LMFDB - Embedded newform 690.2.r.b.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(49,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 16]))

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

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

chi := DirichletCharacter("690.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.r (of order $22$, degree $10$, 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:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	690.49
Dual form			690.2.r.b.169.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(0.981376 + 2.00920i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(2.34067 + 3.64216i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(0.981376 + 2.00920i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(2.34067 + 3.64216i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-1.25733 - 1.84909i) q^{10} +(-0.630409 + 4.38459i) q^{11} +(0.989821 + 0.142315i) q^{12} +(2.80393 - 4.36300i) q^{13} +(-2.83518 - 3.27197i) q^{14} +(0.0580378 + 2.23531i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.0366362 - 0.124771i) q^{17} +(-0.755750 - 0.654861i) q^{18} +(-4.41094 + 1.29517i) q^{19} +(1.50768 + 1.65133i) q^{20} +(0.616144 + 4.28537i) q^{21} -4.42968i q^{22} +(-3.10096 - 3.65842i) q^{23} -1.00000 q^{24} +(-3.07380 + 3.94357i) q^{25} +(-2.15447 + 4.71763i) q^{26} +(0.281733 + 0.959493i) q^{27} +(3.27197 + 2.83518i) q^{28} +(-3.51741 - 1.03280i) q^{29} +(-0.375565 - 2.20430i) q^{30} +(-3.45167 - 7.55811i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(-2.39486 + 3.72648i) q^{33} +(-0.0185065 + 0.128715i) q^{34} +(-5.02076 + 8.27722i) q^{35} +(0.841254 + 0.540641i) q^{36} +(8.53579 - 7.39630i) q^{37} +(4.18173 - 1.90973i) q^{38} +(4.36300 - 2.80393i) q^{39} +(-1.72734 - 1.41996i) q^{40} +(5.06753 - 5.84824i) q^{41} +(-1.21974 - 4.15407i) q^{42} +(4.40797 + 2.01305i) q^{43} +(0.630409 + 4.38459i) q^{44} +(-0.875790 + 2.05742i) q^{45} +(3.59004 + 3.17987i) q^{46} +9.46833i q^{47} +(0.989821 - 0.142315i) q^{48} +(-4.87866 + 10.6828i) q^{49} +(2.48129 - 4.34088i) q^{50} +(0.0851574 - 0.0982769i) q^{51} +(1.46115 - 4.97622i) q^{52} +(3.26756 + 5.08442i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-9.42820 + 3.03631i) q^{55} +(-3.64216 - 2.34067i) q^{56} +(-4.55037 - 0.654244i) q^{57} +(3.62859 + 0.521712i) q^{58} +(-4.79503 - 3.08158i) q^{59} +(0.685448 + 2.12842i) q^{60} +(-0.903633 - 1.97868i) q^{61} +(4.49217 + 6.98995i) q^{62} +(-1.21974 + 4.15407i) q^{63} +(0.654861 - 0.755750i) q^{64} +(11.5179 + 1.35192i) q^{65} +(1.84015 - 4.02937i) q^{66} +(6.46450 - 0.929455i) q^{67} -0.130039i q^{68} +(-1.30097 - 4.61600i) q^{69} +(3.79168 - 8.90750i) q^{70} +(-0.336289 - 2.33894i) q^{71} +(-0.909632 - 0.415415i) q^{72} +(0.190467 + 0.648670i) q^{73} +(-7.39630 + 8.53579i) q^{74} +(-4.43425 + 2.31029i) q^{75} +(-3.86738 + 2.48541i) q^{76} +(-17.4449 + 7.96684i) q^{77} +(-3.91955 + 3.39631i) q^{78} +(8.85021 + 5.68769i) q^{79} +(1.91184 + 1.15968i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-4.18366 + 6.50989i) q^{82} +(2.45486 - 2.12715i) q^{83} +(1.79852 + 3.93820i) q^{84} +(0.286645 - 0.0488381i) q^{85} +(-4.64959 - 1.36524i) q^{86} +(-2.77050 - 2.40065i) q^{87} +(-1.24798 - 4.25024i) q^{88} +(-4.68820 + 10.2657i) q^{89} +(0.574074 - 2.16112i) q^{90} +22.4538 q^{91} +(-4.00604 - 2.63659i) q^{92} -8.30897i q^{93} +(-1.34748 - 9.37195i) q^{94} +(-6.93106 - 7.59144i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(-5.09682 - 4.41642i) q^{97} +(3.30869 - 11.2683i) q^{98} +(-3.72648 + 2.39486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.989821	+	0.142315i	−0.699909	+	0.100632i
$2$	−0.989821	+	0.142315i	−0.699909	+	0.100632i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$4$	0.959493	−	0.281733i	0.479746	−	0.140866i
$5$	0.981376	+	2.00920i	0.438885	+	0.898543i
$5$	0.981376	+	2.00920i	0.438885	+	0.898543i
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	2.34067	+	3.64216i	0.884691	+	1.37661i	0.926025	+	0.377461i	$0.123203\pi$
$7$	2.34067	+	3.64216i	0.884691	+	1.37661i	−0.0413342	+	0.999145i	$0.513161\pi$
$8$	−0.909632	+	0.415415i	−0.321603	+	0.146871i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−1.25733	−	1.84909i	−0.397602	−	0.584733i
$11$	−0.630409	+	4.38459i	−0.190075	+	1.32200i	0.641728	+	0.766932i	$0.278218\pi$
$11$	−0.630409	+	4.38459i	−0.190075	+	1.32200i	−0.831803	+	0.555071i	$0.812691\pi$
$12$	0.989821	+	0.142315i	0.285737	+	0.0410828i
$13$	2.80393	−	4.36300i	0.777670	−	1.21008i	−0.195661	−	0.980672i	$-0.562685\pi$
$13$	2.80393	−	4.36300i	0.777670	−	1.21008i	0.973331	−	0.229406i	$-0.0736784\pi$
$14$	−2.83518	−	3.27197i	−0.757734	−	0.874472i
$15$	0.0580378	+	2.23531i	0.0149853	+	0.577156i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	0.0366362	−	0.124771i	0.00888559	−	0.0302615i	−0.954931	−	0.296828i	$-0.904071\pi$
$17$	0.0366362	−	0.124771i	0.00888559	−	0.0302615i	0.963816	+	0.266567i	$0.0858893\pi$
$18$	−0.755750	−	0.654861i	−0.178132	−	0.154352i
$19$	−4.41094	+	1.29517i	−1.01194	+	0.297132i	−0.745347	−	0.666677i	$-0.767716\pi$
$19$	−4.41094	+	1.29517i	−1.01194	+	0.297132i	−0.266593	+	0.963809i	$0.585898\pi$
$20$	1.50768	+	1.65133i	0.337128	+	0.369249i
$21$	0.616144	+	4.28537i	0.134454	+	0.935145i
$22$		−	4.42968i		−	0.944410i
$23$	−3.10096	−	3.65842i	−0.646594	−	0.762834i
$23$	−3.10096	−	3.65842i	−0.646594	−	0.762834i
$24$	−1.00000			−0.204124
$25$	−3.07380	+	3.94357i	−0.614760	+	0.788714i
$26$	−2.15447	+	4.71763i	−0.422526	+	0.925203i
$27$	0.281733	+	0.959493i	0.0542195	+	0.184655i
$28$	3.27197	+	2.83518i	0.618345	+	0.535799i
$29$	−3.51741	−	1.03280i	−0.653166	−	0.191787i	−0.0616723	−	0.998096i	$-0.519643\pi$
$29$	−3.51741	−	1.03280i	−0.653166	−	0.191787i	−0.591494	+	0.806310i	$0.701462\pi$
$30$	−0.375565	−	2.20430i	−0.0685686	−	0.402449i
$31$	−3.45167	−	7.55811i	−0.619939	−	1.35748i	−0.915564	−	0.402172i	$-0.868255\pi$
$31$	−3.45167	−	7.55811i	−0.619939	−	1.35748i	0.295625	−	0.955304i	$-0.404472\pi$
$32$	−0.755750	+	0.654861i	−0.133599	+	0.115764i
$33$	−2.39486	+	3.72648i	−0.416892	+	0.648697i
$34$	−0.0185065	+	0.128715i	−0.00317383	+	0.0220745i
$35$	−5.02076	+	8.27722i	−0.848663	+	1.39911i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	8.53579	−	7.39630i	1.40328	−	1.21594i	0.458302	−	0.888796i	$-0.348458\pi$
$37$	8.53579	−	7.39630i	1.40328	−	1.21594i	0.944973	−	0.327149i	$-0.106088\pi$
$38$	4.18173	−	1.90973i	0.678365	−	0.309799i
$39$	4.36300	−	2.80393i	0.698639	−	0.448988i
$40$	−1.72734	−	1.41996i	−0.273117	−	0.224515i
$41$	5.06753	−	5.84824i	0.791415	−	0.913341i	−0.206463	−	0.978454i	$-0.566195\pi$
$41$	5.06753	−	5.84824i	0.791415	−	0.913341i	0.997878	+	0.0651131i	$0.0207408\pi$
$42$	−1.21974	−	4.15407i	−0.188211	−	0.640987i
$43$	4.40797	+	2.01305i	0.672208	+	0.306987i	0.722121	−	0.691766i	$-0.243167\pi$
$43$	4.40797	+	2.01305i	0.672208	+	0.306987i	−0.0499131	+	0.998754i	$0.515894\pi$
$44$	0.630409	+	4.38459i	0.0950377	+	0.661002i
$45$	−0.875790	+	2.05742i	−0.130555	+	0.306703i
$46$	3.59004	+	3.17987i	0.529323	+	0.468847i
$47$			9.46833i			1.38110i	0.723286	+	0.690549i	$0.242631\pi$
$47$			9.46833i			1.38110i	−0.723286	+	0.690549i	$0.757369\pi$
$48$	0.989821	−	0.142315i	0.142868	−	0.0205414i
$49$	−4.87866	+	10.6828i	−0.696952	+	1.52611i
$50$	2.48129	−	4.34088i	0.350907	−	0.613893i
$51$	0.0851574	−	0.0982769i	0.0119244	−	0.0137615i
$52$	1.46115	−	4.97622i	0.202625	−	0.690078i
$53$	3.26756	+	5.08442i	0.448833	+	0.698398i	0.989771	−	0.142664i	$-0.0455669\pi$
$53$	3.26756	+	5.08442i	0.448833	+	0.698398i	−0.540938	+	0.841063i	$0.681931\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	−9.42820	+	3.03631i	−1.27130	+	0.409416i
$56$	−3.64216	−	2.34067i	−0.486704	−	0.312786i
$57$	−4.55037	−	0.654244i	−0.602711	−	0.0866568i
$58$	3.62859	+	0.521712i	0.476457	+	0.0685042i
$59$	−4.79503	−	3.08158i	−0.624260	−	0.401187i	0.189921	−	0.981799i	$-0.439177\pi$
$59$	−4.79503	−	3.08158i	−0.624260	−	0.401187i	−0.814180	+	0.580612i	$0.802813\pi$
$60$	0.685448	+	2.12842i	0.0884909	+	0.274778i
$61$	−0.903633	−	1.97868i	−0.115698	−	0.253344i	0.842920	−	0.538039i	$-0.180835\pi$
$61$	−0.903633	−	1.97868i	−0.115698	−	0.253344i	−0.958618	+	0.284695i	$0.908108\pi$
$62$	4.49217	+	6.98995i	0.570506	+	0.887725i
$63$	−1.21974	+	4.15407i	−0.153673	+	0.523364i
$64$	0.654861	−	0.755750i	0.0818576	−	0.0944687i
$65$	11.5179	+	1.35192i	1.42861	+	0.167685i
$66$	1.84015	−	4.02937i	0.226507	−	0.495982i
$67$	6.46450	−	0.929455i	0.789765	−	0.113551i	0.264383	−	0.964418i	$-0.414832\pi$
$67$	6.46450	−	0.929455i	0.789765	−	0.113551i	0.525382	+	0.850867i	$0.323923\pi$
$68$		−	0.130039i		−	0.0157695i
$69$	−1.30097	−	4.61600i	−0.156618	−	0.555702i
$70$	3.79168	−	8.90750i	0.453193	−	1.06465i
$71$	−0.336289	−	2.33894i	−0.0399101	−	0.277581i	0.960088	−	0.279699i	$-0.0902348\pi$
$71$	−0.336289	−	2.33894i	−0.0399101	−	0.277581i	−0.999998	+	0.00211837i	$0.999326\pi$
$72$	−0.909632	−	0.415415i	−0.107201	−	0.0489571i
$73$	0.190467	+	0.648670i	0.0222925	+	0.0759211i	0.969888	−	0.243551i	$-0.0783125\pi$
$73$	0.190467	+	0.648670i	0.0222925	+	0.0759211i	−0.947596	+	0.319473i	$0.896494\pi$
$74$	−7.39630	+	8.53579i	−0.859803	+	0.992265i
$75$	−4.43425	+	2.31029i	−0.512023	+	0.266770i
