LMFDB - Embedded newform 725.2.bd.a.543.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(43,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([21, 13]))

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

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

chi := DirichletCharacter("725.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.bd (of order $28$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			543.2
Character	$\chi$	$=$	725.543
Dual form			725.2.bd.a.482.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.778326 - 1.61621i) q^{2} +(-0.539890 - 0.677001i) q^{3} +(-0.759368 + 0.952217i) q^{4} +(-0.673965 + 1.39950i) q^{6} +(-0.0496935 - 0.00559911i) q^{7} +(-1.36775 - 0.312179i) q^{8} +(0.500714 - 2.19377i) q^{9} +(1.35429 + 0.850959i) q^{11} +1.05463 q^{12} +(-3.21958 - 2.02300i) q^{13} +(0.0296284 + 0.0846731i) q^{14} +(1.10204 + 4.82834i) q^{16} -3.45060i q^{17} +(-3.93532 + 0.898211i) q^{18} +(-2.86087 + 0.322342i) q^{19} +(0.0230384 + 0.0366654i) q^{21} +(0.321247 - 2.85115i) q^{22} +(-0.177124 - 0.506191i) q^{23} +(0.527087 + 1.09451i) q^{24} +(-0.763706 + 6.77808i) q^{26} +(-4.09601 + 1.97253i) q^{27} +(0.0430672 - 0.0430672i) q^{28} +(-5.37491 - 0.332224i) q^{29} +(-0.572869 + 1.63716i) q^{31} +(4.75217 - 3.78973i) q^{32} +(-0.155070 - 1.37628i) q^{33} +(-5.57689 + 2.68569i) q^{34} +(1.70872 + 2.14267i) q^{36} +(-1.35942 + 5.95603i) q^{37} +(2.74766 + 4.37288i) q^{38} +(0.368650 + 3.27185i) q^{39} +(-1.91127 - 1.91127i) q^{41} +(0.0413277 - 0.0657726i) q^{42} +(-2.29605 - 1.10572i) q^{43} +(-1.83870 + 0.643391i) q^{44} +(-0.680251 + 0.680251i) q^{46} +(0.820205 + 3.59355i) q^{47} +(2.67381 - 3.35285i) q^{48} +(-6.82206 - 1.55709i) q^{49} +(-2.33605 + 1.86294i) q^{51} +(4.37118 - 1.52954i) q^{52} +(3.19279 + 1.11721i) q^{53} +(6.37606 + 5.08474i) q^{54} +(0.0662202 + 0.0231715i) q^{56} +(1.76278 + 1.76278i) q^{57} +(3.64649 + 8.94556i) q^{58} -4.31330i q^{59} +(7.71955 + 0.869785i) q^{61} +(3.09188 - 0.348372i) q^{62} +(-0.0371654 + 0.106213i) q^{63} +(-0.899637 - 0.433242i) q^{64} +(-2.10367 + 1.32182i) q^{66} +(-7.23181 + 4.54405i) q^{67} +(3.28571 + 2.62027i) q^{68} +(-0.247064 + 0.393200i) q^{69} +(8.28838 - 1.89177i) q^{71} +(-1.36970 + 2.84421i) q^{72} +(0.955706 - 1.98454i) q^{73} +(10.6843 - 2.43862i) q^{74} +(1.86551 - 2.96894i) q^{76} +(-0.0625350 - 0.0498700i) q^{77} +(5.00108 - 3.14239i) q^{78} +(-1.97211 + 1.23916i) q^{79} +(-2.53525 - 1.22091i) q^{81} +(-1.60143 + 4.57661i) q^{82} +(11.3425 - 1.27799i) q^{83} +(-0.0524080 - 0.00590497i) q^{84} +4.57151i q^{86} +(2.67694 + 3.81818i) q^{87} +(-1.58668 - 1.58668i) q^{88} +(2.11636 + 0.740547i) q^{89} +(0.148665 + 0.118557i) q^{91} +(0.616506 + 0.215725i) q^{92} +(1.41765 - 0.496056i) q^{93} +(5.16955 - 4.12258i) q^{94} +(-5.13130 - 1.17119i) q^{96} +(-6.48824 + 8.13599i) q^{97} +(2.79320 + 12.2378i) q^{98} +(2.54493 - 2.54493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 28 q^{9} - 12 q^{11} + 20 q^{16} - 4 q^{19} + 4 q^{21} - 12 q^{29} - 32 q^{31} + 40 q^{34} - 16 q^{36} + 184 q^{39} - 4 q^{41} - 36 q^{44} + 76 q^{46} + 84 q^{49} + 112 q^{51} - 168 q^{54}+ \cdots + 208 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 28 * q^9 - 12 * q^11 + 20 * q^16 - 4 * q^19 + 4 * q^21 - 12 * q^29 - 32 * q^31 + 40 * q^34 - 16 * q^36 + 184 * q^39 - 4 * q^41 - 36 * q^44 + 76 * q^46 + 84 * q^49 + 112 * q^51 - 168 * q^54 + 180 * q^56 + 124 * q^61 + 196 * q^64 + 144 * q^66 - 152 * q^69 + 56 * q^71 + 112 * q^74 + 12 * q^76 - 220 * q^79 - 76 * q^81 - 136 * q^84 + 208 * q^89 - 84 * q^94 - 84 * q^96 + 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.778326	−	1.61621i	−0.550360	−	1.14283i	−0.971763	−	0.235960i	$-0.924176\pi$
$2$	−0.778326	−	1.61621i	−0.550360	−	1.14283i	0.421403	−	0.906874i	$-0.361538\pi$
$3$	−0.539890	−	0.677001i	−0.311706	−	0.390866i	0.601159	−	0.799130i	$-0.294706\pi$
$3$	−0.539890	−	0.677001i	−0.311706	−	0.390866i	−0.912864	+	0.408263i	$0.866135\pi$
$4$	−0.759368	+	0.952217i	−0.379684	+	0.476108i
$5$		0			0
$5$		0			0
$6$	−0.673965	+	1.39950i	−0.275145	+	0.571345i
$7$	−0.0496935	−	0.00559911i	−0.0187824	−	0.00211626i	0.102568	−	0.994726i	$-0.467294\pi$
$7$	−0.0496935	−	0.00559911i	−0.0187824	−	0.00211626i	−0.121351	+	0.992610i	$0.538723\pi$
$8$	−1.36775	−	0.312179i	−0.483572	−	0.110372i
$9$	0.500714	−	2.19377i	0.166905	−	0.731257i
$10$		0			0
$11$	1.35429	+	0.850959i	0.408335	+	0.256574i	0.720501	−	0.693454i	$-0.243912\pi$
$11$	1.35429	+	0.850959i	0.408335	+	0.256574i	−0.312166	+	0.950027i	$0.601055\pi$
$12$	1.05463			0.304444
$13$	−3.21958	−	2.02300i	−0.892951	−	0.561079i	0.00558163	−	0.999984i	$-0.498223\pi$
$13$	−3.21958	−	2.02300i	−0.892951	−	0.561079i	−0.898533	+	0.438906i	$0.855366\pi$
$14$	0.0296284	+	0.0846731i	0.00791852	+	0.0226298i
$15$		0			0
$16$	1.10204	+	4.82834i	0.275509	+	1.20708i
$17$		−	3.45060i		−	0.836892i	−0.908242	−	0.418446i	$-0.862575\pi$
$17$		−	3.45060i		−	0.836892i	0.908242	−	0.418446i	$-0.137425\pi$
$18$	−3.93532	+	0.898211i	−0.927563	+	0.211710i
$19$	−2.86087	+	0.322342i	−0.656328	+	0.0739504i	−0.433847	−	0.900987i	$-0.642844\pi$
$19$	−2.86087	+	0.322342i	−0.656328	+	0.0739504i	−0.222481	+	0.974937i	$0.571416\pi$
$20$		0			0
$21$	0.0230384	+	0.0366654i	0.00502739	+	0.00800105i
$22$	0.321247	−	2.85115i	0.0684902	−	0.607867i
$23$	−0.177124	−	0.506191i	−0.0369329	−	0.105548i	0.923940	−	0.382536i	$-0.124949\pi$
$23$	−0.177124	−	0.506191i	−0.0369329	−	0.105548i	−0.960873	+	0.276988i	$0.910664\pi$
$24$	0.527087	+	1.09451i	0.107591	+	0.223416i
$25$		0			0
$26$	−0.763706	+	6.77808i	−0.149775	+	1.32929i
$27$	−4.09601	+	1.97253i	−0.788277	+	0.379614i
$28$	0.0430672	−	0.0430672i	0.00813893	−	0.00813893i
$29$	−5.37491	−	0.332224i	−0.998095	−	0.0616925i
$29$	−5.37491	−	0.332224i	−0.998095	−	0.0616925i
$30$		0			0
$31$	−0.572869	+	1.63716i	−0.102890	+	0.294043i	−0.983808	−	0.179226i	$-0.942641\pi$
$31$	−0.572869	+	1.63716i	−0.102890	+	0.294043i	0.880918	+	0.473270i	$0.156926\pi$
$32$	4.75217	−	3.78973i	0.840073	−	0.669936i
$33$	−0.155070	−	1.37628i	−0.0269942	−	0.239580i
$34$	−5.57689	+	2.68569i	−0.956429	+	0.460592i
$35$		0			0
$36$	1.70872	+	2.14267i	0.284787	+	0.357111i
$37$	−1.35942	+	5.95603i	−0.223488	+	0.979165i	0.731342	+	0.682011i	$0.238894\pi$
$37$	−1.35942	+	5.95603i	−0.223488	+	0.979165i	−0.954830	+	0.297154i	$0.903963\pi$
$38$	2.74766	+	4.37288i	0.445729	+	0.709374i
$39$	0.368650	+	3.27185i	0.0590312	+	0.523916i
$40$		0			0
$41$	−1.91127	−	1.91127i	−0.298490	−	0.298490i	0.541932	−	0.840422i	$-0.317693\pi$
$41$	−1.91127	−	1.91127i	−0.298490	−	0.298490i	−0.840422	+	0.541932i	$0.817693\pi$
$42$	0.0413277	−	0.0657726i	0.00637700	−	0.0101489i
$43$	−2.29605	−	1.10572i	−0.350144	−	0.168621i	0.250541	−	0.968106i	$-0.419391\pi$
$43$	−2.29605	−	1.10572i	−0.350144	−	0.168621i	−0.600686	+	0.799485i	$0.705106\pi$
$44$	−1.83870	+	0.643391i	−0.277195	+	0.0969948i
$45$		0			0
$46$	−0.680251	+	0.680251i	−0.100298	+	0.100298i
$47$	0.820205	+	3.59355i	0.119639	+	0.524173i	0.998859	+	0.0477571i	$0.0152073\pi$
$47$	0.820205	+	3.59355i	0.119639	+	0.524173i	−0.879220	+	0.476416i	$0.841936\pi$
$48$	2.67381	−	3.35285i	0.385931	−	0.483942i
$49$	−6.82206	−	1.55709i	−0.974580	−	0.222441i
$50$		0			0
$51$	−2.33605	+	1.86294i	−0.327113	+	0.260864i
$52$	4.37118	−	1.52954i	0.606173	−	0.212109i
$53$	3.19279	+	1.11721i	0.438563	+	0.153460i	0.540524	−	0.841328i	$-0.318226\pi$
$53$	3.19279	+	1.11721i	0.438563	+	0.153460i	−0.101961	+	0.994788i	$0.532512\pi$
$54$	6.37606	+	5.08474i	0.867672	+	0.691945i
$55$		0			0
$56$	0.0662202	+	0.0231715i	0.00884905	+	0.00309642i
$57$	1.76278	+	1.76278i	0.233486	+	0.233486i
$58$	3.64649	+	8.94556i	0.478807	+	1.17461i
$59$		−	4.31330i		−	0.561544i	−0.959774	−	0.280772i	$-0.909410\pi$
$59$		−	4.31330i		−	0.561544i	0.959774	−	0.280772i	$-0.0905905\pi$
$60$		0			0
$61$	7.71955	+	0.869785i	0.988387	+	0.111365i	0.591330	−	0.806429i	$-0.298603\pi$
$61$	7.71955	+	0.869785i	0.988387	+	0.111365i	0.397057	+	0.917794i	$0.370031\pi$
$62$	3.09188	−	0.348372i	0.392670	−	0.0442432i
$63$	−0.0371654	+	0.106213i	−0.00468240	+	0.0133815i
$64$	−0.899637	−	0.433242i	−0.112455	−	0.0541553i
$65$		0			0
$66$	−2.10367	+	1.32182i	−0.258944	+	0.162705i
$67$	−7.23181	+	4.54405i	−0.883506	+	0.555144i	−0.895639	−	0.444783i	$-0.853281\pi$
$67$	−7.23181	+	4.54405i	−0.883506	+	0.555144i	0.0121324	+	0.999926i	$0.496138\pi$
$68$	3.28571	+	2.62027i	0.398451	+	0.317754i
$69$	−0.247064	+	0.393200i	−0.0297430	+	0.0473358i
$70$		0			0
