LMFDB - Embedded newform 1323.2.s.d.656.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.3
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05485 + 1.18637i) q^{2} +(1.81495 - 3.14358i) q^{4} -3.43548 q^{5} +3.86732i q^{8} +O(q^{10})$	\(q+(-2.05485 + 1.18637i) q^{2} +(1.81495 - 3.14358i) q^{4} -3.43548 q^{5} +3.86732i q^{8} +(7.05942 - 4.07576i) q^{10} +0.313957i q^{11} +(-5.09882 + 2.94381i) q^{13} +(-0.958178 - 1.65961i) q^{16} +(0.476712 + 0.825689i) q^{17} +(-1.09214 - 0.630546i) q^{19} +(-6.23523 + 10.7997i) q^{20} +(-0.372470 - 0.645137i) q^{22} +6.82815i q^{23} +6.80255 q^{25} +(6.98489 - 12.0982i) q^{26} +(-3.43518 - 1.98330i) q^{29} +(-4.53388 - 2.61764i) q^{31} +(-2.76057 - 1.59381i) q^{32} +(-1.95915 - 1.13111i) q^{34} +(-2.68802 + 4.65579i) q^{37} +2.99224 q^{38} -13.2861i q^{40} +(-0.0699627 - 0.121179i) q^{41} +(1.44078 - 2.49550i) q^{43} +(0.986951 + 0.569817i) q^{44} +(-8.10072 - 14.0309i) q^{46} +(1.00695 + 1.74409i) q^{47} +(-13.9783 + 8.07035i) q^{50} +21.3714i q^{52} +(10.3749 - 5.98997i) q^{53} -1.07860i q^{55} +9.41172 q^{58} +(-0.824459 + 1.42801i) q^{59} +(-2.57423 + 1.48623i) q^{61} +12.4219 q^{62} +11.3961 q^{64} +(17.5169 - 10.1134i) q^{65} +(0.934059 - 1.61784i) q^{67} +3.46083 q^{68} -10.9981i q^{71} +(-0.354655 + 0.204760i) q^{73} -12.7560i q^{74} +(-3.96435 + 2.28882i) q^{76} +(-5.23325 - 9.06426i) q^{79} +(3.29181 + 5.70158i) q^{80} +(0.287526 + 0.166003i) q^{82} +(4.00094 - 6.92984i) q^{83} +(-1.63774 - 2.83664i) q^{85} +6.83718i q^{86} -1.21417 q^{88} +(-1.05931 + 1.83478i) q^{89} +(21.4649 + 12.3927i) q^{92} +(-4.13828 - 2.38924i) q^{94} +(3.75202 + 2.16623i) q^{95} +(10.5054 + 6.06531i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.05485	+	1.18637i	−1.45300	+	0.838890i	−0.998651	−	0.0519328i	$-0.983462\pi$
$2$	−2.05485	+	1.18637i	−1.45300	+	0.838890i	−0.454350	+	0.890823i	$0.650129\pi$
$3$		0			0
$3$		0			0
$4$	1.81495	−	3.14358i	0.907474	−	1.57179i
$5$	−3.43548			−1.53640			−0.768198	−	0.640213i	$-0.778846\pi$
$5$	−3.43548			−1.53640			−0.768198	+	0.640213i	$0.778846\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			3.86732i			1.36730i
$9$		0			0
$10$	7.05942	−	4.07576i	2.23238	−	1.28887i
$11$			0.313957i			0.0946617i	0.998879	+	0.0473309i	$0.0150715\pi$
$11$			0.313957i			0.0946617i	−0.998879	+	0.0473309i	$0.984928\pi$
$12$		0			0
$13$	−5.09882	+	2.94381i	−1.41416	+	0.816465i	−0.995777	−	0.0918054i	$-0.970736\pi$
$13$	−5.09882	+	2.94381i	−1.41416	+	0.816465i	−0.418383	+	0.908271i	$0.637403\pi$
$14$		0			0
$15$		0			0
$16$	−0.958178	−	1.65961i	−0.239545	−	0.414903i
$17$	0.476712	+	0.825689i	0.115620	+	0.200259i	0.918027	−	0.396517i	$-0.129781\pi$
$17$	0.476712	+	0.825689i	0.115620	+	0.200259i	−0.802408	+	0.596776i	$0.796448\pi$
$18$		0			0
$19$	−1.09214	−	0.630546i	−0.250553	−	0.144657i	0.369464	−	0.929245i	$-0.379541\pi$
$19$	−1.09214	−	0.630546i	−0.250553	−	0.144657i	−0.620018	+	0.784588i	$0.712875\pi$
$20$	−6.23523	+	10.7997i	−1.39424	+	2.41489i
$21$		0			0
$22$	−0.372470	−	0.645137i	−0.0794108	−	0.137544i
$23$			6.82815i			1.42377i	0.702297	+	0.711884i	$0.252158\pi$
$23$			6.82815i			1.42377i	−0.702297	+	0.711884i	$0.747842\pi$
$24$		0			0
$25$	6.80255			1.36051
$26$	6.98489	−	12.0982i	1.36985	−	2.37265i
$27$		0			0
$28$		0			0
$29$	−3.43518	−	1.98330i	−0.637897	−	0.368290i	0.145907	−	0.989298i	$-0.453390\pi$
$29$	−3.43518	−	1.98330i	−0.637897	−	0.368290i	−0.783804	+	0.621008i	$0.786723\pi$
$30$		0			0
$31$	−4.53388	−	2.61764i	−0.814309	−	0.470141i	0.0341412	−	0.999417i	$-0.489130\pi$
$31$	−4.53388	−	2.61764i	−0.814309	−	0.470141i	−0.848450	+	0.529276i	$0.822464\pi$
$32$	−2.76057	−	1.59381i	−0.488004	−	0.281749i
$33$		0			0
$34$	−1.95915	−	1.13111i	−0.335991	−	0.193984i
$35$		0			0
$36$		0			0
$37$	−2.68802	+	4.65579i	−0.441908	+	0.765407i	−0.997831	−	0.0658264i	$-0.979032\pi$
$37$	−2.68802	+	4.65579i	−0.441908	+	0.765407i	0.555923	+	0.831234i	$0.312365\pi$
$38$	2.99224			0.485406
$39$		0			0
$40$		−	13.2861i		−	2.10072i
$41$	−0.0699627	−	0.121179i	−0.0109263	−	0.0189250i	0.860511	−	0.509433i	$-0.170145\pi$
$41$	−0.0699627	−	0.121179i	−0.0109263	−	0.0189250i	−0.871437	+	0.490508i	$0.836811\pi$
$42$		0			0
$43$	1.44078	−	2.49550i	0.219716	−	0.380560i	−0.735005	−	0.678062i	$-0.762820\pi$
$43$	1.44078	−	2.49550i	0.219716	−	0.380560i	0.954721	+	0.297502i	$0.0961535\pi$
$44$	0.986951	+	0.569817i	0.148788	+	0.0859031i
$45$		0			0
$46$	−8.10072	−	14.0309i	−1.19439	−	2.06874i
$47$	1.00695	+	1.74409i	0.146879	+	0.254402i	0.930072	−	0.367376i	$-0.119744\pi$
$47$	1.00695	+	1.74409i	0.146879	+	0.254402i	−0.783193	+	0.621778i	$0.786411\pi$
$48$		0			0
$49$		0			0
$50$	−13.9783	+	8.07035i	−1.97682	+	1.14132i
$51$		0			0
$52$			21.3714i			2.96369i
$53$	10.3749	−	5.98997i	1.42511	−	0.822786i	0.428378	−	0.903599i	$-0.359085\pi$
$53$	10.3749	−	5.98997i	1.42511	−	0.822786i	0.996729	+	0.0808132i	$0.0257517\pi$
$54$		0			0
$55$		−	1.07860i		−	0.145438i
$56$		0			0
$57$		0			0
$58$	9.41172			1.23582
$59$	−0.824459	+	1.42801i	−0.107335	+	0.185910i	−0.914690	−	0.404156i	$-0.867565\pi$
$59$	−0.824459	+	1.42801i	−0.107335	+	0.185910i	0.807355	+	0.590067i	$0.200899\pi$
$60$		0			0
$61$	−2.57423	+	1.48623i	−0.329597	+	0.190293i	−0.655662	−	0.755055i	$-0.727610\pi$
$61$	−2.57423	+	1.48623i	−0.329597	+	0.190293i	0.326065	+	0.945347i	$0.394277\pi$
$62$	12.4219			1.57759
$63$		0			0
$64$	11.3961			1.42452
$65$	17.5169	−	10.1134i	2.17271	−	1.25441i
$66$		0			0
$67$	0.934059	−	1.61784i	0.114113	−	0.197650i	−0.803312	−	0.595559i	$-0.796931\pi$
$67$	0.934059	−	1.61784i	0.114113	−	0.197650i	0.917425	+	0.397909i	$0.130264\pi$
$68$	3.46083			0.419687
$69$		0			0
$70$		0			0
$71$		−	10.9981i		−	1.30524i	−0.757686	−	0.652619i	$-0.773670\pi$
$71$		−	10.9981i		−	1.30524i	0.757686	−	0.652619i	$-0.226330\pi$
$72$		0			0
$73$	−0.354655	+	0.204760i	−0.0415092	+	0.0239653i	−0.520611	−	0.853794i	$-0.674296\pi$
$73$	−0.354655	+	0.204760i	−0.0415092	+	0.0239653i	0.479102	+	0.877759i	$0.340962\pi$
$74$		−	12.7560i		−	1.48285i
$75$		0			0
$76$	−3.96435	+	2.28882i	−0.454742	+	0.262545i
$77$		0			0
$78$		0			0
$79$	−5.23325	−	9.06426i	−0.588787	−	1.01981i	−0.994392	−	0.105760i	$-0.966272\pi$
$79$	−5.23325	−	9.06426i	−0.588787	−	1.01981i	0.405605	−	0.914049i	$-0.367061\pi$
$80$	3.29181	+	5.70158i	0.368035	+	0.637456i
$81$		0			0
$82$	0.287526	+	0.166003i	0.0317519	+	0.0183320i
$83$	4.00094	−	6.92984i	0.439161	−	0.760649i	−0.558464	−	0.829529i	$-0.688609\pi$
$83$	4.00094	−	6.92984i	0.439161	−	0.760649i	0.997625	+	0.0688800i	$0.0219426\pi$
$84$		0			0
$85$	−1.63774	−	2.83664i	−0.177637	−	0.307677i
$86$			6.83718i			0.737272i
$87$		0			0