$76$	−3.86738	+	2.48541i	−0.443619	+	0.285096i
$77$	−17.4449	+	7.96684i	−1.98804	+	0.907906i
$78$	−3.91955	+	3.39631i	−0.443801	+	0.384556i
$79$	8.85021	+	5.68769i	0.995727	+	0.639915i	0.933661	−	0.358157i	$-0.116595\pi$
$79$	8.85021	+	5.68769i	0.995727	+	0.639915i	0.0620656	+	0.998072i	$0.480231\pi$
$80$	1.91184	+	1.15968i	0.213751	+	0.129656i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−4.18366	+	6.50989i	−0.462007	+	0.718898i
$83$	2.45486	−	2.12715i	0.269456	−	0.233485i	−0.509643	−	0.860386i	$-0.670222\pi$
$83$	2.45486	−	2.12715i	0.269456	−	0.233485i	0.779099	+	0.626901i	$0.215677\pi$
$84$	1.79852	+	3.93820i	0.196234	+	0.429693i
$85$	0.286645	−	0.0488381i	0.0310910	−	0.00529724i
$86$	−4.64959	−	1.36524i	−0.501378	−	0.147218i
$87$	−2.77050	−	2.40065i	−0.297029	−	0.257377i
$88$	−1.24798	−	4.25024i	−0.133036	−	0.453077i
$89$	−4.68820	+	10.2657i	−0.496948	+	1.08816i	0.480501	+	0.876994i	$0.340455\pi$
$89$	−4.68820	+	10.2657i	−0.496948	+	1.08816i	−0.977449	+	0.211170i	$0.932273\pi$
$90$	0.574074	−	2.16112i	0.0605127	−	0.227802i
$91$	22.4538			2.35380
$92$	−4.00604	−	2.63659i	−0.417659	−	0.274884i
$93$		−	8.30897i		−	0.861600i
$94$	−1.34748	−	9.37195i	−0.138982	−	0.966643i
$95$	−6.93106	−	7.59144i	−0.711111	−	0.778865i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	−5.09682	−	4.41642i	−0.517504	−	0.448419i	0.356531	−	0.934284i	$-0.383960\pi$
$97$	−5.09682	−	4.41642i	−0.517504	−	0.448419i	−0.874034	+	0.485864i	$0.838505\pi$
$98$	3.30869	−	11.2683i	0.334228	−	1.13828i
$99$	−3.72648	+	2.39486i	−0.374525	+	0.240693i
$100$	−1.83826	+	4.64982i	−0.183826	+	0.464982i
$101$	7.83312	+	9.03990i	0.779424	+	0.899504i	0.997068	−	0.0765246i	$-0.0243824\pi$
$101$	7.83312	+	9.03990i	0.779424	+	0.899504i	−0.217643	+	0.976028i	$0.569837\pi$
$102$	−0.0703044	+	0.109396i	−0.00696117	+	0.0108318i
$103$	12.0663	+	1.73487i	1.18893	+	0.170942i	0.708253	−	0.705959i	$-0.249484\pi$
$103$	12.0663	+	1.73487i	1.18893	+	0.170942i	0.480672	+	0.876900i	$0.340393\pi$
$104$	−0.738088	+	5.13352i	−0.0723755	+	0.503383i
$105$	−8.00552	+	5.44352i	−0.781259	+	0.531233i
$106$	−3.95788	−	4.56764i	−0.384424	−	0.443649i
$107$	−14.2426	+	6.50436i	−1.37688	+	0.628800i	−0.959959	−	0.280142i	$-0.909619\pi$
$107$	−14.2426	+	6.50436i	−1.37688	+	0.628800i	−0.416922	+	0.908942i	$0.636891\pi$
$108$	0.540641	+	0.841254i	0.0520232	+	0.0809497i
$109$	−8.36349	−	2.45574i	−0.801077	−	0.235217i	−0.144528	−	0.989501i	$-0.546166\pi$
$109$	−8.36349	−	2.45574i	−0.801077	−	0.235217i	−0.656549	+	0.754283i	$0.727984\pi$
$110$	8.90012	−	4.34718i	0.848593	−	0.414487i
$111$	10.8370	−	3.18202i	1.02860	−	0.302024i
$112$	3.93820	+	1.79852i	0.372125	+	0.169944i
$113$	14.6613	−	2.10797i	1.37922	−	0.198301i	0.587516	−	0.809212i	$-0.300106\pi$
$113$	14.6613	−	2.10797i	1.37922	−	0.198301i	0.791699	+	0.610911i	$0.209197\pi$
$114$	4.59716			0.430564
$115$	4.30732	−	9.82075i	0.401659	−	0.915789i
$116$	−3.66590			−0.340370
$117$	5.13352	−	0.738088i	0.474594	−	0.0682363i
$118$	5.18478	+	2.36781i	0.477297	+	0.217974i
$119$	0.540191	−	0.158614i	0.0495192	−	0.0145402i
$120$	−0.981376	−	2.00920i	−0.0895870	−	0.183414i
$121$	−8.27278	−	2.42911i	−0.752071	−	0.220828i
$122$	1.17603	+	1.82994i	0.106473	+	0.165675i
$123$	7.03903	−	3.21462i	0.634688	−	0.289852i
$124$	−5.44122	−	6.27950i	−0.488636	−	0.563916i
$125$	−10.9400	−	2.30577i	−0.978503	−	0.206234i
$126$	0.616144	−	4.28537i	0.0548905	−	0.381771i
$127$	0.165368	+	0.0237764i	0.0146741	+	0.00210981i	0.149648	−	0.988739i	$-0.452186\pi$
$127$	0.165368	+	0.0237764i	0.0146741	+	0.00210981i	−0.134974	+	0.990849i	$0.543095\pi$
$128$	−0.540641	+	0.841254i	−0.0477863	+	0.0743570i
$129$	3.17337	+	3.66227i	0.279400	+	0.322445i
$130$	−11.5930	+	0.301002i	−1.01678	+	0.0263996i
$131$	11.4101	−	7.33283i	0.996905	−	0.640672i	0.0629330	−	0.998018i	$-0.479955\pi$
$131$	11.4101	−	7.33283i	0.996905	−	0.640672i	0.933972	+	0.357346i	$0.116318\pi$
$132$	−1.24798	+	4.25024i	−0.108623	+	0.369936i
$133$	−15.0418	−	13.0338i	−1.30429	−	1.13017i
$134$	−6.26643	+	1.83999i	−0.541337	+	0.158951i
$135$	−1.65133	+	1.50768i	−0.142124	+	0.129761i
$136$	0.0185065	+	0.128715i	0.00158692	+	0.0110373i
$137$		−	17.0033i		−	1.45269i	−0.687331	−	0.726345i	$-0.741218\pi$
$137$		−	17.0033i		−	1.45269i	0.687331	−	0.726345i	$-0.258782\pi$
$138$	1.94465	+	4.38387i	0.165540	+	0.373180i
$139$	−1.40019			−0.118763			−0.0593814	−	0.998235i	$-0.518913\pi$
$139$	−1.40019			−0.118763			−0.0593814	+	0.998235i	$0.518913\pi$
$140$	−2.48542	+	9.35644i	−0.210056	+	0.790764i
$141$	−3.93329	+	8.61269i	−0.331242	+	0.725320i
$142$	0.665731	+	2.26727i	0.0558669	+	0.190265i
$143$	17.3623	+	15.0445i	1.45191	+	1.25809i
$144$	0.959493	+	0.281733i	0.0799577	+	0.0234777i
$145$	−1.37679	−	8.08076i	−0.114336	−	0.671070i
$146$	−0.280844	−	0.614962i	−0.0232428	−	0.0508946i
$147$	−8.87557	+	7.69073i	−0.732045	+	0.634321i
$148$	6.10625	−	9.50151i	0.501931	−	0.781019i
$149$	1.48561	−	10.3326i	0.121706	−	0.846482i	−0.833917	−	0.551890i	$-0.813907\pi$
$149$	1.48561	−	10.3326i	0.121706	−	0.846482i	0.955623	−	0.294593i	$-0.0951839\pi$
$150$	4.06032	−	2.91784i	0.331524	−	0.238240i
$151$	−1.26507	−	0.813014i	−0.102950	−	0.0661621i	0.488153	−	0.872758i	$-0.337671\pi$
$151$	−1.26507	−	0.813014i	−0.102950	−	0.0661621i	−0.591103	+	0.806596i	$0.701307\pi$
$152$	3.47430	−	3.01050i	0.281803	−	0.244184i
$153$	0.118288	−	0.0540201i	0.00956299	−	0.00436727i
$154$	16.1336	−	10.3684i	1.30008	−	0.835511i
$155$	11.7984	−	14.3525i	0.947669	−	1.15282i
$156$	3.39631	−	3.91955i	0.271922	−	0.313815i
$157$	4.00150	+	13.6279i	0.319355	+	1.08762i	0.950181	+	0.311698i	$0.100898\pi$
$157$	4.00150	+	13.6279i	0.319355	+	1.08762i	−0.630827	+	0.775924i	$0.717284\pi$
$158$	−9.56957	−	4.37028i	−0.761314	−	0.347681i
$159$	0.860131	+	5.98234i	0.0682128	+	0.474430i
$160$	−2.05742	−	0.875790i	−0.162654	−	0.0692373i
$161$	6.06623	−	19.8573i	0.478086	−	1.56498i
$162$		−	1.00000i		−	0.0785674i
$163$	−5.35398	+	0.769786i	−0.419356	+	0.0602943i	−0.348763	−	0.937211i	$-0.613398\pi$
$163$	−5.35398	+	0.769786i	−0.419356	+	0.0602943i	−0.0705929	+	0.997505i	$0.522489\pi$
$164$	3.21462	−	7.03903i	0.251019	−	0.549656i
$165$	−9.83752	−	1.15469i	−0.765850	−	0.0898925i
$166$	−2.12715	+	2.45486i	−0.165099	+	0.190534i
$167$	−2.04558	+	6.96662i	−0.158292	+	0.539093i	−1.00000		0.000840578i	$-0.999732\pi$
$167$	−2.04558	+	6.96662i	−0.158292	+	0.539093i	0.841708	+	0.539933i	$0.181551\pi$
$168$	−2.34067	−	3.64216i	−0.180587	−	0.280999i
$169$	−5.77334	−	12.6418i	−0.444103	−	0.972450i
$170$	−0.276777	+	0.0891349i	−0.0212278	+	0.00683634i
$171$	−3.86738	−	2.48541i	−0.295746	−	0.190064i
$172$	4.79655	+	0.689640i	0.365734	+	0.0525846i
$173$	−3.33220	−	0.479098i	−0.253342	−	0.0364251i	0.0144735	−	0.999895i	$-0.495393\pi$
$173$	−3.33220	−	0.479098i	−0.253342	−	0.0364251i	−0.267816	+	0.963470i	$0.586302\pi$
$174$	3.08395	+	1.98194i	0.233794	+	0.150250i
$175$	−21.5579	−	1.96466i	−1.62962	−	0.148515i
$176$	1.84015	+	4.02937i	0.138707	+	0.303726i
$177$	−3.08158	−	4.79503i	−0.231626	−	0.360416i
$178$	3.17951	−	10.8284i	0.238315	−	0.811625i
$179$	5.11153	−	5.89903i	0.382054	−	0.440914i	−0.531853	−	0.846836i	$-0.678504\pi$
$179$	5.11153	−	5.89903i	0.382054	−	0.440914i	0.913907	+	0.405923i	$0.133050\pi$
$180$	−0.260671	+	2.22082i	−0.0194293	+	0.165530i
$181$	4.65068	−	10.1836i	0.345682	−	0.756939i	−0.654317	−	0.756220i	$-0.727044\pi$
$181$	4.65068	−	10.1836i	0.345682	−	0.756939i	1.00000		0.000718616i	$-0.000228743\pi$
$182$	−22.2253	+	3.19551i	−1.64745	+	0.236867i
$183$		−	2.17525i		−	0.160799i
$184$	4.34049	+	2.03964i	0.319985	+	0.150364i
$185$	23.2375	+	9.89159i	1.70846	+	0.727244i
$186$	1.18249	+	8.22440i	0.0867044	+	0.603042i
$187$	0.523976	+	0.239292i	0.0383169	+	0.0174987i
$188$	2.66754	+	9.08479i	0.194550	+	0.662577i
$189$	−2.83518	+	3.27197i	−0.206229	+	0.238001i
$190$	7.94088	+	6.52778i	0.576092	+	0.473575i
$191$	4.34290	−	2.79101i	0.314241	−	0.201951i	−0.374007	−	0.927426i	$-0.622016\pi$
$191$	4.34290	−	2.79101i	0.314241	−	0.201951i	0.688248	+	0.725475i	$0.258380\pi$
$192$	0.909632	−	0.415415i	0.0656470	−	0.0299800i
$193$	10.6649	−	9.24120i	0.767677	−	0.665196i	−0.180272	−	0.983617i	$-0.557698\pi$
$193$	10.6649	−	9.24120i	0.767677	−	0.665196i	0.947950	+	0.318421i	$0.103152\pi$
$194$	5.67346	+	3.64611i	0.407331	+	0.261776i
$195$	9.91541	+	6.01444i	0.710057	+	0.430703i
$196$	−1.67135	+	11.6245i	−0.119382	+	0.830324i
$197$	12.5825	−	19.5787i	0.896465	−	1.39493i	−0.0221415	−	0.999755i	$-0.507048\pi$
$197$	12.5825	−	19.5787i	0.896465	−	1.39493i	0.918607	−	0.395173i	$-0.129315\pi$
$198$	3.34773	−	2.90082i	0.237913	−	0.206152i
$199$	−0.854686	−	1.87150i	−0.0605871	−	0.132667i	0.876917	−	0.480643i	$-0.159597\pi$
$199$	−0.854686	−	1.87150i	−0.0605871	−	0.132667i	−0.937504	+	0.347975i	$0.886869\pi$
$200$	1.15781	−	4.86410i	0.0818695	−	0.343944i
$201$	6.26643	+	1.83999i	0.442000	+	0.129783i
$202$	−9.03990	−	7.83312i	−0.636045	−	0.551136i
$203$	−4.47146	−	15.2284i	−0.313835	−	1.06882i
$204$	0.0540201	−	0.118288i	0.00378217	−	0.00828179i
$205$	16.7235	+	4.44237i	1.16802	+	0.310269i
$206$	−12.1904			−0.849342
$207$	0.734158	−	4.73931i	0.0510275	−	0.329404i
$208$		−	5.18630i		−	0.359606i
$209$	−2.89809	−	20.1567i	−0.200465	−	1.39427i
