LMFDB - Embedded newform 864.2.bh.b.47.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(47,864)]

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, 9, 7]))

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

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

chi := DirichletCharacter("864.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bh (of order $18$, degree $6$, not 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:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.11
Character	$\chi$	$=$	864.47
Dual form			864.2.bh.b.239.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.608611 - 1.62160i) q^{3} +(-0.398052 - 2.25746i) q^{5} +(-0.655732 + 0.781471i) q^{7} +(-2.25918 + 1.97385i) q^{9} +O(q^{10})$	\(q+(-0.608611 - 1.62160i) q^{3} +(-0.398052 - 2.25746i) q^{5} +(-0.655732 + 0.781471i) q^{7} +(-2.25918 + 1.97385i) q^{9} +(-2.26514 - 0.399405i) q^{11} +(-1.76237 + 4.84208i) q^{13} +(-3.41845 + 2.01940i) q^{15} +(-3.17019 + 1.83031i) q^{17} +(2.84684 - 4.93086i) q^{19} +(1.66632 + 0.587724i) q^{21} +(-3.84409 + 3.22558i) q^{23} +(-0.239232 + 0.0870733i) q^{25} +(4.57576 + 2.46219i) q^{27} +(-5.56385 + 2.02508i) q^{29} +(2.75110 + 3.27864i) q^{31} +(0.730913 + 3.91623i) q^{33} +(2.02516 + 1.16923i) q^{35} +(-1.87388 + 1.08189i) q^{37} +(8.92452 - 0.0890776i) q^{39} +(4.01923 - 11.0427i) q^{41} +(-0.311848 + 1.76858i) q^{43} +(5.35517 + 4.31433i) q^{45} +(2.74155 + 2.30043i) q^{47} +(1.03482 + 5.86878i) q^{49} +(4.89745 + 4.02684i) q^{51} +3.86392 q^{53} +5.27245i q^{55} +(-9.72851 - 1.61545i) q^{57} +(-9.59630 + 1.69209i) q^{59} +(-8.86954 + 10.5703i) q^{61} +(-0.0610873 - 3.05981i) q^{63} +(11.6323 + 2.05109i) q^{65} +(-12.1912 - 4.43722i) q^{67} +(7.57016 + 4.27046i) q^{69} +(-5.23407 - 9.06567i) q^{71} +(-0.953385 + 1.65131i) q^{73} +(0.286797 + 0.334945i) q^{75} +(1.79745 - 1.50824i) q^{77} +(3.04001 + 8.35237i) q^{79} +(1.20783 - 8.91858i) q^{81} +(1.15723 + 3.17946i) q^{83} +(5.39376 + 6.42804i) q^{85} +(6.67009 + 7.78987i) q^{87} +(-3.39099 - 1.95779i) q^{89} +(-2.62830 - 4.55235i) q^{91} +(3.64229 - 6.45661i) q^{93} +(-12.2644 - 4.46389i) q^{95} +(0.0624115 - 0.353953i) q^{97} +(5.90573 - 3.56871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) $ 192 * q + 12 * q^3 - 12 * q^9	$ 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) $ 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$-1$

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
$3$	−0.608611	−	1.62160i	−0.351382	−	0.936232i
$3$	−0.608611	−	1.62160i	−0.351382	−	0.936232i
$4$		0			0
$5$	−0.398052	−	2.25746i	−0.178014	−	1.00957i	−0.934607	−	0.355682i	$-0.884249\pi$
$5$	−0.398052	−	2.25746i	−0.178014	−	1.00957i	0.756593	−	0.653886i	$-0.226863\pi$
$6$		0			0
$7$	−0.655732	+	0.781471i	−0.247844	+	0.295368i	−0.875596	−	0.483045i	$-0.839531\pi$
$7$	−0.655732	+	0.781471i	−0.247844	+	0.295368i	0.627752	+	0.778413i	$0.283975\pi$
$8$		0			0
$9$	−2.25918	+	1.97385i	−0.753061	+	0.657950i
$10$		0			0
$11$	−2.26514	−	0.399405i	−0.682965	−	0.120425i	−0.178608	−	0.983920i	$-0.557159\pi$
$11$	−2.26514	−	0.399405i	−0.682965	−	0.120425i	−0.504357	+	0.863495i	$0.668270\pi$
$12$		0			0
$13$	−1.76237	+	4.84208i	−0.488794	+	1.34295i	0.412979	+	0.910741i	$0.364488\pi$
$13$	−1.76237	+	4.84208i	−0.488794	+	1.34295i	−0.901773	+	0.432210i	$0.857734\pi$
$14$		0			0
$15$	−3.41845	+	2.01940i	−0.882639	+	0.521407i
$16$		0			0
$17$	−3.17019	+	1.83031i	−0.768885	+	0.443916i	−0.832477	−	0.554060i	$-0.813078\pi$
$17$	−3.17019	+	1.83031i	−0.768885	+	0.443916i	0.0635917	+	0.997976i	$0.479744\pi$
$18$		0			0
$19$	2.84684	−	4.93086i	0.653109	−	1.13122i	−0.329255	−	0.944241i	$-0.606798\pi$
$19$	2.84684	−	4.93086i	0.653109	−	1.13122i	0.982364	−	0.186977i	$-0.0598690\pi$
$20$		0			0
$21$	1.66632	+	0.587724i	0.363621	+	0.128252i
$22$		0			0
$23$	−3.84409	+	3.22558i	−0.801548	+	0.672579i	−0.948575	−	0.316554i	$-0.897474\pi$
$23$	−3.84409	+	3.22558i	−0.801548	+	0.672579i	0.147026	+	0.989133i	$0.453030\pi$
$24$		0			0
$25$	−0.239232	+	0.0870733i	−0.0478464	+	0.0174147i
$26$		0			0
$27$	4.57576	+	2.46219i	0.880606	+	0.473849i
$28$		0			0
$29$	−5.56385	+	2.02508i	−1.03318	+	0.376047i	−0.802291	−	0.596932i	$-0.796386\pi$
$29$	−5.56385	+	2.02508i	−1.03318	+	0.376047i	−0.230890	+	0.972980i	$0.574164\pi$
$30$		0			0
$31$	2.75110	+	3.27864i	0.494113	+	0.588861i	0.954258	−	0.298983i	$-0.0966473\pi$
$31$	2.75110	+	3.27864i	0.494113	+	0.588861i	−0.460146	+	0.887843i	$0.652203\pi$
$32$		0			0
$33$	0.730913	+	3.91623i	0.127236	+	0.681729i
$34$		0			0
$35$	2.02516	+	1.16923i	0.342314	+	0.197635i
$36$		0			0
$37$	−1.87388	+	1.08189i	−0.308065	+	0.177861i	−0.646060	−	0.763287i	$-0.723584\pi$
$37$	−1.87388	+	1.08189i	−0.308065	+	0.177861i	0.337995	+	0.941148i	$0.390251\pi$
$38$		0			0
$39$	8.92452	−	0.0890776i	1.42907	−	0.0142638i
$40$		0			0
$41$	4.01923	−	11.0427i	0.627698	−	1.72459i	−0.0596112	−	0.998222i	$-0.518986\pi$
$41$	4.01923	−	11.0427i	0.627698	−	1.72459i	0.687309	−	0.726365i	$-0.258792\pi$
$42$		0			0
$43$	−0.311848	+	1.76858i	−0.0475564	+	0.269706i	−0.999309	−	0.0371595i	$-0.988169\pi$
$43$	−0.311848	+	1.76858i	−0.0475564	+	0.269706i	0.951753	+	0.306865i	$0.0992801\pi$
$44$		0			0
$45$	5.35517	+	4.31433i	0.798301	+	0.643143i
$46$		0			0
$47$	2.74155	+	2.30043i	0.399896	+	0.335552i	0.820453	−	0.571713i	$-0.193721\pi$
$47$	2.74155	+	2.30043i	0.399896	+	0.335552i	−0.420558	+	0.907266i	$0.638166\pi$
$48$		0			0
$49$	1.03482	+	5.86878i	0.147832	+	0.838397i
$50$		0			0
$51$	4.89745	+	4.02684i	0.685781	+	0.563871i
$52$		0			0
$53$	3.86392			0.530750			0.265375	−	0.964145i	$-0.414504\pi$
$53$	3.86392			0.530750			0.265375	+	0.964145i	$0.414504\pi$
$54$		0			0
$55$			5.27245i			0.710937i
$56$		0			0
$57$	−9.72851	−	1.61545i	−1.28857	−	0.213972i
$58$		0			0
$59$	−9.59630	+	1.69209i	−1.24933	+	0.220291i	−0.758911	−	0.651195i	$-0.774268\pi$
$59$	−9.59630	+	1.69209i	−1.24933	+	0.220291i	−0.490421	+	0.871486i	$0.663157\pi$
$60$		0			0
$61$	−8.86954	+	10.5703i	−1.13563	+	1.35339i	−0.208776	+	0.977963i	$0.566948\pi$
$61$	−8.86954	+	10.5703i	−1.13563	+	1.35339i	−0.926852	+	0.375426i	$0.877496\pi$
$62$		0			0
$63$	−0.0610873	−	3.05981i	−0.00769627	−	0.385499i
$64$		0			0
$65$	11.6323	+	2.05109i	1.44281	+	0.254407i
$66$		0			0
$67$	−12.1912	−	4.43722i	−1.48939	−	0.542093i	−0.536099	−	0.844155i	$-0.680103\pi$
$67$	−12.1912	−	4.43722i	−1.48939	−	0.542093i	−0.953288	+	0.302062i	$0.902325\pi$
$68$		0			0
$69$	7.57016	+	4.27046i	0.911340	+	0.514103i
$70$		0			0
$71$	−5.23407	−	9.06567i	−0.621170	−	1.07590i	−0.989268	−	0.146110i	$-0.953324\pi$
$71$	−5.23407	−	9.06567i	−0.621170	−	1.07590i	0.368099	−	0.929787i	$-0.380009\pi$
$72$		0			0
$73$	−0.953385	+	1.65131i	−0.111585	+	0.193271i	−0.916410	−	0.400242i	$-0.868926\pi$
$73$	−0.953385	+	1.65131i	−0.111585	+	0.193271i	0.804824	+	0.593513i	$0.202259\pi$
