LMFDB - Embedded newform 756.2.l.b.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(289,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 2]))

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

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

chi := DirichletCharacter("756.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.l (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.3
Root			$-1.73040 + 0.0755709i$ of defining polynomial
Character	$\chi$	$=$	756.361
Dual form			756.2.l.b.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.967857 q^{5} +(-1.11482 - 2.39941i) q^{7} +O(q^{10})$	$q-0.967857 q^{5} +(-1.11482 - 2.39941i) q^{7} -0.728244 q^{11} +(1.81066 - 3.13615i) q^{13} +(-3.49948 + 6.06128i) q^{17} +(-0.348050 - 0.602841i) q^{19} -6.43796 q^{23} -4.06325 q^{25} +(-3.34727 - 5.79764i) q^{29} +(-4.58310 - 7.93816i) q^{31} +(1.07899 + 2.32229i) q^{35} +(0.854506 + 1.48005i) q^{37} +(3.62444 - 6.27771i) q^{41} +(-0.348050 - 0.602841i) q^{43} +(3.83120 - 6.63583i) q^{47} +(-4.51435 + 5.34983i) q^{49} +(-2.05637 + 3.56174i) q^{53} +0.704836 q^{55} +(-2.38809 - 4.13629i) q^{59} +(-2.46287 + 4.26582i) q^{61} +(-1.75246 + 3.03535i) q^{65} +(2.91035 + 5.04087i) q^{67} -0.304424 q^{71} +(5.33879 - 9.24705i) q^{73} +(0.811862 + 1.74736i) q^{77} +(1.61945 - 2.80497i) q^{79} +(-0.618759 - 1.07172i) q^{83} +(3.38700 - 5.86646i) q^{85} +(5.78679 + 10.0230i) q^{89} +(-9.54349 - 0.848265i) q^{91} +(0.336863 + 0.583464i) q^{95} +(1.32933 + 2.30247i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{5} - 3 q^{7}+O(q^{10}) $ 14 * q - 4 * q^5 - 3 * q^7	$ 14 q - 4 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} - q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 13 q^{49} + 15 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65} + 6 q^{67} - 2 q^{71} + 21 q^{73} - 19 q^{77} - 10 q^{79} + 25 q^{83} + 8 q^{85} + 6 q^{89} + 2 q^{91} + 28 q^{95} - 18 q^{97}+O(q^{100}) $ 14 * q - 4 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 - q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 13 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 19 * q^77 - 10 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 - 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	−0.967857			−0.432839			−0.216419	−	0.976300i	$-0.569438\pi$
$5$	−0.967857			−0.432839			−0.216419	+	0.976300i	$0.569438\pi$
$6$		0			0
$7$	−1.11482	−	2.39941i	−0.421363	−	0.906892i
$7$	−1.11482	−	2.39941i	−0.421363	−	0.906892i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.728244			−0.219574			−0.109787	−	0.993955i	$-0.535017\pi$
$11$	−0.728244			−0.219574			−0.109787	+	0.993955i	$0.535017\pi$
$12$		0			0
$13$	1.81066	−	3.13615i	0.502187	−	0.869813i	−0.497810	−	0.867286i	$-0.665862\pi$
$13$	1.81066	−	3.13615i	0.502187	−	0.869813i	0.999997	−	0.00252677i	$-0.000804296\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.49948	+	6.06128i	−0.848749	+	1.47008i	0.0335755	+	0.999436i	$0.489311\pi$
$17$	−3.49948	+	6.06128i	−0.848749	+	1.47008i	−0.882325	+	0.470641i	$0.844023\pi$
$18$		0			0
$19$	−0.348050	−	0.602841i	−0.0798483	−	0.138301i	0.823336	−	0.567554i	$-0.192110\pi$
$19$	−0.348050	−	0.602841i	−0.0798483	−	0.138301i	−0.903184	+	0.429253i	$0.858777\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.43796			−1.34241			−0.671204	−	0.741273i	$-0.734222\pi$
$23$	−6.43796			−1.34241			−0.671204	+	0.741273i	$0.734222\pi$
$24$		0			0
$25$	−4.06325			−0.812650
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.34727	−	5.79764i	−0.621573	−	1.07660i	−0.989193	−	0.146619i	$-0.953161\pi$
$29$	−3.34727	−	5.79764i	−0.621573	−	1.07660i	0.367620	−	0.929976i	$-0.380173\pi$
$30$		0			0
$31$	−4.58310	−	7.93816i	−0.823149	−	1.42574i	−0.903326	−	0.428956i	$-0.858882\pi$
$31$	−4.58310	−	7.93816i	−0.823149	−	1.42574i	0.0801762	−	0.996781i	$-0.474452\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.07899	+	2.32229i	0.182382	+	0.392538i
$36$		0			0
$37$	0.854506	+	1.48005i	0.140480	+	0.243318i	0.927677	−	0.373383i	$-0.121802\pi$
$37$	0.854506	+	1.48005i	0.140480	+	0.243318i	−0.787197	+	0.616701i	$0.788469\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.62444	−	6.27771i	0.566042	−	0.980413i	−0.430910	−	0.902395i	$-0.641807\pi$
$41$	3.62444	−	6.27771i	0.566042	−	0.980413i	0.996952	−	0.0780185i	$-0.0248593\pi$
$42$		0			0
$43$	−0.348050	−	0.602841i	−0.0530772	−	0.0919324i	0.838266	−	0.545261i	$-0.183570\pi$
$43$	−0.348050	−	0.602841i	−0.0530772	−	0.0919324i	−0.891343	+	0.453329i	$0.850236\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.83120	−	6.63583i	0.558838	−	0.967936i	−0.438756	−	0.898606i	$-0.644581\pi$
$47$	3.83120	−	6.63583i	0.558838	−	0.967936i	0.997594	−	0.0693294i	$-0.0220860\pi$
$48$		0			0
$49$	−4.51435	+	5.34983i	−0.644907	+	0.764261i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.05637	+	3.56174i	−0.282465	+	0.489243i	−0.971991	−	0.235017i	$-0.924485\pi$
$53$	−2.05637	+	3.56174i	−0.282465	+	0.489243i	0.689527	+	0.724260i	$0.257819\pi$
$54$		0			0
$55$	0.704836			0.0950401
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.38809	−	4.13629i	−0.310903	−	0.538500i	0.667655	−	0.744471i	$-0.267298\pi$
$59$	−2.38809	−	4.13629i	−0.310903	−	0.538500i	−0.978558	+	0.205971i	$0.933965\pi$
$60$		0			0
$61$	−2.46287	+	4.26582i	−0.315338	+	0.546182i	−0.979509	−	0.201399i	$-0.935451\pi$
$61$	−2.46287	+	4.26582i	−0.315338	+	0.546182i	0.664171	+	0.747581i	$0.268785\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.75246	+	3.03535i	−0.217366	+	0.376489i
$66$		0			0
$67$	2.91035	+	5.04087i	0.355556	+	0.615841i	0.987213	−	0.159407i	$-0.0509583\pi$
$67$	2.91035	+	5.04087i	0.355556	+	0.615841i	−0.631657	+	0.775248i	$0.717625\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.304424			−0.0361285			−0.0180642	−	0.999837i	$-0.505750\pi$
$71$	−0.304424			−0.0361285			−0.0180642	+	0.999837i	$0.505750\pi$
$72$		0			0
$73$	5.33879	−	9.24705i	0.624858	−	1.08229i	−0.363711	−	0.931512i	$-0.618490\pi$
$73$	5.33879	−	9.24705i	0.624858	−	1.08229i	0.988568	−	0.150773i	$-0.0481763\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.811862	+	1.74736i	0.0925202	+	0.199130i
