LMFDB - Embedded newform 2100.2.bi.l.101.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(101,2100)]

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, 0, 1]))

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

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

chi := DirichletCharacter("2100.101");

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.bi (of order $6$, degree $2$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 9 x^{14} - 18 x^{13} + 32 x^{12} - 36 x^{11} + 51 x^{9} - 167 x^{8} + 153 x^{7} + \cdots + 6561 $ x^16 - 3x^15 + 9x^14 - 18x^13 + 32x^12 - 36x^11 + 51x^9 - 167x^8 + 153x^7 - 972x^5 + 2592x^4 - 4374x^3 + 6561x^2 - 6561*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.7
Root			$-0.734734 - 1.56849i$ of defining polynomial
Character	$\chi$	$=$	2100.101
Dual form			2100.2.bi.l.1601.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.734734 - 1.56849i) q^{3} +(-2.64111 - 0.156656i) q^{7} +(-1.92033 - 2.30485i) q^{9} +O(q^{10})$	\(q+(0.734734 - 1.56849i) q^{3} +(-2.64111 - 0.156656i) q^{7} +(-1.92033 - 2.30485i) q^{9} +(4.92449 + 2.84316i) q^{11} -1.43616i q^{13} +(1.62414 - 2.81310i) q^{17} +(5.43583 - 3.13838i) q^{19} +(-2.18623 + 4.02746i) q^{21} +(-0.884443 + 0.510633i) q^{23} +(-5.02607 + 1.31858i) q^{27} -4.95680i q^{29} +(-2.28384 - 1.31858i) q^{31} +(8.07766 - 5.63506i) q^{33} +(4.55098 + 7.88253i) q^{37} +(-2.25260 - 1.05519i) q^{39} +0.203153 q^{41} -3.91245 q^{43} +(-5.76577 - 9.98660i) q^{47} +(6.95092 + 0.827492i) q^{49} +(-3.21901 - 4.61434i) q^{51} +(-9.21721 - 5.32156i) q^{53} +(-0.928633 - 10.8319i) q^{57} +(0.739701 - 1.28120i) q^{59} +(7.62492 - 4.40225i) q^{61} +(4.71074 + 6.38819i) q^{63} +(2.34108 - 4.05487i) q^{67} +(0.151094 + 1.76242i) q^{69} -1.08138i q^{71} +(-7.82857 - 4.51983i) q^{73} +(-12.5607 - 8.28054i) q^{77} +(-5.80981 - 10.0629i) q^{79} +(-1.62464 + 8.85215i) q^{81} +10.1512 q^{83} +(-7.77471 - 3.64193i) q^{87} +(-7.53465 - 13.0504i) q^{89} +(-0.224982 + 3.79304i) q^{91} +(-3.74619 + 2.61339i) q^{93} -10.5540i q^{97} +(-2.90362 - 16.8100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9}+O(q^{10}) $ 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9	$ 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9} - 18 q^{19} - 11 q^{21} - 18 q^{31} - 12 q^{33} + 6 q^{37} + 12 q^{39} - 4 q^{43} - 18 q^{49} - q^{51} - 6 q^{57} + 36 q^{61} - 19 q^{63} - 30 q^{67} - 54 q^{73} + 7 q^{81} - 81 q^{87} + 20 q^{91} + 34 q^{93} - 30 q^{99}+O(q^{100}) $ 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9 - 18 * q^19 - 11 * q^21 - 18 * q^31 - 12 * q^33 + 6 * q^37 + 12 * q^39 - 4 * q^43 - 18 * q^49 - q^51 - 6 * q^57 + 36 * q^61 - 19 * q^63 - 30 * q^67 - 54 * q^73 + 7 * q^81 - 81 * q^87 + 20 * q^91 + 34 * q^93 - 30 * 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
$3$	0.734734	−	1.56849i	0.424199	−	0.905569i
$3$	0.734734	−	1.56849i	0.424199	−	0.905569i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.64111	−	0.156656i	−0.998246	−	0.0592104i
$7$	−2.64111	−	0.156656i	−0.998246	−	0.0592104i
$8$		0			0
$9$	−1.92033	−	2.30485i	−0.640111	−	0.768282i
$10$		0			0
$11$	4.92449	+	2.84316i	1.48479	+	0.857244i	0.999850	−	0.0173038i	$-0.00550823\pi$
$11$	4.92449	+	2.84316i	1.48479	+	0.857244i	0.484940	+	0.874548i	$0.338842\pi$
$12$		0			0
$13$		−	1.43616i		−	0.398318i	−0.979967	−	0.199159i	$-0.936179\pi$
$13$		−	1.43616i		−	0.398318i	0.979967	−	0.199159i	$-0.0638210\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.62414	−	2.81310i	0.393913	−	0.682277i	−0.599049	−	0.800712i	$-0.704455\pi$
$17$	1.62414	−	2.81310i	0.393913	−	0.682277i	0.992962	+	0.118435i	$0.0377879\pi$
$18$		0			0
$19$	5.43583	−	3.13838i	1.24707	−	0.719994i	0.276543	−	0.961002i	$-0.410811\pi$
$19$	5.43583	−	3.13838i	1.24707	−	0.719994i	0.970523	+	0.241008i	$0.0774779\pi$
$20$		0			0
$21$	−2.18623	+	4.02746i	−0.477074	+	0.878863i
$22$		0			0
$23$	−0.884443	+	0.510633i	−0.184419	+	0.106474i	−0.589367	−	0.807865i	$-0.700623\pi$
$23$	−0.884443	+	0.510633i	−0.184419	+	0.106474i	0.404948	+	0.914340i	$0.367290\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.02607	+	1.31858i	−0.967267	+	0.253760i
$28$		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	0.280681	−	0.959801i	$-0.409440\pi$
$31$	−2.28384	−	1.31858i	−0.410190	−	0.236823i	−0.690871	+	0.722978i	$0.742773\pi$
$32$		0			0
$33$	8.07766	−	5.63506i	1.40614	−	0.980938i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.55098	+	7.88253i	0.748176	+	1.29588i	0.948696	+	0.316190i	$0.102404\pi$
$37$	4.55098	+	7.88253i	0.748176	+	1.29588i	−0.200520	+	0.979690i	$0.564263\pi$
$38$		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
$43$	−3.91245			−0.596642			−0.298321	−	0.954466i	$-0.596427\pi$
$43$	−3.91245			−0.596642			−0.298321	+	0.954466i	$0.596427\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.76577	−	9.98660i	−0.841024	−	1.45670i	−0.889030	−	0.457849i	$-0.848620\pi$
$47$	−5.76577	−	9.98660i	−0.841024	−	1.45670i	0.0480062	−	0.998847i	$-0.484713\pi$
$48$		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
$53$	−9.21721	−	5.32156i	−1.26608	−	0.730972i	−0.291837	−	0.956468i	$-0.594266\pi$
$53$	−9.21721	−	5.32156i	−1.26608	−	0.730972i	−0.974244	+	0.225496i	$0.927600\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.928633	−	10.8319i	−0.123000	−	1.43472i
$58$		0			0
$59$	0.739701	−	1.28120i	0.0963009	−	0.166798i	−0.813850	−	0.581075i	$-0.802632\pi$
$59$	0.739701	−	1.28120i	0.0963009	−	0.166798i	0.910151	+	0.414277i	$0.135966\pi$
$60$		0			0
$61$	7.62492	−	4.40225i	0.976271	−	0.563650i	0.0751289	−	0.997174i	$-0.476063\pi$
$61$	7.62492	−	4.40225i	0.976271	−	0.563650i	0.901142	+	0.433523i	$0.142730\pi$
$62$		0			0
$63$	4.71074	+	6.38819i	0.593498	+	0.804836i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.34108	−	4.05487i	0.286008	−	0.495381i	−0.686845	−	0.726804i	$-0.741005\pi$
