LMFDB - Embedded newform 2646.2.l.c.521.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(521,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("2646.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.l (of order $6$, degree $2$, 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.10
Character	$\chi$	$=$	2646.521
Dual form			2646.2.l.c.1097.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.724499 - 1.25487i) q^{5} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.724499 - 1.25487i) q^{5} +1.00000i q^{8} +(-1.25487 - 0.724499i) q^{10} +(-1.21051 + 0.698887i) q^{11} +(3.03494 - 1.75222i) q^{13} +1.00000 q^{16} +(-3.95277 + 6.84639i) q^{17} +(-3.61019 + 2.08434i) q^{19} +(-0.724499 + 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(-3.13371 - 1.80925i) q^{23} +(1.45020 + 2.51182i) q^{25} +(-1.75222 - 3.03494i) q^{26} +(-4.06467 - 2.34674i) q^{29} -0.917280i q^{31} -1.00000i q^{32} +(6.84639 + 3.95277i) q^{34} +(2.14176 + 3.70963i) q^{37} +(2.08434 + 3.61019i) q^{38} +(1.25487 + 0.724499i) q^{40} +(-0.343727 - 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} +(1.21051 - 0.698887i) q^{44} +(-1.80925 + 3.13371i) q^{46} -8.31745 q^{47} +(2.51182 - 1.45020i) q^{50} +(-3.03494 + 1.75222i) q^{52} +(5.16176 + 2.98014i) q^{53} +2.02537i q^{55} +(-2.34674 + 4.06467i) q^{58} -9.44130 q^{59} -9.85957i q^{61} -0.917280 q^{62} -1.00000 q^{64} -5.07794i q^{65} -2.97079 q^{67} +(3.95277 - 6.84639i) q^{68} +12.9436i q^{71} +(-9.79071 - 5.65267i) q^{73} +(3.70963 - 2.14176i) q^{74} +(3.61019 - 2.08434i) q^{76} +15.6342 q^{79} +(0.724499 - 1.25487i) q^{80} +(-0.595352 + 0.343727i) q^{82} +(4.11183 - 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(10.4182 + 6.01497i) q^{86} +(-0.698887 - 1.21051i) q^{88} +(0.533417 + 0.923906i) q^{89} +(3.13371 + 1.80925i) q^{92} +8.31745i q^{94} +6.04043i q^{95} +(-10.9670 - 6.33179i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} + 48 q^{11} + 48 q^{16} + 48 q^{23} - 24 q^{25} - 48 q^{44} + 48 q^{50} - 96 q^{53} - 48 q^{64} - 96 q^{79} + 48 q^{85} + 96 q^{86} - 48 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 + 48 * q^11 + 48 * q^16 + 48 * q^23 - 24 * q^25 - 48 * q^44 + 48 * q^50 - 96 * q^53 - 48 * q^64 - 96 * q^79 + 48 * q^85 + 96 * q^86 - 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.724499	−	1.25487i	0.324006	−	0.561195i	−0.657305	−	0.753625i	$-0.728304\pi$
$5$	0.724499	−	1.25487i	0.324006	−	0.561195i	0.981311	+	0.192430i	$0.0616369\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.25487	−	0.724499i	−0.396825	−	0.229107i
$11$	−1.21051	+	0.698887i	−0.364982	+	0.210722i	−0.671264	−	0.741218i	$-0.734248\pi$
$11$	−1.21051	+	0.698887i	−0.364982	+	0.210722i	0.306282	+	0.951941i	$0.400915\pi$
$12$		0			0
$13$	3.03494	−	1.75222i	0.841740	−	0.485979i	−0.0161150	−	0.999870i	$-0.505130\pi$
$13$	3.03494	−	1.75222i	0.841740	−	0.485979i	0.857855	+	0.513891i	$0.171796\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.95277	+	6.84639i	−0.958687	+	1.66049i	−0.232990	+	0.972479i	$0.574851\pi$
$17$	−3.95277	+	6.84639i	−0.958687	+	1.66049i	−0.725697	+	0.688015i	$0.758482\pi$
$18$		0			0
$19$	−3.61019	+	2.08434i	−0.828235	+	0.478181i	−0.853248	−	0.521506i	$-0.825371\pi$
$19$	−3.61019	+	2.08434i	−0.828235	+	0.478181i	0.0250133	+	0.999687i	$0.492037\pi$
$20$	−0.724499	+	1.25487i	−0.162003	+	0.280597i
$21$		0			0
$22$	0.698887	+	1.21051i	0.149003	+	0.258081i
$23$	−3.13371	−	1.80925i	−0.653424	−	0.377255i	0.136343	−	0.990662i	$-0.456465\pi$
$23$	−3.13371	−	1.80925i	−0.653424	−	0.377255i	−0.789767	+	0.613407i	$0.789798\pi$
$24$		0			0
$25$	1.45020	+	2.51182i	0.290040	+	0.502364i
$26$	−1.75222	−	3.03494i	−0.343639	−	0.595200i
$27$		0			0
$28$		0			0
$29$	−4.06467	−	2.34674i	−0.754791	−	0.435779i	0.0726316	−	0.997359i	$-0.476860\pi$
$29$	−4.06467	−	2.34674i	−0.754791	−	0.435779i	−0.827422	+	0.561580i	$0.810194\pi$
$30$		0			0
$31$		−	0.917280i		−	0.164748i	−0.996601	−	0.0823741i	$-0.973750\pi$
$31$		−	0.917280i		−	0.164748i	0.996601	−	0.0823741i	$-0.0262502\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	6.84639	+	3.95277i	1.17415	+	0.677894i
$35$		0			0
$36$		0			0
$37$	2.14176	+	3.70963i	0.352103	+	0.609860i	0.986618	−	0.163051i	$-0.0521334\pi$
$37$	2.14176	+	3.70963i	0.352103	+	0.609860i	−0.634515	+	0.772911i	$0.718800\pi$
$38$	2.08434	+	3.61019i	0.338125	+	0.585650i
$39$		0			0
$40$	1.25487	+	0.724499i	0.198412	+	0.114553i
$41$	−0.343727	−	0.595352i	−0.0536811	−	0.0929784i	0.837936	−	0.545768i	$-0.183762\pi$
$41$	−0.343727	−	0.595352i	−0.0536811	−	0.0929784i	−0.891617	+	0.452790i	$0.850429\pi$
$42$		0			0
$43$	−6.01497	+	10.4182i	−0.917275	+	1.58877i	−0.113739	+	0.993511i	$0.536283\pi$
$43$	−6.01497	+	10.4182i	−0.917275	+	1.58877i	−0.803536	+	0.595256i	$0.797051\pi$
$44$	1.21051	−	0.698887i	0.182491	−	0.105361i
$45$		0			0
$46$	−1.80925	+	3.13371i	−0.266759	+	0.462041i
$47$	−8.31745			−1.21322			−0.606612	−	0.794998i	$-0.707472\pi$
$47$	−8.31745			−1.21322			−0.606612	+	0.794998i	$0.707472\pi$
$48$		0			0
$49$		0			0
$50$	2.51182	−	1.45020i	0.355225	−	0.205089i
$51$		0			0
$52$	−3.03494	+	1.75222i	−0.420870	+	0.242990i
$53$	5.16176	+	2.98014i	0.709022	+	0.409354i	0.810699	−	0.585463i	$-0.199087\pi$
$53$	5.16176	+	2.98014i	0.709022	+	0.409354i	−0.101677	+	0.994818i	$0.532421\pi$
$54$		0			0
$55$			2.02537i			0.273101i
$56$		0			0
$57$		0			0
$58$	−2.34674	+	4.06467i	−0.308142	+	0.533718i
$59$	−9.44130			−1.22915			−0.614577	−	0.788857i	$-0.710673\pi$
$59$	−9.44130			−1.22915			−0.614577	+	0.788857i	$0.710673\pi$
$60$		0			0
$61$		−	9.85957i		−	1.26239i	−0.775625	−	0.631194i	$-0.782565\pi$
$61$		−	9.85957i		−	1.26239i	0.775625	−	0.631194i	$-0.217435\pi$
$62$	−0.917280			−0.116495
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	5.07794i		−	0.629840i
$66$		0			0
$67$	−2.97079			−0.362940			−0.181470	−	0.983396i	$-0.558086\pi$
$67$	−2.97079			−0.362940			−0.181470	+	0.983396i	$0.558086\pi$
$68$	3.95277	−	6.84639i	0.479343	−	0.830247i
$69$		0			0
$70$		0			0
$71$			12.9436i			1.53612i	0.640377	+	0.768061i	$0.278778\pi$
$71$			12.9436i			1.53612i	−0.640377	+	0.768061i	$0.721222\pi$
$72$		0			0
$73$	−9.79071	−	5.65267i	−1.14592	−	0.661595i	−0.198027	−	0.980197i	$-0.563453\pi$
$73$	−9.79071	−	5.65267i	−1.14592	−	0.661595i	−0.947889	+	0.318602i	$0.896787\pi$
$74$	3.70963	−	2.14176i	0.431236	−	0.248974i
$75$		0			0
$76$	3.61019	−	2.08434i	0.414117	−	0.239091i
$77$		0			0
$78$		0			0
$79$	15.6342			1.75898			0.879491	−	0.475915i	$-0.157883\pi$
$79$	15.6342			1.75898			0.879491	+	0.475915i	$0.157883\pi$
$80$	0.724499	−	1.25487i	0.0810015	−	0.140299i
$81$		0			0
$82$	−0.595352	+	0.343727i	−0.0657457	+	0.0379583i
$83$	4.11183	−	7.12189i	0.451332	−	0.781729i	−0.547137	−	0.837043i	$-0.684282\pi$
