LMFDB - Embedded newform 23.19.d.a.14.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,19,Mod(5,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("23.5"); S:= CuspForms(chi, 19); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 19, names="a")

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	23.d (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.2388116732$
Analytic rank:	$0$
Dimension:	$350$
Relative dimension:	$35$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.10
Character	$\chi$	$=$	23.14
Dual form			23.19.d.a.5.10

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-583.928 + 171.457i) q^{2} +(-9265.85 - 10693.4i) q^{3} +(91045.2 - 58511.2i) q^{4} +(-1.09148e6 + 156932. i) q^{5} +(7.24404e6 + 4.65546e6i) q^{6} +(6.93679e7 + 3.16793e7i) q^{7} +(6.13419e7 - 7.07923e7i) q^{8} +(2.66437e7 - 1.85311e8i) q^{9} +(6.10441e8 - 2.78779e8i) q^{10} +(3.39847e8 - 1.15741e9i) q^{11} +(-1.46929e9 - 4.31423e8i) q^{12} +(5.10751e9 + 1.11839e10i) q^{13} +(-4.59375e10 - 6.60482e9i) q^{14} +(1.17916e10 + 1.02175e10i) q^{15} +(-3.54670e10 + 7.76620e10i) q^{16} +(7.15621e10 - 1.11353e11i) q^{17} +(1.62148e10 + 1.12776e11i) q^{18} +(9.40679e10 + 1.46372e11i) q^{19} +(-9.01920e10 + 7.81518e10i) q^{20} +(-3.03995e11 - 1.03531e12i) q^{21} +7.34114e11i q^{22} +(-1.73896e12 + 4.69230e11i) q^{23} -1.32539e12 q^{24} +(-2.49347e12 + 7.32148e11i) q^{25} +(-4.89997e12 - 5.65487e12i) q^{26} +(-6.84001e12 + 4.39581e12i) q^{27} +(8.16921e12 - 1.17456e12i) q^{28} +(-5.04458e12 - 3.24196e12i) q^{29} +(-8.63734e12 - 3.94454e12i) q^{30} +(2.54791e13 - 2.94045e13i) q^{31} +(3.89993e12 - 2.71246e13i) q^{32} +(-1.55256e13 + 7.09030e12i) q^{33} +(-2.26949e13 + 7.72919e13i) q^{34} +(-8.06854e13 - 2.36914e13i) q^{35} +(-8.41698e12 - 1.84306e13i) q^{36} +(1.50162e14 + 2.15901e13i) q^{37} +(-8.00254e13 - 6.93424e13i) q^{38} +(7.22679e13 - 1.58245e14i) q^{39} +(-5.58441e13 + 8.68951e13i) q^{40} +(-3.60729e13 - 2.50892e14i) q^{41} +(3.55023e14 + 5.52426e14i) q^{42} +(-4.50330e14 + 3.90213e14i) q^{43} +(-3.67801e13 - 1.25262e14i) q^{44} +2.06445e14i q^{45} +(9.34974e14 - 5.72153e14i) q^{46} +5.25844e14 q^{47} +(1.15910e15 - 3.40343e14i) q^{48} +(2.74195e15 + 3.16438e15i) q^{49} +(1.33047e15 - 8.55044e14i) q^{50} +(-1.85382e15 + 2.66539e14i) q^{51} +(1.11940e15 + 7.19393e14i) q^{52} +(2.51278e15 + 1.14755e15i) q^{53} +(3.24039e15 - 3.73960e15i) q^{54} +(-1.89302e14 + 1.31663e15i) q^{55} +(6.49781e15 - 2.96745e15i) q^{56} +(6.93595e14 - 2.36217e15i) q^{57} +(3.50153e15 + 1.02814e15i) q^{58} +(8.97809e14 + 1.96593e15i) q^{59} +(1.67141e15 + 2.40313e14i) q^{60} +(-6.51784e15 - 5.64774e15i) q^{61} +(-9.83639e15 + 2.15387e16i) q^{62} +(7.71873e15 - 1.20106e16i) q^{63} +(-8.11755e14 - 5.64588e15i) q^{64} +(-7.32986e15 - 1.14055e16i) q^{65} +(7.85015e15 - 6.80220e15i) q^{66} +(7.61769e15 + 2.59435e16i) q^{67} -1.43253e16i q^{68} +(2.11306e16 + 1.42475e16i) q^{69} +5.11765e16 q^{70} +(2.16685e16 - 6.36245e15i) q^{71} +(-1.14842e16 - 1.32535e16i) q^{72} +(-5.07974e16 + 3.26455e16i) q^{73} +(-9.13858e16 + 1.31393e16i) q^{74} +(3.09332e16 + 1.98796e16i) q^{75} +(1.71289e16 + 7.82249e15i) q^{76} +(6.02404e16 - 6.95212e16i) q^{77} +(-1.50672e16 + 1.04794e17i) q^{78} +(1.43682e17 - 6.56174e16i) q^{79} +(2.65241e16 - 9.03326e16i) q^{80} +(4.07911e16 + 1.19774e16i) q^{81} +(6.40812e16 + 1.40318e17i) q^{82} +(-4.67350e16 - 6.71948e15i) q^{83} +(-8.82547e16 - 7.64731e16i) q^{84} +(-6.06340e16 + 1.32770e17i) q^{85} +(1.96056e17 - 3.05069e17i) q^{86} +(1.20749e16 + 8.39831e16i) q^{87} +(-6.10890e16 - 9.50563e16i) q^{88} +(3.24483e17 - 2.81166e17i) q^{89} +(-3.53964e16 - 1.20549e17i) q^{90} +9.37605e17i q^{91} +(-1.30869e17 + 1.44470e17i) q^{92} -5.50519e17 q^{93} +(-3.07055e17 + 9.01596e16i) q^{94} +(-1.25644e17 - 1.45001e17i) q^{95} +(-3.26189e17 + 2.09629e17i) q^{96} +(-1.16027e18 + 1.66822e17i) q^{97} +(-2.14366e18 - 1.37764e18i) q^{98} +(-2.05426e17 - 9.38150e16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 350 q - 179 q^{2} + 20119 q^{3} - 4092083 q^{4} - 11 q^{5} - 2318126 q^{6} - 11 q^{7} - 18825206 q^{8} - 4214797052 q^{9} - 11 q^{10} - 11 q^{11} + 5321755786 q^{12} + 655768935 q^{13} - 11 q^{14} + 253448904621 q^{15}+ \cdots - 95\!\cdots\!51 q^{99}+O(q^{100}) $ 350 * q - 179 * q^2 + 20119 * q^3 - 4092083 * q^4 - 11 * q^5 - 2318126 * q^6 - 11 * q^7 - 18825206 * q^8 - 4214797052 * q^9 - 11 * q^10 - 11 * q^11 + 5321755786 * q^12 + 655768935 * q^13 - 11 * q^14 + 253448904621 * q^15 - 121059691035 * q^16 - 296340696091 * q^17 + 845128269786 * q^18 + 34950057109 * q^19 - 4104516534283 * q^20 + 5306405877949 * q^21 - 8788512317886 * q^23 + 16248757876058 * q^24 + 15898871892338 * q^25 - 12820353995934 * q^26 - 13015455785135 * q^27 + 105657239863285 * q^28 + 24125383566071 * q^29 - 190975720579083 * q^30 + 21755707682535 * q^31 - 243907502265099 * q^32 + 261034241184453 * q^33 - 129972082436273 * q^34 - 266152601718391 * q^35 + 559915831168033 * q^36 + 428874756612181 * q^37 - 1776255039233686 * q^38 + 549617987179705 * q^39 + 3407519671874989 * q^40 + 453667246412903 * q^41 - 6199000632151481 * q^42 + 1284249744062989 * q^43 + 7033574851458386 * q^44 - 11529170898896835 * q^46 - 2752011365749412 * q^47 + 7346362951210082 * q^48 + 14923872408166082 * q^49 - 8729688416622456 * q^50 - 15827415309093971 * q^51 - 11781732119049248 * q^52 + 10327001802201029 * q^53 + 16483884134652258 * q^54 - 6495140540052155 * q^55 - 112789689088256488 * q^56 + 79316406647596261 * q^57 + 80750695224012275 * q^58 - 103310090431970893 * q^59 + 56789760614471819 * q^60 + 64312558011025621 * q^61 + 78525812725681666 * q^62 - 56271156969207411 * q^63 - 224715274461002686 * q^64 - 45304722356970395 * q^65 + 206405045580983832 * q^66 + 65297330513632789 * q^67 - 143603139268291161 * q^69 - 403103996477716918 * q^70 - 7242816485765057 * q^71 + 620604439361873263 * q^72 + 69596528836762215 * q^73 + 102815849039067692 * q^74 + 116102034703195999 * q^75 - 930398829208773122 * q^76 - 693643966535804563 * q^77 + 2957501787035331408 * q^78 + 960132297145477093 * q^79 - 2513912900105850122 * q^80 - 3453140773055113594 * q^81 + 841776961191439844 * q^82 + 2134251156441149669 * q^83 + 1875963344476894475 * q^84 - 2497986830714303135 * q^85 - 709961756623859245 * q^86 - 2620179835179103895 * q^87 + 746914657235259645 * q^88 + 2323216414828777369 * q^89 + 6947866797842083322 * q^90 - 2374143188353425254 * q^92 - 8687469182791611658 * q^93 - 3156566639060022579 * q^94 + 1273876168349301101 * q^95 + 19129033188570894661 * q^96 + 2956262222729055625 * q^97 - 5708307230013551083 * q^98 - 9593810550169008251 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{21}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−583.928	+	171.457i	−1.14048	+	0.334877i	−0.796821	−	0.604216i	$-0.793486\pi$
$2$	−583.928	+	171.457i	−1.14048	+	0.334877i	−0.343664	+	0.939093i	$0.611668\pi$
$3$	−9265.85	−	10693.4i	−0.470754	−	0.543279i	0.469867	−	0.882737i	$-0.344302\pi$
$3$	−9265.85	−	10693.4i	−0.470754	−	0.543279i	−0.940621	+	0.339458i	$0.889756\pi$
$4$	91045.2	−	58511.2i	0.347310	−	0.223203i
$5$	−1.09148e6	+	156932.i	−0.558839	+	0.0803489i	−0.415946	−	0.909389i	$-0.636550\pi$
$5$	−1.09148e6	+	156932.i	−0.558839	+	0.0803489i	−0.142893	+	0.989738i	$0.545640\pi$
$6$	7.24404e6	+	4.65546e6i	0.718819	+	0.461957i
$7$	6.93679e7	+	3.16793e7i	1.71900	+	0.785042i	0.995504	+	0.0947157i	$0.0301942\pi$
$7$	6.93679e7	+	3.16793e7i	1.71900	+	0.785042i	0.723498	+	0.690326i	$0.242533\pi$
$8$	6.13419e7	−	7.07923e7i	0.457033	−	0.527444i
$9$	2.66437e7	−	1.85311e8i	0.0687720	−	0.478320i
$10$	6.10441e8	−	2.78779e8i	0.610441	−	0.278779i
$11$	3.39847e8	−	1.15741e9i	0.144128	−	0.490855i	−0.855509	−	0.517788i	$-0.826756\pi$
$11$	3.39847e8	−	1.15741e9i	0.144128	−	0.490855i	0.999637	+	0.0269323i	$0.00857386\pi$
$12$	−1.46929e9	−	4.31423e8i	−0.284759	−	0.0836127i
$13$	5.10751e9	+	1.11839e10i	0.481636	+	1.05464i	0.982010	+	0.188827i	$0.0604684\pi$
$13$	5.10751e9	+	1.11839e10i	0.481636	+	1.05464i	−0.500374	+	0.865809i	$0.666804\pi$
$14$	−4.59375e10	−	6.60482e9i	−2.22339	−	0.319675i
$15$	1.17916e10	+	1.02175e10i	0.306728	+	0.265781i
$16$	−3.54670e10	+	7.76620e10i	−0.516113	+	1.13013i
$17$	7.15621e10	−	1.11353e11i	0.603452	−	0.938990i	−0.396330	−	0.918108i	$-0.629716\pi$
$17$	7.15621e10	−	1.11353e11i	0.603452	−	0.938990i	0.999782	−	0.0208816i	$-0.00664729\pi$
$18$	1.62148e10	+	1.12776e11i	0.0817446	+	0.568546i
$19$	9.40679e10	+	1.46372e11i	0.291514	+	0.453604i	0.955861	−	0.293820i	$-0.0949267\pi$
$19$	9.40679e10	+	1.46372e11i	0.291514	+	0.453604i	−0.664347	+	0.747424i	$0.731290\pi$
$20$	−9.01920e10	+	7.81518e10i	−0.176156	+	0.152640i
$21$	−3.03995e11	−	1.03531e12i	−0.382730	−	1.30346i
$22$			7.34114e11i			0.608078i
$23$	−1.73896e12	+	4.69230e11i	−0.965469	+	0.260517i
$23$	−1.73896e12	+	4.69230e11i	−0.965469	+	0.260517i
$24$	−1.32539e12			−0.501699
$25$	−2.49347e12	+	7.32148e11i	−0.653648	+	0.191928i
$26$	−4.89997e12	−	5.65487e12i	−0.902471	−	1.04151i
$27$	−6.84001e12	+	4.39581e12i	−0.896980	+	0.576454i
$28$	8.16921e12	−	1.17456e12i	0.772250	−	0.111033i
$29$	−5.04458e12	−	3.24196e12i	−0.347731	−	0.223473i	0.355103	−	0.934827i	$-0.384446\pi$
$29$	−5.04458e12	−	3.24196e12i	−0.347731	−	0.223473i	−0.702834	+	0.711354i	$0.748082\pi$
$30$	−8.63734e12	−	3.94454e12i	−0.438822	−	0.200403i
$31$	2.54791e13	−	2.94045e13i	0.963672	−	1.11214i	−0.0299696	−	0.999551i	$-0.509541\pi$
$31$	2.54791e13	−	2.94045e13i	0.963672	−	1.11214i	0.993642	−	0.112586i	$-0.0359135\pi$
$32$	3.89993e12	−	2.71246e13i	0.110843	−	0.770927i
$33$	−1.55256e13	+	7.09030e12i	−0.334521	+	0.152770i
$34$	−2.26949e13	+	7.72919e13i	−0.373782	+	1.27299i
$35$	−8.06854e13	−	2.36914e13i	−1.02372	−	0.300592i
$36$	−8.41698e12	−	1.84306e13i	−0.0828769	−	0.181475i
$37$	1.50162e14	+	2.15901e13i	1.15544	+	0.166126i	0.693277	−	0.720671i	$-0.256166\pi$
$37$	1.50162e14	+	2.15901e13i	1.15544	+	0.166126i	0.462158	+	0.886798i	$0.347075\pi$
$38$	−8.00254e13	−	6.93424e13i	−0.484368	−	0.419708i
$39$	7.22679e13	−	1.58245e14i	0.346230	−	0.758137i
$40$	−5.58441e13	+	8.68951e13i	−0.213028	+	0.331478i
$41$	−3.60729e13	−	2.50892e14i	−0.110186	−	0.766360i	−0.967737	−	0.251961i	$-0.918924\pi$
$41$	−3.60729e13	−	2.50892e14i	−0.110186	−	0.766360i	0.857551	−	0.514398i	$-0.171985\pi$
$42$	3.55023e14	+	5.52426e14i	0.872997	+	1.35841i
$43$	−4.50330e14	+	3.90213e14i	−0.896014	+	0.776400i	−0.975400	−	0.220444i	$-0.929249\pi$
$43$	−4.50330e14	+	3.90213e14i	−0.896014	+	0.776400i	0.0793860	+	0.996844i	$0.474704\pi$
$44$	−3.67801e13	−	1.25262e14i	−0.0595030	−	0.202649i
$45$			2.06445e14i			0.272829i
$46$	9.34974e14	−	5.72153e14i	1.01386	−	0.620428i
