LMFDB - Embedded newform 690.2.w.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	690.7
Dual form			690.2.w.a.493.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-0.160701 - 2.23029i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(1.09028 - 1.99670i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-0.160701 - 2.23029i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(1.09028 - 1.99670i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(0.319399 + 2.21314i) q^{10} +(-1.01510 + 0.879593i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(4.15840 - 2.27066i) q^{13} +(-0.945060 + 2.06939i) q^{14} +(-2.21348 - 0.317052i) q^{15} +(0.959493 - 0.281733i) q^{16} +(0.746984 + 0.997854i) q^{17} +(0.936950 + 0.349464i) q^{18} +(-1.03326 - 7.18646i) q^{19} +(-0.476468 - 2.18471i) q^{20} +(-1.71931 - 1.48979i) q^{21} +(0.949768 - 0.949768i) q^{22} +(1.40009 + 4.58691i) q^{23} +1.00000i q^{24} +(-4.94835 + 0.716820i) q^{25} +(-3.98582 + 2.56153i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(0.795024 - 2.13154i) q^{28} +(-3.31635 - 0.476819i) q^{29} +(2.23045 + 0.158337i) q^{30} +(-1.63406 - 1.05015i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(0.643715 + 1.17888i) q^{33} +(-0.816267 - 0.942022i) q^{34} +(-4.62842 - 2.11077i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.63793 + 7.07258i) q^{37} +(1.54330 + 7.09444i) q^{38} +(-1.33484 - 4.54603i) q^{39} +(0.631110 + 2.14516i) q^{40} +(-1.59716 - 3.49728i) q^{41} +(1.82121 + 1.36334i) q^{42} +(-2.60088 - 0.565788i) q^{43} +(-0.879593 + 1.01510i) q^{44} +(-0.780315 + 2.09550i) q^{45} +(-1.72375 - 4.47534i) q^{46} +(-1.64917 - 1.64917i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(0.986384 + 1.53484i) q^{49} +(4.88460 - 1.06800i) q^{50} +(1.13383 - 0.517804i) q^{51} +(3.79293 - 2.83935i) q^{52} +(-6.22598 - 3.39964i) q^{53} +(0.540641 - 0.841254i) q^{54} +(2.12487 + 2.12262i) q^{55} +(-0.640936 + 2.18283i) q^{56} +(-7.24187 - 0.517948i) q^{57} +(3.34192 + 0.239019i) q^{58} +(2.06066 - 7.01798i) q^{59} +(-2.23607 + 0.00118518i) q^{60} +(4.62425 - 7.19548i) q^{61} +(1.70482 + 0.930900i) q^{62} +(-1.82121 + 1.36334i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-5.73248 - 8.90952i) q^{65} +(-0.726175 - 1.12995i) q^{66} +(-0.0387574 - 0.541900i) q^{67} +(0.881390 + 0.881390i) q^{68} +(4.77970 - 0.393076i) q^{69} +(4.76721 + 1.77520i) q^{70} +(-3.82861 + 4.41845i) q^{71} +(0.977147 + 0.212565i) q^{72} +(-2.33119 - 1.74511i) q^{73} +(-3.13577 - 6.86637i) q^{74} +(-0.351409 + 4.98764i) q^{75} +(-2.04548 - 6.96627i) q^{76} +(0.649535 + 2.98586i) q^{77} +(1.65574 + 4.43922i) q^{78} +(-4.55944 - 1.33877i) q^{79} +(-0.782536 - 2.09467i) q^{80} +(0.654861 + 0.755750i) q^{81} +(1.84258 + 3.37443i) q^{82} +(-7.07921 + 2.64041i) q^{83} +(-1.91383 - 1.22995i) q^{84} +(2.10546 - 1.82634i) q^{85} +(2.63462 + 0.378801i) q^{86} +(-1.17086 + 3.13921i) q^{87} +(0.804935 - 1.07527i) q^{88} +(1.22772 - 0.789005i) q^{89} +(0.628836 - 2.14583i) q^{90} -10.7787i q^{91} +(2.03862 + 4.34097i) q^{92} +(-1.37349 + 1.37349i) q^{93} +(1.76262 + 1.52732i) q^{94} +(-15.8618 + 3.45933i) q^{95} +(0.142315 + 0.989821i) q^{96} +(14.4916 + 5.40508i) q^{97} +(-1.09337 - 1.46057i) q^{98} +(1.28877 - 0.378416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

Coefficient data

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

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

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

$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−0.160701	−	2.23029i	−0.0718679	−	0.997414i
$5$	−0.160701	−	2.23029i	−0.0718679	−	0.997414i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	1.09028	−	1.99670i	0.412088	−	0.754682i	−0.586379	−	0.810037i	$-0.699447\pi$
$7$	1.09028	−	1.99670i	0.412088	−	0.754682i	0.998467	+	0.0553547i	$0.0176289\pi$
$8$	−0.977147	+	0.212565i	−0.345474	+	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	0.319399	+	2.21314i	0.101003	+	0.699856i
$11$	−1.01510	+	0.879593i	−0.306065	+	0.265207i	−0.794327	−	0.607490i	$-0.792177\pi$
$11$	−1.01510	+	0.879593i	−0.306065	+	0.265207i	0.488262	+	0.872697i	$0.337631\pi$
$12$	0.0713392	−	0.997452i	0.0205938	−	0.287940i
$13$	4.15840	−	2.27066i	1.15333	−	0.629767i	0.215380	−	0.976530i	$-0.430901\pi$
$13$	4.15840	−	2.27066i	1.15333	−	0.629767i	0.937953	+	0.346763i	$0.112719\pi$
$14$	−0.945060	+	2.06939i	−0.252578	+	0.553069i
$15$	−2.21348	−	0.317052i	−0.571517	−	0.0818626i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	0.746984	+	0.997854i	0.181170	+	0.242015i	0.881928	−	0.471384i	$-0.156245\pi$
$17$	0.746984	+	0.997854i	0.181170	+	0.242015i	−0.700758	+	0.713399i	$0.747155\pi$
$18$	0.936950	+	0.349464i	0.220841	+	0.0823695i
$19$	−1.03326	−	7.18646i	−0.237046	−	1.64869i	−0.666431	−	0.745567i	$-0.732179\pi$
$19$	−1.03326	−	7.18646i	−0.237046	−	1.64869i	0.429386	−	0.903121i	$-0.358730\pi$
$20$	−0.476468	−	2.18471i	−0.106542	−	0.488517i
$21$	−1.71931	−	1.48979i	−0.375185	−	0.325100i
$22$	0.949768	−	0.949768i	0.202491	−	0.202491i
$23$	1.40009	+	4.58691i	0.291939	+	0.956437i
$23$	1.40009	+	4.58691i	0.291939	+	0.956437i
$24$			1.00000i			0.204124i
$25$	−4.94835	+	0.716820i	−0.989670	+	0.143364i
$26$	−3.98582	+	2.56153i	−0.781683	+	0.502357i
$27$	−0.599278	+	0.800541i	−0.115331	+	0.154064i
$28$	0.795024	−	2.13154i	0.150245	−	0.402823i
$29$	−3.31635	−	0.476819i	−0.615831	−	0.0885431i	−0.172662	−	0.984981i	$-0.555237\pi$
$29$	−3.31635	−	0.476819i	−0.615831	−	0.0885431i	−0.443169	+	0.896438i	$0.646146\pi$
$30$	2.23045	+	0.158337i	0.407223	+	0.0289083i
$31$	−1.63406	−	1.05015i	−0.293486	−	0.188612i	0.385609	−	0.922662i	$-0.373991\pi$
$31$	−1.63406	−	1.05015i	−0.293486	−	0.188612i	−0.679095	+	0.734050i	$0.737628\pi$
$32$	−0.936950	+	0.349464i	−0.165631	+	0.0617771i
$33$	0.643715	+	1.17888i	0.112056	+	0.205216i
$34$	−0.816267	−	0.942022i	−0.139989	−	0.161555i
$35$	−4.62842	−	2.11077i	−0.782346	−	0.356785i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	2.63793	+	7.07258i	0.433674	+	1.16272i	0.951611	+	0.307306i	$0.0994274\pi$
$37$	2.63793	+	7.07258i	0.433674	+	1.16272i	−0.517937	+	0.855419i	$0.673300\pi$
$38$	1.54330	+	7.09444i	0.250357	+	1.15087i
$39$	−1.33484	−	4.54603i	−0.213745	−	0.727948i
$40$	0.631110	+	2.14516i	0.0997873	+	0.339179i
$41$	−1.59716	−	3.49728i	−0.249434	−	0.546184i	0.742953	−	0.669344i	$-0.233425\pi$
$41$	−1.59716	−	3.49728i	−0.249434	−	0.546184i	−0.992387	+	0.123160i	$0.960697\pi$
$42$	1.82121	+	1.36334i	0.281019	+	0.210369i
$43$	−2.60088	−	0.565788i	−0.396631	−	0.0862818i	0.00982587	−	0.999952i	$-0.496872\pi$
$43$	−2.60088	−	0.565788i	−0.396631	−	0.0862818i	−0.406457	+	0.913670i	$0.633236\pi$
$44$	−0.879593	+	1.01510i	−0.132604	+	0.153033i
$45$	−0.780315	+	2.09550i	−0.116323	+	0.312378i
$46$	−1.72375	−	4.47534i	−0.254153	−	0.659853i
$47$	−1.64917	−	1.64917i	−0.240556	−	0.240556i	0.576524	−	0.817080i	$-0.304409\pi$
$47$	−1.64917	−	1.64917i	−0.240556	−	0.240556i	−0.817080	+	0.576524i	$0.804409\pi$
$48$	−0.0713392	−	0.997452i	−0.0102969	−	0.143970i
$49$	0.986384	+	1.53484i	0.140912	+	0.219263i
$50$	4.88460	−	1.06800i	0.690787	−	0.151039i
$51$	1.13383	−	0.517804i	0.158768	−	0.0725071i
$52$	3.79293	−	2.83935i	0.525984	−	0.393747i
$53$	−6.22598	−	3.39964i	−0.855205	−	0.466977i	−0.00907793	−	0.999959i	$-0.502890\pi$
$53$	−6.22598	−	3.39964i	−0.855205	−	0.466977i	−0.846127	+	0.532982i	$0.821071\pi$
$54$	0.540641	−	0.841254i	0.0735719	−	0.114480i
$55$	2.12487	+	2.12262i	0.286518	+	0.286214i
$56$	−0.640936	+	2.18283i	−0.0856486	+	0.291692i
$57$	−7.24187	−	0.517948i	−0.959209	−	0.0686039i
$58$	3.34192	+	0.239019i	0.438815	+	0.0313847i
$59$	2.06066	−	7.01798i	0.268276	−	0.913663i	−0.709623	−	0.704582i	$-0.751135\pi$
$59$	2.06066	−	7.01798i	0.268276	−	0.913663i	0.977898	−	0.209081i	$-0.0670472\pi$
$60$	−2.23607	+	0.00118518i	−0.288675	+	0.000153006i
$61$	4.62425	−	7.19548i	0.592075	−	0.921286i	−0.407891	−	0.913031i	$-0.633736\pi$
$61$	4.62425	−	7.19548i	0.592075	−	0.921286i	0.999966	−	0.00825570i	$-0.00262790\pi$
$62$	1.70482	+	0.930900i	0.216512	+	0.118224i
$63$	−1.82121	+	1.36334i	−0.229451	+	0.171765i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−5.73248	−	8.90952i	−0.711026	−	1.10509i
$66$	−0.726175	−	1.12995i	−0.0893860	−	0.139087i
$67$	−0.0387574	−	0.541900i	−0.00473497	−	0.0662036i	0.994535	−	0.104402i	$-0.0332928\pi$
$67$	−0.0387574	−	0.541900i	−0.00473497	−	0.0662036i	−0.999270	+	0.0381981i	$0.987838\pi$
$68$	0.881390	+	0.881390i	0.106884	+	0.106884i
$69$	4.77970	−	0.393076i	0.575408	−	0.0473208i
$70$	4.76721	+	1.77520i	0.569791	+	0.212177i
$71$	−3.82861	+	4.41845i	−0.454372	+	0.524374i	−0.935999	−	0.352003i	$-0.885501\pi$
$71$	−3.82861	+	4.41845i	−0.454372	+	0.524374i	0.481627	+	0.876377i	$0.340046\pi$
$72$	0.977147	+	0.212565i	0.115158	+	0.0250511i
$73$	−2.33119	−	1.74511i	−0.272845	−	0.204249i	0.454089	−	0.890956i	$-0.349965\pi$
$73$	−2.33119	−	1.74511i	−0.272845	−	0.204249i	−0.726934	+	0.686707i	$0.759056\pi$
$74$	−3.13577	−	6.86637i	−0.364525	−	0.798199i
$75$	−0.351409	+	4.98764i	−0.0405772	+	0.575923i
$76$	−2.04548	−	6.96627i	−0.234633	−	0.799086i
$77$	0.649535	+	2.98586i	0.0740213	+	0.340271i
$78$	1.65574	+	4.43922i	0.187476	+	0.502643i
$79$	−4.55944	−	1.33877i	−0.512977	−	0.150624i	0.0149915	−	0.999888i	$-0.495228\pi$
