LMFDB - Embedded newform 700.2.r.a.249.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(149,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,0,0,0,0,0,0,0,-4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	700.249
Dual form			700.2.r.a.149.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 2.50000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-3.00000 + 5.19615i) q^{11} +2.00000i q^{13} +(-5.19615 - 3.00000i) q^{17} +(4.00000 + 6.92820i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(2.59808 - 1.50000i) q^{23} +5.00000i q^{27} -3.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(5.19615 - 3.00000i) q^{33} +(-6.92820 + 4.00000i) q^{37} +(1.00000 - 1.73205i) q^{39} -3.00000 q^{41} +5.00000i q^{43} +(-5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(-10.3923 - 6.00000i) q^{53} -8.00000i q^{57} +(0.500000 + 0.866025i) q^{61} +(-3.46410 + 4.00000i) q^{63} +(-6.06218 - 3.50000i) q^{67} -3.00000 q^{69} +(8.66025 + 5.00000i) q^{73} +(15.5885 + 3.00000i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.00000i q^{83} +(2.59808 + 1.50000i) q^{87} +(-1.50000 - 2.59808i) q^{89} +(5.00000 - 1.73205i) q^{91} +(1.73205 - 1.00000i) q^{93} +10.0000i q^{97} +12.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{9} - 12 q^{11} + 16 q^{19} - 2 q^{21} - 12 q^{29} - 4 q^{31} + 4 q^{39} - 12 q^{41} - 22 q^{49} + 12 q^{51} + 2 q^{61} - 12 q^{69} - 8 q^{79} - 2 q^{81} - 6 q^{89} + 20 q^{91} + 48 q^{99}+O(q^{100}) $ 4 * q - 4 * q^9 - 12 * q^11 + 16 * q^19 - 2 * q^21 - 12 * q^29 - 4 * q^31 + 4 * q^39 - 12 * q^41 - 22 * q^49 + 12 * q^51 + 2 * q^61 - 12 * q^69 - 8 * q^79 - 2 * q^81 - 6 * q^89 + 20 * q^91 + 48 * q^99

Character values

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

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	0.228714	−	0.973494i	$-0.426548\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	−0.728714	+	0.684819i	$0.759881\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$		0			0
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		0			0
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.287129	−	0.957892i	$-0.592701\pi$
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.973123	+	0.230285i	$0.926034\pi$
$18$		0			0
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.802955	+	0.596040i	$0.203260\pi$
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$		0			0
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	−0.204046	−	0.978961i	$-0.565409\pi$
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	0.745782	+	0.666190i	$0.232076\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			5.00000i			0.962250i
$28$		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	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$		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	−0.946180	−	0.323640i	$-0.895093\pi$
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.192809	+	0.981236i	$0.561760\pi$
$38$		0			0
$39$	1.00000	−	1.73205i	0.160128	−	0.277350i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$			5.00000i			0.762493i	0.924473	+	0.381246i	$0.124505\pi$
$43$			5.00000i			0.762493i	−0.924473	+	0.381246i	$0.875495\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$		0			0
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	3.00000	+	5.19615i	0.420084	+	0.727607i
$52$		0			0
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.430570	−	0.902557i	$-0.641688\pi$
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.996922	+	0.0783936i	$0.975021\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	8.00000i		−	1.05963i
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	−3.46410	+	4.00000i	−0.436436	+	0.503953i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.06218	−	3.50000i	−0.740613	−	0.427593i	0.0816792	−	0.996659i	$-0.473972\pi$
$67$	−6.06218	−	3.50000i	−0.740613	−	0.427593i	−0.822292	+	0.569066i	$0.807305\pi$
$68$		0			0
$69$	−3.00000			−0.361158
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.912245	−	0.409644i	$-0.134347\pi$
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.101361	+	0.994850i	$0.467680\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	15.5885	+	3.00000i	1.77647	+	0.341882i
$78$		0			0
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			3.00000i			0.329293i	0.986353	+	0.164646i	$0.0526483\pi$
$83$			3.00000i			0.329293i	−0.986353	+	0.164646i	$0.947352\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.59808	+	1.50000i	0.278543	+	0.160817i
$88$		0			0
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	0.775509	−	0.631337i	$-0.217494\pi$
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	−0.934508	+	0.355942i	$0.884160\pi$
$90$		0			0
$91$	5.00000	−	1.73205i	0.524142	−	0.181568i
$92$		0			0
$93$	1.73205	−	1.00000i	0.179605	−	0.103695i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$		0			0
$99$	12.0000			1.20605
$100$		0			0
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		0			0
$103$	−6.06218	+	3.50000i	−0.597324	+	0.344865i	−0.767988	−	0.640464i	$-0.778742\pi$