$47$	5.25844e14			0.469869			0.234934	−	0.972011i	$-0.424513\pi$
$47$	5.25844e14			0.469869			0.234934	+	0.972011i	$0.424513\pi$
$48$	1.15910e15	−	3.40343e14i	0.856939	−	0.251620i
$49$	2.74195e15	+	3.16438e15i	1.68382	+	1.94323i
$50$	1.33047e15	−	8.55044e14i	0.681203	−	0.437783i
$51$	−1.85382e15	+	2.66539e14i	−0.794211	+	0.114190i
$52$	1.11940e15	+	7.19393e14i	0.402674	+	0.258783i
$53$	2.51278e15	+	1.14755e15i	0.761504	+	0.347767i	0.758024	−	0.652227i	$-0.226165\pi$
$53$	2.51278e15	+	1.14755e15i	0.761504	+	0.347767i	0.00348032	+	0.999994i	$0.498892\pi$
$54$	3.24039e15	−	3.73960e15i	0.829952	−	0.957815i
$55$	−1.89302e14	+	1.31663e15i	−0.0411048	+	0.285890i
$56$	6.49781e15	−	2.96745e15i	1.19971	−	0.547887i
$57$	6.93595e14	−	2.36217e15i	0.109202	−	0.371909i
$58$	3.50153e15	+	1.02814e15i	0.471418	+	0.138421i
$59$	8.97809e14	+	1.96593e15i	0.103637	+	0.226934i	0.954346	−	0.298703i	$-0.0965541\pi$
$59$	8.97809e14	+	1.96593e15i	0.103637	+	0.226934i	−0.850709	+	0.525637i	$0.823827\pi$
$60$	1.67141e15	+	2.40313e14i	0.165853	+	0.0238460i
$61$	−6.51784e15	−	5.64774e15i	−0.557359	−	0.482954i	0.330034	−	0.943969i	$-0.392940\pi$
$61$	−6.51784e15	−	5.64774e15i	−0.557359	−	0.482954i	−0.887392	+	0.461015i	$0.847485\pi$
$62$	−9.83639e15	+	2.15387e16i	−0.726625	+	1.59109i
$63$	7.71873e15	−	1.20106e16i	0.493720	−	0.768244i
$64$	−8.11755e14	−	5.64588e15i	−0.0450615	−	0.313409i
$65$	−7.32986e15	−	1.14055e16i	−0.353896	−	0.550673i
$66$	7.85015e15	−	6.80220e15i	0.330356	−	0.286255i
$67$	7.61769e15	+	2.59435e16i	0.279995	+	0.953575i	0.972644	+	0.232301i	$0.0746253\pi$
$67$	7.61769e15	+	2.59435e16i	0.279995	+	0.953575i	−0.692649	+	0.721275i	$0.743557\pi$
$68$		−	1.43253e16i		−	0.460812i
$69$	2.11306e16	+	1.42475e16i	0.596032	+	0.401880i
$70$	5.11765e16			1.26820
$71$	2.16685e16	−	6.36245e15i	0.472611	−	0.138771i	−0.0367490	−	0.999325i	$-0.511700\pi$
$71$	2.16685e16	−	6.36245e15i	0.472611	−	0.138771i	0.509360	+	0.860553i	$0.329882\pi$
$72$	−1.14842e16	−	1.32535e16i	−0.220856	−	0.254881i
$73$	−5.07974e16	+	3.26455e16i	−0.862850	+	0.554520i	−0.895558	−	0.444945i	$-0.853223\pi$
$73$	−5.07974e16	+	3.26455e16i	−0.862850	+	0.554520i	0.0327078	+	0.999465i	$0.489587\pi$
$74$	−9.13858e16	+	1.31393e16i	−1.37339	+	0.197463i
$75$	3.09332e16	+	1.98796e16i	0.411978	+	0.264762i
$76$	1.71289e16	+	7.82249e15i	0.202491	+	0.0924746i
$77$	6.02404e16	−	6.95212e16i	0.633099	−	0.730635i
$78$	−1.50672e16	+	1.04794e17i	−0.140987	+	0.980588i
$79$	1.43682e17	−	6.56174e16i	1.19883	−	0.547488i	0.286952	−	0.957945i	$-0.407358\pi$
$79$	1.43682e17	−	6.56174e16i	1.19883	−	0.547488i	0.911880	+	0.410456i	$0.134631\pi$
$80$	2.65241e16	−	9.03326e16i	0.197620	−	0.673031i
$81$	4.07911e16	+	1.19774e16i	0.271769	+	0.0797987i
$82$	6.40812e16	+	1.40318e17i	0.382301	+	0.837123i
$83$	−4.67350e16	−	6.71948e15i	−0.250000	−	0.0359445i	0.0161757	−	0.999869i	$-0.494851\pi$
$83$	−4.67350e16	−	6.71948e15i	−0.250000	−	0.0359445i	−0.266175	+	0.963925i	$0.585760\pi$
$84$	−8.82547e16	−	7.64731e16i	−0.423862	−	0.367278i
$85$	−6.06340e16	+	1.32770e17i	−0.261786	+	0.573231i
$86$	1.96056e17	−	3.05069e17i	0.761892	−	1.18553i
$87$	1.20749e16	+	8.39831e16i	0.0422875	+	0.294116i
$88$	−6.10890e16	−	9.50563e16i	−0.193027	−	0.300356i
$89$	3.24483e17	−	2.81166e17i	0.926150	−	0.802514i	−0.0544530	−	0.998516i	$-0.517342\pi$
$89$	3.24483e17	−	2.81166e17i	0.926150	−	0.802514i	0.980603	+	0.196002i	$0.0627961\pi$
$90$	−3.53964e16	−	1.20549e17i	−0.0913642	−	0.311158i
$91$			9.37605e17i			2.19103i
$92$	−1.30869e17	+	1.44470e17i	−0.277169	+	0.305975i
$93$	−5.50519e17			−1.05785
$94$	−3.07055e17	+	9.01596e16i	−0.535878	+	0.157348i
$95$	−1.25644e17	−	1.45001e17i	−0.199356	−	0.230069i
$96$	−3.26189e17	+	2.09629e17i	−0.471008	+	0.302699i
$97$	−1.16027e18	+	1.66822e17i	−1.52621	+	0.219435i	−0.853743	−	0.520695i	$-0.825673\pi$
$97$	−1.16027e18	+	1.66822e17i	−1.52621	+	0.219435i	−0.672463	+	0.740130i	$0.734764\pi$
$98$	−2.14366e18	−	1.37764e18i	−2.57111	−	1.65235i
$99$	−2.05426e17	−	9.38150e16i	−0.224874	−	0.102696i
$100$	−1.84179e17	+	2.12554e17i	−0.184179	+	0.212554i
$101$	−2.26374e17	+	1.57447e18i	−0.206983	+	1.43960i	0.575946	+	0.817488i	$0.304634\pi$
$101$	−2.26374e17	+	1.57447e18i	−0.206983	+	1.43960i	−0.782929	+	0.622111i	$0.786275\pi$
$102$	1.03680e18	−	4.73490e17i	0.867546	−	0.396195i
$103$	6.90212e17	−	2.35064e18i	0.528990	−	1.80157i	−0.0659748	−	0.997821i	$-0.521016\pi$
$103$	6.90212e17	−	2.35064e18i	0.528990	−	1.80157i	0.594964	−	0.803752i	$-0.297166\pi$
$104$	1.10504e18	+	3.24468e17i	0.776384	+	0.227967i
$105$	4.94279e17	+	1.08232e18i	0.318616	+	0.697673i
$106$	−1.66404e18	−	2.39253e17i	−0.984943	−	0.141613i
$107$	−1.61142e18	−	1.39630e18i	−0.876503	−	0.759494i	0.0952600	−	0.995452i	$-0.469632\pi$
$107$	−1.61142e18	−	1.39630e18i	−0.876503	−	0.759494i	−0.971763	+	0.235958i	$0.924177\pi$
$108$	−3.65546e17	+	8.00435e17i	−0.182864	+	0.400417i
$109$	2.02892e18	−	3.15707e18i	0.934172	−	1.45360i	0.0434485	−	0.999056i	$-0.486166\pi$
$109$	2.02892e18	−	3.15707e18i	0.934172	−	1.45360i	0.890724	−	0.454545i	$-0.150198\pi$
$110$	−1.15206e17	−	8.01273e17i	−0.0488585	−	0.339818i
$111$	−1.16051e18	−	1.80579e18i	−0.453673	−	0.705929i
$112$	−4.92055e18	+	4.26368e18i	−1.77440	+	1.53753i
$113$	1.29228e18	+	4.40112e18i	0.430182	+	1.46506i	0.834787	+	0.550573i	$0.185591\pi$
$113$	1.29228e18	+	4.40112e18i	0.430182	+	1.46506i	−0.404605	+	0.914491i	$0.632591\pi$
$114$			1.49826e18i			0.460726i
$115$	1.82441e18	−	7.85054e17i	0.518610	−	0.223161i
$116$	−6.48976e17			−0.170650
$117$	2.20858e18	−	6.48497e17i	0.537576	−	0.157847i
$118$	−8.61328e17	−	9.94025e17i	−0.194192	−	0.224109i
$119$	8.49169e18	−	5.45728e18i	1.77448	−	1.14039i
$120$	1.44664e18	−	2.07996e17i	0.280369	−	0.0403110i
$121$	3.45319e18	+	2.21923e18i	0.621087	+	0.399149i
$122$	4.77429e18	+	2.18035e18i	0.797389	+	0.364155i
$123$	−2.34864e18	+	2.71047e18i	−0.364477	+	0.420629i
$124$	5.99261e17	−	4.16795e18i	0.0864611	−	0.601350i
$125$	6.43304e18	−	2.93787e18i	0.863428	−	0.394314i
$126$	−2.44789e18	+	8.33674e18i	−0.305814	+	1.04151i
$127$	−1.99056e17	−	5.84482e16i	−0.0231602	−	0.00680045i	0.270132	−	0.962823i	$-0.412933\pi$
$127$	−1.99056e17	−	5.84482e16i	−0.0231602	−	0.00680045i	−0.293292	+	0.956023i	$0.594751\pi$
$128$	4.42623e18	+	9.69210e18i	0.479893	+	1.05082i
$129$	8.34538e18	+	1.19988e18i	0.843604	+	0.121292i
$130$	6.23566e18	+	5.40323e18i	0.588020	+	0.509523i
$131$	3.13459e18	−	6.86379e18i	0.275892	−	0.604118i	−0.720070	−	0.693902i	$-0.755890\pi$
$131$	3.13459e18	−	6.86379e18i	0.275892	−	0.604118i	0.995961	+	0.0897834i	$0.0286175\pi$
$132$	−9.98669e17	+	1.55396e18i	−0.0820835	+	0.127724i
$133$	1.88832e18	+	1.31336e19i	0.145014	+	1.00860i
$134$	−8.89637e18	−	1.38430e19i	−0.638660	−	0.993774i
$135$	6.77591e18	−	5.87136e18i	0.454950	−	0.394217i
$136$	−3.49317e18	−	1.18966e19i	−0.219467	−	0.747436i
$137$			1.17439e19i			0.690763i	0.938462	+	0.345381i	$0.112250\pi$
$137$			1.17439e19i			0.690763i	−0.938462	+	0.345381i	$0.887750\pi$
$138$	−1.47816e19	−	4.69653e18i	−0.814346	−	0.258741i
$139$	−3.19196e18			−0.164788			−0.0823938	−	0.996600i	$-0.526257\pi$
$139$	−3.19196e18			−0.164788			−0.0823938	+	0.996600i	$0.526257\pi$
$140$	−8.73223e18	+	2.56401e18i	−0.422642	+	0.124099i
$141$	−4.87240e18	−	5.62304e18i	−0.221193	−	0.255270i
$142$	−1.15620e19	+	7.43043e18i	−0.492535	+	0.316533i
$143$	1.46801e19	−	2.11068e18i	0.587091	−	0.0844110i
$144$	1.34466e19	+	8.64163e18i	0.505070	+	0.324589i
$145$	6.01484e18	+	2.74689e18i	0.212282	+	0.0969457i
$146$	2.40647e19	−	2.77722e19i	0.798372	−	0.921370i
$147$	8.43136e18	−	5.86414e19i	0.263052	−	1.82957i
$148$	1.49348e19	−	6.82051e18i	0.438374	−	0.200199i
$149$	−1.08722e19	+	3.70272e19i	−0.300358	+	1.02293i	0.661629	+	0.749832i	$0.269866\pi$
$149$	−1.08722e19	+	3.70272e19i	−0.300358	+	1.02293i	−0.961987	+	0.273095i	$0.911953\pi$
$150$	−2.14713e19	−	6.30454e18i	−0.558517	−	0.163995i
$151$	−1.12880e19	−	2.47173e19i	−0.276583	−	0.605631i	0.719458	−	0.694536i	$-0.244391\pi$
$151$	−1.12880e19	−	2.47173e19i	−0.276583	−	0.605631i	−0.996040	+	0.0889050i	$0.971663\pi$
$152$	1.61323e19	+	2.31948e18i	0.372482	+	0.0535548i
$153$	−1.87282e19	−	1.62281e19i	−0.407637	−	0.353219i
$154$	−2.32562e19	+	5.09240e19i	−0.477367	+	1.04529i
$155$	−2.31955e19	+	3.60930e19i	−0.449179	+	0.698936i
$156$	−2.67944e18	−	1.86359e19i	−0.0489691	−	0.340588i
$157$	2.47500e19	+	3.85117e19i	0.427049	+	0.664501i	0.986387	−	0.164438i	$-0.0525812\pi$
$157$	2.47500e19	+	3.85117e19i	0.427049	+	0.664501i	−0.559339	+	0.828939i	$0.688945\pi$
$158$	−7.26494e19	+	6.29511e19i	−1.18391	+	1.02586i
$159$	−1.10119e19	−	3.75032e19i	−0.169547	−	0.577423i
$160$			3.02180e19i			0.439730i
$161$	−1.35493e20	−	2.25394e19i	−1.86416	−	0.310105i
$162$	−2.58727e19			−0.336671
$163$	9.98607e19	−	2.93217e19i	1.22944	−	0.360995i	0.398399	−	0.917212i	$-0.369566\pi$
$163$	9.98607e19	−	2.93217e19i	1.22944	−	0.360995i	0.831037	+	0.556217i	$0.187748\pi$
$164$	−1.79643e19	−	2.07319e19i	−0.209322	−	0.241571i
$165$	1.58332e19	−	1.01754e19i	0.174668	−	0.112252i
$166$	2.84420e19	−	4.08934e18i	0.297158	−	0.0427248i
$167$	1.15496e20	+	7.42245e19i	1.14319	+	0.734681i	0.968271	−	0.249902i	$-0.0803985\pi$
$167$	1.15496e20	+	7.42245e19i	1.14319	+	0.734681i	0.174915	+	0.984583i	$0.444035\pi$
$168$	−9.19398e19	−	4.19875e19i	−0.862422	−	0.393855i
$169$	−2.53500e19	+	2.92555e19i	−0.225423	+	0.260152i
$170$	1.26416e19	−	8.79243e19i	0.106601	−	0.741427i
$171$	2.96307e19	−	1.35319e19i	0.237016	−	0.108241i
$172$	−1.81685e19	+	6.18764e19i	−0.137900	+	0.469644i
$173$	1.75682e20	+	5.15849e19i	1.26565	+	0.371628i	0.844593	−	0.535408i	$-0.179842\pi$
$173$	1.75682e20	+	5.15849e19i	1.26565	+	0.371628i	0.421054	+	0.907036i	$0.361660\pi$
$174$	−2.14504e19	−	4.69698e19i	−0.146721	−	0.321274i
$175$	−1.96161e20	−	2.82036e19i	−1.27429	−	0.183216i
$176$	7.78335e19	+	6.74431e19i	0.480344	+	0.416221i
$177$	1.27034e19	−	2.78166e19i	0.0745008	−	0.163134i
$178$	−1.41267e20	+	2.19815e20i	−0.787517	+	1.22540i
$179$	−7.75182e18	−	5.39151e19i	−0.0410891	−	0.285781i	−0.999998	−	0.00206634i	$-0.999342\pi$
$179$	−7.75182e18	−	5.39151e19i	−0.0410891	−	0.285781i	0.958909	−	0.283715i	$-0.0915668\pi$
$180$	1.20793e19	+	1.87958e19i	0.0608962	+	0.0947564i
$181$	3.46321e19	−	3.00089e19i	0.166101	−	0.143927i	−0.567844	−	0.823136i	$-0.692222\pi$
$181$	3.46321e19	−	3.00089e19i	0.166101	−	0.143927i	0.733945	+	0.679209i	$0.237677\pi$
$182$	−1.60759e20	−	5.47494e20i	−0.733723	−	2.49883i
$183$			1.22029e20i			0.530154i
$184$	−7.34531e19	+	1.51888e20i	−0.303843	+	0.628295i
$185$	−1.67288e20			−0.659051
$186$	3.21463e20	−	9.43902e19i	1.20647	−	0.354250i
$187$	−1.04561e20	−	1.20670e20i	−0.373934	−	0.431543i