$79$	−4.55944	−	1.33877i	−0.512977	−	0.150624i	−0.527968	+	0.849264i	$0.677046\pi$
$80$	−0.782536	−	2.09467i	−0.0874902	−	0.234191i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	1.84258	+	3.37443i	0.203479	+	0.372644i
$83$	−7.07921	+	2.64041i	−0.777044	+	0.289823i	−0.706525	−	0.707688i	$-0.749738\pi$
$83$	−7.07921	+	2.64041i	−0.777044	+	0.289823i	−0.0705191	+	0.997510i	$0.522466\pi$
$84$	−1.91383	−	1.22995i	−0.208816	−	0.134198i
$85$	2.10546	−	1.82634i	0.228369	−	0.198095i
$86$	2.63462	+	0.378801i	0.284098	+	0.0408472i
$87$	−1.17086	+	3.13921i	−0.125530	+	0.336558i
$88$	0.804935	−	1.07527i	0.0858063	−	0.114624i
$89$	1.22772	−	0.789005i	0.130138	−	0.0836344i	−0.473952	−	0.880551i	$-0.657173\pi$
$89$	1.22772	−	0.789005i	0.130138	−	0.0836344i	0.604090	+	0.796916i	$0.293537\pi$
$90$	0.628836	−	2.14583i	0.0662851	−	0.226190i
$91$		−	10.7787i		−	1.12992i
$92$	2.03862	+	4.34097i	0.212541	+	0.452577i
$93$	−1.37349	+	1.37349i	−0.142425	+	0.142425i
$94$	1.76262	+	1.52732i	0.181800	+	0.157531i
$95$	−15.8618	+	3.45933i	−1.62739	+	0.354920i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	14.4916	+	5.40508i	1.47140	+	0.548803i	0.952099	−	0.305790i	$-0.0989207\pi$
$97$	14.4916	+	5.40508i	1.47140	+	0.548803i	0.519298	+	0.854593i	$0.326193\pi$
$98$	−1.09337	−	1.46057i	−0.110447	−	0.147539i
$99$	1.28877	−	0.378416i	0.129526	−	0.0380323i
$100$	−4.79597	+	1.41375i	−0.479597	+	0.141375i
$101$	0.854318	−	1.87070i	0.0850078	−	0.186141i	−0.862354	−	0.506305i	$-0.831011\pi$
$101$	0.854318	−	1.87070i	0.0850078	−	0.186141i	0.947362	+	0.320164i	$0.103738\pi$
$102$	−1.09400	+	0.597371i	−0.108323	+	0.0591486i
$103$	0.506077	−	7.07588i	0.0498652	−	0.697207i	−0.909619	−	0.415444i	$-0.863626\pi$
$103$	0.506077	−	7.07588i	0.0498652	−	0.697207i	0.959484	−	0.281763i	$-0.0909192\pi$
$104$	−3.58070	+	3.10270i	−0.351117	+	0.304245i
$105$	−3.04637	+	4.07397i	−0.297295	+	0.397579i
$106$	6.45265	+	2.94683i	0.626737	+	0.286221i
$107$	14.3235	−	3.11589i	1.38470	−	0.301224i	0.542352	−	0.840151i	$-0.317534\pi$
$107$	14.3235	−	3.11589i	1.38470	−	0.301224i	0.842352	+	0.538927i	$0.181170\pi$
$108$	−0.479249	+	0.877679i	−0.0461158	+	0.0844547i
$109$	1.28668	−	8.94904i	0.123241	−	0.857162i	−0.830604	−	0.556864i	$-0.812005\pi$
$109$	1.28668	−	8.94904i	0.123241	−	0.857162i	0.953845	−	0.300299i	$-0.0970863\pi$
$110$	−2.27088	−	1.96563i	−0.216520	−	0.187415i
$111$	7.47168	−	1.07427i	0.709180	−	0.101965i
$112$	0.483581	−	2.22299i	0.0456942	−	0.210053i
$113$	4.45802	−	0.318844i	0.419375	−	0.0299943i	0.139942	−	0.990160i	$-0.455308\pi$
$113$	4.45802	−	0.318844i	0.419375	−	0.0299943i	0.279432	+	0.960165i	$0.409854\pi$
$114$	7.26036			0.679995
$115$	10.0051	−	3.85972i	0.932983	−	0.359921i
$116$	−3.35045			−0.311082
$117$	−4.72588	+	0.338002i	−0.436908	+	0.0312483i
$118$	−1.55476	+	7.14710i	−0.143127	+	0.657944i
$119$	2.80684	−	0.403562i	0.257302	−	0.0369945i
$120$	2.23029	−	0.160701i	0.203596	−	0.0146700i
$121$	−1.30871	+	9.10228i	−0.118974	+	0.827480i
$122$	−4.09915	+	7.50703i	−0.371120	+	0.679655i
$123$	−3.75686	+	0.817255i	−0.338745	+	0.0736894i
$124$	−1.76688	−	0.806908i	−0.158671	−	0.0724625i
$125$	2.39392	+	10.9210i	0.214119	+	0.976808i
$126$	1.71931	−	1.48979i	0.153169	−	0.132721i
$127$	−1.33082	+	18.6073i	−0.118091	+	1.65113i	0.500735	+	0.865601i	$0.333063\pi$
$127$	−1.33082	+	18.6073i	−0.118091	+	1.65113i	−0.618826	+	0.785528i	$0.712391\pi$
$128$	−0.877679	+	0.479249i	−0.0775766	+	0.0423600i
$129$	−1.10572	+	2.42118i	−0.0973528	+	0.213173i
$130$	6.35347	+	8.47787i	0.557236	+	0.743559i
$131$	6.90207	−	2.02663i	0.603037	−	0.177068i	0.0340580	−	0.999420i	$-0.489157\pi$
$131$	6.90207	−	2.02663i	0.603037	−	0.177068i	0.568979	+	0.822352i	$0.307339\pi$
$132$	0.804935	+	1.07527i	0.0700606	+	0.0935900i
$133$	−15.4758	−	5.77216i	−1.34192	−	0.500510i
$134$	0.0773174	+	0.537754i	0.00667920	+	0.0464549i
$135$	1.88174	+	1.20791i	0.161954	+	0.103961i
$136$	−0.942022	−	0.816267i	−0.0807777	−	0.0699943i
$137$	8.85986	−	8.85986i	0.756949	−	0.756949i	−0.218817	−	0.975766i	$-0.570220\pi$
$137$	8.85986	−	8.85986i	0.756949	−	0.756949i	0.975766	+	0.218817i	$0.0702199\pi$
$138$	−4.73948	+	0.733054i	−0.403451	+	0.0624017i
$139$			5.52111i			0.468294i	0.972201	+	0.234147i	$0.0752297\pi$
$139$			5.52111i			0.468294i	−0.972201	+	0.234147i	$0.924770\pi$
$140$	−4.88171	−	1.43059i	−0.412579	−	0.120907i
$141$	−1.96204	+	1.26093i	−0.165233	+	0.106189i
$142$	3.50365	−	4.68032i	0.294019	−	0.392764i
$143$	−2.22395	+	5.96265i	−0.185976	+	0.498622i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	−0.530501	+	7.47303i	−0.0440557	+	0.620602i
$146$	2.44974	+	1.57435i	0.202742	+	0.130294i
$147$	1.70944	−	0.637588i	0.140992	−	0.0525873i
$148$	3.61762	+	6.62517i	0.297366	+	0.544586i
$149$	2.32435	+	2.68244i	0.190418	+	0.219754i	0.842928	−	0.538026i	$-0.180830\pi$
$149$	2.32435	+	2.68244i	0.190418	+	0.219754i	−0.652511	+	0.757780i	$0.726284\pi$
$150$	−0.00530027	−	5.00000i	−0.000432766	−	0.408248i
$151$	−2.00883	−	0.589846i	−0.163476	−	0.0480010i	0.198970	−	0.980006i	$-0.436240\pi$
$151$	−2.00883	−	0.589846i	−0.163476	−	0.0480010i	−0.362447	+	0.932005i	$0.618058\pi$
$152$	2.53724	+	6.80260i	0.205797	+	0.551763i
$153$	−0.264957	−	1.21799i	−0.0214205	−	0.0984685i
$154$	−0.860889	−	2.93192i	−0.0693724	−	0.236261i
$155$	−2.07954	+	3.81319i	−0.167032	+	0.306283i
$156$	−1.96822	−	4.30979i	−0.157583	−	0.345060i
$157$	16.9501	+	12.6887i	1.35277	+	1.01267i	0.996944	+	0.0781142i	$0.0248899\pi$
$157$	16.9501	+	12.6887i	1.35277	+	1.01267i	0.355822	+	0.934554i	$0.384201\pi$
$158$	4.64333	+	1.01009i	0.369403	+	0.0803588i
$159$	−4.64538	+	5.36105i	−0.368403	+	0.425159i
$160$	0.929974	+	2.03351i	0.0735209	+	0.160763i
$161$	10.6852	+	2.20546i	0.842110	+	0.173815i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−1.41631	−	19.8026i	−0.110934	−	1.55106i	−0.682733	−	0.730668i	$-0.739209\pi$
$163$	−1.41631	−	19.8026i	−0.110934	−	1.55106i	0.571799	−	0.820394i	$-0.306246\pi$
$164$	−2.07861	−	3.23439i	−0.162312	−	0.252563i
$165$	2.52579	−	1.62512i	0.196632	−	0.126515i
$166$	6.87281	−	3.13871i	0.533433	−	0.243611i
$167$	15.3458	−	11.4877i	1.18750	−	0.888948i	0.191782	−	0.981438i	$-0.438573\pi$
$167$	15.3458	−	11.4877i	1.18750	−	0.888948i	0.995714	+	0.0924897i	$0.0294825\pi$
$168$	1.99670	+	1.09028i	0.154049	+	0.0841170i
$169$	5.10807	−	7.94831i	0.392929	−	0.611409i
$170$	−1.96980	+	1.97189i	−0.151077	+	0.151237i
$171$	−2.04548	+	6.96627i	−0.156422	+	0.532724i
$172$	−2.65493	−	0.189884i	−0.202437	−	0.0144786i
$173$	14.9766	+	1.07115i	1.13865	+	0.0814379i	0.627902	−	0.778292i	$-0.283914\pi$
$173$	14.9766	+	1.07115i	1.13865	+	0.0814379i	0.510749	+	0.859730i	$0.329368\pi$
$174$	0.943932	−	3.21474i	0.0715593	−	0.243708i
$175$	−3.96382	+	10.6619i	−0.299636	+	0.805965i
$176$	−0.726175	+	1.12995i	−0.0547375	+	0.0851732i
$177$	−6.41957	−	3.50535i	−0.482524	−	0.263478i
$178$	−1.16830	+	0.874579i	−0.0875679	+	0.0655525i
$179$	−17.7984	+	8.12825i	−1.33031	+	0.607534i	−0.948521	−	0.316714i	$-0.897420\pi$
$179$	−17.7984	+	8.12825i	−1.33031	+	0.607534i	−0.381792	+	0.924248i	$0.624693\pi$
$180$	−0.474152	+	2.18522i	−0.0353412	+	0.162877i
$181$	8.24855	+	12.8350i	0.613110	+	0.954017i	0.999498	+	0.0316810i	$0.0100861\pi$
$181$	8.24855	+	12.8350i	0.613110	+	0.954017i	−0.386388	+	0.922336i	$0.626278\pi$
$182$	0.768946	+	10.7513i	0.0569981	+	0.796937i
$183$	−6.04808	−	6.04808i	−0.447087	−	0.447087i
$184$	−2.34311	−	4.18447i	−0.172736	−	0.308484i
$185$	15.3499	−	7.01992i	1.12855	−	0.516115i
$186$	1.27201	−	1.46798i	0.0932684	−	0.107637i
$187$	−1.63597	−	0.355884i	−0.119634	−	0.0260248i
$188$	−1.86709	−	1.39768i	−0.136171	−	0.101937i
$189$	0.945060	+	2.06939i	0.0687430	+	0.150526i
$190$	15.5746	−	4.58209i	1.12990	−	0.332420i
$191$	−0.319169	−	1.08699i	−0.0230943	−	0.0786518i	0.947140	−	0.320822i	$-0.103959\pi$
$191$	−0.319169	−	1.08699i	−0.0230943	−	0.0786518i	−0.970234	+	0.242170i	$0.922141\pi$
$192$	−0.212565	−	0.977147i	−0.0153406	−	0.0705195i
$193$	8.57683	+	22.9954i	0.617374	+	1.65524i	0.747910	+	0.663800i	$0.231057\pi$
$193$	8.57683	+	22.9954i	0.617374	+	1.65524i	−0.130536	+	0.991444i	$0.541670\pi$
$194$	−14.8403	−	4.35749i	−1.06547	−	0.312850i
$195$	−9.92444	+	3.70762i	−0.710704	+	0.265508i
$196$	1.19478	+	1.37884i	0.0853411	+	0.0984889i
$197$	12.7005	+	23.2593i	0.904876	+	1.65716i	0.741883	+	0.670529i	$0.233933\pi$
$197$	12.7005	+	23.2593i	0.904876	+	1.65716i	0.162993	+	0.986627i	$0.447885\pi$
$198$	−1.25849	+	0.469392i	−0.0894368	+	0.0333582i
$199$	−9.30223	−	5.97818i	−0.659418	−	0.423782i	0.167679	−	0.985842i	$-0.446373\pi$
$199$	−9.30223	−	5.97818i	−0.659418	−	0.423782i	−0.827097	+	0.562060i	$0.810009\pi$
$200$	4.68289	−	1.75229i	0.331131	−	0.123905i
$201$	−0.537754	−	0.0773174i	−0.0379303	−	0.00545355i
$202$	−0.718688	+	1.92688i	−0.0505667	+	0.135575i
$203$	−4.56782	+	6.10189i	−0.320598	+	0.428269i
$204$	1.04860	−	0.673895i	0.0734167	−	0.0471821i
$205$	−7.54328	+	4.12413i	−0.526845	+	0.288042i
$206$			7.09395i			0.494259i
$207$	0.631905	−	4.75402i	0.0439204	−	0.330427i
$208$	3.35024	−	3.35024i	0.232297	−	0.232297i
$209$	7.37002	+	6.38616i	0.509795	+	0.441740i
$210$	2.74797	−	4.28092i	0.189628	−	0.295412i
$211$	1.78074	+	12.3854i	0.122592	+	0.852643i	0.954602	+	0.297883i	$0.0962806\pi$
