LMFDB - Embedded newform 525.2.bc.d.418.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, 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:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			418.4
Character	$\chi$	$=$	525.418
Dual form			525.2.bc.d.157.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.159531 + 0.595377i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(1.40303 - 0.810038i) q^{4} -0.616380i q^{6} +(-1.43432 - 2.22322i) q^{7} +(1.57780 + 1.57780i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.159531 + 0.595377i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(1.40303 - 0.810038i) q^{4} -0.616380i q^{6} +(-1.43432 - 2.22322i) q^{7} +(1.57780 + 1.57780i) q^{8} +(0.866025 + 0.500000i) q^{9} +(2.27624 + 3.94256i) q^{11} +(-1.56487 + 0.419306i) q^{12} +(-0.0478013 + 0.0478013i) q^{13} +(1.09484 - 1.20864i) q^{14} +(0.932399 - 1.61496i) q^{16} +(1.07994 - 4.03037i) q^{17} +(-0.159531 + 0.595377i) q^{18} +(3.38472 - 5.86251i) q^{19} +(0.810038 + 2.51870i) q^{21} +(-1.98418 + 1.98418i) q^{22} +(3.94144 - 1.05611i) q^{23} +(-1.11567 - 1.93240i) q^{24} +(-0.0360856 - 0.0208340i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-3.81329 - 1.95738i) q^{28} -6.68768i q^{29} +(-2.56760 + 1.48241i) q^{31} +(5.42088 + 1.45252i) q^{32} +(-1.17827 - 4.39735i) q^{33} +2.57188 q^{34} +1.62008 q^{36} +(1.91159 + 7.13416i) q^{37} +(4.03037 + 1.07994i) q^{38} +(0.0585444 - 0.0338006i) q^{39} +0.956914i q^{41} +(-1.37035 + 0.884088i) q^{42} +(-3.47918 - 3.47918i) q^{43} +(6.38724 + 3.68768i) q^{44} +(1.25756 + 2.17816i) q^{46} +(8.79471 - 2.35653i) q^{47} +(-1.31861 + 1.31861i) q^{48} +(-2.88543 + 6.37764i) q^{49} +(-2.08628 + 3.61353i) q^{51} +(-0.0283456 + 0.105787i) q^{52} +(-3.24567 + 12.1130i) q^{53} +(0.308190 - 0.533801i) q^{54} +(1.24472 - 5.77086i) q^{56} +(-4.78672 + 4.78672i) q^{57} +(3.98169 - 1.06689i) q^{58} +(-1.09484 - 1.89631i) q^{59} +(0.569886 + 0.329024i) q^{61} +(-1.29220 - 1.29220i) q^{62} +(-0.130550 - 2.64253i) q^{63} -0.270405i q^{64} +(2.43011 - 1.40303i) q^{66} +(-10.1513 - 2.72003i) q^{67} +(-1.74958 - 6.52951i) q^{68} -4.08048 q^{69} +3.58273 q^{71} +(0.577514 + 2.15531i) q^{72} +(7.42573 + 1.98972i) q^{73} +(-3.94256 + 2.27624i) q^{74} -10.9670i q^{76} +(5.50032 - 10.7155i) q^{77} +(0.0294638 + 0.0294638i) q^{78} +(-4.84093 - 2.79491i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.569725 + 0.152657i) q^{82} +(-7.19308 + 7.19308i) q^{83} +(3.17675 + 2.87764i) q^{84} +(1.51639 - 2.62646i) q^{86} +(-1.73090 + 6.45980i) q^{87} +(-2.62912 + 9.81200i) q^{88} +(-7.86428 + 13.6213i) q^{89} +(0.174835 + 0.0377104i) q^{91} +(4.67446 - 4.67446i) q^{92} +(2.86379 - 0.767349i) q^{93} +(2.80605 + 4.86023i) q^{94} +(-4.86023 - 2.80605i) q^{96} +(4.60689 + 4.60689i) q^{97} +(-4.25742 - 0.700490i) q^{98} +4.55247i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 24 q^{11} + 48 q^{16} - 24 q^{21} - 144 q^{26} - 36 q^{31} - 48 q^{36} + 48 q^{46} + 24 q^{51} + 168 q^{56} + 144 q^{61} - 72 q^{66} + 96 q^{71} + 12 q^{81} - 168 q^{86} + 12 q^{91} + 144 q^{96}+O(q^{100}) $ 24 * q + 24 * q^11 + 48 * q^16 - 24 * q^21 - 144 * q^26 - 36 * q^31 - 48 * q^36 + 48 * q^46 + 24 * q^51 + 168 * q^56 + 144 * q^61 - 72 * q^66 + 96 * q^71 + 12 * q^81 - 168 * q^86 + 12 * q^91 + 144 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.159531	+	0.595377i	0.112805	+	0.420995i	0.999113	−	0.0421009i	$-0.0134051\pi$
$2$	0.159531	+	0.595377i	0.112805	+	0.420995i	−0.886308	+	0.463096i	$0.846738\pi$
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	1.40303	−	0.810038i	0.701513	−	0.405019i
$5$		0			0
$5$		0			0
$6$		−	0.616380i		−	0.251636i
$7$	−1.43432	−	2.22322i	−0.542123	−	0.840299i
$7$	−1.43432	−	2.22322i	−0.542123	−	0.840299i
$8$	1.57780	+	1.57780i	0.557835	+	0.557835i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	2.27624	+	3.94256i	0.686311	+	1.18873i	0.973023	+	0.230709i	$0.0741046\pi$
$11$	2.27624	+	3.94256i	0.686311	+	1.18873i	−0.286711	+	0.958017i	$0.592562\pi$
$12$	−1.56487	+	0.419306i	−0.451740	+	0.121043i
$13$	−0.0478013	+	0.0478013i	−0.0132577	+	0.0132577i	−0.713705	−	0.700447i	$-0.752984\pi$
$13$	−0.0478013	+	0.0478013i	−0.0132577	+	0.0132577i	0.700447	+	0.713705i	$0.252984\pi$
$14$	1.09484	−	1.20864i	0.292607	−	0.323022i
$15$		0			0
$16$	0.932399	−	1.61496i	0.233100	−	0.403741i
$17$	1.07994	−	4.03037i	0.261923	−	0.977509i	−0.702184	−	0.711995i	$-0.747792\pi$
$17$	1.07994	−	4.03037i	0.261923	−	0.977509i	0.964107	−	0.265514i	$-0.0855416\pi$
$18$	−0.159531	+	0.595377i	−0.0376018	+	0.140332i
$19$	3.38472	−	5.86251i	0.776509	−	1.34495i	−0.157434	−	0.987530i	$-0.550322\pi$
$19$	3.38472	−	5.86251i	0.776509	−	1.34495i	0.933943	−	0.357423i	$-0.116345\pi$
$20$		0			0
$21$	0.810038	+	2.51870i	0.176765	+	0.549625i
$22$	−1.98418	+	1.98418i	−0.423029	+	0.423029i
$23$	3.94144	−	1.05611i	0.821848	−	0.220213i	0.176694	−	0.984266i	$-0.443460\pi$
$23$	3.94144	−	1.05611i	0.821848	−	0.220213i	0.645154	+	0.764053i	$0.276793\pi$
$24$	−1.11567	−	1.93240i	−0.227735	−	0.394449i
$25$		0			0
$26$	−0.0360856	−	0.0208340i	−0.00707697	−	0.00408589i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−3.81329	−	1.95738i	−0.720644	−	0.369911i
$29$		−	6.68768i		−	1.24187i	−0.783862	−	0.620935i	$-0.786753\pi$
$29$		−	6.68768i		−	1.24187i	0.783862	−	0.620935i	$-0.213247\pi$
$30$		0			0
$31$	−2.56760	+	1.48241i	−0.461155	+	0.266248i	−0.712530	−	0.701642i	$-0.752451\pi$
$31$	−2.56760	+	1.48241i	−0.461155	+	0.266248i	0.251375	+	0.967890i	$0.419117\pi$
$32$	5.42088	+	1.45252i	0.958285	+	0.256772i
$33$	−1.17827	−	4.39735i	−0.205110	−	0.765481i
$34$	2.57188			0.441073
$35$		0			0
$36$	1.62008			0.270013
$37$	1.91159	+	7.13416i	0.314264	+	1.17285i	0.924673	+	0.380762i	$0.124338\pi$
$37$	1.91159	+	7.13416i	0.314264	+	1.17285i	−0.610409	+	0.792086i	$0.708995\pi$
$38$	4.03037	+	1.07994i	0.653813	+	0.175189i
$39$	0.0585444	−	0.0338006i	0.00937461	−	0.00541243i
$40$		0			0
$41$			0.956914i			0.149445i	0.997204	+	0.0747224i	$0.0238071\pi$
$41$			0.956914i			0.149445i	−0.997204	+	0.0747224i	$0.976193\pi$
$42$	−1.37035	+	0.884088i	−0.211449	+	0.136418i
$43$	−3.47918	−	3.47918i	−0.530570	−	0.530570i	0.390172	−	0.920742i	$-0.372416\pi$
$43$	−3.47918	−	3.47918i	−0.530570	−	0.530570i	−0.920742	+	0.390172i	$0.872416\pi$
$44$	6.38724	+	3.68768i	0.962913	+	0.555938i
$45$		0			0
$46$	1.25756	+	2.17816i	0.185418	+	0.321153i
$47$	8.79471	−	2.35653i	1.28284	−	0.343736i	0.447903	−	0.894082i	$-0.352171\pi$
$47$	8.79471	−	2.35653i	1.28284	−	0.343736i	0.834937	+	0.550346i	$0.185504\pi$
$48$	−1.31861	+	1.31861i	−0.190325	+	0.190325i
$49$	−2.88543	+	6.37764i	−0.412205	+	0.911091i
$50$		0			0
$51$	−2.08628	+	3.61353i	−0.292137	+	0.505996i
$52$	−0.0283456	+	0.105787i	−0.00393083	+	0.0146701i
$53$	−3.24567	+	12.1130i	−0.445827	+	1.66385i	0.267916	+	0.963442i	$0.413665\pi$
$53$	−3.24567	+	12.1130i	−0.445827	+	1.66385i	−0.713743	+	0.700408i	$0.753002\pi$
$54$	0.308190	−	0.533801i	0.0419393	−	0.0726411i
$55$		0			0
$56$	1.24472	−	5.77086i	0.166333	−	0.771164i
$57$	−4.78672	+	4.78672i	−0.634017	+	0.634017i
$58$	3.98169	−	1.06689i	0.522822	−	0.140090i
$59$	−1.09484	−	1.89631i	−0.142536	−	0.246879i	0.785915	−	0.618334i	$-0.212192\pi$
$59$	−1.09484	−	1.89631i	−0.142536	−	0.246879i	−0.928451	+	0.371455i	$0.878859\pi$
$60$		0			0
$61$	0.569886	+	0.329024i	0.0729665	+	0.0421272i	0.536039	−	0.844193i	$-0.319920\pi$
$61$	0.569886	+	0.329024i	0.0729665	+	0.0421272i	−0.463073	+	0.886320i	$0.653253\pi$
$62$	−1.29220	−	1.29220i	−0.164110	−	0.164110i
$63$	−0.130550	−	2.64253i	−0.0164477	−	0.332927i
$64$		−	0.270405i		−	0.0338006i
$65$		0			0
$66$	2.43011	−	1.40303i	0.299126	−	0.172701i
$67$	−10.1513	−	2.72003i	−1.24018	−	0.332305i	−0.421643	−	0.906762i	$-0.638547\pi$
$67$	−10.1513	−	2.72003i	−1.24018	−	0.332305i	−0.818535	+	0.574457i	$0.805213\pi$
$68$	−1.74958	−	6.52951i	−0.212167	−	0.791820i
$69$	−4.08048			−0.491232
$70$		0			0
$71$	3.58273			0.425192			0.212596	−	0.977140i	$-0.431808\pi$
$71$	3.58273			0.425192			0.212596	+	0.977140i	$0.431808\pi$
$72$	0.577514	+	2.15531i	0.0680607	+	0.254006i
$73$	7.42573	+	1.98972i	0.869115	+	0.232879i	0.665705	−	0.746215i	$-0.268131\pi$
$73$	7.42573	+	1.98972i	0.869115	+	0.232879i	0.203410	+	0.979094i	$0.434797\pi$