$78$		0			0
$79$	1.61945	−	2.80497i	0.182203	−	0.315584i	−0.760428	−	0.649423i	$-0.775011\pi$
$79$	1.61945	−	2.80497i	0.182203	−	0.315584i	0.942630	+	0.333839i	$0.108344\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.618759	−	1.07172i	−0.0679176	−	0.117637i	0.830067	−	0.557664i	$-0.188302\pi$
$83$	−0.618759	−	1.07172i	−0.0679176	−	0.117637i	−0.897985	+	0.440027i	$0.854969\pi$
$84$		0			0
$85$	3.38700	−	5.86646i	0.367372	−	0.636307i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.78679	+	10.0230i	0.613399	+	1.06244i	0.990663	+	0.136333i	$0.0435316\pi$
$89$	5.78679	+	10.0230i	0.613399	+	1.06244i	−0.377264	+	0.926106i	$0.623135\pi$
$90$		0			0
$91$	−9.54349	−	0.848265i	−1.00043	−	0.0889223i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.336863	+	0.583464i	0.0345614	+	0.0598622i
$96$		0			0
$97$	1.32933	+	2.30247i	0.134973	+	0.233780i	0.925587	−	0.378534i	$-0.123572\pi$
$97$	1.32933	+	2.30247i	0.134973	+	0.233780i	−0.790614	+	0.612315i	$0.790238\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.61394			−0.160593			−0.0802964	−	0.996771i	$-0.525587\pi$
$101$	−1.61394			−0.160593			−0.0802964	+	0.996771i	$0.525587\pi$
$102$		0			0
$103$	10.8401			1.06811			0.534055	−	0.845450i	$-0.320668\pi$
$103$	10.8401			1.06811			0.534055	+	0.845450i	$0.320668\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.97630	−	8.61920i	−0.481077	−	0.833249i	0.518688	−	0.854964i	$-0.326421\pi$
$107$	−4.97630	−	8.61920i	−0.481077	−	0.833249i	−0.999764	+	0.0217146i	$0.993087\pi$
$108$		0			0
$109$	−9.27835	+	16.0706i	−0.888705	+	1.53928i	−0.0472974	+	0.998881i	$0.515061\pi$
$109$	−9.27835	+	16.0706i	−0.888705	+	1.53928i	−0.841407	+	0.540401i	$0.818272\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.75824	+	9.97356i	−0.541689	+	0.938234i	0.457118	+	0.889406i	$0.348882\pi$
$113$	−5.75824	+	9.97356i	−0.541689	+	0.938234i	−0.998807	+	0.0488275i	$0.984452\pi$
$114$		0			0
$115$	6.23103			0.581046
$116$		0			0
$117$		0			0
$118$		0			0
$119$	18.4448	+	1.63945i	1.69083	+	0.150288i
$120$		0			0
$121$	−10.4697			−0.951787
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.77193			0.784586
$126$		0			0
$127$	9.06977			0.804812			0.402406	−	0.915461i	$-0.368174\pi$
$127$	9.06977			0.804812			0.402406	+	0.915461i	$0.368174\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−13.0851			−1.14325			−0.571625	−	0.820515i	$-0.693687\pi$
$131$	−13.0851			−1.14325			−0.571625	+	0.820515i	$0.693687\pi$
$132$		0			0
$133$	−1.05845	+	1.50718i	−0.0917792	+	0.130689i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	20.0764			1.71525			0.857623	−	0.514279i	$-0.171940\pi$
$137$	20.0764			1.71525			0.857623	+	0.514279i	$0.171940\pi$
$138$		0			0
$139$	0.337832	−	0.585143i	0.0286546	−	0.0496312i	−0.851343	−	0.524610i	$-0.824211\pi$
$139$	0.337832	−	0.585143i	0.0286546	−	0.0496312i	0.879997	+	0.474979i	$0.157544\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.31860	+	2.28388i	−0.110267	+	0.190988i
$144$		0			0
$145$	3.23968	+	5.61129i	0.269041	+	0.465992i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−21.5088			−1.76207			−0.881034	−	0.473054i	$-0.843152\pi$
$149$	−21.5088			−1.76207			−0.881034	+	0.473054i	$0.843152\pi$
$150$		0			0
$151$	14.1705			1.15318			0.576588	−	0.817035i	$-0.304384\pi$
$151$	14.1705			1.15318			0.576588	+	0.817035i	$0.304384\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.43579	+	7.68301i	0.356291	+	0.617114i
$156$		0			0
$157$	7.99845	+	13.8537i	0.638346	+	1.10565i	0.985796	+	0.167949i	$0.0537143\pi$
$157$	7.99845	+	13.8537i	0.638346	+	1.10565i	−0.347450	+	0.937699i	$0.612952\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.17717	+	15.4473i	0.565641	+	1.21742i
$162$		0			0
$163$	−10.0904	−	17.4771i	−0.790340	−	1.36891i	−0.925757	−	0.378120i	$-0.876571\pi$
$163$	−10.0904	−	17.4771i	−0.790340	−	1.36891i	0.135417	−	0.990789i	$-0.456763\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.2299	−	21.1828i	0.946378	−	1.63917i	0.193410	−	0.981118i	$-0.438045\pi$
$167$	12.2299	−	21.1828i	0.946378	−	1.63917i	0.752968	−	0.658057i	$-0.228621\pi$
$168$		0			0
$169$	−0.0569772	−	0.0986874i	−0.00438286	−	0.00759134i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.87800	−	17.1092i	0.751010	−	1.30079i	−0.196323	−	0.980539i	$-0.562900\pi$
$173$	9.87800	−	17.1092i	0.751010	−	1.30079i	0.947333	−	0.320249i	$-0.103767\pi$
$174$		0			0
$175$	4.52980	+	9.74941i	0.342421	+	0.736986i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.32439	−	10.9542i	0.472707	−	0.818753i	−0.526805	−	0.849986i	$-0.676610\pi$
$179$	6.32439	−	10.9542i	0.472707	−	0.818753i	0.999512	+	0.0312332i	$0.00994346\pi$
$180$		0			0
$181$	12.5654			0.933975			0.466988	−	0.884264i	$-0.345339\pi$
$181$	12.5654			0.933975			0.466988	+	0.884264i	$0.345339\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.827040	−	1.43248i	−0.0608052	−	0.105318i
$186$		0			0
$187$	2.54848	−	4.41409i	0.186363	−	0.322790i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.70316	+	6.41407i	−0.267951	+	0.464105i	−0.968333	−	0.249663i	$-0.919680\pi$
$191$	−3.70316	+	6.41407i	−0.267951	+	0.464105i	0.700381	+	0.713769i	$0.253013\pi$
$192$		0			0
$193$	0.813937	+	1.40978i	0.0585885	+	0.101478i	0.893832	−	0.448402i	$-0.148007\pi$
$193$	0.813937	+	1.40978i	0.0585885	+	0.101478i	−0.835244	+	0.549880i	$0.814673\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.27125			0.589302			0.294651	−	0.955605i	$-0.404797\pi$
$197$	8.27125			0.589302			0.294651	+	0.955605i	$0.404797\pi$
$198$		0			0
$199$	5.34411	−	9.25627i	0.378834	−	0.656159i	−0.612059	−	0.790812i	$-0.709659\pi$
$199$	5.34411	−	9.25627i	0.378834	−	0.656159i	0.990893	+	0.134653i	$0.0429919\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.1793	+	14.4948i	−0.714448	+	1.01734i
$204$		0			0
$205$	−3.50794	+	6.07593i	−0.245005	+	0.424361i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.253466	+	0.439015i	0.0175326	+	0.0303673i
$210$		0			0
$211$	−11.2725	+	19.5246i	−0.776034	+	1.34413i	0.158178	+	0.987411i	$0.449438\pi$
