LMFDB - Embedded newform 525.2.bc.d.82.4

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			82.4
Character	$\chi$	$=$	525.82
Dual form			525.2.bc.d.493.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.595377 - 0.159531i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-1.40303 + 0.810038i) q^{4} -0.616380i q^{6} +(-2.22322 + 1.43432i) q^{7} +(-1.57780 + 1.57780i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.595377 - 0.159531i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-1.40303 + 0.810038i) q^{4} -0.616380i q^{6} +(-2.22322 + 1.43432i) q^{7} +(-1.57780 + 1.57780i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.27624 + 3.94256i) q^{11} +(0.419306 + 1.56487i) q^{12} +(-0.0478013 - 0.0478013i) q^{13} +(-1.09484 + 1.20864i) q^{14} +(0.932399 - 1.61496i) q^{16} +(-4.03037 - 1.07994i) q^{17} +(-0.595377 - 0.159531i) q^{18} +(-3.38472 + 5.86251i) q^{19} +(0.810038 + 2.51870i) q^{21} +(1.98418 + 1.98418i) q^{22} +(1.05611 + 3.94144i) q^{23} +(1.11567 + 1.93240i) q^{24} +(-0.0360856 - 0.0208340i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.95738 - 3.81329i) q^{28} +6.68768i q^{29} +(-2.56760 + 1.48241i) q^{31} +(1.45252 - 5.42088i) q^{32} +(4.39735 - 1.17827i) q^{33} -2.57188 q^{34} +1.62008 q^{36} +(7.13416 - 1.91159i) q^{37} +(-1.07994 + 4.03037i) q^{38} +(-0.0585444 + 0.0338006i) q^{39} +0.956914i q^{41} +(0.884088 + 1.37035i) q^{42} +(3.47918 - 3.47918i) q^{43} +(-6.38724 - 3.68768i) q^{44} +(1.25756 + 2.17816i) q^{46} +(-2.35653 - 8.79471i) q^{47} +(-1.31861 - 1.31861i) q^{48} +(2.88543 - 6.37764i) q^{49} +(-2.08628 + 3.61353i) q^{51} +(0.105787 + 0.0283456i) q^{52} +(-12.1130 - 3.24567i) q^{53} +(-0.308190 + 0.533801i) q^{54} +(1.24472 - 5.77086i) q^{56} +(4.78672 + 4.78672i) q^{57} +(1.06689 + 3.98169i) q^{58} +(1.09484 + 1.89631i) q^{59} +(0.569886 + 0.329024i) q^{61} +(-1.29220 + 1.29220i) q^{62} +(2.64253 - 0.130550i) q^{63} +0.270405i q^{64} +(2.43011 - 1.40303i) q^{66} +(-2.72003 + 10.1513i) q^{67} +(6.52951 - 1.74958i) q^{68} +4.08048 q^{69} +3.58273 q^{71} +(2.15531 - 0.577514i) q^{72} +(-1.98972 + 7.42573i) q^{73} +(3.94256 - 2.27624i) q^{74} -10.9670i q^{76} +(-10.7155 - 5.50032i) q^{77} +(-0.0294638 + 0.0294638i) q^{78} +(4.84093 + 2.79491i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.152657 + 0.569725i) q^{82} +(-7.19308 - 7.19308i) q^{83} +(-3.17675 - 2.87764i) q^{84} +(1.51639 - 2.62646i) q^{86} +(6.45980 + 1.73090i) q^{87} +(-9.81200 - 2.62912i) q^{88} +(7.86428 - 13.6213i) q^{89} +(0.174835 + 0.0377104i) q^{91} +(-4.67446 - 4.67446i) q^{92} +(0.767349 + 2.86379i) q^{93} +(-2.80605 - 4.86023i) q^{94} +(-4.86023 - 2.80605i) q^{96} +(4.60689 - 4.60689i) q^{97} +(0.700490 - 4.25742i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.595377	−	0.159531i	0.420995	−	0.112805i	−0.0421009	−	0.999113i	$-0.513405\pi$
$2$	0.595377	−	0.159531i	0.420995	−	0.112805i	0.463096	+	0.886308i	$0.346738\pi$
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	−1.40303	+	0.810038i	−0.701513	+	0.405019i
$5$		0			0
$5$		0			0
$6$		−	0.616380i		−	0.251636i
$7$	−2.22322	+	1.43432i	−0.840299	+	0.542123i
$7$	−2.22322	+	1.43432i	−0.840299	+	0.542123i
$8$	−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	$0.592562\pi$
$12$	0.419306	+	1.56487i	0.121043	+	0.451740i
$13$	−0.0478013	−	0.0478013i	−0.0132577	−	0.0132577i	0.700447	−	0.713705i	$-0.252984\pi$
$13$	−0.0478013	−	0.0478013i	−0.0132577	−	0.0132577i	−0.713705	+	0.700447i	$0.752984\pi$
$14$	−1.09484	+	1.20864i	−0.292607	+	0.323022i
$15$		0			0
$16$	0.932399	−	1.61496i	0.233100	−	0.403741i
$17$	−4.03037	−	1.07994i	−0.977509	−	0.261923i	−0.265514	−	0.964107i	$-0.585542\pi$
$17$	−4.03037	−	1.07994i	−0.977509	−	0.261923i	−0.711995	+	0.702184i	$0.752208\pi$
$18$	−0.595377	−	0.159531i	−0.140332	−	0.0376018i
$19$	−3.38472	+	5.86251i	−0.776509	+	1.34495i	0.157434	+	0.987530i	$0.449678\pi$
$19$	−3.38472	+	5.86251i	−0.776509	+	1.34495i	−0.933943	+	0.357423i	$0.883655\pi$
$20$		0			0
$21$	0.810038	+	2.51870i	0.176765	+	0.549625i
$22$	1.98418	+	1.98418i	0.423029	+	0.423029i
$23$	1.05611	+	3.94144i	0.220213	+	0.821848i	0.984266	+	0.176694i	$0.0565401\pi$
$23$	1.05611	+	3.94144i	0.220213	+	0.821848i	−0.764053	+	0.645154i	$0.776793\pi$
$24$	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
$28$	1.95738	−	3.81329i	0.369911	−	0.720644i
$29$			6.68768i			1.24187i	0.783862	+	0.620935i	$0.213247\pi$
$29$			6.68768i			1.24187i	−0.783862	+	0.620935i	$0.786753\pi$
$30$		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	$0.419117\pi$
$32$	1.45252	−	5.42088i	0.256772	−	0.958285i
$33$	4.39735	−	1.17827i	0.765481	−	0.205110i
$34$	−2.57188			−0.441073
$35$		0			0
$36$	1.62008			0.270013
$37$	7.13416	−	1.91159i	1.17285	−	0.314264i	0.380762	−	0.924673i	$-0.375662\pi$
$37$	7.13416	−	1.91159i	1.17285	−	0.314264i	0.792086	+	0.610409i	$0.208995\pi$
$38$	−1.07994	+	4.03037i	−0.175189	+	0.653813i
$39$	−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	$0.976193\pi$
$42$	0.884088	+	1.37035i	0.136418	+	0.211449i
$43$	3.47918	−	3.47918i	0.530570	−	0.530570i	−0.390172	−	0.920742i	$-0.627584\pi$
$43$	3.47918	−	3.47918i	0.530570	−	0.530570i	0.920742	+	0.390172i	$0.127584\pi$
$44$	−6.38724	−	3.68768i	−0.962913	−	0.555938i
$45$		0			0
$46$	1.25756	+	2.17816i	0.185418	+	0.321153i
$47$	−2.35653	−	8.79471i	−0.343736	−	1.28284i	−0.894082	−	0.447903i	$-0.852171\pi$
$47$	−2.35653	−	8.79471i	−0.343736	−	1.28284i	0.550346	−	0.834937i	$-0.314496\pi$
$48$	−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
$52$	0.105787	+	0.0283456i	0.0146701	+	0.00393083i
$53$	−12.1130	−	3.24567i	−1.66385	−	0.445827i	−0.700408	−	0.713743i	$-0.746998\pi$
$53$	−12.1130	−	3.24567i	−1.66385	−	0.445827i	−0.963442	+	0.267916i	$0.913665\pi$
$54$	−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
$58$	1.06689	+	3.98169i	0.140090	+	0.522822i
$59$	1.09484	+	1.89631i	0.142536	+	0.246879i	0.928451	−	0.371455i	$-0.121141\pi$
$59$	1.09484	+	1.89631i	0.142536	+	0.246879i	−0.785915	+	0.618334i	$0.787808\pi$
$60$		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
$63$	2.64253	−	0.130550i	0.332927	−	0.0164477i
$64$			0.270405i			0.0338006i
$65$		0			0
$66$	2.43011	−	1.40303i	0.299126	−	0.172701i
$67$	−2.72003	+	10.1513i	−0.332305	+	1.24018i	0.574457	+	0.818535i	$0.305213\pi$
