LMFDB - Embedded newform 864.2.bi.a.95.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.16
Character	$\chi$	$=$	864.95
Dual form			864.2.bi.a.191.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.246052 + 1.71448i) q^{3} +(0.0151145 - 0.0180127i) q^{5} +(1.23843 - 3.40255i) q^{7} +(-2.87892 - 0.843705i) q^{9} +O(q^{10})$	\(q+(-0.246052 + 1.71448i) q^{3} +(0.0151145 - 0.0180127i) q^{5} +(1.23843 - 3.40255i) q^{7} +(-2.87892 - 0.843705i) q^{9} +(-1.09788 + 0.921232i) q^{11} +(-0.995812 + 5.64753i) q^{13} +(0.0271636 + 0.0303456i) q^{15} +(5.80991 + 3.35435i) q^{17} +(-6.74443 + 3.89390i) q^{19} +(5.52890 + 2.96046i) q^{21} +(0.942566 - 0.343066i) q^{23} +(0.868145 + 4.92349i) q^{25} +(2.15488 - 4.72826i) q^{27} +(9.41639 - 1.66036i) q^{29} +(1.96605 + 5.40168i) q^{31} +(-1.30930 - 2.10897i) q^{33} +(-0.0425710 - 0.0737351i) q^{35} +(-1.70852 + 2.95924i) q^{37} +(-9.43759 - 3.09689i) q^{39} +(-6.80617 - 1.20011i) q^{41} +(4.05697 + 4.83491i) q^{43} +(-0.0587107 + 0.0391050i) q^{45} +(0.845478 + 0.307729i) q^{47} +(-4.68131 - 3.92808i) q^{49} +(-7.18053 + 9.13566i) q^{51} +9.38837i q^{53} +0.0336998i q^{55} +(-5.01655 - 12.5213i) q^{57} +(-10.0270 - 8.41368i) q^{59} +(1.21782 + 0.443250i) q^{61} +(-6.43607 + 8.75078i) q^{63} +(0.0866763 + 0.103297i) q^{65} +(5.80459 + 1.02351i) q^{67} +(0.356261 + 1.70043i) q^{69} +(0.203892 - 0.353151i) q^{71} +(-2.79675 - 4.84411i) q^{73} +(-8.65487 + 0.276986i) q^{75} +(1.77489 + 4.87647i) q^{77} +(-10.7972 + 1.90384i) q^{79} +(7.57633 + 4.85791i) q^{81} +(-1.56717 - 8.88783i) q^{83} +(0.148235 - 0.0539530i) q^{85} +(0.529748 + 16.5528i) q^{87} +(1.11291 - 0.642542i) q^{89} +(17.9827 + 10.3823i) q^{91} +(-9.74485 + 2.04167i) q^{93} +(-0.0317988 + 0.180340i) q^{95} +(-3.01023 + 2.52588i) q^{97} +(3.93796 - 1.72586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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
$3$	−0.246052	+	1.71448i	−0.142058	+	0.989858i
$3$	−0.246052	+	1.71448i	−0.142058	+	0.989858i
$4$		0			0
$5$	0.0151145	−	0.0180127i	0.00675939	−	0.00805553i	−0.762654	−	0.646806i	$-0.776104\pi$
$5$	0.0151145	−	0.0180127i	0.00675939	−	0.00805553i	0.769414	+	0.638751i	$0.220549\pi$
$6$		0			0
$7$	1.23843	−	3.40255i	0.468081	−	1.28604i	−0.451194	−	0.892426i	$-0.649002\pi$
$7$	1.23843	−	3.40255i	0.468081	−	1.28604i	0.919275	−	0.393616i	$-0.128776\pi$
$8$		0			0
$9$	−2.87892	−	0.843705i	−0.959639	−	0.281235i
$10$		0			0
$11$	−1.09788	+	0.921232i	−0.331024	+	0.277762i	−0.793117	−	0.609070i	$-0.791543\pi$
$11$	−1.09788	+	0.921232i	−0.331024	+	0.277762i	0.462093	+	0.886831i	$0.347099\pi$
$12$		0			0
$13$	−0.995812	+	5.64753i	−0.276189	+	1.56634i	0.458972	+	0.888451i	$0.348218\pi$
$13$	−0.995812	+	5.64753i	−0.276189	+	1.56634i	−0.735161	+	0.677893i	$0.762893\pi$
$14$		0			0
$15$	0.0271636	+	0.0303456i	0.00701361	+	0.00783520i
$16$		0			0
$17$	5.80991	+	3.35435i	1.40911	+	0.813550i	0.995302	−	0.0968141i	$-0.0308652\pi$
$17$	5.80991	+	3.35435i	1.40911	+	0.813550i	0.413808	+	0.910364i	$0.364199\pi$
$18$		0			0
$19$	−6.74443	+	3.89390i	−1.54728	+	0.893322i	−0.548931	+	0.835868i	$0.684965\pi$
$19$	−6.74443	+	3.89390i	−1.54728	+	0.893322i	−0.998348	+	0.0574542i	$0.981702\pi$
$20$		0			0
$21$	5.52890	+	2.96046i	1.20650	+	0.646026i
$22$		0			0
$23$	0.942566	−	0.343066i	0.196539	−	0.0715342i	−0.241875	−	0.970307i	$-0.577763\pi$
$23$	0.942566	−	0.343066i	0.196539	−	0.0715342i	0.438414	+	0.898773i	$0.355540\pi$
$24$		0			0
$25$	0.868145	+	4.92349i	0.173629	+	0.984699i
$26$		0			0
$27$	2.15488	−	4.72826i	0.414707	−	0.909955i
$28$		0			0
$29$	9.41639	−	1.66036i	1.74858	−	0.308322i	0.794365	−	0.607441i	$-0.207804\pi$
$29$	9.41639	−	1.66036i	1.74858	−	0.308322i	0.954216	+	0.299119i	$0.0966928\pi$
$30$		0			0
$31$	1.96605	+	5.40168i	0.353113	+	0.970170i	0.981364	+	0.192159i	$0.0615490\pi$
$31$	1.96605	+	5.40168i	0.353113	+	0.970170i	−0.628251	+	0.778011i	$0.716229\pi$
$32$		0			0
$33$	−1.30930	−	2.10897i	−0.227920	−	0.367125i
$34$		0			0
$35$	−0.0425710	−	0.0737351i	−0.00719581	−	0.0124635i
$36$		0			0
$37$	−1.70852	+	2.95924i	−0.280878	+	0.486496i	−0.971601	−	0.236624i	$-0.923959\pi$
$37$	−1.70852	+	2.95924i	−0.280878	+	0.486496i	0.690723	+	0.723120i	$0.257292\pi$
$38$		0			0
$39$	−9.43759	−	3.09689i	−1.51122	−	0.495900i
$40$		0			0
$41$	−6.80617	−	1.20011i	−1.06294	−	0.187426i	−0.385282	−	0.922799i	$-0.625896\pi$
$41$	−6.80617	−	1.20011i	−1.06294	−	0.187426i	−0.677663	+	0.735373i	$0.737007\pi$
$42$		0			0
$43$	4.05697	+	4.83491i	0.618682	+	0.737316i	0.980843	−	0.194799i	$-0.0624055\pi$
$43$	4.05697	+	4.83491i	0.618682	+	0.737316i	−0.362161	+	0.932115i	$0.617961\pi$
$44$		0			0
$45$	−0.0587107	+	0.0391050i	−0.00875207	+	0.00582943i
$46$		0			0
$47$	0.845478	+	0.307729i	0.123326	+	0.0448869i	0.402946	−	0.915224i	$-0.367986\pi$
$47$	0.845478	+	0.307729i	0.123326	+	0.0448869i	−0.279620	+	0.960111i	$0.590209\pi$
$48$		0			0
$49$	−4.68131	−	3.92808i	−0.668758	−	0.561155i
$50$		0			0
$51$	−7.18053	+	9.13566i	−1.00548	+	1.27925i
$52$		0			0
$53$			9.38837i			1.28959i	0.764355	+	0.644796i	$0.223058\pi$
$53$			9.38837i			1.28959i	−0.764355	+	0.644796i	$0.776942\pi$
$54$		0			0
$55$			0.0336998i			0.00454407i
$56$		0			0
$57$	−5.01655	−	12.5213i	−0.664459	−	1.65849i
$58$		0			0
$59$	−10.0270	−	8.41368i	−1.30541	−	1.09537i	−0.989183	−	0.146684i	$-0.953140\pi$
$59$	−10.0270	−	8.41368i	−1.30541	−	1.09537i	−0.316225	−	0.948684i	$-0.602416\pi$
$60$		0			0
$61$	1.21782	+	0.443250i	0.155926	+	0.0567524i	0.418804	−	0.908077i	$-0.362449\pi$
$61$	1.21782	+	0.443250i	0.155926	+	0.0567524i	−0.262878	+	0.964829i	$0.584672\pi$
$62$		0			0
$63$	−6.43607	+	8.75078i	−0.810868	+	1.10249i
$64$		0			0
$65$	0.0866763	+	0.103297i	0.0107509	+	0.0128124i
$66$		0			0
$67$	5.80459	+	1.02351i	0.709144	+	0.125041i	0.516574	−	0.856242i	$-0.327207\pi$
$67$	5.80459	+	1.02351i	0.709144	+	0.125041i	0.192569	+	0.981283i	$0.438318\pi$
$68$		0			0
$69$	0.356261	+	1.70043i	0.0428888	+	0.204707i
$70$		0			0
$71$	0.203892	−	0.353151i	0.0241975	−	0.0419113i	−0.853673	−	0.520809i	$-0.825630\pi$
$71$	0.203892	−	0.353151i	0.0241975	−	0.0419113i	0.877871	+	0.478898i	$0.158964\pi$
$72$		0			0
$73$	−2.79675	−	4.84411i	−0.327334	−	0.566960i	0.654648	−	0.755934i	$-0.272817\pi$
$73$	−2.79675	−	4.84411i	−0.327334	−	0.566960i	−0.981982	+	0.188974i	$0.939484\pi$
$74$		0			0
$75$	−8.65487	+	0.276986i	−0.999378	+	0.0319836i
$76$		0			0
$77$	1.77489	+	4.87647i	0.202267	+	0.555725i
$78$		0			0
$79$	−10.7972	+	1.90384i	−1.21478	+	0.214198i	−0.744077	−	0.668094i	$-0.767110\pi$
$79$	−10.7972	+	1.90384i	−1.21478	+	0.214198i	−0.470702	+	0.882292i	$0.655999\pi$
$80$		0			0
$81$	7.57633	+	4.85791i	0.841814	+	0.539768i
$82$		0			0
$83$	−1.56717	−	8.88783i	−0.172019	−	0.975567i	−0.941529	−	0.336932i	$-0.890611\pi$
