LMFDB - Embedded newform 700.2.r.c.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(149,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("700.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	700.149
Dual form			700.2.r.c.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.59808 - 1.50000i) q^{3} +(2.59808 + 0.500000i) q^{7} +(3.00000 - 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{11} +6.00000i q^{13} +(1.73205 - 1.00000i) q^{17} +(7.50000 - 2.59808i) q^{21} +(-7.79423 - 4.50000i) q^{23} -9.00000i q^{27} -3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(5.19615 + 3.00000i) q^{33} +(-6.92820 - 4.00000i) q^{37} +(9.00000 + 15.5885i) q^{39} +5.00000 q^{41} -1.00000i q^{43} +(-6.92820 - 4.00000i) q^{47} +(6.50000 + 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{51} +(-3.46410 + 2.00000i) q^{53} +(-4.00000 - 6.92820i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(10.3923 - 12.0000i) q^{63} +(-2.59808 + 1.50000i) q^{67} -27.0000 q^{69} +8.00000 q^{71} +(-12.1244 + 7.00000i) q^{73} +(1.73205 + 5.00000i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-4.50000 - 7.79423i) q^{81} +1.00000i q^{83} +(-7.79423 + 4.50000i) q^{87} +(6.50000 - 11.2583i) q^{89} +(-3.00000 + 15.5885i) q^{91} +(-5.19615 - 3.00000i) q^{93} -10.0000i q^{97} +12.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{9} + 4 q^{11} + 30 q^{21} - 12 q^{29} - 4 q^{31} + 36 q^{39} + 20 q^{41} + 26 q^{49} + 12 q^{51} - 16 q^{59} - 14 q^{61} - 108 q^{69} + 32 q^{71} + 8 q^{79} - 18 q^{81} + 26 q^{89} - 12 q^{91}+ \cdots + 48 q^{99}+O(q^{100}) $ 4 * q + 12 * q^9 + 4 * q^11 + 30 * q^21 - 12 * q^29 - 4 * q^31 + 36 * q^39 + 20 * q^41 + 26 * q^49 + 12 * q^51 - 16 * q^59 - 14 * q^61 - 108 * q^69 + 32 * q^71 + 8 * q^79 - 18 * q^81 + 26 * q^89 - 12 * q^91 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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
$3$	2.59808	−	1.50000i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	2.59808	−	1.50000i	1.50000	−	0.866025i	1.00000			$0$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.59808	+	0.500000i	0.981981	+	0.188982i
$7$	2.59808	+	0.500000i	0.981981	+	0.188982i
$8$		0			0
$9$	3.00000	−	5.19615i	1.00000	−	1.73205i
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		0			0
$13$			6.00000i			1.66410i	0.554700	+	0.832050i	$0.312833\pi$
$13$			6.00000i			1.66410i	−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	−0.275029	−	0.961436i	$-0.588688\pi$
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	0.695113	+	0.718900i	$0.255354\pi$
$18$		0			0
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$		0			0
$21$	7.50000	−	2.59808i	1.63663	−	0.566947i
$22$		0			0
$23$	−7.79423	−	4.50000i	−1.62521	−	0.938315i	−0.985496	−	0.169701i	$-0.945720\pi$
$23$	−7.79423	−	4.50000i	−1.62521	−	0.938315i	−0.639713	−	0.768613i	$-0.720947\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	9.00000i		−	1.73205i
$28$		0			0
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$		0			0
$33$	5.19615	+	3.00000i	0.904534	+	0.522233i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.192809	−	0.981236i	$-0.561760\pi$
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.946180	+	0.323640i	$0.895093\pi$
$38$		0			0
$39$	9.00000	+	15.5885i	1.44115	+	2.49615i
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$		0			0
$43$		−	1.00000i		−	0.152499i	−0.997089	−	0.0762493i	$-0.975706\pi$
$43$		−	1.00000i		−	0.152499i	0.997089	−	0.0762493i	$-0.0242945\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.0992202	−	0.995066i	$-0.531635\pi$
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.911362	+	0.411606i	$0.864968\pi$
$48$		0			0
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$		0			0
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$		0			0
$53$	−3.46410	+	2.00000i	−0.475831	+	0.274721i	−0.718677	−	0.695344i	$-0.755252\pi$
$53$	−3.46410	+	2.00000i	−0.475831	+	0.274721i	0.242846	+	0.970065i	$0.421919\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		0			0
$63$	10.3923	−	12.0000i	1.30931	−	1.51186i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	−0.650236	−	0.759733i	$-0.725330\pi$
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	0.332830	+	0.942987i	$0.391996\pi$
$68$		0			0
$69$	−27.0000			−3.25042
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	−12.1244	+	7.00000i	−1.41905	+	0.819288i	−0.996215	−	0.0869195i	$-0.972298\pi$
$73$	−12.1244	+	7.00000i	−1.41905	+	0.819288i	−0.422833	+	0.906208i	$0.638964\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.73205	+	5.00000i	0.197386	+	0.569803i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$			1.00000i			0.109764i	0.998493	+	0.0548821i	$0.0174783\pi$
$83$			1.00000i			0.109764i	−0.998493	+	0.0548821i	$0.982522\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−7.79423	+	4.50000i	−0.835629	+	0.482451i
$88$		0			0
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	−0.283164	−	0.959072i	$-0.591384\pi$
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	0.972162	−	0.234309i	$-0.0752827\pi$
$90$		0			0
$91$	−3.00000	+	15.5885i	−0.314485	+	1.63411i
$92$		0			0
$93$	−5.19615	−	3.00000i	−0.538816	−	0.311086i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	10.0000i		−	1.01535i	−0.861550	−	0.507673i	$-0.830506\pi$
$97$		−	10.0000i		−	1.01535i	0.861550	−	0.507673i	$-0.169494\pi$
