LMFDB - Embedded newform 690.2.w.b.493.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			493.6
Character	$\chi$	$=$	690.493
Dual form			690.2.w.b.7.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.98312 - 1.03307i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.653533 - 1.19686i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.98312 - 1.03307i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.653533 - 1.19686i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(-2.05177 + 0.888964i) q^{10} +(-1.60153 - 1.38774i) q^{11} +(-0.0713392 - 0.997452i) q^{12} +(-4.94879 - 2.70224i) q^{13} +(0.566485 + 1.24043i) q^{14} +(-1.43100 - 1.71821i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-1.26500 + 1.68984i) q^{17} +(0.936950 - 0.349464i) q^{18} +(0.299333 - 2.08191i) q^{19} +(2.10996 - 0.740327i) q^{20} +(-1.03059 + 0.893008i) q^{21} +(1.49845 + 1.49845i) q^{22} +(-4.28351 + 2.15673i) q^{23} +1.00000i q^{24} +(2.86553 - 4.09740i) q^{25} +(4.74340 + 3.04840i) q^{26} +(0.599278 + 0.800541i) q^{27} +(-0.476551 - 1.27768i) q^{28} +(5.11643 - 0.735631i) q^{29} +(1.30478 + 1.81591i) q^{30} +(-0.875710 + 0.562784i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(-1.01559 + 1.85992i) q^{33} +(1.38233 - 1.59529i) q^{34} +(-2.53247 - 1.69837i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(3.05803 - 8.19889i) q^{37} +(-0.447092 + 2.05525i) q^{38} +(-1.58855 + 5.41009i) q^{39} +(-2.15739 + 0.587919i) q^{40} +(-3.31299 + 7.25445i) q^{41} +(1.09167 - 0.817212i) q^{42} +(-6.00468 + 1.30624i) q^{43} +(-1.38774 - 1.60153i) q^{44} +(-1.37476 + 1.76353i) q^{45} +(4.42646 - 1.84566i) q^{46} +(-1.39772 + 1.39772i) q^{47} +(0.0713392 - 0.997452i) q^{48} +(2.77913 - 4.32440i) q^{49} +(-3.15054 + 3.88254i) q^{50} +(1.92012 + 0.876889i) q^{51} +(-4.51385 - 3.37902i) q^{52} +(-2.68667 + 1.46703i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-4.60966 - 1.09755i) q^{55} +(0.384188 + 1.30842i) q^{56} +(-2.09796 + 0.150049i) q^{57} +(-5.15587 + 0.368755i) q^{58} +(-0.317333 - 1.08074i) q^{59} +(-1.17191 - 1.90437i) q^{60} +(0.435960 + 0.678367i) q^{61} +(0.913627 - 0.498878i) q^{62} +(1.09167 + 0.817212i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-12.6056 - 0.246428i) q^{65} +(1.14569 - 1.78273i) q^{66} +(1.14642 - 16.0291i) q^{67} +(-1.49261 + 1.49261i) q^{68} +(3.01797 + 3.72718i) q^{69} +(2.40486 + 1.87470i) q^{70} +(-7.09421 - 8.18716i) q^{71} +(0.977147 - 0.212565i) q^{72} +(0.494176 - 0.369936i) q^{73} +(-3.63514 + 7.95985i) q^{74} +(-4.61288 - 1.92908i) q^{75} +(0.592572 - 2.01812i) q^{76} +(-0.614267 + 2.82374i) q^{77} +(1.97045 - 5.28298i) q^{78} +(-13.0887 + 3.84319i) q^{79} +(2.19384 - 0.432514i) q^{80} +(0.654861 - 0.755750i) q^{81} +(3.82208 - 6.99962i) q^{82} +(-1.39625 - 0.520776i) q^{83} +(-1.14718 + 0.737251i) q^{84} +(-0.762922 + 4.65799i) q^{85} +(6.08257 - 0.874542i) q^{86} +(-1.80640 - 4.84313i) q^{87} +(1.26995 + 1.69645i) q^{88} +(14.7728 + 9.49392i) q^{89} +(1.49706 - 1.66096i) q^{90} +7.68899i q^{91} +(-4.54685 + 1.52517i) q^{92} +(0.736068 + 0.736068i) q^{93} +(1.49388 - 1.29445i) q^{94} +(-1.55714 - 4.43790i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(10.5759 - 3.94462i) q^{97} +(-3.08054 + 4.11513i) q^{98} +(2.03329 + 0.597029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$3$	−0.212565	−	0.977147i	−0.122725	−	0.564156i
$3$	−0.212565	−	0.977147i	−0.122725	−	0.564156i
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	1.98312	−	1.03307i	0.886878	−	0.462003i
$5$	1.98312	−	1.03307i	0.886878	−	0.462003i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−0.653533	−	1.19686i	−0.247012	−	0.452369i	0.724527	−	0.689246i	$-0.242058\pi$
$7$	−0.653533	−	1.19686i	−0.247012	−	0.452369i	−0.971540	+	0.236877i	$0.923876\pi$
$8$	−0.977147	−	0.212565i	−0.345474	−	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	−2.05177	+	0.888964i	−0.648825	+	0.281115i
$11$	−1.60153	−	1.38774i	−0.482881	−	0.418418i	0.379103	−	0.925354i	$-0.376233\pi$
$11$	−1.60153	−	1.38774i	−0.482881	−	0.418418i	−0.861984	+	0.506936i	$0.830778\pi$
$12$	−0.0713392	−	0.997452i	−0.0205938	−	0.287940i
$13$	−4.94879	−	2.70224i	−1.37255	−	0.749467i	−0.387519	−	0.921862i	$-0.626668\pi$
$13$	−4.94879	−	2.70224i	−1.37255	−	0.749467i	−0.985028	+	0.172395i	$0.944849\pi$
$14$	0.566485	+	1.24043i	0.151400	+	0.331519i
$15$	−1.43100	−	1.71821i	−0.369484	−	0.443639i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−1.26500	+	1.68984i	−0.306808	+	0.409847i	−0.927272	−	0.374387i	$-0.877853\pi$
$17$	−1.26500	+	1.68984i	−0.306808	+	0.409847i	0.620465	+	0.784234i	$0.286944\pi$
$18$	0.936950	−	0.349464i	0.220841	−	0.0823695i
$19$	0.299333	−	2.08191i	0.0686717	−	0.477622i	−0.926245	−	0.376922i	$-0.876983\pi$
$19$	0.299333	−	2.08191i	0.0686717	−	0.477622i	0.994917	−	0.100700i	$-0.0321083\pi$
$20$	2.10996	−	0.740327i	0.471801	−	0.165542i
$21$	−1.03059	+	0.893008i	−0.224892	+	0.194870i
$22$	1.49845	+	1.49845i	0.319471	+	0.319471i
$23$	−4.28351	+	2.15673i	−0.893175	+	0.449710i
$23$	−4.28351	+	2.15673i	−0.893175	+	0.449710i
$24$			1.00000i			0.204124i
$25$	2.86553	−	4.09740i	0.573107	−	0.819481i
$26$	4.74340	+	3.04840i	0.930258	+	0.597840i
$27$	0.599278	+	0.800541i	0.115331	+	0.154064i
$28$	−0.476551	−	1.27768i	−0.0900596	−	0.241459i
$29$	5.11643	−	0.735631i	0.950097	−	0.136603i	0.350195	−	0.936677i	$-0.386115\pi$
$29$	5.11643	−	0.735631i	0.950097	−	0.136603i	0.599902	+	0.800073i	$0.295206\pi$
$30$	1.30478	+	1.81591i	0.238220	+	0.331539i
$31$	−0.875710	+	0.562784i	−0.157282	+	0.101079i	−0.616914	−	0.787030i	$-0.711618\pi$
$31$	−0.875710	+	0.562784i	−0.157282	+	0.101079i	0.459632	+	0.888109i	$0.347981\pi$
$32$	−0.936950	−	0.349464i	−0.165631	−	0.0617771i
$33$	−1.01559	+	1.85992i	−0.176792	+	0.323770i
$34$	1.38233	−	1.59529i	0.237067	−	0.273590i
$35$	−2.53247	−	1.69837i	−0.428066	−	0.287076i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	3.05803	−	8.19889i	0.502737	−	1.34789i	−0.399533	−	0.916719i	$-0.630828\pi$
$37$	3.05803	−	8.19889i	0.502737	−	1.34789i	0.902270	−	0.431171i	$-0.141899\pi$
$38$	−0.447092	+	2.05525i	−0.0725278	+	0.333405i
$39$	−1.58855	+	5.41009i	−0.254371	+	0.866308i
$40$	−2.15739	+	0.587919i	−0.341114	+	0.0929581i
$41$	−3.31299	+	7.25445i	−0.517403	+	1.13295i	0.453011	+	0.891505i	$0.350350\pi$
$41$	−3.31299	+	7.25445i	−0.517403	+	1.13295i	−0.970414	+	0.241449i	$0.922377\pi$
$42$	1.09167	−	0.817212i	0.168448	−	0.126098i
$43$	−6.00468	+	1.30624i	−0.915706	+	0.199200i	−0.645640	−	0.763642i	$-0.723409\pi$
$43$	−6.00468	+	1.30624i	−0.915706	+	0.199200i	−0.270066	+	0.962842i	$0.587046\pi$
$44$	−1.38774	−	1.60153i	−0.209209	−	0.241440i
$45$	−1.37476	+	1.76353i	−0.204937	+	0.262892i
$46$	4.42646	−	1.84566i	0.652646	−	0.272127i
$47$	−1.39772	+	1.39772i	−0.203879	+	0.203879i	−0.801660	−	0.597781i	$-0.796049\pi$
$47$	−1.39772	+	1.39772i	−0.203879	+	0.203879i	0.597781	+	0.801660i	$0.296049\pi$
$48$	0.0713392	−	0.997452i	0.0102969	−	0.143970i
$49$	2.77913	−	4.32440i	0.397018	−	0.617772i
$50$	−3.15054	+	3.88254i	−0.445553	+	0.549074i
$51$	1.92012	+	0.876889i	0.268870	+	0.122789i
$52$	−4.51385	−	3.37902i	−0.625958	−	0.468586i
$53$	−2.68667	+	1.46703i	−0.369042	+	0.201512i	−0.653059	−	0.757307i	$-0.726515\pi$
$53$	−2.68667	+	1.46703i	−0.369042	+	0.201512i	0.284017	+	0.958819i	$0.408333\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	−4.60966	−	1.09755i	−0.621567	−	0.147994i
$56$	0.384188	+	1.30842i	0.0513392	+	0.174845i
$57$	−2.09796	+	0.150049i	−0.277881	+	0.0198744i
$58$	−5.15587	+	0.368755i	−0.676999	+	0.0484199i
$59$	−0.317333	−	1.08074i	−0.0413132	−	0.140700i	0.936254	−	0.351324i	$-0.114269\pi$
$59$	−0.317333	−	1.08074i	−0.0413132	−	0.140700i	−0.977567	+	0.210624i	$0.932450\pi$
$60$	−1.17191	−	1.90437i	−0.151293	−	0.245853i
$61$	0.435960	+	0.678367i	0.0558189	+	0.0868559i	0.868041	−	0.496492i	$-0.165379\pi$
$61$	0.435960	+	0.678367i	0.0558189	+	0.0868559i	−0.812222	+	0.583348i	$0.801742\pi$
$62$	0.913627	−	0.498878i	0.116031	−	0.0633576i
$63$	1.09167	+	0.817212i	0.137537	+	0.102959i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	−12.6056	−	0.246428i	−1.56354	−	0.0305657i
$66$	1.14569	−	1.78273i	0.141025	−	0.219439i
$67$	1.14642	−	16.0291i	0.140058	−	1.95826i	−0.120265	−	0.992742i	$-0.538374\pi$
$67$	1.14642	−	16.0291i	0.140058	−	1.95826i	0.260322	−	0.965522i	$-0.416171\pi$
$68$	−1.49261	+	1.49261i	−0.181006	+	0.181006i
$69$	3.01797	+	3.72718i	0.363321	+	0.448699i
$70$	2.40486	+	1.87470i	0.287436	+	0.224070i
$71$	−7.09421	−	8.18716i	−0.841928	−	0.971637i	0.157947	−	0.987448i	$-0.449513\pi$
$71$	−7.09421	−	8.18716i	−0.841928	−	0.971637i	−0.999875	+	0.0158106i	$0.994967\pi$
$72$	0.977147	−	0.212565i	0.115158	−	0.0250511i
$73$	0.494176	−	0.369936i	0.0578389	−	0.0432977i	−0.569967	−	0.821668i	$-0.693044\pi$
$73$	0.494176	−	0.369936i	0.0578389	−	0.0432977i	0.627806	+	0.778370i	$0.283953\pi$
$74$	−3.63514	+	7.95985i	−0.422576	+	0.925313i
$75$	−4.61288	−	1.92908i	−0.532649	−	0.222751i
$76$	0.592572	−	2.01812i	0.0679727	−	0.231494i
$77$	−0.614267	+	2.82374i	−0.0700022	+	0.321795i
$78$	1.97045	−	5.28298i	0.223110	−	0.598180i
$79$	−13.0887	+	3.84319i	−1.47259	+	0.432392i	−0.916941	−	0.399023i	$-0.869349\pi$
$79$	−13.0887	+	3.84319i	−1.47259	+	0.432392i	−0.555652	+	0.831415i	$0.687531\pi$
