LMFDB - Embedded newform 1014.2.g.c.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.c.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} +(0.524648 - 1.65068i) 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} +(-0.317946 + 1.00034i) q^{15} -1.00000 q^{16} -5.24723 q^{17} +(0.507306 + 2.95680i) q^{18} +(2.41216 + 2.41216i) q^{19} +(-0.428520 - 0.428520i) q^{20} +(-0.399317 + 1.25636i) q^{21} +4.20241 q^{22} +1.86661 q^{23} +(-1.65068 - 0.524648i) 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} +(6.93684 + 2.20478i) 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} +(-0.307437 - 1.79187i) 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} +(-3.13461 - 4.14418i) q^{54} -2.54674 q^{55} +0.761114 q^{56} +(-5.63097 - 1.78973i) q^{57} +(-6.15628 - 6.15628i) q^{58} +(-6.10925 - 6.10925i) q^{59} +(1.00034 + 0.317946i) q^{60} -8.13061 q^{61} +3.79348 q^{62} +(-0.386118 - 2.25046i) 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} +(2.95680 - 0.507306i) 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} +(1.25636 + 0.399317i) 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} +(6.26182 + 1.99024i) q^{93} +8.11015 q^{94} +2.06731 q^{95} +(-0.524648 + 1.65068i) q^{96} +(11.1369 + 11.1369i) q^{97} +(-4.54012 - 4.54012i) q^{98} +(-12.4257 + 2.13191i) 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	$0.206733\pi$
$6$	0.524648	−	1.65068i	0.214186	−	0.673887i
$7$	0.538189	−	0.538189i	0.203416	−	0.203416i	−0.598046	−	0.801462i	$-0.704056\pi$
$7$	0.538189	−	0.538189i	0.203416	−	0.203416i	0.801462	+	0.598046i	$0.204056\pi$
$8$	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
$15$	−0.317946	+	1.00034i	−0.0820933	+	0.258287i
$16$	−1.00000			−0.250000
$17$	−5.24723			−1.27264			−0.636320	−	0.771425i	$-0.719544\pi$
$17$	−5.24723			−1.27264			−0.636320	+	0.771425i	$0.719544\pi$
$18$	0.507306	+	2.95680i	0.119573	+	0.696923i
$19$	2.41216	+	2.41216i	0.553387	+	0.553387i	0.927417	−	0.374030i	$-0.122024\pi$
$19$	2.41216	+	2.41216i	0.553387	+	0.553387i	−0.374030	+	0.927417i	$0.622024\pi$
$20$	−0.428520	−	0.428520i	−0.0958199	−	0.0958199i
$21$	−0.399317	+	1.25636i	−0.0871381	+	0.274159i
$22$	4.20241			0.895957
$23$	1.86661			0.389216			0.194608	−	0.980881i	$-0.437657\pi$
$23$	1.86661			0.389216			0.194608	+	0.980881i	$0.437657\pi$
$24$	−1.65068	−	0.524648i	−0.336944	−	0.107093i
$25$			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	$0.299644\pi$
$29$			8.70629i			1.61672i	−0.588690	+	0.808359i	$0.700356\pi$
$30$	−0.482527	−	0.932171i	−0.0880970	−	0.170190i
$31$	−2.68240	−	2.68240i	−0.481773	−	0.481773i	0.423925	−	0.905697i	$-0.360652\pi$
$31$	−2.68240	−	2.68240i	−0.481773	−	0.481773i	−0.905697	+	0.423925i	$0.860652\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	6.93684	+	2.20478i	1.20755	+	0.383804i
$34$	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	−0.277452	−	0.960740i	$-0.589490\pi$
$37$	4.15628	−	4.15628i	0.683288	−	0.683288i	0.960740	+	0.277452i	$0.0894898\pi$
$38$	−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
$45$	−0.307437	−	1.79187i	−0.0458300	−	0.267117i
$46$	−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	$0.212524\pi$
$53$			9.01501i			1.23831i	−0.785270	+	0.619153i	$0.787476\pi$
$54$	−3.13461	−	4.14418i	−0.426566	−	0.563952i
$55$	−2.54674			−0.343402
$56$	0.761114			0.101708
$57$	−5.63097	−	1.78973i	−0.745841	−	0.237056i
$58$	−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	$0.940123\pi$
$60$	1.00034	+	0.317946i	0.129144	+	0.0410467i
$61$	−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
$63$	−0.386118	−	2.25046i	−0.0486463	−	0.283531i
$64$			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	0.711618	−	0.702567i	$-0.247963\pi$
$67$	0.0740874	+	0.0740874i	0.00905121	+	0.00905121i	−0.702567	+	0.711618i	$0.747963\pi$
$68$			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	$0.462432\pi$
$72$	2.95680	−	0.507306i	0.348462	−	0.0597866i
$73$	5.57806	−	5.57806i	0.652863	−	0.652863i	−0.300819	−	0.953681i	$-0.597260\pi$
$73$	5.57806	−	5.57806i	0.652863	−	0.652863i	0.953681	+	0.300819i	$0.0972599\pi$
$74$			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	$0.274654\pi$
$84$	1.25636	+	0.399317i	0.137080	+	0.0435690i
$85$	−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
