LMFDB - Embedded newform 570.2.bb.b.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	570.71
Dual form			570.2.bb.b.281.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-1.63144 + 0.581714i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(-1.33410 + 1.10462i) q^{6} +(-0.223800 - 0.387633i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.32322 - 1.89807i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-1.63144 + 0.581714i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(-1.33410 + 1.10462i) q^{6} +(-0.223800 - 0.387633i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.32322 - 1.89807i) q^{9} +(-0.342020 + 0.939693i) q^{10} +(-0.390566 - 0.225494i) q^{11} +(-0.875839 + 1.49429i) q^{12} +(5.90687 - 1.04154i) q^{13} +(-0.342882 - 0.287712i) q^{14} +(0.603053 - 1.62368i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.247206 - 0.679193i) q^{17} +(1.53393 - 2.57819i) q^{18} +(2.18478 + 3.77184i) q^{19} +1.00000i q^{20} +(0.590610 + 0.502214i) q^{21} +(-0.444136 - 0.0783131i) q^{22} +(5.75335 + 6.85657i) q^{23} +(-0.311942 + 1.70373i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(5.19441 - 2.99900i) q^{26} +(-2.68606 + 4.44804i) q^{27} +(-0.420607 - 0.153088i) q^{28} +(2.76773 + 1.00737i) q^{29} +(0.0113538 - 1.73201i) q^{30} +(8.10581 - 4.67989i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.768360 + 0.140682i) q^{33} +(-0.464596 - 0.553684i) q^{34} +(0.440800 + 0.0777250i) q^{35} +(0.559632 - 2.94734i) q^{36} -1.68156i q^{37} +(3.34306 + 2.79713i) q^{38} +(-9.03084 + 5.13532i) q^{39} +(0.342020 + 0.939693i) q^{40} +(1.61909 - 9.18231i) q^{41} +(0.726759 + 0.269927i) q^{42} +(-8.00266 - 6.71503i) q^{43} +(-0.444136 + 0.0783131i) q^{44} +(-0.0393299 + 2.99974i) q^{45} +(7.75146 + 4.47531i) q^{46} +(-2.87126 + 7.88871i) q^{47} +(0.289580 + 1.70767i) q^{48} +(3.39983 - 5.88867i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.798400 + 0.964262i) q^{51} +(3.85543 - 4.59473i) q^{52} +(-10.1621 + 8.52704i) q^{53} +(-1.00275 + 5.09848i) q^{54} +(0.423789 - 0.154247i) q^{55} -0.447601 q^{56} +(-5.75848 - 4.88262i) q^{57} +2.94535 q^{58} +(-3.26613 + 1.18877i) q^{59} +(-0.581714 - 1.63144i) q^{60} +(7.13607 - 5.98787i) q^{61} +(6.01635 - 7.17001i) q^{62} +(-1.25569 - 0.475768i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.99900 + 5.19441i) q^{65} +(0.770138 - 0.130597i) q^{66} +(-3.41429 + 9.38067i) q^{67} +(-0.625948 - 0.361391i) q^{68} +(-13.3748 - 7.83931i) q^{69} +(0.440800 - 0.0777250i) q^{70} +(-1.93015 - 1.61959i) q^{71} +(-0.482167 - 2.96100i) q^{72} +(0.481319 - 2.72969i) q^{73} +(-0.575129 - 1.58015i) q^{74} +(0.856174 + 1.50564i) q^{75} +(4.09813 + 1.48504i) q^{76} +0.201862i q^{77} +(-6.72983 + 7.91436i) q^{78} +(-3.65055 - 0.643690i) q^{79} +(0.642788 + 0.766044i) q^{80} +(1.79467 - 8.81925i) q^{81} +(-1.61909 - 9.18231i) q^{82} +(6.55508 - 3.78457i) q^{83} +(0.775250 + 0.00508197i) q^{84} +(0.679193 + 0.247206i) q^{85} +(-9.81672 - 3.57299i) q^{86} +(-5.10139 - 0.0334409i) q^{87} +(-0.390566 + 0.225494i) q^{88} +(1.14121 + 6.47214i) q^{89} +(0.989014 + 2.83229i) q^{90} +(-1.72569 - 2.05660i) q^{91} +(8.81464 + 1.55426i) q^{92} +(-10.5018 + 12.3502i) q^{93} +8.39499i q^{94} +(-4.29374 - 0.750851i) q^{95} +(0.856174 + 1.50564i) q^{96} +(6.08526 + 16.7191i) q^{97} +(1.18075 - 6.69635i) q^{98} +(-1.33537 + 0.217451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) $ 84 * q - 6 * q^6 + 42 * q^8	$ 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−1.63144	+	0.581714i	−0.941914	+	0.335853i
$3$	−1.63144	+	0.581714i	−0.941914	+	0.335853i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.642788	+	0.766044i	−0.287463	+	0.342585i
$5$	−0.642788	+	0.766044i	−0.287463	+	0.342585i
$6$	−1.33410	+	1.10462i	−0.544643	+	0.450959i
$7$	−0.223800	−	0.387633i	−0.0845886	−	0.146512i	0.820627	−	0.571464i	$-0.193624\pi$
$7$	−0.223800	−	0.387633i	−0.0845886	−	0.146512i	−0.905216	+	0.424952i	$0.860291\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.32322	−	1.89807i	0.774406	−	0.632690i
$10$	−0.342020	+	0.939693i	−0.108156	+	0.297157i
$11$	−0.390566	−	0.225494i	−0.117760	−	0.0679889i	0.439963	−	0.898016i	$-0.354992\pi$
$11$	−0.390566	−	0.225494i	−0.117760	−	0.0679889i	−0.557723	+	0.830027i	$0.688325\pi$
$12$	−0.875839	+	1.49429i	−0.252833	+	0.431365i
$13$	5.90687	−	1.04154i	1.63827	−	0.288871i	0.722740	−	0.691120i	$-0.242882\pi$
$13$	5.90687	−	1.04154i	1.63827	−	0.288871i	0.915530	+	0.402249i	$0.131771\pi$
$14$	−0.342882	−	0.287712i	−0.0916390	−	0.0768943i
$15$	0.603053	−	1.62368i	0.155708	−	0.419232i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.247206	−	0.679193i	−0.0599563	−	0.164729i	0.906098	−	0.423068i	$-0.139047\pi$
$17$	−0.247206	−	0.679193i	−0.0599563	−	0.164729i	−0.966054	+	0.258340i	$0.916825\pi$
$18$	1.53393	−	2.57819i	0.361551	−	0.607685i
$19$	2.18478	+	3.77184i	0.501223	+	0.865318i
$19$	2.18478	+	3.77184i	0.501223	+	0.865318i
$20$			1.00000i			0.223607i
$21$	0.590610	+	0.502214i	0.128882	+	0.109592i
$22$	−0.444136	−	0.0783131i	−0.0946901	−	0.0166964i
$23$	5.75335	+	6.85657i	1.19966	+	1.42969i	0.875178	+	0.483801i	$0.160744\pi$
$23$	5.75335	+	6.85657i	1.19966	+	1.42969i	0.324478	+	0.945893i	$0.394811\pi$
$24$	−0.311942	+	1.70373i	−0.0636750	+	0.347772i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	5.19441	−	2.99900i	1.01871	−	0.588151i
$27$	−2.68606	+	4.44804i	−0.516933	+	0.856026i
$28$	−0.420607	−	0.153088i	−0.0794872	−	0.0289310i
$29$	2.76773	+	1.00737i	0.513954	+	0.187064i	0.585960	−	0.810340i	$-0.300718\pi$
$29$	2.76773	+	1.00737i	0.513954	+	0.187064i	−0.0720056	+	0.997404i	$0.522940\pi$
$30$	0.0113538	−	1.73201i	0.00207291	−	0.316221i
$31$	8.10581	−	4.67989i	1.45585	−	0.840533i	0.457043	−	0.889445i	$-0.348908\pi$
$31$	8.10581	−	4.67989i	1.45585	−	0.840533i	0.998803	+	0.0489113i	$0.0155752\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	0.768360	+	0.140682i	0.133754	+	0.0244896i
$34$	−0.464596	−	0.553684i	−0.0796775	−	0.0949559i
$35$	0.440800	+	0.0777250i	0.0745089	+	0.0131379i
$36$	0.559632	−	2.94734i	0.0932720	−	0.491223i
$37$		−	1.68156i		−	0.276447i	−0.990401	−	0.138224i	$-0.955861\pi$
$37$		−	1.68156i		−	0.276447i	0.990401	−	0.138224i	$-0.0441393\pi$
$38$	3.34306	+	2.79713i	0.542317	+	0.453754i
$39$	−9.03084	+	5.13532i	−1.44609	+	0.822310i
$40$	0.342020	+	0.939693i	0.0540781	+	0.148578i
$41$	1.61909	−	9.18231i	0.252859	−	1.43404i	−0.548649	−	0.836053i	$-0.684858\pi$
$41$	1.61909	−	9.18231i	0.252859	−	1.43404i	0.801508	−	0.597983i	$-0.204031\pi$
$42$	0.726759	+	0.269927i	0.112141	+	0.0416506i
$43$	−8.00266	−	6.71503i	−1.22039	−	1.02403i	−0.998804	−	0.0488925i	$-0.984431\pi$
$43$	−8.00266	−	6.71503i	−1.22039	−	1.02403i	−0.221590	−	0.975140i	$-0.571125\pi$
$44$	−0.444136	+	0.0783131i	−0.0669560	+	0.0118061i
$45$	−0.0393299	+	2.99974i	−0.00586295	+	0.447175i
$46$	7.75146	+	4.47531i	1.14289	+	0.659848i
$47$	−2.87126	+	7.88871i	−0.418816	+	1.15069i	0.533560	+	0.845762i	$0.320854\pi$
$47$	−2.87126	+	7.88871i	−0.418816	+	1.15069i	−0.952376	+	0.304925i	$0.901369\pi$
$48$	0.289580	+	1.70767i	0.0417972	+	0.246481i
$49$	3.39983	−	5.88867i	0.485690	−	0.841239i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	0.798400	+	0.964262i	0.111798	+	0.135024i
$52$	3.85543	−	4.59473i	0.534653	−	0.637174i
$53$	−10.1621	+	8.52704i	−1.39588	+	1.17128i	−0.432980	+	0.901404i	$0.642538\pi$
$53$	−10.1621	+	8.52704i	−1.39588	+	1.17128i	−0.962895	+	0.269875i	$0.913018\pi$
$54$	−1.00275	+	5.09848i	−0.136458	+	0.693815i
$55$	0.423789	−	0.154247i	0.0571438	−	0.0207986i
$56$	−0.447601			−0.0598131
$57$	−5.75848	−	4.88262i	−0.762729	−	0.646719i
$58$	2.94535			0.386744
$59$	−3.26613	+	1.18877i	−0.425213	+	0.154765i	−0.545758	−	0.837943i	$-0.683758\pi$
$59$	−3.26613	+	1.18877i	−0.425213	+	0.154765i	0.120544	+	0.992708i	$0.461536\pi$
$60$	−0.581714	−	1.63144i	−0.0750990	−	0.210618i
$61$	7.13607	−	5.98787i	0.913680	−	0.766669i	−0.0591355	−	0.998250i	$-0.518834\pi$
$61$	7.13607	−	5.98787i	0.913680	−	0.766669i	0.972816	+	0.231581i	$0.0743900\pi$
$62$	6.01635	−	7.17001i	0.764077	−	0.910592i
$63$	−1.25569	−	0.475768i	−0.158202	−	0.0599412i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.99900	+	5.19441i	−0.371980	+	0.644288i
$66$	0.770138	−	0.130597i	0.0947975	−	0.0160754i
$67$	−3.41429	+	9.38067i	−0.417121	+	1.14603i	0.536204	+	0.844088i	$0.319858\pi$
$67$	−3.41429	+	9.38067i	−0.417121	+	1.14603i	−0.953326	+	0.301944i	$0.902365\pi$
$68$	−0.625948	−	0.361391i	−0.0759073	−	0.0438251i
$69$	−13.3748	−	7.83931i	−1.61014	−	0.943742i
$70$	0.440800	−	0.0777250i	0.0526857	−	0.00928992i
$71$	−1.93015	−	1.61959i	−0.229066	−	0.192209i	0.521029	−	0.853539i	$-0.325548\pi$
$71$	−1.93015	−	1.61959i	−0.229066	−	0.192209i	−0.750096	+	0.661329i	$0.769993\pi$
$72$	−0.482167	−	2.96100i	−0.0568240	−	0.348957i
$73$	0.481319	−	2.72969i	0.0563341	−	0.319487i	−0.943599	−	0.331092i	$-0.892583\pi$
$73$	0.481319	−	2.72969i	0.0563341	−	0.319487i	0.999933	+	0.0116052i	$0.00369413\pi$
$74$	−0.575129	−	1.58015i	−0.0668574	−	0.183689i
$75$	0.856174	+	1.50564i	0.0988625	+	0.173857i
$76$	4.09813	+	1.48504i	0.470087	+	0.170346i
$77$			0.201862i			0.0230043i
$78$	−6.72983	+	7.91436i	−0.762003	+	0.896124i
$79$	−3.65055	−	0.643690i	−0.410719	−	0.0724208i	−0.0355285	−	0.999369i	$-0.511311\pi$
