LMFDB - Embedded newform 4.11.b.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,11,Mod(3,4)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 11, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.54142901069$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.26777625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} + 59x^{2} - 58x + 336 $ x^4 - 2x^3 + 59x^2 - 58*x + 336
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{12}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.4
Root			$0.500000 + 2.50555i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.11.b.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19.4722 + 25.3936i) q^{2} +120.267i q^{3} +(-265.666 + 988.937i) q^{4} +2486.44 q^{5} +(-3054.00 + 2341.85i) q^{6} -29129.9i q^{7} +(-30285.8 + 12510.6i) q^{8} +44585.0 q^{9} +O(q^{10})$	\(q+(19.4722 + 25.3936i) q^{2} +120.267i q^{3} +(-265.666 + 988.937i) q^{4} +2486.44 q^{5} +(-3054.00 + 2341.85i) q^{6} -29129.9i q^{7} +(-30285.8 + 12510.6i) q^{8} +44585.0 q^{9} +(48416.5 + 63139.6i) q^{10} +88446.8i q^{11} +(-118936. - 31950.8i) q^{12} -300736. q^{13} +(739713. - 567224. i) q^{14} +299036. i q^{15} +(-907419. - 525455. i) q^{16} -152151. q^{17} +(868167. + 1.13217e6i) q^{18} -47611.7i q^{19} +(-660564. + 2.45894e6i) q^{20} +3.50336e6 q^{21} +(-2.24598e6 + 1.72225e6i) q^{22} -7.60258e6i q^{23} +(-1.50460e6 - 3.64236e6i) q^{24} -3.58323e6 q^{25} +(-5.85600e6 - 7.63677e6i) q^{26} +1.24637e7i q^{27} +(2.88077e7 + 7.73885e6i) q^{28} -6.49949e6 q^{29} +(-7.59359e6 + 5.82289e6i) q^{30} +3.06960e7i q^{31} +(-4.32626e6 - 3.32744e7i) q^{32} -1.06372e7 q^{33} +(-2.96271e6 - 3.86365e6i) q^{34} -7.24299e7i q^{35} +(-1.18447e7 + 4.40917e7i) q^{36} +5.72034e7 q^{37} +(1.20903e6 - 927104. i) q^{38} -3.61685e7i q^{39} +(-7.53038e7 + 3.11068e7i) q^{40} -2.49734e7 q^{41} +(6.82181e7 + 8.89627e7i) q^{42} +1.22346e8i q^{43} +(-8.74683e7 - 2.34973e7i) q^{44} +1.10858e8 q^{45} +(1.93057e8 - 1.48039e8i) q^{46} +1.03820e7i q^{47} +(6.31947e7 - 1.09132e8i) q^{48} -5.66078e8 q^{49} +(-6.97734e7 - 9.09910e7i) q^{50} -1.82987e7i q^{51} +(7.98956e7 - 2.97409e8i) q^{52} +5.65361e8 q^{53} +(-3.16498e8 + 2.42696e8i) q^{54} +2.19918e8i q^{55} +(3.64432e8 + 8.82222e8i) q^{56} +5.72609e6 q^{57} +(-1.26559e8 - 1.65045e8i) q^{58} -3.70040e8i q^{59} +(-2.95728e8 - 7.94438e7i) q^{60} +3.89997e8 q^{61} +(-7.79482e8 + 5.97719e8i) q^{62} -1.29876e9i q^{63} +(7.60713e8 - 7.57785e8i) q^{64} -7.47764e8 q^{65} +(-2.07130e8 - 2.70116e8i) q^{66} +1.36745e9i q^{67} +(4.04214e7 - 1.50468e8i) q^{68} +9.14336e8 q^{69} +(1.83925e9 - 1.41037e9i) q^{70} +1.93751e9i q^{71} +(-1.35029e9 + 5.57783e8i) q^{72} -3.26332e9 q^{73} +(1.11388e9 + 1.45260e9i) q^{74} -4.30943e8i q^{75} +(4.70850e7 + 1.26488e7i) q^{76} +2.57645e9 q^{77} +(9.18448e8 - 7.04281e8i) q^{78} +2.38865e8i q^{79} +(-2.25624e9 - 1.30651e9i) q^{80} +1.13373e9 q^{81} +(-4.86288e8 - 6.34164e8i) q^{82} -6.66076e9i q^{83} +(-9.30725e8 + 3.46460e9i) q^{84} -3.78314e8 q^{85} +(-3.10681e9 + 2.38235e9i) q^{86} -7.81671e8i q^{87} +(-1.10652e9 - 2.67868e9i) q^{88} +2.76291e9 q^{89} +(2.15865e9 + 2.81508e9i) q^{90} +8.76043e9i q^{91} +(7.51847e9 + 2.01975e9i) q^{92} -3.69171e9 q^{93} +(-2.63636e8 + 2.02160e8i) q^{94} -1.18384e8i q^{95} +(4.00179e9 - 5.20305e8i) q^{96} +1.47035e9 q^{97} +(-1.10228e10 - 1.43747e10i) q^{98} +3.94340e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{2} + 16 q^{4} - 1560 q^{5} + 7200 q^{6} - 36288 q^{8} - 28764 q^{9}+O(q^{10}) $ 4 * q - 12 * q^2 + 16 * q^4 - 1560 * q^5 + 7200 * q^6 - 36288 * q^8 - 28764 * q^9	\( 4 q - 12 q^{2} + 16 q^{4} - 1560 q^{5} + 7200 q^{6} - 36288 q^{8} - 28764 q^{9} + 263240 q^{10} - 915840 q^{12} + 212264 q^{13} + 1901760 q^{14} - 3612416 q^{16} - 171384 q^{17} + 4740372 q^{18} - 3108960 q^{20} - 483840 q^{21} - 1996320 q^{22} + 17902080 q^{24} - 5358420 q^{25} - 32439672 q^{26} + 36099840 q^{28} + 30046632 q^{29} - 58656960 q^{30} + 58057728 q^{32} - 65537280 q^{33} - 9311128 q^{34} - 55964016 q^{36} + 134408936 q^{37} + 150268320 q^{38} - 229928320 q^{40} - 340180152 q^{41} + 327237120 q^{42} - 302075520 q^{44} + 606940200 q^{45} + 241181760 q^{46} - 244684800 q^{48} - 804921404 q^{49} - 185601540 q^{50} + 382483616 q^{52} + 1437571944 q^{53} - 631903680 q^{54} + 1392491520 q^{56} - 2610835200 q^{57} - 1349585656 q^{58} + 1623087360 q^{60} + 3412083368 q^{61} - 1633009920 q^{62} - 36368384 q^{64} - 4153551600 q^{65} + 713214720 q^{66} + 117217824 q^{68} + 4399188480 q^{69} + 2298979200 q^{70} - 4132504512 q^{72} - 2988510136 q^{73} + 1718257992 q^{74} - 7437974400 q^{76} + 3748200960 q^{77} + 7251497280 q^{78} + 1359198720 q^{80} - 4715780796 q^{81} + 6420307496 q^{82} - 3911362560 q^{84} - 1190796080 q^{85} - 8760249120 q^{86} + 1708439040 q^{88} + 5274721992 q^{89} - 5495216760 q^{90} + 22420389120 q^{92} - 6070118400 q^{93} - 7391671680 q^{94} + 5494579200 q^{96} + 14343199496 q^{97} - 30380986188 q^{98}+O(q^{100}) \) 4 * q - 12 * q^2 + 16 * q^4 - 1560 * q^5 + 7200 * q^6 - 36288 * q^8 - 28764 * q^9 + 263240 * q^10 - 915840 * q^12 + 212264 * q^13 + 1901760 * q^14 - 3612416 * q^16 - 171384 * q^17 + 4740372 * q^18 - 3108960 * q^20 - 483840 * q^21 - 1996320 * q^22 + 17902080 * q^24 - 5358420 * q^25 - 32439672 * q^26 + 36099840 * q^28 + 30046632 * q^29 - 58656960 * q^30 + 58057728 * q^32 - 65537280 * q^33 - 9311128 * q^34 - 55964016 * q^36 + 134408936 * q^37 + 150268320 * q^38 - 229928320 * q^40 - 340180152 * q^41 + 327237120 * q^42 - 302075520 * q^44 + 606940200 * q^45 + 241181760 * q^46 - 244684800 * q^48 - 804921404 * q^49 - 185601540 * q^50 + 382483616 * q^52 + 1437571944 * q^53 - 631903680 * q^54 + 1392491520 * q^56 - 2610835200 * q^57 - 1349585656 * q^58 + 1623087360 * q^60 + 3412083368 * q^61 - 1633009920 * q^62 - 36368384 * q^64 - 4153551600 * q^65 + 713214720 * q^66 + 117217824 * q^68 + 4399188480 * q^69 + 2298979200 * q^70 - 4132504512 * q^72 - 2988510136 * q^73 + 1718257992 * q^74 - 7437974400 * q^76 + 3748200960 * q^77 + 7251497280 * q^78 + 1359198720 * q^80 - 4715780796 * q^81 + 6420307496 * q^82 - 3911362560 * q^84 - 1190796080 * q^85 - 8760249120 * q^86 + 1708439040 * q^88 + 5274721992 * q^89 - 5495216760 * q^90 + 22420389120 * q^92 - 6070118400 * q^93 - 7391671680 * q^94 + 5494579200 * q^96 + 14343199496 * q^97 - 30380986188 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	19.4722	+	25.3936i	0.608506	+	0.793549i
$2$	19.4722	+	25.3936i	0.608506	+	0.793549i
$3$			120.267i			0.494924i	0.968898	+	0.247462i	$0.0795965\pi$
$3$			120.267i			0.494924i	−0.968898	+	0.247462i	$0.920403\pi$
$4$	−265.666	+	988.937i	−0.259440	+	0.965759i
$5$	2486.44			0.795662			0.397831	−	0.917459i	$-0.369763\pi$
$5$	2486.44			0.795662			0.397831	+	0.917459i	$0.369763\pi$
$6$	−3054.00	+	2341.85i	−0.392746	+	0.301164i
$7$		−	29129.9i		−	1.73320i	−0.499001	−	0.866601i	$-0.666300\pi$
$7$		−	29129.9i		−	1.73320i	0.499001	−	0.866601i	$-0.333700\pi$
$8$	−30285.8	+	12510.6i	−0.924248	+	0.381792i
$9$	44585.0			0.755050
$10$	48416.5	+	63139.6i	0.484165	+	0.631396i
$11$			88446.8i			0.549185i	0.961561	+	0.274592i	$0.0885429\pi$
$11$			88446.8i			0.549185i	−0.961561	+	0.274592i	$0.911457\pi$
$12$	−118936.	−	31950.8i	−0.477977	−	0.128403i
$13$	−300736.			−0.809971			−0.404985	−	0.914323i	$-0.632723\pi$
$13$	−300736.			−0.809971			−0.404985	+	0.914323i	$0.632723\pi$
$14$	739713.	−	567224.i	1.37538	−	1.05467i
$15$			299036.i			0.393792i
$16$	−907419.	−	525455.i	−0.865382	−	0.501113i
$17$	−152151.			−0.107159			−0.0535796	−	0.998564i	$-0.517063\pi$
$17$	−152151.			−0.107159			−0.0535796	+	0.998564i	$0.517063\pi$
$18$	868167.	+	1.13217e6i	0.459453	+	0.599169i
$19$		−	47611.7i		−	0.0192285i	−0.999954	−	0.00961425i	$-0.996940\pi$
$19$		−	47611.7i		−	0.0192285i	0.999954	−	0.00961425i	$-0.00306036\pi$
$20$	−660564.	+	2.45894e6i	−0.206426	+	0.768417i
$21$	3.50336e6			0.857804
$22$	−2.24598e6	+	1.72225e6i	−0.435805	+	0.334183i
$23$		−	7.60258e6i		−	1.18120i	−0.806966	−	0.590598i	$-0.798892\pi$
$23$		−	7.60258e6i		−	1.18120i	0.806966	−	0.590598i	$-0.201108\pi$
$24$	−1.50460e6	−	3.64236e6i	−0.188958	−	0.457433i
$25$	−3.58323e6			−0.366923
$26$	−5.85600e6	−	7.63677e6i	−0.492872	−	0.642751i
$27$			1.24637e7i			0.868617i
$28$	2.88077e7	+	7.73885e6i	1.67386	+	0.449662i
$29$	−6.49949e6			−0.316876			−0.158438	−	0.987369i	$-0.550646\pi$
$29$	−6.49949e6			−0.316876			−0.158438	+	0.987369i	$0.550646\pi$
$30$	−7.59359e6	+	5.82289e6i	−0.312493	+	0.239625i
$31$			3.06960e7i			1.07220i	0.844156	+	0.536098i	$0.180102\pi$
$31$			3.06960e7i			1.07220i	−0.844156	+	0.536098i	$0.819898\pi$
$32$	−4.32626e6	−	3.32744e7i	−0.128933	−	0.991653i
$33$	−1.06372e7			−0.271805
$34$	−2.96271e6	−	3.86365e6i	−0.0652071	−	0.0850361i
$35$		−	7.24299e7i		−	1.37904i
$36$	−1.18447e7	+	4.40917e7i	−0.195890	+	0.729197i
$37$	5.72034e7			0.824923			0.412462	−	0.910975i	$-0.364669\pi$
$37$	5.72034e7			0.824923			0.412462	+	0.910975i	$0.364669\pi$
$38$	1.20903e6	−	927104.i	0.0152588	−	0.0117007i
$39$		−	3.61685e7i		−	0.400874i
$40$	−7.53038e7	+	3.11068e7i	−0.735389	+	0.303778i
$41$	−2.49734e7			−0.215555			−0.107778	−	0.994175i	$-0.534373\pi$