$98$		0			0
$99$	12.0000			1.20605
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	11.2583	+	6.50000i	1.10932	+	0.640464i	0.938652	−	0.344865i	$-0.112075\pi$
$103$	11.2583	+	6.50000i	1.10932	+	0.640464i	0.170664	+	0.985329i	$0.445409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.9904	+	7.50000i	1.25583	+	0.725052i	0.972261	−	0.233900i	$-0.0751489\pi$
$107$	12.9904	+	7.50000i	1.25583	+	0.725052i	0.283567	+	0.958952i	$0.408482\pi$
$108$		0			0
$109$	4.50000	+	7.79423i	0.431022	+	0.746552i	0.996962	−	0.0778949i	$-0.0248199\pi$
$109$	4.50000	+	7.79423i	0.431022	+	0.746552i	−0.565940	+	0.824447i	$0.691487\pi$
$110$		0			0
$111$	−24.0000			−2.27798
$112$		0			0
$113$			4.00000i			0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	31.1769	+	18.0000i	2.88231	+	1.66410i
$118$		0			0
$119$	5.00000	−	1.73205i	0.458349	−	0.158777i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	12.9904	−	7.50000i	1.17130	−	0.676252i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$		0			0
$129$	−1.50000	−	2.59808i	−0.132068	−	0.228748i
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.873247	−	0.487278i	$-0.837990\pi$
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.0146279	+	0.999893i	$0.504656\pi$
$138$		0			0
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$		0			0
$141$	−24.0000			−2.02116
$142$		0			0
$143$	−10.3923	+	6.00000i	−0.869048	+	0.501745i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	20.7846	−	3.00000i	1.71429	−	0.247436i
$148$		0			0
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$		−	12.0000i		−	0.970143i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.73205	+	1.00000i	−0.138233	+	0.0798087i	−0.567521	−	0.823359i	$-0.692098\pi$
$157$	−1.73205	+	1.00000i	−0.138233	+	0.0798087i	0.429289	+	0.903167i	$0.358764\pi$
$158$		0			0
$159$	−6.00000	+	10.3923i	−0.475831	+	0.824163i
$160$		0			0
$161$	−18.0000	−	15.5885i	−1.41860	−	1.22854i
$162$		0			0
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	0.746156	−	0.665771i	$-0.231897\pi$
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	−0.203497	+	0.979076i	$0.565231\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	9.00000i		−	0.696441i	−0.937413	−	0.348220i	$-0.886786\pi$
$167$		−	9.00000i		−	0.696441i	0.937413	−	0.348220i	$-0.113214\pi$
$168$		0			0
$169$	−23.0000			−1.76923
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−13.8564	−	8.00000i	−1.05348	−	0.608229i	−0.129861	−	0.991532i	$-0.541453\pi$
$173$	−13.8564	−	8.00000i	−1.05348	−	0.608229i	−0.923622	+	0.383304i	$0.874786\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−20.7846	−	12.0000i	−1.56227	−	0.901975i
$178$		0			0
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$		0			0
$181$	1.00000			0.0743294			0.0371647	−	0.999309i	$-0.488167\pi$
$181$	1.00000			0.0743294			0.0371647	+	0.999309i	$0.488167\pi$
$182$		0			0
$183$			21.0000i			1.55236i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.46410	+	2.00000i	0.253320	+	0.146254i
$188$		0			0
$189$	4.50000	−	23.3827i	0.327327	−	1.70084i
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	−1.73205	+	1.00000i	−0.124676	+	0.0719816i	−0.561041	−	0.827788i	$-0.689599\pi$
$193$	−1.73205	+	1.00000i	−0.124676	+	0.0719816i	0.436365	+	0.899770i	$0.356266\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			14.0000i			0.997459i	0.866758	+	0.498729i	$0.166200\pi$
$197$			14.0000i			0.997459i	−0.866758	+	0.498729i	$0.833800\pi$
$198$		0			0
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	0.965272	+	0.261245i	$0.0841331\pi$
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	−0.256391	+	0.966573i	$0.582534\pi$
$200$		0			0
$201$	−4.50000	+	7.79423i	−0.317406	+	0.549762i
$202$		0			0
$203$	−7.79423	−	1.50000i	−0.547048	−	0.105279i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−46.7654	+	27.0000i	−3.25042	+	1.87663i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		0			0
$213$	20.7846	−	12.0000i	1.42414	−	0.822226i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.73205	−	5.00000i	−0.117579	−	0.339422i
$218$		0			0
$219$	−21.0000	+	36.3731i	−1.41905	+	2.45786i
$220$		0			0
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$		−	16.0000i		−	1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$		−	16.0000i		−	1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	−0.610535	−	0.791989i	$-0.709046\pi$
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	0.380615	+	0.924734i	$0.375712\pi$
$228$		0			0
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$	12.0000	+	10.3923i	0.789542	+	0.683763i
$232$		0			0
$233$	−15.5885	−	9.00000i	−1.02123	−	0.589610i	−0.106773	−	0.994283i	$-0.534052\pi$
$233$	−15.5885	−	9.00000i	−1.02123	−	0.589610i	−0.914461	+	0.404674i	$0.867385\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	12.0000i		−	0.779484i
$238$		0			0
$239$	26.0000			1.68180			0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000			1.68180			0.840900	+	0.541190i	$0.182026\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	1.50000	+	2.59808i	0.0950586	+	0.164646i
$250$		0			0
$251$	30.0000			1.89358			0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000			1.89358			0.946792	+	0.321847i	$0.104304\pi$
$252$		0			0
$253$		−	18.0000i		−	1.13165i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.92820	−	4.00000i	−0.432169	−	0.249513i	0.268101	−	0.963391i	$-0.413604\pi$