$71$	8.28838	−	1.89177i	0.983650	−	0.224512i	0.299694	−	0.954035i	$-0.403115\pi$
$71$	8.28838	−	1.89177i	0.983650	−	0.224512i	0.683956	+	0.729524i	$0.260258\pi$
$72$	−1.36970	+	2.84421i	−0.161421	+	0.335194i
$73$	0.955706	−	1.98454i	0.111857	−	0.232273i	−0.837524	−	0.546401i	$-0.815998\pi$
$73$	0.955706	−	1.98454i	0.111857	−	0.232273i	0.949381	+	0.314127i	$0.101712\pi$
$74$	10.6843	−	2.43862i	1.24202	−	0.283483i
$75$		0			0
$76$	1.86551	−	2.96894i	0.213989	−	0.340561i
$77$	−0.0625350	−	0.0498700i	−0.00712652	−	0.00568321i
$78$	5.00108	−	3.14239i	0.566261	−	0.355805i
$79$	−1.97211	+	1.23916i	−0.221880	+	0.139416i	−0.638386	−	0.769717i	$-0.720397\pi$
$79$	−1.97211	+	1.23916i	−0.221880	+	0.139416i	0.416506	+	0.909133i	$0.363255\pi$
$80$		0			0
$81$	−2.53525	−	1.22091i	−0.281695	−	0.135657i
$82$	−1.60143	+	4.57661i	−0.176848	+	0.505402i
$83$	11.3425	−	1.27799i	1.24500	−	0.140278i	0.535226	−	0.844709i	$-0.320227\pi$
$83$	11.3425	−	1.27799i	1.24500	−	0.140278i	0.709772	+	0.704432i	$0.248798\pi$
$84$	−0.0524080	−	0.00590497i	−0.00571819	−	0.000644285i
$85$		0			0
$86$			4.57151i			0.492959i
$87$	2.67694	+	3.81818i	0.286998	+	0.409352i
$88$	−1.58668	−	1.58668i	−0.169141	−	0.169141i
$89$	2.11636	+	0.740547i	0.224334	+	0.0784978i	0.440106	−	0.897946i	$-0.354941\pi$
$89$	2.11636	+	0.740547i	0.224334	+	0.0784978i	−0.215772	+	0.976444i	$0.569227\pi$
$90$		0			0
$91$	0.148665	+	0.118557i	0.0155844	+	0.0124281i
$92$	0.616506	+	0.215725i	0.0642752	+	0.0224909i
$93$	1.41765	−	0.496056i	0.147003	−	0.0514386i
$94$	5.16955	−	4.12258i	0.533199	−	0.425212i
$95$		0			0
$96$	−5.13130	−	1.17119i	−0.523711	−	0.119534i
$97$	−6.48824	+	8.13599i	−0.658781	+	0.826085i	−0.993210	−	0.116336i	$-0.962885\pi$
$97$	−6.48824	+	8.13599i	−0.658781	+	0.826085i	0.334429	+	0.942421i	$0.391456\pi$
$98$	2.79320	+	12.2378i	0.282156	+	1.23621i
$99$	2.54493	−	2.54493i	0.255775	−	0.255775i
$100$		0			0
$101$	−10.7478	+	3.76081i	−1.06944	+	0.374215i	−0.806890	−	0.590702i	$-0.798851\pi$
$101$	−10.7478	+	3.76081i	−1.06944	+	0.374215i	−0.262555	+	0.964917i	$0.584565\pi$
$102$	4.82912	+	2.32558i	0.478154	+	0.230267i
$103$	0.363416	−	0.578374i	0.0358085	−	0.0569889i	−0.828340	−	0.560225i	$-0.810715\pi$
$103$	0.363416	−	0.578374i	0.0358085	−	0.0569889i	0.864149	+	0.503236i	$0.167857\pi$
$104$	3.77204	+	3.77204i	0.369879	+	0.369879i
$105$		0			0
$106$	−0.679392	−	6.02977i	−0.0659884	−	0.585663i
$107$	−7.04093	−	11.2056i	−0.680673	−	1.08328i	−0.991156	−	0.132706i	$-0.957634\pi$
$107$	−7.04093	−	11.2056i	−0.680673	−	1.08328i	0.310483	−	0.950579i	$-0.399509\pi$
$108$	1.23210	−	5.39816i	0.118558	−	0.519438i
$109$	−10.9158	−	13.6879i	−1.04554	−	1.31107i	−0.948842	−	0.315752i	$-0.897743\pi$
$109$	−10.9158	−	13.6879i	−1.04554	−	1.31107i	−0.0966979	−	0.995314i	$-0.530828\pi$
$110$		0			0
$111$	4.76617	−	2.29527i	0.452385	−	0.217857i
$112$	−0.0277296	−	0.246107i	−0.00262020	−	0.0232549i
$113$	2.07410	−	1.65404i	0.195114	−	0.155599i	−0.521060	−	0.853520i	$-0.674463\pi$
$113$	2.07410	−	1.65404i	0.195114	−	0.155599i	0.716174	+	0.697922i	$0.245892\pi$
$114$	1.47701	−	4.22104i	0.138334	−	0.395337i
$115$		0			0
$116$	4.39788	−	4.86580i	0.408333	−	0.451778i
$117$	−6.05009	+	6.05009i	−0.559331	+	0.559331i
$118$	−6.97121	+	3.35716i	−0.641752	+	0.309051i
$119$	−0.0193203	+	0.171472i	−0.00177109	+	0.0157188i
$120$		0			0
$121$	−3.66274	−	7.60576i	−0.332976	−	0.691433i
$122$	−4.60258	−	13.1534i	−0.416698	−	1.19085i
$123$	−0.262056	+	2.32581i	−0.0236288	+	0.209711i
$124$	−1.12392	−	1.78870i	−0.100931	−	0.160630i
$125$		0			0
$126$	0.200589	−	0.0226009i	0.0178699	−	0.00201345i
$127$	11.6454	−	2.65798i	1.03336	−	0.235857i	0.327977	−	0.944686i	$-0.393633\pi$
$127$	11.6454	−	2.65798i	1.03336	−	0.235857i	0.705381	+	0.708828i	$0.250776\pi$
$128$		−	10.3653i		−	0.916172i
$129$	0.491041	+	2.15139i	0.0432338	+	0.189420i
$130$		0			0
$131$	−5.93311	−	16.9558i	−0.518378	−	1.48144i	−0.844211	−	0.536011i	$-0.819930\pi$
$131$	−5.93311	−	16.9558i	−0.518378	−	1.48144i	0.325833	−	0.945427i	$-0.394355\pi$
$132$	1.42827	+	0.897444i	0.124315	+	0.0781125i
$133$	0.143971			0.0124839
$134$	12.9728	+	8.15138i	1.12068	+	0.704172i
$135$		0			0
$136$	−1.07721	+	4.71954i	−0.0923696	+	0.404698i
$137$	8.91949	+	2.03582i	0.762044	+	0.173932i	0.585845	−	0.810423i	$-0.300763\pi$
$137$	8.91949	+	2.03582i	0.762044	+	0.173932i	0.176199	+	0.984355i	$0.443620\pi$
$138$	0.827791	+	0.0932697i	0.0704663	+	0.00793964i
$139$	−8.09430	+	16.8080i	−0.686550	+	1.42564i	0.207756	+	0.978181i	$0.433384\pi$
$139$	−8.09430	+	16.8080i	−0.686550	+	1.42564i	−0.894306	+	0.447455i	$0.852330\pi$
$140$		0			0
$141$	1.99002	−	2.49540i	0.167590	−	0.210151i
$142$	−9.50856	−	11.9234i	−0.797941	−	1.00059i
$143$	−2.63877	−	5.47947i	−0.220665	−	0.458216i
$144$	11.1441			0.928673
$145$		0			0
$146$	−3.95129			−0.327011
$147$	2.62901	+	5.45919i	0.216837	+	0.450267i
$148$	−4.63913	−	5.81728i	−0.381334	−	0.478177i
$149$	7.09534	−	8.89728i	0.581273	−	0.728893i	−0.401056	−	0.916053i	$-0.631357\pi$
$149$	7.09534	−	8.89728i	0.581273	−	0.728893i	0.982329	+	0.187160i	$0.0599283\pi$
$150$		0			0
$151$	7.35606	−	15.2750i	0.598627	−	1.24306i	−0.352947	−	0.935643i	$-0.614820\pi$
$151$	7.35606	−	15.2750i	0.598627	−	1.24306i	0.951574	−	0.307419i	$-0.0994654\pi$
$152$	4.01357	+	0.452221i	0.325544	+	0.0366800i
$153$	−7.56982	−	1.72776i	−0.611984	−	0.139681i
$154$	−0.0319278	+	0.139885i	−0.00257282	+	0.0112722i
$155$		0			0
$156$	−3.39546	−	2.13351i	−0.271854	−	0.170817i
$157$	−21.8717			−1.74555			−0.872776	−	0.488120i	$-0.837683\pi$
$157$	−21.8717			−1.74555			−0.872776	+	0.488120i	$0.837683\pi$
$158$	3.53769	+	2.22288i	0.281444	+	0.176843i
$159$	−0.967406	−	2.76469i	−0.0767203	−	0.219254i
$160$		0			0
$161$	0.00596768	+	0.0261461i	0.000470319	+	0.00206060i
$162$			5.04777i			0.396591i
$163$	−11.5587	+	2.63820i	−0.905347	+	0.206640i	−0.649754	−	0.760145i	$-0.725128\pi$
$163$	−11.5587	+	2.63820i	−0.905347	+	0.206640i	−0.255593	+	0.966784i	$0.582271\pi$
$164$	3.27130	−	0.368587i	0.255446	−	0.0287818i
$165$		0			0
$166$	−10.8936	−	17.3371i	−0.845510	−	1.34562i
$167$	2.75695	−	24.4686i	0.213339	−	1.89344i	−0.195302	−	0.980743i	$-0.562569\pi$
$167$	2.75695	−	24.4686i	0.213339	−	1.89344i	0.408641	−	0.912695i	$-0.366003\pi$
$168$	−0.0200645	−	0.0573412i	−0.00154801	−	0.00442397i
$169$	0.632702	+	1.31382i	0.0486694	+	0.101063i
$170$		0			0
$171$	−0.725331	+	6.43749i	−0.0554674	+	0.492287i
$172$	2.79643	−	1.34669i	0.213226	−	0.102684i
$173$	−8.89672	+	8.89672i	−0.676405	+	0.676405i	−0.959185	−	0.282780i	$-0.908744\pi$
$173$	−8.89672	+	8.89672i	−0.676405	+	0.676405i	0.282780	+	0.959185i	$0.408744\pi$
$174$	4.08745	−	7.29829i	0.309869	−	0.553282i
$175$		0			0
$176$	−2.61624	+	7.47678i	−0.197206	+	0.563583i
$177$	−2.92011	+	2.32871i	−0.219489	+	0.175036i
$178$	−0.450339	−	3.99687i	−0.0337544	−	0.299578i
$179$	−1.78074	+	0.857561i	−0.133099	+	0.0640971i	−0.499248	−	0.866459i	$-0.666390\pi$
$179$	−1.78074	+	0.857561i	−0.133099	+	0.0640971i	0.366149	+	0.930556i	$0.380676\pi$
$180$		0			0
$181$	−8.08934	−	10.1437i	−0.601276	−	0.753976i	0.384300	−	0.923208i	$-0.374443\pi$
$181$	−8.08934	−	10.1437i	−0.601276	−	0.753976i	−0.985576	+	0.169232i	$0.945871\pi$
$182$	0.0759024	−	0.332550i	0.00562626	−	0.0246503i
$183$	−3.57886	−	5.69573i	−0.264557	−	0.421040i
$184$	0.0842383	+	0.747636i	0.00621013	+	0.0551165i
$185$		0			0
$186$	−1.90512	−	1.90512i	−0.139690	−	0.139690i
$187$	2.93632	−	4.67312i	0.214725	−	0.341732i
$188$	−4.04468	−	1.94781i	−0.294988	−	0.142059i
$189$	0.214589	−	0.0750880i	0.0156091	−	0.00546185i
$190$		0			0
$191$	9.41763	−	9.41763i	0.681436	−	0.681436i	−0.278888	−	0.960324i	$-0.589966\pi$
$191$	9.41763	−	9.41763i	0.681436	−	0.681436i	0.960324	+	0.278888i	$0.0899658\pi$
$192$	0.192400	+	0.842958i	0.0138853	+	0.0608353i
$193$	−7.09495	+	8.89678i	−0.510705	+	0.640404i	−0.968607	−	0.248599i	$-0.920030\pi$
$193$	−7.09495	+	8.89678i	−0.510705	+	0.640404i	0.457901	+	0.889003i	$0.348601\pi$
$194$	18.1994	+	4.15391i	1.30664	+	0.298233i
$195$		0			0
$196$	6.66314	−	5.31367i	0.475938	−	0.379548i
$197$	21.6856	−	7.58813i	1.54504	−	0.540632i	0.582746	−	0.812654i	$-0.301978\pi$
$197$	21.6856	−	7.58813i	1.54504	−	0.540632i	0.962291	+	0.272022i	$0.0876925\pi$
$198$	−6.09392	−	2.13235i	−0.433076	−	0.151540i
$199$	−1.71680	−	1.36910i	−0.121701	−	0.0970531i	0.560748	−	0.827986i	$-0.310514\pi$
$199$	−1.71680	−	1.36910i	−0.121701	−	0.0970531i	−0.682449	+	0.730933i	$0.739085\pi$
$200$		0			0
$201$	6.98070	+	2.44265i	0.492381	+	0.172292i
