LMFDB - Embedded newform 387.2.v.a.242.4

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			242.4
Character	$\chi$	$=$	387.242
Dual form			387.2.v.a.8.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.362744 - 1.58929i) q^{2} +(-0.592310 + 0.285241i) q^{4} +(-0.0283185 - 0.0355103i) q^{5} -1.92060i q^{7} +(-1.36459 - 1.71114i) q^{8} +O(q^{10})$	\(q+(-0.362744 - 1.58929i) q^{2} +(-0.592310 + 0.285241i) q^{4} +(-0.0283185 - 0.0355103i) q^{5} -1.92060i q^{7} +(-1.36459 - 1.71114i) q^{8} +(-0.0461637 + 0.0578874i) q^{10} +(1.40618 - 2.91997i) q^{11} +(3.68962 + 4.62664i) q^{13} +(-3.05238 + 0.696685i) q^{14} +(-3.04427 + 3.81740i) q^{16} +(-5.91025 - 4.71327i) q^{17} +(-1.98970 - 4.13166i) q^{19} +(0.0269023 + 0.0129555i) q^{20} +(-5.15074 - 1.17562i) q^{22} +(0.680401 - 1.41287i) q^{23} +(1.11215 - 4.87263i) q^{25} +(6.01466 - 7.54215i) q^{26} +(0.547833 + 1.13759i) q^{28} +(1.62192 + 7.10610i) q^{29} +(-0.0534253 - 0.234072i) q^{31} +(3.22746 + 1.55426i) q^{32} +(-5.34682 + 11.1028i) q^{34} +(-0.0682009 + 0.0543884i) q^{35} +0.222810i q^{37} +(-5.84464 + 4.66094i) q^{38} +(-0.0221199 + 0.0969137i) q^{40} +(-1.16238 + 0.265306i) q^{41} +(-6.38482 - 1.49466i) q^{43} +2.13062i q^{44} +(-2.49226 - 0.568843i) q^{46} +(1.06796 + 2.21765i) q^{47} +3.31131 q^{49} -8.14743 q^{50} +(-3.50510 - 1.68797i) q^{52} +(7.58804 + 6.05126i) q^{53} +(-0.143510 + 0.0327552i) q^{55} +(-3.28640 + 2.62082i) q^{56} +(10.7053 - 5.15539i) q^{58} +(7.61935 + 6.07623i) q^{59} +(-3.27552 - 0.747616i) q^{61} +(-0.352627 + 0.169816i) q^{62} +(-0.873550 + 3.82727i) q^{64} +(0.0598087 - 0.262039i) q^{65} +(11.1421 - 5.36575i) q^{67} +(4.84512 + 1.10587i) q^{68} +(0.111178 + 0.0886617i) q^{70} +(8.28733 - 3.99097i) q^{71} +(0.908984 - 0.724891i) q^{73} +(0.354109 - 0.0808230i) q^{74} +(2.35704 + 1.87968i) q^{76} +(-5.60807 - 2.70071i) q^{77} +12.1324 q^{79} +0.221766 q^{80} +(0.843294 + 1.75112i) q^{82} +(0.792357 + 0.180850i) q^{83} +0.343348i q^{85} +(-0.0593890 + 10.6895i) q^{86} +(-6.91532 + 1.57838i) q^{88} +(0.974793 - 4.27085i) q^{89} +(8.88590 - 7.08627i) q^{91} +1.03093i q^{92} +(3.13708 - 2.50174i) q^{94} +(-0.0903711 + 0.187657i) q^{95} +(-12.6444 - 6.08921i) q^{97} +(-1.20116 - 5.26262i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.875906\pi$
$2$	−0.362744	−	1.58929i	−0.256499	−	1.12380i	0.668466	−	0.743743i	$-0.266951\pi$
$3$		0			0
$3$		0			0
$4$	−0.592310	+	0.285241i	−0.296155	+	0.142621i
$5$	−0.0283185	−	0.0355103i	−0.0126644	−	0.0158807i	0.775459	−	0.631398i	$-0.217519\pi$
$5$	−0.0283185	−	0.0355103i	−0.0126644	−	0.0158807i	−0.788123	+	0.615517i	$0.788947\pi$
$6$		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	$-0.694655\pi$
$11$	1.40618	−	2.91997i	0.423980	−	0.880403i	0.998099	−	0.0616311i	$-0.0196302\pi$
$12$		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	$-0.916538\pi$
$17$	−5.91025	−	4.71327i	−1.43345	−	1.14314i	−0.467625	−	0.883927i	$-0.654890\pi$
$18$		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	−0.817909	−	0.575347i	$-0.804867\pi$
$23$	0.680401	−	1.41287i	0.141873	−	0.294603i	0.959783	+	0.280744i	$0.0905812\pi$
$24$		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	$0.165185\pi$
$29$	1.62192	+	7.10610i	0.301183	+	1.31957i	−0.567161	+	0.823607i	$0.691958\pi$
$30$		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	−0.312321	−	0.949977i	$-0.601107\pi$
$41$	−1.16238	+	0.265306i	−0.181533	+	0.0414338i	0.130788	+	0.991410i	$0.458249\pi$
