LMFDB - Embedded newform 570.2.bh.a.67.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, 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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			67.8
Character	$\chi$	$=$	570.67
Dual form			570.2.bh.a.553.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-0.598083 - 2.15460i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.0495570 + 0.0132788i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})$	\(q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-0.598083 - 2.15460i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.0495570 + 0.0132788i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(0.745906 - 2.10799i) q^{10} +(-2.40961 - 4.17357i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(0.173715 + 1.98557i) q^{13} +(-0.0482111 - 0.0175474i) q^{14} +(0.408021 + 2.19853i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(4.52112 - 6.45683i) q^{17} +(0.707107 + 0.707107i) q^{18} +(1.44646 - 4.11190i) q^{19} +(1.82010 - 1.29893i) q^{20} +(0.0505258 - 0.00890906i) q^{21} +(0.420023 - 4.80089i) q^{22} +(1.72629 - 3.70204i) q^{23} +(0.342020 - 0.939693i) q^{24} +(-4.28459 + 2.57726i) q^{25} +(-0.996576 + 1.72612i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(-0.0294275 - 0.0420268i) q^{28} +(-0.543857 + 3.08437i) q^{29} +(-0.926792 + 2.03496i) q^{30} +(-7.01416 - 4.04963i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(2.03669 + 4.36770i) q^{33} +(7.40697 - 2.69592i) q^{34} +(0.0582496 + 0.0988337i) q^{35} +(0.173648 + 0.984808i) q^{36} +(-0.423514 + 0.423514i) q^{37} +(3.54336 - 2.53862i) q^{38} -1.99315i q^{39} +(2.23598 - 0.0200524i) q^{40} +(3.07225 + 3.66136i) q^{41} +(0.0464983 + 0.0216825i) q^{42} +(11.2562 - 5.24884i) q^{43} +(3.09774 - 3.69174i) q^{44} +(-0.214854 - 2.22572i) q^{45} +(3.53750 - 2.04237i) q^{46} +(4.34011 - 3.03898i) q^{47} +(0.819152 - 0.573576i) q^{48} +(-6.05990 + 3.49868i) q^{49} +(-4.98799 - 0.346376i) q^{50} +(-5.06667 + 6.03822i) q^{51} +(-1.80641 + 0.842342i) q^{52} +(-4.47646 - 2.08741i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(-7.55122 + 7.68789i) q^{55} -0.0513052i q^{56} +(-1.79933 + 3.97019i) q^{57} +(-2.21462 + 2.21462i) q^{58} +(1.50376 + 8.52824i) q^{59} +(-1.92639 + 1.13535i) q^{60} +(11.1255 - 4.04933i) q^{61} +(-3.42289 - 7.34041i) q^{62} +(-0.0511100 + 0.00447154i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(4.17421 - 1.56182i) q^{65} +(-0.836850 + 4.74601i) q^{66} +(-4.17215 - 5.95845i) q^{67} +(7.61375 + 2.04010i) q^{68} +(-2.04237 + 3.53750i) q^{69} +(-0.00897340 + 0.114370i) q^{70} +(-1.20049 + 3.29831i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(-1.25344 + 14.3269i) q^{73} +(-0.589839 + 0.104005i) q^{74} +(4.49291 - 2.19402i) q^{75} +(4.35864 - 0.0471284i) q^{76} +(0.174833 + 0.174833i) q^{77} +(1.14322 - 1.63269i) q^{78} +(-12.7795 + 10.7233i) q^{79} +(1.84311 + 1.26608i) q^{80} +(0.939693 + 0.342020i) q^{81} +(0.416567 + 4.76138i) q^{82} +(-0.831140 - 3.10186i) q^{83} +(0.0256526 + 0.0444316i) q^{84} +(-16.6159 - 5.87949i) q^{85} +(12.2311 + 2.15668i) q^{86} +(0.810607 - 3.02523i) q^{87} +(4.65501 - 1.24731i) q^{88} +(9.01493 + 7.56443i) q^{89} +(1.10062 - 1.94644i) q^{90} +(-0.0349747 - 0.0960921i) q^{91} +(4.06920 + 0.356009i) q^{92} +(6.63452 + 4.64554i) q^{93} +5.29829 q^{94} +(-9.72461 - 0.657277i) q^{95} +1.00000 q^{96} +(0.535833 + 0.375195i) q^{97} +(-6.97074 - 0.609861i) q^{98} +(-1.64827 - 4.52859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q - 12 * q^5 + 12 * q^7	$ 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−0.598083	−	2.15460i	−0.267471	−	0.963566i
$5$	−0.598083	−	2.15460i	−0.267471	−	0.963566i
$6$	−0.766044	−	0.642788i	−0.312736	−	0.262417i
$7$	−0.0495570	+	0.0132788i	−0.0187308	+	0.00501890i	−0.268172	−	0.963371i	$-0.586420\pi$
$7$	−0.0495570	+	0.0132788i	−0.0187308	+	0.00501890i	0.249441	+	0.968390i	$0.419753\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	0.984808	+	0.173648i	0.328269	+	0.0578827i
$10$	0.745906	−	2.10799i	0.235876	−	0.666605i
$11$	−2.40961	−	4.17357i	−0.726525	−	1.25838i	−0.958343	−	0.285620i	$-0.907801\pi$
$11$	−2.40961	−	4.17357i	−0.726525	−	1.25838i	0.231818	−	0.972759i	$-0.425533\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	0.173715	+	1.98557i	0.0481798	+	0.550697i	0.981475	+	0.191588i	$0.0613638\pi$
$13$	0.173715	+	1.98557i	0.0481798	+	0.550697i	−0.933296	+	0.359109i	$0.883081\pi$
$14$	−0.0482111	−	0.0175474i	−0.0128850	−	0.00468974i
$15$	0.408021	+	2.19853i	0.105351	+	0.567657i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	4.52112	−	6.45683i	1.09653	−	1.56601i	0.307618	−	0.951510i	$-0.400468\pi$
$17$	4.52112	−	6.45683i	1.09653	−	1.56601i	0.788915	−	0.614502i	$-0.210643\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	1.44646	−	4.11190i	0.331840	−	0.943336i
$19$	1.44646	−	4.11190i	0.331840	−	0.943336i
$20$	1.82010	−	1.29893i	0.406988	−	0.290450i
$21$	0.0505258	−	0.00890906i	0.0110256	−	0.00194412i
$22$	0.420023	−	4.80089i	0.0895492	−	1.02355i
$23$	1.72629	−	3.70204i	0.359956	−	0.771928i	−0.640037	−	0.768344i	$-0.721081\pi$
$23$	1.72629	−	3.70204i	0.359956	−	0.771928i	0.999994	−	0.00358470i	$-0.00114105\pi$
$24$	0.342020	−	0.939693i	0.0698146	−	0.191814i
$25$	−4.28459	+	2.57726i	−0.856919	+	0.515451i
$26$	−0.996576	+	1.72612i	−0.195445	+	0.338520i
$27$	−0.965926	−	0.258819i	−0.185893	−	0.0498097i
$28$	−0.0294275	−	0.0420268i	−0.00556127	−	0.00794231i
$29$	−0.543857	+	3.08437i	−0.100992	+	0.572752i	0.891754	+	0.452520i	$0.149475\pi$
$29$	−0.543857	+	3.08437i	−0.100992	+	0.572752i	−0.992746	+	0.120232i	$0.961636\pi$
$30$	−0.926792	+	2.03496i	−0.169208	+	0.371531i
$31$	−7.01416	−	4.04963i	−1.25978	−	0.727334i	−0.286748	−	0.958006i	$-0.592574\pi$
$31$	−7.01416	−	4.04963i	−1.25978	−	0.727334i	−0.973032	+	0.230672i	$0.925908\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$	2.03669	+	4.36770i	0.354543	+	0.760319i
$34$	7.40697	−	2.69592i	1.27029	−	0.462346i
$35$	0.0582496	+	0.0988337i	0.00984598	+	0.0167059i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	−0.423514	+	0.423514i	−0.0696252	+	0.0696252i	−0.741062	−	0.671437i	$-0.765678\pi$
$37$	−0.423514	+	0.423514i	−0.0696252	+	0.0696252i	0.671437	+	0.741062i	$0.265678\pi$
$38$	3.54336	−	2.53862i	0.574809	−	0.411819i
$39$		−	1.99315i		−	0.319160i
$40$	2.23598	−	0.0200524i	0.353539	−	0.00317056i
$41$	3.07225	+	3.66136i	0.479804	+	0.571808i	0.950594	−	0.310437i	$-0.100475\pi$
$41$	3.07225	+	3.66136i	0.479804	+	0.571808i	−0.470790	+	0.882245i	$0.656031\pi$
$42$	0.0464983	+	0.0216825i	0.00717485	+	0.00334569i
$43$	11.2562	−	5.24884i	1.71655	−	0.800441i	0.722520	−	0.691350i	$-0.242984\pi$
$43$	11.2562	−	5.24884i	1.71655	−	0.800441i	0.994032	−	0.109091i	$-0.0347939\pi$
$44$	3.09774	−	3.69174i	0.467002	−	0.556551i
$45$	−0.214854	−	2.22572i	−0.0320286	−	0.331791i
$46$	3.53750	−	2.04237i	0.521575	−	0.301132i
$47$	4.34011	−	3.03898i	0.633070	−	0.443280i	−0.212488	−	0.977164i	$-0.568157\pi$
$47$	4.34011	−	3.03898i	0.633070	−	0.443280i	0.845558	+	0.533883i	$0.179268\pi$
$48$	0.819152	−	0.573576i	0.118234	−	0.0827886i
$49$	−6.05990	+	3.49868i	−0.865700	+	0.499812i
$50$	−4.98799	−	0.346376i	−0.705408	−	0.0489850i
$51$	−5.06667	+	6.03822i	−0.709476	+	0.845520i
$52$	−1.80641	+	0.842342i	−0.250504	+	0.116812i
$53$	−4.47646	−	2.08741i	−0.614889	−	0.286727i	0.0901144	−	0.995931i	$-0.471277\pi$
$53$	−4.47646	−	2.08741i	−0.614889	−	0.286727i	−0.705003	+	0.709204i	$0.749055\pi$
$54$	−0.642788	−	0.766044i	−0.0874723	−	0.104245i
$55$	−7.55122	+	7.68789i	−1.01821	+	1.03663i
$56$		−	0.0513052i		−	0.00685595i
$57$	−1.79933	+	3.97019i	−0.238327	+	0.525865i
$58$	−2.21462	+	2.21462i	−0.290794	+	0.290794i
$59$	1.50376	+	8.52824i	0.195773	+	1.11028i	0.911314	+	0.411712i	$0.135069\pi$
$59$	1.50376	+	8.52824i	0.195773	+	1.11028i	−0.715541	+	0.698570i	$0.753820\pi$
$60$	−1.92639	+	1.13535i	−0.248696	+	0.146574i
$61$	11.1255	−	4.04933i	1.42447	−	0.518464i	0.489128	−	0.872212i	$-0.337315\pi$
$61$	11.1255	−	4.04933i	1.42447	−	0.518464i	0.935341	+	0.353748i	$0.115093\pi$
$62$	−3.42289	−	7.34041i	−0.434708	−	0.932234i
$63$	−0.0511100	+	0.00447154i	−0.00643925	+	0.000563362i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	4.17421	−	1.56182i	0.517746	−	0.193720i
$66$	−0.836850	+	4.74601i	−0.103009	+	0.584193i
$67$	−4.17215	−	5.95845i	−0.509709	−	0.727940i	0.478995	−	0.877817i	$-0.341001\pi$
$67$	−4.17215	−	5.95845i	−0.509709	−	0.727940i	−0.988705	+	0.149877i	$0.952112\pi$
$68$	7.61375	+	2.04010i	0.923303	+	0.247398i
$69$	−2.04237	+	3.53750i	−0.245873	+	0.425864i
$70$	−0.00897340	+	0.114370i	−0.00107253	+	0.0136699i
$71$	−1.20049	+	3.29831i	−0.142472	+	0.391438i	−0.990320	−	0.138800i	$-0.955675\pi$
$71$	−1.20049	+	3.29831i	−0.142472	+	0.391438i	0.847849	+	0.530238i	$0.177898\pi$
$72$	−0.422618	+	0.906308i	−0.0498060	+	0.106809i
$73$	−1.25344	+	14.3269i	−0.146704	+	1.67684i	0.464662	+	0.885488i	$0.346176\pi$
$73$	−1.25344	+	14.3269i	−0.146704	+	1.67684i	−0.611367	+	0.791348i	$0.709380\pi$
$74$	−0.589839	+	0.104005i	−0.0685674	+	0.0120903i
$75$	4.49291	−	2.19402i	0.518797	−	0.253344i
$76$	4.35864	−	0.0471284i	0.499971	−	0.00540600i
$77$	0.174833	+	0.174833i	0.0199241	+	0.0199241i
$78$	1.14322	−	1.63269i	0.129445	−	0.184866i
$79$	−12.7795	+	10.7233i	−1.43780	+	1.20646i	−0.496891	+	0.867813i	$0.665525\pi$
