LMFDB - Embedded newform 961.2.g.o.235.1

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			235.1
Root			$-0.946294 - 1.05097i$ of defining polynomial
Character	$\chi$	$=$	961.235
Dual form			961.2.g.o.732.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.335106 + 0.243469i) q^{2} +(0.378403 - 0.168476i) q^{3} +(-0.565015 + 1.73894i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(-0.277163 - 0.307821i) q^{7} +(-0.490035 - 1.50817i) q^{8} +(-1.89259 + 2.10193i) q^{9} +O(q^{10})$	\(q+(-0.335106 + 0.243469i) q^{2} +(0.378403 - 0.168476i) q^{3} +(-0.565015 + 1.73894i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(-0.277163 - 0.307821i) q^{7} +(-0.490035 - 1.50817i) q^{8} +(-1.89259 + 2.10193i) q^{9} +(0.378403 + 0.168476i) q^{10} +(-3.17178 + 0.674183i) q^{11} +(0.0791656 + 0.753210i) q^{12} +(0.400180 - 3.80745i) q^{13} +(0.167824 + 0.0356720i) q^{14} +(-0.335106 - 0.243469i) q^{15} +(-2.42705 - 1.76336i) q^{16} +(5.70106 + 1.21180i) q^{17} +(0.122463 - 1.16515i) q^{18} +(-0.461411 - 4.39003i) q^{19} +(1.78847 - 0.380151i) q^{20} +(-0.156740 - 0.0697850i) q^{21} +(0.898740 - 0.998152i) q^{22} +(-1.23607 - 3.80423i) q^{23} +(-0.439521 - 0.488138i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.792893 + 1.37333i) q^{26} +(-0.746033 + 2.29605i) q^{27} +(0.691882 - 0.308046i) q^{28} +(5.52431 - 4.01365i) q^{29} +0.171573 q^{30} +4.41421 q^{32} +(-1.08663 + 0.789481i) q^{33} +(-2.20549 + 0.981949i) q^{34} +(-0.127999 + 0.393941i) q^{35} +(-2.58579 - 4.47871i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(1.22346 + 1.35879i) q^{38} +(-0.490035 - 1.50817i) q^{39} +(-1.06110 + 1.17847i) q^{40} +(-6.83814 - 3.04454i) q^{41} +(0.0695148 - 0.0147758i) q^{42} +(1.13931 + 10.8398i) q^{43} +(0.619742 - 5.89645i) q^{44} +(2.76662 + 0.588063i) q^{45} +(1.34042 + 0.973874i) q^{46} +(-7.81256 - 5.67616i) q^{47} +(-1.21549 - 0.258360i) q^{48} +(0.713765 - 6.79102i) q^{49} +(0.173188 + 1.64778i) q^{50} +(2.36146 - 0.501943i) q^{51} +(6.39482 + 2.84716i) q^{52} +(3.89998 - 4.33137i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(2.16975 + 2.40975i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(-0.914214 - 1.58346i) q^{57} +(-0.874032 + 2.68999i) q^{58} +(3.71911 - 1.65585i) q^{59} +(0.612717 - 0.445165i) q^{60} -2.82843 q^{61} +1.17157 q^{63} +(3.37487 - 2.45199i) q^{64} +(-3.49744 + 1.55716i) q^{65} +(0.171921 - 0.529120i) q^{66} +(-1.62132 - 2.80821i) q^{67} +(-5.32843 + 9.22911i) q^{68} +(-1.10865 - 1.23128i) q^{69} +(-0.0530189 - 0.163176i) q^{70} +(0.0475536 - 0.0528137i) q^{71} +(4.09751 + 1.82433i) q^{72} +(1.78847 - 0.380151i) q^{73} +(-0.0432971 - 0.411944i) q^{74} +(0.173188 - 1.64778i) q^{75} +(7.89470 + 1.67807i) q^{76} +(1.08663 + 0.789481i) q^{77} +(0.531406 + 0.386089i) q^{78} +(6.60969 + 1.40493i) q^{79} +(-0.313585 + 2.98357i) q^{80} +(-0.782425 - 7.44428i) q^{81} +(3.03275 - 0.644631i) q^{82} +(-9.20038 - 4.09627i) q^{83} +(0.209912 - 0.233131i) q^{84} +(-1.80108 - 5.54316i) q^{85} +(-3.02094 - 3.35509i) q^{86} +(1.41421 - 2.44949i) q^{87} +(2.57107 + 4.45322i) q^{88} +(1.38603 - 4.26576i) q^{89} +(-1.07029 + 0.476522i) q^{90} +(-1.28293 + 0.932102i) q^{91} +7.31371 q^{92} +4.00000 q^{94} +(-3.57117 + 2.59461i) q^{95} +(1.67035 - 0.743688i) 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{15}\right)$

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	−0.699926	−	0.714215i	$-0.746784\pi$
$2$	−0.335106	+	0.243469i	−0.236956	+	0.172158i	0.462970	+	0.886374i	$0.346784\pi$
$3$	0.378403	−	0.168476i	0.218471	−	0.0972696i	−0.294583	−	0.955626i	$-0.595181\pi$
$3$	0.378403	−	0.168476i	0.218471	−	0.0972696i	0.513054	+	0.858356i	$0.328514\pi$
$4$	−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
$7$	−0.277163	−	0.307821i	−0.104758	−	0.116345i	0.688486	−	0.725250i	$-0.258276\pi$
$7$	−0.277163	−	0.307821i	−0.104758	−	0.116345i	−0.793243	+	0.608905i	$0.791609\pi$
$8$	−0.490035	−	1.50817i	−0.173254	−	0.533220i
$9$	−1.89259	+	2.10193i	−0.630862	+	0.700644i
$10$	0.378403	+	0.168476i	0.119662	+	0.0532767i
$11$	−3.17178	+	0.674183i	−0.956328	+	0.203274i	−0.659540	−	0.751670i	$-0.729249\pi$
$11$	−3.17178	+	0.674183i	−0.956328	+	0.203274i	−0.296788	+	0.954943i	$0.595916\pi$
$12$	0.0791656	+	0.753210i	0.0228531	+	0.217433i
$13$	0.400180	−	3.80745i	0.110990	−	1.05600i	−0.787293	−	0.616579i	$-0.788518\pi$
$13$	0.400180	−	3.80745i	0.110990	−	1.05600i	0.898283	−	0.439418i	$-0.144815\pi$
$14$	0.167824	+	0.0356720i	0.0448527	+	0.00953374i
$15$	−0.335106	−	0.243469i	−0.0865239	−	0.0628633i
$16$	−2.42705	−	1.76336i	−0.606763	−	0.440839i
$17$	5.70106	+	1.21180i	1.38271	+	0.293904i	0.838435	−	0.545002i	$-0.183471\pi$
$17$	5.70106	+	1.21180i	1.38271	+	0.293904i	0.544276	+	0.838906i	$0.316804\pi$
$18$	0.122463	−	1.16515i	0.0288647	−	0.274630i
$19$	−0.461411	−	4.39003i	−0.105855	−	1.00714i	−0.910535	−	0.413433i	$-0.864330\pi$
$19$	−0.461411	−	4.39003i	−0.105855	−	1.00714i	0.804680	−	0.593709i	$-0.202337\pi$
$20$	1.78847	−	0.380151i	0.399914	−	0.0850044i
$21$	−0.156740	−	0.0697850i	−0.0342034	−	0.0152283i
$22$	0.898740	−	0.998152i	0.191612	−	0.212807i
$23$	−1.23607	−	3.80423i	−0.257738	−	0.793236i	−0.993278	−	0.115755i	$-0.963071\pi$
$23$	−1.23607	−	3.80423i	−0.257738	−	0.793236i	0.735540	−	0.677481i	$-0.236929\pi$
$24$	−0.439521	−	0.488138i	−0.0897169	−	0.0996407i
$25$	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
$28$	0.691882	−	0.308046i	0.130753	−	0.0582152i
$29$	5.52431	−	4.01365i	1.02584	−	0.745316i	0.0583676	−	0.998295i	$-0.481410\pi$
$29$	5.52431	−	4.01365i	1.02584	−	0.745316i	0.967472	+	0.252979i	$0.0814105\pi$
$30$	0.171573			0.0313248
$31$		0			0
$31$		0			0
$32$	4.41421			0.780330
$33$	−1.08663	+	0.789481i	−0.189158	+	0.137431i
$34$	−2.20549	+	0.981949i	−0.378239	+	0.168403i
$35$	−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	$0.192861\pi$
$38$	1.22346	+	1.35879i	0.198471	+	0.220424i
$39$	−0.490035	−	1.50817i	−0.0784684	−	0.241501i
$40$	−1.06110	+	1.17847i	−0.167774	+	0.186332i
$41$	−6.83814	−	3.04454i	−1.06794	−	0.475477i	−0.203947	−	0.978982i	$-0.565377\pi$
$41$	−6.83814	−	3.04454i	−1.06794	−	0.475477i	−0.863992	+	0.503505i	$0.832044\pi$
$42$	0.0695148	−	0.0147758i	0.0107264	−	0.00227996i
$43$	1.13931	+	10.8398i	0.173743	+	1.65305i	0.639980	+	0.768392i	$0.278943\pi$
$43$	1.13931	+	10.8398i	0.173743	+	1.65305i	−0.466237	+	0.884660i	$0.654391\pi$
$44$	0.619742	−	5.89645i	0.0934296	−	0.888924i
$45$	2.76662	+	0.588063i	0.412423	+	0.0876633i
$46$	1.34042	+	0.973874i	0.197635	+	0.143590i
$47$	−7.81256	−	5.67616i	−1.13958	−	0.827953i	−0.152518	−	0.988301i	$-0.548738\pi$
$47$	−7.81256	−	5.67616i	−1.13958	−	0.827953i	−0.987061	+	0.160348i	$0.948738\pi$
$48$	−1.21549	−	0.258360i	−0.175440	−	0.0372910i
$49$	0.713765	−	6.79102i	0.101966	−	0.970146i
$50$	0.173188	+	1.64778i	0.0244925	+	0.233031i
$51$	2.36146	−	0.501943i	0.330670	−	0.0702861i
$52$	6.39482	+	2.84716i	0.886802	+	0.394830i
$53$	3.89998	−	4.33137i	0.535703	−	0.594959i	−0.413155	−	0.910661i	$-0.635573\pi$
$53$	3.89998	−	4.33137i	0.535703	−	0.594959i	0.948858	+	0.315702i	$0.102240\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	2.16975	+	2.40975i	0.292569	+	0.324931i
$56$	−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
$59$	3.71911	−	1.65585i	0.484186	−	0.215574i	−0.150102	−	0.988671i	$-0.547960\pi$
$59$	3.71911	−	1.65585i	0.484186	−	0.215574i	0.634288	+	0.773097i	$0.281293\pi$
$60$	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
$65$	−3.49744	+	1.55716i	−0.433804	+	0.193142i
$66$	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
$69$	−1.10865	−	1.23128i	−0.133466	−	0.148229i
$70$	−0.0530189	−	0.163176i	−0.00633697	−	0.0195032i
$71$	0.0475536	−	0.0528137i	0.00564358	−	0.00626783i	−0.740316	−	0.672259i	$-0.765324\pi$
