LMFDB - Embedded newform 725.2.y.a.18.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(18,725)]

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, 11]))

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

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

chi := DirichletCharacter("725.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.y (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			18.2
Character	$\chi$	$=$	725.18
Dual form			725.2.y.a.282.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61621 - 0.778326i) q^{2} +(0.677001 + 0.539890i) q^{3} +(0.759368 + 0.952217i) q^{4} +(-0.673965 - 1.39950i) q^{6} +(-0.00559911 - 0.0496935i) q^{7} +(0.312179 + 1.36775i) q^{8} +(-0.500714 - 2.19377i) q^{9} +(1.35429 - 0.850959i) q^{11} +1.05463i q^{12} +(2.02300 + 3.21958i) q^{13} +(-0.0296284 + 0.0846731i) q^{14} +(1.10204 - 4.82834i) q^{16} -3.45060 q^{17} +(-0.898211 + 3.93532i) q^{18} +(2.86087 + 0.322342i) q^{19} +(0.0230384 - 0.0366654i) q^{21} +(-2.85115 + 0.321247i) q^{22} +(0.506191 + 0.177124i) q^{23} +(-0.527087 + 1.09451i) q^{24} +(-0.763706 - 6.77808i) q^{26} +(1.97253 - 4.09601i) q^{27} +(0.0430672 - 0.0430672i) q^{28} +(5.37491 - 0.332224i) q^{29} +(-0.572869 - 1.63716i) q^{31} +(-3.78973 + 4.75217i) q^{32} +(1.37628 + 0.155070i) q^{33} +(5.57689 + 2.68569i) q^{34} +(1.70872 - 2.14267i) q^{36} +(5.95603 - 1.35942i) q^{37} +(-4.37288 - 2.74766i) q^{38} +(-0.368650 + 3.27185i) q^{39} +(-1.91127 + 1.91127i) q^{41} +(-0.0657726 + 0.0413277i) q^{42} +(1.10572 + 2.29605i) q^{43} +(1.83870 + 0.643391i) q^{44} +(-0.680251 - 0.680251i) q^{46} +(3.59355 + 0.820205i) q^{47} +(3.35285 - 2.67381i) q^{48} +(6.82206 - 1.55709i) q^{49} +(-2.33605 - 1.86294i) q^{51} +(-1.52954 + 4.37118i) q^{52} +(-1.11721 - 3.19279i) q^{53} +(-6.37606 + 5.08474i) q^{54} +(0.0662202 - 0.0231715i) q^{56} +(1.76278 + 1.76278i) q^{57} +(-8.94556 - 3.64649i) q^{58} -4.31330i q^{59} +(7.71955 - 0.869785i) q^{61} +(-0.348372 + 3.09188i) q^{62} +(-0.106213 + 0.0371654i) q^{63} +(0.899637 - 0.433242i) q^{64} +(-2.10367 - 1.32182i) q^{66} +(4.54405 - 7.23181i) q^{67} +(-2.62027 - 3.28571i) q^{68} +(0.247064 + 0.393200i) q^{69} +(8.28838 + 1.89177i) q^{71} +(2.84421 - 1.36970i) q^{72} +(1.98454 - 0.955706i) q^{73} +(-10.6843 - 2.43862i) q^{74} +(1.86551 + 2.96894i) q^{76} +(-0.0498700 - 0.0625350i) q^{77} +(3.14239 - 5.00108i) q^{78} +(1.97211 + 1.23916i) q^{79} +(-2.53525 + 1.22091i) q^{81} +(4.57661 - 1.60143i) q^{82} +(1.27799 - 11.3425i) q^{83} +(0.0524080 - 0.00590497i) q^{84} -4.57151i q^{86} +(3.81818 + 2.67694i) q^{87} +(1.58668 + 1.58668i) q^{88} +(-2.11636 + 0.740547i) q^{89} +(0.148665 - 0.118557i) q^{91} +(0.215725 + 0.616506i) q^{92} +(0.496056 - 1.41765i) q^{93} +(-5.16955 - 4.12258i) q^{94} +(-5.13130 + 1.17119i) q^{96} +(8.13599 - 6.48824i) q^{97} +(-12.2378 - 2.79320i) 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 $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.61621	−	0.778326i	−1.14283	−	0.550360i	−0.235960	−	0.971763i	$-0.575824\pi$
$2$	−1.61621	−	0.778326i	−1.14283	−	0.550360i	−0.906874	+	0.421403i	$0.861538\pi$
$3$	0.677001	+	0.539890i	0.390866	+	0.311706i	0.799130	−	0.601159i	$-0.205294\pi$
$3$	0.677001	+	0.539890i	0.390866	+	0.311706i	−0.408263	+	0.912864i	$0.633865\pi$
$4$	0.759368	+	0.952217i	0.379684	+	0.476108i
$5$		0			0
$5$		0			0
$6$	−0.673965	−	1.39950i	−0.275145	−	0.571345i
$7$	−0.00559911	−	0.0496935i	−0.00211626	−	0.0187824i	0.992610	−	0.121351i	$-0.0387226\pi$
$7$	−0.00559911	−	0.0496935i	−0.00211626	−	0.0187824i	−0.994726	+	0.102568i	$0.967294\pi$
$8$	0.312179	+	1.36775i	0.110372	+	0.483572i
$9$	−0.500714	−	2.19377i	−0.166905	−	0.731257i
$10$		0			0
$11$	1.35429	−	0.850959i	0.408335	−	0.256574i	−0.312166	−	0.950027i	$-0.601055\pi$
$11$	1.35429	−	0.850959i	0.408335	−	0.256574i	0.720501	+	0.693454i	$0.243912\pi$
$12$			1.05463i			0.304444i
$13$	2.02300	+	3.21958i	0.561079	+	0.892951i	0.999984	−	0.00558163i	$-0.00177670\pi$
$13$	2.02300	+	3.21958i	0.561079	+	0.892951i	−0.438906	+	0.898533i	$0.644634\pi$
$14$	−0.0296284	+	0.0846731i	−0.00791852	+	0.0226298i
$15$		0			0
$16$	1.10204	−	4.82834i	0.275509	−	1.20708i
$17$	−3.45060			−0.836892			−0.418446	−	0.908242i	$-0.637425\pi$
$17$	−3.45060			−0.836892			−0.418446	+	0.908242i	$0.637425\pi$
$18$	−0.898211	+	3.93532i	−0.211710	+	0.927563i
$19$	2.86087	+	0.322342i	0.656328	+	0.0739504i	0.433847	−	0.900987i	$-0.357156\pi$
$19$	2.86087	+	0.322342i	0.656328	+	0.0739504i	0.222481	+	0.974937i	$0.428584\pi$
$20$		0			0
$21$	0.0230384	−	0.0366654i	0.00502739	−	0.00800105i
$22$	−2.85115	+	0.321247i	−0.607867	+	0.0684902i
$23$	0.506191	+	0.177124i	0.105548	+	0.0369329i	0.382536	−	0.923940i	$-0.375051\pi$
$23$	0.506191	+	0.177124i	0.105548	+	0.0369329i	−0.276988	+	0.960873i	$0.589336\pi$
$24$	−0.527087	+	1.09451i	−0.107591	+	0.223416i
$25$		0			0
$26$	−0.763706	−	6.77808i	−0.149775	−	1.32929i
$27$	1.97253	−	4.09601i	0.379614	−	0.788277i
$28$	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	0.880918	−	0.473270i	$-0.156926\pi$
$31$	−0.572869	−	1.63716i	−0.102890	−	0.294043i	−0.983808	+	0.179226i	$0.942641\pi$
$32$	−3.78973	+	4.75217i	−0.669936	+	0.840073i
$33$	1.37628	+	0.155070i	0.239580	+	0.0269942i
$34$	5.57689	+	2.68569i	0.956429	+	0.460592i
$35$		0			0
$36$	1.70872	−	2.14267i	0.284787	−	0.357111i
$37$	5.95603	−	1.35942i	0.979165	−	0.223488i	0.297154	−	0.954830i	$-0.403963\pi$
$37$	5.95603	−	1.35942i	0.979165	−	0.223488i	0.682011	+	0.731342i	$0.261106\pi$
$38$	−4.37288	−	2.74766i	−0.709374	−	0.445729i
$39$	−0.368650	+	3.27185i	−0.0590312	+	0.523916i
$40$		0			0
$41$	−1.91127	+	1.91127i	−0.298490	+	0.298490i	−0.840422	−	0.541932i	$-0.817693\pi$
$41$	−1.91127	+	1.91127i	−0.298490	+	0.298490i	0.541932	+	0.840422i	$0.317693\pi$
$42$	−0.0657726	+	0.0413277i	−0.0101489	+	0.00637700i
$43$	1.10572	+	2.29605i	0.168621	+	0.350144i	0.968106	−	0.250541i	$-0.0806086\pi$
$43$	1.10572	+	2.29605i	0.168621	+	0.350144i	−0.799485	+	0.600686i	$0.794894\pi$
$44$	1.83870	+	0.643391i	0.277195	+	0.0969948i
$45$		0			0
$46$	−0.680251	−	0.680251i	−0.100298	−	0.100298i
$47$	3.59355	+	0.820205i	0.524173	+	0.119639i	0.476416	−	0.879220i	$-0.341936\pi$
$47$	3.59355	+	0.820205i	0.524173	+	0.119639i	0.0477571	+	0.998859i	$0.484793\pi$
$48$	3.35285	−	2.67381i	0.483942	−	0.385931i
$49$	6.82206	−	1.55709i	0.974580	−	0.222441i
$50$		0			0
$51$	−2.33605	−	1.86294i	−0.327113	−	0.260864i
$52$	−1.52954	+	4.37118i	−0.212109	+	0.606173i
$53$	−1.11721	−	3.19279i	−0.153460	−	0.438563i	0.841328	−	0.540524i	$-0.181774\pi$
$53$	−1.11721	−	3.19279i	−0.153460	−	0.438563i	−0.994788	+	0.101961i	$0.967488\pi$
$54$	−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
$58$	−8.94556	−	3.64649i	−1.17461	−	0.478807i
$59$		−	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	0.397057	−	0.917794i	$-0.370031\pi$
$61$	7.71955	−	0.869785i	0.988387	−	0.111365i	0.591330	+	0.806429i	$0.298603\pi$
$62$	−0.348372	+	3.09188i	−0.0442432	+	0.392670i
$63$	−0.106213	+	0.0371654i	−0.0133815	+	0.00468240i
$64$	0.899637	−	0.433242i	0.112455	−	0.0541553i
$65$		0			0
$66$	−2.10367	−	1.32182i	−0.258944	−	0.162705i
$67$	4.54405	−	7.23181i	0.555144	−	0.883506i	−0.444783	−	0.895639i	$-0.646719\pi$
$67$	4.54405	−	7.23181i	0.555144	−	0.883506i	0.999926	+	0.0121324i	$0.00386195\pi$
$68$	−2.62027	−	3.28571i	−0.317754	−	0.398451i
$69$	0.247064	+	0.393200i	0.0297430	+	0.0473358i
$70$		0			0
$71$	8.28838	+	1.89177i	0.983650	+	0.224512i	0.683956	−	0.729524i	$-0.260258\pi$
$71$	8.28838	+	1.89177i	0.983650	+	0.224512i	0.299694	+	0.954035i	$0.403115\pi$
$72$	2.84421	−	1.36970i	0.335194	−	0.161421i
$73$	1.98454	−	0.955706i	0.232273	−	0.111857i	−0.314127	−	0.949381i	$-0.601712\pi$