$79$	−3.65055	−	0.643690i	−0.410719	−	0.0724208i	−0.375190	+	0.926948i	$0.622423\pi$
$80$	0.642788	+	0.766044i	0.0718658	+	0.0856464i
$81$	1.79467	−	8.81925i	0.199408	−	0.979917i
$82$	−1.61909	−	9.18231i	−0.178799	−	1.01402i
$83$	6.55508	−	3.78457i	0.719513	−	0.415411i	−0.0950604	−	0.995472i	$-0.530304\pi$
$83$	6.55508	−	3.78457i	0.719513	−	0.415411i	0.814573	+	0.580060i	$0.196971\pi$
$84$	0.775250	+	0.00508197i	0.0845867	+	0.000554488i
$85$	0.679193	+	0.247206i	0.0736689	+	0.0268133i
$86$	−9.81672	−	3.57299i	−1.05856	−	0.385286i
$87$	−5.10139	−	0.0334409i	−0.546927	−	0.00358525i
$88$	−0.390566	+	0.225494i	−0.0416345	+	0.0240377i
$89$	1.14121	+	6.47214i	0.120968	+	0.686046i	0.983621	+	0.180249i	$0.0576903\pi$
$89$	1.14121	+	6.47214i	0.120968	+	0.686046i	−0.862653	+	0.505797i	$0.831199\pi$
$90$	0.989014	+	2.83229i	0.104251	+	0.298549i
$91$	−1.72569	−	2.05660i	−0.180902	−	0.215591i
$92$	8.81464	+	1.55426i	0.918990	+	0.162043i
$93$	−10.5018	+	12.3502i	−1.08899	+	1.28066i
$94$			8.39499i			0.865878i
$95$	−4.29374	−	0.750851i	−0.440529	−	0.0770357i
$96$	0.856174	+	1.50564i	0.0873829	+	0.153669i
$97$	6.08526	+	16.7191i	0.617865	+	1.69757i	0.712152	+	0.702025i	$0.247721\pi$
$97$	6.08526	+	16.7191i	0.617865	+	1.69757i	−0.0942871	+	0.995545i	$0.530057\pi$
$98$	1.18075	−	6.69635i	0.119274	−	0.676434i
$99$	−1.33537	+	0.217451i	−0.134210	+	0.0218547i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	2.29052	−	0.403880i	0.227915	−	0.0401876i	−0.0585241	−	0.998286i	$-0.518639\pi$
$101$	2.29052	−	0.403880i	0.227915	−	0.0401876i	0.286439	+	0.958098i	$0.407528\pi$
$102$	1.08005	+	0.633041i	0.106941	+	0.0626804i
$103$	−9.46164	−	5.46268i	−0.932283	−	0.538254i	−0.0447499	−	0.998998i	$-0.514249\pi$
$103$	−9.46164	−	5.46268i	−0.932283	−	0.538254i	−0.887533	+	0.460745i	$0.847582\pi$
$104$	2.05143	−	5.63627i	0.201160	−	0.552682i
$105$	−0.764355	+	0.129616i	−0.0745934	+	0.0126492i
$106$	−6.63286	+	11.4884i	−0.644240	+	1.11586i
$107$	−3.90029	−	6.75550i	−0.377055	−	0.653079i	0.613577	−	0.789635i	$-0.289730\pi$
$107$	−3.90029	−	6.75550i	−0.377055	−	0.653079i	−0.990632	+	0.136556i	$0.956397\pi$
$108$	0.801502	+	5.13396i	0.0771246	+	0.494016i
$109$	−7.82118	+	9.32092i	−0.749133	+	0.892782i	−0.997109	−	0.0759842i	$-0.975790\pi$
$109$	−7.82118	+	9.32092i	−0.749133	+	0.892782i	0.247976	+	0.968766i	$0.420235\pi$
$110$	0.345476	−	0.289889i	0.0329399	−	0.0276398i
$111$	0.978190	+	2.74338i	0.0928457	+	0.260390i
$112$	−0.420607	+	0.153088i	−0.0397436	+	0.0144655i
$113$	−7.03077			−0.661399			−0.330699	−	0.943736i	$-0.607285\pi$
$113$	−7.03077			−0.661399			−0.330699	+	0.943736i	$0.607285\pi$
$114$	−7.08115	−	2.61865i	−0.663211	−	0.245259i
$115$	−8.95062			−0.834650
$116$	2.76773	−	1.00737i	0.256977	−	0.0935320i
$117$	11.7460	−	13.6314i	1.08592	−	1.26022i
$118$	−2.66257	+	2.23416i	−0.245110	+	0.205671i
$119$	−0.207953	+	0.247829i	−0.0190630	+	0.0227185i
$120$	−1.10462	−	1.33410i	−0.100837	−	0.121786i
$121$	−5.39831	−	9.35014i	−0.490755	−	0.850013i
$122$	4.65774	−	8.06744i	0.421692	−	0.730392i
$123$	2.70003	+	15.9223i	0.243454	+	1.43566i
$124$	3.20123	−	8.79532i	0.287479	−	0.789843i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	−1.34269	−	0.0176041i	−0.119616	−	0.00156829i
$127$	2.99597	−	0.528271i	0.265850	−	0.0468764i	−0.0391344	−	0.999234i	$-0.512460\pi$
$127$	2.99597	−	0.528271i	0.265850	−	0.0468764i	0.304984	+	0.952358i	$0.401349\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	16.9621	+	6.29993i	1.49343	+	0.554678i
$130$	−1.04154	+	5.90687i	−0.0913491	+	0.518067i
$131$	1.33200	+	3.65963i	0.116377	+	0.319743i	0.984182	−	0.177162i	$-0.0566917\pi$
$131$	1.33200	+	3.65963i	0.116377	+	0.319743i	−0.867805	+	0.496906i	$0.834470\pi$
$132$	0.679027	−	0.386124i	0.0591017	−	0.0336077i
$133$	0.973135	−	1.69103i	0.0843815	−	0.146631i
$134$			9.98271i			0.862374i
$135$	−1.68083	−	4.91679i	−0.144663	−	0.423170i
$136$	−0.711802	−	0.125510i	−0.0610365	−	0.0107624i
$137$	−10.1807	−	12.1329i	−0.869794	−	1.03658i	−0.998989	−	0.0449611i	$-0.985684\pi$
$137$	−10.1807	−	12.1329i	−0.869794	−	1.03658i	0.129195	−	0.991619i	$-0.458761\pi$
$138$	−15.2494	−	2.79208i	−1.29812	−	0.237677i
$139$	−0.599610	−	3.40056i	−0.0508583	−	0.288431i	0.948762	−	0.315992i	$-0.102337\pi$
$139$	−0.599610	−	3.40056i	−0.0508583	−	0.288431i	−0.999620	+	0.0275604i	$0.991226\pi$
$140$	0.387633	−	0.223800i	0.0327610	−	0.0189146i
$141$	0.0953151	−	14.5402i	0.00802698	−	1.22451i
$142$	−2.36768	−	0.861764i	−0.198691	−	0.0723176i
$143$	−2.54189	−	0.925171i	−0.212563	−	0.0773666i
$144$	−1.46581	−	2.61752i	−0.122151	−	0.218126i
$145$	−2.55075	+	1.47268i	−0.211828	+	0.122299i
$146$	−0.481319	−	2.72969i	−0.0398342	−	0.225911i
$147$	−2.12110	+	11.5848i	−0.174945	+	0.955495i
$148$	−1.08089	−	1.28815i	−0.0888485	−	0.105886i
$149$	−10.5841	−	1.86625i	−0.867079	−	0.152889i	−0.277623	−	0.960690i	$-0.589547\pi$
$149$	−10.5841	−	1.86625i	−0.867079	−	0.152889i	−0.589456	+	0.807800i	$0.700658\pi$
$150$	1.31950	+	1.12201i	0.107737	+	0.0916121i
$151$			2.81544i			0.229118i	0.993416	+	0.114559i	$0.0365454\pi$
$151$			2.81544i			0.229118i	−0.993416	+	0.114559i	$0.963455\pi$
$152$	4.35889	−	0.00615684i	0.353553	−	0.000499385i
$153$	−1.86347	−	1.10870i	−0.150653	−	0.0896330i
$154$	0.0690409	+	0.189688i	0.00556348	+	0.0152855i
$155$	−1.62531	+	9.21759i	−0.130548	+	0.740374i
$156$	−3.61710	+	9.73880i	−0.289600	+	0.779728i
$157$	3.64654	+	3.05981i	0.291026	+	0.244200i	0.776597	−	0.629997i	$-0.216944\pi$
$157$	3.64654	+	3.05981i	0.291026	+	0.244200i	−0.485571	+	0.874197i	$0.661388\pi$
$158$	−3.65055	+	0.643690i	−0.290422	+	0.0512092i
$159$	11.6186	−	19.8228i	0.921418	−	1.57205i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	1.37024	−	3.76469i	0.107990	−	0.296699i
$162$	−1.32992	−	8.90120i	−0.104489	−	0.699344i
$163$	−6.06142	+	10.4987i	−0.474767	+	0.822321i	−0.999582	−	0.0288954i	$-0.990801\pi$
$163$	−6.06142	+	10.4987i	−0.474767	+	0.822321i	0.524815	+	0.851216i	$0.324134\pi$
$164$	−4.66198	−	8.07479i	−0.364040	−	0.630535i
$165$	−0.601661	+	0.498169i	−0.0468392	+	0.0387824i
$166$	4.86536	−	5.79830i	0.377625	−	0.450036i
$167$	−8.56382	+	7.18590i	−0.662688	+	0.556062i	−0.910891	−	0.412647i	$-0.864604\pi$
$167$	−8.56382	+	7.18590i	−0.662688	+	0.556062i	0.248203	+	0.968708i	$0.420160\pi$
$168$	0.730235	−	0.260376i	0.0563389	−	0.0200884i
$169$	21.5903	−	7.85822i	1.66079	−	0.604478i
$170$	0.722782			0.0554349
$171$	12.2349	+	4.61593i	0.935628	+	0.352989i
$172$	−10.4467			−0.796556
$173$	17.4922	−	6.36664i	1.32991	−	0.484046i	0.423287	−	0.905996i	$-0.360876\pi$
$173$	17.4922	−	6.36664i	1.32991	−	0.484046i	0.906619	+	0.421949i	$0.138654\pi$
$174$	−4.80518	+	1.71335i	−0.364280	+	0.129889i
$175$	−0.342882	+	0.287712i	−0.0259194	+	0.0217490i
$176$	−0.289889	+	0.345476i	−0.0218512	+	0.0260413i
$177$	4.63697	−	3.83937i	0.348536	−	0.288585i
$178$	3.28599	+	5.69151i	0.246296	+	0.426596i
$179$	−9.91629	+	17.1755i	−0.741178	+	1.28376i	0.210781	+	0.977533i	$0.432399\pi$
$179$	−9.91629	+	17.1755i	−0.741178	+	1.28376i	−0.951959	+	0.306225i	$0.900934\pi$
$180$	1.89807	+	2.32322i	0.141474	+	0.173162i
$181$	−1.35995	+	3.73642i	−0.101084	+	0.277726i	−0.979918	−	0.199402i	$-0.936100\pi$
$181$	−1.35995	+	3.73642i	−0.101084	+	0.277726i	0.878834	+	0.477128i	$0.158322\pi$
$182$	−2.32502	−	1.34235i	−0.172342	−	0.0995018i
$183$	−8.15886	+	13.9200i	−0.603120	+	1.02900i
$184$	8.81464	−	1.55426i	0.649824	−	0.114581i
$185$	1.28815	+	1.08089i	0.0947069	+	0.0794685i
$186$	−5.64444	+	15.1973i	−0.413871	+	1.11432i
$187$	−0.0566034	+	0.321014i	−0.00413925	+	0.0234748i
$188$	2.87126	+	7.88871i	0.209408	+	0.575344i
$189$	2.32535	+	0.0457351i	0.169144	+	0.00332674i
$190$	−4.29160	+	0.762977i	−0.311346	+	0.0553522i
$191$		−	8.39875i		−	0.607712i	−0.952718	−	0.303856i	$-0.901726\pi$
$191$		−	8.39875i		−	0.607712i	0.952718	−	0.303856i	$-0.0982742\pi$
$192$	1.31950	+	1.12201i	0.0952268	+	0.0809744i
$193$	10.3436	+	1.82386i	0.744549	+	0.131284i	0.533037	−	0.846092i	$-0.321050\pi$
$193$	10.3436	+	1.82386i	0.744549	+	0.131284i	0.211511	+	0.977376i	$0.432162\pi$
$194$	11.4366	+	13.6296i	0.821097	+	0.978545i
$195$	1.87103	−	10.2190i	0.133987	−	0.731794i
$196$	−1.18075	−	6.69635i	−0.0843391	−	0.478311i
$197$	18.6545	−	10.7702i	1.32908	−	0.767345i	0.343923	−	0.938998i	$-0.388244\pi$
$197$	18.6545	−	10.7702i	1.32908	−	0.767345i	0.985157	+	0.171653i	$0.0549109\pi$
$198$	−1.18047	+	0.661062i	−0.0838922	+	0.0469796i
$199$	5.77245	+	2.10100i	0.409198	+	0.148936i	0.538414	−	0.842681i	$-0.319024\pi$
$199$	5.77245	+	2.10100i	0.409198	+	0.148936i	−0.129216	+	0.991616i	$0.541246\pi$
$200$	−0.939693	−	0.342020i	−0.0664463	−	0.0241845i
$201$	0.113342	−	17.2902i	0.00799450	−	1.21956i
$202$	2.01425	−	1.16293i	0.141722	−	0.0818233i
$203$	−0.228928	−	1.29831i	−0.0160676	−	0.0911237i
$204$	1.23143	+	0.225466i	0.0862170	+	0.0157858i
$205$	5.99333	+	7.14257i	0.418592	+	0.498859i
$206$	−10.7594	−	1.89717i	−0.749641	−	0.132182i
$207$	26.3805	+	5.00905i	1.83357	+	0.348153i
$208$		−	5.99799i		−	0.415886i
$209$	−0.00277666	−	1.96581i	−0.000192065	−	0.135978i
$210$	−0.673927	+	0.383224i	−0.0465054	+	0.0264450i
$211$	6.42334	+	17.6480i	0.442201	+	1.21494i	0.938041	+	0.346523i	$0.112638\pi$