$103$	−6.06218	+	3.50000i	−0.597324	+	0.344865i	0.170664	+	0.985329i	$0.445409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	−0.369132	−	0.929377i	$-0.620345\pi$
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	0.620298	+	0.784366i	$0.287012\pi$
$108$		0			0
$109$	8.50000	−	14.7224i	0.814152	−	1.41015i	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	8.50000	−	14.7224i	0.814152	−	1.41015i	0.909935	−	0.414751i	$-0.136131\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$		0			0
$113$		−	12.0000i		−	1.12887i	−0.825479	−	0.564433i	$-0.809095\pi$
$113$		−	12.0000i		−	1.12887i	0.825479	−	0.564433i	$-0.190905\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.46410	−	2.00000i	0.320256	−	0.184900i
$118$		0			0
$119$	−3.00000	+	15.5885i	−0.275010	+	1.42899i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$		0			0
$123$	2.59808	+	1.50000i	0.234261	+	0.135250i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$		0			0
$129$	2.50000	−	4.33013i	0.220113	−	0.381246i
$130$		0			0
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$	13.8564	−	16.0000i	1.20150	−	1.38738i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.0146279	−	0.999893i	$-0.504656\pi$
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.873247	+	0.487278i	$0.837990\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−10.3923	−	6.00000i	−0.869048	−	0.501745i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.92820	−	1.00000i	0.571429	−	0.0824786i
$148$		0			0
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	−0.990485	−	0.137619i	$-0.956055\pi$
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	0.376061	−	0.926595i	$-0.377278\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$		0			0
$153$			12.0000i			0.970143i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.1244	+	7.00000i	0.967629	+	0.558661i	0.898513	−	0.438948i	$-0.144649\pi$
$157$	12.1244	+	7.00000i	0.967629	+	0.558661i	0.0691164	+	0.997609i	$0.477982\pi$
$158$		0			0
$159$	6.00000	+	10.3923i	0.475831	+	0.824163i
$160$		0			0
$161$	−6.00000	−	5.19615i	−0.472866	−	0.409514i
$162$		0			0
$163$	−13.8564	+	8.00000i	−1.08532	+	0.626608i	−0.932326	−	0.361619i	$-0.882224\pi$
$163$	−13.8564	+	8.00000i	−1.08532	+	0.626608i	−0.152992	+	0.988227i	$0.548891\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			21.0000i			1.62503i	0.582941	+	0.812514i	$0.301902\pi$
$167$			21.0000i			1.62503i	−0.582941	+	0.812514i	$0.698098\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	8.00000	−	13.8564i	0.611775	−	1.05963i
$172$		0			0
$173$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$173$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	−0.956088	−	0.293079i	$-0.905320\pi$
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	0.731858	+	0.681457i	$0.238654\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$		0			0
$183$		−	1.00000i		−	0.0739221i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	31.1769	−	18.0000i	2.27988	−	1.31629i
$188$		0			0
$189$	12.5000	−	4.33013i	0.909241	−	0.314970i
$190$		0			0
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$		0			0
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	0.436365	−	0.899770i	$-0.356266\pi$
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	−0.561041	+	0.827788i	$0.689599\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$		0			0
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$		0			0
$203$	2.59808	+	7.50000i	0.182349	+	0.526397i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−5.19615	−	3.00000i	−0.361158	−	0.208514i
$208$		0			0
$209$	−48.0000			−3.32023
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.19615	+	1.00000i	0.352738	+	0.0678844i
$218$		0			0
$219$	−5.00000	−	8.66025i	−0.337869	−	0.585206i
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	0.113761	−	0.993508i	$-0.463710\pi$
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	−0.803523	+	0.595274i	$0.797043\pi$
$228$		0			0
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	0.897173	−	0.441679i	$-0.145617\pi$
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	−0.831092	+	0.556136i	$0.812283\pi$
$230$		0			0
$231$	−12.0000	−	10.3923i	−0.789542	−	0.683763i
$232$		0			0
$233$	5.19615	−	3.00000i	0.340411	−	0.196537i	−0.320043	−	0.947403i	$-0.603697\pi$
$233$	5.19615	−	3.00000i	0.340411	−	0.196537i	0.660454	+	0.750867i	$0.270364\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			4.00000i			0.259828i
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	0.0546547	+	0.998505i	$0.482594\pi$
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	−0.892058	+	0.451920i	$0.850739\pi$
$242$		0			0
$243$	13.8564	−	8.00000i	0.888889	−	0.513200i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.8564	+	8.00000i	−0.881662	+	0.509028i
$248$		0			0
$249$	1.50000	−	2.59808i	0.0950586	−	0.164646i
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$			18.0000i			1.13165i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	20.7846	−	12.0000i	1.29651	−	0.748539i	0.316709	−	0.948523i	$-0.397422\pi$