$188$	4.78756e19	−	3.07678e19i	0.163190	−	0.104876i
$189$	−6.13734e20	+	8.82416e19i	−1.99445	+	0.286759i
$190$	9.82284e19	+	6.31276e19i	0.304407	+	0.195631i
$191$	2.37827e20	+	1.08612e20i	0.703009	+	0.321053i	0.734650	−	0.678446i	$-0.237346\pi$
$191$	2.37827e20	+	1.08612e20i	0.703009	+	0.321053i	−0.0316415	+	0.999499i	$0.510073\pi$
$192$	−5.28519e19	+	6.09943e19i	−0.149056	+	0.172020i
$193$	−1.53590e19	+	1.06824e20i	−0.0413377	+	0.287510i	0.958658	+	0.284561i	$0.0918479\pi$
$193$	−1.53590e19	+	1.06824e20i	−0.0413377	+	0.287510i	−0.999996	+	0.00294924i	$0.999061\pi$
$194$	6.48911e20	−	2.96348e20i	1.66713	−	0.761353i
$195$	−5.40456e19	+	1.84062e20i	−0.132571	+	0.451496i
$196$	4.34793e20	+	1.27667e20i	1.01854	+	0.299070i
$197$	−9.29716e19	−	2.03579e20i	−0.208044	−	0.455552i	0.776631	−	0.629956i	$-0.216927\pi$
$197$	−9.29716e19	−	2.03579e20i	−0.208044	−	0.455552i	−0.984674	+	0.174405i	$0.944200\pi$
$198$	1.36039e20	+	1.95595e19i	0.290856	+	0.0418187i
$199$	2.13788e20	+	1.85249e20i	0.436824	+	0.378510i	0.845329	−	0.534246i	$-0.179404\pi$
$199$	2.13788e20	+	1.85249e20i	0.436824	+	0.378510i	−0.408505	+	0.912756i	$0.633950\pi$
$200$	−1.01124e20	+	2.21430e20i	−0.197507	+	0.432480i
$201$	2.06839e20	−	3.21847e20i	0.386249	−	0.601015i
$202$	−1.37767e20	−	9.58190e20i	−0.246027	−	1.71115i
$203$	−2.47230e20	−	3.84697e20i	−0.422315	−	0.657134i
$204$	−1.53186e20	+	1.32736e20i	−0.250350	+	0.216929i
$205$	7.87458e19	+	2.68184e20i	0.123152	+	0.419419i
$206$			1.49095e21i			2.23181i
$207$	4.06212e19	+	3.34750e20i	0.0582129	+	0.479719i
$208$	−1.04971e21			−1.44046
$209$	2.01382e20	−	5.91310e19i	0.264669	−	0.0777139i
$210$	−4.74194e20	−	5.47249e20i	−0.597011	−	0.688988i
$211$	4.67424e20	−	3.00395e20i	0.563857	−	0.362369i	−0.227448	−	0.973790i	$-0.573038\pi$
$211$	4.67424e20	−	3.00395e20i	0.563857	−	0.362369i	0.791305	+	0.611421i	$0.209402\pi$
$212$	2.95922e20	−	4.25471e19i	0.342101	−	0.0491866i
$213$	−2.68813e20	−	1.72756e20i	−0.297875	−	0.191433i
$214$	1.18036e21	+	5.39051e20i	1.25398	+	0.572671i
$215$	4.30291e20	−	4.96582e20i	0.438345	−	0.505877i
$216$	−1.08390e20	+	7.53867e20i	−0.105902	+	0.736565i
$217$	2.69895e21	−	1.23257e21i	2.52963	−	1.15524i
$218$	−6.43445e20	+	2.19137e21i	−0.578633	+	1.97064i
$219$	8.19771e20	+	2.40706e20i	0.707450	+	0.207726i
$220$	5.98024e19	+	1.30949e20i	0.0495352	+	0.108467i
$221$	1.61086e21	+	2.31607e20i	1.28094	+	0.184171i
$222$	9.87271e20	+	8.55475e20i	0.753806	+	0.653177i
$223$	−4.28763e20	+	9.38860e20i	−0.314393	+	0.688425i	−0.999187	−	0.0403115i	$-0.987165\pi$
$223$	−4.28763e20	+	9.38860e20i	−0.314393	+	0.688425i	0.684794	+	0.728737i	$0.259892\pi$
$224$	1.12982e21	−	1.75803e21i	0.795749	−	1.23821i
$225$	6.92398e19	+	4.81574e20i	0.0468504	+	0.325852i
$226$	−1.50920e21	−	2.34836e21i	−0.981232	−	1.52683i
$227$	8.00888e20	−	6.93973e20i	0.500425	−	0.433621i	−0.367716	−	0.929938i	$-0.619860\pi$
$227$	8.00888e20	−	6.93973e20i	0.500425	−	0.433621i	0.868141	+	0.496317i	$0.165315\pi$
$228$	−7.50648e19	−	2.55647e20i	−0.0450840	−	0.153542i
$229$		−	1.78570e21i		−	1.03107i	−0.856868	−	0.515536i	$-0.827593\pi$
$229$		−	1.78570e21i		−	1.03107i	0.856868	−	0.515536i	$-0.172407\pi$
$230$	−9.30719e20	+	7.71222e20i	−0.516735	+	0.428182i
$231$	−1.30159e21			−0.694973
$232$	−5.38950e20	+	1.58250e20i	−0.276794	+	0.0812740i
$233$	−1.04906e21	−	1.21068e21i	−0.518320	−	0.598173i	0.434890	−	0.900484i	$-0.356787\pi$
$233$	−1.04906e21	−	1.21068e21i	−0.518320	−	0.598173i	−0.953209	+	0.302311i	$0.902242\pi$
$234$	−1.17846e21	+	7.57351e20i	−0.560238	+	0.360043i
$235$	−5.73950e20	+	8.25215e19i	−0.262581	+	0.0377534i
$236$	1.96770e20	+	1.26456e20i	0.0866465	+	0.0556843i
$237$	−2.03301e21	−	9.28443e20i	−0.861794	−	0.393568i
$238$	−4.02285e21	+	4.64262e21i	−1.64188	+	1.89483i
$239$	3.11104e20	−	2.16378e21i	0.122271	−	0.850417i	−0.832701	−	0.553723i	$-0.813207\pi$
$239$	3.11104e20	−	2.16378e21i	0.122271	−	0.850417i	0.954973	−	0.296694i	$-0.0958841\pi$
$240$	−1.21173e21	+	5.53378e20i	−0.458674	+	0.209469i
$241$	−4.41444e20	+	1.50342e21i	−0.160962	+	0.548185i	0.839030	+	0.544085i	$0.183123\pi$
$241$	−4.41444e20	+	1.50342e21i	−0.160962	+	0.548185i	−0.999992	+	0.00409993i	$0.998695\pi$
$242$	−2.39692e21	−	7.03799e20i	−0.842006	−	0.247235i
$243$	1.05868e21	+	2.31818e21i	0.358350	+	0.784676i
$244$	−9.23873e20	−	1.32833e20i	−0.301373	−	0.0433309i
$245$	−3.48938e21	−	3.02357e21i	−1.09712	−	0.950660i
$246$	9.06707e20	−	1.98541e21i	0.274822	−	0.601776i
$247$	−1.15656e21	+	1.79964e21i	−0.337984	+	0.525913i
$248$	−5.18673e20	−	3.60745e21i	−0.146160	−	1.01657i
$249$	3.61186e20	+	5.62016e20i	0.0981604	+	0.152741i
$250$	−3.25272e21	+	2.81849e21i	−0.852680	+	0.738851i
$251$	−3.73315e20	−	1.27139e21i	−0.0944087	−	0.321527i	0.898725	−	0.438513i	$-0.144495\pi$
$251$	−3.73315e20	−	1.27139e21i	−0.0944087	−	0.321527i	−0.993133	+	0.116987i	$0.962677\pi$
$252$		−	1.54514e21i		−	0.377018i
$253$	−4.78866e19	+	2.17216e21i	−0.0112753	+	0.511454i
$254$	1.26256e20			0.0286912
$255$	1.98158e21	−	5.81846e20i	0.434661	−	0.127628i
$256$	−3.26720e21	−	3.77055e21i	−0.691856	−	0.798444i
$257$	5.64409e21	−	3.62724e21i	1.15397	−	0.741614i	0.183548	−	0.983011i	$-0.441242\pi$
$257$	5.64409e21	−	3.62724e21i	1.15397	−	0.741614i	0.970427	+	0.241397i	$0.0776055\pi$
$258$	−5.07883e21	+	7.30226e20i	−1.00274	+	0.144172i
$259$	9.73250e21	+	6.25470e21i	1.85578	+	1.19264i
$260$	−1.33470e21	−	6.09536e20i	−0.245823	−	0.112264i
$261$	−7.35176e20	+	8.48438e20i	−0.130806	+	0.150958i
$262$	−6.53531e20	+	4.54540e21i	−0.112345	+	0.781378i
$263$	6.82037e21	−	3.11476e21i	1.13294	−	0.517396i	0.241439	−	0.970416i	$-0.422381\pi$
$263$	6.82037e21	−	3.11476e21i	1.13294	−	0.517396i	0.891500	+	0.453020i	$0.149654\pi$
$264$	−4.50430e20	+	1.53402e21i	−0.0723090	+	0.246262i
$265$	−2.92275e21	−	8.58196e20i	−0.453501	−	0.133160i
$266$	−3.35448e21	−	7.34529e21i	−0.503142	−	1.10173i
$267$	−6.01322e21	−	8.64570e20i	−0.871978	−	0.125372i
$268$	2.21154e21	+	1.91631e21i	0.310085	+	0.268691i
$269$	8.19738e20	−	1.79498e21i	0.111149	−	0.243382i	−0.845881	−	0.533372i	$-0.820925\pi$
$269$	8.19738e20	−	1.79498e21i	0.111149	−	0.243382i	0.957030	+	0.289990i	$0.0936520\pi$
$270$	−2.94996e21	+	4.59023e21i	−0.386850	+	0.601950i
$271$	1.31133e21	+	9.12053e21i	0.166337	+	1.15690i	0.886375	+	0.462967i	$0.153215\pi$
$271$	1.31133e21	+	9.12053e21i	0.166337	+	1.15690i	−0.720038	+	0.693935i	$0.755876\pi$
$272$	6.10979e21	+	9.50701e21i	0.749732	+	1.16661i
$273$	1.00262e22	−	8.68771e21i	1.19034	−	1.03143i
$274$	−2.01358e21	−	6.85762e21i	−0.231320	−	0.787805i
$275$			3.13479e21i			0.348509i
$276$	2.75748e21	+	6.07904e19i	0.296708	+	0.00654114i
$277$	1.62161e22			1.68899			0.844496	−	0.535562i	$-0.179900\pi$
$277$	1.62161e22			1.68899			0.844496	+	0.535562i	$0.179900\pi$
$278$	1.86388e21	−	5.47284e20i	0.187938	−	0.0551835i
$279$	−4.77011e21	−	5.50500e21i	−0.465683	−	0.537427i
$280$	−6.62656e21	+	4.25863e21i	−0.626420	+	0.402576i
$281$	1.78664e22	−	2.56879e21i	1.63561	−	0.235165i	0.737630	−	0.675205i	$-0.235945\pi$
$281$	1.78664e22	−	2.56879e21i	1.63561	−	0.235165i	0.897978	+	0.440040i	$0.145036\pi$
$282$	3.80924e21	+	2.44805e21i	0.337751	+	0.217059i
$283$	5.10840e21	+	2.33293e21i	0.438740	+	0.200366i	0.622524	−	0.782601i	$-0.286107\pi$
$283$	5.10840e21	+	2.33293e21i	0.438740	+	0.200366i	−0.183784	+	0.982967i	$0.558835\pi$
$284$	1.60054e21	−	1.84712e21i	0.133169	−	0.153685i
$285$	−3.86348e20	+	2.68711e21i	−0.0311441	+	0.216612i
$286$	−8.21025e21	+	3.74950e21i	−0.641301	+	0.292872i
$287$	5.44579e21	−	1.85467e22i	0.412215	−	1.40387i
$288$	−4.92257e21	−	1.44540e21i	−0.361127	−	0.106036i
$289$	−1.43630e21	−	3.14505e21i	−0.102132	−	0.223639i
$290$	−3.98321e21	−	5.72699e20i	−0.274569	−	0.0394770i
$291$	1.25348e22	+	1.08614e22i	0.837682	+	0.725856i
$292$	−2.71473e21	+	5.94443e21i	−0.175906	+	0.385181i
$293$	−2.72548e21	+	4.24093e21i	−0.171251	+	0.266472i	−0.916261	−	0.400581i	$-0.868808\pi$
$293$	−2.72548e21	+	4.24093e21i	−0.171251	+	0.266472i	0.745010	+	0.667053i	$0.232445\pi$
$294$	5.13116e21	+	3.56880e22i	0.312672	+	2.17468i
$295$	−1.28846e21	−	2.00488e21i	−0.0761505	−	0.118492i
$296$	1.07397e22	−	9.30596e21i	0.615694	−	0.533502i
$297$	2.76320e21	+	9.41061e21i	0.153676	+	0.523371i
$298$		−	2.34853e22i		−	1.26722i
$299$	−1.41296e22	−	1.70517e22i	−0.739755	−	0.892744i
$300$	3.97950e21			0.202180
$301$	−4.36001e22	+	1.28022e22i	−2.14976	+	0.631225i
$302$	1.08293e22	+	1.24977e22i	0.518250	+	0.598092i
$303$	1.89339e22	−	1.21681e22i	0.879542	−	0.565248i
$304$	−1.47039e22	+	2.11410e21i	−0.663086	+	0.0953374i
$305$	8.00041e21	+	5.14155e21i	0.350279	+	0.225111i
$306$	1.37183e22	+	6.26496e21i	0.583188	+	0.266333i
$307$	6.18491e21	−	7.13777e21i	0.255322	−	0.294657i	−0.613589	−	0.789625i	$-0.710275\pi$
$307$	6.18491e21	−	7.13777e21i	0.255322	−	0.294657i	0.868911	+	0.494968i	$0.164820\pi$
$308$	1.41684e21	−	9.85431e21i	0.0568019	−	0.395066i
$309$	−3.15317e22	+	1.44000e22i	−1.22778	+	0.560709i
$310$	7.35615e21	−	2.50527e22i	0.278224	−	0.947545i
$311$	−1.01816e22	−	2.98959e21i	−0.374087	−	0.109842i	0.0892839	−	0.996006i	$-0.471542\pi$
$311$	−1.01816e22	−	2.98959e21i	−0.374087	−	0.109842i	−0.463371	+	0.886164i	$0.653360\pi$
$312$	−6.76946e21	−	1.48230e22i	−0.241636	−	0.529110i
$313$	−1.02455e22	−	1.47309e21i	−0.355333	−	0.0510892i	−0.0376631	−	0.999290i	$-0.511991\pi$
$313$	−1.02455e22	−	1.47309e21i	−0.355333	−	0.0510892i	−0.317670	+	0.948201i	$0.602900\pi$
$314$	−2.10553e22	−	1.82445e22i	−0.709568	−	0.614845i
$315$	−6.54002e21	+	1.43207e22i	−0.214183	+	0.468995i
$316$	9.24220e21	−	1.43812e22i	0.294166	−	0.457731i
$317$	−5.99094e21	−	4.16679e22i	−0.185337	−	1.28905i	−0.843892	−	0.536513i	$-0.819741\pi$
$317$	−5.99094e21	−	4.16679e22i	−0.185337	−	1.28905i	0.658555	−	0.752533i	$-0.271168\pi$
$318$	1.28603e22	+	2.00111e22i	0.386731	+	0.601764i
$319$	−5.46667e21	+	4.73689e21i	−0.159811	+	0.138477i
$320$	1.77203e21	+	6.03499e21i	0.0503642	+	0.171525i
$321$			3.01694e22i			0.833721i
$322$	8.29826e22	−	1.00698e22i	2.22989	−	0.270593i
$323$	2.30307e22			0.601844
$324$	4.41464e21	−	1.29626e21i	0.112199	−	0.0329447i
$325$	−2.09237e22	−	2.41472e22i	−0.517235	−	0.596921i
$326$	−5.32841e22	+	3.42436e22i	−1.28126	+	0.823419i
$327$	−5.25594e22	+	7.55689e21i	−1.22948	+	0.176772i
$328$	−1.99740e22	−	1.28365e22i	−0.454570	−	0.292135i
$329$	3.64767e22	+	1.66584e22i	0.807705	+	0.368867i
$330$	−7.50083e21	+	8.65642e21i	−0.161616	+	0.186515i
$331$	−9.53718e21	+	6.63325e22i	−0.199971	+	1.39083i	0.604388	+	0.796690i	$0.293418\pi$
$331$	−9.53718e21	+	6.63325e22i	−0.199971	+	1.39083i	−0.804360	+	0.594142i	$0.797492\pi$
$332$	−4.64816e21	+	2.12274e21i	−0.0948502	+	0.0433167i
$333$	8.00175e21	−	2.72515e22i	0.158923	−	0.541242i