$83$	4.11183	−	7.12189i	0.451332	−	0.781729i	0.998469	+	0.0553135i	$0.0176158\pi$
$84$		0			0
$85$	5.72755	+	9.92041i	0.621240	+	1.07602i
$86$	10.4182	+	6.01497i	1.12343	+	0.648611i
$87$		0			0
$88$	−0.698887	−	1.21051i	−0.0745016	−	0.129041i
$89$	0.533417	+	0.923906i	0.0565421	+	0.0979338i	0.892911	−	0.450233i	$-0.148659\pi$
$89$	0.533417	+	0.923906i	0.0565421	+	0.0979338i	−0.836369	+	0.548167i	$0.815326\pi$
$90$		0			0
$91$		0			0
$92$	3.13371	+	1.80925i	0.326712	+	0.188627i
$93$		0			0
$94$			8.31745i			0.857879i
$95$			6.04043i			0.619735i
$96$		0			0
$97$	−10.9670	−	6.33179i	−1.11353	−	0.642895i	−0.173787	−	0.984783i	$-0.555600\pi$
$97$	−10.9670	−	6.33179i	−1.11353	−	0.642895i	−0.939741	+	0.341888i	$0.888934\pi$
$98$		0			0
$99$		0			0
$100$	−1.45020	−	2.51182i	−0.145020	−	0.251182i
$101$	8.77726	+	15.2027i	0.873370	+	1.51272i	0.858489	+	0.512831i	$0.171403\pi$
$101$	8.77726	+	15.2027i	0.873370	+	1.51272i	0.0148801	+	0.999889i	$0.495263\pi$
$102$		0			0
$103$	3.86082	+	2.22905i	0.380418	+	0.219635i	0.678000	−	0.735062i	$-0.262847\pi$
$103$	3.86082	+	2.22905i	0.380418	+	0.219635i	−0.297582	+	0.954696i	$0.596180\pi$
$104$	1.75222	+	3.03494i	0.171820	+	0.297600i
$105$		0			0
$106$	2.98014	−	5.16176i	0.289457	−	0.501355i
$107$	2.04566	−	1.18106i	0.197762	−	0.114178i	−0.397849	−	0.917451i	$-0.630243\pi$
$107$	2.04566	−	1.18106i	0.197762	−	0.114178i	0.595611	+	0.803273i	$0.296910\pi$
$108$		0			0
$109$	−6.49776	+	11.2545i	−0.622373	+	1.07798i	0.366670	+	0.930351i	$0.380498\pi$
$109$	−6.49776	+	11.2545i	−0.622373	+	1.07798i	−0.989043	+	0.147630i	$0.952836\pi$
$110$	2.02537			0.193112
$111$		0			0
$112$		0			0
$113$	−2.90616	+	1.67787i	−0.273388	+	0.157841i	−0.630426	−	0.776249i	$-0.717120\pi$
$113$	−2.90616	+	1.67787i	−0.273388	+	0.157841i	0.357038	+	0.934090i	$0.383787\pi$
$114$		0			0
$115$	−4.54074	+	2.62160i	−0.423427	+	0.244465i
$116$	4.06467	+	2.34674i	0.377395	+	0.217889i
$117$		0			0
$118$			9.44130i			0.869143i
$119$		0			0
$120$		0			0
$121$	−4.52311	+	7.83426i	−0.411192	+	0.712206i
$122$	−9.85957			−0.892644
$123$		0			0
$124$			0.917280i			0.0823741i
$125$	11.4477			1.02391
$126$		0			0
$127$	−12.9075			−1.14535			−0.572677	−	0.819781i	$-0.694095\pi$
$127$	−12.9075			−1.14535			−0.572677	+	0.819781i	$0.694095\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−5.07794			−0.445364
$131$	4.12856	−	7.15088i	0.360714	−	0.624775i	−0.627364	−	0.778726i	$-0.715866\pi$
$131$	4.12856	−	7.15088i	0.360714	−	0.624775i	0.988079	+	0.153951i	$0.0491996\pi$
$132$		0			0
$133$		0			0
$134$			2.97079i			0.256637i
$135$		0			0
$136$	−6.84639	−	3.95277i	−0.587073	−	0.338947i
$137$	11.3267	−	6.53946i	0.967703	−	0.558703i	0.0691676	−	0.997605i	$-0.477966\pi$
$137$	11.3267	−	6.53946i	0.967703	−	0.558703i	0.898535	+	0.438902i	$0.144632\pi$
$138$		0			0
$139$	−10.6722	+	6.16162i	−0.905207	+	0.522621i	−0.878886	−	0.477032i	$-0.841713\pi$
$139$	−10.6722	+	6.16162i	−0.905207	+	0.522621i	−0.0263210	+	0.999654i	$0.508379\pi$
$140$		0			0
$141$		0			0
$142$	12.9436			1.08620
$143$	−2.44921	+	4.24216i	−0.204813	+	0.354747i
$144$		0			0
$145$	−5.88971	+	3.40042i	−0.489113	+	0.282390i
$146$	−5.65267	+	9.79071i	−0.467818	+	0.810285i
$147$		0			0
$148$	−2.14176	−	3.70963i	−0.176051	−	0.304930i
$149$	−0.538692	−	0.311014i	−0.0441314	−	0.0254792i	0.477772	−	0.878484i	$-0.341445\pi$
$149$	−0.538692	−	0.311014i	−0.0441314	−	0.0254792i	−0.521903	+	0.853005i	$0.674778\pi$
$150$		0			0
$151$	10.5911	+	18.3443i	0.861889	+	1.49284i	0.870103	+	0.492870i	$0.164052\pi$
$151$	10.5911	+	18.3443i	0.861889	+	1.49284i	−0.00821353	+	0.999966i	$0.502614\pi$
$152$	−2.08434	−	3.61019i	−0.169063	−	0.292825i
$153$		0			0
$154$		0			0
$155$	−1.15107	−	0.664569i	−0.0924559	−	0.0533794i
$156$		0			0
$157$			15.0294i			1.19947i	0.800197	+	0.599737i	$0.204728\pi$
$157$			15.0294i			1.19947i	−0.800197	+	0.599737i	$0.795272\pi$
$158$		−	15.6342i		−	1.24379i
$159$		0			0
$160$	−1.25487	−	0.724499i	−0.0992062	−	0.0572767i
$161$		0			0
$162$		0			0
$163$	1.51764	+	2.62863i	0.118871	+	0.205890i	0.919320	−	0.393510i	$-0.128739\pi$
$163$	1.51764	+	2.62863i	0.118871	+	0.205890i	−0.800450	+	0.599400i	$0.795406\pi$
$164$	0.343727	+	0.595352i	0.0268406	+	0.0464892i
$165$		0			0
$166$	−7.12189	−	4.11183i	−0.552766	−	0.319140i
$167$	−3.05895	−	5.29826i	−0.236709	−	0.409992i	0.723059	−	0.690786i	$-0.242735\pi$
$167$	−3.05895	−	5.29826i	−0.236709	−	0.409992i	−0.959768	+	0.280794i	$0.909402\pi$
$168$		0			0
$169$	−0.359433	+	0.622557i	−0.0276487	+	0.0478890i
$170$	9.92041	−	5.72755i	0.760861	−	0.439283i
$171$		0			0
$172$	6.01497	−	10.4182i	0.458637	−	0.794383i
$173$	2.29515			0.174497			0.0872484	−	0.996187i	$-0.472193\pi$
$173$	2.29515			0.174497			0.0872484	+	0.996187i	$0.472193\pi$
$174$		0			0
$175$		0			0
$176$	−1.21051	+	0.698887i	−0.0912454	+	0.0526806i
$177$		0			0
$178$	0.923906	−	0.533417i	0.0692497	−	0.0399813i
$179$	2.92364	+	1.68796i	0.218523	+	0.126164i	0.605266	−	0.796023i	$-0.293067\pi$
$179$	2.92364	+	1.68796i	0.218523	+	0.126164i	−0.386743	+	0.922187i	$0.626400\pi$
$180$		0			0
$181$			1.68857i			0.125511i	0.998029	+	0.0627553i	$0.0199888\pi$
$181$			1.68857i			0.125511i	−0.998029	+	0.0627553i	$0.980011\pi$
$182$		0			0
$183$		0			0
$184$	1.80925	−	3.13371i	0.133380	−	0.231020i
$185$	6.20681			0.456334
$186$		0			0
$187$		−	11.0501i		−	0.808067i
$188$	8.31745			0.606612
$189$		0			0
$190$	6.04043			0.438219
$191$		−	8.94832i		−	0.647478i	−0.946146	−	0.323739i	$-0.895060\pi$
$191$		−	8.94832i		−	0.647478i	0.946146	−	0.323739i	$-0.104940\pi$
$192$		0			0
$193$	25.6055			1.84313			0.921564	−	0.388227i	$-0.126912\pi$
$193$	25.6055			1.84313			0.921564	+	0.388227i	$0.126912\pi$
$194$	−6.33179	+	10.9670i	−0.454596	+	0.787383i
$195$		0			0
$196$		0			0
$197$			23.5602i			1.67860i	0.543670	+	0.839299i	$0.317034\pi$
$197$			23.5602i			1.67860i	−0.543670	+	0.839299i	$0.682966\pi$
$198$		0			0
$199$	−11.7989	−	6.81212i	−0.836404	−	0.482898i	0.0196362	−	0.999807i	$-0.493749\pi$
$199$	−11.7989	−	6.81212i	−0.836404	−	0.482898i	−0.856040	+	0.516909i	$0.827083\pi$
$200$	−2.51182	+	1.45020i	−0.177613	+	0.102545i
$201$		0			0
$202$	15.2027	−	8.77726i	1.06965	−	0.617566i
$203$		0			0
$204$		0			0
$205$	−0.996120			−0.0695720
$206$	2.22905	−	3.86082i	0.155305	−	0.268996i
$207$		0			0
$208$	3.03494	−	1.75222i	0.210435	−	0.121495i
$209$	2.91344	−	5.04623i	0.201527	−	0.349055i
$210$		0			0
$211$	−10.7961	−	18.6994i	−0.743235	−	1.28732i	−0.951015	−	0.309145i	$-0.899957\pi$
$211$	−10.7961	−	18.6994i	−0.743235	−	1.28732i	0.207780	−	0.978176i	$-0.433376\pi$
$212$	−5.16176	−	2.98014i	−0.354511	−	0.204677i
$213$		0			0
$214$	−1.18106	−	2.04566i	−0.0807359	−	0.139839i
$215$	8.71569	+	15.0960i	0.594405	+	1.02954i
$216$		0			0
$217$		0			0
$218$	11.2545	+	6.49776i	0.762248	+	0.440084i