$257$	20.7846	−	12.0000i	1.29651	−	0.748539i	0.979799	+	0.199983i	$0.0640888\pi$
$258$		0			0
$259$	16.0000	+	13.8564i	0.994192	+	0.860995i
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$	2.59808	+	1.50000i	0.160204	+	0.0924940i	0.577959	−	0.816066i	$-0.303849\pi$
$263$	2.59808	+	1.50000i	0.160204	+	0.0924940i	−0.417755	+	0.908560i	$0.637183\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			3.00000i			0.183597i
$268$		0			0
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	−0.998816	−	0.0486418i	$-0.984511\pi$
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	0.541533	+	0.840679i	$0.317844\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$		0			0
$273$	−5.19615	−	1.00000i	−0.314485	−	0.0605228i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−19.0526	−	11.0000i	−1.14476	−	0.660926i	−0.197153	−	0.980373i	$-0.563170\pi$
$277$	−19.0526	−	11.0000i	−1.14476	−	0.660926i	−0.947604	+	0.319447i	$0.896503\pi$
$278$		0			0
$279$	4.00000			0.239474
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−17.3205	−	10.0000i	−1.02960	−	0.594438i	−0.112728	−	0.993626i	$-0.535959\pi$
$283$	−17.3205	−	10.0000i	−1.02960	−	0.594438i	−0.916869	+	0.399188i	$0.869292\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.59808	+	7.50000i	0.153360	+	0.442711i
$288$		0			0
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$		0			0
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$		0			0
$293$		−	12.0000i		−	0.701047i	−0.936554	−	0.350524i	$-0.886004\pi$
$293$		−	12.0000i		−	0.701047i	0.936554	−	0.350524i	$-0.113996\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−25.9808	−	15.0000i	−1.50756	−	0.870388i
$298$		0			0
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	12.5000	−	4.33013i	0.720488	−	0.249584i
$302$		0			0
$303$	−2.59808	+	1.50000i	−0.149256	+	0.0861727i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			19.0000i			1.08439i	0.840254	+	0.542194i	$0.182406\pi$
$307$			19.0000i			1.08439i	−0.840254	+	0.542194i	$0.817594\pi$
$308$		0			0
$309$	7.00000			0.398216
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	−3.46410	+	2.00000i	−0.195803	+	0.113047i	−0.594696	−	0.803951i	$-0.702728\pi$
$313$	−3.46410	+	2.00000i	−0.195803	+	0.113047i	0.398894	+	0.916997i	$0.369394\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.5885	+	9.00000i	−0.875535	+	0.505490i	−0.869184	−	0.494489i	$-0.835355\pi$
$317$	−15.5885	+	9.00000i	−0.875535	+	0.505490i	−0.00635137	+	0.999980i	$0.502022\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	−3.00000			−0.167444
$322$		0			0
$323$		−	48.0000i		−	2.67079i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−14.7224	+	8.50000i	−0.814152	+	0.470051i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	0.992112	+	0.125353i	$0.0400062\pi$
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	−0.387498	+	0.921871i	$0.626660\pi$
$332$		0			0
$333$	13.8564	+	8.00000i	0.759326	+	0.438397i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	20.0000i		−	1.08947i	−0.838608	−	0.544735i	$-0.816630\pi$
$337$		−	20.0000i		−	1.08947i	0.838608	−	0.544735i	$-0.183370\pi$
$338$		0			0
$339$	−6.00000	+	10.3923i	−0.325875	+	0.564433i
$340$		0			0
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−23.3827	−	13.5000i	−1.25525	−	0.724718i	−0.283101	−	0.959090i	$-0.591363\pi$
$347$	−23.3827	−	13.5000i	−1.25525	−	0.724718i	−0.972147	+	0.234372i	$0.924697\pi$
$348$		0			0
$349$	1.00000			0.0535288			0.0267644	−	0.999642i	$-0.491480\pi$
$349$	1.00000			0.0535288			0.0267644	+	0.999642i	$0.491480\pi$
$350$		0			0
$351$	−10.0000			−0.533761
$352$		0			0
$353$	10.3923	+	6.00000i	0.553127	+	0.319348i	0.750382	−	0.661004i	$-0.229870\pi$
$353$	10.3923	+	6.00000i	0.553127	+	0.319348i	−0.197256	+	0.980352i	$0.563203\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	10.3923	−	12.0000i	0.550019	−	0.635107i
$358$		0			0
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$		0			0
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$		0			0
$363$			25.0000i			1.31216i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	4.33013	+	2.50000i	0.226031	+	0.130499i	0.608740	−	0.793370i	$-0.291675\pi$
$367$	4.33013	+	2.50000i	0.226031	+	0.130499i	−0.382709	+	0.923869i	$0.625009\pi$
$368$		0			0
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$		0			0
$371$	−6.00000	+	31.1769i	−0.311504	+	1.61862i
$372$		0			0
$373$	−13.8564	+	8.00000i	−0.717458	+	0.414224i	−0.813816	−	0.581122i	$-0.802614\pi$
$373$	−13.8564	+	8.00000i	−0.717458	+	0.414224i	0.0963587	+	0.995347i	$0.469280\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	6.00000i		−	0.309016i
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$		0			0
$383$	2.59808	−	1.50000i	0.132755	−	0.0766464i	−0.432151	−	0.901801i	$-0.642245\pi$
$383$	2.59808	−	1.50000i	0.132755	−	0.0766464i	0.564907	+	0.825155i	$0.308912\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.66025	−	5.00000i	0.440225	−	0.254164i
