LMFDB - Embedded newform 2100.2.ce.d.1993.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(157,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("2100.157");

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.ce (of order $12$, degree $4$, 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1993.1
Character	$\chi$	$=$	2100.1993
Dual form			2100.2.ce.d.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{3} +(2.25190 - 1.38886i) q^{7} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{3} +(2.25190 - 1.38886i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-2.42437 - 4.19914i) q^{11} +(2.27726 - 2.27726i) q^{13} +(0.574714 - 2.14486i) q^{17} +(-0.107324 + 0.185890i) q^{19} +(-2.53463 + 0.758702i) q^{21} +(-6.64641 + 1.78090i) q^{23} +(-0.707107 - 0.707107i) q^{27} -9.28979i q^{29} +(-7.78979 + 4.49744i) q^{31} +(1.25495 + 4.68353i) q^{33} +(2.62192 + 9.78514i) q^{37} +(-2.78906 + 1.61026i) q^{39} +2.32866i q^{41} +(5.01729 + 5.01729i) q^{43} +(9.36705 - 2.50989i) q^{47} +(3.14213 - 6.25516i) q^{49} +(-1.11026 + 1.92303i) q^{51} +(0.785466 - 2.93140i) q^{53} +(0.151779 - 0.151779i) q^{57} +(-2.68173 - 4.64490i) q^{59} +(-13.2321 - 7.63957i) q^{61} +(2.64464 - 0.0768377i) q^{63} +(-4.97338 - 1.33261i) q^{67} +6.88087 q^{69} -12.9873 q^{71} +(-0.146102 - 0.0391479i) q^{73} +(-11.2915 - 6.08893i) q^{77} +(-0.0599887 - 0.0346345i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.467804 + 0.467804i) q^{83} +(-2.40438 + 8.97325i) q^{87} +(-0.997017 + 1.72688i) q^{89} +(1.96537 - 8.29095i) q^{91} +(8.68839 - 2.32805i) q^{93} +(-7.51529 - 7.51529i) q^{97} -4.84874i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{11} + 8 q^{21} - 12 q^{31} - 8 q^{51} - 48 q^{61} + 64 q^{71} + 12 q^{81} + 116 q^{91}+O(q^{100}) $ 24 * q - 8 * q^11 + 8 * q^21 - 12 * q^31 - 8 * q^51 - 48 * q^61 + 64 * q^71 + 12 * q^81 + 116 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.25190	−	1.38886i	0.851139	−	0.524940i
$7$	2.25190	−	1.38886i	0.851139	−	0.524940i
$8$		0			0
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−2.42437	−	4.19914i	−0.730976	−	1.26609i	−0.956467	−	0.291842i	$-0.905732\pi$
$11$	−2.42437	−	4.19914i	−0.730976	−	1.26609i	0.225491	−	0.974245i	$-0.427601\pi$
$12$		0			0
$13$	2.27726	−	2.27726i	0.631597	−	0.631597i	−0.316872	−	0.948468i	$-0.602632\pi$
$13$	2.27726	−	2.27726i	0.631597	−	0.631597i	0.948468	+	0.316872i	$0.102632\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.574714	−	2.14486i	0.139389	−	0.520206i	−0.860553	−	0.509362i	$-0.829882\pi$
$17$	0.574714	−	2.14486i	0.139389	−	0.520206i	0.999941	−	0.0108439i	$-0.00345178\pi$
$18$		0			0
$19$	−0.107324	+	0.185890i	−0.0246218	+	0.0426462i	−0.878074	−	0.478525i	$-0.841171\pi$
$19$	−0.107324	+	0.185890i	−0.0246218	+	0.0426462i	0.853452	+	0.521172i	$0.174505\pi$
$20$		0			0
$21$	−2.53463	+	0.758702i	−0.553103	+	0.165562i
$22$		0			0
$23$	−6.64641	+	1.78090i	−1.38587	+	0.371343i	−0.873251	−	0.487272i	$-0.837992\pi$
$23$	−6.64641	+	1.78090i	−1.38587	+	0.371343i	−0.512621	+	0.858615i	$0.671326\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	9.28979i		−	1.72507i	−0.505996	−	0.862536i	$-0.668875\pi$
$29$		−	9.28979i		−	1.72507i	0.505996	−	0.862536i	$-0.331125\pi$
$30$		0			0
$31$	−7.78979	+	4.49744i	−1.39909	+	0.807764i	−0.994297	−	0.106645i	$-0.965989\pi$
$31$	−7.78979	+	4.49744i	−1.39909	+	0.807764i	−0.404791	+	0.914409i	$0.632656\pi$
$32$		0			0
$33$	1.25495	+	4.68353i	0.218458	+	0.815297i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.62192	+	9.78514i	0.431041	+	1.60867i	0.750367	+	0.661022i	$0.229877\pi$
$37$	2.62192	+	9.78514i	0.431041	+	1.60867i	−0.319326	+	0.947645i	$0.603456\pi$
$38$		0			0
$39$	−2.78906	+	1.61026i	−0.446606	+	0.257848i
$40$		0			0
$41$			2.32866i			0.363675i	0.983329	+	0.181838i	$0.0582046\pi$
$41$			2.32866i			0.363675i	−0.983329	+	0.181838i	$0.941795\pi$
$42$		0			0
$43$	5.01729	+	5.01729i	0.765129	+	0.765129i	0.977245	−	0.212115i	$-0.0680353\pi$
$43$	5.01729	+	5.01729i	0.765129	+	0.765129i	−0.212115	+	0.977245i	$0.568035\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.36705	−	2.50989i	1.36633	−	0.366106i	0.500190	−	0.865916i	$-0.333263\pi$
$47$	9.36705	−	2.50989i	1.36633	−	0.366106i	0.866135	+	0.499810i	$0.166597\pi$
$48$		0			0
$49$	3.14213	−	6.25516i	0.448876	−	0.893594i
$50$		0			0
$51$	−1.11026	+	1.92303i	−0.155468	+	0.269278i
$52$		0			0
$53$	0.785466	−	2.93140i	0.107892	−	0.402658i	−0.890765	−	0.454464i	$-0.849831\pi$
$53$	0.785466	−	2.93140i	0.107892	−	0.402658i	0.998657	+	0.0518054i	$0.0164976\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.151779	−	0.151779i	0.0201036	−	0.0201036i
$58$		0			0
$59$	−2.68173	−	4.64490i	−0.349132	−	0.604714i	0.636964	−	0.770894i	$-0.280190\pi$
$59$	−2.68173	−	4.64490i	−0.349132	−	0.604714i	−0.986095	+	0.166180i	$0.946857\pi$
$60$		0			0
$61$	−13.2321	−	7.63957i	−1.69420	−	0.978147i	−0.951058	−	0.309013i	$-0.900001\pi$
$61$	−13.2321	−	7.63957i	−1.69420	−	0.978147i	−0.743142	−	0.669134i	$-0.766665\pi$
$62$		0			0
$63$	2.64464	−	0.0768377i	0.333193	−	0.00968064i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.97338	−	1.33261i	−0.607595	−	0.162804i	−0.0581126	−	0.998310i	$-0.518508\pi$
$67$	−4.97338	−	1.33261i	−0.607595	−	0.162804i	−0.549482	+	0.835506i	$0.685175\pi$
$68$		0			0
$69$	6.88087			0.828359
$70$		0			0
$71$	−12.9873			−1.54131			−0.770653	−	0.637255i	$-0.780070\pi$
$71$	−12.9873			−1.54131			−0.770653	+	0.637255i	$0.780070\pi$
$72$		0			0
$73$	−0.146102	−	0.0391479i	−0.0170999	−	0.00458192i	0.250259	−	0.968179i	$-0.419484\pi$
$73$	−0.146102	−	0.0391479i	−0.0170999	−	0.00458192i	−0.267359	+	0.963597i	$0.586151\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.2915	−	6.08893i	−1.28678	−	0.693898i
$78$		0			0
$79$	−0.0599887	−	0.0346345i	−0.00674926	−	0.00389669i	0.496622	−	0.867967i	$-0.334574\pi$
$79$	−0.0599887	−	0.0346345i	−0.00674926	−	0.00389669i	−0.503371	+	0.864070i	$0.667907\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	−0.467804	+	0.467804i	−0.0513482	+	0.0513482i	−0.732315	−	0.680966i	$-0.761560\pi$
$83$	−0.467804	+	0.467804i	−0.0513482	+	0.0513482i	0.680966	+	0.732315i	$0.261560\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.40438	+	8.97325i	−0.257776	+	0.962034i
