LMFDB - Embedded newform 2100.2.ce.d.1657.1

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			1657.1
Character	$\chi$	$=$	2100.1657
Dual form			2100.2.ce.d.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{3} +(1.38886 + 2.25190i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{3} +(1.38886 + 2.25190i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(-2.42437 - 4.19914i) q^{11} +(-2.27726 - 2.27726i) q^{13} +(2.14486 + 0.574714i) q^{17} +(0.107324 - 0.185890i) q^{19} +(-2.53463 + 0.758702i) q^{21} +(1.78090 + 6.64641i) q^{23} +(0.707107 - 0.707107i) q^{27} +9.28979i q^{29} +(-7.78979 + 4.49744i) q^{31} +(4.68353 - 1.25495i) q^{33} +(-9.78514 + 2.62192i) q^{37} +(2.78906 - 1.61026i) q^{39} +2.32866i q^{41} +(5.01729 - 5.01729i) q^{43} +(2.50989 + 9.36705i) q^{47} +(-3.14213 + 6.25516i) q^{49} +(-1.11026 + 1.92303i) q^{51} +(-2.93140 - 0.785466i) q^{53} +(0.151779 + 0.151779i) q^{57} +(2.68173 + 4.64490i) q^{59} +(-13.2321 - 7.63957i) q^{61} +(-0.0768377 - 2.64464i) q^{63} +(1.33261 - 4.97338i) q^{67} -6.88087 q^{69} -12.9873 q^{71} +(-0.0391479 + 0.146102i) q^{73} +(6.08893 - 11.2915i) q^{77} +(0.0599887 + 0.0346345i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.467804 + 0.467804i) q^{83} +(-8.97325 - 2.40438i) q^{87} +(0.997017 - 1.72688i) q^{89} +(1.96537 - 8.29095i) q^{91} +(-2.32805 - 8.68839i) q^{93} +(7.51529 - 7.51529i) q^{97} +4.84874i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.38886	+	2.25190i	0.524940	+	0.851139i
$7$	1.38886	+	2.25190i	0.524940	+	0.851139i
$8$		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	$-0.397368\pi$
$13$	−2.27726	−	2.27726i	−0.631597	−	0.631597i	−0.948468	+	0.316872i	$0.897368\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.14486	+	0.574714i	0.520206	+	0.139389i	0.509362	−	0.860553i	$-0.329882\pi$
$17$	2.14486	+	0.574714i	0.520206	+	0.139389i	0.0108439	+	0.999941i	$0.496548\pi$
$18$		0			0
$19$	0.107324	−	0.185890i	0.0246218	−	0.0426462i	−0.853452	−	0.521172i	$-0.825495\pi$
$19$	0.107324	−	0.185890i	0.0246218	−	0.0426462i	0.878074	+	0.478525i	$0.158829\pi$
$20$		0			0
$21$	−2.53463	+	0.758702i	−0.553103	+	0.165562i
$22$		0			0
$23$	1.78090	+	6.64641i	0.371343	+	1.38587i	0.858615	+	0.512621i	$0.171326\pi$
$23$	1.78090	+	6.64641i	0.371343	+	1.38587i	−0.487272	+	0.873251i	$0.662008\pi$
$24$		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	$0.331125\pi$
$29$			9.28979i			1.72507i	−0.505996	+	0.862536i	$0.668875\pi$
$30$		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
$33$	4.68353	−	1.25495i	0.815297	−	0.218458i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−9.78514	+	2.62192i	−1.60867	+	0.431041i	−0.947645	−	0.319326i	$-0.896544\pi$
$37$	−9.78514	+	2.62192i	−1.60867	+	0.431041i	−0.661022	+	0.750367i	$0.729877\pi$
$38$		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	−0.212115	−	0.977245i	$-0.568035\pi$
$43$	5.01729	−	5.01729i	0.765129	−	0.765129i	0.977245	+	0.212115i	$0.0680353\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.50989	+	9.36705i	0.366106	+	1.36633i	0.865916	+	0.500190i	$0.166737\pi$
$47$	2.50989	+	9.36705i	0.366106	+	1.36633i	−0.499810	+	0.866135i	$0.666597\pi$
$48$		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
$53$	−2.93140	−	0.785466i	−0.402658	−	0.107892i	0.0518054	−	0.998657i	$-0.483502\pi$
$53$	−2.93140	−	0.785466i	−0.402658	−	0.107892i	−0.454464	+	0.890765i	$0.650169\pi$
$54$		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	0.986095	−	0.166180i	$-0.0531432\pi$
$59$	2.68173	+	4.64490i	0.349132	+	0.604714i	−0.636964	+	0.770894i	$0.719810\pi$
$60$		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
$63$	−0.0768377	−	2.64464i	−0.00968064	−	0.333193i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.33261	−	4.97338i	0.162804	−	0.607595i	−0.835506	−	0.549482i	$-0.814825\pi$
$67$	1.33261	−	4.97338i	0.162804	−	0.607595i	0.998310	−	0.0581126i	$-0.0185082\pi$
$68$		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
$73$	−0.0391479	+	0.146102i	−0.00458192	+	0.0170999i	−0.968179	−	0.250259i	$-0.919484\pi$
$73$	−0.0391479	+	0.146102i	−0.00458192	+	0.0170999i	0.963597	+	0.267359i	$0.0861509\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.08893	−	11.2915i	0.693898	−	1.28678i
$78$		0			0
$79$	0.0599887	+	0.0346345i	0.00674926	+	0.00389669i	0.503371	−	0.864070i	$-0.332093\pi$
$79$	0.0599887	+	0.0346345i	0.00674926	+	0.00389669i	−0.496622	+	0.867967i	$0.665426\pi$
$80$		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	$-0.238440\pi$