$41$	−2.49734e7			−0.215555			−0.107778	+	0.994175i	$0.534373\pi$
$42$	6.82181e7	+	8.89627e7i	0.521979	+	0.680709i
$43$			1.22346e8i			0.832239i	0.909310	+	0.416120i	$0.136610\pi$
$43$			1.22346e8i			0.832239i	−0.909310	+	0.416120i	$0.863390\pi$
$44$	−8.74683e7	−	2.34973e7i	−0.530380	−	0.142480i
$45$	1.10858e8			0.600764
$46$	1.93057e8	−	1.48039e8i	0.937336	−	0.718765i
$47$			1.03820e7i			0.0452681i	0.999744	+	0.0226340i	$0.00720525\pi$
$47$			1.03820e7i			0.0452681i	−0.999744	+	0.0226340i	$0.992795\pi$
$48$	6.31947e7	−	1.09132e8i	0.248013	−	0.428298i
$49$	−5.66078e8			−2.00399
$50$	−6.97734e7	−	9.09910e7i	−0.223275	−	0.291171i
$51$		−	1.82987e7i		−	0.0530357i
$52$	7.98956e7	−	2.97409e8i	0.210139	−	0.782237i
$53$	5.65361e8			1.35191			0.675953	−	0.736945i	$-0.263732\pi$
$53$	5.65361e8			1.35191			0.675953	+	0.736945i	$0.263732\pi$
$54$	−3.16498e8	+	2.42696e8i	−0.689290	+	0.528559i
$55$			2.19918e8i			0.436965i
$56$	3.64432e8	+	8.82222e8i	0.661724	+	1.60191i
$57$	5.72609e6			0.00951664
$58$	−1.26559e8	−	1.65045e8i	−0.192821	−	0.251457i
$59$		−	3.70040e8i		−	0.517593i	−0.965932	−	0.258797i	$-0.916674\pi$
$59$		−	3.70040e8i		−	0.517593i	0.965932	−	0.258797i	$-0.0833260\pi$
$60$	−2.95728e8	−	7.94438e7i	−0.380308	−	0.102165i
$61$	3.89997e8			0.461756			0.230878	−	0.972983i	$-0.425840\pi$
$61$	3.89997e8			0.461756			0.230878	+	0.972983i	$0.425840\pi$
$62$	−7.79482e8	+	5.97719e8i	−0.850839	+	0.652438i
$63$		−	1.29876e9i		−	1.30866i
$64$	7.60713e8	−	7.57785e8i	0.708469	−	0.705742i
$65$	−7.47764e8			−0.644462
$66$	−2.07130e8	−	2.70116e8i	−0.165395	−	0.215690i
$67$			1.36745e9i			1.01284i	0.862288	+	0.506418i	$0.169031\pi$
$67$			1.36745e9i			1.01284i	−0.862288	+	0.506418i	$0.830969\pi$
$68$	4.04214e7	−	1.50468e8i	0.0278014	−	0.103490i
$69$	9.14336e8			0.584602
$70$	1.83925e9	−	1.41037e9i	1.09434	−	0.839156i
$71$			1.93751e9i			1.07387i	0.843623	+	0.536936i	$0.180418\pi$
$71$			1.93751e9i			1.07387i	−0.843623	+	0.536936i	$0.819582\pi$
$72$	−1.35029e9	+	5.57783e8i	−0.697854	+	0.288272i
$73$	−3.26332e9			−1.57415			−0.787073	−	0.616860i	$-0.788405\pi$
$73$	−3.26332e9			−1.57415			−0.787073	+	0.616860i	$0.788405\pi$
$74$	1.11388e9	+	1.45260e9i	0.501971	+	0.654617i
$75$		−	4.30943e8i		−	0.181599i
$76$	4.70850e7	+	1.26488e7i	0.0185701	+	0.00498864i
$77$	2.57645e9			0.951849
$78$	9.18448e8	−	7.04281e8i	0.318113	−	0.243934i
$79$			2.38865e8i			0.0776277i	0.999246	+	0.0388139i	$0.0123579\pi$
$79$			2.38865e8i			0.0776277i	−0.999246	+	0.0388139i	$0.987642\pi$
$80$	−2.25624e9	−	1.30651e9i	−0.688551	−	0.398716i
$81$	1.13373e9			0.325151
$82$	−4.86288e8	−	6.34164e8i	−0.131167	−	0.171054i
$83$		−	6.66076e9i		−	1.69096i	−0.534007	−	0.845480i	$-0.679314\pi$
$83$		−	6.66076e9i		−	1.69096i	0.534007	−	0.845480i	$-0.320686\pi$
$84$	−9.30725e8	+	3.46460e9i	−0.222549	+	0.828432i
$85$	−3.78314e8			−0.0852625
$86$	−3.10681e9	+	2.38235e9i	−0.660423	+	0.506423i
$87$		−	7.81671e8i		−	0.156830i
$88$	−1.10652e9	−	2.67868e9i	−0.209675	−	0.507583i
$89$	2.76291e9			0.494786			0.247393	−	0.968915i	$-0.420426\pi$
$89$	2.76291e9			0.494786			0.247393	+	0.968915i	$0.420426\pi$
$90$	2.15865e9	+	2.81508e9i	0.365569	+	0.476736i
$91$			8.76043e9i			1.40384i
$92$	7.51847e9	+	2.01975e9i	1.14075	+	0.306449i
$93$	−3.69171e9			−0.530655
$94$	−2.63636e8	+	2.02160e8i	−0.0359224	+	0.0275459i
$95$		−	1.18384e8i		−	0.0152994i
$96$	4.00179e9	−	5.20305e8i	0.490793	−	0.0638119i
$97$	1.47035e9			0.171224			0.0856118	−	0.996329i	$-0.472716\pi$
$97$	1.47035e9			0.171224			0.0856118	+	0.996329i	$0.472716\pi$
$98$	−1.10228e10	−	1.43747e10i	−1.21944	−	1.59027i
$99$			3.94340e9i			0.414662i
$100$	9.51944e8	−	3.54359e9i	0.0951944	−	0.354359i
$101$	−1.43515e10			−1.36550			−0.682748	−	0.730654i	$-0.739215\pi$
$101$	−1.43515e10			−1.36550			−0.682748	+	0.730654i	$0.739215\pi$
$102$	4.64668e8	−	3.56315e8i	0.0420864	−	0.0322726i
$103$		−	6.62493e9i		−	0.571472i	−0.958308	−	0.285736i	$-0.907762\pi$
$103$		−	6.62493e9i		−	0.571472i	0.958308	−	0.285736i	$-0.0922381\pi$
$104$	9.10803e9	−	3.76239e9i	0.748614	−	0.309241i
$105$	8.71090e9			0.682521
$106$	1.10088e10	+	1.43565e10i	0.822643	+	1.07280i
$107$		−	1.71569e9i		−	0.122326i	−0.998128	−	0.0611632i	$-0.980519\pi$
$107$		−	1.71569e9i		−	0.122326i	0.998128	−	0.0611632i	$-0.0194810\pi$
$108$	−1.23258e10	−	3.31119e9i	−0.838874	−	0.225354i
$109$	7.23418e9			0.470172			0.235086	−	0.971975i	$-0.424463\pi$
$109$	7.23418e9			0.470172			0.235086	+	0.971975i	$0.424463\pi$
$110$	−5.58450e9	+	4.28228e9i	−0.346753	+	0.265896i
$111$			6.87966e9i			0.408274i
$112$	−1.53065e10	+	2.64331e10i	−0.868530	+	1.49988i
$113$	1.31399e10			0.713182			0.356591	−	0.934261i	$-0.383939\pi$
$113$	1.31399e10			0.713182			0.356591	+	0.934261i	$0.383939\pi$
$114$	1.11500e8	+	1.45406e8i	0.00579094	+	0.00755192i
$115$		−	1.89034e10i		−	0.939832i
$116$	1.72670e9	−	6.42759e9i	0.0822103	−	0.306026i
$117$	−1.34083e10			−0.611568
$118$	9.39664e9	−	7.20550e9i	0.410736	−	0.314959i
$119$			4.43214e9i			0.185729i
$120$	−3.74111e9	−	9.05653e9i	−0.150347	−	0.363961i
$121$	1.81146e10			0.698396
$122$	7.59410e9	+	9.90342e9i	0.280981	+	0.366426i
$123$		−	3.00347e9i		−	0.106683i
$124$	−3.03565e10	−	8.15491e9i	−1.03548	−	0.278170i
$125$	−3.31912e10			−1.08761
$126$	3.29801e10	−	2.52897e10i	1.03848	−	0.796325i
$127$		−	1.22226e10i		−	0.369952i	−0.982743	−	0.184976i	$-0.940779\pi$
$127$		−	1.22226e10i		−	0.369952i	0.982743	−	0.184976i	$-0.0592207\pi$
$128$	3.40556e10	+	4.56148e9i	0.991149	+	0.132756i
$129$	−1.47142e10			−0.411895
$130$	−1.45606e10	−	1.89884e10i	−0.392160	−	0.511412i
$131$			7.26784e10i			1.88386i	0.335807	+	0.941931i	$0.390991\pi$
$131$			7.26784e10i			1.88386i	−0.335807	+	0.941931i	$0.609009\pi$
$132$	2.82594e9	−	1.05195e10i	0.0705170	−	0.262498i
$133$	−1.38692e9			−0.0333269
$134$	−3.47246e10	+	2.66274e10i	−0.803735	+	0.616317i
$135$			3.09903e10i			0.691125i
$136$	4.60800e9	−	1.90349e9i	0.0990417	−	0.0409126i
$137$	4.05392e10			0.839987			0.419994	−	0.907527i	$-0.362032\pi$
$137$	4.05392e10			0.839987			0.419994	+	0.907527i	$0.362032\pi$
$138$	1.78041e10	+	2.32182e10i	0.355734	+	0.463910i
$139$		−	7.47862e10i		−	1.44128i	−0.693311	−	0.720638i	$-0.743849\pi$
$139$		−	7.47862e10i		−	1.44128i	0.693311	−	0.720638i	$-0.256151\pi$
$140$	7.16287e10	+	1.92422e10i	1.33182	+	0.357779i
$141$	−1.24861e9			−0.0224042
$142$	−4.92003e10	+	3.77276e10i	−0.852170	+	0.653458i
$143$		−	2.65992e10i		−	0.444824i
$144$	−4.04572e10	−	2.34274e10i	−0.653407	−	0.378365i
$145$	−1.61606e10			−0.252126
$146$	−6.35440e10	−	8.28673e10i	−0.957878	−	1.24916i
$147$		−	6.80803e10i		−	0.991824i
$148$	−1.51970e10	+	5.65706e10i	−0.214018	+	0.796677i
$149$	3.20644e10			0.436608			0.218304	−	0.975881i	$-0.429948\pi$
$149$	3.20644e10			0.436608			0.218304	+	0.975881i	$0.429948\pi$
$150$	1.09432e10	−	8.39140e9i	0.144108	−	0.110504i
$151$		−	8.95240e9i		−	0.114039i	−0.998373	−	0.0570197i	$-0.981840\pi$
$151$		−	8.95240e9i		−	0.114039i	0.998373	−	0.0570197i	$-0.0181598\pi$
$152$	5.95649e8	+	1.44196e9i	0.00734129	+	0.0177719i
$153$	−6.78364e9			−0.0809106
$154$	5.01692e10	+	6.54252e10i	0.579206	+	0.755339i
$155$			7.63239e10i			0.853104i
$156$	3.57684e10	+	9.60876e9i	0.387148	+	0.104003i
$157$	1.20190e11			1.26000			0.630001	−	0.776594i	$-0.283054\pi$
$157$	1.20190e11			1.26000			0.630001	+	0.776594i	$0.283054\pi$
$158$	−6.06563e9	+	4.65123e9i	−0.0616014	+	0.0472370i
$159$			6.79940e10i			0.669090i
$160$	−1.07570e10	−	8.27348e10i	−0.102587	−	0.789020i
$161$	−2.21463e11			−2.04725
$162$	2.20763e10	+	2.87895e10i	0.197857	+	0.258023i
$163$			1.53878e11i			1.33733i	0.743564	+	0.668665i	$0.233134\pi$
$163$			1.53878e11i			1.33733i	−0.743564	+	0.668665i	$0.766866\pi$
$164$	6.63460e9	−	2.46971e10i	0.0559236	−	0.208175i
$165$	−2.64488e10			−0.216265
$166$	1.69140e11	−	1.29700e11i	1.34186	−	1.02896i
$167$		−	1.90444e11i		−	1.46618i	−0.680134	−	0.733088i	$-0.738078\pi$
$167$		−	1.90444e11i		−	1.46618i	0.680134	−	0.733088i	$-0.261922\pi$
$168$	−1.06102e11	+	4.38290e10i	−0.792823	+	0.327503i
$169$	−4.74161e10			−0.343948
$170$	−7.36661e9	−	9.60675e9i	−0.0518828	−	0.0676600i
$171$		−	2.12276e9i		−	0.0145185i
$172$	−1.20993e11	−	3.25033e10i	−0.803743	−	0.215916i
$173$	2.01458e11			1.30003			0.650017	−	0.759919i	$-0.274762\pi$
$173$	2.01458e11			1.30003			0.650017	+	0.759919i	$0.274762\pi$
$174$	1.98494e10	−	1.52209e10i	0.124452	−	0.0954318i
$175$			1.04379e11i			0.635952i
$176$	4.64748e10	−	8.02583e10i	0.275204	−	0.475255i
$177$	4.45034e10			0.256169
$178$	5.38000e10	+	7.01602e10i	0.301080	+	0.392637i
$179$		−	2.60541e11i		−	1.41779i	−0.705315	−	0.708894i	$-0.749194\pi$
$179$		−	2.60541e11i		−	1.41779i	0.705315	−	0.708894i	$-0.250806\pi$
$180$	−2.94512e10	+	1.09632e11i	−0.155862	+	0.580194i
$181$	−1.97225e11			−1.01524			−0.507620	−	0.861581i	$-0.669475\pi$
$181$	−1.97225e11			−1.01524			−0.507620	+	0.861581i	$0.669475\pi$
$182$	−2.22459e11	+	1.70585e11i	−1.11402	+	0.854248i
$183$			4.69036e10i			0.228534i
$184$	9.51126e10	+	2.30250e11i	0.450971	+	1.09172i
$185$	1.42233e11			0.656360
$186$	−7.18857e10	−	9.37456e10i	−0.322907	−	0.421101i
$187$		−	1.34572e10i		−	0.0588502i