$210$	7.14934	−	6.52742i	0.493352	−	0.450435i
$211$	−8.24475	+	2.42088i	−0.567592	+	0.166660i	−0.552923	−	0.833232i	$-0.686488\pi$
$211$	−8.24475	+	2.42088i	−0.567592	+	0.166660i	−0.0146690	+	0.999892i	$0.504669\pi$
$212$	4.56764	+	3.95788i	0.313707	+	0.271829i
$213$	0.665731	−	2.26727i	0.0456152	−	0.155351i
$214$	13.1719	−	8.46509i	0.900415	−	0.578661i
$215$	0.281244	+	10.8321i	0.0191807	+	0.738740i
$216$	−0.654861	−	0.755750i	−0.0445576	−	0.0514222i
$217$	19.4486	−	30.2626i	1.32026	−	2.05436i
$218$	8.62785	+	1.24050i	0.584352	+	0.0840171i
$219$	−0.0962127	+	0.669174i	−0.00650145	+	0.0452186i
$220$	−8.19086	+	5.56955i	−0.552228	+	0.375499i
$221$	−0.441652	−	0.509694i	−0.0297087	−	0.0342857i
$222$	−10.2738	+	4.69189i	−0.689533	+	0.314899i
$223$	0.0747794	+	0.116359i	0.00500760	+	0.00779197i	0.843748	−	0.536739i	$-0.180344\pi$
$223$	0.0747794	+	0.116359i	0.00500760	+	0.00779197i	−0.838741	+	0.544531i	$0.816708\pi$
$224$	−4.15407	−	1.21974i	−0.277555	−	0.0814976i
$225$	−4.99326	+	0.259465i	−0.332884	+	0.0172977i
$226$	−14.2120	+	4.17303i	−0.945370	+	0.277586i
$227$	−20.9240	−	9.55568i	−1.38878	−	0.634233i	−0.426047	−	0.904701i	$-0.640094\pi$
$227$	−20.9240	−	9.55568i	−1.38878	−	0.634233i	−0.962729	+	0.270468i	$0.912822\pi$
$228$	−4.55037	+	0.654244i	−0.301356	+	0.0433284i
$229$	−24.7397			−1.63484			−0.817422	−	0.576039i	$-0.804598\pi$
$229$	−24.7397			−1.63484			−0.817422	+	0.576039i	$0.804598\pi$
$230$	−2.86583	+	10.3338i	−0.188968	+	0.681389i
$231$	−19.1780			−1.26182
$232$	3.62859	−	0.521712i	0.238228	−	0.0342521i
$233$	−2.04958	−	0.936013i	−0.134273	−	0.0613202i	0.347146	−	0.937811i	$-0.387151\pi$
$233$	−2.04958	−	0.936013i	−0.134273	−	0.0613202i	−0.481418	+	0.876491i	$0.659878\pi$
$234$	−4.97622	+	1.46115i	−0.325306	+	0.0955184i
$235$	−19.0238	+	9.29199i	−1.24098	+	0.606143i
$236$	−5.46898	−	1.60584i	−0.356000	−	0.104531i
$237$	5.68769	+	8.85021i	0.369455	+	0.574883i
$238$	−0.512119	+	0.233877i	−0.0331958	+	0.0151600i
$239$	1.57070	+	1.81268i	0.101600	+	0.117253i	0.804272	−	0.594261i	$-0.202555\pi$
$239$	1.57070	+	1.81268i	0.101600	+	0.117253i	−0.702672	+	0.711514i	$0.748010\pi$
$240$	1.25733	+	1.84909i	0.0811601	+	0.119358i
$241$	−0.872905	+	6.07119i	−0.0562288	+	0.391080i	0.942200	+	0.335050i	$0.108753\pi$
$241$	−0.872905	+	6.07119i	−0.0562288	+	0.391080i	−0.998429	+	0.0560296i	$0.982156\pi$
$242$	8.53427	+	1.22704i	0.548604	+	0.0788773i
$243$	−0.540641	+	0.841254i	−0.0346821	+	0.0539664i
$244$	−1.42449	−	1.64395i	−0.0911935	−	0.105243i
$245$	−26.2517	+	0.681599i	−1.67716	+	0.0435458i
$246$	−6.50989	+	4.18366i	−0.415056	+	0.266740i
$247$	−6.71715	+	22.8765i	−0.427402	+	1.45560i
$248$	6.27950	+	5.44122i	0.398749	+	0.345518i
$249$	3.11667	−	0.915137i	0.197511	−	0.0579944i
$250$	11.1568	+	0.725375i	0.705617	+	0.0458767i
$251$	0.669302	+	4.65509i	0.0422459	+	0.293827i	0.999981	+	0.00617495i	$0.00196556\pi$
$251$	0.669302	+	4.65509i	0.0422459	+	0.293827i	−0.957735	+	0.287652i	$0.907125\pi$
$252$			4.32944i			0.272729i
$253$	17.9956	−	11.2901i	1.13137	−	0.709804i
$254$	−0.167069			−0.0104828
$255$	0.281030	+	0.0746520i	0.0175988	+	0.00467489i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−7.38123	−	25.1382i	−0.460428	−	1.56808i	−0.783307	−	0.621635i	$-0.786469\pi$
$257$	−7.38123	−	25.1382i	−0.460428	−	1.56808i	0.322879	−	0.946440i	$-0.395349\pi$
$258$	−3.66227	−	3.17337i	−0.228003	−	0.197566i
$259$	46.9180	+	13.7764i	2.91534	+	0.856022i
$260$	11.4322	−	1.94780i	0.708994	−	0.120797i
$261$	−1.52287	−	3.33462i	−0.0942633	−	0.206408i
$262$	−10.2504	+	8.88202i	−0.633271	+	0.548733i
$263$	−12.5138	+	19.4718i	−0.771633	+	1.20068i	0.203502	+	0.979074i	$0.434768\pi$
$263$	−12.5138	+	19.4718i	−0.771633	+	1.20068i	−0.975135	+	0.221610i	$0.928869\pi$
$264$	0.630409	−	4.38459i	0.0387990	−	0.269853i
$265$	−7.00893	+	11.5549i	−0.430555	+	0.709813i
$266$	16.7436	+	10.7605i	1.02662	+	0.659766i
$267$	−8.52907	+	7.39048i	−0.521971	+	0.452290i
$268$	5.94079	−	2.71307i	0.362891	−	0.165727i
$269$	8.98322	−	5.77316i	0.547716	−	0.351996i	−0.237334	−	0.971428i	$-0.576273\pi$
$269$	8.98322	−	5.77316i	0.547716	−	0.351996i	0.785050	+	0.619432i	$0.212637\pi$
$270$	1.41996	−	1.72734i	0.0864159	−	0.105123i
$271$	−15.7156	+	18.1368i	−0.954656	+	1.10173i	0.0400732	+	0.999197i	$0.487241\pi$
$271$	−15.7156	+	18.1368i	−0.954656	+	1.10173i	−0.994729	+	0.102535i	$0.967305\pi$
$272$	−0.0366362	−	0.124771i	−0.00222140	−	0.00756538i
$273$	20.4247	+	9.32765i	1.23616	+	0.564535i
$274$	2.41982	+	16.8302i	0.146187	+	1.01675i
$275$	−15.3532	−	15.9634i	−0.925832	−	0.962630i
$276$	−2.54875	−	4.06250i	−0.153416	−	0.244534i
$277$			21.0021i			1.26189i	0.775826	+	0.630947i	$0.217334\pi$
$277$			21.0021i			1.26189i	−0.775826	+	0.630947i	$0.782666\pi$
$278$	1.38594	−	0.199268i	0.0831233	−	0.0119513i
$279$	3.45167	−	7.55811i	0.206646	−	0.452492i
$280$	1.12856	−	9.61492i	0.0674445	−	0.574601i
$281$	−10.4306	+	12.0375i	−0.622235	+	0.718098i	−0.976130	−	0.217188i	$-0.930312\pi$
$281$	−10.4306	+	12.0375i	−0.622235	+	0.718098i	0.353895	+	0.935285i	$0.384857\pi$
$282$	2.66754	−	9.08479i	0.158849	−	0.540992i
$283$	17.1654	+	26.7098i	1.02038	+	1.58774i	0.788543	+	0.614979i	$0.210836\pi$
$283$	17.1654	+	26.7098i	1.02038	+	1.58774i	0.231832	+	0.972756i	$0.425528\pi$
$284$	−0.981622	−	2.14945i	−0.0582485	−	0.127547i
$285$	−3.15111	−	9.78468i	−0.186656	−	0.579594i
$286$	−19.3267	−	12.4205i	−1.14281	−	0.734439i
$287$	33.1616	+	4.76792i	1.95747	+	0.281442i
$288$	−0.989821	−	0.142315i	−0.0583258	−	0.00838598i
$289$	14.2871	+	9.18175i	0.840417	+	0.540103i
$290$	2.51278	+	7.80257i	0.147556	+	0.458183i
$291$	−2.80158	−	6.13461i	−0.164232	−	0.359617i
$292$	0.365503	+	0.568734i	0.0213895	+	0.0332826i
$293$	5.59145	−	19.0427i	0.326656	−	1.11249i	−0.618477	−	0.785803i	$-0.712250\pi$
$293$	5.59145	−	19.0427i	0.326656	−	1.11249i	0.945133	−	0.326686i	$-0.105932\pi$
$294$	7.69073	−	8.87557i	0.448532	−	0.517634i
$295$	1.48579	−	12.6584i	0.0865061	−	0.736999i
$296$	−4.69189	+	10.2738i	−0.272711	+	0.597153i
$297$	−4.38459	+	0.630409i	−0.254420	+	0.0365800i
$298$			10.4389i			0.604708i
$299$	−24.6566	+	3.27151i	−1.42593	+	0.189196i
$300$	−3.60374	+	3.46598i	−0.208062	+	0.200109i
$301$	2.98576	+	20.7664i	0.172096	+	1.19696i
$302$	1.36790	+	0.624700i	0.0787139	+	0.0359474i
$303$	3.36994	+	11.4770i	0.193598	+	0.659335i
$304$	−3.01050	+	3.47430i	−0.172664	+	0.199265i
$305$	3.08877	−	3.75741i	0.176862	−	0.215149i
$306$	−0.109396	+	0.0703044i	−0.00625374	+	0.00401903i
$307$	14.0742	−	6.42745i	0.803255	−	0.366834i	0.0288971	−	0.999582i	$-0.490800\pi$
$307$	14.0742	−	6.42745i	0.803255	−	0.366834i	0.774358	+	0.632748i	$0.218073\pi$
$308$	−14.4938	+	12.5589i	−0.825860	+	0.715612i
$309$	10.2552	+	6.59060i	0.583397	+	0.374926i
$310$	−9.63573	+	15.8855i	−0.547273	+	0.902233i
$311$	2.03509	−	14.1544i	0.115399	−	0.802621i	−0.847119	−	0.531404i	$-0.821665\pi$
$311$	2.03509	−	14.1544i	0.115399	−	0.802621i	0.962518	−	0.271217i	$-0.0874262\pi$
$312$	−2.80393	+	4.36300i	−0.158741	+	0.247006i
$313$	−21.6139	+	18.7286i	−1.22169	+	1.05860i	−0.225252	+	0.974301i	$0.572320\pi$
$313$	−21.6139	+	18.7286i	−1.22169	+	1.05860i	−0.996440	+	0.0843014i	$0.973134\pi$
$314$	−5.90022	−	12.9197i	−0.332969	−	0.729100i
$315$	−9.54340	+	1.62599i	−0.537710	+	0.0916141i
$316$	10.0941	+	2.96390i	0.567839	+	0.166733i
$317$	−20.1190	−	17.4332i	−1.12999	−	0.979145i	−0.130070	−	0.991505i	$-0.541520\pi$
$317$	−20.1190	−	17.4332i	−1.12999	−	0.979145i	−0.999924	+	0.0123598i	$0.996066\pi$
$318$	−1.70275	−	5.79904i	−0.0954855	−	0.325194i
$319$	6.74582	−	14.7713i	0.377694	−	0.827033i
$320$	2.16112	+	0.574074i	0.120810	+	0.0320917i
$321$	−15.6575			−0.873917
$322$	−3.17849	+	20.5185i	−0.177130	+	1.14345i
$323$			0.597810i			0.0332630i
$324$	0.142315	+	0.989821i	0.00790638	+	0.0549901i
$325$	8.58707	+	24.4685i	0.476325	+	1.35727i
$326$	5.18993	−	1.52390i	0.287444	−	0.0844011i
$327$	−6.58754	−	5.70814i	−0.364292	−	0.315661i
$328$	−2.18014	+	7.42487i	−0.120378	+	0.409970i
$329$	−34.4852	+	22.1623i	−1.90123	+	1.22185i
$330$	9.90172	−	0.257088i	0.545072	−	0.0141523i
$331$	−2.88719	−	3.33200i	−0.158694	−	0.183143i	0.670834	−	0.741607i	$-0.265936\pi$
$331$	−2.88719	−	3.33200i	−0.158694	−	0.183143i	−0.829529	+	0.558464i	$0.811391\pi$
$332$	1.75613	−	2.73260i	0.0963804	−	0.149971i
$333$	11.1795	+	1.60737i	0.612633	+	0.0880834i
$334$	1.03331	−	7.18682i	0.0565402	−	0.393245i
$335$	8.21158	+	12.0764i	0.448646	+	0.659802i
$336$	2.83518	+	3.27197i	0.154672	+	0.178501i
$337$	−28.8079	+	13.1561i	−1.56927	+	0.716661i	−0.994798	−	0.101864i	$-0.967519\pi$
$337$	−28.8079	+	13.1561i	−1.56927	+	0.716661i	−0.574470	+	0.818525i	$0.694792\pi$
$338$	7.51369	+	11.6915i	0.408691	+	0.635936i
$339$	14.2120	+	4.17303i	0.771892	+	0.226648i
$340$	0.261275	−	0.127617i	0.0141696	−	0.00692101i
$341$	35.3152	−	10.3695i	1.91242	−	0.561538i
$342$	4.18173	+	1.90973i	0.226122	+	0.103266i
$343$	−20.3301	+	2.92303i	−1.09772	+	0.157829i
$344$	−4.84588			−0.261272
$345$	7.99776	−	7.14394i	0.430585	−	0.384617i
$346$	3.36646			0.180982
$347$	28.1428	−	4.04632i	1.51078	−	0.217218i	0.663427	−	0.748241i	$-0.269101\pi$
$347$	28.1428	−	4.04632i	1.51078	−	0.217218i	0.847357	+	0.531023i	$0.178192\pi$