$211$	−11.2725	+	19.5246i	−0.776034	+	1.34413i	−0.934211	+	0.356720i	$0.883895\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.336863	+	0.583464i	0.0229739	+	0.0397919i
$216$		0			0
$217$	−13.9376	+	19.8464i	−0.946145	+	1.34726i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	12.6727	+	21.9498i	0.852461	+	1.47651i
$222$		0			0
$223$	3.70093	+	6.41020i	0.247832	+	0.429258i	0.962924	−	0.269772i	$-0.0869484\pi$
$223$	3.70093	+	6.41020i	0.247832	+	0.429258i	−0.715092	+	0.699031i	$0.753615\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.598173			0.0397021			0.0198511	−	0.999803i	$-0.493681\pi$
$227$	0.598173			0.0397021			0.0198511	+	0.999803i	$0.493681\pi$
$228$		0			0
$229$	−4.03717			−0.266783			−0.133392	−	0.991063i	$-0.542587\pi$
$229$	−4.03717			−0.266783			−0.133392	+	0.991063i	$0.542587\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.59754	+	9.69523i	0.366707	+	0.635155i	0.989049	−	0.147591i	$-0.0471518\pi$
$233$	5.59754	+	9.69523i	0.366707	+	0.635155i	−0.622341	+	0.782746i	$0.713818\pi$
$234$		0			0
$235$	−3.70805	+	6.42254i	−0.241887	+	0.418960i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.8171	−	22.1999i	0.829069	−	1.43599i	−0.0697006	−	0.997568i	$-0.522204\pi$
$239$	12.8171	−	22.1999i	0.829069	−	1.43599i	0.898769	−	0.438421i	$-0.144462\pi$
$240$		0			0
$241$	−6.59180			−0.424615			−0.212307	−	0.977203i	$-0.568098\pi$
$241$	−6.59180			−0.424615			−0.212307	+	0.977203i	$0.568098\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.36924	−	5.17787i	0.279141	−	0.330802i
$246$		0			0
$247$	−2.52080			−0.160395
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−25.0438			−1.58075			−0.790374	−	0.612624i	$-0.790114\pi$
$251$	−25.0438			−1.58075			−0.790374	+	0.612624i	$0.790114\pi$
$252$		0			0
$253$	4.68840			0.294757
$254$		0			0
$255$		0			0
$256$		0			0
$257$	18.1407			1.13159			0.565794	−	0.824547i	$-0.308570\pi$
$257$	18.1407			1.13159			0.565794	+	0.824547i	$0.308570\pi$
$258$		0			0
$259$	2.59862	−	3.70030i	0.161471	−	0.229926i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.8088			−0.789822			−0.394911	−	0.918719i	$-0.629225\pi$
$263$	−12.8088			−0.789822			−0.394911	+	0.918719i	$0.629225\pi$
$264$		0			0
$265$	1.99028	−	3.44726i	0.122262	−	0.211763i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.4412	−	25.0129i	0.880497	−	1.52507i	0.0297079	−	0.999559i	$-0.490542\pi$
$269$	14.4412	−	25.0129i	0.880497	−	1.52507i	0.850789	−	0.525507i	$-0.176124\pi$
$270$		0			0
$271$	4.59579	+	7.96015i	0.279175	+	0.483544i	0.971180	−	0.238348i	$-0.0766059\pi$
$271$	4.59579	+	7.96015i	0.279175	+	0.483544i	−0.692005	+	0.721892i	$0.743273\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.95904			0.178437
$276$		0			0
$277$	−3.91557			−0.235264			−0.117632	−	0.993057i	$-0.537530\pi$
$277$	−3.91557			−0.235264			−0.117632	+	0.993057i	$0.537530\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.64654	−	13.2442i	−0.456154	−	0.790082i	0.542600	−	0.839991i	$-0.317440\pi$
$281$	−7.64654	−	13.2442i	−0.456154	−	0.790082i	−0.998754	+	0.0499093i	$0.984107\pi$
$282$		0			0
$283$	−12.4890	−	21.6315i	−0.742392	−	1.28586i	−0.951403	−	0.307947i	$-0.900358\pi$
$283$	−12.4890	−	21.6315i	−0.742392	−	1.28586i	0.209011	−	0.977913i	$-0.432975\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−19.1034	−	1.69799i	−1.12764	−	0.100229i
$288$		0			0
$289$	−15.9928	−	27.7003i	−0.940751	−	1.62943i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.08092	−	7.06835i	0.238410	−	0.412938i	−0.721848	−	0.692051i	$-0.756707\pi$
$293$	4.08092	−	7.06835i	0.238410	−	0.412938i	0.960258	+	0.279114i	$0.0900406\pi$
$294$		0			0
$295$	2.31133	+	4.00334i	0.134571	+	0.233084i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.6570	+	20.1904i	−0.674139	+	1.16764i
$300$		0			0
$301$	−1.05845	+	1.50718i	−0.0610080	+	0.0868722i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.38371	−	4.12870i	0.136491	−	0.236409i
$306$		0			0
$307$	18.0692			1.03126			0.515631	−	0.856811i	$-0.327558\pi$
$307$	18.0692			1.03126			0.515631	+	0.856811i	$0.327558\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.00384	−	8.66691i	−0.283742	−	0.491456i	0.688561	−	0.725178i	$-0.258243\pi$
$311$	−5.00384	−	8.66691i	−0.283742	−	0.491456i	−0.972303	+	0.233723i	$0.924909\pi$
$312$		0			0
$313$	−1.49532	+	2.58998i	−0.0845207	+	0.146394i	−0.905187	−	0.425014i	$-0.860269\pi$
$313$	−1.49532	+	2.58998i	−0.0845207	+	0.146394i	0.820666	+	0.571408i	$0.193603\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.9246	+	20.6541i	−0.669754	+	1.16005i	0.308219	+	0.951315i	$0.400267\pi$
$317$	−11.9246	+	20.6541i	−0.669754	+	1.16005i	−0.977973	+	0.208732i	$0.933066\pi$
$318$		0			0
$319$	2.43763	+	4.22210i	0.136481	+	0.236392i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.87199			0.271085
$324$		0			0
$325$	−7.35717	+	12.7430i	−0.408102	+	0.706854i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−20.1932	−	1.79486i	−1.11329	−	0.0989536i
$330$		0			0
$331$	8.01886	−	13.8891i	0.440757	−	0.763413i	−0.556989	−	0.830520i	$-0.688044\pi$
$331$	8.01886	−	13.8891i	0.440757	−	0.763413i	0.997746	+	0.0671069i	$0.0213768\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.81680	−	4.87884i	−0.153898	−	0.266560i
$336$		0			0
$337$	16.8985	−	29.2691i	0.920520	−	1.59439i	0.121907	−	0.992542i	$-0.461099\pi$
$337$	16.8985	−	29.2691i	0.920520	−	1.59439i	0.798613	−	0.601845i	$-0.205568\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.33761	+	5.78092i	0.180742	+	0.313054i
$342$		0			0
$343$	17.8691	+	4.86767i	0.964842	+	0.262829i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.6637	+	30.5944i	0.948237	+	1.64240i	0.749136	+	0.662417i	$0.230469\pi$
$347$	17.6637	+	30.5944i	0.948237	+	1.64240i	0.199102	+	0.979979i	$0.436198\pi$
$348$		0			0
$349$	−5.75344	−	9.96526i	−0.307975	−	0.533428i	0.669944	−	0.742411i	$-0.266318\pi$
$349$	−5.75344	−	9.96526i	−0.307975	−	0.533428i	−0.977919	+	0.208983i	$0.932985\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−24.8863			−1.32457			−0.662283	−	0.749254i	$-0.730412\pi$
$353$	−24.8863			−1.32457			−0.662283	+	0.749254i	$0.730412\pi$
$354$		0			0
$355$	0.294639			0.0156378