$74$	−3.94256	+	2.27624i	−0.458313	+	0.264607i
$75$		0			0
$76$		−	10.9670i		−	1.25800i
$77$	5.50032	−	10.7155i	0.626820	−	1.22114i
$78$	0.0294638	+	0.0294638i	0.00333611	+	0.00333611i
$79$	−4.84093	−	2.79491i	−0.544647	−	0.314452i	0.202313	−	0.979321i	$-0.435154\pi$
$79$	−4.84093	−	2.79491i	−0.544647	−	0.314452i	−0.746960	+	0.664869i	$0.768487\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.569725	+	0.152657i	−0.0629156	+	0.0168582i
$83$	−7.19308	+	7.19308i	−0.789543	+	0.789543i	−0.981419	−	0.191876i	$-0.938543\pi$
$83$	−7.19308	+	7.19308i	−0.789543	+	0.789543i	0.191876	+	0.981419i	$0.438543\pi$
$84$	3.17675	+	2.87764i	0.346611	+	0.313976i
$85$		0			0
$86$	1.51639	−	2.62646i	0.163516	−	0.283219i
$87$	−1.73090	+	6.45980i	−0.185572	+	0.692563i
$88$	−2.62912	+	9.81200i	−0.280265	+	1.04596i
$89$	−7.86428	+	13.6213i	−0.833612	+	1.44386i	0.0615429	+	0.998104i	$0.480398\pi$
$89$	−7.86428	+	13.6213i	−0.833612	+	1.44386i	−0.895155	+	0.445755i	$0.852935\pi$
$90$		0			0
$91$	0.174835	+	0.0377104i	0.0183277	+	0.00395312i
$92$	4.67446	−	4.67446i	0.487346	−	0.487346i
$93$	2.86379	−	0.767349i	0.296961	−	0.0795704i
$94$	2.80605	+	4.86023i	0.289422	+	0.501294i
$95$		0			0
$96$	−4.86023	−	2.80605i	−0.496045	−	0.286392i
$97$	4.60689	+	4.60689i	0.467759	+	0.467759i	0.901188	−	0.433429i	$-0.142696\pi$
$97$	4.60689	+	4.60689i	0.467759	+	0.467759i	−0.433429	+	0.901188i	$0.642696\pi$
$98$	−4.25742	−	0.700490i	−0.430064	−	0.0707602i
$99$			4.55247i			0.457541i
$100$		0			0
$101$	−16.8241	+	9.71342i	−1.67406	+	0.966522i	−0.708740	+	0.705470i	$0.750736\pi$
$101$	−16.8241	+	9.71342i	−1.67406	+	0.966522i	−0.965325	+	0.261052i	$0.915931\pi$
$102$	−2.48424	−	0.665651i	−0.245977	−	0.0659092i
$103$	−4.38124	−	16.3510i	−0.431697	−	1.61111i	−0.748850	−	0.662740i	$-0.769393\pi$
$103$	−4.38124	−	16.3510i	−0.431697	−	1.61111i	0.317153	−	0.948374i	$-0.397273\pi$
$104$	−0.150841			−0.0147912
$105$		0			0
$106$	−7.72960			−0.750765
$107$	0.159531	+	0.595377i	0.0154224	+	0.0575573i	0.973208	−	0.229926i	$-0.0738483\pi$
$107$	0.159531	+	0.595377i	0.0154224	+	0.0575573i	−0.957786	+	0.287483i	$0.907182\pi$
$108$	−1.56487	−	0.419306i	−0.150580	−	0.0403478i
$109$	−1.49392	+	0.862513i	−0.143091	+	0.0826137i	−0.569836	−	0.821758i	$-0.692993\pi$
$109$	−1.49392	+	0.862513i	−0.143091	+	0.0826137i	0.426745	+	0.904372i	$0.359660\pi$
$110$		0			0
$111$		−	7.38583i		−	0.701032i
$112$	−4.92778	+	0.243449i	−0.465631	+	0.0230037i
$113$	9.57344	+	9.57344i	0.900594	+	0.900594i	0.995487	−	0.0948937i	$-0.0302511\pi$
$113$	9.57344	+	9.57344i	0.900594	+	0.900594i	−0.0948937	+	0.995487i	$0.530251\pi$
$114$	−3.61353	−	2.08628i	−0.338439	−	0.195398i
$115$		0			0
$116$	−5.41727	−	9.38299i	−0.502981	−	0.871189i
$117$	−0.0652978	+	0.0174965i	−0.00603678	+	0.00161755i
$118$	0.954361	−	0.954361i	0.0878561	−	0.0878561i
$119$	−10.5094	+	3.37992i	−0.963395	+	0.309837i
$120$		0			0
$121$	−4.86251	+	8.42212i	−0.442047	+	0.765647i
$122$	−0.104979	+	0.391787i	−0.00950435	+	0.0354707i
$123$	0.247668	−	0.924308i	0.0223314	−	0.0833420i
$124$	−2.40161	+	4.15971i	−0.215671	+	0.373553i
$125$		0			0
$126$	1.55247	−	0.499291i	0.138305	−	0.0444804i
$127$	−3.23839	+	3.23839i	−0.287360	+	0.287360i	−0.836036	−	0.548675i	$-0.815132\pi$
$127$	−3.23839	+	3.23839i	−0.287360	+	0.287360i	0.548675	+	0.836036i	$0.315132\pi$
$128$	11.0028	−	2.94818i	0.972515	−	0.260585i
$129$	2.46015	+	4.26111i	0.216604	+	0.375170i
$130$		0			0
$131$	3.79263	+	2.18967i	0.331363	+	0.191313i	0.656446	−	0.754373i	$-0.272059\pi$
$131$	3.79263	+	2.18967i	0.331363	+	0.191313i	−0.325083	+	0.945686i	$0.605392\pi$
$132$	−5.21516	−	5.21516i	−0.453922	−	0.453922i
$133$	−17.8885	+	0.883749i	−1.55113	+	0.0766307i
$134$		−	6.47778i		−	0.559595i
$135$		0			0
$136$	8.06303	−	4.65519i	0.691399	−	0.399180i
$137$	−9.13612	−	2.44802i	−0.780552	−	0.209148i	−0.153524	−	0.988145i	$-0.549062\pi$
$137$	−9.13612	−	2.44802i	−0.780552	−	0.209148i	−0.627028	+	0.778997i	$0.715729\pi$
$138$	−0.650963	−	2.42943i	−0.0554136	−	0.206806i
$139$	−21.5411			−1.82709			−0.913546	−	0.406735i	$-0.866667\pi$
$139$	−21.5411			−1.82709			−0.913546	+	0.406735i	$0.866667\pi$
$140$		0			0
$141$	−9.10495			−0.766775
$142$	0.571556	+	2.13307i	0.0479639	+	0.179004i
$143$	−0.297267	−	0.0796523i	−0.0248587	−	0.00666086i
$144$	1.61496	−	0.932399i	0.134580	−	0.0776999i
$145$		0			0
$146$			4.73853i			0.392163i
$147$	4.43777	−	5.41352i	0.366021	−	0.446500i
$148$	8.46096	+	8.46096i	0.695486	+	0.695486i
$149$	4.53810	+	2.62008i	0.371776	+	0.214645i	0.674234	−	0.738518i	$-0.264474\pi$
$149$	4.53810	+	2.62008i	0.371776	+	0.214645i	−0.302458	+	0.953163i	$0.597807\pi$
$150$		0			0
$151$	−0.325165	−	0.563202i	−0.0264615	−	0.0458327i	0.852491	−	0.522741i	$-0.175091\pi$
$151$	−0.325165	−	0.563202i	−0.0264615	−	0.0458327i	−0.878953	+	0.476909i	$0.841757\pi$
$152$	14.5903	−	3.90945i	1.18343	−	0.317098i
$153$	2.95044	−	2.95044i	0.238529	−	0.238529i
$154$	7.25723	+	1.56532i	0.584804	+	0.126137i
$155$		0			0
$156$	0.0547596	−	0.0948464i	0.00438427	−	0.00759379i
$157$	0.428319	−	1.59851i	0.0341836	−	0.127575i	−0.946726	−	0.322042i	$-0.895631\pi$
$157$	0.428319	−	1.59851i	0.0341836	−	0.127575i	0.980909	+	0.194467i	$0.0622976\pi$
$158$	0.891749	−	3.32805i	0.0709438	−	0.264766i
$159$	6.27016	−	10.8602i	0.497256	−	0.861272i
$160$		0			0
$161$	−8.00126	−	7.24790i	−0.630588	−	0.571215i
$162$	−0.435846	+	0.435846i	−0.0342433	+	0.0342433i
$163$	22.8091	−	6.11167i	1.78654	−	0.478703i	0.794793	−	0.606881i	$-0.207579\pi$
$163$	22.8091	−	6.11167i	1.78654	−	0.478703i	0.991751	+	0.128178i	$0.0409128\pi$
$164$	0.775137	+	1.34258i	0.0605280	+	0.104838i
$165$		0			0
$166$	−5.43011	−	3.13508i	−0.421459	−	0.243329i
$167$	−2.95044	−	2.95044i	−0.228312	−	0.228312i	0.583675	−	0.811987i	$-0.301614\pi$
$167$	−2.95044	−	2.95044i	−0.228312	−	0.228312i	−0.811987	+	0.583675i	$0.801614\pi$
$168$	−2.69592	+	5.25207i	−0.207995	+	0.405206i
$169$			12.9954i			0.999648i
$170$		0			0
$171$	5.86251	−	3.38472i	0.448318	−	0.258836i
$172$	−7.69966	−	2.06312i	−0.587093	−	0.157311i
$173$	−2.65818	−	9.92045i	−0.202097	−	0.754238i	−0.990315	−	0.138841i	$-0.955662\pi$
$173$	−2.65818	−	9.92045i	−0.202097	−	0.754238i	0.788217	−	0.615397i	$-0.211004\pi$
$174$	−4.12215			−0.312499
$175$		0			0
$176$	8.48944			0.639916
$177$	0.566729	+	2.11506i	0.0425980	+	0.158978i
$178$	−9.36443	−	2.50919i	−0.701894	−	0.188072i
$179$	−1.49787	+	0.864798i	−0.111956	+	0.0646380i	−0.554933	−	0.831895i	$-0.687256\pi$
$179$	−1.49787	+	0.864798i	−0.111956	+	0.0646380i	0.442976	+	0.896533i	$0.353923\pi$
$180$		0			0
$181$			6.53527i			0.485763i	0.970056	+	0.242881i	$0.0780926\pi$
$181$			6.53527i			0.485763i	−0.970056	+	0.242881i	$0.921907\pi$
$182$	0.00543975	+	0.110109i	0.000403221	+	0.00816182i
$183$	−0.465310	−	0.465310i	−0.0343967	−	0.0343967i
$184$	7.88512	+	4.55247i	0.581299	+	0.335613i
$185$		0			0
$186$	0.913725	+	1.58262i	0.0669976	+	0.116043i
$187$	18.3482	−	4.91638i	1.34175	−	0.359521i
$188$	10.4303	−	10.4303i	0.760710	−	0.760710i
$189$	−0.557835	+	2.58628i	−0.0405766	+	0.188124i
$190$		0			0
$191$	7.17255	−	12.4232i	0.518988	−	0.898913i	−0.480769	−	0.876847i	$-0.659642\pi$
$191$	7.17255	−	12.4232i	0.518988	−	0.898913i	0.999757	−	0.0220655i	$-0.00702423\pi$
$192$	−0.0699860	+	0.261191i	−0.00505080	+	0.0188498i
$193$	1.65314	−	6.16960i	0.118996	−	0.444098i	−0.880559	−	0.473936i	$-0.842833\pi$
$193$	1.65314	−	6.16960i	0.118996	−	0.444098i	0.999555	+	0.0298386i	$0.00949932\pi$
$194$	−2.00790	+	3.47778i	−0.144159	+	0.249690i
$195$		0			0
$196$	1.11779	+	11.2853i	0.0798422	+	0.806093i
$197$	−9.36211	+	9.36211i	−0.667023	+	0.667023i	−0.957026	−	0.290003i	$-0.906344\pi$
$197$	−9.36211	+	9.36211i	−0.667023	+	0.667023i	0.290003	+	0.957026i	$0.406344\pi$
$198$	−2.71044	+	0.726260i	−0.192623	+	0.0516131i
$199$	−6.44042	−	11.1551i	−0.456549	−	0.790767i	0.542226	−	0.840232i	$-0.317582\pi$
$199$	−6.44042	−	11.1551i	−0.456549	−	0.790767i	−0.998776	+	0.0494656i	$0.984248\pi$
$200$		0			0
$201$	9.10140	+	5.25470i	0.641963	+	0.370638i
$202$	−8.46712	−	8.46712i	−0.595745	−	0.595745i
$203$	−14.8682	+	9.59229i	−1.04354	+	0.673247i
$204$			6.75985i			0.473284i
$205$		0			0
$206$	9.03609	−	5.21699i	0.629574	−	0.363485i
