LMFDB - Embedded newform 570.2.bb.a.71.4

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			71.4
Character	$\chi$	$=$	570.71
Dual form			570.2.bb.a.281.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-1.33410 - 1.10462i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(1.63144 + 0.581714i) q^{6} +(-0.223800 - 0.387633i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.559632 + 2.94734i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.33410 - 1.10462i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(1.63144 + 0.581714i) q^{6} +(-0.223800 - 0.387633i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.559632 + 2.94734i) q^{9} +(-0.342020 + 0.939693i) q^{10} +(0.390566 + 0.225494i) q^{11} +(-1.73201 + 0.0113538i) q^{12} +(5.90687 - 1.04154i) q^{13} +(0.342882 + 0.287712i) q^{14} +(-1.70373 + 0.311942i) 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} +(-0.129616 + 0.764355i) q^{21} +(-0.444136 - 0.0783131i) q^{22} +(-5.75335 - 6.85657i) q^{23} +(1.62368 - 0.603053i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(-5.19441 + 2.99900i) q^{26} +(2.50908 - 4.55022i) q^{27} +(-0.420607 - 0.153088i) q^{28} +(-2.76773 - 1.00737i) q^{29} +(1.49429 - 0.875839i) q^{30} +(8.10581 - 4.67989i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.271969 - 0.732258i) q^{33} +(-0.464596 - 0.553684i) q^{34} +(-0.440800 - 0.0777250i) q^{35} +(2.32322 + 1.89807i) 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} +(-0.139626 - 0.762590i) q^{42} +(-8.00266 - 6.71503i) q^{43} +(0.444136 - 0.0783131i) q^{44} +(2.61752 + 1.46581i) q^{45} +(7.75146 + 4.47531i) q^{46} +(2.87126 - 7.88871i) q^{47} +(-1.31950 + 1.12201i) q^{48} +(3.39983 - 5.88867i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.420453 - 1.17918i) q^{51} +(3.85543 - 4.59473i) q^{52} +(10.1621 - 8.52704i) q^{53} +(-0.801502 + 5.13396i) q^{54} +(0.423789 - 0.154247i) q^{55} +0.447601 q^{56} +(1.25173 - 7.44535i) q^{57} +2.94535 q^{58} +(3.26613 - 1.18877i) q^{59} +(-1.10462 + 1.33410i) q^{60} +(7.13607 - 5.98787i) q^{61} +(-6.01635 + 7.17001i) q^{62} +(1.01724 - 0.876548i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.99900 - 5.19441i) q^{65} +(0.506014 + 0.595078i) q^{66} +(-3.41429 + 9.38067i) q^{67} +(0.625948 + 0.361391i) q^{68} +(0.101624 + 15.5026i) q^{69} +(0.440800 - 0.0777250i) q^{70} +(1.93015 + 1.61959i) q^{71} +(-2.83229 - 0.989014i) 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} +(10.2426 + 1.73690i) q^{78} +(-3.65055 - 0.643690i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(-8.37362 + 3.29885i) q^{81} +(-1.61909 - 9.18231i) q^{82} +(-6.55508 + 3.78457i) q^{83} +(0.392026 + 0.668845i) q^{84} +(0.679193 + 0.247206i) q^{85} +(9.81672 + 3.57299i) q^{86} +(2.57966 + 4.40121i) q^{87} +(-0.390566 + 0.225494i) q^{88} +(-1.14121 - 6.47214i) q^{89} +(-2.96100 - 0.482167i) q^{90} +(-1.72569 - 2.05660i) q^{91} +(-8.81464 - 1.55426i) q^{92} +(-15.9834 - 2.71040i) 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} +(-0.446033 + 1.27733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * 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
$3$	−1.33410	−	1.10462i	−0.770242	−	0.637752i
$3$	−1.33410	−	1.10462i	−0.770242	−	0.637752i
$4$	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
$6$	1.63144	+	0.581714i	0.666034	+	0.237484i
$7$	−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
$9$	0.559632	+	2.94734i	0.186544	+	0.982447i
$10$	−0.342020	+	0.939693i	−0.108156	+	0.297157i
$11$	0.390566	+	0.225494i	0.117760	+	0.0679889i	0.557723	−	0.830027i	$-0.311675\pi$
$11$	0.390566	+	0.225494i	0.117760	+	0.0679889i	−0.439963	+	0.898016i	$0.645008\pi$
$12$	−1.73201	+	0.0113538i	−0.499989	+	0.00327756i
$13$	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
$15$	−1.70373	+	0.311942i	−0.439901	+	0.0805432i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.247206	+	0.679193i	0.0599563	+	0.164729i	0.966054	−	0.258340i	$-0.0831753\pi$
$17$	0.247206	+	0.679193i	0.0599563	+	0.164729i	−0.906098	+	0.423068i	$0.860953\pi$
$18$	−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
$21$	−0.129616	+	0.764355i	−0.0282845	+	0.166796i
$22$	−0.444136	−	0.0783131i	−0.0946901	−	0.0166964i
$23$	−5.75335	−	6.85657i	−1.19966	−	1.42969i	−0.875178	−	0.483801i	$-0.839256\pi$
$23$	−5.75335	−	6.85657i	−1.19966	−	1.42969i	−0.324478	−	0.945893i	$-0.605189\pi$
$24$	1.62368	−	0.603053i	0.331432	−	0.123098i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	−5.19441	+	2.99900i	−1.01871	+	0.588151i
$27$	2.50908	−	4.55022i	0.482874	−	0.875690i
$28$	−0.420607	−	0.153088i	−0.0794872	−	0.0289310i
$29$	−2.76773	−	1.00737i	−0.513954	−	0.187064i	0.0720056	−	0.997404i	$-0.477060\pi$
$29$	−2.76773	−	1.00737i	−0.513954	−	0.187064i	−0.585960	+	0.810340i	$0.699282\pi$
$30$	1.49429	−	0.875839i	0.272819	−	0.159906i
$31$	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
$33$	−0.271969	−	0.732258i	−0.0473437	−	0.127470i
$34$	−0.464596	−	0.553684i	−0.0796775	−	0.0949559i
$35$	−0.440800	−	0.0777250i	−0.0745089	−	0.0131379i
$36$	2.32322	+	1.89807i	0.387203	+	0.316345i
$37$		−	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	$0.315142\pi$
$41$	−1.61909	+	9.18231i	−0.252859	+	1.43404i	−0.801508	+	0.597983i	$0.795969\pi$
$42$	−0.139626	−	0.762590i	−0.0215447	−	0.117670i
$43$	−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
$45$	2.61752	+	1.46581i	0.390197	+	0.218510i
$46$	7.75146	+	4.47531i	1.14289	+	0.659848i
$47$	2.87126	−	7.88871i	0.418816	−	1.15069i	−0.533560	−	0.845762i	$-0.679146\pi$
$47$	2.87126	−	7.88871i	0.418816	−	1.15069i	0.952376	−	0.304925i	$-0.0986315\pi$
$48$	−1.31950	+	1.12201i	−0.190454	+	0.161949i
$49$	3.39983	−	5.88867i	0.485690	−	0.841239i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	0.420453	−	1.17918i	0.0588752	−	0.165118i
$52$	3.85543	−	4.59473i	0.534653	−	0.637174i
$53$	10.1621	−	8.52704i	1.39588	−	1.17128i	0.432980	−	0.901404i	$-0.357462\pi$
$53$	10.1621	−	8.52704i	1.39588	−	1.17128i	0.962895	−	0.269875i	$-0.0869824\pi$
$54$	−0.801502	+	5.13396i	−0.109071	+	0.698644i
$55$	0.423789	−	0.154247i	0.0571438	−	0.0207986i
$56$	0.447601			0.0598131
$57$	1.25173	−	7.44535i	0.165796	−	0.986160i
$58$	2.94535			0.386744
$59$	3.26613	−	1.18877i	0.425213	−	0.154765i	−0.120544	−	0.992708i	$-0.538464\pi$
$59$	3.26613	−	1.18877i	0.425213	−	0.154765i	0.545758	+	0.837943i	$0.316242\pi$
$60$	−1.10462	+	1.33410i	−0.142606	+	0.172231i
$61$	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
$63$	1.01724	−	0.876548i	0.128160	−	0.110435i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.99900	−	5.19441i	0.371980	−	0.644288i
$66$	0.506014	+	0.595078i	0.0622860	+	0.0732491i
$67$	−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
$69$	0.101624	+	15.5026i	0.0122340	+	1.86629i
$70$	0.440800	−	0.0777250i	0.0526857	−	0.00928992i
$71$	1.93015	+	1.61959i	0.229066	+	0.192209i	0.750096	−	0.661329i	$-0.230007\pi$
$71$	1.93015	+	1.61959i	0.229066	+	0.192209i	−0.521029	+	0.853539i	$0.674452\pi$
