LMFDB - Embedded newform 65.2.t.a.58.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(7,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

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

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

chi := DirichletCharacter("65.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.t (of order $12$, degree $4$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			58.5
Root			$2.08794i$ of defining polynomial
Character	$\chi$	$=$	65.58
Dual form			65.2.t.a.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80821 + 1.04397i) q^{2} +(-2.66159 + 0.713171i) q^{3} +(1.17974 + 2.04338i) q^{4} +(2.22760 + 0.194361i) q^{5} +(-5.55724 - 1.48906i) q^{6} +(-1.45563 - 2.52122i) q^{7} +0.750585i q^{8} +(3.97738 - 2.29634i) q^{9} +O(q^{10})$	\(q+(1.80821 + 1.04397i) q^{2} +(-2.66159 + 0.713171i) q^{3} +(1.17974 + 2.04338i) q^{4} +(2.22760 + 0.194361i) q^{5} +(-5.55724 - 1.48906i) q^{6} +(-1.45563 - 2.52122i) q^{7} +0.750585i q^{8} +(3.97738 - 2.29634i) q^{9} +(3.82506 + 2.67700i) q^{10} +(-0.0254491 + 0.00681908i) q^{11} +(-4.59727 - 4.59727i) q^{12} +(-3.56631 + 0.530479i) q^{13} -6.07853i q^{14} +(-6.06759 + 1.07135i) q^{15} +(1.57590 - 2.72954i) q^{16} +(-0.741318 + 2.76664i) q^{17} +9.58924 q^{18} +(-1.23878 + 4.62320i) q^{19} +(2.23085 + 4.78113i) q^{20} +(5.67236 + 5.67236i) q^{21} +(-0.0531363 - 0.0142378i) q^{22} +(-0.0961080 - 0.358680i) q^{23} +(-0.535296 - 1.99775i) q^{24} +(4.92445 + 0.865921i) q^{25} +(-7.00244 - 2.76390i) q^{26} +(-3.10321 + 3.10321i) q^{27} +(3.43454 - 5.94879i) q^{28} +(-3.62262 - 2.09152i) q^{29} +(-12.0899 - 4.39714i) q^{30} +(-0.835277 + 0.835277i) q^{31} +(6.99915 - 4.04096i) q^{32} +(0.0628721 - 0.0362992i) q^{33} +(-4.22874 + 4.22874i) q^{34} +(-2.75254 - 5.89921i) q^{35} +(9.38457 + 5.41819i) q^{36} +(-3.22588 + 5.58739i) q^{37} +(-7.06645 + 7.06645i) q^{38} +(9.11375 - 3.95531i) q^{39} +(-0.145885 + 1.67201i) q^{40} +(-2.02930 - 7.57344i) q^{41} +(4.33503 + 16.1786i) q^{42} +(6.69664 + 1.79436i) q^{43} +(-0.0439574 - 0.0439574i) q^{44} +(9.30635 - 4.34229i) q^{45} +(0.200668 - 0.748902i) q^{46} +0.833377 q^{47} +(-2.24777 + 8.38880i) q^{48} +(-0.737715 + 1.27776i) q^{49} +(8.00043 + 6.70674i) q^{50} -7.89234i q^{51} +(-5.29130 - 6.66149i) q^{52} +(0.902268 + 0.902268i) q^{53} +(-8.85092 + 2.37160i) q^{54} +(-0.0580160 + 0.0102439i) q^{55} +(1.89239 - 1.09257i) q^{56} -13.1885i q^{57} +(-4.36697 - 7.56381i) q^{58} +(-1.44647 - 0.387581i) q^{59} +(-9.34737 - 11.1344i) q^{60} +(5.35090 + 9.26802i) q^{61} +(-2.38236 + 0.638351i) q^{62} +(-11.5792 - 6.68524i) q^{63} +10.5710 q^{64} +(-8.04744 + 0.488545i) q^{65} +0.151581 q^{66} +(10.6667 + 6.15845i) q^{67} +(-6.52784 + 1.74913i) q^{68} +(0.511601 + 0.886118i) q^{69} +(1.18143 - 13.5406i) q^{70} +(-3.57441 - 0.957759i) q^{71} +(1.72360 + 2.98536i) q^{72} -15.0844i q^{73} +(-11.6661 + 6.73544i) q^{74} +(-13.7244 + 1.20725i) q^{75} +(-10.9084 + 2.92289i) q^{76} +(0.0542370 + 0.0542370i) q^{77} +(20.6088 + 2.36245i) q^{78} +4.25039i q^{79} +(4.04100 - 5.77403i) q^{80} +(-0.842658 + 1.45953i) q^{81} +(4.23705 - 15.8129i) q^{82} +1.31611 q^{83} +(-4.89883 + 18.2827i) q^{84} +(-2.18909 + 6.01889i) q^{85} +(10.2357 + 10.2357i) q^{86} +(11.1335 + 2.98322i) q^{87} +(-0.00511830 - 0.0191018i) q^{88} +(-0.867319 - 3.23688i) q^{89} +(21.3610 + 1.86378i) q^{90} +(6.52869 + 8.21929i) q^{91} +(0.619535 - 0.619535i) q^{92} +(1.62747 - 2.81886i) q^{93} +(1.50692 + 0.870020i) q^{94} +(-3.65809 + 10.0579i) q^{95} +(-15.7470 + 15.7470i) q^{96} +(0.351145 - 0.202734i) q^{97} +(-2.66788 + 1.54030i) q^{98} +(-0.0855620 + 0.0855620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9	$ 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24} + 18 q^{25} - 24 q^{26} + 4 q^{27} + 18 q^{28} - 26 q^{30} + 48 q^{32} + 18 q^{33} + 2 q^{34} + 40 q^{35} + 36 q^{36} - 4 q^{37} - 8 q^{38} + 4 q^{39} - 16 q^{40} + 10 q^{41} + 40 q^{42} + 10 q^{43} - 36 q^{44} + 4 q^{46} - 40 q^{47} - 56 q^{48} + 18 q^{49} + 36 q^{50} - 30 q^{52} - 10 q^{53} - 48 q^{54} - 10 q^{55} - 16 q^{59} + 28 q^{60} - 16 q^{61} - 44 q^{62} - 36 q^{63} + 20 q^{64} - 14 q^{65} - 32 q^{66} + 18 q^{67} + 22 q^{68} - 16 q^{69} - 12 q^{70} - 16 q^{71} + 4 q^{72} + 18 q^{74} - 38 q^{75} - 64 q^{76} - 28 q^{77} + 68 q^{78} - 2 q^{80} - 14 q^{81} + 56 q^{82} + 48 q^{83} - 40 q^{84} - 26 q^{85} + 60 q^{86} - 34 q^{87} + 82 q^{88} - 6 q^{89} + 46 q^{90} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 48 q^{94} - 26 q^{95} + 56 q^{96} + 66 q^{97} - 30 q^{98} + 60 q^{99}+O(q^{100}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	1.80821	+	1.04397i	1.27860	+	0.738198i	0.976590	−	0.215108i	$-0.0690105\pi$
$2$	1.80821	+	1.04397i	1.27860	+	0.738198i	0.302006	+	0.953306i	$0.402344\pi$
$3$	−2.66159	+	0.713171i	−1.53667	+	0.411750i	−0.925188	−	0.379508i	$-0.876093\pi$
$3$	−2.66159	+	0.713171i	−1.53667	+	0.411750i	−0.611482	+	0.791258i	$0.709426\pi$
$4$	1.17974	+	2.04338i	0.589872	+	1.02169i
$5$	2.22760	+	0.194361i	0.996215	+	0.0869210i
$5$	2.22760	+	0.194361i	0.996215	+	0.0869210i
$6$	−5.55724	−	1.48906i	−2.26873	−	0.607905i
$7$	−1.45563	−	2.52122i	−0.550176	−	0.952933i	−0.998261	−	0.0589424i	$-0.981227\pi$
$7$	−1.45563	−	2.52122i	−0.550176	−	0.952933i	0.448085	−	0.893991i	$-0.352106\pi$
$8$			0.750585i			0.265372i
$9$	3.97738	−	2.29634i	1.32579	−	0.765447i
$10$	3.82506	+	2.67700i	1.20959	+	0.846541i
$11$	−0.0254491	+	0.00681908i	−0.00767321	+	0.00205603i	−0.262654	−	0.964890i	$-0.584598\pi$
$11$	−0.0254491	+	0.00681908i	−0.00767321	+	0.00205603i	0.254980	+	0.966946i	$0.417931\pi$
$12$	−4.59727	−	4.59727i	−1.32712	−	1.32712i
$13$	−3.56631	+	0.530479i	−0.989117	+	0.147129i
$13$	−3.56631	+	0.530479i	−0.989117	+	0.147129i
$14$		−	6.07853i		−	1.62456i
$15$	−6.06759	+	1.07135i	−1.56664	+	0.276622i
$16$	1.57590	−	2.72954i	0.393975	−	0.682384i
$17$	−0.741318	+	2.76664i	−0.179796	+	0.671008i	0.815889	+	0.578209i	$0.196248\pi$
$17$	−0.741318	+	2.76664i	−0.179796	+	0.671008i	−0.995685	+	0.0927992i	$0.970419\pi$
$18$	9.58924			2.26020
$19$	−1.23878	+	4.62320i	−0.284196	+	1.06063i	0.665229	+	0.746640i	$0.268334\pi$
$19$	−1.23878	+	4.62320i	−0.284196	+	1.06063i	−0.949425	+	0.313995i	$0.898333\pi$
$20$	2.23085	+	4.78113i	0.498833	+	1.06909i
$21$	5.67236	+	5.67236i	1.23781	+	1.23781i
$22$	−0.0531363	−	0.0142378i	−0.0113287	−	0.00303551i
$23$	−0.0961080	−	0.358680i	−0.0200399	−	0.0747899i	0.955182	−	0.296020i	$-0.0956595\pi$
$23$	−0.0961080	−	0.358680i	−0.0200399	−	0.0747899i	−0.975222	+	0.221230i	$0.928993\pi$
$24$	−0.535296	−	1.99775i	−0.109267	−	0.407789i
$25$	4.92445	+	0.865921i	0.984889	+	0.173184i
$26$	−7.00244	−	2.76390i	−1.37329	−	0.542046i
$27$	−3.10321	+	3.10321i	−0.597214	+	0.597214i
$28$	3.43454	−	5.94879i	0.649067	−	1.12422i
$29$	−3.62262	−	2.09152i	−0.672703	−	0.388386i	0.124397	−	0.992233i	$-0.460300\pi$
$29$	−3.62262	−	2.09152i	−0.672703	−	0.388386i	−0.797100	+	0.603847i	$0.793634\pi$
$30$	−12.0899	−	4.39714i	−2.20731	−	0.802805i
$31$	−0.835277	+	0.835277i	−0.150020	+	0.150020i	−0.778127	−	0.628107i	$-0.783830\pi$
$31$	−0.835277	+	0.835277i	−0.150020	+	0.150020i	0.628107	+	0.778127i	$0.283830\pi$
$32$	6.99915	−	4.04096i	1.23729	−	0.714348i
$33$	0.0628721	−	0.0362992i	0.0109446	−	0.00631888i
$34$	−4.22874	+	4.22874i	−0.725223	+	0.725223i
$35$	−2.75254	−	5.89921i	−0.465264	−	0.997148i
$36$	9.38457	+	5.41819i	1.56410	+	0.903031i
$37$	−3.22588	+	5.58739i	−0.530332	+	0.918561i	0.469042	+	0.883176i	$0.344599\pi$
$37$	−3.22588	+	5.58739i	−0.530332	+	0.918561i	−0.999374	+	0.0353856i	$0.988734\pi$
$38$	−7.06645	+	7.06645i	−1.14633	+	1.14633i
$39$	9.11375	−	3.95531i	1.45937	−	0.633357i
$40$	−0.145885	+	1.67201i	−0.0230664	+	0.264368i
