LMFDB - Embedded newform 1323.2.s.d.656.4

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			656.4
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.4

$q$-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	$-0.221154\pi$
$5$	3.43548			1.53640			0.768198	+	0.640213i	$0.221154\pi$
$6$		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	0.418383	−	0.908271i	$-0.362597\pi$
$13$	5.09882	−	2.94381i	1.41416	−	0.816465i	0.995777	+	0.0918054i	$0.0292638\pi$
$14$		0			0
$15$		0			0
$16$	−0.958178	−	1.65961i	−0.239545	−	0.414903i
$17$	−0.476712	−	0.825689i	−0.115620	−	0.200259i	0.802408	−	0.596776i	$-0.203552\pi$
$17$	−0.476712	−	0.825689i	−0.115620	−	0.200259i	−0.918027	+	0.396517i	$0.870219\pi$
$18$		0			0
$19$	1.09214	+	0.630546i	0.250553	+	0.144657i	0.620018	−	0.784588i	$-0.287125\pi$
$19$	1.09214	+	0.630546i	0.250553	+	0.144657i	−0.369464	+	0.929245i	$0.620459\pi$
$20$	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	0.848450	−	0.529276i	$-0.177536\pi$
$31$	4.53388	+	2.61764i	0.814309	+	0.470141i	−0.0341412	+	0.999417i	$0.510870\pi$
$32$	−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	0.871437	−	0.490508i	$-0.163189\pi$
$41$	0.0699627	+	0.121179i	0.0109263	+	0.0189250i	−0.860511	+	0.509433i	$0.829855\pi$
$42$		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	0.783193	−	0.621778i	$-0.213589\pi$
$47$	−1.00695	−	1.74409i	−0.146879	−	0.254402i	−0.930072	+	0.367376i	$0.880256\pi$
$48$		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	−0.807355	−	0.590067i	$-0.799101\pi$
$59$	0.824459	−	1.42801i	0.107335	−	0.185910i	0.914690	+	0.404156i	$0.132435\pi$
$60$		0			0
$61$	2.57423	−	1.48623i	0.329597	−	0.190293i	−0.326065	−	0.945347i	$-0.605723\pi$
$61$	2.57423	−	1.48623i	0.329597	−	0.190293i	0.655662	+	0.755055i	$0.272390\pi$
$62$	−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	−0.479102	−	0.877759i	$-0.659038\pi$
$73$	0.354655	−	0.204760i	0.0415092	−	0.0239653i	0.520611	+	0.853794i	$0.325704\pi$
$74$		−	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	−0.997625	−	0.0688800i	$-0.978057\pi$
$83$	−4.00094	+	6.92984i	−0.439161	+	0.760649i	0.558464	+	0.829529i	$0.311391\pi$
$84$		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	−0.804405	−	0.594081i	$-0.797516\pi$
$89$	1.05931	−	1.83478i	0.112287	−	0.194487i	0.916692	+	0.399595i	$0.130849\pi$
$90$		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	−0.139396	−	0.990237i	$-0.544516\pi$
$97$	−10.5054	−	6.06531i	−1.06666	−	0.615839i	−0.927268	+	0.374398i	$0.877850\pi$
$98$		0			0
$99$		0			0
$100$	12.3463	−	21.3844i	1.23463	−	2.13844i
$101$	12.5208			1.24586			0.622932	−	0.782276i	$-0.285941\pi$
$101$	12.5208			1.24586			0.622932	+	0.782276i	$0.285941\pi$
$102$		0			0
$103$			18.0179i			1.77536i	0.460461	+	0.887680i	$0.347684\pi$
$103$			18.0179i			1.77536i	−0.460461	+	0.887680i	$0.652316\pi$
$104$	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	$-0.636098\pi$
$131$	−9.49188			−0.829309			−0.414655	+	0.909979i	$0.636098\pi$
$132$		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	−0.680966	−	0.732315i	$-0.738440\pi$
$139$	−4.56556	+	2.63593i	−0.387246	+	0.223577i	0.293720	+	0.955891i	$0.405107\pi$
$140$		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	0.257087	−	0.966388i	$-0.417237\pi$
$157$	−5.65459	−	3.26468i	−0.451286	−	0.260550i	−0.708373	+	0.705838i	$0.750570\pi$
$158$	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	$0.0155055\pi$
$167$	6.99871	+	12.1221i	0.541576	+	0.938037i	−0.457238	+	0.889345i	$0.651161\pi$
$168$		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	0.581022	−	0.813888i	$-0.302653\pi$
$173$	−5.44974	−	9.43923i	−0.414336	−	0.717651i	−0.995359	+	0.0962363i	$0.969320\pi$
$174$		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	$0.225529\pi$
$181$			17.5088i			1.30142i	−0.759326	+	0.650710i	$0.774471\pi$