$72$	−2.83229	−	0.989014i	−0.333788	−	0.116556i
$73$	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
$78$	10.2426	+	1.73690i	1.15975	+	0.196665i
$79$	−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
$81$	−8.37362	+	3.29885i	−0.930403	+	0.366539i
$82$	−1.61909	−	9.18231i	−0.178799	−	1.01402i
$83$	−6.55508	+	3.78457i	−0.719513	+	0.415411i	−0.814573	−	0.580060i	$-0.803029\pi$
$83$	−6.55508	+	3.78457i	−0.719513	+	0.415411i	0.0950604	+	0.995472i	$0.469696\pi$
$84$	0.392026	+	0.668845i	0.0427736	+	0.0729770i
$85$	0.679193	+	0.247206i	0.0736689	+	0.0268133i
$86$	9.81672	+	3.57299i	1.05856	+	0.385286i
$87$	2.57966	+	4.40121i	0.276568	+	0.471860i
$88$	−0.390566	+	0.225494i	−0.0416345	+	0.0240377i
$89$	−1.14121	−	6.47214i	−0.120968	−	0.686046i	−0.983621	−	0.180249i	$-0.942310\pi$
$89$	−1.14121	−	6.47214i	−0.120968	−	0.686046i	0.862653	−	0.505797i	$-0.168801\pi$
$90$	−2.96100	−	0.482167i	−0.312117	−	0.0508249i
$91$	−1.72569	−	2.05660i	−0.180902	−	0.215591i
$92$	−8.81464	−	1.55426i	−0.918990	−	0.162043i
$93$	−15.9834	−	2.71040i	−1.65741	−	0.281056i
$94$			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
$99$	−0.446033	+	1.27733i	−0.0448280	+	0.128376i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	−2.29052	+	0.403880i	−0.227915	+	0.0401876i	−0.286439	−	0.958098i	$-0.592472\pi$
$101$	−2.29052	+	0.403880i	−0.227915	+	0.0401876i	0.0585241	+	0.998286i	$0.481361\pi$
$102$	0.00820632	+	1.25187i	0.000812547	+	0.123954i
$103$	−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
$105$	0.502214	+	0.590610i	0.0490111	+	0.0576376i
$106$	−6.63286	+	11.4884i	−0.644240	+	1.11586i
$107$	3.90029	+	6.75550i	0.377055	+	0.653079i	0.990632	−	0.136556i	$-0.0436033\pi$
$107$	3.90029	+	6.75550i	0.377055	+	0.653079i	−0.613577	+	0.789635i	$0.710270\pi$
$108$	−1.00275	−	5.09848i	−0.0964900	−	0.490601i
$109$	−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
$111$	−1.85749	+	2.24337i	−0.176305	+	0.212931i
$112$	−0.420607	+	0.153088i	−0.0397436	+	0.0144655i
$113$	7.03077			0.661399			0.330699	−	0.943736i	$-0.392715\pi$
$113$	7.03077			0.661399			0.330699	+	0.943736i	$0.392715\pi$
$114$	1.37021	+	7.42445i	0.128332	+	0.695364i
$115$	−8.95062			−0.834650
$116$	−2.76773	+	1.00737i	−0.256977	+	0.0935320i
$117$	6.37545	+	16.8267i	0.589410	+	1.55563i
$118$	−2.66257	+	2.23416i	−0.245110	+	0.205671i
$119$	0.207953	−	0.247829i	0.0190630	−	0.0227185i
$120$	0.581714	−	1.63144i	0.0531030	−	0.148930i
$121$	−5.39831	−	9.35014i	−0.490755	−	0.850013i
$122$	−4.65774	+	8.06744i	−0.421692	+	0.730392i
$123$	12.3030	−	10.4616i	1.10932	−	0.943293i
$124$	3.20123	−	8.79532i	0.287479	−	0.789843i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	−0.656098	+	1.17160i	−0.0584498	+	0.104375i
$127$	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
$129$	3.25878	+	17.7984i	0.286919	+	1.56706i
$130$	−1.04154	+	5.90687i	−0.0913491	+	0.518067i
$131$	−1.33200	−	3.65963i	−0.116377	−	0.319743i	0.867805	−	0.496906i	$-0.165530\pi$
$131$	−1.33200	−	3.65963i	−0.116377	−	0.319743i	−0.984182	+	0.177162i	$0.943308\pi$
$132$	−0.679027	−	0.386124i	−0.0591017	−	0.0336077i
$133$	0.973135	−	1.69103i	0.0843815	−	0.146631i
$134$		−	9.98271i		−	0.862374i
$135$	−1.87286	−	4.84689i	−0.161190	−	0.417154i
$136$	−0.711802	−	0.125510i	−0.0610365	−	0.0107624i
$137$	10.1807	+	12.1329i	0.869794	+	1.03658i	0.998989	+	0.0449611i	$0.0143164\pi$
$137$	10.1807	+	12.1329i	0.869794	+	1.03658i	−0.129195	+	0.991619i	$0.541239\pi$
$138$	−5.39769	−	14.5329i	−0.459482	−	1.23712i
$139$	−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
$141$	−12.5446	+	7.35267i	−1.05644	+	0.619206i
$142$	−2.36768	−	0.861764i	−0.198691	−	0.0723176i
$143$	2.54189	+	0.925171i	0.212563	+	0.0773666i
$144$	2.99974	−	0.0393299i	0.249979	−	0.00327749i
$145$	−2.55075	+	1.47268i	−0.211828	+	0.122299i
$146$	0.481319	+	2.72969i	0.0398342	+	0.225911i
$147$	−11.0404	+	4.10055i	−0.910600	+	0.338208i
$148$	−1.08089	−	1.28815i	−0.0888485	−	0.105886i
$149$	10.5841	+	1.86625i	0.867079	+	0.152889i	0.589456	−	0.807800i	$-0.299342\pi$
$149$	10.5841	+	1.86625i	0.867079	+	0.152889i	0.277623	+	0.960690i	$0.410453\pi$
$150$	0.289580	−	1.70767i	0.0236441	−	0.139431i
$151$			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
$156$	−10.2190	+	1.87103i	−0.818171	+	0.149802i
$157$	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
$159$	−22.9764	+	0.150616i	−1.82215	+	0.0119446i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−1.37024	+	3.76469i	−0.107990	+	0.296699i
$162$	6.74036	−	5.96385i	0.529573	−	0.468565i
$163$	−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
$165$	−0.735760	−	0.262346i	−0.0572789	−	0.0204236i
$166$	4.86536	−	5.79830i	0.377625	−	0.450036i
$167$	8.56382	−	7.18590i	0.662688	−	0.556062i	−0.248203	−	0.968708i	$-0.579840\pi$
$167$	8.56382	−	7.18590i	0.662688	−	0.556062i	0.910891	+	0.412647i	$0.135396\pi$
$168$	−0.597143	−	0.494428i	−0.0460706	−	0.0381460i
$169$	21.5903	−	7.85822i	1.66079	−	0.604478i
$170$	−0.722782			−0.0554349
$171$	−9.89421	+	8.55013i	−0.756629	+	0.653845i
$172$	−10.4467			−0.796556
$173$	−17.4922	+	6.36664i	−1.32991	+	0.484046i	−0.906619	−	0.421949i	$-0.861346\pi$
$173$	−17.4922	+	6.36664i	−1.32991	+	0.484046i	−0.423287	+	0.905996i	$0.639124\pi$
$174$	−3.92939	−	3.25349i	−0.297886	−	0.246647i
$175$	−0.342882	+	0.287712i	−0.0259194	+	0.0217490i
$176$	0.289889	−	0.345476i	0.0218512	−	0.0260413i
$177$	−5.67047	−	2.02189i	−0.426219	−	0.151974i
$178$	3.28599	+	5.69151i	0.246296	+	0.426596i
$179$	9.91629	−	17.1755i	0.741178	−	1.28376i	−0.210781	−	0.977533i	$-0.567601\pi$
$179$	9.91629	−	17.1755i	0.741178	−	1.28376i	0.951959	−	0.306225i	$-0.0990661\pi$
$180$	2.94734	−	0.559632i	0.219682	−	0.0417125i
$181$	−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
$183$	−16.1345	+	0.105766i	−1.19270	+	0.00781845i
$184$	8.81464	−	1.55426i	0.649824	−	0.114581i
$185$	−1.28815	−	1.08089i	−0.0947069	−	0.0794685i
$186$	15.9465	−	2.91971i	1.16926	−	0.214084i
$187$	−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	$0.0982742\pi$
$191$			8.39875i			0.607712i	−0.952718	+	0.303856i	$0.901726\pi$
$192$	−0.289580	+	1.70767i	−0.0208986	+	0.123241i
$193$	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
$195$	−9.73880	+	3.61710i	−0.697410	+	0.259026i
$196$	−1.18075	−	6.69635i	−0.0843391	−	0.478311i
$197$	−18.6545	+	10.7702i	−1.32908	+	0.767345i	−0.985157	−	0.171653i	$-0.945089\pi$
$197$	−18.6545	+	10.7702i	−1.32908	+	0.767345i	−0.343923	+	0.938998i	$0.611756\pi$
$198$	−0.0177373	−	1.35285i	−0.00126053	−	0.0961425i
$199$	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
$201$	14.9171	−	8.74325i	1.05217	−	0.616701i
$202$	2.01425	−	1.16293i	0.141722	−	0.0818233i
$203$	0.228928	+	1.29831i	0.0160676	+	0.0911237i
$204$	−0.435876	−	1.17357i	−0.0305174	−	0.0821660i
$205$	5.99333	+	7.14257i	0.418592	+	0.498859i
$206$	10.7594	+	1.89717i	0.749641	+	0.132182i
$207$	16.9889	−	20.7942i	1.18081	−	1.44530i
$208$		−	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
