LMFDB - Embedded newform 2100.2.bo.h.1949.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1349,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("2100.1349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bo (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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 16 x^{16} + 87 x^{14} + 91 x^{12} - 1104 x^{10} + 819 x^{8} + 7047 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 16x^16 + 87x^14 + 91x^12 - 1104x^10 + 819x^8 + 7047x^6 - 11664x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1949.9
Root			$-1.64368 + 0.546177i$ of defining polynomial
Character	$\chi$	$=$	2100.1949
Dual form			2100.2.bo.h.1349.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64368 - 0.546177i) q^{3} +(-2.41433 - 1.08214i) q^{7} +(2.40338 - 1.79548i) q^{9} +O(q^{10})$	\(q+(1.64368 - 0.546177i) q^{3} +(-2.41433 - 1.08214i) q^{7} +(2.40338 - 1.79548i) q^{9} +(-1.17086 - 0.675999i) q^{11} +4.94296 q^{13} +(-4.97280 - 2.87105i) q^{17} +(-2.84694 + 1.64368i) q^{19} +(-4.55943 - 0.460035i) q^{21} +(-2.50270 - 4.33480i) q^{23} +(2.96974 - 4.26388i) q^{27} -5.68630i q^{29} +(-2.45160 - 1.41543i) q^{31} +(-2.29374 - 0.471628i) q^{33} +(3.33498 - 1.92545i) q^{37} +(8.12466 - 2.69973i) q^{39} +3.73802 q^{41} -4.06339i q^{43} +(-4.92419 + 2.84298i) q^{47} +(4.65797 + 5.22526i) q^{49} +(-9.74181 - 2.00306i) q^{51} +(-0.730773 + 1.26574i) q^{53} +(-3.78172 + 4.25662i) q^{57} +(-4.34239 + 7.52123i) q^{59} +(1.65306 - 0.954394i) q^{61} +(-7.74551 + 1.73410i) q^{63} +(-4.36371 - 2.51939i) q^{67} +(-6.48121 - 5.75812i) q^{69} -3.38259i q^{71} +(8.16364 - 14.1398i) q^{73} +(2.09533 + 2.89912i) q^{77} +(2.41693 + 4.18625i) q^{79} +(2.55248 - 8.63046i) q^{81} -16.6525i q^{83} +(-3.10572 - 9.34646i) q^{87} +(-8.08150 - 13.9976i) q^{89} +(-11.9339 - 5.34895i) q^{91} +(-4.80272 - 0.987510i) q^{93} +12.0577 q^{97} +(-4.02778 + 0.477584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{9}+O(q^{10}) $ 20 * q + 6 * q^9	$ 20 q + 6 q^{9} - 12 q^{11} - 6 q^{19} + 20 q^{21} + 30 q^{31} - 30 q^{39} - 16 q^{41} + 26 q^{49} - 88 q^{51} + 84 q^{61} + 28 q^{69} - 2 q^{79} + 82 q^{81} - 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) $ 20 * q + 6 * q^9 - 12 * q^11 - 6 * q^19 + 20 * q^21 + 30 * q^31 - 30 * q^39 - 16 * q^41 + 26 * q^49 - 88 * q^51 + 84 * q^61 + 28 * q^69 - 2 * q^79 + 82 * q^81 - 56 * q^89 - 22 * q^91 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.64368	−	0.546177i	0.948980	−	0.315336i
$3$	1.64368	−	0.546177i	0.948980	−	0.315336i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.41433	−	1.08214i	−0.912531	−	0.409009i
$7$	−2.41433	−	1.08214i	−0.912531	−	0.409009i
$8$		0			0
$9$	2.40338	−	1.79548i	0.801127	−	0.598494i
$10$		0			0
$11$	−1.17086	−	0.675999i	−0.353029	−	0.203821i	0.312990	−	0.949757i	$-0.398669\pi$
$11$	−1.17086	−	0.675999i	−0.353029	−	0.203821i	−0.666018	+	0.745935i	$0.732003\pi$
$12$		0			0
$13$	4.94296			1.37093			0.685466	−	0.728105i	$-0.259599\pi$
$13$	4.94296			1.37093			0.685466	+	0.728105i	$0.259599\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.97280	−	2.87105i	−1.20608	−	0.696332i	−0.244181	−	0.969730i	$-0.578519\pi$
$17$	−4.97280	−	2.87105i	−1.20608	−	0.696332i	−0.961901	+	0.273398i	$0.911852\pi$
$18$		0			0
$19$	−2.84694	+	1.64368i	−0.653133	+	0.377087i	−0.789656	−	0.613550i	$-0.789741\pi$
$19$	−2.84694	+	1.64368i	−0.653133	+	0.377087i	0.136523	+	0.990637i	$0.456407\pi$
$20$		0			0
$21$	−4.55943	−	0.460035i	−0.994948	−	0.100388i
$22$		0			0
$23$	−2.50270	−	4.33480i	−0.521849	−	0.903868i	−0.999677	−	0.0254150i	$-0.991909\pi$
$23$	−2.50270	−	4.33480i	−0.521849	−	0.903868i	0.477828	−	0.878453i	$-0.341424\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.96974	−	4.26388i	0.571527	−	0.820583i
$28$		0			0
$29$		−	5.68630i		−	1.05592i	−0.849270	−	0.527959i	$-0.822957\pi$
$29$		−	5.68630i		−	1.05592i	0.849270	−	0.527959i	$-0.177043\pi$
$30$		0			0
$31$	−2.45160	−	1.41543i	−0.440320	−	0.254219i	0.263414	−	0.964683i	$-0.415152\pi$
$31$	−2.45160	−	1.41543i	−0.440320	−	0.254219i	−0.703733	+	0.710464i	$0.748485\pi$
$32$		0			0
$33$	−2.29374	−	0.471628i	−0.399289	−	0.0820998i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.33498	−	1.92545i	0.548267	−	0.316542i	−0.200156	−	0.979764i	$-0.564145\pi$
$37$	3.33498	−	1.92545i	0.548267	−	0.316542i	0.748423	+	0.663222i	$0.230811\pi$
$38$		0			0
$39$	8.12466	−	2.69973i	1.30099	−	0.432303i
$40$		0			0
$41$	3.73802			0.583781			0.291890	−	0.956452i	$-0.405716\pi$
$41$	3.73802			0.583781			0.291890	+	0.956452i	$0.405716\pi$
$42$		0			0
$43$		−	4.06339i		−	0.619661i	−0.950792	−	0.309830i	$-0.899728\pi$
$43$		−	4.06339i		−	0.619661i	0.950792	−	0.309830i	$-0.100272\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.92419	+	2.84298i	−0.718266	+	0.414691i	−0.814114	−	0.580705i	$-0.802777\pi$
$47$	−4.92419	+	2.84298i	−0.718266	+	0.414691i	0.0958478	+	0.995396i	$0.469444\pi$
$48$		0			0
$49$	4.65797	+	5.22526i	0.665424	+	0.746466i
$50$		0			0
$51$	−9.74181	−	2.00306i	−1.36413	−	0.280484i
$52$		0			0
$53$	−0.730773	+	1.26574i	−0.100379	+	0.173862i	−0.911841	−	0.410544i	$-0.865339\pi$
$53$	−0.730773	+	1.26574i	−0.100379	+	0.173862i	0.811462	+	0.584406i	$0.198672\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.78172	+	4.25662i	−0.500902	+	0.563804i
$58$		0			0
$59$	−4.34239	+	7.52123i	−0.565330	+	0.979181i	0.431688	+	0.902023i	$0.357918\pi$
$59$	−4.34239	+	7.52123i	−0.565330	+	0.979181i	−0.997019	+	0.0771582i	$0.975415\pi$
$60$		0			0
$61$	1.65306	−	0.954394i	0.211653	−	0.122198i	−0.390427	−	0.920634i	$-0.627672\pi$
$61$	1.65306	−	0.954394i	0.211653	−	0.122198i	0.602079	+	0.798436i	$0.294339\pi$
$62$		0			0
$63$	−7.74551	+	1.73410i	−0.975842	+	0.218477i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.36371	−	2.51939i	−0.533113	−	0.307793i	0.209170	−	0.977879i	$-0.432924\pi$
$67$	−4.36371	−	2.51939i	−0.533113	−	0.307793i	−0.742283	+	0.670086i	$0.766257\pi$
$68$		0			0
$69$	−6.48121	−	5.75812i	−0.780246	−	0.693196i
$70$		0			0
$71$		−	3.38259i		−	0.401440i	−0.979649	−	0.200720i	$-0.935672\pi$
$71$		−	3.38259i		−	0.401440i	0.979649	−	0.200720i	$-0.0643281\pi$
$72$		0			0
$73$	8.16364	−	14.1398i	0.955481	−	1.65494i	0.222218	−	0.974997i	$-0.428670\pi$
$73$	8.16364	−	14.1398i	0.955481	−	1.65494i	0.733263	−	0.679945i	$-0.237996\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.09533	+	2.89912i	0.238785	+	0.330385i