$88$		0			0
$89$	−0.997017	+	1.72688i	−0.105684	+	0.183049i	−0.914017	−	0.405675i	$-0.867036\pi$
$89$	−0.997017	+	1.72688i	−0.105684	+	0.183049i	0.808334	+	0.588725i	$0.200370\pi$
$90$		0			0
$91$	1.96537	−	8.29095i	0.206026	−	0.869127i
$92$		0			0
$93$	8.68839	−	2.32805i	0.900944	−	0.241407i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.51529	−	7.51529i	−0.763062	−	0.763062i	0.213813	−	0.976875i	$-0.431412\pi$
$97$	−7.51529	−	7.51529i	−0.763062	−	0.763062i	−0.976875	+	0.213813i	$0.931412\pi$
$98$		0			0
$99$		−	4.84874i		−	0.487317i
$100$		0			0
$101$	4.35510	−	2.51442i	0.433349	−	0.250194i	−0.267423	−	0.963579i	$-0.586172\pi$
$101$	4.35510	−	2.51442i	0.433349	−	0.250194i	0.700772	+	0.713385i	$0.252839\pi$
$102$		0			0
$103$	1.51377	+	5.64945i	0.149156	+	0.556657i	0.999535	+	0.0304870i	$0.00970582\pi$
$103$	1.51377	+	5.64945i	0.149156	+	0.556657i	−0.850379	+	0.526170i	$0.823628\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.908827	+	3.39179i	0.0878596	+	0.327896i	0.995840	−	0.0911154i	$-0.0290432\pi$
$107$	0.908827	+	3.39179i	0.0878596	+	0.327896i	−0.907981	+	0.419012i	$0.862377\pi$
$108$		0			0
$109$	10.1903	−	5.88338i	0.976055	−	0.563525i	0.0749780	−	0.997185i	$-0.476111\pi$
$109$	10.1903	−	5.88338i	0.976055	−	0.563525i	0.901077	+	0.433660i	$0.142778\pi$
$110$		0			0
$111$		−	10.1303i		−	0.961528i
$112$		0			0
$113$	−9.96763	−	9.96763i	−0.937676	−	0.937676i	0.0604926	−	0.998169i	$-0.480733\pi$
$113$	−9.96763	−	9.96763i	−0.937676	−	0.937676i	−0.998169	+	0.0604926i	$0.980733\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.11079	−	0.833533i	0.287592	−	0.0770602i
$118$		0			0
$119$	−1.68472	−	5.62822i	−0.154438	−	0.515938i
$120$		0			0
$121$	−6.25516	+	10.8343i	−0.568651	+	0.984932i
$122$		0			0
$123$	0.602701	−	2.24931i	0.0543437	−	0.202814i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	3.70771	−	3.70771i	0.329006	−	0.329006i	−0.523203	−	0.852208i	$-0.675263\pi$
$127$	3.70771	−	3.70771i	0.329006	−	0.329006i	0.852208	+	0.523203i	$0.175263\pi$
$128$		0			0
$129$	−3.54776	−	6.14490i	−0.312363	−	0.541028i
$130$		0			0
$131$	−9.28979	−	5.36347i	−0.811653	−	0.468608i	0.0358765	−	0.999356i	$-0.488578\pi$
$131$	−9.28979	−	5.36347i	−0.811653	−	0.468608i	−0.847530	+	0.530748i	$0.821911\pi$
$132$		0			0
$133$	0.0164930	+	0.567665i	0.00143013	+	0.0492228i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.7532	+	3.68516i	1.17502	+	0.314845i	0.792948	−	0.609290i	$-0.208545\pi$
$137$	13.7532	+	3.68516i	1.17502	+	0.314845i	0.382068	+	0.924134i	$0.375212\pi$
$138$		0			0
$139$	−13.9764			−1.18546			−0.592731	−	0.805401i	$-0.701950\pi$
$139$	−13.9764			−1.18546			−0.592731	+	0.805401i	$0.701950\pi$
$140$		0			0
$141$	−9.69749			−0.816676
$142$		0			0
$143$	−15.0834	−	4.04159i	−1.26134	−	0.337975i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.65402	+	5.22878i	−0.383857	+	0.431262i
$148$		0			0
$149$	9.74836	+	5.62822i	0.798617	+	0.461082i	0.842987	−	0.537933i	$-0.180795\pi$
$149$	9.74836	+	5.62822i	0.798617	+	0.461082i	−0.0443704	+	0.999015i	$0.514128\pi$
$150$		0			0
$151$	−4.16285	−	7.21027i	−0.338768	−	0.586764i	0.645433	−	0.763817i	$-0.276677\pi$
$151$	−4.16285	−	7.21027i	−0.338768	−	0.586764i	−0.984201	+	0.177053i	$0.943344\pi$
$152$		0			0
$153$	1.57015	−	1.57015i	0.126939	−	0.126939i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.66707	+	6.22158i	−0.133046	+	0.496536i	−0.999998	−	0.00185597i	$-0.999409\pi$
$157$	−1.66707	+	6.22158i	−0.133046	+	0.496536i	0.866952	+	0.498392i	$0.166076\pi$
$158$		0			0
$159$	−1.51740	+	2.62822i	−0.120338	+	0.208431i
$160$		0			0
$161$	−12.4936	+	13.2413i	−0.984637	+	1.04356i
$162$		0			0
$163$	−10.0382	+	2.68973i	−0.786252	+	0.210676i	−0.629539	−	0.776969i	$-0.716756\pi$
$163$	−10.0382	+	2.68973i	−0.786252	+	0.210676i	−0.156713	+	0.987644i	$0.550090\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.1957	−	13.1957i	−1.02112	−	1.02112i	−0.999772	−	0.0213437i	$-0.993206\pi$
$167$	−13.1957	−	13.1957i	−1.02112	−	1.02112i	−0.0213437	−	0.999772i	$-0.506794\pi$
$168$		0			0
$169$			2.62822i			0.202171i
$170$		0			0
$171$	−0.185890	+	0.107324i	−0.0142154	+	0.00820726i
$172$		0			0
$173$	−3.46687	−	12.9386i	−0.263582	−	0.983700i	−0.963113	−	0.269098i	$-0.913274\pi$
$173$	−3.46687	−	12.9386i	−0.263582	−	0.983700i	0.699531	−	0.714602i	$-0.253392\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.38817	+	5.18071i	0.104341	+	0.389406i
$178$		0			0
$179$	5.19615	−	3.00000i	0.388379	−	0.224231i	−0.293079	−	0.956088i	$-0.594680\pi$
$179$	5.19615	−	3.00000i	0.388379	−	0.224231i	0.681457	+	0.731858i	$0.261346\pi$
$180$		0			0
$181$			6.61889i			0.491978i	0.969273	+	0.245989i	$0.0791127\pi$
$181$			6.61889i			0.491978i	−0.969273	+	0.245989i	$0.920887\pi$
$182$		0			0
$183$	10.8040	+	10.8040i	0.798653	+	0.798653i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10.3999	+	2.78664i	−0.760515	+	0.203779i
$188$		0			0
$189$	−2.57441	−	0.610262i	−0.187261	−	0.0443901i
$190$		0			0
$191$	−5.22052	+	9.04221i	−0.377744	+	0.654272i	−0.990734	−	0.135819i	$-0.956633\pi$
$191$	−5.22052	+	9.04221i	−0.377744	+	0.654272i	0.612990	+	0.790091i	$0.289967\pi$
$192$		0			0
$193$	0.154414	−	0.576279i	0.0111149	−	0.0414815i	−0.960146	−	0.279500i	$-0.909831\pi$
$193$	0.154414	−	0.576279i	0.0111149	−	0.0414815i	0.971261	+	0.238019i	$0.0764979\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.5058	−	16.5058i	1.17599	−	1.17599i	0.195236	−	0.980756i	$-0.437453\pi$
$197$	16.5058	−	16.5058i	1.17599	−	1.17599i	0.980756	−	0.195236i	$-0.0625474\pi$
$198$		0			0
$199$	−12.8357	−	22.2321i	−0.909900	−	1.57599i	−0.814201	−	0.580583i	$-0.802825\pi$
$199$	−12.8357	−	22.2321i	−0.909900	−	1.57599i	−0.0956992	−	0.995410i	$-0.530509\pi$
$200$		0			0
$201$	4.45901	+	2.57441i	0.314514	+	0.181585i
$202$		0			0
$203$	−12.9022	−	20.9197i	−0.905559	−	1.46828i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.64641	−	1.78090i	−0.461957	−	0.123781i
$208$		0			0
$209$	1.04077			0.0719917
$210$		0			0
$211$	11.8847			0.818174			0.409087	−	0.912495i	$-0.365847\pi$
$211$	11.8847			0.818174			0.409087	+	0.912495i	$0.365847\pi$
$212$		0			0
$213$	12.5448	+	3.36136i	0.859552	+	0.230316i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−11.2955	+	20.9467i	−0.766791	+	1.42196i
