LMFDB - Embedded newform 400.2.q.e.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(149,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("400.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			349.1
Root			$-0.507829 - 1.31989i$ of defining polynomial
Character	$\chi$	$=$	400.349
Dual form			400.2.q.e.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31989 - 0.507829i) q^{2} +(0.0623209 - 0.0623209i) q^{3} +(1.48422 + 1.34056i) q^{4} +(-0.113905 + 0.0506084i) q^{6} -0.375877 q^{7} +(-1.27824 - 2.52312i) q^{8} +2.99223i q^{9} +O(q^{10})$	\(q+(-1.31989 - 0.507829i) q^{2} +(0.0623209 - 0.0623209i) q^{3} +(1.48422 + 1.34056i) q^{4} +(-0.113905 + 0.0506084i) q^{6} -0.375877 q^{7} +(-1.27824 - 2.52312i) q^{8} +2.99223i q^{9} +(2.36756 - 2.36756i) q^{11} +(0.176043 - 0.00895328i) q^{12} +(1.76442 - 1.76442i) q^{13} +(0.496116 + 0.190881i) q^{14} +(0.405819 + 3.97936i) q^{16} +4.64955i q^{17} +(1.51954 - 3.94942i) q^{18} +(2.34965 + 2.34965i) q^{19} +(-0.0234250 + 0.0234250i) q^{21} +(-4.32723 + 1.92260i) q^{22} +2.07779 q^{23} +(-0.236904 - 0.0775821i) q^{24} +(-3.22487 + 1.43282i) q^{26} +(0.373441 + 0.373441i) q^{27} +(-0.557884 - 0.503884i) q^{28} +(-2.55422 - 2.55422i) q^{29} +8.51714 q^{31} +(1.48520 - 5.45841i) q^{32} -0.295096i q^{33} +(2.36118 - 6.13690i) q^{34} +(-4.01125 + 4.44113i) q^{36} +(7.62613 + 7.62613i) q^{37} +(-1.90806 - 4.29450i) q^{38} -0.219921i q^{39} -3.77709i q^{41} +(0.0428143 - 0.0190225i) q^{42} +(6.21191 + 6.21191i) q^{43} +(6.68782 - 0.340133i) q^{44} +(-2.74246 - 1.05516i) q^{46} -9.71696i q^{47} +(0.273288 + 0.222706i) q^{48} -6.85872 q^{49} +(0.289764 + 0.289764i) q^{51} +(4.98410 - 0.253484i) q^{52} +(3.03609 + 3.03609i) q^{53} +(-0.303257 - 0.682545i) q^{54} +(0.480459 + 0.948381i) q^{56} +0.292864 q^{57} +(2.07418 + 4.66840i) q^{58} +(8.11663 - 8.11663i) q^{59} +(0.728329 + 0.728329i) q^{61} +(-11.2417 - 4.32525i) q^{62} -1.12471i q^{63} +(-4.73223 + 6.45027i) q^{64} +(-0.149858 + 0.389495i) q^{66} +(-0.969239 + 0.969239i) q^{67} +(-6.23299 + 6.90096i) q^{68} +(0.129490 - 0.129490i) q^{69} -9.14230i q^{71} +(7.54975 - 3.82478i) q^{72} -7.56793 q^{73} +(-6.19289 - 13.9384i) q^{74} +(0.337561 + 6.63723i) q^{76} +(-0.889909 + 0.889909i) q^{77} +(-0.111682 + 0.290271i) q^{78} -11.8065 q^{79} -8.93015 q^{81} +(-1.91811 + 4.98534i) q^{82} +(-10.6393 + 10.6393i) q^{83} +(-0.0661703 + 0.00336533i) q^{84} +(-5.04445 - 11.3536i) q^{86} -0.318363 q^{87} +(-8.99991 - 2.94733i) q^{88} +15.7111i q^{89} +(-0.663205 + 0.663205i) q^{91} +(3.08390 + 2.78540i) q^{92} +(0.530796 - 0.530796i) q^{93} +(-4.93455 + 12.8253i) q^{94} +(-0.247614 - 0.432731i) q^{96} +3.86020i q^{97} +(9.05275 + 3.48305i) q^{98} +(7.08428 + 7.08428i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8	$ 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8} - 2 q^{11} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 2 q^{16} + 18 q^{18} + 14 q^{19} - 20 q^{21} + 20 q^{22} - 12 q^{23} + 14 q^{24} - 16 q^{26} - 10 q^{27} + 10 q^{28} - 4 q^{31} - 2 q^{32} + 6 q^{34} + 2 q^{36} + 8 q^{37} - 28 q^{38} - 10 q^{42} + 44 q^{44} - 10 q^{46} + 58 q^{48} - 4 q^{49} + 10 q^{51} + 16 q^{53} - 10 q^{54} + 6 q^{56} + 16 q^{57} - 4 q^{58} - 20 q^{59} + 4 q^{61} - 22 q^{62} - 38 q^{64} + 32 q^{66} - 50 q^{67} - 50 q^{68} + 54 q^{72} - 40 q^{73} - 10 q^{74} + 60 q^{76} + 8 q^{77} + 48 q^{78} - 12 q^{79} - 8 q^{81} + 12 q^{82} - 2 q^{83} - 34 q^{84} + 6 q^{86} + 64 q^{87} - 56 q^{88} - 50 q^{92} - 44 q^{93} - 32 q^{94} - 34 q^{96} + 30 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8 - 2 * q^11 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 2 * q^16 + 18 * q^18 + 14 * q^19 - 20 * q^21 + 20 * q^22 - 12 * q^23 + 14 * q^24 - 16 * q^26 - 10 * q^27 + 10 * q^28 - 4 * q^31 - 2 * q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 28 * q^38 - 10 * q^42 + 44 * q^44 - 10 * q^46 + 58 * q^48 - 4 * q^49 + 10 * q^51 + 16 * q^53 - 10 * q^54 + 6 * q^56 + 16 * q^57 - 4 * q^58 - 20 * q^59 + 4 * q^61 - 22 * q^62 - 38 * q^64 + 32 * q^66 - 50 * q^67 - 50 * q^68 + 54 * q^72 - 40 * q^73 - 10 * q^74 + 60 * q^76 + 8 * q^77 + 48 * q^78 - 12 * q^79 - 8 * q^81 + 12 * q^82 - 2 * q^83 - 34 * q^84 + 6 * q^86 + 64 * q^87 - 56 * q^88 - 50 * q^92 - 44 * q^93 - 32 * q^94 - 34 * q^96 + 30 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.31989	−	0.507829i	−0.933303	−	0.359089i
$2$	−1.31989	−	0.507829i	−0.933303	−	0.359089i
$3$	0.0623209	−	0.0623209i	0.0359810	−	0.0359810i	−0.688887	−	0.724868i	$-0.741901\pi$
$3$	0.0623209	−	0.0623209i	0.0359810	−	0.0359810i	0.724868	+	0.688887i	$0.241901\pi$
$4$	1.48422	+	1.34056i	0.742110	+	0.670278i
$5$		0			0
$5$		0			0
$6$	−0.113905	+	0.0506084i	−0.0465015	+	0.0206608i
$7$	−0.375877			−0.142068			−0.0710340	−	0.997474i	$-0.522630\pi$
$7$	−0.375877			−0.142068			−0.0710340	+	0.997474i	$0.522630\pi$
$8$	−1.27824	−	2.52312i	−0.451924	−	0.892056i
$9$			2.99223i			0.997411i
$10$		0			0
$11$	2.36756	−	2.36756i	0.713845	−	0.713845i	−0.253492	−	0.967337i	$-0.581579\pi$
$11$	2.36756	−	2.36756i	0.713845	−	0.713845i	0.967337	+	0.253492i	$0.0815793\pi$
$12$	0.176043	−	0.00895328i	0.0508191	−	0.00258459i
$13$	1.76442	−	1.76442i	0.489363	−	0.489363i	−0.418742	−	0.908105i	$-0.637529\pi$
$13$	1.76442	−	1.76442i	0.489363	−	0.489363i	0.908105	+	0.418742i	$0.137529\pi$
$14$	0.496116	+	0.190881i	0.132593	+	0.0510151i
$15$		0			0
$16$	0.405819	+	3.97936i	0.101455	+	0.994840i
$17$			4.64955i			1.12768i	0.825883	+	0.563841i	$0.190677\pi$
$17$			4.64955i			1.12768i	−0.825883	+	0.563841i	$0.809323\pi$
$18$	1.51954	−	3.94942i	0.358159	−	0.930887i
$19$	2.34965	+	2.34965i	0.539047	+	0.539047i	0.923249	−	0.384202i	$-0.125524\pi$
$19$	2.34965	+	2.34965i	0.539047	+	0.539047i	−0.384202	+	0.923249i	$0.625524\pi$
$20$		0			0
$21$	−0.0234250	+	0.0234250i	−0.00511175	+	0.00511175i
$22$	−4.32723	+	1.92260i	−0.922568	+	0.409900i
$23$	2.07779			0.433250			0.216625	−	0.976255i	$-0.430495\pi$
$23$	2.07779			0.433250			0.216625	+	0.976255i	$0.430495\pi$
$24$	−0.236904	−	0.0775821i	−0.0483577	−	0.0158364i
$25$		0			0
$26$	−3.22487	+	1.43282i	−0.632449	+	0.280999i
$27$	0.373441	+	0.373441i	0.0718688	+	0.0718688i
$28$	−0.557884	−	0.503884i	−0.105430	−	0.0952251i
$29$	−2.55422	−	2.55422i	−0.474307	−	0.474307i	0.428998	−	0.903305i	$-0.358867\pi$
$29$	−2.55422	−	2.55422i	−0.474307	−	0.474307i	−0.903305	+	0.428998i	$0.858867\pi$
$30$		0			0
$31$	8.51714			1.52972			0.764862	−	0.644194i	$-0.222807\pi$
$31$	8.51714			1.52972			0.764862	+	0.644194i	$0.222807\pi$
$32$	1.48520	−	5.45841i	0.262548	−	0.964919i
$33$		−	0.295096i		−	0.0513697i
$34$	2.36118	−	6.13690i	0.404938	−	1.05247i
$35$		0			0
$36$	−4.01125	+	4.44113i	−0.668542	+	0.740189i
$37$	7.62613	+	7.62613i	1.25373	+	1.25373i	0.954036	+	0.299691i	$0.0968837\pi$
$37$	7.62613	+	7.62613i	1.25373	+	1.25373i	0.299691	+	0.954036i	$0.403116\pi$
$38$	−1.90806	−	4.29450i	−0.309528	−	0.696660i
$39$		−	0.219921i		−	0.0352155i
$40$		0			0
$41$		−	3.77709i		−	0.589882i	−0.955515	−	0.294941i	$-0.904700\pi$
$41$		−	3.77709i		−	0.589882i	0.955515	−	0.294941i	$-0.0953001\pi$
$42$	0.0428143	−	0.0190225i	0.00660638	−	0.00293524i
$43$	6.21191	+	6.21191i	0.947307	+	0.947307i	0.998680	−	0.0513725i	$-0.0163596\pi$
$43$	6.21191	+	6.21191i	0.947307	+	0.947307i	−0.0513725	+	0.998680i	$0.516360\pi$
$44$	6.68782	−	0.340133i	1.00823	−	0.0512770i
$45$		0			0
$46$	−2.74246	−	1.05516i	−0.404353	−	0.155575i
$47$		−	9.71696i		−	1.41736i	−0.705528	−	0.708682i	$-0.749290\pi$
$47$		−	9.71696i		−	1.41736i	0.705528	−	0.708682i	$-0.250710\pi$
$48$	0.273288	+	0.222706i	0.0394458	+	0.0321449i
$49$	−6.85872			−0.979817
$50$		0			0
$51$	0.289764	+	0.289764i	0.0405751	+	0.0405751i
$52$	4.98410	−	0.253484i	0.691170	−	0.0351520i
$53$	3.03609	+	3.03609i	0.417040	+	0.417040i	0.884182	−	0.467143i	$-0.154717\pi$
$53$	3.03609	+	3.03609i	0.417040	+	0.417040i	−0.467143	+	0.884182i	$0.654717\pi$
$54$	−0.303257	−	0.682545i	−0.0412681	−	0.0928827i
$55$		0			0
$56$	0.480459	+	0.948381i	0.0642040	+	0.126733i
$57$	0.292864			0.0387908
$58$	2.07418	+	4.66840i	0.272354	+	0.612991i
$59$	8.11663	−	8.11663i	1.05670	−	1.05670i	0.0584019	−	0.998293i	$-0.481400\pi$
$59$	8.11663	−	8.11663i	1.05670	−	1.05670i	0.998293	−	0.0584019i	$-0.0186005\pi$
