LMFDB - Embedded newform 288.2.s.a.95.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(95,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("288.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.s (of order $6$, degree $2$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.12
Character	$\chi$	$=$	288.95
Dual form			288.2.s.a.191.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71910 + 0.211392i) q^{3} +(-0.135038 - 0.0779642i) q^{5} +(-0.349281 + 0.201658i) q^{7} +(2.91063 + 0.726809i) q^{9} +O(q^{10})$	\(q+(1.71910 + 0.211392i) q^{3} +(-0.135038 - 0.0779642i) q^{5} +(-0.349281 + 0.201658i) q^{7} +(2.91063 + 0.726809i) q^{9} +(2.28556 + 3.95871i) q^{11} +(2.14257 - 3.71104i) q^{13} +(-0.215663 - 0.162574i) q^{15} -2.84030i q^{17} +0.958898i q^{19} +(-0.643079 + 0.272835i) q^{21} +(-2.71342 + 4.69978i) q^{23} +(-2.48784 - 4.30907i) q^{25} +(4.85002 + 1.86474i) q^{27} +(-4.88928 + 2.82283i) q^{29} +(-8.53685 - 4.92876i) q^{31} +(3.09228 + 7.28859i) q^{33} +0.0628883 q^{35} +9.89523 q^{37} +(4.46778 - 5.92674i) q^{39} +(-7.79267 - 4.49910i) q^{41} +(2.59514 - 1.49831i) q^{43} +(-0.336380 - 0.325072i) q^{45} +(-1.22684 - 2.12495i) q^{47} +(-3.41867 + 5.92131i) q^{49} +(0.600416 - 4.88276i) q^{51} +9.45890i q^{53} -0.712769i q^{55} +(-0.202703 + 1.64844i) q^{57} +(-1.18560 + 2.05352i) q^{59} +(-4.10147 - 7.10395i) q^{61} +(-1.16319 + 0.333090i) q^{63} +(-0.578657 + 0.334088i) q^{65} +(-11.4813 - 6.62872i) q^{67} +(-5.65814 + 7.50581i) q^{69} +2.19993 q^{71} -4.53280 q^{73} +(-3.36595 - 7.93364i) q^{75} +(-1.59661 - 0.921804i) q^{77} +(2.84683 - 1.64362i) q^{79} +(7.94350 + 4.23094i) q^{81} +(0.812395 + 1.40711i) q^{83} +(-0.221442 + 0.383548i) q^{85} +(-9.00190 + 3.81918i) q^{87} -9.45890i q^{89} +1.72826i q^{91} +(-13.6338 - 10.2777i) q^{93} +(0.0747597 - 0.129488i) q^{95} +(-0.162474 - 0.281413i) q^{97} +(3.77520 + 13.1835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^9	$ 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) $ 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	1.71910	+	0.211392i	0.992524	+	0.122047i
$3$	1.71910	+	0.211392i	0.992524	+	0.122047i
$4$		0			0
$5$	−0.135038	−	0.0779642i	−0.0603908	−	0.0348667i	0.469501	−	0.882932i	$-0.344434\pi$
$5$	−0.135038	−	0.0779642i	−0.0603908	−	0.0348667i	−0.529891	+	0.848066i	$0.677767\pi$
$6$		0			0
$7$	−0.349281	+	0.201658i	−0.132016	+	0.0762195i	−0.564554	−	0.825396i	$-0.690952\pi$
$7$	−0.349281	+	0.201658i	−0.132016	+	0.0762195i	0.432538	+	0.901616i	$0.357618\pi$
$8$		0			0
$9$	2.91063	+	0.726809i	0.970209	+	0.242270i
$10$		0			0
$11$	2.28556	+	3.95871i	0.689124	+	1.19360i	0.972122	+	0.234477i	$0.0753377\pi$
$11$	2.28556	+	3.95871i	0.689124	+	1.19360i	−0.282998	+	0.959121i	$0.591329\pi$
$12$		0			0
$13$	2.14257	−	3.71104i	0.594242	−	1.02926i	−0.399411	−	0.916772i	$-0.630785\pi$
$13$	2.14257	−	3.71104i	0.594242	−	1.02926i	0.993653	−	0.112486i	$-0.0358812\pi$
$14$		0			0
$15$	−0.215663	−	0.162574i	−0.0556840	−	0.0419765i
$16$		0			0
$17$		−	2.84030i		−	0.688874i	−0.938810	−	0.344437i	$-0.888070\pi$
$17$		−	2.84030i		−	0.688874i	0.938810	−	0.344437i	$-0.111930\pi$
$18$		0			0
$19$			0.958898i			0.219986i	0.993932	+	0.109993i	$0.0350829\pi$
$19$			0.958898i			0.219986i	−0.993932	+	0.109993i	$0.964917\pi$
$20$		0			0
$21$	−0.643079	+	0.272835i	−0.140331	+	0.0595375i
$22$		0			0
$23$	−2.71342	+	4.69978i	−0.565787	+	0.979972i	0.431189	+	0.902262i	$0.358094\pi$
$23$	−2.71342	+	4.69978i	−0.565787	+	0.979972i	−0.996976	+	0.0777105i	$0.975239\pi$
$24$		0			0
$25$	−2.48784	−	4.30907i	−0.497569	−	0.861814i
$26$		0			0
$27$	4.85002	+	1.86474i	0.933388	+	0.358870i
$28$		0			0
$29$	−4.88928	+	2.82283i	−0.907917	+	0.524186i	−0.879760	−	0.475417i	$-0.842297\pi$
$29$	−4.88928	+	2.82283i	−0.907917	+	0.524186i	−0.0281566	+	0.999604i	$0.508964\pi$
$30$		0			0
$31$	−8.53685	−	4.92876i	−1.53326	−	0.885231i	−0.999208	−	0.0397815i	$-0.987334\pi$
$31$	−8.53685	−	4.92876i	−1.53326	−	0.885231i	−0.534056	−	0.845449i	$-0.679333\pi$
$32$		0			0
$33$	3.09228	+	7.28859i	0.538297	+	1.26878i
$34$		0			0
$35$	0.0628883			0.0106301
$36$		0			0
$37$	9.89523			1.62677			0.813383	−	0.581729i	$-0.197624\pi$
$37$	9.89523			1.62677			0.813383	+	0.581729i	$0.197624\pi$
$38$		0			0
$39$	4.46778	−	5.92674i	0.715418	−	0.949037i
$40$		0			0
$41$	−7.79267	−	4.49910i	−1.21701	−	0.702642i	−0.252733	−	0.967536i	$-0.581330\pi$
$41$	−7.79267	−	4.49910i	−1.21701	−	0.702642i	−0.964277	+	0.264894i	$0.914663\pi$
$42$		0			0
$43$	2.59514	−	1.49831i	0.395756	−	0.228490i	−0.288895	−	0.957361i	$-0.593288\pi$
$43$	2.59514	−	1.49831i	0.395756	−	0.228490i	0.684651	+	0.728871i	$0.259955\pi$
$44$		0			0
$45$	−0.336380	−	0.325072i	−0.0501446	−	0.0484588i
$46$		0			0
$47$	−1.22684	−	2.12495i	−0.178953	−	0.309956i	0.762569	−	0.646907i	$-0.223938\pi$
$47$	−1.22684	−	2.12495i	−0.178953	−	0.309956i	−0.941522	+	0.336951i	$0.890604\pi$
$48$		0			0
$49$	−3.41867	+	5.92131i	−0.488381	+	0.845901i
$50$		0			0
$51$	0.600416	−	4.88276i	0.0840751	−	0.683724i
$52$		0			0
$53$			9.45890i			1.29928i	0.760242	+	0.649640i	$0.225080\pi$
$53$			9.45890i			1.29928i	−0.760242	+	0.649640i	$0.774920\pi$
$54$		0			0
$55$		−	0.712769i		−	0.0961098i
$56$		0			0
$57$	−0.202703	+	1.64844i	−0.0268487	+	0.218342i
$58$		0			0
$59$	−1.18560	+	2.05352i	−0.154352	+	0.267346i	−0.932823	−	0.360335i	$-0.882662\pi$
$59$	−1.18560	+	2.05352i	−0.154352	+	0.267346i	0.778471	+	0.627681i	$0.215996\pi$
$60$		0			0
$61$	−4.10147	−	7.10395i	−0.525139	−	0.909568i	−0.999571	−	0.0292756i	$-0.990680\pi$
$61$	−4.10147	−	7.10395i	−0.525139	−	0.909568i	0.474432	−	0.880292i	$-0.342653\pi$
$62$		0			0
$63$	−1.16319	+	0.333090i	−0.146549	+	0.0419653i
$64$		0			0
$65$	−0.578657	+	0.334088i	−0.0717735	+	0.0414385i
$66$		0			0
$67$	−11.4813	−	6.62872i	−1.40266	−	0.809827i	−0.407997	−	0.912983i	$-0.633772\pi$
$67$	−11.4813	−	6.62872i	−1.40266	−	0.809827i	−0.994665	+	0.103156i	$0.967106\pi$
$68$		0			0
$69$	−5.65814	+	7.50581i	−0.681160	+	0.903594i
$70$		0			0
$71$	2.19993			0.261083			0.130542	−	0.991443i	$-0.458328\pi$
$71$	2.19993			0.261083			0.130542	+	0.991443i	$0.458328\pi$
$72$		0			0
$73$	−4.53280			−0.530524			−0.265262	−	0.964176i	$-0.585459\pi$
$73$	−4.53280			−0.530524			−0.265262	+	0.964176i	$0.585459\pi$
$74$		0			0
$75$	−3.36595	−	7.93364i	−0.388667	−	0.916098i
$76$		0			0
$77$	−1.59661	−	0.921804i	−0.181951	−	0.105049i
$78$		0			0
$79$	2.84683	−	1.64362i	0.320293	−	0.184921i	−0.331230	−	0.943550i	$-0.607464\pi$
$79$	2.84683	−	1.64362i	0.320293	−	0.184921i	0.651523	+	0.758629i	$0.274130\pi$
$80$		0			0
$81$	7.94350	+	4.23094i	0.882611	+	0.470104i
$82$		0			0