$80$	2.19384	−	0.432514i	0.245279	−	0.0483565i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	3.82208	−	6.99962i	0.422078	−	0.772978i
$83$	−1.39625	−	0.520776i	−0.153259	−	0.0571626i	0.271664	−	0.962392i	$-0.412426\pi$
$83$	−1.39625	−	0.520776i	−0.153259	−	0.0571626i	−0.424923	+	0.905230i	$0.639699\pi$
$84$	−1.14718	+	0.737251i	−0.125168	+	0.0804407i
$85$	−0.762922	+	4.65799i	−0.0827505	+	0.505230i
$86$	6.08257	−	0.874542i	0.655900	−	0.0943042i
$87$	−1.80640	−	4.84313i	−0.193666	−	0.519238i
$88$	1.26995	+	1.69645i	0.135377	+	0.180843i
$89$	14.7728	+	9.49392i	1.56592	+	1.00635i	0.980710	+	0.195470i	$0.0626233\pi$
$89$	14.7728	+	9.49392i	1.56592	+	1.00635i	0.585207	+	0.810884i	$0.301013\pi$
$90$	1.49706	−	1.66096i	0.157804	−	0.175081i
$91$			7.68899i			0.806025i
$92$	−4.54685	+	1.52517i	−0.474042	+	0.159010i
$93$	0.736068	+	0.736068i	0.0763267	+	0.0763267i
$94$	1.49388	−	1.29445i	0.154082	−	0.133512i
$95$	−1.55714	−	4.43790i	−0.159759	−	0.455319i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	10.5759	−	3.94462i	1.07382	−	0.400516i	0.250517	−	0.968112i	$-0.419399\pi$
$97$	10.5759	−	3.94462i	1.07382	−	0.400516i	0.823307	+	0.567597i	$0.192127\pi$
$98$	−3.08054	+	4.11513i	−0.311182	+	0.415690i
$99$	2.03329	+	0.597029i	0.204354	+	0.0600037i
$100$	3.41949	−	3.64789i	0.341949	−	0.364789i
$101$	−2.33578	−	5.11464i	−0.232418	−	0.508925i	0.757106	−	0.653292i	$-0.226613\pi$
$101$	−2.33578	−	5.11464i	−0.232418	−	0.508925i	−0.989524	+	0.144367i	$0.953885\pi$
$102$	−1.85267	−	1.01163i	−0.183442	−	0.100167i
$103$	−1.15802	−	16.1912i	−0.114103	−	1.59537i	−0.655891	−	0.754855i	$-0.727707\pi$
$103$	−1.15802	−	16.1912i	−0.114103	−	1.59537i	0.541788	−	0.840515i	$-0.317748\pi$
$104$	4.26129	+	3.69243i	0.417854	+	0.362072i
$105$	−1.12124	+	2.83561i	−0.109422	+	0.276727i
$106$	2.78448	−	1.27163i	0.270453	−	0.123512i
$107$	−0.888161	−	0.193208i	−0.0858617	−	0.0186781i	0.169429	−	0.985542i	$-0.445808\pi$
$107$	−0.888161	−	0.193208i	−0.0858617	−	0.0186781i	−0.255291	+	0.966864i	$0.582171\pi$
$108$	0.479249	+	0.877679i	0.0461158	+	0.0844547i
$109$	2.27156	+	15.7991i	0.217576	+	1.51328i	0.746945	+	0.664886i	$0.231520\pi$
$109$	2.27156	+	15.7991i	0.217576	+	1.51328i	−0.529369	+	0.848392i	$0.677571\pi$
$110$	4.51962	+	1.42361i	0.430929	+	0.135736i
$111$	−8.66155	−	1.24534i	−0.822118	−	0.118203i
$112$	−0.289867	−	1.33250i	−0.0273899	−	0.125909i
$113$	−0.974393	−	0.0696900i	−0.0916632	−	0.00655588i	0.0254322	−	0.999677i	$-0.491904\pi$
$113$	−0.974393	−	0.0696900i	−0.0916632	−	0.00655588i	−0.117095	+	0.993121i	$0.537358\pi$
$114$	2.10331			0.196993
$115$	−6.26667	+	8.70223i	−0.584370	+	0.811487i
$116$	5.16904			0.479934
$117$	5.62413	+	0.402245i	0.519951	+	0.0371876i
$118$	0.239425	+	1.10062i	0.0220409	+	0.101320i
$119$	2.84922	+	0.409656i	0.261187	+	0.0375531i
$120$	1.03307	+	1.98312i	0.0943060	+	0.181033i
$121$	−0.926366	−	6.44302i	−0.0842151	−	0.585729i
$122$	−0.386455	−	0.707739i	−0.0349880	−	0.0640757i
$123$	7.79289	+	1.69524i	0.702661	+	0.152855i
$124$	−0.946889	+	0.432430i	−0.0850331	+	0.0388333i
$125$	1.44979	−	11.0859i	0.129673	−	0.991557i
$126$	−1.03059	−	0.893008i	−0.0918119	−	0.0795555i
$127$	0.944260	+	13.2025i	0.0837895	+	1.17153i	0.849230	+	0.528023i	$0.177067\pi$
$127$	0.944260	+	13.2025i	0.0837895	+	1.17153i	−0.765440	+	0.643507i	$0.777479\pi$
$128$	−0.877679	−	0.479249i	−0.0775766	−	0.0423600i
$129$	2.55277	+	5.58980i	0.224759	+	0.492154i
$130$	12.5559	+	1.14508i	1.10123	+	0.100430i
$131$	11.4494	+	3.36186i	1.00034	+	0.293727i	0.740596	−	0.671950i	$-0.234543\pi$
$131$	11.4494	+	3.36186i	1.00034	+	0.293727i	0.259745	+	0.965677i	$0.416361\pi$
$132$	−1.26995	+	1.69645i	−0.110535	+	0.147657i
$133$	−2.68737	+	1.00234i	−0.233024	+	0.0869136i
$134$	−2.28700	+	15.9065i	−0.197567	+	1.37411i
$135$	2.01545	+	0.968474i	0.173463	+	0.0833530i
$136$	1.59529	−	1.38233i	0.136795	−	0.118534i
$137$	3.33262	+	3.33262i	0.284725	+	0.284725i	0.834990	−	0.550265i	$-0.185473\pi$
$137$	3.33262	+	3.33262i	0.284725	+	0.284725i	−0.550265	+	0.834990i	$0.685473\pi$
$138$	−2.74439	−	3.93298i	−0.233618	−	0.334797i
$139$		−	18.7352i		−	1.58910i	−0.607202	−	0.794548i	$-0.707708\pi$
$139$		−	18.7352i		−	1.58910i	0.607202	−	0.794548i	$-0.292292\pi$
$140$	−2.26499	−	2.04149i	−0.191427	−	0.172537i
$141$	1.66289	+	1.06867i	0.140041	+	0.0899986i
$142$	6.49207	+	8.67239i	0.544803	+	0.727771i
$143$	4.17565	+	11.1953i	0.349185	+	0.936202i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	9.38654	−	6.74447i	0.779509	−	0.560098i
$146$	−0.519308	+	0.333739i	−0.0429782	+	0.0276204i
$147$	−4.81632	−	1.79640i	−0.397244	−	0.148164i
$148$	4.19373	−	7.68024i	0.344722	−	0.631312i
$149$	2.61159	−	3.01394i	0.213950	−	0.246912i	−0.638623	−	0.769520i	$-0.720496\pi$
$149$	2.61159	−	3.01394i	0.213950	−	0.246912i	0.852573	+	0.522608i	$0.175041\pi$
$150$	4.46351	+	2.25324i	0.364444	+	0.183977i
$151$	23.1009	−	6.78303i	1.87992	−	0.551995i	0.883405	−	0.468609i	$-0.155245\pi$
$151$	23.1009	−	6.78303i	1.87992	−	0.551995i	0.996517	−	0.0833858i	$-0.0265734\pi$
$152$	−0.735033	+	1.97070i	−0.0596191	+	0.159845i
$153$	0.448699	−	2.06263i	0.0362751	−	0.166754i
$154$	0.814145	−	2.77272i	0.0656057	−	0.223432i
$155$	−1.15524	+	2.02074i	−0.0927913	+	0.162310i
$156$	−2.34231	+	5.12895i	−0.187535	+	0.410645i
$157$	4.62531	−	3.46246i	0.369140	−	0.276334i	−0.398563	−	0.917141i	$-0.630491\pi$
$157$	4.62531	−	3.46246i	0.369140	−	0.276334i	0.767702	+	0.640807i	$0.221400\pi$
$158$	13.3295	−	2.89966i	1.06044	−	0.230684i
$159$	2.00460	+	2.31343i	0.158975	+	0.183467i
$160$	−2.21911	+	0.274905i	−0.175436	+	0.0217332i
$161$	5.38072	+	3.71726i	0.424060	+	0.292961i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−0.731963	+	10.2342i	−0.0573317	+	0.801602i	0.884717	+	0.466128i	$0.154351\pi$
$163$	−0.731963	+	10.2342i	−0.0573317	+	0.801602i	−0.942049	+	0.335475i	$0.891103\pi$
$164$	−4.31169	+	6.70912i	−0.336686	+	0.523894i
$165$	−0.0926160	+	4.73762i	−0.00721014	+	0.368823i
$166$	1.35554	+	0.619057i	0.105211	+	0.0480481i
$167$	0.805932	+	0.603313i	0.0623649	+	0.0466858i	0.630005	−	0.776591i	$-0.283053\pi$
$167$	0.805932	+	0.603313i	0.0623649	+	0.0466858i	−0.567640	+	0.823277i	$0.692144\pi$
$168$	1.19686	−	0.653533i	0.0923395	−	0.0504212i
$169$	10.1600	+	15.8093i	0.781542	+	1.21610i
$170$	1.09328	−	4.59170i	0.0838504	−	0.352167i
$171$	0.592572	+	2.01812i	0.0453151	+	0.154329i
$172$	−6.12946	+	0.438388i	−0.467367	+	0.0334268i
$173$	12.8275	−	0.917444i	0.975260	−	0.0697519i	0.425397	−	0.905007i	$-0.360135\pi$
$173$	12.8275	−	0.917444i	0.975260	−	0.0697519i	0.549863	+	0.835255i	$0.314680\pi$
$174$	1.45629	+	4.95966i	0.110401	+	0.375991i
$175$	−6.77673	−	0.751843i	−0.512272	−	0.0568340i
$176$	−1.14569	−	1.78273i	−0.0863596	−	0.134378i
$177$	−0.988584	+	0.539808i	−0.0743065	+	0.0405744i
$178$	−14.0579	−	10.5236i	−1.05368	−	0.788778i
$179$	6.56520	+	2.99823i	0.490706	+	0.224098i	0.645372	−	0.763869i	$-0.276703\pi$
$179$	6.56520	+	2.99823i	0.490706	+	0.224098i	−0.154665	+	0.987967i	$0.549430\pi$
$180$	−1.61174	+	1.54993i	−0.120132	+	0.115525i
$181$	−5.43211	+	8.45252i	−0.403765	+	0.628271i	−0.982284	−	0.187398i	$-0.939995\pi$
$181$	−5.43211	+	8.45252i	−0.403765	+	0.628271i	0.578519	+	0.815669i	$0.303631\pi$
$182$	0.548526	−	7.66940i	0.0406595	−	0.568494i
$183$	0.570194	−	0.570194i	0.0421499	−	0.0421499i
$184$	4.64407	−	1.19692i	0.342365	−	0.0882380i
$185$	−2.40559	−	19.4185i	−0.176863	−	1.42768i
$186$	−0.681683	−	0.786704i	−0.0499834	−	0.0576839i
$187$	4.37100	−	0.950852i	0.319639	−	0.0695332i
$188$	−1.58241	+	1.18458i	−0.115409	+	0.0863944i
$189$	0.566485	−	1.24043i	0.0412057	−	0.0902280i
$190$	1.23658	+	4.53768i	0.0897108	+	0.329198i
$191$	3.02438	−	10.3001i	0.218837	−	0.745290i	−0.774755	−	0.632262i	$-0.782127\pi$
$191$	3.02438	−	10.3001i	0.218837	−	0.745290i	0.993592	−	0.113028i	$-0.0360550\pi$
$192$	0.212565	−	0.977147i	0.0153406	−	0.0705195i
$193$	−0.622100	+	1.66791i	−0.0447797	+	0.120059i	−0.957415	−	0.288717i	$-0.906771\pi$
$193$	−0.622100	+	1.66791i	−0.0447797	+	0.120059i	0.912635	+	0.408776i	$0.134044\pi$
$194$	−10.8304	+	3.18009i	−0.777577	+	0.228317i
$195$	2.43873	+	12.3699i	0.174641	+	0.885830i
$196$	3.36626	−	3.88488i	0.240447	−	0.277491i
$197$	9.93209	−	18.1893i	0.707632	−	1.29593i	−0.238181	−	0.971221i	$-0.576551\pi$
$197$	9.93209	−	18.1893i	0.707632	−	1.29593i	0.945813	−	0.324711i	$-0.105267\pi$
$198$	−1.98552	−	0.740561i	−0.141105	−	0.0526294i
$199$	−5.08030	+	3.26491i	−0.360133	+	0.231443i	−0.708177	−	0.706035i	$-0.750482\pi$
$199$	−5.08030	+	3.26491i	−0.360133	+	0.231443i	0.348044	+	0.937478i	$0.386846\pi$
$200$	−3.67101	+	3.39465i	−0.259580	+	0.240038i
$201$	−15.9065	+	2.28700i	−1.12195	+	0.161313i
$202$	1.96495	+	5.26824i	0.138253	+	0.370672i
$203$	−4.22420	−	5.64287i	−0.296481	−	0.396052i
$204$	1.77578	+	1.14122i	0.124329	+	0.0799017i
$205$	0.924283	+	17.8090i	0.0645547	+	1.24383i
$206$			16.2326i			1.13098i
$207$	3.00048	−	3.74127i	0.208548	−	0.260036i
$208$	−3.98702	−	3.98702i	−0.276450	−	0.276450i
$209$	−3.36853	+	2.91885i	−0.233006	+	0.201901i
$210$	1.32067	−	2.74840i	0.0911349	−	0.189657i
$211$	1.36152	−	9.46958i	0.0937309	−	0.651913i	−0.887746	−	0.460333i	$-0.847730\pi$
$211$	1.36152	−	9.46958i	0.0937309	−	0.651913i	0.981477	−	0.191580i	$-0.0613610\pi$
$212$	−2.86810	+	1.06975i	−0.196982	+	0.0734705i
