LMFDB - Embedded newform 140.2.s.a.19.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(19,140)] 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("140.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(140, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			19.4
Root			$1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	140.19
Dual form			140.2.s.a.59.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 1.22474i) q^{2} +(0.308646 - 0.178197i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -0.504017i q^{6} +(0.308646 - 2.62769i) q^{7} -2.82843 q^{8} +(-1.43649 + 2.48808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(-0.617292 - 0.356394i) q^{12} +(-3.00000 - 2.23607i) q^{14} +0.796921 q^{15} +(-2.00000 + 3.46410i) q^{16} +(2.03151 + 3.51867i) q^{18} -4.47214i q^{20} +(-0.372983 - 0.866025i) q^{21} +(-3.75437 + 6.50275i) q^{23} +(-0.872983 + 0.504017i) q^{24} +(2.50000 + 4.33013i) q^{25} +2.09310i q^{27} +(-4.85993 + 2.09310i) q^{28} +4.74597 q^{29} +(0.563508 - 0.976025i) q^{30} +(2.82843 + 4.89898i) q^{32} +(3.53553 - 4.74342i) q^{35} +5.74597 q^{36} +(-5.47723 - 3.16228i) q^{40} -12.6284i q^{41} +(-1.32440 - 0.155563i) q^{42} -9.10257 q^{43} +(-5.56351 + 3.21209i) q^{45} +(5.30948 + 9.19628i) q^{46} +(8.21584 + 4.74342i) q^{47} +1.42558i q^{48} +(-6.80948 - 1.62205i) q^{49} +7.07107 q^{50} +(2.56351 + 1.48004i) q^{54} +(-0.872983 + 7.43222i) q^{56} +(3.35591 - 5.81260i) q^{58} +(-0.796921 - 1.38031i) q^{60} +(-11.8095 - 6.81820i) q^{61} +(6.09452 + 4.54259i) q^{63} +8.00000 q^{64} +(-7.90719 - 13.6957i) q^{67} +2.67607i q^{69} +(-3.30948 - 7.68423i) q^{70} +(4.06301 - 7.03734i) q^{72} +(1.54323 + 0.890985i) q^{75} +(-7.74597 + 4.47214i) q^{80} +(-3.93649 - 6.81820i) q^{81} +(-15.4665 - 8.92961i) q^{82} -18.2156i q^{83} +(-1.12702 + 1.51205i) q^{84} +(-6.43649 + 11.1483i) q^{86} +(1.46482 - 0.845717i) q^{87} +(12.2460 + 7.07021i) q^{89} +9.08517i q^{90} +15.0175 q^{92} +(11.6190 - 6.70820i) q^{94} +(1.74597 + 1.00803i) q^{96} +(-6.80162 + 7.19291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{9} - 24 q^{14} - 16 q^{16} + 28 q^{21} + 24 q^{24} + 20 q^{25} - 24 q^{29} + 20 q^{30} - 16 q^{36} - 60 q^{45} - 4 q^{46} - 8 q^{49} + 36 q^{54} + 24 q^{56} - 48 q^{61} + 64 q^{64}+ \cdots - 48 q^{96}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^9 - 24 * q^14 - 16 * q^16 + 28 * q^21 + 24 * q^24 + 20 * q^25 - 24 * q^29 + 20 * q^30 - 16 * q^36 - 60 * q^45 - 4 * q^46 - 8 * q^49 + 36 * q^54 + 24 * q^56 - 48 * q^61 + 64 * q^64 + 20 * q^70 - 16 * q^81 - 40 * q^84 - 36 * q^86 + 36 * q^89 - 48 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$3$	0.308646	−	0.178197i	0.178197	−	0.102882i	−0.408248	−	0.912871i	$-0.633860\pi$
$3$	0.308646	−	0.178197i	0.178197	−	0.102882i	0.586445	+	0.809989i	$0.300527\pi$
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	1.93649	+	1.11803i	0.866025	+	0.500000i
$5$	1.93649	+	1.11803i	0.866025	+	0.500000i
$6$		−	0.504017i		−	0.205764i
$7$	0.308646	−	2.62769i	0.116657	−	0.993172i
$7$	0.308646	−	2.62769i	0.116657	−	0.993172i
$8$	−2.82843			−1.00000
$9$	−1.43649	+	2.48808i	−0.478831	+	0.829359i
$10$	2.73861	−	1.58114i	0.866025	−	0.500000i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	−0.617292	−	0.356394i	−0.178197	−	0.102882i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−3.00000	−	2.23607i	−0.801784	−	0.597614i
$15$	0.796921			0.205764
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	2.03151	+	3.51867i	0.478831	+	0.829359i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$		−	4.47214i		−	1.00000i
$21$	−0.372983	−	0.866025i	−0.0813916	−	0.188982i
$22$		0			0
$23$	−3.75437	+	6.50275i	−0.782839	+	1.35592i	0.147442	+	0.989071i	$0.452896\pi$
$23$	−3.75437	+	6.50275i	−0.782839	+	1.35592i	−0.930281	+	0.366847i	$0.880437\pi$
$24$	−0.872983	+	0.504017i	−0.178197	+	0.102882i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$		0			0
$27$			2.09310i			0.402816i
$28$	−4.85993	+	2.09310i	−0.918441	+	0.395558i
$29$	4.74597			0.881304			0.440652	−	0.897678i	$-0.354747\pi$
$29$	4.74597			0.881304			0.440652	+	0.897678i	$0.354747\pi$
$30$	0.563508	−	0.976025i	0.102882	−	0.178197i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	2.82843	+	4.89898i	0.500000	+	0.866025i
$33$		0			0
$34$		0			0
$35$	3.53553	−	4.74342i	0.597614	−	0.801784i
$36$	5.74597			0.957661
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$		0			0
$39$		0			0
$40$	−5.47723	−	3.16228i	−0.866025	−	0.500000i
$41$		−	12.6284i		−	1.97222i	−0.166092	−	0.986110i	$-0.553115\pi$
$41$		−	12.6284i		−	1.97222i	0.166092	−	0.986110i	$-0.446885\pi$
$42$	−1.32440	−	0.155563i	−0.204359	−	0.0240039i
$43$	−9.10257			−1.38813			−0.694065	−	0.719913i	$-0.744182\pi$
$43$	−9.10257			−1.38813			−0.694065	+	0.719913i	$0.744182\pi$
$44$		0			0
$45$	−5.56351	+	3.21209i	−0.829359	+	0.478831i
$46$	5.30948	+	9.19628i	0.782839	+	1.35592i
$47$	8.21584	+	4.74342i	1.19840	+	0.691898i	0.960199	−	0.279317i	$-0.0901079\pi$
$47$	8.21584	+	4.74342i	1.19840	+	0.691898i	0.238204	+	0.971215i	$0.423441\pi$
$48$			1.42558i			0.205764i
$49$	−6.80948	−	1.62205i	−0.972782	−	0.231722i
$50$	7.07107			1.00000
$51$		0			0
$52$		0			0
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	2.56351	+	1.48004i	0.348849	+	0.201408i
$55$		0			0
$56$	−0.872983	+	7.43222i	−0.116657	+	0.993172i
$57$		0			0
$58$	3.35591	−	5.81260i	0.440652	−	0.763232i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	−0.796921	−	1.38031i	−0.102882	−	0.178197i
$61$	−11.8095	−	6.81820i	−1.51205	−	0.872982i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−11.8095	−	6.81820i	−1.51205	−	0.872982i	−0.512148	−	0.858898i	$-0.671150\pi$