$67$	2.34108	−	4.05487i	0.286008	−	0.495381i	0.972853	+	0.231423i	$0.0743382\pi$
$68$		0			0
$69$	0.151094	+	1.76242i	0.0181896	+	0.212171i
$70$		0			0
$71$		−	1.08138i		−	0.128336i	−0.997939	−	0.0641680i	$-0.979561\pi$
$71$		−	1.08138i		−	0.128336i	0.997939	−	0.0641680i	$-0.0204394\pi$
$72$		0			0
$73$	−7.82857	−	4.51983i	−0.916265	−	0.529006i	−0.0338235	−	0.999428i	$-0.510768\pi$
$73$	−7.82857	−	4.51983i	−0.916265	−	0.529006i	−0.882442	+	0.470422i	$0.844102\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.5607	−	8.28054i	−1.43143	−	0.943655i
$78$		0			0
$79$	−5.80981	−	10.0629i	−0.653655	−	1.13216i	−0.982229	−	0.187685i	$-0.939902\pi$
$79$	−5.80981	−	10.0629i	−0.653655	−	1.13216i	0.328575	−	0.944478i	$-0.393432\pi$
$80$		0			0
$81$	−1.62464	+	8.85215i	−0.180516	+	0.983572i
$82$		0			0
$83$	10.1512			1.11424			0.557118	−	0.830433i	$-0.311907\pi$
$83$	10.1512			1.11424			0.557118	+	0.830433i	$0.311907\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−7.77471	−	3.64193i	−0.833536	−	0.390456i
$88$		0			0
$89$	−7.53465	−	13.0504i	−0.798672	−	1.38334i	−0.920481	−	0.390787i	$-0.872203\pi$
$89$	−7.53465	−	13.0504i	−0.798672	−	1.38334i	0.121810	−	0.992553i	$-0.461130\pi$
$90$		0			0
$91$	−0.224982	+	3.79304i	−0.0235846	+	0.397619i
$92$		0			0
$93$	−3.74619	+	2.61339i	−0.388462	+	0.270995i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	10.5540i		−	1.07159i	−0.844347	−	0.535797i	$-0.820011\pi$
$97$		−	10.5540i		−	1.07159i	0.844347	−	0.535797i	$-0.179989\pi$
$98$		0			0
$99$	−2.90362	−	16.8100i	−0.291825	−	1.68947i
$100$		0			0
$101$	−7.49149	+	12.9756i	−0.745431	+	1.29112i	0.204562	+	0.978854i	$0.434423\pi$
$101$	−7.49149	+	12.9756i	−0.745431	+	1.29112i	−0.949993	+	0.312271i	$0.898910\pi$
$102$		0			0
$103$	3.43283	−	1.98195i	0.338247	−	0.195287i	−0.321249	−	0.946995i	$-0.604103\pi$
$103$	3.43283	−	1.98195i	0.338247	−	0.195287i	0.659497	+	0.751708i	$0.270769\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.28071	−	4.78087i	0.800526	−	0.462184i	−0.0431288	−	0.999070i	$-0.513733\pi$
$107$	8.28071	−	4.78087i	0.800526	−	0.462184i	0.843655	+	0.536885i	$0.180399\pi$
$108$		0			0
$109$	−7.03847	+	12.1910i	−0.674163	+	1.16769i	0.302549	+	0.953134i	$0.402162\pi$
$109$	−7.03847	+	12.1910i	−0.674163	+	1.16769i	−0.976713	+	0.214551i	$0.931171\pi$
$110$		0			0
$111$	15.7074	−	1.34661i	1.49088	−	0.127815i
$112$		0			0
$113$		−	5.91796i		−	0.556715i	−0.960478	−	0.278357i	$-0.910210\pi$
$113$		−	5.91796i		−	0.556715i	0.960478	−	0.278357i	$-0.0897900\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.31012	+	2.75790i	−0.306021	+	0.254968i
$118$		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
$123$	0.149263	−	0.318643i	0.0134586	−	0.0287311i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.35916			0.741756			0.370878	−	0.928682i	$-0.379057\pi$
$127$	8.35916			0.741756			0.370878	+	0.928682i	$0.379057\pi$
$128$		0			0
$129$	−2.87461	+	6.13664i	−0.253095	+	0.540301i
$130$		0			0
$131$	8.27436	+	14.3316i	0.722934	+	1.25216i	0.959819	+	0.280620i	$0.0905402\pi$
$131$	8.27436	+	14.3316i	0.722934	+	1.25216i	−0.236885	+	0.971538i	$0.576126\pi$
$132$		0			0
$133$	−14.8483	+	7.43725i	−1.28751	+	0.644891i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.96454	−	5.17568i	−0.765892	−	0.442188i	0.0655150	−	0.997852i	$-0.479131\pi$
$137$	−8.96454	−	5.17568i	−0.765892	−	0.442188i	−0.831407	+	0.555663i	$0.812464\pi$
$138$		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
$143$	4.08321	−	7.07233i	0.341455	−	0.591418i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.40499	−	10.2945i	0.528274	−	0.849074i
$148$		0			0
$149$	−3.71301	+	2.14370i	−0.304181	+	0.175619i	−0.644320	−	0.764756i	$-0.722859\pi$
$149$	−3.71301	+	2.14370i	−0.304181	+	0.175619i	0.340138	+	0.940375i	$0.389526\pi$
$150$		0			0
$151$	6.06606	−	10.5067i	0.493649	−	0.855025i	−0.506324	−	0.862343i	$-0.668996\pi$
$151$	6.06606	−	10.5067i	0.493649	−	0.855025i	0.999973	+	0.00731794i	$0.00232939\pi$
$152$		0			0
$153$	−9.60266	+	1.65868i	−0.776329	+	0.134097i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	10.7317	+	6.19593i	0.856480	+	0.494489i	0.862832	−	0.505491i	$-0.168689\pi$
$157$	10.7317	+	6.19593i	0.856480	+	0.494489i	−0.00635192	+	0.999980i	$0.502022\pi$
$158$		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
$163$	10.2811	+	17.8074i	0.805279	+	1.39478i	0.916103	+	0.400944i	$0.131318\pi$
$163$	10.2811	+	17.8074i	0.805279	+	1.39478i	−0.110824	+	0.993840i	$0.535349\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.95678			−0.306185			−0.153093	−	0.988212i	$-0.548923\pi$
$167$	−3.95678			−0.306185			−0.153093	+	0.988212i	$0.548923\pi$
$168$		0			0
$169$	10.9375			0.841343
$170$		0			0
$171$	−17.6721	−	6.50203i	−1.35142	−	0.497223i
$172$		0			0
$173$	−6.50547	−	11.2678i	−0.494602	−	0.856675i	0.505379	−	0.862898i	$-0.331353\pi$
$173$	−6.50547	−	11.2678i	−0.494602	−	0.856675i	−0.999981	+	0.00622220i	$0.998019\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.46607	−	2.10156i	−0.110196	−	0.157963i
$178$		0			0
$179$	−20.2033	−	11.6644i	−1.51007	−	0.871837i	−0.999931	−	0.0117426i	$-0.996262\pi$
$179$	−20.2033	−	11.6644i	−1.51007	−	0.871837i	−0.510135	−	0.860094i	$-0.670405\pi$
$180$		0			0
$181$		−	0.770872i		−	0.0572984i	−0.999590	−	0.0286492i	$-0.990879\pi$
$181$		−	0.770872i		−	0.0572984i	0.999590	−	0.0286492i	$-0.00912058\pi$
$182$		0			0
$183$	−1.30261	−	15.1941i	−0.0962915	−	1.12318i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	15.9962	−	9.23539i	1.16976	−	0.675359i
$188$		0			0
$189$	13.4810	−	2.69514i	0.980595	−	0.196043i
$190$		0			0
$191$	−2.02156	+	1.16715i	−0.146275	+	0.0844517i	−0.571351	−	0.820706i	$-0.693581\pi$
$191$	−2.02156	+	1.16715i	−0.146275	+	0.0844517i	0.425076	+	0.905157i	$0.360247\pi$
$192$		0			0
$193$	0.351009	−	0.607965i	0.0252662	−	0.0437623i	−0.853116	−	0.521722i	$-0.825290\pi$