$213$	−6.49207	+	8.67239i	−0.444830	+	0.594223i
$214$	0.872114	+	0.256076i	0.0596165	+	0.0175050i
$215$	−10.5586	+	8.79369i	−0.720089	+	0.599725i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	1.24588	+	0.680301i	0.0845757	+	0.0461818i
$218$	−1.13868	−	15.9209i	−0.0771214	−	1.07830i
$219$	−0.466526	−	0.404247i	−0.0315249	−	0.0273165i
$220$	−4.40655	−	1.74241i	−0.297089	−	0.117473i
$221$	10.8266	−	4.94433i	0.728274	−	0.332592i
$222$	8.55064	+	1.86008i	0.573882	+	0.124840i
$223$	12.6411	+	23.1505i	0.846512	+	1.55027i	0.834942	+	0.550337i	$0.185501\pi$
$223$	12.6411	+	23.1505i	0.846512	+	1.55027i	0.0115693	+	0.999933i	$0.496317\pi$
$224$	0.194069	+	1.34978i	0.0129668	+	0.0901860i
$225$	−0.904457	+	4.91752i	−0.0602972	+	0.327834i
$226$	0.966939	+	0.139025i	0.0643198	+	0.00924779i
$227$	−0.369312	−	1.69770i	−0.0245121	−	0.112680i	0.963265	−	0.268552i	$-0.0865451\pi$
$227$	−0.369312	−	1.69770i	−0.0245121	−	0.112680i	−0.987777	+	0.155871i	$0.950181\pi$
$228$	−2.09796	−	0.150049i	−0.138940	−	0.00993722i
$229$	−0.510875			−0.0337596			−0.0168798	−	0.999858i	$-0.505373\pi$
$229$	−0.510875			−0.0337596			−0.0168798	+	0.999858i	$0.505373\pi$
$230$	6.87151	−	8.23300i	0.453094	−	0.542868i
$231$	2.88978			0.190134
$232$	−5.15587	−	0.368755i	−0.338500	−	0.0242100i
$233$	3.42515	+	15.7452i	0.224389	+	1.03150i	0.942145	+	0.335205i	$0.108806\pi$
$233$	3.42515	+	15.7452i	0.224389	+	1.03150i	−0.717756	+	0.696294i	$0.754831\pi$
$234$	−5.58110	−	0.802441i	−0.364848	−	0.0524572i
$235$	−1.32791	+	4.21580i	−0.0866232	+	0.275009i
$236$	−0.160298	−	1.11490i	−0.0104345	−	0.0725736i
$237$	6.53756	+	11.9726i	0.424660	+	0.777707i
$238$	−2.81273	−	0.611873i	−0.182322	−	0.0396618i
$239$	−9.76023	+	4.45735i	−0.631336	+	0.288322i	−0.705267	−	0.708942i	$-0.749173\pi$
$239$	−9.76023	+	4.45735i	−0.631336	+	0.288322i	0.0739306	+	0.997263i	$0.476446\pi$
$240$	−0.888964	−	2.05177i	−0.0573824	−	0.132441i
$241$	−13.9160	−	12.0583i	−0.896407	−	0.776741i	0.0790638	−	0.996870i	$-0.474807\pi$
$241$	−13.9160	−	12.0583i	−0.896407	−	0.776741i	−0.975471	+	0.220128i	$0.929352\pi$
$242$	0.464366	+	6.49269i	0.0298506	+	0.417366i
$243$	−0.877679	−	0.479249i	−0.0563031	−	0.0307438i
$244$	0.334981	+	0.733505i	0.0214449	+	0.0469579i
$245$	1.04393	−	11.4468i	0.0666942	−	0.731312i
$246$	−7.65209	−	2.24686i	−0.487880	−	0.143254i
$247$	−7.10715	+	9.49404i	−0.452217	+	0.604091i
$248$	0.975325	−	0.363778i	0.0619332	−	0.0230999i
$249$	−0.212079	+	1.47504i	−0.0134400	+	0.0934771i
$250$	−2.23696	+	10.9543i	−0.141478	+	0.692809i
$251$	7.38404	−	6.39831i	0.466076	−	0.403858i	−0.389912	−	0.920852i	$-0.627495\pi$
$251$	7.38404	−	6.39831i	0.466076	−	0.403858i	0.855989	+	0.516994i	$0.172949\pi$
$252$	0.964254	+	0.964254i	0.0607423	+	0.0607423i
$253$	9.85317	+	2.49031i	0.619464	+	0.156564i
$254$		−	13.2362i		−	0.830513i
$255$	4.71371	−	0.244641i	0.295184	−	0.0153200i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−14.3339	−	19.1479i	−0.894126	−	1.19441i	−0.980177	−	0.198121i	$-0.936516\pi$
$257$	−14.3339	−	19.1479i	−0.894126	−	1.19441i	0.0860518	−	0.996291i	$-0.472575\pi$
$258$	−2.14750	−	5.75767i	−0.133697	−	0.358457i
$259$	−11.8114	+	1.69823i	−0.733926	+	0.105523i
$260$	−12.4423	−	2.03789i	−0.771637	−	0.126385i
$261$	−4.34848	+	2.79460i	−0.269164	+	0.172981i
$262$	−11.1804	−	4.17008i	−0.690729	−	0.257629i
$263$	4.09008	−	7.49042i	0.252205	−	0.461879i	−0.720649	−	0.693301i	$-0.756156\pi$
$263$	4.09008	−	7.49042i	0.252205	−	0.461879i	0.972854	+	0.231422i	$0.0743376\pi$
$264$	1.38774	−	1.60153i	0.0854093	−	0.0985676i
$265$	−3.81244	+	5.68482i	−0.234196	+	0.349216i
$266$	2.75203	−	0.808068i	0.168738	−	0.0495458i
$267$	6.13677	−	16.4533i	0.375564	−	1.00693i
$268$	3.41593	−	15.7028i	0.208661	−	0.959200i
$269$	7.59924	−	25.8806i	0.463334	−	1.57797i	−0.314345	−	0.949309i	$-0.601785\pi$
$269$	7.59924	−	25.8806i	0.463334	−	1.57797i	0.777679	−	0.628662i	$-0.216397\pi$
$270$	−1.94123	−	1.10979i	−0.118139	−	0.0675395i
$271$	2.14310	−	4.69272i	0.130184	−	0.285063i	−0.833304	−	0.552815i	$-0.813554\pi$
$271$	2.14310	−	4.69272i	0.130184	−	0.285063i	0.963488	+	0.267752i	$0.0862809\pi$
$272$	−1.68984	+	1.26500i	−0.102462	+	0.0767019i
$273$	7.51328	−	1.63441i	0.454724	−	0.0989192i
$274$	−3.08638	−	3.56187i	−0.186455	−	0.215180i
$275$	−10.2754	+	2.58553i	−0.619628	+	0.155913i
$276$	2.45682	+	4.11874i	0.147883	+	0.247919i
$277$	4.40279	−	4.40279i	0.264538	−	0.264538i	−0.562357	−	0.826895i	$-0.690105\pi$
$277$	4.40279	−	4.40279i	0.264538	−	0.264538i	0.826895	+	0.562357i	$0.190105\pi$
$278$	−1.33655	+	18.6874i	−0.0801610	+	1.12080i
$279$	0.562784	−	0.875710i	0.0336930	−	0.0524274i
$280$	2.11358	+	2.19787i	0.126311	+	0.131348i
$281$	7.19335	+	3.28509i	0.429120	+	0.195972i	0.618253	−	0.785979i	$-0.287841\pi$
$281$	7.19335	+	3.28509i	0.429120	+	0.195972i	−0.189134	+	0.981951i	$0.560568\pi$
$282$	−1.58241	−	1.18458i	−0.0942314	−	0.0705408i
$283$	−2.36015	+	1.28874i	−0.140296	+	0.0766077i	−0.547864	−	0.836567i	$-0.684559\pi$
$283$	−2.36015	+	1.28874i	−0.140296	+	0.0766077i	0.407568	+	0.913175i	$0.366377\pi$
$284$	−5.85685	−	9.11344i	−0.347540	−	0.540783i
$285$	−4.00549	+	2.46490i	−0.237265	+	0.146008i
$286$	−3.36634	−	11.4647i	−0.199056	−	0.677923i
$287$	10.8477	−	0.775842i	0.640318	−	0.0457965i
$288$	0.997452	−	0.0713392i	0.0587754	−	0.00420370i
$289$	3.53411	+	12.0361i	0.207889	+	0.708005i
$290$	−9.84377	+	6.05766i	−0.578046	+	0.355718i
$291$	−6.10255	−	9.49576i	−0.357738	−	0.556651i
$292$	0.541794	−	0.295842i	0.0317061	−	0.0173128i
$293$	11.7197	+	8.77329i	0.684675	+	0.512541i	0.884056	−	0.467381i	$-0.154802\pi$
$293$	11.7197	+	8.77329i	0.684675	+	0.512541i	−0.199381	+	0.979922i	$0.563893\pi$
$294$	4.67590	+	2.13541i	0.272704	+	0.124540i
$295$	−1.74579	−	1.81540i	−0.101644	−	0.105697i
$296$	−4.73094	+	7.36149i	−0.274981	+	0.427878i
$297$	0.151177	−	2.11373i	0.00877219	−	0.122651i
$298$	−2.81995	+	2.81995i	−0.163355	+	0.163355i
$299$	27.0262	+	0.901879i	1.56297	+	0.0521570i
$300$	−4.29139	−	2.56593i	−0.247763	−	0.148144i
$301$	5.48764	+	6.33308i	0.316302	+	0.365032i
$302$	−23.5259	+	5.11775i	−1.35376	+	0.294493i
$303$	−4.50125	+	3.36959i	−0.258590	+	0.193578i
$304$	0.873748	−	1.91324i	0.0501129	−	0.109732i
$305$	1.56536	+	0.894906i	0.0896323	+	0.0512422i
$306$	−0.594702	+	2.02537i	−0.0339968	+	0.115783i
$307$	2.72208	−	12.5132i	0.155358	−	0.714167i	−0.831886	−	0.554947i	$-0.812738\pi$
$307$	2.72208	−	12.5132i	0.155358	−	0.714167i	0.987243	−	0.159220i	$-0.0508979\pi$
$308$	−1.00987	+	2.70758i	−0.0575429	+	0.154279i
$309$	−15.5751	+	4.57325i	−0.886035	+	0.260163i
$310$	1.29646	−	1.93318i	0.0736338	−	0.109797i
$311$	−8.61434	+	9.94148i	−0.488474	+	0.563729i	−0.945457	−	0.325746i	$-0.894385\pi$
$311$	−8.61434	+	9.94148i	−0.488474	+	0.563729i	0.456983	+	0.889475i	$0.348930\pi$
$312$	2.70224	−	4.94879i	0.152984	−	0.280170i
$313$	−18.8901	−	7.04565i	−1.06773	−	0.398244i	−0.246680	−	0.969097i	$-0.579340\pi$
$313$	−18.8901	−	7.04565i	−1.06773	−	0.398244i	−0.821052	+	0.570853i	$0.806612\pi$
$314$	−4.86053	+	3.12367i	−0.274296	+	0.176279i
$315$	3.00914	+	0.492861i	0.169546	+	0.0277696i
$316$	−13.5024	+	1.94135i	−0.759570	+	0.109210i
$317$	6.32400	+	16.9553i	0.355191	+	0.952304i	0.984537	+	0.175178i	$0.0560502\pi$
$317$	6.32400	+	16.9553i	0.355191	+	0.952304i	−0.629346	+	0.777125i	$0.716677\pi$
$318$	−1.83445	−	2.45054i	−0.102871	−	0.137420i
$319$	−9.21500	−	5.92212i	−0.515941	−	0.331575i
$320$	2.23306	−	0.115895i	0.124832	−	0.00647876i
$321$			0.908933i			0.0507317i
$322$	−5.10182	−	4.09164i	−0.284314	−	0.228018i
$323$	3.13944	+	3.13944i	0.174683	+	0.174683i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	−25.2531	+	12.5338i	−1.40079	+	0.695251i
$326$	1.46020	−	10.1559i	0.0808727	−	0.562482i
$327$	14.9552	−	5.57799i	0.827023	−	0.308463i
$328$	4.77933	−	6.38443i	0.263894	−	0.352521i
$329$	2.58634	+	0.759417i	0.142589	+	0.0418680i
$330$	0.430358	−	4.71894i	0.0236904	−	0.259769i
$331$	2.31398	+	5.06691i	0.127188	+	0.278502i	0.962504	−	0.271267i	$-0.0874427\pi$
$331$	2.31398	+	5.06691i	0.127188	+	0.278502i	−0.835316	+	0.549770i	$0.814715\pi$
$332$	−1.30793	−	0.714183i	−0.0717819	−	0.0391959i
$333$	0.624262	+	8.72833i	0.0342094	+	0.478309i
$334$	−0.760838	−	0.659270i	−0.0416312	−	0.0360737i
$335$	−14.2857	−	32.9719i	−0.780509	−	1.80145i
$336$	−1.24043	+	0.566485i	−0.0676710	+	0.0309043i
$337$	33.3144	+	7.24711i	1.81475	+	0.394775i	0.986257	−	0.165220i	$-0.0528333\pi$
$337$	33.3144	+	7.24711i	1.81475	+	0.394775i	0.828496	+	0.559995i	$0.189197\pi$
$338$	−9.00633	−	16.4939i	−0.489880	−	0.897148i
$339$	0.139025	+	0.966939i	0.00755079	+	0.0525169i
$340$	−1.41806	+	4.50201i	−0.0769050	+	0.244156i
$341$	2.18348	+	0.313936i	0.118242	+	0.0170006i
$342$	−0.447092	−	2.05525i	−0.0241759	−	0.111135i
$343$	−16.5132	−	1.18105i	−0.891632	−	0.0637707i
$344$	6.14512			0.331323
$345$	9.83544	+	4.27366i	0.529522	+	0.230086i
$346$	−12.8603			−0.691374
$347$	−25.2518	−	1.80605i	−1.35559	−	0.0969537i	−0.625457	−	0.780259i	$-0.715087\pi$
$347$	−25.2518	−	1.80605i	−1.35559	−	0.0969537i	−0.730133	+	0.683305i	$0.760542\pi$
$348$	−1.09876	−	5.05091i	−0.0588997	−	0.270757i
$349$	−14.6196	−	2.10198i	−0.782567	−	0.112516i	−0.260561	−	0.965458i	$-0.583907\pi$
$349$	−14.6196	−	2.10198i	−0.782567	−	0.112516i	−0.522007	+	0.852941i	$0.674816\pi$