$78$		0			0
$79$	2.41693	+	4.18625i	0.271926	+	0.470990i	0.969355	−	0.245664i	$-0.0790059\pi$
$79$	2.41693	+	4.18625i	0.271926	+	0.470990i	−0.697429	+	0.716654i	$0.745673\pi$
$80$		0			0
$81$	2.55248	−	8.63046i	0.283609	−	0.958940i
$82$		0			0
$83$		−	16.6525i		−	1.82785i	−0.405879	−	0.913927i	$-0.633035\pi$
$83$		−	16.6525i		−	1.82785i	0.405879	−	0.913927i	$-0.366965\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.10572	−	9.34646i	−0.332969	−	1.00205i
$88$		0			0
$89$	−8.08150	−	13.9976i	−0.856637	−	1.48374i	−0.875118	−	0.483909i	$-0.839216\pi$
$89$	−8.08150	−	13.9976i	−0.856637	−	1.48374i	0.0184813	−	0.999829i	$-0.494117\pi$
$90$		0			0
$91$	−11.9339	−	5.34895i	−1.25102	−	0.560723i
$92$		0			0
$93$	−4.80272	−	0.987510i	−0.498019	−	0.102400i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12.0577			1.22427			0.612137	−	0.790751i	$-0.290310\pi$
$97$	12.0577			1.22427			0.612137	+	0.790751i	$0.290310\pi$
$98$		0			0
$99$	−4.02778	+	0.477584i	−0.404807	+	0.0479990i
$100$		0			0
$101$	−9.01683	+	15.6176i	−0.897208	+	1.55401i	−0.0661605	+	0.997809i	$0.521075\pi$
$101$	−9.01683	+	15.6176i	−0.897208	+	1.55401i	−0.831048	+	0.556201i	$0.812258\pi$
$102$		0			0
$103$	−0.308083	−	0.533615i	−0.0303563	−	0.0525787i	0.850448	−	0.526059i	$-0.176331\pi$
$103$	−0.308083	−	0.533615i	−0.0303563	−	0.0525787i	−0.880804	+	0.473480i	$0.842998\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.85503	+	15.3374i	0.856048	+	1.48272i	0.875669	+	0.482912i	$0.160421\pi$
$107$	8.85503	+	15.3374i	0.856048	+	1.48272i	−0.0196209	+	0.999807i	$0.506246\pi$
$108$		0			0
$109$	−0.855282	+	1.48139i	−0.0819211	+	0.141892i	−0.904075	−	0.427374i	$-0.859439\pi$
$109$	−0.855282	+	1.48139i	−0.0819211	+	0.141892i	0.822154	+	0.569265i	$0.192772\pi$
$110$		0			0
$111$	4.43001	−	4.98632i	0.420478	−	0.473280i
$112$		0			0
$113$	−13.1214			−1.23436			−0.617180	−	0.786822i	$-0.711725\pi$
$113$	−13.1214			−1.23436			−0.617180	+	0.786822i	$0.711725\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	11.8798	−	8.87501i	1.09829	−	0.820495i
$118$		0			0
$119$	8.89912	+	12.3129i	0.815781	+	1.12872i
$120$		0			0
$121$	−4.58605	−	7.94327i	−0.416914	−	0.722116i
$122$		0			0
$123$	6.14412	−	2.04162i	0.553996	−	0.184087i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	15.5324i		−	1.37828i	−0.724629	−	0.689139i	$-0.757989\pi$
$127$		−	15.5324i		−	1.37828i	0.724629	−	0.689139i	$-0.242011\pi$
$128$		0			0
$129$	−2.21933	−	6.67892i	−0.195401	−	0.588046i
$130$		0			0
$131$	4.47822	+	7.75651i	0.391264	+	0.677689i	0.992617	−	0.121295i	$-0.0387046\pi$
$131$	4.47822	+	7.75651i	0.391264	+	0.677689i	−0.601353	+	0.798984i	$0.705371\pi$
$132$		0			0
$133$	8.65214	−	0.887614i	0.750235	−	0.0769659i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.73923	−	13.4047i	0.661207	−	1.14524i	−0.319092	−	0.947724i	$-0.603378\pi$
$137$	7.73923	−	13.4047i	0.661207	−	1.14524i	0.980299	−	0.197520i	$-0.0632888\pi$
$138$		0			0
$139$			20.1547i			1.70950i	0.519044	+	0.854748i	$0.326288\pi$
$139$			20.1547i			1.70950i	−0.519044	+	0.854748i	$0.673712\pi$
$140$		0			0
$141$	−6.54103	+	7.36243i	−0.550854	+	0.620029i
$142$		0			0
$143$	−5.78754	−	3.34144i	−0.483978	−	0.279425i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	10.5101	+	6.04459i	0.866861	+	0.498549i
$148$		0			0
$149$	−1.24947	+	0.721384i	−0.102361	+	0.0590981i	−0.550307	−	0.834963i	$-0.685489\pi$
$149$	−1.24947	+	0.721384i	−0.102361	+	0.0590981i	0.447946	+	0.894061i	$0.352156\pi$
$150$		0			0
$151$	−8.12108	+	14.0661i	−0.660884	+	1.14468i	0.319500	+	0.947586i	$0.396485\pi$
$151$	−8.12108	+	14.0661i	−0.660884	+	1.14468i	−0.980384	+	0.197098i	$0.936848\pi$
$152$		0			0
$153$	−17.1065	+	2.02836i	−1.38298	+	0.163983i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.11876	+	15.7942i	−0.727756	+	1.26051i	0.230073	+	0.973173i	$0.426103\pi$
$157$	−9.11876	+	15.7942i	−0.727756	+	1.26051i	−0.957829	+	0.287338i	$0.907230\pi$
$158$		0			0
$159$	−0.509842	+	2.47960i	−0.0404331	+	0.196645i
$160$		0			0
$161$	1.35150	+	13.1739i	0.106513	+	1.03825i
$162$		0			0
$163$	21.0669	−	12.1630i	1.65009	−	0.952679i	0.673055	−	0.739592i	$-0.264982\pi$
$163$	21.0669	−	12.1630i	1.65009	−	0.952679i	0.977033	−	0.213087i	$-0.0683517\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	12.5007i		−	0.967336i	−0.875252	−	0.483668i	$-0.839304\pi$
$167$		−	12.5007i		−	0.967336i	0.875252	−	0.483668i	$-0.160696\pi$
$168$		0			0
$169$	11.4329			0.879453
$170$		0			0
$171$	−3.89108	+	9.06203i	−0.297558	+	0.692991i
$172$		0			0
$173$	12.8534	−	7.42089i	0.977223	−	0.564200i	0.0757927	−	0.997124i	$-0.475851\pi$
$173$	12.8534	−	7.42089i	0.977223	−	0.564200i	0.901431	+	0.432923i	$0.142518\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.02957	+	14.7342i	−0.227717	+	1.10749i
$178$		0			0
$179$	9.93533	+	5.73617i	0.742602	+	0.428741i	0.823015	−	0.568020i	$-0.192291\pi$
$179$	9.93533	+	5.73617i	0.742602	+	0.428741i	−0.0804127	+	0.996762i	$0.525624\pi$
$180$		0			0
$181$			5.91099i			0.439361i	0.975572	+	0.219680i	$0.0705014\pi$
$181$			5.91099i			0.439361i	−0.975572	+	0.219680i	$0.929499\pi$
$182$		0			0
$183$	2.19584	−	2.47158i	0.162321	−	0.182705i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.88165	+	6.72322i	0.283854	+	0.491650i
$188$		0			0
$189$	−11.7840	+	7.08073i	−0.857162	+	0.515048i
$190$		0			0
$191$	−9.15764	+	5.28716i	−0.662623	+	0.382566i	−0.793276	−	0.608862i	$-0.791626\pi$
$191$	−9.15764	+	5.28716i	−0.662623	+	0.382566i	0.130652	+	0.991428i	$0.458293\pi$
$192$		0			0
$193$	10.4483	+	6.03231i	0.752082	+	0.434215i	0.826446	−	0.563016i	$-0.190359\pi$
$193$	10.4483	+	6.03231i	0.752082	+	0.434215i	−0.0743635	+	0.997231i	$0.523693\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−17.2423			−1.22846			−0.614231	−	0.789126i	$-0.710534\pi$
$197$	−17.2423			−1.22846			−0.614231	+	0.789126i	$0.710534\pi$
$198$		0			0
$199$	−2.46400	−	1.42259i	−0.174668	−	0.100845i	0.410117	−	0.912033i	$-0.365488\pi$
$199$	−2.46400	−	1.42259i	−0.174668	−	0.100845i	−0.584785	+	0.811188i	$0.698821\pi$
$200$		0			0
$201$	−8.54859	−	1.75772i	−0.602971	−	0.123980i
$202$		0			0
$203$	−6.15334	+	13.7286i	−0.431880	+	0.963558i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−13.7980	−	5.92462i	−0.959027	−	0.411790i