$188$	−1.02672e10	−	2.75815e9i	−0.0437180	−	0.0117443i
$189$	3.63067e11			1.50549
$190$	3.00618e9	−	2.30519e9i	0.0121408	−	0.00930977i
$191$			1.06272e11i			0.418074i	0.977908	+	0.209037i	$0.0670329\pi$
$191$			1.06272e11i			0.418074i	−0.977908	+	0.209037i	$0.932967\pi$
$192$	9.11361e10	+	9.14883e10i	0.349289	+	0.350638i
$193$	−3.13091e11			−1.16919			−0.584593	−	0.811327i	$-0.698746\pi$
$193$	−3.13091e11			−1.16919			−0.584593	+	0.811327i	$0.698746\pi$
$194$	2.86311e10	+	3.73376e10i	0.104191	+	0.135874i
$195$		−	8.99309e10i		−	0.318960i
$196$	1.50388e11	−	5.59816e11i	0.519916	−	1.93537i
$197$	−1.13079e11			−0.381109			−0.190555	−	0.981677i	$-0.561029\pi$
$197$	−1.13079e11			−0.381109			−0.190555	+	0.981677i	$0.561029\pi$
$198$	−1.00137e11	+	7.67866e10i	−0.329055	+	0.252325i
$199$			9.62447e10i			0.308398i	0.988040	+	0.154199i	$0.0492797\pi$
$199$			9.62447e10i			0.308398i	−0.988040	+	0.154199i	$0.950720\pi$
$200$	1.08521e11	−	4.48283e10i	0.339128	−	0.140088i
$201$	−1.64459e11			−0.501277
$202$	−2.79455e11	−	3.64436e11i	−0.830913	−	1.08359i
$203$			1.89330e11i			0.549211i
$204$	1.80962e10	+	4.86134e9i	0.0512197	+	0.0137596i
$205$	−6.20950e10			−0.171509
$206$	1.68231e11	−	1.29002e11i	0.453491	−	0.347744i
$207$		−	3.38961e11i		−	0.891862i
$208$	2.72894e11	+	1.58023e11i	0.700934	+	0.405887i
$209$	4.21110e9			0.0105600
$210$	1.69620e11	+	2.21201e11i	0.415319	+	0.541614i
$211$			5.61001e11i			1.34138i	0.741739	+	0.670689i	$0.234001\pi$
$211$			5.61001e11i			1.34138i	−0.741739	+	0.670689i	$0.765999\pi$
$212$	−1.50197e11	+	5.59106e11i	−0.350738	+	1.30561i
$213$	−2.33018e11			−0.531485
$214$	4.35675e10	−	3.34083e10i	0.0970721	−	0.0744364i
$215$			3.04207e11i			0.662181i
$216$	−1.55928e11	−	3.77473e11i	−0.331631	−	0.802817i
$217$	8.94174e11			1.85833
$218$	1.40865e11	+	1.83702e11i	0.286103	+	0.373105i
$219$		−	3.92468e11i		−	0.779083i
$220$	−2.17485e11	−	5.84248e10i	−0.422003	−	0.113366i
$221$	4.57573e10			0.0867958
$222$	−1.74699e11	+	1.33962e11i	−0.323986	+	0.248438i
$223$		−	7.84419e11i		−	1.42241i	−0.702986	−	0.711203i	$-0.748150\pi$
$223$		−	7.84419e11i		−	1.42241i	0.702986	−	0.711203i	$-0.251850\pi$
$224$	−9.69280e11	+	1.26024e11i	−1.71874	+	0.223467i
$225$	−1.59758e11			−0.277045
$226$	2.55863e11	+	3.33669e11i	0.433976	+	0.565945i
$227$		−	5.68954e11i		−	0.943947i	−0.881613	−	0.471974i	$-0.843542\pi$
$227$		−	5.68954e11i		−	0.943947i	0.881613	−	0.471974i	$-0.156458\pi$
$228$	−1.52123e9	+	5.66274e9i	−0.00246900	+	0.00919079i
$229$	−7.23418e11			−1.14871			−0.574357	−	0.818605i	$-0.694748\pi$
$229$	−7.23418e11			−1.14871			−0.574357	+	0.818605i	$0.694748\pi$
$230$	4.80024e11	−	3.68090e11i	0.745802	−	0.571894i
$231$			3.09861e11i			0.471093i
$232$	1.96842e11	−	8.13124e10i	0.292872	−	0.120981i
$233$	9.79824e11			1.42682			0.713409	−	0.700748i	$-0.247150\pi$
$233$	9.79824e11			1.42682			0.713409	+	0.700748i	$0.247150\pi$
$234$	−2.61090e11	−	3.40485e11i	−0.372143	−	0.485310i
$235$			2.58143e10i			0.0360181i
$236$	3.65946e11	+	9.83072e10i	0.499871	+	0.134284i
$237$	−2.87275e10			−0.0384198
$238$	−1.12548e11	+	8.63036e10i	−0.147385	+	0.113017i
$239$			6.74650e11i			0.865145i	0.901599	+	0.432573i	$0.142394\pi$
$239$			6.74650e11i			0.865145i	−0.901599	+	0.432573i	$0.857606\pi$
$240$	1.57130e11	−	2.71351e11i	0.197334	−	0.340780i
$241$	−3.30697e11			−0.406767			−0.203383	−	0.979099i	$-0.565194\pi$
$241$	−3.30697e11			−0.406767			−0.203383	+	0.979099i	$0.565194\pi$
$242$	3.52731e11	+	4.59994e11i	0.424978	+	0.554211i
$243$			8.72319e11i			1.02954i
$244$	−1.03609e11	+	3.85683e11i	−0.119798	+	0.445945i
$245$	−1.40752e12			−1.59450
$246$	7.62687e10	−	5.84841e10i	0.0846586	−	0.0649176i
$247$			1.43186e10i			0.0155745i
$248$	−3.84025e11	−	9.29653e11i	−0.409356	−	0.990974i
$249$	8.01066e11			0.836897
$250$	−6.46305e11	−	8.42842e11i	−0.661816	−	0.863070i
$251$			6.29664e11i			0.632033i	0.948754	+	0.316017i	$0.102346\pi$
$251$			6.29664e11i			0.632033i	−0.948754	+	0.316017i	$0.897654\pi$
$252$	1.28439e12	+	3.45036e11i	1.26385	+	0.339517i
$253$	6.72424e11			0.648695
$254$	3.10375e11	−	2.38001e11i	0.293575	−	0.225118i
$255$		−	4.54985e10i		−	0.0421985i
$256$	5.47306e11	+	9.53615e11i	0.497772	+	0.867308i
$257$	−1.03988e12			−0.927506			−0.463753	−	0.885964i	$-0.653498\pi$
$257$	−1.03988e12			−0.927506			−0.463753	+	0.885964i	$0.653498\pi$
$258$	−2.86517e11	−	3.73645e11i	−0.250641	−	0.326859i
$259$		−	1.66633e12i		−	1.42976i
$260$	1.98656e11	−	7.39492e11i	0.167199	−	0.622396i
$261$	−2.89780e11			−0.239257
$262$	−1.84556e12	+	1.41521e12i	−1.49494	+	1.14634i
$263$		−	1.57735e12i		−	1.25357i	−0.779191	−	0.626787i	$-0.784370\pi$
$263$		−	1.57735e12i		−	1.25357i	0.779191	−	0.626787i	$-0.215630\pi$
$264$	3.22155e11	−	1.33077e11i	0.251215	−	0.103773i
$265$	1.40574e12			1.07566
$266$	−2.70065e10	−	3.52190e10i	−0.0202796	−	0.0264465i
$267$			3.32286e11i			0.244881i
$268$	−1.35233e12	−	3.63287e11i	−0.978155	−	0.262770i
$269$	1.08951e12			0.773514			0.386757	−	0.922182i	$-0.373595\pi$
$269$	1.08951e12			0.773514			0.386757	+	0.922182i	$0.373595\pi$
$270$	−7.86953e11	+	6.03449e11i	−0.548441	+	0.420554i
$271$			8.87154e11i			0.606949i	0.952840	+	0.303475i	$0.0981468\pi$
$271$			8.87154e11i			0.606949i	−0.952840	+	0.303475i	$0.901853\pi$
$272$	1.38064e11	+	7.99484e10i	0.0927337	+	0.0536989i
$273$	−1.05359e12			−0.694796
$274$	7.89388e11	+	1.02944e12i	0.511138	+	0.666571i
$275$		−	3.16925e11i		−	0.201508i
$276$	−2.42908e11	+	9.04221e11i	−0.151669	+	0.564585i
$277$	8.23317e11			0.504857			0.252428	−	0.967616i	$-0.418771\pi$
$277$	8.23317e11			0.504857			0.252428	+	0.967616i	$0.418771\pi$
$278$	1.89909e12	−	1.45625e12i	1.14372	−	0.877026i
$279$			1.36858e12i			0.809561i
$280$	9.06140e11	+	2.19360e12i	0.526508	+	1.27458i
$281$	1.09369e11			0.0624253			0.0312127	−	0.999513i	$-0.490063\pi$
$281$	1.09369e11			0.0624253			0.0312127	+	0.999513i	$0.490063\pi$
$282$	−2.43131e10	−	3.17066e10i	−0.0136331	−	0.0177789i
$283$		−	7.72106e11i		−	0.425348i	−0.977123	−	0.212674i	$-0.931783\pi$
$283$		−	7.72106e11i		−	0.425348i	0.977123	−	0.212674i	$-0.0682173\pi$
$284$	−1.91608e12	−	5.14731e11i	−1.03710	−	0.278605i
$285$	1.42376e10			0.00757203
$286$	6.75448e11	−	5.17944e11i	0.352989	−	0.270678i
$287$			7.27474e11i			0.373601i
$288$	−1.92886e11	−	1.48354e12i	−0.0973507	−	0.748748i
$289$	−1.99284e12			−0.988517
$290$	−3.14683e11	−	4.10376e11i	−0.153420	−	0.200074i
$291$			1.76834e11i			0.0847426i
$292$	8.66954e11	−	3.22722e12i	0.408396	−	1.52025i
$293$	−2.10032e12			−0.972629			−0.486315	−	0.873784i	$-0.661659\pi$
$293$	−2.10032e12			−0.972629			−0.486315	+	0.873784i	$0.661659\pi$
$294$	1.72880e12	−	1.32567e12i	0.787061	−	0.603531i
$295$		−	9.20083e11i		−	0.411829i
$296$	−1.73245e12	+	7.15648e11i	−0.762434	+	0.314949i
$297$	−1.10237e12			−0.477031
$298$	6.24364e11	+	8.14229e11i	0.265679	+	0.346470i
$299$			2.28637e12i			0.956733i
$300$	4.26175e11	+	1.14487e11i	0.175381	+	0.0471140i
$301$	3.56394e12			1.44244
$302$	2.27333e11	−	1.74323e11i	0.0904958	−	0.0693937i
$303$		−	1.72601e12i		−	0.675817i
$304$	−2.50178e10	+	4.32037e10i	−0.00963565	+	0.0166400i
$305$	9.69705e11			0.367401
$306$	−1.32092e11	−	1.72261e11i	−0.0492346	−	0.0642065i
$307$			3.09674e12i			1.13557i	0.823177	+	0.567784i	$0.192199\pi$
$307$			3.09674e12i			1.13557i	−0.823177	+	0.567784i	$0.807801\pi$
$308$	−6.84476e11	+	2.54795e12i	−0.246948	+	0.919257i
$309$	7.96757e11			0.282835
$310$	−1.93814e12	+	1.48619e12i	−0.676980	+	0.519119i
$311$		−	1.73424e12i		−	0.596083i	−0.954553	−	0.298041i	$-0.903667\pi$
$311$		−	1.73424e12i		−	0.596083i	0.954553	−	0.298041i	$-0.0963333\pi$
$312$	4.52489e11	+	1.09539e12i	0.153051	+	0.370507i
$313$	−3.25879e12			−1.08476			−0.542381	−	0.840133i	$-0.682477\pi$
$313$	−3.25879e12			−1.08476			−0.542381	+	0.840133i	$0.682477\pi$
$314$	2.34037e12	+	3.05206e12i	0.766720	+	0.999874i
$315$		−	3.22929e12i		−	1.04125i
$316$	−2.36222e11	−	6.34584e10i	−0.0749697	−	0.0201397i
$317$	3.07857e12			0.961730			0.480865	−	0.876795i	$-0.340323\pi$
$317$	3.07857e12			0.961730			0.480865	+	0.876795i	$0.340323\pi$
$318$	−1.72661e12	+	1.32399e12i	−0.530956	+	0.407146i
$319$		−	5.74859e11i		−	0.174024i
$320$	1.89147e12	−	1.88419e12i	0.563702	−	0.561532i
$321$	2.06340e11			0.0605423
$322$	−4.31237e12	−	5.62373e12i	−1.24577	−	1.62459i
$323$			7.24415e9i			0.00206051i
$324$	−3.01194e11	+	1.12119e12i	−0.0843572	+	0.314018i
$325$	1.07761e12			0.297197
$326$	−3.90751e12	+	2.99634e12i	−1.06124	+	0.813774i
$327$			8.70030e11i			0.232700i
$328$	7.56339e11	−	3.12432e11i	0.199227	−	0.0822974i
$329$	3.02427e11			0.0784587
$330$	−5.15016e11	−	6.71628e11i	−0.131598	−	0.171617i
$331$		−	5.53059e12i		−	1.39197i	−0.718054	−	0.695987i	$-0.754967\pi$
$331$		−	5.53059e12i		−	1.39197i	0.718054	−	0.695987i	$-0.245033\pi$
$332$	6.58707e12	+	1.76954e12i	1.63306	+	0.438702i
$333$	2.55041e12			0.622858
$334$	4.83606e12	−	3.70837e12i	1.16348	−	0.892177i
$335$			3.40010e12i			0.805874i
$336$	−3.17901e12	−	1.84086e12i	−0.742328	−	0.429857i
$337$	−7.76924e12			−1.78743			−0.893715	−	0.448635i	$-0.851910\pi$
$337$	−7.76924e12			−1.78743			−0.893715	+	0.448635i	$0.851910\pi$
