LMFDB - Embedded newform 387.2.v.a.242.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(8,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 13]))

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

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

chi := DirichletCharacter("387.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.v (of order $14$, degree $6$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			242.13
Character	$\chi$	$=$	387.242
Dual form			387.2.v.a.8.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.362744 + 1.58929i) q^{2} +(-0.592310 + 0.285241i) q^{4} +(0.0283185 + 0.0355103i) q^{5} -1.92060i q^{7} +(1.36459 + 1.71114i) q^{8} +O(q^{10})$	\(q+(0.362744 + 1.58929i) q^{2} +(-0.592310 + 0.285241i) q^{4} +(0.0283185 + 0.0355103i) q^{5} -1.92060i q^{7} +(1.36459 + 1.71114i) q^{8} +(-0.0461637 + 0.0578874i) q^{10} +(-1.40618 + 2.91997i) q^{11} +(3.68962 + 4.62664i) q^{13} +(3.05238 - 0.696685i) q^{14} +(-3.04427 + 3.81740i) q^{16} +(5.91025 + 4.71327i) q^{17} +(-1.98970 - 4.13166i) q^{19} +(-0.0269023 - 0.0129555i) q^{20} +(-5.15074 - 1.17562i) q^{22} +(-0.680401 + 1.41287i) q^{23} +(1.11215 - 4.87263i) q^{25} +(-6.01466 + 7.54215i) q^{26} +(0.547833 + 1.13759i) q^{28} +(-1.62192 - 7.10610i) q^{29} +(-0.0534253 - 0.234072i) q^{31} +(-3.22746 - 1.55426i) q^{32} +(-5.34682 + 11.1028i) q^{34} +(0.0682009 - 0.0543884i) q^{35} +0.222810i q^{37} +(5.84464 - 4.66094i) q^{38} +(-0.0221199 + 0.0969137i) q^{40} +(1.16238 - 0.265306i) q^{41} +(-6.38482 - 1.49466i) q^{43} -2.13062i q^{44} +(-2.49226 - 0.568843i) q^{46} +(-1.06796 - 2.21765i) q^{47} +3.31131 q^{49} +8.14743 q^{50} +(-3.50510 - 1.68797i) q^{52} +(-7.58804 - 6.05126i) q^{53} +(-0.143510 + 0.0327552i) q^{55} +(3.28640 - 2.62082i) q^{56} +(10.7053 - 5.15539i) q^{58} +(-7.61935 - 6.07623i) q^{59} +(-3.27552 - 0.747616i) q^{61} +(0.352627 - 0.169816i) q^{62} +(-0.873550 + 3.82727i) q^{64} +(-0.0598087 + 0.262039i) q^{65} +(11.1421 - 5.36575i) q^{67} +(-4.84512 - 1.10587i) q^{68} +(0.111178 + 0.0886617i) q^{70} +(-8.28733 + 3.99097i) q^{71} +(0.908984 - 0.724891i) q^{73} +(-0.354109 + 0.0808230i) q^{74} +(2.35704 + 1.87968i) q^{76} +(5.60807 + 2.70071i) q^{77} +12.1324 q^{79} -0.221766 q^{80} +(0.843294 + 1.75112i) q^{82} +(-0.792357 - 0.180850i) q^{83} +0.343348i q^{85} +(0.0593890 - 10.6895i) q^{86} +(-6.91532 + 1.57838i) q^{88} +(-0.974793 + 4.27085i) q^{89} +(8.88590 - 7.08627i) q^{91} -1.03093i q^{92} +(3.13708 - 2.50174i) q^{94} +(0.0903711 - 0.187657i) q^{95} +(-12.6444 - 6.08921i) q^{97} +(1.20116 + 5.26262i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 20 q^{4}+O(q^{10}) $ 96 * q - 20 * q^4	$ 96 q - 20 q^{4} + 16 q^{10} - 4 q^{13} - 36 q^{16} - 16 q^{25} - 48 q^{31} - 104 q^{40} + 28 q^{43} - 28 q^{46} - 160 q^{49} - 44 q^{52} + 84 q^{55} + 20 q^{58} + 52 q^{64} + 40 q^{67} - 140 q^{70} - 28 q^{73} + 112 q^{76} + 64 q^{79} + 168 q^{88} + 56 q^{91} + 112 q^{94} - 108 q^{97}+O(q^{100}) $ 96 * q - 20 * q^4 + 16 * q^10 - 4 * q^13 - 36 * q^16 - 16 * q^25 - 48 * q^31 - 104 * q^40 + 28 * q^43 - 28 * q^46 - 160 * q^49 - 44 * q^52 + 84 * q^55 + 20 * q^58 + 52 * q^64 + 40 * q^67 - 140 * q^70 - 28 * q^73 + 112 * q^76 + 64 * q^79 + 168 * q^88 + 56 * q^91 + 112 * q^94 - 108 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$-1$

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 $

$2$	0.362744	+	1.58929i	0.256499	+	1.12380i	0.924965	+	0.380052i	$0.124094\pi$
$2$	0.362744	+	1.58929i	0.256499	+	1.12380i	−0.668466	+	0.743743i	$0.733049\pi$
$3$		0			0
$3$		0			0
$4$	−0.592310	+	0.285241i	−0.296155	+	0.142621i
$5$	0.0283185	+	0.0355103i	0.0126644	+	0.0158807i	0.788123	−	0.615517i	$-0.211053\pi$
$5$	0.0283185	+	0.0355103i	0.0126644	+	0.0158807i	−0.775459	+	0.631398i	$0.782481\pi$
$6$		0			0
$7$		−	1.92060i		−	0.725917i	−0.931805	−	0.362959i	$-0.881767\pi$
$7$		−	1.92060i		−	0.725917i	0.931805	−	0.362959i	$-0.118233\pi$
$8$	1.36459	+	1.71114i	0.482454	+	0.604978i
$9$		0			0
$10$	−0.0461637	+	0.0578874i	−0.0145982	+	0.0183056i
$11$	−1.40618	+	2.91997i	−0.423980	+	0.880403i	0.574119	+	0.818772i	$0.305345\pi$
$11$	−1.40618	+	2.91997i	−0.423980	+	0.880403i	−0.998099	+	0.0616311i	$0.980370\pi$
$12$		0			0
$13$	3.68962	+	4.62664i	1.02332	+	1.28320i	0.958437	+	0.285305i	$0.0920948\pi$
$13$	3.68962	+	4.62664i	1.02332	+	1.28320i	0.0648791	+	0.997893i	$0.479334\pi$
$14$	3.05238	−	0.696685i	0.815782	−	0.186197i
$15$		0			0
$16$	−3.04427	+	3.81740i	−0.761068	+	0.954349i
$17$	5.91025	+	4.71327i	1.43345	+	1.14314i	0.965821	+	0.259208i	$0.0834616\pi$
$17$	5.91025	+	4.71327i	1.43345	+	1.14314i	0.467625	+	0.883927i	$0.345110\pi$
$18$		0			0
$19$	−1.98970	−	4.13166i	−0.456469	−	0.947868i	−0.994480	−	0.104930i	$-0.966538\pi$
$19$	−1.98970	−	4.13166i	−0.456469	−	0.947868i	0.538011	−	0.842938i	$-0.319176\pi$
$20$	−0.0269023	−	0.0129555i	−0.00601555	−	0.00289693i
$21$		0			0
$22$	−5.15074	−	1.17562i	−1.09814	−	0.250644i
$23$	−0.680401	+	1.41287i	−0.141873	+	0.294603i	−0.959783	−	0.280744i	$-0.909419\pi$
$23$	−0.680401	+	1.41287i	−0.141873	+	0.294603i	0.817909	+	0.575347i	$0.195133\pi$
$24$		0			0
$25$	1.11215	−	4.87263i	0.222429	−	0.974526i
$26$	−6.01466	+	7.54215i	−1.17957	+	1.47914i
$27$		0			0
$28$	0.547833	+	1.13759i	0.103531	+	0.214984i
$29$	−1.62192	−	7.10610i	−0.301183	−	1.31957i	−0.868344	−	0.495963i	$-0.834815\pi$
$29$	−1.62192	−	7.10610i	−0.301183	−	1.31957i	0.567161	−	0.823607i	$-0.308042\pi$
$30$		0			0
$31$	−0.0534253	−	0.234072i	−0.00959547	−	0.0420405i	0.969904	−	0.243489i	$-0.0782921\pi$
$31$	−0.0534253	−	0.234072i	−0.00959547	−	0.0420405i	−0.979499	+	0.201449i	$0.935435\pi$
$32$	−3.22746	−	1.55426i	−0.570540	−	0.274758i
$33$		0			0
$34$	−5.34682	+	11.1028i	−0.916972	+	1.90411i
$35$	0.0682009	−	0.0543884i	0.0115281	−	0.00919332i
$36$		0			0
$37$			0.222810i			0.0366297i	0.999832	+	0.0183149i	$0.00583013\pi$
$37$			0.222810i			0.0366297i	−0.999832	+	0.0183149i	$0.994170\pi$
$38$	5.84464	−	4.66094i	0.948125	−	0.756105i
$39$		0			0
$40$	−0.0221199	+	0.0969137i	−0.00349747	+	0.0153234i
$41$	1.16238	−	0.265306i	0.181533	−	0.0414338i	−0.130788	−	0.991410i	$-0.541751\pi$
$41$	1.16238	−	0.265306i	0.181533	−	0.0414338i	0.312321	+	0.949977i	$0.398893\pi$
$42$		0			0
$43$	−6.38482	−	1.49466i	−0.973677	−	0.227934i
$43$	−6.38482	−	1.49466i	−0.973677	−	0.227934i
$44$		−	2.13062i		−	0.321204i
$45$		0			0
$46$	−2.49226	−	0.568843i	−0.367464	−	0.0838713i
$47$	−1.06796	−	2.21765i	−0.155778	−	0.323477i	0.808443	−	0.588574i	$-0.200310\pi$
$47$	−1.06796	−	2.21765i	−0.155778	−	0.323477i	−0.964222	+	0.265097i	$0.914596\pi$
$48$		0			0
$49$	3.31131			0.473044
$50$	8.14743			1.15222
$51$		0			0
$52$	−3.50510	−	1.68797i	−0.486071	−	0.234079i
$53$	−7.58804	−	6.05126i	−1.04230	−	0.831204i	−0.0563749	−	0.998410i	$-0.517954\pi$
$53$	−7.58804	−	6.05126i	−1.04230	−	0.831204i	−0.985922	+	0.167206i	$0.946526\pi$
$54$		0			0
$55$	−0.143510	+	0.0327552i	−0.0193509	+	0.00441671i
$56$	3.28640	−	2.62082i	0.439164	−	0.350222i
$57$		0			0
$58$	10.7053	−	5.15539i	1.40567	−	0.676936i
$59$	−7.61935	−	6.07623i	−0.991955	−	0.791058i	−0.0140059	−	0.999902i	$-0.504458\pi$
$59$	−7.61935	−	6.07623i	−0.991955	−	0.791058i	−0.977949	+	0.208844i	$0.933030\pi$
$60$		0			0
$61$	−3.27552	−	0.747616i	−0.419387	−	0.0957224i	0.00761914	−	0.999971i	$-0.497575\pi$
$61$	−3.27552	−	0.747616i	−0.419387	−	0.0957224i	−0.427007	+	0.904249i	$0.640432\pi$
$62$	0.352627	−	0.169816i	0.0447837	−	0.0215667i
$63$		0			0
$64$	−0.873550	+	3.82727i	−0.109194	+	0.478409i
$65$	−0.0598087	+	0.262039i	−0.00741835	+	0.0325019i
$66$		0			0
$67$	11.1421	−	5.36575i	1.36122	−	0.655530i	0.396314	−	0.918115i	$-0.370289\pi$