$207$	3.94144	+	1.05611i	0.273949	+	0.0734045i
$208$	0.0326274	+	0.121767i	0.00226230	+	0.00844303i
$209$	30.8177			2.13171
$210$		0			0
$211$	12.7250			0.876027			0.438013	−	0.898968i	$-0.355682\pi$
$211$	12.7250			0.876027			0.438013	+	0.898968i	$0.355682\pi$
$212$	5.25823	+	19.6240i	0.361137	+	1.34778i
$213$	−3.46065	−	0.927278i	−0.237120	−	0.0635361i
$214$	−0.329024	+	0.189962i	−0.0224916	+	0.0129855i
$215$		0			0
$216$		−	2.23134i		−	0.151824i
$217$	6.97849	+	3.58210i	0.473731	+	0.243169i
$218$	−0.751846	−	0.751846i	−0.0509214	−	0.0509214i
$219$	−6.65772	−	3.84384i	−0.449887	−	0.259743i
$220$		0			0
$221$	0.141035	+	0.244279i	0.00948703	+	0.0164320i
$222$	4.39735	−	1.17827i	0.295131	−	0.0790801i
$223$	−17.7519	+	17.7519i	−1.18875	+	1.18875i	−0.211342	+	0.977412i	$0.567783\pi$
$223$	−17.7519	+	17.7519i	−1.18875	+	1.18875i	−0.977412	+	0.211342i	$0.932217\pi$
$224$	−4.54602	−	14.1352i	−0.303744	−	0.944448i
$225$		0			0
$226$	−4.17255	+	7.22707i	−0.277554	+	0.480738i
$227$	−5.79300	+	21.6198i	−0.384495	+	1.43496i	0.454466	+	0.890764i	$0.349830\pi$
$227$	−5.79300	+	21.6198i	−0.384495	+	1.43496i	−0.838961	+	0.544191i	$0.816837\pi$
$228$	−2.83847	+	10.5933i	−0.187982	+	0.701560i
$229$	4.82942	−	8.36480i	0.319137	−	0.552761i	−0.661171	−	0.750235i	$-0.729940\pi$
$229$	4.82942	−	8.36480i	0.319137	−	0.552761i	0.980308	+	0.197474i	$0.0632737\pi$
$230$		0			0
$231$	−8.08628	+	8.92678i	−0.532038	+	0.587339i
$232$	10.5518	−	10.5518i	0.692759	−	0.692759i
$233$	15.7658	−	4.22443i	1.03285	−	0.276751i	0.297703	−	0.954659i	$-0.403780\pi$
$233$	15.7658	−	4.22443i	1.03285	−	0.276751i	0.735147	+	0.677907i	$0.237113\pi$
$234$	−0.0208340	−	0.0360856i	−0.00136196	−	0.00235899i
$235$		0			0
$236$	−3.07217	−	1.77372i	−0.199981	−	0.115459i
$237$	3.95260	+	3.95260i	0.256749	+	0.256749i
$238$	−3.68890	−	5.71785i	−0.239116	−	0.370633i
$239$		−	26.5550i		−	1.71770i	−0.512227	−	0.858850i	$-0.671179\pi$
$239$		−	26.5550i		−	1.71770i	0.512227	−	0.858850i	$-0.328821\pi$
$240$		0			0
$241$	7.15971	−	4.13366i	0.461197	−	0.266272i	−0.251350	−	0.967896i	$-0.580875\pi$
$241$	7.15971	−	4.13366i	0.461197	−	0.266272i	0.712548	+	0.701624i	$0.247541\pi$
$242$	−5.79006	−	1.55144i	−0.372199	−	0.0997304i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	1.06609			0.0682493
$245$		0			0
$246$	0.589823			0.0376057
$247$	0.118442	+	0.442030i	0.00753626	+	0.0281257i
$248$	−6.39009	−	1.71222i	−0.405771	−	0.108726i
$249$	8.80969	−	5.08628i	0.558291	−	0.322330i
$250$		0			0
$251$			26.3550i			1.66352i	0.555138	+	0.831758i	$0.312665\pi$
$251$			26.3550i			1.66352i	−0.555138	+	0.831758i	$0.687335\pi$
$252$	−2.32371	−	3.60179i	−0.146380	−	0.226891i
$253$	13.1354	+	13.1354i	0.825817	+	0.825817i
$254$	−2.44469	−	1.41144i	−0.153393	−	0.0885616i
$255$		0			0
$256$	3.24015	+	5.61211i	0.202509	+	0.350757i
$257$	−22.3537	+	5.98967i	−1.39439	+	0.373625i	−0.876326	−	0.481718i	$-0.840013\pi$
$257$	−22.3537	+	5.98967i	−1.39439	+	0.373625i	−0.518062	+	0.855343i	$0.673346\pi$
$258$	−2.14450	+	2.14450i	−0.133511	+	0.133511i
$259$	13.1190	−	14.4826i	0.815174	−	0.899904i
$260$		0			0
$261$	3.34384	−	5.79170i	0.206978	−	0.358497i
$262$	−0.698641	+	2.60736i	−0.0431622	+	0.161083i
$263$	−5.29727	+	19.7697i	−0.326644	+	1.21905i	0.586005	+	0.810307i	$0.300700\pi$
$263$	−5.29727	+	19.7697i	−0.326644	+	1.21905i	−0.912649	+	0.408744i	$0.865967\pi$
$264$	5.07906	−	8.79720i	0.312595	−	0.541430i
$265$		0			0
$266$	−3.37992	−	10.5094i	−0.207236	−	0.644372i
$267$	11.1218	−	11.1218i	0.680642	−	0.680642i
$268$	−16.4459	+	4.40666i	−1.00459	+	0.269179i
$269$	11.6898	+	20.2472i	0.712737	+	1.23450i	0.963826	+	0.266532i	$0.0858779\pi$
$269$	11.6898	+	20.2472i	0.712737	+	1.23450i	−0.251089	+	0.967964i	$0.580789\pi$
$270$		0			0
$271$	5.63292	+	3.25217i	0.342175	+	0.197555i	0.661234	−	0.750180i	$-0.270033\pi$
$271$	5.63292	+	3.25217i	0.342175	+	0.197555i	−0.319058	+	0.947735i	$0.603367\pi$
$272$	−5.50197	−	5.50197i	−0.333606	−	0.333606i
$273$	−0.159118	−	0.0816762i	−0.00963025	−	0.00494327i
$274$		−	5.82997i		−	0.352202i
$275$		0			0
$276$	−5.72503	+	3.30534i	−0.344606	+	0.198958i
$277$	−14.0525	−	3.76535i	−0.844332	−	0.226238i	−0.189376	−	0.981905i	$-0.560646\pi$
$277$	−14.0525	−	3.76535i	−0.844332	−	0.226238i	−0.654957	+	0.755667i	$0.727313\pi$
$278$	−3.43647	−	12.8251i	−0.206106	−	0.769197i
$279$	−2.96481			−0.177499
$280$		0			0
$281$	7.37535			0.439977			0.219988	−	0.975502i	$-0.429398\pi$
$281$	7.37535			0.439977			0.219988	+	0.975502i	$0.429398\pi$
$282$	−1.45252	−	5.42088i	−0.0864963	−	0.322809i
$283$	18.4135	+	4.93388i	1.09457	+	0.293288i	0.760551	−	0.649279i	$-0.224929\pi$
$283$	18.4135	+	4.93388i	1.09457	+	0.293288i	0.334017	+	0.942567i	$0.391596\pi$
$284$	5.02666	−	2.90215i	0.298278	−	0.172211i
$285$		0			0
$286$		−	0.189693i		−	0.0112168i
$287$	2.12743	−	1.37252i	0.125578	−	0.0810176i
$288$	3.96836	+	3.96836i	0.233838	+	0.233838i
$289$	−0.355224	−	0.205089i	−0.0208955	−	0.0120640i
$290$		0			0
$291$	−3.25756	−	5.64227i	−0.190962	−	0.330755i
$292$	12.0302	−	3.22349i	0.704016	−	0.188641i
$293$	−5.21516	+	5.21516i	−0.304673	+	0.304673i	−0.842839	−	0.538166i	$-0.819117\pi$
$293$	−5.21516	+	5.21516i	−0.304673	+	0.304673i	0.538166	+	0.842839i	$0.319117\pi$
$294$	3.93105	+	1.77852i	0.229263	+	0.103726i
$295$		0			0
$296$	−8.24015	+	14.2724i	−0.478949	+	0.829564i
$297$	1.17827	−	4.39735i	0.0683700	−	0.255160i
$298$	−0.835966	+	3.11987i	−0.0484262	+	0.180729i
$299$	−0.137923	+	0.238889i	−0.00797628	+	0.0138153i
$300$		0			0
$301$	−2.74472	+	12.7253i	−0.158203	+	0.733472i
$302$	0.283444	−	0.283444i	0.0163103	−	0.0163103i
$303$	18.7649	−	5.02804i	1.07801	−	0.288853i
$304$	−6.31182	−	10.9324i	−0.362008	−	0.627016i
$305$		0			0
$306$	2.22731	+	1.28594i	0.127327	+	0.0735122i
$307$	13.7482	+	13.7482i	0.784654	+	0.784654i	0.980612	−	0.195958i	$-0.0627818\pi$
$307$	13.7482	+	13.7482i	0.784654	+	0.784654i	−0.195958	+	0.980612i	$0.562782\pi$
$308$	−0.962850	−	19.4896i	−0.0548634	−	1.11052i
$309$			16.9278i			0.962991i
$310$		0			0
$311$	1.62134	−	0.936080i	0.0919377	−	0.0530802i	−0.453326	−	0.891345i	$-0.649763\pi$
$311$	1.62134	−	0.936080i	0.0919377	−	0.0530802i	0.545264	+	0.838264i	$0.316429\pi$
$312$	0.145702	+	0.0390407i	0.00824873	+	0.00221024i
$313$	−2.79334	−	10.4249i	−0.157889	−	0.589249i	−0.998841	−	0.0481390i	$-0.984671\pi$
$313$	−2.79334	−	10.4249i	−0.157889	−	0.589249i	0.840952	−	0.541110i	$-0.181996\pi$
$314$	1.02005			0.0575646
$315$		0			0
$316$	−9.05594			−0.509436
$317$	−4.49962	−	16.7928i	−0.252724	−	0.943178i	−0.969343	−	0.245713i	$-0.920978\pi$
$317$	−4.49962	−	16.7928i	−0.252724	−	0.943178i	0.716619	−	0.697465i	$-0.245689\pi$
$318$	7.46622	+	2.00057i	0.418685	+	0.112186i
$319$	26.3666	−	15.2227i	1.47624	−	0.852310i
$320$		0			0
$321$		−	0.616380i		−	0.0344030i
$322$	3.03879	−	5.92003i	0.169345	−	0.329911i
$323$	−19.9728	−	19.9728i	−1.11132	−	1.11132i
$324$	1.40303	+	0.810038i	0.0779459	+	0.0450021i
$325$		0			0
$326$	7.27750	+	12.6050i	0.403063	+	0.698126i
$327$	1.66625	−	0.446469i	0.0921436	−	0.0246898i
$328$	−1.50982	+	1.50982i	−0.0833657	+	0.0833657i
$329$	−17.8536	−	16.1726i	−0.984298	−	0.891622i
$330$		0			0
$331$	10.7402	−	18.6025i	0.590332	−	1.02249i	−0.403855	−	0.914823i	$-0.632330\pi$
$331$	10.7402	−	18.6025i	0.590332	−	1.02249i	0.994188	−	0.107662i	$-0.0343366\pi$
$332$	−4.26542	+	15.9188i	−0.234095	+	0.873655i
$333$	−1.91159	+	7.13416i	−0.104755	+	0.390950i
$334$	1.28594	−	2.22731i	0.0703634	−	0.121873i
$335$		0			0
$336$	4.82288	+	1.04025i	0.263110	+	0.0567503i
$337$	−8.13737	+	8.13737i	−0.443271	+	0.443271i	−0.893110	−	0.449839i	$-0.851481\pi$
$337$	−8.13737	+	8.13737i	−0.443271	+	0.443271i	0.449839	+	0.893110i	$0.351481\pi$
$338$	−7.73718	+	2.07317i	−0.420847	+	0.112766i
$339$	−6.76945	−	11.7250i	−0.367666	−	0.636816i
$340$		0			0
$341$	−11.6889	−	6.74861i	−0.632992	−	0.365458i
$342$	2.95044	+	2.95044i	0.159541	+	0.159541i
$343$	18.3176	−	2.73264i	0.989055	−	0.147549i
$344$		−	10.9789i		−	0.591942i
$345$		0			0
$346$	5.48235	−	3.16524i	0.294733	−	0.170164i
$347$	−15.2329	−	4.08164i	−0.817744	−	0.219114i	−0.174384	−	0.984678i	$-0.555793\pi$
$347$	−15.2329	−	4.08164i	−0.817744	−	0.219114i	−0.643360	+	0.765564i	$0.722460\pi$
