LMFDB - Embedded newform 1014.2.g.d.437.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1014,2,Mod(239,1014)] 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("1014.239"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1014, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.9349208943630483456.9
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.1
Root			$0.500000 + 1.00333i$ of defining polynomial
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.d.239.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.53819 - 0.796225i) q^{3} -1.00000i q^{4} +(0.428520 - 0.428520i) q^{5} +(1.65068 - 0.524648i) q^{6} +(-0.538189 + 0.538189i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.73205 + 2.44949i) q^{9} +0.606018i q^{10} +(-2.97155 - 2.97155i) q^{11} +(-0.796225 + 1.53819i) q^{12} -0.761114i q^{14} +(-1.00034 + 0.317946i) q^{15} -1.00000 q^{16} +5.24723 q^{17} +(-2.95680 - 0.507306i) q^{18} +(-2.41216 - 2.41216i) q^{19} +(-0.428520 - 0.428520i) q^{20} +(1.25636 - 0.399317i) q^{21} +4.20241 q^{22} -1.86661 q^{23} +(-0.524648 - 1.65068i) q^{24} +4.63274i q^{25} +(-0.713876 - 5.14688i) q^{27} +(0.538189 + 0.538189i) q^{28} -8.70629i q^{29} +(0.482527 - 0.932171i) q^{30} +(2.68240 + 2.68240i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.20478 + 6.93684i) q^{33} +(-3.71035 + 3.71035i) q^{34} +0.461249i q^{35} +(2.44949 - 1.73205i) q^{36} +(-4.15628 + 4.15628i) q^{37} +3.41130 q^{38} +0.606018 q^{40} +(-6.27128 + 6.27128i) q^{41} +(-0.606018 + 1.17074i) q^{42} +1.95035i q^{43} +(-2.97155 + 2.97155i) q^{44} +(1.79187 + 0.307437i) q^{45} +(1.31989 - 1.31989i) q^{46} +(-5.73474 - 5.73474i) q^{47} +(1.53819 + 0.796225i) q^{48} +6.42071i q^{49} +(-3.27584 - 3.27584i) q^{50} +(-8.07123 - 4.17798i) q^{51} -9.01501i q^{53} +(4.14418 + 3.13461i) q^{54} -2.54674 q^{55} -0.761114 q^{56} +(1.78973 + 5.63097i) q^{57} +(6.15628 + 6.15628i) q^{58} +(-6.10925 - 6.10925i) q^{59} +(0.317946 + 1.00034i) q^{60} -8.13061 q^{61} -3.79348 q^{62} +(-2.25046 - 0.386118i) q^{63} +1.00000i q^{64} +(-6.46410 - 3.34607i) q^{66} +(-0.0740874 - 0.0740874i) q^{67} -5.24723i q^{68} +(2.87120 + 1.48624i) q^{69} +(-0.326152 - 0.326152i) q^{70} +(-7.37536 + 7.37536i) q^{71} +(-0.507306 + 2.95680i) q^{72} +(-5.57806 + 5.57806i) q^{73} -5.87787i q^{74} +(3.68871 - 7.12603i) q^{75} +(-2.41216 + 2.41216i) q^{76} +3.19851 q^{77} -13.5805 q^{79} +(-0.428520 + 0.428520i) q^{80} +(-3.00000 + 8.48528i) q^{81} -8.86892i q^{82} +(-0.996926 + 0.996926i) q^{83} +(-0.399317 - 1.25636i) q^{84} +(2.24854 - 2.24854i) q^{85} +(-1.37910 - 1.37910i) q^{86} +(-6.93217 + 13.3919i) q^{87} -4.20241i q^{88} +(-4.62980 - 4.62980i) q^{89} +(-1.48444 + 1.04965i) q^{90} +1.86661i q^{92} +(-1.99024 - 6.26182i) q^{93} +8.11015 q^{94} -2.06731 q^{95} +(-1.65068 + 0.524648i) q^{96} +(-11.1369 - 11.1369i) q^{97} +(-4.54012 - 4.54012i) q^{98} +(2.13191 - 12.4257i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{7} + 24 q^{15} - 16 q^{16} - 32 q^{19} + 24 q^{21} - 16 q^{28} - 16 q^{31} - 24 q^{33} - 24 q^{34} + 8 q^{37} + 48 q^{45} + 48 q^{55} + 24 q^{57} + 24 q^{58} + 24 q^{60} + 48 q^{61} - 48 q^{66}+ \cdots - 16 q^{97}+O(q^{100}) $ 16 * q + 16 * q^7 + 24 * q^15 - 16 * q^16 - 32 * q^19 + 24 * q^21 - 16 * q^28 - 16 * q^31 - 24 * q^33 - 24 * q^34 + 8 * q^37 + 48 * q^45 + 48 * q^55 + 24 * q^57 + 24 * q^58 + 24 * q^60 + 48 * q^61 - 48 * q^66 - 32 * q^67 - 56 * q^73 - 32 * q^76 - 96 * q^79 - 48 * q^81 - 24 * q^84 - 24 * q^85 - 96 * q^87 - 48 * q^93 + 48 * q^94 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.53819	−	0.796225i	−0.888074	−	0.459701i
$3$	−1.53819	−	0.796225i	−0.888074	−	0.459701i
$4$		−	1.00000i		−	0.500000i
$5$	0.428520	−	0.428520i	0.191640	−	0.191640i	−0.604765	−	0.796404i	$-0.706733\pi$
$5$	0.428520	−	0.428520i	0.191640	−	0.191640i	0.796404	+	0.604765i	$0.206733\pi$
$6$	1.65068	−	0.524648i	0.673887	−	0.214186i
$7$	−0.538189	+	0.538189i	−0.203416	+	0.203416i	−0.801462	−	0.598046i	$-0.795944\pi$
$7$	−0.538189	+	0.538189i	−0.203416	+	0.203416i	0.598046	+	0.801462i	$0.295944\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.73205	+	2.44949i	0.577350	+	0.816497i
$10$			0.606018i			0.191640i
$11$	−2.97155	−	2.97155i	−0.895957	−	0.895957i	0.0991187	−	0.995076i	$-0.468398\pi$
$11$	−2.97155	−	2.97155i	−0.895957	−	0.895957i	−0.995076	+	0.0991187i	$0.968398\pi$
$12$	−0.796225	+	1.53819i	−0.229850	+	0.444037i
$13$		0			0
$13$		0			0
$14$		−	0.761114i		−	0.203416i
$15$	−1.00034	+	0.317946i	−0.258287	+	0.0820933i
$16$	−1.00000			−0.250000
$17$	5.24723			1.27264			0.636320	−	0.771425i	$-0.280456\pi$
$17$	5.24723			1.27264			0.636320	+	0.771425i	$0.280456\pi$
$18$	−2.95680	−	0.507306i	−0.696923	−	0.119573i
$19$	−2.41216	−	2.41216i	−0.553387	−	0.553387i	0.374030	−	0.927417i	$-0.377976\pi$
$19$	−2.41216	−	2.41216i	−0.553387	−	0.553387i	−0.927417	+	0.374030i	$0.877976\pi$
$20$	−0.428520	−	0.428520i	−0.0958199	−	0.0958199i
$21$	1.25636	−	0.399317i	0.274159	−	0.0871381i
$22$	4.20241			0.895957
$23$	−1.86661			−0.389216			−0.194608	−	0.980881i	$-0.562343\pi$
$23$	−1.86661			−0.389216			−0.194608	+	0.980881i	$0.562343\pi$
$24$	−0.524648	−	1.65068i	−0.107093	−	0.336944i
$25$			4.63274i			0.926548i
$26$		0			0
$27$	−0.713876	−	5.14688i	−0.137386	−	0.990518i
$28$	0.538189	+	0.538189i	0.101708	+	0.101708i
$29$		−	8.70629i		−	1.61672i	−0.588690	−	0.808359i	$-0.700356\pi$
$29$		−	8.70629i		−	1.61672i	0.588690	−	0.808359i	$-0.299644\pi$
$30$	0.482527	−	0.932171i	0.0880970	−	0.170190i
$31$	2.68240	+	2.68240i	0.481773	+	0.481773i	0.905697	−	0.423925i	$-0.139348\pi$
$31$	2.68240	+	2.68240i	0.481773	+	0.481773i	−0.423925	+	0.905697i	$0.639348\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.20478	+	6.93684i	0.383804	+	1.20755i
$34$	−3.71035	+	3.71035i	−0.636320	+	0.636320i
$35$			0.461249i			0.0779653i
$36$	2.44949	−	1.73205i	0.408248	−	0.288675i
$37$	−4.15628	+	4.15628i	−0.683288	+	0.683288i	−0.960740	−	0.277452i	$-0.910510\pi$
$37$	−4.15628	+	4.15628i	−0.683288	+	0.683288i	0.277452	+	0.960740i	$0.410510\pi$
$38$	3.41130			0.553387
$39$		0			0
$40$	0.606018			0.0958199
$41$	−6.27128	+	6.27128i	−0.979409	+	0.979409i	−0.999792	−	0.0203836i	$-0.993511\pi$
$41$	−6.27128	+	6.27128i	−0.979409	+	0.979409i	0.0203836	+	0.999792i	$0.493511\pi$
$42$	−0.606018	+	1.17074i	−0.0935107	+	0.180649i
$43$			1.95035i			0.297425i	0.988880	+	0.148712i	$0.0475129\pi$
$43$			1.95035i			0.297425i	−0.988880	+	0.148712i	$0.952487\pi$
$44$	−2.97155	+	2.97155i	−0.447978	+	0.447978i
$45$	1.79187	+	0.307437i	0.267117	+	0.0458300i
$46$	1.31989	−	1.31989i	0.194608	−	0.194608i
$47$	−5.73474	−	5.73474i	−0.836498	−	0.836498i	0.151898	−	0.988396i	$-0.451461\pi$
$47$	−5.73474	−	5.73474i	−0.836498	−	0.836498i	−0.988396	+	0.151898i	$0.951461\pi$
$48$	1.53819	+	0.796225i	0.222018	+	0.114925i
$49$			6.42071i			0.917244i
$50$	−3.27584	−	3.27584i	−0.463274	−	0.463274i
$51$	−8.07123	−	4.17798i	−1.13020	−	0.585034i
$52$		0			0
$53$		−	9.01501i		−	1.23831i	−0.785270	−	0.619153i	$-0.787476\pi$
$53$		−	9.01501i		−	1.23831i	0.785270	−	0.619153i	$-0.212524\pi$
$54$	4.14418	+	3.13461i	0.563952	+	0.426566i
$55$	−2.54674			−0.343402
$56$	−0.761114			−0.101708
$57$	1.78973	+	5.63097i	0.237056	+	0.745841i
$58$	6.15628	+	6.15628i	0.808359	+	0.808359i
$59$	−6.10925	−	6.10925i	−0.795357	−	0.795357i	0.187002	−	0.982359i	$-0.440123\pi$
$59$	−6.10925	−	6.10925i	−0.795357	−	0.795357i	−0.982359	+	0.187002i	$0.940123\pi$
$60$	0.317946	+	1.00034i	0.0410467	+	0.129144i
$61$	−8.13061			−1.04102			−0.520509	−	0.853856i	$-0.674258\pi$
$61$	−8.13061			−1.04102			−0.520509	+	0.853856i	$0.674258\pi$
$62$	−3.79348			−0.481773
$63$	−2.25046	−	0.386118i	−0.283531	−	0.0486463i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−6.46410	−	3.34607i	−0.795676	−	0.411872i
$67$	−0.0740874	−	0.0740874i	−0.00905121	−	0.00905121i	0.702567	−	0.711618i	$-0.252037\pi$
$67$	−0.0740874	−	0.0740874i	−0.00905121	−	0.00905121i	−0.711618	+	0.702567i	$0.752037\pi$
$68$		−	5.24723i		−	0.636320i
$69$	2.87120	+	1.48624i	0.345652	+	0.178923i
$70$	−0.326152	−	0.326152i	−0.0389827	−	0.0389827i
$71$	−7.37536	+	7.37536i	−0.875294	+	0.875294i	−0.993043	−	0.117749i	$-0.962432\pi$