$73$	1.98454	−	0.955706i	0.232273	−	0.111857i	0.546401	+	0.837524i	$0.315998\pi$
$74$	−10.6843	−	2.43862i	−1.24202	−	0.283483i
$75$		0			0
$76$	1.86551	+	2.96894i	0.213989	+	0.340561i
$77$	−0.0498700	−	0.0625350i	−0.00568321	−	0.00712652i
$78$	3.14239	−	5.00108i	0.355805	−	0.566261i
$79$	1.97211	+	1.23916i	0.221880	+	0.139416i	0.638386	−	0.769717i	$-0.279603\pi$
$79$	1.97211	+	1.23916i	0.221880	+	0.139416i	−0.416506	+	0.909133i	$0.636745\pi$
$80$		0			0
$81$	−2.53525	+	1.22091i	−0.281695	+	0.135657i
$82$	4.57661	−	1.60143i	0.505402	−	0.176848i
$83$	1.27799	−	11.3425i	0.140278	−	1.24500i	−0.704432	−	0.709772i	$-0.748798\pi$
$83$	1.27799	−	11.3425i	0.140278	−	1.24500i	0.844709	−	0.535226i	$-0.179773\pi$
$84$	0.0524080	−	0.00590497i	0.00571819	−	0.000644285i
$85$		0			0
$86$		−	4.57151i		−	0.492959i
$87$	3.81818	+	2.67694i	0.409352	+	0.286998i
$88$	1.58668	+	1.58668i	0.169141	+	0.169141i
$89$	−2.11636	+	0.740547i	−0.224334	+	0.0784978i	−0.440106	−	0.897946i	$-0.645059\pi$
$89$	−2.11636	+	0.740547i	−0.224334	+	0.0784978i	0.215772	+	0.976444i	$0.430773\pi$
$90$		0			0
$91$	0.148665	−	0.118557i	0.0155844	−	0.0124281i
$92$	0.215725	+	0.616506i	0.0224909	+	0.0642752i
$93$	0.496056	−	1.41765i	0.0514386	−	0.147003i
$94$	−5.16955	−	4.12258i	−0.533199	−	0.425212i
$95$		0			0
$96$	−5.13130	+	1.17119i	−0.523711	+	0.119534i
$97$	8.13599	−	6.48824i	0.826085	−	0.658781i	−0.116336	−	0.993210i	$-0.537115\pi$
$97$	8.13599	−	6.48824i	0.826085	−	0.658781i	0.942421	+	0.334429i	$0.108544\pi$
$98$	−12.2378	−	2.79320i	−1.23621	−	0.282156i
$99$	−2.54493	−	2.54493i	−0.255775	−	0.255775i
$100$		0			0
$101$	−10.7478	−	3.76081i	−1.06944	−	0.374215i	−0.262555	−	0.964917i	$-0.584565\pi$
$101$	−10.7478	−	3.76081i	−1.06944	−	0.374215i	−0.806890	+	0.590702i	$0.798851\pi$
$102$	2.32558	+	4.82912i	0.230267	+	0.478154i
$103$	0.578374	−	0.363416i	0.0569889	−	0.0358085i	−0.503236	−	0.864149i	$-0.667857\pi$
$103$	0.578374	−	0.363416i	0.0569889	−	0.0358085i	0.560225	+	0.828340i	$0.310715\pi$
$104$	−3.77204	+	3.77204i	−0.369879	+	0.369879i
$105$		0			0
$106$	−0.679392	+	6.02977i	−0.0659884	+	0.585663i
$107$	−11.2056	−	7.04093i	−1.08328	−	0.680673i	−0.132706	−	0.991156i	$-0.542366\pi$
$107$	−11.2056	−	7.04093i	−1.08328	−	0.680673i	−0.950579	+	0.310483i	$0.899509\pi$
$108$	5.39816	−	1.23210i	0.519438	−	0.118558i
$109$	10.9158	−	13.6879i	1.04554	−	1.31107i	0.0966979	−	0.995314i	$-0.469172\pi$
$109$	10.9158	−	13.6879i	1.04554	−	1.31107i	0.948842	−	0.315752i	$-0.102257\pi$
$110$		0			0
$111$	4.76617	+	2.29527i	0.452385	+	0.217857i
$112$	−0.246107	−	0.0277296i	−0.0232549	−	0.00262020i
$113$	1.65404	−	2.07410i	0.155599	−	0.195114i	−0.697922	−	0.716174i	$-0.745892\pi$
$113$	1.65404	−	2.07410i	0.155599	−	0.195114i	0.853520	+	0.521060i	$0.174463\pi$
$114$	−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
$118$	−3.35716	+	6.97121i	−0.309051	+	0.641752i
$119$	0.0193203	+	0.171472i	0.00177109	+	0.0157188i
$120$		0			0
$121$	−3.66274	+	7.60576i	−0.332976	+	0.691433i
$122$	−13.1534	−	4.60258i	−1.19085	−	0.416698i
$123$	−2.32581	+	0.262056i	−0.209711	+	0.0236288i
$124$	1.12392	−	1.78870i	0.100931	−	0.160630i
$125$		0			0
$126$	0.200589	+	0.0226009i	0.0178699	+	0.00201345i
$127$	−2.65798	+	11.6454i	−0.235857	+	1.03336i	0.708828	+	0.705381i	$0.249224\pi$
$127$	−2.65798	+	11.6454i	−0.235857	+	1.03336i	−0.944686	+	0.327977i	$0.893633\pi$
$128$	10.3653			0.916172
$129$	−0.491041	+	2.15139i	−0.0432338	+	0.189420i
$130$		0			0
$131$	−5.93311	+	16.9558i	−0.518378	+	1.48144i	0.325833	+	0.945427i	$0.394355\pi$
$131$	−5.93311	+	16.9558i	−0.518378	+	1.48144i	−0.844211	+	0.536011i	$0.819930\pi$
$132$	0.897444	+	1.42827i	0.0781125	+	0.124315i
$133$		−	0.143971i		−	0.0124839i
$134$	−12.9728	+	8.15138i	−1.12068	+	0.704172i
$135$		0			0
$136$	−1.07721	−	4.71954i	−0.0923696	−	0.404698i
$137$	2.03582	+	8.91949i	0.173932	+	0.762044i	0.984355	+	0.176199i	$0.0563801\pi$
$137$	2.03582	+	8.91949i	0.173932	+	0.762044i	−0.810423	+	0.585845i	$0.800763\pi$
$138$	−0.0932697	−	0.827791i	−0.00793964	−	0.0704663i
$139$	8.09430	+	16.8080i	0.686550	+	1.42564i	0.894306	+	0.447455i	$0.147670\pi$
$139$	8.09430	+	16.8080i	0.686550	+	1.42564i	−0.207756	+	0.978181i	$0.566616\pi$
$140$		0			0
$141$	1.99002	+	2.49540i	0.167590	+	0.210151i
$142$	−11.9234	−	9.50856i	−1.00059	−	0.797941i
$143$	5.47947	+	2.63877i	0.458216	+	0.220665i
$144$	−11.1441			−0.928673
$145$		0			0
$146$	−3.95129			−0.327011
$147$	5.45919	+	2.62901i	0.450267	+	0.216837i
$148$	5.81728	+	4.63913i	0.478177	+	0.381334i
$149$	−7.09534	−	8.89728i	−0.581273	−	0.728893i	0.401056	−	0.916053i	$-0.368643\pi$
$149$	−7.09534	−	8.89728i	−0.581273	−	0.728893i	−0.982329	+	0.187160i	$0.940072\pi$
$150$		0			0
$151$	7.35606	+	15.2750i	0.598627	+	1.24306i	0.951574	+	0.307419i	$0.0994654\pi$
$151$	7.35606	+	15.2750i	0.598627	+	1.24306i	−0.352947	+	0.935643i	$0.614820\pi$
$152$	0.452221	+	4.01357i	0.0366800	+	0.325544i
$153$	1.72776	+	7.56982i	0.139681	+	0.611984i
$154$	0.0319278	+	0.139885i	0.00257282	+	0.0112722i
$155$		0			0
$156$	−3.39546	+	2.13351i	−0.271854	+	0.170817i
$157$		−	21.8717i		−	1.74555i	−0.488120	−	0.872776i	$-0.662317\pi$
$157$		−	21.8717i		−	1.74555i	0.488120	−	0.872776i	$-0.337683\pi$
$158$	−2.22288	−	3.53769i	−0.176843	−	0.281444i
$159$	0.967406	−	2.76469i	0.0767203	−	0.219254i
$160$		0			0
$161$	0.00596768	−	0.0261461i	0.000470319	−	0.00206060i
$162$	5.04777			0.396591
$163$	−2.63820	+	11.5587i	−0.206640	+	0.905347i	0.760145	+	0.649754i	$0.225128\pi$
$163$	−2.63820	+	11.5587i	−0.206640	+	0.905347i	−0.966784	+	0.255593i	$0.917729\pi$
$164$	−3.27130	−	0.368587i	−0.255446	−	0.0287818i
$165$		0			0
$166$	−10.8936	+	17.3371i	−0.845510	+	1.34562i
$167$	−24.4686	+	2.75695i	−1.89344	+	0.213339i	−0.980743	−	0.195302i	$-0.937431\pi$
$167$	−24.4686	+	2.75695i	−1.89344	+	0.213339i	−0.912695	+	0.408641i	$0.866003\pi$
$168$	0.0573412	+	0.0200645i	0.00442397	+	0.00154801i
$169$	−0.632702	+	1.31382i	−0.0486694	+	0.101063i
$170$		0			0
$171$	−0.725331	−	6.43749i	−0.0554674	−	0.492287i
$172$	−1.34669	+	2.79643i	−0.102684	+	0.213226i
$173$	−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
$177$	2.32871	−	2.92011i	0.175036	−	0.219489i
$178$	3.99687	+	0.450339i	0.299578	+	0.0337544i
$179$	1.78074	+	0.857561i	0.133099	+	0.0640971i	0.499248	−	0.866459i	$-0.333610\pi$
$179$	1.78074	+	0.857561i	0.133099	+	0.0640971i	−0.366149	+	0.930556i	$0.619324\pi$
$180$		0			0
$181$	−8.08934	+	10.1437i	−0.601276	+	0.753976i	−0.985576	−	0.169232i	$-0.945871\pi$
$181$	−8.08934	+	10.1437i	−0.601276	+	0.753976i	0.384300	+	0.923208i	$0.374443\pi$
$182$	−0.332550	+	0.0759024i	−0.0246503	+	0.00562626i
$183$	5.69573	+	3.57886i	0.421040	+	0.264557i
$184$	−0.0842383	+	0.747636i	−0.00621013	+	0.0551165i
$185$		0			0
$186$	−1.90512	+	1.90512i	−0.139690	+	0.139690i
$187$	−4.67312	+	2.93632i	−0.341732	+	0.214725i
$188$	1.94781	+	4.04468i	0.142059	+	0.294988i
$189$	−0.214589	−	0.0750880i	−0.0156091	−	0.00546185i
$190$		0			0
$191$	9.41763	+	9.41763i	0.681436	+	0.681436i	0.960324	−	0.278888i	$-0.0899658\pi$
$191$	9.41763	+	9.41763i	0.681436	+	0.681436i	−0.278888	+	0.960324i	$0.589966\pi$
$192$	0.842958	+	0.192400i	0.0608353	+	0.0138853i
$193$	−8.89678	+	7.09495i	−0.640404	+	0.510705i	−0.889003	−	0.457901i	$-0.848601\pi$
$193$	−8.89678	+	7.09495i	−0.640404	+	0.510705i	0.248599	+	0.968607i	$0.420030\pi$
$194$	−18.1994	+	4.15391i	−1.30664	+	0.298233i
$195$		0			0
$196$	6.66314	+	5.31367i	0.475938	+	0.379548i
$197$	−7.58813	+	21.6856i	−0.540632	+	1.54504i	0.272022	+	0.962291i	$0.412308\pi$
$197$	−7.58813	+	21.6856i	−0.540632	+	1.54504i	−0.812654	+	0.582746i	$0.801978\pi$