$83$	0.467804	+	0.467804i	0.0513482	+	0.0513482i	−0.680966	+	0.732315i	$0.738440\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−8.97325	−	2.40438i	−0.962034	−	0.257776i
$88$		0			0
$89$	0.997017	−	1.72688i	0.105684	−	0.183049i	−0.808334	−	0.588725i	$-0.799630\pi$
$89$	0.997017	−	1.72688i	0.105684	−	0.183049i	0.914017	+	0.405675i	$0.132964\pi$
$90$		0			0
$91$	1.96537	−	8.29095i	0.206026	−	0.869127i
$92$		0			0
$93$	−2.32805	−	8.68839i	−0.241407	−	0.900944i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.51529	−	7.51529i	0.763062	−	0.763062i	−0.213813	−	0.976875i	$-0.568588\pi$
$97$	7.51529	−	7.51529i	0.763062	−	0.763062i	0.976875	+	0.213813i	$0.0685883\pi$
$98$		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
$103$	5.64945	−	1.51377i	0.556657	−	0.149156i	0.0304870	−	0.999535i	$-0.490294\pi$
$103$	5.64945	−	1.51377i	0.556657	−	0.149156i	0.526170	+	0.850379i	$0.323628\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.39179	+	0.908827i	−0.327896	+	0.0878596i	−0.419012	−	0.907981i	$-0.637623\pi$
$107$	−3.39179	+	0.908827i	−0.327896	+	0.0878596i	0.0911154	+	0.995840i	$0.470957\pi$
$108$		0			0
$109$	−10.1903	+	5.88338i	−0.976055	+	0.563525i	−0.901077	−	0.433660i	$-0.857222\pi$
$109$	−10.1903	+	5.88338i	−0.976055	+	0.563525i	−0.0749780	+	0.997185i	$0.523889\pi$
$110$		0			0
$111$		−	10.1303i		−	0.961528i
$112$		0			0
$113$	−9.96763	+	9.96763i	−0.937676	+	0.937676i	−0.998169	−	0.0604926i	$-0.980733\pi$
$113$	−9.96763	+	9.96763i	−0.937676	+	0.937676i	0.0604926	+	0.998169i	$0.480733\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.833533	+	3.11079i	0.0770602	+	0.287592i
$118$		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
$123$	−2.24931	−	0.602701i	−0.202814	−	0.0543437i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	3.70771	+	3.70771i	0.329006	+	0.329006i	0.852208	−	0.523203i	$-0.175263\pi$
$127$	3.70771	+	3.70771i	0.329006	+	0.329006i	−0.523203	+	0.852208i	$0.675263\pi$
$128$		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
$133$	0.567665	−	0.0164930i	0.0492228	−	0.00143013i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.68516	+	13.7532i	−0.314845	+	1.17502i	0.609290	+	0.792948i	$0.291455\pi$
$137$	−3.68516	+	13.7532i	−0.314845	+	1.17502i	−0.924134	+	0.382068i	$0.875212\pi$
$138$		0			0
$139$	13.9764			1.18546			0.592731	−	0.805401i	$-0.298050\pi$
$139$	13.9764			1.18546			0.592731	+	0.805401i	$0.298050\pi$
$140$		0			0
$141$	−9.69749			−0.816676
$142$		0			0
$143$	−4.04159	+	15.0834i	−0.337975	+	1.26134i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.22878	−	4.65402i	−0.431262	−	0.383857i
$148$		0			0
$149$	−9.74836	−	5.62822i	−0.798617	−	0.461082i	0.0443704	−	0.999015i	$-0.485872\pi$
$149$	−9.74836	−	5.62822i	−0.798617	−	0.461082i	−0.842987	+	0.537933i	$0.819205\pi$
$150$		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
$157$	−6.22158	−	1.66707i	−0.496536	−	0.133046i	0.00185597	−	0.999998i	$-0.499409\pi$
$157$	−6.22158	−	1.66707i	−0.496536	−	0.133046i	−0.498392	+	0.866952i	$0.666076\pi$
$158$		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
$163$	2.68973	+	10.0382i	0.210676	+	0.786252i	0.987644	+	0.156713i	$0.0500897\pi$
$163$	2.68973	+	10.0382i	0.210676	+	0.786252i	−0.776969	+	0.629539i	$0.783244\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.1957	−	13.1957i	1.02112	−	1.02112i	0.0213437	−	0.999772i	$-0.493206\pi$
$167$	13.1957	−	13.1957i	1.02112	−	1.02112i	0.999772	−	0.0213437i	$-0.00679444\pi$
$168$		0			0
$169$		−	2.62822i		−	0.202171i
$170$		0			0
$171$	−0.185890	+	0.107324i	−0.0142154	+	0.00820726i
$172$		0			0
$173$	−12.9386	+	3.46687i	−0.983700	+	0.263582i	−0.714602	−	0.699531i	$-0.753392\pi$
$173$	−12.9386	+	3.46687i	−0.983700	+	0.263582i	−0.269098	+	0.963113i	$0.586726\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.18071	+	1.38817i	−0.389406	+	0.104341i
$178$		0			0
$179$	−5.19615	+	3.00000i	−0.388379	+	0.224231i	−0.681457	−	0.731858i	$-0.738654\pi$
$179$	−5.19615	+	3.00000i	−0.388379	+	0.224231i	0.293079	+	0.956088i	$0.405320\pi$
$180$		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
$187$	−2.78664	−	10.3999i	−0.203779	−	0.760515i
$188$		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
$193$	−0.576279	−	0.154414i	−0.0414815	−	0.0111149i	0.238019	−	0.971261i	$-0.423502\pi$
$193$	−0.576279	−	0.154414i	−0.0414815	−	0.0111149i	−0.279500	+	0.960146i	$0.590169\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.5058	+	16.5058i	1.17599	+	1.17599i	0.980756	+	0.195236i	$0.0625474\pi$