$211$	1.78074	+	12.3854i	0.122592	+	0.852643i	−0.832011	+	0.554759i	$0.812810\pi$
$212$	−6.64643	−	2.47899i	−0.456479	−	0.170258i
$213$	3.50365	+	4.68032i	0.240066	+	0.320690i
$214$	−14.0647	+	4.12977i	−0.961444	+	0.282306i
$215$	−0.843903	+	5.89164i	−0.0575537	+	0.401806i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	−3.87842	+	2.11778i	−0.263284	+	0.143764i
$218$	−0.644982	+	9.01802i	−0.0436837	+	0.610778i
$219$	−2.20075	+	1.90696i	−0.148713	+	0.128861i
$220$	2.40532	+	1.79861i	0.162167	+	0.121263i
$221$	5.37204	+	2.45333i	0.361363	+	0.165029i
$222$	−7.37600	+	1.60455i	−0.495045	+	0.107690i
$223$	−1.66947	+	3.05741i	−0.111796	+	0.204739i	−0.927587	−	0.373608i	$-0.878120\pi$
$223$	−1.66947	+	3.05741i	−0.111796	+	0.204739i	0.815790	+	0.578348i	$0.196302\pi$
$224$	−0.323763	+	2.25182i	−0.0216323	+	0.150456i
$225$	4.79896	+	1.40358i	0.319930	+	0.0935718i
$226$	−4.42391	+	0.636062i	−0.294274	+	0.0423102i
$227$	5.83544	−	26.8251i	0.387312	−	1.78044i	−0.209234	−	0.977866i	$-0.567097\pi$
$227$	5.83544	−	26.8251i	0.387312	−	1.78044i	0.596546	−	0.802579i	$-0.296539\pi$
$228$	−7.24187	+	0.517948i	−0.479604	+	0.0343020i
$229$	8.14063			0.537948			0.268974	−	0.963147i	$-0.413315\pi$
$229$	8.14063			0.537948			0.268974	+	0.963147i	$0.413315\pi$
$230$	−9.70428	+	4.56365i	−0.639882	+	0.300918i
$231$	3.05569			0.201050
$232$	3.34192	−	0.239019i	0.219408	−	0.0156923i
$233$	−2.69394	+	12.3838i	−0.176486	+	0.811291i	0.800727	+	0.599029i	$0.204447\pi$
$233$	−2.69394	+	12.3838i	−0.176486	+	0.811291i	−0.977213	+	0.212262i	$0.931917\pi$
$234$	4.68973	−	0.674281i	0.306577	−	0.0440791i
$235$	−3.41310	+	3.94315i	−0.222646	+	0.257222i
$236$	1.04093	−	7.23981i	0.0677586	−	0.471271i
$237$	−2.27735	+	4.17066i	−0.147930	+	0.270914i
$238$	−2.77090	+	0.602772i	−0.179611	+	0.0390719i
$239$	−10.0727	−	4.60004i	−0.651548	−	0.297552i	0.0620860	−	0.998071i	$-0.480225\pi$
$239$	−10.0727	−	4.60004i	−0.651548	−	0.297552i	−0.713634	+	0.700519i	$0.752952\pi$
$240$	−2.21314	+	0.319399i	−0.142858	+	0.0206171i
$241$	16.5919	−	14.3769i	1.06878	−	0.926100i	0.0713248	−	0.997453i	$-0.477277\pi$
$241$	16.5919	−	14.3769i	1.06878	−	0.926100i	0.997451	+	0.0713535i	$0.0227318\pi$
$242$	0.656027	−	9.17245i	0.0421710	−	0.589627i
$243$	0.877679	−	0.479249i	0.0563031	−	0.0307438i
$244$	3.55316	−	7.78034i	0.227468	−	0.498085i
$245$	3.26463	−	2.44657i	0.208569	−	0.156306i
$246$	3.68898	−	1.08318i	0.235201	−	0.0690613i
$247$	−20.6147	−	27.5380i	−1.31168	−	1.75220i
$248$	1.81995	+	0.678804i	0.115567	+	0.0431041i
$249$	1.07527	+	7.47869i	0.0681426	+	0.473943i
$250$	−3.16692	−	10.7224i	−0.200294	−	0.678146i
$251$	8.74204	+	7.57502i	0.551793	+	0.478131i	0.885560	−	0.464524i	$-0.153775\pi$
$251$	8.74204	+	7.57502i	0.551793	+	0.478131i	−0.333768	+	0.942655i	$0.608320\pi$
$252$	−1.60865	+	1.60865i	−0.101336	+	0.101336i
$253$	−5.45585	−	3.42468i	−0.343006	−	0.215308i
$254$		−	18.6548i		−	1.17051i
$255$	−1.33706	−	2.44556i	−0.0837299	−	0.153147i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	5.98260	−	7.99182i	0.373184	−	0.498516i	−0.574155	−	0.818746i	$-0.694669\pi$
$257$	5.98260	−	7.99182i	0.373184	−	0.498516i	0.947340	+	0.320230i	$0.103760\pi$
$258$	0.930173	−	2.49389i	0.0579101	−	0.155263i
$259$	16.9979	+	2.44393i	1.05620	+	0.151858i
$260$	−6.94209	−	8.00302i	−0.430530	−	0.496326i
$261$	2.81858	+	1.81139i	0.174466	+	0.112122i
$262$	−6.73991	+	2.51385i	−0.416393	+	0.155306i
$263$	11.7051	+	21.4363i	0.721766	+	1.32182i	0.938396	+	0.345562i	$0.112312\pi$
$263$	11.7051	+	21.4363i	0.721766	+	1.32182i	−0.216630	+	0.976254i	$0.569506\pi$
$264$	−0.879593	−	1.01510i	−0.0541352	−	0.0624753i
$265$	−6.58165	+	14.4321i	−0.404308	+	0.886554i
$266$	15.8481	+	4.65343i	0.971710	+	0.285320i
$267$	−0.510004	−	1.36737i	−0.0312118	−	0.0836820i
$268$	−0.115483	−	0.530868i	−0.00705427	−	0.0324279i
$269$	−7.53209	−	25.6520i	−0.459240	−	1.56403i	−0.785571	−	0.618772i	$-0.787631\pi$
$269$	−7.53209	−	25.6520i	−0.459240	−	1.56403i	0.326331	−	0.945256i	$-0.394188\pi$
$270$	−1.96312	−	1.07059i	−0.119472	−	0.0651542i
$271$	−11.3077	−	24.7604i	−0.686894	−	1.50409i	−0.855170	−	0.518348i	$-0.826547\pi$
$271$	−11.3077	−	24.7604i	−0.686894	−	1.50409i	0.168276	−	0.985740i	$-0.446180\pi$
$272$	0.997854	+	0.746984i	0.0605038	+	0.0452926i
$273$	−10.5324	−	2.29119i	−0.637450	−	0.138669i
$274$	−8.20523	+	9.46934i	−0.495696	+	0.572064i
$275$	4.39258	−	5.08018i	0.264883	−	0.306346i
$276$	4.67510	−	1.06930i	0.281408	−	0.0643641i
$277$	−2.70962	−	2.70962i	−0.162805	−	0.162805i	0.621003	−	0.783808i	$-0.286725\pi$
$277$	−2.70962	−	2.70962i	−0.162805	−	0.162805i	−0.783808	+	0.621003i	$0.786725\pi$
$278$	−0.393871	−	5.50704i	−0.0236228	−	0.330290i
$279$	1.05015	+	1.63406i	0.0628708	+	0.0978288i
$280$	4.97133	+	1.07869i	0.297094	+	0.0644638i
$281$	5.08660	−	2.32297i	0.303441	−	0.138577i	−0.257875	−	0.966178i	$-0.583022\pi$
$281$	5.08660	−	2.32297i	0.303441	−	0.138577i	0.561316	+	0.827601i	$0.310295\pi$
$282$	1.86709	−	1.39768i	0.111183	−	0.0832308i
$283$	−6.98388	−	3.81349i	−0.415149	−	0.226688i	0.258079	−	0.966124i	$-0.416911\pi$
$283$	−6.98388	−	3.81349i	−0.415149	−	0.226688i	−0.673227	+	0.739436i	$0.735092\pi$
$284$	−3.16083	+	4.91834i	−0.187561	+	0.291850i
$285$	0.00860482	+	16.2347i	0.000509706	+	0.961659i
$286$	1.79292	−	6.10612i	0.106017	−	0.361062i
$287$	−8.72438	−	0.623980i	−0.514984	−	0.0368324i
$288$	0.997452	+	0.0713392i	0.0587754	+	0.00420370i
$289$	4.35173	−	14.8206i	0.255984	−	0.871801i
$290$	−0.00397088	−	7.49184i	−0.000233178	−	0.439936i
$291$	8.36196	−	13.0115i	0.490187	−	0.762746i
$292$	−2.55581	−	1.39558i	−0.149568	−	0.0816701i
$293$	−11.7800	+	8.81837i	−0.688193	+	0.515175i	−0.885190	−	0.465229i	$-0.845972\pi$
$293$	−11.7800	+	8.81837i	−0.688193	+	0.515175i	0.196997	+	0.980404i	$0.436881\pi$
$294$	−1.65960	+	0.757913i	−0.0967897	+	0.0442024i
$295$	−15.9832	−	3.46807i	−0.930580	−	0.201919i
$296$	−4.08103	−	6.35021i	−0.237205	−	0.369099i
$297$	−0.0958210	−	1.33975i	−0.00556010	−	0.0777403i
$298$	−2.50979	−	2.50979i	−0.145388	−	0.145388i
$299$	16.2374	+	15.8951i	0.939035	+	0.919236i
$300$	0.361982	+	4.98688i	0.0208991	+	0.287918i
$301$	−3.96540	+	4.57632i	−0.228562	+	0.263775i
$302$	2.04579	+	0.445035i	0.117722	+	0.0256089i
$303$	−1.64635	−	1.23244i	−0.0945801	−	0.0708018i
$304$	−3.01606	−	6.60426i	−0.172983	−	0.378780i
$305$	−16.7911	−	9.15708i	−0.961455	−	0.524333i
$306$	0.351172	+	1.19598i	0.0200752	+	0.0683698i
$307$	−4.09149	−	18.8083i	−0.233513	−	1.07344i	−0.933302	−	0.359094i	$-0.883086\pi$
$307$	−4.09149	−	18.8083i	−0.233513	−	1.07344i	0.699788	−	0.714351i	$-0.253278\pi$
$308$	1.06786	+	2.86303i	0.0608467	+	0.163136i
$309$	−6.80659	−	1.99860i	−0.387214	−	0.113696i
$310$	1.80221	−	3.95183i	0.102359	−	0.224449i
$311$	−15.5901	−	17.9919i	−0.884033	−	1.02023i	−0.999637	−	0.0269333i	$-0.991426\pi$
$311$	−15.5901	−	17.9919i	−0.884033	−	1.02023i	0.115604	−	0.993295i	$-0.463120\pi$
$312$	2.27066	+	4.15840i	0.128551	+	0.235423i
$313$	−21.1147	+	7.87537i	−1.19347	+	0.445142i	−0.866156	−	0.499773i	$-0.833417\pi$
$313$	−21.1147	+	7.87537i	−1.19347	+	0.445142i	−0.327315	+	0.944915i	$0.606144\pi$
$314$	−17.8121	−	11.4472i	−1.00520	−	0.646000i
$315$	3.33332	+	3.84274i	0.187811	+	0.216514i
$316$	−4.70356	−	0.676269i	−0.264596	−	0.0380431i
$317$	4.09066	−	10.9675i	0.229754	−	0.615995i	−0.770003	−	0.638041i	$-0.779745\pi$
$317$	4.09066	−	10.9675i	0.229754	−	0.615995i	0.999757	+	0.0220457i	$0.00701794\pi$
$318$	4.25109	−	5.67879i	0.238389	−	0.318451i
$319$	3.78585	−	2.43302i	0.211967	−	0.136223i
$320$	−1.07267	−	1.96198i	−0.0599643	−	0.109678i
$321$		−	14.6585i		−	0.818157i
$322$	−10.8153	−	1.43757i	−0.602713	−	0.0801126i
$323$	6.39921	−	6.39921i	0.356062	−	0.356062i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	−18.9496	+	14.2168i	−1.05113	+	0.788608i
$326$	2.82541	+	19.6511i	0.156485	+	1.08838i
$327$	−8.47102	−	3.15953i	−0.468448	−	0.174722i
$328$	2.30406	+	3.07786i	0.127220	+	0.169946i
$329$	−5.09096	+	1.49484i	−0.280674	+	0.0824132i
$330$	−2.40342	+	1.80116i	−0.132304	+	0.0991508i
$331$	−13.5557	+	29.6828i	−0.745087	+	1.63151i	0.0299136	+	0.999552i	$0.490477\pi$
$331$	−13.5557	+	29.6828i	−0.745087	+	1.63151i	−0.775001	+	0.631960i	$0.782250\pi$
$332$	−6.63138	+	3.62101i	−0.363944	+	0.198729i
$333$	0.538505	−	7.52928i	0.0295099	−	0.412602i
$334$	−14.4872	+	12.5532i	−0.792704	+	0.686882i
$335$	−1.20236	+	0.173524i	−0.0656921	+	0.00948064i
$336$	−2.06939	−	0.945060i	−0.112895	−	0.0515573i
$337$	10.8802	−	2.36683i	0.592680	−	0.128930i	0.0937857	−	0.995592i	$-0.470103\pi$
$337$	10.8802	−	2.36683i	0.592680	−	0.128930i	0.498894	+	0.866663i	$0.333740\pi$
$338$	−4.52803	+	8.29247i	−0.246292	+	0.451051i
$339$	0.636062	−	4.42391i	0.0345462	−	0.240274i
$340$	1.82411	−	2.10739i	0.0989263	−	0.114289i
$341$	2.58245	−	0.371300i	0.139847	−	0.0201070i
$342$	1.54330	−	7.09444i	0.0834522	−	0.383623i
$343$	20.0243	−	1.43217i	1.08121	−	0.0773298i
$344$	2.66171			0.143510
$345$	−1.64478	−	10.5969i	−0.0885517	−	0.570519i
$346$	−15.0149			−0.807205
$347$	21.5527	−	1.54148i	1.15701	−	0.0827510i	0.520390	−	0.853929i	$-0.325786\pi$
$347$	21.5527	−	1.54148i	1.15701	−	0.0827510i	0.636620	+	0.771178i	$0.280332\pi$
$348$	−0.712190	+	3.27388i	−0.0381774	+	0.175499i
$349$	−4.65299	+	0.668999i	−0.249069	+	0.0358107i	−0.265718	−	0.964051i	$-0.585609\pi$
