LMFDB - Embedded newform 961.2.g.o.816.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.26873856000000000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			816.1
Root			$1.38331 + 0.294032i$ of defining polynomial
Character	$\chi$	$=$	961.816
Dual form			961.2.g.o.338.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.335106 - 0.243469i) q^{2} +(-0.0432971 - 0.411944i) q^{3} +(-0.565015 - 1.73894i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(0.405162 + 0.0861198i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(2.76662 - 0.588063i) q^{9} +O(q^{10})$	\(q+(-0.335106 - 0.243469i) q^{2} +(-0.0432971 - 0.411944i) q^{3} +(-0.565015 - 1.73894i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(0.405162 + 0.0861198i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(2.76662 - 0.588063i) q^{9} +(-0.0432971 + 0.411944i) q^{10} +(2.16975 - 2.40975i) q^{11} +(-0.691882 + 0.308046i) q^{12} +(-3.49744 - 1.55716i) q^{13} +(-0.114805 - 0.127503i) q^{14} +(-0.335106 + 0.243469i) q^{15} +(-2.42705 + 1.76336i) q^{16} +(-3.89998 - 4.33137i) q^{17} +(-1.07029 - 0.476522i) q^{18} +(4.03258 - 1.79542i) q^{19} +(-1.22346 + 1.35879i) q^{20} +(0.0179342 - 0.170633i) q^{21} +(-1.31379 + 0.279256i) q^{22} +(-1.23607 + 3.80423i) q^{23} +(0.642500 + 0.136568i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.792893 + 1.37333i) q^{26} +(-0.746033 - 2.29605i) q^{27} +(-0.0791656 - 0.753210i) q^{28} +(5.52431 + 4.01365i) q^{29} +0.171573 q^{30} +4.41421 q^{32} +(-1.08663 - 0.789481i) q^{33} +(0.252354 + 2.40099i) q^{34} +(-0.127999 - 0.393941i) q^{35} +(-2.58579 - 4.47871i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(-1.78847 - 0.380151i) q^{38} +(-0.490035 + 1.50817i) q^{39} +(1.55113 - 0.329704i) q^{40} +(0.782425 - 7.44428i) q^{41} +(-0.0475536 + 0.0528137i) q^{42} +(-9.95718 + 4.43322i) q^{43} +(-5.41635 - 2.41151i) q^{44} +(-1.89259 - 2.10193i) q^{45} +(1.34042 - 0.973874i) q^{46} +(-7.81256 + 5.67616i) q^{47} +(0.831489 + 0.923462i) q^{48} +(-6.23808 - 2.77737i) q^{49} +(-1.51361 + 0.673903i) q^{50} +(-1.61542 + 1.79411i) q^{51} +(-0.731699 + 6.96165i) q^{52} +(-5.70106 + 1.21180i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-3.17178 - 0.674183i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(-0.914214 - 1.58346i) q^{57} +(-0.874032 - 2.68999i) q^{58} +(-0.425542 - 4.04877i) q^{59} +(0.612717 + 0.445165i) q^{60} -2.82843 q^{61} +1.17157 q^{63} +(3.37487 + 2.45199i) q^{64} +(0.400180 + 3.80745i) q^{65} +(0.171921 + 0.529120i) q^{66} +(-1.62132 - 2.80821i) q^{67} +(-5.32843 + 9.22911i) q^{68} +(1.62065 + 0.344479i) q^{69} +(-0.0530189 + 0.163176i) q^{70} +(-0.0695148 + 0.0147758i) q^{71} +(-0.468840 + 4.46071i) q^{72} +(-1.22346 + 1.35879i) q^{73} +(0.378403 - 0.168476i) q^{74} +(-1.51361 - 0.673903i) q^{75} +(-5.40060 - 5.99797i) q^{76} +(1.08663 - 0.789481i) q^{77} +(0.531406 - 0.386089i) q^{78} +(-4.52156 - 5.02170i) q^{79} +(2.74064 + 1.22021i) q^{80} +(6.83814 - 3.04454i) q^{81} +(-2.07464 + 2.30412i) q^{82} +(1.05271 - 10.0159i) q^{83} +(-0.306853 + 0.0652237i) q^{84} +(-1.80108 + 5.54316i) q^{85} +(4.41606 + 0.938663i) q^{86} +(1.41421 - 2.44949i) q^{87} +(2.57107 + 4.45322i) q^{88} +(1.38603 + 4.26576i) q^{89} +(0.122463 + 1.16515i) q^{90} +(-1.28293 - 0.932102i) q^{91} +7.31371 q^{92} +4.00000 q^{94} +(-3.57117 - 2.59461i) q^{95} +(-0.191123 - 1.81841i) q^{96} +(1.59810 + 4.91846i) q^{97} +(1.41421 + 2.44949i) q^{98} +(4.58579 - 7.94282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21} + 14 q^{22} + 16 q^{23} + 10 q^{24} + 32 q^{25} + 24 q^{26} + 4 q^{27} + 10 q^{28} + 16 q^{29} + 48 q^{30} + 48 q^{32} - 28 q^{33} - 2 q^{34} - 4 q^{35} - 64 q^{36} - 8 q^{37} - 2 q^{38} + 12 q^{39} - 6 q^{40} + 2 q^{41} + 14 q^{42} - 2 q^{43} - 26 q^{44} - 16 q^{46} - 16 q^{47} - 6 q^{48} - 8 q^{49} + 8 q^{50} - 2 q^{51} + 14 q^{52} + 6 q^{53} + 4 q^{54} - 2 q^{55} + 40 q^{56} + 8 q^{57} - 6 q^{59} + 20 q^{60} + 64 q^{63} + 28 q^{64} - 2 q^{65} + 60 q^{66} + 8 q^{67} - 40 q^{68} + 8 q^{69} + 12 q^{70} - 14 q^{71} - 8 q^{72} + 2 q^{73} - 2 q^{74} + 8 q^{75} - 2 q^{76} + 28 q^{77} - 20 q^{78} - 22 q^{79} + 6 q^{80} - 2 q^{81} - 26 q^{82} - 6 q^{83} - 22 q^{84} + 12 q^{85} - 26 q^{86} - 72 q^{88} + 16 q^{89} - 8 q^{90} - 12 q^{91} - 64 q^{92} + 64 q^{94} - 12 q^{95} - 2 q^{96} - 32 q^{97} + 96 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	−0.335106	−	0.243469i	−0.236956	−	0.172158i	0.462970	−	0.886374i	$-0.346784\pi$
$2$	−0.335106	−	0.243469i	−0.236956	−	0.172158i	−0.699926	+	0.714215i	$0.746784\pi$
$3$	−0.0432971	−	0.411944i	−0.0249976	−	0.237836i	−0.999885	−	0.0151396i	$-0.995181\pi$
$3$	−0.0432971	−	0.411944i	−0.0249976	−	0.237836i	0.974888	−	0.222697i	$-0.0714859\pi$
$4$	−0.565015	−	1.73894i	−0.282508	−	0.869469i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	−0.0857864	+	0.148586i	−0.0350222	+	0.0606602i
$7$	0.405162	+	0.0861198i	0.153137	+	0.0325502i	0.283842	−	0.958871i	$-0.408391\pi$
$7$	0.405162	+	0.0861198i	0.153137	+	0.0325502i	−0.130705	+	0.991421i	$0.541724\pi$
$8$	−0.490035	+	1.50817i	−0.173254	+	0.533220i
$9$	2.76662	−	0.588063i	0.922206	−	0.196021i
$10$	−0.0432971	+	0.411944i	−0.0136917	+	0.130268i
$11$	2.16975	−	2.40975i	0.654204	−	0.726567i	−0.321195	−	0.947013i	$-0.604084\pi$
$11$	2.16975	−	2.40975i	0.654204	−	0.726567i	0.975399	+	0.220446i	$0.0707512\pi$
$12$	−0.691882	+	0.308046i	−0.199729	+	0.0889252i
$13$	−3.49744	−	1.55716i	−0.970016	−	0.431879i	−0.140327	−	0.990105i	$-0.544815\pi$
$13$	−3.49744	−	1.55716i	−0.970016	−	0.431879i	−0.829689	+	0.558226i	$0.811482\pi$
$14$	−0.114805	−	0.127503i	−0.0306828	−	0.0340767i
$15$	−0.335106	+	0.243469i	−0.0865239	+	0.0628633i
$16$	−2.42705	+	1.76336i	−0.606763	+	0.440839i
$17$	−3.89998	−	4.33137i	−0.945884	−	1.05051i	−0.998652	−	0.0519036i	$-0.983471\pi$
$17$	−3.89998	−	4.33137i	−0.945884	−	1.05051i	0.0527683	−	0.998607i	$-0.483196\pi$
$18$	−1.07029	−	0.476522i	−0.252269	−	0.112317i
$19$	4.03258	−	1.79542i	0.925138	−	0.411898i	0.111828	−	0.993728i	$-0.464330\pi$
$19$	4.03258	−	1.79542i	0.925138	−	0.411898i	0.813311	+	0.581829i	$0.197663\pi$
$20$	−1.22346	+	1.35879i	−0.273573	+	0.303834i
$21$	0.0179342	−	0.170633i	0.00391357	−	0.0372352i
$22$	−1.31379	+	0.279256i	−0.280102	+	0.0595375i
$23$	−1.23607	+	3.80423i	−0.257738	+	0.793236i	0.735540	+	0.677481i	$0.236929\pi$
$23$	−1.23607	+	3.80423i	−0.257738	+	0.793236i	−0.993278	+	0.115755i	$0.963071\pi$
$24$	0.642500	+	0.136568i	0.131150	+	0.0278768i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	0.792893	+	1.37333i	0.155499	+	0.269332i
$27$	−0.746033	−	2.29605i	−0.143574	−	0.441876i
$28$	−0.0791656	−	0.753210i	−0.0149609	−	0.142343i
$29$	5.52431	+	4.01365i	1.02584	+	0.745316i	0.967472	−	0.252979i	$-0.0814105\pi$
$29$	5.52431	+	4.01365i	1.02584	+	0.745316i	0.0583676	+	0.998295i	$0.481410\pi$
$30$	0.171573			0.0313248
$31$		0			0
$31$		0			0
$32$	4.41421			0.780330
$33$	−1.08663	−	0.789481i	−0.189158	−	0.137431i
$34$	0.252354	+	2.40099i	0.0432784	+	0.411766i
$35$	−0.127999	−	0.393941i	−0.0216358	−	0.0665881i
$36$	−2.58579	−	4.47871i	−0.430964	−	0.746452i
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$	−1.78847	−	0.380151i	−0.290128	−	0.0616687i
$39$	−0.490035	+	1.50817i	−0.0784684	+	0.241501i
$40$	1.55113	−	0.329704i	0.245256	−	0.0521307i
$41$	0.782425	−	7.44428i	0.122194	−	1.16260i	−0.745850	−	0.666114i	$-0.767956\pi$
$41$	0.782425	−	7.44428i	0.122194	−	1.16260i	0.868044	−	0.496487i	$-0.165377\pi$
$42$	−0.0475536	+	0.0528137i	−0.00733769	+	0.00814933i
$43$	−9.95718	+	4.43322i	−1.51846	+	0.676060i	−0.985437	−	0.170043i	$-0.945609\pi$
$43$	−9.95718	+	4.43322i	−1.51846	+	0.676060i	−0.533020	+	0.846103i	$0.678943\pi$
$44$	−5.41635	−	2.41151i	−0.816545	−	0.363549i
$45$	−1.89259	−	2.10193i	−0.282130	−	0.313337i
$46$	1.34042	−	0.973874i	0.197635	−	0.143590i
$47$	−7.81256	+	5.67616i	−1.13958	+	0.827953i	−0.987061	−	0.160348i	$-0.948738\pi$
$47$	−7.81256	+	5.67616i	−1.13958	+	0.827953i	−0.152518	+	0.988301i	$0.548738\pi$
$48$	0.831489	+	0.923462i	0.120015	+	0.133290i
$49$	−6.23808	−	2.77737i	−0.891154	−	0.396767i
$50$	−1.51361	+	0.673903i	−0.214057	+	0.0953043i
$51$	−1.61542	+	1.79411i	−0.226205	+	0.251226i
$52$	−0.731699	+	6.96165i	−0.101468	+	0.965408i
$53$	−5.70106	+	1.21180i	−0.783101	+	0.166453i	−0.582078	−	0.813133i	$-0.697760\pi$
$53$	−5.70106	+	1.21180i	−0.783101	+	0.166453i	−0.201023	+	0.979586i	$0.564427\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−3.17178	−	0.674183i	−0.427683	−	0.0909068i
$56$	−0.328427	+	0.568852i	−0.0438879	+	0.0760161i
$57$	−0.914214	−	1.58346i	−0.121091	−	0.209735i
$58$	−0.874032	−	2.68999i	−0.114766	−	0.353214i
$59$	−0.425542	−	4.04877i	−0.0554009	−	0.527104i	−0.986666	−	0.162761i	$-0.947960\pi$
$59$	−0.425542	−	4.04877i	−0.0554009	−	0.527104i	0.931265	−	0.364344i	$-0.118707\pi$
$60$	0.612717	+	0.445165i	0.0791014	+	0.0574705i
$61$	−2.82843			−0.362143			−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843			−0.362143			−0.181071	+	0.983470i	$0.557957\pi$
$62$		0			0
$63$	1.17157			0.147604
$64$	3.37487	+	2.45199i	0.421859	+	0.306499i
$65$	0.400180	+	3.80745i	0.0496362	+	0.472257i
$66$	0.171921	+	0.529120i	0.0211621	+	0.0651301i
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	0.749829	−	0.661632i	$-0.230136\pi$
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	−0.947904	+	0.318555i	$0.896803\pi$
$68$	−5.32843	+	9.22911i	−0.646167	+	1.11919i
$69$	1.62065	+	0.344479i	0.195103	+	0.0414704i
$70$	−0.0530189	+	0.163176i	−0.00633697	+	0.0195032i
$71$	−0.0695148	+	0.0147758i	−0.00824989	+	0.00175357i	−0.212035	−	0.977262i	$-0.568009\pi$