$42$		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	0.964222	−	0.265097i	$-0.0854038\pi$
$47$	1.06796	+	2.21765i	0.155778	+	0.323477i	−0.808443	+	0.588574i	$0.799690\pi$
$48$		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	0.985922	−	0.167206i	$-0.0534744\pi$
$53$	7.58804	+	6.05126i	1.04230	+	0.831204i	0.0563749	+	0.998410i	$0.482046\pi$
$54$		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	0.977949	−	0.208844i	$-0.0669702\pi$
$59$	7.61935	+	6.07623i	0.991955	+	0.791058i	0.0140059	+	0.999902i	$0.495542\pi$
$60$		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	0.128209	−	0.991747i	$-0.459077\pi$
$71$	8.28733	−	3.99097i	0.983525	−	0.473641i	0.855316	+	0.518107i	$0.173363\pi$
$72$		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	0.265786	−	0.964032i	$-0.414369\pi$
$83$	0.792357	+	0.180850i	0.0869725	+	0.0198509i	−0.178813	+	0.983883i	$0.557226\pi$
$84$		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	$-0.853987\pi$
$89$	0.974793	−	4.27085i	0.103328	−	0.452709i	0.999951	−	0.00991423i	$-0.00315585\pi$
$90$		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	$0.0184240\pi$
$101$	4.23208	+	8.78800i	0.421107	+	0.874438i	−0.577218	+	0.816590i	$0.695862\pi$
$102$		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	−0.0974839	−	0.995237i	$-0.531079\pi$
$107$	−6.38365	−	1.45703i	−0.617131	−	0.140856i	−0.519647	+	0.854381i	$0.673937\pi$
$108$		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	−0.648534	−	0.761186i	$-0.724618\pi$
$113$	2.52870	−	3.17088i	0.237880	−	0.298292i	0.886414	+	0.462894i	$0.153189\pi$
$114$		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	$0.356745\pi$
$131$	4.96460	+	21.7514i	0.433760	+	1.90042i	−0.00125075	+	0.999999i	$0.500398\pi$
$132$		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	0.687197	−	0.726471i	$-0.258841\pi$
$137$	−2.03633	−	2.55347i	−0.173975	−	0.218158i	−0.861172	+	0.508313i	$0.830269\pi$
$138$		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	−0.240558	−	0.970635i	$-0.577330\pi$
$149$	−14.0304	−	6.75669i	−1.14942	−	0.553530i	−0.908858	+	0.417105i	$0.863045\pi$
$150$		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	−0.350685	−	0.936494i	$-0.614051\pi$
$167$	6.25846	−	4.99095i	0.484294	−	0.386212i	0.834979	+	0.550282i	$0.185480\pi$
$168$		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	$0.0918839\pi$
$173$			7.48849i			0.569339i	−0.958626	+	0.284670i	$0.908116\pi$
$174$		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	$-0.420047\pi$
$179$	6.65065			0.497093			0.248546	+	0.968620i	$0.420047\pi$
$180$		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	0.0765333	−	0.997067i	$-0.475615\pi$
$191$	12.4906	−	6.01517i	0.903789	−	0.435242i	0.827256	+	0.561825i	$0.189901\pi$
$192$		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	−0.146240	−	0.989249i	$-0.546717\pi$
$197$	−9.92626	−	2.26560i	−0.707217	−	0.161418i	−0.560977	+	0.827832i	$0.689574\pi$
$198$		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	$0.0599969\pi$
$227$	2.69050	+	11.7879i	0.178575	+	0.782387i	−0.803714	+	0.595015i	$0.797146\pi$
$228$		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	$0.457874\pi$
$233$	−6.36556	+	27.8893i	−0.417022	+	1.82709i	−0.548979	+	0.835836i	$0.684983\pi$
$234$		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	0.921843	−	0.387563i	$-0.126683\pi$
$239$	0.681376	+	1.41489i	0.0440745	+	0.0915217i	−0.877769	+	0.479085i	$0.840969\pi$
$240$		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	$-0.947013\pi$
