LMFDB - Embedded newform 400.2.l.g.301.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(101,400)]

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, 0]))

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

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

chi := DirichletCharacter("400.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, 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			301.2
Root			$-0.507829 + 1.31989i$ of defining polynomial
Character	$\chi$	$=$	400.301
Dual form			400.2.l.g.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	−0.507829	+	1.31989i	−0.359089	+	0.933303i
$2$	−0.507829	+	1.31989i	−0.359089	+	0.933303i
$3$	0.0623209	+	0.0623209i	0.0359810	+	0.0359810i	0.724868	−	0.688887i	$-0.241901\pi$
$3$	0.0623209	+	0.0623209i	0.0359810	+	0.0359810i	−0.688887	+	0.724868i	$0.741901\pi$
$4$	−1.48422	−	1.34056i	−0.742110	−	0.670278i
$5$		0			0
$5$		0			0
$6$	−0.113905	+	0.0506084i	−0.0465015	+	0.0206608i
$7$			0.375877i			0.142068i	0.997474	+	0.0710340i	$0.0226299\pi$
$7$			0.375877i			0.142068i	−0.997474	+	0.0710340i	$0.977370\pi$
$8$	2.52312	−	1.27824i	0.892056	−	0.451924i
$9$		−	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	$0.0815793\pi$
$12$	−0.00895328	−	0.176043i	−0.00258459	−	0.0508191i
$13$	1.76442	+	1.76442i	0.489363	+	0.489363i	0.908105	−	0.418742i	$-0.137529\pi$
$13$	1.76442	+	1.76442i	0.489363	+	0.489363i	−0.418742	+	0.908105i	$0.637529\pi$
$14$	−0.496116	−	0.190881i	−0.132593	−	0.0510151i
$15$		0			0
$16$	0.405819	+	3.97936i	0.101455	+	0.994840i
$17$	4.64955			1.12768			0.563841	−	0.825883i	$-0.309323\pi$
$17$	4.64955			1.12768			0.563841	+	0.825883i	$0.309323\pi$
$18$	3.94942	+	1.51954i	0.930887	+	0.358159i
$19$	−2.34965	−	2.34965i	−0.539047	−	0.539047i	0.384202	−	0.923249i	$-0.374476\pi$
$19$	−2.34965	−	2.34965i	−0.539047	−	0.539047i	−0.923249	+	0.384202i	$0.874476\pi$
$20$		0			0
$21$	−0.0234250	+	0.0234250i	−0.00511175	+	0.00511175i
$22$	1.92260	+	4.32723i	0.409900	+	0.922568i
$23$			2.07779i			0.433250i	0.976255	+	0.216625i	$0.0695048\pi$
$23$			2.07779i			0.433250i	−0.976255	+	0.216625i	$0.930495\pi$
$24$	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
$28$	0.503884	−	0.557884i	0.0952251	−	0.105430i
$29$	2.55422	+	2.55422i	0.474307	+	0.474307i	0.903305	−	0.428998i	$-0.141133\pi$
$29$	2.55422	+	2.55422i	0.474307	+	0.474307i	−0.428998	+	0.903305i	$0.641133\pi$
$30$		0			0
$31$	8.51714			1.52972			0.764862	−	0.644194i	$-0.222807\pi$
$31$	8.51714			1.52972			0.764862	+	0.644194i	$0.222807\pi$
$32$	−5.45841	−	1.48520i	−0.964919	−	0.262548i
$33$	0.295096			0.0513697
$34$	−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	0.299691	−	0.954036i	$-0.403116\pi$
$37$	7.62613	−	7.62613i	1.25373	−	1.25373i	0.954036	−	0.299691i	$-0.0968837\pi$
$38$	4.29450	−	1.90806i	0.696660	−	0.309528i
$39$			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	$-0.0953001\pi$
$42$	−0.0190225	−	0.0428143i	−0.00293524	−	0.00660638i
$43$	−6.21191	+	6.21191i	−0.947307	+	0.947307i	−0.998680	−	0.0513725i	$-0.983640\pi$
$43$	−6.21191	+	6.21191i	−0.947307	+	0.947307i	0.0513725	+	0.998680i	$0.483640\pi$
$44$	−6.68782	+	0.340133i	−1.00823	+	0.0512770i
$45$		0			0
$46$	−2.74246	−	1.05516i	−0.404353	−	0.155575i
$47$	−9.71696			−1.41736			−0.708682	−	0.705528i	$-0.750710\pi$
$47$	−9.71696			−1.41736			−0.708682	+	0.705528i	$0.750710\pi$
$48$	−0.222706	+	0.273288i	−0.0321449	+	0.0394458i
$49$	6.85872			0.979817
$50$		0			0
$51$	0.289764	+	0.289764i	0.0405751	+	0.0405751i
$52$	−0.253484	−	4.98410i	−0.0351520	−	0.691170i
$53$	−3.03609	+	3.03609i	−0.417040	+	0.417040i	−0.884182	−	0.467143i	$-0.845283\pi$
$53$	−3.03609	+	3.03609i	−0.417040	+	0.417040i	0.467143	+	0.884182i	$0.345283\pi$
$54$	0.303257	+	0.682545i	0.0412681	+	0.0928827i
$55$		0			0
$56$	0.480459	+	0.948381i	0.0642040	+	0.126733i
$57$		−	0.292864i		−	0.0387908i
$58$	−4.66840	+	2.07418i	−0.612991	+	0.272354i
$59$	−8.11663	+	8.11663i	−1.05670	+	1.05670i	−0.0584019	+	0.998293i	$0.518600\pi$
$59$	−8.11663	+	8.11663i	−1.05670	+	1.05670i	−0.998293	+	0.0584019i	$0.981400\pi$
$60$		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	$0.728995\pi$
$62$	−4.32525	+	11.2417i	−0.549307	+	1.42770i
$63$	1.12471			0.141700
$64$	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	$-0.223317\pi$
$67$	0.969239	+	0.969239i	0.118411	+	0.118411i	−0.645418	+	0.763829i	$0.723317\pi$
$68$	−6.90096	−	6.23299i	−0.836864	−	0.755860i
$69$	−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	$-0.182521\pi$
$72$	−3.82478	−	7.54975i	−0.450754	−	0.889747i
$73$		−	7.56793i		−	0.885759i	−0.896581	−	0.442879i	$-0.853957\pi$
$73$		−	7.56793i		−	0.885759i	0.896581	−	0.442879i	$-0.146043\pi$
$74$	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
$78$	−0.290271	−	0.111682i	−0.0328667	−	0.0126455i
$79$	11.8065			1.32834			0.664169	−	0.747583i	$-0.268786\pi$
$79$	11.8065			1.32834			0.664169	+	0.747583i	$0.268786\pi$
$80$		0			0
$81$	−8.93015			−0.992239
$82$	4.98534	+	1.91811i	0.550539	+	0.211820i
$83$	−10.6393	−	10.6393i	−1.16782	−	1.16782i	−0.982720	−	0.185101i	$-0.940739\pi$
$83$	−10.6393	−	10.6393i	−1.16782	−	1.16782i	−0.185101	−	0.982720i	$-0.559261\pi$
$84$	0.0661703	−	0.00336533i	0.00721977	−	0.000367188i
$85$		0			0
$86$	−5.04445	−	11.3536i	−0.543957	−	1.22429i
$87$			0.318363i			0.0341320i
$88$	2.94733	−	8.99991i	0.314186	−	0.959394i
$89$		−	15.7111i		−	1.66538i	−0.553741	−	0.832689i	$-0.686800\pi$
$89$		−	15.7111i		−	1.66538i	0.553741	−	0.832689i	$-0.313200\pi$
$90$		0			0
$91$	−0.663205	+	0.663205i	−0.0695228	+	0.0695228i
$92$	2.78540	−	3.08390i	0.290398	−	0.321519i