$71$	−0.0695148	+	0.0147758i	−0.00824989	+	0.00175357i	0.203785	+	0.979016i	$0.434676\pi$
$72$	−0.468840	+	4.46071i	−0.0552533	+	0.525700i
$73$	−1.22346	+	1.35879i	−0.143195	+	0.159034i	−0.810476	−	0.585772i	$-0.800791\pi$
$73$	−1.22346	+	1.35879i	−0.143195	+	0.159034i	0.667281	+	0.744806i	$0.267458\pi$
$74$	0.378403	−	0.168476i	0.0439884	−	0.0195849i
$75$	−1.51361	−	0.673903i	−0.174777	−	0.0778157i
$76$	−5.40060	−	5.99797i	−0.619491	−	0.688015i
$77$	1.08663	−	0.789481i	0.123833	−	0.0899697i
$78$	0.531406	−	0.386089i	0.0601699	−	0.0437160i
$79$	−4.52156	−	5.02170i	−0.508715	−	0.564985i	0.433001	−	0.901393i	$-0.357454\pi$
$79$	−4.52156	−	5.02170i	−0.508715	−	0.564985i	−0.941716	+	0.336408i	$0.890788\pi$
$80$	2.74064	+	1.22021i	0.306412	+	0.136424i
$81$	6.83814	−	3.04454i	0.759794	−	0.338282i
$82$	−2.07464	+	2.30412i	−0.229106	+	0.254448i
$83$	1.05271	−	10.0159i	0.115550	−	1.09939i	−0.771026	−	0.636804i	$-0.780256\pi$
$83$	1.05271	−	10.0159i	0.115550	−	1.09939i	0.886576	−	0.462583i	$-0.153077\pi$
$84$	−0.306853	+	0.0652237i	−0.0334804	+	0.00711649i
$85$	−1.80108	+	5.54316i	−0.195355	+	0.601241i
$86$	4.41606	+	0.938663i	0.476196	+	0.101219i
$87$	1.41421	−	2.44949i	0.151620	−	0.262613i
$88$	2.57107	+	4.45322i	0.274077	+	0.474715i
$89$	1.38603	+	4.26576i	0.146919	+	0.452169i	0.997253	−	0.0740741i	$-0.0236001\pi$
$89$	1.38603	+	4.26576i	0.146919	+	0.452169i	−0.850334	+	0.526243i	$0.823600\pi$
$90$	0.122463	+	1.16515i	0.0129087	+	0.122818i
$91$	−1.28293	−	0.932102i	−0.134487	−	0.0977108i
$92$	7.31371			0.762507
$93$		0			0
$94$	4.00000			0.412568
$95$	−3.57117	−	2.59461i	−0.366395	−	0.266201i
$96$	−0.191123	−	1.81841i	−0.0195064	−	0.185591i
$97$	1.59810	+	4.91846i	0.162263	+	0.499394i	0.998824	−	0.0484796i	$-0.0154376\pi$
$97$	1.59810	+	4.91846i	0.162263	+	0.499394i	−0.836561	+	0.547873i	$0.815438\pi$
$98$	1.41421	+	2.44949i	0.142857	+	0.247436i
$99$	4.58579	−	7.94282i	0.460889	−	0.798283i
$100$	−7.15389	−	1.52061i	−0.715389	−	0.152061i
$101$	−2.62210	+	8.06998i	−0.260908	+	0.802993i	0.731700	+	0.681627i	$0.238727\pi$
$101$	−2.62210	+	8.06998i	−0.260908	+	0.802993i	−0.992608	+	0.121366i	$0.961273\pi$
$102$	0.978148	−	0.207912i	0.0968510	−	0.0205863i
$103$	−0.216486	+	2.05972i	−0.0213310	+	0.202950i	−0.999997	−	0.00250768i	$-0.999202\pi$
$103$	−0.216486	+	2.05972i	−0.0213310	+	0.202950i	0.978666	+	0.205458i	$0.0658684\pi$
$104$	4.06234	−	4.51168i	0.398345	−	0.442407i
$105$	−0.156740	+	0.0697850i	−0.0152962	+	0.00681032i
$106$	2.20549	+	0.981949i	0.214216	+	0.0953753i
$107$	8.30673	+	9.22556i	0.803042	+	0.891868i	0.996001	−	0.0893383i	$-0.0284752\pi$
$107$	8.30673	+	9.22556i	0.803042	+	0.891868i	−0.192959	+	0.981207i	$0.561809\pi$
$108$	−3.57117	+	2.59461i	−0.343636	+	0.249666i
$109$	8.76038	−	6.36479i	0.839092	−	0.609636i	−0.0830246	−	0.996547i	$-0.526458\pi$
$109$	8.76038	−	6.36479i	0.839092	−	0.609636i	0.922117	+	0.386911i	$0.126458\pi$
$110$	0.898740	+	0.998152i	0.0856915	+	0.0951700i
$111$	0.378403	+	0.168476i	0.0359164	+	0.0159910i
$112$	−1.13521	+	0.505428i	−0.107267	+	0.0477584i
$113$	11.1456	−	12.3785i	1.04849	−	1.16447i	0.0624356	−	0.998049i	$-0.480113\pi$
$113$	11.1456	−	12.3785i	1.04849	−	1.16447i	0.986055	−	0.166418i	$-0.0532201\pi$
$114$	−0.0791656	+	0.753210i	−0.00741454	+	0.0705446i
$115$	3.91259	−	0.831647i	0.364851	−	0.0775515i
$116$	3.85816	−	11.8742i	0.358222	−	1.10249i
$117$	−10.5918	−	2.25136i	−0.979212	−	0.208138i
$118$	−0.843146	+	1.46037i	−0.0776179	+	0.134438i
$119$	−1.20711	−	2.09077i	−0.110655	−	0.191661i
$120$	−0.202979	−	0.624706i	−0.0185294	−	0.0570276i
$121$	0.0507257	+	0.482623i	0.00461143	+	0.0438748i
$122$	0.947822	+	0.688633i	0.0858118	+	0.0623459i
$123$	−3.10051			−0.279563
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−0.392601	−	0.285241i	−0.0349757	−	0.0254113i
$127$	−0.930251	−	8.85074i	−0.0825464	−	0.785376i	−0.954985	−	0.296653i	$-0.904129\pi$
$127$	−0.930251	−	8.85074i	−0.0825464	−	0.785376i	0.872439	−	0.488723i	$-0.162537\pi$
$128$	−3.26209	−	10.0397i	−0.288331	−	0.887391i
$129$	2.25736	+	3.90986i	0.198749	+	0.344244i
$130$	0.792893	−	1.37333i	0.0695413	−	0.120449i
$131$	12.9533	+	2.75330i	1.13173	+	0.240557i	0.735454	−	0.677574i	$-0.236969\pi$
$131$	12.9533	+	2.75330i	1.13173	+	0.240557i	0.396277	+	0.918131i	$0.370302\pi$
$132$	−0.758898	+	2.33565i	−0.0660536	+	0.203292i
$133$	1.78847	−	0.380151i	0.155080	−	0.0329633i
$134$	−0.140397	+	1.33579i	−0.0121285	+	0.115394i
$135$	−1.61542	+	1.79411i	−0.139034	+	0.154412i
$136$	8.44357	−	3.75932i	0.724030	−	0.322359i
$137$	8.66524	+	3.85801i	0.740321	+	0.329612i	0.742012	−	0.670386i	$-0.233872\pi$
$137$	8.66524	+	3.85801i	0.740321	+	0.329612i	−0.00169113	+	0.999999i	$0.500538\pi$
$138$	−0.459219	−	0.510014i	−0.0390913	−	0.0434153i
$139$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$139$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$140$	−0.612717	+	0.445165i	−0.0517840	+	0.0376233i
$141$	2.67652	+	2.97258i	0.225404	+	0.250336i
$142$	0.0268923	+	0.0119732i	0.00225675	+	0.00100477i
$143$	−11.3409	+	5.04932i	−0.948378	+	0.422245i
$144$	−5.67776	+	6.30579i	−0.473147	+	0.525483i
$145$	0.713765	−	6.79102i	0.0592750	−	0.563964i
$146$	0.740809	−	0.157464i	0.0613098	−	0.0130318i
$147$	−0.874032	+	2.68999i	−0.0720889	+	0.221867i
$148$	1.78847	+	0.380151i	0.147011	+	0.0312483i
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$	0.343146	+	0.594346i	0.0280177	+	0.0485281i
$151$	1.64203	+	5.05364i	0.133626	+	0.411259i	0.995374	−	0.0960781i	$-0.0306299\pi$
$151$	1.64203	+	5.05364i	0.133626	+	0.411259i	−0.861748	+	0.507337i	$0.830630\pi$
$152$	0.731699	+	6.96165i	0.0593486	+	0.564665i
$153$	−13.3369	−	9.68981i	−1.07822	−	0.783374i
$154$	−0.556349			−0.0448319
$155$		0			0
$156$	2.89949			0.232145
$157$	−7.41996	−	5.39092i	−0.592177	−	0.430242i	0.250916	−	0.968009i	$-0.419268\pi$
$157$	−7.41996	−	5.39092i	−0.592177	−	0.430242i	−0.843094	+	0.537767i	$0.819268\pi$
$158$	0.292574	+	2.78366i	0.0232759	+	0.221456i
$159$	0.746033	+	2.29605i	0.0591643	+	0.182089i
$160$	−2.20711	−	3.82282i	−0.174487	−	0.302221i
$161$	−0.828427	+	1.43488i	−0.0652892	+	0.113084i
$162$	−3.03275	−	0.644631i	−0.238275	−	0.0506470i
$163$	6.48026	−	19.9442i	0.507573	−	1.56215i	−0.288828	−	0.957381i	$-0.593266\pi$
$163$	6.48026	−	19.9442i	0.507573	−	1.56215i	0.796401	−	0.604769i	$-0.206734\pi$
$164$	−13.3872	+	2.84554i	−1.04537	+	0.222199i
$165$	−0.140397	+	1.33579i	−0.0109299	+	0.103991i
$166$	−2.79133	+	3.10008i	−0.216649	+	0.240613i
$167$	20.6063	−	9.17449i	1.59456	−	0.709944i	0.598711	−	0.800965i	$-0.295680\pi$
$167$	20.6063	−	9.17449i	1.59456	−	0.709944i	0.995849	+	0.0910218i	$0.0290133\pi$
$168$	0.248556	+	0.110664i	0.0191765	+	0.00853792i
$169$	1.10865	+	1.23128i	0.0852809	+	0.0947141i
$170$	1.95314	−	1.41904i	0.149799	−	0.108835i
$171$	10.1008	−	7.33866i	0.772428	−	0.561202i
$172$	13.3351	+	14.8101i	1.01679	+	1.12926i
$173$	7.59495	+	3.38149i	0.577433	+	0.257090i	0.674606	−	0.738178i	$-0.264313\pi$
$173$	7.59495	+	3.38149i	0.577433	+	0.257090i	−0.0971730	+	0.995268i	$0.530980\pi$
$174$	−1.07029	+	0.476522i	−0.0811381	+	0.0361250i
$175$	1.10865	−	1.23128i	0.0838062	−	0.0930762i
$176$	−1.01684	+	9.67463i	−0.0766476	+	0.729253i
$177$	−1.64944	+	0.350600i	−0.123980	+	0.0263527i
$178$	0.574112	−	1.76693i	0.0430315	−	0.132437i
$179$	14.9096	+	3.16912i	1.11439	+	0.236871i	0.728077	−	0.685495i	$-0.240414\pi$
$179$	14.9096	+	3.16912i	1.11439	+	0.236871i	0.386315	+	0.922367i	$0.373748\pi$
$180$	−2.58579	+	4.47871i	−0.192733	+	0.333824i
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	0.541200	−	0.840894i	$-0.317970\pi$
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	−0.998835	+	0.0482461i	$0.984637\pi$
$182$	0.202979	+	0.624706i	0.0150458	+	0.0463063i
$183$	0.122463	+	1.16515i	0.00905270	+	0.0861307i
$184$	−5.13171	−	3.72841i	−0.378315	−	0.274862i
$185$	1.00000			0.0735215
$186$		0			0
$187$	−18.8995			−1.38207
$188$	14.2847	+	10.3784i	1.04182	+	0.756925i
$189$	−0.104528	−	0.994522i	−0.00760333	−	0.0723408i
$190$	0.565015	+	1.73894i	0.0409905	+	0.126156i
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	0.944817	+	0.327599i	$0.106239\pi$
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	−0.188700	+	0.982035i	$0.560427\pi$
$192$	0.863961	−	1.49642i	0.0623510	−	0.107995i
$193$	−6.98606	−	1.48493i	−0.502868	−	0.106888i	−0.0505085	−	0.998724i	$-0.516084\pi$
$193$	−6.98606	−	1.48493i	−0.502868	−	0.106888i	−0.452359	+	0.891836i	$0.649418\pi$
$194$	0.661956	−	2.03729i	0.0475257	−	0.146269i
$195$	1.55113	−	0.329704i	0.111079	−	0.0236106i
$196$	−1.30507	+	12.4169i	−0.0932191	+	0.886920i
$197$	−9.02341	+	10.0215i	−0.642892	+	0.714004i	−0.973223	−	0.229861i	$-0.926173\pi$
$197$	−9.02341	+	10.0215i	−0.642892	+	0.714004i	0.330332	+	0.943865i	$0.392839\pi$
$198$	−3.47055	+	1.54519i	−0.246641	+	0.109812i
$199$	16.8222	+	7.48974i	1.19250	+	0.530933i	0.904407	−	0.426671i	$-0.140314\pi$
$199$	16.8222	+	7.48974i	1.19250	+	0.530933i	0.288089	+	0.957604i	$0.406980\pi$
$200$	4.24439	+	4.71388i	0.300124	+	0.333321i
$201$	−1.08663	+	0.789481i	−0.0766448	+	0.0556857i
$202$	2.84347	−	2.06590i	0.200066	−	0.145356i
$203$	1.89259	+	2.10193i	0.132834	+	0.147527i
$204$	4.03258	+	1.79542i	0.282337	+	0.125705i
$205$	−6.83814	+	3.04454i	−0.477597	+	0.212640i
$206$	0.574023	−	0.637517i	0.0399941	−	0.0444179i
$207$	−1.18260	+	11.2517i	−0.0821967	+	0.782049i
$208$	11.2343	−	2.38792i	0.778959	−	0.165573i
$209$	4.42318	−	13.6131i	0.305958	−	0.941641i
$210$	0.0695148	+	0.0147758i	0.00479698	+	0.00101963i
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	−0.987706	−	0.156324i	$-0.950035\pi$