$67$	−2.72003	+	10.1513i	−0.332305	+	1.24018i	−0.906762	+	0.421643i	$0.861453\pi$
$68$	6.52951	−	1.74958i	0.791820	−	0.212167i
$69$	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	$0.431808\pi$
$72$	2.15531	−	0.577514i	0.254006	−	0.0680607i
$73$	−1.98972	+	7.42573i	−0.232879	+	0.869115i	0.746215	+	0.665705i	$0.231869\pi$
$73$	−1.98972	+	7.42573i	−0.232879	+	0.869115i	−0.979094	+	0.203410i	$0.934797\pi$
$74$	3.94256	−	2.27624i	0.458313	−	0.264607i
$75$		0			0
$76$		−	10.9670i		−	1.25800i
$77$	−10.7155	−	5.50032i	−1.22114	−	0.626820i
$78$	−0.0294638	+	0.0294638i	−0.00333611	+	0.00333611i
$79$	4.84093	+	2.79491i	0.544647	+	0.314452i	0.746960	−	0.664869i	$-0.231513\pi$
$79$	4.84093	+	2.79491i	0.544647	+	0.314452i	−0.202313	+	0.979321i	$0.564846\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	0.152657	+	0.569725i	0.0168582	+	0.0629156i
$83$	−7.19308	−	7.19308i	−0.789543	−	0.789543i	0.191876	−	0.981419i	$-0.438543\pi$
$83$	−7.19308	−	7.19308i	−0.789543	−	0.789543i	−0.981419	+	0.191876i	$0.938543\pi$
$84$	−3.17675	−	2.87764i	−0.346611	−	0.313976i
$85$		0			0
$86$	1.51639	−	2.62646i	0.163516	−	0.283219i
$87$	6.45980	+	1.73090i	0.692563	+	0.185572i
$88$	−9.81200	−	2.62912i	−1.04596	−	0.280265i
$89$	7.86428	−	13.6213i	0.833612	−	1.44386i	−0.0615429	−	0.998104i	$-0.519602\pi$
$89$	7.86428	−	13.6213i	0.833612	−	1.44386i	0.895155	−	0.445755i	$-0.147065\pi$
$90$		0			0
$91$	0.174835	+	0.0377104i	0.0183277	+	0.00395312i
$92$	−4.67446	−	4.67446i	−0.487346	−	0.487346i
$93$	0.767349	+	2.86379i	0.0795704	+	0.296961i
$94$	−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	−0.433429	−	0.901188i	$-0.642696\pi$
$97$	4.60689	−	4.60689i	0.467759	−	0.467759i	0.901188	+	0.433429i	$0.142696\pi$
$98$	0.700490	−	4.25742i	0.0707602	−	0.430064i
$99$		−	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	$0.915931\pi$
$102$	−0.665651	+	2.48424i	−0.0659092	+	0.245977i
$103$	16.3510	−	4.38124i	1.61111	−	0.431697i	0.662740	−	0.748850i	$-0.269393\pi$
$103$	16.3510	−	4.38124i	1.61111	−	0.431697i	0.948374	+	0.317153i	$0.102727\pi$
$104$	0.150841			0.0147912
$105$		0			0
$106$	−7.72960			−0.750765
$107$	0.595377	−	0.159531i	0.0575573	−	0.0154224i	−0.229926	−	0.973208i	$-0.573848\pi$
$107$	0.595377	−	0.159531i	0.0575573	−	0.0154224i	0.287483	+	0.957786i	$0.407182\pi$
$108$	0.419306	−	1.56487i	0.0403478	−	0.150580i
$109$	1.49392	−	0.862513i	0.143091	−	0.0826137i	−0.426745	−	0.904372i	$-0.640340\pi$
$109$	1.49392	−	0.862513i	0.143091	−	0.0826137i	0.569836	+	0.821758i	$0.307007\pi$
$110$		0			0
$111$		−	7.38583i		−	0.701032i
$112$	0.243449	+	4.92778i	0.0230037	+	0.465631i
$113$	−9.57344	+	9.57344i	−0.900594	+	0.900594i	−0.995487	−	0.0948937i	$-0.969749\pi$
$113$	−9.57344	+	9.57344i	−0.900594	+	0.900594i	0.0948937	+	0.995487i	$0.469749\pi$
$114$	3.61353	+	2.08628i	0.338439	+	0.195398i
$115$		0			0
$116$	−5.41727	−	9.38299i	−0.502981	−	0.871189i
$117$	0.0174965	+	0.0652978i	0.00161755	+	0.00603678i
$118$	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
$122$	0.391787	+	0.104979i	0.0354707	+	0.00950435i
$123$	0.924308	+	0.247668i	0.0833420	+	0.0223314i
$124$	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	$-0.184868\pi$
$127$	3.23839	+	3.23839i	0.287360	+	0.287360i	−0.548675	+	0.836036i	$0.684868\pi$
$128$	2.94818	+	11.0028i	0.260585	+	0.972515i
$129$	−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
$133$	−0.883749	−	17.8885i	−0.0766307	−	1.55113i
$134$			6.47778i			0.559595i
$135$		0			0
$136$	8.06303	−	4.65519i	0.691399	−	0.399180i
$137$	−2.44802	+	9.13612i	−0.209148	+	0.780552i	0.778997	+	0.627028i	$0.215729\pi$
$137$	−2.44802	+	9.13612i	−0.209148	+	0.780552i	−0.988145	+	0.153524i	$0.950938\pi$
$138$	2.42943	−	0.650963i	0.206806	−	0.0554136i
$139$	21.5411			1.82709			0.913546	−	0.406735i	$-0.133333\pi$
$139$	21.5411			1.82709			0.913546	+	0.406735i	$0.133333\pi$
$140$		0			0
$141$	−9.10495			−0.766775
$142$	2.13307	−	0.571556i	0.179004	−	0.0479639i
$143$	0.0796523	−	0.297267i	0.00666086	−	0.0248587i
$144$	−1.61496	+	0.932399i	−0.134580	+	0.0776999i
$145$		0			0
$146$			4.73853i			0.392163i
$147$	−5.41352	−	4.43777i	−0.446500	−	0.366021i
$148$	−8.46096	+	8.46096i	−0.695486	+	0.695486i
$149$	−4.53810	−	2.62008i	−0.371776	−	0.214645i	0.302458	−	0.953163i	$-0.402193\pi$
$149$	−4.53810	−	2.62008i	−0.371776	−	0.214645i	−0.674234	+	0.738518i	$0.735526\pi$
$150$		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	$0.841757\pi$
$152$	−3.90945	−	14.5903i	−0.317098	−	1.18343i
$153$	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
$157$	−1.59851	−	0.428319i	−0.127575	−	0.0341836i	0.194467	−	0.980909i	$-0.437702\pi$
$157$	−1.59851	−	0.428319i	−0.127575	−	0.0341836i	−0.322042	+	0.946726i	$0.604369\pi$
$158$	3.32805	+	0.891749i	0.264766	+	0.0709438i
$159$	−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
$163$	6.11167	+	22.8091i	0.478703	+	1.78654i	0.606881	+	0.794793i	$0.292421\pi$
$163$	6.11167	+	22.8091i	0.478703	+	1.78654i	−0.128178	+	0.991751i	$0.540913\pi$
$164$	−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	−0.811987	−	0.583675i	$-0.801614\pi$
$167$	−2.95044	+	2.95044i	−0.228312	+	0.228312i	0.583675	+	0.811987i	$0.301614\pi$
$168$	−5.25207	−	2.69592i	−0.405206	−	0.207995i
$169$		−	12.9954i		−	0.999648i
$170$		0			0
$171$	5.86251	−	3.38472i	0.448318	−	0.258836i
$172$	−2.06312	+	7.69966i	−0.157311	+	0.587093i
$173$	9.92045	−	2.65818i	0.754238	−	0.202097i	0.138841	−	0.990315i	$-0.455662\pi$
$173$	9.92045	−	2.65818i	0.754238	−	0.202097i	0.615397	+	0.788217i	$0.288996\pi$
$174$	4.12215			0.312499
$175$		0			0
$176$	8.48944			0.639916
$177$	2.11506	−	0.566729i	0.158978	−	0.0425980i
$178$	2.50919	−	9.36443i	0.188072	−	0.701894i
$179$	1.49787	−	0.864798i	0.111956	−	0.0646380i	−0.442976	−	0.896533i	$-0.646077\pi$
$179$	1.49787	−	0.864798i	0.111956	−	0.0646380i	0.554933	+	0.831895i	$0.312744\pi$
$180$		0			0
$181$			6.53527i			0.485763i	0.970056	+	0.242881i	$0.0780926\pi$
$181$			6.53527i			0.485763i	−0.970056	+	0.242881i	$0.921907\pi$
$182$	0.110109	−	0.00543975i	0.00816182	−	0.000403221i
$183$	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
$187$	−4.91638	−	18.3482i	−0.359521	−	1.34175i
$188$	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	$-0.00702423\pi$
