LMFDB - Embedded newform 19.13.d.a.8.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,13,Mod(8,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 13, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.8"); S:= CuspForms(chi, 13); N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	19.d (of order $6$, degree $2$, 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:	$17.3658825282$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	19.8
Dual form			19.13.d.a.12.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-101.162 - 58.4061i) q^{2} +(-509.434 - 294.122i) q^{3} +(4774.55 + 8269.76i) q^{4} +(-5618.03 + 9730.71i) q^{5} +(34357.0 + 59508.1i) q^{6} +37646.3 q^{7} -636988. i q^{8} +(-92705.3 - 160570. i) q^{9} +(1.13667e6 - 656254. i) q^{10} +783956. q^{11} -5.61719e6i q^{12} +(4.05828e6 - 2.34305e6i) q^{13} +(-3.80839e6 - 2.19877e6i) q^{14} +(5.72403e6 - 3.30477e6i) q^{15} +(-1.76474e7 + 3.05663e7i) q^{16} +(-1.39779e7 + 2.42104e7i) q^{17} +2.16582e7i q^{18} +(2.46524e7 - 4.00696e7i) q^{19} -1.07294e8 q^{20} +(-1.91783e7 - 1.10726e7i) q^{21} +(-7.93068e7 - 4.57878e7i) q^{22} +(2.62275e7 + 4.54274e7i) q^{23} +(-1.87352e8 + 3.24503e8i) q^{24} +(5.89458e7 + 1.02097e8i) q^{25} -5.47393e8 q^{26} +4.21683e8i q^{27} +(1.79744e8 + 3.11326e8i) q^{28} +(-1.20694e8 + 6.96827e7i) q^{29} -7.72075e8 q^{30} -1.51983e9i q^{31} +(1.31097e9 - 7.56886e8i) q^{32} +(-3.99374e8 - 2.30578e8i) q^{33} +(2.82807e9 - 1.63279e9i) q^{34} +(-2.11498e8 + 3.66325e8i) q^{35} +(8.85251e8 - 1.53330e9i) q^{36} -1.25519e9i q^{37} +(-4.83421e9 + 2.61368e9i) q^{38} -2.75657e9 q^{39} +(6.19835e9 + 3.57862e9i) q^{40} +(2.33054e9 + 1.34554e9i) q^{41} +(1.29341e9 + 2.24026e9i) q^{42} +(-4.89343e9 + 8.47567e9i) q^{43} +(3.74303e9 + 6.48313e9i) q^{44} +2.08328e9 q^{45} -6.12740e9i q^{46} +(-9.65315e9 - 1.67197e10i) q^{47} +(1.79804e10 - 1.03810e10i) q^{48} -1.24240e10 q^{49} -1.37712e10i q^{50} +(1.42416e10 - 8.22240e9i) q^{51} +(3.87529e10 + 2.23740e10i) q^{52} +(-3.54098e10 + 2.04438e10i) q^{53} +(2.46289e10 - 4.26585e10i) q^{54} +(-4.40429e9 + 7.62845e9i) q^{55} -2.39802e10i q^{56} +(-2.43441e10 + 1.31620e10i) q^{57} +1.62796e10 q^{58} +(-2.66705e10 - 1.53982e10i) q^{59} +(5.46593e10 + 3.15576e10i) q^{60} +(-3.69317e10 - 6.39676e10i) q^{61} +(-8.87673e10 + 1.53749e11i) q^{62} +(-3.49001e9 - 6.04487e9i) q^{63} -3.22592e10 q^{64} +5.26532e10i q^{65} +(2.69344e10 + 4.66517e10i) q^{66} +(1.32272e10 - 7.63673e9i) q^{67} -2.66952e11 q^{68} -3.08564e10i q^{69} +(4.27913e10 - 2.47055e10i) q^{70} +(1.39702e9 + 8.06569e8i) q^{71} +(-1.02281e11 + 5.90522e10i) q^{72} +(3.02395e10 - 5.23763e10i) q^{73} +(-7.33107e10 + 1.26978e11i) q^{74} -6.93490e10i q^{75} +(4.49070e11 + 1.25554e10i) q^{76} +2.95130e10 q^{77} +(2.78861e11 + 1.61000e11i) q^{78} +(2.16844e11 + 1.25195e11i) q^{79} +(-1.98288e11 - 3.43444e11i) q^{80} +(7.47589e10 - 1.29486e11i) q^{81} +(-1.57175e11 - 2.72236e11i) q^{82} -3.72314e10 q^{83} -2.11466e11i q^{84} +(-1.57056e11 - 2.72030e11i) q^{85} +(9.90062e11 - 5.71613e11i) q^{86} +8.19808e10 q^{87} -4.99371e11i q^{88} +(-3.57320e10 + 2.06299e10i) q^{89} +(-2.10750e11 - 1.21676e11i) q^{90} +(1.52779e11 - 8.82071e10i) q^{91} +(-2.50449e11 + 4.33791e11i) q^{92} +(-4.47015e11 + 7.74252e11i) q^{93} +2.25521e12i q^{94} +(2.51408e11 + 4.64998e11i) q^{95} -8.90467e11 q^{96} +(4.94218e11 + 2.85337e11i) q^{97} +(1.25685e12 + 7.25640e11i) q^{98} +(-7.26768e10 - 1.25880e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 3 q^{2} + 1377 q^{3} + 37325 q^{4} + 3023 q^{5} - 26867 q^{6} + 202236 q^{7} + 3465518 q^{9} - 4210176 q^{10} + 225284 q^{11} + 212517 q^{13} - 21278490 q^{14} + 46075869 q^{15} - 72759187 q^{16}+ \cdots + 231693405580 q^{99}+O(q^{100}) $ 38 * q - 3 * q^2 + 1377 * q^3 + 37325 * q^4 + 3023 * q^5 - 26867 * q^6 + 202236 * q^7 + 3465518 * q^9 - 4210176 * q^10 + 225284 * q^11 + 212517 * q^13 - 21278490 * q^14 + 46075869 * q^15 - 72759187 * q^16 - 12325321 * q^17 - 73131462 * q^19 + 111917588 * q^20 + 156027138 * q^21 - 211346691 * q^22 - 279329041 * q^23 + 780422281 * q^24 - 372278836 * q^25 - 1597211628 * q^26 + 1073400576 * q^28 - 27282963 * q^29 - 5212471136 * q^30 + 2949918615 * q^32 + 3065041014 * q^33 + 8227712886 * q^34 - 6067993466 * q^35 - 7289473398 * q^36 + 20872085082 * q^38 - 10046427734 * q^39 - 11767148976 * q^40 + 17339304201 * q^41 - 18287327036 * q^42 + 19260286759 * q^43 - 11548377481 * q^44 + 53989159292 * q^45 - 44833646161 * q^47 - 133220290647 * q^48 + 102879628914 * q^49 - 15378013731 * q^51 + 103936340214 * q^52 + 52675070037 * q^53 - 45133036831 * q^54 - 45561195026 * q^55 + 174832261397 * q^57 - 208993675116 * q^58 - 59214662175 * q^59 + 258683654406 * q^60 - 121685590881 * q^61 + 107382291300 * q^62 - 124406826124 * q^63 - 436230170914 * q^64 - 179836732273 * q^66 + 293404150857 * q^67 - 6303456364 * q^68 - 772542532014 * q^70 - 30935350443 * q^71 + 1069728037986 * q^72 - 57455549261 * q^73 - 463964866074 * q^74 + 400484677011 * q^76 + 774791288632 * q^77 + 366171761466 * q^78 + 817499583117 * q^79 + 875293519598 * q^80 - 1180846958651 * q^81 - 1049473265553 * q^82 - 1792056205804 * q^83 - 65622331559 * q^85 + 3947361258426 * q^86 + 1119067320794 * q^87 - 3024866183331 * q^89 - 5555491205910 * q^90 - 983383383558 * q^91 + 4405076379092 * q^92 - 1829505362200 * q^93 + 7666034903 * q^95 + 4922340461862 * q^96 + 1304474752257 * q^97 + 9971274266091 * q^98 + 231693405580 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−101.162	−	58.4061i	−1.58066	−	0.912595i	−0.994763	−	0.102211i	$-0.967408\pi$
$2$	−101.162	−	58.4061i	−1.58066	−	0.912595i	−0.585899	−	0.810384i	$-0.699258\pi$
$3$	−509.434	−	294.122i	−0.698812	−	0.403459i	0.108093	−	0.994141i	$-0.465526\pi$
$3$	−509.434	−	294.122i	−0.698812	−	0.403459i	−0.806905	+	0.590682i	$0.798859\pi$
$4$	4774.55	+	8269.76i	1.16566	+	2.01898i
$5$	−5618.03	+	9730.71i	−0.359554	+	0.622765i	−0.987886	−	0.155179i	$-0.950404\pi$
$5$	−5618.03	+	9730.71i	−0.359554	+	0.622765i	0.628332	+	0.777945i	$0.283738\pi$
$6$	34357.0	+	59508.1i	0.736390	+	1.27547i
$7$	37646.3			0.319988			0.159994	−	0.987118i	$-0.448852\pi$
$7$	37646.3			0.319988			0.159994	+	0.987118i	$0.448852\pi$
$8$		−	636988.i		−	2.42992i
$9$	−92705.3	−	160570.i	−0.174441	−	0.302141i
$10$	1.13667e6	−	656254.i	1.13667	−	0.656254i
$11$	783956.			0.442523			0.221261	−	0.975215i	$-0.428983\pi$
$11$	783956.			0.442523			0.221261	+	0.975215i	$0.428983\pi$
$12$		−	5.61719e6i		−	1.88119i
$13$	4.05828e6	−	2.34305e6i	0.840779	−	0.485424i	−0.0167501	−	0.999860i	$-0.505332\pi$
$13$	4.05828e6	−	2.34305e6i	0.840779	−	0.485424i	0.857529	+	0.514436i	$0.171999\pi$
$14$	−3.80839e6	−	2.19877e6i	−0.505793	−	0.292020i
$15$	5.72403e6	−	3.30477e6i	0.502521	−	0.290131i
$16$	−1.76474e7	+	3.05663e7i	−1.05187	+	1.82189i
$17$	−1.39779e7	+	2.42104e7i	−0.579093	+	1.00302i	0.416491	+	0.909140i	$0.363260\pi$
$17$	−1.39779e7	+	2.42104e7i	−0.579093	+	1.00302i	−0.995584	+	0.0938780i	$0.970074\pi$
$18$			2.16582e7i			0.636777i
$19$	2.46524e7	−	4.00696e7i	0.524008	−	0.851713i
$19$	2.46524e7	−	4.00696e7i	0.524008	−	0.851713i
$20$	−1.07294e8			−1.67647
$21$	−1.91783e7	−	1.10726e7i	−0.223612	−	0.129102i
$22$	−7.93068e7	−	4.57878e7i	−0.699479	−	0.403844i
$23$	2.62275e7	+	4.54274e7i	0.177170	+	0.306868i	0.940910	−	0.338656i	$-0.109972\pi$
$23$	2.62275e7	+	4.54274e7i	0.177170	+	0.306868i	−0.763740	+	0.645524i	$0.776639\pi$
$24$	−1.87352e8	+	3.24503e8i	−0.980372	+	1.69805i
$25$	5.89458e7	+	1.02097e8i	0.241442	+	0.418190i
$26$	−5.47393e8			−1.77198
$27$			4.21683e8i			1.08844i
$28$	1.79744e8	+	3.11326e8i	0.372998	+	0.646051i
$29$	−1.20694e8	+	6.96827e7i	−0.202907	+	0.117149i	−0.598011	−	0.801488i	$-0.704042\pi$
$29$	−1.20694e8	+	6.96827e7i	−0.202907	+	0.117149i	0.395104	+	0.918637i	$0.370709\pi$
$30$	−7.72075e8			−1.05909
$31$		−	1.51983e9i		−	1.71248i	−0.516582	−	0.856238i	$-0.672796\pi$
$31$		−	1.51983e9i		−	1.71248i	0.516582	−	0.856238i	$-0.327204\pi$
$32$	1.31097e9	−	7.56886e8i	1.22093	−	0.704905i
$33$	−3.99374e8	−	2.30578e8i	−0.309240	−	0.178540i
$34$	2.82807e9	−	1.63279e9i	1.83070	−	1.05695i
$35$	−2.11498e8	+	3.66325e8i	−0.115053	+	0.199278i
$36$	8.85251e8	−	1.53330e9i	0.406679	−	0.704388i
$37$		−	1.25519e9i		−	0.489214i	−0.969622	−	0.244607i	$-0.921341\pi$
$37$		−	1.25519e9i		−	0.489214i	0.969622	−	0.244607i	$-0.0786589\pi$
$38$	−4.83421e9	+	2.61368e9i	−1.60555	+	0.868063i
$39$	−2.75657e9			−0.783395
$40$	6.19835e9	+	3.57862e9i	1.51327	+	0.873686i
$41$	2.33054e9	+	1.34554e9i	0.490630	+	0.283265i	0.724836	−	0.688922i	$-0.241916\pi$
$41$	2.33054e9	+	1.34554e9i	0.490630	+	0.283265i	−0.234206	+	0.972187i	$0.575249\pi$
$42$	1.29341e9	+	2.24026e9i	0.235636	+	0.408134i
$43$	−4.89343e9	+	8.47567e9i	−0.774110	+	1.34080i	0.161183	+	0.986925i	$0.448469\pi$
$43$	−4.89343e9	+	8.47567e9i	−0.774110	+	1.34080i	−0.935293	+	0.353874i	$0.884864\pi$
$44$	3.74303e9	+	6.48313e9i	0.515831	+	0.893446i
$45$	2.08328e9			0.250884
$46$		−	6.12740e9i		−	0.646739i
$47$	−9.65315e9	−	1.67197e10i	−0.895534	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$47$	−9.65315e9	−	1.67197e10i	−0.895534	−	1.55111i	−0.0623906	−	0.998052i	$-0.519872\pi$
$48$	1.79804e10	−	1.03810e10i	1.47012	−	0.848773i
$49$	−1.24240e10			−0.897608
$50$		−	1.37712e10i		−	0.881356i
$51$	1.42416e10	−	8.22240e9i	0.809354	−	0.467280i
$52$	3.87529e10	+	2.23740e10i	1.96013	+	1.13168i
$53$	−3.54098e10	+	2.04438e10i	−1.59760	+	0.922375i	−0.605652	+	0.795730i	$0.707087\pi$
$53$	−3.54098e10	+	2.04438e10i	−1.59760	+	0.922375i	−0.991948	+	0.126645i	$0.959579\pi$
$54$	2.46289e10	−	4.26585e10i	0.993304	−	1.72045i
$55$	−4.40429e9	+	7.62845e9i	−0.159111	+	0.275588i