$251$		−	5.25027i		−	0.331394i	0.986177	−	0.165697i	$-0.0529874\pi$
$252$		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	$-0.888769\pi$
$257$	−30.1247			−1.87913			−0.939563	+	0.342375i	$0.888769\pi$
$258$		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	$-0.977674\pi$
$263$	−13.6856	−	17.1612i	−0.843891	−	1.05821i	0.153650	−	0.988125i	$-0.450897\pi$
$264$		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	−0.914328	−	0.404975i	$-0.867280\pi$
$269$	−0.453192	+	0.941062i	−0.0276316	+	0.0573776i	0.886696	+	0.462353i	$0.152995\pi$
$270$		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	−0.800755	−	0.598992i	$-0.795568\pi$
$281$	2.79638	−	5.80674i	0.166818	−	0.346401i	0.967573	+	0.252591i	$0.0812826\pi$
$282$		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	−0.636573	−	0.771216i	$-0.719649\pi$
$293$	−0.450937	+	0.359610i	−0.0263440	+	0.0210086i	0.610229	+	0.792225i	$0.291077\pi$
$294$		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	0.190728	−	0.981643i	$-0.438915\pi$
$311$	−12.7655	−	10.1801i	−0.723862	−	0.577261i	−0.914590	+	0.404382i	$0.867487\pi$
$312$		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	0.779375	−	0.626557i	$-0.215537\pi$
$317$	6.08833	+	4.85528i	0.341954	+	0.272700i	−0.437421	+	0.899257i	$0.644108\pi$
$318$		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	$-0.822757\pi$
$347$	2.70541	−	11.8532i	0.145234	−	0.636311i	0.994171	−	0.107817i	$-0.0343860\pi$
$348$		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	$-0.640598\pi$
$353$	10.2555	−	21.2958i	0.545845	−	1.13346i	0.973324	−	0.229433i	$-0.0736873\pi$
$354$		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	0.907987	−	0.418999i	$-0.137619\pi$
$359$	0.270563	+	0.561829i	0.0142797	+	0.0296522i	−0.893707	+	0.448651i	$0.851905\pi$
$360$		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	−0.138273	−	0.990394i	$-0.544155\pi$
$383$	10.7605	−	5.18198i	0.549836	−	0.264787i	0.688109	+	0.725607i	$0.258441\pi$
$384$		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	$-0.861817\pi$
$389$	−5.37138	−	23.5335i	−0.272340	−	1.19320i	0.634903	−	0.772591i	$-0.281040\pi$
$390$		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	−0.00303660	−	0.999995i	$-0.500967\pi$
$401$	8.57288	−	1.95670i	0.428109	−	0.0977131i	0.431146	+	0.902282i	$0.358109\pi$
$402$		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	0.327779	−	0.944754i	$-0.393700\pi$
$419$	−4.22680	−	2.03552i	−0.206493	−	0.0994416i	−0.534272	+	0.845313i	$0.679414\pi$
$420$		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	$0.339182\pi$
$431$			36.3337i			1.75013i	−0.484005	+	0.875065i	$0.660818\pi$
$432$		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	−0.907992	−	0.418987i	$-0.862385\pi$
$443$	−14.7661	+	11.7755i	−0.701557	+	0.559473i	0.206435	+	0.978460i	$0.433814\pi$
$444$		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	−0.746335	−	0.665570i	$-0.768189\pi$
$449$	−14.6485	+	7.05434i	−0.691305	+	0.332915i	0.0550310	+	0.998485i	$0.482474\pi$
$450$		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	0.323925	−	0.946083i	$-0.394998\pi$
$461$	22.0347	−	5.02929i	1.02626	−	0.234237i	0.702336	+	0.711846i	$0.252140\pi$
$462$		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	$-0.377232\pi$
$467$	16.2593			0.752392			0.376196	+	0.926540i	$0.377232\pi$
$468$		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	$0.116215\pi$
$479$			15.6285i			0.714084i	−0.934088	+	0.357042i	$0.883785\pi$
$480$		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	$-0.566831\pi$