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.22681	−	15.9813i	−0.486972	−	0.843461i	0.512916	−	0.858439i	$-0.328565\pi$
$359$	−9.22681	−	15.9813i	−0.486972	−	0.843461i	−0.999888	+	0.0149785i	$0.995232\pi$
$360$		0			0
$361$	9.25772	−	16.0348i	0.487249	−	0.843939i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.16718	+	8.94982i	−0.270463	+	0.468455i
$366$		0			0
$367$	−18.2138			−0.950750			−0.475375	−	0.879783i	$-0.657688\pi$
$367$	−18.2138			−0.950750			−0.475375	+	0.879783i	$0.657688\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	10.8386	+	0.963378i	0.562711	+	0.0500161i
$372$		0			0
$373$	−18.1999			−0.942355			−0.471177	−	0.882038i	$-0.656171\pi$
$373$	−18.1999			−0.942355			−0.471177	+	0.882038i	$0.656171\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−24.2431			−1.24858
$378$		0			0
$379$	−24.1061			−1.23825			−0.619124	−	0.785293i	$-0.712512\pi$
$379$	−24.1061			−1.23825			−0.619124	+	0.785293i	$0.712512\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6.43694			0.328912			0.164456	−	0.986384i	$-0.447413\pi$
$383$	6.43694			0.328912			0.164456	+	0.986384i	$0.447413\pi$
$384$		0			0
$385$	−0.785766	−	1.69119i	−0.0400463	−	0.0861911i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−33.8597			−1.71676			−0.858379	−	0.513017i	$-0.828528\pi$
$389$	−33.8597			−1.71676			−0.858379	+	0.513017i	$0.828528\pi$
$390$		0			0
$391$	22.5295	−	39.0223i	1.13937	−	1.97344i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.56740	+	2.71481i	−0.0788643	+	0.136597i
$396$		0			0
$397$	−0.808630	−	1.40059i	−0.0405840	−	0.0702935i	0.845020	−	0.534735i	$-0.179588\pi$
$397$	−0.808630	−	1.40059i	−0.0405840	−	0.0702935i	−0.885604	+	0.464441i	$0.846255\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.75382			−0.287332			−0.143666	−	0.989626i	$-0.545889\pi$
$401$	−5.75382			−0.287332			−0.143666	+	0.989626i	$0.545889\pi$
$402$		0			0
$403$	−33.1937			−1.65350
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.622289	−	1.07784i	−0.0308457	−	0.0534263i
$408$		0			0
$409$	2.88631	+	4.99923i	0.142719	+	0.247196i	0.928520	−	0.371284i	$-0.121082\pi$
$409$	2.88631	+	4.99923i	0.142719	+	0.247196i	−0.785801	+	0.618480i	$0.787749\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−7.26237	+	10.3412i	−0.357358	+	0.508859i
$414$		0			0
$415$	0.598871	+	1.03727i	0.0293974	+	0.0509178i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.29032	−	16.0913i	0.453862	−	0.786111i	−0.544760	−	0.838592i	$-0.683379\pi$
$419$	9.29032	−	16.0913i	0.453862	−	0.786111i	0.998622	+	0.0524804i	$0.0167127\pi$
$420$		0			0
$421$	−8.05788	−	13.9567i	−0.392717	−	0.680206i	0.600090	−	0.799933i	$-0.295131\pi$
$421$	−8.05788	−	13.9567i	−0.392717	−	0.680206i	−0.992807	+	0.119727i	$0.961798\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	14.2193	−	24.6285i	0.689737	−	1.19466i
$426$		0			0
$427$	12.9811	+	1.15382i	0.628200	+	0.0558371i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.82664	+	3.16383i	−0.0879860	+	0.152396i	−0.906660	−	0.421863i	$-0.861376\pi$
$431$	−1.82664	+	3.16383i	−0.0879860	+	0.152396i	0.818674	+	0.574259i	$0.194710\pi$
$432$		0			0
$433$	12.6697			0.608865			0.304432	−	0.952534i	$-0.401533\pi$
$433$	12.6697			0.608865			0.304432	+	0.952534i	$0.401533\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.24073	+	3.88107i	0.107189	+	0.185657i
$438$		0			0
$439$	−5.85810	+	10.1465i	−0.279592	+	0.484267i	−0.971283	−	0.237926i	$-0.923532\pi$
$439$	−5.85810	+	10.1465i	−0.279592	+	0.484267i	0.691692	+	0.722193i	$0.256866\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.8735	+	25.7617i	−0.706661	+	1.22397i	0.259428	+	0.965763i	$0.416466\pi$
$443$	−14.8735	+	25.7617i	−0.706661	+	1.22397i	−0.966089	+	0.258210i	$0.916867\pi$
$444$		0			0
$445$	−5.60079	−	9.70085i	−0.265503	−	0.459865i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11.0193			−0.520034			−0.260017	−	0.965604i	$-0.583728\pi$
$449$	−11.0193			−0.520034			−0.260017	+	0.965604i	$0.583728\pi$
$450$		0			0
$451$	−2.63947	+	4.57170i	−0.124288	+	0.215273i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	9.23673	+	0.820999i	0.433025	+	0.0384890i
$456$		0			0
$457$	−0.258224	+	0.447257i	−0.0120792	+	0.0209218i	−0.872002	−	0.489503i	$-0.837178\pi$
$457$	−0.258224	+	0.447257i	−0.0120792	+	0.0209218i	0.859923	+	0.510424i	$0.170512\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.54962	+	6.14813i	0.165322	+	0.286347i	0.936770	−	0.349946i	$-0.113800\pi$
$461$	3.54962	+	6.14813i	0.165322	+	0.286347i	−0.771447	+	0.636293i	$0.780467\pi$
$462$		0			0
$463$	−4.91148	+	8.50693i	−0.228256	+	0.395351i	−0.957291	−	0.289125i	$-0.906636\pi$
$463$	−4.91148	+	8.50693i	−0.228256	+	0.395351i	0.729035	+	0.684476i	$0.239969\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.79604	+	8.30698i	0.221934	+	0.384401i	0.955395	−	0.295330i	$-0.0954297\pi$
$467$	4.79604	+	8.30698i	0.221934	+	0.384401i	−0.733461	+	0.679731i	$0.762096\pi$
$468$		0			0
$469$	8.85061	−	12.6028i	0.408683	−	0.581943i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.253466	+	0.439015i	0.0116544	+	0.0201859i
$474$		0			0
$475$	1.41422	+	2.44950i	0.0648887	+	0.112391i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−16.2724			−0.743506			−0.371753	−	0.928332i	$-0.621243\pi$
$479$	−16.2724			−0.743506			−0.371753	+	0.928332i	$0.621243\pi$
$480$		0			0
$481$	6.18888			0.282189
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.28660	−	2.22846i	−0.0584217	−	0.101189i
$486$		0			0
$487$	−9.50511	+	16.4633i	−0.430718	+	0.746025i	−0.996935	−	0.0782307i	$-0.975073\pi$
$487$	−9.50511	+	16.4633i	−0.430718	+	0.746025i	0.566217	+	0.824256i	$0.308406\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.55413	+	4.42387i	−0.115266	+	0.199647i	−0.917886	−	0.396844i	$-0.870105\pi$
$491$	−2.55413	+	4.42387i	−0.115266	+	0.199647i	0.802620	+	0.596491i	$0.203439\pi$
$492$		0			0
$493$	46.8549			2.11024
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.339378	+	0.730439i	0.0152232	+	0.0327646i
$498$		0			0
$499$	−28.5276			−1.27707			−0.638536	−	0.769592i	$-0.720459\pi$