$83$	−1.56717	−	8.88783i	−0.172019	−	0.975567i	0.769510	−	0.638634i	$-0.220500\pi$
$84$		0			0
$85$	0.148235	−	0.0539530i	0.0160783	−	0.00585203i
$86$		0			0
$87$	0.529748	+	16.5528i	0.0567949	+	1.77465i
$88$		0			0
$89$	1.11291	−	0.642542i	0.117969	−	0.0681093i	−0.439855	−	0.898069i	$-0.644970\pi$
$89$	1.11291	−	0.642542i	0.117969	−	0.0681093i	0.557823	+	0.829960i	$0.311637\pi$
$90$		0			0
$91$	17.9827	+	10.3823i	1.88510	+	1.08837i
$92$		0			0
$93$	−9.74485	+	2.04167i	−1.01049	+	0.211711i
$94$		0			0
$95$	−0.0317988	+	0.180340i	−0.00326249	+	0.0185025i
$96$		0			0
$97$	−3.01023	+	2.52588i	−0.305643	+	0.256465i	−0.782688	−	0.622414i	$-0.786152\pi$
$97$	−3.01023	+	2.52588i	−0.305643	+	0.256465i	0.477046	+	0.878879i	$0.341708\pi$
$98$		0			0
$99$	3.93796	−	1.72586i	0.395779	−	0.173456i
$100$		0			0
$101$	2.60635	−	7.16089i	0.259342	−	0.712536i	−0.739867	−	0.672754i	$-0.765111\pi$
$101$	2.60635	−	7.16089i	0.259342	−	0.712536i	0.999208	−	0.0397820i	$-0.0126663\pi$
$102$		0			0
$103$	7.01114	−	8.35555i	0.690828	−	0.823297i	−0.300628	−	0.953742i	$-0.597196\pi$
$103$	7.01114	−	8.35555i	0.690828	−	0.823297i	0.991456	+	0.130445i	$0.0416406\pi$
$104$		0			0
$105$	0.136892	−	0.0548446i	0.0133593	−	0.00535229i
$106$		0			0
$107$	−3.63233			−0.351150			−0.175575	−	0.984466i	$-0.556178\pi$
$107$	−3.63233			−0.351150			−0.175575	+	0.984466i	$0.556178\pi$
$108$		0			0
$109$	6.63917			0.635917			0.317958	−	0.948105i	$-0.397003\pi$
$109$	6.63917			0.635917			0.317958	+	0.948105i	$0.397003\pi$
$110$		0			0
$111$	−4.65319	−	3.65735i	−0.441661	−	0.347141i
$112$		0			0
$113$	7.55112	−	8.99908i	0.710350	−	0.846562i	−0.283306	−	0.959030i	$-0.591431\pi$
$113$	7.55112	−	8.99908i	0.710350	−	0.846562i	0.993655	+	0.112468i	$0.0358755\pi$
$114$		0			0
$115$	0.00806683	−	0.0221634i	0.000752236	−	0.00206675i
$116$		0			0
$117$	7.63171	−	15.4186i	0.705552	−	1.42545i
$118$		0			0
$119$	18.6085	−	15.6144i	1.70584	−	1.43137i
$120$		0			0
$121$	−1.55345	+	8.81008i	−0.141223	+	0.800916i
$122$		0			0
$123$	3.73224	−	11.3738i	0.336525	−	1.02554i
$124$		0			0
$125$	0.203625	+	0.117563i	0.0182128	+	0.0105152i
$126$		0			0
$127$	10.2285	−	5.90544i	0.907635	−	0.524023i	0.0279655	−	0.999609i	$-0.491097\pi$
$127$	10.2285	−	5.90544i	0.907635	−	0.524023i	0.879669	+	0.475586i	$0.157764\pi$
$128$		0			0
$129$	−9.28760	+	5.76597i	−0.817728	+	0.507666i
$130$		0			0
$131$	7.36505	−	2.68066i	0.643487	−	0.234210i	0.000396255	−	1.00000i	$-0.499874\pi$
$131$	7.36505	−	2.68066i	0.643487	−	0.234210i	0.643091	+	0.765790i	$0.277652\pi$
$132$		0			0
$133$	4.89670	+	27.7705i	0.424597	+	2.40801i
$134$		0			0
$135$	−0.0525990	−	0.110280i	−0.00452700	−	0.00949143i
$136$		0			0
$137$	1.71687	−	0.302731i	0.146682	−	0.0258641i	−0.0998248	−	0.995005i	$-0.531828\pi$
$137$	1.71687	−	0.302731i	0.146682	−	0.0258641i	0.246507	+	0.969141i	$0.420717\pi$
$138$		0			0
$139$	−2.27912	−	6.26183i	−0.193312	−	0.531121i	0.804732	−	0.593639i	$-0.202309\pi$
$139$	−2.27912	−	6.26183i	−0.193312	−	0.531121i	−0.998044	+	0.0625177i	$0.980087\pi$
$140$		0			0
$141$	−0.735628	+	1.37384i	−0.0619511	+	0.115698i
$142$		0			0
$143$	−4.10940	−	7.11769i	−0.343646	−	0.595212i
$144$		0			0
$145$	0.112416	−	0.194710i	0.00933565	−	0.0161698i
$146$		0			0
$147$	7.88648	−	7.05952i	0.650466	−	0.582259i
$148$		0			0
$149$	10.5495	+	1.86015i	0.864245	+	0.152390i	0.588161	−	0.808744i	$-0.299852\pi$
$149$	10.5495	+	1.86015i	0.864245	+	0.152390i	0.276084	+	0.961134i	$0.410963\pi$
$150$		0			0
$151$	−1.07374	−	1.27963i	−0.0873794	−	0.104135i	0.720583	−	0.693368i	$-0.243874\pi$
$151$	−1.07374	−	1.27963i	−0.0873794	−	0.104135i	−0.807963	+	0.589234i	$0.799430\pi$
$152$		0			0
$153$	−13.8962	−	14.5588i	−1.12344	−	1.17701i
$154$		0			0
$155$	0.127015	+	0.0462296i	0.0102021	+	0.00371325i
$156$		0			0
$157$	−16.5577	−	13.8936i	−1.32145	−	1.10883i	−0.985995	−	0.166774i	$-0.946665\pi$
$157$	−16.5577	−	13.8936i	−1.32145	−	1.10883i	−0.335456	−	0.942056i	$-0.608890\pi$
$158$		0			0
$159$	−16.0962	−	2.31003i	−1.27651	−	0.183197i
$160$		0			0
$161$		−	3.63199i		−	0.286241i
$162$		0			0
$163$			15.5786i			1.22021i	0.792320	+	0.610106i	$0.208873\pi$
$163$			15.5786i			1.22021i	−0.792320	+	0.610106i	$0.791127\pi$
$164$		0			0
$165$	−0.0577777	−	0.00829189i	−0.00449799	−	0.000645523i
$166$		0			0
$167$	5.53919	+	4.64793i	0.428635	+	0.359668i	0.831436	−	0.555620i	$-0.187519\pi$
$167$	5.53919	+	4.64793i	0.428635	+	0.359668i	−0.402801	+	0.915287i	$0.631963\pi$
$168$		0			0
$169$	−18.6870	−	6.80151i	−1.43746	−	0.523193i
$170$		0			0
$171$	22.7020	−	5.51991i	1.73606	−	0.422118i
$172$		0			0
$173$	0.936172	+	1.11569i	0.0711759	+	0.0848241i	0.800457	−	0.599390i	$-0.204590\pi$
$173$	0.936172	+	1.11569i	0.0711759	+	0.0848241i	−0.729282	+	0.684214i	$0.760146\pi$
$174$		0			0
$175$	17.8275	+	3.14348i	1.34764	+	0.237625i
$176$		0			0
$177$	16.8923	−	15.1210i	1.26970	−	1.13656i
$178$		0			0
$179$	−0.0633641	+	0.109750i	−0.00473606	+	0.00820309i	−0.868384	−	0.495893i	$-0.834841\pi$
$179$	−0.0633641	+	0.109750i	−0.00473606	+	0.00820309i	0.863648	+	0.504096i	$0.168174\pi$
$180$		0			0
$181$	−0.758506	−	1.31377i	−0.0563793	−	0.0976518i	0.836458	−	0.548031i	$-0.184622\pi$
$181$	−0.758506	−	1.31377i	−0.0563793	−	0.0976518i	−0.892838	+	0.450379i	$0.851289\pi$
$182$		0			0
$183$	−1.05959	+	1.97887i	−0.0783274	+	0.146282i
$184$		0			0
$185$	0.0274806	+	0.0755023i	0.00202041	+	0.00555104i
$186$		0			0
$187$	−9.46873	+	1.66959i	−0.692422	+	0.122093i
$188$		0			0
$189$	−13.4195	−	13.1877i	−0.976123	−	0.959263i
$190$		0			0
$191$	4.23336	+	24.0086i	0.306315	+	1.73720i	0.617247	+	0.786769i	$0.288248\pi$
$191$	4.23336	+	24.0086i	0.306315	+	1.73720i	−0.310932	+	0.950432i	$0.600641\pi$
$192$		0			0
$193$	−19.0843	+	6.94612i	−1.37372	+	0.499992i	−0.920268	−	0.391289i	$-0.872029\pi$
$193$	−19.0843	+	6.94612i	−1.37372	+	0.499992i	−0.453450	+	0.891282i	$0.649807\pi$
$194$		0			0
$195$	−0.198428	+	0.123189i	−0.0142097	+	0.00882173i
$196$		0			0
$197$	13.9623	−	8.06115i	0.994774	−	0.574333i	0.0880758	−	0.996114i	$-0.471928\pi$
$197$	13.9623	−	8.06115i	0.994774	−	0.574333i	0.906698	+	0.421781i	$0.138595\pi$
$198$		0			0
$199$	3.53393	+	2.04031i	0.250513	+	0.144634i	0.619999	−	0.784602i	$-0.287133\pi$
$199$	3.53393	+	2.04031i	0.250513	+	0.144634i	−0.369486	+	0.929236i	$0.620466\pi$
$200$		0			0
$201$	−3.18302	+	9.70005i	−0.224513	+	0.684189i
$202$		0			0
$203$	6.01204	−	34.0959i	0.421962	−	2.39307i
$204$		0			0
$205$	−0.124489	+	0.104459i	−0.00869468	+	0.00729570i
$206$		0			0
$207$	−3.00302	+	0.192411i	−0.208724	+	0.0133735i
$208$		0			0
$209$	3.81740	−	10.4882i	0.264055	−	0.725486i
$210$		0			0
$211$	−4.82034	+	5.74466i	−0.331846	+	0.395479i	−0.906006	−	0.423264i	$-0.860884\pi$