$88$	−1.21417			−0.129431
$89$	−1.05931	+	1.83478i	−0.112287	+	0.194487i	−0.916692	−	0.399595i	$-0.869151\pi$
$89$	−1.05931	+	1.83478i	−0.112287	+	0.194487i	0.804405	+	0.594081i	$0.202484\pi$
$90$		0			0
$91$		0			0
$92$	21.4649	+	12.3927i	2.23787	+	1.29203i
$93$		0			0
$94$	−4.13828	−	2.38924i	−0.426831	−	0.246431i
$95$	3.75202	+	2.16623i	0.384949	+	0.222251i
$96$		0			0
$97$	10.5054	+	6.06531i	1.06666	+	0.615839i	0.927268	−	0.374398i	$-0.122150\pi$
$97$	10.5054	+	6.06531i	1.06666	+	0.615839i	0.139396	+	0.990237i	$0.455484\pi$
$98$		0			0
$99$		0			0
$100$	12.3463	−	21.3844i	1.23463	−	2.13844i
$101$	−12.5208			−1.24586			−0.622932	−	0.782276i	$-0.714059\pi$
$101$	−12.5208			−1.24586			−0.622932	+	0.782276i	$0.714059\pi$
$102$		0			0
$103$		−	18.0179i		−	1.77536i	−0.460461	−	0.887680i	$-0.652316\pi$
$103$		−	18.0179i		−	1.77536i	0.460461	−	0.887680i	$-0.347684\pi$
$104$	−11.3847	−	19.7188i	−1.11636	−	1.93359i
$105$		0			0
$106$	−14.2127	+	24.6170i	−1.38046	+	2.39102i
$107$	3.11610	+	1.79908i	0.301245	+	0.173924i	0.643002	−	0.765864i	$-0.277689\pi$
$107$	3.11610	+	1.79908i	0.301245	+	0.173924i	−0.341757	+	0.939788i	$0.611022\pi$
$108$		0			0
$109$	3.28109	+	5.68302i	0.314271	+	0.544334i	0.979282	−	0.202499i	$-0.0649064\pi$
$109$	3.28109	+	5.68302i	0.314271	+	0.544334i	−0.665011	+	0.746834i	$0.731573\pi$
$110$	1.27961	+	2.21636i	0.122006	+	0.211321i
$111$		0			0
$112$		0			0
$113$	1.87912	−	1.08491i	0.176773	−	0.102060i	−0.409003	−	0.912533i	$-0.634123\pi$
$113$	1.87912	−	1.08491i	0.176773	−	0.102060i	0.585775	+	0.810473i	$0.300790\pi$
$114$		0			0
$115$		−	23.4580i		−	2.18747i
$116$	−12.4694	+	7.19918i	−1.15775	+	0.668427i
$117$		0			0
$118$		−	3.91246i		−	0.360171i
$119$		0			0
$120$		0			0
$121$	10.9014			0.991039
$122$	3.52645	−	6.10798i	0.319269	−	0.552991i
$123$		0			0
$124$	−16.4575	+	9.50175i	−1.47793	+	0.853282i
$125$	−6.19265			−0.553887
$126$		0			0
$127$	2.34967			0.208499			0.104250	−	0.994551i	$-0.466756\pi$
$127$	2.34967			0.208499			0.104250	+	0.994551i	$0.466756\pi$
$128$	−17.8962	+	10.3324i	−1.58182	+	0.913263i
$129$		0			0
$130$	−23.9965	+	41.5631i	−2.10463	+	3.64533i
$131$	9.49188			0.829309			0.414655	−	0.909979i	$-0.363902\pi$
$131$	9.49188			0.829309			0.414655	+	0.909979i	$0.363902\pi$
$132$		0			0
$133$		0			0
$134$			4.43256i			0.382915i
$135$		0			0
$136$	−3.19320	+	1.84360i	−0.273815	+	0.158087i
$137$			10.2244i			0.873527i	0.899576	+	0.436763i	$0.143875\pi$
$137$			10.2244i			0.873527i	−0.899576	+	0.436763i	$0.856125\pi$
$138$		0			0
$139$	4.56556	−	2.63593i	0.387246	−	0.223577i	−0.293720	−	0.955891i	$-0.594893\pi$
$139$	4.56556	−	2.63593i	0.387246	−	0.223577i	0.680966	+	0.732315i	$0.261560\pi$
$140$		0			0
$141$		0			0
$142$	13.0479	+	22.5996i	1.09495	+	1.89651i
$143$	−0.924230	−	1.60081i	−0.0772880	−	0.133867i
$144$		0			0
$145$	11.8015	+	6.81361i	0.980062	+	0.565839i
$146$	0.485842	−	0.841504i	0.0402086	−	0.0696433i
$147$		0			0
$148$	9.75724	+	16.9000i	0.802040	+	1.38917i
$149$		−	18.2617i		−	1.49606i	−0.663666	−	0.748029i	$-0.731000\pi$
$149$		−	18.2617i		−	1.49606i	0.663666	−	0.748029i	$-0.269000\pi$
$150$		0			0
$151$	23.1102			1.88068			0.940340	−	0.340236i	$-0.110507\pi$
$151$	23.1102			1.88068			0.940340	+	0.340236i	$0.110507\pi$
$152$	2.43852	−	4.22365i	0.197790	−	0.342583i
$153$		0			0
$154$		0			0
$155$	15.5761	+	8.99285i	1.25110	+	0.722323i
$156$		0			0
$157$	5.65459	+	3.26468i	0.451286	+	0.260550i	0.708373	−	0.705838i	$-0.249430\pi$
$157$	5.65459	+	3.26468i	0.451286	+	0.260550i	−0.257087	+	0.966388i	$0.582763\pi$
$158$	21.5071	+	12.4172i	1.71102	+	0.987855i
$159$		0			0
$160$	9.48388	+	5.47552i	0.749767	+	0.432878i
$161$		0			0
$162$		0			0
$163$	−12.2623	+	21.2389i	−0.960457	+	1.66356i	−0.239103	+	0.970994i	$0.576853\pi$
$163$	−12.2623	+	21.2389i	−0.960457	+	1.66356i	−0.721354	+	0.692566i	$0.756480\pi$
$164$	−0.507915			−0.0396615
$165$		0			0
$166$			18.9864i			1.47363i
$167$	−6.99871	−	12.1221i	−0.541576	−	0.938037i	−0.998814	−	0.0486928i	$-0.984494\pi$
$167$	−6.99871	−	12.1221i	−0.541576	−	0.938037i	0.457238	−	0.889345i	$-0.348839\pi$
$168$		0			0
$169$	10.8320	−	18.7616i	0.833232	−	1.44320i
$170$	6.73061	+	3.88592i	0.516214	+	0.298037i
$171$		0			0
$172$	−5.22987	−	9.05840i	−0.398774	−	0.690697i
$173$	5.44974	+	9.43923i	0.414336	+	0.717651i	0.995359	−	0.0962363i	$-0.0306805\pi$
$173$	5.44974	+	9.43923i	0.414336	+	0.717651i	−0.581022	+	0.813888i	$0.697347\pi$
$174$		0			0
$175$		0			0
$176$	0.521048	−	0.300827i	0.0392755	−	0.0226757i
$177$		0			0
$178$		−	5.02695i		−	0.376786i
$179$	1.38517	−	0.799726i	0.103532	−	0.0597743i	−0.447340	−	0.894364i	$-0.647629\pi$
$179$	1.38517	−	0.799726i	0.103532	−	0.0597743i	0.550872	+	0.834590i	$0.314295\pi$
$180$		0			0
$181$		−	17.5088i		−	1.30142i	−0.759326	−	0.650710i	$-0.774471\pi$
$181$		−	17.5088i		−	1.30142i	0.759326	−	0.650710i	$-0.225529\pi$
$182$		0			0
$183$		0			0
$184$	−26.4067			−1.94673
$185$	9.23466	−	15.9949i	0.678946	−	1.17597i
$186$		0			0
$187$	−0.259231	+	0.149667i	−0.0189569	+	0.0109447i
$188$	7.31027			0.533156
$189$		0			0
$190$	−10.2798			−0.745775
$191$	−13.9107	+	8.03138i	−1.00655	+	0.581130i	−0.910179	−	0.414216i	$-0.864056\pi$
$191$	−13.9107	+	8.03138i	−1.00655	+	0.581130i	−0.0963679	+	0.995346i	$0.530723\pi$
$192$		0			0
$193$	5.44196	−	9.42575i	0.391721	−	0.678480i	−0.600956	−	0.799282i	$-0.705213\pi$
$193$	5.44196	−	9.42575i	0.391721	−	0.678480i	0.992677	+	0.120802i	$0.0385467\pi$
$194$	−28.7828			−2.06649
$195$		0			0
$196$		0			0
$197$			6.50777i			0.463660i	0.972756	+	0.231830i	$0.0744712\pi$
$197$			6.50777i			0.463660i	−0.972756	+	0.231830i	$0.925529\pi$
$198$		0			0
$199$	15.4217	−	8.90372i	1.09321	−	0.631168i	0.158784	−	0.987313i	$-0.449243\pi$
$199$	15.4217	−	8.90372i	1.09321	−	0.631168i	0.934431	+	0.356145i	$0.115909\pi$
$200$			26.3077i			1.86023i
$201$		0			0
$202$	25.7284	−	14.8543i	1.81024	−	1.04514i
$203$		0			0
$204$		0			0
$205$	0.240356	+	0.416308i	0.0167872	+	0.0290762i
$206$	21.3759	+	37.0242i	1.48933	+	2.57960i
$207$		0			0
$208$	9.77117	+	5.64139i	0.677508	+	0.391160i
$209$	0.197965	−	0.342885i	0.0136935	−	0.0237178i
$210$		0			0
$211$	−0.282402	−	0.489135i	−0.0194414	−	0.0336735i	0.856141	−	0.516742i	$-0.172855\pi$
$211$	−0.282402	−	0.489135i	−0.0194414	−	0.0336735i	−0.875582	+	0.483069i	$0.839522\pi$
$212$		−	43.4860i		−	2.98663i
$213$		0			0
$214$	−8.53751			−0.583612
$215$	−4.94977	+	8.57325i	−0.337571	+	0.584691i
$216$		0			0
$217$		0			0
$218$	−13.4843	−	7.78518i	−0.913273	−	0.527279i
$219$		0			0
$220$	−3.39066	−	1.95760i	−0.228598	−	0.131981i
$221$	−4.86134	−	2.80670i	−0.327009	−	0.188799i
$222$		0			0