$338$	−9.23296e11	−	1.20406e12i	−0.209294	−	0.272939i
$339$			1.58029e12i			0.352971i
$340$	1.00505e11	−	3.74129e11i	0.0221205	−	0.0823430i
$341$	−2.71497e12			−0.588833
$342$	5.39045e10	−	4.13349e10i	0.0115211	−	0.00883459i
$343$			8.26134e12i			1.74012i
$344$	−1.53062e12	−	3.70535e12i	−0.317743	−	0.769196i
$345$	2.27344e12			0.465145
$346$	3.92284e12	+	5.11575e12i	0.791079	+	1.03164i
$347$			1.74639e12i			0.347132i	0.984822	+	0.173566i	$0.0555290\pi$
$347$			1.74639e12i			0.347132i	−0.984822	+	0.173566i	$0.944471\pi$
$348$	7.73024e11	+	2.07664e11i	0.151460	+	0.0406878i
$349$	−4.77133e12			−0.921537			−0.460768	−	0.887520i	$-0.652426\pi$
$349$	−4.77133e12			−0.921537			−0.460768	+	0.887520i	$0.652426\pi$
$350$	−2.65056e12	+	2.03249e12i	−0.504659	+	0.386981i
$351$		−	3.74829e12i		−	0.703554i
$352$	2.94301e12	−	3.82644e11i	0.544601	−	0.0708079i
$353$	7.87216e12			1.43622			0.718109	−	0.695930i	$-0.245008\pi$
$353$	7.87216e12			1.43622			0.718109	+	0.695930i	$0.245008\pi$
$354$	8.66580e11	+	1.13010e12i	0.155881	+	0.203283i
$355$			4.81751e12i			0.854438i
$356$	−7.34013e11	+	2.73235e12i	−0.128367	+	0.477844i
$357$	−5.33039e11			−0.0919216
$358$	6.61608e12	−	5.07332e12i	1.12508	−	0.862734i
$359$		−	8.38030e12i		−	1.40536i	−0.711506	−	0.702680i	$-0.751987\pi$
$359$		−	8.38030e12i		−	1.40536i	0.711506	−	0.702680i	$-0.248013\pi$
$360$	−3.35742e12	+	1.38690e12i	−0.555255	+	0.229367i
$361$	6.12880e12			0.999630
$362$	−3.84041e12	−	5.00825e12i	−0.617781	−	0.805643i
$363$			2.17858e12i			0.345653i
$364$	−8.66352e12	−	2.32735e12i	−1.35577	−	0.364213i
$365$	−8.11405e12			−1.25249
$366$	−1.19105e12	+	9.13316e11i	−0.181353	+	0.139064i
$367$		−	2.03955e12i		−	0.306340i	−0.988200	−	0.153170i	$-0.951052\pi$
$367$		−	2.03955e12i		−	0.306340i	0.988200	−	0.153170i	$-0.0489482\pi$
$368$	−3.99481e12	+	6.89872e12i	−0.591912	+	1.02218i
$369$	−1.11344e12			−0.162755
$370$	2.76959e12	+	3.61180e12i	0.399399	+	0.520854i
$371$		−	1.64689e13i		−	2.34313i
$372$	9.80762e11	−	3.65087e12i	0.137673	−	0.512485i
$373$	4.96883e12			0.688193			0.344096	−	0.938934i	$-0.388185\pi$
$373$	4.96883e12			0.688193			0.344096	+	0.938934i	$0.388185\pi$
$374$	3.41728e11	−	2.62042e11i	0.0467006	−	0.0358108i
$375$		−	3.99179e12i		−	0.538283i
$376$	−1.29885e11	−	3.14427e11i	−0.0172830	−	0.0418389i
$377$	1.95463e12			0.256660
$378$	7.06971e12	+	9.21956e12i	0.916100	+	1.19468i
$379$			9.70064e12i			1.24052i	0.784396	+	0.620261i	$0.212973\pi$
$379$			9.70064e12i			1.24052i	−0.784396	+	0.620261i	$0.787027\pi$
$380$	1.17074e11	+	3.14506e10i	0.0147755	+	0.00396927i
$381$	1.46997e12			0.183098
$382$	−2.69863e12	+	2.06935e12i	−0.331762	+	0.254401i
$383$			1.09603e13i			1.32992i	0.746877	+	0.664962i	$0.231552\pi$
$383$			1.09603e13i			1.32992i	−0.746877	+	0.664962i	$0.768448\pi$
$384$	−5.48593e11	+	4.09575e12i	−0.0657044	+	0.490543i
$385$	6.40619e12			0.757350
$386$	−6.09657e12	−	7.95049e12i	−0.711457	−	0.927807i
$387$			5.45480e12i			0.628383i
$388$	−3.90624e11	+	1.45409e12i	−0.0444222	+	0.165361i
$389$	−2.96322e12			−0.332672			−0.166336	−	0.986069i	$-0.553194\pi$
$389$	−2.96322e12			−0.332672			−0.166336	+	0.986069i	$0.553194\pi$
$390$	2.28367e12	−	1.75115e12i	0.253110	−	0.194089i
$391$			1.15674e12i			0.126576i
$392$	1.71441e13	−	7.08196e12i	1.85219	−	0.765109i
$393$	−8.74078e12			−0.932368
$394$	−2.20189e12	−	2.87147e12i	−0.231907	−	0.302429i
$395$			5.93924e11i			0.0617654i
$396$	−3.89977e12	−	1.04763e12i	−0.400464	−	0.107580i
$397$	−1.59156e13			−1.61387			−0.806936	−	0.590638i	$-0.798876\pi$
$397$	−1.59156e13			−1.61387			−0.806936	+	0.590638i	$0.798876\pi$
$398$	−2.44400e12	+	1.87410e12i	−0.244729	+	0.187662i
$399$		−	1.66801e11i		−	0.0164943i
$400$	3.25149e12	+	1.88283e12i	0.317528	+	0.183870i
$401$	8.90359e12			0.858704			0.429352	−	0.903137i	$-0.358742\pi$
$401$	8.90359e12			0.858704			0.429352	+	0.903137i	$0.358742\pi$
$402$	−3.20238e12	−	4.17620e12i	−0.305030	−	0.397788i
$403$		−	9.23141e12i		−	0.868446i
$404$	3.81271e12	−	1.41927e13i	0.354264	−	1.31874i
$405$	2.81896e12			0.258710
$406$	−4.80776e12	+	3.68667e12i	−0.435825	+	0.334198i
$407$			5.05946e12i			0.453035i
$408$	2.28927e11	+	5.54189e11i	0.0202486	+	0.0490181i
$409$	−1.54383e11			−0.0134891			−0.00674455	−	0.999977i	$-0.502147\pi$
$409$	−1.54383e11			−0.0134891			−0.00674455	+	0.999977i	$0.502147\pi$
$410$	−1.20913e12	−	1.57681e12i	−0.104364	−	0.136101i
$411$			4.87551e12i			0.415730i
$412$	6.55164e12	+	1.76002e12i	0.551904	+	0.148263i
$413$	−1.07792e13			−0.897094
$414$	8.60742e12	−	6.60031e12i	0.707736	−	0.542704i
$415$		−	1.65616e13i		−	1.34543i
$416$	1.30107e12	+	1.00068e13i	0.104432	+	0.803210i
$417$	8.99427e12			0.713322
$418$	8.19994e10	+	1.06935e11i	0.00642583	+	0.00837988i
$419$			1.14268e13i			0.884821i	0.896813	+	0.442411i	$0.145877\pi$
$419$			1.14268e13i			0.884821i	−0.896813	+	0.442411i	$0.854123\pi$
$420$	−2.31419e12	+	8.61453e12i	−0.177073	+	0.659151i
$421$	1.33052e13			1.00603			0.503014	−	0.864279i	$-0.332225\pi$
$421$	1.33052e13			1.00603			0.503014	+	0.864279i	$0.332225\pi$
$422$	−1.42458e13	+	1.09239e13i	−1.06445	+	0.816237i
$423$			4.62881e11i			0.0341797i
$424$	−1.71224e13	+	7.07299e12i	−1.24950	+	0.516147i
$425$	5.45191e11			0.0393192
$426$	−4.53737e12	−	5.91715e12i	−0.323412	−	0.421759i
$427$		−	1.13606e13i		−	0.800316i
$428$	1.69671e12	+	4.55802e11i	0.118138	+	0.0317364i
$429$	3.19899e12			0.220154
$430$	−7.72490e12	+	5.92358e12i	−0.525473	+	0.402941i
$431$			2.02248e12i			0.135987i	0.997686	+	0.0679936i	$0.0216597\pi$
$431$			2.02248e12i			0.135987i	−0.997686	+	0.0679936i	$0.978340\pi$
$432$	6.54911e12	−	1.13098e13i	0.435275	−	0.751685i
$433$	8.28286e12			0.544178			0.272089	−	0.962272i	$-0.412285\pi$
$433$	8.28286e12			0.544178			0.272089	+	0.962272i	$0.412285\pi$
$434$	1.74115e13	+	2.27063e13i	1.13081	+	1.47468i
$435$		−	1.94358e12i		−	0.124783i
$436$	−1.92188e12	+	7.15415e12i	−0.121981	+	0.454073i
$437$	−3.61971e11			−0.0227126
$438$	9.96616e12	−	7.64222e12i	0.618240	−	0.474077i
$439$			4.02387e10i			0.00246786i	0.999999	+	0.00123393i	$0.000392773\pi$
$439$			4.02387e10i			0.00246786i	−0.999999	+	0.00123393i	$0.999607\pi$
$440$	−2.75130e12	−	6.66038e12i	−0.166830	−	0.403864i
$441$	−2.52386e13			−1.51311
$442$	8.90995e11	+	1.16194e12i	0.0528158	+	0.0688767i
$443$		−	9.18481e12i		−	0.538333i	−0.963094	−	0.269167i	$-0.913252\pi$
$443$		−	9.18481e12i		−	0.538333i	0.963094	−	0.269167i	$-0.0867483\pi$
$444$	−6.80355e12	−	1.82769e12i	−0.394295	−	0.105923i
$445$	6.86982e12			0.393682
$446$	1.99192e13	−	1.52744e13i	1.12875	−	0.865544i
$447$			3.85627e12i			0.216088i
$448$	−2.20742e13	−	2.21595e13i	−1.22319	−	1.22792i
$449$	4.73013e12			0.259204			0.129602	−	0.991566i	$-0.458630\pi$
$449$	4.73013e12			0.259204			0.129602	+	0.991566i	$0.458630\pi$
$450$	−3.11084e12	−	4.05683e12i	−0.168584	−	0.219849i
$451$		−	2.20882e12i		−	0.118380i
$452$	−3.49083e12	+	1.29946e13i	−0.185028	+	0.688762i
$453$	1.07667e12			0.0564408
$454$	1.44478e13	−	1.10788e13i	0.749068	−	0.574398i
$455$			2.17823e13i			1.11698i
$456$	−1.73419e11	+	7.16367e10i	−0.00879574	+	0.00363338i
$457$	−2.00212e13			−1.00440			−0.502202	−	0.864750i	$-0.667477\pi$
$457$	−2.00212e13			−1.00440			−0.502202	+	0.864750i	$0.667477\pi$
$458$	−1.40865e13	−	1.83702e13i	−0.699000	−	0.911561i
$459$		−	1.89636e12i		−	0.0930803i
$460$	1.86943e13	+	5.02199e12i	0.907651	+	0.243830i
$461$	−1.25700e13			−0.603713			−0.301857	−	0.953353i	$-0.597606\pi$
$461$	−1.25700e13			−0.603713			−0.301857	+	0.953353i	$0.597606\pi$
$462$	−7.86847e12	+	6.03367e12i	−0.373835	+	0.286663i
$463$			3.27768e12i			0.154050i	0.997029	+	0.0770250i	$0.0245421\pi$
$463$			3.27768e12i			0.154050i	−0.997029	+	0.0770250i	$0.975458\pi$
$464$	5.89776e12	+	3.41519e12i	0.274219	+	0.158791i
$465$	−9.17921e12			−0.422222
$466$	1.90793e13	+	2.48812e13i	0.868228	+	1.13225i
$467$			2.55096e13i			1.14847i	0.818691	+	0.574235i	$0.194700\pi$
$467$			2.55096e13i			1.14847i	−0.818691	+	0.574235i	$0.805300\pi$
$468$	3.56214e12	−	1.32600e13i	0.158665	−	0.590628i
$469$	3.98339e13			1.75545
$470$	−6.55516e11	+	5.02660e11i	−0.0285821	+	0.0219172i
$471$			1.44549e13i			0.623606i
$472$	4.62941e12	+	1.12069e13i	0.197613	+	0.478385i
$473$	−1.08211e13			−0.457053
$474$	−5.59387e11	−	7.29493e11i	−0.0233787	−	0.0304880i
$475$			1.70604e11i			0.00705537i
$476$	−4.38311e12	−	1.17747e12i	−0.179369	−	0.0481854i
$477$	2.52066e13			1.02076
$478$	−1.71318e13	+	1.31369e13i	−0.686535	+	0.526447i
$479$		−	4.10026e13i		−	1.62605i	−0.582228	−	0.813025i	$-0.697819\pi$
$479$		−	4.10026e13i		−	1.62605i	0.582228	−	0.813025i	$-0.302181\pi$
$480$	9.95023e12	−	1.29371e12i	0.390505	−	0.0507727i
$481$	−1.72032e13			−0.668164
$482$	−6.43940e12	−	8.39758e12i	−0.247520	−	0.322789i
$483$		−	2.66345e13i		−	1.01323i
$484$	−4.81244e12	+	1.79142e13i	−0.181192	+	0.674482i
$485$	3.65595e12			0.136236
$486$	−2.21513e13	+	1.69860e13i	−0.816992	+	0.626483i
$487$		−	3.86340e13i		−	1.41034i	−0.709037	−	0.705172i	$-0.750870\pi$
$487$		−	3.86340e13i		−	1.41034i	0.709037	−	0.705172i	$-0.249130\pi$
$488$	−1.18114e13	+	4.87909e12i	−0.426777	+	0.176295i
$489$	−1.85064e13			−0.661877
