LMFDB - Embedded newform 525.2.m.c.307.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(118,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("525.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.m (of order $4$, degree $2$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Character	$\chi$	$=$	525.307
Dual form			525.2.m.c.118.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11266 - 1.11266i) q^{2} +(0.707107 + 0.707107i) q^{3} +0.476024i q^{4} -1.57354i q^{6} +(2.09141 - 1.62049i) q^{7} +(-1.69567 + 1.69567i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.11266 - 1.11266i) q^{2} +(0.707107 + 0.707107i) q^{3} +0.476024i q^{4} -1.57354i q^{6} +(2.09141 - 1.62049i) q^{7} +(-1.69567 + 1.69567i) q^{8} +1.00000i q^{9} +5.20147 q^{11} +(-0.336600 + 0.336600i) q^{12} +(-2.22988 - 2.22988i) q^{13} +(-4.13009 - 0.523976i) q^{14} +4.72545 q^{16} +(-3.11335 + 3.11335i) q^{17} +(1.11266 - 1.11266i) q^{18} +4.13009 q^{19} +(2.62471 + 0.332992i) q^{21} +(-5.78747 - 5.78747i) q^{22} +(2.97914 - 2.97914i) q^{23} -2.39804 q^{24} +4.96218i q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.771392 + 0.995562i) q^{28} +0.249425i q^{29} -10.4242i q^{31} +(-1.86648 - 1.86648i) q^{32} +(3.67800 + 3.67800i) q^{33} +6.92820 q^{34} -0.476024 q^{36} +(1.69567 + 1.69567i) q^{37} +(-4.59538 - 4.59538i) q^{38} -3.15352i q^{39} +6.92820i q^{41} +(-2.54990 - 3.29092i) q^{42} +(4.39191 - 4.39191i) q^{43} +2.47602i q^{44} -6.62954 q^{46} +(3.11335 - 3.11335i) q^{47} +(3.34140 + 3.34140i) q^{48} +(1.74802 - 6.77823i) q^{49} -4.40294 q^{51} +(1.06147 - 1.06147i) q^{52} +(4.89898 - 4.89898i) q^{53} +1.57354 q^{54} +(-0.798528 + 6.29415i) q^{56} +(2.92041 + 2.92041i) q^{57} +(0.277525 - 0.277525i) q^{58} -11.8904 q^{59} +2.16407i q^{61} +(-11.5986 + 11.5986i) q^{62} +(1.62049 + 2.09141i) q^{63} -5.29738i q^{64} -8.18472i q^{66} +(2.50822 + 2.50822i) q^{67} +(-1.48203 - 1.48203i) q^{68} +4.21314 q^{69} -0.798528 q^{71} +(-1.69567 - 1.69567i) q^{72} +(-5.94178 - 5.94178i) q^{73} -3.77340i q^{74} +1.96602i q^{76} +(10.8784 - 8.42894i) q^{77} +(-3.50879 + 3.50879i) q^{78} +5.29738i q^{79} -1.00000 q^{81} +(7.70873 - 7.70873i) q^{82} +(-4.59538 - 4.59538i) q^{83} +(-0.158512 + 1.24943i) q^{84} -9.77340 q^{86} +(-0.176370 + 0.176370i) q^{87} +(-8.81997 + 8.81997i) q^{88} -6.29415 q^{89} +(-8.27708 - 1.05010i) q^{91} +(1.41814 + 1.41814i) q^{92} +(7.37105 - 7.37105i) q^{93} -6.92820 q^{94} -2.63960i q^{96} +(-12.1972 + 12.1972i) q^{97} +(-9.48682 + 5.59692i) q^{98} +5.20147i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 48 q^{11} + 24 q^{16} + 12 q^{21} - 24 q^{36} - 120 q^{46} + 48 q^{51} - 96 q^{56} - 96 q^{71} - 24 q^{81} - 120 q^{86} + 108 q^{91}+O(q^{100}) $ 24 * q + 48 * q^11 + 24 * q^16 + 12 * q^21 - 24 * q^36 - 120 * q^46 + 48 * q^51 - 96 * q^56 - 96 * q^71 - 24 * q^81 - 120 * q^86 + 108 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.11266	−	1.11266i	−0.786769	−	0.786769i	0.194194	−	0.980963i	$-0.437791\pi$
$2$	−1.11266	−	1.11266i	−0.786769	−	0.786769i	−0.980963	+	0.194194i	$0.937791\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			0.476024i			0.238012i
$5$		0			0
$5$		0			0
$6$		−	1.57354i		−	0.642394i
$7$	2.09141	−	1.62049i	0.790480	−	0.612488i
$7$	2.09141	−	1.62049i	0.790480	−	0.612488i
$8$	−1.69567	+	1.69567i	−0.599509	+	0.599509i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	5.20147			1.56830			0.784151	−	0.620569i	$-0.213099\pi$
$11$	5.20147			1.56830			0.784151	+	0.620569i	$0.213099\pi$
$12$	−0.336600	+	0.336600i	−0.0971679	+	0.0971679i
$13$	−2.22988	−	2.22988i	−0.618456	−	0.618456i	0.326679	−	0.945135i	$-0.394070\pi$
$13$	−2.22988	−	2.22988i	−0.618456	−	0.618456i	−0.945135	+	0.326679i	$0.894070\pi$
$14$	−4.13009	−	0.523976i	−1.10381	−	0.140039i
$15$		0			0
$16$	4.72545			1.18136
$17$	−3.11335	+	3.11335i	−0.755099	+	0.755099i	−0.975426	−	0.220327i	$-0.929287\pi$
$17$	−3.11335	+	3.11335i	−0.755099	+	0.755099i	0.220327	+	0.975426i	$0.429287\pi$
$18$	1.11266	−	1.11266i	0.262256	−	0.262256i
$19$	4.13009			0.947507			0.473753	−	0.880658i	$-0.342899\pi$
$19$	4.13009			0.947507			0.473753	+	0.880658i	$0.342899\pi$
$20$		0			0
$21$	2.62471	+	0.332992i	0.572759	+	0.0726649i
$22$	−5.78747	−	5.78747i	−1.23389	−	1.23389i
$23$	2.97914	−	2.97914i	0.621194	−	0.621194i	−0.324643	−	0.945837i	$-0.605244\pi$
$23$	2.97914	−	2.97914i	0.621194	−	0.621194i	0.945837	+	0.324643i	$0.105244\pi$
$24$	−2.39804			−0.489497
$25$		0			0
$26$			4.96218i			0.973164i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.771392	+	0.995562i	0.145779	+	0.188144i
$29$			0.249425i			0.0463171i	0.999732	+	0.0231585i	$0.00737225\pi$
$29$			0.249425i			0.0463171i	−0.999732	+	0.0231585i	$0.992628\pi$
$30$		0			0
$31$		−	10.4242i		−	1.87225i	−0.351669	−	0.936124i	$-0.614386\pi$
$31$		−	10.4242i		−	1.87225i	0.351669	−	0.936124i	$-0.385614\pi$
$32$	−1.86648	−	1.86648i	−0.329951	−	0.329951i
$33$	3.67800	+	3.67800i	0.640257	+	0.640257i
$34$	6.92820			1.18818
$35$		0			0
$36$	−0.476024			−0.0793373
$37$	1.69567	+	1.69567i	0.278766	+	0.278766i	0.832616	−	0.553850i	$-0.186842\pi$
$37$	1.69567	+	1.69567i	0.278766	+	0.278766i	−0.553850	+	0.832616i	$0.686842\pi$
$38$	−4.59538	−	4.59538i	−0.745469	−	0.745469i
$39$		−	3.15352i		−	0.504967i
$40$		0			0
$41$			6.92820i			1.08200i	0.841021	+	0.541002i	$0.181955\pi$
$41$			6.92820i			1.08200i	−0.841021	+	0.541002i	$0.818045\pi$
$42$	−2.54990	−	3.29092i	−0.393459	−	0.507800i
$43$	4.39191	−	4.39191i	0.669760	−	0.669760i	−0.287900	−	0.957660i	$-0.592957\pi$
$43$	4.39191	−	4.39191i	0.669760	−	0.669760i	0.957660	+	0.287900i	$0.0929572\pi$
$44$			2.47602i			0.373275i
$45$		0			0
$46$	−6.62954			−0.977473
$47$	3.11335	−	3.11335i	0.454129	−	0.454129i	−0.442593	−	0.896722i	$-0.645941\pi$
$47$	3.11335	−	3.11335i	0.454129	−	0.454129i	0.896722	+	0.442593i	$0.145941\pi$
$48$	3.34140	+	3.34140i	0.482289	+	0.482289i
$49$	1.74802	−	6.77823i	0.249717	−	0.968319i
$50$		0			0
$51$	−4.40294			−0.616536
$52$	1.06147	−	1.06147i	0.147200	−	0.147200i
$53$	4.89898	−	4.89898i	0.672927	−	0.672927i	−0.285463	−	0.958390i	$-0.592147\pi$
$53$	4.89898	−	4.89898i	0.672927	−	0.672927i	0.958390	+	0.285463i	$0.0921474\pi$
$54$	1.57354			0.214131
$55$		0			0
$56$	−0.798528	+	6.29415i	−0.106708	+	0.841092i
$57$	2.92041	+	2.92041i	0.386818	+	0.386818i
$58$	0.277525	−	0.277525i	0.0364409	−	0.0364409i
$59$	−11.8904			−1.54800			−0.773998	−	0.633188i	$-0.781746\pi$
$59$	−11.8904			−1.54800			−0.773998	+	0.633188i	$0.781746\pi$
$60$		0			0
$61$			2.16407i			0.277080i	0.990357	+	0.138540i	$0.0442410\pi$
$61$			2.16407i			0.277080i	−0.990357	+	0.138540i	$0.955759\pi$
$62$	−11.5986	+	11.5986i	−1.47303	+	1.47303i
$63$	1.62049	+	2.09141i	0.204163	+	0.263493i
$64$		−	5.29738i		−	0.662172i
$65$		0			0
$66$		−	8.18472i		−	1.00747i
$67$	2.50822	+	2.50822i	0.306428	+	0.306428i	0.843522	−	0.537094i	$-0.180478\pi$
$67$	2.50822	+	2.50822i	0.306428	+	0.306428i	−0.537094	+	0.843522i	$0.680478\pi$
$68$	−1.48203	−	1.48203i	−0.179722	−	0.179722i
$69$	4.21314			0.507203
$70$		0			0
$71$	−0.798528			−0.0947678			−0.0473839	−	0.998877i	$-0.515088\pi$
$71$	−0.798528			−0.0947678			−0.0473839	+	0.998877i	$0.515088\pi$
$72$	−1.69567	−	1.69567i	−0.199836	−	0.199836i
$73$	−5.94178	−	5.94178i	−0.695433	−	0.695433i	0.267989	−	0.963422i	$-0.413641\pi$