$197$	16.5058	+	16.5058i	1.17599	+	1.17599i	0.195236	+	0.980756i	$0.437453\pi$
$198$		0			0
$199$	12.8357	+	22.2321i	0.909900	+	1.57599i	0.814201	+	0.580583i	$0.197175\pi$
$199$	12.8357	+	22.2321i	0.909900	+	1.57599i	0.0956992	+	0.995410i	$0.469491\pi$
$200$		0			0
$201$	4.45901	+	2.57441i	0.314514	+	0.181585i
$202$		0			0
$203$	−20.9197	+	12.9022i	−1.46828	+	0.905559i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.78090	−	6.64641i	0.123781	−	0.461957i
$208$		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
$213$	3.36136	−	12.5448i	0.230316	−	0.859552i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−20.9467	−	11.2955i	−1.42196	−	0.766791i
$218$		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	−0.951771	−	0.306809i	$-0.900739\pi$
$223$	−18.7946	−	18.7946i	−1.25858	−	1.25858i	−0.306809	−	0.951771i	$-0.599261\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.8673	+	4.78753i	1.18590	+	0.317760i	0.797262	−	0.603633i	$-0.206281\pi$
$227$	17.8673	+	4.78753i	1.18590	+	0.317760i	0.388633	+	0.921393i	$0.372947\pi$
$228$		0			0
$229$	−6.39680	+	11.0796i	−0.422713	+	0.732160i	−0.996204	−	0.0870520i	$-0.972255\pi$
$229$	−6.39680	+	11.0796i	−0.422713	+	0.732160i	0.573491	+	0.819212i	$0.305589\pi$
$230$		0			0
$231$	9.33079	+	8.80390i	0.613921	+	0.579254i
$232$		0			0
$233$	3.98174	+	14.8600i	0.260852	+	0.973514i	0.964740	+	0.263203i	$0.0847789\pi$
$233$	3.98174	+	14.8600i	0.260852	+	0.973514i	−0.703888	+	0.710311i	$0.748554\pi$
$234$		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	$-0.858196\pi$
$239$		−	13.3231i		−	0.861803i	0.902399	−	0.430901i	$-0.141804\pi$
$240$		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
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.667724	+	0.178916i	−0.0424863	+	0.0113842i
$248$		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
$257$	−4.23404	−	15.8016i	−0.264112	−	0.985679i	−0.962792	−	0.270245i	$-0.912895\pi$
$257$	−4.23404	−	15.8016i	−0.264112	−	0.985679i	0.698680	−	0.715435i	$-0.253771\pi$
$258$		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
$263$	27.8296	+	7.45693i	1.71605	+	0.459814i	0.976894	−	0.213722i	$-0.0685587\pi$
$263$	27.8296	+	7.45693i	1.71605	+	0.459814i	0.739154	+	0.673536i	$0.235225\pi$
$264$		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	0.576359	−	0.817197i	$-0.304473\pi$
$269$	−6.88087	−	11.9180i	−0.419534	−	0.726654i	−0.995893	+	0.0905428i	$0.971140\pi$
$270$		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
$273$	7.49977	+	4.04425i	0.453906	+	0.244769i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.20054	+	19.4087i	−0.312470	+	1.16615i	0.613852	+	0.789421i	$0.289619\pi$
$277$	−5.20054	+	19.4087i	−0.312470	+	1.16615i	−0.926322	+	0.376733i	$0.877048\pi$
$278$		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
$283$	4.65545	−	17.3744i	0.276738	−	1.03280i	−0.677930	−	0.735126i	$-0.737123\pi$
$283$	4.65545	−	17.3744i	0.276738	−	1.03280i	0.954668	−	0.297673i	$-0.0962106\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.24391	+	3.23418i	−0.309538	+	0.190908i
$288$		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	$-0.244611\pi$
$293$	0.409831	+	0.409831i	0.0239426	+	0.0239426i	−0.695034	+	0.718977i	$0.744611\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.68353	−	1.25495i	−0.271766	−	0.0728194i
$298$		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
$303$	1.30156	+	4.85749i	0.0747726	+	0.279055i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−0.747094	+	0.747094i	−0.0426389	+	0.0426389i	−0.728105	−	0.685466i	$-0.759599\pi$
$307$	−0.747094	+	0.747094i	−0.0426389	+	0.0426389i	0.685466	+	0.728105i	$0.259599\pi$
$308$		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
$313$	3.71760	−	0.996128i	0.210131	−	0.0563045i	−0.152218	−	0.988347i	$-0.548642\pi$
$313$	3.71760	−	0.996128i	0.210131	−	0.0563045i	0.362349	+	0.932042i	$0.381975\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.06856	+	0.822219i	−0.172348	+	0.0461804i	−0.343961	−	0.938984i	$-0.611769\pi$
$317$	−3.06856	+	0.822219i	−0.172348	+	0.0461804i	0.171613	+	0.985164i	$0.445102\pi$
$318$		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
$327$	−3.04546	−	11.3658i	−0.168414	−	0.628531i
$328$		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
$333$	9.78514	+	2.62192i	0.536222	+	0.143680i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	18.6413	+	18.6413i	1.01545	+	1.01545i	0.999879	+	0.0155754i	$0.00495802\pi$
$337$	18.6413	+	18.6413i	1.01545	+	1.01545i	0.0155754	+	0.999879i	$0.495042\pi$