$192$	0.261191	+	0.0699860i	0.0188498	+	0.00505080i
$193$	6.16960	+	1.65314i	0.444098	+	0.118996i	0.473936	−	0.880559i	$-0.342833\pi$
$193$	6.16960	+	1.65314i	0.444098	+	0.118996i	−0.0298386	+	0.999555i	$0.509499\pi$
$194$	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	$-0.0936563\pi$
$197$	9.36211	+	9.36211i	0.667023	+	0.667023i	−0.290003	+	0.957026i	$0.593656\pi$
$198$	−0.726260	−	2.71044i	−0.0516131	−	0.192623i
$199$	6.44042	+	11.1551i	0.456549	+	0.790767i	0.998776	−	0.0494656i	$-0.0157518\pi$
$199$	6.44042	+	11.1551i	0.456549	+	0.790767i	−0.542226	+	0.840232i	$0.682418\pi$
$200$		0			0
$201$	9.10140	+	5.25470i	0.641963	+	0.370638i
$202$	−8.46712	+	8.46712i	−0.595745	+	0.595745i
$203$	−9.59229	−	14.8682i	−0.673247	−	1.04354i
$204$		−	6.75985i		−	0.473284i
$205$		0			0
$206$	9.03609	−	5.21699i	0.629574	−	0.363485i
$207$	1.05611	−	3.94144i	0.0734045	−	0.273949i
$208$	−0.121767	+	0.0326274i	−0.00844303	+	0.00226230i
$209$	−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	$0.355682\pi$
$212$	19.6240	−	5.25823i	1.34778	−	0.361137i
$213$	0.927278	−	3.46065i	0.0635361	−	0.237120i
$214$	0.329024	−	0.189962i	0.0224916	−	0.0129855i
$215$		0			0
$216$		−	2.23134i		−	0.151824i
$217$	3.58210	−	6.97849i	0.243169	−	0.473731i
$218$	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
$222$	−1.17827	−	4.39735i	−0.0790801	−	0.295131i
$223$	−17.7519	−	17.7519i	−1.18875	−	1.18875i	−0.977412	−	0.211342i	$-0.932217\pi$
$223$	−17.7519	−	17.7519i	−1.18875	−	1.18875i	−0.211342	−	0.977412i	$-0.567783\pi$
$224$	4.54602	+	14.1352i	0.303744	+	0.944448i
$225$		0			0
$226$	−4.17255	+	7.22707i	−0.277554	+	0.480738i
$227$	21.6198	+	5.79300i	1.43496	+	0.384495i	0.890764	−	0.454466i	$-0.150170\pi$
$227$	21.6198	+	5.79300i	1.43496	+	0.384495i	0.544191	+	0.838961i	$0.316837\pi$
$228$	−10.5933	−	2.83847i	−0.701560	−	0.187982i
$229$	−4.82942	+	8.36480i	−0.319137	+	0.552761i	−0.980308	−	0.197474i	$-0.936726\pi$
$229$	−4.82942	+	8.36480i	−0.319137	+	0.552761i	0.661171	+	0.750235i	$0.270060\pi$
$230$		0			0
$231$	−8.08628	+	8.92678i	−0.532038	+	0.587339i
$232$	−10.5518	−	10.5518i	−0.692759	−	0.692759i
$233$	4.22443	+	15.7658i	0.276751	+	1.03285i	0.954659	+	0.297703i	$0.0962204\pi$
$233$	4.22443	+	15.7658i	0.276751	+	1.03285i	−0.677907	+	0.735147i	$0.737113\pi$
$234$	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
$238$	5.71785	−	3.68890i	0.370633	−	0.239116i
$239$			26.5550i			1.71770i	0.512227	+	0.858850i	$0.328821\pi$
$239$			26.5550i			1.71770i	−0.512227	+	0.858850i	$0.671179\pi$
$240$		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	$0.247541\pi$
$242$	−1.55144	+	5.79006i	−0.0997304	+	0.372199i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−1.06609			−0.0682493
$245$		0			0
$246$	0.589823			0.0376057
$247$	0.442030	−	0.118442i	0.0281257	−	0.00753626i
$248$	1.71222	−	6.39009i	0.108726	−	0.405771i
$249$	−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	$0.687335\pi$
$252$	−3.60179	+	2.32371i	−0.226891	+	0.146380i
$253$	−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
$257$	5.98967	+	22.3537i	0.373625	+	1.39439i	0.855343	+	0.518062i	$0.173346\pi$
$257$	5.98967	+	22.3537i	0.373625	+	1.39439i	−0.481718	+	0.876326i	$0.659987\pi$
$258$	−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
$262$	2.60736	+	0.698641i	0.161083	+	0.0431622i
$263$	−19.7697	−	5.29727i	−1.21905	−	0.326644i	−0.408744	−	0.912649i	$-0.634033\pi$
$263$	−19.7697	−	5.29727i	−1.21905	−	0.326644i	−0.810307	+	0.586005i	$0.800700\pi$
$264$	−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
$268$	−4.40666	−	16.4459i	−0.269179	−	1.00459i
$269$	−11.6898	−	20.2472i	−0.712737	−	1.23450i	−0.963826	−	0.266532i	$-0.914122\pi$
$269$	−11.6898	−	20.2472i	−0.712737	−	1.23450i	0.251089	−	0.967964i	$-0.419211\pi$
$270$		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
$273$	0.0816762	−	0.159118i	0.00494327	−	0.00963025i
$274$			5.82997i			0.352202i
$275$		0			0
$276$	−5.72503	+	3.30534i	−0.344606	+	0.198958i
$277$	−3.76535	+	14.0525i	−0.226238	+	0.844332i	0.755667	+	0.654957i	$0.227313\pi$
$277$	−3.76535	+	14.0525i	−0.226238	+	0.844332i	−0.981905	+	0.189376i	$0.939354\pi$
$278$	12.8251	−	3.43647i	0.769197	−	0.206106i
$279$	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	$0.429398\pi$
$282$	−5.42088	+	1.45252i	−0.322809	+	0.0864963i
$283$	−4.93388	+	18.4135i	−0.293288	+	1.09457i	0.649279	+	0.760551i	$0.275071\pi$
$283$	−4.93388	+	18.4135i	−0.293288	+	1.09457i	−0.942567	+	0.334017i	$0.891596\pi$
$284$	−5.02666	+	2.90215i	−0.298278	+	0.172211i
$285$		0			0
$286$		−	0.189693i		−	0.0112168i
$287$	−1.37252	−	2.12743i	−0.0810176	−	0.125578i
$288$	−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
$292$	−3.22349	−	12.0302i	−0.188641	−	0.704016i
$293$	−5.21516	−	5.21516i	−0.304673	−	0.304673i	0.538166	−	0.842839i	$-0.319117\pi$
$293$	−5.21516	−	5.21516i	−0.304673	−	0.304673i	−0.842839	+	0.538166i	$0.819117\pi$
$294$	−3.93105	−	1.77852i	−0.229263	−	0.103726i
$295$		0			0
$296$	−8.24015	+	14.2724i	−0.478949	+	0.829564i
$297$	−4.39735	−	1.17827i	−0.255160	−	0.0683700i
$298$	−3.11987	−	0.835966i	−0.180729	−	0.0484262i
$299$	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
$303$	5.02804	+	18.7649i	0.288853	+	1.07801i
$304$	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	−0.195958	−	0.980612i	$-0.562782\pi$
$307$	13.7482	−	13.7482i	0.784654	−	0.784654i	0.980612	+	0.195958i	$0.0627818\pi$
$308$	19.4896	−	0.962850i	1.11052	−	0.0548634i
$309$		−	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	$0.316429\pi$
$312$	0.0390407	−	0.145702i	0.00221024	−	0.00824873i
$313$	10.4249	−	2.79334i	0.589249	−	0.157889i	0.0481390	−	0.998841i	$-0.484671\pi$
$313$	10.4249	−	2.79334i	0.589249	−	0.157889i	0.541110	+	0.840952i	$0.318004\pi$
$314$	−1.02005			−0.0575646
$315$		0			0
$316$	−9.05594			−0.509436
$317$	−16.7928	+	4.49962i	−0.943178	+	0.252724i	−0.697465	−	0.716619i	$-0.745689\pi$
$317$	−16.7928	+	4.49962i	−0.943178	+	0.252724i	−0.245713	+	0.969343i	$0.579022\pi$
$318$	−2.00057	+	7.46622i	−0.112186	+	0.418685i
$319$	−26.3666	+	15.2227i	−1.47624	+	0.852310i
$320$		0			0
$321$		−	0.616380i		−	0.0344030i
$322$	−5.92003	−	3.03879i	−0.329911	−	0.169345i
$323$	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