$67$	11.1421	−	5.36575i	1.36122	−	0.655530i	0.964909	+	0.262585i	$0.0845750\pi$
$68$	−4.84512	−	1.10587i	−0.587557	−	0.134106i
$69$		0			0
$70$	0.111178	+	0.0886617i	0.0132883	+	0.0105971i
$71$	−8.28733	+	3.99097i	−0.983525	+	0.473641i	−0.855316	−	0.518107i	$-0.826637\pi$
$71$	−8.28733	+	3.99097i	−0.983525	+	0.473641i	−0.128209	+	0.991747i	$0.540923\pi$
$72$		0			0
$73$	0.908984	−	0.724891i	0.106389	−	0.0848420i	−0.568851	−	0.822441i	$-0.692612\pi$
$73$	0.908984	−	0.724891i	0.106389	−	0.0848420i	0.675239	+	0.737599i	$0.264040\pi$
$74$	−0.354109	+	0.0808230i	−0.0411643	+	0.00939548i
$75$		0			0
$76$	2.35704	+	1.87968i	0.270371	+	0.215614i
$77$	5.60807	+	2.70071i	0.639099	+	0.307774i
$78$		0			0
$79$	12.1324			1.36500			0.682501	−	0.730885i	$-0.260892\pi$
$79$	12.1324			1.36500			0.682501	+	0.730885i	$0.260892\pi$
$80$	−0.221766			−0.0247942
$81$		0			0
$82$	0.843294	+	1.75112i	0.0931263	+	0.193379i
$83$	−0.792357	−	0.180850i	−0.0869725	−	0.0198509i	0.178813	−	0.983883i	$-0.442774\pi$
$83$	−0.792357	−	0.180850i	−0.0869725	−	0.0198509i	−0.265786	+	0.964032i	$0.585631\pi$
$84$		0			0
$85$			0.343348i			0.0372413i
$86$	0.0593890	−	10.6895i	0.00640408	−	1.15268i
$87$		0			0
$88$	−6.91532	+	1.57838i	−0.737175	+	0.168255i
$89$	−0.974793	+	4.27085i	−0.103328	+	0.452709i	0.896623	+	0.442795i	$0.146013\pi$
$89$	−0.974793	+	4.27085i	−0.103328	+	0.452709i	−0.999951	+	0.00991423i	$0.996844\pi$
$90$		0			0
$91$	8.88590	−	7.08627i	0.931495	−	0.742843i
$92$		−	1.03093i		−	0.107482i
$93$		0			0
$94$	3.13708	−	2.50174i	0.323565	−	0.258035i
$95$	0.0903711	−	0.187657i	0.00927188	−	0.0192532i
$96$		0			0
$97$	−12.6444	−	6.08921i	−1.28384	−	0.618266i	−0.337467	−	0.941337i	$-0.609570\pi$
$97$	−12.6444	−	6.08921i	−1.28384	−	0.618266i	−0.946374	+	0.323072i	$0.895284\pi$
$98$	1.20116	+	5.26262i	0.121335	+	0.531605i
$99$		0			0
$100$	0.731140	+	3.20334i	0.0731140	+	0.320334i
$101$	−4.23208	−	8.78800i	−0.421107	−	0.874438i	−0.998325	−	0.0578482i	$-0.981576\pi$
$101$	−4.23208	−	8.78800i	−0.421107	−	0.874438i	0.577218	−	0.816590i	$-0.304138\pi$
$102$		0			0
$103$	2.07244	−	2.59876i	0.204204	−	0.256064i	−0.669175	−	0.743105i	$-0.733352\pi$
$103$	2.07244	−	2.59876i	0.204204	−	0.256064i	0.873379	+	0.487041i	$0.161924\pi$
$104$	−2.88200	+	12.6269i	−0.282604	+	1.23817i
$105$		0			0
$106$	6.86466	−	14.2546i	0.666755	−	1.38453i
$107$	6.38365	+	1.45703i	0.617131	+	0.140856i	0.519647	−	0.854381i	$-0.326063\pi$
$107$	6.38365	+	1.45703i	0.617131	+	0.140856i	0.0974839	+	0.995237i	$0.468921\pi$
$108$		0			0
$109$	14.5570	+	7.01029i	1.39431	+	0.671464i	0.971998	−	0.234987i	$-0.0755048\pi$
$109$	14.5570	+	7.01029i	1.39431	+	0.671464i	0.422311	+	0.906451i	$0.361219\pi$
$110$	−0.104115	−	0.216196i	−0.00992695	−	0.0206135i
$111$		0			0
$112$	7.33168	+	5.84682i	0.692779	+	0.552473i
$113$	−2.52870	+	3.17088i	−0.237880	+	0.298292i	−0.886414	−	0.462894i	$-0.846811\pi$
$113$	−2.52870	+	3.17088i	−0.237880	+	0.298292i	0.648534	+	0.761186i	$0.275382\pi$
$114$		0			0
$115$	−0.0694393	+	0.0158491i	−0.00647525	+	0.00147793i
$116$	2.98763	+	3.74637i	0.277395	+	0.347842i
$117$		0			0
$118$	6.89299	−	14.3134i	0.634551	−	1.31766i
$119$	9.05228	−	11.3512i	0.829822	−	1.04056i
$120$		0			0
$121$	0.309537	+	0.388147i	0.0281397	+	0.0352861i
$122$		−	5.47693i		−	0.495858i
$123$		0			0
$124$	0.0984113	+	0.123404i	0.00883759	+	0.0110820i
$125$	0.409130	−	0.197027i	0.0365937	−	0.0176226i
$126$		0			0
$127$	2.06267	+	9.03714i	0.183032	+	0.801917i	0.980176	+	0.198128i	$0.0634860\pi$
$127$	2.06267	+	9.03714i	0.183032	+	0.801917i	−0.797144	+	0.603789i	$0.793657\pi$
$128$	−13.5639			−1.19889
$129$		0			0
$130$	−0.438150			−0.0384283
$131$	−4.96460	−	21.7514i	−0.433760	−	1.90042i	−0.435010	−	0.900425i	$-0.643255\pi$
$131$	−4.96460	−	21.7514i	−0.433760	−	1.90042i	0.00125075	−	0.999999i	$-0.499602\pi$
$132$		0			0
$133$	−7.93525	+	3.82142i	−0.688074	+	0.331359i
$134$	12.5694	+	15.7616i	1.08583	+	1.36159i
$135$		0			0
$136$			16.5449i			1.41871i
$137$	2.03633	+	2.55347i	0.173975	+	0.218158i	0.861172	−	0.508313i	$-0.169731\pi$
$137$	2.03633	+	2.55347i	0.173975	+	0.218158i	−0.687197	+	0.726471i	$0.741159\pi$
$138$		0			0
$139$	−9.77772	+	12.2609i	−0.829336	+	1.03995i	0.169185	+	0.985584i	$0.445886\pi$
$139$	−9.77772	+	12.2609i	−0.829336	+	1.03995i	−0.998521	+	0.0543699i	$0.982685\pi$
$140$	−0.0248823	+	0.0516685i	−0.00210293	+	0.00436679i
$141$		0			0
$142$	−9.34897	−	11.7232i	−0.784548	−	0.983792i
$143$	−18.6979	+	4.26767i	−1.56360	+	0.356881i
$144$		0			0
$145$	0.206409	−	0.258829i	0.0171414	−	0.0214946i
$146$	1.48179	+	1.18169i	0.122634	+	0.0977970i
$147$		0			0
$148$	−0.0635546	−	0.131972i	−0.00522416	−	0.0108481i
$149$	14.0304	+	6.75669i	1.14942	+	0.553530i	0.908858	−	0.417105i	$-0.136955\pi$
$149$	14.0304	+	6.75669i	1.14942	+	0.553530i	0.240558	+	0.970635i	$0.422670\pi$
$150$		0			0
$151$	−6.24805	−	1.42608i	−0.508459	−	0.116053i	−0.0394076	−	0.999223i	$-0.512547\pi$
$151$	−6.24805	−	1.42608i	−0.508459	−	0.116053i	−0.469052	+	0.883171i	$0.655404\pi$
$152$	4.35472	−	9.04266i	0.353214	−	0.733457i
$153$		0			0
$154$	−2.25790	+	9.89250i	−0.181947	+	0.797160i
$155$	0.00679903	−	0.00852571i	0.000546111	−	0.000684802i
$156$		0			0
$157$	−5.89327	−	12.2375i	−0.470334	−	0.976658i	−0.992319	−	0.123704i	$-0.960523\pi$
$157$	−5.89327	−	12.2375i	−0.470334	−	0.976658i	0.521985	−	0.852955i	$-0.325192\pi$
$158$	4.40096	+	19.2819i	0.350121	+	1.53398i
$159$		0			0
$160$	−0.0362046	−	0.158623i	−0.00286222	−	0.0125402i
$161$	2.71355	+	1.30678i	0.213858	+	0.102988i
$162$		0			0
$163$	8.74554	−	18.1603i	0.685004	−	1.42243i	−0.210600	−	0.977572i	$-0.567542\pi$
$163$	8.74554	−	18.1603i	0.685004	−	1.42243i	0.895604	−	0.444853i	$-0.146744\pi$
$164$	−0.612814	+	0.488703i	−0.0478527	+	0.0381613i
$165$		0			0
$166$		−	1.32488i		−	0.102831i
$167$	−6.25846	+	4.99095i	−0.484294	+	0.386212i	−0.834979	−	0.550282i	$-0.814520\pi$
$167$	−6.25846	+	4.99095i	−0.484294	+	0.386212i	0.350685	+	0.936494i	$0.385949\pi$
$168$		0			0
$169$	−4.89970	+	21.4670i	−0.376900	+	1.65131i
$170$	−0.545677	+	0.124547i	−0.0418516	+	0.00955234i
$171$		0			0
$172$	4.20813	−	0.935913i	0.320867	−	0.0713627i
$173$		−	7.48849i		−	0.569339i	−0.958626	−	0.284670i	$-0.908116\pi$
$173$		−	7.48849i		−	0.569339i	0.958626	−	0.284670i	$-0.0918839\pi$
$174$		0			0
$175$	−9.35835	−	2.13598i	−0.707425	−	0.161465i
$176$	−6.86587	−	14.2571i	−0.517534	−	1.07467i
$177$		0			0
$178$	−7.14120			−0.535256
$179$	−6.65065			−0.497093			−0.248546	−	0.968620i	$-0.579953\pi$
$179$	−6.65065			−0.497093			−0.248546	+	0.968620i	$0.579953\pi$
$180$		0			0
$181$	−10.8360	−	5.21835i	−0.805435	−	0.387877i	−0.0145899	−	0.999894i	$-0.504644\pi$
$181$	−10.8360	−	5.21835i	−0.805435	−	0.387877i	−0.790845	+	0.612017i	$0.790359\pi$
$182$	14.4854	+	11.5517i	1.07373	+	0.856271i
$183$		0			0
$184$	−3.34608	+	0.763720i	−0.246676	+	0.0563022i
$185$	−0.00791205	+	0.00630965i	−0.000581705	+	0.000463894i
$186$		0			0
$187$	−22.0735	+	10.6300i	−1.61417	+	0.777344i
$188$	1.26513	+	1.00891i	0.0922691	+	0.0735822i
$189$		0			0
$190$	0.331023	+	0.0755538i	0.0240149	+	0.00548125i
$191$	−12.4906	+	6.01517i	−0.903789	+	0.435242i	−0.827256	−	0.561825i	$-0.810099\pi$
$191$	−12.4906	+	6.01517i	−0.903789	+	0.435242i	−0.0765333	+	0.997067i	$0.524385\pi$
$192$		0			0
$193$	−3.33277	+	14.6018i	−0.239898	+	1.05106i	0.701210	+	0.712954i	$0.252643\pi$
$193$	−3.33277	+	14.6018i	−0.239898	+	1.05106i	−0.941108	+	0.338106i	$0.890214\pi$
$194$	5.09082	−	22.3044i	0.365500	−	1.60136i
$195$		0			0
$196$	−1.96132	+	0.944522i	−0.140094	+	0.0674659i
$197$	9.92626	+	2.26560i	0.707217	+	0.161418i	0.560977	−	0.827832i	$-0.310426\pi$