$71$	0.0475536	−	0.0528137i	0.00564358	−	0.00626783i	0.745960	+	0.665991i	$0.231991\pi$
$72$	4.09751	+	1.82433i	0.482896	+	0.214999i
$73$	1.78847	−	0.380151i	0.209325	−	0.0444934i	−0.102056	−	0.994779i	$-0.532542\pi$
$73$	1.78847	−	0.380151i	0.209325	−	0.0444934i	0.311380	+	0.950285i	$0.399209\pi$
$74$	−0.0432971	−	0.411944i	−0.00503319	−	0.0478876i
$75$	0.173188	−	1.64778i	0.0199981	−	0.190269i
$76$	7.89470	+	1.67807i	0.905584	+	0.192488i
$77$	1.08663	+	0.789481i	0.123833	+	0.0899697i
$78$	0.531406	+	0.386089i	0.0601699	+	0.0437160i
$79$	6.60969	+	1.40493i	0.743649	+	0.158067i	0.564129	−	0.825687i	$-0.309212\pi$
$79$	6.60969	+	1.40493i	0.743649	+	0.158067i	0.179520	+	0.983754i	$0.442546\pi$
$80$	−0.313585	+	2.98357i	−0.0350599	+	0.333573i
$81$	−0.782425	−	7.44428i	−0.0869361	−	0.827142i
$82$	3.03275	−	0.644631i	0.334911	−	0.0711876i
$83$	−9.20038	−	4.09627i	−1.00987	−	0.449624i	−0.165976	−	0.986130i	$-0.553077\pi$
$83$	−9.20038	−	4.09627i	−1.00987	−	0.449624i	−0.843897	+	0.536506i	$0.819744\pi$
$84$	0.209912	−	0.233131i	0.0229033	−	0.0254367i
$85$	−1.80108	−	5.54316i	−0.195355	−	0.601241i
$86$	−3.02094	−	3.35509i	−0.325756	−	0.361789i
$87$	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	−0.850334	−	0.526243i	$-0.823600\pi$
$89$	1.38603	−	4.26576i	0.146919	−	0.452169i	0.997253	+	0.0740741i	$0.0236001\pi$
$90$	−1.07029	+	0.476522i	−0.112818	+	0.0502298i
$91$	−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
$96$	1.67035	−	0.743688i	0.170480	−	0.0759024i
$97$	1.59810	−	4.91846i	0.162263	−	0.499394i	−0.836561	−	0.547873i	$-0.815438\pi$
$97$	1.59810	−	4.91846i	0.162263	−	0.499394i	0.998824	+	0.0484796i	$0.0154376\pi$
$98$	1.41421	+	2.44949i	0.142857	+	0.247436i
$99$	4.58579	−	7.94282i	0.460889	−	0.798283i
$100$	4.89383	+	5.43514i	0.489383	+	0.543514i
$101$	−2.62210	−	8.06998i	−0.260908	−	0.802993i	−0.992608	−	0.121366i	$-0.961273\pi$
$101$	−2.62210	−	8.06998i	−0.260908	−	0.802993i	0.731700	−	0.681627i	$-0.238727\pi$
$102$	−0.669131	+	0.743145i	−0.0662538	+	0.0735823i
$103$	1.89201	+	0.842379i	0.186426	+	0.0830021i	0.497827	−	0.867277i	$-0.334132\pi$
$103$	1.89201	+	0.842379i	0.186426	+	0.0830021i	−0.311401	+	0.950279i	$0.600798\pi$
$104$	−5.93840	+	1.26225i	−0.582308	+	0.123773i
$105$	0.0179342	+	0.170633i	0.00175020	+	0.0166521i
$106$	−0.252354	+	2.40099i	−0.0245108	+	0.233205i
$107$	−12.1429	−	2.58106i	−1.17390	−	0.249521i	−0.420631	−	0.907232i	$-0.638191\pi$
$107$	−12.1429	−	2.58106i	−1.17390	−	0.249521i	−0.753270	+	0.657711i	$0.771525\pi$
$108$	−3.57117	−	2.59461i	−0.343636	−	0.249666i
$109$	8.76038	+	6.36479i	0.839092	+	0.609636i	0.922117	−	0.386911i	$-0.126458\pi$
$109$	8.76038	+	6.36479i	0.839092	+	0.609636i	−0.0830246	+	0.996547i	$0.526458\pi$
$110$	−1.31379	−	0.279256i	−0.125265	−	0.0266260i
$111$	−0.0432971	+	0.411944i	−0.00410958	+	0.0391000i
$112$	0.129891	+	1.23583i	0.0122736	+	0.116775i
$113$	−16.2929	+	3.46315i	−1.53270	+	0.325786i	−0.895554	−	0.444954i	$-0.853220\pi$
$113$	−16.2929	+	3.46315i	−1.53270	+	0.325786i	−0.637150	+	0.770740i	$0.719887\pi$
$114$	0.691882	+	0.308046i	0.0648007	+	0.0288511i
$115$	−2.67652	+	2.97258i	−0.249587	+	0.277194i
$116$	3.85816	+	11.8742i	0.358222	+	1.10249i
$117$	7.24563	+	8.04709i	0.669859	+	0.743954i
$118$	−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
$121$	−0.443327	+	0.197382i	−0.0403024	+	0.0179438i
$122$	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
$127$	8.13009	−	3.61975i	0.721429	−	0.321201i	−0.0129727	−	0.999916i	$-0.504129\pi$
$127$	8.13009	−	3.61975i	0.721429	−	0.321201i	0.734402	+	0.678715i	$0.237463\pi$
$128$	−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
$131$	−8.86106	−	9.84120i	−0.774194	−	0.859830i	0.219069	−	0.975709i	$-0.429698\pi$
$131$	−8.86106	−	9.84120i	−0.774194	−	0.859830i	−0.993263	+	0.115880i	$0.963031\pi$
$132$	−0.758898	−	2.33565i	−0.0660536	−	0.203292i
$133$	−1.22346	+	1.35879i	−0.106087	+	0.117822i
$134$	1.22702	+	0.546307i	0.105999	+	0.0471937i
$135$	2.36146	−	0.501943i	0.203242	−	0.0432004i
$136$	−0.966119	−	9.19201i	−0.0828440	−	0.788208i
$137$	−0.991482	+	9.43332i	−0.0847080	+	0.805943i	0.866870	+	0.498535i	$0.166128\pi$
$137$	−0.991482	+	9.43332i	−0.0847080	+	0.805943i	−0.951578	+	0.307408i	$0.900538\pi$
$138$	0.671294	+	0.142688i	0.0571444	+	0.0121464i
$139$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$139$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$140$	−0.612717	−	0.445165i	−0.0517840	−	0.0376233i
$141$	−3.91259	−	0.831647i	−0.329500	−	0.0700373i
$142$	−0.00307703	+	0.0292760i	−0.000258219	+	0.00245679i
$143$	1.29764	+	12.3462i	0.108514	+	1.03244i
$144$	8.29986	−	1.76419i	0.691655	−	0.147016i
$145$	−6.23808	−	2.77737i	−0.518044	−	0.230648i
$146$	−0.506772	+	0.562828i	−0.0419408	+	0.0465799i
$147$	−0.874032	−	2.68999i	−0.0720889	−	0.221867i
$148$	−1.22346	−	1.35879i	−0.100568	−	0.111692i
$149$	−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	−0.861748	−	0.507337i	$-0.830630\pi$
$151$	1.64203	−	5.05364i	0.133626	−	0.411259i	0.995374	+	0.0960781i	$0.0306299\pi$
$152$	−6.39482	+	2.84716i	−0.518688	+	0.230935i
$153$	−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	−0.843094	−	0.537767i	$-0.819268\pi$
$157$	−7.41996	+	5.39092i	−0.592177	+	0.430242i	0.250916	+	0.968009i	$0.419268\pi$
$158$	−2.55700	+	1.13845i	−0.203424	+	0.0905704i
$159$	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
$162$	2.07464	+	2.30412i	0.162999	+	0.181029i
$163$	6.48026	+	19.9442i	0.507573	+	1.56215i	0.796401	+	0.604769i	$0.206734\pi$
$163$	6.48026	+	19.9442i	0.507573	+	1.56215i	−0.288828	+	0.957381i	$0.593266\pi$
$164$	9.15792	−	10.1709i	0.715113	−	0.794214i
$165$	1.22702	+	0.546307i	0.0955237	+	0.0425299i
$166$	4.08041	−	0.867319i	0.316702	−	0.0673170i
$167$	−2.35778	−	22.4328i	−0.182451	−	1.73590i	−0.576752	−	0.816920i	$-0.695680\pi$
$167$	−2.35778	−	22.4328i	−0.182451	−	1.73590i	0.394301	−	0.918981i	$-0.370987\pi$
$168$	−0.0284399	+	0.270587i	−0.00219419	+	0.0208763i
$169$	−1.62065	−	0.344479i	−0.124665	−	0.0264984i
$170$	1.95314	+	1.41904i	0.149799	+	0.108835i
$171$	10.1008	+	7.33866i	0.772428	+	0.561202i
$172$	−19.4934	−	4.14346i	−1.48636	−	0.315936i
$173$	−0.869019	+	8.26817i	−0.0660703	+	0.628617i	0.910513	+	0.413479i	$0.135687\pi$
$173$	−0.869019	+	8.26817i	−0.0660703	+	0.628617i	−0.976584	+	0.215138i	$0.930980\pi$
$174$	0.122463	+	1.16515i	0.00928387	+	0.0883302i
$175$	−1.62065	+	0.344479i	−0.122509	+	0.0260402i
$176$	8.88690	+	3.95670i	0.669875	+	0.298248i
$177$	1.12835	−	1.25316i	0.0848119	−	0.0941932i
$178$	0.574112	+	1.76693i	0.0430315	+	0.132437i
$179$	−10.1993	−	11.3275i	−0.762333	−	0.846656i	0.229618	−	0.973281i	$-0.426252\pi$
$179$	−10.1993	−	11.3275i	−0.762333	−	0.846656i	−0.991951	+	0.126625i	$0.959586\pi$
$180$	−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
$183$	−1.07029	+	0.476522i	−0.0791177	+	0.0352255i
$184$	−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
$189$	0.913545	−	0.406737i	0.0664507	−	0.0295857i
$190$	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
$193$	4.77902	+	5.30764i	0.344001	+	0.382052i	0.890174	−	0.455620i	$-0.150582\pi$
$193$	4.77902	+	5.30764i	0.344001	+	0.382052i	−0.546173	+	0.837673i	$0.683916\pi$
$194$	0.661956	+	2.03729i	0.0475257	+	0.146269i
$195$	−1.06110	+	1.17847i	−0.0759868	+	0.0843919i
$196$	11.4059	+	5.07822i	0.814705	+	0.362730i
$197$	13.1906	−	2.80375i	0.939791	−	0.199759i	0.287546	−	0.957767i	$-0.407161\pi$
$197$	13.1906	−	2.80375i	0.939791	−	0.199759i	0.652245	+	0.758008i	$0.273827\pi$
$198$	0.397103	+	3.77818i	0.0282209	+	0.268503i
$199$	−1.92481	+	18.3133i	−0.136446	+	1.29820i	0.685265	+	0.728294i	$0.259686\pi$
$199$	−1.92481	+	18.3133i	−0.136446	+	1.29820i	−0.821711	+	0.569904i	$0.806980\pi$
$200$	−6.20453	−	1.31881i	−0.438727	−	0.0932542i