$198$	2.13235	+	6.09392i	0.151540	+	0.433076i
$199$	1.71680	−	1.36910i	0.121701	−	0.0970531i	−0.560748	−	0.827986i	$-0.689486\pi$
$199$	1.71680	−	1.36910i	0.121701	−	0.0970531i	0.682449	+	0.730933i	$0.260915\pi$
$200$		0			0
$201$	6.98070	−	2.44265i	0.492381	−	0.172292i
$202$	14.4435	+	14.4435i	1.01624	+	1.01624i
$203$	−0.0466041	−	0.265238i	−0.00327097	−	0.0186160i
$204$		−	3.63909i		−	0.254787i
$205$		0			0
$206$	−1.21763	+	0.137194i	−0.0848363	+	0.00955876i
$207$	0.135112	−	1.19916i	0.00939096	−	0.0833471i
$208$	17.7746	−	6.21962i	1.23245	−	0.431253i
$209$	4.14875	−	1.99793i	0.286975	−	0.138200i
$210$		0			0
$211$	8.46368	+	5.31808i	0.582664	+	0.366112i	0.790880	−	0.611971i	$-0.209623\pi$
$211$	8.46368	+	5.31808i	0.582664	+	0.366112i	−0.208216	+	0.978083i	$0.566766\pi$
$212$	2.19186	−	3.48832i	0.150537	−	0.239579i
$213$	4.58989	+	5.75554i	0.314494	+	0.394363i
$214$	12.6304	+	20.1012i	0.863399	+	1.37409i
$215$		0			0
$216$	6.21809	+	1.41924i	0.423087	+	0.0965669i
$217$	−0.0781489	+	0.0376345i	−0.00530509	+	0.00255480i
$218$	−28.2958	+	13.6266i	−1.91644	+	0.922907i
$219$	1.85951	+	0.424422i	0.125654	+	0.0286798i
$220$		0			0
$221$	−6.98055	−	11.1095i	−0.469562	−	0.747304i
$222$	−5.91667	−	7.41927i	−0.397101	−	0.497949i
$223$	−3.30385	+	5.25804i	−0.221242	+	0.352105i	−0.938840	−	0.344352i	$-0.888098\pi$
$223$	−3.30385	+	5.25804i	−0.221242	+	0.352105i	0.717598	+	0.696457i	$0.245241\pi$
$224$	0.257371	+	0.161717i	0.0171963	+	0.0108052i
$225$		0			0
$226$	−4.28759	+	2.06480i	−0.285207	+	0.137348i
$227$	−9.71679	+	3.40005i	−0.644926	+	0.225669i	−0.632870	−	0.774258i	$-0.718123\pi$
$227$	−9.71679	+	3.40005i	−0.644926	+	0.225669i	−0.0120560	+	0.999927i	$0.503838\pi$
$228$	−0.339950	+	3.01714i	−0.0225138	+	0.199815i
$229$	2.88517	−	0.325080i	0.190657	−	0.0214819i	−0.0161195	−	0.999870i	$-0.505131\pi$
$229$	2.88517	−	0.325080i	0.190657	−	0.0214819i	0.206777	+	0.978388i	$0.433703\pi$
$230$		0			0
$231$		−	0.0692605i		−	0.00455701i
$232$	2.13233	+	7.24780i	0.139995	+	0.475842i
$233$	9.72899	+	9.72899i	0.637367	+	0.637367i	0.949905	−	0.312538i	$-0.101179\pi$
$233$	9.72899	+	9.72899i	0.637367	+	0.637367i	−0.312538	+	0.949905i	$0.601179\pi$
$234$	−14.4872	+	5.06928i	−0.947055	+	0.331389i
$235$		0			0
$236$	4.10720	−	3.27538i	0.267356	−	0.213209i
$237$	0.666111	+	1.90364i	0.0432686	+	0.123654i
$238$	0.102236	−	0.292173i	0.00662695	−	0.0189387i
$239$	−13.8791	−	11.0682i	−0.897762	−	0.715941i	0.0616058	−	0.998101i	$-0.480378\pi$
$239$	−13.8791	−	11.0682i	−0.897762	−	0.715941i	−0.959368	+	0.282160i	$0.908949\pi$
$240$		0			0
$241$	−18.2239	+	4.15948i	−1.17390	+	0.267935i	−0.764625	−	0.644475i	$-0.777076\pi$
$241$	−18.2239	+	4.15948i	−1.17390	+	0.267935i	−0.409276	+	0.912411i	$0.634219\pi$
$242$	11.8395	−	9.44171i	0.761074	−	0.606936i
$243$	−15.6722	−	3.57709i	−1.00538	−	0.229470i
$244$	6.69020	+	6.69020i	0.428296	+	0.428296i
$245$		0			0
$246$	3.96296	+	1.38670i	0.252669	+	0.0884128i
$247$	4.74972	+	9.86289i	0.302217	+	0.627561i
$248$	2.06039	−	1.29463i	0.130835	−	0.0822090i
$249$	6.98888	−	6.98888i	0.442902	−	0.442902i
$250$		0			0
$251$	−0.444851	+	3.94816i	−0.0280788	+	0.249206i	0.971830	+	0.235684i	$0.0757329\pi$
$251$	−0.444851	+	3.94816i	−0.0280788	+	0.249206i	−0.999909	+	0.0135222i	$0.995696\pi$
$252$	−0.116044	−	0.0729152i	−0.00731008	−	0.00459323i
$253$	0.836257	−	0.190870i	0.0525750	−	0.0119999i
$254$	13.3597	−	16.7526i	0.838265	−	1.05115i
$255$		0			0
$256$	−18.5518	−	8.93407i	−1.15949	−	0.558380i
$257$	−24.4713	−	2.75726i	−1.52648	−	0.171993i	−0.691542	−	0.722336i	$-0.743068\pi$
$257$	−24.4713	−	2.75726i	−1.52648	−	0.171993i	−0.834939	+	0.550343i	$0.814497\pi$
$258$	2.46811	−	3.09491i	0.153658	−	0.192681i
$259$	−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
$263$	3.52401	−	7.31769i	0.217300	−	0.451228i	−0.763613	−	0.645674i	$-0.776577\pi$
$263$	3.52401	−	7.31769i	0.217300	−	0.451228i	0.980913	+	0.194446i	$0.0622908\pi$
$264$	0.217551	+	1.93082i	0.0133893	+	0.118834i
$265$		0			0
$266$	−0.112057	+	0.232688i	−0.00687063	+	0.0142670i
$267$	−1.83259	−	0.641251i	−0.112153	−	0.0392439i
$268$	10.3369	−	1.16468i	0.631424	−	0.0711444i
$269$	4.23287	−	6.73657i	0.258083	−	0.410736i	−0.692400	−	0.721514i	$-0.743447\pi$
$269$	4.23287	−	6.73657i	0.258083	−	0.410736i	0.950483	+	0.310778i	$0.100589\pi$
$270$		0			0
$271$	25.3607	+	2.85746i	1.54055	+	0.173579i	0.841013	−	0.541015i	$-0.181960\pi$
$271$	25.3607	+	2.85746i	1.54055	+	0.173579i	0.699539	+	0.714594i	$0.253389\pi$
$272$	−3.80268	+	16.6606i	−0.230571	+	1.01020i
$273$	0.164654			0.00996531
$274$	3.65197	−	16.0003i	0.220623	−	0.966614i
$275$		0			0
$276$	−0.186799	+	0.533842i	−0.0112440	+	0.0321335i
$277$	9.73540	+	15.4938i	0.584943	+	0.930932i	0.999779	+	0.0210355i	$0.00669631\pi$
$277$	9.73540	+	15.4938i	0.584943	+	0.930932i	−0.414835	+	0.909896i	$0.636161\pi$
$278$		−	33.4653i		−	2.00711i
$279$	−3.30472	+	2.07650i	−0.197849	+	0.124317i
$280$		0			0
$281$	−5.32480	−	23.3295i	−0.317651	−	1.39172i	−0.841660	−	0.540007i	$-0.818422\pi$
$281$	−5.32480	−	23.3295i	−0.317651	−	1.39172i	0.524009	−	0.851712i	$-0.324436\pi$
$282$	−1.27405	−	5.58198i	−0.0758686	−	0.332402i
$283$	−3.51609	−	31.2062i	−0.209010	−	1.85501i	−0.461148	−	0.887323i	$-0.652562\pi$
$283$	−3.51609	−	31.2062i	−0.209010	−	1.85501i	0.252138	−	0.967691i	$-0.418866\pi$
$284$	4.49255	+	9.32888i	0.266584	+	0.553567i
$285$		0			0
$286$	−6.80215	−	8.52963i	−0.402220	−	0.504367i
$287$	0.105679	+	0.0842763i	0.00623804	+	0.00497467i
$288$	12.3228	+	5.93433i	0.726125	+	0.349683i
$289$	−5.09339			−0.299611
$290$		0			0
$291$	9.01101			0.528234
$292$	2.41704	+	1.16398i	0.141446	+	0.0681170i
$293$	−4.76687	−	3.80145i	−0.278483	−	0.222083i	0.474280	−	0.880374i	$-0.342708\pi$
$293$	−4.76687	−	3.80145i	−0.278483	−	0.222083i	−0.752764	+	0.658291i	$0.771280\pi$
$294$	−6.77698	−	8.49807i	−0.395242	−	0.495617i
$295$		0			0
$296$	3.71870	+	7.72196i	0.216145	+	0.448830i
$297$	−0.814146	−	7.22574i	−0.0472415	−	0.419280i
$298$	4.54259	+	19.9024i	0.263145	+	1.15291i
$299$	0.453758	+	1.98804i	0.0262415	+	0.114972i
$300$		0			0
$301$	0.107908	−	0.0678028i	0.00621969	−	0.00390809i
$302$		−	30.4131i		−	1.75007i
$303$	−5.24583	−	8.34869i	−0.301365	−	0.479620i
$304$	4.70915	−	13.4580i	0.270089	−	0.771869i
$305$		0			0
$306$	3.09936	−	13.5792i	0.177179	−	0.776271i
$307$	−16.3838			−0.935075			−0.467538	−	0.883973i	$-0.654859\pi$
$307$	−16.3838			−0.935075			−0.467538	+	0.883973i	$0.654859\pi$
$308$	0.0216772	−	0.0949741i	0.00123517	−	0.00541165i
$309$	0.587764	+	0.0662251i	0.0334367	+	0.00376741i
$310$		0			0
$311$	10.3934	−	16.5410i	0.589354	−	0.937951i	−0.410308	−	0.911947i	$-0.634579\pi$
$311$	10.3934	−	16.5410i	0.589354	−	0.937951i	0.999662	−	0.0260043i	$-0.00827836\pi$
$312$	−4.59016	+	0.517186i	−0.259866	+	0.0292799i
$313$	−17.7270	−	6.20293i	−1.00199	−	0.350610i	−0.221079	−	0.975256i	$-0.570958\pi$
$313$	−17.7270	−	6.20293i	−1.00199	−	0.350610i	−0.780908	+	0.624646i	$0.785243\pi$
$314$	−17.0233	+	35.3493i	−0.960682	+	1.99488i
$315$		0			0
$316$	0.317609	+	2.81886i	0.0178669	+	0.158573i
$317$	1.86736	−	3.87760i	0.104881	−	0.217788i	−0.841923	−	0.539597i	$-0.818577\pi$
$317$	1.86736	−	3.87760i	0.104881	−	0.217788i	0.946805	+	0.321809i	$0.104291\pi$
$318$	−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
$322$	−0.0299953	+	0.0376129i	−0.00167157	+	0.00209608i
$323$	−9.87169	−	1.11227i	−0.549276	−	0.0618885i
$324$	−3.08776	−	1.48699i	−0.171542	−	0.0826105i
$325$		0			0
$326$	13.2603	−	16.6279i	0.734421	−	0.920935i
$327$	14.7799	−	3.37343i	0.817333	−	0.186551i
$328$	−3.21080	−	2.01748i	−0.177287	−	0.111397i
$329$	0.0206381	−	0.183168i	0.00113782	−	0.0100984i