$213$	−0.785979	−	4.29276i	−0.0538544	−	0.294135i
$214$	−5.97559	−	5.01412i	−0.408483	−	0.342758i
$215$	−10.2880	+	1.81406i	−0.701637	+	0.123718i
$216$	2.68606	+	4.44804i	0.182763	+	0.302651i
$217$	−3.62816	−	2.09472i	−0.246296	−	0.142199i
$218$	4.16156	−	11.4338i	0.281857	−	0.774395i
$219$	−3.65740	+	3.11000i	−0.247144	+	0.210155i
$220$	0.225494	−	0.390566i	0.0152028	−	0.0263320i
$221$	2.16762	+	3.75443i	0.145810	+	0.252550i
$222$	0.978190	−	2.74338i	0.0656518	−	0.184123i
$223$	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
$225$	2.80538	−	1.06293i	0.187026	−	0.0708620i
$226$	−6.60676	+	2.40466i	−0.439475	+	0.159956i
$227$	−8.50175			−0.564281			−0.282140	−	0.959373i	$-0.591044\pi$
$227$	−8.50175			−0.564281			−0.282140	+	0.959373i	$0.591044\pi$
$228$	−3.82689	−	6.50806i	−0.253442	−	0.431007i
$229$	−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
$231$	−0.222981	+	0.269304i	−0.0146711	+	0.0177189i
$232$	2.25627	−	1.89324i	0.148131	−	0.124297i
$233$	−1.58281	+	1.88632i	−0.103693	+	0.123577i	−0.815395	−	0.578905i	$-0.803480\pi$
$233$	−1.58281	+	1.88632i	−0.103693	+	0.123577i	0.711702	+	0.702482i	$0.247925\pi$
$234$	−11.7460	−	13.6314i	−0.767861	−	0.891110i
$235$	−4.19750	−	7.27028i	−0.273815	−	0.474261i
$236$	1.73787	−	3.01008i	0.113126	−	0.195939i
$237$	4.15915	+	4.89121i	0.270166	+	0.317718i
$238$	−0.110650	+	0.304007i	−0.00717235	+	0.0197059i
$239$	22.6835	+	13.0964i	1.46728	+	0.847133i	0.999329	−	0.0366235i	$-0.0116602\pi$
$239$	22.6835	+	13.0964i	1.46728	+	0.847133i	0.467948	+	0.883756i	$0.344994\pi$
$240$	0.0113538	+	1.73201i	0.000732884	+	0.111801i
$241$	−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
$243$	14.8152	+	4.84868i	0.950396	+	0.311043i
$244$	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
$249$	12.9256	+	2.19187i	0.819128	+	0.138904i
$250$	0.984808	+	0.173648i	0.0622847	+	0.0109825i
$251$	−3.59997	−	4.29028i	−0.227228	−	0.270800i	0.640369	−	0.768067i	$-0.278781\pi$
$251$	−3.59997	−	4.29028i	−0.227228	−	0.270800i	−0.867598	+	0.497267i	$0.834337\pi$
$252$	0.215818	−	1.32534i	0.0135953	−	0.0834889i
$253$	−0.700951	−	3.97529i	−0.0440684	−	0.249924i
$254$	−2.63461	+	1.52109i	−0.165310	+	0.0954420i
$255$	−0.633041	−	1.08005i	−0.0396426	−	0.0676352i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	22.7367	+	8.27549i	1.41828	+	0.516211i	0.933548	−	0.358453i	$-0.116696\pi$
$257$	22.7367	+	8.27549i	1.41828	+	0.516211i	0.484730	+	0.874664i	$0.338918\pi$
$258$	−9.14966	−	15.6105i	−0.569633	−	0.971864i
$259$	−0.651831	+	0.376335i	−0.0405028	+	0.0233843i
$260$	−1.04154	−	5.90687i	−0.0645936	−	0.366328i
$261$	1.42015	−	8.72119i	0.0879053	−	0.539828i
$262$	2.50333	+	2.98336i	0.154656	+	0.184312i
$263$	16.6084	+	2.92851i	1.02412	+	0.180579i	0.660387	−	0.750925i	$-0.270392\pi$
$263$	16.6084	+	2.92851i	1.02412	+	0.180579i	0.363730	+	0.931505i	$0.381503\pi$
$264$	0.770138	+	0.130597i	0.0473987	+	0.00803768i
$265$		−	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	−0.952200	−	0.305474i	$-0.901185\pi$
$269$	0.771737	−	4.37674i	0.0470536	−	0.266854i	0.999254	+	0.0386199i	$0.0122961\pi$
$270$	3.41765	+	3.91404i	0.207992	+	0.238201i
$271$	−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
$273$	0.0304816	+	4.64994i	0.00184483	+	0.281427i
$274$	−13.7164	−	7.91916i	−0.828638	−	0.478414i
$275$	0.154247	−	0.423789i	0.00930143	−	0.0255555i
$276$	10.0427	+	11.8104i	0.604501	+	0.710900i
$277$	−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
$279$	18.3295	+	21.2716i	1.09736	+	1.27349i
$280$	0.287712	−	0.342882i	0.0171941	−	0.0204911i
$281$	−4.32925	+	3.63267i	−0.258262	+	0.216707i	−0.762720	−	0.646729i	$-0.776137\pi$
$281$	−4.32925	+	3.63267i	−0.258262	+	0.216707i	0.504459	+	0.863436i	$0.331692\pi$
$282$	9.27327	−	11.1997i	0.552215	−	0.666935i
$283$	−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
$285$	−4.89887	−	5.74466i	−0.290184	−	0.340284i
$286$	−2.70502			−0.159951
$287$	3.92172	−	1.42739i	0.231492	−	0.0842562i
$288$	−2.80538	+	1.06293i	−0.165309	+	0.0626338i
$289$	12.6226	−	10.5916i	0.742504	−	0.623035i
$290$	1.89324	−	2.25627i	0.111175	−	0.132493i
$291$	10.3499	−	29.0268i	0.606724	−	1.70158i
$292$	−1.38590	−	2.40045i	−0.0811038	−	0.140476i
$293$	5.10466	−	8.84153i	0.298217	−	0.516528i	−0.677511	−	0.735513i	$-0.736941\pi$
$293$	5.10466	−	8.84153i	0.298217	−	0.516528i	0.975728	+	0.218985i	$0.0702746\pi$
$294$	8.97215	−	7.62931i	0.523267	−	0.444950i
$295$	1.18877	−	3.26613i	0.0692130	−	0.190161i
$296$	1.45628	+	0.840782i	0.0846444	+	0.0488695i
$297$	2.00601	−	1.21138i	0.116400	−	0.0702914i
$298$	−10.5841	+	1.86625i	−0.613118	+	0.108109i
$299$	−41.1257	−	34.5085i	−2.37836	−	1.99568i
$300$	0.311942	+	1.70373i	0.0180100	+	0.0983648i
$301$	−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
$306$	1.37189	−	1.67918i	0.0784258	−	0.0959923i
$307$	−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
$309$	6.58856	+	17.7393i	0.374810	+	1.00915i
$310$	1.62531	+	9.21759i	0.0923114	+	0.523524i
$311$	−12.4864	+	7.20901i	−0.708037	+	0.408785i	−0.810334	−	0.585969i	$-0.800714\pi$
$311$	−12.4864	+	7.20901i	−0.708037	+	0.408785i	0.102297	+	0.994754i	$0.467381\pi$
$312$	8.96274	−	5.25328i	0.507415	−	0.297408i
$313$	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
$315$	−0.0176041	−	1.34269i	−0.000991877	−	0.0756518i
$316$	−3.21024	+	1.85343i	−0.180590	+	0.104264i
$317$	−1.48613	−	8.42829i	−0.0834696	−	0.473380i	−0.997676	−	0.0681317i	$-0.978296\pi$
$317$	−1.48613	−	8.42829i	−0.0834696	−	0.473380i	0.914207	−	0.405248i	$-0.132815\pi$
$318$	21.5392	−	7.99992i	1.20786	−	0.448613i
$319$	−0.853826	−	1.01755i	−0.0478051	−	0.0569719i
$320$	−0.984808	−	0.173648i	−0.0550524	−	0.00970723i
$321$	2.25889	−	13.3208i	0.126079	−	0.743497i
$322$		−	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
$327$	20.7303	−	3.79559i	1.14639	−	0.209896i
$328$	−7.14257	−	5.99333i	−0.394382	−	0.330926i
$329$	−3.70052	+	0.652501i	−0.204016	+	0.0359735i
$330$	0.781116	−	0.00512042i	0.0429990	−	0.000281870i
$331$	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
$333$	4.95614	−	0.941057i	0.271595	−	0.0515696i
$334$	−5.58964	+	9.68154i	−0.305851	+	0.529750i
$335$	4.99135	+	8.64528i	0.272707	+	0.472342i
$336$	0.730235	+	0.260376i	0.0398376	+	0.0142047i
$337$	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
$339$	−9.37973	−	7.76632i	−0.509437	−	0.421809i
$340$	0.679193	−	0.247206i	0.0368344	−	0.0134066i
$341$	4.22114			0.228588
$342$	6.37320	−	11.4185i	0.344623	−	0.617442i
$343$	−6.17673			−0.333512
$344$	9.81672	−	3.57299i	0.529282	−	0.192643i
$345$	11.9410	+	9.88703i	0.642882	+	0.532300i
$346$	14.2598	−	11.9654i	0.766610	−	0.643262i
$347$	−6.41137	+	7.64077i	−0.344180	+	0.410178i	−0.910171	−	0.414234i	$-0.864050\pi$
$347$	−6.41137	+	7.64077i	−0.344180	+	0.410178i	0.565990	+	0.824412i	$0.308494\pi$
$348$	4.80518	+	1.71335i	0.257585	+	0.0918455i
$349$	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
$351$	10.0816	−	29.4909i	0.538116	−	1.57411i
$352$	−0.154247	+	0.423789i	−0.00822138	+	0.0225881i