$62$		0			0
$63$	6.09452	+	4.54259i	0.767837	+	0.572312i
$64$	8.00000			1.00000
$65$		0			0
$66$		0			0
$67$	−7.90719	−	13.6957i	−0.966017	−	1.67319i	−0.706857	−	0.707357i	$-0.749887\pi$
$67$	−7.90719	−	13.6957i	−0.966017	−	1.67319i	−0.259161	−	0.965834i	$-0.583446\pi$
$68$		0			0
$69$			2.67607i			0.322161i
$70$	−3.30948	−	7.68423i	−0.395558	−	0.918441i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	4.06301	−	7.03734i	0.478831	−	0.829359i
$73$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$73$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$74$		0			0
$75$	1.54323	+	0.890985i	0.178197	+	0.102882i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	−7.74597	+	4.47214i	−0.866025	+	0.500000i
$81$	−3.93649	−	6.81820i	−0.437388	−	0.757578i
$82$	−15.4665	−	8.92961i	−1.70799	−	0.986110i
$83$		−	18.2156i		−	1.99942i	−0.0240199	−	0.999711i	$-0.507647\pi$
$83$		−	18.2156i		−	1.99942i	0.0240199	−	0.999711i	$-0.492353\pi$
$84$	−1.12702	+	1.51205i	−0.122968	+	0.164978i
$85$		0			0
$86$	−6.43649	+	11.1483i	−0.694065	+	1.20216i
$87$	1.46482	−	0.845717i	0.157046	−	0.0906704i
$88$		0			0
$89$	12.2460	+	7.07021i	1.29807	+	0.749441i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	12.2460	+	7.07021i	1.29807	+	0.749441i	0.317999	+	0.948091i	$0.396989\pi$
$90$			9.08517i			0.957661i
$91$		0			0
$92$	15.0175			1.56568
$93$		0			0
$94$	11.6190	−	6.70820i	1.19840	−	0.691898i
$95$		0			0
$96$	1.74597	+	1.00803i	0.178197	+	0.102882i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	−6.80162	+	7.19291i	−0.687068	+	0.726593i
$99$		0			0
$100$	5.00000	−	8.66025i	0.500000	−	0.866025i
$101$	9.62702	−	5.55816i	0.957924	−	0.553058i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.62702	−	5.55816i	0.957924	−	0.553058i	0.895533	+	0.444994i	$0.146794\pi$
$102$		0			0
$103$	16.3925	+	9.46420i	1.61520	+	0.932535i	0.988139	+	0.153564i	$0.0490751\pi$
$103$	16.3925	+	9.46420i	1.61520	+	0.932535i	0.627060	+	0.778971i	$0.284258\pi$
$104$		0			0
$105$	0.245967	−	2.09406i	0.0240039	−	0.204359i
$106$		0			0
$107$	−8.70411	+	15.0760i	−0.841458	+	1.45745i	0.0472033	+	0.998885i	$0.484969\pi$
$107$	−8.70411	+	15.0760i	−0.841458	+	1.45745i	−0.888662	+	0.458563i	$0.848364\pi$
$108$	3.62535	−	2.09310i	0.348849	−	0.201408i
$109$	1.80948	+	3.13410i	0.173316	+	0.300193i	0.939577	−	0.342337i	$-0.111218\pi$
$109$	1.80948	+	3.13410i	0.173316	+	0.300193i	−0.766261	+	0.642529i	$0.777885\pi$
$110$		0			0
$111$		0			0
$112$	8.48528	+	6.32456i	0.801784	+	0.597614i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$	−14.5406	+	8.39502i	−1.35592	+	0.782839i
$116$	−4.74597	−	8.22026i	−0.440652	−	0.763232i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−2.25403			−0.205764
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$	−16.7011	+	9.64240i	−1.51205	+	0.872982i
$123$	−2.25034	−	3.89770i	−0.202906	−	0.351444i
$124$		0			0
$125$			11.1803i			1.00000i
$126$	9.87298	−	4.25214i	0.879555	−	0.378810i
$127$	4.24264			0.376473			0.188237	−	0.982124i	$-0.439723\pi$
$127$	4.24264			0.376473			0.188237	+	0.982124i	$0.439723\pi$
$128$	5.65685	−	9.79796i	0.500000	−	0.866025i
$129$	−2.80948	+	1.62205i	−0.247360	+	0.142814i
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$		0			0
$134$	−22.3649			−1.93203
$135$	−2.34015	+	4.05326i	−0.201408	+	0.348849i
$136$		0			0
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$	3.27750	+	1.89226i	0.278999	+	0.161080i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−11.7514	−	1.38031i	−0.993172	−	0.116657i
$141$	3.38105			0.284736
$142$		0			0
$143$		0			0
$144$	−5.74597	−	9.95231i	−0.478831	−	0.829359i
$145$	9.19052	+	5.30615i	0.763232	+	0.440652i
$146$		0			0
$147$	−2.39076	+	0.712788i	−0.197187	+	0.0587898i
$148$		0			0
$149$	4.06351	−	7.03820i	0.332896	−	0.576592i	−0.650183	−	0.759778i	$-0.725308\pi$
$149$	4.06351	−	7.03820i	0.332896	−	0.576592i	0.983078	+	0.183186i	$0.0586410\pi$
$150$	2.18246	−	1.26004i	0.178197	−	0.102882i
$151$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$151$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$157$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$158$		0			0
$159$		0			0
$160$			12.6491i			1.00000i
$161$	15.9284	+	11.8723i	1.25534	+	0.935672i
$162$	−11.1341			−0.874776
$163$	6.36396	−	11.0227i	0.498464	−	0.863365i	−0.501535	−	0.865138i	$-0.667231\pi$
$163$	6.36396	−	11.0227i	0.498464	−	0.863365i	0.999998	+	0.00177283i	$0.000564310\pi$
$164$	−21.8730	+	12.6284i	−1.70799	+	0.986110i
$165$		0			0
$166$	−22.3095	−	12.8804i	−1.73155	−	0.999711i
$167$			16.0772i			1.24409i	0.782980	+	0.622047i	$0.213699\pi$
$167$			16.0772i			1.24409i	−0.782980	+	0.622047i	$0.786301\pi$
$168$	1.05496	+	2.44949i	0.0813916	+	0.188982i
$169$	−13.0000			−1.00000
$170$		0			0
$171$		0			0
$172$	9.10257	+	15.7661i	0.694065	+	1.20216i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		−	2.39205i		−	0.181341i
$175$	12.1498	−	5.23274i	0.918441	−	0.395558i
$176$		0			0
$177$		0			0
$178$	17.3184	−	9.99879i	1.29807	−	0.749441i
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	11.1270	+	6.42419i	0.829359	+	0.478831i
$181$			15.1485i			1.12598i	0.826465	+	0.562988i	$0.190348\pi$
$181$			15.1485i			1.12598i	−0.826465	+	0.562988i	$0.809652\pi$
$182$		0			0
$183$	−4.85993			−0.359257
$184$	10.6190	−	18.3926i	0.782839	−	1.35592i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		−	18.9737i		−	1.38380i
$189$	5.50000	+	0.646026i	0.400066	+	0.0469915i
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	2.46917	−	1.42558i	0.178197	−	0.102882i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$		0			0