$208$		0			0
$209$	4.44451			0.307433
$210$		0			0
$211$	22.4677			1.54674			0.773372	−	0.633953i	$-0.218569\pi$
$211$	22.4677			1.54674			0.773372	+	0.633953i	$0.218569\pi$
$212$		0			0
$213$	−1.84749	−	5.55991i	−0.126588	−	0.380958i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.38727	+	6.07027i	0.297828	+	0.412077i
$218$		0			0
$219$	5.69557	−	27.7002i	0.384871	−	1.87180i
$220$		0			0
$221$	−24.5804	−	14.1915i	−1.65346	−	0.954623i
$222$		0			0
$223$	5.27620			0.353321			0.176660	−	0.984272i	$-0.443471\pi$
$223$	5.27620			0.353321			0.176660	+	0.984272i	$0.443471\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.8090	−	6.24055i	−0.717416	−	0.414200i	0.0963851	−	0.995344i	$-0.469272\pi$
$227$	−10.8090	−	6.24055i	−0.717416	−	0.414200i	−0.813801	+	0.581144i	$0.802605\pi$
$228$		0			0
$229$	14.0882	−	8.13380i	0.930971	−	0.537496i	0.0438526	−	0.999038i	$-0.486037\pi$
$229$	14.0882	−	8.13380i	0.930971	−	0.537496i	0.887119	+	0.461542i	$0.152703\pi$
$230$		0			0
$231$	5.02749	+	3.62080i	0.330784	+	0.238231i
$232$		0			0
$233$	4.41551	+	7.64788i	0.289269	+	0.501029i	0.973636	−	0.228109i	$-0.0732543\pi$
$233$	4.41551	+	7.64788i	0.289269	+	0.501029i	−0.684366	+	0.729139i	$0.739921\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.25911	+	5.56079i	0.406573	+	0.361212i
$238$		0			0
$239$			12.3333i			0.797773i	0.917000	+	0.398886i	$0.130603\pi$
$239$			12.3333i			0.797773i	−0.917000	+	0.398886i	$0.869397\pi$
$240$		0			0
$241$	6.88815	+	3.97688i	0.443705	+	0.256173i	0.705168	−	0.709040i	$-0.250872\pi$
$241$	6.88815	+	3.97688i	0.443705	+	0.256173i	−0.261463	+	0.965214i	$0.584205\pi$
$242$		0			0
$243$	−0.518295	−	15.5798i	−0.0332486	−	0.999447i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−14.0723	+	8.12466i	−0.895401	+	0.516960i
$248$		0			0
$249$	−9.09524	−	27.3715i	−0.576387	−	1.73460i
$250$		0			0
$251$	7.64756			0.482710			0.241355	−	0.970437i	$-0.422408\pi$
$251$	7.64756			0.482710			0.241355	+	0.970437i	$0.422408\pi$
$252$		0			0
$253$			6.76728i			0.425455i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	23.8118	−	13.7478i	1.48534	−	0.857563i	0.485482	−	0.874247i	$-0.338644\pi$
$257$	23.8118	−	13.7478i	1.48534	−	0.857563i	0.999861	+	0.0166841i	$0.00531095\pi$
$258$		0			0
$259$	−10.1353	+	1.03977i	−0.629779	+	0.0646084i
$260$		0			0
$261$	−10.2096	−	13.6663i	−0.631961	−	0.845925i
$262$		0			0
$263$	−9.51115	+	16.4738i	−0.586483	+	1.01582i	0.408206	+	0.912890i	$0.366155\pi$
$263$	−9.51115	+	16.4738i	−0.586483	+	1.01582i	−0.994689	+	0.102928i	$0.967179\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−20.9286	−	18.5936i	−1.28081	−	1.13791i
$268$		0			0
$269$	4.46010	−	7.72512i	0.271937	−	0.471009i	−0.697421	−	0.716662i	$-0.745669\pi$
$269$	4.46010	−	7.72512i	0.271937	−	0.471009i	0.969358	+	0.245653i	$0.0790024\pi$
$270$		0			0
$271$	6.53123	−	3.77081i	0.396744	−	0.229060i	−0.288334	−	0.957530i	$-0.593101\pi$
$271$	6.53123	−	3.77081i	0.396744	−	0.229060i	0.685078	+	0.728470i	$0.259768\pi$
$272$		0			0
$273$	−22.5371	−	2.27393i	−1.36401	−	0.137625i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.53903	+	0.888562i	0.0924716	+	0.0533885i	0.545523	−	0.838096i	$-0.316331\pi$
$277$	1.53903	+	0.888562i	0.0924716	+	0.0533885i	−0.453051	+	0.891485i	$0.649664\pi$
$278$		0			0
$279$	−8.43350	+	0.999983i	−0.504900	+	0.0598674i
$280$		0			0
$281$		−	25.3819i		−	1.51416i	−0.653324	−	0.757079i	$-0.726626\pi$
$281$		−	25.3819i		−	1.51416i	0.653324	−	0.757079i	$-0.273374\pi$
$282$		0			0
$283$	−8.06987	+	13.9774i	−0.479704	+	0.830872i	−0.999729	−	0.0232795i	$-0.992589\pi$
$283$	−8.06987	+	13.9774i	−0.479704	+	0.830872i	0.520025	+	0.854151i	$0.325923\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.02481	−	4.04504i	−0.532718	−	0.238771i
$288$		0			0
$289$	7.98584	+	13.8319i	0.469755	+	0.813640i
$290$		0			0
$291$	19.8190	−	6.58564i	1.16181	−	0.386057i
$292$		0			0
$293$			19.5542i			1.14237i	0.820821	+	0.571186i	$0.193516\pi$
$293$			19.5542i			1.14237i	−0.820821	+	0.571186i	$0.806484\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−6.35954	+	2.98488i	−0.369018	+	0.173200i
$298$		0			0
$299$	−12.3707	−	21.4268i	−0.715419	−	1.23914i
$300$		0			0
$301$	−4.39713	+	9.81035i	−0.253447	+	0.565459i
$302$		0			0
$303$	−6.29082	+	30.5952i	−0.361398	+	1.75765i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	11.8231			0.674777			0.337389	−	0.941365i	$-0.390456\pi$
$307$	11.8231			0.674777			0.337389	+	0.941365i	$0.390456\pi$
$308$		0			0
$309$	−0.797839	−	0.708826i	−0.0453875	−	0.0403237i
$310$		0			0
$311$	11.1689	−	19.3451i	0.633331	−	1.09696i	−0.353535	−	0.935421i	$-0.615020\pi$
$311$	11.1689	−	19.3451i	0.633331	−	1.09696i	0.986866	−	0.161540i	$-0.0516462\pi$
$312$		0			0
$313$	6.65398	+	11.5250i	0.376105	+	0.651433i	0.990492	−	0.137572i	$-0.0439298\pi$
$313$	6.65398	+	11.5250i	0.376105	+	0.651433i	−0.614387	+	0.789005i	$0.710596\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.9392	+	29.3395i	0.951400	+	1.64787i	0.742399	+	0.669958i	$0.233688\pi$
$317$	16.9392	+	29.3395i	0.951400	+	1.64787i	0.209001	+	0.977915i	$0.432979\pi$
$318$		0			0
$319$	−3.84393	+	6.65788i	−0.215219	+	0.372770i
$320$		0			0
$321$	22.9318	+	20.3733i	1.27993	+	1.13713i
$322$		0			0
$323$	18.8764			1.05031
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.596709	+	2.90207i	−0.0329981	+	0.160485i
$328$		0			0
$329$	14.9651	−	1.53525i	0.825052	−	0.0846413i
$330$		0			0
$331$	0.989824	+	1.71443i	0.0544057	+	0.0942334i	0.891946	−	0.452143i	$-0.149340\pi$
$331$	0.989824	+	1.71443i	0.0544057	+	0.0942334i	−0.837540	+	0.546376i	$0.816007\pi$
$332$		0			0
$333$	4.55811	−	10.6155i	0.249783	−	0.581725i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	12.0217i		−	0.654862i	−0.944875	−	0.327431i	$-0.893817\pi$
$337$		−	12.0217i		−	0.654862i	0.944875	−	0.327431i	$-0.106183\pi$
$338$		0			0
$339$	−21.5674	+	7.16662i	−1.17138	+	0.389237i
$340$		0			0
$341$	1.91366	+	3.31455i	0.103630	+	0.179493i
$342$		0			0
$343$	−5.59143	−	17.6560i	−0.301909	−	0.953337i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.33186	+	12.6992i	−0.393595	+	0.681726i	−0.992921	−	0.118779i	$-0.962102\pi$
$347$	−7.33186	+	12.6992i	−0.393595	+	0.681726i	0.599326	+	0.800505i	$0.295435\pi$
$348$		0			0
$349$			25.0573i			1.34129i	0.741780	+	0.670644i	$0.233982\pi$