$56$		−	2.39802e10i		−	0.777545i
$57$	−2.43441e10	+	1.31620e10i	−0.709815	+	0.383771i
$58$	1.62796e10			0.427637
$59$	−2.66705e10	−	1.53982e10i	−0.632295	−	0.365056i	0.149345	−	0.988785i	$-0.452283\pi$
$59$	−2.66705e10	−	1.53982e10i	−0.632295	−	0.365056i	−0.781640	+	0.623729i	$0.785617\pi$
$60$	5.46593e10	+	3.15576e10i	1.17154	+	0.676388i
$61$	−3.69317e10	−	6.39676e10i	−0.716837	−	1.24160i	−0.962247	−	0.272178i	$-0.912256\pi$
$61$	−3.69317e10	−	6.39676e10i	−0.716837	−	1.24160i	0.245410	−	0.969419i	$-0.421077\pi$
$62$	−8.87673e10	+	1.53749e11i	−1.56280	+	2.70685i
$63$	−3.49001e9	−	6.04487e9i	−0.0558192	−	0.0966816i
$64$	−3.22592e10			−0.469433
$65$			5.26532e10i			0.698144i
$66$	2.69344e10	+	4.66517e10i	0.325869	+	0.564422i
$67$	1.32272e10	−	7.63673e9i	0.146224	−	0.0844226i	−0.425103	−	0.905145i	$-0.639762\pi$
$67$	1.32272e10	−	7.63673e9i	0.146224	−	0.0844226i	0.571327	+	0.820722i	$0.306429\pi$
$68$	−2.66952e11			−2.70010
$69$		−	3.08564e10i		−	0.285924i
$70$	4.27913e10	−	2.47055e10i	0.363720	−	0.209994i
$71$	1.39702e9	+	8.06569e8i	0.0109057	+	0.00629639i	0.505443	−	0.862860i	$-0.331329\pi$
$71$	1.39702e9	+	8.06569e8i	0.0109057	+	0.00629639i	−0.494537	+	0.869156i	$0.664662\pi$
$72$	−1.02281e11	+	5.90522e10i	−0.734178	+	0.423878i
$73$	3.02395e10	−	5.23763e10i	0.199819	−	0.346097i	−0.748650	−	0.662965i	$-0.769298\pi$
$73$	3.02395e10	−	5.23763e10i	0.199819	−	0.346097i	0.948470	+	0.316868i	$0.102631\pi$
$74$	−7.33107e10	+	1.26978e11i	−0.446454	+	0.773281i
$75$		−	6.93490e10i		−	0.389648i
$76$	4.49070e11	+	1.25554e10i	2.33041	+	0.0651553i
$77$	2.95130e10			0.141602
$78$	2.78861e11	+	1.61000e11i	1.23828	+	0.714923i
$79$	2.16844e11	+	1.25195e11i	0.892039	+	0.515019i	0.874609	−	0.484829i	$-0.161118\pi$
$79$	2.16844e11	+	1.25195e11i	0.892039	+	0.515019i	0.0174302	+	0.999848i	$0.494452\pi$
$80$	−1.98288e11	−	3.43444e11i	−0.756408	−	1.31014i
$81$	7.47589e10	−	1.29486e11i	0.264699	−	0.458472i
$82$	−1.57175e11	−	2.72236e11i	−0.517013	−	0.895493i
$83$	−3.72314e10			−0.113878			−0.0569391	−	0.998378i	$-0.518134\pi$
$83$	−3.72314e10			−0.113878			−0.0569391	+	0.998378i	$0.518134\pi$
$84$		−	2.11466e11i		−	0.601957i
$85$	−1.57056e11	−	2.72030e11i	−0.416430	−	0.721278i
$86$	9.90062e11	−	5.71613e11i	2.44721	−	1.41290i
$87$	8.19808e10			0.189059
$88$		−	4.99371e11i		−	1.07529i
$89$	−3.57320e10	+	2.06299e10i	−0.0718981	+	0.0415104i	−0.535518	−	0.844524i	$-0.679884\pi$
$89$	−3.57320e10	+	2.06299e10i	−0.0718981	+	0.0415104i	0.463620	+	0.886034i	$0.346550\pi$
$90$	−2.10750e11	−	1.21676e11i	−0.396563	−	0.228956i
$91$	1.52779e11	−	8.82071e10i	0.269039	−	0.155330i
$92$	−2.50449e11	+	4.33791e11i	−0.413041	+	0.715408i
$93$	−4.47015e11	+	7.74252e11i	−0.690914	+	1.19670i
$94$			2.25521e12i			3.26904i
$95$	2.51408e11	+	4.64998e11i	0.342008	+	0.632571i
$96$	−8.90467e11			−1.13760
$97$	4.94218e11	+	2.85337e11i	0.593319	+	0.342553i	0.766409	−	0.642353i	$-0.222042\pi$
$97$	4.94218e11	+	2.85337e11i	0.593319	+	0.342553i	−0.173090	+	0.984906i	$0.555375\pi$
$98$	1.25685e12	+	7.25640e11i	1.41881	+	0.819153i
$99$	−7.26768e10	−	1.25880e11i	−0.0771942	−	0.133704i
$100$	−5.62879e11	+	9.74936e11i	−0.562879	+	0.974936i
$101$	−1.04680e12	−	1.81312e12i	−0.986137	−	1.70804i	−0.636772	−	0.771053i	$-0.719731\pi$
$101$	−1.04680e12	−	1.81312e12i	−0.986137	−	1.70804i	−0.349365	−	0.936987i	$-0.613603\pi$
$102$	−1.92095e12			−1.70575
$103$		−	1.03180e12i		−	0.864114i	−0.901846	−	0.432057i	$-0.857788\pi$
$103$		−	1.03180e12i		−	0.864114i	0.901846	−	0.432057i	$-0.142212\pi$
$104$	−1.49249e12	−	2.58507e12i	−1.17954	−	2.04302i
$105$	2.15488e11	−	1.24412e11i	0.160801	−	0.0928384i
$106$	4.77618e12			3.36702
$107$		−	4.46163e11i		−	0.297297i	−0.988890	−	0.148648i	$-0.952508\pi$
$107$		−	4.46163e11i		−	0.297297i	0.988890	−	0.148648i	$-0.0474923\pi$
$108$	−3.48722e12	+	2.01335e12i	−2.19754	+	1.26875i
$109$	−6.72005e11	−	3.87982e11i	−0.400695	−	0.231341i	0.286089	−	0.958203i	$-0.407645\pi$
$109$	−6.72005e11	−	3.87982e11i	−0.400695	−	0.231341i	−0.686784	+	0.726862i	$0.740978\pi$
$110$	8.91096e11	−	5.14474e11i	0.503000	−	0.290407i
$111$	−3.69178e11	+	6.39435e11i	−0.197378	+	0.341868i
$112$	−6.64361e11	+	1.15071e12i	−0.336586	+	0.582984i
$113$		−	7.43915e11i		−	0.357316i	−0.983911	−	0.178658i	$-0.942824\pi$
$113$		−	7.43915e11i		−	0.357316i	0.983911	−	0.178658i	$-0.0571756\pi$
$114$	3.23145e12	+	9.03471e10i	1.47220	+	0.0411609i
$115$	−5.89388e11			−0.254809
$116$	−1.15252e12	−	6.65407e11i	−0.473042	−	0.273111i
$117$	−7.52448e11	−	4.34426e11i	−0.293333	−	0.169356i
$118$	1.79870e12	+	3.11545e12i	0.666296	+	1.15406i
$119$	−5.26216e11	+	9.11432e11i	−0.185303	+	0.320954i
$120$	−2.10510e12	−	3.64614e12i	−0.704993	−	1.22108i
$121$	−2.52384e12			−0.804174
$122$			8.62815e12i			2.61673i
$123$	−7.91505e11	−	1.37093e12i	−0.228572	−	0.395898i
$124$	1.25686e13	−	7.25649e12i	3.45746	−	1.99617i
$125$	−4.06782e12			−1.06635
$126$			8.15351e11i			0.203761i
$127$	−3.76769e12	+	2.17527e12i	−0.897950	+	0.518432i	−0.876535	−	0.481339i	$-0.840151\pi$
$127$	−3.76769e12	+	2.17527e12i	−0.897950	+	0.518432i	−0.0214156	+	0.999771i	$0.506817\pi$
$128$	−2.10630e12	−	1.21607e12i	−0.478917	−	0.276503i
$129$	4.98576e12	−	2.87853e12i	1.08191	−	0.624644i
$130$	3.07527e12	−	5.32653e12i	0.637123	−	1.10353i
$131$	−4.47794e12	+	7.75603e12i	−0.886035	+	1.53466i	−0.0415125	+	0.999138i	$0.513218\pi$
$131$	−4.47794e12	+	7.75603e12i	−0.886035	+	1.53466i	−0.844523	+	0.535520i	$0.820116\pi$
$132$		−	4.40363e12i		−	0.832468i
$133$	9.28072e11	−	1.50847e12i	0.167676	−	0.272538i
$134$	−1.78413e12			−0.308175
$135$	−4.10328e12	−	2.36903e12i	−0.677842	−	0.391352i
$136$	1.54217e13	+	8.90375e12i	2.43725	+	1.40715i
$137$	−4.28431e12	−	7.42064e12i	−0.647974	−	1.12232i	−0.983606	−	0.180330i	$-0.942283\pi$
$137$	−4.28431e12	−	7.42064e12i	−0.647974	−	1.12232i	0.335632	−	0.941993i	$-0.391050\pi$
$138$	−1.80220e12	+	3.12150e12i	−0.260933	+	0.451949i
$139$	2.02924e12	+	3.51474e12i	0.281348	+	0.487310i	0.971717	−	0.236148i	$-0.0758850\pi$
$139$	2.02924e12	+	3.51474e12i	0.281348	+	0.487310i	−0.690369	+	0.723458i	$0.742552\pi$
$140$	−4.03923e12			−0.536451
$141$			1.13568e13i			1.44524i
$142$	−9.42171e10	−	1.63189e11i	−0.0114921	−	0.0199049i
$143$	3.18151e12	−	1.83685e12i	0.372064	−	0.214811i
$144$	6.54405e12			0.733958
$145$		−	1.56592e12i		−	0.168485i
$146$	−6.11820e12	+	3.53234e12i	−0.631693	+	0.364708i
$147$	6.32923e12	+	3.65418e12i	0.627259	+	0.362148i
$148$	1.03801e13	−	5.99296e12i	0.987714	−	0.570257i
$149$	9.15682e12	−	1.58601e13i	0.836810	−	1.44940i	−0.0557381	−	0.998445i	$-0.517751\pi$
$149$	9.15682e12	−	1.58601e13i	0.836810	−	1.44940i	0.892548	−	0.450952i	$-0.148915\pi$
$150$	−4.05041e12	+	7.01551e12i	−0.355591	+	0.615902i
$151$		−	7.45324e12i		−	0.628758i	−0.949298	−	0.314379i	$-0.898204\pi$
$151$		−	7.45324e12i		−	0.628758i	0.949298	−	0.314379i	$-0.101796\pi$
$152$	−2.55239e13	−	1.57033e13i	−2.06959	−	1.27330i
$153$	5.18330e12			0.404071
$154$	−2.98561e12	−	1.72374e12i	−0.223825	−	0.129225i
$155$	1.47890e13	+	8.53844e12i	1.06647	+	0.615727i
$156$	−1.31614e13	−	2.27961e13i	−0.913173	−	1.58166i
$157$	−6.04179e12	+	1.04647e13i	−0.403429	+	0.698760i	−0.994137	−	0.108125i	$-0.965515\pi$
$157$	−6.04179e12	+	1.04647e13i	−0.403429	+	0.698760i	0.590708	+	0.806885i	$0.298849\pi$
$158$	−1.46243e13	−	2.53300e13i	−0.940008	−	1.62814i
$159$	2.40519e13			1.48856
$160$			1.70088e13i			1.01381i
$161$	9.87370e11	+	1.71017e12i	0.0566924	+	0.0981941i
$162$	−1.51256e13	+	8.73275e12i	−0.836800	+	0.483126i
$163$	6.25038e12			0.333258			0.166629	−	0.986020i	$-0.446712\pi$
$163$	6.25038e12			0.333258			0.166629	+	0.986020i	$0.446712\pi$
$164$			2.56974e13i			1.32076i
$165$	4.48738e12	−	2.59079e12i	0.222377	−	0.128389i
$166$	3.76641e12	+	2.17454e12i	0.180003	+	0.103925i
$167$	−1.72385e13	+	9.95268e12i	−0.794698	+	0.458819i	−0.841614	−	0.540080i	$-0.818394\pi$
$167$	−1.72385e13	+	9.95268e12i	−0.794698	+	0.458819i	0.0469162	+	0.998899i	$0.485061\pi$
$168$	−7.05311e12	+	1.22163e13i	−0.313708	+	0.543357i
$169$	−6.69295e11	+	1.15925e12i	−0.0287275	+	0.0497574i
$170$			3.66922e13i			1.52013i
$171$	−8.71939e12	−	2.43783e11i	−0.348746	−	0.00975049i
$172$	−9.34557e13			−3.60940
$173$	1.99225e13	+	1.15023e13i	0.743136	+	0.429050i	0.823208	−	0.567739i	$-0.192182\pi$
$173$	1.99225e13	+	1.15023e13i	0.743136	+	0.429050i	−0.0800727	+	0.996789i	$0.525515\pi$
$174$	−8.29337e12	−	4.78818e12i	−0.298838	−	0.172534i
$175$	2.21909e12	+	3.84358e12i	0.0772586	+	0.133816i
$176$	−1.38348e13	+	2.39626e13i	−0.465476	+	0.806229i
$177$	9.05792e12	+	1.56888e13i	0.294570	+	0.510211i
$178$	4.81964e12			0.151529
$179$		−	3.35821e13i		−	1.02092i	−0.859903	−	0.510458i	$-0.829476\pi$
$179$		−	3.35821e13i		−	1.02092i	0.859903	−	0.510458i	$-0.170524\pi$
$180$	9.94673e12	+	1.72282e13i	0.292446	+	0.506531i
$181$	1.83875e13	−	1.06160e13i	0.522939	−	0.301919i	−0.215197	−	0.976571i	$-0.569039\pi$
$181$	1.83875e13	−	1.06160e13i	0.522939	−	0.301919i	0.738136	+	0.674651i	$0.235706\pi$
$182$	−2.06073e13			−0.567013
$183$			4.34497e13i			1.15686i
$184$	2.89367e13	−	1.67066e13i	0.745663	−	0.430509i
$185$	1.22139e13	+	7.05168e12i	0.304665	+	0.175899i
$186$	9.04421e13	−	5.22168e13i	2.18420	−	1.26105i
$187$	−1.09580e13	+	1.89799e13i	−0.256262	+	0.443858i
$188$	9.21788e13	−	1.59658e14i	2.08778	−	3.61614i
$189$			1.58748e13i			0.348287i
$190$	1.72572e12	−	6.17240e13i	0.0366817	−	1.31200i
$191$	5.11740e13			1.05402			0.527010	−	0.849859i	$-0.323313\pi$
$191$	5.11740e13			1.05402			0.527010	+	0.849859i	$0.323313\pi$
$192$	1.64339e13	+	9.48813e12i	0.328045	+	0.189397i