$257$	−6.92820	−	4.00000i	−0.432169	−	0.249513i	−0.700270	+	0.713878i	$0.746937\pi$
$258$		0			0
$259$	−16.0000	−	13.8564i	−0.994192	−	0.860995i
$260$		0			0
$261$	−9.00000	+	15.5885i	−0.557086	+	0.964901i
$262$		0			0
$263$	−14.7224	+	8.50000i	−0.907824	+	0.524132i	−0.879730	−	0.475473i	$-0.842277\pi$
$263$	−14.7224	+	8.50000i	−0.907824	+	0.524132i	−0.0280936	+	0.999605i	$0.508944\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	39.0000i		−	2.38676i
$268$		0			0
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$		0			0
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	−0.228380	−	0.973572i	$-0.573343\pi$
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	0.957328	−	0.289003i	$-0.0933238\pi$
$272$		0			0
$273$	15.5885	+	45.0000i	0.943456	+	2.72352i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	15.5885	−	9.00000i	0.936620	−	0.540758i	0.0477206	−	0.998861i	$-0.484804\pi$
$277$	15.5885	−	9.00000i	0.936620	−	0.540758i	0.888899	+	0.458103i	$0.151471\pi$
$278$		0			0
$279$	−12.0000			−0.718421
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$		0			0
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	−0.393494	−	0.919327i	$-0.628734\pi$
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	0.599414	+	0.800439i	$0.295400\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.9904	+	2.50000i	0.766798	+	0.147570i
$288$		0			0
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$		0			0
$291$	−15.0000	−	25.9808i	−0.879316	−	1.52302i
$292$		0			0
$293$		−	4.00000i		−	0.233682i	−0.993151	−	0.116841i	$-0.962723\pi$
$293$		−	4.00000i		−	0.233682i	0.993151	−	0.116841i	$-0.0372769\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	15.5885	−	9.00000i	0.904534	−	0.522233i
$298$		0			0
$299$	27.0000	−	46.7654i	1.56145	−	2.70451i
$300$		0			0
$301$	0.500000	−	2.59808i	0.0288195	−	0.149751i
$302$		0			0
$303$	7.79423	+	4.50000i	0.447767	+	0.258518i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			1.00000i			0.0570730i	0.999593	+	0.0285365i	$0.00908469\pi$
$307$			1.00000i			0.0570730i	−0.999593	+	0.0285365i	$0.990915\pi$
$308$		0			0
$309$	39.0000			2.21863
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	−3.46410	−	2.00000i	−0.195803	−	0.113047i	0.398894	−	0.916997i	$-0.369394\pi$
$313$	−3.46410	−	2.00000i	−0.195803	−	0.113047i	−0.594696	+	0.803951i	$0.702728\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.66025	−	5.00000i	−0.486408	−	0.280828i	0.236675	−	0.971589i	$-0.423942\pi$
$317$	−8.66025	−	5.00000i	−0.486408	−	0.280828i	−0.723083	+	0.690761i	$0.757276\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$	45.0000			2.51166
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$	23.3827	+	13.5000i	1.29307	+	0.746552i
$328$		0			0
$329$	−16.0000	−	13.8564i	−0.882109	−	0.763928i
$330$		0			0
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$		0			0
$333$	−41.5692	+	24.0000i	−2.27798	+	1.31519i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			28.0000i			1.52526i	0.646837	+	0.762629i	$0.276092\pi$
$337$			28.0000i			1.52526i	−0.646837	+	0.762629i	$0.723908\pi$
$338$		0			0
$339$	6.00000	+	10.3923i	0.325875	+	0.564433i
$340$		0			0
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	21.6506	−	12.5000i	1.16227	−	0.671035i	0.210421	−	0.977611i	$-0.432517\pi$
$347$	21.6506	−	12.5000i	1.16227	−	0.671035i	0.951846	+	0.306576i	$0.0991833\pi$
$348$		0			0
$349$	17.0000			0.909989			0.454995	−	0.890494i	$-0.349641\pi$
$349$	17.0000			0.909989			0.454995	+	0.890494i	$0.349641\pi$
$350$		0			0
$351$	54.0000			2.88231
$352$		0			0
$353$	31.1769	−	18.0000i	1.65938	−	0.958043i	0.686378	−	0.727245i	$-0.259200\pi$
$353$	31.1769	−	18.0000i	1.65938	−	0.958043i	0.973002	−	0.230799i	$-0.0741338\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	10.3923	−	12.0000i	0.550019	−	0.635107i
$358$		0			0
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$		0			0
$363$		−	21.0000i		−	1.10221i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.866025	−	0.500000i	0.0452062	−	0.0260998i	−0.477227	−	0.878780i	$-0.658358\pi$
$367$	0.866025	−	0.500000i	0.0452062	−	0.0260998i	0.522433	+	0.852680i	$0.325025\pi$
$368$		0			0
$369$	15.0000	−	25.9808i	0.780869	−	1.35250i
$370$		0			0
$371$	−10.0000	+	3.46410i	−0.519174	+	0.179847i
$372$		0			0
$373$	27.7128	+	16.0000i	1.43492	+	0.828449i	0.997490	−	0.0708063i	$-0.0225572\pi$
$373$	27.7128	+	16.0000i	1.43492	+	0.828449i	0.437425	+	0.899255i	$0.355891\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	18.0000i		−	0.927047i
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$	24.0000	+	41.5692i	1.22956	+	2.12966i
$382$		0			0
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	0.287469	−	0.957790i	$-0.407186\pi$
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	−0.685736	+	0.727851i	$0.740519\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.19615	−	3.00000i	−0.264135	−	0.152499i
$388$		0			0
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$		−	12.0000i		−	0.605320i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.66025	−	5.00000i	−0.434646	−	0.250943i	0.266678	−	0.963786i	$-0.414074\pi$
$397$	−8.66025	−	5.00000i	−0.434646	−	0.250943i	−0.701324	+	0.712843i	$0.747407\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.5000	−	25.1147i	0.724095	−	1.25417i	−0.235250	−	0.971935i	$-0.575591\pi$