$197$	9.92626	+	2.26560i	0.707217	+	0.161418i	0.146240	+	0.989249i	$0.453283\pi$
$198$		0			0
$199$	−7.12373	−	5.68098i	−0.504988	−	0.402714i	0.337587	−	0.941295i	$-0.390389\pi$
$199$	−7.12373	−	5.68098i	−0.504988	−	0.402714i	−0.842574	+	0.538580i	$0.818961\pi$
$200$	9.85535	−	4.74609i	0.696879	−	0.335599i
$201$		0			0
$202$	12.4315	−	9.91377i	0.874676	−	0.697531i
$203$	−13.6480	+	3.11506i	−0.957898	+	0.218634i
$204$		0			0
$205$	0.0423380	+	0.0337634i	0.00295702	+	0.00235814i
$206$	4.88195	+	2.35102i	0.340141	+	0.163803i
$207$		0			0
$208$	−28.8939			−2.00343
$209$	14.8622			1.02804
$210$		0			0
$211$	2.83114	+	5.87892i	0.194904	+	0.404722i	0.975401	−	0.220437i	$-0.0707485\pi$
$211$	2.83114	+	5.87892i	0.194904	+	0.404722i	−0.780498	+	0.625159i	$0.785034\pi$
$212$	6.22054	+	1.41980i	0.427228	+	0.0975120i
$213$		0			0
$214$			10.6740i			0.729658i
$215$	−0.127733	−	0.269054i	−0.00871131	−	0.0183493i
$216$		0			0
$217$	−0.449557	+	0.102609i	−0.0305179	+	0.00696552i
$218$	−5.86088	+	25.6782i	−0.396949	+	1.73915i
$219$		0			0
$220$	0.0756591	−	0.0603361i	0.00510094	−	0.00406786i
$221$			44.7347i			3.00918i
$222$		0			0
$223$	−20.1856	+	16.0975i	−1.35173	+	1.07797i	−0.362438	+	0.932008i	$0.618056\pi$
$223$	−20.1856	+	16.0975i	−1.35173	+	1.07797i	−0.989290	+	0.145960i	$0.953373\pi$
$224$	−2.98511	+	6.19865i	−0.199451	+	0.414165i
$225$		0			0
$226$	−5.95671	−	2.86860i	−0.396235	−	0.190816i
$227$	−2.69050	−	11.7879i	−0.178575	−	0.782387i	−0.982289	−	0.187372i	$-0.940003\pi$
$227$	−2.69050	−	11.7879i	−0.178575	−	0.782387i	0.803714	−	0.595015i	$-0.202854\pi$
$228$		0			0
$229$	3.65491	+	16.0132i	0.241523	+	1.05818i	0.939631	+	0.342189i	$0.111168\pi$
$229$	3.65491	+	16.0132i	0.241523	+	1.05818i	−0.698108	+	0.715992i	$0.745975\pi$
$230$	−0.0503774	−	0.104610i	−0.00332179	−	0.00689776i
$231$		0			0
$232$	9.94626	−	12.4722i	0.653004	−	0.818841i
$233$	6.36556	−	27.8893i	0.417022	−	1.82709i	−0.131958	−	0.991255i	$-0.542126\pi$
$233$	6.36556	−	27.8893i	0.417022	−	1.82709i	0.548979	−	0.835836i	$-0.315017\pi$
$234$		0			0
$235$	0.0485062	−	0.100724i	0.00316420	−	0.00657053i
$236$	6.24621	+	1.42566i	0.406593	+	0.0928023i
$237$		0			0
$238$	21.3240	+	10.2691i	1.38223	+	0.665646i
$239$	−0.681376	−	1.41489i	−0.0440745	−	0.0915217i	0.877769	−	0.479085i	$-0.159031\pi$
$239$	−0.681376	−	1.41489i	−0.0440745	−	0.0915217i	−0.921843	+	0.387563i	$0.873317\pi$
$240$		0			0
$241$	16.0169	+	12.7730i	1.03174	+	0.822784i	0.984373	−	0.176094i	$-0.0563462\pi$
$241$	16.0169	+	12.7730i	1.03174	+	0.822784i	0.0473648	+	0.998878i	$0.484918\pi$
$242$	−0.504594	+	0.632740i	−0.0324365	+	0.0406741i
$243$		0			0
$244$	2.15337	−	0.491493i	0.137856	−	0.0314646i
$245$	0.0937714	+	0.117586i	0.00599083	+	0.00751227i
$246$		0			0
$247$	11.7744	−	24.4499i	0.749190	−	1.55571i
$248$	0.327625	−	0.410829i	0.0208042	−	0.0260877i
$249$		0			0
$250$	0.461541	+	0.578754i	0.0291904	+	0.0366036i
$251$			5.25027i			0.331394i	0.986177	+	0.165697i	$0.0529874\pi$
$251$			5.25027i			0.331394i	−0.986177	+	0.165697i	$0.947013\pi$
$252$		0			0
$253$	−3.16876	−	3.97349i	−0.199218	−	0.249811i
$254$	−13.6144	+	6.55634i	−0.854243	+	0.411382i
$255$		0			0
$256$	−3.17314	−	13.9024i	−0.198321	−	0.868902i
$257$	30.1247			1.87913			0.939563	−	0.342375i	$-0.111231\pi$
$257$	30.1247			1.87913			0.939563	+	0.342375i	$0.111231\pi$
$258$		0			0
$259$	0.427928			0.0265901
$260$	−0.0393191	−	0.172268i	−0.00243847	−	0.0106836i
$261$		0			0
$262$	32.7682	−	15.7804i	2.02443	−	0.974914i
$263$	13.6856	+	17.1612i	0.843891	+	1.05821i	0.997541	+	0.0700809i	$0.0223258\pi$
$263$	13.6856	+	17.1612i	0.843891	+	1.05821i	−0.153650	+	0.988125i	$0.549103\pi$
$264$		0			0
$265$		−	0.440816i		−	0.0270791i
$266$	−8.95179	−	11.2252i	−0.548870	−	0.688261i
$267$		0			0
$268$	−5.06903	+	6.35637i	−0.309641	+	0.388277i
$269$	0.453192	−	0.941062i	0.0276316	−	0.0573776i	−0.886696	−	0.462353i	$-0.847005\pi$
$269$	0.453192	−	0.941062i	0.0276316	−	0.0573776i	0.914328	+	0.404975i	$0.132720\pi$
$270$		0			0
$271$	−0.601588	−	0.754368i	−0.0365439	−	0.0458246i	0.763224	−	0.646134i	$-0.223615\pi$
$271$	−0.601588	−	0.754368i	−0.0365439	−	0.0458246i	−0.799768	+	0.600310i	$0.795044\pi$
$272$	−35.9848	+	8.21330i	−2.18190	+	0.498005i
$273$		0			0
$274$	−3.31953	+	4.16256i	−0.200540	+	0.251470i
$275$	12.6640	+	10.0992i	0.763670	+	0.609006i
$276$		0			0
$277$	−11.1665	−	23.1875i	−0.670931	−	1.39320i	−0.906860	−	0.421432i	$-0.861527\pi$
$277$	−11.1665	−	23.1875i	−0.670931	−	1.39320i	0.235929	−	0.971770i	$-0.424187\pi$
$278$	−23.0329	−	11.0920i	−1.38142	−	0.665256i
$279$		0			0
$280$	0.186132	+	0.0424835i	0.0111235	+	0.00253887i
$281$	−2.79638	+	5.80674i	−0.166818	+	0.346401i	−0.967573	−	0.252591i	$-0.918717\pi$
$281$	−2.79638	+	5.80674i	−0.166818	+	0.346401i	0.800755	+	0.598992i	$0.204432\pi$
$282$		0			0
$283$	5.55639	−	24.3441i	0.330293	−	1.44711i	−0.488270	−	0.872693i	$-0.662372\pi$
$283$	5.55639	−	24.3441i	0.330293	−	1.44711i	0.818563	−	0.574416i	$-0.194771\pi$
$284$	3.77028	−	4.72778i	0.223725	−	0.280542i
$285$		0			0
$286$	−13.5651	−	28.1682i	−0.802121	−	1.66562i
$287$	−0.509546	−	2.23247i	−0.0300775	−	0.131778i
$288$		0			0
$289$	8.93331	+	39.1394i	0.525489	+	2.30232i
$290$	0.486227	+	0.234155i	0.0285523	+	0.0137500i
$291$		0			0
$292$	−0.331631	+	0.688640i	−0.0194073	+	0.0402996i
$293$	0.450937	−	0.359610i	0.0263440	−	0.0210086i	−0.610229	−	0.792225i	$-0.708923\pi$
$293$	0.450937	−	0.359610i	0.0263440	−	0.0210086i	0.636573	+	0.771216i	$0.280351\pi$
$294$		0			0
$295$		−	0.442635i		−	0.0257712i
$296$	−0.381258	+	0.304043i	−0.0221602	+	0.0176722i
$297$		0			0
$298$	−5.64886	+	24.7493i	−0.327230	+	1.43369i
$299$	−9.04724	+	2.06497i	−0.523215	+	0.119421i
$300$		0			0
$301$	−2.87064	+	12.2627i	−0.165461	+	0.706809i
$302$		−	10.4472i		−	0.601171i
$303$		0			0
$304$	21.8294	+	4.98242i	1.25200	+	0.285761i
$305$	−0.0662098	−	0.137486i	−0.00379116	−	0.00787243i
$306$		0			0
$307$	18.1548			1.03615			0.518075	−	0.855335i	$-0.326649\pi$
$307$	18.1548			1.03615			0.518075	+	0.855335i	$0.326649\pi$
$308$	−4.09207			−0.233167
$309$		0			0
$310$	0.0160161	+	0.00771295i	0.000909654	+	0.000438066i
$311$	12.7655	+	10.1801i	0.723862	+	0.577261i	0.914590	−	0.404382i	$-0.132513\pi$
$311$	12.7655	+	10.1801i	0.723862	+	0.577261i	−0.190728	+	0.981643i	$0.561085\pi$
$312$		0			0
$313$	5.62046	−	1.28283i	0.317687	−	0.0725100i	−0.0607040	−	0.998156i	$-0.519335\pi$
$313$	5.62046	−	1.28283i	0.317687	−	0.0725100i	0.378391	+	0.925646i	$0.376477\pi$
$314$	17.3111	−	13.8052i	0.976924	−	0.779071i
$315$		0			0
$316$	−7.18614	+	3.46066i	−0.404252	+	0.194677i
$317$	−6.08833	−	4.85528i	−0.341954	−	0.272700i	0.437421	−	0.899257i	$-0.355892\pi$
$317$	−6.08833	−	4.85528i	−0.341954	−	0.272700i	−0.779375	+	0.626557i	$0.784463\pi$
$318$		0			0
$319$	23.0303	+	5.25651i	1.28945	+	0.294308i
$320$	−0.160645	+	0.0773627i	−0.00898034	+	0.00432471i
$321$		0			0
$322$	−1.09252	+	4.78663i	−0.0608836	+	0.266748i
$323$	7.71398	−	33.7971i	0.429217	−	1.88052i
$324$		0			0
$325$	26.6473	−	12.8326i	1.47812	−	0.711827i
$326$	32.0343	+	7.31163i	1.77422	+	0.404954i
$327$		0			0
$328$	2.04014	+	1.62696i	0.112648	+	0.0898339i
$329$	−4.25921	+	2.05113i	−0.234818	+	0.113082i
$330$		0			0
$331$	17.2510	−	13.7572i	0.948199	−	0.756163i	−0.0216764	−	0.999765i	$-0.506900\pi$
$331$	17.2510	−	13.7572i	0.948199	−	0.756163i	0.969875	+	0.243602i	$0.0783289\pi$
$332$	0.520907	−	0.118894i	0.0285885	−	0.00652513i
$333$		0			0
$334$	−10.2023	−	8.13604i	−0.558244	−	0.445184i
$335$	0.506067	+	0.243709i	0.0276494	+	0.0133152i
$336$		0			0
$337$	−22.0478			−1.20102			−0.600510	−	0.799617i	$-0.705036\pi$
$337$	−22.0478			−1.20102			−0.600510	+	0.799617i	$0.705036\pi$