$79$	−12.7795	+	10.7233i	−1.43780	+	1.20646i	−0.940913	+	0.338648i	$0.890030\pi$
$80$	1.84311	+	1.26608i	0.206066	+	0.141552i
$81$	0.939693	+	0.342020i	0.104410	+	0.0380022i
$82$	0.416567	+	4.76138i	0.0460021	+	0.525806i
$83$	−0.831140	−	3.10186i	−0.0912294	−	0.340473i	0.905191	−	0.425004i	$-0.139727\pi$
$83$	−0.831140	−	3.10186i	−0.0912294	−	0.340473i	−0.996421	+	0.0845313i	$0.973061\pi$
$84$	0.0256526	+	0.0444316i	0.00279893	+	0.00484789i
$85$	−16.6159	−	5.87949i	−1.80225	−	0.637720i
$86$	12.2311	+	2.15668i	1.31892	+	0.232561i
$87$	0.810607	−	3.02523i	0.0869062	−	0.324339i
$88$	4.65501	−	1.24731i	0.496226	−	0.132963i
$89$	9.01493	+	7.56443i	0.955581	+	0.801828i	0.980229	−	0.197868i	$-0.0634019\pi$
$89$	9.01493	+	7.56443i	0.955581	+	0.801828i	−0.0246475	+	0.999696i	$0.507846\pi$
$90$	1.10062	−	1.94644i	0.116016	−	0.205173i
$91$	−0.0349747	−	0.0960921i	−0.00366634	−	0.0100732i
$92$	4.06920	+	0.356009i	0.424244	+	0.0371165i
$93$	6.63452	+	4.64554i	0.687967	+	0.481720i
$94$	5.29829			0.546477
$95$	−9.72461	−	0.657277i	−0.997724	−	0.0674352i
$96$	1.00000			0.102062
$97$	0.535833	+	0.375195i	0.0544056	+	0.0380952i	0.600463	−	0.799653i	$-0.294983\pi$
$97$	0.535833	+	0.375195i	0.0544056	+	0.0380952i	−0.546057	+	0.837748i	$0.683872\pi$
$98$	−6.97074	−	0.609861i	−0.704151	−	0.0616052i
$99$	−1.64827	−	4.52859i	−0.165658	−	0.455140i
$100$	−3.88725	−	3.14473i	−0.388725	−	0.314473i
$101$	−4.57577	−	3.83952i	−0.455306	−	0.382047i	0.386095	−	0.922459i	$-0.373824\pi$
$101$	−4.57577	−	3.83952i	−0.455306	−	0.382047i	−0.841400	+	0.540412i	$0.818268\pi$
$102$	−7.61375	+	2.04010i	−0.753874	+	0.202000i
$103$	−2.05388	+	7.66519i	−0.202375	+	0.755273i	0.787859	+	0.615856i	$0.211190\pi$
$103$	−2.05388	+	7.66519i	−0.202375	+	0.755273i	−0.990234	+	0.139417i	$0.955477\pi$
$104$	−1.96287	−	0.346107i	−0.192475	−	0.0339386i
$105$	−0.0494140	−	0.103534i	−0.00482232	−	0.0101039i
$106$	−2.46961	−	4.27750i	−0.239870	−	0.415467i
$107$	−1.85409	−	6.91956i	−0.179242	−	0.668939i	−0.995790	−	0.0916620i	$-0.970782\pi$
$107$	−1.85409	−	6.91956i	−0.179242	−	0.668939i	0.816549	−	0.577277i	$-0.195885\pi$
$108$	−0.0871557	−	0.996195i	−0.00838657	−	0.0958589i
$109$	−14.9849	−	5.45405i	−1.43529	−	0.522403i	−0.496848	−	0.867837i	$-0.665509\pi$
$109$	−14.9849	−	5.45405i	−1.43529	−	0.522403i	−0.938443	+	0.345434i	$0.887732\pi$
$110$	−10.5952	+	1.96635i	−1.01021	+	0.187484i
$111$	0.458814	−	0.384990i	0.0435487	−	0.0365417i
$112$	0.0294275	−	0.0420268i	0.00278063	−	0.00397116i
$113$	2.39143	+	2.39143i	0.224967	+	0.224967i	0.810586	−	0.585619i	$-0.199149\pi$
$113$	2.39143	+	2.39143i	0.224967	+	0.224967i	−0.585619	+	0.810586i	$0.699149\pi$
$114$	−3.75113	+	2.22014i	−0.351326	+	0.207935i
$115$	−9.00887	−	1.50533i	−0.840082	−	0.140373i
$116$	−3.08437	+	0.543857i	−0.286376	+	0.0504958i
$117$	−0.173715	+	1.98557i	−0.0160599	+	0.183566i
$118$	−3.65979	+	7.84845i	−0.336911	+	0.722508i
$119$	−0.138315	+	0.380016i	−0.0126793	+	0.0348360i
$120$	−2.22922	−	0.174902i	−0.203499	−	0.0159663i
$121$	−6.11246	+	10.5871i	−0.555679	+	0.962464i
$122$	11.4360	+	3.06428i	1.03537	+	0.277427i
$123$	−2.74145	−	3.91519i	−0.247188	−	0.353021i
$124$	1.40642	−	7.97621i	0.126300	−	0.716284i
$125$	8.11550	+	7.69017i	0.725872	+	0.687830i
$126$	−0.0444316	−	0.0256526i	−0.00395828	−	0.00228532i
$127$	12.5874	−	1.10125i	1.11695	−	0.0977205i	0.486303	−	0.873790i	$-0.338345\pi$
$127$	12.5874	−	1.10125i	1.11695	−	0.0977205i	0.630647	+	0.776070i	$0.282790\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$	−11.6708	+	4.24783i	−1.02756	+	0.374000i
$130$	4.31513	+	1.11486i	0.378462	+	0.0977796i
$131$	−2.39819	−	13.6008i	−0.209531	−	1.18831i	−0.890149	−	0.455670i	$-0.849400\pi$
$131$	−2.39819	−	13.6008i	−0.209531	−	1.18831i	0.680618	−	0.732638i	$-0.261711\pi$
$132$	−3.40771	+	3.40771i	−0.296603	+	0.296603i
$133$	−0.0170811	+	0.222981i	−0.00148112	+	0.0193349i
$134$		−	7.27392i		−	0.628371i
$135$	0.0200524	+	2.23598i	0.00172584	+	0.192442i
$136$	5.06667	+	6.03822i	0.434463	+	0.517773i
$137$	7.89140	+	3.67982i	0.674208	+	0.314388i	0.729400	−	0.684087i	$-0.239799\pi$
$137$	7.89140	+	3.67982i	0.674208	+	0.314388i	−0.0551922	+	0.998476i	$0.517577\pi$
$138$	−3.70204	+	1.72629i	−0.315138	+	0.146951i
$139$	−2.99307	+	3.56700i	−0.253868	+	0.302549i	−0.877894	−	0.478856i	$-0.841052\pi$
$139$	−2.99307	+	3.56700i	−0.253868	+	0.302549i	0.624025	+	0.781404i	$0.285496\pi$
$140$	−0.0729508	+	0.0885399i	−0.00616547	+	0.00748298i
$141$	−4.58846	+	2.64915i	−0.386418	+	0.223098i
$142$	−2.87522	+	2.01325i	−0.241283	+	0.168948i
$143$	7.86832	−	5.50946i	0.657982	−	0.460724i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	6.97084	−	0.672913i	0.578897	−	0.0558824i
$146$	−9.24432	+	11.0170i	−0.765066	+	0.911770i
$147$	6.34177	−	2.95722i	0.523060	−	0.243907i
$148$	−0.542823	−	0.253122i	−0.0446198	−	0.0208065i
$149$	3.62363	+	4.31847i	0.296859	+	0.353783i	0.893771	−	0.448524i	$-0.148050\pi$
$149$	3.62363	+	4.31847i	0.296859	+	0.353783i	−0.596912	+	0.802307i	$0.703606\pi$
$150$	4.93882	+	0.779790i	0.403253	+	0.0636696i
$151$			5.73975i			0.467094i	0.972346	+	0.233547i	$0.0750333\pi$
$151$			5.73975i			0.467094i	−0.972346	+	0.233547i	$0.924967\pi$
$152$	3.59742	+	2.46141i	0.291790	+	0.199647i
$153$	5.57365	−	5.57365i	0.450603	−	0.450603i
$154$	0.0429347	+	0.243495i	0.00345978	+	0.0196214i
$155$	−4.53027	+	17.5347i	−0.363880	+	1.40842i
$156$	1.87295	−	0.681698i	0.149956	−	0.0545795i
$157$	1.88266	+	4.03737i	0.150252	+	0.322217i	0.966999	−	0.254779i	$-0.0820026\pi$
$157$	1.88266	+	4.03737i	0.150252	+	0.322217i	−0.816747	+	0.576996i	$0.804225\pi$
$158$	−16.6189	+	1.45397i	−1.32213	+	0.115672i
$159$	4.27750	+	2.46961i	0.339227	+	0.195853i
$160$	0.783593	+	2.09427i	0.0619484	+	0.165567i
$161$	−0.0363912	+	0.206385i	−0.00286803	+	0.0162654i
$162$	0.573576	+	0.819152i	0.0450644	+	0.0643587i
$163$	14.4217	+	3.86429i	1.12960	+	0.302675i	0.774761	−	0.632254i	$-0.217870\pi$
$163$	14.4217	+	3.86429i	1.12960	+	0.302675i	0.354836	+	0.934929i	$0.384537\pi$
$164$	−2.38978	+	4.13923i	−0.186611	+	0.323219i
$165$	8.19253	−	7.00050i	0.637788	−	0.544988i
$166$	1.09832	−	3.01761i	0.0852463	−	0.234212i
$167$	3.26734	−	7.00684i	0.252834	−	0.542205i	−0.738393	−	0.674370i	$-0.764415\pi$
$167$	3.26734	−	7.00684i	0.252834	−	0.542205i	0.991228	+	0.132165i	$0.0421929\pi$
$168$	−0.00447154	+	0.0511100i	−0.000344987	+	0.00394322i
$169$	8.89020	−	1.56758i	0.683862	−	0.120583i
$170$	−10.2386	−	14.3467i	−0.785265	−	1.10034i
$171$	2.13851	−	3.79826i	0.163536	−	0.290460i
$172$	8.78214	+	8.78214i	0.669632	+	0.669632i
$173$	9.24502	−	13.2033i	0.702886	−	1.00383i	−0.295931	−	0.955209i	$-0.595630\pi$
$173$	9.24502	−	13.2033i	0.702886	−	1.00383i	0.998818	−	0.0486162i	$-0.0154811\pi$
$174$	2.39921	−	2.01318i	0.181884	−	0.152619i
$175$	0.178109	−	0.184615i	0.0134638	−	0.0139556i
$176$	4.52859	+	1.64827i	0.341355	+	0.124243i
$177$	−0.754752	−	8.62685i	−0.0567306	−	0.648434i
$178$	3.04582	+	11.3672i	0.228294	+	0.852005i
$179$	−12.8679	−	22.2879i	−0.961794	−	1.66588i	−0.717993	−	0.696050i	$-0.754939\pi$
$179$	−12.8679	−	22.2879i	−0.961794	−	1.66588i	−0.243801	−	0.969825i	$-0.578394\pi$
$180$	2.01801	−	0.963139i	0.150414	−	0.0717881i
$181$	20.7447	+	3.65786i	1.54194	+	0.271886i	0.879014	−	0.476795i	$-0.158202\pi$
$181$	20.7447	+	3.65786i	1.54194	+	0.271886i	0.662930	+	0.748682i	$0.269313\pi$
$182$	0.0264666	−	0.0987747i	0.00196183	−	0.00732167i
$183$	−11.4360	+	3.06428i	−0.845377	+	0.226518i
$184$	3.12910	+	2.62563i	0.230680	+	0.193564i
$185$	1.16580	+	0.659206i	0.0857112	+	0.0484658i
$186$	2.77011	+	7.61081i	0.203114	+	0.558051i
$187$	−37.8422	−	3.31076i	−2.76730	−	0.242107i
$188$	4.34011	+	3.03898i	0.316535	+	0.221640i
$189$	0.0513052			0.00373190
$190$	−7.58893	−	6.11622i	−0.550559	−	0.443717i
$191$	−3.73041			−0.269923			−0.134962	−	0.990851i	$-0.543091\pi$
$191$	−3.73041			−0.269923			−0.134962	+	0.990851i	$0.543091\pi$
$192$	0.819152	+	0.573576i	0.0591172	+	0.0413943i
$193$	0.251133	+	0.0219713i	0.0180770	+	0.00158153i	0.0961906	−	0.995363i	$-0.469334\pi$
$193$	0.251133	+	0.0219713i	0.0180770	+	0.00158153i	−0.0781137	+	0.996944i	$0.524890\pi$
$194$	0.223726	+	0.614683i	0.0160626	+	0.0441316i
$195$	−4.29444	+	1.19207i	−0.307531	+	0.0853659i
$196$	−5.36029	−	4.49782i	−0.382878	−	0.321273i
$197$	6.63528	−	1.77792i	0.472744	−	0.126671i	−0.0145779	−	0.999894i	$-0.504640\pi$
$197$	6.63528	−	1.77792i	0.472744	−	0.126671i	0.487322	+	0.873222i	$0.337974\pi$
$198$	1.24731	−	4.65501i	0.0886423	−	0.330817i
$199$	7.49501	+	1.32157i	0.531307	+	0.0936838i	0.432865	−	0.901459i	$-0.357503\pi$
$199$	7.49501	+	1.32157i	0.531307	+	0.0936838i	0.0984424	+	0.995143i	$0.468614\pi$
$200$	−1.38051	−	4.80564i	−0.0976164	−	0.339810i
$201$	3.63696	+	6.29940i	0.256532	+	0.444326i
$202$	−1.54599	−	5.76971i	−0.108775	−	0.405955i
$203$	−0.0140046	−	0.160074i	−0.000982933	−	0.0112350i
$204$	−7.40697	−	2.69592i	−0.518592	−	0.188752i
$205$	6.05131	−	8.80926i	0.422642	−	0.615265i
$206$	−6.07901	+	5.10090i	−0.423545	+	0.355396i
$207$	2.34292	−	3.34603i	0.162844	−	0.232565i
$208$	−1.40937	−	1.40937i	−0.0977223	−	0.0977223i
$209$	−20.6467	+	3.87120i	−1.42816	+	0.267777i
$210$	0.0189073	−	0.113153i	0.00130473	−	0.00780831i
$211$	−1.74444	+	0.307591i	−0.120092	+	0.0211754i	−0.233371	−	0.972388i	$-0.574976\pi$
$211$	−1.74444	+	0.307591i	−0.120092	+	0.0211754i	0.113279	+	0.993563i	$0.463865\pi$
