LMFDB - Embedded newform 525.2.bc.d.418.3

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			418.3
Character	$\chi$	$=$	525.418
Dual form			525.2.bc.d.157.3

$q$-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	0.886308	−	0.463096i	$-0.153262\pi$
$2$	−0.159531	−	0.595377i	−0.112805	−	0.420995i	−0.999113	+	0.0421009i	$0.986595\pi$
$3$	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	−0.700447	−	0.713705i	$-0.747016\pi$
$13$	0.0478013	−	0.0478013i	0.0132577	−	0.0132577i	0.713705	+	0.700447i	$0.247016\pi$
$14$	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	$0.252208\pi$
$17$	−1.07994	+	4.03037i	−0.261923	+	0.977509i	−0.964107	+	0.265514i	$0.914458\pi$
$18$	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	−0.645154	−	0.764053i	$-0.723207\pi$
$23$	−3.94144	+	1.05611i	−0.821848	+	0.220213i	−0.176694	+	0.984266i	$0.556540\pi$
$24$	−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	$-0.875662\pi$
$37$	−1.91159	−	7.13416i	−0.314264	−	1.17285i	0.610409	−	0.792086i	$-0.291005\pi$
$38$	−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	0.920742	−	0.390172i	$-0.127584\pi$
$43$	3.47918	+	3.47918i	0.530570	+	0.530570i	−0.390172	+	0.920742i	$0.627584\pi$
$44$	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	−0.834937	−	0.550346i	$-0.814496\pi$
$47$	−8.79471	+	2.35653i	−1.28284	+	0.343736i	−0.447903	+	0.894082i	$0.647829\pi$
$48$	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	$-0.586335\pi$
$53$	3.24567	−	12.1130i	0.445827	−	1.66385i	0.713743	−	0.700408i	$-0.246998\pi$
$54$	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	0.818535	−	0.574457i	$-0.194787\pi$
$67$	10.1513	+	2.72003i	1.24018	+	0.332305i	0.421643	+	0.906762i	$0.361453\pi$
$68$	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	−0.203410	−	0.979094i	$-0.565203\pi$
$73$	−7.42573	−	1.98972i	−0.869115	−	0.232879i	−0.665705	+	0.746215i	$0.731869\pi$
$74$	−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	−0.191876	−	0.981419i	$-0.561457\pi$
$83$	7.19308	−	7.19308i	0.789543	−	0.789543i	0.981419	+	0.191876i	$0.0614572\pi$
$84$	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	0.433429	−	0.901188i	$-0.357304\pi$
$97$	−4.60689	−	4.60689i	−0.467759	−	0.467759i	−0.901188	+	0.433429i	$0.857304\pi$
$98$	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	$0.230607\pi$
$103$	4.38124	+	16.3510i	0.431697	+	1.61111i	−0.317153	+	0.948374i	$0.602727\pi$
$104$	−0.150841			−0.0147912
$105$		0			0
$106$	−7.72960			−0.750765
$107$	−0.159531	−	0.595377i	−0.0154224	−	0.0575573i	0.957786	−	0.287483i	$-0.0928184\pi$
$107$	−0.159531	−	0.595377i	−0.0154224	−	0.0575573i	−0.973208	+	0.229926i	$0.926152\pi$
$108$	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	0.0948937	−	0.995487i	$-0.469749\pi$
$113$	−9.57344	−	9.57344i	−0.900594	−	0.900594i	−0.995487	+	0.0948937i	$0.969749\pi$
$114$	−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	−0.548675	−	0.836036i	$-0.684868\pi$
$127$	3.23839	−	3.23839i	0.287360	−	0.287360i	0.836036	+	0.548675i	$0.184868\pi$
$128$	−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	0.627028	−	0.778997i	$-0.284271\pi$
$137$	9.13612	+	2.44802i	0.780552	+	0.209148i	0.153524	+	0.988145i	$0.450938\pi$
$138$	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	−0.980909	−	0.194467i	$-0.937702\pi$
$157$	−0.428319	+	1.59851i	−0.0341836	+	0.127575i	0.946726	+	0.322042i	$0.104369\pi$
$158$	−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	−0.991751	−	0.128178i	$-0.959087\pi$
$163$	−22.8091	+	6.11167i	−1.78654	+	0.478703i	−0.794793	+	0.606881i	$0.792421\pi$
$164$	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	$-0.198386\pi$
$167$	2.95044	+	2.95044i	0.228312	+	0.228312i	−0.583675	+	0.811987i	$0.698386\pi$
$168$	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	$0.0443376\pi$
$173$	2.65818	+	9.92045i	0.202097	+	0.754238i	−0.788217	+	0.615397i	$0.788996\pi$
$174$	−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	−0.999555	−	0.0298386i	$-0.990501\pi$