$349$			25.0573i			1.34129i	−0.741780	+	0.670644i	$0.766018\pi$
$350$		0			0
$351$	14.6793	−	21.0762i	0.783525	−	1.12496i
$352$		0			0
$353$	6.72669	+	3.88365i	0.358025	+	0.206706i	0.668214	−	0.743969i	$-0.267059\pi$
$353$	6.72669	+	3.88365i	0.358025	+	0.206706i	−0.310189	+	0.950675i	$0.600392\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	21.3523	+	15.3780i	1.13009	+	0.813890i
$358$		0			0
$359$	−3.86952	+	2.23407i	−0.204225	+	0.117910i	−0.598625	−	0.801030i	$-0.704286\pi$
$359$	−3.86952	+	2.23407i	−0.204225	+	0.117910i	0.394399	+	0.918939i	$0.370953\pi$
$360$		0			0
$361$	−4.09662	+	7.09555i	−0.215612	+	0.373450i
$362$		0			0
$363$	−11.8764	−	10.5514i	−0.623352	−	0.553806i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.842240	+	1.45880i	−0.0439646	+	0.0761489i	−0.887170	−	0.461442i	$-0.847332\pi$
$367$	−0.842240	+	1.45880i	−0.0439646	+	0.0761489i	0.843206	+	0.537591i	$0.180666\pi$
$368$		0			0
$369$	8.98389	−	6.71155i	0.467682	−	0.349389i
$370$		0			0
$371$	3.13402	−	2.26511i	0.162710	−	0.117599i
$372$		0			0
$373$	−11.9914	+	6.92322i	−0.620890	+	0.358471i	−0.777215	−	0.629235i	$-0.783368\pi$
$373$	−11.9914	+	6.92322i	−0.620890	+	0.358471i	0.156325	+	0.987706i	$0.450035\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	28.1072i		−	1.44759i
$378$		0			0
$379$	2.15603			0.110748			0.0553739	−	0.998466i	$-0.482365\pi$
$379$	2.15603			0.110748			0.0553739	+	0.998466i	$0.482365\pi$
$380$		0			0
$381$	−8.48345	−	25.5303i	−0.434620	−	1.30796i
$382$		0			0
$383$	3.23197	−	1.86598i	0.165146	−	0.0953471i	−0.415149	−	0.909753i	$-0.636271\pi$
$383$	3.23197	−	1.86598i	0.165146	−	0.0953471i	0.580295	+	0.814406i	$0.302937\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.29574	−	9.76587i	−0.370863	−	0.496427i
$388$		0			0
$389$	−11.9512	−	6.90001i	−0.605948	−	0.349844i	0.165430	−	0.986222i	$-0.447099\pi$
$389$	−11.9512	−	6.90001i	−0.605948	−	0.349844i	−0.771378	+	0.636377i	$0.780432\pi$
$390$		0			0
$391$			28.7415i			1.45352i
$392$		0			0
$393$	11.5972	+	10.3033i	0.585001	+	0.519734i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.17565	−	14.1606i	−0.410324	−	0.710702i	0.584601	−	0.811321i	$-0.301251\pi$
$397$	−8.17565	−	14.1606i	−0.410324	−	0.710702i	−0.994925	+	0.100619i	$0.967918\pi$
$398$		0			0
$399$	13.7366	−	6.18456i	0.687688	−	0.309615i
$400$		0			0
$401$	11.9669	−	6.90910i	0.597599	−	0.345024i	−0.170497	−	0.985358i	$-0.554537\pi$
$401$	11.9669	−	6.90910i	0.597599	−	0.345024i	0.768096	+	0.640334i	$0.221204\pi$
$402$		0			0
$403$	−12.1182	−	6.99642i	−0.603648	−	0.348516i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.20641			−0.258072
$408$		0			0
$409$	8.26987	+	4.77461i	0.408919	+	0.236089i	0.690325	−	0.723499i	$-0.257467\pi$
$409$	8.26987	+	4.77461i	0.408919	+	0.236089i	−0.281406	+	0.959589i	$0.590801\pi$
$410$		0			0
$411$	5.39947	−	26.2601i	0.266336	−	1.29532i
$412$		0			0
$413$	18.6229	−	13.4597i	0.916375	−	0.662307i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	11.0080	+	33.1278i	0.539065	+	1.62228i
$418$		0			0
$419$	9.71886			0.474797			0.237399	−	0.971412i	$-0.423705\pi$
$419$	9.71886			0.474797			0.237399	+	0.971412i	$0.423705\pi$
$420$		0			0
$421$	34.8713			1.69953			0.849763	−	0.527165i	$-0.176745\pi$
$421$	34.8713			1.69953			0.849763	+	0.527165i	$0.176745\pi$
$422$		0			0
$423$	−6.73017	+	15.6741i	−0.327232	+	0.762099i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.02381	+	0.515388i	−0.243119	+	0.0249414i
$428$		0			0
$429$	−11.3379	−	2.33124i	−0.547399	−	0.112553i
$430$		0			0
$431$	1.57279	+	0.908052i	0.0757587	+	0.0437393i	0.537401	−	0.843327i	$-0.319406\pi$
$431$	1.57279	+	0.908052i	0.0757587	+	0.0437393i	−0.461642	+	0.887066i	$0.652740\pi$
$432$		0			0
$433$	10.6773			0.513117			0.256558	−	0.966529i	$-0.417411\pi$
$433$	10.6773			0.513117			0.256558	+	0.966529i	$0.417411\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	14.2501	+	8.22728i	0.681673	+	0.393564i
$438$		0			0
$439$	−26.6759	+	15.4013i	−1.27317	+	0.735066i	−0.975584	−	0.219628i	$-0.929516\pi$
$439$	−26.6759	+	15.4013i	−1.27317	+	0.735066i	−0.297588	+	0.954694i	$0.596182\pi$
$440$		0			0
$441$	20.5767	+	4.19499i	0.979845	+	0.199761i
$442$		0			0
$443$	−8.26640	−	14.3178i	−0.392749	−	0.680260i	0.600062	−	0.799953i	$-0.295142\pi$
$443$	−8.26640	−	14.3178i	−0.392749	−	0.680260i	−0.992811	+	0.119693i	$0.961809\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.65974	+	1.86816i	−0.0785028	+	0.0883610i
$448$		0			0
$449$		−	2.59098i		−	0.122276i	−0.998129	−	0.0611380i	$-0.980527\pi$
$449$		−	2.59098i		−	0.122276i	0.998129	−	0.0611380i	$-0.0194730\pi$
$450$		0			0
$451$	−4.37671	−	2.52690i	−0.206091	−	0.118987i
$452$		0			0
$453$	−5.66588	+	27.5558i	−0.266206	+	1.29468i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−19.2040	+	11.0874i	−0.898323	+	0.518647i	−0.876656	−	0.481118i	$-0.840231\pi$
$457$	−19.2040	+	11.0874i	−0.898323	+	0.518647i	−0.0216672	+	0.999765i	$0.506897\pi$
$458$		0			0
$459$	−27.0097	+	12.6771i	−1.26071	+	0.591718i
$460$		0			0
$461$	30.5304			1.42194			0.710971	−	0.703221i	$-0.248256\pi$
$461$	30.5304			1.42194			0.710971	+	0.703221i	$0.248256\pi$
$462$		0			0
$463$		−	3.54824i		−	0.164901i	−0.996595	−	0.0824504i	$-0.973725\pi$
$463$		−	3.54824i		−	0.164901i	0.996595	−	0.0824504i	$-0.0262746\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−29.7157	+	17.1564i	−1.37508	+	0.793901i	−0.991562	−	0.129633i	$-0.958620\pi$
$467$	−29.7157	+	17.1564i	−1.37508	+	0.793901i	−0.383515	+	0.923534i	$0.625287\pi$
$468$		0			0
$469$	7.80912	+	10.8048i	0.360592	+	0.498918i
$470$		0			0
$471$	−6.36193	+	30.9410i	−0.293142	+	1.42569i
$472$		0			0
$473$	−2.74684	+	4.75767i	−0.126300	+	0.218758i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.516282	+	4.35414i	0.0236389	+	0.199362i
$478$		0			0
$479$	−9.78624	+	16.9503i	−0.447145	+	0.774477i	−0.998199	−	0.0599923i	$-0.980892\pi$
$479$	−9.78624	+	16.9503i	−0.447145	+	0.774477i	0.551054	+	0.834469i	$0.314226\pi$
$480$		0			0
$481$	16.4847	−	9.51743i	0.751637	−	0.433958i
$482$		0			0
$483$	9.41671	+	20.9155i	0.428475	+	0.951689i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−21.8468	−	12.6133i	−0.989973	−	0.571561i	−0.0847071	−	0.996406i	$-0.526995\pi$
$487$	−21.8468	−	12.6133i	−0.989973	−	0.571561i	−0.905266	+	0.424844i	$0.860329\pi$
$488$		0			0
$489$	27.9842	−	31.4984i	1.26549	−	1.42441i