$223$	−7.61261	−	4.39514i	−0.509778	−	0.294321i	0.222964	−	0.974827i	$-0.428427\pi$
$223$	−7.61261	−	4.39514i	−0.509778	−	0.294321i	−0.732742	+	0.680506i	$0.761760\pi$
$224$		0			0
$225$		0			0
$226$	−2.57421	+	4.45866i	−0.171234	+	0.296586i
$227$	−16.9066			−1.12213			−0.561065	−	0.827772i	$-0.689608\pi$
$227$	−16.9066			−1.12213			−0.561065	+	0.827772i	$0.689608\pi$
$228$		0			0
$229$			19.5618i			1.29268i	0.763050	+	0.646339i	$0.223701\pi$
$229$			19.5618i			1.29268i	−0.763050	+	0.646339i	$0.776299\pi$
$230$	27.8299	+	48.2028i	1.83505	+	3.17840i
$231$		0			0
$232$	7.67007	−	13.2849i	0.503565	−	0.872200i
$233$	17.0926	+	9.86840i	1.11977	+	0.646500i	0.941342	−	0.337453i	$-0.109565\pi$
$233$	17.0926	+	9.86840i	1.11977	+	0.646500i	0.178428	+	0.983953i	$0.442899\pi$
$234$		0			0
$235$	−3.45937	−	5.99180i	−0.225664	−	0.390862i
$236$	2.99270	+	5.18351i	0.194808	+	0.337418i
$237$		0			0
$238$		0			0
$239$	16.9761	−	9.80118i	1.09809	−	0.633985i	0.162375	−	0.986729i	$-0.448085\pi$
$239$	16.9761	−	9.80118i	1.09809	−	0.633985i	0.935720	+	0.352744i	$0.114751\pi$
$240$		0			0
$241$			15.9540i			1.02769i	0.857883	+	0.513845i	$0.171779\pi$
$241$			15.9540i			1.02769i	−0.857883	+	0.513845i	$0.828221\pi$
$242$	−22.4008	+	12.9331i	−1.43998	+	0.831373i
$243$		0			0
$244$			10.7897i			0.690743i
$245$		0			0
$246$		0			0
$247$	7.42482			0.472430
$248$	10.1232	−	17.5340i	0.642826	−	1.11341i
$249$		0			0
$250$	12.7250	−	7.34677i	0.804798	−	0.464651i
$251$	−0.976065			−0.0616087			−0.0308044	−	0.999525i	$-0.509807\pi$
$251$	−0.976065			−0.0616087			−0.0308044	+	0.999525i	$0.509807\pi$
$252$		0			0
$253$	−2.14375			−0.134776
$254$	−4.82822	+	2.78758i	−0.302950	+	0.174908i
$255$		0			0
$256$	13.1200	−	22.7244i	0.819998	−	1.42028i
$257$	12.2389			0.763444			0.381722	−	0.924277i	$-0.375331\pi$
$257$	12.2389			0.763444			0.381722	+	0.924277i	$0.375331\pi$
$258$		0			0
$259$		0			0
$260$		−	73.4212i		−	4.55339i
$261$		0			0
$262$	−19.5044	+	11.2609i	−1.20499	+	0.695700i
$263$		−	4.20815i		−	0.259486i	−0.991548	−	0.129743i	$-0.958585\pi$
$263$		−	4.20815i		−	0.259486i	0.991548	−	0.129743i	$-0.0414152\pi$
$264$		0			0
$265$	−35.6429	+	20.5785i	−2.18953	+	1.26413i
$266$		0			0
$267$		0			0
$268$	−3.39054	−	5.87258i	−0.207110	−	0.358725i
$269$	−10.8299	−	18.7579i	−0.660309	−	1.14369i	−0.980534	−	0.196348i	$-0.937092\pi$
$269$	−10.8299	−	18.7579i	−0.660309	−	1.14369i	0.320225	−	0.947341i	$-0.396241\pi$
$270$		0			0
$271$	−17.8987	−	10.3338i	−1.08727	−	0.627736i	−0.154423	−	0.988005i	$-0.549352\pi$
$271$	−17.8987	−	10.3338i	−1.08727	−	0.627736i	−0.932849	+	0.360268i	$0.882685\pi$
$272$	0.913549	−	1.58231i	0.0553921	−	0.0959419i
$273$		0			0
$274$	−12.1299	−	21.0096i	−0.732793	−	1.26923i
$275$			2.13571i			0.128788i
$276$		0			0
$277$	−27.8897			−1.67573			−0.837864	−	0.545879i	$-0.816196\pi$
$277$	−27.8897			−1.67573			−0.837864	+	0.545879i	$0.816196\pi$
$278$	−6.25437	+	10.8329i	−0.375112	+	0.649714i
$279$		0			0
$280$		0			0
$281$	−16.7176	−	9.65190i	−0.997287	−	0.575784i	−0.0898425	−	0.995956i	$-0.528636\pi$
$281$	−16.7176	−	9.65190i	−0.997287	−	0.575784i	−0.907444	+	0.420172i	$0.861970\pi$
$282$		0			0
$283$	15.2703	+	8.81631i	0.907725	+	0.524075i	0.879698	−	0.475532i	$-0.157744\pi$
$283$	15.2703	+	8.81631i	0.907725	+	0.524075i	0.0280263	+	0.999607i	$0.491078\pi$
$284$	−34.5735	−	19.9610i	−2.05156	−	1.18447i
$285$		0			0
$286$	3.79832	+	2.19296i	0.224599	+	0.129672i
$287$		0			0
$288$		0			0
$289$	8.04549	−	13.9352i	0.473264	−	0.819718i
$290$	−32.3338			−1.89871
$291$		0			0
$292$			1.48652i			0.0869917i
$293$	−14.1138	−	24.4458i	−0.824536	−	1.42814i	−0.902273	−	0.431165i	$-0.858103\pi$
$293$	−14.1138	−	24.4458i	−0.824536	−	1.42814i	0.0777369	−	0.996974i	$-0.475231\pi$
$294$		0			0
$295$	2.83242	−	4.90589i	0.164910	−	0.285632i
$296$	−18.0054	−	10.3954i	−1.04655	−	0.604223i
$297$		0			0
$298$	21.6651	+	37.5251i	1.25503	+	2.17377i
$299$	−20.1008	−	34.8156i	−1.16246	−	2.01344i
$300$		0			0
$301$		0			0
$302$	−47.4880	+	27.4172i	−2.73263	+	1.57768i
$303$		0			0
$304$			2.41670i			0.138607i
$305$	8.84374	−	5.10593i	0.506391	−	0.292365i
$306$		0			0
$307$		−	8.56651i		−	0.488917i	−0.969660	−	0.244458i	$-0.921390\pi$
$307$		−	8.56651i		−	0.488917i	0.969660	−	0.244458i	$-0.0786102\pi$
$308$		0			0
$309$		0			0
$310$	−42.6754			−2.42380
$311$	−9.67914	+	16.7648i	−0.548854	+	0.950642i	0.449500	+	0.893280i	$0.351602\pi$
$311$	−9.67914	+	16.7648i	−0.548854	+	0.950642i	−0.998353	+	0.0573619i	$0.981731\pi$
$312$		0			0
$313$	22.9507	−	13.2506i	1.29725	−	0.748967i	0.317321	−	0.948318i	$-0.397217\pi$
$313$	22.9507	−	13.2506i	1.29725	−	0.748967i	0.979928	+	0.199352i	$0.0638836\pi$
$314$	−15.4925			−0.874291
$315$		0			0
$316$	−37.9923			−2.13724
$317$	−7.50458	+	4.33277i	−0.421499	+	0.243353i	−0.695719	−	0.718314i	$-0.744914\pi$
$317$	−7.50458	+	4.33277i	−0.421499	+	0.243353i	0.274219	+	0.961667i	$0.411581\pi$
$318$		0			0
$319$	0.622673	−	1.07850i	0.0348630	−	0.0603844i
$320$	−39.1512			−2.18862
$321$		0			0
$322$		0			0
$323$		−	1.20235i		−	0.0669008i
$324$		0			0
$325$	−34.6850	+	20.0254i	−1.92398	+	1.11081i
$326$		−	58.1905i		−	3.22287i
$327$		0			0
$328$	0.468638	−	0.270568i	0.0258762	−	0.0149396i
$329$		0			0
$330$		0			0
$331$	−9.66912	−	16.7474i	−0.531463	−	0.920521i	−0.999326	−	0.0367197i	$-0.988309\pi$
$331$	−9.66912	−	16.7474i	−0.531463	−	0.920521i	0.467863	−	0.883801i	$-0.345024\pi$
$332$	−14.5230	−	25.1546i	−0.797054	−	1.38054i
$333$		0			0
$334$	28.7626	+	16.6061i	1.57382	+	0.908646i
$335$	−3.20894	+	5.55805i	−0.175323	+	0.303669i
$336$		0			0
$337$	−12.4451	−	21.5556i	−0.677930	−	1.17421i	−0.975603	−	0.219542i	$-0.929544\pi$
$337$	−12.4451	−	21.5556i	−0.677930	−	1.17421i	0.297673	−	0.954668i	$-0.403790\pi$
$338$			51.4031i			2.79596i
$339$		0			0
$340$	−11.8896			−0.644805
$341$	0.821826	−	1.42345i	0.0445044	−	0.0770839i
$342$		0			0
$343$		0			0
$344$	9.65090	+	5.57195i	0.520341	+	0.300419i
$345$		0			0
$346$	−22.3968	−	12.9308i	−1.20406	−	0.695165i
$347$	5.01728	+	2.89673i	0.269342	+	0.155505i	0.628588	−	0.777738i	$-0.283633\pi$
$347$	5.01728	+	2.89673i	0.269342	+	0.155505i	−0.359247	+	0.933243i	$0.616966\pi$
$348$		0			0
$349$	−13.3430	−	7.70360i	−0.714236	−	0.412364i	0.0983918	−	0.995148i	$-0.468630\pi$
$349$	−13.3430	−	7.70360i	−0.714236	−	0.412364i	−0.812627	+	0.582784i	$0.801963\pi$
$350$		0			0
$351$		0			0
$352$	0.500390	−	0.866700i	0.0266709	−	0.0461953i
$353$	17.7453			0.944485			0.472243	−	0.881469i	$-0.343445\pi$
$353$	17.7453			0.944485			0.472243	+	0.881469i	$0.343445\pi$
$354$		0			0
$355$			37.7839i			2.00536i
$356$	3.84519	+	6.66007i	0.203795	+	0.352983i
$357$		0			0