$193$	−8.23020e13	−	4.75171e13i	−1.59245	−	0.919402i	−0.992885	−	0.119078i	$-0.962006\pi$
$193$	−8.23020e13	−	4.75171e13i	−1.59245	−	0.919402i	−0.599567	−	0.800325i	$-0.704660\pi$
$194$	−3.33309e13	−	5.77307e13i	−0.625225	−	1.08292i
$195$	1.54865e13	−	2.68233e13i	0.281673	−	0.487871i
$196$	−5.93192e13	−	1.02744e14i	−1.04631	−	1.81226i
$197$	4.21763e13			0.721557			0.360779	−	0.932652i	$-0.382511\pi$
$197$	4.21763e13			0.721557			0.360779	+	0.932652i	$0.382511\pi$
$198$			1.69791e13i			0.281788i
$199$	4.21129e13	+	7.29418e13i	0.678105	+	1.17451i	0.975551	+	0.219774i	$0.0705320\pi$
$199$	4.21129e13	+	7.29418e13i	0.678105	+	1.17451i	−0.297446	+	0.954739i	$0.596135\pi$
$200$	6.50347e13	−	3.75478e13i	1.01617	−	0.586684i
$201$	−8.98451e12			−0.136244
$202$			2.44559e14i			3.59978i
$203$	−4.54368e12	+	2.62329e12i	−0.0649279	+	0.0374861i
$204$	1.35995e14	+	7.85165e13i	1.88686	+	1.08938i
$205$	−2.61861e13	+	1.51186e13i	−0.352815	+	0.203698i
$206$	−6.02633e13	+	1.04379e14i	−0.788587	+	1.36587i
$207$	4.86286e12	−	8.42273e12i	0.0618116	−	0.107061i
$208$			1.65395e14i			2.04241i
$209$	1.93264e13	−	3.14128e13i	0.231885	−	0.376902i
$210$	−2.90657e13			−0.338895
$211$	−1.00942e14	−	5.82790e13i	−1.14387	−	0.660416i	−0.196487	−	0.980506i	$-0.562953\pi$
$211$	−1.00942e14	−	5.82790e13i	−1.14387	−	0.660416i	−0.947387	+	0.320090i	$0.896287\pi$
$212$	−3.38131e14	−	1.95220e14i	−3.72452	−	2.15035i
$213$	−4.74459e11	−	8.21787e11i	−0.00508067	−	0.00879998i
$214$	−2.60586e13	+	4.51349e13i	−0.271312	+	0.469926i
$215$	−5.49829e13	−	9.52331e13i	−0.556669	−	0.964178i
$216$	2.68607e14			2.64481
$217$		−	5.72159e13i		−	0.547972i
$218$	4.53211e13	+	7.84984e13i	0.422242	+	0.731344i
$219$	−3.08100e13	+	1.77882e13i	−0.279272	+	0.161238i
$220$	−8.41139e13			−0.741877
$221$			1.31003e14i			1.12442i
$222$	7.46939e13	−	4.31245e13i	0.623975	−	0.360252i
$223$	−8.60641e13	−	4.96891e13i	−0.699830	−	0.404047i	0.107454	−	0.994210i	$-0.465730\pi$
$223$	−8.60641e13	−	4.96891e13i	−0.699830	−	0.404047i	−0.807284	+	0.590163i	$0.799064\pi$
$224$	4.93530e13	−	2.84940e13i	0.390684	−	0.225561i
$225$	1.09292e13	−	1.89299e13i	0.0842350	−	0.145899i
$226$	−4.34492e13	+	7.52562e13i	−0.326085	+	0.564796i
$227$			1.27378e14i			0.930981i	0.885053	+	0.465491i	$0.154122\pi$
$227$			1.27378e14i			0.930981i	−0.885053	+	0.465491i	$0.845878\pi$
$228$	−2.25079e14	−	1.38477e14i	−1.60223	−	0.985757i
$229$	−3.92373e13			−0.272073			−0.136037	−	0.990704i	$-0.543436\pi$
$229$	−3.92373e13			−0.272073			−0.136037	+	0.990704i	$0.543436\pi$
$230$	5.96239e13	+	3.44239e13i	0.402767	+	0.232537i
$231$	−1.50349e13	−	8.68042e12i	−0.0989532	−	0.0571306i
$232$	4.43870e13	+	7.68806e13i	0.284661	+	0.493048i
$233$	−9.58251e13	+	1.65974e14i	−0.598885	+	1.03730i	0.394100	+	0.919067i	$0.371056\pi$
$233$	−9.58251e13	+	1.65974e14i	−0.598885	+	1.03730i	−0.992986	+	0.118233i	$0.962277\pi$
$234$	5.07462e13	+	8.78951e13i	0.309107	+	0.535389i
$235$	2.16927e14			1.28797
$236$		−	2.94079e14i		−	1.70212i
$237$	−7.36450e13	−	1.27557e14i	−0.415578	−	0.719803i
$238$	1.06466e14	−	6.14684e13i	0.585802	−	0.338213i
$239$	−2.37136e14			−1.27236			−0.636180	−	0.771541i	$-0.719486\pi$
$239$	−2.37136e14			−1.27236			−0.636180	+	0.771541i	$0.719486\pi$
$240$			2.33283e14i			1.22072i
$241$	−5.24726e13	+	3.02951e13i	−0.267812	+	0.154621i	−0.627893	−	0.778300i	$-0.716082\pi$
$241$	−5.24726e13	+	3.02951e13i	−0.267812	+	0.154621i	0.360081	+	0.932921i	$0.382749\pi$
$242$	2.55318e14	+	1.47408e14i	1.27113	+	0.733885i
$243$	1.17907e14	−	6.80735e13i	0.572665	−	0.330629i
$244$	3.52664e14	−	6.10832e14i	1.67118	−	2.89456i
$245$	6.97986e13	−	1.20895e14i	0.322738	−	0.558999i
$246$			1.84915e14i			0.834374i
$247$	6.16141e12	−	2.20375e14i	0.0271330	−	0.970468i
$248$	−9.68113e14			−4.16117
$249$	1.89669e13	+	1.09506e13i	0.0795794	+	0.0459452i
$250$	4.11510e14	+	2.37585e14i	1.68554	+	0.973149i
$251$	−9.67343e13	−	1.67549e14i	−0.386846	−	0.670037i	0.605177	−	0.796091i	$-0.293102\pi$
$251$	−9.67343e13	−	1.67549e14i	−0.386846	−	0.670037i	−0.992023	+	0.126054i	$0.959769\pi$
$252$	3.33264e13	−	5.77231e13i	0.130132	−	0.225396i
$253$	2.05612e13	+	3.56131e13i	0.0784018	+	0.135796i
$254$	5.08197e14			1.89247
$255$			1.84775e14i			0.672050i
$256$	2.08119e14	+	3.60472e14i	0.739387	+	1.28066i
$257$	1.17943e13	−	6.80942e12i	0.0409329	−	0.0236326i	−0.479394	−	0.877600i	$-0.659143\pi$
$257$	1.17943e13	−	6.80942e12i	0.0409329	−	0.0236326i	0.520327	+	0.853967i	$0.325810\pi$
$258$	−6.72495e14			−2.28019
$259$		−	4.72532e13i		−	0.156543i
$260$	−4.35430e14	+	2.51395e14i	−1.40954	+	0.813799i
$261$	2.23779e13	+	1.29199e13i	0.0707908	+	0.0408711i
$262$	9.05999e14	−	5.23079e14i	2.80104	−	1.61718i
$263$	−1.30642e14	+	2.26279e14i	−0.394775	+	0.683771i	−0.993072	−	0.117503i	$-0.962511\pi$
$263$	−1.30642e14	+	2.26279e14i	−0.394775	+	0.683771i	0.598297	+	0.801274i	$0.295844\pi$
$264$	−1.46876e14	+	2.54396e14i	−0.433837	+	0.751428i
$265$		−	4.59416e14i		−	1.32657i
$266$	−1.81990e14	+	9.83954e13i	−0.513757	+	0.277770i
$267$	2.42708e13			0.0669910
$268$	1.26308e14	+	7.29238e13i	0.340896	+	0.196816i
$269$	2.47563e14	+	1.42930e14i	0.653389	+	0.377234i	0.789753	−	0.613424i	$-0.210208\pi$
$269$	2.47563e14	+	1.42930e14i	0.653389	+	0.377234i	−0.136364	+	0.990659i	$0.543542\pi$
$270$	2.76731e14	+	4.79313e14i	0.714292	+	1.23719i
$271$	−6.97244e13	+	1.20766e14i	−0.176023	+	0.304881i	−0.940515	−	0.339753i	$-0.889657\pi$
$271$	−6.97244e13	+	1.20766e14i	−0.176023	+	0.304881i	0.764492	+	0.644633i	$0.222990\pi$
$272$	−4.93348e14	−	8.54504e14i	−1.21826	−	2.11009i
$273$	−1.03774e14			−0.250677
$274$			1.00092e15i			2.36535i
$275$	4.62109e13	+	8.00397e13i	0.106844	+	0.185059i
$276$	2.55175e14	−	1.47325e14i	0.577276	−	0.333290i
$277$	4.04998e14			0.896550			0.448275	−	0.893896i	$-0.352039\pi$
$277$	4.04998e14			0.896550			0.448275	+	0.893896i	$0.352039\pi$
$278$		−	4.74080e14i		−	1.02703i
$279$	−2.44039e14	+	1.40896e14i	−0.517410	+	0.298727i
$280$	2.33345e14	+	1.34722e14i	0.484228	+	0.279569i
$281$	2.32565e14	−	1.34271e14i	0.472396	−	0.272738i	−0.244846	−	0.969562i	$-0.578737\pi$
$281$	2.32565e14	−	1.34271e14i	0.472396	−	0.272738i	0.717242	+	0.696824i	$0.245404\pi$
$282$	6.63307e14	−	1.14888e15i	1.31892	−	2.28444i
$283$	−2.42375e14	+	4.19805e14i	−0.471811	+	0.817201i	−0.999480	−	0.0322492i	$-0.989733\pi$
$283$	−2.42375e14	+	4.19805e14i	−0.471811	+	0.817201i	0.527669	+	0.849450i	$0.323066\pi$
$284$			1.54040e13i			0.0293578i
$285$	8.69040e12	−	3.10830e14i	0.0162170	−	0.580035i
$286$	−4.29132e14			−0.784142
$287$	8.77362e13	+	5.06545e13i	0.156996	+	0.0906415i
$288$	−2.43067e14	−	1.40335e14i	−0.425962	−	0.245929i
$289$	−9.94516e13	−	1.72255e14i	−0.170696	−	0.295655i
$290$	−9.14591e13	+	1.58412e14i	−0.153758	+	0.266317i
$291$	−1.67848e14	−	2.90721e14i	−0.276412	−	0.478760i
$292$	5.77520e14			0.931686
$293$		−	1.17429e15i		−	1.85596i	−0.372627	−	0.927981i	$-0.621543\pi$
$293$		−	1.17429e15i		−	1.85596i	0.372627	−	0.927981i	$-0.378457\pi$
$294$	−4.26853e14	−	7.39331e14i	−0.660989	−	1.14487i
$295$	2.99672e14	−	1.73016e14i	0.454688	−	0.262514i
$296$	−7.99540e14			−1.18875
$297$			3.30581e14i			0.481659i
$298$	−1.85265e15	+	1.06963e15i	−2.64543	+	1.52734i
$299$	2.12877e14	+	1.22905e14i	0.297922	+	0.172005i
$300$	5.73500e14	−	3.31110e14i	0.786693	−	0.454198i
$301$	−1.84220e14	+	3.19078e14i	−0.247706	+	0.429040i
$302$	−4.35315e14	+	7.53987e14i	−0.573802	+	0.993854i
$303$			1.23155e15i			1.59146i
$304$	7.89726e14	+	1.46066e15i	1.00054	+	1.85058i
$305$	8.29933e14			1.03097
$306$	−5.24354e14	−	3.02736e14i	−0.638699	−	0.368753i
$307$	7.26525e14	+	4.19460e14i	0.867802	+	0.501026i	0.866617	−	0.498974i	$-0.166290\pi$
$307$	7.26525e14	+	4.19460e14i	0.867802	+	0.501026i	0.00118462	+	0.999999i	$0.499623\pi$
$308$	1.40911e14	+	2.44066e14i	0.165060	+	0.285892i
$309$	−3.03474e14	+	5.25633e14i	−0.348635	+	0.603853i
$310$	−9.97394e14	−	1.72754e15i	−1.12382	−	1.94651i
$311$	−5.09177e14			−0.562738			−0.281369	−	0.959600i	$-0.590788\pi$
$311$	−5.09177e14			−0.562738			−0.281369	+	0.959600i	$0.590788\pi$
$312$			1.75590e15i			1.90358i
$313$	−7.86067e14	−	1.36151e15i	−0.835976	−	1.44795i	−0.893233	−	0.449593i	$-0.851569\pi$
$313$	−7.86067e14	−	1.36151e15i	−0.835976	−	1.44795i	0.0572575	−	0.998359i	$-0.481764\pi$
$314$	1.22240e15	−	7.05755e14i	1.27537	−	0.736336i
$315$	7.84279e13			0.0802800
$316$			2.39099e15i			2.40135i
$317$	−2.39228e14	+	1.38118e14i	−0.235752	+	0.136112i	−0.613223	−	0.789910i	$-0.710127\pi$
$317$	−2.39228e14	+	1.38118e14i	−0.235752	+	0.136112i	0.377471	+	0.926022i	$0.376794\pi$
$318$	−2.43315e15	−	1.40478e15i	−2.35291	−	1.35846i
$319$	−9.46187e13	+	5.46281e13i	−0.0897910	+	0.0518409i
$320$	1.81233e14	−	3.13905e14i	0.168786	−	0.292347i
$321$	−1.31226e14	+	2.27290e14i	−0.119947	+	0.207755i
$322$		−	2.30674e14i		−	0.206949i
$323$	6.25513e14	+	1.15693e15i	0.550834	+	1.01881i
$324$	1.42776e15			1.23420
$325$	4.78437e14	+	2.76226e14i	0.405999	+	0.234403i
$326$	−6.32304e14	−	3.65061e14i	−0.526769	−	0.304130i
$327$	2.28228e14	+	3.95303e14i	0.186673	+	0.323328i
$328$	8.57092e14	−	1.48453e15i	0.688311	−	1.19219i
$329$	−3.63405e14	−	6.29436e14i	−0.286560	−	0.496337i
$330$	−6.05273e14			−0.468670
$331$		−	1.38176e15i		−	1.05067i	−0.850896	−	0.525334i	$-0.823940\pi$
$331$		−	1.38176e15i		−	1.05067i	0.850896	−	0.525334i	$-0.176060\pi$
$332$	−1.77763e14	−	3.07895e14i	−0.132743	−	0.229918i
$333$	−2.01546e14	+	1.16363e14i	−0.147812	+	0.0853391i
$334$	2.32519e15			1.67486
$335$			1.71613e14i			0.121418i
$336$	6.76896e14	−	3.90806e14i	0.470420	−	0.271597i
$337$	−1.43436e15	−	8.28126e14i	−0.979213	−	0.565349i	−0.0771809	−	0.997017i	$-0.524592\pi$