$490$		0			0
$491$		−	38.6556i		−	1.74450i	−0.489057	−	0.872252i	$-0.662659\pi$
$491$		−	38.6556i		−	1.74450i	0.489057	−	0.872252i	$-0.337341\pi$
$492$		0			0
$493$	−16.3256	+	28.2768i	−0.735269	+	1.27352i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.66042	+	8.16669i	−0.164192	+	0.366326i
$498$		0			0
$499$	2.80910	+	4.86551i	0.125753	+	0.217810i	0.922027	−	0.387126i	$-0.126532\pi$
$499$	2.80910	+	4.86551i	0.125753	+	0.217810i	−0.796274	+	0.604936i	$0.793199\pi$
$500$		0			0
$501$	−6.82761	−	20.5472i	−0.305035	−	0.917982i
$502$		0			0
$503$			25.8655i			1.15329i	0.816996	+	0.576644i	$0.195638\pi$
$503$			25.8655i			1.15329i	−0.816996	+	0.576644i	$0.804362\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	18.7920	−	6.24438i	0.834584	−	0.277323i
$508$		0			0
$509$	15.2306	+	26.3801i	0.675082	+	1.16928i	0.976445	+	0.215767i	$0.0692253\pi$
$509$	15.2306	+	26.3801i	0.675082	+	1.16928i	−0.301362	+	0.953510i	$0.597441\pi$
$510$		0			0
$511$	−35.0109	+	25.3040i	−1.54879	+	1.11939i
$512$		0			0
$513$	−1.44622	+	17.0203i	−0.0638524	+	0.751465i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	7.68740			0.338092
$518$		0			0
$519$	17.0737	−	19.2178i	0.749453	−	0.843568i
$520$		0			0
$521$	10.6182	−	18.3913i	0.465192	−	0.805737i	−0.534018	−	0.845473i	$-0.679319\pi$
$521$	10.6182	−	18.3913i	0.465192	−	0.805737i	0.999210	+	0.0397366i	$0.0126519\pi$
$522$		0			0
$523$	6.19077	+	10.7227i	0.270704	+	0.468872i	0.969042	−	0.246895i	$-0.0794103\pi$
$523$	6.19077	+	10.7227i	0.270704	+	0.468872i	−0.698339	+	0.715768i	$0.746077\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.12754	+	14.0773i	0.354041	+	0.613217i
$528$		0			0
$529$	−1.02699	+	1.77880i	−0.0446518	+	0.0773392i
$530$		0			0
$531$	3.06784	+	25.8731i	0.133133	+	1.12280i
$532$		0			0
$533$	18.4769			0.800323
$534$		0			0
$535$		0			0
$536$		0			0
$537$	19.4635	+	4.00198i	0.839912	+	0.172698i
$538$		0			0
$539$	−1.92158	−	9.26685i	−0.0827682	−	0.399151i
$540$		0			0
$541$	−6.93001	−	12.0031i	−0.297944	−	0.516055i	0.677721	−	0.735319i	$-0.262968\pi$
$541$	−6.93001	−	12.0031i	−0.297944	−	0.516055i	−0.975665	+	0.219264i	$0.929634\pi$
$542$		0			0
$543$	3.22845	+	9.71579i	0.138546	+	0.416945i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			17.7100i			0.757226i	0.925555	+	0.378613i	$0.123599\pi$
$547$			17.7100i			0.757226i	−0.925555	+	0.378613i	$0.876401\pi$
$548$		0			0
$549$	2.25933	−	5.26181i	0.0964260	−	0.224569i
$550$		0			0
$551$	9.34646	+	16.1885i	0.398173	+	0.689655i
$552$		0			0
$553$	−1.30518	−	12.7224i	−0.0555020	−	0.541013i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.73857	−	3.01129i	0.0736656	−	0.127593i	−0.826840	−	0.562438i	$-0.809864\pi$
$557$	1.73857	−	3.01129i	0.0736656	−	0.127593i	0.900505	+	0.434845i	$0.143197\pi$
$558$		0			0
$559$		−	20.0852i		−	0.849512i
$560$		0			0
$561$	10.0523	+	8.93076i	0.424407	+	0.377057i
$562$		0			0
$563$	−10.4425	−	6.02897i	−0.440098	−	0.254091i	0.263541	−	0.964648i	$-0.415110\pi$
$563$	−10.4425	−	6.02897i	−0.440098	−	0.254091i	−0.703639	+	0.710557i	$0.748443\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−15.5019	+	18.0746i	−0.651017	+	0.759064i
$568$		0			0
$569$	−11.8065	+	6.81650i	−0.494955	+	0.285762i	−0.726628	−	0.687031i	$-0.758913\pi$
$569$	−11.8065	+	6.81650i	−0.494955	+	0.285762i	0.231673	+	0.972794i	$0.425580\pi$
$570$		0			0
$571$	22.0474	−	38.1873i	0.922657	−	1.59809i	0.127369	−	0.991855i	$-0.459347\pi$
$571$	22.0474	−	38.1873i	0.922657	−	1.59809i	0.795287	−	0.606233i	$-0.207320\pi$
$572$		0			0
$573$	−12.1645	+	13.6921i	−0.508180	+	0.571996i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	3.49934	−	6.06103i	0.145679	−	0.252324i	−0.783947	−	0.620828i	$-0.786797\pi$
$577$	3.49934	−	6.06103i	0.145679	−	0.252324i	0.929626	+	0.368504i	$0.120130\pi$
$578$		0			0
$579$	20.4683	+	4.20859i	0.850635	+	0.174903i
$580$		0			0
$581$	−18.0203	+	40.2047i	−0.747608	+	1.66797i
$582$		0			0
$583$	1.71127	−	0.988003i	0.0708736	−	0.0409189i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	29.9161i		−	1.23477i	−0.786661	−	0.617385i	$-0.788192\pi$
$587$		−	29.9161i		−	1.23477i	0.786661	−	0.617385i	$-0.211808\pi$
$588$		0			0
$589$	9.30607			0.383450
$590$		0			0
$591$	−28.3408	+	9.41734i	−1.16579	+	0.387378i
$592$		0			0
$593$	20.8583	−	12.0426i	0.856549	−	0.494529i	−0.00630583	−	0.999980i	$-0.502007\pi$
$593$	20.8583	−	12.0426i	0.856549	−	0.494529i	0.862855	+	0.505451i	$0.168674\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.82702	−	0.992506i	−0.197557	−	0.0406206i
$598$		0			0
$599$	−5.14773	−	2.97205i	−0.210331	−	0.121434i	0.391134	−	0.920334i	$-0.372083\pi$
$599$	−5.14773	−	2.97205i	−0.210331	−	0.121434i	−0.601465	+	0.798899i	$0.705416\pi$
$600$		0			0
$601$			46.9992i			1.91714i	0.284863	+	0.958568i	$0.408052\pi$
$601$			46.9992i			1.91714i	−0.284863	+	0.958568i	$0.591948\pi$
$602$		0			0
$603$	−15.0112	+	1.77992i	−0.611303	+	0.0724839i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.97322	−	8.61387i	−0.201857	−	0.349626i	0.747270	−	0.664521i	$-0.231364\pi$
$607$	−4.97322	−	8.61387i	−0.201857	−	0.349626i	−0.949127	+	0.314894i	$0.898031\pi$
$608$		0			0
$609$	−2.61589	+	25.9262i	−0.106001	+	1.05058i
$610$		0			0
$611$	−24.3401	+	14.0528i	−0.984694	+	0.568513i
$612$		0			0
$613$	−28.1873	−	16.2739i	−1.13847	−	0.657298i	−0.192421	−	0.981312i	$-0.561634\pi$
$613$	−28.1873	−	16.2739i	−1.13847	−	0.657298i	−0.946052	+	0.324014i	$0.894967\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.69843			0.309927			0.154964	−	0.987920i	$-0.450474\pi$
$617$	7.69843			0.309927			0.154964	+	0.987920i	$0.450474\pi$
$618$		0			0
$619$	−2.76170	−	1.59447i	−0.111002	−	0.0640872i	0.443471	−	0.896289i	$-0.353747\pi$
$619$	−2.76170	−	1.59447i	−0.111002	−	0.0640872i	−0.554473	+	0.832202i	$0.687080\pi$
$620$		0			0
$621$	−25.9154	−	2.20205i	−1.03995	−	0.0883650i
$622$		0			0
$623$	4.36414	+	42.5400i	0.174845	+	1.70433i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	7.30536	−	2.42749i	0.291748	−	0.0969446i
$628$		0			0
$629$	−22.1122			−0.881673
$630$		0			0
$631$	7.97461			0.317464			0.158732	−	0.987322i	$-0.449259\pi$
$631$	7.97461			0.317464			0.158732	+	0.987322i	$0.449259\pi$
$632$		0			0
$633$	36.9298	−	12.2714i	1.46783	−	0.487743i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	23.0242	+	25.8283i	0.912251	+	1.02335i
