LMFDB - Embedded newform 2100.2.bo.i.1349.3

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1349.3
Character	$\chi$	$=$	2100.1349
Dual form			2100.2.bo.i.1949.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56849 + 0.734734i) q^{3} +(0.156656 + 2.64111i) q^{7} +(1.92033 - 2.30485i) q^{9} +O(q^{10})$	\(q+(-1.56849 + 0.734734i) q^{3} +(0.156656 + 2.64111i) q^{7} +(1.92033 - 2.30485i) q^{9} +(4.92449 - 2.84316i) q^{11} -1.43616 q^{13} +(2.81310 - 1.62414i) q^{17} +(-5.43583 - 3.13838i) q^{19} +(-2.18623 - 4.02746i) q^{21} +(0.510633 - 0.884443i) q^{23} +(-1.31858 + 5.02607i) q^{27} -4.95680i q^{29} +(-2.28384 + 1.31858i) q^{31} +(-5.63506 + 8.07766i) q^{33} +(-7.88253 - 4.55098i) q^{37} +(2.25260 - 1.05519i) q^{39} +0.203153 q^{41} -3.91245i q^{43} +(9.98660 + 5.76577i) q^{47} +(-6.95092 + 0.827492i) q^{49} +(-3.21901 + 4.61434i) q^{51} +(-5.32156 - 9.21721i) q^{53} +(10.8319 + 0.928633i) q^{57} +(-0.739701 - 1.28120i) q^{59} +(7.62492 + 4.40225i) q^{61} +(6.38819 + 4.71074i) q^{63} +(4.05487 - 2.34108i) q^{67} +(-0.151094 + 1.76242i) q^{69} +1.08138i q^{71} +(-4.51983 - 7.82857i) q^{73} +(8.28054 + 12.5607i) q^{77} +(5.80981 - 10.0629i) q^{79} +(-1.62464 - 8.85215i) q^{81} +10.1512i q^{83} +(3.64193 + 7.77471i) q^{87} +(7.53465 - 13.0504i) q^{89} +(-0.224982 - 3.79304i) q^{91} +(2.61339 - 3.74619i) q^{93} +10.5540 q^{97} +(2.90362 - 16.8100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 18 q^{9}+O(q^{10}) $ 32 * q + 18 * q^9	$ 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) $ 32 * q + 18 * q^9 + 36 * q^19 - 22 * q^21 - 36 * q^31 - 24 * q^39 + 36 * q^49 - 2 * q^51 + 72 * q^61 + 14 * q^81 + 40 * q^91 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.56849	+	0.734734i	−0.905569	+	0.424199i
$3$	−1.56849	+	0.734734i	−0.905569	+	0.424199i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.156656	+	2.64111i	0.0592104	+	0.998246i
$7$	0.156656	+	2.64111i	0.0592104	+	0.998246i
$8$		0			0
$9$	1.92033	−	2.30485i	0.640111	−	0.768282i
$10$		0			0
$11$	4.92449	−	2.84316i	1.48479	−	0.857244i	0.484940	−	0.874548i	$-0.338842\pi$
$11$	4.92449	−	2.84316i	1.48479	−	0.857244i	0.999850	+	0.0173038i	$0.00550823\pi$
$12$		0			0
$13$	−1.43616			−0.398318			−0.199159	−	0.979967i	$-0.563821\pi$
$13$	−1.43616			−0.398318			−0.199159	+	0.979967i	$0.563821\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.81310	−	1.62414i	0.682277	−	0.393913i	−0.118435	−	0.992962i	$-0.537788\pi$
$17$	2.81310	−	1.62414i	0.682277	−	0.393913i	0.800712	+	0.599049i	$0.204455\pi$
$18$		0			0
$19$	−5.43583	−	3.13838i	−1.24707	−	0.719994i	−0.276543	−	0.961002i	$-0.589189\pi$
$19$	−5.43583	−	3.13838i	−1.24707	−	0.719994i	−0.970523	+	0.241008i	$0.922522\pi$
$20$		0			0
$21$	−2.18623	−	4.02746i	−0.477074	−	0.878863i
$22$		0			0
$23$	0.510633	−	0.884443i	0.106474	−	0.184419i	−0.807865	−	0.589367i	$-0.799377\pi$
$23$	0.510633	−	0.884443i	0.106474	−	0.184419i	0.914340	+	0.404948i	$0.132710\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.31858	+	5.02607i	−0.253760	+	0.967267i
$28$		0			0
$29$		−	4.95680i		−	0.920456i	−0.887801	−	0.460228i	$-0.847768\pi$
$29$		−	4.95680i		−	0.920456i	0.887801	−	0.460228i	$-0.152232\pi$
$30$		0			0
$31$	−2.28384	+	1.31858i	−0.410190	+	0.236823i	−0.690871	−	0.722978i	$-0.742773\pi$
$31$	−2.28384	+	1.31858i	−0.410190	+	0.236823i	0.280681	+	0.959801i	$0.409440\pi$
$32$		0			0
$33$	−5.63506	+	8.07766i	−0.980938	+	1.40614i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.88253	−	4.55098i	−1.29588	−	0.748176i	−0.316190	−	0.948696i	$-0.602404\pi$
$37$	−7.88253	−	4.55098i	−1.29588	−	0.748176i	−0.979690	+	0.200520i	$0.935737\pi$
$38$		0			0
$39$	2.25260	−	1.05519i	0.360704	−	0.168966i
$40$		0			0
$41$	0.203153			0.0317271			0.0158636	−	0.999874i	$-0.494950\pi$
$41$	0.203153			0.0317271			0.0158636	+	0.999874i	$0.494950\pi$
$42$		0			0
$43$		−	3.91245i		−	0.596642i	−0.954466	−	0.298321i	$-0.903573\pi$
$43$		−	3.91245i		−	0.596642i	0.954466	−	0.298321i	$-0.0964267\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.98660	+	5.76577i	1.45670	+	0.841024i	0.998847	−	0.0480062i	$-0.0152867\pi$
$47$	9.98660	+	5.76577i	1.45670	+	0.841024i	0.457849	+	0.889030i	$0.348620\pi$
$48$		0			0
$49$	−6.95092	+	0.827492i	−0.992988	+	0.118213i
$50$		0			0
$51$	−3.21901	+	4.61434i	−0.450752	+	0.646136i
$52$		0			0
$53$	−5.32156	−	9.21721i	−0.730972	−	1.26608i	−0.956468	−	0.291837i	$-0.905734\pi$
$53$	−5.32156	−	9.21721i	−0.730972	−	1.26608i	0.225496	−	0.974244i	$-0.427600\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	10.8319	+	0.928633i	1.43472	+	0.123000i
$58$		0			0
$59$	−0.739701	−	1.28120i	−0.0963009	−	0.166798i	0.813850	−	0.581075i	$-0.197368\pi$
$59$	−0.739701	−	1.28120i	−0.0963009	−	0.166798i	−0.910151	+	0.414277i	$0.864034\pi$
$60$		0			0
$61$	7.62492	+	4.40225i	0.976271	+	0.563650i	0.901142	−	0.433523i	$-0.142730\pi$
$61$	7.62492	+	4.40225i	0.976271	+	0.563650i	0.0751289	+	0.997174i	$0.476063\pi$
$62$		0			0
$63$	6.38819	+	4.71074i	0.804836	+	0.593498i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.05487	−	2.34108i	0.495381	−	0.286008i	−0.231423	−	0.972853i	$-0.574338\pi$
$67$	4.05487	−	2.34108i	0.495381	−	0.286008i	0.726804	+	0.686845i	$0.241005\pi$
$68$		0			0
$69$	−0.151094	+	1.76242i	−0.0181896	+	0.212171i
$70$		0			0
$71$			1.08138i			0.128336i	0.997939	+	0.0641680i	$0.0204394\pi$
$71$			1.08138i			0.128336i	−0.997939	+	0.0641680i	$0.979561\pi$
$72$		0			0
$73$	−4.51983	−	7.82857i	−0.529006	−	0.916265i	−0.999428	−	0.0338235i	$-0.989232\pi$
$73$	−4.51983	−	7.82857i	−0.529006	−	0.916265i	0.470422	−	0.882442i	$-0.344102\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.28054	+	12.5607i	0.943655	+	1.43143i
$78$		0			0
$79$	5.80981	−	10.0629i	0.653655	−	1.13216i	−0.328575	−	0.944478i	$-0.606568\pi$
$79$	5.80981	−	10.0629i	0.653655	−	1.13216i	0.982229	−	0.187685i	$-0.0600984\pi$
$80$		0			0
$81$	−1.62464	−	8.85215i	−0.180516	−	0.983572i
$82$		0			0
$83$			10.1512i			1.11424i	0.830433	+	0.557118i	$0.188093\pi$
$83$			10.1512i			1.11424i	−0.830433	+	0.557118i	$0.811907\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.64193	+	7.77471i	0.390456	+	0.833536i
$88$		0			0
$89$	7.53465	−	13.0504i	0.798672	−	1.38334i	−0.121810	−	0.992553i	$-0.538870\pi$