$353$	7.55118	+	4.35967i	0.401909	+	0.232042i	0.687307	−	0.726367i	$-0.258793\pi$
$353$	7.55118	+	4.35967i	0.401909	+	0.232042i	−0.285399	+	0.958409i	$0.592126\pi$
$354$	6.02003	−	0.0394628i	0.319961	−	0.00209743i
$355$	2.48135	−	0.437529i	0.131696	−	0.0232216i
$356$	−5.03443	−	4.22439i	−0.266824	−	0.223892i
$357$	−0.551187	+	0.100919i	−0.0291719	+	0.00534119i
$358$	−3.44389	+	19.5313i	−0.182015	+	1.03226i
$359$	4.75634	+	13.0679i	0.251030	+	0.689700i	0.999644	+	0.0266930i	$0.00849764\pi$
$359$	4.75634	+	13.0679i	0.251030	+	0.689700i	−0.748614	+	0.663007i	$0.769280\pi$
$360$	−2.57819	+	1.53393i	−0.135882	+	0.0808453i
$361$	−9.45348	+	16.4813i	−0.497552	+	0.867434i
$362$		−	3.97622i		−	0.208985i
$363$	−3.12648	+	18.4371i	−0.164098	+	0.967695i
$364$	−2.64392	−	0.466194i	−0.138579	−	0.0244352i
$365$	−1.78168	−	2.12333i	−0.0932575	−	0.111140i
$366$	15.1253	−	5.61772i	0.790613	−	0.293643i
$367$	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
$369$	−27.9695	+	0.366710i	−1.45603	+	0.0190902i
$370$	1.58015	+	0.575129i	0.0821483	+	0.0298995i
$371$	−5.57965	−	2.03083i	−0.289681	−	0.105435i
$372$	−13.9862	+	8.19767i	−0.725153	+	0.425029i
$373$	−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
$375$	0.603053	+	1.62368i	0.0311415	+	0.0838463i
$376$	5.39620	+	6.43094i	0.278288	+	0.331650i
$377$	−17.3978	−	3.06770i	−0.896033	−	0.157995i
$378$	2.16947	−	0.838294i	0.111586	−	0.0431172i
$379$			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	$0.199015\pi$
$383$	−2.96057	+	16.7902i	−0.151278	+	0.857941i	−0.962110	+	0.272662i	$0.912096\pi$
$384$	−0.311942	−	1.70373i	−0.0159187	−	0.0869430i
$385$	−0.154635	−	0.129754i	−0.00788095	−	0.00661290i
$386$	−10.3436	+	1.82386i	−0.526475	+	0.0928318i
$387$	15.3129	−	27.3445i	0.778400	−	1.39000i
$388$	15.4084	+	8.89606i	0.782245	+	0.451629i
$389$	8.55726	−	23.5109i	0.433870	−	1.19205i	−0.509547	−	0.860443i	$-0.670187\pi$
$389$	8.55726	−	23.5109i	0.433870	−	1.19205i	0.943418	−	0.331607i	$-0.107591\pi$
$390$	7.91436	−	6.72983i	0.400759	−	0.340778i
$391$	3.23468	−	5.60262i	0.163585	−	0.283337i
$392$	3.39983	+	5.88867i	0.171717	+	0.297423i
$393$	−2.26548	+	6.35365i	−0.114279	+	0.320499i
$394$	13.8459	−	16.5009i	0.697546	−	0.831303i
$395$	−2.83962	+	2.38272i	−0.142877	+	0.119888i
$396$	0.479368	+	1.26519i	0.0240891	+	0.0635783i
$397$	−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
$399$	−3.16620	+	1.18106i	−0.158508	+	0.0591268i
$400$	−1.00000			−0.0500000
$401$	−9.87117	+	3.59281i	−0.492943	+	0.179416i	−0.576517	−	0.817085i	$-0.695589\pi$
$401$	−9.87117	+	3.59281i	−0.492943	+	0.179416i	0.0835745	+	0.996502i	$0.473366\pi$
$402$	−11.0271	+	13.3179i	−0.549981	+	0.664237i
$403$	43.0057	−	36.0860i	2.14226	−	1.79757i
$404$	−1.49503	+	1.78171i	−0.0743806	+	0.0886433i
$405$	−2.85539	+	8.53503i	−0.141886	+	0.424109i
$406$	−0.659171	−	1.14172i	−0.0327141	−	0.0566625i
$407$	0.379182	−	0.656763i	0.0187954	−	0.0325545i
$408$	0.810972	+	0.953712i	0.0401491	+	0.0472158i
$409$	−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
$411$	−0.179825	−	27.4322i	−0.00887012	−	1.35313i
$412$	−10.7594	+	1.89717i	−0.530076	+	0.0934668i
$413$	−1.19177	−	1.00001i	−0.0586431	−	0.0492074i
$414$	−8.85229	+	25.3507i	−0.435066	+	1.24592i
$415$	−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	$-0.952932\pi$
$419$		−	6.03152i		−	0.294659i	0.989087	−	0.147330i	$-0.0470678\pi$
$420$	0.764355	+	0.129616i	0.0372967	+	0.00632461i
$421$	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
$423$	24.8576	+	4.04779i	1.20862	+	0.196810i
$424$	2.30357	+	13.0642i	0.111871	+	0.634453i
$425$	0.625948	−	0.361391i	0.0303629	−	0.0175301i
$426$	2.20679	+	3.76506i	0.106919	+	0.182418i
$427$	−3.91815	−	1.42609i	−0.189613	−	0.0690134i
$428$	7.33015	+	2.66796i	0.354316	+	0.128961i
$429$	−2.36916	−	4.04208i	−0.114384	−	0.195154i
$430$	9.04713	−	5.22337i	0.436292	−	0.251893i
$431$	1.65413	+	9.38105i	0.0796768	+	0.451869i	0.998379	+	0.0569181i	$0.0181274\pi$
$431$	1.65413	+	9.38105i	0.0796768	+	0.451869i	−0.918702	+	0.394951i	$0.870761\pi$
$432$	−4.04539	−	3.26110i	−0.194634	−	0.156900i
$433$	−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
$435$	5.02970	+	0.852915i	0.241156	+	0.0408941i
$436$			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
$441$	19.2586	+	6.72495i	0.917075	+	0.320236i
$442$	−3.32099	−	2.78664i	−0.157963	−	0.132547i
$443$	−11.8982	+	2.09797i	−0.565299	+	0.0996774i	−0.448992	−	0.893536i	$-0.648217\pi$
$443$	−11.8982	+	2.09797i	−0.565299	+	0.0996774i	−0.116307	+	0.993213i	$0.537106\pi$
$444$	0.0190921	+	2.91249i	0.000906073	+	0.138221i
$445$	−5.69151	−	3.28599i	−0.269803	−	0.155771i
$446$	−7.17402	+	19.7105i	−0.339700	+	0.933317i
$447$	−12.0587	−	14.1811i	−0.570355	−	0.670744i
$448$	−0.223800	+	0.387633i	−0.0105736	+	0.0183140i
$449$	−12.6422	−	21.8969i	−0.596621	−	1.03338i	−0.993316	−	0.115427i	$-0.963176\pi$
$449$	−12.6422	−	21.8969i	−0.596621	−	1.03338i	0.396695	−	0.917950i	$-0.370157\pi$
$450$	−2.27266	+	1.95833i	−0.107134	+	0.0923164i
$451$	−2.70291	+	3.22121i	−0.127275	+	0.151681i
$452$	5.38588	−	4.51929i	0.253330	−	0.212569i
$453$	3.10999	−	3.75608i	0.146120	−	0.176476i
$454$	7.98903	−	2.90777i	0.374944	−	0.136468i
$455$	−2.68470			−0.125861
$456$	5.82199	+	4.80671i	0.272640	+	0.225095i
$457$	−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
$459$	3.71074	+	0.579312i	0.173203	+	0.0270399i
$460$	−6.85657	+	5.75335i	−0.319689	+	0.268251i
$461$	−22.7627	+	27.1275i	−1.06016	+	1.26345i	−0.0967850	+	0.995305i	$0.530856\pi$
$461$	−22.7627	+	27.1275i	−1.06016	+	1.26345i	−0.963378	+	0.268148i	$0.913589\pi$
$462$	0.117426	−	0.329327i	0.00546316	−	0.0153217i
$463$	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
$465$	−12.3502	+	10.5018i	−0.572729	+	0.487010i
$466$	0.842195	−	2.31391i	0.0390139	−	0.107190i
$467$	−21.8121	−	12.5932i	−1.00935	−	0.582746i	−0.0983456	−	0.995152i	$-0.531355\pi$
$467$	−21.8121	−	12.5932i	−1.00935	−	0.582746i	−0.911000	+	0.412406i	$0.864688\pi$
$468$	15.6998	+	8.79192i	0.725726	+	0.406407i
$469$	4.40038	−	0.775906i	0.203191	−	0.0358280i
$470$	6.43094	+	5.39620i	0.296637	+	0.248908i
$471$	−1.48492	−	8.11013i	−0.0684213	−	0.373695i
$472$	−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
$477$	30.8191	+	25.1792i	1.41111	+	1.15288i
$478$	−25.7948	−	4.54832i	−1.17983	−	0.208035i
$479$	6.92808	+	8.25656i	0.316552	+	0.377252i	0.900734	−	0.434370i	$-0.143029\pi$
$479$	6.92808	+	8.25656i	0.316552	+	0.377252i	−0.584182	+	0.811623i	$0.698585\pi$
$480$	−0.603053	−	1.62368i	−0.0275255	−	0.0741104i
$481$	−1.75142	−	9.93278i	−0.0798577	−	0.452896i
$482$	7.98222	−	4.60854i	0.363580	−	0.209913i
$483$	5.98658	−	3.50888i	0.272399	−	0.159659i
$484$	−10.1455	−	3.69266i	−0.461159	−	0.167848i
$485$	16.7191	+	6.08526i	0.759176	+	0.276318i
$486$	−15.5801	+	0.510833i	−0.706727	+	0.0231719i
$487$	−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
$489$	19.6836	−	7.31071i	0.890122	−	0.330602i
$490$	4.37073	+	5.20884i	0.197450	+	0.235311i