$330$		0			0
$331$	−7.44773	+	7.44773i	−0.409364	+	0.409364i	−0.881517	−	0.472153i	$-0.843477\pi$
$331$	−7.44773	+	7.44773i	−0.409364	+	0.409364i	0.472153	+	0.881517i	$0.343477\pi$
$332$	11.7709	−	7.39618i	0.646015	−	0.405918i
$333$	−5.96453	−	12.3855i	−0.326854	−	0.678720i
$334$	41.6923	+	14.5888i	2.28130	+	0.798261i
$335$		0			0
$336$	−0.151644	−	0.151644i	−0.00827285	−	0.00827285i
$337$	23.2516	+	5.30703i	1.26660	+	0.289092i	0.802479	−	0.596681i	$-0.203514\pi$
$337$	23.2516	+	5.30703i	1.26660	+	0.289092i	0.464118	+	0.885773i	$0.346371\pi$
$338$	2.04516	−	1.63096i	0.111242	−	0.0887125i
$339$	2.23957	−	0.511166i	0.121637	−	0.0277627i
$340$		0			0
$341$	−2.16899	−	1.72971i	−0.117458	−	0.0936693i
$342$	−3.83818	+	10.9689i	−0.207545	+	0.593130i
$343$	−0.231191	−	0.660705i	−0.0124831	−	0.0356747i
$344$	−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	$0.425142\pi$
$348$	0.350372	+	5.66852i	0.0187819	+	0.303864i
$349$		−	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
$352$	−1.08850	+	9.66074i	−0.0580175	+	0.514919i
$353$	29.8092	−	10.4307i	1.58658	−	0.555169i	0.614319	−	0.789058i	$-0.289431\pi$
$353$	29.8092	−	10.4307i	1.58658	−	0.555169i	0.972263	+	0.233889i	$0.0751452\pi$
$354$	−6.03648	+	2.90702i	−0.320835	+	0.154506i
$355$		0			0
$356$	−2.31226	−	1.45289i	−0.122549	−	0.0770029i
$357$	−0.0794962	+	0.126518i	−0.00420739	+	0.00669602i
$358$	−2.21060	−	2.77200i	−0.116834	−	0.146505i
$359$	10.9969	+	17.5015i	0.580397	+	0.923696i	0.999873	+	0.0159298i	$0.00507083\pi$
$359$	10.9969	+	17.5015i	0.580397	+	0.923696i	−0.419476	+	0.907766i	$0.637786\pi$
$360$		0			0
$361$	−10.4430	−	2.38354i	−0.549631	−	0.125450i
$362$	20.9692	−	10.0982i	1.10212	−	0.530752i
$363$	−6.58595	+	3.17163i	−0.345673	+	0.166467i
$364$	0.225783	+	0.0515335i	0.0118343	+	0.00270109i
$365$		0			0
$366$	−6.41998	−	10.2173i	−0.335578	−	0.534069i
$367$	−18.7845	−	23.5550i	−0.980542	−	1.22956i	−0.973288	−	0.229588i	$-0.926262\pi$
$367$	−18.7845	−	23.5550i	−0.980542	−	1.22956i	−0.00725434	−	0.999974i	$-0.502309\pi$
$368$	1.41305	−	2.24886i	0.0736606	−	0.117230i
$369$	5.14989	+	3.23589i	0.268093	+	0.168454i
$370$		0			0
$371$	−0.152405	+	0.0733946i	−0.00791250	+	0.00381046i
$372$	1.72660	−	0.604162i	0.0895199	−	0.0313244i
$373$	4.14321	−	36.7720i	0.214527	−	1.90398i	−0.177652	−	0.984093i	$-0.556850\pi$
$373$	4.14321	−	36.7720i	0.214527	−	1.90398i	0.392179	−	0.919889i	$-0.371721\pi$
$374$	9.83816	−	1.10849i	0.508719	−	0.0573189i
$375$		0			0
$376$			5.17112i			0.266680i
$377$	11.9430	+	16.6329i	0.615098	+	0.856636i
$378$	0.288379	+	0.288379i	0.0148326	+	0.0148326i
$379$	−22.8719	+	8.00324i	−1.17485	+	0.411099i	−0.845949	−	0.533264i	$-0.820965\pi$
$379$	−22.8719	+	8.00324i	−1.17485	+	0.411099i	−0.328904	+	0.944363i	$0.606679\pi$
$380$		0			0
$381$	−8.08666	+	6.44890i	−0.414292	+	0.330387i
$382$	−7.89089	−	22.5509i	−0.403733	−	1.15380i
$383$	1.63819	−	4.68168i	0.0837077	−	0.239223i	−0.894420	−	0.447228i	$-0.852411\pi$
$383$	1.63819	−	4.68168i	0.0837077	−	0.239223i	0.978128	+	0.208005i	$0.0666970\pi$
$384$	7.01732	+	5.59612i	0.358101	+	0.285576i
$385$		0			0
$386$	19.9013	−	4.54233i	1.01295	−	0.231199i
$387$	4.48336	−	3.57536i	0.227902	−	0.181746i
$388$	12.3564	+	2.82027i	0.627302	+	0.143178i
$389$	23.2351	+	23.2351i	1.17807	+	1.17807i	0.980236	+	0.197832i	$0.0633900\pi$
$389$	23.2351	+	23.2351i	1.17807	+	1.17807i	0.197832	+	0.980236i	$0.436610\pi$
$390$		0			0
$391$	−1.74666	−	0.611183i	−0.0883324	−	0.0309088i
$392$	4.25941	+	8.84476i	0.215133	+	0.446728i
$393$	−13.1710	+	8.27589i	−0.664389	+	0.417463i
$394$	29.1425	−	29.1425i	1.46818	−	1.46818i
$395$		0			0
$396$	0.490787	−	4.35585i	0.0246630	−	0.218890i
$397$	−17.7209	−	11.1348i	−0.889386	−	0.558838i	0.00805748	−	0.999968i	$-0.497435\pi$
$397$	−17.7209	−	11.1348i	−0.889386	−	0.558838i	−0.897444	+	0.441129i	$0.854578\pi$
$398$	−3.84032	+	0.876528i	−0.192498	+	0.0439364i
$399$	0.0777286	−	0.0974686i	0.00389130	−	0.00487953i
$400$		0			0
$401$	−11.6907	−	5.62994i	−0.583806	−	0.281146i	0.118578	−	0.992945i	$-0.462166\pi$
$401$	−11.6907	−	5.62994i	−0.583806	−	0.281146i	−0.702383	+	0.711799i	$0.747881\pi$
$402$	−13.1835	−	1.48542i	−0.657532	−	0.0740861i
$403$	4.11207	−	5.15638i	0.204837	−	0.256857i
$404$	−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
$408$	1.81877	−	3.77671i	0.0900423	−	0.186975i
$409$	−0.292252	−	2.59381i	−0.0144509	−	0.128256i	0.984415	−	0.175859i	$-0.0562702\pi$
$409$	−0.292252	−	2.59381i	−0.0144509	−	0.128256i	−0.998866	+	0.0476033i	$0.984842\pi$
$410$		0			0
$411$	−3.43730	+	7.13762i	−0.169549	+	0.352073i
$412$	0.785249	+	0.274771i	0.0386865	+	0.0135370i
$413$	−0.214343	+	0.0241507i	−0.0105471	+	0.00118838i
$414$	−1.15171	+	1.83293i	−0.0566032	+	0.0900835i
$415$		0			0
$416$	−22.9666	−	2.58772i	−1.12603	−	0.126873i
$417$	−3.59462	+	15.7491i	−0.176029	+	0.771235i
$418$	−8.26031			−0.404025
$419$	−3.84687	+	16.8542i	−0.187932	+	0.823384i	0.789773	+	0.613399i	$0.210198\pi$
$419$	−3.84687	+	16.8542i	−0.187932	+	0.823384i	−0.977705	+	0.209984i	$0.932659\pi$
$420$		0			0
$421$	−3.22153	+	9.20660i	−0.157008	+	0.448702i	−0.995337	−	0.0964625i	$-0.969247\pi$
$421$	−3.22153	+	9.20660i	−0.157008	+	0.448702i	0.838329	+	0.545165i	$0.183533\pi$
$422$	−9.53990	−	15.1827i	−0.464395	−	0.739080i
$423$		−	8.29412i		−	0.403274i
$424$	4.01816	−	2.52478i	0.195139	−	0.122614i
$425$		0			0
$426$	−2.93854	−	12.8746i	−0.142373	−	0.623777i
$427$	−0.0864453	−	0.378741i	−0.00418338	−	0.0183286i
$428$	−1.80466	−	16.0168i	−0.0872315	−	0.774201i
$429$	2.28496	+	4.74476i	0.110319	+	0.229079i
$430$		0			0
$431$	−10.7212	−	13.4440i	−0.516424	−	0.647575i	0.453422	−	0.891296i	$-0.350203\pi$
$431$	−10.7212	−	13.4440i	−0.516424	−	0.647575i	−0.969845	+	0.243721i	$0.921632\pi$
$432$	−17.6031	−	14.0380i	−0.846929	−	0.675404i
$433$	4.96082	+	2.38901i	0.238402	+	0.114808i	0.549271	−	0.835645i	$-0.314906\pi$
$433$	4.96082	+	2.38901i	0.238402	+	0.114808i	−0.310869	+	0.950453i	$0.600620\pi$
$434$	0.155597			0.00746889
$435$		0			0
$436$	21.3229			1.02118
$437$	1.39105	+	0.669894i	0.0665430	+	0.0320454i
$438$	−2.67503	−	2.13326i	−0.127818	−	0.101931i
$439$	2.44429	+	3.06504i	0.116659	+	0.146286i	0.836732	−	0.547612i	$-0.184463\pi$
$439$	2.44429	+	3.06504i	0.116659	+	0.146286i	−0.720073	+	0.693898i	$0.755892\pi$
$440$		0			0
$441$	−6.83180	−	14.1864i	−0.325324	−	0.675542i
$442$	2.63524	+	23.3884i	0.125346	+	1.11247i
$443$	7.11646	+	31.1792i	0.338113	+	1.48137i	0.802988	+	0.595995i	$0.203242\pi$
$443$	7.11646	+	31.1792i	0.338113	+	1.48137i	−0.464875	+	0.885376i	$0.653901\pi$
$444$	1.43368	+	6.28138i	0.0680396	+	0.298101i
$445$		0			0
$446$	9.43219	−	5.92664i	0.446627	−	0.280634i
$447$		−	9.85416i		−	0.466086i
$448$	−0.0265665	−	0.0422803i	−0.00125515	−	0.00199756i
$449$	2.93533	−	8.38870i	0.138527	−	0.395887i	−0.853631	−	0.520878i	$-0.825605\pi$
$449$	2.93533	−	8.38870i	0.138527	−	0.395887i	0.992158	+	0.124991i	$0.0398902\pi$
$450$		0			0
$451$	−0.962009	+	4.21484i	−0.0452992	+	0.198469i
$452$	3.23101			0.151974
$453$	−3.26677	+	14.3127i	−0.153486	+	0.672467i
$454$	18.3507	+	2.06763i	0.861243	+	0.0970388i
$455$		0			0
$456$	−1.86073	+	2.96134i	−0.0871368	+	0.138677i
$457$	−30.5147	+	3.43818i	−1.42742	+	0.160831i	−0.791614	−	0.611021i	$-0.790759\pi$
$457$	−30.5147	+	3.43818i	−1.42742	+	0.160831i	−0.635802	+	0.771852i	$0.719331\pi$
$458$	−4.91606	−	1.72020i	−0.229712	−	0.0803798i
$459$	−6.80641	+	14.1337i	−0.317696	+	0.659703i
$460$		0			0
$461$	−0.686954	−	6.09689i	−0.0319946	−	0.283960i	−0.999514	−	0.0311644i	$-0.990078\pi$
$461$	−0.686954	−	6.09689i	−0.0319946	−	0.283960i	0.967520	−	0.252796i	$-0.0813501\pi$
$462$	−0.0539073	+	0.111940i	−0.00250799	+	0.00520790i