$71$	−7.37536	+	7.37536i	−0.875294	+	0.875294i	0.117749	+	0.993043i	$0.462432\pi$
$72$	−0.507306	+	2.95680i	−0.0597866	+	0.348462i
$73$	−5.57806	+	5.57806i	−0.652863	+	0.652863i	−0.953681	−	0.300819i	$-0.902740\pi$
$73$	−5.57806	+	5.57806i	−0.652863	+	0.652863i	0.300819	+	0.953681i	$0.402740\pi$
$74$		−	5.87787i		−	0.683288i
$75$	3.68871	−	7.12603i	0.425935	−	0.822843i
$76$	−2.41216	+	2.41216i	−0.276693	+	0.276693i
$77$	3.19851			0.364505
$78$		0			0
$79$	−13.5805			−1.52793			−0.763963	−	0.645260i	$-0.776749\pi$
$79$	−13.5805			−1.52793			−0.763963	+	0.645260i	$0.776749\pi$
$80$	−0.428520	+	0.428520i	−0.0479100	+	0.0479100i
$81$	−3.00000	+	8.48528i	−0.333333	+	0.942809i
$82$		−	8.86892i		−	0.979409i
$83$	−0.996926	+	0.996926i	−0.109427	+	0.109427i	−0.759700	−	0.650273i	$-0.774654\pi$
$83$	−0.996926	+	0.996926i	−0.109427	+	0.109427i	0.650273	+	0.759700i	$0.274654\pi$
$84$	−0.399317	−	1.25636i	−0.0435690	−	0.137080i
$85$	2.24854	−	2.24854i	0.243889	−	0.243889i
$86$	−1.37910	−	1.37910i	−0.148712	−	0.148712i
$87$	−6.93217	+	13.3919i	−0.743207	+	1.43577i
$88$		−	4.20241i		−	0.447978i
$89$	−4.62980	−	4.62980i	−0.490758	−	0.490758i	0.417787	−	0.908545i	$-0.362806\pi$
$89$	−4.62980	−	4.62980i	−0.490758	−	0.490758i	−0.908545	+	0.417787i	$0.862806\pi$
$90$	−1.48444	+	1.04965i	−0.156473	+	0.110643i
$91$		0			0
$92$			1.86661i			0.194608i
$93$	−1.99024	−	6.26182i	−0.206378	−	0.649321i
$94$	8.11015			0.836498
$95$	−2.06731			−0.212102
$96$	−1.65068	+	0.524648i	−0.168472	+	0.0535466i
$97$	−11.1369	−	11.1369i	−1.13078	−	1.13078i	−0.990048	−	0.140730i	$-0.955055\pi$
$97$	−11.1369	−	11.1369i	−1.13078	−	1.13078i	−0.140730	−	0.990048i	$-0.544945\pi$
$98$	−4.54012	−	4.54012i	−0.458622	−	0.458622i
$99$	2.13191	−	12.4257i	0.214265	−	1.24883i
$100$	4.63274			0.463274
$101$	3.27260			0.325636			0.162818	−	0.986656i	$-0.447942\pi$
$101$	3.27260			0.325636			0.162818	+	0.986656i	$0.447942\pi$
$102$	8.66150	−	2.75295i	0.857616	−	0.272582i
$103$		−	4.79880i		−	0.472840i	−0.971651	−	0.236420i	$-0.924026\pi$
$103$		−	4.79880i		−	0.472840i	0.971651	−	0.236420i	$-0.0759741\pi$
$104$		0			0
$105$	0.367258	−	0.709488i	0.0358407	−	0.0692390i
$106$	6.37457	+	6.37457i	0.619153	+	0.619153i
$107$		−	3.12505i		−	0.302110i	−0.988525	−	0.151055i	$-0.951733\pi$
$107$		−	3.12505i		−	0.302110i	0.988525	−	0.151055i	$-0.0482671\pi$
$108$	−5.14688	+	0.713876i	−0.495259	+	0.0686928i
$109$	0.913996	+	0.913996i	0.0875449	+	0.0875449i	0.749523	−	0.661978i	$-0.230283\pi$
$109$	0.913996	+	0.913996i	0.0875449	+	0.0875449i	−0.661978	+	0.749523i	$0.730283\pi$
$110$	1.80082	−	1.80082i	0.171701	−	0.171701i
$111$	9.70248	−	3.08381i	0.920918	−	0.292702i
$112$	0.538189	−	0.538189i	0.0508541	−	0.0508541i
$113$		−	6.97128i		−	0.655802i	−0.944712	−	0.327901i	$-0.893659\pi$
$113$		−	6.97128i		−	0.655802i	0.944712	−	0.327901i	$-0.106341\pi$
$114$	−5.24723	−	2.71617i	−0.491448	−	0.254392i
$115$	−0.799880	+	0.799880i	−0.0745892	+	0.0745892i
$116$	−8.70629			−0.808359
$117$		0			0
$118$	8.63979			0.795357
$119$	−2.82400	+	2.82400i	−0.258876	+	0.258876i
$120$	−0.932171	−	0.482527i	−0.0850952	−	0.0440485i
$121$			6.66025i			0.605478i
$122$	5.74921	−	5.74921i	0.520509	−	0.520509i
$123$	14.6398	−	4.65306i	1.32002	−	0.419552i
$124$	2.68240	−	2.68240i	0.240886	−	0.240886i
$125$	4.12782	+	4.12782i	0.369203	+	0.369203i
$126$	1.86434	−	1.31829i	0.166089	−	0.117442i
$127$			2.23497i			0.198321i	0.995071	+	0.0991607i	$0.0316158\pi$
$127$			2.23497i			0.198321i	−0.995071	+	0.0991607i	$0.968384\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	1.55291	−	3.00000i	0.136726	−	0.264135i
$130$		0			0
$131$			22.0856i			1.92963i	0.262938	+	0.964813i	$0.415308\pi$
$131$			22.0856i			1.92963i	−0.262938	+	0.964813i	$0.584692\pi$
$132$	6.93684	−	2.20478i	0.603774	−	0.191902i
$133$	2.59639			0.225136
$134$	0.104775			0.00905121
$135$	−2.51145	−	1.89963i	−0.216151	−	0.163494i
$136$	3.71035	+	3.71035i	0.318160	+	0.318160i
$137$	−7.05984	−	7.05984i	−0.603162	−	0.603162i	0.337988	−	0.941150i	$-0.390254\pi$
$137$	−7.05984	−	7.05984i	−0.603162	−	0.603162i	−0.941150	+	0.337988i	$0.890254\pi$
$138$	−3.08118	+	0.979314i	−0.262287	+	0.0833647i
$139$	−3.76503			−0.319346			−0.159673	−	0.987170i	$-0.551044\pi$
$139$	−3.76503			−0.319346			−0.159673	+	0.987170i	$0.551044\pi$
$140$	0.461249			0.0389827
$141$	4.25497	+	13.3873i	0.358333	+	1.12741i
$142$		−	10.4303i		−	0.875294i
$143$		0			0
$144$	−1.73205	−	2.44949i	−0.144338	−	0.204124i
$145$	−3.73082	−	3.73082i	−0.309828	−	0.309828i
$146$		−	7.88857i		−	0.652863i
$147$	5.11233	−	9.87626i	0.421658	−	0.814580i
$148$	4.15628	+	4.15628i	0.341644	+	0.341644i
$149$	−6.17093	+	6.17093i	−0.505542	+	0.505542i	−0.913155	−	0.407613i	$-0.866361\pi$
$149$	−6.17093	+	6.17093i	−0.505542	+	0.505542i	0.407613	+	0.913155i	$0.366361\pi$
$150$	2.43056	+	7.64717i	0.198454	+	0.624389i
$151$	17.3671	−	17.3671i	1.41331	−	1.41331i	0.681429	−	0.731885i	$-0.261359\pi$
$151$	17.3671	−	17.3671i	1.41331	−	1.41331i	0.731885	−	0.681429i	$-0.238641\pi$
$152$		−	3.41130i		−	0.276693i
$153$	9.08847	+	12.8530i	0.734759	+	1.03911i
$154$	−2.26169	+	2.26169i	−0.182252	+	0.182252i
$155$	2.29892			0.184654
$156$		0			0
$157$	11.0713			0.883589			0.441794	−	0.897116i	$-0.354342\pi$
$157$	11.0713			0.883589			0.441794	+	0.897116i	$0.354342\pi$
$158$	9.60287	−	9.60287i	0.763963	−	0.763963i
$159$	−7.17798	+	13.8668i	−0.569251	+	1.09971i
$160$		−	0.606018i		−	0.0479100i
$161$	1.00459	−	1.00459i	0.0791728	−	0.0791728i
$162$	−3.87868	−	8.12132i	−0.304738	−	0.638071i
$163$	−3.71617	+	3.71617i	−0.291073	+	0.291073i	−0.837504	−	0.546431i	$-0.815986\pi$
$163$	−3.71617	+	3.71617i	−0.291073	+	0.291073i	0.546431	+	0.837504i	$0.315986\pi$
$164$	6.27128	+	6.27128i	0.489704	+	0.489704i
$165$	3.91736	+	2.02778i	0.304966	+	0.157862i
$166$		−	1.40987i		−	0.109427i
$167$	11.1219	+	11.1219i	0.860635	+	0.860635i	0.991412	−	0.130777i	$-0.0417471\pi$
$167$	11.1219	+	11.1219i	0.860635	+	0.860635i	−0.130777	+	0.991412i	$0.541747\pi$
$168$	1.17074	+	0.606018i	0.0903244	+	0.0467553i
$169$		0			0
$170$			3.17992i			0.243889i
$171$	1.73057	−	10.0865i	0.132340	−	0.771336i
$172$	1.95035			0.148712
$173$	−5.42372			−0.412358			−0.206179	−	0.978514i	$-0.566103\pi$
$173$	−5.42372			−0.412358			−0.206179	+	0.978514i	$0.566103\pi$
$174$	−4.56774	−	14.3713i	−0.346279	−	1.08949i
$175$	−2.49329	−	2.49329i	−0.188475	−	0.188475i
$176$	2.97155	+	2.97155i	0.223989	+	0.223989i
$177$	4.53284	+	14.2615i	0.340709	+	1.07196i
$178$	6.54753			0.490758
$179$	−10.3808			−0.775900			−0.387950	−	0.921680i	$-0.626817\pi$
$179$	−10.3808			−0.775900			−0.387950	+	0.921680i	$0.626817\pi$
$180$	0.307437	−	1.79187i	0.0229150	−	0.133558i
$181$			11.1172i			0.826335i	0.910655	+	0.413167i	$0.135578\pi$
$181$			11.1172i			0.826335i	−0.910655	+	0.413167i	$0.864422\pi$
$182$		0			0
$183$	12.5064	+	6.47380i	0.924501	+	0.478557i
$184$	−1.31989	−	1.31989i	−0.0973039	−	0.0973039i
$185$			3.56209i			0.261890i
$186$	5.83509	+	3.02047i	0.427850	+	0.221471i
$187$	−15.5924	−	15.5924i	−1.14023	−	1.14023i
$188$	−5.73474	+	5.73474i	−0.418249	+	0.418249i
$189$	3.15419	+	2.38579i	0.229434	+	0.173541i
$190$	1.46181	−	1.46181i	0.106051	−	0.106051i
$191$		−	5.73244i		−	0.414785i	−0.978258	−	0.207392i	$-0.933502\pi$
$191$		−	5.73244i		−	0.414785i	0.978258	−	0.207392i	$-0.0664977\pi$
$192$	0.796225	−	1.53819i	0.0574626	−	0.111009i
$193$	8.02170	−	8.02170i	0.577414	−	0.577414i	−0.356776	−	0.934190i	$-0.616124\pi$
$193$	8.02170	−	8.02170i	0.577414	−	0.577414i	0.934190	+	0.356776i	$0.116124\pi$
$194$	15.7499			1.13078
$195$		0			0
$196$	6.42071			0.458622
$197$	−3.31151	+	3.31151i	−0.235935	+	0.235935i	−0.815165	−	0.579229i	$-0.803354\pi$
$197$	−3.31151	+	3.31151i	−0.235935	+	0.235935i	0.579229	+	0.815165i	$0.303354\pi$
$198$	7.27879	+	10.2938i	0.517281	+	0.731546i
$199$			12.9027i			0.914648i	0.889300	+	0.457324i	$0.151192\pi$
$199$			12.9027i			0.914648i	−0.889300	+	0.457324i	$0.848808\pi$
$200$	−3.27584	+	3.27584i	−0.231637	+	0.231637i
$201$	0.0549702	+	0.172951i	0.00387730	+	0.0121990i
$202$	−2.31408	+	2.31408i	−0.162818	+	0.162818i
$203$	4.68563	+	4.68563i	0.328867	+	0.328867i
$204$	−4.17798	+	8.07123i	−0.292517	+	0.565099i
$205$			5.37473i			0.375387i