$218$		0			0
$219$	0.130991	+	0.0756280i	0.00885158	+	0.00511046i
$220$		0			0
$221$	−3.57563	−	6.19317i	−0.240523	−	0.416598i
$222$		0			0
$223$	18.7946	−	18.7946i	1.25858	−	1.25858i	0.306809	−	0.951771i	$-0.400739\pi$
$223$	18.7946	−	18.7946i	1.25858	−	1.25858i	0.951771	−	0.306809i	$-0.0992612\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.78753	−	17.8673i	0.317760	−	1.18590i	−0.603633	−	0.797262i	$-0.706281\pi$
$227$	4.78753	−	17.8673i	0.317760	−	1.18590i	0.921393	−	0.388633i	$-0.127053\pi$
$228$		0			0
$229$	6.39680	−	11.0796i	0.422713	−	0.732160i	−0.573491	−	0.819212i	$-0.694411\pi$
$229$	6.39680	−	11.0796i	0.422713	−	0.732160i	0.996204	+	0.0870520i	$0.0277446\pi$
$230$		0			0
$231$	9.33079	+	8.80390i	0.613921	+	0.579254i
$232$		0			0
$233$	−14.8600	+	3.98174i	−0.973514	+	0.260852i	−0.710311	−	0.703888i	$-0.751446\pi$
$233$	−14.8600	+	3.98174i	−0.973514	+	0.260852i	−0.263203	+	0.964740i	$0.584779\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.0489806	+	0.0489806i	0.00318163	+	0.00318163i
$238$		0			0
$239$			13.3231i			0.861803i	0.902399	+	0.430901i	$0.141804\pi$
$239$			13.3231i			0.861803i	−0.902399	+	0.430901i	$0.858196\pi$
$240$		0			0
$241$	2.71925	−	1.56996i	0.175162	−	0.101130i	−0.409856	−	0.912150i	$-0.634421\pi$
$241$	2.71925	−	1.56996i	0.175162	−	0.101130i	0.585018	+	0.811021i	$0.301088\pi$
$242$		0			0
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.178916	+	0.667724i	0.0113842	+	0.0424863i
$248$		0			0
$249$	0.572941	−	0.330787i	0.0363086	−	0.0209628i
$250$		0			0
$251$		−	16.4250i		−	1.03674i	−0.855157	−	0.518369i	$-0.826539\pi$
$251$		−	16.4250i		−	1.03674i	0.855157	−	0.518369i	$-0.173461\pi$
$252$		0			0
$253$	23.5916	+	23.5916i	1.48319	+	1.48319i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.8016	+	4.23404i	−0.985679	+	0.264112i	−0.715435	−	0.698680i	$-0.753771\pi$
$257$	−15.8016	+	4.23404i	−0.985679	+	0.264112i	−0.270245	+	0.962792i	$0.587105\pi$
$258$		0			0
$259$	19.4945	+	18.3937i	1.21133	+	1.14293i
$260$		0			0
$261$	4.64490	−	8.04520i	0.287512	−	0.497985i
$262$		0			0
$263$	−7.45693	+	27.8296i	−0.459814	+	1.71605i	0.213722	+	0.976894i	$0.431441\pi$
$263$	−7.45693	+	27.8296i	−0.459814	+	1.71605i	−0.673536	+	0.739154i	$0.735225\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.40999	−	1.40999i	0.0862903	−	0.0862903i
$268$		0			0
$269$	6.88087	+	11.9180i	0.419534	+	0.726654i	0.995893	−	0.0905428i	$-0.0288602\pi$
$269$	6.88087	+	11.9180i	0.419534	+	0.726654i	−0.576359	+	0.817197i	$0.695527\pi$
$270$		0			0
$271$	−10.3141	−	5.95485i	−0.626538	−	0.361732i	0.152872	−	0.988246i	$-0.451148\pi$
$271$	−10.3141	−	5.95485i	−0.626538	−	0.361732i	−0.779410	+	0.626514i	$0.784481\pi$
$272$		0			0
$273$	−4.04425	+	7.49977i	−0.244769	+	0.453906i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	19.4087	+	5.20054i	1.16615	+	0.312470i	0.789421	−	0.613852i	$-0.210381\pi$
$277$	19.4087	+	5.20054i	1.16615	+	0.312470i	0.376733	+	0.926322i	$0.377048\pi$
$278$		0			0
$279$	−8.99488			−0.538509
$280$		0			0
$281$	12.5796			0.750435			0.375218	−	0.926937i	$-0.377568\pi$
$281$	12.5796			0.750435			0.375218	+	0.926937i	$0.377568\pi$
$282$		0			0
$283$	17.3744	+	4.65545i	1.03280	+	0.276738i	0.735126	−	0.677930i	$-0.237123\pi$
$283$	17.3744	+	4.65545i	1.03280	+	0.276738i	0.297673	+	0.954668i	$0.403789\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.23418	+	5.24391i	0.190908	+	0.309538i
$288$		0			0
$289$	10.4523	+	6.03463i	0.614841	+	0.354978i
$290$		0			0
$291$	5.31411	+	9.20431i	0.311519	+	0.539566i
$292$		0			0
$293$	−0.409831	+	0.409831i	−0.0239426	+	0.0239426i	−0.718977	−	0.695034i	$-0.755389\pi$
$293$	−0.409831	+	0.409831i	−0.0239426	+	0.0239426i	0.695034	+	0.718977i	$0.255389\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.25495	+	4.68353i	−0.0728194	+	0.271766i
$298$		0			0
$299$	−11.0800	+	19.1911i	−0.640773	+	1.10985i
$300$		0			0
$301$	18.2668	+	4.33013i	1.05288	+	0.249584i
$302$		0			0
$303$	−4.85749	+	1.30156i	−0.279055	+	0.0747726i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.747094	+	0.747094i	0.0426389	+	0.0426389i	0.728105	−	0.685466i	$-0.240401\pi$
$307$	0.747094	+	0.747094i	0.0426389	+	0.0426389i	−0.685466	+	0.728105i	$0.740401\pi$
$308$		0			0
$309$		−	5.84874i		−	0.332723i
$310$		0			0
$311$	16.2731	−	9.39529i	0.922764	−	0.532758i	0.0382480	−	0.999268i	$-0.487822\pi$
$311$	16.2731	−	9.39529i	0.922764	−	0.532758i	0.884516	+	0.466510i	$0.154489\pi$
$312$		0			0
$313$	0.996128	+	3.71760i	0.0563045	+	0.210131i	0.988347	−	0.152218i	$-0.0486415\pi$
$313$	0.996128	+	3.71760i	0.0563045	+	0.210131i	−0.932042	+	0.362349i	$0.881975\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.822219	+	3.06856i	0.0461804	+	0.172348i	0.985164	−	0.171613i	$-0.0548979\pi$
$317$	0.822219	+	3.06856i	0.0461804	+	0.172348i	−0.938984	+	0.343961i	$0.888231\pi$
$318$		0			0
$319$	−39.0091	+	22.5219i	−2.18409	+	1.26099i
$320$		0			0
$321$		−	3.51144i		−	0.195989i
$322$		0			0
$323$	0.337029	+	0.337029i	0.0187528	+	0.0187528i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−11.3658	+	3.04546i	−0.628531	+	0.168414i
$328$		0			0
$329$	17.6078	−	18.6616i	0.970749	−	1.02885i
$330$		0			0
$331$	8.01032	−	13.8743i	0.440287	−	0.762599i	−0.557424	−	0.830228i	$-0.688210\pi$
$331$	8.01032	−	13.8743i	0.440287	−	0.762599i	0.997711	+	0.0676289i	$0.0215434\pi$
$332$		0			0
$333$	−2.62192	+	9.78514i	−0.143680	+	0.536222i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	18.6413	−	18.6413i	1.01545	−	1.01545i	0.0155754	−	0.999879i	$-0.495042\pi$
$337$	18.6413	−	18.6413i	1.01545	−	1.01545i	0.999879	−	0.0155754i	$-0.00495802\pi$
$338$		0			0
$339$	7.04818	+	12.2078i	0.382805	+	0.663037i
$340$		0			0
$341$	37.7707	+	21.8069i	2.04540	+	1.18091i
$342$		0			0
$343$	−1.61178	−	18.4500i	−0.0870278	−	0.996206i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	22.0870	+	5.91820i	1.18569	+	0.317705i	0.797182	−	0.603739i	$-0.206323\pi$
$347$	22.0870	+	5.91820i	1.18569	+	0.317705i	0.388511	+	0.921444i	$0.372990\pi$
$348$		0			0
$349$	7.69212			0.411750			0.205875	−	0.978578i	$-0.433996\pi$
$349$	7.69212			0.411750			0.205875	+	0.978578i	$0.433996\pi$
$350$		0			0