$388$		0			0
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$			12.0000i			0.605320i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−22.5167	+	13.0000i	−1.13008	+	0.652451i	−0.943955	−	0.330075i	$-0.892926\pi$
$397$	−22.5167	+	13.0000i	−1.13008	+	0.652451i	−0.186124	+	0.982526i	$0.559593\pi$
$398$		0			0
$399$	−20.0000	+	6.92820i	−1.00125	+	0.346844i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	−3.46410	−	2.00000i	−0.172559	−	0.0996271i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	48.0000i		−	2.37927i
$408$		0			0
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	−0.697406	−	0.716677i	$-0.745662\pi$
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	0.969363	+	0.245633i	$0.0789957\pi$
$410$		0			0
$411$	6.00000	+	10.3923i	0.295958	+	0.512615i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.73205	+	1.00000i	0.0848189	+	0.0489702i
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	23.0000			1.12095			0.560476	−	0.828171i	$-0.310618\pi$
$421$	23.0000			1.12095			0.560476	+	0.828171i	$0.310618\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.73205	−	2.00000i	0.0838198	−	0.0967868i
$428$		0			0
$429$	6.00000	+	10.3923i	0.289683	+	0.501745i
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$		0			0
$433$		−	28.0000i		−	1.34559i	−0.739827	−	0.672797i	$-0.765093\pi$
$433$		−	28.0000i		−	1.34559i	0.739827	−	0.672797i	$-0.234907\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	20.7846	+	12.0000i	0.994263	+	0.574038i
$438$		0			0
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$	13.0000	+	5.19615i	0.619048	+	0.247436i
$442$		0			0
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			15.0000i			0.709476i
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$		0			0
$453$	−8.66025	+	5.00000i	−0.406894	+	0.234920i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.46410	−	2.00000i	0.162044	−	0.0935561i	−0.416785	−	0.909005i	$-0.636843\pi$
$457$	3.46410	−	2.00000i	0.162044	−	0.0935561i	0.578829	+	0.815449i	$0.303510\pi$
$458$		0			0
$459$	15.0000	−	25.9808i	0.700140	−	1.21268i
$460$		0			0
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$			29.0000i			1.34774i	0.738848	+	0.673872i	$0.235370\pi$
$463$			29.0000i			1.34774i	−0.738848	+	0.673872i	$0.764630\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−28.5788	+	16.5000i	−1.32247	+	0.763529i	−0.984122	−	0.177492i	$-0.943202\pi$
$467$	−28.5788	+	16.5000i	−1.32247	+	0.763529i	−0.338349	+	0.941021i	$0.609868\pi$
$468$		0			0
$469$	−3.50000	+	18.1865i	−0.161615	+	0.839776i
$470$		0			0
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$		0			0
$473$	−25.9808	−	15.0000i	−1.19460	−	0.689701i
$474$		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	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$		0			0
$483$	2.59808	+	7.50000i	0.118217	+	0.341262i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.92820	+	4.00000i	0.313947	+	0.181257i	0.648691	−	0.761052i	$-0.275317\pi$
$487$	6.92820	+	4.00000i	0.313947	+	0.181257i	−0.334744	+	0.942309i	$0.608650\pi$
$488$		0			0
$489$	16.0000			0.723545
$490$		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
$493$	15.5885	+	9.00000i	0.702069	+	0.405340i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.00000	+	1.73205i	0.0447661	+	0.0775372i	0.887540	−	0.460730i	$-0.152412\pi$
$499$	1.00000	+	1.73205i	0.0447661	+	0.0775372i	−0.842774	+	0.538267i	$0.819079\pi$
$500$		0			0
$501$	10.5000	−	18.1865i	0.469105	−	0.812514i
$502$		0			0
$503$		−	9.00000i		−	0.401290i	−0.979664	−	0.200645i	$-0.935696\pi$
$503$		−	9.00000i		−	0.401290i	0.979664	−	0.200645i	$-0.0643038\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.79423	−	4.50000i	−0.346154	−	0.199852i
$508$		0			0
$509$	19.5000	+	33.7750i	0.864322	+	1.49705i	0.867719	+	0.497056i	$0.165586\pi$
$509$	19.5000	+	33.7750i	0.864322	+	1.49705i	−0.00339621	+	0.999994i	$0.501081\pi$
$510$		0			0
$511$	5.00000	−	25.9808i	0.221187	−	1.14932i
$512$		0			0
$513$	−34.6410	+	20.0000i	−1.52944	+	0.883022i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	0.324185	+	0.945994i	$0.394910\pi$
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	−0.981347	+	0.192244i	$0.938423\pi$
$522$		0			0
$523$	38.1051	−	22.0000i	1.66622	−	0.961993i	0.696573	−	0.717486i	$-0.254707\pi$
$523$	38.1051	−	22.0000i	1.66622	−	0.961993i	0.969648	−	0.244507i	$-0.0786260\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.3923	−	6.00000i	0.452696	−	0.261364i
$528$		0			0
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	6.00000i		−	0.259889i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.19615	−	3.00000i	0.224231	−	0.129460i
$538$		0			0
$539$	−6.00000	−	41.5692i	−0.258438	−	1.79051i
$540$		0			0
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	0.623404	−	0.781900i	$-0.285749\pi$
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	−0.988847	+	0.148933i	$0.952416\pi$
$542$		0			0
$543$	−14.7224	−	8.50000i	−0.631800	−	0.364770i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			19.0000i			0.812381i	0.913788	+	0.406191i	$0.133143\pi$