$73$	−5.94178	−	5.94178i	−0.695433	−	0.695433i	−0.963422	+	0.267989i	$0.913641\pi$
$74$		−	3.77340i		−	0.438649i
$75$		0			0
$76$			1.96602i			0.225518i
$77$	10.8784	−	8.42894i	1.23971	−	0.960567i
$78$	−3.50879	+	3.50879i	−0.397293	+	0.397293i
$79$			5.29738i			0.596002i	0.954566	+	0.298001i	$0.0963198\pi$
$79$			5.29738i			0.596002i	−0.954566	+	0.298001i	$0.903680\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	7.70873	−	7.70873i	0.851287	−	0.851287i
$83$	−4.59538	−	4.59538i	−0.504409	−	0.504409i	0.408396	−	0.912805i	$-0.366088\pi$
$83$	−4.59538	−	4.59538i	−0.504409	−	0.504409i	−0.912805	+	0.408396i	$0.866088\pi$
$84$	−0.158512	+	1.24943i	−0.0172951	+	0.136323i
$85$		0			0
$86$	−9.77340			−1.05389
$87$	−0.176370	+	0.176370i	−0.0189089	+	0.0189089i
$88$	−8.81997	+	8.81997i	−0.940212	+	0.940212i
$89$	−6.29415			−0.667179			−0.333590	−	0.942718i	$-0.608260\pi$
$89$	−6.29415			−0.667179			−0.333590	+	0.942718i	$0.608260\pi$
$90$		0			0
$91$	−8.27708	−	1.05010i	−0.867674	−	0.110080i
$92$	1.41814	+	1.41814i	0.147852	+	0.147852i
$93$	7.37105	−	7.37105i	0.764342	−	0.764342i
$94$	−6.92820			−0.714590
$95$		0			0
$96$		−	2.63960i		−	0.269404i
$97$	−12.1972	+	12.1972i	−1.23844	+	1.23844i	−0.277797	+	0.960640i	$0.589604\pi$
$97$	−12.1972	+	12.1972i	−1.23844	+	1.23844i	−0.960640	+	0.277797i	$0.910396\pi$
$98$	−9.48682	+	5.59692i	−0.958313	+	0.565374i
$99$			5.20147i			0.522768i
$100$		0			0
$101$		−	6.29415i		−	0.626292i	−0.949705	−	0.313146i	$-0.898617\pi$
$101$		−	6.29415i		−	0.626292i	0.949705	−	0.313146i	$-0.101383\pi$
$102$	4.89898	+	4.89898i	0.485071	+	0.485071i
$103$	10.5372	+	10.5372i	1.03826	+	1.03826i	0.999238	+	0.0390188i	$0.0124232\pi$
$103$	10.5372	+	10.5372i	1.03826	+	1.03826i	0.0390188	+	0.999238i	$0.487577\pi$
$104$	7.56225			0.741540
$105$		0			0
$106$	−10.9018			−1.05888
$107$	10.8573	+	10.8573i	1.04961	+	1.04961i	0.998703	+	0.0509079i	$0.0162115\pi$
$107$	10.8573	+	10.8573i	1.04961	+	1.04961i	0.0509079	+	0.998703i	$0.483788\pi$
$108$	−0.336600	−	0.336600i	−0.0323893	−	0.0323893i
$109$			15.9018i			1.52312i	0.648097	+	0.761558i	$0.275565\pi$
$109$			15.9018i			1.52312i	−0.648097	+	0.761558i	$0.724435\pi$
$110$		0			0
$111$			2.39804i			0.227611i
$112$	9.88287	−	7.65755i	0.933843	−	0.723570i
$113$	−8.47834	+	8.47834i	−0.797575	+	0.797575i	−0.982713	−	0.185138i	$-0.940727\pi$
$113$	−8.47834	+	8.47834i	−0.797575	+	0.797575i	0.185138	+	0.982713i	$0.440727\pi$
$114$		−	6.49885i		−	0.608673i
$115$		0			0
$116$	−0.118732			−0.0110240
$117$	2.22988	−	2.22988i	0.206152	−	0.206152i
$118$	13.2300	+	13.2300i	1.21792	+	1.21792i
$119$	−1.46615	+	11.5565i	−0.134401	+	1.05938i
$120$		0			0
$121$	16.0553			1.45957
$122$	2.40787	−	2.40787i	0.217998	−	0.217998i
$123$	−4.89898	+	4.89898i	−0.441726	+	0.441726i
$124$	4.96218			0.445617
$125$		0			0
$126$	0.523976	−	4.13009i	0.0466795	−	0.367937i
$127$	12.3288	+	12.3288i	1.09400	+	1.09400i	0.995097	+	0.0989036i	$0.0315335\pi$
$127$	12.3288	+	12.3288i	1.09400	+	1.09400i	0.0989036	+	0.995097i	$0.468466\pi$
$128$	−9.62714	+	9.62714i	−0.850927	+	0.850927i
$129$	6.21110			0.546857
$130$		0			0
$131$			15.8863i			1.38799i	0.719979	+	0.693996i	$0.244152\pi$
$131$			15.8863i			1.38799i	−0.719979	+	0.693996i	$0.755848\pi$
$132$	−1.75081	+	1.75081i	−0.152389	+	0.152389i
$133$	8.63772	−	6.69277i	0.748985	−	0.580337i
$134$		−	5.58159i		−	0.482176i
$135$		0			0
$136$		−	10.5584i		−	0.905377i
$137$	−3.95713	−	3.95713i	−0.338081	−	0.338081i	0.517564	−	0.855645i	$-0.326839\pi$
$137$	−3.95713	−	3.95713i	−0.338081	−	0.338081i	−0.855645	+	0.517564i	$0.826839\pi$
$138$	−4.68779	−	4.68779i	−0.399052	−	0.399052i
$139$	11.8904			1.00853			0.504265	−	0.863549i	$-0.331764\pi$
$139$	11.8904			1.00853			0.504265	+	0.863549i	$0.331764\pi$
$140$		0			0
$141$	4.40294			0.370795
$142$	0.888490	+	0.888490i	0.0745604	+	0.0745604i
$143$	−11.5986	−	11.5986i	−0.969926	−	0.969926i
$144$			4.72545i			0.393787i
$145$		0			0
$146$			13.2224i			1.09429i
$147$	6.02897	−	3.55690i	0.497261	−	0.293368i
$148$	−0.807178	+	0.807178i	−0.0663496	+	0.0663496i
$149$		−	0.249425i		−	0.0204337i	−0.999948	−	0.0102169i	$-0.996748\pi$
$149$		−	0.249425i		−	0.0204337i	0.999948	−	0.0102169i	$-0.00325218\pi$
$150$		0			0
$151$	2.35499			0.191647			0.0958233	−	0.995398i	$-0.469452\pi$
$151$	2.35499			0.191647			0.0958233	+	0.995398i	$0.469452\pi$
$152$	−7.00325	+	7.00325i	−0.568039	+	0.568039i
$153$	−3.11335	−	3.11335i	−0.251700	−	0.251700i
$154$	−21.4825	−	2.72545i	−1.73111	−	0.219623i
$155$		0			0
$156$	1.50115			0.120188
$157$	−5.34323	+	5.34323i	−0.426436	+	0.426436i	−0.887412	−	0.460976i	$-0.847499\pi$
$157$	−5.34323	+	5.34323i	−0.426436	+	0.426436i	0.460976	+	0.887412i	$0.347499\pi$
$158$	5.89418	−	5.89418i	0.468916	−	0.468916i
$159$	6.92820			0.549442
$160$		0			0
$161$	1.40294	−	11.0583i	0.110568	−	0.871515i
$162$	1.11266	+	1.11266i	0.0874188	+	0.0874188i
$163$	−15.2130	+	15.2130i	−1.19158	+	1.19158i	−0.214951	+	0.976625i	$0.568959\pi$
$163$	−15.2130	+	15.2130i	−1.19158	+	1.19158i	−0.976625	+	0.214951i	$0.931041\pi$
$164$	−3.29799			−0.257530
$165$		0			0
$166$			10.2262i			0.793706i
$167$	4.74468	−	4.74468i	0.367154	−	0.367154i	−0.499284	−	0.866438i	$-0.666404\pi$
$167$	4.74468	−	4.74468i	0.367154	−	0.367154i	0.866438	+	0.499284i	$0.166404\pi$
$168$	−5.01528	+	3.88599i	−0.386938	+	0.299811i
$169$		−	3.05531i		−	0.235024i
$170$		0			0
$171$			4.13009i			0.315836i
$172$	2.09065	+	2.09065i	0.159411	+	0.159411i
$173$	6.07741	+	6.07741i	0.462057	+	0.462057i	0.899329	−	0.437272i	$-0.144055\pi$
$173$	6.07741	+	6.07741i	0.462057	+	0.462057i	−0.437272	+	0.899329i	$0.644055\pi$
$174$	0.392480			0.0297538
$175$		0			0
$176$	24.5793			1.85273
$177$	−8.40777	−	8.40777i	−0.631967	−	0.631967i
$178$	7.00325	+	7.00325i	0.524916	+	0.524916i
$179$			2.30704i			0.172436i	0.996276	+	0.0862181i	$0.0274782\pi$
$179$			2.30704i			0.172436i	−0.996276	+	0.0862181i	$0.972522\pi$
$180$		0			0
$181$			0.134178i			0.00997334i	0.999988	+	0.00498667i	$0.00158731\pi$
$181$			0.134178i			0.00997334i	−0.999988	+	0.00498667i	$0.998413\pi$
$182$	8.04117	+	10.3780i	0.596052	+	0.769267i
$183$	−1.53023	+	1.53023i	−0.113118	+	0.113118i
$184$			10.1033i			0.744823i
$185$		0			0
$186$	−16.4029			−1.20272
$187$	−16.1940	+	16.1940i	−1.18422	+	1.18422i
$188$	1.48203	+	1.48203i	0.108088	+	0.108088i
$189$	−0.332992	+	2.62471i	−0.0242216	+	0.190920i
$190$		0			0
$191$	−27.3047			−1.97570			−0.987851	−	0.155405i	$-0.950332\pi$
$191$	−27.3047			−1.97570			−0.987851	+	0.155405i	$0.950332\pi$
$192$	3.74581	−	3.74581i	0.270331	−	0.270331i
$193$	3.67423	−	3.67423i	0.264477	−	0.264477i	−0.562393	−	0.826870i	$-0.690119\pi$
$193$	3.67423	−	3.67423i	0.264477	−	0.264477i	0.826870	+	0.562393i	$0.190119\pi$
$194$	27.1426			1.94873
$195$		0			0
$196$	3.22660	+	0.832098i	0.230471	+	0.0594356i
$197$	−11.9871	−	11.9871i	−0.854048	−	0.854048i	0.136581	−	0.990629i	$-0.456389\pi$
$197$	−11.9871	−	11.9871i	−0.854048	−	0.854048i	−0.990629	+	0.136581i	$0.956389\pi$
$198$	5.78747	−	5.78747i	0.411298	−	0.411298i
$199$	−24.2806			−1.72121			−0.860605	−	0.509274i	$-0.829914\pi$
$199$	−24.2806			−1.72121			−0.860605	+	0.509274i	$0.829914\pi$
$200$		0			0
$201$			3.54716i			0.250197i
$202$	−7.00325	+	7.00325i	−0.492747	+	0.492747i
$203$	0.404191	+	0.521651i	0.0283687	+	0.0366127i
$204$		−	2.09591i		−	0.146743i
$205$		0			0
$206$		−	23.4485i		−	1.63374i