$348$	−3.33462	−	1.52287i	−0.178754	−	0.0816344i
$349$	−18.4777	+	5.42555i	−0.989089	+	0.290423i	−0.735971	−	0.677013i	$-0.763274\pi$
$349$	−18.4777	+	5.42555i	−0.989089	+	0.290423i	−0.253118	+	0.967435i	$0.581456\pi$
$350$	21.6180	−	1.12334i	1.15553	−	0.0600450i
$351$	4.97622	+	1.46115i	0.265611	+	0.0779905i
$352$	−2.39486	−	3.72648i	−0.127647	−	0.198622i
$353$	21.1927	−	9.67839i	1.12798	−	0.515129i	0.238058	−	0.971251i	$-0.423489\pi$
$353$	21.1927	−	9.67839i	1.12798	−	0.515129i	0.889917	+	0.456122i	$0.150762\pi$
$354$	3.73262	+	4.30767i	0.198386	+	0.228950i
$355$	4.36938	−	2.97105i	0.231903	−	0.157687i
$356$	−1.60610	+	11.1707i	−0.0851234	+	0.592046i
$357$	0.557266	+	0.0801227i	0.0294936	+	0.00424054i
$358$	−4.21999	+	6.56643i	−0.223033	+	0.347047i
$359$	2.58966	+	2.98863i	0.136677	+	0.157734i	0.819962	−	0.572418i	$-0.193995\pi$
$359$	2.58966	+	2.98863i	0.136677	+	0.157734i	−0.683285	+	0.730152i	$0.739449\pi$
$360$	−0.0580378	−	2.23531i	−0.00305886	−	0.117811i
$361$	1.79514	−	1.15367i	0.0944813	−	0.0607194i
$362$	−3.15407	+	10.7418i	−0.165774	+	0.564575i
$363$	−6.51609	−	5.64623i	−0.342006	−	0.296350i
$364$	21.5443	−	6.32597i	1.12923	−	0.331571i
$365$	−1.11639	+	1.01928i	−0.0584346	+	0.0533514i
$366$	0.309571	+	2.15311i	0.0161815	+	0.112545i
$367$			11.7978i			0.615841i	0.951412	+	0.307921i	$0.0996331\pi$
$367$			11.7978i			0.615841i	−0.951412	+	0.307921i	$0.900367\pi$
$368$	−4.58658	−	1.40116i	−0.239092	−	0.0730404i
$369$	7.73833			0.402841
$370$	−24.4087	−	6.48386i	−1.26895	−	0.337080i
$371$	−10.8700	+	23.8019i	−0.564341	+	1.23573i
$372$	−2.34091	−	7.97240i	−0.121370	−	0.413350i
$373$	1.12204	+	0.972249i	0.0580968	+	0.0503411i	0.683425	−	0.730021i	$-0.260490\pi$
$373$	1.12204	+	0.972249i	0.0580968	+	0.0503411i	−0.625328	+	0.780362i	$0.715035\pi$
$374$	−0.552697	−	0.162287i	−0.0285793	−	0.00839164i
$375$	−8.99352	−	6.64204i	−0.464423	−	0.342993i
$376$	−3.93329	−	8.61269i	−0.202844	−	0.444166i
$377$	−14.3687	+	12.4505i	−0.740024	+	0.641235i
$378$	2.34067	−	3.64216i	0.120391	−	0.187332i
$379$	4.83760	−	33.6463i	0.248491	−	1.72829i	−0.358452	−	0.933548i	$-0.616695\pi$
$379$	4.83760	−	33.6463i	0.248491	−	1.72829i	0.606943	−	0.794745i	$-0.292396\pi$
$380$	−8.78906	−	5.33123i	−0.450869	−	0.273486i
$381$	0.140547	+	0.0903243i	0.00720046	+	0.00462745i
$382$	−3.90150	+	3.38067i	−0.199618	+	0.172970i
$383$	7.87154	−	3.59481i	0.402217	−	0.183686i	−0.204027	−	0.978965i	$-0.565403\pi$
$383$	7.87154	−	3.59481i	0.402217	−	0.183686i	0.606244	+	0.795279i	$0.292676\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	−33.1271	−	27.2320i	−1.68831	−	1.38787i
$386$	−9.24120	+	10.6649i	−0.470365	+	0.542830i
$387$	1.36524	+	4.64959i	0.0693991	+	0.236352i
$388$	−6.13461	−	2.80158i	−0.311438	−	0.142229i
$389$	0.163107	+	1.13444i	0.00826986	+	0.0575181i	0.993538	−	0.113496i	$-0.0362048\pi$
$389$	0.163107	+	1.13444i	0.00826986	+	0.0575181i	−0.985269	+	0.171014i	$0.945296\pi$
$390$	−10.6704	−	4.54212i	−0.540318	−	0.229999i
$391$	−0.570074	+	0.252880i	−0.0288299	+	0.0127887i
$392$		−	11.7441i		−	0.593165i
$393$	13.4252	−	1.93025i	0.677210	−	0.0973681i
$394$	−9.66807	+	21.1701i	−0.487071	+	1.06654i
$395$	−2.74233	+	23.3636i	−0.137982	+	1.17555i
$396$	−2.90082	+	3.34773i	−0.145772	+	0.168230i
$397$	3.28363	−	11.1830i	0.164801	−	0.561260i	−0.835136	−	0.550043i	$-0.814611\pi$
$397$	3.28363	−	11.1830i	0.164801	−	0.561260i	0.999937	−	0.0112170i	$-0.00357055\pi$
$398$	1.11233	+	1.73082i	0.0557560	+	0.0867581i
$399$	−8.26806	−	18.1045i	−0.413921	−	0.906360i
$400$	−0.453791	+	4.97936i	−0.0226896	+	0.248968i
$401$	4.53485	+	2.91437i	0.226460	+	0.145537i	0.648951	−	0.760830i	$-0.275208\pi$
$401$	4.53485	+	2.91437i	0.226460	+	0.145537i	−0.422491	+	0.906367i	$0.638844\pi$
$402$	−6.46450	−	0.929455i	−0.322420	−	0.0463570i
$403$	−42.6542	−	6.13275i	−2.12476	−	0.305494i
$404$	10.0627	+	6.46688i	0.500636	+	0.321739i
$405$	−2.12842	+	0.685448i	−0.105762	+	0.0340602i
$406$	6.59318	+	14.4370i	0.327214	+	0.716499i
$407$	27.0487	+	42.0886i	1.34075	+	2.08626i
$408$	−0.0366362	+	0.124771i	−0.00181376	+	0.00617711i
$409$	−10.9905	+	12.6838i	−0.543447	+	0.627171i	−0.959344	−	0.282240i	$-0.908922\pi$
$409$	−10.9905	+	12.6838i	−0.543447	+	0.627171i	0.415897	+	0.909412i	$0.363468\pi$
$410$	−17.1854	−	2.01716i	−0.848729	−	0.0996205i
$411$	7.06342	−	15.4667i	0.348413	−	0.762918i
$412$	12.0663	−	1.73487i	0.594463	−	0.0854708i
$413$		−	24.6772i		−	1.21429i
$414$	−0.0522116	+	4.79555i	−0.00256606	+	0.235688i
$415$	6.68302	+	2.84478i	0.328056	+	0.139645i
$416$	0.738088	+	5.13352i	0.0361877	+	0.251691i
$417$	−1.27366	−	0.581662i	−0.0623715	−	0.0284841i
$418$	5.73718	+	19.5391i	0.280615	+	0.955686i
$419$	−3.01980	+	3.48503i	−0.147527	+	0.170255i	−0.824703	−	0.565566i	$-0.808658\pi$
$419$	−3.01980	+	3.48503i	−0.147527	+	0.170255i	0.677176	+	0.735821i	$0.263203\pi$
$420$	−6.14762	+	7.47844i	−0.299973	+	0.364910i
$421$	26.0890	−	16.7664i	1.27150	−	0.817144i	0.281686	−	0.959507i	$-0.409106\pi$
$421$	26.0890	−	16.7664i	1.27150	−	0.817144i	0.989815	+	0.142363i	$0.0454700\pi$
$422$	7.81630	−	3.56959i	0.380492	−	0.173765i
$423$	−7.15569	+	6.20044i	−0.347921	+	0.301476i
$424$	−5.08442	−	3.26756i	−0.246921	−	0.158687i
$425$	0.379433	+	0.528000i	0.0184052	+	0.0256118i
$426$	−0.336289	+	2.33894i	−0.0162932	+	0.113322i
$427$	5.09156	−	7.92262i	0.246398	−	0.383402i
$428$	−11.8332	+	10.2535i	−0.571977	+	0.495621i
$429$	9.54360	+	20.8976i	0.460769	+	1.00894i
$430$	−1.81994	−	10.6818i	−0.0877655	−	0.515121i
$431$	2.18634	+	0.641967i	0.105312	+	0.0309225i	0.333964	−	0.942586i	$-0.391614\pi$
$431$	2.18634	+	0.641967i	0.105312	+	0.0309225i	−0.228652	+	0.973508i	$0.573432\pi$
$432$	0.755750	+	0.654861i	0.0363610	+	0.0315070i
$433$	−11.1407	−	37.9416i	−0.535386	−	1.82336i	−0.566805	−	0.823852i	$-0.691821\pi$
$433$	−11.1407	−	37.9416i	−0.535386	−	1.82336i	0.0314192	−	0.999506i	$-0.489997\pi$
$434$	−14.9438	+	32.7224i	−0.717326	+	1.57072i
$435$	2.10450	−	7.92245i	0.100903	−	0.379852i
$436$	−8.71657			−0.417448
$437$	18.4164	+	12.1208i	0.880977	+	0.579818i
$438$		−	0.676055i		−	0.0323032i
$439$	4.84726	+	33.7134i	0.231347	+	1.60905i	0.692286	+	0.721623i	$0.256604\pi$
$439$	4.84726	+	33.7134i	0.231347	+	1.60905i	−0.460939	+	0.887432i	$0.652487\pi$
$440$	7.31486	−	6.67854i	0.348722	−	0.318387i
$441$	−11.2683	+	3.30869i	−0.536588	+	0.157556i
$442$	0.509694	+	0.441652i	0.0242437	+	0.0210073i
$443$	4.12157	−	14.0368i	0.195821	−	0.666907i	−0.801776	−	0.597625i	$-0.796111\pi$
$443$	4.12157	−	14.0368i	0.195821	−	0.666907i	0.997597	−	0.0692816i	$-0.0220707\pi$
$444$	9.50151	−	6.10625i	0.450922	−	0.289790i
$445$	−25.2268	+	0.654990i	−1.19587	+	0.0310495i
$446$	−0.0905778	−	0.104532i	−0.00428898	−	0.00494975i
$447$	5.64369	−	8.78175i	0.266937	−	0.415362i
$448$	4.28537	+	0.616144i	0.202465	+	0.0291101i
$449$	1.11520	−	7.75640i	0.0526296	−	0.366047i	−0.946438	−	0.322884i	$-0.895347\pi$
$449$	1.11520	−	7.75640i	0.0526296	−	0.366047i	0.999068	−	0.0431628i	$-0.0137434\pi$
$450$	4.90551	−	0.967440i	0.231248	−	0.0456055i
$451$	22.4475	+	25.9058i	1.05701	+	1.21986i
$452$	13.4735	−	6.15314i	0.633740	−	0.289419i
$453$	−0.813014	−	1.26507i	−0.0381987	−	0.0594384i
$454$	22.0710	+	6.48062i	1.03584	+	0.304151i
$455$	22.0356	+	45.1143i	1.03305	+	2.11499i
$456$	4.41094	−	1.29517i	0.206561	−	0.0606519i
$457$	26.9106	+	12.2897i	1.25883	+	0.574887i	0.929323	−	0.369268i	$-0.120391\pi$
$457$	26.9106	+	12.2897i	1.25883	+	0.574887i	0.329503	+	0.944154i	$0.393119\pi$
$458$	24.4879	−	3.52082i	1.14424	−	0.164517i
$459$	0.130039			0.00606970
$460$	1.36601	−	10.6364i	0.0636908	−	0.495927i
$461$	−5.53416			−0.257752			−0.128876	−	0.991661i	$-0.541137\pi$
$461$	−5.53416			−0.257752			−0.128876	+	0.991661i	$0.541137\pi$
$462$	18.9828	−	2.72932i	0.883161	−	0.126979i
$463$	−13.2473	−	6.04986i	−0.615656	−	0.281161i	0.0830772	−	0.996543i	$-0.473525\pi$
$463$	−13.2473	−	6.04986i	−0.615656	−	0.281161i	−0.698733	+	0.715382i	$0.746252\pi$
$464$	−3.51741	+	1.03280i	−0.163291	+	0.0479467i
$465$	16.6944	−	8.15423i	0.774185	−	0.378143i
$466$	2.16193	+	0.634800i	0.100149	+	0.0294065i
$467$	−9.90652	−	15.4148i	−0.458419	−	0.713314i	0.532698	−	0.846305i	$-0.321178\pi$
$467$	−9.90652	−	15.4148i	−0.458419	−	0.713314i	−0.991117	+	0.132991i	$0.957542\pi$
$468$	4.71763	−	2.15447i	0.218072	−	0.0995904i
$469$	18.5165	+	21.3692i	0.855013	+	0.986738i
$470$	17.5078	−	11.9048i	0.807574	−	0.549127i
$471$	−2.02132	+	14.0586i	−0.0931377	+	0.647787i
$472$	5.64185	+	0.811175i	0.259687	+	0.0373374i
$473$	−11.6052	+	18.0581i	−0.533608	+	0.830311i
$474$	−6.88931	−	7.95069i	−0.316437	−	0.365187i
$475$	8.45077	−	21.3760i	0.387748	−	0.980796i
$476$	0.473622	−	0.304379i	0.0217085	−	0.0139512i
$477$	−1.70275	+	5.79904i	−0.0779636	+	0.265520i
$478$	−1.81268	−	1.57070i	−0.0829100	−	0.0718420i
$479$	0.555061	−	0.162981i	0.0253614	−	0.00744677i	−0.269027	−	0.963133i	$-0.586702\pi$
$479$	0.555061	−	0.162981i	0.0253614	−	0.00744677i	0.294389	+	0.955686i	$0.404884\pi$
$480$	−1.50768	−	1.65133i	−0.0688159	−	0.0753726i
$481$	−8.33631	−	57.9803i	−0.380103	−	2.64368i
$482$		−	6.13362i		−	0.279379i
$483$	13.7671	−	15.5429i	0.626424	−	0.707225i
$484$	−8.62203			−0.391910