$201$	−1.08663	−	0.789481i	−0.0766448	−	0.0556857i
$202$	2.84347	+	2.06590i	0.200066	+	0.145356i
$203$	−2.76662	−	0.588063i	−0.194179	−	0.0412739i
$204$	−0.461411	+	4.39003i	−0.0323052	+	0.307364i
$205$	0.782425	+	7.44428i	0.0546469	+	0.519931i
$206$	−0.839118	+	0.178360i	−0.0584641	+	0.0124269i
$207$	10.3356	+	4.60170i	0.718373	+	0.319840i
$208$	−7.68515	+	8.53523i	−0.532870	+	0.591812i
$209$	4.42318	+	13.6131i	0.305958	+	0.941641i
$210$	−0.0475536	−	0.0528137i	−0.00328151	−	0.00364449i
$211$	−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
$214$	4.69757	−	2.09149i	0.321120	−	0.142972i
$215$	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
$220$	−5.41635	+	2.41151i	−0.365170	+	0.162584i
$221$	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	$-0.125584\pi$
$224$	−1.22346	−	1.35879i	−0.0817456	−	0.0907877i
$225$	3.49613	+	10.7600i	0.233075	+	0.717332i
$226$	4.61666	−	5.12732i	0.307096	−	0.341065i
$227$	−16.8222	−	7.48974i	−1.11653	−	0.497111i	−0.236310	−	0.971678i	$-0.575938\pi$
$227$	−16.8222	−	7.48974i	−1.11653	−	0.497111i	−0.880220	+	0.474566i	$0.842605\pi$
$228$	3.27009	−	0.695079i	0.216567	−	0.0460327i
$229$	0.573368	+	5.45523i	0.0378892	+	0.360492i	0.996996	+	0.0774486i	$0.0246774\pi$
$229$	0.573368	+	5.45523i	0.0378892	+	0.360492i	−0.959107	+	0.283043i	$0.908656\pi$
$230$	0.173188	−	1.64778i	0.0114197	−	0.108651i
$231$	0.544192	+	0.115671i	0.0358052	+	0.00761063i
$232$	−8.76038	−	6.36479i	−0.575147	−	0.417869i
$233$	7.41996	+	5.39092i	0.486098	+	0.353171i	0.803682	−	0.595060i	$-0.202872\pi$
$233$	7.41996	+	5.39092i	0.486098	+	0.353171i	−0.317584	+	0.948230i	$0.602872\pi$
$234$	−4.38727	−	0.932542i	−0.286805	−	0.0609622i
$235$	−1.00942	+	9.60395i	−0.0658470	+	0.626493i
$236$	0.778073	+	7.40287i	0.0506483	+	0.481886i
$237$	2.73783	−	0.581943i	0.177841	−	0.0378012i
$238$	0.913545	+	0.406737i	0.0592164	+	0.0263648i
$239$	−14.2141	+	15.7864i	−0.919434	+	1.02113i	0.0802695	+	0.996773i	$0.474422\pi$
$239$	−14.2141	+	15.7864i	−0.919434	+	1.02113i	−0.999703	+	0.0243614i	$0.992245\pi$
$240$	0.383997	+	1.18182i	0.0247869	+	0.0762863i
$241$	8.92831	+	9.91589i	0.575123	+	0.638739i	0.958581	−	0.284820i	$-0.0919337\pi$
$241$	8.92831	+	9.91589i	0.575123	+	0.638739i	−0.383458	+	0.923558i	$0.625267\pi$
$242$	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
$245$	−6.23808	+	2.77737i	−0.398536	+	0.177440i
$246$	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
$251$	5.85968	−	2.60890i	0.369859	−	0.164672i	−0.213386	−	0.976968i	$-0.568449\pi$
$251$	5.85968	−	2.60890i	0.369859	−	0.164672i	0.583246	+	0.812296i	$0.301783\pi$
$252$	−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
$255$	−1.61542	−	1.79411i	−0.101162	−	0.112352i
$256$	1.22697	+	3.77623i	0.0766857	+	0.236014i
$257$	14.9308	−	16.5823i	0.931357	−	1.03438i	−0.0679699	−	0.997687i	$-0.521652\pi$
$257$	14.9308	−	16.5823i	0.931357	−	1.03438i	0.999327	−	0.0366891i	$-0.0116811\pi$
$258$	−1.70838	−	0.760621i	−0.106359	−	0.0473542i
$259$	0.405162	−	0.0861198i	0.0251755	−	0.00535123i
$260$	−0.731699	−	6.96165i	−0.0453781	−	0.431743i
$261$	−2.01883	+	19.2079i	−0.124963	+	1.18894i
$262$	5.36541	+	1.14045i	0.331476	+	0.0704575i
$263$	18.8612	+	13.7035i	1.16303	+	0.844991i	0.990158	−	0.139953i	$-0.0446952\pi$
$263$	18.8612	+	13.7035i	1.16303	+	0.844991i	0.172872	+	0.984944i	$0.444695\pi$
$264$	1.72316	+	1.25195i	0.106053	+	0.0770521i
$265$	−5.70106	−	1.21180i	−0.350213	−	0.0744402i
$266$	0.0791656	−	0.753210i	0.00485395	−	0.0461823i
$267$	−0.194200	−	1.84769i	−0.0118848	−	0.113077i
$268$	5.79937	−	1.23269i	0.354253	−	0.0752988i
$269$	−23.9089	−	10.6449i	−1.45775	−	0.649033i	−0.483675	−	0.875248i	$-0.660698\pi$
$269$	−23.9089	−	10.6449i	−1.45775	−	0.649033i	−0.974078	+	0.226214i	$0.927365\pi$
$270$	−0.669131	+	0.743145i	−0.0407220	+	0.0452264i
$271$	−0.212076	−	0.652702i	−0.0128827	−	0.0396488i	0.944409	−	0.328774i	$-0.106636\pi$
$271$	−0.212076	−	0.652702i	−0.0128827	−	0.0396488i	−0.957291	+	0.289125i	$0.906636\pi$
$272$	−11.6999	−	12.9941i	−0.709413	−	0.787883i
$273$	−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
$276$	2.76753	−	1.23218i	0.166586	−	0.0741687i
$277$	−11.4412	+	8.31254i	−0.687437	+	0.499452i	−0.875817	−	0.482644i	$-0.839676\pi$
$277$	−11.4412	+	8.31254i	−0.687437	+	0.499452i	0.188380	+	0.982096i	$0.439676\pi$
$278$		0			0
$279$		0			0
$280$	0.656854			0.0392545
$281$	−1.61803	+	1.17557i	−0.0965238	+	0.0701287i	−0.635000	−	0.772512i	$-0.719000\pi$
$281$	−1.61803	+	1.17557i	−0.0965238	+	0.0701287i	0.538477	+	0.842641i	$0.319000\pi$
$282$	1.51361	−	0.673903i	0.0901343	−	0.0401304i
$283$	−4.22020	+	12.9884i	−0.250865	+	0.772083i	0.743751	+	0.668456i	$0.233045\pi$
$283$	−4.22020	+	12.9884i	−0.250865	+	0.772083i	−0.994616	+	0.103626i	$0.966955\pi$
$284$	0.0649712	+	0.112533i	0.00385533	+	0.00667763i
$285$	−0.914214	+	1.58346i	−0.0541533	+	0.0937963i
$286$	−3.44076	−	3.82135i	−0.203456	−	0.225961i
$287$	0.958109	+	2.94876i	0.0565554	+	0.174060i
$288$	−8.35428	+	9.27837i	−0.492281	+	0.546733i
$289$	15.5034	+	6.90255i	0.911964	+	0.406032i
$290$	2.76662	−	0.588063i	0.162461	−	0.0345323i
$291$	−0.223914	−	2.13040i	−0.0131261	−	0.124886i
$292$	−0.349454	+	3.32483i	−0.0204502	+	0.194571i
$293$	−14.4756	−	3.07688i	−0.845673	−	0.179753i	−0.235355	−	0.971910i	$-0.575625\pi$
$293$	−14.4756	−	3.07688i	−0.845673	−	0.179753i	−0.610319	+	0.792156i	$0.708959\pi$
$294$	0.947822	+	0.688633i	0.0552781	+	0.0401619i
$295$	−3.29356	−	2.39291i	−0.191759	−	0.139321i
$296$	1.55113	+	0.329704i	0.0901578	+	0.0191636i
$297$	0.818293	−	7.78554i	0.0474822	−	0.451763i
$298$	−0.0432971	−	0.411944i	−0.00250813	−	0.0238633i
$299$	−14.9791	+	3.18390i	−0.866262	+	0.184130i
$300$	2.76753	+	1.23218i	0.159783	+	0.0711401i
$301$	3.02094	−	3.35509i	0.174124	−	0.193384i
$302$	0.680150	+	2.09329i	0.0391382	+	0.120455i
$303$	−2.35181	−	2.61194i	−0.135108	−	0.150052i
$304$	−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
$307$	−10.2707	+	4.57279i	−0.586178	+	0.260983i	−0.678325	−	0.734762i	$-0.737294\pi$
$307$	−10.2707	+	4.57279i	−0.586178	+	0.260983i	0.0921470	+	0.995745i	$0.470627\pi$
$308$	−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
$313$	−1.67035	+	0.743688i	−0.0944138	+	0.0420357i	−0.453400	−	0.891307i	$-0.649789\pi$
$313$	−1.67035	+	0.743688i	−0.0944138	+	0.0420357i	0.358986	+	0.933343i	$0.383122\pi$
$314$	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
$317$	−5.23824	−	5.81766i	−0.294209	−	0.326752i	0.577859	−	0.816136i	$-0.303888\pi$
$317$	−5.23824	−	5.81766i	−0.294209	−	0.326752i	−0.872068	+	0.489384i	$0.837222\pi$
$318$	0.309017	+	0.951057i	0.0173288	+	0.0533326i
$319$	−14.8160	+	16.4548i	−0.829536	+	0.921293i
$320$	−3.81092	−	1.69673i	−0.213037	−	0.0948502i
$321$	−5.02977	+	1.06911i	−0.280734	+	0.0596719i
$322$	−0.0717370	−	0.682532i	−0.00399775	−	0.0380360i
$323$	2.68930	−	25.5870i	0.149637	−	1.42370i
$324$	13.3872	+	2.84554i	0.743734	+	0.158086i
$325$	−12.3891	−	9.00117i	−0.687221	−	0.499295i
$326$	−7.02736	−	5.10567i	−0.389209	−	0.282777i
$327$	4.38727	+	0.932542i	0.242616	+	0.0515697i
$328$	−1.24076	+	11.8050i	−0.0685094	+	0.651824i
$329$	0.418114	+	3.97809i	0.0230514	+	0.219319i
$330$	−0.544192	+	0.115671i	−0.0299568	+	0.00636751i
$331$	8.44357	+	3.75932i	0.464101	+	0.206631i	0.625447	−	0.780267i	$-0.284917\pi$
$331$	8.44357	+	3.75932i	0.464101	+	0.206631i	−0.161346	+	0.986898i	$0.551583\pi$
$332$	12.3215	−	13.6844i	0.676231	−	0.751031i
$333$	−0.874032	−	2.68999i	−0.0478967	−	0.147411i
$334$	6.25178	+	6.94331i	0.342082	+	0.379921i
$335$	−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	−0.841557	−	0.540168i	$-0.818361\pi$
$337$	2.87809	−	8.85786i	0.156780	−	0.482519i	0.998337	+	0.0576496i	$0.0183606\pi$
$338$	0.626958	−	0.279140i	0.0341020	−	0.0151832i