$93$	6.26182	+	1.99024i	0.649321	+	0.206378i
$94$	8.11015			0.836498
$95$	2.06731			0.212102
$96$	−0.524648	+	1.65068i	−0.0535466	+	0.168472i
$97$	11.1369	+	11.1369i	1.13078	+	1.13078i	0.990048	+	0.140730i	$0.0449449\pi$
$97$	11.1369	+	11.1369i	1.13078	+	1.13078i	0.140730	+	0.990048i	$0.455055\pi$
$98$	−4.54012	−	4.54012i	−0.458622	−	0.458622i
$99$	−12.4257	+	2.13191i	−1.24883	+	0.214265i
$100$	4.63274			0.463274
$101$	−3.27260			−0.325636			−0.162818	−	0.986656i	$-0.552058\pi$
$101$	−3.27260			−0.325636			−0.162818	+	0.986656i	$0.552058\pi$
$102$	−2.75295	+	8.66150i	−0.272582	+	0.857616i
$103$		−	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	$0.0482671\pi$
$107$			3.12505i			0.302110i	−0.988525	+	0.151055i	$0.951733\pi$
$108$	5.14688	+	0.713876i	0.495259	+	0.0686928i
$109$	−0.913996	−	0.913996i	−0.0875449	−	0.0875449i	0.661978	−	0.749523i	$-0.269717\pi$
$109$	−0.913996	−	0.913996i	−0.0875449	−	0.0875449i	−0.749523	+	0.661978i	$0.769717\pi$
$110$	1.80082	−	1.80082i	0.171701	−	0.171701i
$111$	−3.08381	+	9.70248i	−0.292702	+	0.920918i
$112$	−0.538189	+	0.538189i	−0.0508541	+	0.0508541i
$113$			6.97128i			0.655802i	0.944712	+	0.327901i	$0.106341\pi$
$113$			6.97128i			0.655802i	−0.944712	+	0.327901i	$0.893659\pi$
$114$	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
$123$	4.65306	−	14.6398i	0.419552	−	1.32002i
$124$	−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	$-0.584692\pi$
$131$		−	22.0856i		−	1.92963i	0.262938	−	0.964813i	$-0.415308\pi$
$132$	2.20478	−	6.93684i	0.191902	−	0.603774i
$133$	2.59639			0.225136
$134$	−0.104775			−0.00905121
$135$	1.89963	+	2.51145i	0.163494	+	0.216151i
$136$	−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	$0.890254\pi$
$138$	0.979314	−	3.08118i	0.0833647	−	0.262287i
$139$	−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
$141$	13.3873	+	4.25497i	1.12741	+	0.358333i
$142$		−	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	$0.366361\pi$
$150$	7.64717	+	2.43056i	0.624389	+	0.198454i
$151$	−17.3671	+	17.3671i	−1.41331	+	1.41331i	−0.681429	+	0.731885i	$0.738641\pi$
$151$	−17.3671	+	17.3671i	−1.41331	+	1.41331i	−0.731885	+	0.681429i	$0.761359\pi$
$152$			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
$162$	8.12132	+	3.87868i	0.638071	+	0.304738i
$163$	3.71617	−	3.71617i	0.291073	−	0.291073i	−0.546431	−	0.837504i	$-0.684014\pi$
$163$	3.71617	−	3.71617i	0.291073	−	0.291073i	0.837504	+	0.546431i	$0.184014\pi$
$164$	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
$171$	10.0865	−	1.73057i	0.771336	−	0.132340i
$172$	1.95035			0.148712
$173$	5.42372			0.412358			0.206179	−	0.978514i	$-0.433897\pi$
$173$	5.42372			0.412358			0.206179	+	0.978514i	$0.433897\pi$
$174$	14.3713	+	4.56774i	1.08949	+	0.346279i
$175$	2.49329	+	2.49329i	0.188475	+	0.188475i
$176$	2.97155	+	2.97155i	0.223989	+	0.223989i
$177$	14.2615	+	4.53284i	1.07196	+	0.340709i
$178$	6.54753			0.490758
$179$	10.3808			0.775900			0.387950	−	0.921680i	$-0.373183\pi$
$179$	10.3808			0.775900			0.387950	+	0.921680i	$0.373183\pi$
$180$	−1.79187	+	0.307437i	−0.133558	+	0.0229150i
$181$			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
$189$	2.38579	+	3.15419i	0.173541	+	0.229434i
$190$	−1.46181	+	1.46181i	−0.106051	+	0.106051i
$191$			5.73244i			0.414785i	0.978258	+	0.207392i	$0.0664977\pi$
$191$			5.73244i			0.414785i	−0.978258	+	0.207392i	$0.933502\pi$
$192$	−0.796225	−	1.53819i	−0.0574626	−	0.111009i
$193$	−8.02170	+	8.02170i	−0.577414	+	0.577414i	−0.934190	−	0.356776i	$-0.883876\pi$
$193$	−8.02170	+	8.02170i	−0.577414	+	0.577414i	0.356776	+	0.934190i	$0.383876\pi$
$194$	−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
$201$	−0.172951	−	0.0549702i	−0.0121990	−	0.00387730i
$202$	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
$210$	−0.761375	−	0.241993i	−0.0525399	−	0.0166991i
$211$	−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
$213$	5.47225	−	17.2171i	0.374952	−	1.17970i
$214$	−2.20975	−	2.20975i	−0.151055	−	0.151055i
$215$	0.835761	+	0.835761i	0.0569985	+	0.0569985i
$216$	−4.14418	+	3.13461i	−0.281976	+	0.213283i
$217$	−2.88727			−0.196001
$218$	1.29259			0.0875449
$219$	−4.13872	+	13.0215i	−0.279669	+	0.879912i
$220$			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	0.786147	−	0.618039i	$-0.212073\pi$