$41$	−2.02930	−	7.57344i	−0.316923	−	1.18277i	−0.922186	−	0.386747i	$-0.873599\pi$
$41$	−2.02930	−	7.57344i	−0.316923	−	1.18277i	0.605263	−	0.796026i	$-0.293068\pi$
$42$	4.33503	+	16.1786i	0.668910	+	2.49641i
$43$	6.69664	+	1.79436i	1.02123	+	0.273637i	0.730314	−	0.683112i	$-0.239374\pi$
$43$	6.69664	+	1.79436i	1.02123	+	0.273637i	0.290915	+	0.956749i	$0.406040\pi$
$44$	−0.0439574	−	0.0439574i	−0.00662683	−	0.00662683i
$45$	9.30635	−	4.34229i	1.38731	−	0.647311i
$46$	0.200668	−	0.748902i	0.0295868	−	0.110420i
$47$	0.833377			0.121561			0.0607803	−	0.998151i	$-0.480641\pi$
$47$	0.833377			0.121561			0.0607803	+	0.998151i	$0.480641\pi$
$48$	−2.24777	+	8.38880i	−0.324438	+	1.21082i
$49$	−0.737715	+	1.27776i	−0.105388	+	0.182537i
$50$	8.00043	+	6.70674i	1.13143	+	0.948476i
$51$		−	7.89234i		−	1.10515i
$52$	−5.29130	−	6.66149i	−0.733772	−	0.923782i
$53$	0.902268	+	0.902268i	0.123936	+	0.123936i	0.766354	−	0.642418i	$-0.222069\pi$
$53$	0.902268	+	0.902268i	0.123936	+	0.123936i	−0.642418	+	0.766354i	$0.722069\pi$
$54$	−8.85092	+	2.37160i	−1.20446	+	0.322733i
$55$	−0.0580160	+	0.0102439i	−0.00782288	+	0.00138128i
$56$	1.89239	−	1.09257i	0.252882	−	0.146001i
$57$		−	13.1885i		−	1.74686i
$58$	−4.36697	−	7.56381i	−0.573411	−	0.993176i
$59$	−1.44647	−	0.387581i	−0.188315	−	0.0504588i	0.163429	−	0.986555i	$-0.447745\pi$
$59$	−1.44647	−	0.387581i	−0.188315	−	0.0504588i	−0.351744	+	0.936096i	$0.614411\pi$
$60$	−9.34737	−	11.1344i	−1.20674	−	1.43745i
$61$	5.35090	+	9.26802i	0.685112	+	1.18665i	0.973402	+	0.229105i	$0.0735801\pi$
$61$	5.35090	+	9.26802i	0.685112	+	1.18665i	−0.288290	+	0.957543i	$0.593087\pi$
$62$	−2.38236	+	0.638351i	−0.302560	+	0.0810706i
$63$	−11.5792	−	6.68524i	−1.45884	−	0.842262i
$64$	10.5710			1.32137
$65$	−8.04744	+	0.488545i	−0.998162	+	0.0605966i
$66$	0.151581			0.0186583
$67$	10.6667	+	6.15845i	1.30315	+	0.752374i	0.980943	−	0.194295i	$-0.0622419\pi$
$67$	10.6667	+	6.15845i	1.30315	+	0.752374i	0.322207	+	0.946669i	$0.395575\pi$
$68$	−6.52784	+	1.74913i	−0.791617	+	0.212113i
$69$	0.511601	+	0.886118i	0.0615895	+	0.106676i
$70$	1.18143	−	13.5406i	0.141208	−	1.61841i
$71$	−3.57441	−	0.957759i	−0.424204	−	0.113665i	0.0404002	−	0.999184i	$-0.487137\pi$
$71$	−3.57441	−	0.957759i	−0.424204	−	0.113665i	−0.464604	+	0.885518i	$0.653803\pi$
$72$	1.72360	+	2.98536i	0.203128	+	0.351828i
$73$		−	15.0844i		−	1.76550i	−0.469844	−	0.882750i	$-0.655690\pi$
$73$		−	15.0844i		−	1.76550i	0.469844	−	0.882750i	$-0.344310\pi$
$74$	−11.6661	+	6.73544i	−1.35616	+	0.782979i
$75$	−13.7244	+	1.20725i	−1.58476	+	0.139401i
$76$	−10.9084	+	2.92289i	−1.25128	+	0.335279i
$77$	0.0542370	+	0.0542370i	0.00618088	+	0.00618088i
$78$	20.6088	+	2.36245i	2.33348	+	0.267494i
$79$			4.25039i			0.478207i	0.970994	+	0.239103i	$0.0768534\pi$
$79$			4.25039i			0.478207i	−0.970994	+	0.239103i	$0.923147\pi$
$80$	4.04100	−	5.77403i	0.451797	−	0.645557i
$81$	−0.842658	+	1.45953i	−0.0936286	+	0.162170i
$82$	4.23705	−	15.8129i	0.467904	−	1.74624i
$83$	1.31611			0.144462			0.0722311	−	0.997388i	$-0.476988\pi$
$83$	1.31611			0.144462			0.0722311	+	0.997388i	$0.476988\pi$
$84$	−4.89883	+	18.2827i	−0.534506	+	1.99480i
$85$	−2.18909	+	6.01889i	−0.237440	+	0.652840i
$86$	10.2357	+	10.2357i	1.10374	+	1.10374i
$87$	11.1335	+	2.98322i	1.19364	+	0.319835i
$88$	−0.00511830	−	0.0191018i	−0.000545613	−	0.00203625i
$89$	−0.867319	−	3.23688i	−0.0919357	−	0.343109i	0.904601	−	0.426259i	$-0.140169\pi$
$89$	−0.867319	−	3.23688i	−0.0919357	−	0.343109i	−0.996537	+	0.0831499i	$0.973502\pi$
$90$	21.3610	+	1.86378i	2.25165	+	0.196459i
$91$	6.52869	+	8.21929i	0.684393	+	0.861616i
$92$	0.619535	−	0.619535i	0.0645910	−	0.0645910i
$93$	1.62747	−	2.81886i	0.168761	−	0.292302i
$94$	1.50692	+	0.870020i	0.155427	+	0.0897357i
$95$	−3.65809	+	10.0579i	−0.375312	+	1.03192i
$96$	−15.7470	+	15.7470i	−1.60717	+	1.60717i
$97$	0.351145	−	0.202734i	0.0356534	−	0.0205845i	−0.482067	−	0.876134i	$-0.660114\pi$
$97$	0.351145	−	0.202734i	0.0356534	−	0.0205845i	0.517721	+	0.855550i	$0.326781\pi$
$98$	−2.66788	+	1.54030i	−0.269497	+	0.155594i
$99$	−0.0855620	+	0.0855620i	−0.00859930	+	0.00859930i
$100$	4.04018	+	11.0841i	0.404018	+	1.10841i
$101$	2.46663	+	1.42411i	0.245439	+	0.141704i	0.617674	−	0.786434i	$-0.288075\pi$
$101$	2.46663	+	1.42411i	0.245439	+	0.141704i	−0.372235	+	0.928139i	$0.621408\pi$
$102$	8.23936	−	14.2710i	0.815819	−	1.41304i
$103$	−5.63497	+	5.63497i	−0.555230	+	0.555230i	−0.927946	−	0.372716i	$-0.878427\pi$
$103$	−5.63497	+	5.63497i	−0.555230	+	0.555230i	0.372716	+	0.927946i	$0.378427\pi$
$104$	−0.398170	−	2.67682i	−0.0390438	−	0.262484i
$105$	11.5333	+	13.7383i	1.12553	+	1.34072i
$106$	0.689548	+	2.57343i	0.0669748	+	0.249953i
$107$	−3.38214	−	12.6223i	−0.326964	−	1.22025i	−0.912323	−	0.409472i	$-0.865713\pi$
$107$	−3.38214	−	12.6223i	−0.326964	−	1.22025i	0.585359	−	0.810774i	$-0.300954\pi$
$108$	−10.0020	−	2.68004i	−0.962446	−	0.257887i
$109$	−7.66343	−	7.66343i	−0.734024	−	0.734024i	0.237391	−	0.971414i	$-0.423708\pi$
$109$	−7.66343	−	7.66343i	−0.734024	−	0.734024i	−0.971414	+	0.237391i	$0.923708\pi$
$110$	−0.115599	−	0.0420439i	−0.0110220	−	0.00400872i
$111$	4.60121	−	17.1720i	0.436728	−	1.62989i
$112$	−9.17570			−0.867022
$113$	2.24906	−	8.39360i	0.211574	−	0.789604i	−0.775771	−	0.631014i	$-0.782639\pi$
$113$	2.24906	−	8.39360i	0.211574	−	0.789604i	0.987345	−	0.158589i	$-0.0506945\pi$
$114$	13.7684	−	23.8476i	1.28953	−	2.23353i
$115$	−0.144377	−	0.817677i	−0.0134632	−	0.0762488i
$116$		−	9.86983i		−	0.916390i
$117$	−12.9664	+	10.2994i	−1.19875	+	0.952179i
$118$	−2.21090	−	2.21090i	−0.203530	−	0.203530i
$119$	8.05440	−	2.15817i	0.738345	−	0.197839i
$120$	−0.804142	−	4.55424i	−0.0734078	−	0.415744i
$121$	−9.52568	+	5.49965i	−0.865971	+	0.499968i
$122$			22.3447i			2.02299i
$123$	10.8023	+	18.7102i	0.974012	+	1.68704i
$124$	−2.69220	−	0.721372i	−0.241766	−	0.0647811i
$125$	10.8014	+	2.88605i	0.966109	+	0.258136i
$126$	−13.9584	−	24.1766i	−1.24351	−	2.15382i
$127$	−14.5154	+	3.88938i	−1.28803	+	0.345126i	−0.836912	−	0.547338i	$-0.815641\pi$
$127$	−14.5154	+	3.88938i	−1.28803	+	0.345126i	−0.451118	+	0.892464i	$0.648975\pi$
$128$	5.11621	+	2.95384i	0.452213	+	0.261085i
$129$	−19.1034			−1.68196
$130$	−15.0615	−	7.51789i	−1.32098	−	0.659363i
$131$	9.04438			0.790211			0.395105	−	0.918636i	$-0.370708\pi$
$131$	9.04438			0.790211			0.395105	+	0.918636i	$0.370708\pi$
$132$	0.148346	+	0.0856475i	0.0129118	+	0.00745466i
$133$	13.4593	−	3.60642i	1.16707	−	0.312716i
$134$	12.8585	+	22.2715i	1.11080	+	1.92397i
$135$	−7.51588	+	6.30959i	−0.646864	+	0.543043i
$136$	−2.07660	−	0.556423i	−0.178067	−	0.0477128i
$137$	7.28411	+	12.6164i	0.622323	+	1.07790i	0.989052	+	0.147568i	$0.0471444\pi$
$137$	7.28411	+	12.6164i	0.622323	+	1.07790i	−0.366729	+	0.930328i	$0.619522\pi$
$138$			2.13638i			0.181861i
$139$	−5.98819	+	3.45728i	−0.507911	+	0.293243i	−0.731975	−	0.681332i	$-0.761401\pi$
$139$	−5.98819	+	3.45728i	−0.507911	+	0.293243i	0.224063	+	0.974575i	$0.428068\pi$
$140$	8.80701	−	12.5840i	0.744328	−	1.06354i
$141$	−2.21811	+	0.594341i	−0.186799	+	0.0500525i
$142$	−5.46340	−	5.46340i	−0.458478	−	0.458478i
$143$	0.0871423	−	0.0378192i	0.00728720	−	0.00316260i
$144$		−	14.4752i		−	1.20627i
$145$	−7.66325	−	5.36318i	−0.636399	−	0.445388i
$146$	15.7477	−	27.2758i	1.30329	−	2.25736i
$147$	1.05223	−	3.92699i	0.0867868	−	0.323893i
$148$	−15.2228			−1.25131
$149$	1.51600	−	5.65780i	0.124196	−	0.463505i	−0.875614	−	0.483012i	$-0.839543\pi$
$149$	1.51600	−	5.65780i	0.124196	−	0.463505i	0.999810	+	0.0195066i	$0.00620954\pi$
$150$	−26.0769	−	12.1449i	−2.12917	−	0.991628i
$151$	−2.92436	−	2.92436i	−0.237981	−	0.237981i	0.578033	−	0.816014i	$-0.303821\pi$
$151$	−2.92436	−	2.92436i	−0.237981	−	0.237981i	−0.816014	+	0.578033i	$0.803821\pi$