$83$	0.812395	+	1.40711i	0.0891720	+	0.154450i	0.907161	−	0.420783i	$-0.138245\pi$
$83$	0.812395	+	1.40711i	0.0891720	+	0.154450i	−0.817989	+	0.575233i	$0.804911\pi$
$84$		0			0
$85$	−0.221442	+	0.383548i	−0.0240187	+	0.0416016i
$86$		0			0
$87$	−9.00190	+	3.81918i	−0.965105	+	0.409459i
$88$		0			0
$89$		−	9.45890i		−	1.00264i	−0.865261	−	0.501321i	$-0.832848\pi$
$89$		−	9.45890i		−	1.00264i	0.865261	−	0.501321i	$-0.167152\pi$
$90$		0			0
$91$			1.72826i			0.181171i
$92$		0			0
$93$	−13.6338	−	10.2777i	−1.41376	−	1.06574i
$94$		0			0
$95$	0.0747597	−	0.129488i	0.00767018	−	0.0132851i
$96$		0			0
$97$	−0.162474	−	0.281413i	−0.0164967	−	0.0285732i	0.857659	−	0.514219i	$-0.171918\pi$
$97$	−0.162474	−	0.281413i	−0.0164967	−	0.0285732i	−0.874156	+	0.485645i	$0.838585\pi$
$98$		0			0
$99$	3.77520	+	13.1835i	0.379422	+	1.32499i
$100$		0			0
$101$	−5.03402	+	2.90639i	−0.500903	+	0.289197i	−0.729087	−	0.684421i	$-0.760055\pi$
$101$	−5.03402	+	2.90639i	−0.500903	+	0.289197i	0.228183	+	0.973618i	$0.426722\pi$
$102$		0			0
$103$	6.03931	+	3.48680i	0.595071	+	0.343564i	0.767100	−	0.641527i	$-0.221699\pi$
$103$	6.03931	+	3.48680i	0.595071	+	0.343564i	−0.172029	+	0.985092i	$0.555032\pi$
$104$		0			0
$105$	0.108112	+	0.0132941i	0.0105506	+	0.00129737i
$106$		0			0
$107$	−14.2022			−1.37298			−0.686490	−	0.727139i	$-0.740850\pi$
$107$	−14.2022			−1.37298			−0.686490	+	0.727139i	$0.740850\pi$
$108$		0			0
$109$	11.8130			1.13148			0.565741	−	0.824583i	$-0.308590\pi$
$109$	11.8130			1.13148			0.565741	+	0.824583i	$0.308590\pi$
$110$		0			0
$111$	17.0109	+	2.09177i	1.61460	+	0.198542i
$112$		0			0
$113$	7.06455	+	4.07872i	0.664577	+	0.383694i	0.794019	−	0.607893i	$-0.207985\pi$
$113$	7.06455	+	4.07872i	0.664577	+	0.383694i	−0.129442	+	0.991587i	$0.541319\pi$
$114$		0			0
$115$	0.732830	−	0.423099i	0.0683367	−	0.0394542i
$116$		0			0
$117$	8.93344	−	9.24421i	0.825897	−	0.854628i
$118$		0			0
$119$	0.572768	+	0.992063i	0.0525056	+	0.0909423i
$120$		0			0
$121$	−4.94761	+	8.56952i	−0.449783	+	0.779047i
$122$		0			0
$123$	−12.4453	−	9.38172i	−1.12216	−	0.845922i
$124$		0			0
$125$			1.55549i			0.139128i
$126$		0			0
$127$			15.6814i			1.39150i	0.718282	+	0.695752i	$0.244929\pi$
$127$			15.6814i			1.39150i	−0.718282	+	0.695752i	$0.755071\pi$
$128$		0			0
$129$	4.77805	−	2.02715i	0.420684	−	0.178481i
$130$		0			0
$131$	10.2084	−	17.6815i	0.891913	−	1.54484i	0.0543338	−	0.998523i	$-0.482696\pi$
$131$	10.2084	−	17.6815i	0.891913	−	1.54484i	0.837579	−	0.546316i	$-0.183970\pi$
$132$		0			0
$133$	−0.193369	−	0.334925i	−0.0167672	−	0.0290417i
$134$		0			0
$135$	−0.509554	−	0.629939i	−0.0438555	−	0.0542165i
$136$		0			0
$137$	12.9617	−	7.48346i	1.10740	−	0.639355i	0.169242	−	0.985575i	$-0.445868\pi$
$137$	12.9617	−	7.48346i	1.10740	−	0.639355i	0.938153	+	0.346220i	$0.112535\pi$
$138$		0			0
$139$	7.32288	+	4.22786i	0.621118	+	0.358603i	0.777304	−	0.629125i	$-0.216587\pi$
$139$	7.32288	+	4.22786i	0.621118	+	0.358603i	−0.156186	+	0.987728i	$0.549920\pi$
$140$		0			0
$141$	−1.65987	−	3.91235i	−0.139786	−	0.329480i
$142$		0			0
$143$	19.5879			1.63803
$144$		0			0
$145$	0.880318			0.0731065
$146$		0			0
$147$	−7.12876	+	9.45666i	−0.587970	+	0.779972i
$148$		0			0
$149$	17.3267	+	10.0036i	1.41946	+	0.819524i	0.996251	−	0.0865089i	$-0.0275711\pi$
$149$	17.3267	+	10.0036i	1.41946	+	0.819524i	0.423207	+	0.906033i	$0.360904\pi$
$150$		0			0
$151$	16.6516	−	9.61383i	1.35509	−	0.782362i	0.366133	−	0.930562i	$-0.380681\pi$
$151$	16.6516	−	9.61383i	1.35509	−	0.782362i	0.988957	+	0.148200i	$0.0473481\pi$
$152$		0			0
$153$	2.06435	−	8.26705i	0.166893	−	0.668351i
$154$		0			0
$155$	0.768533	+	1.33114i	0.0617301	+	0.106920i
$156$		0			0
$157$	−4.61167	+	7.98765i	−0.368052	+	0.637484i	−0.989261	−	0.146161i	$-0.953308\pi$
$157$	−4.61167	+	7.98765i	−0.368052	+	0.637484i	0.621209	+	0.783645i	$0.286642\pi$
$158$		0			0
$159$	−1.99954	+	16.2608i	−0.158573	+	1.28957i
$160$		0			0
$161$		−	2.18873i		−	0.172496i
$162$		0			0
$163$			13.7636i			1.07805i	0.842289	+	0.539026i	$0.181208\pi$
$163$			13.7636i			1.07805i	−0.842289	+	0.539026i	$0.818792\pi$
$164$		0			0
$165$	0.150674	−	1.22532i	0.0117299	−	0.0953913i
$166$		0			0
$167$	−5.48611	+	9.50223i	−0.424528	+	0.735304i	−0.996376	−	0.0850551i	$-0.972893\pi$
$167$	−5.48611	+	9.50223i	−0.424528	+	0.735304i	0.571848	+	0.820360i	$0.306227\pi$
$168$		0			0
$169$	−2.68121	−	4.64400i	−0.206247	−	0.357230i
$170$		0			0
$171$	−0.696935	+	2.79099i	−0.0532960	+	0.213433i
$172$		0			0
$173$	17.1614	−	9.90813i	1.30476	−	0.753302i	0.323541	−	0.946214i	$-0.395127\pi$
$173$	17.1614	−	9.90813i	1.30476	−	0.753302i	0.981216	+	0.192913i	$0.0617934\pi$
$174$		0			0
$175$	1.73791	+	1.00339i	0.131374	+	0.0758488i
$176$		0			0
$177$	−2.47227	+	3.27959i	−0.185827	+	0.246509i
$178$		0			0
$179$	−2.71217			−0.202717			−0.101359	−	0.994850i	$-0.532319\pi$
$179$	−2.71217			−0.202717			−0.101359	+	0.994850i	$0.532319\pi$
$180$		0			0
$181$	0.0561450			0.00417323			0.00208661	−	0.999998i	$-0.499336\pi$
$181$	0.0561450			0.00417323			0.00208661	+	0.999998i	$0.499336\pi$
$182$		0			0
$183$	−5.54913	−	13.0794i	−0.410203	−	0.966860i
$184$		0			0
$185$	−1.33623	−	0.771474i	−0.0982417	−	0.0567199i
$186$		0			0
$187$	11.2439	−	6.49169i	0.822238	−	0.474719i
$188$		0			0
$189$	−2.07006	+	0.326725i	−0.150575	+	0.0237658i
$190$		0			0
$191$	−10.3810	−	17.9804i	−0.751141	−	1.30101i	−0.947270	−	0.320436i	$-0.896171\pi$
$191$	−10.3810	−	17.9804i	−0.751141	−	1.30101i	0.196129	−	0.980578i	$-0.437163\pi$
$192$		0			0
$193$	−5.81321	+	10.0688i	−0.418444	+	0.724767i	−0.995783	−	0.0917380i	$-0.970758\pi$
$193$	−5.81321	+	10.0688i	−0.418444	+	0.724767i	0.577339	+	0.816505i	$0.304091\pi$
$194$		0			0
$195$	−1.06539	+	0.452007i	−0.0762944	+	0.0323689i
$196$		0			0
$197$		−	5.65685i		−	0.403034i	−0.979485	−	0.201517i	$-0.935413\pi$
$197$		−	5.65685i		−	0.403034i	0.979485	−	0.201517i	$-0.0645872\pi$
$198$		0			0
$199$			10.3363i			0.732718i	0.930474	+	0.366359i	$0.119396\pi$
$199$			10.3363i			0.732718i	−0.930474	+	0.366359i	$0.880604\pi$
$200$		0			0
$201$	−18.3362	−	13.8225i	−1.29334	−	0.974964i
$202$		0			0
$203$	1.13849	−	1.97192i	0.0799064	−	0.138402i
$204$		0			0
$205$	0.701538	+	1.21510i	0.0489975	+	0.0848662i
$206$		0			0
$207$	−11.3136	+	11.7072i	−0.786349	+	0.813705i
$208$		0			0
$209$	−3.79600	+	2.19162i	−0.262575	+	0.151598i
$210$		0			0
$211$	−3.02408	−	1.74596i	−0.208187	−	0.120197i	0.392282	−	0.919845i	$-0.371686\pi$
$211$	−3.02408	−	1.74596i	−0.208187	−	0.120197i	−0.600468	+	0.799649i	$0.705019\pi$
$212$		0			0
$213$	3.78190	+	0.465046i	0.259131	+	0.0318645i
$214$		0			0