$206$	3.39327	+	3.39327i	0.236420	+	0.236420i
$207$	−3.23307	−	4.57225i	−0.224714	−	0.317793i
$208$		0			0
$209$			14.3357i			0.991621i
$210$	0.241993	+	0.761375i	0.0166991	+	0.0525399i
$211$	−5.27958			−0.363461			−0.181731	−	0.983348i	$-0.558170\pi$
$211$	−5.27958			−0.363461			−0.181731	+	0.983348i	$0.558170\pi$
$212$	−9.01501			−0.619153
$213$	17.2171	−	5.47225i	1.17970	−	0.374952i
$214$	2.20975	+	2.20975i	0.151055	+	0.151055i
$215$	0.835761	+	0.835761i	0.0569985	+	0.0569985i
$216$	3.13461	−	4.14418i	0.213283	−	0.281976i
$217$	−2.88727			−0.196001
$218$	−1.29259			−0.0875449
$219$	13.0215	−	4.13872i	0.879912	−	0.279669i
$220$			2.54674i			0.171701i
$221$		0			0
$222$	−4.68011	+	9.04127i	−0.314108	+	0.606810i
$223$	−2.51039	−	2.51039i	−0.168108	−	0.168108i	0.618039	−	0.786147i	$-0.287927\pi$
$223$	−2.51039	−	2.51039i	−0.168108	−	0.168108i	−0.786147	+	0.618039i	$0.787927\pi$
$224$			0.761114i			0.0508541i
$225$	−11.3479	+	8.02414i	−0.756524	+	0.534943i
$226$	4.92944	+	4.92944i	0.327901	+	0.327901i
$227$	3.55443	−	3.55443i	0.235916	−	0.235916i	−0.579241	−	0.815157i	$-0.696651\pi$
$227$	3.55443	−	3.55443i	0.235916	−	0.235916i	0.815157	+	0.579241i	$0.196651\pi$
$228$	5.63097	−	1.78973i	0.372920	−	0.118528i
$229$	−11.3889	+	11.3889i	−0.752602	+	0.752602i	−0.974964	−	0.222362i	$-0.928623\pi$
$229$	−11.3889	+	11.3889i	−0.752602	+	0.752602i	0.222362	+	0.974964i	$0.428623\pi$
$230$		−	1.13120i		−	0.0745892i
$231$	−4.91992	−	2.54674i	−0.323707	−	0.167563i
$232$	6.15628	−	6.15628i	0.404180	−	0.404180i
$233$	22.3807			1.46621			0.733103	−	0.680117i	$-0.238071\pi$
$233$	22.3807			1.46621			0.733103	+	0.680117i	$0.238071\pi$
$234$		0			0
$235$	−4.91490			−0.320613
$236$	−6.10925	+	6.10925i	−0.397679	+	0.397679i
$237$	20.8894	+	10.8131i	1.35691	+	0.702389i
$238$		−	3.99374i		−	0.258876i
$239$	6.08236	−	6.08236i	0.393435	−	0.393435i	−0.482475	−	0.875910i	$-0.660262\pi$
$239$	6.08236	−	6.08236i	0.393435	−	0.393435i	0.875910	+	0.482475i	$0.160262\pi$
$240$	1.00034	−	0.317946i	0.0645718	−	0.0205233i
$241$	4.34556	−	4.34556i	0.279922	−	0.279922i	−0.553156	−	0.833078i	$-0.686577\pi$
$241$	4.34556	−	4.34556i	0.279922	−	0.279922i	0.833078	+	0.553156i	$0.186577\pi$
$242$	−4.70951	−	4.70951i	−0.302739	−	0.302739i
$243$	11.3708	−	10.6633i	0.729435	−	0.684050i
$244$			8.13061i			0.520509i
$245$	2.75140	+	2.75140i	0.175780	+	0.175780i
$246$	−7.06166	+	13.6421i	−0.450235	+	0.869787i
$247$		0			0
$248$			3.79348i			0.240886i
$249$	2.32724	−	0.739683i	0.147483	−	0.0468755i
$250$	−5.83762			−0.369203
$251$	−12.5562			−0.792538			−0.396269	−	0.918134i	$-0.629695\pi$
$251$	−12.5562			−0.792538			−0.396269	+	0.918134i	$0.629695\pi$
$252$	−0.386118	+	2.25046i	−0.0243231	+	0.141766i
$253$	5.54674	+	5.54674i	0.348720	+	0.348720i
$254$	−1.58036	−	1.58036i	−0.0991607	−	0.0991607i
$255$	−5.24903	+	1.66834i	−0.328707	+	0.104475i
$256$	1.00000			0.0625000
$257$	4.73782			0.295537			0.147768	−	0.989022i	$-0.452791\pi$
$257$	4.73782			0.295537			0.147768	+	0.989022i	$0.452791\pi$
$258$	1.02324	+	3.21940i	0.0637044	+	0.200431i
$259$		−	4.47373i		−	0.277984i
$260$		0			0
$261$	21.3260	−	15.0797i	1.32004	−	0.933413i
$262$	−15.6169	−	15.6169i	−0.964813	−	0.964813i
$263$			5.66894i			0.349562i	0.984607	+	0.174781i	$0.0559218\pi$
$263$			5.66894i			0.349562i	−0.984607	+	0.174781i	$0.944078\pi$
$264$	−3.34607	+	6.46410i	−0.205936	+	0.397838i
$265$	−3.86311	−	3.86311i	−0.237309	−	0.237309i
$266$	−1.83593	+	1.83593i	−0.112568	+	0.112568i
$267$	3.43514	+	10.8079i	0.210227	+	0.661431i
$268$	−0.0740874	+	0.0740874i	−0.00452561	+	0.00452561i
$269$		−	7.30591i		−	0.445449i	−0.974881	−	0.222725i	$-0.928505\pi$
$269$		−	7.30591i		−	0.445449i	0.974881	−	0.222725i	$-0.0714951\pi$
$270$	3.11910	−	0.432622i	0.189823	−	0.0263285i
$271$	17.3439	−	17.3439i	1.05356	−	1.05356i	0.0550829	−	0.998482i	$-0.482458\pi$
$271$	17.3439	−	17.3439i	1.05356	−	1.05356i	0.998482	−	0.0550829i	$-0.0175423\pi$
$272$	−5.24723			−0.318160
$273$		0			0
$274$	9.98412			0.603162
$275$	13.7664	−	13.7664i	0.830147	−	0.830147i
$276$	1.48624	−	2.87120i	0.0894614	−	0.172826i
$277$		−	8.74626i		−	0.525512i	−0.964862	−	0.262756i	$-0.915369\pi$
$277$		−	8.74626i		−	0.525512i	0.964862	−	0.262756i	$-0.0846314\pi$
$278$	2.66228	−	2.66228i	0.159673	−	0.159673i
$279$	−1.92446	+	11.2165i	−0.115214	+	0.671517i
$280$	−0.326152	+	0.326152i	−0.0194913	+	0.0194913i
$281$	9.49571	+	9.49571i	0.566467	+	0.566467i	0.931137	−	0.364670i	$-0.118818\pi$
$281$	9.49571	+	9.49571i	0.566467	+	0.566467i	−0.364670	+	0.931137i	$0.618818\pi$
$282$	−12.4749	−	6.45750i	−0.742872	−	0.384539i
$283$		−	31.4361i		−	1.86868i	−0.356378	−	0.934342i	$-0.615988\pi$
$283$		−	31.4361i		−	1.86868i	0.356378	−	0.934342i	$-0.384012\pi$
$284$	7.37536	+	7.37536i	0.437647	+	0.437647i
$285$	3.17992	+	1.64605i	0.188362	+	0.0975034i
$286$		0			0
$287$		−	6.75026i		−	0.398455i
$288$	2.95680	+	0.507306i	0.174231	+	0.0298933i
$289$	10.5334			0.619614
$290$	5.27617			0.309828
$291$	8.26316	+	25.9981i	0.484395	+	1.52403i
$292$	5.57806	+	5.57806i	0.326431	+	0.326431i
$293$	−1.48128	−	1.48128i	−0.0865371	−	0.0865371i	0.662513	−	0.749050i	$-0.269490\pi$
$293$	−1.48128	−	1.48128i	−0.0865371	−	0.0865371i	−0.749050	+	0.662513i	$0.769490\pi$
$294$	3.36861	+	10.5985i	0.196461	+	0.618119i
$295$	−5.23587			−0.304844
$296$	−5.87787			−0.341644
$297$	−13.1729	+	17.4155i	−0.764370	+	1.01055i
$298$		−	8.72701i		−	0.505542i
$299$		0			0
$300$	−7.12603	−	3.68871i	−0.411422	−	0.212968i
$301$	−1.04965	−	1.04965i	−0.0605011	−	0.0605011i
$302$			24.5608i			1.41331i
$303$	−5.03388	−	2.60573i	−0.289189	−	0.149695i
$304$	2.41216	+	2.41216i	0.138347	+	0.138347i
$305$	−3.48413	+	3.48413i	−0.199501	+	0.199501i
$306$	−15.5150	−	2.66195i	−0.886933	−	0.152174i
$307$	−1.91340	+	1.91340i	−0.109203	+	0.109203i	−0.759597	−	0.650394i	$-0.774604\pi$
$307$	−1.91340	+	1.91340i	−0.109203	+	0.109203i	0.650394	+	0.759597i	$0.274604\pi$
$308$		−	3.19851i		−	0.182252i
$309$	−3.82093	+	7.38147i	−0.217365	+	0.419917i
$310$	−1.62558	+	1.62558i	−0.0923268	+	0.0923268i
$311$	−7.19354			−0.407908			−0.203954	−	0.978980i	$-0.565379\pi$
$311$	−7.19354			−0.407908			−0.203954	+	0.978980i	$0.565379\pi$
$312$		0			0
$313$	−14.6520			−0.828180			−0.414090	−	0.910236i	$-0.635900\pi$
$313$	−14.6520			−0.828180			−0.414090	+	0.910236i	$0.635900\pi$
$314$	−7.82861	+	7.82861i	−0.441794	+	0.441794i
$315$	−1.12983	+	0.798907i	−0.0636584	+	0.0450133i
$316$			13.5805i			0.763963i
$317$	3.93077	−	3.93077i	0.220774	−	0.220774i	−0.588050	−	0.808824i	$-0.700104\pi$
$317$	3.93077	−	3.93077i	0.220774	−	0.220774i	0.808824	+	0.588050i	$0.200104\pi$
$318$	−4.72970	−	14.8809i	−0.265229	−	0.834479i
$319$	−25.8712	+	25.8712i	−1.44851	+	1.44851i
$320$	0.428520	+	0.428520i	0.0239550	+	0.0239550i
$321$	−2.48825	+	4.80692i	−0.138880	+	0.268296i
$322$			1.42071i			0.0791728i
$323$	−12.6571	−	12.6571i	−0.704262	−	0.704262i
$324$	8.48528	+	3.00000i	0.471405	+	0.166667i
$325$		0			0
$326$		−	5.25545i		−	0.291073i
$327$	−0.678152	−	2.13364i	−0.0375019	−	0.117991i
$328$	−8.86892			−0.489704
$329$	6.17275			0.340315
$330$	−4.20385	+	1.33614i	−0.231414	+	0.0735521i
$331$	13.9674	+	13.9674i	0.767720	+	0.767720i	0.977705	−	0.209985i	$-0.0673414\pi$
$331$	13.9674	+	13.9674i	0.767720	+	0.767720i	−0.209985	+	0.977705i	$0.567341\pi$
$332$	0.996926	+	0.996926i	0.0547134	+	0.0547134i
$333$	−17.3797	−	2.98188i	−0.952399	−	0.163406i
$334$	−15.7287			−0.860635
$335$	−0.0634958			−0.00346915
$336$	−1.25636	+	0.399317i	−0.0685398	+	0.0217845i
$337$			16.3889i			0.892762i	0.894843	+	0.446381i	$0.147287\pi$
$337$			16.3889i			0.892762i	−0.894843	+	0.446381i	$0.852713\pi$
$338$		0			0
$339$	−5.55071	+	10.7231i	−0.301473	+	0.582401i
$340$	−2.24854	−	2.24854i	−0.121944	−	0.121944i
$341$		−	15.9418i		−	0.863295i
$342$	5.90855	+	8.35596i	0.319498	+	0.451838i
$343$	−7.22288	−	7.22288i	−0.389999	−	0.389999i
$344$	−1.37910	+	1.37910i	−0.0743562	+	0.0743562i
$345$	1.86725	−	0.593482i	0.100529	−	0.0319520i
$346$	3.83515	−	3.83515i	0.206179	−	0.206179i
$347$		−	21.6243i		−	1.16085i	−0.814312	−	0.580427i	$-0.802886\pi$
$347$		−	21.6243i		−	1.16085i	0.814312	−	0.580427i	$-0.197114\pi$
$348$	13.3919	+	6.93217i	0.717883	+	0.371603i