$334$	−8.01674e22	−	2.35393e22i	−1.54981	−	0.455067i
$335$	−1.23859e22	−	2.71214e22i	−0.233091	−	0.510398i
$336$	9.11862e22	+	1.31106e22i	1.67061	+	0.240198i
$337$	−1.26356e21	−	1.09488e21i	−0.0225385	−	0.0195297i	0.643519	−	0.765430i	$-0.277474\pi$
$337$	−1.26356e21	−	1.09488e21i	−0.0225385	−	0.0195297i	−0.666057	+	0.745901i	$0.732019\pi$
$338$	9.78654e21	−	2.14295e22i	0.169973	−	0.372188i
$339$	3.50886e22	−	5.45990e22i	0.593429	−	0.923394i
$340$	2.24809e21	+	1.56358e22i	0.0370258	+	0.257520i
$341$	−2.53741e22	−	3.94829e22i	−0.407006	−	0.633314i
$342$	−1.49821e22	+	1.29820e22i	−0.234065	+	0.202819i
$343$	5.49722e22	+	1.87218e23i	0.836558	+	2.84905i
$344$			5.58163e22i			0.827437i
$345$	−2.52995e22	−	1.22348e22i	−0.365377	−	0.176696i
$346$	−1.11430e23			−1.56790
$347$	−3.20758e22	+	9.41830e21i	−0.439756	+	0.129124i	−0.494113	−	0.869397i	$-0.664507\pi$
$347$	−3.20758e22	+	9.41830e21i	−0.439756	+	0.129124i	0.0543571	+	0.998522i	$0.482689\pi$
$348$	6.01332e21	+	6.93974e21i	0.0803343	+	0.0927107i
$349$	8.33130e22	−	5.35420e22i	1.08464	−	0.697053i	0.129012	−	0.991643i	$-0.458819\pi$
$349$	8.33130e22	−	5.35420e22i	1.08464	−	0.697053i	0.955624	+	0.294590i	$0.0951831\pi$
$350$	1.19379e23	−	1.71642e22i	1.51467	−	0.217776i
$351$	−8.40976e22	−	5.40463e22i	−1.03997	−	0.668347i
$352$	−3.00689e22	−	1.37320e22i	−0.362438	−	0.165520i
$353$	−1.35034e22	+	1.55838e22i	−0.158661	+	0.183105i	−0.829514	−	0.558485i	$-0.811383\pi$
$353$	−1.35034e22	+	1.55838e22i	−0.158661	+	0.183105i	0.670853	+	0.741590i	$0.265928\pi$
$354$	−2.64854e21	+	1.84210e22i	−0.0303373	+	0.211001i
$355$	−2.26524e22	+	1.03450e22i	−0.252964	+	0.115525i
$356$	1.30912e22	−	4.45847e22i	0.142538	−	0.485440i
$357$	−1.37039e23	−	4.02384e22i	−1.45490	−	0.427196i
$358$	1.37706e22	+	3.01535e22i	0.142563	+	0.312169i
$359$	−1.48873e23	−	2.14047e22i	−1.50302	−	0.216102i	−0.658890	−	0.752239i	$-0.728974\pi$
$359$	−1.48873e23	−	2.14047e22i	−1.50302	−	0.216102i	−0.844131	+	0.536138i	$0.819883\pi$
$360$	1.46147e22	+	1.26637e22i	0.143902	+	0.124692i
$361$	3.06799e22	−	6.71797e22i	0.294639	−	0.645168i
$362$	−1.50774e22	+	2.34609e22i	−0.141238	+	0.219770i
$363$	−8.26572e21	−	5.74894e22i	−0.0755303	−	0.525325i
$364$	5.48604e22	+	8.53645e22i	0.489043	+	0.760965i
$365$	5.03213e22	−	4.36037e22i	0.437639	−	0.379217i
$366$	−2.09226e22	−	7.12560e22i	−0.177536	−	0.604633i
$367$			1.12464e23i			0.931145i	0.885010	+	0.465573i	$0.154152\pi$
$367$			1.12464e23i			0.931145i	−0.885010	+	0.465573i	$0.845848\pi$
$368$	2.52343e22	−	1.51693e23i	0.203874	−	1.22556i
$369$	−4.74542e22			−0.374143
$370$	9.76841e22	−	2.86826e22i	0.751637	−	0.220701i
$371$	1.37953e23	+	1.59206e23i	1.03602	+	1.19563i
$372$	−5.01221e22	+	3.22115e22i	−0.367403	+	0.236116i
$373$	2.11209e22	−	3.03672e21i	0.151124	−	0.0217283i	−0.0663378	−	0.997797i	$-0.521131\pi$
$373$	2.11209e22	−	3.03672e21i	0.151124	−	0.0217283i	0.217461	+	0.976069i	$0.430222\pi$
$374$	8.17457e22	+	5.25348e22i	0.570979	+	0.366946i
$375$	−9.10233e22	−	4.15690e22i	−0.620685	−	0.283457i
$376$	3.22563e22	−	3.72257e22i	0.214745	−	0.247829i
$377$	1.04924e22	−	7.29764e22i	0.0682030	−	0.474362i
$378$	3.43247e23	−	1.56756e23i	2.17861	−	0.994940i
$379$	−1.62726e22	+	5.54193e22i	−0.100856	+	0.343486i	−0.994426	−	0.105440i	$-0.966375\pi$
$379$	−1.62726e22	+	5.54193e22i	−0.100856	+	0.343486i	0.893569	+	0.448925i	$0.148193\pi$
$380$	−1.99234e22	−	5.85005e21i	−0.120590	−	0.0354085i
$381$	1.21942e21	+	2.67015e21i	0.00720822	+	0.0157838i
$382$	−1.57496e23	−	2.26445e22i	−0.909284	−	0.130735i
$383$	5.44048e22	+	4.71420e22i	0.306795	+	0.265839i	0.794627	−	0.607098i	$-0.207667\pi$
$383$	5.44048e22	+	4.71420e22i	0.306795	+	0.265839i	−0.487832	+	0.872938i	$0.662212\pi$
$384$	6.26283e22	−	1.37137e23i	0.344977	−	0.755394i
$385$	−5.48413e22	+	8.53348e22i	−0.295095	+	0.459176i
$386$	−9.34717e21	−	6.50110e22i	−0.0491354	−	0.341744i
$387$	6.03122e22	+	9.38477e22i	0.309747	+	0.481975i
$388$	−9.58760e22	+	8.30770e22i	−0.481088	+	0.416865i
$389$	1.71352e22	+	5.83571e22i	0.0840122	+	0.286119i	0.990774	−	0.135524i	$-0.0432717\pi$
$389$	1.71352e22	+	5.83571e22i	0.0840122	+	0.286119i	−0.906762	+	0.421643i	$0.861454\pi$
$390$		−	1.16746e23i		−	0.559319i
$391$	−7.21934e22	+	2.27217e23i	−0.337992	+	1.06378i
$392$	3.92210e23			1.79450
$393$	−1.02442e23	+	3.00796e22i	−0.458082	+	0.134505i
$394$	8.91938e22	+	1.02935e23i	0.389824	+	0.449881i
$395$	−1.46529e23	+	9.41685e22i	−0.625964	+	0.402283i
$396$	−2.41923e22	+	3.47833e21i	−0.101023	+	0.0145249i
$397$	2.99521e23	+	1.92491e23i	1.22268	+	0.785769i	0.982735	−	0.185018i	$-0.0592343\pi$
$397$	2.99521e23	+	1.92491e23i	1.22268	+	0.785769i	0.239945	+	0.970787i	$0.422871\pi$
$398$	−1.56599e23	−	7.15165e22i	−0.624945	−	0.285403i
$399$	1.22945e23	−	1.41886e23i	0.479684	−	0.553585i
$400$	3.15758e22	−	2.19615e23i	0.120452	−	0.837764i
$401$	−2.50650e23	+	1.14468e23i	−0.934906	+	0.426957i	−0.823819	−	0.566853i	$-0.808161\pi$
$401$	−2.50650e23	+	1.14468e23i	−0.934906	+	0.426957i	−0.111088	+	0.993811i	$0.535433\pi$
$402$	−6.55960e22	+	2.23400e23i	−0.239245	+	0.814794i
$403$	4.58991e23	+	1.34772e23i	1.63704	+	0.480678i
$404$	7.15137e22	+	1.56593e23i	0.249435	+	0.546186i
$405$	−4.64024e22	−	6.67166e21i	−0.158287	−	0.0227582i
$406$	2.10323e23	+	1.82246e23i	0.701702	+	0.608029i
$407$	7.60208e22	−	1.66462e23i	0.248075	−	0.543208i
$408$	−9.48479e22	+	1.47586e23i	−0.302751	+	0.471090i
$409$	−6.07391e22	−	4.22450e23i	−0.189653	−	1.31906i	−0.832908	−	0.553411i	$-0.813326\pi$
$409$	−6.07391e22	−	4.22450e23i	−0.189653	−	1.31906i	0.643255	−	0.765652i	$-0.277583\pi$
$410$	−9.19639e22	−	1.43099e23i	−0.280907	−	0.437100i
$411$	1.25582e23	−	1.08818e23i	0.375277	−	0.325179i
$412$	−7.46986e22	−	2.54400e23i	−0.218392	−	0.743776i
$413$			1.64814e23i			0.471460i
$414$	−8.11150e22	−	1.88505e23i	−0.227038	−	0.527618i
$415$	5.20649e22			0.142598
$416$	3.23277e23	−	9.49227e22i	0.866433	−	0.254408i
$417$	2.95763e22	+	3.41328e22i	0.0775745	+	0.0895257i
$418$	−1.07454e23	+	6.90566e22i	−0.275827	+	0.177263i
$419$	−4.89921e23	+	7.04401e22i	−1.23084	+	0.176967i	−0.726882	−	0.686763i	$-0.759031\pi$
$419$	−4.89921e23	+	7.04401e22i	−1.23084	+	0.176967i	−0.503954	+	0.863730i	$0.668122\pi$
$420$	1.08329e23	+	6.96191e22i	0.266381	+	0.171193i
$421$	8.15806e22	+	3.72566e22i	0.196358	+	0.0896736i	0.511167	−	0.859481i	$-0.329213\pi$
$421$	8.15806e22	+	3.72566e22i	0.196358	+	0.0896736i	−0.314809	+	0.949155i	$0.601941\pi$
$422$	−2.21437e23	+	2.55552e23i	−0.521722	+	0.602099i
$423$	1.40104e22	−	9.74446e22i	0.0323138	−	0.224747i
$424$	2.35377e23	−	1.07493e23i	0.531460	−	0.242710i
$425$	−9.69110e22	+	3.30049e23i	−0.214226	+	0.729588i
$426$	1.86588e23	+	5.47872e22i	0.403829	+	0.118575i
$427$	−2.73213e23	−	5.98252e23i	−0.578962	−	1.26775i
$428$	−2.28411e23	−	3.28405e22i	−0.473939	−	0.0681422i
$429$	−1.58594e23	−	1.37423e23i	−0.322234	−	0.279218i
$430$	−1.66116e23	+	3.63744e23i	−0.330519	+	0.723736i
$431$	−1.16016e22	+	1.80524e22i	−0.0226059	+	0.0351754i	−0.852373	−	0.522935i	$-0.824837\pi$
$431$	−1.16016e22	+	1.80524e22i	−0.0226059	+	0.0351754i	0.829767	+	0.558110i	$0.188473\pi$
$432$	−9.87923e22	−	6.87115e23i	−0.188525	−	1.31122i
$433$	−2.58989e23	−	4.02995e23i	−0.484051	−	0.753197i	0.510225	−	0.860041i	$-0.329562\pi$
$433$	−2.58989e23	−	4.02995e23i	−0.484051	−	0.753197i	−0.994276	+	0.106843i	$0.965926\pi$
$434$	−1.36466e24	+	1.18248e24i	−2.49814	+	2.16465i
$435$	−2.63592e22	−	8.97712e22i	−0.0472638	−	0.160966i
$436$		−	4.06150e23i		−	0.713359i
$437$	−2.32262e23	−	2.10396e23i	−0.399619	−	0.361997i
$438$	−5.19958e23			−0.876398
$439$	−2.90993e23	+	8.54433e22i	−0.480509	+	0.141090i	−0.513012	−	0.858381i	$-0.671470\pi$
$439$	−2.90993e23	+	8.54433e22i	−0.480509	+	0.141090i	0.0325028	+	0.999472i	$0.489652\pi$
$440$	8.15949e22	+	9.41656e22i	0.132005	+	0.152341i
$441$	6.59450e23	−	4.23802e23i	1.04528	−	0.671763i
$442$	−9.80338e23	+	1.40951e23i	−1.52256	+	0.218912i
$443$	7.68121e23	+	4.93642e23i	1.16895	+	0.751239i	0.973323	−	0.229439i	$-0.0736891\pi$
$443$	7.68121e23	+	4.93642e23i	1.16895	+	0.751239i	0.195628	+	0.980678i	$0.437325\pi$
$444$	−2.11318e23	−	9.65057e22i	−0.315130	−	0.143915i
$445$	−3.10044e23	+	3.57809e23i	−0.453088	+	0.522891i
$446$	8.93929e22	−	6.21741e23i	0.128023	−	0.890422i
$447$	4.96685e23	−	2.26829e23i	0.697130	−	0.318369i
$448$	1.22548e23	−	4.17359e23i	0.168579	−	0.574127i
$449$	1.25529e23	+	3.68586e22i	0.169249	+	0.0496961i	0.365259	−	0.930906i	$-0.380980\pi$
$449$	1.25529e23	+	3.68586e22i	0.169249	+	0.0496961i	−0.196010	+	0.980602i	$0.562799\pi$
$450$	−1.23000e23	−	2.69333e23i	−0.162552	−	0.355940i
$451$	−3.02645e23	−	4.35138e22i	−0.392053	−	0.0563687i
$452$	3.75171e23	+	3.25087e23i	0.476412	+	0.412814i
$453$	−1.59718e23	+	3.49734e23i	−0.198825	+	0.435365i
$454$	−3.48675e23	+	5.42548e23i	−0.425518	+	0.662119i
$455$	−1.47140e23	−	1.02338e24i	−0.176047	−	1.22443i
$456$	−1.24677e23	−	1.94001e23i	−0.146252	−	0.227573i
$457$	−1.56372e23	+	1.35497e23i	−0.179851	+	0.155842i	−0.740134	−	0.672459i	$-0.765238\pi$
$457$	−1.56372e23	+	1.35497e23i	−0.179851	+	0.155842i	0.560283	+	0.828301i	$0.310692\pi$
$458$	3.06170e23	+	1.04272e24i	0.345282	+	1.17592i
$459$			1.07623e24i			1.19012i
$460$	1.20169e23	−	1.78224e23i	0.130308	−	0.193261i
$461$	−8.22372e23			−0.874500			−0.437250	−	0.899340i	$-0.644048\pi$
$461$	−8.22372e23			−0.874500			−0.437250	+	0.899340i	$0.644048\pi$
$462$	7.60038e23	−	2.23167e23i	0.792606	−	0.232730i
$463$	−6.27791e23	−	7.24509e23i	−0.642075	−	0.740994i	0.337665	−	0.941266i	$-0.390363\pi$
$463$	−6.27791e23	−	7.24509e23i	−0.642075	−	0.740994i	−0.979740	+	0.200272i	$0.935817\pi$
$464$	4.30693e23	−	2.76790e23i	0.432023	−	0.277644i
$465$	6.00882e23	−	8.63938e22i	0.591170	−	0.0849974i
$466$	8.20157e23	+	5.27083e23i	0.791450	+	0.508634i
$467$	−6.87330e23	−	3.13893e23i	−0.650599	−	0.297119i	0.0626436	−	0.998036i	$-0.480047\pi$
$467$	−6.87330e23	−	3.13893e23i	−0.650599	−	0.297119i	−0.713242	+	0.700917i	$0.752774\pi$
$468$	1.63136e23	−	1.88269e23i	0.151474	−	0.174810i
$469$	−2.93447e23	+	2.04097e24i	−0.267285	+	1.85901i
$470$	3.20997e23	−	1.46594e23i	0.286827	−	0.130989i
$471$	1.82490e23	−	6.21504e23i	0.159975	−	0.544823i
$472$	1.94246e23	+	5.70357e22i	0.167060	+	0.0490534i
$473$	2.98594e23	+	6.53830e23i	0.251960	+	0.551714i
$474$	1.34632e24	+	1.93571e23i	1.11466	+	0.160264i
$475$	−3.41722e23	−	2.96103e23i	−0.277607	−	0.240548i
$476$	4.53816e23	−	9.93718e23i	0.361757	−	0.792138i
$477$	2.79603e23	−	4.35071e23i	0.218714	−	0.340326i
$478$	1.89332e23	+	1.31683e24i	0.145336	+	1.01083i
$479$	−5.22018e23	−	8.12275e23i	−0.393247	−	0.611904i	0.587022	−	0.809571i	$-0.300300\pi$
$479$	−5.22018e23	−	8.12275e23i	−0.393247	−	0.611904i	−0.980269	+	0.197666i	$0.936664\pi$