$215$	−0.467257			−0.0318667
$216$		0			0
$217$	3.97569			0.269887
$218$		0			0
$219$	−7.79235	−	0.958198i	−0.526558	−	0.0647490i
$220$		0			0
$221$	−10.5405	−	6.08554i	−0.709028	−	0.409358i
$222$		0			0
$223$	−8.87018	+	5.12120i	−0.593991	+	0.342941i	−0.766674	−	0.642037i	$-0.778090\pi$
$223$	−8.87018	+	5.12120i	−0.593991	+	0.342941i	0.172683	+	0.984977i	$0.444756\pi$
$224$		0			0
$225$	−4.10931	−	14.3503i	−0.273954	−	0.956686i
$226$		0			0
$227$	0.779959	+	1.35093i	0.0517677	+	0.0896643i	0.890748	−	0.454497i	$-0.150181\pi$
$227$	0.779959	+	1.35093i	0.0517677	+	0.0896643i	−0.838980	+	0.544162i	$0.816848\pi$
$228$		0			0
$229$	−7.09018	+	12.2806i	−0.468533	+	0.811522i	−0.999353	−	0.0359620i	$-0.988550\pi$
$229$	−7.09018	+	12.2806i	−0.468533	+	0.811522i	0.530821	+	0.847484i	$0.321884\pi$
$230$		0			0
$231$	−2.54988	−	1.92219i	−0.167770	−	0.126471i
$232$		0			0
$233$			17.3465i			1.13641i	0.822888	+	0.568204i	$0.192361\pi$
$233$			17.3465i			1.13641i	−0.822888	+	0.568204i	$0.807639\pi$
$234$		0			0
$235$			0.382599i			0.0249580i
$236$		0			0
$237$	5.24143	−	2.22375i	0.340468	−	0.144448i
$238$		0			0
$239$	6.74548	−	11.6835i	0.436329	−	0.755744i	−0.561074	−	0.827766i	$-0.689612\pi$
$239$	6.74548	−	11.6835i	0.436329	−	0.755744i	0.997403	+	0.0720215i	$0.0229450\pi$
$240$		0			0
$241$	1.71016	+	2.96208i	0.110161	+	0.190804i	0.915835	−	0.401555i	$-0.131530\pi$
$241$	1.71016	+	2.96208i	0.110161	+	0.190804i	−0.805674	+	0.592359i	$0.798197\pi$
$242$		0			0
$243$	12.7613	+	8.95261i	0.818638	+	0.574310i
$244$		0			0
$245$	0.923300	−	0.533068i	0.0589875	−	0.0340564i
$246$		0			0
$247$	3.55851	+	2.05451i	0.226422	+	0.130725i
$248$		0			0
$249$	1.09914	+	2.59070i	0.0696551	+	0.164179i
$250$		0			0
$251$	−8.10511			−0.511590			−0.255795	−	0.966731i	$-0.582337\pi$
$251$	−8.10511			−0.511590			−0.255795	+	0.966731i	$0.582337\pi$
$252$		0			0
$253$	−24.8068			−1.55959
$254$		0			0
$255$	−0.461760	+	0.612548i	−0.0289165	+	0.0383592i
$256$		0			0
$257$	14.0484	+	8.11087i	0.876318	+	0.505942i	0.869443	−	0.494034i	$-0.164478\pi$
$257$	14.0484	+	8.11087i	0.876318	+	0.505942i	0.00687532	+	0.999976i	$0.497812\pi$
$258$		0			0
$259$	−3.45622	+	1.99545i	−0.214759	+	0.123991i
$260$		0			0
$261$	−16.2825	+	4.66263i	−1.00786	+	0.288609i
$262$		0			0
$263$	−13.4734	−	23.3366i	−0.830805	−	1.43900i	−0.897401	−	0.441216i	$-0.854547\pi$
$263$	−13.4734	−	23.3366i	−0.830805	−	1.43900i	0.0665964	−	0.997780i	$-0.478786\pi$
$264$		0			0
$265$	0.737456	−	1.27731i	0.0453016	−	0.0784646i
$266$		0			0
$267$	1.99954	−	16.2608i	0.122370	−	0.995146i
$268$		0			0
$269$			9.15987i			0.558487i	0.960220	+	0.279243i	$0.0900836\pi$
$269$			9.15987i			0.558487i	−0.960220	+	0.279243i	$0.909916\pi$
$270$		0			0
$271$		−	23.7150i		−	1.44058i	−0.693670	−	0.720292i	$-0.744008\pi$
$271$		−	23.7150i		−	1.44058i	0.693670	−	0.720292i	$-0.255992\pi$
$272$		0			0
$273$	−0.365341	+	2.97106i	−0.0221114	+	0.179817i
$274$		0			0
$275$	11.3723	−	19.6973i	0.685773	−	1.18779i
$276$		0			0
$277$	4.07340	+	7.05533i	0.244747	+	0.423914i	0.962060	−	0.272837i	$-0.0879619\pi$
$277$	4.07340	+	7.05533i	0.244747	+	0.423914i	−0.717314	+	0.696750i	$0.754629\pi$
$278$		0			0
$279$	−21.2653	−	20.5504i	−1.27312	−	1.23032i
$280$		0			0
$281$	−6.27676	+	3.62389i	−0.374440	+	0.216183i	−0.675397	−	0.737455i	$-0.736028\pi$
$281$	−6.27676	+	3.62389i	−0.374440	+	0.216183i	0.300956	+	0.953638i	$0.402694\pi$
$282$		0			0
$283$	10.8055	+	6.23858i	0.642323	+	0.370845i	0.785509	−	0.618851i	$-0.212401\pi$
$283$	10.8055	+	6.23858i	0.642323	+	0.370845i	−0.143186	+	0.989696i	$0.545735\pi$
$284$		0			0
$285$	0.155892	−	0.206799i	0.00923426	−	0.0122497i
$286$		0			0
$287$	3.62911			0.214220
$288$		0			0
$289$	8.93270			0.525453
$290$		0			0
$291$	−0.219821	−	0.518123i	−0.0128861	−	0.0303729i
$292$		0			0
$293$	−7.93127	−	4.57912i	−0.463350	−	0.267515i	0.250102	−	0.968220i	$-0.419536\pi$
$293$	−7.93127	−	4.57912i	−0.463350	−	0.267515i	−0.713452	+	0.700704i	$0.752869\pi$
$294$		0			0
$295$	0.320203	−	0.184869i	0.0186429	−	0.0107635i
$296$		0			0
$297$	3.70307	+	23.4619i	0.214874	+	1.36139i
$298$		0			0
$299$	11.6274	+	20.1392i	0.672429	+	1.16468i
$300$		0			0
$301$	−0.604290	+	1.04666i	−0.0348307	+	0.0603286i
$302$		0			0
$303$	−9.26838	+	3.93223i	−0.532454	+	0.225901i
$304$		0			0
$305$			1.27907i			0.0732394i
$306$		0			0
$307$		−	8.99247i		−	0.513228i	−0.966514	−	0.256614i	$-0.917393\pi$
$307$		−	8.99247i		−	0.513228i	0.966514	−	0.256614i	$-0.0826069\pi$
$308$		0			0
$309$	9.64511	+	7.27082i	0.548691	+	0.413623i
$310$		0			0
$311$	−17.0122	+	29.4659i	−0.964671	+	1.67086i	−0.254175	+	0.967158i	$0.581804\pi$
$311$	−17.0122	+	29.4659i	−0.964671	+	1.67086i	−0.710496	+	0.703701i	$0.751530\pi$
$312$		0			0
$313$	0.190546	+	0.330036i	0.0107703	+	0.0186547i	0.871360	−	0.490644i	$-0.163238\pi$
$313$	0.190546	+	0.330036i	0.0107703	+	0.0186547i	−0.860590	+	0.509298i	$0.829905\pi$
$314$		0			0
$315$	0.183045	+	0.0457078i	0.0103134	+	0.00257534i
$316$		0			0
$317$	−7.76598	+	4.48369i	−0.436181	+	0.251829i	−0.701976	−	0.712200i	$-0.747699\pi$
$317$	−7.76598	+	4.48369i	−0.436181	+	0.251829i	0.265796	+	0.964029i	$0.414365\pi$
$318$		0			0
$319$	−22.3495	−	12.9035i	−1.25133	−	0.722458i
$320$		0			0
$321$	−24.4151	−	3.00223i	−1.36272	−	0.167568i
$322$		0			0
$323$	2.72356			0.151543
$324$		0			0
$325$	−21.3215			−1.18270
$326$		0			0
$327$	20.3078	+	2.49718i	1.12302	+	0.138094i
$328$		0			0
$329$	0.857025	+	0.494804i	0.0472493	+	0.0272794i
$330$		0			0
$331$	11.8854	−	6.86204i	0.653281	−	0.377172i	−0.136431	−	0.990650i	$-0.543563\pi$
$331$	11.8854	−	6.86204i	0.653281	−	0.377172i	0.789712	+	0.613478i	$0.210230\pi$
$332$		0			0
$333$	28.8013	+	7.19194i	1.57830	+	0.394116i
$334$		0			0
$335$	1.03361	+	1.79026i	0.0564719	+	0.0978122i
$336$		0			0
$337$	13.2393	−	22.9312i	0.721193	−	1.24914i	−0.239330	−	0.970938i	$-0.576928\pi$
$337$	13.2393	−	22.9312i	0.721193	−	1.24914i	0.960522	−	0.278204i	$-0.0897390\pi$
$338$		0			0
$339$	11.2825	+	8.50513i	0.612780	+	0.461935i
$340$		0			0
$341$		−	45.0600i		−	2.44013i
$342$		0			0
$343$		−	5.58081i		−	0.301335i
$344$		0			0
$345$	1.34925	−	0.572437i	0.0726411	−	0.0308190i
$346$		0			0
$347$	−4.11490	+	7.12721i	−0.220899	+	0.382609i	−0.955081	−	0.296344i	$-0.904233\pi$
$347$	−4.11490	+	7.12721i	−0.220899	+	0.382609i	0.734182	+	0.678953i	$0.237566\pi$
$348$		0			0
$349$	0.635988	+	1.10156i	0.0340437	+	0.0589654i	0.882545	−	0.470227i	$-0.155828\pi$
$349$	0.635988	+	1.10156i	0.0340437	+	0.0589654i	−0.848502	+	0.529193i	$0.822495\pi$
$350$		0			0
$351$	17.3116	−	14.0033i	0.924027	−	0.747441i
$352$		0			0