$401$	14.5000	−	25.1147i	0.724095	−	1.25417i	0.959345	−	0.282235i	$-0.0910758\pi$
$402$		0			0
$403$	10.3923	−	6.00000i	0.517678	−	0.298881i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	16.0000i		−	0.793091i
$408$		0			0
$409$	1.50000	+	2.59808i	0.0741702	+	0.128467i	0.900725	−	0.434389i	$-0.143036\pi$
$409$	1.50000	+	2.59808i	0.0741702	+	0.128467i	−0.826555	+	0.562856i	$0.809703\pi$
$410$		0			0
$411$	−18.0000	+	31.1769i	−0.887875	+	1.53784i
$412$		0			0
$413$	−6.92820	−	20.0000i	−0.340915	−	0.984136i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−25.9808	+	15.0000i	−1.27228	+	0.734553i
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$		0			0
$423$	−41.5692	+	24.0000i	−2.02116	+	1.16692i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−12.1244	+	14.0000i	−0.586739	+	0.677507i
$428$		0			0
$429$	−18.0000	+	31.1769i	−0.869048	+	1.50524i
$430$		0			0
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$432$		0			0
$433$			4.00000i			0.192228i	0.995370	+	0.0961139i	$0.0306413\pi$
$433$			4.00000i			0.192228i	−0.995370	+	0.0961139i	$0.969359\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	−0.814344	−	0.580383i	$-0.802903\pi$
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	0.909798	+	0.415051i	$0.136236\pi$
$440$		0			0
$441$	33.0000	−	25.9808i	1.57143	−	1.23718i
$442$		0			0
$443$	32.0429	+	18.5000i	1.52241	+	0.878962i	0.999649	+	0.0264796i	$0.00842970\pi$
$443$	32.0429	+	18.5000i	1.52241	+	0.878962i	0.522757	+	0.852482i	$0.324904\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	27.0000i		−	1.27706i
$448$		0			0
$449$	−15.0000			−0.707894			−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000			−0.707894			−0.353947	+	0.935266i	$0.615161\pi$
$450$		0			0
$451$	5.00000	+	8.66025i	0.235441	+	0.407795i
$452$		0			0
$453$	25.9808	+	15.0000i	1.22068	+	0.704761i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−24.2487	−	14.0000i	−1.13431	−	0.654892i	−0.189292	−	0.981921i	$-0.560619\pi$
$457$	−24.2487	−	14.0000i	−1.13431	−	0.654892i	−0.945015	+	0.327028i	$0.893953\pi$
$458$		0			0
$459$	−9.00000	−	15.5885i	−0.420084	−	0.727607i
$460$		0			0
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$		0			0
$463$		−	17.0000i		−	0.790057i	−0.918669	−	0.395029i	$-0.870735\pi$
$463$		−	17.0000i		−	0.790057i	0.918669	−	0.395029i	$-0.129265\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.33013	−	2.50000i	−0.200374	−	0.115686i	0.396456	−	0.918054i	$-0.370240\pi$
$467$	−4.33013	−	2.50000i	−0.200374	−	0.115686i	−0.596830	+	0.802368i	$0.703573\pi$
$468$		0			0
$469$	−7.50000	+	2.59808i	−0.346318	+	0.119968i
$470$		0			0
$471$	−3.00000	+	5.19615i	−0.138233	+	0.239426i
$472$		0			0
$473$	1.73205	−	1.00000i	0.0796398	−	0.0459800i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			24.0000i			1.09888i
$478$		0			0
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	−0.973321	−	0.229447i	$-0.926308\pi$
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	0.287954	−	0.957644i	$-0.407025\pi$
$480$		0			0
$481$	24.0000	−	41.5692i	1.09431	−	1.89539i
$482$		0			0
$483$	−70.1481	−	13.5000i	−3.19185	−	0.614271i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	27.7128	−	16.0000i	1.25579	−	0.725029i	0.283535	−	0.958962i	$-0.408493\pi$
$487$	27.7128	−	16.0000i	1.25579	−	0.725029i	0.972253	+	0.233933i	$0.0751596\pi$
$488$		0			0
$489$	24.0000			1.08532
$490$		0			0
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$		0			0
$493$	−5.19615	+	3.00000i	−0.234023	+	0.135113i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.7846	+	4.00000i	0.932317	+	0.179425i
$498$		0			0
$499$	−3.00000	+	5.19615i	−0.134298	+	0.232612i	−0.925329	−	0.379165i	$-0.876211\pi$
$499$	−3.00000	+	5.19615i	−0.134298	+	0.232612i	0.791031	+	0.611776i	$0.209545\pi$
$500$		0			0
$501$	−13.5000	−	23.3827i	−0.603136	−	1.04466i
$502$		0			0
$503$		−	27.0000i		−	1.20387i	−0.798545	−	0.601935i	$-0.794397\pi$
$503$		−	27.0000i		−	1.20387i	0.798545	−	0.601935i	$-0.205603\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−59.7558	+	34.5000i	−2.65385	+	1.53220i
$508$		0			0
$509$	−20.5000	+	35.5070i	−0.908647	+	1.57382i	−0.0927004	+	0.995694i	$0.529550\pi$
$509$	−20.5000	+	35.5070i	−0.908647	+	1.57382i	−0.815946	+	0.578128i	$0.803783\pi$
$510$		0			0
$511$	−35.0000	+	12.1244i	−1.54831	+	0.536350i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	16.0000i		−	0.703679i
$518$		0			0
$519$	−48.0000			−2.10697
$520$		0			0
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	0.670957	−	0.741496i	$-0.265883\pi$
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	−0.977633	+	0.210318i	$0.932550\pi$
$522$		0			0
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	0.573822	−	0.818980i	$-0.305460\pi$
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	−0.422347	+	0.906434i	$0.638794\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.46410	−	2.00000i	−0.150899	−	0.0871214i
$528$		0			0
$529$	29.0000	+	50.2295i	1.26087	+	2.18389i
$530$		0			0
$531$	−48.0000			−2.08302
$532$		0			0
$533$			30.0000i			1.29944i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−15.5885	−	9.00000i	−0.672692	−	0.388379i
$538$		0			0
$539$	2.00000	+	13.8564i	0.0861461	+	0.596838i
$540$		0			0
$541$	−16.5000	+	28.5788i	−0.709390	+	1.22870i	0.255693	+	0.966758i	$0.417696\pi$
$541$	−16.5000	+	28.5788i	−0.709390	+	1.22870i	−0.965084	+	0.261942i	$0.915637\pi$