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	0.629234	+	0.777216i	$0.283369\pi$
$212$	5.32843	+	9.22911i	0.365958	+	0.633858i
$213$	0.00909661	+	0.0279965i	0.000623290	+	0.00191829i
$214$	−0.537500	−	5.11397i	−0.0367427	−	0.349584i
$215$	8.81788	+	6.40656i	0.601374	+	0.436924i
$216$	3.82843			0.260491
$217$		0			0
$218$	−4.48528			−0.303782
$219$	0.612717	+	0.445165i	0.0414035	+	0.0300814i
$220$	0.619742	+	5.89645i	0.0417830	+	0.397539i
$221$	6.89532	+	21.2216i	0.463829	+	1.42752i
$222$	−0.0857864	−	0.148586i	−0.00575761	−	0.00997247i
$223$	11.8640	−	20.5490i	0.794470	−	1.37606i	−0.128706	−	0.991683i	$-0.541082\pi$
$223$	11.8640	−	20.5490i	0.794470	−	1.37606i	0.923175	−	0.384379i	$-0.125584\pi$
$224$	1.78847	+	0.380151i	0.119497	+	0.0253999i
$225$	3.49613	−	10.7600i	0.233075	−	0.717332i
$226$	−6.74872	+	1.43449i	−0.448918	+	0.0954206i
$227$	1.92481	−	18.3133i	0.127754	−	1.21550i	−0.723342	−	0.690490i	$-0.757395\pi$
$227$	1.92481	−	18.3133i	0.127754	−	1.21550i	0.851096	−	0.525009i	$-0.175938\pi$
$228$	−2.23700	+	2.48444i	−0.148149	+	0.164536i
$229$	−5.01105	+	2.23106i	−0.331140	+	0.147433i	−0.565571	−	0.824700i	$-0.691344\pi$
$229$	−5.01105	+	2.23106i	−0.331140	+	0.147433i	0.234431	+	0.972133i	$0.424677\pi$
$230$	−1.51361	−	0.673903i	−0.0998046	−	0.0444359i
$231$	−0.372270	−	0.413448i	−0.0244936	−	0.0272029i
$232$	−8.76038	+	6.36479i	−0.575147	+	0.417869i
$233$	7.41996	−	5.39092i	0.486098	−	0.353171i	−0.317584	−	0.948230i	$-0.602872\pi$
$233$	7.41996	−	5.39092i	0.486098	−	0.353171i	0.803682	+	0.595060i	$0.202872\pi$
$234$	3.00124	+	3.33321i	0.196197	+	0.217899i
$235$	8.82198	+	3.92780i	0.575482	+	0.256221i
$236$	−6.80011	+	3.02761i	−0.442650	+	0.197080i
$237$	−1.87289	+	2.08005i	−0.121657	+	0.135114i
$238$	−0.104528	+	0.994522i	−0.00677557	+	0.0644653i
$239$	20.7784	−	4.41659i	1.34405	−	0.285686i	0.520949	−	0.853588i	$-0.325578\pi$
$239$	20.7784	−	4.41659i	1.34405	−	0.285686i	0.823096	+	0.567902i	$0.192245\pi$
$240$	0.383997	−	1.18182i	0.0247869	−	0.0762863i
$241$	−13.0516	−	2.77420i	−0.840725	−	0.178702i	−0.232630	−	0.972565i	$-0.574733\pi$
$241$	−13.0516	−	2.77420i	−0.840725	−	0.178702i	−0.608096	+	0.793864i	$0.708066\pi$
$242$	0.100505	−	0.174080i	0.00646071	−	0.0111903i
$243$	−5.17157	−	8.95743i	−0.331757	−	0.574619i
$244$	1.59810	+	4.91846i	0.102308	+	0.314872i
$245$	0.713765	+	6.79102i	0.0456008	+	0.433862i
$246$	1.03900	+	0.754876i	0.0662440	+	0.0481291i
$247$	−16.8995			−1.07529
$248$		0			0
$249$	−4.17157			−0.264363
$250$	3.01595	+	2.19122i	0.190746	+	0.138585i
$251$	−0.670468	−	6.37908i	−0.0423196	−	0.402644i	−0.995092	−	0.0989575i	$-0.968449\pi$
$251$	−0.670468	−	6.37908i	−0.0423196	−	0.402644i	0.952772	−	0.303686i	$-0.0982174\pi$
$252$	−0.661956	−	2.03729i	−0.0416993	−	0.128337i
$253$	6.48528	+	11.2328i	0.407726	+	0.706202i
$254$	−1.84315	+	3.19242i	−0.115649	+	0.200310i
$255$	2.36146	+	0.501943i	0.147880	+	0.0314329i
$256$	1.22697	−	3.77623i	0.0766857	−	0.236014i
$257$	−21.8261	+	4.63928i	−1.36147	+	0.289390i	−0.830038	−	0.557707i	$-0.811681\pi$
$257$	−21.8261	+	4.63928i	−1.36147	+	0.289390i	−0.531437	+	0.847098i	$0.678348\pi$
$258$	0.195474	−	1.85981i	0.0121697	−	0.115787i
$259$	−0.277163	+	0.307821i	−0.0172221	+	0.0191270i
$260$	6.39482	−	2.84716i	0.396590	−	0.176573i
$261$	17.6440	+	7.85559i	1.09213	+	0.486249i
$262$	−3.67037	−	4.07636i	−0.226756	−	0.251838i
$263$	18.8612	−	13.7035i	1.16303	−	0.844991i	0.172872	−	0.984944i	$-0.444695\pi$
$263$	18.8612	−	13.7035i	1.16303	−	0.844991i	0.990158	+	0.139953i	$0.0446952\pi$
$264$	1.72316	−	1.25195i	0.106053	−	0.0770521i
$265$	3.89998	+	4.33137i	0.239574	+	0.266074i
$266$	−0.691882	−	0.308046i	−0.0424220	−	0.0188875i
$267$	1.69724	−	0.755662i	0.103870	−	0.0462457i
$268$	−3.96723	+	4.40606i	−0.242337	+	0.269143i
$269$	2.73567	−	26.0282i	0.166797	−	1.58697i	−0.516149	−	0.856499i	$-0.672635\pi$
$269$	2.73567	−	26.0282i	0.166797	−	1.58697i	0.682946	−	0.730469i	$-0.260698\pi$
$270$	0.978148	−	0.207912i	0.0595282	−	0.0126531i
$271$	−0.212076	+	0.652702i	−0.0128827	+	0.0396488i	−0.957291	−	0.289125i	$-0.906636\pi$
$271$	−0.212076	+	0.652702i	−0.0128827	+	0.0396488i	0.944409	+	0.328774i	$0.106636\pi$
$272$	17.1032	+	3.63539i	1.03703	+	0.220428i
$273$	−0.328427	+	0.568852i	−0.0198773	+	0.0344285i
$274$	−1.96447	−	3.40256i	−0.118678	−	0.205556i
$275$	−4.00812	−	12.3357i	−0.241699	−	0.743873i
$276$	−0.316662	−	3.01284i	−0.0190608	−	0.181352i
$277$	−11.4412	−	8.31254i	−0.687437	−	0.499452i	0.188380	−	0.982096i	$-0.439676\pi$
$277$	−11.4412	−	8.31254i	−0.687437	−	0.499452i	−0.875817	+	0.482644i	$0.839676\pi$
$278$		0			0
$279$		0			0
$280$	0.656854			0.0392545
$281$	−1.61803	−	1.17557i	−0.0965238	−	0.0701287i	0.538477	−	0.842641i	$-0.319000\pi$
$281$	−1.61803	−	1.17557i	−0.0965238	−	0.0701287i	−0.635000	+	0.772512i	$0.719000\pi$
$282$	−0.173188	−	1.64778i	−0.0103132	−	0.0981237i
$283$	−4.22020	−	12.9884i	−0.250865	−	0.772083i	−0.994616	−	0.103626i	$-0.966955\pi$
$283$	−4.22020	−	12.9884i	−0.250865	−	0.772083i	0.743751	−	0.668456i	$-0.233045\pi$
$284$	0.0649712	+	0.112533i	0.00385533	+	0.00667763i
$285$	−0.914214	+	1.58346i	−0.0541533	+	0.0937963i
$286$	5.02977	+	1.06911i	0.297416	+	0.0632178i
$287$	0.958109	−	2.94876i	0.0565554	−	0.174060i
$288$	12.2124	−	2.59584i	0.719625	−	0.152961i
$289$	−1.77391	+	16.8776i	−0.104347	+	0.992800i
$290$	−1.89259	+	2.10193i	−0.111137	+	0.123430i
$291$	1.95694	−	0.871285i	0.114718	−	0.0510756i
$292$	3.05412	+	1.35978i	0.178729	+	0.0795751i
$293$	9.90246	+	10.9978i	0.578508	+	0.642498i	0.959376	−	0.282131i	$-0.0910414\pi$
$293$	9.90246	+	10.9978i	0.578508	+	0.642498i	−0.380868	+	0.924629i	$0.624375\pi$
$294$	0.947822	−	0.688633i	0.0552781	−	0.0401619i
$295$	−3.29356	+	2.39291i	−0.191759	+	0.139321i
$296$	−1.06110	−	1.17847i	−0.0616751	−	0.0684971i
$297$	−7.15162	−	3.18411i	−0.414979	−	0.184761i
$298$	0.378403	−	0.168476i	0.0219203	−	0.00975954i
$299$	10.2469	−	11.3803i	0.592592	−	0.658140i
$300$	−0.316662	+	3.01284i	−0.0182825	+	0.173946i
$301$	−4.41606	+	0.938663i	−0.254538	+	0.0541036i
$302$	0.680150	−	2.09329i	0.0391382	−	0.120455i
$303$	3.43791	+	0.730751i	0.197503	+	0.0419806i
$304$	−6.62132	+	11.4685i	−0.379759	+	0.657761i
$305$	1.41421	+	2.44949i	0.0809776	+	0.140257i
$306$	2.11010	+	6.49422i	0.120626	+	0.371250i
$307$	1.17518	+	11.1811i	0.0670708	+	0.638136i	0.975485	+	0.220065i	$0.0706270\pi$
$307$	1.17518	+	11.1811i	0.0670708	+	0.638136i	−0.908414	+	0.418071i	$0.862706\pi$
$308$	−1.98682	−	1.44351i	−0.113210	−	0.0822516i
$309$	0.857864			0.0488022
$310$		0			0
$311$	11.3137			0.641542			0.320771	−	0.947157i	$-0.396058\pi$
$311$	11.3137			0.641542			0.320771	+	0.947157i	$0.396058\pi$
$312$	−2.03445	−	1.47811i	−0.115178	−	0.0836818i
$313$	0.191123	+	1.81841i	0.0108029	+	0.102783i	0.998595	−	0.0529975i	$-0.0168775\pi$
$313$	0.191123	+	1.81841i	0.0108029	+	0.102783i	−0.987792	+	0.155780i	$0.950211\pi$
$314$	1.17395	+	3.61305i	0.0662500	+	0.203896i
$315$	−0.585786	−	1.01461i	−0.0330053	−	0.0571669i
$316$	−6.17767	+	10.7000i	−0.347521	+	0.601924i
$317$	7.65736	+	1.62762i	0.430080	+	0.0914163i	0.417865	−	0.908509i	$-0.362778\pi$
$317$	7.65736	+	1.62762i	0.430080	+	0.0914163i	0.0122149	+	0.999925i	$0.496112\pi$
$318$	0.309017	−	0.951057i	0.0173288	−	0.0533326i
$319$	21.6583	−	4.60361i	1.21263	−	0.257753i
$320$	0.436048	−	4.14872i	0.0243758	−	0.231921i
$321$	3.44076	−	3.82135i	0.192045	−	0.213287i
$322$	0.626958	−	0.279140i	0.0349390	−	0.0155559i
$323$	−23.5036	−	10.4645i	−1.30778	−	0.582260i
$324$	−9.15792	−	10.1709i	−0.508773	−	0.565050i
$325$	−12.3891	+	9.00117i	−0.687221	+	0.499295i
$326$	−7.02736	+	5.10567i	−0.389209	+	0.282777i
$327$	−3.00124	−	3.33321i	−0.165969	−	0.184327i
$328$	10.8438	+	4.82799i	0.598751	+	0.266581i
$329$	−3.65418	+	1.62695i	−0.201462	+	0.0896965i
$330$	0.372270	−	0.413448i	0.0204928	−	0.0227596i
$331$	−0.966119	+	9.19201i	−0.0531027	+	0.505238i	0.935352	+	0.353719i	$0.115083\pi$
$331$	−0.966119	+	9.19201i	−0.0531027	+	0.505238i	−0.988454	+	0.151519i	$0.951583\pi$
$332$	−18.0118	+	3.82853i	−0.988527	+	0.210118i
$333$	−0.874032	+	2.68999i	−0.0478967	+	0.147411i
$334$	−9.13898	−	1.94255i	−0.500062	−	0.106292i
$335$	−1.62132	+	2.80821i	−0.0885822	+	0.153429i
$336$	0.257359	+	0.445759i	0.0140401	+	0.0243182i
$337$	2.87809	+	8.85786i	0.156780	+	0.482519i	0.998337	−	0.0576496i	$-0.0183606\pi$
$337$	2.87809	+	8.85786i	0.156780	+	0.482519i	−0.841557	+	0.540168i	$0.818361\pi$
$338$	−0.0717370	−	0.682532i	−0.00390198	−	0.0371248i
$339$	−5.58181	−	4.05542i	−0.303162	−	0.220260i
$340$	10.6569			0.577949
$341$		0			0
$342$	−5.17157			−0.279647
$343$	−4.63399	−	3.36679i	−0.250212	−	0.181789i
$344$	−1.80670	−	17.1896i	−0.0974106	−	0.926800i
$345$	−0.511996	−	1.57576i	−0.0275649	−	0.0848362i
$346$	−1.72183	−	2.98229i	−0.0925659	−	0.160329i
$347$	4.27817	−	7.41002i	0.229664	−	0.397790i	−0.728044	−	0.685530i	$-0.759570\pi$
$347$	4.27817	−	7.41002i	0.229664	−	0.397790i	0.957709	+	0.287740i	$0.0929038\pi$
$348$	−5.05856	−	1.07523i	−0.271167	−	0.0576384i
$349$	−8.37828	+	25.7857i	−0.448479	+	1.38028i	0.430143	+	0.902761i	$0.358463\pi$
$349$	−8.37828	+	25.7857i	−0.448479	+	1.38028i	−0.878623	+	0.477517i	$0.841537\pi$
$350$	−0.671294	+	0.142688i	−0.0358822	+	0.00762700i
$351$	−0.966119	+	9.19201i	−0.0515676	+	0.490633i
$352$	9.57774	−	10.6372i	0.510495	−	0.566962i
$353$	2.74064	−	1.22021i	0.145869	−	0.0649452i	−0.332504	−	0.943102i	$-0.607893\pi$
$353$	2.74064	−	1.22021i	0.145869	−	0.0649452i	0.478373	+	0.878157i	$0.341227\pi$
$354$	0.638098	+	0.284099i	0.0339145	+	0.0150997i
$355$	0.0475536	+	0.0528137i	0.00252389	+	0.00280306i
$356$	6.63476	−	4.82043i	0.351641	−	0.255482i