$211$	6.42334	+	17.6480i	0.442201	+	1.21494i	−0.495841	+	0.868413i	$0.665140\pi$
$212$	−2.30357	+	13.0642i	−0.158210	+	0.897251i
$213$	4.09106	+	1.51947i	0.280315	+	0.104112i
$214$	−5.97559	−	5.01412i	−0.408483	−	0.342758i
$215$	10.2880	−	1.81406i	0.701637	−	0.123718i
$216$	2.50908	+	4.55022i	0.170722	+	0.309603i
$217$	−3.62816	−	2.09472i	−0.246296	−	0.142199i
$218$	−4.16156	+	11.4338i	−0.281857	+	0.774395i
$219$	0.802658	+	4.73333i	0.0542386	+	0.319849i
$220$	0.225494	−	0.390566i	0.0152028	−	0.0263320i
$221$	−2.16762	−	3.75443i	−0.145810	−	0.252550i
$222$	1.85749	+	2.24337i	0.124666	+	0.150565i
$223$	13.4827	−	16.0681i	0.902871	−	1.07600i	−0.0938899	−	0.995583i	$-0.529930\pi$
$223$	13.4827	−	16.0681i	0.902871	−	1.07600i	0.996761	−	0.0804176i	$-0.0256254\pi$
$224$	−0.342882	+	0.287712i	−0.0229098	+	0.0192236i
$225$	−2.27266	−	1.95833i	−0.151510	−	0.130555i
$226$	−6.60676	+	2.40466i	−0.439475	+	0.159956i
$227$	8.50175			0.564281			0.282140	−	0.959373i	$-0.408956\pi$
$227$	8.50175			0.564281			0.282140	+	0.959373i	$0.408956\pi$
$228$	−7.54973	−	0.0388263i	−0.499993	−	0.00257133i
$229$	−3.36659			−0.222470			−0.111235	−	0.993794i	$-0.535481\pi$
$229$	−3.36659			−0.222470			−0.111235	+	0.993794i	$0.535481\pi$
$230$	−8.41083	+	3.06129i	−0.554594	+	0.201856i
$231$	−0.117426	−	0.329327i	−0.00772607	−	0.0216681i
$232$	2.25627	−	1.89324i	0.148131	−	0.124297i
$233$	1.58281	−	1.88632i	0.103693	−	0.123577i	−0.711702	−	0.702482i	$-0.752075\pi$
$233$	1.58281	−	1.88632i	0.103693	−	0.123577i	0.815395	+	0.578905i	$0.196520\pi$
$234$	6.37545	−	16.8267i	0.416776	−	1.09999i
$235$	−4.19750	−	7.27028i	−0.273815	−	0.474261i
$236$	−1.73787	+	3.01008i	−0.113126	+	0.195939i
$237$	6.33010	−	1.07343i	0.411184	−	0.0697269i
$238$	−0.110650	+	0.304007i	−0.00717235	+	0.0197059i
$239$	−22.6835	−	13.0964i	−1.46728	−	0.847133i	−0.467948	−	0.883756i	$-0.655006\pi$
$239$	−22.6835	−	13.0964i	−1.46728	−	0.847133i	−0.999329	+	0.0366235i	$0.988340\pi$
$240$	−1.49429	−	0.875839i	−0.0964561	−	0.0565352i
$241$	−9.07705	+	1.60053i	−0.584704	+	0.103099i	−0.458172	−	0.888863i	$-0.651496\pi$
$241$	−9.07705	+	1.60053i	−0.584704	+	0.103099i	−0.126532	+	0.991963i	$0.540385\pi$
$242$	−8.27068	−	6.93993i	−0.531660	−	0.446115i
$243$	2.20238	+	15.4321i	0.141283	+	0.989969i
$244$	1.61762	−	9.17395i	0.103557	−	0.587302i
$245$	2.32562	+	6.38958i	0.148578	+	0.408216i
$246$	7.98294	+	14.0386i	0.508973	+	0.895067i
$247$	16.8337	+	20.0042i	1.07110	+	1.27284i
$248$		−	9.35978i		−	0.594347i
$249$	−8.49269	+	9.98750i	−0.538203	+	0.632932i
$250$	0.984808	+	0.173648i	0.0622847	+	0.0109825i
$251$	3.59997	+	4.29028i	0.227228	+	0.270800i	0.867598	−	0.497267i	$-0.165663\pi$
$251$	3.59997	+	4.29028i	0.227228	+	0.270800i	−0.640369	+	0.768067i	$0.721219\pi$
$252$	−1.26773	+	0.442683i	−0.0798597	+	0.0278864i
$253$	−0.700951	−	3.97529i	−0.0440684	−	0.249924i
$254$	2.63461	−	1.52109i	0.165310	−	0.0954420i
$255$	−1.25187	−	0.00820632i	−0.0783951	−	0.000513900i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−22.7367	−	8.27549i	−1.41828	−	0.516211i	−0.484730	−	0.874664i	$-0.661082\pi$
$257$	−22.7367	−	8.27549i	−1.41828	−	0.516211i	−0.933548	+	0.358453i	$0.883304\pi$
$258$	18.0939	+	0.118610i	1.12648	+	0.00738434i
$259$	−0.651831	+	0.376335i	−0.0405028	+	0.0233843i
$260$	1.04154	+	5.90687i	0.0645936	+	0.366328i
$261$	8.34209	−	2.91300i	0.516362	−	0.180310i
$262$	2.50333	+	2.98336i	0.154656	+	0.184312i
$263$	−16.6084	−	2.92851i	−1.02412	−	0.180579i	−0.363730	−	0.931505i	$-0.618497\pi$
$263$	−16.6084	−	2.92851i	−1.02412	−	0.180579i	−0.660387	+	0.750925i	$0.729608\pi$
$264$	0.506014	−	0.595078i	0.0311430	−	0.0366245i
$265$		−	13.2657i		−	0.814906i
$266$	0.336081	−	1.92188i	0.0206065	−	0.117838i
$267$	−5.62676	−	9.89507i	−0.344352	−	0.605569i
$268$	3.41429	+	9.38067i	0.208561	+	0.573016i
$269$	−0.771737	+	4.37674i	−0.0470536	+	0.266854i	−0.999254	−	0.0386199i	$-0.987704\pi$
$269$	−0.771737	+	4.37674i	−0.0470536	+	0.266854i	0.952200	+	0.305474i	$0.0988150\pi$
$270$	−3.26110	−	4.04539i	−0.198464	−	0.246195i
$271$	−21.1699	−	17.7637i	−1.28598	−	1.07907i	−0.992390	−	0.123135i	$-0.960705\pi$
$271$	−21.1699	−	17.7637i	−1.28598	−	1.07907i	−0.293591	−	0.955931i	$-0.594850\pi$
$272$	−0.711802	+	0.125510i	−0.0431593	+	0.00761015i
$273$	4.01173	+	2.35137i	0.242801	+	0.142311i
$274$	−13.7164	−	7.91916i	−0.828638	−	0.478414i
$275$	−0.154247	+	0.423789i	−0.00930143	+	0.0255555i
$276$	−15.2847	+	2.59192i	−0.920032	+	0.156015i
$277$	−0.777677	+	1.34698i	−0.0467261	+	0.0809319i	−0.888443	−	0.458988i	$-0.848212\pi$
$277$	−0.777677	+	1.34698i	−0.0467261	+	0.0809319i	0.841716	+	0.539920i	$0.181545\pi$
$278$	−1.72651	−	2.99040i	−0.103549	−	0.179352i
$279$	9.94880	−	26.2578i	0.595619	−	1.57201i
$280$	0.287712	−	0.342882i	0.0171941	−	0.0204911i
$281$	4.32925	−	3.63267i	0.258262	−	0.216707i	−0.504459	−	0.863436i	$-0.668308\pi$
$281$	4.32925	−	3.63267i	0.258262	−	0.216707i	0.762720	+	0.646729i	$0.223863\pi$
$282$	−4.88349	−	13.6960i	−0.290808	−	0.815583i
$283$	−20.7270	+	7.54401i	−1.23209	+	0.448445i	−0.874313	−	0.485362i	$-0.838688\pi$
$283$	−20.7270	+	7.54401i	−1.23209	+	0.448445i	−0.357778	+	0.933807i	$0.616466\pi$
$284$	−2.51963			−0.149512
$285$	7.44178	−	1.27276i	0.440813	−	0.0753919i
$286$	−2.70502			−0.159951
$287$	−3.92172	+	1.42739i	−0.231492	+	0.0842562i
$288$	−2.27266	−	1.95833i	−0.133917	−	0.115395i
$289$	12.6226	−	10.5916i	0.742504	−	0.623035i
$290$	−1.89324	+	2.25627i	−0.111175	+	0.132493i
$291$	−19.6535	−	23.7364i	−1.15211	−	1.39145i
$292$	−1.38590	−	2.40045i	−0.0811038	−	0.140476i
$293$	−5.10466	+	8.84153i	−0.298217	+	0.516528i	−0.975728	−	0.218985i	$-0.929725\pi$
$293$	−5.10466	+	8.84153i	−0.298217	+	0.516528i	0.677511	+	0.735513i	$0.263059\pi$
$294$	1.96904	+	11.6116i	0.114837	+	0.677201i
$295$	1.18877	−	3.26613i	0.0692130	−	0.190161i
$296$	−1.45628	−	0.840782i	−0.0846444	−	0.0488695i
$297$	2.05209	−	1.13157i	0.119074	−	0.0656601i
$298$	−10.5841	+	1.86625i	−0.613118	+	0.108109i
$299$	41.1257	+	34.5085i	2.37836	+	1.99568i
$300$	1.62368	+	0.603053i	0.0937430	+	0.0348173i
$301$	−0.811972	+	4.60492i	−0.0468013	+	0.265423i
$302$	0.962939	+	2.64565i	0.0554109	+	0.152240i
$303$	−3.50191	+	1.99134i	−0.201180	+	0.114399i
$304$	4.09392	−	1.49662i	0.234802	−	0.0858368i
$305$			9.31548i			0.533403i
$306$	−2.13029	−	0.404492i	−0.121780	−	0.0231233i
$307$	−9.52716	−	1.67990i	−0.543744	−	0.0958767i	−0.104972	−	0.994475i	$-0.533475\pi$
$307$	−9.52716	−	1.67990i	−0.543744	−	0.0958767i	−0.438772	+	0.898598i	$0.644586\pi$
$308$	0.129754	+	0.154635i	0.00739345	+	0.00881117i
$309$	18.6138	+	3.40808i	1.05890	+	0.193879i
$310$	1.62531	+	9.21759i	0.0923114	+	0.523524i
$311$	12.4864	−	7.20901i	0.708037	−	0.408785i	−0.102297	−	0.994754i	$-0.532619\pi$
$311$	12.4864	−	7.20901i	0.708037	−	0.408785i	0.810334	+	0.585969i	$0.199286\pi$
$312$	−0.0681000	+	10.3886i	−0.00385540	+	0.588139i
$313$	5.38079	+	1.95845i	0.304140	+	0.110698i	0.489582	−	0.871957i	$-0.337149\pi$
$313$	5.38079	+	1.95845i	0.304140	+	0.110698i	−0.185442	+	0.982655i	$0.559372\pi$
$314$	4.47315	+	1.62809i	0.252434	+	0.0918786i
$315$	1.17160	−	0.656098i	0.0660123	−	0.0369669i
$316$	−3.21024	+	1.85343i	−0.180590	+	0.104264i
$317$	1.48613	+	8.42829i	0.0834696	+	0.473380i	0.997676	+	0.0681317i	$0.0217038\pi$
$317$	1.48613	+	8.42829i	0.0834696	+	0.473380i	−0.914207	+	0.405248i	$0.867185\pi$
$318$	4.13814	−	22.6012i	0.232055	−	1.26741i
$319$	−0.853826	−	1.01755i	−0.0478051	−	0.0569719i
$320$	0.984808	+	0.173648i	0.0550524	+	0.00970723i
$321$	10.2929	+	8.75237i	0.574492	+	0.488509i
$322$		−	4.00630i		−	0.223262i
$323$	2.02171	−	2.41631i	0.112491	−	0.134447i
$324$	−4.29411	−	7.90953i	−0.238561	−	0.439418i
$325$	−2.05143	−	5.63627i	−0.113793	−	0.312644i
$326$	−2.10511	+	11.9387i	−0.116591	+	0.661222i
$327$	7.33770	−	19.7562i	0.405776	−	1.09252i
$328$	−7.14257	−	5.99333i	−0.394382	−	0.330926i
$329$	3.70052	−	0.652501i	0.204016	−	0.0359735i
$330$	−0.394992	+	0.673906i	−0.0217436	+	0.0370973i
$331$	14.4127	+	8.32117i	0.792193	+	0.457373i	0.840734	−	0.541448i	$-0.182124\pi$
$331$	14.4127	+	8.32117i	0.792193	+	0.457373i	−0.0485411	+	0.998821i	$0.515457\pi$
$332$	2.58880	−	7.11267i	0.142079	−	0.390359i
$333$	−3.19172	−	3.90664i	−0.174905	−	0.214082i
$334$	−5.58964	+	9.68154i	−0.305851	+	0.529750i
$335$	−4.99135	−	8.64528i	−0.272707	−	0.472342i
$336$	0.597143	−	0.494428i	0.0325768	−	0.0269733i
$337$	11.8502	−	14.1225i	0.645519	−	0.769300i	−0.339712	−	0.940530i	$-0.610330\pi$
$337$	11.8502	−	14.1225i	0.645519	−	0.769300i	0.985231	+	0.171229i	$0.0547740\pi$
$338$	17.6006	−	14.7686i	0.957344	−	0.803307i
$339$	11.4703	−	4.08990i	0.622981	−	0.222133i
$340$	0.679193	−	0.247206i	0.0368344	−	0.0134066i
$341$	−4.22114			−0.228588
$342$	13.0758	+	0.152966i	0.707058	+	0.00827144i
$343$	−6.17673			−0.333512
$344$	−9.81672	+	3.57299i	−0.529282	+	0.192643i
$345$	14.6024	−	5.20670i	0.786168	−	0.280320i
$346$	14.2598	−	11.9654i	0.766610	−	0.643262i
$347$	6.41137	−	7.64077i	0.344180	−	0.410178i	−0.565990	−	0.824412i	$-0.691506\pi$
$347$	6.41137	−	7.64077i	0.344180	−	0.410178i	0.910171	+	0.414234i	$0.135950\pi$
$348$	−3.92939	+	3.25349i	−0.210637	+	0.174406i
$349$	0.330289	+	0.572077i	0.0176800	+	0.0306226i	0.874730	−	0.484611i	$-0.161039\pi$