$485$	3.87159	−	14.5747i	0.175800	−	0.661804i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	2.53374	+	8.62912i	0.114815	+	0.391023i	0.996770	−	0.0803104i	$-0.0255911\pi$
$487$	2.53374	+	8.62912i	0.114815	+	0.391023i	−0.881955	+	0.471333i	$0.843773\pi$
$488$	1.64395	+	1.42449i	0.0744180	+	0.0644835i
$489$	−5.18993	−	1.52390i	−0.234697	−	0.0689132i
$490$	25.8875	−	4.41067i	1.16948	−	0.199254i
$491$	−7.68195	−	16.8211i	−0.346682	−	0.759127i	−0.999998	−	0.00204183i	$-0.999350\pi$
$491$	−7.68195	−	16.8211i	−0.346682	−	0.759127i	0.653316	−	0.757085i	$-0.273377\pi$
$492$	5.84824	−	5.06753i	0.263659	−	0.228462i
$493$	−0.257729	+	0.401034i	−0.0116075	+	0.0180617i
$494$	3.39311	−	23.5996i	0.152663	−	1.06180i
$495$	−8.46885	−	5.13700i	−0.380646	−	0.230891i
$496$	−6.98995	−	4.49217i	−0.313858	−	0.201704i
$497$	7.73164	−	6.69951i	0.346812	−	0.300514i
$498$	−2.95471	+	1.34937i	−0.132404	+	0.0604667i
$499$	5.44176	−	3.49721i	0.243607	−	0.156557i	−0.413141	−	0.910667i	$-0.635568\pi$
$499$	5.44176	−	3.49721i	0.243607	−	0.156557i	0.656747	+	0.754111i	$0.271932\pi$
$500$	−11.1465	+	0.869784i	−0.498485	+	0.0388979i
$501$	−4.75476	+	5.48729i	−0.212427	+	0.245154i
$502$	−1.32498	−	4.51246i	−0.0591367	−	0.201401i
$503$	8.33024	+	3.80429i	0.371427	+	0.169625i	0.592379	−	0.805660i	$-0.298189\pi$
$503$	8.33024	+	3.80429i	0.371427	+	0.169625i	−0.220952	+	0.975285i	$0.570916\pi$
$504$	−0.616144	−	4.28537i	−0.0274452	−	0.190886i
$505$	−10.4758	+	24.6099i	−0.466166	+	1.09513i
$506$	−16.2056	+	13.7362i	−0.720428	+	0.610650i
$507$		−	13.8978i		−	0.617221i
$508$	0.165368	−	0.0237764i	0.00733704	−	0.00105491i
$509$	−6.14887	+	13.4641i	−0.272544	+	0.596787i	−0.995569	−	0.0940342i	$-0.970024\pi$
$509$	−6.14887	+	13.4641i	−0.272544	+	0.596787i	0.723025	+	0.690822i	$0.242751\pi$
$510$	−0.288793	−	0.0338974i	−0.0127880	−	0.00150100i
$511$	−1.91674	+	2.21204i	−0.0847916	+	0.0978547i
$512$	−0.281733	+	0.959493i	−0.0124509	+	0.0424040i
$513$	−2.48541	−	3.86738i	−0.109734	−	0.170749i
$514$	10.8836	+	23.8318i	0.480056	+	1.05118i
$515$	8.35585	+	25.9462i	0.368203	+	1.14332i
$516$	4.07661	+	2.61988i	0.179463	+	0.115334i
$517$	−41.5147	−	5.96892i	−1.82582	−	0.262513i
$518$	−48.4010	−	6.95902i	−2.12662	−	0.305762i
$519$	−2.83205	−	1.82005i	−0.124313	−	0.0798912i
$520$	−11.0386	+	3.55494i	−0.484076	+	0.155894i
$521$	−11.9923	−	26.2594i	−0.525390	−	1.15044i	−0.967358	−	0.253413i	$-0.918447\pi$
$521$	−11.9923	−	26.2594i	−0.525390	−	1.15044i	0.441968	−	0.897031i	$-0.354280\pi$
$522$	1.98194	+	3.08395i	0.0867470	+	0.134981i
$523$	−1.62971	+	5.55030i	−0.0712624	+	0.242697i	−0.987420	−	0.158122i	$-0.949456\pi$
$523$	−1.62971	+	5.55030i	−0.0712624	+	0.242697i	0.916157	+	0.400819i	$0.131274\pi$
$524$	8.88202	−	10.2504i	0.388013	−	0.447790i
$525$	−18.7936	−	10.7426i	−0.820219	−	0.468845i
$526$	9.61528	−	21.0545i	0.419246	−	0.918021i
$527$	−1.06949	+	0.153770i	−0.0465878	+	0.00669832i
$528$			4.42968i			0.192777i
$529$	−3.76813	+	22.6892i	−0.163832	+	0.986488i
$530$	5.29315	−	12.4348i	0.229920	−	0.540132i
$531$	−0.811175	−	5.64185i	−0.0352020	−	0.244835i
$532$	−18.1045	−	8.26806i	−0.784931	−	0.358466i
$533$	−11.3069	−	38.5076i	−0.489755	−	1.66795i
$534$	7.39048	−	8.52907i	0.319817	−	0.369089i
$535$	−27.0459	−	22.2330i	−1.16930	−	0.961216i
$536$	−5.49421	+	3.53091i	−0.237314	+	0.152512i
$537$	7.10016	−	3.24253i	0.306394	−	0.139926i
$538$	−8.07017	+	6.99285i	−0.347930	+	0.301483i
$539$	−43.7640	−	28.1254i	−1.88505	−	1.21145i
$540$	−1.15968	+	1.91184i	−0.0499046	+	0.0822727i
$541$	1.10210	−	7.66528i	0.0473830	−	0.329556i	−0.952318	−	0.305107i	$-0.901308\pi$
$541$	1.10210	−	7.66528i	0.0473830	−	0.329556i	0.999701	−	0.0244491i	$-0.00778315\pi$
$542$	12.9745	−	20.1888i	0.557304	−	0.867181i
$543$	8.46081	−	7.33134i	0.363088	−	0.314618i
$544$	0.0540201	+	0.118288i	0.00231609	+	0.00507154i
$545$	−3.27364	−	19.2140i	−0.140227	−	0.823036i
$546$	−21.5443	−	6.32597i	−0.922010	−	0.270726i
$547$	−33.9771	−	29.4414i	−1.45276	−	1.25882i	−0.907168	−	0.420769i	$-0.861760\pi$
$547$	−33.9771	−	29.4414i	−1.45276	−	1.25882i	−0.545590	−	0.838052i	$-0.683694\pi$
$548$	−4.79038	−	16.3145i	−0.204635	−	0.696923i
$549$	0.903633	−	1.97868i	0.0385661	−	0.0844480i
$550$	17.4687	+	13.6159i	0.744869	+	0.580586i
$551$	16.8527			0.717951
$552$	3.10096	+	3.65842i	0.131985	+	0.155713i
$553$			45.5469i			1.93685i
$554$	−2.98891	−	20.7883i	−0.126987	−	0.883212i
$555$	17.0285	+	18.6509i	0.722818	+	0.791687i
$556$	−1.34348	+	0.394480i	−0.0569761	+	0.0167297i
$557$	−4.92060	−	4.26372i	−0.208492	−	0.180660i	0.544355	−	0.838855i	$-0.316775\pi$
$557$	−4.92060	−	4.26372i	−0.208492	−	0.180660i	−0.752847	+	0.658195i	$0.771320\pi$
$558$	−2.34091	+	7.97240i	−0.0990985	+	0.337499i
$559$	21.1425	−	13.5875i	0.894235	−	0.574690i
$560$	0.251271	+	9.67766i	0.0106181	+	0.408956i
$561$	0.377220	+	0.435335i	0.0159262	+	0.0183798i
$562$	8.61128	−	13.3994i	0.363245	−	0.565220i
$563$	22.1368	+	3.18279i	0.932953	+	0.134138i	0.591996	−	0.805941i	$-0.298340\pi$
$563$	22.1368	+	3.18279i	0.932953	+	0.134138i	0.340957	+	0.940079i	$0.389249\pi$
$564$	−1.34748	+	9.37195i	−0.0567393	+	0.394630i
$565$	18.6236	+	27.3888i	0.783499	+	1.15225i
$566$	−20.7919	−	23.9951i	−0.873947	−	1.00859i
$567$	−3.93820	+	1.79852i	−0.165389	+	0.0755305i
$568$	1.27753	+	1.98787i	0.0536039	+	0.0834094i
$569$	−20.4960	−	6.01817i	−0.859237	−	0.252295i	−0.177705	−	0.984084i	$-0.556867\pi$
$569$	−20.4960	−	6.01817i	−0.859237	−	0.252295i	−0.681531	+	0.731789i	$0.738686\pi$
$570$	4.51155	+	9.23663i	0.188968	+	0.386880i
$571$	−34.9176	+	10.2527i	−1.46126	+	0.429064i	−0.913247	−	0.407407i	$-0.866433\pi$
$571$	−34.9176	+	10.2527i	−1.46126	+	0.429064i	−0.548011	+	0.836471i	$0.684615\pi$
$572$	20.8976	+	9.54360i	0.873771	+	0.399038i
$573$	5.10987	−	0.734689i	0.213468	−	0.0306921i
$574$	−33.5026			−1.39837
$575$	23.9590	−	0.983572i	0.999158	−	0.0410178i
$576$	1.00000			0.0416667
$577$	−1.02641	+	0.147576i	−0.0427302	+	0.00614367i	−0.163647	−	0.986519i	$-0.552326\pi$
$577$	−1.02641	+	0.147576i	−0.0427302	+	0.00614367i	0.120917	+	0.992663i	$0.461417\pi$
$578$	−15.4484	−	7.05503i	−0.642567	−	0.293451i
$579$	13.5401	−	3.97573i	0.562706	−	0.165226i
$580$	−3.59763	−	7.36554i	−0.149383	−	0.305838i
$581$	13.4934	+	3.96203i	0.559802	+	0.164373i
$582$	3.64611	+	5.67346i	0.151136	+	0.235173i
$583$	−24.3530	+	11.1216i	−1.00860	+	0.460611i
$584$	−0.442722	−	0.510929i	−0.0183200	−	0.0211424i
$585$	6.52088	+	9.58994i	0.269605	+	0.396495i
$586$	−2.82448	+	19.6447i	−0.116678	+	0.811513i
$587$	−36.0409	−	5.18190i	−1.48757	−	0.213880i	−0.649883	−	0.760035i	$-0.725182\pi$
$587$	−36.0409	−	5.18190i	−1.48757	−	0.213880i	−0.837684	+	0.546155i	$0.816091\pi$
$588$	−6.34932	+	9.87974i	−0.261842	+	0.407434i
$589$	25.0142	+	28.8679i	1.03069	+	1.18948i
$590$	0.330807	+	12.7410i	0.0136191	+	0.524538i
$591$	19.5787	−	12.5825i	0.805362	−	0.517575i
$592$	3.18202	−	10.8370i	0.130780	−	0.445396i
$593$	13.7923	+	11.9511i	0.566383	+	0.490774i	0.890339	−	0.455298i	$-0.150467\pi$
$593$	13.7923	+	11.9511i	0.566383	+	0.490774i	−0.323956	+	0.946072i	$0.605013\pi$
$594$	4.25024	−	1.24798i	0.174390	−	0.0512054i
$595$	0.848819	+	0.929693i	0.0347982	+	0.0381137i
$596$	−1.48561	−	10.3326i	−0.0608529	−	0.423241i
$597$		−	2.05743i		−	0.0842049i
$598$	23.9400	−	6.74720i	0.978979	−	0.275914i
$599$	−34.3827			−1.40484			−0.702419	−	0.711763i	$-0.747897\pi$
$599$	−34.3827			−1.40484			−0.702419	+	0.711763i	$0.747897\pi$
$600$	3.07380	−	3.94357i	0.125487	−	0.160996i
$601$	7.34116	−	16.0749i	0.299452	−	0.655708i	−0.698768	−	0.715348i	$-0.746268\pi$
$601$	7.34116	−	16.0749i	0.299452	−	0.655708i	0.998220	+	0.0596400i	$0.0189953\pi$
$602$	−5.91073	−	20.1301i	−0.240904	−	0.820442i
$603$	4.93578	+	4.27688i	0.201001	+	0.174168i
$604$	−1.44288	−	0.423668i	−0.0587101	−	0.0172388i
$605$	−3.23814	−	19.0056i	−0.131649	−	0.772686i
$606$	−4.96899	−	10.8806i	−0.201851	−	0.441993i
$607$	29.6813	−	25.7190i	1.20473	−	1.04390i	0.206878	−	0.978367i	$-0.433670\pi$
$607$	29.6813	−	25.7190i	1.20473	−	1.04390i	0.997850	−	0.0655361i	$-0.0208758\pi$
$608$	2.48541	−	3.86738i	0.100797	−	0.156843i
$609$	2.25872	−	15.7098i	0.0915280	−	0.636592i
$610$	−2.52259	+	4.15874i	−0.102137	+	0.168383i
$611$	41.3103	+	26.5485i	1.67124	+	1.07404i
$612$	0.0982769	−	0.0851574i	0.00397261	−	0.00344228i
$613$	−16.5249	+	7.54666i	−0.667434	+	0.304807i	−0.720166	−	0.693802i	$-0.755934\pi$
$613$	−16.5249	+	7.54666i	−0.667434	+	0.304807i	0.0527321	+	0.998609i	$0.483207\pi$
$614$	−13.0162	+	8.36499i	−0.525290	+	0.337584i
$615$	13.3668	+	10.9881i	0.539000	+	0.443083i
$616$	12.5589	−	14.4938i	0.506014	−	0.583971i
$617$	1.17812	+	4.01232i	0.0474295	+	0.161530i	0.979803	−	0.199968i	$-0.0640837\pi$
$617$	1.17812	+	4.01232i	0.0474295	+	0.161530i	−0.932373	+	0.361498i	$0.882266\pi$
$618$	−11.0887	−	5.06405i	−0.446054	−	0.203706i
$619$	−3.71707	−	25.8528i	−0.149402	−	1.03911i	−0.917202	−	0.398423i	$-0.869558\pi$
$619$	−3.71707	−	25.8528i	−0.149402	−	1.03911i	0.767800	−	0.640690i	$-0.221351\pi$
$620$	7.27692	−	17.0951i	0.292248	−	0.686555i
$621$	2.63659	−	4.00604i	0.105803	−	0.160757i
$622$			14.2999i			0.573375i
$623$	−48.3629	+	6.95354i	−1.93762	+	0.278588i
$624$	2.15447	−	4.71763i	0.0862478	−	0.188856i
$625$	−6.10349	−	24.2435i	−0.244140	−	0.969740i
