LMFDB - Embedded newform 875.2.q.b.326.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(51,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 10]))

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

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

chi := DirichletCharacter("875.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.q (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			326.12
Character	$\chi$	$=$	875.326
Dual form			875.2.q.b.51.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.141734 + 1.34851i) q^{2} +(-0.281305 - 0.0597933i) q^{3} +(0.157907 + 0.0335641i) q^{4} +(0.120502 - 0.370868i) q^{6} +(2.50606 - 0.848315i) q^{7} +(-0.905658 + 2.78733i) q^{8} +(-2.66508 - 1.18657i) q^{9} +O(q^{10})$	\(q+(-0.141734 + 1.34851i) q^{2} +(-0.281305 - 0.0597933i) q^{3} +(0.157907 + 0.0335641i) q^{4} +(0.120502 - 0.370868i) q^{6} +(2.50606 - 0.848315i) q^{7} +(-0.905658 + 2.78733i) q^{8} +(-2.66508 - 1.18657i) q^{9} +(-0.130473 + 0.0580902i) q^{11} +(-0.0424131 - 0.0188835i) q^{12} +(-3.89078 + 2.82682i) q^{13} +(0.788766 + 3.49969i) q^{14} +(-3.33542 - 1.48502i) q^{16} +(3.39745 + 3.77325i) q^{17} +(1.97783 - 3.42571i) q^{18} +(-0.807335 + 0.171604i) q^{19} +(-0.755693 + 0.0887897i) q^{21} +(-0.0598427 - 0.184177i) q^{22} +(-0.745995 + 7.09767i) q^{23} +(0.421430 - 0.729938i) q^{24} +(-3.26053 - 5.64741i) q^{26} +(1.37675 + 1.00027i) q^{27} +(0.424197 - 0.0498408i) q^{28} +(1.86695 + 5.74589i) q^{29} +(0.249623 + 0.277235i) q^{31} +(-0.455459 + 0.788877i) q^{32} +(0.0401761 - 0.00853969i) q^{33} +(-5.56980 + 4.04670i) q^{34} +(-0.381008 - 0.276818i) q^{36} +(8.27395 + 3.68380i) q^{37} +(-0.116983 - 1.11302i) q^{38} +(1.26352 - 0.562556i) q^{39} +(2.77346 - 2.01504i) q^{41} +(-0.0126263 - 1.03164i) q^{42} +1.35463 q^{43} +(-0.0225523 + 0.00479363i) q^{44} +(-9.46554 - 2.01196i) q^{46} +(-4.67231 + 5.18913i) q^{47} +(0.849477 + 0.617181i) q^{48} +(5.56072 - 4.25187i) q^{49} +(-0.730107 - 1.26458i) q^{51} +(-0.709260 + 0.315783i) q^{52} +(2.21476 + 0.470762i) q^{53} +(-1.54400 + 1.71479i) q^{54} +(0.0948953 + 7.75351i) q^{56} +0.237368 q^{57} +(-8.01299 + 1.70321i) q^{58} +(-0.344714 - 3.27973i) q^{59} +(0.179533 - 1.70814i) q^{61} +(-0.409234 + 0.297326i) q^{62} +(-7.68545 - 0.712794i) q^{63} +(-6.90681 - 5.01809i) q^{64} +(0.00582153 + 0.0553882i) q^{66} +(-7.51641 - 8.34782i) q^{67} +(0.409835 + 0.709855i) q^{68} +(0.634245 - 1.95201i) q^{69} +(1.44811 + 4.45682i) q^{71} +(5.72101 - 6.35382i) q^{72} +(-9.25719 + 4.12157i) q^{73} +(-6.14034 + 10.6354i) q^{74} -0.133243 q^{76} +(-0.277694 + 0.256260i) q^{77} +(0.579528 + 1.78360i) q^{78} +(-7.64875 + 8.49480i) q^{79} +(5.52867 + 6.14021i) q^{81} +(2.32420 + 4.02564i) q^{82} +(4.81947 - 14.8328i) q^{83} +(-0.122309 - 0.0113437i) q^{84} +(-0.191997 + 1.82673i) q^{86} +(-0.181618 - 1.72798i) q^{87} +(-0.0437528 - 0.416280i) q^{88} +(1.42961 - 13.6018i) q^{89} +(-7.35251 + 10.3848i) q^{91} +(-0.356024 + 1.09573i) q^{92} +(-0.0536436 - 0.0929134i) q^{93} +(-6.33536 - 7.03613i) q^{94} +(0.175293 - 0.194682i) q^{96} +(-1.35738 - 4.17760i) q^{97} +(4.94554 + 8.10132i) q^{98} +0.416648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9}+O(q^{10}) $ 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9	$ 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9} + 36 q^{14} + 10 q^{16} + 22 q^{19} - 18 q^{21} - 100 q^{24} - 120 q^{26} + 48 q^{29} + 30 q^{31} + 40 q^{34} + 32 q^{36} - 26 q^{39} - 124 q^{41} + 30 q^{44} - 54 q^{46} + 76 q^{49} - 16 q^{51} + 58 q^{54} + 64 q^{56} + 78 q^{59} + 14 q^{61} - 68 q^{64} + 22 q^{66} - 148 q^{69} - 92 q^{71} - 12 q^{74} + 360 q^{76} - 18 q^{79} - 118 q^{81} + 102 q^{84} + 22 q^{86} + 84 q^{89} + 44 q^{91} - 10 q^{94} + 106 q^{96} + 88 q^{99}+O(q^{100}) $ 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9 + 36 * q^14 + 10 * q^16 + 22 * q^19 - 18 * q^21 - 100 * q^24 - 120 * q^26 + 48 * q^29 + 30 * q^31 + 40 * q^34 + 32 * q^36 - 26 * q^39 - 124 * q^41 + 30 * q^44 - 54 * q^46 + 76 * q^49 - 16 * q^51 + 58 * q^54 + 64 * q^56 + 78 * q^59 + 14 * q^61 - 68 * q^64 + 22 * q^66 - 148 * q^69 - 92 * q^71 - 12 * q^74 + 360 * q^76 - 18 * q^79 - 118 * q^81 + 102 * q^84 + 22 * q^86 + 84 * q^89 + 44 * q^91 - 10 * q^94 + 106 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.141734	+	1.34851i	−0.100221	+	0.953540i	0.822680	+	0.568504i	$0.192478\pi$
$2$	−0.141734	+	1.34851i	−0.100221	+	0.953540i	−0.922902	+	0.385036i	$0.874189\pi$
$3$	−0.281305	−	0.0597933i	−0.162412	−	0.0345217i	0.125988	−	0.992032i	$-0.459790\pi$
$3$	−0.281305	−	0.0597933i	−0.162412	−	0.0345217i	−0.288400	+	0.957510i	$0.593123\pi$
$4$	0.157907	+	0.0335641i	0.0789534	+	0.0167821i
$5$		0			0
$5$		0			0
$6$	0.120502	−	0.370868i	0.0491949	−	0.151406i
$7$	2.50606	−	0.848315i	0.947204	−	0.320633i
$7$	2.50606	−	0.848315i	0.947204	−	0.320633i
$8$	−0.905658	+	2.78733i	−0.320198	+	0.985469i
$9$	−2.66508	−	1.18657i	−0.888360	−	0.395523i
$10$		0			0
$11$	−0.130473	+	0.0580902i	−0.0393390	+	0.0175149i	−0.426312	−	0.904576i	$-0.640187\pi$
$11$	−0.130473	+	0.0580902i	−0.0393390	+	0.0175149i	0.386973	+	0.922091i	$0.373521\pi$
$12$	−0.0424131	−	0.0188835i	−0.0122436	−	0.00545121i
$13$	−3.89078	+	2.82682i	−1.07911	+	0.784018i	−0.977527	−	0.210810i	$-0.932390\pi$
$13$	−3.89078	+	2.82682i	−1.07911	+	0.784018i	−0.101581	+	0.994827i	$0.532390\pi$
$14$	0.788766	+	3.49969i	0.210807	+	0.935331i
$15$		0			0
$16$	−3.33542	−	1.48502i	−0.833855	−	0.371256i
$17$	3.39745	+	3.77325i	0.824004	+	0.915149i	0.997570	−	0.0696735i	$-0.0221958\pi$
$17$	3.39745	+	3.77325i	0.824004	+	0.915149i	−0.173566	+	0.984822i	$0.555529\pi$
$18$	1.97783	−	3.42571i	0.466180	−	0.807447i
$19$	−0.807335	+	0.171604i	−0.185215	+	0.0393687i	−0.299585	−	0.954069i	$-0.596848\pi$
$19$	−0.807335	+	0.171604i	−0.185215	+	0.0393687i	0.114370	+	0.993438i	$0.463515\pi$
$20$		0			0
$21$	−0.755693	+	0.0887897i	−0.164906	+	0.0193755i
$22$	−0.0598427	−	0.184177i	−0.0127585	−	0.0392667i
$23$	−0.745995	+	7.09767i	−0.155551	+	1.47997i	0.586679	+	0.809820i	$0.300435\pi$
$23$	−0.745995	+	7.09767i	−0.155551	+	1.47997i	−0.742229	+	0.670146i	$0.766231\pi$
$24$	0.421430	−	0.729938i	0.0860240	−	0.148998i
$25$		0			0
$26$	−3.26053	−	5.64741i	−0.639443	−	1.10755i
$27$	1.37675	+	1.00027i	0.264955	+	0.192501i
$28$	0.424197	−	0.0498408i	0.0801658	−	0.00941903i
$29$	1.86695	+	5.74589i	0.346684	+	1.06698i	0.960676	+	0.277672i	$0.0895628\pi$
$29$	1.86695	+	5.74589i	0.346684	+	1.06698i	−0.613992	+	0.789312i	$0.710437\pi$
$30$		0			0
$31$	0.249623	+	0.277235i	0.0448336	+	0.0497928i	0.765144	−	0.643859i	$-0.222668\pi$
$31$	0.249623	+	0.277235i	0.0448336	+	0.0497928i	−0.720311	+	0.693651i	$0.756001\pi$
$32$	−0.455459	+	0.788877i	−0.0805145	+	0.139455i
$33$	0.0401761	−	0.00853969i	0.00699376	−	0.00148657i
$34$	−5.56980	+	4.04670i	−0.955213	+	0.694003i
$35$		0			0
$36$	−0.381008	−	0.276818i	−0.0635013	−	0.0461364i
$37$	8.27395	+	3.68380i	1.36023	+	0.605613i	0.951671	−	0.307119i	$-0.0993649\pi$
$37$	8.27395	+	3.68380i	1.36023	+	0.605613i	0.408559	+	0.912732i	$0.366032\pi$
$38$	−0.116983	−	1.11302i	−0.0189772	−	0.180556i
$39$	1.26352	−	0.562556i	0.202325	−	0.0900811i
$40$		0			0
$41$	2.77346	−	2.01504i	0.433142	−	0.314696i	−0.349762	−	0.936839i	$-0.613738\pi$
$41$	2.77346	−	2.01504i	0.433142	−	0.314696i	0.782904	+	0.622142i	$0.213738\pi$
$42$	−0.0126263	−	1.03164i	−0.00194828	−	0.159186i
$43$	1.35463			0.206579			0.103290	−	0.994651i	$-0.467063\pi$
$43$	1.35463			0.206579			0.103290	+	0.994651i	$0.467063\pi$
$44$	−0.0225523	+	0.00479363i	−0.00339988	+	0.000722667i
$45$		0			0
$46$	−9.46554	−	2.01196i	−1.39562	−	0.296648i
$47$	−4.67231	+	5.18913i	−0.681527	+	0.756912i	−0.980322	−	0.197405i	$-0.936749\pi$
$47$	−4.67231	+	5.18913i	−0.681527	+	0.756912i	0.298795	+	0.954317i	$0.403415\pi$
$48$	0.849477	+	0.617181i	0.122611	+	0.0890824i
$49$	5.56072	−	4.25187i	0.794389	−	0.607409i
$50$		0			0
$51$	−0.730107	−	1.26458i	−0.102235	−	0.177077i
$52$	−0.709260	+	0.315783i	−0.0983566	+	0.0437912i
$53$	2.21476	+	0.470762i	0.304221	+	0.0646642i	0.357493	−	0.933916i	$-0.383632\pi$
$53$	2.21476	+	0.470762i	0.304221	+	0.0646642i	−0.0532718	+	0.998580i	$0.516965\pi$
$54$	−1.54400	+	1.71479i	−0.210112	+	0.233353i
$55$		0			0
$56$	0.0948953	+	7.75351i	0.0126809	+	1.03611i
$57$	0.237368			0.0314402
$58$	−8.01299	+	1.70321i	−1.05216	+	0.223643i
$59$	−0.344714	−	3.27973i	−0.0448779	−	0.426985i	−0.993776	−	0.111401i	$-0.964466\pi$
$59$	−0.344714	−	3.27973i	−0.0448779	−	0.426985i	0.948898	−	0.315584i	$-0.102200\pi$
$60$		0			0
$61$	0.179533	−	1.70814i	0.0229868	−	0.218705i	−0.976998	−	0.213247i	$-0.931596\pi$
$61$	0.179533	−	1.70814i	0.0229868	−	0.218705i	0.999985	−	0.00545771i	$-0.00173725\pi$
$62$	−0.409234	+	0.297326i	−0.0519727	+	0.0377604i
