LMFDB - Embedded newform 400.2.l.f.101.5

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			101.5
Root			$-0.507829 - 1.31989i$ of defining polynomial
Character	$\chi$	$=$	400.101
Dual form			400.2.l.f.301.5

$q$-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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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	$-0.758099\pi$
$3$	−0.0623209	+	0.0623209i	−0.0359810	+	0.0359810i	0.688887	+	0.724868i	$0.258099\pi$
$4$	−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	0.967337	−	0.253492i	$-0.0815793\pi$
$11$	2.36756	+	2.36756i	0.713845	+	0.713845i	−0.253492	+	0.967337i	$0.581579\pi$
$12$	0.00895328	−	0.176043i	0.00258459	−	0.0508191i
$13$	−1.76442	+	1.76442i	−0.489363	+	0.489363i	−0.908105	−	0.418742i	$-0.862471\pi$
$13$	−1.76442	+	1.76442i	−0.489363	+	0.489363i	0.418742	+	0.908105i	$0.362471\pi$
$14$	−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	$-0.690677\pi$
$17$	−4.64955			−1.12768			−0.563841	+	0.825883i	$0.690677\pi$
$18$	−3.94942	+	1.51954i	−0.930887	+	0.358159i
$19$	−2.34965	+	2.34965i	−0.539047	+	0.539047i	−0.923249	−	0.384202i	$-0.874476\pi$
$19$	−2.34965	+	2.34965i	−0.539047	+	0.539047i	0.384202	+	0.923249i	$0.374476\pi$
$20$		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	−0.428998	−	0.903305i	$-0.641133\pi$
$29$	2.55422	−	2.55422i	0.474307	−	0.474307i	0.903305	+	0.428998i	$0.141133\pi$
$30$		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	−0.954036	−	0.299691i	$-0.903116\pi$
$37$	−7.62613	−	7.62613i	−1.25373	−	1.25373i	−0.299691	−	0.954036i	$-0.596884\pi$
$38$	−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	$0.0953001\pi$
$41$			3.77709i			0.589882i	−0.955515	+	0.294941i	$0.904700\pi$
$42$	0.0190225	−	0.0428143i	0.00293524	−	0.00660638i
$43$	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
$47$	9.71696			1.41736			0.708682	−	0.705528i	$-0.249290\pi$
$47$	9.71696			1.41736			0.708682	+	0.705528i	$0.249290\pi$
$48$	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	$-0.154717\pi$
$53$	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
$57$		−	0.292864i		−	0.0387908i
$58$	4.66840	+	2.07418i	0.612991	+	0.272354i
$59$	−8.11663	−	8.11663i	−1.05670	−	1.05670i	−0.998293	−	0.0584019i	$-0.981400\pi$
$59$	−8.11663	−	8.11663i	−1.05670	−	1.05670i	−0.0584019	−	0.998293i	$-0.518600\pi$
$60$		0			0
$61$	0.728329	−	0.728329i	0.0932529	−	0.0932529i	−0.658941	−	0.752194i	$-0.728995\pi$
$61$	0.728329	−	0.728329i	0.0932529	−	0.0932529i	0.752194	+	0.658941i	$0.228995\pi$
$62$	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	$-0.776683\pi$
$67$	−0.969239	+	0.969239i	−0.118411	+	0.118411i	0.645418	+	0.763829i	$0.276683\pi$
$68$	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	$0.182521\pi$
$71$			9.14230i			1.08499i	−0.840058	+	0.542496i	$0.817479\pi$
$72$	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	0.185101	−	0.982720i	$-0.440739\pi$
$83$	10.6393	−	10.6393i	1.16782	−	1.16782i	0.982720	−	0.185101i	$-0.0592611\pi$
$84$	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	$0.313200\pi$
$89$			15.7111i			1.66538i	−0.553741	+	0.832689i	$0.686800\pi$
$90$		0			0
$91$	−0.663205	−	0.663205i	−0.0695228	−	0.0695228i
$92$	−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	$-0.562786\pi$
$97$	−3.86020			−0.391943			−0.195972	+	0.980610i	$0.562786\pi$
$98$	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	0.276879	−	0.960905i	$-0.410700\pi$
$101$	−6.87437	−	6.87437i	−0.684026	−	0.684026i	−0.960905	+	0.276879i	$0.910700\pi$
$102$	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	$-0.122495\pi$
$107$	5.70435	+	5.70435i	0.551460	+	0.551460i	−0.375402	+	0.926862i	$0.622495\pi$