$358$	−1.89754	+	3.28664i	−0.100288	+	0.173704i
$359$	−19.8490	−	11.4599i	−1.04759	−	0.604828i	−0.125618	−	0.992079i	$-0.540091\pi$
$359$	−19.8490	−	11.4599i	−1.04759	−	0.604828i	−0.921974	+	0.387251i	$0.873425\pi$
$360$		0			0
$361$	−8.70482	−	15.0772i	−0.458149	−	0.793537i
$362$	20.7719	+	35.9781i	1.09175	+	1.89096i
$363$		0			0
$364$		0			0
$365$	1.21841	−	0.703450i	0.0637745	−	0.0368203i
$366$		0			0
$367$		−	5.00277i		−	0.261143i	−0.991439	−	0.130571i	$-0.958319\pi$
$367$		−	5.00277i		−	0.261143i	0.991439	−	0.130571i	$-0.0416811\pi$
$368$	11.3321	−	6.54259i	0.590726	−	0.341056i
$369$		0			0
$370$			43.8229i			2.27824i
$371$		0			0
$372$		0			0
$373$	9.52560			0.493217			0.246608	−	0.969115i	$-0.420684\pi$
$373$	9.52560			0.493217			0.246608	+	0.969115i	$0.420684\pi$
$374$	0.355121	−	0.615088i	0.0183629	−	0.0318055i
$375$		0			0
$376$	−6.74497	+	3.89421i	−0.347845	+	0.200828i
$377$	23.3538			1.20278
$378$		0			0
$379$	−13.8369			−0.710756			−0.355378	−	0.934723i	$-0.615648\pi$
$379$	−13.8369			−0.710756			−0.355378	+	0.934723i	$0.615648\pi$
$380$	13.6194	−	7.86319i	0.698663	−	0.403373i
$381$		0			0
$382$	19.0564	−	33.0066i	0.975009	−	1.68876i
$383$	21.2320			1.08490			0.542452	−	0.840087i	$-0.317496\pi$
$383$	21.2320			1.08490			0.542452	+	0.840087i	$0.317496\pi$
$384$		0			0
$385$		0			0
$386$			25.8247i			1.31444i
$387$		0			0
$388$	38.1336	−	22.0165i	1.93594	−	1.11772i
$389$		−	4.51972i		−	0.229159i	−0.993414	−	0.114579i	$-0.963448\pi$
$389$		−	4.51972i		−	0.229159i	0.993414	−	0.114579i	$-0.0365521\pi$
$390$		0			0
$391$	−5.63793	+	3.25506i	−0.285122	+	0.164616i
$392$		0			0
$393$		0			0
$394$	−7.72063	−	13.3725i	−0.388960	−	0.673698i
$395$	17.9788	+	31.1401i	0.904610	+	1.56683i
$396$		0			0
$397$	−13.5830	−	7.84214i	−0.681710	−	0.393586i	0.118789	−	0.992920i	$-0.462099\pi$
$397$	−13.5830	−	7.84214i	−0.681710	−	0.393586i	−0.800499	+	0.599334i	$0.795432\pi$
$398$	−21.1262	+	36.5917i	−1.05896	+	1.83417i
$399$		0			0
$400$	−6.51806	−	11.2896i	−0.325903	−	0.564480i
$401$		−	10.7883i		−	0.538741i	−0.963037	−	0.269370i	$-0.913184\pi$
$401$		−	10.7883i		−	0.538741i	0.963037	−	0.269370i	$-0.0868156\pi$
$402$		0			0
$403$	30.8233			1.53542
$404$	−22.7246	+	39.3601i	−1.13059	+	1.95824i
$405$		0			0
$406$		0			0
$407$	−1.46172	−	0.843925i	−0.0724548	−	0.0418318i
$408$		0			0
$409$	16.9860	+	9.80689i	0.839906	+	0.484920i	0.857232	−	0.514930i	$-0.172182\pi$
$409$	16.9860	+	9.80689i	0.839906	+	0.484920i	−0.0173265	+	0.999850i	$0.505515\pi$
$410$	−0.987791	−	0.570302i	−0.0487835	−	0.0281652i
$411$		0			0
$412$	−56.6409	−	32.7016i	−2.79050	−	1.61109i
$413$		0			0
$414$		0			0
$415$	−13.7452	+	23.8074i	−0.674724	+	1.16866i
$416$	18.7675			0.920154
$417$		0			0
$418$			0.939437i			0.0459494i
$419$	8.83829	+	15.3084i	0.431779	+	0.747862i	0.997027	−	0.0770586i	$-0.0245528\pi$
$419$	8.83829	+	15.3084i	0.431779	+	0.747862i	−0.565248	+	0.824921i	$0.691220\pi$
$420$		0			0
$421$	−16.9507	+	29.3594i	−0.826124	+	1.43089i	0.0749327	+	0.997189i	$0.476126\pi$
$421$	−16.9507	+	29.3594i	−0.826124	+	1.43089i	−0.901057	+	0.433701i	$0.857208\pi$
$422$	1.16059	+	0.670068i	0.0564967	+	0.0326184i
$423$		0			0
$424$	23.1652	+	40.1232i	1.12500	+	1.94856i
$425$	3.24286	+	5.61679i	0.157302	+	0.272454i
$426$		0			0
$427$		0			0
$428$	11.3111	−	6.53048i	0.546744	−	0.315663i
$429$		0			0
$430$		−	23.4890i		−	1.13274i
$431$	−12.2317	+	7.06195i	−0.589178	+	0.340162i	−0.764772	−	0.644300i	$-0.777149\pi$
$431$	−12.2317	+	7.06195i	−0.589178	+	0.340162i	0.175594	+	0.984463i	$0.443815\pi$
$432$		0			0
$433$			9.10088i			0.437360i	0.975797	+	0.218680i	$0.0701752\pi$
$433$			9.10088i			0.437360i	−0.975797	+	0.218680i	$0.929825\pi$
$434$		0			0
$435$		0			0
$436$	23.8200			1.14077
$437$	4.30546	−	7.45728i	0.205958	−	0.356730i
$438$		0			0
$439$	10.1520	−	5.86126i	0.484529	−	0.279743i	−0.237773	−	0.971321i	$-0.576417\pi$
$439$	10.1520	−	5.86126i	0.484529	−	0.279743i	0.722302	+	0.691578i	$0.243084\pi$
$440$	4.17128			0.198858
$441$		0			0
$442$	13.3191			0.633526
$443$	−6.17796	+	3.56685i	−0.293524	+	0.169466i	−0.639530	−	0.768766i	$-0.720871\pi$
$443$	−6.17796	+	3.56685i	−0.293524	+	0.169466i	0.346006	+	0.938232i	$0.387538\pi$
$444$		0			0
$445$	3.63925	−	6.30337i	0.172517	−	0.298808i
$446$	20.8571			0.987611
$447$		0			0
$448$		0			0
$449$		−	3.17445i		−	0.149811i	−0.997191	−	0.0749057i	$-0.976134\pi$
$449$		−	3.17445i		−	0.149811i	0.997191	−	0.0749057i	$-0.0238656\pi$
$450$		0			0
$451$	0.0380450	−	0.0219653i	0.00179147	−	0.00103431i
$452$		−	7.87622i		−	0.370466i
$453$		0			0
$454$	34.7406	−	20.0575i	1.63045	−	0.941344i
$455$		0			0
$456$		0			0
$457$	−12.0745	−	20.9137i	−0.564821	−	0.978299i	−0.997066	−	0.0765431i	$-0.975612\pi$
$457$	−12.0745	−	20.9137i	−0.564821	−	0.978299i	0.432245	−	0.901756i	$-0.357722\pi$
$458$	−23.2075	−	40.1966i	−1.08442	−	1.87826i
$459$		0			0
$460$	−73.7422	−	42.5751i	−3.43825	−	1.98507i
$461$	−6.87281	+	11.9041i	−0.320099	+	0.554427i	−0.980508	−	0.196478i	$-0.937049\pi$
$461$	−6.87281	+	11.9041i	−0.320099	+	0.554427i	0.660409	+	0.750906i	$0.270383\pi$
$462$		0			0
$463$	10.3157	+	17.8673i	0.479411	+	0.830364i	0.999721	−	0.0236135i	$-0.00751711\pi$
$463$	10.3157	+	17.8673i	0.479411	+	0.830364i	−0.520310	+	0.853977i	$0.674184\pi$
$464$			7.60143i			0.352887i
$465$		0			0
$466$	−46.8303			−2.16937
$467$	−0.465894	+	0.806952i	−0.0215590	+	0.0373413i	−0.876604	−	0.481213i	$-0.840196\pi$
$467$	−0.465894	+	0.806952i	−0.0215590	+	0.0373413i	0.855045	+	0.518554i	$0.173530\pi$
$468$		0			0
$469$		0			0
$470$	14.2170	+	8.20819i	0.655781	+	0.378615i
$471$		0			0
$472$	−5.52256	−	3.18845i	−0.254196	−	0.146760i
$473$	0.783481	+	0.452343i	0.0360245	+	0.0207987i
$474$		0			0
$475$	−7.42932	−	4.28932i	−0.340881	−	0.196808i
$476$		0			0
$477$		0			0
$478$	−23.2556	+	40.2800i	−1.06369	+	1.84236i
$479$	32.4063			1.48068			0.740340	−	0.672232i	$-0.234664\pi$
$479$	32.4063			1.48068			0.740340	+	0.672232i	$0.234664\pi$
$480$		0			0
$481$		−	31.6521i		−	1.44321i
$482$	−18.9274	−	32.7832i	−0.862120	−	1.49324i
$483$		0			0
$484$	19.7855	−	34.2695i	0.899342	−	1.55771i
$485$	−36.0912	−	20.8373i	−1.63882	−	0.946172i
$486$		0			0
$487$	17.1867	+	29.7682i	0.778802	+	1.34892i	0.932633	+	0.360828i	$0.117506\pi$
$487$	17.1867	+	29.7682i	0.778802	+	1.34892i	−0.153830	+	0.988097i	$0.549161\pi$
$488$	−5.74774	−	9.95538i	−0.260188	−	0.450659i
$489$		0			0
$490$		0			0
$491$	7.31048	−	4.22071i	0.329917	−	0.190478i	−0.325887	−	0.945409i	$-0.605663\pi$
$491$	7.31048	−	4.22071i	0.329917	−	0.190478i	0.655804	+	0.754931i	$0.272330\pi$
$492$		0			0
$493$		−	3.78185i		−	0.170326i
$494$	−15.2569	+	8.80859i	−0.686441	+	0.396317i