$490$	−2.74075e13	−	3.57420e13i	−0.970263	−	1.26531i
$491$			2.00168e13i			0.701434i	0.936481	+	0.350717i	$0.114062\pi$
$491$			2.00168e13i			0.701434i	−0.936481	+	0.350717i	$0.885938\pi$
$492$	2.97024e12	+	7.97920e11i	0.103031	+	0.0276780i
$493$	9.88903e11			0.0339562
$494$	−3.63599e11	+	2.78814e11i	−0.0123591	+	0.00947719i
$495$			9.80503e12i			0.329931i
$496$	1.61294e13	−	2.78542e13i	0.537291	−	0.927858i
$497$	5.64396e13			1.86124
$498$	1.55985e13	+	2.03419e13i	0.509257	+	0.664118i
$499$			1.92978e13i			0.623743i	0.950124	+	0.311872i	$0.100956\pi$
$499$			1.92978e13i			0.623743i	−0.950124	+	0.311872i	$0.899044\pi$
$500$	8.81778e12	−	3.28240e13i	0.282169	−	1.05037i
$501$	2.29041e13			0.725646
$502$	−1.59894e13	+	1.22609e13i	−0.501549	+	0.384596i
$503$		−	4.41413e13i		−	1.37090i	−0.728120	−	0.685449i	$-0.759606\pi$
$503$		−	4.41413e13i		−	1.37090i	0.728120	−	0.685449i	$-0.240394\pi$
$504$	1.62482e13	+	3.93339e13i	0.499635	+	1.20952i
$505$	−3.56842e13			−1.08647
$506$	1.30936e13	+	1.70752e13i	0.394735	+	0.514771i
$507$		−	5.70257e12i		−	0.170228i
$508$	1.20874e13	+	3.24714e12i	0.357284	+	0.0959802i
$509$	−5.16632e13			−1.51214			−0.756070	−	0.654491i	$-0.772883\pi$
$509$	−5.16632e13			−1.51214			−0.756070	+	0.654491i	$0.772883\pi$
$510$	1.15537e12	−	8.85957e11i	0.0334865	−	0.0256780i
$511$			9.50603e13i			2.72832i
$512$	−1.35584e13	+	3.24670e13i	−0.385354	+	0.922769i
$513$	5.93417e11			0.0167022
$514$	−2.02487e13	−	2.64062e13i	−0.564394	−	0.736022i
$515$		−	1.64725e13i		−	0.454698i
$516$	3.90906e12	−	1.45514e13i	0.106862	−	0.397792i
$517$	−9.18255e11			−0.0248605
$518$	4.23141e13	−	3.24472e13i	1.13458	−	0.870018i
$519$			2.42287e13i			0.643418i
$520$	2.26466e13	−	9.35495e12i	0.595643	−	0.246051i
$521$	1.13579e13			0.295877			0.147938	−	0.988997i	$-0.452736\pi$
$521$	1.13579e13			0.295877			0.147938	+	0.988997i	$0.452736\pi$
$522$	−5.64265e12	−	7.35854e12i	−0.145590	−	0.189862i
$523$			1.85848e13i			0.474951i	0.971394	+	0.237476i	$0.0763200\pi$
$523$			1.85848e13i			0.474951i	−0.971394	+	0.237476i	$0.923680\pi$
$524$	−7.18744e13	−	1.93082e13i	−1.81936	−	0.488749i
$525$	−1.25533e13			−0.314748
$526$	4.00546e13	−	3.07145e13i	0.994772	−	0.762807i
$527$		−	4.67043e12i		−	0.114896i
$528$	9.65238e12	+	5.58936e12i	0.235215	+	0.136205i
$529$	−1.63727e13			−0.395222
$530$	2.73728e13	+	3.56967e13i	0.654545	+	0.853588i
$531$		−	1.64982e13i		−	0.390809i
$532$	3.68459e11	−	1.37158e12i	0.00864632	−	0.0321857i
$533$	7.51042e12			0.174593
$534$	−8.43793e12	+	6.47034e12i	−0.194325	+	0.149012i
$535$		−	4.26597e12i		−	0.0973305i
$536$	−1.71076e13	−	4.14144e13i	−0.386693	−	0.936112i
$537$	3.13344e13			0.701698
$538$	2.12151e13	+	2.76664e13i	0.470688	+	0.613821i
$539$		−	5.00678e13i		−	1.10056i
$540$	−3.06474e13	−	8.23307e12i	−0.667460	−	0.179305i
$541$	−2.03744e13			−0.439641			−0.219821	−	0.975540i	$-0.570547\pi$
$541$	−2.03744e13			−0.439641			−0.219821	+	0.975540i	$0.570547\pi$
$542$	−2.25280e13	+	1.72748e13i	−0.481644	+	0.369333i
$543$		−	2.37196e13i		−	0.502467i
$544$	6.58245e11	+	5.06272e12i	0.0138163	+	0.106265i
$545$	1.79874e13			0.374098
$546$	−2.05157e13	−	2.67543e13i	−0.422788	−	0.551354i
$547$		−	1.07691e13i		−	0.219910i	−0.993937	−	0.109955i	$-0.964929\pi$
$547$		−	1.07691e13i		−	0.219910i	0.993937	−	0.109955i	$-0.0350706\pi$
$548$	−1.07699e13	+	4.00908e13i	−0.217926	+	0.811225i
$549$	1.73880e13			0.348649
$550$	8.04786e12	−	6.17123e12i	0.159907	−	0.122619i
$551$			3.09452e11i			0.00609305i
$552$	−2.76914e13	+	1.14389e13i	−0.540317	+	0.223197i
$553$	6.95812e12			0.134545
$554$	1.60318e13	+	2.09069e13i	0.307208	+	0.400628i
$555$			1.71059e13i			0.324848i
$556$	7.39589e13	+	1.98682e13i	1.39193	+	0.373925i
$557$	−2.58247e13			−0.481682			−0.240841	−	0.970565i	$-0.577423\pi$
$557$	−2.58247e13			−0.481682			−0.240841	+	0.970565i	$0.577423\pi$
$558$	−3.47532e13	+	2.66493e13i	−0.642426	+	0.492623i
$559$		−	3.67940e13i		−	0.674089i
$560$	−3.80587e13	+	6.57243e13i	−0.691056	+	1.19340i
$561$	1.61846e12			0.0291264
$562$	2.12965e12	+	2.77726e12i	0.0379862	+	0.0495375i
$563$			8.59720e13i			1.51990i	0.649981	+	0.759950i	$0.274777\pi$
$563$			8.59720e13i			1.51990i	−0.649981	+	0.759950i	$0.725223\pi$
$564$	3.31713e11	−	1.23479e12i	0.00581256	−	0.0216371i
$565$	3.26716e13			0.567451
$566$	1.96065e13	−	1.50346e13i	0.337535	−	0.258827i
$567$		−	3.30255e13i		−	0.563553i
$568$	−2.42394e13	−	5.86790e13i	−0.409996	−	0.992524i
$569$	1.09169e14			1.83037			0.915184	−	0.403036i	$-0.132045\pi$
$569$	1.09169e14			1.83037			0.915184	+	0.403036i	$0.132045\pi$
$570$	2.77237e11	+	3.61543e11i	0.00460763	+	0.00600877i
$571$			3.59534e12i			0.0592324i	0.999561	+	0.0296162i	$0.00942851\pi$
$571$			3.59534e12i			0.0592324i	−0.999561	+	0.0296162i	$0.990571\pi$
$572$	2.63049e13	+	7.06651e12i	0.429593	+	0.115405i
$573$	−1.27810e13			−0.206915
$574$	−1.84732e13	+	1.41655e13i	−0.296471	+	0.227339i
$575$			2.72418e13i			0.433407i
$576$	3.39164e13	−	3.37858e13i	0.534930	−	0.532871i
$577$	−4.29147e13			−0.671008			−0.335504	−	0.942039i	$-0.608907\pi$
$577$	−4.29147e13			−0.671008			−0.335504	+	0.942039i	$0.608907\pi$
$578$	−3.88051e13	−	5.06054e13i	−0.601519	−	0.784437i
$579$		−	3.76543e13i		−	0.578658i
$580$	4.29333e12	−	1.59818e13i	0.0654116	−	0.243493i
$581$	−1.94028e14			−2.93078
$582$	−4.49046e12	+	3.44336e12i	−0.0672474	+	0.0515664i
$583$			5.00043e13i			0.742446i
$584$	9.88321e13	−	4.08260e13i	1.45490	−	0.600997i
$585$	−3.33390e13			−0.486601
$586$	−4.08979e13	−	5.33346e13i	−0.591851	−	0.771829i
$587$		−	4.91035e13i		−	0.704567i	−0.935893	−	0.352283i	$-0.885405\pi$
$587$		−	4.91035e13i		−	0.704567i	0.935893	−	0.352283i	$-0.114595\pi$
$588$	6.73271e13	+	1.80866e13i	0.957863	+	0.257319i
$589$	1.46149e12			0.0206167
$590$	2.33642e13	−	1.79160e13i	0.326807	−	0.250601i
$591$		−	1.35996e13i		−	0.188620i
$592$	−5.19075e13	−	3.00578e13i	−0.713874	−	0.413380i
$593$	1.04747e14			1.42846			0.714230	−	0.699911i	$-0.246777\pi$
$593$	1.04747e14			1.42846			0.714230	+	0.699911i	$0.246777\pi$
$594$	−2.14657e13	−	2.79932e13i	−0.290276	−	0.378548i
$595$			1.10203e13i			0.147777i
$596$	−8.51843e12	+	3.17097e13i	−0.113273	+	0.421658i
$597$	−1.15750e13			−0.152634
$598$	−5.80591e13	+	4.45207e13i	−0.759215	+	0.582178i
$599$			1.24568e14i			1.61537i	0.589613	+	0.807686i	$0.299280\pi$
$599$			1.24568e14i			1.61537i	−0.589613	+	0.807686i	$0.700720\pi$
$600$	5.39134e12	+	1.30514e13i	0.0693331	+	0.167842i
$601$	2.99672e13			0.382185			0.191093	−	0.981572i	$-0.438797\pi$
$601$	2.99672e13			0.382185			0.191093	+	0.981572i	$0.438797\pi$
$602$	6.93977e13	+	9.05011e13i	0.877734	+	1.14465i
$603$			6.09679e13i			0.764742i
$604$	8.85336e12	+	2.37835e12i	0.110135	+	0.0295864i
$605$	4.50409e13			0.555687
$606$	4.38294e13	−	3.36091e13i	0.536294	−	0.411239i
$607$		−	1.00566e14i		−	1.22041i	−0.792242	−	0.610206i	$-0.791087\pi$
$607$		−	1.00566e14i		−	1.22041i	0.792242	−	0.610206i	$-0.208913\pi$
$608$	−1.58425e12	+	2.05981e11i	−0.0190680	+	0.00247918i
$609$	−2.27700e13			−0.271817
$610$	1.88823e13	+	2.46243e13i	0.223566	+	0.291551i
$611$		−	3.12225e12i		−	0.0366658i
$612$	1.80219e12	−	6.70859e12i	0.0209914	−	0.0781402i
$613$	−1.20215e13			−0.138886			−0.0694428	−	0.997586i	$-0.522122\pi$
$613$	−1.20215e13			−0.138886			−0.0694428	+	0.997586i	$0.522122\pi$
$614$	−7.86374e13	+	6.03004e13i	−0.901129	+	0.691001i
$615$		−	7.46795e12i		−	0.0848840i
$616$	−7.80297e13	+	3.22329e13i	−0.879745	+	0.363409i
$617$	8.00567e12			0.0895307			0.0447654	−	0.998998i	$-0.485746\pi$
$617$	8.00567e12			0.0895307			0.0447654	+	0.998998i	$0.485746\pi$
$618$	1.55146e13	+	2.02325e13i	0.172107	+	0.224444i
$619$		−	2.24599e13i		−	0.247147i	−0.992335	−	0.123573i	$-0.960565\pi$
$619$		−	2.24599e13i		−	0.247147i	0.992335	−	0.123573i	$-0.0394354\pi$
$620$	−7.54796e13	−	2.02767e13i	−0.823893	−	0.221329i
$621$	9.47562e13			1.02601
$622$	4.40385e13	−	3.37694e13i	0.473021	−	0.362720i
$623$		−	8.04835e13i		−	0.857564i
$624$	−1.90049e13	+	3.28200e13i	−0.200883	+	0.346909i
$625$	−4.75354e13			−0.498445
$626$	−6.34558e13	−	8.27523e13i	−0.660085	−	0.860812i
$627$			5.06454e11i			0.00522640i
$628$	−3.19306e13	+	1.18861e14i	−0.326895	+	1.21686i
$629$	−8.70355e12			−0.0883982
$630$	8.20031e13	−	6.28813e13i	0.826280	−	0.633605i
$631$		−	1.73303e14i		−	1.73245i	−0.499658	−	0.866223i	$-0.666541\pi$
$631$		−	1.73303e14i		−	1.73245i	0.499658	−	0.866223i	$-0.333459\pi$
$632$	−2.98834e12	−	7.23421e12i	−0.0296377	−	0.0717473i
$633$	−6.74696e13			−0.663880
$634$	5.99466e13	+	7.81759e13i	0.585219	+	0.763180i
$635$		−	3.03908e13i		−	0.294356i
$636$	−6.72418e13	−	1.80637e13i	−0.646180	−	0.173589i
$637$	1.70240e14			1.62317
$638$	1.45977e13	−	1.11938e13i	0.138096	−	0.105894i
$639$			8.63838e13i			0.810827i
$640$	8.46773e13	+	1.13419e13i	0.788619	+	0.105629i
$641$	−6.47807e13			−0.598625			−0.299313	−	0.954155i	$-0.596757\pi$
$641$	−6.47807e13			−0.598625			−0.299313	+	0.954155i	$0.596757\pi$
$642$	4.01790e12	+	5.23972e12i	0.0368404	+	0.0480433i
$643$			2.11865e13i			0.192755i	0.995345	+	0.0963774i	$0.0307256\pi$
$643$			2.11865e13i			0.192755i	−0.995345	+	0.0963774i	$0.969274\pi$
$644$	5.88352e13	−	2.19013e14i	0.531139	−	1.97715i