$348$	2.80419	+	10.4654i	0.150320	+	0.561003i
$349$	5.69544			0.304870			0.152435	−	0.988313i	$-0.451289\pi$
$349$	5.69544			0.304870			0.152435	+	0.988313i	$0.451289\pi$
$350$		0			0
$351$	0.0676012			0.00360829
$352$	6.61256	+	24.6784i	0.352451	+	1.31536i
$353$	−9.62318	−	2.57852i	−0.512190	−	0.137241i	−0.00653851	−	0.999979i	$-0.502081\pi$
$353$	−9.62318	−	2.57852i	−0.512190	−	0.137241i	−0.505652	+	0.862738i	$0.668748\pi$
$354$	−1.16885	+	0.674835i	−0.0621236	+	0.0358671i
$355$		0			0
$356$			25.4815i			1.35052i
$357$	11.0261	−	0.544725i	0.583562	−	0.0288299i
$358$	−0.753838	−	0.753838i	−0.0398416	−	0.0398416i
$359$	−4.60061	−	2.65616i	−0.242811	−	0.140187i	0.373657	−	0.927567i	$-0.378104\pi$
$359$	−4.60061	−	2.65616i	−0.242811	−	0.140187i	−0.616468	+	0.787380i	$0.711437\pi$
$360$		0			0
$361$	−13.4127	−	23.2315i	−0.705932	−	1.22271i
$362$	−3.89095	+	1.04258i	−0.204504	+	0.0547966i
$363$	6.87663	−	6.87663i	0.360930	−	0.360930i
$364$	0.275846	−	0.0887147i	0.0144582	−	0.00464991i
$365$		0			0
$366$	0.202804	−	0.351266i	0.0106007	−	0.0183610i
$367$	8.76433	−	32.7089i	0.457494	−	1.70739i	−0.223156	−	0.974783i	$-0.571636\pi$
$367$	8.76433	−	32.7089i	0.457494	−	1.70739i	0.680650	−	0.732608i	$-0.261697\pi$
$368$	1.96942	−	7.34999i	0.102663	−	0.383145i
$369$	−0.478457	+	0.828712i	−0.0249075	+	0.0431410i
$370$		0			0
$371$	31.5853	−	10.1581i	1.63982	−	0.527384i
$372$	3.39639	−	3.39639i	0.176095	−	0.176095i
$373$	5.38828	−	1.44378i	0.278994	−	0.0747563i	−0.116609	−	0.993178i	$-0.537202\pi$
$373$	5.38828	−	1.44378i	0.278994	−	0.0747563i	0.395603	+	0.918422i	$0.370536\pi$
$374$	5.85420	+	10.1398i	0.302713	+	0.524315i
$375$		0			0
$376$	17.5944	+	10.1581i	0.907362	+	0.523865i
$377$	0.319680	+	0.319680i	0.0164643	+	0.0164643i
$378$	−1.62880	+	0.0804681i	−0.0837765	+	0.00413883i
$379$			27.2704i			1.40079i	0.713757	+	0.700393i	$0.246992\pi$
$379$			27.2704i			1.40079i	−0.713757	+	0.700393i	$0.753008\pi$
$380$		0			0
$381$	3.96620	−	2.28989i	0.203195	−	0.117314i
$382$	8.54075	+	2.28849i	0.436983	+	0.117089i
$383$	−1.25127	−	4.66981i	−0.0639370	−	0.238616i	0.926561	−	0.376145i	$-0.122751\pi$
$383$	−1.25127	−	4.66981i	−0.0639370	−	0.238616i	−0.990498	+	0.137529i	$0.956084\pi$
$384$	−11.3909			−0.581289
$385$		0			0
$386$	3.93697			0.200386
$387$	−1.27347	−	4.75265i	−0.0647341	−	0.241591i
$388$	10.1953	+	2.73183i	0.517590	+	0.138688i
$389$	−20.0641	+	11.5840i	−1.01729	+	0.587332i	−0.913317	−	0.407249i	$-0.866488\pi$
$389$	−20.0641	+	11.5840i	−1.01729	+	0.587332i	−0.103971	+	0.994580i	$0.533155\pi$
$390$		0			0
$391$		−	17.0260i		−	0.861043i
$392$	−14.6152	+	5.50999i	−0.738181	+	0.278297i
$393$	−3.09667	−	3.09667i	−0.156206	−	0.156206i
$394$	−7.06753	−	4.08044i	−0.356057	−	0.205570i
$395$		0			0
$396$	3.68768	+	6.38724i	0.185313	+	0.320971i
$397$	12.4873	−	3.34597i	0.626721	−	0.167929i	0.0685396	−	0.997648i	$-0.478166\pi$
$397$	12.4873	−	3.34597i	0.626721	−	0.167929i	0.558181	+	0.829719i	$0.311499\pi$
$398$	5.61407	−	5.61407i	0.281408	−	0.281408i
$399$	17.5077	+	3.77624i	0.876479	+	0.189048i
$400$		0			0
$401$	−5.52222	+	9.56477i	−0.275767	+	0.477642i	−0.970328	−	0.241791i	$-0.922265\pi$
$401$	−5.52222	+	9.56477i	−0.275767	+	0.477642i	0.694562	+	0.719433i	$0.255598\pi$
$402$	−1.67657	+	6.25705i	−0.0836198	+	0.312073i
$403$	0.0518738	−	0.193596i	0.00258402	−	0.00964368i
$404$	−15.7365	+	27.2564i	−0.782919	+	1.35606i
$405$		0			0
$406$	−8.08297	−	7.32192i	−0.401151	−	0.363381i
$407$	−23.7756	+	23.7756i	−1.17851	+	1.17851i
$408$	−8.99314	+	2.40971i	−0.445227	+	0.119298i
$409$	8.59239	+	14.8824i	0.424866	+	0.735890i	0.996408	−	0.0846832i	$-0.0269878\pi$
$409$	8.59239	+	14.8824i	0.424866	+	0.735890i	−0.571542	+	0.820573i	$0.693654\pi$
$410$		0			0
$411$	8.19122	+	4.72921i	0.404043	+	0.233275i
$412$	−19.3920	−	19.3920i	−0.955373	−	0.955373i
$413$	−2.64557	+	5.15399i	−0.130180	+	0.253611i
$414$			2.51513i			0.123612i
$415$		0			0
$416$	−0.328557	+	0.189693i	−0.0161089	+	0.00930045i
$417$	20.8071	+	5.57525i	1.01893	+	0.273021i
$418$	4.91638	+	18.3482i	0.240468	+	0.897439i
$419$	36.0246			1.75992			0.879959	−	0.475050i	$-0.157570\pi$
$419$	36.0246			1.75992			0.879959	+	0.475050i	$0.157570\pi$
$420$		0			0
$421$	−31.9349			−1.55641			−0.778206	−	0.628009i	$-0.783870\pi$
$421$	−31.9349			−1.55641			−0.778206	+	0.628009i	$0.783870\pi$
$422$	2.03003	+	7.57619i	0.0988205	+	0.368803i
$423$	8.79471	+	2.35653i	0.427613	+	0.114579i
$424$	−24.2329	+	13.9909i	−1.17685	+	0.679456i
$425$		0			0
$426$		−	2.20832i		−	0.106994i
$427$	−0.0859079	−	1.73891i	−0.00415737	−	0.0841518i
$428$	0.706104	+	0.706104i	0.0341308	+	0.0341308i
$429$	0.266522	+	0.153876i	0.0128678	+	0.00742923i
$430$		0			0
$431$	−15.4127	−	26.6956i	−0.742404	−	1.28588i	−0.951398	−	0.307964i	$-0.900352\pi$
$431$	−15.4127	−	26.6956i	−0.742404	−	1.28588i	0.208994	−	0.977917i	$-0.432981\pi$
$432$	−1.80126	+	0.482645i	−0.0866630	+	0.0232213i
$433$	11.1638	−	11.1638i	0.536500	−	0.536500i	−0.385999	−	0.922499i	$-0.626143\pi$
$433$	11.1638	−	11.1638i	0.536500	−	0.536500i	0.922499	+	0.385999i	$0.126143\pi$
$434$	−1.01942	+	4.72629i	−0.0489335	+	0.226869i
$435$		0			0
$436$	−1.39734	+	2.42026i	−0.0669202	+	0.115909i
$437$	7.14926	−	26.6814i	0.341995	−	1.27634i
$438$	1.22642	−	4.57707i	0.0586007	−	0.218701i
$439$	1.40303	−	2.43011i	0.0669628	−	0.115983i	−0.830600	−	0.556869i	$-0.812002\pi$
$439$	1.40303	−	2.43011i	0.0669628	−	0.115983i	0.897563	+	0.440886i	$0.145336\pi$
$440$		0			0
$441$	−5.68768	+	4.08048i	−0.270842	+	0.194309i
$442$	−0.122939	+	0.122939i	−0.00584761	+	0.00584761i
$443$	−12.9971	+	3.48255i	−0.617509	+	0.165461i	−0.553995	−	0.832520i	$-0.686897\pi$
$443$	−12.9971	+	3.48255i	−0.617509	+	0.165461i	−0.0635141	+	0.997981i	$0.520231\pi$
$444$	−5.98280	−	10.3625i	−0.283931	−	0.491783i
$445$		0			0
$446$	−13.4010	−	7.73709i	−0.634558	−	0.366362i
$447$	−3.70535	−	3.70535i	−0.175257	−	0.175257i
$448$	−0.601170	+	0.387848i	−0.0284026	+	0.0183241i
$449$			1.58525i			0.0748127i	0.999300	+	0.0374063i	$0.0119096\pi$
$449$			1.58525i			0.0748127i	−0.999300	+	0.0374063i	$0.988090\pi$
$450$		0			0
$451$	−3.77269	+	2.17816i	−0.177649	+	0.102566i
$452$	21.1866	+	5.67695i	0.996536	+	0.267021i
$453$	0.168318	+	0.628170i	0.00790825	+	0.0295140i
$454$	−13.7961			−0.647483
$455$		0			0
$456$	−15.1049			−0.707354
$457$	−8.07792	−	30.1472i	−0.377869	−	1.41023i	−0.849107	−	0.528220i	$-0.822860\pi$
$457$	−8.07792	−	30.1472i	−0.377869	−	1.41023i	0.471238	−	0.882006i	$-0.343807\pi$
$458$	5.75065	+	1.54088i	0.268710	+	0.0720007i
$459$	−3.61353	+	2.08628i	−0.168665	+	0.0973790i
$460$		0			0
$461$		−	30.2660i		−	1.40963i	−0.709391	−	0.704815i	$-0.751030\pi$
$461$		−	30.2660i		−	1.40963i	0.709391	−	0.704815i	$-0.248970\pi$
$462$	−6.60481	−	3.39029i	−0.307284	−	0.157730i
$463$	−8.84347	−	8.84347i	−0.410991	−	0.410991i	0.471093	−	0.882084i	$-0.343860\pi$
$463$	−8.84347	−	8.84347i	−0.410991	−	0.410991i	−0.882084	+	0.471093i	$0.843860\pi$
$464$	−10.8003	−	6.23558i	−0.501393	−	0.289480i
$465$		0			0
$466$	5.03025	+	8.71265i	0.233022	+	0.403606i
$467$	−28.1044	+	7.53055i	−1.30052	+	0.348472i	−0.841645	−	0.540031i	$-0.818413\pi$
$467$	−28.1044	+	7.53055i	−1.30052	+	0.348472i	−0.458871	+	0.888503i	$0.651746\pi$
$468$	−0.0774417	+	0.0774417i	−0.00357975	+	0.00357975i
$469$	8.51301	+	26.4700i	0.393094	+	1.22227i
$470$		0			0
$471$	−0.827450	+	1.43318i	−0.0381269	+	0.0660377i
$472$	1.26457	−	4.71943i	0.0582064	−	0.217229i
$473$	5.79744	−	21.6363i	0.266566	−	0.994839i
$474$	−1.72273	+	2.98385i	−0.0791275	+	0.137053i
$475$		0			0
$476$	−12.0071	+	13.2551i	−0.550344	+	0.607548i
$477$	−8.86734	+	8.86734i	−0.406008	+	0.406008i
$478$	15.8102	−	4.23634i	0.723144	−	0.193766i
$479$	−8.04387	−	13.9324i	−0.367534	−	0.636588i	0.621645	−	0.783299i	$-0.286465\pi$
$479$	−8.04387	−	13.9324i	−0.367534	−	0.636588i	−0.989179	+	0.146711i	$0.953131\pi$
$480$		0			0
$481$	−0.432399	−	0.249646i	−0.0197157	−	0.0113829i
$482$	3.60328	+	3.60328i	0.164125	+	0.164125i
$483$	5.85273	+	9.07182i	0.266308	+	0.412782i
$484$			15.7553i			0.716149i
$485$		0			0
$486$	0.533801	−	0.308190i	0.0242137	−	0.0139798i
$487$	17.1141	+	4.58571i	0.775514	+	0.207798i	0.624806	−	0.780780i	$-0.285178\pi$