$351$	−3.22052			−0.171899
$352$		0			0
$353$	−29.4584	−	7.89336i	−1.56791	−	0.420121i	−0.632755	−	0.774352i	$-0.718076\pi$
$353$	−29.4584	−	7.89336i	−1.56791	−	0.420121i	−0.935158	+	0.354231i	$0.884743\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.170620	+	5.87248i	0.00903017	+	0.310805i
$358$		0			0
$359$	−17.1496	−	9.90134i	−0.905122	−	0.522572i	−0.0262636	−	0.999655i	$-0.508361\pi$
$359$	−17.1496	−	9.90134i	−0.905122	−	0.522572i	−0.878858	+	0.477083i	$0.841694\pi$
$360$		0			0
$361$	9.47696	+	16.4146i	0.498788	+	0.863925i
$362$		0			0
$363$	8.84613	−	8.84613i	0.464301	−	0.464301i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−8.44151	+	31.5042i	−0.440643	+	1.64450i	0.286546	+	0.958067i	$0.407493\pi$
$367$	−8.44151	+	31.5042i	−0.440643	+	1.64450i	−0.727189	+	0.686437i	$0.759174\pi$
$368$		0			0
$369$	−1.16433	+	2.01668i	−0.0606126	+	0.104984i
$370$		0			0
$371$	−2.30251	−	7.69212i	−0.119540	−	0.399355i
$372$		0			0
$373$	26.0194	−	6.97189i	1.34724	−	0.360991i	0.488122	−	0.872776i	$-0.337682\pi$
$373$	26.0194	−	6.97189i	1.34724	−	0.360991i	0.859114	+	0.511785i	$0.171016\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−21.1552	−	21.1552i	−1.08955	−	1.08955i
$378$		0			0
$379$			7.13854i			0.366682i	0.983049	+	0.183341i	$0.0586913\pi$
$379$			7.13854i			0.366682i	−0.983049	+	0.183341i	$0.941309\pi$
$380$		0			0
$381$	−4.54099	+	2.62174i	−0.232642	+	0.134316i
$382$		0			0
$383$	−2.50989	−	9.36705i	−0.128250	−	0.478634i	0.871685	−	0.490067i	$-0.163028\pi$
$383$	−2.50989	−	9.36705i	−0.128250	−	0.478634i	−0.999935	+	0.0114324i	$0.996361\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.83645	+	6.85374i	0.0933522	+	0.348395i
$388$		0			0
$389$	4.84308	−	2.79615i	0.245554	−	0.141771i	−0.372173	−	0.928163i	$-0.621387\pi$
$389$	4.84308	−	2.79615i	0.245554	−	0.141771i	0.617727	+	0.786393i	$0.288054\pi$
$390$		0			0
$391$			15.2791i			0.772699i
$392$		0			0
$393$	7.58508	+	7.58508i	0.382617	+	0.382617i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	27.8857	−	7.47195i	1.39954	−	0.375006i	0.521362	−	0.853336i	$-0.325424\pi$
$397$	27.8857	−	7.47195i	1.39954	−	0.375006i	0.878180	+	0.478330i	$0.158758\pi$
$398$		0			0
$399$	0.130991	−	0.552591i	0.00655778	−	0.0276642i
$400$		0			0
$401$	−6.40769	+	11.0985i	−0.319985	+	0.554230i	−0.980485	−	0.196596i	$-0.937011\pi$
$401$	−6.40769	+	11.0985i	−0.319985	+	0.554230i	0.660500	+	0.750826i	$0.270345\pi$
$402$		0			0
$403$	−7.49753	+	27.9812i	−0.373479	+	1.39384i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	34.7326	−	34.7326i	1.72163	−	1.72163i
$408$		0			0
$409$	5.58555	+	9.67445i	0.276188	+	0.478371i	0.970434	−	0.241366i	$-0.0775956\pi$
$409$	5.58555	+	9.67445i	0.276188	+	0.478371i	−0.694247	+	0.719737i	$0.744262\pi$
$410$		0			0
$411$	−12.3308	−	7.11918i	−0.608233	−	0.351163i
$412$		0			0
$413$	−12.4901	−	6.73530i	−0.614598	−	0.331423i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	13.5002	+	3.61735i	0.661105	+	0.177143i
$418$		0			0
$419$	−33.2585			−1.62478			−0.812391	−	0.583113i	$-0.801834\pi$
$419$	−33.2585			−1.62478			−0.812391	+	0.583113i	$0.801834\pi$
$420$		0			0
$421$	8.64886			0.421519			0.210760	−	0.977538i	$-0.432406\pi$
$421$	8.64886			0.421519			0.210760	+	0.977538i	$0.432406\pi$
$422$		0			0
$423$	9.36705	+	2.50989i	0.455442	+	0.122035i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−40.4078	+	1.17401i	−1.95547	+	0.0568145i
$428$		0			0
$429$	13.5234	+	7.80775i	0.652917	+	0.376962i
$430$		0			0
$431$	−0.0819870	−	0.142006i	−0.00394917	−	0.00684017i	0.864044	−	0.503416i	$-0.167924\pi$
$431$	−0.0819870	−	0.142006i	−0.00394917	−	0.00684017i	−0.867993	+	0.496576i	$0.834590\pi$
$432$		0			0
$433$	−13.2611	+	13.2611i	−0.637288	+	0.637288i	−0.949886	−	0.312597i	$-0.898801\pi$
$433$	−13.2611	+	13.2611i	−0.637288	+	0.637288i	0.312597	+	0.949886i	$0.398801\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.382266	−	1.42664i	0.0182863	−	0.0682453i
$438$		0			0
$439$	−10.1355	+	17.5553i	−0.483743	+	0.837867i	−0.999826	−	0.0186713i	$-0.994056\pi$
$439$	−10.1355	+	17.5553i	−0.483743	+	0.837867i	0.516083	+	0.856539i	$0.327390\pi$
$440$		0			0
$441$	5.84874	−	3.84606i	0.278512	−	0.183146i
$442$		0			0
$443$	−29.1938	+	7.82246i	−1.38704	+	0.371656i	−0.873673	−	0.486513i	$-0.838269\pi$
$443$	−29.1938	+	7.82246i	−1.38704	+	0.371656i	−0.513366	+	0.858169i	$0.671602\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.95950	−	7.95950i	−0.376472	−	0.376472i
$448$		0			0
$449$		−	5.18461i		−	0.244677i	−0.992488	−	0.122338i	$-0.960961\pi$
$449$		−	5.18461i		−	0.244677i	0.992488	−	0.122338i	$-0.0390393\pi$
$450$		0			0
$451$	9.77835	−	5.64554i	0.460445	−	0.265838i
$452$		0			0
$453$	2.15485	+	8.04202i	0.101244	+	0.377847i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.15027	+	11.7570i	0.147363	+	0.549967i	0.999639	+	0.0268740i	$0.00855528\pi$
$457$	3.15027	+	11.7570i	0.147363	+	0.549967i	−0.852276	+	0.523093i	$0.824778\pi$
$458$		0			0
$459$	−1.92303	+	1.11026i	−0.0897594	+	0.0518226i
$460$		0			0
$461$			21.8254i			1.01651i	0.861207	+	0.508255i	$0.169709\pi$
$461$			21.8254i			1.01651i	−0.861207	+	0.508255i	$0.830291\pi$
$462$		0			0
$463$	−10.2272	−	10.2272i	−0.475299	−	0.475299i	0.428326	−	0.903624i	$-0.359104\pi$
$463$	−10.2272	−	10.2272i	−0.475299	−	0.475299i	−0.903624	+	0.428326i	$0.859104\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	37.3988	−	10.0210i	1.73061	−	0.463716i	0.750288	−	0.661111i	$-0.229915\pi$
$467$	37.3988	−	10.0210i	1.73061	−	0.463716i	0.980324	+	0.197395i	$0.0632482\pi$
$468$		0			0
$469$	−13.0504	+	3.90642i	−0.602610	+	0.180382i
$470$		0			0
$471$	3.22052	−	5.57811i	0.148394	−	0.257026i
$472$		0			0
$473$	8.90450	−	33.2320i	0.409429	−	1.52801i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.14593	−	2.14593i	0.0982555	−	0.0982555i
$478$		0			0
$479$	9.04221	+	15.6616i	0.413149	+	0.715596i	0.995232	−	0.0975338i	$-0.0310954\pi$
$479$	9.04221	+	15.6616i	0.413149	+	0.715596i	−0.582083	+	0.813129i	$0.697762\pi$
$480$		0			0
$481$	28.2540	+	16.3125i	1.28827	+	0.743785i
$482$		0			0
$483$	15.4950	−	9.55657i	0.705049	−	0.434839i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.95527	+	1.86366i	0.315173	+	0.0844504i	0.412938	−	0.910759i	$-0.364503\pi$