$547$			19.0000i			0.812381i	−0.913788	+	0.406191i	$0.866857\pi$
$548$		0			0
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$		0			0
$551$	−12.0000	−	20.7846i	−0.511217	−	0.885454i
$552$		0			0
$553$	−6.92820	+	8.00000i	−0.294617	+	0.340195i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	25.9808	+	15.0000i	1.10084	+	0.635570i	0.936442	−	0.350824i	$-0.114098\pi$
$557$	25.9808	+	15.0000i	1.10084	+	0.635570i	0.164399	+	0.986394i	$0.447432\pi$
$558$		0			0
$559$	−10.0000			−0.422955
$560$		0			0
$561$	−36.0000			−1.51992
$562$		0			0
$563$	7.79423	+	4.50000i	0.328488	+	0.189652i	0.655169	−	0.755482i	$-0.272597\pi$
$563$	7.79423	+	4.50000i	0.328488	+	0.189652i	−0.326682	+	0.945134i	$0.605931\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.59808	+	0.500000i	0.109109	+	0.0209980i
$568$		0			0
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	0.983444	+	0.181210i	$0.0580014\pi$
$572$		0			0
$573$		−	18.0000i		−	0.751961i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−8.66025	−	5.00000i	−0.360531	−	0.208153i	0.308783	−	0.951133i	$-0.400078\pi$
$577$	−8.66025	−	5.00000i	−0.360531	−	0.208153i	−0.669314	+	0.742980i	$0.733412\pi$
$578$		0			0
$579$	1.00000	+	1.73205i	0.0415586	+	0.0719816i
$580$		0			0
$581$	7.50000	−	2.59808i	0.311152	−	0.107786i
$582$		0			0
$583$	62.3538	−	36.0000i	2.58243	−	1.49097i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		0			0
$589$	−16.0000			−0.659269
$590$		0			0
$591$	9.00000	−	15.5885i	0.370211	−	0.641223i
$592$		0			0
$593$	−10.3923	+	6.00000i	−0.426761	+	0.246390i	−0.697966	−	0.716131i	$-0.745911\pi$
$593$	−10.3923	+	6.00000i	−0.426761	+	0.246390i	0.271205	+	0.962522i	$0.412578\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−17.3205	+	10.0000i	−0.708881	+	0.409273i
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$			14.0000i			0.570124i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	37.2391	−	21.5000i	1.51149	−	0.872658i	0.511578	−	0.859237i	$-0.329061\pi$
$607$	37.2391	−	21.5000i	1.51149	−	0.872658i	0.999910	−	0.0134214i	$-0.00427228\pi$
$608$		0			0
$609$	1.50000	−	7.79423i	0.0607831	−	0.315838i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.73205	−	1.00000i	−0.0699569	−	0.0403896i	0.464614	−	0.885514i	$-0.346193\pi$
$613$	−1.73205	−	1.00000i	−0.0699569	−	0.0403896i	−0.534570	+	0.845124i	$0.679527\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			12.0000i			0.483102i	0.970388	+	0.241551i	$0.0776561\pi$
$617$			12.0000i			0.483102i	−0.970388	+	0.241551i	$0.922344\pi$
$618$		0			0
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	−0.690365	−	0.723462i	$-0.742550\pi$
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	0.971718	+	0.236143i	$0.0758832\pi$
$620$		0			0
$621$	7.50000	+	12.9904i	0.300965	+	0.521286i
$622$		0			0
$623$	−5.19615	+	6.00000i	−0.208179	+	0.240385i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	41.5692	+	24.0000i	1.66011	+	0.958468i
$628$		0			0
$629$	48.0000			1.91389
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$		0			0
$633$	3.46410	+	2.00000i	0.137686	+	0.0794929i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−8.66025	−	11.0000i	−0.343132	−	0.435836i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$		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
$647$	18.1865	+	10.5000i	0.714986	+	0.412798i	0.812905	−	0.582397i	$-0.197885\pi$
$647$	18.1865	+	10.5000i	0.714986	+	0.412798i	−0.0979182	+	0.995194i	$0.531218\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−4.00000	−	3.46410i	−0.156772	−	0.135769i
$652$		0			0
$653$	−36.3731	+	21.0000i	−1.42339	+	0.821794i	−0.996587	−	0.0825519i	$-0.973693\pi$
$653$	−36.3731	+	21.0000i	−1.42339	+	0.821794i	−0.426801	+	0.904345i	$0.640360\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	20.0000i		−	0.780274i
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	−0.513680	−	0.857982i	$-0.671718\pi$
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	0.999874	+	0.0158695i	$0.00505163\pi$
$662$		0			0
$663$	−10.3923	+	6.00000i	−0.403604	+	0.233021i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.79423	+	4.50000i	−0.301794	+	0.174241i
$668$		0			0
$669$	4.00000	−	6.92820i	0.154649	−	0.267860i
$670$		0			0
$671$	−6.00000			−0.231627
$672$		0			0
$673$			32.0000i			1.23351i	0.787155	+	0.616755i	$0.211553\pi$
$673$			32.0000i			1.23351i	−0.787155	+	0.616755i	$0.788447\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.5885	−	9.00000i	0.599113	−	0.345898i	−0.169580	−	0.985517i	$-0.554241\pi$
$677$	15.5885	−	9.00000i	0.599113	−	0.345898i	0.768693	+	0.639618i	$0.220908\pi$
$678$		0			0
$679$	25.0000	−	8.66025i	0.959412	−	0.332350i
$680$		0			0
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$		0			0
$683$	12.9904	+	7.50000i	0.497063	+	0.286980i	0.727500	−	0.686108i	$-0.240682\pi$
$683$	12.9904	+	7.50000i	0.497063	+	0.286980i	−0.230437	+	0.973087i	$0.574015\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	2.00000i		−	0.0763048i