$357$	−0.809017	+	0.587785i	−0.0428177	+	0.0311089i
$358$	−4.22470	−	4.69200i	−0.223282	−	0.247980i
$359$	6.48663	+	2.88804i	0.342351	+	0.152425i	0.570708	−	0.821153i	$-0.306669\pi$
$359$	6.48663	+	2.88804i	0.342351	+	0.152425i	−0.228357	+	0.973577i	$0.573335\pi$
$360$	4.09751	−	1.82433i	0.215958	−	0.0961505i
$361$	0.324717	−	0.360634i	0.0170903	−	0.0189808i
$362$	−0.533148	+	5.07256i	−0.0280216	+	0.266608i
$363$	0.196618	−	0.0417924i	0.0103197	−	0.00219353i
$364$	−0.895993	+	2.75758i	−0.0469628	+	0.144537i
$365$	1.78847	+	0.380151i	0.0936129	+	0.0198980i
$366$	0.242641	−	0.420266i	0.0126830	−	0.0219677i
$367$	12.1066	+	20.9692i	0.631959	+	1.09459i	0.987151	+	0.159792i	$0.0510824\pi$
$367$	12.1066	+	20.9692i	0.631959	+	1.09459i	−0.355191	+	0.934794i	$0.615584\pi$
$368$	−3.70820	−	11.4127i	−0.193303	−	0.594927i
$369$	−2.21303	−	21.0556i	−0.115206	−	1.09611i
$370$	−0.335106	−	0.243469i	−0.0174213	−	0.0126573i
$371$	−2.41421			−0.125340
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	6.33333	+	4.60143i	0.327489	+	0.237934i
$375$	0.389674	+	3.70750i	0.0201227	+	0.191454i
$376$	−4.73220	−	14.5642i	−0.244044	−	0.751091i
$377$	−13.0711	−	22.6398i	−0.673194	−	1.16601i
$378$	−0.207107	+	0.358719i	−0.0106524	+	0.0184505i
$379$	−7.22340	−	1.53538i	−0.371041	−	0.0788672i	0.0186172	−	0.999827i	$-0.494074\pi$
$379$	−7.22340	−	1.53538i	−0.371041	−	0.0788672i	−0.389658	+	0.920959i	$0.627407\pi$
$380$	−2.49410	+	7.67604i	−0.127944	+	0.393773i
$381$	−3.60574	+	0.766423i	−0.184728	+	0.0392650i
$382$	0.904888	−	8.60943i	0.0462981	−	0.440497i
$383$	3.41290	−	3.79041i	0.174391	−	0.193681i	−0.649612	−	0.760266i	$-0.725069\pi$
$383$	3.41290	−	3.79041i	0.174391	−	0.193681i	0.824004	+	0.566584i	$0.191735\pi$
$384$	−3.99455	+	1.77849i	−0.203846	+	0.0907582i
$385$	−1.22702	−	0.546307i	−0.0625350	−	0.0278424i
$386$	1.97954	+	2.19850i	0.100756	+	0.111901i
$387$	−24.9407	+	18.1205i	−1.26781	+	0.921117i
$388$	7.64994	−	5.55801i	0.388367	−	0.282165i
$389$	−7.45554	−	8.28022i	−0.378011	−	0.419824i	0.523877	−	0.851794i	$-0.324485\pi$
$389$	−7.45554	−	8.28022i	−0.378011	−	0.419824i	−0.901888	+	0.431970i	$0.857819\pi$
$390$	−0.600066	−	0.267167i	−0.0303855	−	0.0135285i
$391$	21.2981	−	9.48254i	1.07709	−	0.479553i
$392$	7.24563	−	8.04709i	0.365960	−	0.406439i
$393$	0.573368	−	5.45523i	0.0289226	−	0.275180i
$394$	5.46372	−	1.16135i	0.275258	−	0.0585080i
$395$	−2.08814	+	6.42663i	−0.105066	+	0.323359i
$396$	−16.4031	−	3.48659i	−0.824287	−	0.175208i
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	−0.0493613	−	0.998781i	$-0.515719\pi$
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	0.889650	−	0.456642i	$-0.150948\pi$
$398$	−3.81371	−	6.60554i	−0.191164	−	0.331106i
$399$	−0.234037	−	0.720292i	−0.0117165	−	0.0360597i
$400$	1.25434	+	11.9343i	0.0627171	+	0.596713i
$401$	21.7047	+	15.7694i	1.08388	+	0.787484i	0.978355	−	0.206933i	$-0.0663482\pi$
$401$	21.7047	+	15.7694i	1.08388	+	0.787484i	0.105524	+	0.994417i	$0.466348\pi$
$402$	0.556349			0.0277482
$403$		0			0
$404$	15.5147			0.771886
$405$	−6.05572	−	4.39974i	−0.300911	−	0.218625i
$406$	−0.122463	−	1.16515i	−0.00607772	−	0.0578257i
$407$	1.00203	+	3.08393i	0.0496688	+	0.152865i
$408$	−1.91421	−	3.31552i	−0.0947677	−	0.164142i
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	0.489215	+	0.872163i	$0.337283\pi$
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	−0.999923	+	0.0124088i	$0.996050\pi$
$410$	3.03275	+	0.644631i	0.149777	+	0.0318361i
$411$	1.21411	−	3.73664i	0.0598875	−	0.184315i
$412$	3.70405	−	0.787319i	0.182485	−	0.0387884i
$413$	0.176265	−	1.67705i	0.00867346	−	0.0825224i
$414$	3.13574	−	3.48259i	0.154113	−	0.171160i
$415$	−9.20038	+	4.09627i	−0.451629	+	0.201078i
$416$	−15.4385	−	6.87364i	−0.756933	−	0.337008i
$417$		0			0
$418$	−4.79661	+	3.48494i	−0.234610	+	0.170454i
$419$	−22.6525	+	16.4580i	−1.10665	+	0.804025i	−0.982132	−	0.188193i	$-0.939737\pi$
$419$	−22.6525	+	16.4580i	−1.10665	+	0.804025i	−0.124514	+	0.992218i	$0.539737\pi$
$420$	0.209912	+	0.233131i	0.0102427	+	0.0113756i
$421$	−28.4498	−	12.6666i	−1.38656	−	0.617335i	−0.428402	−	0.903588i	$-0.640923\pi$
$421$	−28.4498	−	12.6666i	−1.38656	−	0.617335i	−0.958154	+	0.286253i	$0.907590\pi$
$422$	3.94077	−	1.75454i	0.191834	−	0.0854098i
$423$	−18.2764	+	20.2980i	−0.888631	+	0.986925i
$424$	0.966119	−	9.19201i	0.0469189	−	0.446403i
$425$	−22.8042	+	4.84719i	−1.10617	+	0.235123i
$426$	0.00376794	−	0.0115965i	0.000182557	−	0.000561854i
$427$	−1.14597	−	0.243584i	−0.0554574	−	0.0117878i
$428$	11.3492	−	19.6575i	0.548586	−	0.950179i
$429$	2.57107	+	4.45322i	0.124132	+	0.215003i
$430$	−1.39512	−	4.29375i	−0.0672789	−	0.207063i
$431$	1.75162	+	16.6656i	0.0843726	+	0.802752i	0.952116	+	0.305738i	$0.0989033\pi$
$431$	1.75162	+	16.6656i	0.0843726	+	0.802752i	−0.867743	+	0.497013i	$0.834430\pi$
$432$	5.85942	+	4.25712i	0.281911	+	0.204821i
$433$	27.1127			1.30295			0.651477	−	0.758669i	$-0.274150\pi$
$433$	27.1127			1.30295			0.651477	+	0.758669i	$0.274150\pi$
$434$		0			0
$435$	−2.82843			−0.135613
$436$	−16.0177	−	11.6376i	−0.767110	−	0.557338i
$437$	1.84564	+	17.5601i	0.0882891	+	0.840015i
$438$	−0.0969413	−	0.298355i	−0.00463203	−	0.0142559i
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	0.840255	−	0.542191i	$-0.182405\pi$
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	−0.889679	+	0.456587i	$0.849072\pi$
$440$	2.57107	−	4.45322i	0.122571	−	0.212299i
$441$	−18.8917	−	4.01555i	−0.899603	−	0.191216i
$442$	2.85613	−	8.79027i	0.135852	−	0.418111i
$443$	4.65340	−	0.989111i	0.221090	−	0.0469941i	−0.0960348	−	0.995378i	$-0.530616\pi$
$443$	4.65340	−	0.989111i	0.221090	−	0.0469941i	0.317125	+	0.948384i	$0.397283\pi$
$444$	0.0791656	−	0.753210i	0.00375703	−	0.0357458i
$445$	3.00124	−	3.33321i	0.142272	−	0.158009i
$446$	−8.97871	+	3.99758i	−0.425154	+	0.189291i
$447$	0.378403	+	0.168476i	0.0178978	+	0.00796863i
$448$	1.15621	+	1.28410i	0.0546256	+	0.0606678i
$449$	32.8683	−	23.8802i	1.55115	−	1.12698i	0.608324	−	0.793688i	$-0.291842\pi$
$449$	32.8683	−	23.8802i	1.55115	−	1.12698i	0.942825	−	0.333288i	$-0.108158\pi$
$450$	−3.79129	+	2.75453i	−0.178723	+	0.129850i
$451$	−16.2412	−	18.0377i	−0.764768	−	0.849361i
$452$	−27.8228	−	12.3875i	−1.30867	−	0.582659i
$453$	2.01072	−	0.895231i	0.0944720	−	0.0420616i
$454$	−5.10374	+	5.66828i	−0.239530	+	0.266025i
$455$	−0.165760	+	1.57710i	−0.00777094	+	0.0739356i
$456$	2.83613	−	0.602839i	0.132814	−	0.0282305i
$457$	−9.61435	+	29.5899i	−0.449740	+	1.38416i	0.427460	+	0.904034i	$0.359409\pi$
$457$	−9.61435	+	29.5899i	−0.449740	+	1.38416i	−0.877200	+	0.480124i	$0.840591\pi$
$458$	2.22243	+	0.472392i	0.103847	+	0.0220734i
$459$	−7.03553	+	12.1859i	−0.328391	+	0.568789i
$460$	−3.65685	−	6.33386i	−0.170502	−	0.295318i
$461$	−0.661956	−	2.03729i	−0.0308304	−	0.0948862i	0.934457	−	0.356075i	$-0.115885\pi$
$461$	−0.661956	−	2.03729i	−0.0308304	−	0.0948862i	−0.965288	+	0.261189i	$0.915885\pi$
$462$	0.0240883	+	0.229185i	0.00112069	+	0.0106626i
$463$	7.25734	+	5.27276i	0.337277	+	0.245046i	0.743512	−	0.668722i	$-0.233159\pi$
$463$	7.25734	+	5.27276i	0.337277	+	0.245046i	−0.406235	+	0.913769i	$0.633159\pi$
$464$	−20.4853			−0.951005
$465$		0			0
$466$	−3.79899			−0.175985
$467$	6.47214	+	4.70228i	0.299495	+	0.217596i	0.727376	−	0.686239i	$-0.240740\pi$
$467$	6.47214	+	4.70228i	0.299495	+	0.217596i	−0.427881	+	0.903835i	$0.640740\pi$
$468$	2.06956	+	19.6905i	0.0956654	+	0.910195i
$469$	−0.415055	−	1.27741i	−0.0191655	−	0.0589852i
$470$	−2.00000	−	3.46410i	−0.0922531	−	0.159787i
$471$	−1.89949	+	3.29002i	−0.0875241	+	0.151596i
$472$	6.31477	+	1.34225i	0.290661	+	0.0617819i
$473$	−10.9216	+	33.6133i	−0.502177	+	1.54554i
$474$	1.13404	−	0.241049i	0.0520884	−	0.0110717i
$475$	1.84564	−	17.5601i	0.0846839	−	0.805714i
$476$	−2.95369	+	3.28040i	−0.135382	+	0.150357i
$477$	−15.0601	+	6.70517i	−0.689552	+	0.307009i
$478$	−8.03828	−	3.57887i	−0.367662	−	0.163694i
$479$	−10.5240	−	11.6881i	−0.480855	−	0.534044i	0.453088	−	0.891466i	$-0.350322\pi$
$479$	−10.5240	−	11.6881i	−0.480855	−	0.534044i	−0.933943	+	0.357422i	$0.883656\pi$
$480$	−1.47923	+	1.07472i	−0.0675172	+	0.0490541i
$481$	3.09726	−	2.25029i	0.141223	−	0.102605i
$482$	3.69823	+	4.10730i	0.168450	+	0.187082i
$483$	0.626958	+	0.279140i	0.0285276	+	0.0127013i
$484$	0.810590	−	0.360898i	0.0368450	−	0.0164045i
$485$	3.46046	−	3.84323i	0.157131	−	0.174512i
$486$	−0.447828	+	4.26080i	−0.0203139	+	0.193274i
$487$	−18.9612	+	4.03032i	−0.859213	+	0.182631i	−0.616392	−	0.787440i	$-0.711406\pi$
$487$	−18.9612	+	4.03032i	−0.859213	+	0.182631i	−0.242821	+	0.970071i	$0.578073\pi$
$488$	1.38603	−	4.26576i	0.0627425	−	0.193102i
$489$	−8.49648	−	1.80598i	−0.384224	−	0.0816693i
$490$	1.41421	−	2.44949i	0.0638877	−	0.110657i
$491$	−0.792893	−	1.37333i	−0.0357828	−	0.0619776i	0.847579	−	0.530669i	$-0.178059\pi$
$491$	−0.792893	−	1.37333i	−0.0357828	−	0.0619776i	−0.883362	+	0.468691i	$0.844726\pi$
$492$	1.75183	+	5.39158i	0.0789787	+	0.243071i
$493$	−4.16013	−	39.5810i	−0.187363	−	1.78264i
$494$	5.66312	+	4.11450i	0.254796	+	0.185120i
$495$	−9.17157			−0.412232
$496$		0			0
$497$	−0.0294373			−0.00132044
$498$	1.39792	+	1.01565i	0.0626422	+	0.0455122i
$499$	0.231343	+	2.20108i	0.0103563	+	0.0985338i	0.998479	−	0.0551332i	$-0.0175583\pi$
$499$	0.231343	+	2.20108i	0.0103563	+	0.0985338i	−0.988123	+	0.153667i	$0.950892\pi$
$500$	5.08514	+	15.6504i	0.227414	+	0.699909i
$501$	−4.67157	−	8.09140i	−0.208710	−	0.361497i
$502$	−1.32843	+	2.30090i	−0.0592906	+	0.102694i
$503$	13.0923	+	2.78285i	0.583756	+	0.124081i	0.490318	−	0.871544i	$-0.336881\pi$
$503$	13.0923	+	2.78285i	0.583756	+	0.124081i	0.0934386	+	0.995625i	$0.470214\pi$