$487$	6.95527	+	1.86366i	0.315173	+	0.0844504i	−0.0977647	+	0.995210i	$0.531169\pi$
$488$		0			0
$489$	10.3923			0.469956
$490$		0			0
$491$	43.9746			1.98454			0.992272	−	0.124081i	$-0.0395981\pi$
$491$	43.9746			1.98454			0.992272	+	0.124081i	$0.0395981\pi$
$492$		0			0
$493$	−19.9253	−	5.33898i	−0.897392	−	0.240455i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−29.2461	+	18.0375i	−1.31187	+	0.809094i
$498$		0			0
$499$	19.0704	+	11.0103i	0.853710	+	0.492890i	0.861901	−	0.507077i	$-0.169274\pi$
$499$	19.0704	+	11.0103i	0.853710	+	0.492890i	−0.00819105	+	0.999966i	$0.502607\pi$
$500$		0			0
$501$	9.33079	+	16.1614i	0.416869	+	0.722038i
$502$		0			0
$503$	12.7279	−	12.7279i	0.567510	−	0.567510i	−0.363920	−	0.931430i	$-0.618562\pi$
$503$	12.7279	−	12.7279i	0.567510	−	0.567510i	0.931430	+	0.363920i	$0.118562\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.680233	−	2.53866i	0.0302102	−	0.112746i
$508$		0			0
$509$	−9.74836	+	16.8847i	−0.432089	+	0.748399i	−0.997053	−	0.0767160i	$-0.975557\pi$
$509$	−9.74836	+	16.8847i	−0.432089	+	0.748399i	0.564964	+	0.825115i	$0.308890\pi$
$510$		0			0
$511$	−0.383379	+	0.114758i	−0.0169597	+	0.00507660i
$512$		0			0
$513$	0.207334	−	0.0555549i	0.00915401	−	0.00245281i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−33.2486	−	33.2486i	−1.46227	−	1.46227i
$518$		0			0
$519$			13.3950i			0.587974i
$520$		0			0
$521$	33.9514	−	19.6018i	1.48744	−	0.858772i	0.487539	−	0.873101i	$-0.337895\pi$
$521$	33.9514	−	19.6018i	1.48744	−	0.858772i	0.999897	+	0.0143293i	$0.00456131\pi$
$522$		0			0
$523$	3.34343	+	12.4778i	0.146198	+	0.545618i	0.999699	+	0.0245272i	$0.00780803\pi$
$523$	3.34343	+	12.4778i	0.146198	+	0.545618i	−0.853501	+	0.521091i	$0.825525\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.16948	+	19.2928i	0.225186	+	0.840407i
$528$		0			0
$529$	21.0846	−	12.1732i	0.916720	−	0.529268i
$530$		0			0
$531$		−	5.36347i		−	0.232755i
$532$		0			0
$533$	5.30295	+	5.30295i	0.229696	+	0.229696i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−5.79555	+	1.55291i	−0.250097	+	0.0670132i
$538$		0			0
$539$	−33.8840	+	1.97060i	−1.45949	+	0.0848799i
$540$		0			0
$541$	3.09231	−	5.35603i	0.132949	−	0.230274i	−0.791863	−	0.610698i	$-0.790889\pi$
$541$	3.09231	−	5.35603i	0.132949	−	0.230274i	0.924812	+	0.380425i	$0.124222\pi$
$542$		0			0
$543$	1.71309	−	6.39335i	0.0735159	−	0.274365i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	6.87524	−	6.87524i	0.293964	−	0.293964i	−0.544680	−	0.838644i	$-0.683349\pi$
$547$	6.87524	−	6.87524i	0.293964	−	0.293964i	0.838644	+	0.544680i	$0.183349\pi$
$548$		0			0
$549$	−7.63957	−	13.2321i	−0.326049	−	0.564733i
$550$		0			0
$551$	1.72688	+	0.997017i	0.0735677	+	0.0424743i
$552$		0			0
$553$	−0.183191	+	0.00532247i	−0.00779008	+	0.000226334i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−27.2321	−	7.29681i	−1.15386	−	0.309176i	−0.369349	−	0.929291i	$-0.620419\pi$
$557$	−27.2321	−	7.29681i	−1.15386	−	0.309176i	−0.784511	+	0.620115i	$0.787086\pi$
$558$		0			0
$559$	22.8513			0.966506
$560$		0			0
$561$	10.7668			0.454573
$562$		0			0
$563$	24.5297	+	6.57270i	1.03380	+	0.277006i	0.735543	−	0.677478i	$-0.236927\pi$
$563$	24.5297	+	6.57270i	1.03380	+	0.277006i	0.298259	+	0.954485i	$0.403594\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.32874	+	1.25577i	0.0977979	+	0.0527376i
$568$		0			0
$569$	15.7373	+	9.08595i	0.659743	+	0.380903i	0.792179	−	0.610289i	$-0.208947\pi$
$569$	15.7373	+	9.08595i	0.659743	+	0.380903i	−0.132436	+	0.991192i	$0.542280\pi$
$570$		0			0
$571$	3.37306	+	5.84231i	0.141158	+	0.244493i	0.927933	−	0.372747i	$-0.121584\pi$
$571$	3.37306	+	5.84231i	0.141158	+	0.244493i	−0.786775	+	0.617240i	$0.788251\pi$
$572$		0			0
$573$	7.38294	−	7.38294i	0.308427	−	0.308427i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−0.641085	+	2.39256i	−0.0266887	+	0.0996037i	−0.977985	−	0.208673i	$-0.933086\pi$
$577$	−0.641085	+	2.39256i	−0.0266887	+	0.0996037i	0.951297	+	0.308277i	$0.0997522\pi$
$578$		0			0
$579$	−0.298304	+	0.516678i	−0.0123971	+	0.0214724i
$580$		0			0
$581$	−0.403734	+	1.70316i	−0.0167497	+	0.0706591i
$582$		0			0
$583$	−14.2136	+	3.80852i	−0.588667	+	0.157733i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.92874	−	5.92874i	−0.244705	−	0.244705i	0.574088	−	0.818793i	$-0.305357\pi$
$587$	−5.92874	−	5.92874i	−0.244705	−	0.244705i	−0.818793	+	0.574088i	$0.805357\pi$
$588$		0			0
$589$		−	1.93073i		−	0.0795544i
$590$		0			0
$591$	−20.2154	+	11.6714i	−0.831552	+	0.480097i
$592$		0			0
$593$	2.32008	+	8.65864i	0.0952741	+	0.355568i	0.997061	−	0.0766134i	$-0.0244107\pi$
$593$	2.32008	+	8.65864i	0.0952741	+	0.355568i	−0.901787	+	0.432181i	$0.857744\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	6.64426	+	24.7967i	0.271931	+	1.01486i
$598$		0			0
$599$	7.89633	−	4.55895i	0.322635	−	0.186274i	−0.329931	−	0.944005i	$-0.607026\pi$
$599$	7.89633	−	4.55895i	0.322635	−	0.186274i	0.652567	+	0.757731i	$0.273692\pi$
$600$		0			0
$601$		−	45.0586i		−	1.83798i	−0.394281	−	0.918990i	$-0.629006\pi$
$601$		−	45.0586i		−	1.83798i	0.394281	−	0.918990i	$-0.370994\pi$
$602$		0			0
$603$	−3.64076	−	3.64076i	−0.148263	−	0.148263i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−2.45700	+	0.658351i	−0.0997266	+	0.0267217i	−0.308337	−	0.951277i	$-0.599773\pi$
$607$	−2.45700	+	0.658351i	−0.0997266	+	0.0267217i	0.208611	+	0.977999i	$0.433106\pi$
$608$		0			0
$609$	7.04818	+	23.5462i	0.285607	+	0.954141i
$610$		0			0
$611$	15.6155	−	27.0468i	0.631736	−	1.09420i
$612$		0			0
$613$	0.306125	−	1.14248i	0.0123643	−	0.0461442i	−0.959468	−	0.281817i	$-0.909063\pi$
$613$	0.306125	−	1.14248i	0.0123643	−	0.0461442i	0.971832	+	0.235673i	$0.0757295\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.58337	−	2.58337i	0.104003	−	0.104003i	−0.653191	−	0.757193i	$-0.726570\pi$
$617$	2.58337	−	2.58337i	0.104003	−	0.104003i	0.757193	+	0.653191i	$0.226570\pi$
$618$		0			0
$619$	−3.51887	−	6.09486i	−0.141435	−	0.244973i	0.786602	−	0.617460i	$-0.211838\pi$
$619$	−3.51887	−	6.09486i	−0.141435	−	0.244973i	−0.928037	+	0.372487i	$0.878505\pi$
$620$		0			0
$621$	5.95901	+	3.44043i	0.239127	+	0.138060i
$622$		0			0