$338$		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
$343$	−18.4500	+	1.61178i	−0.996206	+	0.0870278i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.91820	+	22.0870i	−0.317705	+	1.18569i	0.603739	+	0.797182i	$0.293677\pi$
$347$	−5.91820	+	22.0870i	−0.317705	+	1.18569i	−0.921444	+	0.388511i	$0.872990\pi$
$348$		0			0
$349$	−7.69212			−0.411750			−0.205875	−	0.978578i	$-0.566004\pi$
$349$	−7.69212			−0.411750			−0.205875	+	0.978578i	$0.566004\pi$
$350$		0			0
$351$	−3.22052			−0.171899
$352$		0			0
$353$	−7.89336	+	29.4584i	−0.420121	+	1.56791i	0.354231	+	0.935158i	$0.384743\pi$
$353$	−7.89336	+	29.4584i	−0.420121	+	1.56791i	−0.774352	+	0.632755i	$0.781924\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−5.87248	+	0.170620i	−0.310805	+	0.00903017i
$358$		0			0
$359$	17.1496	+	9.90134i	0.905122	+	0.522572i	0.878858	−	0.477083i	$-0.158306\pi$
$359$	17.1496	+	9.90134i	0.905122	+	0.522572i	0.0262636	+	0.999655i	$0.491639\pi$
$360$		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
$367$	−31.5042	−	8.44151i	−1.64450	−	0.440643i	−0.686437	−	0.727189i	$-0.740826\pi$
$367$	−31.5042	−	8.44151i	−1.64450	−	0.440643i	−0.958067	+	0.286546i	$0.907493\pi$
$368$		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
$373$	−6.97189	−	26.0194i	−0.360991	−	1.34724i	−0.872776	−	0.488122i	$-0.837682\pi$
$373$	−6.97189	−	26.0194i	−0.360991	−	1.34724i	0.511785	−	0.859114i	$-0.328984\pi$
$374$		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	$-0.941309\pi$
$379$		−	7.13854i		−	0.366682i	0.983049	−	0.183341i	$-0.0586913\pi$
$380$		0			0
$381$	−4.54099	+	2.62174i	−0.232642	+	0.134316i
$382$		0			0
$383$	−9.36705	+	2.50989i	−0.478634	+	0.128250i	−0.490067	−	0.871685i	$-0.663028\pi$
$383$	−9.36705	+	2.50989i	−0.478634	+	0.128250i	0.0114324	+	0.999935i	$0.496361\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.85374	+	1.83645i	−0.348395	+	0.0933522i
$388$		0			0
$389$	−4.84308	+	2.79615i	−0.245554	+	0.141771i	−0.617727	−	0.786393i	$-0.711946\pi$
$389$	−4.84308	+	2.79615i	−0.245554	+	0.141771i	0.372173	+	0.928163i	$0.378613\pi$
$390$		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
$397$	7.47195	+	27.8857i	0.375006	+	1.39954i	0.853336	+	0.521362i	$0.174576\pi$
$397$	7.47195	+	27.8857i	0.375006	+	1.39954i	−0.478330	+	0.878180i	$0.658758\pi$
$398$		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
$403$	27.9812	+	7.49753i	1.39384	+	0.373479i
$404$		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	0.694247	−	0.719737i	$-0.255738\pi$
$409$	−5.58555	−	9.67445i	−0.276188	−	0.478371i	−0.970434	+	0.241366i	$0.922404\pi$
$410$		0			0
$411$	−12.3308	−	7.11918i	−0.608233	−	0.351163i
$412$		0			0
$413$	−6.73530	+	12.4901i	−0.331423	+	0.614598i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−3.61735	+	13.5002i	−0.177143	+	0.661105i
$418$		0			0
$419$	33.2585			1.62478			0.812391	−	0.583113i	$-0.198166\pi$
$419$	33.2585			1.62478			0.812391	+	0.583113i	$0.198166\pi$
$420$		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
$423$	2.50989	−	9.36705i	0.122035	−	0.455442i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.17401	−	40.4078i	−0.0568145	−	1.95547i
$428$		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	$-0.101199\pi$
$433$	13.2611	+	13.2611i	0.637288	+	0.637288i	−0.312597	+	0.949886i	$0.601199\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.42664	+	0.382266i	0.0682453	+	0.0182863i
$438$		0			0
$439$	10.1355	−	17.5553i	0.483743	−	0.837867i	−0.516083	−	0.856539i	$-0.672610\pi$
$439$	10.1355	−	17.5553i	0.483743	−	0.837867i	0.999826	+	0.0186713i	$0.00594362\pi$
$440$		0			0
$441$	5.84874	−	3.84606i	0.278512	−	0.183146i
$442$		0			0
$443$	7.82246	+	29.1938i	0.371656	+	1.38704i	0.858169	+	0.513366i	$0.171602\pi$
$443$	7.82246	+	29.1938i	0.371656	+	1.38704i	−0.486513	+	0.873673i	$0.661731\pi$
$444$		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	$0.0390393\pi$
$449$			5.18461i			0.244677i	−0.992488	+	0.122338i	$0.960961\pi$
$450$		0			0
$451$	9.77835	−	5.64554i	0.460445	−	0.265838i
$452$		0			0
$453$	8.04202	−	2.15485i	0.377847	−	0.101244i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−11.7570	+	3.15027i	−0.549967	+	0.147363i	−0.523093	−	0.852276i	$-0.675222\pi$
$457$	−11.7570	+	3.15027i	−0.549967	+	0.147363i	−0.0268740	+	0.999639i	$0.508555\pi$
$458$		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	−0.903624	−	0.428326i	$-0.859104\pi$