$487$	17.1141	+	4.58571i	0.775514	+	0.207798i	0.150708	+	0.988578i	$0.451845\pi$
$488$	0.380032	+	1.41830i	0.0172032	+	0.0642033i
$489$	−23.6137			−1.06785
$490$		0			0
$491$	24.0656			1.08606			0.543032	−	0.839712i	$-0.317276\pi$
$491$	24.0656			1.08606			0.543032	+	0.839712i	$0.317276\pi$
$492$	−0.401240	−	1.49745i	−0.0180893	−	0.0675102i
$493$	−26.9538	−	7.22226i	−1.21394	−	0.325274i
$494$	−0.244279	+	0.141035i	−0.0109907	+	0.00634546i
$495$		0			0
$496$			5.52877i			0.248249i
$497$	−5.13879	−	7.96520i	−0.230506	−	0.357288i
$498$	4.43367	+	4.43367i	0.198677	+	0.198677i
$499$	−25.5307	−	14.7402i	−1.14291	−	0.659860i	−0.195761	−	0.980652i	$-0.562718\pi$
$499$	−25.5307	−	14.7402i	−1.14291	−	0.659860i	−0.947150	+	0.320792i	$0.896051\pi$
$500$		0			0
$501$	2.08628	+	3.61353i	0.0932079	+	0.161441i
$502$	−15.6912	+	4.20444i	−0.700332	+	0.187653i
$503$	−13.0248	+	13.0248i	−0.580745	+	0.580745i	−0.935108	−	0.354363i	$-0.884698\pi$
$503$	−13.0248	+	13.0248i	−0.580745	+	0.580745i	0.354363	+	0.935108i	$0.384698\pi$
$504$	3.96339	−	4.37535i	0.176544	−	0.194894i
$505$		0			0
$506$	−5.72503	+	9.91603i	−0.254508	+	0.440821i
$507$	3.36346	−	12.5526i	0.149377	−	0.557481i
$508$	−1.92033	+	7.16676i	−0.0852008	+	0.317974i
$509$	−13.9318	+	24.1306i	−0.617517	+	1.06957i	0.372420	+	0.928064i	$0.378528\pi$
$509$	−13.9318	+	24.1306i	−0.617517	+	1.06957i	−0.989937	+	0.141507i	$0.954805\pi$
$510$		0			0
$511$	−6.22731	−	19.3629i	−0.275480	−	0.856566i
$512$	13.2847	−	13.2847i	0.587108	−	0.587108i
$513$	−6.53878	+	1.75206i	−0.288694	+	0.0773554i
$514$	−7.13222	−	12.3534i	−0.314589	−	0.544884i
$515$		0			0
$516$	6.90332	+	3.98564i	0.303902	+	0.175458i
$517$	29.3096	+	29.3096i	1.28904	+	1.28904i
$518$	10.7155	+	5.50032i	0.470811	+	0.241670i
$519$			10.2704i			0.450821i
$520$		0			0
$521$	−11.4102	+	6.58767i	−0.499889	+	0.288611i	−0.728668	−	0.684867i	$-0.759860\pi$
$521$	−11.4102	+	6.58767i	−0.499889	+	0.288611i	0.228779	+	0.973478i	$0.426527\pi$
$522$	3.98169	+	1.06689i	0.174274	+	0.0466965i
$523$	3.14266	+	11.7286i	0.137419	+	0.512854i	0.999976	+	0.00689484i	$0.00219471\pi$
$523$	3.14266	+	11.7286i	0.137419	+	0.512854i	−0.862557	+	0.505959i	$0.831139\pi$
$524$	7.09488			0.309941
$525$		0			0
$526$	−12.6155			−0.550062
$527$	3.20180	+	11.9493i	0.139473	+	0.520520i
$528$	−8.20017	−	2.19723i	−0.356867	−	0.0956221i
$529$	−5.49898	+	3.17484i	−0.239086	+	0.138036i
$530$		0			0
$531$		−	2.18967i		−	0.0950238i
$532$	−24.3821	+	15.7302i	−1.05710	+	0.681993i
$533$	−0.0457417	−	0.0457417i	−0.00198129	−	0.00198129i
$534$	8.39592	+	4.84739i	0.363327	+	0.209767i
$535$		0			0
$536$	−11.7250	−	20.3083i	−0.506444	−	0.877187i
$537$	1.67066	−	0.447652i	0.0720943	−	0.0193176i
$538$	−10.1899	+	10.1899i	−0.439317	+	0.439317i
$539$	−31.7121	+	3.14103i	−1.36594	+	0.135294i
$540$		0			0
$541$	13.2926	−	23.0235i	0.571495	−	0.989858i	−0.424918	−	0.905232i	$-0.639697\pi$
$541$	13.2926	−	23.0235i	0.571495	−	0.989858i	0.996413	−	0.0846260i	$-0.0269695\pi$
$542$	−1.03764	+	3.87253i	−0.0445705	+	0.166339i
$543$	1.69145	−	6.31258i	0.0725872	−	0.270899i
$544$	11.7084	−	20.2795i	0.501994	−	0.869478i
$545$		0			0
$546$	0.0232439	−	0.107765i	0.000994748	−	0.00461192i
$547$	−2.78067	+	2.78067i	−0.118893	+	0.118893i	−0.764050	−	0.645157i	$-0.776792\pi$
$547$	−2.78067	+	2.78067i	−0.118893	+	0.118893i	0.645157	+	0.764050i	$0.276792\pi$
$548$	−14.8012	+	3.96597i	−0.632277	+	0.169418i
$549$	0.329024	+	0.569886i	0.0140424	+	0.0243222i
$550$		0			0
$551$	−39.2066	−	22.6359i	−1.67026	−	0.964323i
$552$	−6.43817	−	6.43817i	−0.274027	−	0.274027i
$553$	0.729749	+	14.7713i	0.0310321	+	0.628138i
$554$		−	8.96722i		−	0.380981i
$555$		0			0
$556$	−30.2227	+	17.4491i	−1.28173	+	0.740007i
$557$	15.1524	+	4.06007i	0.642027	+	0.172031i	0.565121	−	0.825008i	$-0.308829\pi$
$557$	15.1524	+	4.06007i	0.642027	+	0.172031i	0.0769056	+	0.997038i	$0.475496\pi$
$558$	−0.472979	−	1.76518i	−0.0200228	−	0.0747261i
$559$	0.332619			0.0140683
$560$		0			0
$561$	−18.9954			−0.801988
$562$	1.17660	+	4.39112i	0.0496317	+	0.185228i
$563$	7.26347	+	1.94624i	0.306119	+	0.0820243i	0.408608	−	0.912710i	$-0.366014\pi$
$563$	7.26347	+	1.94624i	0.306119	+	0.0820243i	−0.102490	+	0.994734i	$0.532681\pi$
$564$	−12.7745	+	7.37535i	−0.537903	+	0.310558i
$565$		0			0
$566$			11.7501i			0.493892i
$567$	1.20820	−	2.35377i	0.0507398	−	0.0988491i
$568$	5.65282	+	5.65282i	0.237187	+	0.237187i
$569$	22.8780	+	13.2086i	0.959097	+	0.553735i	0.895895	−	0.444266i	$-0.146535\pi$
$569$	22.8780	+	13.2086i	0.959097	+	0.553735i	0.0632019	+	0.998001i	$0.479869\pi$
$570$		0			0
$571$	10.2076	+	17.6801i	0.427175	+	0.739889i	0.996621	−	0.0821397i	$-0.0261754\pi$
$571$	10.2076	+	17.6801i	0.427175	+	0.739889i	−0.569445	+	0.822029i	$0.692842\pi$
$572$	−0.481594	+	0.129043i	−0.0201365	+	0.00539555i
$573$	−10.1435	+	10.1435i	−0.423752	+	0.423752i
$574$	1.15656	+	1.04766i	0.0482739	+	0.0437287i
$575$		0			0
$576$	0.135202	−	0.234178i	0.00563344	−	0.00975740i
$577$	−4.05126	+	15.1195i	−0.168656	+	0.629433i	0.828890	+	0.559412i	$0.188973\pi$
$577$	−4.05126	+	15.1195i	−0.168656	+	0.629433i	−0.997546	+	0.0700205i	$0.977694\pi$
$578$	0.0654360	−	0.244210i	0.00272178	−	0.0101578i
$579$	−3.19362	+	5.53152i	−0.132722	+	0.229882i
$580$		0			0
$581$	26.3090	+	5.67461i	1.09148	+	0.235422i
$582$	2.83959	−	2.83959i	0.117705	−	0.117705i
$583$	−55.1442	+	14.7758i	−2.28384	+	0.611953i
$584$	8.57692	+	14.8557i	0.354915	+	0.614731i
$585$		0			0
$586$	−3.93697	−	2.27301i	−0.162635	−	0.0938972i
$587$	11.1489	+	11.1489i	0.460165	+	0.460165i	0.898709	−	0.438545i	$-0.144506\pi$
$587$	11.1489	+	11.1489i	0.460165	+	0.460165i	−0.438545	+	0.898709i	$0.644506\pi$
$588$	1.84115	−	11.1901i	0.0759277	−	0.461471i
$589$			20.0701i			0.826975i
$590$		0			0
$591$	11.4662	−	6.62001i	0.471656	−	0.272311i
$592$	13.3038	+	3.56473i	0.546781	+	0.146510i
$593$	10.9127	+	40.7267i	0.448131	+	1.67245i	0.707536	+	0.706678i	$0.249807\pi$
$593$	10.9127	+	40.7267i	0.448131	+	1.67245i	−0.259405	+	0.965769i	$0.583526\pi$
$594$	2.80605			0.115134
$595$		0			0
$596$	8.48944			0.347741
$597$	3.33381	+	12.4419i	0.136444	+	0.509215i
$598$	−0.164232	−	0.0440059i	−0.00671595	−	0.00179953i
$599$	−15.5885	+	9.00000i	−0.636927	+	0.367730i	−0.783430	−	0.621480i	$-0.786532\pi$
$599$	−15.5885	+	9.00000i	−0.636927	+	0.367730i	0.146503	+	0.989210i	$0.453198\pi$
$600$		0			0
$601$		−	0.158757i		−	0.00647583i	−0.999995	−	0.00323791i	$-0.998969\pi$
$601$		−	0.158757i		−	0.00647583i	0.999995	−	0.00323791i	$-0.00103066\pi$
$602$	−8.01420	+	0.395928i	−0.326635	+	0.0161368i
$603$	−7.43126	−	7.43126i	−0.302624	−	0.302624i
$604$	−0.912429	−	0.526791i	−0.0371262	−	0.0214348i
$605$		0			0
$606$	5.98716	+	10.3701i	0.243212	+	0.421255i
$607$	−26.6522	+	7.14142i	−1.08178	+	0.289861i	−0.755324	−	0.655352i	$-0.772520\pi$
$607$	−26.6522	+	7.14142i	−1.08178	+	0.289861i	−0.326454	+	0.945213i	$0.605854\pi$
$608$	26.8636	−	26.8636i	1.08946	−	1.08946i
$609$	16.8442	−	5.41727i	0.682563	−	0.219519i
$610$		0			0
$611$	−0.307753	+	0.533044i	−0.0124504	+	0.0215646i
$612$	1.74958	−	6.52951i	0.0707225	−	0.263940i
$613$	7.89886	−	29.4790i	0.319032	−	1.19064i	−0.601144	−	0.799140i	$-0.705288\pi$
$613$	7.89886	−	29.4790i	0.319032	−	1.19064i	0.920177	−	0.391504i	$-0.128045\pi$
$614$	−5.99212	+	10.3787i	−0.241822	+	0.418849i
$615$		0			0
$616$	25.5853	−	8.22847i	1.03086	−	0.331534i
$617$	3.74384	−	3.74384i	0.150721	−	0.150721i	−0.627719	−	0.778440i	$-0.716011\pi$
$617$	3.74384	−	3.74384i	0.150721	−	0.150721i	0.778440	+	0.627719i	$0.216011\pi$
$618$	−10.0784	+	2.70051i	−0.405414	+	0.108630i
$619$	1.58876	+	2.75182i	0.0638577	+	0.110605i	0.896187	−	0.443677i	$-0.146326\pi$
$619$	1.58876	+	2.75182i	0.0638577	+	0.110605i	−0.832329	+	0.554282i	$0.812993\pi$
$620$		0			0
$621$	−3.53380	−	2.04024i	−0.141807	−	0.0818720i
$622$	0.815974	+	0.815974i	0.0327176	+	0.0327176i
$623$	41.5632	−	2.05336i	1.66519	−	0.0822661i
$624$		−	0.126063i		−	0.00504654i
$625$		0			0
$626$	5.76111	−	3.32618i	0.230260	−	0.132941i
$627$	−29.7676	−	7.97622i	−1.18881	−	0.318539i
$628$	−0.693910	−	2.58971i	−0.0276900	−	0.103341i
$629$	30.8177			1.22878
$630$		0			0
$631$	2.40561			0.0957657			0.0478829	−	0.998853i	$-0.484753\pi$
$631$	2.40561			0.0957657			0.0478829	+	0.998853i	$0.484753\pi$