$219$		0			0
$220$		−	2.02537i		−	0.136551i
$221$			27.7045i			1.86361i
$222$		0			0
$223$	−14.5710	−	8.41256i	−0.975745	−	0.563347i	−0.0747620	−	0.997201i	$-0.523820\pi$
$223$	−14.5710	−	8.41256i	−0.975745	−	0.563347i	−0.900983	+	0.433855i	$0.857153\pi$
$224$		0			0
$225$		0			0
$226$	1.67787	+	2.90616i	0.111610	+	0.193315i
$227$	−6.11065	−	10.5840i	−0.405578	−	0.702482i	0.588810	−	0.808271i	$-0.299596\pi$
$227$	−6.11065	−	10.5840i	−0.405578	−	0.702482i	−0.994389	+	0.105789i	$0.966263\pi$
$228$		0			0
$229$	16.8458	+	9.72591i	1.11320	+	0.642706i	0.939656	−	0.342120i	$-0.111145\pi$
$229$	16.8458	+	9.72591i	1.11320	+	0.642706i	0.173543	+	0.984826i	$0.444478\pi$
$230$	2.62160	+	4.54074i	0.172863	+	0.299408i
$231$		0			0
$232$	2.34674	−	4.06467i	0.154071	−	0.266859i
$233$	24.7381	−	14.2825i	1.62065	−	0.935681i	0.633900	−	0.773415i	$-0.281453\pi$
$233$	24.7381	−	14.2825i	1.62065	−	0.935681i	0.986747	−	0.162265i	$-0.0518801\pi$
$234$		0			0
$235$	−6.02598	+	10.4373i	−0.393092	+	0.680855i
$236$	9.44130			0.614577
$237$		0			0
$238$		0			0
$239$	10.0020	−	5.77465i	0.646975	−	0.373531i	−0.140322	−	0.990106i	$-0.544814\pi$
$239$	10.0020	−	5.77465i	0.646975	−	0.373531i	0.787296	+	0.616575i	$0.211480\pi$
$240$		0			0
$241$	0.0299000	−	0.0172628i	0.00192603	−	0.00111199i	−0.499037	−	0.866581i	$-0.666313\pi$
$241$	0.0299000	−	0.0172628i	0.00192603	−	0.00111199i	0.500963	+	0.865469i	$0.332979\pi$
$242$	7.83426	+	4.52311i	0.503606	+	0.290757i
$243$		0			0
$244$			9.85957i			0.631194i
$245$		0			0
$246$		0			0
$247$	−7.30447	+	12.6517i	−0.464772	+	0.805009i
$248$	0.917280			0.0582473
$249$		0			0
$250$		−	11.4477i		−	0.724014i
$251$	−3.26317			−0.205969			−0.102985	−	0.994683i	$-0.532839\pi$
$251$	−3.26317			−0.205969			−0.102985	+	0.994683i	$0.532839\pi$
$252$		0			0
$253$	5.05784			0.317984
$254$			12.9075i			0.809887i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−9.89851	+	17.1447i	−0.617452	+	1.06946i	0.372497	+	0.928034i	$0.378502\pi$
$257$	−9.89851	+	17.1447i	−0.617452	+	1.06946i	−0.989949	+	0.141425i	$0.954832\pi$
$258$		0			0
$259$		0			0
$260$			5.07794i			0.314920i
$261$		0			0
$262$	−7.15088	−	4.12856i	−0.441783	−	0.255063i
$263$	−15.2576	+	8.80897i	−0.940823	+	0.543184i	−0.890218	−	0.455535i	$-0.849448\pi$
$263$	−15.2576	+	8.80897i	−0.940823	+	0.543184i	−0.0506045	+	0.998719i	$0.516115\pi$
$264$		0			0
$265$	7.47939	−	4.31823i	0.459455	−	0.265266i
$266$		0			0
$267$		0			0
$268$	2.97079			0.181470
$269$	3.83672	−	6.64540i	0.233929	−	0.405177i	−0.725032	−	0.688715i	$-0.758175\pi$
$269$	3.83672	−	6.64540i	0.233929	−	0.405177i	0.958961	+	0.283538i	$0.0915083\pi$
$270$		0			0
$271$	−6.09146	+	3.51690i	−0.370030	+	0.213637i	−0.673471	−	0.739213i	$-0.735198\pi$
$271$	−6.09146	+	3.51690i	−0.370030	+	0.213637i	0.303442	+	0.952850i	$0.401864\pi$
$272$	−3.95277	+	6.84639i	−0.239672	+	0.415123i
$273$		0			0
$274$	−6.53946	−	11.3267i	−0.395063	−	0.684269i
$275$	−3.51096	−	2.02705i	−0.211719	−	0.122236i
$276$		0			0
$277$	−8.65364	−	14.9885i	−0.519947	−	0.900575i	−0.999731	−	0.0231880i	$-0.992618\pi$
$277$	−8.65364	−	14.9885i	−0.519947	−	0.900575i	0.479784	−	0.877387i	$-0.340715\pi$
$278$	6.16162	+	10.6722i	0.369549	+	0.640078i
$279$		0			0
$280$		0			0
$281$	−14.3155	−	8.26508i	−0.853994	−	0.493053i	0.00800273	−	0.999968i	$-0.497453\pi$
$281$	−14.3155	−	8.26508i	−0.853994	−	0.493053i	−0.861996	+	0.506915i	$0.830786\pi$
$282$		0			0
$283$			3.16284i			0.188011i	0.995572	+	0.0940057i	$0.0299672\pi$
$283$			3.16284i			0.188011i	−0.995572	+	0.0940057i	$0.970033\pi$
$284$		−	12.9436i		−	0.768061i
$285$		0			0
$286$	4.24216	+	2.44921i	0.250844	+	0.144825i
$287$		0			0
$288$		0			0
$289$	−22.7487	−	39.4019i	−1.33816	−	2.31776i
$290$	3.40042	+	5.88971i	0.199680	+	0.345855i
$291$		0			0
$292$	9.79071	+	5.65267i	0.572958	+	0.330797i
$293$	−4.26045	−	7.37932i	−0.248898	−	0.431104i	0.714322	−	0.699817i	$-0.246735\pi$
$293$	−4.26045	−	7.37932i	−0.248898	−	0.431104i	−0.963220	+	0.268713i	$0.913402\pi$
$294$		0			0
$295$	−6.84022	+	11.8476i	−0.398253	+	0.689794i
$296$	−3.70963	+	2.14176i	−0.215618	+	0.124487i
$297$		0			0
$298$	−0.311014	+	0.538692i	−0.0180165	+	0.0312056i
$299$	−12.6808			−0.733351
$300$		0			0
$301$		0			0
$302$	18.3443	−	10.5911i	1.05559	−	0.609448i
$303$		0			0
$304$	−3.61019	+	2.08434i	−0.207059	+	0.119545i
$305$	−12.3725	−	7.14325i	−0.708446	−	0.409022i
$306$		0			0
$307$			25.0805i			1.43142i	0.698398	+	0.715710i	$0.253897\pi$
$307$			25.0805i			1.43142i	−0.698398	+	0.715710i	$0.746103\pi$
$308$		0			0
$309$		0			0
$310$	−0.664569	+	1.15107i	−0.0377450	+	0.0653762i
$311$	3.57355			0.202638			0.101319	−	0.994854i	$-0.467694\pi$
$311$	3.57355			0.202638			0.101319	+	0.994854i	$0.467694\pi$
$312$		0			0
$313$			13.6293i			0.770372i	0.922839	+	0.385186i	$0.125863\pi$
$313$			13.6293i			0.770372i	−0.922839	+	0.385186i	$0.874137\pi$
$314$	15.0294			0.848157
$315$		0			0
$316$	−15.6342			−0.879491
$317$			4.28994i			0.240947i	0.992717	+	0.120474i	$0.0384413\pi$
$317$			4.28994i			0.240947i	−0.992717	+	0.120474i	$0.961559\pi$
$318$		0			0
$319$	6.56042			0.367313
$320$	−0.724499	+	1.25487i	−0.0405007	+	0.0701494i
$321$		0			0
$322$		0			0
$323$		−	32.9557i		−	1.83370i
$324$		0			0
$325$	8.80254	+	5.08215i	0.488277	+	0.281907i
$326$	2.62863	−	1.51764i	0.145586	−	0.0840542i
$327$		0			0
$328$	0.595352	−	0.343727i	0.0328728	−	0.0189791i
$329$		0			0
$330$		0			0
$331$	8.93923			0.491345			0.245672	−	0.969353i	$-0.420991\pi$
$331$	8.93923			0.491345			0.245672	+	0.969353i	$0.420991\pi$
$332$	−4.11183	+	7.12189i	−0.225666	+	0.390865i
$333$		0			0
$334$	−5.29826	+	3.05895i	−0.289908	+	0.167379i
$335$	−2.15234	+	3.72796i	−0.117595	+	0.203680i
$336$		0			0
$337$	0.0729773	+	0.126400i	0.00397532	+	0.00688546i	0.868006	−	0.496553i	$-0.165401\pi$
$337$	0.0729773	+	0.126400i	0.00397532	+	0.00688546i	−0.864031	+	0.503439i	$0.832068\pi$
$338$	0.622557	+	0.359433i	0.0338626	+	0.0195506i
$339$		0			0
$340$	−5.72755	−	9.92041i	−0.310620	−	0.538010i
$341$	0.641075	+	1.11037i	0.0347161	+	0.0601301i
$342$		0			0
$343$		0			0
$344$	−10.4182	−	6.01497i	−0.561714	−	0.324306i
$345$		0			0
$346$		−	2.29515i		−	0.123388i
$347$			22.2844i			1.19629i	0.801389	+	0.598144i	$0.204095\pi$
$347$			22.2844i			1.19629i	−0.801389	+	0.598144i	$0.795905\pi$
$348$		0			0
$349$	−2.79851	−	1.61572i	−0.149801	−	0.0864876i	0.423226	−	0.906024i	$-0.360898\pi$
$349$	−2.79851	−	1.61572i	−0.149801	−	0.0864876i	−0.573027	+	0.819537i	$0.694231\pi$
$350$		0			0
$351$		0			0
$352$	0.698887	+	1.21051i	0.0372508	+	0.0645203i
$353$	3.13232	+	5.42533i	0.166716	+	0.288761i	0.937263	−	0.348622i	$-0.113350\pi$
$353$	3.13232	+	5.42533i	0.166716	+	0.288761i	−0.770547	+	0.637383i	$0.780017\pi$
$354$		0			0