$202$	14.4435	+	14.4435i	1.01624	+	1.01624i
$203$	0.265238	+	0.0466041i	0.0186160	+	0.00327097i
$204$		−	3.63909i		−	0.254787i
$205$		0			0
$206$	−1.21763	−	0.137194i	−0.0848363	−	0.00955876i
$207$	−1.19916	+	0.135112i	−0.0833471	+	0.00939096i
$208$	6.21962	−	17.7746i	0.431253	−	1.23245i
$209$	−4.14875	−	1.99793i	−0.286975	−	0.138200i
$210$		0			0
$211$	8.46368	−	5.31808i	0.582664	−	0.366112i	−0.208216	−	0.978083i	$-0.566766\pi$
$211$	8.46368	−	5.31808i	0.582664	−	0.366112i	0.790880	+	0.611971i	$0.209623\pi$
$212$	−3.48832	+	2.19186i	−0.239579	+	0.150537i
$213$	−5.75554	−	4.58989i	−0.394363	−	0.314494i
$214$	−12.6304	+	20.1012i	−0.863399	+	1.37409i
$215$		0			0
$216$	6.21809	−	1.41924i	0.423087	−	0.0965669i
$217$	0.0376345	−	0.0781489i	0.00255480	−	0.00530509i
$218$	−13.6266	+	28.2958i	−0.922907	+	1.91644i
$219$	−1.85951	+	0.424422i	−0.125654	+	0.0286798i
$220$		0			0
$221$	−6.98055	+	11.1095i	−0.469562	+	0.747304i
$222$	−7.41927	−	5.91667i	−0.497949	−	0.397101i
$223$	−5.25804	+	3.30385i	−0.352105	+	0.221242i	−0.696457	−	0.717598i	$-0.745241\pi$
$223$	−5.25804	+	3.30385i	−0.352105	+	0.221242i	0.344352	+	0.938840i	$0.388098\pi$
$224$	−0.257371	+	0.161717i	−0.0171963	+	0.0108052i
$225$		0			0
$226$	−4.28759	−	2.06480i	−0.285207	−	0.137348i
$227$	3.40005	−	9.71679i	0.225669	−	0.644926i	−0.774258	−	0.632870i	$-0.781877\pi$
$227$	3.40005	−	9.71679i	0.225669	−	0.644926i	0.999927	−	0.0120560i	$-0.00383765\pi$
$228$	−3.01714	+	0.339950i	−0.199815	+	0.0225138i
$229$	−2.88517	−	0.325080i	−0.190657	−	0.0214819i	0.0161195	−	0.999870i	$-0.494869\pi$
$229$	−2.88517	−	0.325080i	−0.190657	−	0.0214819i	−0.206777	+	0.978388i	$0.566297\pi$
$230$		0			0
$231$			0.0692605i			0.00455701i
$232$	7.24780	+	2.13233i	0.475842	+	0.139995i
$233$	−9.72899	−	9.72899i	−0.637367	−	0.637367i	0.312538	−	0.949905i	$-0.398821\pi$
$233$	−9.72899	−	9.72899i	−0.637367	−	0.637367i	−0.949905	+	0.312538i	$0.898821\pi$
$234$	14.4872	+	5.06928i	0.947055	+	0.331389i
$235$		0			0
$236$	4.10720	+	3.27538i	0.267356	+	0.213209i
$237$	1.90364	+	0.666111i	0.123654	+	0.0432686i
$238$	0.292173	−	0.102236i	0.0189387	−	0.00662695i
$239$	13.8791	−	11.0682i	0.897762	−	0.715941i	−0.0616058	−	0.998101i	$-0.519622\pi$
$239$	13.8791	−	11.0682i	0.897762	−	0.715941i	0.959368	+	0.282160i	$0.0910507\pi$
$240$		0			0
$241$	−18.2239	−	4.15948i	−1.17390	−	0.267935i	−0.409276	−	0.912411i	$-0.634219\pi$
$241$	−18.2239	−	4.15948i	−1.17390	−	0.267935i	−0.764625	+	0.644475i	$0.777076\pi$
$242$	−9.44171	+	11.8395i	−0.606936	+	0.761074i
$243$	3.57709	+	15.6722i	0.229470	+	1.00538i
$244$	−6.69020	+	6.69020i	−0.428296	+	0.428296i
$245$		0			0
$246$	3.96296	−	1.38670i	0.252669	−	0.0884128i
$247$	9.86289	+	4.74972i	0.627561	+	0.302217i
$248$	1.29463	−	2.06039i	0.0822090	−	0.130835i
$249$	−6.98888	−	6.98888i	−0.442902	−	0.442902i
$250$		0			0
$251$	−0.444851	−	3.94816i	−0.0280788	−	0.249206i	−0.999909	−	0.0135222i	$-0.995696\pi$
$251$	−0.444851	−	3.94816i	−0.0280788	−	0.249206i	0.971830	−	0.235684i	$-0.0757329\pi$
$252$	−0.0729152	−	0.116044i	−0.00459323	−	0.00731008i
$253$	0.190870	−	0.836257i	0.0119999	−	0.0525750i
$254$	−13.3597	−	16.7526i	−0.838265	−	1.05115i
$255$		0			0
$256$	−18.5518	+	8.93407i	−1.15949	+	0.558380i
$257$	−2.75726	−	24.4713i	−0.171993	−	1.52648i	−0.722336	−	0.691542i	$-0.756932\pi$
$257$	−2.75726	−	24.4713i	−0.171993	−	1.52648i	0.550343	−	0.834939i	$-0.314497\pi$
$258$	3.09491	−	2.46811i	0.192681	−	0.153658i
$259$	0.100903	−	0.288364i	0.00626980	−	0.0179181i
$260$		0			0
$261$	−3.42012	+	11.6250i	−0.211700	+	0.719568i
$262$	−22.7863	+	22.7863i	−1.40774	+	1.40774i
$263$	7.31769	−	3.52401i	0.451228	−	0.217300i	−0.194446	−	0.980913i	$-0.562291\pi$
$263$	7.31769	−	3.52401i	0.451228	−	0.217300i	0.645674	+	0.763613i	$0.276577\pi$
$264$	−0.217551	+	1.93082i	−0.0133893	+	0.118834i
$265$		0			0
$266$	−0.112057	−	0.232688i	−0.00687063	−	0.0142670i
$267$	−0.641251	−	1.83259i	−0.0392439	−	0.112153i
$268$	1.16468	−	10.3369i	0.0711444	−	0.631424i
$269$	−4.23287	−	6.73657i	−0.258083	−	0.410736i	0.692400	−	0.721514i	$-0.256553\pi$
$269$	−4.23287	−	6.73657i	−0.258083	−	0.410736i	−0.950483	+	0.310778i	$0.899411\pi$
$270$		0			0
$271$	25.3607	−	2.85746i	1.54055	−	0.173579i	0.699539	−	0.714594i	$-0.253389\pi$
$271$	25.3607	−	2.85746i	1.54055	−	0.173579i	0.841013	+	0.541015i	$0.181960\pi$
$272$	16.6606	−	3.80268i	1.01020	−	0.230571i
$273$		−	0.164654i		−	0.00996531i
$274$	−3.65197	−	16.0003i	−0.220623	−	0.966614i
$275$		0			0
$276$	−0.186799	−	0.533842i	−0.0112440	−	0.0321335i
$277$	15.4938	+	9.73540i	0.930932	+	0.584943i	0.909896	−	0.414835i	$-0.136161\pi$
$277$	15.4938	+	9.73540i	0.930932	+	0.584943i	0.0210355	+	0.999779i	$0.493304\pi$
$278$	33.4653			2.00711
$279$	3.30472	+	2.07650i	0.197849	+	0.124317i
$280$		0			0
$281$	−5.32480	+	23.3295i	−0.317651	+	1.39172i	0.524009	+	0.851712i	$0.324436\pi$
$281$	−5.32480	+	23.3295i	−0.317651	+	1.39172i	−0.841660	+	0.540007i	$0.818422\pi$
$282$	−5.58198	−	1.27405i	−0.332402	−	0.0758686i
$283$	31.2062	+	3.51609i	1.85501	+	0.209010i	0.967691	−	0.252138i	$-0.0811335\pi$
$283$	31.2062	+	3.51609i	1.85501	+	0.209010i	0.887323	+	0.461148i	$0.152562\pi$
$284$	−4.49255	+	9.32888i	−0.266584	+	0.553567i
$285$		0			0
$286$	−6.80215	+	8.52963i	−0.402220	+	0.504367i
$287$	0.0842763	+	0.105679i	0.00497467	+	0.00623804i
$288$	−5.93433	−	12.3228i	−0.349683	−	0.726125i
$289$	5.09339			0.299611
$290$		0			0
$291$	9.01101			0.528234
$292$	1.16398	+	2.41704i	0.0681170	+	0.141446i
$293$	3.80145	+	4.76687i	0.222083	+	0.278483i	0.880374	−	0.474280i	$-0.157292\pi$
$293$	3.80145	+	4.76687i	0.222083	+	0.278483i	−0.658291	+	0.752764i	$0.728720\pi$
$294$	6.77698	−	8.49807i	0.395242	−	0.495617i
$295$		0			0
$296$	3.71870	−	7.72196i	0.216145	−	0.448830i
$297$	−7.22574	−	0.814146i	−0.419280	−	0.0472415i
$298$	−19.9024	−	4.54259i	−1.15291	−	0.263145i
$299$	−0.453758	+	1.98804i	−0.0262415	+	0.114972i
$300$		0			0
$301$	0.107908	+	0.0678028i	0.00621969	+	0.00390809i
$302$	−30.4131			−1.75007
$303$	8.34869	+	5.24583i	0.479620	+	0.301365i
$304$	−4.70915	−	13.4580i	−0.270089	−	0.771869i
$305$		0			0
$306$	3.09936	+	13.5792i	0.177179	+	0.776271i
$307$		−	16.3838i		−	0.935075i	−0.883973	−	0.467538i	$-0.845141\pi$
$307$		−	16.3838i		−	0.935075i	0.883973	−	0.467538i	$-0.154859\pi$
$308$	0.0949741	−	0.0216772i	0.00541165	−	0.00123517i
$309$	−0.587764	+	0.0662251i	−0.0334367	+	0.00376741i
$310$		0			0
$311$	10.3934	+	16.5410i	0.589354	+	0.937951i	0.999662	+	0.0260043i	$0.00827836\pi$
$311$	10.3934	+	16.5410i	0.589354	+	0.937951i	−0.410308	+	0.911947i	$0.634579\pi$
$312$	0.517186	−	4.59016i	0.0292799	−	0.259866i
$313$	6.20293	+	17.7270i	0.350610	+	1.00199i	0.975256	+	0.221079i	$0.0709577\pi$
$313$	6.20293	+	17.7270i	0.350610	+	1.00199i	−0.624646	+	0.780908i	$0.714757\pi$
$314$	17.0233	+	35.3493i	0.960682	+	1.99488i
$315$		0			0
$316$	0.317609	−	2.81886i	0.0178669	−	0.158573i
$317$	−3.87760	+	1.86736i	−0.217788	+	0.104881i	−0.539597	−	0.841923i	$-0.681423\pi$
$317$	−3.87760	+	1.86736i	−0.217788	+	0.104881i	0.321809	+	0.946805i	$0.395709\pi$
$318$	−3.71536	+	3.71536i	−0.208347	+	0.208347i
$319$	−6.99650	−	5.02376i	−0.391729	−	0.281276i
$320$		0			0
$321$	−3.78486	+	10.8165i	−0.211250	+	0.603718i
$322$	0.0376129	−	0.0299953i	0.00209608	−	0.00167157i
$323$	1.11227	+	9.87169i	0.0618885	+	0.549276i
$324$	3.08776	−	1.48699i	0.171542	−	0.0826105i
$325$		0			0
$326$	13.2603	+	16.6279i	0.734421	+	0.920935i
$327$	−3.37343	+	14.7799i	−0.186551	+	0.817333i
$328$	2.01748	+	3.21080i	0.111397	+	0.177287i
$329$	−0.0206381	−	0.183168i	−0.00113782	−	0.0100984i
$330$		0			0
$331$	−7.44773	−	7.44773i	−0.409364	−	0.409364i	0.472153	−	0.881517i	$-0.343477\pi$
$331$	−7.44773	−	7.44773i	−0.409364	−	0.409364i	−0.881517	+	0.472153i	$0.843477\pi$
$332$	−7.39618	+	11.7709i	−0.405918	+	0.646015i
$333$	12.3855	+	5.96453i	0.678720	+	0.326854i
$334$	−41.6923	+	14.5888i	−2.28130	+	0.798261i
$335$		0			0
$336$	−0.151644	+	0.151644i	−0.00827285	+	0.00827285i
$337$	5.30703	+	23.2516i	0.289092	+	1.26660i	0.885773	+	0.464118i	$0.153629\pi$
$337$	5.30703	+	23.2516i	0.289092	+	1.26660i	−0.596681	+	0.802479i	$0.703514\pi$
$338$	1.63096	−	2.04516i	0.0887125	−	0.111242i
$339$	−2.23957	−	0.511166i	−0.121637	−	0.0277627i
$340$		0			0
$341$	−2.16899	+	1.72971i	−0.117458	+	0.0936693i
$342$	10.9689	−	3.83818i	0.593130	−	0.207545i
$343$	0.660705	+	0.231191i	0.0356747	+	0.0124831i
$344$	2.79523	+	2.22912i	0.150709	+	0.120186i
$345$		0			0