$349$	0.330289	+	0.572077i	0.0176800	+	0.0306226i	−0.857050	+	0.515233i	$0.827705\pi$
$350$	−0.223800	+	0.387633i	−0.0119626	+	0.0207199i
$351$	−11.2334	+	29.0716i	−0.599595	+	1.55173i
$352$	−0.154247	+	0.423789i	−0.00822138	+	0.0225881i
$353$	−7.55118	−	4.35967i	−0.401909	−	0.232042i	0.285399	−	0.958409i	$-0.407874\pi$
$353$	−7.55118	−	4.35967i	−0.401909	−	0.232042i	−0.687307	+	0.726367i	$0.741207\pi$
$354$	3.04419	−	5.19377i	0.161797	−	0.276046i
$355$	2.48135	−	0.437529i	0.131696	−	0.0232216i
$356$	5.03443	+	4.22439i	0.266824	+	0.223892i
$357$	0.195098	−	0.525289i	0.0103257	−	0.0278012i
$358$	−3.44389	+	19.5313i	−0.182015	+	1.03226i
$359$	−4.75634	−	13.0679i	−0.251030	−	0.689700i	−0.999644	−	0.0266930i	$-0.991502\pi$
$359$	−4.75634	−	13.0679i	−0.251030	−	0.689700i	0.748614	−	0.663007i	$-0.230720\pi$
$360$	2.57819	+	1.53393i	0.135882	+	0.0808453i
$361$	−9.45348	+	16.4813i	−0.497552	+	0.867434i
$362$			3.97622i			0.208985i
$363$	14.2461	+	12.1140i	0.747729	+	0.635818i
$364$	−2.64392	−	0.466194i	−0.138579	−	0.0244352i
$365$	1.78168	+	2.12333i	0.0932575	+	0.111140i
$366$	−2.90589	+	15.8710i	−0.151893	+	0.829593i
$367$	2.46383	+	13.9731i	0.128611	+	0.729388i	0.979097	+	0.203391i	$0.0651964\pi$
$367$	2.46383	+	13.9731i	0.128611	+	0.729388i	−0.850487	+	0.525997i	$0.823692\pi$
$368$	7.75146	−	4.47531i	0.404073	−	0.233292i
$369$	−13.6672	−	24.4056i	−0.711484	−	1.27051i
$370$	1.58015	+	0.575129i	0.0821483	+	0.0298995i
$371$	5.57965	+	2.03083i	0.289681	+	0.105435i
$372$	−0.106269	+	16.2113i	−0.00550979	+	0.840515i
$373$	−26.6703	+	15.3981i	−1.38094	+	0.797284i	−0.992270	−	0.124095i	$-0.960397\pi$
$373$	−26.6703	+	15.3981i	−1.38094	+	0.797284i	−0.388666	+	0.921379i	$0.627064\pi$
$374$	0.0566034	+	0.321014i	0.00292689	+	0.0165992i
$375$	−1.70373	−	0.311942i	−0.0879802	−	0.0161086i
$376$	5.39620	+	6.43094i	0.278288	+	0.331650i
$377$	17.3978	+	3.06770i	0.896033	+	0.157995i
$378$	2.20076	−	0.752340i	0.113195	−	0.0386962i
$379$			3.34690i			0.171919i	0.996299	+	0.0859593i	$0.0273955\pi$
$379$			3.34690i			0.171919i	−0.996299	+	0.0859593i	$0.972605\pi$
$380$	−3.77184	+	2.18478i	−0.193491	+	0.112077i
$381$	−4.58046	+	2.60464i	−0.234664	+	0.133440i
$382$	−2.87254	−	7.89225i	−0.146972	−	0.403802i
$383$	2.96057	−	16.7902i	0.151278	−	0.857941i	−0.810832	−	0.585279i	$-0.800985\pi$
$383$	2.96057	−	16.7902i	0.151278	−	0.857941i	0.962110	−	0.272662i	$-0.0879041\pi$
$384$	1.62368	+	0.603053i	0.0828579	+	0.0307744i
$385$	−0.154635	−	0.129754i	−0.00788095	−	0.00661290i
$386$	10.3436	−	1.82386i	0.526475	−	0.0928318i
$387$	−31.3375	−	0.410868i	−1.59297	−	0.0208856i
$388$	15.4084	+	8.89606i	0.782245	+	0.451629i
$389$	−8.55726	+	23.5109i	−0.433870	+	1.19205i	0.509547	+	0.860443i	$0.329813\pi$
$389$	−8.55726	+	23.5109i	−0.433870	+	1.19205i	−0.943418	+	0.331607i	$0.892409\pi$
$390$	−1.73690	−	10.2426i	−0.0879512	−	0.518654i
$391$	3.23468	−	5.60262i	0.163585	−	0.283337i
$392$	−3.39983	−	5.88867i	−0.171717	−	0.297423i
$393$	−4.30194	−	5.19564i	−0.217004	−	0.262085i
$394$	13.8459	−	16.5009i	0.697546	−	0.831303i
$395$	2.83962	−	2.38272i	0.142877	−	0.119888i
$396$	−0.883180	+	1.02494i	−0.0443815	+	0.0515051i
$397$	−34.9459	+	12.7193i	−1.75388	+	0.638362i	−0.999830	−	0.0184497i	$-0.994127\pi$
$397$	−34.9459	+	12.7193i	−1.75388	+	0.638362i	−0.754055	+	0.656811i	$0.771905\pi$
$398$	6.14291			0.307916
$399$	−0.603918	+	3.32491i	−0.0302337	+	0.166454i
$400$	−1.00000			−0.0500000
$401$	9.87117	−	3.59281i	0.492943	−	0.179416i	−0.0835745	−	0.996502i	$-0.526634\pi$
$401$	9.87117	−	3.59281i	0.492943	−	0.179416i	0.576517	+	0.817085i	$0.304411\pi$
$402$	−5.80708	−	16.2862i	−0.289631	−	0.812283i
$403$	43.0057	−	36.0860i	2.14226	−	1.79757i
$404$	1.49503	−	1.78171i	0.0743806	−	0.0886433i
$405$	5.60234	+	7.04370i	0.278383	+	0.350004i
$406$	−0.659171	−	1.14172i	−0.0327141	−	0.0566625i
$407$	−0.379182	+	0.656763i	−0.0187954	+	0.0325545i
$408$	1.23428	−	0.209303i	0.0611057	−	0.0103620i
$409$	−3.63005	+	9.97349i	−0.179495	+	0.493158i	−0.996511	−	0.0834564i	$-0.973404\pi$
$409$	−3.63005	+	9.97349i	−0.179495	+	0.493158i	0.817017	+	0.576614i	$0.195626\pi$
$410$	8.07479	+	4.66198i	0.398785	+	0.230239i
$411$	23.6671	+	13.8718i	1.16741	+	0.684247i
$412$	−10.7594	+	1.89717i	−0.530076	+	0.0934668i
$413$	1.19177	+	1.00001i	0.0586431	+	0.0492074i
$414$	26.5028	−	4.31570i	1.30254	−	0.212105i
$415$	−1.31437	+	7.45416i	−0.0645198	+	0.365910i
$416$	−2.05143	−	5.63627i	−0.100580	−	0.276341i
$417$	2.95638	+	5.19902i	0.144775	+	0.254597i
$418$	−0.674954	−	1.84630i	−0.0330131	−	0.0903057i
$419$			6.03152i			0.294659i	0.989087	+	0.147330i	$0.0470678\pi$
$419$			6.03152i			0.294659i	−0.989087	+	0.147330i	$0.952932\pi$
$420$	−0.502214	+	0.590610i	−0.0245055	+	0.0288188i
$421$	3.19225	+	0.562881i	0.155581	+	0.0274331i	0.250896	−	0.968014i	$-0.419275\pi$
$421$	3.19225	+	0.562881i	0.155581	+	0.0274331i	−0.0953151	+	0.995447i	$0.530386\pi$
$422$	12.0719	+	14.3868i	0.587652	+	0.700336i
$423$	8.30277	+	23.7770i	0.403694	+	1.15608i
$424$	2.30357	+	13.0642i	0.111871	+	0.634453i
$425$	−0.625948	+	0.361391i	−0.0303629	+	0.0175301i
$426$	4.36403	+	0.0286073i	0.211438	+	0.00138603i
$427$	−3.91815	−	1.42609i	−0.189613	−	0.0690134i
$428$	−7.33015	−	2.66796i	−0.354316	−	0.128961i
$429$	4.68513	+	0.0307122i	0.226200	+	0.00148280i
$430$	9.04713	−	5.22337i	0.436292	−	0.251893i
$431$	−1.65413	−	9.38105i	−0.0796768	−	0.451869i	−0.998379	−	0.0569181i	$-0.981873\pi$
$431$	−1.65413	−	9.38105i	−0.0796768	−	0.451869i	0.918702	−	0.394951i	$-0.129239\pi$
$432$	3.91404	+	3.41765i	0.188314	+	0.164432i
$433$	−10.9890	−	13.0962i	−0.528098	−	0.629362i	0.434378	−	0.900731i	$-0.356968\pi$
$433$	−10.9890	−	13.0962i	−0.528098	−	0.629362i	−0.962476	+	0.271368i	$0.912524\pi$
$434$	−4.12580	−	0.727489i	−0.198045	−	0.0349206i
$435$	3.30473	−	3.88640i	0.158450	−	0.186339i
$436$			12.1676i			0.582722i
$437$	−13.2921	+	36.6808i	−0.635846	+	1.75468i
$438$	2.37315	+	4.17335i	0.113393	+	0.199411i
$439$	−1.47812	−	4.06111i	−0.0705470	−	0.193826i	0.899408	−	0.437109i	$-0.143998\pi$
$439$	−1.47812	−	4.06111i	−0.0705470	−	0.193826i	−0.969955	+	0.243283i	$0.921776\pi$
$440$	0.0783131	−	0.444136i	0.00373343	−	0.0211733i
$441$	−3.27857	−	20.1338i	−0.156122	−	0.958751i
$442$	−3.32099	−	2.78664i	−0.157963	−	0.132547i
$443$	11.8982	−	2.09797i	0.565299	−	0.0996774i	0.116307	−	0.993213i	$-0.462894\pi$
$443$	11.8982	−	2.09797i	0.565299	−	0.0996774i	0.448992	+	0.893536i	$0.351783\pi$
$444$	2.51275	+	1.47278i	0.119250	+	0.0698951i
$445$	−5.69151	−	3.28599i	−0.269803	−	0.155771i
$446$	7.17402	−	19.7105i	0.339700	−	0.933317i
$447$	18.3529	−	3.11221i	0.868063	−	0.147202i
$448$	−0.223800	+	0.387633i	−0.0105736	+	0.0183140i
$449$	12.6422	+	21.8969i	0.596621	+	1.03338i	0.993316	+	0.115427i	$0.0368236\pi$
$449$	12.6422	+	21.8969i	0.596621	+	1.03338i	−0.396695	+	0.917950i	$0.629843\pi$
$450$	−2.80538	−	1.06293i	−0.132247	−	0.0501070i
$451$	−2.70291	+	3.22121i	−0.127275	+	0.151681i
$452$	−5.38588	+	4.51929i	−0.253330	+	0.212569i
$453$	−1.63778	−	4.59324i	−0.0769498	−	0.215809i
$454$	7.98903	−	2.90777i	0.374944	−	0.136468i
$455$	2.68470			0.125861
$456$	−7.10771	+	2.54568i	−0.332849	+	0.119212i
$457$	−35.7380			−1.67175			−0.835876	−	0.548918i	$-0.815040\pi$
$457$	−35.7380			−1.67175			−0.835876	+	0.548918i	$0.815040\pi$
$458$	−3.16356	+	1.15144i	−0.147823	+	0.0538033i
$459$	3.68509	+	0.724773i	0.172005	+	0.0338295i
$460$	−6.85657	+	5.75335i	−0.319689	+	0.268251i
$461$	22.7627	−	27.1275i	1.06016	−	1.26345i	0.0967850	−	0.995305i	$-0.469144\pi$
$461$	22.7627	−	27.1275i	1.06016	−	1.26345i	0.963378	−	0.268148i	$-0.0864115\pi$
$462$	−0.222981	−	0.269304i	−0.0103740	−	0.0125291i
$463$	14.7573	+	25.5604i	0.685829	+	1.18789i	0.973176	+	0.230064i	$0.0738934\pi$
$463$	14.7573	+	25.5604i	0.685829	+	1.18789i	−0.287347	+	0.957827i	$0.592773\pi$
$464$	1.47268	−	2.55075i	0.0683673	−	0.118416i
$465$	−2.71040	−	15.9834i	−0.125692	−	0.741214i
$466$	0.842195	−	2.31391i	0.0390139	−	0.107190i
$467$	21.8121	+	12.5932i	1.00935	+	0.582746i	0.911000	−	0.412406i	$-0.135312\pi$
$467$	21.8121	+	12.5932i	1.00935	+	0.582746i	0.0983456	+	0.995152i	$0.468645\pi$
$468$	0.235900	−	17.9924i	0.0109045	−	0.831700i
$469$	4.40038	−	0.775906i	0.203191	−	0.0358280i
$470$	−6.43094	−	5.39620i	−0.296637	−	0.248908i
$471$	−7.72907	−	2.87067i	−0.356137	−	0.132273i
$472$	−0.603556	+	3.42294i	−0.0277809	+	0.157553i
$473$	1.61137	+	4.42721i	0.0740911	+	0.203564i
$474$	5.58122	−	3.17372i	0.256354	−	0.145774i
$475$	3.33515	−	2.80656i	0.153027	−	0.128774i
$476$			0.323518i			0.0148284i
$477$	−7.42392	+	39.0986i	−0.339918	+	1.79020i
$478$	−25.7948	−	4.54832i	−1.17983	−	0.208035i
$479$	−6.92808	−	8.25656i	−0.316552	−	0.377252i	0.584182	−	0.811623i	$-0.301415\pi$
$479$	−6.92808	−	8.25656i	−0.316552	−	0.377252i	−0.900734	+	0.434370i	$0.856971\pi$
$480$	−1.70373	−	0.311942i	−0.0777642	−	0.0142382i
$481$	−1.75142	−	9.93278i	−0.0798577	−	0.452896i
$482$	−7.98222	+	4.60854i	−0.363580	+	0.209913i
$483$	−0.0454867	+	6.93897i	−0.00206972	+	0.315734i
$484$	−10.1455	−	3.69266i	−0.461159	−	0.167848i
$485$	−16.7191	−	6.08526i	−0.759176	−	0.276318i
$486$	7.34765	+	13.7482i	0.333296	+	0.623629i
$487$	−18.9144	+	10.9202i	−0.857094	+	0.494843i	−0.863038	−	0.505139i	$-0.831441\pi$