$349$	−4.65299	+	0.668999i	−0.249069	+	0.0358107i	0.0166496	+	0.999861i	$0.494700\pi$
$350$	3.19311	−	10.9175i	0.170679	−	0.583566i
$351$	−0.674281	+	4.68973i	−0.0359904	+	0.250319i
$352$	0.643715	−	1.17888i	0.0343101	−	0.0628343i
$353$	32.8220	−	7.14000i	1.74694	−	0.380024i	0.778184	−	0.628036i	$-0.216141\pi$
$353$	32.8220	−	7.14000i	1.74694	−	0.380024i	0.968757	+	0.248013i	$0.0797775\pi$
$354$	6.65328	+	3.03845i	0.353618	+	0.161492i
$355$	10.4697	+	7.82884i	0.555672	+	0.415512i
$356$	1.10293	−	0.955697i	0.0584553	−	0.0506518i
$357$	0.202297	−	2.82848i	0.0107067	−	0.149699i
$358$	17.1732	−	9.37726i	0.907630	−	0.495604i
$359$	4.36232	−	9.55214i	0.230234	−	0.504143i	−0.758891	−	0.651218i	$-0.774259\pi$
$359$	4.36232	−	9.55214i	0.230234	−	0.504143i	0.989125	+	0.147075i	$0.0469858\pi$
$360$	0.317052	−	2.21348i	0.0167101	−	0.116660i
$361$	−32.3473	+	9.49802i	−1.70249	+	0.499896i
$362$	−9.14317	−	12.2138i	−0.480554	−	0.641945i
$363$	8.61608	+	3.21363i	0.452227	+	0.168672i
$364$	−1.53397	−	10.6690i	−0.0804021	−	0.559209i
$365$	−3.51746	+	5.47966i	−0.184112	+	0.286818i
$366$	6.46414	+	5.60121i	0.337886	+	0.292780i
$367$	0.190320	−	0.190320i	0.00993465	−	0.00993465i	−0.702122	−	0.712057i	$-0.747764\pi$
$367$	0.190320	−	0.190320i	0.00993465	−	0.00993465i	0.712057	+	0.702122i	$0.247764\pi$
$368$	2.63566	+	4.00666i	0.137393	+	0.208861i
$369$			3.84472i			0.200148i
$370$	−14.8100	+	8.09709i	−0.769937	+	0.420948i
$371$	−13.5761	+	8.72486i	−0.704838	+	0.452972i
$372$	−1.16405	+	1.55498i	−0.0603530	+	0.0806221i
$373$	11.5268	−	30.9045i	0.596834	−	1.60017i	−0.189164	−	0.981946i	$-0.560578\pi$
$373$	11.5268	−	30.9045i	0.596834	−	1.60017i	0.785998	−	0.618229i	$-0.212150\pi$
$374$	1.65719	+	0.238268i	0.0856913	+	0.0123206i
$375$	11.1803	−	0.0177777i	0.577350	−	0.000918034i
$376$	1.96204	+	1.26093i	0.101184	+	0.0650273i
$377$	−14.8734	+	5.54749i	−0.766019	+	0.285710i
$378$	−1.09028	−	1.99670i	−0.0560780	−	0.102699i
$379$	7.21415	+	8.32558i	0.370566	+	0.427656i	0.910152	−	0.414274i	$-0.135965\pi$
$379$	7.21415	+	8.32558i	0.370566	+	0.427656i	−0.539586	+	0.841931i	$0.681419\pi$
$380$	−15.2081	+	5.68150i	−0.780157	+	0.291455i
$381$	17.8992	+	5.25567i	0.917002	+	0.269256i
$382$	0.395901	+	1.06145i	0.0202561	+	0.0543086i
$383$	−7.83030	−	35.9953i	−0.400109	−	1.83927i	−0.530334	−	0.847789i	$-0.677933\pi$
$383$	−7.83030	−	35.9953i	−0.400109	−	1.83927i	0.130224	−	0.991485i	$-0.458430\pi$
$384$	0.281733	+	0.959493i	0.0143771	+	0.0489639i
$385$	6.55495	−	1.92848i	0.334071	−	0.0982845i
$386$	−10.1955	−	22.3249i	−0.518935	−	1.13631i
$387$	2.13081	+	1.59511i	0.108315	+	0.0810837i
$388$	15.1133	+	3.28770i	0.767262	+	0.166908i
$389$	22.1811	−	25.5984i	1.12463	−	1.29789i	0.174980	−	0.984572i	$-0.444014\pi$
$389$	22.1811	−	25.5984i	1.12463	−	1.29789i	0.949648	−	0.313318i	$-0.101441\pi$
$390$	9.63465	−	4.40617i	0.487870	−	0.223115i
$391$	−3.53122	+	4.82343i	−0.178582	+	0.243932i
$392$	−1.29010	−	1.29010i	−0.0651597	−	0.0651597i
$393$	−0.513175	−	7.17513i	−0.0258863	−	0.361937i
$394$	−14.3275	−	22.2940i	−0.721808	−	1.12315i
$395$	−2.25314	+	10.3840i	−0.113368	+	0.522475i
$396$	1.22180	−	0.557975i	0.0613975	−	0.0280393i
$397$	−26.9492	+	20.1739i	−1.35254	+	1.01250i	−0.355578	+	0.934646i	$0.615716\pi$
$397$	−26.9492	+	20.1739i	−1.35254	+	1.01250i	−0.996965	+	0.0778546i	$0.975193\pi$
$398$	9.70501	+	5.29934i	0.486468	+	0.265632i
$399$	−8.92986	+	13.8951i	−0.447052	+	0.695627i
$400$	−4.54596	+	2.08190i	−0.227298	+	0.104095i
$401$	−6.73600	+	22.9407i	−0.336380	+	1.14561i	0.601566	+	0.798823i	$0.294544\pi$
$401$	−6.73600	+	22.9407i	−0.336380	+	1.14561i	−0.937946	+	0.346782i	$0.887274\pi$
$402$	0.541900	+	0.0387574i	0.0270275	+	0.00193305i
$403$	−9.17962	−	0.656539i	−0.457269	−	0.0327046i
$404$	0.579395	−	1.97324i	0.0288260	−	0.0981722i
$405$	1.58030	−	1.58198i	0.0785258	−	0.0786091i
$406$	4.12088	−	6.41221i	0.204516	−	0.318233i
$407$	−8.89876	−	4.85909i	−0.441095	−	0.240856i
$408$	−0.997854	+	0.746984i	−0.0494011	+	0.0369812i
$409$	29.0709	−	13.2762i	1.43746	−	0.656468i	0.464111	−	0.885777i	$-0.346374\pi$
$409$	29.0709	−	13.2762i	1.43746	−	0.656468i	0.973354	+	0.229309i	$0.0736467\pi$
$410$	7.22984	−	4.65176i	0.357057	−	0.229734i
$411$	−6.77408	−	10.5407i	−0.334141	−	0.519933i
$412$	−0.506077	−	7.07588i	−0.0249326	−	0.348603i
$413$	−11.7661	−	11.7661i	−0.578972	−	0.578972i
$414$	−0.291147	+	4.78699i	−0.0143091	+	0.235268i
$415$	7.02651	+	15.3643i	0.344918	+	0.754206i
$416$	−3.10270	+	3.58070i	−0.152122	+	0.175558i
$417$	5.39493	+	1.17360i	0.264191	+	0.0574712i
$418$	−7.80683	−	5.84412i	−0.381845	−	0.285845i
$419$	−1.49851	−	3.28127i	−0.0732068	−	0.160301i	0.869491	−	0.493950i	$-0.164447\pi$
$419$	−1.49851	−	3.28127i	−0.0732068	−	0.160301i	−0.942697	+	0.333649i	$0.891720\pi$
$420$	−2.43558	+	4.46605i	−0.118844	+	0.217921i
$421$	4.47904	+	15.2542i	0.218295	+	0.743445i	0.993709	+	0.111992i	$0.0357230\pi$
$421$	4.47904	+	15.2542i	0.218295	+	0.743445i	−0.775414	+	0.631453i	$0.782459\pi$
$422$	−2.65977	−	12.2268i	−0.129476	−	0.595189i
$423$	0.815048	+	2.18523i	0.0396290	+	0.106249i
$424$	6.80635	+	1.99852i	0.330545	+	0.0970569i
$425$	−4.41162	−	4.40228i	−0.213995	−	0.213542i
$426$	−3.82861	−	4.41845i	−0.185497	−	0.214075i
$427$	−9.32548	−	17.0783i	−0.451292	−	0.826479i
$428$	13.7343	−	5.12262i	0.663871	−	0.247611i
$429$	5.35365	+	3.44058i	0.258477	+	0.166113i
$430$	0.421448	−	5.93683i	0.0203240	−	0.286299i
$431$	−27.3839	−	3.93722i	−1.31904	−	0.189649i	−0.553397	−	0.832917i	$-0.686669\pi$
$431$	−27.3839	−	3.93722i	−1.31904	−	0.189649i	−0.765641	+	0.643268i	$0.777578\pi$
$432$	−0.349464	+	0.936950i	−0.0168136	+	0.0450790i
$433$	−20.5050	+	27.3914i	−0.985407	+	1.31635i	−0.0369921	+	0.999316i	$0.511778\pi$
$433$	−20.5050	+	27.3914i	−0.985407	+	1.31635i	−0.948414	+	0.317033i	$0.897313\pi$
$434$	3.71746	−	2.38907i	0.178444	−	0.114679i
$435$	7.18949	+	2.10688i	0.344709	+	0.101017i
$436$		−	9.04106i		−	0.432988i
$437$	31.5170	−	14.8012i	1.50766	−	0.708035i
$438$	2.05911	−	2.05911i	0.0983878	−	0.0983878i
$439$	10.2486	+	8.88042i	0.489137	+	0.423839i	0.864191	−	0.503163i	$-0.167831\pi$
$439$	10.2486	+	8.88042i	0.489137	+	0.423839i	−0.375055	+	0.927003i	$0.622376\pi$
$440$	−2.52751	−	1.62244i	−0.120494	−	0.0773467i
$441$	−0.259649	−	1.80590i	−0.0123643	−	0.0859953i
$442$	−5.53338	−	2.06384i	−0.263196	−	0.0981670i
$443$	11.1624	+	14.9112i	0.530342	+	0.708454i	0.983077	−	0.183191i	$-0.0586427\pi$
$443$	11.1624	+	14.9112i	0.530342	+	0.708454i	−0.452735	+	0.891645i	$0.649552\pi$
$444$	7.24274	−	2.12666i	0.343725	−	0.100927i
$445$	−1.95700	−	2.61136i	−0.0927709	−	0.123791i
$446$	1.44711	−	3.16872i	0.0685225	−	0.150043i
$447$	3.11521	−	1.70103i	0.147344	−	0.0804561i
$448$	0.162295	−	2.26918i	0.00766772	−	0.107209i
$449$	−1.34450	+	1.16501i	−0.0634507	+	0.0549803i	−0.686009	−	0.727593i	$-0.740639\pi$
$449$	−1.34450	+	1.16501i	−0.0634507	+	0.0549803i	0.622558	+	0.782574i	$0.286093\pi$
$450$	−4.88686	−	1.05765i	−0.230369	−	0.0498579i
$451$	4.69746	+	2.14526i	0.221195	+	0.101016i
$452$	4.36726	−	0.950040i	0.205419	−	0.0446861i
$453$	−1.00337	+	1.83754i	−0.0471426	+	0.0863352i
$454$	−3.90689	+	27.1730i	−0.183360	+	1.27529i
$455$	−24.0397	+	1.73216i	−1.12700	+	0.0812048i
$456$	7.18646	−	1.03326i	0.336537	−	0.0483867i
$457$	−1.28448	+	5.90467i	−0.0600855	+	0.276209i	−0.997381	−	0.0723272i	$-0.976957\pi$
$457$	−1.28448	+	5.90467i	−0.0600855	+	0.276209i	0.937295	+	0.348536i	$0.113321\pi$
$458$	−8.11988	+	0.580746i	−0.379417	+	0.0271365i
$459$	−1.24647			−0.0581804
$460$	9.35399	−	5.24432i	0.436132	−	0.244517i
$461$	15.4136			0.717884			0.358942	−	0.933360i	$-0.383138\pi$
$461$	15.4136			0.717884			0.358942	+	0.933360i	$0.383138\pi$
$462$	−3.04791	+	0.217991i	−0.141802	+	0.0101418i
$463$	5.75204	−	26.4417i	0.267320	−	1.22885i	−0.626141	−	0.779710i	$-0.715366\pi$
$463$	5.75204	−	26.4417i	0.267320	−	1.22885i	0.893461	−	0.449141i	$-0.148270\pi$
$464$	−3.31635	+	0.476819i	−0.153958	+	0.0221358i
$465$	3.28401	+	2.84256i	0.152292	+	0.131821i
$466$	1.80362	−	12.5445i	0.0835511	−	0.581111i
$467$	1.74675	−	3.19893i	0.0808299	−	0.148029i	−0.834138	−	0.551556i	$-0.814034\pi$
$467$	1.74675	−	3.19893i	0.0808299	−	0.148029i	0.914968	+	0.403527i	$0.132216\pi$
$468$	−4.62967	+	1.00712i	−0.214007	+	0.0465543i
$469$	−1.12427	−	0.513436i	−0.0519139	−	0.0237083i
$470$	3.12310	−	4.17659i	0.144058	−	0.192652i
$471$	16.0017	−	13.8656i	0.737320	−	0.638892i
$472$	−0.521793	+	7.29562i	−0.0240175	+	0.335808i
$473$	3.13783	−	1.71339i	0.144278	−	0.0787815i
$474$	1.97402	−	4.32250i	0.0906698	−	0.198539i
$475$	10.2643	+	34.8205i	0.470959	+	1.59767i
$476$	2.72084	−	0.798910i	0.124709	−	0.0366180i
$477$	4.25109	+	5.67879i	0.194644	+	0.260014i
$478$	10.3752	+	3.86974i	0.474550	+	0.176998i
$479$	5.44125	+	37.8447i	0.248617	+	1.72917i	0.606222	+	0.795296i	$0.292684\pi$
$479$	5.44125	+	37.8447i	0.248617	+	1.72917i	−0.357605	+	0.933873i	$0.616406\pi$
$480$	2.18471	−	0.476468i	0.0997181	−	0.0217477i
$481$	27.0290	+	23.4208i	1.23242	+	1.06789i
$482$	−15.5240	+	15.5240i	−0.707097	+	0.707097i
$483$	4.42636	−	9.97219i	0.201406	−	0.453750i
$484$			9.19588i			0.417995i
$485$	9.72606	−	33.1890i	0.441637	−	1.50703i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	−21.1605	+	28.2671i	−0.958873	+	1.28090i	0.000862493		1.00000i	$0.499725\pi$