$193$	0.351009	−	0.607965i	0.0252662	−	0.0437623i	0.878382	+	0.477959i	$0.158623\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			19.3932i			1.38171i	0.722993	+	0.690855i	$0.242766\pi$
$197$			19.3932i			1.38171i	−0.722993	+	0.690855i	$0.757234\pi$
$198$		0			0
$199$	16.0457	+	9.26397i	1.13745	+	0.656706i	0.945797	−	0.324758i	$-0.105283\pi$
$199$	16.0457	+	9.26397i	1.13745	+	0.656706i	0.191650	+	0.981463i	$0.438616\pi$
$200$		0			0
$201$	−4.63996	−	6.65121i	−0.327277	−	0.469140i
$202$		0			0
$203$	−0.776514	+	13.0915i	−0.0545006	+	0.918841i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.87536	+	1.05792i	0.199851	+	0.0735305i
$208$		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
$213$	−1.69613	−	0.794525i	−0.116217	−	0.0544400i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.82532	+	3.84028i	0.395448	+	0.260696i
$218$		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
$223$		−	14.7072i		−	0.984868i	−0.870350	−	0.492434i	$-0.836107\pi$
$223$		−	14.7072i		−	0.984868i	0.870350	−	0.492434i	$-0.163893\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.47751	−	14.6835i	0.562672	−	0.974577i	−0.434590	−	0.900628i	$-0.643107\pi$
$227$	8.47751	−	14.6835i	0.562672	−	0.974577i	0.997262	−	0.0739481i	$-0.0235599\pi$
$228$		0			0
$229$	−19.4690	+	11.2404i	−1.28655	+	0.742789i	−0.978037	−	0.208432i	$-0.933164\pi$
$229$	−19.4690	+	11.2404i	−1.28655	+	0.742789i	−0.308511	+	0.951221i	$0.599831\pi$
$230$		0			0
$231$	−22.2167	+	13.6174i	−1.46175	+	0.895959i
$232$		0			0
$233$	−22.2249	+	12.8315i	−1.45600	+	0.840621i	−0.998811	−	0.0487486i	$-0.984477\pi$
$233$	−22.2249	+	12.8315i	−1.45600	+	0.840621i	−0.457188	+	0.889370i	$0.651143\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−20.0522	+	1.71910i	−1.30253	+	0.111667i
$238$		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	0.717526	−	0.696532i	$-0.245275\pi$
$241$	7.34408	+	4.24011i	0.473074	+	0.273129i	−0.244452	+	0.969661i	$0.578608\pi$
$242$		0			0
$243$	12.6908	+	9.05221i	0.814118	+	0.580700i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.50720	−	7.80670i	−0.286786	−	0.496729i
$248$		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
$253$	−5.80724			−0.365098
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.66857	+	4.62211i	0.166461	+	0.288319i	0.937173	−	0.348864i	$-0.113433\pi$
$257$	2.66857	+	4.62211i	0.166461	+	0.288319i	−0.770712	+	0.637184i	$0.780099\pi$
$258$		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
$263$	13.2573	+	7.65408i	0.817478	+	0.471971i	0.849546	−	0.527515i	$-0.176876\pi$
$263$	13.2573	+	7.65408i	0.817478	+	0.471971i	−0.0320683	+	0.999486i	$0.510209\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−26.0054	+	2.22947i	−1.59151	+	0.136441i
$268$		0			0
$269$	−3.50096	+	6.06384i	−0.213457	+	0.369719i	−0.952794	−	0.303617i	$-0.901806\pi$
$269$	−3.50096	+	6.06384i	−0.213457	+	0.369719i	0.739337	+	0.673336i	$0.235139\pi$
$270$		0			0
$271$	11.1722	−	6.45029i	0.678665	−	0.391827i	−0.120687	−	0.992691i	$-0.538510\pi$
$271$	11.1722	−	6.45029i	0.678665	−	0.391827i	0.799352	+	0.600863i	$0.205176\pi$
$272$		0			0
$273$	5.78405	+	3.13976i	0.350067	+	0.190027i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.56717	+	9.64261i	−0.334499	+	0.579369i	−0.983388	−	0.181514i	$-0.941900\pi$
$277$	−5.56717	+	9.64261i	−0.334499	+	0.579369i	0.648890	+	0.760882i	$0.275234\pi$
$278$		0			0
$279$	1.34662	+	7.79602i	0.0806200	+	0.466735i
$280$		0			0
$281$		−	22.5391i		−	1.34457i	−0.740291	−	0.672286i	$-0.765312\pi$
$281$		−	22.5391i		−	1.34457i	0.740291	−	0.672286i	$-0.234688\pi$
$282$		0			0
$283$	−15.8420	−	9.14640i	−0.941710	−	0.543697i	−0.0512144	−	0.998688i	$-0.516309\pi$
$283$	−15.8420	−	9.14640i	−0.941710	−	0.543697i	−0.890496	+	0.454991i	$0.849643\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.536549	−	0.0318251i	−0.0316715	−	0.00187858i
$288$		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
$293$	17.0413			0.995566			0.497783	−	0.867302i	$-0.334148\pi$
$293$	17.0413			0.995566			0.497783	+	0.867302i	$0.334148\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−28.4997	−	7.79657i	−1.65372	−	0.452403i
$298$		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
$303$	14.8479	+	21.2840i	0.852992	+	1.22273i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			16.9629i			0.968124i	0.875034	+	0.484062i	$0.160839\pi$
$307$			16.9629i			0.968124i	−0.875034	+	0.484062i	$0.839161\pi$
$308$		0			0
$309$	−0.586450	−	6.84058i	−0.0333620	−	0.389147i
$310$		0			0
$311$	16.7519	−	29.0151i	0.949911	−	1.64529i	0.204305	−	0.978907i	$-0.434507\pi$
$311$	16.7519	−	29.0151i	0.949911	−	1.64529i	0.745606	−	0.666387i	$-0.232160\pi$
$312$		0			0
$313$	5.92768	−	3.42235i	0.335052	−	0.193443i	−0.323030	−	0.946389i	$-0.604701\pi$
$313$	5.92768	−	3.42235i	0.335052	−	0.193443i	0.658082	+	0.752946i	$0.271368\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.2908	−	6.51876i	0.634156	−	0.366130i	−0.148204	−	0.988957i	$-0.547349\pi$
$317$	11.2908	−	6.51876i	0.634156	−	0.366130i	0.782360	+	0.622827i	$0.214016\pi$
$318$		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
$323$		−	20.3887i		−	1.13446i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	13.9501	+	19.9969i	0.771440	+	1.10583i
$328$		0			0
$329$	13.6636	+	27.2790i	0.753297	+	1.50394i
$330$		0			0
$331$	3.35727	+	5.81496i	0.184532	+	0.319619i	0.943419	−	0.331604i	$-0.107590\pi$
$331$	3.35727	+	5.81496i	0.184532	+	0.319619i	−0.758887	+	0.651223i	$0.774256\pi$
$332$		0			0
$333$	9.42863	−	25.6264i	0.516686	−	1.40432i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0783052			0.00426556			0.00213278	−	0.999998i	$-0.499321\pi$
$337$	0.0783052			0.00426556			0.00213278	+	0.999998i	$0.499321\pi$
$338$		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
$343$	−18.2285	−	3.27440i	−0.984247	−	0.176801i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	24.1913	+	13.9669i	1.29866	+	0.749780i	0.980172	−	0.198148i	$-0.0634927\pi$