$152$	−3.47011	−	0.929812i	−0.281463	−	0.0754177i
$153$	3.40464	+	12.7063i	0.275249	+	1.02724i
$154$	0.0414500	+	0.154693i	0.00334013	+	0.0124655i
$155$	−2.02301	+	1.69832i	−0.162492	+	0.136412i
$156$	18.8341	+	13.9566i	1.50793	+	1.11742i
$157$	−4.59859	+	4.59859i	−0.367007	+	0.367007i	−0.866385	−	0.499377i	$-0.833562\pi$
$157$	−4.59859	+	4.59859i	−0.367007	+	0.367007i	0.499377	+	0.866385i	$0.333562\pi$
$158$	−4.43728	+	7.68559i	−0.353011	+	0.611433i
$159$	−3.04494	−	1.75800i	−0.241480	−	0.139418i
$160$	16.3768	−	7.64131i	1.29470	−	0.604098i
$161$	−0.764415	+	0.764415i	−0.0602443	+	0.0602443i
$162$	−3.04740	+	1.75942i	−0.239426	+	0.138233i
$163$	3.48809	−	2.01385i	0.273208	−	0.157737i	−0.357137	−	0.934052i	$-0.616247\pi$
$163$	3.48809	−	2.01385i	0.273208	−	0.157737i	0.630345	+	0.776315i	$0.282914\pi$
$164$	13.0813	−	13.0813i	1.02148	−	1.02148i
$165$	0.147109	−	0.0686404i	0.0114524	−	0.00534365i
$166$	2.37981	+	1.37398i	0.184709	+	0.106642i
$167$	11.9198	−	20.6458i	0.922385	−	1.59762i	0.126670	−	0.991945i	$-0.459571\pi$
$167$	11.9198	−	20.6458i	0.922385	−	1.59762i	0.795714	−	0.605672i	$-0.207096\pi$
$168$	−4.25759	+	4.25759i	−0.328480	+	0.328480i
$169$	12.4372	−	3.78371i	0.956706	−	0.291055i
$170$	−10.2419	+	8.59806i	−0.785515	+	0.659441i
$171$	5.68933	+	21.2329i	0.435074	+	1.62372i
$172$	4.23377	+	15.8006i	0.322822	+	1.20479i
$173$	0.784743	+	0.210271i	0.0596629	+	0.0159866i	0.288527	−	0.957472i	$-0.406834\pi$
$173$	0.784743	+	0.210271i	0.0596629	+	0.0159866i	−0.228864	+	0.973458i	$0.573501\pi$
$174$	17.0174	+	17.0174i	1.29008	+	1.29008i
$175$	−4.98499	−	13.6761i	−0.376830	−	1.03382i
$176$	−0.0214923	+	0.0802105i	−0.00162005	+	0.00604610i
$177$	4.12633			0.310154
$178$	1.81091	−	6.75841i	0.135733	−	0.506564i
$179$	−3.28130	+	5.68337i	−0.245256	+	0.424795i	−0.962203	−	0.272332i	$-0.912205\pi$
$179$	−3.28130	+	5.68337i	−0.245256	+	0.424795i	0.716948	+	0.697127i	$0.245539\pi$
$180$	19.8520	+	13.8936i	1.47968	+	1.03557i
$181$			1.56627i			0.116420i	0.998304	+	0.0582099i	$0.0185393\pi$
$181$			1.56627i			0.116420i	−0.998304	+	0.0582099i	$0.981461\pi$
$182$	3.22453	+	21.6779i	0.239018	+	1.60688i
$183$	−20.8516	−	20.8516i	−1.54139	−	1.54139i
$184$	0.269220	−	0.0721373i	0.0198472	−	0.00531803i
$185$	−8.27196	+	11.8195i	−0.608167	+	0.868988i
$186$	5.88561	−	3.39806i	0.431554	−	0.249158i
$187$		−	0.0754637i		−	0.00551845i
$188$	0.983171	+	1.70290i	0.0717051	+	0.124197i
$189$	12.3410	+	3.30677i	0.897678	+	0.240532i
$190$	−17.1147	+	14.3678i	−1.24163	+	1.04235i
$191$	−2.31024	−	4.00145i	−0.167163	−	0.289535i	0.770258	−	0.637732i	$-0.220127\pi$
$191$	−2.31024	−	4.00145i	−0.167163	−	0.289535i	−0.937421	+	0.348197i	$0.886794\pi$
$192$	−28.1356	+	7.53891i	−2.03051	+	0.544074i
$193$	14.4037	+	8.31597i	1.03680	+	0.598597i	0.918925	−	0.394432i	$-0.129058\pi$
$193$	14.4037	+	8.31597i	1.03680	+	0.598597i	0.117875	+	0.993028i	$0.462392\pi$
$194$	0.846590			0.0607816
$195$	21.0706	−	7.03951i	1.50890	−	0.504110i
$196$	−3.48126			−0.248661
$197$	−22.2821	−	12.8646i	−1.58753	−	0.916563i	−0.993712	−	0.111966i	$-0.964285\pi$
$197$	−22.2821	−	12.8646i	−1.58753	−	0.916563i	−0.593821	−	0.804597i	$-0.702381\pi$
$198$	−0.244038	+	0.0653898i	−0.0173430	+	0.00464705i
$199$	−13.8914	−	24.0606i	−0.984736	−	1.70561i	−0.643104	−	0.765779i	$-0.722354\pi$
$199$	−13.8914	−	24.0606i	−0.984736	−	1.70561i	−0.341632	−	0.939834i	$-0.610980\pi$
$200$	−0.649947	+	3.69622i	−0.0459582	+	0.261362i
$201$	−32.7825	−	8.78406i	−2.31230	−	0.619580i
$202$	2.97346	+	5.15018i	0.209212	+	0.362365i
$203$			12.1779i			0.854722i
$204$	16.1270	−	9.31094i	1.12912	−	0.651896i
$205$	−3.04849	−	17.2650i	−0.212916	−	1.20584i
$206$	−16.0719	+	4.30646i	−1.11978	+	0.300045i
$207$	−1.20591	−	1.20591i	−0.0838165	−	0.0838165i
$208$	−4.17218	+	10.5704i	−0.289289	+	0.732923i
$209$		−	0.126104i		−	0.00872278i
$210$	6.51225	+	36.8820i	0.449388	+	2.54510i
$211$	−7.38830	+	12.7969i	−0.508632	+	0.880976i	0.491318	+	0.870980i	$0.336515\pi$
$211$	−7.38830	+	12.7969i	−0.508632	+	0.880976i	−0.999950	+	0.00999576i	$0.996818\pi$
$212$	−0.779228	+	2.90812i	−0.0535176	+	0.199730i
$213$	10.1967			0.698663
$214$	7.06170	−	26.3546i	0.482728	−	1.80157i
$215$	14.5687	+	5.29869i	0.993579	+	0.361368i
$216$	−2.32923	−	2.32923i	−0.158484	−	0.158484i
$217$	3.32178	+	0.890067i	0.225497	+	0.0604217i
$218$	−5.85669	−	21.8575i	−0.396665	−	1.48037i
$219$	10.7578	+	40.1486i	0.726944	+	2.71299i
$220$	−0.0893761	−	0.106463i	−0.00602573	−	0.00717776i
$221$	1.17613	−	10.2599i	0.0791150	−	0.690159i
$222$	26.2469	−	26.2469i	1.76158	−	1.76158i
$223$	−7.01198	+	12.1451i	−0.469557	+	0.813296i	−0.999394	−	0.0348032i	$-0.988920\pi$
$223$	−7.01198	+	12.1451i	−0.469557	+	0.813296i	0.529838	+	0.848099i	$0.322253\pi$
$224$	−20.3764	−	11.7643i	−1.36145	−	0.786035i
$225$	21.5748	−	7.86412i	1.43832	−	0.524274i
$226$	12.8294	−	12.8294i	0.853401	−	0.853401i
$227$	13.8488	−	7.99560i	0.919176	−	0.530687i	0.0358042	−	0.999359i	$-0.488601\pi$
$227$	13.8488	−	7.99560i	0.919176	−	0.530687i	0.883372	+	0.468672i	$0.155267\pi$
$228$	26.9491	−	15.5591i	1.78475	−	1.03043i
$229$	2.31063	−	2.31063i	0.152691	−	0.152691i	−0.626628	−	0.779319i	$-0.715565\pi$
$229$	2.31063	−	2.31063i	0.152691	−	0.152691i	0.779319	+	0.626628i	$0.215565\pi$
$230$	0.592566	−	1.62926i	0.0390726	−	0.107430i
$231$	−0.183037	−	0.105676i	−0.0120429	−	0.00695300i
$232$	1.56986	−	2.71909i	0.103067	−	0.178517i
$233$	−17.8141	+	17.8141i	−1.16704	+	1.16704i	−0.184143	+	0.982899i	$0.558951\pi$
$233$	−17.8141	+	17.8141i	−1.16704	+	1.16704i	−0.982899	+	0.184143i	$0.941049\pi$
$234$	−34.1982	+	5.08689i	−2.23561	+	0.332541i
$235$	1.85644	+	0.161976i	0.121100	+	0.0105662i
$236$	−0.914493	−	3.41293i	−0.0595284	−	0.222163i
$237$	−3.03126	−	11.3128i	−0.196901	−	0.734846i
$238$	16.8171	+	4.50612i	1.09009	+	0.292089i
$239$	4.31403	+	4.31403i	0.279052	+	0.279052i	0.832730	−	0.553679i	$-0.186776\pi$
$239$	4.31403	+	4.31403i	0.279052	+	0.279052i	−0.553679	+	0.832730i	$0.686776\pi$
$240$	−6.63760	+	18.2500i	−0.428455	+	1.17804i
$241$	2.34253	−	8.74246i	0.150896	−	0.563151i	−0.848526	−	0.529154i	$-0.822509\pi$
$241$	2.34253	−	8.74246i	0.150896	−	0.563151i	0.999422	−	0.0339976i	$-0.0108239\pi$
$242$	−22.9659			−1.47630
$243$	4.60948	−	17.2028i	0.295699	−	1.10356i
$244$	−12.6254	+	21.8678i	−0.808256	+	1.39994i
$245$	−1.89168	+	2.70296i	−0.120855	+	0.172686i
$246$			45.1091i			2.87605i
$247$	1.96537	−	17.1449i	0.125054	−	1.09091i
$248$	−0.626947	−	0.626947i	−0.0398112	−	0.0398112i
$249$	−3.50296	+	0.938615i	−0.221991	+	0.0594823i
$250$	16.5183	+	16.4949i	1.04471	+	1.04323i
$251$	0.503450	−	0.290667i	0.0317775	−	0.0183467i	−0.484027	−	0.875053i	$-0.660826\pi$
$251$	0.503450	−	0.290667i	0.0317775	−	0.0183467i	0.515805	+	0.856706i	$0.327493\pi$
$252$		−	31.5475i		−	1.98730i
$253$	0.00489173	+	0.00847273i	0.000307541	+	0.000532676i
$254$	−30.3072	−	8.12078i	−1.90164	−	0.509543i
$255$	1.53397	−	17.5810i	0.0960607	−	1.10097i
$256$	−4.40353	−	7.62714i	−0.275221	−	0.476696i
$257$	16.8089	−	4.50394i	1.04851	−	0.280948i	0.306876	−	0.951750i	$-0.400716\pi$
$257$	16.8089	−	4.50394i	1.04851	−	0.280948i	0.741637	+	0.670801i	$0.234050\pi$
$258$	−34.5429	−	19.9434i	−2.15055	−	1.24162i
$259$	18.7828			1.16710
$260$	−10.4922	−	15.8676i	−0.650698	−	0.984066i
$261$	−19.2114			−1.18915
$262$	16.3541	+	9.44205i	1.01036	+	0.583332i
$263$	26.6449	−	7.13948i	1.64299	−	0.440239i	0.685355	−	0.728209i	$-0.259647\pi$
$263$	26.6449	−	7.13948i	1.64299	−	0.440239i	0.957639	+	0.287970i	$0.0929803\pi$
$264$	0.0272457	+	0.0471909i	0.00167685	+	0.00290440i
$265$	1.83453	+	2.18526i	0.112694	+	0.134240i
$266$	28.1023	+	7.52998i	1.72306	+	0.461692i
$267$	4.61690	+	7.99671i	0.282550	+	0.489390i
$268$			29.0615i			1.77522i
$269$	−15.9495	+	9.20844i	−0.972457	+	0.561448i	−0.899984	−	0.435922i	$-0.856422\pi$