$353$	−11.2765	+	6.51051i	−0.600189	+	0.346519i	−0.769116	−	0.639109i	$-0.779303\pi$
$353$	−11.2765	+	6.51051i	−0.600189	+	0.346519i	0.168927	+	0.985629i	$0.445970\pi$
$354$		0			0
$355$	−0.297073	−	0.171515i	−0.0157670	−	0.00910310i
$356$		0			0
$357$	0.774933	+	1.82654i	0.0410138	+	0.0966706i
$358$		0			0
$359$	−8.69181			−0.458736			−0.229368	−	0.973340i	$-0.573666\pi$
$359$	−8.69181			−0.458736			−0.229368	+	0.973340i	$0.573666\pi$
$360$		0			0
$361$	18.0805			0.951606
$362$		0			0
$363$	−10.3170	+	13.6860i	−0.541501	+	0.718328i
$364$		0			0
$365$	0.612101	+	0.353396i	0.0320388	+	0.0184976i
$366$		0			0
$367$	−28.6395	+	16.5350i	−1.49497	+	0.863120i	−0.999983	−	0.00578127i	$-0.998160\pi$
$367$	−28.6395	+	16.5350i	−1.49497	+	0.863120i	−0.494985	+	0.868902i	$0.664826\pi$
$368$		0			0
$369$	−19.4116	−	18.7590i	−1.01053	−	0.976554i
$370$		0			0
$371$	−1.90746	−	3.30382i	−0.0990304	−	0.171526i
$372$		0			0
$373$	5.02649	−	8.70613i	0.260262	−	0.450786i	−0.706050	−	0.708162i	$-0.749525\pi$
$373$	5.02649	−	8.70613i	0.260262	−	0.450786i	0.966311	+	0.257376i	$0.0828579\pi$
$374$		0			0
$375$	−0.328819	+	2.67405i	−0.0169801	+	0.138087i
$376$		0			0
$377$			24.1924i			1.24597i
$378$		0			0
$379$			10.2627i			0.527160i	0.964638	+	0.263580i	$0.0849033\pi$
$379$			10.2627i			0.527160i	−0.964638	+	0.263580i	$0.915097\pi$
$380$		0			0
$381$	−3.31493	+	26.9580i	−0.169829	+	1.38110i
$382$		0			0
$383$	3.97279	−	6.88107i	0.203000	−	0.351607i	−0.746494	−	0.665393i	$-0.768264\pi$
$383$	3.97279	−	6.88107i	0.203000	−	0.351607i	0.949494	+	0.313786i	$0.101597\pi$
$384$		0			0
$385$	0.143735	+	0.248957i	0.00732543	+	0.0126880i
$386$		0			0
$387$	8.64248	−	2.47484i	0.439322	−	0.125803i
$388$		0			0
$389$	−2.19438	+	1.26692i	−0.111259	+	0.0642356i	−0.554597	−	0.832119i	$-0.687128\pi$
$389$	−2.19438	+	1.26692i	−0.111259	+	0.0642356i	0.443338	+	0.896355i	$0.353794\pi$
$390$		0			0
$391$	13.3488	+	7.70692i	0.675077	+	0.389756i
$392$		0			0
$393$	21.2870	−	28.2383i	1.07379	−	1.42443i
$394$		0			0
$395$	−0.512573			−0.0257903
$396$		0			0
$397$	16.8586			0.846109			0.423054	−	0.906104i	$-0.360958\pi$
$397$	16.8586			0.846109			0.423054	+	0.906104i	$0.360958\pi$
$398$		0			0
$399$	−0.261621	−	0.616647i	−0.0130974	−	0.0308710i
$400$		0			0
$401$	−20.3709	−	11.7612i	−1.01728	−	0.587324i	−0.103962	−	0.994581i	$-0.533152\pi$
$401$	−20.3709	−	11.7612i	−1.01728	−	0.587324i	−0.913314	+	0.407257i	$0.866485\pi$
$402$		0			0
$403$	−36.5816	+	21.1204i	−1.82226	+	1.05208i
$404$		0			0
$405$	−0.742812	−	1.19065i	−0.0369106	−	0.0591637i
$406$		0			0
$407$	22.6162	+	39.1724i	1.12104	+	1.94170i
$408$		0			0
$409$	15.6804	−	27.1592i	0.775344	−	1.34294i	−0.159257	−	0.987237i	$-0.550910\pi$
$409$	15.6804	−	27.1592i	0.775344	−	1.34294i	0.934601	−	0.355698i	$-0.115757\pi$
$410$		0			0
$411$	23.8645	−	10.1248i	1.17715	−	0.499421i
$412$		0			0
$413$		−	0.956343i		−	0.0470586i
$414$		0			0
$415$		−	0.253351i		−	0.0124365i
$416$		0			0
$417$	11.6950	+	8.81613i	0.572709	+	0.431728i
$418$		0			0
$419$	−8.53096	+	14.7761i	−0.416765	+	0.721858i	−0.995612	−	0.0935782i	$-0.970169\pi$
$419$	−8.53096	+	14.7761i	−0.416765	+	0.721858i	0.578847	+	0.815436i	$0.303503\pi$
$420$		0			0
$421$	−10.2100	−	17.6843i	−0.497606	−	0.861879i	0.502390	−	0.864641i	$-0.332454\pi$
$421$	−10.2100	−	17.6843i	−0.497606	−	0.861879i	−0.999996	+	0.00276183i	$0.999121\pi$
$422$		0			0
$423$	−2.02644	−	7.07662i	−0.0985291	−	0.344077i
$424$		0			0
$425$	−12.2390	+	7.06622i	−0.593681	+	0.342762i
$426$		0			0
$427$	2.86513	+	1.65419i	0.138653	+	0.0800516i
$428$		0			0
$429$	33.6737	+	4.14073i	1.62578	+	0.199916i
$430$		0			0
$431$	−2.66939			−0.128580			−0.0642899	−	0.997931i	$-0.520478\pi$
$431$	−2.66939			−0.128580			−0.0642899	+	0.997931i	$0.520478\pi$
$432$		0			0
$433$	−5.41857			−0.260400			−0.130200	−	0.991488i	$-0.541562\pi$
$433$	−5.41857			−0.260400			−0.130200	+	0.991488i	$0.541562\pi$
$434$		0			0
$435$	1.51336	+	0.186092i	0.0725599	+	0.00892244i
$436$		0			0
$437$	−4.50661	−	2.60189i	−0.215580	−	0.124465i
$438$		0			0
$439$	19.2837	−	11.1334i	0.920360	−	0.531370i	0.0366099	−	0.999330i	$-0.488344\pi$
$439$	19.2837	−	11.1334i	0.920360	−	0.531370i	0.883750	+	0.467960i	$0.155011\pi$
$440$		0			0
$441$	−14.2541	+	14.7500i	−0.678768	+	0.702381i
$442$		0			0
$443$	12.2064	+	21.1421i	0.579944	+	1.00449i	0.995485	+	0.0949180i	$0.0302589\pi$
$443$	12.2064	+	21.1421i	0.579944	+	1.00449i	−0.415541	+	0.909574i	$0.636408\pi$
$444$		0			0
$445$	−0.737456	+	1.27731i	−0.0349588	+	0.0605504i
$446$		0			0
$447$	27.6717	+	20.8599i	1.30883	+	0.986639i
$448$		0			0
$449$		−	8.22186i		−	0.388013i	−0.981000	−	0.194007i	$-0.937852\pi$
$449$		−	8.22186i		−	0.388013i	0.981000	−	0.194007i	$-0.0621484\pi$
$450$		0			0
$451$		−	41.1320i		−	1.93683i
$452$		0			0
$453$	30.6582	−	13.0071i	1.44045	−	0.611128i
$454$		0			0
$455$	0.134743	−	0.233381i	0.00631683	−	0.0109411i
$456$		0			0
$457$	8.59988	+	14.8954i	0.402285	+	0.696779i	0.994001	−	0.109368i	$-0.0348826\pi$
$457$	8.59988	+	14.8954i	0.402285	+	0.696779i	−0.591716	+	0.806147i	$0.701549\pi$
$458$		0			0
$459$	5.29642	−	13.7755i	0.247216	−	0.642986i
$460$		0			0
$461$	29.5488	−	17.0600i	1.37622	−	0.794563i	0.384521	−	0.923116i	$-0.374367\pi$
$461$	29.5488	−	17.0600i	1.37622	−	0.794563i	0.991703	+	0.128554i	$0.0410334\pi$
$462$		0			0
$463$	3.40301	+	1.96473i	0.158151	+	0.0913086i	0.576987	−	0.816753i	$-0.304228\pi$
$463$	3.40301	+	1.96473i	0.158151	+	0.0913086i	−0.418836	+	0.908062i	$0.637562\pi$
$464$		0			0
$465$	1.03980	+	2.45082i	0.0482194	+	0.113654i
$466$		0			0
$467$	7.80148			0.361010			0.180505	−	0.983574i	$-0.442227\pi$
$467$	7.80148			0.361010			0.180505	+	0.983574i	$0.442227\pi$
$468$		0			0
$469$	5.34693			0.246898
$470$		0			0
$471$	−9.61647	+	12.7567i	−0.443103	+	0.587799i
$472$		0			0
$473$	11.8627	+	6.84896i	0.545449	+	0.314915i
$474$		0			0
$475$	4.13196	−	2.38559i	0.189587	−	0.109458i
$476$		0			0
$477$	−6.87481	+	27.5313i	−0.314776	+	1.26057i
$478$		0			0
$479$	−5.16002	−	8.93741i	−0.235767	−	0.408361i	0.723728	−	0.690085i	$-0.242427\pi$
$479$	−5.16002	−	8.93741i	−0.235767	−	0.408361i	−0.959495	+	0.281724i	$0.909094\pi$
$480$		0			0
$481$	21.2012	−	36.7216i	0.966692	−	1.67436i
$482$		0			0
$483$	0.462679	−	3.76265i	0.0210526	−	0.171206i
$484$		0			0
$485$			0.0506686i			0.00230074i
$486$		0			0
$487$			2.25172i			0.102035i	0.998698	+	0.0510177i	$0.0162465\pi$
$487$			2.25172i			0.102035i	−0.998698	+	0.0510177i	$0.983754\pi$
$488$		0			0
$489$	−2.90952	+	23.6611i	−0.131573	+	1.06999i
$490$		0			0
$491$	−12.3393	+	21.3722i	−0.556863	+	0.964516i	0.440893	+	0.897560i	$0.354662\pi$