$63$	−7.68545	−	0.712794i	−0.968275	−	0.0898036i
$64$	−6.90681	−	5.01809i	−0.863351	−	0.627261i
$65$		0			0
$66$	0.00582153	+	0.0553882i	0.000716581	+	0.00681781i
$67$	−7.51641	−	8.34782i	−0.918276	−	1.01985i	−0.999731	−	0.0231719i	$-0.992623\pi$
$67$	−7.51641	−	8.34782i	−0.918276	−	1.01985i	0.0814554	−	0.996677i	$-0.474043\pi$
$68$	0.409835	+	0.709855i	0.0496998	+	0.0860825i
$69$	0.634245	−	1.95201i	0.0763542	−	0.234994i
$70$		0			0
$71$	1.44811	+	4.45682i	0.171859	+	0.528928i	0.999476	−	0.0323654i	$-0.0103040\pi$
$71$	1.44811	+	4.45682i	0.171859	+	0.528928i	−0.827617	+	0.561293i	$0.810304\pi$
$72$	5.72101	−	6.35382i	0.674227	−	0.748805i
$73$	−9.25719	+	4.12157i	−1.08347	+	0.482393i	−0.869240	−	0.494390i	$-0.835392\pi$
$73$	−9.25719	+	4.12157i	−1.08347	+	0.482393i	−0.214232	+	0.976783i	$0.568725\pi$
$74$	−6.14034	+	10.6354i	−0.713800	+	1.23634i
$75$		0			0
$76$	−0.133243			−0.0152841
$77$	−0.277694	+	0.256260i	−0.0316462	+	0.0292035i
$78$	0.579528	+	1.78360i	0.0656186	+	0.201953i
$79$	−7.64875	+	8.49480i	−0.860552	+	0.955740i	−0.999402	−	0.0345738i	$-0.988993\pi$
$79$	−7.64875	+	8.49480i	−0.860552	+	0.955740i	0.138850	+	0.990313i	$0.455659\pi$
$80$		0			0
$81$	5.52867	+	6.14021i	0.614297	+	0.682246i
$82$	2.32420	+	4.02564i	0.256665	+	0.444558i
$83$	4.81947	−	14.8328i	0.529005	−	1.62811i	−0.227252	−	0.973836i	$-0.572974\pi$
$83$	4.81947	−	14.8328i	0.529005	−	1.62811i	0.756257	−	0.654275i	$-0.227026\pi$
$84$	−0.122309	−	0.0113437i	−0.0133450	−	0.00123770i
$85$		0			0
$86$	−0.191997	+	1.82673i	−0.0207036	+	0.196982i
$87$	−0.181618	−	1.72798i	−0.0194715	−	0.185259i
$88$	−0.0437528	−	0.416280i	−0.00466406	−	0.0443756i
$89$	1.42961	−	13.6018i	0.151538	−	1.44179i	−0.609346	−	0.792905i	$-0.708568\pi$
$89$	1.42961	−	13.6018i	0.151538	−	1.44179i	0.760884	−	0.648888i	$-0.224765\pi$
$90$		0			0
$91$	−7.35251	+	10.3848i	−0.770753	+	1.08862i
$92$	−0.356024	+	1.09573i	−0.0371181	+	0.114238i
$93$	−0.0536436	−	0.0929134i	−0.00556258	−	0.00963467i
$94$	−6.33536	−	7.03613i	−0.653443	−	0.725722i
$95$		0			0
$96$	0.175293	−	0.194682i	0.0178907	−	0.0198697i
$97$	−1.35738	−	4.17760i	−0.137821	−	0.424171i	0.858197	−	0.513321i	$-0.171585\pi$
$97$	−1.35738	−	4.17760i	−0.137821	−	0.424171i	−0.996018	+	0.0891501i	$0.971585\pi$
$98$	4.94554	+	8.10132i	0.499575	+	0.818357i
$99$	0.416648			0.0418747
$100$		0			0
$101$	3.76146	−	6.51503i	0.374279	−	0.648270i	−0.615940	−	0.787793i	$-0.711224\pi$
$101$	3.76146	−	6.51503i	0.374279	−	0.648270i	0.990219	+	0.139523i	$0.0445570\pi$
$102$	1.80878	−	0.805321i	0.179096	−	0.0797387i
$103$	12.3540	−	13.7205i	1.21727	−	1.35192i	0.299862	−	0.953983i	$-0.403059\pi$
$103$	12.3540	−	13.7205i	1.21727	−	1.35192i	0.917413	−	0.397937i	$-0.130274\pi$
$104$	−4.35555	−	13.4050i	−0.427097	−	1.31447i
$105$		0			0
$106$	−0.948734	+	2.91990i	−0.0921492	+	0.283606i
$107$	1.55232	+	2.68869i	0.150068	+	0.259926i	0.931252	−	0.364375i	$-0.118717\pi$
$107$	1.55232	+	2.68869i	0.150068	+	0.259926i	−0.781184	+	0.624301i	$0.785384\pi$
$108$	0.183825	+	0.204158i	0.0176885	+	0.0196451i
$109$	0.389344	+	3.70436i	0.0372924	+	0.354814i	0.997217	+	0.0745548i	$0.0237536\pi$
$109$	0.389344	+	3.70436i	0.0372924	+	0.354814i	−0.959925	+	0.280259i	$0.909580\pi$
$110$		0			0
$111$	−2.10724	−	1.53100i	−0.200011	−	0.145316i
$112$	−9.61854	−	0.892081i	−0.908867	−	0.0842937i
$113$	−6.02127	+	4.37471i	−0.566434	+	0.411538i	−0.833808	−	0.552055i	$-0.813844\pi$
$113$	−6.02127	+	4.37471i	−0.566434	+	0.411538i	0.267374	+	0.963593i	$0.413844\pi$
$114$	−0.0336432	+	0.320094i	−0.00315097	+	0.0299795i
$115$		0			0
$116$	0.101949	+	0.969977i	0.00946570	+	0.0900601i
$117$	13.7234	−	2.91701i	1.26873	−	0.269678i
$118$	4.47161			0.411645
$119$	11.7151	+	6.57391i	1.07393	+	0.602629i
$120$		0			0
$121$	−7.34679	+	8.15943i	−0.667890	+	0.741767i
$122$	2.27799	+	0.484203i	0.206240	+	0.0438377i
$123$	−0.900676	+	0.401007i	−0.0812112	+	0.0361576i
$124$	0.0301120	+	0.0521556i	0.00270414	+	0.00468371i
$125$		0			0
$126$	2.05050	−	10.2629i	0.182673	−	0.914289i
$127$	−11.7448	−	8.53310i	−1.04218	−	0.757190i	−0.0714722	−	0.997443i	$-0.522770\pi$
$127$	−11.7448	−	8.53310i	−1.04218	−	0.757190i	−0.970710	+	0.240253i	$0.922770\pi$
$128$	6.52683	−	7.24878i	0.576895	−	0.640707i
$129$	−0.381065	−	0.0809979i	−0.0335509	−	0.00713147i
$130$		0			0
$131$	14.7815	−	3.14191i	1.29147	−	0.274510i	0.489565	−	0.871967i	$-0.337155\pi$
$131$	14.7815	−	3.14191i	1.29147	−	0.274510i	0.801901	+	0.597457i	$0.203822\pi$
$132$	0.00663070			0.000577128
$133$	−1.87766	+	1.11493i	−0.162814	+	0.0966763i
$134$	12.3224	−	8.95278i	1.06450	−	0.773403i
$135$		0			0
$136$	−13.5942	+	6.05254i	−1.16570	+	0.519001i
$137$	−1.67649	−	15.9508i	−0.143233	−	1.36277i	−0.796041	−	0.605243i	$-0.793076\pi$
$137$	−1.67649	−	15.9508i	−0.143233	−	1.36277i	0.652808	−	0.757523i	$-0.273591\pi$
$138$	2.54240	+	1.13195i	0.216424	+	0.0963581i
$139$	2.65128	+	1.92627i	0.224879	+	0.163384i	0.694520	−	0.719473i	$-0.255617\pi$
$139$	2.65128	+	1.92627i	0.224879	+	0.163384i	−0.469641	+	0.882857i	$0.655617\pi$
$140$		0			0
$141$	1.62462	−	1.18036i	0.136818	−	0.0994040i
$142$	−6.21531	+	1.32111i	−0.521578	+	0.110865i
$143$	0.343430	−	0.594838i	0.0287191	−	0.0497429i
$144$	7.12707	+	7.91541i	0.593922	+	0.659618i
$145$		0			0
$146$	−4.24591	−	13.0676i	−0.351394	−	1.08148i
$147$	−1.81849	+	0.863579i	−0.149987	+	0.0712268i
$148$	1.18287	+	0.859405i	0.0972313	+	0.0706427i
$149$	5.39761	+	9.34893i	0.442189	+	0.765894i	0.997852	−	0.0655140i	$-0.0208687\pi$
$149$	5.39761	+	9.34893i	0.442189	+	0.765894i	−0.555663	+	0.831408i	$0.687535\pi$
$150$		0			0
$151$	8.70042	−	15.0696i	0.708030	−	1.22634i	−0.257557	−	0.966263i	$-0.582917\pi$
$151$	8.70042	−	15.0696i	0.708030	−	1.22634i	0.965587	−	0.260081i	$-0.0837492\pi$
$152$	0.252851	−	2.40572i	0.0205090	−	0.195130i
$153$	−4.57725	−	14.0873i	−0.370049	−	1.13889i
$154$	−0.306210	−	0.410794i	−0.0246751	−	0.0331027i
$155$		0			0
$156$	0.218400	−	0.0464224i	0.0174860	−	0.00371677i
$157$	−4.15820	+	7.20222i	−0.331861	+	0.574800i	−0.982877	−	0.184264i	$-0.941010\pi$
$157$	−4.15820	+	7.20222i	−0.331861	+	0.574800i	0.651016	+	0.759064i	$0.274343\pi$
$158$	−10.3712	−	11.5184i	−0.825090	−	0.916356i
$159$	−0.594876	−	0.264856i	−0.0471768	−	0.0210044i
$160$		0			0
$161$	4.15155	+	18.4201i	0.327188	+	1.45170i
$162$	−9.06373	+	6.58519i	−0.712114	+	0.517381i
$163$	12.5198	+	5.57419i	0.980630	+	0.436604i	0.833504	−	0.552513i	$-0.186331\pi$
$163$	12.5198	+	5.57419i	0.980630	+	0.436604i	0.147126	+	0.989118i	$0.452998\pi$
$164$	0.505581	−	0.225099i	0.0394793	−	0.0175773i
$165$		0			0
$166$	19.3191	+	8.60141i	1.49945	+	0.667599i
$167$	−5.33231	+	16.4112i	−0.412626	+	1.26993i	0.501730	+	0.865024i	$0.332697\pi$
$167$	−5.33231	+	16.4112i	−0.412626	+	1.26993i	−0.914357	+	0.404910i	$0.867303\pi$
$168$	0.436913	−	2.18678i	0.0337086	−	0.168714i
$169$	3.13005	−	9.63330i	0.240773	−	0.741023i
$170$		0			0
$171$	2.35523	+	0.500620i	0.180109	+	0.0382834i
$172$	0.213905	+	0.0454670i	0.0163101	+	0.00346683i
$173$	−0.603206	+	5.73912i	−0.0458609	+	0.436337i	0.947367	+	0.320151i	$0.103734\pi$
$173$	−0.603206	+	5.73912i	−0.0458609	+	0.436337i	−0.993227	+	0.116186i	$0.962933\pi$
$174$	2.35594			0.178603
$175$		0			0
$176$	0.521446			0.0393055
$177$	−0.0991363	+	0.943219i	−0.00745154	+	0.0708967i
$178$	18.1396	+	3.85569i	1.35962	+	0.288996i
$179$	12.8846	+	2.73871i	0.963043	+	0.204701i	0.662496	−	0.749066i	$-0.269497\pi$
$179$	12.8846	+	2.73871i	0.963043	+	0.204701i	0.300548	+	0.953767i	$0.402831\pi$
$180$		0			0
$181$	5.86832	−	18.0608i	0.436189	−	1.34245i	−0.455674	−	0.890147i	$-0.650602\pi$
$181$	5.86832	−	18.0608i	0.436189	−	1.34245i	0.891863	−	0.452305i	$-0.149398\pi$
$182$	−12.9619	−	11.3868i	−0.960799	−	0.844047i
$183$	−0.152639	+	0.469774i	−0.0112834	+	0.0347267i
$184$	−19.1079	−	8.50739i	−1.40865	−	0.627173i
$185$		0			0
$186$	0.132898	−	0.0591699i	0.00974453	−	0.00433854i
$187$	−0.662464	−	0.294948i	−0.0484442	−	0.0215687i
$188$	−0.911958	+	0.662576i	−0.0665114	+	0.0483234i
$189$	4.29876	+	1.33881i	0.312689	+	0.0973845i
$190$		0			0
$191$	13.4652	+	5.99510i	0.974309	+	0.433790i	0.831235	−	0.555922i	$-0.187635\pi$
$191$	13.4652	+	5.99510i	0.974309	+	0.433790i	0.143074	+	0.989712i	$0.454301\pi$
$192$	1.64287	+	1.82460i	0.118564	+	0.131679i
$193$	1.98215	−	3.43318i	0.142678	−	0.247125i	−0.785826	−	0.618447i	$-0.787762\pi$
$193$	1.98215	−	3.43318i	0.142678	−	0.247125i	0.928504	+	0.371322i	$0.121095\pi$
$194$	5.82591	−	1.23834i	0.418276	−	0.0889074i
$195$		0			0
$196$	1.02079	−	0.484757i	0.0729133	−	0.0346255i
$197$	6.16564	+	18.9759i	0.439283	+	1.35198i	0.888633	+	0.458619i	$0.151656\pi$
$197$	6.16564	+	18.9759i	0.439283	+	1.35198i	−0.449350	+	0.893356i	$0.648344\pi$
$198$	−0.0590532	+	0.561854i	−0.00419673	+	0.0399292i