$349$	1.37688	−	1.37688i	0.0737029	−	0.0737029i	−0.669294	−	0.742997i	$-0.733403\pi$
$349$	1.37688	−	1.37688i	0.0737029	−	0.0737029i	0.742997	+	0.669294i	$0.233403\pi$
$350$	3.52605			0.188475
$351$		0			0
$352$	−4.20241			−0.223989
$353$	16.4570	−	16.4570i	0.875919	−	0.875919i	−0.117191	−	0.993109i	$-0.537389\pi$
$353$	16.4570	−	16.4570i	0.875919	−	0.875919i	0.993109	+	0.117191i	$0.0373888\pi$
$354$	−13.2896	−	6.87922i	−0.706336	−	0.365626i
$355$			6.32097i			0.335482i
$356$	−4.62980	+	4.62980i	−0.245379	+	0.245379i
$357$	6.59239	−	2.09531i	0.348906	−	0.110895i
$358$	7.34036	−	7.34036i	0.387950	−	0.387950i
$359$	−15.8859	−	15.8859i	−0.838428	−	0.838428i	0.150224	−	0.988652i	$-0.452000\pi$
$359$	−15.8859	−	15.8859i	−0.838428	−	0.838428i	−0.988652	+	0.150224i	$0.952000\pi$
$360$	1.04965	+	1.48444i	0.0553216	+	0.0782366i
$361$		−	7.36300i		−	0.387526i
$362$	−7.86104	−	7.86104i	−0.413167	−	0.413167i
$363$	5.30306	−	10.2447i	0.278339	−	0.537709i
$364$		0			0
$365$			4.78062i			0.250229i
$366$	−13.4210	+	4.26571i	−0.701529	+	0.222972i
$367$	0.601762			0.0314117			0.0157059	−	0.999877i	$-0.495000\pi$
$367$	0.601762			0.0314117			0.0157059	+	0.999877i	$0.495000\pi$
$368$	1.86661			0.0973039
$369$	−26.2236	−	4.49926i	−1.36515	−	0.234222i
$370$	−2.51878	−	2.51878i	−0.130945	−	0.130945i
$371$	4.85178	+	4.85178i	0.251892	+	0.251892i
$372$	−6.26182	+	1.99024i	−0.324660	+	0.103189i
$373$	11.4157			0.591080			0.295540	−	0.955330i	$-0.404500\pi$
$373$	11.4157			0.591080			0.295540	+	0.955330i	$0.404500\pi$
$374$	22.0510			1.14023
$375$	−3.06269	−	9.63604i	−0.158157	−	0.497603i
$376$		−	8.11015i		−	0.418249i
$377$		0			0
$378$	−3.91736	+	0.543341i	−0.201487	+	0.0279465i
$379$	26.5622	+	26.5622i	1.36441	+	1.36441i	0.868211	+	0.496196i	$0.165270\pi$
$379$	26.5622	+	26.5622i	1.36441	+	1.36441i	0.496196	+	0.868211i	$0.334730\pi$
$380$			2.06731i			0.106051i
$381$	1.77954	−	3.43780i	0.0911685	−	0.176124i
$382$	4.05345	+	4.05345i	0.207392	+	0.207392i
$383$	8.93292	−	8.93292i	0.456451	−	0.456451i	−0.441038	−	0.897489i	$-0.645390\pi$
$383$	8.93292	−	8.93292i	0.456451	−	0.456451i	0.897489	+	0.441038i	$0.145390\pi$
$384$	0.524648	+	1.65068i	0.0267733	+	0.0842359i
$385$	1.37063	−	1.37063i	0.0698536	−	0.0698536i
$386$			11.3444i			0.577414i
$387$	−4.77735	+	3.37810i	−0.242846	+	0.171718i
$388$	−11.1369	+	11.1369i	−0.565389	+	0.565389i
$389$	−18.8229			−0.954361			−0.477180	−	0.878805i	$-0.658341\pi$
$389$	−18.8229			−0.954361			−0.477180	+	0.878805i	$0.658341\pi$
$390$		0			0
$391$	−9.79455			−0.495332
$392$	−4.54012	+	4.54012i	−0.229311	+	0.229311i
$393$	17.5851	−	33.9718i	0.887050	−	1.71365i
$394$		−	4.68319i		−	0.235935i
$395$	−5.81951	+	5.81951i	−0.292812	+	0.292812i
$396$	−12.4257	−	2.13191i	−0.624413	−	0.107132i
$397$	8.43859	−	8.43859i	0.423521	−	0.423521i	−0.462893	−	0.886414i	$-0.653189\pi$
$397$	8.43859	−	8.43859i	0.423521	−	0.423521i	0.886414	+	0.462893i	$0.153189\pi$
$398$	−9.12358	−	9.12358i	−0.457324	−	0.457324i
$399$	−3.99374	−	2.06731i	−0.199937	−	0.103495i
$400$		−	4.63274i		−	0.231637i
$401$	17.1270	+	17.1270i	0.855280	+	0.855280i	0.990778	−	0.135497i	$-0.0432632\pi$
$401$	17.1270	+	17.1270i	0.855280	+	0.855280i	−0.135497	+	0.990778i	$0.543263\pi$
$402$	−0.161164	−	0.0834248i	−0.00803815	−	0.00416085i
$403$		0			0
$404$		−	3.27260i		−	0.162818i
$405$	2.35055	+	4.92167i	0.116800	+	0.244560i
$406$	−6.62648			−0.328867
$407$	24.7012			1.22439
$408$	−2.75295	−	8.66150i	−0.136291	−	0.428808i
$409$	−18.9725	−	18.9725i	−0.938128	−	0.938128i	0.0600662	−	0.998194i	$-0.480869\pi$
$409$	−18.9725	−	18.9725i	−0.938128	−	0.938128i	−0.998194	+	0.0600662i	$0.980869\pi$
$410$	−3.80051	−	3.80051i	−0.187694	−	0.187694i
$411$	5.23814	+	16.4806i	0.258379	+	0.812927i
$412$	−4.79880			−0.236420
$413$	6.57587			0.323577
$414$	5.51919	+	0.946944i	0.271253	+	0.0465397i
$415$			0.854405i			0.0419411i
$416$		0			0
$417$	5.79133	+	2.99781i	0.283603	+	0.146804i
$418$	−10.1369	−	10.1369i	−0.495811	−	0.495811i
$419$			10.8367i			0.529409i	0.964330	+	0.264704i	$0.0852743\pi$
$419$			10.8367i			0.529409i	−0.964330	+	0.264704i	$0.914726\pi$
$420$	−0.709488	−	0.367258i	−0.0346195	−	0.0179204i
$421$	22.8984	+	22.8984i	1.11600	+	1.11600i	0.992323	+	0.123676i	$0.0394684\pi$
$421$	22.8984	+	22.8984i	1.11600	+	1.11600i	0.123676	+	0.992323i	$0.460532\pi$
$422$	3.73322	−	3.73322i	0.181731	−	0.181731i
$423$	4.11433	−	23.9801i	0.200045	−	1.16595i
$424$	6.37457	−	6.37457i	0.309577	−	0.309577i
$425$			24.3091i			1.17916i
$426$	−8.30489	+	16.0438i	−0.402373	+	0.777326i
$427$	4.37581	−	4.37581i	0.211760	−	0.211760i
$428$	−3.12505			−0.151055
$429$		0			0
$430$	−1.18195			−0.0569985
$431$	−23.7339	+	23.7339i	−1.14322	+	1.14322i	−0.155362	+	0.987858i	$0.549654\pi$
$431$	−23.7339	+	23.7339i	−1.14322	+	1.14322i	−0.987858	+	0.155362i	$0.950346\pi$
$432$	0.713876	+	5.14688i	0.0343464	+	0.247629i
$433$		−	23.7562i		−	1.14165i	−0.821072	−	0.570825i	$-0.806623\pi$
$433$		−	23.7562i		−	1.14165i	0.821072	−	0.570825i	$-0.193377\pi$
$434$	2.04161	−	2.04161i	0.0980004	−	0.0980004i
$435$	2.76813	+	8.70927i	0.132722	+	0.417578i
$436$	0.913996	−	0.913996i	0.0437725	−	0.0437725i
$437$	4.50256	+	4.50256i	0.215387	+	0.215387i
$438$	−6.28108	+	12.1341i	−0.300122	+	0.579790i
$439$		−	14.8663i		−	0.709532i	−0.934955	−	0.354766i	$-0.884561\pi$
$439$		−	14.8663i		−	0.709532i	0.934955	−	0.354766i	$-0.115439\pi$
$440$	−1.80082	−	1.80082i	−0.0858505	−	0.0858505i
$441$	−15.7275	+	11.1210i	−0.748926	+	0.529571i
$442$		0			0
$443$		−	40.3416i		−	1.91669i	−0.285619	−	0.958343i	$-0.592199\pi$
$443$		−	40.3416i		−	1.91669i	0.285619	−	0.958343i	$-0.407801\pi$
$444$	−3.08381	−	9.70248i	−0.146351	−	0.460459i
$445$	−3.96792			−0.188097
$446$	3.55022			0.168108
$447$	14.4055	−	4.57860i	0.681357	−	0.216560i
$448$	−0.538189	−	0.538189i	−0.0254270	−	0.0254270i
$449$	3.22808	+	3.22808i	0.152343	+	0.152343i	0.779163	−	0.626821i	$-0.215644\pi$
$449$	3.22808	+	3.22808i	0.152343	+	0.152343i	−0.626821	+	0.779163i	$0.715644\pi$
$450$	2.35022	−	13.6981i	0.110790	−	0.645733i
$451$	37.2709			1.75502
$452$	−6.97128			−0.327901
$453$	−40.5420	+	12.8857i	−1.90483	+	0.605425i
$454$			5.02672i			0.235916i
$455$		0			0
$456$	−2.71617	+	5.24723i	−0.127196	+	0.245724i
$457$	18.5918	+	18.5918i	0.869687	+	0.869687i	0.992438	−	0.122750i	$-0.0391714\pi$
$457$	18.5918	+	18.5918i	0.869687	+	0.869687i	−0.122750	+	0.992438i	$0.539171\pi$
$458$		−	16.1064i		−	0.752602i
$459$	−3.74587	−	27.0069i	−0.174842	−	1.26057i
$460$	0.799880	+	0.799880i	0.0372946	+	0.0372946i
$461$	10.6532	−	10.6532i	0.496168	−	0.496168i	−0.414075	−	0.910243i	$-0.635895\pi$
$461$	10.6532	−	10.6532i	0.496168	−	0.496168i	0.910243	+	0.414075i	$0.135895\pi$
$462$	5.27972	−	1.67809i	0.245635	−	0.0780719i
$463$	12.8578	−	12.8578i	0.597552	−	0.597552i	−0.342108	−	0.939661i	$-0.611141\pi$
$463$	12.8578	−	12.8578i	0.597552	−	0.597552i	0.939661	+	0.342108i	$0.111141\pi$
$464$			8.70629i			0.404180i
$465$	−3.53617	−	1.83046i	−0.163986	−	0.0848854i
$466$	−15.8255	+	15.8255i	−0.733103	+	0.733103i
$467$	−12.7104			−0.588168			−0.294084	−	0.955780i	$-0.595015\pi$
$467$	−12.7104			−0.588168			−0.294084	+	0.955780i	$0.595015\pi$
$468$		0			0
$469$	0.0797460			0.00368233
$470$	3.47536	−	3.47536i	0.160306	−	0.160306i
$471$	−17.0298	−	8.81527i	−0.784692	−	0.406186i
$472$		−	8.63979i		−	0.397679i
$473$	5.79555	−	5.79555i	0.266480	−	0.266480i
$474$	−22.4171	+	7.12498i	−1.02965	+	0.327261i
$475$	11.1749	−	11.1749i	0.512739	−	0.512739i
$476$	2.82400	+	2.82400i	0.129438	+	0.129438i
$477$	22.0822	−	15.6145i	1.01107	−	0.714937i
$478$			8.60176i			0.393435i
$479$	−25.3340	−	25.3340i	−1.15754	−	1.15754i	−0.985003	−	0.172535i	$-0.944804\pi$
$479$	−25.3340	−	25.3340i	−1.15754	−	1.15754i	−0.172535	−	0.985003i	$-0.555196\pi$
$480$	−0.482527	+	0.932171i	−0.0220242	+	0.0425476i
$481$		0			0
$482$			6.14555i			0.279922i
$483$	−2.34513	+	0.745370i	−0.106707	+	0.0339155i
$484$	6.66025			0.302739
$485$	−9.54474			−0.433404
$486$	−0.500258	+	15.5804i	−0.0226921	+	0.706743i
$487$	4.75849	+	4.75849i	0.215628	+	0.215628i	0.806653	−	0.591025i	$-0.201277\pi$
$487$	4.75849	+	4.75849i	0.215628	+	0.215628i	−0.591025	+	0.806653i	$0.701277\pi$