$638$		0			0
$639$	−6.07339	−	8.12966i	−0.240259	−	0.321604i
$640$		0			0
$641$	23.7774	+	13.7279i	0.939152	+	0.542219i	0.889694	−	0.456557i	$-0.150917\pi$
$641$	23.7774	+	13.7279i	0.939152	+	0.542219i	0.0494573	+	0.998776i	$0.484251\pi$
$642$		0			0
$643$	29.0919			1.14727			0.573637	−	0.819110i	$-0.305532\pi$
$643$	29.0919			1.14727			0.573637	+	0.819110i	$0.305532\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	37.4122	+	21.5999i	1.47082	+	0.849181i	0.999463	−	0.0327597i	$-0.0104296\pi$
$647$	37.4122	+	21.5999i	1.47082	+	0.849181i	0.471361	+	0.881940i	$0.343763\pi$
$648$		0			0
$649$	10.1687	−	5.87089i	0.399156	−	0.230453i
$650$		0			0
$651$	10.5267	+	7.58137i	0.412575	+	0.297137i
$652$		0			0
$653$	−3.62080	−	6.27142i	−0.141693	−	0.245420i	0.786441	−	0.617665i	$-0.211921\pi$
$653$	−3.62080	−	6.27142i	−0.141693	−	0.245420i	−0.928134	+	0.372246i	$0.878588\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−5.76750	−	48.6411i	−0.225012	−	1.89767i
$658$		0			0
$659$			5.29324i			0.206196i	0.994671	+	0.103098i	$0.0328755\pi$
$659$			5.29324i			0.206196i	−0.994671	+	0.103098i	$0.967125\pi$
$660$		0			0
$661$	43.2638	+	24.9783i	1.68276	+	0.971545i	0.959810	+	0.280649i	$0.0905497\pi$
$661$	43.2638	+	24.9783i	1.68276	+	0.971545i	0.722954	+	0.690896i	$0.242784\pi$
$662$		0			0
$663$	−48.1534	−	9.90105i	−1.87012	−	0.384525i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−24.6490	+	14.2311i	−0.954411	+	0.551030i
$668$		0			0
$669$	8.67240	−	2.88174i	0.335294	−	0.111415i
$670$		0			0
$671$	−2.58068			−0.0996259
$672$		0			0
$673$			21.8855i			0.843625i	0.906683	+	0.421812i	$0.138606\pi$
$673$			21.8855i			0.843625i	−0.906683	+	0.421812i	$0.861394\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.9033	+	6.87236i	−0.457480	+	0.264126i	−0.710984	−	0.703208i	$-0.751750\pi$
$677$	−11.9033	+	6.87236i	−0.457480	+	0.264126i	0.253504	+	0.967334i	$0.418417\pi$
$678$		0			0
$679$	−29.1113	−	13.0481i	−1.11719	−	0.500739i
$680$		0			0
$681$	−21.1749	−	4.35388i	−0.811425	−	0.166841i
$682$		0			0
$683$	21.4513	−	37.1547i	0.820811	−	1.42169i	−0.0842682	−	0.996443i	$-0.526855\pi$
$683$	21.4513	−	37.1547i	0.820811	−	1.42169i	0.905079	−	0.425243i	$-0.139811\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	18.7139	−	21.0640i	0.713982	−	0.803642i
$688$		0			0
$689$	−3.61218	+	6.25649i	−0.137613	+	0.238353i
$690$		0			0
$691$	−20.5494	+	11.8642i	−0.781735	+	0.451335i	−0.837045	−	0.547134i	$-0.815719\pi$
$691$	−20.5494	+	11.8642i	−0.781735	+	0.451335i	0.0553098	+	0.998469i	$0.482385\pi$
$692$		0			0
$693$	10.2412	+	3.20555i	0.389031	+	0.121769i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−18.5884	−	10.7320i	−0.704087	−	0.406505i
$698$		0			0
$699$	11.4348	+	10.1590i	0.432503	+	0.384250i
$700$		0			0
$701$			21.2721i			0.803436i	0.915763	+	0.401718i	$0.131587\pi$
$701$			21.2721i			0.803436i	−0.915763	+	0.401718i	$0.868413\pi$
$702$		0			0
$703$	−6.32966	+	10.9633i	−0.238728	+	0.413488i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	38.6700	−	27.9486i	1.45433	−	1.05112i
$708$		0			0
$709$	−22.8069	−	39.5026i	−0.856529	−	1.48355i	−0.875219	−	0.483727i	$-0.839283\pi$
$709$	−22.8069	−	39.5026i	−0.856529	−	1.48355i	0.0186897	−	0.999825i	$-0.494051\pi$
$710$		0			0
$711$	13.3252	+	5.72160i	0.499733	+	0.214577i
$712$		0			0
$713$			14.1696i			0.530655i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6.73615	+	20.2720i	0.251566	+	0.757071i
$718$		0			0
$719$	−9.50850	−	16.4692i	−0.354607	−	0.614198i	0.632443	−	0.774607i	$-0.282052\pi$
$719$	−9.50850	−	16.4692i	−0.354607	−	0.614198i	−0.987051	+	0.160409i	$0.948719\pi$
$720$		0			0
$721$	0.166370	+	1.62171i	0.00619593	+	0.0603956i
$722$		0			0
$723$	13.4940	+	2.77457i	0.501848	+	0.103187i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	34.0540			1.26299			0.631496	−	0.775379i	$-0.282441\pi$
$727$	34.0540			1.26299			0.631496	+	0.775379i	$0.282441\pi$
$728$		0			0
$729$	−9.36126	−	25.3252i	−0.346714	−	0.937971i
$730$		0			0
$731$	−11.6662	+	20.2064i	−0.431489	+	0.747361i
$732$		0			0
$733$	3.87885	+	6.71837i	0.143269	+	0.248148i	0.928726	−	0.370768i	$-0.120905\pi$
$733$	3.87885	+	6.71837i	0.143269	+	0.248148i	−0.785457	+	0.618916i	$0.787572\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.40621	+	5.89973i	0.125469	+	0.217319i
$738$		0			0
$739$	−4.19659	+	7.26871i	−0.154374	+	0.267384i	−0.932831	−	0.360314i	$-0.882669\pi$
$739$	−4.19659	+	7.26871i	−0.154374	+	0.267384i	0.778457	+	0.627698i	$0.216003\pi$
$740$		0			0
$741$	−18.6929	+	21.0403i	−0.686702	+	0.772936i
$742$		0			0
$743$	−14.7540			−0.541273			−0.270636	−	0.962682i	$-0.587234\pi$
$743$	−14.7540			−0.541273			−0.270636	+	0.962682i	$0.587234\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−29.8994	−	40.0224i	−1.09396	−	1.46434i
$748$		0			0
$749$	−4.78186	−	46.6118i	−0.174725	−	1.70316i
$750$		0			0
$751$	−20.6067	−	35.6918i	−0.751948	−	1.30241i	−0.946877	−	0.321595i	$-0.895781\pi$
$751$	−20.6067	−	35.6918i	−0.751948	−	1.30241i	0.194929	−	0.980817i	$-0.437552\pi$
$752$		0			0
$753$	12.5702	−	4.17692i	0.458082	−	0.152216i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	11.8681i		−	0.431354i	−0.976465	−	0.215677i	$-0.930804\pi$
$757$		−	11.8681i		−	0.431354i	0.976465	−	0.215677i	$-0.0691958\pi$
$758$		0			0
$759$	3.69613	+	11.1233i	0.134161	+	0.403749i
$760$		0			0
$761$	−17.7705	−	30.7795i	−0.644181	−	1.11575i	−0.984490	−	0.175441i	$-0.943865\pi$
$761$	−17.7705	−	30.7795i	−0.644181	−	1.11575i	0.340309	−	0.940314i	$-0.389468\pi$
$762$		0			0
$763$	3.66800	−	2.65104i	0.132790	−	0.0959739i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−21.4643	+	37.1772i	−0.775029	+	1.34239i
$768$		0			0
$769$		−	6.25608i		−	0.225600i	−0.993618	−	0.112800i	$-0.964018\pi$
$769$		−	6.25608i		−	0.225600i	0.993618	−	0.112800i	$-0.0359820\pi$
$770$		0			0
$771$	31.6304	−	35.6025i	1.13914	−	1.28219i
$772$		0			0
$773$	−17.3483	−	10.0161i	−0.623977	−	0.360253i	0.154439	−	0.988002i	$-0.450643\pi$
$773$	−17.3483	−	10.0161i	−0.623977	−	0.360253i	−0.778416	+	0.627749i	$0.783976\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−16.0914	+	7.24474i	−0.577274	+	0.259904i
$778$		0			0
$779$	−10.6419	+	6.14412i	−0.381286	+	0.220136i
$780$		0			0
$781$	−2.28663	+	3.96056i	−0.0818220	+	0.141720i
$782$		0			0