$487$	−21.1605	+	28.2671i	−0.958873	+	1.28090i	−0.959736	+	0.280905i	$0.909365\pi$
$488$	−2.98906	+	8.01399i	−0.135309	+	0.362776i
$489$	−19.6511	−	2.82541i	−0.888655	−	0.127769i
$490$	−3.08177	+	2.67323i	−0.139220	+	0.120764i
$491$	−4.89169	−	3.14370i	−0.220759	−	0.141873i	0.425587	−	0.904917i	$-0.360067\pi$
$491$	−4.89169	−	3.14370i	−0.220759	−	0.141873i	−0.646346	+	0.763044i	$0.723704\pi$
$492$	−3.60231	+	1.34359i	−0.162405	+	0.0605738i
$493$	−2.00146	−	3.66541i	−0.0901414	−	0.165082i
$494$	22.5267	+	25.9972i	1.01352	+	1.16967i
$495$	−1.05108	−	2.81351i	−0.0472427	−	0.126458i
$496$	−1.86373	−	0.547242i	−0.0836841	−	0.0245719i
$497$	4.64806	+	12.4619i	0.208494	+	0.558994i
$498$	−1.60606	−	7.38292i	−0.0719691	−	0.330837i
$499$	3.34777	+	11.4015i	0.149867	+	0.510400i	0.999866	−	0.0163848i	$-0.00521567\pi$
$499$	3.34777	+	11.4015i	0.149867	+	0.510400i	−0.849999	+	0.526785i	$0.823397\pi$
$500$	3.92378	+	10.4692i	0.175477	+	0.468196i
$501$	−7.96322	−	17.4370i	−0.355770	−	0.779028i
$502$	−9.26016	−	6.93207i	−0.413301	−	0.309394i
$503$	−28.3851	−	6.17480i	−1.26563	−	0.275321i	−0.470847	−	0.882215i	$-0.656052\pi$
$503$	−28.3851	−	6.17480i	−1.26563	−	0.275321i	−0.794783	+	0.606894i	$0.792415\pi$
$504$	1.48979	−	1.71931i	0.0663607	−	0.0765843i
$505$	−4.30948	−	1.60475i	−0.191769	−	0.0714105i
$506$	5.68626	+	3.02674i	0.252785	+	0.134555i
$507$	−6.68087	−	6.68087i	−0.296708	−	0.296708i
$508$	1.33082	+	18.6073i	0.0590455	+	0.825564i
$509$	0.413907	+	0.644052i	0.0183461	+	0.0285471i	0.850305	−	0.526289i	$-0.176417\pi$
$509$	0.413907	+	0.644052i	0.0183461	+	0.0285471i	−0.831959	+	0.554837i	$0.812781\pi$
$510$	1.50812	+	2.34394i	0.0667806	+	0.103792i
$511$	−6.02610	+	2.75203i	−0.266579	+	0.121743i
$512$	−0.800541	+	0.599278i	−0.0353793	+	0.0264846i
$513$	6.37227	+	3.47952i	0.281343	+	0.153625i
$514$	−5.39723	+	8.39825i	−0.238062	+	0.370431i
$515$	−15.8626	+	0.00840759i	−0.698988	+	0.000370483i
$516$	−0.749891	+	2.55389i	−0.0330121	+	0.112429i
$517$	3.12468	+	0.223481i	0.137423	+	0.00982870i
$518$	−17.1289	−	1.22509i	−0.752603	−	0.0538272i
$519$	4.23018	−	14.4067i	0.185684	−	0.632382i
$520$	7.49533	+	7.48739i	0.328692	+	0.328344i
$521$	−3.23996	+	5.04147i	−0.141945	+	0.220871i	−0.904946	−	0.425527i	$-0.860089\pi$
$521$	−3.23996	+	5.04147i	−0.141945	+	0.220871i	0.763001	+	0.646398i	$0.223725\pi$
$522$	−2.94062	−	1.60570i	−0.128708	−	0.0702796i
$523$	13.1733	−	9.86138i	0.576027	−	0.431208i	−0.271137	−	0.962541i	$-0.587400\pi$
$523$	13.1733	−	9.86138i	0.576027	−	0.431208i	0.847163	+	0.531333i	$0.178309\pi$
$524$	6.54340	−	2.98827i	0.285850	−	0.130543i
$525$	9.57568	+	6.13958i	0.417917	+	0.267953i
$526$	−13.2045	−	20.5466i	−0.575744	−	0.895875i
$527$	−0.172724	−	2.41500i	−0.00752399	−	0.105199i
$528$	0.949768	+	0.949768i	0.0413334	+	0.0413334i
$529$	−19.0795	+	12.8442i	−0.829543	+	0.558442i
$530$	5.53531	−	14.8648i	0.240439	−	0.645686i
$531$	−4.78982	+	5.52774i	−0.207860	+	0.239884i
$532$	−16.1397	−	3.51098i	−0.699745	−	0.152220i
$533$	−14.5827	−	10.9165i	−0.631649	−	0.472846i
$534$	0.606252	+	1.32751i	0.0262351	+	0.0574469i
$535$	−9.25112	−	31.4448i	−0.399961	−	1.35948i
$536$	0.153061	+	0.521277i	0.00661122	+	0.0225157i
$537$	4.15917	+	19.1194i	0.179482	+	0.825064i
$538$	9.34289	+	25.0493i	0.402801	+	1.07995i
$539$	−2.35132	−	0.690410i	−0.101279	−	0.0297381i
$540$	2.03449	+	0.927818i	0.0875506	+	0.0399269i
$541$	−16.0531	−	18.5263i	−0.690178	−	0.796508i	0.297212	−	0.954811i	$-0.403943\pi$
$541$	−16.0531	−	18.5263i	−0.690178	−	0.796508i	−0.987391	+	0.158303i	$0.949398\pi$
$542$	13.0453	+	23.8906i	0.560343	+	1.02619i
$543$	14.2950	−	5.33177i	0.613458	−	0.228808i
$544$	−1.04860	−	0.673895i	−0.0449584	−	0.0288930i
$545$	−20.1657	−	1.43154i	−0.863803	−	0.0613202i
$546$	10.6690	+	1.53397i	0.456592	+	0.0656480i
$547$	3.18847	−	8.54863i	0.136329	−	0.365513i	−0.850788	−	0.525508i	$-0.823875\pi$
$547$	3.18847	−	8.54863i	0.136329	−	0.365513i	0.987118	+	0.159995i	$0.0511479\pi$
$548$	7.50879	−	10.0306i	0.320759	−	0.428484i
$549$	−7.19548	+	4.62425i	−0.307095	+	0.197358i
$550$	−4.01897	+	5.38060i	−0.171370	+	0.229430i
$551$			24.3255i			1.03630i
$552$	−4.58691	+	1.40009i	−0.195232	+	0.0595918i
$553$	−7.64420	+	7.64420i	−0.325064	+	0.325064i
$554$	2.89601	+	2.50941i	0.123040	+	0.106615i
$555$	−3.59663	−	16.4913i	−0.152668	−	0.700019i
$556$	0.785736	+	5.46491i	0.0333226	+	0.231764i
$557$	26.4041	+	9.84824i	1.11878	+	0.417283i	0.839736	−	0.542995i	$-0.182710\pi$
$557$	26.4041	+	9.84824i	1.11878	+	0.417283i	0.279044	+	0.960278i	$0.409983\pi$
$558$	−1.16405	−	1.55498i	−0.0492780	−	0.0658277i
$559$	−12.1002	+	3.55295i	−0.511785	+	0.150274i
$560$	−5.03561	−	0.721288i	−0.212793	−	0.0304800i
$561$	−0.695502	+	1.52294i	−0.0293641	+	0.0642984i
$562$	−4.90792	+	2.67993i	−0.207028	+	0.113046i
$563$	−1.85235	+	25.8992i	−0.0780672	+	1.09152i	0.795865	+	0.605474i	$0.207017\pi$
$563$	−1.85235	+	25.8992i	−0.0780672	+	1.09152i	−0.873932	+	0.486048i	$0.838438\pi$
$564$	−1.76262	+	1.52732i	−0.0742197	+	0.0643117i
$565$	−1.42752	−	9.89141i	−0.0600563	−	0.416135i
$566$	7.23814	+	3.30555i	0.304242	+	0.138943i
$567$	2.22299	−	0.483581i	0.0933567	−	0.0203085i
$568$	2.80190	−	5.13130i	0.117565	−	0.215305i
$569$	−3.65181	+	25.3989i	−0.153092	+	1.06478i	0.757905	+	0.652364i	$0.226223\pi$
$569$	−3.65181	+	25.3989i	−0.153092	+	1.06478i	−0.910997	+	0.412412i	$0.864686\pi$
$570$	−1.16675	−	16.1927i	−0.0488698	−	0.678237i
$571$	28.7531	−	4.13407i	1.20328	−	0.173005i	0.488631	−	0.872490i	$-0.337496\pi$
$571$	28.7531	−	4.13407i	1.20328	−	0.173005i	0.714647	+	0.699485i	$0.246587\pi$
$572$	−1.35274	+	6.21846i	−0.0565611	+	0.260007i
$573$	−1.12999	+	0.0808187i	−0.0472061	+	0.00337625i
$574$	8.74666			0.365079
$575$	−10.2161	−	21.6940i	−0.426042	−	0.904703i
$576$	−1.00000			−0.0416667
$577$	−23.0725	+	1.65018i	−0.960521	+	0.0686978i	−0.542786	−	0.839871i	$-0.682630\pi$
$577$	−23.0725	+	1.65018i	−0.960521	+	0.0686978i	−0.417735	+	0.908569i	$0.637176\pi$
$578$	−3.28335	+	15.0933i	−0.136569	+	0.627799i
$579$	24.2930	−	3.49281i	1.00958	−	0.145156i
$580$	0.538422	+	7.47247i	0.0223568	+	0.310277i
$581$	−2.44622	+	17.0139i	−0.101486	+	0.705854i
$582$	−7.41243	+	13.5749i	−0.307255	+	0.562696i
$583$	9.31032	−	2.02534i	0.385594	−	0.0838809i
$584$	2.64886	+	1.20969i	0.109611	+	0.0500575i
$585$	1.51330	+	10.4857i	0.0625671	+	0.433532i
$586$	11.1209	−	9.63628i	0.459398	−	0.398071i
$587$	1.64004	−	22.9308i	0.0676918	−	0.946455i	−0.844201	−	0.536027i	$-0.819925\pi$
$587$	1.64004	−	22.9308i	0.0676918	−	0.946455i	0.911893	−	0.410429i	$-0.134621\pi$
$588$	1.60130	−	0.874376i	0.0660365	−	0.0360587i
$589$	−5.85845	+	12.8282i	−0.241393	+	0.528577i
$590$	16.1899	+	2.31900i	0.666529	+	0.0954718i
$591$	25.4274	−	7.46617i	1.04595	−	0.307117i
$592$	4.52365	+	6.04290i	0.185921	+	0.248361i
$593$	3.40466	+	1.26987i	0.139813	+	0.0521475i	0.418397	−	0.908264i	$-0.362592\pi$
$593$	3.40466	+	1.26987i	0.139813	+	0.0521475i	−0.278584	+	0.960412i	$0.589865\pi$
$594$	0.191154	+	1.32950i	0.00784313	+	0.0545502i
$595$	−1.35112	−	6.19520i	−0.0553906	−	0.253978i
$596$	2.68244	+	2.32435i	0.109877	+	0.0952089i
$597$	−7.81889	+	7.81889i	−0.320006	+	0.320006i
$598$	−17.3300	−	14.6962i	−0.708677	−	0.600973i
$599$			9.09232i			0.371502i	0.982597	+	0.185751i	$0.0594718\pi$
$599$			9.09232i			0.371502i	−0.982597	+	0.185751i	$0.940528\pi$
$600$	−0.716820	−	4.94835i	−0.0292641	−	0.202016i
$601$	−20.1451	+	12.9465i	−0.821738	+	0.528099i	−0.882643	−	0.470045i	$-0.844238\pi$
$601$	−20.1451	+	12.9465i	−0.821738	+	0.528099i	0.0609048	+	0.998144i	$0.480601\pi$
$602$	3.62883	−	4.84755i	0.147900	−	0.197571i
$603$	−0.189858	+	0.509030i	−0.00773163	+	0.0207293i
$604$	−2.07233	−	0.297956i	−0.0843218	−	0.0121236i
$605$	20.5110	+	1.45605i	0.833891	+	0.0591968i
$606$	1.73007	+	1.11185i	0.0702794	+	0.0451658i
$607$	−39.2893	+	14.6541i	−1.59470	+	0.594793i	−0.980873	−	0.194647i	$-0.937644\pi$
$607$	−39.2893	+	14.6541i	−1.59470	+	0.594793i	−0.613828	+	0.789440i	$0.710371\pi$
$608$	3.47952	+	6.37227i	0.141113	+	0.258430i
$609$	4.99148	+	5.76048i	0.202265	+	0.233426i
$610$	17.4016	+	7.93589i	0.704569	+	0.321315i
$611$	−10.6026	−	3.11321i	−0.428936	−	0.125947i
$612$	−0.435598	−	1.16788i	−0.0176080	−	0.0472089i
$613$	−2.83795	−	13.0459i	−0.114624	−	0.526917i	−0.998272	−	0.0587654i	$-0.981284\pi$
$613$	−2.83795	−	13.0459i	−0.114624	−	0.526917i	0.883648	−	0.468152i	$-0.155080\pi$
$614$	5.42283	+	18.4685i	0.218848	+	0.745326i
$615$	2.42644	+	8.24754i	0.0978437	+	0.332573i
$616$	−1.26938	−	2.77956i	−0.0511448	−	0.111992i
$617$	32.2332	+	24.1295i	1.29766	+	0.971416i	0.999859	+	0.0167887i	$0.00534425\pi$
$617$	32.2332	+	24.1295i	1.29766	+	0.971416i	0.297801	+	0.954628i	$0.403747\pi$
$618$	6.93183	+	1.50793i	0.278839	+	0.0606577i
$619$	1.90213	−	2.19518i	0.0764531	−	0.0882316i	−0.716234	−	0.697860i	$-0.754136\pi$
$619$	1.90213	−	2.19518i	0.0764531	−	0.0882316i	0.792687	+	0.609628i	$0.208681\pi$
$620$	−1.51570	+	4.07033i	−0.0608718	+	0.163468i
$621$	−4.51105	−	1.62800i	−0.181022	−	0.0653295i
$622$	16.8339	+	16.8339i	0.674978	+	0.674978i
$623$	−0.236852	−	3.31162i	−0.00948927	−	0.132677i
$624$	−2.56153	−	3.98582i	−0.102543	−	0.159560i
$625$	23.9723	−	7.09415i	0.958894	−	0.283766i
$626$	20.4991	−	9.36160i	0.819307	−	0.374165i
$627$	7.80683	−	5.84412i	0.311775	−	0.233392i