$337$	−1.43436e15	−	8.28126e14i	−0.979213	−	0.565349i	−0.902033	+	0.431668i	$0.857925\pi$
$338$	1.35415e14	−	7.81818e13i	0.0908168	−	0.0524331i
$339$	−2.18802e14	+	3.78976e14i	−0.144163	+	0.249697i
$340$	1.49975e15	−	2.59764e15i	0.970832	−	1.68153i
$341$		−	1.19148e15i		−	0.757809i
$342$	8.67836e14	+	5.33928e14i	0.542352	+	0.333677i
$343$	−9.88792e14			−0.607212
$344$	5.39890e15	+	3.11706e15i	3.25803	+	1.88102i
$345$	3.00254e14	+	1.73352e14i	0.178063	+	0.102805i
$346$	−1.34361e15	−	2.32720e15i	−0.783097	−	1.35636i
$347$	−1.19841e15	+	2.07571e15i	−0.686483	+	1.18902i	0.286486	+	0.958085i	$0.407513\pi$
$347$	−1.19841e15	+	2.07571e15i	−0.686483	+	1.18902i	−0.972968	+	0.230938i	$0.925820\pi$
$348$	3.91421e14	+	6.77961e14i	0.220378	+	0.381706i
$349$	3.75166e14			0.207621			0.103811	−	0.994597i	$-0.466896\pi$
$349$	3.75166e14			0.207621			0.103811	+	0.994597i	$0.466896\pi$
$350$		−	5.18434e14i		−	0.282023i
$351$	9.88024e14	+	1.71131e15i	0.528354	+	0.915136i
$352$	1.02774e15	−	5.93365e14i	0.540290	−	0.311937i
$353$	−6.54938e14			−0.338495			−0.169247	−	0.985574i	$-0.554134\pi$
$353$	−6.54938e14			−0.338495			−0.169247	+	0.985574i	$0.554134\pi$
$354$		−	2.11615e15i		−	1.07529i
$355$	−1.56970e13	+	9.06265e12i	−0.00784234	+	0.00452778i
$356$	−3.41208e14	−	1.96997e14i	−0.167618	−	0.0967740i
$357$	5.36144e14	−	3.09543e14i	0.258984	−	0.149524i
$358$	−1.96140e15	+	3.39725e15i	−0.931684	+	1.61372i
$359$	8.36967e14	−	1.44967e15i	0.390968	−	0.677177i	−0.601609	−	0.798791i	$-0.705473\pi$
$359$	8.36967e14	−	1.44967e15i	0.390968	−	0.677177i	0.992578	+	0.121613i	$0.0388068\pi$
$360$		−	1.32703e15i		−	0.609628i
$361$	−9.97831e14	−	1.97563e15i	−0.450831	−	0.892609i
$362$	−2.48016e15			−1.10212
$363$	1.28573e15	+	7.42317e14i	0.561966	+	0.324451i
$364$	1.45890e15	+	8.42298e14i	0.627217	+	0.362124i
$365$	3.39773e14	+	5.88504e14i	0.143692	+	0.248881i
$366$	2.53773e15	−	4.39547e15i	1.05574	−	1.82860i
$367$	2.20477e15	+	3.81878e15i	0.902335	+	1.56289i	0.824455	+	0.565927i	$0.191482\pi$
$367$	2.20477e15	+	3.81878e15i	0.902335	+	1.56289i	0.0778793	+	0.996963i	$0.475185\pi$
$368$	−1.85140e15			−0.745440
$369$		−	4.98954e14i		−	0.197653i
$370$	−8.23723e14	−	1.42673e15i	−0.321049	−	0.556072i
$371$	−1.33305e15	+	7.69635e14i	−0.511213	+	0.295149i
$372$	−8.53717e15			−3.22149
$373$		−	3.72549e15i		−	1.38334i	−0.722212	−	0.691672i	$-0.756874\pi$
$373$		−	3.72549e15i		−	1.38334i	0.722212	−	0.691672i	$-0.243126\pi$
$374$	2.21708e15	−	1.28003e15i	0.810126	−	0.467726i
$375$	2.07228e15	+	1.19643e15i	0.745180	+	0.430230i
$376$	−1.06503e16	+	6.14894e15i	−3.76907	+	2.17607i
$377$	−3.26540e14	+	5.65583e14i	−0.113733	+	0.196992i
$378$	9.27186e14	−	1.60593e15i	0.317845	−	0.550525i
$379$			5.49965e14i			0.185567i	0.995686	+	0.0927833i	$0.0295764\pi$
$379$			5.49965e14i			0.185567i	−0.995686	+	0.0927833i	$0.970424\pi$
$380$	−2.64506e15	+	4.29923e15i	−0.878485	+	1.42787i
$381$	2.55918e15			0.836664
$382$	−5.17688e15	−	2.98887e15i	−1.66605	−	0.961894i
$383$	2.33043e15	+	1.34547e15i	0.738316	+	0.426267i	0.821457	−	0.570271i	$-0.193162\pi$
$383$	2.33043e15	+	1.34547e15i	0.738316	+	0.426267i	−0.0831404	+	0.996538i	$0.526495\pi$
$384$	7.15346e14	+	1.23902e15i	0.223115	+	0.386447i
$385$	−1.65805e14	+	2.87183e14i	−0.0509135	+	0.0881848i
$386$	5.55057e15	+	9.61387e15i	1.67809	+	2.90653i
$387$	1.81459e15			0.540147
$388$			5.44942e15i			1.59720i
$389$	8.59955e14	+	1.48949e15i	0.248186	+	0.429872i	0.963023	−	0.269420i	$-0.0868321\pi$
$389$	8.59955e14	+	1.48949e15i	0.248186	+	0.429872i	−0.714836	+	0.699292i	$0.753499\pi$
$390$	−3.13329e15	+	1.80901e15i	−0.890458	+	0.514106i
$391$	−1.46642e15			−0.410392
$392$			7.91397e15i			2.18111i
$393$	4.56243e15	−	2.63412e15i	1.23834	−	0.714958i
$394$	−4.26665e15	−	2.46335e15i	−1.14054	−	0.658490i
$395$	−2.43647e15	+	1.40669e15i	−0.641472	+	0.370354i
$396$	6.93998e14	−	1.20204e15i	0.179965	−	0.311708i
$397$	1.73560e15	−	3.00615e15i	0.443309	−	0.767834i	−0.554624	−	0.832101i	$-0.687138\pi$
$397$	1.73560e15	−	3.00615e15i	0.443309	−	0.767834i	0.997933	+	0.0642674i	$0.0204710\pi$
$398$		−	9.83861e15i		−	2.47534i
$399$	−9.16466e14	+	4.95500e14i	−0.227132	+	0.122802i
$400$	−4.16097e15			−1.01586
$401$	4.82917e14	+	2.78812e14i	0.116147	+	0.0670573i	0.556948	−	0.830547i	$-0.311972\pi$
$401$	4.82917e14	+	2.78812e14i	0.116147	+	0.0670573i	−0.440801	+	0.897605i	$0.645306\pi$
$402$	9.08894e14	+	5.24750e14i	0.215356	+	0.124336i
$403$	−3.56103e15	−	6.16789e15i	−0.831277	−	1.43981i
$404$	9.99603e15	−	1.73136e16i	2.29900	−	3.98199i
$405$	8.39995e14	+	1.45491e15i	0.190347	+	0.329691i
$406$	6.12866e14			0.136839
$407$		−	9.84012e14i		−	0.216488i
$408$	−5.23757e15	−	9.07174e15i	−1.13545	−	1.96666i
$409$	2.56826e15	−	1.48279e15i	0.548655	−	0.316766i	−0.199924	−	0.979811i	$-0.564070\pi$
$409$	2.56826e15	−	1.48279e15i	0.548655	−	0.316766i	0.748579	+	0.663045i	$0.230736\pi$
$410$	3.53206e15			0.743576
$411$			5.04043e15i			1.04572i
$412$	8.53272e15	−	4.92637e15i	1.74463	−	1.00726i
$413$	−1.00405e15	−	5.79687e14i	−0.202327	−	0.116814i
$414$	−9.83878e14	+	5.68042e14i	−0.195406	+	0.112818i
$415$	2.09167e14	−	3.62288e14i	0.0409453	−	0.0709194i
$416$	3.54684e15	−	6.14331e15i	0.684356	−	1.18534i
$417$		−	2.38737e15i		−	0.454050i
$418$	−3.78980e15	+	2.04901e15i	−0.710492	+	0.384138i
$419$	5.97330e15			1.10390			0.551951	−	0.833877i	$-0.313884\pi$
$419$	5.97330e15			1.10390			0.551951	+	0.833877i	$0.313884\pi$
$420$	2.05772e15	+	1.18802e15i	0.374878	+	0.216436i
$421$	−6.82989e15	−	3.94324e15i	−1.22665	−	0.708208i	−0.260324	−	0.965521i	$-0.583829\pi$
$421$	−6.82989e15	−	3.94324e15i	−1.22665	−	0.708208i	−0.966328	+	0.257314i	$0.917163\pi$
$422$	6.80770e15	+	1.17913e16i	1.20539	+	2.08779i
$423$	−1.78980e15	+	3.10002e15i	−0.312436	+	0.541155i
$424$	1.30225e16	+	2.25556e16i	2.24129	+	3.88203i
$425$	−3.29575e15			−0.559269
$426$			1.10845e14i			0.0185464i
$427$	−1.39034e15	−	2.40814e15i	−0.229379	−	0.397296i
$428$	3.68966e15	−	2.13022e15i	0.600238	−	0.346547i
$429$	−2.16103e15			−0.346670
$430$			1.28453e16i			2.03205i
$431$	−5.98141e15	+	3.45337e15i	−0.933125	+	0.538740i	−0.887798	−	0.460233i	$-0.847766\pi$
$431$	−5.98141e15	+	3.45337e15i	−0.933125	+	0.538740i	−0.0453261	+	0.998972i	$0.514433\pi$
$432$	−1.28893e16	−	7.44163e15i	−1.98302	−	1.14490i
$433$	−4.25158e15	+	2.45465e15i	−0.645094	+	0.372445i	−0.786574	−	0.617496i	$-0.788147\pi$
$433$	−4.25158e15	+	2.45465e15i	−0.645094	+	0.372445i	0.141480	+	0.989941i	$0.454814\pi$
$434$	−3.34176e15	+	5.78810e15i	−0.500077	+	0.866158i
$435$	−4.60570e14	+	7.97731e14i	−0.0679767	+	0.117739i
$436$		−	7.40976e15i		−	1.07866i
$437$	2.46683e15	+	6.89694e13i	0.354202	+	0.00990303i
$438$	4.15576e15			0.588580
$439$	−6.72553e15	−	3.88299e15i	−0.939592	−	0.542474i	−0.0497597	−	0.998761i	$-0.515846\pi$
$439$	−6.72553e15	−	3.88299e15i	−0.939592	−	0.542474i	−0.889832	+	0.456287i	$0.849179\pi$
$440$	4.85923e15	+	2.80548e15i	0.669655	+	0.386626i
$441$	1.15177e15	+	1.99493e15i	0.156580	+	0.271204i
$442$	7.65140e15	−	1.32526e16i	1.02614	−	1.77733i
$443$	1.05226e15	+	1.82257e15i	0.139220	+	0.241136i	0.927202	−	0.374562i	$-0.122207\pi$
$443$	1.05226e15	+	1.82257e15i	0.139220	+	0.241136i	−0.787981	+	0.615699i	$0.788874\pi$
$444$	−7.05063e15			−0.920302
$445$		−	4.63597e14i		−	0.0597009i
$446$	5.80430e15	+	1.00533e16i	0.737463	+	1.27732i
$447$	−9.32958e15	+	5.38644e15i	−1.16955	+	0.675237i
$448$	−1.21444e15			−0.150213
$449$		−	1.07758e16i		−	1.31513i	−0.753396	−	0.657567i	$-0.771586\pi$
$449$		−	1.07758e16i		−	1.31513i	0.753396	−	0.657567i	$-0.228414\pi$
$450$	−2.21124e15	+	1.27666e15i	−0.266294	+	0.153745i
$451$	1.82704e15	+	1.05484e15i	0.217115	+	0.125351i
$452$	6.15200e15	−	3.55186e15i	0.721416	−	0.416510i
$453$	−2.19216e15	+	3.79693e15i	−0.253678	+	0.439383i
$454$	7.43968e15	−	1.28859e16i	0.849609	−	1.47157i
$455$			1.98220e15i			0.223398i
$456$	8.38403e15	+	1.55069e16i	0.932532	+	1.72479i
$457$	−1.12808e15			−0.123834			−0.0619172	−	0.998081i	$-0.519721\pi$
$457$	−1.12808e15			−0.123834			−0.0619172	+	0.998081i	$0.519721\pi$
$458$	3.96933e15	+	2.29170e15i	0.430056	+	0.248293i
$459$	−1.02091e16	−	5.89424e15i	−1.09172	−	0.630307i
$460$	−2.81406e15	−	4.87410e15i	−0.297021	−	0.514455i
$461$	6.88601e15	−	1.19269e16i	0.717401	−	1.24257i	−0.244625	−	0.969618i	$-0.578665\pi$
$461$	6.88601e15	−	1.19269e16i	0.717401	−	1.24257i	0.962026	−	0.272957i	$-0.0880017\pi$
$462$	1.01398e15	+	1.75626e15i	0.104274	+	0.180608i
$463$	−1.55119e16			−1.57464			−0.787318	−	0.616547i	$-0.788531\pi$
$463$	−1.55119e16			−1.57464			−0.787318	+	0.616547i	$0.788531\pi$
$464$		−	4.91889e15i		−	0.492900i
$465$	−5.02268e15	−	8.69954e15i	−0.496842	−	0.860555i
$466$	1.93878e16	−	1.11935e16i	1.89327	−	1.09308i
$467$	5.09338e15			0.491026			0.245513	−	0.969393i	$-0.421044\pi$
$467$	5.09338e15			0.491026			0.245513	+	0.969393i	$0.421044\pi$
$468$		−	8.29675e15i		−	0.789646i
$469$	4.97955e14	−	2.87494e14i	0.0467900	−	0.0270142i
$470$	−2.19448e16	−	1.26698e16i	−2.03584	−	1.17540i
$471$	6.15578e15	−	3.55404e15i	0.563842	−	0.325535i
$472$	−9.80850e15	+	1.69888e16i	−0.887055	+	1.53642i
$473$	−3.83623e15	+	6.64455e15i	−0.342561	+	0.593334i
$474$			1.72053e16i			1.51702i
$475$	5.54415e15	+	1.55007e14i	0.482696	+	0.0134955i
$476$	−1.00498e16			−0.864001
$477$	6.56535e15	+	3.79050e15i	0.557375	+	0.321801i
$478$	2.39892e16	+	1.38502e16i	2.01117	+	1.16115i
$479$	5.85545e15	+	1.01419e16i	0.484782	+	0.839668i	0.999847	−	0.0174834i	$-0.00556543\pi$
$479$	5.85545e15	+	1.01419e16i	0.484782	+	0.839668i	−0.515065	+	0.857151i	$0.672232\pi$
$480$	5.00267e15	−	8.66487e15i	0.409029	−	0.708459i
$481$	−2.94097e15	−	5.09390e15i	−0.237476	−	0.411320i