$783$	−24.2457	−	16.8868i	−0.866469	−	0.603486i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.738053	−	1.27835i	0.0263088	−	0.0455681i	−0.852571	−	0.522611i	$-0.824958\pi$
$787$	0.738053	−	1.27835i	0.0263088	−	0.0455681i	0.878880	+	0.477043i	$0.158291\pi$
$788$		0			0
$789$	−6.63570	+	32.2725i	−0.236237	+	1.14893i
$790$		0			0
$791$	31.6794	+	14.1991i	1.12639	+	0.504863i
$792$		0			0
$793$	8.17101	−	4.71754i	0.290161	−	0.167525i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			22.9470i			0.812823i	0.913690	+	0.406411i	$0.133220\pi$
$797$			22.9470i			0.812823i	−0.913690	+	0.406411i	$0.866780\pi$
$798$		0			0
$799$	32.6493			1.15505
$800$		0			0
$801$	−44.5553	−	19.1313i	−1.57428	−	0.675971i
$802$		0			0
$803$	−19.1170	+	11.0372i	−0.674625	+	0.389495i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.11170	−	15.1336i	0.109537	−	0.532729i
$808$		0			0
$809$	19.5613	+	11.2937i	0.687739	+	0.397066i	0.802764	−	0.596296i	$-0.203362\pi$
$809$	19.5613	+	11.2937i	0.687739	+	0.397066i	−0.115026	+	0.993363i	$0.536695\pi$
$810$		0			0
$811$		−	41.9366i		−	1.47259i	−0.676659	−	0.736296i	$-0.736573\pi$
$811$		−	41.9366i		−	1.47259i	0.676659	−	0.736296i	$-0.263427\pi$
$812$		0			0
$813$	8.67573	−	9.76522i	0.304271	−	0.342481i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	6.67892	+	11.5682i	0.233666	+	0.404721i
$818$		0			0
$819$	−38.2858	+	8.57161i	−1.33781	+	0.299516i
$820$		0			0
$821$	−0.447025	+	0.258090i	−0.0156013	+	0.00900741i	−0.507780	−	0.861487i	$-0.669534\pi$
$821$	−0.447025	+	0.258090i	−0.0156013	+	0.00900741i	0.492179	+	0.870494i	$0.336201\pi$
$822$		0			0
$823$	−17.8125	−	10.2841i	−0.620906	−	0.358480i	0.156316	−	0.987707i	$-0.450038\pi$
$823$	−17.8125	−	10.2841i	−0.620906	−	0.358480i	−0.777222	+	0.629227i	$0.783372\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−24.0587			−0.836603			−0.418301	−	0.908308i	$-0.637374\pi$
$827$	−24.0587			−0.836603			−0.418301	+	0.908308i	$0.637374\pi$
$828$		0			0
$829$	39.3074	+	22.6941i	1.36520	+	0.788200i	0.990311	−	0.138869i	$-0.0443468\pi$
$829$	39.3074	+	22.6941i	1.36520	+	0.788200i	0.374891	+	0.927069i	$0.377680\pi$
$830$		0			0
$831$	3.01500	+	0.619928i	0.104589	+	0.0215051i
$832$		0			0
$833$	−8.16117	−	39.3574i	−0.282768	−	1.36365i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−13.3158	+	6.24984i	−0.460262	+	0.216026i
$838$		0			0
$839$	39.8758			1.37666			0.688332	−	0.725395i	$-0.258343\pi$
$839$	39.8758			1.37666			0.688332	+	0.725395i	$0.258343\pi$
$840$		0			0
$841$	−3.33396			−0.114964
$842$		0			0
$843$	−13.8630	−	41.7198i	−0.477468	−	1.43691i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	2.47654	+	24.1404i	0.0850949	+	0.829474i
$848$		0			0
$849$	−5.63015	+	27.3820i	−0.193226	+	0.939748i
$850$		0			0
$851$	−16.6929	−	9.63764i	−0.572225	−	0.330374i
$852$		0			0
$853$	16.9504			0.580372			0.290186	−	0.956970i	$-0.406283\pi$
$853$	16.9504			0.580372			0.290186	+	0.956970i	$0.406283\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.546711	+	0.315644i	0.0186753	+	0.0107822i	0.509309	−	0.860584i	$-0.329901\pi$
$857$	0.546711	+	0.315644i	0.0186753	+	0.0107822i	−0.490633	+	0.871366i	$0.663235\pi$
$858$		0			0
$859$	5.59642	−	3.23109i	0.190947	−	0.110243i	−0.401479	−	0.915868i	$-0.631504\pi$
$859$	5.59642	−	3.23109i	0.190947	−	0.110243i	0.592426	+	0.805625i	$0.298170\pi$
$860$		0			0
$861$	−17.0432	−	1.71962i	−0.580832	−	0.0586045i
$862$		0			0
$863$	−3.64782	−	6.31821i	−0.124173	−	0.215074i	0.797236	−	0.603667i	$-0.206295\pi$
$863$	−3.64782	−	6.31821i	−0.124173	−	0.215074i	−0.921409	+	0.388593i	$0.872961\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	20.6808	+	18.3735i	0.702358	+	0.623998i
$868$		0			0
$869$		−	6.53538i		−	0.221698i
$870$		0			0
$871$	−21.5697	−	12.4533i	−0.730861	−	0.421963i
$872$		0			0
$873$	28.9793	−	21.6494i	0.980800	−	0.732722i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.7109	−	14.8442i	0.868196	−	0.501253i	0.00144772	−	0.999999i	$-0.499539\pi$
$877$	25.7109	−	14.8442i	0.868196	−	0.501253i	0.866748	+	0.498746i	$0.166206\pi$
$878$		0			0
$879$	10.6801	+	32.1410i	0.360230	+	1.08409i
$880$		0			0
$881$	21.6272			0.728638			0.364319	−	0.931274i	$-0.381302\pi$
$881$	21.6272			0.728638			0.364319	+	0.931274i	$0.381302\pi$
$882$		0			0
$883$			29.9462i			1.00777i	0.863771	+	0.503884i	$0.168096\pi$
$883$			29.9462i			1.00777i	−0.863771	+	0.503884i	$0.831904\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.2160	+	5.89821i	−0.343020	+	0.198043i	−0.661607	−	0.749851i	$-0.730125\pi$
$887$	−10.2160	+	5.89821i	−0.343020	+	0.198043i	0.318587	+	0.947894i	$0.396792\pi$
$888$		0			0
$889$	−16.8082	+	37.5003i	−0.563728	+	1.25772i
$890$		0			0
$891$	−8.82279	+	8.37962i	−0.295574	+	0.280728i
$892$		0			0
$893$	9.34591	−	16.1876i	0.312749	−	0.541697i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−32.0364	−	28.4622i	−1.06966	−	0.950324i
$898$		0			0
$899$	−8.04855	+	13.9405i	−0.268434	+	0.464942i
$900$		0			0
$901$	7.26798	−	4.19617i	0.242131	−	0.139795i
$902$		0			0
$903$	−1.86930	+	18.5267i	−0.0622064	+	0.616530i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	24.6739	+	14.2455i	0.819284	+	0.473014i	0.850169	−	0.526509i	$-0.176499\pi$
$907$	24.6739	+	14.2455i	0.819284	+	0.473014i	−0.0308855	+	0.999523i	$0.509833\pi$
$908$		0			0
$909$	6.37028	+	53.7246i	0.211289	+	1.78193i
$910$		0			0
$911$		−	14.4884i		−	0.480023i	−0.970770	−	0.240011i	$-0.922849\pi$
$911$		−	14.4884i		−	0.480023i	0.970770	−	0.240011i	$-0.0771511\pi$
$912$		0			0
$913$	−11.2571	+	19.4979i	−0.372555	+	0.645285i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.41831	−	23.5728i	−0.0798597	−	0.778442i
$918$		0			0
$919$	−2.83403	−	4.90869i	−0.0934861	−	0.161923i	0.815490	−	0.578772i	$-0.196468\pi$
$919$	−2.83403	−	4.90869i	−0.0934861	−	0.161923i	−0.908976	+	0.416849i	$0.863134\pi$
$920$		0			0
$921$	19.4333	−	6.45748i	0.640350	−	0.212781i
$922$		0			0
$923$		−	16.7200i		−	0.550346i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.69854	−	0.729323i	−0.0557873	−	0.0239541i
$928$		0			0
$929$	8.51159	+	14.7425i	0.279256	+	0.483686i	0.971200	−	0.238265i	$-0.0765788\pi$
$929$	8.51159	+	14.7425i	0.279256	+	0.483686i	−0.691944	+	0.721951i	$0.743245\pi$
$930$		0			0
$931$	−21.8496	−	7.21979i	−0.716092	−	0.236619i
$932$		0			0