$93$	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
$97$	3.86020			0.391943			0.195972	−	0.980610i	$-0.437214\pi$
$97$	3.86020			0.391943			0.195972	+	0.980610i	$0.437214\pi$
$98$	−3.48305	+	9.05275i	−0.351841	+	0.914466i
$99$	−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	$0.410700\pi$
$102$	−0.529607	+	0.235306i	−0.0524390	+	0.0232988i
$103$		−	1.15407i		−	0.113714i	−0.998382	−	0.0568571i	$-0.981892\pi$
$103$		−	1.15407i		−	0.113714i	0.998382	−	0.0568571i	$-0.0181079\pi$
$104$	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	−0.926862	−	0.375402i	$-0.877505\pi$
$107$	−5.70435	+	5.70435i	−0.551460	+	0.551460i	0.375402	+	0.926862i	$0.377505\pi$
$108$	−1.05489	+	0.0536502i	−0.101507	+	0.00516249i
$109$	11.1863	+	11.1863i	1.07145	+	1.07145i	0.997243	+	0.0742092i	$0.0236433\pi$
$109$	11.1863	+	11.1863i	1.07145	+	1.07145i	0.0742092	+	0.997243i	$0.476357\pi$
$110$		0			0
$111$	0.950534			0.0902207
$112$	−1.49575	+	0.152538i	−0.141335	+	0.0144135i
$113$	4.08163			0.383967			0.191984	−	0.981398i	$-0.438508\pi$
$113$	4.08163			0.383967			0.191984	+	0.981398i	$0.438508\pi$
$114$	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
$118$	−6.59120	−	14.8349i	−0.606769	−	1.36566i
$119$			1.74766i			0.160208i
$120$		0			0
$121$		−	0.210643i		−	0.0191493i
$122$	−1.33118	+	0.591448i	−0.120519	+	0.0535472i
$123$	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
$127$	−17.0918			−1.51665			−0.758326	−	0.651876i	$-0.773982\pi$
$127$	−17.0918			−1.51665			−0.758326	+	0.651876i	$0.773982\pi$
$128$	6.11049	+	9.52166i	0.540096	+	0.841603i
$129$	−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	$0.820671\pi$
$132$	−0.437988	−	0.395593i	−0.0381220	−	0.0344320i
$133$	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
$137$			16.6995i			1.42673i	0.700792	+	0.713366i	$0.252830\pi$
$137$			16.6995i			1.42673i	−0.700792	+	0.713366i	$0.747170\pi$
$138$	−0.105154	−	0.236671i	−0.00895128	−	0.0201468i
$139$	−7.56455	+	7.56455i	−0.641616	+	0.641616i	−0.950953	−	0.309336i	$-0.899893\pi$
$139$	−7.56455	+	7.56455i	−0.641616	+	0.641616i	0.309336	+	0.950953i	$0.399893\pi$
$140$		0			0
$141$	−0.605569	−	0.605569i	−0.0509982	−	0.0509982i
$142$	12.0668	+	4.64272i	1.01263	+	0.389609i
$143$	8.35474			0.698658
$144$	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
$148$	−21.5421	+	1.09560i	−1.77075	+	0.0900579i
$149$	−10.2542	+	10.2542i	−0.840056	+	0.840056i	−0.988866	−	0.148810i	$-0.952456\pi$
$149$	−10.2542	+	10.2542i	−0.840056	+	0.840056i	0.148810	+	0.988866i	$0.452456\pi$
$150$		0			0
$151$			19.0430i			1.54970i	0.632147	+	0.774849i	$0.282174\pi$
$151$			19.0430i			1.54970i	−0.632147	+	0.774849i	$0.717826\pi$
$152$	−8.93184	−	2.92503i	−0.724468	−	0.237252i
$153$		−	13.9125i		−	1.12476i
$154$	−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	$-0.443780\pi$
$157$	−10.1335	−	10.1335i	−0.808741	−	0.808741i	−0.984443	+	0.175702i	$0.943780\pi$
$158$	−5.99569	+	15.5833i	−0.476991	+	1.23974i
$159$	−0.378424			−0.0300110
$160$		0			0
$161$	−0.780994			−0.0615509
$162$	4.53499	−	11.7868i	0.356302	−	0.926060i
$163$	7.35501	+	7.35501i	0.576089	+	0.576089i	0.933823	−	0.357735i	$-0.116451\pi$
$163$	7.35501	+	7.35501i	0.576089	+	0.576089i	−0.357735	+	0.933823i	$0.616451\pi$
$164$	−5.06340	+	5.60603i	−0.395385	+	0.437758i
$165$		0			0
$166$	19.4457	−	8.63981i	1.50928	−	0.670579i
$167$			8.02936i			0.621331i	0.950519	+	0.310665i	$0.100552\pi$
$167$			8.02936i			0.621331i	−0.950519	+	0.310665i	$0.899448\pi$
$168$	−0.0291613	+	0.0890465i	−0.00224984	+	0.00687009i
$169$		−	6.77363i		−	0.521048i
$170$		0			0
$171$	−7.03070	+	7.03070i	−0.537651	+	0.537651i
$172$	17.5472	−	0.892429i	1.33797	−	0.0680471i
$173$	10.4326	+	10.4326i	0.793177	+	0.793177i	0.982009	−	0.188832i	$-0.0604702\pi$
$173$	10.4326	+	10.4326i	0.793177	+	0.793177i	−0.188832	+	0.982009i	$0.560470\pi$
$174$	−0.420204	−	0.161674i	−0.0318556	−	0.0122564i
$175$		0			0
$176$	10.3822	+	8.46056i	0.782585	+	0.637739i
$177$	−1.01167			−0.0760418
$178$	20.7370	+	7.97857i	1.55430	+	0.598019i
$179$	−8.30280	−	8.30280i	−0.620580	−	0.620580i	0.325099	−	0.945680i	$-0.394602\pi$
$179$	−8.30280	−	8.30280i	−0.620580	−	0.620580i	−0.945680	+	0.325099i	$0.894602\pi$
$180$		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	$0.435628\pi$
$182$	−0.538564	−	1.21215i	−0.0399210	−	0.0898508i
$183$			0.0907802i			0.00671066i
$184$	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
$188$	14.4221	+	13.0261i	1.05184	+	0.950028i
$189$	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	$0.480632\pi$
$192$	0.696903	−	0.107070i	0.0502947	−	0.00772710i
$193$	1.61403			0.116181			0.0580903	−	0.998311i	$-0.481499\pi$
$193$	1.61403			0.116181			0.0580903	+	0.998311i	$0.481499\pi$
$194$	−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	−0.865133	−	0.501543i	$-0.832766\pi$
$197$	−5.10322	+	5.10322i	−0.363589	+	0.363589i	0.501543	+	0.865133i	$0.332766\pi$
$198$	12.9481	−	5.75287i	0.920179	−	0.408839i
$199$			11.1545i			0.790725i	0.918525	+	0.395362i	$0.129381\pi$
$199$			11.1545i			0.790725i	−0.918525	+	0.395362i	$0.870619\pi$
$200$		0			0
$201$			0.120808i			0.00852111i
$202$	−5.58241	−	12.5644i	−0.392777	−	0.884030i
$203$	−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
$207$	6.21724			0.432128
$208$	−6.30524	+	7.73731i	−0.437189	+	0.536486i
$209$	−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	$0.788581\pi$
$212$	8.57628	−	0.436178i	0.589022	−	0.0299568i
$213$	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
$217$			3.20140i			0.217325i
$218$	−20.4454	+	9.08395i	−1.38474	+	0.615243i