$74$		0			0
$75$	0.286797	+	0.334945i	0.0331165	+	0.0386761i
$76$		0			0
$77$	1.79745	−	1.50824i	0.204838	−	0.171880i
$78$		0			0
$79$	3.04001	+	8.35237i	0.342028	+	0.939715i	0.984805	+	0.173662i	$0.0555600\pi$
$79$	3.04001	+	8.35237i	0.342028	+	0.939715i	−0.642777	+	0.766053i	$0.722218\pi$
$80$		0			0
$81$	1.20783	−	8.91858i	0.134203	−	0.990954i
$82$		0			0
$83$	1.15723	+	3.17946i	0.127022	+	0.348991i	0.986860	−	0.161576i	$-0.0516578\pi$
$83$	1.15723	+	3.17946i	0.127022	+	0.348991i	−0.859838	+	0.510567i	$0.829436\pi$
$84$		0			0
$85$	5.39376	+	6.42804i	0.585036	+	0.697219i
$86$		0			0
$87$	6.67009	+	7.78987i	0.715109	+	0.835162i
$88$		0			0
$89$	−3.39099	−	1.95779i	−0.359445	−	0.207526i	0.309392	−	0.950934i	$-0.399874\pi$
$89$	−3.39099	−	1.95779i	−0.359445	−	0.207526i	−0.668837	+	0.743409i	$0.733208\pi$
$90$		0			0
$91$	−2.62830	−	4.55235i	−0.275521	−	0.477216i
$92$		0			0
$93$	3.64229	−	6.45661i	0.377688	−	0.669519i
$94$		0			0
$95$	−12.2644	−	4.46389i	−1.25830	−	0.457985i
$96$		0			0
$97$	0.0624115	−	0.353953i	0.00633693	−	0.0359385i	−0.981475	−	0.191589i	$-0.938636\pi$
$97$	0.0624115	−	0.353953i	0.00633693	−	0.0359385i	0.987812	+	0.155650i	$0.0497472\pi$
$98$		0			0
$99$	5.90573	−	3.56871i	0.593548	−	0.358669i
$100$		0			0
$101$	−2.40504	−	2.01807i	−0.239310	−	0.200805i	0.515243	−	0.857044i	$-0.327702\pi$
$101$	−2.40504	−	2.01807i	−0.239310	−	0.200805i	−0.754553	+	0.656239i	$0.772146\pi$
$102$		0			0
$103$	−9.20855	+	1.62372i	−0.907346	+	0.159990i	−0.607798	−	0.794092i	$-0.707947\pi$
$103$	−9.20855	+	1.62372i	−0.907346	+	0.159990i	−0.299548	+	0.954081i	$0.596836\pi$
$104$		0			0
$105$	0.663484	−	3.99560i	0.0647494	−	0.389931i
$106$		0			0
$107$			6.72552i			0.650181i	0.945683	+	0.325090i	$0.105395\pi$
$107$			6.72552i			0.650181i	−0.945683	+	0.325090i	$0.894605\pi$
$108$		0			0
$109$		−	9.28279i		−	0.889130i	−0.895747	−	0.444565i	$-0.853358\pi$
$109$		−	9.28279i		−	0.889130i	0.895747	−	0.444565i	$-0.146642\pi$
$110$		0			0
$111$	2.89486	+	2.38025i	0.274768	+	0.225923i
$112$		0			0
$113$	−0.445994	+	0.0786407i	−0.0419555	+	0.00739789i	−0.194587	−	0.980885i	$-0.562337\pi$
$113$	−0.445994	+	0.0786407i	−0.0419555	+	0.00739789i	0.152631	+	0.988283i	$0.451225\pi$
$114$		0			0
$115$	8.81177	+	7.39395i	0.821701	+	0.689489i
$116$		0			0
$117$	−5.57601	−	14.4178i	−0.515502	−	1.33293i
$118$		0			0
$119$	0.648462	−	3.67761i	0.0594444	−	0.337126i
$120$		0			0
$121$	−5.36529	−	1.95281i	−0.487754	−	0.177528i
$122$		0			0
$123$	−20.3531	+	0.203149i	−1.83518	+	0.0183173i
$124$		0			0
$125$	−5.43893	−	9.42050i	−0.486473	−	0.842595i
$126$		0			0
$127$	2.33880	+	1.35030i	0.207535	+	0.119820i	0.600165	−	0.799876i	$-0.295102\pi$
$127$	2.33880	+	1.35030i	0.207535	+	0.119820i	−0.392631	+	0.919696i	$0.628435\pi$
$128$		0			0
$129$	3.05773	−	0.570684i	0.269218	−	0.0502459i
$130$		0			0
$131$	5.38585	+	6.41861i	0.470564	+	0.560797i	0.948164	−	0.317781i	$-0.102938\pi$
$131$	5.38585	+	6.41861i	0.470564	+	0.560797i	−0.477600	+	0.878577i	$0.658493\pi$
$132$		0			0
$133$	1.98657	+	5.45805i	0.172257	+	0.473273i
$134$		0			0
$135$	3.73691	−	11.3097i	0.321622	−	0.973384i
$136$		0			0
$137$	1.05558	+	2.90018i	0.0901843	+	0.247779i	0.976582	−	0.215145i	$-0.0690224\pi$
$137$	1.05558	+	2.90018i	0.0901843	+	0.247779i	−0.886398	+	0.462924i	$0.846800\pi$
$138$		0			0
$139$	−6.25108	+	5.24528i	−0.530210	+	0.444899i	−0.868174	−	0.496260i	$-0.834706\pi$
$139$	−6.25108	+	5.24528i	−0.530210	+	0.444899i	0.337964	+	0.941159i	$0.390262\pi$
$140$		0			0
$141$	2.06185	−	5.84577i	0.173639	−	0.492302i
$142$		0			0
$143$	5.92596	−	10.2641i	0.495554	−	0.858325i
$144$		0			0
$145$	6.78624	+	11.7541i	0.563566	+	0.976126i
$146$		0			0
$147$	8.88702	−	5.24988i	0.732989	−	0.433003i
$148$		0			0
$149$	−17.1000	−	6.22387i	−1.40088	−	0.509880i	−0.472443	−	0.881361i	$-0.656628\pi$
$149$	−17.1000	−	6.22387i	−1.40088	−	0.509880i	−0.928440	+	0.371482i	$0.878850\pi$
$150$		0			0
$151$	−23.1361	−	4.07953i	−1.88279	−	0.331987i	−0.890408	−	0.455163i	$-0.849581\pi$
$151$	−23.1361	−	4.07953i	−1.88279	−	0.331987i	−0.992385	+	0.123176i	$0.960692\pi$
$152$		0			0
$153$	3.54929	−	10.3925i	0.286943	−	0.840184i
$154$		0			0
$155$	6.30632	−	7.51558i	0.506536	−	0.603666i
$156$		0			0
$157$	22.8321	−	4.02592i	1.82220	−	0.321303i	0.845187	−	0.534471i	$-0.179489\pi$
$157$	22.8321	−	4.02592i	1.82220	−	0.321303i	0.977016	+	0.213168i	$0.0683781\pi$
$158$		0			0
$159$	−2.35163	−	6.26574i	−0.186496	−	0.496906i
$160$		0			0
$161$		−	5.11916i		−	0.403446i
$162$		0			0
$163$	−5.02882			−0.393887			−0.196944	−	0.980415i	$-0.563102\pi$
$163$	−5.02882			−0.393887			−0.196944	+	0.980415i	$0.563102\pi$
$164$		0			0
$165$	8.54981	−	3.20887i	0.665602	−	0.249810i
$166$		0			0
$167$	−3.26193	−	18.4993i	−0.252415	−	1.43152i	−0.802621	−	0.596490i	$-0.796562\pi$
$167$	−3.26193	−	18.4993i	−0.252415	−	1.43152i	0.550205	−	0.835030i	$-0.314550\pi$
$168$		0			0
$169$	−10.3812	−	8.71084i	−0.798552	−	0.670064i
$170$		0			0
$171$	3.30126	+	16.7590i	0.252454	+	1.28159i
$172$		0			0
$173$	−2.72791	+	15.4708i	−0.207400	+	1.17622i	0.686219	+	0.727395i	$0.259269\pi$
$173$	−2.72791	+	15.4708i	−0.207400	+	1.17622i	−0.893619	+	0.448826i	$0.851842\pi$
$174$		0			0
$175$	0.0888268	−	0.244050i	0.00671467	−	0.0184484i
$176$		0			0
$177$	8.58431	+	14.5316i	0.645236	+	1.09226i
$178$		0			0
$179$	21.3312	−	12.3156i	1.59437	−	0.920508i	0.601821	−	0.798631i	$-0.294442\pi$
$179$	21.3312	−	12.3156i	1.59437	−	0.920508i	0.992545	−	0.121877i	$-0.0388913\pi$
$180$		0			0
$181$	−7.76298	−	4.48196i	−0.577018	−	0.333142i	0.182929	−	0.983126i	$-0.441442\pi$
$181$	−7.76298	−	4.48196i	−0.577018	−	0.333142i	−0.759947	+	0.649985i	$0.774775\pi$
$182$		0			0
$183$	22.5389	+	7.94966i	1.66613	+	0.587655i
$184$		0			0
$185$	3.18822	+	3.79958i	0.234403	+	0.279351i
$186$		0			0
$187$	7.91196	−	2.87972i	0.578580	−	0.210586i
$188$		0			0
$189$	−4.92461	+	1.96129i	−0.358212	+	0.142663i
$190$		0			0
$191$	−4.37135	+	1.59104i	−0.316300	+	0.115124i	−0.495292	−	0.868727i	$-0.664939\pi$
$191$	−4.37135	+	1.59104i	−0.316300	+	0.115124i	0.178992	+	0.983851i	$0.442717\pi$
$192$		0			0
$193$	16.5086	−	13.8524i	1.18832	−	0.997117i	0.188431	−	0.982086i	$-0.439660\pi$
$193$	16.5086	−	13.8524i	1.18832	−	0.997117i	0.999887	−	0.0150310i	$-0.00478471\pi$
$194$		0			0
$195$	−3.75351	−	20.1113i	−0.268794	−	1.44020i
$196$		0			0
$197$	7.16801	−	12.4153i	0.510699	−	0.884557i	−0.489224	−	0.872158i	$-0.662720\pi$
$197$	7.16801	−	12.4153i	0.510699	−	0.884557i	0.999923	−	0.0123988i	$-0.00394676\pi$
$198$		0			0
$199$	5.83426	−	3.36841i	0.413580	−	0.238781i	−0.278747	−	0.960365i	$-0.589919\pi$
$199$	5.83426	−	3.36841i	0.413580	−	0.238781i	0.692327	+	0.721584i	$0.256586\pi$
$200$		0			0
$201$	0.224276	+	22.4698i	0.0158192	+	1.58489i
$202$		0			0
$203$	2.06586	−	5.67590i	0.144995	−	0.398370i
$204$		0			0