$488$	−5.74921	−	5.74921i	−0.260255	−	0.260255i
$489$	8.67507	−	2.75726i	0.392300	−	0.124688i
$490$	−3.89106			−0.175780
$491$	−29.8138			−1.34548			−0.672740	−	0.739879i	$-0.734883\pi$
$491$	−29.8138			−1.34548			−0.672740	+	0.739879i	$0.734883\pi$
$492$	−4.65306	−	14.6398i	−0.209776	−	0.660011i
$493$		−	45.6839i		−	2.05750i
$494$		0			0
$495$	−4.41108	−	6.23821i	−0.198263	−	0.280387i
$496$	−2.68240	−	2.68240i	−0.120443	−	0.120443i
$497$		−	7.93867i		−	0.356098i
$498$	−1.12257	+	2.16864i	−0.0503036	+	0.0971791i
$499$	−25.5487	−	25.5487i	−1.14372	−	1.14372i	−0.987764	−	0.155954i	$-0.950155\pi$
$499$	−25.5487	−	25.5487i	−1.14372	−	1.14372i	−0.155954	−	0.987764i	$-0.549845\pi$
$500$	4.12782	−	4.12782i	0.184602	−	0.184602i
$501$	−8.25202	−	25.9630i	−0.368673	−	1.15994i
$502$	8.87855	−	8.87855i	0.396269	−	0.396269i
$503$			42.5984i			1.89937i	0.313210	+	0.949684i	$0.398596\pi$
$503$			42.5984i			1.89937i	−0.313210	+	0.949684i	$0.601404\pi$
$504$	−1.31829	−	1.86434i	−0.0587212	−	0.0830444i
$505$	1.40238	−	1.40238i	0.0624049	−	0.0624049i
$506$	−7.84427			−0.348720
$507$		0			0
$508$	2.23497			0.0991607
$509$	11.9455	−	11.9455i	0.529477	−	0.529477i	−0.390940	−	0.920416i	$-0.627850\pi$
$509$	11.9455	−	11.9455i	0.529477	−	0.529477i	0.920416	+	0.390940i	$0.127850\pi$
$510$	2.53193	−	4.89131i	0.112116	−	0.216591i
$511$		−	6.00410i		−	0.265606i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−10.6931	+	14.1371i	−0.472112	+	0.624167i
$514$	−3.35014	+	3.35014i	−0.147768	+	0.147768i
$515$	−2.05638	−	2.05638i	−0.0906150	−	0.0906150i
$516$	−3.00000	−	1.55291i	−0.132068	−	0.0683632i
$517$			34.0822i			1.49893i
$518$	3.16340	+	3.16340i	0.138992	+	0.138992i
$519$	8.34271	+	4.31851i	0.366204	+	0.189561i
$520$		0			0
$521$		−	18.8358i		−	0.825213i	−0.910909	−	0.412607i	$-0.864618\pi$
$521$		−	18.8358i		−	0.825213i	0.910909	−	0.412607i	$-0.135382\pi$
$522$	−4.41675	+	25.7427i	−0.193316	+	1.12673i
$523$	−11.9533			−0.522683			−0.261342	−	0.965246i	$-0.584165\pi$
$523$	−11.9533			−0.522683			−0.261342	+	0.965246i	$0.584165\pi$
$524$	22.0856			0.964813
$525$	1.84993	+	5.82037i	0.0807376	+	0.254022i
$526$	−4.00855	−	4.00855i	−0.174781	−	0.174781i
$527$	14.0752	+	14.0752i	0.613123	+	0.613123i
$528$	−2.20478	−	6.93684i	−0.0959509	−	0.301887i
$529$	−19.5158			−0.848511
$530$	5.46326			0.237309
$531$	4.38302	−	25.5461i	0.190207	−	1.10861i
$532$		−	2.59639i		−	0.112568i
$533$		0			0
$534$	−10.0713	−	5.21331i	−0.435829	−	0.225602i
$535$	−1.33915	−	1.33915i	−0.0578964	−	0.0578964i
$536$		−	0.104775i		−	0.00452561i
$537$	15.9677	+	8.26548i	0.689057	+	0.356682i
$538$	5.16606	+	5.16606i	0.222725	+	0.222725i
$539$	19.0795	−	19.0795i	0.821811	−	0.821811i
$540$	−1.89963	+	2.51145i	−0.0817470	+	0.108076i
$541$	−13.7056	+	13.7056i	−0.589250	+	0.589250i	−0.937428	−	0.348179i	$-0.886800\pi$
$541$	−13.7056	+	13.7056i	−0.589250	+	0.589250i	0.348179	+	0.937428i	$0.386800\pi$
$542$			24.5279i			1.05356i
$543$	8.85179	−	17.1003i	0.379867	−	0.733846i
$544$	3.71035	−	3.71035i	0.159080	−	0.159080i
$545$	0.783330			0.0335542
$546$		0			0
$547$	−14.6259			−0.625359			−0.312679	−	0.949859i	$-0.601227\pi$
$547$	−14.6259			−0.625359			−0.312679	+	0.949859i	$0.601227\pi$
$548$	−7.05984	+	7.05984i	−0.301581	+	0.301581i
$549$	−14.0826	−	19.9159i	−0.601032	−	0.849988i
$550$			19.4687i			0.830147i
$551$	−21.0009	+	21.0009i	−0.894670	+	0.894670i
$552$	0.979314	+	3.08118i	0.0416824	+	0.131144i
$553$	7.30888	−	7.30888i	0.310805	−	0.310805i
$554$	6.18454	+	6.18454i	0.262756	+	0.262756i
$555$	2.83623	−	5.47918i	0.120391	−	0.232578i
$556$			3.76503i			0.159673i
$557$	0.855215	+	0.855215i	0.0362366	+	0.0362366i	0.724993	−	0.688756i	$-0.241843\pi$
$557$	0.855215	+	0.855215i	0.0362366	+	0.0362366i	−0.688756	+	0.724993i	$0.741843\pi$
$558$	−6.57050	−	9.29209i	−0.278152	−	0.393366i
$559$		0			0
$560$		−	0.461249i		−	0.0194913i
$561$	11.5690	+	36.3992i	0.488444	+	1.53677i
$562$	−13.4290			−0.566467
$563$	−24.4117			−1.02883			−0.514416	−	0.857541i	$-0.671991\pi$
$563$	−24.4117			−1.02883			−0.514416	+	0.857541i	$0.671991\pi$
$564$	13.3873	−	4.25497i	0.563705	−	0.179167i
$565$	−2.98733	−	2.98733i	−0.125678	−	0.125678i
$566$	22.2287	+	22.2287i	0.934342	+	0.934342i
$567$	−2.95212	−	6.18125i	−0.123977	−	0.259588i
$568$	−10.4303			−0.437647
$569$	5.97665			0.250554			0.125277	−	0.992122i	$-0.460018\pi$
$569$	5.97665			0.250554			0.125277	+	0.992122i	$0.460018\pi$
$570$	−3.41247	+	1.08461i	−0.142933	+	0.0454293i
$571$			35.8068i			1.49847i	0.662307	+	0.749233i	$0.269578\pi$
$571$			35.8068i			1.49847i	−0.662307	+	0.749233i	$0.730422\pi$
$572$		0			0
$573$	−4.56431	+	8.81758i	−0.190677	+	0.368360i
$574$	4.77316	+	4.77316i	0.199228	+	0.199228i
$575$		−	8.64753i		−	0.360627i
$576$	−2.44949	+	1.73205i	−0.102062	+	0.0721688i
$577$	−13.8142	−	13.8142i	−0.575094	−	0.575094i	0.358453	−	0.933548i	$-0.383304\pi$
$577$	−13.8142	−	13.8142i	−0.575094	−	0.575094i	−0.933548	+	0.358453i	$0.883304\pi$
$578$	−7.44826	+	7.44826i	−0.309807	+	0.309807i
$579$	−18.7260	+	5.95181i	−0.778225	+	0.247349i
$580$	−3.73082	+	3.73082i	−0.154914	+	0.154914i
$581$		−	1.07307i		−	0.0445184i
$582$	−24.2263	−	12.5405i	−1.00421	−	0.519820i
$583$	−26.7886	+	26.7886i	−1.10947	+	1.10947i
$584$	−7.88857			−0.326431
$585$		0			0
$586$	2.09484			0.0865371
$587$	−10.9112	+	10.9112i	−0.450353	+	0.450353i	−0.895472	−	0.445119i	$-0.853162\pi$
$587$	−10.9112	+	10.9112i	−0.450353	+	0.450353i	0.445119	+	0.895472i	$0.353162\pi$
$588$	−9.87626	−	5.11233i	−0.407290	−	0.210829i
$589$		−	12.9407i		−	0.533213i
$590$	3.70232	−	3.70232i	0.152422	−	0.152422i
$591$	7.73044	−	2.45702i	0.317988	−	0.101068i
$592$	4.15628	−	4.15628i	0.170822	−	0.170822i
$593$	−19.1066	−	19.1066i	−0.784613	−	0.784613i	0.195992	−	0.980605i	$-0.437207\pi$
$593$	−19.1066	−	19.1066i	−0.784613	−	0.784613i	−0.980605	+	0.195992i	$0.937207\pi$
$594$	−3.00000	−	21.6293i	−0.123091	−	0.887461i
$595$			2.42028i			0.0992218i
$596$	6.17093	+	6.17093i	0.252771	+	0.252771i
$597$	10.2734	−	19.8468i	0.420464	−	0.812275i
$598$		0			0
$599$			15.6579i			0.639764i	0.947457	+	0.319882i	$0.103643\pi$
$599$			15.6579i			0.639764i	−0.947457	+	0.319882i	$0.896357\pi$
$600$	7.64717	−	2.43056i	0.312195	−	0.0992271i
$601$	−13.3171			−0.543217			−0.271609	−	0.962408i	$-0.587556\pi$
$601$	−13.3171			−0.543217			−0.271609	+	0.962408i	$0.587556\pi$
$602$	1.48444			0.0605011
$603$	0.0531532	−	0.309799i	0.00216456	−	0.0126160i
$604$	−17.3671	−	17.3671i	−0.706657	−	0.706657i
$605$	2.85405	+	2.85405i	0.116034	+	0.116034i
$606$	5.40202	−	1.71696i	0.219442	−	0.0697469i
$607$	12.2930			0.498957			0.249479	−	0.968380i	$-0.419741\pi$
$607$	12.2930			0.498957			0.249479	+	0.968380i	$0.419741\pi$
$608$	−3.41130			−0.138347
$609$	−3.47657	−	10.9382i	−0.140878	−	0.443238i
$610$		−	4.92730i		−	0.199501i
$611$		0			0
$612$	12.8530	−	9.08847i	0.519553	−	0.367380i
$613$	−7.60371	−	7.60371i	−0.307111	−	0.307111i	0.536677	−	0.843788i	$-0.319679\pi$
$613$	−7.60371	−	7.60371i	−0.307111	−	0.307111i	−0.843788	+	0.536677i	$0.819679\pi$
$614$		−	2.70595i		−	0.109203i
$615$	4.27950	−	8.26735i	0.172566	−	0.333372i
$616$	2.26169	+	2.26169i	0.0911261	+	0.0911261i
$617$	−8.90722	+	8.90722i	−0.358591	+	0.358591i	−0.863294	−	0.504702i	$-0.831602\pi$
$617$	−8.90722	+	8.90722i	−0.358591	+	0.358591i	0.504702	+	0.863294i	$0.331602\pi$
$618$	−2.51768	−	7.92129i	−0.101276	−	0.318641i
$619$	5.08096	−	5.08096i	0.204221	−	0.204221i	−0.597585	−	0.801806i	$-0.703873\pi$
$619$	5.08096	−	5.08096i	0.204221	−	0.204221i	0.801806	+	0.597585i	$0.203873\pi$
$620$		−	2.29892i		−	0.0923268i
$621$	1.33253	+	9.60723i	0.0534726	+	0.385525i
$622$	5.08660	−	5.08660i	0.203954	−	0.203954i
$623$	4.98342			0.199656
$624$		0			0
$625$	−19.6260			−0.785040
$626$	10.3605	−	10.3605i	0.414090	−	0.414090i
$627$	11.4144	−	22.0510i	0.455849	−	0.880633i
$628$		−	11.0713i		−	0.441794i
$629$	−21.8090	+	21.8090i	−0.869580	+	0.869580i
$630$	0.233994	−	1.36382i	0.00932256	−	0.0543359i
$631$	−17.5431	+	17.5431i	−0.698378	+	0.698378i	−0.964061	−	0.265682i	$-0.914403\pi$
$631$	−17.5431	+	17.5431i	−0.698378	+	0.698378i	0.265682	+	0.964061i	$0.414403\pi$
$632$	−9.60287	−	9.60287i	−0.381982	−	0.381982i
$633$	8.12099	+	4.20373i	0.322780	+	0.167083i