$327$	−0.446469	−	1.66625i	−0.0246898	−	0.0921436i
$328$	−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	$-0.0343366\pi$
$332$	15.9188	+	4.26542i	0.873655	+	0.234095i
$333$	−7.13416	−	1.91159i	−0.390950	−	0.104755i
$334$	−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	$-0.148519\pi$
$337$	8.13737	+	8.13737i	0.443271	+	0.443271i	−0.449839	+	0.893110i	$0.648519\pi$
$338$	−2.07317	−	7.73718i	−0.112766	−	0.420847i
$339$	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
$343$	2.73264	+	18.3176i	0.147549	+	0.989055i
$344$			10.9789i			0.591942i
$345$		0			0
$346$	5.48235	−	3.16524i	0.294733	−	0.170164i
$347$	−4.08164	+	15.2329i	−0.219114	+	0.817744i	0.765564	+	0.643360i	$0.222460\pi$
$347$	−4.08164	+	15.2329i	−0.219114	+	0.817744i	−0.984678	+	0.174384i	$0.944207\pi$
$348$	−10.4654	+	2.80419i	−0.561003	+	0.150320i
$349$	−5.69544			−0.304870			−0.152435	−	0.988313i	$-0.548711\pi$
$349$	−5.69544			−0.304870			−0.152435	+	0.988313i	$0.548711\pi$
$350$		0			0
$351$	0.0676012			0.00360829
$352$	24.6784	−	6.61256i	1.31536	−	0.352451i
$353$	2.57852	−	9.62318i	0.137241	−	0.512190i	−0.862738	−	0.505652i	$-0.831252\pi$
$353$	2.57852	−	9.62318i	0.137241	−	0.512190i	0.999979	−	0.00653851i	$-0.00208129\pi$
$354$	1.16885	−	0.674835i	0.0621236	−	0.0358671i
$355$		0			0
$356$			25.4815i			1.35052i
$357$	−0.544725	−	11.0261i	−0.0288299	−	0.583562i
$358$	0.753838	−	0.753838i	0.0398416	−	0.0398416i
$359$	4.60061	+	2.65616i	0.242811	+	0.140187i	0.616468	−	0.787380i	$-0.288563\pi$
$359$	4.60061	+	2.65616i	0.242811	+	0.140187i	−0.373657	+	0.927567i	$0.621896\pi$
$360$		0			0
$361$	−13.4127	−	23.2315i	−0.705932	−	1.22271i
$362$	1.04258	+	3.89095i	0.0547966	+	0.204504i
$363$	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
$367$	−32.7089	−	8.76433i	−1.70739	−	0.457494i	−0.732608	−	0.680650i	$-0.761697\pi$
$367$	−32.7089	−	8.76433i	−1.70739	−	0.457494i	−0.974783	+	0.223156i	$0.928364\pi$
$368$	7.34999	+	1.96942i	0.383145	+	0.102663i
$369$	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
$373$	1.44378	+	5.38828i	0.0747563	+	0.278994i	0.993178	−	0.116609i	$-0.0372023\pi$
$373$	1.44378	+	5.38828i	0.0747563	+	0.278994i	−0.918422	+	0.395603i	$0.870536\pi$
$374$	−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
$378$	−0.0804681	−	1.62880i	−0.00413883	−	0.0837765i
$379$		−	27.2704i		−	1.40079i	−0.713757	−	0.700393i	$-0.753008\pi$
$379$		−	27.2704i		−	1.40079i	0.713757	−	0.700393i	$-0.246992\pi$
$380$		0			0
$381$	3.96620	−	2.28989i	0.203195	−	0.117314i
$382$	2.28849	−	8.54075i	0.117089	−	0.436983i
$383$	4.66981	−	1.25127i	0.238616	−	0.0639370i	−0.137529	−	0.990498i	$-0.543916\pi$
$383$	4.66981	−	1.25127i	0.238616	−	0.0639370i	0.376145	+	0.926561i	$0.377249\pi$
$384$	11.3909			0.581289
$385$		0			0
$386$	3.93697			0.200386
$387$	−4.75265	+	1.27347i	−0.241591	+	0.0647341i
$388$	−2.73183	+	10.1953i	−0.138688	+	0.517590i
$389$	20.0641	−	11.5840i	1.01729	−	0.587332i	0.103971	−	0.994580i	$-0.466845\pi$
$389$	20.0641	−	11.5840i	1.01729	−	0.587332i	0.913317	+	0.407249i	$0.133512\pi$
$390$		0			0
$391$		−	17.0260i		−	0.861043i
$392$	5.50999	+	14.6152i	0.278297	+	0.738181i
$393$	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
$397$	−3.34597	−	12.4873i	−0.167929	−	0.626721i	−0.997648	−	0.0685396i	$-0.978166\pi$
$397$	−3.34597	−	12.4873i	−0.167929	−	0.626721i	0.829719	−	0.558181i	$-0.188501\pi$
$398$	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	$0.255598\pi$
$402$	6.25705	+	1.67657i	0.312073	+	0.0836198i
$403$	0.193596	+	0.0518738i	0.00964368	+	0.00258402i
$404$	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
$408$	−2.40971	−	8.99314i	−0.119298	−	0.445227i
$409$	−8.59239	−	14.8824i	−0.424866	−	0.735890i	0.571542	−	0.820573i	$-0.306346\pi$
$409$	−8.59239	−	14.8824i	−0.424866	−	0.735890i	−0.996408	+	0.0846832i	$0.973012\pi$
$410$		0			0
$411$	8.19122	+	4.72921i	0.404043	+	0.233275i
$412$	−19.3920	+	19.3920i	−0.955373	+	0.955373i
$413$	−5.15399	−	2.64557i	−0.253611	−	0.130180i
$414$		−	2.51513i		−	0.123612i
$415$		0			0
$416$	−0.328557	+	0.189693i	−0.0161089	+	0.00930045i
$417$	5.57525	−	20.8071i	0.273021	−	1.01893i
$418$	−18.3482	+	4.91638i	−0.897439	+	0.240468i
$419$	−36.0246			−1.75992			−0.879959	−	0.475050i	$-0.842430\pi$
$419$	−36.0246			−1.75992			−0.879959	+	0.475050i	$0.842430\pi$
$420$		0			0
$421$	−31.9349			−1.55641			−0.778206	−	0.628009i	$-0.783870\pi$
$421$	−31.9349			−1.55641			−0.778206	+	0.628009i	$0.783870\pi$
$422$	7.57619	−	2.03003i	0.368803	−	0.0988205i
$423$	−2.35653	+	8.79471i	−0.114579	+	0.427613i
$424$	24.2329	−	13.9909i	1.17685	−	0.679456i
$425$		0			0
$426$		−	2.20832i		−	0.106994i
$427$	−1.73891	+	0.0859079i	−0.0841518	+	0.00415737i
$428$	−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	$-0.432981\pi$
$432$	0.482645	+	1.80126i	0.0232213	+	0.0866630i
$433$	11.1638	+	11.1638i	0.536500	+	0.536500i	0.922499	−	0.385999i	$-0.126143\pi$
$433$	11.1638	+	11.1638i	0.536500	+	0.536500i	−0.385999	+	0.922499i	$0.626143\pi$
$434$	1.01942	−	4.72629i	0.0489335	−	0.226869i
$435$		0			0
$436$	−1.39734	+	2.42026i	−0.0669202	+	0.115909i
$437$	−26.6814	−	7.14926i	−1.27634	−	0.341995i
$438$	4.57707	+	1.22642i	0.218701	+	0.0586007i
$439$	−1.40303	+	2.43011i	−0.0669628	+	0.115983i	−0.897563	−	0.440886i	$-0.854664\pi$
$439$	−1.40303	+	2.43011i	−0.0669628	+	0.115983i	0.830600	+	0.556869i	$0.187998\pi$
$440$		0			0
$441$	−5.68768	+	4.08048i	−0.270842	+	0.194309i
$442$	0.122939	+	0.122939i	0.00584761	+	0.00584761i
$443$	−3.48255	−	12.9971i	−0.165461	−	0.617509i	−0.997981	−	0.0635141i	$-0.979769\pi$
$443$	−3.48255	−	12.9971i	−0.165461	−	0.617509i	0.832520	−	0.553995i	$-0.186897\pi$
$444$	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
$448$	−0.387848	−	0.601170i	−0.0183241	−	0.0284026i
$449$		−	1.58525i		−	0.0748127i	−0.999300	−	0.0374063i	$-0.988090\pi$
$449$		−	1.58525i		−	0.0748127i	0.999300	−	0.0374063i	$-0.0119096\pi$
$450$		0			0
$451$	−3.77269	+	2.17816i	−0.177649	+	0.102566i
$452$	5.67695	−	21.1866i	0.267021	−	0.996536i
$453$	−0.628170	+	0.168318i	−0.0295140	+	0.00790825i
$454$	13.7961			0.647483
$455$		0			0
$456$	−15.1049			−0.707354
$457$	−30.1472	+	8.07792i	−1.41023	+	0.377869i	−0.882006	−	0.471238i	$-0.843807\pi$
$457$	−30.1472	+	8.07792i	−1.41023	+	0.377869i	−0.528220	+	0.849107i	$0.677140\pi$