$482$	7.07767e15			0.564427
$483$		−	1.16163e15i		−	0.0914922i
$484$	−1.20502e16	−	2.08716e16i	−0.937394	−	1.62361i
$485$	−5.55306e15	+	3.20606e15i	−0.426660	+	0.246332i
$486$	−1.59036e16			−1.20692
$487$			1.67662e16i			1.25678i	0.777898	+	0.628391i	$0.216286\pi$
$487$			1.67662e16i			1.25678i	−0.777898	+	0.628391i	$0.783714\pi$
$488$	−4.07466e16	+	2.35250e16i	−3.01698	+	1.74185i
$489$	−3.18416e15	−	1.83837e15i	−0.232885	−	0.134456i
$490$	−1.41220e16	+	8.15333e15i	−1.02028	+	0.589059i
$491$	5.93099e15	−	1.02728e16i	0.423290	−	0.733160i	−0.572969	−	0.819577i	$-0.694208\pi$
$491$	5.93099e15	−	1.02728e16i	0.423290	−	0.733160i	0.996259	+	0.0864170i	$0.0275418\pi$
$492$	7.55815e15	−	1.30911e16i	0.532875	−	0.922966i
$493$		−	3.89607e15i		−	0.271359i
$494$	−1.34946e16	+	2.19338e16i	−0.928533	+	1.50922i
$495$	1.63320e15			0.111022
$496$	4.64555e16	+	2.68211e16i	3.11995	+	1.80130i
$497$	5.25926e13	+	3.03643e13i	0.00348968	+	0.00201477i
$498$	−1.27916e15	−	2.21557e15i	−0.0838588	−	0.145248i
$499$	−7.61576e15	+	1.31909e16i	−0.493299	+	0.854419i	−0.999970	−	0.00772051i	$-0.997542\pi$
$499$	−7.61576e15	+	1.31909e16i	−0.493299	+	0.854419i	0.506671	+	0.862139i	$0.330876\pi$
$500$	−1.94220e16	−	3.36398e16i	−1.24301	−	2.15295i
$501$	1.17092e16			0.740459
$502$			2.25995e16i			1.41214i
$503$	−4.05213e15	−	7.01849e15i	−0.250193	−	0.433347i	0.713386	−	0.700771i	$-0.247161\pi$
$503$	−4.05213e15	−	7.01849e15i	−0.250193	−	0.433347i	−0.963579	+	0.267425i	$0.913827\pi$
$504$	−3.85051e15	+	2.22309e15i	−0.234928	+	0.135636i
$505$	2.35239e16			1.41828
$506$		−	4.80361e15i		−	0.286197i
$507$	6.81923e14	−	3.93709e14i	0.0401502	−	0.0231807i
$508$	−3.59780e16	−	2.07719e16i	−2.09341	−	1.20863i
$509$	−2.02625e16	+	1.16986e16i	−1.16516	+	0.672708i	−0.952536	−	0.304425i	$-0.901536\pi$
$509$	−2.02625e16	+	1.16986e16i	−1.16516	+	0.672708i	−0.212628	+	0.977133i	$0.568202\pi$
$510$	1.07920e16	−	1.86922e16i	0.613310	−	1.06228i
$511$	1.13840e15	−	1.97177e15i	0.0639398	−	0.110747i
$512$		−	3.86596e16i		−	2.14604i
$513$	1.68967e16	+	1.03955e16i	0.927037	+	0.570351i
$514$	−1.59085e15			−0.0862680
$515$	1.00401e16	+	5.79667e15i	0.538141	+	0.310696i
$516$	4.76095e16	+	2.74874e16i	2.52229	+	1.45625i
$517$	−7.56764e15	−	1.31075e16i	−0.396294	−	0.686401i
$518$	−2.75987e15	+	4.78024e15i	−0.142860	+	0.247441i
$519$	−6.76614e15	−	1.17193e16i	−0.346208	−	0.599650i
$520$	3.35395e16			1.69643
$521$			1.73131e16i			0.865665i	0.901474	+	0.432832i	$0.142486\pi$
$521$			1.73131e16i			0.865665i	−0.901474	+	0.432832i	$0.857514\pi$
$522$	−1.50920e15	−	2.61402e15i	−0.0745975	−	0.129207i
$523$	3.29798e16	−	1.90409e16i	1.61153	−	0.930417i	0.622514	−	0.782609i	$-0.286111\pi$
$523$	3.29798e16	−	1.90409e16i	1.61153	−	0.930417i	0.989016	−	0.147808i	$-0.0472219\pi$
$524$	−8.55206e16			−4.13127
$525$		−	2.61073e15i		−	0.124683i
$526$	2.64322e16	−	1.52606e16i	1.24801	−	0.720540i
$527$	3.67957e16	+	2.12440e16i	1.71764	+	0.991682i
$528$	1.40959e16	−	8.13824e15i	0.650561	−	0.375601i
$529$	9.58154e15	−	1.65957e16i	0.437221	−	0.757290i
$530$	−2.68327e16	+	4.64756e16i	−1.21062	+	2.09686i
$531$			5.70999e15i			0.254723i
$532$	1.69058e16	+	4.72665e14i	0.745704	+	0.0208489i
$533$	1.26106e16			0.550015
$534$	−2.45529e15	−	1.41756e15i	−0.105890	−	0.0611357i
$535$	4.34148e15	+	2.50655e15i	0.185146	+	0.106894i
$536$	−4.86451e15	−	8.42557e15i	−0.205140	−	0.355313i
$537$	−9.87724e15	+	1.71079e16i	−0.411898	+	0.713428i
$538$	−1.66960e16	−	2.89184e16i	−0.688525	−	1.19256i
$539$	−9.73990e15			−0.397212
$540$		−	4.52442e16i		−	1.82474i
$541$	−3.08725e15	−	5.34728e15i	−0.123137	−	0.213280i	0.797866	−	0.602835i	$-0.205962\pi$
$541$	−3.08725e15	−	5.34728e15i	−0.123137	−	0.213280i	−0.921003	+	0.389555i	$0.872629\pi$
$542$	1.41070e16	−	8.14466e15i	0.556465	−	0.321275i
$543$	−1.24896e16			−0.487248
$544$			4.23187e16i			1.63282i
$545$	7.55068e15	−	4.35939e15i	0.288142	−	0.166359i
$546$	1.04981e16	+	6.06106e15i	0.396236	+	0.228767i
$547$	4.01445e16	−	2.31774e16i	1.49866	−	0.865249i	0.498657	−	0.866800i	$-0.333827\pi$
$547$	4.01445e16	−	2.31774e16i	1.49866	−	0.865249i	0.999999	+	0.00155044i	$0.000493521\pi$
$548$	4.09113e16	−	7.08604e16i	1.51064	−	2.61650i
$549$	−6.84752e15	+	1.18603e16i	−0.250092	+	0.433172i
$550$		−	1.07960e16i		−	0.390020i
$551$	−1.83241e14	+	6.55401e15i	−0.00654808	+	0.234206i
$552$	−1.96551e16			−0.694771
$553$	8.16335e15	+	4.71311e15i	0.285442	+	0.164800i
$554$	−4.09706e16	−	2.36544e16i	−1.41714	−	0.818188i
$555$	−4.14811e15	−	7.18473e15i	−0.141936	−	0.245840i
$556$	−1.93774e16	+	3.35626e16i	−0.655914	+	1.13608i
$557$	1.11166e16	+	1.92546e16i	0.372257	+	0.644767i	0.989912	−	0.141681i	$-0.0452508\pi$
$557$	1.11166e16	+	1.92546e16i	0.372257	+	0.644767i	−0.617656	+	0.786449i	$0.711917\pi$
$558$	3.29168e16			1.09047
$559$			4.58622e16i			1.50309i
$560$	−7.46480e15	−	1.29294e16i	−0.242042	−	0.419228i
$561$	1.11648e16	−	6.44600e15i	0.358157	−	0.206782i
$562$	−3.13691e16			−0.995598
$563$		−	1.30898e16i		−	0.411037i	−0.978653	−	0.205519i	$-0.934112\pi$
$563$		−	1.30898e16i		−	0.411037i	0.978653	−	0.205519i	$-0.0658881\pi$
$564$	−9.39180e16	+	5.42236e16i	−2.91793	+	1.68467i
$565$	7.23883e15	+	4.17934e15i	0.222524	+	0.128474i
$566$	4.90383e16	−	2.83123e16i	1.49155	−	0.861146i
$567$	2.81439e15	−	4.87467e15i	0.0847006	−	0.146706i
$568$	5.13775e14	−	8.89884e14i	0.0152997	−	0.0264998i
$569$		−	1.70997e16i		−	0.503866i	−0.967745	−	0.251933i	$-0.918934\pi$
$569$		−	1.70997e16i		−	0.503866i	0.967745	−	0.251933i	$-0.0810663\pi$
$570$	−1.90335e16	+	3.09367e16i	−0.554970	+	0.902039i
$571$	−5.37718e16			−1.55145			−0.775725	−	0.631071i	$-0.782616\pi$
$571$	−5.37718e16			−1.55145			−0.775725	+	0.631071i	$0.782616\pi$
$572$	3.03805e16	+	1.75402e16i	0.867400	+	0.500794i
$573$	−2.60698e16	−	1.50514e16i	−0.736562	−	0.425254i
$574$	−5.91707e15	−	1.02487e16i	−0.165438	−	0.286547i
$575$	−3.09201e15	+	5.35552e15i	−0.0855527	+	0.148182i
$576$	2.99060e15	+	5.17987e15i	0.0818885	+	0.141835i
$577$	−4.55825e16			−1.23522			−0.617609	−	0.786485i	$-0.711899\pi$
$577$	−4.55825e16			−1.23522			−0.617609	+	0.786485i	$0.711899\pi$
$578$			2.32343e16i			0.623107i
$579$	2.79516e16	+	4.84136e16i	0.741883	+	1.28498i
$580$	1.29498e16	−	7.47655e15i	0.340168	−	0.196396i
$581$	−1.40162e15			−0.0364397
$582$			3.92133e16i			1.00901i
$583$	−2.77597e16	+	1.60271e16i	−0.706974	+	0.408172i
$584$	−3.33631e16	−	1.92622e16i	−0.840987	−	0.485544i
$585$	8.45454e15	−	4.88123e15i	0.210938	−	0.121785i
$586$	−6.85856e16	+	1.18794e17i	−1.69374	+	2.93365i
$587$	8.71419e15	−	1.50934e16i	0.213009	−	0.368943i	−0.739646	−	0.672997i	$-0.765007\pi$
$587$	8.71419e15	−	1.50934e16i	0.213009	−	0.368943i	0.952655	+	0.304054i	$0.0983402\pi$
$588$			6.97883e16i			1.68857i
$589$	−6.08989e16	−	3.74675e16i	−1.45854	−	0.897351i
$590$	−4.04207e16			−0.958278
$591$	−2.14860e16	−	1.24050e16i	−0.504233	−	0.291119i
$592$	3.83664e16	+	2.21509e16i	0.891294	+	0.514589i
$593$	2.83545e16	+	4.91115e16i	0.652070	+	1.12942i	0.982620	+	0.185630i	$0.0594327\pi$
$593$	2.83545e16	+	4.91115e16i	0.652070	+	1.12942i	−0.330549	+	0.943789i	$0.607234\pi$
$594$	1.93080e16	−	3.34424e16i	0.439559	−	0.761339i
$595$	−5.91259e15	−	1.02409e16i	−0.133253	−	0.230800i
$596$	1.74879e17			3.90175
$597$		−	4.95453e16i		−	1.09435i
$598$	−1.43568e16	−	2.48667e16i	−0.313942	−	0.543764i
$599$	−8.96533e15	+	5.17614e15i	−0.194091	+	0.112059i	−0.593896	−	0.804542i	$-0.702411\pi$
$599$	−8.96533e15	+	5.17614e15i	−0.194091	+	0.112059i	0.399805	+	0.916600i	$0.369078\pi$
$600$	−4.41745e16			−0.946813
$601$			5.12183e16i			1.08687i	0.839450	+	0.543436i	$0.182877\pi$
$601$			5.12183e16i			1.08687i	−0.839450	+	0.543436i	$0.817123\pi$
$602$	3.72722e16	−	2.15191e16i	0.783079	−	0.452111i
$603$	−2.45246e15	−	1.41593e15i	−0.0510151	−	0.0294536i
$604$	6.16365e16	−	3.55859e16i	1.26945	−	0.732919i
$605$	1.41790e16	−	2.45588e16i	0.289144	−	0.500812i
$606$	7.19301e16	−	1.24587e17i	1.45236	−	2.51557i
$607$		−	1.08597e16i		−	0.217112i	−0.994090	−	0.108556i	$-0.965377\pi$
$607$		−	1.08597e16i		−	0.217112i	0.994090	−	0.108556i	$-0.0346227\pi$
$608$	1.99035e15	−	7.11889e16i	0.0394011	−	1.40926i
$609$	3.08627e15			0.0604965
$610$	−8.39580e16	−	4.84732e16i	−1.62961	−	0.940854i
$611$	−7.83503e16	−	4.52356e16i	−1.50589	−	0.869427i
$612$	2.47479e16	+	4.28646e16i	0.471009	+	0.815812i
$613$	1.09419e16	−	1.89519e16i	0.206219	−	0.357181i	−0.744302	−	0.667844i	$-0.767217\pi$
$613$	1.09419e16	−	1.89519e16i	0.206219	−	0.357181i	0.950520	+	0.310662i	$0.100551\pi$
$614$	−4.89980e16	−	8.48670e16i	−0.914467	−	1.58390i
$615$	1.77868e16			0.328736
$616$		−	1.87994e16i		−	0.344081i
$617$	−3.61848e16	−	6.26740e16i	−0.655867	−	1.13599i	−0.981676	−	0.190559i	$-0.938970\pi$
$617$	−3.61848e16	−	6.26740e16i	−0.655867	−	1.13599i	0.325809	−	0.945436i	$-0.394363\pi$
$618$	6.14003e16	−	3.54495e16i	1.10215	−	0.636325i
$619$	6.99148e16			1.24287			0.621434	−	0.783466i	$-0.286550\pi$
$619$	6.99148e16			1.24287			0.621434	+	0.783466i	$0.286550\pi$
$620$			1.63069e17i			2.87092i
$621$	−1.91560e16	+	1.10597e16i	−0.334007	+	0.192839i
$622$	5.15095e16	+	2.97390e16i	0.889498	+	0.513552i
$623$	−1.34518e15	+	7.76638e14i	−0.0230065	+	0.0132828i
$624$	4.86464e16	−	8.42580e16i	0.824029	−	1.42726i
$625$	8.46203e15	−	1.46567e16i	0.141969	−	0.245898i
$626$			1.83645e17i			3.05163i
$627$	−1.90847e16	+	1.03184e16i	−0.314109	+	0.169828i
$628$	−1.15387e17			−1.88105
$629$	3.03886e16	+	1.75449e16i	0.490690	+	0.283300i
$630$	−7.93395e15	−	4.58067e15i	−0.126895	−	0.0732631i
$631$	1.71128e16	+	2.96403e16i	0.271110	+	0.469576i	0.969146	−	0.246486i	$-0.0792760\pi$