$632$	−3.22820	−	12.0478i	−0.128411	−	0.479236i
$633$	−12.2914	−	3.29348i	−0.488540	−	0.130904i
$634$	9.28023	−	5.35794i	0.368565	−	0.212791i
$635$		0			0
$636$		−	20.3163i		−	0.805592i
$637$	−0.166932	−	0.442787i	−0.00661409	−	0.0175439i
$638$	13.2696	+	13.2696i	0.525347	+	0.525347i
$639$	3.10273	+	1.79136i	0.122742	+	0.0708653i
$640$		0			0
$641$	13.1037	+	22.6963i	0.517565	+	0.896448i	0.999792	+	0.0204019i	$0.00649458\pi$
$641$	13.1037	+	22.6963i	0.517565	+	0.896448i	−0.482227	+	0.876046i	$0.660172\pi$
$642$	0.366979	−	0.0983316i	0.0144835	−	0.00388084i
$643$	17.3152	−	17.3152i	0.682845	−	0.682845i	−0.277795	−	0.960640i	$-0.589604\pi$
$643$	17.3152	−	17.3152i	0.682845	−	0.682845i	0.960640	+	0.277795i	$0.0896037\pi$
$644$	−17.0971	−	3.68768i	−0.673719	−	0.145315i
$645$		0			0
$646$	8.70509	−	15.0777i	0.342497	−	0.593222i
$647$	−1.43590	+	5.35886i	−0.0564512	+	0.210679i	−0.988390	−	0.151936i	$-0.951449\pi$
$647$	−1.43590	+	5.35886i	−0.0564512	+	0.210679i	0.931939	+	0.362615i	$0.118116\pi$
$648$	−0.577514	+	2.15531i	−0.0226869	+	0.0846686i
$649$	4.98422	−	8.63292i	0.195648	−	0.338872i
$650$		0			0
$651$	−5.81359	−	5.26621i	−0.227852	−	0.206399i
$652$	27.0510	−	27.0510i	1.05940	−	1.05940i
$653$	−6.83511	+	1.83146i	−0.267479	+	0.0716707i	−0.390065	−	0.920787i	$-0.627548\pi$
$653$	−6.83511	+	1.83146i	−0.267479	+	0.0716707i	0.122587	+	0.992458i	$0.460881\pi$
$654$	0.531635	+	0.920819i	0.0207886	+	0.0360069i
$655$		0			0
$656$	1.54538	+	0.892226i	0.0603369	+	0.0348356i
$657$	5.43601	+	5.43601i	0.212079	+	0.212079i
$658$	6.78058	−	13.2096i	0.264334	−	0.514965i
$659$		−	32.2008i		−	1.25436i	−0.778873	−	0.627182i	$-0.784208\pi$
$659$		−	32.2008i		−	1.25436i	0.778873	−	0.627182i	$-0.215792\pi$
$660$		0			0
$661$	9.61527	−	5.55138i	0.373991	−	0.215924i	−0.301210	−	0.953558i	$-0.597390\pi$
$661$	9.61527	−	5.55138i	0.373991	−	0.215924i	0.675200	+	0.737634i	$0.264057\pi$
$662$	12.7889	+	3.42677i	0.497054	+	0.133185i
$663$	−0.0730050	−	0.272458i	−0.00283528	−	0.0105814i
$664$	−22.6984			−0.880870
$665$		0			0
$666$	−4.55247			−0.176405
$667$	−7.06290	−	26.3591i	−0.273477	−	1.02063i
$668$	−6.52951	−	1.74958i	−0.252634	−	0.0676932i
$669$	21.7415	−	12.5525i	0.840576	−	0.485307i
$670$		0			0
$671$			2.99575i			0.115650i
$672$	0.732658	+	14.8302i	0.0282629	+	0.572086i
$673$	−34.4082	−	34.4082i	−1.32634	−	1.32634i	−0.908539	−	0.417800i	$-0.862801\pi$
$673$	−34.4082	−	34.4082i	−1.32634	−	1.32634i	−0.417800	−	0.908539i	$-0.637199\pi$
$674$	−6.14296	−	3.54664i	−0.236618	−	0.136612i
$675$		0			0
$676$	10.5268	+	18.2329i	0.404877	+	0.701267i
$677$	39.8037	−	10.6654i	1.52978	−	0.409904i	0.606834	−	0.794829i	$-0.292439\pi$
$677$	39.8037	−	10.6654i	1.52978	−	0.409904i	0.922948	+	0.384925i	$0.125773\pi$
$678$	5.90088	−	5.90088i	0.226622	−	0.226622i
$679$	3.63437	−	16.8499i	0.139474	−	0.646640i
$680$		0			0
$681$	11.1912	−	19.3838i	0.428849	−	0.742788i
$682$	2.15322	−	8.03594i	0.0824512	−	0.307712i
$683$	2.74551	−	10.2464i	0.105054	−	0.392067i	−0.893297	−	0.449466i	$-0.851614\pi$
$683$	2.74551	−	10.2464i	0.105054	−	0.392067i	0.998351	+	0.0573994i	$0.0182808\pi$
$684$	5.48351	−	9.49772i	0.209667	−	0.363154i
$685$		0			0
$686$	4.54917	+	10.4699i	0.173688	+	0.399743i
$687$	−6.82983	+	6.82983i	−0.260574	+	0.260574i
$688$	−8.86273	+	2.37476i	−0.337889	+	0.0905370i
$689$	−0.423870	−	0.734165i	−0.0161482	−	0.0279695i
$690$		0			0
$691$	25.9455	+	14.9796i	0.987013	+	0.569852i	0.904380	−	0.426728i	$-0.140334\pi$
$691$	25.9455	+	14.9796i	0.987013	+	0.569852i	0.0826326	+	0.996580i	$0.473667\pi$
$692$	−11.7654	−	11.7654i	−0.447255	−	0.447255i
$693$	10.1212	−	6.52972i	0.384471	−	0.248044i
$694$		−	9.72046i		−	0.368983i
$695$		0			0
$696$	−12.9233	+	7.46125i	−0.489855	+	0.282818i
$697$	3.85672	+	1.03341i	0.146084	+	0.0391430i
$698$	0.908599	+	3.39094i	0.0343910	+	0.128349i
$699$	−16.3219			−0.617352
$700$		0			0
$701$	23.9278			0.903742			0.451871	−	0.892083i	$-0.350757\pi$
$701$	23.9278			0.903742			0.451871	+	0.892083i	$0.350757\pi$
$702$	0.0107845	+	0.0402482i	0.000407034	+	0.00151907i
$703$	48.2943	+	12.9404i	1.82145	+	0.488057i
$704$	1.06609	−	0.615506i	0.0401797	−	0.0231978i
$705$		0			0
$706$		−	6.14078i		−	0.231111i
$707$	45.7264	+	23.4716i	1.71972	+	0.882741i
$708$	2.50842	+	2.50842i	0.0942721	+	0.0942721i
$709$	35.0268	+	20.2227i	1.31546	+	0.759481i	0.982995	−	0.183635i	$-0.0587863\pi$
$709$	35.0268	+	20.2227i	1.31546	+	0.759481i	0.332465	+	0.943116i	$0.392120\pi$
$710$		0			0
$711$	−2.79491	−	4.84093i	−0.104817	−	0.181549i
$712$	−33.8999	+	9.08346i	−1.27045	+	0.340417i
$713$	−8.55447	+	8.55447i	−0.320368	+	0.320368i
$714$	2.08332	+	6.47778i	0.0779662	+	0.242425i
$715$		0			0
$716$	−1.40104	+	2.42667i	−0.0523592	+	0.0906888i
$717$	−6.87294	+	25.6502i	−0.256675	+	0.957923i
$718$	0.847479	−	3.16284i	0.0316276	−	0.118036i
$719$	19.2343	−	33.3148i	0.717320	−	1.24243i	−0.244738	−	0.969589i	$-0.578702\pi$
$719$	19.2343	−	33.3148i	0.717320	−	1.24243i	0.962058	−	0.272845i	$-0.0879646\pi$
$720$		0			0
$721$	−30.0678	+	33.1931i	−1.11978	+	1.23618i
$722$	11.6918	−	11.6918i	0.435122	−	0.435122i
$723$	−7.98562	+	2.13974i	−0.296988	+	0.0795778i
$724$	5.29382	+	9.16916i	0.196743	+	0.340769i
$725$		0			0
$726$	5.19122	+	2.99715i	0.192664	+	0.111235i
$727$	−15.0422	−	15.0422i	−0.557886	−	0.557886i	0.370819	−	0.928705i	$-0.379077\pi$
$727$	−15.0422	−	15.0422i	−0.557886	−	0.557886i	−0.928705	+	0.370819i	$0.879077\pi$
$728$	0.216356	+	0.335354i	0.00801867	+	0.0124291i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−17.7797	+	10.2651i	−0.657606	+	0.379669i
$732$	−1.02976	−	0.275924i	−0.0380611	−	0.0101984i
$733$	9.08767	+	33.9156i	0.335661	+	1.25270i	0.903151	+	0.429323i	$0.141248\pi$
$733$	9.08767	+	33.9156i	0.335661	+	1.25270i	−0.567491	+	0.823380i	$0.692086\pi$
$734$	20.8723			0.770411
$735$		0			0
$736$	22.9001			0.844109
$737$	−12.3829	−	46.2135i	−0.456129	−	1.70230i
$738$	−0.569725	−	0.152657i	−0.0209719	−	0.00561939i
$739$	−0.177820	+	0.102664i	−0.00654120	+	0.00377657i	−0.503267	−	0.864131i	$-0.667869\pi$
$739$	−0.177820	+	0.102664i	−0.00654120	+	0.00377657i	0.496726	+	0.867908i	$0.334535\pi$
$740$		0			0
$741$		−	0.457623i		−	0.0168112i
$742$	11.0867	+	17.1846i	0.407007	+	0.630867i
$743$	−16.1701	−	16.1701i	−0.593222	−	0.593222i	0.345278	−	0.938500i	$-0.387785\pi$
$743$	−16.1701	−	16.1701i	−0.593222	−	0.593222i	−0.938500	+	0.345278i	$0.887785\pi$
$744$	5.72920	+	3.30775i	0.210043	+	0.121268i
$745$		0			0
$746$	1.71919	+	2.97773i	0.0629441	+	0.109022i
$747$	−9.82593	+	2.63285i	−0.359512	+	0.0963309i
$748$	21.7605	−	21.7605i	0.795644	−	0.795644i
$749$	1.09484	−	1.20864i	0.0400045	−	0.0441626i
$750$		0			0
$751$	−13.4324	+	23.2656i	−0.490155	+	0.848974i	−0.999936	−	0.0113307i	$-0.996393\pi$
$751$	−13.4324	+	23.2656i	−0.490155	+	0.848974i	0.509781	+	0.860304i	$0.329727\pi$
$752$	4.39446	−	16.4003i	0.160249	−	0.598059i
$753$	6.82119	−	25.4570i	0.248578	−	0.927705i
$754$	−0.139331	+	0.241329i	−0.00507414	+	0.00878868i
$755$		0			0
$756$	1.31232	+	4.08048i	0.0477287	+	0.148406i
$757$	−17.3120	+	17.3120i	−0.629216	+	0.629216i	−0.947871	−	0.318655i	$-0.896769\pi$
$757$	−17.3120	+	17.3120i	−0.629216	+	0.629216i	0.318655	+	0.947871i	$0.396769\pi$
$758$	−16.2362	+	4.35047i	−0.589725	+	0.158016i
$759$	−9.28814	−	16.0875i	−0.337138	−	0.583941i
$760$		0			0
$761$	−18.8287	−	10.8708i	−0.682540	−	0.394065i	0.118271	−	0.992981i	$-0.462265\pi$
$761$	−18.8287	−	10.8708i	−0.682540	−	0.394065i	−0.800811	+	0.598917i	$0.795598\pi$
$762$	1.99608	+	1.99608i	0.0723103	+	0.0723103i
$763$	4.06032	+	2.08418i	0.146993	+	0.0754525i
$764$		−	23.2402i		−	0.840799i
$765$		0			0
$766$	2.58068	−	1.48996i	0.0932439	−	0.0538344i
$767$	0.142981	+	0.0383116i	0.00516274	+	0.00138335i
$768$	−1.67723	−	6.25949i	−0.0605217	−	0.225870i
$769$	0.923161			0.0332901			0.0166450	−	0.999861i	$-0.494701\pi$
$769$	0.923161			0.0332901			0.0166450	+	0.999861i	$0.494701\pi$
$770$		0			0
$771$	23.1423			0.833449
$772$	−2.67821	−	9.99523i	−0.0963910	−	0.359736i
$773$	4.23312	+	1.13426i	0.152255	+	0.0407965i	0.334141	−	0.942523i	$-0.391554\pi$
$773$	4.23312	+	1.13426i	0.152255	+	0.0407965i	−0.181887	+	0.983320i	$0.558220\pi$
$774$	2.62646	−	1.51639i	0.0944063	−	0.0545055i