$688$		0			0
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	−7.00000	−	12.1244i	−0.266293	−	0.461232i	0.701609	−	0.712562i	$-0.252465\pi$
$691$	−7.00000	−	12.1244i	−0.266293	−	0.461232i	−0.967901	+	0.251330i	$0.919132\pi$
$692$		0			0
$693$	−10.3923	−	30.0000i	−0.394771	−	1.13961i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	15.5885	+	9.00000i	0.590455	+	0.340899i
$698$		0			0
$699$	−6.00000			−0.226941
$700$		0			0
$701$	27.0000			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$702$		0			0
$703$	−55.4256	−	32.0000i	−2.09042	−	1.20690i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.79423	−	1.50000i	−0.293132	−	0.0564133i
$708$		0			0
$709$	−0.500000	−	0.866025i	−0.0187779	−	0.0325243i	0.856484	−	0.516174i	$-0.172644\pi$
$709$	−0.500000	−	0.866025i	−0.0187779	−	0.0325243i	−0.875262	+	0.483650i	$0.839311\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$		0			0
$713$			6.00000i			0.224702i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.19615	+	3.00000i	0.194054	+	0.112037i
$718$		0			0
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	−0.997546	−	0.0700124i	$-0.977696\pi$
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	0.438141	−	0.898906i	$-0.355637\pi$
$720$		0			0
$721$	14.0000	+	12.1244i	0.521387	+	0.451535i
$722$		0			0
$723$	22.5167	−	13.0000i	0.837404	−	0.483475i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	23.0000i		−	0.853023i	−0.904482	−	0.426511i	$-0.859742\pi$
$727$		−	23.0000i		−	0.853023i	0.904482	−	0.426511i	$-0.140258\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	15.0000	−	25.9808i	0.554795	−	0.960933i
$732$		0			0
$733$	1.73205	−	1.00000i	0.0639748	−	0.0369358i	−0.467671	−	0.883902i	$-0.654907\pi$
$733$	1.73205	−	1.00000i	0.0639748	−	0.0369358i	0.531646	+	0.846967i	$0.321574\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	36.3731	−	21.0000i	1.33982	−	0.773545i
$738$		0			0
$739$	−23.0000	+	39.8372i	−0.846069	+	1.46543i	0.0386212	+	0.999254i	$0.487703\pi$
$739$	−23.0000	+	39.8372i	−0.846069	+	1.46543i	−0.884690	+	0.466180i	$0.845630\pi$
$740$		0			0
$741$	16.0000			0.587775
$742$		0			0
$743$		−	39.0000i		−	1.43077i	−0.698730	−	0.715386i	$-0.746251\pi$
$743$		−	39.0000i		−	1.43077i	0.698730	−	0.715386i	$-0.253749\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.19615	−	3.00000i	0.190117	−	0.109764i
$748$		0			0
$749$	−6.00000	−	5.19615i	−0.219235	−	0.189863i
$750$		0			0
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	0.623856	−	0.781540i	$-0.285565\pi$
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	−0.988761	+	0.149505i	$0.952232\pi$
$752$		0			0
$753$	15.5885	+	9.00000i	0.568075	+	0.327978i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$		0			0
$759$	9.00000	−	15.5885i	0.326679	−	0.565825i
$760$		0			0
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	−0.998684	−	0.0512772i	$-0.983671\pi$
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	0.454935	−	0.890525i	$-0.349663\pi$
$762$		0			0
$763$	−44.1673	−	8.50000i	−1.59896	−	0.307721i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$		0			0
$773$	36.3731	+	21.0000i	1.30825	+	0.755318i	0.981804	−	0.189899i	$-0.0608160\pi$
$773$	36.3731	+	21.0000i	1.30825	+	0.755318i	0.326445	+	0.945216i	$0.394149\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−6.92820	−	20.0000i	−0.248548	−	0.717496i
$778$		0			0
$779$	−12.0000	−	20.7846i	−0.429945	−	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	15.0000i		−	0.536056i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−26.8468	−	15.5000i	−0.956985	−	0.552515i	−0.0617409	−	0.998092i	$-0.519665\pi$
$787$	−26.8468	−	15.5000i	−0.956985	−	0.552515i	−0.895244	+	0.445577i	$0.852999\pi$
$788$		0			0
$789$	−1.50000	−	2.59808i	−0.0534014	−	0.0924940i
$790$		0			0
$791$	−30.0000	+	10.3923i	−1.06668	+	0.369508i
$792$		0			0
$793$	−1.73205	+	1.00000i	−0.0615069	+	0.0355110i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			12.0000i			0.425062i	0.977154	+	0.212531i	$0.0681706\pi$
$797$			12.0000i			0.425062i	−0.977154	+	0.212531i	$0.931829\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$		0			0
$803$	−51.9615	+	30.0000i	−1.83368	+	1.05868i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.9904	−	7.50000i	0.457283	−	0.264013i
$808$		0			0
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.0646355	+	0.997909i	$0.520588\pi$
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.831897	+	0.554930i	$0.812745\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$		−	16.0000i		−	0.561144i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−34.6410	+	20.0000i	−1.21194	+	0.699711i
$818$		0			0
$819$	−8.00000	−	6.92820i	−0.279543	−	0.242091i
$820$		0			0
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	42.4352	+	24.5000i	1.47920	+	0.854016i	0.999723	−	0.0235383i	$-0.00749316\pi$
$823$	42.4352	+	24.5000i	1.47920	+	0.854016i	0.479477	+	0.877555i	$0.340826\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			45.0000i			1.56480i	0.622774	+	0.782402i	$0.286006\pi$