$205$	−26.5284	−	4.67768i	−1.85283	−	0.326703i
$206$		0			0
$207$	2.31771	−	14.8748i	0.161092	−	1.03387i
$208$		0			0
$209$	−8.41789	+	10.0320i	−0.582278	+	0.693931i
$210$		0			0
$211$	0.713133	+	4.04438i	0.0490941	+	0.278427i	0.999466	−	0.0326911i	$-0.0104078\pi$
$211$	0.713133	+	4.04438i	0.0490941	+	0.278427i	−0.950371	+	0.311118i	$0.899297\pi$
$212$		0			0
$213$	−11.5154	+	14.0050i	−0.789022	+	0.959610i
$214$		0			0
$215$	4.11663			0.280752
$216$		0			0
$217$	−4.36615			−0.296393
$218$		0			0
$219$	3.25801	+	0.541004i	0.220156	+	0.0365577i
$220$		0			0
$221$	−3.27545	−	18.5760i	−0.220331	−	1.24956i
$222$		0			0
$223$	0.584747	−	0.696875i	0.0391576	−	0.0466662i	−0.746110	−	0.665822i	$-0.768081\pi$
$223$	0.584747	−	0.696875i	0.0391576	−	0.0466662i	0.785268	+	0.619156i	$0.212525\pi$
$224$		0			0
$225$	0.368599	−	0.668923i	0.0245733	−	0.0445948i
$226$		0			0
$227$	−12.6025	−	2.22216i	−0.836457	−	0.147490i	−0.261017	−	0.965334i	$-0.584058\pi$
$227$	−12.6025	−	2.22216i	−0.836457	−	0.147490i	−0.575440	+	0.817844i	$0.695169\pi$
$228$		0			0
$229$	−6.54665	+	17.9868i	−0.432615	+	1.18860i	0.511587	+	0.859231i	$0.329058\pi$
$229$	−6.54665	+	17.9868i	−0.432615	+	1.18860i	−0.944202	+	0.329368i	$0.893164\pi$
$230$		0			0
$231$	−3.53971	−	1.99681i	−0.232896	−	0.131381i
$232$		0			0
$233$	−22.5612	+	13.0257i	−1.47804	+	0.853344i	−0.999692	−	0.0248287i	$-0.992096\pi$
$233$	−22.5612	+	13.0257i	−1.47804	+	0.853344i	−0.478344	+	0.878173i	$0.658763\pi$
$234$		0			0
$235$	4.10186	−	7.10463i	0.267576	−	0.463455i
$236$		0			0
$237$	11.6940	−	10.0130i	0.759609	−	0.650417i
$238$		0			0
$239$	−2.86909	+	2.40746i	−0.185586	+	0.155725i	−0.730847	−	0.682541i	$-0.760875\pi$
$239$	−2.86909	+	2.40746i	−0.185586	+	0.155725i	0.545261	+	0.838266i	$0.316430\pi$
$240$		0			0
$241$	−12.5599	+	4.57143i	−0.809054	+	0.294472i	−0.713233	−	0.700927i	$-0.752770\pi$
$241$	−12.5599	+	4.57143i	−0.809054	+	0.294472i	−0.0958210	+	0.995399i	$0.530548\pi$
$242$		0			0
$243$	−15.1975	+	3.46933i	−0.974919	+	0.222558i
$244$		0			0
$245$	12.8366	−	4.67216i	0.820103	−	0.298493i
$246$		0			0
$247$	18.8584	+	22.4746i	1.19993	+	1.43003i
$248$		0			0
$249$	4.45151	−	3.81161i	0.282103	−	0.241551i
$250$		0			0
$251$	−13.2001	−	7.62110i	−0.833185	−	0.481040i	0.0217568	−	0.999763i	$-0.493074\pi$
$251$	−13.2001	−	7.62110i	−0.833185	−	0.481040i	−0.854942	+	0.518724i	$0.826407\pi$
$252$		0			0
$253$	9.99571	−	5.77103i	0.628425	−	0.362821i
$254$		0			0
$255$	7.14101	−	12.6587i	0.447187	−	0.792719i
$256$		0			0
$257$	1.66823	−	4.58341i	0.104061	−	0.285905i	−0.876725	−	0.480992i	$-0.840277\pi$
$257$	1.66823	−	4.58341i	0.104061	−	0.285905i	0.980786	+	0.195087i	$0.0624988\pi$
$258$		0			0
$259$	0.383302	−	2.17382i	0.0238172	−	0.135074i
$260$		0			0
$261$	8.57257	−	15.5572i	0.530629	−	0.962969i
$262$		0			0
$263$	8.66118	+	7.26759i	0.534071	+	0.448139i	0.869504	−	0.493925i	$-0.164438\pi$
$263$	8.66118	+	7.26759i	0.534071	+	0.448139i	−0.335433	+	0.942064i	$0.608883\pi$
$264$		0			0
$265$	−1.53804	−	8.72266i	−0.0944811	−	0.535829i
$266$		0			0
$267$	−1.11096	+	6.69038i	−0.0679897	+	0.409444i
$268$		0			0
$269$	15.2494			0.929769			0.464885	−	0.885371i	$-0.346096\pi$
$269$	15.2494			0.929769			0.464885	+	0.885371i	$0.346096\pi$
$270$		0			0
$271$		−	30.9881i		−	1.88239i	−0.337860	−	0.941196i	$-0.609703\pi$
$271$		−	30.9881i		−	1.88239i	0.337860	−	0.941196i	$-0.390297\pi$
$272$		0			0
$273$	−5.78248	+	7.03267i	−0.349972	+	0.425636i
$274$		0			0
$275$	0.576671	−	0.101683i	0.0347746	−	0.00613169i
$276$		0			0
$277$	14.1054	−	16.8102i	0.847512	−	1.01003i	−0.152253	−	0.988342i	$-0.548653\pi$
$277$	14.1054	−	16.8102i	0.847512	−	1.01003i	0.999765	−	0.0216842i	$-0.00690284\pi$
$278$		0			0
$279$	−12.6868	−	1.97678i	−0.759538	−	0.118347i
$280$		0			0
$281$	−17.2683	−	3.04486i	−1.03014	−	0.181641i	−0.367065	−	0.930195i	$-0.619637\pi$
$281$	−17.2683	−	3.04486i	−1.03014	−	0.181641i	−0.663074	+	0.748554i	$0.730748\pi$
$282$		0			0
$283$	30.4151	+	11.0702i	1.80799	+	0.658055i	0.997369	+	0.0724860i	$0.0230933\pi$
$283$	30.4151	+	11.0702i	1.80799	+	0.658055i	0.810622	+	0.585569i	$0.199129\pi$
$284$		0			0
$285$	0.225623	+	22.6048i	0.0133648	+	1.33899i
$286$		0			0
$287$	5.99405	+	10.3820i	0.353817	+	0.612830i
$288$		0			0
$289$	−1.79991	+	3.11754i	−0.105877	+	0.183385i
$290$		0			0
$291$	−0.611956	+	0.114213i	−0.0358735	+	0.00669531i
$292$		0			0
$293$	−18.5355	+	15.5532i	−1.08286	+	0.908625i	−0.996155	−	0.0876094i	$-0.972077\pi$
$293$	−18.5355	+	15.5532i	−1.08286	+	0.908625i	−0.0867021	+	0.996234i	$0.527633\pi$
$294$		0			0
$295$	7.63965	+	20.9898i	0.444797	+	1.22207i
$296$		0			0
$297$	−9.38133	−	7.40478i	−0.544360	−	0.429669i
$298$		0			0
$299$	−8.84377	−	24.2980i	−0.511448	−	1.40519i
$300$		0			0
$301$	−1.17761	−	1.40342i	−0.0678760	−	0.0808915i
$302$		0			0
$303$	−1.80877	+	5.12823i	−0.103911	+	0.294609i
$304$		0			0
$305$	27.3926	+	15.8151i	1.56850	+	0.905572i
$306$		0			0
$307$	1.31824	+	2.28327i	0.0752362	+	0.130313i	0.901189	−	0.433426i	$-0.142696\pi$
$307$	1.31824	+	2.28327i	0.0752362	+	0.130313i	−0.825953	+	0.563739i	$0.809362\pi$
$308$		0			0
$309$	8.23745	+	13.9444i	0.468612	+	0.793269i
$310$		0			0
$311$	−7.71143	−	2.80673i	−0.437275	−	0.159155i	0.113996	−	0.993481i	$-0.463635\pi$
$311$	−7.71143	−	2.80673i	−0.437275	−	0.159155i	−0.551271	+	0.834326i	$0.685857\pi$
$312$		0			0
$313$	2.94996	−	16.7300i	0.166741	−	0.945637i	−0.780509	−	0.625144i	$-0.785040\pi$
$313$	2.94996	−	16.7300i	0.166741	−	0.945637i	0.947251	−	0.320493i	$-0.103849\pi$
$314$		0			0
$315$	−6.88308	+	1.35586i	−0.387818	+	0.0763942i
$316$		0			0
$317$	5.58073	+	4.68279i	0.313445	+	0.263012i	0.785914	−	0.618336i	$-0.212193\pi$
$317$	5.58073	+	4.68279i	0.313445	+	0.263012i	−0.472469	+	0.881347i	$0.656637\pi$
$318$		0			0
$319$	13.4117	−	2.36485i	0.750912	−	0.132406i
$320$		0			0
$321$	10.9061	−	4.09323i	0.608720	−	0.228462i
$322$		0			0
$323$			20.8424i			1.15970i
$324$		0			0
$325$		−	1.31183i		−	0.0727675i
$326$		0			0
$327$	−15.0530	+	5.64961i	−0.832432	+	0.312424i
$328$		0			0
$329$	−3.59544	+	0.633974i	−0.198223	+	0.0349521i
$330$		0			0
$331$	−1.18992	−	0.998461i	−0.0654039	−	0.0548804i	0.609500	−	0.792786i	$-0.291370\pi$
$331$	−1.18992	−	0.998461i	−0.0654039	−	0.0548804i	−0.674904	+	0.737906i	$0.735815\pi$
$332$		0			0
$333$	2.09797	−	6.14295i	0.114968	−	0.336632i
$334$		0			0
$335$	−5.16415	+	29.2873i	−0.282148	+	1.60014i
$336$		0			0
$337$	21.3220	+	7.76056i	1.16148	+	0.422744i	0.849626	−	0.527385i	$-0.176828\pi$
$337$	21.3220	+	7.76056i	1.16148	+	0.422744i	0.311855	+	0.950130i	$0.399050\pi$
$338$		0			0
$339$	0.398961	+	0.675362i	0.0216686	+	0.0366806i
$340$		0			0
$341$	−4.92212	−	8.52537i	−0.266548	−	0.461675i
$342$		0			0
$343$	−11.4491	−	6.61015i	−0.618194	−	0.356914i
$344$		0			0
$345$	6.62710	−	18.7892i	0.356791	−	1.01158i
$346$		0			0