$355$	16.2425	+	9.37762i	0.862063	+	0.497712i
$356$	−0.533417	−	0.923906i	−0.0282711	−	0.0489669i
$357$		0			0
$358$	1.68796	−	2.92364i	0.0892116	−	0.154519i
$359$	−10.4523	+	6.03463i	−0.551651	+	0.318496i	−0.749787	−	0.661679i	$-0.769844\pi$
$359$	−10.4523	+	6.03463i	−0.551651	+	0.318496i	0.198137	+	0.980174i	$0.436511\pi$
$360$		0			0
$361$	−0.811015	+	1.40472i	−0.0426850	+	0.0739326i
$362$	1.68857			0.0887494
$363$		0			0
$364$		0			0
$365$	−14.1867	+	8.19071i	−0.742567	+	0.428721i
$366$		0			0
$367$	14.7907	−	8.53940i	0.772067	−	0.445753i	−0.0615446	−	0.998104i	$-0.519603\pi$
$367$	14.7907	−	8.53940i	0.772067	−	0.445753i	0.833611	+	0.552351i	$0.186269\pi$
$368$	−3.13371	−	1.80925i	−0.163356	−	0.0943136i
$369$		0			0
$370$		−	6.20681i		−	0.322677i
$371$		0			0
$372$		0			0
$373$	−1.93680	+	3.35463i	−0.100284	+	0.173696i	−0.911801	−	0.410631i	$-0.865308\pi$
$373$	−1.93680	+	3.35463i	−0.100284	+	0.173696i	0.811518	+	0.584328i	$0.198642\pi$
$374$	−11.0501			−0.571389
$375$		0			0
$376$		−	8.31745i		−	0.428939i
$377$	−16.4480			−0.847117
$378$		0			0
$379$	8.21884			0.422173			0.211087	−	0.977467i	$-0.432300\pi$
$379$	8.21884			0.422173			0.211087	+	0.977467i	$0.432300\pi$
$380$		−	6.04043i		−	0.309867i
$381$		0			0
$382$	−8.94832			−0.457836
$383$	15.1513	−	26.2428i	0.774195	−	1.34095i	−0.161050	−	0.986946i	$-0.551488\pi$
$383$	15.1513	−	26.2428i	0.774195	−	1.34095i	0.935246	−	0.353999i	$-0.115179\pi$
$384$		0			0
$385$		0			0
$386$		−	25.6055i		−	1.30329i
$387$		0			0
$388$	10.9670	+	6.33179i	0.556764	+	0.321448i
$389$	18.2352	−	10.5281i	0.924562	−	0.533796i	0.0394744	−	0.999221i	$-0.487432\pi$
$389$	18.2352	−	10.5281i	0.924562	−	0.533796i	0.885088	+	0.465424i	$0.154098\pi$
$390$		0			0
$391$	24.7737	−	14.3031i	1.25286	−	0.723338i
$392$		0			0
$393$		0			0
$394$	23.5602			1.18695
$395$	11.3269	−	19.6189i	0.569921	−	0.987132i
$396$		0			0
$397$	−0.516521	+	0.298214i	−0.0259235	+	0.0149669i	−0.512906	−	0.858445i	$-0.671431\pi$
$397$	−0.516521	+	0.298214i	−0.0259235	+	0.0149669i	0.486982	+	0.873412i	$0.338098\pi$
$398$	−6.81212	+	11.7989i	−0.341461	+	0.591427i
$399$		0			0
$400$	1.45020	+	2.51182i	0.0725101	+	0.125591i
$401$	−2.02316	−	1.16807i	−0.101032	−	0.0583309i	0.448633	−	0.893716i	$-0.351911\pi$
$401$	−2.02316	−	1.16807i	−0.101032	−	0.0583309i	−0.549665	+	0.835385i	$0.685245\pi$
$402$		0			0
$403$	−1.60728	−	2.78389i	−0.0800642	−	0.138675i
$404$	−8.77726	−	15.2027i	−0.436685	−	0.756360i
$405$		0			0
$406$		0			0
$407$	−5.18523	−	2.99369i	−0.257022	−	0.148392i
$408$		0			0
$409$		−	9.64564i		−	0.476946i	−0.971149	−	0.238473i	$-0.923353\pi$
$409$		−	9.64564i		−	0.476946i	0.971149	−	0.238473i	$-0.0766469\pi$
$410$			0.996120i			0.0491948i
$411$		0			0
$412$	−3.86082	−	2.22905i	−0.190209	−	0.109817i
$413$		0			0
$414$		0			0
$415$	−5.95803	−	10.3196i	−0.292468	−	0.506570i
$416$	−1.75222	−	3.03494i	−0.0859098	−	0.148800i
$417$		0			0
$418$	−5.04623	−	2.91344i	−0.246819	−	0.142501i
$419$	−14.4297	−	24.9930i	−0.704939	−	1.22099i	−0.966714	−	0.255861i	$-0.917641\pi$
$419$	−14.4297	−	24.9930i	−0.704939	−	1.22099i	0.261775	−	0.965129i	$-0.415692\pi$
$420$		0			0
$421$	6.14672	−	10.6464i	0.299573	−	0.518875i	−0.676466	−	0.736474i	$-0.736489\pi$
$421$	6.14672	−	10.6464i	0.299573	−	0.518875i	0.976038	+	0.217599i	$0.0698226\pi$
$422$	−18.6994	+	10.7961i	−0.910273	+	0.525546i
$423$		0			0
$424$	−2.98014	+	5.16176i	−0.144729	+	0.250677i
$425$	−22.9292			−1.11223
$426$		0			0
$427$		0			0
$428$	−2.04566	+	1.18106i	−0.0988808	+	0.0570889i
$429$		0			0
$430$	15.0960	−	8.71569i	0.727995	−	0.420308i
$431$	−24.0435	−	13.8815i	−1.15814	−	0.668650i	−0.207280	−	0.978282i	$-0.566461\pi$
$431$	−24.0435	−	13.8815i	−1.15814	−	0.668650i	−0.950857	+	0.309631i	$0.899794\pi$
$432$		0			0
$433$		−	21.3927i		−	1.02807i	−0.857769	−	0.514035i	$-0.828150\pi$
$433$		−	21.3927i		−	1.02807i	0.857769	−	0.514035i	$-0.171850\pi$
$434$		0			0
$435$		0			0
$436$	6.49776	−	11.2545i	0.311186	−	0.538990i
$437$	15.0844			0.721585
$438$		0			0
$439$			2.63916i			0.125960i	0.998015	+	0.0629801i	$0.0200605\pi$
$439$			2.63916i			0.125960i	−0.998015	+	0.0629801i	$0.979940\pi$
$440$	−2.02537			−0.0965558
$441$		0			0
$442$	27.7045			1.31777
$443$			12.1750i			0.578452i	0.957261	+	0.289226i	$0.0933979\pi$
$443$			12.1750i			0.578452i	−0.957261	+	0.289226i	$0.906602\pi$
$444$		0			0
$445$	1.54584			0.0732799
$446$	−8.41256	+	14.5710i	−0.398346	+	0.689956i
$447$		0			0
$448$		0			0
$449$		−	14.2454i		−	0.672283i	−0.941811	−	0.336142i	$-0.890878\pi$
$449$		−	14.2454i		−	0.672283i	0.941811	−	0.336142i	$-0.109122\pi$
$450$		0			0
$451$	0.832168	+	0.480452i	0.0391853	+	0.0226236i
$452$	2.90616	−	1.67787i	0.136694	−	0.0789204i
$453$		0			0
$454$	−10.5840	+	6.11065i	−0.496730	+	0.286787i
$455$		0			0
$456$		0			0
$457$	−11.5631			−0.540900			−0.270450	−	0.962734i	$-0.587172\pi$
$457$	−11.5631			−0.540900			−0.270450	+	0.962734i	$0.587172\pi$
$458$	9.72591	−	16.8458i	0.454462	−	0.787151i
$459$		0			0
$460$	4.54074	−	2.62160i	0.211713	−	0.122233i
$461$	11.0041	−	19.0597i	0.512513	−	0.887698i	−0.487382	−	0.873189i	$-0.662048\pi$
$461$	11.0041	−	19.0597i	0.512513	−	0.887698i	0.999895	−	0.0145095i	$-0.00461867\pi$
$462$		0			0
$463$	6.47862	+	11.2213i	0.301087	+	0.521498i	0.976382	−	0.216049i	$-0.0693171\pi$
$463$	6.47862	+	11.2213i	0.301087	+	0.521498i	−0.675295	+	0.737547i	$0.735984\pi$
$464$	−4.06467	−	2.34674i	−0.188698	−	0.108945i
$465$		0			0
$466$	−14.2825	−	24.7381i	−0.661626	−	1.14597i
$467$	1.42545	+	2.46895i	0.0659619	+	0.114249i	0.897120	−	0.441786i	$-0.145655\pi$
$467$	1.42545	+	2.46895i	0.0659619	+	0.114249i	−0.831158	+	0.556036i	$0.812322\pi$
$468$		0			0
$469$		0			0
$470$	10.4373	+	6.02598i	0.481437	+	0.277958i
$471$		0			0
$472$		−	9.44130i		−	0.434571i
$473$		−	16.8151i		−	0.773161i
$474$		0			0
$475$	−10.4710	−	6.04544i	−0.480443	−	0.277384i
$476$		0			0
$477$		0			0
$478$	−5.77465	−	10.0020i	−0.264126	−	0.457480i
$479$	−16.6352	−	28.8130i	−0.760081	−	1.31650i	−0.942808	−	0.333336i	$-0.891826\pi$
$479$	−16.6352	−	28.8130i	−0.760081	−	1.31650i	0.182727	−	0.983164i	$-0.441508\pi$
$480$		0			0
$481$	13.0002	+	7.50567i	0.592758	+	0.342229i
$482$	−0.0172628	−	0.0299000i	−0.000786298	−	0.00136191i
$483$		0			0
$484$	4.52311	−	7.83426i	0.205596	−	0.356103i
$485$	−15.8911	+	9.17475i	−0.721579	+	0.416604i
$486$		0			0
$487$	5.22500	−	9.04997i	0.236767	−	0.410093i	−0.723017	−	0.690830i	$-0.757245\pi$
$487$	5.22500	−	9.04997i	0.236767	−	0.410093i	0.959785	+	0.280737i	$0.0905788\pi$
$488$	9.85957			0.446322
$489$		0			0
$490$		0			0
$491$	−2.03404	+	1.17436i	−0.0917952	+	0.0529980i	−0.545195	−	0.838309i	$-0.683544\pi$
$491$	−2.03404	+	1.17436i	−0.0917952	+	0.0529980i	0.453400	+	0.891307i	$0.350211\pi$
$492$		0			0