$504$	−0.574112	+	1.76693i	−0.0255730	+	0.0787055i
$505$	8.29986	−	1.76419i	0.369339	−	0.0785054i
$506$	0.561588	−	5.34315i	0.0249656	−	0.237532i
$507$	0.459219	−	0.510014i	0.0203946	−	0.0226505i
$508$	−14.8653	+	6.61845i	−0.659540	+	0.293646i
$509$	−29.9634	−	13.3406i	−1.32810	−	0.591310i	−0.384726	−	0.923031i	$-0.625704\pi$
$509$	−29.9634	−	13.3406i	−1.32810	−	0.591310i	−0.943377	+	0.331721i	$0.892371\pi$
$510$	−0.669131	−	0.743145i	−0.0296296	−	0.0329070i
$511$	−0.612717	+	0.445165i	−0.0271050	+	0.0196929i
$512$	−18.4111	+	13.3764i	−0.813663	+	0.591161i
$513$	−7.13083	−	7.91959i	−0.314834	−	0.349658i
$514$	8.44357	+	3.75932i	0.372430	+	0.165817i
$515$	1.89201	−	0.842379i	0.0833721	−	0.0371197i
$516$	5.52356	−	6.13454i	0.243161	−	0.270058i
$517$	−3.27317	+	31.1422i	−0.143954	+	1.36963i
$518$	0.167824	−	0.0356720i	0.00737375	−	0.00156734i
$519$	1.06415	−	3.27511i	0.0467109	−	0.143761i
$520$	−5.93840	−	1.26225i	−0.260416	−	0.0553531i
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	−0.550169	−	0.835054i	$-0.685437\pi$
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	0.998262	+	0.0589331i	$0.0187699\pi$
$522$	−4.00000	−	6.92820i	−0.175075	−	0.303239i
$523$	−2.47214	−	7.60845i	−0.108099	−	0.332694i	0.882346	−	0.470601i	$-0.155963\pi$
$523$	−2.47214	−	7.60845i	−0.108099	−	0.332694i	−0.990445	+	0.137906i	$0.955963\pi$
$524$	−2.53097	−	24.0806i	−0.110566	−	1.05196i
$525$	−0.555221	−	0.403392i	−0.0242319	−	0.0176055i
$526$	−9.65685			−0.421059
$527$		0			0
$528$	4.02944			0.175359
$529$	5.66312	+	4.11450i	0.246223	+	0.178891i
$530$	−0.252354	−	2.40099i	−0.0109616	−	0.104292i
$531$	−3.55824	−	10.9511i	−0.154415	−	0.475239i
$532$	−1.67157	−	2.89525i	−0.0724719	−	0.125525i
$533$	−14.3284	+	24.8176i	−0.620633	+	1.07497i
$534$	−0.752736	−	0.159999i	−0.0325741	−	0.00692383i
$535$	3.83620	−	11.8066i	0.165854	−	0.510445i
$536$	5.02977	−	1.06911i	0.217253	−	0.0461785i
$537$	0.659962	−	6.27912i	0.0284795	−	0.270964i
$538$	−7.25379	+	8.05615i	−0.312733	+	0.347325i
$539$	−20.2278	+	9.00602i	−0.871275	+	0.387917i
$540$	4.03258	+	1.79542i	0.173535	+	0.0772627i
$541$	−20.9333	−	23.2487i	−0.899991	−	0.999542i	−0.999990	−	0.00455398i	$-0.998550\pi$
$541$	−20.9333	−	23.2487i	−0.899991	−	0.999542i	0.0999983	−	0.994988i	$-0.468116\pi$
$542$	0.229980	−	0.167090i	0.00987850	−	0.00717715i
$543$	−4.12640	+	2.99800i	−0.177081	+	0.128657i
$544$	−17.2153	−	19.1196i	−0.738102	−	0.819745i
$545$	−9.89226	−	4.40432i	−0.423738	−	0.188660i
$546$	0.248556	−	0.110664i	0.0106372	−	0.00473598i
$547$	−13.2006	+	14.6607i	−0.564415	+	0.626846i	−0.956025	−	0.293285i	$-0.905252\pi$
$547$	−13.2006	+	14.6607i	−0.564415	+	0.626846i	0.391610	+	0.920131i	$0.371918\pi$
$548$	1.81285	−	17.2481i	0.0774412	−	0.736804i
$549$	−7.82518	+	1.66329i	−0.333971	+	0.0709876i
$550$	−1.66022	+	5.10963i	−0.0707920	+	0.217875i
$551$	29.4835	+	6.26690i	1.25604	+	0.266979i
$552$	−1.31371	+	2.27541i	−0.0559151	+	0.0968479i
$553$	−1.39949	−	2.42400i	−0.0595126	−	0.103079i
$554$	1.81018	+	5.57116i	0.0769072	+	0.236696i
$555$	−0.0432971	−	0.411944i	−0.00183786	−	0.0174861i
$556$		0			0
$557$	27.5147			1.16584			0.582918	−	0.812531i	$-0.301911\pi$
$557$	27.5147			1.16584			0.582918	+	0.812531i	$0.301911\pi$
$558$		0			0
$559$	41.7279			1.76490
$560$	1.00532	+	0.730406i	0.0424824	+	0.0308653i
$561$	0.818293	+	7.78554i	0.0345484	+	0.328706i
$562$	0.255998	+	0.787881i	0.0107986	+	0.0332348i
$563$	−6.62132	−	11.4685i	−0.279055	−	0.483338i	0.692095	−	0.721807i	$-0.256688\pi$
$563$	−6.62132	−	11.4685i	−0.279055	−	0.483338i	−0.971150	+	0.238468i	$0.923355\pi$
$564$	3.65685	−	6.33386i	0.153981	−	0.266704i
$565$	−16.2929	−	3.46315i	−0.685446	−	0.145696i
$566$	−1.74806	+	5.37999i	−0.0734766	+	0.226138i
$567$	3.03275	−	0.644631i	0.127364	−	0.0270720i
$568$	0.0117802	−	0.112081i	0.000494286	−	0.00470281i
$569$	−8.79381	+	9.76651i	−0.368655	+	0.409433i	−0.898719	−	0.438524i	$-0.855501\pi$
$569$	−8.79381	+	9.76651i	−0.368655	+	0.409433i	0.530064	+	0.847958i	$0.322168\pi$
$570$	0.691882	−	0.308046i	0.0289798	−	0.0129026i
$571$	−19.2763	−	8.58235i	−0.806687	−	0.359160i	−0.0383972	−	0.999263i	$-0.512225\pi$
$571$	−19.2763	−	8.58235i	−0.806687	−	0.359160i	−0.768290	+	0.640102i	$0.778892\pi$
$572$	15.1883	+	16.8683i	0.635053	+	0.705297i
$573$	7.00354	−	5.08837i	0.292577	−	0.212570i
$574$	−1.03900	+	0.754876i	−0.0433669	+	0.0315079i
$575$	10.7061	+	11.8903i	0.446475	+	0.495861i
$576$	10.7789	+	4.79908i	0.449121	+	0.199962i
$577$	−0.0268923	+	0.0119732i	−0.00111954	+	0.000498451i	−0.407296	−	0.913296i	$-0.633528\pi$
$577$	−0.0268923	+	0.0119732i	−0.00111954	+	0.000498451i	0.406177	+	0.913795i	$0.366862\pi$
$578$	4.70361	−	5.22389i	0.195644	−	0.217285i
$579$	−0.309234	+	2.94216i	−0.0128513	+	0.122272i
$580$	−12.2124	+	2.59584i	−0.507094	+	0.107786i
$581$	1.28909	−	3.96740i	0.0534803	−	0.164596i
$582$	−0.867912	−	0.184480i	−0.0359761	−	0.00764696i
$583$	−9.44975	+	16.3674i	−0.391369	+	0.677870i
$584$	−1.44975	−	2.51104i	−0.0599910	−	0.103907i
$585$	3.34617	+	10.2984i	0.138347	+	0.425788i
$586$	−0.640753	−	6.09636i	−0.0264693	−	0.251838i
$587$	25.6109	+	18.6074i	1.05708	+	0.768011i	0.973545	−	0.228494i	$-0.0733802\pi$
$587$	25.6109	+	18.6074i	1.05708	+	0.768011i	0.0835311	+	0.996505i	$0.473380\pi$
$588$	5.17157			0.213272
$589$		0			0
$590$	1.68629			0.0694235
$591$	4.51900	+	3.28324i	0.185887	+	0.135055i
$592$	−0.313585	−	2.98357i	−0.0128883	−	0.122624i
$593$	−0.405958	−	1.24941i	−0.0166707	−	0.0513072i	0.942375	−	0.334558i	$-0.108587\pi$
$593$	−0.405958	−	1.24941i	−0.0166707	−	0.0513072i	−0.959046	+	0.283251i	$0.908587\pi$
$594$	1.62132	+	2.80821i	0.0665236	+	0.115222i
$595$	−1.20711	+	2.09077i	−0.0494866	+	0.0857132i
$596$	1.78847	+	0.380151i	0.0732587	+	0.0155716i
$597$	2.35700	−	7.25410i	0.0964656	−	0.296891i
$598$	−6.20453	+	1.31881i	−0.253722	+	0.0539303i
$599$	−1.57843	+	15.0178i	−0.0644930	+	0.613610i	0.913769	+	0.406235i	$0.133159\pi$
$599$	−1.57843	+	15.0178i	−0.0644930	+	0.613610i	−0.978262	+	0.207375i	$0.933508\pi$
$600$	1.75809	−	1.95255i	0.0717735	−	0.0797126i
$601$	−5.95149	+	2.64977i	−0.242766	+	0.108087i	−0.524513	−	0.851402i	$-0.675753\pi$
$601$	−5.95149	+	2.64977i	−0.242766	+	0.108087i	0.281747	+	0.959489i	$0.409086\pi$
$602$	1.70838	+	0.760621i	0.0696285	+	0.0310006i
$603$	−6.13698	−	6.81581i	−0.249917	−	0.277561i
$604$	7.86019	−	5.71076i	0.319827	−	0.232368i
$605$	0.392601	−	0.285241i	0.0159615	−	0.0115967i
$606$	−0.974150	−	1.08190i	−0.0395721	−	0.0439493i
$607$	−1.44869	−	0.644997i	−0.0588004	−	0.0261796i	0.377126	−	0.926162i	$-0.376912\pi$
$607$	−1.44869	−	0.644997i	−0.0588004	−	0.0261796i	−0.435926	+	0.899982i	$0.643579\pi$
$608$	17.8007	−	7.92538i	0.721913	−	0.321417i
$609$	0.783935	−	0.870648i	0.0317667	−	0.0352805i
$610$	0.122463	−	1.16515i	0.00495837	−	0.0471757i
$611$	36.1627	−	7.68661i	1.46298	−	0.310967i
$612$	−9.31443	+	28.6669i	−0.376514	+	1.15879i
$613$	−12.0446	−	2.56016i	−0.486478	−	0.103404i	−0.0418582	−	0.999124i	$-0.513328\pi$
$613$	−12.0446	−	2.56016i	−0.486478	−	0.103404i	−0.444620	+	0.895720i	$0.646661\pi$
$614$	2.32843	−	4.03295i	0.0939677	−	0.162757i
$615$	1.55025	+	2.68512i	0.0625122	+	0.108274i
$616$	0.658188	+	2.02570i	0.0265192	+	0.0816176i
$617$	3.47915	+	33.1019i	0.140065	+	1.33263i	0.808339	+	0.588718i	$0.200367\pi$
$617$	3.47915	+	33.1019i	0.140065	+	1.33263i	−0.668273	+	0.743916i	$0.732966\pi$
$618$	−0.287475	−	0.208863i	−0.0115640	−	0.00840170i
$619$	−20.3431			−0.817660			−0.408830	−	0.912611i	$-0.634063\pi$
$619$	−20.3431			−0.817660			−0.408830	+	0.912611i	$0.634063\pi$
$620$		0			0
$621$	9.65685			0.387516
$622$	−3.79129	−	2.75453i	−0.152017	−	0.110447i
$623$	0.194200	+	1.84769i	0.00778045	+	0.0740260i
$624$	−1.47010	−	4.52452i	−0.0588513	−	0.181126i
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	0.378680	−	0.655892i	0.0151351	−	0.0262147i
$627$	−5.79937	−	1.23269i	−0.231605	−	0.0492291i
$628$	−5.18208	+	15.9488i	−0.206787	+	0.636426i
$629$	5.70106	−	1.21180i	0.227316	−	0.0483176i
$630$	−0.0507257	+	0.482623i	−0.00202096	+	0.0192282i
$631$	33.4647	−	37.1663i	1.33221	−	1.47957i	0.595503	−	0.803353i	$-0.296953\pi$
$631$	33.4647	−	37.1663i	1.33221	−	1.47957i	0.736705	−	0.676214i	$-0.236381\pi$
$632$	9.78931	−	4.35848i	0.389398	−	0.173371i
$633$	3.94077	+	1.75454i	0.156631	+	0.0697368i
$634$	−2.16975	−	2.40975i	−0.0861718	−	0.0957035i
$635$	−7.19984	+	5.23099i	−0.285717	+	0.207586i
$636$	3.57117	−	2.59461i	0.141606	−	0.102883i
$637$	17.4925	+	19.4274i	0.693078	+	0.769741i
$638$	−8.37865	−	3.73041i	−0.331714	−	0.147689i
$639$	−0.183632	+	0.0817582i	−0.00726437	+	0.00323430i
$640$	−7.06358	+	7.84490i	−0.279212	+	0.310097i
$641$	1.46032	−	13.8940i	0.0576792	−	0.548781i	−0.927081	−	0.374862i	$-0.877690\pi$
$641$	1.46032	−	13.8940i	0.0576792	−	0.548781i	0.984760	−	0.173919i	$-0.0556432\pi$
$642$	−2.08340	+	0.442840i	−0.0822252	+	0.0174775i
$643$	10.9125	−	33.5853i	0.430348	−	1.32448i	−0.467430	−	0.884030i	$-0.654820\pi$
$643$	10.9125	−	33.5853i	0.430348	−	1.32448i	0.897779	−	0.440446i	$-0.145180\pi$
$644$	2.96324	+	0.629855i	0.116768	+	0.0248198i
$645$	2.25736	−	3.90986i	0.0888834	−	0.153951i
$646$	5.32843	+	9.22911i	0.209644	+	0.363114i
$647$	−14.0027	−	43.0959i	−0.550503	−	1.69427i	−0.707533	−	0.706681i	$-0.750192\pi$
$647$	−14.0027	−	43.0959i	−0.550503	−	1.69427i	0.157029	−	0.987594i	$-0.449808\pi$
$648$	1.24076	+	11.8050i	0.0487416	+	0.463745i
$649$	−10.6798	−	7.75936i	−0.419220	−	0.304581i
$650$	6.34315			0.248799
$651$		0			0
$652$	−38.3431			−1.50163
$653$	4.96909	+	3.61026i	0.194456	+	0.141280i	0.680753	−	0.732513i	$-0.261653\pi$