$212$	0.430482	−	4.92043i	0.0295656	−	0.337937i
$213$	1.48339	−	3.18113i	0.101640	−	0.217968i
$214$	2.45011	−	6.73163i	0.167486	−	0.460165i
$215$	−18.0413	−	21.1133i	−1.23041	−	1.43992i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	0.401375	+	0.107548i	0.0272471	+	0.00730084i
$218$	−9.14658	−	13.0627i	−0.619485	−	0.884716i
$219$	2.49734	−	14.1631i	0.168755	−	0.957055i
$220$	−9.80692	−	4.46642i	−0.661183	−	0.301126i
$221$	13.6059	+	7.85535i	0.915229	+	0.528408i
$222$	0.596659	−	0.0522009i	0.0400452	−	0.00350350i
$223$	10.9643	+	23.5131i	0.734225	+	1.57455i	0.816102	+	0.577908i	$0.196131\pi$
$223$	10.9643	+	23.5131i	0.734225	+	1.57455i	−0.0818765	+	0.996642i	$0.526091\pi$
$224$	0.0482111	−	0.0175474i	0.00322124	−	0.00117244i
$225$	−4.66704	+	1.79409i	−0.311136	+	0.119606i
$226$	0.587277	+	3.33061i	0.0390651	+	0.221549i
$227$	4.88986	−	4.88986i	0.324552	−	0.324552i	−0.525959	−	0.850510i	$-0.676293\pi$
$227$	4.88986	−	4.88986i	0.324552	−	0.324552i	0.850510	+	0.525959i	$0.176293\pi$
$228$	−4.34617	−	0.332932i	−0.287832	−	0.0220489i
$229$			22.8216i			1.50809i	0.656821	+	0.754047i	$0.271901\pi$
$229$			22.8216i			1.50809i	−0.656821	+	0.754047i	$0.728099\pi$
$230$	−6.51621	−	6.40038i	−0.429666	−	0.422028i
$231$	−0.158930	−	0.189406i	−0.0104568	−	0.0124620i
$232$	−2.83851	−	1.32362i	−0.186357	−	0.0868998i
$233$	22.0022	−	10.2598i	1.44141	−	0.672142i	0.464459	−	0.885595i	$-0.346249\pi$
$233$	22.0022	−	10.2598i	1.44141	−	0.672142i	0.976953	+	0.213453i	$0.0684710\pi$
$234$	−1.28117	+	1.52684i	−0.0837529	+	0.0998128i
$235$	−9.14352	−	7.53363i	−0.596457	−	0.491440i
$236$	−7.49961	+	4.32990i	−0.488183	+	0.281853i
$237$	13.6654	−	9.56865i	0.887666	−	0.621550i
$238$	−0.331269	+	0.231957i	−0.0214730	+	0.0150355i
$239$	−2.89683	+	1.67249i	−0.187380	+	0.108184i	−0.590756	−	0.806851i	$-0.701170\pi$
$239$	−2.89683	+	1.67249i	−0.187380	+	0.108184i	0.403375	+	0.915035i	$0.367837\pi$
$240$	−1.72575	−	1.42190i	−0.111397	−	0.0917831i
$241$	14.1399	−	16.8513i	0.910833	−	1.08549i	−0.0851873	−	0.996365i	$-0.527149\pi$
$241$	14.1399	−	16.8513i	0.910833	−	1.08549i	0.996021	−	0.0891238i	$-0.0284067\pi$
$242$	−11.0795	+	5.16648i	−0.712220	+	0.332114i
$243$	−0.906308	−	0.422618i	−0.0581397	−	0.0271110i
$244$	7.61026	+	9.06955i	0.487197	+	0.580619i
$245$	11.1626	+	10.9641i	0.713151	+	0.700474i
$246$		−	4.77957i		−	0.304734i
$247$	8.41573	+	2.15774i	0.535480	+	0.137294i
$248$	5.72704	−	5.72704i	0.363667	−	0.363667i
$249$	0.557633	+	3.16249i	0.0353385	+	0.200415i
$250$	2.23693	+	10.9543i	0.141476	+	0.692809i
$251$	−9.05512	+	3.29579i	−0.571554	+	0.208029i	−0.611597	−	0.791169i	$-0.709473\pi$
$251$	−9.05512	+	3.29579i	−0.571554	+	0.208029i	0.0400431	+	0.999198i	$0.487250\pi$
$252$	−0.0216825	−	0.0464983i	−0.00136587	−	0.00292912i
$253$	−19.6104	+	1.71569i	−1.23290	+	0.107864i
$254$	10.9426	+	6.31774i	0.686602	+	0.396410i
$255$	16.0402	+	7.30528i	1.00448	+	0.457475i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	7.07372	+	10.1023i	0.441246	+	0.630165i	0.976753	−	0.214366i	$-0.0687684\pi$
$257$	7.07372	+	10.1023i	0.441246	+	0.630165i	−0.535507	+	0.844531i	$0.679879\pi$
$258$	−11.9966	−	3.21449i	−0.746877	−	0.200125i
$259$	0.0153643	−	0.0266118i	0.000954693	−	0.00165358i
$260$	2.89529	+	3.38830i	0.179558	+	0.210133i
$261$	−1.07119	+	2.94307i	−0.0663049	+	0.182171i
$262$	5.83662	−	12.5167i	0.360588	−	0.773283i
$263$	−2.32068	+	26.5255i	−0.143100	+	1.63564i	0.497290	+	0.867585i	$0.334329\pi$
$263$	−2.32068	+	26.5255i	−0.143100	+	1.63564i	−0.640389	+	0.768051i	$0.721227\pi$
$264$	−4.74601	+	0.836850i	−0.292097	+	0.0515045i
$265$	−1.82023	+	10.8934i	−0.111816	+	0.669177i
$266$	−0.141889	+	0.172858i	−0.00869975	+	0.0105986i
$267$	−8.32135	−	8.32135i	−0.509258	−	0.509258i
$268$	4.17215	−	5.95845i	0.254855	−	0.363970i
$269$	12.0097	−	10.0773i	0.732245	−	0.614427i	−0.198498	−	0.980101i	$-0.563606\pi$
$269$	12.0097	−	10.0773i	0.732245	−	0.614427i	0.930743	+	0.365675i	$0.119162\pi$
$270$	−1.26608	+	1.84311i	−0.0770511	+	0.112168i
$271$	−0.678495	−	0.246952i	−0.0412156	−	0.0150013i	0.321330	−	0.946967i	$-0.395870\pi$
$271$	−0.678495	−	0.246952i	−0.0412156	−	0.0150013i	−0.362546	+	0.931966i	$0.618092\pi$
$272$	0.686991	+	7.85234i	0.0416549	+	0.476118i
$273$	0.0264666	+	0.0987747i	0.00160183	+	0.00597812i
$274$	4.35360	+	7.54065i	0.263010	+	0.455548i
$275$	21.0806	+	11.6719i	1.27121	+	0.703840i
$276$	−4.02269	−	0.709309i	−0.242138	−	0.0426954i
$277$	4.83600	−	18.0482i	0.290567	−	1.08441i	−0.654107	−	0.756402i	$-0.726955\pi$
$277$	4.83600	−	18.0482i	0.290567	−	1.08441i	0.944674	−	0.328010i	$-0.106378\pi$
$278$	−4.49772	+	1.20516i	−0.269755	+	0.0722807i
$279$	−6.20439	−	5.20610i	−0.371447	−	0.311681i
$280$	−0.110542	+	0.0306848i	−0.00660616	+	0.00183377i
$281$	1.82300	+	5.00865i	0.108751	+	0.298791i	0.982116	−	0.188274i	$-0.0602895\pi$
$281$	1.82300	+	5.00865i	0.108751	+	0.298791i	−0.873365	+	0.487066i	$0.838067\pi$
$282$	−5.27813	−	0.461777i	−0.314308	−	0.0274984i
$283$	8.30220	+	5.81326i	0.493514	+	0.345563i	0.793691	−	0.608321i	$-0.208157\pi$
$283$	8.30220	+	5.81326i	0.493514	+	0.345563i	−0.300177	+	0.953884i	$0.597046\pi$
$284$	−3.50999			−0.208280
$285$	9.63032	+	1.50233i	0.570451	+	0.0889904i
$286$	9.60545			0.567982
$287$	−0.200870	−	0.140650i	−0.0118570	−	0.00830234i
$288$	−0.996195	−	0.0871557i	−0.0587013	−	0.00513570i
$289$	−15.4358	−	42.4095i	−0.907988	−	2.49468i
$290$	6.09615	+	3.44709i	0.357978	+	0.202420i
$291$	−0.501094	−	0.420468i	−0.0293746	−	0.0246483i
$292$	−13.8916	+	3.72224i	−0.812943	+	0.217827i
$293$	−0.000543581		0.00202867i	−3.17563e−5		0.000118516i	−0.965942	−	0.258760i	$-0.916686\pi$
$293$	−0.000543581		0.00202867i	−3.17563e−5		0.000118516i	0.965910	+	0.258878i	$0.0833529\pi$
$294$	6.89106	+	1.21508i	0.401895	+	0.0708649i
$295$	17.4756	−	8.34059i	1.01747	−	0.485608i
$296$	−0.299469	−	0.518696i	−0.0174063	−	0.0301486i
$297$	1.24731	+	4.65501i	0.0723761	+	0.270111i
$298$	0.491328	+	5.61591i	0.0284619	+	0.325321i
$299$	7.65053	+	2.78456i	0.442441	+	0.161036i
$300$	3.59837	+	3.47156i	0.207752	+	0.200430i
$301$	−0.488125	+	0.409585i	−0.0281350	+	0.0236081i
$302$	−3.29218	+	4.70173i	−0.189444	+	0.270554i
$303$	4.22372	+	4.22372i	0.242646	+	0.242646i
$304$	1.53503	+	4.07967i	0.0880400	+	0.233985i
$305$	−15.3786	−	21.5491i	−0.880578	−	1.23390i
$306$	7.76259	−	1.36875i	0.443758	−	0.0782464i
$307$	0.525851	−	6.01050i	0.0300119	−	0.343038i	−0.966312	−	0.257373i	$-0.917143\pi$
$307$	0.525851	−	6.01050i	0.0300119	−	0.343038i	0.996324	−	0.0856645i	$-0.0273013\pi$
$308$	−0.104493	+	0.224086i	−0.00595404	+	0.0127685i
$309$	2.71413	−	7.45701i	0.154401	−	0.424214i
$310$	−13.7685	+	11.7651i	−0.781997	+	0.668215i
$311$	−8.33690	+	14.4399i	−0.472742	+	0.818813i	−0.999513	−	0.0311937i	$-0.990069\pi$
$311$	−8.33690	+	14.4399i	−0.472742	+	0.818813i	0.526771	+	0.850007i	$0.323402\pi$
$312$	1.92524	+	0.515866i	0.108995	+	0.0292051i
$313$	−9.63242	−	13.7565i	−0.544456	−	0.777564i	0.448784	−	0.893640i	$-0.351857\pi$
$313$	−9.63242	−	13.7565i	−0.544456	−	0.777564i	−0.993240	+	0.116076i	$0.962968\pi$
$314$	−0.773559	+	4.38707i	−0.0436544	+	0.247577i
$315$	0.0402024	+	0.107447i	0.00226515	+	0.00605396i
$316$	−14.4474	−	8.34121i	−0.812730	−	0.469230i
$317$	−10.5770	+	0.925367i	−0.594063	+	0.0519738i	−0.380223	−	0.924895i	$-0.624153\pi$
$317$	−10.5770	+	0.925367i	−0.594063	+	0.0519738i	−0.213840	+	0.976869i	$0.568597\pi$
$318$	2.08741	+	4.47646i	0.117056	+	0.251027i
$319$	14.1833	−	5.16230i	0.794113	−	0.289033i
$320$	−0.559345	+	2.16498i	−0.0312683	+	0.121026i
$321$	1.24396	+	7.05482i	0.0694308	+	0.393762i
$322$	−0.148188	+	0.148188i	−0.00825817	+	0.00825817i
$323$	−20.0103	−	27.9300i	−1.11340	−	1.55406i
$324$			1.00000i			0.0555556i
$325$	−5.86161	−	8.05964i	−0.325144	−	0.447068i
$326$	9.59712	+	11.4374i	0.531535	+	0.633459i
$327$	14.4525	+	6.73932i	0.799226	+	0.372685i
$328$	−4.33176	+	2.01993i	−0.239181	+	0.111532i
$329$	−0.174729	+	0.208234i	−0.00963312	+	0.0114803i
$330$	10.7263	−	1.03543i	0.590461	−	0.0569986i
$331$	11.1512	−	6.43817i	0.612928	−	0.353874i	−0.161183	−	0.986925i	$-0.551531\pi$
$331$	11.1512	−	6.43817i	0.612928	−	0.353874i	0.774110	+	0.633051i	$0.218197\pi$
$332$	2.63052	−	1.84191i	0.144369	−	0.101088i
$333$	−0.490622	+	0.343537i	−0.0268859	+	0.0188257i
$334$	6.69540	−	3.86559i	0.366356	−	0.211516i
$335$	−10.3428	+	12.5530i	−0.565086	+	0.685841i
$336$	−0.0329784	+	0.0393021i	−0.00179912	+	0.00214410i
$337$	12.6417	−	5.89492i	0.688637	−	0.321117i	−0.0466126	−	0.998913i	$-0.514843\pi$
$337$	12.6417	−	5.89492i	0.688637	−	0.321117i	0.735250	+	0.677796i	$0.237065\pi$
$338$	8.18155	+	3.81512i	0.445018	+	0.207515i
$339$	−2.17390	−	2.59076i	−0.118070	−	0.140711i
$340$	−0.158060	−	17.6247i	−0.00857200	−	0.955835i
$341$			39.0321i			2.11371i
$342$	3.93036	−	1.88476i	0.212529	−	0.101916i
$343$	0.507800	−	0.507800i	0.0274186	−	0.0274186i
$344$	2.15668	+	12.2311i	0.116280	+	0.659459i
$345$	8.84339	+	2.28478i	0.476112	+	0.123008i
$346$	15.1462	−	5.51275i	0.814263	−	0.296367i
$347$	−8.87684	−	19.0364i	−0.476534	−	1.02193i	−0.986805	−	0.161916i	$-0.948233\pi$
$347$	−8.87684	−	19.0364i	−0.476534	−	1.02193i	0.510271	−	0.860014i	$-0.329545\pi$
$348$	3.12003	−	0.272967i	0.167251	−	0.0146326i
$349$	13.9578	+	8.05854i	0.747144	+	0.431364i	0.824661	−	0.565627i	$-0.191366\pi$
$349$	13.9578	+	8.05854i	0.747144	+	0.431364i	−0.0775171	+	0.996991i	$0.524699\pi$