$645$	−3.65859e13			−0.327729
$646$	−1.83955e11	+	1.41060e11i	−0.00163512	+	0.00125383i
$647$			1.16826e14i			1.03043i	0.857062	+	0.515214i	$0.172287\pi$
$647$			1.16826e14i			1.03043i	−0.857062	+	0.515214i	$0.827713\pi$
$648$	−3.43359e13	+	1.41836e13i	−0.300520	+	0.124140i
$649$	3.27288e13			0.284254
$650$	2.09834e13	+	2.73643e13i	0.180846	+	0.235840i
$651$			1.07539e14i			0.919733i
$652$	−1.52176e14	−	4.08802e13i	−1.29154	−	0.346957i
$653$	−1.13028e14			−0.951966			−0.475983	−	0.879455i	$-0.657908\pi$
$653$	−1.13028e14			−0.951966			−0.475983	+	0.879455i	$0.657908\pi$
$654$	−2.20932e13	+	1.69414e13i	−0.184658	+	0.141599i
$655$			1.80711e14i			1.49892i
$656$	2.26613e13	+	1.31224e13i	0.186538	+	0.108018i
$657$	−1.45495e14			−1.18856
$658$	5.88892e12	+	7.67970e12i	0.0477426	+	0.0622608i
$659$		−	1.46878e14i		−	1.18176i	−0.806758	−	0.590881i	$-0.798780\pi$
$659$		−	1.46878e14i		−	1.18176i	0.806758	−	0.590881i	$-0.201220\pi$
$660$	7.02655e12	−	2.61562e13i	0.0561077	−	0.208860i
$661$	9.00092e13			0.713313			0.356656	−	0.934236i	$-0.383917\pi$
$661$	9.00092e13			0.713313			0.356656	+	0.934236i	$0.383917\pi$
$662$	1.40441e14	−	1.07693e14i	1.10460	−	0.847026i
$663$			5.50307e12i			0.0429573i
$664$	8.33299e13	+	2.01726e14i	0.645596	+	1.56287i
$665$	−3.44851e12			−0.0265169
$666$	4.96622e13	+	6.47641e13i	0.379013	+	0.494269i
$667$			4.94129e13i			0.374292i
$668$	1.88338e14	+	5.05947e13i	1.41597	+	0.380385i
$669$	9.43394e13			0.703983
$670$	−8.63406e13	+	6.62074e13i	−0.639501	+	0.490380i
$671$			3.44940e13i			0.253589i
$672$	−1.51565e13	−	1.16572e14i	−0.110599	−	0.850644i
$673$	−4.04707e13			−0.293134			−0.146567	−	0.989201i	$-0.546822\pi$
$673$	−4.04707e13			−0.293134			−0.146567	+	0.989201i	$0.546822\pi$
$674$	−1.51284e14	−	1.97289e14i	−1.08766	−	1.41841i
$675$		−	4.46603e13i		−	0.318715i
$676$	1.25969e13	−	4.68916e13i	0.0892338	−	0.332171i
$677$	−7.14287e13			−0.502261			−0.251131	−	0.967953i	$-0.580802\pi$
$677$	−7.14287e13			−0.502261			−0.251131	+	0.967953i	$0.580802\pi$
$678$	−4.01292e13	+	3.07718e13i	−0.280100	+	0.214785i
$679$		−	4.28314e13i		−	0.296765i
$680$	1.14575e13	−	4.73293e12i	0.0788037	−	0.0325526i
$681$	6.84261e13			0.467182
$682$	−5.28664e13	−	6.89427e13i	−0.358309	−	0.467268i
$683$		−	3.94409e13i		−	0.265365i	−0.991159	−	0.132682i	$-0.957641\pi$
$683$		−	3.94409e13i		−	0.265365i	0.991159	−	0.132682i	$-0.0423590\pi$
$684$	2.09928e12	+	5.63947e11i	0.0140214	+	0.00376667i
$685$	1.00798e14			0.668345
$686$	−2.09785e14	+	1.60867e14i	−1.38087	+	1.05888i
$687$		−	8.70030e13i		−	0.568526i
$688$	6.42874e13	−	1.11019e14i	0.417046	−	0.720205i
$689$	−1.70025e14			−1.09500
$690$	4.42689e13	+	5.77308e13i	0.283044	+	0.369115i
$691$		−	2.34608e14i		−	1.48920i	−0.667511	−	0.744600i	$-0.732640\pi$
$691$		−	2.34608e14i		−	1.48920i	0.667511	−	0.744600i	$-0.267360\pi$
$692$	−5.35207e13	+	1.99230e14i	−0.337281	+	1.25552i
$693$	1.14871e14			0.718694
$694$	−4.43471e13	+	3.40061e13i	−0.275466	+	0.211232i
$695$		−	1.85952e14i		−	1.14677i
$696$	9.77916e12	+	2.36735e13i	0.0598763	+	0.144949i
$697$	3.79973e12			0.0230987
$698$	−9.29084e13	−	1.21161e14i	−0.560761	−	0.731285i
$699$			1.17840e14i			0.706166i
$700$	−1.03225e14	−	2.77301e13i	−0.614176	−	0.164991i
$701$	3.05949e14			1.80742			0.903710	−	0.428144i	$-0.140833\pi$
$701$	3.05949e14			1.80742			0.903710	+	0.428144i	$0.140833\pi$
$702$	9.51824e13	−	7.29874e13i	0.558304	−	0.428117i
$703$		−	2.72355e12i		−	0.0158620i
$704$	6.70236e13	+	6.72826e13i	0.387583	+	0.389081i
$705$	−3.10459e12			−0.0178262
$706$	1.53288e14	+	1.99902e14i	0.873948	+	1.13971i
$707$			4.18058e14i			2.36668i
$708$	−1.18231e13	+	4.40111e13i	−0.0664606	+	0.247398i
$709$	−3.15185e14			−1.75928			−0.879638	−	0.475643i	$-0.842215\pi$
$709$	−3.15185e14			−1.75928			−0.879638	+	0.475643i	$0.842215\pi$
$710$	−1.22334e14	+	9.38075e13i	−0.678038	+	0.519931i
$711$			1.06498e13i			0.0586128i
$712$	−8.36769e13	+	3.45656e13i	−0.457305	+	0.188905i
$713$	2.33369e14			1.26647
$714$	−1.03794e13	−	1.35358e13i	−0.0559349	−	0.0729443i
$715$		−	6.61373e13i		−	0.353929i
$716$	2.57659e14	+	6.92171e13i	1.36924	+	0.367831i
$717$	−8.11378e13			−0.428181
$718$	2.12806e14	−	1.63183e14i	1.11522	−	0.855170i
$719$		−	9.33623e13i		−	0.485878i	−0.970042	−	0.242939i	$-0.921889\pi$
$719$		−	9.33623e13i		−	0.485878i	0.970042	−	0.242939i	$-0.0781115\pi$
$720$	−1.00595e14	−	5.82509e13i	−0.519891	−	0.301051i
$721$	−1.92984e14			−0.990477
$722$	1.19341e14	+	1.55632e14i	0.608281	+	0.793256i
$723$		−	3.97718e13i		−	0.201319i
$724$	5.23961e13	−	1.95043e14i	0.263394	−	0.980478i
$725$	2.32892e13			0.116269
$726$	−5.53219e13	+	4.24217e13i	−0.274292	+	0.210332i
$727$			2.69930e14i			1.32916i	0.747216	+	0.664582i	$0.231390\pi$
$727$			2.69930e14i			1.32916i	−0.747216	+	0.664582i	$0.768610\pi$
$728$	−1.09598e14	−	2.65316e14i	−0.535977	−	1.29750i
$729$	−3.79650e13			−0.184394
$730$	−1.57998e14	−	2.06045e14i	−0.762147	−	0.993910i
$731$		−	1.86151e13i		−	0.0891821i
$732$	−4.63847e13	−	1.24607e13i	−0.220709	−	0.0592908i
$733$	−2.61050e13			−0.123368			−0.0616842	−	0.998096i	$-0.519647\pi$
$733$	−2.61050e13			−0.123368			−0.0616842	+	0.998096i	$0.519647\pi$
$734$	5.17914e13	−	3.97145e13i	0.243096	−	0.186410i
$735$		−	1.69278e14i		−	0.789156i
$736$	−2.52971e14	+	3.28908e13i	−1.17134	+	0.152295i
$737$	−1.20947e14			−0.556234
$738$	−2.16811e13	−	2.82742e13i	−0.0990375	−	0.129154i
$739$			2.34717e14i			1.06493i	0.846451	+	0.532467i	$0.178735\pi$
$739$			2.34717e14i			1.06493i	−0.846451	+	0.532467i	$0.821265\pi$
$740$	−3.77866e13	+	1.40660e14i	−0.170286	+	0.633885i
$741$	−1.72204e12			−0.00770820
$742$	4.18205e14	−	3.20686e14i	1.85939	−	1.42581i
$743$			1.48102e13i			0.0654058i	0.999465	+	0.0327029i	$0.0104115\pi$
$743$			1.48102e13i			0.0654058i	−0.999465	+	0.0327029i	$0.989588\pi$
$744$	1.11806e14	−	4.61854e13i	0.490457	−	0.202600i
$745$	7.97262e13			0.347392
$746$	9.67541e13	+	1.26176e14i	0.418770	+	0.546115i
$747$		−	2.96970e14i		−	1.27676i
$748$	1.33084e13	+	3.57514e12i	0.0568352	+	0.0152681i
$749$	−4.99780e13			−0.212017
$750$	1.01366e14	−	7.77289e13i	0.427154	−	0.327549i
$751$			1.61819e14i			0.677378i	0.940898	+	0.338689i	$0.109983\pi$
$751$			1.61819e14i			0.677378i	−0.940898	+	0.338689i	$0.890017\pi$
$752$	5.45528e12	−	9.42082e12i	0.0226844	−	0.0391742i
$753$	−7.57275e13			−0.312808
$754$	3.80610e13	+	4.96351e13i	0.156179	+	0.203672i
$755$		−	2.22596e13i		−	0.0907367i
$756$	−9.64547e13	+	3.59050e14i	−0.390584	+	1.45394i
$757$	4.32506e13			0.173985			0.0869926	−	0.996209i	$-0.472274\pi$
$757$	4.32506e13			0.173985			0.0869926	+	0.996209i	$0.472274\pi$
$758$	−2.46334e14	+	1.88893e14i	−0.984415	+	0.754865i
$759$			8.08700e13i			0.321055i
$760$	1.48105e12	+	3.58534e12i	0.00584118	+	0.0141404i
$761$	3.30081e14			1.29329			0.646647	−	0.762790i	$-0.276171\pi$
$761$	3.30081e14			1.29329			0.646647	+	0.762790i	$0.276171\pi$
$762$	2.86236e13	+	3.73278e13i	0.111416	+	0.145297i
$763$		−	2.10731e14i		−	0.814904i
$764$	−1.05097e14	−	2.82330e13i	−0.403759	−	0.108465i
$765$	−1.68671e13			−0.0643775
$766$	−2.78320e14	+	2.13420e14i	−1.05536	+	0.809268i
$767$			1.11285e14i			0.419235i
$768$	−1.14688e14	+	6.58226e13i	−0.429252	+	0.246359i
$769$	2.97669e14			1.10688			0.553442	−	0.832887i	$-0.313314\pi$
$769$	2.97669e14			1.10688			0.553442	+	0.832887i	$0.313314\pi$
$770$	1.24743e14	+	1.62676e14i	0.460852	+	0.600994i
$771$		−	1.25063e14i		−	0.459045i
$772$	8.31777e13	−	3.09627e14i	0.303334	−	1.12915i
$773$	−4.07713e14			−1.47726			−0.738630	−	0.674111i	$-0.764527\pi$
$773$	−4.07713e14			−1.47726			−0.738630	+	0.674111i	$0.764527\pi$
$774$	−1.38517e14	+	1.06217e14i	−0.498652	+	0.382375i
$775$		−	1.09991e14i		−	0.393413i
$776$	−4.45308e13	+	1.83950e13i	−0.158253	+	0.0653719i
$777$	2.00404e14			0.707622
$778$	−5.77005e13	−	7.52468e13i	−0.202433	−	0.263991i
$779$			1.18903e12i			0.00414480i
$780$	8.89361e13	+	2.38916e13i	0.308038	+	0.0827509i
$781$	−1.71367e14			−0.589754
$782$	−2.93737e13	+	2.25242e13i	−0.100444	+	0.0770223i
$783$		−	8.10077e13i		−	0.275244i
$784$	5.13670e14	+	2.97449e14i	1.73422	+	1.00423i
$785$	2.98846e14			1.00254
$786$	−1.70202e14	−	2.21960e14i	−0.567352	−	0.739880i
$787$			2.31524e14i			0.766870i	0.923568	+	0.383435i	$0.125259\pi$
$787$			2.31524e14i			0.766870i	−0.923568	+	0.383435i	$0.874741\pi$
$788$	3.00412e13	−	1.11828e14i	0.0988749	−	0.368060i
$789$	1.89703e14			0.620424
$790$	−1.50818e13	+	1.15650e13i	−0.0490139	+	0.0375846i
$791$		−	3.82765e14i		−	1.23609i
$792$	−4.93342e13	−	1.19429e14i	−0.158315	−	0.383251i
$793$	−1.17286e14			−0.374008
$794$	−3.09911e14	−	4.04153e14i	−0.982052	−	1.28069i
$795$			1.69063e14i			0.532369i
$796$	−9.51800e13	−	2.55690e13i	−0.297838	−	0.0800107i
$797$	−2.56317e14			−0.797050			−0.398525	−	0.917157i	$-0.630478\pi$
$797$	−2.56317e14			−0.797050			−0.398525	+	0.917157i	$0.630478\pi$
$798$	4.23566e12	−	3.24798e12i	0.0130890	−	0.0100369i
$799$		−	1.57963e12i		−	0.00485089i
$800$	1.55020e13	+	1.19230e14i	0.0473084	+	0.363860i
$801$	1.23184e14			0.373588
$802$	1.73373e14	+	2.26094e14i	0.522527	+	0.681424i
$803$		−	2.88630e14i		−	0.864498i
$804$	4.36913e13	−	1.62640e14i	0.130051	−	0.484113i