$269$	−15.9495	+	9.20844i	−0.972457	+	0.561448i	−0.0724726	+	0.997370i	$0.523089\pi$
$270$	−20.1773	+	3.56270i	−1.22795	+	0.216819i
$271$	25.0269	−	6.70594i	1.52028	−	0.407357i	0.600444	−	0.799667i	$-0.294990\pi$
$271$	25.0269	−	6.70594i	1.52028	−	0.407357i	0.919833	+	0.392310i	$0.128324\pi$
$272$	6.38339	+	6.38339i	0.387050	+	0.387050i
$273$	−23.2385	−	17.2203i	−1.40646	−	1.04222i
$274$			30.4175i			1.83759i
$275$	−0.131228	+	0.0115433i	−0.00791333	+	0.000696084i
$276$	−1.20711	+	2.09078i	−0.0726598	+	0.125850i
$277$	−6.06254	+	22.6257i	−0.364263	+	1.35945i	0.504155	+	0.863613i	$0.331804\pi$
$277$	−6.06254	+	22.6257i	−0.364263	+	1.35945i	−0.868418	+	0.495833i	$0.834863\pi$
$278$	−14.4372			−0.865884
$279$	−1.40413	+	5.24030i	−0.0840632	+	0.313728i
$280$	4.42786	−	2.06602i	0.264615	−	0.123468i
$281$	−9.93011	−	9.93011i	−0.592381	−	0.592381i	0.345893	−	0.938274i	$-0.387576\pi$
$281$	−9.93011	−	9.93011i	−0.592381	−	0.592381i	−0.938274	+	0.345893i	$0.887576\pi$
$282$	−4.63128	−	1.24095i	−0.275789	−	0.0738973i
$283$	1.06421	+	3.97170i	0.0632610	+	0.236093i	0.990316	−	0.138832i	$-0.0443349\pi$
$283$	1.06421	+	3.97170i	0.0632610	+	0.236093i	−0.927055	+	0.374926i	$0.877668\pi$
$284$	−2.25982	−	8.43376i	−0.134096	−	0.500452i
$285$	2.56334	−	29.3788i	0.151839	−	1.74025i
$286$	0.197053	+	0.0225888i	0.0116520	+	0.00133571i
$287$	−16.1404	+	16.1404i	−0.952740	+	0.952740i
$288$	18.5589	−	32.1449i	1.09359	−	1.89416i
$289$	7.61770	+	4.39808i	0.448100	+	0.258711i
$290$	−8.25776	−	17.6979i	−0.484912	−	1.03926i
$291$	−0.790020	+	0.790020i	−0.0463118	+	0.0463118i
$292$	30.8232	−	17.7958i	1.80379	−	1.04142i
$293$	−18.9253	+	10.9265i	−1.10563	+	0.638336i	−0.937694	−	0.347462i	$-0.887043\pi$
$293$	−18.9253	+	10.9265i	−1.10563	+	0.638336i	−0.167936	+	0.985798i	$0.553710\pi$
$294$	6.00232	−	6.00232i	0.350062	−	0.350062i
$295$	−3.14684	−	1.14452i	−0.183216	−	0.0666363i
$296$	−4.19381	−	2.42130i	−0.243761	−	0.140735i
$297$	0.0578131	−	0.100135i	0.00335466	−	0.00581044i
$298$	8.64782	−	8.64782i	0.500955	−	0.500955i
$299$	0.533024	+	1.22818i	0.0308256	+	0.0710276i
$300$	−18.6581	−	26.6199i	−1.07723	−	1.53690i
$301$	−5.22385	−	19.4957i	−0.301098	−	1.12371i
$302$	−2.23491	−	8.34078i	−0.128604	−	0.479958i
$303$	−7.58081	−	2.03127i	−0.435506	−	0.116693i
$304$	10.6670	+	10.6670i	0.611794	+	0.611794i
$305$	10.1183	+	21.6855i	0.579374	+	1.24171i
$306$	−7.10868	+	26.5299i	−0.406376	+	1.51662i
$307$	−6.98281			−0.398530			−0.199265	−	0.979946i	$-0.563855\pi$
$307$	−6.98281			−0.398530			−0.199265	+	0.979946i	$0.563855\pi$
$308$	−0.0468408	+	0.174812i	−0.00266900	+	0.00996085i
$309$	10.9793	−	19.0167i	0.624590	−	1.08182i
$310$	−5.43102	+	0.958955i	−0.308461	+	0.0544650i
$311$			21.2824i			1.20681i	0.797434	+	0.603406i	$0.206190\pi$
$311$			21.2824i			1.20681i	−0.797434	+	0.603406i	$0.793810\pi$
$312$	2.96880	+	6.84065i	0.168075	+	0.387275i
$313$	17.6647	+	17.6647i	0.998470	+	0.998470i	0.999999	−	0.00152850i	$-0.000486538\pi$
$313$	17.6647	+	17.6647i	0.998470	+	0.998470i	−0.00152850	+	0.999999i	$0.500487\pi$
$314$	−13.1160	+	3.51442i	−0.740177	+	0.198330i
$315$	−24.4945	−	17.1426i	−1.38011	−	0.965878i
$316$	−8.68515	+	5.01437i	−0.488578	+	0.282080i
$317$			15.6715i			0.880198i	0.897949	+	0.440099i	$0.145057\pi$
$317$			15.6715i			0.880198i	−0.897949	+	0.440099i	$0.854943\pi$
$318$	−3.67059	−	6.35765i	−0.205836	−	0.356519i
$319$	0.106455	+	0.0285245i	0.00596032	+	0.00159706i
$320$	23.5480	+	2.05459i	1.31637	+	0.114855i
$321$	18.0038	+	31.1834i	1.00487	+	1.74049i
$322$	−2.18025	+	0.584195i	−0.121500	+	0.0325559i
$323$	−11.8724	−	6.85452i	−0.660597	−	0.381396i
$324$	−3.97648			−0.220915
$325$	−18.0215	−	0.475827i	−0.999652	−	0.0263941i
$326$	8.40958			0.465763
$327$	25.8623	+	14.9316i	1.43019	+	0.825719i
$328$	5.68451	−	1.52316i	0.313875	−	0.0841025i
$329$	−1.21309	−	2.10113i	−0.0668797	−	0.115839i
$330$	0.337663	+	0.0294615i	0.0185877	+	0.00162180i
$331$	3.25207	+	0.871389i	0.178750	+	0.0478959i	0.347084	−	0.937834i	$-0.387172\pi$
$331$	3.25207	+	0.871389i	0.178750	+	0.0478959i	−0.168334	+	0.985730i	$0.553839\pi$
$332$	1.55268	+	2.68932i	0.0852142	+	0.147595i
$333$			29.6309i			1.62376i
$334$	43.1071	−	24.8879i	2.35871	−	1.36180i
$335$	22.5643	+	15.7918i	1.23282	+	0.862798i
$336$	24.4220	−	6.54384i	1.33233	−	0.356996i
$337$	7.20813	+	7.20813i	0.392652	+	0.392652i	0.875631	−	0.482980i	$-0.160446\pi$
$337$	7.20813	+	7.20813i	0.392652	+	0.392652i	−0.482980	+	0.875631i	$0.660446\pi$
$338$	26.4391	+	6.14230i	1.43810	+	0.334097i
$339$			23.9443i			1.30048i
$340$	−14.8814	+	2.62761i	−0.807058	+	0.142502i
$341$	0.0155613	−	0.0269529i	0.000842690	−	0.00145958i
$342$	−11.8790	+	44.3330i	−0.642342	+	2.39725i
$343$	−16.0835			−0.868425
$344$	−1.34682	+	5.02640i	−0.0726157	+	0.271005i
$345$	0.967417	+	2.07336i	0.0520840	+	0.111626i
$346$	1.19946	+	1.19946i	0.0644835	+	0.0644835i
$347$	−18.9253	−	5.07101i	−1.01596	−	0.272226i	−0.287844	−	0.957677i	$-0.592938\pi$
$347$	−18.9253	−	5.07101i	−1.01596	−	0.272226i	−0.728119	+	0.685451i	$0.759605\pi$
$348$	7.03888	+	26.2694i	0.377323	+	1.40819i
$349$	−2.15644	−	8.04794i	−0.115432	−	0.430796i	0.883887	−	0.467700i	$-0.154917\pi$
$349$	−2.15644	−	8.04794i	−0.115432	−	0.430796i	−0.999319	+	0.0369035i	$0.988251\pi$
$350$	5.26352	−	29.9334i	0.281347	−	1.60001i
$351$	9.42084	−	12.7132i	0.502847	−	0.678582i
$352$	−0.150567	+	0.150567i	−0.00802524	+	0.00802524i
$353$	2.58427	−	4.47609i	0.137547	−	0.238238i	−0.789021	−	0.614367i	$-0.789412\pi$
$353$	2.58427	−	4.47609i	0.137547	−	0.238238i	0.926567	+	0.376129i	$0.122745\pi$
$354$	7.46127	+	4.30777i	0.396562	+	0.228955i
$355$	−7.77621	−	2.82824i	−0.412719	−	0.150107i
$356$	5.59095	−	5.59095i	0.296320	−	0.296320i
$357$	−19.8984	+	11.4883i	−1.05313	+	0.608027i
$358$	−11.8665	+	6.85114i	−0.627166	+	0.362094i
$359$	11.2145	−	11.2145i	0.591877	−	0.591877i	−0.346261	−	0.938138i	$-0.612549\pi$
$359$	11.2145	−	11.2145i	0.591877	−	0.591877i	0.938138	+	0.346261i	$0.112549\pi$
$360$	3.25926	+	6.98521i	0.171778	+	0.368153i
$361$	−3.38491	−	1.95428i	−0.178153	−	0.102857i
$362$	−1.63513	+	2.83214i	−0.0859408	+	0.148854i
$363$	21.4313	−	21.4313i	1.12485	−	1.12485i
$364$	−9.09293	+	23.0372i	−0.476599	+	1.20748i
$365$	2.93183	−	33.6022i	0.153459	−	1.75882i
$366$	−15.9356	−	59.4724i	−0.832966	−	3.10867i
$367$	3.14803	+	11.7486i	0.164326	+	0.613272i	0.998125	+	0.0612047i	$0.0194942\pi$
$367$	3.14803	+	11.7486i	0.164326	+	0.613272i	−0.833799	+	0.552067i	$0.813839\pi$
$368$	−1.13049	−	0.302913i	−0.0589307	−	0.0157904i
$369$	−25.4625	−	25.4625i	−1.32552	−	1.32552i
$370$	−27.2966	+	12.7365i	−1.41908	+	0.662137i
$371$	0.961452	−	3.58819i	0.0499161	−	0.186289i
$372$	7.67999			0.398189
$373$	0.0887099	−	0.331070i	0.00459322	−	0.0171421i	−0.963591	−	0.267380i	$-0.913842\pi$
$373$	0.0887099	−	0.331070i	0.00459322	−	0.0171421i	0.968184	+	0.250238i	$0.0805088\pi$
$374$	0.0787817	−	0.136454i	0.00407371	−	0.00705587i
$375$	−30.8072	+	0.0217739i	−1.59088	+	0.00112440i
$376$			0.625521i			0.0322588i
$377$	14.0289	+	5.53729i	0.722525	+	0.285185i
$378$	18.8630	+	18.8630i	0.970207	+	0.970207i
$379$	−14.9855	+	4.01535i	−0.769754	+	0.206255i	−0.622263	−	0.782809i	$-0.713786\pi$
$379$	−14.9855	+	4.01535i	−0.769754	+	0.206255i	−0.147491	+	0.989063i	$0.547120\pi$
$380$	−24.8676	+	4.39088i	−1.27568	+	0.225247i
$381$	35.8602	−	20.7039i	1.83717	−	1.06069i
$382$		−	9.64728i		−	0.493598i
$383$	−11.2034	−	19.4048i	−0.572465	−	0.991538i	−0.996312	−	0.0858043i	$-0.972654\pi$
$383$	−11.2034	−	19.4048i	−0.572465	−	0.991538i	0.423847	−	0.905734i	$-0.360679\pi$
$384$	−15.7238	−	4.21319i	−0.802404	−	0.215004i
$385$	0.110277	+	0.131360i	0.00562023	+	0.00669473i
$386$	17.3632	+	30.0740i	0.883766	+	1.53073i