$350$	0.251789	−	0.0490689i	0.0134587	−	0.00262285i
$351$	0.346107	−	1.96287i	0.0184738	−	0.104770i
$352$	2.76419	+	3.94768i	0.147332	+	0.210412i
$353$	2.09972	+	0.562618i	0.111757	+	0.0299452i	0.314264	−	0.949336i	$-0.398242\pi$
$353$	2.09972	+	0.562618i	0.111757	+	0.0299452i	−0.202507	+	0.979281i	$0.564909\pi$
$354$	4.32990	−	7.49961i	0.230132	−	0.398600i
$355$	7.82453	+	0.613905i	0.415283	+	0.0325827i
$356$	−4.02495	+	11.0585i	−0.213322	+	0.586097i
$357$	0.170909	−	0.366515i	0.00904546	−	0.0193980i
$358$	2.24303	−	25.6379i	0.118548	−	1.35501i
$359$	−7.78576	+	1.37284i	−0.410917	+	0.0724557i	−0.375285	−	0.926909i	$-0.622455\pi$
$359$	−7.78576	+	1.37284i	−0.410917	+	0.0724557i	−0.0356313	+	0.999365i	$0.511344\pi$
$360$	2.20549	+	0.368526i	0.116240	+	0.0194230i
$361$	−14.8155	−	11.8954i	−0.779764	−	0.626073i
$362$	14.8950	+	14.8950i	0.782866	+	0.782866i
$363$	7.01193	−	10.0141i	0.368031	−	0.525603i
$364$	0.0783350	−	0.0657309i	0.00410587	−	0.00344523i
$365$	31.6184	−	5.86800i	1.65498	−	0.307145i
$366$	−11.1255	−	4.04933i	−0.581537	−	0.211662i
$367$	−1.07695	−	12.3096i	−0.0562164	−	0.642556i	−0.971074	−	0.238779i	$-0.923253\pi$
$367$	−1.07695	−	12.3096i	−0.0562164	−	0.642556i	0.914858	−	0.403777i	$-0.132303\pi$
$368$	1.05721	+	3.94556i	0.0551109	+	0.205677i
$369$	2.38978	+	4.13923i	0.124407	+	0.215480i
$370$	0.576861	+	1.20866i	0.0299896	+	0.0628355i
$371$	0.249558	+	0.0440038i	0.0129564	+	0.00228457i
$372$	−2.09624	+	7.82328i	−0.108685	+	0.405618i
$373$	−26.1855	+	7.01638i	−1.35583	+	0.363294i	−0.862285	−	0.506424i	$-0.830967\pi$
$373$	−26.1855	+	7.01638i	−1.35583	+	0.363294i	−0.493548	+	0.869718i	$0.664300\pi$
$374$	−29.0995	−	24.4174i	−1.50470	−	1.26259i
$375$	−7.41437	−	8.36822i	−0.382877	−	0.432133i
$376$	1.81212	+	4.97877i	0.0934531	+	0.256760i
$377$	−6.21869	−	0.544065i	−0.320279	−	0.0280208i
$378$	0.0420268	+	0.0294275i	0.00216162	+	0.00151359i
$379$	10.9904			0.564538			0.282269	−	0.959335i	$-0.408913\pi$
$379$	10.9904			0.564538			0.282269	+	0.959335i	$0.408913\pi$
$380$	−2.70837	−	9.36294i	−0.138937	−	0.480309i
$381$	−12.6355			−0.647335
$382$	−3.05577	−	2.13968i	−0.156347	−	0.109475i
$383$	−4.07694	−	0.356686i	−0.208322	−	0.0182258i	−0.0174830	−	0.999847i	$-0.505565\pi$
$383$	−4.07694	−	0.356686i	−0.208322	−	0.0182258i	−0.190839	+	0.981621i	$0.561121\pi$
$384$	0.342020	+	0.939693i	0.0174536	+	0.0479535i
$385$	0.272131	−	0.481260i	0.0138691	−	0.0245273i
$386$	0.193114	+	0.162042i	0.00982925	+	0.00824772i
$387$	11.9966	−	3.21449i	0.609823	−	0.163402i
$388$	−0.169302	+	0.631843i	−0.00859499	+	0.0320770i
$389$	−0.554792	−	0.0978248i	−0.0281291	−	0.00495991i	0.159566	−	0.987187i	$-0.448991\pi$
$389$	−0.554792	−	0.0978248i	−0.0281291	−	0.00495991i	−0.187695	+	0.982227i	$0.560102\pi$
$390$	−4.20154	−	1.48670i	−0.212753	−	0.0752822i
$391$	−16.0987	−	27.8837i	−0.814145	−	1.41014i
$392$	−1.81105	−	6.75894i	−0.0914719	−	0.341378i
$393$	1.20368	+	13.7581i	0.0607174	+	0.694003i
$394$	6.45508	+	2.34946i	0.325202	+	0.118364i
$395$	30.7475	+	21.1213i	1.54708	+	1.06273i
$396$	3.69174	−	3.09774i	0.185517	−	0.155667i
$397$	−8.89693	+	12.7061i	−0.446524	+	0.637703i	−0.977811	−	0.209489i	$-0.932820\pi$
$397$	−8.89693	+	12.7061i	−0.446524	+	0.637703i	0.531287	+	0.847192i	$0.321709\pi$
$398$	5.38153	+	5.38153i	0.269752	+	0.269752i
$399$	0.0364502	−	0.220644i	0.00182479	−	0.0110460i
$400$	1.62556	−	4.72838i	0.0812780	−	0.236419i
$401$	−35.1992	+	6.20657i	−1.75776	+	0.309941i	−0.957226	−	0.289342i	$-0.906564\pi$
$401$	−35.1992	+	6.20657i	−1.75776	+	0.309941i	−0.800537	+	0.599283i	$0.795453\pi$
$402$	−0.633964	+	7.24624i	−0.0316193	+	0.361410i
$403$	6.82234	−	14.6306i	0.339845	−	0.728800i
$404$	2.04297	−	5.61301i	0.101641	−	0.279258i
$405$	0.174902	−	2.22922i	0.00869096	−	0.110771i
$406$	0.0803426	−	0.139157i	0.00398734	−	0.00690627i
$407$	2.78807	+	0.747060i	0.138199	+	0.0370304i
$408$	−4.52112	−	6.45683i	−0.223829	−	0.319661i
$409$	−5.00471	+	28.3831i	−0.247467	+	1.40346i	0.567225	+	0.823563i	$0.308017\pi$
$409$	−5.00471	+	28.3831i	−0.247467	+	1.40346i	−0.814693	+	0.579893i	$0.803094\pi$
$410$	10.0097	−	3.74523i	0.494345	−	0.184964i
$411$	−7.54065	−	4.35360i	−0.371953	−	0.214747i
$412$	−7.90539	+	0.691632i	−0.389470	+	0.0340743i
$413$	−0.187766	−	0.402666i	−0.00923938	−	0.0198139i
$414$	3.83841	−	1.39707i	0.188647	−	0.0686620i
$415$	−6.18617	+	3.64594i	−0.303667	+	0.178972i
$416$	−0.346107	−	1.96287i	−0.0169693	−	0.0962377i
$417$	3.29256	−	3.29256i	0.161237	−	0.161237i
$418$	−19.1332	−	8.67137i	−0.935837	−	0.424131i
$419$		−	5.09458i		−	0.248886i	−0.992227	−	0.124443i	$-0.960286\pi$
$419$		−	5.09458i		−	0.248886i	0.992227	−	0.124443i	$-0.0397144\pi$
$420$	0.0803899	−	0.0818449i	0.00392263	−	0.00399362i
$421$	−3.22782	−	3.84677i	−0.157314	−	0.187480i	0.681630	−	0.731697i	$-0.261271\pi$
$421$	−3.22782	−	3.84677i	−0.157314	−	0.187480i	−0.838945	+	0.544217i	$0.816827\pi$
$422$	−1.60538	−	0.748603i	−0.0781489	−	0.0364414i
$423$	4.80188	−	2.23916i	0.233476	−	0.108871i
$424$	3.17487	−	3.78367i	0.154185	−	0.183751i
$425$	−2.73026	+	39.3170i	−0.132437	+	1.90715i
$426$	3.03974	−	1.75500i	0.147276	−	0.0850298i
$427$	−0.497574	+	0.348405i	−0.0240793	+	0.0168605i
$428$	5.86812	−	4.10890i	0.283646	−	0.198611i
$429$	−8.31856	+	4.80272i	−0.401624	+	0.231878i
$430$	−2.66845	−	27.6431i	−0.128684	−	1.33307i
$431$	25.9835	−	30.9659i	1.25158	−	1.49158i	0.450792	−	0.892629i	$-0.351142\pi$
$431$	25.9835	−	30.9659i	1.25158	−	1.49158i	0.800789	−	0.598947i	$-0.204414\pi$
$432$	0.906308	−	0.422618i	0.0436048	−	0.0203332i
$433$	6.99541	+	3.26201i	0.336178	+	0.156762i	0.583375	−	0.812203i	$-0.301732\pi$
$433$	6.99541	+	3.26201i	0.336178	+	0.156762i	−0.247197	+	0.968965i	$0.579510\pi$
$434$	0.267100	+	0.318317i	0.0128212	+	0.0152797i
$435$	−7.00296	+	0.0628031i	−0.335766	+	0.00301118i
$436$		−	15.9466i		−	0.763703i
$437$	−12.7254	−	12.4532i	−0.608740	−	0.595716i
$438$	10.1693	−	10.1693i	0.485910	−	0.485910i
$439$	−1.03789	−	5.88618i	−0.0495359	−	0.280932i	0.949971	−	0.312339i	$-0.101112\pi$
$439$	−1.03789	−	5.88618i	−0.0495359	−	0.280932i	−0.999507	+	0.0314066i	$0.990001\pi$
$440$	−5.47153	−	9.28370i	−0.260845	−	0.442583i
$441$	−6.57537	+	2.39324i	−0.313113	+	0.113964i
$442$	6.63963	+	14.2387i	0.315815	+	0.677267i
$443$	−15.6336	+	1.36776i	−0.742776	+	0.0649845i	−0.452260	−	0.891886i	$-0.649382\pi$
$443$	−15.6336	+	1.36776i	−0.742776	+	0.0649845i	−0.290515	+	0.956870i	$0.593827\pi$
$444$	0.518696	+	0.299469i	0.0246162	+	0.0142122i
$445$	10.9066	−	23.9477i	0.517024	−	1.13523i
$446$	−4.50509	+	25.5496i	−0.213322	+	1.20981i
$447$	−3.23346	−	4.61786i	−0.152937	−	0.218417i
$448$	0.0495570	+	0.0132788i	0.00234135	+	0.000627363i
$449$	−2.40054	+	4.15786i	−0.113289	+	0.196222i	−0.917094	−	0.398670i	$-0.869472\pi$
$449$	−2.40054	+	4.15786i	−0.113289	+	0.196222i	0.803806	+	0.594892i	$0.202805\pi$
$450$	−4.85206	−	1.20727i	−0.228728	−	0.0569112i
$451$	7.87803	−	21.6447i	0.370962	−	1.01921i
$452$	−1.42929	+	3.06513i	−0.0672283	+	0.144171i
$453$	0.500252	−	5.71791i	0.0235039	−	0.268651i
$454$	6.81025	−	1.20083i	0.319621	−	0.0563578i
$455$	−0.186122	+	0.132827i	−0.00872554	+	0.00622704i
$456$	−3.36921	−	2.76558i	−0.157778	−	0.129510i
$457$	10.5393	+	10.5393i	0.493006	+	0.493006i	0.909252	−	0.416246i	$-0.136654\pi$
$457$	10.5393	+	10.5393i	0.493006	+	0.493006i	−0.416246	+	0.909252i	$0.636654\pi$
$458$	−13.0899	+	18.6944i	−0.611652	+	0.873530i
$459$	−6.03822	+	5.06667i	−0.281840	+	0.236492i
$460$	−1.66666	−	8.98043i	−0.0777086	−	0.418715i
$461$	2.78062	+	1.01206i	0.129506	+	0.0471365i	0.405960	−	0.913891i	$-0.366937\pi$
$461$	2.78062	+	1.01206i	0.129506	+	0.0471365i	−0.276454	+	0.961027i	$0.589159\pi$
$462$	−0.0215494	−	0.246310i	−0.00100257	−	0.0114594i
$463$	−0.370048	−	1.38104i	−0.0171976	−	0.0641823i	0.956794	−	0.290767i	$-0.0939106\pi$
$463$	−0.370048	−	1.38104i	−0.0171976	−	0.0641823i	−0.973991	+	0.226585i	$0.927244\pi$
$464$	−1.56597	−	2.71235i	−0.0726985	−	0.125917i
$465$	6.04128	−	17.0731i	0.280158	−	0.791748i
$466$	23.9079	+	4.21561i	1.10751	+	0.195285i
$467$	−1.81454	+	6.77195i	−0.0839668	+	0.313368i	−0.995117	−	0.0987071i	$-0.968529\pi$
$467$	−1.81454	+	6.77195i	−0.0839668	+	0.313368i	0.911150	+	0.412075i	$0.135196\pi$
$468$	−1.92524	+	0.515866i	−0.0889941	+	0.0238459i
$469$	0.285880	+	0.239882i	0.0132007	+	0.0110767i
$470$	−3.16882	−	11.4157i	−0.146167	−	0.526567i
$471$	−1.52361	−	4.18609i	−0.0702044	−	0.192885i
$472$	−8.62685	−	0.754752i	−0.397083	−	0.0347403i
$473$	−49.0295	−	34.3308i	−2.25438	−	1.57853i
$474$	16.6824			0.766249
$475$	4.39995	+	21.3457i	0.201884	+	0.979410i
$476$	−0.404405			−0.0185359
$477$	−4.04598	−	2.83302i	−0.185253	−	0.129715i
$478$	−3.33224	−	0.291534i	−0.152413	−	0.0133344i
$479$	3.80461	+	10.4531i	0.173837	+	0.477613i	0.995760	−	0.0919850i	$-0.0293212\pi$
$479$	3.80461	+	10.4531i	0.173837	+	0.477613i	−0.821924	+	0.569598i	$0.807099\pi$
$480$	−0.598083	−	2.15460i	−0.0272986	−	0.0983435i
$481$	−0.914485	−	0.767344i	−0.0416969	−	0.0349879i
$482$	21.2483	−	5.69346i	0.967832	−	0.259330i
$483$	0.0542404	−	0.202428i	0.00246802	−	0.00921079i
$484$	−12.0392	−	2.12284i	−0.547237	−	0.0964926i
$485$	0.487921	−	1.37890i	0.0221554	−	0.0626128i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	7.27611	+	27.1548i	0.329712	+	1.23050i	0.909489	+	0.415727i	$0.136473\pi$