$223$	2.51039	+	2.51039i	0.168108	+	0.168108i	−0.618039	+	0.786147i	$0.712073\pi$
$224$		−	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	$0.196651\pi$
$228$	−1.78973	+	5.63097i	−0.118528	+	0.372920i
$229$	11.3889	−	11.3889i	0.752602	−	0.752602i	−0.222362	−	0.974964i	$-0.571377\pi$
$229$	11.3889	−	11.3889i	0.752602	−	0.752602i	0.974964	+	0.222362i	$0.0713767\pi$
$230$			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	$-0.761929\pi$
$233$	−22.3807			−1.46621			−0.733103	+	0.680117i	$0.761929\pi$
$234$		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	$0.160262\pi$
$240$	0.317946	−	1.00034i	0.0205233	−	0.0645718i
$241$	−4.34556	+	4.34556i	−0.279922	+	0.279922i	−0.833078	−	0.553156i	$-0.813423\pi$
$241$	−4.34556	+	4.34556i	−0.279922	+	0.279922i	0.553156	+	0.833078i	$0.313423\pi$
$242$	−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
$249$	0.739683	−	2.32724i	0.0468755	−	0.147483i
$250$	−5.83762			−0.369203
$251$	12.5562			0.792538			0.396269	−	0.918134i	$-0.370305\pi$
$251$	12.5562			0.792538			0.396269	+	0.918134i	$0.370305\pi$
$252$	−2.25046	+	0.386118i	−0.141766	+	0.0243231i
$253$	−5.54674	−	5.54674i	−0.348720	−	0.348720i
$254$	−1.58036	−	1.58036i	−0.0991607	−	0.0991607i
$255$	1.66834	−	5.24903i	0.104475	−	0.328707i
$256$	1.00000			0.0625000
$257$	−4.73782			−0.295537			−0.147768	−	0.989022i	$-0.547209\pi$
$257$	−4.73782			−0.295537			−0.147768	+	0.989022i	$0.547209\pi$
$258$	3.21940	+	1.02324i	0.200431	+	0.0637044i
$259$		−	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	$-0.944078\pi$
$263$		−	5.66894i		−	0.349562i	0.984607	−	0.174781i	$-0.0559218\pi$
$264$	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
$267$	10.8079	+	3.43514i	0.661431	+	0.210227i
$268$	0.0740874	−	0.0740874i	0.00452561	−	0.00452561i
$269$			7.30591i			0.445449i	0.974881	+	0.222725i	$0.0714951\pi$
$269$			7.30591i			0.445449i	−0.974881	+	0.222725i	$0.928505\pi$
$270$	−3.11910	−	0.432622i	−0.189823	−	0.0263285i
$271$	−17.3439	+	17.3439i	−1.05356	+	1.05356i	−0.0550829	+	0.998482i	$0.517542\pi$
$271$	−17.3439	+	17.3439i	−1.05356	+	1.05356i	−0.998482	+	0.0550829i	$0.982458\pi$
$272$	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
$279$	−11.2165	+	1.92446i	−0.671517	+	0.115214i
$280$	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
$288$	−0.507306	−	2.95680i	−0.0298933	−	0.174231i
$289$	10.5334			0.619614
$290$	−5.27617			−0.309828
$291$	−25.9981	−	8.26316i	−1.52403	−	0.484395i
$292$	−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	$0.769490\pi$
$294$	10.5985	+	3.36861i	0.618119	+	0.196461i
$295$	−5.23587			−0.304844
$296$	5.87787			0.341644
$297$	17.4155	−	13.1729i	1.01055	−	0.764370i
$298$		−	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
$306$	−2.66195	−	15.5150i	−0.152174	−	0.886933i
$307$	1.91340	−	1.91340i	0.109203	−	0.109203i	−0.650394	−	0.759597i	$-0.725396\pi$
$307$	1.91340	−	1.91340i	0.109203	−	0.109203i	0.759597	+	0.650394i	$0.225396\pi$
$308$			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	$-0.434621\pi$
$311$	7.19354			0.407908			0.203954	+	0.978980i	$0.434621\pi$
$312$		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	$0.200104\pi$
$318$	14.8809	+	4.72970i	0.834479	+	0.265229i
$319$	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
$327$	2.13364	+	0.678152i	0.117991	+	0.0375019i
$328$	−8.86892			−0.489704
$329$	−6.17275			−0.340315
$330$	−1.33614	+	4.20385i	−0.0735521	+	0.231414i
$331$	−13.9674	−	13.9674i	−0.767720	−	0.767720i	0.209985	−	0.977705i	$-0.432659\pi$
$331$	−13.9674	−	13.9674i	−0.767720	−	0.767720i	−0.977705	+	0.209985i	$0.932659\pi$
$332$	0.996926	+	0.996926i	0.0547134	+	0.0547134i
$333$	−2.98188	−	17.3797i	−0.163406	−	0.952399i
$334$	−15.7287			−0.860635
$335$	0.0634958			0.00346915
$336$	0.399317	−	1.25636i	0.0217845	−	0.0685398i
$337$			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
$345$	−0.593482	+	1.86725i	−0.0319520	+	0.100529i
$346$	−3.83515	+	3.83515i	−0.206179	+	0.206179i
$347$			21.6243i			1.16085i	0.814312	+	0.580427i	$0.197114\pi$
$347$			21.6243i			1.16085i	−0.814312	+	0.580427i	$0.802886\pi$
$348$	−13.3919	+	6.93217i	−0.717883	+	0.371603i
$349$	−1.37688	+	1.37688i	−0.0737029	+	0.0737029i	−0.742997	−	0.669294i	$-0.766597\pi$