$211$	−4.82034	+	5.74466i	−0.331846	+	0.395479i	0.574160	+	0.818743i	$0.305329\pi$
$212$		0			0
$213$	0.555304	+	0.436463i	0.0380488	+	0.0299060i
$214$		0			0
$215$	0.148409			0.0101214
$216$		0			0
$217$	20.8143			1.41296
$218$		0			0
$219$	8.99329	−	3.60308i	0.607710	−	0.243473i
$220$		0			0
$221$	−24.7294	+	29.4714i	−1.66348	+	1.98246i
$222$		0			0
$223$	0.778668	−	2.13937i	0.0521434	−	0.143263i	−0.910887	−	0.412656i	$-0.864601\pi$
$223$	0.778668	−	2.13937i	0.0521434	−	0.143263i	0.963030	+	0.269394i	$0.0868232\pi$
$224$		0			0
$225$	1.65466	−	14.9068i	0.110311	−	0.993786i
$226$		0			0
$227$	−10.0293	+	8.41561i	−0.665670	+	0.558564i	−0.911780	−	0.410678i	$-0.865292\pi$
$227$	−10.0293	+	8.41561i	−0.665670	+	0.558564i	0.246110	+	0.969242i	$0.420848\pi$
$228$		0			0
$229$	3.51693	−	19.9455i	0.232405	−	1.31804i	−0.615605	−	0.788055i	$-0.711088\pi$
$229$	3.51693	−	19.9455i	0.232405	−	1.31804i	0.848010	−	0.529980i	$-0.177801\pi$
$230$		0			0
$231$	−8.79734	+	1.84316i	−0.578823	+	0.121271i
$232$		0			0
$233$	20.9640	+	12.1036i	1.37340	+	0.792930i	0.991354	−	0.131215i	$-0.0418877\pi$
$233$	20.9640	+	12.1036i	1.37340	+	0.792930i	0.382042	+	0.924145i	$0.375221\pi$
$234$		0			0
$235$	0.0183220	−	0.0105782i	0.00119519	−	0.000690046i
$236$		0			0
$237$	−0.607429	−	18.9801i	−0.0394567	−	1.23289i
$238$		0			0
$239$	11.0354	−	4.01654i	0.713818	−	0.259808i	0.0405188	−	0.999179i	$-0.487099\pi$
$239$	11.0354	−	4.01654i	0.713818	−	0.259808i	0.673299	+	0.739370i	$0.264877\pi$
$240$		0			0
$241$	−0.165047	−	0.936031i	−0.0106316	−	0.0602950i	0.979030	−	0.203714i	$-0.0653014\pi$
$241$	−0.165047	−	0.936031i	−0.0106316	−	0.0602950i	−0.989662	+	0.143419i	$0.954190\pi$
$242$		0			0
$243$	−10.1930	+	11.7942i	−0.653880	+	0.756598i
$244$		0			0
$245$	−0.141511	+	0.0249522i	−0.00904080	+	0.00159414i
$246$		0			0
$247$	−15.2747	−	41.9670i	−0.971908	−	2.67030i
$248$		0			0
$249$	15.6237	−	0.500012i	0.990109	−	0.0316870i
$250$		0			0
$251$	0.503134	+	0.871453i	0.0317575	+	0.0550056i	0.881467	−	0.472245i	$-0.156556\pi$
$251$	0.503134	+	0.871453i	0.0317575	+	0.0550056i	−0.849710	+	0.527251i	$0.823223\pi$
$252$		0			0
$253$	−0.718783	+	1.24497i	−0.0451895	+	0.0782705i
$254$		0			0
$255$	0.0560282	+	0.267421i	0.00350862	+	0.0167466i
$256$		0			0
$257$	−18.0030	−	3.17442i	−1.12300	−	0.198015i	−0.418842	−	0.908059i	$-0.637564\pi$
$257$	−18.0030	−	3.17442i	−1.12300	−	0.198015i	−0.704157	+	0.710044i	$0.748675\pi$
$258$		0			0
$259$	7.95307	+	9.47810i	0.494180	+	0.588941i
$260$		0			0
$261$	−28.5099	−	3.16460i	−1.76472	−	0.195884i
$262$		0			0
$263$	18.9920	+	6.91252i	1.17110	+	0.426244i	0.853049	−	0.521830i	$-0.174751\pi$
$263$	18.9920	+	6.91252i	1.17110	+	0.426244i	0.318048	+	0.948075i	$0.396973\pi$
$264$		0			0
$265$	0.169110	+	0.141900i	0.0103883	+	0.00871686i
$266$		0			0
$267$	0.827793	+	2.06617i	0.0506601	+	0.126448i
$268$		0			0
$269$		−	10.9338i		−	0.666647i	−0.942813	−	0.333323i	$-0.891830\pi$
$269$		−	10.9338i		−	0.666647i	0.942813	−	0.333323i	$-0.108170\pi$
$270$		0			0
$271$			4.60890i			0.279971i	0.990154	+	0.139985i	$0.0447056\pi$
$271$			4.60890i			0.279971i	−0.990154	+	0.139985i	$0.955294\pi$
$272$		0			0
$273$	−22.2251	+	28.2766i	−1.34512	+	1.71138i
$274$		0			0
$275$	−5.48880	−	4.60565i	−0.330987	−	0.277731i
$276$		0			0
$277$	−6.10890	−	2.22346i	−0.367048	−	0.133595i	0.151910	−	0.988394i	$-0.451458\pi$
$277$	−6.10890	−	2.22346i	−0.367048	−	0.133595i	−0.518958	+	0.854800i	$0.673680\pi$
$278$		0			0
$279$	−1.10267	−	17.2098i	−0.0660154	−	1.03032i
$280$		0			0
$281$	−6.60328	−	7.86948i	−0.393919	−	0.469454i	0.532237	−	0.846595i	$-0.321352\pi$
$281$	−6.60328	−	7.86948i	−0.393919	−	0.469454i	−0.926156	+	0.377141i	$0.876907\pi$
$282$		0			0
$283$	16.7061	+	2.94574i	0.993077	+	0.175106i	0.646499	−	0.762915i	$-0.276233\pi$
$283$	16.7061	+	2.94574i	0.993077	+	0.175106i	0.346578	+	0.938021i	$0.387344\pi$
$284$		0			0
$285$	−0.301366	−	0.0988915i	−0.0178514	−	0.00585782i
$286$		0			0
$287$	−12.5124	+	21.6720i	−0.738581	+	1.27926i
$288$		0			0
$289$	14.0034	+	24.2546i	0.823728	+	1.42674i
$290$		0			0
$291$	−3.58992	−	5.78250i	−0.210445	−	0.338976i
$292$		0			0
$293$	−9.34623	−	25.6786i	−0.546013	−	1.50016i	−0.839049	−	0.544056i	$-0.816888\pi$
$293$	−9.34623	−	25.6786i	−0.546013	−	1.50016i	0.293036	−	0.956101i	$-0.405334\pi$
$294$		0			0
$295$	−0.303107	+	0.0534459i	−0.0176475	+	0.00311174i
$296$		0			0
$297$	1.99002	+	7.17622i	0.115473	+	0.416406i
$298$		0			0
$299$	0.998858	+	5.66480i	0.0577654	+	0.327604i
$300$		0			0
$301$	21.4752	−	7.81635i	1.23781	−	0.450527i
$302$		0			0
$303$	11.6359	+	6.23050i	0.668468	+	0.357933i
$304$		0			0
$305$	0.0263908	−	0.0152368i	0.00151114	−	0.000872455i
$306$		0			0
$307$	0.926384	+	0.534848i	0.0528715	+	0.0305254i	0.526203	−	0.850359i	$-0.323615\pi$
$307$	0.926384	+	0.534848i	0.0528715	+	0.0305254i	−0.473331	+	0.880885i	$0.656949\pi$
$308$		0			0
$309$	12.6004	+	14.0764i	0.716809	+	0.800778i
$310$		0			0
$311$	5.86318	−	33.2517i	0.332470	−	1.88553i	−0.118436	−	0.992962i	$-0.537788\pi$
$311$	5.86318	−	33.2517i	0.332470	−	1.88553i	0.450907	−	0.892571i	$-0.351101\pi$
$312$		0			0
$313$	2.14164	−	1.79705i	0.121053	−	0.101575i	−0.580252	−	0.814437i	$-0.697046\pi$
$313$	2.14164	−	1.79705i	0.121053	−	0.101575i	0.701304	+	0.712862i	$0.252601\pi$
$314$		0			0
$315$	0.0603476	+	0.248194i	0.00340020	+	0.0139842i
$316$		0			0
$317$	6.89745	−	18.9506i	0.387399	−	1.06437i	−0.580768	−	0.814069i	$-0.697248\pi$
$317$	6.89745	−	18.9506i	0.387399	−	1.06437i	0.968168	−	0.250302i	$-0.0805300\pi$
$318$		0			0
$319$	−8.80850	+	10.4976i	−0.493181	+	0.587751i
$320$		0			0
$321$	0.893741	−	6.22757i	0.0498837	−	0.347589i
$322$		0			0
$323$	−52.2461			−2.90705
$324$		0			0
$325$	−28.6701			−1.59033
$326$		0			0
$327$	−1.63358	+	11.3828i	−0.0903372	+	0.629468i
$328$		0			0
$329$	2.09412	−	2.49568i	0.115453	−	0.137591i
$330$		0			0
$331$	−3.09489	+	8.50313i	−0.170110	+	0.467375i	−0.995227	−	0.0975881i	$-0.968887\pi$
$331$	−3.09489	+	8.50313i	−0.170110	+	0.467375i	0.825116	+	0.564963i	$0.191109\pi$
$332$		0			0
$333$	7.41540	−	7.07792i	0.406361	−	0.387867i
$334$		0			0
$335$	0.106169	−	0.0890867i	0.00580065	−	0.00486733i
$336$		0			0
$337$	−1.44103	+	8.17248i	−0.0784978	+	0.445183i	0.920073	+	0.391746i	$0.128129\pi$
$337$	−1.44103	+	8.17248i	−0.0784978	+	0.445183i	−0.998571	+	0.0534371i	$0.982982\pi$
$338$		0			0
$339$	13.5708	+	15.1605i	0.737065	+	0.823407i
$340$		0			0
$341$	−7.13469	−	4.11921i	−0.386365	−	0.223068i
$342$		0			0
$343$	2.78769	−	1.60947i	0.150521	−	0.0869033i
$344$		0			0
$345$	0.0360140	+	0.0192838i	0.00193893	+	0.00103821i
$346$		0			0
$347$	−23.1278	+	8.41785i	−1.24157	+	0.451894i	−0.877544	−	0.479496i	$-0.840819\pi$