$631$	1.71128e16	+	2.96403e16i	0.271110	+	0.469576i	−0.698037	+	0.716062i	$0.745943\pi$
$632$	7.97475e16	−	1.38127e17i	1.25145	−	2.16758i
$633$	3.42823e16	+	5.93786e16i	0.532902	+	0.923013i
$634$	3.22678e16			0.496859
$635$		−	4.88830e16i		−	0.745617i
$636$	1.14837e17	+	1.98904e17i	1.73516	+	3.00538i
$637$	−5.04202e16	+	2.91101e16i	−0.754689	+	0.435720i
$638$	1.27625e16			0.189239
$639$		−	2.99093e14i		−	0.00439340i
$640$	2.36665e16	−	1.36638e16i	0.344393	−	0.198835i
$641$	1.38503e16	+	7.99649e15i	0.199670	+	0.115279i	0.596501	−	0.802612i	$-0.296557\pi$
$641$	1.38503e16	+	7.99649e15i	0.199670	+	0.115279i	−0.396832	+	0.917891i	$0.629890\pi$
$642$	2.65503e16	−	1.53288e16i	0.379192	−	0.218927i
$643$	4.99199e15	−	8.64639e15i	0.0706331	−	0.122340i	−0.828546	−	0.559921i	$-0.810831\pi$
$643$	4.99199e15	−	8.64639e15i	0.0706331	−	0.122340i	0.899179	+	0.437581i	$0.144165\pi$
$644$	−9.42849e15	+	1.63306e16i	−0.132168	+	0.228922i
$645$			6.46866e16i			0.898372i
$646$	4.29367e15	−	1.53572e17i	0.0590791	−	2.11308i
$647$	−4.57253e16			−0.623348			−0.311674	−	0.950189i	$-0.600890\pi$
$647$	−4.57253e16			−0.623348			−0.311674	+	0.950189i	$0.600890\pi$
$648$	−8.24811e16	−	4.76205e16i	−1.11405	−	0.643197i
$649$	−2.09085e16	−	1.20715e16i	−0.279805	−	0.161545i
$650$	−3.22665e16	−	5.58873e16i	−0.427831	−	0.741025i
$651$	−1.68284e16	+	2.91477e16i	−0.221084	+	0.382929i
$652$	2.98428e16	+	5.16892e16i	0.388466	+	0.672843i
$653$	−3.81932e16			−0.492614			−0.246307	−	0.969192i	$-0.579217\pi$
$653$	−3.81932e16			−0.492614			−0.246307	+	0.969192i	$0.579217\pi$
$654$		−	5.33196e16i		−	0.681429i
$655$	−5.03144e16	−	8.71472e16i	−0.637155	−	1.10358i
$656$	−8.22562e16	+	4.74907e16i	−1.03216	+	0.595916i
$657$	−1.12134e16			−0.139427
$658$			8.49003e16i			1.04605i
$659$	7.33618e16	−	4.23554e16i	0.895689	−	0.517126i	0.0198902	−	0.999802i	$-0.493668\pi$
$659$	7.33618e16	−	4.23554e16i	0.895689	−	0.517126i	0.875799	+	0.482676i	$0.160335\pi$
$660$	4.28505e16	+	2.47397e16i	0.518432	+	0.299317i
$661$	2.16609e16	−	1.25059e16i	0.259698	−	0.149937i	−0.364499	−	0.931204i	$-0.618760\pi$
$661$	2.16609e16	−	1.25059e16i	0.259698	−	0.149937i	0.624197	+	0.781267i	$0.285426\pi$
$662$	−8.07034e16	+	1.39782e17i	−0.958835	+	1.66075i
$663$	3.85310e16	−	6.67376e16i	0.453658	−	0.785759i
$664$			2.37159e16i			0.276715i
$665$	9.46456e15	+	1.75054e16i	0.109439	+	0.202415i
$666$	2.71851e16			0.311520
$667$	−6.33101e15	−	3.65521e15i	−0.0718982	−	0.0415105i
$668$	−1.64613e17	−	9.50391e16i	−1.85270	−	1.06965i
$669$	2.92293e16	+	5.06266e16i	0.326033	+	0.564706i
$670$	1.00233e16	−	1.73608e16i	0.110805	−	0.191920i
$671$	−2.89528e16	−	5.01477e16i	−0.317216	−	0.549435i
$672$	−3.35228e16			−0.364019
$673$			9.05831e16i			0.974893i	0.873153	+	0.487446i	$0.162072\pi$
$673$			9.05831e16i			0.974893i	−0.873153	+	0.487446i	$0.837928\pi$
$674$	9.67352e16	+	1.67550e17i	1.03187	+	1.78725i
$675$	−4.30527e16	+	2.48565e16i	−0.455174	+	0.262795i
$676$	−1.27823e16			−0.133946
$677$			1.18655e16i			0.123240i	0.998100	+	0.0616202i	$0.0196268\pi$
$677$			1.18655e16i			0.123240i	−0.998100	+	0.0616202i	$0.980373\pi$
$678$	4.42690e16	−	2.55587e16i	0.455745	−	0.263124i
$679$	1.86055e16	+	1.07419e16i	0.189855	+	0.109613i
$680$	−1.73280e17	+	1.00043e17i	−1.75264	+	1.01189i
$681$	3.74648e16	−	6.48909e16i	0.375613	−	0.650581i
$682$	−6.95896e16	+	1.20533e17i	−0.691573	+	1.19784i
$683$		−	1.32993e17i		−	1.31010i	−0.755585	−	0.655050i	$-0.772647\pi$
$683$		−	1.32993e17i		−	1.31010i	0.755585	−	0.655050i	$-0.227353\pi$
$684$	−3.96151e16	−	7.32712e16i	−0.386834	−	0.715479i
$685$	9.62775e16			0.931926
$686$	1.00029e17	+	5.77515e16i	0.959797	+	0.554139i
$687$	1.99888e16	+	1.15405e16i	0.190128	+	0.109770i
$688$	−1.72713e17	−	2.99148e17i	−1.62853	−	2.82069i
$689$	−9.58018e16	+	1.65934e17i	−0.895485	+	1.55103i
$690$	−2.02496e16	−	3.50734e16i	−0.187639	−	0.325000i
$691$	9.45369e16			0.868426			0.434213	−	0.900810i	$-0.357026\pi$
$691$	9.45369e16			0.868426			0.434213	+	0.900810i	$0.357026\pi$
$692$			2.19673e17i			2.00051i
$693$	−2.73601e15	−	4.73891e15i	−0.0247012	−	0.0427838i
$694$	2.42468e17	−	1.39989e17i	2.17019	−	1.25296i
$695$	−4.56013e16			−0.404639
$696$		−	5.22208e16i		−	0.459397i
$697$	−6.51521e16	+	3.76156e16i	−0.568240	+	0.328073i
$698$	−3.79527e16	−	2.19120e16i	−0.328179	−	0.189474i
$699$	9.76331e16	−	5.63685e16i	0.837017	−	0.483252i
$700$	−2.11903e16	+	3.67027e16i	−0.180115	+	0.311968i
$701$	5.01058e16	−	8.67858e16i	0.422260	−	0.731376i	−0.573900	−	0.818925i	$-0.694570\pi$
$701$	5.01058e16	−	8.67858e16i	0.422260	−	0.731376i	0.996160	+	0.0875492i	$0.0279035\pi$
$702$		−	2.30827e17i		−	1.92869i
$703$	−5.02949e16	−	3.09434e16i	−0.416670	−	0.256352i
$704$	−2.52898e16			−0.207735
$705$	−1.10510e17	−	6.38028e16i	−0.900049	−	0.519643i
$706$	6.62550e16	+	3.82524e16i	0.535045	+	0.308909i
$707$	−3.94083e16	−	6.82572e16i	−0.315552	−	0.546552i
$708$	−8.64949e16	+	1.49814e17i	−0.686738	+	1.18947i
$709$	1.15585e17	+	2.00198e17i	0.909960	+	1.57610i	0.814117	+	0.580700i	$0.197221\pi$
$709$	1.15585e17	+	2.00198e17i	0.909960	+	1.57610i	0.0958426	+	0.995397i	$0.469445\pi$
$710$	2.11726e15			0.0165281
$711$		−	4.64248e16i		−	0.359362i
$712$	1.31410e16	+	2.27609e16i	0.100867	+	0.174706i
$713$	6.90419e16	−	3.98614e16i	0.525504	−	0.303400i
$714$	−7.23168e16			−0.545821
$715$			4.12778e16i			0.308944i
$716$	2.77716e17	−	1.60339e17i	2.06121	−	1.19004i
$717$	1.20805e17	+	6.97468e16i	0.889140	+	0.513345i
$718$	−1.69339e17	+	9.77680e16i	−1.23598	+	0.713592i
$719$	4.06336e16	−	7.03795e16i	0.294111	−	0.509416i	−0.680666	−	0.732594i	$-0.738310\pi$
$719$	4.06336e16	−	7.03795e16i	0.294111	−	0.509416i	0.974778	+	0.223178i	$0.0716430\pi$
$720$	−3.67646e16	+	6.36782e16i	−0.263898	+	0.457084i
$721$		−	3.88434e16i		−	0.276506i
$722$	−1.44457e16	+	2.58138e17i	−0.101980	+	1.82234i
$723$	3.56418e16			0.249534
$724$	1.75584e17	+	1.01373e17i	1.21914	+	0.703871i
$725$	−1.42288e16	−	8.21501e15i	−0.0979807	−	0.0565692i
$726$	−8.67117e16	−	1.50189e17i	−0.592186	−	1.02570i
$727$	−2.93731e15	+	5.08758e15i	−0.0198950	+	0.0344591i	−0.875801	−	0.482671i	$-0.839667\pi$
$727$	−2.93731e15	+	5.08758e15i	−0.0198950	+	0.0344591i	0.855906	+	0.517131i	$0.173000\pi$
$728$	−5.61868e16	−	9.73185e16i	−0.377439	−	0.653743i
$729$	−1.59547e17			−1.06298
$730$		−	7.93792e16i		−	0.524529i
$731$	−1.36800e17	−	2.36944e17i	−0.896563	−	1.55289i
$732$	−3.59318e17	+	2.07452e17i	−2.33568	+	1.34850i
$733$	−1.59536e14			−0.00102857			−0.000514286	−	1.00000i	$-0.500164\pi$
$733$	−1.59536e14			−0.00102857			−0.000514286		1.00000i	$0.500164\pi$
$734$		−	5.15089e17i		−	3.29387i
$735$	−7.11156e16	+	4.10586e16i	−0.451067	+	0.260423i
$736$	6.87668e16	+	3.97025e16i	0.432625	+	0.249776i
$737$	1.03695e16	−	5.98686e15i	0.0647075	−	0.0373589i
$738$	−2.91420e16	+	5.04754e16i	−0.180377	+	0.312422i
$739$	−6.96944e16	+	1.20714e17i	−0.427889	+	0.741126i	−0.996685	−	0.0813528i	$-0.974076\pi$
$739$	−6.96944e16	+	1.20714e17i	−0.427889	+	0.741126i	0.568796	+	0.822478i	$0.307409\pi$
$740$			1.34674e17i			0.820153i
$741$	−6.79560e16	+	1.10454e17i	−0.410505	+	0.667228i
$742$	1.79806e17			1.07741
$743$	5.06537e16	+	2.92449e16i	0.301077	+	0.173827i	0.642927	−	0.765928i	$-0.277720\pi$
$743$	5.06537e16	+	2.92449e16i	0.301077	+	0.173827i	−0.341849	+	0.939755i	$0.611053\pi$
$744$	4.93189e17	+	2.84743e17i	2.90788	+	1.67886i
$745$	1.02887e17	+	1.78205e17i	0.601756	+	1.04227i
$746$	−2.17591e17	+	3.76879e17i	−1.26243	+	2.18660i
$747$	3.45155e15	+	5.97825e15i	0.0198651	+	0.0344073i
$748$	−2.09279e17			−1.19486
$749$		−	1.67964e16i		−	0.0951315i
$750$	−1.39758e17	−	2.42068e17i	−0.785252	−	1.36010i
$751$	1.51957e17	−	8.77325e16i	0.846996	−	0.489014i	−0.0126400	−	0.999920i	$-0.504024\pi$
$751$	1.51957e17	−	8.77325e16i	0.846996	−	0.489014i	0.859636	+	0.510907i	$0.170690\pi$
$752$	6.81414e17			3.76794
$753$			1.13807e17i			0.624306i
$754$	6.60671e16	−	3.81438e16i	0.359548	−	0.207585i
$755$	7.25253e16	+	4.18725e16i	0.391569	+	0.226072i
$756$	−1.31281e17	+	7.57950e16i	−0.703187	+	0.405985i
$757$	−1.62010e17	+	2.80609e17i	−0.860927	+	1.49117i	0.0101092	+	0.999949i	$0.496782\pi$
$757$	−1.62010e17	+	2.80609e17i	−0.860927	+	1.49117i	−0.871036	+	0.491220i	$0.836551\pi$
$758$	3.21213e16	−	5.56358e16i	0.169347	−	0.293318i
$759$		−	2.41900e16i		−	0.126528i
$760$	2.96198e17	−	1.60144e17i	1.53709	−	0.831052i
$761$	6.83647e16			0.351985			0.175992	−	0.984392i	$-0.443687\pi$
$761$	6.83647e16			0.351985			0.175992	+	0.984392i	$0.443687\pi$
$762$	−2.58893e17	−	1.49472e17i	−1.32248	−	0.763536i
$763$	−2.52985e16	−	1.46061e16i	−0.128218	−	0.0740264i
$764$	2.44333e17	+	4.23196e17i	1.22863	+	2.12805i
$765$	−2.91199e16	+	5.04371e16i	−0.145285	+	0.251641i
$766$	−1.57168e17	−	2.72222e17i	−0.778019	−	1.34757i
$767$	−1.44315e17			−0.708827
$768$		−	2.44849e17i		−	1.19325i
$769$	−1.13662e16	−	1.96869e16i	−0.0549615	−	0.0951961i	0.837236	−	0.546842i	$-0.184170\pi$
$769$	−1.13662e16	−	1.96869e16i	−0.0549615	−	0.0951961i	−0.892197	+	0.451646i	$0.850837\pi$
$770$	3.35465e16	−	1.93681e16i	0.160954	−	0.0929269i
$771$	−8.01120e15			−0.0381392
$772$		−	9.07490e17i		−	4.28685i
$773$	−9.75370e16	+	5.63130e16i	−0.457186	+	0.263956i	−0.710860	−	0.703333i	$-0.751694\pi$
$773$	−9.75370e16	+	5.63130e16i	−0.457186	+	0.263956i	0.253674	+	0.967290i	$0.418361\pi$
$774$	−1.83568e17	−	1.05983e17i	−0.853790	−	0.492936i
$775$	1.55170e17	−	8.95876e16i	0.716140	−	0.413464i
$776$	1.81756e17	−	3.14811e17i	0.832375	−	1.44172i
$777$	−1.38982e16	+	2.40724e16i	−0.0631585	+	0.109394i
$778$		−	2.00906e17i		−	0.905975i
$779$	1.11369e17	−	6.02131e16i	0.498355	−	0.269442i
$780$	2.95763e17			1.31334
$781$	1.09520e15	+	6.32314e14i	0.00482600	+	0.00278629i