$349$	−1.37688	+	1.37688i	−0.0737029	+	0.0737029i	0.669294	+	0.742997i	$0.266597\pi$
$350$	−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
$357$	2.09531	−	6.59239i	0.110895	−	0.348906i
$358$	−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
$366$	−4.26571	+	13.4210i	−0.222972	+	0.701529i
$367$	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
$369$	4.49926	+	26.2236i	0.234222	+	1.36515i
$370$	2.51878	+	2.51878i	0.130945	+	0.130945i
$371$	4.85178	+	4.85178i	0.251892	+	0.251892i
$372$	1.99024	−	6.26182i	0.103189	−	0.324660i
$373$	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
$375$	−9.63604	−	3.06269i	−0.497603	−	0.158157i
$376$		−	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	$-0.834730\pi$
$379$	−26.5622	−	26.5622i	−1.36441	−	1.36441i	−0.496196	−	0.868211i	$-0.665270\pi$
$380$		−	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	$0.145390\pi$
$384$	1.65068	+	0.524648i	0.0842359	+	0.0267733i
$385$	−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	$-0.341659\pi$
$389$	18.8229			0.954361			0.477180	+	0.878805i	$0.341659\pi$
$390$		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
$396$	2.13191	+	12.4257i	0.107132	+	0.624413i
$397$	−8.43859	+	8.43859i	−0.423521	+	0.423521i	−0.886414	−	0.462893i	$-0.846811\pi$
$397$	−8.43859	+	8.43859i	−0.423521	+	0.423521i	0.462893	+	0.886414i	$0.346811\pi$
$398$	−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
$405$	−4.92167	−	2.35055i	−0.244560	−	0.116800i
$406$	−6.62648			−0.328867
$407$	−24.7012			−1.22439
$408$	8.66150	+	2.75295i	0.428808	+	0.136291i
$409$	18.9725	+	18.9725i	0.938128	+	0.938128i	0.998194	−	0.0600662i	$-0.0191312\pi$
$409$	18.9725	+	18.9725i	0.938128	+	0.938128i	−0.0600662	+	0.998194i	$0.519131\pi$
$410$	−3.80051	−	3.80051i	−0.187694	−	0.187694i
$411$	16.4806	+	5.23814i	0.812927	+	0.258379i
$412$	−4.79880			−0.236420
$413$	−6.57587			−0.323577
$414$	0.946944	+	5.51919i	0.0465397	+	0.271253i
$415$			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	$-0.914726\pi$
$419$		−	10.8367i		−	0.529409i	0.964330	−	0.264704i	$-0.0852743\pi$
$420$	0.709488	−	0.367258i	0.0346195	−	0.0179204i
$421$	−22.8984	−	22.8984i	−1.11600	−	1.11600i	−0.992323	−	0.123676i	$-0.960532\pi$
$421$	−22.8984	−	22.8984i	−1.11600	−	1.11600i	−0.123676	−	0.992323i	$-0.539468\pi$
$422$	3.73322	−	3.73322i	0.181731	−	0.181731i
$423$	−23.9801	+	4.11433i	−1.16595	+	0.200045i
$424$	−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
$435$	−8.70927	−	2.76813i	−0.417578	−	0.132722i
$436$	−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	$0.407801\pi$
$443$			40.3416i			1.91669i	−0.285619	+	0.958343i	$0.592199\pi$
$444$	9.70248	+	3.08381i	0.460459	+	0.146351i
$445$	−3.96792			−0.188097
$446$	−3.55022			−0.168108
$447$	4.57860	−	14.4055i	0.216560	−	0.681357i
$448$	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	$0.715644\pi$
$450$	−13.6981	+	2.35022i	−0.645733	+	0.110790i
$451$	37.2709			1.75502
$452$	6.97128			0.327901
$453$	12.8857	−	40.5420i	0.605425	−	1.90483i
$454$			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	0.122750	−	0.992438i	$-0.460829\pi$
$457$	−18.5918	−	18.5918i	−0.869687	−	0.869687i	−0.992438	+	0.122750i	$0.960829\pi$
$458$			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	$0.135895\pi$
$462$	−1.67809	+	5.27972i	−0.0780719	+	0.245635i
$463$	−12.8578	+	12.8578i	−0.597552	+	0.597552i	−0.939661	−	0.342108i	$-0.888859\pi$
$463$	−12.8578	+	12.8578i	−0.597552	+	0.597552i	0.342108	+	0.939661i	$0.388859\pi$
$464$		−	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	$-0.404985\pi$
$467$	12.7104			0.588168			0.294084	+	0.955780i	$0.404985\pi$
$468$		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
$474$	−7.12498	+	22.4171i	−0.327261	+	1.02965i
$475$	−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
$483$	−0.745370	+	2.34513i	−0.0339155	+	0.106707i
$484$	6.66025			0.302739
$485$	9.54474			0.433404
$486$	−15.5804	+	0.500258i	−0.706743	+	0.0226921i
$487$	−4.75849	−	4.75849i	−0.215628	−	0.215628i	0.591025	−	0.806653i	$-0.298723\pi$
$487$	−4.75849	−	4.75849i	−0.215628	−	0.215628i	−0.806653	+	0.591025i	$0.798723\pi$
$488$	−5.74921	−	5.74921i	−0.260255	−	0.260255i
$489$	−2.75726	+	8.67507i	−0.124688	+	0.392300i
$490$	−3.89106			−0.175780