$60$		0			0
$61$	0.728329	+	0.728329i	0.0932529	+	0.0932529i	0.752194	−	0.658941i	$-0.228995\pi$
$61$	0.728329	+	0.728329i	0.0932529	+	0.0932529i	−0.658941	+	0.752194i	$0.728995\pi$
$62$	−11.2417	−	4.32525i	−1.42770	−	0.549307i
$63$		−	1.12471i		−	0.141700i
$64$	−4.73223	+	6.45027i	−0.591529	+	0.806284i
$65$		0			0
$66$	−0.149858	+	0.389495i	−0.0184463	+	0.0479435i
$67$	−0.969239	+	0.969239i	−0.118411	+	0.118411i	−0.763829	−	0.645418i	$-0.776683\pi$
$67$	−0.969239	+	0.969239i	−0.118411	+	0.118411i	0.645418	+	0.763829i	$0.276683\pi$
$68$	−6.23299	+	6.90096i	−0.755860	+	0.836864i
$69$	0.129490	−	0.129490i	0.0155887	−	0.0155887i
$70$		0			0
$71$		−	9.14230i		−	1.08499i	−0.840058	−	0.542496i	$-0.817479\pi$
$71$		−	9.14230i		−	1.08499i	0.840058	−	0.542496i	$-0.182521\pi$
$72$	7.54975	−	3.82478i	0.889747	−	0.450754i
$73$	−7.56793			−0.885759			−0.442879	−	0.896581i	$-0.646043\pi$
$73$	−7.56793			−0.885759			−0.442879	+	0.896581i	$0.646043\pi$
$74$	−6.19289	−	13.9384i	−0.719908	−	1.62031i
$75$		0			0
$76$	0.337561	+	6.63723i	0.0387209	+	0.761343i
$77$	−0.889909	+	0.889909i	−0.101415	+	0.101415i
$78$	−0.111682	+	0.290271i	−0.0126455	+	0.0328667i
$79$	−11.8065			−1.32834			−0.664169	−	0.747583i	$-0.731214\pi$
$79$	−11.8065			−1.32834			−0.664169	+	0.747583i	$0.731214\pi$
$80$		0			0
$81$	−8.93015			−0.992239
$82$	−1.91811	+	4.98534i	−0.211820	+	0.550539i
$83$	−10.6393	+	10.6393i	−1.16782	+	1.16782i	−0.185101	+	0.982720i	$0.559261\pi$
$83$	−10.6393	+	10.6393i	−1.16782	+	1.16782i	−0.982720	+	0.185101i	$0.940739\pi$
$84$	−0.0661703	+	0.00336533i	−0.00721977	+	0.000367188i
$85$		0			0
$86$	−5.04445	−	11.3536i	−0.543957	−	1.22429i
$87$	−0.318363			−0.0341320
$88$	−8.99991	−	2.94733i	−0.959394	−	0.314186i
$89$			15.7111i			1.66538i	0.553741	+	0.832689i	$0.313200\pi$
$89$			15.7111i			1.66538i	−0.553741	+	0.832689i	$0.686800\pi$
$90$		0			0
$91$	−0.663205	+	0.663205i	−0.0695228	+	0.0695228i
$92$	3.08390	+	2.78540i	0.321519	+	0.290398i
$93$	0.530796	−	0.530796i	0.0550410	−	0.0550410i
$94$	−4.93455	+	12.8253i	−0.508960	+	1.32283i
$95$		0			0
$96$	−0.247614	−	0.432731i	−0.0252720	−	0.0441655i
$97$			3.86020i			0.391943i	0.980610	+	0.195972i	$0.0627861\pi$
$97$			3.86020i			0.391943i	−0.980610	+	0.195972i	$0.937214\pi$
$98$	9.05275	+	3.48305i	0.914466	+	0.351841i
$99$	7.08428	+	7.08428i	0.711997	+	0.711997i
$100$		0			0
$101$	−6.87437	+	6.87437i	−0.684026	+	0.684026i	−0.960905	−	0.276879i	$-0.910700\pi$
$101$	−6.87437	+	6.87437i	−0.684026	+	0.684026i	0.276879	+	0.960905i	$0.410700\pi$
$102$	−0.235306	−	0.529607i	−0.0232988	−	0.0524390i
$103$	−1.15407			−0.113714			−0.0568571	−	0.998382i	$-0.518108\pi$
$103$	−1.15407			−0.113714			−0.0568571	+	0.998382i	$0.518108\pi$
$104$	−6.70719	−	2.19650i	−0.657694	−	0.215384i
$105$		0			0
$106$	−2.46549	−	5.54913i	−0.239470	−	0.538979i
$107$	−5.70435	−	5.70435i	−0.551460	−	0.551460i	0.375402	−	0.926862i	$-0.377505\pi$
$107$	−5.70435	−	5.70435i	−0.551460	−	0.551460i	−0.926862	+	0.375402i	$0.877505\pi$
$108$	0.0536502	+	1.05489i	0.00516249	+	0.101507i
$109$	−11.1863	−	11.1863i	−1.07145	−	1.07145i	−0.997243	−	0.0742092i	$-0.976357\pi$
$109$	−11.1863	−	11.1863i	−1.07145	−	1.07145i	−0.0742092	−	0.997243i	$-0.523643\pi$
$110$		0			0
$111$	0.950534			0.0902207
$112$	−0.152538	−	1.49575i	−0.0144135	−	0.141335i
$113$		−	4.08163i		−	0.383967i	−0.981398	−	0.191984i	$-0.938508\pi$
$113$		−	4.08163i		−	0.383967i	0.981398	−	0.191984i	$-0.0614920\pi$
$114$	−0.386549	−	0.148725i	−0.0362036	−	0.0139294i
$115$		0			0
$116$	−0.366950	−	7.21510i	−0.0340705	−	0.669905i
$117$	5.27956	+	5.27956i	0.488096	+	0.488096i
$118$	−14.8349	+	6.59120i	−1.36566	+	0.606769i
$119$		−	1.74766i		−	0.160208i
$120$		0			0
$121$		−	0.210643i		−	0.0191493i
$122$	−0.591448	−	1.33118i	−0.0535472	−	0.120519i
$123$	−0.235392	−	0.235392i	−0.0212245	−	0.0212245i
$124$	12.6413	+	11.4177i	1.13522	+	1.02534i
$125$		0			0
$126$	−0.571160	+	1.48449i	−0.0508830	+	0.132249i
$127$		−	17.0918i		−	1.51665i	−0.651876	−	0.758326i	$-0.726018\pi$
$127$		−	17.0918i		−	1.51665i	0.651876	−	0.758326i	$-0.273982\pi$
$128$	9.52166	−	6.11049i	0.841603	−	0.540096i
$129$	0.774263			0.0681701
$130$		0			0
$131$	−3.56424	−	3.56424i	−0.311409	−	0.311409i	0.534046	−	0.845455i	$-0.320671\pi$
$131$	−3.56424	−	3.56424i	−0.311409	−	0.311409i	−0.845455	+	0.534046i	$0.820671\pi$
$132$	0.395593	−	0.437988i	0.0344320	−	0.0381220i
$133$	−0.883179	−	0.883179i	−0.0765813	−	0.0765813i
$134$	1.77150	−	0.787081i	0.153034	−	0.0679935i
$135$		0			0
$136$	11.7314	−	5.94322i	1.00596	−	0.509627i
$137$	−16.6995			−1.42673			−0.713366	−	0.700792i	$-0.752830\pi$
$137$	−16.6995			−1.42673			−0.713366	+	0.700792i	$0.752830\pi$
$138$	−0.236671	+	0.105154i	−0.0201468	+	0.00895128i
$139$	7.56455	−	7.56455i	0.641616	−	0.641616i	−0.309336	−	0.950953i	$-0.600107\pi$
$139$	7.56455	−	7.56455i	0.641616	−	0.641616i	0.950953	+	0.309336i	$0.100107\pi$
$140$		0			0
$141$	−0.605569	−	0.605569i	−0.0509982	−	0.0509982i
$142$	−4.64272	+	12.0668i	−0.389609	+	1.01263i
$143$		−	8.35474i		−	0.698658i
$144$	−11.9072	+	1.21431i	−0.992264	+	0.101192i
$145$		0			0
$146$	9.98883	+	3.84321i	0.826682	+	0.318066i
$147$	−0.427441	+	0.427441i	−0.0352548	+	0.0352548i
$148$	1.09560	+	21.5421i	0.0900579	+	1.77075i
$149$	10.2542	−	10.2542i	0.840056	−	0.840056i	−0.148810	−	0.988866i	$-0.547544\pi$
$149$	10.2542	−	10.2542i	0.840056	−	0.840056i	0.988866	+	0.148810i	$0.0475444\pi$
$150$		0			0
$151$			19.0430i			1.54970i	0.632147	+	0.774849i	$0.282174\pi$
$151$			19.0430i			1.54970i	−0.632147	+	0.774849i	$0.717826\pi$
$152$	2.92503	−	8.93184i	0.237252	−	0.724468i
$153$	−13.9125			−1.12476
$154$	1.62650	−	0.722661i	0.131067	−	0.0582337i
$155$		0			0
$156$	0.294816	−	0.326411i	0.0236042	−	0.0261338i
$157$	10.1335	−	10.1335i	0.808741	−	0.808741i	−0.175702	−	0.984443i	$-0.556220\pi$
$157$	10.1335	−	10.1335i	0.808741	−	0.808741i	0.984443	+	0.175702i	$0.0562196\pi$
$158$	15.5833	+	5.99569i	1.23974	+	0.476991i
$159$	0.378424			0.0300110
$160$		0			0
$161$	−0.780994			−0.0615509
$162$	11.7868	+	4.53499i	0.926060	+	0.356302i
$163$	7.35501	−	7.35501i	0.576089	−	0.576089i	−0.357735	−	0.933823i	$-0.616451\pi$
$163$	7.35501	−	7.35501i	0.576089	−	0.576089i	0.933823	+	0.357735i	$0.116451\pi$
$164$	5.06340	−	5.60603i	0.395385	−	0.437758i
$165$		0			0
$166$	19.4457	−	8.63981i	1.50928	−	0.670579i
$167$	−8.02936			−0.621331			−0.310665	−	0.950519i	$-0.600552\pi$
$167$	−8.02936			−0.621331			−0.310665	+	0.950519i	$0.600552\pi$
$168$	0.0890465	+	0.0291613i	0.00687009	+	0.00224984i
$169$			6.77363i			0.521048i
$170$		0			0
$171$	−7.03070	+	7.03070i	−0.537651	+	0.537651i
$172$	0.892429	+	17.5472i	0.0680471	+	1.33797i
$173$	10.4326	−	10.4326i	0.793177	−	0.793177i	−0.188832	−	0.982009i	$-0.560470\pi$
$173$	10.4326	−	10.4326i	0.793177	−	0.793177i	0.982009	+	0.188832i	$0.0604702\pi$
$174$	0.420204	+	0.161674i	0.0318556	+	0.0122564i
$175$		0			0
$176$	10.3822	+	8.46056i	0.782585	+	0.637739i
$177$		−	1.01167i		−	0.0760418i
$178$	7.97857	−	20.7370i	0.598019	−	1.55430i
$179$	8.30280	+	8.30280i	0.620580	+	0.620580i	0.945680	−	0.325099i	$-0.105398\pi$
$179$	8.30280	+	8.30280i	0.620580	+	0.620580i	−0.325099	+	0.945680i	$0.605398\pi$
$180$		0			0
$181$	−10.4772	+	10.4772i	−0.778765	+	0.778765i	−0.979621	−	0.200856i	$-0.935628\pi$
$181$	−10.4772	+	10.4772i	−0.778765	+	0.778765i	0.200856	+	0.979621i	$0.435628\pi$
$182$	1.21215	−	0.538564i	0.0898508	−	0.0399210i
$183$	0.0907802			0.00671066
$184$	−2.65591	−	5.24251i	−0.195796	−	0.386483i
$185$		0			0
$186$	−0.970145	+	0.431039i	−0.0711345	+	0.0316053i
$187$	11.0081	+	11.0081i	0.804990	+	0.804990i
$188$	13.0261	−	14.4221i	0.950028	−	1.05184i
$189$	−0.140368	−	0.140368i	−0.0102103	−	0.0102103i
$190$		0			0
$191$	1.68079			0.121618			0.0608089	−	0.998149i	$-0.480632\pi$
$191$	1.68079			0.121618			0.0608089	+	0.998149i	$0.480632\pi$
$192$	0.107070	+	0.696903i	0.00772710	+	0.0502947i
$193$		−	1.61403i		−	0.116181i	−0.998311	−	0.0580903i	$-0.981499\pi$
$193$		−	1.61403i		−	0.116181i	0.998311	−	0.0580903i	$-0.0185011\pi$
$194$	1.96032	−	5.09503i	0.140743	−	0.365802i
$195$		0			0
$196$	−10.1798	−	9.19449i	−0.727132	−	0.656750i
$197$	−5.10322	−	5.10322i	−0.363589	−	0.363589i	0.501543	−	0.865133i	$-0.332766\pi$