$108$	1.05489	+	0.0536502i	0.101507	+	0.00516249i
$109$	11.1863	−	11.1863i	1.07145	−	1.07145i	0.0742092	−	0.997243i	$-0.476357\pi$
$109$	11.1863	−	11.1863i	1.07145	−	1.07145i	0.997243	−	0.0742092i	$-0.0236433\pi$
$110$		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	$-0.561492\pi$
$113$	−4.08163			−0.383967			−0.191984	+	0.981398i	$0.561492\pi$
$114$	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	$-0.226018\pi$
$127$	17.0918			1.51665			0.758326	+	0.651876i	$0.226018\pi$
$128$	−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	−0.845455	−	0.534046i	$-0.820671\pi$
$131$	−3.56424	+	3.56424i	−0.311409	+	0.311409i	0.534046	+	0.845455i	$0.320671\pi$
$132$	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	0.309336	−	0.950953i	$-0.399893\pi$
$139$	−7.56455	−	7.56455i	−0.641616	−	0.641616i	−0.950953	+	0.309336i	$0.899893\pi$
$140$		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	0.148810	−	0.988866i	$-0.452456\pi$
$149$	−10.2542	−	10.2542i	−0.840056	−	0.840056i	−0.988866	+	0.148810i	$0.952456\pi$
$150$		0			0
$151$		−	19.0430i		−	1.54970i	−0.632147	−	0.774849i	$-0.717826\pi$
$151$		−	19.0430i		−	1.54970i	0.632147	−	0.774849i	$-0.282174\pi$
$152$	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	$-0.556220\pi$
$157$	10.1335	−	10.1335i	0.808741	−	0.808741i	0.984443	+	0.175702i	$0.0562196\pi$
$158$	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	$-0.883549\pi$
$163$	−7.35501	+	7.35501i	−0.576089	+	0.576089i	0.357735	+	0.933823i	$0.383549\pi$
$164$	−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	$-0.939530\pi$
$173$	−10.4326	+	10.4326i	−0.793177	+	0.793177i	0.188832	+	0.982009i	$0.439530\pi$
$174$	−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	−0.945680	−	0.325099i	$-0.894602\pi$
$179$	−8.30280	+	8.30280i	−0.620580	+	0.620580i	0.325099	+	0.945680i	$0.394602\pi$
$180$		0			0
$181$	−10.4772	−	10.4772i	−0.778765	−	0.778765i	0.200856	−	0.979621i	$-0.435628\pi$
$181$	−10.4772	−	10.4772i	−0.778765	−	0.778765i	−0.979621	+	0.200856i	$0.935628\pi$
$182$	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	$-0.518501\pi$
$193$	−1.61403			−0.116181			−0.0580903	+	0.998311i	$0.518501\pi$
$194$	−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	$-0.167234\pi$
$197$	5.10322	+	5.10322i	0.363589	+	0.363589i	−0.501543	+	0.865133i	$0.667234\pi$
$198$	−12.9481	−	5.75287i	−0.920179	−	0.408839i
$199$		−	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
$202$	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	−0.787414	−	0.616425i	$-0.788581\pi$
$211$	−2.48377	+	2.48377i	−0.170989	+	0.170989i	0.616425	+	0.787414i	$0.288581\pi$
$212$	−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	$-0.750297\pi$
$223$	−21.1384			−1.41553			−0.707765	+	0.706448i	$0.750297\pi$
$224$	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	$0.488011\pi$
$228$	0.392601	+	0.434675i	0.0260006	+	0.0287871i
$229$	−10.0956	−	10.0956i	−0.667138	−	0.667138i	0.289914	−	0.957053i	$-0.406373\pi$
$229$	−10.0956	−	10.0956i	−0.667138	−	0.667138i	−0.957053	+	0.289914i	$0.906373\pi$
$230$		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	0.355348	−	0.934734i	$-0.384362\pi$
$251$	−9.17919	−	9.17919i	−0.579386	−	0.579386i	−0.934734	+	0.355348i	$0.884362\pi$
$252$	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	$-0.330363\pi$
$257$	16.2897			1.01612			0.508061	+	0.861321i	$0.330363\pi$
$258$	−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	−0.916420	−	0.400217i	$-0.868935\pi$
$269$	−8.46636	+	8.46636i	−0.516203	+	0.516203i	0.400217	+	0.916420i	$0.368935\pi$
$270$		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	$-0.119756\pi$