$491$	29.8138			1.34548			0.672740	−	0.739879i	$-0.265117\pi$
$491$	29.8138			1.34548			0.672740	+	0.739879i	$0.265117\pi$
$492$	−14.6398	−	4.65306i	−0.660011	−	0.209776i
$493$		−	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	$0.0498453\pi$
$499$	25.5487	+	25.5487i	1.14372	+	1.14372i	0.155954	+	0.987764i	$0.450155\pi$
$500$	4.12782	−	4.12782i	0.184602	−	0.184602i
$501$	−25.9630	−	8.25202i	−1.15994	−	0.368673i
$502$	−8.87855	+	8.87855i	−0.396269	+	0.396269i
$503$		−	42.5984i		−	1.89937i	−0.313210	−	0.949684i	$-0.601404\pi$
$503$		−	42.5984i		−	1.89937i	0.313210	−	0.949684i	$-0.398596\pi$
$504$	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
$513$	−14.1371	+	10.6931i	−0.624167	+	0.472112i
$514$	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	$0.135382\pi$
$521$			18.8358i			0.825213i	−0.910909	+	0.412607i	$0.864618\pi$
$522$	−25.7427	+	4.41675i	−1.12673	+	0.193316i
$523$	−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
$525$	−5.82037	−	1.84993i	−0.254022	−	0.0807376i
$526$	4.00855	+	4.00855i	0.174781	+	0.174781i
$527$	14.0752	+	14.0752i	0.613123	+	0.613123i
$528$	−6.93684	−	2.20478i	−0.301887	−	0.0959509i
$529$	−19.5158			−0.848511
$530$	−5.46326			−0.237309
$531$	−25.5461	+	4.38302i	−1.10861	+	0.190207i
$532$		−	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
$540$	2.51145	−	1.89963i	0.108076	−	0.0817470i
$541$	13.7056	−	13.7056i	0.589250	−	0.589250i	−0.348179	−	0.937428i	$-0.613200\pi$
$541$	13.7056	−	13.7056i	0.589250	−	0.589250i	0.937428	+	0.348179i	$0.113200\pi$
$542$		−	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
$552$	−3.08118	−	0.979314i	−0.131144	−	0.0416824i
$553$	−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
$561$	−36.3992	−	11.5690i	−1.53677	−	0.488444i
$562$	−13.4290			−0.566467
$563$	24.4117			1.02883			0.514416	−	0.857541i	$-0.328009\pi$
$563$	24.4117			1.02883			0.514416	+	0.857541i	$0.328009\pi$
$564$	4.25497	−	13.3873i	0.179167	−	0.563705i
$565$	2.98733	+	2.98733i	0.125678	+	0.125678i
$566$	22.2287	+	22.2287i	0.934342	+	0.934342i
$567$	−6.18125	−	2.95212i	−0.259588	−	0.123977i
$568$	−10.4303			−0.437647
$569$	−5.97665			−0.250554			−0.125277	−	0.992122i	$-0.539982\pi$
$569$	−5.97665			−0.250554			−0.125277	+	0.992122i	$0.539982\pi$
$570$	1.08461	−	3.41247i	0.0454293	−	0.142933i
$571$			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	0.933548	−	0.358453i	$-0.116696\pi$
$577$	13.8142	+	13.8142i	0.575094	+	0.575094i	−0.358453	+	0.933548i	$0.616696\pi$
$578$	−7.44826	+	7.44826i	−0.309807	+	0.309807i
$579$	5.95181	−	18.7260i	0.247349	−	0.778225i
$580$	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
$591$	2.45702	−	7.73044i	0.101068	−	0.317988i
$592$	−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	$-0.896357\pi$
$599$		−	15.6579i		−	0.639764i	0.947457	−	0.319882i	$-0.103643\pi$
$600$	2.43056	−	7.64717i	0.0992271	−	0.312195i
$601$	−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
$603$	0.309799	−	0.0531532i	0.0126160	−	0.00216456i
$604$	17.3671	+	17.3671i	0.706657	+	0.706657i
$605$	2.85405	+	2.85405i	0.116034	+	0.116034i
$606$	−1.71696	+	5.40202i	−0.0697469	+	0.219442i
$607$	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
$609$	−10.9382	−	3.47657i	−0.443238	−	0.140878i
$610$		−	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	0.843788	−	0.536677i	$-0.180321\pi$
$613$	7.60371	+	7.60371i	0.307111	+	0.307111i	−0.536677	+	0.843788i	$0.680321\pi$
$614$			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	$0.331602\pi$
$618$	−7.92129	−	2.51768i	−0.318641	−	0.101276i
$619$	−5.08096	+	5.08096i	−0.204221	+	0.204221i	−0.801806	−	0.597585i	$-0.796127\pi$
$619$	−5.08096	+	5.08096i	−0.204221	+	0.204221i	0.597585	+	0.801806i	$0.296127\pi$
$620$			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
$630$	1.36382	−	0.233994i	0.0543359	−	0.00932256i
$631$	17.5431	−	17.5431i	0.698378	−	0.698378i	−0.265682	−	0.964061i	$-0.585597\pi$
$631$	17.5431	−	17.5431i	0.698378	−	0.698378i	0.964061	+	0.265682i	$0.0855973\pi$
$632$	−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
$639$	5.29137	+	30.8404i	0.209323	+	1.22003i
$640$	−0.606018			−0.0239550
$641$	−11.8520			−0.468127			−0.234064	−	0.972221i	$-0.575202\pi$
$641$	−11.8520			−0.468127			−0.234064	+	0.972221i	$0.575202\pi$