$634$			5.55894i			0.220774i
$635$	0.957728	+	0.957728i	0.0380063	+	0.0380063i
$636$	13.8668	+	7.17798i	0.549854	+	0.284625i
$637$		0			0
$638$		−	36.5874i		−	1.44851i
$639$	−30.8404	−	5.29137i	−1.22003	−	0.209323i
$640$	−0.606018			−0.0239550
$641$	11.8520			0.468127			0.234064	−	0.972221i	$-0.424798\pi$
$641$	11.8520			0.468127			0.234064	+	0.972221i	$0.424798\pi$
$642$	−1.63955	−	5.15846i	−0.0647079	−	0.203588i
$643$	19.6347	+	19.6347i	0.774319	+	0.774319i	0.978858	−	0.204540i	$-0.0655697\pi$
$643$	19.6347	+	19.6347i	0.774319	+	0.774319i	−0.204540	+	0.978858i	$0.565570\pi$
$644$	−1.00459	−	1.00459i	−0.0395864	−	0.0395864i
$645$	−0.620105	−	1.95101i	−0.0244166	−	0.0768211i
$646$	17.8999			0.704262
$647$	19.6923			0.774182			0.387091	−	0.922041i	$-0.373480\pi$
$647$	19.6923			0.774182			0.387091	+	0.922041i	$0.373480\pi$
$648$	−8.12132	+	3.87868i	−0.319036	+	0.152369i
$649$			36.3079i			1.42521i
$650$		0			0
$651$	4.44117	+	2.29892i	0.174063	+	0.0901017i
$652$	3.71617	+	3.71617i	0.145536	+	0.145536i
$653$			48.6132i			1.90238i	0.308602	+	0.951191i	$0.400139\pi$
$653$			48.6132i			1.90238i	−0.308602	+	0.951191i	$0.599861\pi$
$654$	1.98824	+	1.02919i	0.0777464	+	0.0402445i
$655$	9.46410	+	9.46410i	0.369793	+	0.369793i
$656$	6.27128	−	6.27128i	0.244852	−	0.244852i
$657$	−23.3249	−	4.00192i	−0.909991	−	0.156130i
$658$	−4.36479	+	4.36479i	−0.170157	+	0.170157i
$659$		−	3.70793i		−	0.144440i	−0.997389	−	0.0722202i	$-0.976992\pi$
$659$		−	3.70793i		−	0.144440i	0.997389	−	0.0722202i	$-0.0230084\pi$
$660$	2.02778	−	3.91736i	0.0789311	−	0.152483i
$661$	−4.54658	+	4.54658i	−0.176842	+	0.176842i	−0.789977	−	0.613136i	$-0.789908\pi$
$661$	−4.54658	+	4.54658i	−0.176842	+	0.176842i	0.613136	+	0.789977i	$0.289908\pi$
$662$	−19.7529			−0.767720
$663$		0			0
$664$	−1.40987			−0.0547134
$665$	1.11261	−	1.11261i	0.0431450	−	0.0431450i
$666$	14.3978	−	10.1808i	0.557902	−	0.394497i
$667$			16.2513i			0.629252i
$668$	11.1219	−	11.1219i	0.430318	−	0.430318i
$669$	1.86262	+	5.86029i	0.0720129	+	0.226572i
$670$	0.0448983	−	0.0448983i	0.00173457	−	0.00173457i
$671$	24.1605	+	24.1605i	0.932708	+	0.932708i
$672$	0.606018	−	1.17074i	0.0233777	−	0.0451622i
$673$		−	5.93825i		−	0.228903i	−0.993429	−	0.114451i	$-0.963489\pi$
$673$		−	5.93825i		−	0.228903i	0.993429	−	0.114451i	$-0.0365110\pi$
$674$	−11.5887	−	11.5887i	−0.446381	−	0.446381i
$675$	23.8442	−	3.30720i	0.917763	−	0.127294i
$676$		0			0
$677$		−	24.5297i		−	0.942753i	−0.881932	−	0.471376i	$-0.843757\pi$
$677$		−	24.5297i		−	0.942753i	0.881932	−	0.471376i	$-0.156243\pi$
$678$	−3.65746	−	11.5073i	−0.140464	−	0.441937i
$679$	11.9875			0.460037
$680$	3.17992			0.121944
$681$	−8.29751	+	2.63726i	−0.317961	+	0.101060i
$682$	11.2725	+	11.2725i	0.431647	+	0.431647i
$683$	18.9705	+	18.9705i	0.725885	+	0.725885i	0.969797	−	0.243912i	$-0.0784308\pi$
$683$	18.9705	+	18.9705i	0.725885	+	0.725885i	−0.243912	+	0.969797i	$0.578431\pi$
$684$	−10.0865	−	1.73057i	−0.385668	−	0.0661702i
$685$	−6.05056			−0.231180
$686$	10.2147			0.389999
$687$	26.5865	−	8.45018i	1.01434	−	0.322394i
$688$		−	1.95035i		−	0.0743562i
$689$		0			0
$690$	−0.900691	+	1.74000i	−0.0342887	+	0.0662407i
$691$	−7.45140	−	7.45140i	−0.283464	−	0.283464i	0.551025	−	0.834489i	$-0.314237\pi$
$691$	−7.45140	−	7.45140i	−0.283464	−	0.283464i	−0.834489	+	0.551025i	$0.814237\pi$
$692$			5.42372i			0.206179i
$693$	5.53999	+	7.83473i	0.210447	+	0.297617i
$694$	15.2907	+	15.2907i	0.580427	+	0.580427i
$695$	−1.61339	+	1.61339i	−0.0611994	+	0.0611994i
$696$	−14.3713	+	4.56774i	−0.544743	+	0.173140i
$697$	−32.9068	+	32.9068i	−1.24644	+	1.24644i
$698$			1.94721i			0.0737029i
$699$	−34.4257	−	17.8201i	−1.30210	−	0.674016i
$700$	−2.49329	+	2.49329i	−0.0942375	+	0.0942375i
$701$	−48.3500			−1.82616			−0.913078	−	0.407785i	$-0.866301\pi$
$701$	−48.3500			−1.82616			−0.913078	+	0.407785i	$0.866301\pi$
$702$		0			0
$703$	20.0512			0.756245
$704$	2.97155	−	2.97155i	0.111995	−	0.111995i
$705$	7.56004	+	3.91337i	0.284728	+	0.147386i
$706$			23.2737i			0.875919i
$707$	−1.76128	+	1.76128i	−0.0662397	+	0.0662397i
$708$	14.2615	−	4.53284i	0.535981	−	0.170355i
$709$	20.8103	−	20.8103i	0.781546	−	0.781546i	−0.198545	−	0.980092i	$-0.563622\pi$
$709$	20.8103	−	20.8103i	0.781546	−	0.781546i	0.980092	+	0.198545i	$0.0636217\pi$
$710$	−4.46960	−	4.46960i	−0.167741	−	0.167741i
$711$	−23.5221	−	33.2653i	−0.882149	−	1.24755i
$712$		−	6.54753i		−	0.245379i
$713$	−5.00699	−	5.00699i	−0.187513	−	0.187513i
$714$	−3.17992	+	6.14313i	−0.119005	+	0.229901i
$715$		0			0
$716$			10.3808i			0.387950i
$717$	−14.1988	+	4.51289i	−0.530262	+	0.168537i
$718$	22.4661			0.838428
$719$	42.8472			1.59793			0.798966	−	0.601376i	$-0.205381\pi$
$719$	42.8472			1.59793			0.798966	+	0.601376i	$0.205381\pi$
$720$	−1.79187	−	0.307437i	−0.0667791	−	0.0114575i
$721$	2.58266	+	2.58266i	0.0961834	+	0.0961834i
$722$	5.20643	+	5.20643i	0.193763	+	0.193763i
$723$	−10.1443	+	3.22425i	−0.377272	+	0.119911i
$724$	11.1172			0.413167
$725$	40.3340			1.49797
$726$	3.49429	+	10.9939i	0.129685	+	0.408024i
$727$		−	1.92620i		−	0.0714389i	−0.999362	−	0.0357194i	$-0.988628\pi$
$727$		−	1.92620i		−	0.0714389i	0.999362	−	0.0357194i	$-0.0113723\pi$
$728$		0			0
$729$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$730$	−3.38041	−	3.38041i	−0.125115	−	0.125115i
$731$			10.2339i			0.378515i
$732$	6.47380	−	12.5064i	0.239279	−	0.462251i
$733$	22.6065	+	22.6065i	0.834990	+	0.834990i	0.988195	−	0.153204i	$-0.0489593\pi$
$733$	22.6065	+	22.6065i	0.834990	+	0.834990i	−0.153204	+	0.988195i	$0.548959\pi$
$734$	−0.425510	+	0.425510i	−0.0157059	+	0.0157059i
$735$	−2.04144	−	6.42290i	−0.0752996	−	0.236912i
$736$	−1.31989	+	1.31989i	−0.0486519	+	0.0486519i
$737$			0.440309i			0.0162190i
$738$	21.7243	−	15.3614i	0.799684	−	0.565462i
$739$	1.02751	−	1.02751i	0.0377976	−	0.0377976i	−0.687955	−	0.725753i	$-0.741492\pi$
$739$	1.02751	−	1.02751i	0.0377976	−	0.0377976i	0.725753	+	0.687955i	$0.241492\pi$
$740$	3.56209			0.130945
$741$		0			0
$742$	−6.86145			−0.251892
$743$	26.1830	−	26.1830i	0.960561	−	0.960561i	−0.0386900	−	0.999251i	$-0.512318\pi$
$743$	26.1830	−	26.1830i	0.960561	−	0.960561i	0.999251	+	0.0386900i	$0.0123185\pi$
$744$	3.02047	−	5.83509i	0.110736	−	0.213925i
$745$			5.28873i			0.193764i
$746$	−8.07209	+	8.07209i	−0.295540	+	0.295540i
$747$	−4.16869	−	0.715233i	−0.152524	−	0.0261690i
$748$	−15.5924	+	15.5924i	−0.570116	+	0.570116i
$749$	1.68187	+	1.68187i	0.0614542	+	0.0614542i
$750$	8.97936	+	4.64806i	0.327880	+	0.169723i
$751$			15.3439i			0.559906i	0.960014	+	0.279953i	$0.0903188\pi$
$751$			15.3439i			0.559906i	−0.960014	+	0.279953i	$0.909681\pi$
$752$	5.73474	+	5.73474i	0.209124	+	0.209124i
$753$	19.3138	+	9.99753i	0.703832	+	0.364330i
$754$		0			0
$755$		−	14.8843i		−	0.541694i
$756$	2.38579	−	3.15419i	0.0867705	−	0.114717i
$757$	22.4708			0.816715			0.408357	−	0.912822i	$-0.366102\pi$
$757$	22.4708			0.816715			0.408357	+	0.912822i	$0.366102\pi$
$758$	−37.5646			−1.36441
$759$	−4.11548	−	12.9484i	−0.149382	−	0.469997i
$760$	−1.46181	−	1.46181i	−0.0530255	−	0.0530255i
$761$	−0.574247	−	0.574247i	−0.0208164	−	0.0208164i	0.696622	−	0.717438i	$-0.254686\pi$
$761$	−0.574247	−	0.574247i	−0.0208164	−	0.0208164i	−0.717438	+	0.696622i	$0.754686\pi$
$762$	1.17257	+	3.68922i	0.0424777	+	0.133646i
$763$	−0.983805			−0.0356161
$764$	−5.73244			−0.207392
$765$	9.40237	+	1.61319i	0.339943	+	0.0583251i
$766$			12.6331i			0.456451i
$767$		0			0
$768$	−1.53819	−	0.796225i	−0.0555046	−	0.0287313i
$769$	−8.84388	−	8.84388i	−0.318918	−	0.318918i	0.529433	−	0.848352i	$-0.322405\pi$
$769$	−8.84388	−	8.84388i	−0.318918	−	0.318918i	−0.848352	+	0.529433i	$0.822405\pi$
$770$			1.93836i			0.0698536i
$771$	−7.28766	−	3.77237i	−0.262458	−	0.135859i
$772$	−8.02170	−	8.02170i	−0.288707	−	0.288707i
$773$	10.7358	−	10.7358i	0.386139	−	0.386139i	−0.487169	−	0.873308i	$-0.661970\pi$
$773$	10.7358	−	10.7358i	0.386139	−	0.386139i	0.873308	+	0.487169i	$0.161970\pi$
$774$	0.989422	−	5.76677i	0.0355640	−	0.207282i
$775$	−12.4268	+	12.4268i	−0.446386	+	0.446386i
$776$		−	15.7499i		−	0.565389i
$777$	−3.56209	+	6.88144i	−0.127789	+	0.246870i
$778$	13.3098	−	13.3098i	0.477180	−	0.477180i