$197$	−5.10322	−	5.10322i	−0.363589	−	0.363589i	−0.865133	+	0.501543i	$0.832766\pi$
$198$	−5.75287	−	12.9481i	−0.408839	−	0.920179i
$199$		−	11.1545i		−	0.790725i	−0.918525	−	0.395362i	$-0.870619\pi$
$199$		−	11.1545i		−	0.790725i	0.918525	−	0.395362i	$-0.129381\pi$
$200$		0			0
$201$			0.120808i			0.00852111i
$202$	12.5644	−	5.58241i	0.884030	−	0.392777i
$203$	0.960072	+	0.960072i	0.0673839	+	0.0673839i
$204$	0.0416288	+	0.818519i	0.00291460	+	0.0573078i
$205$		0			0
$206$	1.52325	+	0.586072i	0.106130	+	0.0408335i
$207$			6.21724i			0.432128i
$208$	7.73731	+	6.30524i	0.536486	+	0.437189i
$209$	11.1259			0.769591
$210$		0			0
$211$	−2.48377	−	2.48377i	−0.170989	−	0.170989i	0.616425	−	0.787414i	$-0.288581\pi$
$211$	−2.48377	−	2.48377i	−0.170989	−	0.170989i	−0.787414	+	0.616425i	$0.788581\pi$
$212$	0.436178	+	8.57628i	0.0299568	+	0.589022i
$213$	−0.569756	−	0.569756i	−0.0390391	−	0.0390391i
$214$	4.63228	+	10.4259i	0.316656	+	0.712703i
$215$		0			0
$216$	0.464890	−	1.41958i	0.0316317	−	0.0965903i
$217$	−3.20140			−0.217325
$218$	9.08395	+	20.4454i	0.615243	+	1.38474i
$219$	−0.471640	+	0.471640i	−0.0318705	+	0.0318705i
$220$		0			0
$221$	8.20377	+	8.20377i	0.551846	+	0.551846i
$222$	−1.25460	−	0.482708i	−0.0842033	−	0.0323973i
$223$		−	21.1384i		−	1.41553i	−0.706448	−	0.707765i	$-0.749703\pi$
$223$		−	21.1384i		−	1.41553i	0.706448	−	0.707765i	$-0.250297\pi$
$224$	−0.558251	+	2.05169i	−0.0372997	+	0.137084i
$225$		0			0
$226$	−2.07277	+	5.38730i	−0.137878	+	0.358358i
$227$	−14.4885	+	14.4885i	−0.961634	+	0.961634i	−0.999291	−	0.0376566i	$-0.988011\pi$
$227$	−14.4885	+	14.4885i	−0.961634	+	0.961634i	0.0376566	+	0.999291i	$0.488011\pi$
$228$	0.434675	+	0.392601i	0.0287871	+	0.0260006i
$229$	10.0956	−	10.0956i	0.667138	−	0.667138i	−0.289914	−	0.957053i	$-0.593627\pi$
$229$	10.0956	−	10.0956i	0.667138	−	0.667138i	0.957053	+	0.289914i	$0.0936268\pi$
$230$		0			0
$231$			0.110920i			0.00729799i
$232$	−3.17970	+	9.70949i	−0.208758	+	0.637459i
$233$	3.44995			0.226014			0.113007	−	0.993594i	$-0.463952\pi$
$233$	3.44995			0.226014			0.113007	+	0.993594i	$0.463952\pi$
$234$	−4.28733	−	9.64955i	−0.280271	−	0.630811i
$235$		0			0
$236$	22.9277	−	1.16607i	1.49246	−	0.0759047i
$237$	−0.735793	+	0.735793i	−0.0477949	+	0.0477949i
$238$	−0.887511	+	2.30672i	−0.0575288	+	0.149522i
$239$	−18.0060			−1.16471			−0.582354	−	0.812935i	$-0.697868\pi$
$239$	−18.0060			−1.16471			−0.582354	+	0.812935i	$0.697868\pi$
$240$		0			0
$241$	12.6235			0.813154			0.406577	−	0.913617i	$-0.366722\pi$
$241$	12.6235			0.813154			0.406577	+	0.913617i	$0.366722\pi$
$242$	−0.106970	+	0.278025i	−0.00687632	+	0.0178721i
$243$	−1.67686	+	1.67686i	−0.107571	+	0.107571i
$244$	0.104635	+	2.05737i	0.00669856	+	0.131709i
$245$		0			0
$246$	0.191152	+	0.430230i	0.0121874	+	0.0274304i
$247$	8.29155			0.527578
$248$	−10.8869	−	21.4897i	−0.691320	−	1.36460i
$249$			1.32611i			0.0840386i
$250$		0			0
$251$	−9.17919	+	9.17919i	−0.579386	+	0.579386i	−0.934734	−	0.355348i	$-0.884362\pi$
$251$	−9.17919	+	9.17919i	−0.579386	+	0.579386i	0.355348	+	0.934734i	$0.384362\pi$
$252$	1.50774	−	1.66932i	0.0949785	−	0.105157i
$253$	4.91929	−	4.91929i	0.309273	−	0.309273i
$254$	−8.67970	+	22.5593i	−0.544613	+	1.41550i
$255$		0			0
$256$	−15.6706	+	3.22980i	−0.979414	+	0.201863i
$257$		−	16.2897i		−	1.01612i	−0.861321	−	0.508061i	$-0.830363\pi$
$257$		−	16.2897i		−	1.01612i	0.861321	−	0.508061i	$-0.169637\pi$
$258$	−1.02194	−	0.393193i	−0.0636233	−	0.0244791i
$259$	−2.86648	−	2.86648i	−0.178115	−	0.178115i
$260$		0			0
$261$	7.64282	−	7.64282i	0.473079	−	0.473079i
$262$	2.89438	+	6.51442i	0.178815	+	0.402462i
$263$	−10.4898			−0.646831			−0.323416	−	0.946257i	$-0.604831\pi$
$263$	−10.4898			−0.646831			−0.323416	+	0.946257i	$0.604831\pi$
$264$	−0.744562	+	0.377202i	−0.0458246	+	0.0232152i
$265$		0			0
$266$	0.717196	+	1.61420i	0.0439741	+	0.0989731i
$267$	0.979132	+	0.979132i	0.0599219	+	0.0599219i
$268$	−2.73788	+	0.139245i	−0.167243	+	0.00850574i
$269$	8.46636	+	8.46636i	0.516203	+	0.516203i	0.916420	−	0.400217i	$-0.131065\pi$
$269$	8.46636	+	8.46636i	0.516203	+	0.516203i	−0.400217	+	0.916420i	$0.631065\pi$
$270$		0			0
$271$	−8.92117			−0.541923			−0.270961	−	0.962590i	$-0.587342\pi$
$271$	−8.92117			−0.541923			−0.270961	+	0.962590i	$0.587342\pi$
$272$	−18.5022	+	1.88688i	−1.12186	+	0.114409i
$273$			0.0826631i			0.00500300i
$274$	22.0415	+	8.48047i	1.33157	+	0.512324i
$275$		0			0
$276$	0.365780	−	0.0186031i	0.0220174	−	0.00111977i
$277$	−9.36430	−	9.36430i	−0.562646	−	0.562646i	0.367412	−	0.930058i	$-0.380244\pi$
$277$	−9.36430	−	9.36430i	−0.562646	−	0.562646i	−0.930058	+	0.367412i	$0.880244\pi$
$278$	−13.8259	+	6.14288i	−0.829220	+	0.368425i
$279$			25.4853i			1.52576i
$280$		0			0
$281$		−	3.12921i		−	0.186673i	−0.995635	−	0.0933365i	$-0.970247\pi$
$281$		−	3.12921i		−	0.186673i	0.995635	−	0.0933365i	$-0.0297532\pi$
$282$	0.491760	+	1.10681i	0.0292839	+	0.0659096i
$283$	−2.07308	−	2.07308i	−0.123232	−	0.123232i	0.642801	−	0.766033i	$-0.277772\pi$
$283$	−2.07308	−	2.07308i	−0.123232	−	0.123232i	−0.766033	+	0.642801i	$0.777772\pi$
$284$	12.2558	−	13.5692i	0.727246	−	0.805183i
$285$		0			0
$286$	−4.24277	+	11.0273i	−0.250880	+	0.652060i
$287$			1.41972i			0.0838035i
$288$	16.3328	+	4.44405i	0.962420	+	0.261868i
$289$	−4.61834			−0.271667
$290$		0			0
$291$	0.240571	+	0.240571i	0.0141025	+	0.0141025i
$292$	−11.2325	−	10.1452i	−0.657331	−	0.593705i
$293$	12.3528	+	12.3528i	0.721659	+	0.721659i	0.968943	−	0.247284i	$-0.0795382\pi$
$293$	12.3528	+	12.3528i	0.721659	+	0.721659i	−0.247284	+	0.968943i	$0.579538\pi$
$294$	0.781242	−	0.347109i	0.0455630	−	0.0202438i
$295$		0			0
$296$	9.49362	−	28.9896i	0.551806	−	1.68499i
$297$	1.76829			0.102606
$298$	−18.7418	+	8.32703i	−1.08568	+	0.482372i
$299$	3.66610	−	3.66610i	0.212016	−	0.212016i
$300$		0			0
$301$	−2.33491	−	2.33491i	−0.134582	−	0.134582i
$302$	9.67058	−	25.1347i	0.556479	−	1.44634i
$303$			0.856834i			0.0492238i
$304$	−8.39657	+	10.3036i	−0.481576	+	0.590954i
$305$		0			0
$306$	18.3630	+	7.06519i	1.04974	+	0.403890i
$307$	10.5938	−	10.5938i	0.604619	−	0.604619i	−0.336916	−	0.941535i	$-0.609384\pi$
$307$	10.5938	−	10.5938i	0.604619	−	0.604619i	0.941535	+	0.336916i	$0.109384\pi$
$308$	−2.51379	+	0.127848i	−0.143237	+	0.00728483i
$309$	−0.0719229	+	0.0719229i	−0.00409155	+	0.00409155i
$310$		0			0
$311$		−	19.4153i		−	1.10094i	−0.834854	−	0.550471i	$-0.814448\pi$
$311$		−	19.4153i		−	1.10094i	0.834854	−	0.550471i	$-0.185552\pi$
$312$	−0.554885	+	0.281110i	−0.0314142	+	0.0159147i
$313$	2.56569			0.145022			0.0725108	−	0.997368i	$-0.476899\pi$
$313$	2.56569			0.145022			0.0725108	+	0.997368i	$0.476899\pi$
$314$	−18.5212	+	8.22902i	−1.04521	+	0.464391i
$315$		0			0
$316$	−17.5235	−	15.8273i	−0.985773	−	0.890355i
$317$	−7.32418	+	7.32418i	−0.411367	+	0.411367i	−0.882215	−	0.470848i	$-0.843948\pi$
$317$	−7.32418	+	7.32418i	−0.411367	+	0.411367i	0.470848	+	0.882215i	$0.343948\pi$
$318$	−0.499478	−	0.192175i	−0.0280093	−	0.0107766i
$319$	−12.0945			−0.677163
$320$		0			0
$321$	−0.711000			−0.0396842
$322$	1.03083	+	0.396611i	0.0574457	+	0.0221023i
$323$	−10.9248	+	10.9248i	−0.607873	+	0.607873i
$324$	−13.2543	−	11.9714i	−0.736351	−	0.665076i
$325$		0			0
$326$	−13.4429	+	5.97272i	−0.744533	+	0.330798i
$327$	−1.39428			−0.0771038
$328$	−9.53004	+	4.82801i	−0.526208	+	0.266582i
$329$			3.65238i			0.201362i
$330$		0			0
$331$	4.17652	−	4.17652i	0.229562	−	0.229562i	−0.582948	−	0.812510i	$-0.698101\pi$
$331$	4.17652	−	4.17652i	0.229562	−	0.229562i	0.812510	+	0.582948i	$0.198101\pi$
$332$	−30.0538	+	1.52849i	−1.64942	+	0.0838870i
$333$	−22.8191	+	22.8191i	−1.25048	+	1.25048i
$334$	10.5979	+	4.07754i	0.579890	+	0.223113i
$335$		0			0
$336$	−0.102723	−	0.0837101i	−0.00560398	−	0.00456676i
$337$		−	12.4540i		−	0.678410i	−0.940712	−	0.339205i	$-0.889842\pi$
$337$		−	12.4540i		−	0.678410i	0.940712	−	0.339205i	$-0.110158\pi$
$338$	3.43984	−	8.94045i	0.187103	−	0.486296i
$339$	−0.254371	−	0.254371i	−0.0138155	−	0.0138155i
$340$		0			0
$341$	20.1648	−	20.1648i	1.09199	−	1.09199i
$342$	12.8501	−	5.70936i	0.694856	−	0.308727i
$343$	5.20917			0.281269
$344$	7.73309	−	23.6136i	0.416940	−	1.27316i