$347$	−23.1278	+	8.41785i	−1.24157	+	0.451894i	−0.364024	+	0.931390i	$0.618597\pi$
$348$		0			0
$349$	0.421268	+	2.38913i	0.0225499	+	0.127887i	0.994005	−	0.109338i	$-0.0348732\pi$
$349$	0.421268	+	2.38913i	0.0225499	+	0.127887i	−0.971455	+	0.237225i	$0.923762\pi$
$350$		0			0
$351$	24.5572	+	16.8782i	1.31076	+	0.900893i
$352$		0			0
$353$	−1.29418	+	0.228200i	−0.0688825	+	0.0121458i	−0.207983	−	0.978132i	$-0.566690\pi$
$353$	−1.29418	+	0.228200i	−0.0688825	+	0.0121458i	0.139101	+	0.990278i	$0.455579\pi$
$354$		0			0
$355$	−0.00327949	−	0.00901034i	−0.000174058	−	0.000478219i
$356$		0			0
$357$	22.1919	+	35.7459i	1.17452	+	1.89187i
$358$		0			0
$359$	6.97428	+	12.0798i	0.368089	+	0.637548i	0.989267	−	0.146121i	$-0.0466789\pi$
$359$	6.97428	+	12.0798i	0.368089	+	0.637548i	−0.621178	+	0.783669i	$0.713346\pi$
$360$		0			0
$361$	20.8249	−	36.0698i	1.09605	−	1.89841i
$362$		0			0
$363$	−14.7225	−	4.83111i	−0.772732	−	0.253568i
$364$		0			0
$365$	−0.129527	−	0.0228391i	−0.00677975	−	0.00119545i
$366$		0			0
$367$	−11.8673	−	14.1430i	−0.619471	−	0.738256i	0.361509	−	0.932369i	$-0.382262\pi$
$367$	−11.8673	−	14.1430i	−0.619471	−	0.738256i	−0.980979	+	0.194112i	$0.937817\pi$
$368$		0			0
$369$	18.5818	+	9.19741i	0.967332	+	0.478798i
$370$		0			0
$371$	31.9444	+	11.6268i	1.65847	+	0.603633i
$372$		0			0
$373$	−15.0899	−	12.6620i	−0.781327	−	0.655612i	0.162255	−	0.986749i	$-0.448123\pi$
$373$	−15.0899	−	12.6620i	−0.781327	−	0.655612i	−0.943583	+	0.331137i	$0.892568\pi$
$374$		0			0
$375$	−0.251663	+	0.320186i	−0.0129958	+	0.0165343i
$376$		0			0
$377$			54.8328i			2.82403i
$378$		0			0
$379$			13.8218i			0.709979i	0.934870	+	0.354989i	$0.115516\pi$
$379$			13.8218i			0.709979i	−0.934870	+	0.354989i	$0.884484\pi$
$380$		0			0
$381$	7.60804	+	18.9897i	0.389772	+	0.972872i
$382$		0			0
$383$	−14.4928	−	12.1609i	−0.740545	−	0.621391i	0.192439	−	0.981309i	$-0.438360\pi$
$383$	−14.4928	−	12.1609i	−0.740545	−	0.621391i	−0.932984	+	0.359918i	$0.882805\pi$
$384$		0			0
$385$	0.114665	+	0.0417346i	0.00584387	+	0.00212699i
$386$		0			0
$387$	−7.60044	−	17.3422i	−0.386352	−	0.881553i
$388$		0			0
$389$	−7.25900	−	8.65094i	−0.368046	−	0.438620i	0.549958	−	0.835193i	$-0.314644\pi$
$389$	−7.25900	−	8.65094i	−0.368046	−	0.438620i	−0.918003	+	0.396573i	$0.870199\pi$
$390$		0			0
$391$	6.62699	+	1.16852i	0.335141	+	0.0590945i
$392$		0			0
$393$	2.78376	+	13.2868i	0.140422	+	0.670233i
$394$		0			0
$395$	−0.128901	+	0.223262i	−0.00648569	+	0.0112335i
$396$		0			0
$397$	2.49572	+	4.32272i	0.125257	+	0.216951i	0.921833	−	0.387587i	$-0.126691\pi$
$397$	2.49572	+	4.32272i	0.125257	+	0.216951i	−0.796577	+	0.604538i	$0.793358\pi$
$398$		0			0
$399$	−48.8170	+	1.56232i	−2.44391	+	0.0782136i
$400$		0			0
$401$	2.14749	+	5.90018i	0.107241	+	0.294641i	0.981693	−	0.190470i	$-0.0610013\pi$
$401$	2.14749	+	5.90018i	0.107241	+	0.294641i	−0.874452	+	0.485111i	$0.838779\pi$
$402$		0			0
$403$	−32.4640	+	5.72428i	−1.61715	+	0.285146i
$404$		0			0
$405$	0.202016	−	0.0630455i	0.0100383	−	0.00313276i
$406$		0			0
$407$	−0.850395	−	4.82283i	−0.0421525	−	0.239059i
$408$		0			0
$409$	29.8711	−	10.8722i	1.47703	−	0.537595i	0.527031	−	0.849846i	$-0.323305\pi$
$409$	29.8711	−	10.8722i	1.47703	−	0.537595i	0.950000	+	0.312250i	$0.101083\pi$
$410$		0			0
$411$	0.0965879	+	3.01804i	0.00476433	+	0.148869i
$412$		0			0
$413$	−41.0457	+	23.6977i	−2.01973	+	1.16609i
$414$		0			0
$415$	−0.183781	−	0.106106i	−0.00902145	−	0.00520854i
$416$		0			0
$417$	11.2966	−	2.36678i	0.553196	−	0.115902i
$418$		0			0
$419$	−5.43695	+	30.8345i	−0.265612	+	1.50636i	0.501674	+	0.865057i	$0.332718\pi$
$419$	−5.43695	+	30.8345i	−0.265612	+	1.50636i	−0.767286	+	0.641305i	$0.778393\pi$
$420$		0			0
$421$	−18.5973	+	15.6050i	−0.906377	+	0.760540i	−0.971426	−	0.237342i	$-0.923724\pi$
$421$	−18.5973	+	15.6050i	−0.906377	+	0.760540i	0.0650496	+	0.997882i	$0.479279\pi$
$422$		0			0
$423$	−2.17443	−	1.59926i	−0.105724	−	0.0777587i
$424$		0			0
$425$	−11.4713	+	31.5171i	−0.556440	+	1.52881i
$426$		0			0
$427$	3.01636	−	3.59476i	0.145972	−	0.173962i
$428$		0			0
$429$	13.2143	−	5.29419i	0.637993	−	0.255606i
$430$		0			0
$431$	20.7065			0.997396			0.498698	−	0.866776i	$-0.333812\pi$
$431$	20.7065			0.997396			0.498698	+	0.866776i	$0.333812\pi$
$432$		0			0
$433$	21.5474			1.03550			0.517750	−	0.855532i	$-0.326770\pi$
$433$	21.5474			1.03550			0.517750	+	0.855532i	$0.326770\pi$
$434$		0			0
$435$	0.306168	+	0.240645i	0.0146796	+	0.0115380i
$436$		0			0
$437$	−5.02121	+	5.98405i	−0.240197	+	0.286256i
$438$		0			0
$439$	2.25676	−	6.20039i	0.107709	−	0.295928i	−0.874116	−	0.485718i	$-0.838558\pi$
$439$	2.25676	−	6.20039i	0.107709	−	0.295928i	0.981825	+	0.189789i	$0.0607805\pi$
$440$		0			0
$441$	10.1630	+	15.2583i	0.483950	+	0.726584i
$442$		0			0
$443$	15.5893	−	13.0810i	0.740669	−	0.621495i	−0.192348	−	0.981327i	$-0.561610\pi$
$443$	15.5893	−	13.0810i	0.740669	−	0.621495i	0.933017	+	0.359831i	$0.117166\pi$
$444$		0			0
$445$	0.00524719	−	0.0297583i	0.000248741	−	0.00141068i
$446$		0			0
$447$	−5.78492	+	17.6292i	−0.273617	+	0.833832i
$448$		0			0
$449$	6.86064	+	3.96099i	0.323774	+	0.186931i	0.653073	−	0.757295i	$-0.273479\pi$
$449$	6.86064	+	3.96099i	0.323774	+	0.186931i	−0.329300	+	0.944225i	$0.606813\pi$
$450$		0			0
$451$	8.57794	−	4.95248i	0.403920	−	0.233203i
$452$		0			0
$453$	2.45810	−	1.52605i	0.115492	−	0.0717000i
$454$		0			0
$455$	0.458814	−	0.166995i	0.0215095	−	0.00782883i
$456$		0			0
$457$	1.93734	+	10.9872i	0.0906248	+	0.513959i	0.996001	+	0.0893475i	$0.0284782\pi$
$457$	1.93734	+	10.9872i	0.0906248	+	0.513959i	−0.905376	+	0.424611i	$0.860411\pi$
$458$		0			0
$459$	28.3799	−	20.2426i	1.32466	−	0.944842i
$460$		0			0
$461$	30.0749	−	5.30301i	1.40073	−	0.246986i	0.578284	−	0.815835i	$-0.303722\pi$
$461$	30.0749	−	5.30301i	1.40073	−	0.246986i	0.822442	+	0.568850i	$0.192611\pi$
$462$		0			0
$463$	−9.28159	−	25.5010i	−0.431352	−	1.18513i	−0.944983	−	0.327119i	$-0.893922\pi$
$463$	−9.28159	−	25.5010i	−0.431352	−	1.18513i	0.513631	−	0.858011i	$-0.328300\pi$
$464$		0			0
$465$	−0.110512	+	0.206390i	−0.00512488	+	0.00957110i
$466$		0			0
$467$	−2.11956	−	3.67119i	−0.0980816	−	0.169882i	0.812809	−	0.582530i	$-0.197937\pi$
$467$	−2.11956	−	3.67119i	−0.0980816	−	0.169882i	−0.910891	+	0.412648i	$0.864604\pi$
$468$		0			0
$469$	10.6711	−	18.4828i	0.492745	−	0.853459i
$470$		0			0
$471$	27.8944	−	24.9694i	1.28531	−	1.15053i
$472$		0			0
$473$	−8.90814	−	1.57075i	−0.409597	−	0.0722230i
$474$		0			0
$475$	−25.0267	−	29.8257i	−1.14831	−	1.36850i
$476$		0			0
$477$	7.92101	−	27.0283i	0.362678	−	1.23754i
$478$		0			0
$479$	4.56144	+	1.66023i	0.208417	+	0.0758577i	0.444119	−	0.895968i	$-0.353517\pi$