$827$			45.0000i			1.56480i	−0.622774	+	0.782402i	$0.713994\pi$
$828$		0			0
$829$	−5.00000	+	8.66025i	−0.173657	+	0.300783i	−0.939696	−	0.342012i	$-0.888892\pi$
$829$	−5.00000	+	8.66025i	−0.173657	+	0.300783i	0.766039	+	0.642795i	$0.222225\pi$
$830$		0			0
$831$	11.0000	+	19.0526i	0.381586	+	0.660926i
$832$		0			0
$833$	41.5692	−	6.00000i	1.44029	−	0.207888i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.66025	−	5.00000i	−0.299342	−	0.172825i
$838$		0			0
$839$	42.0000			1.45000			0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000			1.45000			0.725001	+	0.688748i	$0.241839\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		0			0
$843$	5.19615	+	3.00000i	0.178965	+	0.103325i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−43.3013	+	50.0000i	−1.48785	+	1.71802i
$848$		0			0
$849$	10.0000	+	17.3205i	0.343199	+	0.594438i
$850$		0			0
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$		0			0
$853$			32.0000i			1.09566i	0.836590	+	0.547830i	$0.184546\pi$
$853$			32.0000i			1.09566i	−0.836590	+	0.547830i	$0.815454\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	36.3731	+	21.0000i	1.24248	+	0.717346i	0.969599	−	0.244701i	$-0.0786899\pi$
$857$	36.3731	+	21.0000i	1.24248	+	0.717346i	0.272882	+	0.962048i	$0.412023\pi$
$858$		0			0
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$		0			0
$861$	1.50000	−	7.79423i	0.0511199	−	0.265627i
$862$		0			0
$863$	28.5788	−	16.5000i	0.972835	−	0.561667i	0.0727356	−	0.997351i	$-0.476827\pi$
$863$	28.5788	−	16.5000i	0.972835	−	0.561667i	0.900099	+	0.435685i	$0.143494\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	19.0000i		−	0.645274i
$868$		0			0
$869$	24.0000			0.814144
$870$		0			0
$871$	7.00000	−	12.1244i	0.237186	−	0.410818i
$872$		0			0
$873$	17.3205	−	10.0000i	0.586210	−	0.338449i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	34.6410	−	20.0000i	1.16974	−	0.675352i	0.216124	−	0.976366i	$-0.430658\pi$
$877$	34.6410	−	20.0000i	1.16974	−	0.675352i	0.953620	+	0.301014i	$0.0973250\pi$
$878$		0			0
$879$	−6.00000	+	10.3923i	−0.202375	+	0.350524i
$880$		0			0
$881$	9.00000			0.303218			0.151609	−	0.988441i	$-0.451555\pi$
$881$	9.00000			0.303218			0.151609	+	0.988441i	$0.451555\pi$
$882$		0			0
$883$		−	28.0000i		−	0.942275i	−0.882060	−	0.471138i	$-0.843844\pi$
$883$		−	28.0000i		−	0.942275i	0.882060	−	0.471138i	$-0.156156\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−49.3634	+	28.5000i	−1.65746	+	0.956936i	−0.683582	+	0.729873i	$0.739579\pi$
$887$	−49.3634	+	28.5000i	−1.65746	+	0.956936i	−0.973880	+	0.227063i	$0.927088\pi$
$888$		0			0
$889$	−20.0000	+	6.92820i	−0.670778	+	0.232364i
$890$		0			0
$891$	−3.00000	−	5.19615i	−0.100504	−	0.174078i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	6.00000i		−	0.200334i
$898$		0			0
$899$	3.00000	−	5.19615i	0.100056	−	0.173301i
$900$		0			0
$901$	36.0000	+	62.3538i	1.19933	+	2.07731i
$902$		0			0
$903$	−12.9904	−	2.50000i	−0.432293	−	0.0831948i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	19.9186	+	11.5000i	0.661386	+	0.381851i	0.792805	−	0.609476i	$-0.208620\pi$
$907$	19.9186	+	11.5000i	0.661386	+	0.381851i	−0.131419	+	0.991327i	$0.541953\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$	−15.5885	−	9.00000i	−0.515903	−	0.297857i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.7846	+	24.0000i	−0.686368	+	0.792550i
$918$		0			0
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	0.924427	−	0.381358i	$-0.124544\pi$
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	−0.792480	+	0.609898i	$0.791210\pi$
$920$		0			0
$921$	9.50000	−	16.4545i	0.313036	−	0.542194i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	12.1244	+	7.00000i	0.398216	+	0.229910i
$928$		0			0
$929$	−22.5000	−	38.9711i	−0.738201	−	1.27860i	−0.953305	−	0.302010i	$-0.902342\pi$
$929$	−22.5000	−	38.9711i	−0.738201	−	1.27860i	0.215104	−	0.976591i	$-0.430991\pi$
$930$		0			0
$931$	−52.0000	−	20.7846i	−1.70423	−	0.681188i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	44.0000i		−	1.43742i	−0.695311	−	0.718709i	$-0.744734\pi$
$937$		−	44.0000i		−	1.43742i	0.695311	−	0.718709i	$-0.255266\pi$
$938$		0			0
$939$	4.00000			0.130535
$940$		0			0
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.0290288	+	0.999579i	$0.509241\pi$
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.851146	+	0.524929i	$0.824092\pi$
$942$		0			0
$943$	−7.79423	+	4.50000i	−0.253815	+	0.146540i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.79423	+	4.50000i	−0.253278	+	0.146230i	−0.621264	−	0.783601i	$-0.713381\pi$
$947$	−7.79423	+	4.50000i	−0.253278	+	0.146230i	0.367986	+	0.929831i	$0.380047\pi$
$948$		0			0
$949$	−10.0000	+	17.3205i	−0.324614	+	0.562247i
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$			36.0000i			1.16615i	0.812417	+	0.583077i	$0.198151\pi$
$953$			36.0000i			1.16615i	−0.812417	+	0.583077i	$0.801849\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−15.5885	+	9.00000i	−0.503903	+	0.290929i
$958$		0			0