$350$	6.70582	+	1.23337i	0.358441	+	0.0659266i
$351$	−0.802441	−	5.58110i	−0.0428311	−	0.297897i
$352$	1.01559	+	1.85992i	0.0541313	+	0.0991340i
$353$	−1.04608	−	0.227561i	−0.0556772	−	0.0121118i	0.184640	−	0.982806i	$-0.440888\pi$
$353$	−1.04608	−	0.227561i	−0.0556772	−	0.0121118i	−0.240318	+	0.970694i	$0.577252\pi$
$354$	1.02457	−	0.467908i	0.0544555	−	0.0248690i
$355$	−22.5266	−	8.90730i	−1.19559	−	0.472751i
$356$	13.2713	+	11.4997i	0.703380	+	0.609482i
$357$	−0.205351	−	2.87118i	−0.0108683	−	0.151959i
$358$	−6.33459	−	3.45895i	−0.334793	−	0.182811i
$359$	1.12498	+	2.46337i	0.0593744	+	0.130012i	0.936993	−	0.349347i	$-0.113597\pi$
$359$	1.12498	+	2.46337i	0.0593744	+	0.130012i	−0.877619	+	0.479359i	$0.840869\pi$
$360$	1.71821	−	1.43100i	0.0905574	−	0.0754205i
$361$	13.9856	+	4.10655i	0.736086	+	0.216134i
$362$	6.02126	−	8.04346i	0.316470	−	0.422755i
$363$	−6.09886	+	2.27476i	−0.320107	+	0.119394i
$364$	−1.09426	+	7.61073i	−0.0573547	+	0.398911i
$365$	0.597841	−	1.24415i	0.0312925	−	0.0651216i
$366$	−0.609418	+	0.528064i	−0.0318548	+	0.0276023i
$367$	−3.64681	−	3.64681i	−0.190362	−	0.190362i	0.605491	−	0.795852i	$-0.292977\pi$
$367$	−3.64681	−	3.64681i	−0.190362	−	0.190362i	−0.795852	+	0.605491i	$0.792977\pi$
$368$	−4.71762	+	0.862565i	−0.245923	+	0.0449643i
$369$		−	7.97514i		−	0.415169i
$370$	1.01416	+	19.5407i	0.0527235	+	1.01587i
$371$	3.51165	+	2.25680i	0.182316	+	0.117167i
$372$	0.623823	+	0.833330i	0.0323437	+	0.0432061i
$373$	−1.62871	−	4.36673i	−0.0843312	−	0.226101i	0.887939	−	0.459961i	$-0.152137\pi$
$373$	−1.62871	−	4.36673i	−0.0843312	−	0.226101i	−0.972270	+	0.233861i	$0.924864\pi$
$374$	−4.42769	+	0.636606i	−0.228951	+	0.0329181i
$375$	−11.1408	+	0.939827i	−0.575307	+	0.0485325i
$376$	1.66289	−	1.06867i	0.0857570	−	0.0551127i
$377$	−27.3080	−	10.1853i	−1.40643	−	0.524572i
$378$	−0.653533	+	1.19686i	−0.0336141	+	0.0615597i
$379$	7.72162	−	8.91122i	0.396633	−	0.457739i	−0.521945	−	0.852979i	$-0.674793\pi$
$379$	7.72162	−	8.91122i	0.396633	−	0.457739i	0.918578	+	0.395241i	$0.129339\pi$
$380$	−0.909713	−	4.61433i	−0.0466673	−	0.236710i
$381$	12.7000	−	3.72907i	0.650643	−	0.191046i
$382$	−3.75148	+	10.0581i	−0.191942	+	0.514617i
$383$	−0.296861	+	1.36465i	−0.0151689	+	0.0697302i	−0.984109	−	0.177565i	$-0.943178\pi$
$383$	−0.296861	+	1.36465i	−0.0151689	+	0.0697302i	0.968940	+	0.247295i	$0.0795417\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	1.69895	+	6.23439i	0.0865867	+	0.317734i
$386$	0.739502	−	1.61928i	0.0376397	−	0.0824194i
$387$	4.91942	−	3.68263i	0.250068	−	0.187199i
$388$	11.0297	−	2.39936i	0.559947	−	0.121809i
$389$	−20.1673	−	23.2743i	−1.02252	−	1.18006i	−0.983517	−	0.180817i	$-0.942126\pi$
$389$	−20.1673	−	23.2743i	−1.02252	−	1.18006i	−0.0390075	−	0.999239i	$-0.512420\pi$
$390$	−1.55005	−	12.5124i	−0.0784898	−	0.633590i
$391$	1.77411	−	9.96673i	0.0897204	−	0.504039i
$392$	−3.63483	+	3.63483i	−0.183587	+	0.183587i
$393$	0.851276	−	11.9024i	0.0429412	−	0.600396i
$394$	−11.2044	+	17.4344i	−0.564469	+	0.878331i
$395$	−21.9862	+	21.1430i	−1.10624	+	1.06382i
$396$	1.92763	+	0.880320i	0.0968671	+	0.0442377i
$397$	11.2269	+	8.40433i	0.563461	+	0.421801i	0.842671	−	0.538428i	$-0.180982\pi$
$397$	11.2269	+	8.40433i	0.563461	+	0.421801i	−0.279210	+	0.960230i	$0.590073\pi$
$398$	5.30027	−	2.89417i	0.265679	−	0.145072i
$399$	1.55067	+	2.41289i	0.0776306	+	0.120796i
$400$	3.90383	−	3.12412i	0.195192	−	0.156206i
$401$	0.481013	+	1.63818i	0.0240206	+	0.0818067i	0.970631	−	0.240573i	$-0.0773354\pi$
$401$	0.481013	+	1.63818i	0.0240206	+	0.0818067i	−0.946610	+	0.322380i	$0.895517\pi$
$402$	16.0291	−	1.14642i	0.799458	−	0.0571783i
$403$	5.85448	−	0.418721i	0.291632	−	0.0208580i
$404$	−1.58411	−	5.39499i	−0.0788126	−	0.268411i
$405$	0.517925	−	2.17526i	0.0257359	−	0.108090i
$406$	3.81088	+	5.92985i	0.189131	+	0.294293i
$407$	−16.2754	+	8.88707i	−0.806744	+	0.440515i
$408$	−1.68984	−	1.26500i	−0.0836596	−	0.0626268i
$409$	−1.33912	−	0.611554i	−0.0662150	−	0.0302394i	0.382032	−	0.924149i	$-0.375224\pi$
$409$	−1.33912	−	0.611554i	−0.0662150	−	0.0302394i	−0.448247	+	0.893910i	$0.647952\pi$
$410$	0.348551	−	17.8296i	0.0172137	−	0.880539i
$411$	2.54806	−	3.96485i	0.125686	−	0.195572i
$412$	1.15802	−	16.1912i	0.0570516	−	0.797685i
$413$	−1.08610	+	1.08610i	−0.0534434	+	0.0534434i
$414$	−3.25974	+	3.51769i	−0.160207	+	0.172885i
$415$	−3.30694	+	0.409667i	−0.162331	+	0.0201098i
$416$	3.69243	+	4.26129i	0.181036	+	0.208927i
$417$	−18.3070	+	3.98244i	−0.896498	+	0.195021i
$418$	3.56818	−	2.67110i	0.174525	−	0.130648i
$419$	4.63401	−	10.1471i	0.226386	−	0.495717i	−0.762019	−	0.647555i	$-0.775792\pi$
$419$	4.63401	−	10.1471i	0.226386	−	0.495717i	0.988405	+	0.151838i	$0.0485191\pi$
$420$	−1.51337	+	2.64718i	−0.0738451	+	0.129169i
$421$	3.03356	−	10.3314i	0.147847	−	0.503520i	−0.851951	−	0.523621i	$-0.824581\pi$
$421$	3.03356	−	10.3314i	0.147847	−	0.503520i	0.999798	+	0.0201014i	$0.00639892\pi$
$422$	−2.03360	+	9.34832i	−0.0989943	+	0.455069i
$423$	0.690779	−	1.85205i	0.0335868	−	0.0900498i
$424$	2.93711	−	0.862413i	0.142639	−	0.0418825i
$425$	3.29907	+	10.0255i	0.160028	+	0.486309i
$426$	7.09421	−	8.18716i	0.343716	−	0.396669i
$427$	0.526993	−	0.965116i	0.0255030	−	0.0467053i
$428$	−0.851624	−	0.317639i	−0.0411648	−	0.0153537i
$429$	10.0519	−	6.45996i	0.485310	−	0.311890i
$430$	11.1590	−	8.01804i	0.538135	−	0.386664i
$431$	0.686463	−	0.0986985i	0.0330658	−	0.00475414i	−0.125762	−	0.992060i	$-0.540138\pi$
$431$	0.686463	−	0.0986985i	0.0330658	−	0.00475414i	0.158828	+	0.987306i	$0.449229\pi$
$432$	0.349464	+	0.936950i	0.0168136	+	0.0450790i
$433$	−4.29264	−	5.73430i	−0.206291	−	0.275573i	0.685449	−	0.728121i	$-0.259606\pi$
$433$	−4.29264	−	5.73430i	−0.206291	−	0.275573i	−0.891740	+	0.452548i	$0.850515\pi$
$434$	−1.19417	−	0.767447i	−0.0573220	−	0.0368386i
$435$	−8.58559	−	7.73838i	−0.411648	−	0.371027i
$436$			15.9615i			0.764419i
$437$	3.20792	+	9.56346i	0.153456	+	0.457482i
$438$	0.436499	+	0.436499i	0.0208567	+	0.0208567i
$439$	−0.738650	+	0.640044i	−0.0352539	+	0.0305476i	−0.672310	−	0.740270i	$-0.734698\pi$
$439$	−0.738650	+	0.640044i	−0.0352539	+	0.0305476i	0.637056	+	0.770818i	$0.280152\pi$
$440$	4.27102	+	2.05233i	0.203613	+	0.0978408i
$441$	−0.731559	+	5.08811i	−0.0348362	+	0.242291i
$442$	−11.1517	+	4.15937i	−0.530433	+	0.197841i
$443$	−16.9697	+	22.6689i	−0.806255	+	1.07703i	0.189213	+	0.981936i	$0.439406\pi$
$443$	−16.9697	+	22.6689i	−0.806255	+	1.07703i	−0.995468	+	0.0950943i	$0.969685\pi$
$444$	−8.39616	−	2.46534i	−0.398464	−	0.117000i
$445$	39.1042	+	3.56622i	1.85372	+	0.169055i
$446$	−10.9574	−	23.9933i	−0.518847	−	1.13612i
$447$	−3.50020	−	1.91125i	−0.165554	−	0.0903991i
$448$	−0.0972825	−	1.36019i	−0.00459616	−	0.0642628i
$449$	−19.9243	−	17.2645i	−0.940288	−	0.814764i	0.0425770	−	0.999093i	$-0.486443\pi$
$449$	−19.9243	−	17.2645i	−0.940288	−	0.814764i	−0.982865	+	0.184329i	$0.940989\pi$
$450$	1.25296	−	4.84046i	0.0590653	−	0.228182i
$451$	15.3731	−	7.02068i	0.723893	−	0.330591i
$452$	−0.954557	−	0.207651i	−0.0448986	−	0.00976709i
$453$	−11.5385	−	21.1311i	−0.542124	−	0.992826i
$454$	0.247259	+	1.71972i	0.0116044	+	0.0807105i
$455$	7.94327	+	15.2482i	0.372386	+	0.714847i
$456$	2.08191	+	0.299333i	0.0974942	+	0.0140175i
$457$	7.70254	+	35.4080i	0.360310	+	1.65632i	0.698778	+	0.715339i	$0.253728\pi$
$457$	7.70254	+	35.4080i	0.360310	+	1.65632i	−0.338468	+	0.940978i	$0.609909\pi$
$458$	0.509574	+	0.0364454i	0.0238108	+	0.00170298i
$459$	−2.11087			−0.0985272
$460$	−7.44134	+	7.72182i	−0.346954	+	0.360032i
$461$	−9.52809			−0.443767			−0.221884	−	0.975073i	$-0.571221\pi$
$461$	−9.52809			−0.443767			−0.221884	+	0.975073i	$0.571221\pi$
$462$	−2.88242	−	0.206154i	−0.134102	−	0.00959118i
$463$	−4.51561	−	20.7579i	−0.209858	−	0.964702i	−0.954725	−	0.297489i	$-0.903851\pi$
$463$	−4.51561	−	20.7579i	−0.209858	−	0.964702i	0.744867	−	0.667213i	$-0.232513\pi$
$464$	5.11643	+	0.735631i	0.237524	+	0.0341508i
$465$	2.22012	+	0.699302i	0.102956	+	0.0324294i
$466$	−2.29317	−	15.9494i	−0.106229	−	0.738841i
$467$	18.0134	+	32.9891i	0.833561	+	1.52655i	0.850058	+	0.526689i	$0.176567\pi$
$467$	18.0134	+	32.9891i	0.833561	+	1.52655i	−0.0164971	+	0.999864i	$0.505251\pi$
$468$	5.50964	+	1.19855i	0.254683	+	0.0554029i
$469$	−19.9337	+	9.10343i	−0.920454	+	0.420357i
$470$	1.62528	−	4.11033i	0.0749685	−	0.189595i
$471$	−4.36651	−	3.78360i	−0.201198	−	0.174339i
$472$	0.0803537	+	1.12349i	0.00369858	+	0.0517129i
$473$	11.4294	+	6.24094i	0.525525	+	0.286959i
$474$	−5.66678	−	12.4085i	−0.260284	−	0.569942i
$475$	−7.67266	−	7.19226i	−0.352046	−	0.330003i
$476$	2.76192	+	0.810972i	0.126592	+	0.0371708i
$477$	1.83445	−	2.45054i	0.0839938	−	0.112203i
$478$	10.0533	−	3.74970i	0.459829	−	0.171507i
$479$	4.54229	−	31.5923i	0.207543	−	1.44349i	−0.573599	−	0.819136i	$-0.694453\pi$
$479$	4.54229	−	31.5923i	0.207543	−	1.44349i	0.781142	−	0.624354i	$-0.214638\pi$
$480$	0.740327	+	2.10996i	0.0337912	+	0.0963059i
$481$	−37.2889	+	32.3110i	−1.70023	+	1.47326i
$482$	13.0203	+	13.0203i	0.593058	+	0.593058i
$483$	2.48855	−	6.04791i	0.113233	−	0.275190i
$484$		−	6.50927i		−	0.295876i
$485$	16.8983	−	18.7483i	0.767312	−	0.851318i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	5.08167	+	6.78831i	0.230272	+	0.307608i	0.900764	−	0.434309i	$-0.143008\pi$