$626$	18.7286	−	21.6139i	0.748545	−	0.863867i
$627$	5.73718	−	19.5391i	0.229121	−	0.780315i
$628$	7.67882	+	11.9485i	0.306418	+	0.476796i
$629$	−0.610129	−	1.33600i	−0.0243274	−	0.0532696i
$630$	9.21486	−	2.96761i	0.367129	−	0.118232i
$631$	14.2367	+	9.14936i	0.566754	+	0.364230i	0.792422	−	0.609974i	$-0.208820\pi$
$631$	14.2367	+	9.14936i	0.566754	+	0.364230i	−0.225668	+	0.974204i	$0.572456\pi$
$632$	−10.4132	−	1.49719i	−0.414214	−	0.0595550i
$633$	−8.50536	−	1.22289i	−0.338058	−	0.0486053i
$634$	22.3952	+	14.3925i	0.889426	+	0.571600i
$635$	0.114517	+	0.355592i	0.00454447	+	0.0141113i
$636$	2.51071	+	5.49769i	0.0995561	+	0.217997i
$637$	32.9295	+	51.2393i	1.30472	+	2.03018i
$638$	−4.57499	+	15.5810i	−0.181125	+	0.616857i
$639$	1.54743	−	1.78583i	0.0612154	−	0.0706463i
$640$	−2.22082	−	0.260671i	−0.0877857	−	0.0103039i
$641$	6.14154	−	13.4481i	0.242576	−	0.531168i	−0.748709	−	0.662899i	$-0.769326\pi$
$641$	6.14154	−	13.4481i	0.242576	−	0.531168i	0.991286	+	0.131730i	$0.0420533\pi$
$642$	15.4981	−	2.22830i	0.611663	−	0.0879438i
$643$		−	42.2702i		−	1.66697i	−0.552539	−	0.833487i	$-0.686341\pi$
$643$		−	42.2702i		−	1.66697i	0.552539	−	0.833487i	$-0.313659\pi$
$644$	0.226047	−	20.7620i	0.00890750	−	0.818139i
$645$	−4.24397	+	9.97002i	−0.167106	+	0.392569i
$646$	−0.0850772	−	0.591725i	−0.00334732	−	0.0232811i
$647$	6.49002	+	2.96389i	0.255149	+	0.116523i	0.538884	−	0.842380i	$-0.318846\pi$
$647$	6.49002	+	2.96389i	0.255149	+	0.116523i	−0.283735	+	0.958903i	$0.591573\pi$
$648$	−0.281733	−	0.959493i	−0.0110675	−	0.0376924i
$649$	16.5343	−	19.0816i	0.649027	−	0.749017i
$650$	−11.9819	−	22.9974i	−0.469968	−	0.902030i
$651$	30.2626	−	19.4486i	1.18608	−	0.762250i
$652$	−4.92023	+	2.24699i	−0.192691	+	0.0879991i
$653$	−13.6017	+	11.7860i	−0.532277	+	0.461220i	−0.879051	−	0.476728i	$-0.841823\pi$
$653$	−13.6017	+	11.7860i	−0.532277	+	0.461220i	0.346774	+	0.937949i	$0.387277\pi$
$654$	7.33284	+	4.71253i	0.286737	+	0.184275i
$655$	25.9307	+	15.7290i	1.01320	+	0.614581i
$656$	1.10128	−	7.65956i	0.0429977	−	0.299056i
$657$	−0.365503	+	0.568734i	−0.0142596	+	0.0221884i
$658$	30.9801	−	26.8444i	1.20773	−	1.04650i
$659$	11.7345	+	25.6950i	0.457112	+	1.00094i	0.988136	+	0.153580i	$0.0490802\pi$
$659$	11.7345	+	25.6950i	0.457112	+	1.00094i	−0.531024	+	0.847357i	$0.678193\pi$
$660$	−9.76435	+	1.66363i	−0.380077	+	0.0647568i
$661$	−1.78876	−	0.525227i	−0.0695747	−	0.0204290i	0.246760	−	0.969077i	$-0.420634\pi$
$661$	−1.78876	−	0.525227i	−0.0695747	−	0.0204290i	−0.316335	+	0.948648i	$0.602452\pi$
$662$	3.33200	+	2.88719i	0.129502	+	0.112214i
$663$	−0.190007	−	0.647103i	−0.00737924	−	0.0251314i
$664$	−1.34937	+	2.95471i	−0.0523657	+	0.114665i
$665$	11.4259	−	43.0131i	0.443077	−	1.66798i
$666$	−11.2945			−0.437652
$667$	7.12889	+	16.0708i	0.276032	+	0.622266i
$668$			7.26073i			0.280926i
$669$	0.0196844	+	0.136908i	0.000761045	+	0.00529318i
$670$	−9.84664	−	10.7848i	−0.380409	−	0.416654i
$671$	9.24535	−	2.71468i	0.356913	−	0.104799i
$672$	−3.27197	−	2.83518i	−0.126219	−	0.109370i
$673$	−7.40395	+	25.2155i	−0.285401	+	0.971987i	0.684607	+	0.728913i	$0.259974\pi$
$673$	−7.40395	+	25.2155i	−0.285401	+	0.971987i	−0.970008	+	0.243074i	$0.921844\pi$
$674$	26.6424	−	17.1220i	1.02623	−	0.659516i
$675$	−4.64982	−	1.83826i	−0.178972	−	0.0707546i
$676$	−9.10110	−	10.5032i	−0.350042	−	0.403970i
$677$	−1.41379	+	2.19989i	−0.0543362	+	0.0845488i	−0.867359	−	0.497683i	$-0.834184\pi$
$677$	−1.41379	+	2.19989i	−0.0543362	+	0.0845488i	0.813023	+	0.582232i	$0.197821\pi$
$678$	−14.6613	−	2.10797i	−0.563062	−	0.0809561i
$679$	4.15531	−	28.9008i	0.159466	−	1.10911i
$680$	−0.240454	+	0.163501i	−0.00922097	+	0.00627000i
$681$	−15.0636	−	17.3843i	−0.577238	−	0.666168i
$682$	−33.4800	+	15.2898i	−1.28201	+	0.585476i
$683$	20.7875	+	32.3459i	0.795410	+	1.23768i	0.967568	+	0.252612i	$0.0812897\pi$
$683$	20.7875	+	32.3459i	0.795410	+	1.23768i	−0.172158	+	0.985069i	$0.555074\pi$
$684$	−4.41094	−	1.29517i	−0.168657	−	0.0495221i
$685$	34.1631	−	16.6866i	1.30530	−	0.637563i
$686$	19.7072	−	5.78655i	0.752424	−	0.220932i
$687$	−22.5040	−	10.2772i	−0.858582	−	0.392101i
$688$	4.79655	−	0.689640i	0.182867	−	0.0262923i
$689$	31.3453			1.19416
$690$	−6.89966	+	8.20943i	−0.262666	+	0.312527i
$691$	−9.12064			−0.346966			−0.173483	−	0.984837i	$-0.555502\pi$
$691$	−9.12064			−0.346966			−0.173483	+	0.984837i	$0.555502\pi$
$692$	−3.33220	+	0.479098i	−0.126671	+	0.0182126i
$693$	−17.4449	−	7.96684i	−0.662679	−	0.302635i
$694$	−27.2805	+	8.01027i	−1.03555	+	0.304066i
$695$	−1.37412	−	2.81328i	−0.0521232	−	0.106714i
$696$	3.51741	+	1.03280i	0.133327	+	0.0391483i
$697$	−0.544038	−	0.846540i	−0.0206069	−	0.0320650i
$698$	17.5175	−	7.99997i	0.663047	−	0.302803i
$699$	−1.47553	−	1.70285i	−0.0558097	−	0.0644079i
$700$	−21.2381	+	4.18847i	−0.802726	+	0.158309i
$701$	−0.761652	+	5.29741i	−0.0287672	+	0.200080i	−0.999137	−	0.0415459i	$-0.986772\pi$
$701$	−0.761652	+	5.29741i	−0.0287672	+	0.200080i	0.970369	+	0.241626i	$0.0776808\pi$
$702$	−5.13352	−	0.738088i	−0.193752	−	0.0278573i
$703$	−28.0714	+	43.6800i	−1.05873	+	1.64742i
$704$	2.90082	+	3.34773i	0.109329	+	0.126172i
$705$	−21.1647	+	0.549521i	−0.797108	+	0.0206961i
$706$	−19.5996	+	12.5959i	−0.737642	+	0.474054i
$707$	−14.5900	+	49.6889i	−0.548713	+	1.86874i
$708$	−4.30767	−	3.73262i	−0.161892	−	0.140280i
$709$	44.8921	−	13.1815i	1.68596	−	0.495042i	0.708417	−	0.705794i	$-0.249410\pi$
$709$	44.8921	−	13.1815i	1.68596	−	0.495042i	0.977540	+	0.210752i	$0.0675913\pi$
$710$	−3.90208	+	3.56264i	−0.146442	+	0.133703i
$711$	1.49719	+	10.4132i	0.0561490	+	0.390525i
$712$		−	11.2856i		−	0.422945i
$713$	−16.9473	+	36.0650i	−0.634681	+	1.35065i
$714$	−0.562996			−0.0210696
$715$	−13.1886	+	49.6488i	−0.493225	+	1.85676i
$716$	3.24253	−	7.10016i	0.121179	−	0.265345i
$717$	0.675741	+	2.30136i	0.0252360	+	0.0859460i
$718$	−2.98863	−	2.58966i	−0.111535	−	0.0966454i
$719$	8.83106	+	2.59303i	0.329343	+	0.0967039i	0.442224	−	0.896905i	$-0.354190\pi$
$719$	8.83106	+	2.59303i	0.329343	+	0.0967039i	−0.112881	+	0.993609i	$0.536008\pi$
$720$	0.375565	+	2.20430i	0.0139965	+	0.0821495i
$721$	21.9245	+	48.0080i	0.816512	+	1.78791i
$722$	−1.61269	+	1.39740i	−0.0600181	+	0.0520059i
$723$	−3.31609	+	5.15993i	−0.123327	+	0.191900i
$724$	1.59325	−	11.0813i	0.0592127	−	0.411834i
$725$	14.8847	−	10.6965i	0.552805	−	0.397258i
$726$	7.25331	+	4.66142i	0.269196	+	0.173002i
$727$	8.80672	−	7.63107i	0.326623	−	0.283021i	−0.476077	−	0.879404i	$-0.657942\pi$
$727$	8.80672	−	7.63107i	0.326623	−	0.283021i	0.802700	+	0.596383i	$0.203396\pi$
$728$	−20.4247	+	9.32765i	−0.756990	+	0.345706i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	0.959970	−	1.16778i	0.0355301	−	0.0432215i
$731$	0.412662	−	0.476238i	0.0152629	−	0.0176143i
$732$	−0.612840	−	2.08714i	−0.0226512	−	0.0771429i
$733$	−8.45428	−	3.86094i	−0.312266	−	0.142607i	0.253117	−	0.967436i	$-0.418544\pi$
$733$	−8.45428	−	3.86094i	−0.312266	−	0.142607i	−0.565383	+	0.824829i	$0.691272\pi$
$734$	−1.67901	−	11.6777i	−0.0619732	−	0.431033i
$735$	−24.1625	−	10.2853i	−0.891248	−	0.379380i
$736$	4.73931	+	0.734158i	0.174693	+	0.0270614i
$737$			28.9301i			1.06565i
$738$	−7.65956	+	1.10128i	−0.281952	+	0.0405386i
$739$	13.3152	−	29.1563i	0.489808	−	1.07253i	−0.489841	−	0.871812i	$-0.662945\pi$
$739$	13.3152	−	29.1563i	0.489808	−	1.07253i	0.979649	−	0.200718i	$-0.0643276\pi$
$740$	25.0830	+	2.94415i	0.922070	+	0.108229i
$741$	−15.6134	+	18.0188i	−0.573572	+	0.661937i
$742$	7.37196	−	25.1066i	0.270633	−	0.921692i
$743$	−1.77028	−	2.75461i	−0.0649453	−	0.101057i	0.807262	−	0.590193i	$-0.200948\pi$
$743$	−1.77028	−	2.75461i	−0.0649453	−	0.101057i	−0.872207	+	0.489136i	$0.837312\pi$
$744$	3.45167	+	7.55811i	0.126544	+	0.277094i
$745$	22.2183	−	7.15531i	0.814016	−	0.262150i
$746$	−1.24898	−	0.802671i	−0.0457284	−	0.0293879i
$747$	3.21518	+	0.462274i	0.117637	+	0.0169137i
$748$	0.570167	+	0.0819777i	0.0208474	+	0.00299740i
$749$	−57.0271	−	36.6491i	−2.08373	−	1.33913i
$750$	9.84724	+	5.29452i	0.359570	+	0.193329i
$751$	9.25348	+	20.2623i	0.337664	+	0.739381i	0.999951	−	0.00986870i	$-0.00314135\pi$
$751$	9.25348	+	20.2623i	0.337664	+	0.739381i	−0.662287	+	0.749250i	$0.730414\pi$
$752$	5.11896	+	7.96527i	0.186669	+	0.290463i
$753$	−1.32498	+	4.51246i	−0.0482849	+	0.164443i
$754$	12.4505	−	14.3687i	0.453421	−	0.523276i
$755$	0.391997	−	3.33966i	0.0142662	−	0.121543i
$756$	−1.79852	+	3.93820i	−0.0654114	+	0.143231i
$757$	−9.17184	+	1.31871i	−0.333356	+	0.0479294i	−0.306961	−	0.951722i	$-0.599312\pi$
$757$	−9.17184	+	1.31871i	−0.333356	+	0.0479294i	−0.0263956	+	0.999652i	$0.508403\pi$
$758$			33.9923i			1.23465i
$759$	21.0594	−	2.79423i	0.764408	−	0.101424i
$760$	9.45831	+	4.02615i	0.343089	+	0.146044i
$761$	−1.44846	−	10.0742i	−0.0525065	−	0.365191i	−0.999087	−	0.0427231i	$-0.986397\pi$
$761$	−1.44846	−	10.0742i	−0.0525065	−	0.365191i	0.946580	−	0.322468i	$-0.104512\pi$
$762$	−0.151971	−	0.0694029i	−0.00550534	−	0.00251420i
$763$	−10.6320	−	36.2092i	−0.384904	−	1.31086i
$764$	3.38067	−	3.90150i	0.122308	−	0.141151i
$765$	0.224622	+	0.184650i	0.00812123	+	0.00667603i
$766$	−7.27982	+	4.67846i	−0.263031	+	0.169040i
$767$	−26.8898	+	12.2802i	−0.970936	+	0.443411i
$768$	0.755750	−	0.654861i	0.0272708	−	0.0236303i