$347$	6.31120	+	7.52140i	0.338803	+	0.403770i	0.908365	−	0.418179i	$-0.137331\pi$
$347$	6.31120	+	7.52140i	0.338803	+	0.403770i	−0.569562	+	0.821949i	$0.692887\pi$
$348$		0			0
$349$	8.79630	+	24.1676i	0.470855	+	1.29366i	0.917066	+	0.398736i	$0.130551\pi$
$349$	8.79630	+	24.1676i	0.470855	+	1.29366i	−0.446211	+	0.894928i	$0.647227\pi$
$350$		0			0
$351$	−19.9863	+	17.8169i	−1.06679	+	0.950996i
$352$		0			0
$353$	−1.22454	−	3.36438i	−0.0651754	−	0.179068i	0.902830	−	0.429998i	$-0.141486\pi$
$353$	−1.22454	−	3.36438i	−0.0651754	−	0.179068i	−0.968005	+	0.250930i	$0.919264\pi$
$354$		0			0
$355$	−18.3820	+	15.4243i	−0.975615	+	0.818638i
$356$		0			0
$357$	−6.35828	+	1.18669i	−0.336516	+	0.0628062i
$358$		0			0
$359$	9.38169	−	16.2496i	0.495146	−	0.857619i	−0.504838	−	0.863214i	$-0.668448\pi$
$359$	9.38169	−	16.2496i	0.495146	−	0.857619i	0.999984	+	0.00559540i	$0.00178108\pi$
$360$		0			0
$361$	−6.70895	−	11.6202i	−0.353103	−	0.611592i
$362$		0			0
$363$	0.0987030	+	9.88887i	0.00518056	+	0.519031i
$364$		0			0
$365$	4.10727	+	1.49492i	0.214984	+	0.0782479i
$366$		0			0
$367$	−26.0267	−	4.58921i	−1.35858	−	0.239555i	−0.553565	−	0.832806i	$-0.686733\pi$
$367$	−26.0267	−	4.58921i	−1.35858	−	0.239555i	−0.805017	+	0.593251i	$0.797844\pi$
$368$		0			0
$369$	12.7165	+	32.8809i	0.661997	+	1.71171i
$370$		0			0
$371$	−2.53370	+	3.01954i	−0.131543	+	0.156767i
$372$		0			0
$373$	−2.99876	+	0.528763i	−0.155270	+	0.0273783i	−0.250743	−	0.968054i	$-0.580675\pi$
$373$	−2.99876	+	0.528763i	−0.155270	+	0.0273783i	0.0954727	+	0.995432i	$0.469564\pi$
$374$		0			0
$375$	−11.9661	+	14.5532i	−0.617927	+	0.751524i
$376$		0			0
$377$		−	30.5095i		−	1.57132i
$378$		0			0
$379$	16.2636			0.835404			0.417702	−	0.908584i	$-0.362836\pi$
$379$	16.2636			0.835404			0.417702	+	0.908584i	$0.362836\pi$
$380$		0			0
$381$	0.766238	−	4.61440i	0.0392556	−	0.236403i
$382$		0			0
$383$	3.79043	+	21.4966i	0.193682	+	1.09842i	0.914283	+	0.405075i	$0.132755\pi$
$383$	3.79043	+	21.4966i	0.193682	+	1.09842i	−0.720602	+	0.693349i	$0.756134\pi$
$384$		0			0
$385$	−4.12027	−	3.45732i	−0.209988	−	0.176201i
$386$		0			0
$387$	−2.78639	−	4.61109i	−0.141640	−	0.234395i
$388$		0			0
$389$	−1.31304	+	7.44664i	−0.0665740	+	0.377560i	0.933258	+	0.359208i	$0.116953\pi$
$389$	−1.31304	+	7.44664i	−0.0665740	+	0.377560i	−0.999832	+	0.0183520i	$0.994158\pi$
$390$		0			0
$391$	6.28270	−	17.2616i	0.317730	−	0.872956i
$392$		0			0
$393$	7.13054	−	12.6401i	0.359688	−	0.637611i
$394$		0			0
$395$	17.6451	−	10.1874i	0.887821	−	0.512584i
$396$		0			0
$397$	−4.30902	−	2.48781i	−0.216264	−	0.124860i	0.387955	−	0.921678i	$-0.373181\pi$
$397$	−4.30902	−	2.48781i	−0.216264	−	0.124860i	−0.604219	+	0.796818i	$0.706515\pi$
$398$		0			0
$399$	7.64173	−	6.54325i	0.382565	−	0.327572i
$400$		0			0
$401$	9.87857	+	11.7728i	0.493312	+	0.587907i	0.954057	−	0.299626i	$-0.0968619\pi$
$401$	9.87857	+	11.7728i	0.493312	+	0.587907i	−0.460744	+	0.887533i	$0.652418\pi$
$402$		0			0
$403$	−20.7239	+	7.54287i	−1.03233	+	0.375737i
$404$		0			0
$405$	−20.6142	+	0.823428i	−1.02433	+	0.0409165i
$406$		0			0
$407$	4.67672	−	1.70219i	0.231816	−	0.0843742i
$408$		0			0
$409$	−13.1872	+	11.0654i	−0.652066	+	0.547148i	−0.907697	−	0.419626i	$-0.862161\pi$
$409$	−13.1872	+	11.0654i	−0.652066	+	0.547148i	0.255631	+	0.966774i	$0.417717\pi$
$410$		0			0
$411$	4.06050	−	3.47681i	0.200290	−	0.171499i
$412$		0			0
$413$	4.97029	−	8.60879i	0.244572	−	0.423611i
$414$		0			0
$415$	6.71687	−	3.87798i	0.329718	−	0.190363i
$416$		0			0
$417$	12.3102	+	6.94443i	0.602835	+	0.340070i
$418$		0			0
$419$	−1.79105	+	4.92087i	−0.0874984	+	0.240400i	−0.975722	−	0.219011i	$-0.929717\pi$
$419$	−1.79105	+	4.92087i	−0.0874984	+	0.240400i	0.888224	+	0.459411i	$0.151939\pi$
$420$		0			0
$421$	−20.5157	−	3.61747i	−0.999873	−	0.176305i	−0.350327	−	0.936627i	$-0.613930\pi$
$421$	−20.5157	−	3.61747i	−0.999873	−	0.176305i	−0.649545	+	0.760323i	$0.725041\pi$
$422$		0			0
$423$	−10.7344	+	0.214306i	−0.521923	+	0.0104199i
$424$		0			0
$425$	0.599040	−	0.713908i	0.0290577	−	0.0346296i
$426$		0			0
$427$	−2.44435	−	13.8626i	−0.118290	−	0.670858i
$428$		0			0
$429$	−20.2508	−	3.36272i	−0.977720	−	0.162354i
$430$		0			0
$431$	18.2756			0.880306			0.440153	−	0.897923i	$-0.354924\pi$
$431$	18.2756			0.880306			0.440153	+	0.897923i	$0.354924\pi$
$432$		0			0
$433$	−9.27958			−0.445948			−0.222974	−	0.974824i	$-0.571577\pi$
$433$	−9.27958			−0.445948			−0.222974	+	0.974824i	$0.571577\pi$
$434$		0			0
$435$	14.9303	−	18.1583i	0.715853	−	0.870622i
$436$		0			0
$437$	4.96138	+	28.1374i	0.237335	+	1.34599i
$438$		0			0
$439$	−6.79506	+	8.09803i	−0.324310	+	0.386498i	−0.903424	−	0.428749i	$-0.858954\pi$
$439$	−6.79506	+	8.09803i	−0.324310	+	0.386498i	0.579113	+	0.815247i	$0.303399\pi$
$440$		0			0
$441$	−13.9220	−	11.2161i	−0.662950	−	0.534099i
$442$		0			0
$443$	−4.18440	−	0.737822i	−0.198807	−	0.0350550i	0.0733580	−	0.997306i	$-0.476628\pi$
$443$	−4.18440	−	0.737822i	−0.198807	−	0.0350550i	−0.272165	+	0.962251i	$0.587740\pi$
$444$		0			0
$445$	−3.06985	+	8.43435i	−0.145525	+	0.399826i
$446$		0			0
$447$	0.314580	+	31.5172i	0.0148791	+	1.49071i
$448$		0			0
$449$	−2.30729	+	1.33212i	−0.108888	+	0.0628665i	−0.553455	−	0.832879i	$-0.686691\pi$
$449$	−2.30729	+	1.33212i	−0.108888	+	0.0628665i	0.444567	+	0.895746i	$0.353358\pi$
$450$		0			0
$451$	−13.5146	+	23.4080i	−0.636379	+	1.10224i
$452$		0			0
$453$	7.46555	+	40.0005i	0.350762	+	1.87939i
$454$		0			0
$455$	−9.23056	+	7.74536i	−0.432735	+	0.363108i
$456$		0			0
$457$	7.57163	−	2.75585i	0.354186	−	0.128913i	−0.158799	−	0.987311i	$-0.550762\pi$
$457$	7.57163	−	2.75585i	0.354186	−	0.128913i	0.512985	+	0.858398i	$0.328540\pi$
$458$		0			0
$459$	−19.0126	+	0.569459i	−0.887434	+	0.0265801i
$460$		0			0
$461$	−18.6527	+	6.78902i	−0.868742	+	0.316196i	−0.737658	−	0.675175i	$-0.764068\pi$
$461$	−18.6527	+	6.78902i	−0.868742	+	0.316196i	−0.131085	+	0.991371i	$0.541846\pi$
$462$		0			0
$463$	9.71616	+	11.5793i	0.451548	+	0.538134i	0.943010	−	0.332765i	$-0.107982\pi$
$463$	9.71616	+	11.5793i	0.451548	+	0.538134i	−0.491461	+	0.870899i	$0.663537\pi$
$464$		0			0
$465$	−16.0254	−	5.65227i	−0.743159	−	0.262118i
$466$		0			0
$467$	5.72534	+	3.30553i	0.264937	+	0.152961i	0.626585	−	0.779353i	$-0.284452\pi$
$467$	5.72534	+	3.30553i	0.264937	+	0.152961i	−0.361648	+	0.932315i	$0.617786\pi$
$468$		0			0
$469$	11.4617	−	6.61742i	0.529252	−	0.305564i
$470$		0			0
$471$	−20.4243	−	34.5744i	−0.941104	−	1.59310i
$472$		0			0
$473$	1.41276	−	3.88152i	0.0649587	−	0.178473i
$474$		0			0
$475$	−0.251707	+	1.42750i	−0.0115491	+	0.0654983i
$476$		0			0
$477$	−8.72931	+	7.62680i	−0.399688	+	0.349207i
$478$		0			0
$479$	1.07806	+	0.904601i	0.0492579	+	0.0413323i	0.667084	−	0.744982i	$-0.267542\pi$
$479$	1.07806	+	0.904601i	0.0492579	+	0.0413323i	−0.617826	+	0.786315i	$0.711987\pi$