$628$	18.5834	+	10.1473i	0.741557	+	0.404921i
$629$	−5.08690	+	7.91538i	−0.202828	+	0.315607i
$630$	−3.59896	−	3.59515i	−0.143386	−	0.143234i
$631$	−2.96766	+	10.1069i	−0.118141	+	0.402350i	−0.997236	−	0.0742952i	$-0.976329\pi$
$631$	−2.96766	+	10.1069i	−0.118141	+	0.402350i	0.879096	+	0.476646i	$0.158147\pi$
$632$	4.73982	+	0.338998i	0.188540	+	0.0134846i
$633$	12.4808	+	0.892647i	0.496069	+	0.0354795i
$634$	−3.29782	+	11.2314i	−0.130973	+	0.446054i
$635$	41.7134	−	0.0221093i	1.65535	−	0.000877379i
$636$	−3.83514	+	5.96759i	−0.152073	+	0.236630i
$637$	7.58688	+	4.14275i	0.300603	+	0.164142i
$638$	−3.60263	+	2.69690i	−0.142630	+	0.106771i
$639$	5.31812	−	2.42870i	0.210381	−	0.0960780i
$640$	1.20991	+	1.88046i	0.0478258	+	0.0743317i
$641$	5.81533	+	9.04883i	0.229692	+	0.357407i	0.936900	−	0.349598i	$-0.113682\pi$
$641$	5.81533	+	9.04883i	0.229692	+	0.357407i	−0.707208	+	0.707006i	$0.750046\pi$
$642$	1.04572	+	14.6211i	0.0412715	+	0.577050i
$643$	0.515757	+	0.515757i	0.0203395	+	0.0203395i	0.717203	−	0.696864i	$-0.245422\pi$
$643$	0.515757	+	0.515757i	0.0203395	+	0.0203395i	−0.696864	+	0.717203i	$0.745422\pi$
$644$	10.8903	+	0.662353i	0.429138	+	0.0261004i
$645$	5.57761	+	2.07697i	0.219618	+	0.0817808i
$646$	−5.92640	+	6.83943i	−0.233171	+	0.269094i
$647$	−24.6344	−	5.35888i	−0.968477	−	0.210679i	−0.299610	−	0.954062i	$-0.596857\pi$
$647$	−24.6344	−	5.35888i	−0.968477	−	0.210679i	−0.668867	+	0.743382i	$0.733220\pi$
$648$	−0.800541	−	0.599278i	−0.0314482	−	0.0235419i
$649$	4.08117	+	8.93652i	0.160200	+	0.350789i
$650$	17.8871	−	15.5325i	0.701588	−	0.609233i
$651$	1.24496	+	4.23995i	0.0487939	+	0.166177i
$652$	−4.22010	−	19.3995i	−0.165272	−	0.759743i
$653$	0.721677	+	1.93489i	0.0282414	+	0.0757181i	0.950305	−	0.311320i	$-0.100771\pi$
$653$	0.721677	+	1.93489i	0.0282414	+	0.0757181i	−0.922064	+	0.387038i	$0.873498\pi$
$654$	8.67483	+	2.54716i	0.339213	+	0.0996019i
$655$	−5.62914	−	15.0679i	−0.219949	−	0.588752i
$656$	−2.51776	−	2.90565i	−0.0983019	−	0.113446i
$657$	1.39558	+	2.55581i	0.0544468	+	0.0997118i
$658$	4.97135	−	1.85422i	0.193803	−	0.0722849i
$659$	21.5046	+	13.8202i	0.837701	+	0.538358i	0.887716	−	0.460391i	$-0.152291\pi$
$659$	21.5046	+	13.8202i	0.837701	+	0.538358i	−0.0500154	+	0.998748i	$0.515927\pi$
$660$	2.26880	−	1.96803i	0.0883129	−	0.0766055i
$661$	−8.79915	−	1.26513i	−0.342247	−	0.0492077i	−0.0309518	−	0.999521i	$-0.509854\pi$
$661$	−8.79915	−	1.26513i	−0.342247	−	0.0492077i	−0.311296	+	0.950313i	$0.600763\pi$
$662$	11.4036	−	30.5742i	0.443213	−	1.18830i
$663$	3.53917	−	4.72778i	0.137450	−	0.183612i
$664$	6.35617	−	4.08486i	0.246667	−	0.158523i
$665$	−10.3866	+	35.4430i	−0.402775	+	1.37442i
$666$			7.54851i			0.292499i
$667$	−2.45606	−	15.8794i	−0.0950991	−	0.614852i
$668$	13.5547	−	13.5547i	0.524449	−	0.524449i
$669$	2.63267	+	2.28122i	0.101785	+	0.0881971i
$670$	1.18692	−	0.258858i	0.0458547	−	0.0100005i
$671$	1.63499	+	11.3716i	0.0631181	+	0.438996i
$672$	2.13154	+	0.795024i	0.0822260	+	0.0306687i
$673$	−6.31352	−	8.43387i	−0.243368	−	0.325102i	0.662180	−	0.749344i	$-0.269631\pi$
$673$	−6.31352	−	8.43387i	−0.243368	−	0.325102i	−0.905549	+	0.424243i	$0.860540\pi$
$674$	−10.6836	+	3.13699i	−0.411517	+	0.120832i
$675$	2.39159	−	4.39093i	0.0920524	−	0.169007i
$676$	3.92492	−	8.59437i	0.150958	−	0.330553i
$677$	−5.62608	+	3.07207i	−0.216228	+	0.118069i	−0.583713	−	0.811960i	$-0.698401\pi$
$677$	−5.62608	+	3.07207i	−0.216228	+	0.118069i	0.367485	+	0.930029i	$0.380219\pi$
$678$	−0.318844	+	4.45802i	−0.0122451	+	0.171209i
$679$	26.5922	−	23.0423i	1.02052	−	0.884282i
$680$	−1.66912	+	2.23215i	−0.0640080	+	0.0855992i
$681$	−24.9716	−	11.4042i	−0.956916	−	0.437009i
$682$	−2.54938	+	0.554584i	−0.0976208	+	0.0212361i
$683$	−9.84980	+	18.0386i	−0.376892	+	0.690227i	−0.995426	−	0.0955313i	$-0.969545\pi$
$683$	−9.84980	+	18.0386i	−0.376892	+	0.690227i	0.618534	+	0.785758i	$0.287727\pi$
$684$	−1.03326	+	7.18646i	−0.0395076	+	0.274781i
$685$	−21.1838	−	18.3362i	−0.809391	−	0.700591i
$686$	−19.8711	+	2.85704i	−0.758684	+	0.109082i
$687$	1.73041	−	7.95459i	0.0660194	−	0.303486i
$688$	−2.65493	+	0.189884i	−0.101218	+	0.00723928i
$689$	−33.6096			−1.28042
$690$	2.39656	+	10.4526i	0.0912355	+	0.397923i
$691$	28.7268			1.09282			0.546409	−	0.837518i	$-0.315994\pi$
$691$	28.7268			1.09282			0.546409	+	0.837518i	$0.315994\pi$
$692$	14.9766	−	1.07115i	0.569326	−	0.0407190i
$693$	0.649535	−	2.98586i	0.0246738	−	0.113424i
$694$	−21.3878	+	3.07511i	−0.811871	+	0.116729i
$695$	12.3136	−	0.887250i	0.467083	−	0.0336553i
$696$	0.476819	−	3.31635i	0.0180738	−	0.125706i
$697$	2.29673	−	4.20614i	0.0869948	−	0.159319i
$698$	4.59341	−	0.999235i	0.173863	−	0.0378216i
$699$	11.5282	+	5.26474i	0.436036	+	0.199131i
$700$	−2.40612	+	11.1175i	−0.0909429	+	0.420202i
$701$	9.68512	−	8.39220i	0.365802	−	0.316969i	−0.452493	−	0.891768i	$-0.649465\pi$
$701$	9.68512	−	8.39220i	0.365802	−	0.316969i	0.818295	+	0.574799i	$0.194920\pi$
$702$	0.338002	−	4.72588i	0.0127570	−	0.178367i
$703$	48.1011	−	26.2652i	1.81417	−	0.990611i
$704$	−0.557975	+	1.22180i	−0.0210295	+	0.0460481i
$705$	3.12753	+	4.17327i	0.117789	+	0.157175i
$706$	−32.2290	+	9.46330i	−1.21296	+	0.356156i
$707$	−2.80377	−	3.74540i	−0.105447	−	0.140860i
$708$	−6.85309	−	2.55607i	−0.257555	−	0.0960630i
$709$	−3.32437	−	23.1215i	−0.124849	−	0.868347i	−0.951941	−	0.306280i	$-0.900916\pi$
$709$	−3.32437	−	23.1215i	−0.124849	−	0.868347i	0.827092	−	0.562067i	$-0.189994\pi$
$710$	−11.0015	−	7.06200i	−0.412879	−	0.265032i
$711$	3.59126	+	3.11185i	0.134683	+	0.116703i
$712$	−1.03194	+	1.03194i	−0.0386737	+	0.0386737i
$713$	2.52910	−	8.96561i	0.0947156	−	0.335765i
$714$			2.83570i			0.106123i
$715$	13.6558	+	4.00185i	0.510698	+	0.149661i
$716$	−16.4604	+	10.5785i	−0.615156	+	0.395337i
$717$	−6.63602	+	8.86469i	−0.247827	+	0.331058i
$718$	−3.66976	+	9.83901i	−0.136954	+	0.367189i
$719$	−40.7835	−	5.86378i	−1.52097	−	0.218682i	−0.669389	−	0.742912i	$-0.733444\pi$
$719$	−40.7835	−	5.86378i	−1.52097	−	0.218682i	−0.851577	+	0.524230i	$0.824353\pi$
$720$	−0.158337	+	2.23045i	−0.00590087	+	0.0831241i
$721$	−13.5766	−	8.72518i	−0.505621	−	0.324943i
$722$	31.5873	−	11.7814i	1.17556	−	0.438460i
$723$	−10.5215	−	19.2687i	−0.391300	−	0.716612i
$724$	9.99120	+	11.5305i	0.371320	+	0.428526i
$725$	16.7523	−	0.0177583i	0.622163	−	0.000659527i
$726$	−8.82338	−	2.59078i	−0.327466	−	0.0961528i
$727$	9.70361	+	26.0164i	0.359887	+	0.964894i	0.983137	+	0.182871i	$0.0585392\pi$
$727$	9.70361	+	26.0164i	0.359887	+	0.964894i	−0.623250	+	0.782023i	$0.714188\pi$
$728$	2.29119	+	10.5324i	0.0849170	+	0.390357i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	3.11758	−	5.71663i	0.115387	−	0.211582i
$731$	−1.37825	−	3.01794i	−0.0509763	−	0.111622i
$732$	−6.84725	−	5.12579i	−0.253082	−	0.189455i
$733$	−21.9339	−	4.77143i	−0.810147	−	0.176237i	−0.211633	−	0.977349i	$-0.567878\pi$
$733$	−21.9339	−	4.77143i	−0.810147	−	0.176237i	−0.598514	+	0.801112i	$0.704242\pi$
$734$	−0.176258	+	0.203413i	−0.00650581	+	0.00750810i
$735$	−1.69671	−	3.71008i	−0.0625842	−	0.136848i
$736$	−2.91478	−	3.80842i	−0.107440	−	0.140380i
$737$	0.515994	+	0.515994i	0.0190069	+	0.0190069i
$738$	−0.274279	−	3.83493i	−0.0100964	−	0.141166i
$739$	10.8802	+	16.9299i	0.400234	+	0.622777i	0.981619	−	0.190852i	$-0.0611251\pi$
$739$	10.8802	+	16.9299i	0.400234	+	0.622777i	−0.581384	+	0.813629i	$0.697489\pi$
$740$	14.1947	−	9.13299i	0.521806	−	0.335736i
$741$	−31.2907	+	14.2900i	−1.14949	+	0.524955i
$742$	12.9191	−	9.67114i	0.474276	−	0.355039i
$743$	−31.3254	−	17.1050i	−1.14922	−	0.627520i	−0.212346	−	0.977195i	$-0.568110\pi$
$743$	−31.3254	−	17.1050i	−1.14922	−	0.627520i	−0.936871	+	0.349674i	$0.886292\pi$
$744$	1.05015	−	1.63406i	0.0385003	−	0.0599077i
$745$	5.60908	−	5.61503i	0.205501	−	0.205719i
$746$	−9.29271	+	31.6481i	−0.340230	+	1.15872i
$747$	7.53634	+	0.539010i	0.275740	+	0.0197213i
$748$	−1.66997	−	0.119438i	−0.0610601	−	0.00436710i
$749$	9.39515	−	31.9969i	0.343291	−	1.16914i
$750$	−11.1506	+	0.815328i	−0.407161	+	0.0297716i
$751$	25.1298	−	39.1027i	0.916999	−	1.42688i	0.0127287	−	0.999919i	$-0.495948\pi$
$751$	25.1298	−	39.1027i	0.916999	−	1.42688i	0.904271	−	0.426960i	$-0.140415\pi$
$752$	−2.04699	−	1.11774i	−0.0746461	−	0.0407599i
$753$	9.26016	−	6.93207i	0.337459	−	0.252619i
$754$	14.4398	−	6.59441i	0.525865	−	0.240154i
$755$	−0.992703	+	4.57506i	−0.0361282	+	0.166503i
$756$	1.22995	+	1.91383i	0.0447327	+	0.0696055i
$757$	−1.19893	−	16.7632i	−0.0435759	−	0.609271i	−0.971582	−	0.236705i	$-0.923933\pi$
$757$	−1.19893	−	16.7632i	−0.0435759	−	0.609271i	0.928006	−	0.372566i	$-0.121522\pi$
$758$	−7.78971	−	7.78971i	−0.282935	−	0.282935i
$759$	−4.50614	+	4.60320i	−0.163563	+	0.167086i
$760$	14.7640	−	6.75195i	0.535546	−	0.244919i
$761$	−3.10067	+	3.57836i	−0.112399	+	0.129716i	−0.809161	−	0.587587i	$-0.800078\pi$
$761$	−3.10067	+	3.57836i	−0.112399	+	0.129716i	0.696762	+	0.717303i	$0.254623\pi$
$762$	−18.2285	−	3.96536i	−0.660348	−	0.143650i
$763$	−16.4657	−	12.3261i	−0.596099	−	0.446234i
$764$	−0.470615	−	1.03050i	−0.0170263	−	0.0372823i
$765$	−2.67388	+	0.786663i	−0.0966744	+	0.0284418i
$766$	10.3782	+	35.3450i	0.374980	+	1.27707i
$767$	−7.36636	−	33.8626i	−0.265984	−	1.22271i
$768$	−0.349464	−	0.936950i	−0.0126102	−	0.0338093i