$219$	0.471640	−	0.471640i	0.0318705	−	0.0318705i
$220$		0			0
$221$	8.20377	+	8.20377i	0.551846	+	0.551846i
$222$	−0.482708	+	1.25460i	−0.0323973	+	0.0842033i
$223$	21.1384			1.41553			0.707765	−	0.706448i	$-0.249703\pi$
$223$	21.1384			1.41553			0.707765	+	0.706448i	$0.249703\pi$
$224$	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	$-0.0119893\pi$
$227$	14.4885	+	14.4885i	0.961634	+	0.961634i	−0.0376566	+	0.999291i	$0.511989\pi$
$228$	−0.392601	+	0.434675i	−0.0260006	+	0.0287871i
$229$	−10.0956	+	10.0956i	−0.667138	+	0.667138i	−0.957053	−	0.289914i	$-0.906373\pi$
$229$	−10.0956	+	10.0956i	−0.667138	+	0.667138i	0.289914	+	0.957053i	$0.406373\pi$
$230$		0			0
$231$			0.110920i			0.00729799i
$232$	9.70949	+	3.17970i	0.637459	+	0.208758i
$233$			3.44995i			0.226014i	0.993594	+	0.113007i	$0.0360482\pi$
$233$			3.44995i			0.226014i	−0.993594	+	0.113007i	$0.963952\pi$
$234$	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
$238$	−2.30672	−	0.887511i	−0.149522	−	0.0575288i
$239$	18.0060			1.16471			0.582354	−	0.812935i	$-0.302132\pi$
$239$	18.0060			1.16471			0.582354	+	0.812935i	$0.302132\pi$
$240$		0			0
$241$	12.6235			0.813154			0.406577	−	0.913617i	$-0.366722\pi$
$241$	12.6235			0.813154			0.406577	+	0.913617i	$0.366722\pi$
$242$	0.278025	+	0.106970i	0.0178721	+	0.00687632i
$243$	−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
$247$		−	8.29155i		−	0.527578i
$248$	21.4897	−	10.8869i	1.36460	−	0.691320i
$249$		−	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	$0.384362\pi$
$252$	−1.66932	−	1.50774i	−0.105157	−	0.0949785i
$253$	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
$257$	−16.2897			−1.01612			−0.508061	−	0.861321i	$-0.669637\pi$
$257$	−16.2897			−1.01612			−0.508061	+	0.861321i	$0.669637\pi$
$258$	0.393193	−	1.02194i	0.0244791	−	0.0636233i
$259$	2.86648	+	2.86648i	0.178115	+	0.178115i
$260$		0			0
$261$	7.64282	−	7.64282i	0.473079	−	0.473079i
$262$	6.51442	−	2.89438i	0.402462	−	0.178815i
$263$		−	10.4898i		−	0.646831i	−0.946257	−	0.323416i	$-0.895169\pi$
$263$		−	10.4898i		−	0.646831i	0.946257	−	0.323416i	$-0.104831\pi$
$264$	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
$268$	−0.139245	−	2.73788i	−0.00850574	−	0.167243i
$269$	−8.46636	−	8.46636i	−0.516203	−	0.516203i	0.400217	−	0.916420i	$-0.368935\pi$
$269$	−8.46636	−	8.46636i	−0.516203	−	0.516203i	−0.916420	+	0.400217i	$0.868935\pi$
$270$		0			0
$271$	−8.92117			−0.541923			−0.270961	−	0.962590i	$-0.587342\pi$
$271$	−8.92117			−0.541923			−0.270961	+	0.962590i	$0.587342\pi$
$272$	1.88688	+	18.5022i	0.114409	+	1.12186i
$273$	−0.0826631			−0.00500300
$274$	−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	−0.930058	−	0.367412i	$-0.880244\pi$
$277$	−9.36430	+	9.36430i	−0.562646	+	0.562646i	0.367412	+	0.930058i	$0.380244\pi$
$278$	−6.14288	−	13.8259i	−0.368425	−	0.829220i
$279$		−	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	$-0.0297532\pi$
$282$	1.10681	−	0.491760i	0.0659096	−	0.0292839i
$283$	2.07308	−	2.07308i	0.123232	−	0.123232i	−0.642801	−	0.766033i	$-0.722228\pi$
$283$	2.07308	−	2.07308i	0.123232	−	0.123232i	0.766033	+	0.642801i	$0.222228\pi$
$284$	−12.2558	+	13.5692i	−0.727246	+	0.805183i
$285$		0			0
$286$	−4.24277	+	11.0273i	−0.250880	+	0.652060i
$287$	1.41972			0.0838035
$288$	−4.44405	+	16.3328i	−0.261868	+	0.962420i
$289$	4.61834			0.271667
$290$		0			0
$291$	0.240571	+	0.240571i	0.0141025	+	0.0141025i
$292$	−10.1452	+	11.2325i	−0.593705	+	0.657331i
$293$	−12.3528	+	12.3528i	−0.721659	+	0.721659i	−0.968943	−	0.247284i	$-0.920462\pi$
$293$	−12.3528	+	12.3528i	−0.721659	+	0.721659i	0.247284	+	0.968943i	$0.420462\pi$
$294$	−0.781242	+	0.347109i	−0.0455630	+	0.0202438i
$295$		0			0
$296$	9.49362	−	28.9896i	0.551806	−	1.68499i
$297$		−	1.76829i		−	0.102606i
$298$	−8.32703	−	18.7418i	−0.482372	−	1.08568i
$299$	−3.66610	+	3.66610i	−0.212016	+	0.212016i
$300$		0			0
$301$	−2.33491	−	2.33491i	−0.134582	−	0.134582i
$302$	−25.1347	−	9.67058i	−1.44634	−	0.556479i
$303$	−0.856834			−0.0492238
$304$	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	$-0.390616\pi$
$307$	−10.5938	−	10.5938i	−0.604619	−	0.604619i	−0.941535	+	0.336916i	$0.890616\pi$
$308$	−0.127848	−	2.51379i	−0.00728483	−	0.143237i
$309$	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	$-0.185552\pi$
$312$	0.281110	+	0.554885i	0.0159147	+	0.0314142i
$313$			2.56569i			0.145022i	0.997368	+	0.0725108i	$0.0231012\pi$
$313$			2.56569i			0.145022i	−0.997368	+	0.0725108i	$0.976899\pi$
$314$	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	$-0.156052\pi$
$317$	7.32418	+	7.32418i	0.411367	+	0.411367i	−0.470848	+	0.882215i	$0.656052\pi$
$318$	0.192175	−	0.499478i	0.0107766	−	0.0280093i
$319$	12.0945			0.677163
$320$		0			0
$321$	−0.711000			−0.0396842
$322$	0.396611	−	1.03083i	0.0221023	−	0.0574457i
$323$	−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
$327$			1.39428i			0.0771038i
$328$	−4.82801	−	9.53004i	−0.266582	−	0.526208i
$329$		−	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	$0.198101\pi$
$332$	1.52849	+	30.0538i	0.0838870	+	1.64942i
$333$	−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
$337$	−12.4540			−0.678410			−0.339205	−	0.940712i	$-0.610158\pi$
$337$	−12.4540			−0.678410			−0.339205	+	0.940712i	$0.610158\pi$
$338$	8.94045	+	3.43984i	0.486296	+	0.187103i
$339$	0.254371	+	0.254371i	0.0138155	+	0.0138155i
$340$		0			0
$341$	20.1648	−	20.1648i	1.09199	−	1.09199i
$342$	−5.70936	−	12.8501i	−0.308727	−	0.694856i
$343$			5.20917i			0.281269i
$344$	−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	−0.0582766	−	0.998300i	$-0.518561\pi$