$493$	32.1334	−	18.5522i	1.44722	−	0.835550i
$494$	12.6517	+	7.30447i	0.569228	+	0.328644i
$495$		0			0
$496$		−	0.917280i		−	0.0411871i
$497$		0			0
$498$		0			0
$499$	−17.3895	+	30.1195i	−0.778462	+	1.34834i	0.154366	+	0.988014i	$0.450667\pi$
$499$	−17.3895	+	30.1195i	−0.778462	+	1.34834i	−0.932828	+	0.360322i	$0.882667\pi$
$500$	−11.4477			−0.511956
$501$		0			0
$502$			3.26317i			0.145642i
$503$	−17.8290			−0.794956			−0.397478	−	0.917612i	$-0.630114\pi$
$503$	−17.8290			−0.794956			−0.397478	+	0.917612i	$0.630114\pi$
$504$		0			0
$505$	25.4365			1.13191
$506$		−	5.05784i		−	0.224849i
$507$		0			0
$508$	12.9075			0.572677
$509$	7.78061	−	13.4764i	0.344869	−	0.597331i	−0.640461	−	0.767991i	$-0.721257\pi$
$509$	7.78061	−	13.4764i	0.344869	−	0.597331i	0.985330	+	0.170660i	$0.0545899\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	17.1447	+	9.89851i	0.756222	+	0.436605i
$515$	5.59433	−	3.22989i	0.246516	−	0.142326i
$516$		0			0
$517$	10.0683	−	5.81295i	0.442805	−	0.255653i
$518$		0			0
$519$		0			0
$520$	5.07794			0.222682
$521$	−14.8188	+	25.6669i	−0.649222	+	1.12449i	0.334087	+	0.942542i	$0.391572\pi$
$521$	−14.8188	+	25.6669i	−0.649222	+	1.12449i	−0.983309	+	0.181944i	$0.941761\pi$
$522$		0			0
$523$	−19.2353	+	11.1055i	−0.841101	+	0.485610i	−0.857638	−	0.514253i	$-0.828069\pi$
$523$	−19.2353	+	11.1055i	−0.841101	+	0.485610i	0.0165371	+	0.999863i	$0.494736\pi$
$524$	−4.12856	+	7.15088i	−0.180357	+	0.312388i
$525$		0			0
$526$	8.80897	+	15.2576i	0.384089	+	0.665262i
$527$	6.28006	+	3.62579i	0.273564	+	0.157942i
$528$		0			0
$529$	−4.95323	−	8.57925i	−0.215358	−	0.373011i
$530$	−4.31823	−	7.47939i	−0.187572	−	0.324884i
$531$		0			0
$532$		0			0
$533$	−2.08638	−	1.20457i	−0.0903711	−	0.0521758i
$534$		0			0
$535$		−	3.42272i		−	0.147977i
$536$		−	2.97079i		−	0.128319i
$537$		0			0
$538$	−6.64540	−	3.83672i	−0.286503	−	0.165413i
$539$		0			0
$540$		0			0
$541$	−11.0171	−	19.0822i	−0.473662	−	0.820406i	0.525884	−	0.850557i	$-0.323735\pi$
$541$	−11.0171	−	19.0822i	−0.473662	−	0.820406i	−0.999545	+	0.0301502i	$0.990401\pi$
$542$	3.51690	+	6.09146i	0.151064	+	0.261650i
$543$		0			0
$544$	6.84639	+	3.95277i	0.293537	+	0.169473i
$545$	9.41525	+	16.3077i	0.403305	+	0.698545i
$546$		0			0
$547$	−14.5256	+	25.1592i	−0.621072	+	1.07573i	0.368215	+	0.929741i	$0.379969\pi$
$547$	−14.5256	+	25.1592i	−0.621072	+	1.07573i	−0.989286	+	0.145987i	$0.953364\pi$
$548$	−11.3267	+	6.53946i	−0.483851	+	0.279352i
$549$		0			0
$550$	−2.02705	+	3.51096i	−0.0864338	+	0.149708i
$551$	19.5657			0.833525
$552$		0			0
$553$		0			0
$554$	−14.9885	+	8.65364i	−0.636802	+	0.367658i
$555$		0			0
$556$	10.6722	−	6.16162i	0.452603	−	0.261311i
$557$	−14.9946	−	8.65716i	−0.635344	−	0.366816i	0.147475	−	0.989066i	$-0.452885\pi$
$557$	−14.9946	−	8.65716i	−0.635344	−	0.366816i	−0.782819	+	0.622250i	$0.786219\pi$
$558$		0			0
$559$			42.1583i			1.78311i
$560$		0			0
$561$		0			0
$562$	−8.26508	+	14.3155i	−0.348641	+	0.603865i
$563$	20.7668			0.875216			0.437608	−	0.899166i	$-0.355826\pi$
$563$	20.7668			0.875216			0.437608	+	0.899166i	$0.355826\pi$
$564$		0			0
$565$			4.86247i			0.204566i
$566$	3.16284			0.132944
$567$		0			0
$568$	−12.9436			−0.543101
$569$			14.7604i			0.618789i	0.950934	+	0.309394i	$0.100126\pi$
$569$			14.7604i			0.618789i	−0.950934	+	0.309394i	$0.899874\pi$
$570$		0			0
$571$	−22.2416			−0.930781			−0.465390	−	0.885106i	$-0.654086\pi$
$571$	−22.2416			−0.930781			−0.465390	+	0.885106i	$0.654086\pi$
$572$	2.44921	−	4.24216i	0.102407	−	0.177373i
$573$		0			0
$574$		0			0
$575$		−	10.4951i		−	0.437676i
$576$		0			0
$577$	16.2104	+	9.35911i	0.674850	+	0.389625i	0.797912	−	0.602774i	$-0.205938\pi$
$577$	16.2104	+	9.35911i	0.674850	+	0.389625i	−0.123062	+	0.992399i	$0.539271\pi$
$578$	−39.4019	+	22.7487i	−1.63890	+	0.946222i
$579$		0			0
$580$	5.88971	−	3.40042i	0.244557	−	0.141195i
$581$		0			0
$582$		0			0
$583$	−8.33113			−0.345040
$584$	5.65267	−	9.79071i	0.233909	−	0.405142i
$585$		0			0
$586$	−7.37932	+	4.26045i	−0.304837	+	0.175998i
$587$	−10.7433	+	18.6079i	−0.443423	+	0.768031i	−0.997941	−	0.0641405i	$-0.979569\pi$
$587$	−10.7433	+	18.6079i	−0.443423	+	0.768031i	0.554518	+	0.832172i	$0.312903\pi$
$588$		0			0
$589$	1.91193	+	3.31155i	0.0787796	+	0.136450i
$590$	11.8476	+	6.84022i	0.487758	+	0.281607i
$591$		0			0
$592$	2.14176	+	3.70963i	0.0880257	+	0.152465i
$593$	−7.04746	−	12.2066i	−0.289404	−	0.501263i	0.684263	−	0.729235i	$-0.260124\pi$
$593$	−7.04746	−	12.2066i	−0.289404	−	0.501263i	−0.973668	+	0.227972i	$0.926791\pi$
$594$		0			0
$595$		0			0
$596$	0.538692	+	0.311014i	0.0220657	+	0.0127396i
$597$		0			0
$598$			12.6808i			0.518558i
$599$		−	19.1707i		−	0.783296i	−0.920115	−	0.391648i	$-0.871905\pi$
$599$		−	19.1707i		−	0.783296i	0.920115	−	0.391648i	$-0.128095\pi$
$600$		0			0
$601$	−34.6795	−	20.0222i	−1.41460	−	0.816723i	−0.418787	−	0.908084i	$-0.637545\pi$
$601$	−34.6795	−	20.0222i	−1.41460	−	0.816723i	−0.995818	+	0.0913619i	$0.970878\pi$
$602$		0			0
$603$		0			0
$604$	−10.5911	−	18.3443i	−0.430945	−	0.746418i
$605$	6.55399	+	11.3518i	0.266457	+	0.461518i
$606$		0			0
$607$	−39.6529	−	22.8936i	−1.60946	−	0.929223i	−0.989490	−	0.144599i	$-0.953811\pi$
$607$	−39.6529	−	22.8936i	−1.60946	−	0.929223i	−0.619971	−	0.784625i	$-0.712856\pi$
$608$	2.08434	+	3.61019i	0.0845313	+	0.146413i
$609$		0			0
$610$	−7.14325	+	12.3725i	−0.289222	+	0.500947i
$611$	−25.2429	+	14.5740i	−1.02122	+	0.589601i
$612$		0			0
$613$	22.6481	−	39.2276i	0.914748	−	1.58439i	0.107477	−	0.994208i	$-0.465723\pi$
$613$	22.6481	−	39.2276i	0.914748	−	1.58439i	0.807270	−	0.590182i	$-0.200944\pi$
$614$	25.0805			1.01217
$615$		0			0
$616$		0			0
$617$	28.6323	−	16.5308i	1.15269	−	0.665506i	0.203149	−	0.979148i	$-0.434882\pi$
$617$	28.6323	−	16.5308i	1.15269	−	0.665506i	0.949542	+	0.313641i	$0.101549\pi$
$618$		0			0
$619$	9.35801	−	5.40285i	0.376130	−	0.217159i	−0.300003	−	0.953938i	$-0.596988\pi$
$619$	9.35801	−	5.40285i	0.376130	−	0.217159i	0.676133	+	0.736779i	$0.263654\pi$
$620$	1.15107	+	0.664569i	0.0462279	+	0.0266897i
$621$		0			0
$622$		−	3.57355i		−	0.143286i
$623$		0			0
$624$		0			0
$625$	1.04283	−	1.80623i	0.0417131	−	0.0722491i
$626$	13.6293			0.544736
$627$		0			0
$628$		−	15.0294i		−	0.599737i
$629$	−33.8635			−1.35022
$630$		0			0
$631$	−30.0554			−1.19648			−0.598242	−	0.801315i	$-0.704134\pi$
$631$	−30.0554			−1.19648			−0.598242	+	0.801315i	$0.704134\pi$
$632$			15.6342i			0.621894i
$633$		0			0
$634$	4.28994			0.170375
$635$	−9.35146	+	16.1972i	−0.371101	+	0.642767i
$636$		0			0
$637$		0			0
$638$		−	6.56042i		−	0.259730i
$639$		0			0
$640$	1.25487	+	0.724499i	0.0496031	+	0.0286384i
$641$	−9.66957	+	5.58273i	−0.381925	+	0.220505i	−0.678655	−	0.734457i	$-0.737437\pi$