$933$	7.79228	−	37.8974i	0.255108	−	1.24071i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	11.1936			0.365678			0.182839	−	0.983143i	$-0.441471\pi$
$937$	11.1936			0.365678			0.182839	+	0.983143i	$0.441471\pi$
$938$		0			0
$939$	17.2317	+	15.3092i	0.562336	+	0.499598i
$940$		0			0
$941$	−11.0101	+	19.0700i	−0.358919	+	0.621665i	−0.987780	−	0.155852i	$-0.950188\pi$
$941$	−11.0101	+	19.0700i	−0.358919	+	0.621665i	0.628862	+	0.777517i	$0.283521\pi$
$942$		0			0
$943$	−9.35513	−	16.2036i	−0.304645	−	0.527661i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.3035	−	24.7743i	−0.464800	−	0.805057i	0.534393	−	0.845236i	$-0.320540\pi$
$947$	−14.3035	−	24.7743i	−0.464800	−	0.805057i	−0.999192	+	0.0401795i	$0.987207\pi$
$948$		0			0
$949$	40.3526	−	69.8927i	1.30990	−	2.26881i
$950$		0			0
$951$	43.8672	+	38.9731i	1.42249	+	1.26379i
$952$		0			0
$953$	−45.2210			−1.46485			−0.732426	−	0.680846i	$-0.761612\pi$
$953$	−45.2210			−1.46485			−0.732426	+	0.680846i	$0.761612\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.68181	+	13.0429i	−0.0866907	+	0.421617i
$958$		0			0
$959$	−33.1908	+	23.9886i	−1.07179	+	0.774631i
$960$		0			0
$961$	−11.4931	−	19.9067i	−0.370746	−	0.642150i
$962$		0			0
$963$	48.8200	+	20.9625i	1.57320	+	0.675506i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	54.5961i		−	1.75569i	−0.478943	−	0.877846i	$-0.658980\pi$
$967$		−	54.5961i		−	1.75569i	0.478943	−	0.877846i	$-0.341020\pi$
$968$		0			0
$969$	31.0267	−	10.3098i	0.996722	−	0.331200i
$970$		0			0
$971$	−12.1591	−	21.0603i	−0.390206	−	0.675856i	0.602271	−	0.798292i	$-0.294263\pi$
$971$	−12.1591	−	21.0603i	−0.390206	−	0.675856i	−0.992476	+	0.122436i	$0.960929\pi$
$972$		0			0
$973$	21.8101	−	48.6600i	0.699198	−	1.55997i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.58898	−	7.94835i	0.146815	−	0.254290i	−0.783234	−	0.621727i	$-0.786431\pi$
$977$	4.58898	−	7.94835i	0.146815	−	0.254290i	0.930048	+	0.367437i	$0.119765\pi$
$978$		0			0
$979$			21.8523i			0.698403i
$980$		0			0
$981$	0.604246	+	5.09599i	0.0192921	+	0.162703i
$982$		0			0
$983$	14.3720	+	8.29768i	0.458396	+	0.264655i	0.711369	−	0.702818i	$-0.248075\pi$
$983$	14.3720	+	8.29768i	0.458396	+	0.264655i	−0.252974	+	0.967473i	$0.581409\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	23.7593	−	10.6971i	0.756268	−	0.340491i
$988$		0			0
$989$	−17.6140	+	10.1694i	−0.560092	+	0.323369i
$990$		0			0
$991$	−9.44914	+	16.3664i	−0.300162	+	0.519895i	−0.976172	−	0.216996i	$-0.930374\pi$
$991$	−9.44914	+	16.3664i	−0.300162	+	0.519895i	0.676011	+	0.736892i	$0.263707\pi$
$992$		0			0
$993$	2.56334	+	2.27735i	0.0813450	+	0.0722696i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−7.37103	+	12.7670i	−0.233443	+	0.404335i	−0.958819	−	0.284018i	$-0.908333\pi$
$997$	−7.37103	+	12.7670i	−0.233443	+	0.404335i	0.725376	+	0.688353i	$0.241666\pi$
$998$		0			0
$999$	1.69414	−	19.9380i	0.0536003	−	0.630811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.h.1949.9		20
3.2	odd	2		2100.2.bo.g.1949.5		20
5.2	odd	4		2100.2.bi.k.101.2		10
5.3	odd	4		420.2.bh.a.101.4	✓	10
5.4	even	2	inner	2100.2.bo.h.1949.2		20
7.5	odd	6		2100.2.bo.g.1349.6		20
15.2	even	4		2100.2.bi.j.101.1		10
15.8	even	4		420.2.bh.b.101.5	yes	10
15.14	odd	2		2100.2.bo.g.1949.6		20
21.5	even	6	inner	2100.2.bo.h.1349.2		20
35.3	even	12		2940.2.d.a.881.4		10
35.12	even	12		2100.2.bi.j.1601.1		10
35.18	odd	12		2940.2.d.b.881.7		10
35.19	odd	6		2100.2.bo.g.1349.5		20
35.33	even	12		420.2.bh.b.341.5	yes	10
105.38	odd	12		2940.2.d.b.881.8		10
105.47	odd	12		2100.2.bi.k.1601.2		10
105.53	even	12		2940.2.d.a.881.3		10
105.68	odd	12		420.2.bh.a.341.4	yes	10
105.89	even	6	inner	2100.2.bo.h.1349.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.4	✓	10	5.3	odd	4
420.2.bh.a.341.4	yes	10	105.68	odd	12
420.2.bh.b.101.5	yes	10	15.8	even	4
420.2.bh.b.341.5	yes	10	35.33	even	12
2100.2.bi.j.101.1		10	15.2	even	4
2100.2.bi.j.1601.1		10	35.12	even	12
2100.2.bi.k.101.2		10	5.2	odd	4
2100.2.bi.k.1601.2		10	105.47	odd	12
2100.2.bo.g.1349.5		20	35.19	odd	6
2100.2.bo.g.1349.6		20	7.5	odd	6
2100.2.bo.g.1949.5		20	3.2	odd	2
2100.2.bo.g.1949.6		20	15.14	odd	2
2100.2.bo.h.1349.2		20	21.5	even	6	inner
2100.2.bo.h.1349.9		20	105.89	even	6	inner
2100.2.bo.h.1949.2		20	5.4	even	2	inner
2100.2.bo.h.1949.9		20	1.1	even	1	trivial
2940.2.d.a.881.3		10	105.53	even	12
2940.2.d.a.881.4		10	35.3	even	12
2940.2.d.b.881.7		10	35.18	odd	12
2940.2.d.b.881.8		10	105.38	odd	12

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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bo (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.64368 - 0.546177i) q^{3} +(-2.41433 - 1.08214i) q^{7} +(2.40338 - 1.79548i) q^{9} +O(q^{10})\)	\(q+(1.64368 - 0.546177i) q^{3} +(-2.41433 - 1.08214i) q^{7} +(2.40338 - 1.79548i) q^{9} +(-1.17086 - 0.675999i) q^{11} +4.94296 q^{13} +(-4.97280 - 2.87105i) q^{17} +(-2.84694 + 1.64368i) q^{19} +(-4.55943 - 0.460035i) q^{21} +(-2.50270 - 4.33480i) q^{23} +(2.96974 - 4.26388i) q^{27} -5.68630i q^{29} +(-2.45160 - 1.41543i) q^{31} +(-2.29374 - 0.471628i) q^{33} +(3.33498 - 1.92545i) q^{37} +(8.12466 - 2.69973i) q^{39} +3.73802 q^{41} -4.06339i q^{43} +(-4.92419 + 2.84298i) q^{47} +(4.65797 + 5.22526i) q^{49} +(-9.74181 - 2.00306i) q^{51} +(-0.730773 + 1.26574i) q^{53} +(-3.78172 + 4.25662i) q^{57} +(-4.34239 + 7.52123i) q^{59} +(1.65306 - 0.954394i) q^{61} +(-7.74551 + 1.73410i) q^{63} +(-4.36371 - 2.51939i) q^{67} +(-6.48121 - 5.75812i) q^{69} -3.38259i q^{71} +(8.16364 - 14.1398i) q^{73} +(2.09533 + 2.89912i) q^{77} +(2.41693 + 4.18625i) q^{79} +(2.55248 - 8.63046i) q^{81} -16.6525i q^{83} +(-3.10572 - 9.34646i) q^{87} +(-8.08150 - 13.9976i) q^{89} +(-11.9339 - 5.34895i) q^{91} +(-4.80272 - 0.987510i) q^{93} +12.0577 q^{97} +(-4.02778 + 0.477584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{9}+O(q^{10}) \) 20 * q + 6 * q^9	\( 20 q + 6 q^{9} - 12 q^{11} - 6 q^{19} + 20 q^{21} + 30 q^{31} - 30 q^{39} - 16 q^{41} + 26 q^{49} - 88 q^{51} + 84 q^{61} + 28 q^{69} - 2 q^{79} + 82 q^{81} - 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) \) 20 * q + 6 * q^9 - 12 * q^11 - 6 * q^19 + 20 * q^21 + 30 * q^31 - 30 * q^39 - 16 * q^41 + 26 * q^49 - 88 * q^51 + 84 * q^61 + 28 * q^69 - 2 * q^79 + 82 * q^81 - 56 * q^89 - 22 * q^91 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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