$463$	−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
$467$	3.56319	−	4.46810i	0.164885	−	0.206759i	−0.692524	−	0.721395i	$-0.743501\pi$
$467$	3.56319	−	4.46810i	0.164885	−	0.206759i	0.857409	+	0.514636i	$0.172073\pi$
$468$	10.3552	+	1.16675i	0.478671	+	0.0539332i
$469$	−0.384816	−	0.185318i	−0.0177692	−	0.00855718i
$470$		0			0
$471$	11.8083	−	14.8072i	0.544099	−	0.682278i
$472$	5.89951	−	1.34652i	0.271547	−	0.0619788i
$473$	3.45131	+	2.16860i	0.158692	+	0.0997125i
$474$	0.405074	−	3.59513i	0.0186057	−	0.165130i
$475$		0			0
$476$	−0.148607	+	0.148607i	−0.00681141	+	0.00681141i
$477$	−6.44485	+	4.04957i	−0.295090	+	0.185417i
$478$	13.8168	+	28.6910i	0.631967	+	1.31229i
$479$	−0.512120	−	0.179198i	−0.0233993	−	0.00818778i	0.318554	−	0.947905i	$-0.396803\pi$
$479$	−0.512120	−	0.179198i	−0.0233993	−	0.00818778i	−0.341953	+	0.939717i	$0.611088\pi$
$480$		0			0
$481$	16.4258	+	16.4258i	0.748952	+	0.748952i
$482$	32.6910	+	7.46151i	1.48904	+	0.339863i
$483$	0.0181562	−	0.0144791i	0.000826134	−	0.000658820i
$484$	−10.0237	+	2.28784i	−0.455623	+	0.103993i
$485$		0			0
$486$	22.5455	+	17.9795i	1.02269	+	0.815565i
$487$	−12.2890	+	35.1198i	−0.556866	+	1.59143i	0.229261	+	0.973365i	$0.426369\pi$
$487$	−12.2890	+	35.1198i	−0.556866	+	1.59143i	−0.786127	+	0.618065i	$0.787917\pi$
$488$	3.59953	+	10.2869i	0.162943	+	0.465665i
$489$	−8.02648	+	6.40091i	−0.362970	+	0.289459i
$490$		0			0
$491$	17.2250	−	6.02730i	0.777355	−	0.272008i	0.0877005	−	0.996147i	$-0.472048\pi$
$491$	17.2250	−	6.02730i	0.777355	−	0.272008i	0.689654	+	0.724139i	$0.257762\pi$
$492$	−2.01568	−	2.01568i	−0.0908737	−	0.0908737i
$493$	−18.5466	+	1.14637i	−0.835298	+	0.0516300i
$494$		−	19.6373i		−	0.883526i
$495$		0			0
$496$	−8.53610	+	0.961788i	−0.383282	+	0.0431856i
$497$	0.0476010	−	0.422471i	0.00213520	−	0.0189504i
$498$	−16.7351	+	5.85588i	−0.749920	+	0.262408i
$499$	−8.25425	+	3.97504i	−0.369511	+	0.177947i	−0.609419	−	0.792849i	$-0.708597\pi$
$499$	−8.25425	+	3.97504i	−0.369511	+	0.177947i	0.239908	+	0.970796i	$0.422883\pi$
$500$		0			0
$501$	−18.0537	−	11.3439i	−0.806581	−	0.506808i
$502$	3.79193	−	6.03483i	0.169242	−	0.269348i
$503$	11.8551	+	14.8659i	0.528594	+	0.662836i	0.972409	−	0.233282i	$-0.0749466\pi$
$503$	11.8551	+	14.8659i	0.528594	+	0.662836i	−0.443815	+	0.896119i	$0.646375\pi$
$504$	−0.0839903	−	0.133670i	−0.00374122	−	0.00595413i
$505$		0			0
$506$	−1.50013	−	0.342394i	−0.0666888	−	0.0152213i
$507$	−1.13766	+	0.547867i	−0.0505251	+	0.0243316i
$508$	−13.1073	+	6.31214i	−0.581542	+	0.280056i
$509$	−36.0022	−	8.21727i	−1.59577	−	0.364224i	−0.670014	−	0.742348i	$-0.733712\pi$
$509$	−36.0022	−	8.21727i	−1.59577	−	0.364224i	−0.925755	+	0.378124i	$0.876569\pi$
$510$		0			0
$511$	−0.0586040	−	0.0932678i	−0.00259249	−	0.00412592i
$512$	10.1047	+	12.6709i	0.446568	+	0.559978i
$513$	6.96347	−	11.0823i	0.307445	−	0.489295i
$514$	37.4048	+	23.5030i	1.64986	+	1.03667i
$515$		0			0
$516$	−2.42147	+	1.16612i	−0.106599	+	0.0513356i
$517$	5.56469	−	1.94717i	0.244735	−	0.0856363i
$518$	−0.0613609	+	0.544593i	−0.00269604	+	0.0239280i
$519$	−10.8263	+	1.21984i	−0.475224	+	0.0535448i
$520$		0			0
$521$		−	12.6825i		−	0.555630i	−0.960635	−	0.277815i	$-0.910390\pi$
$521$		−	12.6825i		−	0.555630i	0.960635	−	0.277815i	$-0.0896102\pi$
$522$	−3.52039	+	21.4504i	−0.154083	+	0.938858i
$523$	24.6658	+	24.6658i	1.07856	+	1.07856i	0.996639	+	0.0819190i	$0.0261049\pi$
$523$	24.6658	+	24.6658i	1.07856	+	1.07856i	0.0819190	+	0.996639i	$0.473895\pi$
$524$	−20.6510	+	7.22611i	−0.902145	+	0.315674i
$525$		0			0
$526$	−11.3911	+	9.08410i	−0.496676	+	0.396086i
$527$	1.97674	+	5.64919i	0.0861081	+	0.246083i
$528$	2.26544	−	6.47426i	0.0985907	−	0.281756i
$529$	−17.7573	−	14.1609i	−0.772055	−	0.615693i
$530$		0			0
$531$	−9.46240	+	2.15973i	−0.410633	+	0.0937244i
$532$	0.137092	−	0.109327i	0.00594368	−	0.00473993i
$533$	−10.0200	−	2.28700i	−0.434014	−	0.0990609i
$534$	2.46275	+	2.46275i	0.106574	+	0.106574i
$535$		0			0
$536$	11.3098	+	3.95749i	0.488511	+	0.170937i
$537$	0.742576	+	1.54197i	0.0320445	+	0.0665411i
$538$	−12.0845	+	7.59317i	−0.520998	+	0.327365i
$539$	7.91405	−	7.91405i	0.340882	−	0.340882i
$540$		0			0
$541$	1.45294	−	12.8952i	0.0624669	−	0.554409i	−0.923032	−	0.384724i	$-0.874297\pi$
$541$	1.45294	−	12.8952i	0.0624669	−	0.554409i	0.985498	−	0.169685i	$-0.0542749\pi$
$542$	−38.7642	−	24.3572i	−1.66506	−	1.04623i
$543$	−10.9530	+	2.49995i	−0.470037	+	0.107283i
$544$	13.0768	−	16.3978i	0.560664	−	0.703051i
$545$		0			0
$546$	−0.266116	−	0.128155i	−0.0113887	−	0.00548451i
$547$	12.2767	+	1.38325i	0.524913	+	0.0591435i	0.370445	−	0.928854i	$-0.379205\pi$
$547$	12.2767	+	1.38325i	0.524913	+	0.0591435i	0.154468	+	0.987998i	$0.450634\pi$
$548$	−6.94736	+	8.71171i	−0.296776	+	0.372146i
$549$	−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
$553$	0.0505361	−	0.104939i	0.00214901	−	0.00446247i
$554$	−3.67523	−	32.6186i	−0.156146	−	1.38583i
$555$		0			0
$556$	−9.85830	+	20.4710i	−0.418085	+	0.868163i
$557$	−17.3588	−	6.07412i	−0.735518	−	0.257369i	−0.0635804	−	0.997977i	$-0.520252\pi$
$557$	−17.3588	−	6.07412i	−0.735518	−	0.257369i	−0.671937	+	0.740608i	$0.734538\pi$
$558$	6.95732	−	0.783902i	0.294527	−	0.0331852i
$559$	−5.15545	+	8.20485i	−0.218052	+	0.347028i
$560$		0			0
$561$	−4.74899	−	0.535083i	−0.200503	−	0.0225912i
$562$	−9.55194	+	41.8498i	−0.402924	+	1.76533i
$563$	33.1694			1.39792			0.698962	−	0.715159i	$-0.253646\pi$
$563$	33.1694			1.39792			0.698962	+	0.715159i	$0.253646\pi$
$564$	−0.865009	+	3.78985i	−0.0364235	+	0.159582i
$565$		0			0
$566$	−18.6058	+	53.1724i	−0.782062	+	2.23500i
$567$	0.0748666	+	0.119150i	0.00314410	+	0.00500381i
$568$			11.9270i			0.500445i
$569$	12.1703	−	7.64712i	0.510207	−	0.320584i	−0.252208	−	0.967673i	$-0.581157\pi$
$569$	12.1703	−	7.64712i	0.510207	−	0.320584i	0.762414	+	0.647089i	$0.224014\pi$
$570$		0			0
$571$	2.48794	+	10.9004i	0.104117	+	0.456166i	0.999931	+	0.0117373i	$0.00373617\pi$
$571$	2.48794	+	10.9004i	0.104117	+	0.456166i	−0.895814	+	0.444429i	$0.853407\pi$
$572$	1.64825	+	7.22144i	0.0689166	+	0.301944i
$573$	1.29126	+	11.4602i	0.0539430	+	0.478758i
$574$	−0.105205	−	0.218461i	−0.00439119	−	0.00911839i
$575$		0			0
$576$	−1.40090	−	1.75667i	−0.0583707	−	0.0731945i
$577$	−20.7764	−	16.5686i	−0.864933	−	0.689761i	0.0869530	−	0.996212i	$-0.472287\pi$
$577$	−20.7764	−	16.5686i	−0.864933	−	0.689761i	−0.951886	+	0.306451i	$0.900858\pi$
$578$	8.23200	+	3.96432i	0.342406	+	0.164894i
$579$	−9.85362			−0.409502
$580$		0			0
$581$	−0.570802			−0.0236809
$582$	−14.5637	−	7.01350i	−0.603684	−	0.290719i
$583$	−4.22996	−	3.37328i	−0.175187	−	0.139707i
$584$	1.92670	+	2.41600i	0.0797273	+	0.0999749i
$585$		0			0
$586$	4.74549	+	9.85412i	0.196035	+	0.407070i
$587$	0.901390	+	8.00006i	0.0372044	+	0.330198i	0.998503	+	0.0546906i	$0.0174172\pi$
$587$	0.901390	+	8.00006i	0.0372044	+	0.330198i	−0.961299	+	0.275507i	$0.911154\pi$
$588$	1.64215	+	7.19472i	0.0677210	+	0.296705i
$589$	−1.11117	−	4.86837i	−0.0457851	−	0.200598i
$590$		0			0
$591$	−16.8450	+	10.5844i	−0.692912	+	0.435385i
$592$		−	30.2558i		−	1.24351i
$593$	20.3482	+	32.3840i	0.835600	+	1.32985i	0.942030	+	0.335529i	$0.108915\pi$
$593$	20.3482	+	32.3840i	0.835600	+	1.32985i	−0.106430	+	0.994320i	$0.533942\pi$
$594$	−4.30815	+	12.3120i	−0.176766	+	0.505167i
$595$		0			0
$596$	3.08416	−	13.5126i	0.126332	−	0.553498i
$597$	1.90144			0.0778207
$598$	0.813978	−	3.56627i	0.0332861	−	0.145836i
$599$	−46.8364	−	5.27719i	−1.91368	−	0.215620i	−0.926625	−	0.375986i	$-0.877304\pi$
$599$	−46.8364	−	5.27719i	−1.91368	−	0.215620i	−0.987058	+	0.160366i	$0.948733\pi$
$600$		0			0