$775$		0			0
$776$			14.5375i			0.521865i
$777$	−16.4203	+	10.5937i	−0.589076	+	0.380046i
$778$	−10.0977	−	10.0977i	−0.362019	−	0.362019i
$779$	5.60992	+	3.23889i	0.200996	+	0.116045i
$780$		0			0
$781$	8.15514	+	14.1251i	0.291814	+	0.505436i
$782$	10.1369	−	2.71617i	0.362495	−	0.0971302i
$783$	−4.72890	+	4.72890i	−0.168997	+	0.168997i
$784$	7.60927	+	10.6064i	0.271760	+	0.378799i
$785$		0			0
$786$	1.34967	−	2.33770i	0.0481412	−	0.0833829i
$787$	−9.95944	+	37.1691i	−0.355016	+	1.32494i	0.525449	+	0.850825i	$0.323897\pi$
$787$	−9.95944	+	37.1691i	−0.355016	+	1.32494i	−0.880465	+	0.474111i	$0.842769\pi$
$788$	−5.55163	+	20.7190i	−0.197769	+	0.738082i
$789$	10.2335	−	17.7250i	0.364324	−	0.631028i
$790$		0			0
$791$	7.55247	−	35.0153i	0.268535	−	1.24500i
$792$	−7.18288	+	7.18288i	−0.255233	+	0.255233i
$793$	−0.0429691	+	0.0115135i	−0.00152588	+	0.000408857i
$794$	3.98423	+	6.90088i	0.141395	+	0.244903i
$795$		0			0
$796$	−18.0722	−	10.4340i	−0.640551	−	0.369822i
$797$	−0.616521	−	0.616521i	−0.0218383	−	0.0218383i	0.696103	−	0.717942i	$-0.254916\pi$
$797$	−0.616521	−	0.616521i	−0.0218383	−	0.0218383i	−0.717942	+	0.696103i	$0.754916\pi$
$798$	0.544725	+	11.0261i	0.0192830	+	0.390319i
$799$		−	37.9909i		−	1.34402i
$800$		0			0
$801$	−13.6213	+	7.86428i	−0.481286	+	0.277871i
$802$	−6.57561	−	1.76193i	−0.232193	−	0.0622159i
$803$	9.05814	+	33.8054i	0.319655	+	1.19297i
$804$	17.0260			0.600461
$805$		0			0
$806$	0.123538			0.00435144
$807$	−6.05106	−	22.5829i	−0.213007	−	0.794955i
$808$	−41.8709	−	11.2193i	−1.47301	−	0.394693i
$809$	4.71988	−	2.72503i	0.165942	−	0.0958068i	−0.414729	−	0.909945i	$-0.636124\pi$
$809$	4.71988	−	2.72503i	0.165942	−	0.0958068i	0.580671	+	0.814138i	$0.302790\pi$
$810$		0			0
$811$			0.938267i			0.0329470i	0.999864	+	0.0164735i	$0.00524391\pi$
$811$			0.938267i			0.0329470i	−0.999864	+	0.0164735i	$0.994756\pi$
$812$	−13.0904	+	25.5020i	−0.459381	+	0.894946i
$813$	−4.59926	−	4.59926i	−0.161303	−	0.161303i
$814$	−17.9484	−	10.3625i	−0.629091	−	0.363206i
$815$		0			0
$816$	3.89048	+	6.73851i	0.136194	+	0.235895i
$817$	−32.1728	+	8.62068i	−1.12558	+	0.301599i
$818$	−7.48992	+	7.48992i	−0.261879	+	0.261879i
$819$	0.132557	+	0.120076i	0.00463191	+	0.00419579i
$820$		0			0
$821$	−12.1667	+	21.0734i	−0.424621	+	0.735466i	−0.996385	−	0.0849526i	$-0.972926\pi$
$821$	−12.1667	+	21.0734i	−0.424621	+	0.735466i	0.571764	+	0.820418i	$0.306259\pi$
$822$	−1.50891	+	5.63132i	−0.0526292	+	0.196415i
$823$	2.41566	−	9.01538i	0.0842047	−	0.314256i	−0.910958	−	0.412500i	$-0.864656\pi$
$823$	2.41566	−	9.01538i	0.0842047	−	0.314256i	0.995162	+	0.0982435i	$0.0313224\pi$
$824$	18.8859	−	32.7113i	0.657921	−	1.13955i
$825$		0			0
$826$	−3.49062	−	0.752894i	−0.121454	−	0.0261965i
$827$	30.1477	−	30.1477i	1.04834	−	1.04834i	0.0495680	−	0.998771i	$-0.484216\pi$
$827$	30.1477	−	30.1477i	1.04834	−	1.04834i	0.998771	−	0.0495680i	$-0.0157845\pi$
$828$	6.38544	−	1.71097i	0.221909	−	0.0594604i
$829$	−27.5731	−	47.7580i	−0.957654	−	1.65871i	−0.728174	−	0.685392i	$-0.759631\pi$
$829$	−27.5731	−	47.7580i	−0.957654	−	1.65871i	−0.229480	−	0.973313i	$-0.573702\pi$
$830$		0			0
$831$	12.5991	+	7.27410i	0.437059	+	0.252336i
$832$	0.0129257	+	0.0129257i	0.000448118	+	0.000448118i
$833$	22.5882	+	18.5168i	0.782634	+	0.641569i
$834$			13.2775i			0.459762i
$835$		0			0
$836$	43.2381	−	24.9635i	1.49542	−	0.863382i
$837$	2.86379	+	0.767349i	0.0989870	+	0.0265235i
$838$	5.74704	+	21.4482i	0.198528	+	0.740917i
$839$	7.33343			0.253178			0.126589	−	0.991955i	$-0.459597\pi$
$839$	7.33343			0.253178			0.126589	+	0.991955i	$0.459597\pi$
$840$		0			0
$841$	−15.7250			−0.542242
$842$	−5.09461	−	19.0133i	−0.175572	−	0.655242i
$843$	−7.12405	−	1.90888i	−0.245365	−	0.0657454i
$844$	17.8536	−	10.3078i	0.614545	−	0.354807i
$845$		0			0
$846$			5.61211i			0.192948i
$847$	25.6987	−	1.26960i	0.883016	−	0.0436239i
$848$	16.5358	+	16.5358i	0.567841	+	0.567841i
$849$	−16.5091	−	9.53152i	−0.566590	−	0.327121i
$850$		0			0
$851$	15.0689	+	26.1000i	0.516554	+	0.894698i
$852$	−5.60651	+	1.50226i	−0.192076	+	0.0514666i
$853$	−6.61623	+	6.61623i	−0.226535	+	0.226535i	−0.811244	−	0.584708i	$-0.801209\pi$
$853$	−6.61623	+	6.61623i	−0.226535	+	0.226535i	0.584708	+	0.811244i	$0.301209\pi$
$854$	1.02160	−	0.328557i	0.0349585	−	0.0112430i
$855$		0			0
$856$	−0.687677	+	1.19109i	−0.0235043	+	0.0407107i
$857$	13.2149	−	49.3187i	0.451412	−	1.68469i	−0.247014	−	0.969012i	$-0.579449\pi$
$857$	13.2149	−	49.3187i	0.451412	−	1.68469i	0.698426	−	0.715682i	$-0.253884\pi$
$858$	−0.0490961	+	0.183229i	−0.00167611	+	0.00625534i
$859$	−11.9017	+	20.6143i	−0.406080	+	0.703352i	−0.994447	−	0.105243i	$-0.966438\pi$
$859$	−11.9017	+	20.6143i	−0.406080	+	0.703352i	0.588366	+	0.808595i	$0.299771\pi$
$860$		0			0
$861$	−2.41018	+	0.775137i	−0.0821386	+	0.0264166i
$862$	13.4351	−	13.4351i	0.457603	−	0.457603i
$863$	−17.6949	+	4.74133i	−0.602341	+	0.161397i	−0.547087	−	0.837076i	$-0.684263\pi$
$863$	−17.6949	+	4.74133i	−0.602341	+	0.161397i	−0.0552536	+	0.998472i	$0.517597\pi$
$864$	−2.80605	−	4.86023i	−0.0954639	−	0.165348i
$865$		0			0
$866$	8.42767	+	4.86572i	0.286384	+	0.165344i
$867$	0.290039	+	0.290039i	0.00985025	+	0.00985025i
$868$	12.6926	−	0.627058i	0.430816	−	0.0212837i
$869$		−	25.4475i		−	0.863248i
$870$		0			0
$871$	0.615266	−	0.355224i	0.0208475	−	0.0120363i
$872$	−3.71797	−	0.996226i	−0.125906	−	0.0337365i
$873$	1.68624	+	6.29313i	0.0570705	+	0.212990i
$874$	17.0260			0.575914
$875$		0			0
$876$	−12.4546			−0.420803
$877$	2.80539	+	10.4699i	0.0947313	+	0.353542i	0.996979	−	0.0776770i	$-0.0247503\pi$
$877$	2.80539	+	10.4699i	0.0947313	+	0.353542i	−0.902247	+	0.431219i	$0.858084\pi$
$878$	1.67066	+	0.447652i	0.0563821	+	0.0151075i
$879$	6.38724	−	3.68768i	0.215436	−	0.124382i
$880$		0			0
$881$		−	0.400850i		−	0.0135050i	−0.999977	−	0.00675249i	$-0.997851\pi$
$881$		−	0.400850i		−	0.0135050i	0.999977	−	0.00675249i	$-0.00214940\pi$
$882$	−3.33679	−	2.73535i	−0.112355	−	0.0921041i
$883$	1.45235	+	1.45235i	0.0488756	+	0.0488756i	0.731122	−	0.682247i	$-0.238997\pi$
$883$	1.45235	+	1.45235i	0.0488756	+	0.0488756i	−0.682247	+	0.731122i	$0.738997\pi$
$884$	0.395751	+	0.228487i	0.0133106	+	0.00768485i
$885$		0			0
$886$	−4.14687	−	7.18258i	−0.139317	−	0.241304i
$887$	−6.09282	+	1.63257i	−0.204577	+	0.0548162i	−0.359652	−	0.933086i	$-0.617105\pi$
$887$	−6.09282	+	1.63257i	−0.204577	+	0.0548162i	0.155075	+	0.987903i	$0.450438\pi$
$888$	11.6533	−	11.6533i	0.391060	−	0.391060i
$889$	11.8446	+	2.55476i	0.397254	+	0.0856839i
$890$		0			0
$891$	−2.27624	+	3.94256i	−0.0762568	+	0.132081i
$892$	−10.5267	+	39.2861i	−0.352459	+	1.31539i
$893$	15.9524	−	59.5353i	0.533828	−	1.99227i
$894$	1.61496	−	2.79720i	0.0540124	−	0.0935522i
$895$		0			0
$896$	−22.3360	−	20.2329i	−0.746192	−	0.675934i
$897$	0.195052	−	0.195052i	0.00651261	−	0.00651261i
$898$	−0.943823	+	0.252897i	−0.0314958	+	0.00843927i
$899$	9.91385	+	17.1713i	0.330645	+	0.572695i
$900$		0			0
$901$	45.3148	+	26.1625i	1.50966	+	0.871601i
$902$	−1.89869	−	1.89869i	−0.0632194	−	0.0632194i
$903$	5.94474	−	11.5813i	0.197829	−	0.385401i
$904$			30.2099i			1.00477i
$905$		0			0
$906$	−0.347146	+	0.200425i	−0.0115332	+	0.00665867i
$907$	−31.6461	−	8.47956i	−1.05079	−	0.281559i	−0.308214	−	0.951317i	$-0.599731\pi$
$907$	−31.6461	−	8.47956i	−1.05079	−	0.281559i	−0.742579	+	0.669758i	$0.766398\pi$
$908$	9.38511	+	35.0257i	0.311456	+	1.16237i
$909$	−19.4268			−0.644348
$910$		0			0
$911$	1.59187			0.0527409			0.0263705	−	0.999652i	$-0.491605\pi$
$911$	1.59187			0.0527409			0.0263705	+	0.999652i	$0.491605\pi$
$912$	3.26724	+	12.1935i	0.108189	+	0.403767i
$913$	−44.7323	−	11.9860i	−1.48042	−	0.396678i
$914$	16.6603	−	9.61881i	0.551073	−	0.318162i
$915$		0			0
$916$		−	15.6480i		−	0.517026i
$917$	−0.571722	−	11.5726i	−0.0188799	−	0.382159i
$918$	−1.81859	−	1.81859i	−0.0600224	−	0.0600224i
$919$	37.2959	+	21.5328i	1.23028	+	0.710301i	0.967088	−	0.254443i	$-0.0818922\pi$
$919$	37.2959	+	21.5328i	1.23028	+	0.710301i	0.263189	+	0.964744i	$0.415226\pi$
$920$		0			0
$921$	−9.72148	−	16.8381i	−0.320334	−	0.554834i
$922$	18.0197	−	4.82837i	0.593448	−	0.159014i
$923$	−0.171259	+	0.171259i	−0.00563706	+	0.00563706i