$207$	2.97914	+	2.97914i	0.207065	+	0.207065i
$208$	−10.5372	−	10.5372i	−0.730621	−	0.730621i
$209$	21.4825			1.48598
$210$		0			0
$211$	−26.0553			−1.79372			−0.896861	−	0.442313i	$-0.854158\pi$
$211$	−26.0553			−1.79372			−0.896861	+	0.442313i	$0.854158\pi$
$212$	2.33203	+	2.33203i	0.160164	+	0.160164i
$213$	−0.564644	−	0.564644i	−0.0386888	−	0.0386888i
$214$		−	24.1609i		−	1.65160i
$215$		0			0
$216$		−	2.39804i		−	0.163166i
$217$	−16.8924	−	21.8014i	−1.14673	−	1.47998i
$218$	17.6933	−	17.6933i	1.19834	−	1.19834i
$219$		−	8.40294i		−	0.567818i
$220$		0			0
$221$	13.8848			0.933991
$222$	2.66820	−	2.66820i	0.179078	−	0.179078i
$223$	−3.99683	−	3.99683i	−0.267647	−	0.267647i	0.560504	−	0.828152i	$-0.310607\pi$
$223$	−3.99683	−	3.99683i	−0.267647	−	0.267647i	−0.828152	+	0.560504i	$0.810607\pi$
$224$	−6.92820	−	0.878968i	−0.462910	−	0.0587285i
$225$		0			0
$226$	18.8670			1.25501
$227$	16.1940	−	16.1940i	1.07483	−	1.07483i	0.0778711	−	0.996963i	$-0.475188\pi$
$227$	16.1940	−	16.1940i	1.07483	−	1.07483i	0.996963	−	0.0778711i	$-0.0248122\pi$
$228$	−1.39019	+	1.39019i	−0.0920673	+	0.0920673i
$229$	−11.7562			−0.776872			−0.388436	−	0.921476i	$-0.626985\pi$
$229$	−11.7562			−0.776872			−0.388436	+	0.921476i	$0.626985\pi$
$230$		0			0
$231$	13.6524	+	1.73205i	0.898260	+	0.113961i
$232$	−0.422942	−	0.422942i	−0.0277675	−	0.0277675i
$233$	12.4806	−	12.4806i	0.817634	−	0.817634i	−0.168131	−	0.985765i	$-0.553773\pi$
$233$	12.4806	−	12.4806i	0.817634	−	0.817634i	0.985765	+	0.168131i	$0.0537732\pi$
$234$	−4.96218			−0.324388
$235$		0			0
$236$		−	5.66011i		−	0.368441i
$237$	−3.74581	+	3.74581i	−0.243317	+	0.243317i
$238$	14.4897	−	11.2271i	0.939230	−	0.727744i
$239$			8.80589i			0.569606i	0.958586	+	0.284803i	$0.0919281\pi$
$239$			8.80589i			0.569606i	−0.958586	+	0.284803i	$0.908072\pi$
$240$		0			0
$241$			22.3146i			1.43741i	0.695314	+	0.718706i	$0.255265\pi$
$241$			22.3146i			1.43741i	−0.695314	+	0.718706i	$0.744735\pi$
$242$	−17.8641	−	17.8641i	−1.14835	−	1.14835i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−1.03015			−0.0659484
$245$		0			0
$246$	10.9018			0.695073
$247$	−9.20958	−	9.20958i	−0.585991	−	0.585991i
$248$	17.6760	+	17.6760i	1.12243	+	1.12243i
$249$		−	6.49885i		−	0.411848i
$250$		0			0
$251$		−	15.8863i		−	1.00273i	−0.865235	−	0.501367i	$-0.832831\pi$
$251$		−	15.8863i		−	1.00273i	0.865235	−	0.501367i	$-0.167169\pi$
$252$	−0.995562	+	0.771392i	−0.0627145	+	0.0485931i
$253$	15.4959	−	15.4959i	0.974220	−	0.974220i
$254$		−	27.4354i		−	1.72145i
$255$		0			0
$256$	10.8287			0.676795
$257$	2.25858	−	2.25858i	0.140886	−	0.140886i	−0.633146	−	0.774032i	$-0.718237\pi$
$257$	2.25858	−	2.25858i	0.140886	−	0.140886i	0.774032	+	0.633146i	$0.218237\pi$
$258$	−6.91084	−	6.91084i	−0.430250	−	0.430250i
$259$	6.29415	+	0.798528i	0.391100	+	0.0496181i
$260$		0			0
$261$	−0.249425			−0.0154390
$262$	17.6760	−	17.6760i	1.09203	−	1.09203i
$263$	2.03730	−	2.03730i	0.125625	−	0.125625i	−0.641499	−	0.767124i	$-0.721687\pi$
$263$	2.03730	−	2.03730i	0.125625	−	0.125625i	0.767124	+	0.641499i	$0.221687\pi$
$264$	−12.4733			−0.767680
$265$		0			0
$266$	−17.0576	−	2.16407i	−1.04587	−	0.132688i
$267$	−4.45064	−	4.45064i	−0.272375	−	0.272375i
$268$	−1.19397	+	1.19397i	−0.0729334	+	0.0729334i
$269$	−15.1884			−0.926052			−0.463026	−	0.886345i	$-0.653236\pi$
$269$	−15.1884			−0.926052			−0.463026	+	0.886345i	$0.653236\pi$
$270$		0			0
$271$		−	14.5543i		−	0.884112i	−0.896987	−	0.442056i	$-0.854249\pi$
$271$		−	14.5543i		−	0.884112i	0.896987	−	0.442056i	$-0.145751\pi$
$272$	−14.7120	+	14.7120i	−0.892045	+	0.892045i
$273$	−5.11025	−	6.59531i	−0.309286	−	0.399166i
$274$			8.80589i			0.531983i
$275$		0			0
$276$			2.00556i			0.120720i
$277$	0.353463	+	0.353463i	0.0212375	+	0.0212375i	0.717646	−	0.696408i	$-0.245220\pi$
$277$	0.353463	+	0.353463i	0.0212375	+	0.0212375i	−0.696408	+	0.717646i	$0.745220\pi$
$278$	−13.2300	−	13.2300i	−0.793480	−	0.793480i
$279$	10.4242			0.624083
$280$		0			0
$281$	6.03829			0.360214			0.180107	−	0.983647i	$-0.442356\pi$
$281$	6.03829			0.360214			0.180107	+	0.983647i	$0.442356\pi$
$282$	−4.89898	−	4.89898i	−0.291730	−	0.291730i
$283$	−1.37510	−	1.37510i	−0.0817412	−	0.0817412i	0.665054	−	0.746795i	$-0.268409\pi$
$283$	−1.37510	−	1.37510i	−0.0817412	−	0.0817412i	−0.746795	+	0.665054i	$0.768409\pi$
$284$		−	0.380118i		−	0.0225559i
$285$		0			0
$286$			25.8107i			1.52622i
$287$	11.2271	+	14.4897i	0.662714	+	0.855302i
$288$	1.86648	−	1.86648i	0.109984	−	0.109984i
$289$		−	2.38592i		−	0.140348i
$290$		0			0
$291$	−17.2494			−1.01118
$292$	2.82843	−	2.82843i	0.165521	−	0.165521i
$293$	11.5986	+	11.5986i	0.677599	+	0.677599i	0.959456	−	0.281857i	$-0.0909504\pi$
$293$	11.5986	+	11.5986i	0.677599	+	0.677599i	−0.281857	+	0.959456i	$0.590950\pi$
$294$	−10.6658	−	2.75057i	−0.622043	−	0.160417i
$295$		0			0
$296$	−5.75057			−0.334245
$297$	−3.67800	+	3.67800i	−0.213419	+	0.213419i
$298$	−0.277525	+	0.277525i	−0.0160766	+	0.0160766i
$299$	−13.2862			−0.768362
$300$		0			0
$301$	2.06825	−	16.3023i	0.119212	−	0.939652i
$302$	−2.62030	−	2.62030i	−0.150782	−	0.150782i
$303$	4.45064	−	4.45064i	0.255683	−	0.255683i
$304$	19.5165			1.11935
$305$		0			0
$306$			6.92820i			0.396059i
$307$	6.82526	−	6.82526i	0.389538	−	0.389538i	−0.484985	−	0.874523i	$-0.661175\pi$
$307$	6.82526	−	6.82526i	0.389538	−	0.389538i	0.874523	+	0.484985i	$0.161175\pi$
$308$	4.01237	+	5.17839i	0.228626	+	0.295066i
$309$			14.9018i			0.847733i
$310$		0			0
$311$			24.1465i			1.36922i	0.728909	+	0.684610i	$0.240028\pi$
$311$			24.1465i			1.36922i	−0.728909	+	0.684610i	$0.759972\pi$
$312$	5.34732	+	5.34732i	0.302732	+	0.302732i
$313$	0.598552	+	0.598552i	0.0338322	+	0.0338322i	0.723820	−	0.689988i	$-0.242384\pi$
$313$	0.598552	+	0.598552i	0.0338322	+	0.0338322i	−0.689988	+	0.723820i	$0.742384\pi$
$314$	11.8904			0.671013
$315$		0			0
$316$	−2.52168			−0.141855
$317$	−13.5399	−	13.5399i	−0.760479	−	0.760479i	0.215930	−	0.976409i	$-0.430722\pi$
$317$	−13.5399	−	13.5399i	−0.760479	−	0.760479i	−0.976409	+	0.215930i	$0.930722\pi$
$318$	−7.70873	−	7.70873i	−0.432284	−	0.432284i
$319$			1.29738i			0.0726392i
$320$		0			0
$321$			15.3545i			0.857004i
$322$	−13.8651	+	10.7431i	−0.772673	+	0.598690i
$323$	−12.8584	+	12.8584i	−0.715461	+	0.715461i
$324$		−	0.476024i		−	0.0264458i
$325$		0			0
$326$	33.8538			1.87499
$327$	−11.2443	+	11.2443i	−0.621809	+	0.621809i
$328$	−11.7479	−	11.7479i	−0.648671	−	0.648671i
$329$	1.46615	−	11.5565i	0.0808313	−	0.637128i
$330$		0			0
$331$	22.4103			1.23178			0.615891	−	0.787831i	$-0.288796\pi$
$331$	22.4103			1.23178			0.615891	+	0.787831i	$0.288796\pi$
$332$	2.18751	−	2.18751i	0.120055	−	0.120055i
$333$	−1.69567	+	1.69567i	−0.0929220	+	0.0929220i
$334$	−10.5584			−0.577731
$335$		0			0
$336$	12.4029	+	1.57354i	0.676636	+	0.0858436i
$337$	−0.588382	−	0.588382i	−0.0320512	−	0.0320512i	0.690900	−	0.722951i	$-0.257215\pi$
$337$	−0.588382	−	0.588382i	−0.0320512	−	0.0320512i	−0.722951	+	0.690900i	$0.757215\pi$
$338$	−3.39953	+	3.39953i	−0.184910	+	0.184910i
$339$	−11.9902			−0.651217
$340$		0			0
$341$		−	54.2214i		−	2.93625i
$342$	4.59538	−	4.59538i	0.248490	−	0.248490i
$343$	−7.32823	−	17.0087i	−0.395687	−	0.918385i
$344$			14.8944i			0.803054i
$345$		0			0
$346$		−	13.5242i		−	0.727064i
$347$	−21.0674	−	21.0674i	−1.13096	−	1.13096i	−0.990018	−	0.140940i	$-0.954988\pi$