$89$	7.53465	−	13.0504i	0.798672	−	1.38334i	0.920481	−	0.390787i	$-0.127797\pi$
$90$		0			0
$91$	−0.224982	−	3.79304i	−0.0235846	−	0.397619i
$92$		0			0
$93$	2.61339	−	3.74619i	0.270995	−	0.388462i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	10.5540			1.07159			0.535797	−	0.844347i	$-0.320011\pi$
$97$	10.5540			1.07159			0.535797	+	0.844347i	$0.320011\pi$
$98$		0			0
$99$	2.90362	−	16.8100i	0.291825	−	1.68947i
$100$		0			0
$101$	−7.49149	−	12.9756i	−0.745431	−	1.29112i	−0.949993	−	0.312271i	$-0.898910\pi$
$101$	−7.49149	−	12.9756i	−0.745431	−	1.29112i	0.204562	−	0.978854i	$-0.434423\pi$
$102$		0			0
$103$	−1.98195	+	3.43283i	−0.195287	+	0.338247i	−0.946995	−	0.321249i	$-0.895897\pi$
$103$	−1.98195	+	3.43283i	−0.195287	+	0.338247i	0.751708	+	0.659497i	$0.229231\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.78087	−	8.28071i	0.462184	−	0.800526i	−0.536885	−	0.843655i	$-0.680399\pi$
$107$	4.78087	−	8.28071i	0.462184	−	0.800526i	0.999070	+	0.0431288i	$0.0137326\pi$
$108$		0			0
$109$	7.03847	+	12.1910i	0.674163	+	1.16769i	0.976713	+	0.214551i	$0.0688290\pi$
$109$	7.03847	+	12.1910i	0.674163	+	1.16769i	−0.302549	+	0.953134i	$0.597838\pi$
$110$		0			0
$111$	15.7074	+	1.34661i	1.49088	+	0.127815i
$112$		0			0
$113$	−5.91796			−0.556715			−0.278357	−	0.960478i	$-0.589790\pi$
$113$	−5.91796			−0.556715			−0.278357	+	0.960478i	$0.589790\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.75790	+	3.31012i	−0.254968	+	0.306021i
$118$		0			0
$119$	4.73023	+	7.17527i	0.433620	+	0.657756i
$120$		0			0
$121$	10.6671	−	18.4759i	0.969734	−	1.67963i
$122$		0			0
$123$	−0.318643	+	0.149263i	−0.0287311	+	0.0134586i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	8.35916i		−	0.741756i	−0.928682	−	0.370878i	$-0.879057\pi$
$127$		−	8.35916i		−	0.741756i	0.928682	−	0.370878i	$-0.120943\pi$
$128$		0			0
$129$	2.87461	+	6.13664i	0.253095	+	0.540301i
$130$		0			0
$131$	8.27436	−	14.3316i	0.722934	−	1.25216i	−0.236885	−	0.971538i	$-0.576126\pi$
$131$	8.27436	−	14.3316i	0.722934	−	1.25216i	0.959819	−	0.280620i	$-0.0905402\pi$
$132$		0			0
$133$	7.43725	−	14.8483i	0.644891	−	1.28751i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.17568	+	8.96454i	0.442188	+	0.765892i	0.997852	−	0.0655150i	$-0.0208690\pi$
$137$	5.17568	+	8.96454i	0.442188	+	0.765892i	−0.555663	+	0.831407i	$0.687536\pi$
$138$		0			0
$139$			9.17498i			0.778212i	0.921193	+	0.389106i	$0.127216\pi$
$139$			9.17498i			0.778212i	−0.921193	+	0.389106i	$0.872784\pi$
$140$		0			0
$141$	−19.9002	−	1.70607i	−1.67590	−	0.143677i
$142$		0			0
$143$	−7.07233	+	4.08321i	−0.591418	+	0.341455i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	10.2945	−	6.40499i	0.849074	−	0.528274i
$148$		0			0
$149$	3.71301	+	2.14370i	0.304181	+	0.175619i	0.644320	−	0.764756i	$-0.277141\pi$
$149$	3.71301	+	2.14370i	0.304181	+	0.175619i	−0.340138	+	0.940375i	$0.610474\pi$
$150$		0			0
$151$	6.06606	+	10.5067i	0.493649	+	0.855025i	0.999973	−	0.00731794i	$-0.00232939\pi$
$151$	6.06606	+	10.5067i	0.493649	+	0.855025i	−0.506324	+	0.862343i	$0.668996\pi$
$152$		0			0
$153$	1.65868	−	9.60266i	0.134097	−	0.776329i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−6.19593	−	10.7317i	−0.494489	−	0.856480i	0.505491	−	0.862832i	$-0.331311\pi$
$157$	−6.19593	−	10.7317i	−0.494489	−	0.856480i	−0.999980	+	0.00635192i	$0.997978\pi$
$158$		0			0
$159$	15.1190	+	10.5472i	1.19902	+	0.836447i
$160$		0			0
$161$	2.41590	+	1.21009i	0.190400	+	0.0953681i
$162$		0			0
$163$	17.8074	+	10.2811i	1.39478	+	0.805279i	0.993840	−	0.110824i	$-0.0353488\pi$
$163$	17.8074	+	10.2811i	1.39478	+	0.805279i	0.400944	+	0.916103i	$0.368682\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			3.95678i			0.306185i	0.988212	+	0.153093i	$0.0489232\pi$
$167$			3.95678i			0.306185i	−0.988212	+	0.153093i	$0.951077\pi$
$168$		0			0
$169$	−10.9375			−0.841343
$170$		0			0
$171$	−17.6721	+	6.50203i	−1.35142	+	0.497223i
$172$		0			0
$173$	−11.2678	−	6.50547i	−0.856675	−	0.494602i	0.00622220	−	0.999981i	$-0.498019\pi$
$173$	−11.2678	−	6.50547i	−0.856675	−	0.494602i	−0.862898	+	0.505379i	$0.831353\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.10156	+	1.46607i	0.157963	+	0.110196i
$178$		0			0
$179$	20.2033	−	11.6644i	1.51007	−	0.871837i	0.510135	−	0.860094i	$-0.329595\pi$
$179$	20.2033	−	11.6644i	1.51007	−	0.871837i	0.999931	−	0.0117426i	$-0.00373787\pi$
$180$		0			0
$181$			0.770872i			0.0572984i	0.999590	+	0.0286492i	$0.00912058\pi$
$181$			0.770872i			0.0572984i	−0.999590	+	0.0286492i	$0.990879\pi$
$182$		0			0
$183$	−15.1941	−	1.30261i	−1.12318	−	0.0962915i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	9.23539	−	15.9962i	0.675359	−	1.16976i
$188$		0			0
$189$	−13.4810	−	2.69514i	−0.980595	−	0.196043i
$190$		0			0
$191$	−2.02156	−	1.16715i	−0.146275	−	0.0844517i	0.425076	−	0.905157i	$-0.360247\pi$
$191$	−2.02156	−	1.16715i	−0.146275	−	0.0844517i	−0.571351	+	0.820706i	$0.693581\pi$
$192$		0			0
$193$	−0.607965	+	0.351009i	−0.0437623	+	0.0252662i	−0.521722	−	0.853116i	$-0.674710\pi$
$193$	−0.607965	+	0.351009i	−0.0437623	+	0.0252662i	0.477959	+	0.878382i	$0.341377\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−19.3932			−1.38171			−0.690855	−	0.722993i	$-0.742766\pi$
$197$	−19.3932			−1.38171			−0.690855	+	0.722993i	$0.742766\pi$
$198$		0			0
$199$	−16.0457	+	9.26397i	−1.13745	+	0.656706i	−0.945797	−	0.324758i	$-0.894717\pi$
$199$	−16.0457	+	9.26397i	−1.13745	+	0.656706i	−0.191650	+	0.981463i	$0.561384\pi$
$200$		0			0
$201$	−4.63996	+	6.65121i	−0.327277	+	0.469140i
$202$		0			0
$203$	13.0915	−	0.776514i	0.918841	−	0.0545006i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.05792	−	2.87536i	−0.0735305	−	0.199851i
$208$		0			0
$209$	−35.6916			−2.46884
$210$		0			0
$211$	22.5538			1.55267			0.776335	−	0.630321i	$-0.217077\pi$
$211$	22.5538			1.55267			0.776335	+	0.630321i	$0.217077\pi$
$212$		0			0
$213$	−0.794525	−	1.69613i	−0.0544400	−	0.116217i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.84028	−	5.82532i	−0.260696	−	0.395448i
$218$		0			0
$219$	12.8412	+	8.95818i	0.867730	+	0.605338i
$220$		0			0
$221$	−4.04005	+	2.33252i	−0.271763	+	0.156902i
$222$		0			0