$463$	−10.2272	+	10.2272i	−0.475299	+	0.475299i	0.428326	+	0.903624i	$0.359104\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.0210	+	37.3988i	0.463716	+	1.73061i	0.661111	+	0.750288i	$0.270085\pi$
$467$	10.0210	+	37.3988i	0.463716	+	1.73061i	−0.197395	+	0.980324i	$0.563248\pi$
$468$		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
$473$	−33.2320	−	8.90450i	−1.52801	−	0.409429i
$474$		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	0.582083	−	0.813129i	$-0.302238\pi$
$479$	−9.04221	−	15.6616i	−0.413149	−	0.715596i	−0.995232	+	0.0975338i	$0.968905\pi$
$480$		0			0
$481$	28.2540	+	16.3125i	1.28827	+	0.743785i
$482$		0			0
$483$	−9.55657	−	15.4950i	−0.434839	−	0.705049i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.86366	+	6.95527i	−0.0844504	+	0.315173i	−0.995210	−	0.0977647i	$-0.968831\pi$
$487$	−1.86366	+	6.95527i	−0.0844504	+	0.315173i	0.910759	+	0.412938i	$0.135497\pi$
$488$		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
$493$	−5.33898	+	19.9253i	−0.240455	+	0.897392i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−18.0375	−	29.2461i	−0.809094	−	1.31187i
$498$		0			0
$499$	−19.0704	−	11.0103i	−0.853710	−	0.492890i	0.00819105	−	0.999966i	$-0.497393\pi$
$499$	−19.0704	−	11.0103i	−0.853710	−	0.492890i	−0.861901	+	0.507077i	$0.830726\pi$
$500$		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	$-0.381438\pi$
$503$	−12.7279	−	12.7279i	−0.567510	−	0.567510i	−0.931430	+	0.363920i	$0.881438\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.53866	+	0.680233i	0.112746	+	0.0302102i
$508$		0			0
$509$	9.74836	−	16.8847i	0.432089	−	0.748399i	−0.564964	−	0.825115i	$-0.691110\pi$
$509$	9.74836	−	16.8847i	0.432089	−	0.748399i	0.997053	+	0.0767160i	$0.0244435\pi$
$510$		0			0
$511$	−0.383379	+	0.114758i	−0.0169597	+	0.00507660i
$512$		0			0
$513$	−0.0555549	−	0.207334i	−0.00245281	−	0.00915401i
$514$		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
$523$	12.4778	−	3.34343i	0.545618	−	0.146198i	0.0245272	−	0.999699i	$-0.492192\pi$
$523$	12.4778	−	3.34343i	0.545618	−	0.146198i	0.521091	+	0.853501i	$0.325525\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−19.2928	+	5.16948i	−0.840407	+	0.225186i
$528$		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
$537$	−1.55291	−	5.79555i	−0.0670132	−	0.250097i
$538$		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
$543$	−6.39335	−	1.71309i	−0.274365	−	0.0735159i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	6.87524	+	6.87524i	0.293964	+	0.293964i	0.838644	−	0.544680i	$-0.183349\pi$
$547$	6.87524	+	6.87524i	0.293964	+	0.293964i	−0.544680	+	0.838644i	$0.683349\pi$
$548$		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
$553$	0.00532247	+	0.183191i	0.000226334	+	0.00779008i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.29681	−	27.2321i	0.309176	−	1.15386i	−0.620115	−	0.784511i	$-0.712914\pi$
$557$	7.29681	−	27.2321i	0.309176	−	1.15386i	0.929291	−	0.369349i	$-0.120419\pi$
$558$		0			0
$559$	−22.8513			−0.966506
$560$		0			0
$561$	10.7668			0.454573
$562$		0			0
$563$	6.57270	−	24.5297i	0.277006	−	1.03380i	−0.677478	−	0.735543i	$-0.736927\pi$
$563$	6.57270	−	24.5297i	0.277006	−	1.03380i	0.954485	−	0.298259i	$-0.0964061\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.25577	+	2.32874i	−0.0527376	+	0.0977979i
$568$		0			0
$569$	−15.7373	−	9.08595i	−0.659743	−	0.380903i	0.132436	−	0.991192i	$-0.457720\pi$
$569$	−15.7373	−	9.08595i	−0.659743	−	0.380903i	−0.792179	+	0.610289i	$0.791053\pi$
$570$		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
$577$	−2.39256	−	0.641085i	−0.0996037	−	0.0266887i	0.208673	−	0.977985i	$-0.433086\pi$
$577$	−2.39256	−	0.641085i	−0.0996037	−	0.0266887i	−0.308277	+	0.951297i	$0.599752\pi$
$578$		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
$583$	3.80852	+	14.2136i	0.157733	+	0.588667i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.92874	−	5.92874i	0.244705	−	0.244705i	−0.574088	−	0.818793i	$-0.694643\pi$
$587$	5.92874	−	5.92874i	0.244705	−	0.244705i	0.818793	+	0.574088i	$0.194643\pi$
$588$		0			0
$589$			1.93073i			0.0795544i
$590$		0			0
$591$	−20.2154	+	11.6714i	−0.831552	+	0.480097i
$592$		0			0
$593$	8.65864	−	2.32008i	0.355568	−	0.0952741i	−0.0766134	−	0.997061i	$-0.524411\pi$
$593$	8.65864	−	2.32008i	0.355568	−	0.0952741i	0.432181	+	0.901787i	$0.357744\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−24.7967	+	6.64426i	−1.01486	+	0.271931i
$598$		0			0
$599$	−7.89633	+	4.55895i	−0.322635	+	0.186274i	−0.652567	−	0.757731i	$-0.726308\pi$
$599$	−7.89633	+	4.55895i	−0.322635	+	0.186274i	0.329931	+	0.944005i	$0.392974\pi$