$491$	−12.3393	+	21.3722i	−0.556863	+	0.964516i	−0.997756	+	0.0669558i	$0.978671\pi$
$492$		0			0
$493$	8.01768	+	13.8870i	0.361098	+	0.625440i
$494$		0			0
$495$	0.518047	−	2.07460i	0.0232845	−	0.0932466i
$496$		0			0
$497$	−0.768393	+	0.443632i	−0.0344671	+	0.0198996i
$498$		0			0
$499$	−20.0746	−	11.5901i	−0.898663	−	0.518843i	−0.0218966	−	0.999760i	$-0.506970\pi$
$499$	−20.0746	−	11.5901i	−0.898663	−	0.518843i	−0.876766	+	0.480917i	$0.840304\pi$
$500$		0			0
$501$	−11.4399	+	15.1756i	−0.511096	+	0.677995i
$502$		0			0
$503$	27.8228			1.24056			0.620279	−	0.784381i	$-0.287019\pi$
$503$	27.8228			1.24056			0.620279	+	0.784381i	$0.287019\pi$
$504$		0			0
$505$	0.906378			0.0403333
$506$		0			0
$507$	−3.62758	−	8.55029i	−0.161106	−	0.379732i
$508$		0			0
$509$	−30.8321	−	17.8009i	−1.36661	−	0.789013i	−0.376117	−	0.926572i	$-0.622741\pi$
$509$	−30.8321	−	17.8009i	−1.36661	−	0.789013i	−0.990493	+	0.137560i	$0.956074\pi$
$510$		0			0
$511$	1.58322	−	0.914075i	0.0700377	−	0.0404363i
$512$		0			0
$513$	−1.78810	+	4.65068i	−0.0789464	+	0.205332i
$514$		0			0
$515$	−0.543691	−	0.941700i	−0.0239579	−	0.0414963i
$516$		0			0
$517$	5.60805	−	9.71343i	0.246642	−	0.427196i
$518$		0			0
$519$	31.5967	−	13.4053i	1.38694	−	0.588428i
$520$		0			0
$521$			9.35452i			0.409829i	0.978780	+	0.204914i	$0.0656916\pi$
$521$			9.35452i			0.409829i	−0.978780	+	0.204914i	$0.934308\pi$
$522$		0			0
$523$		−	3.18845i		−	0.139421i	−0.997567	−	0.0697106i	$-0.977792\pi$
$523$		−	3.18845i		−	0.139421i	0.997567	−	0.0697106i	$-0.0222076\pi$
$524$		0			0
$525$	2.77555	+	2.09230i	0.121135	+	0.0913156i
$526$		0			0
$527$	−13.9991	+	24.2472i	−0.609812	+	1.05623i
$528$		0			0
$529$	−3.22530	−	5.58638i	−0.140230	−	0.242886i
$530$		0			0
$531$	−4.94336	+	5.11533i	−0.214524	+	0.221987i
$532$		0			0
$533$	−33.3927	+	19.2793i	−1.44640	+	0.835078i
$534$		0			0
$535$	1.91784	+	1.10726i	0.0829154	+	0.0478712i
$536$		0			0
$537$	−4.66250	−	0.573331i	−0.201202	−	0.0247411i
$538$		0			0
$539$	−31.2544			−1.34622
$540$		0			0
$541$	−17.5925			−0.756359			−0.378180	−	0.925732i	$-0.623450\pi$
$541$	−17.5925			−0.756359			−0.378180	+	0.925732i	$0.623450\pi$
$542$		0			0
$543$	0.0965191	+	0.0118686i	0.00414203	+	0.000509331i
$544$		0			0
$545$	−1.59521	−	0.920993i	−0.0683312	−	0.0394510i
$546$		0			0
$547$	−15.6730	+	9.04882i	−0.670130	+	0.386900i	−0.796126	−	0.605131i	$-0.793121\pi$
$547$	−15.6730	+	9.04882i	−0.670130	+	0.386900i	0.125996	+	0.992031i	$0.459787\pi$
$548$		0			0
$549$	−6.77463	−	23.6579i	−0.289134	−	1.00970i
$550$		0			0
$551$	−2.70680	−	4.68832i	−0.115314	−	0.199729i
$552$		0			0
$553$	−0.662895	+	1.14817i	−0.0281892	+	0.0488251i
$554$		0			0
$555$	−2.13404	−	1.60871i	−0.0905848	−	0.0682860i
$556$		0			0
$557$			20.5638i			0.871318i	0.900112	+	0.435659i	$0.143485\pi$
$557$			20.5638i			0.871318i	−0.900112	+	0.435659i	$0.856515\pi$
$558$		0			0
$559$		−	12.8409i		−	0.543113i
$560$		0			0
$561$	20.7018	−	8.78300i	0.874029	−	0.370819i
$562$		0			0
$563$	15.1630	−	26.2631i	0.639043	−	1.10686i	−0.346600	−	0.938013i	$-0.612664\pi$
$563$	15.1630	−	26.2631i	0.639043	−	1.10686i	0.985643	−	0.168842i	$-0.0540029\pi$
$564$		0			0
$565$	−0.635988	−	1.10156i	−0.0267562	−	0.0463432i
$566$		0			0
$567$	−3.62772	+	0.124080i	−0.152350	+	0.00521086i
$568$		0			0
$569$	12.6128	−	7.28198i	0.528755	−	0.305277i	−0.211755	−	0.977323i	$-0.567918\pi$
$569$	12.6128	−	7.28198i	0.528755	−	0.305277i	0.740509	+	0.672046i	$0.234584\pi$
$570$		0			0
$571$	−2.25820	−	1.30377i	−0.0945028	−	0.0545612i	0.452004	−	0.892016i	$-0.350709\pi$
$571$	−2.25820	−	1.30377i	−0.0945028	−	0.0545612i	−0.546507	+	0.837455i	$0.684043\pi$
$572$		0			0
$573$	−14.0451	−	33.1046i	−0.586740	−	1.38296i
$574$		0			0
$575$	27.0023			1.12607
$576$		0			0
$577$	−20.1253			−0.837826			−0.418913	−	0.908026i	$-0.637589\pi$
$577$	−20.1253			−0.837826			−0.418913	+	0.908026i	$0.637589\pi$
$578$		0			0
$579$	−12.1220	+	16.0804i	−0.503772	+	0.668279i
$580$		0			0
$581$	−0.567509	−	0.327652i	−0.0235442	−	0.0135933i
$582$		0			0
$583$	−37.4451	+	21.6189i	−1.55082	+	0.895365i
$584$		0			0
$585$	−1.92707	+	0.551832i	−0.0796746	+	0.0228154i
$586$		0			0
$587$	−20.4379	−	35.3995i	−0.843564	−	1.46110i	−0.886863	−	0.462033i	$-0.847120\pi$
$587$	−20.4379	−	35.3995i	−0.843564	−	1.46110i	0.0432988	−	0.999062i	$-0.486213\pi$
$588$		0			0
$589$	4.72617	−	8.18597i	0.194739	−	0.337297i
$590$		0			0
$591$	1.19581	−	9.72471i	0.0491892	−	0.400021i
$592$		0			0
$593$			3.73552i			0.153399i	0.997054	+	0.0766997i	$0.0244383\pi$
$593$			3.73552i			0.153399i	−0.997054	+	0.0766997i	$0.975562\pi$
$594$		0			0
$595$		−	0.178622i		−	0.00732277i
$596$		0			0
$597$	−2.18500	+	17.7691i	−0.0894262	+	0.727240i
$598$		0			0
$599$	−2.77394	+	4.80461i	−0.113340	+	0.196311i	−0.917115	−	0.398623i	$-0.869488\pi$
$599$	−2.77394	+	4.80461i	−0.113340	+	0.196311i	0.803775	+	0.594934i	$0.202822\pi$
$600$		0			0
$601$	17.1869	+	29.7687i	0.701070	+	1.21429i	0.968091	+	0.250599i	$0.0806274\pi$
$601$	17.1869	+	29.7687i	0.701070	+	1.21429i	−0.267021	+	0.963691i	$0.586039\pi$
$602$		0			0
$603$	−28.5999	−	27.6384i	−1.16468	−	1.12552i
$604$		0			0
$605$	1.33623	−	0.771474i	0.0543255	−	0.0313649i
$606$		0			0
$607$	23.5586	+	13.6016i	0.956216	+	0.552071i	0.895006	−	0.446054i	$-0.147171\pi$
$607$	23.5586	+	13.6016i	0.956216	+	0.552071i	0.0612094	+	0.998125i	$0.480504\pi$
$608$		0			0
$609$	2.37403	−	3.14927i	0.0962006	−	0.127615i
$610$		0			0
$611$	−10.5144			−0.425366
$612$		0			0
$613$	−37.5348			−1.51602			−0.758008	−	0.652245i	$-0.773827\pi$
$613$	−37.5348			−1.51602			−0.758008	+	0.652245i	$0.773827\pi$
$614$		0			0
$615$	0.949153	+	2.23718i	0.0382736	+	0.0902118i
$616$		0			0
$617$	−20.2495	−	11.6910i	−0.815213	−	0.470663i	0.0335499	−	0.999437i	$-0.489319\pi$
$617$	−20.2495	−	11.6910i	−0.815213	−	0.470663i	−0.848763	+	0.528774i	$0.822652\pi$
$618$		0			0
$619$	−18.7503	+	10.8255i	−0.753637	+	0.435113i	−0.827007	−	0.562192i	$-0.809958\pi$
$619$	−18.7503	+	10.8255i	−0.753637	+	0.435113i	0.0733695	+	0.997305i	$0.476625\pi$
$620$		0			0
$621$	−21.9240	+	17.7342i	−0.879781	+	0.711650i
$622$		0			0
$623$	1.90746	+	3.30382i	0.0764208	+	0.132365i
$624$		0			0
$625$	−12.3179	+	21.3353i	−0.492718	+	0.853412i
$626$		0			0
$627$	−6.98901	+	2.96518i	−0.279114	+	0.118418i
$628$		0			0
$629$		−	28.1054i		−	1.12064i
$630$		0			0
$631$		−	36.5039i		−	1.45320i	−0.687062	−	0.726599i	$-0.741100\pi$
$631$		−	36.5039i		−	1.45320i	0.687062	−	0.726599i	$-0.258900\pi$
$632$		0			0
$633$	−4.82963	−	3.64074i	−0.191961	−	0.144707i
$634$		0			0
$635$	1.22259	−	2.11759i	0.0485171	−	0.0840340i
$636$		0			0
$637$	14.6495	+	25.3736i	0.580433	+	1.00534i