$277$	9.36430	+	9.36430i	0.562646	+	0.562646i	−0.367412	+	0.930058i	$0.619756\pi$
$278$	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	$0.0297532\pi$
$281$			3.12921i			0.186673i	−0.995635	+	0.0933365i	$0.970247\pi$
$282$	−1.10681	−	0.491760i	−0.0659096	−	0.0292839i
$283$	−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
$287$	−1.41972			−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	$-0.0795382\pi$
$293$	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
$297$		−	1.76829i		−	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	$-0.609384\pi$
$307$	10.5938	−	10.5938i	0.604619	−	0.604619i	0.941535	+	0.336916i	$0.109384\pi$
$308$	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	$0.185552\pi$
$311$			19.4153i			1.10094i	−0.834854	+	0.550471i	$0.814448\pi$
$312$	−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	$-0.843948\pi$
$317$	−7.32418	+	7.32418i	−0.411367	+	0.411367i	0.470848	+	0.882215i	$0.343948\pi$
$318$	−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	0.812510	−	0.582948i	$-0.198101\pi$
$331$	4.17652	+	4.17652i	0.229562	+	0.229562i	−0.582948	+	0.812510i	$0.698101\pi$
$332$	−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	$-0.389842\pi$
$337$	12.4540			0.678410			0.339205	+	0.940712i	$0.389842\pi$
$338$	−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	$-0.481439\pi$
$347$	−17.5107	−	17.5107i	−0.940024	−	0.940024i	−0.998300	+	0.0582766i	$0.981439\pi$
$348$	−0.426783	−	0.472520i	−0.0228780	−	0.0253297i
$349$	8.42042	−	8.42042i	0.450735	−	0.450735i	−0.444863	−	0.895598i	$-0.646748\pi$
$349$	8.42042	−	8.42042i	0.450735	−	0.450735i	0.895598	+	0.444863i	$0.146748\pi$
$350$		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	$-0.416777\pi$
$353$	9.71293			0.516967			0.258484	+	0.966016i	$0.416777\pi$
$354$	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	$-0.942779\pi$
$359$		−	6.77551i		−	0.357598i	0.983886	−	0.178799i	$-0.0572212\pi$
$360$		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	$-0.855979\pi$
$367$	−34.4591			−1.79875			−0.899376	+	0.437176i	$0.855979\pi$
$368$	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	$-0.208488\pi$
$373$	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
$377$			9.01345i			0.464216i
$378$	0.256553	+	0.113987i	0.0131957	+	0.00586288i
$379$	26.4464	+	26.4464i	1.35846	+	1.35846i	0.875817	+	0.482644i	$0.160323\pi$
$379$	26.4464	+	26.4464i	1.35846	+	1.35846i	0.482644	+	0.875817i	$0.339677\pi$
$380$		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	$-0.210872\pi$
$383$	30.8614			1.57695			0.788473	+	0.615069i	$0.210872\pi$
$384$	−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	0.905819	−	0.423664i	$-0.139256\pi$
$389$	9.50959	+	9.50959i	0.482155	+	0.482155i	−0.423664	+	0.905819i	$0.639256\pi$
$390$		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	0.290518	−	0.956870i	$-0.406172\pi$
$397$	24.8540	−	24.8540i	1.24739	−	1.24739i	0.956870	−	0.290518i	$-0.0938276\pi$
$398$	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	$-0.753724\pi$
$409$		−	28.2641i		−	1.39757i	0.715331	−	0.698786i	$-0.246276\pi$
$410$		0			0
$411$	−1.04073	−	1.04073i	−0.0513352	−	0.0513352i
$412$	1.54710	+	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	0.134433	−	0.990923i	$-0.457079\pi$
$419$	23.0355	−	23.0355i	1.12536	−	1.12536i	0.990923	−	0.134433i	$-0.0429213\pi$
$420$		0			0
$421$	5.40760	+	5.40760i	0.263550	+	0.263550i	0.826495	−	0.562945i	$-0.190332\pi$
$421$	5.40760	+	5.40760i	0.263550	+	0.263550i	−0.562945	+	0.826495i	$0.690332\pi$
$422$	−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	$-0.305739\pi$