$347$	−21.0674	−	21.0674i	−1.13096	−	1.13096i	−0.140940	−	0.990018i	$-0.545012\pi$
$348$	−0.0839564	−	0.0839564i	−0.00450053	−	0.00450053i
$349$	23.1467			1.23902			0.619508	−	0.784990i	$-0.287332\pi$
$349$	23.1467			1.23902			0.619508	+	0.784990i	$0.287332\pi$
$350$		0			0
$351$	3.15352			0.168322
$352$	−9.70846	−	9.70846i	−0.517462	−	0.517462i
$353$	10.8221	+	10.8221i	0.576001	+	0.576001i	0.933799	−	0.357798i	$-0.116472\pi$
$353$	10.8221	+	10.8221i	0.576001	+	0.576001i	−0.357798	+	0.933799i	$0.616472\pi$
$354$			18.7100i			0.994424i
$355$		0			0
$356$		−	2.99617i		−	0.158796i
$357$	−9.20838	+	7.13493i	−0.487359	+	0.377621i
$358$	2.56695	−	2.56695i	0.135668	−	0.135668i
$359$			12.7985i			0.675480i	0.941239	+	0.337740i	$0.109663\pi$
$359$			12.7985i			0.675480i	−0.941239	+	0.337740i	$0.890337\pi$
$360$		0			0
$361$	−1.94239			−0.102231
$362$	0.149294	−	0.149294i	0.00784671	−	0.00784671i
$363$	11.3528	+	11.3528i	0.595869	+	0.595869i
$364$	0.499871	−	3.94009i	0.0262004	−	0.206517i
$365$		0			0
$366$	3.40524			0.177995
$367$	4.14612	−	4.14612i	0.216426	−	0.216426i	−0.590565	−	0.806990i	$-0.701095\pi$
$367$	4.14612	−	4.14612i	0.216426	−	0.216426i	0.806990	+	0.590565i	$0.201095\pi$
$368$	14.0778	−	14.0778i	0.733855	−	0.733855i
$369$	−6.92820			−0.360668
$370$		0			0
$371$	2.30704	−	18.1845i	0.119776	−	0.944094i
$372$	3.50879	+	3.50879i	0.181923	+	0.181923i
$373$	−22.8670	+	22.8670i	−1.18401	+	1.18401i	−0.205310	+	0.978697i	$0.565820\pi$
$373$	−22.8670	+	22.8670i	−1.18401	+	1.18401i	−0.978697	+	0.205310i	$0.934180\pi$
$374$	36.0369			1.86342
$375$		0			0
$376$			10.5584i			0.544509i
$377$	0.556187	−	0.556187i	0.0286451	−	0.0286451i
$378$	3.29092	−	2.54990i	0.169267	−	0.131153i
$379$		−	21.3527i		−	1.09681i	−0.836212	−	0.548407i	$-0.815234\pi$
$379$		−	21.3527i		−	1.09681i	0.836212	−	0.548407i	$-0.184766\pi$
$380$		0			0
$381$			17.4355i			0.893248i
$382$	30.3809	+	30.3809i	1.55442	+	1.55442i
$383$	21.7152	+	21.7152i	1.10960	+	1.10960i	0.993203	+	0.116394i	$0.0371334\pi$
$383$	21.7152	+	21.7152i	1.10960	+	1.10960i	0.116394	+	0.993203i	$0.462867\pi$
$384$	−13.6148			−0.694779
$385$		0			0
$386$	−8.17635			−0.416165
$387$	4.39191	+	4.39191i	0.223253	+	0.223253i
$388$	−5.80615	−	5.80615i	−0.294763	−	0.294763i
$389$		−	28.0530i		−	1.42234i	−0.703018	−	0.711172i	$-0.748165\pi$
$389$		−	28.0530i		−	1.42234i	0.703018	−	0.711172i	$-0.251835\pi$
$390$		0			0
$391$			18.5502i			0.938126i
$392$	8.52957	+	14.4577i	0.430808	+	0.730223i
$393$	−11.2333	+	11.2333i	−0.566645	+	0.566645i
$394$			26.6752i			1.34388i
$395$		0			0
$396$	−2.47602			−0.124425
$397$	1.37510	−	1.37510i	0.0690143	−	0.0690143i	−0.671757	−	0.740771i	$-0.734460\pi$
$397$	1.37510	−	1.37510i	0.0690143	−	0.0690143i	0.740771	+	0.671757i	$0.234460\pi$
$398$	27.0161	+	27.0161i	1.35419	+	1.35419i
$399$	10.8403	+	1.37529i	0.542693	+	0.0688505i
$400$		0			0
$401$	−4.15352			−0.207417			−0.103708	−	0.994608i	$-0.533071\pi$
$401$	−4.15352			−0.207417			−0.103708	+	0.994608i	$0.533071\pi$
$402$	3.94678	−	3.94678i	0.196848	−	0.196848i
$403$	−23.2448	+	23.2448i	−1.15790	+	1.15790i
$404$	2.99617			0.149065
$405$		0			0
$406$	0.130693	−	1.03015i	0.00648618	−	0.0511254i
$407$	8.81997	+	8.81997i	0.437189	+	0.437189i
$408$	7.46593	−	7.46593i	0.369619	−	0.369619i
$409$	6.79403			0.335943			0.167971	−	0.985792i	$-0.446278\pi$
$409$	6.79403			0.335943			0.167971	+	0.985792i	$0.446278\pi$
$410$		0			0
$411$		−	5.59623i		−	0.276042i
$412$	−5.01594	+	5.01594i	−0.247117	+	0.247117i
$413$	−24.8677	+	19.2683i	−1.22366	+	0.948129i
$414$		−	6.62954i		−	0.325824i
$415$		0			0
$416$			8.32404i			0.408120i
$417$	8.40777	+	8.40777i	0.411730	+	0.411730i
$418$	−23.9027	−	23.9027i	−1.16912	−	1.16912i
$419$	−23.4485			−1.14554			−0.572768	−	0.819717i	$-0.694131\pi$
$419$	−23.4485			−1.14554			−0.572768	+	0.819717i	$0.694131\pi$
$420$		0			0
$421$	10.9594			0.534129			0.267064	−	0.963679i	$-0.413946\pi$
$421$	10.9594			0.534129			0.267064	+	0.963679i	$0.413946\pi$
$422$	28.9907	+	28.9907i	1.41125	+	1.41125i
$423$	3.11335	+	3.11335i	0.151376	+	0.151376i
$424$			16.6141i			0.806851i
$425$		0			0
$426$			1.25651i			0.0608783i
$427$	3.50685	+	4.52596i	0.169708	+	0.219027i
$428$	−5.16831	+	5.16831i	−0.249820	+	0.249820i
$429$		−	16.4029i		−	0.791942i
$430$		0			0
$431$	−3.30474			−0.159184			−0.0795919	−	0.996828i	$-0.525362\pi$
$431$	−3.30474			−0.159184			−0.0795919	+	0.996828i	$0.525362\pi$
$432$	−3.34140	+	3.34140i	−0.160763	+	0.160763i
$433$	−12.3328	−	12.3328i	−0.592677	−	0.592677i	0.345676	−	0.938354i	$-0.387649\pi$
$433$	−12.3328	−	12.3328i	−0.592677	−	0.592677i	−0.938354	+	0.345676i	$0.887649\pi$
$434$	−5.46206	+	43.0530i	−0.262187	+	2.06661i
$435$		0			0
$436$	−7.56963			−0.362520
$437$	12.3041	−	12.3041i	0.588586	−	0.588586i
$438$	−9.34962	+	9.34962i	−0.446742	+	0.446742i
$439$	33.1749			1.58335			0.791675	−	0.610942i	$-0.209209\pi$
$439$	33.1749			1.58335			0.791675	+	0.610942i	$0.209209\pi$
$440$		0			0
$441$	6.77823	+	1.74802i	0.322773	+	0.0832390i
$442$	−15.4490	−	15.4490i	−0.734835	−	0.734835i
$443$	−14.8596	+	14.8596i	−0.705999	+	0.705999i	−0.965691	−	0.259692i	$-0.916379\pi$
$443$	−14.8596	+	14.8596i	−0.705999	+	0.705999i	0.259692	+	0.965691i	$0.416379\pi$
$444$	−1.14152			−0.0541742
$445$		0			0
$446$			8.89422i			0.421154i
$447$	0.176370	−	0.176370i	0.00834202	−	0.00834202i
$448$	−8.58435	−	11.0790i	−0.405573	−	0.523434i
$449$		−	7.84648i		−	0.370298i	−0.982710	−	0.185149i	$-0.940723\pi$
$449$		−	7.84648i		−	0.370298i	0.982710	−	0.185149i	$-0.0592768\pi$
$450$		0			0
$451$			36.0369i			1.69691i
$452$	−4.03589	−	4.03589i	−0.189832	−	0.189832i
$453$	1.66523	+	1.66523i	0.0782394	+	0.0782394i
$454$	−36.0369			−1.69129
$455$		0			0
$456$	−9.90409			−0.463802
$457$	6.52235	+	6.52235i	0.305103	+	0.305103i	0.843006	−	0.537904i	$-0.180784\pi$
$457$	6.52235	+	6.52235i	0.305103	+	0.305103i	−0.537904	+	0.843006i	$0.680784\pi$
$458$	13.0807	+	13.0807i	0.611219	+	0.611219i
$459$		−	4.40294i		−	0.205512i
$460$		0			0
$461$		−	0.966276i		−	0.0450039i	−0.999747	−	0.0225020i	$-0.992837\pi$
$461$		−	0.966276i		−	0.0450039i	0.999747	−	0.0225020i	$-0.00716320\pi$
$462$	−13.2633	−	17.1176i	−0.617063	−	0.796384i
$463$	−7.79681	+	7.79681i	−0.362348	+	0.362348i	−0.864677	−	0.502328i	$-0.832477\pi$
$463$	−7.79681	+	7.79681i	−0.362348	+	0.362348i	0.502328	+	0.864677i	$0.332477\pi$
$464$			1.17865i			0.0547173i
$465$		0			0
$466$	−27.7734			−1.28658
$467$	−19.3074	+	19.3074i	−0.893438	+	0.893438i	−0.994845	−	0.101407i	$-0.967666\pi$
$467$	−19.3074	+	19.3074i	−0.893438	+	0.893438i	0.101407	+	0.994845i	$0.467666\pi$
$468$	1.06147	+	1.06147i	0.0490666	+	0.0490666i
$469$	9.31027	+	1.18118i	0.429908	+	0.0545417i
$470$		0			0
$471$	−7.55646			−0.348183
$472$	20.1621	−	20.1621i	0.928038	−	0.928038i
$473$	22.8444	−	22.8444i	1.05039	−	1.05039i
$474$	8.33563			0.382868
$475$		0			0
$476$	−5.50115	−	0.697921i	−0.252145	−	0.0319891i
$477$	4.89898	+	4.89898i	0.224309	+	0.224309i
$478$	9.79796	−	9.79796i	0.448148	−	0.448148i
$479$	4.62996			0.211548			0.105774	−	0.994390i	$-0.466268\pi$
$479$	4.62996			0.211548			0.105774	+	0.994390i	$0.466268\pi$
$480$		0			0
$481$		−	7.56225i		−	0.344809i
$482$	24.8286	−	24.8286i	1.13091	−	1.13091i
$483$	8.81142	−	6.82736i	0.400934	−	0.310656i
$484$			7.64271i			0.347396i
$485$		0			0
$486$			1.57354i			0.0713772i