$479$	4.56144	+	1.66023i	0.208417	+	0.0758577i	−0.235702	+	0.971825i	$0.575739\pi$
$480$		0			0
$481$	−15.0110	−	12.5958i	−0.684444	−	0.574317i
$482$		0			0
$483$	6.22699	+	0.893657i	0.283338	+	0.0406628i
$484$		0			0
$485$			0.0923999i			0.00419566i
$486$		0			0
$487$			22.8600i			1.03588i	0.855415	+	0.517942i	$0.173302\pi$
$487$			22.8600i			1.03588i	−0.855415	+	0.517942i	$0.826698\pi$
$488$		0			0
$489$	−26.7093	−	3.83315i	−1.20784	−	0.173341i
$490$		0			0
$491$	17.3229	+	14.5356i	0.781772	+	0.655985i	0.943694	−	0.330819i	$-0.107325\pi$
$491$	17.3229	+	14.5356i	0.781772	+	0.655985i	−0.161922	+	0.986804i	$0.551769\pi$
$492$		0			0
$493$	60.2779	+	21.9393i	2.71478	+	0.988098i
$494$		0			0
$495$	0.0284326	−	0.0970188i	0.00127795	−	0.00436067i
$496$		0			0
$497$	−0.949108	−	1.13110i	−0.0425733	−	0.0507369i
$498$		0			0
$499$	12.1872	+	2.14893i	0.545573	+	0.0961993i	0.439640	−	0.898174i	$-0.355106\pi$
$499$	12.1872	+	2.14893i	0.545573	+	0.0961993i	0.105933	+	0.994373i	$0.466217\pi$
$500$		0			0
$501$	−9.33173	+	8.35322i	−0.416911	+	0.373194i
$502$		0			0
$503$	−15.4946	+	26.8374i	−0.690870	+	1.19662i	0.280683	+	0.959800i	$0.409439\pi$
$503$	−15.4946	+	26.8374i	−0.690870	+	1.19662i	−0.971553	+	0.236822i	$0.923894\pi$
$504$		0			0
$505$	−0.0895935	−	0.155181i	−0.00398686	−	0.00690544i
$506$		0			0
$507$	16.2590	−	30.3650i	0.722090	−	1.34856i
$508$		0			0
$509$	5.40132	+	14.8400i	0.239409	+	0.657772i	0.999964	+	0.00849776i	$0.00270495\pi$
$509$	5.40132	+	14.8400i	0.239409	+	0.657772i	−0.760555	+	0.649274i	$0.775073\pi$
$510$		0			0
$511$	−19.9459	+	3.51699i	−0.882353	+	0.155583i
$512$		0			0
$513$	3.87793	+	40.2804i	0.171215	+	1.77842i
$514$		0			0
$515$	−0.0445365	−	0.252579i	−0.00196251	−	0.0111300i
$516$		0			0
$517$	−1.21172	+	0.441032i	−0.0532916	+	0.0193965i
$518$		0			0
$519$	−2.14318	+	1.33054i	−0.0940749	+	0.0584041i
$520$		0			0
$521$	37.4289	−	21.6096i	1.63979	−	0.946733i	0.658886	−	0.752243i	$-0.271028\pi$
$521$	37.4289	−	21.6096i	1.63979	−	0.946733i	0.980904	−	0.194491i	$-0.0623054\pi$
$522$		0			0
$523$	−32.0786	−	18.5206i	−1.40270	−	0.809849i	−0.408031	−	0.912968i	$-0.633784\pi$
$523$	−32.0786	−	18.5206i	−1.40270	−	0.809849i	−0.994669	+	0.103119i	$0.967118\pi$
$524$		0			0
$525$	−9.77595	+	29.7916i	−0.426657	+	1.30021i
$526$		0			0
$527$	−6.69656	+	37.9781i	−0.291707	+	1.65435i
$528$		0			0
$529$	−16.8483	+	14.1374i	−0.732534	+	0.614669i
$530$		0			0
$531$	21.7683	+	32.6821i	0.944665	+	1.41828i
$532$		0			0
$533$	13.5553	−	37.2430i	0.587147	−	1.61317i
$534$		0			0
$535$	−0.0549007	+	0.0654281i	−0.00237356	+	0.00282870i
$536$		0			0
$537$	−0.172574	−	0.135641i	−0.00744711	−	0.00585334i
$538$		0			0
$539$	8.75820			0.377242
$540$		0			0
$541$	5.72646			0.246200			0.123100	−	0.992394i	$-0.460716\pi$
$541$	5.72646			0.246200			0.123100	+	0.992394i	$0.460716\pi$
$542$		0			0
$543$	2.43907	−	0.977191i	0.104671	−	0.0419353i
$544$		0			0
$545$	0.100347	−	0.119589i	0.00429841	−	0.00512265i
$546$		0			0
$547$	−7.58943	+	20.8518i	−0.324500	+	0.891558i	0.664976	+	0.746865i	$0.268442\pi$
$547$	−7.58943	+	20.8518i	−0.324500	+	0.891558i	−0.989477	+	0.144693i	$0.953781\pi$
$548$		0			0
$549$	−3.13203	−	2.30356i	−0.133672	−	0.0983136i
$550$		0			0
$551$	−57.0429	+	47.8647i	−2.43011	+	2.03911i
$552$		0			0
$553$	−6.89363	+	39.0957i	−0.293147	+	1.66252i
$554$		0			0
$555$	−0.136209	+	0.0285376i	−0.00578176	+	0.00121135i
$556$		0			0
$557$	7.51400	+	4.33821i	0.318379	+	0.183816i	0.650670	−	0.759361i	$-0.274488\pi$
$557$	7.51400	+	4.33821i	0.318379	+	0.183816i	−0.332291	+	0.943177i	$0.607822\pi$
$558$		0			0
$559$	−31.3453	+	18.0972i	−1.32576	+	0.765430i
$560$		0			0
$561$	−0.532692	−	16.6448i	−0.0224903	−	0.702744i
$562$		0			0
$563$	−9.94382	+	3.61925i	−0.419082	+	0.152533i	−0.542949	−	0.839765i	$-0.682692\pi$
$563$	−9.94382	+	3.61925i	−0.419082	+	0.152533i	0.123867	+	0.992299i	$0.460470\pi$
$564$		0			0
$565$	−0.0479667	−	0.272032i	−0.00201797	−	0.0114445i
$566$		0			0
$567$	25.9120	−	19.7626i	1.08820	−	0.829953i
$568$		0			0
$569$	−36.2970	+	6.40013i	−1.52165	+	0.268308i	−0.871080	−	0.491141i	$-0.836580\pi$
$569$	−36.2970	+	6.40013i	−1.52165	+	0.268308i	−0.650568	+	0.759448i	$0.725469\pi$
$570$		0			0
$571$	−5.28465	−	14.5195i	−0.221156	−	0.607621i	0.778647	−	0.627462i	$-0.215906\pi$
$571$	−5.28465	−	14.5195i	−0.221156	−	0.607621i	−0.999803	+	0.0198411i	$0.993684\pi$
$572$		0			0
$573$	−42.2040	+	1.35068i	−1.76310	+	0.0564253i
$574$		0			0
$575$	2.50737	+	4.34289i	0.104564	+	0.181111i
$576$		0			0
$577$	9.99160	−	17.3060i	0.415956	−	0.720456i	−0.579573	−	0.814921i	$-0.696781\pi$
$577$	9.99160	−	17.3060i	0.415956	−	0.720456i	0.995528	+	0.0944644i	$0.0301139\pi$
$578$		0			0
$579$	−7.21328	−	34.4288i	−0.299774	−	1.43081i
$580$		0			0
$581$	−32.1821	−	5.67457i	−1.33514	−	0.235421i
$582$		0			0
$583$	−8.64886	−	10.3073i	−0.358199	−	0.426885i
$584$		0			0
$585$	−0.162382	−	0.370512i	−0.00671366	−	0.0153188i
$586$		0			0
$587$	−31.5964	−	11.5002i	−1.30412	−	0.474662i	−0.405786	−	0.913968i	$-0.633002\pi$
$587$	−31.5964	−	11.5002i	−1.30412	−	0.474662i	−0.898338	+	0.439306i	$0.855224\pi$
$588$		0			0
$589$	−34.2935	−	28.7757i	−1.41304	−	1.18568i
$590$		0			0
$591$	10.3853	+	25.9216i	0.427192	+	1.06627i
$592$		0			0
$593$		−	25.8332i		−	1.06084i	−0.847734	−	0.530422i	$-0.822034\pi$
$593$		−	25.8332i		−	1.06084i	0.847734	−	0.530422i	$-0.177966\pi$
$594$		0			0
$595$		−	0.571192i		−	0.0234166i
$596$		0			0
$597$	−4.36762	+	5.55684i	−0.178755	+	0.227426i
$598$		0			0
$599$	0.147684	+	0.123922i	0.00603421	+	0.00506330i	0.645800	−	0.763507i	$-0.276524\pi$
$599$	0.147684	+	0.123922i	0.00603421	+	0.00506330i	−0.639766	+	0.768570i	$0.720969\pi$
$600$		0			0
$601$	31.2533	+	11.3753i	1.27485	+	0.464007i	0.888725	−	0.458440i	$-0.151592\pi$
$601$	31.2533	+	11.3753i	1.27485	+	0.464007i	0.386123	+	0.922447i	$0.373814\pi$
$602$		0			0
$603$	−15.8474	−	7.84395i	−0.645356	−	0.319430i
$604$		0			0
$605$	0.135214	+	0.161142i	0.00549722	+	0.00655134i
$606$		0			0
$607$	−7.48727	−	1.32021i	−0.303899	−	0.0535856i	0.0196193	−	0.999808i	$-0.493755\pi$
$607$	−7.48727	−	1.32021i	−0.303899	−	0.0535856i	−0.323518	+	0.946222i	$0.604866\pi$
$608$		0			0
$609$	56.9777	+	18.6969i	2.30885	+	0.757637i
$610$		0			0
$611$	−2.57985	+	4.46843i	−0.104369	+	0.180773i
$612$		0			0
$613$	−13.1895	−	22.8448i	−0.532717	−	0.922693i	−0.999270	−	0.0381996i	$-0.987838\pi$
$613$	−13.1895	−	22.8448i	−0.532717	−	0.922693i	0.466553	−	0.884493i	$-0.345496\pi$
$614$		0			0
$615$	−0.148462	−	0.239136i	−0.00598656	−	0.00964291i
$616$		0			0
$617$	−13.8011	−	37.9183i	−0.555612	−	1.52653i	−0.825937	−	0.563763i	$-0.809353\pi$
$617$	−13.8011	−	37.9183i	−0.555612	−	1.52653i	0.270324	−	0.962769i	$-0.412869\pi$
$618$		0			0