$805$	−5.50654e14			−1.62892
$806$	2.34419e14	−	1.79756e14i	0.689155	−	0.528455i
$807$			1.31031e14i			0.382831i
$808$	4.34646e14	−	1.79546e14i	1.26206	−	0.521336i
$809$	−2.76271e14			−0.797247			−0.398624	−	0.917115i	$-0.630512\pi$
$809$	−2.76271e14			−0.797247			−0.398624	+	0.917115i	$0.630512\pi$
$810$	5.48913e13	+	7.15834e13i	0.157427	+	0.205299i
$811$			3.41060e14i			0.972136i	0.873921	+	0.486068i	$0.161569\pi$
$811$			3.41060e14i			0.972136i	−0.873921	+	0.486068i	$0.838431\pi$
$812$	−1.87235e14	−	5.02986e13i	−0.530405	−	0.142487i
$813$	−1.06695e14			−0.300394
$814$	−1.28478e14	+	9.85189e13i	−0.359506	+	0.275675i
$815$			3.82609e14i			1.06406i
$816$	−9.61512e12	+	1.66045e13i	−0.0265769	+	0.0458961i
$817$	5.82511e12			0.0160027
$818$	−3.00618e12	−	3.92033e12i	−0.00820820	−	0.0107043i
$819$			3.90584e14i			1.05997i
$820$	1.64965e13	−	6.14080e13i	0.0444963	−	0.165636i
$821$	5.08697e14			1.36378			0.681889	−	0.731456i	$-0.261159\pi$
$821$	5.08697e14			1.36378			0.681889	+	0.731456i	$0.261159\pi$
$822$	−1.23807e14	+	9.49370e13i	−0.329902	+	0.252974i
$823$			2.54957e14i			0.675255i	0.941280	+	0.337628i	$0.109624\pi$
$823$			2.54957e14i			0.675255i	−0.941280	+	0.337628i	$0.890376\pi$
$824$	8.28816e13	+	2.00641e14i	0.218184	+	0.528182i
$825$	3.81155e13			0.0997314
$826$	−2.09896e14	−	2.73723e14i	−0.545888	−	0.711888i
$827$		−	1.46659e14i		−	0.379125i	−0.981869	−	0.189563i	$-0.939293\pi$
$827$		−	1.46659e14i		−	0.379125i	0.981869	−	0.189563i	$-0.0607070\pi$
$828$	3.35211e14	+	9.00505e13i	0.861324	+	0.231385i
$829$	5.09908e14			1.30232			0.651162	−	0.758939i	$-0.274282\pi$
$829$	5.09908e14			1.30232			0.651162	+	0.758939i	$0.274282\pi$
$830$	4.20558e14	−	3.22491e14i	1.06767	−	0.818704i
$831$			9.90174e13i			0.249866i
$832$	−2.28774e14	+	2.27893e14i	−0.573839	+	0.571630i
$833$	8.61293e13			0.214746
$834$	1.75138e14	+	2.28397e14i	0.434061	+	0.566056i
$835$		−	4.73529e14i		−	1.16658i
$836$	−1.11875e12	+	4.16451e12i	−0.00273969	+	0.0101984i
$837$	−3.82586e14			−0.931326
$838$	−2.90168e14	+	2.22506e14i	−0.702149	+	0.538419i
$839$		−	3.90267e14i		−	0.938754i	−0.882998	−	0.469377i	$-0.844479\pi$
$839$		−	3.90267e14i		−	0.938754i	0.882998	−	0.469377i	$-0.155521\pi$
$840$	−2.63816e14	+	1.08978e14i	−0.630819	+	0.260582i
$841$	−3.78464e14			−0.899590
$842$	2.59081e14	+	3.37866e14i	0.612174	+	0.798332i
$843$			1.31534e13i			0.0308958i
$844$	−5.54794e14	−	1.49039e14i	−1.29545	−	0.348007i
$845$	−1.17897e14			−0.273666
$846$	−1.17542e13	+	9.01332e12i	−0.0271232	+	0.0207985i
$847$		−	5.27677e14i		−	1.21046i
$848$	−5.13019e14	−	2.97072e14i	−1.16991	−	0.677457i
$849$	9.28585e13			0.210515
$850$	1.06161e13	+	1.38444e13i	0.0239260	+	0.0312017i
$851$		−	4.34894e14i		−	0.974395i
$852$	6.19050e13	−	2.30440e14i	0.137888	−	0.513286i
$853$	6.20925e14			1.37497			0.687486	−	0.726198i	$-0.258714\pi$
$853$	6.20925e14			1.37497			0.687486	+	0.726198i	$0.258714\pi$
$854$	2.88486e14	−	2.21216e14i	0.635090	−	0.486998i
$855$		−	5.27813e12i		−	0.0115518i
$856$	2.14643e13	+	5.19610e13i	0.0467033	+	0.113060i
$857$	−1.62792e14			−0.352150			−0.176075	−	0.984377i	$-0.556340\pi$
$857$	−1.62792e14			−0.352150			−0.176075	+	0.984377i	$0.556340\pi$
$858$	6.22914e13	+	8.12338e13i	0.133965	+	0.174703i
$859$			2.90683e13i			0.0621518i	0.999517	+	0.0310759i	$0.00989336\pi$
$859$			2.90683e13i			0.0621518i	−0.999517	+	0.0310759i	$0.990107\pi$
$860$	−3.00842e14	−	8.08175e13i	−0.639507	−	0.171796i
$861$	−8.74908e13			−0.184904
$862$	−5.13580e13	+	3.93821e13i	−0.107912	+	0.0827491i
$863$			4.43331e14i			0.926136i	0.886323	+	0.463068i	$0.153251\pi$
$863$			4.43331e14i			0.926136i	−0.886323	+	0.463068i	$0.846749\pi$
$864$	4.14722e14	−	5.39213e13i	0.861366	−	0.111993i
$865$	5.00915e14			1.03439
$866$	1.61286e14	+	2.10331e14i	0.331136	+	0.431832i
$867$		−	2.39672e14i		−	0.489241i
$868$	−2.37552e14	+	8.84282e14i	−0.482125	+	1.79470i
$869$	−2.11268e13			−0.0426320
$870$	4.93544e13	−	3.78458e13i	0.0990216	−	0.0759314i
$871$		−	4.11243e14i		−	0.820367i
$872$	−2.19093e14	+	9.05038e13i	−0.434556	+	0.179508i
$873$	6.55557e13			0.129282
$874$	−7.04838e12	−	9.19174e12i	−0.0138208	−	0.0180236i
$875$			9.66856e14i			1.88505i
$876$	3.88126e14	+	1.04266e14i	0.752407	+	0.202125i
$877$	1.63092e14			0.314365			0.157183	−	0.987570i	$-0.449759\pi$
$877$	1.63092e14			0.314365			0.157183	+	0.987570i	$0.449759\pi$
$878$	−1.02180e12	+	7.83536e11i	−0.00195837	+	0.00150171i
$879$		−	2.52598e14i		−	0.481378i
$880$	1.15557e14	−	1.99558e14i	0.218969	−	0.378142i
$881$	−6.93892e14			−1.30741			−0.653706	−	0.756748i	$-0.726787\pi$
$881$	−6.93892e14			−1.30741			−0.653706	+	0.756748i	$0.726787\pi$
$882$	−4.91451e14	−	6.40898e14i	−0.920740	−	1.20073i
$883$			7.89644e14i			1.47105i	0.677497	+	0.735526i	$0.263065\pi$
$883$			7.89644e14i			1.47105i	−0.677497	+	0.735526i	$0.736935\pi$
$884$	−1.21562e13	+	4.52511e13i	−0.0225183	+	0.0838239i
$885$	1.10655e14			0.203824
$886$	2.33235e14	−	1.78848e14i	0.427194	−	0.327579i
$887$			6.79201e14i			1.23703i	0.785773	+	0.618515i	$0.212265\pi$
$887$			6.79201e14i			1.23703i	−0.785773	+	0.618515i	$0.787735\pi$
$888$	−8.60685e13	−	2.08356e14i	−0.155876	−	0.377347i
$889$	−3.56044e14			−0.641201
$890$	1.33771e14	+	1.74449e14i	0.239558	+	0.312406i
$891$			1.00275e14i			0.178568i
$892$	7.75741e14	+	2.08394e14i	1.37370	+	0.369029i
$893$	4.94304e11			0.000870437
$894$	−9.79245e13	+	7.50901e13i	−0.171476	+	0.131491i
$895$		−	6.47821e14i		−	1.12808i
$896$	1.32876e14	−	9.92038e14i	0.230094	−	1.71786i
$897$	−2.74974e14			−0.473510
$898$	9.21062e13	+	1.20115e14i	0.157727	+	0.205691i
$899$		−	1.99509e14i		−	0.339753i
$900$	4.24424e13	−	1.57991e14i	0.0718766	−	0.267559i
$901$	−8.60201e13			−0.144869
$902$	5.60898e13	−	4.30106e13i	0.0939401	−	0.0720348i
$903$			4.28623e14i			0.713898i
$904$	−3.97952e14	+	1.64388e14i	−0.659157	+	0.272287i
$905$	−4.90389e14			−0.807788
$906$	2.09652e13	+	2.73406e13i	0.0343446	+	0.0447885i
$907$		−	1.16301e15i		−	1.89473i	−0.320154	−	0.947365i	$-0.603735\pi$
$907$		−	1.16301e15i		−	1.89473i	0.320154	−	0.947365i	$-0.396265\pi$
$908$	5.62660e14	+	1.51152e14i	0.911626	+	0.244898i
$909$	−6.39861e14			−1.03102
$910$	−5.53131e14	+	4.24150e14i	−0.886382	+	0.679692i
$911$			5.13156e14i			0.817819i	0.912575	+	0.408909i	$0.134091\pi$
$911$			5.13156e14i			0.817819i	−0.912575	+	0.408909i	$0.865909\pi$
$912$	−5.19596e12	−	3.00880e12i	−0.00823553	−	0.00476891i
$913$	5.89123e14			0.928650
$914$	−3.89857e14	−	5.08409e14i	−0.611187	−	0.797044i
$915$			1.16623e14i			0.181836i
$916$	1.92188e14	−	7.15415e14i	0.298022	−	1.10938i
$917$	2.11712e15			3.26511
$918$	4.81554e13	−	3.69263e13i	0.0738638	−	0.0566400i
$919$			3.05396e14i			0.465893i	0.972490	+	0.232947i	$0.0748367\pi$
$919$			3.05396e14i			0.465893i	−0.972490	+	0.232947i	$0.925163\pi$
$920$	2.36492e14	+	5.72503e14i	0.358821	+	0.868638i
$921$	−3.72435e14			−0.562020
$922$	−2.44766e14	−	3.19197e14i	−0.367363	−	0.479076i
$923$		−	5.82680e14i		−	0.869804i
$924$	−3.06433e14	−	8.23196e13i	−0.454962	−	0.122220i
$925$	−2.04973e14			−0.302683
$926$	−8.32320e13	+	6.38236e13i	−0.122246	+	0.0937404i
$927$		−	2.95372e14i		−	0.431490i
$928$	2.81185e13	+	2.16266e14i	0.0408557	+	0.314231i
$929$	−7.46473e14			−1.07879			−0.539393	−	0.842054i	$-0.681346\pi$
$929$	−7.46473e14			−1.07879			−0.539393	+	0.842054i	$0.681346\pi$
$930$	−1.78740e14	−	2.33093e14i	−0.256925	−	0.335054i
$931$			2.69519e13i			0.0385338i
$932$	−2.60306e14	+	9.68985e14i	−0.370173	+	1.37796i
$933$	2.08571e14			0.295016
$934$	−6.47780e14	+	4.96728e14i	−0.911367	+	0.698851i
$935$		−	3.34607e13i		−	0.0468249i
$936$	4.06081e14	−	1.67746e14i	0.565241	−	0.233492i
$937$	−2.42971e14			−0.336400			−0.168200	−	0.985753i	$-0.553795\pi$
$937$	−2.42971e14			−0.336400			−0.168200	+	0.985753i	$0.553795\pi$
$938$	7.75654e14	+	1.01152e15i	1.06820	+	1.39304i
$939$		−	3.91923e14i		−	0.536875i
$940$	−2.55287e13	−	6.85798e12i	−0.0347848	−	0.00934452i
$941$	−8.54747e13			−0.115848			−0.0579241	−	0.998321i	$-0.518448\pi$
$941$	−8.54747e13			−0.115848			−0.0579241	+	0.998321i	$0.518448\pi$
$942$	−3.67061e14	+	2.81468e14i	−0.494862	+	0.379468i
$943$			1.89862e14i			0.254613i
$944$	−1.94439e14	+	3.35781e14i	−0.259373	+	0.447916i
$945$	9.02745e14			1.19786
$946$	−2.10711e14	−	2.74787e14i	−0.278120	−	0.362694i
$947$			1.40626e14i			0.184636i	0.995730	+	0.0923181i	$0.0294277\pi$
$947$			1.40626e14i			0.184636i	−0.995730	+	0.0923181i	$0.970572\pi$
$948$	7.63192e12	−	2.84097e13i	0.00996764	−	0.0371043i
$949$	9.81399e14			1.27501
$950$	−4.33223e12	+	3.32203e12i	−0.00559878	+	0.00429324i
$951$			3.70249e14i			0.475983i
$952$	−5.54487e13	−	1.34231e14i	−0.0709098	−	0.171659i
$953$	−2.42303e14			−0.308244			−0.154122	−	0.988052i	$-0.549255\pi$
$953$	−2.42303e14			−0.308244			−0.154122	+	0.988052i	$0.549255\pi$
$954$	4.90828e14	+	6.40085e14i	0.621137	+	0.810020i
$955$			2.64240e14i			0.332645i
$956$	−6.67187e14	−	1.79232e14i	−0.835522	−	0.224453i
$957$	6.91363e13			0.0861284
$958$	1.04120e15	−	7.98411e14i	1.29035	−	0.989462i
$959$		−	1.18091e15i		−	1.45587i
$960$	2.26605e14	+	2.27480e14i	0.277915	+	0.278989i
$961$	−1.22618e14			−0.149602