$491$	24.6451	+	4.34560i	1.11222	+	0.196114i	0.699422	−	0.714709i	$-0.253441\pi$
$491$	24.6451	+	4.34560i	1.11222	+	0.196114i	0.412797	+	0.910823i	$0.364552\pi$
$492$	2.70003	−	15.9223i	0.121727	−	0.717831i
$493$		−	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
$498$	−12.8958	+	2.36114i	−0.577874	+	0.105805i
$499$	−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
$501$	−19.3627	+	0.126927i	−0.865060	+	0.00567069i
$502$	4.85023	+	2.80028i	0.216476	+	0.124983i
$503$	−10.5421	+	28.9642i	−0.470049	+	1.29145i	0.447663	+	0.894202i	$0.352256\pi$
$503$	−10.5421	+	28.9642i	−0.470049	+	1.29145i	−0.917712	+	0.397246i	$0.869966\pi$
$504$	0.250492	+	1.31923i	0.0111578	+	0.0587632i
$505$	−1.16293	+	2.01425i	−0.0517496	+	0.0896329i
$506$	2.01831	+	3.49581i	0.0897247	+	0.155408i
$507$	−37.4839	−	13.3654i	−1.66472	−	0.593579i
$508$	1.95548	−	2.33045i	0.0867605	−	0.103397i
$509$	18.6127	−	15.6179i	0.824992	−	0.692251i	−0.129143	−	0.991626i	$-0.541223\pi$
$509$	18.6127	−	15.6179i	0.824992	−	0.692251i	0.954135	+	0.299375i	$0.0967783\pi$
$510$	0.964262	+	0.798400i	0.0426983	+	0.0353537i
$511$	−1.16584	+	0.424331i	−0.0515737	+	0.0187713i
$512$	1.00000			0.0441942
$513$	22.6445	−	0.477370i	0.999778	−	0.0210764i
$514$	−24.1959			−1.06724
$515$	−10.2665	+	3.73669i	−0.452395	+	0.164658i
$516$	13.9370	+	11.5397i	0.613540	+	0.508005i
$517$	2.90027	−	2.43362i	0.127554	−	0.107030i
$518$	0.483806	−	0.576578i	0.0212572	−	0.0253334i
$519$	30.3690	+	10.8285i	1.33305	+	0.475318i
$520$	2.99900	+	5.19441i	0.131515	+	0.227790i
$521$	4.79563	−	8.30627i	0.210100	−	0.363904i	−0.741646	−	0.670792i	$-0.765954\pi$
$521$	4.79563	−	8.30627i	0.210100	−	0.363904i	0.951746	+	0.306888i	$0.0992877\pi$
$522$	1.64831	+	8.68096i	0.0721448	+	0.379955i
$523$	−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
$525$	0.775250	−	0.00508197i	0.0338347	−	0.000221795i
$526$	−16.6084	+	2.92851i	−0.724160	+	0.127689i
$527$	5.18236	+	4.34851i	0.225747	+	0.189424i
$528$	−0.768360	+	0.140682i	−0.0334386	+	0.00612240i
$529$	−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
$534$	1.90311	−	11.2228i	0.0823558	−	0.485658i
$535$	7.68207	+	1.35456i	0.332125	+	0.0585626i
$536$	−6.41676	−	7.64720i	−0.277162	−	0.330309i
$537$	−32.2017	+	11.9601i	−1.38961	+	0.516116i
$538$	0.771737	+	4.37674i	0.0332719	+	0.188695i
$539$	2.65572	−	1.53328i	0.114390	−	0.0660430i
$540$	−4.55022	−	2.50908i	−0.195810	−	0.107974i
$541$	−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
$543$	5.94162	−	3.48253i	0.254979	−	0.149450i
$544$	−0.625948	+	0.361391i	−0.0268373	+	0.0154945i
$545$	2.11288	+	11.9827i	0.0905059	+	0.513284i
$546$	−1.61902	−	4.35909i	−0.0692876	−	0.186552i
$547$	−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
$549$	21.6419	+	17.6814i	0.923652	+	0.754624i
$550$			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
$555$	0.524551	+	2.86493i	0.0222660	+	0.121610i
$556$	−2.64516	−	2.21956i	−0.112180	−	0.0941301i
$557$	−4.27875	+	0.754459i	−0.181296	+	0.0319675i	−0.263559	−	0.964643i	$-0.584896\pi$
$557$	−4.27875	+	0.754459i	−0.181296	+	0.0319675i	0.0822628	+	0.996611i	$0.473785\pi$
$558$	−24.4994	−	13.7197i	−1.03714	−	0.580800i
$559$	−54.2646	−	31.3297i	−2.29515	−	1.32511i
$560$	−0.153088	+	0.420607i	−0.00646917	+	0.0177739i
$561$	0.430112	−	0.365738i	0.0181594	−	0.0154415i
$562$	2.82572	−	4.89429i	0.119196	−	0.206453i
$563$	20.0759	+	34.7726i	0.846100	+	1.46549i	0.884662	+	0.466233i	$0.154389\pi$
$563$	20.0759	+	34.7726i	0.846100	+	1.46549i	−0.0385618	+	0.999256i	$0.512278\pi$
$564$	−4.88349	+	13.6960i	−0.205632	+	0.576704i
$565$	4.51929	−	5.38588i	0.190128	−	0.226586i
$566$	16.8968	−	14.1781i	0.710225	−	0.595950i
$567$	3.15276	+	2.50761i	0.132404	+	0.105310i
$568$	−2.36768	+	0.861764i	−0.0993455	+	0.0361588i
$569$	27.9741			1.17273			0.586367	−	0.810046i	$-0.300558\pi$
$569$	27.9741			1.17273			0.586367	+	0.810046i	$0.300558\pi$
$570$	6.56822	+	3.72270i	0.275112	+	0.155927i
$571$	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
$573$	9.27743	−	11.2048i	0.387570	−	0.468085i
$574$	−3.19702	+	2.68262i	−0.133441	+	0.111970i
$575$	−5.75335	+	6.85657i	−0.239931	+	0.285939i
$576$	2.27266	−	1.95833i	0.0946940	−	0.0815969i
$577$	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
$579$	−11.7847	−	13.8589i	−0.489756	−	0.575958i
$580$	−1.00737	+	2.76773i	−0.0418288	+	0.114924i
$581$	2.93406	+	1.69398i	0.121725	+	0.0702780i
$582$	0.202008	+	30.8162i	0.00837351	+	1.27737i
$583$	5.89178	−	1.03888i	0.244013	−	0.0430260i
$584$	2.12333	+	1.78168i	0.0878638	+	0.0737265i
$585$	16.9880	+	5.93210i	0.702369	+	0.245262i
$586$	−1.77283	+	10.0542i	−0.0732349	+	0.415336i
$587$	11.1397	+	30.6061i	0.459785	+	1.26325i	0.925646	+	0.378390i	$0.123522\pi$
$587$	11.1397	+	30.6061i	0.459785	+	1.26325i	−0.465862	+	0.884858i	$0.654256\pi$
$588$	−5.82169	+	10.2379i	−0.240082	+	0.422202i
$589$	35.3612	+	20.3492i	1.45703	+	0.838476i
$590$			3.47574i			0.143094i
$591$	36.7839	+	6.23766i	1.51309	+	0.256583i
$592$	−1.65602	−	0.292001i	−0.0680619	−	0.0120012i
$593$	−3.01254	−	3.59020i	−0.123710	−	0.147432i	0.700634	−	0.713520i	$-0.252900\pi$
$593$	−3.01254	−	3.59020i	−0.123710	−	0.147432i	−0.824344	+	0.566089i	$0.808456\pi$
$594$	−1.47072	+	1.82442i	−0.0603442	+	0.0748569i
$595$	−0.0561783	−	0.318603i	−0.00230309	−	0.0130614i
$596$	9.30746	−	5.37366i	0.381248	−	0.220114i
$597$	−5.38020	−	9.17929i	−0.220197	−	0.375683i
$598$	50.4481	+	18.3616i	2.06298	+	0.750862i
$599$	−9.79347	−	3.56453i	−0.400150	−	0.145643i	0.134103	−	0.990967i	$-0.457185\pi$
$599$	−9.79347	−	3.56453i	−0.400150	−	0.145643i	−0.534253	+	0.845325i	$0.679407\pi$
$600$	−0.875839	−	1.49429i	−0.0357560	−	0.0610042i
$601$	−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
$603$	−29.5588	−	4.81334i	−1.20373	−	0.196014i
$604$	1.80973	+	2.15676i	0.0736370	+	0.0877571i
$605$	−10.6326	−	1.87481i	−0.432276	−	0.0762219i
$606$	−3.97180	−	0.673520i	−0.161343	−	0.0273599i
$607$		−	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
$612$	−0.714842	+	2.04713i	−0.0288958	+	0.0827502i
$613$	−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
$615$	−0.105862	−	16.1492i	−0.00426878	−	0.651200i
$616$	0.174818	+	0.100931i	0.00704361	+	0.00406663i
$617$	7.93745	−	21.8080i	0.319550	−	0.877956i	−0.671080	−	0.741385i	$-0.734170\pi$
$617$	7.93745	−	21.8080i	0.319550	−	0.877956i	0.990630	−	0.136571i	$-0.0436083\pi$
$618$	−12.2584	−	14.4160i	−0.493105	−	0.579897i
$619$	−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
$621$	−45.6345	+	8.97527i	−1.83125	+	0.360165i
$622$	9.26772	−	11.0448i	0.371602	−	0.442858i
$623$	−2.25341	+	1.89084i	−0.0902812	+	0.0757549i
$624$	−6.62550	+	8.00190i	−0.265232	+	0.320333i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	−5.72612			−0.228862
$627$	2.16776	−	2.62564i	0.0865721	−	0.104858i
$628$	4.76022			0.189954
$629$	1.14211	−	0.415693i	0.0455388	−	0.0165748i
$630$	0.475768	+	1.25569i	0.0189551	+	0.0500279i
$631$	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