$619$	24.6015	−	4.33791i	0.988817	−	0.174355i	0.344230	−	0.938886i	$-0.388140\pi$
$619$	24.6015	−	4.33791i	0.988817	−	0.174355i	0.644588	+	0.764530i	$0.277029\pi$
$620$		0			0
$621$	0.409012	−	5.19597i	0.0164131	−	0.208507i
$622$		0			0
$623$	−0.808016	−	4.58248i	−0.0323725	−	0.183593i
$624$		0			0
$625$	−23.4845	+	8.54767i	−0.939381	+	0.341907i
$626$		0			0
$627$	17.0426	+	9.12553i	0.680617	+	0.364438i
$628$		0			0
$629$	−19.8527	+	11.4619i	−0.791577	+	0.457017i
$630$		0			0
$631$	0.958554	+	0.553421i	0.0381594	+	0.0220314i	0.518958	−	0.854800i	$-0.326320\pi$
$631$	0.958554	+	0.553421i	0.0381594	+	0.0220314i	−0.480799	+	0.876831i	$0.659653\pi$
$632$		0			0
$633$	−8.66308	−	9.67789i	−0.344326	−	0.384661i
$634$		0			0
$635$	0.0482256	−	0.273501i	0.00191378	−	0.0108536i
$636$		0			0
$637$	26.8457	−	22.5262i	1.06366	−	0.892521i
$638$		0			0
$639$	−0.884943	+	0.844668i	−0.0350078	+	0.0334146i
$640$		0			0
$641$	6.97372	−	19.1601i	0.275445	−	0.756779i	−0.722419	−	0.691456i	$-0.756970\pi$
$641$	6.97372	−	19.1601i	0.275445	−	0.756779i	0.997864	−	0.0653238i	$-0.0208080\pi$
$642$		0			0
$643$	−5.56859	+	6.63639i	−0.219604	+	0.261714i	−0.864587	−	0.502483i	$-0.832420\pi$
$643$	−5.56859	+	6.63639i	−0.219604	+	0.261714i	0.644983	+	0.764197i	$0.276864\pi$
$644$		0			0
$645$	−0.0365163	+	0.254445i	−0.00143783	+	0.0100187i
$646$		0			0
$647$	20.8500			0.819698			0.409849	−	0.912153i	$-0.365581\pi$
$647$	20.8500			0.819698			0.409849	+	0.912153i	$0.365581\pi$
$648$		0			0
$649$	18.7594			0.736372
$650$		0			0
$651$	−5.12139	+	35.6857i	−0.200723	+	1.39863i
$652$		0			0
$653$	−16.2368	+	19.3503i	−0.635395	+	0.757235i	−0.983635	−	0.180171i	$-0.942335\pi$
$653$	−16.2368	+	19.3503i	−0.635395	+	0.757235i	0.348240	+	0.937405i	$0.386779\pi$
$654$		0			0
$655$	0.0630328	−	0.173181i	0.00246290	−	0.00676675i
$656$		0			0
$657$	3.96461	+	16.3054i	0.154674	+	0.636135i
$658$		0			0
$659$	14.8493	−	12.4600i	0.578446	−	0.485374i	−0.305990	−	0.952035i	$-0.598988\pi$
$659$	14.8493	−	12.4600i	0.578446	−	0.485374i	0.884436	+	0.466661i	$0.154543\pi$
$660$		0			0
$661$	−3.47920	+	19.7315i	−0.135325	+	0.767468i	0.839307	+	0.543657i	$0.182961\pi$
$661$	−3.47920	+	19.7315i	−0.135325	+	0.767468i	−0.974633	+	0.223811i	$0.928150\pi$
$662$		0			0
$663$	−44.4435	−	49.6497i	−1.72604	−	1.92823i
$664$		0			0
$665$	0.574234	+	0.331534i	0.0222678	+	0.0128563i
$666$		0			0
$667$	8.30596	−	4.79545i	0.321608	−	0.185681i
$668$		0			0
$669$	3.47633	+	1.86141i	0.134403	+	0.0719663i
$670$		0			0
$671$	−1.74536	+	0.635259i	−0.0673788	+	0.0245239i
$672$		0			0
$673$	−7.45572	−	42.2835i	−0.287397	−	1.62991i	−0.696595	−	0.717464i	$-0.745303\pi$
$673$	−7.45572	−	42.2835i	−0.287397	−	1.62991i	0.409198	−	0.912445i	$-0.365808\pi$
$674$		0			0
$675$	25.1503	+	6.50473i	0.968037	+	0.250367i
$676$		0			0
$677$	3.93681	−	0.694165i	0.151304	−	0.0266789i	−0.0974832	−	0.995237i	$-0.531079\pi$
$677$	3.93681	−	0.694165i	0.151304	−	0.0266789i	0.248787	+	0.968558i	$0.419968\pi$
$678$		0			0
$679$	4.86649	+	13.3706i	0.186759	+	0.513115i
$680$		0			0
$681$	−11.9607	−	19.2658i	−0.458335	−	0.738268i
$682$		0			0
$683$	20.1473	+	34.8961i	0.770915	+	1.33526i	0.937062	+	0.349162i	$0.113534\pi$
$683$	20.1473	+	34.8961i	0.770915	+	1.33526i	−0.166148	+	0.986101i	$0.553133\pi$
$684$		0			0
$685$	0.0204966	−	0.0355012i	0.000783135	−	0.00135643i
$686$		0			0
$687$	33.3309	+	10.9373i	1.27165	+	0.417286i
$688$		0			0
$689$	−53.0211	−	9.34906i	−2.01994	−	0.356171i
$690$		0			0
$691$	−25.8294	−	30.7822i	−0.982595	−	1.17101i	−0.985268	−	0.171015i	$-0.945295\pi$
$691$	−25.8294	−	30.7822i	−0.982595	−	1.17101i	0.00267318	−	0.999996i	$-0.499149\pi$
$692$		0			0
$693$	−0.995460	−	15.5364i	−0.0378144	−	0.590180i
$694$		0			0
$695$	−0.147240	−	0.0535910i	−0.00558514	−	0.00203282i
$696$		0			0
$697$	−35.5176	−	29.8028i	−1.34533	−	1.12886i
$698$		0			0
$699$	−25.9096	+	32.9643i	−0.979991	+	1.24682i
$700$		0			0
$701$		−	1.10033i		−	0.0415589i	−0.999784	−	0.0207794i	$-0.993385\pi$
$701$		−	1.10033i		−	0.0415589i	0.999784	−	0.0207794i	$-0.00661478\pi$
$702$		0			0
$703$		−	26.6112i		−	1.00366i
$704$		0			0
$705$	0.0136280	+	0.0340156i	0.000513261	+	0.00128110i
$706$		0			0
$707$	−21.1375	−	17.7365i	−0.794957	−	0.667048i
$708$		0			0
$709$	−0.457077	−	0.166362i	−0.0171659	−	0.00624787i	0.333423	−	0.942777i	$-0.391796\pi$
$709$	−0.457077	−	0.166362i	−0.0171659	−	0.00624787i	−0.350589	+	0.936529i	$0.614019\pi$
$710$		0			0
$711$	32.6905	+	3.62865i	1.22599	+	0.136085i
$712$		0			0
$713$	3.70627	+	4.41696i	0.138801	+	0.165416i
$714$		0			0
$715$	−0.190320	−	0.0335586i	−0.00711758	−	0.00125502i
$716$		0			0
$717$	4.17103	+	19.9082i	0.155770	+	0.743486i
$718$		0			0
$719$	−0.125185	+	0.216826i	−0.00466860	+	0.00808625i	−0.868350	−	0.495951i	$-0.834819\pi$
$719$	−0.125185	+	0.216826i	−0.00466860	+	0.00808625i	0.863682	+	0.504038i	$0.168153\pi$
$720$		0			0
$721$	−19.7474	−	34.2034i	−0.735430	−	1.27380i
$722$		0			0
$723$	1.64542	−	0.0526593i	0.0611939	−	0.00195842i
$724$		0			0
$725$	16.3496	+	44.9201i	0.607209	+	1.66829i
$726$		0			0
$727$	43.3028	−	7.63546i	1.60601	−	0.283183i	0.702480	−	0.711703i	$-0.252076\pi$
$727$	43.3028	−	7.63546i	1.60601	−	0.283183i	0.903532	+	0.428520i	$0.140965\pi$
$728$		0			0
$729$	−17.7130	−	20.3777i	−0.656036	−	0.754730i
$730$		0			0
$731$	7.35264	+	41.6989i	0.271947	+	1.54229i
$732$		0			0
$733$	43.7876	−	15.9374i	1.61733	−	0.588661i	0.634462	−	0.772954i	$-0.281222\pi$
$733$	43.7876	−	15.9374i	1.61733	−	0.588661i	0.982871	+	0.184293i	$0.0589995\pi$
$734$		0			0
$735$	−0.00796113	−	0.248758i	−0.000293651	−	0.00917557i
$736$		0			0
$737$	−7.31564	+	4.22368i	−0.269475	+	0.155581i
$738$		0			0
$739$	15.8277	+	9.13810i	0.582230	+	0.336151i	0.762019	−	0.647555i	$-0.224208\pi$
$739$	15.8277	+	9.13810i	0.582230	+	0.336151i	−0.179789	+	0.983705i	$0.557542\pi$
$740$		0			0
$741$	75.7102	−	15.8622i	2.78128	−	0.582714i
$742$		0			0
$743$	2.75056	−	15.5992i	0.100908	−	0.572279i	−0.891868	−	0.452296i	$-0.850605\pi$
$743$	2.75056	−	15.5992i	0.100908	−	0.572279i	0.992776	−	0.119983i	$-0.0382839\pi$
$744$		0			0
$745$	0.192956	−	0.161909i	0.00706935	−	0.00593189i
$746$		0			0
$747$	−2.98697	+	26.9096i	−0.109287	+	0.984569i
$748$		0			0
$749$	−4.49836	+	12.3592i	−0.164367	+	0.451594i
$750$		0			0
$751$	8.56138	−	10.2031i	0.312409	−	0.372315i	−0.586876	−	0.809677i	$-0.699643\pi$
$751$	8.56138	−	10.2031i	0.312409	−	0.372315i	0.899286	+	0.437362i	$0.144087\pi$
$752$		0			0
$753$	−1.61789	+	0.648192i	−0.0589592	+	0.0236214i
$754$		0			0
$755$	−0.0392785			−0.00142949
$756$		0			0
$757$	23.8412			0.866522			0.433261	−	0.901268i	$-0.357363\pi$
$757$	23.8412			0.866522			0.433261	+	0.901268i	$0.357363\pi$
$758$		0			0
$759$	−1.95762	−	1.53867i	−0.0710571	−	0.0558501i