$480$	3.23133e23	−	2.79996e23i	0.238896	−	0.207005i
$481$	5.25495e23	+	1.78967e24i	0.381296	+	1.29858i
$482$		−	9.53579e23i		−	0.679099i
$483$	1.01443e24	+	1.65772e24i	0.709087	+	1.15874i
$484$	4.44247e23			0.304801
$485$	1.24023e24	−	3.64166e23i	0.835272	−	0.245258i
$486$	−1.01566e24	−	1.17213e24i	−0.671462	−	0.774909i
$487$	2.35052e24	−	1.51059e24i	1.52547	−	0.980359i	0.534662	−	0.845066i	$-0.320439\pi$
$487$	2.35052e24	−	1.51059e24i	1.52547	−	0.980359i	0.990806	−	0.135293i	$-0.0431975\pi$
$488$	−7.99632e23	+	1.14970e23i	−0.509462	+	0.0732496i
$489$	−1.23884e24	−	7.96156e23i	−0.774883	−	0.497987i
$490$	2.55596e24	+	1.16727e24i	1.56960	+	0.716813i
$491$	6.80889e23	−	7.85788e23i	0.410528	−	0.473775i	−0.512400	−	0.858747i	$-0.671243\pi$
$491$	6.80889e23	−	7.85788e23i	0.410528	−	0.473775i	0.922928	+	0.384972i	$0.125789\pi$
$492$	−5.52392e22	+	3.84197e23i	−0.0327010	+	0.227441i
$493$	−7.22002e23	+	3.29727e23i	−0.419678	+	0.191661i
$494$	3.66787e23	−	1.24916e24i	0.209349	−	0.712978i
$495$	2.38942e23	+	7.01596e22i	0.133920	+	0.0393224i
$496$	1.37994e24	+	3.02165e24i	0.759496	+	1.66306i
$497$	1.70466e24	+	2.45093e23i	0.921361	+	0.132472i
$498$	−3.07268e23	−	2.66249e23i	−0.163100	−	0.141327i
$499$	5.07862e22	−	1.11206e23i	0.0264753	−	0.0579729i	−0.895932	−	0.444190i	$-0.853491\pi$
$499$	5.07862e22	−	1.11206e23i	0.0264753	−	0.0579729i	0.922408	+	0.386218i	$0.126219\pi$
$500$	4.13799e23	−	6.43884e23i	0.211865	−	0.329669i
$501$	−2.76455e23	−	1.92279e24i	−0.139023	−	0.966924i
$502$	4.35979e23	+	6.78396e23i	0.215343	+	0.335081i
$503$	−9.90669e23	+	8.58419e23i	−0.480636	+	0.416474i	−0.861189	−	0.508286i	$-0.830279\pi$
$503$	−9.90669e23	+	8.58419e23i	−0.480636	+	0.416474i	0.380552	+	0.924759i	$0.375734\pi$
$504$	−3.76775e23	−	1.28318e24i	−0.179559	−	0.611522i
$505$		−	1.75403e24i		−	0.821135i
$506$	−3.44469e23	−	1.27659e24i	−0.158415	−	0.587081i
$507$	5.47729e23			0.247454
$508$	−2.15430e22	+	6.32560e21i	−0.00956165	+	0.00280755i
$509$	2.88112e24	+	3.32500e24i	1.25633	+	1.44988i	0.841756	+	0.539859i	$0.181522\pi$
$509$	2.88112e24	+	3.32500e24i	1.25633	+	1.44988i	0.414569	+	0.910018i	$0.363932\pi$
$510$	−1.05734e24	+	6.79512e23i	−0.452985	+	0.291116i
$511$	−4.55789e24	+	6.55326e23i	−1.91856	+	0.275848i
$512$	2.04559e23	+	1.31462e23i	0.0846036	+	0.0543714i
$513$	−1.28685e24	−	5.87685e23i	−0.522964	−	0.238830i
$514$	−2.67383e24	+	3.08577e24i	−1.06774	+	1.23224i
$515$	−3.84464e23	+	2.67400e24i	−0.150866	+	1.04929i
$516$	8.30014e23	−	3.79054e23i	0.320065	−	0.146169i
$517$	1.78706e23	−	6.08618e23i	0.0677213	−	0.230638i
$518$	−6.75549e24	−	1.98359e24i	−2.51587	−	0.738727i
$519$	−1.07623e24	−	2.35661e24i	−0.393911	−	0.862545i
$520$	−1.25705e24	−	1.80736e23i	−0.452191	−	0.0650153i
$521$	−1.57173e24	−	1.36191e24i	−0.555698	−	0.481515i	0.331149	−	0.943579i	$-0.392564\pi$
$521$	−1.57173e24	−	1.36191e24i	−0.555698	−	0.481515i	−0.886847	+	0.462063i	$0.847109\pi$
$522$	2.83820e23	−	6.21478e23i	0.0986297	−	0.215969i
$523$	−1.06897e24	+	1.66334e24i	−0.365131	+	0.568155i	−0.974404	−	0.224806i	$-0.927825\pi$
$523$	−1.06897e24	+	1.66334e24i	−0.365131	+	0.568155i	0.609273	+	0.792961i	$0.291462\pi$
$524$	−1.16219e23	−	8.08323e23i	−0.0390209	−	0.271396i
$525$	1.51600e24	+	2.35895e24i	0.500342	+	0.778547i
$526$	−3.44856e24	+	2.98820e24i	−1.11884	+	0.969477i
$527$	−1.45093e24	−	4.94142e24i	−0.462755	−	1.57600i
$528$		−	1.45722e24i		−	0.456899i
$529$	2.80380e24	−	1.63194e24i	0.864262	−	0.503042i
$530$	1.85382e24			0.561804
$531$	3.88229e23	−	1.13994e23i	0.115674	−	0.0339650i
$532$	9.40383e23	+	1.08526e24i	0.275486	+	0.317928i
$533$	2.62171e24	−	1.68487e24i	0.755161	−	0.485313i
$534$	3.65952e24	−	5.26160e23i	1.03646	−	0.149021i
$535$	1.97796e24	+	1.27116e24i	0.550849	+	0.354009i
$536$	2.30388e24	+	1.05215e24i	0.630924	+	0.288133i
$537$	−5.04707e23	+	5.82463e23i	−0.135916	+	0.156855i
$538$	−1.70907e23	+	1.18869e24i	−0.0452606	+	0.314794i
$539$	4.59433e24	−	2.09816e24i	1.19653	−	0.546437i
$540$	2.73374e23	−	9.31026e23i	0.0700186	−	0.238461i
$541$	−6.98175e24	−	2.05003e24i	−1.75869	−	0.516398i	−0.766621	−	0.642100i	$-0.778063\pi$
$541$	−6.98175e24	−	2.05003e24i	−1.75869	−	0.516398i	−0.992068	+	0.125702i	$0.959882\pi$
$542$	−2.32950e24	−	5.10090e24i	−0.577125	−	1.26373i
$543$	−6.41792e23	−	9.22757e22i	−0.156385	−	0.0224848i
$544$	−2.74131e24	−	2.37536e24i	−0.657004	−	0.569298i
$545$	−1.71909e24	+	3.76428e24i	−0.405257	+	0.887389i
$546$	−4.36499e24	+	6.79205e24i	−1.01216	+	1.57495i
$547$	7.64647e23	+	5.31823e24i	0.174411	+	1.21306i	0.869426	+	0.494063i	$0.164489\pi$
$547$	7.64647e23	+	5.31823e24i	0.174411	+	1.21306i	−0.695015	+	0.718995i	$0.744602\pi$
$548$	6.87152e23	+	1.06923e24i	0.154180	+	0.239909i
$549$	−1.22025e24	+	1.05735e24i	−0.269337	+	0.233382i
$550$	−5.37481e23	−	1.83049e24i	−0.116707	−	0.397469i
$551$		−	1.04335e24i		−	0.222878i
$552$	2.30480e24	−	6.21914e23i	0.484375	−	0.130701i
$553$	1.20456e25			2.49060
$554$	−9.46902e24	+	2.78036e24i	−1.92627	+	0.565604i
$555$	1.55006e24	+	1.78887e24i	0.310251	+	0.358048i
$556$	−2.90613e23	+	1.86766e23i	−0.0572324	+	0.0367810i
$557$	4.41047e24	−	6.34130e23i	0.854650	−	0.122880i	0.298956	−	0.954267i	$-0.403362\pi$
$557$	4.41047e24	−	6.34130e23i	0.854650	−	0.122880i	0.555694	+	0.831387i	$0.312452\pi$
$558$	3.72927e24	+	2.39666e24i	0.711077	+	0.456981i
$559$	−6.66416e24	−	3.04342e24i	−1.25037	−	0.571026i
$560$	4.70159e24	−	5.42593e24i	0.868066	−	1.00180i
$561$	−3.21519e23	+	2.23622e24i	−0.0584173	+	0.406301i
$562$	−9.99224e24	+	4.56330e24i	−1.78663	+	0.815929i
$563$	3.09080e23	−	1.05263e24i	0.0543870	−	0.185225i	−0.927819	−	0.373030i	$-0.878319\pi$
$563$	3.09080e23	−	1.05263e24i	0.0543870	−	0.185225i	0.982206	+	0.187805i	$0.0601372\pi$
$564$	−7.72619e23	−	2.26861e23i	−0.133799	−	0.0392870i
$565$	−2.10118e24	−	4.60094e24i	−0.358119	−	0.784171i
$566$	−3.38294e24	−	4.86393e23i	−0.567474	−	0.0815905i
$567$	2.45016e24	+	2.12308e24i	0.404527	+	0.350524i
$568$	8.78775e23	−	1.92425e24i	0.142805	−	0.312699i
$569$	5.12579e24	−	7.97588e24i	0.819880	−	1.27576i	−0.138529	−	0.990358i	$-0.544237\pi$
$569$	5.12579e24	−	7.97588e24i	0.819880	−	1.27576i	0.958409	−	0.285400i	$-0.0921263\pi$
$570$	−2.35124e23	−	1.63532e24i	−0.0370189	−	0.257472i
$571$	3.58390e24	+	5.57666e24i	0.555432	+	0.864269i	0.999497	−	0.0317257i	$-0.0101003\pi$
$571$	3.58390e24	+	5.57666e24i	0.555432	+	0.864269i	−0.444065	+	0.895995i	$0.646464\pi$
$572$	1.21306e24	−	1.05112e24i	0.185062	−	0.160357i
$573$	−1.04224e24	−	3.54955e24i	−0.156523	−	0.533067i
$574$			1.17636e25i			1.73914i
$575$	3.99249e24	−	2.44319e24i	0.581076	−	0.355587i
$576$	−1.06787e24			−0.153009
$577$	−1.73165e23	+	5.08458e22i	−0.0244274	+	0.00717253i	−0.293923	−	0.955829i	$-0.594961\pi$
$577$	−1.73165e23	+	5.08458e22i	−0.0244274	+	0.00717253i	0.269496	+	0.963002i	$0.413143\pi$
$578$	1.37793e24	+	1.59022e24i	0.191372	+	0.220855i
$579$	1.28462e24	−	8.25577e23i	0.175658	−	0.112889i
$580$	7.08346e23	−	1.01845e23i	0.0953660	−	0.0137116i
$581$	−3.02904e24	−	1.94665e24i	−0.401532	−	0.258049i
$582$	−9.18167e24	−	4.19313e24i	−1.19844	−	0.547308i
$583$	2.18215e24	−	2.51833e24i	0.280458	−	0.323666i
$584$	−8.04957e23	+	5.59860e24i	−0.101872	+	0.708539i
$585$	−2.30885e24	+	1.05442e24i	−0.287736	+	0.131405i
$586$	8.64348e23	−	2.94370e24i	0.106074	−	0.361256i
$587$	1.78912e24	+	5.25334e23i	0.216221	+	0.0634881i	0.388049	−	0.921639i	$-0.373149\pi$
$587$	1.78912e24	+	5.25334e23i	0.216221	+	0.0634881i	−0.171828	+	0.985127i	$0.554967\pi$
$588$	−2.66354e24	−	5.83234e24i	−0.317003	−	0.694140i
$589$	6.70078e24	+	9.63426e23i	0.785394	+	0.112923i
$590$	1.09612e24	+	9.49792e23i	0.126529	+	0.109638i
$591$	−1.31549e24	+	2.88052e24i	−0.149554	+	0.327479i
$592$	−7.00255e24	+	1.08962e25i	−0.784080	+	1.22005i
$593$	−6.71871e23	−	4.67296e24i	−0.0740958	−	0.515347i	−0.992742	−	0.120266i	$-0.961625\pi$
$593$	−6.71871e23	−	4.67296e24i	−0.0740958	−	0.515347i	0.918646	−	0.395082i	$-0.129284\pi$
$594$	−3.22703e24	−	5.02135e24i	−0.350529	−	0.545434i
$595$	−8.41212e24	+	7.28914e24i	−0.900021	+	0.779873i
$596$	1.17665e24	+	4.00729e24i	0.124002	+	0.422313i
$597$		−	4.00261e24i		−	0.415503i
$598$	1.11743e25	+	7.53436e24i	1.14264	+	0.770435i
$599$	−1.43350e25			−1.44396			−0.721981	−	0.691912i	$-0.756768\pi$
$599$	−1.43350e25			−1.44396			−0.721981	+	0.691912i	$0.756768\pi$
$600$	3.30482e24	−	9.70384e23i	0.327935	−	0.0962903i
$601$	−3.56573e24	−	4.11507e24i	−0.348560	−	0.402260i	0.554214	−	0.832374i	$-0.313019\pi$
$601$	−3.56573e24	−	4.11507e24i	−0.348560	−	0.402260i	−0.902775	+	0.430114i	$0.858473\pi$
$602$	2.32643e25	−	1.49511e25i	2.24038	−	1.43981i
$603$	5.01057e24	−	7.20411e23i	0.475370	−	0.0683478i
$604$	−2.47396e24	−	1.58992e24i	−0.231238	−	0.148608i
$605$	−4.11737e24	−	1.88034e24i	−0.379159	−	0.173156i
$606$	−8.96975e24	+	1.03516e25i	−0.813817	+	0.939194i
$607$	5.19851e22	−	3.61564e23i	0.00464708	−	0.0323212i	−0.987366	−	0.158456i	$-0.949348\pi$
$607$	5.19851e22	−	3.61564e23i	0.00464708	−	0.0323212i	0.992013	+	0.126135i	$0.0402573\pi$
$608$	4.33715e24	−	1.98071e24i	0.382008	−	0.174457i
$609$	−1.82291e24	+	6.20826e24i	−0.158201	+	0.538784i
$610$	−5.55322e24	−	1.63057e24i	−0.474872	−	0.139435i
$611$	2.68575e24	+	5.88098e24i	0.226306	+	0.495540i
$612$	−2.65464e24	−	3.81679e23i	−0.220416	−	0.0316910i
$613$	1.41371e25	+	1.22498e25i	1.15668	+	1.00227i	0.999893	+	0.0146413i	$0.00466062\pi$
$613$	1.41371e25	+	1.22498e25i	1.15668	+	1.00227i	0.156792	+	0.987632i	$0.449885\pi$
$614$	−2.38773e24	+	5.22839e24i	−0.192517	+	0.421553i
$615$	2.13814e24	−	3.32701e24i	0.169887	−	0.264349i
$616$	−1.22630e24	−	8.52912e24i	−0.0960221	−	0.667848i
$617$	−9.85610e24	−	1.53364e25i	−0.760569	−	1.18347i	−0.978246	−	0.207448i	$-0.933484\pi$
$617$	−9.85610e24	−	1.53364e25i	−0.760569	−	1.18347i	0.217677	−	0.976021i	$-0.430152\pi$
$618$	1.59433e25	−	1.38149e25i	1.21250	−	1.05064i
$619$	4.34158e24	+	1.47861e25i	0.325411	+	1.10825i	0.946015	+	0.324123i	$0.105069\pi$
$619$	4.34158e24	+	1.47861e25i	0.325411	+	1.10825i	−0.620604	+	0.784124i	$0.713113\pi$
$620$			4.64329e24i			0.343005i
$621$	9.83185e24	−	1.08537e25i	0.715831	−	0.790227i
$622$	6.45792e24			0.463424
$623$	3.14158e25	−	9.22452e24i	2.22206	−	0.652456i
$624$	9.72647e24	+	1.12249e25i	0.678100	+	0.782570i
$625$	1.77916e24	−	1.14340e24i	0.122263	−	0.0785738i
$626$	6.23523e24	−	8.96491e23i	0.422361	−	0.0607263i
$627$	−2.49828e24	−	1.60555e24i	−0.166815	−	0.107205i
$628$	4.50673e24	+	2.05815e24i	0.296637	+	0.135469i
$629$	1.31501e25	−	1.51760e25i	0.853241	−	0.984692i
$630$	1.36353e24	−	9.48356e24i	0.0872168	−	0.606606i
$631$	−3.09899e24	+	1.41526e24i	−0.195414	+	0.0892427i	−0.510719	−	0.859748i	$-0.670621\pi$