$223$	−14.7072			−0.984868			−0.492434	−	0.870350i	$-0.663893\pi$
$223$	−14.7072			−0.984868			−0.492434	+	0.870350i	$0.663893\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	14.6835	−	8.47751i	0.974577	−	0.562672i	0.0739481	−	0.997262i	$-0.476440\pi$
$227$	14.6835	−	8.47751i	0.974577	−	0.562672i	0.900628	+	0.434590i	$0.143107\pi$
$228$		0			0
$229$	19.4690	+	11.2404i	1.28655	+	0.742789i	0.978037	−	0.208432i	$-0.0668360\pi$
$229$	19.4690	+	11.2404i	1.28655	+	0.742789i	0.308511	+	0.951221i	$0.400169\pi$
$230$		0			0
$231$	−22.2167	−	13.6174i	−1.46175	−	0.895959i
$232$		0			0
$233$	12.8315	−	22.2249i	0.840621	−	1.45600i	−0.0487486	−	0.998811i	$-0.515523\pi$
$233$	12.8315	−	22.2249i	0.840621	−	1.45600i	0.889370	−	0.457188i	$-0.151143\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.71910	+	20.0522i	−0.111667	+	1.30253i
$238$		0			0
$239$		−	7.58286i		−	0.490494i	−0.969461	−	0.245247i	$-0.921131\pi$
$239$		−	7.58286i		−	0.490494i	0.969461	−	0.245247i	$-0.0788691\pi$
$240$		0			0
$241$	7.34408	−	4.24011i	0.473074	−	0.273129i	−0.244452	−	0.969661i	$-0.578608\pi$
$241$	7.34408	−	4.24011i	0.473074	−	0.273129i	0.717526	+	0.696532i	$0.245275\pi$
$242$		0			0
$243$	9.05221	+	12.6908i	0.580700	+	0.814118i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.80670	+	4.50720i	0.496729	+	0.286786i
$248$		0			0
$249$	−7.45841	−	15.9220i	−0.472657	−	1.00902i
$250$		0			0
$251$	−1.17721			−0.0743051			−0.0371526	−	0.999310i	$-0.511829\pi$
$251$	−1.17721			−0.0743051			−0.0371526	+	0.999310i	$0.511829\pi$
$252$		0			0
$253$		−	5.80724i		−	0.365098i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.62211	−	2.66857i	−0.288319	−	0.166461i	0.348864	−	0.937173i	$-0.386567\pi$
$257$	−4.62211	−	2.66857i	−0.288319	−	0.166461i	−0.637184	+	0.770712i	$0.719901\pi$
$258$		0			0
$259$	10.7848	−	21.5316i	0.670134	−	1.33791i
$260$		0			0
$261$	−11.4247	−	9.51871i	−0.707170	−	0.589194i
$262$		0			0
$263$	7.65408	+	13.2573i	0.471971	+	0.817478i	0.999486	−	0.0320683i	$-0.0102094\pi$
$263$	7.65408	+	13.2573i	0.471971	+	0.817478i	−0.527515	+	0.849546i	$0.676876\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.22947	+	26.0054i	−0.136441	+	1.59151i
$268$		0			0
$269$	3.50096	+	6.06384i	0.213457	+	0.369719i	0.952794	−	0.303617i	$-0.0981943\pi$
$269$	3.50096	+	6.06384i	0.213457	+	0.369719i	−0.739337	+	0.673336i	$0.764861\pi$
$270$		0			0
$271$	11.1722	+	6.45029i	0.678665	+	0.391827i	0.799352	−	0.600863i	$-0.205176\pi$
$271$	11.1722	+	6.45029i	0.678665	+	0.391827i	−0.120687	+	0.992691i	$0.538510\pi$
$272$		0			0
$273$	3.13976	+	5.78405i	0.190027	+	0.350067i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.64261	+	5.56717i	−0.579369	+	0.334499i	−0.760882	−	0.648890i	$-0.775234\pi$
$277$	−9.64261	+	5.56717i	−0.579369	+	0.334499i	0.181514	+	0.983388i	$0.441900\pi$
$278$		0			0
$279$	−1.34662	+	7.79602i	−0.0806200	+	0.466735i
$280$		0			0
$281$			22.5391i			1.34457i	0.740291	+	0.672286i	$0.234688\pi$
$281$			22.5391i			1.34457i	−0.740291	+	0.672286i	$0.765312\pi$
$282$		0			0
$283$	−9.14640	−	15.8420i	−0.543697	−	0.941710i	−0.998688	−	0.0512144i	$-0.983691\pi$
$283$	−9.14640	−	15.8420i	−0.543697	−	0.941710i	0.454991	−	0.890496i	$-0.349643\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.0318251	+	0.536549i	0.00187858	+	0.0316715i
$288$		0			0
$289$	−3.22431	+	5.58467i	−0.189665	+	0.328510i
$290$		0			0
$291$	−16.5538	+	7.75436i	−0.970402	+	0.454568i
$292$		0			0
$293$			17.0413i			0.995566i	0.867302	+	0.497783i	$0.165852\pi$
$293$			17.0413i			0.995566i	−0.867302	+	0.497783i	$0.834148\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	7.79657	+	28.4997i	0.452403	+	1.65372i
$298$		0			0
$299$	−0.733349	+	1.27020i	−0.0424106	+	0.0734574i
$300$		0			0
$301$	10.3332	−	0.612909i	0.595596	−	0.0353275i
$302$		0			0
$303$	21.2840	+	14.8479i	1.22273	+	0.852992i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−16.9629			−0.968124			−0.484062	−	0.875034i	$-0.660839\pi$
$307$	−16.9629			−0.968124			−0.484062	+	0.875034i	$0.660839\pi$
$308$		0			0
$309$	0.586450	−	6.84058i	0.0333620	−	0.389147i
$310$		0			0
$311$	16.7519	+	29.0151i	0.949911	+	1.64529i	0.745606	+	0.666387i	$0.232160\pi$
$311$	16.7519	+	29.0151i	0.949911	+	1.64529i	0.204305	+	0.978907i	$0.434507\pi$
$312$		0			0
$313$	−3.42235	+	5.92768i	−0.193443	+	0.335052i	−0.946389	−	0.323030i	$-0.895299\pi$
$313$	−3.42235	+	5.92768i	−0.193443	+	0.335052i	0.752946	+	0.658082i	$0.228632\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.51876	−	11.2908i	0.366130	−	0.634156i	−0.622827	−	0.782360i	$-0.714016\pi$
$317$	6.51876	−	11.2908i	0.366130	−	0.634156i	0.988957	+	0.148204i	$0.0473492\pi$
$318$		0			0
$319$	−14.0930	−	24.4097i	−0.789055	−	1.36668i
$320$		0			0
$321$	−1.41464	+	16.5009i	−0.0789574	+	0.920990i
$322$		0			0
$323$	−20.3887			−1.13446
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−19.9969	−	13.9501i	−1.10583	−	0.771440i
$328$		0			0
$329$	−13.6636	+	27.2790i	−0.753297	+	1.50394i
$330$		0			0
$331$	3.35727	−	5.81496i	0.184532	−	0.319619i	−0.758887	−	0.651223i	$-0.774256\pi$
$331$	3.35727	−	5.81496i	0.184532	−	0.319619i	0.943419	+	0.331604i	$0.107590\pi$
$332$		0			0
$333$	−25.6264	+	9.42863i	−1.40432	+	0.516686i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	0.0783052i		−	0.00426556i	−0.999998	−	0.00213278i	$-0.999321\pi$
$337$		−	0.0783052i		−	0.00426556i	0.999998	−	0.00213278i	$-0.000678885\pi$
$338$		0			0
$339$	9.28227	−	4.34812i	0.504144	−	0.236158i
$340$		0			0
$341$	−7.49784	+	12.9866i	−0.406031	+	0.703266i
$342$		0			0
$343$	−3.27440	−	18.2285i	−0.176801	−	0.984247i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.9669	−	24.1913i	−0.749780	−	1.29866i	−0.947928	−	0.318485i	$-0.896826\pi$
$347$	−13.9669	−	24.1913i	−0.749780	−	1.29866i	0.198148	−	0.980172i	$-0.436507\pi$
$348$		0			0
$349$		−	18.8292i		−	1.00790i	−0.863732	−	0.503952i	$-0.831879\pi$
$349$		−	18.8292i		−	1.00790i	0.863732	−	0.503952i	$-0.168121\pi$
$350$		0			0
$351$	1.89368	−	7.21821i	0.101077	−	0.385280i
$352$		0			0
$353$	24.0565	−	13.8890i	1.28040	−	0.739239i	0.303477	−	0.952839i	$-0.401852\pi$
$353$	24.0565	−	13.8890i	1.28040	−	0.739239i	0.976921	+	0.213600i	$0.0685190\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−12.6912	−	7.77890i	−0.671692	−	0.411703i