$339$	−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
$344$	15.7900	−	7.03015i	0.851338	−	0.379040i
$345$	−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	$0.0929038\pi$
$348$	3.46046	+	3.84323i	0.185500	+	0.206019i
$349$	−8.37828	−	25.7857i	−0.448479	−	1.38028i	−0.878623	−	0.477517i	$-0.841537\pi$
$349$	−8.37828	−	25.7857i	−0.448479	−	1.38028i	0.430143	−	0.902761i	$-0.358463\pi$
$350$	0.459219	−	0.510014i	0.0245463	−	0.0272614i
$351$	8.44357	+	3.75932i	0.450685	+	0.200658i
$352$	−14.0009	+	2.97599i	−0.746252	+	0.158621i
$353$	−0.313585	−	2.98357i	−0.0166905	−	0.158799i	0.983002	−	0.183594i	$-0.0587733\pi$
$353$	−0.313585	−	2.98357i	−0.0166905	−	0.158799i	−0.999693	+	0.0247952i	$0.992107\pi$
$354$	−0.0730115	+	0.694658i	−0.00388052	+	0.0369207i
$355$	−0.0695148	−	0.0147758i	−0.00368946	−	0.000784220i
$356$	6.63476	+	4.82043i	0.351641	+	0.255482i
$357$	−0.809017	−	0.587785i	−0.0428177	−	0.0311089i
$358$	6.17574	+	1.31269i	0.326398	+	0.0693780i
$359$	−0.742205	+	7.06161i	−0.0391721	+	0.372697i	0.957321	+	0.289026i	$0.0933313\pi$
$359$	−0.742205	+	7.06161i	−0.0391721	+	0.372697i	−0.996493	+	0.0836716i	$0.973335\pi$
$360$	−0.468840	−	4.46071i	−0.0247100	−	0.235100i
$361$	−0.474677	+	0.100896i	−0.0249830	+	0.00531030i
$362$	4.65954	+	2.07456i	0.244900	+	0.109037i
$363$	−0.134502	+	0.149380i	−0.00705953	+	0.00784040i
$364$	−0.895993	−	2.75758i	−0.0469628	−	0.144537i
$365$	−1.22346	−	1.35879i	−0.0640386	−	0.0711221i
$366$	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
$369$	19.3412	−	8.61125i	1.00686	−	0.448284i
$370$	−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
$375$	−3.40563	+	1.51628i	−0.175866	+	0.0783005i
$376$	−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
$379$	4.94138	+	5.48796i	0.253822	+	0.281897i	0.856567	−	0.516036i	$-0.172593\pi$
$379$	4.94138	+	5.48796i	0.253822	+	0.281897i	−0.602745	+	0.797934i	$0.705926\pi$
$380$	−2.49410	−	7.67604i	−0.127944	−	0.393773i
$381$	2.46661	−	2.73945i	0.126368	−	0.140346i
$382$	−7.90843	−	3.52106i	−0.404630	−	0.180153i
$383$	−4.98905	+	1.06045i	−0.254928	+	0.0541867i	−0.333603	−	0.942714i	$-0.608265\pi$
$383$	−4.98905	+	1.06045i	−0.254928	+	0.0541867i	0.0786746	+	0.996900i	$0.474931\pi$
$384$	0.457059	+	4.34863i	0.0233242	+	0.221915i
$385$	0.140397	−	1.33579i	0.00715529	−	0.0680781i
$386$	−2.89372	−	0.615080i	−0.147287	−	0.0313067i
$387$	−24.9407	−	18.1205i	−1.26781	−	0.921117i
$388$	7.64994	+	5.55801i	0.388367	+	0.282165i
$389$	10.8987	+	2.31658i	0.552584	+	0.117455i	0.475737	−	0.879588i	$-0.342181\pi$
$389$	10.8987	+	2.31658i	0.552584	+	0.117455i	0.0768468	+	0.997043i	$0.475515\pi$
$390$	0.0686600	−	0.653256i	0.00347673	−	0.0330789i
$391$	−2.43695	−	23.1860i	−0.123242	−	1.17257i
$392$	−10.5918	+	2.25136i	−0.534967	+	0.113711i
$393$	−5.01105	−	2.23106i	−0.252774	−	0.112542i
$394$	−3.73762	+	4.15105i	−0.188299	+	0.209127i
$395$	−2.08814	−	6.42663i	−0.105066	−	0.323359i
$396$	11.2210	+	12.4622i	0.563878	+	0.626249i
$397$	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
$400$	−10.9625	+	4.88084i	−0.548127	+	0.244042i
$401$	21.7047	−	15.7694i	1.08388	−	0.787484i	0.105524	−	0.994417i	$-0.466348\pi$
$401$	21.7047	−	15.7694i	1.08388	−	0.787484i	0.978355	+	0.206933i	$0.0663482\pi$
$402$	0.556349			0.0277482
$403$		0			0
$404$	15.5147			0.771886
$405$	−6.05572	+	4.39974i	−0.300911	+	0.218625i
$406$	1.07029	−	0.476522i	0.0531174	−	0.0236494i
$407$	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	$0.996050\pi$
$410$	−2.07464	−	2.30412i	−0.102459	−	0.113793i
$411$	1.21411	+	3.73664i	0.0598875	+	0.184315i
$412$	−2.53386	+	2.81414i	−0.124834	+	0.138643i
$413$	−1.54050	−	0.685877i	−0.0758032	−	0.0337498i
$414$	−4.58388	+	0.974335i	−0.225286	+	0.0478859i
$415$	1.05271	+	10.0159i	0.0516757	+	0.491661i
$416$	1.76648	−	16.8069i	0.0866087	−	0.824027i
$417$		0			0
$418$	−4.79661	−	3.48494i	−0.234610	−	0.170454i
$419$	−22.6525	−	16.4580i	−1.10665	−	0.804025i	−0.124514	−	0.992218i	$-0.539737\pi$
$419$	−22.6525	−	16.4580i	−1.10665	−	0.804025i	−0.982132	+	0.188193i	$0.939737\pi$
$420$	−0.306853	−	0.0652237i	−0.0149729	−	0.00318259i
$421$	3.25524	−	30.9715i	0.158651	−	1.50946i	−0.568329	−	0.822801i	$-0.692410\pi$
$421$	3.25524	−	30.9715i	0.158651	−	1.50946i	0.726980	−	0.686659i	$-0.240923\pi$
$422$	−0.450905	−	4.29008i	−0.0219497	−	0.208838i
$423$	26.7168	−	5.67884i	1.29902	−	0.276115i
$424$	−8.44357	−	3.75932i	−0.410056	−	0.182569i
$425$	15.5999	−	17.3255i	0.756707	−	0.840408i
$426$	0.00376794	+	0.0115965i	0.000182557	+	0.000561854i
$427$	0.783935	+	0.870648i	0.0379373	+	0.0421336i
$428$	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
$431$	−15.3086	+	6.81583i	−0.737390	+	0.328307i	−0.740835	−	0.671687i	$-0.765570\pi$
$431$	−15.3086	+	6.81583i	−0.737390	+	0.328307i	0.00344529	+	0.999994i	$0.498903\pi$
$432$	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
$437$	−16.1303	+	7.18169i	−0.771619	+	0.343547i
$438$	−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
$441$	12.9234	+	14.3529i	0.615400	+	0.683471i
$442$	2.85613	+	8.79027i	0.135852	+	0.418111i
$443$	−3.18329	+	3.53541i	−0.151243	+	0.167972i	−0.814005	−	0.580858i	$-0.802717\pi$
$443$	−3.18329	+	3.53541i	−0.151243	+	0.167972i	0.662762	+	0.748830i	$0.269384\pi$
$444$	−0.691882	−	0.308046i	−0.0328353	−	0.0146192i
$445$	−4.38727	+	0.932542i	−0.207976	+	0.0442068i
$446$	1.02735	+	9.77459i	0.0486465	+	0.462840i
$447$	−0.0432971	+	0.411944i	−0.00204788	+	0.0194843i
$448$	−1.69016	−	0.359255i	−0.0798527	−	0.0169732i
$449$	32.8683	+	23.8802i	1.55115	+	1.12698i	0.942825	+	0.333288i	$0.108158\pi$
$449$	32.8683	+	23.8802i	1.55115	+	1.12698i	0.608324	+	0.793688i	$0.291842\pi$
$450$	−3.79129	−	2.75453i	−0.178723	−	0.129850i
$451$	23.7417	+	5.04645i	1.11795	+	0.237628i
$452$	3.18350	−	30.2890i	0.149739	−	1.42467i
$453$	−0.230068	−	2.18895i	−0.0108095	−	0.102846i
$454$	7.46074	−	1.58583i	0.350150	−	0.0744267i
$455$	1.44869	+	0.644997i	0.0679155	+	0.0302379i
$456$	−1.94014	+	2.15474i	−0.0908554	+	0.100905i
$457$	−9.61435	−	29.5899i	−0.449740	−	1.38416i	−0.877200	−	0.480124i	$-0.840591\pi$
$457$	−9.61435	−	29.5899i	−0.449740	−	1.38416i	0.427460	−	0.904034i	$-0.359409\pi$
$458$	−1.52032	−	1.68848i	−0.0710397	−	0.0788976i
$459$	−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	−0.965288	−	0.261189i	$-0.915885\pi$
$461$	−0.661956	+	2.03729i	−0.0308304	+	0.0948862i	0.934457	+	0.356075i	$0.115885\pi$
$462$	−0.210524	+	0.0937314i	−0.00979447	+	0.00436078i
$463$	7.25734	−	5.27276i	0.337277	−	0.245046i	−0.406235	−	0.913769i	$-0.633159\pi$
$463$	7.25734	−	5.27276i	0.337277	−	0.245046i	0.743512	+	0.668722i	$0.233159\pi$
$464$	−20.4853			−0.951005
$465$		0			0
$466$	−3.79899			−0.175985
$467$	6.47214	−	4.70228i	0.299495	−	0.217596i	−0.427881	−	0.903835i	$-0.640740\pi$
$467$	6.47214	−	4.70228i	0.299495	−	0.217596i	0.727376	+	0.686239i	$0.240740\pi$
$468$	−18.0873	+	8.05297i	−0.836085	+	0.372249i
$469$	−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
$472$	−4.31980	−	4.79763i	−0.198835	−	0.220829i
$473$	−10.9216	−	33.6133i	−0.502177	−	1.54554i
$474$	−0.775776	+	0.861587i	−0.0356326	+	0.0395740i
$475$	−16.1303	−	7.18169i	−0.740111	−	0.329519i
$476$	4.31775	−	0.917767i	0.197904	−	0.0420658i
$477$	1.72318	+	16.3950i	0.0788990	+	0.750674i
$478$	0.919745	−	8.75079i	0.0420682	−	0.400252i
$479$	15.3842	+	3.27002i	0.702923	+	0.149411i	0.545488	−	0.838118i	$-0.316344\pi$
$479$	15.3842	+	3.27002i	0.702923	+	0.149411i	0.157435	+	0.987529i	$0.449678\pi$
$480$	−1.47923	−	1.07472i	−0.0675172	−	0.0490541i
$481$	3.09726	+	2.25029i	0.141223	+	0.102605i
$482$	−5.40614	−	1.14911i	−0.246243	−	0.0523405i
$483$	−0.0717370	+	0.682532i	−0.00326415	+	0.0310563i
$484$	−0.0927483	−	0.882441i	−0.00421583	−	0.0401109i
$485$	−5.05856	+	1.07523i	−0.229697	+	0.0488237i