$631$	−3.09899e24	+	1.41526e24i	−0.195414	+	0.0892427i	0.315304	+	0.948991i	$0.397893\pi$
$632$	4.16852e24	−	1.41967e25i	0.259136	−	0.882537i
$633$	−7.54332e24	−	2.21492e24i	−0.462306	−	0.135745i
$634$	1.06425e25	+	2.33039e25i	0.643045	+	1.40807i
$635$	2.26439e23	+	3.25570e22i	0.0134892	+	0.00193946i
$636$	−3.19694e24	−	2.77016e24i	−0.187767	−	0.162701i
$637$	−2.13855e25	+	4.68278e25i	−1.23841	+	2.71174i
$638$	2.37997e24	−	3.70330e24i	0.135889	−	0.211448i
$639$	−6.01702e23	−	4.18493e24i	−0.0338746	−	0.235603i
$640$	−6.35216e24	−	9.88415e24i	−0.352615	−	0.548680i
$641$	−2.42211e25	+	2.09877e25i	−1.32578	+	1.14879i	−0.348388	+	0.937351i	$0.613271\pi$
$641$	−2.42211e25	+	2.09877e25i	−1.32578	+	1.14879i	−0.977390	+	0.211443i	$0.932184\pi$
$642$	−5.17274e24	−	1.76167e25i	−0.279194	−	0.950846i
$643$			2.44368e25i			1.30061i	0.759675	+	0.650303i	$0.225358\pi$
$643$			2.44368e25i			1.30061i	−0.759675	+	0.650303i	$0.774642\pi$
$644$	−1.36548e25	+	5.87574e24i	−0.716658	+	0.308383i
$645$	−9.29714e24			−0.481185
$646$	−1.34483e25	+	3.94877e24i	−0.686394	+	0.201544i
$647$	−1.30612e25	−	1.50735e25i	−0.657424	−	0.758708i	0.324930	−	0.945738i	$-0.394659\pi$
$647$	−1.30612e25	−	1.50735e25i	−0.657424	−	0.758708i	−0.982354	+	0.187030i	$0.940114\pi$
$648$	3.35011e24	−	2.15298e24i	0.166297	−	0.106872i
$649$	2.58051e24	−	3.71021e23i	0.126329	−	0.0181633i
$650$	1.63581e25	+	1.05127e25i	0.789793	+	0.507569i
$651$	−3.81884e25	−	1.74400e25i	−1.81845	−	0.830460i
$652$	7.37619e24	−	8.51257e24i	0.346420	−	0.399790i
$653$	−3.43726e24	+	2.39066e25i	−0.159218	+	1.10739i	0.740860	+	0.671660i	$0.234418\pi$
$653$	−3.43726e24	+	2.39066e25i	−0.159218	+	1.10739i	−0.900078	+	0.435729i	$0.856491\pi$
$654$	2.93952e25	−	1.34243e25i	1.34300	−	0.613329i
$655$	−2.34420e24	+	7.98362e24i	−0.105639	+	0.359773i
$656$	2.07642e25	+	6.09692e24i	0.922955	+	0.271004i
$657$	4.69613e24	+	1.02831e25i	0.205898	+	0.450854i
$658$	−2.41560e25	−	3.47311e24i	−1.04470	−	0.150205i
$659$	7.42646e24	+	6.43506e24i	0.316820	+	0.274526i	0.798724	−	0.601698i	$-0.205509\pi$
$659$	7.42646e24	+	6.43506e24i	0.316820	+	0.274526i	−0.481903	+	0.876224i	$0.660054\pi$
$660$	8.46165e23	−	1.85284e24i	0.0356090	−	0.0779728i
$661$	−3.36249e24	+	5.23214e24i	−0.139588	+	0.217203i	−0.904008	−	0.427515i	$-0.859389\pi$
$661$	−3.36249e24	+	5.23214e24i	−0.139588	+	0.217203i	0.764420	+	0.644718i	$0.223025\pi$
$662$	−5.80414e24	−	4.03687e25i	−0.237693	−	1.65319i
$663$	−1.24493e25	−	1.93716e25i	−0.502950	−	0.782605i
$664$	−3.34250e24	+	2.89629e24i	−0.133217	+	0.115433i
$665$	−4.12214e24	−	1.40387e25i	−0.162079	−	0.551992i
$666$			1.72849e25i			0.670498i
$667$	1.02935e25	+	3.27056e24i	0.393942	+	0.125167i
$668$	1.48583e25			0.561023
$669$	1.40124e25	−	4.11442e24i	0.522009	−	0.153276i
$670$	1.18826e25	+	1.37133e25i	0.436757	+	0.504044i
$671$	−8.75182e24	+	5.62445e24i	−0.317392	+	0.203975i
$672$	−2.92680e25	+	4.20810e24i	−1.04730	+	0.150578i
$673$	1.02884e25	+	6.61197e24i	0.363257	+	0.233451i	0.709518	−	0.704687i	$-0.248913\pi$
$673$	1.02884e25	+	6.61197e24i	0.363257	+	0.233451i	−0.346262	+	0.938138i	$0.612549\pi$
$674$	9.25550e23	+	4.22684e23i	0.0322449	+	0.0147257i
$675$	1.38370e25	−	1.59687e25i	0.475671	−	0.548954i
$676$	−5.96224e23	+	4.14683e24i	−0.0202250	+	0.140668i
$677$	−1.94535e25	+	8.88413e24i	−0.651179	+	0.297384i	−0.713482	−	0.700674i	$-0.752883\pi$
$677$	−1.94535e25	+	8.88413e24i	−0.651179	+	0.297384i	0.0623026	+	0.998057i	$0.480156\pi$
$678$	−1.11279e25	+	3.78981e25i	−0.367574	+	1.25184i
$679$	−8.57703e25	−	2.51844e25i	−2.79582	−	0.820926i
$680$	5.67969e24	+	1.24368e25i	0.182702	+	0.400063i
$681$	−1.48418e25	−	2.13393e24i	−0.471154	−	0.0677418i
$682$	2.15863e25	+	1.87046e25i	0.676267	+	0.585988i
$683$	1.31554e25	−	2.88064e25i	0.406742	−	0.890640i	−0.589800	−	0.807549i	$-0.700793\pi$
$683$	1.31554e25	−	2.88064e25i	0.406742	−	0.890640i	0.996542	−	0.0830910i	$-0.0264792\pi$
$684$	1.90597e24	−	2.96574e24i	0.0581581	−	0.0904958i
$685$	−1.84300e24	−	1.28183e25i	−0.0555021	−	0.386025i
$686$	−6.41996e25	−	9.98966e25i	−1.90816	−	2.96916i
$687$	−1.90951e25	+	1.65460e25i	−0.560160	+	0.485381i
$688$	−1.43329e25	−	4.88132e25i	−0.414989	−	1.41332i
$689$			3.39638e25i			0.970607i
$690$	1.68709e25	+	2.80649e24i	0.475878	+	0.0791629i
$691$	−2.58086e24			−0.0718557			−0.0359278	−	0.999354i	$-0.511439\pi$
$691$	−2.58086e24			−0.0718557			−0.0359278	+	0.999354i	$0.511439\pi$
$692$	1.90133e25	−	5.58281e24i	0.522520	−	0.153426i
$693$	−1.12780e25	−	1.30155e25i	−0.305938	−	0.353071i
$694$	1.71151e25	−	1.09992e25i	0.458295	−	0.294528i
$695$	3.48397e24	−	5.00920e23i	0.0920898	−	0.0132405i
$696$	6.68606e24	+	4.29687e24i	0.174456	+	0.112116i
$697$	−3.05190e25	−	1.39376e25i	−0.786096	−	0.358998i
$698$	−3.94687e25	+	4.55493e25i	−1.00358	+	1.15820i
$699$	−3.22581e24	+	2.24360e25i	−0.0809738	+	0.563185i
$700$	−1.95097e25	+	8.90979e24i	−0.483469	+	0.220793i
$701$	1.55048e25	−	5.28046e25i	0.379319	−	1.29184i	−0.519856	−	0.854254i	$-0.674014\pi$
$701$	1.55048e25	−	5.28046e25i	0.379319	−	1.29184i	0.899175	−	0.437589i	$-0.144167\pi$
$702$	5.83736e25	+	1.71400e25i	1.40988	+	0.413978i
$703$	1.09653e25	+	2.40106e25i	0.261469	+	0.572538i
$704$	−6.81048e24	−	9.79199e23i	−0.160333	−	0.0230525i
$705$	6.20057e24	+	5.37282e24i	0.144122	+	0.124882i
$706$	5.21308e24	−	1.14150e25i	0.119633	−	0.261960i
$707$	−6.55811e25	+	1.02046e26i	−1.48595	+	2.31218i
$708$	−4.70998e23	−	3.27586e24i	−0.0105371	−	0.0732868i
$709$	−2.21195e25	−	3.44186e25i	−0.488606	−	0.760286i	0.506163	−	0.862438i	$-0.331064\pi$
$709$	−2.21195e25	−	3.44186e25i	−0.488606	−	0.760286i	−0.994769	+	0.102152i	$0.967427\pi$
$710$	1.14536e25	−	9.92463e24i	0.249815	−	0.216466i
$711$	−8.33139e24	−	2.83741e25i	−0.179428	−	0.611077i
$712$		−	4.02181e25i		−	0.855267i
$713$	−3.05097e25	+	6.30887e25i	−0.640666	+	1.32479i
$714$	8.69204e25			1.80234
$715$	−1.56919e25	+	4.60755e24i	−0.321307	+	0.0943443i
$716$	−3.86040e24	−	4.45514e24i	−0.0780577	−	0.0900834i
$717$	−2.60207e25	+	1.67225e25i	−0.519573	+	0.333910i
$718$	9.06009e25	−	1.30264e25i	1.78654	−	0.256866i
$719$	8.23881e25	+	5.29476e25i	1.60437	+	1.03107i	0.965030	+	0.262141i	$0.0844285\pi$
$719$	8.23881e25	+	5.29476e25i	1.60437	+	1.03107i	0.639340	+	0.768924i	$0.279208\pi$
$720$	−1.60329e25	−	7.32199e24i	−0.308333	−	0.140811i
$721$	1.22345e26	−	1.41194e26i	2.32365	−	2.68163i
$722$	−6.39647e24	+	4.44884e25i	−0.119979	+	0.834472i
$723$	2.01670e25	−	9.20996e24i	0.373591	−	0.170613i
$724$	1.39723e24	−	4.75853e24i	0.0255635	−	0.0870614i
$725$	1.49521e25	+	4.39033e24i	0.270184	+	0.0793333i
$726$	1.46835e25	+	3.21524e25i	0.262060	+	0.573832i
$727$	9.47275e25	+	1.36198e25i	1.66981	+	0.240082i	0.911347	−	0.411638i	$-0.135043\pi$
$727$	9.47275e25	+	1.36198e25i	1.66981	+	0.240082i	0.758459	+	0.651720i	$0.225952\pi$
$728$	6.63752e25	+	5.75145e25i	1.15564	+	1.00137i
$729$	2.18217e25	−	4.77828e25i	0.375267	−	0.821720i
$730$	−2.19079e25	+	3.40894e25i	−0.372130	+	0.579046i
$731$	1.12248e25	+	7.80700e25i	0.188331	+	1.30987i
$732$	7.14004e24	+	1.11101e25i	0.118332	+	0.184128i
$733$	−2.19392e25	+	1.90104e25i	−0.359157	+	0.311212i	−0.815684	−	0.578498i	$-0.803639\pi$
$733$	−2.19392e25	+	1.90104e25i	−0.359157	+	0.311212i	0.456526	+	0.889710i	$0.349093\pi$
$734$	−1.92826e25	−	6.56707e25i	−0.311819	−	1.06196i
$735$			6.53292e25i			1.04357i
$736$	5.94587e24	+	4.89985e25i	0.0938242	+	0.773183i
$737$	3.26161e25			0.508423
$738$	2.77098e25	−	8.13634e24i	0.426704	−	0.125292i
$739$	1.42131e25	+	1.64028e25i	0.216216	+	0.249527i	0.853488	−	0.521112i	$-0.174483\pi$
$739$	1.42131e25	+	1.64028e25i	0.216216	+	0.249527i	−0.637272	+	0.770639i	$0.719937\pi$
$740$	−1.52308e25	+	9.78821e24i	−0.228895	+	0.147102i
$741$	2.99608e25	−	4.30771e24i	0.444825	−	0.0639561i
$742$	−1.07852e26	−	6.93121e25i	−1.58195	−	1.01666i
$743$	−9.41908e25	−	4.30155e25i	−1.36493	−	0.623341i	−0.407815	−	0.913064i	$-0.633709\pi$
$743$	−9.41908e25	−	4.30155e25i	−1.36493	−	0.623341i	−0.957110	+	0.289724i	$0.906437\pi$
$744$	−3.37699e25	+	3.89725e25i	−0.483474	+	0.557958i
$745$	6.05605e24	−	4.21207e25i	0.0856610	−	0.595785i
$746$	−1.18124e25	+	5.39454e24i	−0.165078	+	0.0753885i
$747$	−2.49038e24	+	8.48147e24i	−0.0343859	+	0.117108i
$748$	−1.65803e25	−	4.86841e24i	−0.226192	−	0.0664161i
$749$	−6.75468e25	−	1.47907e26i	−0.910476	−	1.99366i
$750$	6.02784e25	+	8.66672e24i	0.802805	+	0.115426i
$751$	1.40235e25	+	1.21514e25i	0.184543	+	0.159907i	0.742233	−	0.670142i	$-0.233767\pi$
$751$	1.40235e25	+	1.21514e25i	0.184543	+	0.159907i	−0.557690	+	0.830049i	$0.688312\pi$
$752$	−1.86501e25	+	4.08381e25i	−0.242505	+	0.531013i
$753$	−1.01364e25	+	1.57726e25i	−0.130235	+	0.202650i
$754$	6.38548e24	+	4.44120e25i	0.0810683	+	0.563843i
$755$	1.61996e25	+	2.52071e25i	0.203227	+	0.316227i
$756$	−5.07144e25	+	4.39443e25i	−0.628688	+	0.544761i
$757$	1.38487e25	+	4.71643e25i	0.169647	+	0.577764i	0.999796	+	0.0202218i	$0.00643722\pi$
$757$	1.38487e25	+	4.71643e25i	0.169647	+	0.577764i	−0.830149	+	0.557542i	$0.811745\pi$
$758$		−	3.51510e25i		−	0.425515i
$759$	2.36714e25	−	1.96148e25i	0.283170	−	0.234643i
$760$	−1.79722e25			−0.212461
$761$	4.29218e25	−	1.26030e25i	0.501437	−	0.147235i	−0.0212257	−	0.999775i	$-0.506757\pi$
$761$	4.29218e25	−	1.26030e25i	0.501437	−	0.147235i	0.522663	+	0.852539i	$0.324939\pi$
$762$	−1.16987e24	−	1.35010e24i	−0.0135065	−	0.0155873i
$763$	2.40756e26	−	1.54724e26i	2.74698	−	1.76538i
$764$	2.80080e25	−	4.02694e24i	0.315822	−	0.0454083i
$765$	2.29882e25	+	1.47736e25i	0.256184	+	0.164640i
$766$	−3.98513e25	−	1.81995e25i	−0.438918	−	0.200447i
$767$	−1.74011e25	+	2.00820e25i	−0.189417	+	0.218599i
$768$	−1.00465e25	+	6.98747e25i	−0.108084	+	0.751742i
$769$	3.84012e25	−	1.75372e25i	0.408326	−	0.186476i	−0.200653	−	0.979662i	$-0.564306\pi$
$769$	3.84012e25	−	1.75372e25i	0.408326	−	0.186476i	0.608979	+	0.793186i	$0.291579\pi$
$770$	1.73922e25	−	5.92323e25i	0.182784	−	0.622504i
$771$	−9.10847e25	−	2.67449e25i	−0.946142	−	0.277812i
$772$	4.85204e24	+	1.06245e25i	0.0498160	+	0.109082i
$773$	1.15844e26	+	1.66558e25i	1.17559	+	0.169025i	0.702301	−	0.711880i	$-0.252156\pi$
$773$	1.15844e26	+	1.66558e25i	1.17559	+	0.169025i	0.473293	+	0.880905i	$0.343065\pi$
$774$	−5.13089e25	−	4.44594e25i	−0.514664	−	0.445959i
$775$	−4.20030e25	+	9.19736e25i	−0.416452	+	0.911902i
$776$	−5.93634e25	+	9.23713e25i	−0.581786	+	0.905277i
$777$	−2.32961e25	−	1.62028e26i	−0.225681	−	1.56965i
$778$	−2.00114e25	−	3.11384e25i	−0.191629	−	0.298181i
$779$	3.33304e25	−	2.88810e25i	0.315503	−	0.273385i
$780$	5.84912e24	+	1.99203e25i	0.0547317	+	0.186399i
$781$		−	2.72417e25i		−	0.251985i
$782$	3.19787e24	−	1.45056e26i	0.0292415	−	1.32641i
$783$	4.87561e25			0.440730
$784$	−3.43001e26	+	1.00714e26i	−3.06514	+	0.900008i