$338$	−35.8945			−1.95240
$339$		0			0
$340$	−0.0979369	−	0.203368i	−0.00531137	−	0.0110292i
$341$	0.758607	+	0.173147i	0.0410809	+	0.00937644i
$342$		0			0
$343$		−	19.8039i		−	1.06931i
$344$	−6.15507	−	12.9649i	−0.331859	−	0.699021i
$345$		0			0
$346$	11.9013	−	2.71641i	0.639820	−	0.146035i
$347$	−2.70541	+	11.8532i	−0.145234	+	0.636311i	0.848937	+	0.528494i	$0.177243\pi$
$347$	−2.70541	+	11.8532i	−0.145234	+	0.636311i	−0.994171	+	0.107817i	$0.965614\pi$
$348$		0			0
$349$	−13.6143	+	10.8570i	−0.728756	+	0.581163i	−0.916014	−	0.401147i	$-0.868612\pi$
$349$	−13.6143	+	10.8570i	−0.728756	+	0.581163i	0.187258	+	0.982311i	$0.440040\pi$
$350$		−	15.6479i		−	0.836416i
$351$		0			0
$352$	9.07679	−	7.23850i	0.483795	−	0.385813i
$353$	−10.2555	+	21.2958i	−0.545845	+	1.13346i	0.427480	+	0.904025i	$0.359402\pi$
$353$	−10.2555	+	21.2958i	−0.545845	+	1.13346i	−0.973324	+	0.229433i	$0.926313\pi$
$354$		0			0
$355$	−0.376405	−	0.181267i	−0.0199775	−	0.00962066i
$356$	−0.640843	−	2.80772i	−0.0339646	−	0.148809i
$357$		0			0
$358$	−2.41248	−	10.5698i	−0.127504	−	0.558630i
$359$	−0.270563	−	0.561829i	−0.0142797	−	0.0296522i	0.893707	−	0.448651i	$-0.148095\pi$
$359$	−0.270563	−	0.561829i	−0.0142797	−	0.0296522i	−0.907987	+	0.418999i	$0.862381\pi$
$360$		0			0
$361$	−1.26539	+	1.58675i	−0.0665997	+	0.0835134i
$362$	4.36275	−	19.1145i	0.229301	−	1.00463i
$363$		0			0
$364$	−3.24191	+	6.73189i	−0.169922	+	0.352847i
$365$	0.0514822	+	0.0117505i	0.00269470	+	0.000615048i
$366$		0			0
$367$	11.8303	+	5.69718i	0.617537	+	0.297390i	0.716377	−	0.697713i	$-0.245799\pi$
$367$	11.8303	+	5.69718i	0.617537	+	0.297390i	−0.0988402	+	0.995103i	$0.531513\pi$
$368$	−3.32215	−	6.89852i	−0.173179	−	0.359610i
$369$		0			0
$370$	−0.0128979	−	0.0102857i	−0.000670529	−	0.000534729i
$371$	−11.6220	+	14.5736i	−0.603385	+	0.756621i
$372$		0			0
$373$	−4.85410	+	1.10792i	−0.251336	+	0.0573657i	−0.346332	−	0.938112i	$-0.612573\pi$
$373$	−4.85410	+	1.10792i	−0.251336	+	0.0573657i	0.0949968	+	0.995478i	$0.469716\pi$
$374$	−24.9012	−	31.2251i	−1.28761	−	1.61461i
$375$		0			0
$376$	2.33737	−	4.85361i	0.120541	−	0.250306i
$377$	26.8931	−	33.7228i	1.38506	−	1.73681i
$378$		0			0
$379$	−1.99945	−	2.50723i	−0.102705	−	0.128788i	0.727823	−	0.685765i	$-0.240532\pi$
$379$	−1.99945	−	2.50723i	−0.102705	−	0.128788i	−0.830528	+	0.556977i	$0.811961\pi$
$380$			0.136929i			0.00702430i
$381$		0			0
$382$	−14.0907	−	17.6692i	−0.720944	−	0.904035i
$383$	−10.7605	+	5.18198i	−0.549836	+	0.264787i	−0.688109	−	0.725607i	$-0.741559\pi$
$383$	−10.7605	+	5.18198i	−0.549836	+	0.264787i	0.138273	+	0.990394i	$0.455845\pi$
$384$		0			0
$385$	0.0629095	+	0.275624i	0.00320616	+	0.0140471i
$386$	−24.4154			−1.24271
$387$		0			0
$388$	9.22628			0.468393
$389$	5.37138	+	23.5335i	0.272340	+	1.19320i	0.907243	+	0.420607i	$0.138183\pi$
$389$	5.37138	+	23.5335i	0.272340	+	1.19320i	−0.634903	+	0.772591i	$0.718960\pi$
$390$		0			0
$391$	−10.6806	+	5.14349i	−0.540139	+	0.260117i
$392$	4.51857	+	5.66611i	0.228222	+	0.286182i
$393$		0			0
$394$			16.5975i			0.836170i
$395$	0.343572	+	0.430825i	0.0172870	+	0.0216772i
$396$		0			0
$397$	−0.630100	+	0.790120i	−0.0316238	+	0.0396550i	−0.797392	−	0.603462i	$-0.793788\pi$
$397$	−0.630100	+	0.790120i	−0.0316238	+	0.0396550i	0.765768	+	0.643117i	$0.222359\pi$
$398$	6.44462	−	13.3824i	0.323040	−	0.670798i
$399$		0			0
$400$	15.2151	+	19.0791i	0.760754	+	0.953956i
$401$	−8.57288	+	1.95670i	−0.428109	+	0.0977131i	−0.431146	−	0.902282i	$-0.641891\pi$
$401$	−8.57288	+	1.95670i	−0.428109	+	0.0977131i	0.00303660	+	0.999995i	$0.499033\pi$
$402$		0			0
$403$	0.885845	−	1.11081i	0.0441271	−	0.0553336i
$404$	5.01340	+	3.99805i	0.249426	+	0.198911i
$405$		0			0
$406$	−9.90143	−	20.5605i	−0.491400	−	1.02040i
$407$	−0.650597	−	0.313311i	−0.0322489	−	0.0155303i
$408$		0			0
$409$	−18.8676	−	4.30640i	−0.932942	−	0.212938i	−0.271074	−	0.962559i	$-0.587379\pi$
$409$	−18.8676	−	4.30640i	−0.932942	−	0.212938i	−0.661868	+	0.749621i	$0.730236\pi$
$410$	−0.0383019	+	0.0795347i	−0.00189160	+	0.00392794i
$411$		0			0
$412$	−0.486254	+	2.13042i	−0.0239560	+	0.104958i
$413$	−11.6700	+	14.6337i	−0.574242	+	0.720077i
$414$		0			0
$415$	−0.0160163	−	0.0332582i	−0.000786210	−	0.00163258i
$416$	−4.71709	−	20.6669i	−0.231274	−	1.01328i
$417$		0			0
$418$	5.39117	+	23.6203i	0.263691	+	1.15531i
$419$	4.22680	+	2.03552i	0.206493	+	0.0994416i	0.534272	−	0.845313i	$-0.320586\pi$
$419$	4.22680	+	2.03552i	0.206493	+	0.0994416i	−0.327779	+	0.944754i	$0.606300\pi$
$420$		0			0
$421$	−5.77689	+	11.9958i	−0.281548	+	0.584641i	−0.993003	−	0.118091i	$-0.962323\pi$
$421$	−5.77689	+	11.9958i	−0.281548	+	0.584641i	0.711454	+	0.702732i	$0.248037\pi$
$422$	−8.31631	+	6.63203i	−0.404831	+	0.322842i
$423$		0			0
$424$		−	21.2416i		−	1.03158i
$425$	29.5391	−	23.5566i	1.43285	−	1.14266i
$426$		0			0
$427$	−1.43587	+	6.29095i	−0.0694866	+	0.304441i
$428$	−4.19670	+	0.957870i	−0.202855	+	0.0463004i
$429$		0			0
$430$	0.381269	−	0.300602i	0.0183864	−	0.0144963i
$431$		−	36.3337i		−	1.75013i	−0.484005	−	0.875065i	$-0.660818\pi$
$431$		−	36.3337i		−	1.75013i	0.484005	−	0.875065i	$-0.339182\pi$
$432$		0			0
$433$	10.0965	+	2.30447i	0.485208	+	0.110746i	0.458125	−	0.888888i	$-0.348521\pi$
$433$	10.0965	+	2.30447i	0.485208	+	0.110746i	0.0270828	+	0.999633i	$0.491378\pi$
$434$	−0.326149	−	0.677255i	−0.0156556	−	0.0325093i
$435$		0			0
$436$	−10.6219			−0.508696
$437$	7.19128			0.344006
$438$		0			0
$439$	−33.3385	−	16.0550i	−1.59116	−	0.766262i	−0.591949	−	0.805976i	$-0.701641\pi$
$439$	−33.3385	−	16.0550i	−1.59116	−	0.766262i	−0.999211	+	0.0397133i	$0.987356\pi$
$440$	−0.251880	−	0.200868i	−0.0120079	−	0.00957599i
$441$		0			0
$442$	−71.0963	+	16.2273i	−3.38171	+	0.771852i
$443$	14.7661	−	11.7755i	0.701557	−	0.559473i	−0.206435	−	0.978460i	$-0.566186\pi$
$443$	14.7661	−	11.7755i	0.701557	−	0.559473i	0.907992	+	0.418987i	$0.137615\pi$
$444$		0			0
$445$	−0.179264	+	0.0863289i	−0.00849792	+	0.00409238i
$446$	−32.9057	−	26.2415i	−1.55813	−	1.24257i
$447$		0			0
$448$	7.35065	+	1.67774i	0.347285	+	0.0792656i
$449$	14.6485	−	7.05434i	0.691305	−	0.332915i	−0.0550310	−	0.998485i	$-0.517526\pi$
$449$	14.6485	−	7.05434i	0.691305	−	0.332915i	0.746335	+	0.665570i	$0.231811\pi$
$450$		0			0
$451$	−0.859835	+	3.76718i	−0.0404880	+	0.177390i
$452$	0.593304	−	2.59943i	0.0279067	−	0.122267i
$453$		0			0
$454$	17.7583	−	8.55195i	0.833439	−	0.401363i
$455$	0.503271	+	0.114868i	0.0235937	+	0.00538511i
$456$		0			0
$457$	20.6183	+	16.4426i	0.964484	+	0.769150i	0.972998	−	0.230813i	$-0.0741387\pi$
$457$	20.6183	+	16.4426i	0.964484	+	0.769150i	−0.00851405	+	0.999964i	$0.502710\pi$
$458$	−24.1237	+	11.6174i	−1.12723	+	0.542845i
$459$		0			0
$460$	0.0366088	−	0.0291945i	0.00170689	−	0.00136120i
$461$	−22.0347	+	5.02929i	−1.02626	+	0.234237i	−0.702336	−	0.711846i	$-0.747860\pi$
$461$	−22.0347	+	5.02929i	−1.02626	+	0.234237i	−0.323925	+	0.946083i	$0.605002\pi$
$462$		0			0
$463$	−8.03196	−	6.40528i	−0.373277	−	0.297678i	0.418825	−	0.908067i	$-0.362442\pi$
$463$	−8.03196	−	6.40528i	−0.373277	−	0.297678i	−0.792102	+	0.610388i	$0.791013\pi$
$464$	32.0644	+	15.4414i	1.48855	+	0.716849i
$465$		0			0
$466$	46.6332			2.16024
$467$	−16.2593			−0.752392			−0.376196	−	0.926540i	$-0.622768\pi$
$467$	−16.2593			−0.752392			−0.376196	+	0.926540i	$0.622768\pi$
$468$		0			0
$469$	−10.3054	−	21.3995i	−0.475861	−	0.988135i
$470$	0.177675	+	0.0405532i	0.00819554	+	0.00187058i
$471$		0			0
$472$		−	21.3293i		−	0.981760i
$473$	13.3426	−	16.5417i	0.613493	−	0.760588i
$474$		0			0
$475$	−22.3449	+	5.10007i	−1.02525	+	0.234007i
$476$	−2.12392	+	9.30552i	−0.0973499	+	0.426518i