$345$		0			0
$346$	−19.0679	+	8.47193i	−1.02510	+	0.455454i
$347$	17.5107	+	17.5107i	0.940024	+	0.940024i	0.998300	−	0.0582766i	$-0.0185605\pi$
$347$	17.5107	+	17.5107i	0.940024	+	0.940024i	−0.0582766	+	0.998300i	$0.518561\pi$
$348$	−0.472520	−	0.426783i	−0.0253297	−	0.0228780i
$349$	−8.42042	−	8.42042i	−0.450735	−	0.450735i	0.444863	−	0.895598i	$-0.353252\pi$
$349$	−8.42042	−	8.42042i	−0.450735	−	0.450735i	−0.895598	+	0.444863i	$0.853252\pi$
$350$		0			0
$351$	1.31782			0.0703398
$352$	−9.40680	−	16.4394i	−0.501384	−	0.876221i
$353$			9.71293i			0.516967i	0.966016	+	0.258484i	$0.0832228\pi$
$353$			9.71293i			0.516967i	−0.966016	+	0.258484i	$0.916777\pi$
$354$	−0.513755	+	1.33529i	−0.0273058	+	0.0709701i
$355$		0			0
$356$	−21.0617	+	23.3188i	−1.11627	+	1.23589i
$357$	−0.108916	−	0.108916i	−0.00576443	−	0.00576443i
$358$	−6.74238	−	15.1752i	−0.356346	−	0.802033i
$359$		−	6.77551i		−	0.357598i	−0.983886	−	0.178799i	$-0.942779\pi$
$359$		−	6.77551i		−	0.357598i	0.983886	−	0.178799i	$-0.0572212\pi$
$360$		0			0
$361$		−	7.95830i		−	0.418858i
$362$	19.1494	−	8.50814i	1.00647	−	0.447178i
$363$	−0.0131274	−	0.0131274i	−0.000689012	−	0.000689012i
$364$	−1.87341	+	0.0952789i	−0.0981932	+	0.00499397i
$365$		0			0
$366$	−0.119820	−	0.0461008i	−0.00626308	−	0.00240973i
$367$			34.4591i			1.79875i	0.437176	+	0.899376i	$0.355979\pi$
$367$			34.4591i			1.79875i	−0.437176	+	0.899376i	$0.644021\pi$
$368$	0.843208	+	8.26828i	0.0439553	+	0.431014i
$369$	11.3019			0.588355
$370$		0			0
$371$	−1.14120	−	1.14120i	−0.0592480	−	0.0592480i
$372$	1.49938	−	0.0762564i	0.0777392	−	0.00395371i
$373$	3.55187	+	3.55187i	0.183909	+	0.183909i	0.793057	−	0.609148i	$-0.208488\pi$
$373$	3.55187	+	3.55187i	0.183909	+	0.183909i	−0.609148	+	0.793057i	$0.708488\pi$
$374$	−8.93924	−	20.1197i	−0.462237	−	1.04036i
$375$		0			0
$376$	−24.5170	+	12.4206i	−1.26437	+	0.640541i
$377$	−9.01345			−0.464216
$378$	0.113987	+	0.256553i	0.00586288	+	0.0131957i
$379$	−26.4464	+	26.4464i	−1.35846	+	1.35846i	−0.482644	+	0.875817i	$0.660323\pi$
$379$	−26.4464	+	26.4464i	−1.35846	+	1.35846i	−0.875817	+	0.482644i	$0.839677\pi$
$380$		0			0
$381$	−1.06518	−	1.06518i	−0.0545706	−	0.0545706i
$382$	−2.21846	−	0.853554i	−0.113506	−	0.0436716i
$383$			30.8614i			1.57695i	0.615069	+	0.788473i	$0.289128\pi$
$383$			30.8614i			1.57695i	−0.615069	+	0.788473i	$0.710872\pi$
$384$	0.212587	−	0.974209i	0.0108485	−	0.0497149i
$385$		0			0
$386$	−0.819651	+	2.13034i	−0.0417192	+	0.108432i
$387$	−18.5875	+	18.5875i	−0.944854	+	0.944854i
$388$	−5.17481	+	5.72938i	−0.262711	+	0.290865i
$389$	−9.50959	+	9.50959i	−0.482155	+	0.482155i	−0.905819	−	0.423664i	$-0.860744\pi$
$389$	−9.50959	+	9.50959i	−0.482155	+	0.482155i	0.423664	+	0.905819i	$0.360744\pi$
$390$		0			0
$391$			9.66080i			0.488568i
$392$	8.76705	+	17.3053i	0.442803	+	0.874052i
$393$	−0.444253			−0.0224096
$394$	4.14413	+	9.32725i	0.208778	+	0.469900i
$395$		0			0
$396$	1.01776	+	20.0115i	0.0511442	+	1.00562i
$397$	24.8540	−	24.8540i	1.24739	−	1.24739i	0.290518	−	0.956870i	$-0.406172\pi$
$397$	24.8540	−	24.8540i	1.24739	−	1.24739i	0.956870	−	0.290518i	$-0.0938276\pi$
$398$	−5.66460	+	14.7228i	−0.283941	+	0.737986i
$399$	−0.110081			−0.00551094
$400$		0			0
$401$	4.69303			0.234359			0.117179	−	0.993111i	$-0.462615\pi$
$401$	4.69303			0.234359			0.117179	+	0.993111i	$0.462615\pi$
$402$	0.0613496	−	0.159453i	0.00305984	−	0.00795278i
$403$	15.0278	−	15.0278i	0.748590	−	0.748590i
$404$	−19.4186	+	0.987602i	−0.966110	+	0.0491350i
$405$		0			0
$406$	−0.779638	−	1.75474i	−0.0386928	−	0.0870864i
$407$	36.1106			1.78993
$408$	0.360722	−	1.10150i	0.0178584	−	0.0545322i
$409$		−	28.2641i		−	1.39757i	−0.715331	−	0.698786i	$-0.753724\pi$
$409$		−	28.2641i		−	1.39757i	0.715331	−	0.698786i	$-0.246276\pi$
$410$		0			0
$411$	−1.04073	+	1.04073i	−0.0513352	+	0.0513352i
$412$	−1.71290	−	1.54710i	−0.0843885	−	0.0762202i
$413$	−3.05085	+	3.05085i	−0.150123	+	0.150123i
$414$	3.15729	−	8.20607i	0.155172	−	0.403306i
$415$		0			0
$416$	−7.01042	−	12.2514i	−0.343714	−	0.600676i
$417$		−	0.942858i		−	0.0461720i
$418$	−14.6849	−	5.65003i	−0.718262	−	0.276352i
$419$	−23.0355	−	23.0355i	−1.12536	−	1.12536i	−0.990923	−	0.134433i	$-0.957079\pi$
$419$	−23.0355	−	23.0355i	−1.12536	−	1.12536i	−0.134433	−	0.990923i	$-0.542921\pi$
$420$		0			0
$421$	5.40760	−	5.40760i	0.263550	−	0.263550i	−0.562945	−	0.826495i	$-0.690332\pi$
$421$	5.40760	−	5.40760i	0.263550	−	0.263550i	0.826495	+	0.562945i	$0.190332\pi$
$422$	2.01697	+	4.53962i	0.0981846	+	0.220985i
$423$	29.0754			1.41369
$424$	3.77958	−	11.5413i	0.183552	−	0.560493i
$425$		0			0
$426$	0.462677	+	1.04135i	0.0224168	+	0.0504538i
$427$	−0.273762	−	0.273762i	−0.0132483	−	0.0132483i
$428$	−0.819511	−	16.1135i	−0.0396126	−	0.778876i
$429$	−0.520675	−	0.520675i	−0.0251384	−	0.0251384i
$430$		0			0
$431$	−12.6839			−0.610961			−0.305481	−	0.952198i	$-0.598817\pi$
$431$	−12.6839			−0.610961			−0.305481	+	0.952198i	$0.598817\pi$
$432$	−1.33451	+	1.63761i	−0.0642065	+	0.0787894i
$433$			23.8511i			1.14621i	0.819482	+	0.573104i	$0.194261\pi$
$433$			23.8511i			1.14621i	−0.819482	+	0.573104i	$0.805739\pi$
$434$	4.22549	+	1.62576i	0.202830	+	0.0780390i
$435$		0			0
$436$	−1.60707	−	31.5988i	−0.0769647	−	1.51331i
$437$	4.88208	+	4.88208i	0.233542	+	0.233542i
$438$	0.862025	−	0.383001i	0.0411891	−	0.0183005i
$439$		−	4.65878i		−	0.222352i	−0.993801	−	0.111176i	$-0.964538\pi$
$439$		−	4.65878i		−	0.222352i	0.993801	−	0.111176i	$-0.0354617\pi$
$440$		0			0
$441$		−	20.5229i		−	0.977280i
$442$	−6.66197	−	14.9942i	−0.316878	−	0.713201i
$443$	−8.74048	−	8.74048i	−0.415273	−	0.415273i	0.468298	−	0.883571i	$-0.344867\pi$
$443$	−8.74048	−	8.74048i	−0.415273	−	0.415273i	−0.883571	+	0.468298i	$0.844867\pi$
$444$	1.41080	+	1.27424i	0.0669537	+	0.0604729i
$445$		0			0
$446$	−10.7347	+	27.9003i	−0.508302	+	1.32112i
$447$		−	1.27810i		−	0.0604520i
$448$	1.77874	−	2.42451i	0.0840374	−	0.114547i
$449$	7.28525			0.343812			0.171906	−	0.985113i	$-0.445007\pi$
$449$	7.28525			0.343812			0.171906	+	0.985113i	$0.445007\pi$
$450$		0			0
$451$	−8.94247	−	8.94247i	−0.421085	−	0.421085i
$452$	5.47165	−	6.05803i	0.257365	−	0.284946i
$453$	1.18678	+	1.18678i	0.0557596	+	0.0557596i
$454$	26.4809	−	11.7655i	1.24281	−	0.552184i
$455$		0			0
$456$	−0.374350	−	0.738931i	−0.0175305	−	0.0346036i
$457$	25.2194			1.17971			0.589857	−	0.807508i	$-0.299184\pi$
$457$	25.2194			1.17971			0.589857	+	0.807508i	$0.299184\pi$
$458$	−18.4520	+	8.19828i	−0.862204	+	0.383080i
$459$	−1.73633	+	1.73633i	−0.0810451	+	0.0810451i
$460$		0			0
$461$	13.6698	+	13.6698i	0.636667	+	0.636667i	0.949732	−	0.313064i	$-0.101356\pi$
$461$	13.6698	+	13.6698i	0.636667	+	0.636667i	−0.313064	+	0.949732i	$0.601356\pi$
$462$	0.0563283	−	0.146402i	0.00262063	−	0.00681124i
$463$		−	2.77045i		−	0.128754i	−0.997926	−	0.0643768i	$-0.979494\pi$
$463$		−	2.77045i		−	0.128754i	0.997926	−	0.0643768i	$-0.0205060\pi$
$464$	9.12761	−	11.2007i	0.423739	−	0.519980i
$465$		0			0
$466$	−4.55355	−	1.75198i	−0.210939	−	0.0811590i
$467$	17.9587	−	17.9587i	0.831031	−	0.831031i	−0.156627	−	0.987658i	$-0.550062\pi$
$467$	17.9587	−	17.9587i	0.831031	−	0.831031i	0.987658	+	0.156627i	$0.0500621\pi$
$468$	0.758484	+	14.9136i	0.0350609	+	0.689380i
$469$	0.364314	−	0.364314i	0.0168225	−	0.0168225i
$470$		0			0
$471$		−	1.26306i		−	0.0581986i
$472$	−30.8542	−	10.1042i	−1.42018	−	0.465085i
$473$	29.4141			1.35246
$474$	1.34482	−	0.597509i	0.0617697	−	0.0274445i
$475$		0			0
$476$	2.34283	−	2.59391i	0.107384	−	0.118892i
$477$	−9.08470	+	9.08470i	−0.415960	+	0.415960i
$478$	23.7659	+	9.14394i	1.08703	+	0.418234i
$479$	22.4540			1.02595			0.512975	−	0.858403i	$-0.328543\pi$
$479$	22.4540			1.02595			0.512975	+	0.858403i	$0.328543\pi$
$480$		0			0
$481$	26.9114			1.22705
$482$	−16.6617	−	6.41059i	−0.758919	−	0.291995i
$483$	−0.0486722	+	0.0486722i	−0.00221466	+	0.00221466i
$484$	0.282378	−	0.312640i	0.0128354	−	0.0142109i
$485$		0			0
$486$	3.06483	−	1.36171i	0.139023	−	0.0617685i
$487$	−27.7615			−1.25799			−0.628997	−	0.777408i	$-0.716534\pi$
$487$	−27.7615			−1.25799			−0.628997	+	0.777408i	$0.716534\pi$
$488$	0.906683	−	2.76863i	0.0410436	−	0.125330i
$489$		−	0.916741i		−	0.0414565i