$199$	2.37463	−	4.11297i	0.168333	−	0.291561i	−0.769501	−	0.638646i	$-0.779495\pi$
$199$	2.37463	−	4.11297i	0.168333	−	0.291561i	0.937834	+	0.347085i	$0.112828\pi$
$200$		0			0
$201$	1.61526	+	2.79772i	0.113932	+	0.197336i
$202$	8.25245	+	5.99576i	0.580641	+	0.421860i
$203$	9.55303	+	12.8158i	0.670491	+	0.899493i
$204$	−0.0728442	−	0.224191i	−0.00510011	−	0.0156965i
$205$		0			0
$206$	16.7512	+	18.6041i	1.16711	+	1.29621i
$207$	10.4100	−	18.0307i	0.723546	−	1.25322i
$208$	17.1753	−	3.65072i	1.19089	−	0.253132i
$209$	0.0953666	−	0.0692879i	0.00659665	−	0.00479274i
$210$		0			0
$211$	−1.61068	−	1.17023i	−0.110884	−	0.0805619i	0.530961	−	0.847396i	$-0.321831\pi$
$211$	−1.61068	−	1.17023i	−0.110884	−	0.0805619i	−0.641845	+	0.766834i	$0.721831\pi$
$212$	0.333925	+	0.148673i	0.0229341	+	0.0102109i
$213$	−0.140873	−	1.34032i	−0.00965245	−	0.0918369i
$214$	−3.84574	+	1.71224i	−0.262890	+	0.117046i
$215$		0			0
$216$	−4.03493	+	2.93155i	−0.274542	+	0.199467i
$217$	0.860754	+	0.483009i	0.0584318	+	0.0327888i
$218$	−5.05055			−0.342066
$219$	2.85054	−	0.605901i	0.192622	−	0.0409430i
$220$		0			0
$221$	−23.8850	−	5.07692i	−1.60668	−	0.341511i
$222$	2.36324	−	2.62464i	0.158610	−	0.176154i
$223$	−13.1770	−	9.57365i	−0.882397	−	0.641099i	0.0514874	−	0.998674i	$-0.483604\pi$
$223$	−13.1770	−	9.57365i	−0.882397	−	0.641099i	−0.933885	+	0.357575i	$0.883604\pi$
$224$	−0.472192	+	2.36335i	−0.0315497	+	0.157908i
$225$		0			0
$226$	−5.04592	−	8.73979i	−0.335649	−	0.581362i
$227$	−1.00627	+	0.448022i	−0.0667888	+	0.0297363i	−0.439859	−	0.898067i	$-0.644972\pi$
$227$	−1.00627	+	0.448022i	−0.0667888	+	0.0297363i	0.373070	+	0.927803i	$0.378305\pi$
$228$	0.0374821	+	0.00796706i	0.00248231	+	0.000527632i
$229$	−4.12813	+	4.58476i	−0.272795	+	0.302969i	−0.863939	−	0.503597i	$-0.832010\pi$
$229$	−4.12813	+	4.58476i	−0.272795	+	0.302969i	0.591144	+	0.806566i	$0.298676\pi$
$230$		0			0
$231$	0.0934395	−	0.0554830i	0.00614787	−	0.00365051i
$232$	−17.7065			−1.16249
$233$	−10.1348	+	2.15421i	−0.663950	+	0.141127i	−0.527546	−	0.849526i	$-0.676888\pi$
$233$	−10.1348	+	2.15421i	−0.663950	+	0.141127i	−0.136404	+	0.990653i	$0.543554\pi$
$234$	1.98853	+	18.9196i	0.129995	+	1.23682i
$235$		0			0
$236$	0.0556487	−	0.529462i	0.00362242	−	0.0344651i
$237$	2.65957	−	1.93229i	0.172757	−	0.125516i
$238$	−10.5254	+	14.8662i	−0.682261	+	0.963635i
$239$	5.80855	+	4.22016i	0.375724	+	0.272979i	0.759580	−	0.650413i	$-0.225404\pi$
$239$	5.80855	+	4.22016i	0.375724	+	0.272979i	−0.383857	+	0.923393i	$0.625404\pi$
$240$		0			0
$241$	−2.10935	−	20.0691i	−0.135875	−	1.29277i	−0.823757	−	0.566943i	$-0.808126\pi$
$241$	−2.10935	−	20.0691i	−0.135875	−	1.29277i	0.687882	−	0.725822i	$-0.258541\pi$
$242$	−9.96178	−	11.0637i	−0.640368	−	0.711200i
$243$	−3.74073	−	6.47914i	−0.239968	−	0.415637i
$244$	0.0856816	−	0.263701i	0.00548520	−	0.0168817i
$245$		0			0
$246$	−0.413105	−	1.27141i	−0.0263386	−	0.0810619i
$247$	2.65607	−	2.94986i	0.169002	−	0.187695i
$248$	−0.998817	+	0.444702i	−0.0634249	+	0.0282386i
$249$	−2.24264	+	3.88437i	−0.142122	+	0.246162i
$250$		0			0
$251$	26.6764			1.68380			0.841901	−	0.539632i	$-0.181437\pi$
$251$	26.6764			1.68380			0.841901	+	0.539632i	$0.181437\pi$
$252$	−1.18966	−	0.370510i	−0.0749415	−	0.0233399i
$253$	−0.314973	−	0.969387i	−0.0198022	−	0.0609448i
$254$	13.1716	−	14.6285i	0.826460	−	0.917876i
$255$		0			0
$256$	−2.57515	−	2.86000i	−0.160947	−	0.178750i
$257$	−0.886703	−	1.53581i	−0.0553110	−	0.0958015i	0.837044	−	0.547135i	$-0.184282\pi$
$257$	−0.886703	−	1.53581i	−0.0553110	−	0.0958015i	−0.892355	+	0.451334i	$0.850948\pi$
$258$	0.163236	−	0.502390i	0.0101626	−	0.0312774i
$259$	23.8601	+	2.21293i	1.48259	+	0.137505i
$260$		0			0
$261$	1.84232	−	17.5285i	0.114037	−	1.08499i
$262$	2.14185	+	20.3783i	0.132324	+	1.25898i
$263$	−0.00712606	−	0.0677999i	−0.000439412	−	0.00418072i	0.994300	−	0.106619i	$-0.0340024\pi$
$263$	−0.00712606	−	0.0677999i	−0.000439412	−	0.00418072i	−0.994739	+	0.102438i	$0.967336\pi$
$264$	−0.0125829	+	0.119718i	−0.000774422	+	0.00736813i
$265$		0			0
$266$	−1.23736	−	2.69006i	−0.0758674	−	0.164938i
$267$	−1.21546	+	3.74079i	−0.0743847	+	0.228933i
$268$	−0.906705	−	1.57046i	−0.0553858	−	0.0959311i
$269$	−3.65949	−	4.06427i	−0.223123	−	0.247803i	0.621182	−	0.783666i	$-0.286653\pi$
$269$	−3.65949	−	4.06427i	−0.223123	−	0.247803i	−0.844305	+	0.535863i	$0.819986\pi$
$270$		0			0
$271$	2.12393	−	2.35887i	0.129020	−	0.143291i	−0.675173	−	0.737659i	$-0.735931\pi$
$271$	2.12393	−	2.35887i	0.129020	−	0.143291i	0.804193	+	0.594368i	$0.202598\pi$
$272$	−5.72856	−	17.6307i	−0.347345	−	1.06902i
$273$	2.68924	−	2.48167i	0.162760	−	0.150197i
$274$	21.7474			1.31381
$275$		0			0
$276$	0.165669	−	0.286947i	0.00997210	−	0.0172722i
$277$	8.96419	−	3.99112i	0.538606	−	0.239803i	−0.119359	−	0.992851i	$-0.538084\pi$
$277$	8.96419	−	3.99112i	0.538606	−	0.239803i	0.657965	+	0.753048i	$0.271417\pi$
$278$	−2.97337	+	3.30226i	−0.178331	+	0.198057i
$279$	−0.336307	−	1.03505i	−0.0201342	−	0.0619667i
$280$		0			0
$281$	−6.68442	+	20.5725i	−0.398759	+	1.22725i	0.527236	+	0.849719i	$0.323228\pi$
$281$	−6.68442	+	20.5725i	−0.398759	+	1.22725i	−0.925995	+	0.377536i	$0.876772\pi$
$282$	1.36146	+	2.35811i	0.0810737	+	0.140424i
$283$	14.2949	+	15.8761i	0.849746	+	0.943738i	0.998984	−	0.0450630i	$-0.0143489\pi$
$283$	14.2949	+	15.8761i	0.849746	+	0.943738i	−0.149238	+	0.988801i	$0.547682\pi$
$284$	0.0790770	+	0.752367i	0.00469235	+	0.0446448i
$285$		0			0
$286$	0.753469	+	0.547428i	0.0445536	+	0.0323701i
$287$	5.24109	−	7.40259i	0.309372	−	0.436961i
$288$	2.14989	−	1.56199i	0.126684	−	0.0920410i
$289$	−0.917775	+	8.73204i	−0.0539868	+	0.513650i
$290$		0			0
$291$	0.132047	+	1.25634i	0.00774073	+	0.0736481i
$292$	−1.60011	+	0.340114i	−0.0936393	+	0.0199037i
$293$	3.83275			0.223911			0.111956	−	0.993713i	$-0.464289\pi$
$293$	3.83275			0.223911			0.111956	+	0.993713i	$0.464289\pi$
$294$	−0.906801	−	2.57466i	−0.0528857	−	0.150157i
$295$		0			0
$296$	−17.7613	+	19.7260i	−1.03236	+	1.14655i
$297$	−0.237734	−	0.0505318i	−0.0137947	−	0.00293215i
$298$	−13.3721	+	5.95366i	−0.774627	+	0.344886i
$299$	−17.1613	−	29.7242i	−0.992464	−	1.71900i
$300$		0			0
$301$	3.39479	−	1.14915i	0.195673	−	0.0662362i
$302$	19.0883	+	13.8685i	1.09841	+	0.798041i
$303$	−1.44767	+	1.60780i	−0.0831667	+	0.0923659i
$304$	2.94764	+	0.626539i	0.169059	+	0.0359345i
$305$		0			0
$306$	19.6457	−	4.17581i	1.12307	−	0.238715i
$307$	19.4072			1.10763			0.553814	−	0.832641i	$-0.313172\pi$
$307$	19.4072			1.10763			0.553814	+	0.832641i	$0.313172\pi$
$308$	−0.0524509	+	0.0311446i	−0.00298867	+	0.00177463i
$309$	−4.29564	+	3.12096i	−0.244370	+	0.177545i
$310$		0			0
$311$	2.48883	−	1.10810i	0.141128	−	0.0628344i	−0.334957	−	0.942233i	$-0.608722\pi$
$311$	2.48883	−	1.10810i	0.141128	−	0.0628344i	0.476086	+	0.879399i	$0.342055\pi$
$312$	0.423710	+	4.03133i	0.0239879	+	0.228229i
$313$	23.3332	+	10.3886i	1.31887	+	0.587200i	0.940921	−	0.338626i	$-0.109962\pi$
$313$	23.3332	+	10.3886i	1.31887	+	0.587200i	0.377951	+	0.925826i	$0.376629\pi$
$314$	−9.12290	−	6.62817i	−0.514835	−	0.374049i
$315$		0			0
$316$	−1.49291	+	1.08466i	−0.0839827	+	0.0610170i
$317$	10.1468	−	2.15677i	0.569903	−	0.121137i	0.0860574	−	0.996290i	$-0.472573\pi$
$317$	10.1468	−	2.15677i	0.569903	−	0.121137i	0.483845	+	0.875154i	$0.339240\pi$
$318$	0.441475	−	0.764657i	0.0247567	−	0.0428798i
$319$	−0.577366	−	0.641230i	−0.0323263	−	0.0359020i
$320$		0			0
$321$	−0.275909	−	0.849162i	−0.0153998	−	0.0473956i
$322$	−25.4280	+	2.98765i	−1.41705	+	0.166495i
$323$	−3.39039	−	2.46326i	−0.188646	−	0.137060i
$324$	0.666924	+	1.15515i	0.0370513	+	0.0641748i
$325$		0			0
$326$	−9.29134	+	16.0931i	−0.514600	+	0.891313i
$327$	0.111971	−	1.06534i	0.00619204	−	0.0589133i
$328$	3.10476	+	9.55548i	0.171432	+	0.527613i
$329$	−7.30710	+	16.9679i	−0.402854	+	0.935470i
$330$		0			0
$331$	12.8193	−	2.72482i	0.704611	−	0.149770i	0.158348	−	0.987383i	$-0.449383\pi$
$331$	12.8193	−	2.72482i	0.704611	−	0.149770i	0.546263	+	0.837614i	$0.316050\pi$
$332$	1.25888	−	2.18044i	0.0690898	−	0.119667i
$333$	−17.6797	−	19.6352i	−0.968839	−	1.07600i
$334$	−21.3748	−	9.51669i	−1.16958	−	0.520730i
$335$		0			0
$336$	2.65241	+	0.826072i	0.144701	+	0.0450659i
$337$	−8.34261	+	6.06126i	−0.454451	+	0.330178i	−0.791351	−	0.611363i	$-0.790622\pi$
$337$	−8.34261	+	6.06126i	−0.454451	+	0.330178i	0.336899	+	0.941541i	$0.390622\pi$
$338$	12.5470	+	5.58627i	0.682465	+	0.303853i
$339$	1.95539	−	0.870598i	0.106202	−	0.0472844i
$340$		0			0
$341$	−0.0486736	−	0.0216709i	−0.00263582	−	0.00117354i
$342$	−1.00891	+	3.10510i	−0.0545554	+	0.167904i
$343$	10.3286	−	15.3727i	0.557693	−	0.830048i
$344$	−1.22683	+	3.77580i	−0.0661464	+	0.203578i
$345$		0			0
$346$	−7.65376	−	1.62686i	−0.411469	−	0.0874603i