$347$	17.5107	−	17.5107i	0.940024	−	0.940024i	0.998300	+	0.0582766i	$0.0185605\pi$
$348$	0.426783	−	0.472520i	0.0228780	−	0.0253297i
$349$	8.42042	+	8.42042i	0.450735	+	0.450735i	0.895598	−	0.444863i	$-0.146748\pi$
$349$	8.42042	+	8.42042i	0.450735	+	0.450735i	−0.444863	+	0.895598i	$0.646748\pi$
$350$		0			0
$351$	1.31782			0.0703398
$352$	−16.4394	+	9.40680i	−0.876221	+	0.501384i
$353$	−9.71293			−0.516967			−0.258484	−	0.966016i	$-0.583223\pi$
$353$	−9.71293			−0.516967			−0.258484	+	0.966016i	$0.583223\pi$
$354$	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
$358$	15.1752	−	6.74238i	0.802033	−	0.356346i
$359$			6.77551i			0.357598i	0.983886	+	0.178799i	$0.0572212\pi$
$359$			6.77551i			0.357598i	−0.983886	+	0.178799i	$0.942779\pi$
$360$		0			0
$361$		−	7.95830i		−	0.418858i
$362$	−8.50814	−	19.1494i	−0.447178	−	1.00647i
$363$	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
$367$	34.4591			1.79875			0.899376	−	0.437176i	$-0.144021\pi$
$367$	34.4591			1.79875			0.899376	+	0.437176i	$0.144021\pi$
$368$	−8.26828	+	0.843208i	−0.431014	+	0.0439553i
$369$	−11.3019			−0.588355
$370$		0			0
$371$	−1.14120	−	1.14120i	−0.0592480	−	0.0592480i
$372$	−0.0762564	−	1.49938i	−0.00395371	−	0.0777392i
$373$	−3.55187	+	3.55187i	−0.183909	+	0.183909i	−0.793057	−	0.609148i	$-0.791512\pi$
$373$	−3.55187	+	3.55187i	−0.183909	+	0.183909i	0.609148	+	0.793057i	$0.291512\pi$
$374$	8.93924	+	20.1197i	0.462237	+	1.04036i
$375$		0			0
$376$	−24.5170	+	12.4206i	−1.26437	+	0.640541i
$377$			9.01345i			0.464216i
$378$	−0.256553	+	0.113987i	−0.0131957	+	0.00586288i
$379$	26.4464	−	26.4464i	1.35846	−	1.35846i	0.482644	−	0.875817i	$-0.339677\pi$
$379$	26.4464	−	26.4464i	1.35846	−	1.35846i	0.875817	−	0.482644i	$-0.160323\pi$
$380$		0			0
$381$	−1.06518	−	1.06518i	−0.0545706	−	0.0545706i
$382$	−0.853554	+	2.21846i	−0.0436716	+	0.113506i
$383$	−30.8614			−1.57695			−0.788473	−	0.615069i	$-0.789128\pi$
$383$	−30.8614			−1.57695			−0.788473	+	0.615069i	$0.789128\pi$
$384$	−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
$388$	−5.72938	−	5.17481i	−0.290865	−	0.262711i
$389$	9.50959	−	9.50959i	0.482155	−	0.482155i	−0.423664	−	0.905819i	$-0.639256\pi$
$389$	9.50959	−	9.50959i	0.482155	−	0.482155i	0.905819	+	0.423664i	$0.139256\pi$
$390$		0			0
$391$			9.66080i			0.488568i
$392$	17.3053	−	8.76705i	0.874052	−	0.442803i
$393$		−	0.444253i		−	0.0224096i
$394$	−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	−0.956870	−	0.290518i	$-0.906172\pi$
$397$	−24.8540	−	24.8540i	−1.24739	−	1.24739i	−0.290518	−	0.956870i	$-0.593828\pi$
$398$	−14.7228	−	5.66460i	−0.737986	−	0.283941i
$399$	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	$0.462615\pi$
$402$	−0.159453	−	0.0613496i	−0.00795278	−	0.00305984i
$403$	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
$407$		−	36.1106i		−	1.78993i
$408$	1.10150	+	0.360722i	0.0545322	+	0.0178584i
$409$			28.2641i			1.39757i	0.715331	+	0.698786i	$0.246276\pi$
$409$			28.2641i			1.39757i	−0.715331	+	0.698786i	$0.753724\pi$
$410$		0			0
$411$	−1.04073	+	1.04073i	−0.0513352	+	0.0513352i
$412$	−1.54710	+	1.71290i	−0.0762202	+	0.0843885i
$413$	−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
$417$	−0.942858			−0.0461720
$418$	5.65003	−	14.6849i	0.276352	−	0.718262i
$419$	23.0355	+	23.0355i	1.12536	+	1.12536i	0.990923	+	0.134433i	$0.0429213\pi$
$419$	23.0355	+	23.0355i	1.12536	+	1.12536i	0.134433	+	0.990923i	$0.457079\pi$
$420$		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	$0.190332\pi$
$422$	4.53962	−	2.01697i	0.220985	−	0.0981846i
$423$			29.0754i			1.41369i
$424$	−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
$428$	16.1135	−	0.819511i	0.778876	−	0.0396126i
$429$	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	$0.598817\pi$
$432$	1.63761	+	1.33451i	0.0787894	+	0.0642065i
$433$	−23.8511			−1.14621			−0.573104	−	0.819482i	$-0.694261\pi$
$433$	−23.8511			−1.14621			−0.573104	+	0.819482i	$0.694261\pi$
$434$	−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
$438$	0.383001	+	0.862025i	0.0183005	+	0.0411891i
$439$			4.65878i			0.222352i	0.993801	+	0.111176i	$0.0354617\pi$
$439$			4.65878i			0.222352i	−0.993801	+	0.111176i	$0.964538\pi$
$440$		0			0
$441$		−	20.5229i		−	0.977280i
$442$	−14.9942	+	6.66197i	−0.713201	+	0.316878i
$443$	8.74048	−	8.74048i	0.415273	−	0.415273i	−0.468298	−	0.883571i	$-0.655133\pi$
$443$	8.74048	−	8.74048i	0.415273	−	0.415273i	0.883571	+	0.468298i	$0.155133\pi$
$444$	−1.41080	−	1.27424i	−0.0669537	−	0.0604729i
$445$		0			0
$446$	−10.7347	+	27.9003i	−0.508302	+	1.32112i
$447$	−1.27810			−0.0604520
$448$	2.42451	+	1.77874i	0.114547	+	0.0840374i
$449$	−7.28525			−0.343812			−0.171906	−	0.985113i	$-0.554993\pi$
$449$	−7.28525			−0.343812			−0.171906	+	0.985113i	$0.554993\pi$
$450$		0			0
$451$	−8.94247	−	8.94247i	−0.421085	−	0.421085i
$452$	−6.05803	−	5.47165i	−0.284946	−	0.257365i
$453$	−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
$457$		−	25.2194i		−	1.17971i	−0.807508	−	0.589857i	$-0.799184\pi$
$457$		−	25.2194i		−	1.17971i	0.807508	−	0.589857i	$-0.200816\pi$
$458$	−8.19828	−	18.4520i	−0.383080	−	0.862204i
$459$	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	$0.601356\pi$
$462$	−0.146402	−	0.0563283i	−0.00681124	−	0.00262063i
$463$	2.77045			0.128754			0.0643768	−	0.997926i	$-0.479494\pi$
$463$	2.77045			0.128754			0.0643768	+	0.997926i	$0.479494\pi$
$464$	−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	$-0.449938\pi$
$467$	−17.9587	−	17.9587i	−0.831031	−	0.831031i	−0.987658	+	0.156627i	$0.949938\pi$