$458$	−1.54088	+	5.75065i	−0.0720007	+	0.268710i
$459$	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	$-0.248970\pi$
$462$	−3.39029	+	6.60481i	−0.157730	+	0.307284i
$463$	8.84347	−	8.84347i	0.410991	−	0.410991i	−0.471093	−	0.882084i	$-0.656140\pi$
$463$	8.84347	−	8.84347i	0.410991	−	0.410991i	0.882084	+	0.471093i	$0.156140\pi$
$464$	10.8003	+	6.23558i	0.501393	+	0.289480i
$465$		0			0
$466$	5.03025	+	8.71265i	0.233022	+	0.403606i
$467$	7.53055	+	28.1044i	0.348472	+	1.30052i	0.888503	+	0.458871i	$0.151746\pi$
$467$	7.53055	+	28.1044i	0.348472	+	1.30052i	−0.540031	+	0.841645i	$0.681587\pi$
$468$	−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
$472$	−4.71943	−	1.26457i	−0.217229	−	0.0582064i
$473$	21.6363	+	5.79744i	0.994839	+	0.266566i
$474$	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
$478$	4.23634	+	15.8102i	0.193766	+	0.723144i
$479$	8.04387	+	13.9324i	0.367534	+	0.636588i	0.989179	−	0.146711i	$-0.0468688\pi$
$479$	8.04387	+	13.9324i	0.367534	+	0.636588i	−0.621645	+	0.783299i	$0.713535\pi$
$480$		0			0
$481$	−0.432399	−	0.249646i	−0.0197157	−	0.0113829i
$482$	3.60328	−	3.60328i	0.164125	−	0.164125i
$483$	−9.07182	+	5.85273i	−0.412782	+	0.266308i
$484$		−	15.7553i		−	0.716149i
$485$		0			0
$486$	0.533801	−	0.308190i	0.0242137	−	0.0139798i
$487$	4.58571	−	17.1141i	0.207798	−	0.775514i	−0.780780	−	0.624806i	$-0.785178\pi$
$487$	4.58571	−	17.1141i	0.207798	−	0.775514i	0.988578	−	0.150708i	$-0.0481552\pi$
$488$	−1.41830	+	0.380032i	−0.0642033	+	0.0172032i
$489$	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	$0.317276\pi$
$492$	−1.49745	+	0.401240i	−0.0675102	+	0.0180893i
$493$	7.22226	−	26.9538i	0.325274	−	1.21394i
$494$	0.244279	−	0.141035i	0.0109907	−	0.00634546i
$495$		0			0
$496$			5.52877i			0.248249i
$497$	−7.96520	+	5.13879i	−0.357288	+	0.230506i
$498$	−4.43367	+	4.43367i	−0.198677	+	0.198677i
$499$	25.5307	+	14.7402i	1.14291	+	0.659860i	0.947150	−	0.320792i	$-0.103949\pi$
$499$	25.5307	+	14.7402i	1.14291	+	0.659860i	0.195761	+	0.980652i	$0.437282\pi$
$500$		0			0
$501$	2.08628	+	3.61353i	0.0932079	+	0.161441i
$502$	4.20444	+	15.6912i	0.187653	+	0.700332i
$503$	−13.0248	−	13.0248i	−0.580745	−	0.580745i	0.354363	−	0.935108i	$-0.384698\pi$
$503$	−13.0248	−	13.0248i	−0.580745	−	0.580745i	−0.935108	+	0.354363i	$0.884698\pi$
$504$	−3.96339	+	4.37535i	−0.176544	+	0.194894i
$505$		0			0
$506$	−5.72503	+	9.91603i	−0.254508	+	0.440821i
$507$	−12.5526	−	3.36346i	−0.557481	−	0.149377i
$508$	−7.16676	−	1.92033i	−0.317974	−	0.0852008i
$509$	13.9318	−	24.1306i	0.617517	−	1.06957i	−0.372420	−	0.928064i	$-0.621472\pi$
$509$	13.9318	−	24.1306i	0.617517	−	1.06957i	0.989937	−	0.141507i	$-0.0451948\pi$
$510$		0			0
$511$	−6.22731	−	19.3629i	−0.275480	−	0.856566i
$512$	−13.2847	−	13.2847i	−0.587108	−	0.587108i
$513$	−1.75206	−	6.53878i	−0.0773554	−	0.288694i
$514$	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
$518$	−5.50032	+	10.7155i	−0.241670	+	0.470811i
$519$		−	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	$0.426527\pi$
$522$	1.06689	−	3.98169i	0.0466965	−	0.174274i
$523$	−11.7286	+	3.14266i	−0.512854	+	0.137419i	−0.505959	−	0.862557i	$-0.668861\pi$
$523$	−11.7286	+	3.14266i	−0.512854	+	0.137419i	−0.00689484	+	0.999976i	$0.502195\pi$
$524$	−7.09488			−0.309941
$525$		0			0
$526$	−12.6155			−0.550062
$527$	11.9493	−	3.20180i	0.520520	−	0.139473i
$528$	2.19723	−	8.20017i	0.0956221	−	0.356867i
$529$	5.49898	−	3.17484i	0.239086	−	0.138036i
$530$		0			0
$531$		−	2.18967i		−	0.0950238i
$532$	15.7302	+	24.3821i	0.681993	+	1.05710i
$533$	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
$537$	−0.447652	−	1.67066i	−0.0193176	−	0.0720943i
$538$	−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	$-0.0269695\pi$
$542$	3.87253	+	1.03764i	0.166339	+	0.0445705i
$543$	6.31258	+	1.69145i	0.270899	+	0.0725872i
$544$	−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	$-0.223208\pi$
$547$	2.78067	+	2.78067i	0.118893	+	0.118893i	−0.645157	+	0.764050i	$0.723208\pi$
$548$	−3.96597	−	14.8012i	−0.169418	−	0.632277i
$549$	−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
$553$	−14.7713	+	0.729749i	−0.628138	+	0.0310321i
$554$			8.96722i			0.380981i
$555$		0			0
$556$	−30.2227	+	17.4491i	−1.28173	+	0.740007i
$557$	4.06007	−	15.1524i	0.172031	−	0.642027i	−0.825008	−	0.565121i	$-0.808829\pi$
$557$	4.06007	−	15.1524i	0.172031	−	0.642027i	0.997038	−	0.0769056i	$-0.0245040\pi$
$558$	1.76518	−	0.472979i	0.0747261	−	0.0200228i
$559$	−0.332619			−0.0140683
$560$		0			0
$561$	−18.9954			−0.801988
$562$	4.39112	−	1.17660i	0.185228	−	0.0496317i
$563$	−1.94624	+	7.26347i	−0.0820243	+	0.306119i	−0.994734	−	0.102490i	$-0.967319\pi$
$563$	−1.94624	+	7.26347i	−0.0820243	+	0.306119i	0.912710	+	0.408608i	$0.133986\pi$
$564$	12.7745	−	7.37535i	0.537903	−	0.310558i
$565$		0			0
$566$			11.7501i			0.493892i
$567$	−2.35377	−	1.20820i	−0.0988491	−	0.0507398i
$568$	−5.65282	+	5.65282i	−0.237187	+	0.237187i
$569$	−22.8780	−	13.2086i	−0.959097	−	0.553735i	−0.0632019	−	0.998001i	$-0.520131\pi$
$569$	−22.8780	−	13.2086i	−0.959097	−	0.553735i	−0.895895	+	0.444266i	$0.853465\pi$
$570$		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	$0.692842\pi$
$572$	0.129043	+	0.481594i	0.00539555	+	0.0201365i
$573$	−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
$577$	15.1195	+	4.05126i	0.629433	+	0.168656i	0.559412	−	0.828890i	$-0.311027\pi$
$577$	15.1195	+	4.05126i	0.629433	+	0.168656i	0.0700205	+	0.997546i	$0.477694\pi$
$578$	0.244210	+	0.0654360i	0.0101578	+	0.00272178i
$579$	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
$583$	−14.7758	−	55.1442i	−0.611953	−	2.28384i
$584$	−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	−0.438545	−	0.898709i	$-0.644506\pi$
$587$	11.1489	−	11.1489i	0.460165	−	0.460165i	0.898709	+	0.438545i	$0.144506\pi$
$588$	11.1901	+	1.84115i	0.461471	+	0.0759277i
$589$		−	20.0701i		−	0.826975i
$590$		0			0
$591$	11.4662	−	6.62001i	0.471656	−	0.272311i
$592$	3.56473	−	13.3038i	0.146510	−	0.546781i
$593$	−40.7267	+	10.9127i	−1.67245	+	0.448131i	−0.965769	−	0.259405i	$-0.916474\pi$
$593$	−40.7267	+	10.9127i	−1.67245	+	0.448131i	−0.706678	+	0.707536i	$0.749807\pi$
$594$	−2.80605			−0.115134
$595$		0			0
$596$	8.48944			0.347741