$638$		0			0
$639$	6.40316	+	1.59892i	0.253305	+	0.0632525i
$640$		0			0
$641$	−35.4336	+	20.4576i	−1.39954	+	0.808027i	−0.994345	−	0.106201i	$-0.966131\pi$
$641$	−35.4336	+	20.4576i	−1.39954	+	0.808027i	−0.405199	+	0.914228i	$0.632798\pi$
$642$		0			0
$643$	25.3014	+	14.6078i	0.997791	+	0.576075i	0.907594	−	0.419849i	$-0.137917\pi$
$643$	25.3014	+	14.6078i	0.997791	+	0.576075i	0.0901973	+	0.995924i	$0.471250\pi$
$644$		0			0
$645$	−0.803263	−	0.0987744i	−0.0316285	−	0.00388924i
$646$		0			0
$647$	−45.9293			−1.80567			−0.902834	−	0.429988i	$-0.858518\pi$
$647$	−45.9293			−1.80567			−0.902834	+	0.429988i	$0.858518\pi$
$648$		0			0
$649$	−10.8391			−0.425471
$650$		0			0
$651$	6.83461	+	0.840428i	0.267870	+	0.0329390i
$652$		0			0
$653$	27.3513	+	15.7913i	1.07034	+	0.617961i	0.928274	−	0.371896i	$-0.121292\pi$
$653$	27.3513	+	15.7913i	1.07034	+	0.617961i	0.142066	+	0.989857i	$0.454626\pi$
$654$		0			0
$655$	−2.75705	+	1.59178i	−0.107727	+	0.0621961i
$656$		0			0
$657$	−13.1933	−	3.29448i	−0.514720	−	0.128530i
$658$		0			0
$659$	5.19029	+	8.98985i	0.202185	+	0.350195i	0.949232	−	0.314576i	$-0.101862\pi$
$659$	5.19029	+	8.98985i	0.202185	+	0.350195i	−0.747047	+	0.664771i	$0.768529\pi$
$660$		0			0
$661$	8.73963	−	15.1375i	0.339932	−	0.588780i	−0.644488	−	0.764615i	$-0.722929\pi$
$661$	8.73963	−	15.1375i	0.339932	−	0.588780i	0.984420	+	0.175835i	$0.0562626\pi$
$662$		0			0
$663$	−16.8337	−	12.6898i	−0.653767	−	0.492832i
$664$		0			0
$665$			0.0603035i			0.00233847i
$666$		0			0
$667$		−	30.6381i		−	1.18631i
$668$		0			0
$669$	−16.3313	+	6.92878i	−0.631405	+	0.267882i
$670$		0			0
$671$	18.7483	−	32.4731i	0.723772	−	1.25361i
$672$		0			0
$673$	−10.9029	−	18.8843i	−0.420275	−	0.727937i	0.575691	−	0.817667i	$-0.304733\pi$
$673$	−10.9029	−	18.8843i	−0.420275	−	0.727937i	−0.995966	+	0.0897298i	$0.971400\pi$
$674$		0			0
$675$	−4.03080	−	25.5383i	−0.155145	−	0.982969i
$676$		0			0
$677$	−1.62547	+	0.938463i	−0.0624717	+	0.0360681i	−0.530911	−	0.847428i	$-0.678150\pi$
$677$	−1.62547	+	0.938463i	−0.0624717	+	0.0360681i	0.468439	+	0.883496i	$0.344817\pi$
$678$		0			0
$679$	0.113498	+	0.0655282i	0.00435566	+	0.00251474i
$680$		0			0
$681$	1.05525	+	2.48726i	0.0404374	+	0.0953121i
$682$		0			0
$683$	25.5634			0.978157			0.489078	−	0.872240i	$-0.337333\pi$
$683$	25.5634			0.978157			0.489078	+	0.872240i	$0.337333\pi$
$684$		0			0
$685$	−2.33377			−0.0891687
$686$		0			0
$687$	−14.7848	+	19.6127i	−0.564074	+	0.748272i
$688$		0			0
$689$	35.1024	+	20.2664i	1.33729	+	0.772087i
$690$		0			0
$691$	26.6721	−	15.3992i	1.01466	−	0.585811i	0.102104	−	0.994774i	$-0.467443\pi$
$691$	26.6721	−	15.3992i	1.01466	−	0.585811i	0.912551	+	0.408962i	$0.134109\pi$
$692$		0			0
$693$	−3.97716	−	3.84346i	−0.151080	−	0.146001i
$694$		0			0
$695$	−0.659244	−	1.14184i	−0.0250066	−	0.0433126i
$696$		0			0
$697$	−12.7788	+	22.1335i	−0.484031	+	0.838367i
$698$		0			0
$699$	−3.66691	+	29.8204i	−0.138695	+	1.12791i
$700$		0			0
$701$			26.4594i			0.999356i	0.866211	+	0.499678i	$0.166548\pi$
$701$			26.4594i			0.999356i	−0.866211	+	0.499678i	$0.833452\pi$
$702$		0			0
$703$			9.48851i			0.357866i
$704$		0			0
$705$	−0.0808783	+	0.657727i	−0.00304605	+	0.0247714i
$706$		0			0
$707$	1.17219	−	2.03030i	0.0440848	−	0.0763572i
$708$		0			0
$709$	6.22853	+	10.7881i	0.233917	+	0.405157i	0.958958	−	0.283550i	$-0.0915121\pi$
$709$	6.22853	+	10.7881i	0.233917	+	0.405157i	−0.725040	+	0.688707i	$0.758179\pi$
$710$		0			0
$711$	9.48064	−	2.71485i	0.355552	−	0.101815i
$712$		0			0
$713$	46.3281	−	26.7476i	1.73500	−	1.00170i
$714$		0			0
$715$	−2.64511	−	1.52716i	−0.0989217	−	0.0571125i
$716$		0			0
$717$	14.0660	−	18.6592i	0.525304	−	0.696842i
$718$		0			0
$719$	−10.9461			−0.408222			−0.204111	−	0.978948i	$-0.565430\pi$
$719$	−10.9461			−0.408222			−0.204111	+	0.978948i	$0.565430\pi$
$720$		0			0
$721$	−2.81256			−0.104745
$722$		0			0
$723$	2.31378	+	5.45363i	0.0860503	+	0.202823i
$724$		0			0
$725$	24.3275	+	14.0455i	0.903502	+	0.521637i
$726$		0			0
$727$	41.4945	−	23.9569i	1.53895	−	0.888511i	0.540045	−	0.841636i	$-0.318407\pi$
$727$	41.4945	−	23.9569i	1.53895	−	0.888511i	0.998901	−	0.0468743i	$-0.0149260\pi$
$728$		0			0
$729$	20.0455	+	18.0881i	0.742425	+	0.669929i
$730$		0			0
$731$	−4.25564	−	7.37098i	−0.157401	−	0.272626i
$732$		0			0
$733$	0.392838	−	0.680415i	0.0145098	−	0.0251317i	−0.858679	−	0.512513i	$-0.828715\pi$
$733$	0.392838	−	0.680415i	0.0145098	−	0.0251317i	0.873189	+	0.487382i	$0.162048\pi$
$734$		0			0
$735$	1.69993	−	0.721220i	0.0627030	−	0.0266026i
$736$		0			0
$737$		−	60.6015i		−	2.23228i
$738$		0			0
$739$			34.1281i			1.25542i	0.778446	+	0.627711i	$0.216008\pi$
$739$			34.1281i			1.25542i	−0.778446	+	0.627711i	$0.783992\pi$
$740$		0			0
$741$	5.68313	+	4.28415i	0.208775	+	0.157382i
$742$		0			0
$743$	20.1056	−	34.8239i	0.737603	−	1.27757i	−0.215969	−	0.976400i	$-0.569291\pi$
$743$	20.1056	−	34.8239i	0.737603	−	1.27757i	0.953572	−	0.301165i	$-0.0973756\pi$
$744$		0			0
$745$	−1.55984	−	2.70172i	−0.0571481	−	0.0989835i
$746$		0			0
$747$	1.34188	+	4.68603i	0.0490968	+	0.171453i
$748$		0			0
$749$	4.96057	−	2.86399i	0.181255	−	0.104648i
$750$		0			0
$751$	−1.65200	−	0.953783i	−0.0602824	−	0.0348040i	0.469556	−	0.882903i	$-0.344414\pi$
$751$	−1.65200	−	0.953783i	−0.0602824	−	0.0348040i	−0.529838	+	0.848099i	$0.677747\pi$
$752$		0			0
$753$	−13.9335	−	1.71336i	−0.507766	−	0.0624381i
$754$		0			0
$755$	−2.99814			−0.109113
$756$		0			0
$757$	24.7403			0.899201			0.449600	−	0.893230i	$-0.351566\pi$
$757$	24.7403			0.899201			0.449600	+	0.893230i	$0.351566\pi$
$758$		0			0
$759$	−42.6454	−	5.24395i	−1.54793	−	0.190343i
$760$		0			0
$761$	−21.8526	−	12.6166i	−0.792158	−	0.457353i	0.0485638	−	0.998820i	$-0.484536\pi$
$761$	−21.8526	−	12.6166i	−0.792158	−	0.457353i	−0.840722	+	0.541468i	$0.817869\pi$
$762$		0			0
$763$	−4.12607	+	2.38219i	−0.149374	+	0.0862410i
$764$		0			0
$765$	−0.923300	+	0.955420i	−0.0333820	+	0.0345433i
$766$		0			0
$767$	5.08047	+	8.79963i	0.183445	+	0.317736i
$768$		0			0
$769$	−20.2057	+	34.9973i	−0.728636	+	1.26203i	0.228824	+	0.973468i	$0.426512\pi$
$769$	−20.2057	+	34.9973i	−0.728636	+	1.26203i	−0.957460	+	0.288566i	$0.906821\pi$
$770$		0			0
$771$	22.4361	+	16.9132i	0.808018	+	0.609112i
$772$		0			0
$773$			37.0731i			1.33343i	0.745314	+	0.666714i	$0.232300\pi$
$773$			37.0731i			1.33343i	−0.745314	+	0.666714i	$0.767700\pi$
$774$		0			0
$775$			49.0479i			1.76185i
$776$		0			0
$777$	−6.36342	+	2.69976i	−0.228286	+	0.0968535i
$778$		0			0
$779$	4.31418	−	7.47238i	0.154571	−	0.267726i
$780$		0			0
$781$	5.02807	+	8.70888i	0.179919	+	0.311628i