$347$	24.1913	+	13.9669i	1.29866	+	0.749780i	0.318485	+	0.947928i	$0.396826\pi$
$348$		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
$353$	−13.8890	+	24.0565i	−0.739239	+	1.28040i	0.213600	+	0.976921i	$0.431481\pi$
$353$	−13.8890	+	24.0565i	−0.739239	+	1.28040i	−0.952839	+	0.303477i	$0.901852\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	7.77890	+	12.6912i	0.411703	+	0.671692i
$358$		0			0
$359$	−24.6446	+	14.2286i	−1.30069	+	0.750954i	−0.980523	−	0.196406i	$-0.937073\pi$
$359$	−24.6446	+	14.2286i	−1.30069	+	0.750954i	−0.320168	+	0.947361i	$0.603740\pi$
$360$		0			0
$361$	10.1989	−	17.6650i	0.536782	−	0.929734i
$362$		0			0
$363$	36.8168	−	3.15634i	1.93238	−	0.165665i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	13.5818	+	7.84147i	0.708966	+	0.409321i	0.810678	−	0.585492i	$-0.199099\pi$
$367$	13.5818	+	7.84147i	0.708966	+	0.409321i	−0.101712	+	0.994814i	$0.532432\pi$
$368$		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
$373$	1.31769	+	2.28231i	0.0682274	+	0.118173i	0.898121	−	0.439748i	$-0.144932\pi$
$373$	1.31769	+	2.28231i	0.0682274	+	0.118173i	−0.829894	+	0.557922i	$0.811599\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.11874			−0.366634
$378$		0			0
$379$	26.3684			1.35445			0.677227	−	0.735774i	$-0.263181\pi$
$379$	26.3684			1.35445			0.677227	+	0.735774i	$0.263181\pi$
$380$		0			0
$381$	6.14176	−	13.1113i	0.314652	−	0.671711i
$382$		0			0
$383$	8.95565	+	15.5116i	0.457612	+	0.792607i	0.998834	−	0.0482722i	$-0.0153715\pi$
$383$	8.95565	+	15.5116i	0.457612	+	0.792607i	−0.541222	+	0.840880i	$0.682038\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.51320	+	9.01759i	0.381917	+	0.458390i
$388$		0			0
$389$	17.6243	+	10.1754i	0.893590	+	0.515914i	0.875115	−	0.483915i	$-0.160786\pi$
$389$	17.6243	+	10.1754i	0.893590	+	0.515914i	0.0184749	+	0.999829i	$0.494119\pi$
$390$		0			0
$391$			3.31737i			0.167767i
$392$		0			0
$393$	28.5585	−	2.44835i	1.44058	−	0.123503i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	14.3014	−	8.25692i	0.717767	−	0.414403i	−0.0961632	−	0.995366i	$-0.530657\pi$
$397$	14.3014	−	8.25692i	0.717767	−	0.414403i	0.813930	+	0.580963i	$0.197324\pi$
$398$		0			0
$399$	0.755733	+	28.7538i	0.0378340	+	1.43949i
$400$		0			0
$401$	−26.0643	+	15.0482i	−1.30159	+	0.751473i	−0.980677	−	0.195636i	$-0.937323\pi$
$401$	−26.0643	+	15.0482i	−1.30159	+	0.751473i	−0.320912	+	0.947109i	$0.603990\pi$
$402$		0			0
$403$	−1.89368	+	3.27995i	−0.0943310	+	0.163386i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			51.7566i			2.56548i
$408$		0			0
$409$	19.1623	+	11.0634i	0.947515	+	0.547048i	0.892308	−	0.451427i	$-0.149085\pi$
$409$	19.1623	+	11.0634i	0.947515	+	0.547048i	0.0552067	+	0.998475i	$0.482418\pi$
$410$		0			0
$411$	−14.7046	+	10.2581i	−0.725322	+	0.505993i
$412$		0			0
$413$	−2.15434	+	3.26791i	−0.106008	+	0.160803i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	14.3909	+	6.74117i	0.704724	+	0.330116i
$418$		0			0
$419$	24.3632			1.19022			0.595111	−	0.803643i	$-0.297108\pi$
$419$	24.3632			1.19022			0.595111	+	0.803643i	$0.297108\pi$
$420$		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
$423$	−11.9454	+	32.4668i	−0.580805	+	1.57859i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−20.8279	+	10.4323i	−1.00793	+	0.504856i
$428$		0			0
$429$	−8.09282	−	11.6008i	−0.390725	−	0.560090i
$430$		0			0
$431$	−18.2369	−	10.5291i	−0.878439	−	0.507167i	−0.00829574	−	0.999966i	$-0.502641\pi$
$431$	−18.2369	−	10.5291i	−0.878439	−	0.507167i	−0.870143	+	0.492798i	$0.835974\pi$
$432$		0			0
$433$		−	2.13627i		−	0.102663i	−0.998682	−	0.0513313i	$-0.983654\pi$
$433$		−	2.13627i		−	0.102663i	0.998682	−	0.0513313i	$-0.0163465\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.20512	+	5.55144i	−0.153322	+	0.265561i
$438$		0			0
$439$	13.0942	−	7.55996i	0.624954	−	0.360817i	−0.153841	−	0.988096i	$-0.549164\pi$
$439$	13.0942	−	7.55996i	0.624954	−	0.360817i	0.778795	+	0.627278i	$0.215831\pi$
$440$		0			0
$441$	−11.4408	−	17.6099i	−0.544802	−	0.838565i
$442$		0			0
$443$	12.8040	−	7.39238i	0.608335	−	0.351223i	−0.163978	−	0.986464i	$-0.552433\pi$
$443$	12.8040	−	7.39238i	0.608335	−	0.351223i	0.772314	+	0.635241i	$0.219099\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.634313	+	7.39887i	0.0300020	+	0.349955i
$448$		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
$453$	−12.0228	−	17.2342i	−0.564879	−	0.809734i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.19577	+	10.7314i	0.289826	+	0.501993i	0.973768	−	0.227543i	$-0.0730693\pi$
$457$	6.19577	+	10.7314i	0.289826	+	0.501993i	−0.683942	+	0.729536i	$0.739736\pi$
$458$		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
$463$	−12.8360			−0.596542			−0.298271	−	0.954481i	$-0.596410\pi$
$463$	−12.8360			−0.596542			−0.298271	+	0.954481i	$0.596410\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.9741	+	25.9359i	0.692918	+	1.20017i	0.970878	+	0.239576i	$0.0770086\pi$
$467$	14.9741	+	25.9359i	0.692918	+	1.20017i	−0.277959	+	0.960593i	$0.589658\pi$
$468$		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
$473$	−19.2668	−	11.1237i	−0.885889	−	0.511468i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	5.43473	+	31.4634i	0.248839	+	1.44061i
$478$		0			0
$479$	−10.0585	+	17.4218i	−0.459584	+	0.796023i	−0.998939	−	0.0460557i	$-0.985335\pi$
$479$	−10.0585	+	17.4218i	−0.459584	+	0.796023i	0.539355	+	0.842079i	$0.318668\pi$
$480$		0			0
$481$	11.3205	−	6.53591i	0.516172	−	0.298012i
$482$		0			0
$483$	−0.122962	−	4.67842i	−0.00559498	−	0.212875i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−12.4697	+	21.5981i	−0.565055	+	0.978704i	0.431989	+	0.901879i	$0.357812\pi$
$487$	−12.4697	+	21.5981i	−0.565055	+	0.978704i	−0.997045	+	0.0768256i	$0.975522\pi$
$488$		0			0
$489$	35.4847	−	3.04214i	1.60467	−	0.137570i