$347$	4.83296	+	1.02728i	0.259447	+	0.0551471i	0.335799	−	0.941934i	$-0.390994\pi$
$347$	4.83296	+	1.02728i	0.259447	+	0.0551471i	−0.0763517	+	0.997081i	$0.524327\pi$
$348$	0.0293194	−	0.278956i	0.00157169	−	0.0149536i
$349$	−16.4954			−0.882977			−0.441488	−	0.897267i	$-0.645549\pi$
$349$	−16.4954			−0.882977			−0.441488	+	0.897267i	$0.645549\pi$
$350$		0			0
$351$	−8.18419			−0.436840
$352$	0.0135989	−	0.129385i	0.000724822	−	0.00689622i
$353$	−30.9736	−	6.58363i	−1.64856	−	0.350411i	−0.712340	−	0.701835i	$-0.752364\pi$
$353$	−30.9736	−	6.58363i	−1.64856	−	0.350411i	−0.936217	+	0.351423i	$0.885698\pi$
$354$	−1.25789	−	0.267372i	−0.0668560	−	0.0142107i
$355$		0			0
$356$	0.682279	−	2.09984i	0.0361607	−	0.111291i
$357$	−2.90246	−	2.54976i	−0.153614	−	0.134948i
$358$	−5.51937	+	16.9869i	−0.291708	+	0.897785i
$359$	24.7508	+	11.0198i	1.30630	+	0.581602i	0.937525	−	0.347918i	$-0.113111\pi$
$359$	24.7508	+	11.0198i	1.30630	+	0.581602i	0.368773	+	0.929519i	$0.379778\pi$
$360$		0			0
$361$	−16.7350	+	7.45091i	−0.880791	+	0.392153i
$362$	23.5235	+	10.4733i	1.23637	+	0.550466i
$363$	2.55457	−	1.85600i	0.134080	−	0.0974150i
$364$	−1.50957	+	1.39305i	−0.0791228	+	0.0730156i
$365$		0			0
$366$	−0.611860	−	0.272418i	−0.0319824	−	0.0142395i
$367$	−14.0175	−	15.5681i	−0.731710	−	0.812646i	0.256371	−	0.966578i	$-0.417473\pi$
$367$	−14.0175	−	15.5681i	−0.731710	−	0.812646i	−0.988081	+	0.153932i	$0.950806\pi$
$368$	13.0284	−	22.5659i	0.679153	−	1.17633i
$369$	−9.78248	+	2.07933i	−0.509256	+	0.108246i
$370$		0			0
$371$	5.94969	−	0.699056i	0.308893	−	0.0362932i
$372$	−0.00535213	−	0.0164721i	−0.000277495	−	0.000854041i
$373$	−0.146187	+	1.39088i	−0.00756927	+	0.0720168i	−0.997654	−	0.0684515i	$-0.978194\pi$
$373$	−0.146187	+	1.39088i	−0.00756927	+	0.0720168i	0.990085	+	0.140468i	$0.0448608\pi$
$374$	0.491634	−	0.851535i	0.0254218	−	0.0440318i
$375$		0			0
$376$	−10.2323	−	17.7228i	−0.527690	−	0.913986i
$377$	−23.5065	−	17.0784i	−1.21064	−	0.879585i
$378$	−2.41468	+	5.60716i	−0.124198	+	0.288401i
$379$	−4.54620	−	13.9918i	−0.233522	−	0.718708i	−0.997314	−	0.0732451i	$-0.976664\pi$
$379$	−4.54620	−	13.9918i	−0.233522	−	0.718708i	0.763792	−	0.645463i	$-0.223336\pi$
$380$		0			0
$381$	2.79365	+	3.10267i	0.143123	+	0.158954i
$382$	−9.99293	+	17.3083i	−0.511283	+	0.885568i
$383$	−23.7268	+	5.04328i	−1.21238	+	0.257700i	−0.769363	−	0.638812i	$-0.779426\pi$
$383$	−23.7268	+	5.04328i	−1.21238	+	0.257700i	−0.443019	+	0.896512i	$0.646093\pi$
$384$	−2.26946	+	1.64886i	−0.115813	+	0.0841430i
$385$		0			0
$386$	4.34873	+	3.15954i	0.221345	+	0.160816i
$387$	−3.61020	−	1.60736i	−0.183517	−	0.0817069i
$388$	−0.0741227	−	0.705230i	−0.00376301	−	0.0358026i
$389$	−23.3117	+	10.3790i	−1.18195	+	0.526238i	−0.901141	−	0.433526i	$-0.857269\pi$
$389$	−23.3117	+	10.3790i	−1.18195	+	0.526238i	−0.280809	+	0.959764i	$0.590603\pi$
$390$		0			0
$391$	−29.3158	+	21.2992i	−1.48256	+	1.07715i
$392$	6.81523	+	19.3503i	0.344221	+	0.977337i
$393$	−4.34598			−0.219226
$394$	−26.4630	+	5.62489i	−1.33319	+	0.283378i
$395$		0			0
$396$	0.0657915	+	0.0139844i	0.00330615	+	0.000702744i
$397$	−3.37001	+	3.74278i	−0.169136	+	0.187844i	−0.821754	−	0.569843i	$-0.807004\pi$
$397$	−3.37001	+	3.74278i	−0.169136	+	0.187844i	0.652618	+	0.757687i	$0.273671\pi$
$398$	5.20982	+	3.78515i	0.261145	+	0.189733i
$399$	0.594861	−	0.201363i	0.0297803	−	0.0100808i
$400$		0			0
$401$	−14.8506	−	25.7220i	−0.741605	−	1.28450i	−0.951764	−	0.306830i	$-0.900732\pi$
$401$	−14.8506	−	25.7220i	−0.741605	−	1.28450i	0.210159	−	0.977667i	$-0.432602\pi$
$402$	−4.00169	+	1.78167i	−0.199586	+	0.0888614i
$403$	−1.75492	−	0.373020i	−0.0874188	−	0.0185814i
$404$	0.812630	−	0.902517i	0.0404299	−	0.0449019i
$405$		0			0
$406$	−18.6362	+	11.0659i	−0.924900	+	0.549192i
$407$	−1.29352			−0.0641173
$408$	4.18603	−	0.889768i	0.207239	−	0.0440501i
$409$	−2.23540	−	21.2684i	−0.110533	−	1.05165i	−0.899411	−	0.437103i	$-0.856004\pi$
$409$	−2.23540	−	21.2684i	−0.110533	−	1.05165i	0.788878	−	0.614550i	$-0.210662\pi$
$410$		0			0
$411$	−0.482143	+	4.58728i	−0.0237823	+	0.226274i
$412$	2.41129	−	1.75191i	0.118796	−	0.0863103i
$413$	−3.64612	−	7.92680i	−0.179414	−	0.390052i
$414$	22.8391	+	16.5936i	1.12248	+	0.815529i
$415$		0			0
$416$	−0.457923	−	4.35684i	−0.0224515	−	0.213612i
$417$	−0.630642	−	0.700399i	−0.0308827	−	0.0342987i
$418$	0.0799187	+	0.138423i	0.00390895	+	0.00677050i
$419$	−7.11650	+	21.9023i	−0.347664	+	1.07000i	0.612479	+	0.790487i	$0.290173\pi$
$419$	−7.11650	+	21.9023i	−0.347664	+	1.07000i	−0.960142	+	0.279512i	$0.909827\pi$
$420$		0			0
$421$	5.15258	+	15.8580i	0.251121	+	0.772872i	0.994569	+	0.104078i	$0.0331892\pi$
$421$	5.15258	+	15.8580i	0.251121	+	0.772872i	−0.743448	+	0.668794i	$0.766811\pi$
$422$	1.80635	−	2.00616i	0.0879319	−	0.0976583i
$423$	18.6093	−	8.28542i	0.904817	−	0.402851i
$424$	−3.31798	+	5.74692i	−0.161136	+	0.279095i
$425$		0			0
$426$	1.82739			0.0885376
$427$	−0.999120	−	4.43301i	−0.0483508	−	0.214528i
$428$	0.154878	+	0.476665i	0.00748630	+	0.0230405i
$429$	−0.132176	+	0.146796i	−0.00638152	+	0.00708740i
$430$		0			0
$431$	−4.71885	−	5.24082i	−0.227299	−	0.252441i	0.618698	−	0.785629i	$-0.287661\pi$
$431$	−4.71885	−	5.24082i	−0.227299	−	0.252441i	−0.845997	+	0.533188i	$0.820994\pi$
$432$	−3.10661	−	5.38081i	−0.149467	−	0.258884i
$433$	0.324227	−	0.997867i	0.0155813	−	0.0479544i	−0.942964	−	0.332896i	$-0.891974\pi$
$433$	0.324227	−	0.997867i	0.0155813	−	0.0479544i	0.958545	+	0.284942i	$0.0919742\pi$
$434$	−0.773340	+	1.09228i	−0.0371215	+	0.0524309i
$435$		0			0
$436$	−0.0628536	+	0.598012i	−0.00301014	+	0.0286396i
$437$	−0.615723	−	5.85821i	−0.0294540	−	0.280236i
$438$	0.413045	+	3.92986i	0.0197360	+	0.187776i
$439$	−0.830281	+	7.89959i	−0.0396271	+	0.377027i	0.956678	+	0.291147i	$0.0940368\pi$
$439$	−0.830281	+	7.89959i	−0.0396271	+	0.377027i	−0.996305	+	0.0858800i	$0.972630\pi$
$440$		0			0
$441$	−19.8649	+	4.73337i	−0.945948	+	0.225399i
$442$	10.2316	−	31.4896i	0.486668	−	1.49781i
$443$	−10.2938	−	17.8294i	−0.489073	−	0.847099i	0.510848	−	0.859671i	$-0.329331\pi$
$443$	−10.2938	−	17.8294i	−0.489073	−	0.847099i	−0.999921	+	0.0125723i	$0.995998\pi$
$444$	−0.281361	−	0.312483i	−0.0133528	−	0.0148298i
$445$		0			0
$446$	14.7778	−	16.4124i	0.699748	−	0.777149i
$447$	−0.959372	−	2.95264i	−0.0453768	−	0.139655i
$448$	−21.5658	−	6.71651i	−1.01889	−	0.317325i
$449$	−14.6499			−0.691371			−0.345685	−	0.938350i	$-0.612354\pi$
$449$	−14.6499			−0.691371			−0.345685	+	0.938350i	$0.612354\pi$
$450$		0			0
$451$	−0.244807	+	0.424019i	−0.0115275	+	0.0199663i
$452$	−1.09763	+	0.488698i	−0.0516283	+	0.0229864i
$453$	−3.34853	+	3.71892i	−0.157328	+	0.174730i
$454$	−0.461539	−	1.42047i	−0.0216611	−	0.0666660i
$455$		0			0
$456$	−0.214975	+	0.661624i	−0.0100671	+	0.0309834i
$457$	17.2850	+	29.9385i	0.808557	+	1.40046i	0.913863	+	0.406023i	$0.133085\pi$
$457$	17.2850	+	29.9385i	0.808557	+	1.40046i	−0.105306	+	0.994440i	$0.533582\pi$
$458$	−5.59749	−	6.21664i	−0.261554	−	0.290485i
$459$	0.903179	+	8.59318i	0.0421568	+	0.401095i
$460$		0			0
$461$	−12.8239	−	9.31709i	−0.597267	−	0.433940i	0.247641	−	0.968852i	$-0.420345\pi$
$461$	−12.8239	−	9.31709i	−0.597267	−	0.433940i	−0.844908	+	0.534912i	$0.820345\pi$
$462$	0.0615758	+	0.133868i	0.00286476	+	0.00622810i
$463$	10.5429	−	7.65984i	0.489969	−	0.355983i	−0.315204	−	0.949024i	$-0.602073\pi$
$463$	10.5429	−	7.65984i	0.489969	−	0.355983i	0.805172	+	0.593041i	$0.202073\pi$
$464$	2.30571	−	21.9374i	0.107040	−	1.01842i
$465$		0			0
$466$	−1.46853	−	13.9721i	−0.0680283	−	0.647246i
$467$	29.8787	−	6.35092i	1.38262	−	0.293885i	0.544222	−	0.838941i	$-0.316825\pi$
$467$	29.8787	−	6.35092i	1.38262	−	0.293885i	0.838400	+	0.545056i	$0.183492\pi$
$468$	2.26493			0.104696
$469$	−25.9182	−	14.5439i	−1.19679	−	0.671575i
$470$		0			0
$471$	1.60037	−	1.77739i	0.0737411	−	0.0818978i
$472$	9.45389	+	2.00949i	0.435150	+	0.0924941i
$473$	−0.176742	+	0.0786908i	−0.00812663	+	0.00361821i
$474$	2.22876	+	3.86032i	0.102370	+	0.177310i
$475$		0			0
$476$	1.62925	+	1.43127i	0.0746767	+	0.0656023i
$477$	−5.34392	−	3.88259i	−0.244681	−	0.177772i
$478$	−6.51419	+	7.23474i	−0.297952	+	0.330909i
$479$	6.64926	+	1.41334i	0.303812	+	0.0645773i	0.357295	−	0.933991i	$-0.383699\pi$
$479$	6.64926	+	1.41334i	0.303812	+	0.0645773i	−0.0534830	+	0.998569i	$0.517032\pi$
$480$		0			0
$481$	−42.6056	+	9.05609i	−1.94265	+	0.412922i
$482$	27.3623			1.24632
$483$	−0.0664566	−	5.42990i	−0.00302388	−	0.247069i
$484$	−1.43397	+	1.04184i	−0.0651805	+	0.0473564i
$485$		0			0
$486$	9.26737	−	4.12610i	0.420376	−	0.187164i
$487$	−2.87545	−	27.3581i	−0.130299	−	1.23971i	−0.842872	−	0.538114i	$-0.819137\pi$
$487$	−2.87545	−	27.3581i	−0.130299	−	1.23971i	0.712573	−	0.701598i	$-0.247530\pi$
$488$	4.59855	+	2.04740i	0.208166	+	0.0926817i