$433$	23.8511			1.14621			0.573104	+	0.819482i	$0.305739\pi$
$434$	−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	$-0.964538\pi$
$439$		−	4.65878i		−	0.222352i	0.993801	−	0.111176i	$-0.0354617\pi$
$440$		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	$-0.344867\pi$
$443$	−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
$447$	1.27810			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	−0.313064	−	0.949732i	$-0.601356\pi$
$461$	13.6698	−	13.6698i	0.636667	−	0.636667i	0.949732	+	0.313064i	$0.101356\pi$
$462$	0.146402	−	0.0563283i	0.00681124	−	0.00262063i
$463$	−2.77045			−0.128754			−0.0643768	−	0.997926i	$-0.520506\pi$
$463$	−2.77045			−0.128754			−0.0643768	+	0.997926i	$0.520506\pi$
$464$	−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	$0.0500621\pi$
$468$	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	0.976802	−	0.214146i	$-0.0686968\pi$
$491$	16.8993	+	16.8993i	0.762656	+	0.762656i	−0.214146	+	0.976802i	$0.568697\pi$
$492$	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	−0.746659	−	0.665207i	$-0.768343\pi$
$499$	−1.81950	+	1.81950i	−0.0814520	+	0.0814520i	0.665207	+	0.746659i	$0.268343\pi$
$500$		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	−0.999680	−	0.0252980i	$-0.991947\pi$
$509$	−21.9831	+	21.9831i	−0.974382	+	0.974382i	0.0252980	+	0.999680i	$0.491947\pi$
$510$		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	$-0.788567\pi$
$521$		−	28.1418i		−	1.23291i	0.787388	−	0.616457i	$-0.211433\pi$
$522$	−6.20644	+	13.9689i	−0.271649	+	0.611403i
$523$	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
$527$	−39.6009			−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	−0.171972	+	0.985102i	$0.555014\pi$
$541$	−26.9128	+	26.9128i	−1.15707	+	1.15707i	−0.985102	+	0.171972i	$0.944986\pi$
$542$	−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	$-0.645520\pi$
$547$	10.6627	−	10.6627i	0.455902	−	0.455902i	0.897308	+	0.441406i	$0.145520\pi$
$548$	−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	$-0.989452\pi$
$557$	−22.8060	+	22.8060i	−0.966320	+	0.966320i	0.0331307	+	0.999451i	$0.489452\pi$
$558$	−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	$-0.745518\pi$
$563$	0.472513	−	0.472513i	0.0199140	−	0.0199140i	0.716994	+	0.697080i	$0.245518\pi$
$564$	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	$-0.978981\pi$
$569$		−	3.14792i		−	0.131967i	0.997821	−	0.0659837i	$-0.0210185\pi$
$570$		0			0
$571$	5.78162	+	5.78162i	0.241953	+	0.241953i	0.817658	−	0.575704i	$-0.195272\pi$
$571$	5.78162	+	5.78162i	0.241953	+	0.241953i	−0.575704	+	0.817658i	$0.695272\pi$
$572$	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	$-0.706376\pi$
$577$	−29.0110			−1.20774			−0.603872	+	0.797081i	$0.706376\pi$
$578$	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	$-0.0468857\pi$
$587$	20.4099	+	20.4099i	0.842408	+	0.842408i	−0.146764	+	0.989172i	$0.546886\pi$
$588$	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	$-0.702291\pi$
$593$	−28.9098			−1.18718			−0.593592	+	0.804766i	$0.702291\pi$
$594$	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	$0.0774256\pi$
$599$			11.7893i			0.481696i	−0.970563	+	0.240848i	$0.922574\pi$
$600$		0			0
$601$		−	17.7398i		−	0.723621i	−0.932252	−	0.361810i	$-0.882159\pi$
$601$		−	17.7398i		−	0.723621i	0.932252	−	0.361810i	$-0.117841\pi$
$602$	−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	$-0.324293\pi$
$607$	25.8393			1.04878			0.524392	+	0.851477i	$0.324293\pi$
$608$	−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	−0.944006	−	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
$617$		−	15.0637i		−	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	0.463938	−	0.885868i	$-0.346436\pi$