$769$	−37.2050	−	23.9102i	−1.34165	−	0.862223i	−0.344579	−	0.938757i	$-0.611978\pi$
$769$	−37.2050	−	23.9102i	−1.34165	−	0.862223i	−0.997067	+	0.0765341i	$0.975615\pi$
$770$	36.6654	+	22.2403i	1.32133	+	0.801486i
$771$	3.72857	−	25.9327i	0.134281	−	0.933945i
$772$	7.62936	−	11.8715i	0.274587	−	0.427265i
$773$	−25.6222	+	22.2018i	−0.921566	+	0.798541i	−0.979845	−	0.199759i	$-0.935984\pi$
$773$	−25.6222	+	22.2018i	−0.921566	+	0.798541i	0.0582791	+	0.998300i	$0.481439\pi$
$774$	−2.01305	−	4.40797i	−0.0723576	−	0.158441i
$775$	40.4157	+	9.62021i	1.45177	+	0.345568i
$776$	6.47088	+	1.90002i	0.232291	+	0.0682068i
$777$	36.9552	+	32.0219i	1.32576	+	1.14878i
$778$	−0.322894	−	1.09968i	−0.0115763	−	0.0394253i
$779$	−14.7781	+	32.3596i	−0.529481	+	1.15940i
$780$	11.2082	+	2.97732i	0.401319	+	0.106605i
$781$	10.4673			0.374549
$782$	0.528283	−	0.331436i	0.0188914	−	0.0118521i
$783$		−	3.66590i		−	0.131009i
$784$	1.67135	+	11.6245i	0.0596912	+	0.415162i
$785$	−23.4542	+	21.4139i	−0.837115	+	0.764295i
$786$	−13.0138	+	3.82120i	−0.464187	+	0.136298i
$787$	13.5718	+	11.7600i	0.483781	+	0.419199i	0.862302	−	0.506394i	$-0.169022\pi$
$787$	13.5718	+	11.7600i	0.483781	+	0.419199i	−0.378521	+	0.925593i	$0.623567\pi$
$788$	6.55684	−	22.3306i	0.233578	−	0.795493i
$789$	−19.4718	+	12.5138i	−0.693215	+	0.445503i
$790$	−0.610573	−	23.5161i	−0.0217232	−	0.836666i
$791$	41.9948	+	48.4646i	1.49316	+	1.72320i
$792$	2.39486	−	3.72648i	0.0850978	−	0.132415i
$793$	−11.1667	−	1.60553i	−0.396541	−	0.0570140i
$794$	−1.65870	+	11.5365i	−0.0588651	+	0.409415i
$795$	−11.1756	+	7.59910i	−0.396359	+	0.269512i
$796$	−1.34733	−	1.55490i	−0.0477548	−	0.0551120i
$797$	−11.9443	+	5.45479i	−0.423089	+	0.193218i	−0.615570	−	0.788082i	$-0.711074\pi$
$797$	−11.9443	+	5.45479i	−0.423089	+	0.193218i	0.192480	+	0.981301i	$0.438347\pi$
$798$	10.7605	+	16.7436i	0.380916	+	0.592717i
$799$	1.18138	+	0.346884i	0.0417941	+	0.0122719i
$800$	−0.259465	−	4.99326i	−0.00917348	−	0.176539i
$801$	−10.8284	+	3.17951i	−0.382604	+	0.112343i
$802$	−4.90345	−	2.23933i	−0.173147	−	0.0790735i
$803$	−2.96422	+	0.426191i	−0.104605	+	0.0150400i
$804$	6.53098			0.230330
$805$	45.8507	−	7.29923i	1.61603	−	0.257264i
$806$	43.0929			1.51788
$807$	10.5697	−	1.51969i	0.372070	−	0.0534956i
$808$	−10.8806	−	4.96899i	−0.382777	−	0.174808i
$809$	−20.3229	+	5.96735i	−0.714517	+	0.209801i	−0.618733	−	0.785601i	$-0.712354\pi$
$809$	−20.3229	+	5.96735i	−0.714517	+	0.209801i	−0.0957834	+	0.995402i	$0.530536\pi$
$810$	2.00920	−	0.981376i	0.0705962	−	0.0344820i
$811$	−44.9167	−	13.1887i	−1.57724	−	0.463119i	−0.628141	−	0.778100i	$-0.716184\pi$
$811$	−44.9167	−	13.1887i	−1.57724	−	0.463119i	−0.949098	+	0.314981i	$0.898002\pi$
$812$	−8.58068	−	13.3518i	−0.301123	−	0.468556i
$813$	−21.8297	+	9.96930i	−0.765602	+	0.349639i
$814$	−32.7632	−	37.8108i	−1.14835	−	1.32527i
$815$	−6.80093	−	10.0018i	−0.238226	−	0.350347i
$816$	0.0185065	−	0.128715i	0.000647856	−	0.00450594i
$817$	−22.0505	−	3.17039i	−0.771450	−	0.110918i
$818$	9.07358	−	14.1188i	0.317250	−	0.493651i
$819$	14.7041	+	16.9695i	0.513803	+	0.592961i
$820$	17.2976	−	0.449115i	0.604058	−	0.0156838i
$821$	12.5207	−	8.04654i	0.436974	−	0.280826i	−0.303602	−	0.952799i	$-0.598189\pi$
$821$	12.5207	−	8.04654i	0.436974	−	0.280826i	0.740576	+	0.671973i	$0.234553\pi$
$822$	−4.79038	+	16.3145i	−0.167084	+	0.569035i
$823$	6.72049	+	5.82334i	0.234262	+	0.202989i	0.764079	−	0.645123i	$-0.223194\pi$
$823$	6.72049	+	5.82334i	0.234262	+	0.202989i	−0.529817	+	0.848112i	$0.677739\pi$
$824$	−11.6966	+	3.43442i	−0.407469	+	0.119644i
$825$	−7.33430	−	20.8988i	−0.255348	−	0.727602i
$826$	3.51193	+	24.4260i	0.122196	+	0.849891i
$827$		−	52.2852i		−	1.81813i	−0.416650	−	0.909067i	$-0.636796\pi$
$827$		−	52.2852i		−	1.81813i	0.416650	−	0.909067i	$-0.363204\pi$
$828$	−0.630797	−	4.75417i	−0.0219217	−	0.165219i
$829$	−11.2534			−0.390846			−0.195423	−	0.980719i	$-0.562608\pi$
$829$	−11.2534			−0.390846			−0.195423	+	0.980719i	$0.562608\pi$
$830$	−7.01985	−	1.86473i	−0.243663	−	0.0647259i
$831$	−8.72459	+	19.1042i	−0.302653	+	0.662717i
$832$	−1.46115	−	4.97622i	−0.0506563	−	0.172519i
$833$	1.15417	+	1.00009i	0.0399896	+	0.0346512i
$834$	1.34348	+	0.394480i	0.0465208	+	0.0136597i
$835$	−16.0048	+	2.72688i	−0.553870	+	0.0943675i
$836$	−8.45948	−	18.5237i	−0.292577	−	0.640655i
$837$	6.27950	−	5.44122i	0.217051	−	0.188076i
$838$	2.49309	−	3.87932i	0.0861224	−	0.134009i
$839$	−0.139634	+	0.971177i	−0.00482071	+	0.0335288i	−0.992090	−	0.125530i	$-0.959937\pi$
$839$	−0.139634	+	0.971177i	−0.00482071	+	0.0335288i	0.987269	+	0.159059i	$0.0508459\pi$
$840$	5.02076	−	8.27722i	0.173233	−	0.285591i
$841$	−13.0909	−	8.41300i	−0.451410	−	0.290104i
$842$	−23.4374	+	20.3086i	−0.807705	+	0.699880i
$843$	−14.4885	+	6.61669i	−0.499012	+	0.227891i
$844$	−7.22874	+	4.64563i	−0.248823	+	0.159909i
$845$	19.7342	−	24.0062i	0.678878	−	0.825839i
$846$	6.20044	−	7.15569i	0.213175	−	0.246018i
$847$	−10.5167	−	35.8165i	−0.361357	−	1.23067i
$848$	5.49769	+	2.51071i	0.188791	+	0.0862181i
$849$	4.51850	+	31.4269i	0.155075	+	1.07857i
$850$	−0.450713	−	0.468627i	−0.0154593	−	0.0160738i
$851$	−53.5279	−	8.29192i	−1.83491	−	0.284243i
$852$		−	2.36299i		−	0.0809547i
$853$	15.8223	−	2.27490i	0.541744	−	0.0778911i	0.133990	−	0.990983i	$-0.457221\pi$
$853$	15.8223	−	2.27490i	0.541744	−	0.0778911i	0.407754	+	0.913092i	$0.366312\pi$
$854$	−3.91223	+	8.56658i	−0.133874	+	0.293142i
$855$	1.19835	−	10.2095i	0.0409827	−	0.349157i
$856$	10.2535	−	11.8332i	0.350457	−	0.404449i
$857$	−1.57066	+	5.34918i	−0.0536528	+	0.182725i	−0.981960	−	0.189090i	$-0.939446\pi$
$857$	−1.57066	+	5.34918i	−0.0536528	+	0.182725i	0.928307	+	0.371815i	$0.121264\pi$
$858$	−12.4205	−	19.3267i	−0.424029	−	0.659801i
$859$	−10.8981	−	23.8636i	−0.371839	−	0.814214i	−0.999365	−	0.0356188i	$-0.988660\pi$
$859$	−10.8981	−	23.8636i	−0.371839	−	0.814214i	0.627526	−	0.778595i	$-0.284067\pi$
$860$	3.32160	+	10.3141i	0.113265	+	0.351706i
$861$	28.1842	+	18.1129i	0.960515	+	0.617286i
$862$	−2.25545	−	0.324284i	−0.0768208	−	0.0110452i
$863$	51.7280	+	7.43736i	1.76084	+	0.253171i	0.945456	−	0.325749i	$-0.105616\pi$
$863$	51.7280	+	7.43736i	1.76084	+	0.253171i	0.815385	+	0.578919i	$0.196525\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	−2.30754	−	7.16524i	−0.0784586	−	0.243626i
$866$	16.4269	+	35.9699i	0.558210	+	1.22231i
$867$	9.18175	+	14.2871i	0.311829	+	0.485215i
$868$	10.1348	−	34.5160i	0.343998	−	1.17155i
$869$	−30.5174	+	35.2190i	−1.03523	+	1.19472i
$870$	−0.955596	+	8.14131i	−0.0323977	+	0.276016i
$871$	14.0708	−	30.8107i	0.476771	−	1.04398i
$872$	8.62785	−	1.24050i	0.292176	−	0.0420085i
$873$		−	6.74406i		−	0.228252i
$874$	−19.9540	−	9.37653i	−0.674952	−	0.317166i
$875$	−17.2090	−	45.2422i	−0.581770	−	1.52947i
$876$	0.0962127	+	0.669174i	0.00325073	+	0.0226093i
$877$	−2.39636	−	1.09438i	−0.0809194	−	0.0369547i	0.374544	−	0.927209i	$-0.377799\pi$
$877$	−2.39636	−	1.09438i	−0.0809194	−	0.0369547i	−0.455464	+	0.890254i	$0.650526\pi$
$878$	−9.59584	−	32.6804i	−0.323844	−	1.10291i
$879$	12.9968	−	14.9991i	0.438371	−	0.505907i
$880$	−6.28995	+	7.65158i	−0.212034	+	0.257935i
$881$	−15.3036	+	9.83502i	−0.515591	+	0.331350i	−0.772426	−	0.635105i	$-0.780957\pi$
$881$	−15.3036	+	9.83502i	−0.515591	+	0.331350i	0.256835	+	0.966455i	$0.417320\pi$
$882$	10.6828	−	4.87866i	0.359708	−	0.164273i
$883$	−33.5584	+	29.0785i	−1.12933	+	0.978570i	−0.999915	−	0.0130207i	$-0.995855\pi$
$883$	−33.5584	+	29.0785i	−1.12933	+	0.978570i	−0.129415	+	0.991591i	$0.541310\pi$
$884$	−0.567360	−	0.364620i	−0.0190824	−	0.0122635i
$885$	6.61000	−	10.8972i	0.222193	−	0.366307i
$886$	−2.08197	+	14.4804i	−0.0699453	+	0.486480i
$887$	11.6940	−	18.1963i	0.392647	−	0.610971i	−0.587504	−	0.809221i	$-0.699890\pi$
$887$	11.6940	−	18.1963i	0.392647	−	0.610971i	0.980151	+	0.198250i	$0.0635259\pi$
$888$	−8.53579	+	7.39630i	−0.286442	+	0.248204i
$889$	0.300476	+	0.657951i	0.0100776	+	0.0220670i
$890$	24.8768	−	4.23847i	0.833873	−	0.142074i
$891$	−4.25024	−	1.24798i	−0.142388	−	0.0418090i
$892$	0.104532	+	0.0905778i	0.00350000	+	0.00303277i
$893$	−12.2631	−	41.7643i	−0.410369	−	1.39759i
$894$	−4.33647	+	9.49554i	−0.145033	+	0.317578i
$895$	16.8687	+	4.48095i	0.563858	+	0.149782i
$896$	−4.32944			−0.144637
$897$	−23.7874	−	7.26683i	−0.794239	−	0.242633i
$898$			7.83616i			0.261496i
$899$	4.33489	+	30.1498i	0.144577	+	1.00555i
$900$	−4.71790	+	1.65572i	−0.157263	+	0.0551907i
$901$	0.754101	−	0.221424i	0.0251227	−	0.00737670i
$902$	−25.9058	−	22.4475i	−0.862569	−	0.747420i
$903$	−5.91073	+	20.1301i	−0.196697	+	0.669888i
$904$	−12.4607	+	8.00799i	−0.414436	+	0.266342i
$905$	25.0249	−	0.649748i	0.831857	−	0.0215983i
$906$	0.984777	+	1.13649i	0.0327170	+	0.0377575i
$907$	23.8467	−	37.1061i	0.791815	−	1.23209i	−0.176977	−	0.984215i	$-0.556632\pi$
$907$	23.8467	−	37.1061i	0.791815	−	1.23209i	0.968792	−	0.247874i	$-0.0797317\pi$
$908$	−22.7686	−	3.27363i	−0.755603	−	0.108639i
$909$	−1.70230	+	11.8398i	−0.0564617	+	0.392700i
$910$	−28.2318	−	41.5191i	−0.935874	−	1.37634i
$911$	0.229458	+	0.264808i	0.00760228	+	0.00877350i	0.759538	−	0.650463i	$-0.225425\pi$
$911$	0.229458	+	0.264808i	0.00760228	+	0.00877350i	−0.751936	+	0.659236i	$0.770880\pi$