$641$	−9.66957	+	5.58273i	−0.381925	+	0.220505i	0.296730	+	0.954961i	$0.404104\pi$
$642$		0			0
$643$	4.40588	−	2.54373i	0.173751	−	0.100315i	−0.410602	−	0.911814i	$-0.634682\pi$
$643$	4.40588	−	2.54373i	0.173751	−	0.100315i	0.584353	+	0.811499i	$0.301348\pi$
$644$		0			0
$645$		0			0
$646$	−32.9557			−1.29662
$647$	6.45711	−	11.1840i	0.253855	−	0.439690i	−0.710729	−	0.703466i	$-0.751635\pi$
$647$	6.45711	−	11.1840i	0.253855	−	0.439690i	0.964584	+	0.263776i	$0.0849680\pi$
$648$		0			0
$649$	11.4288	−	6.59840i	0.448618	−	0.259010i
$650$	5.08215	−	8.80254i	0.199338	−	0.345264i
$651$		0			0
$652$	−1.51764	−	2.62863i	−0.0594353	−	0.102945i
$653$	−31.5843	−	18.2352i	−1.23599	−	0.713598i	−0.267716	−	0.963498i	$-0.586269\pi$
$653$	−31.5843	−	18.2352i	−1.23599	−	0.713598i	−0.968272	+	0.249900i	$0.919602\pi$
$654$		0			0
$655$	−5.98228	−	10.3616i	−0.233747	−	0.404862i
$656$	−0.343727	−	0.595352i	−0.0134203	−	0.0232446i
$657$		0			0
$658$		0			0
$659$	−2.04111	−	1.17844i	−0.0795104	−	0.0459054i	0.459718	−	0.888065i	$-0.347951\pi$
$659$	−2.04111	−	1.17844i	−0.0795104	−	0.0459054i	−0.539228	+	0.842160i	$0.681284\pi$
$660$		0			0
$661$			7.76114i			0.301873i	0.988543	+	0.150937i	$0.0482290\pi$
$661$			7.76114i			0.301873i	−0.988543	+	0.150937i	$0.951771\pi$
$662$		−	8.93923i		−	0.347433i
$663$		0			0
$664$	7.12189	+	4.11183i	0.276383	+	0.159570i
$665$		0			0
$666$		0			0
$667$	8.49167	+	14.7080i	0.328799	+	0.569497i
$668$	3.05895	+	5.29826i	0.118354	+	0.204996i
$669$		0			0
$670$	3.72796	+	2.15234i	0.144024	+	0.0831520i
$671$	6.89072	+	11.9351i	0.266013	+	0.460749i
$672$		0			0
$673$	17.5783	−	30.4465i	0.677594	−	1.17363i	−0.298109	−	0.954532i	$-0.596356\pi$
$673$	17.5783	−	30.4465i	0.677594	−	1.17363i	0.975703	−	0.219096i	$-0.0703106\pi$
$674$	0.126400	−	0.0729773i	0.00486876	−	0.00281098i
$675$		0			0
$676$	0.359433	−	0.622557i	0.0138244	−	0.0239445i
$677$	−14.0615			−0.540427			−0.270213	−	0.962800i	$-0.587094\pi$
$677$	−14.0615			−0.540427			−0.270213	+	0.962800i	$0.587094\pi$
$678$		0			0
$679$		0			0
$680$	−9.92041	+	5.72755i	−0.380430	+	0.219642i
$681$		0			0
$682$	1.11037	−	0.641075i	0.0425184	−	0.0245480i
$683$	−29.1299	−	16.8182i	−1.11462	−	0.643529i	−0.174601	−	0.984639i	$-0.555864\pi$
$683$	−29.1299	−	16.8182i	−1.11462	−	0.643529i	−0.940023	+	0.341110i	$0.889197\pi$
$684$		0			0
$685$		−	18.9513i		−	0.724093i
$686$		0			0
$687$		0			0
$688$	−6.01497	+	10.4182i	−0.229319	+	0.397192i
$689$	20.8875			0.795751
$690$		0			0
$691$			4.40252i			0.167480i	0.996488	+	0.0837399i	$0.0266865\pi$
$691$			4.40252i			0.167480i	−0.996488	+	0.0837399i	$0.973314\pi$
$692$	−2.29515			−0.0872484
$693$		0			0
$694$	22.2844			0.845903
$695$			17.8563i			0.677330i
$696$		0			0
$697$	5.43469			0.205853
$698$	−1.61572	+	2.79851i	−0.0611560	+	0.105925i
$699$		0			0
$700$		0			0
$701$			31.5424i			1.19134i	0.803229	+	0.595670i	$0.203113\pi$
$701$			31.5424i			1.19134i	−0.803229	+	0.595670i	$0.796887\pi$
$702$		0			0
$703$	−15.4643	−	8.92832i	−0.583247	−	0.336738i
$704$	1.21051	−	0.698887i	0.0456227	−	0.0263403i
$705$		0			0
$706$	5.42533	−	3.13232i	0.204185	−	0.117886i
$707$		0			0
$708$		0			0
$709$	4.34537			0.163194			0.0815970	−	0.996665i	$-0.473998\pi$
$709$	4.34537			0.163194			0.0815970	+	0.996665i	$0.473998\pi$
$710$	9.37762	−	16.2425i	0.351936	−	0.609571i
$711$		0			0
$712$	−0.923906	+	0.533417i	−0.0346248	+	0.0199907i
$713$	−1.65959	+	2.87449i	−0.0621520	+	0.107651i
$714$		0			0
$715$	3.54890	+	6.14688i	0.132721	+	0.229880i
$716$	−2.92364	−	1.68796i	−0.109261	−	0.0630821i
$717$		0			0
$718$	6.03463	+	10.4523i	0.225210	+	0.390076i
$719$	14.1500	+	24.5086i	0.527707	+	0.914016i	0.999478	+	0.0322946i	$0.0102815\pi$
$719$	14.1500	+	24.5086i	0.527707	+	0.914016i	−0.471771	+	0.881721i	$0.656385\pi$
$720$		0			0
$721$		0			0
$722$	1.40472	+	0.811015i	0.0522782	+	0.0301829i
$723$		0			0
$724$		−	1.68857i		−	0.0627553i
$725$		−	13.6130i		−	0.505573i
$726$		0			0
$727$	11.7770	+	6.79945i	0.436784	+	0.252178i	0.702233	−	0.711948i	$-0.252187\pi$
$727$	11.7770	+	6.79945i	0.436784	+	0.252178i	−0.265448	+	0.964125i	$0.585520\pi$
$728$		0			0
$729$		0			0
$730$	8.19071	+	14.1867i	0.303152	+	0.525074i
$731$	−47.5516	−	82.3617i	−1.75876	−	3.04626i
$732$		0			0
$733$	−41.0236	−	23.6850i	−1.51524	−	0.874825i	−0.999840	−	0.0178757i	$-0.994310\pi$
$733$	−41.0236	−	23.6850i	−1.51524	−	0.874825i	−0.515401	−	0.856949i	$-0.672357\pi$
$734$	−8.53940	−	14.7907i	−0.315195	−	0.545934i
$735$		0			0
$736$	−1.80925	+	3.13371i	−0.0666898	+	0.115510i
$737$	3.59617	−	2.07625i	0.132466	−	0.0764796i
$738$		0			0
$739$	−16.8601	+	29.2026i	−0.620210	+	1.07424i	0.369236	+	0.929336i	$0.379619\pi$
$739$	−16.8601	+	29.2026i	−0.620210	+	1.07424i	−0.989446	+	0.144900i	$0.953714\pi$
$740$	−6.20681			−0.228167
$741$		0			0
$742$		0			0
$743$	−6.86253	+	3.96208i	−0.251762	+	0.145355i	−0.620571	−	0.784151i	$-0.713099\pi$
$743$	−6.86253	+	3.96208i	−0.251762	+	0.145355i	0.368809	+	0.929505i	$0.379766\pi$
$744$		0			0
$745$	−0.780564	+	0.450659i	−0.0285976	+	0.0165109i
$746$	3.35463	+	1.93680i	0.122822	+	0.0709112i
$747$		0			0
$748$			11.0501i			0.404033i
$749$		0			0
$750$		0			0
$751$	−2.06865	+	3.58301i	−0.0754861	+	0.130746i	−0.901298	−	0.433201i	$-0.857384\pi$
$751$	−2.06865	+	3.58301i	−0.0754861	+	0.130746i	0.825811	+	0.563946i	$0.190718\pi$
$752$	−8.31745			−0.303306
$753$		0			0
$754$			16.4480i			0.599002i
$755$	30.6929			1.11703
$756$		0			0
$757$	35.2411			1.28086			0.640430	−	0.768017i	$-0.278756\pi$
$757$	35.2411			1.28086			0.640430	+	0.768017i	$0.278756\pi$
$758$		−	8.21884i		−	0.298522i
$759$		0			0
$760$	−6.04043			−0.219109
$761$	4.93597	−	8.54935i	0.178929	−	0.309914i	−0.762585	−	0.646888i	$-0.776070\pi$
$761$	4.93597	−	8.54935i	0.178929	−	0.309914i	0.941514	+	0.336974i	$0.109404\pi$
$762$		0			0
$763$		0			0
$764$			8.94832i			0.323739i
$765$		0			0
$766$	−26.2428	−	15.1513i	−0.948192	−	0.547439i
$767$	−28.6538	+	16.5433i	−1.03463	+	0.597343i
$768$		0			0
$769$	−18.6213	+	10.7510i	−0.671503	+	0.387692i	−0.796646	−	0.604446i	$-0.793394\pi$
$769$	−18.6213	+	10.7510i	−0.671503	+	0.387692i	0.125143	+	0.992139i	$0.460061\pi$
$770$		0			0
$771$		0			0
$772$	−25.6055			−0.921564
$773$	−3.69775	+	6.40468i	−0.132999	+	0.230360i	−0.924831	−	0.380378i	$-0.875794\pi$
$773$	−3.69775	+	6.40468i	−0.132999	+	0.230360i	0.791832	+	0.610738i	$0.209127\pi$
$774$		0			0
$775$	2.30404	−	1.33024i	0.0827637	−	0.0477836i
$776$	6.33179	−	10.9670i	0.227298	−	0.393691i
$777$		0			0
$778$	−10.5281	−	18.2352i	−0.377451	−	0.653764i
$779$	2.48184	+	1.43289i	0.0889211	+	0.0513386i
$780$		0			0
$781$	−9.04610	−	15.6683i	−0.323695	−	0.560656i
$782$	−14.3031	−	24.7737i	−0.511477	−	0.885904i
$783$		0			0
$784$		0			0
$785$	18.8599	+	10.8888i	0.673139	+	0.388637i
$786$		0			0