$487$	−18.9144	+	10.9202i	−0.857094	+	0.494843i	0.00594424	+	0.999982i	$0.498108\pi$
$488$	−1.61762	−	9.17395i	−0.0732260	−	0.415285i
$489$	3.78163	−	20.6540i	0.171011	−	0.934008i
$490$	4.37073	+	5.20884i	0.197450	+	0.235311i
$491$	−24.6451	−	4.34560i	−1.11222	−	0.196114i	−0.412797	−	0.910823i	$-0.635448\pi$
$491$	−24.6451	−	4.34560i	−1.11222	−	0.196114i	−0.699422	+	0.714709i	$0.746559\pi$
$492$	12.3030	+	10.4616i	0.554661	+	0.471646i
$493$		−	2.12885i		−	0.0958786i
$494$	22.6604	+	13.0403i	1.01954	+	0.586712i
$495$	0.691784	−	1.16273i	0.0310934	−	0.0522608i
$496$	−3.20123	−	8.79532i	−0.143740	−	0.394921i
$497$	−0.195838	+	1.11065i	−0.00878454	+	0.0498196i
$498$	−4.56460	+	12.2899i	−0.204544	+	0.550722i
$499$	−22.0479	−	18.5004i	−0.986998	−	0.828189i	−0.00186745	−	0.999998i	$-0.500594\pi$
$499$	−22.0479	−	18.5004i	−0.986998	−	0.828189i	−0.985130	+	0.171809i	$0.945039\pi$
$500$	0.984808	−	0.173648i	0.0440419	−	0.00776578i
$501$	9.79125	−	16.7051i	0.437441	−	0.746328i
$502$	4.85023	+	2.80028i	0.216476	+	0.124983i
$503$	10.5421	−	28.9642i	0.470049	−	1.29145i	−0.447663	−	0.894202i	$-0.647744\pi$
$503$	10.5421	−	28.9642i	0.470049	−	1.29145i	0.917712	−	0.397246i	$-0.130034\pi$
$504$	−1.03987	+	0.849577i	−0.0463196	+	0.0378431i
$505$	−1.16293	+	2.01425i	−0.0517496	+	0.0896329i
$506$	−2.01831	−	3.49581i	−0.0897247	−	0.155408i
$507$	−30.6521	+	25.3796i	−1.36131	+	1.12715i
$508$	1.95548	−	2.33045i	0.0867605	−	0.103397i
$509$	−18.6127	+	15.6179i	−0.824992	+	0.692251i	−0.954135	−	0.299375i	$-0.903222\pi$
$509$	−18.6127	+	15.6179i	−0.824992	+	0.692251i	0.129143	+	0.991626i	$0.458777\pi$
$510$	−1.17918	+	0.420453i	−0.0522149	+	0.0186180i
$511$	−1.16584	+	0.424331i	−0.0515737	+	0.0187713i
$512$	−1.00000			−0.0441942
$513$	−22.6457	−	0.413399i	−0.999833	−	0.0182520i
$514$	−24.1959			−1.06724
$515$	10.2665	−	3.73669i	0.452395	−	0.164658i
$516$	17.0433	−	6.07701i	0.750287	−	0.267526i
$517$	2.90027	−	2.43362i	0.127554	−	0.107030i
$518$	−0.483806	+	0.576578i	−0.0212572	+	0.0253334i
$519$	−24.8340	+	20.5623i	−1.09009	+	0.902583i
$520$	2.99900	+	5.19441i	0.131515	+	0.227790i
$521$	−4.79563	+	8.30627i	−0.210100	+	0.363904i	−0.951746	−	0.306888i	$-0.900712\pi$
$521$	−4.79563	+	8.30627i	−0.210100	+	0.363904i	0.741646	+	0.670792i	$0.234046\pi$
$522$	6.84269	−	5.59048i	0.299497	−	0.244689i
$523$	−13.6257	+	37.4362i	−0.595808	+	1.63697i	0.163728	+	0.986506i	$0.447648\pi$
$523$	−13.6257	+	37.4362i	−0.595808	+	1.63697i	−0.759536	+	0.650465i	$0.774574\pi$
$524$	3.37273	+	1.94725i	0.147339	+	0.0850659i
$525$	0.392026	−	0.668845i	0.0171094	−	0.0291908i
$526$	−16.6084	+	2.92851i	−0.724160	+	0.127689i
$527$	−5.18236	−	4.34851i	−0.225747	−	0.189424i
$528$	0.271969	−	0.732258i	0.0118359	−	0.0318674i
$529$	−9.91767	+	56.2459i	−0.431203	+	2.44547i
$530$	−4.53714	−	12.4657i	−0.197081	−	0.541475i
$531$	−5.33155	+	8.96111i	−0.231369	+	0.388879i
$532$	−0.341509	−	1.92092i	−0.0148063	−	0.0832826i
$533$		−	55.9251i		−	2.42238i
$534$	−8.67174	−	7.37386i	−0.375263	−	0.319098i
$535$	7.68207	+	1.35456i	0.332125	+	0.0585626i
$536$	6.41676	+	7.64720i	0.277162	+	0.330309i
$537$	6.18662	−	33.7893i	0.266972	−	1.45812i
$538$	0.771737	+	4.37674i	0.0332719	+	0.188695i
$539$	−2.65572	+	1.53328i	−0.114390	+	0.0660430i
$540$	−4.44804	−	2.68606i	−0.191413	−	0.115590i
$541$	−10.0900	−	3.67245i	−0.433802	−	0.157891i	0.115883	−	0.993263i	$-0.463030\pi$
$541$	−10.0900	−	3.67245i	−0.433802	−	0.157891i	−0.549685	+	0.835372i	$0.685252\pi$
$542$	−25.9687	−	9.45185i	−1.11545	−	0.405992i
$543$	0.0451451	−	6.88686i	0.00193736	−	0.295543i
$544$	−0.625948	+	0.361391i	−0.0268373	+	0.0154945i
$545$	−2.11288	−	11.9827i	−0.0905059	−	0.513284i
$546$	4.57401	+	0.837473i	0.195749	+	0.0358405i
$547$	−4.91727	−	5.86017i	−0.210247	−	0.250563i	0.650607	−	0.759415i	$-0.274515\pi$
$547$	−4.91727	−	5.86017i	−0.210247	−	0.250563i	−0.860854	+	0.508852i	$0.830070\pi$
$548$	−15.5977	−	2.75030i	−0.666301	−	0.117487i
$549$	5.21324	−	27.4559i	0.222496	−	1.17179i
$550$			0.450987i			0.0192302i
$551$	2.24724	+	12.6403i	0.0957356	+	0.538495i
$552$	−13.4765	+	7.66329i	−0.573596	+	0.326171i
$553$	0.567478	+	1.55913i	0.0241316	+	0.0663010i
$554$	−0.270084	+	1.53172i	−0.0114748	+	0.0650767i
$555$	−2.73032	−	1.01407i	−0.115896	−	0.0430450i
$556$	−2.64516	−	2.21956i	−0.112180	−	0.0941301i
$557$	4.27875	−	0.754459i	0.181296	−	0.0319675i	−0.0822628	−	0.996611i	$-0.526215\pi$
$557$	4.27875	−	0.754459i	0.181296	−	0.0319675i	0.263559	+	0.964643i	$0.415104\pi$
$558$	0.368119	−	28.0769i	0.0155837	−	1.18859i
$559$	−54.2646	−	31.3297i	−2.29515	−	1.32511i
$560$	0.153088	−	0.420607i	0.00646917	−	0.0177739i
$561$	−0.0943931	−	0.556643i	−0.00398528	−	0.0235015i
$562$	2.82572	−	4.89429i	0.119196	−	0.206453i
$563$	−20.0759	−	34.7726i	−0.846100	−	1.46549i	−0.884662	−	0.466233i	$-0.845611\pi$
$563$	−20.0759	−	34.7726i	−0.846100	−	1.46549i	0.0385618	−	0.999256i	$-0.487722\pi$
$564$	−9.27327	−	11.1997i	−0.390475	−	0.471594i
$565$	4.51929	−	5.38588i	0.190128	−	0.226586i
$566$	−16.8968	+	14.1781i	−0.710225	+	0.595950i
$567$	−3.82028	+	1.27808i	−0.160437	+	0.0536742i
$568$	−2.36768	+	0.861764i	−0.0993455	+	0.0361588i
$569$	−27.9741			−1.17273			−0.586367	−	0.810046i	$-0.699442\pi$
$569$	−27.9741			−1.17273			−0.586367	+	0.810046i	$0.699442\pi$
$570$	6.55768	−	3.74124i	0.274671	−	0.156703i
$571$	2.88023			0.120534			0.0602669	−	0.998182i	$-0.480805\pi$
$571$	2.88023			0.120534			0.0602669	+	0.998182i	$0.480805\pi$
$572$	−2.54189	+	0.925171i	−0.106282	+	0.0386833i
$573$	4.88568	+	13.7021i	0.204102	+	0.572413i
$574$	−3.19702	+	2.68262i	−0.133441	+	0.111970i
$575$	5.75335	−	6.85657i	0.239931	−	0.285939i
$576$	−2.80538	−	1.06293i	−0.116891	−	0.0442888i
$577$	10.4675	+	18.1303i	0.435769	+	0.754774i	0.997358	−	0.0726424i	$-0.0231432\pi$
$577$	10.4675	+	18.1303i	0.435769	+	0.754774i	−0.561589	+	0.827416i	$0.689810\pi$
$578$	8.23879	−	14.2700i	0.342689	−	0.593554i
$579$	−17.9360	+	3.04150i	−0.745393	+	0.126401i
$580$	−1.00737	+	2.76773i	−0.0418288	+	0.114924i
$581$	−2.93406	−	1.69398i	−0.121725	−	0.0702780i
$582$	−26.5866	−	15.5830i	−1.10205	−	0.645938i
$583$	5.89178	−	1.03888i	0.244013	−	0.0430260i
$584$	−2.12333	−	1.78168i	−0.0878638	−	0.0737265i
$585$	2.89204	+	17.7600i	0.119571	+	0.734288i
$586$	−1.77283	+	10.0542i	−0.0732349	+	0.415336i
$587$	−11.1397	−	30.6061i	−0.459785	−	1.26325i	−0.925646	−	0.378390i	$-0.876478\pi$
$587$	−11.1397	−	30.6061i	−0.459785	−	1.26325i	0.465862	−	0.884858i	$-0.345744\pi$
$588$	5.82169	+	10.2379i	0.240082	+	0.422202i
$589$	35.3612	+	20.3492i	1.45703	+	0.838476i
$590$		−	3.47574i		−	0.143094i
$591$	−24.1686	+	28.4226i	−0.994165	+	1.16915i
$592$	−1.65602	−	0.292001i	−0.0680619	−	0.0120012i
$593$	3.01254	+	3.59020i	0.123710	+	0.147432i	0.824344	−	0.566089i	$-0.191544\pi$
$593$	3.01254	+	3.59020i	0.123710	+	0.147432i	−0.700634	+	0.713520i	$0.747100\pi$
$594$	1.54132	−	1.76518i	0.0632410	−	0.0724262i
$595$	−0.0561783	−	0.318603i	−0.00230309	−	0.0130614i
$596$	−9.30746	+	5.37366i	−0.381248	+	0.220114i
$597$	−10.6396	−	0.0697453i	−0.435450	−	0.00285449i
$598$	50.4481	+	18.3616i	2.06298	+	0.750862i
$599$	9.79347	+	3.56453i	0.400150	+	0.145643i	0.534253	−	0.845325i	$-0.320593\pi$
$599$	9.79347	+	3.56453i	0.400150	+	0.145643i	−0.134103	+	0.990967i	$0.542815\pi$
$600$	1.73201	+	0.0113538i	0.0707092	+	0.000463517i
$601$	−11.9916	+	6.92336i	−0.489148	+	0.282410i	−0.724221	−	0.689568i	$-0.757800\pi$
$601$	−11.9916	+	6.92336i	−0.489148	+	0.282410i	0.235073	+	0.971978i	$0.424467\pi$
$602$	0.811972	+	4.60492i	0.0330935	+	0.187683i
$603$	9.87304	+	28.2739i	0.402061	+	1.15140i
$604$	1.80973	+	2.15676i	0.0736370	+	0.0877571i
$605$	10.6326	+	1.87481i	0.432276	+	0.0762219i
$606$	−2.60964	+	3.06897i	−0.106009	+	0.124668i
$607$		−	34.9298i		−	1.41776i	−0.705330	−	0.708879i	$-0.749201\pi$
$607$		−	34.9298i		−	1.41776i	0.705330	−	0.708879i	$-0.250799\pi$
$608$	3.33515	−	2.80656i	0.135258	−	0.113821i
$609$	1.12873	+	1.98495i	0.0457385	+	0.0804344i
$610$	3.18608	+	8.75368i	0.129001	+	0.354426i
$611$	−8.74372	+	49.5881i	−0.353733	+	2.00612i
$612$	−2.14016	+	0.348502i	−0.0865108	+	0.0140874i
$613$	−14.0861	−	11.8197i	−0.568934	−	0.477392i	0.312358	−	0.949964i	$-0.398881\pi$
$613$	−14.0861	−	11.8197i	−0.568934	−	0.477392i	−0.881292	+	0.472572i	$0.843326\pi$
$614$	−9.52716	+	1.67990i	−0.384485	+	0.0677951i
$615$	−13.9327	−	8.16630i	−0.561821	−	0.329297i
$616$	0.174818	+	0.100931i	0.00704361	+	0.00406663i
$617$	−7.93745	+	21.8080i	−0.319550	+	0.877956i	0.671080	+	0.741385i	$0.265830\pi$
$617$	−7.93745	+	21.8080i	−0.319550	+	0.877956i	−0.990630	+	0.136571i	$0.956392\pi$
$618$	18.6569	−	3.16376i	0.750492	−	0.127265i
$619$	−11.8569	+	20.5367i	−0.476569	+	0.825442i	−0.999640	−	0.0268478i	$-0.991453\pi$
$619$	−11.8569	+	20.5367i	−0.476569	+	0.825442i	0.523071	+	0.852289i	$0.324786\pi$
$620$	4.67989	+	8.10581i	0.187949	+	0.325537i
$621$	−45.9522	+	7.17394i	−1.84400	+	0.287880i
$622$	9.26772	−	11.0448i	0.371602	−	0.442858i
$623$	2.25341	−	1.89084i	0.0902812	−	0.0757549i
$624$	3.48912	+	9.78538i	0.139677	+	0.391729i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	5.72612			0.228862
$627$	1.14807	+	3.20549i	0.0458494	+	0.128015i
$628$	4.76022			0.189954