$487$	7.85554	+	7.85554i	0.355968	+	0.355968i	0.862325	−	0.506356i	$-0.169008\pi$
$487$	7.85554	+	7.85554i	0.355968	+	0.355968i	−0.506356	+	0.862325i	$0.669008\pi$
$488$	−3.66954	−	3.66954i	−0.166112	−	0.166112i
$489$	−21.5145			−0.972918
$490$		0			0
$491$	−5.48919			−0.247724			−0.123862	−	0.992299i	$-0.539528\pi$
$491$	−5.48919			−0.247724			−0.123862	+	0.992299i	$0.539528\pi$
$492$	−2.33203	−	2.33203i	−0.105136	−	0.105136i
$493$	−0.776548	−	0.776548i	−0.0349740	−	0.0349740i
$494$			20.4943i			0.922080i
$495$		0			0
$496$		−	49.2592i		−	2.21180i
$497$	−1.67005	+	1.29401i	−0.0749120	+	0.0580441i
$498$	−7.23101	+	7.23101i	−0.324029	+	0.324029i
$499$		−	15.5565i		−	0.696403i	−0.937420	−	0.348201i	$-0.886793\pi$
$499$		−	15.5565i		−	0.696403i	0.937420	−	0.348201i	$-0.113207\pi$
$500$		0			0
$501$	6.70998			0.299780
$502$	−17.6760	+	17.6760i	−0.788920	+	0.788920i
$503$	−23.1973	−	23.1973i	−1.03432	−	1.03432i	−0.999390	−	0.0349251i	$-0.988881\pi$
$503$	−23.1973	−	23.1973i	−1.03432	−	1.03432i	−0.0349251	−	0.999390i	$-0.511119\pi$
$504$	−6.29415	−	0.798528i	−0.280364	−	0.0355692i
$505$		0			0
$506$	−34.4834			−1.53297
$507$	2.16043	−	2.16043i	0.0959482	−	0.0959482i
$508$	−5.86878	+	5.86878i	−0.260385	+	0.260385i
$509$	−11.8904			−0.527032			−0.263516	−	0.964655i	$-0.584882\pi$
$509$	−11.8904			−0.527032			−0.263516	+	0.964655i	$0.584882\pi$
$510$		0			0
$511$	−22.0553	−	2.79812i	−0.975670	−	0.123781i
$512$	7.20561	+	7.20561i	0.318446	+	0.318446i
$513$	−2.92041	+	2.92041i	−0.128939	+	0.128939i
$514$	−5.02606			−0.221690
$515$		0			0
$516$			2.95663i			0.130158i
$517$	16.1940	−	16.1940i	0.712212	−	0.712212i
$518$	−6.11476	−	7.89174i	−0.268667	−	0.346743i
$519$			8.59476i			0.377268i
$520$		0			0
$521$			5.59623i			0.245175i	0.992458	+	0.122588i	$0.0391193\pi$
$521$			5.59623i			0.245175i	−0.992458	+	0.122588i	$0.960881\pi$
$522$	0.277525	+	0.277525i	0.0121470	+	0.0121470i
$523$	12.6314	+	12.6314i	0.552333	+	0.552333i	0.927113	−	0.374781i	$-0.122282\pi$
$523$	12.6314	+	12.6314i	0.552333	+	0.552333i	−0.374781	+	0.927113i	$0.622282\pi$
$524$	−7.56225			−0.330359
$525$		0			0
$526$	−4.53364			−0.197676
$527$	32.4543	+	32.4543i	1.41373	+	1.41373i
$528$	17.3802	+	17.3802i	0.756375	+	0.756375i
$529$			5.24943i			0.228236i
$530$		0			0
$531$		−	11.8904i		−	0.515999i
$532$	3.18592	+	4.11176i	0.138127	+	0.178267i
$533$	15.4490	−	15.4490i	0.669172	−	0.669172i
$534$			9.90409i			0.428592i
$535$		0			0
$536$	−8.50621			−0.367412
$537$	−1.63132	+	1.63132i	−0.0703968	+	0.0703968i
$538$	16.8995	+	16.8995i	0.728589	+	0.728589i
$539$	9.09227	−	35.2568i	0.391632	−	1.51862i
$540$		0			0
$541$	−0.712283			−0.0306234			−0.0153117	−	0.999883i	$-0.504874\pi$
$541$	−0.712283			−0.0306234			−0.0153117	+	0.999883i	$0.504874\pi$
$542$	−16.1940	+	16.1940i	−0.695592	+	0.695592i
$543$	−0.0948778	+	0.0948778i	−0.00407160	+	0.00407160i
$544$	11.6220			0.498291
$545$		0			0
$546$	−1.65237	+	13.0243i	−0.0707149	+	0.557389i
$547$	14.8234	+	14.8234i	0.633803	+	0.633803i	0.949020	−	0.315216i	$-0.102077\pi$
$547$	14.8234	+	14.8234i	0.633803	+	0.633803i	−0.315216	+	0.949020i	$0.602077\pi$
$548$	1.88369	−	1.88369i	0.0804672	−	0.0804672i
$549$	−2.16407			−0.0923602
$550$		0			0
$551$			1.03015i			0.0438858i
$552$	−7.14409	+	7.14409i	−0.304073	+	0.304073i
$553$	8.58435	+	11.0790i	0.365044	+	0.471127i
$554$		−	0.786567i		−	0.0334180i
$555$		0			0
$556$			5.66011i			0.240042i
$557$	−17.4971	−	17.4971i	−0.741375	−	0.741375i	0.231468	−	0.972843i	$-0.425647\pi$
$557$	−17.4971	−	17.4971i	−0.741375	−	0.741375i	−0.972843	+	0.231468i	$0.925647\pi$
$558$	−11.5986	−	11.5986i	−0.491009	−	0.491009i
$559$	−19.5868			−0.828434
$560$		0			0
$561$	−22.9018			−0.966915
$562$	−6.71856	−	6.71856i	−0.283406	−	0.283406i
$563$	−9.81802	−	9.81802i	−0.413780	−	0.413780i	0.469273	−	0.883053i	$-0.344516\pi$
$563$	−9.81802	−	9.81802i	−0.413780	−	0.413780i	−0.883053	+	0.469273i	$0.844516\pi$
$564$			2.09591i			0.0882535i
$565$		0			0
$566$			3.06004i			0.128623i
$567$	−2.09141	+	1.62049i	−0.0878311	+	0.0680542i
$568$	1.35404	−	1.35404i	0.0568141	−	0.0568141i
$569$			23.1512i			0.970550i	0.874362	+	0.485275i	$0.161280\pi$
$569$			23.1512i			0.970550i	−0.874362	+	0.485275i	$0.838720\pi$
$570$		0			0
$571$	−38.1586			−1.59689			−0.798443	−	0.602070i	$-0.794343\pi$
$571$	−38.1586			−1.59689			−0.798443	+	0.602070i	$0.794343\pi$
$572$	5.52122	−	5.52122i	0.230854	−	0.230854i
$573$	−19.3074	−	19.3074i	−0.806577	−	0.806577i
$574$	3.63021	−	28.6141i	0.151522	−	1.19433i
$575$		0			0
$576$	5.29738			0.220724
$577$	0.598552	−	0.598552i	0.0249180	−	0.0249180i	−0.694538	−	0.719456i	$-0.744391\pi$
$577$	0.598552	−	0.598552i	0.0249180	−	0.0249180i	0.719456	+	0.694538i	$0.244391\pi$
$578$	−2.65472	+	2.65472i	−0.110422	+	0.110422i
$579$	5.19615			0.215945
$580$		0			0
$581$	−17.0576	−	2.16407i	−0.707669	−	0.0897807i
$582$	19.1927	+	19.1927i	0.795565	+	0.795565i
$583$	25.4819	−	25.4819i	1.05535	−	1.05535i
$584$	20.1506			0.833836
$585$		0			0
$586$		−	25.8107i		−	1.06623i
$587$	15.4885	−	15.4885i	0.639280	−	0.639280i	−0.311098	−	0.950378i	$-0.600697\pi$
$587$	15.4885	−	15.4885i	0.639280	−	0.639280i	0.950378	+	0.311098i	$0.100697\pi$
$588$	1.69317	+	2.86993i	0.0698250	+	0.118354i
$589$		−	43.0530i		−	1.77397i
$590$		0			0
$591$		−	16.9524i		−	0.697327i
$592$	8.01279	+	8.01279i	0.329324	+	0.329324i
$593$	6.22670	+	6.22670i	0.255700	+	0.255700i	0.823303	−	0.567603i	$-0.192129\pi$
$593$	6.22670	+	6.22670i	0.255700	+	0.255700i	−0.567603	+	0.823303i	$0.692129\pi$
$594$	8.18472			0.335823
$595$		0			0
$596$	0.118732			0.00486346
$597$	−17.1690	−	17.1690i	−0.702681	−	0.702681i
$598$	14.7831	+	14.7831i	0.604524	+	0.604524i
$599$		−	19.0097i		−	0.776714i	−0.921509	−	0.388357i	$-0.873043\pi$
$599$		−	19.0097i		−	0.776714i	0.921509	−	0.388357i	$-0.126957\pi$
$600$		0			0
$601$			10.3604i			0.422608i	0.977420	+	0.211304i	$0.0677710\pi$
$601$			10.3604i			0.422608i	−0.977420	+	0.211304i	$0.932229\pi$
$602$	−20.4402	+	15.8377i	−0.833081	+	0.645497i
$603$	−2.50822	+	2.50822i	−0.102143	+	0.102143i
$604$			1.12103i			0.0456141i
$605$		0			0
$606$	−9.90409			−0.402326
$607$	10.4015	−	10.4015i	0.422185	−	0.422185i	−0.463770	−	0.885955i	$-0.653504\pi$
$607$	10.4015	−	10.4015i	0.422185	−	0.422185i	0.885955	+	0.463770i	$0.153504\pi$
$608$	−7.70873	−	7.70873i	−0.312630	−	0.312630i
$609$	−0.0830567	+	0.654669i	−0.00336563	+	0.0265285i
$610$		0			0
$611$	−13.8848			−0.561718
$612$	1.48203	−	1.48203i	0.0599075	−	0.0599075i
$613$	−5.08700	+	5.08700i	−0.205462	+	0.205462i	−0.802335	−	0.596873i	$-0.796409\pi$
$613$	−5.08700	+	5.08700i	−0.205462	+	0.205462i	0.596873	+	0.802335i	$0.296409\pi$
$614$	−15.1884			−0.612953
$615$		0			0
$616$	−4.15352	+	32.7389i	−0.167350	+	1.31909i
$617$	−8.33721	−	8.33721i	−0.335643	−	0.335643i	0.519081	−	0.854725i	$-0.326274\pi$
$617$	−8.33721	−	8.33721i	−0.335643	−	0.335643i	−0.854725	+	0.519081i	$0.826274\pi$
$618$	16.5806	−	16.5806i	0.666971	−	0.666971i
$619$	30.9070			1.24226			0.621129	−	0.783708i	$-0.286674\pi$
$619$	30.9070			1.24226			0.621129	+	0.783708i	$0.286674\pi$
$620$		0			0
$621$			4.21314i			0.169068i
$622$	26.8668	−	26.8668i	1.07726	−	1.07726i
$623$	−13.1637	+	10.1996i	−0.527392	+	0.408639i
$624$		−	14.9018i		−	0.596549i
$625$		0			0
$626$		−	1.33197i		−	0.0532362i
$627$	15.1904	+	15.1904i	0.606648	+	0.606648i