$477$		0			0
$478$	2.00150	−	1.59614i	0.0915466	−	0.0730059i
$479$		−	15.6285i		−	0.714084i	−0.934088	−	0.357042i	$-0.883785\pi$
$479$		−	15.6285i		−	0.714084i	0.934088	−	0.357042i	$-0.116215\pi$
$480$		0			0
$481$	−1.03086	+	0.822084i	−0.0470032	+	0.0374838i
$482$	−14.4900	+	30.0888i	−0.660001	+	1.37051i
$483$		0			0
$484$	−0.294057	−	0.141610i	−0.0133662	−	0.00643684i
$485$	−0.141840	−	0.621443i	−0.00644063	−	0.0282183i
$486$		0			0
$487$	5.40932	+	23.6998i	0.245120	+	1.07394i	0.936285	+	0.351242i	$0.114241\pi$
$487$	5.40932	+	23.6998i	0.245120	+	1.07394i	−0.691165	+	0.722697i	$0.742902\pi$
$488$	−3.19046	−	6.62505i	−0.144425	−	0.299902i
$489$		0			0
$490$	−0.152862	+	0.191683i	−0.00690561	+	0.00865936i
$491$	−8.94575	+	39.1939i	−0.403716	+	1.76880i	0.208417	+	0.978040i	$0.433169\pi$
$491$	−8.94575	+	39.1939i	−0.403716	+	1.76880i	−0.612133	+	0.790755i	$0.709688\pi$
$492$		0			0
$493$	23.9070	−	49.6434i	1.07672	−	2.23583i
$494$	43.1290	+	9.84391i	1.94046	+	0.442898i
$495$		0			0
$496$	1.05619	+	0.508632i	0.0474242	+	0.0228383i
$497$	7.66504	+	15.9166i	0.343824	+	0.713958i
$498$		0			0
$499$	26.2118	+	20.9032i	1.17340	+	0.935755i	0.998804	−	0.0488853i	$-0.0155669\pi$
$499$	26.2118	+	20.9032i	1.17340	+	0.935755i	0.174595	+	0.984640i	$0.444138\pi$
$500$	−0.186132	+	0.233402i	−0.00832406	+	0.0104380i
$501$		0			0
$502$	−8.34418	+	1.90450i	−0.372419	+	0.0850022i
$503$	9.30753	+	11.6713i	0.415002	+	0.520396i	0.944765	−	0.327750i	$-0.106290\pi$
$503$	9.30753	+	11.6713i	0.415002	+	0.520396i	−0.529762	+	0.848146i	$0.677719\pi$
$504$		0			0
$505$	0.192218	−	0.399145i	0.00855360	−	0.0177617i
$506$	5.16557	−	6.47742i	0.229638	−	0.287957i
$507$		0			0
$508$	−3.79951	−	4.76443i	−0.168576	−	0.211387i
$509$			3.26453i			0.144698i	0.997379	+	0.0723488i	$0.0230495\pi$
$509$			3.26453i			0.144698i	−0.997379	+	0.0723488i	$0.976951\pi$
$510$		0			0
$511$	−1.39222	−	1.74579i	−0.0615883	−	0.0772293i
$512$	−3.49747	+	1.68429i	−0.154568	+	0.0744359i
$513$		0			0
$514$	10.9276	+	47.8768i	0.481994	+	2.11175i
$515$	0.150971			0.00665260
$516$		0			0
$517$	7.97721			0.350837
$518$	0.155228	+	0.680100i	0.00682034	+	0.0298819i
$519$		0			0
$520$	−0.529999	+	0.255234i	−0.0232420	+	0.0111927i
$521$	9.21093	+	11.5501i	0.403538	+	0.506021i	0.941530	−	0.336929i	$-0.109388\pi$
$521$	9.21093	+	11.5501i	0.403538	+	0.506021i	−0.537992	+	0.842950i	$0.680817\pi$
$522$		0			0
$523$			41.9480i			1.83426i	0.398591	+	0.917129i	$0.369499\pi$
$523$			41.9480i			1.83426i	−0.398591	+	0.917129i	$0.630501\pi$
$524$	9.14497	+	11.4674i	0.399500	+	0.500957i
$525$		0			0
$526$	−22.3097	+	27.9755i	−0.972750	+	1.21979i
$527$	0.787485	−	1.63523i	0.0343034	−	0.0712318i
$528$		0			0
$529$	12.8070	+	16.0595i	0.556827	+	0.698239i
$530$	0.700583	−	0.159903i	0.0304314	−	0.00694576i
$531$		0			0
$532$	3.61010	−	4.52692i	0.156518	−	0.196267i
$533$	5.51622	+	4.39904i	0.238934	+	0.190543i
$534$		0			0
$535$	0.129036	+	0.267946i	0.00557872	+	0.0115843i
$536$	24.3859	+	11.7436i	1.05331	+	0.507247i
$537$		0			0
$538$	1.66001	+	0.378886i	0.0715681	+	0.0163349i
$539$	−4.65630	+	9.66891i	−0.200561	+	0.416469i
$540$		0			0
$541$	2.16929	−	9.50427i	0.0932650	−	0.408620i	−0.906647	−	0.421890i	$-0.861367\pi$
$541$	2.16929	−	9.50427i	0.0932650	−	0.408620i	0.999912	+	0.0132696i	$0.00422396\pi$
$542$	0.980684	−	1.22974i	0.0421240	−	0.0528218i
$543$		0			0
$544$	−11.7494	−	24.3980i	−0.503753	−	1.04605i
$545$	0.163296	+	0.715445i	0.00699482	+	0.0306463i
$546$		0			0
$547$	−4.28079	−	18.7554i	−0.183033	−	0.801922i	−0.980176	−	0.198130i	$-0.936513\pi$
$547$	−4.28079	−	18.7554i	−0.183033	−	0.801922i	0.797142	−	0.603791i	$-0.206344\pi$
$548$	−1.93449	−	0.931602i	−0.0826374	−	0.0397961i
$549$		0			0
$550$	−11.4568	+	23.7902i	−0.488518	+	1.01442i
$551$	−26.1329	+	20.8403i	−1.11330	+	0.887825i
$552$		0			0
$553$		−	23.3014i		−	0.990878i
$554$	32.8010	−	26.1579i	1.39358	−	1.11134i
$555$		0			0
$556$	2.29413	−	10.0512i	0.0972929	−	0.426268i
$557$	−30.1923	+	6.89119i	−1.27929	+	0.291989i	−0.807576	−	0.589764i	$-0.799221\pi$
$557$	−30.1923	+	6.89119i	−1.27929	+	0.291989i	−0.471712	+	0.881753i	$0.656364\pi$
$558$		0			0
$559$	−16.6423	−	35.0550i	−0.703895	−	1.48267i
$560$			0.425923i			0.0179985i
$561$		0			0
$562$	−10.2429	−	2.33788i	−0.432072	−	0.0986177i
$563$	7.52457	+	15.6249i	0.317123	+	0.658513i	0.997212	−	0.0746167i	$-0.0237733\pi$
$563$	7.52457	+	15.6249i	0.317123	+	0.658513i	−0.680089	+	0.733129i	$0.738059\pi$
$564$		0			0
$565$	−0.184208			−0.00774969
$566$	40.7054			1.71097
$567$		0			0
$568$	−18.1379	−	8.73474i	−0.761048	−	0.366501i
$569$	19.9500	+	15.9096i	0.836350	+	0.666967i	0.944984	−	0.327115i	$-0.106077\pi$
$569$	19.9500	+	15.9096i	0.836350	+	0.666967i	−0.108635	+	0.994082i	$0.534648\pi$
$570$		0			0
$571$	−9.81038	+	2.23916i	−0.410552	+	0.0937058i	−0.422808	−	0.906219i	$-0.638956\pi$
$571$	−9.81038	+	2.23916i	−0.410552	+	0.0937058i	0.0122566	+	0.999925i	$0.496099\pi$
$572$	9.85762	−	7.86119i	0.412168	−	0.328693i
$573$		0			0
$574$	3.36319	−	1.61963i	0.140377	−	0.0676020i
$575$	6.12767	+	4.88666i	0.255542	+	0.203788i
$576$		0			0
$577$	15.9730	+	3.64574i	0.664965	+	0.151774i	0.541664	−	0.840595i	$-0.317795\pi$
$577$	15.9730	+	3.64574i	0.664965	+	0.151774i	0.123301	+	0.992369i	$0.460652\pi$
$578$	−58.9632	+	28.3952i	−2.45255	+	1.18108i
$579$		0			0
$580$	−0.0484295	+	0.212184i	−0.00201093	+	0.00881044i
$581$	−0.347340	+	1.52180i	−0.0144101	+	0.0631348i
$582$		0			0
$583$	28.3396	−	13.6476i	1.17371	−	0.565227i
$584$	2.48077	+	0.566221i	0.102655	+	0.0234304i
$585$		0			0
$586$	0.735098	+	0.586221i	0.0303666	+	0.0242166i
$587$	−38.3918	+	18.4885i	−1.58460	+	0.763102i	−0.998876	−	0.0474091i	$-0.984904\pi$
$587$	−38.3918	+	18.4885i	−1.58460	+	0.763102i	−0.585723	+	0.810511i	$0.699189\pi$
$588$		0			0
$589$	−0.860804	+	0.686468i	−0.0354688	+	0.0282854i
$590$	0.703474	−	0.160563i	0.0289616	−	0.00661029i
$591$		0			0
$592$	−0.850554	−	0.678294i	−0.0349576	−	0.0278777i
$593$	21.2493	+	10.2331i	0.872605	+	0.420225i	0.815918	−	0.578167i	$-0.196232\pi$
$593$	21.2493	+	10.2331i	0.872605	+	0.420225i	0.0566872	+	0.998392i	$0.481946\pi$
$594$		0			0
$595$	0.659432			0.0270341
$596$	−10.2376			−0.419350
$597$		0			0
$598$	−6.56367	−	13.6296i	−0.268408	−	0.557356i
$599$	7.59202	+	1.73283i	0.310202	+	0.0708015i	0.374788	−	0.927111i	$-0.377716\pi$
$599$	7.59202	+	1.73283i	0.310202	+	0.0708015i	−0.0645861	+	0.997912i	$0.520573\pi$
$600$		0			0
$601$			42.1631i			1.71987i	0.510405	+	0.859934i	$0.329496\pi$
$601$			42.1631i			1.71987i	−0.510405	+	0.859934i	$0.670504\pi$
$602$	−20.5302	−	0.114062i	−0.836749	−	0.00464883i
$603$		0			0
$604$	4.10756	−	0.937523i	0.167134	−	0.0381473i
$605$	−0.00501758	+	0.0219835i	−0.000203994	+	0.000893755i
$606$		0			0
$607$	3.82560	−	3.05081i	0.155276	−	0.123829i	−0.542770	−	0.839881i	$-0.682624\pi$
$607$	3.82560	−	3.05081i	0.155276	−	0.123829i	0.698046	+	0.716053i	$0.254053\pi$
$608$			16.4273i			0.666215i
$609$		0			0
$610$	0.194488	−	0.155099i	0.00787457	−	0.00627976i
$611$	6.31988	−	13.1234i	0.255675	−	0.530914i
$612$		0			0
$613$	−24.0715	−	11.5922i	−0.972241	−	0.468206i	−0.120811	−	0.992676i	$-0.538550\pi$
$613$	−24.0715	−	11.5922i	−0.972241	−	0.468206i	−0.851429	+	0.524469i	$0.824264\pi$
$614$	6.58556	+	28.8532i	0.265772	+	1.16442i
$615$		0			0
$616$	3.03142	+	13.2815i	0.122140	+	0.535128i
$617$	1.79631	+	3.73007i	0.0723165	+	0.150167i	0.933993	−	0.357291i	$-0.116300\pi$
$617$	1.79631	+	3.73007i	0.0723165	+	0.150167i	−0.861677	+	0.507458i	$0.830585\pi$
$618$		0			0
$619$	−8.91505	+	11.1791i	−0.358326	+	0.449327i	−0.928020	−	0.372530i	$-0.878490\pi$