$633$	10.9249	−	30.6395i	0.434227	−	1.21781i
$634$	4.27915	+	7.41171i	0.169947	+	0.294357i
$635$	1.52109	−	2.63461i	0.0603628	−	0.104551i
$636$	−17.5041	+	14.8843i	−0.694084	+	0.590202i
$637$	13.9490	−	38.3247i	0.552681	−	1.51848i
$638$	1.15036	+	0.664158i	0.0455430	+	0.0262943i
$639$	−3.69330	+	6.59517i	−0.146105	+	0.260901i
$640$	0.984808	−	0.173648i	0.0389279	−	0.00686405i
$641$	−18.4132	−	15.4505i	−0.727279	−	0.610260i	0.202109	−	0.979363i	$-0.435220\pi$
$641$	−18.4132	−	15.4505i	−0.727279	−	0.610260i	−0.929388	+	0.369103i	$0.879665\pi$
$642$	2.43333	+	13.2901i	0.0960359	+	0.524518i
$643$	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	$0.119218\pi$
$647$			18.6111i			0.731679i	−0.930678	+	0.365840i	$0.880782\pi$
$648$	1.32992	−	8.90120i	0.0522443	−	0.349672i
$649$	1.54370	+	0.272196i	0.0605955	+	0.0106846i
$650$	3.85543	+	4.59473i	0.151223	+	0.180220i
$651$	2.52645	+	6.80230i	0.0990196	+	0.266603i
$652$	2.10511	+	11.9387i	0.0824424	+	0.467554i
$653$	−3.57084	+	2.06162i	−0.139738	+	0.0806776i	−0.568239	−	0.822864i	$-0.692375\pi$
$653$	−3.57084	+	2.06162i	−0.139738	+	0.0806776i	0.428501	+	0.903541i	$0.359042\pi$
$654$	−18.1819	+	10.6569i	−0.710970	+	0.416716i
$655$	−3.65963	−	1.33200i	−0.142994	−	0.0520454i
$656$	8.76166	+	3.18898i	0.342085	+	0.124509i
$657$	8.31470	−	0.109015i	0.324387	−	0.00425307i
$658$	3.25418	−	1.87880i	0.126861	−	0.0732433i
$659$	7.30640	+	41.4366i	0.284617	+	1.61414i	0.706651	+	0.707562i	$0.250205\pi$
$659$	7.30640	+	41.4366i	0.284617	+	1.61414i	−0.422034	+	0.906580i	$0.638684\pi$
$660$	−0.732258	+	0.271969i	−0.0285031	+	0.0105864i
$661$	−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
$663$	1.25540	−	7.40317i	0.0487556	−	0.287515i
$664$		−	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
$669$	−35.7364	+	6.54312i	−1.38165	+	0.252972i
$670$	−7.64720	−	6.41676i	−0.295437	−	0.247901i
$671$	4.13734	−	0.729524i	0.159720	−	0.0281630i
$672$	−0.775250	+	0.00508197i	−0.0299059	+	0.000196041i
$673$	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
$675$	−4.91679	−	1.68083i	−0.189247	−	0.0646951i
$676$	11.4879	−	19.8977i	0.441844	−	0.765297i
$677$	−4.73423	−	8.19993i	−0.181951	−	0.315149i	0.760594	−	0.649228i	$-0.224908\pi$
$677$	−4.73423	−	8.19993i	−0.181951	−	0.315149i	−0.942545	+	0.334079i	$0.891575\pi$
$678$	11.4703	+	4.08990i	0.440514	+	0.157072i
$679$	5.11901	−	6.10060i	0.196450	−	0.234119i
$680$	−0.553684	+	0.464596i	−0.0212328	+	0.0178164i
$681$	11.3422	+	9.39120i	0.434633	+	0.359871i
$682$	−3.96658	+	1.44372i	−0.151888	+	0.0552827i
$683$	3.06787			0.117389			0.0586945	−	0.998276i	$-0.481306\pi$
$683$	3.06787			0.117389			0.0586945	+	0.998276i	$0.481306\pi$
$684$	−2.08349	+	12.9097i	−0.0796641	+	0.493613i
$685$	15.8383			0.605151
$686$	5.80423	−	2.11257i	0.221607	−	0.0806582i
$687$	4.49136	+	3.71880i	0.171356	+	0.141881i
$688$	−8.00266	+	6.71503i	−0.305099	+	0.256008i
$689$	51.1451	−	60.9523i	1.94847	−	2.32210i
$690$	−14.6024	−	5.20670i	−0.555905	−	0.198216i
$691$	−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
$693$	0.594956	−	0.112969i	0.0226005	−	0.00429132i
$694$	3.41142	−	9.37280i	0.129496	−	0.355786i
$695$	−2.99040	−	1.72651i	−0.113432	−	0.0654902i
$696$	−5.10139	+	0.0334409i	−0.193368	+	0.00126758i
$697$	−6.63681	+	1.17025i	−0.251387	+	0.0443264i
$698$	−0.506032	−	0.424611i	−0.0191536	−	0.0160718i
$699$	4.19529	−	0.768131i	0.158680	−	0.0290534i
$700$	−0.0777250	+	0.440800i	−0.00293773	+	0.0166607i
$701$	−4.54025	−	12.4742i	−0.171483	−	0.471145i	0.823944	−	0.566671i	$-0.191769\pi$
$701$	−4.54025	−	12.4742i	−0.171483	−	0.471145i	−0.995427	+	0.0955260i	$0.969547\pi$
$702$	0.612865	+	31.1605i	0.0231311	+	1.17608i
$703$	6.34258	−	3.67385i	0.239215	−	0.138562i
$704$		−	0.450987i		−	0.0169972i
$705$	−2.43102	+	14.3359i	−0.0915575	+	0.539921i
$706$	−8.58688	−	1.51410i	−0.323172	−	0.0569839i
$707$	0.669177	+	0.797494i	0.0251670	+	0.0299928i
$708$	−5.64348	+	2.09605i	−0.212095	+	0.0787745i
$709$	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
$711$	−0.145790	−	11.1196i	−0.00546757	−	0.417019i
$712$	6.17565	+	2.24775i	0.231442	+	0.0842380i
$713$	−78.7235	−	28.6530i	−2.94822	−	1.07306i
$714$	0.483430	−	0.283350i	0.0180919	−	0.0106041i
$715$	2.34261	−	1.35251i	0.0876088	−	0.0505810i
$716$	−3.44389	−	19.5313i	−0.128704	−	0.729918i
$717$	−15.7956	−	42.5285i	−0.589897	−	1.58826i
$718$	−8.93900	−	10.6531i	−0.333600	−	0.397570i
$719$	7.26973	+	1.28185i	0.271115	+	0.0478049i	0.307553	−	0.951531i	$-0.400490\pi$
$719$	7.26973	+	1.28185i	0.271115	+	0.0478049i	−0.0364376	+	0.999336i	$0.511601\pi$
$720$	1.89807	−	2.32322i	0.0707368	−	0.0865812i
$721$			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
$726$	−3.36792	−	18.3945i	−0.124995	−	0.682684i
$727$	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
$729$	−14.4090	−	22.8338i	−0.533666	−	0.845695i
$730$	2.40045	+	1.38590i	0.0888448	+	0.0512945i
$731$	2.58250	−	7.09535i	0.0955171	−	0.262431i
$732$	−12.2918	+	10.4521i	−0.454317	+	0.386321i
$733$	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
$735$	−3.95546	+	11.0933i	−0.145899	+	0.409181i
$736$	5.75335	−	6.85657i	0.212071	−	0.252737i
$737$	−3.44879	+	2.89388i	−0.127038	+	0.106597i
$738$	26.1573	−	9.91072i	0.962863	−	0.364819i
$739$	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
$741$	−0.360802	−	45.2824i	−0.0132544	−	1.66349i
$742$	5.93774			0.217981
$743$	−7.19025	+	2.61704i	−0.263785	+	0.0960097i	−0.470527	−	0.882386i	$-0.655936\pi$
$743$	−7.19025	+	2.61704i	−0.263785	+	0.0960097i	0.206742	+	0.978395i	$0.433714\pi$
$744$	10.3390	−	12.4869i	0.379046	−	0.457791i
$745$	8.23293	−	6.90825i	0.301631	−	0.253099i
$746$	19.7954	−	23.5913i	0.724762	−	0.863738i
$747$	−14.8229	−	17.2021i	−0.542340	−	0.629391i
$748$	0.162983	+	0.282295i	0.00595924	+	0.0103217i
$749$	1.74577	−	3.02377i	0.0637891	−	0.110486i
$750$	−1.12201	−	1.31950i	−0.0409702	−	0.0481814i
$751$	−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
$753$	0.0635877	+	9.70025i	0.00231726	+	0.353497i
$754$	17.3978	−	3.06770i	0.633591	−	0.111719i
$755$	2.15676	+	1.80973i	0.0784924	+	0.0658629i
$756$	−1.75192	+	1.52974i	−0.0637169	+	0.0556362i
$757$	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	$-0.950596\pi$
$761$		−	8.52888i		−	0.309172i	0.987979	−	0.154586i	$-0.0494043\pi$
$762$	5.19506	+	0.880956i	0.188197	+	0.0319137i
$763$	5.36348	+	0.945727i	0.194171	+	0.0342376i
$764$	5.39861	+	6.43382i	0.195315	+	0.232767i
$765$	−0.348502	+	2.14016i	−0.0126001	+	0.0773776i
$766$	−2.96057	−	16.7902i	−0.106970	−	0.606656i
$767$	18.0544	−	10.4237i	0.651907	−	0.376379i
$768$	0.875839	+	1.49429i	0.0316041	+	0.0539206i
$769$	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
$771$	−21.1917	−	36.1557i	−0.763202	−	1.30212i
$772$	9.09601	−	5.25158i	0.327372	−	0.189009i
$773$	5.85221	+	33.1896i	0.210489	+	1.19375i	0.888564	+	0.458752i	$0.151703\pi$
$773$	5.85221	+	33.1896i	0.210489	+	1.19375i	−0.678075	+	0.734993i	$0.737185\pi$
$774$	−5.03707	+	30.9328i	−0.181054	+	1.11186i