$486$	3.91388	+	1.74257i	0.177537	+	0.0790446i
$487$	12.9709	−	14.4057i	0.587770	−	0.652784i	−0.373747	−	0.927531i	$-0.621927\pi$
$487$	12.9709	−	14.4057i	0.587770	−	0.652784i	0.961517	+	0.274746i	$0.0885939\pi$
$488$	1.38603	+	4.26576i	0.0627425	+	0.193102i
$489$	5.81226	+	6.45517i	0.262840	+	0.291913i
$490$	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
$493$	36.3582	−	16.1877i	1.63749	−	0.729058i
$494$	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
$499$	−2.02186	+	0.900191i	−0.0905110	+	0.0402981i	−0.451493	−	0.892275i	$-0.649108\pi$
$499$	−2.02186	+	0.900191i	−0.0905110	+	0.0402981i	0.360982	+	0.932573i	$0.382442\pi$
$500$	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
$503$	−8.95616	−	9.94683i	−0.399336	−	0.443507i	0.509620	−	0.860399i	$-0.329786\pi$
$503$	−8.95616	−	9.94683i	−0.399336	−	0.443507i	−0.908956	+	0.416892i	$0.863119\pi$
$504$	−0.574112	−	1.76693i	−0.0255730	−	0.0787055i
$505$	−5.67776	+	6.30579i	−0.252657	+	0.280604i
$506$	−4.90810	−	2.18523i	−0.218192	−	0.0971452i
$507$	−0.671294	+	0.142688i	−0.0298132	+	0.00633700i
$508$	1.70090	+	16.1829i	0.0754650	+	0.718002i
$509$	3.42843	−	32.6193i	0.151962	−	1.44583i	−0.607006	−	0.794698i	$-0.707629\pi$
$509$	3.42843	−	32.6193i	0.151962	−	1.44583i	0.758968	−	0.651128i	$-0.225704\pi$
$510$	0.978148	+	0.207912i	0.0433131	+	0.00920648i
$511$	−0.612717	−	0.445165i	−0.0271050	−	0.0196929i
$512$	−18.4111	−	13.3764i	−0.813663	−	0.591161i
$513$	10.4240	+	2.21568i	0.460230	+	0.0978249i
$514$	−0.966119	+	9.19201i	−0.0426137	+	0.405442i
$515$	−0.216486	−	2.05972i	−0.00953949	−	0.0907622i
$516$	−8.07445	+	1.71628i	−0.355458	+	0.0755549i
$517$	28.6065	+	12.7364i	1.25811	+	0.560148i
$518$	−0.114805	+	0.127503i	−0.00504423	+	0.00560218i
$519$	1.06415	+	3.27511i	0.0467109	+	0.143761i
$520$	4.06234	+	4.51168i	0.178145	+	0.197850i
$521$	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	−0.990445	−	0.137906i	$-0.955963\pi$
$523$	−2.47214	+	7.60845i	−0.108099	+	0.332694i	0.882346	+	0.470601i	$0.155963\pi$
$524$	22.1199	−	9.84840i	0.966311	−	0.430229i
$525$	−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
$530$	2.20549	−	0.981949i	0.0958005	−	0.0426531i
$531$	−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
$534$	0.514931	+	0.571889i	0.0222833	+	0.0247481i
$535$	3.83620	+	11.8066i	0.165854	+	0.510445i
$536$	−3.44076	+	3.82135i	−0.148618	+	0.165057i
$537$	−5.76786	−	2.56802i	−0.248902	−	0.110818i
$538$	10.6037	−	2.25389i	0.457159	−	0.0971722i
$539$	2.31448	+	22.0208i	0.0996919	+	0.948505i
$540$	−0.461411	+	4.39003i	−0.0198560	+	0.188917i
$541$	30.6006	+	6.50437i	1.31562	+	0.279645i	0.811685	−	0.584095i	$-0.198550\pi$
$541$	30.6006	+	6.50437i	1.31562	+	0.279645i	0.503939	+	0.863739i	$0.331884\pi$
$542$	0.229980	+	0.167090i	0.00987850	+	0.00717715i
$543$	−4.12640	−	2.99800i	−0.177081	−	0.128657i
$544$	25.1657	+	5.34914i	1.07897	+	0.229342i
$545$	1.13188	−	10.7691i	0.0484844	−	0.461298i
$546$	−0.0284399	−	0.270587i	−0.00121711	−	0.0115801i
$547$	19.2968	−	4.10167i	0.825072	−	0.175375i	0.224020	−	0.974584i	$-0.428082\pi$
$547$	19.2968	−	4.10167i	0.825072	−	0.175375i	0.601052	+	0.799210i	$0.294748\pi$
$548$	−15.8438	−	7.05409i	−0.676812	−	0.301336i
$549$	5.35304	−	5.94516i	0.228462	−	0.253733i
$550$	−1.66022	−	5.10963i	−0.0707920	−	0.217875i
$551$	−20.1690	−	22.4000i	−0.859229	−	0.954271i
$552$	−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
$555$	0.378403	−	0.168476i	0.0160623	−	0.00715140i
$556$		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
$561$	−7.15162	+	3.18411i	−0.301942	+	0.134433i
$562$	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
$565$	11.1456	+	12.3785i	0.468899	+	0.520766i
$566$	−1.74806	−	5.37999i	−0.0734766	−	0.226138i
$567$	−2.07464	+	2.30412i	−0.0871268	+	0.0967641i
$568$	−0.102955	−	0.0458386i	−0.00431990	−	0.00192334i
$569$	12.8549	−	2.73240i	0.538907	−	0.114548i	0.0695864	−	0.997576i	$-0.477832\pi$
$569$	12.8549	−	2.73240i	0.538907	−	0.114548i	0.469321	+	0.883028i	$0.344499\pi$
$570$	−0.0791656	−	0.753210i	−0.00331588	−	0.0315485i
$571$	2.20560	−	20.9849i	0.0923016	−	0.878191i	−0.846188	−	0.532884i	$-0.821108\pi$
$571$	2.20560	−	20.9849i	0.0923016	−	0.878191i	0.938490	−	0.345307i	$-0.112225\pi$
$572$	−22.2025	−	4.71928i	−0.928332	−	0.197323i
$573$	7.00354	+	5.08837i	0.292577	+	0.212570i
$574$	−1.03900	−	0.754876i	−0.0433669	−	0.0315079i
$575$	−15.6504	−	3.32659i	−0.652665	−	0.138728i
$576$	−1.23333	+	11.7344i	−0.0513888	+	0.488931i
$577$	0.00307703	+	0.0292760i	0.000128098	+	0.00121878i	0.994586	−	0.103919i	$-0.0331383\pi$
$577$	0.00307703	+	0.0292760i	0.000128098	+	0.00121878i	−0.994458	+	0.105138i	$0.966472\pi$
$578$	−6.87583	+	1.46150i	−0.285997	+	0.0607905i
$579$	2.70260	+	1.20328i	0.112316	+	0.0500065i
$580$	8.35428	−	9.27837i	0.346893	−	0.385263i
$581$	1.28909	+	3.96740i	0.0534803	+	0.164596i
$582$	0.593721	+	0.659394i	0.0246105	+	0.0273327i
$583$	−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
$586$	5.59998	−	2.49327i	0.231333	−	0.102996i
$587$	25.6109	−	18.6074i	1.05708	−	0.768011i	0.0835311	−	0.996505i	$-0.473380\pi$
$587$	25.6109	−	18.6074i	1.05708	−	0.768011i	0.973545	+	0.228494i	$0.0733802\pi$
$588$	5.17157			0.213272
$589$		0			0
$590$	1.68629			0.0694235
$591$	4.51900	−	3.28324i	0.185887	−	0.135055i
$592$	2.74064	−	1.22021i	0.112639	−	0.0501503i
$593$	−0.405958	+	1.24941i	−0.0166707	+	0.0513072i	−0.959046	−	0.283251i	$-0.908587\pi$
$593$	−0.405958	+	1.24941i	−0.0166707	+	0.0513072i	0.942375	+	0.334558i	$0.108587\pi$
$594$	1.62132	+	2.80821i	0.0665236	+	0.115222i
$595$	−1.20711	+	2.09077i	−0.0494866	+	0.0857132i
$596$	−1.22346	−	1.35879i	−0.0501147	−	0.0556580i
$597$	2.35700	+	7.25410i	0.0964656	+	0.296891i
$598$	4.24439	−	4.71388i	0.173566	−	0.192765i
$599$	13.7950	+	6.14193i	0.563648	+	0.250952i	0.668723	−	0.743512i	$-0.266841\pi$
$599$	13.7950	+	6.14193i	0.563648	+	0.250952i	−0.105074	+	0.994464i	$0.533508\pi$
$600$	−2.57000	+	0.546271i	−0.104920	+	0.0223014i
$601$	0.680974	+	6.47903i	0.0277775	+	0.264285i	0.999593	+	0.0285409i	$0.00908609\pi$
$601$	0.680974	+	6.47903i	0.0277775	+	0.264285i	−0.971815	+	0.235744i	$0.924247\pi$
$602$	−0.195474	+	1.85981i	−0.00796694	+	0.0758003i
$603$	8.97115	+	1.90688i	0.365334	+	0.0776540i
$604$	7.86019	+	5.71076i	0.319827	+	0.232368i
$605$	0.392601	+	0.285241i	0.0159615	+	0.0115967i
$606$	1.42403	+	0.302687i	0.0578473	+	0.0122958i
$607$	0.165760	−	1.57710i	0.00672798	−	0.0640125i	−0.990643	−	0.136481i	$-0.956421\pi$
$607$	0.165760	−	1.57710i	0.00672798	−	0.0640125i	0.997371	+	0.0724681i	$0.0230875\pi$
$608$	−2.03677	−	19.3785i	−0.0826018	−	0.785904i
$609$	−1.14597	+	0.243584i	−0.0464371	+	0.00987051i
$610$	−1.07029	−	0.476522i	−0.0433346	−	0.0192938i
$611$	−24.7381	+	27.4745i	−1.00080	+	1.11150i
$612$	−9.31443	−	28.6669i	−0.376514	−	1.15879i
$613$	8.23948	+	9.15087i	0.332789	+	0.369600i	0.886196	−	0.463311i	$-0.153339\pi$
$613$	8.23948	+	9.15087i	0.332789	+	0.369600i	−0.553406	+	0.832912i	$0.686672\pi$
$614$	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
$617$	−30.4067	+	13.5379i	−1.22413	+	0.545017i	−0.914014	−	0.405683i	$-0.867034\pi$
$617$	−30.4067	+	13.5379i	−1.22413	+	0.545017i	−0.310114	+	0.950700i	$0.600367\pi$
$618$	−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
$623$	−1.69724	+	0.755662i	−0.0679986	+	0.0302749i
$624$	−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
$627$	3.96723	+	4.40606i	0.158436	+	0.175961i
$628$	−5.18208	−	15.9488i	−0.206787	−	0.636426i
$629$	−3.89998	+	4.33137i	−0.155502	+	0.172703i
$630$	0.443327	+	0.197382i	0.0176626	+	0.00786388i
$631$	−48.9193	+	10.3981i	−1.94745	+	0.413943i	−0.953971	+	0.299898i	$0.903047\pi$
$631$	−48.9193	+	10.3981i	−1.94745	+	0.413943i	−0.993476	+	0.114044i	$0.963619\pi$
$632$	−1.12010	−	10.6570i	−0.0445551	−	0.423914i