$495$		0			0
$496$			10.0326i			0.450479i
$497$		0			0
$498$		0			0
$499$	−11.4080			−0.510692			−0.255346	−	0.966850i	$-0.582189\pi$
$499$	−11.4080			−0.510692			−0.255346	+	0.966850i	$0.582189\pi$
$500$	−11.2393	+	19.4671i	−0.502638	+	0.870595i
$501$		0			0
$502$	2.00567	−	1.15797i	0.0895175	−	0.0516830i
$503$	32.8028			1.46261			0.731303	−	0.682053i	$-0.238913\pi$
$503$	32.8028			1.46261			0.731303	+	0.682053i	$0.238913\pi$
$504$		0			0
$505$	43.0149			1.91414
$506$	4.40509	−	2.54328i	0.195830	−	0.113063i
$507$		0			0
$508$	4.26453	−	7.38638i	0.189208	−	0.327717i
$509$	−19.5166			−0.865056			−0.432528	−	0.901621i	$-0.642378\pi$
$509$	−19.5166			−0.865056			−0.432528	+	0.901621i	$0.642378\pi$
$510$		0			0
$511$		0			0
$512$			20.9310i			0.925027i
$513$		0			0
$514$	−25.1492	+	14.5199i	−1.10928	+	0.640446i
$515$			61.9003i			2.72765i
$516$		0			0
$517$	−0.547571	+	0.316140i	−0.0240821	+	0.0139038i
$518$		0			0
$519$		0			0
$520$	39.1118	+	67.7436i	1.71517	+	2.97075i
$521$	9.93108	+	17.2011i	0.435088	+	0.753595i	0.997303	−	0.0733964i	$-0.0233838\pi$
$521$	9.93108	+	17.2011i	0.435088	+	0.753595i	−0.562215	+	0.826991i	$0.690050\pi$
$522$		0			0
$523$	−6.71478	−	3.87678i	−0.293617	−	0.169520i	0.345955	−	0.938251i	$-0.387555\pi$
$523$	−6.71478	−	3.87678i	−0.293617	−	0.169520i	−0.639572	+	0.768731i	$0.720888\pi$
$524$	17.2273	−	29.8385i	0.752577	−	1.30350i
$525$		0			0
$526$	4.99242	+	8.64713i	0.217680	+	0.377033i
$527$		−	4.99143i		−	0.217430i
$528$		0			0
$529$	−23.6237			−1.02712
$530$	48.8274	−	84.5715i	2.12092	−	3.67355i
$531$		0			0
$532$		0			0
$533$	0.713455	+	0.411913i	0.0309032	+	0.0178419i
$534$		0			0
$535$	−10.7053	−	6.18072i	−0.462831	−	0.267216i
$536$	6.25670	+	3.61231i	0.270248	+	0.156028i
$537$		0			0
$538$	44.5076	+	25.6965i	1.91886	+	1.10785i
$539$		0			0
$540$		0			0
$541$	9.04616	−	15.6684i	0.388925	−	0.673638i	−0.603380	−	0.797454i	$-0.706180\pi$
$541$	9.04616	−	15.6684i	0.388925	−	0.673638i	0.992305	+	0.123816i	$0.0395133\pi$
$542$	49.0391			2.10641
$543$		0			0
$544$		−	3.03916i		−	0.130303i
$545$	−11.2721	−	19.5239i	−0.482845	−	0.836313i
$546$		0			0
$547$	3.46839	−	6.00743i	0.148298	−	0.256859i	−0.782301	−	0.622901i	$-0.785954\pi$
$547$	3.46839	−	6.00743i	0.148298	−	0.256859i	0.930598	+	0.366042i	$0.119287\pi$
$548$	32.1411	+	18.5567i	1.37300	+	0.792703i
$549$		0			0
$550$	−2.53375	−	4.38858i	−0.108039	−	0.187130i
$551$	2.50113	+	4.33208i	0.106552	+	0.184553i
$552$		0			0
$553$		0			0
$554$	57.3092	−	33.0875i	2.43483	−	1.40575i
$555$		0			0
$556$		−	19.1363i		−	0.811560i
$557$	13.6993	−	7.90931i	0.580459	−	0.335128i	−0.180857	−	0.983509i	$-0.557887\pi$
$557$	13.6993	−	7.90931i	0.580459	−	0.335128i	0.761316	+	0.648381i	$0.224554\pi$
$558$		0			0
$559$			16.9655i			0.717563i
$560$		0			0
$561$		0			0
$562$	45.8029			1.93208
$563$	16.0561	−	27.8101i	0.676686	−	1.17205i	−0.299287	−	0.954163i	$-0.596749\pi$
$563$	16.0561	−	27.8101i	0.676686	−	1.17205i	0.975973	−	0.217891i	$-0.0699178\pi$
$564$		0			0
$565$	−6.45568	+	3.72719i	−0.271593	+	0.156804i
$566$	−41.8376			−1.75857
$567$		0			0
$568$	42.5333			1.78466
$569$	31.3107	−	18.0772i	1.31261	−	0.757837i	0.330084	−	0.943951i	$-0.392923\pi$
$569$	31.3107	−	18.0772i	1.31261	−	0.757837i	0.982528	+	0.186114i	$0.0595894\pi$
$570$		0			0
$571$	−14.1792	+	24.5590i	−0.593380	+	1.02776i	0.400393	+	0.916343i	$0.368873\pi$
$571$	−14.1792	+	24.5590i	−0.593380	+	1.02776i	−0.993773	+	0.111421i	$0.964460\pi$
$572$	−6.70972			−0.280548
$573$		0			0
$574$		0			0
$575$			46.4489i			1.93705i
$576$		0			0
$577$	−36.3589	+	20.9918i	−1.51364	+	0.873901i	−0.513768	+	0.857929i	$0.671751\pi$
$577$	−36.3589	+	20.9918i	−1.51364	+	0.873901i	−0.999872	+	0.0159713i	$0.994916\pi$
$578$			38.1797i			1.58807i
$579$		0			0
$580$	42.8383	−	24.7327i	1.77876	−	1.02697i
$581$		0			0
$582$		0			0
$583$	1.88060	+	3.25729i	0.0778864	+	0.134903i
$584$	−0.791873	−	1.37156i	−0.0327679	−	0.0567557i
$585$		0			0
$586$	58.0035	+	33.4884i	2.39610	+	1.38339i
$587$	−9.79227	+	16.9607i	−0.404170	+	0.700043i	−0.994225	−	0.107320i	$-0.965773\pi$
$587$	−9.79227	+	16.9607i	−0.404170	+	0.700043i	0.590054	+	0.807364i	$0.299106\pi$
$588$		0			0
$589$	3.30108	+	5.71764i	0.136019	+	0.235591i
$590$			13.4412i			0.553365i
$591$		0			0
$592$	10.3024			0.423427
$593$	9.96374	−	17.2577i	0.409162	−	0.708689i	−0.585634	−	0.810575i	$-0.699154\pi$
$593$	9.96374	−	17.2577i	0.409162	−	0.708689i	0.994796	+	0.101886i	$0.0324878\pi$
$594$		0			0
$595$		0			0
$596$	−57.4072	−	33.1441i	−2.35149	−	1.35763i
$597$		0			0
$598$	82.6083	+	47.6939i	3.37810	+	1.95035i
$599$	0.0267639	+	0.0154521i	0.00109354	+	0.000631357i	0.500547	−	0.865710i	$-0.333132\pi$
$599$	0.0267639	+	0.0154521i	0.00109354	+	0.000631357i	−0.499453	+	0.866341i	$0.666466\pi$
$600$		0			0
$601$	25.8633	+	14.9322i	1.05499	+	0.609097i	0.924041	−	0.382293i	$-0.124865\pi$
$601$	25.8633	+	14.9322i	1.05499	+	0.609097i	0.130945	+	0.991390i	$0.458199\pi$
$602$		0			0
$603$		0			0
$604$	41.9438	−	72.6488i	1.70667	−	2.95604i
$605$	−37.4517			−1.52263
$606$		0			0
$607$			31.3960i			1.27433i	0.770729	+	0.637163i	$0.219892\pi$
$607$			31.3960i			1.27433i	−0.770729	+	0.637163i	$0.780108\pi$
$608$	2.00994	+	3.48133i	0.0815140	+	0.141186i
$609$		0			0
$610$	−12.1151	+	20.9839i	−0.490524	+	0.849613i
$611$	−10.2685	−	5.92855i	−0.415421	−	0.239843i
$612$		0			0
$613$	2.23146	+	3.86500i	0.0901278	+	0.156106i	0.907565	−	0.419912i	$-0.137939\pi$
$613$	2.23146	+	3.86500i	0.0901278	+	0.156106i	−0.817437	+	0.576018i	$0.804606\pi$
$614$	10.1631	+	17.6029i	0.410148	+	0.710396i
$615$		0			0
$616$		0			0
$617$	−26.9685	+	15.5703i	−1.08571	+	0.626835i	−0.932431	−	0.361348i	$-0.882317\pi$
$617$	−26.9685	+	15.5703i	−1.08571	+	0.626835i	−0.153279	+	0.988183i	$0.548983\pi$
$618$		0			0
$619$		−	1.31050i		−	0.0526736i	−0.999653	−	0.0263368i	$-0.991616\pi$
$619$		−	1.31050i		−	0.0526736i	0.999653	−	0.0263368i	$-0.00838424\pi$
$620$	56.5395	−	32.6431i	2.27068	−	1.31098i
$621$		0			0
$622$		−	45.9322i		−	1.84171i
$623$		0			0
$624$		0			0
$625$	−12.7380			−0.509521
$626$	−31.4402	+	54.4560i	−1.25660	+	2.17650i
$627$		0			0
$628$	20.5256	−	11.8505i	0.819060	−	0.472884i
$629$	−5.12565			−0.204373
$630$		0			0
$631$	−28.8892			−1.15006			−0.575030	−	0.818132i	$-0.695010\pi$
$631$	−28.8892			−1.15006			−0.575030	+	0.818132i	$0.695010\pi$
$632$	35.0544	−	20.2387i	1.39439	−	0.805051i
$633$		0			0
$634$	10.2805	−	17.8064i	0.408293	−	0.707183i
$635$	−8.07225			−0.320337
$636$		0			0
$637$		0			0
$638$			2.95488i			0.116985i
$639$		0			0
$640$	61.4822	−	35.4968i	2.43030	−	1.40313i
$641$			2.78658i			0.110063i	0.998485	+	0.0550316i	$0.0175260\pi$