$600$		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
$607$	−0.658351	−	2.45700i	−0.0267217	−	0.0997266i	0.951277	−	0.308337i	$-0.0997725\pi$
$607$	−0.658351	−	2.45700i	−0.0267217	−	0.0997266i	−0.977999	+	0.208611i	$0.933106\pi$
$608$		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
$613$	−1.14248	−	0.306125i	−0.0461442	−	0.0123643i	0.235673	−	0.971832i	$-0.424271\pi$
$613$	−1.14248	−	0.306125i	−0.0461442	−	0.0123643i	−0.281817	+	0.959468i	$0.590937\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.58337	+	2.58337i	0.104003	+	0.104003i	0.757193	−	0.653191i	$-0.226570\pi$
$617$	2.58337	+	2.58337i	0.104003	+	0.104003i	−0.653191	+	0.757193i	$0.726570\pi$
$618$		0			0
$619$	3.51887	+	6.09486i	0.141435	+	0.244973i	0.928037	−	0.372487i	$-0.121495\pi$
$619$	3.51887	+	6.09486i	0.141435	+	0.244973i	−0.786602	+	0.617460i	$0.788162\pi$
$620$		0			0
$621$	5.95901	+	3.44043i	0.239127	+	0.138060i
$622$		0			0
$623$	5.27349	−	0.153217i	0.211278	−	0.00613851i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.269372	−	1.00531i	0.0107577	−	0.0401482i
$628$		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
$633$	−3.07598	+	11.4797i	−0.122259	+	0.456277i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	21.4000	−	7.08916i	0.847900	−	0.280883i
$638$		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	$-0.399759\pi$
$643$	−16.2563	−	16.2563i	−0.641085	−	0.641085i	−0.950822	+	0.309737i	$0.899759\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−38.9839	−	10.4457i	−1.53261	−	0.410663i	−0.608743	−	0.793367i	$-0.708326\pi$
$647$	−38.9839	−	10.4457i	−1.53261	−	0.410663i	−0.923871	+	0.382705i	$0.874993\pi$
$648$		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
$653$	10.0233	+	37.4074i	0.392242	+	1.46387i	0.826428	+	0.563043i	$0.190369\pi$
$653$	10.0233	+	37.4074i	0.392242	+	1.46387i	−0.434186	+	0.900823i	$0.642964\pi$
$654$		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	$-0.890889\pi$
$659$		−	17.2564i		−	0.672215i	0.941824	−	0.336108i	$-0.109111\pi$
$660$		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
$663$	6.90758	−	1.85088i	0.268268	−	0.0718823i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−61.7438	+	16.5442i	−2.39073	+	0.640594i
$668$		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	−0.162087	−	0.986777i	$-0.551822\pi$
$673$	21.3943	−	21.3943i	0.824690	−	0.824690i	0.986777	+	0.162087i	$0.0518224\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.06660	−	7.71265i	−0.0794258	−	0.296421i	0.914775	−	0.403965i	$-0.132368\pi$
$677$	−2.06660	−	7.71265i	−0.0794258	−	0.296421i	−0.994200	+	0.107544i	$0.965702\pi$
$678$		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
$683$	9.25458	+	2.47976i	0.354117	+	0.0948853i	0.431492	−	0.902117i	$-0.357987\pi$
$683$	9.25458	+	2.47976i	0.354117	+	0.0948853i	−0.0773753	+	0.997002i	$0.524654\pi$
$684$		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
$693$	−10.9189	+	6.73423i	−0.414775	+	0.255812i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.33831	+	4.99465i	−0.0506922	+	0.189186i
$698$		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
$703$	−0.562789	+	2.10036i	−0.0212260	+	0.0792165i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.7109	+	6.31509i	0.440432	+	0.237503i
$708$		0			0
$709$	29.7847	+	17.1962i	1.11859	+	0.645817i	0.941040	−	0.338295i	$-0.109850\pi$
$709$	29.7847	+	17.1962i	1.11859	+	0.645817i	0.177548	+	0.984112i	$0.443183\pi$
$710$		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
$717$	12.8692	+	3.44828i	0.480608	+	0.128779i
$718$		0			0
$719$	−16.4619	+	28.5129i	−0.613926	+	1.06335i	0.376646	+	0.926357i	$0.377077\pi$
$719$	−16.4619	+	28.5129i	−0.613926	+	1.06335i	−0.990572	+	0.136994i	$0.956256\pi$
$720$		0			0
$721$	11.2552	+	10.6196i	0.419164	+	0.395495i
$722$		0			0
$723$	0.812670	+	3.03292i	0.0302235	+	0.112796i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	34.2948	−	34.2948i	1.27192	−	1.27192i	0.326846	−	0.945078i	$-0.394014\pi$
$727$	34.2948	−	34.2948i	1.27192	−	1.27192i	0.945078	−	0.326846i	$-0.105986\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	13.6449	−	7.87788i	0.504675	−	0.291374i
$732$		0			0
$733$	9.26793	−	2.48333i	0.342319	−	0.0917240i	−0.0835640	−	0.996502i	$-0.526630\pi$
$733$	9.26793	−	2.48333i	0.342319	−	0.0917240i	0.425883	+	0.904778i	$0.359964\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−24.1146	+	6.46149i	−0.888274	+	0.238012i
$738$		0			0
$739$	10.5145	−	6.07055i	0.386782	−	0.223309i	−0.293983	−	0.955811i	$-0.594981\pi$