$633$	−0.450905	+	4.29008i	−0.0179219	+	0.170515i
$634$	3.17178	+	0.674183i	0.125968	+	0.0267752i
$635$	−7.19984	−	5.23099i	−0.285717	−	0.207586i
$636$	3.57117	+	2.59461i	0.141606	+	0.102883i
$637$	−25.5709	−	5.43526i	−1.01315	−	0.215353i
$638$	0.958690	−	9.12133i	0.0379549	−	0.361117i
$639$	0.0210113	+	0.199909i	0.000831193	+	0.00790828i
$640$	10.3257	−	2.19479i	0.408158	−	0.0867566i
$641$	−12.7627	−	5.68234i	−0.504098	−	0.224439i	0.138900	−	0.990306i	$-0.455643\pi$
$641$	−12.7627	−	5.68234i	−0.504098	−	0.224439i	−0.642999	+	0.765867i	$0.722310\pi$
$642$	1.42521	−	1.58286i	0.0562485	−	0.0624703i
$643$	10.9125	+	33.5853i	0.430348	+	1.32448i	0.897779	+	0.440446i	$0.145180\pi$
$643$	10.9125	+	33.5853i	0.430348	+	1.32448i	−0.467430	+	0.884030i	$0.654820\pi$
$644$	−2.02709	−	2.25131i	−0.0798785	−	0.0887141i
$645$	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	0.157029	+	0.987594i	$0.449808\pi$
$647$	−14.0027	+	43.0959i	−0.550503	+	1.69427i	−0.707533	+	0.706681i	$0.750192\pi$
$648$	−10.8438	+	4.82799i	−0.425986	+	0.189661i
$649$	−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	−0.486297	−	0.873793i	$-0.661653\pi$
$653$	4.96909	−	3.61026i	0.194456	−	0.141280i	0.680753	+	0.732513i	$0.261653\pi$
$654$	−1.69724	+	0.755662i	−0.0663675	+	0.0295487i
$655$	−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
$658$	−1.10865	−	1.23128i	−0.0432198	−	0.0480004i
$659$	−0.511996	−	1.57576i	−0.0199445	−	0.0613830i	0.940589	−	0.339548i	$-0.110274\pi$
$659$	−0.511996	−	1.57576i	−0.0199445	−	0.0613830i	−0.960533	+	0.278165i	$0.910274\pi$
$660$	−1.64328	+	1.82505i	−0.0639646	+	0.0710399i
$661$	4.43788	+	1.97587i	0.172614	+	0.0768525i	0.491224	−	0.871033i	$-0.336550\pi$
$661$	4.43788	+	1.97587i	0.172614	+	0.0768525i	−0.318611	+	0.947886i	$0.603216\pi$
$662$	−3.74477	+	0.795975i	−0.145544	+	0.0309364i
$663$	−0.966119	−	9.19201i	−0.0375210	−	0.356988i
$664$	−1.66938	+	15.8831i	−0.0647844	+	0.616383i
$665$	1.78847	+	0.380151i	0.0693540	+	0.0147416i
$666$	0.947822	+	0.688633i	0.0367274	+	0.0266840i
$667$	−22.0973	−	16.0546i	−0.855609	−	0.621636i
$668$	40.3414	+	8.57483i	1.56086	+	0.331770i
$669$	1.02735	−	9.77459i	0.0397197	−	0.377907i
$670$	−0.140397	−	1.33579i	−0.00542401	−	0.0516060i
$671$	8.97115	−	1.90688i	0.346327	−	0.0736142i
$672$	−0.691882	−	0.308046i	−0.0266899	−	0.0118831i
$673$	6.25178	−	6.94331i	0.240989	−	0.267645i	−0.610502	−	0.792015i	$-0.709032\pi$
$673$	6.25178	−	6.94331i	0.240989	−	0.267645i	0.851491	+	0.524370i	$0.175699\pi$
$674$	1.19215	+	3.66905i	0.0459197	+	0.141326i
$675$	6.46170	+	7.17644i	0.248711	+	0.276221i
$676$	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
$679$	−1.95694	+	0.871285i	−0.0751004	+	0.0334369i
$680$	−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
$685$	8.66524	−	3.85801i	0.331082	−	0.147407i
$686$	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
$689$	−14.9308	−	16.5823i	−0.568818	−	0.631736i
$690$	−0.212076	−	0.652702i	−0.00807359	−	0.0248479i
$691$	−0.0475536	+	0.0528137i	−0.00180903	+	0.00200913i	−0.744049	−	0.668125i	$-0.767097\pi$
$691$	−0.0475536	+	0.0528137i	−0.00180903	+	0.00200913i	0.742240	+	0.670135i	$0.233764\pi$
$692$	−13.8868	−	6.18281i	−0.527897	−	0.235035i
$693$	−3.71597	+	0.789854i	−0.141158	+	0.0300041i
$694$	0.370465	+	3.52474i	0.0140627	+	0.133797i
$695$		0			0
$696$	−4.38727	−	0.932542i	−0.166299	−	0.0353479i
$697$	−35.2953	−	25.6436i	−1.33691	−	0.971319i
$698$	9.08562	+	6.60109i	0.343896	+	0.249855i
$699$	3.71597	+	0.789854i	0.140551	+	0.0298750i
$700$	0.316662	−	3.01284i	0.0119687	−	0.113875i
$701$	1.40960	+	13.4114i	0.0532397	+	0.506542i	0.988351	+	0.152189i	$0.0486322\pi$
$701$	1.40960	+	13.4114i	0.0532397	+	0.506542i	−0.935112	+	0.354353i	$0.884701\pi$
$702$	−3.74477	+	0.795975i	−0.141337	+	0.0300421i
$703$	4.03258	+	1.79542i	0.152092	+	0.0677156i
$704$	−9.05127	+	10.0525i	−0.341133	+	0.378866i
$705$	1.23607	+	3.80423i	0.0465530	+	0.143275i
$706$	0.831489	+	0.923462i	0.0312935	+	0.0347550i
$707$	−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	−0.798924	−	0.601432i	$-0.794597\pi$
$709$	5.35023	−	16.4663i	0.200932	−	0.618405i	0.999856	−	0.0169732i	$-0.00540301\pi$
$710$	0.0268923	−	0.0119732i	0.00100925	−	0.000449347i
$711$	−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
$716$	25.4606	−	11.3358i	0.951506	−	0.423638i
$717$	−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	$0.118578\pi$
$720$	−5.67776	−	6.30579i	−0.211598	−	0.235003i
$721$	−0.265095	−	0.815878i	−0.00987264	−	0.0303849i
$722$	0.134502	−	0.149380i	0.00500565	−	0.00555933i
$723$	5.04909	+	2.24800i	0.187778	+	0.0836039i
$724$	22.0227	−	4.68107i	0.818468	−	0.173971i
$725$	−2.85506	−	27.1641i	−0.106034	−	1.00885i
$726$	0.00870316	−	0.0828050i	0.000323004	−	0.00307318i
$727$	−39.9482	−	8.49124i	−1.48160	−	0.314923i	−0.605029	−	0.796204i	$-0.706838\pi$
$727$	−39.9482	−	8.49124i	−1.48160	−	0.314923i	−0.876566	+	0.481281i	$0.840172\pi$
$728$	2.03445	+	1.47811i	0.0754017	+	0.0547826i
$729$	14.7011	+	10.6810i	0.544486	+	0.395592i
$730$	0.740809	+	0.157464i	0.0274186	+	0.00582800i
$731$	−6.64037	+	63.1789i	−0.245603	+	2.33676i
$732$	−0.223914	−	2.13040i	−0.00827610	−	0.0787419i
$733$	−15.2859	+	3.24912i	−0.564598	+	0.120009i	−0.481364	−	0.876521i	$-0.659858\pi$
$733$	−15.2859	+	3.24912i	−0.564598	+	0.120009i	−0.0832345	+	0.996530i	$0.526525\pi$
$734$	−9.16235	−	4.07934i	−0.338188	−	0.150571i
$735$	−1.89259	+	2.10193i	−0.0698091	+	0.0775309i
$736$	−5.45627	−	16.7927i	−0.201121	−	0.618986i
$737$	7.03572	+	7.81396i	0.259164	+	0.287831i
$738$	−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
$741$	−6.39482	+	2.84716i	−0.234920	+	0.104593i
$742$	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
$747$	26.0226	−	11.5860i	0.952117	−	0.423910i
$748$	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
$751$	4.84627	+	5.38233i	0.176843	+	0.196404i	0.825049	−	0.565061i	$-0.191147\pi$
$751$	4.84627	+	5.38233i	0.176843	+	0.196404i	−0.648206	+	0.761465i	$0.724481\pi$
$752$	8.95240	+	27.5526i	0.326460	+	1.00474i
$753$	1.77778	−	1.97443i	0.0647860	−	0.0719521i
$754$	9.89226	+	4.40432i	0.360255	+	0.160396i
$755$	−5.19759	+	1.10478i	−0.189160	+	0.0402071i
$756$	0.191123	+	1.81841i	0.00695106	+	0.0661350i
$757$	−2.44002	+	23.2153i	−0.0886841	+	0.843773i	0.856261	+	0.516544i	$0.172782\pi$
$757$	−2.44002	+	23.2153i	−0.0886841	+	0.843773i	−0.944945	+	0.327229i	$0.893885\pi$
$758$	−2.99203	−	0.635976i	−0.108675	−	0.0230997i
$759$	4.34651	+	3.15793i	0.157768	+	0.114625i
$760$	5.66312	+	4.11450i	0.205423	+	0.149248i
$761$	−29.7903	−	6.33213i	−1.07990	−	0.229539i	−0.366585	−	0.930385i	$-0.619473\pi$
$761$	−29.7903	−	6.33213i	−1.07990	−	0.229539i	−0.713313	+	0.700845i	$0.752806\pi$
$762$	−0.159606	+	1.51855i	−0.00578191	+	0.0550112i
$763$	−0.468840	−	4.46071i	−0.0169731	−	0.161489i
$764$	−37.3782	+	7.94497i	−1.35229	+	0.287439i
$765$	15.0601	+	6.70517i	0.544497	+	0.242426i
$766$	1.41367	−	1.57004i	0.0510780	−	0.0567279i
$767$	−4.81627	−	14.8230i	−0.173906	−	0.535226i
$768$	1.10049	+	1.22222i	0.0397106	+	0.0441031i
$769$	−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
$772$	−11.9299	+	5.31152i	−0.429366	+	0.191166i
$773$	−14.5623	+	10.5801i	−0.523770	+	0.380541i	−0.818022	−	0.575187i	$-0.804929\pi$
$773$	−14.5623	+	10.5801i	−0.523770	+	0.380541i	0.294252	+	0.955728i	$0.404929\pi$
$774$	12.7696			0.458992
$775$		0			0
$776$	−8.20101			−0.294399
$777$	0.138805	−	0.100848i	0.00497961	−	0.00361790i
$778$	−4.21622	+	1.87718i	−0.151159	+	0.0673002i
$779$	−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
$782$	6.46170	+	7.17644i	0.231070	+	0.256629i
$783$	5.09423	+	15.6784i	0.182053	+	0.560302i
$784$	−13.7073	+	15.2235i	−0.489547	+	0.543698i
$785$	8.37865	+	3.73041i	0.299047	+	0.133144i