$779$	30.2546			1.08398
$780$		0			0
$781$	43.8325			1.56845
$782$	6.92579	−	6.92579i	0.247666	−	0.247666i
$783$	−44.8103	+	6.21521i	−1.60139	+	0.222114i
$784$		−	6.42071i		−	0.229311i
$785$	4.74428	−	4.74428i	0.169331	−	0.169331i
$786$	11.5871	+	36.4562i	0.413300	+	1.30035i
$787$	−19.7245	+	19.7245i	−0.703104	+	0.703104i	−0.965076	−	0.261972i	$-0.915627\pi$
$787$	−19.7245	+	19.7245i	−0.703104	+	0.703104i	0.261972	+	0.965076i	$0.415627\pi$
$788$	3.31151	+	3.31151i	0.117968	+	0.117968i
$789$	4.51376	−	8.71991i	0.160694	−	0.310437i
$790$		−	8.23004i		−	0.292812i
$791$	3.75186	+	3.75186i	0.133401	+	0.133401i
$792$	10.2938	−	7.27879i	0.365773	−	0.258640i
$793$		0			0
$794$			11.9340i			0.423521i
$795$	2.86629	+	9.01810i	0.101657	+	0.319839i
$796$	12.9027			0.457324
$797$	−43.8082			−1.55177			−0.775883	−	0.630877i	$-0.782695\pi$
$797$	−43.8082			−1.55177			−0.775883	+	0.630877i	$0.782695\pi$
$798$	4.28581	−	1.36219i	0.151716	−	0.0482210i
$799$	−30.0915	−	30.0915i	−1.06456	−	1.06456i
$800$	3.27584	+	3.27584i	0.115819	+	0.115819i
$801$	3.32160	−	19.3597i	0.117363	−	0.684041i
$802$	−24.2212			−0.855280
$803$	33.1510			1.16987
$804$	0.172951	−	0.0549702i	0.00609950	−	0.00193865i
$805$		−	0.860973i		−	0.0303453i
$806$		0			0
$807$	−5.81715	+	11.2379i	−0.204773	+	0.395592i
$808$	2.31408	+	2.31408i	0.0814091	+	0.0814091i
$809$			0.388416i			0.0136560i	0.999977	+	0.00682798i	$0.00217343\pi$
$809$			0.388416i			0.0136560i	−0.999977	+	0.00682798i	$0.997827\pi$
$810$	−5.14224	−	1.81805i	−0.180680	−	0.0638799i
$811$	5.70744	+	5.70744i	0.200415	+	0.200415i	0.800178	−	0.599763i	$-0.204738\pi$
$811$	5.70744	+	5.70744i	0.200415	+	0.200415i	−0.599763	+	0.800178i	$0.704738\pi$
$812$	4.68563	−	4.68563i	0.164433	−	0.164433i
$813$	−40.4878	+	12.8685i	−1.41997	+	0.451319i
$814$	−17.4664	+	17.4664i	−0.612197	+	0.612197i
$815$			3.18490i			0.111562i
$816$	8.07123	+	4.17798i	0.282550	+	0.146258i
$817$	4.70454	−	4.70454i	0.164591	−	0.164591i
$818$	26.8311			0.938128
$819$		0			0
$820$	5.37473			0.187694
$821$	−24.1892	+	24.1892i	−0.844207	+	0.844207i	−0.989403	−	0.145196i	$-0.953619\pi$
$821$	−24.1892	+	24.1892i	−0.844207	+	0.844207i	0.145196	+	0.989403i	$0.453619\pi$
$822$	−15.3575	−	7.94960i	−0.535653	−	0.277274i
$823$			37.3184i			1.30084i	0.759576	+	0.650418i	$0.225406\pi$
$823$			37.3184i			1.30084i	−0.759576	+	0.650418i	$0.774594\pi$
$824$	3.39327	−	3.39327i	0.118210	−	0.118210i
$825$	−32.1366	+	10.2142i	−1.11885	+	0.355613i
$826$	−4.64984	+	4.64984i	−0.161789	+	0.161789i
$827$	8.16295	+	8.16295i	0.283854	+	0.283854i	0.834644	−	0.550790i	$-0.185674\pi$
$827$	8.16295	+	8.16295i	0.283854	+	0.283854i	−0.550790	+	0.834644i	$0.685674\pi$
$828$	−4.57225	+	3.23307i	−0.158897	+	0.112357i
$829$		−	32.5422i		−	1.13024i	−0.825010	−	0.565118i	$-0.808831\pi$
$829$		−	32.5422i		−	1.13024i	0.825010	−	0.565118i	$-0.191169\pi$
$830$	−0.604155	−	0.604155i	−0.0209705	−	0.0209705i
$831$	−6.96399	+	13.4534i	−0.241578	+	0.466693i
$832$		0			0
$833$			33.6909i			1.16732i
$834$	−6.21486	+	1.97532i	−0.215203	+	0.0683996i
$835$	9.53187			0.329864
$836$	14.3357			0.495811
$837$	11.8911	−	15.7209i	0.411016	−	0.543393i
$838$	−7.66272	−	7.66272i	−0.264704	−	0.264704i
$839$	9.51383	+	9.51383i	0.328454	+	0.328454i	0.851998	−	0.523544i	$-0.175391\pi$
$839$	9.51383	+	9.51383i	0.328454	+	0.328454i	−0.523544	+	0.851998i	$0.675391\pi$
$840$	0.761375	−	0.241993i	0.0262699	−	0.00834956i
$841$	−46.7996			−1.61378
$842$	−32.3832			−1.11600
$843$	−7.04547	−	22.1669i	−0.242659	−	0.763469i
$844$			5.27958i			0.181731i
$845$		0			0
$846$	14.0472	+	19.8657i	0.482952	+	0.682998i
$847$	−3.58448	−	3.58448i	−0.123164	−	0.123164i
$848$			9.01501i			0.309577i
$849$	−25.0302	+	48.3547i	−0.859035	+	1.65953i
$850$	−17.1891	−	17.1891i	−0.589581	−	0.589581i
$851$	7.75816	−	7.75816i	0.265946	−	0.265946i
$852$	−5.47225	−	17.2171i	−0.187476	−	0.589850i
$853$	8.09779	−	8.09779i	0.277263	−	0.277263i	−0.554752	−	0.832015i	$-0.687187\pi$
$853$	8.09779	−	8.09779i	0.277263	−	0.277263i	0.832015	+	0.554752i	$0.187187\pi$
$854$			6.18833i			0.211760i
$855$	−3.58069	−	5.06386i	−0.122457	−	0.173180i
$856$	2.20975	−	2.20975i	0.0755276	−	0.0755276i
$857$	−2.81672			−0.0962173			−0.0481086	−	0.998842i	$-0.515319\pi$
$857$	−2.81672			−0.0962173			−0.0481086	+	0.998842i	$0.515319\pi$
$858$		0			0
$859$	18.5174			0.631807			0.315903	−	0.948791i	$-0.397692\pi$
$859$	18.5174			0.631807			0.315903	+	0.948791i	$0.397692\pi$
$860$	0.835761	−	0.835761i	0.0284992	−	0.0284992i
$861$	−5.37473	+	10.3832i	−0.183170	+	0.353858i
$862$		−	33.5647i		−	1.14322i
$863$	16.9992	−	16.9992i	0.578658	−	0.578658i	−0.355875	−	0.934534i	$-0.615817\pi$
$863$	16.9992	−	16.9992i	0.578658	−	0.578658i	0.934534	+	0.355875i	$0.115817\pi$
$864$	−4.14418	−	3.13461i	−0.140988	−	0.106642i
$865$	−2.32417	+	2.32417i	−0.0790242	+	0.0790242i
$866$	16.7982	+	16.7982i	0.570825	+	0.570825i
$867$	−16.2024	−	8.38698i	−0.550263	−	0.284837i
$868$			2.88727i			0.0980004i
$869$	40.3552	+	40.3552i	1.36896	+	1.36896i
$870$	−8.11575	−	4.20102i	−0.275150	−	0.142428i
$871$		0			0
$872$			1.29259i			0.0437725i
$873$	7.99003	−	46.5693i	0.270421	−	1.57613i
$874$	−6.36758			−0.215387
$875$	−4.44309			−0.150204
$876$	−4.13872	−	13.0215i	−0.139834	−	0.439956i
$877$	21.8195	+	21.8195i	0.736793	+	0.736793i	0.971956	−	0.235163i	$-0.0755623\pi$
$877$	21.8195	+	21.8195i	0.736793	+	0.736793i	−0.235163	+	0.971956i	$0.575562\pi$
$878$	10.5121	+	10.5121i	0.354766	+	0.354766i
$879$	1.09905	+	3.45791i	0.0370702	+	0.116633i
$880$	2.54674			0.0858505
$881$	−46.2624			−1.55862			−0.779310	−	0.626638i	$-0.784430\pi$
$881$	−46.2624			−1.55862			−0.779310	+	0.626638i	$0.784430\pi$
$882$	3.25726	−	18.9847i	0.109678	−	0.639249i
$883$		−	31.0867i		−	1.04615i	−0.852286	−	0.523076i	$-0.824784\pi$
$883$		−	31.0867i		−	1.04615i	0.852286	−	0.523076i	$-0.175216\pi$
$884$		0			0
$885$	8.05376	+	4.16893i	0.270724	+	0.140137i
$886$	28.5258	+	28.5258i	0.958343	+	0.958343i
$887$			36.2495i			1.21714i	0.793500	+	0.608570i	$0.208256\pi$
$887$			36.2495i			1.21714i	−0.793500	+	0.608570i	$0.791744\pi$
$888$	9.04127	+	4.68011i	0.303405	+	0.157054i
$889$	−1.20283	−	1.20283i	−0.0403418	−	0.0403418i
$890$	2.80574	−	2.80574i	0.0940487	−	0.0940487i
$891$	34.1291	−	16.2998i	1.14337	−	0.546064i
$892$	−2.51039	+	2.51039i	−0.0840540	+	0.0840540i
$893$			27.6662i			0.925814i
$894$	−6.94866	+	13.4238i	−0.232398	+	0.448959i
$895$	−4.44839	+	4.44839i	−0.148693	+	0.148693i
$896$	0.761114			0.0254270
$897$		0			0
$898$	−4.56520			−0.152343
$899$	23.3537	−	23.3537i	0.778891	−	0.778891i
$900$	8.02414	+	11.3479i	0.267471	+	0.378262i
$901$		−	47.3038i		−	1.57592i
$902$	−26.3545	+	26.3545i	−0.877508	+	0.877508i
$903$	0.778806	+	2.45033i	0.0259170	+	0.0815418i
$904$	4.92944	−	4.92944i	0.163951	−	0.163951i
$905$	4.76394	+	4.76394i	0.158359	+	0.158359i
$906$	19.5559	−	37.7791i	0.649701	−	1.25513i
$907$			54.8347i			1.82076i	0.413777	+	0.910378i	$0.364209\pi$
$907$			54.8347i			1.82076i	−0.413777	+	0.910378i	$0.635791\pi$
$908$	−3.55443	−	3.55443i	−0.117958	−	0.117958i
$909$	5.66832	+	8.01621i	0.188006	+	0.265881i
$910$		0			0
$911$			12.4963i			0.414022i	0.978339	+	0.207011i	$0.0663737\pi$
$911$			12.4963i			0.414022i	−0.978339	+	0.207011i	$0.933626\pi$
$912$	−1.78973	−	5.63097i	−0.0592640	−	0.186460i
$913$	5.92484			0.196083
$914$	−26.2928			−0.869687
$915$	8.13340	−	2.58510i	0.268882	−	0.0854607i
$916$	11.3889	+	11.3889i	0.376301	+	0.376301i
$917$	−11.8862	−	11.8862i	−0.392517	−	0.392517i
$918$	21.7455	+	16.4480i	0.717708	+	0.542865i
$919$	30.4287			1.00375			0.501874	−	0.864941i	$-0.332644\pi$
$919$	30.4287			1.00375			0.501874	+	0.864941i	$0.332644\pi$
$920$	−1.13120			−0.0372946
$921$	4.46666	−	1.41967i	0.147181	−	0.0467797i
$922$			15.0659i			0.496168i
$923$		0			0
$924$	−2.54674	+	4.91992i	−0.0837815	+	0.161853i
$925$	−19.2550	−	19.2550i	−0.633099	−	0.633099i
$926$			18.1837i			0.597552i
$927$	11.7546	−	8.31177i	0.386072	−	0.272994i
$928$	−6.15628	−	6.15628i	−0.202090	−	0.202090i
$929$	8.30768	−	8.30768i	0.272566	−	0.272566i	−0.557566	−	0.830132i	$-0.688265\pi$
$929$	8.30768	−	8.30768i	0.272566	−	0.272566i	0.830132	+	0.557566i	$0.188265\pi$