$490$		0			0
$491$	16.8993	−	16.8993i	0.762656	−	0.762656i	−0.214146	−	0.976802i	$-0.568697\pi$
$491$	16.8993	−	16.8993i	0.762656	−	0.762656i	0.976802	+	0.214146i	$0.0686968\pi$
$492$	−0.0338174	−	0.664929i	−0.00152460	−	0.0299773i
$493$	11.8760	−	11.8760i	0.534867	−	0.534867i
$494$	−10.9439	−	4.21068i	−0.492391	−	0.189448i
$495$		0			0
$496$	3.45642	+	33.8928i	0.155198	+	1.52183i
$497$			3.43638i			0.154143i
$498$	0.673435	−	1.75032i	0.0301773	−	0.0784335i
$499$	1.81950	+	1.81950i	0.0814520	+	0.0814520i	0.746659	−	0.665207i	$-0.231657\pi$
$499$	1.81950	+	1.81950i	0.0814520	+	0.0814520i	−0.665207	+	0.746659i	$0.731657\pi$
$500$		0			0
$501$	−0.500397	+	0.500397i	−0.0223561	+	0.0223561i
$502$	16.7770	−	7.45407i	0.748794	−	0.332691i
$503$	−42.2076			−1.88195			−0.940973	−	0.338482i	$-0.890087\pi$
$503$	−42.2076			−1.88195			−0.940973	+	0.338482i	$0.890087\pi$
$504$	−2.83778	+	1.43764i	−0.126405	+	0.0640378i
$505$		0			0
$506$	−8.99108	+	3.99477i	−0.399702	+	0.177589i
$507$	0.422139	+	0.422139i	0.0187478	+	0.0187478i
$508$	22.9125	−	25.3680i	1.01658	−	1.12552i
$509$	21.9831	+	21.9831i	0.974382	+	0.974382i	0.999680	−	0.0252980i	$-0.00805345\pi$
$509$	21.9831	+	21.9831i	0.974382	+	0.974382i	−0.0252980	+	0.999680i	$0.508053\pi$
$510$		0			0
$511$	2.84461			0.125838
$512$	22.3237	+	3.69500i	0.986577	+	0.163298i
$513$			1.75491i			0.0774812i
$514$	−8.27236	+	21.5006i	−0.364878	+	0.948349i
$515$		0			0
$516$	1.14918	+	1.03794i	0.0505897	+	0.0456929i
$517$	−23.0054	−	23.0054i	−1.01178	−	1.01178i
$518$	2.32776	+	5.23913i	0.102276	+	0.230194i
$519$		−	1.30034i		−	0.0570786i
$520$		0			0
$521$			28.1418i			1.23291i	0.787388	+	0.616457i	$0.211433\pi$
$521$			28.1418i			1.23291i	−0.787388	+	0.616457i	$0.788567\pi$
$522$	−13.9689	+	6.20644i	−0.611403	+	0.271649i
$523$	9.58093	+	9.58093i	0.418945	+	0.418945i	0.884840	−	0.465895i	$-0.154268\pi$
$523$	9.58093	+	9.58093i	0.418945	+	0.418945i	−0.465895	+	0.884840i	$0.654268\pi$
$524$	−0.512054	−	10.0682i	−0.0223692	−	0.439830i
$525$		0			0
$526$	13.8454	+	5.32704i	0.603690	+	0.232270i
$527$			39.6009i			1.72504i
$528$	1.17429	−	0.119756i	0.0511046	−	0.00521170i
$529$	−18.6828			−0.812295
$530$		0			0
$531$	24.2868	+	24.2868i	1.05396	+	1.05396i
$532$	−0.126881	−	2.49478i	−0.00550100	−	0.108163i
$533$	−6.66438	−	6.66438i	−0.288666	−	0.288666i
$534$	−0.795116	−	1.78958i	−0.0344080	−	0.0774426i
$535$		0			0
$536$	3.68442	+	1.20659i	0.159143	+	0.0521166i
$537$	1.03488			0.0446582
$538$	−6.87521	−	15.4741i	−0.296411	−	0.667137i
$539$	−16.2384	+	16.2384i	−0.699437	+	0.699437i
$540$		0			0
$541$	−26.9128	−	26.9128i	−1.15707	−	1.15707i	−0.985102	−	0.171972i	$-0.944986\pi$
$541$	−26.9128	−	26.9128i	−1.15707	−	1.15707i	−0.171972	−	0.985102i	$-0.555014\pi$
$542$	11.7750	+	4.53043i	0.505778	+	0.194598i
$543$			1.30590i			0.0560415i
$544$	25.3791	+	6.90550i	1.08812	+	0.296071i
$545$		0			0
$546$	0.0419787	−	0.109106i	0.00179652	−	0.00466931i
$547$	10.6627	−	10.6627i	0.455902	−	0.455902i	−0.441406	−	0.897308i	$-0.645520\pi$
$547$	10.6627	−	10.6627i	0.455902	−	0.455902i	0.897308	+	0.441406i	$0.145520\pi$
$548$	−24.7857	−	22.3866i	−1.05879	−	0.956307i
$549$	−2.17933	+	2.17933i	−0.0930115	+	0.0930115i
$550$		0			0
$551$		−	12.0030i		−	0.511347i
$552$	−0.492236	−	0.161199i	−0.0209510	−	0.00686110i
$553$	4.43780			0.188714
$554$	7.60439	+	17.1153i	0.323079	+	0.727159i
$555$		0			0
$556$	21.3681	−	1.08675i	0.906211	−	0.0460887i
$557$	−22.8060	+	22.8060i	−0.966320	+	0.966320i	−0.999451	−	0.0331307i	$-0.989452\pi$
$557$	−22.8060	+	22.8060i	−0.966320	+	0.966320i	0.0331307	+	0.999451i	$0.489452\pi$
$558$	12.9421	−	33.6378i	0.547885	−	1.42400i
$559$	21.9209			0.927153
$560$		0			0
$561$	1.37207			0.0579287
$562$	−1.58910	+	4.13021i	−0.0670322	+	0.174223i
$563$	−0.472513	+	0.472513i	−0.0199140	+	0.0199140i	−0.716994	−	0.697080i	$-0.754482\pi$
$563$	−0.472513	+	0.472513i	−0.0199140	+	0.0199140i	0.697080	+	0.716994i	$0.254482\pi$
$564$	−0.0869987	−	1.71060i	−0.00366331	−	0.0720292i
$565$		0			0
$566$	1.68347	+	3.78900i	0.0707614	+	0.159264i
$567$	3.35664			0.140965
$568$	−23.0671	+	11.6860i	−0.967874	+	0.490334i
$569$		−	3.14792i		−	0.131967i	−0.997821	−	0.0659837i	$-0.978981\pi$
$569$		−	3.14792i		−	0.131967i	0.997821	−	0.0659837i	$-0.0210185\pi$
$570$		0			0
$571$	5.78162	−	5.78162i	0.241953	−	0.241953i	−0.575704	−	0.817658i	$-0.695272\pi$
$571$	5.78162	−	5.78162i	0.241953	−	0.241953i	0.817658	+	0.575704i	$0.195272\pi$
$572$	11.2000	−	12.4003i	0.468295	−	0.518481i
$573$	0.104748	−	0.104748i	0.00437593	−	0.00437593i
$574$	0.720975	−	1.87388i	0.0300929	−	0.0782141i
$575$		0			0
$576$	−19.3007	−	14.1599i	−0.804196	−	0.589997i
$577$			29.0110i			1.20774i	0.797081	+	0.603872i	$0.206376\pi$
$577$			29.0110i			1.20774i	−0.797081	+	0.603872i	$0.793624\pi$
$578$	6.09570	+	2.34532i	0.253548	+	0.0975526i
$579$	−0.100588	−	0.100588i	−0.00418029	−	0.00418029i
$580$		0			0
$581$	3.99908	−	3.99908i	0.165910	−	0.165910i
$582$	−0.195358	−	0.439696i	−0.00809786	−	0.0182260i
$583$	14.3762			0.595403
$584$	9.67359	+	19.0948i	0.400296	+	0.790147i
$585$		0			0
$586$	−10.0312	−	22.5775i	−0.414387	−	0.932666i
$587$	−20.4099	−	20.4099i	−0.842408	−	0.842408i	0.146764	−	0.989172i	$-0.453114\pi$
$587$	−20.4099	−	20.4099i	−0.842408	−	0.842408i	−0.989172	+	0.146764i	$0.953114\pi$
$588$	−1.20743	+	0.0614080i	−0.0497934	+	0.00253242i
$589$	20.0123	+	20.0123i	0.824592	+	0.824592i
$590$		0			0
$591$	−0.636074			−0.0261646
$592$	−27.2523	+	33.4419i	−1.12006	+	1.37446i
$593$		−	28.9098i		−	1.18718i	−0.804766	−	0.593592i	$-0.797709\pi$
$593$		−	28.9098i		−	1.18718i	0.804766	−	0.593592i	$-0.202291\pi$
$594$	−2.33394	−	0.897986i	−0.0957628	−	0.0368448i
$595$		0			0
$596$	28.9658	−	1.47316i	1.18648	−	0.0603430i
$597$	−0.695161	−	0.695161i	−0.0284511	−	0.0284511i
$598$	−6.70060	+	2.97710i	−0.274008	+	0.121743i
$599$			11.7893i			0.481696i	0.970563	+	0.240848i	$0.0774256\pi$
$599$			11.7893i			0.481696i	−0.970563	+	0.240848i	$0.922574\pi$
$600$		0			0
$601$			17.7398i			0.723621i	0.932252	+	0.361810i	$0.117841\pi$
$601$			17.7398i			0.723621i	−0.932252	+	0.361810i	$0.882159\pi$
$602$	1.89609	+	4.26756i	0.0772790	+	0.173933i
$603$	−2.90019	−	2.90019i	−0.118105	−	0.118105i
$604$	−25.5282	+	28.2640i	−1.03873	+	1.15005i
$605$		0			0
$606$	0.435125	−	1.13093i	0.0176757	−	0.0459408i
$607$		−	25.8393i		−	1.04878i	−0.851477	−	0.524392i	$-0.824293\pi$
$607$		−	25.8393i		−	1.04878i	0.851477	−	0.524392i	$-0.175707\pi$
$608$	16.3150	−	9.33565i	0.661662	−	0.378611i
$609$	0.119665			0.00484907
$610$		0			0
$611$	−17.1448	−	17.1448i	−0.693605	−	0.693605i
$612$	−20.6493	−	18.6505i	−0.834697	−	0.753903i
$613$	−31.5411	−	31.5411i	−1.27393	−	1.27393i	−0.944006	−	0.329929i	$-0.892975\pi$
$613$	−31.5411	−	31.5411i	−1.27393	−	1.27393i	−0.329929	−	0.944006i	$-0.607025\pi$
$614$	−19.3625	+	8.60280i	−0.781405	+	0.347181i
$615$		0			0
$616$	3.38286	+	1.10783i	0.136299	+	0.0446358i
$617$	15.0637			0.606440			0.303220	−	0.952921i	$-0.401938\pi$
$617$	15.0637			0.606440			0.303220	+	0.952921i	$0.401938\pi$
$618$	0.131455	−	0.0584058i	0.00528789	−	0.00234943i
$619$	10.4975	−	10.4975i	0.421929	−	0.421929i	−0.463938	−	0.885868i	$-0.653564\pi$
$619$	10.4975	−	10.4975i	0.421929	−	0.421929i	0.885868	+	0.463938i	$0.153564\pi$
$620$		0			0
$621$	0.775933	+	0.775933i	0.0311371	+	0.0311371i
$622$	−9.85966	+	25.6261i	−0.395336	+	1.02751i
$623$		−	5.90545i		−	0.236597i
$624$	0.875144	−	0.0892481i	0.0350338	−	0.00357278i
$625$		0			0
$626$	−3.38644	−	1.30293i	−0.135349	−	0.0520757i
$627$	0.693373	−	0.693373i	0.0276906	−	0.0276906i
$628$	28.6249	−	1.45582i	1.14226	−	0.0580936i
$629$	−35.4581	+	35.4581i	−1.41381	+	1.41381i
$630$		0			0
$631$			43.6349i			1.73708i	0.495621	+	0.868539i	$0.334940\pi$
$631$			43.6349i			1.73708i	−0.495621	+	0.868539i	$0.665060\pi$
$632$	15.0915	+	29.7892i	0.600308	+	1.18495i
$633$	−0.309581			−0.0123047
$634$	13.3865	−	5.94768i	0.531647	−	0.236213i
$635$		0			0
$636$	0.561665	+	0.507299i	0.0222714	+	0.0201157i
$637$	−12.1017	+	12.1017i	−0.479486	+	0.479486i
$638$	15.9634	+	6.14194i	0.631999	+	0.243162i
$639$	27.3559			1.08218
$640$		0			0
$641$	−34.2710			−1.35362			−0.676812	−	0.736156i	$-0.736639\pi$