$195$		0			0
$196$	4.00000	+	13.4164i	0.285714	+	0.958315i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	−7.07107	−	12.2474i	−0.500000	−	0.866025i
$201$	−4.88105	−	2.81808i	−0.344283	−	0.198772i
$202$		−	15.7209i		−	1.10612i
$203$	1.46482	−	12.4709i	0.102811	−	0.875287i
$204$		0			0
$205$	14.1190	−	24.4547i	0.986110	−	1.70799i
$206$	23.1825	−	13.3844i	1.61520	−	0.932535i
$207$	−10.7862	−	18.6823i	−0.749695	−	1.29851i
$208$		0			0
$209$		0			0
$210$	−2.39076	−	1.78197i	−0.164978	−	0.122968i
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$		0			0
$213$		0			0
$214$	12.3095	+	21.3206i	0.841458	+	1.45745i
$215$	−17.6271	−	10.1770i	−1.20216	−	0.694065i
$216$		−	5.92017i		−	0.402816i
$217$		0			0
$218$	5.11797			0.346633
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$			3.16228i			0.211762i	0.994379	+	0.105881i	$0.0337662\pi$
$223$			3.16228i			0.211762i	−0.994379	+	0.105881i	$0.966234\pi$
$224$	13.7460	−	5.92017i	0.918441	−	0.395558i
$225$	−14.3649			−0.957661
$226$		0			0
$227$	24.6475	−	14.2302i	1.63591	−	0.944495i	0.653693	−	0.756760i	$-0.273219\pi$
$227$	24.6475	−	14.2302i	1.63591	−	0.944495i	0.982220	−	0.187735i	$-0.0601147\pi$
$228$		0			0
$229$	−23.2379	−	13.4164i	−1.53560	−	0.886581i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−23.2379	−	13.4164i	−1.53560	−	0.886581i	−0.536515	−	0.843891i	$-0.680260\pi$
$230$			23.7447i			1.56568i
$231$		0			0
$232$	−13.4236			−0.881304
$233$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$233$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$234$		0			0
$235$	10.6066	+	18.3712i	0.691898	+	1.19840i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−1.59384	+	2.76062i	−0.102882	+	0.178197i
$241$	11.6190	−	6.70820i	0.748442	−	0.432113i	−0.0766885	−	0.997055i	$-0.524435\pi$
$241$	11.6190	−	6.70820i	0.748442	−	0.432113i	0.825131	+	0.564942i	$0.191101\pi$
$242$	7.77817	+	13.4722i	0.500000	+	0.866025i
$243$	−7.86799	−	4.54259i	−0.504732	−	0.291407i
$244$			27.2728i			1.74596i
$245$	−11.3730	−	10.7543i	−0.726593	−	0.687068i
$246$	−6.36492			−0.405812
$247$		0			0
$248$		0			0
$249$	−3.24597	−	5.62218i	−0.205705	−	0.356291i
$250$	13.6931	+	7.90569i	0.866025	+	0.500000i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	1.77347	−	15.0986i	0.111718	−	0.951122i
$253$		0			0
$254$	3.00000	−	5.19615i	0.188237	−	0.326036i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$			4.58785i			0.285627i
$259$		0			0
$260$		0			0
$261$	−6.81754	+	11.8083i	−0.421995	+	0.730917i
$262$		0			0
$263$	16.2128	+	28.0815i	0.999727	+	1.73158i	0.520104	+	0.854103i	$0.325893\pi$
$263$	16.2128	+	28.0815i	0.999727	+	1.73158i	0.479623	+	0.877475i	$0.340774\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	5.03956			0.308416
$268$	−15.8144	+	27.3913i	−0.966017	+	1.67319i
$269$	−8.31754	+	4.80213i	−0.507129	+	0.292791i	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−8.31754	+	4.80213i	−0.507129	+	0.292791i	0.224523	+	0.974469i	$0.427917\pi$
$270$	3.30948	+	5.73218i	0.201408	+	0.348849i
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	4.63508	−	2.67607i	0.278999	−	0.161080i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$	−10.0000	+	13.4164i	−0.597614	+	0.801784i
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	2.39076	−	4.14092i	0.142368	−	0.246588i
$283$	−13.6931	+	7.90569i	−0.813968	+	0.469945i	−0.848332	−	0.529465i	$-0.822393\pi$
$283$	−13.6931	+	7.90569i	−0.813968	+	0.469945i	0.0343638	+	0.999409i	$0.489059\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−33.1834	−	3.89770i	−1.95875	−	0.230074i
$288$	−16.2520			−0.957661
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	12.9974	−	7.50403i	0.763232	−	0.440652i
$291$		0			0
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	−0.817542	+	3.43209i	−0.0476800	+	0.200164i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−5.74667	−	9.95352i	−0.332896	−	0.576592i
$299$		0			0
$300$		−	3.56394i		−	0.205764i
$301$	−2.80948	+	23.9187i	−0.161935	+	1.37865i
$302$		0			0
$303$	1.98089	−	3.43101i	0.113799	−	0.197106i
$304$		0			0
$305$	−15.2460	−	26.4068i	−0.872982	−	1.51205i
$306$		0			0
$307$			21.0668i			1.20234i	0.799120	+	0.601172i	$0.205299\pi$
$307$			21.0668i			1.20234i	−0.799120	+	0.601172i	$0.794701\pi$
$308$		0			0
$309$	6.74597			0.383765
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$313$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$314$		0			0
$315$	6.72322	+	15.6106i	0.378810	+	0.879555i
$316$		0			0
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$		0			0
$320$	15.4919	+	8.94427i	0.866025	+	0.500000i
$321$			6.20419i			0.346284i
$322$	25.8037	−	11.1132i	1.43798	−	0.619317i
$323$		0			0
$324$	−7.87298	+	13.6364i	−0.437388	+	0.757578i
$325$		0			0
$326$	−9.00000	−	15.5885i	−0.498464	−	0.863365i
$327$	1.11698	+	0.644886i	0.0617689	+	0.0356623i
$328$			35.7184i			1.97222i
$329$	15.0000	−	20.1246i	0.826977	−	1.10951i
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−31.5504	+	18.2156i	−1.73155	+	0.999711i
$333$		0			0
$334$	19.6905	+	11.3683i	1.07742	+	0.622047i
$335$		−	35.3620i		−	1.93203i
$336$	3.74597	+	0.439999i	0.204359	+	0.0240039i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	−9.19239	+	15.9217i	−0.500000	+	0.866025i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−6.36396	+	17.3925i	−0.343622	+	0.939108i
$344$	25.7460			1.38813
$345$	−2.99193	+	5.18218i	−0.161080	+	0.278999i
$346$		0			0
$347$	6.31335	+	10.9350i	0.338918	+	0.587024i	0.984230	−	0.176896i	$-0.0566056\pi$
$347$	6.31335	+	10.9350i	0.338918	+	0.587024i	−0.645311	+	0.763920i	$0.723272\pi$