$760$		0			0
$761$	11.8416	−	14.1123i	0.429258	−	0.511570i	−0.507450	−	0.861681i	$-0.669412\pi$
$761$	11.8416	−	14.1123i	0.429258	−	0.511570i	0.936708	+	0.350112i	$0.113856\pi$
$762$		0			0
$763$	8.22211	−	22.5901i	0.297661	−	0.817816i
$764$		0			0
$765$	−0.472276	+	0.0302600i	−0.0170752	+	0.00109405i
$766$		0			0
$767$	57.5016	−	48.2496i	2.07626	−	1.74219i
$768$		0			0
$769$	−5.06075	+	28.7010i	−0.182495	+	1.03498i	0.746636	+	0.665233i	$0.231668\pi$
$769$	−5.06075	+	28.7010i	−0.182495	+	1.03498i	−0.929131	+	0.369750i	$0.879443\pi$
$770$		0			0
$771$	9.87219	−	30.0849i	0.355538	−	1.08348i
$772$		0			0
$773$	−38.3542	−	22.1438i	−1.37950	−	0.796457i	−0.387405	−	0.921910i	$-0.626629\pi$
$773$	−38.3542	−	22.1438i	−1.37950	−	0.796457i	−0.992100	+	0.125452i	$0.959962\pi$
$774$		0			0
$775$	−24.8883	+	14.3693i	−0.894015	+	0.516160i
$776$		0			0
$777$	−18.2069	+	11.3033i	−0.653170	+	0.405504i
$778$		0			0
$779$	50.5768	−	18.4085i	1.81210	−	0.659552i
$780$		0			0
$781$	0.101485	+	0.575550i	0.00363142	+	0.0205948i
$782$		0			0
$783$	12.4406	−	48.1011i	0.444590	−	1.71899i
$784$		0			0
$785$	−0.500523	+	0.0882557i	−0.0178644	+	0.00314998i
$786$		0			0
$787$	−8.76062	−	24.0696i	−0.312282	−	0.857989i	−0.992195	−	0.124696i	$-0.960205\pi$
$787$	−8.76062	−	24.0696i	−0.312282	−	0.857989i	0.679913	−	0.733293i	$-0.262018\pi$
$788$		0			0
$789$	−16.5244	+	30.8607i	−0.588285	+	1.09867i
$790$		0			0
$791$	−21.2683	−	36.8377i	−0.756213	−	1.30980i
$792$		0			0
$793$	−3.71599	+	6.43629i	−0.131959	+	0.228559i
$794$		0			0
$795$	−0.284896	+	0.255022i	−0.0101042	+	0.00904469i
$796$		0			0
$797$	24.6001	+	4.33767i	0.871381	+	0.153648i	0.591420	−	0.806363i	$-0.298567\pi$
$797$	24.6001	+	4.33767i	0.871381	+	0.153648i	0.279961	+	0.960011i	$0.409678\pi$
$798$		0			0
$799$	3.87992	+	4.62391i	0.137262	+	0.163582i
$800$		0			0
$801$	−3.74611	+	0.910853i	−0.132362	+	0.0321834i
$802$		0			0
$803$	7.53304	+	2.74180i	0.265835	+	0.0967561i
$804$		0			0
$805$	−0.0654220	−	0.0548955i	−0.00230582	−	0.00193481i
$806$		0			0
$807$	18.7459	+	2.69029i	0.659886	+	0.0947026i
$808$		0			0
$809$			37.1657i			1.30668i	0.757067	+	0.653338i	$0.226632\pi$
$809$			37.1657i			1.30668i	−0.757067	+	0.653338i	$0.773368\pi$
$810$		0			0
$811$			5.32739i			0.187070i	0.995616	+	0.0935350i	$0.0298167\pi$
$811$			5.32739i			0.187070i	−0.995616	+	0.0935350i	$0.970183\pi$
$812$		0			0
$813$	−7.90189	−	1.13403i	−0.277131	−	0.0397721i
$814$		0			0
$815$	0.280613	+	0.235463i	0.00982946	+	0.00824790i
$816$		0			0
$817$	−46.1886	−	16.8113i	−1.61593	−	0.588152i
$818$		0			0
$819$	−43.0112	−	45.0620i	−1.50293	−	1.57460i
$820$		0			0
$821$	−2.08922	−	2.48984i	−0.0729144	−	0.0868960i	0.728354	−	0.685201i	$-0.240286\pi$
$821$	−2.08922	−	2.48984i	−0.0729144	−	0.0868960i	−0.801269	+	0.598305i	$0.795841\pi$
$822$		0			0
$823$	21.5238	+	3.79524i	0.750274	+	0.132294i	0.535693	−	0.844413i	$-0.320050\pi$
$823$	21.5238	+	3.79524i	0.750274	+	0.132294i	0.214581	+	0.976706i	$0.431161\pi$
$824$		0			0
$825$	9.24685	−	8.27723i	0.321934	−	0.288176i
$826$		0			0
$827$	11.4506	−	19.8330i	0.398175	−	0.689660i	−0.595325	−	0.803485i	$-0.702977\pi$
$827$	11.4506	−	19.8330i	0.398175	−	0.689660i	0.993501	+	0.113825i	$0.0363102\pi$
$828$		0			0
$829$	7.02076	+	12.1603i	0.243841	+	0.422345i	0.961805	−	0.273735i	$-0.0882592\pi$
$829$	7.02076	+	12.1603i	0.243841	+	0.422345i	−0.717964	+	0.696080i	$0.754926\pi$
$830$		0			0
$831$	5.31519	−	9.92653i	0.184382	−	0.344347i
$832$		0			0
$833$	−14.0218	−	38.5246i	−0.485827	−	1.33480i
$834$		0			0
$835$	0.167444	−	0.0295248i	0.00579463	−	0.00102175i
$836$		0			0
$837$	29.7772	+	2.34397i	1.02925	+	0.0810196i
$838$		0			0
$839$	−3.24135	−	18.3826i	−0.111904	−	0.634637i	−0.988237	−	0.152932i	$-0.951129\pi$
$839$	−3.24135	−	18.3826i	−0.111904	−	0.634637i	0.876333	−	0.481706i	$-0.159983\pi$
$840$		0			0
$841$	58.6606	−	21.3507i	2.02278	−	0.736231i
$842$		0			0
$843$	15.1169	−	9.38492i	0.520652	−	0.323234i
$844$		0			0
$845$	−0.404957	+	0.233802i	−0.0139310	+	0.00804304i
$846$		0			0
$847$	28.0529	+	16.1963i	0.963908	+	0.556512i
$848$		0			0
$849$	−9.16101	+	27.9176i	−0.314405	+	0.958130i
$850$		0			0
$851$	−0.595176	+	3.37541i	−0.0204024	+	0.115708i
$852$		0			0
$853$	−14.3593	+	12.0489i	−0.491653	+	0.412546i	−0.854618	−	0.519257i	$-0.826209\pi$
$853$	−14.3593	+	12.0489i	−0.491653	+	0.412546i	0.362965	+	0.931803i	$0.381764\pi$
$854$		0			0
$855$	0.243700	−	0.492355i	0.00833435	−	0.0168382i
$856$		0			0
$857$	0.0248203	−	0.0681931i	0.000847844	−	0.00232943i	−0.939268	−	0.343185i	$-0.888494\pi$
$857$	0.0248203	−	0.0681931i	0.000847844	−	0.00232943i	0.940116	+	0.340855i	$0.110717\pi$
$858$		0			0
$859$	−19.4506	+	23.1803i	−0.663646	+	0.790903i	−0.987904	−	0.155066i	$-0.950441\pi$
$859$	−19.4506	+	23.1803i	−0.663646	+	0.790903i	0.324258	+	0.945969i	$0.394885\pi$
$860$		0			0
$861$	−34.0777	−	26.7847i	−1.16136	−	0.912820i
$862$		0			0
$863$	−41.0698			−1.39803			−0.699017	−	0.715106i	$-0.746379\pi$
$863$	−41.0698			−1.39803			−0.699017	+	0.715106i	$0.746379\pi$
$864$		0			0
$865$	0.0342463			0.00116441
$866$		0			0
$867$	−45.0296	+	18.0407i	−1.52929	+	0.612694i
$868$		0			0
$869$	10.1002	−	12.0369i	0.342625	−	0.408324i
$870$		0			0
$871$	−11.5606	+	31.7624i	−0.391715	+	1.07623i
$872$		0			0
$873$	10.7973	−	4.73207i	0.365434	−	0.160156i
$874$		0			0
$875$	0.652189	−	0.547251i	0.0220480	−	0.0185005i
$876$		0			0
$877$	6.05760	−	34.3544i	0.204551	−	1.16006i	−0.693594	−	0.720366i	$-0.743974\pi$
$877$	6.05760	−	34.3544i	0.204551	−	1.16006i	0.898145	−	0.439699i	$-0.144915\pi$
$878$		0			0
$879$	46.3252	−	9.70572i	1.56251	−	0.327366i
$880$		0			0
$881$	14.7219	+	8.49967i	0.495992	+	0.286361i	0.727057	−	0.686577i	$-0.240888\pi$
$881$	14.7219	+	8.49967i	0.495992	+	0.286361i	−0.231065	+	0.972938i	$0.574221\pi$
$882$		0			0
$883$	28.6510	−	16.5417i	0.964184	−	0.556672i	0.0667257	−	0.997771i	$-0.478745\pi$
$883$	28.6510	−	16.5417i	0.964184	−	0.556672i	0.897458	+	0.441100i	$0.145411\pi$
$884$		0			0
$885$	−0.0170522	−	0.532822i	−0.000573203	−	0.0179106i
$886$		0			0
$887$	0.350679	−	0.127637i	0.0117747	−	0.00428563i	−0.336126	−	0.941817i	$-0.609117\pi$
$887$	0.350679	−	0.127637i	0.0117747	−	0.00428563i	0.347901	+	0.937531i	$0.386895\pi$
$888$		0			0
$889$	−7.42627	−	42.1165i	−0.249069	−	1.41254i
$890$		0			0
$891$	−12.7932	+	1.64614i	−0.428587	+	0.0551478i
$892$		0			0
$893$	−6.90054	+	1.21675i	−0.230918	+	0.0407170i
$894$		0			0
$895$	0.00101918	+	0.00280017i	3.40674e−5	+	9.35994e-5i
$896$		0			0
$897$	−9.95799	+	0.318691i	−0.332488	+	0.0106408i
$898$		0			0
$899$	27.4819	+	47.6000i	0.916571	+	1.58755i
$900$		0			0
$901$	−31.4919	+	54.5456i	−1.04915	+	1.81718i
$902$		0			0
$903$	8.11699	+	38.7422i	0.270116	+	1.28926i