$468$	−14.9136	+	0.758484i	−0.689380	+	0.0350609i
$469$	−0.364314	+	0.364314i	−0.0168225	+	0.0168225i
$470$		0			0
$471$		−	1.26306i		−	0.0581986i
$472$	−10.1042	+	30.8542i	−0.465085	+	1.42018i
$473$			29.4141i			1.35246i
$474$	−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
$478$	−9.14394	+	23.7659i	−0.418234	+	1.08703i
$479$	−22.4540			−1.02595			−0.512975	−	0.858403i	$-0.671457\pi$
$479$	−22.4540			−1.02595			−0.512975	+	0.858403i	$0.671457\pi$
$480$		0			0
$481$	26.9114			1.22705
$482$	−6.41059	+	16.6617i	−0.291995	+	0.758919i
$483$	−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
$487$			27.7615i			1.25799i	0.777408	+	0.628997i	$0.216534\pi$
$487$			27.7615i			1.25799i	−0.777408	+	0.628997i	$0.783466\pi$
$488$	2.76863	+	0.906683i	0.125330	+	0.0410436i
$489$			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	$0.0686968\pi$
$492$	−0.664929	+	0.0338174i	−0.0299773	+	0.00152460i
$493$	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
$497$	3.43638			0.154143
$498$	1.75032	+	0.673435i	0.0784335	+	0.0301773i
$499$	−1.81950	−	1.81950i	−0.0814520	−	0.0814520i	0.665207	−	0.746659i	$-0.268343\pi$
$499$	−1.81950	−	1.81950i	−0.0814520	−	0.0814520i	−0.746659	+	0.665207i	$0.768343\pi$
$500$		0			0
$501$	−0.500397	+	0.500397i	−0.0223561	+	0.0223561i
$502$	−7.45407	−	16.7770i	−0.332691	−	0.748794i
$503$		−	42.2076i		−	1.88195i	−0.338482	−	0.940973i	$-0.609913\pi$
$503$		−	42.2076i		−	1.88195i	0.338482	−	0.940973i	$-0.390087\pi$
$504$	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
$508$	25.3680	+	22.9125i	1.12552	+	1.01658i
$509$	−21.9831	−	21.9831i	−0.974382	−	0.974382i	0.0252980	−	0.999680i	$-0.491947\pi$
$509$	−21.9831	−	21.9831i	−0.974382	−	0.974382i	−0.999680	+	0.0252980i	$0.991947\pi$
$510$		0			0
$511$	2.84461			0.125838
$512$	3.69500	−	22.3237i	0.163298	−	0.986577i
$513$	−1.75491			−0.0774812
$514$	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
$518$	−5.23913	+	2.32776i	−0.230194	+	0.102276i
$519$			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	$0.788567\pi$
$522$	6.20644	+	13.9689i	0.271649	+	0.611403i
$523$	−9.58093	+	9.58093i	−0.418945	+	0.418945i	−0.884840	−	0.465895i	$-0.845732\pi$
$523$	−9.58093	+	9.58093i	−0.418945	+	0.418945i	0.465895	+	0.884840i	$0.345732\pi$
$524$	0.512054	+	10.0682i	0.0223692	+	0.439830i
$525$		0			0
$526$	13.8454	+	5.32704i	0.603690	+	0.232270i
$527$	39.6009			1.72504
$528$	0.119756	+	1.17429i	0.00521170	+	0.0511046i
$529$	18.6828			0.812295
$530$		0			0
$531$	24.2868	+	24.2868i	1.05396	+	1.05396i
$532$	−2.49478	+	0.126881i	−0.108163	+	0.00550100i
$533$	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
$537$		−	1.03488i		−	0.0446582i
$538$	15.4741	−	6.87521i	0.667137	−	0.296411i
$539$	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	$-0.555014\pi$
$542$	4.53043	−	11.7750i	0.194598	−	0.505778i
$543$	−1.30590			−0.0560415
$544$	−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	$-0.354480\pi$
$547$	−10.6627	−	10.6627i	−0.455902	−	0.455902i	−0.897308	+	0.441406i	$0.854480\pi$
$548$	22.3866	−	24.7857i	0.956307	−	1.05879i
$549$	2.17933	−	2.17933i	0.0930115	−	0.0930115i
$550$		0			0
$551$		−	12.0030i		−	0.511347i
$552$	−0.161199	+	0.492236i	−0.00686110	+	0.0209510i
$553$			4.43780i			0.188714i
$554$	−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	$-0.0105477\pi$
$557$	22.8060	+	22.8060i	0.966320	+	0.966320i	−0.0331307	+	0.999451i	$0.510548\pi$
$558$	33.6378	+	12.9421i	1.42400	+	0.547885i
$559$	−21.9209			−0.927153
$560$		0			0
$561$	1.37207			0.0579287
$562$	4.13021	+	1.58910i	0.174223	+	0.0670322i
$563$	−0.472513	−	0.472513i	−0.0199140	−	0.0199140i	0.697080	−	0.716994i	$-0.254482\pi$
$563$	−0.472513	−	0.472513i	−0.0199140	−	0.0199140i	−0.716994	+	0.697080i	$0.754482\pi$
$564$	0.0869987	+	1.71060i	0.00366331	+	0.0720292i
$565$		0			0
$566$	1.68347	+	3.78900i	0.0707614	+	0.159264i
$567$		−	3.35664i		−	0.140965i
$568$	−11.6860	−	23.0671i	−0.490334	−	0.967874i
$569$			3.14792i			0.131967i	0.997821	+	0.0659837i	$0.0210185\pi$
$569$			3.14792i			0.131967i	−0.997821	+	0.0659837i	$0.978981\pi$
$570$		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	$0.195272\pi$
$572$	−12.4003	−	11.2000i	−0.518481	−	0.468295i
$573$	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
$577$	29.0110			1.20774			0.603872	−	0.797081i	$-0.293624\pi$
$577$	29.0110			1.20774			0.603872	+	0.797081i	$0.293624\pi$
$578$	−2.34532	+	6.09570i	−0.0975526	+	0.253548i
$579$	0.100588	+	0.100588i	0.00418029	+	0.00418029i
$580$		0			0
$581$	3.99908	−	3.99908i	0.165910	−	0.165910i
$582$	−0.439696	+	0.195358i	−0.0182260	+	0.00809786i
$583$			14.3762i			0.595403i
$584$	−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	−0.989172	−	0.146764i	$-0.953114\pi$
$587$	−20.4099	+	20.4099i	−0.842408	+	0.842408i	0.146764	+	0.989172i	$0.453114\pi$
$588$	−0.0614080	−	1.20743i	−0.00253242	−	0.0497934i
$589$	−20.0123	−	20.0123i	−0.824592	−	0.824592i
$590$		0			0
$591$	−0.636074			−0.0261646
$592$	33.4419	+	27.2523i	1.37446	+	1.12006i
$593$	28.9098			1.18718			0.593592	−	0.804766i	$-0.297709\pi$
$593$	28.9098			1.18718			0.593592	+	0.804766i	$0.297709\pi$
$594$	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
$598$	−2.97710	−	6.70060i	−0.121743	−	0.274008i
$599$		−	11.7893i		−	0.481696i	−0.970563	−	0.240848i	$-0.922574\pi$
$599$		−	11.7893i		−	0.481696i	0.970563	−	0.240848i	$-0.0774256\pi$
$600$		0			0
$601$			17.7398i			0.723621i	0.932252	+	0.361810i	$0.117841\pi$
$601$			17.7398i			0.723621i	−0.932252	+	0.361810i	$0.882159\pi$
$602$	4.26756	−	1.89609i	0.173933	−	0.0772790i
$603$	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