$358$		0			0
$359$	24.6446	+	14.2286i	1.30069	+	0.750954i	0.980523	−	0.196406i	$-0.0629271\pi$
$359$	24.6446	+	14.2286i	1.30069	+	0.750954i	0.320168	+	0.947361i	$0.396260\pi$
$360$		0			0
$361$	10.1989	+	17.6650i	0.536782	+	0.929734i
$362$		0			0
$363$	−3.15634	+	36.8168i	−0.165665	+	1.93238i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.84147	−	13.5818i	−0.409321	−	0.708966i	0.585492	−	0.810678i	$-0.300901\pi$
$367$	−7.84147	−	13.5818i	−0.409321	−	0.708966i	−0.994814	+	0.101712i	$0.967568\pi$
$368$		0			0
$369$	0.390121	−	0.468236i	0.0203089	−	0.0243754i
$370$		0			0
$371$	23.5100	−	15.4988i	1.22058	−	0.804655i
$372$		0			0
$373$	2.28231	+	1.31769i	0.118173	+	0.0682274i	0.557922	−	0.829894i	$-0.311599\pi$
$373$	2.28231	+	1.31769i	0.118173	+	0.0682274i	−0.439748	+	0.898121i	$0.644932\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			7.11874i			0.366634i
$378$		0			0
$379$	−26.3684			−1.35445			−0.677227	−	0.735774i	$-0.736819\pi$
$379$	−26.3684			−1.35445			−0.677227	+	0.735774i	$0.736819\pi$
$380$		0			0
$381$	6.14176	+	13.1113i	0.314652	+	0.671711i
$382$		0			0
$383$	15.5116	+	8.95565i	0.792607	+	0.457612i	0.840880	−	0.541222i	$-0.182038\pi$
$383$	15.5116	+	8.95565i	0.792607	+	0.457612i	−0.0482722	+	0.998834i	$0.515372\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.01759	−	7.51320i	−0.458390	−	0.381917i
$388$		0			0
$389$	−17.6243	+	10.1754i	−0.893590	+	0.515914i	−0.875115	−	0.483915i	$-0.839214\pi$
$389$	−17.6243	+	10.1754i	−0.893590	+	0.515914i	−0.0184749	+	0.999829i	$0.505881\pi$
$390$		0			0
$391$		−	3.31737i		−	0.167767i
$392$		0			0
$393$	−2.44835	+	28.5585i	−0.123503	+	1.44058i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	8.25692	−	14.3014i	0.414403	−	0.717767i	−0.580963	−	0.813930i	$-0.697324\pi$
$397$	8.25692	−	14.3014i	0.414403	−	0.717767i	0.995366	+	0.0961632i	$0.0306571\pi$
$398$		0			0
$399$	−0.755733	+	28.7538i	−0.0378340	+	1.43949i
$400$		0			0
$401$	−26.0643	−	15.0482i	−1.30159	−	0.751473i	−0.320912	−	0.947109i	$-0.603990\pi$
$401$	−26.0643	−	15.0482i	−1.30159	−	0.751473i	−0.980677	+	0.195636i	$0.937323\pi$
$402$		0			0
$403$	3.27995	−	1.89368i	0.163386	−	0.0943310i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−51.7566			−2.56548
$408$		0			0
$409$	−19.1623	+	11.0634i	−0.947515	+	0.547048i	−0.892308	−	0.451427i	$-0.850915\pi$
$409$	−19.1623	+	11.0634i	−0.947515	+	0.547048i	−0.0552067	+	0.998475i	$0.517582\pi$
$410$		0			0
$411$	−14.7046	−	10.2581i	−0.725322	−	0.505993i
$412$		0			0
$413$	3.26791	−	2.15434i	0.160803	−	0.106008i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−6.74117	−	14.3909i	−0.330116	−	0.704724i
$418$		0			0
$419$	−24.3632			−1.19022			−0.595111	−	0.803643i	$-0.702892\pi$
$419$	−24.3632			−1.19022			−0.595111	+	0.803643i	$0.702892\pi$
$420$		0			0
$421$	−13.6655			−0.666018			−0.333009	−	0.942924i	$-0.608064\pi$
$421$	−13.6655			−0.666018			−0.333009	+	0.942924i	$0.608064\pi$
$422$		0			0
$423$	32.4668	−	11.9454i	1.57859	−	0.580805i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.4323	+	20.8279i	−0.504856	+	1.00793i
$428$		0			0
$429$	8.09282	−	11.6008i	0.390725	−	0.560090i
$430$		0			0
$431$	−18.2369	+	10.5291i	−0.878439	+	0.507167i	−0.870143	−	0.492798i	$-0.835974\pi$
$431$	−18.2369	+	10.5291i	−0.878439	+	0.507167i	−0.00829574	+	0.999966i	$0.502641\pi$
$432$		0			0
$433$	−2.13627			−0.102663			−0.0513313	−	0.998682i	$-0.516346\pi$
$433$	−2.13627			−0.102663			−0.0513313	+	0.998682i	$0.516346\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.55144	+	3.20512i	−0.265561	+	0.153322i
$438$		0			0
$439$	−13.0942	−	7.55996i	−0.624954	−	0.360817i	0.153841	−	0.988096i	$-0.450836\pi$
$439$	−13.0942	−	7.55996i	−0.624954	−	0.360817i	−0.778795	+	0.627278i	$0.784169\pi$
$440$		0			0
$441$	−11.4408	+	17.6099i	−0.544802	+	0.838565i
$442$		0			0
$443$	−7.39238	+	12.8040i	−0.351223	+	0.608335i	−0.986464	−	0.163978i	$-0.947567\pi$
$443$	−7.39238	+	12.8040i	−0.351223	+	0.608335i	0.635241	+	0.772314i	$0.280901\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.39887	−	0.634313i	−0.349955	−	0.0300020i
$448$		0			0
$449$		−	24.2040i		−	1.14226i	−0.820860	−	0.571130i	$-0.806505\pi$
$449$		−	24.2040i		−	1.14226i	0.820860	−	0.571130i	$-0.193495\pi$
$450$		0			0
$451$	1.00042	−	0.577595i	0.0471081	−	0.0271979i
$452$		0			0
$453$	−17.2342	−	12.0228i	−0.809734	−	0.564879i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.7314	−	6.19577i	−0.501993	−	0.289826i	0.227543	−	0.973768i	$-0.426931\pi$
$457$	−10.7314	−	6.19577i	−0.501993	−	0.289826i	−0.729536	+	0.683942i	$0.760264\pi$
$458$		0			0
$459$	4.45377	+	16.2804i	0.207884	+	0.759904i
$460$		0			0
$461$	3.34732			0.155900			0.0779502	−	0.996957i	$-0.475162\pi$
$461$	3.34732			0.155900			0.0779502	+	0.996957i	$0.475162\pi$
$462$		0			0
$463$		−	12.8360i		−	0.596542i	−0.954481	−	0.298271i	$-0.903590\pi$
$463$		−	12.8360i		−	0.596542i	0.954481	−	0.298271i	$-0.0964099\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−25.9359	−	14.9741i	−1.20017	−	0.692918i	−0.239576	−	0.970878i	$-0.577009\pi$
$467$	−25.9359	−	14.9741i	−1.20017	−	0.692918i	−0.960593	+	0.277959i	$0.910342\pi$
$468$		0			0
$469$	6.81827	+	10.3426i	0.314838	+	0.477577i
$470$		0			0
$471$	17.6032	+	12.2802i	0.811112	+	0.565840i
$472$		0			0
$473$	−11.1237	−	19.2668i	−0.511468	−	0.885889i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−31.4634	−	5.43473i	−1.44061	−	0.248839i
$478$		0			0
$479$	10.0585	+	17.4218i	0.459584	+	0.796023i	0.998939	−	0.0460557i	$-0.0146652\pi$
$479$	10.0585	+	17.4218i	0.459584	+	0.796023i	−0.539355	+	0.842079i	$0.681332\pi$
$480$		0			0
$481$	11.3205	+	6.53591i	0.516172	+	0.298012i
$482$		0			0
$483$	−4.67842	−	0.122962i	−0.212875	−	0.00559498i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−21.5981	+	12.4697i	−0.978704	+	0.565055i	−0.901879	−	0.431989i	$-0.857812\pi$
$487$	−21.5981	+	12.4697i	−0.978704	+	0.565055i	−0.0768256	+	0.997045i	$0.524478\pi$
$488$		0			0
$489$	−35.4847	−	3.04214i	−1.60467	−	0.137570i
$490$		0			0
$491$			11.2524i			0.507814i	0.967229	+	0.253907i	$0.0817157\pi$
$491$			11.2524i			0.507814i	−0.967229	+	0.253907i	$0.918284\pi$