$480$		0			0
$481$	−1.93610	−	10.9802i	−0.0882786	−	0.500653i
$482$		0			0
$483$	−8.30124	+	3.11558i	−0.377720	+	0.141764i
$484$		0			0
$485$	−0.823880			−0.0374104
$486$		0			0
$487$		−	23.6611i		−	1.07219i	−0.844159	−	0.536093i	$-0.819900\pi$
$487$		−	23.6611i		−	1.07219i	0.844159	−	0.536093i	$-0.180100\pi$
$488$		0			0
$489$	3.06060	+	8.15474i	0.138405	+	0.368770i
$490$		0			0
$491$	−6.29639	+	1.11022i	−0.284152	+	0.0501037i	−0.313908	−	0.949454i	$-0.601638\pi$
$491$	−6.29639	+	1.11022i	−0.284152	+	0.0501037i	0.0297556	+	0.999557i	$0.490527\pi$
$492$		0			0
$493$	13.9320	−	16.6035i	0.627464	−	0.747783i
$494$		0			0
$495$	−10.4070	−	11.9114i	−0.467761	−	0.535379i
$496$		0			0
$497$	10.5167	+	1.85438i	0.471739	+	0.0831803i
$498$		0			0
$499$	−9.65079	−	3.51260i	−0.432029	−	0.157246i	0.116846	−	0.993150i	$-0.462722\pi$
$499$	−9.65079	−	3.51260i	−0.432029	−	0.157246i	−0.548875	+	0.835904i	$0.684944\pi$
$500$		0			0
$501$	−28.0133	+	16.5484i	−1.25154	+	0.739330i
$502$		0			0
$503$	18.3438	+	31.7724i	0.817909	+	1.41666i	0.907220	+	0.420655i	$0.138200\pi$
$503$	18.3438	+	31.7724i	0.817909	+	1.41666i	−0.0893120	+	0.996004i	$0.528467\pi$
$504$		0			0
$505$	−3.59838	+	6.23258i	−0.160126	+	0.277346i
$506$		0			0
$507$	−7.80741	+	22.1356i	−0.346739	+	0.983078i
$508$		0			0
$509$	−1.05295	+	0.883527i	−0.0466710	+	0.0391617i	−0.665825	−	0.746108i	$-0.731920\pi$
$509$	−1.05295	+	0.883527i	−0.0466710	+	0.0391617i	0.619154	+	0.785270i	$0.287476\pi$
$510$		0			0
$511$	−0.665287	−	1.82786i	−0.0294306	−	0.0808598i
$512$		0			0
$513$	25.1672	−	15.5530i	1.11116	−	0.686683i
$514$		0			0
$515$	7.33096	+	20.1417i	0.323041	+	0.887547i
$516$		0			0
$517$	−5.29118	−	6.30578i	−0.232706	−	0.277328i
$518$		0			0
$519$	26.7477	−	4.99210i	1.17409	−	0.219129i
$520$		0			0
$521$	−2.59296	−	1.49704i	−0.113600	−	0.0655867i	0.442124	−	0.896954i	$-0.354225\pi$
$521$	−2.59296	−	1.49704i	−0.113600	−	0.0655867i	−0.555723	+	0.831367i	$0.687559\pi$
$522$		0			0
$523$	7.61202	+	13.1844i	0.332850	+	0.576513i	0.983069	−	0.183233i	$-0.0586563\pi$
$523$	7.61202	+	13.1844i	0.332850	+	0.576513i	−0.650219	+	0.759747i	$0.725323\pi$
$524$		0			0
$525$	−0.449812	+	0.00448968i	−0.0196314	+	0.000195945i
$526$		0			0
$527$	−14.7225	−	5.35854i	−0.641320	−	0.233422i
$528$		0			0
$529$	0.378792	−	2.14824i	0.0164692	−	0.0934017i
$530$		0			0
$531$	18.3399	−	22.7644i	0.795883	−	0.987891i
$532$		0			0
$533$	46.3864	+	38.9228i	2.00922	+	1.68593i
$534$		0			0
$535$	15.1826	−	2.67710i	0.656402	−	0.115741i
$536$		0			0
$537$	−32.9533	−	27.0953i	−1.42204	−	1.16925i
$538$		0			0
$539$		−	13.7069i		−	0.590399i
$540$		0			0
$541$		−	24.1732i		−	1.03929i	−0.854383	−	0.519644i	$-0.826064\pi$
$541$		−	24.1732i		−	1.03929i	0.854383	−	0.519644i	$-0.173936\pi$
$542$		0			0
$543$	−2.54332	+	15.3162i	−0.109144	+	0.657283i
$544$		0			0
$545$	−20.9556	+	3.69503i	−0.897638	+	0.158278i
$546$		0			0
$547$	−21.2524	−	17.8329i	−0.908687	−	0.762479i	0.0631816	−	0.998002i	$-0.479875\pi$
$547$	−21.2524	−	17.8329i	−0.908687	−	0.762479i	−0.971869	+	0.235523i	$0.924320\pi$
$548$		0			0
$549$	−0.826276	−	41.3874i	−0.0352646	−	1.76637i
$550$		0			0
$551$	−5.85400	+	33.1997i	−0.249389	+	1.41435i
$552$		0			0
$553$	−8.52057	−	3.10124i	−0.362332	−	0.131878i
$554$		0			0
$555$	4.22101	−	7.48250i	0.179172	−	0.317614i
$556$		0			0
$557$	16.1966	+	28.0534i	0.686274	+	1.18866i	0.973035	+	0.230659i	$0.0740881\pi$
$557$	16.1966	+	28.0534i	0.686274	+	1.18866i	−0.286761	+	0.958002i	$0.592579\pi$
$558$		0			0
$559$	−8.01400	−	4.62689i	−0.338956	−	0.195696i
$560$		0			0
$561$	−9.48507	−	11.0774i	−0.400460	−	0.467689i
$562$		0			0
$563$	7.47656	+	8.91022i	0.315099	+	0.375521i	0.900227	−	0.435420i	$-0.143400\pi$
$563$	7.47656	+	8.91022i	0.315099	+	0.375521i	−0.585128	+	0.810941i	$0.698956\pi$
$564$		0			0
$565$	0.355057	+	0.975511i	0.0149374	+	0.0410401i
$566$		0			0
$567$	6.17761	+	6.79209i	0.259435	+	0.285241i
$568$		0			0
$569$	10.8888	+	29.9168i	0.456484	+	1.25418i	0.928085	+	0.372368i	$0.121454\pi$
$569$	10.8888	+	29.9168i	0.456484	+	1.25418i	−0.471601	+	0.881812i	$0.656324\pi$
$570$		0			0
$571$	22.3423	−	18.7474i	0.934997	−	0.784556i	−0.0417107	−	0.999130i	$-0.513281\pi$
$571$	22.3423	−	18.7474i	0.934997	−	0.784556i	0.976708	+	0.214574i	$0.0688363\pi$
$572$		0			0
$573$	5.24049	+	6.12027i	0.218925	+	0.255678i
$574$		0			0
$575$	0.638768	−	1.10638i	0.0266385	−	0.0461392i
$576$		0			0
$577$	13.1518	+	22.7796i	0.547517	+	0.948327i	0.998444	+	0.0557659i	$0.0177601\pi$
$577$	13.1518	+	22.7796i	0.547517	+	0.948327i	−0.450927	+	0.892561i	$0.648907\pi$
$578$		0			0
$579$	−32.5104	−	18.3397i	−1.35109	−	0.762173i
$580$		0			0
$581$	−3.24348	−	1.18053i	−0.134562	−	0.0489767i
$582$		0			0
$583$	−8.75232	−	1.54327i	−0.362484	−	0.0639157i
$584$		0			0
$585$	−30.3281	+	18.3267i	−1.25391	+	0.757715i
$586$		0			0
$587$	−18.5909	+	22.1557i	−0.767328	+	0.914466i	−0.998288	−	0.0584977i	$-0.981369\pi$
$587$	−18.5909	+	22.1557i	−0.767328	+	0.914466i	0.230960	+	0.972963i	$0.425813\pi$
$588$		0			0
$589$	23.9984	−	4.23157i	0.988839	−	0.174359i
$590$		0			0
$591$	−24.4953	−	4.06753i	−1.00760	−	0.167316i
$592$		0			0
$593$			6.66759i			0.273805i	0.990585	+	0.136902i	$0.0437147\pi$
$593$			6.66759i			0.273805i	−0.990585	+	0.136902i	$0.956285\pi$
$594$		0			0
$595$	−8.56019			−0.350934
$596$		0			0
$597$	−9.01303	−	7.41080i	−0.368879	−	0.303304i
$598$		0			0
$599$	−4.82715	−	27.3761i	−0.197232	−	1.11856i	−0.909204	−	0.416351i	$-0.863309\pi$
$599$	−4.82715	−	27.3761i	−0.197232	−	1.11856i	0.711972	−	0.702208i	$-0.247802\pi$
$600$		0			0
$601$	32.9708	+	27.6658i	1.34491	+	1.12851i	0.980336	+	0.197336i	$0.0632291\pi$
$601$	32.9708	+	27.6658i	1.34491	+	1.12851i	0.364572	+	0.931175i	$0.381215\pi$
$602$		0			0
$603$	36.3005	−	14.0390i	1.47827	−	0.571714i
$604$		0			0
$605$	−2.27273	+	12.8893i	−0.0923994	+	0.524023i
$606$		0			0
$607$	−6.17503	+	16.9658i	−0.250637	+	0.688619i	0.749023	+	0.662544i	$0.230523\pi$
$607$	−6.17503	+	16.9658i	−0.250637	+	0.688619i	−0.999660	+	0.0260750i	$0.991699\pi$
$608$		0			0
$609$	−10.4614	+	0.104417i	−0.423916	+	0.00423119i
$610$		0			0
$611$	−15.9705	+	9.22057i	−0.646097	+	0.373024i
$612$		0			0
$613$	15.9194	+	9.19108i	0.642979	+	0.371224i	0.785761	−	0.618530i	$-0.212271\pi$
$613$	15.9194	+	9.19108i	0.642979	+	0.371224i	−0.142782	+	0.989754i	$0.545605\pi$
$614$		0			0
$615$	8.56018	+	45.8655i	0.345180	+	1.84947i
$616$		0			0
$617$	−17.1567	−	20.4465i	−0.690701	−	0.823146i	0.300739	−	0.953707i	$-0.402767\pi$
$617$	−17.1567	−	20.4465i	−0.690701	−	0.823146i	−0.991440	+	0.130561i	$0.958322\pi$
$618$		0			0
$619$	27.1693	−	9.88881i	1.09203	−	0.397465i	0.267655	−	0.963515i	$-0.413751\pi$
$619$	27.1693	−	9.88881i	1.09203	−	0.397465i	0.824371	+	0.566050i	$0.191529\pi$
$620$		0			0
$621$	−25.5316	+	5.29459i	−1.02455	+	0.212465i
$622$		0			0