$782$		0			0
$783$	−28.9770	+	4.57354i	−1.03555	+	0.163445i
$784$		0			0
$785$	1.24550	−	0.719091i	0.0444539	−	0.0256655i
$786$		0			0
$787$	22.5009	+	12.9909i	0.802072	+	0.463076i	0.844195	−	0.536036i	$-0.180079\pi$
$787$	22.5009	+	12.9909i	0.802072	+	0.463076i	−0.0421234	+	0.999112i	$0.513412\pi$
$788$		0			0
$789$	−18.2290	−	42.9662i	−0.648968	−	1.52964i
$790$		0			0
$791$	−3.29002			−0.116980
$792$		0			0
$793$	−35.1507			−1.24824
$794$		0			0
$795$	1.53778	−	2.03994i	0.0545393	−	0.0723491i
$796$		0			0
$797$	7.84705	+	4.53050i	0.277957	+	0.160479i	0.632498	−	0.774562i	$-0.282030\pi$
$797$	7.84705	+	4.53050i	0.277957	+	0.160479i	−0.354541	+	0.935040i	$0.615363\pi$
$798$		0			0
$799$	−6.03549	+	3.48459i	−0.213520	+	0.123276i
$800$		0			0
$801$	6.87481	−	27.5313i	0.242910	−	0.972772i
$802$		0			0
$803$	−10.3600	−	17.9441i	−0.365597	−	0.633233i
$804$		0			0
$805$	−0.170643	+	0.295561i	−0.00601436	+	0.0104172i
$806$		0			0
$807$	−1.93632	+	15.7467i	−0.0681617	+	0.554312i
$808$		0			0
$809$			25.2651i			0.888274i	0.895959	+	0.444137i	$0.146490\pi$
$809$			25.2651i			0.888274i	−0.895959	+	0.444137i	$0.853510\pi$
$810$		0			0
$811$			4.43725i			0.155813i	0.996961	+	0.0779064i	$0.0248235\pi$
$811$			4.43725i			0.155813i	−0.996961	+	0.0779064i	$0.975176\pi$
$812$		0			0
$813$	5.01316	−	40.7686i	0.175819	−	1.42982i
$814$		0			0
$815$	1.07307	−	1.85862i	0.0375881	−	0.0651045i
$816$		0			0
$817$	1.43672	+	2.48848i	0.0502646	+	0.0870608i
$818$		0			0
$819$	−1.25612	+	5.03033i	−0.0438923	+	0.175774i
$820$		0			0
$821$	14.2690	−	8.23820i	0.497991	−	0.287515i	−0.229893	−	0.973216i	$-0.573837\pi$
$821$	14.2690	−	8.23820i	0.497991	−	0.287515i	0.727883	+	0.685701i	$0.240504\pi$
$822$		0			0
$823$	25.6912	+	14.8328i	0.895540	+	0.517040i	0.875751	−	0.482764i	$-0.160367\pi$
$823$	25.6912	+	14.8328i	0.895540	+	0.517040i	0.0197897	+	0.999804i	$0.493700\pi$
$824$		0			0
$825$	23.7139	−	31.4577i	0.825613	−	1.09522i
$826$		0			0
$827$	49.6179			1.72538			0.862692	−	0.505730i	$-0.168777\pi$
$827$	49.6179			1.72538			0.862692	+	0.505730i	$0.168777\pi$
$828$		0			0
$829$	21.6521			0.752009			0.376004	−	0.926618i	$-0.377298\pi$
$829$	21.6521			0.752009			0.376004	+	0.926618i	$0.377298\pi$
$830$		0			0
$831$	5.51114	+	12.9899i	0.191179	+	0.450615i
$832$		0			0
$833$	16.8183	+	9.71004i	0.582719	+	0.336433i
$834$		0			0
$835$	1.48167	−	0.855441i	0.0512752	−	0.0296038i
$836$		0			0
$837$	−32.2131	−	39.8236i	−1.11345	−	1.37651i
$838$		0			0
$839$	−15.7930	−	27.3543i	−0.545235	−	0.944375i	−0.998592	−	0.0530461i	$-0.983107\pi$
$839$	−15.7930	−	27.3543i	−0.545235	−	0.944375i	0.453357	−	0.891329i	$-0.350226\pi$
$840$		0			0
$841$	1.43672	−	2.48848i	0.0495422	−	0.0858096i
$842$		0			0
$843$	−11.5565	+	4.90298i	−0.398026	+	0.168868i
$844$		0			0
$845$			0.836154i			0.0287646i
$846$		0			0
$847$		−	3.99090i		−	0.137129i
$848$		0			0
$849$	17.2570	+	13.0090i	0.592260	+	0.446467i
$850$		0			0
$851$	−26.8499	+	46.5054i	−0.920403	+	1.59418i
$852$		0			0
$853$	4.33029	+	7.50029i	0.148266	+	0.256805i	0.930587	−	0.366071i	$-0.119297\pi$
$853$	4.33029	+	7.50029i	0.148266	+	0.256805i	−0.782320	+	0.622876i	$0.785964\pi$
$854$		0			0
$855$	0.311710	−	0.322554i	0.0106603	−	0.0110311i
$856$		0			0
$857$	25.6931	−	14.8339i	0.877658	−	0.506716i	0.00777246	−	0.999970i	$-0.497526\pi$
$857$	25.6931	−	14.8339i	0.877658	−	0.506716i	0.869885	+	0.493254i	$0.164193\pi$
$858$		0			0
$859$	41.4164	+	23.9118i	1.41311	+	0.815859i	0.995680	−	0.0928504i	$-0.0295978\pi$
$859$	41.4164	+	23.9118i	1.41311	+	0.815859i	0.417429	+	0.908709i	$0.362931\pi$
$860$		0			0
$861$	6.23882	+	0.767165i	0.212618	+	0.0261449i
$862$		0			0
$863$	−35.2409			−1.19961			−0.599807	−	0.800144i	$-0.704756\pi$
$863$	−35.2409			−1.19961			−0.599807	+	0.800144i	$0.704756\pi$
$864$		0			0
$865$	−3.08992			−0.105060
$866$		0			0
$867$	15.3562	+	1.88830i	0.521525	+	0.0641301i
$868$		0			0
$869$	13.0132	+	7.51318i	0.441443	+	0.254867i
$870$		0			0
$871$	−49.1989	+	28.4050i	−1.66704	+	0.962467i
$872$		0			0
$873$	−0.268367	−	0.937175i	−0.00908286	−	0.0317186i
$874$		0			0
$875$	−0.313677	−	0.543305i	−0.0106042	−	0.0183671i
$876$		0			0
$877$	9.49592	−	16.4474i	0.320654	−	0.555390i	−0.659969	−	0.751293i	$-0.729431\pi$
$877$	9.49592	−	16.4474i	0.320654	−	0.555390i	0.980623	+	0.195903i	$0.0627638\pi$
$878$		0			0
$879$	−12.6667	−	9.54859i	−0.427237	−	0.322066i
$880$		0			0
$881$		−	54.0736i		−	1.82178i	−0.412644	−	0.910892i	$-0.635395\pi$
$881$		−	54.0736i		−	1.82178i	0.412644	−	0.910892i	$-0.364605\pi$
$882$		0			0
$883$			32.2679i			1.08590i	0.839764	+	0.542951i	$0.182693\pi$
$883$			32.2679i			1.08590i	−0.839764	+	0.542951i	$0.817307\pi$
$884$		0			0
$885$	0.589541	−	0.250121i	0.0198172	−	0.00840771i
$886$		0			0
$887$	7.01404	−	12.1487i	0.235508	−	0.407913i	−0.723912	−	0.689892i	$-0.757658\pi$
$887$	7.01404	−	12.1487i	0.235508	−	0.407913i	0.959420	+	0.281980i	$0.0909911\pi$
$888$		0			0
$889$	−3.16228	−	5.47724i	−0.106060	−	0.183701i
$890$		0			0
$891$	1.40631	+	41.1161i	0.0471130	+	1.37744i
$892$		0			0
$893$	2.03761	−	1.17641i	0.0681860	−	0.0393672i
$894$		0			0
$895$	0.366246	+	0.211452i	0.0122423	+	0.00706807i
$896$		0			0
$897$	15.7314	+	37.0793i	0.525256	+	1.23804i
$898$		0			0
$899$	55.6521			1.85610
$900$		0			0
$901$	26.8661			0.895040
$902$		0			0
$903$	−1.26009	+	1.67158i	−0.0419333	+	0.0556266i
$904$		0			0
$905$	−0.00758171	−	0.00437730i	−0.000252025	−	0.000145507i
$906$		0			0
$907$	17.0198	−	9.82640i	0.565134	−	0.326280i	−0.190070	−	0.981771i	$-0.560871\pi$
$907$	17.0198	−	9.82640i	0.565134	−	0.326280i	0.755204	+	0.655490i	$0.227538\pi$
$908$		0			0
$909$	−16.7645	+	4.80065i	−0.556045	+	0.159228i
$910$		0			0
$911$	7.57865	+	13.1266i	0.251092	+	0.434904i	0.963827	−	0.266530i	$-0.0858770\pi$
$911$	7.57865	+	13.1266i	0.251092	+	0.434904i	−0.712735	+	0.701434i	$0.752544\pi$
$912$		0			0
$913$	−3.71356	+	6.43208i	−0.122901	+	0.212871i
$914$		0			0
$915$	−0.270385	+	2.19885i	−0.00893866	+	0.0726919i
$916$		0			0
$917$			8.23442i			0.271924i
$918$		0			0
$919$		−	42.4353i		−	1.39981i	−0.714236	−	0.699905i	$-0.753226\pi$
$919$		−	42.4353i		−	1.39981i	0.714236	−	0.699905i	$-0.246774\pi$
$920$		0			0
$921$	1.90094	−	15.4590i	0.0626380	−	0.509391i
$922$		0			0
$923$	4.71349	−	8.16401i	0.155147	−	0.268722i
$924$		0			0
$925$	−24.6178	−	42.6392i	−0.809427	−	1.40197i
$926$		0			0
$927$	15.0439	+	14.5382i	0.494108	+	0.477497i
$928$		0			0
$929$	41.1480	−	23.7568i	1.35002	−	0.779435i	0.361770	−	0.932267i	$-0.382173\pi$
$929$	41.1480	−	23.7568i	1.35002	−	0.779435i	0.988252	+	0.152832i	$0.0488393\pi$
$930$		0			0