$387$	30.7556	−	8.24093i	1.56339	−	0.418910i
$388$	0.828521	+	0.478347i	0.0420618	+	0.0242844i
$389$	−7.41149			−0.375777			−0.187889	−	0.982190i	$-0.560164\pi$
$389$	−7.41149			−0.375777			−0.187889	+	0.982190i	$0.560164\pi$
$390$	45.4490	+	9.26814i	2.30140	+	0.469311i
$391$	1.06358			0.0537878
$392$	−0.959068	−	0.553718i	−0.0484402	−	0.0279670i
$393$	−24.0724	+	6.45019i	−1.21429	+	0.325369i
$394$	−26.8604	−	46.5236i	−1.35321	−	2.34383i
$395$	−0.826112	+	9.46820i	−0.0415662	+	0.476397i
$396$	−0.275776	−	0.0738941i	−0.0138583	−	0.00371332i
$397$	−8.77205	−	15.1936i	−0.440257	−	0.762547i	0.557452	−	0.830209i	$-0.311779\pi$
$397$	−8.77205	−	15.1936i	−0.440257	−	0.762547i	−0.997708	+	0.0676626i	$0.978446\pi$
$398$		−	58.0088i		−	2.90772i
$399$	−33.2512	+	19.1976i	−1.66464	+	0.961083i
$400$	10.1240	−	12.0769i	0.506199	−	0.603843i
$401$	−26.5449	+	7.11268i	−1.32559	+	0.355190i	−0.851068	−	0.525055i	$-0.824045\pi$
$401$	−26.5449	+	7.11268i	−1.32559	+	0.355190i	−0.474520	+	0.880245i	$0.657378\pi$
$402$	−50.1074	−	50.1074i	−2.49913	−	2.49913i
$403$	2.53576	−	3.42196i	0.126315	−	0.170460i
$404$			6.72034i			0.334350i
$405$	−2.16078	+	3.08747i	−0.107370	+	0.153417i
$406$	−12.7134	+	22.0202i	−0.630954	+	1.09284i
$407$	0.0439951	−	0.164192i	0.00218076	−	0.00813869i
$408$	5.92388			0.293276
$409$	−4.33151	+	16.1654i	−0.214179	+	0.799329i	0.772274	+	0.635289i	$0.219119\pi$
$409$	−4.33151	+	16.1654i	−0.214179	+	0.799329i	−0.986454	+	0.164039i	$0.947548\pi$
$410$	12.5119	−	34.4013i	0.617918	−	1.69896i
$411$	−28.3850	−	28.3850i	−1.40013	−	1.40013i
$412$	−18.1622	−	4.86654i	−0.894786	−	0.239757i
$413$	1.12835	+	4.21106i	0.0555225	+	0.207213i
$414$	−0.921603	−	3.43947i	−0.0452943	−	0.169041i
$415$	2.93178	+	0.255802i	0.143916	+	0.0125568i
$416$	−22.8175	+	18.1243i	−1.11872	+	0.888615i
$417$	13.4725	−	13.4725i	0.659750	−	0.659750i
$418$	0.131649	−	0.228022i	0.00643914	−	0.0111529i
$419$	24.9349	+	14.3962i	1.21815	+	0.703299i	0.964522	−	0.264003i	$-0.0850429\pi$
$419$	24.9349	+	14.3962i	1.21815	+	0.703299i	0.253627	+	0.967302i	$0.418376\pi$
$420$	−14.4661	+	39.7744i	−0.705873	+	1.94079i
$421$	8.48901	−	8.48901i	0.413729	−	0.413729i	−0.469306	−	0.883035i	$-0.655496\pi$
$421$	8.48901	−	8.48901i	0.413729	−	0.413729i	0.883035	+	0.469306i	$0.155496\pi$
$422$	−26.7192	+	15.4263i	−1.30067	+	0.750941i
$423$	3.31466	−	1.91372i	0.161164	−	0.0930482i
$424$	−0.677229	+	0.677229i	−0.0328892	+	0.0328892i
$425$	−6.04627	+	12.9822i	−0.293287	+	0.629731i
$426$	18.4377	+	10.6450i	0.893308	+	0.515752i
$427$	15.5778	−	26.9816i	0.753865	−	1.30573i
$428$	21.8021	−	21.8021i	1.05384	−	1.05384i
$429$	−0.204966	+	0.162807i	−0.00989583	+	0.00786038i
$430$	20.8116	+	24.7904i	1.00362	+	1.19550i
$431$	3.04457	+	11.3625i	0.146652	+	0.547311i	0.999676	+	0.0254407i	$0.00809891\pi$
$431$	3.04457	+	11.3625i	0.146652	+	0.547311i	−0.853025	+	0.521870i	$0.825234\pi$
$432$	3.57999	+	13.3607i	0.172242	+	0.642816i
$433$	18.7108	+	5.01355i	0.899184	+	0.240936i	0.678666	−	0.734447i	$-0.262558\pi$
$433$	18.7108	+	5.01355i	0.899184	+	0.240936i	0.220518	+	0.975383i	$0.429225\pi$
$434$	5.07726	+	5.07726i	0.243716	+	0.243716i
$435$	24.2213	+	8.80938i	1.16132	+	0.422377i
$436$	6.61838	−	24.7001i	0.316963	−	1.18292i
$437$	1.77731			0.0850201
$438$	−22.4616	+	83.8278i	−1.07326	+	4.00545i
$439$	−11.9244	+	20.6537i	−0.569121	+	0.985747i	0.427532	+	0.904000i	$0.359383\pi$
$439$	−11.9244	+	20.6537i	−0.569121	+	0.985747i	−0.996653	+	0.0817464i	$0.973950\pi$
$440$	−0.00768891	−	0.0435460i	−0.000366554	−	0.00207597i
$441$			6.77618i			0.322675i
$442$	12.8378	−	17.3243i	0.610630	−	0.824032i
$443$	11.8603	+	11.8603i	0.563501	+	0.563501i	0.930300	−	0.366799i	$-0.119546\pi$
$443$	11.8603	+	11.8603i	0.563501	+	0.563501i	−0.366799	+	0.930300i	$0.619546\pi$
$444$	40.5170	−	10.8565i	1.92285	−	0.515227i
$445$	−1.30292	−	7.37906i	−0.0617644	−	0.349801i
$446$	−25.3582	+	14.6406i	−1.20075	+	0.693251i
$447$			16.1399i			0.763392i
$448$	−15.3874	−	26.6518i	−0.726987	−	1.25918i
$449$	39.5246	+	10.5906i	1.86528	+	0.499801i	0.999999	−	0.00148324i	$-0.000472129\pi$
$449$	39.5246	+	10.5906i	1.86528	+	0.499801i	0.865283	+	0.501284i	$0.167139\pi$
$450$	47.2217	+	8.30352i	2.22605	+	0.391432i
$451$	0.103288	+	0.178900i	0.00486363	+	0.00842405i
$452$	19.8046	−	5.30662i	0.931529	−	0.249603i
$453$	9.86901	+	5.69788i	0.463687	+	0.267710i
$454$	33.3886			1.56701
$455$	12.9458	+	19.5783i	0.606910	+	0.917843i
$456$	9.89912			0.463569
$457$	7.15685	+	4.13201i	0.334783	+	0.193287i	0.657963	−	0.753051i	$-0.271418\pi$
$457$	7.15685	+	4.13201i	0.334783	+	0.193287i	−0.323180	+	0.946338i	$0.604752\pi$
$458$	6.59033	−	1.76587i	0.307946	−	0.0825139i
$459$	−6.28500	−	10.8859i	−0.293359	−	0.508112i
$460$	1.50049	−	1.25967i	0.0699608	−	0.0587322i
$461$	−18.3239	−	4.90987i	−0.853429	−	0.228676i	−0.194520	−	0.980899i	$-0.562315\pi$
$461$	−18.3239	−	4.90987i	−0.853429	−	0.228676i	−0.658909	+	0.752223i	$0.728982\pi$
$462$	−0.220646	−	0.382170i	−0.0102654	−	0.0177801i
$463$			24.9284i			1.15852i	0.815142	+	0.579261i	$0.196659\pi$
$463$			24.9284i			1.15852i	−0.815142	+	0.579261i	$0.803341\pi$
$464$	−11.4178	+	6.59205i	−0.530056	+	0.306028i
$465$	4.17324	−	5.96299i	0.193529	−	0.276527i
$466$	−50.8091	+	13.6142i	−2.35368	+	0.630668i
$467$	−25.6059	−	25.6059i	−1.18490	−	1.18490i	−0.978459	−	0.206441i	$-0.933812\pi$
$467$	−25.6059	−	25.6059i	−1.18490	−	1.18490i	−0.206441	−	0.978459i	$-0.566188\pi$
$468$	−36.3426	−	14.3446i	−1.67994	−	0.663081i
$469$		−	35.8577i		−	1.65575i
$470$	3.18772	+	2.23095i	0.147039	+	0.102906i
$471$	8.95998	−	15.5191i	0.412854	−	0.715084i
$472$	0.290913	−	1.08570i	0.0133904	−	0.0499735i
$473$	−0.182660			−0.00839870
$474$	6.32908	−	23.6204i	0.290704	−	1.08492i
$475$	−10.1036	+	21.6940i	−0.463587	+	0.995390i
$476$	13.9121	+	13.9121i	0.637659	+	0.637659i
$477$	5.66058	+	1.51675i	0.259180	+	0.0694471i
$478$	3.29695	+	12.3044i	0.150799	+	0.562789i
$479$	−1.20781	−	4.50760i	−0.0551861	−	0.205957i	0.932828	−	0.360323i	$-0.117333\pi$
$479$	−1.20781	−	4.50760i	−0.0551861	−	0.205957i	−0.988014	+	0.154365i	$0.950667\pi$
$480$	−38.1387	+	32.0175i	−1.74078	+	1.46139i
$481$	8.54051	−	21.6377i	0.389414	−	0.986592i
$482$	13.3626	−	13.3626i	0.608652	−	0.608652i
$483$	1.48940	−	2.57972i	0.0677701	−	0.117381i
$484$	−22.4757	−	12.9764i	−1.02162	−	0.589834i
$485$	0.821616	−	0.383361i	0.0373076	−	0.0174075i
$486$	26.2941	−	26.2941i	1.19273	−	1.19273i
$487$	−12.6563	+	7.30711i	−0.573511	+	0.331117i	−0.758550	−	0.651615i	$-0.774092\pi$
$487$	−12.6563	+	7.30711i	−0.573511	+	0.331117i	0.185040	+	0.982731i	$0.440759\pi$
$488$	−6.95644	+	4.01630i	−0.314903	+	0.181810i
$489$	−7.84764	+	7.84764i	−0.354883	+	0.354883i
$490$	−6.24237	+	2.91265i	−0.282001	+	0.131580i
$491$	−17.4840	−	10.0944i	−0.789042	−	0.455553i	0.0505834	−	0.998720i	$-0.483892\pi$
$491$	−17.4840	−	10.0944i	−0.789042	−	0.455553i	−0.839625	+	0.543166i	$0.817225\pi$
$492$	−25.4879	+	44.1464i	−1.14908	+	1.99027i
$493$	8.47199	−	8.47199i	0.381559	−	0.381559i
$494$	21.4526	−	28.9498i	0.965197	−	1.30251i
$495$	−0.207228	+	0.173968i	−0.00931422	+	0.00781930i
$496$	0.963607	+	3.59623i	0.0432672	+	0.161476i
$497$	2.78829	+	10.4060i	0.125072	+	0.466774i
$498$	−7.31396	−	1.95977i	−0.327746	−	0.0878194i
$499$	−0.519223	−	0.519223i	−0.0232436	−	0.0232436i	0.695389	−	0.718633i	$-0.255232\pi$
$499$	−0.519223	−	0.519223i	−0.0232436	−	0.0232436i	−0.718633	+	0.695389i	$0.755232\pi$
$500$	6.84562	+	25.4762i	0.306145	+	1.13933i
$501$	−17.0018	+	63.4515i	−0.759583	+	2.83480i
$502$	1.21379			0.0541741
$503$	9.77048	−	36.4639i	0.435644	−	1.62585i	−0.303876	−	0.952712i	$-0.598281\pi$
$503$	9.77048	−	36.4639i	0.435644	−	1.62585i	0.739520	−	0.673134i	$-0.235052\pi$
$504$	5.01785	−	8.69117i	0.223513	−	0.387135i