$619$	−8.91505	+	11.1791i	−0.358326	+	0.449327i	0.569694	+	0.821857i	$0.307062\pi$
$620$	−0.00159525	+	0.00698923i	−6.40666e−5	+	0.000280694i
$621$		0			0
$622$	−11.5485	+	23.9807i	−0.463053	+	0.961540i
$623$	8.20258	+	1.87218i	0.328629	+	0.0750075i
$624$		0			0
$625$	−22.4963	−	10.8337i	−0.899854	−	0.433347i
$626$	4.07758	+	8.46718i	0.162973	+	0.338417i
$627$		0			0
$628$	6.98128	+	5.56738i	0.278583	+	0.222163i
$629$	−1.05016	+	1.31686i	−0.0418727	+	0.0525067i
$630$		0			0
$631$	11.2076	−	2.55806i	0.446167	−	0.101835i	0.00646635	−	0.999979i	$-0.497942\pi$
$631$	11.2076	−	2.55806i	0.446167	−	0.101835i	0.439701	+	0.898144i	$0.355085\pi$
$632$	16.5557	+	20.7602i	0.658551	+	0.825797i
$633$		0			0
$634$	5.50792	−	11.4373i	0.218748	−	0.454234i
$635$	−0.262500	+	0.329165i	−0.0104170	+	0.0130625i
$636$		0			0
$637$	12.2175	+	15.3202i	0.484074	+	0.607009i
$638$			38.5085i			1.52457i
$639$		0			0
$640$	−0.384110	−	0.481659i	−0.0151833	−	0.0190393i
$641$	11.4628	−	5.52018i	0.452752	−	0.218034i	−0.193589	−	0.981083i	$-0.562013\pi$
$641$	11.4628	−	5.52018i	0.452752	−	0.218034i	0.646341	+	0.763049i	$0.276298\pi$
$642$		0			0
$643$	−1.67861	−	7.35446i	−0.0661978	−	0.290032i	0.930983	−	0.365061i	$-0.118952\pi$
$643$	−1.67861	−	7.35446i	−0.0661978	−	0.290032i	−0.997181	+	0.0750297i	$0.976095\pi$
$644$	−1.98001			−0.0780232
$645$		0			0
$646$	56.5115			2.22342
$647$	−10.5960	−	46.4241i	−0.416572	−	1.82512i	−0.551389	−	0.834249i	$-0.685902\pi$
$647$	−10.5960	−	46.4241i	−0.416572	−	1.82512i	0.134817	−	0.990870i	$-0.456955\pi$
$648$		0			0
$649$	28.4566	−	13.7040i	1.11702	−	0.537927i
$650$	30.0609	+	37.6952i	1.17909	+	1.47853i
$651$		0			0
$652$			13.2511i			0.518954i
$653$	−23.5788	−	29.5669i	−0.922709	−	1.15704i	−0.987258	−	0.159126i	$-0.949132\pi$
$653$	−23.5788	−	29.5669i	−0.922709	−	1.15704i	0.0645492	−	0.997915i	$-0.479439\pi$
$654$		0			0
$655$	0.631807	−	0.792261i	0.0246867	−	0.0309562i
$656$	−2.52583	+	5.24494i	−0.0986170	+	0.204780i
$657$		0			0
$658$	−4.80483	−	6.02507i	−0.187312	−	0.234882i
$659$	46.3714	−	10.5840i	1.80637	−	0.412293i	0.819407	−	0.573213i	$-0.194303\pi$
$659$	46.3714	−	10.5840i	1.80637	−	0.412293i	0.986968	+	0.160920i	$0.0514460\pi$
$660$		0			0
$661$	−28.0962	+	35.2315i	−1.09281	+	1.37035i	−0.169846	+	0.985471i	$0.554327\pi$
$661$	−28.0962	+	35.2315i	−1.09281	+	1.37035i	−0.922969	+	0.384875i	$0.874244\pi$
$662$	28.1218	+	22.4264i	1.09298	+	0.871626i
$663$		0			0
$664$	−0.771780	−	1.60262i	−0.0299509	−	0.0621936i
$665$	−0.360414	−	0.173566i	−0.0139763	−	0.00673061i
$666$		0			0
$667$	11.1435	+	2.54344i	0.431479	+	0.0984824i
$668$	2.28332	−	4.74136i	0.0883443	−	0.183449i
$669$		0			0
$670$	−0.203750	+	0.892689i	−0.00787156	+	0.0344876i
$671$	6.78899	−	8.51312i	0.262086	−	0.328645i
$672$		0			0
$673$	−9.28777	−	19.2863i	−0.358017	−	0.743430i	0.641706	−	0.766951i	$-0.278227\pi$
$673$	−9.28777	−	19.2863i	−0.358017	−	0.743430i	−0.999723	+	0.0235202i	$0.992513\pi$
$674$	−7.99771	−	35.0403i	−0.308060	−	1.34970i
$675$		0			0
$676$	−3.22113	−	14.1127i	−0.123890	−	0.542796i
$677$	−27.6603	−	13.3205i	−1.06307	−	0.511948i	−0.181203	−	0.983446i	$-0.557999\pi$
$677$	−27.6603	−	13.3205i	−1.06307	−	0.511948i	−0.881867	+	0.471498i	$0.843714\pi$
$678$		0			0
$679$	−11.6949	+	24.2847i	−0.448810	+	0.931963i
$680$	−0.587515	+	0.468527i	−0.0225302	+	0.0179672i
$681$		0			0
$682$			1.26845i			0.0485715i
$683$	−4.33110	+	3.45394i	−0.165725	+	0.132161i	−0.702841	−	0.711347i	$-0.748085\pi$
$683$	−4.33110	+	3.45394i	−0.165725	+	0.132161i	0.537116	+	0.843509i	$0.319514\pi$
$684$		0			0
$685$	−0.0330088	+	0.144621i	−0.00126120	+	0.00552569i
$686$	31.4740	−	7.18374i	1.20168	−	0.274276i
$687$		0			0
$688$	25.1429	−	19.8233i	0.958563	−	0.755754i
$689$		−	57.4339i		−	2.18806i
$690$		0			0
$691$	−48.4910	−	11.0677i	−1.84468	−	0.421037i	−0.850248	−	0.526383i	$-0.823548\pi$
$691$	−48.4910	−	11.0677i	−1.84468	−	0.421037i	−0.994436	+	0.105346i	$0.966405\pi$
$692$	2.13603	+	4.43550i	0.0811995	+	0.168613i
$693$		0			0
$694$	−19.8194			−0.752335
$695$	−0.712278			−0.0270183
$696$		0			0
$697$	8.12042	+	3.91059i	0.307583	+	0.148124i
$698$	−22.1934	−	17.6987i	−0.840034	−	0.669904i
$699$		0			0
$700$	6.15231	−	1.40423i	0.232536	−	0.0530747i
$701$	−0.853940	+	0.680994i	−0.0322529	+	0.0257208i	−0.639484	−	0.768805i	$-0.720852\pi$
$701$	−0.853940	+	0.680994i	−0.0322529	+	0.0257208i	0.607231	+	0.794526i	$0.292280\pi$
$702$		0			0
$703$	0.920575	−	0.443325i	0.0347201	−	0.0167203i
$704$	−9.94714	−	7.93258i	−0.374897	−	0.298970i
$705$		0			0
$706$	−37.5652	−	8.57400i	−1.41378	−	0.322687i
$707$	−16.8782	+	8.12811i	−0.634770	+	0.305689i
$708$		0			0
$709$	−5.65514	+	24.7768i	−0.212383	+	0.930511i	0.750559	+	0.660803i	$0.229784\pi$
$709$	−5.65514	+	24.7768i	−0.212383	+	0.930511i	−0.962942	+	0.269708i	$0.913073\pi$
$710$	0.151547	−	0.663969i	0.00568745	−	0.0249183i
$711$		0			0
$712$	−8.63820	+	4.15994i	−0.323730	+	0.155900i
$713$	0.367063	+	0.0837797i	0.0137466	+	0.00313757i
$714$		0			0
$715$	−0.681043	−	0.543113i	−0.0254696	−	0.0203113i
$716$	3.93924	−	1.89704i	0.147216	−	0.0708957i
$717$		0			0
$718$	0.794762	−	0.633802i	0.0296603	−	0.0236533i
$719$	−35.3400	+	8.06612i	−1.31796	+	0.300816i	−0.822971	−	0.568084i	$-0.807685\pi$
$719$	−35.3400	+	8.06612i	−1.31796	+	0.300816i	−0.494989	+	0.868899i	$0.664828\pi$
$720$		0			0
$721$	−4.99117	−	3.98033i	−0.185881	−	0.148235i
$722$	−2.98082	−	1.43549i	−0.110935	−	0.0534233i
$723$		0			0
$724$	7.90677			0.293853
$725$	−36.4292			−1.35295
$726$		0			0
$727$	18.6988	+	38.8285i	0.693501	+	1.44007i	0.888317	+	0.459231i	$0.151875\pi$
$727$	18.6988	+	38.8285i	0.693501	+	1.44007i	−0.194816	+	0.980840i	$0.562411\pi$
$728$	24.2512	+	5.53517i	0.898807	+	0.205147i
$729$		0			0
$730$			0.0860823i			0.00318605i
$731$	−30.6912	−	38.9272i	−1.13515	−	1.43978i
$732$		0			0
$733$	−39.3838	+	8.98908i	−1.45467	+	0.332019i	−0.875513	−	0.483195i	$-0.839476\pi$
$733$	−39.3838	+	8.98908i	−1.45467	+	0.332019i	−0.579159	+	0.815214i	$0.696619\pi$
$734$	−4.76307	+	20.8684i	−0.175808	+	0.770265i
$735$		0			0
$736$	4.39194	−	3.50245i	0.161889	−	0.129102i
$737$			40.0797i			1.47636i
$738$		0			0
$739$	−4.68377	+	3.73518i	−0.172295	+	0.137401i	−0.705841	−	0.708370i	$-0.749431\pi$
$739$	−4.68377	+	3.73518i	−0.172295	+	0.137401i	0.533546	+	0.845771i	$0.320859\pi$
$740$	0.00288661	−	0.00599411i	0.000106114	−	0.000220348i
$741$		0			0
$742$	−27.3774	−	13.1842i	−1.00505	−	0.484009i
$743$	−2.51360	−	11.0128i	−0.0922150	−	0.404020i	0.907662	−	0.419702i	$-0.137865\pi$
$743$	−2.51360	−	11.0128i	−0.0922150	−	0.404020i	−0.999877	+	0.0156816i	$0.995008\pi$
$744$		0			0
$745$	0.157388	+	0.689563i	0.00576626	+	0.0252636i
$746$	−3.52159	−	7.31266i	−0.128935	−	0.267736i
$747$		0			0
$748$	10.0422	−	12.5925i	0.367179	−	0.460428i
$749$	2.79836	−	12.2604i	0.102250	−	0.447986i
$750$		0			0
$751$	16.8023	−	34.8902i	0.613123	−	1.27316i	−0.331019	−	0.943624i	$-0.607392\pi$
$751$	16.8023	−	34.8902i	0.613123	−	1.27316i	0.944142	−	0.329539i	$-0.106893\pi$
$752$	11.7168	+	2.67429i	0.427269	+	0.0975213i
$753$		0			0
$754$	63.3506	+	30.5080i	2.30709	+	1.11104i
$755$	−0.126295	−	0.262255i	−0.00459635	−	0.00954442i
$756$		0			0
$757$	−4.84799	−	3.86614i	−0.176203	−	0.140517i	0.531417	−	0.847110i	$-0.321660\pi$
$757$	−4.84799	−	3.86614i	−0.176203	−	0.140517i	−0.707620	+	0.706593i	$0.750231\pi$
$758$	3.25942	−	4.08719i	0.118388	−	0.148453i
$759$		0			0
$760$	0.444427	−	0.101438i	0.0161211	−	0.00367952i
$761$	−11.1078	−	13.9287i	−0.402656	−	0.504915i	0.538622	−	0.842548i	$-0.318945\pi$
$761$	−11.1078	−	13.9287i	−0.402656	−	0.504915i	−0.941278	+	0.337633i	$0.890374\pi$
$762$		0			0
$763$	13.4639	−	27.9582i	0.487427	−	1.01215i