$489$	−3.18860	−	2.31665i	−0.144193	−	0.104763i
$490$		0			0
$491$	3.14168	−	2.28256i	0.141782	−	0.103011i	−0.514633	−	0.857410i	$-0.672072\pi$
$491$	3.14168	−	2.28256i	0.141782	−	0.103011i	0.656415	+	0.754400i	$0.272072\pi$
$492$	−0.155682	+	0.0330913i	−0.00701870	+	0.00149187i
$493$	−15.3378	+	26.5659i	−0.690780	+	1.19647i
$494$	3.60146	+	3.99983i	0.162037	+	0.179961i
$495$		0			0
$496$	−0.420898	−	1.29539i	−0.0188989	−	0.0581647i
$497$	7.40985	+	9.94064i	0.332377	+	0.445898i
$498$	−4.92025	−	3.57477i	−0.220482	−	0.160189i
$499$	−9.17007	−	15.8830i	−0.410509	−	0.711022i	0.584437	−	0.811439i	$-0.301316\pi$
$499$	−9.17007	−	15.8830i	−0.410509	−	0.711022i	−0.994945	+	0.100417i	$0.967982\pi$
$500$		0			0
$501$	2.48129	−	4.29771i	0.110856	−	0.192008i
$502$	−3.78096	+	35.9734i	−0.168752	+	1.60557i
$503$	10.5853	+	32.5781i	0.471974	+	1.45259i	0.849995	+	0.526790i	$0.176605\pi$
$503$	10.5853	+	32.5781i	0.471974	+	1.45259i	−0.378021	+	0.925797i	$0.623395\pi$
$504$	8.94717	−	20.7763i	0.398539	−	0.925450i
$505$		0			0
$506$	1.35187	−	0.287349i	0.0600979	−	0.0127742i
$507$	−1.45651	+	2.52274i	−0.0646857	+	0.112039i
$508$	−1.56818	−	1.74164i	−0.0695766	−	0.0772727i
$509$	13.0256	+	5.79939i	0.577352	+	0.257054i	0.674572	−	0.738209i	$-0.264328\pi$
$509$	13.0256	+	5.79939i	0.577352	+	0.257054i	−0.0972200	+	0.995263i	$0.530995\pi$
$510$		0			0
$511$	−19.7027	+	18.1819i	−0.871598	+	0.804321i
$512$	20.0043	−	14.5340i	0.884075	−	0.642318i
$513$	−1.28315	−	0.571294i	−0.0566523	−	0.0252232i
$514$	2.19674	−	0.978050i	0.0968939	−	0.0431399i
$515$		0			0
$516$	−0.0574541	−	0.0255802i	−0.00252928	−	0.00112611i
$517$	0.308172	−	0.948455i	0.0135534	−	0.0417130i
$518$	−6.36594	+	31.8619i	−0.279703	+	1.39993i
$519$	0.512846	−	1.57838i	0.0225114	−	0.0692831i
$520$		0			0
$521$	38.7121	+	8.22852i	1.69601	+	0.360498i	0.951627	−	0.307256i	$-0.0994108\pi$
$521$	38.7121	+	8.22852i	1.69601	+	0.360498i	0.744382	+	0.667754i	$0.232744\pi$
$522$	23.3762	+	4.96877i	1.02315	+	0.217477i
$523$	0.359554	−	3.42093i	0.0157222	−	0.149587i	−0.983844	−	0.179026i	$-0.942705\pi$
$523$	0.359554	−	3.42093i	0.0157222	−	0.149587i	0.999567	+	0.0294391i	$0.00937212\pi$
$524$	2.43956			0.106572
$525$		0			0
$526$	0.0924388			0.00403053
$527$	−0.197994	+	1.88378i	−0.00862474	+	0.0820589i
$528$	−0.146686	−	0.0311790i	−0.00638368	−	0.00135689i
$529$	−27.3230	−	5.80768i	−1.18796	−	0.252508i
$530$		0			0
$531$	−2.97294	+	9.14978i	−0.129015	+	0.397067i
$532$	−0.333916	+	0.113032i	−0.0144771	+	0.00490057i
$533$	−5.09479	+	15.6801i	−0.220680	+	0.679182i
$534$	−4.87222	−	2.16925i	−0.210842	−	0.0938727i
$535$		0			0
$536$	30.0754	−	13.3904i	1.29906	−	0.578379i
$537$	−3.46076	−	1.54083i	−0.149343	−	0.0664918i
$538$	5.99938	−	4.35880i	0.258652	−	0.187921i
$539$	−0.478531	+	0.877776i	−0.0206118	+	0.0378085i
$540$		0			0
$541$	37.5468	+	16.7169i	1.61426	+	0.718717i	0.997648	−	0.0685469i	$-0.0218363\pi$
$541$	37.5468	+	16.7169i	1.61426	+	0.718717i	0.616616	+	0.787264i	$0.288503\pi$
$542$	2.87992	+	3.19847i	0.123703	+	0.137386i
$543$	−2.73071	+	4.72973i	−0.117186	+	0.202972i
$544$	−4.52403	+	0.961613i	−0.193966	+	0.0412288i
$545$		0			0
$546$	2.96539	+	3.97821i	0.126907	+	0.170251i
$547$	−2.63436	−	8.10774i	−0.112637	−	0.346662i	0.878810	−	0.477172i	$-0.158338\pi$
$547$	−2.63436	−	8.10774i	−0.112637	−	0.346662i	−0.991447	+	0.130511i	$0.958338\pi$
$548$	0.270644	−	2.57500i	0.0115613	−	0.109999i
$549$	−2.50529	+	4.33930i	−0.106923	+	0.185197i
$550$		0			0
$551$	−2.49327	−	4.31848i	−0.106217	−	0.183973i
$552$	4.86647	+	3.53570i	0.207131	+	0.150489i
$553$	−11.9620	+	27.7771i	−0.508676	+	1.18120i
$554$	4.11153	+	12.6540i	0.174682	+	0.537616i
$555$		0			0
$556$	0.354002	+	0.393159i	0.0150130	+	0.0166737i
$557$	−17.3425	+	30.0382i	−0.734827	+	1.27276i	0.219972	+	0.975506i	$0.429403\pi$
$557$	−17.3425	+	30.0382i	−0.734827	+	1.27276i	−0.954799	+	0.297252i	$0.903930\pi$
$558$	1.44344	−	0.306812i	0.0611056	−	0.0129884i
$559$	−5.27057	+	3.82929i	−0.222921	+	0.161962i
$560$		0			0
$561$	0.168719	+	0.122581i	0.00712331	+	0.00517539i
$562$	−26.7948	−	11.9298i	−1.13027	−	0.503230i
$563$	−0.0682528	−	0.649382i	−0.00287651	−	0.0273682i	0.992989	−	0.118203i	$-0.0377132\pi$
$563$	−0.0682528	−	0.649382i	−0.00287651	−	0.0273682i	−0.995866	+	0.0908345i	$0.971047\pi$
$564$	0.296156	−	0.131857i	0.0124704	−	0.00555220i
$565$		0			0
$566$	−23.4352	+	17.0267i	−0.985055	+	0.715684i
$567$	19.0640	+	10.6977i	0.800615	+	0.449262i
$568$	−13.7341			−0.576271
$569$	3.24739	−	0.690255i	0.136138	−	0.0289370i	−0.139339	−	0.990245i	$-0.544498\pi$
$569$	3.24739	−	0.690255i	0.136138	−	0.0289370i	0.275477	+	0.961308i	$0.411164\pi$
$570$		0			0
$571$	−27.3242	−	5.80794i	−1.14348	−	0.243055i	−0.403045	−	0.915180i	$-0.632048\pi$
$571$	−27.3242	−	5.80794i	−1.14348	−	0.243055i	−0.740437	+	0.672126i	$0.765381\pi$
$572$	0.0741952	−	0.0824021i	0.00310226	−	0.00344540i
$573$	−3.42937	−	2.49158i	−0.143264	−	0.104087i
$574$	9.23962	+	8.11686i	0.385654	+	0.338791i
$575$		0			0
$576$	12.4529	+	21.5690i	0.518870	+	0.898709i
$577$	10.8694	−	4.83939i	0.452501	−	0.201466i	−0.167815	−	0.985818i	$-0.553671\pi$
$577$	10.8694	−	4.83939i	0.452501	−	0.201466i	0.620316	+	0.784352i	$0.287004\pi$
$578$	−11.6452	−	2.47526i	−0.484375	−	0.102957i
$579$	−0.762869	+	0.847252i	−0.0317038	+	0.0352106i
$580$		0			0
$581$	−0.504987	−	41.2604i	−0.0209504	−	1.71177i
$582$	−1.71291			−0.0710022
$583$	−0.316313	+	0.0672343i	−0.0131003	+	0.00278456i
$584$	−3.10431	−	29.5356i	−0.128457	−	1.22219i
$585$		0			0
$586$	−0.543230	+	5.16849i	−0.0224406	+	0.213508i
$587$	−3.59382	+	2.61107i	−0.148333	+	0.107770i	−0.659477	−	0.751725i	$-0.729222\pi$
$587$	−3.59382	+	2.61107i	−0.148333	+	0.107770i	0.511144	+	0.859495i	$0.329222\pi$
$588$	−0.316138	+	0.0753287i	−0.0130373	+	0.00310651i
$589$	−0.249104	−	0.180985i	−0.0102642	−	0.00745735i
$590$		0			0
$591$	−0.599796	−	5.70668i	−0.0246723	−	0.234741i
$592$	−22.1266	−	24.5740i	−0.909396	−	1.00999i
$593$	−0.996551	−	1.72608i	−0.0409234	−	0.0708815i	0.844838	−	0.535022i	$-0.179697\pi$
$593$	−0.996551	−	1.72608i	−0.0409234	−	0.0708815i	−0.885762	+	0.464140i	$0.846363\pi$
$594$	0.101838	−	0.313424i	0.00417845	−	0.0128599i
$595$		0			0
$596$	0.538530	+	1.65742i	0.0220590	+	0.0678907i
$597$	−0.913924	+	1.01502i	−0.0374044	+	0.0415418i
$598$	42.5158	−	18.9292i	1.73860	−	0.774074i
$599$	4.67970	−	8.10548i	0.191207	−	0.331181i	−0.754443	−	0.656365i	$-0.772093\pi$
$599$	4.67970	−	8.10548i	0.191207	−	0.331181i	0.945651	+	0.325184i	$0.105426\pi$
$600$		0			0
$601$	5.74535			0.234358			0.117179	−	0.993111i	$-0.462615\pi$
$601$	5.74535			0.234358			0.117179	+	0.993111i	$0.462615\pi$
$602$	1.06849	+	4.74079i	0.0435483	+	0.193220i
$603$	10.1266	+	31.1664i	0.412386	+	1.26919i
$604$	1.87965	−	2.08756i	0.0764819	−	0.0849418i
$605$		0			0
$606$	−1.96295	−	2.18008i	−0.0797395	−	0.0885597i
$607$	−5.24441	−	9.08358i	−0.212864	−	0.368691i	0.739746	−	0.672886i	$-0.234946\pi$
$607$	−5.24441	−	9.08358i	−0.212864	−	0.368691i	−0.952610	+	0.304195i	$0.901612\pi$
$608$	0.232333	−	0.715047i	0.00942234	−	0.0289990i
$609$	−1.92102	−	4.17636i	−0.0778436	−	0.169235i
$610$		0			0
$611$	3.51022	−	33.3975i	0.142008	−	1.35112i
$612$	−0.249950	−	2.37812i	−0.0101036	−	0.0961297i
$613$	−1.37033	−	13.0378i	−0.0553470	−	0.526592i	−0.986709	−	0.162497i	$-0.948045\pi$
$613$	−1.37033	−	13.0378i	−0.0553470	−	0.526592i	0.931362	−	0.364095i	$-0.118621\pi$
$614$	−2.75066	+	26.1708i	−0.111008	+	1.05617i
$615$		0			0
$616$	−0.462784	−	1.00611i	−0.0186461	−	0.0405373i
$617$	−13.5049	+	41.5637i	−0.543685	+	1.67329i	0.180410	+	0.983591i	$0.442257\pi$
$617$	−13.5049	+	41.5637i	−0.543685	+	1.67329i	−0.724095	+	0.689700i	$0.757743\pi$
$618$	−3.59981	−	6.23505i	−0.144806	−	0.250811i
$619$	24.8400	+	27.5877i	0.998405	+	1.10884i	0.994058	+	0.108851i	$0.0347171\pi$
$619$	24.8400	+	27.5877i	0.998405	+	1.10884i	0.00434711	+	0.999991i	$0.498616\pi$
$620$		0			0
$621$	−8.12660	+	9.02550i	−0.326109	+	0.362181i
$622$	1.14153	+	3.51326i	0.0457711	+	0.140869i
$623$	−7.95595	−	35.2999i	−0.318748	−	1.41426i
$624$	−5.04978			−0.202153
$625$		0			0
$626$	−17.3163	+	29.9926i	−0.692097	+	1.19875i
$627$	−0.0309701	+	0.0137888i	−0.00123683	+	0.000550671i
$628$	−0.898344	+	0.997712i	−0.0358478	+	0.0398131i
$629$	14.2105	+	43.7353i	0.566608	+	1.74384i
$630$		0			0
$631$	−0.484202	+	1.49022i	−0.0192758	+	0.0593247i	−0.960232	−	0.279204i	$-0.909929\pi$
$631$	−0.484202	+	1.49022i	−0.0192758	+	0.0593247i	0.940956	+	0.338529i	$0.109929\pi$
$632$	−16.7506	−	29.0130i	−0.666304	−	1.15407i
$633$	0.383122	+	0.425500i	0.0152277	+	0.0169121i
$634$	1.47028	+	13.9888i	0.0583923	+	0.555565i
$635$		0			0
$636$	−0.0850453	−	0.0617890i	−0.00337227	−	0.00245009i
$637$	−9.61630	+	32.2622i	−0.381012	+	1.27828i