$490$		0			0
$491$		−	11.2524i		−	0.507814i	−0.967229	−	0.253907i	$-0.918284\pi$
$491$		−	11.2524i		−	0.507814i	0.967229	−	0.253907i	$-0.0817157\pi$
$492$		0			0
$493$	−13.9440	−	8.05057i	−0.628006	−	0.362579i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.169405	+	2.85604i	−0.00759883	+	0.128111i
$498$		0			0
$499$	2.84476	+	4.92727i	0.127349	+	0.220575i	0.922649	−	0.385642i	$-0.126020\pi$
$499$	2.84476	+	4.92727i	0.127349	+	0.220575i	−0.795300	+	0.606216i	$0.792687\pi$
$500$		0			0
$501$	−2.90718	+	6.20618i	−0.129883	+	0.277272i
$502$		0			0
$503$	22.7975			1.01649			0.508245	−	0.861212i	$-0.330294\pi$
$503$	22.7975			1.01649			0.508245	+	0.861212i	$0.330294\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	8.03612	−	17.1553i	0.356897	−	0.761894i
$508$		0			0
$509$	8.17913	+	14.1667i	0.362534	+	0.627927i	0.988377	−	0.152022i	$-0.0485785\pi$
$509$	8.17913	+	14.1667i	0.362534	+	0.627927i	−0.625843	+	0.779949i	$0.715245\pi$
$510$		0			0
$511$	19.9681	+	13.1638i	0.883335	+	0.582330i
$512$		0			0
$513$	−23.1827	+	22.9413i	−1.02354	+	1.01288i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	65.5719i		−	2.88385i
$518$		0			0
$519$	−22.4532	+	1.92494i	−0.985588	+	0.0844955i
$520$		0			0
$521$	−8.67177	+	15.0199i	−0.379917	+	0.658036i	−0.991050	−	0.133492i	$-0.957381\pi$
$521$	−8.67177	+	15.0199i	−0.379917	+	0.658036i	0.611133	+	0.791528i	$0.290714\pi$
$522$		0			0
$523$	11.1701	−	6.44905i	0.488433	−	0.281997i	−0.235491	−	0.971877i	$-0.575670\pi$
$523$	11.1701	−	6.44905i	0.488433	−	0.281997i	0.723924	+	0.689879i	$0.242336\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.41858	+	4.28312i	−0.323158	+	0.186576i
$528$		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
$533$		−	0.291759i		−	0.0126375i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−33.1395	+	23.1185i	−1.43008	+	0.997637i
$538$		0			0
$539$	31.8770	+	23.8375i	1.37304	+	1.02675i
$540$		0			0
$541$	−2.22594	−	3.85543i	−0.0957004	−	0.165758i	0.814200	−	0.580584i	$-0.197176\pi$
$541$	−2.22594	−	3.85543i	−0.0957004	−	0.165758i	−0.909901	+	0.414826i	$0.863842\pi$
$542$		0			0
$543$	−1.20911	−	0.566385i	−0.0518877	−	0.0243059i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−5.58754			−0.238906			−0.119453	−	0.992840i	$-0.538114\pi$
$547$	−5.58754			−0.238906			−0.119453	+	0.992840i	$0.538114\pi$
$548$		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
$553$	13.7679	+	27.4873i	0.585472	+	1.16888i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.1594	+	10.4844i	0.769440	+	0.444236i	0.832675	−	0.553762i	$-0.186808\pi$
$557$	18.1594	+	10.4844i	0.769440	+	0.444236i	−0.0632348	+	0.997999i	$0.520142\pi$
$558$		0			0
$559$			5.61888i			0.237653i
$560$		0			0
$561$	−2.73271	−	31.8754i	−0.115375	−	1.34578i
$562$		0			0
$563$	6.14487	−	10.6432i	0.258975	−	0.448559i	−0.706992	−	0.707221i	$-0.749948\pi$
$563$	6.14487	−	10.6432i	0.258975	−	0.448559i	0.965968	+	0.258663i	$0.0832818\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	5.67760	−	23.1250i	0.238437	−	0.971158i
$568$		0			0
$569$	−37.1989	+	21.4768i	−1.55946	+	0.900355i	−0.562153	+	0.827033i	$0.690027\pi$
$569$	−37.1989	+	21.4768i	−1.55946	+	0.900355i	−0.997308	+	0.0733217i	$0.976640\pi$
$570$		0			0
$571$	−3.24932	+	5.62799i	−0.135980	+	0.235524i	−0.925971	−	0.377594i	$-0.876752\pi$
$571$	−3.24932	+	5.62799i	−0.135980	+	0.235524i	0.789991	+	0.613118i	$0.210085\pi$
$572$		0			0
$573$	0.345353	+	4.02834i	0.0144273	+	0.168286i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.15551	−	0.667135i	−0.0481046	−	0.0277732i	0.475755	−	0.879578i	$-0.342175\pi$
$577$	−1.15551	−	0.667135i	−0.0481046	−	0.0277732i	−0.523859	+	0.851805i	$0.675508\pi$
$578$		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
$583$	−30.2600	−	52.4119i	−1.25324	−	2.17068i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−20.5791			−0.849391			−0.424696	−	0.905336i	$-0.639619\pi$
$587$	−20.5791			−0.849391			−0.424696	+	0.905336i	$0.639619\pi$
$588$		0			0
$589$	−16.5528			−0.682046
$590$		0			0
$591$	30.4181	+	14.2489i	1.25123	+	0.586120i
$592$		0			0
$593$	4.83181	+	8.36894i	0.198419	+	0.343671i	0.948016	−	0.318223i	$-0.103086\pi$
$593$	4.83181	+	8.36894i	0.198419	+	0.343671i	−0.749597	+	0.661894i	$0.769753\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	26.3198	−	18.3610i	1.07720	−	0.751464i
$598$		0			0
$599$	−37.3444	−	21.5608i	−1.52585	−	0.880951i	−0.999530	−	0.0306663i	$-0.990237\pi$
$599$	−37.3444	−	21.5608i	−1.52585	−	0.880951i	−0.526323	−	0.850285i	$-0.676430\pi$
$600$		0			0
$601$			24.0495i			0.980999i	0.871442	+	0.490499i	$0.163186\pi$
$601$			24.0495i			0.980999i	−0.871442	+	0.490499i	$0.836814\pi$
$602$		0			0
$603$	−13.8415	+	2.39087i	−0.563670	+	0.0973636i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	6.56417	−	3.78982i	0.266431	−	0.153824i	−0.360833	−	0.932630i	$-0.617508\pi$
$607$	6.56417	−	3.78982i	0.266431	−	0.153824i	0.627265	+	0.778806i	$0.284174\pi$
$608$		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
$613$	−23.1986	+	40.1812i	−0.936983	+	1.62290i	−0.165925	+	0.986138i	$0.553061\pi$
$613$	−23.1986	+	40.1812i	−0.936983	+	1.62290i	−0.771058	+	0.636764i	$0.780272\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	1.36960i		−	0.0551380i	−0.999620	−	0.0275690i	$-0.991223\pi$
$617$		−	1.36960i		−	0.0551380i	0.999620	−	0.0275690i	$-0.00877660\pi$
$618$		0			0
$619$	−13.0178	−	7.51581i	−0.523228	−	0.302086i	0.215026	−	0.976608i	$-0.431016\pi$
$619$	−13.0178	−	7.51581i	−0.523228	−	0.302086i	−0.738255	+	0.674522i	$0.764350\pi$
$620$		0			0
$621$	3.77196	−	3.73268i	0.151364	−	0.149787i
$622$		0			0
$623$	17.8554	+	35.6479i	0.715362	+	1.42820i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	26.2238	−	55.9820i	1.04728	−	2.23571i
$628$		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