$499$	−28.5276			−1.27707			−0.638536	+	0.769592i	$0.720459\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.05885			−0.180975			−0.0904877	−	0.995898i	$-0.528843\pi$
$503$	−4.05885			−0.180975			−0.0904877	+	0.995898i	$0.528843\pi$
$504$		0			0
$505$	1.56206			0.0695108
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−17.2605			−0.765056			−0.382528	−	0.923944i	$-0.624946\pi$
$509$	−17.2605			−0.765056			−0.382528	+	0.923944i	$0.624946\pi$
$510$		0			0
$511$	−28.1393	−	2.50114i	−1.24481	−	0.110644i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−10.4917			−0.462320
$516$		0			0
$517$	−2.79005	+	4.83250i	−0.122706	+	0.212533i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	17.0525	−	29.5358i	0.747083	−	1.29399i	−0.202132	−	0.979358i	$-0.564787\pi$
$521$	17.0525	−	29.5358i	0.747083	−	1.29399i	0.949215	−	0.314628i	$-0.101880\pi$
$522$		0			0
$523$	−9.44847	−	16.3652i	−0.413153	−	0.715602i	0.582080	−	0.813132i	$-0.302239\pi$
$523$	−9.44847	−	16.3652i	−0.413153	−	0.715602i	−0.995233	+	0.0975299i	$0.968906\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	64.1539			2.79459
$528$		0			0
$529$	18.4473			0.802057
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−13.1252	−	22.7336i	−0.568517	−	0.984701i
$534$		0			0
$535$	4.81634	+	8.34215i	0.208229	+	0.360663i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.28754	−	3.89598i	0.141605	−	0.167812i
$540$		0			0
$541$	0.564117	+	0.977080i	0.0242533	+	0.0420080i	0.877897	−	0.478849i	$-0.158946\pi$
$541$	0.564117	+	0.977080i	0.0242533	+	0.0420080i	−0.853644	+	0.520857i	$0.825613\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.98012	−	15.5540i	0.384666	−	0.666261i
$546$		0			0
$547$	15.8427	+	27.4404i	0.677386	+	1.17327i	0.975765	+	0.218819i	$0.0702205\pi$
$547$	15.8427	+	27.4404i	0.677386	+	1.17327i	−0.298380	+	0.954447i	$0.596446\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.33004	+	4.03575i	−0.0992630	+	0.171929i
$552$		0			0
$553$	−8.53568	−	0.758687i	−0.362974	−	0.0322626i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.8135	−	23.9257i	0.585298	−	1.01377i	−0.409540	−	0.912292i	$-0.634311\pi$
$557$	13.8135	−	23.9257i	0.585298	−	1.01377i	0.994838	−	0.101474i	$-0.0323559\pi$
$558$		0			0
$559$	−2.52080			−0.106619
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.920685	+	1.59467i	0.0388022	+	0.0672074i	0.884774	−	0.466020i	$-0.154312\pi$
$563$	0.920685	+	1.59467i	0.0388022	+	0.0672074i	−0.845972	+	0.533227i	$0.820979\pi$
$564$		0			0
$565$	5.57315	−	9.65298i	0.234464	−	0.406104i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.75524	+	9.96837i	−0.241272	+	0.417896i	−0.961077	−	0.276281i	$-0.910898\pi$
$569$	−5.75524	+	9.96837i	−0.241272	+	0.417896i	0.719805	+	0.694177i	$0.244231\pi$
$570$		0			0
$571$	4.35262	+	7.53896i	0.182152	+	0.315496i	0.942613	−	0.333887i	$-0.108361\pi$
$571$	4.35262	+	7.53896i	0.182152	+	0.315496i	−0.760461	+	0.649383i	$0.775027\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	26.1591			1.09091
$576$		0			0
$577$	−7.24358	+	12.5462i	−0.301554	+	0.522307i	−0.976488	−	0.215571i	$-0.930839\pi$
$577$	−7.24358	+	12.5462i	−0.301554	+	0.522307i	0.674934	+	0.737878i	$0.264172\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.88170	+	2.67944i	−0.0780659	+	0.111162i
$582$		0			0
$583$	1.49754	−	2.59382i	0.0620218	−	0.107425i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.3695	+	24.8886i	0.593091	+	1.02726i	0.993813	+	0.111065i	$0.0354261\pi$
$587$	14.3695	+	24.8886i	0.593091	+	1.02726i	−0.400722	+	0.916200i	$0.631241\pi$
$588$		0			0
$589$	−3.19030	+	5.52576i	−0.131454	+	0.227685i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.82328	−	11.8183i	−0.280199	−	0.485318i	0.691235	−	0.722630i	$-0.257067\pi$
$593$	−6.82328	−	11.8183i	−0.280199	−	0.485318i	−0.971434	+	0.237312i	$0.923734\pi$
$594$		0			0
$595$	−17.8519	−	1.58676i	−0.731858	−	0.0650506i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.64585	+	4.58275i	0.108106	+	0.187246i	0.915003	−	0.403447i	$-0.132188\pi$
$599$	2.64585	+	4.58275i	0.108106	+	0.187246i	−0.806897	+	0.590693i	$0.798855\pi$
$600$		0			0
$601$	17.0522	+	29.5353i	0.695574	+	1.20477i	0.969987	+	0.243158i	$0.0781834\pi$
$601$	17.0522	+	29.5353i	0.695574	+	1.20477i	−0.274412	+	0.961612i	$0.588483\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.1331			0.411971
$606$		0			0
$607$	−9.04464			−0.367111			−0.183555	−	0.983009i	$-0.558761\pi$
$607$	−9.04464			−0.367111			−0.183555	+	0.983009i	$0.558761\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13.8740	−	24.0305i	−0.561282	−	0.972169i
$612$		0			0
$613$	5.97889	−	10.3557i	0.241485	−	0.418264i	−0.719653	−	0.694334i	$-0.755699\pi$
$613$	5.97889	−	10.3557i	0.241485	−	0.418264i	0.961137	+	0.276070i	$0.0890322\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.13220	+	8.88923i	−0.206615	+	0.357867i	−0.950646	−	0.310278i	$-0.899578\pi$
$617$	−5.13220	+	8.88923i	−0.206615	+	0.357867i	0.744031	+	0.668145i	$0.232911\pi$
$618$		0			0
$619$	−43.5605			−1.75085			−0.875423	−	0.483358i	$-0.839417\pi$
$619$	−43.5605			−1.75085			−0.875423	+	0.483358i	$0.839417\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	17.5981	−	25.0588i	0.705053	−	1.00396i
$624$		0			0
$625$	11.8263			0.473051
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−11.9613			−0.476929
$630$		0			0
$631$	19.3703			0.771119			0.385559	−	0.922683i	$-0.374008\pi$
$631$	19.3703			0.771119			0.385559	+	0.922683i	$0.374008\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.77825			−0.348354
$636$		0			0
$637$	8.60395	+	23.8444i	0.340901	+	0.944750i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.50016			−0.177746			−0.0888728	−	0.996043i	$-0.528326\pi$
$641$	−4.50016			−0.177746			−0.0888728	+	0.996043i	$0.528326\pi$
$642$		0			0
$643$	−20.9045	+	36.2077i	−0.824394	+	1.42789i	0.0779869	+	0.996954i	$0.475151\pi$
$643$	−20.9045	+	36.2077i	−0.824394	+	1.42789i	−0.902381	+	0.430939i	$0.858183\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.9381	+	20.6773i	−0.469334	+	0.812910i	−0.999385	−	0.0350555i	$-0.988839\pi$
$647$	−11.9381	+	20.6773i	−0.469334	+	0.812910i	0.530052	+	0.847965i	$0.322173\pi$