$629$	−1.14211	+	0.415693i	−0.0455388	+	0.0165748i
$630$	0.876548	−	1.01724i	0.0349225	−	0.0405279i
$631$	19.0531	−	15.9874i	0.758490	−	0.636449i	−0.179243	−	0.983805i	$-0.557365\pi$
$631$	19.0531	−	15.9874i	0.758490	−	0.636449i	0.937733	+	0.347356i	$0.112920\pi$
$632$	−2.38272	+	2.83962i	−0.0947797	+	0.112954i
$633$	−20.7454	−	25.0551i	−0.824555	−	0.995852i
$634$	4.27915	+	7.41171i	0.169947	+	0.294357i
$635$	−1.52109	+	2.63461i	−0.0603628	+	0.104551i
$636$	−3.84148	−	22.6535i	−0.152325	−	0.898269i
$637$	13.9490	−	38.3247i	0.552681	−	1.51848i
$638$	−1.15036	−	0.664158i	−0.0455430	−	0.0262943i
$639$	−7.55824	−	0.0990966i	−0.298999	−	0.00392020i
$640$	0.984808	−	0.173648i	0.0389279	−	0.00686405i
$641$	18.4132	+	15.4505i	0.727279	+	0.610260i	0.929388	−	0.369103i	$-0.120335\pi$
$641$	18.4132	+	15.4505i	0.727279	+	0.610260i	−0.202109	+	0.979363i	$0.564780\pi$
$642$	12.6656	+	4.70416i	0.499872	+	0.185658i
$643$	5.65604	−	32.0770i	0.223052	−	1.26499i	−0.643321	−	0.765596i	$-0.722444\pi$
$643$	5.65604	−	32.0770i	0.223052	−	1.26499i	0.866374	−	0.499396i	$-0.166445\pi$
$644$	−1.37024	−	3.76469i	−0.0539949	−	0.148350i
$645$	−15.7291	+	8.94422i	−0.619331	+	0.352178i
$646$	1.07336	−	2.96205i	0.0422309	−	0.116540i
$647$		−	18.6111i		−	0.731679i	−0.930678	−	0.365840i	$-0.880782\pi$
$647$		−	18.6111i		−	0.731679i	0.930678	−	0.365840i	$-0.119218\pi$
$648$	−6.74036	−	5.96385i	−0.264786	−	0.234282i
$649$	1.54370	+	0.272196i	0.0605955	+	0.0106846i
$650$	−3.85543	−	4.59473i	−0.151223	−	0.180220i
$651$	7.13768	+	1.30686i	0.279748	+	0.0512201i
$652$	2.10511	+	11.9387i	0.0824424	+	0.467554i
$653$	3.57084	−	2.06162i	0.139738	−	0.0806776i	−0.428501	−	0.903541i	$-0.640958\pi$
$653$	3.57084	−	2.06162i	0.139738	−	0.0806776i	0.568239	+	0.822864i	$0.307625\pi$
$654$	0.138148	−	21.0744i	0.00540203	−	0.824076i
$655$	−3.65963	−	1.33200i	−0.142994	−	0.0520454i
$656$	−8.76166	−	3.18898i	−0.342085	−	0.124509i
$657$	−4.06294	−	7.25525i	−0.158510	−	0.283054i
$658$	3.25418	−	1.87880i	0.126861	−	0.0732433i
$659$	−7.30640	−	41.4366i	−0.284617	−	1.61414i	−0.706651	−	0.707562i	$-0.749795\pi$
$659$	−7.30640	−	41.4366i	−0.284617	−	1.61414i	0.422034	−	0.906580i	$-0.361316\pi$
$660$	−0.140682	+	0.768360i	−0.00547604	+	0.0299084i
$661$	−0.499629	−	0.595435i	−0.0194333	−	0.0231597i	0.756240	−	0.654294i	$-0.227034\pi$
$661$	−0.499629	−	0.595435i	−0.0194333	−	0.0231597i	−0.775674	+	0.631134i	$0.782590\pi$
$662$	16.3895	+	2.88991i	0.636996	+	0.112320i
$663$	5.72036	+	4.86421i	0.222160	+	0.188910i
$664$		−	7.56915i		−	0.293740i
$665$	0.669886	+	1.83244i	0.0259771	+	0.0710589i
$666$	−4.33539	−	2.57941i	−0.167993	−	0.0999499i
$667$	9.01659	+	24.7729i	0.349124	+	0.959209i
$668$	−1.94126	+	11.0094i	−0.0751096	+	0.425968i
$669$	−12.6493	+	34.0573i	−0.489050	+	1.31673i
$670$	−7.64720	−	6.41676i	−0.295437	−	0.247901i
$671$	−4.13734	+	0.729524i	−0.159720	+	0.0281630i
$672$	0.392026	−	0.668845i	0.0151227	−	0.0258013i
$673$	4.06408	+	2.34640i	0.156659	+	0.0904470i	0.576280	−	0.817252i	$-0.304504\pi$
$673$	4.06408	+	2.34640i	0.156659	+	0.0904470i	−0.419621	+	0.907699i	$0.637837\pi$
$674$	6.30534	−	17.3238i	0.242873	−	0.667287i
$675$	4.84689	+	1.87286i	0.186557	+	0.0720865i
$676$	11.4879	−	19.8977i	0.441844	−	0.765297i
$677$	4.73423	+	8.19993i	0.181951	+	0.315149i	0.942545	−	0.334079i	$-0.108425\pi$
$677$	4.73423	+	8.19993i	0.181951	+	0.315149i	−0.760594	+	0.649228i	$0.775092\pi$
$678$	9.37973	−	7.76632i	0.360226	−	0.298264i
$679$	5.11901	−	6.10060i	0.196450	−	0.234119i
$680$	0.553684	−	0.464596i	0.0212328	−	0.0178164i
$681$	−13.8701	+	4.94559i	−0.531504	+	0.189515i
$682$	−3.96658	+	1.44372i	−0.151888	+	0.0552827i
$683$	−3.06787			−0.117389			−0.0586945	−	0.998276i	$-0.518694\pi$
$683$	−3.06787			−0.117389			−0.0586945	+	0.998276i	$0.518694\pi$
$684$	12.3396	−	4.32845i	0.471815	−	0.165502i
$685$	15.8383			0.605151
$686$	−5.80423	+	2.11257i	−0.221607	+	0.0806582i
$687$	5.49240	−	1.95839i	0.209548	−	0.0747173i
$688$	−8.00266	+	6.71503i	−0.305099	+	0.256008i
$689$	−51.1451	+	60.9523i	−1.94847	+	2.32210i
$690$	11.9410	−	9.88703i	0.454586	−	0.376393i
$691$	−4.81731	−	8.34383i	−0.183259	−	0.317414i	0.759729	−	0.650239i	$-0.225331\pi$
$691$	−4.81731	−	8.34383i	−0.183259	−	0.317414i	−0.942989	+	0.332825i	$0.891998\pi$
$692$	9.30740	−	16.1209i	0.353814	−	0.612824i
$693$	0.383148	+	0.468970i	0.0145546	+	0.0178147i
$694$	3.41142	−	9.37280i	0.129496	−	0.355786i
$695$	2.99040	+	1.72651i	0.113432	+	0.0654902i
$696$	−2.57966	+	4.40121i	−0.0977816	+	0.166828i
$697$	−6.63681	+	1.17025i	−0.251387	+	0.0443264i
$698$	0.506032	+	0.424611i	0.0191536	+	0.0160718i
$699$	−1.48497	+	3.99817i	−0.0561666	+	0.151225i
$700$	−0.0777250	+	0.440800i	−0.00293773	+	0.0166607i
$701$	4.54025	+	12.4742i	0.171483	+	0.471145i	0.995427	−	0.0955260i	$-0.0304533\pi$
$701$	4.54025	+	12.4742i	0.171483	+	0.471145i	−0.823944	+	0.566671i	$0.808231\pi$
$702$	−0.612865	+	31.1605i	−0.0231311	+	1.17608i
$703$	6.34258	−	3.67385i	0.239215	−	0.138562i
$704$			0.450987i			0.0169972i
$705$	11.0772	+	9.41930i	0.417192	+	0.354752i
$706$	−8.58688	−	1.51410i	−0.323172	−	0.0569839i
$707$	−0.669177	−	0.797494i	−0.0251670	−	0.0299928i
$708$	1.08423	−	5.92172i	0.0407479	−	0.222552i
$709$	1.62838	+	9.23501i	0.0611551	+	0.346828i	0.999997	+	0.00247917i	$0.000789146\pi$
$709$	1.62838	+	9.23501i	0.0611551	+	0.346828i	−0.938842	+	0.344349i	$0.888100\pi$
$710$	2.18206	−	1.25981i	0.0818913	−	0.0472800i
$711$	−9.70278	+	5.43356i	−0.363883	+	0.203774i
$712$	6.17565	+	2.24775i	0.231442	+	0.0842380i
$713$	78.7235	+	28.6530i	2.94822	+	1.07306i
$714$	0.00367316	−	0.560337i	0.000137464	−	0.0209701i
$715$	2.34261	−	1.35251i	0.0876088	−	0.0505810i
$716$	3.44389	+	19.5313i	0.128704	+	0.729918i
$717$	44.6253	+	8.17061i	1.66656	+	0.305137i
$718$	−8.93900	−	10.6531i	−0.333600	−	0.397570i
$719$	−7.26973	−	1.28185i	−0.271115	−	0.0478049i	0.0364376	−	0.999336i	$-0.488399\pi$
$719$	−7.26973	−	1.28185i	−0.271115	−	0.0478049i	−0.307553	+	0.951531i	$0.599510\pi$
$720$	2.94734	+	0.559632i	0.109841	+	0.0208563i
$721$			4.89020i			0.182120i
$722$	−3.24644	+	18.7206i	−0.120820	+	0.696708i
$723$	13.8776	−	7.89142i	0.516115	−	0.293485i
$724$	1.35995	+	3.73642i	0.0505420	+	0.138863i
$725$	0.511455	−	2.90061i	0.0189950	−	0.107726i
$726$	17.5302	+	6.51092i	0.650607	+	0.241643i
$727$	36.8664	+	30.9346i	1.36730	+	1.14730i	0.973652	+	0.228038i	$0.0732309\pi$
$727$	36.8664	+	30.9346i	1.36730	+	1.14730i	0.393646	+	0.919262i	$0.371214\pi$
$728$	−2.64392	+	0.466194i	−0.0979901	+	0.0172783i
$729$	−12.5701	−	23.8954i	−0.465560	−	0.885016i
$730$	2.40045	+	1.38590i	0.0888448	+	0.0512945i
$731$	−2.58250	+	7.09535i	−0.0955171	+	0.262431i
$732$	2.69757	+	15.9078i	0.0997052	+	0.587968i
$733$	18.2443	−	31.6000i	0.673868	−	1.16717i	−0.302930	−	0.953013i	$-0.597965\pi$
$733$	18.2443	−	31.6000i	0.673868	−	1.16717i	0.976798	−	0.214161i	$-0.0687018\pi$
$734$	7.09431	+	12.2877i	0.261856	+	0.453548i
$735$	−7.51103	−	9.07140i	−0.277048	−	0.334604i
$736$	5.75335	−	6.85657i	0.212071	−	0.252737i
$737$	3.44879	−	2.89388i	0.127038	−	0.106597i
$738$	−21.1902	−	18.2594i	−0.780020	−	0.672136i
$739$	4.26801	−	1.55343i	0.157001	−	0.0571438i	−0.262324	−	0.964980i	$-0.584489\pi$
$739$	4.26801	−	1.55343i	0.157001	−	0.0571438i	0.419325	+	0.907836i	$0.362267\pi$
$740$	1.68156			0.0618155
$741$	−39.1000	−	22.8433i	−1.43637	−	0.839170i
$742$	5.93774			0.217981
$743$	7.19025	−	2.61704i	0.263785	−	0.0960097i	−0.206742	−	0.978395i	$-0.566286\pi$
$743$	7.19025	−	2.61704i	0.263785	−	0.0960097i	0.470527	+	0.882386i	$0.344064\pi$
$744$	5.44472	+	15.2700i	0.199613	+	0.559824i
$745$	8.23293	−	6.90825i	0.301631	−	0.253099i
$746$	−19.7954	+	23.5913i	−0.724762	+	0.863738i
$747$	8.04548	−	21.2344i	0.294369	−	0.776925i
$748$	0.162983	+	0.282295i	0.00595924	+	0.0103217i
$749$	−1.74577	+	3.02377i	−0.0637891	+	0.110486i
$750$	−1.70767	+	0.289580i	−0.0623554	+	0.0105740i
$751$	−10.4494	+	28.7094i	−0.381303	+	1.04762i	0.589505	+	0.807765i	$0.299323\pi$
$751$	−10.4494	+	28.7094i	−0.381303	+	1.04762i	−0.970808	+	0.239857i	$0.922899\pi$
$752$	7.27028	+	4.19750i	0.265120	+	0.153067i
$753$	−8.36887	−	4.90520i	−0.304979	−	0.178755i
$754$	17.3978	−	3.06770i	0.633591	−	0.111719i
$755$	−2.15676	−	1.80973i	−0.0784924	−	0.0658629i
$756$	1.81072	−	1.45967i	0.0658553	−	0.0530877i
$757$	2.06940	−	11.7361i	0.0752135	−	0.426557i	−0.923829	−	0.382806i	$-0.874958\pi$
$757$	2.06940	−	11.7361i	0.0752135	−	0.426557i	0.999042	−	0.0437516i	$-0.0139310\pi$
$758$	1.14471	+	3.14505i	0.0415776	+	0.114233i
$759$	3.45605	+	6.07771i	0.125447	+	0.220607i
$760$	−2.79713	+	3.34306i	−0.101462	+	0.121266i
$761$			8.52888i			0.309172i	0.987979	+	0.154586i	$0.0494043\pi$
$761$			8.52888i			0.309172i	−0.987979	+	0.154586i	$0.950596\pi$
$762$	−3.41338	+	4.01417i	−0.123654	+	0.145418i
$763$	5.36348	+	0.945727i	0.194171	+	0.0342376i
$764$	−5.39861	−	6.43382i	−0.195315	−	0.232767i
$765$	2.04713	−	0.714842i	0.0740141	−	0.0258452i
$766$	−2.96057	−	16.7902i	−0.106970	−	0.606656i
$767$	−18.0544	+	10.4237i	−0.651907	+	0.376379i
$768$	1.73201	+	0.0113538i	0.0624987	+	0.000409695i
$769$	26.4188	+	9.61565i	0.952685	+	0.346749i	0.771163	−	0.636638i	$-0.219675\pi$
$769$	26.4188	+	9.61565i	0.952685	+	0.346749i	0.181522	+	0.983387i	$0.441898\pi$