$542$		0			0
$543$	2.59808	−	1.50000i	0.111494	−	0.0643712i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	15.0000i		−	0.641354i	−0.947189	−	0.320677i	$-0.896090\pi$
$547$		−	15.0000i		−	0.641354i	0.947189	−	0.320677i	$-0.103910\pi$
$548$		0			0
$549$	21.0000	+	36.3731i	0.896258	+	1.55236i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	6.92820	−	8.00000i	0.294617	−	0.340195i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.73205	+	1.00000i	−0.0733893	+	0.0423714i	−0.536246	−	0.844062i	$-0.680158\pi$
$557$	−1.73205	+	1.00000i	−0.0733893	+	0.0423714i	0.462856	+	0.886433i	$0.346825\pi$
$558$		0			0
$559$	6.00000			0.253773
$560$		0			0
$561$	12.0000			0.506640
$562$		0			0
$563$	11.2583	−	6.50000i	0.474482	−	0.273942i	−0.243632	−	0.969868i	$-0.578339\pi$
$563$	11.2583	−	6.50000i	0.474482	−	0.273942i	0.718114	+	0.695925i	$0.245006\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−7.79423	−	22.5000i	−0.327327	−	0.944911i
$568$		0			0
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	−0.358954	−	0.933355i	$-0.616866\pi$
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	0.987786	−	0.155815i	$-0.0498003\pi$
$570$		0			0
$571$	−12.0000	−	20.7846i	−0.502184	−	0.869809i	−0.999997	−	0.00252413i	$-0.999197\pi$
$571$	−12.0000	−	20.7846i	−0.502184	−	0.869809i	0.497812	−	0.867285i	$-0.334137\pi$
$572$		0			0
$573$			18.0000i			0.751961i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	19.0526	−	11.0000i	0.793168	−	0.457936i	−0.0479084	−	0.998852i	$-0.515256\pi$
$577$	19.0526	−	11.0000i	0.793168	−	0.457936i	0.841077	+	0.540916i	$0.181922\pi$
$578$		0			0
$579$	−3.00000	+	5.19615i	−0.124676	+	0.215945i
$580$		0			0
$581$	−0.500000	+	2.59808i	−0.0207435	+	0.107786i
$582$		0			0
$583$	−6.92820	−	4.00000i	−0.286937	−	0.165663i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			20.0000i			0.825488i	0.910847	+	0.412744i	$0.135430\pi$
$587$			20.0000i			0.825488i	−0.910847	+	0.412744i	$0.864570\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	21.0000	+	36.3731i	0.863825	+	1.49619i
$592$		0			0
$593$	−31.1769	−	18.0000i	−1.28028	−	0.739171i	−0.303383	−	0.952869i	$-0.598116\pi$
$593$	−31.1769	−	18.0000i	−1.28028	−	0.739171i	−0.976900	+	0.213697i	$0.931449\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	51.9615	+	30.0000i	2.12664	+	1.22782i
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−6.00000			−0.244745			−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000			−0.244745			−0.122373	+	0.992484i	$0.539050\pi$
$602$		0			0
$603$			18.0000i			0.733017i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.866025	−	0.500000i	−0.0351509	−	0.0202944i	0.482322	−	0.875994i	$-0.339794\pi$
$607$	−0.866025	−	0.500000i	−0.0351509	−	0.0202944i	−0.517472	+	0.855700i	$0.673127\pi$
$608$		0			0
$609$	−22.5000	+	7.79423i	−0.911746	+	0.315838i
$610$		0			0
$611$	24.0000	−	41.5692i	0.970936	−	1.68171i
$612$		0			0
$613$	5.19615	−	3.00000i	0.209871	−	0.121169i	−0.391381	−	0.920229i	$-0.628002\pi$
$613$	5.19615	−	3.00000i	0.209871	−	0.121169i	0.601251	+	0.799060i	$0.294669\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			20.0000i			0.805170i	0.915383	+	0.402585i	$0.131888\pi$
$617$			20.0000i			0.805170i	−0.915383	+	0.402585i	$0.868112\pi$
$618$		0			0
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	0.747873	−	0.663842i	$-0.231075\pi$
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	−0.948840	+	0.315757i	$0.897742\pi$
$620$		0			0
$621$	−40.5000	+	70.1481i	−1.62521	+	2.81494i
$622$		0			0
$623$	22.5167	−	26.0000i	0.902111	−	1.04167i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−16.0000			−0.637962
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$		0			0
$633$	10.3923	−	6.00000i	0.413057	−	0.238479i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−15.5885	+	39.0000i	−0.617637	+	1.54524i
$638$		0			0
$639$	24.0000	−	41.5692i	0.949425	−	1.64445i
$640$		0			0
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	0.990867	+	0.134846i	$0.0430539\pi$
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	−0.378653	+	0.925539i	$0.623613\pi$
$642$		0			0
$643$			20.0000i			0.788723i	0.918955	+	0.394362i	$0.129034\pi$
$643$			20.0000i			0.788723i	−0.918955	+	0.394362i	$0.870966\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.866025	−	0.500000i	0.0340470	−	0.0196570i	−0.482880	−	0.875687i	$-0.660409\pi$
$647$	0.866025	−	0.500000i	0.0340470	−	0.0196570i	0.516927	+	0.856030i	$0.327076\pi$
$648$		0			0
$649$	8.00000	−	13.8564i	0.314027	−	0.543912i
$650$		0			0
$651$	−12.0000	−	10.3923i	−0.470317	−	0.407307i
$652$		0			0
$653$	−29.4449	−	17.0000i	−1.15227	−	0.665261i	−0.202828	−	0.979214i	$-0.565013\pi$
$653$	−29.4449	−	17.0000i	−1.15227	−	0.665261i	−0.949439	+	0.313953i	$0.898347\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			84.0000i			3.27715i
$658$		0			0
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$	−15.5000	−	26.8468i	−0.602880	−	1.04422i	−0.992383	−	0.123194i	$-0.960686\pi$
$661$	−15.5000	−	26.8468i	−0.602880	−	1.04422i	0.389503	−	0.921025i	$-0.372647\pi$
$662$		0			0
$663$	31.1769	+	18.0000i	1.21081	+	0.699062i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	23.3827	+	13.5000i	0.905381	+	0.522722i
$668$		0			0
$669$	−24.0000	−	41.5692i	−0.927894	−	1.60716i
$670$		0			0
$671$	−14.0000			−0.540464