$491$	8.94575	−	39.1939i	0.403716	−	1.76880i	0.612133	−	0.790755i	$-0.290312\pi$
$492$		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	0.529762	−	0.848146i	$-0.322281\pi$
$503$	−9.30753	−	11.6713i	−0.415002	−	0.520396i	−0.944765	+	0.327750i	$0.893710\pi$
$504$		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	$-0.976951\pi$
$509$		−	3.26453i		−	0.144698i	0.997379	−	0.0723488i	$-0.0230495\pi$
$510$		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	0.537992	−	0.842950i	$-0.319183\pi$
$521$	−9.21093	−	11.5501i	−0.403538	−	0.506021i	−0.941530	+	0.336929i	$0.890612\pi$
$522$		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	0.471712	−	0.881753i	$-0.343636\pi$
$557$	30.1923	−	6.89119i	1.27929	−	0.291989i	0.807576	+	0.589764i	$0.200779\pi$
$558$		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	0.680089	−	0.733129i	$-0.261941\pi$
$563$	−7.52457	−	15.6249i	−0.317123	−	0.658513i	−0.997212	+	0.0746167i	$0.976227\pi$
$564$		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	0.108635	−	0.994082i	$-0.465352\pi$
$569$	−19.9500	−	15.9096i	−0.836350	−	0.666967i	−0.944984	+	0.327115i	$0.893923\pi$
$570$		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	0.585723	−	0.810511i	$-0.300811\pi$
$587$	38.3918	−	18.4885i	1.58460	−	0.763102i	0.998876	+	0.0474091i	$0.0150964\pi$
$588$		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	−0.0566872	−	0.998392i	$-0.518054\pi$
$593$	−21.2493	−	10.2331i	−0.872605	−	0.420225i	−0.815918	+	0.578167i	$0.803768\pi$
$594$		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	0.0645861	−	0.997912i	$-0.479427\pi$
$599$	−7.59202	−	1.73283i	−0.310202	−	0.0708015i	−0.374788	+	0.927111i	$0.622284\pi$
$600$		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	0.861677	−	0.507458i	$-0.169415\pi$
$617$	−1.79631	−	3.73007i	−0.0723165	−	0.150167i	−0.933993	+	0.357291i	$0.883700\pi$
$618$		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	−0.646341	−	0.763049i	$-0.723702\pi$
$641$	−11.4628	+	5.52018i	−0.452752	+	0.218034i	0.193589	+	0.981083i	$0.437987\pi$
$642$		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	$0.314098\pi$
$647$	10.5960	+	46.4241i	0.416572	+	1.82512i	−0.134817	+	0.990870i	$0.543045\pi$
$648$		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	$0.0508676\pi$
$653$	23.5788	+	29.5669i	0.922709	+	1.15704i	−0.0645492	+	0.997915i	$0.520561\pi$
$654$		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	−0.986968	−	0.160920i	$-0.948554\pi$
$659$	−46.3714	+	10.5840i	−1.80637	+	0.412293i	−0.819407	+	0.573213i	$0.805697\pi$
$660$		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	0.881867	−	0.471498i	$-0.156286\pi$
$677$	27.6603	+	13.3205i	1.06307	+	0.511948i	0.181203	+	0.983446i	$0.442001\pi$
$678$		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	−0.537116	−	0.843509i	$-0.680486\pi$
$683$	4.33110	−	3.45394i	0.165725	−	0.132161i	0.702841	+	0.711347i	$0.251915\pi$
$684$		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	−0.607231	−	0.794526i	$-0.707720\pi$
$701$	0.853940	−	0.680994i	0.0322529	−	0.0257208i	0.639484	+	0.768805i	$0.279148\pi$
$702$		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	0.494989	−	0.868899i	$-0.335172\pi$
$719$	35.3400	−	8.06612i	1.31796	−	0.300816i	0.822971	+	0.568084i	$0.192315\pi$
$720$		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	0.999877	−	0.0156816i	$-0.00499181\pi$
$743$	2.51360	+	11.0128i	0.0922150	+	0.404020i	−0.907662	+	0.419702i	$0.862135\pi$