$492$		0			0
$493$	−8.05057	−	13.9440i	−0.362579	−	0.628006i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.85604	+	0.169405i	−0.128111	+	0.00759883i
$498$		0			0
$499$	−2.84476	+	4.92727i	−0.127349	+	0.220575i	−0.922649	−	0.385642i	$-0.873980\pi$
$499$	−2.84476	+	4.92727i	−0.127349	+	0.220575i	0.795300	+	0.606216i	$0.207313\pi$
$500$		0			0
$501$	−2.90718	−	6.20618i	−0.129883	−	0.277272i
$502$		0			0
$503$			22.7975i			1.01649i	0.861212	+	0.508245i	$0.169706\pi$
$503$			22.7975i			1.01649i	−0.861212	+	0.508245i	$0.830294\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	17.1553	−	8.03612i	0.761894	−	0.356897i
$508$		0			0
$509$	−8.17913	+	14.1667i	−0.362534	+	0.627927i	−0.988377	−	0.152022i	$-0.951422\pi$
$509$	−8.17913	+	14.1667i	−0.362534	+	0.627927i	0.625843	+	0.779949i	$0.284755\pi$
$510$		0			0
$511$	19.9681	−	13.1638i	0.883335	−	0.582330i
$512$		0			0
$513$	22.9413	−	23.1827i	1.01288	−	1.02354i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	65.5719			2.88385
$518$		0			0
$519$	22.4532	+	1.92494i	0.985588	+	0.0844955i
$520$		0			0
$521$	−8.67177	−	15.0199i	−0.379917	−	0.658036i	0.611133	−	0.791528i	$-0.290714\pi$
$521$	−8.67177	−	15.0199i	−0.379917	−	0.658036i	−0.991050	+	0.133492i	$0.957381\pi$
$522$		0			0
$523$	−6.44905	+	11.1701i	−0.281997	+	0.488433i	−0.971877	−	0.235491i	$-0.924330\pi$
$523$	−6.44905	+	11.1701i	−0.281997	+	0.488433i	0.689879	+	0.723924i	$0.257664\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.28312	+	7.41858i	−0.186576	+	0.323158i
$528$		0			0
$529$	10.9785	+	19.0153i	0.477326	+	0.826754i
$530$		0			0
$531$	−4.37344	−	0.755432i	−0.189791	−	0.0327830i
$532$		0			0
$533$	−0.291759			−0.0126375
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−23.1185	+	33.1395i	−0.997637	+	1.43008i
$538$		0			0
$539$	−31.8770	+	23.8375i	−1.37304	+	1.02675i
$540$		0			0
$541$	−2.22594	+	3.85543i	−0.0957004	+	0.165758i	−0.909901	−	0.414826i	$-0.863842\pi$
$541$	−2.22594	+	3.85543i	−0.0957004	+	0.165758i	0.814200	+	0.580584i	$0.197176\pi$
$542$		0			0
$543$	−0.566385	−	1.20911i	−0.0243059	−	0.0518877i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			5.58754i			0.238906i	0.992840	+	0.119453i	$0.0381141\pi$
$547$			5.58754i			0.238906i	−0.992840	+	0.119453i	$0.961886\pi$
$548$		0			0
$549$	24.7889	−	9.12050i	1.05796	−	0.389253i
$550$		0			0
$551$	−15.5563	+	26.9444i	−0.662722	+	1.14787i
$552$		0			0
$553$	27.4873	+	13.7679i	1.16888	+	0.585472i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.4844	−	18.1594i	−0.444236	−	0.769440i	0.553762	−	0.832675i	$-0.313192\pi$
$557$	−10.4844	−	18.1594i	−0.444236	−	0.769440i	−0.997999	+	0.0632348i	$0.979858\pi$
$558$		0			0
$559$			5.61888i			0.237653i
$560$		0			0
$561$	−2.73271	+	31.8754i	−0.115375	+	1.34578i
$562$		0			0
$563$	−10.6432	+	6.14487i	−0.448559	+	0.258975i	−0.707221	−	0.706992i	$-0.750052\pi$
$563$	−10.6432	+	6.14487i	−0.448559	+	0.258975i	0.258663	+	0.965968i	$0.416718\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	23.1250	−	5.67760i	0.971158	−	0.238437i
$568$		0			0
$569$	37.1989	+	21.4768i	1.55946	+	0.900355i	0.997308	+	0.0733217i	$0.0233600\pi$
$569$	37.1989	+	21.4768i	1.55946	+	0.900355i	0.562153	+	0.827033i	$0.309973\pi$
$570$		0			0
$571$	−3.24932	−	5.62799i	−0.135980	−	0.235524i	0.789991	−	0.613118i	$-0.210085\pi$
$571$	−3.24932	−	5.62799i	−0.135980	−	0.235524i	−0.925971	+	0.377594i	$0.876752\pi$
$572$		0			0
$573$	4.02834	+	0.345353i	0.168286	+	0.0144273i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.667135	+	1.15551i	0.0277732	+	0.0481046i	0.879578	−	0.475755i	$-0.157825\pi$
$577$	0.667135	+	1.15551i	0.0277732	+	0.0481046i	−0.851805	+	0.523859i	$0.824492\pi$
$578$		0			0
$579$	0.695690	−	0.997247i	0.0289119	−	0.0414442i
$580$		0			0
$581$	−26.8104	+	1.59024i	−1.11228	+	0.0659744i
$582$		0			0
$583$	−52.4119	−	30.2600i	−2.17068	−	1.25324i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			20.5791i			0.849391i	0.905336	+	0.424696i	$0.139619\pi$
$587$			20.5791i			0.849391i	−0.905336	+	0.424696i	$0.860381\pi$
$588$		0			0
$589$	16.5528			0.682046
$590$		0			0
$591$	30.4181	−	14.2489i	1.25123	−	0.586120i
$592$		0			0
$593$	8.36894	+	4.83181i	0.343671	+	0.198419i	0.661894	−	0.749597i	$-0.269753\pi$
$593$	8.36894	+	4.83181i	0.343671	+	0.198419i	−0.318223	+	0.948016i	$0.603086\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	18.3610	−	26.3198i	0.751464	−	1.07720i
$598$		0			0
$599$	37.3444	−	21.5608i	1.52585	−	0.880951i	0.526323	−	0.850285i	$-0.323570\pi$
$599$	37.3444	−	21.5608i	1.52585	−	0.880951i	0.999530	−	0.0306663i	$-0.00976291\pi$
$600$		0			0
$601$		−	24.0495i		−	0.980999i	−0.871442	−	0.490499i	$-0.836814\pi$
$601$		−	24.0495i		−	0.980999i	0.871442	−	0.490499i	$-0.163186\pi$
$602$		0			0
$603$	2.39087	−	13.8415i	0.0973636	−	0.563670i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	3.78982	−	6.56417i	0.153824	−	0.266431i	−0.778806	−	0.627265i	$-0.784174\pi$
$607$	3.78982	−	6.56417i	0.153824	−	0.266431i	0.932630	+	0.360833i	$0.117508\pi$
$608$		0			0
$609$	−19.9633	+	10.8367i	−0.808955	+	0.439125i
$610$		0			0
$611$	−14.3423	−	8.28054i	−0.580228	−	0.334995i
$612$		0			0
$613$	40.1812	−	23.1986i	1.62290	−	0.936983i	0.636764	−	0.771058i	$-0.280272\pi$
$613$	40.1812	−	23.1986i	1.62290	−	0.936983i	0.986138	−	0.165925i	$-0.0530609\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.36960			0.0551380			0.0275690	−	0.999620i	$-0.491223\pi$
$617$	1.36960			0.0551380			0.0275690	+	0.999620i	$0.491223\pi$
$618$		0			0
$619$	13.0178	−	7.51581i	0.523228	−	0.302086i	−0.215026	−	0.976608i	$-0.568984\pi$
$619$	13.0178	−	7.51581i	0.523228	−	0.302086i	0.738255	+	0.674522i	$0.235650\pi$
$620$		0			0
$621$	3.77196	+	3.73268i	0.151364	+	0.149787i
$622$		0			0
$623$	35.6479	+	17.8554i	1.42820	+	0.715362i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	55.9820	−	26.2238i	2.23571	−	1.04728i
$628$		0			0
$629$	−29.5658			−1.17886
$630$		0			0
$631$	4.30638			0.171434			0.0857172	−	0.996320i	$-0.472682\pi$
$631$	4.30638			0.171434			0.0857172	+	0.996320i	$0.472682\pi$
$632$		0			0
$633$	−35.3755	+	16.5711i	−1.40605	+	0.658640i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.98260	−	1.18841i	0.395525	−	0.0470864i