$623$	0.153217	+	5.27349i	0.00613851	+	0.211278i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.00531	−	0.269372i	−0.0401482	−	0.0107577i
$628$		0			0
$629$	22.4946			0.896920
$630$		0			0
$631$	1.92817			0.0767594			0.0383797	−	0.999263i	$-0.487780\pi$
$631$	1.92817			0.0767594			0.0383797	+	0.999263i	$0.487780\pi$
$632$		0			0
$633$	−11.4797	−	3.07598i	−0.456277	−	0.122259i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−7.08916	−	21.4000i	−0.280883	−	0.847900i
$638$		0			0
$639$	−11.2473	−	6.49364i	−0.444937	−	0.256884i
$640$		0			0
$641$	−14.7962	−	25.6277i	−0.584413	−	1.01223i	−0.994948	−	0.100388i	$-0.967992\pi$
$641$	−14.7962	−	25.6277i	−0.584413	−	1.01223i	0.410535	−	0.911845i	$-0.365342\pi$
$642$		0			0
$643$	16.2563	−	16.2563i	0.641085	−	0.641085i	−0.309737	−	0.950822i	$-0.600241\pi$
$643$	16.2563	−	16.2563i	0.641085	−	0.641085i	0.950822	+	0.309737i	$0.100241\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.4457	+	38.9839i	−0.410663	+	1.53261i	0.382705	+	0.923871i	$0.374993\pi$
$647$	−10.4457	+	38.9839i	−0.410663	+	1.53261i	−0.793367	+	0.608743i	$0.791674\pi$
$648$		0			0
$649$	−13.0030	+	22.5219i	−0.510414	+	0.884063i
$650$		0			0
$651$	16.3321	−	17.3095i	0.640104	−	0.678413i
$652$		0			0
$653$	−37.4074	+	10.0233i	−1.46387	+	0.392242i	−0.900823	−	0.434186i	$-0.857036\pi$
$653$	−37.4074	+	10.0233i	−1.46387	+	0.392242i	−0.563043	+	0.826428i	$0.690369\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.106954	−	0.106954i	−0.00417268	−	0.00417268i
$658$		0			0
$659$			17.2564i			0.672215i	0.941824	+	0.336108i	$0.109111\pi$
$659$			17.2564i			0.672215i	−0.941824	+	0.336108i	$0.890889\pi$
$660$		0			0
$661$	−21.8475	+	12.6136i	−0.849768	+	0.490614i	−0.860573	−	0.509328i	$-0.829894\pi$
$661$	−21.8475	+	12.6136i	−0.849768	+	0.490614i	0.0108046	+	0.999942i	$0.496561\pi$
$662$		0			0
$663$	1.85088	+	6.90758i	0.0718823	+	0.268268i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	16.5442	+	61.7438i	0.640594	+	2.39073i
$668$		0			0
$669$	−23.0186	+	13.2898i	−0.889950	+	0.513813i
$670$		0			0
$671$			74.0846i			2.86001i
$672$		0			0
$673$	21.3943	+	21.3943i	0.824690	+	0.824690i	0.986777	−	0.162087i	$-0.0518224\pi$
$673$	21.3943	+	21.3943i	0.824690	+	0.824690i	−0.162087	+	0.986777i	$0.551822\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.71265	+	2.06660i	−0.296421	+	0.0794258i	−0.403965	−	0.914775i	$-0.632368\pi$
$677$	−7.71265	+	2.06660i	−0.296421	+	0.0794258i	0.107544	+	0.994200i	$0.465702\pi$
$678$		0			0
$679$	−27.3614	−	6.48600i	−1.05003	−	0.248910i
$680$		0			0
$681$	−9.24880	+	16.0194i	−0.354415	+	0.613864i
$682$		0			0
$683$	−2.47976	+	9.25458i	−0.0948853	+	0.354117i	−0.997002	−	0.0773753i	$-0.975346\pi$
$683$	−2.47976	+	9.25458i	−0.0948853	+	0.354117i	0.902117	+	0.431492i	$0.142013\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−9.04645	+	9.04645i	−0.345143	+	0.345143i
$688$		0			0
$689$	−4.88683	−	8.46425i	−0.186174	−	0.322462i
$690$		0			0
$691$	3.01288	+	1.73949i	0.114615	+	0.0661731i	0.556212	−	0.831041i	$-0.312254\pi$
$691$	3.01288	+	1.73949i	0.114615	+	0.0661731i	−0.441596	+	0.897214i	$0.645588\pi$
$692$		0			0
$693$	−6.73423	−	10.9189i	−0.255812	−	0.414775i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.99465	+	1.33831i	0.189186	+	0.0506922i
$698$		0			0
$699$	15.3842			0.581886
$700$		0			0
$701$	−28.6129			−1.08070			−0.540348	−	0.841442i	$-0.681707\pi$
$701$	−28.6129			−1.08070			−0.540348	+	0.841442i	$0.681707\pi$
$702$		0			0
$703$	−2.10036	−	0.562789i	−0.0792165	−	0.0212260i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.31509	−	11.7109i	0.237503	−	0.440432i
$708$		0			0
$709$	−29.7847	−	17.1962i	−1.11859	−	0.645817i	−0.177548	−	0.984112i	$-0.556817\pi$
$709$	−29.7847	−	17.1962i	−1.11859	−	0.645817i	−0.941040	+	0.338295i	$0.890150\pi$
$710$		0			0
$711$	−0.0346345	−	0.0599887i	−0.00129890	−	0.00224975i
$712$		0			0
$713$	43.7647	−	43.7647i	1.63900	−	1.63900i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.44828	−	12.8692i	0.128779	−	0.480608i
$718$		0			0
$719$	16.4619	−	28.5129i	0.613926	−	1.06335i	−0.376646	−	0.926357i	$-0.622923\pi$
$719$	16.4619	−	28.5129i	0.613926	−	1.06335i	0.990572	−	0.136994i	$-0.0437440\pi$
$720$		0			0
$721$	11.2552	+	10.6196i	0.419164	+	0.395495i
$722$		0			0
$723$	−3.03292	+	0.812670i	−0.112796	+	0.0302235i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−34.2948	−	34.2948i	−1.27192	−	1.27192i	−0.945078	−	0.326846i	$-0.894014\pi$
$727$	−34.2948	−	34.2948i	−1.27192	−	1.27192i	−0.326846	−	0.945078i	$-0.605986\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	13.6449	−	7.87788i	0.504675	−	0.291374i
$732$		0			0
$733$	2.48333	+	9.26793i	0.0917240	+	0.342319i	0.996502	−	0.0835640i	$-0.0266303\pi$
$733$	2.48333	+	9.26793i	0.0917240	+	0.342319i	−0.904778	+	0.425883i	$0.859964\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.46149	+	24.1146i	0.238012	+	0.888274i
$738$		0			0
$739$	−10.5145	+	6.07055i	−0.386782	+	0.223309i	−0.680765	−	0.732502i	$-0.738352\pi$
$739$	−10.5145	+	6.07055i	−0.386782	+	0.223309i	0.293983	+	0.955811i	$0.405019\pi$
$740$		0			0
$741$		−	0.691279i		−	0.0253948i
$742$		0			0
$743$	35.2058	+	35.2058i	1.29158	+	1.29158i	0.933811	+	0.357766i	$0.116461\pi$
$743$	35.2058	+	35.2058i	1.29158	+	1.29158i	0.357766	+	0.933811i	$0.383539\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.639032	+	0.171228i	−0.0233810	+	0.00626491i
$748$		0			0
$749$	6.75731	+	6.37574i	0.246907	+	0.232964i
$750$		0			0
$751$	−7.23084	+	12.5242i	−0.263857	+	0.457014i	−0.967264	−	0.253774i	$-0.918328\pi$
$751$	−7.23084	+	12.5242i	−0.263857	+	0.457014i	0.703406	+	0.710788i	$0.251661\pi$
$752$		0			0
$753$	−4.25111	+	15.8654i	−0.154919	+	0.578166i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.14729	−	1.14729i	0.0416989	−	0.0416989i	−0.685950	−	0.727649i	$-0.740613\pi$
$757$	1.14729	−	1.14729i	0.0416989	−	0.0416989i	0.727649	+	0.685950i	$0.240613\pi$
$758$		0			0
$759$	−16.6818	−	28.8937i	−0.605510	−	1.04877i
$760$		0			0
$761$	−31.6887	−	18.2955i	−1.14872	−	0.663211i	−0.200142	−	0.979767i	$-0.564140\pi$
$761$	−31.6887	−	18.2955i	−1.14872	−	0.663211i	−0.948574	+	0.316556i	$0.897474\pi$
$762$		0			0
$763$	14.7764	−	27.4017i	0.534941	−	0.992009i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.6846	−	4.47063i	−0.602446	−	0.161425i