$182$		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	−0.934431	−	0.356145i	$-0.884091\pi$
$199$	−15.4217	+	8.90372i	−1.09321	+	0.631168i	−0.158784	+	0.987313i	$0.550757\pi$
$200$			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	0.732742	−	0.680506i	$-0.238240\pi$
$223$	7.61261	+	4.39514i	0.509778	+	0.294321i	−0.222964	+	0.974827i	$0.571573\pi$
$224$		0			0
$225$		0			0
$226$	−2.57421	+	4.45866i	−0.171234	+	0.296586i
$227$	16.9066			1.12213			0.561065	−	0.827772i	$-0.310392\pi$
$227$	16.9066			1.12213			0.561065	+	0.827772i	$0.310392\pi$
$228$		0			0
$229$		−	19.5618i		−	1.29268i	−0.763050	−	0.646339i	$-0.776299\pi$
$229$		−	19.5618i		−	1.29268i	0.763050	−	0.646339i	$-0.223701\pi$
$230$	−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	$-0.828221\pi$
$241$		−	15.9540i		−	1.02769i	0.857883	−	0.513845i	$-0.171779\pi$
$242$	−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	$-0.490193\pi$
$251$	0.976065			0.0616087			0.0308044	+	0.999525i	$0.490193\pi$
$252$		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	$-0.624669\pi$
$257$	−12.2389			−0.763444			−0.381722	+	0.924277i	$0.624669\pi$
$258$		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	$0.0629081\pi$
$269$	10.8299	+	18.7579i	0.660309	+	1.14369i	−0.320225	+	0.947341i	$0.603759\pi$
$270$		0			0
$271$	17.8987	+	10.3338i	1.08727	+	0.627736i	0.932849	−	0.360268i	$-0.117315\pi$
$271$	17.8987	+	10.3338i	1.08727	+	0.627736i	0.154423	+	0.988005i	$0.450648\pi$
$272$	−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	−0.0280263	−	0.999607i	$-0.508922\pi$
$283$	−15.2703	−	8.81631i	−0.907725	−	0.524075i	−0.879698	+	0.475532i	$0.842256\pi$
$284$	−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	$0.141897\pi$
$293$	14.1138	+	24.4458i	0.824536	+	1.42814i	−0.0777369	+	0.996974i	$0.524769\pi$
$294$		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	$0.0786102\pi$
$307$			8.56651i			0.488917i	−0.969660	+	0.244458i	$0.921390\pi$
$308$		0			0
$309$		0			0
$310$	−42.6754			−2.42380
$311$	9.67914	−	16.7648i	0.548854	−	0.950642i	−0.449500	−	0.893280i	$-0.648398\pi$
$311$	9.67914	−	16.7648i	0.548854	−	0.950642i	0.998353	−	0.0573619i	$-0.0182689\pi$
$312$		0			0
$313$	−22.9507	+	13.2506i	−1.29725	+	0.748967i	−0.979928	−	0.199352i	$-0.936116\pi$
$313$	−22.9507	+	13.2506i	−1.29725	+	0.748967i	−0.317321	+	0.948318i	$0.602783\pi$
$314$	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	0.812627	−	0.582784i	$-0.198037\pi$
$349$	13.3430	+	7.70360i	0.714236	+	0.412364i	−0.0983918	+	0.995148i	$0.531370\pi$
$350$		0			0
$351$		0			0
$352$	0.500390	−	0.866700i	0.0266709	−	0.0461953i
$353$	−17.7453			−0.944485			−0.472243	−	0.881469i	$-0.656555\pi$
$353$	−17.7453			−0.944485			−0.472243	+	0.881469i	$0.656555\pi$
$354$		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	$0.0416811\pi$
$367$			5.00277i			0.261143i	−0.991439	+	0.130571i	$0.958319\pi$
$368$	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	$-0.682504\pi$
$383$	−21.2320			−1.08490			−0.542452	+	0.840087i	$0.682504\pi$
$384$		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	0.800499	−	0.599334i	$-0.204568\pi$
$397$	13.5830	+	7.84214i	0.681710	+	0.393586i	−0.118789	+	0.992920i	$0.537901\pi$
$398$	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	0.0173265	−	0.999850i	$-0.494485\pi$
$409$	−16.9860	−	9.80689i	−0.839906	−	0.484920i	−0.857232	+	0.514930i	$0.827818\pi$
$410$	−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	0.565248	−	0.824921i	$-0.308780\pi$
$419$	−8.83829	−	15.3084i	−0.431779	−	0.747862i	−0.997027	+	0.0770586i	$0.975447\pi$
$420$		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	$-0.929825\pi$
$433$		−	9.10088i		−	0.437360i	0.975797	−	0.218680i	$-0.0701752\pi$
$434$		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	−0.722302	−	0.691578i	$-0.756916\pi$
$439$	−10.1520	+	5.86126i	−0.484529	+	0.279743i	0.237773	+	0.971321i	$0.423583\pi$