$653$	4.96909	+	3.61026i	0.194456	+	0.141280i	−0.486297	+	0.873793i	$0.661653\pi$
$654$	0.194200	+	1.84769i	0.00759381	+	0.0722503i
$655$	−4.09220	−	12.5945i	−0.159896	−	0.492108i
$656$	11.2279	+	19.4473i	0.438377	+	0.759291i
$657$	−2.58579	+	4.47871i	−0.100881	+	0.174731i
$658$	1.62065	+	0.344479i	0.0631794	+	0.0134292i
$659$	−0.511996	+	1.57576i	−0.0199445	+	0.0613830i	−0.960533	−	0.278165i	$-0.910274\pi$
$659$	−0.511996	+	1.57576i	−0.0199445	+	0.0613830i	0.940589	+	0.339548i	$0.110274\pi$
$660$	2.40218	−	0.510599i	0.0935047	−	0.0198750i
$661$	−0.507785	+	4.83125i	−0.0197506	+	0.187914i	−0.999949	−	0.0101040i	$-0.996784\pi$
$661$	−0.507785	+	4.83125i	−0.0197506	+	0.187914i	0.980198	+	0.198018i	$0.0634504\pi$
$662$	2.56172	−	2.84508i	0.0995640	−	0.110577i
$663$	8.44357	−	3.75932i	0.327921	−	0.146000i
$664$	14.5898	+	6.49581i	0.566195	+	0.252086i
$665$	−1.22346	−	1.35879i	−0.0474436	−	0.0526915i
$666$	0.947822	−	0.688633i	0.0367274	−	0.0266840i
$667$	−22.0973	+	16.0546i	−0.855609	+	0.621636i
$668$	−27.5967	−	30.6493i	−1.06775	−	1.18586i
$669$	−8.97871	−	3.99758i	−0.347137	−	0.154555i
$670$	1.22702	−	0.546307i	0.0474041	−	0.0211057i
$671$	−6.13698	+	6.81581i	−0.236915	+	0.263121i
$672$	0.0791656	−	0.753210i	0.00305388	−	0.0290557i
$673$	−9.13898	+	1.94255i	−0.352282	+	0.0748798i	−0.380654	−	0.924718i	$-0.624301\pi$
$673$	−9.13898	+	1.94255i	−0.352282	+	0.0748798i	0.0283721	+	0.999597i	$0.490968\pi$
$674$	1.19215	−	3.66905i	0.0459197	−	0.141326i
$675$	−9.44583	−	2.00777i	−0.363570	−	0.0772792i
$676$	1.51472	−	2.62357i	0.0582584	−	0.100907i
$677$	19.2990	+	33.4268i	0.741720	+	1.28470i	0.951711	+	0.306994i	$0.0993232\pi$
$677$	19.2990	+	33.4268i	0.741720	+	1.28470i	−0.209991	+	0.977703i	$0.567343\pi$
$678$	0.883129	+	2.71799i	0.0339164	+	0.104384i
$679$	0.223914	+	2.13040i	0.00859304	+	0.0817573i
$680$	−7.47745	−	5.43269i	−0.286747	−	0.208334i
$681$	−7.62742			−0.292283
$682$		0			0
$683$	−1.37258			−0.0525204			−0.0262602	−	0.999655i	$-0.508360\pi$
$683$	−1.37258			−0.0525204			−0.0262602	+	0.999655i	$0.508360\pi$
$684$	−18.4686	−	13.4182i	−0.706164	−	0.513058i
$685$	−0.991482	−	9.43332i	−0.0378826	−	0.360429i
$686$	0.733168	+	2.25646i	0.0279925	+	0.0861521i
$687$	1.13604	+	1.96768i	0.0433426	+	0.0750716i
$688$	16.3492	−	28.3177i	0.623309	−	1.07960i
$689$	21.8261	+	4.63928i	0.831508	+	0.176743i
$690$	−0.212076	+	0.652702i	−0.00807359	+	0.0248479i
$691$	0.0695148	−	0.0147758i	0.00264447	−	0.000562099i	−0.206589	−	0.978428i	$-0.566236\pi$
$691$	0.0695148	−	0.0147758i	0.00264447	−	0.000562099i	0.209234	+	0.977866i	$0.432903\pi$
$692$	1.58894	−	15.1177i	0.0604024	−	0.574690i
$693$	2.54202	−	2.82320i	0.0965634	−	0.107244i
$694$	−3.23775	+	1.44154i	−0.122903	+	0.0547200i
$695$		0			0
$696$	3.00124	+	3.33321i	0.113762	+	0.126345i
$697$	−35.2953	+	25.6436i	−1.33691	+	0.971319i
$698$	9.08562	−	6.60109i	0.343896	−	0.249855i
$699$	−2.54202	−	2.82320i	−0.0961480	−	0.106783i
$700$	−2.76753	−	1.23218i	−0.104603	−	0.0465721i
$701$	−12.3194	+	5.48496i	−0.465298	+	0.207164i	−0.625975	−	0.779843i	$-0.715299\pi$
$701$	−12.3194	+	5.48496i	−0.465298	+	0.207164i	0.160677	+	0.987007i	$0.448632\pi$
$702$	2.56172	−	2.84508i	0.0966858	−	0.107380i
$703$	−0.461411	+	4.39003i	−0.0174024	+	0.165573i
$704$	13.2313	−	2.81240i	0.498674	−	0.105996i
$705$	1.23607	−	3.80423i	0.0465530	−	0.143275i
$706$	−1.21549	−	0.258360i	−0.0457454	−	0.00972349i
$707$	−1.75736	+	3.04384i	−0.0660923	+	0.114475i
$708$	1.54163	+	2.67018i	0.0579380	+	0.100352i
$709$	5.35023	+	16.4663i	0.200932	+	0.618405i	0.999856	+	0.0169732i	$0.00540301\pi$
$709$	5.35023	+	16.4663i	0.200932	+	0.618405i	−0.798924	+	0.601432i	$0.794597\pi$
$710$	−0.00307703	−	0.0292760i	−0.000115479	−	0.00109871i
$711$	−15.4625	−	11.2342i	−0.579889	−	0.421314i
$712$	−7.11270			−0.266560
$713$		0			0
$714$	0.414214			0.0155016
$715$	10.0433	+	7.29689i	0.375598	+	0.272888i
$716$	−2.91321	−	27.7174i	−0.108872	−	1.03585i
$717$	−2.71904	−	8.36834i	−0.101544	−	0.312521i
$718$	−1.47056	−	2.54709i	−0.0548809	−	0.0950565i
$719$	4.03553	−	6.98975i	0.150500	−	0.260674i	−0.780911	−	0.624642i	$-0.785245\pi$
$719$	4.03553	−	6.98975i	0.150500	−	0.260674i	0.931411	+	0.363968i	$0.118578\pi$
$720$	8.29986	+	1.76419i	0.309317	+	0.0657474i
$721$	−0.265095	+	0.815878i	−0.00987264	+	0.0303849i
$722$	−0.196618	+	0.0417924i	−0.00731735	+	0.00155535i
$723$	−0.577720	+	5.49663i	−0.0214856	+	0.204422i
$724$	−15.0653	+	16.7317i	−0.559897	+	0.621829i
$725$	24.9523	−	11.1095i	0.926706	−	0.412596i
$726$	−0.0760628	−	0.0338653i	−0.00282296	−	0.00125686i
$727$	27.3277	+	30.3505i	1.01353	+	1.12564i	0.992047	+	0.125868i	$0.0401717\pi$
$727$	27.3277	+	30.3505i	1.01353	+	1.12564i	0.0214817	+	0.999769i	$0.493162\pi$
$728$	2.03445	−	1.47811i	0.0754017	−	0.0547826i
$729$	14.7011	−	10.6810i	0.544486	−	0.395592i
$730$	−0.506772	−	0.562828i	−0.0187565	−	0.0208312i
$731$	58.0347	+	25.8387i	2.14649	+	0.955680i
$732$	1.95694	−	0.871285i	0.0723305	−	0.0322036i
$733$	10.4568	−	11.6134i	0.386230	−	0.428952i	−0.518407	−	0.855134i	$-0.673475\pi$
$733$	10.4568	−	11.6134i	0.386230	−	0.428952i	0.904638	+	0.426182i	$0.140142\pi$
$734$	1.04836	−	9.97449i	0.0386957	−	0.368165i
$735$	2.76662	−	0.588063i	0.102048	−	0.0216910i
$736$	−5.45627	+	16.7927i	−0.201121	+	0.618986i
$737$	−10.2849	−	2.18613i	−0.378851	−	0.0805272i
$738$	−4.38478	+	7.59466i	−0.161406	+	0.279563i
$739$	−22.9350	−	39.7246i	−0.843679	−	1.46129i	−0.886764	−	0.462223i	$-0.847052\pi$
$739$	−22.9350	−	39.7246i	−0.843679	−	1.46129i	0.0430851	−	0.999071i	$-0.486281\pi$
$740$	−0.565015	−	1.73894i	−0.0207704	−	0.0639246i
$741$	0.731699	+	6.96165i	0.0268796	+	0.255743i
$742$	0.809017	+	0.587785i	0.0296999	+	0.0215783i
$743$	5.65685			0.207530			0.103765	−	0.994602i	$-0.466911\pi$
$743$	5.65685			0.207530			0.103765	+	0.994602i	$0.466911\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	−3.35106	−	2.43469i	−0.122691	−	0.0891402i
$747$	−2.97752	−	28.3292i	−0.108942	−	1.03651i
$748$	10.6785	+	32.8650i	0.390445	+	1.20166i
$749$	2.57107	+	4.45322i	0.0939448	+	0.162717i
$750$	0.772078	−	1.33728i	0.0281923	−	0.0488305i
$751$	−7.08437	−	1.50583i	−0.258512	−	0.0549485i	0.0768322	−	0.997044i	$-0.475519\pi$
$751$	−7.08437	−	1.50583i	−0.258512	−	0.0549485i	−0.335345	+	0.942096i	$0.608853\pi$
$752$	8.95240	−	27.5526i	0.326460	−	1.00474i
$753$	−2.59880	+	0.552391i	−0.0947054	+	0.0201302i
$754$	−1.13188	+	10.7691i	−0.0412206	+	0.392188i
$755$	3.55556	−	3.94885i	0.129400	−	0.143714i
$756$	−1.67035	+	0.743688i	−0.0607501	+	0.0270477i
$757$	21.3250	+	9.49451i	0.775071	+	0.345084i	0.755862	−	0.654732i	$-0.227218\pi$
$757$	21.3250	+	9.49451i	0.775071	+	0.345084i	0.0192097	+	0.999815i	$0.493885\pi$
$758$	2.04679	+	2.27319i	0.0743426	+	0.0825659i
$759$	4.34651	−	3.15793i	0.157768	−	0.114625i
$760$	5.66312	−	4.11450i	0.205423	−	0.149248i
$761$	20.3789	+	22.6331i	0.738736	+	0.820449i	0.989029	−	0.147721i	$-0.0471937\pi$
$761$	20.3789	+	22.6331i	0.738736	+	0.820449i	−0.250293	+	0.968170i	$0.580527\pi$
$762$	1.39490	+	0.621051i	0.0505320	+	0.0224983i
$763$	4.09751	−	1.82433i	0.148340	−	0.0660451i
$764$	25.5696	−	28.3979i	0.925077	−	1.02740i
$765$	−1.72318	+	16.3950i	−0.0623017	+	0.592762i
$766$	−2.06653	+	0.439255i	−0.0746668	+	0.0158709i
$767$	−4.81627	+	14.8230i	−0.173906	+	0.535226i
$768$	−1.60872	−	0.341944i	−0.0580497	−	0.0123388i
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	0.331721	+	0.943378i	$0.392371\pi$
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	−0.982849	+	0.184410i	$0.940963\pi$
$770$	0.278175	+	0.481813i	0.0100247	+	0.0173633i
$771$	2.85613	+	8.79027i	0.102861	+	0.316574i
$772$	1.36502	+	12.9873i	0.0491283	+	0.467424i
$773$	−14.5623	−	10.5801i	−0.523770	−	0.380541i	0.294252	−	0.955728i	$-0.404929\pi$
$773$	−14.5623	−	10.5801i	−0.523770	−	0.380541i	−0.818022	+	0.575187i	$0.804929\pi$
$774$	12.7696			0.458992
$775$		0			0
$776$	−8.20101			−0.294399
$777$	0.138805	+	0.100848i	0.00497961	+	0.00361790i
$778$	0.482422	+	4.58994i	0.0172957	+	0.164557i
$779$	−10.2104	−	31.4245i	−0.365826	−	1.12590i
$780$	−1.44975	−	2.51104i	−0.0519093	−	0.0899095i
$781$	−0.115224	+	0.199573i	−0.00412303	+	0.00714129i
$782$	−9.44583	−	2.00777i	−0.337782	−	0.0717978i
$783$	5.09423	−	15.6784i	0.182053	−	0.560302i
$784$	20.0376	−	4.25913i	0.715630	−	0.152112i
$785$	−0.958690	+	9.12133i	−0.0342171	+	0.325554i
$786$	−1.52032	+	1.68848i	−0.0542279	+	0.0602262i
$787$	38.7473	−	17.2514i	1.38119	−	0.614947i	0.424335	−	0.905505i	$-0.360508\pi$
$787$	38.7473	−	17.2514i	1.38119	−	0.614947i	0.956857	+	0.290559i	$0.0938411\pi$
$788$	22.5252	+	10.0288i	0.802426	+	0.357263i
$789$	−6.46170	−	7.17644i	−0.230042	−	0.255488i
$790$	2.26443	−	1.64520i	0.0805648	−	0.0585338i
$791$	5.58181	−	4.05542i	0.198466	−	0.144194i
$792$	9.73194	+	10.8084i	0.345809	+	0.384060i
$793$	9.89226	+	4.40432i	0.351284	+	0.156402i
$794$	−12.6709	+	5.64146i	−0.449674	+	0.200208i
$795$	1.61542	−	1.79411i	0.0572932	−	0.0636305i
$796$	3.51937	−	33.4846i	0.124741	−	1.18683i
$797$	−27.8340	+	5.91630i	−0.985931	+	0.209566i	−0.672542	−	0.740059i	$-0.734798\pi$
$797$	−27.8340	+	5.91630i	−0.985931	+	0.209566i	−0.313389	+	0.949625i	$0.601464\pi$
$798$	−0.0969413	+	0.298355i	−0.00343168	+	0.0105616i
$799$	55.0543	+	11.7022i	1.94768	+	0.413993i
$800$	8.82843	−	15.2913i	0.312132	−	0.540629i
$801$	6.34315	+	10.9867i	0.224124	+	0.388194i
$802$	−3.43401	−	10.5688i	−0.121259	−	0.373197i
$803$	0.619742	+	5.89645i	0.0218702	+	0.208081i
$804$	1.98682	+	1.44351i	0.0700697	+	0.0509086i
$805$	1.65685			0.0583964
$806$		0			0
$807$	−10.8406			−0.381608
$808$	−10.8860	−	7.90915i	−0.382968	−	0.278243i
$809$	1.25742	+	11.9635i	0.0442085	+	0.420616i	0.994135	+	0.108143i	$0.0344905\pi$