$930$	3.79478	−	1.20612i	0.124436	−	0.0395503i
$931$	15.4877	−	15.4877i	0.507590	−	0.507590i
$932$		−	22.3807i		−	0.733103i
$933$	11.0650	+	5.72768i	0.362253	+	0.187516i
$934$	8.98762	−	8.98762i	0.294084	−	0.294084i
$935$	−13.3633			−0.437027
$936$		0			0
$937$	4.30645			0.140686			0.0703429	−	0.997523i	$-0.477591\pi$
$937$	4.30645			0.140686			0.0703429	+	0.997523i	$0.477591\pi$
$938$	−0.0563890	+	0.0563890i	−0.00184116	+	0.00184116i
$939$	22.5375	+	11.6663i	0.735485	+	0.380715i
$940$			4.91490i			0.160306i
$941$	35.4161	−	35.4161i	1.15453	−	1.15453i	0.168897	−	0.985634i	$-0.445980\pi$
$941$	35.4161	−	35.4161i	1.15453	−	1.15453i	0.985634	−	0.168897i	$-0.0540204\pi$
$942$	18.2752	−	5.80855i	0.595439	−	0.189253i
$943$	11.7060	−	11.7060i	0.381201	−	0.381201i
$944$	6.10925	+	6.10925i	0.198839	+	0.198839i
$945$	2.37399	−	0.329275i	0.0772260	−	0.0107113i
$946$			8.19615i			0.266480i
$947$	39.9302	+	39.9302i	1.29756	+	1.29756i	0.930001	+	0.367557i	$0.119806\pi$
$947$	39.9302	+	39.9302i	1.29756	+	1.29756i	0.367557	+	0.930001i	$0.380194\pi$
$948$	10.8131	−	20.8894i	0.351195	−	0.678456i
$949$		0			0
$950$			15.8037i			0.512739i
$951$	−9.17604	+	2.91649i	−0.297553	+	0.0945735i
$952$	−3.99374			−0.129438
$953$	6.54349			0.211964			0.105982	−	0.994368i	$-0.466201\pi$
$953$	6.54349			0.211964			0.105982	+	0.994368i	$0.466201\pi$
$954$	−4.57337	+	26.6555i	−0.148068	+	0.863005i
$955$	−2.45646	−	2.45646i	−0.0794893	−	0.0794893i
$956$	−6.08236	−	6.08236i	−0.196718	−	0.196718i
$957$	60.3941	−	19.1955i	1.95226	−	0.620502i
$958$	35.8276			1.15754
$959$	7.59905			0.245386
$960$	−0.317946	−	1.00034i	−0.0102617	−	0.0322859i
$961$		−	16.6095i		−	0.535790i
$962$		0			0
$963$	7.65478	−	5.41275i	0.246672	−	0.174423i
$964$	−4.34556	−	4.34556i	−0.139961	−	0.139961i
$965$		−	6.87491i		−	0.221311i
$966$	1.13120	−	2.18531i	0.0363958	−	0.0703113i
$967$	10.8941	+	10.8941i	0.350332	+	0.350332i	0.860233	−	0.509901i	$-0.170318\pi$
$967$	10.8941	+	10.8941i	0.350332	+	0.350332i	−0.509901	+	0.860233i	$0.670318\pi$
$968$	−4.70951	+	4.70951i	−0.151369	+	0.151369i
$969$	9.39114	+	29.5470i	0.301687	+	0.949187i
$970$	6.74915	−	6.74915i	0.216702	−	0.216702i
$971$		−	2.39332i		−	0.0768053i	−0.999262	−	0.0384027i	$-0.987773\pi$
$971$		−	2.39332i		−	0.0768053i	0.999262	−	0.0384027i	$-0.0122270\pi$
$972$	−10.6633	−	11.3708i	−0.342025	−	0.364717i
$973$	2.02630	−	2.02630i	0.0649602	−	0.0649602i
$974$	−6.72951			−0.215628
$975$		0			0
$976$	8.13061			0.260255
$977$	23.8091	−	23.8091i	0.761722	−	0.761722i	−0.214912	−	0.976633i	$-0.568946\pi$
$977$	23.8091	−	23.8091i	0.761722	−	0.761722i	0.976633	+	0.214912i	$0.0689464\pi$
$978$	−4.18452	+	8.08388i	−0.133806	+	0.258494i
$979$			27.5154i			0.879396i
$980$	2.75140	−	2.75140i	0.0878902	−	0.0878902i
$981$	−0.655736	+	3.82191i	−0.0209360	+	0.122024i
$982$	21.0816	−	21.0816i	0.672740	−	0.672740i
$983$	−26.5732	−	26.5732i	−0.847553	−	0.847553i	0.142274	−	0.989827i	$-0.454558\pi$
$983$	−26.5732	−	26.5732i	−0.847553	−	0.847553i	−0.989827	+	0.142274i	$0.954558\pi$
$984$	13.6421	+	7.06166i	0.434894	+	0.225117i
$985$			2.83810i			0.0904293i
$986$	32.3034	+	32.3034i	1.02875	+	1.02875i
$987$	−9.49485	−	4.91490i	−0.302225	−	0.156443i
$988$		0			0
$989$		−	3.64054i		−	0.115762i
$990$	7.53018	+	1.29198i	0.239325	+	0.0410617i
$991$	21.7196			0.689947			0.344974	−	0.938612i	$-0.387888\pi$
$991$	21.7196			0.689947			0.344974	+	0.938612i	$0.387888\pi$
$992$	3.79348			0.120443
$993$	−10.3633	−	32.6058i	−0.328871	−	1.03471i
$994$	5.61349	+	5.61349i	0.178049	+	0.178049i
$995$	5.52906	+	5.52906i	0.175283	+	0.175283i
$996$	−0.739683	−	2.32724i	−0.0234377	−	0.0737413i
$997$	−11.5522			−0.365862			−0.182931	−	0.983126i	$-0.558559\pi$
$997$	−11.5522			−0.365862			−0.182931	+	0.983126i	$0.558559\pi$
$998$	36.1314			1.14372
$999$	24.3589	+	18.4248i	0.770683	+	0.582935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.d.437.1		16
3.2	odd	2	inner	1014.2.g.d.437.5		16
13.5	odd	4	inner	1014.2.g.d.239.5		16
13.7	odd	12		78.2.k.a.41.2	✓	16
13.8	odd	4		1014.2.g.c.239.1		16
13.10	even	6		78.2.k.a.59.4	yes	16
13.12	even	2		1014.2.g.c.437.5		16
39.5	even	4	inner	1014.2.g.d.239.1		16
39.8	even	4		1014.2.g.c.239.5		16
39.20	even	12		78.2.k.a.41.4	yes	16
39.23	odd	6		78.2.k.a.59.2	yes	16
39.38	odd	2		1014.2.g.c.437.1		16
52.7	even	12		624.2.cn.d.353.2		16
52.23	odd	6		624.2.cn.d.449.1		16
156.23	even	6		624.2.cn.d.449.2		16
156.59	odd	12		624.2.cn.d.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.41.2	✓	16	13.7	odd	12
78.2.k.a.41.4	yes	16	39.20	even	12
78.2.k.a.59.2	yes	16	39.23	odd	6
78.2.k.a.59.4	yes	16	13.10	even	6
624.2.cn.d.353.1		16	156.59	odd	12
624.2.cn.d.353.2		16	52.7	even	12
624.2.cn.d.449.1		16	52.23	odd	6
624.2.cn.d.449.2		16	156.23	even	6
1014.2.g.c.239.1		16	13.8	odd	4
1014.2.g.c.239.5		16	39.8	even	4
1014.2.g.c.437.1		16	39.38	odd	2
1014.2.g.c.437.5		16	13.12	even	2
1014.2.g.d.239.1		16	39.5	even	4	inner
1014.2.g.d.239.5		16	13.5	odd	4	inner
1014.2.g.d.437.1		16	1.1	even	1	trivial
1014.2.g.d.437.5		16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.53819 - 0.796225i) q^{3} -1.00000i q^{4} +(0.428520 - 0.428520i) q^{5} +(1.65068 - 0.524648i) q^{6} +(-0.538189 + 0.538189i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.73205 + 2.44949i) q^{9} +0.606018i q^{10} +(-2.97155 - 2.97155i) q^{11} +(-0.796225 + 1.53819i) q^{12} -0.761114i q^{14} +(-1.00034 + 0.317946i) q^{15} -1.00000 q^{16} +5.24723 q^{17} +(-2.95680 - 0.507306i) q^{18} +(-2.41216 - 2.41216i) q^{19} +(-0.428520 - 0.428520i) q^{20} +(1.25636 - 0.399317i) q^{21} +4.20241 q^{22} -1.86661 q^{23} +(-0.524648 - 1.65068i) q^{24} +4.63274i q^{25} +(-0.713876 - 5.14688i) q^{27} +(0.538189 + 0.538189i) q^{28} -8.70629i q^{29} +(0.482527 - 0.932171i) q^{30} +(2.68240 + 2.68240i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.20478 + 6.93684i) q^{33} +(-3.71035 + 3.71035i) q^{34} +0.461249i q^{35} +(2.44949 - 1.73205i) q^{36} +(-4.15628 + 4.15628i) q^{37} +3.41130 q^{38} +0.606018 q^{40} +(-6.27128 + 6.27128i) q^{41} +(-0.606018 + 1.17074i) q^{42} +1.95035i q^{43} +(-2.97155 + 2.97155i) q^{44} +(1.79187 + 0.307437i) q^{45} +(1.31989 - 1.31989i) q^{46} +(-5.73474 - 5.73474i) q^{47} +(1.53819 + 0.796225i) q^{48} +6.42071i q^{49} +(-3.27584 - 3.27584i) q^{50} +(-8.07123 - 4.17798i) q^{51} -9.01501i q^{53} +(4.14418 + 3.13461i) q^{54} -2.54674 q^{55} -0.761114 q^{56} +(1.78973 + 5.63097i) q^{57} +(6.15628 + 6.15628i) q^{58} +(-6.10925 - 6.10925i) q^{59} +(0.317946 + 1.00034i) q^{60} -8.13061 q^{61} -3.79348 q^{62} +(-2.25046 - 0.386118i) q^{63} +1.00000i q^{64} +(-6.46410 - 3.34607i) q^{66} +(-0.0740874 - 0.0740874i) q^{67} -5.24723i q^{68} +(2.87120 + 1.48624i) q^{69} +(-0.326152 - 0.326152i) q^{70} +(-7.37536 + 7.37536i) q^{71} +(-0.507306 + 2.95680i) q^{72} +(-5.57806 + 5.57806i) q^{73} -5.87787i q^{74} +(3.68871 - 7.12603i) q^{75} +(-2.41216 + 2.41216i) q^{76} +3.19851 q^{77} -13.5805 q^{79} +(-0.428520 + 0.428520i) q^{80} +(-3.00000 + 8.48528i) q^{81} -8.86892i q^{82} +(-0.996926 + 0.996926i) q^{83} +(-0.399317 - 1.25636i) q^{84} +(2.24854 - 2.24854i) q^{85} +(-1.37910 - 1.37910i) q^{86} +(-6.93217 + 13.3919i) q^{87} -4.20241i q^{88} +(-4.62980 - 4.62980i) q^{89} +(-1.48444 + 1.04965i) q^{90} +1.86661i q^{92} +(-1.99024 - 6.26182i) q^{93} +8.11015 q^{94} -2.06731 q^{95} +(-1.65068 + 0.524648i) q^{96} +(-11.1369 - 11.1369i) q^{97} +(-4.54012 - 4.54012i) q^{98} +(2.13191 - 12.4257i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{7} + 24 q^{15} - 16 q^{16} - 32 q^{19} + 24 q^{21} - 16 q^{28} - 16 q^{31} - 24 q^{33} - 24 q^{34} + 8 q^{37} + 48 q^{45} + 48 q^{55} + 24 q^{57} + 24 q^{58} + 24 q^{60} + 48 q^{61} - 48 q^{66}+ \cdots - 16 q^{97}+O(q^{100}) \) 16 * q + 16 * q^7 + 24 * q^15 - 16 * q^16 - 32 * q^19 + 24 * q^21 - 16 * q^28 - 16 * q^31 - 24 * q^33 - 24 * q^34 + 8 * q^37 + 48 * q^45 + 48 * q^55 + 24 * q^57 + 24 * q^58 + 24 * q^60 + 48 * q^61 - 48 * q^66 - 32 * q^67 - 56 * q^73 - 32 * q^76 - 96 * q^79 - 48 * q^81 - 24 * q^84 - 24 * q^85 - 96 * q^87 - 48 * q^93 + 48 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

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Database

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