$642$	5.15846	+	1.63955i	0.203588	+	0.0647079i
$643$	−19.6347	−	19.6347i	−0.774319	−	0.774319i	0.204540	−	0.978858i	$-0.434430\pi$
$643$	−19.6347	−	19.6347i	−0.774319	−	0.774319i	−0.978858	+	0.204540i	$0.934430\pi$
$644$	−1.00459	−	1.00459i	−0.0395864	−	0.0395864i
$645$	−1.95101	−	0.620105i	−0.0768211	−	0.0244166i
$646$	17.8999			0.704262
$647$	−19.6923			−0.774182			−0.387091	−	0.922041i	$-0.626520\pi$
$647$	−19.6923			−0.774182			−0.387091	+	0.922041i	$0.626520\pi$
$648$	3.87868	−	8.12132i	0.152369	−	0.319036i
$649$			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	$-0.599861\pi$
$653$		−	48.6132i		−	1.90238i	0.308602	−	0.951191i	$-0.400139\pi$
$654$	−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
$657$	−4.00192	−	23.3249i	−0.156130	−	0.909991i
$658$	4.36479	−	4.36479i	0.170157	−	0.170157i
$659$			3.70793i			0.144440i	0.997389	+	0.0722202i	$0.0230084\pi$
$659$			3.70793i			0.144440i	−0.997389	+	0.0722202i	$0.976992\pi$
$660$	−2.02778	−	3.91736i	−0.0789311	−	0.152483i
$661$	4.54658	−	4.54658i	0.176842	−	0.176842i	−0.613136	−	0.789977i	$-0.710092\pi$
$661$	4.54658	−	4.54658i	0.176842	−	0.176842i	0.789977	+	0.613136i	$0.210092\pi$
$662$	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
$669$	−5.86029	−	1.86262i	−0.226572	−	0.0720129i
$670$	−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	$0.156243\pi$
$677$			24.5297i			0.942753i	−0.881932	+	0.471376i	$0.843757\pi$
$678$	11.5073	+	3.65746i	0.441937	+	0.140464i
$679$	11.9875			0.460037
$680$	−3.17992			−0.121944
$681$	−2.63726	+	8.29751i	−0.101060	+	0.317961i
$682$	−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	$0.578431\pi$
$684$	−1.73057	−	10.0865i	−0.0661702	−	0.385668i
$685$	−6.05056			−0.231180
$686$	−10.2147			−0.389999
$687$	−8.45018	+	26.5865i	−0.322394	+	1.01434i
$688$		−	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	0.834489	−	0.551025i	$-0.185763\pi$
$691$	7.45140	+	7.45140i	0.283464	+	0.283464i	−0.551025	+	0.834489i	$0.685763\pi$
$692$		−	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
$696$	4.56774	−	14.3713i	0.173140	−	0.544743i
$697$	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	$-0.133699\pi$
$701$	48.3500			1.82616			0.913078	+	0.407785i	$0.133699\pi$
$702$		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
$708$	4.53284	−	14.2615i	0.170355	−	0.535981i
$709$	−20.8103	+	20.8103i	−0.781546	+	0.781546i	−0.980092	−	0.198545i	$-0.936378\pi$
$709$	−20.8103	+	20.8103i	−0.781546	+	0.781546i	0.198545	+	0.980092i	$0.436378\pi$
$710$	−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
$717$	−4.51289	+	14.1988i	−0.168537	+	0.530262i
$718$	22.4661			0.838428
$719$	−42.8472			−1.59793			−0.798966	−	0.601376i	$-0.794619\pi$
$719$	−42.8472			−1.59793			−0.798966	+	0.601376i	$0.794619\pi$
$720$	0.307437	+	1.79187i	0.0114575	+	0.0667791i
$721$	−2.58266	−	2.58266i	−0.0961834	−	0.0961834i
$722$	5.20643	+	5.20643i	0.193763	+	0.193763i
$723$	3.22425	−	10.1443i	0.119911	−	0.377272i
$724$	11.1172			0.413167
$725$	−40.3340			−1.49797
$726$	10.9939	+	3.49429i	0.408024	+	0.129685i
$727$		−	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	0.153204	−	0.988195i	$-0.451041\pi$
$733$	−22.6065	−	22.6065i	−0.834990	−	0.834990i	−0.988195	+	0.153204i	$0.951041\pi$
$734$	−0.425510	+	0.425510i	−0.0157059	+	0.0157059i
$735$	−6.42290	−	2.04144i	−0.236912	−	0.0752996i
$736$	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	−0.725753	−	0.687955i	$-0.758508\pi$
$739$	−1.02751	+	1.02751i	−0.0377976	+	0.0377976i	0.687955	+	0.725753i	$0.258508\pi$
$740$	−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
$747$	0.715233	+	4.16869i	0.0261690	+	0.152524i
$748$	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
$756$	3.15419	−	2.38579i	0.114717	−	0.0867705i
$757$	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
$759$	12.9484	+	4.11548i	0.469997	+	0.149382i
$760$	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	$0.754686\pi$
$762$	3.68922	+	1.17257i	0.133646	+	0.0424777i
$763$	−0.983805			−0.0356161
$764$	5.73244			0.207392
$765$	1.61319	+	9.40237i	0.0583251	+	0.339943i
$766$			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	0.848352	−	0.529433i	$-0.177595\pi$
$769$	8.84388	+	8.84388i	0.318918	+	0.318918i	−0.529433	+	0.848352i	$0.677595\pi$