$672$		0			0
$673$		−	16.0000i		−	0.616755i	−0.951264	−	0.308377i	$-0.900214\pi$
$673$		−	16.0000i		−	0.616755i	0.951264	−	0.308377i	$-0.0997859\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.19615	−	3.00000i	−0.199704	−	0.115299i	0.396813	−	0.917899i	$-0.370116\pi$
$677$	−5.19615	−	3.00000i	−0.199704	−	0.115299i	−0.596518	+	0.802600i	$0.703449\pi$
$678$		0			0
$679$	5.00000	−	25.9808i	0.191882	−	0.997050i
$680$		0			0
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$	−25.1147	+	14.5000i	−0.960989	+	0.554827i	−0.896477	−	0.443090i	$-0.853882\pi$
$683$	−25.1147	+	14.5000i	−0.960989	+	0.554827i	−0.0645115	+	0.997917i	$0.520549\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			42.0000i			1.60240i
$688$		0			0
$689$	−12.0000	−	20.7846i	−0.457164	−	0.791831i
$690$		0			0
$691$	13.0000	−	22.5167i	0.494543	−	0.856574i	−0.505437	−	0.862864i	$-0.668669\pi$
$691$	13.0000	−	22.5167i	0.494543	−	0.856574i	0.999980	+	0.00628943i	$0.00200200\pi$
$692$		0			0
$693$	31.1769	+	6.00000i	1.18431	+	0.227921i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	8.66025	−	5.00000i	0.328031	−	0.189389i
$698$		0			0
$699$	−54.0000			−2.04247
$700$		0			0
$701$	−29.0000			−1.09531			−0.547657	−	0.836703i	$-0.684480\pi$
$701$	−29.0000			−1.09531			−0.547657	+	0.836703i	$0.684480\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.59808	+	7.50000i	0.0977107	+	0.282067i
$708$		0			0
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	0.995228	−	0.0975728i	$-0.0311079\pi$
$710$		0			0
$711$	−12.0000	−	20.7846i	−0.450035	−	0.779484i
$712$		0			0
$713$			18.0000i			0.674105i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	67.5500	−	39.0000i	2.52270	−	1.45648i
$718$		0			0
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$	26.0000	+	22.5167i	0.968291	+	0.838564i
$722$		0			0
$723$	−25.9808	−	15.0000i	−0.966235	−	0.557856i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			3.00000i			0.111264i	0.998451	+	0.0556319i	$0.0177173\pi$
$727$			3.00000i			0.111264i	−0.998451	+	0.0556319i	$0.982283\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−1.00000	−	1.73205i	−0.0369863	−	0.0640622i
$732$		0			0
$733$	29.4449	+	17.0000i	1.08757	+	0.627909i	0.932929	−	0.360061i	$-0.117244\pi$
$733$	29.4449	+	17.0000i	1.08757	+	0.627909i	0.154642	+	0.987971i	$0.450578\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.19615	−	3.00000i	−0.191403	−	0.110506i
$738$		0			0
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	0.943215	−	0.332184i	$-0.107785\pi$
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	−0.759287	+	0.650756i	$0.774452\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			3.00000i			0.110059i	0.998485	+	0.0550297i	$0.0175253\pi$
$743$			3.00000i			0.110059i	−0.998485	+	0.0550297i	$0.982475\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.19615	+	3.00000i	0.190117	+	0.109764i
$748$		0			0
$749$	30.0000	+	25.9808i	1.09618	+	0.949316i
$750$		0			0
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$		0			0
$753$	77.9423	−	45.0000i	2.84037	−	1.63989i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	38.0000i		−	1.38113i	−0.723269	−	0.690567i	$-0.757361\pi$
$757$		−	38.0000i		−	1.38113i	0.723269	−	0.690567i	$-0.242639\pi$
$758$		0			0
$759$	−27.0000	−	46.7654i	−0.980038	−	1.69748i
$760$		0			0
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	0.454935	+	0.890525i	$0.349663\pi$
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	−0.998684	+	0.0512772i	$0.983671\pi$
$762$		0			0
$763$	7.79423	+	22.5000i	0.282170	+	0.814555i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	41.5692	−	24.0000i	1.50098	−	0.866590i
$768$		0			0
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$		0			0
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	−0.192740	−	0.981250i	$-0.561737\pi$
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	0.753418	+	0.657542i	$0.228404\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−62.3538	−	12.0000i	−2.23693	−	0.430498i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	8.00000	+	13.8564i	0.286263	+	0.495821i
$782$		0			0
$783$			27.0000i			0.964901i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−9.52628	+	5.50000i	−0.339575	+	0.196054i	−0.660084	−	0.751192i	$-0.729479\pi$
$787$	−9.52628	+	5.50000i	−0.339575	+	0.196054i	0.320509	+	0.947245i	$0.396146\pi$
$788$		0			0
$789$	−25.5000	+	44.1673i	−0.907824	+	1.57240i
$790$		0			0
$791$	−2.00000	+	10.3923i	−0.0711118	+	0.369508i
$792$		0			0
$793$	−36.3731	−	21.0000i	−1.29165	−	0.745732i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			36.0000i			1.27519i	0.770374	+	0.637593i	$0.220070\pi$
$797$			36.0000i			1.27519i	−0.770374	+	0.637593i	$0.779930\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$		0			0
$801$	−39.0000	−	67.5500i	−1.37800	−	2.38676i
$802$		0			0
$803$	−24.2487	−	14.0000i	−0.855718	−	0.494049i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	23.3827	+	13.5000i	0.823110	+	0.475223i
$808$		0			0
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	0.925312	+	0.379206i	$0.123803\pi$
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	−0.134255	+	0.990947i	$0.542864\pi$
$810$		0			0
$811$	50.0000			1.75574			0.877869	−	0.478901i	$-0.158965\pi$
$811$	50.0000			1.75574			0.877869	+	0.478901i	$0.158965\pi$
$812$		0			0