$607$	−25.8393			−1.04878			−0.524392	−	0.851477i	$-0.675707\pi$
$607$	−25.8393			−1.04878			−0.524392	+	0.851477i	$0.675707\pi$
$608$	9.33565	+	16.3150i	0.378611	+	0.661662i
$609$	−0.119665			−0.00484907
$610$		0			0
$611$	−17.1448	−	17.1448i	−0.693605	−	0.693605i
$612$	−18.6505	+	20.6493i	−0.753903	+	0.834697i
$613$	31.5411	−	31.5411i	1.27393	−	1.27393i	0.329929	−	0.944006i	$-0.392975\pi$
$613$	31.5411	−	31.5411i	1.27393	−	1.27393i	0.944006	−	0.329929i	$-0.107025\pi$
$614$	19.3625	−	8.60280i	0.781405	−	0.347181i
$615$		0			0
$616$	3.38286	+	1.10783i	0.136299	+	0.0446358i
$617$		−	15.0637i		−	0.606440i	−0.952921	−	0.303220i	$-0.901938\pi$
$617$		−	15.0637i		−	0.606440i	0.952921	−	0.303220i	$-0.0980618\pi$
$618$	0.0584058	+	0.131455i	0.00234943	+	0.00528789i
$619$	−10.4975	+	10.4975i	−0.421929	+	0.421929i	−0.885868	−	0.463938i	$-0.846436\pi$
$619$	−10.4975	+	10.4975i	−0.421929	+	0.421929i	0.463938	+	0.885868i	$0.346436\pi$
$620$		0			0
$621$	0.775933	+	0.775933i	0.0311371	+	0.0311371i
$622$	25.6261	+	9.85966i	1.02751	+	0.395336i
$623$	5.90545			0.236597
$624$	−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
$628$	1.45582	+	28.6249i	0.0580936	+	1.14226i
$629$	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	$0.665060\pi$
$632$	29.7892	−	15.0915i	1.18495	−	0.600308i
$633$		−	0.309581i		−	0.0123047i
$634$	−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
$638$	−6.14194	+	15.9634i	−0.243162	+	0.631999i
$639$	−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	$0.736639\pi$
$642$	0.361066	−	0.938442i	0.0142501	−	0.0370374i
$643$	30.1937	+	30.1937i	1.19072	+	1.19072i	0.976865	+	0.213857i	$0.0686027\pi$
$643$	30.1937	+	30.1937i	1.19072	+	1.19072i	0.213857	+	0.976865i	$0.431397\pi$
$644$	1.15917	+	1.04697i	0.0456776	+	0.0412562i
$645$		0			0
$646$	19.9675	−	8.87163i	0.785611	−	0.349049i
$647$			15.7474i			0.619096i	0.950884	+	0.309548i	$0.100178\pi$
$647$			15.7474i			0.619096i	−0.950884	+	0.309548i	$0.899822\pi$
$648$	−22.5318	+	11.4148i	−0.885133	+	0.448417i
$649$			38.4331i			1.50863i
$650$		0			0
$651$	−0.199514	+	0.199514i	−0.00781956	+	0.00781956i
$652$	−1.05665	−	20.7763i	−0.0413817	−	0.813661i
$653$	−5.80619	−	5.80619i	−0.227214	−	0.227214i	0.584314	−	0.811528i	$-0.301364\pi$
$653$	−5.80619	−	5.80619i	−0.227214	−	0.227214i	−0.811528	+	0.584314i	$0.801364\pi$
$654$	−1.84029	−	0.708054i	−0.0719612	−	0.0276871i
$655$		0			0
$656$	15.0304	−	1.53282i	0.586839	−	0.0598464i
$657$	−22.6450			−0.883465
$658$	4.82074	+	1.85478i	0.187932	+	0.0723070i
$659$	1.76782	+	1.76782i	0.0688647	+	0.0688647i	0.740700	−	0.671836i	$-0.234494\pi$
$659$	1.76782	+	1.76782i	0.0688647	+	0.0688647i	−0.671836	+	0.740700i	$0.734494\pi$
$660$		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	$0.361547\pi$
$662$	3.39159	+	7.63350i	0.131818	+	0.296685i
$663$			1.02253i			0.0397119i
$664$	−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
$668$	10.7638	−	11.9173i	0.416464	−	0.461096i
$669$	1.31736	+	1.31736i	0.0509322	+	0.0509322i
$670$		0			0
$671$	3.44872			0.133136
$672$	0.162654	−	0.0930723i	0.00627450	−	0.00359034i
$673$	14.1113			0.543950			0.271975	−	0.962304i	$-0.412323\pi$
$673$	14.1113			0.543950			0.271975	+	0.962304i	$0.412323\pi$
$674$	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	−0.529104	−	0.848557i	$-0.677472\pi$
$677$	8.31191	−	8.31191i	0.319453	−	0.319453i	0.848557	+	0.529104i	$0.177472\pi$
$678$	−0.464918	+	0.206565i	−0.0178551	+	0.00793306i
$679$			1.45096i			0.0556827i
$680$		0			0
$681$			1.80587i			0.0692011i
$682$	16.3751	+	36.8556i	0.627034	+	1.41127i
$683$	30.0811	−	30.0811i	1.15102	−	1.15102i	0.164673	−	0.986348i	$-0.447343\pi$
$683$	30.0811	−	30.0811i	1.15102	−	1.15102i	0.986348	−	0.164673i	$-0.0526570\pi$
$684$	19.8601	−	1.01006i	0.759372	−	0.0386206i
$685$		0			0
$686$	−6.87553	−	2.64537i	−0.262509	−	0.101001i
$687$	−1.25834			−0.0480086
$688$	−27.2403	−	22.1985i	−1.03853	−	0.846310i
$689$	−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	$0.526373\pi$
$692$	−1.49879	−	29.4698i	−0.0569756	−	1.12027i
$693$	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
$697$		−	17.5618i		−	0.665200i
$698$	−15.3902	+	6.83790i	−0.582526	+	0.258818i
$699$	−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	$0.663087\pi$
$702$	−0.669225	+	1.73937i	−0.0252583	+	0.0656484i
$703$	−35.8375			−1.35164
$704$	−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
$708$	1.50154	+	1.35620i	0.0564314	+	0.0509692i
$709$	−4.67310	+	4.67310i	−0.175502	+	0.175502i	−0.789392	−	0.613890i	$-0.789604\pi$
$709$	−4.67310	+	4.67310i	−0.175502	+	0.175502i	0.613890	+	0.789392i	$0.289604\pi$
$710$		0			0
$711$		−	35.3279i		−	1.32490i
$712$	−20.0825	−	39.6410i	−0.752625	−	1.48561i
$713$			17.6968i			0.662752i
$714$	−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
$718$	−8.94293	−	3.44080i	−0.333747	−	0.128409i
$719$	−23.5339			−0.877667			−0.438833	−	0.898568i	$-0.644608\pi$
$719$	−23.5339			−0.877667			−0.438833	+	0.898568i	$0.644608\pi$
$720$		0			0
$721$	0.433789			0.0161552
$722$	10.5041	+	4.04145i	0.390921	+	0.150407i
$723$	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
$727$			16.6692i			0.618226i	0.951025	+	0.309113i	$0.100032\pi$
$727$			16.6692i			0.618226i	−0.951025	+	0.309113i	$0.899968\pi$
$728$	−0.825612	+	2.52108i	−0.0305992	+	0.0934373i
$729$			26.5814i			0.984498i
$730$		0			0
$731$	−28.8826	+	28.8826i	−1.06826	+	1.06826i
$732$	0.121696	−	0.134738i	0.00449801	−	0.00498005i
$733$	−27.4684	−	27.4684i	−1.01457	−	1.01457i	−0.999892	−	0.0146760i	$-0.995328\pi$