$628$	−2.54350	−	2.54350i	−0.101497	−	0.101497i
$629$	−10.5584			−0.420992
$630$		0			0
$631$	10.4509			0.416044			0.208022	−	0.978124i	$-0.433297\pi$
$631$	10.4509			0.416044			0.208022	+	0.978124i	$0.433297\pi$
$632$	−8.98259	−	8.98259i	−0.357308	−	0.357308i
$633$	−18.4239	−	18.4239i	−0.732284	−	0.732284i
$634$			30.1307i			1.19664i
$635$		0			0
$636$			3.29799i			0.130774i
$637$	−19.0125	+	11.2167i	−0.753302	+	0.444424i
$638$	1.44354	−	1.44354i	0.0571503	−	0.0571503i
$639$		−	0.798528i		−	0.0315893i
$640$		0			0
$641$	46.2641			1.82732			0.913662	−	0.406475i	$-0.133242\pi$
$641$	46.2641			1.82732			0.913662	+	0.406475i	$0.133242\pi$
$642$	17.0843	−	17.0843i	0.674264	−	0.674264i
$643$	11.8836	+	11.8836i	0.468642	+	0.468642i	0.901474	−	0.432833i	$-0.142486\pi$
$643$	11.8836	+	11.8836i	0.468642	+	0.468642i	−0.432833	+	0.901474i	$0.642486\pi$
$644$	5.26401	+	0.667835i	0.207431	+	0.0263164i
$645$		0			0
$646$	28.6141			1.12581
$647$	−26.1613	+	26.1613i	−1.02851	+	1.02851i	−0.0289263	+	0.999582i	$0.509209\pi$
$647$	−26.1613	+	26.1613i	−1.02851	+	1.02851i	−0.999582	+	0.0289263i	$0.990791\pi$
$648$	1.69567	−	1.69567i	0.0666121	−	0.0666121i
$649$	−61.8475			−2.42773
$650$		0			0
$651$	3.47119	−	27.3606i	0.136047	−	1.07235i
$652$	−7.24176	−	7.24176i	−0.283609	−	0.283609i
$653$	−0.0451641	+	0.0451641i	−0.00176741	+	0.00176741i	−0.707990	−	0.706223i	$-0.750398\pi$
$653$	−0.0451641	+	0.0451641i	−0.00176741	+	0.00176741i	0.706223	+	0.707990i	$0.250398\pi$
$654$	25.0221			0.978441
$655$		0			0
$656$			32.7389i			1.27824i
$657$	5.94178	−	5.94178i	0.231811	−	0.231811i
$658$	−14.4897	+	11.2271i	−0.564869	+	0.437678i
$659$		−	16.1918i		−	0.630743i	−0.948968	−	0.315372i	$-0.897871\pi$
$659$		−	16.1918i		−	0.630743i	0.948968	−	0.315372i	$-0.102129\pi$
$660$		0			0
$661$			17.1544i			0.667229i	0.942710	+	0.333614i	$0.108268\pi$
$661$			17.1544i			0.667229i	−0.942710	+	0.333614i	$0.891732\pi$
$662$	−24.9350	−	24.9350i	−0.969128	−	0.969128i
$663$	9.81802	+	9.81802i	0.381300	+	0.381300i
$664$	15.5845			0.604795
$665$		0			0
$666$	3.77340			0.146216
$667$	0.743073	+	0.743073i	0.0287719	+	0.0287719i
$668$	2.25858	+	2.25858i	0.0873870	+	0.0873870i
$669$		−	5.65237i		−	0.218533i
$670$		0			0
$671$			11.2563i			0.434546i
$672$	−4.27746	−	5.52050i	−0.165006	−	0.212958i
$673$	7.91427	−	7.91427i	0.305073	−	0.305073i	−0.537922	−	0.842995i	$-0.680790\pi$
$673$	7.91427	−	7.91427i	0.305073	−	0.305073i	0.842995	+	0.537922i	$0.180790\pi$
$674$			1.30934i			0.0504338i
$675$		0			0
$676$	1.45440			0.0559385
$677$	16.0447	−	16.0447i	0.616649	−	0.616649i	−0.328022	−	0.944670i	$-0.606382\pi$
$677$	16.0447	−	16.0447i	0.616649	−	0.616649i	0.944670	+	0.328022i	$0.106382\pi$
$678$	13.3410	+	13.3410i	0.512358	+	0.512358i
$679$	−5.74393	+	45.2748i	−0.220432	+	1.73749i
$680$		0			0
$681$	22.9018			0.877599
$682$	−60.3300	+	60.3300i	−2.31015	+	2.31015i
$683$	−10.2553	+	10.2553i	−0.392409	+	0.392409i	−0.875545	−	0.483136i	$-0.839498\pi$
$683$	−10.2553	+	10.2553i	−0.392409	+	0.392409i	0.483136	+	0.875545i	$0.339498\pi$
$684$	−1.96602			−0.0751726
$685$		0			0
$686$	−10.7711	+	27.0788i	−0.411243	+	1.03387i
$687$	−8.31290	−	8.31290i	−0.317157	−	0.317157i
$688$	20.7537	−	20.7537i	0.791229	−	0.791229i
$689$	−21.8482			−0.832351
$690$		0			0
$691$			5.26401i			0.200252i	0.994975	+	0.100126i	$0.0319246\pi$
$691$			5.26401i			0.200252i	−0.994975	+	0.100126i	$0.968075\pi$
$692$	−2.89299	+	2.89299i	−0.109975	+	0.109975i
$693$	8.42894	+	10.8784i	0.320189	+	0.413237i
$694$			46.8817i			1.77961i
$695$		0			0
$696$		−	0.598130i		−	0.0226721i
$697$	−21.5699	−	21.5699i	−0.817020	−	0.817020i
$698$	−25.7544	−	25.7544i	−0.974820	−	0.974820i
$699$	17.6503			0.667595
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−3.50879	−	3.50879i	−0.132431	−	0.132431i
$703$	7.00325	+	7.00325i	0.264133	+	0.264133i
$704$		−	27.5542i		−	1.03849i
$705$		0			0
$706$		−	24.0826i		−	0.906361i
$707$	−10.1996	−	13.1637i	−0.383596	−	0.495071i
$708$	4.00230	−	4.00230i	0.150416	−	0.150416i
$709$		−	24.6694i		−	0.926478i	−0.886233	−	0.463239i	$-0.846687\pi$
$709$		−	24.6694i		−	0.926478i	0.886233	−	0.463239i	$-0.153313\pi$
$710$		0			0
$711$	−5.29738			−0.198667
$712$	10.6728	−	10.6728i	0.399980	−	0.399980i
$713$	−31.0553	−	31.0553i	−1.16303	−	1.16303i
$714$	18.1845	+	2.30704i	0.680539	+	0.0863388i
$715$		0			0
$716$	−1.09821			−0.0410418
$717$	−6.22670	+	6.22670i	−0.232541	+	0.232541i
$718$	14.2404	−	14.2404i	0.531447	−	0.531447i
$719$	17.8523			0.665779			0.332890	−	0.942966i	$-0.391976\pi$
$719$	17.8523			0.665779			0.332890	+	0.942966i	$0.391976\pi$
$720$		0			0
$721$	39.1129	+	4.96218i	1.45664	+	0.184801i
$722$	2.16121	+	2.16121i	0.0804321	+	0.0804321i
$723$	−15.7788	+	15.7788i	−0.586821	+	0.586821i
$724$	−0.0638717			−0.00237377
$725$		0			0
$726$		−	25.2637i		−	0.937622i
$727$	−1.73825	+	1.73825i	−0.0644682	+	0.0644682i	−0.738606	−	0.674138i	$-0.764515\pi$
$727$	−1.73825	+	1.73825i	−0.0644682	+	0.0644682i	0.674138	+	0.738606i	$0.264515\pi$
$728$	15.8158	−	12.2546i	0.586172	−	0.454184i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			27.3471i			1.01147i
$732$	−0.728424	−	0.728424i	−0.0269233	−	0.0269233i
$733$	12.5108	+	12.5108i	0.462097	+	0.462097i	0.899342	−	0.437245i	$-0.144046\pi$
$733$	12.5108	+	12.5108i	0.462097	+	0.462097i	−0.437245	+	0.899342i	$0.644046\pi$
$734$	−9.22645			−0.340554
$735$		0			0
$736$	−11.1210			−0.409927
$737$	13.0464	+	13.0464i	0.480572	+	0.480572i
$738$	7.70873	+	7.70873i	0.283762	+	0.283762i
$739$		−	10.5874i		−	0.389464i	−0.980857	−	0.194732i	$-0.937616\pi$
$739$		−	10.5874i		−	0.389464i	0.980857	−	0.194732i	$-0.0623836\pi$
$740$		0			0
$741$		−	13.0243i		−	0.478460i
$742$	−22.8002	+	17.6663i	−0.837020	+	0.648549i
$743$	−12.5060	+	12.5060i	−0.458802	+	0.458802i	−0.898262	−	0.439460i	$-0.855170\pi$
$743$	−12.5060	+	12.5060i	−0.458802	+	0.458802i	0.439460	+	0.898262i	$0.355170\pi$
$744$			24.9977i			0.916460i
$745$		0			0
$746$	50.8863			1.86308
$747$	4.59538	−	4.59538i	0.168136	−	0.168136i
$748$	−7.70873	−	7.70873i	−0.281859	−	0.281859i
$749$	40.3011	+	5.11293i	1.47257	+	0.186822i
$750$		0			0
$751$	32.0000			1.16770			0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000			1.16770			0.583848	+	0.811863i	$0.301546\pi$
$752$	14.7120	−	14.7120i	0.536491	−	0.536491i
$753$	11.2333	−	11.2333i	0.409365	−	0.409365i
$754$	−1.23769			−0.0450741
$755$		0			0
$756$	−1.24943	−	0.158512i	−0.0454412	−	0.00576503i
$757$	−13.7308	−	13.7308i	−0.499054	−	0.499054i	0.412090	−	0.911143i	$-0.364799\pi$
$757$	−13.7308	−	13.7308i	−0.499054	−	0.499054i	−0.911143	+	0.412090i	$0.864799\pi$
$758$	−23.7583	+	23.7583i	−0.862940	+	0.862940i
$759$	21.9145			0.795448
$760$		0			0
$761$		−	13.8564i		−	0.502294i	−0.967949	−	0.251147i	$-0.919192\pi$
$761$		−	13.8564i		−	0.502294i	0.967949	−	0.251147i	$-0.0808078\pi$
$762$	19.3998	−	19.3998i	0.702780	−	0.702780i
$763$	25.7687	+	33.2572i	0.932890	+	1.20399i
$764$		−	12.9977i		−	0.470240i
$765$		0			0
$766$		−	48.3233i		−	1.74599i
$767$	26.5141	+	26.5141i	0.957368	+	0.957368i
$768$	7.65706	+	7.65706i	0.276300	+	0.276300i
$769$	−25.9448			−0.935595			−0.467797	−	0.883836i	$-0.654952\pi$
$769$	−25.9448			−0.935595			−0.467797	+	0.883836i	$0.654952\pi$
$770$		0			0
$771$	3.19411			0.115033
$772$	1.74902	+	1.74902i	0.0629487	+	0.0629487i