$597$	12.4419	−	3.33381i	0.509215	−	0.136444i
$598$	0.0440059	−	0.164232i	0.00179953	−	0.00671595i
$599$	15.5885	−	9.00000i	0.636927	−	0.367730i	−0.146503	−	0.989210i	$-0.546802\pi$
$599$	15.5885	−	9.00000i	0.636927	−	0.367730i	0.783430	+	0.621480i	$0.213468\pi$
$600$		0			0
$601$		−	0.158757i		−	0.00647583i	−0.999995	−	0.00323791i	$-0.998969\pi$
$601$		−	0.158757i		−	0.00647583i	0.999995	−	0.00323791i	$-0.00103066\pi$
$602$	0.395928	+	8.01420i	0.0161368	+	0.326635i
$603$	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
$607$	7.14142	+	26.6522i	0.289861	+	1.08178i	0.945213	+	0.326454i	$0.105854\pi$
$607$	7.14142	+	26.6522i	0.289861	+	1.08178i	−0.655352	+	0.755324i	$0.727480\pi$
$608$	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
$612$	−6.52951	−	1.74958i	−0.263940	−	0.0707225i
$613$	29.4790	+	7.89886i	1.19064	+	0.319032i	0.799140	−	0.601144i	$-0.205288\pi$
$613$	29.4790	+	7.89886i	1.19064	+	0.319032i	0.391504	+	0.920177i	$0.371955\pi$
$614$	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	$-0.283989\pi$
$617$	−3.74384	−	3.74384i	−0.150721	−	0.150721i	−0.778440	+	0.627719i	$0.783989\pi$
$618$	−2.70051	−	10.0784i	−0.108630	−	0.405414i
$619$	−1.58876	−	2.75182i	−0.0638577	−	0.110605i	0.832329	−	0.554282i	$-0.187007\pi$
$619$	−1.58876	−	2.75182i	−0.0638577	−	0.110605i	−0.896187	+	0.443677i	$0.853674\pi$
$620$		0			0
$621$	−3.53380	−	2.04024i	−0.141807	−	0.0818720i
$622$	0.815974	−	0.815974i	0.0327176	−	0.0327176i
$623$	2.05336	+	41.5632i	0.0822661	+	1.66519i
$624$			0.126063i			0.00504654i
$625$		0			0
$626$	5.76111	−	3.32618i	0.230260	−	0.132941i
$627$	−7.97622	+	29.7676i	−0.318539	+	1.18881i
$628$	2.58971	−	0.693910i	0.103341	−	0.0276900i
$629$	−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	$0.484753\pi$
$632$	−12.0478	+	3.22820i	−0.479236	+	0.128411i
$633$	3.29348	−	12.2914i	0.130904	−	0.488540i
$634$	−9.28023	+	5.35794i	−0.368565	+	0.212791i
$635$		0			0
$636$		−	20.3163i		−	0.805592i
$637$	−0.442787	+	0.166932i	−0.0175439	+	0.00661409i
$638$	−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	$0.660172\pi$
$642$	−0.0983316	−	0.366979i	−0.00388084	−	0.0144835i
$643$	17.3152	+	17.3152i	0.682845	+	0.682845i	0.960640	−	0.277795i	$-0.0896037\pi$
$643$	17.3152	+	17.3152i	0.682845	+	0.682845i	−0.277795	+	0.960640i	$0.589604\pi$
$644$	17.0971	+	3.68768i	0.673719	+	0.145315i
$645$		0			0
$646$	8.70509	−	15.0777i	0.342497	−	0.593222i
$647$	5.35886	+	1.43590i	0.210679	+	0.0564512i	0.362615	−	0.931939i	$-0.381884\pi$
$647$	5.35886	+	1.43590i	0.210679	+	0.0564512i	−0.151936	+	0.988390i	$0.548551\pi$
$648$	−2.15531	−	0.577514i	−0.0846686	−	0.0226869i
$649$	−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
$653$	−1.83146	−	6.83511i	−0.0716707	−	0.267479i	0.920787	−	0.390065i	$-0.127548\pi$
$653$	−1.83146	−	6.83511i	−0.0716707	−	0.267479i	−0.992458	+	0.122587i	$0.960881\pi$
$654$	−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
$658$	13.2096	+	6.78058i	0.514965	+	0.264334i
$659$			32.2008i			1.25436i	0.778873	+	0.627182i	$0.215792\pi$
$659$			32.2008i			1.25436i	−0.778873	+	0.627182i	$0.784208\pi$
$660$		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	$0.264057\pi$
$662$	3.42677	−	12.7889i	0.133185	−	0.497054i
$663$	0.272458	−	0.0730050i	0.0105814	−	0.00283528i
$664$	22.6984			0.880870
$665$		0			0
$666$	−4.55247			−0.176405
$667$	−26.3591	+	7.06290i	−1.02063	+	0.273477i
$668$	1.74958	−	6.52951i	0.0676932	−	0.252634i
$669$	−21.7415	+	12.5525i	−0.840576	+	0.485307i
$670$		0			0
$671$			2.99575i			0.115650i
$672$	14.8302	−	0.732658i	0.572086	−	0.0282629i
$673$	34.4082	−	34.4082i	1.32634	−	1.32634i	0.417800	−	0.908539i	$-0.362801\pi$
$673$	34.4082	−	34.4082i	1.32634	−	1.32634i	0.908539	−	0.417800i	$-0.137199\pi$
$674$	6.14296	+	3.54664i	0.236618	+	0.136612i
$675$		0			0
$676$	10.5268	+	18.2329i	0.404877	+	0.701267i
$677$	−10.6654	−	39.8037i	−0.409904	−	1.52978i	−0.794829	−	0.606834i	$-0.792439\pi$
$677$	−10.6654	−	39.8037i	−0.409904	−	1.52978i	0.384925	−	0.922948i	$-0.374227\pi$
$678$	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
$682$	−8.03594	−	2.15322i	−0.307712	−	0.0824512i
$683$	10.2464	+	2.74551i	0.392067	+	0.105054i	0.449466	−	0.893297i	$-0.351614\pi$
$683$	10.2464	+	2.74551i	0.392067	+	0.105054i	−0.0573994	+	0.998351i	$0.518281\pi$
$684$	−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
$688$	−2.37476	−	8.86273i	−0.0905370	−	0.337889i
$689$	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
$693$	6.52972	+	10.1212i	0.248044	+	0.384471i
$694$			9.72046i			0.368983i
$695$		0			0
$696$	−12.9233	+	7.46125i	−0.489855	+	0.282818i
$697$	1.03341	−	3.85672i	0.0391430	−	0.146084i
$698$	−3.39094	+	0.908599i	−0.128349	+	0.0343910i
$699$	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	$0.350757\pi$
$702$	0.0402482	−	0.0107845i	0.00151907	−	0.000407034i
$703$	−12.9404	+	48.2943i	−0.488057	+	1.82145i
$704$	−1.06609	+	0.615506i	−0.0401797	+	0.0231978i
$705$		0			0
$706$		−	6.14078i		−	0.231111i
$707$	23.4716	−	45.7264i	0.882741	−	1.71972i
$708$	−2.50842	+	2.50842i	−0.0942721	+	0.0942721i
$709$	−35.0268	−	20.2227i	−1.31546	−	0.759481i	−0.332465	−	0.943116i	$-0.607880\pi$
$709$	−35.0268	−	20.2227i	−1.31546	−	0.759481i	−0.982995	+	0.183635i	$0.941214\pi$
$710$		0			0
$711$	−2.79491	−	4.84093i	−0.104817	−	0.181549i
$712$	9.08346	+	33.8999i	0.340417	+	1.27045i
$713$	−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
$717$	25.6502	+	6.87294i	0.957923	+	0.256675i
$718$	3.16284	+	0.847479i	0.118036	+	0.0316276i
$719$	−19.2343	+	33.3148i	−0.717320	+	1.24243i	0.244738	+	0.969589i	$0.421298\pi$
$719$	−19.2343	+	33.3148i	−0.717320	+	1.24243i	−0.962058	+	0.272845i	$0.912035\pi$
$720$		0			0
$721$	−30.0678	+	33.1931i	−1.11978	+	1.23618i
$722$	−11.6918	−	11.6918i	−0.435122	−	0.435122i
$723$	−2.13974	−	7.98562i	−0.0795778	−	0.296988i
$724$	−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	−0.928705	−	0.370819i	$-0.879077\pi$
$727$	−15.0422	+	15.0422i	−0.557886	+	0.557886i	0.370819	+	0.928705i	$0.379077\pi$
$728$	−0.335354	+	0.216356i	−0.0124291	+	0.00801867i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−17.7797	+	10.2651i	−0.657606	+	0.379669i
$732$	−0.275924	+	1.02976i	−0.0101984	+	0.0380611i
$733$	−33.9156	+	9.08767i	−1.25270	+	0.335661i	−0.823380	−	0.567491i	$-0.807914\pi$