$505$	5.21789	+	3.65178i	0.232193	+	0.162502i
$506$			0.0204273i			0.000908103i
$507$	−30.4043	+	18.9405i	−1.35030	+	0.841179i
$508$	−25.0719	−	25.0719i	−1.11238	−	1.11238i
$509$	39.8263	−	10.6714i	1.76527	−	0.473003i	0.777496	−	0.628887i	$-0.216489\pi$
$509$	39.8263	−	10.6714i	1.76527	−	0.473003i	0.987775	+	0.155884i	$0.0498227\pi$
$510$	21.1278	−	30.1887i	0.935554	−	1.33678i
$511$	−38.0312	+	21.9573i	−1.68240	+	0.971336i
$512$		−	30.2040i		−	1.33484i
$513$	−10.5026	−	18.1910i	−0.463700	−	0.803152i
$514$	35.0960	+	9.40395i	1.54802	+	0.414791i
$515$	−13.6477	+	11.4573i	−0.601390	+	0.504867i
$516$	−22.5371	−	39.0354i	−0.992142	−	1.71844i
$517$	−0.0212087	+	0.00568287i	−0.000932759	+	0.000249932i
$518$	33.9631	+	19.6086i	1.49225	+	0.861553i
$519$	−2.23862			−0.0982647
$520$	−0.366695	−	6.04029i	−0.0160806	−	0.264884i
$521$	2.07984			0.0911193			0.0455597	−	0.998962i	$-0.485493\pi$
$521$	2.07984			0.0911193			0.0455597	+	0.998962i	$0.485493\pi$
$522$	−34.7382	−	20.0561i	−1.52045	−	0.877831i
$523$	−37.1287	+	9.94861i	−1.62353	+	0.435022i	−0.952035	−	0.305990i	$-0.901013\pi$
$523$	−37.1287	+	9.94861i	−1.62353	+	0.435022i	−0.671491	+	0.741013i	$0.734346\pi$
$524$	10.6700	+	18.4811i	0.466123	+	0.807349i
$525$	23.0214	+	32.8450i	1.00474	+	1.43347i
$526$	55.6329	+	14.9068i	2.42571	+	0.649967i
$527$	−1.69170	−	2.93011i	−0.0736917	−	0.127638i
$528$		−	0.228815i		−	0.00995791i
$529$	19.7992	−	11.4311i	0.860833	−	0.497002i
$530$	1.03587	+	5.86660i	0.0449951	+	0.254829i
$531$	−6.64319	+	1.78004i	−0.288290	+	0.0772471i
$532$	23.2478	+	23.2478i	1.00792	+	1.00792i
$533$	11.2547	+	25.9328i	0.487494	+	1.12327i
$534$			19.2796i			0.834310i
$535$	−5.08078	−	28.7749i	−0.219661	−	1.24405i
$536$	−4.62244	+	8.00630i	−0.199659	+	0.345820i
$537$	4.68025	−	17.4669i	0.201968	−	0.753754i
$538$	−38.4533			−1.65784
$539$	0.0100611	−	0.0375484i	0.000433361	−	0.00161733i
$540$	−21.7597	−	7.91407i	−0.936387	−	0.340567i
$541$	17.3961	+	17.3961i	0.747916	+	0.747916i	0.974088	−	0.226171i	$-0.0726209\pi$
$541$	17.3961	+	17.3961i	0.747916	+	0.747916i	−0.226171	+	0.974088i	$0.572621\pi$
$542$	52.2547	+	14.0016i	2.24453	+	0.601420i
$543$	−1.11702	−	4.16876i	−0.0479358	−	0.178899i
$544$	5.99128	+	22.3598i	0.256874	+	0.958667i
$545$	−15.5816	−	18.5606i	−0.667443	−	0.795048i
$546$	−24.0425	−	55.3982i	−1.02892	−	2.37082i
$547$	−12.8424	+	12.8424i	−0.549100	+	0.549100i	−0.926180	−	0.377081i	$-0.876928\pi$
$547$	−12.8424	+	12.8424i	−0.549100	+	0.549100i	0.377081	+	0.926180i	$0.376928\pi$
$548$	−17.1868	+	29.7683i	−0.734182	+	1.27164i
$549$	42.5651	+	24.5750i	1.81663	+	1.04883i
$550$	−0.249338	−	0.116125i	−0.0106318	−	0.00495159i
$551$	14.1572	−	14.1572i	0.603115	−	0.603115i
$552$	−0.665107	+	0.384000i	−0.0283089	+	0.0163441i
$553$	10.7162	−	6.18700i	0.455699	−	0.263098i
$554$	−34.5829	+	34.5829i	−1.46928	+	1.46928i
$555$	13.5872	−	37.3580i	0.576747	−	1.58576i
$556$	−14.1290	−	8.15741i	−0.599205	−	0.345951i
$557$	15.0968	−	26.1484i	0.639671	−	1.10794i	−0.345834	−	0.938296i	$-0.612404\pi$
$557$	15.0968	−	26.1484i	0.639671	−	1.10794i	0.985505	−	0.169647i	$-0.0542627\pi$
$558$	−8.00967	+	8.00967i	−0.339076	+	0.339076i
$559$	−24.8342	−	2.84682i	−1.05037	−	0.120408i
$560$	−20.4398	−	1.78340i	−0.863740	−	0.0753624i
$561$	0.0538185	+	0.200853i	0.00227222	+	0.00848004i
$562$	−7.58897	−	28.3224i	−0.320122	−	1.19471i
$563$	−27.4966	−	7.36768i	−1.15884	−	0.310511i	−0.372339	−	0.928097i	$-0.621444\pi$
$563$	−27.4966	−	7.36768i	−1.15884	−	0.310511i	−0.786503	+	0.617586i	$0.788111\pi$
$564$	−3.83126	−	3.83126i	−0.161325	−	0.161325i
$565$	6.64141	−	18.2605i	0.279406	−	0.768225i
$566$	−2.22201	+	8.29267i	−0.0933982	+	0.348567i
$567$	4.90639			0.206049
$568$	0.718880	−	2.68290i	0.0301635	−	0.112572i
$569$	−16.3759	+	28.3638i	−0.686512	+	1.18907i	0.286447	+	0.958096i	$0.407526\pi$
$569$	−16.3759	+	28.3638i	−0.686512	+	1.18907i	−0.972959	+	0.230978i	$0.925807\pi$
$570$	35.3057	−	50.4470i	1.47879	−	2.11299i
$571$		−	7.81838i		−	0.327189i	−0.986528	−	0.163594i	$-0.947691\pi$
$571$		−	7.81838i		−	0.327189i	0.986528	−	0.163594i	$-0.0523088\pi$
$572$	0.180084	+	0.133447i	0.00752970	+	0.00557971i
$573$	9.00264	+	9.00264i	0.376091	+	0.376091i
$574$	−46.0354	+	12.3351i	−1.92148	+	0.514859i
$575$	−0.162690	−	1.84952i	−0.00678466	−	0.0771304i
$576$	42.0448	−	24.2746i	1.75187	−	1.01144i
$577$		−	14.7927i		−	0.615830i	−0.951414	−	0.307915i	$-0.900369\pi$
$577$		−	14.7927i		−	0.615830i	0.951414	−	0.307915i	$-0.0996312\pi$
$578$	9.18293	+	15.9053i	0.381959	+	0.661573i
$579$	−44.2675	−	11.8614i	−1.83969	−	0.492944i
$580$	1.91831	−	21.9861i	0.0796536	−	0.912922i
$581$	−1.91577	−	3.31822i	−0.0794797	−	0.137663i
$582$	−2.25328	+	0.603764i	−0.0934014	+	0.0250268i
$583$	−0.0291146	−	0.0168093i	−0.00120580	−	0.000696171i
$584$	11.3222			0.468514
$585$	−30.8859	+	20.4228i	−1.27697	+	0.844379i
$586$	−45.6279			−1.88487
$587$	−14.4411	−	8.33757i	−0.596048	−	0.344128i	0.171437	−	0.985195i	$-0.445159\pi$
$587$	−14.4411	−	8.33757i	−0.596048	−	0.344128i	−0.767485	+	0.641067i	$0.778492\pi$
$588$	9.26568	−	2.48273i	0.382110	−	0.102386i
$589$	−2.82693	−	4.89638i	−0.116481	−	0.201752i
$590$	−4.49530	−	5.35473i	−0.185069	−	0.220451i
$591$	68.4805	+	18.3493i	2.81691	+	0.754789i
$592$	10.1673	+	17.6103i	0.417874	+	0.723780i
$593$		−	6.40700i		−	0.263104i	−0.991309	−	0.131552i	$-0.958004\pi$
$593$		−	6.40700i		−	0.263104i	0.991309	−	0.131552i	$-0.0419960\pi$
$594$	0.209076	−	0.120710i	0.00857850	−	0.00495280i
$595$	18.3615	−	3.24208i	0.752747	−	0.132913i
$596$	13.3495	−	3.57699i	0.546817	−	0.146519i
$597$	54.1326	+	54.1326i	2.21550	+	2.21550i
$598$	−0.318367	+	2.77727i	−0.0130190	+	0.113571i
$599$		−	37.0014i		−	1.51184i	−0.654667	−	0.755918i	$-0.727191\pi$
$599$		−	37.0014i		−	1.51184i	0.654667	−	0.755918i	$-0.272809\pi$
$600$	−0.906142	−	10.3013i	−0.0369931	−	0.420551i
$601$	0.255112	−	0.441867i	0.0104062	−	0.0180241i	−0.860775	−	0.508985i	$-0.830021\pi$
$601$	0.255112	−	0.441867i	0.0104062	−	0.0180241i	0.871182	+	0.490961i	$0.163354\pi$
$602$	10.9071	−	40.7057i	0.444539	−	1.65904i
$603$	56.5676			2.30361
$604$	2.52557	−	9.42555i	0.102764	−	0.383520i
$605$	−22.2884	+	10.3996i	−0.906151	+	0.422805i
$606$	−11.5871	−	11.5871i	−0.470693	−	0.470693i
$607$	−22.6944	−	6.08093i	−0.921135	−	0.246817i	−0.233065	−	0.972461i	$-0.574875\pi$
$607$	−22.6944	−	6.08093i	−0.921135	−	0.246817i	−0.688071	+	0.725644i	$0.741542\pi$
$608$	10.0118	+	37.3644i	0.406030	+	1.51533i
$609$	−8.68494	−	32.4126i	−0.351931	−	1.31343i
$610$	−4.34294	+	49.7751i	−0.175841	+	2.01534i
$611$	−2.97208	+	0.442089i	−0.120238	+	0.0178850i
$612$	−21.9471	+	21.9471i	−0.887159	+	0.887159i
$613$	6.23084	−	10.7921i	0.251661	−	0.435890i	−0.712322	−	0.701853i	$-0.752356\pi$
$613$	6.23084	−	10.7921i	0.251661	−	0.435890i	0.963983	+	0.265963i	$0.0856898\pi$
$614$	−12.6264	−	7.28984i	−0.509559	−	0.294194i
$615$	20.4268	+	43.7784i	0.823687	+	1.76532i
$616$	−0.0407095	+	0.0407095i	−0.00164023	+	0.00164023i
$617$	−24.1020	+	13.9153i	−0.970311	+	0.560209i	−0.899331	−	0.437268i	$-0.855946\pi$
$617$	−24.1020	+	13.9153i	−0.970311	+	0.560209i	−0.0709800	+	0.997478i	$0.522613\pi$
$618$	39.7057	−	22.9241i	1.59720	−	0.922141i
$619$	9.96152	−	9.96152i	0.400387	−	0.400387i	−0.477982	−	0.878370i	$-0.658632\pi$
$619$	9.96152	−	9.96152i	0.400387	−	0.400387i	0.878370	+	0.477982i	$0.158632\pi$
$620$	−5.85694	−	2.13019i	−0.235221	−	0.0855505i
$621$	1.41130	+	0.814817i	0.0566337	+	0.0326975i
$622$	−22.2181	+	38.4830i	−0.890867	+	1.54303i
$623$	−6.89841	+	6.89841i	−0.276379	+	0.276379i
$624$	3.56617	−	31.1095i	0.142761	−	1.24538i
$625$	23.5004	+	8.52836i	0.940015	+	0.341134i
$626$	13.5001	+	50.3830i	0.539572	+	2.01371i
$627$	0.0899336	+	0.335637i	0.00359160	+	0.0134040i
$628$	−14.8218	−	3.97149i	−0.591454	−	0.158480i