$764$	5.68254	−	7.12568i	0.205587	−	0.257798i
$765$		0			0
$766$	−12.1390	−	15.2218i	−0.438599	−	0.549985i
$767$		−	57.6709i		−	2.08238i
$768$		0			0
$769$	10.4663	+	13.1243i	0.377424	+	0.473275i	0.933872	−	0.357608i	$-0.116407\pi$
$769$	10.4663	+	13.1243i	0.377424	+	0.473275i	−0.556448	+	0.830883i	$0.687836\pi$
$770$	−0.415226	+	0.199962i	−0.0149637	+	0.00720614i
$771$		0			0
$772$	−2.19101	−	9.59943i	−0.0788561	−	0.345491i
$773$	−9.01688			−0.324315			−0.162157	−	0.986765i	$-0.551845\pi$
$773$	−9.01688			−0.324315			−0.162157	+	0.986765i	$0.551845\pi$
$774$		0			0
$775$	−1.19996			−0.0431039
$776$	−6.83487	−	29.9455i	−0.245357	−	1.07498i
$777$		0			0
$778$	−35.4531	+	17.0733i	−1.27106	+	0.612108i
$779$	−3.40895	−	4.27469i	−0.122138	−	0.153156i
$780$		0			0
$781$		−	29.8107i		−	1.06671i
$782$	−12.0488	−	15.1087i	−0.430864	−	0.540286i
$783$		0			0
$784$	−10.0805	+	12.6406i	−0.360019	+	0.451450i
$785$	0.267669	−	0.555819i	0.00955350	−	0.0198380i
$786$		0			0
$787$	12.0773	+	15.1444i	0.430509	+	0.539841i	0.949014	−	0.315233i	$-0.102083\pi$
$787$	12.0773	+	15.1444i	0.430509	+	0.539841i	−0.518505	+	0.855074i	$0.673511\pi$
$788$	−6.52566	+	1.48944i	−0.232467	+	0.0530591i
$789$		0			0
$790$	−0.560076	+	0.702313i	−0.0199266	+	0.0249872i
$791$	6.08999	+	4.85660i	0.216535	+	0.172681i
$792$		0			0
$793$	−8.62647	−	17.9131i	−0.306335	−	0.636111i
$794$	−1.48429	−	0.714797i	−0.0526755	−	0.0253672i
$795$		0			0
$796$	5.83991	+	1.33292i	0.206990	+	0.0472441i
$797$	13.9739	−	29.0171i	0.494980	−	1.02784i	−0.492532	−	0.870294i	$-0.663929\pi$
$797$	13.9739	−	29.0171i	0.494980	−	1.02784i	0.987512	−	0.157543i	$-0.0503571\pi$
$798$		0			0
$799$	4.14044	−	18.1405i	0.146478	−	0.641763i
$800$	−11.1628	+	13.9977i	−0.394663	+	0.494892i
$801$		0			0
$802$	−6.21953	−	12.9150i	−0.219619	−	0.456044i
$803$	0.838459	+	3.67353i	0.0295886	+	0.129636i
$804$		0			0
$805$	0.0304397	+	0.133365i	0.00107286	+	0.00470049i
$806$	2.08674	+	1.00492i	0.0735022	+	0.0353968i
$807$		0			0
$808$	9.26243	−	19.2336i	0.325851	−	0.676637i
$809$	−17.2786	+	13.7792i	−0.607483	+	0.484452i	−0.878255	−	0.478192i	$-0.841292\pi$
$809$	−17.2786	+	13.7792i	−0.607483	+	0.484452i	0.270772	+	0.962643i	$0.412721\pi$
$810$		0			0
$811$			2.24716i			0.0789085i	0.999221	+	0.0394542i	$0.0125619\pi$
$811$			2.24716i			0.0789085i	−0.999221	+	0.0394542i	$0.987438\pi$
$812$	7.19527	−	5.73804i	0.252505	−	0.201366i
$813$		0			0
$814$	0.261941	−	1.14764i	0.00918101	−	0.0402247i
$815$	0.892539	−	0.203716i	0.0312643	−	0.00713587i
$816$		0			0
$817$	6.52846	+	29.3539i	0.228402	+	1.02696i
$818$		−	31.5481i		−	1.10305i
$819$		0			0
$820$	−0.0347079	−	0.00792186i	−0.00121205	−	0.000276643i
$821$	−20.9943	−	43.5951i	−0.732706	−	1.52148i	−0.849074	−	0.528274i	$-0.822839\pi$
$821$	−20.9943	−	43.5951i	−0.732706	−	1.52148i	0.116368	−	0.993206i	$-0.462875\pi$
$822$		0			0
$823$	−34.8258			−1.21395			−0.606976	−	0.794720i	$-0.707618\pi$
$823$	−34.8258			−1.21395			−0.606976	+	0.794720i	$0.707618\pi$
$824$	7.27487			0.253432
$825$		0			0
$826$	−27.4903	−	13.2387i	−0.956512	−	0.460632i
$827$	44.2897	+	35.3199i	1.54011	+	1.22819i	0.877872	+	0.478895i	$0.158962\pi$
$827$	44.2897	+	35.3199i	1.54011	+	1.22819i	0.662233	+	0.749298i	$0.269609\pi$
$828$		0			0
$829$	40.3000	−	9.19820i	1.39968	−	0.319467i	0.544916	−	0.838491i	$-0.316562\pi$
$829$	40.3000	−	9.19820i	1.39968	−	0.319467i	0.854760	+	0.519024i	$0.173704\pi$
$830$	0.0470470	−	0.0375188i	0.00163303	−	0.00130230i
$831$		0			0
$832$	−20.9305	+	10.0796i	−0.725633	+	0.349447i
$833$	19.5707	+	15.6071i	0.678084	+	0.540754i
$834$		0			0
$835$	−0.354461	−	0.0809033i	−0.0122666	−	0.00279977i
$836$	−8.80302	+	4.23931i	−0.304459	+	0.146620i
$837$		0			0
$838$	−1.70178	+	7.45597i	−0.0587869	+	0.257562i
$839$	6.41484	−	28.1053i	0.221465	−	0.970302i	−0.734911	−	0.678163i	$-0.762776\pi$
$839$	6.41484	−	28.1053i	0.221465	−	0.970302i	0.956376	−	0.292138i	$-0.0943667\pi$
$840$		0			0
$841$	−21.7379	+	10.4684i	−0.749584	+	0.360981i
$842$	−21.1603	−	4.82971i	−0.729234	−	0.166443i
$843$		0			0
$844$	−3.35382	−	2.67458i	−0.115443	−	0.0920630i
$845$	−0.901051	+	0.433923i	−0.0309971	+	0.0149274i
$846$		0			0
$847$	0.745473	−	0.594495i	0.0256148	−	0.0204271i
$848$	46.2001	−	10.5449i	1.58652	−	0.362112i
$849$		0			0
$850$	48.1533	+	38.4010i	1.65165	+	1.31714i
$851$	−0.314801	−	0.151600i	−0.0107912	−	0.00519678i
$852$		0			0
$853$	−15.0884			−0.516618			−0.258309	−	0.966062i	$-0.583165\pi$
$853$	−15.0884			−0.516618			−0.258309	+	0.966062i	$0.583165\pi$
$854$	−10.5190			−0.359952
$855$		0			0
$856$	6.21787	+	12.9115i	0.212522	+	0.441307i
$857$	−35.4378	−	8.08845i	−1.21053	−	0.276296i	−0.430822	−	0.902437i	$-0.641776\pi$
$857$	−35.4378	−	8.08845i	−1.21053	−	0.276296i	−0.779710	+	0.626141i	$0.784634\pi$
$858$		0			0
$859$		−	36.4602i		−	1.24401i	−0.783014	−	0.622004i	$-0.786319\pi$
$859$		−	36.4602i		−	1.24401i	0.783014	−	0.622004i	$-0.213681\pi$
$860$	0.152403	+	0.122928i	0.00519689	+	0.00419182i
$861$		0			0
$862$	57.7446	−	13.1798i	1.96679	−	0.448907i
$863$	−9.77305	+	42.8185i	−0.332678	+	1.45756i	0.481245	+	0.876586i	$0.340185\pi$
$863$	−9.77305	+	42.8185i	−0.332678	+	1.45756i	−0.813923	+	0.580973i	$0.802672\pi$
$864$		0			0
$865$	0.265918	−	0.212063i	0.00904150	−	0.00721035i
$866$			16.8822i			0.573681i
$867$		0			0
$868$	0.237009	−	0.189008i	0.00804461	−	0.00641536i
$869$	−17.0604	+	35.4262i	−0.578733	+	1.20175i
$870$		0			0
$871$	65.9354	+	31.7528i	2.23414	+	1.07590i
$872$	7.86874	+	34.4752i	0.266469	+	1.16748i
$873$		0			0
$874$	2.60860	+	11.4290i	0.0882371	+	0.386592i
$875$	−0.378409	−	0.785774i	−0.0127925	−	0.0265640i
$876$		0			0
$877$	2.81770	−	3.53328i	0.0951468	−	0.119310i	−0.731979	−	0.681327i	$-0.761403\pi$
$877$	2.81770	−	3.53328i	0.0951468	−	0.119310i	0.827126	+	0.562017i	$0.189974\pi$
$878$	13.4226	−	58.8083i	0.452991	−	1.98468i
$879$		0			0
$880$	0.311843	−	0.647550i	0.0105122	−	0.0218289i
$881$	−34.7885	−	7.94025i	−1.17206	−	0.267514i	−0.408194	−	0.912895i	$-0.633841\pi$
$881$	−34.7885	−	7.94025i	−1.17206	−	0.267514i	−0.763861	+	0.645381i	$0.776699\pi$
$882$		0			0
$883$	6.36007	+	3.06285i	0.214033	+	0.103073i	0.537829	−	0.843054i	$-0.319245\pi$
$883$	6.36007	+	3.06285i	0.214033	+	0.103073i	−0.323795	+	0.946127i	$0.604959\pi$
$884$	−12.7602	−	26.4968i	−0.429172	−	0.891184i
$885$		0			0
$886$	24.0710	+	19.1960i	0.808682	+	0.644902i
$887$	23.2255	−	29.1239i	0.779837	−	0.977885i	−0.220160	−	0.975464i	$-0.570658\pi$
$887$	23.2255	−	29.1239i	0.779837	−	0.977885i	0.999997	−	0.00242078i	$-0.000770558\pi$
$888$		0			0
$889$	17.3567	−	3.96155i	0.582125	−	0.132866i
$890$	−0.202228	−	0.253586i	−0.00677871	−	0.00850023i
$891$		0			0
$892$	7.36447	−	15.2925i	0.246581	−	0.512030i
$893$	−7.03764	+	8.82493i	−0.235506	+	0.295315i
$894$		0			0
$895$	−0.188336	−	0.236166i	−0.00629539	−	0.00789417i
$896$			26.0508i			0.870297i
$897$		0			0
$898$	16.5250	+	20.7217i	0.551447	+	0.691492i
$899$	−1.57669	+	0.759292i	−0.0525854	+	0.0253238i
$900$		0			0
$901$	−16.3260	−	71.5289i	−0.543898	−	2.38297i
$902$	−6.29903			−0.209735
$903$		0			0
$904$	−8.87644			−0.295226
$905$	−0.121555	−	0.532566i	−0.00404062	−	0.0177031i
$906$		0			0
$907$	−1.03045	+	0.496239i	−0.0342155	+	0.0164773i	−0.450913	−	0.892568i	$-0.648902\pi$
$907$	−1.03045	+	0.496239i	−0.0342155	+	0.0164773i	0.416698	+	0.909045i	$0.363187\pi$
$908$	4.95599	+	6.21462i	0.164470	+	0.206239i
$909$		0			0
$910$			0.841509i			0.0278958i
$911$	8.50740	+	10.6679i	0.281863	+	0.353445i	0.902528	−	0.430631i	$-0.141709\pi$
$911$	8.50740	+	10.6679i	0.281863	+	0.353445i	−0.620666	+	0.784075i	$0.713137\pi$
$912$		0			0
$913$	1.64227	−	2.05935i	0.0543513	−	0.0681544i