$623$	3.75354	−	1.36618i	0.150383	−	0.0547348i
$624$		0			0
$625$	−20.0766	+	16.8463i	−0.803063	+	0.673850i
$626$		0			0
$627$	21.3912	+	7.54484i	0.854283	+	0.301312i
$628$		0			0
$629$	3.96038	−	6.85959i	0.157911	−	0.273510i
$630$		0			0
$631$	16.5682	−	9.56563i	0.659568	−	0.380802i	−0.132544	−	0.991177i	$-0.542315\pi$
$631$	16.5682	−	9.56563i	0.659568	−	0.380802i	0.792112	+	0.610375i	$0.208981\pi$
$632$		0			0
$633$	6.12435	−	3.61787i	0.243421	−	0.143798i
$634$		0			0
$635$	2.11730	−	5.81724i	0.0840225	−	0.230850i
$636$		0			0
$637$	−30.2408	−	5.33228i	−1.19819	−	0.211272i
$638$		0			0
$639$	29.7190	+	10.1498i	1.17567	+	0.401518i
$640$		0			0
$641$	19.0528	−	22.7063i	0.752541	−	0.896843i	−0.244811	−	0.969571i	$-0.578726\pi$
$641$	19.0528	−	22.7063i	0.752541	−	0.896843i	0.997352	+	0.0727276i	$0.0231704\pi$
$642$		0			0
$643$	−1.32021	−	7.48729i	−0.0520641	−	0.295270i	0.947647	−	0.319321i	$-0.103455\pi$
$643$	−1.32021	−	7.48729i	−0.0520641	−	0.295270i	−0.999711	+	0.0240508i	$0.992344\pi$
$644$		0			0
$645$	−2.50543	−	6.67554i	−0.0986512	−	0.262849i
$646$		0			0
$647$	−0.299936			−0.0117917			−0.00589585	−	0.999983i	$-0.501877\pi$
$647$	−0.299936			−0.0117917			−0.00589585	+	0.999983i	$0.501877\pi$
$648$		0			0
$649$	22.4128			0.879778
$650$		0			0
$651$	2.65729	+	7.08015i	0.104147	+	0.277493i
$652$		0			0
$653$	−0.815786	−	4.62655i	−0.0319242	−	0.181051i	0.964676	−	0.263438i	$-0.0848566\pi$
$653$	−0.815786	−	4.62655i	−0.0319242	−	0.181051i	−0.996600	+	0.0823875i	$0.973745\pi$
$654$		0			0
$655$	12.3459	−	14.7133i	0.482395	−	0.574896i
$656$		0			0
$657$	−1.10557	−	5.61246i	−0.0431323	−	0.218963i
$658$		0			0
$659$	41.8965	+	7.38748i	1.63206	+	0.287775i	0.913239	−	0.407425i	$-0.133573\pi$
$659$	41.8965	+	7.38748i	1.63206	+	0.287775i	0.718816	+	0.695200i	$0.244684\pi$
$660$		0			0
$661$	13.6136	−	37.4031i	0.529508	−	1.45481i	−0.330143	−	0.943931i	$-0.607097\pi$
$661$	13.6136	−	37.4031i	0.529508	−	1.45481i	0.859651	−	0.510881i	$-0.170681\pi$
$662$		0			0
$663$	−28.1294	+	16.6171i	−1.09246	+	0.645353i
$664$		0			0
$665$	11.5306	−	6.65719i	0.447137	−	0.258155i
$666$		0			0
$667$	14.8559	−	25.7312i	0.575224	−	0.996317i
$668$		0			0
$669$	−1.48594	−	0.524101i	−0.0574496	−	0.0202629i
$670$		0			0
$671$	24.3126	−	20.4007i	0.938576	−	0.787559i
$672$		0			0
$673$	14.5108	−	5.28149i	0.559349	−	0.203586i	−0.0468463	−	0.998902i	$-0.514917\pi$
$673$	14.5108	−	5.28149i	0.559349	−	0.203586i	0.606196	+	0.795316i	$0.292695\pi$
$674$		0			0
$675$	−1.30906	−	0.190607i	−0.0503857	−	0.00733648i
$676$		0			0
$677$	13.3291	−	4.85138i	0.512277	−	0.186454i	−0.0729307	−	0.997337i	$-0.523235\pi$
$677$	13.3291	−	4.85138i	0.512277	−	0.186454i	0.585208	+	0.810883i	$0.301013\pi$
$678$		0			0
$679$	0.235679	+	0.280871i	0.00904453	+	0.0107789i
$680$		0			0
$681$	4.06656	+	21.7887i	0.155831	+	0.834943i
$682$		0			0
$683$	−42.1162	−	24.3158i	−1.61153	−	0.930418i	−0.989016	−	0.147811i	$-0.952777\pi$
$683$	−42.1162	−	24.3158i	−1.61153	−	0.930418i	−0.622516	−	0.782607i	$-0.713889\pi$
$684$		0			0
$685$	6.12688	−	3.53735i	0.234096	−	0.135155i
$686$		0			0
$687$	33.1517	−	0.330895i	1.26482	−	0.0126244i
$688$		0			0
$689$	−6.80967	+	18.7094i	−0.259428	+	0.712772i
$690$		0			0
$691$	4.54802	−	25.7931i	0.173015	−	0.981216i	−0.767395	−	0.641174i	$-0.778448\pi$
$691$	4.54802	−	25.7931i	0.173015	−	0.981216i	0.940410	−	0.340042i	$-0.110441\pi$
$692$		0			0
$693$	−1.08373	+	6.95528i	−0.0411675	+	0.264209i
$694$		0			0
$695$	14.3293	+	12.0237i	0.543541	+	0.456085i
$696$		0			0
$697$	7.46993	+	42.3641i	0.282944	+	1.60465i
$698$		0			0
$699$	34.8536	+	28.6577i	1.31828	+	1.08393i
$700$		0			0
$701$	22.0114			0.831360			0.415680	−	0.909511i	$-0.363544\pi$
$701$	22.0114			0.831360			0.415680	+	0.909511i	$0.363544\pi$
$702$		0			0
$703$			12.3198i			0.464651i
$704$		0			0
$705$	−14.0173	−	2.32763i	−0.527923	−	0.0876635i
$706$		0			0
$707$	3.15412	−	0.556157i	0.118623	−	0.0209164i
$708$		0			0
$709$	13.2246	−	15.7605i	0.496661	−	0.591897i	−0.458238	−	0.888830i	$-0.651519\pi$
$709$	13.2246	−	15.7605i	0.496661	−	0.591897i	0.954898	+	0.296933i	$0.0959637\pi$
$710$		0			0
$711$	−23.3543	−	12.8690i	−0.875854	−	0.482626i
$712$		0			0
$713$	−21.1510	−	3.72949i	−0.792110	−	0.139670i
$714$		0			0
$715$	−25.5296	−	9.29202i	−0.954753	−	0.347502i
$716$		0			0
$717$	5.65010	+	3.18732i	0.211007	+	0.119033i
$718$		0			0
$719$	−13.4372	−	23.2739i	−0.501124	−	0.867972i	−0.999999	−	0.00129793i	$-0.999587\pi$
$719$	−13.4372	−	23.2739i	−0.501124	−	0.867972i	0.498876	−	0.866674i	$-0.333746\pi$
$720$		0			0
$721$	4.76946	−	8.26094i	0.177624	−	0.307654i
$722$		0			0
$723$	15.0571	+	17.5849i	0.559981	+	0.653990i
$724$		0			0
$725$	1.15472	−	0.968926i	0.0428853	−	0.0359850i
$726$		0			0
$727$	−7.36651	−	20.2393i	−0.273209	−	0.750635i	−0.998091	−	0.0617620i	$-0.980328\pi$
$727$	−7.36651	−	20.2393i	−0.273209	−	0.750635i	0.724882	−	0.688873i	$-0.241894\pi$
$728$		0			0
$729$	14.8752	+	22.5328i	0.550935	+	0.834548i
$730$		0			0
$731$	−2.24843	−	6.17752i	−0.0831613	−	0.228484i
$732$		0			0
$733$	9.80116	+	11.6806i	0.362014	+	0.431432i	0.916052	−	0.401060i	$-0.131358\pi$
$733$	9.80116	+	11.6806i	0.362014	+	0.431432i	−0.554038	+	0.832492i	$0.686914\pi$
$734$		0			0
$735$	−15.3889	−	17.9724i	−0.567628	−	0.662922i
$736$		0			0
$737$	25.8424	+	14.9201i	0.951918	+	0.549590i
$738$		0			0
$739$	−10.6738	−	18.4875i	−0.392642	−	0.680075i	0.600155	−	0.799883i	$-0.295105\pi$
$739$	−10.6738	−	18.4875i	−0.392642	−	0.680075i	−0.992797	+	0.119808i	$0.961772\pi$
$740$		0			0
$741$	24.9674	−	44.2592i	0.917201	−	1.62590i
$742$		0			0
$743$	35.7223	+	13.0019i	1.31052	+	0.476992i	0.900410	−	0.435043i	$-0.143267\pi$
$743$	35.7223	+	13.0019i	1.31052	+	0.476992i	0.410114	+	0.912034i	$0.365489\pi$
$744$		0			0
$745$	−7.24350	+	41.0799i	−0.265381	+	1.50505i
$746$		0			0
$747$	−8.89016	−	4.89878i	−0.325274	−	0.179237i
$748$		0			0
$749$	−5.25580	−	4.41014i	−0.192043	−	0.161143i
$750$		0			0
$751$	8.29178	−	1.46207i	0.302571	−	0.0533515i	−0.0203012	−	0.999794i	$-0.506463\pi$
$751$	8.29178	−	1.46207i	0.302571	−	0.0533515i	0.322873	+	0.946442i	$0.395351\pi$
$752$		0			0
$753$	−4.32464	+	26.0437i	−0.157599	+	0.949083i
$754$		0			0
$755$			53.8529i			1.95991i
$756$		0			0
$757$		−	13.1454i		−	0.477778i	−0.971047	−	0.238889i	$-0.923217\pi$
$757$		−	13.1454i		−	0.477778i	0.971047	−	0.238889i	$-0.0767832\pi$
$758$		0			0
$759$	−15.4418	−	12.6967i	−0.560502	−	0.460863i
$760$		0			0
$761$	37.6562	−	6.63981i	1.36504	−	0.240693i	0.557337	−	0.830287i	$-0.311823\pi$
$761$	37.6562	−	6.63981i	1.36504	−	0.240693i	0.807700	+	0.589594i	$0.200712\pi$
$762$		0			0
$763$	7.25424	+	6.08703i	0.262621	+	0.220365i
$764$		0			0
$765$	−24.8735	−	3.87564i	−0.899303	−	0.140124i
$766$		0			0
$767$	8.71903	−	49.4481i	0.314826	−	1.78547i
$768$		0			0