$346$	21.3035	+	7.45443i	1.14529	+	0.400753i
$347$	22.4557	+	22.4557i	1.20549	+	1.20549i	0.972474	+	0.233012i	$0.0748581\pi$
$347$	22.4557	+	22.4557i	1.20549	+	1.20549i	0.233012	+	0.972474i	$0.425142\pi$
$348$	−5.66852	−	0.350372i	−0.303864	−	0.0187819i
$349$		−	9.37948i		−	0.502072i	−0.967978	−	0.251036i	$-0.919229\pi$
$349$		−	9.37948i		−	0.502072i	0.967978	−	0.251036i	$-0.0807713\pi$
$350$		0			0
$351$	17.1779	+	1.93548i	0.916886	+	0.103308i
$352$	9.66074	−	1.08850i	0.514919	−	0.0580175i
$353$	10.4307	−	29.8092i	0.555169	−	1.58658i	−0.233889	−	0.972263i	$-0.575145\pi$
$353$	10.4307	−	29.8092i	0.555169	−	1.58658i	0.789058	−	0.614319i	$-0.210569\pi$
$354$	6.03648	+	2.90702i	0.320835	+	0.154506i
$355$		0			0
$356$	−2.31226	+	1.45289i	−0.122549	+	0.0770029i
$357$	0.126518	−	0.0794962i	0.00669602	−	0.00420739i
$358$	2.77200	+	2.21060i	0.146505	+	0.116834i
$359$	−10.9969	+	17.5015i	−0.580397	+	0.923696i	0.419476	+	0.907766i	$0.362214\pi$
$359$	−10.9969	+	17.5015i	−0.580397	+	0.923696i	−0.999873	+	0.0159298i	$0.994929\pi$
$360$		0			0
$361$	−10.4430	+	2.38354i	−0.549631	+	0.125450i
$362$	−10.0982	+	20.9692i	−0.530752	+	1.10212i
$363$	−3.17163	+	6.58595i	−0.166467	+	0.345673i
$364$	−0.225783	+	0.0515335i	−0.0118343	+	0.00270109i
$365$		0			0
$366$	−6.41998	+	10.2173i	−0.335578	+	0.534069i
$367$	−23.5550	−	18.7845i	−1.22956	−	0.980542i	−0.999974	−	0.00725434i	$-0.997691\pi$
$367$	−23.5550	−	18.7845i	−1.22956	−	0.980542i	−0.229588	−	0.973288i	$-0.573738\pi$
$368$	2.24886	−	1.41305i	0.117230	−	0.0736606i
$369$	−5.14989	+	3.23589i	−0.268093	+	0.168454i
$370$		0			0
$371$	−0.152405	−	0.0733946i	−0.00791250	−	0.00381046i
$372$	−0.604162	+	1.72660i	−0.0313244	+	0.0895199i
$373$	36.7720	−	4.14321i	1.90398	−	0.214527i	0.919889	−	0.392179i	$-0.128279\pi$
$373$	36.7720	−	4.14321i	1.90398	−	0.214527i	0.984093	+	0.177652i	$0.0568501\pi$
$374$	−9.83816	−	1.10849i	−0.508719	−	0.0573189i
$375$		0			0
$376$		−	5.17112i		−	0.266680i
$377$	16.6329	+	11.9430i	0.856636	+	0.615098i
$378$	−0.288379	−	0.288379i	−0.0148326	−	0.0148326i
$379$	22.8719	+	8.00324i	1.17485	+	0.411099i	0.845949	−	0.533264i	$-0.179035\pi$
$379$	22.8719	+	8.00324i	1.17485	+	0.411099i	0.328904	+	0.944363i	$0.393321\pi$
$380$		0			0
$381$	−8.08666	−	6.44890i	−0.414292	−	0.330387i
$382$	−22.5509	−	7.89089i	−1.15380	−	0.403733i
$383$	4.68168	−	1.63819i	0.239223	−	0.0837077i	−0.208005	−	0.978128i	$-0.566697\pi$
$383$	4.68168	−	1.63819i	0.239223	−	0.0837077i	0.447228	+	0.894420i	$0.352411\pi$
$384$	−7.01732	+	5.59612i	−0.358101	+	0.285576i
$385$		0			0
$386$	19.9013	+	4.54233i	1.01295	+	0.231199i
$387$	−3.57536	+	4.48336i	−0.181746	+	0.227902i
$388$	−2.82027	−	12.3564i	−0.143178	−	0.627302i
$389$	−23.2351	+	23.2351i	−1.17807	+	1.17807i	−0.197832	+	0.980236i	$0.563390\pi$
$389$	−23.2351	+	23.2351i	−1.17807	+	1.17807i	−0.980236	+	0.197832i	$0.936610\pi$
$390$		0			0
$391$	−1.74666	+	0.611183i	−0.0883324	+	0.0309088i
$392$	8.84476	+	4.25941i	0.446728	+	0.215133i
$393$	−8.27589	+	13.1710i	−0.417463	+	0.664389i
$394$	−29.1425	−	29.1425i	−1.46818	−	1.46818i
$395$		0			0
$396$	0.490787	+	4.35585i	0.0246630	+	0.218890i
$397$	−11.1348	−	17.7209i	−0.558838	−	0.889386i	0.441129	−	0.897444i	$-0.354578\pi$
$397$	−11.1348	−	17.7209i	−0.558838	−	0.889386i	−0.999968	+	0.00805748i	$0.997435\pi$
$398$	−0.876528	+	3.84032i	−0.0439364	+	0.192498i
$399$	−0.0777286	−	0.0974686i	−0.00389130	−	0.00487953i
$400$		0			0
$401$	−11.6907	+	5.62994i	−0.583806	+	0.281146i	−0.702383	−	0.711799i	$-0.747881\pi$
$401$	−11.6907	+	5.62994i	−0.583806	+	0.281146i	0.118578	+	0.992945i	$0.462166\pi$
$402$	−1.48542	−	13.1835i	−0.0740861	−	0.657532i
$403$	5.15638	−	4.11207i	0.256857	−	0.204837i
$404$	4.58041	−	13.0901i	0.227884	−	0.651255i
$405$		0			0
$406$	−0.131119	−	0.464953i	−0.00650735	−	0.0230752i
$407$	−6.90940	+	6.90940i	−0.342486	+	0.342486i
$408$	3.77671	−	1.81877i	0.186975	−	0.0900423i
$409$	0.292252	−	2.59381i	0.0144509	−	0.128256i	−0.984415	−	0.175859i	$-0.943730\pi$
$409$	0.292252	−	2.59381i	0.0144509	−	0.128256i	0.998866	+	0.0476033i	$0.0151583\pi$
$410$		0			0
$411$	−3.43730	−	7.13762i	−0.169549	−	0.352073i
$412$	0.274771	+	0.785249i	0.0135370	+	0.0386865i
$413$	−0.0241507	+	0.214343i	−0.00118838	+	0.0105471i
$414$	1.15171	+	1.83293i	0.0566032	+	0.0900835i
$415$		0			0
$416$	−22.9666	+	2.58772i	−1.12603	+	0.126873i
$417$	15.7491	−	3.59462i	0.771235	−	0.176029i
$418$			8.26031i			0.404025i
$419$	3.84687	+	16.8542i	0.187932	+	0.823384i	0.977705	+	0.209984i	$0.0673413\pi$
$419$	3.84687	+	16.8542i	0.187932	+	0.823384i	−0.789773	+	0.613399i	$0.789802\pi$
$420$		0			0
$421$	−3.22153	−	9.20660i	−0.157008	−	0.448702i	0.838329	−	0.545165i	$-0.183533\pi$
$421$	−3.22153	−	9.20660i	−0.157008	−	0.448702i	−0.995337	+	0.0964625i	$0.969247\pi$
$422$	−15.1827	−	9.53990i	−0.739080	−	0.464395i
$423$	8.29412			0.403274
$424$	−4.01816	−	2.52478i	−0.195139	−	0.122614i
$425$		0			0
$426$	−2.93854	+	12.8746i	−0.142373	+	0.623777i
$427$	−0.378741	−	0.0864453i	−0.0183286	−	0.00418338i
$428$	16.0168	+	1.80466i	0.774201	+	0.0872315i
$429$	−2.28496	+	4.74476i	−0.110319	+	0.229079i
$430$		0			0
$431$	−10.7212	+	13.4440i	−0.516424	+	0.647575i	−0.969845	−	0.243721i	$-0.921632\pi$
$431$	−10.7212	+	13.4440i	−0.516424	+	0.647575i	0.453422	+	0.891296i	$0.350203\pi$
$432$	−14.0380	−	17.6031i	−0.675404	−	0.846929i
$433$	−2.38901	−	4.96082i	−0.114808	−	0.238402i	0.835645	−	0.549271i	$-0.185094\pi$
$433$	−2.38901	−	4.96082i	−0.114808	−	0.238402i	−0.950453	+	0.310869i	$0.899380\pi$
$434$	−0.155597			−0.00746889
$435$		0			0
$436$	21.3229			1.02118
$437$	0.669894	+	1.39105i	0.0320454	+	0.0665430i
$438$	2.13326	+	2.67503i	0.101931	+	0.127818i
$439$	−2.44429	+	3.06504i	−0.116659	+	0.146286i	−0.836732	−	0.547612i	$-0.815537\pi$
$439$	−2.44429	+	3.06504i	−0.116659	+	0.146286i	0.720073	+	0.693898i	$0.244108\pi$
$440$		0			0
$441$	−6.83180	+	14.1864i	−0.325324	+	0.675542i
$442$	23.3884	+	2.63524i	1.11247	+	0.125346i
$443$	−31.1792	−	7.11646i	−1.48137	−	0.338113i	−0.595995	−	0.802988i	$-0.703242\pi$
$443$	−31.1792	−	7.11646i	−1.48137	−	0.338113i	−0.885376	+	0.464875i	$0.846099\pi$
$444$	−1.43368	+	6.28138i	−0.0680396	+	0.298101i
$445$		0			0
$446$	9.43219	+	5.92664i	0.446627	+	0.280634i
$447$	−9.85416			−0.466086
$448$	0.0422803	+	0.0265665i	0.00199756	+	0.00125515i
$449$	−2.93533	−	8.38870i	−0.138527	−	0.395887i	0.853631	−	0.520878i	$-0.174395\pi$
$449$	−2.93533	−	8.38870i	−0.138527	−	0.395887i	−0.992158	+	0.124991i	$0.960110\pi$
$450$		0			0
$451$	−0.962009	−	4.21484i	−0.0452992	−	0.198469i
$452$			3.23101i			0.151974i
$453$	−14.3127	+	3.26677i	−0.672467	+	0.153486i
$454$	−18.3507	+	2.06763i	−0.861243	+	0.0970388i
$455$		0			0
$456$	−1.86073	−	2.96134i	−0.0871368	−	0.138677i
$457$	3.43818	−	30.5147i	0.160831	−	1.42742i	−0.611021	−	0.791614i	$-0.709241\pi$
$457$	3.43818	−	30.5147i	0.160831	−	1.42742i	0.771852	−	0.635802i	$-0.219331\pi$
$458$	1.72020	+	4.91606i	0.0803798	+	0.229712i
$459$	6.80641	+	14.1337i	0.317696	+	0.659703i
$460$		0			0
$461$	−0.686954	+	6.09689i	−0.0319946	+	0.283960i	0.967520	+	0.252796i	$0.0813501\pi$
$461$	−0.686954	+	6.09689i	−0.0319946	+	0.283960i	−0.999514	+	0.0311644i	$0.990078\pi$
$462$	0.111940	−	0.0539073i	0.00520790	−	0.00250799i
$463$	−8.48374	+	8.48374i	−0.394273	+	0.394273i	−0.876207	−	0.481935i	$-0.839934\pi$
$463$	−8.48374	+	8.48374i	−0.394273	+	0.394273i	0.481935	+	0.876207i	$0.339934\pi$
$464$	−4.31925	−	26.3180i	−0.200516	−	1.22178i
$465$		0			0
$466$	−8.15177	+	23.2964i	−0.377624	+	1.07919i
$467$	−4.46810	+	3.56319i	−0.206759	+	0.164885i	−0.721395	−	0.692524i	$-0.756499\pi$
$467$	−4.46810	+	3.56319i	−0.206759	+	0.164885i	0.514636	+	0.857409i	$0.327927\pi$
$468$	−1.16675	−	10.3552i	−0.0539332	−	0.478671i
$469$	0.384816	−	0.185318i	0.0177692	−	0.00855718i
$470$		0			0
$471$	11.8083	+	14.8072i	0.544099	+	0.682278i
$472$	−1.34652	+	5.89951i	−0.0619788	+	0.271547i
$473$	−2.16860	−	3.45131i	−0.0997125	−	0.158692i
$474$	−0.405074	−	3.59513i	−0.0186057	−	0.165130i
$475$		0			0
$476$	−0.148607	−	0.148607i	−0.00681141	−	0.00681141i
$477$	4.04957	−	6.44485i	0.185417	−	0.295090i
$478$	−28.6910	−	13.8168i	−1.31229	−	0.631967i
$479$	0.512120	−	0.179198i	0.0233993	−	0.00818778i	−0.318554	−	0.947905i	$-0.603197\pi$
$479$	0.512120	−	0.179198i	0.0233993	−	0.00818778i	0.341953	+	0.939717i	$0.388912\pi$
$480$		0			0
$481$	16.4258	−	16.4258i	0.748952	−	0.748952i
$482$	7.46151	+	32.6910i	0.339863	+	1.48904i
$483$	0.0144791	−	0.0181562i	0.000658820	−	0.000826134i