$633$	16.5711	−	35.3755i	0.658640	−	1.40605i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.18841	−	9.98260i	0.0470864	−	0.395525i
$638$		0			0
$639$	−2.49241	+	2.07661i	−0.0985983	+	0.0821493i
$640$		0			0
$641$	−10.9310	−	6.31100i	−0.431747	−	0.249270i	0.268343	−	0.963323i	$-0.413524\pi$
$641$	−10.9310	−	6.31100i	−0.431747	−	0.249270i	−0.700091	+	0.714054i	$0.746857\pi$
$642$		0			0
$643$			29.2411i			1.15316i	0.817042	+	0.576578i	$0.195612\pi$
$643$			29.2411i			1.15316i	−0.817042	+	0.576578i	$0.804388\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.33150	+	12.6985i	−0.288231	+	0.499231i	−0.973388	−	0.229165i	$-0.926400\pi$
$647$	−7.33150	+	12.6985i	−0.288231	+	0.499231i	0.685157	+	0.728396i	$0.259734\pi$
$648$		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
$653$	−27.7557	+	16.0248i	−1.08617	+	0.627098i	−0.932553	−	0.361033i	$-0.882424\pi$
$653$	−27.7557	+	16.0248i	−1.08617	+	0.627098i	−0.153613	+	0.988131i	$0.549091\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	4.61595	+	26.7232i	0.180085	+	1.04257i
$658$		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	−0.211245	−	0.977433i	$-0.567752\pi$
$661$	−29.9096	−	17.2683i	−1.16335	−	0.671660i	−0.952104	+	0.305773i	$0.901085\pi$
$662$		0			0
$663$	−6.62690	+	4.62300i	−0.257368	+	0.179542i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.53111	+	4.38401i	0.0980050	+	0.169750i
$668$		0			0
$669$	−23.0681	−	10.8059i	−0.891866	−	0.417780i
$670$		0			0
$671$	50.0651			1.93274
$672$		0			0
$673$	−11.0196			−0.424773			−0.212386	−	0.977186i	$-0.568124\pi$
$673$	−11.0196			−0.424773			−0.212386	+	0.977186i	$0.568124\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.78738	+	6.55993i	0.145561	+	0.252119i	0.929582	−	0.368615i	$-0.120168\pi$
$677$	3.78738	+	6.55993i	0.145561	+	0.252119i	−0.784021	+	0.620734i	$0.786835\pi$
$678$		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
$683$	21.9945	+	12.6985i	0.841596	+	0.485896i	0.857807	−	0.513973i	$-0.171827\pi$
$683$	21.9945	+	12.6985i	0.841596	+	0.485896i	−0.0162102	+	0.999869i	$0.505160\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	3.32600	+	38.7957i	0.126895	+	1.48015i
$688$		0			0
$689$	−7.64258	+	13.2373i	−0.291159	+	0.504303i
$690$		0			0
$691$	−2.43241	+	1.40435i	−0.0925332	+	0.0534241i	−0.545553	−	0.838077i	$-0.683680\pi$
$691$	−2.43241	+	1.40435i	−0.0925332	+	0.0534241i	0.453019	+	0.891501i	$0.350347\pi$
$692$		0			0
$693$	5.03539	+	44.8519i	0.191279	+	1.70378i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.329949	−	0.571489i	0.0124977	−	0.0216467i
$698$		0			0
$699$	3.79679	+	44.2873i	0.143608	+	1.67510i
$700$		0			0
$701$		−	18.1659i		−	0.686115i	−0.939314	−	0.343058i	$-0.888537\pi$
$701$		−	18.1659i		−	0.686115i	0.939314	−	0.343058i	$-0.111463\pi$
$702$		0			0
$703$	49.4767	+	28.5654i	1.86605	+	1.07736i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	21.8186	−	33.0965i	0.820571	−	1.24472i
$708$		0			0
$709$	−15.0139	−	26.0048i	−0.563858	−	0.976631i	−0.997155	−	0.0753797i	$-0.975983\pi$
$709$	−15.0139	−	26.0048i	−0.563858	−	0.976631i	0.433297	−	0.901251i	$-0.357350\pi$
$710$		0			0
$711$	−12.0366	+	32.7148i	−0.451409	+	1.22690i
$712$		0			0
$713$	2.69324			0.100863
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−11.8936	−	5.57138i	−0.444176	−	0.208067i
$718$		0			0
$719$	−0.687643	−	1.19103i	−0.0256447	−	0.0444180i	0.852918	−	0.522045i	$-0.174831\pi$
$719$	−0.687643	−	1.19103i	−0.0256447	−	0.0444180i	−0.878563	+	0.477627i	$0.841497\pi$
$720$		0			0
$721$	−9.37697	+	4.69677i	−0.349217	+	0.174917i
$722$		0			0
$723$	12.0465	−	8.40378i	0.448015	−	0.312540i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			33.6733i			1.24887i	0.781076	+	0.624436i	$0.214671\pi$
$727$			33.6733i			1.24887i	−0.781076	+	0.624436i	$0.785329\pi$
$728$		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
$733$	−14.5146	+	8.37999i	−0.536108	+	0.309522i	−0.743500	−	0.668736i	$-0.766836\pi$
$733$	−14.5146	+	8.37999i	−0.536108	+	0.309522i	0.207392	+	0.978258i	$0.433502\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	23.0572	−	13.3121i	0.849325	−	0.490358i
$738$		0			0
$739$	−19.3091	+	33.4444i	−0.710298	+	1.23027i	0.254448	+	0.967087i	$0.418106\pi$
$739$	−19.3091	+	33.4444i	−0.710298	+	1.23027i	−0.964745	+	0.263185i	$0.915227\pi$
$740$		0			0
$741$	−15.5563	+	1.33366i	−0.571476	+	0.0489933i
$742$		0			0
$743$		−	29.3068i		−	1.07516i	−0.843212	−	0.537582i	$-0.819338\pi$
$743$		−	29.3068i		−	1.07516i	0.843212	−	0.537582i	$-0.180662\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−19.4936	−	23.3969i	−0.713234	−	0.856048i
$748$		0			0
$749$	−22.6192	+	11.3296i	−0.826488	+	0.413974i
$750$		0			0
$751$	−5.94534	−	10.2976i	−0.216949	−	0.375766i	0.736925	−	0.675974i	$-0.236277\pi$
$751$	−5.94534	−	10.2976i	−0.216949	−	0.375766i	−0.953874	+	0.300209i	$0.902944\pi$
$752$		0			0
$753$	−0.864939	+	1.84645i	−0.0315201	+	0.0672884i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	44.9755			1.63466			0.817332	−	0.576167i	$-0.195452\pi$
$757$	44.9755			1.63466			0.817332	+	0.576167i	$0.195452\pi$
$758$		0			0
$759$	−4.26678	+	9.10861i	−0.154874	+	0.330622i
$760$		0			0
$761$	1.22673	+	2.12476i	0.0444690	+	0.0770226i	0.887403	−	0.460994i	$-0.152507\pi$
$761$	1.22673	+	2.12476i	0.0444690	+	0.0770226i	−0.842934	+	0.538017i	$0.819174\pi$
$762$		0			0
$763$	20.4992	−	31.0951i	0.742120	−	1.12572i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.84000	−	1.06233i	−0.0664386	−	0.0383584i
$768$		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
$773$	−0.884443	+	1.53190i	−0.0318112	+	0.0550986i	−0.881493	−	0.472198i	$-0.843461\pi$
$773$	−0.884443	+	1.53190i	−0.0318112	+	0.0550986i	0.849682	+	0.527296i	$0.176794\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−41.6960	+	1.09589i	−1.49584	+	0.0393149i
$778$		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