$601$	1.29346	−	2.05853i	0.0527614	−	0.0839693i	−0.819302	−	0.573362i	$-0.805639\pi$
$601$	1.29346	−	2.05853i	0.0527614	−	0.0839693i	0.872063	+	0.489393i	$0.162782\pi$
$602$	−0.227174	+	0.0255964i	−0.00925893	+	0.00104323i
$603$	−18.1402	−	6.34753i	−0.738727	−	0.258492i
$604$	−8.95917	+	18.6039i	−0.364543	+	0.756982i
$605$		0			0
$606$	1.98036	+	17.5762i	0.0804468	+	0.713985i
$607$	12.2672	−	25.4732i	0.497912	−	1.03392i	−0.488943	−	0.872316i	$-0.662617\pi$
$607$	12.2672	−	25.4732i	0.497912	−	1.03392i	0.986855	−	0.161609i	$-0.0516683\pi$
$608$	−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
$612$	−5.89610	+	7.39348i	−0.238336	+	0.298864i
$613$	−23.5041	−	2.64828i	−0.949323	−	0.106963i	−0.376296	−	0.926499i	$-0.622802\pi$
$613$	−23.5041	−	2.64828i	−0.949323	−	0.106963i	−0.573027	+	0.819536i	$0.694231\pi$
$614$	26.4797	+	12.7520i	1.06864	+	0.514628i
$615$		0			0
$616$	0.0699637	−	0.0877317i	0.00281892	−	0.00353481i
$617$	17.3434	−	3.95851i	0.698218	−	0.159364i	0.141344	−	0.989961i	$-0.454858\pi$
$617$	17.3434	−	3.95851i	0.698218	−	0.159364i	0.556874	+	0.830597i	$0.312001\pi$
$618$	−0.898406	−	0.564506i	−0.0361392	−	0.0227078i
$619$	−5.39810	+	47.9094i	−0.216968	+	1.92564i	0.137360	+	0.990521i	$0.456138\pi$
$619$	−5.39810	+	47.9094i	−0.216968	+	1.92564i	−0.354328	+	0.935121i	$0.615290\pi$
$620$		0			0
$621$	1.72398	−	1.72398i	0.0691809	−	0.0691809i
$622$	−29.6721	+	18.6442i	−1.18974	+	0.747566i
$623$	0.0486501	+	0.101023i	0.00194912	+	0.00404740i
$624$	15.3914	+	5.38567i	0.616147	+	0.215599i
$625$		0			0
$626$	23.8226	+	23.8226i	0.952143	+	0.952143i
$627$	3.88737	+	0.887268i	0.155247	+	0.0354341i
$628$	20.8266	−	16.6087i	0.831072	−	0.662758i
$629$	−20.5518	+	4.69082i	−0.819455	+	0.187035i
$630$		0			0
$631$	24.3390	+	19.4097i	0.968921	+	0.772688i	0.973825	−	0.227300i	$-0.0729896\pi$
$631$	24.3390	+	19.4097i	0.968921	+	0.772688i	−0.00490424	+	0.999988i	$0.501561\pi$
$632$	−1.07921	+	3.08419i	−0.0429285	+	0.122683i
$633$	2.85874	+	8.16980i	0.113625	+	0.324721i
$634$	−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
$638$	−15.2179	+	2.67390i	−0.602484	+	0.105861i
$639$		−	19.1301i		−	0.756773i
$640$		0			0
$641$	−47.2768	+	5.32682i	−1.86732	+	0.210397i	−0.971993	−	0.235010i	$-0.924488\pi$
$641$	−47.2768	+	5.32682i	−1.86732	+	0.210397i	−0.895328	+	0.445406i	$0.853059\pi$
$642$	−2.30164	+	20.4276i	−0.0908384	+	0.806213i
$643$	0.213571	−	0.0747317i	0.00842241	−	0.00294713i	−0.326065	−	0.945348i	$-0.605723\pi$
$643$	0.213571	−	0.0747317i	0.00842241	−	0.00294713i	0.334487	+	0.942400i	$0.391437\pi$
$644$	0.0294284	−	0.0141720i	0.00115964	−	0.000558455i
$645$		0			0
$646$	15.0890	+	9.48106i	0.593670	+	0.373028i
$647$	22.1007	−	35.1731i	0.868868	−	1.38280i	−0.0543507	−	0.998522i	$-0.517309\pi$
$647$	22.1007	−	35.1731i	0.868868	−	1.38280i	0.923219	−	0.384274i	$-0.125548\pi$
$648$	−2.46136	−	3.08644i	−0.0966912	−	0.121247i
$649$	−3.67044	−	5.84148i	−0.144078	−	0.229298i
$650$		0			0
$651$	−0.0732253	−	0.0167132i	−0.00286993	−	0.000655042i
$652$	−13.0097	+	6.26516i	−0.509501	+	0.245363i
$653$	15.6929	−	7.55731i	0.614111	−	0.295740i	−0.100853	−	0.994901i	$-0.532157\pi$
$653$	15.6929	−	7.55731i	0.614111	−	0.295740i	0.714964	+	0.699161i	$0.246443\pi$
$654$	−26.5131	−	6.05145i	−1.03675	−	0.236630i
$655$		0			0
$656$	7.12197	+	11.3346i	0.278066	+	0.442540i
$657$	−3.09029	−	3.87510i	−0.120564	−	0.151182i
$658$	−0.175920	+	0.279976i	−0.00685809	+	0.0109146i
$659$	36.8444	+	23.1509i	1.43526	+	0.901831i	0.999999	+	0.00152434i	$0.000485211\pi$
$659$	36.8444	+	23.1509i	1.43526	+	0.901831i	0.435257	+	0.900306i	$0.356658\pi$
$660$		0			0
$661$	−10.9914	+	5.29320i	−0.427518	+	0.205882i	−0.635254	−	0.772303i	$-0.719105\pi$
$661$	−10.9914	+	5.29320i	−0.427518	+	0.205882i	0.207736	+	0.978185i	$0.433390\pi$
$662$	17.8339	−	6.24034i	0.693133	−	0.242538i
$663$	1.27206	−	11.2898i	0.0494027	−	0.438461i
$664$	15.9126	−	1.79292i	0.617528	−	0.0695787i
$665$		0			0
$666$			24.6599i			0.955552i
$667$	2.77957	+	0.783855i	0.107626	+	0.0303510i
$668$	−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
$672$	0.0869310	+	0.248434i	0.00335344	+	0.00958357i
$673$	10.4404	−	29.8369i	0.402447	−	1.15013i	−0.547253	−	0.836967i	$-0.684326\pi$
$673$	10.4404	−	29.8369i	0.402447	−	1.15013i	0.949700	−	0.313161i	$-0.101388\pi$
$674$	−33.4489	−	26.6746i	−1.28841	−	1.02747i
$675$		0			0
$676$	−1.73149	+	0.395202i	−0.0665959	+	0.0152001i
$677$	21.1289	−	16.8498i	0.812051	−	0.647589i	−0.126794	−	0.991929i	$-0.540469\pi$
$677$	21.1289	−	16.8498i	0.812051	−	0.647589i	0.938845	+	0.344340i	$0.111897\pi$
$678$	−4.01747	−	0.916961i	−0.154290	−	0.0352157i
$679$	−0.367977	−	0.367977i	−0.0141217	−	0.0141217i
$680$		0			0
$681$	−8.41393	−	2.94416i	−0.322422	−	0.112821i
$682$	2.15927	+	4.48377i	0.0826827	+	0.171692i
$683$	11.2393	−	7.06210i	0.430058	−	0.270224i	−0.299561	−	0.954077i	$-0.596840\pi$
$683$	11.2393	−	7.06210i	0.430058	−	0.270224i	0.729619	+	0.683854i	$0.239697\pi$
$684$	5.57909	−	5.57909i	0.213322	−	0.213322i
$685$		0			0
$686$	−0.140591	+	1.24778i	−0.00536779	+	0.0476405i
$687$	2.12877	+	1.33759i	0.0812175	+	0.0510323i
$688$	12.3046	−	2.80845i	0.469110	−	0.107071i
$689$	8.01935	−	10.0559i	0.305513	−	0.383101i
$690$		0			0
$691$	−17.7230	−	8.53497i	−0.674216	−	0.324685i	0.0652598	−	0.997868i	$-0.479212\pi$
$691$	−17.7230	−	8.53497i	−0.674216	−	0.324685i	−0.739476	+	0.673183i	$0.764927\pi$
$692$	−15.2275	−	1.71573i	−0.578862	−	0.0652221i
$693$	−0.112217	+	0.140716i	−0.00426277	+	0.00534534i
$694$	−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
$698$	−7.30030	+	15.1592i	−0.276320	+	0.573785i
$699$	1.33395	+	11.8391i	0.0504545	+	0.447796i
$700$		0			0
$701$	1.46305	−	3.03806i	0.0552588	−	0.114746i	−0.871511	−	0.490376i	$-0.836859\pi$
$701$	1.46305	−	3.03806i	0.0552588	−	0.114746i	0.926770	+	0.375630i	$0.122574\pi$
$702$	−29.2695	−	10.2418i	−1.10471	−	0.386553i
$703$	17.4776	−	1.96925i	0.659180	−	0.0742717i
$704$	0.849702	−	1.35229i	0.0320243	−	0.0509664i
$705$		0			0
$706$	−56.2964	−	6.34308i	−2.11874	−	0.238725i
$707$	−0.126710	+	0.555152i	−0.00476541	+	0.0208786i
$708$	4.54892			0.170959
$709$	−0.0430267	+	0.188512i	−0.00161590	+	0.00707973i	−0.975729	−	0.218980i	$-0.929727\pi$
$709$	−0.0430267	+	0.188512i	−0.00161590	+	0.00707973i	0.974114	+	0.226059i	$0.0725843\pi$
$710$		0			0
$711$	1.73097	−	4.94683i	0.0649165	−	0.185521i
$712$	−1.67357	−	2.66346i	−0.0627195	−	0.0998175i
$713$		−	0.930187i		−	0.0348358i
$714$	0.226955	−	0.142605i	0.00849356	−	0.00533686i
$715$		0			0
$716$	0.535655	+	2.34686i	0.0200184	+	0.0877062i
$717$	−3.42053	−	14.9863i	−0.127742	−	0.559675i
$718$	−4.15148	−	36.8454i	−0.154932	−	1.37506i
$719$	−10.8827	−	22.5981i	−0.405856	−	0.842768i	−0.999282	−	0.0378799i	$-0.987940\pi$
$719$	−10.8827	−	22.5981i	−0.405856	−	0.842768i	0.593427	−	0.804888i	$-0.297775\pi$
$720$		0			0
$721$	−0.0212978	−	0.0267066i	−0.000793171	−	0.000994605i
$722$	15.0229	+	11.9804i	0.559094	+	0.445863i
$723$	−14.5832	−	7.02291i	−0.542356	−	0.261185i
$724$	−15.8018			−0.587269
$725$		0			0
$726$	13.1128			0.486663
$727$	13.0524	+	6.28573i	0.484088	+	0.233125i	0.659978	−	0.751285i	$-0.270566\pi$
$727$	13.0524	+	6.28573i	0.484088	+	0.233125i	−0.175889	+	0.984410i	$0.556280\pi$
$728$	0.208566	+	0.166326i	0.00772996	+	0.00616444i
$729$	−3.41554	−	4.28295i	−0.126501	−	0.158628i
$730$		0			0
$731$	−3.81539	−	7.92274i	−0.141117	−	0.293033i
$732$	0.917298	+	8.14124i	0.0339043	+	0.300909i
$733$	−4.89262	−	21.4360i	−0.180713	−	0.791755i	−0.981292	−	0.192528i	$-0.938332\pi$
$733$	−4.89262	−	21.4360i	−0.180713	−	0.791755i	0.800579	−	0.599228i	$-0.204526\pi$
$734$	12.0262	+	52.6903i	0.443896	+	1.94484i
$735$		0			0