$782$	1.48347e17	+	8.56481e16i	0.648691	+	0.374522i
$783$	−2.93840e16	−	5.08946e16i	−0.127509	−	0.220852i
$784$	2.19253e17	−	3.79757e17i	0.944166	−	1.63534i
$785$	−6.78859e16	−	1.17582e17i	−0.290109	−	0.502484i
$786$	−6.15395e17			−2.60987
$787$		−	4.59364e16i		−	0.193334i	−0.995317	−	0.0966670i	$-0.969182\pi$
$787$		−	4.59364e16i		−	0.193334i	0.995317	−	0.0966670i	$-0.0308182\pi$
$788$	2.01373e17	+	3.48787e17i	0.841091	+	1.45681i
$789$	1.33107e17	−	7.68496e16i	0.551747	−	0.318551i
$790$	3.28638e17			1.35193
$791$		−	2.80057e16i		−	0.114337i
$792$	−8.01840e16	+	4.62943e16i	−0.324890	+	0.187576i
$793$	−2.99758e17	−	1.73065e17i	−1.20540	−	0.695939i
$794$	−3.51155e17	+	2.02739e17i	−1.40144	+	0.809124i
$795$	−1.35124e17	+	2.34042e17i	−0.535218	+	0.927025i
$796$	−4.02140e17	+	6.96528e17i	−1.58088	+	2.73817i
$797$		−	1.69281e17i		−	0.660478i	−0.943897	−	0.330239i	$-0.892871\pi$
$797$		−	1.69281e17i		−	0.660478i	0.943897	−	0.330239i	$-0.107129\pi$
$798$	1.21652e17	+	3.40123e15i	0.471088	+	0.0131710i
$799$	5.39723e17			2.07439
$800$	1.54552e17	+	8.92306e16i	0.589569	+	0.340388i
$801$	6.62509e15	+	3.82500e15i	0.0250840	+	0.0144822i
$802$	−3.25687e16	−	5.64106e16i	−0.122392	−	0.211990i
$803$	2.37064e16	−	4.10607e16i	0.0884246	−	0.153156i
$804$	−4.28970e16	−	7.42997e16i	−0.158815	−	0.275075i
$805$	−2.21883e16			−0.0815358
$806$			8.31944e17i			3.03448i
$807$	−8.40779e16	−	1.45627e17i	−0.304397	−	0.527232i
$808$	−1.15493e18	+	6.66802e17i	−4.15039	+	2.39623i
$809$	3.08483e17			1.10037			0.550187	−	0.835041i	$-0.314556\pi$
$809$	3.08483e17			1.10037			0.550187	+	0.835041i	$0.314556\pi$
$810$		−	1.96243e17i		−	0.694840i
$811$	−4.56378e17	+	2.63490e17i	−1.60398	+	0.926060i	−0.613304	+	0.789847i	$0.710160\pi$
$811$	−4.56378e17	+	2.63490e17i	−1.60398	+	0.926060i	−0.990680	+	0.136213i	$0.956507\pi$
$812$	−4.33880e16	−	2.50501e16i	−0.151368	−	0.0873923i
$813$	7.10400e16	−	4.10149e16i	0.246014	−	0.142036i
$814$	−5.74723e16	+	9.95450e16i	−0.197566	+	0.342194i
$815$	−3.51148e16	+	6.08207e16i	−0.119824	+	0.207542i
$816$			5.80418e17i			1.96607i
$817$	2.18982e17	+	4.05024e17i	0.736336	+	1.36191i
$818$	−3.46415e17			−1.15632
$819$	−2.83269e16	−	1.63545e16i	−0.0938631	−	0.0541919i
$820$	−2.50054e17	−	1.44368e17i	−0.822526	−	0.474886i
$821$	−2.34712e16	−	4.06534e16i	−0.0766438	−	0.132751i	0.825156	−	0.564905i	$-0.191087\pi$
$821$	−2.34712e16	−	4.06534e16i	−0.0766438	−	0.132751i	−0.901800	+	0.432154i	$0.857754\pi$
$822$	2.94392e17	−	5.09902e17i	0.954323	−	1.65294i
$823$	2.52975e17	+	4.38166e17i	0.814102	+	1.41007i	0.909971	+	0.414672i	$0.136104\pi$
$823$	2.52975e17	+	4.38166e17i	0.814102	+	1.41007i	−0.0958691	+	0.995394i	$0.530563\pi$
$824$	−6.57243e17			−2.09973
$825$		−	5.43666e16i		−	0.172428i
$826$	6.77145e16	+	1.17285e17i	0.213207	+	0.369285i
$827$	2.48879e17	−	1.43690e17i	0.777957	−	0.449154i	−0.0577489	−	0.998331i	$-0.518392\pi$
$827$	2.48879e17	−	1.43690e17i	0.777957	−	0.449154i	0.835706	+	0.549178i	$0.185059\pi$
$828$	9.28719e16			0.288206
$829$			2.16421e17i			0.666764i	0.942792	+	0.333382i	$0.108190\pi$
$829$			2.16421e17i			0.666764i	−0.942792	+	0.333382i	$0.891810\pi$
$830$	−4.23196e16	+	2.44333e16i	−0.129441	+	0.0747331i
$831$	−2.06320e17	−	1.19119e17i	−0.626520	−	0.361721i
$832$	−1.30917e17	+	7.55849e16i	−0.394689	+	0.227874i
$833$	1.73662e17	−	3.00791e17i	0.519798	−	0.900316i
$834$	−1.39437e17	+	2.41512e17i	−0.414364	+	0.717700i
$835$		−	2.23658e17i		−	0.659880i
$836$	3.52051e17	+	9.84289e15i	1.03126	+	0.0288327i
$837$	6.40886e17			1.86392
$838$	−6.04273e17	−	3.48877e17i	−1.74490	−	1.00742i
$839$	−3.99016e17	−	2.30372e17i	−1.14398	−	0.660477i	−0.196567	−	0.980490i	$-0.562979\pi$
$839$	−3.99016e17	−	2.30372e17i	−1.14398	−	0.660477i	−0.947413	+	0.320013i	$0.896313\pi$
$840$	−7.92491e16	−	1.37264e17i	−0.225589	−	0.390732i
$841$	−1.67196e17	+	2.89592e17i	−0.472552	+	0.818485i
$842$	4.60619e17	+	7.97815e17i	1.29261	+	2.23887i
$843$	−1.57969e17			−0.440155
$844$		−	1.11302e18i		−	3.07929i
$845$	−7.52024e15	−	1.30254e16i	−0.0206581	−	0.0357810i
$846$	3.62120e17	−	2.09070e17i	0.987712	−	0.570256i
$847$	−9.50133e16			−0.257326
$848$		−	1.44313e18i		−	3.88087i
$849$	2.46948e17	−	1.42575e17i	0.659415	−	0.380713i
$850$	3.33406e17	+	1.92492e17i	0.884016	+	0.510387i
$851$	5.70200e16	−	3.29205e16i	0.150124	−	0.0866741i
$852$	4.53065e15	−	7.84732e15i	0.0118447	−	0.0205156i
$853$	1.69481e17	−	2.93550e17i	0.439975	−	0.762059i	−0.557712	−	0.830034i	$-0.688321\pi$
$853$	1.69481e17	−	2.93550e17i	0.439975	−	0.762059i	0.997687	+	0.0679757i	$0.0216540\pi$
$854$			3.24818e17i			0.837322i
$855$	5.13580e16	−	8.34763e16i	0.131465	−	0.213681i
$856$	−2.84200e17			−0.722407
$857$	−5.93988e17	−	3.42939e17i	−1.49931	−	0.865630i	−0.499315	−	0.866420i	$-0.666415\pi$
$857$	−5.93988e17	−	3.42939e17i	−1.49931	−	0.865630i	−1.00000		0.000790677i	$0.999748\pi$
$858$	2.18614e17	+	1.26217e17i	0.547968	+	0.316369i
$859$	3.46896e17	+	6.00842e17i	0.863457	+	1.49555i	0.868571	+	0.495565i	$0.165039\pi$
$859$	3.46896e17	+	6.00842e17i	0.863457	+	1.49555i	−0.00511368	+	0.999987i	$0.501628\pi$
$860$	5.25037e17	−	9.09390e17i	1.29777	−	2.24781i
$861$	−2.97972e16	−	5.16103e16i	−0.0731403	−	0.126683i
$862$	8.06791e17			1.96661
$863$			2.33193e17i			0.564482i	0.959344	+	0.282241i	$0.0910778\pi$
$863$			2.33193e17i			0.564482i	−0.959344	+	0.282241i	$0.908922\pi$
$864$	3.19166e17	+	5.52812e17i	0.767246	+	1.32891i
$865$	−2.23851e17	+	1.29240e17i	−0.534395	+	0.308533i
$866$	5.73466e17			1.35957
$867$			1.17003e17i			0.275476i
$868$	4.73162e17	−	2.73180e17i	1.10635	−	0.638750i
$869$	1.69996e17	+	9.81471e16i	0.394748	+	0.227908i
$870$	9.31847e16	−	5.38002e16i	0.214896	−	0.124071i
$871$	3.57864e16	−	6.19839e16i	0.0819614	−	0.141961i
$872$	−2.47140e17	+	4.28059e17i	−0.562140	+	0.973654i
$873$		−	1.05809e17i		−	0.239022i
$874$	−2.45522e17	−	1.51055e17i	−0.550836	−	0.338896i
$875$	−1.53138e17			−0.341220
$876$	−2.94208e17	−	1.69861e17i	−0.651073	−	0.375897i
$877$	−3.99175e15	−	2.30464e15i	−0.00877336	−	0.00506530i	0.495607	−	0.868547i	$-0.334946\pi$
$877$	−3.99175e15	−	2.30464e15i	−0.00877336	−	0.00506530i	−0.504380	+	0.863482i	$0.668279\pi$
$878$	4.53580e17	+	7.85624e17i	0.990118	+	1.71494i
$879$	−3.45384e17	+	5.98222e17i	−0.748805	+	1.29697i
$880$	−1.55449e17	−	2.69245e17i	−0.334728	−	0.579765i
$881$	2.58718e17			0.553314			0.276657	−	0.960969i	$-0.410773\pi$
$881$	2.58718e17			0.553314			0.276657	+	0.960969i	$0.410773\pi$
$882$		−	2.69083e17i		−	0.571576i
$883$	−6.92161e16	−	1.19886e17i	−0.146030	−	0.252932i	0.783727	−	0.621106i	$-0.213316\pi$
$883$	−6.92161e16	−	1.19886e17i	−0.146030	−	0.252932i	−0.929757	+	0.368174i	$0.879983\pi$
$884$	−1.08337e18	+	6.25482e17i	−2.27019	+	1.31069i
$885$	−2.03551e17			−0.423655
$886$		−	2.45835e17i		−	0.508207i
$887$	6.89047e17	−	3.97822e17i	1.41484	−	0.816858i	0.419000	−	0.907986i	$-0.362381\pi$
$887$	6.89047e17	−	3.97822e17i	1.41484	−	0.816858i	0.995839	+	0.0911281i	$0.0290473\pi$
$888$	4.07313e17	+	2.35162e17i	0.830711	+	0.479611i
$889$	−1.41839e17	+	8.18910e16i	−0.287333	+	0.165892i
$890$	−2.70769e16	+	4.68986e16i	−0.0544827	+	0.0943668i
$891$	5.86076e16	−	1.01511e17i	0.117135	−	0.202884i
$892$		−	9.48972e17i		−	1.88393i
$893$	−9.07927e17	−	2.53845e16i	−1.79037	−	0.0500563i
$894$	1.25840e18			2.46487
$895$	3.26778e17	+	1.88665e17i	0.635791	+	0.367074i
$896$	−7.92943e16	−	4.57806e16i	−0.153248	−	0.0884776i
$897$	−7.22980e16	−	1.25224e17i	−0.138794	−	0.240399i
$898$	−6.29371e17	+	1.09010e18i	−1.20019	+	2.07878i
$899$	1.05906e17	+	1.83434e17i	0.200614	+	0.347474i
$900$	2.08728e17			0.392758
$901$		−	1.14305e18i		−	2.13656i
$902$	−1.23219e17	−	2.13421e17i	−0.228790	−	0.396276i
$903$	1.87695e17	−	1.08366e17i	0.346200	−	0.199879i
$904$	−4.73865e17			−0.868249
$905$			2.38565e17i			0.434225i
$906$	4.43528e17	−	2.56071e17i	0.801959	−	0.463011i
$907$	2.90527e17	+	1.67736e17i	0.521847	+	0.301289i	0.737690	−	0.675140i	$-0.235917\pi$
$907$	2.90527e17	+	1.67736e17i	0.521847	+	0.301289i	−0.215843	+	0.976428i	$0.569250\pi$
$908$	−1.05339e18	+	6.08175e17i	−1.87964	+	1.08521i
$909$	−1.94089e17	+	3.36171e17i	−0.344046	+	0.595905i
$910$	1.15773e17	−	2.00524e17i	0.203872	−	0.353116i
$911$		−	8.25360e17i		−	1.44389i	−0.691952	−	0.721944i	$-0.743249\pi$
$911$		−	8.25360e17i		−	1.44389i	0.691952	−	0.721944i	$-0.256751\pi$
$912$	2.72984e16	−	9.76385e17i	0.0474427	−	1.69688i
$913$	−2.91878e16			−0.0503937
$914$	1.14119e17	+	6.58866e16i	0.195740	+	0.113011i
$915$	−4.22796e17	−	2.44101e17i	−0.720451	−	0.415952i
$916$	−1.87340e17	−	3.24483e17i	−0.317145	−	0.549312i
$917$	−1.68578e17	+	2.91986e17i	−0.283521	+	0.491072i
$918$	6.88519e17	+	1.19255e18i	1.15043	+	1.99260i
$919$	−4.35216e17			−0.722457			−0.361228	−	0.932477i	$-0.617643\pi$
$919$	−4.35216e17			−0.722457			−0.361228	+	0.932477i	$0.617643\pi$
$920$			3.75433e17i			0.619164i
$921$	−2.46744e17	−	4.27374e17i	−0.404287	−	0.700245i
$922$	−1.39321e18	+	8.04370e17i	−2.26794	+	1.30939i
$923$	7.55932e15			0.0122257
$924$		−	1.65780e17i		−	0.266380i
$925$	1.28151e17	−	7.39881e16i	0.204584	−	0.118117i
$926$	1.56923e18	+	9.05993e17i	2.48897	+	1.43701i
$927$	−1.65676e17	+	9.56531e16i	−0.261085	+	0.150737i
$928$	−1.05484e17	+	1.82703e17i	−0.165157	+	0.286061i
$929$	2.10658e17	−	3.64871e17i	0.327706	−	0.567604i	−0.654350	−	0.756192i	$-0.727058\pi$
$929$	2.10658e17	−	3.64871e17i	0.327706	−	0.567604i	0.982056	+	0.188588i	$0.0603911\pi$
$930$			1.17342e18i			1.81366i
$931$	−3.06283e17	+	4.97826e17i	−0.470354	+	0.764504i
$932$	−1.83009e18			−2.79239
$933$	2.59392e17	+	1.49760e17i	0.393248	+	0.227042i
$934$	−5.15258e17	−	2.97484e17i	−0.776146	−	0.448108i