$959$	−6.00000	+	31.1769i	−0.193750	+	1.00676i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$	−5.19615	−	3.00000i	−0.167444	−	0.0966736i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			7.00000i			0.225105i	0.993646	+	0.112552i	$0.0359026\pi$
$967$			7.00000i			0.225105i	−0.993646	+	0.112552i	$0.964097\pi$
$968$		0			0
$969$	−24.0000	+	41.5692i	−0.770991	+	1.33540i
$970$		0			0
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	0.946094	−	0.323891i	$-0.104991\pi$
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	−0.753545	+	0.657396i	$0.771658\pi$
$972$		0			0
$973$	1.73205	+	5.00000i	0.0555270	+	0.160293i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−46.7654	−	27.0000i	−1.49616	−	0.863807i	−0.496167	−	0.868227i	$-0.665259\pi$
$977$	−46.7654	−	27.0000i	−1.49616	−	0.863807i	−0.999990	+	0.00442082i	$0.998593\pi$
$978$		0			0
$979$	18.0000			0.575282
$980$		0			0
$981$	−34.0000			−1.08554
$982$		0			0
$983$	33.7750	+	19.5000i	1.07725	+	0.621953i	0.930155	−	0.367168i	$-0.119673\pi$
$983$	33.7750	+	19.5000i	1.07725	+	0.621953i	0.147100	+	0.989122i	$0.453006\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.50000	+	12.9904i	0.238486	+	0.413070i
$990$		0			0
$991$	−13.0000	+	22.5167i	−0.412959	+	0.715265i	−0.995212	−	0.0977423i	$-0.968838\pi$
$991$	−13.0000	+	22.5167i	−0.412959	+	0.715265i	0.582253	+	0.813008i	$0.302171\pi$
$992$		0			0
$993$		−	22.0000i		−	0.698149i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	27.7128	+	16.0000i	0.877674	+	0.506725i	0.869891	−	0.493245i	$-0.164189\pi$
$997$	27.7128	+	16.0000i	0.877674	+	0.506725i	0.00778294	+	0.999970i	$0.497523\pi$
$998$		0			0
$999$	−20.0000	−	34.6410i	−0.632772	−	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.r.a.249.1		4
5.2	odd	4		140.2.i.a.81.1	✓	2
5.3	odd	4		700.2.i.b.501.1		2
5.4	even	2	inner	700.2.r.a.249.2		4
7.2	even	3	inner	700.2.r.a.149.2		4
7.3	odd	6		4900.2.e.n.2549.1		2
7.4	even	3		4900.2.e.m.2549.2		2
15.2	even	4		1260.2.s.c.361.1		2
20.7	even	4		560.2.q.f.81.1		2
35.2	odd	12		140.2.i.a.121.1	yes	2
35.3	even	12		4900.2.a.q.1.1		1
35.4	even	6		4900.2.e.m.2549.1		2
35.9	even	6	inner	700.2.r.a.149.1		4
35.12	even	12		980.2.i.f.961.1		2
35.17	even	12		980.2.a.e.1.1		1
35.18	odd	12		4900.2.a.i.1.1		1
35.23	odd	12		700.2.i.b.401.1		2
35.24	odd	6		4900.2.e.n.2549.2		2
35.27	even	4		980.2.i.f.361.1		2
35.32	odd	12		980.2.a.g.1.1		1
105.2	even	12		1260.2.s.c.541.1		2
105.17	odd	12		8820.2.a.a.1.1		1
105.32	even	12		8820.2.a.p.1.1		1
140.67	even	12		3920.2.a.k.1.1		1
140.87	odd	12		3920.2.a.w.1.1		1
140.107	even	12		560.2.q.f.401.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.i.a.81.1	✓	2	5.2	odd	4
140.2.i.a.121.1	yes	2	35.2	odd	12
560.2.q.f.81.1		2	20.7	even	4
560.2.q.f.401.1		2	140.107	even	12
700.2.i.b.401.1		2	35.23	odd	12
700.2.i.b.501.1		2	5.3	odd	4
700.2.r.a.149.1		4	35.9	even	6	inner
700.2.r.a.149.2		4	7.2	even	3	inner
700.2.r.a.249.1		4	1.1	even	1	trivial
700.2.r.a.249.2		4	5.4	even	2	inner
980.2.a.e.1.1		1	35.17	even	12
980.2.a.g.1.1		1	35.32	odd	12
980.2.i.f.361.1		2	35.27	even	4
980.2.i.f.961.1		2	35.12	even	12
1260.2.s.c.361.1		2	15.2	even	4
1260.2.s.c.541.1		2	105.2	even	12
3920.2.a.k.1.1		1	140.67	even	12
3920.2.a.w.1.1		1	140.87	odd	12
4900.2.a.i.1.1		1	35.18	odd	12
4900.2.a.q.1.1		1	35.3	even	12
4900.2.e.m.2549.1		2	35.4	even	6
4900.2.e.m.2549.2		2	7.4	even	3
4900.2.e.n.2549.1		2	7.3	odd	6
4900.2.e.n.2549.2		2	35.24	odd	6
8820.2.a.a.1.1		1	105.17	odd	12
8820.2.a.p.1.1		1	105.32	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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 2.50000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-3.00000 + 5.19615i) q^{11} +2.00000i q^{13} +(-5.19615 - 3.00000i) q^{17} +(4.00000 + 6.92820i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(2.59808 - 1.50000i) q^{23} +5.00000i q^{27} -3.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(5.19615 - 3.00000i) q^{33} +(-6.92820 + 4.00000i) q^{37} +(1.00000 - 1.73205i) q^{39} -3.00000 q^{41} +5.00000i q^{43} +(-5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(-10.3923 - 6.00000i) q^{53} -8.00000i q^{57} +(0.500000 + 0.866025i) q^{61} +(-3.46410 + 4.00000i) q^{63} +(-6.06218 - 3.50000i) q^{67} -3.00000 q^{69} +(8.66025 + 5.00000i) q^{73} +(15.5885 + 3.00000i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.00000i q^{83} +(2.59808 + 1.50000i) q^{87} +(-1.50000 - 2.59808i) q^{89} +(5.00000 - 1.73205i) q^{91} +(1.73205 - 1.00000i) q^{93} +10.0000i q^{97} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{9} - 12 q^{11} + 16 q^{19} - 2 q^{21} - 12 q^{29} - 4 q^{31} + 4 q^{39} - 12 q^{41} - 22 q^{49} + 12 q^{51} + 2 q^{61} - 12 q^{69} - 8 q^{79} - 2 q^{81} - 6 q^{89} + 20 q^{91} + 48 q^{99}+O(q^{100}) \) 4 * q - 4 * q^9 - 12 * q^11 + 16 * q^19 - 2 * q^21 - 12 * q^29 - 4 * q^31 + 4 * q^39 - 12 * q^41 - 22 * q^49 + 12 * q^51 + 2 * q^61 - 12 * q^69 - 8 * q^79 - 2 * q^81 - 6 * q^89 + 20 * q^91 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more