$484$	10.0237	+	2.28784i	0.455623	+	0.103993i
$485$		0			0
$486$	22.5455	−	17.9795i	1.02269	−	0.815565i
$487$	35.1198	−	12.2890i	1.59143	−	0.556866i	0.618065	−	0.786127i	$-0.287917\pi$
$487$	35.1198	−	12.2890i	1.59143	−	0.556866i	0.973365	+	0.229261i	$0.0736310\pi$
$488$	−10.2869	−	3.59953i	−0.465665	−	0.162943i
$489$	8.02648	+	6.40091i	0.362970	+	0.289459i
$490$		0			0
$491$	17.2250	+	6.02730i	0.777355	+	0.272008i	0.689654	−	0.724139i	$-0.257762\pi$
$491$	17.2250	+	6.02730i	0.777355	+	0.272008i	0.0877005	+	0.996147i	$0.472048\pi$
$492$	−2.01568	−	2.01568i	−0.0908737	−	0.0908737i
$493$	−1.14637	+	18.5466i	−0.0516300	+	0.835298i
$494$		−	19.6373i		−	0.883526i
$495$		0			0
$496$	−8.53610	−	0.961788i	−0.383282	−	0.0431856i
$497$	−0.422471	+	0.0476010i	−0.0189504	+	0.00213520i
$498$	−5.85588	+	16.7351i	−0.262408	+	0.749920i
$499$	8.25425	+	3.97504i	0.369511	+	0.177947i	0.609419	−	0.792849i	$-0.291403\pi$
$499$	8.25425	+	3.97504i	0.369511	+	0.177947i	−0.239908	+	0.970796i	$0.577117\pi$
$500$		0			0
$501$	−18.0537	+	11.3439i	−0.806581	+	0.506808i
$502$	−6.03483	+	3.79193i	−0.269348	+	0.169242i
$503$	−14.8659	−	11.8551i	−0.662836	−	0.528594i	0.233282	−	0.972409i	$-0.425053\pi$
$503$	−14.8659	−	11.8551i	−0.662836	−	0.528594i	−0.896119	+	0.443815i	$0.853625\pi$
$504$	0.0839903	−	0.133670i	0.00374122	−	0.00595413i
$505$		0			0
$506$	−1.50013	+	0.342394i	−0.0666888	+	0.0152213i
$507$	0.547867	−	1.13766i	0.0243316	−	0.0505251i
$508$	−6.31214	+	13.1073i	−0.280056	+	0.581542i
$509$	36.0022	−	8.21727i	1.59577	−	0.364224i	0.670014	−	0.742348i	$-0.266288\pi$
$509$	36.0022	−	8.21727i	1.59577	−	0.364224i	0.925755	+	0.378124i	$0.123431\pi$
$510$		0			0
$511$	−0.0586040	+	0.0932678i	−0.00259249	+	0.00412592i
$512$	12.6709	+	10.1047i	0.559978	+	0.446568i
$513$	11.0823	−	6.96347i	0.489295	−	0.307445i
$514$	−37.4048	+	23.5030i	−1.64986	+	1.03667i
$515$		0			0
$516$	−2.42147	−	1.16612i	−0.106599	−	0.0513356i
$517$	−1.94717	+	5.56469i	−0.0856363	+	0.244735i
$518$	−0.544593	+	0.0613609i	−0.0239280	+	0.00269604i
$519$	10.8263	+	1.21984i	0.475224	+	0.0535448i
$520$		0			0
$521$			12.6825i			0.555630i	0.960635	+	0.277815i	$0.0896102\pi$
$521$			12.6825i			0.555630i	−0.960635	+	0.277815i	$0.910390\pi$
$522$	21.4504	−	3.52039i	0.938858	−	0.154083i
$523$	−24.6658	−	24.6658i	−1.07856	−	1.07856i	−0.996639	−	0.0819190i	$-0.973895\pi$
$523$	−24.6658	−	24.6658i	−1.07856	−	1.07856i	−0.0819190	−	0.996639i	$-0.526105\pi$
$524$	20.6510	+	7.22611i	0.902145	+	0.315674i
$525$		0			0
$526$	−11.3911	−	9.08410i	−0.496676	−	0.396086i
$527$	5.64919	+	1.97674i	0.246083	+	0.0861081i
$528$	6.47426	−	2.26544i	0.281756	−	0.0985907i
$529$	17.7573	−	14.1609i	0.772055	−	0.615693i
$530$		0			0
$531$	−9.46240	−	2.15973i	−0.410633	−	0.0937244i
$532$	−0.109327	+	0.137092i	−0.00473993	+	0.00594368i
$533$	2.28700	+	10.0200i	0.0990609	+	0.434014i
$534$	−2.46275	+	2.46275i	−0.106574	+	0.106574i
$535$		0			0
$536$	11.3098	−	3.95749i	0.488511	−	0.170937i
$537$	1.54197	+	0.742576i	0.0665411	+	0.0320445i
$538$	−7.59317	+	12.0845i	−0.327365	+	0.520998i
$539$	−7.91405	−	7.91405i	−0.340882	−	0.340882i
$540$		0			0
$541$	1.45294	+	12.8952i	0.0624669	+	0.554409i	0.985498	+	0.169685i	$0.0542749\pi$
$541$	1.45294	+	12.8952i	0.0624669	+	0.554409i	−0.923032	+	0.384724i	$0.874297\pi$
$542$	−24.3572	−	38.7642i	−1.04623	−	1.66506i
$543$	−2.49995	+	10.9530i	−0.107283	+	0.470037i
$544$	−13.0768	−	16.3978i	−0.560664	−	0.703051i
$545$		0			0
$546$	−0.266116	+	0.128155i	−0.0113887	+	0.00548451i
$547$	1.38325	+	12.2767i	0.0591435	+	0.524913i	0.987998	+	0.154468i	$0.0493663\pi$
$547$	1.38325	+	12.2767i	0.0591435	+	0.524913i	−0.928854	+	0.370445i	$0.879205\pi$
$548$	−8.71171	+	6.94736i	−0.372146	+	0.296776i
$549$	5.77340	−	16.4994i	0.246403	−	0.704178i
$550$		0			0
$551$	15.4840	−	0.782110i	0.659640	−	0.0333190i
$552$	0.460671	−	0.460671i	0.0196074	−	0.0196074i
$553$	0.104939	−	0.0505361i	0.00446247	−	0.00214901i
$554$	3.67523	−	32.6186i	0.156146	−	1.38583i
$555$		0			0
$556$	−9.85830	−	20.4710i	−0.418085	−	0.868163i
$557$	−6.07412	−	17.3588i	−0.257369	−	0.735518i	−0.997977	−	0.0635804i	$-0.979748\pi$
$557$	−6.07412	−	17.3588i	−0.257369	−	0.735518i	0.740608	−	0.671937i	$-0.234538\pi$
$558$	0.783902	−	6.95732i	0.0331852	−	0.294527i
$559$	5.15545	+	8.20485i	0.218052	+	0.347028i
$560$		0			0
$561$	−4.74899	+	0.535083i	−0.200503	+	0.0225912i
$562$	41.8498	−	9.55194i	1.76533	−	0.402924i
$563$		−	33.1694i		−	1.39792i	−0.715159	−	0.698962i	$-0.753646\pi$
$563$		−	33.1694i		−	1.39792i	0.715159	−	0.698962i	$-0.246354\pi$
$564$	0.865009	+	3.78985i	0.0364235	+	0.159582i
$565$		0			0
$566$	−18.6058	−	53.1724i	−0.782062	−	2.23500i
$567$	0.119150	+	0.0748666i	0.00500381	+	0.00314410i
$568$	−11.9270			−0.500445
$569$	−12.1703	−	7.64712i	−0.510207	−	0.320584i	0.252208	−	0.967673i	$-0.418843\pi$
$569$	−12.1703	−	7.64712i	−0.510207	−	0.320584i	−0.762414	+	0.647089i	$0.775986\pi$
$570$		0			0
$571$	2.48794	−	10.9004i	0.104117	−	0.456166i	−0.895814	−	0.444429i	$-0.853407\pi$
$571$	2.48794	−	10.9004i	0.104117	−	0.456166i	0.999931	−	0.0117373i	$-0.00373617\pi$
$572$	7.22144	+	1.64825i	0.301944	+	0.0689166i
$573$	−11.4602	−	1.29126i	−0.478758	−	0.0539430i
$574$	0.105205	−	0.218461i	0.00439119	−	0.00911839i
$575$		0			0
$576$	−1.40090	+	1.75667i	−0.0583707	+	0.0731945i
$577$	−16.5686	−	20.7764i	−0.689761	−	0.864933i	0.306451	−	0.951886i	$-0.400858\pi$
$577$	−16.5686	−	20.7764i	−0.689761	−	0.864933i	−0.996212	+	0.0869530i	$0.972287\pi$
$578$	−3.96432	−	8.23200i	−0.164894	−	0.342406i
$579$	9.85362			0.409502
$580$		0			0
$581$	−0.570802			−0.0236809
$582$	−7.01350	−	14.5637i	−0.290719	−	0.603684i
$583$	3.37328	+	4.22996i	0.139707	+	0.175187i
$584$	−1.92670	+	2.41600i	−0.0797273	+	0.0999749i
$585$		0			0
$586$	4.74549	−	9.85412i	0.196035	−	0.407070i
$587$	8.00006	+	0.901390i	0.330198	+	0.0372044i	0.275507	−	0.961299i	$-0.411154\pi$
$587$	8.00006	+	0.901390i	0.330198	+	0.0372044i	0.0546906	+	0.998503i	$0.482583\pi$
$588$	−7.19472	−	1.64215i	−0.296705	−	0.0677210i
$589$	1.11117	−	4.86837i	0.0457851	−	0.200598i
$590$		0			0
$591$	−16.8450	−	10.5844i	−0.692912	−	0.435385i
$592$	−30.2558			−1.24351
$593$	−32.3840	−	20.3482i	−1.32985	−	0.835600i	−0.335529	−	0.942030i	$-0.608915\pi$
$593$	−32.3840	−	20.3482i	−1.32985	−	0.835600i	−0.994320	+	0.106430i	$0.966058\pi$
$594$	4.30815	+	12.3120i	0.176766	+	0.505167i
$595$		0			0
$596$	3.08416	+	13.5126i	0.126332	+	0.553498i
$597$			1.90144i			0.0778207i
$598$	3.56627	−	0.813978i	0.145836	−	0.0332861i
$599$	46.8364	−	5.27719i	1.91368	−	0.215620i	0.926625	−	0.375986i	$-0.122696\pi$
$599$	46.8364	−	5.27719i	1.91368	−	0.215620i	0.987058	+	0.160366i	$0.0512674\pi$
$600$		0			0
$601$	1.29346	+	2.05853i	0.0527614	+	0.0839693i	0.872063	−	0.489393i	$-0.162782\pi$
$601$	1.29346	+	2.05853i	0.0527614	+	0.0839693i	−0.819302	+	0.573362i	$0.805639\pi$
$602$	0.0255964	−	0.227174i	0.00104323	−	0.00925893i
$603$	6.34753	+	18.1402i	0.258492	+	0.738727i
$604$	8.95917	+	18.6039i	0.364543	+	0.756982i
$605$		0			0
$606$	1.98036	−	17.5762i	0.0804468	−	0.713985i
$607$	−25.4732	+	12.2672i	−1.03392	+	0.497912i	−0.872316	−	0.488943i	$-0.837383\pi$
$607$	−25.4732	+	12.2672i	−1.03392	+	0.497912i	−0.161609	+	0.986855i	$0.551668\pi$
$608$	−12.3737	+	12.3737i	−0.501821	+	0.501821i
$609$	−0.111648	−	0.204727i	−0.00452421	−	0.00829596i
$610$		0			0
$611$	4.62903	−	13.2290i	0.187270	−	0.535188i
$612$	7.39348	−	5.89610i	0.298864	−	0.238336i
$613$	2.64828	+	23.5041i	0.106963	+	0.949323i	0.926499	+	0.376296i	$0.122802\pi$
$613$	2.64828	+	23.5041i	0.106963	+	0.949323i	−0.819536	+	0.573027i	$0.805769\pi$
$614$	−26.4797	+	12.7520i	−1.06864	+	0.514628i
$615$		0			0
$616$	0.0699637	+	0.0877317i	0.00281892	+	0.00353481i
$617$	−3.95851	+	17.3434i	−0.159364	+	0.698218i	0.830597	+	0.556874i	$0.187999\pi$
$617$	−3.95851	+	17.3434i	−0.159364	+	0.698218i	−0.989961	+	0.141344i	$0.954858\pi$
$618$	0.564506	+	0.898406i	0.0227078	+	0.0361392i
$619$	5.39810	+	47.9094i	0.216968	+	1.92564i	0.354328	+	0.935121i	$0.384710\pi$
$619$	5.39810	+	47.9094i	0.216968	+	1.92564i	−0.137360	+	0.990521i	$0.543862\pi$
$620$		0			0
$621$	1.72398	+	1.72398i	0.0691809	+	0.0691809i
$622$	18.6442	−	29.6721i	0.747566	−	1.18974i
$623$	−0.101023	−	0.0486501i	−0.00404740	−	0.00194912i
$624$	−15.3914	+	5.38567i	−0.616147	+	0.215599i
$625$		0			0
$626$	23.8226	−	23.8226i	0.952143	−	0.952143i
$627$	0.887268	+	3.88737i	0.0354341	+	0.155247i
$628$	16.6087	−	20.8266i	0.662758	−	0.831072i