$638$		0			0
$639$	2.49241	+	2.07661i	0.0985983	+	0.0821493i
$640$		0			0
$641$	−10.9310	+	6.31100i	−0.431747	+	0.249270i	−0.700091	−	0.714054i	$-0.746857\pi$
$641$	−10.9310	+	6.31100i	−0.431747	+	0.249270i	0.268343	+	0.963323i	$0.413524\pi$
$642$		0			0
$643$	29.2411			1.15316			0.576578	−	0.817042i	$-0.304388\pi$
$643$	29.2411			1.15316			0.576578	+	0.817042i	$0.304388\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.6985	+	7.33150i	−0.499231	+	0.288231i	−0.728396	−	0.685157i	$-0.759734\pi$
$647$	−12.6985	+	7.33150i	−0.499231	+	0.288231i	0.229165	+	0.973388i	$0.426400\pi$
$648$		0			0
$649$	−7.28531	−	4.20617i	−0.285973	−	0.165107i
$650$		0			0
$651$	10.3035	+	6.31537i	0.403826	+	0.247519i
$652$		0			0
$653$	16.0248	−	27.7557i	0.627098	−	1.08617i	−0.361033	−	0.932553i	$-0.617576\pi$
$653$	16.0248	−	27.7557i	0.627098	−	1.08617i	0.988131	−	0.153613i	$-0.0490910\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−26.7232	−	4.61595i	−1.04257	−	0.180085i
$658$		0			0
$659$		−	44.0951i		−	1.71770i	−0.512225	−	0.858851i	$-0.671179\pi$
$659$		−	44.0951i		−	1.71770i	0.512225	−	0.858851i	$-0.328821\pi$
$660$		0			0
$661$	−29.9096	+	17.2683i	−1.16335	+	0.671660i	−0.952104	−	0.305773i	$-0.901085\pi$
$661$	−29.9096	+	17.2683i	−1.16335	+	0.671660i	−0.211245	+	0.977433i	$0.567752\pi$
$662$		0			0
$663$	4.62300	−	6.62690i	0.179542	−	0.257368i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.38401	−	2.53111i	−0.169750	−	0.0980050i
$668$		0			0
$669$	23.0681	−	10.8059i	0.891866	−	0.417780i
$670$		0			0
$671$	50.0651			1.93274
$672$		0			0
$673$		−	11.0196i		−	0.424773i	−0.977186	−	0.212386i	$-0.931876\pi$
$673$		−	11.0196i		−	0.424773i	0.977186	−	0.212386i	$-0.0681235\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.55993	−	3.78738i	−0.252119	−	0.145561i	0.368615	−	0.929582i	$-0.379832\pi$
$677$	−6.55993	−	3.78738i	−0.252119	−	0.145561i	−0.620734	+	0.784021i	$0.713165\pi$
$678$		0			0
$679$	1.65334	+	27.8742i	0.0634495	+	1.06971i
$680$		0			0
$681$	−16.8022	+	24.0853i	−0.643862	+	0.922952i
$682$		0			0
$683$	12.6985	+	21.9945i	0.485896	+	0.841596i	0.999869	−	0.0162102i	$-0.00516008\pi$
$683$	12.6985	+	21.9945i	0.485896	+	0.841596i	−0.513973	+	0.857807i	$0.671827\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−38.7957	−	3.32600i	−1.48015	−	0.126895i
$688$		0			0
$689$	7.64258	+	13.2373i	0.291159	+	0.504303i
$690$		0			0
$691$	−2.43241	−	1.40435i	−0.0925332	−	0.0534241i	0.453019	−	0.891501i	$-0.350347\pi$
$691$	−2.43241	−	1.40435i	−0.0925332	−	0.0534241i	−0.545553	+	0.838077i	$0.683680\pi$
$692$		0			0
$693$	44.8519	+	5.03539i	1.70378	+	0.191279i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.571489	−	0.329949i	0.0216467	−	0.0124977i
$698$		0			0
$699$	−3.79679	+	44.2873i	−0.143608	+	1.67510i
$700$		0			0
$701$			18.1659i			0.686115i	0.939314	+	0.343058i	$0.111463\pi$
$701$			18.1659i			0.686115i	−0.939314	+	0.343058i	$0.888537\pi$
$702$		0			0
$703$	28.5654	+	49.4767i	1.07736	+	1.86605i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	33.0965	−	21.8186i	1.24472	−	0.820571i
$708$		0			0
$709$	15.0139	−	26.0048i	0.563858	−	0.976631i	−0.433297	−	0.901251i	$-0.642650\pi$
$709$	15.0139	−	26.0048i	0.563858	−	0.976631i	0.997155	−	0.0753797i	$-0.0240169\pi$
$710$		0			0
$711$	−12.0366	−	32.7148i	−0.451409	−	1.22690i
$712$		0			0
$713$			2.69324i			0.100863i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.57138	+	11.8936i	0.208067	+	0.444176i
$718$		0			0
$719$	0.687643	−	1.19103i	0.0256447	−	0.0444180i	−0.852918	−	0.522045i	$-0.825169\pi$
$719$	0.687643	−	1.19103i	0.0256447	−	0.0444180i	0.878563	+	0.477627i	$0.158503\pi$
$720$		0			0
$721$	−9.37697	−	4.69677i	−0.349217	−	0.174917i
$722$		0			0
$723$	−8.40378	+	12.0465i	−0.312540	+	0.448015i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−33.6733			−1.24887			−0.624436	−	0.781076i	$-0.714671\pi$
$727$	−33.6733			−1.24887			−0.624436	+	0.781076i	$0.714671\pi$
$728$		0			0
$729$	−23.5227	−	13.2545i	−0.871211	−	0.490908i
$730$		0			0
$731$	−6.35438	−	11.0061i	−0.235025	−	0.407075i
$732$		0			0
$733$	8.37999	−	14.5146i	0.309522	−	0.536108i	−0.668736	−	0.743500i	$-0.733164\pi$
$733$	8.37999	−	14.5146i	0.309522	−	0.536108i	0.978258	+	0.207392i	$0.0664977\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.3121	−	23.0572i	0.490358	−	0.849325i
$738$		0			0
$739$	19.3091	+	33.4444i	0.710298	+	1.23027i	0.964745	+	0.263185i	$0.0847730\pi$
$739$	19.3091	+	33.4444i	0.710298	+	1.23027i	−0.254448	+	0.967087i	$0.581894\pi$
$740$		0			0
$741$	−15.5563	−	1.33366i	−0.571476	−	0.0489933i
$742$		0			0
$743$	−29.3068			−1.07516			−0.537582	−	0.843212i	$-0.680662\pi$
$743$	−29.3068			−1.07516			−0.537582	+	0.843212i	$0.680662\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	23.3969	+	19.4936i	0.856048	+	0.713234i
$748$		0			0
$749$	22.6192	+	11.3296i	0.826488	+	0.413974i
$750$		0			0
$751$	−5.94534	+	10.2976i	−0.216949	+	0.375766i	−0.953874	−	0.300209i	$-0.902944\pi$
$751$	−5.94534	+	10.2976i	−0.216949	+	0.375766i	0.736925	+	0.675974i	$0.236277\pi$
$752$		0			0
$753$	1.84645	−	0.864939i	0.0672884	−	0.0315201i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	44.9755i		−	1.63466i	−0.576167	−	0.817332i	$-0.695452\pi$
$757$		−	44.9755i		−	1.63466i	0.576167	−	0.817332i	$-0.304548\pi$
$758$		0			0
$759$	4.26678	+	9.10861i	0.154874	+	0.330622i
$760$		0			0
$761$	1.22673	−	2.12476i	0.0444690	−	0.0770226i	−0.842934	−	0.538017i	$-0.819174\pi$
$761$	1.22673	−	2.12476i	0.0444690	−	0.0770226i	0.887403	+	0.460994i	$0.152507\pi$
$762$		0			0
$763$	−31.0951	+	20.4992i	−1.12572	+	0.742120i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.06233	+	1.84000i	0.0383584	+	0.0664386i
$768$		0			0
$769$			18.4658i			0.665894i	0.942946	+	0.332947i	$0.108043\pi$
$769$			18.4658i			0.665894i	−0.942946	+	0.332947i	$0.891957\pi$
$770$		0			0
$771$	9.21043	+	0.789620i	0.331705	+	0.0284375i
$772$		0			0
$773$	1.53190	−	0.884443i	0.0550986	−	0.0318112i	−0.472198	−	0.881493i	$-0.656539\pi$
$773$	1.53190	−	0.884443i	0.0550986	−	0.0318112i	0.527296	+	0.849682i	$0.323206\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.09589	+	41.6960i	−0.0393149	+	1.49584i
$778$		0			0