$912$	−4.18173	+	1.90973i	−0.138471	+	0.0632375i
$913$	7.77911	+	12.1045i	0.257451	+	0.400601i
$914$	−28.3857	−	8.33480i	−0.938916	−	0.275691i
$915$	4.37053	−	2.13474i	0.144485	−	0.0705724i
$916$	−23.7376	+	6.96998i	−0.784311	+	0.230294i
$917$	53.4146	+	24.3936i	1.76391	+	0.805549i
$918$	−0.128715	+	0.0185065i	−0.00424824	+	0.000610805i
$919$	21.8468			0.720660			0.360330	−	0.932825i	$-0.382664\pi$
$919$	21.8468			0.720660			0.360330	+	0.932825i	$0.382664\pi$
$920$	0.161613	+	10.7226i	0.00532824	+	0.353513i
$921$	15.4724			0.509832
$922$	5.47783	−	0.787593i	0.180403	−	0.0259380i
$923$	−11.1477	−	5.09099i	−0.366931	−	0.167572i
$924$	−18.4012	+	5.40307i	−0.605354	+	0.177748i
$925$	2.93052	+	56.3963i	0.0963550	+	1.85430i
$926$	13.9735	+	4.10298i	0.459197	+	0.134832i
$927$	6.59060	+	10.2552i	0.216464	+	0.336824i
$928$	3.33462	−	1.52287i	0.109464	−	0.0499907i
$929$	30.7674	+	35.5074i	1.00944	+	1.16496i	0.986255	+	0.165230i	$0.0528368\pi$
$929$	30.7674	+	35.5074i	1.00944	+	1.16496i	0.0231899	+	0.999731i	$0.492618\pi$
$930$	−15.3640	+	10.4471i	−0.503806	+	0.342574i
$931$	7.68349	−	53.4398i	0.251816	−	1.75142i
$932$	−2.23026	−	0.320664i	−0.0730547	−	0.0105037i
$933$	7.73112	−	12.0299i	0.253106	−	0.393840i
$934$	11.9994	+	13.8481i	0.392634	+	0.453124i
$935$	0.0334315	+	1.28761i	0.00109333	+	0.0421093i
$936$	−4.36300	+	2.80393i	−0.142609	+	0.0916493i
$937$	−3.37699	+	11.5010i	−0.110322	+	0.375721i	−0.996083	−	0.0884194i	$-0.971818\pi$
$937$	−3.37699	+	11.5010i	−0.110322	+	0.375721i	0.885762	+	0.464140i	$0.153637\pi$
$938$	−21.3692	−	18.5165i	−0.697729	−	0.604586i
$939$	−27.4409	+	8.05736i	−0.895499	+	0.262942i
$940$	−15.6353	+	14.2752i	−0.509969	+	0.465607i
$941$	−1.44014	−	10.0164i	−0.0469473	−	0.326526i	−0.999738	−	0.0228974i	$-0.992711\pi$
$941$	−1.44014	−	10.0164i	−0.0469473	−	0.326526i	0.952790	−	0.303629i	$-0.0981982\pi$
$942$		−	14.2032i		−	0.462765i
$943$	−37.1095	−	0.404030i	−1.20845	−	0.0131570i
$944$	−5.69986			−0.185515
$945$	−9.35644	−	2.48542i	−0.304365	−	0.0808507i
$946$	8.91716	−	19.5259i	0.289922	−	0.634840i
$947$	−0.650735	−	2.21620i	−0.0211460	−	0.0720168i	0.948244	−	0.317543i	$-0.102858\pi$
$947$	−0.650735	−	2.21620i	−0.0211460	−	0.0720168i	−0.969390	+	0.245526i	$0.921039\pi$
$948$	7.95069	+	6.88931i	0.258226	+	0.223754i
$949$	3.36420	+	0.987819i	0.109207	+	0.0320660i
$950$	−5.32264	+	22.3611i	−0.172689	+	0.725488i
$951$	−11.0588	−	24.2155i	−0.358608	−	0.785241i
$952$	−0.425484	+	0.368684i	−0.0137900	+	0.0119491i
$953$	0.353463	−	0.550000i	0.0114498	−	0.0178162i	−0.835481	−	0.549519i	$-0.814811\pi$
$953$	0.353463	−	0.550000i	0.0114498	−	0.0178162i	0.846931	+	0.531702i	$0.178448\pi$
$954$	0.860131	−	5.98234i	0.0278478	−	0.193685i
$955$	9.86974	+	5.98674i	0.319377	+	0.193726i
$956$	2.01776	+	1.29674i	0.0652591	+	0.0419395i
$957$	12.2724	−	10.6341i	0.396711	−	0.343752i
$958$	−0.526217	+	0.240315i	−0.0170013	+	0.00776423i
$959$	61.9287	−	39.7991i	1.99978	−	1.28518i
$960$	1.72734	+	1.41996i	0.0557498	+	0.0458289i
$961$	−24.9103	+	28.7480i	−0.803557	+	0.927354i
$962$	16.5029	+	56.2038i	0.532076	+	1.81208i
$963$	−14.2426	−	6.50436i	−0.458960	−	0.209600i
$964$	0.872905	+	6.07119i	0.0281144	+	0.195540i
$965$	29.0337	+	12.3589i	0.934629	+	0.397847i
$966$	−11.4150	+	17.3439i	−0.367271	+	0.558032i
$967$		−	2.91319i		−	0.0936820i	−0.998902	−	0.0468410i	$-0.985085\pi$
$967$		−	2.91319i		−	0.0936820i	0.998902	−	0.0468410i	$-0.0149154\pi$
$968$	8.53427	−	1.22704i	0.274302	−	0.0394386i
$969$	−0.248339	+	0.543787i	−0.00797781	+	0.0174690i
$970$	−1.75798	+	14.9774i	−0.0564454	+	0.480894i
$971$	−6.30329	+	7.27439i	−0.202282	+	0.233446i	−0.847823	−	0.530280i	$-0.822087\pi$
$971$	−6.30329	+	7.27439i	−0.202282	+	0.233446i	0.645540	+	0.763726i	$0.276632\pi$
$972$	−0.281733	+	0.959493i	−0.00903658	+	0.0307758i
$973$	−3.27740	−	5.09973i	−0.105068	−	0.163490i
$974$	−3.73600	−	8.18070i	−0.119709	−	0.262126i
$975$	−2.35350	+	25.8245i	−0.0753723	+	0.827046i
$976$	−1.82994	−	1.17603i	−0.0585749	−	0.0376438i
$977$	−2.57381	−	0.370058i	−0.0823434	−	0.0118392i	0.101020	−	0.994884i	$-0.467789\pi$
$977$	−2.57381	−	0.370058i	−0.0823434	−	0.0118392i	−0.183363	+	0.983045i	$0.558698\pi$
$978$	5.35398	+	0.769786i	0.171201	+	0.0246150i
$979$	−42.0555	−	27.0274i	−1.34410	−	0.863800i
$980$	−24.9963	+	8.04994i	−0.798477	+	0.257146i
$981$	−3.62099	−	7.92887i	−0.115609	−	0.253149i
$982$	9.99766	+	15.5567i	0.319038	+	0.496433i
$983$	−8.07853	+	27.5130i	−0.257665	+	0.877527i	0.724463	+	0.689314i	$0.242088\pi$
$983$	−8.07853	+	27.5130i	−0.257665	+	0.877527i	−0.982128	+	0.188213i	$0.939730\pi$
$984$	−5.06753	+	5.84824i	−0.161547	+	0.186435i
$985$	51.6858	+	6.06668i	1.64685	+	0.193301i
$986$	0.198032	−	0.433631i	0.00630664	−	0.0138096i
$987$	−40.5753	+	5.83385i	−1.29153	+	0.185694i
$988$			23.8423i			0.758524i
$989$	−6.30432	−	22.3686i	−0.200466	−	0.711280i
$990$	9.11372	+	3.87947i	0.289653	+	0.123298i
$991$	−1.02432	−	7.12433i	−0.0325387	−	0.226312i	0.967063	−	0.254538i	$-0.0819233\pi$
$991$	−1.02432	−	7.12433i	−0.0325387	−	0.226312i	−0.999602	+	0.0282259i	$0.991014\pi$
$992$	7.55811	+	3.45167i	0.239970	+	0.109591i
$993$	−1.24212	−	4.23027i	−0.0394175	−	0.134244i
$994$	−6.69951	+	7.73164i	−0.212495	+	0.245233i
$995$	2.92146	−	3.55389i	0.0926165	−	0.112666i
$996$	2.73260	−	1.75613i	0.0865857	−	0.0556453i
$997$	18.5863	−	8.48808i	0.588634	−	0.268820i	−0.0987524	−	0.995112i	$-0.531485\pi$
$997$	18.5863	−	8.48808i	0.588634	−	0.268820i	0.687386	+	0.726292i	$0.258758\pi$
$998$	−4.88867	+	4.23606i	−0.154748	+	0.134090i
$999$	9.50151	+	6.10625i	0.300615	+	0.193193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.r.b.49.5	✓	120
5.4	even	2	inner	690.2.r.b.49.8	yes	120
23.8	even	11	inner	690.2.r.b.169.8	yes	120
115.54	even	22	inner	690.2.r.b.169.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.b.49.5	✓	120	1.1	even	1	trivial
690.2.r.b.49.8	yes	120	5.4	even	2	inner
690.2.r.b.169.5	yes	120	115.54	even	22	inner
690.2.r.b.169.8	yes	120	23.8	even	11	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.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(0.981376 + 2.00920i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(2.34067 + 3.64216i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(0.981376 + 2.00920i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(2.34067 + 3.64216i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-1.25733 - 1.84909i) q^{10} +(-0.630409 + 4.38459i) q^{11} +(0.989821 + 0.142315i) q^{12} +(2.80393 - 4.36300i) q^{13} +(-2.83518 - 3.27197i) q^{14} +(0.0580378 + 2.23531i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.0366362 - 0.124771i) q^{17} +(-0.755750 - 0.654861i) q^{18} +(-4.41094 + 1.29517i) q^{19} +(1.50768 + 1.65133i) q^{20} +(0.616144 + 4.28537i) q^{21} -4.42968i q^{22} +(-3.10096 - 3.65842i) q^{23} -1.00000 q^{24} +(-3.07380 + 3.94357i) q^{25} +(-2.15447 + 4.71763i) q^{26} +(0.281733 + 0.959493i) q^{27} +(3.27197 + 2.83518i) q^{28} +(-3.51741 - 1.03280i) q^{29} +(-0.375565 - 2.20430i) q^{30} +(-3.45167 - 7.55811i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(-2.39486 + 3.72648i) q^{33} +(-0.0185065 + 0.128715i) q^{34} +(-5.02076 + 8.27722i) q^{35} +(0.841254 + 0.540641i) q^{36} +(8.53579 - 7.39630i) q^{37} +(4.18173 - 1.90973i) q^{38} +(4.36300 - 2.80393i) q^{39} +(-1.72734 - 1.41996i) q^{40} +(5.06753 - 5.84824i) q^{41} +(-1.21974 - 4.15407i) q^{42} +(4.40797 + 2.01305i) q^{43} +(0.630409 + 4.38459i) q^{44} +(-0.875790 + 2.05742i) q^{45} +(3.59004 + 3.17987i) q^{46} +9.46833i q^{47} +(0.989821 - 0.142315i) q^{48} +(-4.87866 + 10.6828i) q^{49} +(2.48129 - 4.34088i) q^{50} +(0.0851574 - 0.0982769i) q^{51} +(1.46115 - 4.97622i) q^{52} +(3.26756 + 5.08442i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-9.42820 + 3.03631i) q^{55} +(-3.64216 - 2.34067i) q^{56} +(-4.55037 - 0.654244i) q^{57} +(3.62859 + 0.521712i) q^{58} +(-4.79503 - 3.08158i) q^{59} +(0.685448 + 2.12842i) q^{60} +(-0.903633 - 1.97868i) q^{61} +(4.49217 + 6.98995i) q^{62} +(-1.21974 + 4.15407i) q^{63} +(0.654861 - 0.755750i) q^{64} +(11.5179 + 1.35192i) q^{65} +(1.84015 - 4.02937i) q^{66} +(6.46450 - 0.929455i) q^{67} -0.130039i q^{68} +(-1.30097 - 4.61600i) q^{69} +(3.79168 - 8.90750i) q^{70} +(-0.336289 - 2.33894i) q^{71} +(-0.909632 - 0.415415i) q^{72} +(0.190467 + 0.648670i) q^{73} +(-7.39630 + 8.53579i) q^{74} +(-4.43425 + 2.31029i) q^{75} +(-3.86738 + 2.48541i) q^{76} +(-17.4449 + 7.96684i) q^{77} +(-3.91955 + 3.39631i) q^{78} +(8.85021 + 5.68769i) q^{79} +(1.91184 + 1.15968i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-4.18366 + 6.50989i) q^{82} +(2.45486 - 2.12715i) q^{83} +(1.79852 + 3.93820i) q^{84} +(0.286645 - 0.0488381i) q^{85} +(-4.64959 - 1.36524i) q^{86} +(-2.77050 - 2.40065i) q^{87} +(-1.24798 - 4.25024i) q^{88} +(-4.68820 + 10.2657i) q^{89} +(0.574074 - 2.16112i) q^{90} +22.4538 q^{91} +(-4.00604 - 2.63659i) q^{92} -8.30897i q^{93} +(-1.34748 - 9.37195i) q^{94} +(-6.93106 - 7.59144i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(-5.09682 - 4.41642i) q^{97} +(3.30869 - 11.2683i) q^{98} +(-3.72648 + 2.39486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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