$487$	5.08167	+	6.78831i	0.230272	+	0.307608i	−0.670491	+	0.741917i	$0.733917\pi$
$488$	−0.281800	−	0.755534i	−0.0127565	−	0.0342014i
$489$	10.1559	−	1.46020i	0.459265	−	0.0660323i
$490$	−1.85788	+	11.3432i	−0.0839304	+	0.512434i
$491$	−20.9053	+	13.4351i	−0.943445	+	0.606315i	−0.919370	−	0.393395i	$-0.871301\pi$
$491$	−20.9053	+	13.4351i	−0.943445	+	0.606315i	−0.0240755	+	0.999710i	$0.507664\pi$
$492$	7.47231	+	2.78703i	0.336878	+	0.125649i
$493$	−5.22918	+	9.57653i	−0.235510	+	0.431305i
$494$	7.76634	−	8.96283i	0.349424	−	0.403257i
$495$	4.64904	−	0.916554i	0.208959	−	0.0411961i
$496$	−0.998792	+	0.293272i	−0.0448471	+	0.0131683i
$497$	−5.16255	+	13.8413i	−0.231572	+	0.620869i
$498$	0.316767	−	1.45616i	0.0141947	−	0.0652519i
$499$	−7.79598	+	26.5507i	−0.348996	+	1.18857i	0.578796	+	0.815473i	$0.303523\pi$
$499$	−7.79598	+	26.5507i	−0.348996	+	1.18857i	−0.927792	+	0.373099i	$0.878295\pi$
$500$	3.01273	−	10.7668i	0.134733	−	0.481505i
$501$	0.418212	−	0.915757i	0.0186843	−	0.0409130i
$502$	−7.82168	+	5.85523i	−0.349099	+	0.261332i
$503$	19.4937	−	4.24060i	0.869183	−	0.189079i	0.244207	−	0.969723i	$-0.421472\pi$
$503$	19.4937	−	4.24060i	0.869183	−	0.189079i	0.624976	+	0.780644i	$0.285109\pi$
$504$	−0.893008	−	1.03059i	−0.0397777	−	0.0459060i
$505$	−9.91590	−	7.72992i	−0.441252	−	0.343977i
$506$	−9.65041	−	3.18688i	−0.429013	−	0.141674i
$507$	13.2884	−	13.2884i	0.590157	−	0.590157i
$508$	−0.944260	+	13.2025i	−0.0418948	+	0.585765i
$509$	10.0052	−	15.5683i	0.443471	−	0.690055i	−0.545509	−	0.838105i	$-0.683663\pi$
$509$	10.0052	−	15.5683i	0.443471	−	0.690055i	0.988980	+	0.148051i	$0.0472998\pi$
$510$	−4.71916	−	0.0922550i	−0.208968	−	0.00408512i
$511$	−0.765720	−	0.349693i	−0.0338735	−	0.0154695i
$512$	−0.800541	−	0.599278i	−0.0353793	−	0.0264846i
$513$	1.84603	−	1.00801i	0.0815044	−	0.0445048i
$514$	12.9314	+	20.1217i	0.570380	+	0.887529i
$515$	−19.0232	−	30.9129i	−0.838261	−	1.36218i
$516$	1.73128	+	5.89620i	0.0762154	+	0.259566i
$517$	4.17818	−	0.298829i	0.183756	−	0.0131425i
$518$	11.9025	−	0.851282i	0.522965	−	0.0374032i
$519$	−3.62317	−	12.3394i	−0.159039	−	0.541638i
$520$	12.2652	+	2.92032i	0.537864	+	0.128064i
$521$	21.2785	+	33.1100i	0.932227	+	1.45057i	0.892337	+	0.451370i	$0.149064\pi$
$521$	21.2785	+	33.1100i	0.932227	+	1.45057i	0.0398903	+	0.999204i	$0.487299\pi$
$522$	4.53676	−	2.47726i	0.198569	−	0.108427i
$523$	14.9681	+	11.2050i	0.654510	+	0.489960i	0.874172	−	0.485616i	$-0.161405\pi$
$523$	14.9681	+	11.2050i	0.654510	+	0.489960i	−0.219662	+	0.975576i	$0.570495\pi$
$524$	10.8545	+	4.95706i	0.474179	+	0.216550i
$525$	0.705836	+	6.78167i	0.0308052	+	0.295976i
$526$	−4.61402	+	7.17955i	−0.201181	+	0.313043i
$527$	0.156756	−	2.19173i	0.00682839	−	0.0954734i
$528$	−1.49845	+	1.49845i	−0.0652118	+	0.0652118i
$529$	13.6970	−	18.4768i	0.595522	−	0.803339i
$530$	4.20828	−	5.39836i	0.182796	−	0.234490i
$531$	0.737610	+	0.851248i	0.0320096	+	0.0369410i
$532$	−2.80266	+	0.609681i	−0.121511	+	0.0264330i
$533$	35.9986	−	26.9482i	1.55927	−	1.16726i
$534$	−7.29490	+	15.9736i	−0.315681	+	0.691245i
$535$	−1.96093	+	0.534378i	−0.0847782	+	0.0231032i
$536$	−4.52745	+	15.4191i	−0.195556	+	0.666003i
$537$	1.53417	−	7.05249i	0.0662045	−	0.304337i
$538$	−9.42619	+	25.2726i	−0.406392	+	1.08958i
$539$	−10.4520	+	3.06898i	−0.450199	+	0.132190i
$540$	1.85711	+	1.24545i	0.0799174	+	0.0535954i
$541$	−20.6548	+	23.8369i	−0.888019	+	1.02483i	0.111498	+	0.993765i	$0.464435\pi$
$541$	−20.6548	+	23.8369i	−0.888019	+	1.02483i	−0.999517	+	0.0310644i	$0.990110\pi$
$542$	−2.47241	+	4.52788i	−0.106199	+	0.194489i
$543$	9.41403	+	3.51125i	0.403995	+	0.150682i
$544$	1.77578	−	1.14122i	0.0761360	−	0.0489296i
$545$	20.8263	+	28.9848i	0.892102	+	1.24157i
$546$	−7.61073	+	1.09426i	−0.325709	+	0.0468299i
$547$	12.8656	+	34.4941i	0.550094	+	1.47486i	0.853037	+	0.521851i	$0.174758\pi$
$547$	12.8656	+	34.4941i	0.550094	+	1.47486i	−0.302942	+	0.953009i	$0.597969\pi$
$548$	2.82441	+	3.77298i	0.120653	+	0.161174i
$549$	−0.678367	−	0.435960i	−0.0289520	−	0.0186063i
$550$	10.4336	−	1.84590i	0.444892	−	0.0787095i
$551$		−	10.8721i		−	0.463168i
$552$	−2.15673	−	4.28351i	−0.0917967	−	0.182319i
$553$	13.1536	+	13.1536i	0.559349	+	0.559349i
$554$	−4.70566	+	4.07748i	−0.199924	+	0.173236i
$555$	−18.4634	+	6.47832i	−0.783729	+	0.274990i
$556$	2.66629	−	18.5445i	0.113076	−	0.786460i
$557$	−4.18296	+	1.56016i	−0.177238	+	0.0661062i	−0.436516	−	0.899696i	$-0.643788\pi$
$557$	−4.18296	+	1.56016i	−0.177238	+	0.0661062i	0.259279	+	0.965803i	$0.416515\pi$
$558$	−0.623823	+	0.833330i	−0.0264085	+	0.0352777i
$559$	33.2457	+	9.76181i	1.40614	+	0.412881i
$560$	−1.95140	−	2.34305i	−0.0824619	−	0.0990119i
$561$	−1.85824	−	4.06899i	−0.0784551	−	0.171793i
$562$	−6.94067	−	3.78989i	−0.292774	−	0.159867i
$563$	0.793937	+	11.1007i	0.0334605	+	0.467839i	0.986365	+	0.164570i	$0.0526235\pi$
$563$	0.793937	+	11.1007i	0.0334605	+	0.467839i	−0.952905	+	0.303269i	$0.901922\pi$
$564$	1.49388	+	1.29445i	0.0629035	+	0.0545062i
$565$	−2.00433	+	0.868413i	−0.0843230	+	0.0365344i
$566$	2.44608	−	1.11709i	0.102816	−	0.0469546i
$567$	−1.33250	−	0.289867i	−0.0559596	−	0.0121733i
$568$	5.19178	+	9.50804i	0.217842	+	0.398949i
$569$	3.11620	+	21.6736i	0.130638	+	0.908606i	0.944725	+	0.327864i	$0.106329\pi$
$569$	3.11620	+	21.6736i	0.130638	+	0.908606i	−0.814087	+	0.580743i	$0.802762\pi$
$570$	4.17113	−	2.17287i	0.174709	−	0.0910116i
$571$	19.6100	+	2.81949i	0.820651	+	0.117992i	0.539836	−	0.841770i	$-0.318486\pi$
$571$	19.6100	+	2.81949i	0.820651	+	0.117992i	0.280815	+	0.959762i	$0.409395\pi$
$572$	2.53988	+	11.6757i	0.106198	+	0.488184i
$573$	−10.7076	−	0.765822i	−0.447316	−	0.0319927i
$574$	−10.8754			−0.453930
$575$	−3.43754	+	23.7315i	−0.143355	+	0.989671i
$576$	−1.00000			−0.0416667
$577$	13.7421	+	0.982858i	0.572093	+	0.0409169i	0.354389	−	0.935098i	$-0.384689\pi$
$577$	13.7421	+	0.982858i	0.572093	+	0.0409169i	0.217704	+	0.976015i	$0.430143\pi$
$578$	−2.66646	−	12.2575i	−0.110910	−	0.509846i
$579$	1.76203	+	0.253342i	0.0732276	+	0.0105285i
$580$	10.2508	−	5.33998i	0.425643	−	0.221731i
$581$	0.289204	+	2.01146i	0.0119982	+	0.0834494i
$582$	5.40958	+	9.90691i	0.224234	+	0.410655i
$583$	6.33865	+	1.37889i	0.262520	+	0.0571077i
$584$	−0.561518	+	0.256437i	−0.0232358	+	0.0106114i
$585$	11.5689	−	5.01241i	0.478314	−	0.207238i
$586$	−11.0640	−	9.58702i	−0.457050	−	0.396036i
$587$	0.607129	+	8.48878i	0.0250589	+	0.350369i	0.994477	+	0.104954i	$0.0334697\pi$
$587$	0.607129	+	8.48878i	0.0250589	+	0.350369i	−0.969418	+	0.245415i	$0.921076\pi$
$588$	−4.51165	−	2.46355i	−0.186057	−	0.101595i
$589$	0.909535	+	1.99160i	0.0374768	+	0.0820626i
$590$	1.61183	+	1.93532i	0.0663579	+	0.0796759i
$591$	−19.8848	−	5.83871i	−0.817952	−	0.240172i
$592$	5.24405	−	7.00523i	0.215529	−	0.287913i
$593$	−17.4811	+	6.52010i	−0.717862	+	0.267749i	−0.681736	−	0.731599i	$-0.738775\pi$
$593$	−17.4811	+	6.52010i	−0.717862	+	0.267749i	−0.0361262	+	0.999347i	$0.511502\pi$
$594$	−0.301584	+	2.09756i	−0.0123741	+	0.0860641i
$595$	6.07354	−	2.13104i	0.248991	−	0.0873643i
$596$	3.01394	−	2.61159i	0.123456	−	0.106975i
$597$	4.27019	+	4.27019i	0.174767	+	0.174767i
$598$	−26.8930	−	2.82761i	−1.09974	−	0.115630i
$599$		−	26.0165i		−	1.06301i	−0.847056	−	0.531503i	$-0.821627\pi$
$599$		−	26.0165i		−	1.06301i	0.847056	−	0.531503i	$-0.178373\pi$
$600$	4.09740	+	2.86553i	0.167276	+	0.116985i
$601$	−19.5792	−	12.5828i	−0.798654	−	0.513263i	0.0765226	−	0.997068i	$-0.475618\pi$
$601$	−19.5792	−	12.5828i	−0.798654	−	0.513263i	−0.875176	+	0.483804i	$0.839255\pi$
$602$	−5.02186	−	6.70842i	−0.204676	−	0.273415i
$603$	5.61590	+	15.0568i	0.228697	+	0.613160i
$604$	23.8311	−	3.42639i	0.969673	−	0.139418i
$605$	−8.49319	−	11.8203i	−0.345297	−	0.480563i
$606$	4.73016	−	3.03989i	0.192150	−	0.123487i
$607$	−19.4890	−	7.26903i	−0.791035	−	0.295041i	−0.0787165	−	0.996897i	$-0.525082\pi$
$607$	−19.4890	−	7.26903i	−0.791035	−	0.295041i	−0.712319	+	0.701856i	$0.752355\pi$
$608$	−1.00801	+	1.84603i	−0.0408803	+	0.0748666i
$609$	−4.61600	+	5.32714i	−0.187050	+	0.215867i
$610$	−1.49753	−	1.00430i	−0.0606332	−	0.0406628i
$611$	10.6940	−	3.14005i	0.432634	−	0.127033i
$612$	0.737675	−	1.97778i	0.0298187	−	0.0799471i
$613$	−4.58172	+	21.0618i	−0.185054	+	0.850680i	0.787190	+	0.616711i	$0.211535\pi$
$613$	−4.58172	+	21.0618i	−0.185054	+	0.850680i	−0.972244	+	0.233969i	$0.924829\pi$
$614$	−3.60783	+	12.2871i	−0.145600	+	0.495869i
$615$	17.2055	−	4.68873i	0.693794	−	0.189068i
$616$	1.20046	−	2.62864i	0.0483678	−	0.105911i
$617$	27.6152	−	20.6725i	1.11175	−	0.832243i	0.124623	−	0.992204i	$-0.460228\pi$
$617$	27.6152	−	20.6725i	1.11175	−	0.832243i	0.987123	+	0.159961i	$0.0511369\pi$
$618$	15.8616	−	3.45049i	0.638049	−	0.138799i
$619$	−4.73589	−	5.46551i	−0.190352	−	0.219677i	0.652549	−	0.757746i	$-0.273700\pi$
$619$	−4.73589	−	5.46551i	−0.190352	−	0.219677i	−0.842901	+	0.538069i	$0.819154\pi$
$620$	−1.43106	+	1.83576i	−0.0574729	+	0.0737260i
$621$	−4.29357	−	2.13665i	−0.172295	−	0.0857407i
$622$	9.30161	−	9.30161i	0.372960	−	0.372960i
$623$	1.70833	−	23.8856i	0.0684427	−	0.956955i
$624$	−3.04840	+	4.74340i	−0.122034	+	0.189888i
$625$	−8.57744	−	23.4825i	−0.343098	−	0.939300i
$626$	18.3394	+	8.37530i	0.732988	+	0.334744i
$627$	3.56818	+	2.67110i	0.142499	+	0.106674i