$914$	−18.6528	+	38.7328i	−0.616978	+	1.28117i
$915$		0			0
$916$	−6.73246	−	8.44224i	−0.222447	−	0.278939i
$917$	−41.7756	+	9.53500i	−1.37955	+	0.314874i
$918$		0			0
$919$	8.01708	−	10.0531i	0.264459	−	0.331621i	−0.631817	−	0.775118i	$-0.717691\pi$
$919$	8.01708	−	10.0531i	0.264459	−	0.331621i	0.896276	+	0.443496i	$0.146262\pi$
$920$	−0.121876	−	0.0971927i	−0.00401813	−	0.00320435i
$921$		0			0
$922$	−15.9860	−	33.1952i	−0.526469	−	1.09322i
$923$	−49.0418	−	23.6173i	−1.61423	−	0.777373i
$924$		0			0
$925$	1.08567	+	0.247797i	0.0356966	+	0.00814752i
$926$	7.26627	−	15.0886i	0.238784	−	0.495841i
$927$		0			0
$928$	−5.81007	+	25.4556i	−0.190725	+	0.835620i
$929$	21.3149	−	26.7281i	0.699321	−	0.876920i	−0.297652	−	0.954674i	$-0.596204\pi$
$929$	21.3149	−	26.7281i	0.699321	−	0.876920i	0.996973	+	0.0777542i	$0.0247749\pi$
$930$		0			0
$931$	−6.58852	−	13.6812i	−0.215930	−	0.448383i
$932$	4.18481	+	18.3348i	0.137078	+	0.600578i
$933$		0			0
$934$	−5.89798	−	25.8407i	−0.192988	−	0.845534i
$935$	−1.00256	−	0.482809i	−0.0327873	−	0.0157895i
$936$		0			0
$937$	−3.49421	+	7.25580i	−0.114151	+	0.237037i	−0.950215	−	0.311595i	$-0.899137\pi$
$937$	−3.49421	+	7.25580i	−0.114151	+	0.237037i	0.836064	+	0.548632i	$0.184851\pi$
$938$	30.2716	−	24.1408i	0.988403	−	0.788225i
$939$		0			0
$940$			0.0734959i			0.00239717i
$941$	−11.6288	+	9.27362i	−0.379087	+	0.302311i	−0.794433	−	0.607352i	$-0.792232\pi$
$941$	−11.6288	+	9.27362i	−0.379087	+	0.302311i	0.415346	+	0.909663i	$0.363660\pi$
$942$		0			0
$943$	−0.416043	+	1.82281i	−0.0135482	+	0.0593587i
$944$	46.3908	−	10.5884i	1.50989	−	0.344623i
$945$		0			0
$946$	31.1294	+	15.2048i	1.01211	+	0.494350i
$947$			24.0962i			0.783020i	0.920174	+	0.391510i	$0.128047\pi$
$947$			24.0962i			0.783020i	−0.920174	+	0.391510i	$0.871953\pi$
$948$		0			0
$949$	6.70761	+	1.53097i	0.217738	+	0.0496973i
$950$	−16.2110	−	33.6624i	−0.525953	−	1.09215i
$951$		0			0
$952$	31.7761			1.02987
$953$	−3.45365			−0.111875			−0.0559373	−	0.998434i	$-0.517815\pi$
$953$	−3.45365			−0.111875			−0.0559373	+	0.998434i	$0.517815\pi$
$954$		0			0
$955$	−0.567316	−	0.273205i	−0.0183579	−	0.00884071i
$956$	0.807171	+	0.643697i	0.0261058	+	0.0208187i
$957$		0			0
$958$	24.8381	−	5.66914i	0.802484	−	0.183162i
$959$	4.90419	−	3.91096i	0.158365	−	0.126292i
$960$		0			0
$961$	27.8781	−	13.4254i	0.899294	−	0.433077i
$962$	−1.68046	−	1.34013i	−0.0541804	−	0.0432074i
$963$		0			0
$964$	−13.1304	−	2.99692i	−0.422900	−	0.0965242i
$965$	−0.612893	+	0.295154i	−0.0197297	+	0.00950134i
$966$		0			0
$967$	−10.4167	+	45.6386i	−0.334979	+	1.46764i	0.474377	+	0.880322i	$0.342673\pi$
$967$	−10.4167	+	45.6386i	−0.334979	+	1.46764i	−0.809356	+	0.587318i	$0.800184\pi$
$968$	−0.241783	+	1.05932i	−0.00777119	+	0.0340478i
$969$		0			0
$970$	0.936199	−	0.450850i	0.0300595	−	0.0144759i
$971$	35.8340	+	8.17888i	1.14997	+	0.262473i	0.754685	−	0.656087i	$-0.227790\pi$
$971$	35.8340	+	8.17888i	1.14997	+	0.262473i	0.395283	+	0.918560i	$0.370647\pi$
$972$		0			0
$973$	23.5482	+	18.7791i	0.754921	+	0.602029i
$974$	−35.7035	+	17.1939i	−1.14401	+	0.550929i
$975$		0			0
$976$	12.8255	−	10.2280i	0.410535	−	0.327391i
$977$	24.1685	−	5.51629i	0.773217	−	0.176482i	0.182332	−	0.983237i	$-0.441636\pi$
$977$	24.1685	−	5.51629i	0.773217	−	0.176482i	0.590886	+	0.806755i	$0.298778\pi$
$978$		0			0
$979$	−11.1000	−	8.85195i	−0.354757	−	0.282910i
$980$	−0.0890820	−	0.0428996i	−0.00284562	−	0.00137038i
$981$		0			0
$982$	−65.5353			−2.09132
$983$	48.0404			1.53225			0.766125	−	0.642691i	$-0.222182\pi$
$983$	48.0404			1.53225			0.766125	+	0.642691i	$0.222182\pi$
$984$		0			0
$985$	0.200645	+	0.416643i	0.00639307	+	0.0132753i
$986$	87.5697	+	19.9872i	2.78879	+	0.636522i
$987$		0			0
$988$			17.8405i			0.567581i
$989$	6.45600	−	8.00394i	0.205289	−	0.254510i
$990$		0			0
$991$	−6.24573	+	1.42555i	−0.198402	+	0.0452840i	−0.320567	−	0.947226i	$-0.603873\pi$
$991$	−6.24573	+	1.42555i	−0.198402	+	0.0452840i	0.122165	+	0.992510i	$0.461016\pi$
$992$	−0.191381	+	0.838494i	−0.00607635	+	0.0266222i
$993$		0			0
$994$	−22.5156	+	17.9556i	−0.714152	+	0.569517i
$995$		−	0.413843i		−	0.0131197i
$996$		0			0
$997$	34.8978	−	27.8301i	1.10523	−	0.881388i	0.111559	−	0.993758i	$-0.464415\pi$
$997$	34.8978	−	27.8301i	1.10523	−	0.881388i	0.993666	+	0.112370i	$0.0358441\pi$
$998$	−23.7130	+	49.2405i	−0.750621	+	1.55868i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.v.a.242.13	yes	96
3.2	odd	2	inner	387.2.v.a.242.4	yes	96
43.8	odd	14	inner	387.2.v.a.8.4	✓	96
129.8	even	14	inner	387.2.v.a.8.13	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.v.a.8.4	✓	96	43.8	odd	14	inner
387.2.v.a.8.13	yes	96	129.8	even	14	inner
387.2.v.a.242.4	yes	96	3.2	odd	2	inner
387.2.v.a.242.13	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.v (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.362744 + 1.58929i) q^{2} +(-0.592310 + 0.285241i) q^{4} +(0.0283185 + 0.0355103i) q^{5} -1.92060i q^{7} +(1.36459 + 1.71114i) q^{8} +O(q^{10})\)	\(q+(0.362744 + 1.58929i) q^{2} +(-0.592310 + 0.285241i) q^{4} +(0.0283185 + 0.0355103i) q^{5} -1.92060i q^{7} +(1.36459 + 1.71114i) q^{8} +(-0.0461637 + 0.0578874i) q^{10} +(-1.40618 + 2.91997i) q^{11} +(3.68962 + 4.62664i) q^{13} +(3.05238 - 0.696685i) q^{14} +(-3.04427 + 3.81740i) q^{16} +(5.91025 + 4.71327i) q^{17} +(-1.98970 - 4.13166i) q^{19} +(-0.0269023 - 0.0129555i) q^{20} +(-5.15074 - 1.17562i) q^{22} +(-0.680401 + 1.41287i) q^{23} +(1.11215 - 4.87263i) q^{25} +(-6.01466 + 7.54215i) q^{26} +(0.547833 + 1.13759i) q^{28} +(-1.62192 - 7.10610i) q^{29} +(-0.0534253 - 0.234072i) q^{31} +(-3.22746 - 1.55426i) q^{32} +(-5.34682 + 11.1028i) q^{34} +(0.0682009 - 0.0543884i) q^{35} +0.222810i q^{37} +(5.84464 - 4.66094i) q^{38} +(-0.0221199 + 0.0969137i) q^{40} +(1.16238 - 0.265306i) q^{41} +(-6.38482 - 1.49466i) q^{43} -2.13062i q^{44} +(-2.49226 - 0.568843i) q^{46} +(-1.06796 - 2.21765i) q^{47} +3.31131 q^{49} +8.14743 q^{50} +(-3.50510 - 1.68797i) q^{52} +(-7.58804 - 6.05126i) q^{53} +(-0.143510 + 0.0327552i) q^{55} +(3.28640 - 2.62082i) q^{56} +(10.7053 - 5.15539i) q^{58} +(-7.61935 - 6.07623i) q^{59} +(-3.27552 - 0.747616i) q^{61} +(0.352627 - 0.169816i) q^{62} +(-0.873550 + 3.82727i) q^{64} +(-0.0598087 + 0.262039i) q^{65} +(11.1421 - 5.36575i) q^{67} +(-4.84512 - 1.10587i) q^{68} +(0.111178 + 0.0886617i) q^{70} +(-8.28733 + 3.99097i) q^{71} +(0.908984 - 0.724891i) q^{73} +(-0.354109 + 0.0808230i) q^{74} +(2.35704 + 1.87968i) q^{76} +(5.60807 + 2.70071i) q^{77} +12.1324 q^{79} -0.221766 q^{80} +(0.843294 + 1.75112i) q^{82} +(-0.792357 - 0.180850i) q^{83} +0.343348i q^{85} +(0.0593890 - 10.6895i) q^{86} +(-6.91532 + 1.57838i) q^{88} +(-0.974793 + 4.27085i) q^{89} +(8.88590 - 7.08627i) q^{91} -1.03093i q^{92} +(3.13708 - 2.50174i) q^{94} +(0.0903711 - 0.187657i) q^{95} +(-12.6444 - 6.08921i) q^{97} +(1.20116 + 5.26262i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 20 q^{4}+O(q^{10}) \) 96 * q - 20 * q^4	\( 96 q - 20 q^{4} + 16 q^{10} - 4 q^{13} - 36 q^{16} - 16 q^{25} - 48 q^{31} - 104 q^{40} + 28 q^{43} - 28 q^{46} - 160 q^{49} - 44 q^{52} + 84 q^{55} + 20 q^{58} + 52 q^{64} + 40 q^{67} - 140 q^{70} - 28 q^{73} + 112 q^{76} + 64 q^{79} + 168 q^{88} + 56 q^{91} + 112 q^{94} - 108 q^{97}+O(q^{100}) \) 96 * q - 20 * q^4 + 16 * q^10 - 4 * q^13 - 36 * q^16 - 16 * q^25 - 48 * q^31 - 104 * q^40 + 28 * q^43 - 28 * q^46 - 160 * q^49 - 44 * q^52 + 84 * q^55 + 20 * q^58 + 52 * q^64 + 40 * q^67 - 140 * q^70 - 28 * q^73 + 112 * q^76 + 64 * q^79 + 168 * q^88 + 56 * q^91 + 112 * q^94 - 108 * q^97

Introduction

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