$813$		−	72.0000i		−	2.52515i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	72.0000	+	62.3538i	2.51588	+	2.17882i
$820$		0			0
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$		0			0
$823$	−16.4545	+	9.50000i	−0.573567	+	0.331149i	−0.758573	−	0.651588i	$-0.774103\pi$
$823$	−16.4545	+	9.50000i	−0.573567	+	0.331149i	0.185006	+	0.982737i	$0.440770\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			23.0000i			0.799788i	0.916561	+	0.399894i	$0.130953\pi$
$827$			23.0000i			0.799788i	−0.916561	+	0.399894i	$0.869047\pi$
$828$		0			0
$829$	−5.00000	−	8.66025i	−0.173657	−	0.300783i	0.766039	−	0.642795i	$-0.222225\pi$
$829$	−5.00000	−	8.66025i	−0.173657	−	0.300783i	−0.939696	+	0.342012i	$0.888892\pi$
$830$		0			0
$831$	27.0000	−	46.7654i	0.936620	−	1.62227i
$832$		0			0
$833$	13.8564	−	2.00000i	0.480096	−	0.0692959i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−15.5885	+	9.00000i	−0.538816	+	0.311086i
$838$		0			0
$839$	−14.0000			−0.483334			−0.241667	−	0.970359i	$-0.577694\pi$
$839$	−14.0000			−0.483334			−0.241667	+	0.970359i	$0.577694\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		0			0
$843$	−57.1577	+	33.0000i	−1.96861	+	1.13658i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	12.1244	−	14.0000i	0.416598	−	0.481046i
$848$		0			0
$849$	6.00000	−	10.3923i	0.205919	−	0.356663i
$850$		0			0
$851$	36.0000	+	62.3538i	1.23406	+	2.13746i
$852$		0			0
$853$			40.0000i			1.36957i	0.728743	+	0.684787i	$0.240105\pi$
$853$			40.0000i			1.36957i	−0.728743	+	0.684787i	$0.759895\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−46.7654	+	27.0000i	−1.59747	+	0.922302i	−0.605503	+	0.795843i	$0.707028\pi$
$857$	−46.7654	+	27.0000i	−1.59747	+	0.922302i	−0.991972	+	0.126459i	$0.959639\pi$
$858$		0			0
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	0.376381	+	0.926465i	$0.377169\pi$
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	−0.990533	+	0.137277i	$0.956165\pi$
$860$		0			0
$861$	37.5000	−	12.9904i	1.27800	−	0.442711i
$862$		0			0
$863$	32.0429	+	18.5000i	1.09075	+	0.629747i	0.933777	−	0.357855i	$-0.116492\pi$
$863$	32.0429	+	18.5000i	1.09075	+	0.629747i	0.156977	+	0.987602i	$0.449825\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			39.0000i			1.32451i
$868$		0			0
$869$	8.00000			0.271381
$870$		0			0
$871$	−9.00000	−	15.5885i	−0.304953	−	0.528195i
$872$		0			0
$873$	−51.9615	−	30.0000i	−1.75863	−	1.01535i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−27.7128	−	16.0000i	−0.935795	−	0.540282i	−0.0471555	−	0.998888i	$-0.515016\pi$
$877$	−27.7128	−	16.0000i	−0.935795	−	0.540282i	−0.888640	+	0.458606i	$0.848349\pi$
$878$		0			0
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$		0			0
$881$	−31.0000			−1.04442			−0.522208	−	0.852818i	$-0.674892\pi$
$881$	−31.0000			−1.04442			−0.522208	+	0.852818i	$0.674892\pi$
$882$		0			0
$883$			36.0000i			1.21150i	0.795656	+	0.605748i	$0.207126\pi$
$883$			36.0000i			1.21150i	−0.795656	+	0.605748i	$0.792874\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−45.8993	−	26.5000i	−1.54115	−	0.889783i	−0.998767	−	0.0496513i	$-0.984189\pi$
$887$	−45.8993	−	26.5000i	−1.54115	−	0.889783i	−0.542383	−	0.840132i	$-0.682478\pi$
$888$		0			0
$889$	−8.00000	+	41.5692i	−0.268311	+	1.39419i
$890$		0			0
$891$	9.00000	−	15.5885i	0.301511	−	0.522233i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	162.000i		−	5.40902i
$898$		0			0
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$		0			0
$901$	−4.00000	+	6.92820i	−0.133259	+	0.230812i
$902$		0			0
$903$	−2.59808	−	7.50000i	−0.0864586	−	0.249584i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−32.0429	+	18.5000i	−1.06397	+	0.614282i	−0.926527	−	0.376228i	$-0.877221\pi$
$907$	−32.0429	+	18.5000i	−1.06397	+	0.614282i	−0.137441	+	0.990510i	$0.543888\pi$
$908$		0			0
$909$	18.0000			0.597022
$910$		0			0
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$		0			0
$913$	−1.73205	+	1.00000i	−0.0573225	+	0.0330952i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.92820	−	8.00000i	0.228789	−	0.264183i
$918$		0			0
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	−0.471684	−	0.881768i	$-0.656354\pi$
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	0.999475	−	0.0323936i	$-0.0103130\pi$
$920$		0			0
$921$	1.50000	+	2.59808i	0.0494267	+	0.0856095i
$922$		0			0
$923$			48.0000i			1.57994i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	67.5500	−	39.0000i	2.21863	−	1.28093i
$928$		0			0
$929$	−2.50000	+	4.33013i	−0.0820223	+	0.142067i	−0.904118	−	0.427282i	$-0.859471\pi$
$929$	−2.50000	+	4.33013i	−0.0820223	+	0.142067i	0.822096	+	0.569349i	$0.192805\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−62.3538	−	36.0000i	−2.04137	−	1.17859i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	52.0000i		−	1.69877i	−0.527777	−	0.849383i	$-0.676974\pi$
$937$		−	52.0000i		−	1.69877i	0.527777	−	0.849383i	$-0.323026\pi$
$938$		0			0
$939$	−12.0000			−0.391605
$940$		0			0
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	−0.989599	−	0.143856i	$-0.954050\pi$
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	0.370216	−	0.928946i	$-0.379284\pi$
$942$		0			0
$943$	−38.9711	−	22.5000i	−1.26908	−	0.732701i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25.1147	−	14.5000i	−0.816119	−	0.471187i	0.0329571	−	0.999457i	$-0.489508\pi$
$947$	−25.1147	−	14.5000i	−0.816119	−	0.471187i	−0.849076	+	0.528270i	$0.822841\pi$