$648$		0			0
$649$	1.73911	+	3.01223i	0.0682661	+	0.118240i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.33347			0.326114			0.163057	−	0.986617i	$-0.447865\pi$
$653$	8.33347			0.326114			0.163057	+	0.986617i	$0.447865\pi$
$654$		0			0
$655$	12.6645			0.494843
$656$		0			0
$657$		0			0
$658$		0			0
$659$	20.2488	+	35.0719i	0.788781	+	1.36621i	0.926714	+	0.375767i	$0.122621\pi$
$659$	20.2488	+	35.0719i	0.788781	+	1.36621i	−0.137933	+	0.990442i	$0.544046\pi$
$660$		0			0
$661$	3.88559	+	6.73004i	0.151132	+	0.261768i	0.931644	−	0.363373i	$-0.118375\pi$
$661$	3.88559	+	6.73004i	0.151132	+	0.261768i	−0.780512	+	0.625141i	$0.785042\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.02443	−	1.45873i	0.0397256	−	0.0565672i
$666$		0			0
$667$	21.5496	+	37.3250i	0.834404	+	1.44523i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.79357	−	3.10656i	0.0692400	−	0.119927i
$672$		0			0
$673$	−22.7830	−	39.4614i	−0.878221	−	1.52112i	−0.853291	−	0.521435i	$-0.825397\pi$
$673$	−22.7830	−	39.4614i	−0.878221	−	1.52112i	−0.0249302	−	0.999689i	$-0.507936\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.54521	−	11.3366i	0.251553	−	0.435702i	−0.712401	−	0.701773i	$-0.752392\pi$
$677$	6.54521	−	11.3366i	0.251553	−	0.435702i	0.963954	+	0.266071i	$0.0857254\pi$
$678$		0			0
$679$	4.04261	−	5.75646i	0.155141	−	0.220913i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.6506	−	21.9114i	0.484060	−	0.838417i	−0.515772	−	0.856726i	$-0.672495\pi$
$683$	12.6506	−	21.9114i	0.484060	−	0.838417i	0.999832	+	0.0183087i	$0.00582815\pi$
$684$		0			0
$685$	−19.4311			−0.742425
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.44679	+	12.8982i	0.283700	+	0.491383i
$690$		0			0
$691$	12.2016	−	21.1337i	0.464170	−	0.803965i	−0.534994	−	0.844856i	$-0.679686\pi$
$691$	12.2016	−	21.1337i	0.464170	−	0.803965i	0.999164	+	0.0408905i	$0.0130195\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.326974	+	0.566335i	−0.0124028	+	0.0214823i
$696$		0			0
$697$	25.3673	+	43.9375i	0.960855	+	1.66425i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.4137			0.695476			0.347738	−	0.937592i	$-0.386950\pi$
$701$	18.4137			0.695476			0.347738	+	0.937592i	$0.386950\pi$
$702$		0			0
$703$	0.594823	−	1.03026i	0.0224342	−	0.0388571i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.79925	+	3.87250i	0.0676679	+	0.145640i
$708$		0			0
$709$	6.66501	−	11.5441i	0.250310	−	0.433549i	−0.713301	−	0.700858i	$-0.752801\pi$
$709$	6.66501	−	11.5441i	0.250310	−	0.433549i	0.963611	+	0.267308i	$0.0861342\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	29.5058	+	51.1056i	1.10500	+	1.91392i
$714$		0			0
$715$	1.27622	−	2.21047i	0.0477278	−	0.0826671i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	7.84705	+	13.5915i	0.292646	+	0.506877i	0.974434	−	0.224672i	$-0.0721310\pi$
$719$	7.84705	+	13.5915i	0.292646	+	0.506877i	−0.681789	+	0.731549i	$0.738798\pi$
$720$		0			0
$721$	−12.0848	−	26.0099i	−0.450062	−	0.968660i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.6008	+	23.5573i	0.505121	+	0.874896i
$726$		0			0
$727$	−12.8388	−	22.2374i	−0.476163	−	0.824739i	0.523464	−	0.852048i	$-0.324640\pi$
$727$	−12.8388	−	22.2374i	−0.476163	−	0.824739i	−0.999627	+	0.0273090i	$0.991306\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.87199			0.180197
$732$		0			0
$733$	1.17308			0.0433288			0.0216644	−	0.999765i	$-0.493103\pi$
$733$	1.17308			0.0433288			0.0216644	+	0.999765i	$0.493103\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.11944	−	3.67098i	−0.0780707	−	0.135222i
$738$		0			0
$739$	11.6114	−	20.1116i	0.427133	−	0.739816i	−0.569484	−	0.822003i	$-0.692857\pi$
$739$	11.6114	−	20.1116i	0.427133	−	0.739816i	0.996617	+	0.0821861i	$0.0261902\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.7846	+	20.4115i	−0.432335	+	0.748826i	−0.997074	−	0.0764439i	$-0.975643\pi$
$743$	−11.7846	+	20.4115i	−0.432335	+	0.748826i	0.564739	+	0.825269i	$0.308977\pi$
$744$		0			0
$745$	20.8174			0.762691
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−15.1333	+	21.5490i	−0.552959	+	0.787385i
$750$		0			0
$751$	44.1062			1.60946			0.804728	−	0.593643i	$-0.202311\pi$
$751$	44.1062			1.60946			0.804728	+	0.593643i	$0.202311\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−13.7150			−0.499139
$756$		0			0
$757$	−2.71020			−0.0985040			−0.0492520	−	0.998786i	$-0.515684\pi$
$757$	−2.71020			−0.0985040			−0.0492520	+	0.998786i	$0.515684\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−29.0496			−1.05305			−0.526524	−	0.850160i	$-0.676505\pi$
$761$	−29.0496			−1.05305			−0.526524	+	0.850160i	$0.676505\pi$
$762$		0			0
$763$	48.9036	+	4.34676i	1.77043	+	0.157363i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.2961			−0.624525
$768$		0			0
$769$	−5.25175	+	9.09629i	−0.189383	+	0.328021i	−0.945045	−	0.326941i	$-0.893982\pi$
$769$	−5.25175	+	9.09629i	−0.189383	+	0.328021i	0.755662	+	0.654962i	$0.227315\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.9230	−	20.6513i	0.428841	−	0.742774i	−0.567930	−	0.823077i	$-0.692255\pi$
$773$	11.9230	−	20.6513i	0.428841	−	0.742774i	0.996771	+	0.0803029i	$0.0255888\pi$
$774$		0			0
$775$	18.6223	+	32.2548i	0.668933	+	1.15863i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.04595			−0.180790
$780$		0			0
$781$	0.221695			0.00793287
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.74136	−	13.4084i	−0.276301	−	0.478567i
$786$		0			0
$787$	2.19788	+	3.80684i	0.0783460	+	0.135699i	0.902536	−	0.430613i	$-0.141703\pi$
$787$	2.19788	+	3.80684i	0.0783460	+	0.135699i	−0.824190	+	0.566313i	$0.808369\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	30.3501	+	2.69764i	1.07912	+	0.0959171i
$792$		0			0
$793$	8.91885	+	15.4479i	0.316717	+	0.548571i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.56236	−	4.43813i	0.0907633	−	0.157207i	−0.817069	−	0.576540i	$-0.804403\pi$
$797$	2.56236	−	4.43813i	0.0907633	−	0.157207i	0.907833	+	0.419333i	$0.137736\pi$
$798$		0			0
$799$	26.8144	+	46.4440i	0.948627	+	1.64307i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.88794	+	6.73410i	−0.137202	+	0.237641i