$785$	−3.30578e25	−	3.81508e25i	−0.292044	−	0.337036i
$786$	5.46612e25	−	3.51286e25i	0.477393	−	0.306802i
$787$	−2.13767e26	+	3.07351e25i	−1.84573	+	0.265376i	−0.974319	−	0.225173i	$-0.927705\pi$
$787$	−2.13767e26	+	3.07351e25i	−1.84573	+	0.265376i	−0.871414	+	0.490549i	$0.836796\pi$
$788$	−2.03763e25	−	1.30950e25i	−0.173936	−	0.111782i
$789$	−9.65038e25	−	4.40718e25i	−0.814426	−	0.371936i
$790$	6.94166e25	−	8.01110e25i	0.579188	−	0.668418i
$791$	−4.97811e25	+	3.46235e26i	−0.410654	+	2.85616i
$792$	−1.92426e25	+	8.78780e24i	−0.156941	+	0.0716727i
$793$	2.98737e25	−	1.01741e26i	0.240897	−	0.820419i
$794$	−2.07903e26	−	6.10457e25i	−1.65758	−	0.486710i
$795$	1.79048e25	+	3.92059e25i	0.141145	+	0.309063i
$796$	3.03035e25	+	4.35699e24i	0.236198	+	0.0339601i
$797$	1.09349e26	+	9.47517e25i	0.842735	+	0.730234i	0.964996	−	0.262264i	$-0.0844690\pi$
$797$	1.09349e26	+	9.47517e25i	0.842735	+	0.730234i	−0.122261	+	0.992498i	$0.539014\pi$
$798$	−4.74637e25	+	1.03931e26i	−0.361690	+	0.791990i
$799$	3.76305e25	−	5.85542e25i	0.283543	−	0.441202i
$800$	1.01349e25	+	7.04896e25i	0.0755107	+	0.525189i
$801$	−4.34577e25	−	6.76214e25i	−0.320165	−	0.498186i
$802$	1.26735e26	−	1.09817e26i	0.923268	−	0.800017i
$803$	2.05209e25	+	6.98879e25i	0.147828	+	0.503457i
$804$		−	4.14050e25i		−	0.294950i
$805$	1.51425e26	+	3.33827e24i	1.06668	+	0.0235157i
$806$	−2.91126e26			−2.02799
$807$	−2.67899e25	+	7.86622e24i	−0.184548	+	0.0541882i
$808$	9.75740e25	+	1.12606e26i	0.664709	+	0.767116i
$809$	−1.13341e26	+	7.28398e25i	−0.763572	+	0.490718i	−0.863545	−	0.504272i	$-0.831761\pi$
$809$	−1.13341e26	+	7.28398e25i	−0.763572	+	0.490718i	0.0999727	+	0.994990i	$0.468124\pi$
$810$	2.82396e25	−	4.06024e24i	0.188145	−	0.0270512i
$811$	−1.37730e26	−	8.85135e25i	−0.907486	−	0.583206i	0.00151572	−	0.999999i	$-0.499518\pi$
$811$	−1.37730e26	−	8.85135e25i	−0.907486	−	0.583206i	−0.909001	+	0.416793i	$0.863154\pi$
$812$	−4.50181e25	−	2.05591e25i	−0.293348	−	0.133968i
$813$	8.53786e25	−	9.85321e25i	0.550217	−	0.634984i
$814$	−1.58496e25	+	1.10236e26i	−0.101018	+	0.702595i
$815$	−1.04395e26	+	4.76755e25i	−0.658052	+	0.300522i
$816$	4.50496e25	−	1.53425e26i	0.280853	−	0.956498i
$817$	−9.94780e25	−	2.92094e25i	−0.613379	−	0.180104i
$818$	1.07899e26	+	2.36266e26i	0.658019	+	1.44086i
$819$	1.73748e26	+	2.49812e25i	1.04801	+	0.150681i
$820$	2.28612e25	+	1.98093e25i	0.136387	+	0.118180i
$821$	−5.54779e25	+	1.21480e26i	−0.327365	+	0.716829i	−0.999726	−	0.0233942i	$-0.992553\pi$
$821$	−5.54779e25	+	1.21480e26i	−0.327365	+	0.716829i	0.672362	+	0.740223i	$0.265280\pi$
$822$	−5.46735e25	+	8.50737e25i	−0.319103	+	0.496534i
$823$	7.96564e24	+	5.54022e25i	0.0459856	+	0.319837i	0.999810	+	0.0194734i	$0.00619896\pi$
$823$	7.96564e24	+	5.54022e25i	0.0459856	+	0.319837i	−0.953825	+	0.300364i	$0.902892\pi$
$824$	−1.24069e26	−	1.93055e26i	−0.708463	−	1.10239i
$825$	3.35214e25	−	2.90465e25i	0.189338	−	0.164062i
$826$	−2.82585e25	−	9.62397e25i	−0.157881	−	0.537693i
$827$			4.41515e25i			0.244003i	0.992530	+	0.122002i	$0.0389313\pi$
$827$			4.41515e25i			0.244003i	−0.992530	+	0.122002i	$0.961069\pi$
$828$	2.32850e25	+	2.81006e25i	0.127292	+	0.153618i
$829$	2.77511e26			1.50069			0.750343	−	0.661048i	$-0.229888\pi$
$829$	2.77511e26			1.50069			0.750343	+	0.661048i	$0.229888\pi$
$830$	−3.04022e25	+	8.92689e24i	−0.162631	+	0.0477526i
$831$	−1.50256e26	−	1.73404e26i	−0.795100	−	0.917594i
$832$	5.89968e25	−	3.79150e25i	0.308830	−	0.198473i
$833$	5.48582e26	−	7.88742e25i	2.84078	−	0.408442i
$834$	−2.31227e25	−	1.48601e25i	−0.118453	−	0.0761248i
$835$	−1.37710e26	−	6.28899e25i	−0.697888	−	0.318715i
$836$	1.48750e25	−	1.71667e25i	0.0745764	−	0.0860657i
$837$	−4.50211e25	+	3.13128e26i	−0.223299	+	1.55308i
$838$	2.74001e26	−	1.25132e26i	1.34449	−	0.614007i
$839$	2.12247e25	−	7.22848e25i	0.103035	−	0.350905i	−0.891797	−	0.452435i	$-0.850556\pi$
$839$	2.12247e25	−	7.22848e25i	0.103035	−	0.350905i	0.994833	+	0.101530i	$0.0323737\pi$
$840$	1.06940e26	+	3.14004e25i	0.513601	+	0.150807i
$841$	−7.24896e25	−	1.58730e26i	−0.344438	−	0.754215i
$842$	−5.40251e25	−	7.76764e24i	−0.253973	−	0.0365157i
$843$	−1.93016e26	−	1.67249e26i	−0.897729	−	0.777887i
$844$	2.49803e25	−	5.46991e25i	0.114952	−	0.251709i
$845$	2.30780e25	−	3.59101e25i	0.105072	−	0.163495i
$846$	8.52646e24	+	5.93028e25i	0.0384092	+	0.267142i
$847$	1.69237e26	+	2.63338e26i	0.754302	+	1.17372i
$848$	−1.78242e26	+	1.54448e26i	−0.786045	+	0.681112i
$849$	−2.23869e25	−	7.62426e25i	−0.0976841	−	0.332682i
$850$		−	2.09341e26i		−	0.903823i
$851$	−2.71257e26	+	3.29165e25i	−1.15882	+	0.140620i
$852$	−3.45823e25			−0.146183
$853$	3.66588e25	−	1.07640e25i	0.153333	−	0.0450228i	−0.204165	−	0.978936i	$-0.565448\pi$
$853$	3.66588e25	−	1.07640e25i	0.153333	−	0.0450228i	0.357498	+	0.933914i	$0.383630\pi$
$854$	2.62111e26	+	3.02492e26i	1.08484	+	1.25197i
$855$	−3.02178e25	+	1.94198e25i	−0.123757	+	0.0795335i
$856$	−1.97695e26	+	2.84242e25i	−0.801181	+	0.115192i
$857$	1.32136e26	+	8.49187e25i	0.529900	+	0.340546i	0.778077	−	0.628168i	$-0.216195\pi$
$857$	1.32136e26	+	8.49187e25i	0.529900	+	0.340546i	−0.248177	+	0.968715i	$0.579831\pi$
$858$	1.16170e26	+	5.30529e25i	0.461007	+	0.210535i
$859$	1.81242e26	−	2.09165e26i	0.711739	−	0.821390i	−0.278549	−	0.960422i	$-0.589854\pi$
$859$	1.81242e26	−	2.09165e26i	0.711739	−	0.821390i	0.990288	+	0.139032i	$0.0443990\pi$
$860$	1.01203e25	−	7.03882e25i	0.0393285	−	0.273536i
$861$	−2.48786e26	+	1.13617e26i	−0.956748	+	0.436932i
$862$	3.67928e24	−	1.25305e25i	0.0140022	−	0.0476872i
$863$	1.21366e26	+	3.56364e25i	0.457089	+	0.134214i	0.502168	−	0.864770i	$-0.332536\pi$
$863$	1.21366e26	+	3.56364e25i	0.457089	+	0.134214i	−0.0450790	+	0.998983i	$0.514354\pi$
$864$	9.25590e25	+	2.02676e26i	0.344981	+	0.755402i
$865$	−1.99849e26	−	2.87340e25i	−0.737153	−	0.105987i
$866$	2.20327e26	+	1.90915e26i	0.804280	+	0.696913i
$867$	−2.03226e25	+	4.45004e25i	−0.0734190	+	0.160765i
$868$	1.73607e26	−	2.70138e26i	0.620712	−	0.965847i
$869$	−2.71164e25	−	1.88599e26i	−0.0959522	−	0.667362i
$870$	3.07838e25	+	4.79005e25i	0.107807	+	0.167751i
$871$	−2.51241e26	+	2.17702e26i	−0.870819	+	0.754569i
$872$	−9.90380e25	−	3.37292e26i	−0.339745	−	1.15707i
$873$			2.19455e26i			0.745105i
$874$	1.71698e26	+	8.30332e25i	0.576984	+	0.279029i
$875$	5.39316e26			1.79379
$876$	8.87202e25	−	2.60506e25i	0.292069	−	0.0857593i
$877$	−8.27488e25	−	9.54972e25i	−0.269628	−	0.311168i	0.604747	−	0.796417i	$-0.293274\pi$
$877$	−8.27488e25	−	9.54972e25i	−0.269628	−	0.311168i	−0.874376	+	0.485250i	$0.838729\pi$
$878$	1.55269e26	−	9.97855e25i	0.500766	−	0.321823i
$879$	7.06037e25	−	1.01513e25i	0.225386	−	0.0324057i
$880$	−9.55379e25	−	6.13985e25i	−0.301878	−	0.194005i
$881$	−1.94517e26	−	8.88331e25i	−0.608380	−	0.277838i	0.0873085	−	0.996181i	$-0.472173\pi$
$881$	−1.94517e26	−	8.88331e25i	−0.608380	−	0.277838i	−0.695689	+	0.718343i	$0.744901\pi$
$882$	−3.12407e26	+	3.60537e26i	−0.967173	+	1.11618i
$883$	6.73879e25	−	4.68693e26i	0.206507	−	1.43629i	−0.577932	−	0.816085i	$-0.696140\pi$
$883$	6.73879e25	−	4.68693e26i	0.206507	−	1.43629i	0.784439	−	0.620206i	$-0.212951\pi$
$884$	1.60213e26	−	7.31667e25i	0.485989	−	0.221944i
$885$	−9.50026e24	+	3.23549e25i	−0.0285263	+	0.0971518i
$886$	−5.33166e26	−	1.56552e26i	−1.58474	−	0.465323i
$887$	−2.41272e26	−	5.28313e26i	−0.709897	−	1.55446i	−0.827543	−	0.561402i	$-0.810262\pi$
$887$	−2.41272e26	−	5.28313e26i	−0.709897	−	1.55446i	0.117647	−	0.993056i	$-0.462465\pi$
$888$	−1.99024e26	−	2.86153e25i	−0.579681	−	0.0833455i
$889$	−1.19565e25	−	1.03604e25i	−0.0344738	−	0.0298717i
$890$	1.19694e26	−	2.62094e26i	0.341636	−	0.748078i
$891$	2.77254e25	−	4.31416e25i	0.0783392	−	0.121898i
$892$	1.58970e25	+	1.10566e26i	0.0444664	+	0.309270i
$893$	4.94650e25	+	7.69691e25i	0.136973	+	0.213134i
$894$	−2.51137e26	+	2.17612e26i	−0.688452	+	0.596547i
$895$	1.69220e25	+	5.76309e25i	0.0459244	+	0.156404i
$896$			8.12541e26i			2.18310i
$897$	−5.14177e25	+	3.09091e26i	−0.136767	+	0.822157i
$898$	−7.96196e25			−0.209668
$899$	−2.23860e26	+	6.57312e25i	−0.583632	+	0.171370i
$900$	3.44814e25	+	3.97937e25i	0.0890025	+	0.102714i
$901$	3.07603e26	−	1.97684e26i	0.786081	−	0.505184i
$902$	1.84184e26	−	2.64816e25i	0.466007	−	0.0670017i
$903$	5.40890e26	+	3.47609e26i	1.35494	+	0.870766i
$904$	3.90836e26	+	1.78489e26i	0.969346	+	0.442686i
$905$	−3.30910e25	+	3.81891e25i	−0.0812592	+	0.0937781i
$906$	3.32996e25	−	2.31604e26i	0.0809628	−	0.563109i
$907$	−2.83227e26	+	1.29345e26i	−0.681819	+	0.311376i	−0.726047	−	0.687645i	$-0.758645\pi$
$907$	−2.83227e26	+	1.29345e26i	−0.681819	+	0.311376i	0.0442278	+	0.999021i	$0.485917\pi$
$908$	3.23118e25	−	1.10044e26i	0.0770173	−	0.262297i
$909$	2.85734e26	+	8.38992e25i	0.674354	+	0.198008i
$910$	2.61385e26	+	5.72352e26i	0.610812	+	1.33749i
$911$	−2.25356e26	−	3.24013e25i	−0.521439	−	0.0749717i	−0.123430	−	0.992353i	$-0.539390\pi$
$911$	−2.25356e26	−	3.24013e25i	−0.521439	−	0.0749717i	−0.398009	+	0.917382i	$0.630299\pi$
$912$	1.58851e26	+	1.37645e26i	0.363945	+	0.315360i
$913$	−2.36599e25	+	5.18080e25i	−0.0536756	+	0.117533i
$914$	6.80782e25	−	1.05932e26i	0.152930	−	0.237963i
$915$	−1.91501e25	−	1.33192e26i	−0.0425973	−	0.296271i
$916$	−1.04483e26	−	1.62579e26i	−0.230138	−	0.358101i
$917$	4.34880e26	−	3.76825e26i	0.948517	−	0.821894i
$918$	−1.84527e26	−	6.28440e26i	−0.398543	−	1.35731i
$919$		−	4.64423e26i		−	0.993285i	−0.867955	−	0.496642i	$-0.834566\pi$
$919$		−	4.64423e26i		−	0.993285i	0.867955	−	0.496642i	$-0.165434\pi$
$920$	5.63367e25	−	1.77311e26i	0.119317	−	0.375530i
$921$	−1.33635e26			−0.280275
$922$	4.80206e26	−	1.41001e26i	0.997354	−	0.292850i
$923$	1.81829e26	+	2.09842e26i	0.373980	+	0.431596i
$924$	−1.18504e26	+	7.61578e25i	−0.241371	+	0.155120i
$925$	−3.90232e26	+	5.61069e25i	−0.787132	+	0.113172i
$926$	4.90807e26	+	3.15422e26i	0.980419	+	0.630077i
$927$	−4.17210e26	−	1.90533e26i	−0.825348	−	0.376924i
$928$	−1.07610e26	+	1.24189e26i	−0.210825	+	0.243305i
$929$	1.21876e26	−	8.47668e26i	0.236471	−	1.64469i	−0.432667	−	0.901554i	$-0.642427\pi$
$929$	1.21876e26	−	8.47668e26i	0.236471	−	1.64469i	0.669138	−	0.743138i	$-0.266663\pi$
$930$	−3.36059e26	+	1.53473e26i	−0.645757	+	0.294907i
$931$	−2.05249e26	+	6.99013e26i	−0.390601	+	1.33026i
$932$	−1.66351e26	−	4.88449e25i	−0.313531	−	0.0920611i
$933$	6.23725e25	+	1.36577e26i	0.116428	+	0.254942i
$934$	4.55170e26	+	6.54436e25i	0.841496	+	0.120989i
$935$	1.33063e26	+	1.15300e26i	0.243643	+	0.211118i
$936$	8.95697e25	−	1.96130e26i	0.162435	−	0.355682i
$937$	−2.76855e26	+	4.30795e26i	−0.497275	+	0.773775i	−0.995649	−	0.0931874i	$-0.970294\pi$
$937$	−2.76855e26	+	4.30795e26i	−0.497275	+	0.773775i	0.498374	+	0.866962i	$0.333931\pi$