$487$	7.27611	+	27.1548i	0.329712	+	1.23050i	−0.579777	+	0.814775i	$0.696860\pi$
$488$	1.03188	+	11.7944i	0.0467109	+	0.533908i
$489$	−14.0301	−	5.10652i	−0.634461	−	0.230925i
$490$	2.85507	+	15.3839i	0.128979	+	0.694974i
$491$	−11.9877	+	10.0589i	−0.540999	+	0.453952i	−0.871879	−	0.489721i	$-0.837099\pi$
$491$	−11.9877	+	10.0589i	−0.540999	+	0.453952i	0.330881	+	0.943673i	$0.392654\pi$
$492$	2.74145	−	3.91519i	0.123594	−	0.176510i
$493$	17.4564	+	17.4564i	0.786196	+	0.786196i
$494$	5.65614	+	6.59458i	0.254482	+	0.296704i
$495$	−8.77149	+	6.25984i	−0.394249	+	0.281359i
$496$	7.97621	−	1.40642i	0.358142	−	0.0631501i
$497$	0.0156951	−	0.179396i	0.000704021	−	0.00804699i
$498$	−1.35714	+	2.91041i	−0.0608151	+	0.130418i
$499$	−9.86195	+	27.0955i	−0.441481	+	1.21296i	0.497036	+	0.867730i	$0.334422\pi$
$499$	−9.86195	+	27.0955i	−0.441481	+	1.21296i	−0.938518	+	0.345231i	$0.887801\pi$
$500$	−4.45073	+	10.2563i	−0.199043	+	0.458674i
$501$	−3.86559	+	6.69540i	−0.172702	+	0.299129i
$502$	−9.30791	−	2.49405i	−0.415432	−	0.111315i
$503$	0.253327	+	0.361788i	0.0112953	+	0.0161313i	0.824760	−	0.565483i	$-0.191310\pi$
$503$	0.253327	+	0.361788i	0.0112953	+	0.0161313i	−0.813465	+	0.581614i	$0.802421\pi$
$504$	0.00890906	−	0.0505258i	0.000396841	−	0.00225060i
$505$	−5.53595	+	12.1553i	−0.246346	+	0.540904i
$506$	−17.0480	−	9.84266i	−0.757875	−	0.437560i
$507$	−8.99299	+	0.786785i	−0.399393	+	0.0349424i
$508$	5.33998	+	11.4516i	0.236923	+	0.508084i
$509$	−26.0232	+	9.47169i	−1.15346	+	0.419825i	−0.846757	−	0.531980i	$-0.821448\pi$
$509$	−26.0232	+	9.47169i	−1.15346	+	0.419825i	−0.306703	+	0.951805i	$0.599226\pi$
$510$	8.94925	+	15.1844i	0.396279	+	0.672378i
$511$	−0.128127	−	0.726642i	−0.00566799	−	0.0321448i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.46141	+	3.59742i	−0.108674	+	0.158830i
$514$			12.3327i			0.543970i
$515$	17.7438	−	0.159128i	0.781885	−	0.00701200i
$516$	−7.98331	−	9.51413i	−0.351445	−	0.418836i
$517$	−23.1414	−	10.7910i	−1.01776	−	0.474587i
$518$	0.0278496	−	0.0129865i	0.00122364	−	0.000570594i
$519$	−10.3606	+	12.3473i	−0.454779	+	0.541985i
$520$	0.428237	+	4.43620i	0.0187795	+	0.194540i
$521$	20.0898	−	11.5989i	0.880150	−	0.508155i	0.00944214	−	0.999955i	$-0.496994\pi$
$521$	20.0898	−	11.5989i	0.880150	−	0.508155i	0.870708	+	0.491801i	$0.163661\pi$
$522$	−2.56554	+	1.79641i	−0.112291	+	0.0786268i
$523$	22.6498	−	15.8595i	0.990405	−	0.693489i	0.0383016	−	0.999266i	$-0.487805\pi$
$523$	22.6498	−	15.8595i	0.990405	−	0.693489i	0.952103	+	0.305777i	$0.0989163\pi$
$524$	11.9604	−	6.90531i	0.522490	−	0.301660i
$525$	−0.193521	+	0.168390i	−0.00844597	+	0.00734912i
$526$	−17.1154	+	20.3974i	−0.746268	+	0.889367i
$527$	−57.8596	+	26.9804i	−2.52040	+	1.17528i
$528$	−4.36770	−	2.03669i	−0.190080	−	0.0886357i
$529$	4.05910	+	4.83745i	0.176483	+	0.210324i
$530$	−7.73925	+	7.87932i	−0.336172	+	0.342256i
$531$			8.65980i			0.375803i
$532$	−0.215376	+	0.0602130i	−0.00933772	+	0.00261056i
$533$	−6.73618	+	6.73618i	−0.291776	+	0.291776i
$534$	−2.04352	−	11.5894i	−0.0884317	−	0.501521i
$535$	−13.8000	+	8.13329i	−0.596625	+	0.351633i
$536$	6.83525	−	2.48783i	0.295238	−	0.107458i
$537$	10.8764	+	23.3246i	0.469353	+	1.00653i
$538$	15.6179	−	1.36639i	0.673336	−	0.0589093i
$539$	29.2040	+	16.8609i	1.25791	+	0.726252i
$540$	−2.09427	+	0.783593i	−0.0901232	+	0.0337205i
$541$	6.77271	−	38.4099i	0.291181	−	1.65137i	−0.391149	−	0.920327i	$-0.627922\pi$
$541$	6.77271	−	38.4099i	0.291181	−	1.65137i	0.682330	−	0.731044i	$-0.260967\pi$
$542$	−0.414145	−	0.591460i	−0.0177890	−	0.0254054i
$543$	−20.3470	−	5.45196i	−0.873173	−	0.233966i
$544$	−3.94117	+	6.82630i	−0.168976	+	0.292675i
$545$	−2.78909	+	35.5484i	−0.119472	+	1.52273i
$546$	−0.0349747	+	0.0960921i	−0.00149678	+	0.00411236i
$547$	2.14027	−	4.58983i	0.0915114	−	0.196247i	−0.855225	−	0.518257i	$-0.826581\pi$
$547$	2.14027	−	4.58983i	0.0915114	−	0.196247i	0.946736	+	0.322011i	$0.104359\pi$
$548$	−0.758882	+	8.67406i	−0.0324178	+	0.370538i
$549$	11.6596	−	2.05590i	0.497619	−	0.0877437i
$550$	10.5735	+	21.6524i	0.450855	+	0.923260i
$551$	11.8960	+	6.69769i	0.506785	+	0.285331i
$552$	−2.88835	−	2.88835i	−0.122936	−	0.122936i
$553$	0.490921	−	0.701109i	0.0208761	−	0.0298142i
$554$	14.3134	−	12.0104i	0.608120	−	0.510273i
$555$	−1.10391	−	0.758303i	−0.0468583	−	0.0321882i
$556$	−4.37557	−	1.59258i	−0.185565	−	0.0675403i
$557$	2.33140	+	26.6480i	0.0987847	+	1.12911i	0.870172	+	0.492748i	$0.164008\pi$
$557$	2.33140	+	26.6480i	0.0987847	+	1.12911i	−0.771387	+	0.636366i	$0.780437\pi$
$558$	−2.09624	−	7.82328i	−0.0887409	−	0.331186i
$559$	12.3773	+	21.4381i	0.523504	+	0.906735i
$560$	−0.108151	−	0.0382689i	−0.00457021	−	0.00161716i
$561$	37.4097	+	6.59633i	1.57944	+	0.278497i
$562$	−1.37953	+	5.14848i	−0.0581920	+	0.217175i
$563$	23.8348	−	6.38652i	1.00452	−	0.269160i	0.281181	−	0.959655i	$-0.409274\pi$
$563$	23.8348	−	6.38652i	1.00452	−	0.269160i	0.723337	+	0.690495i	$0.242607\pi$
$564$	−4.05873	−	3.40568i	−0.170903	−	0.143405i
$565$	3.72230	−	6.58285i	0.156598	−	0.276942i
$566$	3.46641	+	9.52389i	0.145704	+	0.400319i
$567$	−0.0511100	−	0.00447154i	−0.00214642	−	0.000187787i
$568$	−2.87522	−	2.01325i	−0.120641	−	0.0844740i
$569$	−27.4605			−1.15120			−0.575602	−	0.817730i	$-0.695232\pi$
$569$	−27.4605			−1.15120			−0.575602	+	0.817730i	$0.695232\pi$
$570$	7.02699	+	6.75436i	0.294328	+	0.282909i
$571$	21.5530			0.901966			0.450983	−	0.892533i	$-0.351074\pi$
$571$	21.5530			0.901966			0.450983	+	0.892533i	$0.351074\pi$
$572$	7.86832	+	5.50946i	0.328991	+	0.230362i
$573$	3.71622	+	0.325127i	0.155247	+	0.0135824i
$574$	−0.0838690	−	0.230428i	−0.00350063	−	0.00961789i
$575$	2.14466	+	20.3108i	0.0894385	+	0.847020i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	0.0687285	−	0.0184157i	0.00286120	−	0.000766658i	−0.257388	−	0.966308i	$-0.582862\pi$
$577$	0.0687285	−	0.0184157i	0.00286120	−	0.000766658i	0.260249	+	0.965541i	$0.416195\pi$
$578$	11.6808	−	43.5934i	0.485858	−	1.81325i
$579$	−0.248263	−	0.0437754i	−0.0103174	−	0.00181924i
$580$	3.01650	+	6.32030i	0.125253	+	0.262436i
$581$	0.0823776	+	0.142682i	0.00341760	+	0.00591946i
$582$	−0.169302	−	0.631843i	−0.00701778	−	0.0261907i
$583$	2.07459	+	23.7127i	0.0859207	+	0.982078i
$584$	−13.5143	−	4.91880i	−0.559226	−	0.203541i
$585$	4.38200	−	0.813248i	0.181173	−	0.0336237i
$586$	−0.00160887	+	0.00135000i	−6.64619e−5	+	5.57682e-5i
$587$	−17.6797	+	25.2492i	−0.729719	+	1.04215i	0.267195	+	0.963643i	$0.413903\pi$
$587$	−17.6797	+	25.2492i	−0.729719	+	1.04215i	−0.996914	+	0.0785041i	$0.974986\pi$
$588$	4.94789	+	4.94789i	0.204047	+	0.204047i
$589$	−26.7974	+	22.9839i	−1.10417	+	0.947036i
$590$	19.0991	+	3.19136i	0.786298	+	0.131386i
$591$	−6.76499	+	1.19285i	−0.278274	+	0.0490673i
$592$	0.0522009	−	0.596659i	0.00214545	−	0.0245226i
$593$	−3.29390	+	7.06378i	−0.135264	+	0.290075i	−0.962259	−	0.272134i	$-0.912271\pi$
$593$	−3.29390	+	7.06378i	−0.135264	+	0.290075i	0.826995	+	0.562209i	$0.190048\pi$
$594$	−1.64827	+	4.52859i	−0.0676294	+	0.185810i
$595$	0.901506	+	0.0707313i	0.0369582	+	0.00289970i
$596$	−2.81868	+	4.88210i	−0.115458	+	0.199979i
$597$	−7.35130	−	1.96978i	−0.300869	−	0.0806176i
$598$	4.66979	+	6.66914i	0.190962	+	0.272722i
$599$	−1.06026	+	6.01304i	−0.0433211	+	0.245686i	−0.998777	−	0.0494489i	$-0.984254\pi$
$599$	−1.06026	+	6.01304i	−0.0433211	+	0.245686i	0.955456	+	0.295135i	$0.0953646\pi$
$600$	0.956412	+	4.90768i	0.0390454	+	0.200355i
$601$	−18.3960	−	10.6209i	−0.750388	−	0.433237i	0.0754461	−	0.997150i	$-0.475962\pi$
$601$	−18.3960	−	10.6209i	−0.750388	−	0.433237i	−0.825834	+	0.563913i	$0.809295\pi$
$602$	−0.634777	+	0.0555358i	−0.0258716	+	0.00226347i
$603$	−3.07409	−	6.59241i	−0.125187	−	0.268464i
$604$	−5.39360	+	1.96311i	−0.219462	+	0.0798778i
$605$	26.4667	+	6.83795i	1.07602	+	0.278002i
$606$	1.03724	+	5.88249i	0.0421351	+	0.238960i
$607$	−28.1711	+	28.1711i	−1.14343	+	1.14343i	−0.155611	+	0.987818i	$0.549735\pi$
$607$	−28.1711	+	28.1711i	−1.14343	+	1.14343i	−0.987818	+	0.155611i	$0.950265\pi$
$608$	−1.08258	+	4.22232i	−0.0439043	+	0.171238i
$609$			0.160685i			0.00651129i
$610$	−0.237410	−	26.4728i	−0.00961244	−	1.07185i
$611$	6.78803	+	8.08966i	0.274614	+	0.327273i
$612$	7.14382	+	3.33122i	0.288772	+	0.134657i
$613$	−37.8203	+	17.6359i	−1.52755	+	0.712306i	−0.991284	−	0.131745i	$-0.957942\pi$
$613$	−37.8203	+	17.6359i	−1.52755	+	0.712306i	−0.536262	+	0.844051i	$0.680164\pi$
$614$	3.87823	−	4.62190i	0.156513	−	0.186525i
$615$	−6.79606	+	8.24833i	−0.274043	+	0.332605i
$616$	−0.214126	+	0.123626i	−0.00862738	+	0.00498102i
$617$	3.23143	−	2.26267i	0.130092	−	0.0910916i	−0.506719	−	0.862111i	$-0.669142\pi$
$617$	3.23143	−	2.26267i	0.130092	−	0.0910916i	0.636811	+	0.771020i	$0.280253\pi$
$618$	6.50045	−	4.55166i	0.261486	−	0.183095i
$619$	25.3177	−	14.6172i	1.01760	−	0.587514i	0.104195	−	0.994557i	$-0.466773\pi$
$619$	25.3177	−	14.6172i	1.01760	−	0.587514i	0.913409	+	0.407043i	$0.133440\pi$
$620$	−18.0267	+	1.74016i	−0.723969	+	0.0698865i
$621$	−2.62563	+	3.12910i	−0.105363	+	0.125566i
$622$	−15.1116	+	7.04665i	−0.605920	+	0.282545i
$623$	−0.547200	−	0.255163i	−0.0219231	−	0.0102229i
$624$	1.28117	+	1.52684i	0.0512880	+	0.0611226i
$625$	11.7155	−	22.0850i	0.468620	−	0.883400i
$626$		−	16.7936i		−	0.671207i
$627$	20.9056	−	2.05699i	0.834888	−	0.0821483i
$628$	−3.14998	+	3.14998i	−0.125698	+	0.125698i
$629$	0.819799	+	4.64931i	0.0326875	+	0.185380i