$931$	−5.67793	−	3.27815i	−0.186087	−	0.107437i
$932$		0			0
$933$	−35.4745	+	47.0587i	−1.16138	+	1.54063i
$934$		0			0
$935$	−2.02448			−0.0662075
$936$		0			0
$937$	−25.9106			−0.846462			−0.423231	−	0.906022i	$-0.639104\pi$
$937$	−25.9106			−0.846462			−0.423231	+	0.906022i	$0.639104\pi$
$938$		0			0
$939$	0.257802	+	0.607646i	0.00841304	+	0.0198298i
$940$		0			0
$941$	−26.9910	−	15.5833i	−0.879882	−	0.508000i	−0.00926245	−	0.999957i	$-0.502948\pi$
$941$	−26.9910	−	15.5833i	−0.879882	−	0.508000i	−0.870619	+	0.491957i	$0.836282\pi$
$942$		0			0
$943$	42.2896	−	24.4159i	1.37714	−	0.795091i
$944$		0			0
$945$	0.305010	+	0.117271i	0.00992198	+	0.00381481i
$946$		0			0
$947$	−8.56333	−	14.8321i	−0.278271	−	0.481979i	0.692684	−	0.721241i	$-0.256428\pi$
$947$	−8.56333	−	14.8321i	−0.278271	−	0.481979i	−0.970955	+	0.239262i	$0.923095\pi$
$948$		0			0
$949$	−9.71185	+	16.8214i	−0.315260	+	0.546046i
$950$		0			0
$951$	−14.2983	+	6.06626i	−0.463655	+	0.196712i
$952$		0			0
$953$			5.85610i			0.189698i	0.995492	+	0.0948489i	$0.0302368\pi$
$953$			5.85610i			0.189698i	−0.995492	+	0.0948489i	$0.969763\pi$
$954$		0			0
$955$			3.23738i			0.104759i
$956$		0			0
$957$	−35.6935	−	26.9070i	−1.15381	−	0.869779i
$958$		0			0
$959$	−3.01819	+	5.22766i	−0.0974626	+	0.168810i
$960$		0			0
$961$	33.0853	+	57.3054i	1.06727	+	1.84856i
$962$		0			0
$963$	−41.3374	−	10.3223i	−1.33208	−	0.332631i
$964$		0			0
$965$	1.57001	−	0.906445i	0.0505404	−	0.0291795i
$966$		0			0
$967$	−29.0101	−	16.7490i	−0.932903	−	0.538612i	−0.0451742	−	0.998979i	$-0.514384\pi$
$967$	−29.0101	−	16.7490i	−0.932903	−	0.538612i	−0.887728	+	0.460368i	$0.847718\pi$
$968$		0			0
$969$	4.68207	+	0.575738i	0.150410	+	0.0184954i
$970$		0			0
$971$	−15.6302			−0.501596			−0.250798	−	0.968039i	$-0.580693\pi$
$971$	−15.6302			−0.501596			−0.250798	+	0.968039i	$0.580693\pi$
$972$		0			0
$973$	−3.41033			−0.109330
$974$		0			0
$975$	−36.6539	−	4.50719i	−1.17386	−	0.144346i
$976$		0			0
$977$	12.7594	+	7.36663i	0.408209	+	0.235679i	0.690020	−	0.723791i	$-0.257602\pi$
$977$	12.7594	+	7.36663i	0.408209	+	0.235679i	−0.281811	+	0.959470i	$0.590935\pi$
$978$		0			0
$979$	37.4451	−	21.6189i	1.19675	−	0.690944i
$980$		0			0
$981$	34.3833	+	8.58581i	1.09777	+	0.274124i
$982$		0			0
$983$	20.7082	+	35.8676i	0.660488	+	1.14400i	0.980488	+	0.196581i	$0.0629839\pi$
$983$	20.7082	+	35.8676i	0.660488	+	1.14400i	−0.320000	+	0.947418i	$0.603683\pi$
$984$		0			0
$985$	−0.441032	+	0.763890i	−0.0140525	+	0.0243396i
$986$		0			0
$987$	1.36872	+	1.03179i	0.0435667	+	0.0328421i
$988$		0			0
$989$			16.2621i			0.517106i
$990$		0			0
$991$			23.1798i			0.736331i	0.929760	+	0.368166i	$0.120014\pi$
$991$			23.1798i			0.736331i	−0.929760	+	0.368166i	$0.879986\pi$
$992$		0			0
$993$	21.8828	−	9.28407i	0.694430	−	0.294621i
$994$		0			0
$995$	0.805858	−	1.39579i	0.0255474	−	0.0442494i
$996$		0			0
$997$	9.17878	+	15.8981i	0.290695	+	0.503498i	0.973974	−	0.226659i	$-0.0727802\pi$
$997$	9.17878	+	15.8981i	0.290695	+	0.503498i	−0.683279	+	0.730157i	$0.739447\pi$
$998$		0			0
$999$	47.9921	+	18.4520i	1.51840	+	0.583797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.s.a.95.12	yes	24
3.2	odd	2		864.2.s.a.287.5		24
4.3	odd	2	inner	288.2.s.a.95.1	✓	24
8.3	odd	2		576.2.s.g.383.12		24
8.5	even	2		576.2.s.g.383.1		24
9.2	odd	6	inner	288.2.s.a.191.1	yes	24
9.4	even	3		2592.2.c.c.2591.13		24
9.5	odd	6		2592.2.c.c.2591.11		24
9.7	even	3		864.2.s.a.575.6		24
12.11	even	2		864.2.s.a.287.6		24
24.5	odd	2		1728.2.s.g.1151.7		24
24.11	even	2		1728.2.s.g.1151.8		24
36.7	odd	6		864.2.s.a.575.5		24
36.11	even	6	inner	288.2.s.a.191.12	yes	24
36.23	even	6		2592.2.c.c.2591.12		24
36.31	odd	6		2592.2.c.c.2591.14		24
72.5	odd	6		5184.2.c.m.5183.13		24
72.11	even	6		576.2.s.g.191.1		24
72.13	even	6		5184.2.c.m.5183.11		24
72.29	odd	6		576.2.s.g.191.12		24
72.43	odd	6		1728.2.s.g.575.7		24
72.59	even	6		5184.2.c.m.5183.14		24
72.61	even	6		1728.2.s.g.575.8		24
72.67	odd	6		5184.2.c.m.5183.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.1	✓	24	4.3	odd	2	inner
288.2.s.a.95.12	yes	24	1.1	even	1	trivial
288.2.s.a.191.1	yes	24	9.2	odd	6	inner
288.2.s.a.191.12	yes	24	36.11	even	6	inner
576.2.s.g.191.1		24	72.11	even	6
576.2.s.g.191.12		24	72.29	odd	6
576.2.s.g.383.1		24	8.5	even	2
576.2.s.g.383.12		24	8.3	odd	2
864.2.s.a.287.5		24	3.2	odd	2
864.2.s.a.287.6		24	12.11	even	2
864.2.s.a.575.5		24	36.7	odd	6
864.2.s.a.575.6		24	9.7	even	3
1728.2.s.g.575.7		24	72.43	odd	6
1728.2.s.g.575.8		24	72.61	even	6
1728.2.s.g.1151.7		24	24.5	odd	2
1728.2.s.g.1151.8		24	24.11	even	2
2592.2.c.c.2591.11		24	9.5	odd	6
2592.2.c.c.2591.12		24	36.23	even	6
2592.2.c.c.2591.13		24	9.4	even	3
2592.2.c.c.2591.14		24	36.31	odd	6
5184.2.c.m.5183.11		24	72.13	even	6
5184.2.c.m.5183.12		24	72.67	odd	6
5184.2.c.m.5183.13		24	72.5	odd	6
5184.2.c.m.5183.14		24	72.59	even	6

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71910 + 0.211392i) q^{3} +(-0.135038 - 0.0779642i) q^{5} +(-0.349281 + 0.201658i) q^{7} +(2.91063 + 0.726809i) q^{9} +O(q^{10})\)	\(q+(1.71910 + 0.211392i) q^{3} +(-0.135038 - 0.0779642i) q^{5} +(-0.349281 + 0.201658i) q^{7} +(2.91063 + 0.726809i) q^{9} +(2.28556 + 3.95871i) q^{11} +(2.14257 - 3.71104i) q^{13} +(-0.215663 - 0.162574i) q^{15} -2.84030i q^{17} +0.958898i q^{19} +(-0.643079 + 0.272835i) q^{21} +(-2.71342 + 4.69978i) q^{23} +(-2.48784 - 4.30907i) q^{25} +(4.85002 + 1.86474i) q^{27} +(-4.88928 + 2.82283i) q^{29} +(-8.53685 - 4.92876i) q^{31} +(3.09228 + 7.28859i) q^{33} +0.0628883 q^{35} +9.89523 q^{37} +(4.46778 - 5.92674i) q^{39} +(-7.79267 - 4.49910i) q^{41} +(2.59514 - 1.49831i) q^{43} +(-0.336380 - 0.325072i) q^{45} +(-1.22684 - 2.12495i) q^{47} +(-3.41867 + 5.92131i) q^{49} +(0.600416 - 4.88276i) q^{51} +9.45890i q^{53} -0.712769i q^{55} +(-0.202703 + 1.64844i) q^{57} +(-1.18560 + 2.05352i) q^{59} +(-4.10147 - 7.10395i) q^{61} +(-1.16319 + 0.333090i) q^{63} +(-0.578657 + 0.334088i) q^{65} +(-11.4813 - 6.62872i) q^{67} +(-5.65814 + 7.50581i) q^{69} +2.19993 q^{71} -4.53280 q^{73} +(-3.36595 - 7.93364i) q^{75} +(-1.59661 - 0.921804i) q^{77} +(2.84683 - 1.64362i) q^{79} +(7.94350 + 4.23094i) q^{81} +(0.812395 + 1.40711i) q^{83} +(-0.221442 + 0.383548i) q^{85} +(-9.00190 + 3.81918i) q^{87} -9.45890i q^{89} +1.72826i q^{91} +(-13.6338 - 10.2777i) q^{93} +(0.0747597 - 0.129488i) q^{95} +(-0.162474 - 0.281413i) q^{97} +(3.77520 + 13.1835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^9	\( 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) \) 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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