$628$	5.07099	−	2.76897i	0.202354	−	0.110494i
$629$	9.98643	+	15.5392i	0.398185	+	0.619588i
$630$	−2.96632	−	0.706275i	−0.118181	−	0.0281387i
$631$	−14.0116	−	47.7192i	−0.557794	−	1.89967i	−0.414684	−	0.909966i	$-0.636108\pi$
$631$	−14.0116	−	47.7192i	−0.557794	−	1.89967i	−0.143111	−	0.989707i	$-0.545710\pi$
$632$	13.6065	−	0.973156i	0.541237	−	0.0387101i
$633$	−9.54258	+	0.682499i	−0.379284	+	0.0271269i
$634$	−5.09831	−	17.3632i	−0.202480	−	0.689582i
$635$	15.5117	+	25.2066i	0.615562	+	1.00029i
$636$	1.65496	+	2.57517i	0.0656234	+	0.102112i
$637$	−25.4389	+	13.8907i	−1.00793	+	0.550369i
$638$	8.76904	+	6.56442i	0.347170	+	0.259888i
$639$	9.85419	+	4.50026i	0.389826	+	0.178027i
$640$	−2.23564	−	0.0437046i	−0.0883715	−	0.00172758i
$641$	18.0069	−	28.0193i	0.711231	−	1.10670i	−0.278035	−	0.960571i	$-0.589683\pi$
$641$	18.0069	−	28.0193i	0.711231	−	1.10670i	0.989266	−	0.146126i	$-0.0466805\pi$
$642$	0.0648425	−	0.906617i	0.00255913	−	0.0357813i
$643$	35.1839	−	35.1839i	1.38752	−	1.38752i	0.557018	−	0.830501i	$-0.311946\pi$
$643$	35.1839	−	35.1839i	1.38752	−	1.38752i	0.830501	−	0.557018i	$-0.188054\pi$
$644$	4.79693	+	4.44518i	0.189026	+	0.175164i
$645$	10.8371	+	8.44805i	0.426711	+	0.332641i
$646$	−2.90747	−	3.35540i	−0.114393	−	0.132017i
$647$	−33.2418	+	7.23132i	−1.30687	+	0.284292i	−0.811481	−	0.584379i	$-0.801338\pi$
$647$	−33.2418	+	7.23132i	−1.30687	+	0.284292i	−0.495390	+	0.868671i	$0.664975\pi$
$648$	−0.800541	+	0.599278i	−0.0314482	+	0.0235419i
$649$	−0.991559	+	2.17121i	−0.0389221	+	0.0852275i
$650$	26.0829	−	10.7003i	1.02306	−	0.419702i
$651$	0.399923	−	1.36201i	0.0156742	−	0.0533815i
$652$	−2.18099	+	10.0258i	−0.0854140	+	0.392642i
$653$	−11.0624	+	29.6595i	−0.432906	+	1.16067i	0.519134	+	0.854693i	$0.326255\pi$
$653$	−11.0624	+	29.6595i	−0.432906	+	1.16067i	−0.952040	+	0.305974i	$0.901018\pi$
$654$	−15.3150	+	4.49689i	−0.598864	+	0.175842i
$655$	26.1786	−	5.16110i	1.02288	−	0.201661i
$656$	−5.22261	+	6.02721i	−0.203909	+	0.235323i
$657$	−0.295842	+	0.541794i	−0.0115419	+	0.0211374i
$658$	−2.52557	−	0.941989i	−0.0984570	−	0.0367225i
$659$	17.3319	−	11.1385i	0.675156	−	0.433896i	−0.157625	−	0.987499i	$-0.550384\pi$
$659$	17.3319	−	11.1385i	0.675156	−	0.433896i	0.832781	+	0.553603i	$0.186747\pi$
$660$	−0.765907	+	4.67622i	−0.0298129	+	0.182022i
$661$	−29.8793	+	4.29599i	−1.16217	+	0.167095i	−0.696294	−	0.717756i	$-0.745169\pi$
$661$	−29.8793	+	4.29599i	−1.16217	+	0.167095i	−0.465874	+	0.884851i	$0.654260\pi$
$662$	−1.94661	−	5.21908i	−0.0756573	−	0.202845i
$663$	−7.13269	−	9.52816i	−0.277011	−	0.370043i
$664$	1.25365	+	0.805670i	0.0486509	+	0.0312660i
$665$	−4.29389	+	4.76399i	−0.166510	+	0.184740i
$666$		−	8.75062i		−	0.339080i
$667$	−20.3297	+	14.1859i	−0.787171	+	0.549279i
$668$	0.711868	+	0.711868i	0.0275430	+	0.0275430i
$669$	19.9344	−	17.2732i	0.770707	−	0.667821i
$670$	11.8971	+	33.9070i	0.459624	+	1.30994i
$671$	0.243190	−	1.69142i	0.00938825	−	0.0652967i
$672$	1.27768	−	0.476551i	0.0492876	−	0.0183833i
$673$	3.59910	−	4.80783i	0.138735	−	0.185328i	−0.725793	−	0.687914i	$-0.758527\pi$
$673$	3.59910	−	4.80783i	0.138735	−	0.185328i	0.864528	+	0.502585i	$0.167618\pi$
$674$	−32.7125	−	9.60527i	−1.26004	−	0.369981i
$675$	4.99739	−	0.161505i	0.192350	−	0.00621635i
$676$	7.80673	+	17.0943i	0.300259	+	0.657475i
$677$	−33.8655	−	18.4920i	−1.30156	−	0.710704i	−0.329213	−	0.944256i	$-0.606784\pi$
$677$	−33.8655	−	18.4920i	−1.30156	−	0.710704i	−0.972345	+	0.233551i	$0.924965\pi$
$678$	−0.0696900	−	0.974393i	−0.00267643	−	0.0374213i
$679$	−11.6329	−	10.0799i	−0.446429	−	0.386833i
$680$	1.73561	−	4.38937i	0.0665578	−	0.168325i
$681$	−1.58040	+	0.721745i	−0.0605611	+	0.0276573i
$682$	−2.15552	−	0.468904i	−0.0825390	−	0.0179553i
$683$	17.3029	+	31.6880i	0.662079	+	1.21251i	0.965687	+	0.259710i	$0.0836269\pi$
$683$	17.3029	+	31.6880i	0.662079	+	1.21251i	−0.303608	+	0.952797i	$0.598191\pi$
$684$	0.299333	+	2.08191i	0.0114453	+	0.0796037i
$685$	10.0518	+	3.16615i	0.384060	+	0.120972i
$686$	16.3869	+	2.35608i	0.625655	+	0.0899557i
$687$	0.108594	+	0.499200i	0.00414313	+	0.0190457i
$688$	−6.12946	−	0.438388i	−0.233684	−	0.0167134i
$689$	17.2600			0.657555
$690$	−9.50550	−	4.96443i	−0.361868	−	0.188992i
$691$	44.6041			1.69682			0.848410	−	0.529339i	$-0.177560\pi$
$691$	44.6041			1.69682			0.848410	+	0.529339i	$0.177560\pi$
$692$	12.8275	+	0.917444i	0.487630	+	0.0348760i
$693$	−0.614267	−	2.82374i	−0.0233341	−	0.107265i
$694$	25.0586	+	3.60289i	0.951213	+	0.136764i
$695$	−19.3547	−	37.1541i	−0.734167	−	1.40933i
$696$	0.735631	+	5.11643i	0.0278840	+	0.193938i
$697$	−8.06793	−	14.7753i	−0.305595	−	0.559655i
$698$	14.4324	+	3.13957i	0.546273	+	0.118834i
$699$	14.6573	−	6.69375i	0.554388	−	0.253181i
$700$	−6.60075	−	1.70862i	−0.249485	−	0.0645797i
$701$	32.4796	+	28.1437i	1.22674	+	1.06297i	0.995944	+	0.0899706i	$0.0286773\pi$
$701$	32.4796	+	28.1437i	1.22674	+	1.06297i	0.230793	+	0.973003i	$0.425868\pi$
$702$	0.402245	+	5.62413i	0.0151818	+	0.212269i
$703$	−16.1540	−	8.82073i	−0.609258	−	0.332680i
$704$	−0.880320	−	1.92763i	−0.0331783	−	0.0726503i
$705$	4.40173	+	0.401429i	0.165779	+	0.0151187i
$706$	1.02718	+	0.301607i	0.0386584	+	0.0113511i
$707$	−4.59498	+	6.13817i	−0.172812	+	0.230850i
$708$	−1.05534	+	0.393623i	−0.0396623	+	0.0147933i
$709$	2.64756	−	18.4142i	0.0994312	−	0.691559i	−0.877745	−	0.479128i	$-0.840953\pi$
$709$	2.64756	−	18.4142i	0.0994312	−	0.691559i	0.977176	−	0.212431i	$-0.0681380\pi$
$710$	21.8338	+	10.4916i	0.819406	+	0.393744i
$711$	10.3094	−	8.93312i	0.386632	−	0.335018i
$712$	−12.4171	−	12.4171i	−0.465352	−	0.465352i
$713$	2.53734	−	4.29937i	0.0950241	−	0.161013i
$714$			2.87852i			0.107726i
$715$	19.8464	+	17.8880i	0.742213	+	0.668973i
$716$	6.07169	+	3.90204i	0.226910	+	0.145826i
$717$	6.43017	+	8.58970i	0.240139	+	0.320788i
$718$	−0.946383	−	2.53735i	−0.0353187	−	0.0946931i
$719$	−43.3179	+	6.22817i	−1.61548	+	0.232272i	−0.889998	−	0.455965i	$-0.849294\pi$
$719$	−43.3179	+	6.22817i	−1.61548	+	0.232272i	−0.725486	+	0.688237i	$0.758385\pi$
$720$	−1.81591	+	1.30478i	−0.0676751	+	0.0486264i
$721$	−18.6218	+	11.9675i	−0.693512	+	0.445693i
$722$	−13.6570	−	5.09381i	−0.508263	−	0.189572i
$723$	−8.82464	+	16.1611i	−0.328192	+	0.601039i
$724$	−6.57973	+	7.59342i	−0.244534	+	0.282207i
$725$	11.6471	−	23.0721i	0.432563	−	0.856875i
$726$	6.24560	−	1.83387i	0.231796	−	0.0680615i
$727$	3.27405	−	8.77806i	0.121428	−	0.325560i	−0.861987	−	0.506930i	$-0.830780\pi$
$727$	3.27405	−	8.77806i	0.121428	−	0.325560i	0.983415	+	0.181370i	$0.0580530\pi$
$728$	1.63441	−	7.51328i	0.0605754	−	0.278461i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	−0.685075	+	1.19833i	−0.0253557	+	0.0443520i
$731$	5.38859	−	11.7994i	0.199304	−	0.436415i
$732$	0.645537	−	0.483243i	0.0238597	−	0.0178612i
$733$	5.16028	−	1.12255i	0.190599	−	0.0414624i	−0.116252	−	0.993220i	$-0.537088\pi$
$733$	5.16028	−	1.12255i	0.190599	−	0.0414624i	0.306852	+	0.951757i	$0.400724\pi$
$734$	3.37735	+	3.89767i	0.124660	+	0.143866i
$735$	−11.4072	+	1.41313i	−0.420759	+	0.0521241i
$736$	4.76714	−	0.523816i	0.175719	−	0.0193081i
$737$	−24.0802	+	24.0802i	−0.887005	+	0.887005i
$738$	−0.568940	+	7.95482i	−0.0209430	+	0.292821i
$739$	−15.1429	+	23.5629i	−0.557042	+	0.866775i	−0.999550	−	0.0299899i	$-0.990452\pi$
$739$	−15.1429	+	23.5629i	−0.557042	+	0.866775i	0.442508	+	0.896765i	$0.354089\pi$
$740$	0.382443	−	19.5632i	0.0140589	−	0.719159i
$741$	10.7878	+	4.92662i	0.396300	+	0.180984i
$742$	−3.34171	−	2.50157i	−0.122678	−	0.0918356i
$743$	−14.7384	+	8.04775i	−0.540698	+	0.295243i	−0.726296	−	0.687382i	$-0.758760\pi$
$743$	−14.7384	+	8.04775i	−0.540698	+	0.295243i	0.185598	+	0.982626i	$0.440578\pi$
$744$	−0.562784	−	0.875710i	−0.0206327	−	0.0321051i
$745$	2.06549	−	8.67497i	0.0756739	−	0.317826i
$746$	1.31304	+	4.47180i	0.0480737	+	0.163724i
$747$	1.48642	−	0.106311i	0.0543851	−	0.00388970i
$748$	4.46183	−	0.319116i	0.163141	−	0.0116680i
$749$	0.349201	+	1.18927i	0.0127595	+	0.0434549i
$750$	11.1794	−	0.142659i	0.408215	−	0.00520917i
$751$	−21.4500	−	33.3768i	−0.782721	−	1.21794i	−0.971761	−	0.235968i	$-0.924174\pi$
$751$	−21.4500	−	33.3768i	−0.782721	−	1.21794i	0.189040	−	0.981969i	$-0.439462\pi$
$752$	−1.73489	+	0.947322i	−0.0632650	+	0.0345453i
$753$	−7.82168	−	5.85523i	−0.285038	−	0.213377i
$754$	26.5118	+	12.1075i	0.965502	+	0.440930i
$755$	38.8045	−	37.3164i	1.41224	−	1.35808i
$756$	0.737251	−	1.14718i	0.0268136	−	0.0417227i
$757$	1.89607	−	26.5105i	0.0689139	−	0.963542i	−0.838931	−	0.544237i	$-0.816819\pi$
$757$	1.89607	−	26.5105i	0.0689139	−	0.963542i	0.907845	−	0.419305i	$-0.137726\pi$
$758$	−8.33766	+	8.33766i	−0.302838	+	0.302838i
$759$	0.338956	−	10.1574i	0.0123033	−	0.368689i
$760$	0.578212	+	4.66748i	0.0209739	+	0.169307i
$761$	−22.9650	−	26.5030i	−0.832479	−	0.960732i	0.167203	−	0.985922i	$-0.446526\pi$
$761$	−22.9650	−	26.5030i	−0.832479	−	0.960732i	−0.999683	+	0.0251902i	$0.991981\pi$
$762$	−12.9337	+	2.81356i	−0.468539	+	0.101924i
$763$	17.4247	−	13.0440i	0.630816	−	0.472223i
$764$	4.45946	−	9.76485i	0.161338	−	0.353280i
$765$	−1.24102	−	4.55399i	−0.0448692	−	0.164650i
$766$	0.393457	−	1.33999i	0.0142162	−	0.0484159i
$767$	−1.35000	+	6.20584i	−0.0487456	+	0.224080i
$768$	0.349464	−	0.936950i	0.0126102	−	0.0338093i