$739$	10.5145	−	6.07055i	0.386782	−	0.223309i	0.680765	+	0.732502i	$0.261648\pi$
$740$		0			0
$741$		−	0.691279i		−	0.0253948i
$742$		0			0
$743$	35.2058	−	35.2058i	1.29158	−	1.29158i	0.357766	−	0.933811i	$-0.383539\pi$
$743$	35.2058	−	35.2058i	1.29158	−	1.29158i	0.933811	−	0.357766i	$-0.116461\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.171228	−	0.639032i	−0.00626491	−	0.0233810i
$748$		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
$753$	15.8654	+	4.25111i	0.578166	+	0.154919i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.14729	+	1.14729i	0.0416989	+	0.0416989i	0.727649	−	0.685950i	$-0.240613\pi$
$757$	1.14729	+	1.14729i	0.0416989	+	0.0416989i	−0.685950	+	0.727649i	$0.740613\pi$
$758$		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
$763$	−27.4017	−	14.7764i	−0.992009	−	0.534941i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.47063	−	16.6846i	0.161425	−	0.602446i
$768$		0			0
$769$	−9.84303			−0.354949			−0.177474	−	0.984125i	$-0.556793\pi$
$769$	−9.84303			−0.354949			−0.177474	+	0.984125i	$0.556793\pi$
$770$		0			0
$771$	16.3591			0.589157
$772$		0			0
$773$	−9.48871	+	35.4124i	−0.341285	+	1.27369i	0.555607	+	0.831445i	$0.312486\pi$
$773$	−9.48871	+	35.4124i	−0.341285	+	1.27369i	−0.896892	+	0.442249i	$0.854181\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	22.8125	−	14.0696i	0.818394	−	0.504744i
$778$		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
$787$	22.0134	+	5.89847i	0.784693	+	0.210258i	0.628853	−	0.777524i	$-0.283525\pi$
$787$	22.0134	+	5.89847i	0.784693	+	0.210258i	0.155840	+	0.987782i	$0.450191\pi$
$788$		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
$793$	12.7357	+	47.5302i	0.452257	+	1.68785i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	31.7293	−	31.7293i	1.12391	−	1.12391i	0.132760	−	0.991148i	$-0.457616\pi$
$797$	31.7293	−	31.7293i	1.12391	−	1.12391i	0.991148	−	0.132760i	$-0.0423838\pi$
$798$		0			0
$799$			21.5335i			0.761801i
$800$		0			0
$801$	−1.72688	+	0.997017i	−0.0610164	+	0.0352279i
$802$		0			0
$803$	0.708411	−	0.189818i	0.0249993	−	0.00669854i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	13.2928	−	3.56180i	0.467929	−	0.125381i
$808$		0			0
$809$	−14.9445	+	8.62822i	−0.525421	+	0.303352i	−0.739150	−	0.673541i	$-0.764772\pi$
$809$	−14.9445	+	8.62822i	−0.525421	+	0.303352i	0.213729	+	0.976893i	$0.431439\pi$
$810$		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
$817$	−0.394191	−	1.47114i	−0.0137910	−	0.0514687i
$818$		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
$823$	−28.6978	−	7.68955i	−1.00034	−	0.268041i	−0.278753	−	0.960363i	$-0.589921\pi$
$823$	−28.6978	−	7.68955i	−1.00034	−	0.268041i	−0.721589	+	0.692322i	$0.756588\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	20.1361	+	20.1361i	0.700201	+	0.700201i	0.964453	−	0.264253i	$-0.0851254\pi$
$827$	20.1361	+	20.1361i	0.700201	+	0.700201i	−0.264253	+	0.964453i	$0.585125\pi$
$828$		0			0
$829$	−23.6174	−	40.9066i	−0.820267	−	1.42074i	−0.905483	−	0.424382i	$-0.860492\pi$
$829$	−23.6174	−	40.9066i	−0.820267	−	1.42074i	0.0852165	−	0.996362i	$-0.472842\pi$
$830$		0			0
$831$	−17.4013	−	10.0467i	−0.603646	−	0.348515i
$832$		0			0
$833$	−10.3344	+	11.6106i	−0.358065	+	0.402284i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.32805	+	8.68839i	−0.0804690	+	0.300315i
$838$		0			0
$839$	40.5791			1.40094			0.700472	−	0.713680i	$-0.252973\pi$
$839$	40.5791			1.40094			0.700472	+	0.713680i	$0.252973\pi$
$840$		0			0
$841$	−57.3003			−1.97587
$842$		0			0
$843$	−3.25584	+	12.1509i	−0.112137	+	0.418501i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−33.0852	+	0.961264i	−1.13682	+	0.0330294i
$848$		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	−0.981614	−	0.190879i	$-0.938866\pi$
$853$	−34.2440	−	34.2440i	−1.17249	−	1.17249i	−0.190879	−	0.981614i	$-0.561134\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−20.6512	−	5.53347i	−0.705432	−	0.189020i	−0.111769	−	0.993734i	$-0.535652\pi$
$857$	−20.6512	−	5.53347i	−0.705432	−	0.189020i	−0.593662	+	0.804714i	$0.702318\pi$
$858$		0			0
$859$	−19.0104	+	32.9271i	−0.648628	+	1.12346i	0.334823	+	0.942281i	$0.391324\pi$
$859$	−19.0104	+	32.9271i	−0.648628	+	1.12346i	−0.983451	+	0.181175i	$0.942010\pi$
$860$		0			0
$861$	−1.76676	−	5.90230i	−0.0602109	−	0.201150i
$862$		0			0
$863$	−5.72588	−	21.3693i	−0.194911	−	0.727419i	−0.992290	−	0.123939i	$-0.960447\pi$
$863$	−5.72588	−	21.3693i	−0.194911	−	0.727419i	0.797378	−	0.603480i	$-0.206219\pi$