$348$	−2.92965	−	1.69143i	−0.157046	−	0.0906704i
$349$		−	9.10025i		−	0.487125i	−0.969885	−	0.243563i	$-0.921684\pi$
$349$		−	9.10025i		−	0.487125i	0.969885	−	0.243563i	$-0.0783162\pi$
$350$	2.18246	−	18.5806i	0.116657	−	0.993172i
$351$		0			0
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$		0			0
$356$		−	28.2808i		−	1.49888i
$357$		0			0
$358$		0			0
$359$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$359$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$360$	15.7360	−	9.08517i	0.829359	−	0.478831i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	18.5530	+	10.7116i	0.975124	+	0.562988i
$363$			3.92033i			0.205764i
$364$		0			0
$365$		0			0
$366$	−3.43649	+	5.95218i	−0.179628	+	0.311125i
$367$	30.0071	−	17.3246i	1.56636	−	0.904338i	0.569771	−	0.821803i	$-0.307032\pi$
$367$	30.0071	−	17.3246i	1.56636	−	0.904338i	0.996588	−	0.0825348i	$-0.0263016\pi$
$368$	−15.0175	−	26.0110i	−0.782839	−	1.35592i
$369$	31.4204	+	18.1406i	1.63568	+	0.944359i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	1.99230	+	3.45077i	0.102882	+	0.178197i
$376$	−23.2379	−	13.4164i	−1.19840	−	0.691898i
$377$		0			0
$378$	4.68030	−	6.27929i	0.240729	−	0.322972i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	1.30948	−	0.756026i	0.0670864	−	0.0387324i
$382$		0			0
$383$	−32.4763	−	18.7502i	−1.65946	−	0.958091i	−0.972964	−	0.230959i	$-0.925814\pi$
$383$	−32.4763	−	18.7502i	−1.65946	−	0.958091i	−0.686498	−	0.727132i	$-0.740853\pi$
$384$		−	4.03214i		−	0.205764i
$385$		0			0
$386$		0			0
$387$	13.0758	−	22.6479i	0.664679	−	1.15126i
$388$		0			0
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	0.991500	+	0.130105i	$0.0415314\pi$
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	−0.383076	+	0.923717i	$0.625135\pi$
$390$		0			0
$391$		0			0
$392$	19.2601	+	4.58785i	0.972782	+	0.231722i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$397$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$398$		0			0
$399$		0			0
$400$	−20.0000			−1.00000
$401$	−19.9919	+	34.6270i	−0.998350	+	1.72919i	−0.449439	+	0.893311i	$0.648376\pi$
$401$	−19.9919	+	34.6270i	−0.998350	+	1.72919i	−0.548911	+	0.835881i	$0.684957\pi$
$402$	−6.90285	+	3.98536i	−0.344283	+	0.198772i
$403$		0			0
$404$	−19.2540	−	11.1163i	−0.957924	−	0.553058i
$405$		−	17.6045i		−	0.874776i
$406$	−14.2379	−	10.6123i	−0.706615	−	0.526680i
$407$		0			0
$408$		0			0
$409$	−14.4284	+	8.33026i	−0.713440	+	0.411905i	−0.812333	−	0.583193i	$-0.801803\pi$
$409$	−14.4284	+	8.33026i	−0.713440	+	0.411905i	0.0988936	+	0.995098i	$0.468470\pi$
$410$	−19.9672	−	34.5842i	−0.986110	−	1.70799i
$411$		0			0
$412$		−	37.8568i		−	1.86507i
$413$		0			0
$414$	−30.5081			−1.49939
$415$	20.3657	−	35.2744i	0.999711	−	1.73155i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	−3.87298	+	1.66803i	−0.188982	+	0.0813916i
$421$	38.8569			1.89377			0.946883	−	0.321577i	$-0.104213\pi$
$421$	38.8569			1.89377			0.946883	+	0.321577i	$0.104213\pi$
$422$		0			0
$423$	−23.6040	+	13.6278i	−1.14766	+	0.662604i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−21.5611	+	28.9272i	−1.04341	+	1.39988i
$428$	34.8165			1.68292
$429$		0			0
$430$	−24.9284	+	14.3924i	−1.20216	+	0.694065i
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	−7.25070	−	4.18619i	−0.348849	−	0.201408i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$	3.78216			0.181341
$436$	3.61895	−	6.26821i	0.173316	−	0.300193i
$437$		0			0
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	13.8175	−	14.6124i	0.657978	−	0.695830i
$442$		0			0
$443$	6.14513	−	10.6437i	0.291964	−	0.505696i	−0.682310	−	0.731063i	$-0.739025\pi$
$443$	6.14513	−	10.6437i	0.291964	−	0.505696i	0.974274	+	0.225367i	$0.0723580\pi$
$444$		0			0
$445$	15.8095	+	27.3828i	0.749441	+	1.29807i
$446$	3.87298	+	2.23607i	0.183391	+	0.105881i
$447$		−	2.89642i		−	0.136996i
$448$	2.46917	−	21.0215i	0.116657	−	0.993172i
$449$	−1.36492			−0.0644144			−0.0322072	−	0.999481i	$-0.510254\pi$
$449$	−1.36492			−0.0644144			−0.0322072	+	0.999481i	$0.510254\pi$
$450$	−10.1575	+	17.5934i	−0.478831	+	0.829359i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		−	40.2492i		−	1.88899i
$455$		0			0
$456$		0			0
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	−32.8634	+	18.9737i	−1.53560	+	0.886581i
$459$		0			0
$460$	29.0812	+	16.7900i	1.35592	+	0.782839i
$461$		−	8.94427i		−	0.416576i	−0.978068	−	0.208288i	$-0.933211\pi$
$461$		−	8.94427i		−	0.416576i	0.978068	−	0.208288i	$-0.0667892\pi$
$462$		0			0
$463$	29.2380			1.35881			0.679403	−	0.733766i	$-0.262239\pi$
$463$	29.2380			1.35881			0.679403	+	0.733766i	$0.262239\pi$
$464$	−9.49193	+	16.4405i	−0.440652	+	0.763232i
$465$		0			0
$466$		0			0
$467$	12.0714	+	6.96944i	0.558599	+	0.322507i	0.752583	−	0.658497i	$-0.228808\pi$
$467$	12.0714	+	6.96944i	0.558599	+	0.322507i	−0.193984	+	0.981005i	$0.562141\pi$
$468$		0			0
$469$	−38.4284	+	16.5505i	−1.77446	+	0.764232i
$470$	30.0000			1.38380
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	2.25403	+	3.90410i	0.102882	+	0.178197i
$481$		0			0
$482$		−	18.9737i		−	0.864227i
$483$	7.03186	+	0.825958i	0.319961	+	0.0375824i
$484$	22.0000			1.00000
$485$		0			0
$486$	−11.1270	+	6.42419i	−0.504732	+	0.291407i
$487$	−19.0919	−	33.0681i	−0.865136	−	1.49846i	−0.866912	−	0.498461i	$-0.833899\pi$
$487$	−19.0919	−	33.0681i	−0.865136	−	1.49846i	0.00177647	−	0.999998i	$-0.499435\pi$
$488$	33.4022	+	19.2848i	1.51205	+	0.872982i
$489$		−	4.53615i		−	0.205132i
$490$	−21.2132	+	6.32456i	−0.958315	+	0.285714i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	−4.50068	+	7.79540i	−0.202906	+	0.351444i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−9.18098			−0.411410