$809$	1.25742	+	11.9635i	0.0442085	+	0.420616i	−0.949927	+	0.312472i	$0.898843\pi$
$810$	0.958109	+	2.94876i	0.0336645	+	0.103609i
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	0.961007	−	0.276524i	$-0.0891827\pi$
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	−0.719981	+	0.693994i	$0.755849\pi$
$812$	2.58579	−	4.47871i	0.0907433	−	0.157172i
$813$	0.278059	+	0.0591033i	0.00975196	+	0.00207284i
$814$	0.415055	−	1.27741i	0.0145477	−	0.0447731i
$815$	−20.5123	+	4.36003i	−0.718515	+	0.152725i
$816$	0.757062	−	7.20296i	0.0265025	−	0.252154i
$817$	−32.1937	+	35.7547i	−1.12631	+	1.25090i
$818$	7.81661	−	3.48018i	0.273301	−	0.121682i
$819$	−4.09751	−	1.82433i	−0.143179	−	0.0637472i
$820$	9.15792	+	10.1709i	0.319808	+	0.355183i
$821$	−6.86474	+	4.98752i	−0.239581	+	0.174066i	−0.701097	−	0.713066i	$-0.747306\pi$
$821$	−6.86474	+	4.98752i	−0.239581	+	0.174066i	0.461516	+	0.887132i	$0.347306\pi$
$822$	−1.31661	+	0.956572i	−0.0459220	+	0.0333643i
$823$	24.2314	+	26.9117i	0.844652	+	0.938081i	0.998751	−	0.0499742i	$-0.0159139\pi$
$823$	24.2314	+	26.9117i	0.844652	+	0.938081i	−0.154098	+	0.988056i	$0.549247\pi$
$824$	−3.00033	−	1.33583i	−0.104521	−	0.0465360i
$825$	−4.90810	+	2.18523i	−0.170878	+	0.0760798i
$826$	−0.467378	+	0.519075i	−0.0162621	+	0.0180609i
$827$	−3.85705	+	36.6974i	−0.134123	+	1.27609i	0.695809	+	0.718227i	$0.255046\pi$
$827$	−3.85705	+	36.6974i	−0.134123	+	1.27609i	−0.829932	+	0.557865i	$0.811621\pi$
$828$	20.2342	−	4.30092i	0.703189	−	0.149467i
$829$	11.8744	−	36.5457i	0.412415	−	1.26928i	−0.502127	−	0.864794i	$-0.667449\pi$
$829$	11.8744	−	36.5457i	0.412415	−	1.26928i	0.914542	−	0.404490i	$-0.132551\pi$
$830$	4.08041	+	0.867319i	0.141633	+	0.0301051i
$831$	−2.92893	+	5.07306i	−0.101604	+	0.175982i
$832$	−7.98528	−	13.8309i	−0.276840	−	0.479501i
$833$	12.2986	+	37.8511i	0.426120	+	1.31146i
$834$		0			0
$835$	−18.2485	−	13.2583i	−0.631514	−	0.458822i
$836$	−26.1716			−0.905163
$837$		0			0
$838$	11.5980			0.400646
$839$	11.8338	+	8.59778i	0.408549	+	0.296828i	0.773014	−	0.634389i	$-0.218748\pi$
$839$	11.8338	+	8.59778i	0.408549	+	0.296828i	−0.364465	+	0.931217i	$0.618748\pi$
$840$	−0.0284399	−	0.270587i	−0.000981269	−	0.00933615i
$841$	5.44717	+	16.7647i	0.187833	+	0.578092i
$842$	6.44975	+	11.1713i	0.222273	+	0.384988i
$843$	−0.414214	+	0.717439i	−0.0142663	+	0.0247099i
$844$	18.6255	+	3.95898i	0.641117	+	0.136274i
$845$	0.511996	−	1.57576i	0.0176132	−	0.0542079i
$846$	11.0665	−	2.35225i	0.380473	−	0.0808721i
$847$	−0.0210113	+	0.199909i	−0.000721956	+	0.00686895i
$848$	11.6999	−	12.9941i	0.401777	−	0.446219i
$849$	−5.16779	+	2.30085i	−0.177358	+	0.0789650i
$850$	8.82198	+	3.92780i	0.302591	+	0.134722i
$851$	−2.67652	−	2.97258i	−0.0917500	−	0.101899i
$852$	0.0435444	−	0.0316369i	0.00149181	−	0.00108386i
$853$	12.5517	−	9.11932i	0.429761	−	0.312240i	−0.351792	−	0.936078i	$-0.614428\pi$
$853$	12.5517	−	9.11932i	0.429761	−	0.312240i	0.781553	+	0.623838i	$0.214428\pi$
$854$	0.324717	+	0.360634i	0.0111116	+	0.0123407i
$855$	−11.4059	−	5.07822i	−0.390073	−	0.173672i
$856$	−17.9843	+	8.00714i	−0.614691	+	0.273678i
$857$	−13.0382	+	14.4804i	−0.445376	+	0.494641i	−0.923471	−	0.383668i	$-0.874661\pi$
$857$	−13.0382	+	14.4804i	−0.445376	+	0.494641i	0.478095	+	0.878308i	$0.341328\pi$
$858$	0.222640	−	2.11827i	0.00760079	−	0.0723167i
$859$	48.3056	−	10.2677i	1.64817	−	0.350328i	0.712079	−	0.702099i	$-0.247754\pi$
$859$	48.3056	−	10.2677i	1.64817	−	0.350328i	0.936086	+	0.351770i	$0.114420\pi$
$860$	6.15838	−	18.9535i	0.209999	−	0.646310i
$861$	−1.25621	−	0.267015i	−0.0428114	−	0.00909985i
$862$	3.47056	−	6.01119i	0.118208	−	0.204742i
$863$	1.30761	+	2.26485i	0.0445116	+	0.0770964i	0.887423	−	0.460956i	$-0.152493\pi$
$863$	1.30761	+	2.26485i	0.0445116	+	0.0770964i	−0.842911	+	0.538053i	$0.819160\pi$
$864$	−3.29315	−	10.1353i	−0.112035	−	0.344809i
$865$	−0.869019	−	8.26817i	−0.0295475	−	0.281126i
$866$	−9.08562	−	6.60109i	−0.308742	−	0.224314i
$867$	7.02944			0.238732
$868$		0			0
$869$	−21.9117			−0.743303
$870$	0.947822	+	0.688633i	0.0321342	+	0.0233469i
$871$	1.29764	+	12.3462i	0.0439688	+	0.418335i
$872$	5.30631	+	16.3311i	0.179694	+	0.553042i
$873$	7.31371	+	12.6677i	0.247532	+	0.428737i
$874$	3.65685	−	6.33386i	0.123695	−	0.214246i
$875$	−3.64646	−	0.775079i	−0.123273	−	0.0262024i
$876$	0.427919	−	1.31700i	0.0144581	−	0.0444973i
$877$	−52.6521	+	11.1916i	−1.77794	+	0.377912i	−0.975703	−	0.219098i	$-0.929689\pi$
$877$	−52.6521	+	11.1916i	−1.77794	+	0.377912i	−0.802234	+	0.597010i	$0.796355\pi$
$878$	−0.0896712	+	0.853165i	−0.00302626	+	0.0287929i
$879$	4.10173	−	4.55543i	0.138348	−	0.153651i
$880$	8.88690	−	3.95670i	0.299577	−	0.133380i
$881$	10.6760	+	4.75324i	0.359682	+	0.160141i	0.578619	−	0.815598i	$-0.303592\pi$
$881$	10.6760	+	4.75324i	0.359682	+	0.160141i	−0.218936	+	0.975739i	$0.570259\pi$
$882$	5.35304	+	5.94516i	0.180246	+	0.200184i
$883$	24.5005	−	17.8006i	0.824507	−	0.599040i	−0.0934928	−	0.995620i	$-0.529803\pi$
$883$	24.5005	−	17.8006i	0.824507	−	0.599040i	0.918000	+	0.396580i	$0.129803\pi$
$884$	33.0071	−	23.9810i	1.11015	−	0.806570i
$885$	1.12835	+	1.25316i	0.0379290	+	0.0421245i
$886$	−1.80020	−	0.801500i	−0.0604789	−	0.0269269i
$887$	−46.8885	+	20.8761i	−1.57436	+	0.700952i	−0.993583	−	0.113108i	$-0.963919\pi$
$887$	−46.8885	+	20.8761i	−1.57436	+	0.700952i	−0.580781	+	0.814060i	$0.697253\pi$
$888$	−0.439521	+	0.488138i	−0.0147494	+	0.0163808i
$889$	0.385322	−	3.66610i	0.0129233	−	0.122957i
$890$	−1.81727	+	0.386272i	−0.0609149	+	0.0129479i
$891$	7.50048	−	23.0841i	0.251276	−	0.773347i
$892$	−42.4367	−	9.02020i	−1.42089	−	0.302019i
$893$	−21.3137	+	36.9164i	−0.713236	+	1.23536i
$894$	−0.0857864	−	0.148586i	−0.00286913	−	0.00496947i
$895$	−4.71024	−	14.4966i	−0.157446	−	0.484568i
$896$	−0.457059	−	4.34863i	−0.0152693	−	0.145278i
$897$	−5.13171	−	3.72841i	−0.171343	−	0.124488i
$898$	−16.8284			−0.561572
$899$		0			0
$900$	−20.6863			−0.689543
$901$	27.4828	+	19.9674i	0.915584	+	0.665210i
$902$	1.05091	+	9.99875i	0.0349915	+	0.332922i
$903$	0.577880	+	1.77853i	0.0192306	+	0.0591858i
$904$	13.2071	+	22.8754i	0.439262	+	0.760824i
$905$	−6.15685	+	10.6640i	−0.204661	+	0.354483i
$906$	−0.891766	−	0.189551i	−0.0296269	−	0.00629740i
$907$	10.1006	−	31.0865i	0.335386	−	1.03221i	−0.631146	−	0.775664i	$-0.717415\pi$
$907$	10.1006	−	31.0865i	0.335386	−	1.03221i	0.966532	−	0.256547i	$-0.0825848\pi$
$908$	−32.9333	+	7.00019i	−1.09293	+	0.232309i
$909$	−2.50868	+	23.8685i	−0.0832078	+	0.791669i
$910$	0.439521	−	0.488138i	0.0145700	−	0.0161816i
$911$	0.875514	−	0.389804i	0.0290071	−	0.0129148i	−0.392182	−	0.919888i	$-0.628280\pi$
$911$	0.875514	−	0.389804i	0.0290071	−	0.0129148i	0.421189	+	0.906973i	$0.361613\pi$
$912$	5.01105	+	2.23106i	0.165933	+	0.0738779i
$913$	−21.8517	−	24.2688i	−0.723186	−	0.803179i
$914$	10.4260	−	7.57497i	0.344863	−	0.250558i
$915$	0.947822	−	0.688633i	0.0313340	−	0.0227655i
$916$	6.71100	+	7.45332i	0.221738	+	0.246265i
$917$	5.01105	+	2.23106i	0.165480	+	0.0736763i
$918$	5.32453	−	2.37063i	0.175736	−	0.0782426i
$919$	−23.3523	+	25.9354i	−0.770322	+	0.855529i	−0.992846	−	0.119398i	$-0.961904\pi$
$919$	−23.3523	+	25.9354i	−0.770322	+	0.855529i	0.222525	+	0.974927i	$0.428570\pi$
$920$	−0.663039	+	6.30840i	−0.0218598	+	0.207982i
$921$	4.55509	−	0.968214i	0.150095	−	0.0319038i
$922$	−0.274191	+	0.843874i	−0.00903001	+	0.0277915i
$923$	0.266132	+	0.0565682i	0.00875985	+	0.00186196i
$924$	−0.508622	+	0.880959i	−0.0167324	+	0.0289814i
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	−1.14822	−	3.53387i	−0.0377330	−	0.116130i
$927$	0.612314	+	5.82577i	0.0201110	+	0.191344i
$928$	24.3855	+	17.7171i	0.800493	+	0.581592i
$929$	7.51472			0.246550			0.123275	−	0.992373i	$-0.460660\pi$
$929$	7.51472			0.246550			0.123275	+	0.992373i	$0.460660\pi$
$930$		0			0
$931$	−30.1421			−0.987869
$932$	−13.5669	−	9.85690i	−0.444397	−	0.322873i
$933$	−0.489851	−	4.66062i	−0.0160370	−	0.152582i
$934$	−1.02399	−	3.15152i	−0.0335060	−	0.103121i
$935$	9.44975	+	16.3674i	0.309040	+	0.535273i
$936$	8.58579	−	14.8710i	0.280635	−	0.486074i
$937$	−15.3435	−	3.26136i	−0.501251	−	0.106544i	−0.0496542	−	0.998766i	$-0.515812\pi$
$937$	−15.3435	−	3.26136i	−0.501251	−	0.106544i	−0.451596	+	0.892222i	$0.649145\pi$
$938$	−0.171921	+	0.529120i	−0.00561343	+	0.0172764i
$939$	0.740809	−	0.157464i	0.0241754	−	0.00513864i
$940$	1.84564	−	17.5601i	0.0601983	−	0.572748i
$941$	−23.4196	+	26.0101i	−0.763456	+	0.847904i	−0.992080	−	0.125611i	$-0.959911\pi$
$941$	−23.4196	+	26.0101i	−0.763456	+	0.847904i	0.228623	+	0.973515i	$0.426578\pi$
$942$	1.43755	−	0.640038i	0.0468379	−	0.0208536i
$943$	27.3526	+	12.1782i	0.890723	+	0.396575i
$944$	8.17223	+	9.07618i	0.265983	+	0.295404i
$945$	−0.809017	+	0.587785i	−0.0263173	+	0.0191207i
$946$	11.8437	−	8.60495i	0.385072	−	0.279771i
$947$	12.7807	+	14.1944i	0.415318	+	0.461257i	0.914111	−	0.405464i	$-0.132890\pi$
$947$	12.7807	+	14.1944i	0.415318	+	0.461257i	−0.498793	+	0.866721i	$0.666223\pi$
$948$	4.67530	+	2.08158i	0.151847	+	0.0676064i
$949$	6.39482	−	2.84716i	0.207585	−	0.0924226i
$950$	−4.89383	+	5.43514i	−0.158777	+	0.176339i
$951$	0.338948	−	3.22488i	0.0109912	−	0.104574i
$952$	3.74477	−	0.795975i	0.121369	−	0.0257977i
$953$	1.08611	−	3.34270i	0.0351825	−	0.108281i	−0.931923	−	0.362656i	$-0.881870\pi$
$953$	1.08611	−	3.34270i	0.0351825	−	0.108281i	0.967106	+	0.254376i	$0.0818699\pi$
$954$	6.67921	+	1.41971i	0.216247	+	0.0459648i
$955$	10.4497	−	18.0995i	0.338146	−	0.585686i
$956$	−19.4203	−	33.6370i	−0.628098	−	1.08790i
$957$	−2.83417	−	8.72268i	−0.0916158	−	0.281964i