$733$	−33.9156	+	9.08767i	−1.25270	+	0.335661i	−0.429323	+	0.903151i	$0.641248\pi$
$734$	−20.8723			−0.770411
$735$		0			0
$736$	22.9001			0.844109
$737$	−46.2135	+	12.3829i	−1.70230	+	0.456129i
$738$	0.152657	−	0.569725i	0.00561939	−	0.0209719i
$739$	0.177820	−	0.102664i	0.00654120	−	0.00377657i	−0.496726	−	0.867908i	$-0.665465\pi$
$739$	0.177820	−	0.102664i	0.00654120	−	0.00377657i	0.503267	+	0.864131i	$0.332131\pi$
$740$		0			0
$741$		−	0.457623i		−	0.0168112i
$742$	17.1846	−	11.0867i	0.630867	−	0.407007i
$743$	16.1701	−	16.1701i	0.593222	−	0.593222i	−0.345278	−	0.938500i	$-0.612215\pi$
$743$	16.1701	−	16.1701i	0.593222	−	0.593222i	0.938500	+	0.345278i	$0.112215\pi$
$744$	−5.72920	−	3.30775i	−0.210043	−	0.121268i
$745$		0			0
$746$	1.71919	+	2.97773i	0.0629441	+	0.109022i
$747$	2.63285	+	9.82593i	0.0963309	+	0.359512i
$748$	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	$0.329727\pi$
$752$	−16.4003	−	4.39446i	−0.598059	−	0.160249i
$753$	25.4570	+	6.82119i	0.927705	+	0.248578i
$754$	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	$-0.103231\pi$
$757$	17.3120	+	17.3120i	0.629216	+	0.629216i	−0.318655	+	0.947871i	$0.603231\pi$
$758$	−4.35047	−	16.2362i	−0.158016	−	0.589725i
$759$	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
$763$	−2.08418	+	4.06032i	−0.0754525	+	0.146993i
$764$			23.2402i			0.840799i
$765$		0			0
$766$	2.58068	−	1.48996i	0.0932439	−	0.0538344i
$767$	0.0383116	−	0.142981i	0.00138335	−	0.00516274i
$768$	6.25949	−	1.67723i	0.225870	−	0.0605217i
$769$	−0.923161			−0.0332901			−0.0166450	−	0.999861i	$-0.505299\pi$
$769$	−0.923161			−0.0332901			−0.0166450	+	0.999861i	$0.505299\pi$
$770$		0			0
$771$	23.1423			0.833449
$772$	−9.99523	+	2.67821i	−0.359736	+	0.0963910i
$773$	−1.13426	+	4.23312i	−0.0407965	+	0.152255i	−0.983320	−	0.181887i	$-0.941780\pi$
$773$	−1.13426	+	4.23312i	−0.0407965	+	0.152255i	0.942523	+	0.334141i	$0.108446\pi$
$774$	−2.62646	+	1.51639i	−0.0944063	+	0.0545055i
$775$		0			0
$776$			14.5375i			0.521865i
$777$	10.5937	+	16.4203i	0.380046	+	0.589076i
$778$	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
$782$	−2.71617	−	10.1369i	−0.0971302	−	0.362495i
$783$	−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
$787$	37.1691	+	9.95944i	1.32494	+	0.355016i	0.850825	−	0.525449i	$-0.176103\pi$
$787$	37.1691	+	9.95944i	1.32494	+	0.355016i	0.474111	+	0.880465i	$0.342769\pi$
$788$	−20.7190	−	5.55163i	−0.738082	−	0.197769i
$789$	−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
$793$	−0.0115135	−	0.0429691i	−0.000408857	−	0.00152588i
$794$	−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	−0.717942	−	0.696103i	$-0.754916\pi$
$797$	−0.616521	+	0.616521i	−0.0218383	+	0.0218383i	0.696103	+	0.717942i	$0.254916\pi$
$798$	−11.0261	+	0.544725i	−0.390319	+	0.0192830i
$799$			37.9909i			1.34402i
$800$		0			0
$801$	−13.6213	+	7.86428i	−0.481286	+	0.277871i
$802$	−1.76193	+	6.57561i	−0.0622159	+	0.232193i
$803$	−33.8054	+	9.05814i	−1.19297	+	0.319655i
$804$	−17.0260			−0.600461
$805$		0			0
$806$	0.123538			0.00435144
$807$	−22.5829	+	6.05106i	−0.794955	+	0.213007i
$808$	11.2193	−	41.8709i	0.394693	−	1.47301i
$809$	−4.71988	+	2.72503i	−0.165942	+	0.0958068i	−0.580671	−	0.814138i	$-0.697210\pi$
$809$	−4.71988	+	2.72503i	−0.165942	+	0.0958068i	0.414729	+	0.909945i	$0.363876\pi$
$810$		0			0
$811$			0.938267i			0.0329470i	0.999864	+	0.0164735i	$0.00524391\pi$
$811$			0.938267i			0.0329470i	−0.999864	+	0.0164735i	$0.994756\pi$
$812$	25.5020	+	13.0904i	0.894946	+	0.459381i
$813$	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
$817$	8.62068	+	32.1728i	0.301599	+	1.12558i
$818$	−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	$0.306259\pi$
$822$	5.63132	+	1.50891i	0.196415	+	0.0526292i
$823$	9.01538	+	2.41566i	0.314256	+	0.0842047i	0.412500	−	0.910958i	$-0.364656\pi$
$823$	9.01538	+	2.41566i	0.314256	+	0.0842047i	−0.0982435	+	0.995162i	$0.531322\pi$
$824$	−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	−0.998771	−	0.0495680i	$-0.984216\pi$
$827$	−30.1477	−	30.1477i	−1.04834	−	1.04834i	−0.0495680	−	0.998771i	$-0.515784\pi$
$828$	1.71097	+	6.38544i	0.0594604	+	0.221909i
$829$	27.5731	+	47.7580i	0.957654	+	1.65871i	0.728174	+	0.685392i	$0.240369\pi$
$829$	27.5731	+	47.7580i	0.957654	+	1.65871i	0.229480	+	0.973313i	$0.426298\pi$
$830$		0			0
$831$	12.5991	+	7.27410i	0.437059	+	0.252336i
$832$	0.0129257	−	0.0129257i	0.000448118	−	0.000448118i
$833$	−18.5168	+	22.5882i	−0.641569	+	0.782634i
$834$		−	13.2775i		−	0.459762i
$835$		0			0
$836$	43.2381	−	24.9635i	1.49542	−	0.863382i
$837$	0.767349	−	2.86379i	0.0265235	−	0.0989870i
$838$	−21.4482	+	5.74704i	−0.740917	+	0.198528i
$839$	−7.33343			−0.253178			−0.126589	−	0.991955i	$-0.540403\pi$
$839$	−7.33343			−0.253178			−0.126589	+	0.991955i	$0.540403\pi$
$840$		0			0
$841$	−15.7250			−0.542242
$842$	−19.0133	+	5.09461i	−0.655242	+	0.175572i
$843$	1.90888	−	7.12405i	0.0657454	−	0.245365i
$844$	−17.8536	+	10.3078i	−0.614545	+	0.354807i
$845$		0			0
$846$			5.61211i			0.192948i
$847$	−1.26960	−	25.6987i	−0.0436239	−	0.883016i
$848$	−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
$852$	1.50226	+	5.60651i	0.0514666	+	0.192076i
$853$	−6.61623	−	6.61623i	−0.226535	−	0.226535i	0.584708	−	0.811244i	$-0.301209\pi$
$853$	−6.61623	−	6.61623i	−0.226535	−	0.226535i	−0.811244	+	0.584708i	$0.801209\pi$
$854$	−1.02160	+	0.328557i	−0.0349585	+	0.0112430i
$855$		0			0
$856$	−0.687677	+	1.19109i	−0.0235043	+	0.0407107i
$857$	−49.3187	−	13.2149i	−1.68469	−	0.451412i	−0.715682	−	0.698426i	$-0.753884\pi$
$857$	−49.3187	−	13.2149i	−1.68469	−	0.451412i	−0.969012	+	0.247014i	$0.920551\pi$
$858$	−0.183229	−	0.0490961i	−0.00625534	−	0.00167611i
$859$	11.9017	−	20.6143i	0.406080	−	0.703352i	−0.588366	−	0.808595i	$-0.700229\pi$
$859$	11.9017	−	20.6143i	0.406080	−	0.703352i	0.994447	+	0.105243i	$0.0335620\pi$
$860$		0			0
$861$	−2.41018	+	0.775137i	−0.0821386	+	0.0264166i
$862$	−13.4351	−	13.4351i	−0.457603	−	0.457603i
$863$	−4.74133	−	17.6949i	−0.161397	−	0.602341i	−0.998472	−	0.0552536i	$-0.982403\pi$
$863$	−4.74133	−	17.6949i	−0.161397	−	0.602341i	0.837076	−	0.547087i	$-0.184263\pi$
$864$	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
$868$	0.627058	+	12.6926i	0.0212837	+	0.430816i