$779$	−1.10430	−	0.637571i	−0.0395658	−	0.0228433i
$780$		0			0
$781$	3.07453	+	5.32524i	0.110015	+	0.190552i
$782$		0			0
$783$	24.9132	+	6.53593i	0.890326	+	0.233575i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−26.5888	−	46.0531i	−0.947788	−	1.64162i	−0.750070	−	0.661358i	$-0.769980\pi$
$787$	−26.5888	−	46.0531i	−0.947788	−	1.64162i	−0.197718	−	0.980259i	$-0.563353\pi$
$788$		0			0
$789$	−21.7459	−	15.1702i	−0.774175	−	0.540073i
$790$		0			0
$791$	−0.927084	−	15.6300i	−0.0329633	−	0.555738i
$792$		0			0
$793$	−10.9506	−	6.32231i	−0.388866	−	0.224512i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			33.8237i			1.19810i	0.800713	+	0.599049i	$0.204454\pi$
$797$			33.8237i			1.19810i	−0.800713	+	0.599049i	$0.795546\pi$
$798$		0			0
$799$	37.4578			1.32516
$800$		0			0
$801$	−15.6101	−	42.4273i	−0.551557	−	1.49910i
$802$		0			0
$803$	−44.5157	−	25.7012i	−1.57093	−	0.906974i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−9.94653	−	6.93881i	−0.350135	−	0.244258i
$808$		0			0
$809$	−23.8866	+	13.7909i	−0.839807	+	0.484863i	−0.857199	−	0.514986i	$-0.827797\pi$
$809$	−23.8866	+	13.7909i	−0.839807	+	0.484863i	0.0173917	+	0.999849i	$0.494464\pi$
$810$		0			0
$811$		−	3.97378i		−	0.139538i	−0.997563	−	0.0697692i	$-0.977774\pi$
$811$		−	3.97378i		−	0.139538i	0.997563	−	0.0697692i	$-0.0222263\pi$
$812$		0			0
$813$	−22.2628	−	1.90861i	−0.780790	−	0.0669380i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−12.2787	+	21.2674i	−0.429579	+	0.744052i
$818$		0			0
$819$	−9.17443	−	6.76535i	−0.320580	−	0.236401i
$820$		0			0
$821$	45.8143	+	26.4509i	1.59893	+	0.923143i	0.991694	+	0.128623i	$0.0410556\pi$
$821$	45.8143	+	26.4509i	1.59893	+	0.923143i	0.607237	+	0.794521i	$0.292278\pi$
$822$		0			0
$823$	−8.98823	+	5.18936i	−0.313310	+	0.180890i	−0.648407	−	0.761294i	$-0.724564\pi$
$823$	−8.98823	+	5.18936i	−0.313310	+	0.180890i	0.335097	+	0.942184i	$0.391231\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	50.8249			1.76736			0.883678	−	0.468095i	$-0.155059\pi$
$827$	50.8249			1.76736			0.883678	+	0.468095i	$0.155059\pi$
$828$		0			0
$829$	1.33850	−	0.772785i	0.0464881	−	0.0268399i	−0.476576	−	0.879133i	$-0.658122\pi$
$829$	1.33850	−	0.772785i	0.0464881	−	0.0268399i	0.523064	+	0.852293i	$0.324789\pi$
$830$		0			0
$831$	11.0340	−	15.8168i	0.382764	−	0.548679i
$832$		0			0
$833$	−18.2097	+	13.6171i	−0.630927	+	0.471805i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.61584	−	13.2174i	−0.124982	−	0.456860i
$838$		0			0
$839$	−24.0738			−0.831118			−0.415559	−	0.909566i	$-0.636414\pi$
$839$	−24.0738			−0.831118			−0.415559	+	0.909566i	$0.636414\pi$
$840$		0			0
$841$	4.43009			0.152762
$842$		0			0
$843$	−16.5603	−	35.3525i	−0.570366	−	1.21760i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	50.4680	+	25.2785i	1.73410	+	0.868581i
$848$		0			0
$849$	25.9857	+	18.1279i	0.891827	+	0.622148i
$850$		0			0
$851$	−8.05016	+	4.64776i	−0.275956	+	0.159323i
$852$		0			0
$853$	−16.6929			−0.571555			−0.285777	−	0.958296i	$-0.592252\pi$
$853$	−16.6929			−0.571555			−0.285777	+	0.958296i	$0.592252\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24.3974	+	14.0858i	−0.833398	+	0.481163i	−0.855015	−	0.518604i	$-0.826452\pi$
$857$	−24.3974	+	14.0858i	−0.833398	+	0.481163i	0.0216164	+	0.999766i	$0.493119\pi$
$858$		0			0
$859$	−48.0897	−	27.7646i	−1.64080	−	0.947315i	−0.980550	−	0.196268i	$-0.937118\pi$
$859$	−48.0897	−	27.7646i	−1.64080	−	0.947315i	−0.660248	−	0.751048i	$-0.729549\pi$
$860$		0			0
$861$	−0.444138	−	0.818189i	−0.0151362	−	0.0278838i
$862$		0			0
$863$	14.6517	−	25.3774i	0.498748	−	0.863857i	−0.501251	−	0.865302i	$-0.667127\pi$
$863$	14.6517	−	25.3774i	0.498748	−	0.863857i	0.999999	+	0.00144510i	$0.000459991\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.954060	−	11.1285i	0.0324016	−	0.377944i
$868$		0			0
$869$		−	66.0728i		−	2.24137i
$870$		0			0
$871$	−5.82342	+	3.36215i	−0.197319	+	0.113922i
$872$		0			0
$873$	20.2671	−	24.3253i	0.685939	−	0.823286i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	43.2276	+	24.9574i	1.45969	+	0.842753i	0.998996	−	0.0448051i	$-0.0142667\pi$
$877$	43.2276	+	24.9574i	1.45969	+	0.842753i	0.460695	+	0.887558i	$0.347600\pi$
$878$		0			0
$879$	−12.5209	−	26.7292i	−0.422318	−	0.901554i
$880$		0			0
$881$	57.0594			1.92238			0.961191	−	0.275885i	$-0.0889709\pi$
$881$	57.0594			1.92238			0.961191	+	0.275885i	$0.0889709\pi$
$882$		0			0
$883$			39.2846i			1.32203i	0.750371	+	0.661017i	$0.229875\pi$
$883$			39.2846i			1.32203i	−0.750371	+	0.661017i	$0.770125\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.6684	−	7.89144i	−0.458939	−	0.264969i	0.252659	−	0.967555i	$-0.418695\pi$
$887$	−13.6684	−	7.89144i	−0.458939	−	0.264969i	−0.711598	+	0.702587i	$0.752028\pi$
$888$		0			0
$889$	22.0775	−	1.30951i	0.740454	−	0.0439197i
$890$		0			0
$891$	−33.1686	−	38.9732i	−1.11119	−	1.30565i
$892$		0			0
$893$	−36.1904	−	62.6835i	−1.21106	−	2.09762i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.216995	−	2.53111i	0.00724524	−	0.0845113i
$898$		0			0
$899$	6.53593	+	11.3206i	0.217985	+	0.377562i
$900$		0			0
$901$	−29.9402	−	17.2860i	−0.997451	−	0.575879i
$902$		0			0
$903$	−15.7572	+	8.55349i	−0.524367	+	0.284642i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−39.8965	+	23.0343i	−1.32474	+	0.764840i	−0.984481	−	0.175490i	$-0.943849\pi$
$907$	−39.8965	+	23.0343i	−1.32474	+	0.764840i	−0.340261	+	0.940331i	$0.610516\pi$
$908$		0			0
$909$	−44.2930	−	7.65081i	−1.46911	−	0.253761i
$910$		0			0
$911$		−	26.6500i		−	0.882953i	−0.897273	−	0.441477i	$-0.854455\pi$
$911$		−	26.6500i		−	0.882953i	0.897273	−	0.441477i	$-0.145545\pi$
$912$		0			0
$913$	28.8614	+	49.9893i	0.955172	+	1.65441i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	39.1476	+	19.6083i	1.29277	+	0.647525i
$918$		0			0
$919$	1.65362	−	2.86415i	0.0545478	−	0.0944795i	−0.837462	−	0.546495i	$-0.815962\pi$
$919$	1.65362	−	2.86415i	0.0545478	−	0.0944795i	0.892010	+	0.452016i	$0.149295\pi$
$920$		0			0
$921$	26.6062	−	12.4632i	0.876704	−	0.410677i
$922$		0			0
$923$		−	1.55303i		−	0.0511185i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	4.10616	+	11.1603i	0.134864	+	0.366551i
$928$		0			0