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	19.3649	−	11.1803i	0.866025	−	0.500000i
$501$	2.86492	+	4.96218i	0.127995	+	0.221694i
$502$		0			0
$503$			33.2237i			1.48137i	0.671852	+	0.740685i	$0.265499\pi$
$503$			33.2237i			1.48137i	−0.671852	+	0.740685i	$0.734501\pi$
$504$	−17.2379	−	12.8484i	−0.767837	−	0.572312i
$505$	24.8569			1.10612
$506$		0			0
$507$	−4.01240	+	2.31656i	−0.178197	+	0.102882i
$508$	−4.24264	−	7.34847i	−0.188237	−	0.326036i
$509$	−14.8649	−	8.58226i	−0.658876	−	0.380402i	0.132973	−	0.991120i	$-0.457548\pi$
$509$	−14.8649	−	8.58226i	−0.658876	−	0.380402i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$		0			0
$512$	−22.6274			−1.00000
$513$		0			0
$514$		0			0
$515$	21.1626	+	36.6547i	0.932535	+	1.61520i
$516$	5.61895	+	3.24410i	0.247360	+	0.142814i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.4919	+	8.94427i	−0.678714	+	0.391856i	−0.799370	−	0.600839i	$-0.794833\pi$
$521$	−15.4919	+	8.94427i	−0.678714	+	0.391856i	0.120656	+	0.992694i	$0.461500\pi$
$522$	9.64146	+	16.6995i	0.421995	+	0.730917i
$523$	−30.1247	−	17.3925i	−1.31726	−	0.760522i	−0.333975	−	0.942582i	$-0.608390\pi$
$523$	−30.1247	−	17.3925i	−1.31726	−	0.760522i	−0.983287	+	0.182060i	$0.941724\pi$
$524$		0			0
$525$	2.81754	−	3.78013i	0.122968	−	0.164978i
$526$	45.8569			1.99945
$527$		0			0
$528$		0			0
$529$	−16.6905	−	28.9088i	−0.725675	−	1.25691i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	3.56351	−	6.17218i	0.154208	−	0.267096i
$535$	−33.7109	+	19.4630i	−1.45745	+	0.841458i
$536$	22.3649	+	38.7372i	0.966017	+	1.67319i
$537$		0			0
$538$			13.5825i			0.585583i
$539$		0			0
$540$	9.36061			0.402816
$541$	21.1190	−	36.5791i	0.907975	−	1.57266i	0.0911008	−	0.995842i	$-0.470961\pi$
$541$	21.1190	−	36.5791i	0.907975	−	1.57266i	0.816874	−	0.576816i	$-0.195705\pi$
$542$		0			0
$543$	2.69941	+	4.67551i	0.115843	+	0.200646i
$544$		0			0
$545$			8.09222i			0.346633i
$546$		0			0
$547$	20.5959			0.880618			0.440309	−	0.897846i	$-0.354869\pi$
$547$	20.5959			0.880618			0.440309	+	0.897846i	$0.354869\pi$
$548$		0			0
$549$	33.9284	−	19.5886i	1.44803	−	0.836020i
$550$		0			0
$551$		0			0
$552$		−	7.56906i		−	0.322161i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$		0			0
$560$	9.36061	+	21.7343i	0.395558	+	0.918441i
$561$		0			0
$562$	−8.48528	+	14.6969i	−0.357930	+	0.619953i
$563$	19.4789	−	11.2462i	0.820939	−	0.473970i	−0.0298010	−	0.999556i	$-0.509487\pi$
$563$	19.4789	−	11.2462i	0.820939	−	0.473970i	0.850740	+	0.525586i	$0.176154\pi$
$564$	−3.38105	−	5.85615i	−0.142368	−	0.246588i
$565$		0			0
$566$			22.3607i			0.939889i
$567$	−19.1311	+	8.23945i	−0.803430	+	0.346025i
$568$		0			0
$569$	−18.0000	+	31.1769i	−0.754599	+	1.30700i	0.190974	+	0.981595i	$0.438835\pi$
$569$	−18.0000	+	31.1769i	−0.754599	+	1.30700i	−0.945573	+	0.325409i	$0.894498\pi$
$570$		0			0
$571$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$571$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$572$		0			0
$573$		0			0
$574$	−28.2379	+	37.8851i	−1.17863	+	1.58129i
$575$	−37.5437			−1.56568
$576$	−11.4919	+	19.9046i	−0.478831	+	0.829359i
$577$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$577$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$578$	−12.0208	−	20.8207i	−0.500000	−	0.866025i
$579$		0			0
$580$		−	21.2246i		−	0.881304i
$581$	−47.8649	−	5.62218i	−1.98577	−	0.233247i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$			47.4342i			1.95782i	0.204298	+	0.978909i	$0.434509\pi$
$587$			47.4342i			1.95782i	−0.204298	+	0.978909i	$0.565491\pi$
$588$	3.62535	+	3.42814i	0.149507	+	0.141374i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$		0			0
$595$		0			0
$596$	−16.2540			−0.665791
$597$		0			0
$598$		0			0
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$	−4.36492	−	2.52009i	−0.178197	−	0.102882i
$601$		−	40.2492i		−	1.64180i	−0.571072	−	0.820900i	$-0.693472\pi$
$601$		−	40.2492i		−	1.64180i	0.571072	−	0.820900i	$-0.306528\pi$
$602$	27.3077	+	20.3540i	1.11298	+	0.829566i
$603$	45.4345			1.85023
$604$		0			0
$605$	−21.3014	+	12.2984i	−0.866025	+	0.500000i
$606$	−2.80141	−	4.85218i	−0.113799	−	0.197106i
$607$	−28.1553	−	16.2554i	−1.14279	−	0.659788i	−0.195667	−	0.980670i	$-0.562687\pi$
$607$	−28.1553	−	16.2554i	−1.14279	−	0.659788i	−0.947119	+	0.320882i	$0.896021\pi$
$608$		0			0
$609$	−1.77017	−	4.11013i	−0.0717308	−	0.166551i
$610$	−43.1221			−1.74596
$611$		0			0
$612$		0			0
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	25.8014	+	14.8965i	1.04126	+	0.601172i
$615$		−	10.0638i		−	0.405812i
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$	4.77012	−	8.26209i	0.191882	−	0.332350i
$619$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$619$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$	−13.6109	−	7.85825i	−0.546186	−	0.315341i
$622$		0			0
$623$	22.3580	−	29.9964i	0.895753	−	1.20178i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	23.8730	+	2.80410i	0.951122	+	0.111718i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.21584	+	4.74342i	0.326036	+	0.188237i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	21.9089	−	12.6491i	0.866025	−	0.500000i
$641$	−18.3014	−	31.6990i	−0.722862	−	1.25203i	−0.959848	−	0.280521i	$-0.909493\pi$
$641$	−18.3014	−	31.6990i	−0.722862	−	1.25203i	0.236986	−	0.971513i	$-0.423841\pi$
$642$	7.59855	+	4.38702i	0.299891	+	0.173142i
$643$		−	41.1096i		−	1.62120i	−0.585597	−	0.810602i	$-0.699140\pi$
$643$		−	41.1096i		−	1.62120i	0.585597	−	0.810602i	$-0.300860\pi$
$644$	4.63508	−	39.4612i	0.182648	−	1.55499i