$783$	6.53593	+	24.9132i	0.233575	+	0.890326i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	46.0531	+	26.5888i	1.64162	+	0.947788i	0.980259	+	0.197718i	$0.0633529\pi$
$787$	46.0531	+	26.5888i	1.64162	+	0.947788i	0.661358	+	0.750070i	$0.269980\pi$
$788$		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
$793$	−6.32231	−	10.9506i	−0.224512	−	0.388866i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−33.8237			−1.19810			−0.599049	−	0.800713i	$-0.704454\pi$
$797$	−33.8237			−1.19810			−0.599049	+	0.800713i	$0.704454\pi$
$798$		0			0
$799$	−37.4578			−1.32516
$800$		0			0
$801$	−15.6101	+	42.4273i	−0.551557	+	1.49910i
$802$		0			0
$803$	−25.7012	−	44.5157i	−0.906974	−	1.57093i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.93881	+	9.94653i	0.244258	+	0.350135i
$808$		0			0
$809$	23.8866	+	13.7909i	0.839807	+	0.484863i	0.857199	−	0.514986i	$-0.172203\pi$
$809$	23.8866	+	13.7909i	0.839807	+	0.484863i	−0.0173917	+	0.999849i	$0.505536\pi$
$810$		0			0
$811$			3.97378i			0.139538i	0.997563	+	0.0697692i	$0.0222263\pi$
$811$			3.97378i			0.139538i	−0.997563	+	0.0697692i	$0.977774\pi$
$812$		0			0
$813$	−1.90861	−	22.2628i	−0.0669380	−	0.780790i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−21.2674	+	12.2787i	−0.744052	+	0.429579i
$818$		0			0
$819$	9.17443	−	6.76535i	0.320580	−	0.236401i
$820$		0			0
$821$	45.8143	−	26.4509i	1.59893	−	0.923143i	0.607237	−	0.794521i	$-0.292278\pi$
$821$	45.8143	−	26.4509i	1.59893	−	0.923143i	0.991694	−	0.128623i	$-0.0410556\pi$
$822$		0			0
$823$	5.18936	−	8.98823i	0.180890	−	0.313310i	−0.761294	−	0.648407i	$-0.775436\pi$
$823$	5.18936	−	8.98823i	0.180890	−	0.313310i	0.942184	+	0.335097i	$0.108769\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	50.8249i		−	1.76736i	−0.468095	−	0.883678i	$-0.655059\pi$
$827$		−	50.8249i		−	1.76736i	0.468095	−	0.883678i	$-0.344941\pi$
$828$		0			0
$829$	−1.33850	−	0.772785i	−0.0464881	−	0.0268399i	0.476576	−	0.879133i	$-0.341878\pi$
$829$	−1.33850	−	0.772785i	−0.0464881	−	0.0268399i	−0.523064	+	0.852293i	$0.675211\pi$
$830$		0			0
$831$	11.0340	+	15.8168i	0.382764	+	0.548679i
$832$		0			0
$833$	13.6171	−	18.2097i	0.471805	−	0.630927i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	13.2174	+	3.61584i	0.456860	+	0.124982i
$838$		0			0
$839$	24.0738			0.831118			0.415559	−	0.909566i	$-0.363586\pi$
$839$	24.0738			0.831118			0.415559	+	0.909566i	$0.363586\pi$
$840$		0			0
$841$	4.43009			0.152762
$842$		0			0
$843$	−35.3525	−	16.5603i	−1.21760	−	0.570366i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−25.2785	−	50.4680i	−0.868581	−	1.73410i
$848$		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
$853$		−	16.6929i		−	0.571555i	−0.958296	−	0.285777i	$-0.907748\pi$
$853$		−	16.6929i		−	0.571555i	0.958296	−	0.285777i	$-0.0922518\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.0858	+	24.3974i	−0.481163	+	0.833398i	−0.999766	−	0.0216164i	$-0.993119\pi$
$857$	−14.0858	+	24.3974i	−0.481163	+	0.833398i	0.518604	+	0.855015i	$0.326452\pi$
$858$		0			0
$859$	48.0897	−	27.7646i	1.64080	−	0.947315i	0.660248	−	0.751048i	$-0.270451\pi$
$859$	48.0897	−	27.7646i	1.64080	−	0.947315i	0.980550	−	0.196268i	$-0.0628821\pi$
$860$		0			0
$861$	−0.444138	+	0.818189i	−0.0151362	+	0.0278838i
$862$		0			0
$863$	−25.3774	+	14.6517i	−0.863857	+	0.498748i	−0.865302	−	0.501251i	$-0.832873\pi$
$863$	−25.3774	+	14.6517i	−0.863857	+	0.498748i	0.00144510	+	0.999999i	$0.499540\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	11.1285	−	0.954060i	0.377944	−	0.0324016i
$868$		0			0
$869$		−	66.0728i		−	2.24137i
$870$		0			0
$871$	−5.82342	−	3.36215i	−0.197319	−	0.113922i
$872$		0			0
$873$	−24.3253	+	20.2671i	−0.823286	+	0.685939i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−24.9574	−	43.2276i	−0.842753	−	1.45969i	−0.887558	−	0.460695i	$-0.847600\pi$
$877$	−24.9574	−	43.2276i	−0.842753	−	1.45969i	0.0448051	−	0.998996i	$-0.485733\pi$
$878$		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
$883$	39.2846			1.32203			0.661017	−	0.750371i	$-0.270125\pi$
$883$	39.2846			1.32203			0.661017	+	0.750371i	$0.270125\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.89144	+	13.6684i	0.264969	+	0.458939i	0.967555	−	0.252659i	$-0.0813050\pi$
$887$	7.89144	+	13.6684i	0.264969	+	0.458939i	−0.702587	+	0.711598i	$0.747972\pi$
$888$		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
$893$	−62.6835	−	36.1904i	−2.09762	−	1.21106i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.53111	−	0.216995i	0.0845113	−	0.00724524i
$898$		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
$903$	8.55349	−	15.7572i	0.284642	−	0.524367i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−23.0343	+	39.8965i	−0.764840	+	1.32474i	0.175490	+	0.984481i	$0.443849\pi$
$907$	−23.0343	+	39.8965i	−0.764840	+	1.32474i	−0.940331	+	0.340261i	$0.889484\pi$
$908$		0			0
$909$	44.2930	−	7.65081i	1.46911	−	0.253761i
$910$		0			0
$911$			26.6500i			0.882953i	0.897273	+	0.441477i	$0.145545\pi$
$911$			26.6500i			0.882953i	−0.897273	+	0.441477i	$0.854455\pi$
$912$		0			0
$913$	49.9893	+	28.8614i	1.65441	+	0.955172i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−19.6083	−	39.1476i	−0.647525	−	1.29277i
$918$		0			0
$919$	−1.65362	−	2.86415i	−0.0545478	−	0.0944795i	0.837462	−	0.546495i	$-0.184038\pi$
$919$	−1.65362	−	2.86415i	−0.0545478	−	0.0944795i	−0.892010	+	0.452016i	$0.850705\pi$
$920$		0			0
$921$	26.6062	+	12.4632i	0.876704	+	0.410677i
$922$		0			0
$923$	−1.55303			−0.0511185
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−11.1603	−	4.10616i	−0.366551	−	0.134864i
$928$		0			0
$929$	−11.3962	−	19.7388i	−0.373898	−	0.647610i	0.616264	−	0.787540i	$-0.288646\pi$
$929$	−11.3962	−	19.7388i	−0.373898	−	0.647610i	−0.990161	+	0.139930i	$0.955312\pi$
$930$		0			0
$931$	40.3810	−	17.3165i	1.32343	−	0.567526i
$932$		0			0
$933$	−33.2018	−	47.5935i	−1.08698	−	1.55814i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	33.2636i		−	1.08667i	−0.839515	−	0.543336i	$-0.817161\pi$