$929$	11.3962	−	19.7388i	0.373898	−	0.647610i	−0.616264	−	0.787540i	$-0.711354\pi$
$929$	11.3962	−	19.7388i	0.373898	−	0.647610i	0.990161	+	0.139930i	$0.0446878\pi$
$930$		0			0
$931$	40.3810	+	17.3165i	1.32343	+	0.567526i
$932$		0			0
$933$	−47.5935	−	33.2018i	−1.55814	−	1.08698i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	33.2636			1.08667			0.543336	−	0.839515i	$-0.317161\pi$
$937$	33.2636			1.08667			0.543336	+	0.839515i	$0.317161\pi$
$938$		0			0
$939$	1.01266	−	11.8120i	0.0330468	−	0.385471i
$940$		0			0
$941$	−23.1677	−	40.1277i	−0.755246	−	1.30812i	−0.945252	−	0.326341i	$-0.894184\pi$
$941$	−23.1677	−	40.1277i	−0.755246	−	1.30812i	0.190006	−	0.981783i	$-0.439149\pi$
$942$		0			0
$943$	0.103737	−	0.179677i	0.00337813	−	0.00585109i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.8743	−	36.1553i	0.678322	−	1.17489i	−0.297164	−	0.954826i	$-0.596041\pi$
$947$	20.8743	−	36.1553i	0.678322	−	1.17489i	0.975486	−	0.220062i	$-0.0706259\pi$
$948$		0			0
$949$	6.49117	+	11.2430i	0.210712	+	0.364965i
$950$		0			0
$951$	−1.92887	+	22.4991i	−0.0625480	+	0.729584i
$952$		0			0
$953$	−5.47667			−0.177407			−0.0887034	−	0.996058i	$-0.528272\pi$
$953$	−5.47667			−0.177407			−0.0887034	+	0.996058i	$0.528272\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	40.0394	+	27.9319i	1.29429	+	0.902910i
$958$		0			0
$959$	−22.8655	+	15.0739i	−0.738366	+	0.486761i
$960$		0			0
$961$	−12.0227	+	20.8239i	−0.387829	+	0.671740i
$962$		0			0
$963$	−9.90491	−	26.9209i	−0.319181	−	0.867514i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			60.2148i			1.93638i	0.250223	+	0.968188i	$0.419496\pi$
$967$			60.2148i			1.93638i	−0.250223	+	0.968188i	$0.580504\pi$
$968$		0			0
$969$	31.9796	−	14.9803i	1.02733	−	0.481236i
$970$		0			0
$971$	13.2636	−	22.9732i	0.425650	−	0.737247i	−0.570831	−	0.821067i	$-0.693379\pi$
$971$	13.2636	−	22.9732i	0.425650	−	0.737247i	0.996481	+	0.0838207i	$0.0267123\pi$
$972$		0			0
$973$	−24.2321	+	1.43732i	−0.776846	+	0.0460782i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.07480	−	5.32572i	−0.0983717	−	0.170385i	0.812639	−	0.582767i	$-0.198030\pi$
$977$	−3.07480	−	5.32572i	−0.0983717	−	0.170385i	−0.911011	+	0.412383i	$0.864697\pi$
$978$		0			0
$979$		−	85.6888i		−	2.73863i
$980$		0			0
$981$	41.6146	+	7.18816i	1.32865	+	0.229500i
$982$		0			0
$983$	39.4877	−	22.7982i	1.25946	−	0.727150i	0.286492	−	0.958083i	$-0.407511\pi$
$983$	39.4877	−	22.7982i	1.25946	−	0.727150i	0.972970	+	0.230932i	$0.0741776\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.38842	−	52.8259i	0.0441938	−	1.68147i
$988$		0			0
$989$	−3.46033	−	1.99783i	−0.110032	−	0.0635271i
$990$		0			0
$991$	11.0880	+	19.2049i	0.352221	+	0.610065i	0.986638	−	0.162926i	$-0.0520931\pi$
$991$	11.0880	+	19.2049i	0.352221	+	0.610065i	−0.634417	+	0.772991i	$0.718760\pi$
$992$		0			0
$993$	−0.993401	+	11.5874i	−0.0315246	+	0.367715i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−5.84211	−	10.1188i	−0.185021	−	0.320466i	0.758562	−	0.651600i	$-0.225902\pi$
$997$	−5.84211	−	10.1188i	−0.185021	−	0.320466i	−0.943584	+	0.331134i	$0.892569\pi$
$998$		0			0
$999$	33.2672	−	33.6173i	1.05253	−	1.06360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.i.1349.3		32
3.2	odd	2	inner	2100.2.bo.i.1349.12		32
5.2	odd	4		2100.2.bi.l.1601.7	yes	16
5.3	odd	4		2100.2.bi.m.1601.2	yes	16
5.4	even	2	inner	2100.2.bo.i.1349.14		32
7.3	odd	6	inner	2100.2.bo.i.1949.5		32
15.2	even	4		2100.2.bi.l.1601.3	yes	16
15.8	even	4		2100.2.bi.m.1601.6	yes	16
15.14	odd	2	inner	2100.2.bo.i.1349.5		32
21.17	even	6	inner	2100.2.bo.i.1949.14		32
35.3	even	12		2100.2.bi.m.101.6	yes	16
35.17	even	12		2100.2.bi.l.101.3	✓	16
35.24	odd	6	inner	2100.2.bo.i.1949.12		32
105.17	odd	12		2100.2.bi.l.101.7	yes	16
105.38	odd	12		2100.2.bi.m.101.2	yes	16
105.59	even	6	inner	2100.2.bo.i.1949.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.3	✓	16	35.17	even	12
2100.2.bi.l.101.7	yes	16	105.17	odd	12
2100.2.bi.l.1601.3	yes	16	15.2	even	4
2100.2.bi.l.1601.7	yes	16	5.2	odd	4
2100.2.bi.m.101.2	yes	16	105.38	odd	12
2100.2.bi.m.101.6	yes	16	35.3	even	12
2100.2.bi.m.1601.2	yes	16	5.3	odd	4
2100.2.bi.m.1601.6	yes	16	15.8	even	4
2100.2.bo.i.1349.3		32	1.1	even	1	trivial
2100.2.bo.i.1349.5		32	15.14	odd	2	inner
2100.2.bo.i.1349.12		32	3.2	odd	2	inner
2100.2.bo.i.1349.14		32	5.4	even	2	inner
2100.2.bo.i.1949.3		32	105.59	even	6	inner
2100.2.bo.i.1949.5		32	7.3	odd	6	inner
2100.2.bo.i.1949.12		32	35.24	odd	6	inner
2100.2.bo.i.1949.14		32	21.17	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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bo (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.56849 + 0.734734i) q^{3} +(0.156656 + 2.64111i) q^{7} +(1.92033 - 2.30485i) q^{9} +O(q^{10})\)	\(q+(-1.56849 + 0.734734i) q^{3} +(0.156656 + 2.64111i) q^{7} +(1.92033 - 2.30485i) q^{9} +(4.92449 - 2.84316i) q^{11} -1.43616 q^{13} +(2.81310 - 1.62414i) q^{17} +(-5.43583 - 3.13838i) q^{19} +(-2.18623 - 4.02746i) q^{21} +(0.510633 - 0.884443i) q^{23} +(-1.31858 + 5.02607i) q^{27} -4.95680i q^{29} +(-2.28384 + 1.31858i) q^{31} +(-5.63506 + 8.07766i) q^{33} +(-7.88253 - 4.55098i) q^{37} +(2.25260 - 1.05519i) q^{39} +0.203153 q^{41} -3.91245i q^{43} +(9.98660 + 5.76577i) q^{47} +(-6.95092 + 0.827492i) q^{49} +(-3.21901 + 4.61434i) q^{51} +(-5.32156 - 9.21721i) q^{53} +(10.8319 + 0.928633i) q^{57} +(-0.739701 - 1.28120i) q^{59} +(7.62492 + 4.40225i) q^{61} +(6.38819 + 4.71074i) q^{63} +(4.05487 - 2.34108i) q^{67} +(-0.151094 + 1.76242i) q^{69} +1.08138i q^{71} +(-4.51983 - 7.82857i) q^{73} +(8.28054 + 12.5607i) q^{77} +(5.80981 - 10.0629i) q^{79} +(-1.62464 - 8.85215i) q^{81} +10.1512i q^{83} +(3.64193 + 7.77471i) q^{87} +(7.53465 - 13.0504i) q^{89} +(-0.224982 - 3.79304i) q^{91} +(2.61339 - 3.74619i) q^{93} +10.5540 q^{97} +(2.90362 - 16.8100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 18 q^{9}+O(q^{10}) \) 32 * q + 18 * q^9	\( 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) \) 32 * q + 18 * q^9 + 36 * q^19 - 22 * q^21 - 36 * q^31 - 24 * q^39 + 36 * q^49 - 2 * q^51 + 72 * q^61 + 14 * q^81 + 40 * q^91 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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