$787$			17.8154i			0.635049i	0.948250	+	0.317524i	$0.102852\pi$
$787$			17.8154i			0.635049i	−0.948250	+	0.317524i	$0.897148\pi$
$788$		−	23.5602i		−	0.839299i
$789$		0			0
$790$	−19.6189	−	11.3269i	−0.698007	−	0.402995i
$791$		0			0
$792$		0			0
$793$	−17.2762	−	29.9232i	−0.613495	−	1.06260i
$794$	0.298214	+	0.516521i	0.0105832	+	0.0183307i
$795$		0			0
$796$	11.7989	+	6.81212i	0.418202	+	0.241449i
$797$	27.0403	+	46.8351i	0.957815	+	1.65898i	0.727790	+	0.685800i	$0.240548\pi$
$797$	27.0403	+	46.8351i	0.957815	+	1.65898i	0.230025	+	0.973185i	$0.426119\pi$
$798$		0			0
$799$	32.8769	−	56.9445i	1.16310	−	2.01455i
$800$	2.51182	−	1.45020i	0.0888063	−	0.0512724i
$801$		0			0
$802$	−1.16807	+	2.02316i	−0.0412462	+	0.0714404i
$803$	15.8023			0.557651
$804$		0			0
$805$		0			0
$806$	−2.78389	+	1.60728i	−0.0980582	+	0.0566140i
$807$		0			0
$808$	−15.2027	+	8.77726i	−0.534827	+	0.308783i
$809$	36.0795	+	20.8305i	1.26849	+	0.732363i	0.974702	−	0.223508i	$-0.0717510\pi$
$809$	36.0795	+	20.8305i	1.26849	+	0.732363i	0.293787	+	0.955871i	$0.405084\pi$
$810$		0			0
$811$		−	24.8645i		−	0.873111i	−0.899677	−	0.436556i	$-0.856198\pi$
$811$		−	24.8645i		−	0.873111i	0.899677	−	0.436556i	$-0.143802\pi$
$812$		0			0
$813$		0			0
$814$	−2.99369	+	5.18523i	−0.104929	+	0.181742i
$815$	4.39811			0.154059
$816$		0			0
$817$		−	50.1491i		−	1.75450i
$818$	−9.64564			−0.337252
$819$		0			0
$820$	0.996120			0.0347860
$821$		−	34.5967i		−	1.20743i	−0.797199	−	0.603716i	$-0.793686\pi$
$821$		−	34.5967i		−	1.20743i	0.797199	−	0.603716i	$-0.206314\pi$
$822$		0			0
$823$	15.7623			0.549438			0.274719	−	0.961525i	$-0.411415\pi$
$823$	15.7623			0.549438			0.274719	+	0.961525i	$0.411415\pi$
$824$	−2.22905	+	3.86082i	−0.0776526	+	0.134498i
$825$		0			0
$826$		0			0
$827$			17.6523i			0.613830i	0.951737	+	0.306915i	$0.0992967\pi$
$827$			17.6523i			0.613830i	−0.951737	+	0.306915i	$0.900703\pi$
$828$		0			0
$829$	32.6295	+	18.8387i	1.13327	+	0.654294i	0.944756	−	0.327776i	$-0.106299\pi$
$829$	32.6295	+	18.8387i	1.13327	+	0.654294i	0.188516	+	0.982070i	$0.439632\pi$
$830$	−10.3196	+	5.95803i	−0.358199	+	0.206806i
$831$		0			0
$832$	−3.03494	+	1.75222i	−0.105218	+	0.0607474i
$833$		0			0
$834$		0			0
$835$	−8.86484			−0.306781
$836$	−2.91344	+	5.04623i	−0.100763	+	0.174527i
$837$		0			0
$838$	−24.9930	+	14.4297i	−0.863370	+	0.498467i
$839$	10.5777	−	18.3211i	0.365183	−	0.632516i	−0.623622	−	0.781726i	$-0.714340\pi$
$839$	10.5777	−	18.3211i	0.365183	−	0.632516i	0.988806	+	0.149210i	$0.0476730\pi$
$840$		0			0
$841$	−3.48563	−	6.03728i	−0.120194	−	0.208182i
$842$	−10.6464	−	6.14672i	−0.366900	−	0.211830i
$843$		0			0
$844$	10.7961	+	18.6994i	0.371617	+	0.643660i
$845$	0.520818	+	0.902084i	0.0179167	+	0.0310326i
$846$		0			0
$847$		0			0
$848$	5.16176	+	2.98014i	0.177256	+	0.102339i
$849$		0			0
$850$			22.9292i			0.786466i
$851$		−	15.4999i		−	0.531329i
$852$		0			0
$853$	34.7061	+	20.0376i	1.18831	+	0.686073i	0.957923	−	0.287026i	$-0.0926665\pi$
$853$	34.7061	+	20.0376i	1.18831	+	0.686073i	0.230390	+	0.973098i	$0.426000\pi$
$854$		0			0
$855$		0			0
$856$	1.18106	+	2.04566i	0.0403679	+	0.0699193i
$857$	3.73018	+	6.46087i	0.127421	+	0.220699i	0.922677	−	0.385575i	$-0.125997\pi$
$857$	3.73018	+	6.46087i	0.127421	+	0.220699i	−0.795256	+	0.606274i	$0.792664\pi$
$858$		0			0
$859$	41.2721	+	23.8285i	1.40819	+	0.813017i	0.995213	−	0.0977257i	$-0.0311568\pi$
$859$	41.2721	+	23.8285i	1.40819	+	0.813017i	0.412974	+	0.910743i	$0.364490\pi$
$860$	−8.71569	−	15.0960i	−0.297203	−	0.514770i
$861$		0			0
$862$	−13.8815	+	24.0435i	−0.472807	+	0.818926i
$863$	−37.1822	+	21.4671i	−1.26570	+	0.730750i	−0.974171	−	0.225813i	$-0.927496\pi$
$863$	−37.1822	+	21.4671i	−1.26570	+	0.730750i	−0.291525	+	0.956563i	$0.594163\pi$
$864$		0			0
$865$	1.66283	−	2.88011i	0.0565380	−	0.0979267i
$866$	−21.3927			−0.726955
$867$		0			0
$868$		0			0
$869$	−18.9253	+	10.9265i	−0.641996	+	0.370657i
$870$		0			0
$871$	−9.01617	+	5.20549i	−0.305501	+	0.176381i
$872$	−11.2545	−	6.49776i	−0.381124	−	0.220042i
$873$		0			0
$874$		−	15.0844i		−	0.510237i
$875$		0			0
$876$		0			0
$877$	−13.0702	+	22.6382i	−0.441349	+	0.764438i	−0.997790	−	0.0664486i	$-0.978833\pi$
$877$	−13.0702	+	22.6382i	−0.441349	+	0.764438i	0.556441	+	0.830887i	$0.312166\pi$
$878$	2.63916			0.0890674
$879$		0			0
$880$			2.02537i			0.0682753i
$881$	11.2385			0.378636			0.189318	−	0.981916i	$-0.439372\pi$
$881$	11.2385			0.378636			0.189318	+	0.981916i	$0.439372\pi$
$882$		0			0
$883$	−0.253239			−0.00852217			−0.00426108	−	0.999991i	$-0.501356\pi$
$883$	−0.253239			−0.00852217			−0.00426108	+	0.999991i	$0.501356\pi$
$884$		−	27.7045i		−	0.931803i
$885$		0			0
$886$	12.1750			0.409027
$887$	2.86053	−	4.95458i	0.0960472	−	0.166359i	−0.813998	−	0.580868i	$-0.802713\pi$
$887$	2.86053	−	4.95458i	0.0960472	−	0.166359i	0.910045	+	0.414509i	$0.136047\pi$
$888$		0			0
$889$		0			0
$890$		−	1.54584i		−	0.0518167i
$891$		0			0
$892$	14.5710	+	8.41256i	0.487872	+	0.281673i
$893$	30.0276	−	17.3364i	1.00483	−	0.580141i
$894$		0			0
$895$	4.23635	−	2.44586i	0.141605	−	0.0817559i
$896$		0			0
$897$		0			0
$898$	−14.2454			−0.475376
$899$	−2.15262	+	3.72844i	−0.0717938	+	0.124350i
$900$		0			0
$901$	−40.8065	+	23.5596i	−1.35946	+	0.784885i
$902$	0.480452	−	0.832168i	0.0159973	−	0.0277082i
$903$		0			0
$904$	−1.67787	−	2.90616i	−0.0558052	−	0.0966574i
$905$	2.11894	+	1.22337i	0.0704359	+	0.0406662i
$906$		0			0
$907$	−11.8731	−	20.5648i	−0.394241	−	0.682845i	0.598763	−	0.800926i	$-0.295659\pi$
$907$	−11.8731	−	20.5648i	−0.394241	−	0.682845i	−0.993004	+	0.118081i	$0.962326\pi$
$908$	6.11065	+	10.5840i	0.202789	+	0.351241i
$909$		0			0
$910$		0			0
$911$	−17.0673	−	9.85384i	−0.565466	−	0.326472i	0.189870	−	0.981809i	$-0.439193\pi$
$911$	−17.0673	−	9.85384i	−0.565466	−	0.326472i	−0.755337	+	0.655337i	$0.772527\pi$
$912$		0			0
$913$			11.4948i			0.380423i
$914$			11.5631i			0.382474i
$915$		0			0
$916$	−16.8458	−	9.72591i	−0.556600	−	0.321353i
$917$		0			0
$918$		0			0
$919$	27.3077	+	47.2983i	0.900797	+	1.56023i	0.826461	+	0.562994i	$0.190350\pi$
$919$	27.3077	+	47.2983i	0.900797	+	1.56023i	0.0743361	+	0.997233i	$0.476316\pi$
$920$	−2.62160	−	4.54074i	−0.0864316	−	0.149704i
$921$		0			0
$922$	−19.0597	−	11.0041i	−0.627698	−	0.362401i
$923$	22.6800	+	39.2830i	0.746523	+	1.29302i
$924$		0			0
$925$	−6.21196	+	10.7594i	−0.204248	+	0.353768i
$926$	11.2213	−	6.47862i	0.368755	−	0.212901i
$927$		0			0
$928$	−2.34674	+	4.06467i	−0.0770355	+	0.133429i
$929$	22.7720			0.747124			0.373562	−	0.927605i	$-0.378136\pi$
$929$	22.7720			0.747124			0.373562	+	0.927605i	$0.378136\pi$
$930$		0			0
$931$		0			0
$932$	−24.7381	+	14.2825i	−0.810323	+	0.467840i
$933$		0			0
$934$	2.46895	−	1.42545i	0.0807865	−	0.0466421i