$770$	−0.189688	−	0.0690409i	−0.00683589	−	0.00248806i
$771$	41.9077	+	0.274716i	1.50927	+	0.00989364i
$772$	9.09601	−	5.25158i	0.327372	−	0.189009i
$773$	−5.85221	−	33.1896i	−0.210489	−	1.19375i	−0.888564	−	0.458752i	$-0.848297\pi$
$773$	−5.85221	−	33.1896i	−0.210489	−	1.19375i	0.678075	−	0.734993i	$-0.262815\pi$
$774$	−29.5881	+	10.3320i	−1.06352	+	0.371375i
$775$	−6.01635	−	7.17001i	−0.216114	−	0.257554i
$776$	17.5218	+	3.08957i	0.628997	+	0.110909i
$777$	0.844506	−	0.993148i	0.0302965	−	0.0356290i
$778$			25.0198i			0.897002i
$779$	38.1715	−	13.9544i	1.36764	−	0.499968i
$780$	−5.13532	−	9.03084i	−0.183874	−	0.323356i
$781$	0.388644	+	1.06779i	0.0139068	+	0.0382086i
$782$	1.12339	−	6.37107i	0.0401724	−	0.227829i
$783$	−11.9151	+	9.60510i	−0.425811	+	0.343258i
$784$	−5.20884	−	4.37073i	−0.186030	−	0.156098i
$785$	−4.68791	+	0.826604i	−0.167319	+	0.0295028i
$786$	−5.81951	−	3.41095i	−0.207575	−	0.121665i
$787$	20.2290	+	11.6792i	0.721084	+	0.416318i	0.815152	−	0.579248i	$-0.196654\pi$
$787$	20.2290	+	11.6792i	0.721084	+	0.416318i	−0.0940674	+	0.995566i	$0.529987\pi$
$788$	7.36725	−	20.2413i	0.262447	−	0.721068i
$789$	28.7992	−	4.88364i	1.02528	−	0.173862i
$790$	1.85343	−	3.21024i	0.0659421	−	0.114215i
$791$	1.57349	+	2.72536i	0.0559468	+	0.0969026i
$792$	−0.479368	+	1.26519i	−0.0170336	+	0.0449567i
$793$	35.9152	−	42.8021i	1.27539	−	1.51995i
$794$	−28.4882	+	23.9044i	−1.01101	+	0.848336i
$795$	7.71686	+	21.6423i	0.273689	+	0.767572i
$796$	5.77245	−	2.10100i	0.204599	−	0.0744679i
$797$	−28.9848			−1.02669			−0.513347	−	0.858181i	$-0.671594\pi$
$797$	−28.9848			−1.02669			−0.513347	+	0.858181i	$0.671594\pi$
$798$	0.569689	+	3.33094i	0.0201668	+	0.117914i
$799$	6.06775			0.214662
$800$	−0.939693	+	0.342020i	−0.0332232	+	0.0120922i
$801$	14.9359	+	12.8701i	0.527733	+	0.454742i
$802$	8.04705	−	6.75228i	0.284151	−	0.238431i
$803$	−0.803516	+	0.957593i	−0.0283555	+	0.0337927i
$804$	−11.0271	−	13.3179i	−0.388895	−	0.469686i
$805$	2.00315	+	3.46956i	0.0706018	+	0.122286i
$806$	28.0699	−	48.6186i	0.988722	−	1.71252i
$807$	−1.28697	−	7.58933i	−0.0453033	−	0.267157i
$808$	0.795489	−	2.18559i	0.0279852	−	0.0768887i
$809$	30.1621	+	17.4141i	1.06044	+	0.612248i	0.925555	−	0.378613i	$-0.123599\pi$
$809$	30.1621	+	17.4141i	1.06044	+	0.612248i	0.134889	+	0.990861i	$0.456932\pi$
$810$	7.67357	+	4.70280i	0.269622	+	0.165240i
$811$	2.26469	−	0.399326i	0.0795240	−	0.0140222i	−0.133745	−	0.991016i	$-0.542700\pi$
$811$	2.26469	−	0.399326i	0.0795240	−	0.0140222i	0.213269	+	0.976994i	$0.431589\pi$
$812$	−1.00991	−	0.847414i	−0.0354408	−	0.0297384i
$813$	44.8709	+	16.6656i	1.57369	+	0.584487i
$814$	−0.131689	+	0.746843i	−0.00461568	+	0.0261768i
$815$	−4.14626	−	11.3917i	−0.145237	−	0.399035i
$816$	1.08825	−	0.618828i	0.0380965	−	0.0216633i
$817$	7.84394	−	44.8556i	0.274425	−	1.56930i
$818$			10.6136i			0.371095i
$819$	−7.91274	−	1.50245i	−0.276493	−	0.0524997i
$820$	9.18231	+	1.61909i	0.320660	+	0.0565411i
$821$	−5.05095	−	6.01949i	−0.176280	−	0.210082i	0.670669	−	0.741757i	$-0.266007\pi$
$821$	−5.05095	−	6.01949i	−0.176280	−	0.210082i	−0.846948	+	0.531675i	$0.821563\pi$
$822$	26.9842	+	4.94064i	0.941183	+	0.172325i
$823$	−2.66593	−	15.1192i	−0.0929284	−	0.527023i	−0.995362	−	0.0961951i	$-0.969333\pi$
$823$	−2.66593	−	15.1192i	−0.0929284	−	0.527023i	0.902434	−	0.430828i	$-0.141778\pi$
$824$	−9.46164	+	5.46268i	−0.329612	+	0.190301i
$825$	0.00512042	−	0.781116i	0.000178270	−	0.0271950i
$826$	1.46192	+	0.532095i	0.0508667	+	0.0185140i
$827$	−14.2558	−	5.18869i	−0.495723	−	0.180428i	0.0820464	−	0.996629i	$-0.473854\pi$
$827$	−14.2558	−	5.18869i	−0.495723	−	0.180428i	−0.577769	+	0.816200i	$0.696077\pi$
$828$	23.4284	−	13.1199i	0.814193	−	0.455948i
$829$	−20.4353	+	11.7983i	−0.709748	+	0.409773i	−0.810968	−	0.585091i	$-0.801059\pi$
$829$	−20.4353	+	11.7983i	−0.709748	+	0.409773i	0.101220	+	0.994864i	$0.467725\pi$
$830$	1.31437	+	7.45416i	0.0456224	+	0.258738i
$831$	0.485181	−	2.64990i	0.0168307	−	0.0919240i
$832$	−3.85543	−	4.59473i	−0.133663	−	0.159294i
$833$	−4.84001	−	0.853424i	−0.167696	−	0.0295694i
$834$	4.55626	+	3.87433i	0.157770	+	0.134157i
$835$		−	11.1793i		−	0.386875i
$836$	−1.26572	−	1.50411i	−0.0437759	−	0.0520207i
$837$	−0.956367	+	48.6255i	−0.0330569	+	1.68074i
$838$	2.06290	+	5.66778i	0.0712618	+	0.195790i
$839$	6.14495	−	34.8497i	0.212147	−	1.20315i	−0.673642	−	0.739058i	$-0.735271\pi$
$839$	6.14495	−	34.8497i	0.212147	−	1.20315i	0.885789	−	0.464088i	$-0.153618\pi$
$840$	−0.269927	+	0.726759i	−0.00931336	+	0.0250756i
$841$	−15.5698	−	13.0646i	−0.536889	−	0.450503i
$842$	3.19225	−	0.562881i	0.110012	−	0.0193981i
$843$	−4.94975	+	8.44489i	−0.170479	+	0.290858i
$844$	16.2645	+	9.39029i	0.559846	+	0.323227i
$845$	−7.85822	+	21.5903i	−0.270331	+	0.742728i
$846$	15.9343	+	19.5034i	0.547832	+	0.670540i
$847$	−2.41628	+	4.18513i	−0.0830245	+	0.143803i
$848$	6.63286	+	11.4884i	0.227773	+	0.394515i
$849$	29.4265	−	24.3648i	1.00991	−	0.836198i
$850$	−0.464596	+	0.553684i	−0.0159355	+	0.0189912i
$851$	11.5298	−	9.67462i	0.395235	−	0.331642i
$852$	4.11063	−	1.46570i	0.140828	−	0.0502142i
$853$	−9.26824	+	3.37336i	−0.317338	+	0.115502i	−0.495778	−	0.868449i	$-0.665117\pi$
$853$	−9.26824	+	3.37336i	−0.317338	+	0.115502i	0.178440	+	0.983951i	$0.442895\pi$
$854$	−4.16961			−0.142681
$855$	−11.4005	+	6.40543i	−0.389887	+	0.219061i
$856$	−7.80058			−0.266618
$857$	45.4685	−	16.5492i	1.55317	−	0.565309i	0.584015	−	0.811743i	$-0.301481\pi$
$857$	45.4685	−	16.5492i	1.55317	−	0.565309i	0.969160	+	0.246433i	$0.0792587\pi$
$858$	4.41308	−	1.57355i	0.150660	−	0.0537200i
$859$	−2.97754	+	2.49845i	−0.101592	+	0.0852460i	−0.692169	−	0.721735i	$-0.743345\pi$
$859$	−2.97754	+	2.49845i	−0.101592	+	0.0852460i	0.590577	+	0.806981i	$0.298900\pi$
$860$	6.71503	−	8.00266i	0.228981	−	0.272888i
$861$	5.56774	−	4.61003i	0.189748	−	0.157109i
$862$	−4.76288	−	8.24956i	−0.162224	−	0.280981i
$863$	2.84088	−	4.92055i	0.0967048	−	0.167498i	−0.813614	−	0.581405i	$-0.802503\pi$
$863$	2.84088	−	4.92055i	0.0967048	−	0.167498i	0.910319	+	0.413908i	$0.135836\pi$
$864$	4.84689	+	1.87286i	0.164895	+	0.0637160i
$865$	−6.36664	+	17.4922i	−0.216472	+	0.594752i
$866$	−14.8054	−	8.54793i	−0.503109	−	0.290470i
$867$	−14.4317	+	24.6223i	−0.490127	+	0.836217i
$868$	−4.12580	+	0.727489i	−0.140039	+	0.0246926i
$869$	1.28063	+	1.07458i	0.0434425	+	0.0364526i
$870$	1.77620	−	4.78230i	0.0602189	−	0.162135i
$871$	−10.3974	+	58.9665i	−0.352302	+	1.99800i
$872$	4.16156	+	11.4338i	0.140928	+	0.387197i
$873$	45.8714	+	27.2919i	1.55251	+	0.923691i
$874$	0.0551075	+	39.0148i	0.00186404	+	1.31970i
$875$		−	0.447601i		−	0.0151317i
$876$	3.65740	+	3.11000i	0.123572	+	0.105077i
$877$	−0.465569	−	0.0820925i	−0.0157212	−	0.00277207i	0.165782	−	0.986162i	$-0.446985\pi$
$877$	−0.465569	−	0.0820925i	−0.0157212	−	0.00277207i	−0.181503	+	0.983390i	$0.558096\pi$
$878$	−2.77796	−	3.31065i	−0.0937517	−	0.111729i
$879$	3.18472	−	17.3939i	0.107418	−	0.586682i
$880$	−0.0783131	−	0.444136i	−0.00263993	−	0.0149718i
$881$	−25.9578	+	14.9868i	−0.874541	+	0.504917i	−0.868855	−	0.495067i	$-0.835143\pi$
$881$	−25.9578	+	14.9868i	−0.874541	+	0.504917i	−0.00568654	+	0.999984i	$0.501810\pi$
$882$	−9.96700	−	17.7982i	−0.335606	−	0.599297i
$883$	−25.1371	−	9.14914i	−0.845929	−	0.307893i	−0.117550	−	0.993067i	$-0.537504\pi$
$883$	−25.1371	−	9.14914i	−0.845929	−	0.307893i	−0.728380	+	0.685174i	$0.759726\pi$
$884$	−4.07380	−	1.48274i	−0.137017	−	0.0498700i
$885$	−0.0394628	+	6.02003i	−0.00132653	+	0.202361i
$886$	10.4631	−	6.04086i	0.351514	−	0.202947i
$887$	4.09494	+	23.2235i	0.137495	+	0.779770i	0.973090	+	0.230425i	$0.0740117\pi$
$887$	4.09494	+	23.2235i	0.137495	+	0.779770i	−0.835596	+	0.549345i	$0.814877\pi$
$888$	2.86493	+	0.524551i	0.0961408	+	0.0176028i
$889$	−0.875275	−	1.04311i	−0.0293558	−	0.0349848i
$890$	−6.47214	−	1.14121i	−0.216947	−	0.0382536i
$891$	−2.68962	+	3.03982i	−0.0901058	+	0.101838i
$892$		−	20.9754i		−	0.702309i
$893$	−36.0280	+	6.40519i	−1.20563	+	0.214342i
$894$	16.1817	−	9.20158i	0.541196	−	0.307747i
$895$	−6.78314	−	18.6365i	−0.226735	−	0.622951i
$896$	−0.0777250	+	0.440800i	−0.00259661	+	0.0147261i
$897$	−87.1683	−	32.3753i	−2.91046	−	1.08098i
$898$	19.3689	+	16.2525i	0.646349	+	0.542351i
$899$	27.1490	−	4.78711i	0.905471	−	0.159659i
$900$	−2.99974	−	0.0393299i	−0.0999914	−	0.00131100i
$901$	8.30365	+	4.79411i	0.276635	+	0.159715i
$902$	−1.43819	+	3.95140i	−0.0478865	+	0.131567i
$903$	−1.35406	−	7.98501i	−0.0450604	−	0.265724i
$904$	−3.51538	+	6.08882i	−0.116920	+	0.202511i
$905$	−1.98811	−	3.44350i	−0.0660869	−	0.114466i
$906$	−3.10999	−	3.75608i	−0.103323	−	0.124787i
$907$	4.99145	−	5.94858i	0.165738	−	0.197519i	−0.676782	−	0.736183i	$-0.736626\pi$
$907$	4.99145	−	5.94858i	0.165738	−	0.197519i	0.842521	+	0.538664i	$0.181071\pi$
$908$	6.51272	−	5.46482i	0.216132	−	0.181356i
$909$	4.55478	−	5.28587i	0.151073	−	0.175321i
$910$	2.52280	−	0.918223i	0.0836299	−	0.0304388i
$911$	−26.5167			−0.878538			−0.439269	−	0.898356i	$-0.644763\pi$
$911$	−26.5167			−0.878538			−0.439269	+	0.898356i	$0.644763\pi$
$912$	−5.80839	+	4.82313i	−0.192335	+	0.159710i
$913$	−3.41359			−0.112973
$914$	−33.5827	+	12.2231i	−1.11082	+	0.404304i
$915$	−5.41895	−	15.1977i	−0.179145	−	0.502420i