$440$	−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	−0.660409	−	0.750906i	$-0.729617\pi$
$461$	6.87281	−	11.9041i	0.320099	−	0.554427i	0.980508	+	0.196478i	$0.0629505\pi$
$462$		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	−0.855045	−	0.518554i	$-0.826470\pi$
$467$	0.465894	−	0.806952i	0.0215590	−	0.0373413i	0.876604	+	0.481213i	$0.159804\pi$
$468$		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	$-0.765336\pi$
$479$	−32.4063			−1.48068			−0.740340	+	0.672232i	$0.765336\pi$
$480$		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	$-0.761087\pi$
$503$	−32.8028			−1.46261			−0.731303	+	0.682053i	$0.761087\pi$
$504$		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	$-0.357622\pi$
$509$	19.5166			0.865056			0.432528	+	0.901621i	$0.357622\pi$
$510$		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	0.562215	−	0.826991i	$-0.309950\pi$
$521$	−9.93108	−	17.2011i	−0.435088	−	0.753595i	−0.997303	+	0.0733964i	$0.976616\pi$
$522$		0			0
$523$	6.71478	+	3.87678i	0.293617	+	0.169520i	0.639572	−	0.768731i	$-0.279112\pi$
$523$	6.71478	+	3.87678i	0.293617	+	0.169520i	−0.345955	+	0.938251i	$0.612445\pi$
$524$	−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	$0.403251\pi$
$563$	−16.0561	+	27.8101i	−0.676686	+	1.17205i	−0.975973	+	0.217891i	$0.930082\pi$
$564$		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	$-0.328249\pi$
$577$	36.3589	−	20.9918i	1.51364	−	0.873901i	0.999872	−	0.0159713i	$-0.00508404\pi$
$578$			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	−0.590054	−	0.807364i	$-0.700894\pi$
$587$	9.79227	−	16.9607i	0.404170	−	0.700043i	0.994225	+	0.107320i	$0.0342270\pi$
$588$		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	−0.994796	−	0.101886i	$-0.967512\pi$
$593$	−9.96374	+	17.2577i	−0.409162	+	0.708689i	0.585634	+	0.810575i	$0.300846\pi$
$594$		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	−0.130945	−	0.991390i	$-0.541801\pi$
$601$	−25.8633	−	14.9322i	−1.05499	−	0.609097i	−0.924041	+	0.382293i	$0.875135\pi$
$602$		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	$-0.780108\pi$
$607$		−	31.3960i		−	1.27433i	0.770729	−	0.637163i	$-0.219892\pi$
$608$	−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	$0.00838424\pi$
$619$			1.31050i			0.0526736i	−0.999653	+	0.0263368i	$0.991616\pi$
$620$	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	−0.493586	−	0.869697i	$-0.664314\pi$
$643$	0.324584	−	0.187399i	0.0128004	−	0.00739029i	0.506387	+	0.862307i	$0.330981\pi$
$644$		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	$-0.713550\pi$
$647$	−25.1608	−	43.5798i	−0.989172	−	1.71330i	−0.367490	−	0.930027i	$-0.619783\pi$
$648$		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	0.682606	−	0.730787i	$-0.260847\pi$
$661$	10.0533	+	5.80428i	0.391028	+	0.225760i	−0.291577	+	0.956547i	$0.594180\pi$
$662$	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	0.907087	−	0.420942i	$-0.138300\pi$
$677$	2.31563	+	4.01080i	0.0889970	+	0.154147i	−0.818090	+	0.575090i	$0.804967\pi$
$678$		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	−0.824340	−	0.566095i	$-0.808454\pi$
$691$	−19.6168	+	11.3258i	−0.746258	+	0.430852i	0.0780825	+	0.996947i	$0.475120\pi$
$692$	−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	−0.692629	−	0.721294i	$-0.743547\pi$
$719$	7.46359	−	12.9273i	0.278345	−	0.482108i	0.970974	+	0.239187i	$0.0768808\pi$
$720$		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	0.583390	−	0.812192i	$-0.301726\pi$
$727$	4.62968	+	2.67295i	0.171705	+	0.0991341i	−0.411684	+	0.911326i	$0.635059\pi$
$728$		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	$-0.886202\pi$
$733$		−	18.9486i		−	0.699881i	0.936772	−	0.349941i	$-0.113798\pi$
$734$	−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	$-0.529425\pi$
$761$	−5.09302			−0.184622			−0.0923109	+	0.995730i	$0.529425\pi$
$762$		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	−0.961939	−	0.273264i	$-0.911897\pi$