$733$	−27.4684	−	27.4684i	−1.01457	−	1.01457i	−0.0146760	−	0.999892i	$-0.504672\pi$
$734$	−17.4993	+	45.4823i	−0.645912	+	1.67878i
$735$		0			0
$736$	3.08593	−	11.3414i	0.113749	−	0.418051i
$737$	4.58945			0.169055
$738$	5.73944	−	14.9173i	0.211272	−	0.549114i
$739$	22.7939	+	22.7939i	0.838486	+	0.838486i	0.988660	−	0.150174i	$-0.0479832\pi$
$739$	22.7939	+	22.7939i	0.838486	+	0.838486i	−0.150174	+	0.988660i	$0.547983\pi$
$740$		0			0
$741$	0.516736	−	0.516736i	0.0189828	−	0.0189828i
$742$	2.08579	−	0.926722i	0.0765717	−	0.0340210i
$743$			16.4964i			0.605196i	0.953118	+	0.302598i	$0.0978539\pi$
$743$			16.4964i			0.605196i	−0.953118	+	0.302598i	$0.902146\pi$
$744$	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
$748$	−31.0954	+	1.58147i	−1.13696	+	0.0578242i
$749$	−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	$0.629573\pi$
$752$	−3.94333	−	38.6673i	−0.143798	−	1.41005i
$753$	−1.14411			−0.0416937
$754$	−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	−0.674813	−	0.737989i	$-0.735776\pi$
$757$	1.73819	−	1.73819i	0.0631757	−	0.0631757i	0.737989	+	0.674813i	$0.235776\pi$
$758$	21.4761	+	48.3366i	0.780047	+	1.75566i
$759$			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	$0.680565\pi$
$762$	1.94684	−	0.864989i	0.0705266	−	0.0313352i
$763$	−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
$767$	−28.6423			−1.03421
$768$	−1.17789	−	0.775323i	−0.0425035	−	0.0279770i
$769$	15.4731			0.557976			0.278988	−	0.960295i	$-0.410001\pi$
$769$	15.4731			0.557976			0.278988	+	0.960295i	$0.410001\pi$
$770$		0			0
$771$	−1.01519	−	1.01519i	−0.0365610	−	0.0365610i
$772$	−2.39558	−	2.16370i	−0.0862187	−	0.0778732i
$773$	−5.69848	+	5.69848i	−0.204960	+	0.204960i	−0.802121	−	0.597161i	$-0.796295\pi$
$773$	−5.69848	+	5.69848i	−0.204960	+	0.204960i	0.597161	+	0.802121i	$0.296295\pi$
$774$	−33.9727	+	15.0942i	−1.22112	+	0.542549i
$775$		0			0
$776$	9.73972	−	4.93424i	0.349636	−	0.177129i
$777$			0.357284i			0.0128175i
$778$	7.72237	+	17.3808i	0.276860	+	0.623134i
$779$	−8.87484	+	8.87484i	−0.317974	+	0.317974i
$780$		0			0
$781$	−21.6449	−	21.6449i	−0.774516	−	0.774516i
$782$	−12.7512	−	4.90603i	−0.455982	−	0.175439i
$783$	1.90770			0.0681757
$784$	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	$-0.401115\pi$
$787$	−18.1351	−	18.1351i	−0.646448	−	0.646448i	−0.952133	+	0.305685i	$0.901115\pi$
$788$	14.4155	−	0.733151i	0.513529	−	0.0261174i
$789$	0.653736	−	0.653736i	0.0232736	−	0.0232736i
$790$		0			0
$791$			1.53419i			0.0545495i
$792$	−26.9298	−	8.81908i	−0.956910	−	0.313372i
$793$			2.57016i			0.0912690i
$794$	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	$-0.286080\pi$
$797$	−4.51575	−	4.51575i	−0.159956	−	0.159956i	−0.782547	+	0.622591i	$0.786080\pi$
$798$	−0.0559023	+	0.145295i	−0.00197892	+	0.00514338i
$799$	−45.1795			−1.59834
$800$		0			0
$801$	−47.0114			−1.66107
$802$	−2.38326	+	6.19429i	−0.0841557	+	0.218728i
$803$	−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
$807$		−	1.05526i		−	0.0371470i
$808$	−8.55778	+	26.1319i	−0.301062	+	0.919317i
$809$			3.33368i			0.117206i	0.998281	+	0.0586030i	$0.0186646\pi$
$809$			3.33368i			0.117206i	−0.998281	+	0.0586030i	$0.981335\pi$
$810$		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	$-0.124721\pi$
$812$	2.71199	−	0.137928i	0.0951722	−	0.00484033i
$813$	−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
$817$	29.1916			1.02129
$818$	−37.3055	−	14.3533i	−1.30436	−	0.501853i
$819$	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	$0.466937\pi$
$822$	−0.845133	−	1.90215i	−0.0294774	−	0.0663452i
$823$		−	16.8858i		−	0.588603i	−0.955713	−	0.294301i	$-0.904913\pi$
$823$		−	16.8858i		−	0.588603i	0.955713	−	0.294301i	$-0.0950870\pi$
$824$	−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	−0.879133	−	0.476577i	$-0.841877\pi$
$827$	−11.5765	+	11.5765i	−0.402556	+	0.402556i	0.476577	+	0.879133i	$0.341877\pi$
$828$	−9.22775	−	8.33455i	−0.320686	−	0.289646i
$829$	5.97296	+	5.97296i	0.207449	+	0.207449i	0.803182	−	0.595733i	$-0.203138\pi$
$829$	5.97296	+	5.97296i	0.207449	+	0.207449i	−0.595733	+	0.803182i	$0.703138\pi$
$830$		0			0
$831$	−1.16718			−0.0404891
$832$	19.7307	−	3.03135i	0.684037	−	0.105093i
$833$	31.8900			1.10492
$834$	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
$838$	−42.1023	+	18.7062i	−1.45440	+	0.646195i
$839$			27.2960i			0.942362i	0.882037	+	0.471181i	$0.156172\pi$
$839$			27.2960i			0.942362i	−0.882037	+	0.471181i	$0.843828\pi$
$840$		0			0
$841$		−	15.9519i		−	0.550066i
$842$	4.39130	+	9.88356i	0.151334	+	0.340610i
$843$	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
$847$	0.0791757			0.00272051
$848$	−13.3138	−	10.8496i	−0.457198	−	0.372577i
$849$	0.258392			0.00886799
$850$		0			0
$851$	15.8455	+	15.8455i	0.543177	+	0.543177i
$852$	−1.60943	+	0.0818536i	−0.0551383	+	0.00280426i
$853$	29.1167	−	29.1167i	0.996938	−	0.996938i	−0.00305738	−	0.999995i	$-0.500973\pi$
$853$	29.1167	−	29.1167i	0.996938	−	0.996938i	0.999995	+	0.00305738i	$0.000973195\pi$
$854$	−0.222311	−	0.500360i	−0.00760734	−	0.0171220i
$855$		0			0
$856$	−7.10124	+	21.6842i	−0.242715	+	0.741152i
$857$		−	22.0170i		−	0.752087i	−0.926602	−	0.376044i	$-0.877284\pi$
$857$		−	22.0170i		−	0.752087i	0.926602	−	0.376044i	$-0.122716\pi$
$858$	−0.951647	+	0.422820i	−0.0324887	+	0.0144348i
$859$	16.8910	−	16.8910i	0.576312	−	0.576312i	−0.357573	−	0.933885i	$-0.616396\pi$
$859$	16.8910	−	16.8910i	0.576312	−	0.576312i	0.933885	+	0.357573i	$0.116396\pi$
$860$		0			0
$861$	0.0884782	+	0.0884782i	0.00301533	+	0.00301533i
$862$	6.44124	−	16.7413i	0.219390	−	0.570212i