$193$	−1.65314	+	6.16960i	−0.118996	+	0.444098i	0.880559	+	0.473936i	$0.157167\pi$
$194$	−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	−0.290003	−	0.957026i	$-0.593656\pi$
$197$	9.36211	−	9.36211i	0.667023	−	0.667023i	0.957026	+	0.290003i	$0.0936563\pi$
$198$	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	$-0.432217\pi$
$223$	17.7519	−	17.7519i	1.18875	−	1.18875i	0.977412	−	0.211342i	$-0.0677832\pi$
$224$	−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	$-0.650170\pi$
$227$	5.79300	−	21.6198i	0.384495	−	1.43496i	0.838961	−	0.544191i	$-0.183163\pi$
$228$	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	−0.735147	−	0.677907i	$-0.762887\pi$
$233$	−15.7658	+	4.22443i	−1.03285	+	0.276751i	−0.297703	+	0.954659i	$0.596220\pi$
$234$	−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	0.518062	−	0.855343i	$-0.326654\pi$
$257$	22.3537	−	5.98967i	1.39439	−	0.373625i	0.876326	+	0.481718i	$0.159987\pi$
$258$	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	$-0.699300\pi$
$263$	5.29727	−	19.7697i	0.326644	−	1.21905i	0.912649	−	0.408744i	$-0.134033\pi$
$264$	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	0.654957	−	0.755667i	$-0.272687\pi$
$277$	14.0525	+	3.76535i	0.844332	+	0.226238i	0.189376	+	0.981905i	$0.439354\pi$
$278$	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	−0.334017	−	0.942567i	$-0.608404\pi$
$283$	−18.4135	−	4.93388i	−1.09457	−	0.293288i	−0.760551	+	0.649279i	$0.775071\pi$
$284$	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	−0.538166	−	0.842839i	$-0.680883\pi$
$293$	5.21516	−	5.21516i	0.304673	−	0.304673i	0.842839	+	0.538166i	$0.180883\pi$
$294$	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	0.195958	−	0.980612i	$-0.437218\pi$
$307$	−13.7482	−	13.7482i	−0.784654	−	0.784654i	−0.980612	+	0.195958i	$0.937218\pi$
$308$	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	$0.0153290\pi$
$313$	2.79334	+	10.4249i	0.157889	+	0.589249i	−0.840952	+	0.541110i	$0.818004\pi$
$314$	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	$0.0790221\pi$
$317$	4.49962	+	16.7928i	0.252724	+	0.943178i	−0.716619	+	0.697465i	$0.754311\pi$
$318$	−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	−0.449839	−	0.893110i	$-0.648519\pi$
$337$	8.13737	−	8.13737i	0.443271	−	0.443271i	0.893110	+	0.449839i	$0.148519\pi$
$338$	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	0.643360	−	0.765564i	$-0.277540\pi$
$347$	15.2329	+	4.08164i	0.817744	+	0.219114i	0.174384	+	0.984678i	$0.444207\pi$
$348$	−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	0.505652	−	0.862738i	$-0.331252\pi$
$353$	9.62318	+	2.57852i	0.512190	+	0.137241i	0.00653851	+	0.999979i	$0.497919\pi$
$354$	−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	$0.428364\pi$
$367$	−8.76433	+	32.7089i	−0.457494	+	1.70739i	−0.680650	+	0.732608i	$0.738303\pi$
$368$	−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	−0.395603	−	0.918422i	$-0.629464\pi$
$373$	−5.38828	+	1.44378i	−0.278994	+	0.0747563i	0.116609	+	0.993178i	$0.462798\pi$
$374$	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	0.990498	−	0.137529i	$-0.0439160\pi$
$383$	1.25127	+	4.66981i	0.0639370	+	0.238616i	−0.926561	+	0.376145i	$0.877249\pi$
$384$	−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	−0.558181	−	0.829719i	$-0.688501\pi$
$397$	−12.4873	+	3.34597i	−0.626721	+	0.167929i	−0.0685396	+	0.997648i	$0.521834\pi$
$398$	−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	−0.922499	−	0.385999i	$-0.873857\pi$
$433$	−11.1638	+	11.1638i	−0.536500	+	0.536500i	0.385999	+	0.922499i	$0.373857\pi$
$434$	−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	0.0635141	−	0.997981i	$-0.479769\pi$
$443$	12.9971	−	3.48255i	0.617509	−	0.165461i	0.553995	+	0.832520i	$0.313103\pi$
$444$	−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	$0.177140\pi$
$457$	8.07792	+	30.1472i	0.377869	+	1.41023i	−0.471238	+	0.882006i	$0.656193\pi$
$458$	−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	0.882084	−	0.471093i	$-0.156140\pi$