$770$		−	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	$0.161970\pi$
$774$	−5.76677	+	0.989422i	−0.207282	+	0.0355640i
$775$	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
$786$	−36.4562	−	11.5871i	−1.30035	−	0.413300i
$787$	19.7245	−	19.7245i	0.703104	−	0.703104i	−0.261972	−	0.965076i	$-0.584373\pi$
$787$	19.7245	−	19.7245i	0.703104	−	0.703104i	0.965076	+	0.261972i	$0.0843727\pi$
$788$	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
$795$	−9.01810	−	2.86629i	−0.319839	−	0.101657i
$796$	12.9027			0.457324
$797$	43.8082			1.55177			0.775883	−	0.630877i	$-0.217305\pi$
$797$	43.8082			1.55177			0.775883	+	0.630877i	$0.217305\pi$
$798$	1.36219	−	4.28581i	0.0482210	−	0.151716i
$799$	30.0915	+	30.0915i	1.06456	+	1.06456i
$800$	3.27584	+	3.27584i	0.115819	+	0.115819i
$801$	−19.3597	+	3.32160i	−0.684041	+	0.117363i
$802$	−24.2212			−0.855280
$803$	−33.1510			−1.16987
$804$	−0.0549702	+	0.172951i	−0.00193865	+	0.00609950i
$805$		−	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	$-0.997827\pi$
$809$		−	0.388416i		−	0.0136560i	0.999977	−	0.00682798i	$-0.00217343\pi$
$810$	5.14224	−	1.81805i	0.180680	−	0.0638799i
$811$	−5.70744	−	5.70744i	−0.200415	−	0.200415i	0.599763	−	0.800178i	$-0.295262\pi$
$811$	−5.70744	−	5.70744i	−0.200415	−	0.200415i	−0.800178	+	0.599763i	$0.795262\pi$
$812$	4.68563	−	4.68563i	0.164433	−	0.164433i
$813$	12.8685	−	40.4878i	0.451319	−	1.41997i
$814$	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
$825$	−10.2142	+	32.1366i	−0.355613	+	1.11885i
$826$	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
$834$	−1.97532	+	6.21486i	−0.0683996	+	0.215203i
$835$	9.53187			0.329864
$836$	−14.3357			−0.495811
$837$	15.7209	−	11.8911i	0.543393	−	0.411016i
$838$	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	$0.675391\pi$
$840$	−0.241993	+	0.761375i	−0.00834956	+	0.0262699i
$841$	−46.7996			−1.61378
$842$	32.3832			1.11600
$843$	−22.1669	−	7.04547i	−0.763469	−	0.242659i
$844$			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
$852$	−17.2171	−	5.47225i	−0.589850	−	0.187476i
$853$	−8.09779	+	8.09779i	−0.277263	+	0.277263i	−0.832015	−	0.554752i	$-0.812813\pi$
$853$	−8.09779	+	8.09779i	−0.277263	+	0.277263i	0.554752	+	0.832015i	$0.312813\pi$
$854$		−	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	$-0.484681\pi$
$857$	2.81672			0.0962173			0.0481086	+	0.998842i	$0.484681\pi$
$858$		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	$0.115817\pi$
$864$	3.13461	+	4.14418i	0.106642	+	0.140988i
$865$	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
$873$	46.5693	−	7.99003i	1.57613	−	0.270421i
$874$	−6.36758			−0.215387
$875$	4.44309			0.150204
$876$	13.0215	+	4.13872i	0.439956	+	0.139834i
$877$	−21.8195	−	21.8195i	−0.736793	−	0.736793i	0.235163	−	0.971956i	$-0.424438\pi$
$877$	−21.8195	−	21.8195i	−0.736793	−	0.736793i	−0.971956	+	0.235163i	$0.924438\pi$
$878$	10.5121	+	10.5121i	0.354766	+	0.354766i
$879$	3.45791	+	1.09905i	0.116633	+	0.0370702i
$880$	2.54674			0.0858505
$881$	46.2624			1.55862			0.779310	−	0.626638i	$-0.215570\pi$
$881$	46.2624			1.55862			0.779310	+	0.626638i	$0.215570\pi$
$882$	−18.9847	+	3.25726i	−0.639249	+	0.109678i
$883$		−	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	$-0.791744\pi$
$887$		−	36.2495i		−	1.21714i	0.793500	−	0.608570i	$-0.208256\pi$
$888$	−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
$891$	−16.2998	+	34.1291i	−0.546064	+	1.14337i
$892$	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
$903$	−2.45033	−	0.778806i	−0.0815418	−	0.0259170i
$904$	−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	$-0.933626\pi$
$911$		−	12.4963i		−	0.414022i	0.978339	−	0.207011i	$-0.0663737\pi$
$912$	5.63097	+	1.78973i	0.186460	+	0.0592640i
$913$	5.92484			0.196083
$914$	26.2928			0.869687
$915$	2.58510	−	8.13340i	0.0854607	−	0.268882i
$916$	−11.3889	−	11.3889i	−0.376301	−	0.376301i
$917$	−11.8862	−	11.8862i	−0.392517	−	0.392517i
$918$	16.4480	+	21.7455i	0.542865	+	0.717708i
$919$	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
$921$	−1.41967	+	4.46666i	−0.0467797	+	0.147181i
$922$			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	$0.188265\pi$
$930$	−1.20612	+	3.79478i	−0.0395503	+	0.124436i
$931$	−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	$-0.0540204\pi$