$641$	−34.2710			−1.35362			−0.676812	+	0.736156i	$0.736639\pi$
$642$	0.938442	+	0.361066i	0.0370374	+	0.0142501i
$643$	30.1937	−	30.1937i	1.19072	−	1.19072i	0.213857	−	0.976865i	$-0.431397\pi$
$643$	30.1937	−	30.1937i	1.19072	−	1.19072i	0.976865	−	0.213857i	$-0.0686027\pi$
$644$	−1.15917	−	1.04697i	−0.0456776	−	0.0412562i
$645$		0			0
$646$	19.9675	−	8.87163i	0.785611	−	0.349049i
$647$	−15.7474			−0.619096			−0.309548	−	0.950884i	$-0.600178\pi$
$647$	−15.7474			−0.619096			−0.309548	+	0.950884i	$0.600178\pi$
$648$	11.4148	+	22.5318i	0.448417	+	0.885133i
$649$		−	38.4331i		−	1.50863i
$650$		0			0
$651$	−0.199514	+	0.199514i	−0.00781956	+	0.00781956i
$652$	20.7763	−	1.05665i	0.813661	−	0.0413817i
$653$	−5.80619	+	5.80619i	−0.227214	+	0.227214i	−0.811528	−	0.584314i	$-0.801364\pi$
$653$	−5.80619	+	5.80619i	−0.227214	+	0.227214i	0.584314	+	0.811528i	$0.301364\pi$
$654$	1.84029	+	0.708054i	0.0719612	+	0.0276871i
$655$		0			0
$656$	15.0304	−	1.53282i	0.586839	−	0.0598464i
$657$		−	22.6450i		−	0.883465i
$658$	1.85478	−	4.82074i	0.0723070	−	0.187932i
$659$	−1.76782	−	1.76782i	−0.0688647	−	0.0688647i	0.671836	−	0.740700i	$-0.265506\pi$
$659$	−1.76782	−	1.76782i	−0.0688647	−	0.0688647i	−0.740700	+	0.671836i	$0.765506\pi$
$660$		0			0
$661$	−12.4824	+	12.4824i	−0.485509	+	0.485509i	−0.906886	−	0.421377i	$-0.861547\pi$
$661$	−12.4824	+	12.4824i	−0.485509	+	0.485509i	0.421377	+	0.906886i	$0.361547\pi$
$662$	−7.63350	+	3.39159i	−0.296685	+	0.131818i
$663$	1.02253			0.0397119
$664$	40.4439	+	13.2447i	1.56953	+	0.513995i
$665$		0			0
$666$	41.7070	−	18.5306i	1.61611	−	0.718044i
$667$	−5.30714	−	5.30714i	−0.205493	−	0.205493i
$668$	−11.9173	−	10.7638i	−0.461096	−	0.416464i
$669$	−1.31736	−	1.31736i	−0.0509322	−	0.0509322i
$670$		0			0
$671$	3.44872			0.133136
$672$	0.0930723	+	0.162654i	0.00359034	+	0.00627450i
$673$		−	14.1113i		−	0.543950i	−0.962304	−	0.271975i	$-0.912323\pi$
$673$		−	14.1113i		−	0.543950i	0.962304	−	0.271975i	$-0.0876768\pi$
$674$	−6.32447	+	16.4379i	−0.243610	+	0.633162i
$675$		0			0
$676$	−9.08043	+	10.0536i	−0.349247	+	0.386675i
$677$	8.31191	+	8.31191i	0.319453	+	0.319453i	0.848557	−	0.529104i	$-0.177472\pi$
$677$	8.31191	+	8.31191i	0.319453	+	0.319453i	−0.529104	+	0.848557i	$0.677472\pi$
$678$	0.206565	+	0.464918i	0.00793306	+	0.0178551i
$679$		−	1.45096i		−	0.0556827i
$680$		0			0
$681$			1.80587i			0.0692011i
$682$	−36.8556	+	16.3751i	−1.41127	+	0.627034i
$683$	−30.0811	−	30.0811i	−1.15102	−	1.15102i	−0.986348	−	0.164673i	$-0.947343\pi$
$683$	−30.0811	−	30.0811i	−1.15102	−	1.15102i	−0.164673	−	0.986348i	$-0.552657\pi$
$684$	−19.8601	+	1.01006i	−0.759372	+	0.0386206i
$685$		0			0
$686$	−6.87553	−	2.64537i	−0.262509	−	0.101001i
$687$		−	1.25834i		−	0.0480086i
$688$	−22.1985	+	27.2403i	−0.846310	+	1.03853i
$689$	10.7139			0.408167
$690$		0			0
$691$	24.0212	+	24.0212i	0.913810	+	0.913810i	0.996570	−	0.0827600i	$-0.0263735\pi$
$691$	24.0212	+	24.0212i	0.913810	+	0.913810i	−0.0827600	+	0.996570i	$0.526373\pi$
$692$	29.4698	−	1.49879i	1.12027	−	0.0569756i
$693$	−2.66282	−	2.66282i	−0.101152	−	0.101152i
$694$	−14.2198	−	32.0046i	−0.539775	−	1.21488i
$695$		0			0
$696$	0.406942	+	0.803266i	0.0154251	+	0.0304477i
$697$	17.5618			0.665200
$698$	6.83790	+	15.3902i	0.258818	+	0.582526i
$699$	0.215004	−	0.215004i	0.00813219	−	0.00813219i
$700$		0			0
$701$	10.0971	+	10.0971i	0.381363	+	0.381363i	0.871593	−	0.490230i	$-0.163087\pi$
$701$	10.0971	+	10.0971i	0.381363	+	0.381363i	−0.490230	+	0.871593i	$0.663087\pi$
$702$	−1.73937	−	0.669225i	−0.0656484	−	0.0252583i
$703$			35.8375i			1.35164i
$704$	4.06756	+	26.4752i	0.153302	+	0.997822i
$705$		0			0
$706$	4.93251	−	12.8200i	0.185637	−	0.482487i
$707$	2.58392	−	2.58392i	0.0971782	−	0.0971782i
$708$	1.35620	−	1.50154i	0.0509692	−	0.0564314i
$709$	4.67310	−	4.67310i	0.175502	−	0.175502i	−0.613890	−	0.789392i	$-0.710396\pi$
$709$	4.67310	−	4.67310i	0.175502	−	0.175502i	0.789392	+	0.613890i	$0.210396\pi$
$710$		0			0
$711$		−	35.3279i		−	1.32490i
$712$	39.6410	−	20.0825i	1.48561	−	0.752625i
$713$	17.6968			0.662752
$714$	0.0884462	+	0.199067i	0.00331002	+	0.00744990i
$715$		0			0
$716$	1.19282	+	23.4536i	0.0445776	+	0.876500i
$717$	−1.12215	+	1.12215i	−0.0419074	+	0.0419074i
$718$	−3.44080	+	8.94293i	−0.128409	+	0.333747i
$719$	23.5339			0.877667			0.438833	−	0.898568i	$-0.355392\pi$
$719$	23.5339			0.877667			0.438833	+	0.898568i	$0.355392\pi$
$720$		0			0
$721$	0.433789			0.0161552
$722$	−4.04145	+	10.5041i	−0.150407	+	0.390921i
$723$	0.786710	−	0.786710i	0.0292581	−	0.0292581i
$724$	−29.5958	+	1.50520i	−1.09992	+	0.0559404i
$725$		0			0
$726$	0.0106603	+	0.0239933i	0.000395641	+	0.000890474i
$727$	−16.6692			−0.618226			−0.309113	−	0.951025i	$-0.600032\pi$
$727$	−16.6692			−0.618226			−0.309113	+	0.951025i	$0.600032\pi$
$728$	2.52108	+	0.825612i	0.0934373	+	0.0305992i
$729$		−	26.5814i		−	0.984498i
$730$		0			0
$731$	−28.8826	+	28.8826i	−1.06826	+	1.06826i
$732$	0.134738	+	0.121696i	0.00498005	+	0.00449801i
$733$	−27.4684	+	27.4684i	−1.01457	+	1.01457i	−0.0146760	+	0.999892i	$0.504672\pi$
$733$	−27.4684	+	27.4684i	−1.01457	+	1.01457i	−0.999892	+	0.0146760i	$0.995328\pi$
$734$	17.4993	−	45.4823i	0.645912	−	1.67878i
$735$		0			0
$736$	3.08593	−	11.3414i	0.113749	−	0.418051i
$737$			4.58945i			0.169055i
$738$	−14.9173	−	5.73944i	−0.549114	−	0.211272i
$739$	−22.7939	−	22.7939i	−0.838486	−	0.838486i	0.150174	−	0.988660i	$-0.452017\pi$
$739$	−22.7939	−	22.7939i	−0.838486	−	0.838486i	−0.988660	+	0.150174i	$0.952017\pi$
$740$		0			0
$741$	0.516736	−	0.516736i	0.0189828	−	0.0189828i
$742$	0.926722	+	2.08579i	0.0340210	+	0.0765717i
$743$	16.4964			0.605196			0.302598	−	0.953118i	$-0.402146\pi$
$743$	16.4964			0.605196			0.302598	+	0.953118i	$0.402146\pi$
$744$	−2.01774	−	0.660778i	−0.0739740	−	0.0242253i
$745$		0			0
$746$	−2.88434	−	6.49181i	−0.105603	−	0.237682i
$747$	−31.8354	−	31.8354i	−1.16480	−	1.16480i
$748$	1.58147	+	31.0954i	0.0578242	+	1.13696i
$749$	2.14413	+	2.14413i	0.0783449	+	0.0783449i
$750$		0			0
$751$	−21.6997			−0.791833			−0.395917	−	0.918286i	$-0.629573\pi$
$751$	−21.6997			−0.791833			−0.395917	+	0.918286i	$0.629573\pi$
$752$	38.6673	−	3.94333i	1.41005	−	0.143798i
$753$			1.14411i			0.0416937i
$754$	11.8968	+	4.57729i	0.433254	+	0.166695i
$755$		0			0
$756$	−0.0201658	−	0.396508i	−0.000733425	−	0.0144209i
$757$	1.73819	+	1.73819i	0.0631757	+	0.0631757i	0.737989	−	0.674813i	$-0.235776\pi$
$757$	1.73819	+	1.73819i	0.0631757	+	0.0631757i	−0.674813	+	0.737989i	$0.735776\pi$
$758$	48.3366	−	21.4761i	1.75566	−	0.780047i
$759$		−	0.613149i		−	0.0222559i
$760$		0			0
$761$			46.5311i			1.68675i	0.537323	+	0.843376i	$0.319435\pi$
$761$			46.5311i			1.68675i	−0.537323	+	0.843376i	$0.680565\pi$
$762$	0.864989	+	1.94684i	0.0313352	+	0.0705266i
$763$	4.20467	+	4.20467i	0.152219	+	0.152219i
$764$	2.49467	+	2.25320i	0.0902538	+	0.0815178i
$765$		0			0
$766$	15.6723	−	40.7337i	0.566264	−	1.47177i
$767$		−	28.6423i		−	1.03421i
$768$	−0.775323	+	1.17789i	−0.0279770	+	0.0425035i
$769$	−15.4731			−0.557976			−0.278988	−	0.960295i	$-0.589999\pi$
$769$	−15.4731			−0.557976			−0.278988	+	0.960295i	$0.589999\pi$
$770$		0			0
$771$	−1.01519	−	1.01519i	−0.0365610	−	0.0365610i
$772$	2.16370	−	2.39558i	0.0778732	−	0.0862187i
$773$	5.69848	+	5.69848i	0.204960	+	0.204960i	0.802121	−	0.597161i	$-0.203705\pi$
$773$	5.69848	+	5.69848i	0.204960	+	0.204960i	−0.597161	+	0.802121i	$0.703705\pi$
$774$	33.9727	−	15.0942i	1.22112	−	0.542549i
$775$		0			0
$776$	9.73972	−	4.93424i	0.349636	−	0.177129i
$777$	−0.357284			−0.0128175
$778$	17.3808	−	7.72237i	0.623134	−	0.276860i
$779$	8.87484	−	8.87484i	0.317974	−	0.317974i
$780$		0			0
$781$	−21.6449	−	21.6449i	−0.774516	−	0.774516i
$782$	4.90603	−	12.7512i	0.175439	−	0.455982i
$783$		−	1.90770i		−	0.0681757i
$784$	−2.78340	−	27.2933i	−0.0994072	−	0.974761i
$785$		0			0
$786$	0.586365	+	0.225604i	0.0209149	+	0.00804704i
$787$	18.1351	−	18.1351i	0.646448	−	0.646448i	−0.305685	−	0.952133i	$-0.598885\pi$
$787$	18.1351	−	18.1351i	0.646448	−	0.646448i	0.952133	+	0.305685i	$0.0988855\pi$
$788$	−0.733151	−	14.4155i	−0.0261174	−	0.513529i
$789$	−0.653736	+	0.653736i	−0.0232736	+	0.0232736i
$790$		0			0
$791$			1.53419i			0.0545495i