$463$	8.84347	+	8.84347i	0.410991	+	0.410991i	−0.471093	+	0.882084i	$0.656140\pi$
$464$	−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	0.458871	−	0.888503i	$-0.348254\pi$
$467$	28.1044	−	7.53055i	1.30052	−	0.348472i	0.841645	+	0.540031i	$0.181587\pi$
$468$	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	−0.150708	−	0.988578i	$-0.548155\pi$
$487$	−17.1141	−	4.58571i	−0.775514	−	0.207798i	−0.624806	+	0.780780i	$0.714822\pi$
$488$	−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	−0.354363	−	0.935108i	$-0.615302\pi$
$503$	13.0248	−	13.0248i	0.580745	−	0.580745i	0.935108	+	0.354363i	$0.115302\pi$
$504$	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	$-0.997805\pi$
$523$	−3.14266	−	11.7286i	−0.137419	−	0.512854i	0.862557	−	0.505959i	$-0.168861\pi$
$524$	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	−0.645157	−	0.764050i	$-0.723208\pi$
$547$	2.78067	−	2.78067i	0.118893	−	0.118893i	0.764050	+	0.645157i	$0.223208\pi$
$548$	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	−0.0769056	−	0.997038i	$-0.524504\pi$
$557$	−15.1524	−	4.06007i	−0.642027	−	0.172031i	−0.565121	+	0.825008i	$0.691171\pi$
$558$	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	0.102490	−	0.994734i	$-0.467319\pi$
$563$	−7.26347	−	1.94624i	−0.306119	−	0.0820243i	−0.408608	+	0.912710i	$0.633986\pi$
$564$	−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	$-0.811027\pi$
$577$	4.05126	−	15.1195i	0.168656	−	0.629433i	0.997546	−	0.0700205i	$-0.0223065\pi$
$578$	−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	0.438545	−	0.898709i	$-0.355494\pi$
$587$	−11.1489	−	11.1489i	−0.460165	−	0.460165i	−0.898709	+	0.438545i	$0.855494\pi$
$588$	−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	$-0.750193\pi$
$593$	−10.9127	−	40.7267i	−0.448131	−	1.67245i	0.259405	−	0.965769i	$-0.416474\pi$
$594$	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	0.326454	−	0.945213i	$-0.394146\pi$
$607$	26.6522	−	7.14142i	1.08178	−	0.289861i	0.755324	+	0.655352i	$0.227480\pi$
$608$	−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	$0.294712\pi$
$613$	−7.89886	+	29.4790i	−0.319032	+	1.19064i	−0.920177	+	0.391504i	$0.871955\pi$
$614$	−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	−0.778440	−	0.627719i	$-0.783989\pi$
$617$	−3.74384	+	3.74384i	−0.150721	+	0.150721i	0.627719	+	0.778440i	$0.283989\pi$
$618$	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	−0.960640	−	0.277795i	$-0.910396\pi$
$643$	−17.3152	+	17.3152i	−0.682845	+	0.682845i	0.277795	+	0.960640i	$0.410396\pi$
$644$	−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	−0.931939	−	0.362615i	$-0.881884\pi$
$647$	1.43590	−	5.35886i	0.0564512	−	0.210679i	0.988390	+	0.151936i	$0.0485508\pi$
$648$	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	−0.122587	−	0.992458i	$-0.539119\pi$
$653$	6.83511	−	1.83146i	0.267479	−	0.0716707i	0.390065	+	0.920787i	$0.372452\pi$
$654$	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	$0.137199\pi$
$673$	34.4082	+	34.4082i	1.32634	+	1.32634i	0.417800	+	0.908539i	$0.362801\pi$
$674$	−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	−0.922948	−	0.384925i	$-0.874227\pi$
$677$	−39.8037	+	10.6654i	−1.52978	+	0.409904i	−0.606834	+	0.794829i	$0.707561\pi$
$678$	−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	−0.998351	−	0.0573994i	$-0.981719\pi$
$683$	−2.74551	+	10.2464i	−0.105054	+	0.392067i	0.893297	+	0.449466i	$0.148386\pi$
$684$	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	0.928705	−	0.370819i	$-0.120923\pi$
$727$	15.0422	+	15.0422i	0.557886	+	0.557886i	−0.370819	+	0.928705i	$0.620923\pi$
$728$	−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	$-0.858752\pi$
$733$	−9.08767	−	33.9156i	−0.335661	−	1.25270i	0.567491	−	0.823380i	$-0.307914\pi$
$734$	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	0.938500	−	0.345278i	$-0.112215\pi$
$743$	16.1701	+	16.1701i	0.593222	+	0.593222i	−0.345278	+	0.938500i	$0.612215\pi$