$769$	−24.7734	−	9.01679i	−0.893353	−	0.325154i	−0.145767	−	0.989319i	$-0.546565\pi$
$769$	−24.7734	−	9.01679i	−0.893353	−	0.325154i	−0.747586	+	0.664165i	$0.768787\pi$
$770$		0			0
$771$	−8.44777	+	0.0843191i	−0.304239	+	0.00303668i
$772$		0			0
$773$	−9.13472	−	15.8218i	−0.328553	−	0.569071i	0.653672	−	0.756778i	$-0.273228\pi$
$773$	−9.13472	−	15.8218i	−0.328553	−	0.569071i	−0.982225	+	0.187708i	$0.939894\pi$
$774$		0			0
$775$	−0.943633	−	0.544807i	−0.0338963	−	0.0195700i
$776$		0			0
$777$	−3.75835	+	0.701445i	−0.134830	+	0.0251642i
$778$		0			0
$779$	−43.0082	−	51.2551i	−1.54093	−	1.83641i
$780$		0			0
$781$	8.23501	+	22.6255i	0.294672	+	0.809604i
$782$		0			0
$783$	−30.4450	−	4.43299i	−1.08802	−	0.158422i
$784$		0			0
$785$	−18.1767	−	49.9402i	−0.648755	−	1.78244i
$786$		0			0
$787$	9.05964	−	7.60194i	0.322941	−	0.270980i	−0.466875	−	0.884323i	$-0.654620\pi$
$787$	9.05964	−	7.60194i	0.322941	−	0.270980i	0.789816	+	0.613343i	$0.210176\pi$
$788$		0			0
$789$	6.51385	−	18.4681i	0.231899	−	0.657482i
$790$		0			0
$791$	0.230997	−	0.400098i	0.00821331	−	0.0142259i
$792$		0			0
$793$	−35.5508	−	61.5758i	−1.26245	−	2.18662i
$794$		0			0
$795$	−13.2086	+	7.80280i	−0.468461	+	0.276737i
$796$		0			0
$797$	−20.3529	−	7.40784i	−0.720936	−	0.262399i	−0.0446129	−	0.999004i	$-0.514205\pi$
$797$	−20.3529	−	7.40784i	−0.720936	−	0.262399i	−0.676323	+	0.736605i	$0.736428\pi$
$798$		0			0
$799$	−12.9017	−	2.27493i	−0.456431	−	0.0804811i
$800$		0			0
$801$	11.5253	−	2.27030i	0.407225	−	0.0802172i
$802$		0			0
$803$	2.81909	−	3.35966i	0.0994835	−	0.118560i
$804$		0			0
$805$	−11.5563	+	2.03769i	−0.407307	+	0.0718192i
$806$		0			0
$807$	−9.28093	−	24.7284i	−0.326704	−	0.870480i
$808$		0			0
$809$		−	16.0122i		−	0.562958i	−0.959567	−	0.281479i	$-0.909175\pi$
$809$		−	16.0122i		−	0.562958i	0.959567	−	0.281479i	$-0.0908249\pi$
$810$		0			0
$811$	21.9288			0.770023			0.385012	−	0.922912i	$-0.374197\pi$
$811$	21.9288			0.770023			0.385012	+	0.922912i	$0.374197\pi$
$812$		0			0
$813$	−50.2504	+	18.8597i	−1.76236	+	0.661439i
$814$		0			0
$815$	2.00173	+	11.3524i	0.0701175	+	0.397656i
$816$		0			0
$817$	7.83284	+	6.57254i	0.274037	+	0.229944i
$818$		0			0
$819$	14.9235	+	5.09673i	0.521468	+	0.178094i
$820$		0			0
$821$	1.41374	−	8.01771i	0.0493398	−	0.279820i	−0.950149	−	0.311797i	$-0.899069\pi$
$821$	1.41374	−	8.01771i	0.0493398	−	0.279820i	0.999489	+	0.0319769i	$0.0101803\pi$
$822$		0			0
$823$	12.5890	−	34.5880i	0.438825	−	1.20566i	−0.501432	−	0.865197i	$-0.667193\pi$
$823$	12.5890	−	34.5880i	0.438825	−	1.20566i	0.940257	−	0.340465i	$-0.110585\pi$
$824$		0			0
$825$	−0.515857	−	0.873245i	−0.0179598	−	0.0304025i
$826$		0			0
$827$	−19.5617	+	11.2939i	−0.680226	+	0.392728i	−0.799940	−	0.600080i	$-0.795135\pi$
$827$	−19.5617	+	11.2939i	−0.680226	+	0.392728i	0.119714	+	0.992808i	$0.461802\pi$
$828$		0			0
$829$	−26.7278	−	15.4313i	−0.928294	−	0.535951i	−0.0420222	−	0.999117i	$-0.513380\pi$
$829$	−26.7278	−	15.4313i	−0.928294	−	0.535951i	−0.886272	+	0.463166i	$0.846713\pi$
$830$		0			0
$831$	−35.8441	−	12.6425i	−1.24342	−	0.438563i
$832$		0			0
$833$	−14.0223	−	16.7111i	−0.485844	−	0.579006i
$834$		0			0
$835$	−40.4631	+	14.7274i	−1.40028	+	0.509661i
$836$		0			0
$837$	4.51577	+	21.7760i	0.156088	+	0.752689i
$838$		0			0
$839$	−20.8563	+	7.59109i	−0.720041	+	0.262073i	−0.675943	−	0.736954i	$-0.736263\pi$
$839$	−20.8563	+	7.59109i	−0.720041	+	0.262073i	−0.0440977	+	0.999027i	$0.514041\pi$
$840$		0			0
$841$	4.64024	−	3.89362i	0.160008	−	0.134263i
$842$		0			0
$843$	5.57211	+	29.8554i	0.191914	+	1.02827i
$844$		0			0
$845$	−15.5322	+	26.9025i	−0.534322	+	0.925473i
$846$		0			0
$847$	5.04426	−	2.91230i	0.173323	−	0.100068i
$848$		0			0
$849$	−0.559534	−	56.0587i	−0.0192032	−	1.92393i
$850$		0			0
$851$	3.71367	−	10.2032i	0.127303	−	0.349762i
$852$		0			0
$853$	−22.3662	−	3.94377i	−0.765806	−	0.135032i	−0.222918	−	0.974837i	$-0.571558\pi$
$853$	−22.3662	−	3.94377i	−0.765806	−	0.135032i	−0.542888	+	0.839805i	$0.682669\pi$
$854$		0			0
$855$	36.5187	−	14.1234i	1.24891	−	0.483010i
$856$		0			0
$857$	3.47977	−	4.14703i	0.118867	−	0.141660i	−0.703329	−	0.710864i	$-0.748304\pi$
$857$	3.47977	−	4.14703i	0.118867	−	0.141660i	0.822196	+	0.569204i	$0.192749\pi$
$858$		0			0
$859$	5.65784	+	32.0872i	0.193043	+	1.09480i	0.915178	+	0.403049i	$0.132050\pi$
$859$	5.65784	+	32.0872i	0.193043	+	1.09480i	−0.722135	+	0.691752i	$0.756839\pi$
$860$		0			0
$861$	13.1874	−	16.0386i	0.449426	−	0.546593i
$862$		0			0
$863$	−13.2192			−0.449986			−0.224993	−	0.974360i	$-0.572236\pi$
$863$	−13.2192			−0.449986			−0.224993	+	0.974360i	$0.572236\pi$
$864$		0			0
$865$	36.0106			1.22440
$866$		0			0
$867$	6.15086	+	1.02137i	0.208894	+	0.0346876i
$868$		0			0
$869$	−3.55007	−	20.1335i	−0.120428	−	0.682981i
$870$		0			0
$871$	42.9707	−	51.2105i	1.45601	−	1.73520i
$872$		0			0
$873$	0.557652	+	0.922837i	0.0188737	+	0.0312333i
$874$		0			0
$875$	10.9283	+	1.92696i	0.369445	+	0.0651431i
$876$		0			0
$877$	2.29892	−	6.31624i	0.0776291	−	0.213284i	−0.894807	−	0.446453i	$-0.852687\pi$
$877$	2.29892	−	6.31624i	0.0776291	−	0.213284i	0.972436	+	0.233168i	$0.0749093\pi$
$878$		0			0
$879$	36.5020	+	20.5914i	1.23118	+	0.694531i
$880$		0			0
$881$	−8.26078	+	4.76936i	−0.278313	+	0.160684i	−0.632659	−	0.774430i	$-0.718037\pi$
$881$	−8.26078	+	4.76936i	−0.278313	+	0.160684i	0.354347	+	0.935114i	$0.384703\pi$
$882$		0			0
$883$	−15.7656	+	27.3069i	−0.530555	+	0.918949i	0.468809	+	0.883300i	$0.344683\pi$
$883$	−15.7656	+	27.3069i	−0.530555	+	0.918949i	−0.999364	+	0.0356494i	$0.988650\pi$
$884$		0			0
$885$	29.3874	−	25.1631i	0.987848	−	0.845847i
$886$		0			0
$887$	−31.1111	+	26.1054i	−1.04461	+	0.876532i	−0.992517	−	0.122110i	$-0.961034\pi$
$887$	−31.1111	+	26.1054i	−1.04461	+	0.876532i	−0.0520935	+	0.998642i	$0.516589\pi$
$888$		0			0
$889$	−2.58885	+	0.942263i	−0.0868272	+	0.0316025i
$890$		0			0
$891$	−6.29803	+	19.7194i	−0.210992	+	0.660625i
$892$		0			0
$893$	19.1479	−	6.96925i	0.640758	−	0.233217i
$894$		0			0
$895$	−36.2928	−	43.2521i	−1.21314	−	1.44576i
$896$		0			0
$897$	−34.0193	+	29.1291i	−1.13587	+	0.972593i
$898$		0			0
$899$	−21.9462	−	12.6707i	−0.731948	−	0.422590i
$900$		0			0
$901$	−12.2494	+	7.07218i	−0.408086	+	0.235609i
$902$		0			0
$903$	−1.55908	+	2.76374i	−0.0518828	+	0.0919715i
$904$		0			0
$905$	−7.02779	+	19.3087i	−0.233612	+	0.641843i
$906$		0			0
$907$	−0.671160	+	3.80634i	−0.0222855	+	0.126387i	−0.993921	−	0.110097i	$-0.964884\pi$
$907$	−0.671160	+	3.80634i	−0.0222855	+	0.126387i	0.971635	+	0.236484i	$0.0759951\pi$
$908$		0			0
$909$	9.41678	−	0.188001i	0.312335	−	0.00623559i
$910$		0			0
$911$	3.22343	+	2.70478i	0.106797	+	0.0896132i	0.694622	−	0.719374i	$-0.255571\pi$
$911$	3.22343	+	2.70478i	0.106797	+	0.0896132i	−0.587826	+	0.808988i	$0.700016\pi$
$912$		0			0
$913$	−1.35139	−	7.66411i	−0.0447244	−	0.253645i
$914$		0			0