$641$			2.78658i			0.110063i	−0.998485	+	0.0550316i	$0.982474\pi$
$642$		0			0
$643$	−0.324584	+	0.187399i	−0.0128004	+	0.00739029i	−0.506387	−	0.862307i	$-0.669019\pi$
$643$	−0.324584	+	0.187399i	−0.0128004	+	0.00739029i	0.493586	+	0.869697i	$0.335686\pi$
$644$		0			0
$645$		0			0
$646$	1.42644	+	2.47066i	0.0561224	+	0.0972069i
$647$	25.1608	+	43.5798i	0.989172	+	1.71330i	0.621682	+	0.783270i	$0.286450\pi$
$647$	25.1608	+	43.5798i	0.989172	+	1.71330i	0.367490	+	0.930027i	$0.380217\pi$
$648$		0			0
$649$	−0.448333	−	0.258845i	−0.0175986	−	0.0101606i
$650$	47.5151	−	82.2986i	1.86370	−	3.22802i
$651$		0			0
$652$	44.5109	+	77.0951i	1.74318	+	3.01928i
$653$			28.9270i			1.13200i	0.824405	+	0.566000i	$0.191510\pi$
$653$			28.9270i			1.13200i	−0.824405	+	0.566000i	$0.808490\pi$
$654$		0			0
$655$	−32.6092			−1.27415
$656$	−0.134073	+	0.232222i	−0.00523469	+	0.00906674i
$657$		0			0
$658$		0			0
$659$	22.8449	+	13.1895i	0.889910	+	0.513790i	0.873913	−	0.486082i	$-0.161574\pi$
$659$	22.8449	+	13.1895i	0.889910	+	0.513790i	0.0159971	+	0.999872i	$0.494908\pi$
$660$		0			0
$661$	−10.0533	−	5.80428i	−0.391028	−	0.225760i	0.291577	−	0.956547i	$-0.405820\pi$
$661$	−10.0533	−	5.80428i	−0.391028	−	0.225760i	−0.682606	+	0.730787i	$0.739153\pi$
$662$	39.7373	+	22.9423i	1.54443	+	0.891678i
$663$		0			0
$664$	26.7999	+	15.4729i	1.04004	+	0.600466i
$665$		0			0
$666$		0			0
$667$	13.5423	−	23.4559i	0.524360	−	0.908218i
$668$	−50.8092			−1.96587
$669$		0			0
$670$		−	15.2280i		−	0.588308i
$671$	−0.466614	−	0.808199i	−0.0180134	−	0.0312002i
$672$		0			0
$673$	−13.7692	+	23.8490i	−0.530764	+	0.919310i	0.468592	+	0.883415i	$0.344761\pi$
$673$	−13.7692	+	23.8490i	−0.530764	+	0.919310i	−0.999356	+	0.0358949i	$0.988572\pi$
$674$	51.1459	+	29.5291i	1.97007	+	1.13742i
$675$		0			0
$676$	−39.3191	−	68.1026i	−1.51227	−	2.61933i
$677$	−2.31563	−	4.01080i	−0.0889970	−	0.154147i	0.818090	−	0.575090i	$-0.195033\pi$
$677$	−2.31563	−	4.01080i	−0.0889970	−	0.154147i	−0.907087	+	0.420942i	$0.861700\pi$
$678$		0			0
$679$		0			0
$680$	10.9702	−	6.33365i	0.420688	−	0.242884i
$681$		0			0
$682$			3.89996i			0.149337i
$683$	12.0197	−	6.93959i	0.459922	−	0.265536i	−0.252089	−	0.967704i	$-0.581118\pi$
$683$	12.0197	−	6.93959i	0.459922	−	0.265536i	0.712012	+	0.702168i	$0.247784\pi$
$684$		0			0
$685$		−	35.1257i		−	1.34208i
$686$		0			0
$687$		0			0
$688$	−5.52208			−0.210527
$689$	−35.2667	+	61.0837i	−1.34355	+	2.32710i
$690$		0			0
$691$	19.6168	−	11.3258i	0.746258	−	0.430852i	−0.0780825	−	0.996947i	$-0.524880\pi$
$691$	19.6168	−	11.3258i	0.746258	−	0.430852i	0.824340	+	0.566095i	$0.191546\pi$
$692$	39.5640			1.50400
$693$		0			0
$694$	−13.7464			−0.521805
$695$	−15.6849	+	9.05569i	−0.594963	+	0.343502i
$696$		0			0
$697$	0.0667040	−	0.115535i	0.00252660	−	0.00437619i
$698$	36.5573			1.38371
$699$		0			0
$700$		0			0
$701$			16.3485i			0.617474i	0.951147	+	0.308737i	$0.0999063\pi$
$701$			16.3485i			0.617474i	−0.951147	+	0.308737i	$0.900094\pi$
$702$		0			0
$703$	5.87138	−	3.38984i	0.221443	−	0.127850i
$704$			3.57790i			0.134847i
$705$		0			0
$706$	−36.4639	+	21.0525i	−1.37234	+	0.792320i
$707$		0			0
$708$		0			0
$709$	−7.65356	−	13.2564i	−0.287435	−	0.497853i	0.685761	−	0.727826i	$-0.259469\pi$
$709$	−7.65356	−	13.2564i	−0.287435	−	0.497853i	−0.973197	+	0.229974i	$0.926136\pi$
$710$	−44.8257	−	77.6404i	−1.68228	−	2.91379i
$711$		0			0
$712$	−7.09569	−	4.09670i	−0.265922	−	0.153530i
$713$	17.8736	−	30.9580i	0.669372	−	1.15939i
$714$		0			0
$715$	3.17518	+	5.49957i	0.118745	+	0.205672i
$716$		−	5.80585i		−	0.216975i
$717$		0			0
$718$	54.3825			2.02954
$719$	−7.46359	+	12.9273i	−0.278345	+	0.482108i	−0.970974	−	0.239187i	$-0.923119\pi$
$719$	−7.46359	+	12.9273i	−0.278345	+	0.482108i	0.692629	+	0.721294i	$0.256453\pi$
$720$		0			0
$721$		0			0
$722$	35.7743	+	20.6543i	1.33138	+	0.768673i
$723$		0			0
$724$	−55.0404	−	31.7776i	−2.04556	−	1.18101i
$725$	−23.3680	−	13.4915i	−0.867866	−	0.501063i
$726$		0			0
$727$	−4.62968	−	2.67295i	−0.171705	−	0.0991341i	0.411684	−	0.911326i	$-0.364941\pi$
$727$	−4.62968	−	2.67295i	−0.171705	−	0.0991341i	−0.583390	+	0.812192i	$0.698274\pi$
$728$		0			0
$729$		0			0
$730$	−1.66910	+	2.89097i	−0.0617763	+	0.107000i
$731$	2.74734			0.101614
$732$		0			0
$733$			18.9486i			0.699881i	0.936772	+	0.349941i	$0.113798\pi$
$733$			18.9486i			0.699881i	−0.936772	+	0.349941i	$0.886202\pi$
$734$	5.93514	+	10.2800i	0.219070	+	0.379440i
$735$		0			0
$736$	10.8828	−	18.8496i	0.401145	−	0.694804i
$737$	0.507932	+	0.293255i	0.0187099	+	0.0108022i
$738$		0			0
$739$	−22.8430	−	39.5653i	−0.840295	−	1.45543i	−0.889646	−	0.456651i	$-0.849049\pi$
$739$	−22.8430	−	39.5653i	−0.840295	−	1.45543i	0.0493510	−	0.998781i	$-0.484285\pi$
$740$	−33.5209	−	58.0598i	−1.23225	−	2.13432i
$741$		0			0
$742$		0			0
$743$	25.0448	−	14.4596i	0.918804	−	0.530472i	0.0355508	−	0.999368i	$-0.488681\pi$
$743$	25.0448	−	14.4596i	0.918804	−	0.530472i	0.883253	+	0.468896i	$0.155348\pi$
$744$		0			0
$745$			62.7378i			2.29854i
$746$	−19.5737	+	11.3009i	−0.716644	+	0.413755i
$747$		0			0
$748$			1.08655i			0.0397283i
$749$		0			0
$750$		0			0
$751$	44.2014			1.61293			0.806465	−	0.591281i	$-0.201378\pi$
$751$	44.2014			1.61293			0.806465	+	0.591281i	$0.201378\pi$
$752$	1.92968	−	3.34230i	0.0703682	−	0.121881i
$753$		0			0
$754$	−47.9887	+	27.7063i	−1.74765	+	1.00900i
$755$	−79.3947			−2.88947
$756$		0			0
$757$	−27.5029			−0.999611			−0.499805	−	0.866138i	$-0.666595\pi$
$757$	−27.5029			−0.999611			−0.499805	+	0.866138i	$0.666595\pi$
$758$	28.4329	−	16.4157i	1.03273	−	0.596246i
$759$		0			0
$760$	−8.37751	+	14.5103i	−0.303884	+	0.526343i
$761$	5.09302			0.184622			0.0923109	−	0.995730i	$-0.470575\pi$
$761$	5.09302			0.184622			0.0923109	+	0.995730i	$0.470575\pi$
$762$		0			0
$763$		0			0
$764$			58.3061i			2.10944i
$765$		0			0
$766$	−43.6286	+	25.1890i	−1.57637	+	0.910115i
$767$		−	9.70820i		−	0.350543i
$768$		0			0
$769$	33.4505	−	19.3126i	1.20626	−	0.696432i	0.244316	−	0.969696i	$-0.421436\pi$
$769$	33.4505	−	19.3126i	1.20626	−	0.696432i	0.961939	+	0.273264i	$0.0881031\pi$
$770$		0			0
$771$		0			0
$772$	−19.7537	−	34.2145i	−0.710953	−	1.23141i
$773$	−17.1754	−	29.7486i	−0.617754	−	1.06998i	−0.989895	−	0.141806i	$-0.954709\pi$
$773$	−17.1754	−	29.7486i	−0.617754	−	1.06998i	0.372140	−	0.928177i	$-0.378624\pi$
$774$		0			0
$775$	−30.8420	−	17.8066i	−1.10788	−	0.639632i
$776$	−23.4565	+	40.6279i	−0.842040	+	1.45846i
$777$		0			0
$778$	5.36206	+	9.28736i	0.192239	+	0.332968i
$779$			0.176459i			0.00632229i
$780$		0			0
$781$	3.45295			0.123556
$782$	7.72341	−	13.3773i	0.276189	−	0.478373i