$769$	−23.8974	+	7.01691i	−0.861762	+	0.253036i	−0.682608	−	0.730785i	$-0.739154\pi$
$769$	−23.8974	+	7.01691i	−0.861762	+	0.253036i	−0.179154	+	0.983821i	$0.557336\pi$
$770$	−1.24987	−	6.33971i	−0.0450422	−	0.228467i
$771$	−15.6634	+	18.0765i	−0.564103	+	0.651010i
$772$	−0.853136	+	1.56240i	−0.0307051	+	0.0562321i
$773$	−28.9247	−	10.7884i	−1.04035	−	0.388030i	−0.229514	−	0.973305i	$-0.573714\pi$
$773$	−28.9247	−	10.7884i	−1.04035	−	0.388030i	−0.810835	+	0.585275i	$0.800986\pi$
$774$	−5.16960	+	3.32230i	−0.185818	+	0.119418i
$775$	−0.203420	+	5.20081i	−0.00730705	+	0.186819i
$776$	−11.1727	+	1.60640i	−0.401078	+	0.0576663i
$777$	4.17011	+	11.1805i	0.149602	+	0.401099i
$778$	18.4556	+	24.6538i	0.661664	+	0.883880i
$779$	14.1114	+	9.06884i	0.505593	+	0.324925i
$780$	0.653476	+	12.5911i	0.0233982	+	0.450834i
$781$			22.9569i			0.821463i
$782$	−2.48060	+	9.81477i	−0.0887062	+	0.350976i
$783$	3.65506	+	3.65506i	0.130621	+	0.130621i
$784$	3.88488	−	3.36626i	0.138746	−	0.120224i
$785$	5.59558	−	11.6447i	0.199715	−	0.415619i
$786$	−1.69821	+	11.8113i	−0.0605733	+	0.421296i
$787$	10.0805	−	3.75983i	0.359331	−	0.134024i	−0.163313	−	0.986574i	$-0.552218\pi$
$787$	10.0805	−	3.75983i	0.359331	−	0.134024i	0.522645	+	0.852551i	$0.324945\pi$
$788$	12.4196	−	16.5906i	0.442430	−	0.591017i
$789$	−8.18865	−	2.40440i	−0.291524	−	0.0855991i
$790$	23.4385	−	19.5207i	0.833903	−	0.694515i
$791$	0.553389	+	1.21175i	0.0196763	+	0.0430850i
$792$	−1.85992	−	1.01559i	−0.0660893	−	0.0360875i
$793$	−0.324361	−	4.53516i	−0.0115184	−	0.161048i
$794$	−10.5987	−	9.18384i	−0.376134	−	0.325922i
$795$	6.36529	+	2.51692i	0.225754	+	0.0892659i
$796$	−5.49324	+	2.50868i	−0.194703	+	0.0889177i
$797$	27.8438	+	6.05705i	0.986278	+	0.214552i	0.676649	−	0.736306i	$-0.263432\pi$
$797$	27.8438	+	6.05705i	0.986278	+	0.214552i	0.309629	+	0.950858i	$0.399795\pi$
$798$	−1.37459	−	2.51737i	−0.0486598	−	0.0891138i
$799$	−0.593812	−	4.13006i	−0.0210076	−	0.146111i
$800$	−4.11676	+	2.83766i	−0.145549	+	0.100326i
$801$	−17.3818	−	2.49912i	−0.614154	−	0.0883021i
$802$	−0.362921	−	1.66832i	−0.0128152	−	0.0589104i
$803$	−1.30481	−	0.0933221i	−0.0460459	−	0.00329327i
$804$	−16.0700			−0.566746
$805$	14.5108	+	1.81311i	0.511439	+	0.0639036i
$806$	−5.86943			−0.206742
$807$	−26.9045	−	1.92425i	−0.947084	−	0.0677368i
$808$	1.19520	+	5.49426i	0.0420471	+	0.193287i
$809$	−30.8122	−	4.43013i	−1.08330	−	0.155755i	−0.422534	−	0.906347i	$-0.638859\pi$
$809$	−30.8122	−	4.43013i	−1.08330	−	0.155755i	−0.660766	+	0.750592i	$0.729768\pi$
$810$	−0.671787	+	2.13277i	−0.0236042	+	0.0749379i
$811$	0.289843	+	2.01590i	0.0101778	+	0.0707878i	0.994277	−	0.106830i	$-0.0340700\pi$
$811$	0.289843	+	2.01590i	0.0101778	+	0.0707878i	−0.984100	+	0.177618i	$0.943161\pi$
$812$	−3.37814	−	6.18660i	−0.118549	−	0.217107i
$813$	−5.04103	−	1.09661i	−0.176797	−	0.0384597i
$814$	16.8680	−	7.70335i	0.591222	−	0.270002i
$815$	9.12105	+	21.0518i	0.319496	+	0.737411i
$816$	1.59529	+	1.38233i	0.0558464	+	0.0483912i
$817$	0.922067	+	12.8922i	0.0322591	+	0.451041i
$818$	1.29208	+	0.705527i	0.0451764	+	0.0246682i
$819$	−3.19412	−	6.99415i	−0.111612	−	0.244396i
$820$	−1.61961	+	17.7593i	−0.0565592	+	0.620180i
$821$	−47.6283	−	13.9849i	−1.66224	−	0.488077i	−0.690341	−	0.723484i	$-0.742539\pi$
$821$	−47.6283	−	13.9849i	−1.66224	−	0.488077i	−0.971897	+	0.235407i	$0.924358\pi$
$822$	−2.82441	+	3.77298i	−0.0985127	+	0.131598i
$823$	−3.05121	+	1.13804i	−0.106359	+	0.0396697i	−0.402080	−	0.915604i	$-0.631713\pi$
$823$	−3.05121	+	1.13804i	−0.106359	+	0.0396697i	0.295722	+	0.955274i	$0.404440\pi$
$824$	−2.31014	+	16.0674i	−0.0804775	+	0.559734i
$825$	4.71062	+	9.49095i	0.164003	+	0.330432i
$826$	1.16081	−	1.00585i	0.0403899	−	0.0349980i
$827$	16.7074	+	16.7074i	0.580973	+	0.580973i	0.935171	−	0.354198i	$-0.115246\pi$
$827$	16.7074	+	16.7074i	0.580973	+	0.580973i	−0.354198	+	0.935171i	$0.615246\pi$
$828$	3.50238	−	3.27618i	0.121716	−	0.113855i
$829$		−	23.6448i		−	0.821217i	−0.911812	−	0.410608i	$-0.865316\pi$
$829$		−	23.6448i		−	0.821217i	0.911812	−	0.410608i	$-0.134684\pi$
$830$	3.32774	−	0.172709i	0.115507	−	0.00599481i
$831$	−5.23805	−	3.36629i	−0.181706	−	0.116775i
$832$	−3.37902	−	4.51385i	−0.117147	−	0.156489i
$833$	3.79197	+	10.1667i	0.131384	+	0.352254i
$834$	18.5445	−	2.66629i	0.642142	−	0.0923261i
$835$	2.22152	+	0.363858i	0.0768790	+	0.0125918i
$836$	−3.74964	+	2.40975i	−0.129684	+	0.0833428i
$837$	−0.975325	−	0.363778i	−0.0337122	−	0.0125740i
$838$	−5.34609	+	9.79063i	−0.184678	+	0.338212i
$839$	−14.0059	+	16.1637i	−0.483538	+	0.558033i	−0.944127	−	0.329581i	$-0.893093\pi$
$839$	−14.0059	+	16.1637i	−0.483538	+	0.558033i	0.460589	+	0.887613i	$0.347638\pi$
$840$	1.69837	−	2.53247i	0.0585992	−	0.0873786i
$841$	−2.18860	+	0.642632i	−0.0754691	+	0.0221597i
$842$	−3.76286	+	10.0886i	−0.129677	+	0.347677i
$843$	1.68096	−	7.72726i	0.0578954	−	0.266141i
$844$	2.69532	−	9.17943i	0.0927769	−	0.315969i
$845$	36.4807	+	20.8558i	1.25498	+	0.717461i
$846$	−0.821143	+	1.79805i	−0.0282315	+	0.0618183i
$847$	−7.10596	+	5.31945i	−0.244164	+	0.182779i
$848$	−2.99115	+	0.650685i	−0.102717	+	0.0223446i
$849$	1.76097	+	2.03227i	0.0604365	+	0.0697474i
$850$	−2.57545	−	10.2353i	−0.0883372	−	0.351069i
$851$	4.58372	+	41.7154i	0.157128	+	1.42999i
$852$	−7.66020	+	7.66020i	−0.262434	+	0.262434i
$853$	3.15722	−	44.1437i	0.108101	−	1.51145i	−0.596940	−	0.802286i	$-0.703617\pi$
$853$	3.15722	−	44.1437i	0.108101	−	1.51145i	0.705041	−	0.709166i	$-0.250928\pi$
$854$	−0.594501	+	0.925062i	−0.0203434	+	0.0316550i
$855$	3.26000	+	3.39000i	0.111490	+	0.115935i
$856$	0.826794	+	0.377584i	0.0282592	+	0.0129056i
$857$	−38.8151	−	29.0566i	−1.32590	−	0.992556i	−0.998869	−	0.0475417i	$-0.984861\pi$
$857$	−38.8151	−	29.0566i	−1.32590	−	0.992556i	−0.327030	−	0.945014i	$-0.606048\pi$
$858$	−10.4871	+	5.72641i	−0.358025	+	0.195496i
$859$	−17.8696	−	27.8056i	−0.609702	−	0.948714i	−0.999612	−	0.0278614i	$-0.991130\pi$
$859$	−17.8696	−	27.8056i	−0.609702	−	0.948714i	0.389910	−	0.920853i	$-0.372506\pi$
$860$	−11.7026	+	7.20154i	−0.399055	+	0.245570i
$861$	−3.06395	−	10.4349i	−0.104419	−	0.355619i
$862$	−0.691755	+	0.0494753i	−0.0235613	+	0.00168514i
$863$	−47.1734	+	3.37391i	−1.60580	+	0.114849i	−0.845229	−	0.534405i	$-0.820536\pi$
$863$	−47.1734	+	3.37391i	−1.60580	+	0.114849i	−0.760572	+	0.649254i	$0.775081\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	24.4908	−	15.0711i	0.832711	−	0.512434i
$866$	3.87263	+	6.02592i	0.131597	+	0.204769i
$867$	11.0098	−	6.01180i	0.373912	−	0.204171i
$868$	1.13638	+	0.850683i	0.0385712	+	0.0288741i
$869$	26.2953	+	12.0087i	0.892007	+	0.407366i
$870$	8.01167	+	8.33116i	0.271621	+	0.282453i
$871$	−48.9878	+	76.2266i	−1.65989	+	2.58284i
$872$	1.13868	−	15.9209i	0.0385607	−	0.539149i
$873$	−7.98156	+	7.98156i	−0.270135	+	0.270135i
$874$	−2.51750	−	9.76794i	−0.0851556	−	0.330405i
$875$	−14.2158	+	5.50984i	−0.480581	+	0.186267i
$876$	−0.404247	−	0.466526i	−0.0136582	−	0.0157625i
$877$	−46.2216	+	10.0549i	−1.56079	+	0.339530i	−0.908318	−	0.418281i	$-0.862633\pi$
$877$	−46.2216	+	10.0549i	−1.56079	+	0.339530i	−0.652475	+	0.757811i	$0.726269\pi$
$878$	0.782429	−	0.585719i	0.0264057	−	0.0197670i
$879$	6.08158	−	13.3168i	0.205127	−	0.449165i
$880$	−4.11372	−	2.35179i	−0.138674	−	0.0792787i
$881$	10.1715	−	34.6408i	0.342685	−	1.16708i	−0.590307	−	0.807179i	$-0.700993\pi$
$881$	10.1715	−	34.6408i	0.342685	−	1.16708i	0.932992	−	0.359898i	$-0.117189\pi$
$882$	1.09268	−	5.02295i	0.0367923	−	0.169132i
$883$	−12.1700	+	32.6291i	−0.409554	+	1.09806i	0.554462	+	0.832209i	$0.312924\pi$
$883$	−12.1700	+	32.6291i	−0.409554	+	1.09806i	−0.964015	+	0.265846i	$0.914349\pi$
$884$	11.4200	−	3.35322i	0.384097	−	0.112781i
$885$	−1.40282	+	2.09178i	−0.0471554	+	0.0703144i
$886$	18.5436	−	21.4005i	0.622986	−	0.718964i
$887$	−21.9545	+	40.2067i	−0.737161	+	1.35001i	0.192392	+	0.981318i	$0.438376\pi$
$887$	−21.9545	+	40.2067i	−0.737161	+	1.35001i	−0.929552	+	0.368691i	$0.879806\pi$
$888$	8.19889	+	3.05803i	0.275137	+	0.102621i
$889$	15.1844	−	9.75840i	0.509267	−	0.327286i
$890$	−38.7501	−	6.34680i	−1.29891	−	0.212745i
$891$	−2.09756	+	0.301584i	−0.0702710	+	0.0101034i
$892$	9.21779	+	24.7139i	0.308634	+	0.827481i
$893$	2.49155	+	3.32832i	0.0833764	+	0.111378i
$894$	3.35493	+	2.15608i	0.112206	+	0.0721102i
$895$	16.1170	−	0.836468i	0.538731	−	0.0279600i
$896$			1.36366i			0.0455567i
$897$	−4.86357	−	26.6003i	−0.162390	−	0.888158i
$898$	18.6419	+	18.6419i	0.622089	+	0.622089i
$899$	−4.06650	+	3.52365i	−0.135626	+	0.117520i
$900$	−1.59509	+	4.73874i	−0.0531696	+	0.157958i
$901$	0.919583	−	6.39584i	0.0306358	−	0.213076i
$902$	−15.8348	+	5.90608i	−0.527242	+	0.196651i
$903$	5.02186	−	6.70842i	0.167117	−	0.223242i
$904$	0.937312	+	0.275220i	0.0311745	+	0.00915367i
$905$	−2.04047	+	22.3741i	−0.0678276	+	0.743741i
$906$	10.0016	+	21.9004i	0.332280	+	0.727593i
$907$	4.29267	+	2.34398i	0.142536	+	0.0778305i	0.548934	−	0.835865i	$-0.315034\pi$
$907$	4.29267	+	2.34398i	0.142536	+	0.0778305i	−0.406398	+	0.913696i	$0.633216\pi$
$908$	−0.123945	−	1.73298i	−0.00411326	−	0.0575109i
$909$	4.24939	+	3.68212i	0.140943	+	0.122128i
$910$	−6.83523	−	15.7760i	−0.226586	−	0.522970i
$911$	−30.8803	+	14.1025i	−1.02311	+	0.467238i	−0.855054	−	0.518539i	$-0.826476\pi$