$792$	8.81908	−	26.9298i	0.313372	−	0.956910i
$793$	2.57016			0.0912690
$794$	−45.4262	+	20.1830i	−1.61211	+	0.716268i
$795$		0			0
$796$	14.9533	−	16.5558i	0.530005	−	0.586805i
$797$	4.51575	−	4.51575i	0.159956	−	0.159956i	−0.622591	−	0.782547i	$-0.713920\pi$
$797$	4.51575	−	4.51575i	0.159956	−	0.159956i	0.782547	+	0.622591i	$0.213920\pi$
$798$	0.145295	+	0.0559023i	0.00514338	+	0.00197892i
$799$	45.1795			1.59834
$800$		0			0
$801$	−47.0114			−1.66107
$802$	−6.19429	−	2.38326i	−0.218728	−	0.0841557i
$803$	−17.9175	+	17.9175i	−0.632294	+	0.632294i
$804$	−0.161949	+	0.179305i	−0.00571151	+	0.00632360i
$805$		0			0
$806$	−27.4667	+	12.2035i	−0.967472	+	0.429851i
$807$	1.05526			0.0371470
$808$	26.1319	+	8.55778i	0.919317	+	0.301062i
$809$		−	3.33368i		−	0.117206i	−0.998281	−	0.0586030i	$-0.981335\pi$
$809$		−	3.33368i		−	0.117206i	0.998281	−	0.0586030i	$-0.0186646\pi$
$810$		0			0
$811$	37.1948	−	37.1948i	1.30609	−	1.30609i	0.381873	−	0.924215i	$-0.375279\pi$
$811$	37.1948	−	37.1948i	1.30609	−	1.30609i	0.924215	−	0.381873i	$-0.124721\pi$
$812$	0.137928	+	2.71199i	0.00484033	+	0.0951722i
$813$	−0.555975	+	0.555975i	−0.0194989	+	0.0194989i
$814$	−47.6620	−	18.3380i	−1.67055	−	0.642746i
$815$		0			0
$816$	−1.03548	+	1.27067i	−0.0362492	+	0.0444823i
$817$			29.1916i			1.02129i
$818$	−14.3533	+	37.3055i	−0.501853	+	1.30436i
$819$	−1.98446	−	1.98446i	−0.0693428	−	0.0693428i
$820$		0			0
$821$	−25.5278	+	25.5278i	−0.890926	+	0.890926i	−0.994610	−	0.103684i	$-0.966937\pi$
$821$	−25.5278	+	25.5278i	−0.890926	+	0.890926i	0.103684	+	0.994610i	$0.466937\pi$
$822$	1.90215	−	0.845133i	0.0663452	−	0.0294774i
$823$	−16.8858			−0.588603			−0.294301	−	0.955713i	$-0.595087\pi$
$823$	−16.8858			−0.588603			−0.294301	+	0.955713i	$0.595087\pi$
$824$	1.47518	+	2.91186i	0.0513902	+	0.101440i
$825$		0			0
$826$	5.57610	−	2.47748i	0.194017	−	0.0862026i
$827$	−11.5765	−	11.5765i	−0.402556	−	0.402556i	0.476577	−	0.879133i	$-0.341877\pi$
$827$	−11.5765	−	11.5765i	−0.402556	−	0.402556i	−0.879133	+	0.476577i	$0.841877\pi$
$828$	−8.33455	+	9.22775i	−0.289646	+	0.320686i
$829$	−5.97296	−	5.97296i	−0.207449	−	0.207449i	0.595733	−	0.803182i	$-0.296862\pi$
$829$	−5.97296	−	5.97296i	−0.207449	−	0.207449i	−0.803182	+	0.595733i	$0.796862\pi$
$830$		0			0
$831$	−1.16718			−0.0404891
$832$	3.03135	+	19.7307i	0.105093	+	0.684037i
$833$		−	31.8900i		−	1.10492i
$834$	−0.478810	+	1.24447i	−0.0165798	+	0.0430925i
$835$		0			0
$836$	16.5132	+	14.9148i	0.571122	+	0.515840i
$837$	3.18065	+	3.18065i	0.109939	+	0.109939i
$838$	18.7062	+	42.1023i	0.646195	+	1.45440i
$839$		−	27.2960i		−	0.942362i	−0.882037	−	0.471181i	$-0.843828\pi$
$839$		−	27.2960i		−	0.942362i	0.882037	−	0.471181i	$-0.156172\pi$
$840$		0			0
$841$		−	15.9519i		−	0.550066i
$842$	−9.88356	+	4.39130i	−0.340610	+	0.151334i
$843$	−0.195015	−	0.195015i	−0.00671668	−	0.00671668i
$844$	−0.356828	−	7.01608i	−0.0122825	−	0.241503i
$845$		0			0
$846$	−38.3763	−	14.7653i	−1.31941	−	0.507642i
$847$			0.0791757i			0.00272051i
$848$	−10.8496	+	13.3138i	−0.372577	+	0.457198i
$849$	−0.258392			−0.00886799
$850$		0			0
$851$	15.8455	+	15.8455i	0.543177	+	0.543177i
$852$	−0.0818536	−	1.60943i	−0.00280426	−	0.0551383i
$853$	−29.1167	−	29.1167i	−0.996938	−	0.996938i	0.00305738	−	0.999995i	$-0.499027\pi$
$853$	−29.1167	−	29.1167i	−0.996938	−	0.996938i	−0.999995	+	0.00305738i	$0.999027\pi$
$854$	0.222311	+	0.500360i	0.00760734	+	0.0171220i
$855$		0			0
$856$	−7.10124	+	21.6842i	−0.242715	+	0.741152i
$857$	22.0170			0.752087			0.376044	−	0.926602i	$-0.377284\pi$
$857$	22.0170			0.752087			0.376044	+	0.926602i	$0.377284\pi$
$858$	0.422820	+	0.951647i	0.0144348	+	0.0324887i
$859$	−16.8910	+	16.8910i	−0.576312	+	0.576312i	−0.933885	−	0.357573i	$-0.883604\pi$
$859$	−16.8910	+	16.8910i	−0.576312	+	0.576312i	0.357573	+	0.933885i	$0.383604\pi$
$860$		0			0
$861$	0.0884782	+	0.0884782i	0.00301533	+	0.00301533i
$862$	16.7413	+	6.44124i	0.570212	+	0.219390i
$863$			46.2073i			1.57292i	0.617644	+	0.786458i	$0.288087\pi$
$863$			46.2073i			1.57292i	−0.617644	+	0.786458i	$0.711913\pi$
$864$	2.59303	−	1.48376i	0.0882166	−	0.0504785i
$865$		0			0
$866$	12.1122	−	31.4808i	0.411591	−	1.06976i
$867$	−0.287819	+	0.287819i	−0.00977484	+	0.00977484i
$868$	−4.75158	−	4.29165i	−0.161279	−	0.145668i
$869$	−27.9526	+	27.9526i	−0.948227	+	0.948227i
$870$		0			0
$871$			3.42029i			0.115892i
$872$	−13.9256	+	42.5230i	−0.471580	+	1.44001i
$873$	−11.5506			−0.390929
$874$	−3.96455	−	8.92307i	−0.134103	−	0.301827i
$875$		0			0
$876$	−1.33228	+	0.0677578i	−0.0450135	+	0.00228932i
$877$	−21.6380	+	21.6380i	−0.730664	+	0.730664i	−0.970751	−	0.240087i	$-0.922824\pi$
$877$	−21.6380	+	21.6380i	−0.730664	+	0.730664i	0.240087	+	0.970751i	$0.422824\pi$
$878$	−2.36586	+	6.14908i	−0.0798440	+	0.207521i
$879$	1.53968			0.0519320
$880$		0			0
$881$	−35.6649			−1.20158			−0.600790	−	0.799407i	$-0.705147\pi$
$881$	−35.6649			−1.20158			−0.600790	+	0.799407i	$0.705147\pi$
$882$	−10.4221	+	27.0879i	−0.350930	+	0.912098i
$883$	−17.5681	+	17.5681i	−0.591213	+	0.591213i	−0.937959	−	0.346746i	$-0.887287\pi$
$883$	−17.5681	+	17.5681i	−0.591213	+	0.591213i	0.346746	+	0.937959i	$0.387287\pi$
$884$	1.17859	+	23.1738i	0.0396402	+	0.779420i
$885$		0			0
$886$	7.09781	+	15.9751i	0.238456	+	0.536695i
$887$	51.2454			1.72065			0.860326	−	0.509744i	$-0.170260\pi$
$887$	51.2454			1.72065			0.860326	+	0.509744i	$0.170260\pi$
$888$	−1.21501	−	2.39831i	−0.0407729	−	0.0804819i
$889$			6.42441i			0.215468i
$890$		0			0
$891$	−21.1426	+	21.1426i	−0.708305	+	0.708305i
$892$	28.3372	−	31.3740i	0.948799	−	1.05048i
$893$	22.8315	−	22.8315i	0.764025	−	0.764025i
$894$	−0.649055	+	1.68695i	−0.0217077	+	0.0564201i
$895$		0			0
$896$	−3.57897	+	2.29679i	−0.119565	+	0.0767304i
$897$		−	0.456949i		−	0.0152571i
$898$	−9.61574	−	3.69966i	−0.320881	−	0.123459i
$899$	−21.7547	−	21.7547i	−0.725559	−	0.725559i
$900$		0			0
$901$	−14.1165	+	14.1165i	−0.470288	+	0.470288i
$902$	7.26184	+	16.3443i	0.241793	+	0.544207i
$903$	−0.291028			−0.00968479
$904$	−10.2984	+	5.21728i	−0.342520	+	0.173524i
$905$		0			0
$906$	−0.963736	−	2.16909i	−0.0320180	−	0.0720633i
$907$	−29.6745	−	29.6745i	−0.985324	−	0.985324i	0.0145695	−	0.999894i	$-0.495362\pi$
$907$	−29.6745	−	29.6745i	−0.985324	−	0.985324i	−0.999894	+	0.0145695i	$0.995362\pi$
$908$	−40.9267	+	2.08148i	−1.35820	+	0.0690762i
$909$	−20.5697	−	20.5697i	−0.682255	−	0.682255i
$910$		0			0
$911$	−24.9064			−0.825187			−0.412593	−	0.910915i	$-0.635377\pi$
$911$	−24.9064			−0.825187			−0.412593	+	0.910915i	$0.635377\pi$
$912$	0.118850	+	1.16541i	0.00393552	+	0.0385907i
$913$			50.3785i			1.66729i
$914$	−33.2869	−	12.8071i	−1.10103	−	0.423623i
$915$		0			0
$916$	28.5179	−	1.45038i	0.942258	−	0.0479220i
$917$	1.33971	+	1.33971i	0.0442413	+	0.0442413i
$918$	3.17353	−	1.41001i	0.104742	−	0.0465373i
$919$		−	15.6940i		−	0.517696i	−0.965918	−	0.258848i	$-0.916657\pi$
$919$		−	15.6940i		−	0.517696i	0.965918	−	0.258848i	$-0.0833429\pi$
$920$		0			0
$921$		−	1.32043i		−	0.0435096i
$922$	−11.1007	−	24.9846i	−0.365584	−	0.822824i
$923$	−16.1309	−	16.1309i	−0.530954	−	0.530954i
$924$	−0.148694	+	0.164630i	−0.00489168	+	0.00541591i
$925$		0			0
$926$	−1.40691	+	3.65669i	−0.0462340	+	0.120166i
$927$		−	3.45326i		−	0.113420i
$928$	−17.7355	+	10.1485i	−0.582196	+	0.333139i
$929$	−6.00598			−0.197050			−0.0985249	−	0.995135i	$-0.531412\pi$
$929$	−6.00598			−0.197050			−0.0985249	+	0.995135i	$0.531412\pi$
$930$		0			0
$931$	−16.1156	−	16.1156i	−0.528167	−	0.528167i
$932$	5.12048	+	4.62485i	0.167727	+	0.151492i
$933$	−1.20998	−	1.20998i	−0.0396130	−	0.0396130i
$934$	−32.8235	+	14.5836i	−1.07402	+	0.477190i
$935$		0			0
$936$	6.57243	−	20.0695i	0.214826	−	0.655991i
$937$	−4.83037			−0.157801			−0.0789006	−	0.996882i	$-0.525141\pi$
$937$	−4.83037			−0.157801			−0.0789006	+	0.996882i	$0.525141\pi$
$938$	−0.665864	+	0.295846i	−0.0217412	+	0.00965970i
$939$	0.159896	−	0.159896i	0.00521802	−	0.00521802i
$940$		0			0
$941$	−3.63878	−	3.63878i	−0.118621	−	0.118621i	0.645305	−	0.763925i	$-0.276730\pi$
$941$	−3.63878	−	3.63878i	−0.118621	−	0.118621i	−0.763925	+	0.645305i	$0.776730\pi$
$942$	−0.641416	+	1.66710i	−0.0208985	+	0.0543169i
$943$		−	7.84801i		−	0.255566i