$958$	0.680974	+	6.47903i	0.0220013	+	0.209328i
$959$	3.17857	+	2.30937i	0.102641	+	0.0745734i
$960$	−1.72792			−0.0557684
$961$		0			0
$962$	−1.58579			−0.0511278
$963$	28.4068	+	20.6387i	0.915395	+	0.665074i
$964$	2.55018	+	24.2633i	0.0821357	+	0.781469i
$965$	2.20704	+	6.79257i	0.0710472	+	0.218661i
$966$	−0.142136	−	0.246186i	−0.00457314	−	0.00792091i
$967$	7.72183	−	13.3746i	0.248317	−	0.430098i	−0.714742	−	0.699388i	$-0.753456\pi$
$967$	7.72183	−	13.3746i	0.248317	−	0.430098i	0.963059	+	0.269290i	$0.0867892\pi$
$968$	−0.752736	−	0.159999i	−0.0241939	−	0.00514256i
$969$	−3.29315	+	10.1353i	−0.105791	+	0.325592i
$970$	−2.09532	+	0.445375i	−0.0672768	+	0.0143001i
$971$	0.0730115	−	0.694658i	0.00234305	−	0.0222927i	−0.993288	−	0.115668i	$-0.963099\pi$
$971$	0.0730115	−	0.694658i	0.00234305	−	0.0222927i	0.995631	+	0.0933756i	$0.0297657\pi$
$972$	−12.6544	+	14.0541i	−0.405890	+	0.450786i
$973$		0			0
$974$	7.33526	+	3.26587i	0.235037	+	0.104645i
$975$	4.24439	+	4.71388i	0.135929	+	0.150965i
$976$	6.86474	−	4.98752i	0.219735	−	0.159647i
$977$	0.392601	−	0.285241i	0.0125604	−	0.00912568i	−0.581487	−	0.813555i	$-0.697529\pi$
$977$	0.392601	−	0.285241i	0.0125604	−	0.00912568i	0.594048	+	0.804430i	$0.297529\pi$
$978$	2.40752	+	2.67382i	0.0769839	+	0.0854993i
$979$	13.2867	+	5.91564i	0.424646	+	0.189065i
$980$	11.4059	−	5.07822i	0.364347	−	0.162218i
$981$	20.4937	−	22.7606i	0.654315	−	0.726690i
$982$	−0.0686600	+	0.653256i	−0.00219103	+	0.0208462i
$983$	37.9919	−	8.07542i	1.21175	−	0.257566i	0.442652	−	0.896694i	$-0.354038\pi$
$983$	37.9919	−	8.07542i	1.21175	−	0.257566i	0.769101	+	0.639128i	$0.220705\pi$
$984$	1.51936	−	4.67610i	0.0484353	−	0.149069i
$985$	13.1906	+	2.80375i	0.420287	+	0.0893348i
$986$	−8.24264	+	14.2767i	−0.262499	+	0.454662i
$987$	0.828427	+	1.43488i	0.0263691	+	0.0456727i
$988$	9.54847	+	29.3872i	0.303777	+	0.934930i
$989$	−4.55723	−	43.3591i	−0.144911	−	1.37874i
$990$	3.07345	+	2.23299i	0.0976806	+	0.0709691i
$991$	47.9411			1.52290			0.761450	−	0.648224i	$-0.224488\pi$
$991$	47.9411			1.52290			0.761450	+	0.648224i	$0.224488\pi$
$992$		0			0
$993$	3.82843			0.121491
$994$	0.00986459	+	0.00716705i	0.000312886	+	0.000227325i
$995$	−1.92481	−	18.3133i	−0.0610206	−	0.580572i
$996$	2.35700	+	7.25410i	0.0746844	+	0.229855i
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	−0.999823	−	0.0188015i	$-0.994015\pi$
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	0.483629	−	0.875273i	$-0.339318\pi$
$998$	0.458369	−	0.793919i	0.0145094	−	0.0251311i
$999$	2.36146	+	0.501943i	0.0747132	+	0.0158808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.o.816.1		16
31.2	even	5	inner	961.2.g.o.846.2		16
31.3	odd	30		961.2.g.r.338.1		16
31.4	even	5		31.2.c.a.5.2	✓	4
31.5	even	3		961.2.d.l.374.1		8
31.6	odd	6		961.2.g.r.732.1		16
31.7	even	15		31.2.c.a.25.2	yes	4
31.8	even	5	inner	961.2.g.o.547.2		16
31.9	even	15		961.2.d.l.531.2		8
31.10	even	15		961.2.d.l.628.2		8
31.11	odd	30		961.2.a.c.1.2		2
31.12	odd	30		961.2.g.r.448.2		16
31.13	odd	30		961.2.d.i.388.1		8
31.14	even	15	inner	961.2.g.o.844.2		16
31.15	odd	10		961.2.g.r.235.1		16
31.16	even	5	inner	961.2.g.o.235.1		16
31.17	odd	30		961.2.g.r.844.2		16
31.18	even	15		961.2.d.l.388.1		8
31.19	even	15	inner	961.2.g.o.448.2		16
31.20	even	15		961.2.a.a.1.2		2
31.21	odd	30		961.2.d.i.628.2		8
31.22	odd	30		961.2.d.i.531.2		8
31.23	odd	10		961.2.g.r.547.2		16
31.24	odd	30		961.2.c.a.521.2		4
31.25	even	3	inner	961.2.g.o.732.1		16
31.26	odd	6		961.2.d.i.374.1		8
31.27	odd	10		961.2.c.a.439.2		4
31.28	even	15	inner	961.2.g.o.338.1		16
31.29	odd	10		961.2.g.r.846.2		16
31.30	odd	2		961.2.g.r.816.1		16
93.11	even	30		8649.2.a.k.1.1		2
93.20	odd	30		8649.2.a.l.1.1		2
93.35	odd	10		279.2.h.c.253.1		4
93.38	odd	30		279.2.h.c.118.1		4
124.7	odd	30		496.2.i.h.273.2		4
124.35	odd	10		496.2.i.h.129.2		4
155.4	even	10		775.2.e.e.501.1		4
155.7	odd	60		775.2.o.d.149.3		8
155.38	odd	60		775.2.o.d.149.2		8
155.69	even	30		775.2.e.e.676.1		4
155.97	odd	20		775.2.o.d.749.3		8
155.128	odd	20		775.2.o.d.749.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.2	✓	4	31.4	even	5
31.2.c.a.25.2	yes	4	31.7	even	15
279.2.h.c.118.1		4	93.38	odd	30
279.2.h.c.253.1		4	93.35	odd	10
496.2.i.h.129.2		4	124.35	odd	10
496.2.i.h.273.2		4	124.7	odd	30
775.2.e.e.501.1		4	155.4	even	10
775.2.e.e.676.1		4	155.69	even	30
775.2.o.d.149.2		8	155.38	odd	60
775.2.o.d.149.3		8	155.7	odd	60
775.2.o.d.749.2		8	155.128	odd	20
775.2.o.d.749.3		8	155.97	odd	20
961.2.a.a.1.2		2	31.20	even	15
961.2.a.c.1.2		2	31.11	odd	30
961.2.c.a.439.2		4	31.27	odd	10
961.2.c.a.521.2		4	31.24	odd	30
961.2.d.i.374.1		8	31.26	odd	6
961.2.d.i.388.1		8	31.13	odd	30
961.2.d.i.531.2		8	31.22	odd	30
961.2.d.i.628.2		8	31.21	odd	30
961.2.d.l.374.1		8	31.5	even	3
961.2.d.l.388.1		8	31.18	even	15
961.2.d.l.531.2		8	31.9	even	15
961.2.d.l.628.2		8	31.10	even	15
961.2.g.o.235.1		16	31.16	even	5	inner
961.2.g.o.338.1		16	31.28	even	15	inner
961.2.g.o.448.2		16	31.19	even	15	inner
961.2.g.o.547.2		16	31.8	even	5	inner
961.2.g.o.732.1		16	31.25	even	3	inner
961.2.g.o.816.1		16	1.1	even	1	trivial
961.2.g.o.844.2		16	31.14	even	15	inner
961.2.g.o.846.2		16	31.2	even	5	inner
961.2.g.r.235.1		16	31.15	odd	10
961.2.g.r.338.1		16	31.3	odd	30
961.2.g.r.448.2		16	31.12	odd	30
961.2.g.r.547.2		16	31.23	odd	10
961.2.g.r.732.1		16	31.6	odd	6
961.2.g.r.816.1		16	31.30	odd	2
961.2.g.r.844.2		16	31.17	odd	30
961.2.g.r.846.2		16	31.29	odd	10
8649.2.a.k.1.1		2	93.11	even	30
8649.2.a.l.1.1		2	93.20	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.335106 - 0.243469i) q^{2} +(-0.0432971 - 0.411944i) q^{3} +(-0.565015 - 1.73894i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(0.405162 + 0.0861198i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(2.76662 - 0.588063i) q^{9} +O(q^{10})\)	\(q+(-0.335106 - 0.243469i) q^{2} +(-0.0432971 - 0.411944i) q^{3} +(-0.565015 - 1.73894i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(0.405162 + 0.0861198i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(2.76662 - 0.588063i) q^{9} +(-0.0432971 + 0.411944i) q^{10} +(2.16975 - 2.40975i) q^{11} +(-0.691882 + 0.308046i) q^{12} +(-3.49744 - 1.55716i) q^{13} +(-0.114805 - 0.127503i) q^{14} +(-0.335106 + 0.243469i) q^{15} +(-2.42705 + 1.76336i) q^{16} +(-3.89998 - 4.33137i) q^{17} +(-1.07029 - 0.476522i) q^{18} +(4.03258 - 1.79542i) q^{19} +(-1.22346 + 1.35879i) q^{20} +(0.0179342 - 0.170633i) q^{21} +(-1.31379 + 0.279256i) q^{22} +(-1.23607 + 3.80423i) q^{23} +(0.642500 + 0.136568i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.792893 + 1.37333i) q^{26} +(-0.746033 - 2.29605i) q^{27} +(-0.0791656 - 0.753210i) q^{28} +(5.52431 + 4.01365i) q^{29} +0.171573 q^{30} +4.41421 q^{32} +(-1.08663 - 0.789481i) q^{33} +(0.252354 + 2.40099i) q^{34} +(-0.127999 - 0.393941i) q^{35} +(-2.58579 - 4.47871i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(-1.78847 - 0.380151i) q^{38} +(-0.490035 + 1.50817i) q^{39} +(1.55113 - 0.329704i) q^{40} +(0.782425 - 7.44428i) q^{41} +(-0.0475536 + 0.0528137i) q^{42} +(-9.95718 + 4.43322i) q^{43} +(-5.41635 - 2.41151i) q^{44} +(-1.89259 - 2.10193i) q^{45} +(1.34042 - 0.973874i) q^{46} +(-7.81256 + 5.67616i) q^{47} +(0.831489 + 0.923462i) q^{48} +(-6.23808 - 2.77737i) q^{49} +(-1.51361 + 0.673903i) q^{50} +(-1.61542 + 1.79411i) q^{51} +(-0.731699 + 6.96165i) q^{52} +(-5.70106 + 1.21180i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-3.17178 - 0.674183i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(-0.914214 - 1.58346i) q^{57} +(-0.874032 - 2.68999i) q^{58} +(-0.425542 - 4.04877i) q^{59} +(0.612717 + 0.445165i) q^{60} -2.82843 q^{61} +1.17157 q^{63} +(3.37487 + 2.45199i) q^{64} +(0.400180 + 3.80745i) q^{65} +(0.171921 + 0.529120i) q^{66} +(-1.62132 - 2.80821i) q^{67} +(-5.32843 + 9.22911i) q^{68} +(1.62065 + 0.344479i) q^{69} +(-0.0530189 + 0.163176i) q^{70} +(-0.0695148 + 0.0147758i) q^{71} +(-0.468840 + 4.46071i) q^{72} +(-1.22346 + 1.35879i) q^{73} +(0.378403 - 0.168476i) q^{74} +(-1.51361 - 0.673903i) q^{75} +(-5.40060 - 5.99797i) q^{76} +(1.08663 - 0.789481i) q^{77} +(0.531406 - 0.386089i) q^{78} +(-4.52156 - 5.02170i) q^{79} +(2.74064 + 1.22021i) q^{80} +(6.83814 - 3.04454i) q^{81} +(-2.07464 + 2.30412i) q^{82} +(1.05271 - 10.0159i) q^{83} +(-0.306853 + 0.0652237i) q^{84} +(-1.80108 + 5.54316i) q^{85} +(4.41606 + 0.938663i) q^{86} +(1.41421 - 2.44949i) q^{87} +(2.57107 + 4.45322i) q^{88} +(1.38603 + 4.26576i) q^{89} +(0.122463 + 1.16515i) q^{90} +(-1.28293 - 0.932102i) q^{91} +7.31371 q^{92} +4.00000 q^{94} +(-3.57117 - 2.59461i) q^{95} +(-0.191123 - 1.81841i) q^{96} +(1.59810 + 4.91846i) q^{97} +(1.41421 + 2.44949i) q^{98} +(4.58579 - 7.94282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21} + 14 q^{22} + 16 q^{23} + 10 q^{24} + 32 q^{25} + 24 q^{26} + 4 q^{27} + 10 q^{28} + 16 q^{29} + 48 q^{30} + 48 q^{32} - 28 q^{33} - 2 q^{34} - 4 q^{35} - 64 q^{36} - 8 q^{37} - 2 q^{38} + 12 q^{39} - 6 q^{40} + 2 q^{41} + 14 q^{42} - 2 q^{43} - 26 q^{44} - 16 q^{46} - 16 q^{47} - 6 q^{48} - 8 q^{49} + 8 q^{50} - 2 q^{51} + 14 q^{52} + 6 q^{53} + 4 q^{54} - 2 q^{55} + 40 q^{56} + 8 q^{57} - 6 q^{59} + 20 q^{60} + 64 q^{63} + 28 q^{64} - 2 q^{65} + 60 q^{66} + 8 q^{67} - 40 q^{68} + 8 q^{69} + 12 q^{70} - 14 q^{71} - 8 q^{72} + 2 q^{73} - 2 q^{74} + 8 q^{75} - 2 q^{76} + 28 q^{77} - 20 q^{78} - 22 q^{79} + 6 q^{80} - 2 q^{81} - 26 q^{82} - 6 q^{83} - 22 q^{84} + 12 q^{85} - 26 q^{86} - 72 q^{88} + 16 q^{89} - 8 q^{90} - 12 q^{91} - 64 q^{92} + 64 q^{94} - 12 q^{95} - 2 q^{96} - 32 q^{97} + 96 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more