$629$	−13.0669	−	13.0669i	−0.521011	−	0.521011i
$630$	−26.3948	−	56.5689i	−1.05159	−	2.25376i
$631$	8.57363	−	31.9972i	0.341311	−	1.27379i	−0.555552	−	0.831482i	$-0.687493\pi$
$631$	8.57363	−	31.9972i	0.341311	−	1.27379i	0.896863	−	0.442308i	$-0.145840\pi$
$632$	−3.19028			−0.126903
$633$	10.5382	−	39.3293i	0.418858	−	1.56320i
$634$	−16.3605	+	28.3373i	−0.649760	+	1.12542i
$635$	−33.0904	+	5.84277i	−1.31315	+	0.231863i
$636$		−	8.29594i		−	0.328955i
$637$	1.95310	−	4.94823i	0.0773845	−	0.196056i
$638$	0.162714	+	0.162714i	0.00644190	+	0.00644190i
$639$	−16.4161	+	4.39868i	−0.649411	+	0.174009i
$640$	10.8228	+	7.57439i	0.427808	+	0.299404i
$641$	39.0498	−	22.5454i	1.54238	−	0.890491i	0.543688	−	0.839288i	$-0.317028\pi$
$641$	39.0498	−	22.5454i	1.54238	−	0.890491i	0.998688	−	0.0512035i	$-0.0163057\pi$
$642$			75.1815i			2.96718i
$643$	−8.71256	−	15.0906i	−0.343590	−	0.595115i	0.641507	−	0.767117i	$-0.278310\pi$
$643$	−8.71256	−	15.0906i	−0.343590	−	0.595115i	−0.985097	+	0.172003i	$0.944976\pi$
$644$	−2.46380	−	0.660173i	−0.0970873	−	0.0260145i
$645$	−42.5549	−	3.71297i	−1.67560	−	0.146198i
$646$	−14.3118	−	24.7888i	−0.563091	−	0.975302i
$647$	−24.0485	+	6.44377i	−0.945442	+	0.253331i	−0.698427	−	0.715681i	$-0.746116\pi$
$647$	−24.0485	+	6.44377i	−0.945442	+	0.253331i	−0.247015	+	0.969012i	$0.579450\pi$
$648$	−1.09550	−	0.632487i	−0.0430353	−	0.0248464i
$649$	0.0394545			0.00154872
$650$	−32.0898	−	19.6743i	−1.25867	−	0.771688i
$651$	−9.47598			−0.371393
$652$	8.23009	+	4.75164i	0.322315	+	0.186089i
$653$	−17.6610	+	4.73226i	−0.691129	+	0.185188i	−0.587254	−	0.809403i	$-0.699791\pi$
$653$	−17.6610	+	4.73226i	−0.691129	+	0.185188i	−0.103875	+	0.994590i	$0.533124\pi$
$654$	31.1762	+	53.9988i	1.21909	+	2.11152i
$655$	20.1473	+	1.75788i	0.787220	+	0.0686860i
$656$	−23.8699	−	6.39593i	−0.931965	−	0.249719i
$657$	−34.6390	−	59.9965i	−1.35140	−	2.34069i
$658$		−	5.06571i		−	0.197482i
$659$	24.6502	−	14.2318i	0.960234	−	0.554391i	0.0639889	−	0.997951i	$-0.479618\pi$
$659$	24.6502	−	14.2318i	0.960234	−	0.554391i	0.896245	+	0.443559i	$0.146284\pi$
$660$	0.313809	+	0.219621i	0.0122150	+	0.00854875i
$661$	24.2172	−	6.48898i	0.941941	−	0.252392i	0.245002	−	0.969523i	$-0.421211\pi$
$661$	24.2172	−	6.48898i	0.941941	−	0.252392i	0.696939	+	0.717130i	$0.254545\pi$
$662$	4.97071	+	4.97071i	0.193192	+	0.193192i
$663$	4.18673	+	28.1466i	0.162599	+	1.09312i
$664$			0.987856i			0.0383363i
$665$	30.6830	−	5.41770i	1.18984	−	0.210089i
$666$	−30.9337	+	53.5788i	−1.19866	+	2.07614i
$667$	−0.402024	+	1.50037i	−0.0155664	+	0.0580947i
$668$	56.2494			2.17635
$669$	10.0015	−	37.3260i	0.386680	−	1.44311i
$670$	24.3148	+	52.1113i	0.939365	+	2.01324i
$671$	−0.199375	−	0.199375i	−0.00769679	−	0.00769679i
$672$	62.6235	+	16.7799i	2.41575	+	0.647299i
$673$	−7.36105	−	27.4718i	−0.283748	−	1.05896i	−0.949750	−	0.313010i	$-0.898663\pi$
$673$	−7.36105	−	27.4718i	−0.283748	−	1.05896i	0.666002	−	0.745950i	$-0.268004\pi$
$674$	5.50873	+	20.5588i	0.212188	+	0.791897i
$675$	−17.9688	+	12.5945i	−0.691618	+	0.484762i
$676$	22.4042	+	20.9500i	0.861701	+	0.805770i
$677$	−2.88008	+	2.88008i	−0.110691	+	0.110691i	−0.760283	−	0.649592i	$-0.774940\pi$
$677$	−2.88008	+	2.88008i	−0.110691	+	0.110691i	0.649592	+	0.760283i	$0.274940\pi$
$678$	−24.9971	+	43.2963i	−0.960008	+	1.66278i
$679$	−1.02227	−	0.590210i	−0.0392313	−	0.0226502i
$680$	−4.51769	−	1.64310i	−0.173246	−	0.0630100i
$681$	−31.1576	+	31.1576i	−1.19396	+	1.19396i
$682$	0.0562760	−	0.0324910i	0.00215492	−	0.00124414i
$683$	18.6936	−	10.7928i	0.715292	−	0.412974i	−0.0977251	−	0.995213i	$-0.531157\pi$
$683$	18.6936	−	10.7928i	0.715292	−	0.412974i	0.813018	+	0.582239i	$0.197823\pi$
$684$	−36.6748	+	36.6748i	−1.40230	+	1.40230i
$685$	13.7740	+	29.5202i	0.526276	+	1.12791i
$686$	−29.0822	−	16.7906i	−1.11036	−	0.641069i
$687$	−4.50208	+	7.79784i	−0.171765	+	0.297506i
$688$	15.4510	−	15.4510i	0.589064	−	0.589064i
$689$	−3.69641	−	2.73914i	−0.140822	−	0.104353i
$690$	−0.415230	+	4.75901i	−0.0158075	+	0.181172i
$691$	9.34901	+	34.8910i	0.355653	+	1.32732i	0.879661	+	0.475602i	$0.157770\pi$
$691$	9.34901	+	34.8910i	0.355653	+	1.32732i	−0.524008	+	0.851713i	$0.675564\pi$
$692$	0.496132	+	1.85159i	0.0188601	+	0.0703869i
$693$	0.340268	+	0.0911744i	0.0129257	+	0.00346343i
$694$	−28.9269	−	28.9269i	−1.09805	−	1.09805i
$695$	−14.0113	+	6.53758i	−0.531478	+	0.247985i
$696$	−2.23916	+	8.35668i	−0.0848753	+	0.316759i
$697$	22.4573			0.850631
$698$	4.50251	−	16.8036i	0.170423	−	0.636026i
$699$	34.7094	−	60.1185i	1.31283	−	2.27389i
$700$	22.0644	−	26.3205i	0.833955	−	0.994821i
$701$			16.0544i			0.606367i	0.952932	+	0.303184i	$0.0980496\pi$
$701$			16.0544i			0.606367i	−0.952932	+	0.303184i	$0.901950\pi$
$702$	30.3071	−	13.1531i	1.14387	−	0.496431i
$703$	−21.8355	−	21.8355i	−0.823540	−	0.823540i
$704$	−0.269022	+	0.0720843i	−0.0101392	+	0.00271678i
$705$	−5.05659	+	0.892842i	−0.190442	+	0.0336264i
$706$	9.34579	−	5.39580i	0.351734	−	0.203073i
$707$		−	8.29192i		−	0.311850i
$708$	4.86801	+	8.43165i	0.182951	+	0.316881i
$709$	−25.0659	−	6.71639i	−0.941370	−	0.252239i	−0.244674	−	0.969605i	$-0.578681\pi$
$709$	−25.0659	−	6.71639i	−0.941370	−	0.252239i	−0.696696	+	0.717366i	$0.745348\pi$
$710$	−11.1084	−	13.2322i	−0.416892	−	0.496594i
$711$	9.76035	+	16.9054i	0.366042	+	0.634003i
$712$	2.42956	−	0.650997i	0.0910514	−	0.0243972i
$713$	0.379874	+	0.219320i	0.0142264	+	0.00821361i
$714$	−47.9738			−1.79538
$715$	0.201469	−	0.0673092i	0.00753452	−	0.00251722i
$716$	−15.4843			−0.578677
$717$	−14.5588	−	8.40555i	−0.543710	−	0.313911i
$718$	31.9856	−	8.57052i	1.19369	−	0.319849i
$719$	21.6867	+	37.5624i	0.808776	+	1.40084i	0.913712	+	0.406362i	$0.133203\pi$
$719$	21.6867	+	37.5624i	0.808776	+	1.40084i	−0.104936	+	0.994479i	$0.533464\pi$
$720$	2.81342	−	32.2450i	0.104850	−	1.20170i
$721$	22.4094	+	6.00459i	0.834571	+	0.223623i
$722$	−4.08041	−	7.06747i	−0.151857	−	0.263024i
$723$			24.9395i			0.927509i
$724$	−3.20047	+	1.84779i	−0.118945	+	0.0686727i
$725$	−16.0283	−	13.4365i	−0.595276	−	0.499018i
$726$	61.1258	−	16.3786i	2.26859	−	0.607867i
$727$	−5.51970	−	5.51970i	−0.204714	−	0.204714i	0.597302	−	0.802016i	$-0.296239\pi$
$727$	−5.51970	−	5.51970i	−0.204714	−	0.204714i	−0.802016	+	0.597302i	$0.796239\pi$
$728$	−6.16928	+	4.90034i	−0.228649	+	0.181619i
$729$			44.0183i			1.63031i
$730$	40.3810	−	57.6989i	1.49457	−	2.13553i
$731$	−9.92869	+	17.1970i	−0.367226	+	0.636054i
$732$	18.0081	−	67.2071i	0.665598	−	2.48405i
$733$	14.7183			0.543633			0.271817	−	0.962349i	$-0.412376\pi$
$733$	14.7183			0.543633			0.271817	+	0.962349i	$0.412376\pi$
$734$	−6.57289	+	24.5304i	−0.242610	+	0.905432i
$735$	3.10722	−	8.54327i	0.114611	−	0.315123i
$736$	−2.12209	−	2.12209i	−0.0782212	−	0.0782212i
$737$	−0.313455	−	0.0839899i	−0.0115462	−	0.00309381i
$738$	−19.4594	−	72.6235i	−0.716311	−	2.67331i
$739$	8.68701	+	32.4204i	0.319557	+	1.19260i	0.919672	+	0.392688i	$0.128455\pi$
$739$	8.68701	+	32.4204i	0.319557	+	1.19260i	−0.600115	+	0.799914i	$0.704878\pi$
$740$	−33.9105	−	2.95873i	−1.24657	−	0.108765i
$741$	6.99624	+	47.0344i	0.257013	+	1.72785i
$742$	5.48446	−	5.48446i	0.201341	−	0.201341i
$743$	−10.4647	+	18.1254i	−0.383914	+	0.664958i	−0.991618	−	0.129206i	$-0.958757\pi$
$743$	−10.4647	+	18.1254i	−0.383914	+	0.664958i	0.607704	+	0.794163i	$0.292091\pi$
$744$	2.11580	+	1.22156i	0.0775689	+	0.0447844i
$745$	4.47671	−	12.3087i	0.164014	−	0.450956i
$746$	0.506032	−	0.506032i	0.0185272	−	0.0185272i
$747$	5.23469	−	3.02225i	0.191527	−	0.110578i
$748$	0.154201	−	0.0890277i	0.00563813	−	0.00325518i
$749$	−26.9006	+	26.9006i	−0.982925	+	0.982925i
$750$	−55.7286	−	32.1224i	−2.03492	−	1.17294i
$751$	28.8409	+	16.6513i	1.05242	+	0.607614i	0.923325	−	0.384019i	$-0.125460\pi$