$630$	−0.0286973	+	0.111075i	−0.00114333	+	0.00442532i
$631$	−10.8854	+	3.96197i	−0.433342	+	0.157724i	−0.549475	−	0.835510i	$-0.685172\pi$
$631$	−10.8854	+	3.96197i	−0.433342	+	0.157724i	0.116133	+	0.993234i	$0.462950\pi$
$632$	−7.05030	−	15.1194i	−0.280446	−	0.601418i
$633$	1.76461	−	0.154383i	0.0701368	−	0.00613617i
$634$	−9.19493	−	5.30870i	−0.365177	−	0.210835i
$635$	−9.90106	−	26.4621i	−0.392912	−	1.05012i
$636$	−0.857688	+	4.86419i	−0.0340095	+	0.192878i
$637$	−7.99956	−	11.4246i	−0.316954	−	0.452658i
$638$	14.5793	+	3.90650i	0.577198	+	0.154660i
$639$	−1.75500	+	3.03974i	−0.0694266	+	0.120250i
$640$	−1.69997	+	1.45262i	−0.0671972	+	0.0574198i
$641$	1.16589	−	3.20325i	0.0460497	−	0.126521i	−0.914536	−	0.404505i	$-0.867444\pi$
$641$	1.16589	−	3.20325i	0.0460497	−	0.126521i	0.960586	+	0.277984i	$0.0896662\pi$
$642$	−3.02749	+	6.49247i	−0.119486	+	0.256237i
$643$	−0.801360	+	9.15959i	−0.0316026	+	0.361219i	0.963884	+	0.266321i	$0.0858081\pi$
$643$	−0.801360	+	9.15959i	−0.0316026	+	0.361219i	−0.995487	+	0.0948981i	$0.969747\pi$
$644$	−0.206385	+	0.0363912i	−0.00813271	+	0.00143402i
$645$	16.1325	+	22.6054i	0.635216	+	0.890086i
$646$	−0.371482	−	34.3563i	−0.0146158	−	1.35173i
$647$	2.46456	+	2.46456i	0.0968917	+	0.0968917i	0.753891	−	0.656999i	$-0.228175\pi$
$647$	2.46456	+	2.46456i	0.0968917	+	0.0968917i	−0.656999	+	0.753891i	$0.728175\pi$
$648$	−0.573576	+	0.819152i	−0.0225322	+	0.0321793i
$649$	31.9697	−	26.8258i	1.25492	−	1.05300i
$650$	−0.178733	−	9.96416i	−0.00701048	−	0.390826i
$651$	−0.390474	−	0.142121i	−0.0153039	−	0.00557016i
$652$	1.30128	+	14.8737i	0.0509619	+	0.582497i
$653$	−2.68088	−	10.0052i	−0.104911	−	0.391533i	0.893424	−	0.449214i	$-0.148296\pi$
$653$	−2.68088	−	10.0052i	−0.104911	−	0.391533i	−0.998335	+	0.0576809i	$0.981629\pi$
$654$	7.97329	+	13.8101i	0.311780	+	0.540019i
$655$	−27.8700	+	13.3015i	−1.08897	+	0.519734i
$656$	−4.70695	−	0.829963i	−0.183776	−	0.0324046i
$657$	−3.72224	+	13.8916i	−0.145218	+	0.541962i
$658$	−0.262568	+	0.0703548i	−0.0102360	+	0.00274272i
$659$	−37.4927	−	31.4601i	−1.46051	−	1.22551i	−0.924436	−	0.381338i	$-0.875464\pi$
$659$	−37.4927	−	31.4601i	−1.46051	−	1.22551i	−0.536071	−	0.844173i	$-0.680092\pi$
$660$	9.38033	+	5.30415i	0.365129	+	0.206464i
$661$	−2.26266	−	6.21660i	−0.0880072	−	0.241798i	0.887879	−	0.460076i	$-0.152178\pi$
$661$	−2.26266	−	6.21660i	−0.0880072	−	0.241798i	−0.975886	+	0.218279i	$0.929956\pi$
$662$	12.8273	+	1.12225i	0.498549	+	0.0436174i
$663$	−12.8694	−	9.01128i	−0.499808	−	0.349969i
$664$	3.21128			0.124622
$665$	0.490650	−	0.0965581i	0.0190266	−	0.00374436i
$666$	−0.598939			−0.0232084
$667$	10.4796	+	7.33789i	0.405771	+	0.284124i
$668$	7.70177	+	0.673817i	0.297990	+	0.0260708i
$669$	−8.87330	−	24.3792i	−0.343062	−	0.942554i
$670$	−15.6724	+	4.35041i	−0.605477	+	0.168071i
$671$	−43.7082	−	36.6756i	−1.68734	−	1.41584i
$672$	−0.0495570	+	0.0132788i	−0.00191170	+	0.000512239i
$673$	4.53910	−	16.9401i	0.174969	−	0.652995i	−0.821587	−	0.570082i	$-0.806911\pi$
$673$	4.53910	−	16.9401i	0.174969	−	0.652995i	0.996557	−	0.0829122i	$-0.0264221\pi$
$674$	13.7367	+	2.42214i	0.529116	+	0.0932975i
$675$	4.80564	−	1.38051i	0.184969	−	0.0531357i
$676$	4.51367	+	7.81791i	0.173603	+	0.300689i
$677$	5.31144	+	19.8226i	0.204135	+	0.761843i	0.989711	+	0.143078i	$0.0457001\pi$
$677$	5.31144	+	19.8226i	0.204135	+	0.761843i	−0.785576	+	0.618765i	$0.787633\pi$
$678$	−0.294760	−	3.36912i	−0.0113202	−	0.129390i
$679$	−0.0315364	−	0.0114783i	−0.00121026	−	0.000440497i
$680$	9.97966	−	14.5280i	0.382702	−	0.557123i
$681$	−5.29743	+	4.44507i	−0.202998	+	0.170336i
$682$	−22.3879	+	31.9732i	−0.857277	+	1.22432i
$683$	12.3897	+	12.3897i	0.474080	+	0.474080i	0.903232	−	0.429152i	$-0.141188\pi$
$683$	12.3897	+	12.3897i	0.474080	+	0.474080i	−0.429152	+	0.903232i	$0.641188\pi$
$684$	4.30061	+	0.710458i	0.164438	+	0.0271650i
$685$	3.20883	−	19.2036i	0.122603	−	0.733733i
$686$	0.707228	−	0.124703i	0.0270021	−	0.00476120i
$687$	1.98903	−	22.7348i	0.0758864	−	0.867385i
$688$	−5.24884	+	11.2562i	−0.200110	+	0.429138i
$689$	3.36706	−	9.25092i	0.128275	−	0.352432i
$690$	5.93359	+	6.94395i	0.225888	+	0.264351i
$691$	−25.0174	+	43.3315i	−0.951708	+	1.64841i	−0.209980	+	0.977706i	$0.567340\pi$
$691$	−25.0174	+	43.3315i	−0.951708	+	1.64841i	−0.741728	+	0.670701i	$0.765993\pi$
$692$	15.5690	+	4.17170i	0.591844	+	0.158584i
$693$	0.141818	+	0.202536i	0.00538720	+	0.00769372i
$694$	3.64737	−	20.6853i	0.138452	−	0.785203i
$695$	9.47555	+	4.31550i	0.359428	+	0.163696i
$696$	2.71235	+	1.56597i	0.102811	+	0.0593581i
$697$	37.5308	−	3.28352i	1.42158	−	0.124372i
$698$	6.81137	+	14.6070i	0.257814	+	0.552884i
$699$	−22.8127	+	8.30314i	−0.862855	+	0.314054i
$700$	0.234399	+	0.104225i	0.00885943	+	0.00393935i
$701$	−4.62423	−	26.2253i	−0.174655	−	0.990516i	−0.938542	−	0.345166i	$-0.887823\pi$
$701$	−4.62423	−	26.2253i	−0.174655	−	0.990516i	0.763887	−	0.645350i	$-0.223289\pi$
$702$	1.40937	−	1.40937i	0.0531933	−	0.0531933i
$703$	1.12885	+	2.35404i	0.0425755	+	0.0887844i
$704$			4.81922i			0.181631i
$705$	8.45213	+	8.30188i	0.318325	+	0.312667i
$706$	1.39729	+	1.66522i	0.0525875	+	0.0626714i
$707$	0.277746	+	0.129515i	0.0104457	+	0.00487091i
$708$	7.84845	−	3.65979i	0.294963	−	0.137543i
$709$	12.8661	−	15.3332i	0.483195	−	0.575849i	−0.468278	−	0.883581i	$-0.655126\pi$
$709$	12.8661	−	15.3332i	0.483195	−	0.575849i	0.951473	+	0.307732i	$0.0995700\pi$
$710$	6.05736	+	4.99085i	0.227329	+	0.187303i
$711$	−14.4474	+	8.34121i	−0.541820	+	0.312820i
$712$	−9.63991	+	6.74994i	−0.361271	+	0.252965i
$713$	−27.1003	+	18.9759i	−1.01492	+	0.710651i
$714$	0.350225	−	0.202202i	0.0131068	−	0.00756724i
$715$	−16.5766	−	13.6580i	−0.619929	−	0.510779i
$716$	16.5427	−	19.7148i	0.618229	−	0.736777i
$717$	3.03157	−	1.41365i	0.113216	−	0.0527936i
$718$	−7.16515	−	3.34116i	−0.267401	−	0.124691i
$719$	−0.343068	−	0.408853i	−0.0127943	−	0.0152476i	0.759609	−	0.650380i	$-0.225390\pi$
$719$	−0.343068	−	0.408853i	−0.0127943	−	0.0152476i	−0.772404	+	0.635132i	$0.780946\pi$
$720$	1.59525	+	1.56690i	0.0594516	+	0.0583948i
$721$		−	0.407137i		−	0.0151626i
$722$	−5.31325	−	18.2420i	−0.197739	−	0.678896i
$723$	−15.5548	+	15.5548i	−0.578490	+	0.578490i
$724$	3.65786	+	20.7447i	0.135943	+	0.770972i
$725$	−5.61900	−	14.6169i	−0.208684	−	0.542859i
$726$	11.4877	−	4.18117i	0.426348	−	0.155178i
$727$	20.2526	+	43.4318i	0.751127	+	1.61080i	0.791168	+	0.611599i	$0.209474\pi$
$727$	20.2526	+	43.4318i	0.751127	+	1.61080i	−0.0400405	+	0.999198i	$0.512749\pi$
$728$	0.101870	−	0.00891247i	0.00377555	−	0.000330318i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	29.2660	+	13.3288i	1.08318	+	0.493319i
$731$	16.9997	−	96.4099i	0.628756	−	3.56585i
$732$	−6.79084	−	9.69832i	−0.250997	−	0.358460i
$733$	−23.5736	−	6.31652i	−0.870709	−	0.233306i	−0.204315	−	0.978905i	$-0.565497\pi$
$733$	−23.5736	−	6.31652i	−0.870709	−	0.233306i	−0.666394	+	0.745599i	$0.732163\pi$
$734$	6.17831	−	10.7011i	0.228046	−	0.394987i
$735$	−10.1645	−	11.8953i	−0.374924	−	0.438765i
$736$	−1.39707	+	3.83841i	−0.0514965	+	0.141486i
$737$	−14.8147	+	31.7703i	−0.545708	+	1.17027i
$738$	−0.416567	+	4.76138i	−0.0153340	+	0.175269i
$739$	29.0538	−	5.12296i	1.06876	−	0.188451i	0.388519	−	0.921441i	$-0.372987\pi$
$739$	29.0538	−	5.12296i	1.06876	−	0.188451i	0.680240	+	0.732989i	$0.261876\pi$
$740$	−0.220724	+	1.32095i	−0.00811399	+	0.0485592i
$741$	−8.19565	−	2.88301i	−0.301075	−	0.105910i
$742$	0.179187	+	0.179187i	0.00657814	+	0.00657814i
$743$	−3.17978	+	4.54120i	−0.116655	+	0.166601i	−0.873233	−	0.487303i	$-0.837981\pi$
$743$	−3.17978	+	4.54120i	−0.116655	+	0.166601i	0.756578	+	0.653903i	$0.226870\pi$
$744$	−6.20439	+	5.20610i	−0.227464	+	0.190865i
$745$	7.13734	−	10.3903i	0.261492	−	0.380670i
$746$	−25.4743	−	9.27189i	−0.932681	−	0.339468i
$747$	−0.279881	−	3.19906i	−0.0102403	−	0.117047i
$748$	−9.83170	−	36.6924i	−0.359482	−	1.34161i
$749$	0.183766	+	0.318293i	0.00671468	+	0.0116302i
$750$	−1.27369	−	11.1076i	−0.0465085	−	0.405590i
$751$	−10.4626	−	1.84485i	−0.381787	−	0.0673194i	−0.0205389	−	0.999789i	$-0.506538\pi$
$751$	−10.4626	−	1.84485i	−0.381787	−	0.0673194i	−0.361248	+	0.932470i	$0.617649\pi$
$752$	−1.37130	+	5.11776i	−0.0500061	+	0.186625i
$753$	9.30791	−	2.49405i	0.339199	−	0.0908881i
$754$	−4.78199	−	4.01257i	−0.174150	−	0.146129i
$755$	12.3669	−	3.43285i	0.450076	−	0.124934i
$756$	0.0175474	+	0.0482111i	0.000638193	+	0.00175342i
$757$	−28.5589	−	2.49858i	−1.03799	−	0.0908125i	−0.444602	−	0.895728i	$-0.646655\pi$
$757$	−28.5589	−	2.49858i	−1.03799	−	0.0908125i	−0.593389	+	0.804916i	$0.702211\pi$
$758$	9.00280	+	6.30383i	0.326996	+	0.228965i
$759$	19.6853			0.714532
$760$	3.15179	−	9.22313i	0.114328	−	0.334558i
$761$	10.5212			0.381392			0.190696	−	0.981649i	$-0.438925\pi$
$761$	10.5212			0.381392			0.190696	+	0.981649i	$0.438925\pi$
$762$	−10.3504	−	7.24741i	−0.374954	−	0.262546i
$763$	0.815029	+	0.0713058i	0.0295060	+	0.00258144i
$764$	−1.27588	−	3.50544i	−0.0461596	−	0.126822i
$765$	−15.3425	−	8.67548i	−0.554709	−	0.313663i
$766$	−3.13505	−	2.63062i	−0.113274	−	0.0950481i
$767$	−16.6722	+	4.46729i	−0.601997	+	0.161305i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	20.0156	+	3.52930i	0.721782	+	0.127270i	0.522459	−	0.852664i	$-0.325015\pi$
$769$	20.0156	+	3.52930i	0.721782	+	0.127270i	0.199323	+	0.979934i	$0.436126\pi$