$916$	−2.57896	+	2.16400i	−0.0852111	+	0.0715006i
$917$	1.12049	−	1.33535i	0.0370020	−	0.0440972i
$918$	3.71074	−	0.579312i	0.122473	−	0.0191201i
$919$	−21.0750	−	36.5030i	−0.695201	−	1.20412i	−0.970113	−	0.242654i	$-0.921982\pi$
$919$	−21.0750	−	36.5030i	−0.695201	−	1.20412i	0.274912	−	0.961469i	$-0.411351\pi$
$920$	−4.47531	+	7.75146i	−0.147547	+	0.255558i
$921$	16.5202	−	2.80143i	0.544361	−	0.0923103i
$922$	12.1118	−	33.2768i	0.398880	−	1.09591i
$923$	−13.0880	−	7.55635i	−0.430796	−	0.248720i
$924$	−0.301641	−	0.176799i	−0.00992325	−	0.00581625i
$925$	−1.65602	+	0.292001i	−0.0544495	+	0.00960092i
$926$	22.6095	+	18.9716i	0.742993	+	0.623445i
$927$	−32.3500	+	5.26785i	−1.06251	+	0.173019i
$928$	0.511455	−	2.90061i	0.0167893	−	0.0952171i
$929$	3.92496	+	10.7837i	0.128774	+	0.353803i	0.987278	−	0.159003i	$-0.0508280\pi$
$929$	3.92496	+	10.7837i	0.128774	+	0.353803i	−0.858504	+	0.512807i	$0.828606\pi$
$930$	−8.01360	−	14.0925i	−0.262776	−	0.462111i
$931$	29.6390	−	0.0418644i	0.971378	−	0.00137205i
$932$		−	2.46241i		−	0.0806591i
$933$	−16.1772	+	19.0246i	−0.529618	+	0.622837i
$934$	24.8039	+	4.37359i	0.811607	+	0.143108i
$935$	−0.209527	−	0.249704i	−0.00685226	−	0.00816620i
$936$	−5.93210	−	16.9880i	−0.193897	−	0.555271i
$937$	4.03064	+	22.8589i	0.131675	+	0.746767i	0.977117	+	0.212700i	$0.0682259\pi$
$937$	4.03064	+	22.8589i	0.131675	+	0.746767i	−0.845442	+	0.534067i	$0.820663\pi$
$938$	3.86963	−	2.23413i	0.126348	−	0.0729470i
$939$	−9.91772	−	0.0650132i	−0.323653	−	0.00212163i
$940$	−7.88871	−	2.87126i	−0.257301	−	0.0936501i
$941$	24.8719	+	9.05263i	0.810800	+	0.295107i	0.713954	−	0.700192i	$-0.246902\pi$
$941$	24.8719	+	9.05263i	0.810800	+	0.295107i	0.0968459	+	0.995299i	$0.469125\pi$
$942$	−8.24477	−	0.0540466i	−0.268629	−	0.00176093i
$943$	72.2744	−	41.7276i	2.35358	−	1.35884i
$944$	0.603556	+	3.42294i	0.0196441	+	0.111407i
$945$	−1.52974	+	1.75192i	−0.0497625	+	0.0569901i
$946$	3.02839	+	3.60910i	0.0984615	+	0.117342i
$947$	52.5926	+	9.27349i	1.70903	+	0.301348i	0.940834	−	0.338867i	$-0.110044\pi$
$947$	52.5926	+	9.27349i	1.70903	+	0.301348i	0.768196	+	0.640215i	$0.221155\pi$
$948$	4.15915	−	4.89121i	0.135083	−	0.158859i
$949$		−	16.6253i		−	0.539679i
$950$	2.17412	−	3.77799i	0.0705376	−	0.122574i
$951$	−7.32740	−	12.8858i	−0.237607	−	0.417850i
$952$	0.110650	+	0.304007i	0.00358617	+	0.00985293i
$953$	−6.62663	+	37.5815i	−0.214658	+	1.21738i	0.666842	+	0.745199i	$0.267646\pi$
$953$	−6.62663	+	37.5815i	−0.214658	+	1.21738i	−0.881500	+	0.472185i	$0.843466\pi$
$954$	6.39629	+	39.2798i	0.207088	+	1.27173i
$955$	6.43382	+	5.39861i	0.208193	+	0.174695i
$956$	−25.7948	+	4.54832i	−0.834263	+	0.147103i
$957$	1.98489	+	1.16339i	0.0641624	+	0.0376071i
$958$	−9.33418	−	5.38909i	−0.301574	−	0.174114i
$959$	−2.42466	+	6.66171i	−0.0782965	+	0.215118i
$960$	−1.70767	+	0.289580i	−0.0551149	+	0.00934614i
$961$	28.3028	−	49.0218i	0.912992	−	1.58135i
$962$	−5.04300	−	8.73474i	−0.162593	−	0.281619i
$963$	−21.8836	−	8.29147i	−0.705190	−	0.267189i
$964$	−5.92462	+	7.06069i	−0.190819	+	0.227410i
$965$	−8.04589	+	6.75130i	−0.259006	+	0.217332i
$966$	2.33052	+	6.53606i	0.0749834	+	0.210294i
$967$	41.1718	−	14.9853i	1.32399	−	0.481895i	0.419259	−	0.907867i	$-0.362290\pi$
$967$	41.1718	−	14.9853i	1.32399	−	0.481895i	0.904736	+	0.425972i	$0.140068\pi$
$968$	−10.7966			−0.347016
$969$	−1.89271	+	5.11813i	−0.0608027	+	0.164418i
$970$	−17.7921			−0.571271
$971$	22.4944	−	8.18730i	0.721880	−	0.262743i	0.0451565	−	0.998980i	$-0.485621\pi$
$971$	22.4944	−	8.18730i	0.721880	−	0.262743i	0.676724	+	0.736237i	$0.263399\pi$
$972$	11.6067	+	10.4060i	0.372284	+	0.333773i
$973$	−1.18398	+	0.993474i	−0.0379566	+	0.0318493i
$974$	−14.0388	+	16.7308i	−0.449832	+	0.536089i
$975$	6.62550	+	8.00190i	0.212186	+	0.256266i
$976$	−4.65774	−	8.06744i	−0.149091	−	0.258232i
$977$	15.4386	−	26.7405i	0.493926	−	0.855504i	−0.506050	−	0.862504i	$-0.668895\pi$
$977$	15.4386	−	26.7405i	0.493926	−	0.855504i	0.999975	+	0.00700008i	$0.00222821\pi$
$978$	−3.51053	−	20.7018i	−0.112254	−	0.661972i
$979$	1.01371	−	2.78514i	0.0323982	−	0.0890134i
$980$	5.88867	+	3.39983i	0.188107	+	0.108603i
$981$	−0.478550	+	36.4996i	−0.0152789	+	1.16534i
$982$	−24.6451	+	4.34560i	−0.786458	+	0.138674i
$983$	−5.78769	−	4.85645i	−0.184599	−	0.154897i	0.545805	−	0.837912i	$-0.316224\pi$
$983$	−5.78769	−	4.85645i	−0.184599	−	0.154897i	−0.730404	+	0.683015i	$0.760668\pi$
$984$	15.1391	+	5.62284i	0.482617	+	0.179250i
$985$	−3.74045	+	21.2131i	−0.119181	+	0.675907i
$986$	−0.728110	−	2.00046i	−0.0231877	−	0.0637078i
$987$	−5.65762	+	3.21716i	−0.180084	+	0.102403i
$988$	25.7538	+	4.50360i	0.819338	+	0.143278i
$989$		−	93.5047i		−	2.97328i
$990$	0.252387	−	1.32921i	0.00802138	−	0.0422452i
$991$	−7.54866	−	1.33103i	−0.239791	−	0.0422817i	0.0524609	−	0.998623i	$-0.483294\pi$
$991$	−7.54866	−	1.33103i	−0.239791	−	0.0422817i	−0.292252	+	0.956341i	$0.594405\pi$
$992$	−6.01635	−	7.17001i	−0.191019	−	0.227648i
$993$	−28.3540	−	5.19145i	−0.899788	−	0.164746i
$994$	0.195838	+	1.11065i	0.00621161	+	0.0352278i
$995$	−5.31992	+	3.07145i	−0.168653	+	0.0973717i
$996$	−0.0859386	+	13.1099i	−0.00272307	+	0.415402i
$997$	29.1664	+	10.6157i	0.923709	+	0.336203i	0.759713	−	0.650258i	$-0.225339\pi$
$997$	29.1664	+	10.6157i	0.923709	+	0.336203i	0.163996	+	0.986461i	$0.447562\pi$
$998$	−27.0457	−	9.84383i	−0.856117	−	0.311601i
$999$	7.47967	+	4.51679i	0.236646	+	0.142905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.b.71.2	yes	84
3.2	odd	2		570.2.bb.a.71.4	✓	84
19.15	odd	18		570.2.bb.a.281.4	yes	84
57.53	even	18	inner	570.2.bb.b.281.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.71.4	✓	84	3.2	odd	2
570.2.bb.a.281.4	yes	84	19.15	odd	18
570.2.bb.b.71.2	yes	84	1.1	even	1	trivial
570.2.bb.b.281.2	yes	84	57.53	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.63144 + 0.581714i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(-1.33410 + 1.10462i) q^{6} +(-0.223800 - 0.387633i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.32322 - 1.89807i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.63144 + 0.581714i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(-1.33410 + 1.10462i) q^{6} +(-0.223800 - 0.387633i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.32322 - 1.89807i) q^{9} +(-0.342020 + 0.939693i) q^{10} +(-0.390566 - 0.225494i) q^{11} +(-0.875839 + 1.49429i) q^{12} +(5.90687 - 1.04154i) q^{13} +(-0.342882 - 0.287712i) q^{14} +(0.603053 - 1.62368i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.247206 - 0.679193i) q^{17} +(1.53393 - 2.57819i) q^{18} +(2.18478 + 3.77184i) q^{19} +1.00000i q^{20} +(0.590610 + 0.502214i) q^{21} +(-0.444136 - 0.0783131i) q^{22} +(5.75335 + 6.85657i) q^{23} +(-0.311942 + 1.70373i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(5.19441 - 2.99900i) q^{26} +(-2.68606 + 4.44804i) q^{27} +(-0.420607 - 0.153088i) q^{28} +(2.76773 + 1.00737i) q^{29} +(0.0113538 - 1.73201i) q^{30} +(8.10581 - 4.67989i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.768360 + 0.140682i) q^{33} +(-0.464596 - 0.553684i) q^{34} +(0.440800 + 0.0777250i) q^{35} +(0.559632 - 2.94734i) q^{36} -1.68156i q^{37} +(3.34306 + 2.79713i) q^{38} +(-9.03084 + 5.13532i) q^{39} +(0.342020 + 0.939693i) q^{40} +(1.61909 - 9.18231i) q^{41} +(0.726759 + 0.269927i) q^{42} +(-8.00266 - 6.71503i) q^{43} +(-0.444136 + 0.0783131i) q^{44} +(-0.0393299 + 2.99974i) q^{45} +(7.75146 + 4.47531i) q^{46} +(-2.87126 + 7.88871i) q^{47} +(0.289580 + 1.70767i) q^{48} +(3.39983 - 5.88867i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.798400 + 0.964262i) q^{51} +(3.85543 - 4.59473i) q^{52} +(-10.1621 + 8.52704i) q^{53} +(-1.00275 + 5.09848i) q^{54} +(0.423789 - 0.154247i) q^{55} -0.447601 q^{56} +(-5.75848 - 4.88262i) q^{57} +2.94535 q^{58} +(-3.26613 + 1.18877i) q^{59} +(-0.581714 - 1.63144i) q^{60} +(7.13607 - 5.98787i) q^{61} +(6.01635 - 7.17001i) q^{62} +(-1.25569 - 0.475768i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.99900 + 5.19441i) q^{65} +(0.770138 - 0.130597i) q^{66} +(-3.41429 + 9.38067i) q^{67} +(-0.625948 - 0.361391i) q^{68} +(-13.3748 - 7.83931i) q^{69} +(0.440800 - 0.0777250i) q^{70} +(-1.93015 - 1.61959i) q^{71} +(-0.482167 - 2.96100i) q^{72} +(0.481319 - 2.72969i) q^{73} +(-0.575129 - 1.58015i) q^{74} +(0.856174 + 1.50564i) q^{75} +(4.09813 + 1.48504i) q^{76} +0.201862i q^{77} +(-6.72983 + 7.91436i) q^{78} +(-3.65055 - 0.643690i) q^{79} +(0.642788 + 0.766044i) q^{80} +(1.79467 - 8.81925i) q^{81} +(-1.61909 - 9.18231i) q^{82} +(6.55508 - 3.78457i) q^{83} +(0.775250 + 0.00508197i) q^{84} +(0.679193 + 0.247206i) q^{85} +(-9.81672 - 3.57299i) q^{86} +(-5.10139 - 0.0334409i) q^{87} +(-0.390566 + 0.225494i) q^{88} +(1.14121 + 6.47214i) q^{89} +(0.989014 + 2.83229i) q^{90} +(-1.72569 - 2.05660i) q^{91} +(8.81464 + 1.55426i) q^{92} +(-10.5018 + 12.3502i) q^{93} +8.39499i q^{94} +(-4.29374 - 0.750851i) q^{95} +(0.856174 + 1.50564i) q^{96} +(6.08526 + 16.7191i) q^{97} +(1.18075 - 6.69635i) q^{98} +(-1.33537 + 0.217451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) \) 84 * q - 6 * q^6 + 42 * q^8	\( 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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