$619$	−10.4975	−	10.4975i	−0.421929	−	0.421929i	−0.885868	+	0.463938i	$0.846436\pi$
$620$		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	$-0.665060\pi$
$631$		−	43.6349i		−	1.73708i	0.495621	−	0.868539i	$-0.334940\pi$
$632$	−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	−0.213857	+	0.976865i	$0.568603\pi$
$643$	−30.1937	+	30.1937i	−1.19072	+	1.19072i	−0.976865	+	0.213857i	$0.931397\pi$
$644$	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	$-0.698636\pi$
$653$	5.80619	−	5.80619i	0.227214	−	0.227214i	0.811528	+	0.584314i	$0.198636\pi$
$654$	−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	−0.671836	−	0.740700i	$-0.734494\pi$
$659$	1.76782	−	1.76782i	0.0688647	−	0.0688647i	0.740700	+	0.671836i	$0.234494\pi$
$660$		0			0
$661$	−12.4824	−	12.4824i	−0.485509	−	0.485509i	0.421377	−	0.906886i	$-0.361547\pi$
$661$	−12.4824	−	12.4824i	−0.485509	−	0.485509i	−0.906886	+	0.421377i	$0.861547\pi$
$662$	−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	$-0.587677\pi$
$673$	−14.1113			−0.543950			−0.271975	+	0.962304i	$0.587677\pi$
$674$	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	$-0.322528\pi$
$677$	−8.31191	−	8.31191i	−0.319453	−	0.319453i	−0.848557	+	0.529104i	$0.822528\pi$
$678$	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	−0.986348	−	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
$687$	1.25834			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	−0.0827600	−	0.996570i	$-0.526373\pi$
$691$	24.0212	−	24.0212i	0.913810	−	0.913810i	0.996570	+	0.0827600i	$0.0263735\pi$
$692$	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	−0.490230	−	0.871593i	$-0.663087\pi$
$701$	10.0971	−	10.0971i	0.381363	−	0.381363i	0.871593	+	0.490230i	$0.163087\pi$
$702$	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	0.613890	−	0.789392i	$-0.289604\pi$
$709$	−4.67310	−	4.67310i	−0.175502	−	0.175502i	−0.789392	+	0.613890i	$0.789604\pi$
$710$		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	0.0146760	−	0.999892i	$-0.495328\pi$
$733$	27.4684	−	27.4684i	1.01457	−	1.01457i	0.999892	−	0.0146760i	$-0.00467168\pi$
$734$	−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	−0.150174	−	0.988660i	$-0.547983\pi$
$739$	22.7939	−	22.7939i	0.838486	−	0.838486i	0.988660	+	0.150174i	$0.0479832\pi$
$740$		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	$-0.264224\pi$
$757$	−1.73819	−	1.73819i	−0.0631757	−	0.0631757i	−0.737989	+	0.674813i	$0.764224\pi$
$758$	−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	$-0.680565\pi$
$761$		−	46.5311i		−	1.68675i	0.537323	−	0.843376i	$-0.319435\pi$
$762$	−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	$-0.203705\pi$
$773$	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
$777$			0.357284i			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	$-0.598885\pi$
$787$	18.1351	−	18.1351i	0.646448	−	0.646448i	0.952133	+	0.305685i	$0.0988855\pi$
$788$	−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	$-0.713920\pi$
$797$	4.51575	−	4.51575i	0.159956	−	0.159956i	0.782547	+	0.622591i	$0.213920\pi$
$798$	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	$-0.981335\pi$
$809$		−	3.33368i		−	0.117206i	0.998281	−	0.0586030i	$-0.0186646\pi$
$810$		0			0
$811$	37.1948	+	37.1948i	1.30609	+	1.30609i	0.924215	+	0.381873i	$0.124721\pi$
$811$	37.1948	+	37.1948i	1.30609	+	1.30609i	0.381873	+	0.924215i	$0.375279\pi$
$812$	−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	0.103684	−	0.994610i	$-0.466937\pi$
$821$	−25.5278	−	25.5278i	−0.890926	−	0.890926i	−0.994610	+	0.103684i	$0.966937\pi$
$822$	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	$-0.158123\pi$