$629$	20.5518	+	4.69082i	0.819455	+	0.187035i
$630$		0			0
$631$	24.3390	−	19.4097i	0.968921	−	0.772688i	−0.00490424	−	0.999988i	$-0.501561\pi$
$631$	24.3390	−	19.4097i	0.968921	−	0.772688i	0.973825	+	0.227300i	$0.0729896\pi$
$632$	3.08419	−	1.07921i	0.122683	−	0.0429285i
$633$	−8.16980	−	2.85874i	−0.324721	−	0.113625i
$634$	6.03608	+	4.81361i	0.239723	+	0.191173i
$635$		0			0
$636$	3.36720	+	1.17823i	0.133518	+	0.0467200i
$637$	18.8142	+	18.8142i	0.745445	+	0.745445i
$638$	−2.67390	+	15.2179i	−0.105861	+	0.602484i
$639$		−	19.1301i		−	0.756773i
$640$		0			0
$641$	−47.2768	−	5.32682i	−1.86732	−	0.210397i	−0.895328	−	0.445406i	$-0.853059\pi$
$641$	−47.2768	−	5.32682i	−1.86732	−	0.210397i	−0.971993	+	0.235010i	$0.924488\pi$
$642$	20.4276	−	2.30164i	0.806213	−	0.0908384i
$643$	0.0747317	−	0.213571i	0.00294713	−	0.00842241i	−0.942400	−	0.334487i	$-0.891437\pi$
$643$	0.0747317	−	0.213571i	0.00294713	−	0.00842241i	0.945348	+	0.326065i	$0.105723\pi$
$644$	−0.0294284	−	0.0141720i	−0.00115964	−	0.000558455i
$645$		0			0
$646$	15.0890	−	9.48106i	0.593670	−	0.373028i
$647$	−35.1731	+	22.1007i	−1.38280	+	0.868868i	−0.998522	−	0.0543507i	$-0.982691\pi$
$647$	−35.1731	+	22.1007i	−1.38280	+	0.868868i	−0.384274	+	0.923219i	$0.625548\pi$
$648$	3.08644	+	2.46136i	0.121247	+	0.0966912i
$649$	3.67044	−	5.84148i	0.144078	−	0.229298i
$650$		0			0
$651$	−0.0732253	+	0.0167132i	−0.00286993	+	0.000655042i
$652$	6.26516	−	13.0097i	0.245363	−	0.509501i
$653$	7.55731	−	15.6929i	0.295740	−	0.614111i	−0.699161	−	0.714964i	$-0.746443\pi$
$653$	7.55731	−	15.6929i	0.295740	−	0.614111i	0.994901	+	0.100853i	$0.0321572\pi$
$654$	26.5131	−	6.05145i	1.03675	−	0.236630i
$655$		0			0
$656$	7.12197	−	11.3346i	0.278066	−	0.442540i
$657$	−3.87510	−	3.09029i	−0.151182	−	0.120564i
$658$	−0.279976	+	0.175920i	−0.0109146	+	0.00685809i
$659$	−36.8444	+	23.1509i	−1.43526	+	0.901831i	−0.435257	+	0.900306i	$0.643342\pi$
$659$	−36.8444	+	23.1509i	−1.43526	+	0.901831i	−0.999999	+	0.00152434i	$0.999515\pi$
$660$		0			0
$661$	−10.9914	−	5.29320i	−0.427518	−	0.205882i	0.207736	−	0.978185i	$-0.433390\pi$
$661$	−10.9914	−	5.29320i	−0.427518	−	0.205882i	−0.635254	+	0.772303i	$0.719105\pi$
$662$	−6.24034	+	17.8339i	−0.242538	+	0.693133i
$663$	11.2898	−	1.27206i	0.438461	−	0.0494027i
$664$	−15.9126	−	1.79292i	−0.617528	−	0.0695787i
$665$		0			0
$666$		−	24.6599i		−	0.955552i
$667$	0.783855	+	2.77957i	0.0303510	+	0.107626i
$668$	21.2059	+	21.2059i	0.820480	+	0.820480i
$669$	5.07547	+	1.77598i	0.196229	+	0.0686635i
$670$		0			0
$671$	9.71439	+	7.74697i	0.375020	+	0.299068i
$672$	0.248434	+	0.0869310i	0.00958357	+	0.00335344i
$673$	29.8369	−	10.4404i	1.15013	−	0.402447i	0.313161	−	0.949700i	$-0.398612\pi$
$673$	29.8369	−	10.4404i	1.15013	−	0.402447i	0.836967	+	0.547253i	$0.184326\pi$
$674$	33.4489	−	26.6746i	1.28841	−	1.02747i
$675$		0			0
$676$	−1.73149	−	0.395202i	−0.0665959	−	0.0152001i
$677$	−16.8498	+	21.1289i	−0.647589	+	0.812051i	−0.991929	−	0.126794i	$-0.959531\pi$
$677$	−16.8498	+	21.1289i	−0.647589	+	0.812051i	0.344340	+	0.938845i	$0.388103\pi$
$678$	0.916961	+	4.01747i	0.0352157	+	0.154290i
$679$	0.367977	−	0.367977i	0.0141217	−	0.0141217i
$680$		0			0
$681$	−8.41393	+	2.94416i	−0.322422	+	0.112821i
$682$	4.48377	+	2.15927i	0.171692	+	0.0826827i
$683$	7.06210	−	11.2393i	0.270224	−	0.430058i	−0.683854	−	0.729619i	$-0.739697\pi$
$683$	7.06210	−	11.2393i	0.270224	−	0.430058i	0.954077	+	0.299561i	$0.0968402\pi$
$684$	−5.57909	−	5.57909i	−0.213322	−	0.213322i
$685$		0			0
$686$	−0.140591	−	1.24778i	−0.00536779	−	0.0476405i
$687$	1.33759	+	2.12877i	0.0510323	+	0.0812175i
$688$	2.80845	−	12.3046i	0.107071	−	0.469110i
$689$	−8.01935	−	10.0559i	−0.305513	−	0.383101i
$690$		0			0
$691$	−17.7230	+	8.53497i	−0.674216	+	0.324685i	−0.739476	−	0.673183i	$-0.764927\pi$
$691$	−17.7230	+	8.53497i	−0.674216	+	0.324685i	0.0652598	+	0.997868i	$0.479212\pi$
$692$	−1.71573	−	15.2275i	−0.0652221	−	0.578862i
$693$	−0.140716	+	0.112217i	−0.00534534	+	0.00426277i
$694$	18.8153	−	53.7711i	0.714219	−	2.04112i
$695$		0			0
$696$	−2.46942	−	6.05799i	−0.0936033	−	0.229628i
$697$	−6.59502	+	6.59502i	−0.249804	+	0.249804i
$698$	−15.1592	+	7.30030i	−0.573785	+	0.276320i
$699$	−1.33395	+	11.8391i	−0.0504545	+	0.447796i
$700$		0			0
$701$	1.46305	+	3.03806i	0.0552588	+	0.114746i	0.926770	−	0.375630i	$-0.122574\pi$
$701$	1.46305	+	3.03806i	0.0552588	+	0.114746i	−0.871511	+	0.490376i	$0.836859\pi$
$702$	−10.2418	−	29.2695i	−0.386553	−	1.10471i
$703$	1.96925	−	17.4776i	0.0742717	−	0.659180i
$704$	−0.849702	−	1.35229i	−0.0320243	−	0.0509664i
$705$		0			0
$706$	−56.2964	+	6.34308i	−2.11874	+	0.238725i
$707$	0.555152	−	0.126710i	0.0208786	−	0.00476541i
$708$		−	4.54892i		−	0.170959i
$709$	0.0430267	+	0.188512i	0.00161590	+	0.00707973i	0.975729	−	0.218980i	$-0.0702728\pi$
$709$	0.0430267	+	0.188512i	0.00161590	+	0.00707973i	−0.974114	+	0.226059i	$0.927416\pi$
$710$		0			0
$711$	1.73097	+	4.94683i	0.0649165	+	0.185521i
$712$	−2.66346	−	1.67357i	−0.0998175	−	0.0627195i
$713$	0.930187			0.0348358
$714$	−0.226955	−	0.142605i	−0.00849356	−	0.00533686i
$715$		0			0
$716$	0.535655	−	2.34686i	0.0200184	−	0.0877062i
$717$	−14.9863	−	3.42053i	−0.559675	−	0.127742i
$718$	36.8454	+	4.15148i	1.37506	+	0.154932i
$719$	10.8827	−	22.5981i	0.405856	−	0.842768i	−0.593427	−	0.804888i	$-0.702225\pi$
$719$	10.8827	−	22.5981i	0.405856	−	0.842768i	0.999282	−	0.0378799i	$-0.0120604\pi$
$720$		0			0
$721$	−0.0212978	+	0.0267066i	−0.000793171	+	0.000994605i
$722$	11.9804	+	15.0229i	0.445863	+	0.559094i
$723$	7.02291	+	14.5832i	0.261185	+	0.542356i
$724$	15.8018			0.587269
$725$		0			0
$726$	13.1128			0.486663
$727$	6.28573	+	13.0524i	0.233125	+	0.484088i	0.984410	−	0.175889i	$-0.0562800\pi$
$727$	6.28573	+	13.0524i	0.233125	+	0.484088i	−0.751285	+	0.659978i	$0.770566\pi$
$728$	−0.166326	−	0.208566i	−0.00616444	−	0.00772996i
$729$	3.41554	−	4.28295i	0.126501	−	0.158628i
$730$		0			0
$731$	−3.81539	+	7.92274i	−0.141117	+	0.293033i
$732$	8.14124	+	0.917298i	0.300909	+	0.0339043i
$733$	21.4360	+	4.89262i	0.791755	+	0.180713i	0.599228	−	0.800579i	$-0.295474\pi$
$733$	21.4360	+	4.89262i	0.791755	+	0.180713i	0.192528	+	0.981292i	$0.438332\pi$
$734$	−12.0262	+	52.6903i	−0.443896	+	1.94484i
$735$		0			0
$736$	−2.76005	−	1.73425i	−0.101737	−	0.0639255i
$737$	−13.6608			−0.503202
$738$	9.23819	+	5.80474i	0.340062	+	0.213675i
$739$	12.6498	+	36.1512i	0.465332	+	1.32984i	0.902588	+	0.430505i	$0.141664\pi$
$739$	12.6498	+	36.1512i	0.465332	+	1.32984i	−0.437257	+	0.899337i	$0.644050\pi$
$740$		0			0
$741$	−2.10931	−	9.24151i	−0.0774876	−	0.339495i
$742$			0.303444i			0.0111398i
$743$	−25.7547	+	5.87833i	−0.944847	+	0.215655i	−0.667074	−	0.744992i	$-0.732453\pi$
$743$	−25.7547	+	5.87833i	−0.944847	+	0.215655i	−0.277773	+	0.960647i	$0.589596\pi$
$744$	−2.09384	+	0.235919i	−0.0767640	+	0.00864922i
$745$		0			0
$746$	−35.3169	−	56.2066i	−1.29304	−	2.05787i
$747$	2.87572	−	25.5227i	0.105217	−	0.933827i
$748$	2.22008	+	6.34463i	0.0811742	+	0.231982i
$749$	0.287147	+	0.596267i	0.0104921	+	0.0217871i
$750$		0			0
$751$	2.42708	−	21.5409i	0.0885654	−	0.786039i	−0.868405	−	0.495855i	$-0.834855\pi$
$751$	2.42708	−	21.5409i	0.0885654	−	0.786039i	0.956971	−	0.290184i	$-0.0937167\pi$
$752$	−16.4470	+	7.92045i	−0.599760	+	0.288829i
$753$	−2.43274	+	2.43274i	−0.0886539	+	0.0886539i
$754$	6.35669	−	36.1778i	0.231497	−	1.31752i
$755$		0			0
$756$	−0.0914520	+	0.261355i	−0.00332608	+	0.00950538i
$757$	15.4075	−	12.2870i	0.559993	−	0.446580i	−0.302138	−	0.953264i	$-0.597700\pi$
$757$	15.4075	−	12.2870i	0.559993	−	0.446580i	0.862132	+	0.506684i	$0.169129\pi$
$758$	−4.86691	−	43.1950i	−0.176774	−	1.56891i
$759$	−0.669195	+	0.322267i	−0.0242902	+	0.0116976i
$760$		0			0
$761$	11.8638	+	14.8768i	0.430063	+	0.539282i	0.948894	−	0.315595i	$-0.102204\pi$
$761$	11.8638	+	14.8768i	0.430063	+	0.539282i	−0.518831	+	0.854877i	$0.673633\pi$
$762$	−4.12872	+	18.0891i	−0.149568	+	0.655299i
$763$	0.465802	+	0.741319i	0.0168632	+	0.0268376i
$764$	1.81618	+	16.1191i	0.0657072	+	0.583167i
$765$		0			0
$766$	−6.29154	−	6.29154i	−0.227323	−	0.227323i
$767$	−8.72580	+	13.8870i	−0.315070	+	0.501432i
$768$	16.0643	+	7.73616i	0.579670	+	0.279155i
$769$	−24.2753	+	8.49430i	−0.875390	+	0.306312i	−0.730317	−	0.683109i	$-0.760628\pi$
$769$	−24.2753	+	8.49430i	−0.875390	+	0.306312i	−0.145073	+	0.989421i	$0.546342\pi$
$770$		0			0
$771$	−15.0785	+	15.0785i	−0.543039	+	0.543039i
$772$	−3.08399	−	13.5119i	−0.110995	−	0.486302i