$773$	−11.7479	−	11.7479i	−0.422544	−	0.422544i	0.463535	−	0.886079i	$-0.346581\pi$
$773$	−11.7479	−	11.7479i	−0.422544	−	0.422544i	−0.886079	+	0.463535i	$0.846581\pi$
$774$		−	9.77340i		−	0.351298i
$775$		0			0
$776$		−	41.3647i		−	1.48491i
$777$	3.88599	+	5.01528i	0.139409	+	0.179922i
$778$	−31.2135	+	31.2135i	−1.11906	+	1.11906i
$779$			28.6141i			1.02521i
$780$		0			0
$781$	−4.15352			−0.148625
$782$	20.6401	−	20.6401i	0.738089	−	0.738089i
$783$	−0.176370	−	0.176370i	−0.00630296	−	0.00630296i
$784$	8.26017	−	32.0302i	0.295006	−	1.14394i
$785$		0			0
$786$	24.9977			0.891638
$787$	−20.3401	+	20.3401i	−0.725048	+	0.725048i	−0.969629	−	0.244581i	$-0.921350\pi$
$787$	−20.3401	+	20.3401i	−0.725048	+	0.725048i	0.244581	+	0.969629i	$0.421350\pi$
$788$	5.70616	−	5.70616i	0.203273	−	0.203273i
$789$	2.88117			0.102572
$790$		0			0
$791$	−3.99264	+	31.4708i	−0.141962	+	1.11897i
$792$	−8.81997	−	8.81997i	−0.313404	−	0.313404i
$793$	4.82560	−	4.82560i	0.171362	−	0.171362i
$794$	−3.06004			−0.108597
$795$		0			0
$796$		−	11.5582i		−	0.409668i
$797$	−16.4926	+	16.4926i	−0.584198	+	0.584198i	−0.936054	−	0.351856i	$-0.885551\pi$
$797$	−16.4926	+	16.4926i	−0.584198	+	0.584198i	0.351856	+	0.936054i	$0.385551\pi$
$798$	−10.5313	−	13.5918i	−0.372805	−	0.481144i
$799$			19.3859i			0.685825i
$800$		0			0
$801$		−	6.29415i		−	0.222393i
$802$	4.62145	+	4.62145i	0.163189	+	0.163189i
$803$	−30.9060	−	30.9060i	−1.09065	−	1.09065i
$804$	−1.68853			−0.0595499
$805$		0			0
$806$	51.7270			1.82201
$807$	−10.7398	−	10.7398i	−0.378059	−	0.378059i
$808$	10.6728	+	10.6728i	0.375467	+	0.375467i
$809$			49.9571i			1.75640i	0.478295	+	0.878199i	$0.341255\pi$
$809$			49.9571i			1.75640i	−0.478295	+	0.878199i	$0.658745\pi$
$810$		0			0
$811$		−	28.5449i		−	1.00235i	−0.865347	−	0.501174i	$-0.832902\pi$
$811$		−	28.5449i		−	1.00235i	0.865347	−	0.501174i	$-0.167098\pi$
$812$	−0.248318	+	0.192405i	−0.00871426	+	0.00675208i
$813$	10.2915	−	10.2915i	0.360937	−	0.360937i
$814$		−	19.6272i		−	0.687935i
$815$		0			0
$816$	−20.8059			−0.728352
$817$	18.1390	−	18.1390i	0.634602	−	0.634602i
$818$	−7.55944	−	7.55944i	−0.264310	−	0.264310i
$819$	1.05010	−	8.27708i	0.0366934	−	0.289225i
$820$		0			0
$821$	6.00000			0.209401			0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000			0.209401			0.104701	+	0.994504i	$0.466612\pi$
$822$	−6.22670	+	6.22670i	−0.217181	+	0.217181i
$823$	16.8020	−	16.8020i	0.585680	−	0.585680i	−0.350778	−	0.936459i	$-0.614083\pi$
$823$	16.8020	−	16.8020i	0.585680	−	0.585680i	0.936459	+	0.350778i	$0.114083\pi$
$824$	−35.7350			−1.24489
$825$		0			0
$826$	49.1083	+	6.23028i	1.70870	+	0.216779i
$827$	−39.8118	−	39.8118i	−1.38439	−	1.38439i	−0.836641	−	0.547751i	$-0.815484\pi$
$827$	−39.8118	−	39.8118i	−1.38439	−	1.38439i	−0.547751	−	0.836641i	$-0.684516\pi$
$828$	−1.41814	+	1.41814i	−0.0492838	+	0.0492838i
$829$	−27.0788			−0.940484			−0.470242	−	0.882537i	$-0.655833\pi$
$829$	−27.0788			−0.940484			−0.470242	+	0.882537i	$0.655833\pi$
$830$		0			0
$831$			0.499871i			0.0173403i
$832$	−11.8125	+	11.8125i	−0.409524	+	0.409524i
$833$	15.6608	+	26.5452i	0.542615	+	0.919737i
$834$		−	18.7100i		−	0.647874i
$835$		0			0
$836$			10.2262i			0.353680i
$837$	7.37105	+	7.37105i	0.254781	+	0.254781i
$838$	26.0903	+	26.0903i	0.901273	+	0.901273i
$839$	−54.8554			−1.89382			−0.946910	−	0.321498i	$-0.895814\pi$
$839$	−54.8554			−1.89382			−0.946910	+	0.321498i	$0.895814\pi$
$840$		0			0
$841$	28.9378			0.997855
$842$	−12.1941	−	12.1941i	−0.420236	−	0.420236i
$843$	4.26972	+	4.26972i	0.147057	+	0.147057i
$844$		−	12.4029i		−	0.426927i
$845$		0			0
$846$		−	6.92820i		−	0.238197i
$847$	33.5783	−	26.0175i	1.15376	−	0.893972i
$848$	23.1499	−	23.1499i	0.794970	−	0.794970i
$849$		−	1.94469i		−	0.0667414i
$850$		0			0
$851$	10.1033			0.346336
$852$	0.268784	−	0.268784i	0.00920839	−	0.00920839i
$853$	9.36876	+	9.36876i	0.320780	+	0.320780i	0.849066	−	0.528286i	$-0.177165\pi$
$853$	9.36876	+	9.36876i	0.320780	+	0.320780i	−0.528286	+	0.849066i	$0.677165\pi$
$854$	1.13392	−	8.93779i	0.0388020	−	0.305845i
$855$		0			0
$856$	−36.8206			−1.25850
$857$	−20.6401	+	20.6401i	−0.705052	+	0.705052i	−0.965491	−	0.260438i	$-0.916133\pi$
$857$	−20.6401	+	20.6401i	−0.705052	+	0.705052i	0.260438	+	0.965491i	$0.416133\pi$
$858$	−18.2509	+	18.2509i	−0.623075	+	0.623075i
$859$	15.5206			0.529556			0.264778	−	0.964309i	$-0.414701\pi$
$859$	15.5206			0.529556			0.264778	+	0.964309i	$0.414701\pi$
$860$		0			0
$861$	−2.30704	+	18.1845i	−0.0786237	+	0.619728i
$862$	3.67705	+	3.67705i	0.125241	+	0.125241i
$863$	22.6925	−	22.6925i	0.772462	−	0.772462i	−0.206074	−	0.978536i	$-0.566069\pi$
$863$	22.6925	−	22.6925i	0.772462	−	0.772462i	0.978536	+	0.206074i	$0.0660688\pi$
$864$	2.63960			0.0898012
$865$		0			0
$866$			27.4445i			0.932601i
$867$	1.68710	−	1.68710i	0.0572970	−	0.0572970i
$868$	10.3780	−	8.04117i	0.352252	−	0.272935i
$869$			27.5542i			0.934711i
$870$		0			0
$871$		−	11.1860i		−	0.379024i
$872$	−26.9642	−	26.9642i	−0.913121	−	0.913121i
$873$	−12.1972	−	12.1972i	−0.412812	−	0.412812i
$874$	−27.3806			−0.926162
$875$		0			0
$876$	4.00000			0.135147
$877$	−10.1514	−	10.1514i	−0.342789	−	0.342789i	0.514626	−	0.857415i	$-0.327931\pi$
$877$	−10.1514	−	10.1514i	−0.342789	−	0.342789i	−0.857415	+	0.514626i	$0.827931\pi$
$878$	−36.9123	−	36.9123i	−1.24573	−	1.24573i
$879$			16.4029i			0.553258i
$880$		0			0
$881$		−	5.66011i		−	0.190694i	−0.995444	−	0.0953469i	$-0.969604\pi$
$881$		−	5.66011i		−	0.190694i	0.995444	−	0.0953469i	$-0.0303960\pi$
$882$	−5.59692	−	9.48682i	−0.188458	−	0.319438i
$883$	−18.2373	+	18.2373i	−0.613735	+	0.613735i	−0.943917	−	0.330182i	$-0.892890\pi$
$883$	−18.2373	+	18.2373i	−0.613735	+	0.613735i	0.330182	+	0.943917i	$0.392890\pi$
$884$			6.60948i			0.222301i
$885$		0			0
$886$	33.0673			1.11092
$887$	−9.11254	+	9.11254i	−0.305969	+	0.305969i	−0.843344	−	0.537375i	$-0.819416\pi$
$887$	−9.11254	+	9.11254i	−0.305969	+	0.305969i	0.537375	+	0.843344i	$0.319416\pi$
$888$	−4.06627	−	4.06627i	−0.136455	−	0.136455i
$889$	45.7632	+	5.80589i	1.53485	+	0.194723i
$890$		0			0
$891$	−5.20147			−0.174256
$892$	1.90258	−	1.90258i	0.0637033	−	0.0637033i
$893$	12.8584	−	12.8584i	0.430290	−	0.430290i
$894$	−0.392480			−0.0131265
$895$		0			0
$896$	−4.53364	+	35.7350i	−0.151458	+	1.19382i
$897$	−9.39478	−	9.39478i	−0.313683	−	0.313683i
$898$	−8.73046	+	8.73046i	−0.291339	+	0.291339i
$899$	2.60007			0.0867171
$900$		0			0
$901$			30.5045i			1.01625i
$902$	40.0968	−	40.0968i	1.33508	−	1.33508i
$903$	12.9900	−	10.0650i	0.432279	−	0.334943i
$904$		−	28.7529i		−	0.956306i
$905$		0			0
$906$		−	3.70567i		−	0.123113i
$907$	−21.5971	−	21.5971i	−0.717119	−	0.717119i	0.250895	−	0.968014i	$-0.419275\pi$
$907$	−21.5971	−	21.5971i	−0.717119	−	0.717119i	−0.968014	+	0.250895i	$0.919275\pi$
$908$	7.70873	+	7.70873i	0.255823	+	0.255823i
$909$	6.29415			0.208764
$910$		0			0
$911$	−29.7003			−0.984016			−0.492008	−	0.870591i	$-0.663737\pi$
$911$	−29.7003			−0.984016			−0.492008	+	0.870591i	$0.663737\pi$
$912$	13.8003	+	13.8003i	0.456972	+	0.456972i
$913$	−23.9027	−	23.9027i	−0.791065	−	0.791065i
$914$		−	14.5143i		−	0.480091i
$915$		0			0
$916$		−	5.59623i		−	0.184905i
$917$	25.7436	+	33.2248i	0.850129	+	1.09718i
$918$	−4.89898	+	4.89898i	−0.161690	+	0.161690i
$919$			14.2591i			0.470364i	0.971951	+	0.235182i	$0.0755686\pi$
$919$			14.2591i			0.470364i	−0.971951	+	0.235182i	$0.924431\pi$