$736$	−2.76005	+	1.73425i	−0.101737	+	0.0639255i
$737$		−	13.6608i		−	0.503202i
$738$	−5.80474	−	9.23819i	−0.213675	−	0.340062i
$739$	−12.6498	+	36.1512i	−0.465332	+	1.32984i	0.437257	+	0.899337i	$0.355950\pi$
$739$	−12.6498	+	36.1512i	−0.465332	+	1.32984i	−0.902588	+	0.430505i	$0.858336\pi$
$740$		0			0
$741$	−2.10931	+	9.24151i	−0.0774876	+	0.339495i
$742$	0.303444			0.0111398
$743$	−5.87833	+	25.7547i	−0.215655	+	0.944847i	0.744992	+	0.667074i	$0.232453\pi$
$743$	−5.87833	+	25.7547i	−0.215655	+	0.944847i	−0.960647	+	0.277773i	$0.910404\pi$
$744$	2.09384	+	0.235919i	0.0767640	+	0.00864922i
$745$		0			0
$746$	−35.3169	+	56.2066i	−1.29304	+	2.05787i
$747$	−25.5227	+	2.87572i	−0.933827	+	0.105217i
$748$	−6.34463	−	2.22008i	−0.231982	−	0.0811742i
$749$	−0.287147	+	0.596267i	−0.0104921	+	0.0217871i
$750$		0			0
$751$	2.42708	+	21.5409i	0.0885654	+	0.786039i	0.956971	+	0.290184i	$0.0937167\pi$
$751$	2.42708	+	21.5409i	0.0885654	+	0.786039i	−0.868405	+	0.495855i	$0.834855\pi$
$752$	7.92045	−	16.4470i	0.288829	−	0.599760i
$753$	−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
$757$	−12.2870	+	15.4075i	−0.446580	+	0.559993i	−0.953264	−	0.302138i	$-0.902300\pi$
$757$	−12.2870	+	15.4075i	−0.446580	+	0.559993i	0.506684	+	0.862132i	$0.330871\pi$
$758$	43.1950	+	4.86691i	1.56891	+	0.176774i
$759$	0.669195	+	0.322267i	0.0242902	+	0.0116976i
$760$		0			0
$761$	11.8638	−	14.8768i	0.430063	−	0.539282i	−0.518831	−	0.854877i	$-0.673633\pi$
$761$	11.8638	−	14.8768i	0.430063	−	0.539282i	0.948894	+	0.315595i	$0.102204\pi$
$762$	18.0891	−	4.12872i	0.655299	−	0.149568i
$763$	−0.741319	−	0.465802i	−0.0268376	−	0.0168632i
$764$	−1.81618	+	16.1191i	−0.0657072	+	0.583167i
$765$		0			0
$766$	−6.29154	+	6.29154i	−0.227323	+	0.227323i
$767$	13.8870	−	8.72580i	0.501432	−	0.315070i
$768$	−7.73616	−	16.0643i	−0.279155	−	0.579670i
$769$	24.2753	+	8.49430i	0.875390	+	0.306312i	0.730317	−	0.683109i	$-0.239372\pi$
$769$	24.2753	+	8.49430i	0.875390	+	0.306312i	0.145073	+	0.989421i	$0.453658\pi$
$770$		0			0
$771$	−15.0785	−	15.0785i	−0.543039	−	0.543039i
$772$	−13.5119	−	3.08399i	−0.486302	−	0.110995i
$773$	5.38261	−	4.29249i	0.193599	−	0.154390i	−0.521893	−	0.853011i	$-0.674774\pi$
$773$	5.38261	−	4.29249i	0.193599	−	0.154390i	0.715492	+	0.698621i	$0.246203\pi$
$774$	−10.0289	+	2.28902i	−0.360480	+	0.0822771i
$775$		0			0
$776$	11.4142	+	9.10249i	0.409745	+	0.326760i
$777$	0.0873735	−	0.249699i	0.00313451	−	0.00895791i
$778$	−19.4684	−	55.6374i	−0.697975	−	1.99470i
$779$	−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
$783$	9.24139	−	22.6710i	0.330260	−	0.810195i
$784$		−	34.6552i		−	1.23768i
$785$		0			0
$786$	27.7285	−	3.12425i	0.989042	−	0.111438i
$787$	4.01476	−	35.6320i	0.143111	−	1.27014i	−0.692740	−	0.721187i	$-0.743597\pi$
$787$	4.01476	−	35.6320i	0.143111	−	1.27014i	0.835851	−	0.548957i	$-0.184975\pi$
$788$	−26.4116	+	9.24182i	−0.940874	+	0.329226i
$789$	6.33651	−	3.05150i	0.225586	−	0.108636i
$790$		0			0
$791$	−0.112330	−	0.0705817i	−0.00399400	−	0.00250960i
$792$	2.68634	−	4.27529i	0.0954550	−	0.151916i
$793$	18.4170	+	23.0942i	0.654006	+	0.820098i
$794$	19.9742	+	31.7888i	0.708859	+	1.12814i
$795$		0			0
$796$	2.60736	+	0.595114i	0.0924156	+	0.0210933i
$797$	39.7334	−	19.1346i	1.40743	−	0.677782i	0.432775	−	0.901502i	$-0.357534\pi$
$797$	39.7334	−	19.1346i	1.40743	−	0.677782i	0.974654	+	0.223720i	$0.0718200\pi$
$798$	−0.201488	+	0.0970316i	−0.00713261	+	0.00343488i
$799$	−12.3999	−	2.83019i	−0.438677	−	0.100125i
$800$		0			0
$801$	2.68428	+	4.27201i	0.0948445	+	0.150944i
$802$	14.5127	+	18.1984i	0.512461	+	0.642606i
$803$	1.87439	−	2.98307i	0.0661457	−	0.105270i
$804$	7.62686	+	4.79227i	0.268978	+	0.169010i
$805$		0			0
$806$	−10.6593	+	5.13326i	−0.375459	+	0.180811i
$807$	6.50266	−	2.27538i	0.228905	−	0.0800972i
$808$	1.78860	−	15.8743i	0.0629229	−	0.558456i
$809$	−27.0462	+	3.04738i	−0.950895	+	0.107140i	−0.573765	−	0.819020i	$-0.694518\pi$
$809$	−27.0462	+	3.04738i	−0.950895	+	0.107140i	−0.377130	+	0.926160i	$0.623089\pi$
$810$		0			0
$811$		−	15.8296i		−	0.555851i	−0.960603	−	0.277926i	$-0.910353\pi$
$811$		−	15.8296i		−	0.555851i	0.960603	−	0.277926i	$-0.0896469\pi$
$812$	0.217174	−	0.245790i	0.00762132	−	0.00862554i
$813$	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
$817$	2.42320	+	6.92511i	0.0847770	+	0.242279i
$818$	−1.54649	+	4.41961i	−0.0540717	+	0.154528i
$819$	−0.334525	−	0.266775i	−0.0116892	−	0.00932186i
$820$		0			0
$821$	−9.19783	+	2.09935i	−0.321007	+	0.0732677i	−0.379988	−	0.924991i	$-0.624072\pi$
$821$	−9.19783	+	2.09935i	−0.321007	+	0.0732677i	0.0589814	+	0.998259i	$0.481215\pi$
$822$	11.1108	−	8.86056i	0.387533	−	0.309048i
$823$	−38.7440	−	8.84307i	−1.35053	−	0.308250i	−0.514763	−	0.857332i	$-0.672120\pi$
$823$	−38.7440	−	8.84307i	−1.35053	−	0.308250i	−0.835768	+	0.549083i	$0.814977\pi$
$824$	0.677618	+	0.677618i	0.0236059	+	0.0236059i
$825$		0			0
$826$	0.365221	+	0.127796i	0.0127077	+	0.00444660i
$827$	19.2297	+	39.9309i	0.668683	+	1.38853i	0.908570	+	0.417734i	$0.137175\pi$
$827$	19.2297	+	39.9309i	0.668683	+	1.38853i	−0.239887	+	0.970801i	$0.577110\pi$
$828$	1.24446	−	0.781944i	0.0432479	−	0.0271744i
$829$	17.1511	−	17.1511i	0.595681	−	0.595681i	−0.343479	−	0.939160i	$-0.611606\pi$
$829$	17.1511	−	17.1511i	0.595681	−	0.595681i	0.939160	+	0.343479i	$0.111606\pi$
$830$		0			0
$831$	−1.77408	+	15.7454i	−0.0615420	+	0.546200i
$832$	3.21482	+	2.02001i	0.111454	+	0.0700312i
$833$	−23.5402	+	5.37289i	−0.815618	+	0.186160i
$834$	18.0676	−	22.6560i	0.625629	−	0.784514i
$835$		0			0
$836$	5.05290	+	2.43335i	0.174758	+	0.0841591i
$837$	−7.83584	−	0.882887i	−0.270846	−	0.0305170i
$838$	19.3355	−	24.2459i	0.667932	−	0.837561i
$839$	−11.9236	−	34.0758i	−0.411650	−	1.17643i	−0.944012	−	0.329911i	$-0.892981\pi$
$839$	−11.9236	−	34.0758i	−0.411650	−	1.17643i	0.532362	−	0.846517i	$-0.321305\pi$
$840$		0			0
$841$	28.7793	−	3.57135i	0.992388	−	0.123150i
$842$	12.3724	−	12.3724i	0.426381	−	0.426381i
$843$	8.99045	−	18.6689i	0.309648	−	0.642990i
$844$	1.36308	+	12.0976i	0.0469190	+	0.416418i
$845$		0			0
$846$	−6.45553	+	13.4051i	−0.221946	+	0.460875i
$847$	0.398465	+	0.139429i	0.0136914	+	0.00479083i
$848$	−16.6471	+	1.87567i	−0.571663	+	0.0644109i
$849$	14.4675	−	23.0249i	0.496524	−	0.790213i
$850$		0			0
$851$	3.25567	+	0.366826i	0.111603	+	0.0125746i
$852$	−1.99511	+	8.74114i	−0.0683513	+	0.299467i
$853$	−6.64060			−0.227370			−0.113685	−	0.993517i	$-0.536265\pi$
$853$	−6.64060			−0.227370			−0.113685	+	0.993517i	$0.536265\pi$
$854$	−0.155071	+	0.679409i	−0.00530641	+	0.0232489i
$855$		0			0
$856$	6.13207	−	17.5244i	0.209590	−	0.598973i
$857$	4.11164	+	6.54364i	0.140451	+	0.223527i	0.909541	−	0.415614i	$-0.136433\pi$
$857$	4.11164	+	6.54364i	0.140451	+	0.223527i	−0.769090	+	0.639140i	$0.779290\pi$
$858$		−	9.44698i		−	0.322514i
$859$	−24.3070	+	15.2731i	−0.829346	+	0.521113i	−0.878536	−	0.477677i	$-0.841479\pi$
$859$	−24.3070	+	15.2731i	−0.829346	+	0.521113i	0.0491898	+	0.998789i	$0.484336\pi$
$860$		0			0
$861$	0.0260449	+	0.114110i	0.000887608	+	0.00388887i
$862$	6.86396	+	30.0730i	0.233787	+	1.02429i
$863$	−0.144916	−	1.28617i	−0.00493300	−	0.0437816i	0.991005	−	0.133828i	$-0.0427270\pi$
$863$	−0.144916	−	1.28617i	−0.00493300	−	0.0437816i	−0.995938	+	0.0900465i	$0.971298\pi$
$864$	11.9896	+	24.8966i	0.407893	+	0.846999i
$865$		0			0
$866$	−6.15831	−	7.72228i	−0.209268	−	0.262414i
$867$	−3.44823	−	2.74987i	−0.117108	−	0.0933905i
$868$	−0.0951799	−	0.0458362i	−0.00323062	−	0.00155578i
$869$	3.72530			0.126372
$870$		0			0
$871$	32.4760			1.10041
$872$	22.1293	+	10.6569i	0.749393	+	0.360888i
$873$	−18.3075	−	14.5998i	−0.619616	−	0.494127i