$773$	4.29249	−	5.38261i	0.154390	−	0.193599i	−0.698621	−	0.715492i	$-0.746203\pi$
$773$	4.29249	−	5.38261i	0.154390	−	0.193599i	0.853011	+	0.521893i	$0.174774\pi$
$774$	10.0289	+	2.28902i	0.360480	+	0.0822771i
$775$		0			0
$776$	11.4142	−	9.10249i	0.409745	−	0.326760i
$777$	−0.249699	+	0.0873735i	−0.00895791	+	0.00313451i
$778$	55.6374	+	19.4684i	1.99470	+	0.697975i
$779$	6.08397	+	4.85181i	0.217981	+	0.173834i
$780$		0			0
$781$	12.8347	+	4.49106i	0.459263	+	0.160703i
$782$	2.34727	+	2.34727i	0.0839383	+	0.0839383i
$783$	22.6710	−	9.24139i	0.810195	−	0.330260i
$784$		−	34.6552i		−	1.23768i
$785$		0			0
$786$	27.7285	+	3.12425i	0.989042	+	0.111438i
$787$	−35.6320	+	4.01476i	−1.27014	+	0.143111i	−0.721187	−	0.692740i	$-0.756403\pi$
$787$	−35.6320	+	4.01476i	−1.27014	+	0.143111i	−0.548957	+	0.835851i	$0.684975\pi$
$788$	−9.24182	+	26.4116i	−0.329226	+	0.940874i
$789$	−6.33651	−	3.05150i	−0.225586	−	0.108636i
$790$		0			0
$791$	−0.112330	+	0.0705817i	−0.00399400	+	0.00250960i
$792$	−4.27529	+	2.68634i	−0.151916	+	0.0954550i
$793$	−23.0942	−	18.4170i	−0.820098	−	0.654006i
$794$	−19.9742	+	31.7888i	−0.708859	+	1.12814i
$795$		0			0
$796$	2.60736	−	0.595114i	0.0924156	−	0.0210933i
$797$	−19.1346	+	39.7334i	−0.677782	+	1.40743i	0.223720	+	0.974654i	$0.428180\pi$
$797$	−19.1346	+	39.7334i	−0.677782	+	1.40743i	−0.901502	+	0.432775i	$0.857534\pi$
$798$	−0.0970316	+	0.201488i	−0.00343488	+	0.00713261i
$799$	12.3999	−	2.83019i	0.438677	−	0.100125i
$800$		0			0
$801$	2.68428	−	4.27201i	0.0948445	−	0.150944i
$802$	18.1984	+	14.5127i	0.642606	+	0.512461i
$803$	2.98307	−	1.87439i	0.105270	−	0.0661457i
$804$	−7.62686	+	4.79227i	−0.268978	+	0.169010i
$805$		0			0
$806$	−10.6593	−	5.13326i	−0.375459	−	0.180811i
$807$	−2.27538	+	6.50266i	−0.0800972	+	0.228905i
$808$	15.8743	−	1.78860i	0.558456	−	0.0629229i
$809$	27.0462	+	3.04738i	0.950895	+	0.107140i	0.573765	−	0.819020i	$-0.305482\pi$
$809$	27.0462	+	3.04738i	0.950895	+	0.107140i	0.377130	+	0.926160i	$0.376911\pi$
$810$		0			0
$811$			15.8296i			0.555851i	0.960603	+	0.277926i	$0.0896469\pi$
$811$			15.8296i			0.555851i	−0.960603	+	0.277926i	$0.910353\pi$
$812$	−0.245790	+	0.217174i	−0.00862554	+	0.00762132i
$813$	−15.6265	−	15.6265i	−0.548045	−	0.548045i
$814$	16.5448	+	5.78928i	0.579895	+	0.202914i
$815$		0			0
$816$	−11.5693	−	9.22623i	−0.405007	−	0.322983i
$817$	6.92511	+	2.42320i	0.242279	+	0.0847770i
$818$	−4.41961	+	1.54649i	−0.154528	+	0.0540717i
$819$	0.334525	−	0.266775i	0.0116892	−	0.00932186i
$820$		0			0
$821$	−9.19783	−	2.09935i	−0.321007	−	0.0732677i	0.0589814	−	0.998259i	$-0.481215\pi$
$821$	−9.19783	−	2.09935i	−0.321007	−	0.0732677i	−0.379988	+	0.924991i	$0.624072\pi$
$822$	−8.86056	+	11.1108i	−0.309048	+	0.387533i
$823$	8.84307	+	38.7440i	0.308250	+	1.35053i	0.857332	+	0.514763i	$0.172120\pi$
$823$	8.84307	+	38.7440i	0.308250	+	1.35053i	−0.549083	+	0.835768i	$0.685023\pi$
$824$	−0.677618	+	0.677618i	−0.0236059	+	0.0236059i
$825$		0			0
$826$	0.365221	−	0.127796i	0.0127077	−	0.00444660i
$827$	39.9309	+	19.2297i	1.38853	+	0.668683i	0.970801	−	0.239887i	$-0.0771103\pi$
$827$	39.9309	+	19.2297i	1.38853	+	0.668683i	0.417734	+	0.908570i	$0.362825\pi$
$828$	0.781944	−	1.24446i	0.0271744	−	0.0432479i
$829$	−17.1511	−	17.1511i	−0.595681	−	0.595681i	0.343479	−	0.939160i	$-0.388394\pi$
$829$	−17.1511	−	17.1511i	−0.595681	−	0.595681i	−0.939160	+	0.343479i	$0.888394\pi$
$830$		0			0
$831$	−1.77408	−	15.7454i	−0.0615420	−	0.546200i
$832$	2.02001	+	3.21482i	0.0700312	+	0.111454i
$833$	−5.37289	+	23.5402i	−0.186160	+	0.815618i
$834$	−18.0676	−	22.6560i	−0.625629	−	0.784514i
$835$		0			0
$836$	5.05290	−	2.43335i	0.174758	−	0.0841591i
$837$	−0.882887	−	7.83584i	−0.0305170	−	0.270846i
$838$	24.2459	−	19.3355i	0.837561	−	0.667932i
$839$	11.9236	−	34.0758i	0.411650	−	1.17643i	−0.532362	−	0.846517i	$-0.678695\pi$
$839$	11.9236	−	34.0758i	0.411650	−	1.17643i	0.944012	−	0.329911i	$-0.107019\pi$
$840$		0			0
$841$	28.7793	+	3.57135i	0.992388	+	0.123150i
$842$	−12.3724	+	12.3724i	−0.426381	+	0.426381i
$843$	18.6689	−	8.99045i	0.642990	−	0.309648i
$844$	−1.36308	+	12.0976i	−0.0469190	+	0.416418i
$845$		0			0
$846$	−6.45553	−	13.4051i	−0.221946	−	0.460875i
$847$	0.139429	+	0.398465i	0.00479083	+	0.0136914i
$848$	−1.87567	+	16.6471i	−0.0644109	+	0.571663i
$849$	−14.4675	−	23.0249i	−0.496524	−	0.790213i
$850$		0			0
$851$	3.25567	−	0.366826i	0.111603	−	0.0125746i
$852$	8.74114	−	1.99511i	0.299467	−	0.0683513i
$853$			6.64060i			0.227370i	0.993517	+	0.113685i	$0.0362654\pi$
$853$			6.64060i			0.227370i	−0.993517	+	0.113685i	$0.963735\pi$
$854$	0.155071	+	0.679409i	0.00530641	+	0.0232489i
$855$		0			0
$856$	6.13207	+	17.5244i	0.209590	+	0.598973i
$857$	6.54364	+	4.11164i	0.223527	+	0.140451i	0.639140	−	0.769090i	$-0.279290\pi$
$857$	6.54364	+	4.11164i	0.223527	+	0.140451i	−0.415614	+	0.909541i	$0.636433\pi$
$858$	9.44698			0.322514
$859$	24.3070	+	15.2731i	0.829346	+	0.521113i	0.878536	−	0.477677i	$-0.158521\pi$
$859$	24.3070	+	15.2731i	0.829346	+	0.521113i	−0.0491898	+	0.998789i	$0.515664\pi$
$860$		0			0
$861$	0.0260449	−	0.114110i	0.000887608	−	0.00388887i
$862$	30.0730	+	6.86396i	1.02429	+	0.233787i
$863$	1.28617	+	0.144916i	0.0437816	+	0.00493300i	0.133828	−	0.991005i	$-0.457273\pi$
$863$	1.28617	+	0.144916i	0.0437816	+	0.00493300i	−0.0900465	+	0.995938i	$0.528702\pi$
$864$	−11.9896	+	24.8966i	−0.407893	+	0.846999i
$865$		0			0
$866$	−6.15831	+	7.72228i	−0.209268	+	0.262414i
$867$	−2.74987	−	3.44823i	−0.0933905	−	0.117108i
$868$	0.0458362	+	0.0951799i	0.00155578	+	0.00323062i
$869$	−3.72530			−0.126372
$870$		0			0
$871$	32.4760			1.10041
$872$	10.6569	+	22.1293i	0.360888	+	0.749393i
$873$	14.5998	+	18.3075i	0.494127	+	0.619616i
$874$	1.72683	−	2.16538i	0.0584110	−	0.0732451i
$875$		0			0
$876$	1.00791	−	2.09295i	0.0340542	−	0.0707143i
$877$	−45.0188	−	5.07240i	−1.52018	−	0.171283i	−0.687966	−	0.725743i	$-0.741496\pi$
$877$	−45.0188	−	5.07240i	−1.52018	−	0.171283i	−0.832210	+	0.554460i	$0.812925\pi$
$878$	6.85620	+	1.56488i	0.231385	+	0.0528122i
$879$	1.17481	−	5.14717i	0.0396253	−	0.173610i
$880$		0			0
$881$	−29.8952	−	18.7844i	−1.00720	−	0.632863i	−0.0758960	−	0.997116i	$-0.524182\pi$
$881$	−29.8952	−	18.7844i	−1.00720	−	0.632863i	−0.931300	+	0.364252i	$0.881325\pi$
$882$	28.2456			0.951078
$883$	−24.8153	−	15.5925i	−0.835101	−	0.524729i	0.0452919	−	0.998974i	$-0.485578\pi$
$883$	−24.8153	−	15.5925i	−0.835101	−	0.524729i	−0.880393	+	0.474245i	$0.842721\pi$
$884$	−5.27783	−	15.0832i	−0.177513	−	0.507302i
$885$		0			0
$886$	12.7659	+	55.9312i	0.428880	+	1.87904i
$887$		−	31.6025i		−	1.06111i	−0.847651	−	0.530555i	$-0.821984\pi$
$887$		−	31.6025i		−	1.06111i	0.847651	−	0.530555i	$-0.178016\pi$
$888$	−7.23546	+	1.65145i	−0.242806	+	0.0554189i
$889$	−0.593581	+	0.0668805i	−0.0199081	+	0.00224310i
$890$		0			0
$891$	−2.39453	−	3.81087i	−0.0802198	−	0.127669i
$892$	0.846808	−	7.51563i	0.0283532	−	0.251642i
$893$	−3.50485	−	10.0163i	−0.117285	−	0.335182i
$894$	7.66976	+	15.9264i	0.256515	+	0.532659i
$895$		0			0
$896$	−0.0580365	+	0.515088i	−0.00193886	+	0.0172079i
$897$	1.59089	−	0.766131i	0.0531182	−	0.0255804i
$898$	−11.2733	+	11.2733i	−0.376194	+	0.376194i
$899$	3.62302	−	8.60929i	0.120835	−	0.287136i
$900$		0			0
$901$	3.85502	−	11.0170i	0.128429	−	0.367030i
$902$	−6.06331	+	4.83533i	−0.201886	+	0.160999i
$903$	−0.0123557	−	0.109660i	−0.000411171	−	0.00364924i
$904$	−3.35319	+	1.61481i	−0.111526	+	0.0537079i
$905$		0			0
$906$	16.4197	+	20.5897i	0.545508	+	0.684046i
$907$	−1.31997	+	5.78318i	−0.0438290	+	0.192027i	−0.992103	−	0.125426i	$-0.959970\pi$
$907$	−1.31997	+	5.78318i	−0.0438290	+	0.192027i	0.948274	+	0.317453i	$0.102828\pi$
$908$	6.67060	+	10.6162i	0.221372	+	0.352311i
$909$	2.86880	+	25.4613i	0.0951520	+	0.844497i
$910$		0			0
$911$	−3.72458	−	3.72458i	−0.123401	−	0.123401i	0.642709	−	0.766110i	$-0.277810\pi$
$911$	−3.72458	−	3.72458i	−0.123401	−	0.123401i	−0.766110	+	0.642709i	$0.777810\pi$
$912$	−6.56864	+	10.4539i	−0.217509	+	0.346164i
$913$	16.4486	+	7.92120i	0.544368	+	0.262154i
$914$	−51.9942	+	18.1936i	−1.71982	+	0.601789i
$915$		0			0
$916$	2.50045	−	2.50045i	0.0826171	−	0.0826171i
$917$	0.199899	+	0.875815i	0.00660125	+	0.0289220i
$918$	17.5454	−	22.0012i	0.579084	−	0.726148i
$919$	33.9679	+	7.75296i	1.12050	+	0.255747i	0.742359	−	0.670002i	$-0.233707\pi$
$919$	33.9679	+	7.75296i	1.12050	+	0.255747i	0.378140	+	0.925749i	$0.376564\pi$
$920$		0			0
$921$	−11.0919	+	8.84547i	−0.365489	+	0.291468i