$775$	−6.01635	−	7.17001i	−0.216114	−	0.257554i
$776$	−17.5218	−	3.08957i	−0.628997	−	0.110909i
$777$	1.28531	+	0.217958i	0.0461103	+	0.00781919i
$778$			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
$783$	−11.5282	+	10.0662i	−0.411985	+	0.359736i
$784$	−5.20884	−	4.37073i	−0.186030	−	0.156098i
$785$	4.68791	−	0.826604i	0.167319	−	0.0295028i
$786$	−0.0442173	−	6.74532i	−0.00157718	−	0.240598i
$787$	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
$789$	−18.9223	−	22.2529i	−0.673652	−	0.792223i
$790$	1.85343	−	3.21024i	0.0659421	−	0.114215i
$791$	−1.57349	−	2.72536i	−0.0559468	−	0.0969026i
$792$	−0.883180	−	1.02494i	−0.0313824	−	0.0364196i
$793$	35.9152	−	42.8021i	1.27539	−	1.51995i
$794$	28.4882	−	23.9044i	1.01101	−	0.848336i
$795$	−14.6536	+	17.6978i	−0.519708	+	0.627675i
$796$	5.77245	−	2.10100i	0.204599	−	0.0744679i
$797$	28.9848			1.02669			0.513347	−	0.858181i	$-0.328406\pi$
$797$	28.9848			1.02669			0.513347	+	0.858181i	$0.328406\pi$
$798$	2.57131	−	2.19274i	0.0910235	−	0.0776220i
$799$	6.06775			0.214662
$800$	0.939693	−	0.342020i	0.0332232	−	0.0120922i
$801$	18.4369	−	6.98556i	0.651437	−	0.246823i
$802$	8.04705	−	6.75228i	0.284151	−	0.238431i
$803$	0.803516	−	0.957593i	0.0283555	−	0.0337927i
$804$	5.80708	−	16.2862i	0.204800	−	0.574371i
$805$	2.00315	+	3.46956i	0.0706018	+	0.122286i
$806$	−28.0699	+	48.6186i	−0.988722	+	1.71252i
$807$	−5.86420	+	4.98652i	−0.206430	+	0.175534i
$808$	0.795489	−	2.18559i	0.0279852	−	0.0768887i
$809$	−30.1621	−	17.4141i	−1.06044	−	0.612248i	−0.134889	−	0.990861i	$-0.543068\pi$
$809$	−30.1621	−	17.4141i	−1.06044	−	0.612248i	−0.925555	+	0.378613i	$0.876401\pi$
$810$	−0.235959	−	8.99691i	−0.00829075	−	0.316119i
$811$	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
$813$	8.62064	+	47.0832i	0.302339	+	1.65128i
$814$	−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
$819$	5.09575	−	6.23715i	0.178060	−	0.217944i
$820$	9.18231	+	1.61909i	0.320660	+	0.0565411i
$821$	5.05095	+	6.01949i	0.176280	+	0.210082i	0.846948	−	0.531675i	$-0.178437\pi$
$821$	5.05095	+	6.01949i	0.176280	+	0.210082i	−0.670669	+	0.741757i	$0.733993\pi$
$822$	9.55134	+	25.7163i	0.333141	+	0.896960i
$823$	−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
$825$	−0.673906	+	0.394992i	−0.0234624	+	0.0137519i
$826$	1.46192	+	0.532095i	0.0508667	+	0.0185140i
$827$	14.2558	+	5.18869i	0.495723	+	0.180428i	0.577769	−	0.816200i	$-0.303923\pi$
$827$	14.2558	+	5.18869i	0.495723	+	0.180428i	−0.0820464	+	0.996629i	$0.526146\pi$
$828$	−0.352027	−	26.8496i	−0.0122338	−	0.933086i
$829$	−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
$831$	2.52539	−	0.937960i	0.0876049	−	0.0325375i
$832$	−3.85543	−	4.59473i	−0.133663	−	0.159294i
$833$	4.84001	+	0.853424i	0.167696	+	0.0295694i
$834$	0.999923	−	5.89662i	0.0346245	−	0.204183i
$835$		−	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	$0.264729\pi$
$839$	−6.14495	+	34.8497i	−0.212147	+	1.20315i	−0.885789	+	0.464088i	$0.846382\pi$
$840$	−0.762590	+	0.139626i	−0.0263119	+	0.00481754i
$841$	−15.5698	−	13.0646i	−0.536889	−	0.450503i
$842$	−3.19225	+	0.562881i	−0.110012	+	0.0193981i
$843$	9.78837	−	0.0641653i	0.337129	−	0.00220997i
$844$	16.2645	+	9.39029i	0.559846	+	0.323227i
$845$	7.85822	−	21.5903i	0.270331	−	0.742728i
$846$	−24.7429	+	4.69811i	−0.850678	+	0.161524i
$847$	−2.41628	+	4.18513i	−0.0830245	+	0.143803i
$848$	−6.63286	−	11.4884i	−0.227773	−	0.394515i
$849$	35.9851	+	12.8310i	1.23500	+	0.440359i
$850$	−0.464596	+	0.553684i	−0.0159355	+	0.0189912i
$851$	−11.5298	+	9.67462i	−0.395235	+	0.331642i
$852$	−3.36143	−	2.78323i	−0.115161	−	0.0953519i
$853$	−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
$855$	0.189904	+	13.0753i	0.00649457	+	0.447166i
$856$	−7.80058			−0.266618
$857$	−45.4685	+	16.5492i	−1.55317	+	0.565309i	−0.969160	−	0.246433i	$-0.920741\pi$
$857$	−45.4685	+	16.5492i	−1.55317	+	0.565309i	−0.584015	+	0.811743i	$0.698519\pi$
$858$	3.60876	+	2.98801i	0.123201	+	0.102009i
$859$	−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
$861$	−6.80869	−	2.42773i	−0.232039	−	0.0827369i
$862$	−4.76288	−	8.24956i	−0.162224	−	0.280981i
$863$	−2.84088	+	4.92055i	−0.0967048	+	0.167498i	−0.910319	−	0.413908i	$-0.864164\pi$
$863$	−2.84088	+	4.92055i	−0.0967048	+	0.167498i	0.813614	+	0.581405i	$0.197497\pi$
$864$	4.91679	+	1.68083i	0.167273	+	0.0571830i
$865$	−6.36664	+	17.4922i	−0.216472	+	0.594752i
$866$	14.8054	+	8.54793i	0.503109	+	0.290470i
$867$	−28.5394	+	0.187083i	−0.969249	+	0.00635368i
$868$	−4.12580	+	0.727489i	−0.140039	+	0.0246926i
$869$	−1.28063	−	1.07458i	−0.0434425	−	0.0364526i
$870$	−5.01808	+	0.918780i	−0.170129	+	0.0311496i
$871$	−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
$876$	−0.802658	+	4.73333i	−0.0271193	+	0.159925i
$877$	−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
$879$	−16.5766	+	6.15676i	−0.559116	+	0.207662i
$880$	−0.0783131	−	0.444136i	−0.00263993	−	0.0149718i
$881$	25.9578	−	14.9868i	0.874541	−	0.504917i	0.00568654	−	0.999984i	$-0.498190\pi$
$881$	25.9578	−	14.9868i	0.874541	−	0.504917i	0.868855	+	0.495067i	$0.164857\pi$
$882$	−20.3972	+	0.267429i	−0.686810	+	0.00900482i
$883$	−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
$885$	−5.19377	+	3.04419i	−0.174587	+	0.102329i
$886$	10.4631	−	6.04086i	0.351514	−	0.202947i
$887$	−4.09494	−	23.2235i	−0.137495	−	0.779770i	−0.973090	−	0.230425i	$-0.925988\pi$
$887$	−4.09494	−	23.2235i	−0.137495	−	0.779770i	0.835596	−	0.549345i	$-0.185123\pi$
$888$	−1.01407	−	2.73032i	−0.0340300	−	0.0916235i
$889$	−0.875275	−	1.04311i	−0.0293558	−	0.0349848i
$890$	6.47214	+	1.14121i	0.216947	+	0.0382536i
$891$	−4.01433	−	0.599778i	−0.134485	−	0.0200933i
$892$		−	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
$897$	16.7469	+	91.4659i	0.559161	+	3.05396i
$898$	19.3689	+	16.2525i	0.646349	+	0.542351i
$899$	−27.1490	+	4.78711i	−0.905471	+	0.159659i
$900$	1.46581	−	2.61752i	0.0488603	−	0.0872506i
$901$	8.30365	+	4.79411i	0.276635	+	0.159715i
$902$	1.43819	−	3.95140i	0.0478865	−	0.131567i
$903$	6.16994	−	5.24650i	0.205323	−	0.174592i
$904$	−3.51538	+	6.08882i	−0.116920	+	0.202511i
$905$	1.98811	+	3.44350i	0.0660869	+	0.114466i
$906$	−1.63778	+	4.59324i	−0.0544118	+	0.152600i
$907$	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
$909$	−2.47222	−	6.52492i	−0.0819984	−	0.216418i
$910$	2.52280	−	0.918223i	0.0836299	−	0.0304388i
$911$	26.5167			0.878538			0.439269	−	0.898356i	$-0.355237\pi$
$911$	26.5167			0.878538			0.439269	+	0.898356i	$0.355237\pi$
$912$	−7.11487	−	2.52559i	−0.235597	−	0.0836306i
$913$	−3.41359			−0.112973
$914$	33.5827	−	12.2231i	1.11082	−	0.404304i
$915$	−10.2901	+	12.4278i	−0.340179	+	0.410849i
$916$	−2.57896	+	2.16400i	−0.0852111	+	0.0715006i
$917$	−1.12049	+	1.33535i	−0.0370020	+	0.0440972i
$918$	−3.68509	+	0.724773i	−0.121626	+	0.0239211i
$919$	−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
$921$	10.8545	+	12.7650i	0.357668	+	0.420622i
$922$	12.1118	−	33.2768i	0.398880	−	1.09591i