$638$	0.946537	−	0.687699i	0.0374737	−	0.0272263i
$639$	1.42900	−	13.5961i	0.0565305	−	0.537852i
$640$		0			0
$641$	−3.49220	−	33.2260i	−0.137933	−	1.31235i	−0.816301	−	0.577627i	$-0.803979\pi$
$641$	−3.49220	−	33.2260i	−0.137933	−	1.31235i	0.678368	−	0.734723i	$-0.262688\pi$
$642$	1.18421	−	0.251711i	0.0467370	−	0.00993425i
$643$	−1.80161			−0.0710485			−0.0355242	−	0.999369i	$-0.511310\pi$
$643$	−1.80161			−0.0710485			−0.0355242	+	0.999369i	$0.511310\pi$
$644$	0.0373045	+	3.04799i	0.00147000	+	0.120108i
$645$		0			0
$646$	3.80227	−	4.22284i	0.149598	−	0.166146i
$647$	−0.421377	−	0.0895664i	−0.0165660	−	0.00352122i	0.199621	−	0.979873i	$-0.436029\pi$
$647$	−0.421377	−	0.0895664i	−0.0165660	−	0.00352122i	−0.216187	+	0.976352i	$0.569362\pi$
$648$	−22.1219	+	9.84929i	−0.869029	+	0.386917i
$649$	0.235496	+	0.407891i	0.00924403	+	0.0160111i
$650$		0			0
$651$	−0.213254	−	0.187340i	−0.00835809	−	0.00734245i
$652$	1.78987	+	1.30042i	0.0700969	+	0.0509284i
$653$	25.1961	−	27.9831i	0.985999	−	1.09506i	−0.00946787	−	0.999955i	$-0.503014\pi$
$653$	25.1961	−	27.9831i	0.985999	−	1.09506i	0.995467	−	0.0951078i	$-0.0303196\pi$
$654$	1.42075	+	0.301989i	0.0555556	+	0.0118087i
$655$		0			0
$656$	−12.2430	+	2.60234i	−0.478010	+	0.101604i
$657$	29.5617			1.15331
$658$	−21.8457	−	12.2586i	−0.851634	−	0.477891i
$659$	−11.2546	+	8.17693i	−0.438416	+	0.318528i	−0.785005	−	0.619489i	$-0.787340\pi$
$659$	−11.2546	+	8.17693i	−0.438416	+	0.318528i	0.346589	+	0.938017i	$0.387340\pi$
$660$		0			0
$661$	−38.4504	+	17.1192i	−1.49555	+	0.665860i	−0.981423	−	0.191857i	$-0.938549\pi$
$661$	−38.4504	+	17.1192i	−1.49555	+	0.665860i	−0.514123	+	0.857717i	$0.671882\pi$
$662$	1.85752	+	17.6731i	0.0721945	+	0.686885i
$663$	6.41542	+	2.85633i	0.249154	+	0.110931i
$664$	36.9791	+	26.8669i	1.43507	+	1.04264i
$665$		0			0
$666$	28.9841	−	21.0582i	1.12311	−	0.815988i
$667$	−42.1751	+	8.96460i	−1.63303	+	0.347111i
$668$	−1.39283	+	2.41246i	−0.0538903	+	0.0933408i
$669$	3.13432	+	3.48102i	0.121180	+	0.134584i
$670$		0			0
$671$	0.0758020	+	0.233295i	0.00292630	+	0.00900624i
$672$	0.274143	−	0.636589i	0.0105753	−	0.0245570i
$673$	36.1323	+	26.2517i	1.39280	+	1.01193i	0.995552	+	0.0942163i	$0.0300345\pi$
$673$	36.1323	+	26.2517i	1.39280	+	1.01193i	0.397247	+	0.917712i	$0.369965\pi$
$674$	−6.99124	−	12.1092i	−0.269292	−	0.466428i
$675$		0			0
$676$	0.817589	−	1.41611i	0.0314457	−	0.0544656i
$677$	−0.673286	+	6.40589i	−0.0258765	+	0.246198i	0.973936	+	0.226824i	$0.0728341\pi$
$677$	−0.673286	+	6.40589i	−0.0258765	+	0.246198i	−0.999812	+	0.0193745i	$0.993833\pi$
$678$	0.896863	+	2.76026i	0.0344438	+	0.106007i
$679$	−6.94561	−	9.31784i	−0.266548	−	0.357586i
$680$		0			0
$681$	0.309859	−	0.0658626i	0.0118738	−	0.00252386i
$682$	0.0361221	−	0.0625653i	0.00138319	−	0.00239575i
$683$	25.1007	+	27.8772i	0.960453	+	1.06669i	0.997727	+	0.0673864i	$0.0214660\pi$
$683$	25.1007	+	27.8772i	0.960453	+	1.06669i	−0.0372736	+	0.999305i	$0.511867\pi$
$684$	0.355104	+	0.158102i	0.0135777	+	0.00604520i
$685$		0			0
$686$	19.2663	+	16.1071i	0.735591	+	0.614970i
$687$	1.43540	−	1.04288i	0.0547641	−	0.0397884i
$688$	−4.51826	−	2.01166i	−0.172257	−	0.0766938i
$689$	−9.94791	+	4.42909i	−0.378985	+	0.168735i
$690$		0			0
$691$	16.4183	+	7.30988i	0.624580	+	0.278081i	0.694524	−	0.719470i	$-0.255615\pi$
$691$	16.4183	+	7.30988i	0.624580	+	0.278081i	−0.0699433	+	0.997551i	$0.522282\pi$
$692$	−0.287879	+	0.885999i	−0.0109435	+	0.0336806i
$693$	1.04415	−	0.353449i	0.0396639	−	0.0134264i
$694$	−2.07029	+	6.37169i	−0.0785870	+	0.241866i
$695$		0			0
$696$	4.98093	+	1.05873i	0.188802	+	0.0401310i
$697$	17.0260	+	3.61898i	0.644904	+	0.137079i
$698$	2.33795	−	22.2442i	0.0884929	−	0.841954i
$699$	2.97977			0.112705
$700$		0			0
$701$	−14.1055			−0.532756			−0.266378	−	0.963869i	$-0.585827\pi$
$701$	−14.1055			−0.532756			−0.266378	+	0.963869i	$0.585827\pi$
$702$	1.15998	−	11.0365i	0.0437805	−	0.416544i
$703$	−7.31201	−	1.55422i	−0.275778	−	0.0586183i
$704$	1.19265	+	0.253506i	0.0449498	+	0.00955437i
$705$		0			0
$706$	13.2681	−	40.8350i	0.499351	−	1.53685i
$707$	3.89965	−	19.5180i	0.146661	−	0.734050i
$708$	−0.0473126	+	0.145613i	−0.00177812	+	0.00547248i
$709$	41.2318	+	18.3576i	1.54849	+	0.689433i	0.990128	−	0.140163i	$-0.0447626\pi$
$709$	41.2318	+	18.3576i	1.54849	+	0.689433i	0.558364	+	0.829596i	$0.311429\pi$
$710$		0			0
$711$	30.4642	−	13.5635i	1.14250	−	0.508672i
$712$	36.6180	+	16.3034i	1.37232	+	0.610996i
$713$	−2.15394	+	1.56493i	−0.0806656	+	0.0586070i
$714$	3.84976	−	3.55260i	0.144074	−	0.132953i
$715$		0			0
$716$	1.94265	+	0.864923i	0.0726002	+	0.0323237i
$717$	−1.38164	−	1.53447i	−0.0515982	−	0.0573057i
$718$	−18.3683	+	31.8148i	−0.685499	+	1.18732i
$719$	−0.0315305	+	0.00670202i	−0.00117589	+	0.000249943i	−0.208500	−	0.978022i	$-0.566858\pi$
$719$	−0.0315305	+	0.00670202i	−0.00117589	+	0.000249943i	0.207324	+	0.978272i	$0.433525\pi$
$720$		0			0
$721$	19.3206	−	44.8645i	0.719536	−	1.67084i
$722$	−7.67570	−	23.6234i	−0.285660	−	0.879171i
$723$	−0.606627	+	5.77168i	−0.0225607	+	0.214651i
$724$	1.53284	−	2.65496i	0.0569677	−	0.0986709i
$725$		0			0
$726$	2.14077	+	3.70792i	0.0794514	+	0.137614i
$727$	−28.8050	−	20.9280i	−1.06832	−	0.776178i	−0.0927080	−	0.995693i	$-0.529552\pi$
$727$	−28.8050	−	20.9280i	−1.06832	−	0.776178i	−0.975609	+	0.219516i	$0.929552\pi$
$728$	−22.2870	−	29.8989i	−0.826009	−	1.10813i
$729$	−6.99485	−	21.5279i	−0.259069	−	0.797331i
$730$		0			0
$731$	4.60230	+	5.11137i	0.170222	+	0.189051i
$732$	−0.0398702	+	0.0690573i	−0.00147365	+	0.00255243i
$733$	28.3922	−	6.03495i	1.04869	−	0.222906i	0.348830	−	0.937186i	$-0.386579\pi$
$733$	28.3922	−	6.03495i	1.04869	−	0.222906i	0.699860	+	0.714280i	$0.253246\pi$
$734$	22.9804	−	16.6963i	0.848224	−	0.616270i
$735$		0			0
$736$	−5.25942	−	3.82119i	−0.193865	−	0.140851i
$737$	1.46561	+	0.652533i	0.0539866	+	0.0240364i
$738$	−1.41749	−	13.4865i	−0.0521784	−	0.496444i
$739$	33.6345	−	14.9750i	1.23727	−	0.550866i	0.319348	−	0.947638i	$-0.396536\pi$
$739$	33.6345	−	14.9750i	1.23727	−	0.550866i	0.917917	+	0.396772i	$0.129870\pi$
$740$		0			0
$741$	−0.923548	+	0.670997i	−0.0339274	+	0.0246497i
$742$	0.0994090	+	8.12230i	0.00364942	+	0.298179i
$743$	15.3528			0.563240			0.281620	−	0.959526i	$-0.409128\pi$
$743$	15.3528			0.563240			0.281620	+	0.959526i	$0.409128\pi$
$744$	0.307563	−	0.0653745i	0.0112758	−	0.00239674i
$745$		0			0
$746$	−1.85489	−	0.394269i	−0.0679123	−	0.0144352i
$747$	−30.4444	+	33.8119i	−1.11390	+	1.23711i
$748$	−0.0947079	−	0.0688093i	−0.00346286	−	0.00251592i
$749$	6.17107	+	5.42118i	0.225486	+	0.198086i
$750$		0			0
$751$	22.6383	+	39.2107i	0.826083	+	1.43082i	0.901089	+	0.433634i	$0.142769\pi$
$751$	22.6383	+	39.2107i	0.826083	+	1.43082i	−0.0750064	+	0.997183i	$0.523898\pi$
$752$	23.2901	−	10.3694i	0.849303	−	0.378134i
$753$	−7.50423	−	1.59507i	−0.273469	−	0.0581277i
$754$	26.3621	−	29.2781i	0.960051	−	1.06624i
$755$		0			0
$756$	0.633867	+	0.355692i	0.0230535	+	0.0129364i
$757$	−28.8407			−1.04823			−0.524116	−	0.851647i	$-0.675604\pi$
$757$	−28.8407			−1.04823			−0.524116	+	0.851647i	$0.675604\pi$
$758$	19.5124	−	4.14748i	0.708721	−	0.150643i
$759$	0.0306407	+	0.291527i	0.00111219	+	0.0105818i
$760$		0			0
$761$	2.19935	−	20.9254i	0.0797264	−	0.758546i	−0.879499	−	0.475902i	$-0.842122\pi$
$761$	2.19935	−	20.9254i	0.0797264	−	0.758546i	0.959225	−	0.282644i	$-0.0912115\pi$
$762$	−4.57993	+	3.32751i	−0.165913	+	0.120543i
$763$	4.11819	+	8.95308i	0.149088	+	0.324123i
$764$	1.92503	+	1.39861i	0.0696451	+	0.0506001i
$765$		0			0
$766$	−3.43802	−	32.7106i	−0.124221	−	1.18188i
$767$	10.6124	+	11.7863i	0.383192	+	0.425578i
$768$	0.553396	+	0.958509i	0.0199689	+	0.0345872i
$769$	13.9262	−	42.8606i	0.502193	−	1.54559i	−0.303245	−	0.952913i	$-0.598070\pi$
$769$	13.9262	−	42.8606i	0.502193	−	1.54559i	0.805438	−	0.592680i	$-0.201930\pi$
$770$		0			0
$771$	0.157603	+	0.485052i	0.00567593	+	0.0174687i
$772$	0.428226	−	0.475593i	0.0154122	−	0.0171170i
$773$	−0.945366	+	0.420904i	−0.0340024	+	0.0151389i	−0.423667	−	0.905818i	$-0.639257\pi$
$773$	−0.945366	+	0.420904i	−0.0340024	+	0.0151389i	0.389665	+	0.920957i	$0.372591\pi$
$774$	2.67923	−	4.64057i	0.0963031	−	0.166802i
$775$		0			0
$776$	12.8737			0.462137
$777$	−6.57966	−	2.04918i	−0.236044	−	0.0735140i
$778$	−10.6922	−	32.9071i	−0.383333	−	1.17978i
$779$	−1.89332	+	2.10275i	−0.0678354	+	0.0753388i
$780$		0			0
$781$	−0.447837	−	0.497373i	−0.0160249	−	0.0177974i
$782$	−24.5671	−	42.5514i	−0.878517	−	1.52164i
$783$	−3.17709	+	9.77808i	−0.113540	+	0.349440i
$784$	−24.8615	+	5.92394i	−0.887909	+	0.211569i
$785$		0			0
$786$	0.615974	−	5.86060i	0.0219711	−	0.209041i
$787$	0.397738	+	3.78423i	0.0141778	+	0.134893i	0.999321	−	0.0368413i	$-0.0117296\pi$