$864$		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
$873$	−10.2661	+	2.75079i	−0.347454	+	0.0931000i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.9286	+	6.41164i	−0.808010	+	0.216506i	−0.639098	−	0.769125i	$-0.720692\pi$
$877$	−23.9286	+	6.41164i	−0.808010	+	0.216506i	−0.168912	+	0.985631i	$0.554025\pi$
$878$		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	−0.922909	−	0.385019i	$-0.874195\pi$
$883$	−15.9836	+	15.9836i	−0.537890	+	0.537890i	0.385019	+	0.922909i	$0.374195\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.3416	+	42.3276i	0.380815	+	1.42122i	0.844659	+	0.535305i	$0.179803\pi$
$887$	11.3416	+	42.3276i	0.380815	+	1.42122i	−0.463844	+	0.885917i	$0.653530\pi$
$888$		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
$893$	2.01062	+	0.538743i	0.0672828	+	0.0180284i
$894$		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
$903$	−8.91037	+	16.5236i	−0.296518	+	0.549871i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1.63874	+	6.11585i	−0.0544134	+	0.203074i	−0.987781	−	0.155848i	$-0.950189\pi$
$907$	−1.63874	+	6.11585i	−0.0544134	+	0.203074i	0.933368	+	0.358922i	$0.116856\pi$
$908$		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
$913$	0.830242	−	3.09850i	0.0274770	−	0.102546i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.824233	−	28.3688i	−0.0272186	−	0.936821i
$918$		0			0
$919$	22.2726	+	12.8591i	0.734704	+	0.424181i	0.820140	−	0.572162i	$-0.193895\pi$
$919$	22.2726	+	12.8591i	0.734704	+	0.424181i	−0.0854368	+	0.996344i	$0.527229\pi$
$920$		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
$927$	−5.64945	−	1.51377i	−0.185552	−	0.0497186i
$928$		0			0
$929$	−12.9320	+	22.3989i	−0.424286	+	0.734885i	−0.996353	−	0.0853214i	$-0.972808\pi$
$929$	−12.9320	+	22.3989i	−0.424286	+	0.734885i	0.572067	+	0.820207i	$0.306142\pi$
$930$		0			0
$931$	0.825549	+	1.25542i	0.0270563	+	0.0411447i
$932$		0			0
$933$	4.86336	+	18.1503i	0.159219	+	0.594214i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−37.7290	+	37.7290i	−1.23255	+	1.23255i	−0.269571	+	0.962980i	$0.586882\pi$
$937$	−37.7290	+	37.7290i	−1.23255	+	1.23255i	−0.962980	+	0.269571i	$0.913118\pi$
$938$		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
$943$	−15.4772	+	4.14711i	−0.504008	+	0.135048i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.9420	+	2.93189i	−0.355566	+	0.0952737i	−0.432181	−	0.901787i	$-0.642256\pi$
$947$	−10.9420	+	2.93189i	−0.355566	+	0.0952737i	0.0766141	+	0.997061i	$0.475589\pi$
$948$		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	−0.162981	−	0.986629i	$-0.552111\pi$
$953$	25.4266	−	25.4266i	0.823648	−	0.823648i	0.986629	+	0.162981i	$0.0521109\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	11.6582	+	43.5090i	0.376856	+	1.40645i
$958$		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
$963$	3.39179	+	0.908827i	0.109299	+	0.0292865i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	42.9279	+	42.9279i	1.38047	+	1.38047i	0.843779	+	0.536691i	$0.180326\pi$
$967$	42.9279	+	42.9279i	1.38047	+	1.38047i	0.536691	+	0.843779i	$0.319674\pi$
$968$		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
$973$	19.4113	+	31.4735i	0.622296	+	1.00899i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.0555	+	41.2596i	−0.353696	+	1.32001i	0.528421	+	0.848982i	$0.322784\pi$
$977$	−11.0555	+	41.2596i	−0.353696	+	1.32001i	−0.882117	+	0.471030i	$0.843882\pi$
$978$		0			0
$979$	−9.66856			−0.309009
$980$		0			0
$981$	11.7668			0.375684
$982$		0			0
$983$	1.32066	−	4.92876i	0.0421224	−	0.157203i	−0.941661	−	0.336562i	$-0.890736\pi$
$983$	1.32066	−	4.92876i	0.0421224	−	0.157203i	0.983784	+	0.179359i	$0.0574024\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−13.4685	−	21.8378i	−0.428706	−	0.695105i
$988$		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
$997$	32.1754	+	8.62137i	1.01901	+	0.273042i	0.729388	−	0.684101i	$-0.239805\pi$
$997$	32.1754	+	8.62137i	1.01901	+	0.273042i	0.289618	+	0.957142i	$0.406472\pi$
$998$		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.1657.1	yes	24
5.2	odd	4	inner	2100.2.ce.d.1993.5	yes	24
5.3	odd	4	inner	2100.2.ce.d.1993.1	yes	24
5.4	even	2	inner	2100.2.ce.d.1657.5	yes	24
7.3	odd	6	inner	2100.2.ce.d.157.1	✓	24
35.3	even	12	inner	2100.2.ce.d.493.1	yes	24
35.17	even	12	inner	2100.2.ce.d.493.5	yes	24
35.24	odd	6	inner	2100.2.ce.d.157.6	yes	24

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

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

Related objects

Downloads

Learn more