$938$	−1.78586e26	−	1.24209e27i	−0.317703	−	2.20968i
$939$	7.91814e25	+	1.23209e26i	0.139519	+	0.217096i
$940$	−4.74270e25	+	4.10957e25i	−0.0827703	+	0.0717209i
$941$	2.68729e26	+	9.15206e26i	0.464523	+	1.58202i	0.775336	+	0.631549i	$0.217581\pi$
$941$	2.68729e26	+	9.15206e26i	0.464523	+	1.58202i	−0.310813	+	0.950471i	$0.600601\pi$
$942$			3.94203e26i			0.674934i
$943$	1.80455e26	+	4.19365e26i	0.306031	+	0.711192i
$944$	−1.84521e26			−0.309954
$945$	6.56032e26	−	1.92628e26i	1.09154	−	0.320504i
$946$	−2.86461e26	−	3.30594e26i	−0.472112	−	0.544847i
$947$	−7.31422e26	+	4.70056e26i	−1.19404	+	0.767362i	−0.977915	−	0.209004i	$-0.932978\pi$
$947$	−7.31422e26	+	4.70056e26i	−1.19404	+	0.767362i	−0.216124	+	0.976366i	$0.569341\pi$
$948$	−2.39420e26	+	3.44234e25i	−0.387155	+	0.0556645i
$949$	−6.24551e26	−	4.01375e26i	−1.00040	−	0.642916i
$950$	2.50310e26	+	1.14313e26i	0.397160	+	0.181377i
$951$	−3.90059e26	+	4.50152e26i	−0.613064	+	0.707513i
$952$	1.34563e26	−	9.35906e26i	0.209504	−	1.45714i
$953$	1.06397e24	−	4.85898e23i	0.00164094	−	0.000749391i	−0.414594	−	0.910006i	$-0.636077\pi$
$953$	1.06397e24	−	4.85898e23i	0.00164094	−	0.000749391i	0.416235	+	0.909257i	$0.363349\pi$
$954$	−8.86723e25	+	3.01990e26i	−0.135473	+	0.461379i
$955$	−2.76629e26	−	8.12255e25i	−0.418665	−	0.122931i
$956$	−9.82807e25	−	2.15205e26i	−0.147349	−	0.322649i
$957$	1.01307e26	+	1.45657e25i	0.150463	+	0.0216334i
$958$	4.44091e26	+	3.84807e26i	0.653405	+	0.566178i
$959$	−3.72040e26	+	8.14653e26i	−0.542278	+	1.18742i
$960$	4.81150e25	−	7.48684e25i	0.0694767	−	0.108108i
$961$	−1.15952e26	−	8.06463e26i	−0.165870	−	1.15365i
$962$	−6.13702e26	−	9.54939e26i	−0.869725	−	1.35332i
$963$	−3.01683e26	+	2.61410e26i	−0.423560	+	0.367017i
$964$	4.77756e25	+	1.62709e26i	0.0664527	+	0.226317i
$965$		−	1.19007e26i		−	0.163993i
$966$	−8.76584e26	−	7.94058e26i	−1.19674	−	1.08407i
$967$	6.88554e26			0.931322			0.465661	−	0.884963i	$-0.345817\pi$
$967$	6.88554e26			0.931322			0.465661	+	0.884963i	$0.345817\pi$
$968$	3.68930e26	−	1.08328e26i	0.494386	−	0.145165i
$969$	−2.13399e26	−	2.46275e26i	−0.283321	−	0.326969i
$970$	−6.61769e26	+	4.25293e26i	−0.870484	+	0.559426i
$971$	−1.13214e27	+	1.62777e26i	−1.47545	+	0.212138i	−0.832610	−	0.553859i	$-0.813155\pi$
$971$	−1.13214e27	+	1.62777e26i	−1.47545	+	0.212138i	−0.642844	+	0.765997i	$0.722246\pi$
$972$	2.32027e26	+	1.49115e26i	0.299600	+	0.192541i
$973$	−2.21420e26	−	1.01119e26i	−0.283270	−	0.129365i
$974$	−1.11353e27	+	1.28509e27i	−1.41147	+	1.62893i
$975$	−6.43392e25	+	4.47489e26i	−0.0808042	+	0.562006i
$976$	6.69783e26	−	3.05880e26i	0.833462	−	0.380629i
$977$	5.15660e25	−	1.75618e26i	0.0635788	−	0.216530i	−0.921576	−	0.388198i	$-0.873098\pi$
$977$	5.15660e25	−	1.75618e26i	0.0635788	−	0.216530i	0.985155	+	0.171669i	$0.0549158\pi$
$978$	8.59901e26	+	2.52490e26i	1.05051	+	0.308457i
$979$	−2.15150e26	−	4.71113e26i	−0.260434	−	0.570271i
$980$	−4.94604e26	−	7.11134e25i	−0.593230	−	0.0852936i
$981$	−5.30980e26	−	4.60097e26i	−0.631041	−	0.546800i
$982$	−2.62862e26	+	5.75587e26i	−0.309545	+	0.677809i
$983$	2.54520e25	−	3.96041e25i	0.0296989	−	0.0462124i	−0.826087	−	0.563543i	$-0.809438\pi$
$983$	2.54520e25	−	3.96041e25i	0.0296989	−	0.0462124i	0.855786	+	0.517331i	$0.173074\pi$
$984$	4.78107e25	+	3.32531e26i	0.0552802	+	0.384482i
$985$	1.33425e26	+	2.07613e26i	0.152866	+	0.237864i
$986$	3.65063e26	−	3.16329e26i	0.414454	−	0.359126i
$987$	−1.59854e26	−	5.44413e26i	−0.179833	−	0.612455i
$988$			2.31521e26i			0.258094i
$989$	6.00005e26	−	8.89872e26i	0.662809	−	0.983017i
$990$	−1.51554e26			−0.165902
$991$	9.60416e26	−	2.82004e26i	1.04183	−	0.305909i	0.284317	−	0.958730i	$-0.408233\pi$
$991$	9.60416e26	−	2.82004e26i	1.04183	−	0.305909i	0.757512	+	0.652822i	$0.226415\pi$
$992$	−6.98218e26	−	8.05786e26i	−0.750561	−	0.866193i
$993$	7.97688e26	−	5.12643e26i	0.849748	−	0.546100i
$994$	−1.03742e27	+	1.49159e26i	−1.09516	+	0.157460i
$995$	−2.62418e26	−	1.68646e26i	−0.274527	−	0.176428i
$996$	6.57685e25	+	3.00354e25i	0.0681842	+	0.0311387i
$997$	1.47027e26	−	1.69678e26i	0.151057	−	0.174329i	−0.675178	−	0.737655i	$-0.735933\pi$
$997$	1.47027e26	−	1.69678e26i	0.151057	−	0.174329i	0.826234	+	0.563326i	$0.190479\pi$
$998$	−1.05884e25	+	7.36442e25i	−0.0107809	+	0.0749831i
$999$	−1.12202e27	+	5.12409e26i	−1.13217	+	0.517043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.19.d.a.14.10	yes	350
23.5	odd	22	inner	23.19.d.a.5.10	✓	350

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.19.d.a.5.10	✓	350	23.5	odd	22	inner
23.19.d.a.14.10	yes	350	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-583.928 + 171.457i) q^{2} +(-9265.85 - 10693.4i) q^{3} +(91045.2 - 58511.2i) q^{4} +(-1.09148e6 + 156932. i) q^{5} +(7.24404e6 + 4.65546e6i) q^{6} +(6.93679e7 + 3.16793e7i) q^{7} +(6.13419e7 - 7.07923e7i) q^{8} +(2.66437e7 - 1.85311e8i) q^{9} +(6.10441e8 - 2.78779e8i) q^{10} +(3.39847e8 - 1.15741e9i) q^{11} +(-1.46929e9 - 4.31423e8i) q^{12} +(5.10751e9 + 1.11839e10i) q^{13} +(-4.59375e10 - 6.60482e9i) q^{14} +(1.17916e10 + 1.02175e10i) q^{15} +(-3.54670e10 + 7.76620e10i) q^{16} +(7.15621e10 - 1.11353e11i) q^{17} +(1.62148e10 + 1.12776e11i) q^{18} +(9.40679e10 + 1.46372e11i) q^{19} +(-9.01920e10 + 7.81518e10i) q^{20} +(-3.03995e11 - 1.03531e12i) q^{21} +7.34114e11i q^{22} +(-1.73896e12 + 4.69230e11i) q^{23} -1.32539e12 q^{24} +(-2.49347e12 + 7.32148e11i) q^{25} +(-4.89997e12 - 5.65487e12i) q^{26} +(-6.84001e12 + 4.39581e12i) q^{27} +(8.16921e12 - 1.17456e12i) q^{28} +(-5.04458e12 - 3.24196e12i) q^{29} +(-8.63734e12 - 3.94454e12i) q^{30} +(2.54791e13 - 2.94045e13i) q^{31} +(3.89993e12 - 2.71246e13i) q^{32} +(-1.55256e13 + 7.09030e12i) q^{33} +(-2.26949e13 + 7.72919e13i) q^{34} +(-8.06854e13 - 2.36914e13i) q^{35} +(-8.41698e12 - 1.84306e13i) q^{36} +(1.50162e14 + 2.15901e13i) q^{37} +(-8.00254e13 - 6.93424e13i) q^{38} +(7.22679e13 - 1.58245e14i) q^{39} +(-5.58441e13 + 8.68951e13i) q^{40} +(-3.60729e13 - 2.50892e14i) q^{41} +(3.55023e14 + 5.52426e14i) q^{42} +(-4.50330e14 + 3.90213e14i) q^{43} +(-3.67801e13 - 1.25262e14i) q^{44} +2.06445e14i q^{45} +(9.34974e14 - 5.72153e14i) q^{46} +5.25844e14 q^{47} +(1.15910e15 - 3.40343e14i) q^{48} +(2.74195e15 + 3.16438e15i) q^{49} +(1.33047e15 - 8.55044e14i) q^{50} +(-1.85382e15 + 2.66539e14i) q^{51} +(1.11940e15 + 7.19393e14i) q^{52} +(2.51278e15 + 1.14755e15i) q^{53} +(3.24039e15 - 3.73960e15i) q^{54} +(-1.89302e14 + 1.31663e15i) q^{55} +(6.49781e15 - 2.96745e15i) q^{56} +(6.93595e14 - 2.36217e15i) q^{57} +(3.50153e15 + 1.02814e15i) q^{58} +(8.97809e14 + 1.96593e15i) q^{59} +(1.67141e15 + 2.40313e14i) q^{60} +(-6.51784e15 - 5.64774e15i) q^{61} +(-9.83639e15 + 2.15387e16i) q^{62} +(7.71873e15 - 1.20106e16i) q^{63} +(-8.11755e14 - 5.64588e15i) q^{64} +(-7.32986e15 - 1.14055e16i) q^{65} +(7.85015e15 - 6.80220e15i) q^{66} +(7.61769e15 + 2.59435e16i) q^{67} -1.43253e16i q^{68} +(2.11306e16 + 1.42475e16i) q^{69} +5.11765e16 q^{70} +(2.16685e16 - 6.36245e15i) q^{71} +(-1.14842e16 - 1.32535e16i) q^{72} +(-5.07974e16 + 3.26455e16i) q^{73} +(-9.13858e16 + 1.31393e16i) q^{74} +(3.09332e16 + 1.98796e16i) q^{75} +(1.71289e16 + 7.82249e15i) q^{76} +(6.02404e16 - 6.95212e16i) q^{77} +(-1.50672e16 + 1.04794e17i) q^{78} +(1.43682e17 - 6.56174e16i) q^{79} +(2.65241e16 - 9.03326e16i) q^{80} +(4.07911e16 + 1.19774e16i) q^{81} +(6.40812e16 + 1.40318e17i) q^{82} +(-4.67350e16 - 6.71948e15i) q^{83} +(-8.82547e16 - 7.64731e16i) q^{84} +(-6.06340e16 + 1.32770e17i) q^{85} +(1.96056e17 - 3.05069e17i) q^{86} +(1.20749e16 + 8.39831e16i) q^{87} +(-6.10890e16 - 9.50563e16i) q^{88} +(3.24483e17 - 2.81166e17i) q^{89} +(-3.53964e16 - 1.20549e17i) q^{90} +9.37605e17i q^{91} +(-1.30869e17 + 1.44470e17i) q^{92} -5.50519e17 q^{93} +(-3.07055e17 + 9.01596e16i) q^{94} +(-1.25644e17 - 1.45001e17i) q^{95} +(-3.26189e17 + 2.09629e17i) q^{96} +(-1.16027e18 + 1.66822e17i) q^{97} +(-2.14366e18 - 1.37764e18i) q^{98} +(-2.05426e17 - 9.38150e16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 350 q - 179 q^{2} + 20119 q^{3} - 4092083 q^{4} - 11 q^{5} - 2318126 q^{6} - 11 q^{7} - 18825206 q^{8} - 4214797052 q^{9} - 11 q^{10} - 11 q^{11} + 5321755786 q^{12} + 655768935 q^{13} - 11 q^{14} + 253448904621 q^{15}+ \cdots - 95\!\cdots\!51 q^{99}+O(q^{100}) \) 350 * q - 179 * q^2 + 20119 * q^3 - 4092083 * q^4 - 11 * q^5 - 2318126 * q^6 - 11 * q^7 - 18825206 * q^8 - 4214797052 * q^9 - 11 * q^10 - 11 * q^11 + 5321755786 * q^12 + 655768935 * q^13 - 11 * q^14 + 253448904621 * q^15 - 121059691035 * q^16 - 296340696091 * q^17 + 845128269786 * q^18 + 34950057109 * q^19 - 4104516534283 * q^20 + 5306405877949 * q^21 - 8788512317886 * q^23 + 16248757876058 * q^24 + 15898871892338 * q^25 - 12820353995934 * q^26 - 13015455785135 * q^27 + 105657239863285 * q^28 + 24125383566071 * q^29 - 190975720579083 * q^30 + 21755707682535 * q^31 - 243907502265099 * q^32 + 261034241184453 * q^33 - 129972082436273 * q^34 - 266152601718391 * q^35 + 559915831168033 * q^36 + 428874756612181 * q^37 - 1776255039233686 * q^38 + 549617987179705 * q^39 + 3407519671874989 * q^40 + 453667246412903 * q^41 - 6199000632151481 * q^42 + 1284249744062989 * q^43 + 7033574851458386 * q^44 - 11529170898896835 * q^46 - 2752011365749412 * q^47 + 7346362951210082 * q^48 + 14923872408166082 * q^49 - 8729688416622456 * q^50 - 15827415309093971 * q^51 - 11781732119049248 * q^52 + 10327001802201029 * q^53 + 16483884134652258 * q^54 - 6495140540052155 * q^55 - 112789689088256488 * q^56 + 79316406647596261 * q^57 + 80750695224012275 * q^58 - 103310090431970893 * q^59 + 56789760614471819 * q^60 + 64312558011025621 * q^61 + 78525812725681666 * q^62 - 56271156969207411 * q^63 - 224715274461002686 * q^64 - 45304722356970395 * q^65 + 206405045580983832 * q^66 + 65297330513632789 * q^67 - 143603139268291161 * q^69 - 403103996477716918 * q^70 - 7242816485765057 * q^71 + 620604439361873263 * q^72 + 69596528836762215 * q^73 + 102815849039067692 * q^74 + 116102034703195999 * q^75 - 930398829208773122 * q^76 - 693643966535804563 * q^77 + 2957501787035331408 * q^78 + 960132297145477093 * q^79 - 2513912900105850122 * q^80 - 3453140773055113594 * q^81 + 841776961191439844 * q^82 + 2134251156441149669 * q^83 + 1875963344476894475 * q^84 - 2497986830714303135 * q^85 - 709961756623859245 * q^86 - 2620179835179103895 * q^87 + 746914657235259645 * q^88 + 2323216414828777369 * q^89 + 6947866797842083322 * q^90 - 2374143188353425254 * q^92 - 8687469182791611658 * q^93 - 3156566639060022579 * q^94 + 1273876168349301101 * q^95 + 19129033188570894661 * q^96 + 2956262222729055625 * q^97 - 5708307230013551083 * q^98 - 9593810550169008251 * q^99

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