$923$	13.0880	+	7.55635i	0.430796	+	0.248720i
$924$	0.00229190	+	0.349628i	7.53980e−5	+	0.0115019i
$925$	−1.65602	+	0.292001i	−0.0544495	+	0.00960092i
$926$	−22.6095	−	18.9716i	−0.742993	−	0.623445i
$927$	10.8053	−	30.9437i	0.354894	−	1.01633i
$928$	0.511455	−	2.90061i	0.0167893	−	0.0952171i
$929$	−3.92496	−	10.7837i	−0.128774	−	0.353803i	0.858504	−	0.512807i	$-0.171394\pi$
$929$	−3.92496	−	10.7837i	−0.128774	−	0.353803i	−0.987278	+	0.159003i	$0.949172\pi$
$930$	8.01360	−	14.0925i	0.262776	−	0.462111i
$931$	29.6390	−	0.0418644i	0.971378	−	0.00137205i
$932$			2.46241i			0.0806591i
$933$	24.6212	+	4.17516i	0.806063	+	0.136689i
$934$	24.8039	+	4.37359i	0.811607	+	0.143108i
$935$	0.209527	+	0.249704i	0.00685226	+	0.00816620i
$936$	−17.7600	−	2.89204i	−0.580505	−	0.0945292i
$937$	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
$939$	−5.01516	−	8.55649i	−0.163664	−	0.279230i
$940$	−7.88871	−	2.87126i	−0.257301	−	0.0936501i
$941$	−24.8719	−	9.05263i	−0.810800	−	0.295107i	−0.0968459	−	0.995299i	$-0.530875\pi$
$941$	−24.8719	−	9.05263i	−0.810800	−	0.295107i	−0.713954	+	0.700192i	$0.753098\pi$
$942$	4.16919	+	7.11316i	0.135840	+	0.231759i
$943$	72.2744	−	41.7276i	2.35358	−	1.35884i
$944$	−0.603556	−	3.42294i	−0.0196441	−	0.111407i
$945$	−1.45967	+	1.81072i	−0.0474831	+	0.0589027i
$946$	3.02839	+	3.60910i	0.0984615	+	0.117342i
$947$	−52.5926	−	9.27349i	−1.70903	−	0.301348i	−0.768196	−	0.640215i	$-0.778845\pi$
$947$	−52.5926	−	9.27349i	−1.70903	−	0.301348i	−0.940834	+	0.338867i	$0.889956\pi$
$948$	6.33010	+	1.07343i	0.205592	+	0.0348634i
$949$		−	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	$-0.732354\pi$
$953$	6.62663	−	37.5815i	0.214658	−	1.21738i	0.881500	−	0.472185i	$-0.156534\pi$
$954$	−37.5723	−	13.1200i	−1.21645	−	0.424775i
$955$	6.43382	+	5.39861i	0.208193	+	0.174695i
$956$	25.7948	−	4.54832i	0.834263	−	0.147103i
$957$	0.0150814	+	2.30066i	0.000487514	+	0.0743699i
$958$	−9.33418	−	5.38909i	−0.301574	−	0.174114i
$959$	2.42466	−	6.66171i	0.0782965	−	0.215118i
$960$	1.12201	+	1.31950i	0.0362129	+	0.0425867i
$961$	28.3028	−	49.0218i	0.912992	−	1.58135i
$962$	5.04300	+	8.73474i	0.162593	+	0.281619i
$963$	−17.7280	+	15.2761i	−0.571278	+	0.492265i
$964$	−5.92462	+	7.06069i	−0.190819	+	0.227410i
$965$	8.04589	−	6.75130i	0.259006	−	0.217332i
$966$	−4.42544	+	5.34480i	−0.142386	+	0.171966i
$967$	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
$969$	5.36627	−	0.990366i	0.172389	−	0.0318151i
$970$	−17.7921			−0.571271
$971$	−22.4944	+	8.18730i	−0.721880	+	0.262743i	−0.676724	−	0.736237i	$-0.736601\pi$
$971$	−22.4944	+	8.18730i	−0.721880	+	0.262743i	−0.0451565	+	0.998980i	$0.514379\pi$
$972$	14.4658	−	5.80873i	0.463990	−	0.186315i
$973$	−1.18398	+	0.993474i	−0.0379566	+	0.0318493i
$974$	14.0388	−	16.7308i	0.449832	−	0.536089i
$975$	−3.48912	+	9.78538i	−0.111741	+	0.313383i
$976$	−4.65774	−	8.06744i	−0.149091	−	0.258232i
$977$	−15.4386	+	26.7405i	−0.493926	+	0.855504i	−0.999975	−	0.00700008i	$-0.997772\pi$
$977$	−15.4386	+	26.7405i	−0.493926	+	0.855504i	0.506050	+	0.862504i	$0.331105\pi$
$978$	−15.9961	+	13.6020i	−0.511499	+	0.434944i
$979$	1.01371	−	2.78514i	0.0323982	−	0.0890134i
$980$	−5.88867	−	3.39983i	−0.188107	−	0.108603i
$981$	−31.8489	−	17.8354i	−1.01686	−	0.569440i
$982$	−24.6451	+	4.34560i	−0.786458	+	0.138674i
$983$	5.78769	+	4.85645i	0.184599	+	0.154897i	0.730404	−	0.683015i	$-0.239332\pi$
$983$	5.78769	+	4.85645i	0.184599	+	0.154897i	−0.545805	+	0.837912i	$0.683776\pi$
$984$	2.90854	+	15.8855i	0.0927208	+	0.506411i
$985$	−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
$990$	−1.04774	−	0.856005i	−0.0332994	−	0.0272056i
$991$	−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
$993$	−10.0362	−	27.0218i	−0.318489	−	0.857510i
$994$	0.195838	+	1.11065i	0.00621161	+	0.0352278i
$995$	5.31992	−	3.07145i	0.168653	−	0.0973717i
$996$	11.3105	−	6.62936i	0.358387	−	0.210059i
$997$	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
$999$	−7.65149	−	4.21919i	−0.242082	−	0.133489i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.33410 - 1.10462i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(1.63144 + 0.581714i) q^{6} +(-0.223800 - 0.387633i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.559632 + 2.94734i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.33410 - 1.10462i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(1.63144 + 0.581714i) q^{6} +(-0.223800 - 0.387633i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.559632 + 2.94734i) q^{9} +(-0.342020 + 0.939693i) q^{10} +(0.390566 + 0.225494i) q^{11} +(-1.73201 + 0.0113538i) q^{12} +(5.90687 - 1.04154i) q^{13} +(0.342882 + 0.287712i) q^{14} +(-1.70373 + 0.311942i) 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} +(-0.129616 + 0.764355i) q^{21} +(-0.444136 - 0.0783131i) q^{22} +(-5.75335 - 6.85657i) q^{23} +(1.62368 - 0.603053i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(-5.19441 + 2.99900i) q^{26} +(2.50908 - 4.55022i) q^{27} +(-0.420607 - 0.153088i) q^{28} +(-2.76773 - 1.00737i) q^{29} +(1.49429 - 0.875839i) q^{30} +(8.10581 - 4.67989i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.271969 - 0.732258i) q^{33} +(-0.464596 - 0.553684i) q^{34} +(-0.440800 - 0.0777250i) q^{35} +(2.32322 + 1.89807i) 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} +(-0.139626 - 0.762590i) q^{42} +(-8.00266 - 6.71503i) q^{43} +(0.444136 - 0.0783131i) q^{44} +(2.61752 + 1.46581i) q^{45} +(7.75146 + 4.47531i) q^{46} +(2.87126 - 7.88871i) q^{47} +(-1.31950 + 1.12201i) q^{48} +(3.39983 - 5.88867i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.420453 - 1.17918i) q^{51} +(3.85543 - 4.59473i) q^{52} +(10.1621 - 8.52704i) q^{53} +(-0.801502 + 5.13396i) q^{54} +(0.423789 - 0.154247i) q^{55} +0.447601 q^{56} +(1.25173 - 7.44535i) q^{57} +2.94535 q^{58} +(3.26613 - 1.18877i) q^{59} +(-1.10462 + 1.33410i) q^{60} +(7.13607 - 5.98787i) q^{61} +(-6.01635 + 7.17001i) q^{62} +(1.01724 - 0.876548i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.99900 - 5.19441i) q^{65} +(0.506014 + 0.595078i) q^{66} +(-3.41429 + 9.38067i) q^{67} +(0.625948 + 0.361391i) q^{68} +(0.101624 + 15.5026i) q^{69} +(0.440800 - 0.0777250i) q^{70} +(1.93015 + 1.61959i) q^{71} +(-2.83229 - 0.989014i) 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} +(10.2426 + 1.73690i) q^{78} +(-3.65055 - 0.643690i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(-8.37362 + 3.29885i) q^{81} +(-1.61909 - 9.18231i) q^{82} +(-6.55508 + 3.78457i) q^{83} +(0.392026 + 0.668845i) q^{84} +(0.679193 + 0.247206i) q^{85} +(9.81672 + 3.57299i) q^{86} +(2.57966 + 4.40121i) q^{87} +(-0.390566 + 0.225494i) q^{88} +(-1.14121 - 6.47214i) q^{89} +(-2.96100 - 0.482167i) q^{90} +(-1.72569 - 2.05660i) q^{91} +(-8.81464 - 1.55426i) q^{92} +(-15.9834 - 2.71040i) 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} +(-0.446033 + 1.27733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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