$804$		0			0
$805$	−6.94648	−	14.9508i	−0.244831	−	0.526946i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	16.4612	−	28.5116i	0.578744	−	1.00241i	−0.416880	−	0.908961i	$-0.636877\pi$
$809$	16.4612	−	28.5116i	0.578744	−	1.00241i	0.995624	−	0.0934519i	$-0.0297901\pi$
$810$		0			0
$811$	−31.8830			−1.11956			−0.559781	−	0.828640i	$-0.689115\pi$
$811$	−31.8830			−1.11956			−0.559781	+	0.828640i	$0.689115\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	9.76605	+	16.9153i	0.342090	+	0.592517i
$816$		0			0
$817$	−0.242278	+	0.419638i	−0.00847624	+	0.0146813i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.1139	−	29.6421i	0.597278	−	1.03452i	−0.395943	−	0.918275i	$-0.629582\pi$
$821$	17.1139	−	29.6421i	0.597278	−	1.03452i	0.993221	−	0.116241i	$-0.0370844\pi$
$822$		0			0
$823$	−19.1866	−	33.2321i	−0.668802	−	1.15840i	−0.978239	−	0.207480i	$-0.933474\pi$
$823$	−19.1866	−	33.2321i	−0.668802	−	1.15840i	0.309437	−	0.950920i	$-0.399859\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.23903			−0.321273			−0.160636	−	0.987014i	$-0.551355\pi$
$827$	−9.23903			−0.321273			−0.160636	+	0.987014i	$0.551355\pi$
$828$		0			0
$829$	20.8224	−	36.0654i	0.723191	−	1.25260i	−0.236523	−	0.971626i	$-0.576008\pi$
$829$	20.8224	−	36.0654i	0.723191	−	1.25260i	0.959714	−	0.280978i	$-0.0906589\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−16.6289	−	46.0844i	−0.576159	−	1.59673i
$834$		0			0
$835$	−11.8368	+	20.5019i	−0.409629	+	0.709499i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.4241	+	26.7154i	0.532500	+	0.922318i	0.999280	+	0.0379439i	$0.0120808\pi$
$839$	15.4241	+	26.7154i	0.532500	+	0.922318i	−0.466780	+	0.884374i	$0.654586\pi$
$840$		0			0
$841$	−7.90845	+	13.6978i	−0.272705	+	0.472339i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.0551458	+	0.0955153i	0.00189707	+	0.00328583i
$846$		0			0
$847$	11.6718	+	25.1210i	0.401048	+	0.863168i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.50128	−	9.52849i	−0.188581	−	0.326632i
$852$		0			0
$853$	−11.4171	−	19.7750i	−0.390913	−	0.677082i	0.601657	−	0.798755i	$-0.294507\pi$
$853$	−11.4171	−	19.7750i	−0.390913	−	0.677082i	−0.992570	+	0.121673i	$0.961174\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	53.3441			1.82220			0.911100	−	0.412186i	$-0.135235\pi$
$857$	53.3441			1.82220			0.911100	+	0.412186i	$0.135235\pi$
$858$		0			0
$859$	−23.1757			−0.790743			−0.395372	−	0.918521i	$-0.629384\pi$
$859$	−23.1757			−0.790743			−0.395372	+	0.918521i	$0.629384\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.58456	−	7.94069i	−0.156060	−	0.270304i	0.777384	−	0.629026i	$-0.216546\pi$
$863$	−4.58456	−	7.94069i	−0.156060	−	0.270304i	−0.933445	+	0.358722i	$0.883213\pi$
$864$		0			0
$865$	−9.56049	+	16.5593i	−0.325067	+	0.563032i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.17936	+	2.04270i	−0.0400069	+	0.0692940i
$870$		0			0
$871$	21.0786			0.714221
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−9.77914	−	21.0475i	−0.330595	−	0.711535i
$876$		0			0
$877$	37.2380			1.25744			0.628718	−	0.777633i	$-0.283580\pi$
$877$	37.2380			1.25744			0.628718	+	0.777633i	$0.283580\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−7.15345			−0.241006			−0.120503	−	0.992713i	$-0.538451\pi$
$881$	−7.15345			−0.241006			−0.120503	+	0.992713i	$0.538451\pi$
$882$		0			0
$883$	−39.8688			−1.34169			−0.670846	−	0.741596i	$-0.734069\pi$
$883$	−39.8688			−1.34169			−0.670846	+	0.741596i	$0.734069\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	21.3509			0.716893			0.358447	−	0.933550i	$-0.383306\pi$
$887$	21.3509			0.716893			0.358447	+	0.933550i	$0.383306\pi$
$888$		0			0
$889$	−10.1112	−	21.7621i	−0.339118	−	0.729878i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.33380			−0.178489
$894$		0			0
$895$	−6.12111	+	10.6021i	−0.204606	+	0.354388i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.6818	+	53.1424i	−1.02329	+	1.77240i
$900$		0			0
$901$	−14.3925	−	24.9285i	−0.479483	−	0.830490i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.1615			−0.404261
$906$		0			0
$907$	−22.6024			−0.750499			−0.375250	−	0.926924i	$-0.622443\pi$
$907$	−22.6024			−0.750499			−0.375250	+	0.926924i	$0.622443\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.7594	−	22.0999i	−0.422738	−	0.732203i	0.573468	−	0.819228i	$-0.305598\pi$
$911$	−12.7594	−	22.0999i	−0.422738	−	0.732203i	−0.996206	+	0.0870243i	$0.972264\pi$
$912$		0			0
$913$	0.450607	+	0.780475i	0.0149129	+	0.0258300i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.5876	+	31.3965i	0.481723	+	1.03681i
$918$		0			0
$919$	5.71326	+	9.89566i	0.188463	+	0.326428i	0.944738	−	0.327826i	$-0.106316\pi$
$919$	5.71326	+	9.89566i	0.188463	+	0.326428i	−0.756275	+	0.654254i	$0.772983\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.551208	+	0.954721i	−0.0181432	+	0.0314250i
$924$		0			0
$925$	−3.47207	−	6.01381i	−0.114161	−	0.197733i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.79851	−	11.7754i	0.223052	−	0.386337i	−0.732681	−	0.680572i	$-0.761731\pi$
$929$	6.79851	−	11.7754i	0.223052	−	0.386337i	0.955733	+	0.294235i	$0.0950648\pi$
$930$		0			0
$931$	4.79632	+	0.859423i	0.157193	+	0.0281665i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.46656	+	4.27221i	−0.0806652	+	0.139716i
$936$		0			0
$937$	−11.1455			−0.364109			−0.182054	−	0.983288i	$-0.558275\pi$
$937$	−11.1455			−0.364109			−0.182054	+	0.983288i	$0.558275\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.7310	+	35.9072i	0.675813	+	1.17054i	0.976231	+	0.216734i	$0.0695405\pi$
$941$	20.7310	+	35.9072i	0.675813	+	1.17054i	−0.300418	+	0.953808i	$0.597126\pi$
$942$		0			0
$943$	−23.3340	+	40.4156i	−0.759859	+	1.31611i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	21.2784	−	36.8552i	0.691454	−	1.19763i	−0.279908	−	0.960027i	$-0.590304\pi$
$947$	21.2784	−	36.8552i	0.691454	−	1.19763i	0.971362	−	0.237606i	$-0.0763627\pi$
$948$		0			0
$949$	−19.3335	−	33.4865i	−0.627590	−	1.08702i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−21.2114			−0.687106			−0.343553	−	0.939133i	$-0.611630\pi$