$645$	−7.25403			−0.285627
$646$		0			0
$647$	34.3282	−	19.8194i	1.34958	−	0.779180i	0.361390	−	0.932415i	$-0.382302\pi$
$647$	34.3282	−	19.8194i	1.34958	−	0.779180i	0.988190	+	0.153234i	$0.0489689\pi$
$648$	11.1341	+	19.2848i	0.437388	+	0.757578i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−25.4558			−0.996928
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$	1.57964	−	0.912006i	0.0617689	−	0.0356623i
$655$		0			0
$656$	43.7460	+	25.2567i	1.70799	+	0.986110i
$657$		0			0
$658$	−14.0409	−	32.6014i	−0.547372	−	1.27094i
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$	6.57157	−	3.79410i	0.255605	−	0.147573i	−0.366723	−	0.930330i	$-0.619520\pi$
$661$	6.57157	−	3.79410i	0.255605	−	0.147573i	0.622328	+	0.782757i	$0.286187\pi$
$662$		0			0
$663$		0			0
$664$			51.5215i			1.99942i
$665$		0			0
$666$		0			0
$667$	−17.8181	+	30.8618i	−0.689919	+	1.19498i
$668$	27.8466	−	16.0772i	1.07742	−	0.622047i
$669$	0.563508	+	0.976025i	0.0217865	+	0.0377353i
$670$	−43.3095	−	25.0047i	−1.67319	−	0.966017i
$671$		0			0
$672$	3.18768	−	4.27673i	0.122968	−	0.164978i
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		0			0
$675$	−9.06337	+	5.23274i	−0.348849	+	0.201408i
$676$	13.0000	+	22.5167i	0.500000	+	0.866025i
$677$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$677$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	5.07157	−	8.78423i	0.194343	−	0.336612i
$682$		0			0
$683$	1.36360	+	2.36183i	0.0521768	+	0.0903729i	0.890934	−	0.454132i	$-0.150051\pi$
$683$	1.36360	+	2.36183i	0.0521768	+	0.0903729i	−0.838757	+	0.544505i	$0.816717\pi$
$684$		0			0
$685$		0			0
$686$	16.8014	+	20.0926i	0.641481	+	0.767139i
$687$	−9.56305			−0.364853
$688$	18.2051	−	31.5322i	0.694065	−	1.20216i
$689$		0			0
$690$	4.23123	+	7.32871i	0.161080	+	0.278999i
$691$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$		0			0
$693$		0			0
$694$	17.8569			0.677837
$695$		0			0
$696$	−4.14315	+	2.39205i	−0.157046	+	0.0906704i
$697$		0			0
$698$	−11.1455	−	6.43485i	−0.421863	−	0.243563i
$699$		0			0
$700$	−21.2132	−	15.8114i	−0.801784	−	0.597614i
$701$	−43.3649			−1.63787			−0.818935	−	0.573886i	$-0.805435\pi$
$701$	−43.3649			−1.63787			−0.818935	+	0.573886i	$0.805435\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	6.54738	+	3.78013i	0.246588	+	0.142368i
$706$		0			0
$707$	−11.6338	−	27.0123i	−0.437533	−	1.01590i
$708$		0			0
$709$	0.118950	−	0.206028i	0.00446726	−	0.00773753i	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	0.118950	−	0.206028i	0.00446726	−	0.00773753i	0.868250	+	0.496126i	$0.165245\pi$
$710$		0			0
$711$		0			0
$712$	−34.6368	−	19.9976i	−1.29807	−	0.749441i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		−	25.6967i		−	0.957661i
$721$	29.9284	−	40.1532i	1.11459	−	1.49538i
$722$	26.8701			1.00000
$723$	2.39076	−	4.14092i	0.0889134	−	0.154003i
$724$	26.2379	−	15.1485i	0.975124	−	0.562988i
$725$	11.8649	+	20.5506i	0.440652	+	0.763232i
$726$	4.80141	+	2.77209i	0.178197	+	0.102882i
$727$		−	23.2051i		−	0.860630i	−0.902679	−	0.430315i	$-0.858402\pi$
$727$		−	23.2051i		−	0.860630i	0.902679	−	0.430315i	$-0.141598\pi$
$728$		0			0
$729$	20.3810			0.754854
$730$		0			0
$731$		0			0
$732$	4.85993	+	8.41765i	0.179628	+	0.311125i
$733$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$733$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$734$		−	49.0014i		−	1.80868i
$735$	−5.42661	−	1.29265i	−0.200164	−	0.0476800i
$736$	−42.4758			−1.56568
$737$		0			0
$738$	44.4351	−	25.6546i	1.63568	−	0.944359i
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−27.6442			−1.01417			−0.507083	−	0.861897i	$-0.669276\pi$
$743$	−27.6442			−1.01417			−0.507083	+	0.861897i	$0.669276\pi$
$744$		0			0
$745$	15.7379	−	9.08628i	0.576592	−	0.332896i
$746$		0			0
$747$	45.3218	+	26.1666i	1.65824	+	0.957385i
$748$		0			0
$749$	36.9284	+	27.5248i	1.34934	+	1.00574i
$750$	5.63508			0.205764
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$	−32.8634	+	18.9737i	−1.19840	+	0.691898i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−4.38105	−	10.1723i	−0.159337	−	0.369963i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	30.9839	+	17.8885i	1.12316	+	0.648459i	0.942207	−	0.335032i	$-0.108747\pi$
$761$	30.9839	+	17.8885i	1.12316	+	0.648459i	0.180957	+	0.983491i	$0.442080\pi$
$762$		−	2.13836i		−	0.0774647i
$763$	8.79393	−	3.78740i	0.318362	−	0.137113i
$764$		0			0
$765$		0			0
$766$	−45.9284	+	26.5168i	−1.65946	+	0.958091i
$767$		0			0
$768$	−4.93834	−	2.85115i	−0.178197	−	0.102882i
$769$			53.6656i			1.93523i	0.252426	+	0.967616i	$0.418771\pi$
$769$			53.6656i			1.93523i	−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$773$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$774$	−18.4919	−	32.0290i	−0.664679	−	1.15126i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	33.9411			1.21685
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$			9.93376i			0.355004i
$784$	19.2379	−	20.3446i	0.687068	−	0.726593i
$785$		0			0
$786$		0			0
$787$	10.8368	−	6.25665i	0.386292	−	0.223026i	−0.294260	−	0.955725i	$-0.595073\pi$
$787$	10.8368	−	6.25665i	0.386292	−	0.223026i	0.680552	+	0.732700i	$0.261740\pi$
$788$		0			0
$789$	10.0081	+	5.77816i	0.356297	+	0.205708i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$		0			0
$800$	−14.1421	+	24.4949i	−0.500000	+	0.866025i
$801$	−35.1825	+	20.3126i	−1.24311	+	0.717710i
$802$	28.2729	+	48.9700i	0.998350	+	1.72919i
$803$		0			0
$804$			11.2723i			0.397543i
$805$	17.5716	+	40.7992i	0.619317	+	1.43798i
$806$		0			0
$807$	−1.71145	+	2.96432i	−0.0602460	+	0.104349i
$808$	−27.2293	+	15.7209i	−0.957924	+	0.553058i