$769$	−33.4505	+	19.3126i	−1.20626	+	0.696432i	−0.244316	+	0.969696i	$0.578564\pi$
$770$		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	$0.0452908\pi$
$773$	17.1754	+	29.7486i	0.617754	+	1.06998i	−0.372140	+	0.928177i	$0.621376\pi$
$774$		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	0.0916921	−	0.995787i	$-0.470772\pi$
$787$	−20.3343	−	11.7400i	−0.724839	−	0.418486i	−0.816531	+	0.577301i	$0.804106\pi$
$788$	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	0.744249	−	0.667903i	$-0.232808\pi$
$797$	−5.82399	−	10.0875i	−0.206296	−	0.357316i	−0.950545	+	0.310587i	$0.899474\pi$
$798$		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	$-0.980085\pi$
$811$		−	3.56109i		−	0.125047i	0.998044	−	0.0625233i	$-0.0199148\pi$
$812$		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	−0.879222	−	0.476412i	$-0.841937\pi$
$829$	−26.0930	+	15.0648i	−0.906248	+	0.523223i	−0.0270260	+	0.999635i	$0.508604\pi$
$830$		−	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	−0.748004	−	0.663694i	$-0.768988\pi$
$839$	5.81551	−	10.0728i	0.200774	−	0.347750i	0.948778	+	0.315944i	$0.102321\pi$
$840$		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	0.102160	−	0.994768i	$-0.467425\pi$
$853$	−20.6854	−	11.9427i	−0.708254	−	0.408911i	−0.810414	+	0.585857i	$0.800758\pi$
$854$		0			0
$855$		0			0
$856$	−6.95763	+	12.0510i	−0.237807	+	0.411894i
$857$	34.6724			1.18439			0.592193	−	0.805796i	$-0.298262\pi$
$857$	34.6724			1.18439			0.592193	+	0.805796i	$0.298262\pi$
$858$		0			0
$859$			30.4763i			1.03984i	0.854216	+	0.519918i	$0.174038\pi$
$859$			30.4763i			1.03984i	−0.854216	+	0.519918i	$0.825962\pi$
$860$	−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	$-0.609296\pi$
$881$	−19.9850			−0.673313			−0.336656	+	0.941628i	$0.609296\pi$
$882$		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	$-0.704327\pi$
$887$	−35.6633			−1.19746			−0.598729	+	0.800952i	$0.704327\pi$
$888$		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	$0.113184\pi$
$929$	23.4757	+	40.6611i	0.770213	+	1.33405i	−0.167233	+	0.985917i	$0.553483\pi$
$930$		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	$0.156387\pi$
$937$			28.8826i			0.943555i	−0.881718	+	0.471777i	$0.843613\pi$
$938$		0			0
$939$		0			0
$940$	−25.1143			−0.819138
$941$	0.727044	−	1.25928i	0.0237009	−	0.0410512i	−0.853932	−	0.520385i	$-0.825788\pi$
$941$	0.727044	−	1.25928i	0.0237009	−	0.0410512i	0.877633	+	0.479334i	$0.159122\pi$
$942$		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	−0.915433	−	0.402471i	$-0.868151\pi$
$971$	−3.40171	+	5.89194i	−0.109166	+	0.189081i	0.806267	+	0.591552i	$0.201485\pi$
$972$		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	$-0.769589\pi$
$983$	−46.9826			−1.49851			−0.749256	+	0.662280i	$0.769589\pi$
$984$		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	$0.278174\pi$
$997$			48.4267i			1.53369i	−0.641834	+	0.766844i	$0.721826\pi$
$998$	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.656.4		48
3.2	odd	2		441.2.s.d.362.22		48
7.2	even	3		1323.2.o.e.440.22		48
7.3	odd	6		1323.2.i.d.521.24		48
7.4	even	3		1323.2.i.d.521.4		48
7.5	odd	6		1323.2.o.e.440.21		48
7.6	odd	2	inner	1323.2.s.d.656.3		48
9.4	even	3		441.2.i.d.68.4		48
9.5	odd	6		1323.2.i.d.1097.24		48
21.2	odd	6		441.2.o.e.146.4	yes	48
21.5	even	6		441.2.o.e.146.3	✓	48
21.11	odd	6		441.2.i.d.227.21		48
21.17	even	6		441.2.i.d.227.22		48
21.20	even	2		441.2.s.d.362.21		48
63.4	even	3		441.2.s.d.374.21		48
63.5	even	6		1323.2.o.e.881.22		48
63.13	odd	6		441.2.i.d.68.3		48
63.23	odd	6		1323.2.o.e.881.21		48
63.31	odd	6		441.2.s.d.374.22		48
63.32	odd	6	inner	1323.2.s.d.962.3		48
63.40	odd	6		441.2.o.e.293.4	yes	48
63.41	even	6		1323.2.i.d.1097.4		48
63.58	even	3		441.2.o.e.293.3	yes	48
63.59	even	6	inner	1323.2.s.d.962.4		48

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