$744$		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	0.941278	−	0.337633i	$-0.109626\pi$
$761$	11.1078	+	13.9287i	0.402656	+	0.504915i	−0.538622	+	0.842548i	$0.681055\pi$
$762$		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	$-0.448155\pi$
$773$	9.01688			0.324315			0.162157	+	0.986765i	$0.448155\pi$
$774$		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	$0.336071\pi$
$797$	−13.9739	+	29.0171i	−0.494980	+	1.02784i	−0.987512	+	0.157543i	$0.949643\pi$
$798$		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	−0.270772	−	0.962643i	$-0.587279\pi$
$809$	17.2786	−	13.7792i	0.607483	−	0.484452i	0.878255	+	0.478192i	$0.158708\pi$
$810$		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	$0.177161\pi$
$821$	20.9943	+	43.5951i	0.732706	+	1.52148i	−0.116368	+	0.993206i	$0.537125\pi$
$822$		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	$-0.841038\pi$
$827$	−44.2897	−	35.3199i	−1.54011	−	1.22819i	−0.662233	−	0.749298i	$-0.730391\pi$
$828$		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	$0.237224\pi$
$839$	−6.41484	+	28.1053i	−0.221465	+	0.970302i	−0.956376	+	0.292138i	$0.905633\pi$
$840$		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	0.779710	−	0.626141i	$-0.215366\pi$
$857$	35.4378	+	8.08845i	1.21053	+	0.276296i	0.430822	+	0.902437i	$0.358224\pi$
$858$		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	$-0.659815\pi$
$863$	9.77305	−	42.8185i	0.332678	−	1.45756i	0.813923	−	0.580973i	$-0.197328\pi$
$864$		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	0.763861	−	0.645381i	$-0.223301\pi$
$881$	34.7885	+	7.94025i	1.17206	+	0.267514i	0.408194	+	0.912895i	$0.366159\pi$
$882$		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	$0.429342\pi$
$887$	−23.2255	+	29.1239i	−0.779837	+	0.977885i	−0.999997	+	0.00242078i	$0.999229\pi$
$888$		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	0.620666	−	0.784075i	$-0.286863\pi$
$911$	−8.50740	−	10.6679i	−0.281863	−	0.353445i	−0.902528	+	0.430631i	$0.858291\pi$
$912$		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	−0.996973	−	0.0777542i	$-0.975225\pi$
$929$	−21.3149	+	26.7281i	−0.699321	+	0.876920i	0.297652	+	0.954674i	$0.403796\pi$
$930$		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	−0.415346	−	0.909663i	$-0.636340\pi$
$941$	11.6288	−	9.27362i	0.379087	−	0.302311i	0.794433	+	0.607352i	$0.207768\pi$
$942$		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	$-0.871953\pi$
$947$		−	24.0962i		−	0.783020i	0.920174	−	0.391510i	$-0.128047\pi$
$948$		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	$-0.482185\pi$
$953$	3.45365			0.111875			0.0559373	+	0.998434i	$0.482185\pi$
$954$		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	−0.395283	−	0.918560i	$-0.629353\pi$
$971$	−35.8340	−	8.17888i	−1.14997	−	0.262473i	−0.754685	+	0.656087i	$0.772210\pi$
$972$		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	−0.590886	−	0.806755i	$-0.701222\pi$
$977$	−24.1685	+	5.51629i	−0.773217	+	0.176482i	−0.182332	+	0.983237i	$0.558364\pi$
$978$		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	$-0.777818\pi$
$983$	−48.0404			−1.53225			−0.766125	+	0.642691i	$0.777818\pi$
$984$		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.242.4	yes	96
3.2	odd	2	inner	387.2.v.a.242.13	yes	96
43.8	odd	14	inner	387.2.v.a.8.13	yes	96
129.8	even	14	inner	387.2.v.a.8.4	✓	96

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
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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