$953$	−21.2114			−0.687106			−0.343553	+	0.939133i	$0.611630\pi$
$954$		0			0
$955$	3.58413	−	6.20790i	0.115980	−	0.200883i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−22.3816	−	48.1716i	−0.722741	−	1.55554i
$960$		0			0
$961$	−26.5096	+	45.9160i	−0.855150	+	1.48116i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.787775	−	1.36447i	−0.0253594	−	0.0439237i
$966$		0			0
$967$	−9.83257	+	17.0305i	−0.316194	+	0.547664i	−0.979691	−	0.200515i	$-0.935738\pi$
$967$	−9.83257	+	17.0305i	−0.316194	+	0.547664i	0.663496	+	0.748179i	$0.269072\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	12.2892	+	21.2855i	0.394379	+	0.683084i	0.993022	−	0.117932i	$-0.0376265\pi$
$971$	12.2892	+	21.2855i	0.394379	+	0.683084i	−0.598643	+	0.801016i	$0.704293\pi$
$972$		0			0
$973$	−1.78062	−	0.158269i	−0.0570841	−	0.00507387i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.7359	−	41.1117i	−0.759378	−	1.31528i	−0.943168	−	0.332316i	$-0.892170\pi$
$977$	−23.7359	−	41.1117i	−0.759378	−	1.31528i	0.183790	−	0.982966i	$-0.441163\pi$
$978$		0			0
$979$	−4.21420	−	7.29920i	−0.134686	−	0.233284i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−27.5440			−0.878516			−0.439258	−	0.898361i	$-0.644759\pi$
$983$	−27.5440			−0.878516			−0.439258	+	0.898361i	$0.644759\pi$
$984$		0			0
$985$	−8.00539			−0.255073
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.24073	+	3.88107i	0.0712512	+	0.123411i
$990$		0			0
$991$	19.2335	−	33.3135i	0.610973	−	1.05824i	−0.380103	−	0.924944i	$-0.624112\pi$
$991$	19.2335	−	33.3135i	0.610973	−	1.05824i	0.991077	−	0.133293i	$-0.0425551\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.17233	+	8.95874i	−0.163974	+	0.284011i
$996$		0			0
$997$	−32.4544			−1.02784			−0.513921	−	0.857837i	$-0.671808\pi$
$997$	−32.4544			−1.02784			−0.513921	+	0.857837i	$0.671808\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.l.b.361.3		14
3.2	odd	2		252.2.l.b.193.1	yes	14
4.3	odd	2		3024.2.t.j.1873.3		14
7.2	even	3		756.2.i.b.37.5		14
7.3	odd	6		5292.2.j.g.1765.3		14
7.4	even	3		5292.2.j.h.1765.5		14
7.5	odd	6		5292.2.i.i.1549.3		14
7.6	odd	2		5292.2.l.i.361.5		14
9.2	odd	6		252.2.i.b.25.5	✓	14
9.4	even	3		2268.2.k.f.1621.5		14
9.5	odd	6		2268.2.k.e.1621.3		14
9.7	even	3		756.2.i.b.613.5		14
12.11	even	2		1008.2.t.j.193.7		14
21.2	odd	6		252.2.i.b.121.5	yes	14
21.5	even	6		1764.2.i.i.373.3		14
21.11	odd	6		1764.2.j.g.589.6		14
21.17	even	6		1764.2.j.h.589.2		14
21.20	even	2		1764.2.l.i.949.7		14
28.23	odd	6		3024.2.q.j.2305.5		14
36.7	odd	6		3024.2.q.j.2881.5		14
36.11	even	6		1008.2.q.j.529.3		14
63.2	odd	6		252.2.l.b.205.1	yes	14
63.11	odd	6		1764.2.j.g.1177.6		14
63.16	even	3	inner	756.2.l.b.289.3		14
63.20	even	6		1764.2.i.i.1537.3		14
63.23	odd	6		2268.2.k.e.1297.3		14
63.25	even	3		5292.2.j.h.3529.5		14
63.34	odd	6		5292.2.i.i.2125.3		14
63.38	even	6		1764.2.j.h.1177.2		14
63.47	even	6		1764.2.l.i.961.7		14
63.52	odd	6		5292.2.j.g.3529.3		14
63.58	even	3		2268.2.k.f.1297.5		14
63.61	odd	6		5292.2.l.i.3313.5		14
84.23	even	6		1008.2.q.j.625.3		14
252.79	odd	6		3024.2.t.j.289.3		14
252.191	even	6		1008.2.t.j.961.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.5	✓	14	9.2	odd	6
252.2.i.b.121.5	yes	14	21.2	odd	6
252.2.l.b.193.1	yes	14	3.2	odd	2
252.2.l.b.205.1	yes	14	63.2	odd	6
756.2.i.b.37.5		14	7.2	even	3
756.2.i.b.613.5		14	9.7	even	3
756.2.l.b.289.3		14	63.16	even	3	inner
756.2.l.b.361.3		14	1.1	even	1	trivial
1008.2.q.j.529.3		14	36.11	even	6
1008.2.q.j.625.3		14	84.23	even	6
1008.2.t.j.193.7		14	12.11	even	2
1008.2.t.j.961.7		14	252.191	even	6
1764.2.i.i.373.3		14	21.5	even	6
1764.2.i.i.1537.3		14	63.20	even	6
1764.2.j.g.589.6		14	21.11	odd	6
1764.2.j.g.1177.6		14	63.11	odd	6
1764.2.j.h.589.2		14	21.17	even	6
1764.2.j.h.1177.2		14	63.38	even	6
1764.2.l.i.949.7		14	21.20	even	2
1764.2.l.i.961.7		14	63.47	even	6
2268.2.k.e.1297.3		14	63.23	odd	6
2268.2.k.e.1621.3		14	9.5	odd	6
2268.2.k.f.1297.5		14	63.58	even	3
2268.2.k.f.1621.5		14	9.4	even	3
3024.2.q.j.2305.5		14	28.23	odd	6
3024.2.q.j.2881.5		14	36.7	odd	6
3024.2.t.j.289.3		14	252.79	odd	6
3024.2.t.j.1873.3		14	4.3	odd	2
5292.2.i.i.1549.3		14	7.5	odd	6
5292.2.i.i.2125.3		14	63.34	odd	6
5292.2.j.g.1765.3		14	7.3	odd	6
5292.2.j.g.3529.3		14	63.52	odd	6
5292.2.j.h.1765.5		14	7.4	even	3
5292.2.j.h.3529.5		14	63.25	even	3
5292.2.l.i.361.5		14	7.6	odd	2
5292.2.l.i.3313.5		14	63.61	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.967857 q^{5} +(-1.11482 - 2.39941i) q^{7} +O(q^{10})\)	\(q-0.967857 q^{5} +(-1.11482 - 2.39941i) q^{7} -0.728244 q^{11} +(1.81066 - 3.13615i) q^{13} +(-3.49948 + 6.06128i) q^{17} +(-0.348050 - 0.602841i) q^{19} -6.43796 q^{23} -4.06325 q^{25} +(-3.34727 - 5.79764i) q^{29} +(-4.58310 - 7.93816i) q^{31} +(1.07899 + 2.32229i) q^{35} +(0.854506 + 1.48005i) q^{37} +(3.62444 - 6.27771i) q^{41} +(-0.348050 - 0.602841i) q^{43} +(3.83120 - 6.63583i) q^{47} +(-4.51435 + 5.34983i) q^{49} +(-2.05637 + 3.56174i) q^{53} +0.704836 q^{55} +(-2.38809 - 4.13629i) q^{59} +(-2.46287 + 4.26582i) q^{61} +(-1.75246 + 3.03535i) q^{65} +(2.91035 + 5.04087i) q^{67} -0.304424 q^{71} +(5.33879 - 9.24705i) q^{73} +(0.811862 + 1.74736i) q^{77} +(1.61945 - 2.80497i) q^{79} +(-0.618759 - 1.07172i) q^{83} +(3.38700 - 5.86646i) q^{85} +(5.78679 + 10.0230i) q^{89} +(-9.54349 - 0.848265i) q^{91} +(0.336863 + 0.583464i) q^{95} +(1.32933 + 2.30247i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{5} - 3 q^{7}+O(q^{10}) \) 14 * q - 4 * q^5 - 3 * q^7	\( 14 q - 4 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} - q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 13 q^{49} + 15 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65} + 6 q^{67} - 2 q^{71} + 21 q^{73} - 19 q^{77} - 10 q^{79} + 25 q^{83} + 8 q^{85} + 6 q^{89} + 2 q^{91} + 28 q^{95} - 18 q^{97}+O(q^{100}) \) 14 * q - 4 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 - q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 13 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 19 * q^77 - 10 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 - 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more