$768$		0			0
$769$	9.84303			0.354949			0.177474	−	0.984125i	$-0.443207\pi$
$769$	9.84303			0.354949			0.177474	+	0.984125i	$0.443207\pi$
$770$		0			0
$771$	16.3591			0.589157
$772$		0			0
$773$	−35.4124	−	9.48871i	−1.27369	−	0.341285i	−0.442249	−	0.896892i	$-0.645819\pi$
$773$	−35.4124	−	9.48871i	−1.27369	−	0.341285i	−0.831445	+	0.555607i	$0.812486\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−14.0696	−	22.8125i	−0.504744	−	0.818394i
$778$		0			0
$779$	−0.432875	−	0.249921i	−0.0155094	−	0.00895434i
$780$		0			0
$781$	31.4860	+	54.5354i	1.12666	+	1.95143i
$782$		0			0
$783$	−6.56888	+	6.56888i	−0.234752	+	0.234752i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	5.89847	−	22.0134i	0.210258	−	0.784693i	−0.777524	−	0.628853i	$-0.783525\pi$
$787$	5.89847	−	22.0134i	0.210258	−	0.784693i	0.987782	−	0.155840i	$-0.0498085\pi$
$788$		0			0
$789$	14.4057	−	24.9514i	0.512856	−	0.888292i
$790$		0			0
$791$	−36.2898	−	8.60248i	−1.29032	−	0.305869i
$792$		0			0
$793$	−47.5302	+	12.7357i	−1.68785	+	0.452257i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−31.7293	−	31.7293i	−1.12391	−	1.12391i	−0.991148	−	0.132760i	$-0.957616\pi$
$797$	−31.7293	−	31.7293i	−1.12391	−	1.12391i	−0.132760	−	0.991148i	$-0.542384\pi$
$798$		0			0
$799$		−	21.5335i		−	0.761801i
$800$		0			0
$801$	−1.72688	+	0.997017i	−0.0610164	+	0.0352279i
$802$		0			0
$803$	0.189818	+	0.708411i	0.00669854	+	0.0249993i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.56180	−	13.2928i	−0.125381	−	0.467929i
$808$		0			0
$809$	14.9445	−	8.62822i	0.525421	−	0.303352i	−0.213729	−	0.976893i	$-0.568561\pi$
$809$	14.9445	−	8.62822i	0.525421	−	0.303352i	0.739150	+	0.673541i	$0.235228\pi$
$810$		0			0
$811$		−	46.1720i		−	1.62132i	−0.585517	−	0.810660i	$-0.699109\pi$
$811$		−	46.1720i		−	1.62132i	0.585517	−	0.810660i	$-0.300891\pi$
$812$		0			0
$813$	8.42144	+	8.42144i	0.295353	+	0.295353i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.47114	+	0.394191i	−0.0514687	+	0.0137910i
$818$		0			0
$819$	5.84753	−	6.19749i	0.204329	−	0.216558i
$820$		0			0
$821$	−9.49364	+	16.4435i	−0.331330	+	0.573881i	−0.982773	−	0.184817i	$-0.940831\pi$
$821$	−9.49364	+	16.4435i	−0.331330	+	0.573881i	0.651443	+	0.758698i	$0.274164\pi$
$822$		0			0
$823$	7.68955	−	28.6978i	0.268041	−	1.00034i	−0.692322	−	0.721589i	$-0.743412\pi$
$823$	7.68955	−	28.6978i	0.268041	−	1.00034i	0.960363	−	0.278753i	$-0.0899211\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	20.1361	−	20.1361i	0.700201	−	0.700201i	−0.264253	−	0.964453i	$-0.585125\pi$
$827$	20.1361	−	20.1361i	0.700201	−	0.700201i	0.964453	+	0.264253i	$0.0851254\pi$
$828$		0			0
$829$	23.6174	+	40.9066i	0.820267	+	1.42074i	0.905483	+	0.424382i	$0.139508\pi$
$829$	23.6174	+	40.9066i	0.820267	+	1.42074i	−0.0852165	+	0.996362i	$0.527158\pi$
$830$		0			0
$831$	−17.4013	−	10.0467i	−0.603646	−	0.348515i
$832$		0			0
$833$	−11.6106	−	10.3344i	−0.402284	−	0.358065i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	8.68839	+	2.32805i	0.300315	+	0.0804690i
$838$		0			0
$839$	−40.5791			−1.40094			−0.700472	−	0.713680i	$-0.747027\pi$
$839$	−40.5791			−1.40094			−0.700472	+	0.713680i	$0.747027\pi$
$840$		0			0
$841$	−57.3003			−1.97587
$842$		0			0
$843$	−12.1509	−	3.25584i	−0.418501	−	0.112137i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.961264	+	33.0852i	0.0330294	+	1.13682i
$848$		0			0
$849$	−15.5774	−	8.99364i	−0.534616	−	0.308661i
$850$		0			0
$851$	−34.8527	−	60.3667i	−1.19474	−	2.06934i
$852$		0			0
$853$	34.2440	−	34.2440i	1.17249	−	1.17249i	0.190879	−	0.981614i	$-0.438866\pi$
$853$	34.2440	−	34.2440i	1.17249	−	1.17249i	0.981614	−	0.190879i	$-0.0611337\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.53347	+	20.6512i	−0.189020	+	0.705432i	0.804714	+	0.593662i	$0.202318\pi$
$857$	−5.53347	+	20.6512i	−0.189020	+	0.705432i	−0.993734	+	0.111769i	$0.964348\pi$
$858$		0			0
$859$	19.0104	−	32.9271i	0.648628	−	1.12346i	−0.334823	−	0.942281i	$-0.608676\pi$
$859$	19.0104	−	32.9271i	0.648628	−	1.12346i	0.983451	−	0.181175i	$-0.0579902\pi$
$860$		0			0
$861$	−1.76676	−	5.90230i	−0.0602109	−	0.201150i
$862$		0			0
$863$	21.3693	−	5.72588i	0.727419	−	0.194911i	0.123939	−	0.992290i	$-0.460447\pi$
$863$	21.3693	−	5.72588i	0.727419	−	0.194911i	0.603480	+	0.797378i	$0.293781\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−8.53426	−	8.53426i	−0.289839	−	0.289839i
$868$		0			0
$869$			0.335868i			0.0113935i
$870$		0			0
$871$	−14.3603	+	8.29095i	−0.486582	+	0.280928i
$872$		0			0
$873$	−2.75079	−	10.2661i	−0.0931000	−	0.347454i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.41164	+	23.9286i	0.216506	+	0.808010i	0.985631	+	0.168912i	$0.0540255\pi$
$877$	6.41164	+	23.9286i	0.216506	+	0.808010i	−0.769125	+	0.639098i	$0.779308\pi$
$878$		0			0
$879$	0.501938	−	0.289794i	0.0169299	−	0.00977451i
$880$		0			0
$881$			30.2237i			1.01826i	0.860689	+	0.509130i	$0.170033\pi$
$881$			30.2237i			1.01826i	−0.860689	+	0.509130i	$0.829967\pi$
$882$		0			0
$883$	−15.9836	−	15.9836i	−0.537890	−	0.537890i	0.385019	−	0.922909i	$-0.374195\pi$
$883$	−15.9836	−	15.9836i	−0.537890	−	0.537890i	−0.922909	+	0.385019i	$0.874195\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	42.3276	−	11.3416i	1.42122	−	0.380815i	0.535305	−	0.844659i	$-0.320197\pi$
$887$	42.3276	−	11.3416i	1.42122	−	0.380815i	0.885917	+	0.463844i	$0.153530\pi$
$888$		0			0
$889$	3.19990	−	13.4989i	0.107321	−	0.452738i
$890$		0			0
$891$	2.42437	−	4.19914i	0.0812195	−	0.140676i
$892$		0			0
$893$	−0.538743	+	2.01062i	−0.0180284	+	0.0672828i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	15.6695	−	15.6695i	0.523189	−	0.523189i
$898$		0			0
$899$	41.7803	+	72.3656i	1.39345	+	2.41353i
$900$		0			0
$901$	−5.83603	−	3.36943i	−0.194426	−	0.112252i
$902$		0			0
$903$	−16.5236	−	8.91037i	−0.549871	−	0.296518i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.11585	+	1.63874i	0.203074	+	0.0544134i	0.358922	−	0.933368i	$-0.383144\pi$
$907$	6.11585	+	1.63874i	0.203074	+	0.0544134i	−0.155848	+	0.987781i	$0.549811\pi$
$908$		0			0
$909$	5.02884			0.166796
$910$		0			0
$911$	−3.12582			−0.103563			−0.0517815	−	0.998658i	$-0.516490\pi$
$911$	−3.12582			−0.103563			−0.0517815	+	0.998658i	$0.516490\pi$