$904$		0			0
$905$	−0.0351290	−	0.00619419i	−0.00116773	−	0.000205902i
$906$		0			0
$907$	17.5449	+	20.9092i	0.582569	+	0.694279i	0.974160	−	0.225861i	$-0.0725195\pi$
$907$	17.5449	+	20.9092i	0.582569	+	0.694279i	−0.391591	+	0.920140i	$0.628075\pi$
$908$		0			0
$909$	−13.5451	+	18.4166i	−0.449264	+	0.610841i
$910$		0			0
$911$	13.0043	+	4.73319i	0.430853	+	0.156818i	0.548337	−	0.836257i	$-0.315261\pi$
$911$	13.0043	+	4.73319i	0.430853	+	0.156818i	−0.117485	+	0.993075i	$0.537483\pi$
$912$		0			0
$913$	9.90832	+	8.31406i	0.327917	+	0.275155i
$914$		0			0
$915$	0.0196297	+	0.0489957i	0.000648937	+	0.00161975i
$916$		0			0
$917$		−	28.3797i		−	0.937181i
$918$		0			0
$919$		−	19.8960i		−	0.656308i	−0.944624	−	0.328154i	$-0.893574\pi$
$919$		−	19.8960i		−	0.656308i	0.944624	−	0.328154i	$-0.106426\pi$
$920$		0			0
$921$	−1.14493	+	1.45667i	−0.0377266	+	0.0479989i
$922$		0			0
$923$	1.79139	+	1.50316i	0.0589645	+	0.0494771i
$924$		0			0
$925$	−16.0530	−	5.84283i	−0.527820	−	0.192111i
$926$		0			0
$927$	−27.2341	+	18.1396i	−0.894485	+	0.595783i
$928$		0			0
$929$	−8.54750	−	10.1865i	−0.280435	−	0.334209i	0.607379	−	0.794412i	$-0.292221\pi$
$929$	−8.54750	−	10.1865i	−0.280435	−	0.334209i	−0.887814	+	0.460203i	$0.847776\pi$
$930$		0			0
$931$	46.8683	+	8.26415i	1.53605	+	0.270847i
$932$		0			0
$933$	55.5669	+	18.2340i	1.81918	+	0.596954i
$934$		0			0
$935$	−0.113041	+	0.195793i	−0.00369683	+	0.00640310i
$936$		0			0
$937$	5.48666	+	9.50317i	0.179241	+	0.310455i	0.941621	−	0.336675i	$-0.109302\pi$
$937$	5.48666	+	9.50317i	0.179241	+	0.310455i	−0.762380	+	0.647130i	$0.775969\pi$
$938$		0			0
$939$	2.55406	+	4.11397i	0.0833485	+	0.134254i
$940$		0			0
$941$	5.86888	+	16.1246i	0.191320	+	0.525647i	0.997850	−	0.0655466i	$-0.0208791\pi$
$941$	5.86888	+	16.1246i	0.191320	+	0.525647i	−0.806530	+	0.591194i	$0.798657\pi$
$942$		0			0
$943$	−6.82698	+	1.20378i	−0.222317	+	0.0392005i
$944$		0			0
$945$	−0.440374	+	0.0423964i	−0.0143254	+	0.00137916i
$946$		0			0
$947$	1.51077	+	8.56799i	0.0490934	+	0.278422i	0.999465	−	0.0326933i	$-0.0104085\pi$
$947$	1.51077	+	8.56799i	0.0490934	+	0.278422i	−0.950372	+	0.311116i	$0.899297\pi$
$948$		0			0
$949$	30.1423	−	10.9709i	0.978460	−	0.356130i
$950$		0			0
$951$	30.7934	+	16.4884i	0.998543	+	0.534673i
$952$		0			0
$953$	−25.0470	+	14.4609i	−0.811353	+	0.468435i	−0.847425	−	0.530914i	$-0.821849\pi$
$953$	−25.0470	+	14.4609i	−0.811353	+	0.468435i	0.0360727	+	0.999349i	$0.488515\pi$
$954$		0			0
$955$	0.496445	+	0.286623i	0.0160646	+	0.00927490i
$956$		0			0
$957$	−15.8306	−	17.6850i	−0.511730	−	0.571675i
$958$		0			0
$959$	1.09616	−	6.21665i	0.0353970	−	0.200746i
$960$		0			0
$961$	−1.56540	+	1.31353i	−0.0504969	+	0.0423720i
$962$		0			0
$963$	10.4572	+	3.06461i	0.336977	+	0.0987557i
$964$		0			0
$965$	−0.163331	+	0.448747i	−0.00525780	+	0.0144457i
$966$		0			0
$967$	−31.7268	+	37.8106i	−1.02027	+	1.21591i	−0.0440676	+	0.999029i	$0.514032\pi$
$967$	−31.7268	+	37.8106i	−1.02027	+	1.21591i	−0.976199	+	0.216878i	$0.930413\pi$
$968$		0			0
$969$	12.8552	−	89.5751i	0.412970	−	2.87757i
$970$		0			0
$971$	−39.9179			−1.28103			−0.640514	−	0.767947i	$-0.721279\pi$
$971$	−39.9179			−1.28103			−0.640514	+	0.767947i	$0.721279\pi$
$972$		0			0
$973$	−24.1287			−0.773530
$974$		0			0
$975$	7.05433	−	49.1545i	0.225920	−	1.57420i
$976$		0			0
$977$	27.6131	−	32.9080i	0.883420	−	1.05282i	−0.114812	−	0.993387i	$-0.536627\pi$
$977$	27.6131	−	32.9080i	0.883420	−	1.05282i	0.998232	−	0.0594316i	$-0.0189288\pi$
$978$		0			0
$979$	−0.629919	+	1.73069i	−0.0201323	+	0.0553130i
$980$		0			0
$981$	−19.1136	−	5.60150i	−0.610251	−	0.178842i
$982$		0			0
$983$	−35.3768	+	29.6846i	−1.12834	+	0.946793i	−0.998996	−	0.0448067i	$-0.985733\pi$
$983$	−35.3768	+	29.6846i	−1.12834	+	0.946793i	−0.129348	+	0.991599i	$0.541288\pi$
$984$		0			0
$985$	0.0658298	−	0.373339i	0.00209751	−	0.0118956i
$986$		0			0
$987$	3.76354	+	4.20441i	0.119795	+	0.133828i
$988$		0			0
$989$	5.48266	+	3.16541i	0.174338	+	0.100654i
$990$		0			0
$991$	35.0809	−	20.2540i	1.11438	−	0.643388i	0.174421	−	0.984671i	$-0.444195\pi$
$991$	35.0809	−	20.2540i	1.11438	−	0.643388i	0.939961	+	0.341283i	$0.110861\pi$
$992$		0			0
$993$	−13.8170	−	7.39835i	−0.438469	−	0.234780i
$994$		0			0
$995$	0.0901650	−	0.0328174i	0.00285842	−	0.00104038i
$996$		0			0
$997$	4.18028	+	23.7075i	0.132391	+	0.750825i	0.976641	+	0.214876i	$0.0689348\pi$
$997$	4.18028	+	23.7075i	0.132391	+	0.750825i	−0.844251	+	0.535949i	$0.819954\pi$
$998$		0			0
$999$	10.3104	+	14.4551i	0.326207	+	0.457340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.95.16	✓	216
4.3	odd	2	inner	864.2.bi.a.95.21	yes	216
27.2	odd	18	inner	864.2.bi.a.191.21	yes	216
108.83	even	18	inner	864.2.bi.a.191.16	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.95.16	✓	216	1.1	even	1	trivial
864.2.bi.a.95.21	yes	216	4.3	odd	2	inner
864.2.bi.a.191.16	yes	216	108.83	even	18	inner
864.2.bi.a.191.21	yes	216	27.2	odd	18	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.246052 + 1.71448i) q^{3} +(0.0151145 - 0.0180127i) q^{5} +(1.23843 - 3.40255i) q^{7} +(-2.87892 - 0.843705i) q^{9} +O(q^{10})\)	\(q+(-0.246052 + 1.71448i) q^{3} +(0.0151145 - 0.0180127i) q^{5} +(1.23843 - 3.40255i) q^{7} +(-2.87892 - 0.843705i) q^{9} +(-1.09788 + 0.921232i) q^{11} +(-0.995812 + 5.64753i) q^{13} +(0.0271636 + 0.0303456i) q^{15} +(5.80991 + 3.35435i) q^{17} +(-6.74443 + 3.89390i) q^{19} +(5.52890 + 2.96046i) q^{21} +(0.942566 - 0.343066i) q^{23} +(0.868145 + 4.92349i) q^{25} +(2.15488 - 4.72826i) q^{27} +(9.41639 - 1.66036i) q^{29} +(1.96605 + 5.40168i) q^{31} +(-1.30930 - 2.10897i) q^{33} +(-0.0425710 - 0.0737351i) q^{35} +(-1.70852 + 2.95924i) q^{37} +(-9.43759 - 3.09689i) q^{39} +(-6.80617 - 1.20011i) q^{41} +(4.05697 + 4.83491i) q^{43} +(-0.0587107 + 0.0391050i) q^{45} +(0.845478 + 0.307729i) q^{47} +(-4.68131 - 3.92808i) q^{49} +(-7.18053 + 9.13566i) q^{51} +9.38837i q^{53} +0.0336998i q^{55} +(-5.01655 - 12.5213i) q^{57} +(-10.0270 - 8.41368i) q^{59} +(1.21782 + 0.443250i) q^{61} +(-6.43607 + 8.75078i) q^{63} +(0.0866763 + 0.103297i) q^{65} +(5.80459 + 1.02351i) q^{67} +(0.356261 + 1.70043i) q^{69} +(0.203892 - 0.353151i) q^{71} +(-2.79675 - 4.84411i) q^{73} +(-8.65487 + 0.276986i) q^{75} +(1.77489 + 4.87647i) q^{77} +(-10.7972 + 1.90384i) q^{79} +(7.57633 + 4.85791i) q^{81} +(-1.56717 - 8.88783i) q^{83} +(0.148235 - 0.0539530i) q^{85} +(0.529748 + 16.5528i) q^{87} +(1.11291 - 0.642542i) q^{89} +(17.9827 + 10.3823i) q^{91} +(-9.74485 + 2.04167i) q^{93} +(-0.0317988 + 0.180340i) q^{95} +(-3.01023 + 2.52588i) q^{97} +(3.93796 - 1.72586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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