$769$	46.1229	+	13.5429i	1.66324	+	0.488370i	0.972142	−	0.234395i	$-0.0753108\pi$
$769$	46.1229	+	13.5429i	1.66324	+	0.488370i	0.691094	+	0.722765i	$0.257129\pi$
$770$	−6.40067	+	2.39119i	−0.230664	+	0.0861725i
$771$	−6.53749	−	7.54466i	−0.235442	−	0.271714i
$772$	11.7621	+	21.5407i	0.423328	+	0.775267i
$773$	35.7598	−	13.3377i	1.28619	−	0.479725i	0.388948	−	0.921260i	$-0.372839\pi$
$773$	35.7598	−	13.3377i	1.28619	−	0.479725i	0.897244	+	0.441535i	$0.145566\pi$
$774$	−2.23918	−	1.43903i	−0.0804855	−	0.0517249i
$775$	8.83869	+	4.02517i	0.317495	+	0.144589i
$776$	−15.3093	−	2.20115i	−0.549573	−	0.0790167i
$777$	6.00124	−	16.0900i	0.215293	−	0.577224i
$778$	−20.2985	+	27.1156i	−0.727735	+	0.972140i
$779$	−23.4828	+	15.0915i	−0.841360	+	0.540709i
$780$	−9.29577	+	5.08227i	−0.332842	+	0.181975i
$781$		−	7.85280i		−	0.280995i
$782$	3.17812	−	5.06306i	0.113650	−	0.181055i
$783$	2.36913	−	2.36913i	0.0846657	−	0.0846657i
$784$	1.37884	+	1.19478i	0.0492444	+	0.0426705i
$785$	25.5755	−	39.8427i	0.912829	−	1.42205i
$786$	1.02374	+	7.12024i	0.0365154	+	0.253970i
$787$	44.9435	+	16.7631i	1.60206	+	0.597539i	0.982311	−	0.187258i	$-0.0599599\pi$
$787$	44.9435	+	16.7631i	1.60206	+	0.597539i	0.619753	+	0.784797i	$0.287233\pi$
$788$	15.8814	+	21.2151i	0.565752	+	0.755756i
$789$	23.4345	−	6.88098i	0.834289	−	0.244969i
$790$	1.50661	−	10.5183i	0.0536028	−	0.374223i
$791$	4.22386	−	9.24895i	0.150183	−	0.328855i
$792$	−1.17888	+	0.643715i	−0.0418896	+	0.0228734i
$793$	2.89102	−	40.4218i	0.102663	−	1.43542i
$794$	25.4414	−	22.0451i	0.902881	−	0.782350i
$795$	12.7032	+	9.49900i	0.450536	+	0.336895i
$796$	−10.0583	−	4.59349i	−0.356508	−	0.162812i
$797$	3.93523	−	0.856056i	0.139393	−	0.0303231i	−0.142327	−	0.989820i	$-0.545459\pi$
$797$	3.93523	−	0.856056i	0.139393	−	0.0303231i	0.281720	+	0.959497i	$0.409095\pi$
$798$	7.91584	−	14.4968i	0.280218	−	0.513180i
$799$	0.413727	−	2.87754i	0.0146366	−	0.101800i
$800$	4.38585	−	2.40090i	0.155063	−	0.0848845i
$801$	−1.44453	+	0.207693i	−0.0510401	+	0.00733846i
$802$	5.08227	−	23.3628i	0.179461	−	0.824970i
$803$	3.90138	−	0.279032i	0.137677	−	0.00984683i
$804$	−0.543284			−0.0191601
$805$	3.20168	−	24.1854i	0.112845	−	0.852424i
$806$	9.20307			0.324164
$807$	−26.6668	+	1.90725i	−0.938715	+	0.0671382i
$808$	−0.437149	+	2.00954i	−0.0153789	+	0.0706955i
$809$	−46.8022	+	6.72915i	−1.64548	+	0.236584i	−0.901863	−	0.432022i	$-0.857800\pi$
$809$	−46.8022	+	6.72915i	−1.64548	+	0.236584i	−0.743616	+	0.668607i	$0.766891\pi$
$810$	−1.46342	+	1.69068i	−0.0514192	+	0.0594046i
$811$	−4.50450	+	31.3295i	−0.158174	+	1.10013i	0.743820	+	0.668380i	$0.233012\pi$
$811$	−4.50450	+	31.3295i	−0.158174	+	1.10013i	−0.901995	+	0.431747i	$0.857897\pi$
$812$	−3.65294	+	6.68985i	−0.128193	+	0.234768i
$813$	−26.5982	+	5.78608i	−0.932839	+	0.202927i
$814$	9.22273	+	4.21188i	0.323257	+	0.147626i
$815$	−43.9379	+	6.34109i	−1.53908	+	0.222119i
$816$	0.942022	−	0.816267i	0.0329774	−	0.0285751i
$817$	−1.37863	+	19.2758i	−0.0482322	+	0.674374i
$818$	−28.0497	+	15.3163i	−0.980736	+	0.535522i
$819$	−4.47765	+	9.80468i	−0.156462	+	0.342603i
$820$	−6.87957	+	5.15567i	−0.240245	+	0.180044i
$821$	−31.3667	+	9.21011i	−1.09471	+	0.321435i	−0.778747	−	0.627338i	$-0.784145\pi$
$821$	−31.3667	+	9.21011i	−1.09471	+	0.321435i	−0.315959	+	0.948773i	$0.602326\pi$
$822$	7.50879	+	10.0306i	0.261899	+	0.349856i
$823$	−18.0901	−	6.74726i	−0.630581	−	0.235195i	0.0137931	−	0.999905i	$-0.495609\pi$
$823$	−18.0901	−	6.74726i	−0.630581	−	0.235195i	−0.644374	+	0.764710i	$0.722882\pi$
$824$	1.00957	+	7.02174i	0.0351702	+	0.244614i
$825$	−4.03037	−	5.37207i	−0.140320	−	0.187031i
$826$	12.5755	+	10.8967i	0.437558	+	0.379146i
$827$	−25.5340	+	25.5340i	−0.887904	+	0.887904i	−0.994322	−	0.106417i	$-0.966062\pi$
$827$	−25.5340	+	25.5340i	−0.887904	+	0.887904i	0.106417	+	0.994322i	$0.466062\pi$
$828$	−0.0510947	−	4.79556i	−0.00177566	−	0.166657i
$829$			35.6518i			1.23824i	0.785297	+	0.619119i	$0.212510\pi$
$829$			35.6518i			1.23824i	−0.785297	+	0.619119i	$0.787490\pi$
$830$	−8.10468	−	14.8239i	−0.281318	−	0.514546i
$831$	−3.22366	+	2.07172i	−0.111828	+	0.0718673i
$832$	2.83935	−	3.79293i	0.0984367	−	0.131496i
$833$	−0.794737	+	2.13077i	−0.0275360	+	0.0738268i
$834$	−5.46491	−	0.785736i	−0.189234	−	0.0272078i
$835$	−28.0870	−	32.3795i	−0.971992	−	1.12054i
$836$	8.20385	+	5.27230i	0.283736	+	0.182346i
$837$	1.81995	−	0.678804i	0.0629065	−	0.0234629i
$838$	1.72877	+	3.16601i	0.0597194	+	0.109368i
$839$	1.17228	+	1.35289i	0.0404718	+	0.0467069i	0.775625	−	0.631195i	$-0.217435\pi$
$839$	1.17228	+	1.35289i	0.0404718	+	0.0467069i	−0.735153	+	0.677901i	$0.762890\pi$
$840$	2.11077	−	4.62842i	0.0728284	−	0.159696i
$841$	−17.0545	−	5.00765i	−0.588085	−	0.172677i
$842$	−5.55585	−	14.8958i	−0.191467	−	0.513344i
$843$	−1.18865	−	5.46413i	−0.0409393	−	0.188195i
$844$	3.52524	+	12.0059i	0.121344	+	0.413259i
$845$	−18.5479	−	10.1152i	−0.638067	−	0.347972i
$846$	−0.968864	−	2.12152i	−0.0333102	−	0.0729392i
$847$	16.7477	+	12.5371i	0.575457	+	0.430781i
$848$	−6.93158	−	1.50787i	−0.238031	−	0.0517806i
$849$	−5.21087	+	6.01366i	−0.178837	+	0.206388i
$850$	4.71444	+	4.07634i	0.161704	+	0.139817i
$851$	−28.7479	+	22.0022i	−0.985466	+	0.754226i
$852$	4.13406	+	4.13406i	0.141631	+	0.141631i
$853$	3.99150	+	55.8084i	0.136666	+	1.91084i	0.354828	+	0.934932i	$0.384539\pi$
$853$	3.99150	+	55.8084i	0.136666	+	1.91084i	−0.218162	+	0.975913i	$0.570006\pi$
$854$	10.5201	+	16.3696i	0.359989	+	0.560155i
$855$	15.8655	+	3.44252i	0.542588	+	0.117732i
$856$	−13.3338	+	6.08936i	−0.455741	+	0.208130i
$857$	−18.1963	+	13.6216i	−0.621573	+	0.465303i	−0.863061	−	0.505100i	$-0.831455\pi$
$857$	−18.1963	+	13.6216i	−0.621573	+	0.465303i	0.241488	+	0.970404i	$0.422365\pi$
$858$	−5.58546	−	3.04989i	−0.190684	−	0.104122i
$859$	−12.6023	+	19.6096i	−0.429986	+	0.669071i	−0.986870	−	0.161520i	$-0.948361\pi$
$859$	−12.6023	+	19.6096i	−0.429986	+	0.669071i	0.556884	+	0.830590i	$0.311997\pi$
$860$	0.00315460	+	5.95177i	0.000107571	+	0.202954i
$861$	−2.46422	+	8.39236i	−0.0839804	+	0.286011i
$862$	27.5950	+	1.97364i	0.939891	+	0.0672223i
$863$	15.0385	+	1.07557i	0.511916	+	0.0366130i	0.324908	−	0.945746i	$-0.394667\pi$
$863$	15.0385	+	1.07557i	0.511916	+	0.0366130i	0.187008	+	0.982358i	$0.440121\pi$
$864$	0.281733	−	0.959493i	0.00958474	−	0.0326426i
$865$	−0.0177953	−	33.5743i	−0.000605058	−	1.14156i
$866$	18.4987	−	28.7845i	0.628610	−	0.978136i
$867$	−13.5569	−	7.40262i	−0.460416	−	0.251406i
$868$	−3.53755	+	2.64818i	−0.120072	+	0.0898851i
$869$	5.80588	−	2.65146i	0.196951	−	0.0899445i
$870$	−7.32147	−	1.58862i	−0.248221	−	0.0538594i
$871$	−1.39164	−	2.16543i	−0.0471539	−	0.0733728i
$872$	0.644982	+	9.01802i	0.0218418	+	0.305389i
$873$	−10.9367	−	10.9367i	−0.370150	−	0.370150i
$874$	−30.3808	+	17.0118i	−1.02765	+	0.575434i
$875$	24.4161	+	7.12706i	0.825415	+	0.240939i
$876$	−1.90696	+	2.20075i	−0.0644303	+	0.0743566i
$877$	−23.2115	−	5.04934i	−0.783795	−	0.170504i	−0.197177	−	0.980368i	$-0.563177\pi$
$877$	−23.2115	−	5.04934i	−0.783795	−	0.170504i	−0.586618	+	0.809864i	$0.699541\pi$
$878$	−10.8560	−	8.12667i	−0.366371	−	0.274262i
$879$	6.11283	+	13.3852i	0.206181	+	0.451473i
$880$	2.63681	+	1.43799i	0.0888869	+	0.0484748i
$881$	−9.40424	−	32.0279i	−0.316837	−	1.07905i	−0.951855	−	0.306550i	$-0.900825\pi$
$881$	−9.40424	−	32.0279i	−0.316837	−	1.07905i	0.635018	−	0.772498i	$-0.280993\pi$
$882$	0.387819	+	1.78278i	0.0130586	+	0.0600292i
$883$	7.81135	+	20.9430i	0.262873	+	0.704789i	0.999591	+	0.0285897i	$0.00910162\pi$
$883$	7.81135	+	20.9430i	0.262873	+	0.704789i	−0.736718	+	0.676200i	$0.763626\pi$
$884$	5.66651	+	1.66384i	0.190585	+	0.0559609i
$885$	−6.78630	+	14.8808i	−0.228119	+	0.500212i
$886$	−12.1977	−	14.0769i	−0.409790	−	0.472923i
$887$	−10.4906	−	19.2121i	−0.352239	−	0.645078i	0.640145	−	0.768254i	$-0.278874\pi$
$887$	−10.4906	−	19.2121i	−0.352239	−	0.645078i	−0.992385	+	0.123175i	$0.960692\pi$
$888$	−7.07258	+	2.63793i	−0.237340	+	0.0885233i
$889$	35.7022	+	22.9444i	1.19741	+	0.769531i
$890$	2.13831	+	2.46510i	0.0716763	+	0.0826303i
$891$	−1.32950	−	0.191154i	−0.0445400	−	0.00640389i
$892$	−1.21737	+	3.26388i	−0.0407604	+	0.109283i
$893$	−10.1477	+	13.5557i	−0.339579	+	0.453625i
$894$	−2.98592	+	1.91894i	−0.0998642	+	0.0641788i
$895$	20.9885	+	38.3893i	0.701570	+	1.28321i
$896$			2.27498i			0.0760017i
$897$	18.9833	−	12.4876i	0.633835	−	0.416950i
$898$	1.25796	−	1.25796i	0.0419786	−	0.0419786i
$899$	4.91840	+	4.26181i	0.164038	+	0.142139i
$900$	4.94986	+	0.706327i	0.164995	+	0.0235442i
$901$	−1.25836	−	8.75210i	−0.0419221	−	0.291575i
$902$	−4.83854	−	1.80468i	−0.161106	−	0.0600893i
$903$	3.62883	+	4.84755i	0.120760	+	0.161316i
$904$	−4.28836	+	1.25918i	−0.142629	+	0.0418796i
$905$	27.3001	−	20.4592i	0.907487	−	0.680087i
$906$	0.869729	−	1.90444i	0.0288948	−	0.0632708i
$907$	−33.0483	+	18.0457i	−1.09735	+	0.599199i	−0.922734	−	0.385438i	$-0.874051\pi$
$907$	−33.0483	+	18.0457i	−1.09735	+	0.599199i	−0.174617	+	0.984636i	$0.555869\pi$
$908$	1.95844	−	27.3825i	0.0649930	−	0.908721i
$909$	−1.55423	+	1.34675i	−0.0515506	+	0.0446688i
$910$	23.8548	−	3.44271i	0.790780	−	0.114125i
$911$	18.6339	+	8.50984i	0.617370	+	0.281943i	0.699449	−	0.714682i	$-0.253429\pi$
$911$	18.6339	+	8.50984i	0.617370	+	0.281943i	−0.0820791	+	0.996626i	$0.526156\pi$