$942$	5.80855	−	18.2752i	0.189253	−	0.595439i
$943$	−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
$951$	−2.91649	+	9.17604i	−0.0945735	+	0.297553i
$952$	−3.99374			−0.129438
$953$	−6.54349			−0.211964			−0.105982	−	0.994368i	$-0.533799\pi$
$953$	−6.54349			−0.211964			−0.105982	+	0.994368i	$0.533799\pi$
$954$	−26.6555	+	4.57337i	−0.863005	+	0.148068i
$955$	2.45646	+	2.45646i	0.0794893	+	0.0794893i
$956$	−6.08236	−	6.08236i	−0.196718	−	0.196718i
$957$	−19.1955	+	60.3941i	−0.620502	+	1.95226i
$958$	35.8276			1.15754
$959$	−7.59905			−0.245386
$960$	−1.00034	−	0.317946i	−0.0322859	−	0.0102617i
$961$		−	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	0.509901	−	0.860233i	$-0.329682\pi$
$967$	−10.8941	−	10.8941i	−0.350332	−	0.350332i	−0.860233	+	0.509901i	$0.829682\pi$
$968$	−4.70951	+	4.70951i	−0.151369	+	0.151369i
$969$	29.5470	+	9.39114i	0.949187	+	0.301687i
$970$	−6.74915	+	6.74915i	−0.216702	+	0.216702i
$971$			2.39332i			0.0768053i	0.999262	+	0.0384027i	$0.0122270\pi$
$971$			2.39332i			0.0768053i	−0.999262	+	0.0384027i	$0.987773\pi$
$972$	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
$981$	−3.82191	+	0.655736i	−0.122024	+	0.0209360i
$982$	−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
$990$	−1.29198	−	7.53018i	−0.0410617	−	0.239325i
$991$	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
$993$	32.6058	+	10.3633i	1.03471	+	0.328871i
$994$	−5.61349	−	5.61349i	−0.178049	−	0.178049i
$995$	5.52906	+	5.52906i	0.175283	+	0.175283i
$996$	−2.32724	−	0.739683i	−0.0737413	−	0.0234377i
$997$	−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
$999$	18.4248	+	24.3589i	0.582935	+	0.770683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.c.437.1		16
3.2	odd	2	inner	1014.2.g.c.437.5		16
13.3	even	3		78.2.k.a.59.2	yes	16
13.5	odd	4	inner	1014.2.g.c.239.5		16
13.6	odd	12		78.2.k.a.41.4	yes	16
13.8	odd	4		1014.2.g.d.239.1		16
13.12	even	2		1014.2.g.d.437.5		16
39.5	even	4	inner	1014.2.g.c.239.1		16
39.8	even	4		1014.2.g.d.239.5		16
39.29	odd	6		78.2.k.a.59.4	yes	16
39.32	even	12		78.2.k.a.41.2	✓	16
39.38	odd	2		1014.2.g.d.437.1		16
52.3	odd	6		624.2.cn.d.449.2		16
52.19	even	12		624.2.cn.d.353.1		16
156.71	odd	12		624.2.cn.d.353.2		16
156.107	even	6		624.2.cn.d.449.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.41.2	✓	16	39.32	even	12
78.2.k.a.41.4	yes	16	13.6	odd	12
78.2.k.a.59.2	yes	16	13.3	even	3
78.2.k.a.59.4	yes	16	39.29	odd	6
624.2.cn.d.353.1		16	52.19	even	12
624.2.cn.d.353.2		16	156.71	odd	12
624.2.cn.d.449.1		16	156.107	even	6
624.2.cn.d.449.2		16	52.3	odd	6
1014.2.g.c.239.1		16	39.5	even	4	inner
1014.2.g.c.239.5		16	13.5	odd	4	inner
1014.2.g.c.437.1		16	1.1	even	1	trivial
1014.2.g.c.437.5		16	3.2	odd	2	inner
1014.2.g.d.239.1		16	13.8	odd	4
1014.2.g.d.239.5		16	39.8	even	4
1014.2.g.d.437.1		16	39.38	odd	2
1014.2.g.d.437.5		16	13.12	even	2

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} +(0.524648 - 1.65068i) 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} +(-0.317946 + 1.00034i) q^{15} -1.00000 q^{16} -5.24723 q^{17} +(0.507306 + 2.95680i) q^{18} +(2.41216 + 2.41216i) q^{19} +(-0.428520 - 0.428520i) q^{20} +(-0.399317 + 1.25636i) q^{21} +4.20241 q^{22} +1.86661 q^{23} +(-1.65068 - 0.524648i) 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} +(6.93684 + 2.20478i) 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} +(-0.307437 - 1.79187i) 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} +(-3.13461 - 4.14418i) q^{54} -2.54674 q^{55} +0.761114 q^{56} +(-5.63097 - 1.78973i) q^{57} +(-6.15628 - 6.15628i) q^{58} +(-6.10925 - 6.10925i) q^{59} +(1.00034 + 0.317946i) q^{60} -8.13061 q^{61} +3.79348 q^{62} +(-0.386118 - 2.25046i) 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} +(2.95680 - 0.507306i) 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} +(1.25636 + 0.399317i) 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} +(6.26182 + 1.99024i) q^{93} +8.11015 q^{94} +2.06731 q^{95} +(-0.524648 + 1.65068i) q^{96} +(11.1369 + 11.1369i) q^{97} +(-4.54012 - 4.54012i) q^{98} +(-12.4257 + 2.13191i) 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

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Database

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