$863$	−46.2073			−1.57292			−0.786458	−	0.617644i	$-0.788087\pi$
$863$	−46.2073			−1.57292			−0.786458	+	0.617644i	$0.788087\pi$
$864$	−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
$868$	4.29165	−	4.75158i	0.145668	−	0.161279i
$869$	27.9526	−	27.9526i	0.948227	−	0.948227i
$870$		0			0
$871$			3.42029i			0.115892i
$872$	42.5230	+	13.9256i	1.44001	+	0.471580i
$873$		−	11.5506i		−	0.390929i
$874$	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	$-0.0771760\pi$
$877$	21.6380	+	21.6380i	0.730664	+	0.730664i	−0.240087	+	0.970751i	$0.577176\pi$
$878$	−6.14908	−	2.36586i	−0.207521	−	0.0798440i
$879$	−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	$0.705147\pi$
$882$	27.0879	+	10.4221i	0.912098	+	0.350930i
$883$	−17.5681	−	17.5681i	−0.591213	−	0.591213i	0.346746	−	0.937959i	$-0.387287\pi$
$883$	−17.5681	−	17.5681i	−0.591213	−	0.591213i	−0.937959	+	0.346746i	$0.887287\pi$
$884$	−1.17859	−	23.1738i	−0.0396402	−	0.779420i
$885$		0			0
$886$	7.09781	+	15.9751i	0.238456	+	0.536695i
$887$		−	51.2454i		−	1.72065i	−0.509744	−	0.860326i	$-0.670260\pi$
$887$		−	51.2454i		−	1.72065i	0.509744	−	0.860326i	$-0.329740\pi$
$888$	2.39831	−	1.21501i	0.0804819	−	0.0407729i
$889$		−	6.42441i		−	0.215468i
$890$		0			0
$891$	−21.1426	+	21.1426i	−0.708305	+	0.708305i
$892$	−31.3740	−	28.3372i	−1.05048	−	0.948799i
$893$	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
$897$	−0.456949			−0.0152571
$898$	3.69966	−	9.61574i	0.123459	−	0.320881i
$899$	21.7547	+	21.7547i	0.725559	+	0.725559i
$900$		0			0
$901$	−14.1165	+	14.1165i	−0.470288	+	0.470288i
$902$	16.3443	−	7.26184i	0.544207	−	0.241793i
$903$		−	0.291028i		−	0.00968479i
$904$	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	−0.999894	−	0.0145695i	$-0.995362\pi$
$907$	−29.6745	+	29.6745i	−0.985324	+	0.985324i	0.0145695	+	0.999894i	$0.495362\pi$
$908$	−2.08148	−	40.9267i	−0.0690762	−	1.35820i
$909$	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	$0.635377\pi$
$912$	1.16541	−	0.118850i	0.0385907	−	0.00393552i
$913$	−50.3785			−1.66729
$914$	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
$918$	1.41001	+	3.17353i	0.0465373	+	0.104742i
$919$			15.6940i			0.517696i	0.965918	+	0.258848i	$0.0833429\pi$
$919$			15.6940i			0.517696i	−0.965918	+	0.258848i	$0.916657\pi$
$920$		0			0
$921$		−	1.32043i		−	0.0435096i
$922$	−24.9846	+	11.1007i	−0.822824	+	0.365584i
$923$	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
$927$	−3.45326			−0.113420
$928$	−10.1485	−	17.7355i	−0.333139	−	0.582196i
$929$	6.00598			0.197050			0.0985249	−	0.995135i	$-0.468588\pi$
$929$	6.00598			0.197050			0.0985249	+	0.995135i	$0.468588\pi$
$930$		0			0
$931$	−16.1156	−	16.1156i	−0.528167	−	0.528167i
$932$	4.62485	−	5.12048i	0.151492	−	0.167727i
$933$	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
$937$			4.83037i			0.157801i	0.996882	+	0.0789006i	$0.0251410\pi$
$937$			4.83037i			0.157801i	−0.996882	+	0.0789006i	$0.974859\pi$
$938$	−0.295846	−	0.665864i	−0.00965970	−	0.0217412i
$939$	−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	$0.776730\pi$
$942$	1.66710	+	0.641416i	0.0543169	+	0.0208985i
$943$	7.84801			0.255566
$944$	−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	−0.990187	−	0.139751i	$-0.955370\pi$
$947$	−34.7720	−	34.7720i	−1.12994	−	1.12994i	−0.139751	−	0.990187i	$-0.544630\pi$
$948$	−0.105707	−	2.07845i	−0.00343321	−	0.0675049i
$949$	13.3530	−	13.3530i	0.433457	−	0.433457i
$950$		0			0
$951$			0.912899i			0.0296028i
$952$	2.23392	+	4.40955i	0.0724017	+	0.142914i
$953$		−	1.89827i		−	0.0614910i	−0.999527	−	0.0307455i	$-0.990212\pi$
$953$		−	1.89827i		−	0.0614910i	0.999527	−	0.0307455i	$-0.00978813\pi$
$954$	−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
$958$	11.4028	−	29.6368i	0.368408	−	0.957523i
$959$	−6.27694			−0.202693
$960$		0			0
$961$	41.5417			1.34006
$962$	−13.6664	+	35.5201i	−0.440622	+	1.14521i
$963$	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
$967$			61.5753i			1.98013i	0.140616	+	0.990064i	$0.455092\pi$
$967$			61.5753i			1.98013i	−0.140616	+	0.990064i	$0.544908\pi$
$968$	−0.269251	−	0.531476i	−0.00865406	−	0.0170823i
$969$		−	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	$0.0780913\pi$
$972$	0.240905	+	4.73675i	0.00772702	+	0.151931i
$973$	−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
$977$	25.3240			0.810186			0.405093	−	0.914276i	$-0.367239\pi$
$977$	25.3240			0.810186			0.405093	+	0.914276i	$0.367239\pi$
$978$	−1.21000	−	0.465547i	−0.0386915	−	0.0148866i
$979$	−37.1970	−	37.1970i	−1.18882	−	1.18882i
$980$		0			0
$981$	33.4720	−	33.4720i	1.06868	−	1.06868i
$982$	13.7233	+	30.8872i	0.437928	+	0.985651i
$983$		−	5.01686i		−	0.160013i	−0.996794	−	0.0800065i	$-0.974506\pi$
$983$		−	5.01686i		−	0.160013i	0.996794	−	0.0800065i	$-0.0254941\pi$
$984$	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
$988$	−11.1153	+	12.3065i	−0.353624	+	0.391521i
$989$	−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	$0.272262\pi$
$992$	−46.4900	−	12.6496i	−1.47606	−	0.401626i
$993$	0.520569			0.0165198
$994$	−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	−0.726447	−	0.687223i	$-0.758830\pi$
$997$	−1.23850	+	1.23850i	−0.0392235	+	0.0392235i	0.687223	+	0.726447i	$0.258830\pi$
$998$	3.32553	−	1.47755i	0.105268	−	0.0467709i
$999$		−	5.69582i		−	0.180208i

Twists

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

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

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.l (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

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