$809$	5.75403	+	9.96628i	0.202301	+	0.350396i	0.949269	−	0.314464i	$-0.101825\pi$
$809$	5.75403	+	9.96628i	0.202301	+	0.350396i	−0.746968	+	0.664860i	$0.768491\pi$
$810$	−21.5611	−	12.4483i	−0.757578	−	0.437388i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	−23.0651	+	9.93376i	−0.809426	+	0.348607i
$813$		0			0
$814$		0			0
$815$	24.6475	−	14.2302i	0.863365	−	0.498464i
$816$		0			0
$817$		0			0
$818$			23.5615i			0.823809i
$819$		0			0
$820$	−56.4758			−1.97222
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	−0.0542853	−	0.998525i	$-0.517288\pi$
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	0.891891	−	0.452250i	$-0.149379\pi$
$822$		0			0
$823$	6.94205	+	12.0240i	0.241985	+	0.419130i	0.961280	−	0.275575i	$-0.0888683\pi$
$823$	6.94205	+	12.0240i	0.241985	+	0.419130i	−0.719295	+	0.694705i	$0.755535\pi$
$824$	−46.3649	−	26.7688i	−1.61520	−	0.932535i
$825$		0			0
$826$		0			0
$827$	−57.3426			−1.99400			−0.997000	−	0.0774065i	$-0.975336\pi$
$827$	−57.3426			−1.99400			−0.997000	+	0.0774065i	$0.975336\pi$
$828$	−21.5725	+	37.3646i	−0.749695	+	1.29851i
$829$	11.6190	−	6.70820i	0.403543	−	0.232986i	−0.284469	−	0.958685i	$-0.591817\pi$
$829$	11.6190	−	6.70820i	0.403543	−	0.232986i	0.688012	+	0.725700i	$0.258484\pi$
$830$	−28.8014	−	49.8855i	−0.999711	−	1.73155i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−17.9749	+	31.1335i	−0.622047	+	1.07742i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	−0.695699	+	5.92289i	−0.0240039	+	0.204359i
$841$	−6.47580			−0.223303
$842$	27.4759	−	47.5897i	0.946883	−	1.64005i
$843$	−3.70375	+	2.13836i	−0.127564	+	0.0736492i
$844$		0			0
$845$	−25.1744	−	14.5344i	−0.866025	−	0.500000i
$846$			38.5451i			1.32521i
$847$	23.3345	+	17.3925i	0.801784	+	0.597614i
$848$		0			0
$849$	−2.81754	+	4.88013i	−0.0966978	+	0.167485i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$	20.1825	+	46.8614i	0.690630	+	1.60356i
$855$		0			0
$856$	24.6190	−	42.6413i	0.841458	−	1.45745i
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$			40.7079i			1.38813i
$861$	−10.9365	+	4.71017i	−0.372715	+	0.160522i
$862$		0			0
$863$	−18.6036	+	32.2224i	−0.633274	+	1.09686i	0.353604	+	0.935395i	$0.384956\pi$
$863$	−18.6036	+	32.2224i	−0.633274	+	1.09686i	−0.986878	+	0.161468i	$0.948377\pi$
$864$	−10.2540	+	5.92017i	−0.348849	+	0.201408i
$865$		0			0
$866$		0			0
$867$		−	6.05870i		−	0.205764i
$868$		0			0
$869$		0			0
$870$	2.67439	−	4.63218i	0.0906704	−	0.157046i
$871$		0			0
$872$	−5.11797	−	8.86458i	−0.173316	−	0.300193i
$873$		0			0
$874$		0			0
$875$	29.3784	+	3.45077i	0.993172	+	0.116657i
$876$		0			0
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			18.6766i			0.629230i	0.949219	+	0.314615i	$0.101875\pi$
$881$			18.6766i			0.629230i	−0.949219	+	0.314615i	$0.898125\pi$
$882$	−8.12602	−	27.2555i	−0.273617	−	0.917741i
$883$	−55.1543			−1.85609			−0.928045	−	0.372467i	$-0.878512\pi$
$883$	−55.1543			−1.85609			−0.928045	+	0.372467i	$0.878512\pi$
$884$		0			0
$885$		0			0
$886$	−8.69052	−	15.0524i	−0.291964	−	0.505696i
$887$	26.9207	+	15.5427i	0.903908	+	0.521871i	0.878466	−	0.477805i	$-0.158567\pi$
$887$	26.9207	+	15.5427i	0.903908	+	0.521871i	0.0254417	+	0.999676i	$0.491901\pi$
$888$		0			0
$889$	1.30948	−	11.1483i	0.0439184	−	0.373903i
$890$	44.7159			1.49888
$891$		0			0
$892$	5.47723	−	3.16228i	0.183391	−	0.105881i
$893$		0			0
$894$	−3.54738	−	2.04808i	−0.118642	−	0.0684980i
$895$		0			0
$896$	−24.0000	−	17.8885i	−0.801784	−	0.597614i
$897$		0			0
$898$	−0.965142	+	1.67167i	−0.0322072	+	0.0557845i
$899$		0			0
$900$	14.3649	+	24.8808i	0.478831	+	0.829359i
$901$		0			0
$902$		0			0
$903$	3.39511	+	7.88306i	0.112982	+	0.262332i
$904$		0			0
$905$	−16.9365	+	29.3349i	−0.562988	+	0.975124i
$906$		0			0
$907$	−27.0775	−	46.8996i	−0.899093	−	1.55727i	−0.828656	−	0.559759i	$-0.810894\pi$
$907$	−27.0775	−	46.8996i	−0.899093	−	1.55727i	−0.0704373	−	0.997516i	$-0.522439\pi$
$908$	−49.2950	−	28.4605i	−1.63591	−	0.944495i
$909$			31.9370i			1.05928i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−9.41122	−	5.43357i	−0.311125	−	0.179628i
$916$			53.6656i			1.77316i
$917$		0			0
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$	41.1270	−	23.7447i	1.35592	−	0.782839i
$921$	3.75403	+	6.50218i	0.123700	+	0.214254i
$922$	−10.9545	−	6.32456i	−0.360766	−	0.208288i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	20.6744	−	35.8091i	0.679403	−	1.17676i
$927$	−47.0953	+	27.1905i	−1.54681	+	0.893053i
$928$	13.4236	+	23.2504i	0.440652	+	0.763232i
$929$	−5.69859	−	3.29008i	−0.186965	−	0.107944i	0.403596	−	0.914937i	$-0.367760\pi$
$929$	−5.69859	−	3.29008i	−0.186965	−	0.107944i	−0.590561	+	0.806993i	$0.701093\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	17.0716	−	9.85628i	0.558599	−	0.322507i
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−6.90285	+	58.7680i	−0.225386	+	1.91884i
$939$		0			0
$940$	21.2132	−	36.7423i	0.691898	−	1.19840i
$941$	38.7298	−	22.3607i	1.26256	−	0.728937i	0.288988	−	0.957333i	$-0.406681\pi$
$941$	38.7298	−	22.3607i	1.26256	−	0.728937i	0.973568	+	0.228395i	$0.0733479\pi$
$942$		0			0
$943$	82.1192	+	47.4115i	2.67417	+	1.54393i
$944$		0			0
$945$	9.92843	+	7.40021i	0.322972	+	0.240729i
$946$		0			0
$947$	11.0949	−	19.2169i	0.360535	−	0.624465i	−0.627514	−	0.778605i	$-0.715927\pi$
$947$	11.0949	−	19.2169i	0.360535	−	0.624465i	0.988049	+	0.154140i	$0.0492608\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	6.37537			0.205764
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$		0			0
$963$	−25.0068	−	43.3130i	−0.805832	−	1.39574i
$964$	−23.2379	−	13.4164i	−0.748442	−	0.432113i