$787$	0.397738	+	3.78423i	0.0141778	+	0.134893i	−0.985143	+	0.171734i	$0.945063\pi$
$788$	0.336687	+	3.20336i	0.0119940	+	0.114115i
$789$	−0.00204938	+	0.0194986i	−7.29600e−5	+	0.000694168i
$790$		0			0
$791$	−11.3786	+	16.0712i	−0.404575	+	0.571428i
$792$	−0.377340	+	1.16133i	−0.0134082	+	0.0412662i
$793$	4.13007	+	7.15350i	0.146663	+	0.254028i
$794$	−4.56952	−	5.07497i	−0.162166	−	0.180104i
$795$		0			0
$796$	0.513018	−	0.569764i	0.0181834	−	0.0201948i
$797$	−13.5272	−	41.6324i	−0.479157	−	1.47469i	−0.840268	−	0.542172i	$-0.817602\pi$
$797$	−13.5272	−	41.6324i	−0.479157	−	1.47469i	0.361111	−	0.932523i	$-0.382398\pi$
$798$	0.187228	+	0.830715i	0.00662781	+	0.0294070i
$799$	−35.4539			−1.25427
$800$		0			0
$801$	−19.9496	+	34.5536i	−0.704883	+	1.22089i
$802$	36.7912	−	16.3805i	1.29914	−	0.578416i
$803$	0.968388	−	1.07550i	0.0341737	−	0.0379537i
$804$	0.161158	+	0.495994i	0.00568361	+	0.0174923i
$805$		0			0
$806$	0.751752	−	2.31366i	0.0264793	−	0.0814951i
$807$	0.786417	+	1.36211i	0.0276832	+	0.0479487i
$808$	14.7529	+	16.3848i	0.519006	+	0.576415i
$809$	−1.28858	−	12.2601i	−0.0453042	−	0.431041i	−0.993541	−	0.113476i	$-0.963802\pi$
$809$	−1.28858	−	12.2601i	−0.0453042	−	0.431041i	0.948237	−	0.317565i	$-0.102865\pi$
$810$		0			0
$811$	42.0610	+	30.5591i	1.47696	+	1.07308i	0.978520	+	0.206154i	$0.0660947\pi$
$811$	42.0610	+	30.5591i	1.47696	+	1.07308i	0.498443	+	0.866922i	$0.333905\pi$
$812$	1.07834	+	2.34434i	0.0378422	+	0.0822702i
$813$	−0.738518	+	0.536565i	−0.0259010	+	0.0188181i
$814$	0.183336	−	1.74432i	0.00642591	−	0.0611384i
$815$		0			0
$816$	0.557277	+	5.30214i	0.0195086	+	0.185612i
$817$	−1.09364	+	0.232461i	−0.0382617	+	0.00813277i
$818$	28.9974			1.01387
$819$	31.9173	−	18.9520i	1.11528	−	0.662237i
$820$		0			0
$821$	−4.00582	+	4.44892i	−0.139804	+	0.155268i	−0.808981	−	0.587835i	$-0.799980\pi$
$821$	−4.00582	+	4.44892i	−0.139804	+	0.155268i	0.669177	+	0.743103i	$0.266647\pi$
$822$	−6.11766	−	1.30035i	−0.213378	−	0.0453548i
$823$	17.5363	−	7.80767i	0.611277	−	0.272158i	−0.0776590	−	0.996980i	$-0.524745\pi$
$823$	17.5363	−	7.80767i	0.611277	−	0.272158i	0.688936	+	0.724822i	$0.258078\pi$
$824$	27.0550	+	46.8607i	0.942506	+	1.63247i
$825$		0			0
$826$	11.2061	−	3.79333i	0.389912	−	0.131987i
$827$	5.34080	+	3.88032i	0.185718	+	0.134932i	0.676760	−	0.736204i	$-0.263384\pi$
$827$	5.34080	+	3.88032i	0.185718	+	0.134932i	−0.491042	+	0.871136i	$0.663384\pi$
$828$	2.24899	−	2.49776i	0.0781579	−	0.0868032i
$829$	−5.32594	−	1.13206i	−0.184978	−	0.0393182i	0.114491	−	0.993424i	$-0.463476\pi$
$829$	−5.32594	−	1.13206i	−0.184978	−	0.0393182i	−0.299469	+	0.954106i	$0.596810\pi$
$830$		0			0
$831$	−2.76032	+	0.586724i	−0.0957544	+	0.0203532i
$832$	41.0581			1.42343
$833$	34.9357	+	6.53651i	1.21045	+	0.226477i
$834$	1.03388	−	0.751157i	0.0358003	−	0.0260104i
$835$		0			0
$836$	0.0173846	−	0.00774013i	0.000601260	−	0.000267698i
$837$	0.0663598	+	0.631372i	0.00229373	+	0.0218234i
$838$	−28.5268	−	12.7010i	−0.985444	−	0.438748i
$839$	−32.8580	−	23.8727i	−1.13438	−	0.824178i	−0.148057	−	0.988979i	$-0.547302\pi$
$839$	−32.8580	−	23.8727i	−1.13438	−	0.824178i	−0.986327	+	0.164801i	$0.947302\pi$
$840$		0			0
$841$	−6.06822	+	4.40882i	−0.209249	+	0.152028i
$842$	−22.1150	+	4.70068i	−0.762132	+	0.161996i
$843$	3.11046	−	5.38748i	0.107130	−	0.185555i
$844$	−0.215060	−	0.238848i	−0.00740267	−	0.00822150i
$845$		0			0
$846$	8.53538	+	26.2692i	0.293452	+	0.903154i
$847$	−11.4898	+	26.6805i	−0.394793	+	0.916752i
$848$	−6.68807	−	4.85916i	−0.229669	−	0.166864i
$849$	−3.07196	−	5.32078i	−0.105429	−	0.182609i
$850$		0			0
$851$	−32.3187	+	55.9777i	−1.10787	+	1.91889i
$852$	0.0227417	−	0.216373i	0.000779119	−	0.00741282i
$853$	−0.851704	−	2.62128i	−0.0291618	−	0.0897508i	0.935416	−	0.353548i	$-0.115025\pi$
$853$	−0.851704	−	2.62128i	−0.0291618	−	0.0897508i	−0.964578	+	0.263797i	$0.915025\pi$
$854$	6.11956	−	0.719014i	0.209407	−	0.0246042i
$855$		0			0
$856$	−8.90013	+	1.89178i	−0.304200	+	0.0646598i
$857$	1.44978	−	2.51108i	0.0495234	−	0.0857770i	−0.840201	−	0.542275i	$-0.817563\pi$
$857$	1.44978	−	2.51108i	0.0495234	−	0.0857770i	0.889724	+	0.456498i	$0.150896\pi$
$858$	−0.179223	−	0.199047i	−0.00611856	−	0.00679534i
$859$	−1.67772	−	0.746969i	−0.0572431	−	0.0254863i	0.377915	−	0.925840i	$-0.376641\pi$
$859$	−1.67772	−	0.746969i	−0.0572431	−	0.0254863i	−0.435159	+	0.900354i	$0.643308\pi$
$860$		0			0
$861$	−1.91697	+	1.76901i	−0.0653302	+	0.0602876i
$862$	7.73611	−	5.62061i	0.263493	−	0.191439i
$863$	−4.53148	−	2.01755i	−0.154253	−	0.0686780i	0.328158	−	0.944623i	$-0.393572\pi$
$863$	−4.53148	−	2.01755i	−0.154253	−	0.0686780i	−0.482411	+	0.875945i	$0.660239\pi$
$864$	−1.41614	+	0.630505i	−0.0481780	+	0.0214502i
$865$		0			0
$866$	1.29968	+	0.578654i	0.0441649	+	0.0196635i
$867$	0.780293	−	2.40149i	0.0265001	−	0.0815590i
$868$	0.119707	+	0.105161i	0.00406312	+	0.00356939i
$869$	0.504489	−	1.55266i	0.0171136	−	0.0526703i
$870$		0			0
$871$	52.8425	+	11.2320i	1.79050	+	0.380582i
$872$	−10.6779	−	2.26965i	−0.361599	−	0.0768602i
$873$	−1.33948	+	12.7443i	−0.0453344	+	0.431328i
$874$	7.98712			0.270168
$875$		0			0
$876$	0.470456			0.0158952
$877$	2.12539	−	20.2217i	0.0717692	−	0.682838i	−0.898196	−	0.439595i	$-0.855122\pi$
$877$	2.12539	−	20.2217i	0.0717692	−	0.682838i	0.969965	−	0.243243i	$-0.0782113\pi$
$878$	−10.5350	−	2.23928i	−0.355539	−	0.0755721i
$879$	−1.07817	−	0.229173i	−0.0363658	−	0.00772980i
$880$		0			0
$881$	−1.46453	+	4.50737i	−0.0493413	+	0.151857i	−0.972691	−	0.232102i	$-0.925440\pi$
$881$	−1.46453	+	4.50737i	−0.0493413	+	0.151857i	0.923350	+	0.383959i	$0.125440\pi$
$882$	−3.56746	−	27.4589i	−0.120123	−	0.924589i
$883$	10.3017	−	31.7053i	0.346678	−	1.06697i	−0.614001	−	0.789306i	$-0.710441\pi$
$883$	10.3017	−	31.7053i	0.346678	−	1.06697i	0.960679	−	0.277661i	$-0.0895592\pi$
$884$	−3.60121	−	1.60336i	−0.121122	−	0.0539268i
$885$		0			0
$886$	25.5020	−	11.3542i	0.856758	−	0.381453i
$887$	−46.2868	−	20.6082i	−1.55416	−	0.691956i	−0.563224	−	0.826304i	$-0.690439\pi$
$887$	−46.2868	−	20.6082i	−1.55416	−	0.691956i	−0.990934	+	0.134349i	$0.957106\pi$
$888$	6.17584	−	4.48701i	0.207248	−	0.150574i
$889$	−36.6720	−	11.4212i	−1.22994	−	0.383055i
$890$		0			0
$891$	−1.07803	−	0.479968i	−0.0361153	−	0.0160795i
$892$	−1.75941	−	1.95402i	−0.0589093	−	0.0654254i
$893$	2.88164	−	4.99115i	0.0964305	−	0.167023i
$894$	4.11764	−	0.875232i	0.137715	−	0.0292721i
$895$		0			0
$896$	10.2074	−	23.7027i	0.341005	−	0.791852i
$897$	3.05026	+	9.38772i	0.101845	+	0.313447i
$898$	2.07639	−	19.7555i	0.0692899	−	0.659250i
$899$	−1.12692	+	1.95189i	−0.0375850	+	0.0650992i
$900$		0			0
$901$	5.74825	+	9.95626i	0.191502	+	0.331691i
$902$	−0.537095	−	0.390223i	−0.0178833	−	0.0129930i
$903$	−1.02369	+	0.120277i	−0.0340661	+	0.00400258i
$904$	−6.74054	−	20.7452i	−0.224187	−	0.689977i
$905$		0			0
$906$	−4.54040	−	5.04263i	−0.150845	−	0.167530i
$907$	−25.3907	+	43.9780i	−0.843085	+	1.46027i	0.0441895	+	0.999023i	$0.485929\pi$
$907$	−25.3907	+	43.9780i	−0.843085	+	1.46027i	−0.887274	+	0.461242i	$0.847404\pi$
$908$	−0.173935	+	0.0369710i	−0.00577224	+	0.00122693i
$909$	−17.7551	+	12.8998i	−0.588900	+	0.427861i
$910$		0			0
$911$	−4.32719	−	3.14388i	−0.143366	−	0.104162i	0.513790	−	0.857916i	$-0.328241\pi$
$911$	−4.32719	−	3.14388i	−0.143366	−	0.104162i	−0.657156	+	0.753754i	$0.728241\pi$
$912$	−0.791723	−	0.352498i	−0.0262166	−	0.0116724i
$913$	0.232831	+	2.21524i	0.00770558	+	0.0733137i
$914$	−42.8222	+	19.0657i	−1.41643	+	0.630636i
$915$		0			0
$916$	−0.805743	+	0.585407i	−0.0266225	+	0.0193424i
$917$	34.3781	−	20.4132i	1.13526	−	0.674103i
$918$	−11.7160			−0.386685
$919$	36.0168	−	7.65560i	1.18808	−	0.252535i	0.428864	−	0.903369i	$-0.358914\pi$
$919$	36.0168	−	7.65560i	1.18808	−	0.252535i	0.759220	+	0.650834i	$0.225581\pi$
$920$		0			0
$921$	−5.45935	−	1.16042i	−0.179892	−	0.0382372i
$922$	14.3818	−	15.9726i	0.473638	−	0.526028i
$923$	−18.2329	−	13.2470i	−0.600143	−	0.436030i
$924$	0.0166170	−	0.00562492i	0.000546658	−	0.000185046i
$925$		0			0
$926$	8.83508	+	15.3028i	0.290339	+	0.502882i
$927$	−49.2047	+	21.9073i	−1.61609	+	0.719531i
$928$	−5.38312	−	1.14422i	−0.176710	−	0.0375608i
$929$	−7.25628	+	8.05891i	−0.238071	+	0.264404i	−0.850327	−	0.526255i	$-0.823596\pi$
$929$	−7.25628	+	8.05891i	−0.238071	+	0.264404i	0.612256	+	0.790660i	$0.290262\pi$
$930$		0			0
$931$	−3.75973	+	4.38692i	−0.123220	+	0.143776i
$932$	−1.67265			−0.0547895
$933$	−0.766377	+	0.162899i	−0.0250901	+	0.00533306i
$934$	4.32944	+	41.1919i	0.141664	+	1.34784i
$935$		0			0
$936$	−4.29808	+	40.8935i	−0.140487	+	1.33665i
$937$	−31.1902	+	22.6610i	−1.01894	+	0.740302i	−0.966065	−	0.258299i	$-0.916838\pi$
$937$	−31.1902	+	22.6610i	−1.01894	+	0.740302i	−0.0528734	+	0.998601i	$0.516838\pi$