$770$	0.498956	−	0.238137i	0.0179811	−	0.00858188i
$771$	−6.16633	−	10.6804i	−0.222075	−	0.384645i
$772$	0.0652464	+	0.243503i	0.00234827	+	0.00876386i
$773$	−0.887301	−	10.1419i	−0.0319140	−	0.364779i	−0.995313	−	0.0967068i	$-0.969169\pi$
$773$	−0.887301	−	10.1419i	−0.0319140	−	0.364779i	0.963399	−	0.268072i	$-0.0863865\pi$
$774$	11.6708	+	4.24783i	0.419499	+	0.152685i
$775$	40.4897	−	0.726288i	1.45443	−	0.0260890i
$776$	−0.501094	+	0.420468i	−0.0179882	+	0.0150939i
$777$	−0.0176252	+	0.0251715i	−0.000632302	+	0.000903021i
$778$	−0.398349	−	0.398349i	−0.0142815	−	0.0142815i
$779$	19.4990	−	7.33678i	0.698626	−	0.262867i
$780$	−2.58897	−	3.62774i	−0.0926998	−	0.129894i
$781$	16.6585	−	2.93734i	0.596087	−	0.105106i
$782$	2.80618	−	32.0748i	0.100349	−	1.14699i
$783$	1.32362	−	2.83851i	0.0473022	−	0.101440i
$784$	2.39324	−	6.57537i	0.0854729	−	0.234835i
$785$	7.57293	−	6.47105i	0.270290	−	0.230962i
$786$	−6.90531	+	11.9604i	−0.246304	+	0.426612i
$787$	5.72330	+	1.53355i	0.204014	+	0.0546653i	0.359379	−	0.933192i	$-0.382989\pi$
$787$	5.72330	+	1.53355i	0.204014	+	0.0546653i	−0.155365	+	0.987857i	$0.549655\pi$
$788$	3.94010	+	5.62704i	0.140360	+	0.200455i
$789$	4.62371	−	26.2223i	0.164608	−	0.933540i
$790$	13.0722	+	34.9376i	0.465089	+	1.24302i
$791$	−0.150267	−	0.0867569i	−0.00534290	−	0.00308472i
$792$	4.80089	−	0.420023i	0.170592	−	0.0149249i
$793$	9.97288	+	21.3869i	0.354147	+	0.759472i
$794$	−14.5759	+	5.30519i	−0.517279	+	0.188274i
$795$	2.76273	−	10.6933i	0.0979839	−	0.379253i
$796$	1.32157	+	7.49501i	0.0468419	+	0.265653i
$797$	2.55282	−	2.55282i	0.0904256	−	0.0904256i	−0.660447	−	0.750873i	$-0.729633\pi$
$797$	2.55282	−	2.55282i	0.0904256	−	0.0904256i	0.750873	+	0.660447i	$0.229633\pi$
$798$	0.156414	−	0.159834i	0.00553701	−	0.00565805i
$799$		−	41.7629i		−	1.47747i
$800$	4.04367	−	2.94088i	0.142965	−	0.103976i
$801$	7.56443	+	9.01493i	0.267276	+	0.318527i
$802$	−32.3934	−	15.1053i	−1.14385	−	0.533387i
$803$	62.8146	−	29.2909i	2.21668	−	1.03365i
$804$	−4.67559	+	5.57215i	−0.164895	+	0.196515i
$805$	0.466442	−	0.0450268i	0.0164399	−	0.00158699i
$806$	13.9803	−	8.07152i	0.492434	−	0.284307i
$807$	−12.8423	+	8.99228i	−0.452071	+	0.316543i
$808$	4.89299	−	3.42611i	0.172135	−	0.120530i
$809$	30.5346	−	17.6292i	1.07354	−	0.619809i	0.144394	−	0.989520i	$-0.453877\pi$
$809$	30.5346	−	17.6292i	1.07354	−	0.619809i	0.929147	+	0.369711i	$0.120543\pi$
$810$	1.42190	−	1.72575i	0.0499604	−	0.0606366i
$811$	5.93361	−	7.07140i	0.208357	−	0.248310i	−0.651738	−	0.758444i	$-0.725960\pi$
$811$	5.93361	−	7.07140i	0.208357	−	0.248310i	0.860095	+	0.510134i	$0.170404\pi$
$812$	0.145630	−	0.0679085i	0.00511062	−	0.00238312i
$813$	0.654390	+	0.305147i	0.0229505	+	0.0107020i
$814$	1.85535	+	2.21113i	0.0650302	+	0.0774999i
$815$	−0.299392	−	33.3842i	−0.0104872	−	1.16940i
$816$		−	7.88234i		−	0.275937i
$817$	−5.30115	−	53.8766i	−0.185464	−	1.88490i
$818$	−20.3795	+	20.3795i	−0.712553	+	0.712553i
$819$	−0.0177571	−	0.100706i	−0.000620483	−	0.00351894i
$820$	10.3477	+	2.67342i	0.361356	+	0.0933600i
$821$	−21.9116	+	7.97519i	−0.764722	+	0.278336i	−0.694787	−	0.719216i	$-0.744501\pi$
$821$	−21.9116	+	7.97519i	−0.764722	+	0.278336i	−0.0699347	+	0.997552i	$0.522279\pi$
$822$	−3.67982	−	7.89140i	−0.128348	−	0.275244i
$823$	−31.8768	+	2.78886i	−1.11116	+	0.0972135i	−0.627921	−	0.778277i	$-0.716094\pi$
$823$	−31.8768	+	2.78886i	−1.11116	+	0.0972135i	−0.483235	+	0.875491i	$0.660538\pi$
$824$	−6.87242	−	3.96779i	−0.239412	−	0.138225i
$825$	−19.9831	−	13.4647i	−0.695722	−	0.468782i
$826$	0.0771507	−	0.437543i	0.00268442	−	0.0152241i
$827$	26.0528	+	37.2073i	0.905945	+	1.29382i	0.955482	+	0.295051i	$0.0953365\pi$
$827$	26.0528	+	37.2073i	0.905945	+	1.29382i	−0.0495371	+	0.998772i	$0.515775\pi$
$828$	3.94556	+	1.05721i	0.137118	+	0.0367406i
$829$	−11.0918	+	19.2116i	−0.385236	+	0.667248i	−0.991802	−	0.127785i	$-0.959213\pi$
$829$	−11.0918	+	19.2116i	−0.385236	+	0.667248i	0.606566	+	0.795033i	$0.292547\pi$
$830$	−7.15864	−	0.561660i	−0.248480	−	0.0194955i
$831$	−6.39061	+	17.5580i	−0.221688	+	0.609082i
$832$	0.842342	−	1.80641i	0.0292030	−	0.0626260i
$833$	−4.80713	+	54.9457i	−0.166557	+	1.90376i
$834$	4.58564	−	0.808572i	0.158788	−	0.0279986i
$835$	−17.0511	−	2.84914i	−0.590076	−	0.0985986i
$836$	−10.6993	−	18.0776i	−0.370044	−	0.625225i
$837$	5.72704	+	5.72704i	0.197955	+	0.197955i
$838$	2.92213	−	4.17323i	0.100943	−	0.144162i
$839$	20.1594	−	16.9157i	0.695980	−	0.583996i	−0.224647	−	0.974440i	$-0.572123\pi$
$839$	20.1594	−	16.9157i	0.695980	−	0.583996i	0.920627	+	0.390444i	$0.127678\pi$
$840$	0.112796	−	0.0209336i	0.00389183	−	0.000722278i
$841$	18.0336	+	6.56368i	0.621847	+	0.226334i
$842$	−0.437661	−	5.00249i	−0.0150828	−	0.172397i
$843$	−1.37953	−	5.14848i	−0.0475136	−	0.177323i
$844$	−0.885673	−	1.53403i	−0.0304861	−	0.0528035i
$845$	−8.69459	−	18.2173i	−0.299103	−	0.626693i
$846$	5.21780	+	0.920039i	0.179392	+	0.0316316i
$847$	0.162332	−	0.605831i	0.00557779	−	0.0208166i
$848$	4.77093	−	1.27837i	0.163834	−	0.0438993i
$849$	−7.76395	−	6.51472i	−0.266458	−	0.223585i
$850$	−24.7878	+	30.6406i	−0.850215	+	1.05096i
$851$	0.836757	+	2.29897i	0.0286837	+	0.0788077i
$852$	3.49664	+	0.305916i	0.119793	+	0.0104805i
$853$	38.0216	+	26.6230i	1.30183	+	0.911554i	0.999137	−	0.0415325i	$-0.0132240\pi$
$853$	38.0216	+	26.6230i	1.30183	+	0.911554i	0.302697	+	0.953087i	$0.402113\pi$
$854$	−0.607426			−0.0207857
$855$	−9.46273	−	2.33595i	−0.323619	−	0.0798879i
$856$	7.16365			0.244849
$857$	−37.1499	−	26.0126i	−1.26902	−	0.888575i	−0.271743	−	0.962370i	$-0.587600\pi$
$857$	−37.1499	−	26.0126i	−1.26902	−	0.888575i	−0.997273	+	0.0737951i	$0.976489\pi$
$858$	−9.56890	−	0.837170i	−0.326677	−	0.0285805i
$859$	2.75248	+	7.56238i	0.0939134	+	0.258025i	0.977751	−	0.209769i	$-0.0672712\pi$
$859$	2.75248	+	7.56238i	0.0939134	+	0.258025i	−0.883838	+	0.467794i	$0.845049\pi$
$860$	13.6695	−	24.1744i	0.466128	−	0.824341i
$861$	0.187847	+	0.157622i	0.00640180	+	0.00537175i
$862$	39.0458	−	10.4623i	1.32990	−	0.356347i
$863$	5.58066	−	20.8273i	0.189968	−	0.708970i	−0.803544	−	0.595245i	$-0.797055\pi$
$863$	5.58066	−	20.8273i	0.189968	−	0.708970i	0.993512	−	0.113725i	$-0.0362783\pi$
$864$	0.984808	+	0.173648i	0.0335038	+	0.00590763i
$865$	−33.9770	−	12.0227i	−1.15525	−	0.408783i
$866$	3.85929	+	6.68449i	0.131144	+	0.227148i
$867$	11.6808	+	43.5934i	0.396702	+	1.48051i
$868$	0.0362162	+	0.413953i	0.00122926	+	0.0140505i
$869$	75.5479	+	27.4972i	2.56279	+	0.932778i
$870$	−5.77251	−	3.96529i	−0.195707	−	0.134436i
$871$	11.1061	−	9.31916i	0.376317	−	0.315768i
$872$	9.14658	−	13.0627i	0.309742	−	0.442358i
$873$	0.462541	+	0.462541i	0.0156546	+	0.0156546i
$874$	−3.28121	−	17.5001i	−0.110989	−	0.591948i
$875$	−0.504296	−	0.273338i	−0.0170483	−	0.00924051i
$876$	14.1631	−	2.49734i	0.478528	−	0.0843773i
$877$	−1.36467	+	15.5983i	−0.0460816	+	0.526716i	0.937712	+	0.347413i	$0.112940\pi$
$877$	−1.36467	+	15.5983i	−0.0460816	+	0.526716i	−0.983794	+	0.179303i	$0.942616\pi$
$878$	2.52598	−	5.41699i	0.0852478	−	0.182815i
$879$	0.000718323	−	0.00197358i	2.42284e−5	−	6.65670e-5i
$880$	0.842893	−	10.7431i	0.0284139	−	0.362150i
$881$	12.7119	−	22.0177i	0.428276	−	0.741796i	−0.568444	−	0.822722i	$-0.692454\pi$
$881$	12.7119	−	22.0177i	0.428276	−	0.741796i	0.996720	+	0.0809261i	$0.0257878\pi$
$882$	−6.75894	−	1.81105i	−0.227585	−	0.0609813i
$883$	−18.4976	−	26.4174i	−0.622495	−	0.889015i	0.376810	−	0.926290i	$-0.377021\pi$
$883$	−18.4976	−	26.4174i	−0.622495	−	0.889015i	−0.999305	+	0.0372758i	$0.988132\pi$
$884$	−2.72813	+	15.4720i	−0.0917571	+	0.520380i
$885$	−18.1360	+	6.78576i	−0.609635	+	0.228101i
$886$	−13.5908	−	7.84667i	−0.456593	−	0.263614i
$887$	43.3798	−	3.79524i	1.45655	−	0.127432i	0.668808	−	0.743435i	$-0.266805\pi$
$887$	43.3798	−	3.79524i	1.45655	−	0.127432i	0.787744	+	0.616003i	$0.211249\pi$
$888$	0.253122	+	0.542823i	0.00849423	+	0.0182159i
$889$	−0.609170	+	0.221720i	−0.0204309	+	0.00743624i
$890$	22.6700	−	13.3610i	0.759901	−	0.447863i
$891$	−0.836850	−	4.74601i	−0.0280355	−	0.158997i
$892$	−18.3450	+	18.3450i	−0.614237	+	0.614237i
$893$	−6.21820	−	22.2419i	−0.208084	−	0.744296i
$894$		−	5.63736i		−	0.188542i
$895$	−40.3254	+	41.0552i	−1.34793	+	1.37232i
$896$	0.0329784	+	0.0393021i	0.00110173	+	0.00131299i
$897$	−7.37872	−	3.44076i	−0.246368	−	0.114883i
$898$	−4.35126	+	2.02903i	−0.145203	+	0.0677095i
$899$	16.3052	−	19.4318i	0.543810	−	0.648087i
$900$	−3.28211	−	3.77197i	−0.109404	−	0.125732i
$901$	−33.7167	+	19.4663i	−1.12326	+	0.648517i
$902$	18.8682	−	13.2116i	0.628242	−	0.439900i
$903$	0.521965	−	0.365484i	0.0173699	−	0.0121625i
$904$	−2.92889	+	1.69100i	−0.0974135	+	0.0562417i
$905$	−4.52586	−	46.8843i	−0.150445	−	1.55849i
$906$	3.68944	−	4.39690i	0.122573	−	0.146077i
$907$	23.2826	−	10.8569i	0.773087	−	0.360496i	0.00429114	−	0.999991i	$-0.498634\pi$
$907$	23.2826	−	10.8569i	0.773087	−	0.360496i	0.768796	+	0.639494i	$0.220856\pi$
$908$	6.26740	+	2.92254i	0.207991	+	0.0969878i
$909$	−3.83952	−	4.57577i	−0.127349	−	0.151769i
$910$	−0.228649	+	0.00205054i	−0.00757964	+	6.79748e-5i
$911$		−	29.3237i		−	0.971537i	−0.874088	−	0.485768i	$-0.838540\pi$
$911$		−	29.3237i		−	0.971537i	0.874088	−	0.485768i	$-0.161460\pi$
$912$	−1.17362	−	4.19793i	−0.0388625	−	0.139007i
$913$	−10.9431	+	10.9431i	−0.362164	+	0.362164i
$914$	2.58819	+	14.6783i	0.0856096	+	0.485516i