$874$	−1.72683	−	2.16538i	−0.0584110	−	0.0732451i
$875$		0			0
$876$	1.00791	+	2.09295i	0.0340542	+	0.0707143i
$877$	−5.07240	−	45.0188i	−0.171283	−	1.52018i	−0.725743	−	0.687966i	$-0.758504\pi$
$877$	−5.07240	−	45.0188i	−0.171283	−	1.52018i	0.554460	−	0.832210i	$-0.312925\pi$
$878$	−1.56488	−	6.85620i	−0.0528122	−	0.231385i
$879$	−1.17481	−	5.14717i	−0.0396253	−	0.173610i
$880$		0			0
$881$	−29.8952	+	18.7844i	−1.00720	+	0.632863i	−0.931300	−	0.364252i	$-0.881325\pi$
$881$	−29.8952	+	18.7844i	−1.00720	+	0.632863i	−0.0758960	+	0.997116i	$0.524182\pi$
$882$			28.2456i			0.951078i
$883$	15.5925	+	24.8153i	0.524729	+	0.835101i	0.998974	−	0.0452919i	$-0.0144218\pi$
$883$	15.5925	+	24.8153i	0.524729	+	0.835101i	−0.474245	+	0.880393i	$0.657279\pi$
$884$	5.27783	−	15.0832i	0.177513	−	0.507302i
$885$		0			0
$886$	12.7659	−	55.9312i	0.428880	−	1.87904i
$887$	−31.6025			−1.06111			−0.530555	−	0.847651i	$-0.678016\pi$
$887$	−31.6025			−1.06111			−0.530555	+	0.847651i	$0.678016\pi$
$888$	−1.65145	+	7.23546i	−0.0554189	+	0.242806i
$889$	0.593581	+	0.0668805i	0.0199081	+	0.00224310i
$890$		0			0
$891$	−2.39453	+	3.81087i	−0.0802198	+	0.127669i
$892$	−7.51563	+	0.846808i	−0.251642	+	0.0283532i
$893$	10.0163	+	3.50485i	0.335182	+	0.117285i
$894$	−7.66976	+	15.9264i	−0.256515	+	0.532659i
$895$		0			0
$896$	−0.0580365	−	0.515088i	−0.00193886	−	0.0172079i
$897$	−0.766131	+	1.59089i	−0.0255804	+	0.0531182i
$898$	−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
$902$	4.83533	−	6.06331i	0.160999	−	0.201886i
$903$	0.109660	+	0.0123557i	0.00364924	+	0.000411171i
$904$	3.35319	+	1.61481i	0.111526	+	0.0537079i
$905$		0			0
$906$	16.4197	−	20.5897i	0.545508	−	0.684046i
$907$	5.78318	−	1.31997i	0.192027	−	0.0438290i	−0.125426	−	0.992103i	$-0.540030\pi$
$907$	5.78318	−	1.31997i	0.192027	−	0.0438290i	0.317453	+	0.948274i	$0.397172\pi$
$908$	−10.6162	−	6.67060i	−0.352311	−	0.221372i
$909$	−2.86880	+	25.4613i	−0.0951520	+	0.844497i
$910$		0			0
$911$	−3.72458	+	3.72458i	−0.123401	+	0.123401i	−0.766110	−	0.642709i	$-0.777810\pi$
$911$	−3.72458	+	3.72458i	−0.123401	+	0.123401i	0.642709	+	0.766110i	$0.277810\pi$
$912$	10.4539	−	6.56864i	0.346164	−	0.217509i
$913$	−7.92120	−	16.4486i	−0.262154	−	0.544368i
$914$	51.9942	+	18.1936i	1.71982	+	0.601789i
$915$		0			0
$916$	2.50045	+	2.50045i	0.0826171	+	0.0826171i
$917$	0.875815	+	0.199899i	0.0289220	+	0.00660125i
$918$	22.0012	−	17.5454i	0.726148	−	0.579084i
$919$	−33.9679	+	7.75296i	−1.12050	+	0.255747i	−0.742359	−	0.670002i	$-0.766293\pi$
$919$	−33.9679	+	7.75296i	−1.12050	+	0.255747i	−0.378140	+	0.925749i	$0.623436\pi$
$920$		0			0
$921$	−11.0919	−	8.84547i	−0.365489	−	0.291468i
$922$	−3.63510	+	10.3885i	−0.119716	+	0.342128i
$923$	10.6767	+	30.5122i	0.351427	+	1.00432i
$924$	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
$928$	−18.7907	+	26.8015i	−0.616834	+	0.879803i
$929$			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
$932$	−1.87623	+	16.6520i	−0.0614579	+	0.545454i
$933$	15.9666	−	5.58696i	0.522723	−	0.182909i
$934$	−9.23651	+	4.44807i	−0.302228	+	0.145545i
$935$		0			0
$936$	10.1637	+	6.38628i	0.332211	+	0.208742i
$937$	−17.6180	+	28.0389i	−0.575555	+	0.915990i	0.424390	+	0.905480i	$0.360489\pi$
$937$	−17.6180	+	28.0389i	−0.575555	+	0.915990i	−0.999945	+	0.0105107i	$0.996654\pi$
$938$	0.477707	+	0.599025i	0.0155977	+	0.0195589i
$939$	−8.65226	−	13.7700i	−0.282356	−	0.449367i
$940$		0			0
$941$	−36.8079	−	8.40116i	−1.19990	−	0.273870i	−0.424554	−	0.905403i	$-0.639569\pi$
$941$	−36.8079	−	8.40116i	−1.19990	−	0.273870i	−0.775349	+	0.631533i	$0.782426\pi$
$942$	−30.6095	+	14.7408i	−0.997313	+	0.480281i
$943$	−1.30600	+	0.628936i	−0.0425292	+	0.0204810i
$944$	−20.8261	−	4.75341i	−0.677831	−	0.154710i
$945$		0			0
$946$	−3.89017	−	6.19117i	−0.126480	−	0.201292i
$947$	−5.12052	−	6.42093i	−0.166394	−	0.208652i	0.691642	−	0.722240i	$-0.256887\pi$
$947$	−5.12052	−	6.42093i	−0.166394	−	0.208652i	−0.858037	+	0.513588i	$0.828316\pi$
$948$	−1.30685	+	2.07984i	−0.0424446	+	0.0675501i
$949$	7.09170	+	4.45601i	0.230206	+	0.144648i
$950$		0			0
$951$	3.35768	−	1.61697i	0.108880	−	0.0524339i
$952$	−0.228499	+	0.0799553i	−0.00740570	+	0.00259137i
$953$	−2.26419	+	20.0953i	−0.0733444	+	0.650950i	0.902226	+	0.431263i	$0.141932\pi$
$953$	−2.26419	+	20.0953i	−0.0733444	+	0.650950i	−0.975571	+	0.219687i	$0.929497\pi$
$954$	13.5681	−	1.52876i	0.439285	−	0.0494955i
$955$		0			0
$956$		−	21.6207i		−	0.699263i
$957$	7.44891	+	0.376251i	0.240789	+	0.0121625i
$958$	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
$962$	−13.7629	−	39.3322i	−0.443735	−	1.26812i
$963$	−9.83541	+	28.1080i	−0.316942	+	0.905767i
$964$	−17.7993	−	14.1945i	−0.573278	−	0.457174i
$965$		0			0
$966$	−0.0406136	+	0.00926979i	−0.00130672	+	0.000298251i
$967$	−9.18359	+	7.32367i	−0.295324	+	0.235513i	−0.759931	−	0.650004i	$-0.774767\pi$
$967$	−9.18359	+	7.32367i	−0.295324	+	0.235513i	0.464606	+	0.885517i	$0.346196\pi$
$968$	−11.5462	−	2.63534i	−0.371109	−	0.0847031i
$969$	−6.08264	−	6.08264i	−0.195402	−	0.195402i
$970$		0			0
$971$	25.2257	+	8.82685i	0.809531	+	0.283267i	0.703135	−	0.711057i	$-0.251783\pi$
$971$	25.2257	+	8.82685i	0.809531	+	0.283267i	0.106396	+	0.994324i	$0.466069\pi$
$972$	−8.49483	−	17.6397i	−0.272472	−	0.565794i
$973$	0.789927	−	0.496344i	0.0253239	−	0.0159121i
$974$	47.1962	−	47.1962i	1.51226	−	1.51226i
$975$		0			0
$976$	4.30761	−	38.2311i	0.137883	−	1.22375i
$977$	12.8225	+	8.05689i	0.410227	+	0.257763i	0.721299	−	0.692624i	$-0.243545\pi$
$977$	12.8225	+	8.05689i	0.410227	+	0.257763i	−0.311072	+	0.950386i	$0.600688\pi$
$978$	17.9545	−	4.09799i	0.574121	−	0.131039i
$979$	−2.23600	+	2.80385i	−0.0714629	+	0.0896116i
$980$		0			0
$981$	−35.4939	−	17.0929i	−1.13323	−	0.545736i
$982$	−32.5305	−	3.66531i	−1.03809	−	0.116965i
$983$	−5.50262	+	6.90007i	−0.175506	+	0.220078i	−0.861802	−	0.507244i	$-0.830664\pi$
$983$	−5.50262	+	6.90007i	−0.175506	+	0.220078i	0.686296	+	0.727323i	$0.259236\pi$
$984$	−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
$988$	−5.78483	+	12.0123i	−0.184040	+	0.382163i
$989$	0.153020	+	1.35809i	0.00486575	+	0.0431847i
$990$		0			0
$991$	11.0604	−	22.9671i	0.351345	−	0.729575i	−0.648145	−	0.761517i	$-0.724455\pi$
$991$	11.0604	−	22.9671i	0.351345	−	0.729575i	0.999490	+	0.0319421i	$0.0101692\pi$
$992$	9.95110	+	3.48204i	0.315948	+	0.110555i
$993$	−9.06307	+	1.02116i	−0.287608	+	0.0324056i
$994$	−0.405753	+	0.645753i	−0.0128697	+	0.0204820i
$995$		0			0
$996$	11.9621	+	1.34780i	0.379032	+	0.0427067i
$997$	3.55020	−	15.5544i	0.112436	−	0.492614i	−0.887083	−	0.461609i	$-0.847272\pi$
$997$	3.55020	−	15.5544i	0.112436	−	0.492614i	0.999519	−	0.0310044i	$-0.00987059\pi$
$998$	16.4345			0.520225
$999$	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.y.a.18.2	✓	120
5.2	odd	4		725.2.bd.a.482.9	yes	120
5.3	odd	4		725.2.bd.a.482.2	yes	120
5.4	even	2	inner	725.2.y.a.18.9	yes	120
29.21	odd	28		725.2.bd.a.543.9	yes	120
145.79	odd	28		725.2.bd.a.543.2	yes	120
145.108	even	28	inner	725.2.y.a.282.9	yes	120
145.137	even	28	inner	725.2.y.a.282.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.y.a.18.2	✓	120	1.1	even	1	trivial
725.2.y.a.18.9	yes	120	5.4	even	2	inner
725.2.y.a.282.2	yes	120	145.137	even	28	inner
725.2.y.a.282.9	yes	120	145.108	even	28	inner
725.2.bd.a.482.2	yes	120	5.3	odd	4
725.2.bd.a.482.9	yes	120	5.2	odd	4
725.2.bd.a.543.2	yes	120	145.79	odd	28
725.2.bd.a.543.9	yes	120	29.21	odd	28

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.y (of order \(28\), degree \(12\), minimal)

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

Properties

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