$948$		0			0
$949$	−42.0000	−	72.7461i	−1.36338	−	2.36144i
$950$		0			0
$951$	−30.0000			−0.972817
$952$		0			0
$953$			60.0000i			1.94359i	0.235826	+	0.971795i	$0.424220\pi$
$953$			60.0000i			1.94359i	−0.235826	+	0.971795i	$0.575780\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−15.5885	−	9.00000i	−0.503903	−	0.290929i
$958$		0			0
$959$	−30.0000	+	10.3923i	−0.968751	+	0.335585i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$	77.9423	−	45.0000i	2.51166	−	1.45010i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			37.0000i			1.18984i	0.803785	+	0.594920i	$0.202816\pi$
$967$			37.0000i			1.18984i	−0.803785	+	0.594920i	$0.797184\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$972$		0			0
$973$	−25.9808	−	5.00000i	−0.832905	−	0.160293i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.19615	+	3.00000i	−0.166240	+	0.0959785i	−0.580812	−	0.814038i	$-0.697265\pi$
$977$	−5.19615	+	3.00000i	−0.166240	+	0.0959785i	0.414572	+	0.910017i	$0.363931\pi$
$978$		0			0
$979$	26.0000			0.830964
$980$		0			0
$981$	54.0000			1.72409
$982$		0			0
$983$	16.4545	−	9.50000i	0.524816	−	0.303003i	−0.214087	−	0.976815i	$-0.568677\pi$
$983$	16.4545	−	9.50000i	0.524816	−	0.303003i	0.738903	+	0.673812i	$0.235344\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−62.3538	−	12.0000i	−1.98474	−	0.381964i
$988$		0			0
$989$	−4.50000	+	7.79423i	−0.143092	+	0.247842i
$990$		0			0
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	0.992278	+	0.124033i	$0.0395829\pi$
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	−0.388723	+	0.921355i	$0.627084\pi$
$992$		0			0
$993$			30.0000i			0.952021i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−34.6410	+	20.0000i	−1.09709	+	0.633406i	−0.935456	−	0.353444i	$-0.885010\pi$
$997$	−34.6410	+	20.0000i	−1.09709	+	0.633406i	−0.161636	+	0.986850i	$0.551677\pi$
$998$		0			0
$999$	−36.0000	+	62.3538i	−1.13899	+	1.97279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.r.c.149.2		4
5.2	odd	4		700.2.i.a.401.1		2
5.3	odd	4		140.2.i.b.121.1	yes	2
5.4	even	2	inner	700.2.r.c.149.1		4
7.2	even	3		4900.2.e.c.2549.2		2
7.4	even	3	inner	700.2.r.c.249.1		4
7.5	odd	6		4900.2.e.b.2549.1		2
15.8	even	4		1260.2.s.b.541.1		2
20.3	even	4		560.2.q.a.401.1		2
35.2	odd	12		4900.2.a.v.1.1		1
35.3	even	12		980.2.i.a.361.1		2
35.4	even	6	inner	700.2.r.c.249.2		4
35.9	even	6		4900.2.e.c.2549.1		2
35.12	even	12		4900.2.a.a.1.1		1
35.13	even	4		980.2.i.a.961.1		2
35.18	odd	12		140.2.i.b.81.1	✓	2
35.19	odd	6		4900.2.e.b.2549.2		2
35.23	odd	12		980.2.a.a.1.1		1
35.32	odd	12		700.2.i.a.501.1		2
35.33	even	12		980.2.a.i.1.1		1
105.23	even	12		8820.2.a.w.1.1		1
105.53	even	12		1260.2.s.b.361.1		2
105.68	odd	12		8820.2.a.k.1.1		1
140.23	even	12		3920.2.a.bi.1.1		1
140.103	odd	12		3920.2.a.d.1.1		1
140.123	even	12		560.2.q.a.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.i.b.81.1	✓	2	35.18	odd	12
140.2.i.b.121.1	yes	2	5.3	odd	4
560.2.q.a.81.1		2	140.123	even	12
560.2.q.a.401.1		2	20.3	even	4
700.2.i.a.401.1		2	5.2	odd	4
700.2.i.a.501.1		2	35.32	odd	12
700.2.r.c.149.1		4	5.4	even	2	inner
700.2.r.c.149.2		4	1.1	even	1	trivial
700.2.r.c.249.1		4	7.4	even	3	inner
700.2.r.c.249.2		4	35.4	even	6	inner
980.2.a.a.1.1		1	35.23	odd	12
980.2.a.i.1.1		1	35.33	even	12
980.2.i.a.361.1		2	35.3	even	12
980.2.i.a.961.1		2	35.13	even	4
1260.2.s.b.361.1		2	105.53	even	12
1260.2.s.b.541.1		2	15.8	even	4
3920.2.a.d.1.1		1	140.103	odd	12
3920.2.a.bi.1.1		1	140.23	even	12
4900.2.a.a.1.1		1	35.12	even	12
4900.2.a.v.1.1		1	35.2	odd	12
4900.2.e.b.2549.1		2	7.5	odd	6
4900.2.e.b.2549.2		2	35.19	odd	6
4900.2.e.c.2549.1		2	35.9	even	6
4900.2.e.c.2549.2		2	7.2	even	3
8820.2.a.k.1.1		1	105.68	odd	12
8820.2.a.w.1.1		1	105.23	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.59808 - 1.50000i) q^{3} +(2.59808 + 0.500000i) q^{7} +(3.00000 - 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{11} +6.00000i q^{13} +(1.73205 - 1.00000i) q^{17} +(7.50000 - 2.59808i) q^{21} +(-7.79423 - 4.50000i) q^{23} -9.00000i q^{27} -3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(5.19615 + 3.00000i) q^{33} +(-6.92820 - 4.00000i) q^{37} +(9.00000 + 15.5885i) q^{39} +5.00000 q^{41} -1.00000i q^{43} +(-6.92820 - 4.00000i) q^{47} +(6.50000 + 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{51} +(-3.46410 + 2.00000i) q^{53} +(-4.00000 - 6.92820i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(10.3923 - 12.0000i) q^{63} +(-2.59808 + 1.50000i) q^{67} -27.0000 q^{69} +8.00000 q^{71} +(-12.1244 + 7.00000i) q^{73} +(1.73205 + 5.00000i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-4.50000 - 7.79423i) q^{81} +1.00000i q^{83} +(-7.79423 + 4.50000i) q^{87} +(6.50000 - 11.2583i) q^{89} +(-3.00000 + 15.5885i) q^{91} +(-5.19615 - 3.00000i) q^{93} -10.0000i q^{97} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{9} + 4 q^{11} + 30 q^{21} - 12 q^{29} - 4 q^{31} + 36 q^{39} + 20 q^{41} + 26 q^{49} + 12 q^{51} - 16 q^{59} - 14 q^{61} - 108 q^{69} + 32 q^{71} + 8 q^{79} - 18 q^{81} + 26 q^{89} - 12 q^{91}+ \cdots + 48 q^{99}+O(q^{100}) \) 4 * q + 12 * q^9 + 4 * q^11 + 30 * q^21 - 12 * q^29 - 4 * q^31 + 36 * q^39 + 20 * q^41 + 26 * q^49 + 12 * q^51 - 16 * q^59 - 14 * q^61 - 108 * q^69 + 32 * q^71 + 8 * q^79 - 18 * q^81 + 26 * q^89 - 12 * q^91 + 48 * q^99

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