$938$	23.2861	−	32.8896i	0.760317	−	1.07388i
$939$	−5.94259	−	4.31755i	−0.193929	−	0.140898i
$940$		0			0
$941$	−3.12194	−	29.7033i	−0.101772	−	0.968300i	−0.919605	−	0.392844i	$-0.871491\pi$
$941$	−3.12194	−	29.7033i	−0.101772	−	0.968300i	0.817833	−	0.575456i	$-0.195175\pi$
$942$	2.17000	+	2.41003i	0.0707024	+	0.0785230i
$943$	12.2331	+	21.1883i	0.398364	+	0.689987i
$944$	−3.72072	+	11.4512i	−0.121099	+	0.372705i
$945$		0			0
$946$	−0.0810649	−	0.249492i	−0.00263565	−	0.00811168i
$947$	10.0164	−	11.1243i	0.325489	−	0.361492i	−0.558085	−	0.829784i	$-0.688464\pi$
$947$	10.0164	−	11.1243i	0.325489	−	0.361492i	0.883574	+	0.468292i	$0.155130\pi$
$948$	0.484819	−	0.215855i	0.0157462	−	0.00701066i
$949$	24.3668	−	42.2045i	0.790979	−	1.37002i
$950$		0			0
$951$	−2.98332			−0.0967407
$952$	−28.9335	+	26.7002i	−0.937742	+	0.865360i
$953$	−13.6868	−	42.1237i	−0.443360	−	1.36452i	−0.884273	−	0.466971i	$-0.845345\pi$
$953$	−13.6868	−	42.1237i	−0.443360	−	1.36452i	0.440913	−	0.897550i	$-0.354655\pi$
$954$	5.99312	−	6.65604i	0.194034	−	0.215497i
$955$		0			0
$956$	0.775563	+	0.861350i	0.0250835	+	0.0278580i
$957$	0.124075	+	0.214904i	0.00401077	+	0.00694686i
$958$	−2.84833	+	8.76626i	−0.0920254	+	0.283225i
$959$	−17.7327	−	38.5515i	−0.572618	−	1.24489i
$960$		0			0
$961$	3.22584	−	30.6918i	0.104059	−	0.990057i
$962$	−6.17356	−	58.7375i	−0.199044	−	1.89377i
$963$	−0.946728	−	9.00751i	−0.0305079	−	0.290263i
$964$	0.340522	−	3.23985i	0.0109675	−	0.104348i
$965$		0			0
$966$	7.33168	+	0.679984i	0.235893	+	0.0218781i
$967$	14.0009	−	43.0905i	0.450240	−	1.38570i	−0.426394	−	0.904538i	$-0.640216\pi$
$967$	14.0009	−	43.0905i	0.450240	−	1.38570i	0.876634	−	0.481159i	$-0.159784\pi$
$968$	−16.0893	−	27.8676i	−0.517131	−	0.895697i
$969$	0.806448	+	0.895652i	0.0259069	+	0.0287725i
$970$		0			0
$971$	15.7647	−	17.5085i	0.505914	−	0.561875i	−0.435039	−	0.900412i	$-0.643265\pi$
$971$	15.7647	−	17.5085i	0.505914	−	0.561875i	0.940953	+	0.338537i	$0.109932\pi$
$972$	−0.373220	−	1.14865i	−0.0119710	−	0.0368431i
$973$	8.27837	+	2.57823i	0.265392	+	0.0826544i
$974$	37.3001			1.19517
$975$		0			0
$976$	−3.13544	+	5.43075i	−0.100363	+	0.173834i
$977$	−2.23146	+	0.993512i	−0.0713909	+	0.0317853i	−0.442121	−	0.896955i	$-0.645774\pi$
$977$	−2.23146	+	0.993512i	−0.0713909	+	0.0317853i	0.370731	+	0.928740i	$0.379107\pi$
$978$	3.57596	−	3.97151i	0.114347	−	0.126995i
$979$	0.603608	+	1.85772i	0.0192914	+	0.0593728i
$980$		0			0
$981$	3.35785	−	10.3344i	0.107208	−	0.329952i
$982$	2.63278	+	4.56010i	0.0840153	+	0.145519i
$983$	7.07979	+	7.86290i	0.225810	+	0.250788i	0.845394	−	0.534143i	$-0.179365\pi$
$983$	7.07979	+	7.86290i	0.225810	+	0.250788i	−0.619584	+	0.784930i	$0.712699\pi$
$984$	−0.302033	−	2.87365i	−0.00962847	−	0.0916087i
$985$		0			0
$986$	−33.6504	−	24.4485i	−1.07165	−	0.778598i
$987$	3.07009	−	4.33624i	0.0977222	−	0.138024i
$988$	0.518420	−	0.376654i	0.0164931	−	0.0119830i
$989$	−1.01055	+	9.61472i	−0.0321336	+	0.305730i
$990$		0			0
$991$	5.04243	+	47.9755i	0.160178	+	1.52399i	0.719178	+	0.694826i	$0.244519\pi$
$991$	5.04243	+	47.9755i	0.160178	+	1.52399i	−0.559000	+	0.829168i	$0.688815\pi$
$992$	−0.332397	+	0.0706532i	−0.0105536	+	0.00224324i
$993$	−3.76906			−0.119607
$994$	−14.4553	+	8.58332i	−0.458493	+	0.272246i
$995$		0			0
$996$	−0.484504	+	0.538096i	−0.0153521	+	0.0170502i
$997$	12.9541	+	2.75348i	0.410260	+	0.0872035i	0.408418	−	0.912795i	$-0.366080\pi$
$997$	12.9541	+	2.75348i	0.410260	+	0.0872035i	0.00184172	+	0.999998i	$0.499414\pi$
$998$	22.7181	−	10.1148i	0.719130	−	0.320177i
$999$	7.70637	+	13.3478i	0.243819	+	0.422306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.q.b.326.12		288
5.2	odd	4		175.2.t.a.109.6	yes	144
5.3	odd	4		875.2.u.a.424.13		144
5.4	even	2	inner	875.2.q.b.326.25		288
7.2	even	3	inner	875.2.q.b.576.25		288
25.2	odd	20		875.2.u.a.74.6		144
25.11	even	5	inner	875.2.q.b.676.25		288
25.14	even	10	inner	875.2.q.b.676.12		288
25.23	odd	20		175.2.t.a.39.13	yes	144
35.2	odd	12		175.2.t.a.9.13	✓	144
35.9	even	6	inner	875.2.q.b.576.12		288
35.23	odd	12		875.2.u.a.674.6		144
175.2	odd	60		875.2.u.a.324.13		144
175.23	odd	60		175.2.t.a.114.6	yes	144
175.86	even	15	inner	875.2.q.b.51.12		288
175.114	even	30	inner	875.2.q.b.51.25		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.t.a.9.13	✓	144	35.2	odd	12
175.2.t.a.39.13	yes	144	25.23	odd	20
175.2.t.a.109.6	yes	144	5.2	odd	4
175.2.t.a.114.6	yes	144	175.23	odd	60
875.2.q.b.51.12		288	175.86	even	15	inner
875.2.q.b.51.25		288	175.114	even	30	inner
875.2.q.b.326.12		288	1.1	even	1	trivial
875.2.q.b.326.25		288	5.4	even	2	inner
875.2.q.b.576.12		288	35.9	even	6	inner
875.2.q.b.576.25		288	7.2	even	3	inner
875.2.q.b.676.12		288	25.14	even	10	inner
875.2.q.b.676.25		288	25.11	even	5	inner
875.2.u.a.74.6		144	25.2	odd	20
875.2.u.a.324.13		144	175.2	odd	60
875.2.u.a.424.13		144	5.3	odd	4
875.2.u.a.674.6		144	35.23	odd	12

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.141734 + 1.34851i) q^{2} +(-0.281305 - 0.0597933i) q^{3} +(0.157907 + 0.0335641i) q^{4} +(0.120502 - 0.370868i) q^{6} +(2.50606 - 0.848315i) q^{7} +(-0.905658 + 2.78733i) q^{8} +(-2.66508 - 1.18657i) q^{9} +O(q^{10})\)	\(q+(-0.141734 + 1.34851i) q^{2} +(-0.281305 - 0.0597933i) q^{3} +(0.157907 + 0.0335641i) q^{4} +(0.120502 - 0.370868i) q^{6} +(2.50606 - 0.848315i) q^{7} +(-0.905658 + 2.78733i) q^{8} +(-2.66508 - 1.18657i) q^{9} +(-0.130473 + 0.0580902i) q^{11} +(-0.0424131 - 0.0188835i) q^{12} +(-3.89078 + 2.82682i) q^{13} +(0.788766 + 3.49969i) q^{14} +(-3.33542 - 1.48502i) q^{16} +(3.39745 + 3.77325i) q^{17} +(1.97783 - 3.42571i) q^{18} +(-0.807335 + 0.171604i) q^{19} +(-0.755693 + 0.0887897i) q^{21} +(-0.0598427 - 0.184177i) q^{22} +(-0.745995 + 7.09767i) q^{23} +(0.421430 - 0.729938i) q^{24} +(-3.26053 - 5.64741i) q^{26} +(1.37675 + 1.00027i) q^{27} +(0.424197 - 0.0498408i) q^{28} +(1.86695 + 5.74589i) q^{29} +(0.249623 + 0.277235i) q^{31} +(-0.455459 + 0.788877i) q^{32} +(0.0401761 - 0.00853969i) q^{33} +(-5.56980 + 4.04670i) q^{34} +(-0.381008 - 0.276818i) q^{36} +(8.27395 + 3.68380i) q^{37} +(-0.116983 - 1.11302i) q^{38} +(1.26352 - 0.562556i) q^{39} +(2.77346 - 2.01504i) q^{41} +(-0.0126263 - 1.03164i) q^{42} +1.35463 q^{43} +(-0.0225523 + 0.00479363i) q^{44} +(-9.46554 - 2.01196i) q^{46} +(-4.67231 + 5.18913i) q^{47} +(0.849477 + 0.617181i) q^{48} +(5.56072 - 4.25187i) q^{49} +(-0.730107 - 1.26458i) q^{51} +(-0.709260 + 0.315783i) q^{52} +(2.21476 + 0.470762i) q^{53} +(-1.54400 + 1.71479i) q^{54} +(0.0948953 + 7.75351i) q^{56} +0.237368 q^{57} +(-8.01299 + 1.70321i) q^{58} +(-0.344714 - 3.27973i) q^{59} +(0.179533 - 1.70814i) q^{61} +(-0.409234 + 0.297326i) q^{62} +(-7.68545 - 0.712794i) q^{63} +(-6.90681 - 5.01809i) q^{64} +(0.00582153 + 0.0553882i) q^{66} +(-7.51641 - 8.34782i) q^{67} +(0.409835 + 0.709855i) q^{68} +(0.634245 - 1.95201i) q^{69} +(1.44811 + 4.45682i) q^{71} +(5.72101 - 6.35382i) q^{72} +(-9.25719 + 4.12157i) q^{73} +(-6.14034 + 10.6354i) q^{74} -0.133243 q^{76} +(-0.277694 + 0.256260i) q^{77} +(0.579528 + 1.78360i) q^{78} +(-7.64875 + 8.49480i) q^{79} +(5.52867 + 6.14021i) q^{81} +(2.32420 + 4.02564i) q^{82} +(4.81947 - 14.8328i) q^{83} +(-0.122309 - 0.0113437i) q^{84} +(-0.191997 + 1.82673i) q^{86} +(-0.181618 - 1.72798i) q^{87} +(-0.0437528 - 0.416280i) q^{88} +(1.42961 - 13.6018i) q^{89} +(-7.35251 + 10.3848i) q^{91} +(-0.356024 + 1.09573i) q^{92} +(-0.0536436 - 0.0929134i) q^{93} +(-6.33536 - 7.03613i) q^{94} +(0.175293 - 0.194682i) q^{96} +(-1.35738 - 4.17760i) q^{97} +(4.94554 + 8.10132i) q^{98} +0.416648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9}+O(q^{10}) \) 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9	\( 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9} + 36 q^{14} + 10 q^{16} + 22 q^{19} - 18 q^{21} - 100 q^{24} - 120 q^{26} + 48 q^{29} + 30 q^{31} + 40 q^{34} + 32 q^{36} - 26 q^{39} - 124 q^{41} + 30 q^{44} - 54 q^{46} + 76 q^{49} - 16 q^{51} + 58 q^{54} + 64 q^{56} + 78 q^{59} + 14 q^{61} - 68 q^{64} + 22 q^{66} - 148 q^{69} - 92 q^{71} - 12 q^{74} + 360 q^{76} - 18 q^{79} - 118 q^{81} + 102 q^{84} + 22 q^{86} + 84 q^{89} + 44 q^{91} - 10 q^{94} + 106 q^{96} + 88 q^{99}+O(q^{100}) \) 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9 + 36 * q^14 + 10 * q^16 + 22 * q^19 - 18 * q^21 - 100 * q^24 - 120 * q^26 + 48 * q^29 + 30 * q^31 + 40 * q^34 + 32 * q^36 - 26 * q^39 - 124 * q^41 + 30 * q^44 - 54 * q^46 + 76 * q^49 - 16 * q^51 + 58 * q^54 + 64 * q^56 + 78 * q^59 + 14 * q^61 - 68 * q^64 + 22 * q^66 - 148 * q^69 - 92 * q^71 - 12 * q^74 + 360 * q^76 - 18 * q^79 - 118 * q^81 + 102 * q^84 + 22 * q^86 + 84 * q^89 + 44 * q^91 - 10 * q^94 + 106 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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