$924$	−4.11423	+	19.0747i	−0.135348	+	0.627511i
$925$		0			0
$926$	3.85440	−	6.67601i	0.126663	−	0.219387i
$927$	4.38124	−	16.3510i	0.143899	−	0.537038i
$928$	9.71399	−	36.2531i	0.318877	−	1.19007i
$929$	−16.5662	+	28.6935i	−0.543520	+	0.941404i	0.455179	+	0.890400i	$0.349575\pi$
$929$	−16.5662	+	28.6935i	−0.543520	+	0.941404i	−0.998698	+	0.0510035i	$0.983758\pi$
$930$		0			0
$931$	27.6226	+	38.5024i	0.905294	+	1.26187i
$932$	18.6979	−	18.6979i	0.612469	−	0.612469i
$933$	−1.80837	+	0.484551i	−0.0592033	+	0.0158635i
$934$	−8.96704	−	15.5314i	−0.293410	−	0.508202i
$935$		0			0
$936$	−0.130633	−	0.0754207i	−0.00426986	−	0.00246520i
$937$	7.09425	+	7.09425i	0.231759	+	0.231759i	0.813427	−	0.581668i	$-0.197600\pi$
$937$	7.09425	+	7.09425i	0.231759	+	0.231759i	−0.581668	+	0.813427i	$0.697600\pi$
$938$	−14.4015	+	9.29123i	−0.470227	+	0.303369i
$939$			10.7926i			0.352204i
$940$		0			0
$941$	−13.0129	+	7.51302i	−0.424209	+	0.244917i	−0.696877	−	0.717191i	$-0.745427\pi$
$941$	−13.0129	+	7.51302i	−0.424209	+	0.244917i	0.272667	+	0.962108i	$0.412094\pi$
$942$	−0.985289	−	0.264007i	−0.0321025	−	0.00860183i
$943$	1.01060	+	3.77162i	0.0329098	+	0.122821i
$944$	−4.08330			−0.132900
$945$		0			0
$946$	13.8066			0.448893
$947$	−3.84958	−	14.3668i	−0.125095	−	0.466859i	0.874748	−	0.484577i	$-0.161027\pi$
$947$	−3.84958	−	14.3668i	−0.125095	−	0.466859i	−0.999843	+	0.0177180i	$0.994360\pi$
$948$	8.74736	+	2.34385i	0.284101	+	0.0761247i
$949$	−0.450070	+	0.259848i	−0.0146099	+	0.00843503i
$950$		0			0
$951$			17.3852i			0.563754i
$952$	−21.9145	−	11.2489i	−0.710254	−	0.364577i
$953$	4.93154	+	4.93154i	0.159748	+	0.159748i	0.782455	−	0.622707i	$-0.213967\pi$
$953$	4.93154	+	4.93154i	0.159748	+	0.159748i	−0.622707	+	0.782455i	$0.713967\pi$
$954$	−6.69403	−	3.86480i	−0.216727	−	0.125127i
$955$		0			0
$956$	−21.5106	−	37.2574i	−0.695701	−	1.20499i
$957$	−29.4081	+	7.87987i	−0.950628	+	0.254720i
$958$	7.01179	−	7.01179i	0.226541	−	0.226541i
$959$	7.66167	+	23.8229i	0.247408	+	0.769281i
$960$		0			0
$961$	−11.1049	+	19.2343i	−0.358224	+	0.620462i
$962$	0.0796523	−	0.297267i	0.00256809	−	0.00958426i
$963$	−0.159531	+	0.595377i	−0.00514081	+	0.0191858i
$964$	6.69684	−	11.5993i	0.215691	−	0.373587i
$965$		0			0
$966$	−4.46746	+	4.93182i	−0.143738	+	0.158679i
$967$	−8.91868	+	8.91868i	−0.286805	+	0.286805i	−0.835816	−	0.549010i	$-0.815005\pi$
$967$	−8.91868	+	8.91868i	−0.286805	+	0.286805i	0.549010	+	0.835816i	$0.315005\pi$
$968$	−20.9605	+	5.61634i	−0.673694	+	0.180516i
$969$	14.1229	+	24.4616i	0.453694	+	0.785821i
$970$		0			0
$971$	5.24725	+	3.02950i	0.168392	+	0.0972213i	0.581827	−	0.813312i	$-0.302338\pi$
$971$	5.24725	+	3.02950i	0.168392	+	0.0972213i	−0.413435	+	0.910533i	$0.635671\pi$
$972$	−1.14557	−	1.14557i	−0.0367441	−	0.0367441i
$973$	30.8969	+	47.8906i	0.990509	+	1.53530i
$974$			10.9209i			0.349928i
$975$		0			0
$976$	1.06272	−	0.613563i	0.0340169	−	0.0196397i
$977$	17.7574	+	4.75807i	0.568108	+	0.152224i	0.531429	−	0.847103i	$-0.321655\pi$
$977$	17.7574	+	4.75807i	0.568108	+	0.152224i	0.0366795	+	0.999327i	$0.488322\pi$
$978$	−3.76711	−	14.0590i	−0.120459	−	0.449559i
$979$	−71.6039			−2.28847
$980$		0			0
$981$	−1.72503			−0.0550758
$982$	3.83920	+	14.3281i	0.122514	+	0.457228i
$983$	−18.4812	−	4.95203i	−0.589459	−	0.157945i	−0.0482531	−	0.998835i	$-0.515365\pi$
$983$	−18.4812	−	4.95203i	−0.589459	−	0.157945i	−0.541206	+	0.840890i	$0.682032\pi$
$984$	1.84914	−	1.06760i	0.0589484	−	0.0340339i
$985$		0			0
$986$		−	17.1999i		−	0.547756i
$987$	13.0594	+	20.2423i	0.415687	+	0.644320i
$988$	0.524238	+	0.524238i	0.0166782	+	0.0166782i
$989$	−17.3874	−	10.0386i	−0.552887	−	0.319209i
$990$		0			0
$991$	−17.5573	−	30.4101i	−0.557726	−	0.966009i	−0.997686	−	0.0679917i	$-0.978341\pi$
$991$	−17.5573	−	30.4101i	−0.557726	−	0.966009i	0.439960	−	0.898017i	$-0.354992\pi$
$992$	−16.0719	+	4.30645i	−0.510283	+	0.136730i
$993$	−15.1889	+	15.1889i	−0.482004	+	0.482004i
$994$	3.92250	−	4.33021i	0.124414	−	0.137346i
$995$		0			0
$996$	8.24015	−	14.2724i	0.261099	−	0.452237i
$997$	0.474162	−	1.76959i	0.0150168	−	0.0560436i	−0.958011	−	0.286732i	$-0.907431\pi$
$997$	0.474162	−	1.76959i	0.0150168	−	0.0560436i	0.973028	+	0.230688i	$0.0740978\pi$
$998$	4.70302	−	17.5519i	0.148871	−	0.555596i
$999$	3.69291	−	6.39631i	0.116839	−	0.202370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.d.418.4	yes	24
5.2	odd	4	inner	525.2.bc.d.82.3	✓	24
5.3	odd	4	inner	525.2.bc.d.82.4	yes	24
5.4	even	2	inner	525.2.bc.d.418.3	yes	24
7.3	odd	6	inner	525.2.bc.d.493.3	yes	24
35.3	even	12	inner	525.2.bc.d.157.3	yes	24
35.17	even	12	inner	525.2.bc.d.157.4	yes	24
35.24	odd	6	inner	525.2.bc.d.493.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.d.82.3	✓	24	5.2	odd	4	inner
525.2.bc.d.82.4	yes	24	5.3	odd	4	inner
525.2.bc.d.157.3	yes	24	35.3	even	12	inner
525.2.bc.d.157.4	yes	24	35.17	even	12	inner
525.2.bc.d.418.3	yes	24	5.4	even	2	inner
525.2.bc.d.418.4	yes	24	1.1	even	1	trivial
525.2.bc.d.493.3	yes	24	7.3	odd	6	inner
525.2.bc.d.493.4	yes	24	35.24	odd	6	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.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.159531 + 0.595377i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(1.40303 - 0.810038i) q^{4} -0.616380i q^{6} +(-1.43432 - 2.22322i) q^{7} +(1.57780 + 1.57780i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.159531 + 0.595377i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(1.40303 - 0.810038i) q^{4} -0.616380i q^{6} +(-1.43432 - 2.22322i) q^{7} +(1.57780 + 1.57780i) q^{8} +(0.866025 + 0.500000i) q^{9} +(2.27624 + 3.94256i) q^{11} +(-1.56487 + 0.419306i) q^{12} +(-0.0478013 + 0.0478013i) q^{13} +(1.09484 - 1.20864i) q^{14} +(0.932399 - 1.61496i) q^{16} +(1.07994 - 4.03037i) q^{17} +(-0.159531 + 0.595377i) q^{18} +(3.38472 - 5.86251i) q^{19} +(0.810038 + 2.51870i) q^{21} +(-1.98418 + 1.98418i) q^{22} +(3.94144 - 1.05611i) q^{23} +(-1.11567 - 1.93240i) q^{24} +(-0.0360856 - 0.0208340i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-3.81329 - 1.95738i) q^{28} -6.68768i q^{29} +(-2.56760 + 1.48241i) q^{31} +(5.42088 + 1.45252i) q^{32} +(-1.17827 - 4.39735i) q^{33} +2.57188 q^{34} +1.62008 q^{36} +(1.91159 + 7.13416i) q^{37} +(4.03037 + 1.07994i) q^{38} +(0.0585444 - 0.0338006i) q^{39} +0.956914i q^{41} +(-1.37035 + 0.884088i) q^{42} +(-3.47918 - 3.47918i) q^{43} +(6.38724 + 3.68768i) q^{44} +(1.25756 + 2.17816i) q^{46} +(8.79471 - 2.35653i) q^{47} +(-1.31861 + 1.31861i) q^{48} +(-2.88543 + 6.37764i) q^{49} +(-2.08628 + 3.61353i) q^{51} +(-0.0283456 + 0.105787i) q^{52} +(-3.24567 + 12.1130i) q^{53} +(0.308190 - 0.533801i) q^{54} +(1.24472 - 5.77086i) q^{56} +(-4.78672 + 4.78672i) q^{57} +(3.98169 - 1.06689i) q^{58} +(-1.09484 - 1.89631i) q^{59} +(0.569886 + 0.329024i) q^{61} +(-1.29220 - 1.29220i) q^{62} +(-0.130550 - 2.64253i) q^{63} -0.270405i q^{64} +(2.43011 - 1.40303i) q^{66} +(-10.1513 - 2.72003i) q^{67} +(-1.74958 - 6.52951i) q^{68} -4.08048 q^{69} +3.58273 q^{71} +(0.577514 + 2.15531i) q^{72} +(7.42573 + 1.98972i) q^{73} +(-3.94256 + 2.27624i) q^{74} -10.9670i q^{76} +(5.50032 - 10.7155i) q^{77} +(0.0294638 + 0.0294638i) q^{78} +(-4.84093 - 2.79491i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.569725 + 0.152657i) q^{82} +(-7.19308 + 7.19308i) q^{83} +(3.17675 + 2.87764i) q^{84} +(1.51639 - 2.62646i) q^{86} +(-1.73090 + 6.45980i) q^{87} +(-2.62912 + 9.81200i) q^{88} +(-7.86428 + 13.6213i) q^{89} +(0.174835 + 0.0377104i) q^{91} +(4.67446 - 4.67446i) q^{92} +(2.86379 - 0.767349i) q^{93} +(2.80605 + 4.86023i) q^{94} +(-4.86023 - 2.80605i) q^{96} +(4.60689 + 4.60689i) q^{97} +(-4.25742 - 0.700490i) q^{98} +4.55247i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 24 q^{11} + 48 q^{16} - 24 q^{21} - 144 q^{26} - 36 q^{31} - 48 q^{36} + 48 q^{46} + 24 q^{51} + 168 q^{56} + 144 q^{61} - 72 q^{66} + 96 q^{71} + 12 q^{81} - 168 q^{86} + 12 q^{91} + 144 q^{96}+O(q^{100}) \) 24 * q + 24 * q^11 + 48 * q^16 - 24 * q^21 - 144 * q^26 - 36 * q^31 - 48 * q^36 + 48 * q^46 + 24 * q^51 + 168 * q^56 + 144 * q^61 - 72 * q^66 + 96 * q^71 + 12 * q^81 - 168 * q^86 + 12 * q^91 + 144 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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