$786$	2.22243	−	0.472392i	0.0792714	−	0.0168496i
$787$	−4.43349	−	42.1819i	−0.158037	−	1.50362i	−0.730060	−	0.683383i	$-0.760508\pi$
$787$	−4.43349	−	42.1819i	−0.158037	−	1.50362i	0.572023	−	0.820238i	$-0.306159\pi$
$788$	−2.57734	+	24.5218i	−0.0918140	+	0.873552i
$789$	9.44583	+	2.00777i	0.336280	+	0.0714786i
$790$	2.26443	+	1.64520i	0.0805648	+	0.0585338i
$791$	5.58181	+	4.05542i	0.198466	+	0.144194i
$792$	−14.2263	−	3.02390i	−0.505511	−	0.107450i
$793$	−1.13188	+	10.7691i	−0.0401942	+	0.382422i
$794$	1.44982	+	13.7941i	0.0514520	+	0.489533i
$795$	−2.36146	+	0.501943i	−0.0837523	+	0.0178021i
$796$	−30.7582	−	13.6944i	−1.09020	−	0.485386i
$797$	19.0407	−	21.1468i	0.674455	−	0.749059i	−0.304638	−	0.952468i	$-0.598536\pi$
$797$	19.0407	−	21.1468i	0.674455	−	0.749059i	0.979094	+	0.203410i	$0.0652023\pi$
$798$	−0.0969413	−	0.298355i	−0.00343168	−	0.0105616i
$799$	−37.6615	−	41.8274i	−1.33237	−	1.47975i
$800$	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
$803$	−5.41635	+	2.41151i	−0.191139	+	0.0851005i
$804$	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
$809$	−10.9894	+	4.89281i	−0.386368	+	0.172022i	−0.590722	−	0.806875i	$-0.701157\pi$
$809$	−10.9894	+	4.89281i	−0.386368	+	0.172022i	0.204354	+	0.978897i	$0.434491\pi$
$810$	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
$813$	−0.190215	−	0.211255i	−0.00667112	−	0.00740903i
$814$	0.415055	+	1.27741i	0.0145477	+	0.0447731i
$815$	14.0320	−	15.5842i	0.491521	−	0.545889i
$816$	−6.61648	−	2.94585i	−0.231623	−	0.103125i
$817$	47.0613	−	10.0032i	1.64647	−	0.349967i
$818$	−0.894382	−	8.50948i	−0.0312713	−	0.297527i
$819$	0.468840	−	4.46071i	0.0163826	−	0.155870i
$820$	−13.3872	−	2.84554i	−0.467502	−	0.0993706i
$821$	−6.86474	−	4.98752i	−0.239581	−	0.174066i	0.461516	−	0.887132i	$-0.347306\pi$
$821$	−6.86474	−	4.98752i	−0.239581	−	0.174066i	−0.701097	+	0.713066i	$0.747306\pi$
$822$	−1.31661	−	0.956572i	−0.0459220	−	0.0333643i
$823$	−35.4219	−	7.52915i	−1.23473	−	0.262450i	−0.456096	−	0.889930i	$-0.650753\pi$
$823$	−35.4219	−	7.52915i	−1.23473	−	0.262450i	−0.778632	+	0.627481i	$0.784086\pi$
$824$	0.343300	−	3.26628i	0.0119594	−	0.113786i
$825$	0.561588	+	5.34315i	0.0195520	+	0.186025i
$826$	0.683221	−	0.145223i	0.0237723	−	0.00505296i
$827$	33.7094	+	15.0084i	1.17219	+	0.521892i	0.898091	−	0.439809i	$-0.144954\pi$
$827$	33.7094	+	15.0084i	1.17219	+	0.521892i	0.274098	+	0.961702i	$0.411621\pi$
$828$	−13.8418	+	15.3729i	−0.481037	+	0.534246i
$829$	11.8744	+	36.5457i	0.412415	+	1.26928i	0.914542	+	0.404490i	$0.132551\pi$
$829$	11.8744	+	36.5457i	0.412415	+	1.26928i	−0.502127	+	0.864794i	$0.667449\pi$
$830$	−2.79133	−	3.10008i	−0.0968884	−	0.107605i
$831$	−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	−0.364465	−	0.931217i	$-0.618748\pi$
$839$	11.8338	−	8.59778i	0.408549	−	0.296828i	0.773014	+	0.634389i	$0.218748\pi$
$840$	0.248556	−	0.110664i	0.00857598	−	0.00381827i
$841$	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
$844$	−12.7413	−	14.1507i	−0.438575	−	0.487087i
$845$	0.511996	+	1.57576i	0.0176132	+	0.0542079i
$846$	−7.57035	+	8.40772i	−0.260274	+	0.289064i
$847$	0.183632	+	0.0817582i	0.00630967	+	0.00280924i
$848$	−17.1032	+	3.63539i	−0.587326	+	0.124840i
$849$	0.591302	+	5.62587i	0.0202934	+	0.193079i
$850$	−1.00942	+	9.60395i	−0.0346227	+	0.329413i
$851$	3.91259	+	0.831647i	0.134122	+	0.0285085i
$852$	0.0435444	+	0.0316369i	0.00149181	+	0.00108386i
$853$	12.5517	+	9.11932i	0.429761	+	0.312240i	0.781553	−	0.623838i	$-0.214428\pi$
$853$	12.5517	+	9.11932i	0.429761	+	0.312240i	−0.351792	+	0.936078i	$0.614428\pi$
$854$	−0.474677	−	0.100896i	−0.0162431	−	0.00345258i
$855$	1.30507	−	12.4169i	0.0446324	−	0.424649i
$856$	2.05778	+	19.5784i	0.0703334	+	0.669178i
$857$	19.0595	−	4.05122i	0.651059	−	0.138387i	0.129470	−	0.991583i	$-0.458672\pi$
$857$	19.0595	−	4.05122i	0.651059	−	0.138387i	0.521590	+	0.853196i	$0.325339\pi$
$858$	−1.94580	−	0.866326i	−0.0664285	−	0.0295759i
$859$	−33.0449	+	36.7000i	−1.12748	+	1.25219i	−0.163401	+	0.986560i	$0.552246\pi$
$859$	−33.0449	+	36.7000i	−1.12748	+	1.25219i	−0.964075	+	0.265630i	$0.914420\pi$
$860$	6.15838	+	18.9535i	0.209999	+	0.646310i
$861$	0.859345	+	0.954400i	0.0292864	+	0.0325258i
$862$	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
$865$	7.59495	−	3.38149i	0.258236	−	0.114974i
$866$	−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
$871$	−11.3409	+	5.04932i	−0.384273	+	0.171090i
$872$	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
$875$	2.49447	+	2.77039i	0.0843284	+	0.0936561i
$876$	0.427919	+	1.31700i	0.0144581	+	0.0444973i
$877$	36.0182	−	40.0023i	1.21625	−	1.35078i	0.298107	−	0.954532i	$-0.403645\pi$
$877$	36.0182	−	40.0023i	1.21625	−	1.35078i	0.918143	−	0.396250i	$-0.129689\pi$
$878$	0.783698	+	0.348925i	0.0264485	+	0.0117756i
$879$	−5.99599	+	1.27449i	−0.202240	+	0.0429874i
$880$	−1.01684	−	9.67463i	−0.0342778	−	0.326132i
$881$	−1.22155	+	11.6223i	−0.0411551	+	0.391564i	0.954483	+	0.298265i	$0.0964080\pi$
$881$	−1.22155	+	11.6223i	−0.0411551	+	0.391564i	−0.995638	+	0.0932992i	$0.970259\pi$
$882$	−7.82518	−	1.66329i	−0.263488	−	0.0560060i
$883$	24.5005	+	17.8006i	0.824507	+	0.599040i	0.918000	−	0.396580i	$-0.129803\pi$
$883$	24.5005	+	17.8006i	0.824507	+	0.599040i	−0.0934928	+	0.995620i	$0.529803\pi$
$884$	33.0071	+	23.9810i	1.11015	+	0.806570i
$885$	−1.64944	−	0.350600i	−0.0554454	−	0.0117853i
$886$	0.205980	−	1.95977i	0.00692003	−	0.0658397i
$887$	5.36502	+	51.0447i	0.180140	+	1.71391i	0.594746	+	0.803914i	$0.297253\pi$
$887$	5.36502	+	51.0447i	0.180140	+	1.71391i	−0.414606	+	0.910001i	$0.636081\pi$
$888$	0.642500	−	0.136568i	0.0215609	−	0.00458291i
$889$	−3.36759	−	1.49935i	−0.112946	−	0.0502866i
$890$	1.24315	−	1.38066i	0.0416706	−	0.0462799i
$891$	7.50048	+	23.0841i	0.251276	+	0.773347i
$892$	29.0301	+	32.2412i	0.971999	+	1.07951i
$893$	−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
$896$	3.99455	−	1.77849i	0.133449	−	0.0594152i
$897$	−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
$902$	−9.18463	+	4.08926i	−0.305815	+	0.136157i
$903$	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
$906$	0.610039	+	0.677516i	0.0202672	+	0.0225090i
$907$	10.1006	+	31.0865i	0.335386	+	1.03221i	0.966532	+	0.256547i	$0.0825848\pi$
$907$	10.1006	+	31.0865i	0.335386	+	1.03221i	−0.631146	+	0.775664i	$0.717415\pi$
$908$	22.5290	−	25.0210i	0.747651	−	0.830350i
$909$	21.9251	+	9.76168i	0.727209	+	0.323774i
$910$	−0.642500	+	0.136568i	−0.0212987	+	0.00452717i
$911$	−0.100177	−	0.953119i	−0.00331901	−	0.0315783i	0.992737	−	0.120304i	$-0.0383871\pi$
$911$	−0.100177	−	0.953119i	−0.00331901	−	0.0315783i	−0.996056	+	0.0887262i	$0.971720\pi$
$912$	−0.573368	+	5.45523i	−0.0189861	+	0.180641i
$913$	31.9432	+	6.78974i	1.05717	+	0.224708i
$914$	10.4260	+	7.57497i	0.344863	+	0.250558i
$915$	0.947822	+	0.688633i	0.0313340	+	0.0227655i
$916$	−9.81027	−	2.08524i	−0.324140	−	0.0688982i
$917$	−0.573368	+	5.45523i	−0.0189343	+	0.180148i
$918$	−0.609237	−	5.79650i	−0.0201078	−	0.191313i
$919$	34.1369	−	7.25601i	1.12607	−	0.239354i	0.393022	−	0.919529i	$-0.371430\pi$
$919$	34.1369	−	7.25601i	1.12607	−	0.239354i	0.733049	+	0.680175i	$0.238096\pi$
$920$	5.79475	+	2.57999i	0.191047	+	0.0850597i
$921$	−3.11604	+	3.46072i	−0.102677	+	0.114035i
$922$	−0.274191	−	0.843874i	−0.00903001	−	0.0277915i
$923$	−0.182056	−	0.202193i	−0.00599244	−	0.00665527i
$924$	−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
$927$	−5.35143	+	2.38261i	−0.175764	+	0.0782551i
$928$	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
$933$	4.28114	−	1.90609i	0.140158	−	0.0624025i
$934$	−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
$937$	10.4962	+	11.6572i	0.342895	+	0.380824i	0.889784	−	0.456381i	$-0.150855\pi$