$744$	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	−0.318655	−	0.947871i	$-0.603231\pi$
$757$	17.3120	−	17.3120i	0.629216	−	0.629216i	0.947871	+	0.318655i	$0.103231\pi$
$758$	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	0.181887	−	0.983320i	$-0.441780\pi$
$773$	−4.23312	−	1.13426i	−0.152255	−	0.0407965i	−0.334141	+	0.942523i	$0.608446\pi$
$774$	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	$-0.676103\pi$
$787$	9.95944	−	37.1691i	0.355016	−	1.32494i	0.880465	−	0.474111i	$-0.157231\pi$
$788$	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	0.717942	−	0.696103i	$-0.245084\pi$
$797$	0.616521	+	0.616521i	0.0218383	+	0.0218383i	−0.696103	+	0.717942i	$0.745084\pi$
$798$	−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	−0.995162	−	0.0982435i	$-0.968678\pi$
$823$	−2.41566	+	9.01538i	−0.0842047	+	0.314256i	0.910958	+	0.412500i	$0.135344\pi$
$824$	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	$0.515784\pi$
$827$	−30.1477	+	30.1477i	−1.04834	+	1.04834i	−0.998771	+	0.0495680i	$0.984216\pi$
$828$	−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	−0.584708	−	0.811244i	$-0.698791\pi$
$853$	6.61623	−	6.61623i	0.226535	−	0.226535i	0.811244	+	0.584708i	$0.198791\pi$
$854$	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	$0.420551\pi$
$857$	−13.2149	+	49.3187i	−0.451412	+	1.68469i	−0.698426	+	0.715682i	$0.746116\pi$
$858$	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	0.0552536	−	0.998472i	$-0.482403\pi$
$863$	17.6949	−	4.74133i	0.602341	−	0.161397i	0.547087	+	0.837076i	$0.315737\pi$
$864$	−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	0.902247	−	0.431219i	$-0.141916\pi$
$877$	−2.80539	−	10.4699i	−0.0947313	−	0.353542i	−0.996979	+	0.0776770i	$0.975250\pi$
$878$	−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	0.682247	−	0.731122i	$-0.261003\pi$
$883$	−1.45235	−	1.45235i	−0.0488756	−	0.0488756i	−0.731122	+	0.682247i	$0.761003\pi$
$884$	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	−0.155075	−	0.987903i	$-0.549562\pi$
$887$	6.09282	−	1.63257i	0.204577	−	0.0548162i	0.359652	+	0.933086i	$0.382895\pi$
$888$	−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	0.742579	−	0.669758i	$-0.233602\pi$
$907$	31.6461	+	8.47956i	1.05079	+	0.281559i	0.308214	+	0.951317i	$0.400269\pi$
$908$	−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	0.581668	−	0.813427i	$-0.302400\pi$
$937$	−7.09425	−	7.09425i	−0.231759	−	0.231759i	−0.813427	+	0.581668i	$0.802400\pi$
$938$	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	0.999843	−	0.0177180i	$-0.00564012\pi$
$947$	3.84958	+	14.3668i	0.125095	+	0.466859i	−0.874748	+	0.484577i	$0.838973\pi$
$948$	−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	0.622707	−	0.782455i	$-0.286033\pi$
$953$	−4.93154	−	4.93154i	−0.159748	−	0.159748i	−0.782455	+	0.622707i	$0.786033\pi$
$954$	−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	−0.549010	−	0.835816i	$-0.684995\pi$
$967$	8.91868	−	8.91868i	0.286805	−	0.286805i	0.835816	+	0.549010i	$0.184995\pi$
$968$	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	−0.0366795	−	0.999327i	$-0.511678\pi$
$977$	−17.7574	−	4.75807i	−0.568108	−	0.152224i	−0.531429	+	0.847103i	$0.678345\pi$
$978$	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	0.541206	−	0.840890i	$-0.317968\pi$
$983$	18.4812	+	4.95203i	0.589459	+	0.157945i	0.0482531	+	0.998835i	$0.484635\pi$
$984$	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	−0.973028	−	0.230688i	$-0.925902\pi$
$997$	−0.474162	+	1.76959i	−0.0150168	+	0.0560436i	0.958011	+	0.286732i	$0.0925689\pi$
$998$	−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.418.3	yes	24
5.2	odd	4	inner	525.2.bc.d.82.4	yes	24
5.3	odd	4	inner	525.2.bc.d.82.3	✓	24
5.4	even	2	inner	525.2.bc.d.418.4	yes	24
7.3	odd	6	inner	525.2.bc.d.493.4	yes	24
35.3	even	12	inner	525.2.bc.d.157.4	yes	24
35.17	even	12	inner	525.2.bc.d.157.3	yes	24
35.24	odd	6	inner	525.2.bc.d.493.3	yes	24

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