$869$			25.4475i			0.863248i
$870$		0			0
$871$	0.615266	−	0.355224i	0.0208475	−	0.0120363i
$872$	−0.996226	+	3.71797i	−0.0337365	+	0.125906i
$873$	−6.29313	+	1.68624i	−0.212990	+	0.0570705i
$874$	−17.0260			−0.575914
$875$		0			0
$876$	−12.4546			−0.420803
$877$	10.4699	−	2.80539i	0.353542	−	0.0947313i	−0.0776770	−	0.996979i	$-0.524750\pi$
$877$	10.4699	−	2.80539i	0.353542	−	0.0947313i	0.431219	+	0.902247i	$0.358084\pi$
$878$	−0.447652	+	1.67066i	−0.0151075	+	0.0563821i
$879$	−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	$-0.00214940\pi$
$882$	−2.73535	+	3.33679i	−0.0921041	+	0.112355i
$883$	−1.45235	+	1.45235i	−0.0488756	+	0.0488756i	−0.731122	−	0.682247i	$-0.761003\pi$
$883$	−1.45235	+	1.45235i	−0.0488756	+	0.0488756i	0.682247	+	0.731122i	$0.261003\pi$
$884$	−0.395751	−	0.228487i	−0.0133106	−	0.00768485i
$885$		0			0
$886$	−4.14687	−	7.18258i	−0.139317	−	0.241304i
$887$	1.63257	+	6.09282i	0.0548162	+	0.204577i	0.987903	−	0.155075i	$-0.0495620\pi$
$887$	1.63257	+	6.09282i	0.0548162	+	0.204577i	−0.933086	+	0.359652i	$0.882895\pi$
$888$	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
$892$	39.2861	+	10.5267i	1.31539	+	0.352459i
$893$	59.5353	+	15.9524i	1.99227	+	0.533828i
$894$	−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
$898$	−0.252897	−	0.943823i	−0.00843927	−	0.0314958i
$899$	−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
$903$	11.5813	+	5.94474i	0.385401	+	0.197829i
$904$		−	30.2099i		−	1.00477i
$905$		0			0
$906$	−0.347146	+	0.200425i	−0.0115332	+	0.00665867i
$907$	−8.47956	+	31.6461i	−0.281559	+	1.05079i	0.669758	+	0.742579i	$0.266398\pi$
$907$	−8.47956	+	31.6461i	−0.281559	+	1.05079i	−0.951317	+	0.308214i	$0.900269\pi$
$908$	−35.0257	+	9.38511i	−1.16237	+	0.311456i
$909$	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	$0.491605\pi$
$912$	12.1935	−	3.26724i	0.403767	−	0.108189i
$913$	11.9860	−	44.7323i	0.396678	−	1.48042i
$914$	−16.6603	+	9.61881i	−0.551073	+	0.318162i
$915$		0			0
$916$		−	15.6480i		−	0.517026i
$917$	−11.5726	+	0.571722i	−0.382159	+	0.0188799i
$918$	1.81859	−	1.81859i	0.0600224	−	0.0600224i
$919$	−37.2959	−	21.5328i	−1.23028	−	0.710301i	−0.263189	−	0.964744i	$-0.584774\pi$
$919$	−37.2959	−	21.5328i	−1.23028	−	0.710301i	−0.967088	+	0.254443i	$0.918108\pi$
$920$		0			0
$921$	−9.72148	−	16.8381i	−0.320334	−	0.554834i
$922$	−4.82837	−	18.0197i	−0.159014	−	0.593448i
$923$	−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
$927$	−16.3510	−	4.38124i	−0.537038	−	0.143899i
$928$	36.2531	+	9.71399i	1.19007	+	0.318877i
$929$	16.5662	−	28.6935i	0.543520	−	0.941404i	−0.455179	−	0.890400i	$-0.650425\pi$
$929$	16.5662	−	28.6935i	0.543520	−	0.941404i	0.998698	−	0.0510035i	$-0.0162420\pi$
$930$		0			0
$931$	27.6226	+	38.5024i	0.905294	+	1.26187i
$932$	−18.6979	−	18.6979i	−0.612469	−	0.612469i
$933$	−0.484551	−	1.80837i	−0.0158635	−	0.0592033i
$934$	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	−0.581668	−	0.813427i	$-0.697600\pi$
$937$	7.09425	−	7.09425i	0.231759	−	0.231759i	0.813427	+	0.581668i	$0.197600\pi$
$938$	−9.29123	−	14.4015i	−0.303369	−	0.470227i
$939$		−	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	$0.412094\pi$
$942$	−0.264007	+	0.985289i	−0.00860183	+	0.0321025i
$943$	−3.77162	+	1.01060i	−0.122821	+	0.0329098i
$944$	4.08330			0.132900
$945$		0			0
$946$	13.8066			0.448893
$947$	−14.3668	+	3.84958i	−0.466859	+	0.125095i	−0.484577	−	0.874748i	$-0.661027\pi$
$947$	−14.3668	+	3.84958i	−0.466859	+	0.125095i	0.0177180	+	0.999843i	$0.494360\pi$
$948$	−2.34385	+	8.74736i	−0.0761247	+	0.284101i
$949$	0.450070	−	0.259848i	0.0146099	−	0.00843503i
$950$		0			0
$951$			17.3852i			0.563754i
$952$	−11.2489	+	21.9145i	−0.364577	+	0.710254i
$953$	−4.93154	+	4.93154i	−0.159748	+	0.159748i	−0.782455	−	0.622707i	$-0.786033\pi$
$953$	−4.93154	+	4.93154i	−0.159748	+	0.159748i	0.622707	+	0.782455i	$0.286033\pi$
$954$	6.69403	+	3.86480i	0.216727	+	0.125127i
$955$		0			0
$956$	−21.5106	−	37.2574i	−0.695701	−	1.20499i
$957$	7.87987	+	29.4081i	0.254720	+	0.950628i
$958$	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
$962$	−0.297267	−	0.0796523i	−0.00958426	−	0.00256809i
$963$	−0.595377	−	0.159531i	−0.0191858	−	0.00514081i
$964$	−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	$-0.184995\pi$
$967$	8.91868	+	8.91868i	0.286805	+	0.286805i	−0.549010	+	0.835816i	$0.684995\pi$
$968$	−5.61634	−	20.9605i	−0.180516	−	0.673694i
$969$	−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
$973$	−47.8906	+	30.8969i	−1.53530	+	0.990509i
$974$		−	10.9209i		−	0.349928i
$975$		0			0
$976$	1.06272	−	0.613563i	0.0340169	−	0.0196397i
$977$	4.75807	−	17.7574i	0.152224	−	0.568108i	−0.847103	−	0.531429i	$-0.821655\pi$
$977$	4.75807	−	17.7574i	0.152224	−	0.568108i	0.999327	−	0.0366795i	$-0.0116781\pi$
$978$	14.0590	−	3.76711i	0.449559	−	0.120459i
$979$	71.6039			2.28847
$980$		0			0
$981$	−1.72503			−0.0550758
$982$	14.3281	−	3.83920i	0.457228	−	0.122514i
$983$	4.95203	−	18.4812i	0.157945	−	0.589459i	−0.840890	−	0.541206i	$-0.817968\pi$
$983$	4.95203	−	18.4812i	0.157945	−	0.589459i	0.998835	−	0.0482531i	$-0.0153654\pi$
$984$	−1.84914	+	1.06760i	−0.0589484	+	0.0340339i
$985$		0			0
$986$		−	17.1999i		−	0.547756i
$987$	20.2423	−	13.0594i	0.644320	−	0.415687i
$988$	−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	$-0.354992\pi$
$992$	4.30645	+	16.0719i	0.136730	+	0.510283i
$993$	−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
$997$	−1.76959	−	0.474162i	−0.0560436	−	0.0150168i	0.230688	−	0.973028i	$-0.425902\pi$
$997$	−1.76959	−	0.474162i	−0.0560436	−	0.0150168i	−0.286732	+	0.958011i	$0.592569\pi$
$998$	17.5519	+	4.70302i	0.555596	+	0.148871i
$999$	−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.82.4	yes	24
5.2	odd	4	inner	525.2.bc.d.418.4	yes	24
5.3	odd	4	inner	525.2.bc.d.418.3	yes	24
5.4	even	2	inner	525.2.bc.d.82.3	✓	24
7.3	odd	6	inner	525.2.bc.d.157.3	yes	24
35.3	even	12	inner	525.2.bc.d.493.4	yes	24
35.17	even	12	inner	525.2.bc.d.493.3	yes	24
35.24	odd	6	inner	525.2.bc.d.157.4	yes	24

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

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

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Database

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