$935$	−1.23125e17	−	2.13259e17i	−0.184280	−	0.319182i
$936$	−2.76724e17	+	4.79300e17i	−0.411521	+	0.712775i
$937$	1.77516e17	+	3.07467e17i	0.262301	+	0.454319i	0.966853	−	0.255334i	$-0.0821853\pi$
$937$	1.77516e17	+	3.07467e17i	0.262301	+	0.454319i	−0.704552	+	0.709652i	$0.748852\pi$
$938$	−6.71657e16			−0.0986122
$939$			9.24798e17i			1.34913i
$940$	1.03573e18	+	1.79393e18i	1.50134	+	2.60039i
$941$	1.01156e18	−	5.84023e17i	1.45698	−	0.841187i	0.458117	−	0.888892i	$-0.348524\pi$
$941$	1.01156e18	−	5.84023e17i	1.45698	−	0.841187i	0.998861	+	0.0477049i	$0.0151907\pi$
$942$	−8.30311e17			−1.18833
$943$			1.41161e17i			0.200745i
$944$	9.41334e17	−	5.43480e17i	1.33018	−	0.767982i
$945$	−1.54473e17	−	8.91851e16i	−0.216901	−	0.125228i
$946$	7.76165e17	−	4.48119e17i	1.08295	−	0.625240i
$947$	−1.82351e17	+	3.15841e17i	−0.252818	+	0.437893i	−0.964301	−	0.264810i	$-0.914691\pi$
$947$	−1.82351e17	+	3.15841e17i	−0.252818	+	0.437893i	0.711483	+	0.702704i	$0.248024\pi$
$948$	7.03243e17	−	1.21805e18i	0.968847	−	1.67809i
$949$		−	2.83410e17i		−	0.387988i
$950$	−5.51806e17	−	3.39493e17i	−0.750662	−	0.461838i
$951$	1.62494e17			0.219662
$952$	5.80571e17	+	3.35193e17i	0.779891	+	0.450270i
$953$	−1.14831e18	−	6.62975e17i	−1.53285	−	0.884992i	−0.999229	−	0.0392702i	$-0.987497\pi$
$953$	−1.14831e18	−	6.62975e17i	−1.53285	−	0.884992i	−0.533623	−	0.845722i	$-0.679170\pi$
$954$	−4.42777e17	−	7.66913e17i	−0.587347	−	1.01732i
$955$	−2.87497e17	+	4.97959e17i	−0.378977	+	0.656407i
$956$	−1.13222e18	−	1.96106e18i	−1.48314	−	2.56887i
$957$	6.42693e16			0.0836627
$958$		−	1.36798e18i		−	1.76964i
$959$	−1.61288e17	−	2.79360e17i	−0.207344	−	0.359130i
$960$	−1.84653e17	+	1.06609e17i	−0.235900	+	0.136197i
$961$	−1.52222e18			−1.93257
$962$			6.87082e17i			0.866878i
$963$	−7.16404e16	+	4.13616e16i	−0.0898257	+	0.0518609i
$964$	−5.01066e17	−	2.89290e17i	−0.624356	−	0.360472i
$965$	9.24749e17	−	5.33904e17i	1.14514	−	0.661149i
$966$	−6.78462e16	+	1.17513e17i	−0.0834954	+	0.144618i
$967$	1.02798e17	−	1.78052e17i	0.125726	−	0.217765i	−0.796290	−	0.604915i	$-0.793207\pi$
$967$	1.02798e17	−	1.78052e17i	0.125726	−	0.217765i	0.922017	+	0.387150i	$0.126540\pi$
$968$			1.60766e18i			1.95408i
$969$	2.16221e16	−	7.73358e17i	0.0261189	−	0.934196i
$970$	7.49015e17			0.899207
$971$	−4.60120e17	−	2.65651e17i	−0.548979	−	0.316953i	0.199731	−	0.979851i	$-0.435993\pi$
$971$	−4.60120e17	−	2.65651e17i	−0.548979	−	0.316953i	−0.748710	+	0.662897i	$0.769327\pi$
$972$	1.12590e18	+	6.50040e17i	1.33507	+	0.770802i
$973$	7.63933e16	+	1.32317e17i	0.0900281	+	0.155933i
$974$	9.79246e17	−	1.69610e18i	1.14693	−	1.98655i
$975$	−1.62488e17	−	2.81438e17i	−0.189145	−	0.327608i
$976$	2.60700e18			3.01608
$977$			9.32322e17i			1.07201i	0.844215	+	0.536005i	$0.180067\pi$
$977$			9.32322e17i			1.07201i	−0.844215	+	0.536005i	$0.819933\pi$
$978$	2.14745e17	+	3.71948e17i	0.245408	+	0.425059i
$979$	−2.80123e16	+	1.61729e16i	−0.0318165	+	0.0183693i
$980$	1.33303e18			1.50481
$981$			1.43872e17i			0.161422i
$982$	−1.19999e18	+	6.92812e17i	−1.33816	+	0.772585i
$983$	6.05335e17	+	3.49490e17i	0.670926	+	0.387359i	0.796427	−	0.604734i	$-0.206721\pi$
$983$	6.05335e17	+	3.49490e17i	0.670926	+	0.387359i	−0.125501	+	0.992093i	$0.540054\pi$
$984$	−8.73264e17	+	5.04179e17i	−0.961999	+	0.555411i
$985$	−2.36947e17	+	4.10405e17i	−0.259439	+	0.449361i
$986$	−2.27554e17	+	3.94135e17i	−0.247641	+	0.428927i
$987$			4.27542e17i			0.462461i
$988$	1.85187e18	−	1.00124e18i	1.99099	−	1.07646i
$989$	−5.13371e17			−0.548597
$990$	−1.65219e17	−	9.53890e16i	−0.175488	−	0.101318i
$991$	−7.06798e17	−	4.08070e17i	−0.746197	−	0.430817i	0.0781211	−	0.996944i	$-0.475108\pi$
$991$	−7.06798e17	−	4.08070e17i	−0.746197	−	0.430817i	−0.824318	+	0.566127i	$0.808441\pi$
$992$	−1.15034e18	−	1.99244e18i	−1.20713	−	2.09082i
$993$	−4.06407e17	+	7.03917e17i	−0.423902	+	0.734219i
$994$	−3.54692e15	−	6.14345e15i	−0.00367734	−	0.00636934i
$995$	−9.46367e17			−0.975261
$996$			2.09136e17i			0.214226i
$997$	−2.03160e17	−	3.51883e17i	−0.206855	−	0.358284i	0.743867	−	0.668328i	$-0.232990\pi$
$997$	−2.03160e17	−	3.51883e17i	−0.206855	−	0.358284i	−0.950722	+	0.310044i	$0.899656\pi$
$998$	1.54086e18	−	8.89614e17i	1.55948	−	0.900365i
$999$	5.29292e17			0.532479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.13.d.a.8.2	✓	38
19.12	odd	6	inner	19.13.d.a.12.2	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.13.d.a.8.2	✓	38	1.1	even	1	trivial
19.13.d.a.12.2	yes	38	19.12	odd	6	inner

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	19.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-101.162 - 58.4061i) q^{2} +(-509.434 - 294.122i) q^{3} +(4774.55 + 8269.76i) q^{4} +(-5618.03 + 9730.71i) q^{5} +(34357.0 + 59508.1i) q^{6} +37646.3 q^{7} -636988. i q^{8} +(-92705.3 - 160570. i) q^{9} +(1.13667e6 - 656254. i) q^{10} +783956. q^{11} -5.61719e6i q^{12} +(4.05828e6 - 2.34305e6i) q^{13} +(-3.80839e6 - 2.19877e6i) q^{14} +(5.72403e6 - 3.30477e6i) q^{15} +(-1.76474e7 + 3.05663e7i) q^{16} +(-1.39779e7 + 2.42104e7i) q^{17} +2.16582e7i q^{18} +(2.46524e7 - 4.00696e7i) q^{19} -1.07294e8 q^{20} +(-1.91783e7 - 1.10726e7i) q^{21} +(-7.93068e7 - 4.57878e7i) q^{22} +(2.62275e7 + 4.54274e7i) q^{23} +(-1.87352e8 + 3.24503e8i) q^{24} +(5.89458e7 + 1.02097e8i) q^{25} -5.47393e8 q^{26} +4.21683e8i q^{27} +(1.79744e8 + 3.11326e8i) q^{28} +(-1.20694e8 + 6.96827e7i) q^{29} -7.72075e8 q^{30} -1.51983e9i q^{31} +(1.31097e9 - 7.56886e8i) q^{32} +(-3.99374e8 - 2.30578e8i) q^{33} +(2.82807e9 - 1.63279e9i) q^{34} +(-2.11498e8 + 3.66325e8i) q^{35} +(8.85251e8 - 1.53330e9i) q^{36} -1.25519e9i q^{37} +(-4.83421e9 + 2.61368e9i) q^{38} -2.75657e9 q^{39} +(6.19835e9 + 3.57862e9i) q^{40} +(2.33054e9 + 1.34554e9i) q^{41} +(1.29341e9 + 2.24026e9i) q^{42} +(-4.89343e9 + 8.47567e9i) q^{43} +(3.74303e9 + 6.48313e9i) q^{44} +2.08328e9 q^{45} -6.12740e9i q^{46} +(-9.65315e9 - 1.67197e10i) q^{47} +(1.79804e10 - 1.03810e10i) q^{48} -1.24240e10 q^{49} -1.37712e10i q^{50} +(1.42416e10 - 8.22240e9i) q^{51} +(3.87529e10 + 2.23740e10i) q^{52} +(-3.54098e10 + 2.04438e10i) q^{53} +(2.46289e10 - 4.26585e10i) q^{54} +(-4.40429e9 + 7.62845e9i) q^{55} -2.39802e10i q^{56} +(-2.43441e10 + 1.31620e10i) q^{57} +1.62796e10 q^{58} +(-2.66705e10 - 1.53982e10i) q^{59} +(5.46593e10 + 3.15576e10i) q^{60} +(-3.69317e10 - 6.39676e10i) q^{61} +(-8.87673e10 + 1.53749e11i) q^{62} +(-3.49001e9 - 6.04487e9i) q^{63} -3.22592e10 q^{64} +5.26532e10i q^{65} +(2.69344e10 + 4.66517e10i) q^{66} +(1.32272e10 - 7.63673e9i) q^{67} -2.66952e11 q^{68} -3.08564e10i q^{69} +(4.27913e10 - 2.47055e10i) q^{70} +(1.39702e9 + 8.06569e8i) q^{71} +(-1.02281e11 + 5.90522e10i) q^{72} +(3.02395e10 - 5.23763e10i) q^{73} +(-7.33107e10 + 1.26978e11i) q^{74} -6.93490e10i q^{75} +(4.49070e11 + 1.25554e10i) q^{76} +2.95130e10 q^{77} +(2.78861e11 + 1.61000e11i) q^{78} +(2.16844e11 + 1.25195e11i) q^{79} +(-1.98288e11 - 3.43444e11i) q^{80} +(7.47589e10 - 1.29486e11i) q^{81} +(-1.57175e11 - 2.72236e11i) q^{82} -3.72314e10 q^{83} -2.11466e11i q^{84} +(-1.57056e11 - 2.72030e11i) q^{85} +(9.90062e11 - 5.71613e11i) q^{86} +8.19808e10 q^{87} -4.99371e11i q^{88} +(-3.57320e10 + 2.06299e10i) q^{89} +(-2.10750e11 - 1.21676e11i) q^{90} +(1.52779e11 - 8.82071e10i) q^{91} +(-2.50449e11 + 4.33791e11i) q^{92} +(-4.47015e11 + 7.74252e11i) q^{93} +2.25521e12i q^{94} +(2.51408e11 + 4.64998e11i) q^{95} -8.90467e11 q^{96} +(4.94218e11 + 2.85337e11i) q^{97} +(1.25685e12 + 7.25640e11i) q^{98} +(-7.26768e10 - 1.25880e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 3 q^{2} + 1377 q^{3} + 37325 q^{4} + 3023 q^{5} - 26867 q^{6} + 202236 q^{7} + 3465518 q^{9} - 4210176 q^{10} + 225284 q^{11} + 212517 q^{13} - 21278490 q^{14} + 46075869 q^{15} - 72759187 q^{16}+ \cdots + 231693405580 q^{99}+O(q^{100}) \) 38 * q - 3 * q^2 + 1377 * q^3 + 37325 * q^4 + 3023 * q^5 - 26867 * q^6 + 202236 * q^7 + 3465518 * q^9 - 4210176 * q^10 + 225284 * q^11 + 212517 * q^13 - 21278490 * q^14 + 46075869 * q^15 - 72759187 * q^16 - 12325321 * q^17 - 73131462 * q^19 + 111917588 * q^20 + 156027138 * q^21 - 211346691 * q^22 - 279329041 * q^23 + 780422281 * q^24 - 372278836 * q^25 - 1597211628 * q^26 + 1073400576 * q^28 - 27282963 * q^29 - 5212471136 * q^30 + 2949918615 * q^32 + 3065041014 * q^33 + 8227712886 * q^34 - 6067993466 * q^35 - 7289473398 * q^36 + 20872085082 * q^38 - 10046427734 * q^39 - 11767148976 * q^40 + 17339304201 * q^41 - 18287327036 * q^42 + 19260286759 * q^43 - 11548377481 * q^44 + 53989159292 * q^45 - 44833646161 * q^47 - 133220290647 * q^48 + 102879628914 * q^49 - 15378013731 * q^51 + 103936340214 * q^52 + 52675070037 * q^53 - 45133036831 * q^54 - 45561195026 * q^55 + 174832261397 * q^57 - 208993675116 * q^58 - 59214662175 * q^59 + 258683654406 * q^60 - 121685590881 * q^61 + 107382291300 * q^62 - 124406826124 * q^63 - 436230170914 * q^64 - 179836732273 * q^66 + 293404150857 * q^67 - 6303456364 * q^68 - 772542532014 * q^70 - 30935350443 * q^71 + 1069728037986 * q^72 - 57455549261 * q^73 - 463964866074 * q^74 + 400484677011 * q^76 + 774791288632 * q^77 + 366171761466 * q^78 + 817499583117 * q^79 + 875293519598 * q^80 - 1180846958651 * q^81 - 1049473265553 * q^82 - 1792056205804 * q^83 - 65622331559 * q^85 + 3947361258426 * q^86 + 1119067320794 * q^87 - 3024866183331 * q^89 - 5555491205910 * q^90 - 983383383558 * q^91 + 4405076379092 * q^92 - 1829505362200 * q^93 + 7666034903 * q^95 + 4922340461862 * q^96 + 1304474752257 * q^97 + 9971274266091 * q^98 + 231693405580 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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