$783$		0			0
$784$		0			0
$785$	−19.4263	−	11.2158i	−0.693353	−	0.400308i
$786$		0			0
$787$	20.3343	+	11.7400i	0.724839	+	0.418486i	0.816531	−	0.577301i	$-0.195894\pi$
$787$	20.3343	+	11.7400i	0.724839	+	0.418486i	−0.0916921	+	0.995787i	$0.529228\pi$
$788$	20.4577	+	11.8113i	0.728776	+	0.420759i
$789$		0			0
$790$	−73.8874	−	42.6589i	−2.62880	−	1.51774i
$791$		0			0
$792$		0			0
$793$	8.75037	−	15.1561i	0.310735	−	0.538209i
$794$	37.2147			1.32070
$795$		0			0
$796$		−	64.6392i		−	2.29107i
$797$	5.82399	+	10.0875i	0.206296	+	0.357316i	0.950545	−	0.310587i	$-0.100526\pi$
$797$	5.82399	+	10.0875i	0.206296	+	0.357316i	−0.744249	+	0.667903i	$0.767192\pi$
$798$		0			0
$799$	−0.960052	+	1.66286i	−0.0339642	+	0.0588277i
$800$	−18.7789	−	10.8420i	−0.663934	−	0.383323i
$801$		0			0
$802$	12.7989	+	22.1683i	0.451945	+	0.782791i
$803$	−0.0642859	−	0.111347i	−0.00226860	−	0.00392933i
$804$		0			0
$805$		0			0
$806$	−63.3373	+	36.5678i	−2.23096	+	1.28805i
$807$		0			0
$808$		−	48.4219i		−	1.70348i
$809$	−13.7723	+	7.95147i	−0.484210	+	0.279559i	−0.722169	−	0.691716i	$-0.756855\pi$
$809$	−13.7723	+	7.95147i	−0.484210	+	0.279559i	0.237959	+	0.971275i	$0.423521\pi$
$810$		0			0
$811$			3.56109i			0.125047i	0.998044	+	0.0625233i	$0.0199148\pi$
$811$			3.56109i			0.125047i	−0.998044	+	0.0625233i	$0.980085\pi$
$812$		0			0
$813$		0			0
$814$	4.00483			0.140369
$815$	42.1269	−	72.9660i	1.47564	−	2.55589i
$816$		0			0
$817$	−3.14705	+	1.81695i	−0.110101	+	0.0635671i
$818$	−46.5384			−1.62718
$819$		0			0
$820$	1.74493			0.0609357
$821$	−0.113440	+	0.0654949i	−0.00395910	+	0.00228579i	−0.501978	−	0.864880i	$-0.667394\pi$
$821$	−0.113440	+	0.0654949i	−0.00395910	+	0.00228579i	0.498019	+	0.867166i	$0.334061\pi$
$822$		0			0
$823$	−23.0144	+	39.8621i	−0.802231	+	1.38950i	0.115914	+	0.993259i	$0.463020\pi$
$823$	−23.0144	+	39.8621i	−0.802231	+	1.38950i	−0.918145	+	0.396245i	$0.870313\pi$
$824$	69.6811			2.42746
$825$		0			0
$826$		0			0
$827$		−	40.5836i		−	1.41123i	−0.708595	−	0.705615i	$-0.750671\pi$
$827$		−	40.5836i		−	1.41123i	0.708595	−	0.705615i	$-0.249329\pi$
$828$		0			0
$829$	26.0930	−	15.0648i	0.906248	−	0.523223i	0.0270260	−	0.999635i	$-0.491396\pi$
$829$	26.0930	−	15.0648i	0.906248	−	0.523223i	0.879222	+	0.476412i	$0.158063\pi$
$830$		−	65.2275i		−	2.26408i
$831$		0			0
$832$	−58.1068	+	33.5480i	−2.01449	+	1.16307i
$833$		0			0
$834$		0			0
$835$	24.0439	+	41.6453i	0.832075	+	1.44120i
$836$	−0.718591	−	1.24464i	−0.0248530	−	0.0430466i
$837$		0			0
$838$	−36.3228	−	20.9710i	−1.25475	−	0.724430i
$839$	−5.81551	+	10.0728i	−0.200774	+	0.347750i	−0.948778	−	0.315944i	$-0.897679\pi$
$839$	−5.81551	+	10.0728i	−0.200774	+	0.347750i	0.748004	+	0.663694i	$0.231012\pi$
$840$		0			0
$841$	−6.63302	−	11.4887i	−0.228725	−	0.396163i
$842$		−	80.4390i		−	2.77211i
$843$		0			0
$844$	−2.05018			−0.0705702
$845$	−37.2132	+	64.4552i	−1.28017	+	2.21732i
$846$		0			0
$847$		0			0
$848$	−19.8821	−	11.4789i	−0.682754	−	0.394188i
$849$		0			0
$850$	−13.3272	−	7.69446i	−0.457119	−	0.263918i
$851$	−31.7905	−	18.3542i	−1.08976	−	0.629175i
$852$		0			0
$853$	20.6854	+	11.9427i	0.708254	+	0.408911i	0.810414	−	0.585857i	$-0.199242\pi$
$853$	20.6854	+	11.9427i	0.708254	+	0.408911i	−0.102160	+	0.994768i	$0.532575\pi$
$854$		0			0
$855$		0			0
$856$	−6.95763	+	12.0510i	−0.237807	+	0.411894i
$857$	−34.6724			−1.18439			−0.592193	−	0.805796i	$-0.701738\pi$
$857$	−34.6724			−1.18439			−0.592193	+	0.805796i	$0.701738\pi$
$858$		0			0
$859$		−	30.4763i		−	1.03984i	−0.854216	−	0.519918i	$-0.825962\pi$
$859$		−	30.4763i		−	1.03984i	0.854216	−	0.519918i	$-0.174038\pi$
$860$	17.9671	+	31.1200i	0.612674	+	1.06118i
$861$		0			0
$862$	16.7562	−	29.0225i	0.570717	−	0.988512i
$863$	28.9298	+	16.7026i	0.984781	+	0.568564i	0.903710	−	0.428145i	$-0.140833\pi$
$863$	28.9298	+	16.7026i	0.984781	+	0.568564i	0.0810708	+	0.996708i	$0.474166\pi$
$864$		0			0
$865$	−18.7225	−	32.4283i	−0.636584	−	1.10260i
$866$	−10.7970	−	18.7010i	−0.366898	−	0.635485i
$867$		0			0
$868$		0			0
$869$	2.84579	−	1.64302i	0.0965369	−	0.0557356i
$870$		0			0
$871$			10.9988i			0.372679i
$872$	−21.9780	+	12.6890i	−0.744271	+	0.429705i
$873$		0			0
$874$			20.4315i			0.691106i
$875$		0			0
$876$		0			0
$877$	−55.5200			−1.87478			−0.937389	−	0.348285i	$-0.886764\pi$
$877$	−55.5200			−1.87478			−0.937389	+	0.348285i	$0.886764\pi$
$878$	−13.9073	+	24.0881i	−0.469347	+	0.812933i
$879$		0			0
$880$	−1.79005	+	1.03349i	−0.0603426	+	0.0348388i
$881$	19.9850			0.673313			0.336656	−	0.941628i	$-0.390704\pi$
$881$	19.9850			0.673313			0.336656	+	0.941628i	$0.390704\pi$
$882$		0			0
$883$	35.5837			1.19749			0.598743	−	0.800941i	$-0.295667\pi$
$883$	35.5837			1.19749			0.598743	+	0.800941i	$0.295667\pi$
$884$	−17.6462	+	10.1880i	−0.593504	+	0.342660i
$885$		0			0
$886$	8.46321	−	14.6587i	0.284327	−	0.492469i
$887$	35.6633			1.19746			0.598729	−	0.800952i	$-0.295673\pi$
$887$	35.6633			1.19746			0.598729	+	0.800952i	$0.295673\pi$
$888$		0			0
$889$		0			0
$890$			17.2700i			0.578892i
$891$		0			0
$892$	−27.6330	+	15.9539i	−0.925221	+	0.534177i
$893$		−	2.53972i		−	0.0849884i
$894$		0			0
$895$	−4.75872	+	2.74745i	−0.159066	+	0.0918370i
$896$		0			0
$897$		0			0
$898$	3.76607	+	6.52302i	0.125675	+	0.217676i
$899$	10.3831	+	17.9841i	0.346297	+	0.599804i
$900$		0			0
$901$	9.89171	+	5.71098i	0.329541	+	0.190260i
$902$	−0.0521180	+	0.0902710i	−0.00173534	+	0.00300569i
$903$		0			0
$904$	4.19569	+	7.26715i	0.139547	+	0.241702i
$905$			60.1513i			1.99950i
$906$		0			0
$907$	37.2429			1.23663			0.618315	−	0.785930i	$-0.287815\pi$
$907$	37.2429			1.23663			0.618315	+	0.785930i	$0.287815\pi$
$908$	−30.6846	+	53.1472i	−1.01830	+	1.76375i
$909$		0			0
$910$		0			0
$911$	18.8068	+	10.8581i	0.623098	+	0.359746i	0.778074	−	0.628172i	$-0.216197\pi$
$911$	18.8068	+	10.8581i	0.623098	+	0.359746i	−0.154976	+	0.987918i	$0.549530\pi$
$912$		0			0
$913$	2.17567	+	1.25613i	0.0720043	+	0.0415717i
$914$	49.6227	+	28.6497i	1.64137	+	0.947647i
$915$		0			0
$916$	61.4940	+	35.5036i	2.03182	+	1.17307i
$917$		0			0
$918$		0			0
$919$	−17.1023	+	29.6220i	−0.564153	+	0.977141i	0.432975	+	0.901406i	$0.357464\pi$
$919$	−17.1023	+	29.6220i	−0.564153	+	0.977141i	−0.997128	+	0.0757353i	$0.975870\pi$
$920$	90.7197			2.99094
$921$		0			0
$922$		−	32.6148i		−	1.07411i
$923$	32.3764	+	56.0776i	1.06568	+	1.84582i
$924$		0			0
$925$	−18.2854	+	31.6713i	−0.601221	+	1.04135i
$926$	−42.3945	−	24.4764i	−1.39317	−	0.804346i
$927$		0			0
$928$	6.32203	+	10.9501i	0.207531	+	0.359454i
$929$	−23.4757	−	40.6611i	−0.770213	−	1.33405i	−0.937446	−	0.348131i	$-0.886816\pi$