$915$	13.4420	+	22.8074i	0.444379	+	0.753989i
$916$	−21.4453	+	7.80545i	−0.708572	+	0.257899i
$917$	0.299449	+	0.642171i	0.00988868	+	0.0212063i
$918$	−7.85234	+	0.686991i	−0.259166	+	0.0226741i
$919$	35.9895	+	20.7786i	1.18718	+	0.685421i	0.957666	−	0.287883i	$-0.0929513\pi$
$919$	35.9895	+	20.7786i	1.18718	+	0.685421i	0.229519	+	0.973304i	$0.426285\pi$
$920$	3.78571	−	8.31229i	0.124811	−	0.274048i
$921$	−1.04770	+	5.94180i	−0.0345229	+	0.195789i
$922$	1.69726	+	2.42393i	0.0558962	+	0.0798280i
$923$	−6.75757	−	1.81068i	−0.222428	−	0.0595994i
$924$	0.123626	−	0.214126i	0.00406699	−	0.00704423i
$925$	0.723080	−	2.90609i	0.0237747	−	0.0955516i
$926$	0.489005	−	1.34353i	0.0160697	−	0.0441512i
$927$	−3.35372	+	7.19208i	−0.110151	+	0.236219i
$928$	0.272967	−	3.12003i	0.00896059	−	0.102420i
$929$	−1.57175	+	0.277142i	−0.0515675	+	0.00909274i	−0.199372	−	0.979924i	$-0.563890\pi$
$929$	−1.57175	+	0.277142i	−0.0515675	+	0.00909274i	0.147805	+	0.989017i	$0.452779\pi$
$930$	14.7415	−	10.5204i	0.483392	−	0.344976i
$931$	5.62087	+	29.9784i	0.184216	+	0.982503i
$932$	17.1663	+	17.1663i	0.562299	+	0.562299i
$933$	9.56370	−	13.6584i	0.313101	−	0.447155i
$934$	−5.37061	+	4.50648i	−0.175732	+	0.147456i
$935$	15.4994	+	83.5149i	0.506885	+	2.73123i
$936$	−1.87295	−	0.681698i	−0.0612193	−	0.0222820i
$937$	−2.00491	−	22.9163i	−0.0654977	−	0.748642i	−0.955943	−	0.293552i	$-0.905163\pi$
$937$	−2.00491	−	22.9163i	−0.0654977	−	0.748642i	0.890445	−	0.455090i	$-0.150393\pi$
$938$	0.0965887	+	0.360474i	0.00315373	+	0.0117699i
$939$	8.39680	+	14.5437i	0.274019	+	0.474615i
$940$	3.95203	−	11.1688i	0.128901	−	0.364285i
$941$	43.6204	+	7.69145i	1.42198	+	0.250734i	0.831145	−	0.556055i	$-0.187686\pi$
$941$	43.6204	+	7.69145i	1.42198	+	0.250734i	0.590839	+	0.806789i	$0.298797\pi$
$942$	1.15297	−	4.30295i	0.0375659	−	0.140198i
$943$	18.8581	−	5.05301i	0.614104	−	0.164549i
$944$	−6.63379	−	5.56641i	−0.215912	−	0.181171i
$945$	−0.0306848	−	0.110542i	−0.000998175	−	0.00359594i
$946$	−20.4712	−	56.2443i	−0.665578	−	1.82866i
$947$	−32.5736	−	2.84982i	−1.05850	−	0.0926068i	−0.455412	−	0.890281i	$-0.650508\pi$
$947$	−32.5736	−	2.84982i	−1.05850	−	0.0926068i	−0.603089	+	0.797674i	$0.706063\pi$
$948$	13.6654	+	9.56865i	0.443833	+	0.310775i
$949$	−28.6647			−0.930497
$950$	−8.63918	+	20.0091i	−0.280292	+	0.649181i
$951$	10.6174			0.344293
$952$	−0.331269	−	0.231957i	−0.0107365	−	0.00751777i
$953$	−26.6550	−	2.33201i	−0.863440	−	0.0755412i	−0.353174	−	0.935558i	$-0.614898\pi$
$953$	−26.6550	−	2.33201i	−0.863440	−	0.0755412i	−0.510266	+	0.860017i	$0.670453\pi$
$954$	−1.68931	−	4.64135i	−0.0546936	−	0.150269i
$955$	2.23109	+	8.03754i	0.0721965	+	0.260089i
$956$	−2.56240	−	2.15011i	−0.0828739	−	0.0695394i
$957$	−14.5793	+	3.90650i	−0.471280	+	0.126279i
$958$	−2.87908	+	10.7449i	−0.0930190	+	0.347151i
$959$	−0.439938	−	0.0775729i	−0.0142063	−	0.00250496i
$960$	0.745906	−	2.10799i	0.0240740	−	0.0680351i
$961$	17.2989	+	29.9626i	0.558030	+	0.966536i
$962$	−0.308972	−	1.15310i	−0.00996165	−	0.0371774i
$963$	−0.624353	−	7.13639i	−0.0201195	−	0.229967i
$964$	20.6712	+	7.52370i	0.665775	+	0.242322i
$965$	−0.102859	−	0.554232i	−0.00331115	−	0.0178414i
$966$	0.160539	−	0.134708i	0.00516526	−	0.00433417i
$967$	6.06923	−	8.66775i	0.195173	−	0.278736i	−0.709623	−	0.704582i	$-0.751135\pi$
$967$	6.06923	−	8.66775i	0.195173	−	0.278736i	0.904796	+	0.425846i	$0.140023\pi$
$968$	−8.64433	−	8.64433i	−0.277839	−	0.277839i
$969$	17.4999	+	29.5677i	0.562177	+	0.949851i
$970$	1.19059	−	0.849671i	0.0382275	−	0.0272813i
$971$	−23.6241	+	4.16556i	−0.758133	+	0.133679i	−0.539335	−	0.842091i	$-0.681324\pi$
$971$	−23.6241	+	4.16556i	−0.758133	+	0.133679i	−0.218797	+	0.975770i	$0.570213\pi$
$972$	0.0871557	−	0.996195i	0.00279552	−	0.0319530i
$973$	0.100962	−	0.216514i	0.00323670	−	0.00694112i
$974$	−9.61512	+	26.4173i	−0.308088	+	0.846466i
$975$	5.13687	+	8.53985i	0.164511	+	0.273494i
$976$	−5.91973	+	10.2533i	−0.189486	+	0.328199i
$977$	−14.7006	−	3.93900i	−0.470313	−	0.126020i	0.0158757	−	0.999874i	$-0.494946\pi$
$977$	−14.7006	−	3.93900i	−0.470313	−	0.126020i	−0.486188	+	0.873854i	$0.661613\pi$
$978$	−8.56377	−	12.2303i	−0.273839	−	0.391083i
$979$	9.84818	−	55.8518i	0.314749	−	1.78503i
$980$	−6.48510	+	14.2394i	−0.207159	+	0.454860i
$981$	−13.8101	−	7.97329i	−0.440924	−	0.254568i
$982$	−15.5893	+	1.36389i	−0.497475	+	0.0435235i
$983$	−5.57271	−	11.9507i	−0.177742	−	0.381169i	0.797172	−	0.603753i	$-0.206329\pi$
$983$	−5.57271	−	11.9507i	−0.177742	−	0.381169i	−0.974913	+	0.222584i	$0.928551\pi$
$984$	4.49132	−	1.63471i	0.143178	−	0.0521126i
$985$	−7.79915	−	13.2330i	−0.248502	−	0.421639i
$986$	4.28686	+	24.3120i	0.136522	+	0.774252i
$987$	0.192213	−	0.192213i	0.00611820	−	0.00611820i
$988$	0.850737	+	8.64619i	0.0270655	+	0.275072i
$989$		−	50.7318i		−	1.61318i
$990$	−10.7757	+	0.0966371i	−0.342474	+	0.00307133i
$991$	22.3606	+	26.6483i	0.710308	+	0.846512i	0.993651	−	0.112506i	$-0.0358879\pi$
$991$	22.3606	+	26.6483i	0.710308	+	0.846512i	−0.283343	+	0.959019i	$0.591443\pi$
$992$	7.34041	+	3.42289i	0.233058	+	0.108677i
$993$	−11.6699	+	5.44178i	−0.370334	+	0.172690i
$994$	0.115754	−	0.137950i	0.00367149	−	0.00437551i
$995$	−1.63518	−	16.9391i	−0.0518386	−	0.537007i
$996$	−2.78105	+	1.60564i	−0.0881209	+	0.0508766i
$997$	13.7505	−	9.62823i	0.435484	−	0.304929i	−0.335200	−	0.942147i	$-0.608804\pi$
$997$	13.7505	−	9.62823i	0.435484	−	0.304929i	0.770684	+	0.637218i	$0.219915\pi$
$998$	−23.6198	+	16.5387i	−0.747671	+	0.523525i
$999$	0.518696	−	0.299469i	0.0164108	−	0.00947479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.a.67.8	✓	120
5.3	odd	4	inner	570.2.bh.a.523.6	yes	120
19.2	odd	18	inner	570.2.bh.a.97.6	yes	120
95.78	even	36	inner	570.2.bh.a.553.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.67.8	✓	120	1.1	even	1	trivial
570.2.bh.a.97.6	yes	120	19.2	odd	18	inner
570.2.bh.a.523.6	yes	120	5.3	odd	4	inner
570.2.bh.a.553.8	yes	120	95.78	even	36	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.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-0.598083 - 2.15460i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.0495570 + 0.0132788i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})\)	\(q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-0.598083 - 2.15460i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-0.0495570 + 0.0132788i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(0.745906 - 2.10799i) q^{10} +(-2.40961 - 4.17357i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(0.173715 + 1.98557i) q^{13} +(-0.0482111 - 0.0175474i) q^{14} +(0.408021 + 2.19853i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(4.52112 - 6.45683i) q^{17} +(0.707107 + 0.707107i) q^{18} +(1.44646 - 4.11190i) q^{19} +(1.82010 - 1.29893i) q^{20} +(0.0505258 - 0.00890906i) q^{21} +(0.420023 - 4.80089i) q^{22} +(1.72629 - 3.70204i) q^{23} +(0.342020 - 0.939693i) q^{24} +(-4.28459 + 2.57726i) q^{25} +(-0.996576 + 1.72612i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(-0.0294275 - 0.0420268i) q^{28} +(-0.543857 + 3.08437i) q^{29} +(-0.926792 + 2.03496i) q^{30} +(-7.01416 - 4.04963i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(2.03669 + 4.36770i) q^{33} +(7.40697 - 2.69592i) q^{34} +(0.0582496 + 0.0988337i) q^{35} +(0.173648 + 0.984808i) q^{36} +(-0.423514 + 0.423514i) q^{37} +(3.54336 - 2.53862i) q^{38} -1.99315i q^{39} +(2.23598 - 0.0200524i) q^{40} +(3.07225 + 3.66136i) q^{41} +(0.0464983 + 0.0216825i) q^{42} +(11.2562 - 5.24884i) q^{43} +(3.09774 - 3.69174i) q^{44} +(-0.214854 - 2.22572i) q^{45} +(3.53750 - 2.04237i) q^{46} +(4.34011 - 3.03898i) q^{47} +(0.819152 - 0.573576i) q^{48} +(-6.05990 + 3.49868i) q^{49} +(-4.98799 - 0.346376i) q^{50} +(-5.06667 + 6.03822i) q^{51} +(-1.80641 + 0.842342i) q^{52} +(-4.47646 - 2.08741i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(-7.55122 + 7.68789i) q^{55} -0.0513052i q^{56} +(-1.79933 + 3.97019i) q^{57} +(-2.21462 + 2.21462i) q^{58} +(1.50376 + 8.52824i) q^{59} +(-1.92639 + 1.13535i) q^{60} +(11.1255 - 4.04933i) q^{61} +(-3.42289 - 7.34041i) q^{62} +(-0.0511100 + 0.00447154i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(4.17421 - 1.56182i) q^{65} +(-0.836850 + 4.74601i) q^{66} +(-4.17215 - 5.95845i) q^{67} +(7.61375 + 2.04010i) q^{68} +(-2.04237 + 3.53750i) q^{69} +(-0.00897340 + 0.114370i) q^{70} +(-1.20049 + 3.29831i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(-1.25344 + 14.3269i) q^{73} +(-0.589839 + 0.104005i) q^{74} +(4.49291 - 2.19402i) q^{75} +(4.35864 - 0.0471284i) q^{76} +(0.174833 + 0.174833i) q^{77} +(1.14322 - 1.63269i) q^{78} +(-12.7795 + 10.7233i) q^{79} +(1.84311 + 1.26608i) q^{80} +(0.939693 + 0.342020i) q^{81} +(0.416567 + 4.76138i) q^{82} +(-0.831140 - 3.10186i) q^{83} +(0.0256526 + 0.0444316i) q^{84} +(-16.6159 - 5.87949i) q^{85} +(12.2311 + 2.15668i) q^{86} +(0.810607 - 3.02523i) q^{87} +(4.65501 - 1.24731i) q^{88} +(9.01493 + 7.56443i) q^{89} +(1.10062 - 1.94644i) q^{90} +(-0.0349747 - 0.0960921i) q^{91} +(4.06920 + 0.356009i) q^{92} +(6.63452 + 4.64554i) q^{93} +5.29829 q^{94} +(-9.72461 - 0.657277i) q^{95} +1.00000 q^{96} +(0.535833 + 0.375195i) q^{97} +(-6.97074 - 0.609861i) q^{98} +(-1.64827 - 4.52859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q - 12 * q^5 + 12 * q^7	\( 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more