$937$		−	33.2636i		−	1.08667i	0.839515	−	0.543336i	$-0.182839\pi$
$938$		0			0
$939$	−1.01266	−	11.8120i	−0.0330468	−	0.385471i
$940$		0			0
$941$	−23.1677	+	40.1277i	−0.755246	+	1.30812i	0.190006	+	0.981783i	$0.439149\pi$
$941$	−23.1677	+	40.1277i	−0.755246	+	1.30812i	−0.945252	+	0.326341i	$0.894184\pi$
$942$		0			0
$943$	−0.179677	+	0.103737i	−0.00585109	+	0.00337813i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	36.1553	−	20.8743i	1.17489	−	0.678322i	0.220062	−	0.975486i	$-0.429374\pi$
$947$	36.1553	−	20.8743i	1.17489	−	0.678322i	0.954826	+	0.297164i	$0.0960408\pi$
$948$		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
$953$		−	5.47667i		−	0.177407i	−0.996058	−	0.0887034i	$-0.971728\pi$
$953$		−	5.47667i		−	0.177407i	0.996058	−	0.0887034i	$-0.0282723\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−27.9319	−	40.0394i	−0.902910	−	1.29429i
$958$		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
$963$	−26.9209	−	9.90491i	−0.867514	−	0.319181i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−60.2148			−1.93638			−0.968188	−	0.250223i	$-0.919496\pi$
$967$	−60.2148			−1.93638			−0.968188	+	0.250223i	$0.919496\pi$
$968$		0			0
$969$	−31.9796	−	14.9803i	−1.02733	−	0.481236i
$970$		0			0
$971$	13.2636	+	22.9732i	0.425650	+	0.737247i	0.996481	−	0.0838207i	$-0.0267123\pi$
$971$	13.2636	+	22.9732i	0.425650	+	0.737247i	−0.570831	+	0.821067i	$0.693379\pi$
$972$		0			0
$973$	1.43732	−	24.2321i	0.0460782	−	0.776846i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.32572	+	3.07480i	0.170385	+	0.0983717i	0.582767	−	0.812639i	$-0.301970\pi$
$977$	5.32572	+	3.07480i	0.170385	+	0.0983717i	−0.412383	+	0.911011i	$0.635303\pi$
$978$		0			0
$979$		−	85.6888i		−	2.73863i
$980$		0			0
$981$	41.6146	−	7.18816i	1.32865	−	0.229500i
$982$		0			0
$983$	−22.7982	+	39.4877i	−0.727150	+	1.25946i	0.230932	+	0.972970i	$0.425822\pi$
$983$	−22.7982	+	39.4877i	−0.727150	+	1.25946i	−0.958083	+	0.286492i	$0.907511\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	52.8259	−	1.38842i	1.68147	−	0.0441938i
$988$		0			0
$989$	3.46033	−	1.99783i	0.110032	−	0.0635271i
$990$		0			0
$991$	11.0880	−	19.2049i	0.352221	−	0.610065i	−0.634417	−	0.772991i	$-0.718760\pi$
$991$	11.0880	−	19.2049i	0.352221	−	0.610065i	0.986638	+	0.162926i	$0.0520931\pi$
$992$		0			0
$993$	11.5874	−	0.993401i	0.367715	−	0.0315246i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.1188	+	5.84211i	0.320466	+	0.185021i	0.651600	−	0.758562i	$-0.274098\pi$
$997$	10.1188	+	5.84211i	0.320466	+	0.185021i	−0.331134	+	0.943584i	$0.607431\pi$
$998$		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.bi.l.101.7	yes	16
3.2	odd	2	inner	2100.2.bi.l.101.3	✓	16
5.2	odd	4		2100.2.bo.i.1949.3		32
5.3	odd	4		2100.2.bo.i.1949.14		32
5.4	even	2		2100.2.bi.m.101.2	yes	16
7.5	odd	6	inner	2100.2.bi.l.1601.3	yes	16
15.2	even	4		2100.2.bo.i.1949.12		32
15.8	even	4		2100.2.bo.i.1949.5		32
15.14	odd	2		2100.2.bi.m.101.6	yes	16
21.5	even	6	inner	2100.2.bi.l.1601.7	yes	16
35.12	even	12		2100.2.bo.i.1349.5		32
35.19	odd	6		2100.2.bi.m.1601.6	yes	16
35.33	even	12		2100.2.bo.i.1349.12		32
105.47	odd	12		2100.2.bo.i.1349.14		32
105.68	odd	12		2100.2.bo.i.1349.3		32
105.89	even	6		2100.2.bi.m.1601.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.3	✓	16	3.2	odd	2	inner
2100.2.bi.l.101.7	yes	16	1.1	even	1	trivial
2100.2.bi.l.1601.3	yes	16	7.5	odd	6	inner
2100.2.bi.l.1601.7	yes	16	21.5	even	6	inner
2100.2.bi.m.101.2	yes	16	5.4	even	2
2100.2.bi.m.101.6	yes	16	15.14	odd	2
2100.2.bi.m.1601.2	yes	16	105.89	even	6
2100.2.bi.m.1601.6	yes	16	35.19	odd	6
2100.2.bo.i.1349.3		32	105.68	odd	12
2100.2.bo.i.1349.5		32	35.12	even	12
2100.2.bo.i.1349.12		32	35.33	even	12
2100.2.bo.i.1349.14		32	105.47	odd	12
2100.2.bo.i.1949.3		32	5.2	odd	4
2100.2.bo.i.1949.5		32	15.8	even	4
2100.2.bo.i.1949.12		32	15.2	even	4
2100.2.bo.i.1949.14		32	5.3	odd	4

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.734734 - 1.56849i) q^{3} +(-2.64111 - 0.156656i) q^{7} +(-1.92033 - 2.30485i) q^{9} +O(q^{10})\)	\(q+(0.734734 - 1.56849i) q^{3} +(-2.64111 - 0.156656i) q^{7} +(-1.92033 - 2.30485i) q^{9} +(4.92449 + 2.84316i) q^{11} -1.43616i q^{13} +(1.62414 - 2.81310i) q^{17} +(5.43583 - 3.13838i) q^{19} +(-2.18623 + 4.02746i) q^{21} +(-0.884443 + 0.510633i) q^{23} +(-5.02607 + 1.31858i) q^{27} -4.95680i q^{29} +(-2.28384 - 1.31858i) q^{31} +(8.07766 - 5.63506i) q^{33} +(4.55098 + 7.88253i) q^{37} +(-2.25260 - 1.05519i) q^{39} +0.203153 q^{41} -3.91245 q^{43} +(-5.76577 - 9.98660i) q^{47} +(6.95092 + 0.827492i) q^{49} +(-3.21901 - 4.61434i) q^{51} +(-9.21721 - 5.32156i) q^{53} +(-0.928633 - 10.8319i) q^{57} +(0.739701 - 1.28120i) q^{59} +(7.62492 - 4.40225i) q^{61} +(4.71074 + 6.38819i) q^{63} +(2.34108 - 4.05487i) q^{67} +(0.151094 + 1.76242i) q^{69} -1.08138i q^{71} +(-7.82857 - 4.51983i) q^{73} +(-12.5607 - 8.28054i) q^{77} +(-5.80981 - 10.0629i) q^{79} +(-1.62464 + 8.85215i) q^{81} +10.1512 q^{83} +(-7.77471 - 3.64193i) q^{87} +(-7.53465 - 13.0504i) q^{89} +(-0.224982 + 3.79304i) q^{91} +(-3.74619 + 2.61339i) q^{93} -10.5540i q^{97} +(-2.90362 - 16.8100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9	\( 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9} - 18 q^{19} - 11 q^{21} - 18 q^{31} - 12 q^{33} + 6 q^{37} + 12 q^{39} - 4 q^{43} - 18 q^{49} - q^{51} - 6 q^{57} + 36 q^{61} - 19 q^{63} - 30 q^{67} - 54 q^{73} + 7 q^{81} - 81 q^{87} + 20 q^{91} + 34 q^{93} - 30 q^{99}+O(q^{100}) \) 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9 - 18 * q^19 - 11 * q^21 - 18 * q^31 - 12 * q^33 + 6 * q^37 + 12 * q^39 - 4 * q^43 - 18 * q^49 - q^51 - 6 * q^57 + 36 * q^61 - 19 * q^63 - 30 * q^67 - 54 * q^73 + 7 * q^81 - 81 * q^87 + 20 * q^91 + 34 * q^93 - 30 * q^99

Introduction

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