$827$	11.5765	+	11.5765i	0.402556	+	0.402556i	−0.476577	+	0.879133i	$0.658123\pi$
$828$	9.22775	−	8.33455i	0.320686	−	0.289646i
$829$	5.97296	−	5.97296i	0.207449	−	0.207449i	−0.595733	−	0.803182i	$-0.703138\pi$
$829$	5.97296	−	5.97296i	0.207449	−	0.207449i	0.803182	+	0.595733i	$0.203138\pi$
$830$		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	$-0.843828\pi$
$839$		−	27.2960i		−	0.942362i	0.882037	−	0.471181i	$-0.156172\pi$
$840$		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	$-0.499027\pi$
$853$	−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
$857$		−	22.0170i		−	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	0.933885	−	0.357573i	$-0.116396\pi$
$859$	16.8910	+	16.8910i	0.576312	+	0.576312i	−0.357573	+	0.933885i	$0.616396\pi$
$860$		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	$-0.211913\pi$
$863$	46.2073			1.57292			0.786458	+	0.617644i	$0.211913\pi$
$864$	−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	$-0.922824\pi$
$877$	−21.6380	+	21.6380i	−0.730664	+	0.730664i	0.240087	+	0.970751i	$0.422824\pi$
$878$	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	$-0.612713\pi$
$883$	17.5681	−	17.5681i	0.591213	−	0.591213i	0.937959	+	0.346746i	$0.112713\pi$
$884$	−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	$-0.00463777\pi$
$907$	29.6745	+	29.6745i	0.985324	+	0.985324i	−0.0145695	+	0.999894i	$0.504638\pi$
$908$	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	$-0.916657\pi$
$919$		−	15.6940i		−	0.517696i	0.965918	−	0.258848i	$-0.0833429\pi$
$920$		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	−0.763925	−	0.645305i	$-0.776730\pi$
$941$	−3.63878	+	3.63878i	−0.118621	+	0.118621i	0.645305	+	0.763925i	$0.276730\pi$
$942$	−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	0.139751	−	0.990187i	$-0.455370\pi$
$947$	34.7720	−	34.7720i	1.12994	−	1.12994i	0.990187	−	0.139751i	$-0.0446302\pi$
$948$	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	0.970057	−	0.242878i	$-0.0780913\pi$
$971$	22.6595	+	22.6595i	0.727179	+	0.727179i	−0.242878	+	0.970057i	$0.578091\pi$
$972$	−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	$-0.632761\pi$
$977$	−25.3240			−0.810186			−0.405093	+	0.914276i	$0.632761\pi$
$978$	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	$-0.241170\pi$
$997$	1.23850	+	1.23850i	0.0392235	+	0.0392235i	−0.687223	+	0.726447i	$0.741170\pi$
$998$	−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.f.101.5	✓	12
4.3	odd	2		1600.2.l.g.1201.3		12
5.2	odd	4		400.2.q.e.149.1		12
5.3	odd	4		400.2.q.f.149.6		12
5.4	even	2		400.2.l.g.101.2	yes	12
16.3	odd	4		1600.2.l.g.401.3		12
16.13	even	4	inner	400.2.l.f.301.5	yes	12
20.3	even	4		1600.2.q.f.49.3		12
20.7	even	4		1600.2.q.e.49.4		12
20.19	odd	2		1600.2.l.f.1201.4		12
80.3	even	4		1600.2.q.e.849.4		12
80.13	odd	4		400.2.q.e.349.1		12
80.19	odd	4		1600.2.l.f.401.4		12
80.29	even	4		400.2.l.g.301.2	yes	12
80.67	even	4		1600.2.q.f.849.3		12
80.77	odd	4		400.2.q.f.349.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.5	✓	12	1.1	even	1	trivial
400.2.l.f.301.5	yes	12	16.13	even	4	inner
400.2.l.g.101.2	yes	12	5.4	even	2
400.2.l.g.301.2	yes	12	80.29	even	4
400.2.q.e.149.1		12	5.2	odd	4
400.2.q.e.349.1		12	80.13	odd	4
400.2.q.f.149.6		12	5.3	odd	4
400.2.q.f.349.6		12	80.77	odd	4
1600.2.l.f.401.4		12	80.19	odd	4
1600.2.l.f.1201.4		12	20.19	odd	2
1600.2.l.g.401.3		12	16.3	odd	4
1600.2.l.g.1201.3		12	4.3	odd	2
1600.2.q.e.49.4		12	20.7	even	4
1600.2.q.e.849.4		12	80.3	even	4
1600.2.q.f.49.3		12	20.3	even	4
1600.2.q.f.849.3		12	80.67	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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