$962$	−3.34983e14	−	4.36850e14i	−0.406582	−	0.530220i
$963$		−	7.64941e13i		−	0.0923626i
$964$	8.78551e13	−	3.27039e14i	0.105531	−	0.392839i
$965$	−7.78482e14			−0.930277
$966$	6.76346e14	−	5.18633e14i	0.804051	−	0.616559i
$967$		−	2.24166e14i		−	0.265117i	−0.991175	−	0.132559i	$-0.957681\pi$
$967$		−	2.24166e14i		−	0.265117i	0.991175	−	0.132559i	$-0.0423192\pi$
$968$	−5.48614e14	+	2.26624e14i	−0.645491	+	0.266642i
$969$	−8.71229e11			−0.00101980
$970$	7.11895e13	+	9.28377e13i	0.0829005	+	0.108110i
$971$			1.58784e15i			1.83954i	0.392457	+	0.919770i	$0.371625\pi$
$971$			1.58784e15i			1.83954i	−0.392457	+	0.919770i	$0.628375\pi$
$972$	−8.62669e14	−	2.31746e14i	−0.994289	−	0.267104i
$973$	−2.17852e15			−2.49802
$974$	9.81055e14	−	7.52289e14i	1.11918	−	0.858203i
$975$			1.29600e14i			0.147090i
$976$	−3.53891e14	−	2.04926e14i	−0.399595	−	0.231392i
$977$	6.25059e14			0.702180			0.351090	−	0.936342i	$-0.385811\pi$
$977$	6.25059e14			0.702180			0.351090	+	0.936342i	$0.385811\pi$
$978$	−3.60360e14	−	4.69943e14i	−0.402756	−	0.525232i
$979$			2.44371e14i			0.271729i
$980$	3.73931e14	−	1.39195e15i	0.413677	−	1.53990i
$981$	3.22536e14			0.355004
$982$	−5.08298e14	+	3.89771e14i	−0.556623	+	0.426827i
$983$		−	1.35611e15i		−	1.47750i	−0.673978	−	0.738751i	$-0.735416\pi$
$983$		−	1.35611e15i		−	1.47750i	0.673978	−	0.738751i	$-0.264584\pi$
$984$	3.75751e13	+	9.09623e13i	0.0407310	+	0.0986020i
$985$	−2.81163e14			−0.303234
$986$	1.92561e13	+	2.51118e13i	0.0206626	+	0.0269459i
$987$			3.63719e13i			0.0388311i
$988$	−1.41602e13	−	3.80396e12i	−0.0150412	−	0.00404065i
$989$	9.30147e14			0.983037
$990$	−2.48985e14	+	1.90926e14i	−0.261816	+	0.200765i
$991$			1.33504e15i			1.39677i	0.715723	+	0.698384i	$0.246097\pi$
$991$			1.33504e15i			1.39677i	−0.715723	+	0.698384i	$0.753903\pi$
$992$	1.02139e15	−	1.32799e14i	1.06325	−	0.138241i
$993$	6.65145e14			0.688922
$994$	1.09900e15	+	1.43320e15i	1.13257	+	1.47698i
$995$			2.39307e14i			0.245380i
$996$	−2.12816e14	+	7.92205e14i	−0.217124	+	0.808241i
$997$	−1.09516e15			−1.11174			−0.555869	−	0.831270i	$-0.687614\pi$
$997$	−1.09516e15			−1.11174			−0.555869	+	0.831270i	$0.687614\pi$
$998$	−4.90041e14	+	3.75771e14i	−0.494971	+	0.379552i
$999$			7.12966e14i			0.716542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.11.b.a.3.4	yes	4
3.2	odd	2		36.11.d.c.19.1		4
4.3	odd	2	inner	4.11.b.a.3.3	✓	4
5.2	odd	4		100.11.d.a.99.2		8
5.3	odd	4		100.11.d.a.99.7		8
5.4	even	2		100.11.b.d.51.1		4
8.3	odd	2		64.11.c.d.63.3		4
8.5	even	2		64.11.c.d.63.2		4
12.11	even	2		36.11.d.c.19.2		4
16.3	odd	4		256.11.d.f.127.5		8
16.5	even	4		256.11.d.f.127.6		8
16.11	odd	4		256.11.d.f.127.4		8
16.13	even	4		256.11.d.f.127.3		8
20.3	even	4		100.11.d.a.99.1		8
20.7	even	4		100.11.d.a.99.8		8
20.19	odd	2		100.11.b.d.51.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.11.b.a.3.3	✓	4	4.3	odd	2	inner
4.11.b.a.3.4	yes	4	1.1	even	1	trivial
36.11.d.c.19.1		4	3.2	odd	2
36.11.d.c.19.2		4	12.11	even	2
64.11.c.d.63.2		4	8.5	even	2
64.11.c.d.63.3		4	8.3	odd	2
100.11.b.d.51.1		4	5.4	even	2
100.11.b.d.51.2		4	20.19	odd	2
100.11.d.a.99.1		8	20.3	even	4
100.11.d.a.99.2		8	5.2	odd	4
100.11.d.a.99.7		8	5.3	odd	4
100.11.d.a.99.8		8	20.7	even	4
256.11.d.f.127.3		8	16.13	even	4
256.11.d.f.127.4		8	16.11	odd	4
256.11.d.f.127.5		8	16.3	odd	4
256.11.d.f.127.6		8	16.5	even	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(19.4722 + 25.3936i) q^{2} +120.267i q^{3} +(-265.666 + 988.937i) q^{4} +2486.44 q^{5} +(-3054.00 + 2341.85i) q^{6} -29129.9i q^{7} +(-30285.8 + 12510.6i) q^{8} +44585.0 q^{9} +O(q^{10})\)	\(q+(19.4722 + 25.3936i) q^{2} +120.267i q^{3} +(-265.666 + 988.937i) q^{4} +2486.44 q^{5} +(-3054.00 + 2341.85i) q^{6} -29129.9i q^{7} +(-30285.8 + 12510.6i) q^{8} +44585.0 q^{9} +(48416.5 + 63139.6i) q^{10} +88446.8i q^{11} +(-118936. - 31950.8i) q^{12} -300736. q^{13} +(739713. - 567224. i) q^{14} +299036. i q^{15} +(-907419. - 525455. i) q^{16} -152151. q^{17} +(868167. + 1.13217e6i) q^{18} -47611.7i q^{19} +(-660564. + 2.45894e6i) q^{20} +3.50336e6 q^{21} +(-2.24598e6 + 1.72225e6i) q^{22} -7.60258e6i q^{23} +(-1.50460e6 - 3.64236e6i) q^{24} -3.58323e6 q^{25} +(-5.85600e6 - 7.63677e6i) q^{26} +1.24637e7i q^{27} +(2.88077e7 + 7.73885e6i) q^{28} -6.49949e6 q^{29} +(-7.59359e6 + 5.82289e6i) q^{30} +3.06960e7i q^{31} +(-4.32626e6 - 3.32744e7i) q^{32} -1.06372e7 q^{33} +(-2.96271e6 - 3.86365e6i) q^{34} -7.24299e7i q^{35} +(-1.18447e7 + 4.40917e7i) q^{36} +5.72034e7 q^{37} +(1.20903e6 - 927104. i) q^{38} -3.61685e7i q^{39} +(-7.53038e7 + 3.11068e7i) q^{40} -2.49734e7 q^{41} +(6.82181e7 + 8.89627e7i) q^{42} +1.22346e8i q^{43} +(-8.74683e7 - 2.34973e7i) q^{44} +1.10858e8 q^{45} +(1.93057e8 - 1.48039e8i) q^{46} +1.03820e7i q^{47} +(6.31947e7 - 1.09132e8i) q^{48} -5.66078e8 q^{49} +(-6.97734e7 - 9.09910e7i) q^{50} -1.82987e7i q^{51} +(7.98956e7 - 2.97409e8i) q^{52} +5.65361e8 q^{53} +(-3.16498e8 + 2.42696e8i) q^{54} +2.19918e8i q^{55} +(3.64432e8 + 8.82222e8i) q^{56} +5.72609e6 q^{57} +(-1.26559e8 - 1.65045e8i) q^{58} -3.70040e8i q^{59} +(-2.95728e8 - 7.94438e7i) q^{60} +3.89997e8 q^{61} +(-7.79482e8 + 5.97719e8i) q^{62} -1.29876e9i q^{63} +(7.60713e8 - 7.57785e8i) q^{64} -7.47764e8 q^{65} +(-2.07130e8 - 2.70116e8i) q^{66} +1.36745e9i q^{67} +(4.04214e7 - 1.50468e8i) q^{68} +9.14336e8 q^{69} +(1.83925e9 - 1.41037e9i) q^{70} +1.93751e9i q^{71} +(-1.35029e9 + 5.57783e8i) q^{72} -3.26332e9 q^{73} +(1.11388e9 + 1.45260e9i) q^{74} -4.30943e8i q^{75} +(4.70850e7 + 1.26488e7i) q^{76} +2.57645e9 q^{77} +(9.18448e8 - 7.04281e8i) q^{78} +2.38865e8i q^{79} +(-2.25624e9 - 1.30651e9i) q^{80} +1.13373e9 q^{81} +(-4.86288e8 - 6.34164e8i) q^{82} -6.66076e9i q^{83} +(-9.30725e8 + 3.46460e9i) q^{84} -3.78314e8 q^{85} +(-3.10681e9 + 2.38235e9i) q^{86} -7.81671e8i q^{87} +(-1.10652e9 - 2.67868e9i) q^{88} +2.76291e9 q^{89} +(2.15865e9 + 2.81508e9i) q^{90} +8.76043e9i q^{91} +(7.51847e9 + 2.01975e9i) q^{92} -3.69171e9 q^{93} +(-2.63636e8 + 2.02160e8i) q^{94} -1.18384e8i q^{95} +(4.00179e9 - 5.20305e8i) q^{96} +1.47035e9 q^{97} +(-1.10228e10 - 1.43747e10i) q^{98} +3.94340e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{2} + 16 q^{4} - 1560 q^{5} + 7200 q^{6} - 36288 q^{8} - 28764 q^{9}+O(q^{10}) \) 4 * q - 12 * q^2 + 16 * q^4 - 1560 * q^5 + 7200 * q^6 - 36288 * q^8 - 28764 * q^9	\( 4 q - 12 q^{2} + 16 q^{4} - 1560 q^{5} + 7200 q^{6} - 36288 q^{8} - 28764 q^{9} + 263240 q^{10} - 915840 q^{12} + 212264 q^{13} + 1901760 q^{14} - 3612416 q^{16} - 171384 q^{17} + 4740372 q^{18} - 3108960 q^{20} - 483840 q^{21} - 1996320 q^{22} + 17902080 q^{24} - 5358420 q^{25} - 32439672 q^{26} + 36099840 q^{28} + 30046632 q^{29} - 58656960 q^{30} + 58057728 q^{32} - 65537280 q^{33} - 9311128 q^{34} - 55964016 q^{36} + 134408936 q^{37} + 150268320 q^{38} - 229928320 q^{40} - 340180152 q^{41} + 327237120 q^{42} - 302075520 q^{44} + 606940200 q^{45} + 241181760 q^{46} - 244684800 q^{48} - 804921404 q^{49} - 185601540 q^{50} + 382483616 q^{52} + 1437571944 q^{53} - 631903680 q^{54} + 1392491520 q^{56} - 2610835200 q^{57} - 1349585656 q^{58} + 1623087360 q^{60} + 3412083368 q^{61} - 1633009920 q^{62} - 36368384 q^{64} - 4153551600 q^{65} + 713214720 q^{66} + 117217824 q^{68} + 4399188480 q^{69} + 2298979200 q^{70} - 4132504512 q^{72} - 2988510136 q^{73} + 1718257992 q^{74} - 7437974400 q^{76} + 3748200960 q^{77} + 7251497280 q^{78} + 1359198720 q^{80} - 4715780796 q^{81} + 6420307496 q^{82} - 3911362560 q^{84} - 1190796080 q^{85} - 8760249120 q^{86} + 1708439040 q^{88} + 5274721992 q^{89} - 5495216760 q^{90} + 22420389120 q^{92} - 6070118400 q^{93} - 7391671680 q^{94} + 5494579200 q^{96} + 14343199496 q^{97} - 30380986188 q^{98}+O(q^{100}) \) 4 * q - 12 * q^2 + 16 * q^4 - 1560 * q^5 + 7200 * q^6 - 36288 * q^8 - 28764 * q^9 + 263240 * q^10 - 915840 * q^12 + 212264 * q^13 + 1901760 * q^14 - 3612416 * q^16 - 171384 * q^17 + 4740372 * q^18 - 3108960 * q^20 - 483840 * q^21 - 1996320 * q^22 + 17902080 * q^24 - 5358420 * q^25 - 32439672 * q^26 + 36099840 * q^28 + 30046632 * q^29 - 58656960 * q^30 + 58057728 * q^32 - 65537280 * q^33 - 9311128 * q^34 - 55964016 * q^36 + 134408936 * q^37 + 150268320 * q^38 - 229928320 * q^40 - 340180152 * q^41 + 327237120 * q^42 - 302075520 * q^44 + 606940200 * q^45 + 241181760 * q^46 - 244684800 * q^48 - 804921404 * q^49 - 185601540 * q^50 + 382483616 * q^52 + 1437571944 * q^53 - 631903680 * q^54 + 1392491520 * q^56 - 2610835200 * q^57 - 1349585656 * q^58 + 1623087360 * q^60 + 3412083368 * q^61 - 1633009920 * q^62 - 36368384 * q^64 - 4153551600 * q^65 + 713214720 * q^66 + 117217824 * q^68 + 4399188480 * q^69 + 2298979200 * q^70 - 4132504512 * q^72 - 2988510136 * q^73 + 1718257992 * q^74 - 7437974400 * q^76 + 3748200960 * q^77 + 7251497280 * q^78 + 1359198720 * q^80 - 4715780796 * q^81 + 6420307496 * q^82 - 3911362560 * q^84 - 1190796080 * q^85 - 8760249120 * q^86 + 1708439040 * q^88 + 5274721992 * q^89 - 5495216760 * q^90 + 22420389120 * q^92 - 6070118400 * q^93 - 7391671680 * q^94 + 5494579200 * q^96 + 14343199496 * q^97 - 30380986188 * q^98

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