$944$	35.5929	+	29.0051i	1.15845	+	0.944036i
$945$		0			0
$946$	−38.8234	−	14.9373i	−1.26226	−	0.485654i
$947$	34.7720	−	34.7720i	1.12994	−	1.12994i	0.139751	−	0.990187i	$-0.455370\pi$
$947$	34.7720	−	34.7720i	1.12994	−	1.12994i	0.990187	−	0.139751i	$-0.0446302\pi$
$948$	−2.07845	+	0.105707i	−0.0675049	+	0.00343321i
$949$	−13.3530	+	13.3530i	−0.433457	+	0.433457i
$950$		0			0
$951$			0.912899i			0.0296028i
$952$	−4.40955	+	2.23392i	−0.142914	+	0.0724017i
$953$	−1.89827			−0.0614910			−0.0307455	−	0.999527i	$-0.509788\pi$
$953$	−1.89827			−0.0614910			−0.0307455	+	0.999527i	$0.509788\pi$
$954$	16.6043	−	7.37733i	0.537583	−	0.238850i
$955$		0			0
$956$	−26.7248	−	24.1380i	−0.864342	−	0.780679i
$957$	−0.753741	+	0.753741i	−0.0243650	+	0.0243650i
$958$	−29.6368	−	11.4028i	−0.957523	−	0.368408i
$959$	6.27694			0.202693
$960$		0			0
$961$	41.5417			1.34006
$962$	−35.5201	−	13.6664i	−1.14521	−	0.440622i
$963$	17.0687	−	17.0687i	0.550033	−	0.550033i
$964$	18.7361	+	16.9226i	0.603450	+	0.545039i
$965$		0			0
$966$	0.0889591	−	0.0395248i	0.00286221	−	0.00127169i
$967$	−61.5753			−1.98013			−0.990064	−	0.140616i	$-0.955092\pi$
$967$	−61.5753			−1.98013			−0.990064	+	0.140616i	$0.955092\pi$
$968$	−0.531476	+	0.269251i	−0.0170823	+	0.00865406i
$969$			1.36169i			0.0437437i
$970$		0			0
$971$	22.6595	−	22.6595i	0.727179	−	0.727179i	−0.242878	−	0.970057i	$-0.578091\pi$
$971$	22.6595	−	22.6595i	0.727179	−	0.727179i	0.970057	+	0.242878i	$0.0780913\pi$
$972$	−4.73675	+	0.240905i	−0.151931	+	0.00772702i
$973$	−2.84334	+	2.84334i	−0.0911532	+	0.0911532i
$974$	36.6421	+	14.0981i	1.17409	+	0.451732i
$975$		0			0
$976$	−2.60271	+	3.19385i	−0.0833108	+	0.102233i
$977$			25.3240i			0.810186i	0.914276	+	0.405093i	$0.132761\pi$
$977$			25.3240i			0.810186i	−0.914276	+	0.405093i	$0.867239\pi$
$978$	−0.465547	+	1.21000i	−0.0148866	+	0.0386915i
$979$	37.1970	+	37.1970i	1.18882	+	1.18882i
$980$		0			0
$981$	33.4720	−	33.4720i	1.06868	−	1.06868i
$982$	−30.8872	+	13.7233i	−0.985651	+	0.437928i
$983$	−5.01686			−0.160013			−0.0800065	−	0.996794i	$-0.525494\pi$
$983$	−5.01686			−0.160013			−0.0800065	+	0.996794i	$0.525494\pi$
$984$	−0.293035	+	0.894806i	−0.00934160	+	0.0285254i
$985$		0			0
$986$	−21.7060	+	9.64403i	−0.691259	+	0.307128i
$987$	0.227620	+	0.227620i	0.00724521	+	0.00724521i
$988$	12.3065	+	11.1153i	0.391521	+	0.353624i
$989$	12.9071	+	12.9071i	0.410420	+	0.410420i
$990$		0			0
$991$	41.2998			1.31193			0.655965	−	0.754791i	$-0.272262\pi$
$991$	41.2998			1.31193			0.655965	+	0.754791i	$0.272262\pi$
$992$	12.6496	−	46.4900i	0.401626	−	1.47606i
$993$		−	0.520569i		−	0.0165198i
$994$	1.74509	−	4.53564i	0.0553510	−	0.143862i
$995$		0			0
$996$	−1.77772	+	1.96824i	−0.0563292	+	0.0623659i
$997$	−1.23850	−	1.23850i	−0.0392235	−	0.0392235i	0.687223	−	0.726447i	$-0.258830\pi$
$997$	−1.23850	−	1.23850i	−0.0392235	−	0.0392235i	−0.726447	+	0.687223i	$0.758830\pi$
$998$	−1.47755	−	3.32553i	−0.0467709	−	0.105268i
$999$			5.69582i			0.180208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.e.349.1		12
4.3	odd	2		1600.2.q.e.849.4		12
5.2	odd	4		400.2.l.f.301.5	yes	12
5.3	odd	4		400.2.l.g.301.2	yes	12
5.4	even	2		400.2.q.f.349.6		12
16.5	even	4		400.2.q.f.149.6		12
16.11	odd	4		1600.2.q.f.49.3		12
20.3	even	4		1600.2.l.f.401.4		12
20.7	even	4		1600.2.l.g.401.3		12
20.19	odd	2		1600.2.q.f.849.3		12
80.27	even	4		1600.2.l.g.1201.3		12
80.37	odd	4		400.2.l.f.101.5	✓	12
80.43	even	4		1600.2.l.f.1201.4		12
80.53	odd	4		400.2.l.g.101.2	yes	12
80.59	odd	4		1600.2.q.e.49.4		12
80.69	even	4	inner	400.2.q.e.149.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.5	✓	12	80.37	odd	4
400.2.l.f.301.5	yes	12	5.2	odd	4
400.2.l.g.101.2	yes	12	80.53	odd	4
400.2.l.g.301.2	yes	12	5.3	odd	4
400.2.q.e.149.1		12	80.69	even	4	inner
400.2.q.e.349.1		12	1.1	even	1	trivial
400.2.q.f.149.6		12	16.5	even	4
400.2.q.f.349.6		12	5.4	even	2
1600.2.l.f.401.4		12	20.3	even	4
1600.2.l.f.1201.4		12	80.43	even	4
1600.2.l.g.401.3		12	20.7	even	4
1600.2.l.g.1201.3		12	80.27	even	4
1600.2.q.e.49.4		12	80.59	odd	4
1600.2.q.e.849.4		12	4.3	odd	2
1600.2.q.f.49.3		12	16.11	odd	4
1600.2.q.f.849.3		12	20.19	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.31989 - 0.507829i) q^{2} +(0.0623209 - 0.0623209i) q^{3} +(1.48422 + 1.34056i) q^{4} +(-0.113905 + 0.0506084i) q^{6} -0.375877 q^{7} +(-1.27824 - 2.52312i) q^{8} +2.99223i q^{9} +O(q^{10})\)	\(q+(-1.31989 - 0.507829i) q^{2} +(0.0623209 - 0.0623209i) q^{3} +(1.48422 + 1.34056i) q^{4} +(-0.113905 + 0.0506084i) q^{6} -0.375877 q^{7} +(-1.27824 - 2.52312i) q^{8} +2.99223i q^{9} +(2.36756 - 2.36756i) q^{11} +(0.176043 - 0.00895328i) q^{12} +(1.76442 - 1.76442i) q^{13} +(0.496116 + 0.190881i) q^{14} +(0.405819 + 3.97936i) q^{16} +4.64955i q^{17} +(1.51954 - 3.94942i) q^{18} +(2.34965 + 2.34965i) q^{19} +(-0.0234250 + 0.0234250i) q^{21} +(-4.32723 + 1.92260i) q^{22} +2.07779 q^{23} +(-0.236904 - 0.0775821i) q^{24} +(-3.22487 + 1.43282i) q^{26} +(0.373441 + 0.373441i) q^{27} +(-0.557884 - 0.503884i) q^{28} +(-2.55422 - 2.55422i) q^{29} +8.51714 q^{31} +(1.48520 - 5.45841i) q^{32} -0.295096i q^{33} +(2.36118 - 6.13690i) q^{34} +(-4.01125 + 4.44113i) q^{36} +(7.62613 + 7.62613i) q^{37} +(-1.90806 - 4.29450i) q^{38} -0.219921i q^{39} -3.77709i q^{41} +(0.0428143 - 0.0190225i) q^{42} +(6.21191 + 6.21191i) q^{43} +(6.68782 - 0.340133i) q^{44} +(-2.74246 - 1.05516i) q^{46} -9.71696i q^{47} +(0.273288 + 0.222706i) q^{48} -6.85872 q^{49} +(0.289764 + 0.289764i) q^{51} +(4.98410 - 0.253484i) q^{52} +(3.03609 + 3.03609i) q^{53} +(-0.303257 - 0.682545i) q^{54} +(0.480459 + 0.948381i) q^{56} +0.292864 q^{57} +(2.07418 + 4.66840i) q^{58} +(8.11663 - 8.11663i) q^{59} +(0.728329 + 0.728329i) q^{61} +(-11.2417 - 4.32525i) q^{62} -1.12471i q^{63} +(-4.73223 + 6.45027i) q^{64} +(-0.149858 + 0.389495i) q^{66} +(-0.969239 + 0.969239i) q^{67} +(-6.23299 + 6.90096i) q^{68} +(0.129490 - 0.129490i) q^{69} -9.14230i q^{71} +(7.54975 - 3.82478i) q^{72} -7.56793 q^{73} +(-6.19289 - 13.9384i) q^{74} +(0.337561 + 6.63723i) q^{76} +(-0.889909 + 0.889909i) q^{77} +(-0.111682 + 0.290271i) q^{78} -11.8065 q^{79} -8.93015 q^{81} +(-1.91811 + 4.98534i) q^{82} +(-10.6393 + 10.6393i) q^{83} +(-0.0661703 + 0.00336533i) q^{84} +(-5.04445 - 11.3536i) q^{86} -0.318363 q^{87} +(-8.99991 - 2.94733i) q^{88} +15.7111i q^{89} +(-0.663205 + 0.663205i) q^{91} +(3.08390 + 2.78540i) q^{92} +(0.530796 - 0.530796i) q^{93} +(-4.93455 + 12.8253i) q^{94} +(-0.247614 - 0.432731i) q^{96} +3.86020i q^{97} +(9.05275 + 3.48305i) q^{98} +(7.08428 + 7.08428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8	\( 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8} - 2 q^{11} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 2 q^{16} + 18 q^{18} + 14 q^{19} - 20 q^{21} + 20 q^{22} - 12 q^{23} + 14 q^{24} - 16 q^{26} - 10 q^{27} + 10 q^{28} - 4 q^{31} - 2 q^{32} + 6 q^{34} + 2 q^{36} + 8 q^{37} - 28 q^{38} - 10 q^{42} + 44 q^{44} - 10 q^{46} + 58 q^{48} - 4 q^{49} + 10 q^{51} + 16 q^{53} - 10 q^{54} + 6 q^{56} + 16 q^{57} - 4 q^{58} - 20 q^{59} + 4 q^{61} - 22 q^{62} - 38 q^{64} + 32 q^{66} - 50 q^{67} - 50 q^{68} + 54 q^{72} - 40 q^{73} - 10 q^{74} + 60 q^{76} + 8 q^{77} + 48 q^{78} - 12 q^{79} - 8 q^{81} + 12 q^{82} - 2 q^{83} - 34 q^{84} + 6 q^{86} + 64 q^{87} - 56 q^{88} - 50 q^{92} - 44 q^{93} - 32 q^{94} - 34 q^{96} + 30 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8 - 2 * q^11 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 2 * q^16 + 18 * q^18 + 14 * q^19 - 20 * q^21 + 20 * q^22 - 12 * q^23 + 14 * q^24 - 16 * q^26 - 10 * q^27 + 10 * q^28 - 4 * q^31 - 2 * q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 28 * q^38 - 10 * q^42 + 44 * q^44 - 10 * q^46 + 58 * q^48 - 4 * q^49 + 10 * q^51 + 16 * q^53 - 10 * q^54 + 6 * q^56 + 16 * q^57 - 4 * q^58 - 20 * q^59 + 4 * q^61 - 22 * q^62 - 38 * q^64 + 32 * q^66 - 50 * q^67 - 50 * q^68 + 54 * q^72 - 40 * q^73 - 10 * q^74 + 60 * q^76 + 8 * q^77 + 48 * q^78 - 12 * q^79 - 8 * q^81 + 12 * q^82 - 2 * q^83 - 34 * q^84 + 6 * q^86 + 64 * q^87 - 56 * q^88 - 50 * q^92 - 44 * q^93 - 32 * q^94 - 34 * q^96 + 30 * q^98 - 12 * q^99

Introduction

L-functions

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