$912$	−7.09444	+	1.54330i	−0.234920	+	0.0511038i
$913$	4.86365	−	8.90711i	0.160963	−	0.294782i
$914$	0.859975	−	5.98126i	0.0284454	−	0.197842i
$915$	−12.5170	+	14.4609i	−0.413800	+	0.478062i
$916$	8.05777	−	1.15853i	0.266236	−	0.0382790i
$917$	3.47862	−	15.9910i	0.114874	−	0.528068i
$918$	1.24330	−	0.0889224i	0.0410350	−	0.00293488i
$919$	−31.0632			−1.02468			−0.512339	−	0.858783i	$-0.671221\pi$
$919$	−31.0632			−1.02468			−0.512339	+	0.858783i	$0.671221\pi$
$920$	−8.95603	+	5.89826i	−0.295272	+	0.194460i
$921$	−19.2481			−0.634248
$922$	−15.3744	+	1.09960i	−0.506327	+	0.0362132i
$923$	−5.88810	+	27.0671i	−0.193809	+	0.890926i
$924$	3.02459	−	0.434871i	0.0995018	−	0.0143062i
$925$	−18.1232	−	33.1067i	−0.595887	−	1.08854i
$926$	−3.85106	+	26.7847i	−0.126554	+	0.880200i
$927$	−3.39977	+	6.22621i	−0.111663	+	0.204496i
$928$	3.27388	−	0.712190i	0.107471	−	0.0233788i
$929$	−22.5649	−	10.3050i	−0.740330	−	0.338097i	0.00929822	−	0.999957i	$-0.497040\pi$
$929$	−22.5649	−	10.3050i	−0.740330	−	0.338097i	−0.749628	+	0.661860i	$0.769768\pi$
$930$	−3.47843	−	2.60104i	−0.114062	−	0.0852915i
$931$	10.0109	−	8.67450i	0.328094	−	0.284295i
$932$	−0.904114	+	12.6412i	−0.0296152	+	0.414075i
$933$	−20.8947	+	11.4094i	−0.684061	+	0.373525i
$934$	−1.51409	+	3.31539i	−0.0495425	+	0.108483i
$935$	−0.530820	+	3.70588i	−0.0173597	+	0.121195i
$936$	4.54603	−	1.33484i	0.148592	−	0.0436304i
$937$	−29.0743	−	38.8388i	−0.949817	−	1.26881i	−0.963169	−	0.268896i	$-0.913341\pi$
$937$	−29.0743	−	38.8388i	−0.949817	−	1.26881i	0.0133524	−	0.999911i	$-0.495750\pi$
$938$	1.15803	+	0.431924i	0.0378111	+	0.0141028i
$939$	3.20714	+	22.3062i	0.104661	+	0.727934i
$940$	−2.81719	+	4.38875i	−0.0918866	+	0.143145i
$941$	2.46426	+	2.13530i	0.0803327	+	0.0696087i	0.694102	−	0.719877i	$-0.255802\pi$
$941$	2.46426	+	2.13530i	0.0803327	+	0.0696087i	−0.613769	+	0.789486i	$0.710347\pi$
$942$	−14.9718	+	14.9718i	−0.487807	+	0.487807i
$943$	13.8056	−	12.2225i	0.449571	−	0.398020i
$944$		−	7.31425i		−	0.238059i
$945$	4.46347	−	2.44031i	0.145197	−	0.0793833i
$946$	−3.00760	+	1.93287i	−0.0977857	+	0.0628430i
$947$	8.41118	−	11.2360i	0.273326	−	0.365121i	−0.642784	−	0.766048i	$-0.722221\pi$
$947$	8.41118	−	11.2360i	0.273326	−	0.365121i	0.916110	+	0.400926i	$0.131312\pi$
$948$	−1.66063	+	4.45231i	−0.0539347	+	0.144604i
$949$	−13.6565	−	1.96352i	−0.443310	−	0.0637384i
$950$	−12.7222	−	33.9995i	−0.412764	−	1.10309i
$951$	−9.84730	−	6.32848i	−0.319321	−	0.205215i
$952$	−2.65691	+	0.990976i	−0.0861110	+	0.0321177i
$953$	6.51021	+	11.9226i	0.210886	+	0.386210i	0.961615	−	0.274401i	$-0.0884794\pi$
$953$	6.51021	+	11.9226i	0.210886	+	0.386210i	−0.750729	+	0.660610i	$0.770298\pi$
$954$	−4.64538	−	5.36105i	−0.150400	−	0.173571i
$955$	−2.37301	+	0.886519i	−0.0767887	+	0.0286871i
$956$	−10.6248	−	3.11973i	−0.343631	−	0.100899i
$957$	−1.57267	−	4.21650i	−0.0508373	−	0.136300i
$958$	−8.12719	−	37.3601i	−0.262578	−	1.20705i
$959$	−8.03075	−	27.3502i	−0.259326	−	0.883185i
$960$	−2.14516	+	0.631110i	−0.0692347	+	0.0203690i
$961$	−11.3105	−	24.7666i	−0.364855	−	0.798922i
$962$	−28.6309	−	21.4329i	−0.923099	−	0.691023i
$963$	−14.3235	−	3.11589i	−0.461568	−	0.100408i
$964$	14.3769	−	16.5919i	0.463050	−	0.534388i
$965$	49.9080	−	22.8242i	1.60659	−	0.734736i
$966$	−3.70367	+	10.2626i	−0.119164	+	0.330192i
$967$	6.63006	+	6.63006i	0.213208	+	0.213208i	0.805629	−	0.592421i	$-0.201828\pi$
$967$	6.63006	+	6.63006i	0.213208	+	0.213208i	−0.592421	+	0.805629i	$0.701828\pi$
$968$	−0.656027	−	9.17245i	−0.0210855	−	0.294814i
$969$	−4.89272	−	7.61322i	−0.157177	−	0.244572i
$970$	−7.33360	+	33.7983i	−0.235468	+	1.08520i
$971$	−0.176519	+	0.0806137i	−0.00566477	+	0.00258702i	−0.418245	−	0.908334i	$-0.637355\pi$
$971$	−0.176519	+	0.0806137i	−0.00566477	+	0.00258702i	0.412581	+	0.910921i	$0.364628\pi$
$972$	0.800541	−	0.599278i	0.0256774	−	0.0192218i
$973$	11.0240	+	6.01956i	0.353413	+	0.192978i
$974$	19.0900	−	29.7046i	0.611684	−	0.951798i
$975$	9.86392	+	21.5385i	0.315898	+	0.689785i
$976$	2.40974	−	8.20681i	0.0771338	−	0.262694i
$977$	−29.0045	−	2.07444i	−0.927936	−	0.0663673i	−0.400816	−	0.916158i	$-0.631273\pi$
$977$	−29.0045	−	2.07444i	−0.927936	−	0.0663673i	−0.527120	+	0.849791i	$0.676728\pi$
$978$	19.8026	+	1.41631i	0.633218	+	0.0452887i
$979$	−0.552257	+	1.88081i	−0.0176502	+	0.0601110i
$980$	2.88321	−	2.88627i	0.0921009	−	0.0921986i
$981$	−4.88797	+	7.60582i	−0.156061	+	0.242835i
$982$	5.10349	+	2.78672i	0.162859	+	0.0889278i
$983$	2.27443	−	1.70262i	0.0725430	−	0.0543050i	−0.562391	−	0.826872i	$-0.690118\pi$
$983$	2.27443	−	1.70262i	0.0725430	−	0.0543050i	0.634934	+	0.772567i	$0.281027\pi$
$984$	3.49728	−	1.59716i	0.111489	−	0.0509155i
$985$	49.8339	−	32.0636i	1.58784	−	1.02163i
$986$	2.25785	+	3.51329i	0.0719047	+	0.111886i
$987$	0.378518	+	5.29237i	0.0120483	+	0.168458i
$988$	−24.3239	−	24.3239i	−0.773848	−	0.773848i
$989$	−1.04625	−	12.7222i	−0.0332690	−	0.404542i
$990$	1.24912	+	2.73136i	0.0396996	+	0.0868082i
$991$	32.4761	−	37.4794i	1.03164	−	1.19057i	0.0502110	−	0.998739i	$-0.484011\pi$
$991$	32.4761	−	37.4794i	1.03164	−	1.19057i	0.981427	−	0.191835i	$-0.0614439\pi$
$992$	1.89802	+	0.412890i	0.0602623	+	0.0131093i
$993$	26.1230	+	19.5554i	0.828987	+	0.620572i
$994$	−5.52525	−	12.0986i	−0.175250	−	0.383744i
$995$	−11.8382	+	21.7073i	−0.375295	+	0.688169i
$996$	2.12866	+	7.24954i	0.0674491	+	0.229710i
$997$	−8.40154	−	38.6213i	−0.266079	−	1.22315i	−0.895138	−	0.445789i	$-0.852923\pi$
$997$	−8.40154	−	38.6213i	−0.266079	−	1.22315i	0.629058	−	0.777358i	$-0.283441\pi$
$998$	−4.15261	−	11.1336i	−0.131449	−	0.352428i
$999$	−7.24274	−	2.12666i	−0.229150	−	0.0672846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.7.4	✓	240
5.3	odd	4	inner	690.2.w.a.283.12	yes	240
23.10	odd	22	inner	690.2.w.a.217.12	yes	240
115.33	even	44	inner	690.2.w.a.493.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.4	✓	240	1.1	even	1	trivial
690.2.w.a.217.12	yes	240	23.10	odd	22	inner
690.2.w.a.283.12	yes	240	5.3	odd	4	inner
690.2.w.a.493.4	yes	240	115.33	even	44	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-0.160701 - 2.23029i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(1.09028 - 1.99670i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-0.160701 - 2.23029i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(1.09028 - 1.99670i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(0.319399 + 2.21314i) q^{10} +(-1.01510 + 0.879593i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(4.15840 - 2.27066i) q^{13} +(-0.945060 + 2.06939i) q^{14} +(-2.21348 - 0.317052i) q^{15} +(0.959493 - 0.281733i) q^{16} +(0.746984 + 0.997854i) q^{17} +(0.936950 + 0.349464i) q^{18} +(-1.03326 - 7.18646i) q^{19} +(-0.476468 - 2.18471i) q^{20} +(-1.71931 - 1.48979i) q^{21} +(0.949768 - 0.949768i) q^{22} +(1.40009 + 4.58691i) q^{23} +1.00000i q^{24} +(-4.94835 + 0.716820i) q^{25} +(-3.98582 + 2.56153i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(0.795024 - 2.13154i) q^{28} +(-3.31635 - 0.476819i) q^{29} +(2.23045 + 0.158337i) q^{30} +(-1.63406 - 1.05015i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(0.643715 + 1.17888i) q^{33} +(-0.816267 - 0.942022i) q^{34} +(-4.62842 - 2.11077i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.63793 + 7.07258i) q^{37} +(1.54330 + 7.09444i) q^{38} +(-1.33484 - 4.54603i) q^{39} +(0.631110 + 2.14516i) q^{40} +(-1.59716 - 3.49728i) q^{41} +(1.82121 + 1.36334i) q^{42} +(-2.60088 - 0.565788i) q^{43} +(-0.879593 + 1.01510i) q^{44} +(-0.780315 + 2.09550i) q^{45} +(-1.72375 - 4.47534i) q^{46} +(-1.64917 - 1.64917i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(0.986384 + 1.53484i) q^{49} +(4.88460 - 1.06800i) q^{50} +(1.13383 - 0.517804i) q^{51} +(3.79293 - 2.83935i) q^{52} +(-6.22598 - 3.39964i) q^{53} +(0.540641 - 0.841254i) q^{54} +(2.12487 + 2.12262i) q^{55} +(-0.640936 + 2.18283i) q^{56} +(-7.24187 - 0.517948i) q^{57} +(3.34192 + 0.239019i) q^{58} +(2.06066 - 7.01798i) q^{59} +(-2.23607 + 0.00118518i) q^{60} +(4.62425 - 7.19548i) q^{61} +(1.70482 + 0.930900i) q^{62} +(-1.82121 + 1.36334i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-5.73248 - 8.90952i) q^{65} +(-0.726175 - 1.12995i) q^{66} +(-0.0387574 - 0.541900i) q^{67} +(0.881390 + 0.881390i) q^{68} +(4.77970 - 0.393076i) q^{69} +(4.76721 + 1.77520i) q^{70} +(-3.82861 + 4.41845i) q^{71} +(0.977147 + 0.212565i) q^{72} +(-2.33119 - 1.74511i) q^{73} +(-3.13577 - 6.86637i) q^{74} +(-0.351409 + 4.98764i) q^{75} +(-2.04548 - 6.96627i) q^{76} +(0.649535 + 2.98586i) q^{77} +(1.65574 + 4.43922i) q^{78} +(-4.55944 - 1.33877i) q^{79} +(-0.782536 - 2.09467i) q^{80} +(0.654861 + 0.755750i) q^{81} +(1.84258 + 3.37443i) q^{82} +(-7.07921 + 2.64041i) q^{83} +(-1.91383 - 1.22995i) q^{84} +(2.10546 - 1.82634i) q^{85} +(2.63462 + 0.378801i) q^{86} +(-1.17086 + 3.13921i) q^{87} +(0.804935 - 1.07527i) q^{88} +(1.22772 - 0.789005i) q^{89} +(0.628836 - 2.14583i) q^{90} -10.7787i q^{91} +(2.03862 + 4.34097i) q^{92} +(-1.37349 + 1.37349i) q^{93} +(1.76262 + 1.52732i) q^{94} +(-15.8618 + 3.45933i) q^{95} +(0.142315 + 0.989821i) q^{96} +(14.4916 + 5.40508i) q^{97} +(-1.09337 - 1.46057i) q^{98} +(1.28877 - 0.378416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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