$912$		0			0
$913$	3.09850	+	0.830242i	0.102546	+	0.0274770i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−28.3688	+	0.824233i	−0.936821	+	0.0272186i
$918$		0			0
$919$	−22.2726	−	12.8591i	−0.734704	−	0.424181i	0.0854368	−	0.996344i	$-0.472771\pi$
$919$	−22.2726	−	12.8591i	−0.734704	−	0.424181i	−0.820140	+	0.572162i	$0.806105\pi$
$920$		0			0
$921$	−0.528276	−	0.915000i	−0.0174073	−	0.0301503i
$922$		0			0
$923$	−29.5754	+	29.5754i	−0.973485	+	0.973485i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.51377	+	5.64945i	−0.0497186	+	0.185552i
$928$		0			0
$929$	12.9320	−	22.3989i	0.424286	−	0.734885i	−0.572067	−	0.820207i	$-0.693858\pi$
$929$	12.9320	−	22.3989i	0.424286	−	0.734885i	0.996353	+	0.0853214i	$0.0271917\pi$
$930$		0			0
$931$	0.825549	+	1.25542i	0.0270563	+	0.0411447i
$932$		0			0
$933$	−18.1503	+	4.86336i	−0.594214	+	0.159219i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	37.7290	+	37.7290i	1.23255	+	1.23255i	0.962980	+	0.269571i	$0.0868820\pi$
$937$	37.7290	+	37.7290i	1.23255	+	1.23255i	0.269571	+	0.962980i	$0.413118\pi$
$938$		0			0
$939$		−	3.84874i		−	0.125599i
$940$		0			0
$941$	12.7755	−	7.37595i	0.416470	−	0.240449i	−0.277096	−	0.960842i	$-0.589372\pi$
$941$	12.7755	−	7.37595i	0.416470	−	0.240449i	0.693566	+	0.720393i	$0.256039\pi$
$942$		0			0
$943$	−4.14711	−	15.4772i	−0.135048	−	0.504008i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.93189	+	10.9420i	0.0952737	+	0.355566i	0.997061	−	0.0766141i	$-0.0244110\pi$
$947$	2.93189	+	10.9420i	0.0952737	+	0.355566i	−0.901787	+	0.432181i	$0.857744\pi$
$948$		0			0
$949$	−0.421861	+	0.243562i	−0.0136942	+	0.00790635i
$950$		0			0
$951$		−	3.17681i		−	0.103015i
$952$		0			0
$953$	25.4266	+	25.4266i	0.823648	+	0.823648i	0.986629	−	0.162981i	$-0.0521109\pi$
$953$	25.4266	+	25.4266i	0.823648	+	0.823648i	−0.162981	+	0.986629i	$0.552111\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	43.5090	−	11.6582i	1.40645	−	0.376856i
$958$		0			0
$959$	36.0891	−	10.8027i	1.16538	−	0.348836i
$960$		0			0
$961$	24.9539	−	43.2215i	0.804965	−	1.39424i
$962$		0			0
$963$	−0.908827	+	3.39179i	−0.0292865	+	0.109299i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	42.9279	−	42.9279i	1.38047	−	1.38047i	0.536691	−	0.843779i	$-0.319674\pi$
$967$	42.9279	−	42.9279i	1.38047	−	1.38047i	0.843779	−	0.536691i	$-0.180326\pi$
$968$		0			0
$969$	−0.238315	−	0.412774i	−0.00765579	−	0.0132602i
$970$		0			0
$971$	38.9180	+	22.4693i	1.24894	+	0.721075i	0.970898	−	0.239494i	$-0.0769817\pi$
$971$	38.9180	+	22.4693i	1.24894	+	0.721075i	0.278041	+	0.960569i	$0.410315\pi$
$972$		0			0
$973$	−31.4735	+	19.4113i	−1.00899	+	0.622296i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	41.2596	+	11.0555i	1.32001	+	0.353696i	0.848982	−	0.528421i	$-0.177216\pi$
$977$	41.2596	+	11.0555i	1.32001	+	0.353696i	0.471030	+	0.882117i	$0.343882\pi$
$978$		0			0
$979$	9.66856			0.309009
$980$		0			0
$981$	11.7668			0.375684
$982$		0			0
$983$	4.92876	+	1.32066i	0.157203	+	0.0421224i	0.336562	−	0.941661i	$-0.390736\pi$
$983$	4.92876	+	1.32066i	0.157203	+	0.0421224i	−0.179359	+	0.983784i	$0.557402\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−21.8378	+	13.4685i	−0.695105	+	0.428706i
$988$		0			0
$989$	−42.2822	−	24.4117i	−1.34450	−	0.776245i
$990$		0			0
$991$	−4.44233	−	7.69434i	−0.141115	−	0.244419i	0.786802	−	0.617206i	$-0.211735\pi$
$991$	−4.44233	−	7.69434i	−0.141115	−	0.244419i	−0.927917	+	0.372787i	$0.878402\pi$
$992$		0			0
$993$	−11.3283	+	11.3283i	−0.359493	+	0.359493i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	8.62137	−	32.1754i	0.273042	−	1.01901i	−0.684101	−	0.729388i	$-0.739805\pi$
$997$	8.62137	−	32.1754i	0.273042	−	1.01901i	0.957142	−	0.289618i	$-0.0935282\pi$
$998$		0			0
$999$	5.06516	−	8.77312i	0.160255	−	0.277569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.d.1993.1	yes	24
5.2	odd	4	inner	2100.2.ce.d.1657.1	yes	24
5.3	odd	4	inner	2100.2.ce.d.1657.5	yes	24
5.4	even	2	inner	2100.2.ce.d.1993.5	yes	24
7.3	odd	6	inner	2100.2.ce.d.493.1	yes	24
35.3	even	12	inner	2100.2.ce.d.157.6	yes	24
35.17	even	12	inner	2100.2.ce.d.157.1	✓	24
35.24	odd	6	inner	2100.2.ce.d.493.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.d.157.1	✓	24	35.17	even	12	inner
2100.2.ce.d.157.6	yes	24	35.3	even	12	inner
2100.2.ce.d.493.1	yes	24	7.3	odd	6	inner
2100.2.ce.d.493.5	yes	24	35.24	odd	6	inner
2100.2.ce.d.1657.1	yes	24	5.2	odd	4	inner
2100.2.ce.d.1657.5	yes	24	5.3	odd	4	inner
2100.2.ce.d.1993.1	yes	24	1.1	even	1	trivial
2100.2.ce.d.1993.5	yes	24	5.4	even	2	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.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{3} +(2.25190 - 1.38886i) q^{7} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{3} +(2.25190 - 1.38886i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-2.42437 - 4.19914i) q^{11} +(2.27726 - 2.27726i) q^{13} +(0.574714 - 2.14486i) q^{17} +(-0.107324 + 0.185890i) q^{19} +(-2.53463 + 0.758702i) q^{21} +(-6.64641 + 1.78090i) q^{23} +(-0.707107 - 0.707107i) q^{27} -9.28979i q^{29} +(-7.78979 + 4.49744i) q^{31} +(1.25495 + 4.68353i) q^{33} +(2.62192 + 9.78514i) q^{37} +(-2.78906 + 1.61026i) q^{39} +2.32866i q^{41} +(5.01729 + 5.01729i) q^{43} +(9.36705 - 2.50989i) q^{47} +(3.14213 - 6.25516i) q^{49} +(-1.11026 + 1.92303i) q^{51} +(0.785466 - 2.93140i) q^{53} +(0.151779 - 0.151779i) q^{57} +(-2.68173 - 4.64490i) q^{59} +(-13.2321 - 7.63957i) q^{61} +(2.64464 - 0.0768377i) q^{63} +(-4.97338 - 1.33261i) q^{67} +6.88087 q^{69} -12.9873 q^{71} +(-0.146102 - 0.0391479i) q^{73} +(-11.2915 - 6.08893i) q^{77} +(-0.0599887 - 0.0346345i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.467804 + 0.467804i) q^{83} +(-2.40438 + 8.97325i) q^{87} +(-0.997017 + 1.72688i) q^{89} +(1.96537 - 8.29095i) q^{91} +(8.68839 - 2.32805i) q^{93} +(-7.51529 - 7.51529i) q^{97} -4.84874i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{11} + 8 q^{21} - 12 q^{31} - 8 q^{51} - 48 q^{61} + 64 q^{71} + 12 q^{81} + 116 q^{91}+O(q^{100}) \) 24 * q - 8 * q^11 + 8 * q^21 - 12 * q^31 - 8 * q^51 - 48 * q^61 + 64 * q^71 + 12 * q^81 + 116 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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