$965$		0			0
$966$	5.98387	−	8.02820i	0.192528	−	0.258303i
$967$	58.9365			1.89527			0.947635	−	0.319356i	$-0.103467\pi$
$967$	58.9365			1.89527			0.947635	+	0.319356i	$0.103467\pi$
$968$	15.5563	−	26.9444i	0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$			18.1703i			0.582814i
$973$		0			0
$974$	−54.0000			−1.73027
$975$		0			0
$976$	47.2379	−	27.2728i	1.51205	−	0.872982i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$	−5.55563	−	3.20755i	−0.177650	−	0.102566i
$979$		0			0
$980$	−7.25403	+	30.4529i	−0.231722	+	0.972782i
$981$	−10.3972			−0.331957
$982$		0			0
$983$	−10.2195	+	5.90026i	−0.325953	+	0.188189i	−0.654043	−	0.756457i	$-0.726928\pi$
$983$	−10.2195	+	5.90026i	−0.325953	+	0.188189i	0.328090	+	0.944646i	$0.393595\pi$
$984$	6.36492	+	11.0244i	0.202906	+	0.351444i
$985$		0			0
$986$		0			0
$987$	1.04355	−	8.88434i	0.0332165	−	0.282792i
$988$		0			0
$989$	34.1744	−	59.1918i	1.08668	−	1.88219i
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−6.49193	+	11.2444i	−0.205705	+	0.356291i
$997$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$997$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.s.a.19.4	yes	8
4.3	odd	2	inner	140.2.s.a.19.1	✓	8
5.2	odd	4		700.2.p.b.551.3		8
5.3	odd	4		700.2.p.b.551.2		8
5.4	even	2	inner	140.2.s.a.19.1	✓	8
7.2	even	3		980.2.c.b.979.3		8
7.3	odd	6	inner	140.2.s.a.59.4	yes	8
7.4	even	3		980.2.s.a.619.3		8
7.5	odd	6		980.2.c.b.979.2		8
7.6	odd	2		980.2.s.a.19.3		8
20.3	even	4		700.2.p.b.551.3		8
20.7	even	4		700.2.p.b.551.2		8
20.19	odd	2	CM	140.2.s.a.19.4	yes	8
28.3	even	6	inner	140.2.s.a.59.1	yes	8
28.11	odd	6		980.2.s.a.619.2		8
28.19	even	6		980.2.c.b.979.7		8
28.23	odd	6		980.2.c.b.979.6		8
28.27	even	2		980.2.s.a.19.2		8
35.3	even	12		700.2.p.b.451.3		8
35.4	even	6		980.2.s.a.619.2		8
35.9	even	6		980.2.c.b.979.6		8
35.17	even	12		700.2.p.b.451.2		8
35.19	odd	6		980.2.c.b.979.7		8
35.24	odd	6	inner	140.2.s.a.59.1	yes	8
35.34	odd	2		980.2.s.a.19.2		8
140.3	odd	12		700.2.p.b.451.2		8
140.19	even	6		980.2.c.b.979.2		8
140.39	odd	6		980.2.s.a.619.3		8
140.59	even	6	inner	140.2.s.a.59.4	yes	8
140.79	odd	6		980.2.c.b.979.3		8
140.87	odd	12		700.2.p.b.451.3		8
140.139	even	2		980.2.s.a.19.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.a.19.1	✓	8	4.3	odd	2	inner
140.2.s.a.19.1	✓	8	5.4	even	2	inner
140.2.s.a.19.4	yes	8	1.1	even	1	trivial
140.2.s.a.19.4	yes	8	20.19	odd	2	CM
140.2.s.a.59.1	yes	8	28.3	even	6	inner
140.2.s.a.59.1	yes	8	35.24	odd	6	inner
140.2.s.a.59.4	yes	8	7.3	odd	6	inner
140.2.s.a.59.4	yes	8	140.59	even	6	inner
700.2.p.b.451.2		8	35.17	even	12
700.2.p.b.451.2		8	140.3	odd	12
700.2.p.b.451.3		8	35.3	even	12
700.2.p.b.451.3		8	140.87	odd	12
700.2.p.b.551.2		8	5.3	odd	4
700.2.p.b.551.2		8	20.7	even	4
700.2.p.b.551.3		8	5.2	odd	4
700.2.p.b.551.3		8	20.3	even	4
980.2.c.b.979.2		8	7.5	odd	6
980.2.c.b.979.2		8	140.19	even	6
980.2.c.b.979.3		8	7.2	even	3
980.2.c.b.979.3		8	140.79	odd	6
980.2.c.b.979.6		8	28.23	odd	6
980.2.c.b.979.6		8	35.9	even	6
980.2.c.b.979.7		8	28.19	even	6
980.2.c.b.979.7		8	35.19	odd	6
980.2.s.a.19.2		8	28.27	even	2
980.2.s.a.19.2		8	35.34	odd	2
980.2.s.a.19.3		8	7.6	odd	2
980.2.s.a.19.3		8	140.139	even	2
980.2.s.a.619.2		8	28.11	odd	6
980.2.s.a.619.2		8	35.4	even	6
980.2.s.a.619.3		8	7.4	even	3
980.2.s.a.619.3		8	140.39	odd	6

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(0.308646 - 0.178197i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -0.504017i q^{6} +(0.308646 - 2.62769i) q^{7} -2.82843 q^{8} +(-1.43649 + 2.48808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(-0.617292 - 0.356394i) q^{12} +(-3.00000 - 2.23607i) q^{14} +0.796921 q^{15} +(-2.00000 + 3.46410i) q^{16} +(2.03151 + 3.51867i) q^{18} -4.47214i q^{20} +(-0.372983 - 0.866025i) q^{21} +(-3.75437 + 6.50275i) q^{23} +(-0.872983 + 0.504017i) q^{24} +(2.50000 + 4.33013i) q^{25} +2.09310i q^{27} +(-4.85993 + 2.09310i) q^{28} +4.74597 q^{29} +(0.563508 - 0.976025i) q^{30} +(2.82843 + 4.89898i) q^{32} +(3.53553 - 4.74342i) q^{35} +5.74597 q^{36} +(-5.47723 - 3.16228i) q^{40} -12.6284i q^{41} +(-1.32440 - 0.155563i) q^{42} -9.10257 q^{43} +(-5.56351 + 3.21209i) q^{45} +(5.30948 + 9.19628i) q^{46} +(8.21584 + 4.74342i) q^{47} +1.42558i q^{48} +(-6.80948 - 1.62205i) q^{49} +7.07107 q^{50} +(2.56351 + 1.48004i) q^{54} +(-0.872983 + 7.43222i) q^{56} +(3.35591 - 5.81260i) q^{58} +(-0.796921 - 1.38031i) q^{60} +(-11.8095 - 6.81820i) q^{61} +(6.09452 + 4.54259i) q^{63} +8.00000 q^{64} +(-7.90719 - 13.6957i) q^{67} +2.67607i q^{69} +(-3.30948 - 7.68423i) q^{70} +(4.06301 - 7.03734i) q^{72} +(1.54323 + 0.890985i) q^{75} +(-7.74597 + 4.47214i) q^{80} +(-3.93649 - 6.81820i) q^{81} +(-15.4665 - 8.92961i) q^{82} -18.2156i q^{83} +(-1.12702 + 1.51205i) q^{84} +(-6.43649 + 11.1483i) q^{86} +(1.46482 - 0.845717i) q^{87} +(12.2460 + 7.07021i) q^{89} +9.08517i q^{90} +15.0175 q^{92} +(11.6190 - 6.70820i) q^{94} +(1.74597 + 1.00803i) q^{96} +(-6.80162 + 7.19291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{9} - 24 q^{14} - 16 q^{16} + 28 q^{21} + 24 q^{24} + 20 q^{25} - 24 q^{29} + 20 q^{30} - 16 q^{36} - 60 q^{45} - 4 q^{46} - 8 q^{49} + 36 q^{54} + 24 q^{56} - 48 q^{61} + 64 q^{64}+ \cdots - 48 q^{96}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^9 - 24 * q^14 - 16 * q^16 + 28 * q^21 + 24 * q^24 + 20 * q^25 - 24 * q^29 + 20 * q^30 - 16 * q^36 - 60 * q^45 - 4 * q^46 - 8 * q^49 + 36 * q^54 + 24 * q^56 - 48 * q^61 + 64 * q^64 + 20 * q^70 - 16 * q^81 - 40 * q^84 - 36 * q^86 + 36 * q^89 - 48 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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