$929$	−23.4757	−	40.6611i	−0.770213	−	1.33405i	0.167233	−	0.985917i	$-0.446517\pi$
$930$		0			0
$931$		0			0
$932$	62.0442	−	35.8213i	2.03233	−	1.17336i
$933$		0			0
$934$		−	2.21089i		−	0.0723425i
$935$	0.890585	−	0.514179i	0.0291252	−	0.0168155i
$936$		0			0
$937$		−	28.8826i		−	0.943555i	−0.881718	−	0.471777i	$-0.843613\pi$
$937$		−	28.8826i		−	0.943555i	0.881718	−	0.471777i	$-0.156387\pi$
$938$		0			0
$939$		0			0
$940$	−25.1143			−0.819138
$941$	−0.727044	+	1.25928i	−0.0237009	+	0.0410512i	−0.877633	−	0.479334i	$-0.840878\pi$
$941$	−0.727044	+	1.25928i	−0.0237009	+	0.0410512i	0.853932	+	0.520385i	$0.174212\pi$
$942$		0			0
$943$	0.827428	−	0.477716i	0.0269448	−	0.0155566i
$944$	3.15992			0.102847
$945$		0			0
$946$	−2.14658			−0.0697914
$947$	−36.9596	+	21.3386i	−1.20102	+	0.693412i	−0.960783	−	0.277301i	$-0.910560\pi$
$947$	−36.9596	+	21.3386i	−1.20102	+	0.693412i	−0.240241	+	0.970713i	$0.577227\pi$
$948$		0			0
$949$	1.20555	−	2.08807i	0.0391338	−	0.0677817i
$950$	20.3549			0.660400
$951$		0			0
$952$		0			0
$953$		−	10.8171i		−	0.350401i	−0.984533	−	0.175200i	$-0.943943\pi$
$953$		−	10.8171i		−	0.350401i	0.984533	−	0.175200i	$-0.0560574\pi$
$954$		0			0
$955$	47.7902	−	27.5917i	1.54645	−	0.892845i
$956$		−	71.1545i		−	2.30130i
$957$		0			0
$958$	−66.5902	+	38.4458i	−2.15143	+	1.24213i
$959$		0			0
$960$		0			0
$961$	−1.79596	−	3.11070i	−0.0579342	−	0.100345i
$962$	37.5511	+	65.0404i	1.21070	+	2.09699i
$963$		0			0
$964$	50.1529	+	28.9558i	1.61532	+	0.932603i
$965$	−18.6958	+	32.3820i	−0.601838	+	1.04241i
$966$		0			0
$967$	−22.4942	−	38.9611i	−0.723365	−	1.25290i	−0.959643	−	0.281219i	$-0.909261\pi$
$967$	−22.4942	−	38.9611i	−0.723365	−	1.25290i	0.236279	−	0.971685i	$-0.424072\pi$
$968$			42.1593i			1.35505i
$969$		0			0
$970$	98.8829			3.17494
$971$	3.40171	−	5.89194i	0.109166	−	0.189081i	−0.806267	−	0.591552i	$-0.798515\pi$
$971$	3.40171	−	5.89194i	0.109166	−	0.189081i	0.915433	+	0.402471i	$0.131849\pi$
$972$		0			0
$973$		0			0
$974$	−70.6321	−	40.7795i	−2.26320	−	1.30666i
$975$		0			0
$976$	4.93315	+	2.84815i	0.157906	+	0.0911672i
$977$	−29.2645	−	16.8959i	−0.936254	−	0.540546i	−0.0474698	−	0.998873i	$-0.515116\pi$
$977$	−29.2645	−	16.8959i	−0.936254	−	0.540546i	−0.888784	+	0.458326i	$0.848449\pi$
$978$		0			0
$979$	−0.576044	−	0.332579i	−0.0184104	−	0.0106293i
$980$		0			0
$981$		0			0
$982$	−10.0146	+	17.3459i	−0.319580	+	0.553529i
$983$	46.9826			1.49851			0.749256	−	0.662280i	$-0.230411\pi$
$983$	46.9826			1.49851			0.749256	+	0.662280i	$0.230411\pi$
$984$		0			0
$985$		−	22.3573i		−	0.712364i
$986$	4.48668	+	7.77116i	0.142885	+	0.247484i
$987$		0			0
$988$	13.4757	−	23.3405i	0.428718	−	0.742562i
$989$	17.0397	+	9.83785i	0.541829	+	0.312825i
$990$		0			0
$991$	−0.300449	−	0.520392i	−0.00954406	−	0.0165308i	0.861214	−	0.508243i	$-0.169705\pi$
$991$	−0.300449	−	0.520392i	−0.00954406	−	0.0165308i	−0.870758	+	0.491712i	$0.836371\pi$
$992$	8.34405	+	14.4523i	0.264924	+	0.458861i
$993$		0			0
$994$		0			0
$995$	−52.9810	+	30.5886i	−1.67961	+	0.969723i
$996$		0			0
$997$		−	48.4267i		−	1.53369i	−0.641834	−	0.766844i	$-0.721826\pi$
$997$		−	48.4267i		−	1.53369i	0.641834	−	0.766844i	$-0.278174\pi$
$998$	23.4418	−	13.5341i	0.742036	−	0.428415i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.d.656.3		48
3.2	odd	2		441.2.s.d.362.21		48
7.2	even	3		1323.2.o.e.440.21		48
7.3	odd	6		1323.2.i.d.521.4		48
7.4	even	3		1323.2.i.d.521.24		48
7.5	odd	6		1323.2.o.e.440.22		48
7.6	odd	2	inner	1323.2.s.d.656.4		48
9.4	even	3		441.2.i.d.68.3		48
9.5	odd	6		1323.2.i.d.1097.4		48
21.2	odd	6		441.2.o.e.146.3	✓	48
21.5	even	6		441.2.o.e.146.4	yes	48
21.11	odd	6		441.2.i.d.227.22		48
21.17	even	6		441.2.i.d.227.21		48
21.20	even	2		441.2.s.d.362.22		48
63.4	even	3		441.2.s.d.374.22		48
63.5	even	6		1323.2.o.e.881.21		48
63.13	odd	6		441.2.i.d.68.4		48
63.23	odd	6		1323.2.o.e.881.22		48
63.31	odd	6		441.2.s.d.374.21		48
63.32	odd	6	inner	1323.2.s.d.962.4		48
63.40	odd	6		441.2.o.e.293.3	yes	48
63.41	even	6		1323.2.i.d.1097.24		48
63.58	even	3		441.2.o.e.293.4	yes	48
63.59	even	6	inner	1323.2.s.d.962.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.3		48	9.4	even	3
441.2.i.d.68.4		48	63.13	odd	6
441.2.i.d.227.21		48	21.17	even	6
441.2.i.d.227.22		48	21.11	odd	6
441.2.o.e.146.3	✓	48	21.2	odd	6
441.2.o.e.146.4	yes	48	21.5	even	6
441.2.o.e.293.3	yes	48	63.40	odd	6
441.2.o.e.293.4	yes	48	63.58	even	3
441.2.s.d.362.21		48	3.2	odd	2
441.2.s.d.362.22		48	21.20	even	2
441.2.s.d.374.21		48	63.31	odd	6
441.2.s.d.374.22		48	63.4	even	3
1323.2.i.d.521.4		48	7.3	odd	6
1323.2.i.d.521.24		48	7.4	even	3
1323.2.i.d.1097.4		48	9.5	odd	6
1323.2.i.d.1097.24		48	63.41	even	6
1323.2.o.e.440.21		48	7.2	even	3
1323.2.o.e.440.22		48	7.5	odd	6
1323.2.o.e.881.21		48	63.5	even	6
1323.2.o.e.881.22		48	63.23	odd	6
1323.2.s.d.656.3		48	1.1	even	1	trivial
1323.2.s.d.656.4		48	7.6	odd	2	inner
1323.2.s.d.962.3		48	63.59	even	6	inner
1323.2.s.d.962.4		48	63.32	odd	6	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.05485 + 1.18637i) q^{2} +(1.81495 - 3.14358i) q^{4} -3.43548 q^{5} +3.86732i q^{8} +O(q^{10})\)	\(q+(-2.05485 + 1.18637i) q^{2} +(1.81495 - 3.14358i) q^{4} -3.43548 q^{5} +3.86732i q^{8} +(7.05942 - 4.07576i) q^{10} +0.313957i q^{11} +(-5.09882 + 2.94381i) q^{13} +(-0.958178 - 1.65961i) q^{16} +(0.476712 + 0.825689i) q^{17} +(-1.09214 - 0.630546i) q^{19} +(-6.23523 + 10.7997i) q^{20} +(-0.372470 - 0.645137i) q^{22} +6.82815i q^{23} +6.80255 q^{25} +(6.98489 - 12.0982i) q^{26} +(-3.43518 - 1.98330i) q^{29} +(-4.53388 - 2.61764i) q^{31} +(-2.76057 - 1.59381i) q^{32} +(-1.95915 - 1.13111i) q^{34} +(-2.68802 + 4.65579i) q^{37} +2.99224 q^{38} -13.2861i q^{40} +(-0.0699627 - 0.121179i) q^{41} +(1.44078 - 2.49550i) q^{43} +(0.986951 + 0.569817i) q^{44} +(-8.10072 - 14.0309i) q^{46} +(1.00695 + 1.74409i) q^{47} +(-13.9783 + 8.07035i) q^{50} +21.3714i q^{52} +(10.3749 - 5.98997i) q^{53} -1.07860i q^{55} +9.41172 q^{58} +(-0.824459 + 1.42801i) q^{59} +(-2.57423 + 1.48623i) q^{61} +12.4219 q^{62} +11.3961 q^{64} +(17.5169 - 10.1134i) q^{65} +(0.934059 - 1.61784i) q^{67} +3.46083 q^{68} -10.9981i q^{71} +(-0.354655 + 0.204760i) q^{73} -12.7560i q^{74} +(-3.96435 + 2.28882i) q^{76} +(-5.23325 - 9.06426i) q^{79} +(3.29181 + 5.70158i) q^{80} +(0.287526 + 0.166003i) q^{82} +(4.00094 - 6.92984i) q^{83} +(-1.63774 - 2.83664i) q^{85} +6.83718i q^{86} -1.21417 q^{88} +(-1.05931 + 1.83478i) q^{89} +(21.4649 + 12.3927i) q^{92} +(-4.13828 - 2.38924i) q^{94} +(3.75202 + 2.16623i) q^{95} +(10.5054 + 6.06531i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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