$937$	10.4962	+	11.6572i	0.342895	+	0.380824i	−0.546889	+	0.837205i	$0.684188\pi$
$938$	−0.171921	−	0.529120i	−0.00561343	−	0.0172764i
$939$	−0.506772	+	0.562828i	−0.0165379	+	0.0183672i
$940$	−16.1303	−	7.18169i	−0.526114	−	0.234241i
$941$	34.2352	−	7.27691i	1.11603	−	0.237220i	0.387258	−	0.921972i	$-0.373422\pi$
$941$	34.2352	−	7.27691i	1.11603	−	0.237220i	0.728777	+	0.684751i	$0.240089\pi$
$942$	−0.164485	−	1.56497i	−0.00535922	−	0.0509896i
$943$	−3.12970	+	29.7771i	−0.101917	+	0.969676i
$944$	−11.9463	−	2.53927i	−0.388819	−	0.0826461i
$945$	−0.809017	−	0.587785i	−0.0263173	−	0.0191207i
$946$	11.8437	+	8.60495i	0.385072	+	0.279771i
$947$	−18.6831	−	3.97122i	−0.607120	−	0.129047i	−0.105914	−	0.994375i	$-0.533777\pi$
$947$	−18.6831	−	3.97122i	−0.607120	−	0.129047i	−0.501206	+	0.865328i	$0.667110\pi$
$948$	−0.534950	+	5.08971i	−0.0173744	+	0.165306i
$949$	−0.731699	−	6.96165i	−0.0237520	−	0.225985i
$950$	7.15389	−	1.52061i	0.232103	−	0.0493350i
$951$	−2.96230	−	1.31890i	−0.0960591	−	0.0427683i
$952$	−2.56172	+	2.84508i	−0.0830257	+	0.0922094i
$953$	1.08611	+	3.34270i	0.0351825	+	0.108281i	0.967106	−	0.254376i	$-0.0818699\pi$
$953$	1.08611	+	3.34270i	0.0351825	+	0.108281i	−0.931923	+	0.362656i	$0.881870\pi$
$954$	−4.56911	−	5.07451i	−0.147930	−	0.164293i
$955$	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
$958$	−5.95149	+	2.64977i	−0.192284	+	0.0856103i
$959$	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
$964$	−22.2877	+	9.92314i	−0.717840	+	0.319603i
$965$	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	$0.0867892\pi$
$968$	0.514931	+	0.571889i	0.0165505	+	0.0183812i
$969$	−3.29315	−	10.1353i	−0.105791	−	0.325592i
$970$	1.43337	−	1.59192i	0.0460227	−	0.0511134i
$971$	−0.638098	−	0.284099i	−0.0204775	−	0.00911718i	0.396472	−	0.918047i	$-0.370234\pi$
$971$	−0.638098	−	0.284099i	−0.0204775	−	0.00911718i	−0.416950	+	0.908929i	$0.636901\pi$
$972$	18.4984	−	3.93196i	0.593337	−	0.126118i
$973$		0			0
$974$	−0.839305	+	7.98545i	−0.0268931	+	0.255870i
$975$	−6.20453	−	1.31881i	−0.198704	−	0.0422359i
$976$	6.86474	+	4.98752i	0.219735	+	0.159647i
$977$	0.392601	+	0.285241i	0.0125604	+	0.00912568i	0.594048	−	0.804430i	$-0.297529\pi$
$977$	0.392601	+	0.285241i	0.0125604	+	0.00912568i	−0.581487	+	0.813555i	$0.697529\pi$
$978$	−3.51936	−	0.748062i	−0.112537	−	0.0239204i
$979$	−1.52028	+	14.4645i	−0.0485883	+	0.462287i
$980$	−1.30507	−	12.4169i	−0.0416888	−	0.396643i
$981$	−29.9581	+	6.36780i	−0.956490	+	0.203308i
$982$	0.600066	+	0.267167i	0.0191489	+	0.00852563i
$983$	−25.9894	+	28.8642i	−0.828935	+	0.920625i	−0.997885	−	0.0649993i	$-0.979295\pi$
$983$	−25.9894	+	28.8642i	−0.828935	+	0.920625i	0.168951	+	0.985625i	$0.445962\pi$
$984$	1.51936	+	4.67610i	0.0484353	+	0.149069i
$985$	−9.02341	−	10.0215i	−0.287510	−	0.319312i
$986$	−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
$989$	39.8287	−	17.7329i	1.26648	−	0.563873i
$990$	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
$995$	16.8222	−	7.48974i	0.533300	−	0.237441i
$996$	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
$999$	−1.61542	−	1.79411i	−0.0511098	−	0.0567631i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.2	✓	4	31.8	even	5
31.2.c.a.25.2	yes	4	31.14	even	15
279.2.h.c.118.1		4	93.14	odd	30
279.2.h.c.253.1		4	93.8	odd	10
496.2.i.h.129.2		4	124.39	odd	10
496.2.i.h.273.2		4	124.107	odd	30
775.2.e.e.501.1		4	155.39	even	10
775.2.e.e.676.1		4	155.14	even	30
775.2.o.d.149.2		8	155.138	odd	60
775.2.o.d.149.3		8	155.107	odd	60
775.2.o.d.749.2		8	155.8	odd	20
775.2.o.d.749.3		8	155.132	odd	20
961.2.a.a.1.2		2	31.9	even	15
961.2.a.c.1.2		2	31.22	odd	30
961.2.c.a.439.2		4	31.23	odd	10
961.2.c.a.521.2		4	31.17	odd	30
961.2.d.i.374.1		8	31.21	odd	30
961.2.d.i.388.1		8	31.26	odd	6
961.2.d.i.531.2		8	31.13	odd	30
961.2.d.i.628.2		8	31.11	odd	30
961.2.d.l.374.1		8	31.10	even	15
961.2.d.l.388.1		8	31.5	even	3
961.2.d.l.531.2		8	31.18	even	15
961.2.d.l.628.2		8	31.20	even	15
961.2.g.o.235.1		16	1.1	even	1	trivial
961.2.g.o.338.1		16	31.25	even	3	inner
961.2.g.o.448.2		16	31.7	even	15	inner
961.2.g.o.547.2		16	31.16	even	5	inner
961.2.g.o.732.1		16	31.19	even	15	inner
961.2.g.o.816.1		16	31.2	even	5	inner
961.2.g.o.844.2		16	31.28	even	15	inner
961.2.g.o.846.2		16	31.4	even	5	inner
961.2.g.r.235.1		16	31.30	odd	2
961.2.g.r.338.1		16	31.6	odd	6
961.2.g.r.448.2		16	31.24	odd	30
961.2.g.r.547.2		16	31.15	odd	10
961.2.g.r.732.1		16	31.12	odd	30
961.2.g.r.816.1		16	31.29	odd	10
961.2.g.r.844.2		16	31.3	odd	30
961.2.g.r.846.2		16	31.27	odd	10
8649.2.a.k.1.1		2	93.53	even	30
8649.2.a.l.1.1		2	93.71	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)

\(f(q)\)	\(=\)	\(q+(-0.335106 + 0.243469i) q^{2} +(0.378403 - 0.168476i) q^{3} +(-0.565015 + 1.73894i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(-0.277163 - 0.307821i) q^{7} +(-0.490035 - 1.50817i) q^{8} +(-1.89259 + 2.10193i) q^{9} +O(q^{10})\)	\(q+(-0.335106 + 0.243469i) q^{2} +(0.378403 - 0.168476i) q^{3} +(-0.565015 + 1.73894i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(-0.277163 - 0.307821i) q^{7} +(-0.490035 - 1.50817i) q^{8} +(-1.89259 + 2.10193i) q^{9} +(0.378403 + 0.168476i) q^{10} +(-3.17178 + 0.674183i) q^{11} +(0.0791656 + 0.753210i) q^{12} +(0.400180 - 3.80745i) q^{13} +(0.167824 + 0.0356720i) q^{14} +(-0.335106 - 0.243469i) q^{15} +(-2.42705 - 1.76336i) q^{16} +(5.70106 + 1.21180i) q^{17} +(0.122463 - 1.16515i) q^{18} +(-0.461411 - 4.39003i) q^{19} +(1.78847 - 0.380151i) q^{20} +(-0.156740 - 0.0697850i) q^{21} +(0.898740 - 0.998152i) q^{22} +(-1.23607 - 3.80423i) q^{23} +(-0.439521 - 0.488138i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.792893 + 1.37333i) q^{26} +(-0.746033 + 2.29605i) q^{27} +(0.691882 - 0.308046i) q^{28} +(5.52431 - 4.01365i) q^{29} +0.171573 q^{30} +4.41421 q^{32} +(-1.08663 + 0.789481i) q^{33} +(-2.20549 + 0.981949i) q^{34} +(-0.127999 + 0.393941i) q^{35} +(-2.58579 - 4.47871i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(1.22346 + 1.35879i) q^{38} +(-0.490035 - 1.50817i) q^{39} +(-1.06110 + 1.17847i) q^{40} +(-6.83814 - 3.04454i) q^{41} +(0.0695148 - 0.0147758i) q^{42} +(1.13931 + 10.8398i) q^{43} +(0.619742 - 5.89645i) q^{44} +(2.76662 + 0.588063i) q^{45} +(1.34042 + 0.973874i) q^{46} +(-7.81256 - 5.67616i) q^{47} +(-1.21549 - 0.258360i) q^{48} +(0.713765 - 6.79102i) q^{49} +(0.173188 + 1.64778i) q^{50} +(2.36146 - 0.501943i) q^{51} +(6.39482 + 2.84716i) q^{52} +(3.89998 - 4.33137i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(2.16975 + 2.40975i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(-0.914214 - 1.58346i) q^{57} +(-0.874032 + 2.68999i) q^{58} +(3.71911 - 1.65585i) q^{59} +(0.612717 - 0.445165i) q^{60} -2.82843 q^{61} +1.17157 q^{63} +(3.37487 - 2.45199i) q^{64} +(-3.49744 + 1.55716i) q^{65} +(0.171921 - 0.529120i) q^{66} +(-1.62132 - 2.80821i) q^{67} +(-5.32843 + 9.22911i) q^{68} +(-1.10865 - 1.23128i) q^{69} +(-0.0530189 - 0.163176i) q^{70} +(0.0475536 - 0.0528137i) q^{71} +(4.09751 + 1.82433i) q^{72} +(1.78847 - 0.380151i) q^{73} +(-0.0432971 - 0.411944i) q^{74} +(0.173188 - 1.64778i) q^{75} +(7.89470 + 1.67807i) q^{76} +(1.08663 + 0.789481i) q^{77} +(0.531406 + 0.386089i) q^{78} +(6.60969 + 1.40493i) q^{79} +(-0.313585 + 2.98357i) q^{80} +(-0.782425 - 7.44428i) q^{81} +(3.03275 - 0.644631i) q^{82} +(-9.20038 - 4.09627i) q^{83} +(0.209912 - 0.233131i) q^{84} +(-1.80108 - 5.54316i) q^{85} +(-3.02094 - 3.35509i) q^{86} +(1.41421 - 2.44949i) q^{87} +(2.57107 + 4.45322i) q^{88} +(1.38603 - 4.26576i) q^{89} +(-1.07029 + 0.476522i) q^{90} +(-1.28293 + 0.932102i) q^{91} +7.31371 q^{92} +4.00000 q^{94} +(-3.57117 + 2.59461i) q^{95} +(1.67035 - 0.743688i) 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

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