$911$	−30.8803	+	14.1025i	−1.02311	+	0.467238i	−0.168055	+	0.985778i	$0.553749\pi$
$912$	−2.05525	−	0.447092i	−0.0680560	−	0.0148047i
$913$	1.51345	+	2.77167i	0.0500878	+	0.0917290i
$914$	−5.15694	−	35.8673i	−0.170576	−	1.18638i
$915$	0.541713	−	1.71981i	0.0179085	−	0.0568553i
$916$	−0.505675	−	0.0727051i	−0.0167080	−	0.00240225i
$917$	−3.45892	−	15.9004i	−0.114224	−	0.525078i
$918$	2.10550	+	0.150588i	0.0694917	+	0.00497015i
$919$	19.6337			0.647655			0.323828	−	0.946116i	$-0.395030\pi$
$919$	19.6337			0.647655			0.323828	+	0.946116i	$0.395030\pi$
$920$	7.97325	−	7.17128i	0.262870	−	0.236430i
$921$	−12.8059			−0.421968
$922$	9.50381	+	0.679726i	0.312991	+	0.0223856i
$923$	12.9841	+	59.6868i	0.427376	+	1.96461i
$924$	2.86037	+	0.411258i	0.0940991	+	0.0135294i
$925$	−24.8313	−	36.0242i	−0.816448	−	1.18447i
$926$	3.02325	+	21.0272i	0.0993502	+	0.690996i
$927$	7.77946	+	14.2470i	0.255511	+	0.467933i
$928$	−5.05091	−	1.09876i	−0.165804	−	0.0360685i
$929$	−30.1047	+	13.7484i	−0.987703	+	0.451069i	−0.842712	−	0.538364i	$-0.819042\pi$
$929$	−30.1047	+	13.7484i	−0.987703	+	0.451069i	−0.144991	+	0.989433i	$0.546315\pi$
$930$	−2.16458	−	0.855902i	−0.0709793	−	0.0280661i
$931$	−8.17112	−	7.08031i	−0.267798	−	0.232048i
$932$	1.14952	+	16.0723i	0.0376537	+	0.526467i
$933$	11.5454	+	6.30426i	0.377979	+	0.206392i
$934$	−15.6141	−	34.1901i	−0.510909	−	1.11873i
$935$	7.68592	−	6.40120i	0.251356	−	0.209342i
$936$	−5.41009	−	1.58855i	−0.176834	−	0.0519233i
$937$	33.8683	−	45.2428i	1.10643	−	1.47802i	0.245429	−	0.969415i	$-0.421071\pi$
$937$	33.8683	−	45.2428i	1.10643	−	1.47802i	0.861001	−	0.508603i	$-0.169838\pi$
$938$	20.5324	−	7.65818i	0.670406	−	0.250048i
$939$	−2.86925	+	19.9561i	−0.0936344	+	0.651242i
$940$	−1.91436	+	3.98391i	−0.0624397	+	0.129941i
$941$	9.11489	−	7.89810i	0.297137	−	0.257471i	−0.493514	−	0.869738i	$-0.664288\pi$
$941$	9.11489	−	7.89810i	0.297137	−	0.257471i	0.790651	+	0.612267i	$0.209742\pi$
$942$	4.08547	+	4.08547i	0.133112	+	0.133112i
$943$	−1.45465	−	38.2198i	−0.0473698	−	1.24461i
$944$		−	1.12636i		−	0.0366600i
$945$	−0.158042	−	3.04514i	−0.00514111	−	0.0990584i
$946$	−10.9551	−	7.04040i	−0.356180	−	0.228903i
$947$	4.92613	+	6.58054i	0.160078	+	0.213839i	0.873408	−	0.486989i	$-0.161905\pi$
$947$	4.92613	+	6.58054i	0.160078	+	0.213839i	−0.713330	+	0.700828i	$0.752814\pi$
$948$	4.76713	+	12.7812i	0.154829	+	0.415113i
$949$	−3.44523	+	0.495349i	−0.111837	+	0.0160797i
$950$	7.14002	+	7.72129i	0.231653	+	0.250512i
$951$	15.2235	−	9.78358i	0.493657	−	0.317254i
$952$	−2.69703	−	1.00594i	−0.0874111	−	0.0326027i
$953$	−7.67902	+	14.0631i	−0.248748	+	0.455548i	−0.971982	−	0.235055i	$-0.924473\pi$
$953$	−7.67902	+	14.0631i	−0.248748	+	0.455548i	0.723234	+	0.690603i	$0.242655\pi$
$954$	−2.00460	+	2.31343i	−0.0649013	+	0.0749001i
$955$	−4.64301	−	23.5508i	−0.150244	−	0.762084i
$956$	−10.2952	+	3.02295i	−0.332971	+	0.0977692i
$957$	−3.82799	+	10.2632i	−0.123741	+	0.331764i
$958$	−6.78449	+	31.1878i	−0.219197	+	1.00763i
$959$	1.81069	−	6.16664i	0.0584702	−	0.199131i
$960$	−0.587919	−	2.15739i	−0.0189750	−	0.0696296i
$961$	−12.4277	+	27.2129i	−0.400894	+	0.877836i
$962$	39.4990	−	29.5686i	1.27350	−	0.953328i
$963$	0.888161	−	0.193208i	0.0286206	−	0.00622602i
$964$	−12.0583	−	13.9160i	−0.388371	−	0.448204i
$965$	0.489373	+	3.95035i	0.0157535	+	0.127166i
$966$	−2.91366	+	5.85497i	−0.0937456	+	0.188381i
$967$	18.7717	−	18.7717i	0.603658	−	0.603658i	−0.337623	−	0.941281i	$-0.609623\pi$
$967$	18.7717	−	18.7717i	0.603658	−	0.603658i	0.941281	+	0.337623i	$0.109623\pi$
$968$	−0.464366	+	6.49269i	−0.0149253	+	0.208683i
$969$	2.40035	−	3.73502i	0.0771105	−	0.119986i
$970$	−18.1927	+	17.4951i	−0.584133	+	0.561733i
$971$	1.45944	+	0.666504i	0.0468357	+	0.0213891i	0.438695	−	0.898636i	$-0.355441\pi$
$971$	1.45944	+	0.666504i	0.0468357	+	0.0213891i	−0.391859	+	0.920025i	$0.628168\pi$
$972$	−0.800541	−	0.599278i	−0.0256774	−	0.0192218i
$973$	−22.4233	+	12.2440i	−0.718858	+	0.392526i
$974$	−4.58445	−	7.13354i	−0.146895	−	0.228573i
$975$	17.6153	+	22.0117i	0.564141	+	0.704939i
$976$	0.227182	+	0.773712i	0.00727193	+	0.0247659i
$977$	−9.65324	+	0.690413i	−0.308834	+	0.0220883i	−0.224896	−	0.974383i	$-0.572204\pi$
$977$	−9.65324	+	0.690413i	−0.308834	+	0.0220883i	−0.0839381	+	0.996471i	$0.526750\pi$
$978$	−10.2342	+	0.731963i	−0.327253	+	0.0234056i
$979$	−10.4841	−	35.7056i	−0.335074	−	1.14116i
$980$	2.66236	−	11.1818i	0.0850459	−	0.357188i
$981$	−8.62946	−	13.4277i	−0.275518	−	0.428714i
$982$	21.8105	−	11.9094i	0.696002	−	0.380046i
$983$	30.6385	+	22.9357i	0.977217	+	0.731536i	0.963317	−	0.268368i	$-0.0864842\pi$
$983$	30.6385	+	22.9357i	0.977217	+	0.731536i	0.0139009	+	0.999903i	$0.495575\pi$
$984$	−7.25445	−	3.31299i	−0.231263	−	0.105614i
$985$	0.905748	−	46.3321i	0.0288595	−	1.47626i
$986$	5.89904	−	9.17908i	0.187864	−	0.292322i
$987$	0.192296	−	2.68866i	0.00612086	−	0.0855808i
$988$	−8.38595	+	8.38595i	−0.266793	+	0.266793i
$989$	22.9039	−	18.5458i	0.728303	−	0.589722i
$990$	−4.70258	+	0.582560i	−0.149458	+	0.0185150i
$991$	20.3290	+	23.4609i	0.645771	+	0.745260i	0.980384	−	0.197096i	$-0.0631510\pi$
$991$	20.3290	+	23.4609i	0.645771	+	0.745260i	−0.334613	+	0.942356i	$0.608606\pi$
$992$	1.01717	−	0.221272i	0.0322951	−	0.00702538i
$993$	4.45924	−	3.33815i	0.141510	−	0.105933i
$994$	6.13683	−	13.4378i	0.194648	−	0.426220i
$995$	−6.70197	+	11.7230i	−0.212467	+	0.371645i
$996$	−0.419841	+	1.42985i	−0.0133032	+	0.0453065i
$997$	12.3890	−	56.9512i	0.392363	−	1.80366i	−0.180006	−	0.983665i	$-0.557612\pi$
$997$	12.3890	−	56.9512i	0.392363	−	1.80366i	0.572369	−	0.819996i	$-0.306025\pi$
$998$	9.67022	−	25.9269i	0.306106	−	0.820701i
$999$	8.39616	−	2.46534i	0.265643	−	0.0779998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.493.6	yes	240
5.2	odd	4	inner	690.2.w.b.217.10	yes	240
23.7	odd	22	inner	690.2.w.b.283.10	yes	240
115.7	even	44	inner	690.2.w.b.7.6	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.6	✓	240	115.7	even	44	inner
690.2.w.b.217.10	yes	240	5.2	odd	4	inner
690.2.w.b.283.10	yes	240	23.7	odd	22	inner
690.2.w.b.493.6	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.98312 - 1.03307i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.653533 - 1.19686i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.98312 - 1.03307i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.653533 - 1.19686i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(-2.05177 + 0.888964i) q^{10} +(-1.60153 - 1.38774i) q^{11} +(-0.0713392 - 0.997452i) q^{12} +(-4.94879 - 2.70224i) q^{13} +(0.566485 + 1.24043i) q^{14} +(-1.43100 - 1.71821i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-1.26500 + 1.68984i) q^{17} +(0.936950 - 0.349464i) q^{18} +(0.299333 - 2.08191i) q^{19} +(2.10996 - 0.740327i) q^{20} +(-1.03059 + 0.893008i) q^{21} +(1.49845 + 1.49845i) q^{22} +(-4.28351 + 2.15673i) q^{23} +1.00000i q^{24} +(2.86553 - 4.09740i) q^{25} +(4.74340 + 3.04840i) q^{26} +(0.599278 + 0.800541i) q^{27} +(-0.476551 - 1.27768i) q^{28} +(5.11643 - 0.735631i) q^{29} +(1.30478 + 1.81591i) q^{30} +(-0.875710 + 0.562784i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(-1.01559 + 1.85992i) q^{33} +(1.38233 - 1.59529i) q^{34} +(-2.53247 - 1.69837i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(3.05803 - 8.19889i) q^{37} +(-0.447092 + 2.05525i) q^{38} +(-1.58855 + 5.41009i) q^{39} +(-2.15739 + 0.587919i) q^{40} +(-3.31299 + 7.25445i) q^{41} +(1.09167 - 0.817212i) q^{42} +(-6.00468 + 1.30624i) q^{43} +(-1.38774 - 1.60153i) q^{44} +(-1.37476 + 1.76353i) q^{45} +(4.42646 - 1.84566i) q^{46} +(-1.39772 + 1.39772i) q^{47} +(0.0713392 - 0.997452i) q^{48} +(2.77913 - 4.32440i) q^{49} +(-3.15054 + 3.88254i) q^{50} +(1.92012 + 0.876889i) q^{51} +(-4.51385 - 3.37902i) q^{52} +(-2.68667 + 1.46703i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-4.60966 - 1.09755i) q^{55} +(0.384188 + 1.30842i) q^{56} +(-2.09796 + 0.150049i) q^{57} +(-5.15587 + 0.368755i) q^{58} +(-0.317333 - 1.08074i) q^{59} +(-1.17191 - 1.90437i) q^{60} +(0.435960 + 0.678367i) q^{61} +(0.913627 - 0.498878i) q^{62} +(1.09167 + 0.817212i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-12.6056 - 0.246428i) q^{65} +(1.14569 - 1.78273i) q^{66} +(1.14642 - 16.0291i) q^{67} +(-1.49261 + 1.49261i) q^{68} +(3.01797 + 3.72718i) q^{69} +(2.40486 + 1.87470i) q^{70} +(-7.09421 - 8.18716i) q^{71} +(0.977147 - 0.212565i) q^{72} +(0.494176 - 0.369936i) q^{73} +(-3.63514 + 7.95985i) q^{74} +(-4.61288 - 1.92908i) q^{75} +(0.592572 - 2.01812i) q^{76} +(-0.614267 + 2.82374i) q^{77} +(1.97045 - 5.28298i) q^{78} +(-13.0887 + 3.84319i) q^{79} +(2.19384 - 0.432514i) q^{80} +(0.654861 - 0.755750i) q^{81} +(3.82208 - 6.99962i) q^{82} +(-1.39625 - 0.520776i) q^{83} +(-1.14718 + 0.737251i) q^{84} +(-0.762922 + 4.65799i) q^{85} +(6.08257 - 0.874542i) q^{86} +(-1.80640 - 4.84313i) q^{87} +(1.26995 + 1.69645i) q^{88} +(14.7728 + 9.49392i) q^{89} +(1.49706 - 1.66096i) q^{90} +7.68899i q^{91} +(-4.54685 + 1.52517i) q^{92} +(0.736068 + 0.736068i) q^{93} +(1.49388 - 1.29445i) q^{94} +(-1.55714 - 4.43790i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(10.5759 - 3.94462i) q^{97} +(-3.08054 + 4.11513i) q^{98} +(2.03329 + 0.597029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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