$935$	−13.8665	−	8.00582i	−0.453483	−	0.261818i
$936$		0			0
$937$			19.4429i			0.635173i	0.948229	+	0.317587i	$0.102872\pi$
$937$			19.4429i			0.635173i	−0.948229	+	0.317587i	$0.897128\pi$
$938$		0			0
$939$		0			0
$940$	6.02598	−	10.4373i	0.196546	−	0.340428i
$941$	−19.4602			−0.634383			−0.317192	−	0.948361i	$-0.602740\pi$
$941$	−19.4602			−0.634383			−0.317192	+	0.948361i	$0.602740\pi$
$942$		0			0
$943$			2.48755i			0.0810058i
$944$	−9.44130			−0.307288
$945$		0			0
$946$	−16.8151			−0.546707
$947$			30.2570i			0.983221i	0.870815	+	0.491611i	$0.163592\pi$
$947$			30.2570i			0.983221i	−0.870815	+	0.491611i	$0.836408\pi$
$948$		0			0
$949$	−39.6189			−1.28608
$950$	−6.04544	+	10.4710i	−0.196140	+	0.339724i
$951$		0			0
$952$		0			0
$953$		−	21.4885i		−	0.696082i	−0.937479	−	0.348041i	$-0.886847\pi$
$953$		−	21.4885i		−	0.696082i	0.937479	−	0.348041i	$-0.113153\pi$
$954$		0			0
$955$	−11.2290	−	6.48305i	−0.363361	−	0.209787i
$956$	−10.0020	+	5.77465i	−0.323487	+	0.186765i
$957$		0			0
$958$	−28.8130	+	16.6352i	−0.930906	+	0.537459i
$959$		0			0
$960$		0			0
$961$	30.1586			0.972858
$962$	7.50567	−	13.0002i	0.241992	−	0.419143i
$963$		0			0
$964$	−0.0299000	+	0.0172628i	−0.000963015	+	0.000555997i
$965$	18.5512	−	32.1316i	0.597184	−	1.03435i
$966$		0			0
$967$	−8.76620	−	15.1835i	−0.281902	−	0.488268i	0.689951	−	0.723856i	$-0.257632\pi$
$967$	−8.76620	−	15.1835i	−0.281902	−	0.488268i	−0.971853	+	0.235587i	$0.924299\pi$
$968$	−7.83426	−	4.52311i	−0.251803	−	0.145378i
$969$		0			0
$970$	9.17475	+	15.8911i	0.294583	+	0.510234i
$971$	−12.9458	−	22.4228i	−0.415451	−	0.719582i	0.580025	−	0.814599i	$-0.303043\pi$
$971$	−12.9458	−	22.4228i	−0.415451	−	0.719582i	−0.995476	+	0.0950171i	$0.969709\pi$
$972$		0			0
$973$		0			0
$974$	−9.04997	−	5.22500i	−0.289980	−	0.167420i
$975$		0			0
$976$		−	9.85957i		−	0.315597i
$977$			54.4135i			1.74084i	0.492308	+	0.870421i	$0.336154\pi$
$977$			54.4135i			1.74084i	−0.492308	+	0.870421i	$0.663846\pi$
$978$		0			0
$979$	−1.29141	−	0.745597i	−0.0412737	−	0.0238294i
$980$		0			0
$981$		0			0
$982$	1.17436	+	2.03404i	0.0374752	+	0.0649090i
$983$	23.8665	+	41.3379i	0.761222	+	1.31847i	0.942221	+	0.334991i	$0.108733\pi$
$983$	23.8665	+	41.3379i	0.761222	+	1.31847i	−0.181000	+	0.983483i	$0.557933\pi$
$984$		0			0
$985$	29.5650	+	17.0694i	0.942020	+	0.543876i
$986$	−18.5522	−	32.1334i	−0.590823	−	1.02334i
$987$		0			0
$988$	7.30447	−	12.6517i	0.232386	−	0.402505i
$989$	37.6984	−	21.7652i	1.19874	−	0.692092i
$990$		0			0
$991$	−1.89016	+	3.27386i	−0.0600430	+	0.103997i	−0.894484	−	0.447099i	$-0.852457\pi$
$991$	−1.89016	+	3.27386i	−0.0600430	+	0.103997i	0.834441	+	0.551097i	$0.185790\pi$
$992$	−0.917280			−0.0291237
$993$		0			0
$994$		0			0
$995$	−17.0966	+	9.87075i	−0.542000	+	0.312924i
$996$		0			0
$997$	2.58264	−	1.49109i	0.0817931	−	0.0472233i	−0.458546	−	0.888671i	$-0.651629\pi$
$997$	2.58264	−	1.49109i	0.0817931	−	0.0472233i	0.540339	+	0.841448i	$0.318296\pi$
$998$	30.1195	+	17.3895i	0.953417	+	0.550456i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.l.c.521.10		48
3.2	odd	2		882.2.l.c.227.21		48
7.2	even	3		2646.2.t.c.1979.1		48
7.3	odd	6		2646.2.m.c.1763.21		48
7.4	even	3		2646.2.m.c.1763.22		48
7.5	odd	6		2646.2.t.c.1979.2		48
7.6	odd	2	inner	2646.2.l.c.521.9		48
9.4	even	3		882.2.t.c.815.18		48
9.5	odd	6		2646.2.t.c.2285.2		48
21.2	odd	6		882.2.t.c.803.19		48
21.5	even	6		882.2.t.c.803.18		48
21.11	odd	6		882.2.m.c.587.2	yes	48
21.17	even	6		882.2.m.c.587.11	yes	48
21.20	even	2		882.2.l.c.227.16		48
63.4	even	3		882.2.m.c.293.11	yes	48
63.5	even	6	inner	2646.2.l.c.1097.10		48
63.13	odd	6		882.2.t.c.815.19		48
63.23	odd	6	inner	2646.2.l.c.1097.9		48
63.31	odd	6		882.2.m.c.293.2	✓	48
63.32	odd	6		2646.2.m.c.881.21		48
63.40	odd	6		882.2.l.c.509.9		48
63.41	even	6		2646.2.t.c.2285.1		48
63.58	even	3		882.2.l.c.509.4		48
63.59	even	6		2646.2.m.c.881.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.16		48	21.20	even	2
882.2.l.c.227.21		48	3.2	odd	2
882.2.l.c.509.4		48	63.58	even	3
882.2.l.c.509.9		48	63.40	odd	6
882.2.m.c.293.2	✓	48	63.31	odd	6
882.2.m.c.293.11	yes	48	63.4	even	3
882.2.m.c.587.2	yes	48	21.11	odd	6
882.2.m.c.587.11	yes	48	21.17	even	6
882.2.t.c.803.18		48	21.5	even	6
882.2.t.c.803.19		48	21.2	odd	6
882.2.t.c.815.18		48	9.4	even	3
882.2.t.c.815.19		48	63.13	odd	6
2646.2.l.c.521.9		48	7.6	odd	2	inner
2646.2.l.c.521.10		48	1.1	even	1	trivial
2646.2.l.c.1097.9		48	63.23	odd	6	inner
2646.2.l.c.1097.10		48	63.5	even	6	inner
2646.2.m.c.881.21		48	63.32	odd	6
2646.2.m.c.881.22		48	63.59	even	6
2646.2.m.c.1763.21		48	7.3	odd	6
2646.2.m.c.1763.22		48	7.4	even	3
2646.2.t.c.1979.1		48	7.2	even	3
2646.2.t.c.1979.2		48	7.5	odd	6
2646.2.t.c.2285.1		48	63.41	even	6
2646.2.t.c.2285.2		48	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.724499 - 1.25487i) q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.724499 - 1.25487i) q^{5} +1.00000i q^{8} +(-1.25487 - 0.724499i) q^{10} +(-1.21051 + 0.698887i) q^{11} +(3.03494 - 1.75222i) q^{13} +1.00000 q^{16} +(-3.95277 + 6.84639i) q^{17} +(-3.61019 + 2.08434i) q^{19} +(-0.724499 + 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(-3.13371 - 1.80925i) q^{23} +(1.45020 + 2.51182i) q^{25} +(-1.75222 - 3.03494i) q^{26} +(-4.06467 - 2.34674i) q^{29} -0.917280i q^{31} -1.00000i q^{32} +(6.84639 + 3.95277i) q^{34} +(2.14176 + 3.70963i) q^{37} +(2.08434 + 3.61019i) q^{38} +(1.25487 + 0.724499i) q^{40} +(-0.343727 - 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} +(1.21051 - 0.698887i) q^{44} +(-1.80925 + 3.13371i) q^{46} -8.31745 q^{47} +(2.51182 - 1.45020i) q^{50} +(-3.03494 + 1.75222i) q^{52} +(5.16176 + 2.98014i) q^{53} +2.02537i q^{55} +(-2.34674 + 4.06467i) q^{58} -9.44130 q^{59} -9.85957i q^{61} -0.917280 q^{62} -1.00000 q^{64} -5.07794i q^{65} -2.97079 q^{67} +(3.95277 - 6.84639i) q^{68} +12.9436i q^{71} +(-9.79071 - 5.65267i) q^{73} +(3.70963 - 2.14176i) q^{74} +(3.61019 - 2.08434i) q^{76} +15.6342 q^{79} +(0.724499 - 1.25487i) q^{80} +(-0.595352 + 0.343727i) q^{82} +(4.11183 - 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(10.4182 + 6.01497i) q^{86} +(-0.698887 - 1.21051i) q^{88} +(0.533417 + 0.923906i) q^{89} +(3.13371 + 1.80925i) q^{92} +8.31745i q^{94} +6.04043i q^{95} +(-10.9670 - 6.33179i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} + 48 q^{11} + 48 q^{16} + 48 q^{23} - 24 q^{25} - 48 q^{44} + 48 q^{50} - 96 q^{53} - 48 q^{64} - 96 q^{79} + 48 q^{85} + 96 q^{86} - 48 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 + 48 * q^11 + 48 * q^16 + 48 * q^23 - 24 * q^25 - 48 * q^44 + 48 * q^50 - 96 * q^53 - 48 * q^64 - 96 * q^79 + 48 * q^85 + 96 * q^86 - 48 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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