$920$		0			0
$921$	9.65237			0.318056
$922$	−1.07514	+	1.07514i	−0.0354077	+	0.0354077i
$923$	1.78062	+	1.78062i	0.0586097	+	0.0586097i
$924$	−0.824497	+	6.49885i	−0.0271240	+	0.213796i
$925$		0			0
$926$	17.3504			0.570169
$927$	−10.5372	+	10.5372i	−0.346086	+	0.346086i
$928$	0.465548	−	0.465548i	0.0152823	−	0.0152823i
$929$	54.9832			1.80394			0.901970	−	0.431799i	$-0.142121\pi$
$929$	54.9832			1.80394			0.901970	+	0.431799i	$0.142121\pi$
$930$		0			0
$931$	7.21947	−	27.9947i	0.236609	−	0.917489i
$932$	5.94108	+	5.94108i	0.194606	+	0.194606i
$933$	−17.0741	+	17.0741i	−0.558982	+	0.558982i
$934$	42.9651			1.40586
$935$		0			0
$936$			7.56225i			0.247180i
$937$	14.8900	−	14.8900i	0.486434	−	0.486434i	−0.420745	−	0.907179i	$-0.638231\pi$
$937$	14.8900	−	14.8900i	0.486434	−	0.486434i	0.907179	+	0.420745i	$0.138231\pi$
$938$	−9.04492	−	11.6734i	−0.295327	−	0.381150i
$939$			0.846480i			0.0276238i
$940$		0			0
$941$		−	29.1725i		−	0.950997i	−0.879716	−	0.475499i	$-0.842268\pi$
$941$		−	29.1725i		−	0.950997i	0.879716	−	0.475499i	$-0.157732\pi$
$942$	8.40777	+	8.40777i	0.273940	+	0.273940i
$943$	20.6401	+	20.6401i	0.672134	+	0.672134i
$944$	−56.1874			−1.82874
$945$		0			0
$946$	−50.8361			−1.65282
$947$	−6.00345	−	6.00345i	−0.195086	−	0.195086i	0.602804	−	0.797890i	$-0.294050\pi$
$947$	−6.00345	−	6.00345i	−0.195086	−	0.195086i	−0.797890	+	0.602804i	$0.794050\pi$
$948$	−1.78309	−	1.78309i	−0.0579122	−	0.0579122i
$949$			26.4989i			0.860189i
$950$		0			0
$951$		−	19.1484i		−	0.620928i
$952$	−17.1098	−	22.0820i	−0.554532	−	0.715682i
$953$	11.4936	−	11.4936i	0.372315	−	0.372315i	−0.496005	−	0.868320i	$-0.665200\pi$
$953$	11.4936	−	11.4936i	0.372315	−	0.372315i	0.868320	+	0.496005i	$0.165200\pi$
$954$		−	10.9018i		−	0.352959i
$955$		0			0
$956$	−4.19181			−0.135573
$957$	−0.917385	+	0.917385i	−0.0296548	+	0.0296548i
$958$	−5.15157	−	5.15157i	−0.166440	−	0.166440i
$959$	−14.6885	−	1.86350i	−0.474317	−	0.0601757i
$960$		0			0
$961$	−77.6648			−2.50532
$962$	−8.41421	+	8.41421i	−0.271285	+	0.271285i
$963$	−10.8573	+	10.8573i	−0.349870	+	0.349870i
$964$	−10.6223			−0.342121
$965$		0			0
$966$	−17.4006	−	2.20759i	−0.559857	−	0.0710280i
$967$	31.4854	+	31.4854i	1.01250	+	1.01250i	0.999921	+	0.0125799i	$0.00400440\pi$
$967$	31.4854	+	31.4854i	1.01250	+	1.01250i	0.0125799	+	0.999921i	$0.495996\pi$
$968$	−27.2245	+	27.2245i	−0.875028	+	0.875028i
$969$	−18.1845			−0.584172
$970$		0			0
$971$			47.9272i			1.53806i	0.639214	+	0.769029i	$0.279260\pi$
$971$			47.9272i			1.53806i	−0.639214	+	0.769029i	$0.720740\pi$
$972$	0.336600	−	0.336600i	0.0107964	−	0.0107964i
$973$	24.8677	−	19.2683i	0.797222	−	0.617712i
$974$		−	17.4811i		−	0.560130i
$975$		0			0
$976$			10.2262i			0.327332i
$977$	20.9607	+	20.9607i	0.670592	+	0.670592i	0.957853	−	0.287260i	$-0.0927444\pi$
$977$	20.9607	+	20.9607i	0.670592	+	0.670592i	−0.287260	+	0.957853i	$0.592744\pi$
$978$	23.9383	+	23.9383i	0.765462	+	0.765462i
$979$	−32.7389			−1.04634
$980$		0			0
$981$	−15.9018			−0.507705
$982$	6.10760	+	6.10760i	0.194901	+	0.194901i
$983$	−34.9452	−	34.9452i	−1.11458	−	1.11458i	−0.992523	−	0.122055i	$-0.961051\pi$
$983$	−34.9452	−	34.9452i	−1.11458	−	1.11458i	−0.122055	−	0.992523i	$-0.538949\pi$
$984$		−	16.6141i		−	0.529637i
$985$		0			0
$986$			1.72807i			0.0550329i
$987$	9.20838	−	7.13493i	0.293106	−	0.227107i
$988$	4.38398	−	4.38398i	0.139473	−	0.139473i
$989$		−	26.1682i		−	0.832102i
$990$		0			0
$991$	−28.6620			−0.910479			−0.455240	−	0.890369i	$-0.650446\pi$
$991$	−28.6620			−0.910479			−0.455240	+	0.890369i	$0.650446\pi$
$992$	−19.4567	+	19.4567i	−0.617750	+	0.617750i
$993$	15.8465	+	15.8465i	0.502873	+	0.502873i
$994$	3.29799	+	0.418410i	0.104606	+	0.0132711i
$995$		0			0
$996$	3.09361			0.0980247
$997$	−14.6983	+	14.6983i	−0.465501	+	0.465501i	−0.900453	−	0.434953i	$-0.856765\pi$
$997$	−14.6983	+	14.6983i	−0.465501	+	0.465501i	0.434953	+	0.900453i	$0.356765\pi$
$998$	−17.3091	+	17.3091i	−0.547908	+	0.547908i
$999$	−2.39804			−0.0758705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.m.c.307.4	yes	24
5.2	odd	4	inner	525.2.m.c.118.10	yes	24
5.3	odd	4	inner	525.2.m.c.118.3	✓	24
5.4	even	2	inner	525.2.m.c.307.9	yes	24
7.6	odd	2	inner	525.2.m.c.307.3	yes	24
35.13	even	4	inner	525.2.m.c.118.4	yes	24
35.27	even	4	inner	525.2.m.c.118.9	yes	24
35.34	odd	2	inner	525.2.m.c.307.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.m.c.118.3	✓	24	5.3	odd	4	inner
525.2.m.c.118.4	yes	24	35.13	even	4	inner
525.2.m.c.118.9	yes	24	35.27	even	4	inner
525.2.m.c.118.10	yes	24	5.2	odd	4	inner
525.2.m.c.307.3	yes	24	7.6	odd	2	inner
525.2.m.c.307.4	yes	24	1.1	even	1	trivial
525.2.m.c.307.9	yes	24	5.4	even	2	inner
525.2.m.c.307.10	yes	24	35.34	odd	2	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11266 - 1.11266i) q^{2} +(0.707107 + 0.707107i) q^{3} +0.476024i q^{4} -1.57354i q^{6} +(2.09141 - 1.62049i) q^{7} +(-1.69567 + 1.69567i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.11266 - 1.11266i) q^{2} +(0.707107 + 0.707107i) q^{3} +0.476024i q^{4} -1.57354i q^{6} +(2.09141 - 1.62049i) q^{7} +(-1.69567 + 1.69567i) q^{8} +1.00000i q^{9} +5.20147 q^{11} +(-0.336600 + 0.336600i) q^{12} +(-2.22988 - 2.22988i) q^{13} +(-4.13009 - 0.523976i) q^{14} +4.72545 q^{16} +(-3.11335 + 3.11335i) q^{17} +(1.11266 - 1.11266i) q^{18} +4.13009 q^{19} +(2.62471 + 0.332992i) q^{21} +(-5.78747 - 5.78747i) q^{22} +(2.97914 - 2.97914i) q^{23} -2.39804 q^{24} +4.96218i q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.771392 + 0.995562i) q^{28} +0.249425i q^{29} -10.4242i q^{31} +(-1.86648 - 1.86648i) q^{32} +(3.67800 + 3.67800i) q^{33} +6.92820 q^{34} -0.476024 q^{36} +(1.69567 + 1.69567i) q^{37} +(-4.59538 - 4.59538i) q^{38} -3.15352i q^{39} +6.92820i q^{41} +(-2.54990 - 3.29092i) q^{42} +(4.39191 - 4.39191i) q^{43} +2.47602i q^{44} -6.62954 q^{46} +(3.11335 - 3.11335i) q^{47} +(3.34140 + 3.34140i) q^{48} +(1.74802 - 6.77823i) q^{49} -4.40294 q^{51} +(1.06147 - 1.06147i) q^{52} +(4.89898 - 4.89898i) q^{53} +1.57354 q^{54} +(-0.798528 + 6.29415i) q^{56} +(2.92041 + 2.92041i) q^{57} +(0.277525 - 0.277525i) q^{58} -11.8904 q^{59} +2.16407i q^{61} +(-11.5986 + 11.5986i) q^{62} +(1.62049 + 2.09141i) q^{63} -5.29738i q^{64} -8.18472i q^{66} +(2.50822 + 2.50822i) q^{67} +(-1.48203 - 1.48203i) q^{68} +4.21314 q^{69} -0.798528 q^{71} +(-1.69567 - 1.69567i) q^{72} +(-5.94178 - 5.94178i) q^{73} -3.77340i q^{74} +1.96602i q^{76} +(10.8784 - 8.42894i) q^{77} +(-3.50879 + 3.50879i) q^{78} +5.29738i q^{79} -1.00000 q^{81} +(7.70873 - 7.70873i) q^{82} +(-4.59538 - 4.59538i) q^{83} +(-0.158512 + 1.24943i) q^{84} -9.77340 q^{86} +(-0.176370 + 0.176370i) q^{87} +(-8.81997 + 8.81997i) q^{88} -6.29415 q^{89} +(-8.27708 - 1.05010i) q^{91} +(1.41814 + 1.41814i) q^{92} +(7.37105 - 7.37105i) q^{93} -6.92820 q^{94} -2.63960i q^{96} +(-12.1972 + 12.1972i) q^{97} +(-9.48682 + 5.59692i) q^{98} +5.20147i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 48 q^{11} + 24 q^{16} + 12 q^{21} - 24 q^{36} - 120 q^{46} + 48 q^{51} - 96 q^{56} - 96 q^{71} - 24 q^{81} - 120 q^{86} + 108 q^{91}+O(q^{100}) \) 24 * q + 48 * q^11 + 24 * q^16 + 12 * q^21 - 24 * q^36 - 120 * q^46 + 48 * q^51 - 96 * q^56 - 96 * q^71 - 24 * q^81 - 120 * q^86 + 108 * q^91

Introduction

L-functions

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