$915$	8.97439	−	54.0452i	0.296684	−	1.78668i
$916$		0			0
$917$	−8.54764			−0.282268
$918$		0			0
$919$			14.9699i			0.493812i	0.969039	+	0.246906i	$0.0794139\pi$
$919$			14.9699i			0.493812i	−0.969039	+	0.246906i	$0.920586\pi$
$920$		0			0
$921$	2.90025	−	3.52729i	0.0955665	−	0.116228i
$922$		0			0
$923$	53.1210	−	9.36667i	1.74850	−	0.308308i
$924$		0			0
$925$	0.354089	−	0.421987i	0.0116424	−	0.0138749i
$926$		0			0
$927$	17.5989	−	21.8446i	0.578022	−	0.717470i
$928$		0			0
$929$	−27.8646	−	4.91329i	−0.914209	−	0.161200i	−0.303295	−	0.952897i	$-0.598087\pi$
$929$	−27.8646	−	4.91329i	−0.914209	−	0.161200i	−0.610914	+	0.791697i	$0.709198\pi$
$930$		0			0
$931$	31.8841	+	11.6049i	1.04496	+	0.380335i
$932$		0			0
$933$	0.141864	+	14.2131i	0.00464442	+	0.465315i
$934$		0			0
$935$	−9.65023	−	16.7147i	−0.315596	−	0.546629i
$936$		0			0
$937$	27.7865	−	48.1276i	0.907744	−	1.57226i	0.0905543	−	0.995892i	$-0.471136\pi$
$937$	27.7865	−	48.1276i	0.907744	−	1.57226i	0.817190	−	0.576368i	$-0.195531\pi$
$938$		0			0
$939$	−28.9248	+	5.39843i	−0.943926	+	0.176171i
$940$		0			0
$941$	19.5910	−	16.4388i	0.638649	−	0.535890i	−0.264954	−	0.964261i	$-0.585357\pi$
$941$	19.5910	−	16.4388i	0.638649	−	0.535890i	0.903603	+	0.428371i	$0.140912\pi$
$942$		0			0
$943$	20.1689	+	55.4136i	0.656790	+	1.80452i
$944$		0			0
$945$	6.38779	+	10.3364i	0.207795	+	0.336244i
$946$		0			0
$947$	15.7821	+	43.3609i	0.512849	+	1.40904i	0.878255	+	0.478193i	$0.158708\pi$
$947$	15.7821	+	43.3609i	0.512849	+	1.40904i	−0.365406	+	0.930848i	$0.619070\pi$
$948$		0			0
$949$	−6.31556	−	7.52659i	−0.205012	−	0.244323i
$950$		0			0
$951$	4.19712	−	11.8997i	0.136101	−	0.385875i
$952$		0			0
$953$	17.6438	+	10.1866i	0.571537	+	0.329977i	0.757763	−	0.652530i	$-0.226292\pi$
$953$	17.6438	+	10.1866i	0.571537	+	0.329977i	−0.186226	+	0.982507i	$0.559626\pi$
$954$		0			0
$955$	5.33174	+	9.23485i	0.172531	+	0.298833i
$956$		0			0
$957$	−11.9974	−	20.3092i	−0.387820	−	0.656503i
$958$		0			0
$959$	−2.95859	−	1.07684i	−0.0955377	−	0.0347729i
$960$		0			0
$961$	2.20220	−	12.4893i	0.0710388	−	0.402881i
$962$		0			0
$963$	−13.2752	−	15.1942i	−0.427786	−	0.489626i
$964$		0			0
$965$	−37.8426	−	31.7537i	−1.21820	−	1.02219i
$966$		0			0
$967$	−27.7741	+	4.89732i	−0.893154	+	0.157487i	−0.601345	−	0.798990i	$-0.705368\pi$
$967$	−27.7741	+	4.89732i	−0.893154	+	0.157487i	−0.291809	+	0.956477i	$0.594257\pi$
$968$		0			0
$969$	33.7981	−	12.6849i	1.08575	−	0.407498i
$970$		0			0
$971$			22.6663i			0.727397i	0.931517	+	0.363698i	$0.118486\pi$
$971$			22.6663i			0.727397i	−0.931517	+	0.363698i	$0.881514\pi$
$972$		0			0
$973$		−	8.32454i		−	0.266873i
$974$		0			0
$975$	−2.12727	+	0.798397i	−0.0681273	+	0.0255692i
$976$		0			0
$977$	3.41255	−	0.601725i	0.109177	−	0.0192509i	−0.118793	−	0.992919i	$-0.537902\pi$
$977$	3.41255	−	0.601725i	0.109177	−	0.0192509i	0.227970	+	0.973668i	$0.426791\pi$
$978$		0			0
$979$	6.89912	+	5.78905i	0.220497	+	0.185019i
$980$		0			0
$981$	18.3228	+	20.9715i	0.585003	+	0.669570i
$982$		0			0
$983$	−1.18209	+	6.70399i	−0.0377029	+	0.213824i	−0.997839	−	0.0657099i	$-0.979069\pi$
$983$	−1.18209	+	6.70399i	−0.0377029	+	0.213824i	0.960136	+	0.279534i	$0.0901799\pi$
$984$		0			0
$985$	−30.8804	−	11.2396i	−0.983932	−	0.358122i
$986$		0			0
$987$	3.21628	+	5.44453i	0.102375	+	0.173301i
$988$		0			0
$989$	−4.50591	−	7.80447i	−0.143280	−	0.248168i
$990$		0			0
$991$	2.80756	+	1.62094i	0.0891850	+	0.0514910i	0.543929	−	0.839131i	$-0.316936\pi$
$991$	2.80756	+	1.62094i	0.0891850	+	0.0514910i	−0.454744	+	0.890622i	$0.650269\pi$
$992$		0			0
$993$	−0.894908	+	2.53725i	−0.0283990	+	0.0805172i
$994$		0			0
$995$	−9.92641	−	11.8298i	−0.314688	−	0.375031i
$996$		0			0
$997$	13.6667	+	37.5488i	0.432828	+	1.18918i	0.944069	+	0.329747i	$0.106963\pi$
$997$	13.6667	+	37.5488i	0.432828	+	1.18918i	−0.511242	+	0.859437i	$0.670814\pi$
$998$		0			0
$999$	−11.2383	+	0.336604i	−0.355563	+	0.0106497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.47.11		192
4.3	odd	2		216.2.v.b.155.28	yes	192
8.3	odd	2	inner	864.2.bh.b.47.12		192
8.5	even	2		216.2.v.b.155.3	yes	192
12.11	even	2		648.2.v.b.467.5		192
24.5	odd	2		648.2.v.b.467.30		192
27.23	odd	18	inner	864.2.bh.b.239.12		192
108.23	even	18		216.2.v.b.131.3	✓	192
108.31	odd	18		648.2.v.b.179.30		192
216.77	odd	18		216.2.v.b.131.28	yes	192
216.85	even	18		648.2.v.b.179.5		192
216.131	even	18	inner	864.2.bh.b.239.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.131.3	✓	192	108.23	even	18
216.2.v.b.131.28	yes	192	216.77	odd	18
216.2.v.b.155.3	yes	192	8.5	even	2
216.2.v.b.155.28	yes	192	4.3	odd	2
648.2.v.b.179.5		192	216.85	even	18
648.2.v.b.179.30		192	108.31	odd	18
648.2.v.b.467.5		192	12.11	even	2
648.2.v.b.467.30		192	24.5	odd	2
864.2.bh.b.47.11		192	1.1	even	1	trivial
864.2.bh.b.47.12		192	8.3	odd	2	inner
864.2.bh.b.239.11		192	216.131	even	18	inner
864.2.bh.b.239.12		192	27.23	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.bh (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.608611 - 1.62160i) q^{3} +(-0.398052 - 2.25746i) q^{5} +(-0.655732 + 0.781471i) q^{7} +(-2.25918 + 1.97385i) q^{9} +O(q^{10})\)	\(q+(-0.608611 - 1.62160i) q^{3} +(-0.398052 - 2.25746i) q^{5} +(-0.655732 + 0.781471i) q^{7} +(-2.25918 + 1.97385i) q^{9} +(-2.26514 - 0.399405i) q^{11} +(-1.76237 + 4.84208i) q^{13} +(-3.41845 + 2.01940i) q^{15} +(-3.17019 + 1.83031i) q^{17} +(2.84684 - 4.93086i) q^{19} +(1.66632 + 0.587724i) q^{21} +(-3.84409 + 3.22558i) q^{23} +(-0.239232 + 0.0870733i) q^{25} +(4.57576 + 2.46219i) q^{27} +(-5.56385 + 2.02508i) q^{29} +(2.75110 + 3.27864i) q^{31} +(0.730913 + 3.91623i) q^{33} +(2.02516 + 1.16923i) q^{35} +(-1.87388 + 1.08189i) q^{37} +(8.92452 - 0.0890776i) q^{39} +(4.01923 - 11.0427i) q^{41} +(-0.311848 + 1.76858i) q^{43} +(5.35517 + 4.31433i) q^{45} +(2.74155 + 2.30043i) q^{47} +(1.03482 + 5.86878i) q^{49} +(4.89745 + 4.02684i) q^{51} +3.86392 q^{53} +5.27245i q^{55} +(-9.72851 - 1.61545i) q^{57} +(-9.59630 + 1.69209i) q^{59} +(-8.86954 + 10.5703i) q^{61} +(-0.0610873 - 3.05981i) q^{63} +(11.6323 + 2.05109i) q^{65} +(-12.1912 - 4.43722i) q^{67} +(7.57016 + 4.27046i) q^{69} +(-5.23407 - 9.06567i) q^{71} +(-0.953385 + 1.65131i) q^{73} +(0.286797 + 0.334945i) q^{75} +(1.79745 - 1.50824i) q^{77} +(3.04001 + 8.35237i) q^{79} +(1.20783 - 8.91858i) q^{81} +(1.15723 + 3.17946i) q^{83} +(5.39376 + 6.42804i) q^{85} +(6.67009 + 7.78987i) q^{87} +(-3.39099 - 1.95779i) q^{89} +(-2.62830 - 4.55235i) q^{91} +(3.64229 - 6.45661i) q^{93} +(-12.2644 - 4.46389i) q^{95} +(0.0624115 - 0.353953i) q^{97} +(5.90573 - 3.56871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) 192 * q + 12 * q^3 - 12 * q^9	\( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) \) 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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