$922$	10.3885	−	3.63510i	0.342128	−	0.119716i
$923$	−30.5122	−	10.6767i	−1.00432	−	0.351427i
$924$	−0.0659510	−	0.0525942i	−0.00216963	−	0.00173022i
$925$		0			0
$926$	20.3146	+	7.10840i	0.667580	+	0.233596i
$927$	−1.08685	−	1.08685i	−0.0356969	−	0.0356969i
$928$	−26.8015	+	18.7907i	−0.879803	+	0.616834i
$929$			2.84350i			0.0932921i	0.998911	+	0.0466460i	$0.0148533\pi$
$929$			2.84350i			0.0932921i	−0.998911	+	0.0466460i	$0.985147\pi$
$930$		0			0
$931$	20.0189	+	2.25559i	0.656093	+	0.0739240i
$932$	16.6520	−	1.87623i	0.545454	−	0.0614579i
$933$	5.58696	−	15.9666i	0.182909	−	0.522723i
$934$	9.23651	+	4.44807i	0.302228	+	0.145545i
$935$		0			0
$936$	10.1637	−	6.38628i	0.332211	−	0.208742i
$937$	28.0389	−	17.6180i	0.915990	−	0.575555i	0.0105107	−	0.999945i	$-0.496654\pi$
$937$	28.0389	−	17.6180i	0.915990	−	0.575555i	0.905480	+	0.424390i	$0.139511\pi$
$938$	−0.599025	−	0.477707i	−0.0195589	−	0.0155977i
$939$	8.65226	−	13.7700i	0.282356	−	0.449367i
$940$		0			0
$941$	−36.8079	+	8.40116i	−1.19990	+	0.273870i	−0.775349	−	0.631533i	$-0.782426\pi$
$941$	−36.8079	+	8.40116i	−1.19990	+	0.273870i	−0.424554	+	0.905403i	$0.639569\pi$
$942$	14.7408	−	30.6095i	0.480281	−	0.997313i
$943$	−0.628936	+	1.30600i	−0.0204810	+	0.0425292i
$944$	20.8261	−	4.75341i	0.677831	−	0.154710i
$945$		0			0
$946$	−3.89017	+	6.19117i	−0.126480	+	0.201292i
$947$	−6.42093	−	5.12052i	−0.208652	−	0.166394i	0.513588	−	0.858037i	$-0.328316\pi$
$947$	−6.42093	−	5.12052i	−0.208652	−	0.166394i	−0.722240	+	0.691642i	$0.756887\pi$
$948$	−2.07984	+	1.30685i	−0.0675501	+	0.0424446i
$949$	−7.09170	+	4.45601i	−0.230206	+	0.144648i
$950$		0			0
$951$	3.35768	+	1.61697i	0.108880	+	0.0524339i
$952$	0.0799553	−	0.228499i	0.00259137	−	0.00740570i
$953$	−20.0953	+	2.26419i	−0.650950	+	0.0733444i	−0.431263	−	0.902226i	$-0.641932\pi$
$953$	−20.0953	+	2.26419i	−0.650950	+	0.0733444i	−0.219687	+	0.975571i	$0.570503\pi$
$954$	−13.5681	−	1.52876i	−0.439285	−	0.0494955i
$955$		0			0
$956$			21.6207i			0.699263i
$957$	0.376251	+	7.44891i	0.0121625	+	0.240789i
$958$	−0.688219	−	0.688219i	−0.0222353	−	0.0222353i
$959$	−0.431842	−	0.151108i	−0.0139449	−	0.00487953i
$960$		0			0
$961$	21.8846	+	17.4524i	0.705956	+	0.562981i
$962$	−39.3322	−	13.7629i	−1.26812	−	0.443735i
$963$	−28.1080	+	9.83541i	−0.905767	+	0.316942i
$964$	17.7993	−	14.1945i	0.573278	−	0.457174i
$965$		0			0
$966$	−0.0406136	−	0.00926979i	−0.00130672	−	0.000298251i
$967$	7.32367	−	9.18359i	0.235513	−	0.295324i	−0.650004	−	0.759931i	$-0.725233\pi$
$967$	7.32367	−	9.18359i	0.235513	−	0.295324i	0.885517	+	0.464606i	$0.153804\pi$
$968$	2.63534	+	11.5462i	0.0847031	+	0.371109i
$969$	6.08264	−	6.08264i	0.195402	−	0.195402i
$970$		0			0
$971$	25.2257	−	8.82685i	0.809531	−	0.283267i	0.106396	−	0.994324i	$-0.466069\pi$
$971$	25.2257	−	8.82685i	0.809531	−	0.283267i	0.703135	+	0.711057i	$0.251783\pi$
$972$	−17.6397	−	8.49483i	−0.565794	−	0.272472i
$973$	0.496344	−	0.789927i	0.0159121	−	0.0253239i
$974$	−47.1962	−	47.1962i	−1.51226	−	1.51226i
$975$		0			0
$976$	4.30761	+	38.2311i	0.137883	+	1.22375i
$977$	8.05689	+	12.8225i	0.257763	+	0.410227i	0.950386	−	0.311072i	$-0.100688\pi$
$977$	8.05689	+	12.8225i	0.257763	+	0.410227i	−0.692624	+	0.721299i	$0.743545\pi$
$978$	4.09799	−	17.9545i	0.131039	−	0.574121i
$979$	2.23600	+	2.80385i	0.0714629	+	0.0896116i
$980$		0			0
$981$	−35.4939	+	17.0929i	−1.13323	+	0.545736i
$982$	−3.66531	−	32.5305i	−0.116965	−	1.03809i
$983$	−6.90007	+	5.50262i	−0.220078	+	0.175506i	−0.727323	−	0.686296i	$-0.759236\pi$
$983$	−6.90007	+	5.50262i	−0.220078	+	0.175506i	0.507244	+	0.861802i	$0.330664\pi$
$984$	1.08450	−	3.09931i	0.0345724	−	0.0988024i
$985$		0			0
$986$	30.8675	−	12.5826i	0.983022	−	0.400710i
$987$	−0.112863	+	0.112863i	−0.00359246	+	0.00359246i
$988$	−12.0123	+	5.78483i	−0.382163	+	0.184040i
$989$	−0.153020	+	1.35809i	−0.00486575	+	0.0431847i
$990$		0			0
$991$	11.0604	+	22.9671i	0.351345	+	0.729575i	0.999490	−	0.0319421i	$-0.0101692\pi$
$991$	11.0604	+	22.9671i	0.351345	+	0.729575i	−0.648145	+	0.761517i	$0.724455\pi$
$992$	3.48204	+	9.95110i	0.110555	+	0.315948i
$993$	−1.02116	+	9.06307i	−0.0324056	+	0.287608i
$994$	0.405753	+	0.645753i	0.0128697	+	0.0204820i
$995$		0			0
$996$	11.9621	−	1.34780i	0.379032	−	0.0427067i
$997$	−15.5544	+	3.55020i	−0.492614	+	0.112436i	−0.461609	−	0.887083i	$-0.652728\pi$
$997$	−15.5544	+	3.55020i	−0.492614	+	0.112436i	−0.0310044	+	0.999519i	$0.509871\pi$
$998$		−	16.4345i		−	0.520225i
$999$	−6.18025	−	27.0774i	−0.195534	−	0.856692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.bd.a.543.2	yes	120
5.2	odd	4		725.2.y.a.282.9	yes	120
5.3	odd	4		725.2.y.a.282.2	yes	120
5.4	even	2	inner	725.2.bd.a.543.9	yes	120
29.18	odd	28		725.2.y.a.18.9	yes	120
145.18	even	28	inner	725.2.bd.a.482.9	yes	120
145.47	even	28	inner	725.2.bd.a.482.2	yes	120
145.134	odd	28		725.2.y.a.18.2	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.y.a.18.2	✓	120	145.134	odd	28
725.2.y.a.18.9	yes	120	29.18	odd	28
725.2.y.a.282.2	yes	120	5.3	odd	4
725.2.y.a.282.9	yes	120	5.2	odd	4
725.2.bd.a.482.2	yes	120	145.47	even	28	inner
725.2.bd.a.482.9	yes	120	145.18	even	28	inner
725.2.bd.a.543.2	yes	120	1.1	even	1	trivial
725.2.bd.a.543.9	yes	120	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.bd (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.778326 - 1.61621i) q^{2} +(-0.539890 - 0.677001i) q^{3} +(-0.759368 + 0.952217i) q^{4} +(-0.673965 + 1.39950i) q^{6} +(-0.0496935 - 0.00559911i) q^{7} +(-1.36775 - 0.312179i) q^{8} +(0.500714 - 2.19377i) q^{9} +(1.35429 + 0.850959i) q^{11} +1.05463 q^{12} +(-3.21958 - 2.02300i) q^{13} +(0.0296284 + 0.0846731i) q^{14} +(1.10204 + 4.82834i) q^{16} -3.45060i q^{17} +(-3.93532 + 0.898211i) q^{18} +(-2.86087 + 0.322342i) q^{19} +(0.0230384 + 0.0366654i) q^{21} +(0.321247 - 2.85115i) q^{22} +(-0.177124 - 0.506191i) q^{23} +(0.527087 + 1.09451i) q^{24} +(-0.763706 + 6.77808i) q^{26} +(-4.09601 + 1.97253i) q^{27} +(0.0430672 - 0.0430672i) q^{28} +(-5.37491 - 0.332224i) q^{29} +(-0.572869 + 1.63716i) q^{31} +(4.75217 - 3.78973i) q^{32} +(-0.155070 - 1.37628i) q^{33} +(-5.57689 + 2.68569i) q^{34} +(1.70872 + 2.14267i) q^{36} +(-1.35942 + 5.95603i) q^{37} +(2.74766 + 4.37288i) q^{38} +(0.368650 + 3.27185i) q^{39} +(-1.91127 - 1.91127i) q^{41} +(0.0413277 - 0.0657726i) q^{42} +(-2.29605 - 1.10572i) q^{43} +(-1.83870 + 0.643391i) q^{44} +(-0.680251 + 0.680251i) q^{46} +(0.820205 + 3.59355i) q^{47} +(2.67381 - 3.35285i) q^{48} +(-6.82206 - 1.55709i) q^{49} +(-2.33605 + 1.86294i) q^{51} +(4.37118 - 1.52954i) q^{52} +(3.19279 + 1.11721i) q^{53} +(6.37606 + 5.08474i) q^{54} +(0.0662202 + 0.0231715i) q^{56} +(1.76278 + 1.76278i) q^{57} +(3.64649 + 8.94556i) q^{58} -4.31330i q^{59} +(7.71955 + 0.869785i) q^{61} +(3.09188 - 0.348372i) q^{62} +(-0.0371654 + 0.106213i) q^{63} +(-0.899637 - 0.433242i) q^{64} +(-2.10367 + 1.32182i) q^{66} +(-7.23181 + 4.54405i) q^{67} +(3.28571 + 2.62027i) q^{68} +(-0.247064 + 0.393200i) q^{69} +(8.28838 - 1.89177i) q^{71} +(-1.36970 + 2.84421i) q^{72} +(0.955706 - 1.98454i) q^{73} +(10.6843 - 2.43862i) q^{74} +(1.86551 - 2.96894i) q^{76} +(-0.0625350 - 0.0498700i) q^{77} +(5.00108 - 3.14239i) q^{78} +(-1.97211 + 1.23916i) q^{79} +(-2.53525 - 1.22091i) q^{81} +(-1.60143 + 4.57661i) q^{82} +(11.3425 - 1.27799i) q^{83} +(-0.0524080 - 0.00590497i) q^{84} +4.57151i q^{86} +(2.67694 + 3.81818i) q^{87} +(-1.58668 - 1.58668i) q^{88} +(2.11636 + 0.740547i) q^{89} +(0.148665 + 0.118557i) q^{91} +(0.616506 + 0.215725i) q^{92} +(1.41765 - 0.496056i) q^{93} +(5.16955 - 4.12258i) q^{94} +(-5.13130 - 1.17119i) q^{96} +(-6.48824 + 8.13599i) q^{97} +(2.79320 + 12.2378i) q^{98} +(2.54493 - 2.54493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 28 q^{9} - 12 q^{11} + 20 q^{16} - 4 q^{19} + 4 q^{21} - 12 q^{29} - 32 q^{31} + 40 q^{34} - 16 q^{36} + 184 q^{39} - 4 q^{41} - 36 q^{44} + 76 q^{46} + 84 q^{49} + 112 q^{51} - 168 q^{54}+ \cdots + 208 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 28 * q^9 - 12 * q^11 + 20 * q^16 - 4 * q^19 + 4 * q^21 - 12 * q^29 - 32 * q^31 + 40 * q^34 - 16 * q^36 + 184 * q^39 - 4 * q^41 - 36 * q^44 + 76 * q^46 + 84 * q^49 + 112 * q^51 - 168 * q^54 + 180 * q^56 + 124 * q^61 + 196 * q^64 + 144 * q^66 - 152 * q^69 + 56 * q^71 + 112 * q^74 + 12 * q^76 - 220 * q^79 - 76 * q^81 - 136 * q^84 + 208 * q^89 - 84 * q^94 - 84 * q^96 + 208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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