$751$	28.8409	+	16.6513i	1.05242	+	0.607614i	0.129093	+	0.991633i	$0.458793\pi$
$752$	1.31332	−	2.27473i	0.0478918	−	0.0829510i
$753$	−1.13268	+	1.13268i	−0.0412773	+	0.0412773i
$754$	19.5864	+	24.6583i	0.713295	+	0.898003i
$755$	−5.94593	−	7.08269i	−0.216395	−	0.257766i
$756$	7.80228	+	29.1185i	0.283766	+	1.05903i
$757$	−2.57119	−	9.59581i	−0.0934515	−	0.348766i	0.903329	−	0.428949i	$-0.141116\pi$
$757$	−2.57119	−	9.59581i	−0.0934515	−	0.348766i	−0.996780	+	0.0801834i	$0.974449\pi$
$758$	−31.2888	−	8.38381i	−1.13646	−	0.304514i
$759$	−0.0190623	−	0.0190623i	−0.000691918	−	0.000691918i
$760$	−7.54931	−	2.74571i	−0.273842	−	0.0995973i
$761$	11.0600	−	41.2764i	0.400924	−	1.49627i	−0.410526	−	0.911849i	$-0.634655\pi$
$761$	11.0600	−	41.2764i	0.400924	−	1.49627i	0.811450	−	0.584421i	$-0.198678\pi$
$762$	86.4568			3.13200
$763$	−8.16611	+	30.4763i	−0.295633	+	1.10332i
$764$	5.45098	−	9.44138i	0.197210	−	0.341577i
$765$	5.11458	+	28.9663i	0.184918	+	1.04728i
$766$		−	46.7838i		−	1.69037i
$767$	5.36418	+	0.614912i	0.193689	+	0.0222032i
$768$	17.1599	+	17.1599i	0.619203	+	0.619203i
$769$	−32.2304	+	8.63611i	−1.16226	+	0.311426i	−0.787867	−	0.615845i	$-0.788815\pi$
$769$	−32.2304	+	8.63611i	−1.16226	+	0.311426i	−0.374391	+	0.927271i	$0.622148\pi$
$770$	0.0622677	+	0.352652i	0.00224397	+	0.0127087i
$771$	−41.5264	+	23.9753i	−1.49554	+	0.863450i
$772$			39.2429i			1.41238i
$773$	4.97625	+	8.61912i	0.178983	+	0.310008i	0.941533	−	0.336922i	$-0.109386\pi$
$773$	4.97625	+	8.61912i	0.178983	+	0.310008i	−0.762549	+	0.646930i	$0.776052\pi$
$774$	64.2157	+	17.2065i	2.30819	+	0.618477i
$775$	−4.83656	+	3.38999i	−0.173734	+	0.121772i
$776$	0.152169	+	0.263564i	0.00546254	+	0.00946140i
$777$	−49.9920	+	13.3953i	−1.79345	+	0.480555i
$778$	−13.4015	−	7.73737i	−0.480467	−	0.277398i
$779$	37.5274			1.34456
$780$	39.2422	+	34.7503i	1.40510	+	1.24426i
$781$	0.0974966			0.00348870
$782$	1.92318	+	1.11035i	0.0687728	+	0.0397060i
$783$	17.7322	−	4.75133i	0.633697	−	0.169799i
$784$	2.32513	+	4.02724i	0.0830403	+	0.143830i
$785$	−11.1376	+	9.35004i	−0.397519	+	0.333717i
$786$	−50.2618	−	13.4676i	−1.79278	−	0.480373i
$787$	9.61957	+	16.6616i	0.342901	+	0.593922i	0.984970	−	0.172725i	$-0.0552572\pi$
$787$	9.61957	+	16.6616i	0.342901	+	0.593922i	−0.642069	+	0.766647i	$0.721924\pi$
$788$		−	60.7076i		−	2.16262i
$789$	−65.8262	+	38.0047i	−2.34347	+	1.35300i
$790$	−11.3783	+	16.2580i	−0.404821	+	0.578435i
$791$	−24.4359	+	6.54759i	−0.868842	+	0.232806i
$792$	−0.0642216	−	0.0642216i	−0.00228201	−	0.00228201i
$793$	−23.9995	−	30.2141i	−0.852246	−	1.07294i
$794$		−	36.6310i		−	1.29999i
$795$	−6.44124	−	4.50794i	−0.228447	−	0.159880i
$796$	32.7766	−	56.7707i	1.16174	−	2.01219i
$797$	5.23820	−	19.5492i	0.185546	−	0.692469i	−0.808966	−	0.587855i	$-0.799973\pi$
$797$	5.23820	−	19.5492i	0.185546	−	0.692469i	0.994513	−	0.104614i	$-0.0333607\pi$
$798$	−80.1669			−2.83788
$799$	−0.617798	+	2.30565i	−0.0218561	+	0.0815681i
$800$	37.9661	−	13.8388i	1.34231	−	0.489276i
$801$	−10.8826	−	10.8826i	−0.384519	−	0.384519i
$802$	−55.4241	−	14.8508i	−1.95709	−	0.524401i
$803$	0.102862	+	0.383886i	0.00362992	+	0.0135470i
$804$	−20.7259	−	77.3500i	−0.730945	−	2.72792i
$805$	−1.85139	+	1.55424i	−0.0652528	+	0.0547798i
$806$	8.15760	−	3.54035i	0.287339	−	0.124704i
$807$	35.8838	−	35.8838i	1.26317	−	1.26317i
$808$	−1.06892	+	1.85142i	−0.0376044	+	0.0651327i
$809$	−1.16125	−	0.670445i	−0.0408272	−	0.0235716i	0.479447	−	0.877571i	$-0.340837\pi$
$809$	−1.16125	−	0.670445i	−0.0408272	−	0.0235716i	−0.520275	+	0.853999i	$0.674170\pi$
$810$	−7.13037	+	3.32699i	−0.250536	+	0.116898i
$811$	−26.9316	+	26.9316i	−0.945697	+	0.945697i	−0.998600	−	0.0529030i	$-0.983153\pi$
$811$	−26.9316	+	26.9316i	−0.945697	+	0.945697i	0.0529030	+	0.998600i	$0.483153\pi$
$812$	−24.8840	+	14.3668i	−0.873259	+	0.504176i
$813$	−61.8290	+	35.6970i	−2.16844	+	1.25195i
$814$	0.250964	−	0.250964i	0.00879627	−	0.00879627i
$815$	8.16149	−	3.80811i	0.285885	−	0.133392i
$816$	−21.5424	−	12.4375i	−0.754136	−	0.435401i
$817$	−16.5914	+	28.7371i	−0.580459	+	1.00538i
$818$	−24.7085	+	24.7085i	−0.863912	+	0.863912i
$819$	44.8414	+	17.6992i	1.56688	+	0.618459i
$820$	31.6825	−	26.5975i	1.10640	−	0.928826i
$821$	−4.83545	−	18.0461i	−0.168758	−	0.629815i	−0.997531	−	0.0702292i	$-0.977627\pi$
$821$	−4.83545	−	18.0461i	−0.168758	−	0.629815i	0.828772	−	0.559586i	$-0.189040\pi$
$822$	−21.6929	−	80.9591i	−0.756627	−	2.82377i
$823$	−2.41632	−	0.647451i	−0.0842276	−	0.0225687i	0.216459	−	0.976292i	$-0.430549\pi$
$823$	−2.41632	−	0.647451i	−0.0842276	−	0.0225687i	−0.300687	+	0.953723i	$0.597216\pi$
$824$	−4.22953	−	4.22953i	−0.147342	−	0.147342i
$825$	0.341042	−	0.124311i	0.0118736	−	0.00432796i
$826$	−2.35593	+	8.79243i	−0.0819731	+	0.305928i
$827$	31.5605			1.09747			0.548733	−	0.835998i	$-0.315110\pi$
$827$	31.5605			1.09747			0.548733	+	0.835998i	$0.315110\pi$
$828$	1.04146	−	3.88679i	0.0361933	−	0.135075i
$829$	−12.7105	+	22.0153i	−0.441455	+	0.764622i	−0.997798	−	0.0663305i	$-0.978871\pi$
$829$	−12.7105	+	22.0153i	−0.441455	+	0.764622i	0.556343	+	0.830953i	$0.312204\pi$
$830$	5.03422	+	3.52323i	0.174740	+	0.122293i
$831$		−	64.5440i		−	2.23901i
$832$	−37.6994	+	5.60768i	−1.30699	+	0.194411i
$833$	−2.98822	−	2.98822i	−0.103536	−	0.103536i
$834$	38.4259	−	10.2962i	1.33058	−	0.356528i
$835$	30.5654	−	43.6738i	1.05776	−	1.51140i
$836$	0.257677	−	0.148770i	0.00891196	−	0.00514532i
$837$		−	5.18409i		−	0.179188i
$838$	30.0583	+	52.0625i	1.03835	+	1.79847i
$839$	−18.5670	−	4.97501i	−0.641004	−	0.171757i	−0.0763459	−	0.997081i	$-0.524325\pi$
$839$	−18.5670	−	4.97501i	−0.641004	−	0.171757i	−0.564658	+	0.825325i	$0.690992\pi$
$840$	−10.3117	+	8.65671i	−0.355789	+	0.298685i
$841$	−5.75109	−	9.96118i	−0.198313	−	0.343489i
$842$	24.2121	−	6.48763i	0.834406	−	0.223578i
$843$	33.5118	+	19.3480i	1.15421	+	0.666382i
$844$	−34.8652			−1.20011
$845$	28.4405	−	6.01131i	0.978384	−	0.206795i
$846$	7.99145			0.274752
$847$	27.7317	+	16.0109i	0.952873	+	0.550142i
$848$	3.88466	−	1.04089i	0.133400	−	0.0357443i
$849$	−5.66501	−	9.81208i	−0.194423	−	0.336750i
$850$	−24.4860	+	17.1625i	−0.839862	+	0.588667i
$851$	2.31412	+	0.620066i	0.0793270	+	0.0212556i
$852$	12.0294	+	20.8356i	0.412122	+	0.713816i
$853$		−	38.7388i		−	1.32639i	−0.748445	−	0.663196i	$-0.769199\pi$
$853$		−	38.7388i		−	1.32639i	0.748445	−	0.663196i	$-0.230801\pi$
$854$	56.3359	−	32.5256i	1.92778	−	1.11300i
$855$	8.54674	+	48.4043i	0.292292	+	1.65539i
$856$	9.47413	−	2.53859i	0.323819	−	0.0867671i
$857$	28.3225	+	28.3225i	0.967479	+	0.967479i	0.999488	−	0.0320088i	$-0.0101905\pi$
$857$	28.3225	+	28.3225i	0.967479	+	0.967479i	−0.0320088	+	0.999488i	$0.510190\pi$
$858$	−0.540585	+	0.0804106i	−0.0184553	+	0.00274517i
$859$		−	31.6153i		−	1.07870i	−0.842082	−	0.539350i	$-0.818670\pi$
$859$		−	31.6153i		−	1.07870i	0.842082	−	0.539350i	$-0.181330\pi$
$860$	6.36013	+	36.0205i	0.216879	+	1.22829i
$861$	31.4483	−	54.4701i	1.07176	−	1.85634i
$862$	−6.35687	+	23.7241i	−0.216516	+	0.808048i
$863$	−9.51860			−0.324017			−0.162008	−	0.986789i	$-0.551797\pi$
$863$	−9.51860			−0.324017			−0.162008	+	0.986789i	$0.551797\pi$
$864$	−9.17990	+	34.2599i	−0.312307	+	1.16554i
$865$	1.70723	+	0.620925i	0.0580475	+	0.0211121i
$866$	28.5991	+	28.5991i	0.971835	+	0.971835i
$867$	−23.4118	−	6.27317i	−0.795107	−	0.213048i
$868$	2.10010	+	7.83768i	0.0712821	+	0.266028i
$869$	−0.0289838	−	0.108169i	−0.000983207	−	0.00366938i
$870$	34.6004	+	41.2155i	1.17307	+	1.39734i
$871$	−41.3079	−	16.3045i	−1.39966	−	0.552456i
$872$	5.75206	−	5.75206i	0.194789	−	0.194789i
$873$	0.931091	−	1.61270i	0.0315127	−	0.0545815i
$874$	3.21374	+	1.85545i	0.108706	+	0.0627616i
$875$	−8.44649	−	31.4338i	−0.285543	−	1.06266i
$876$	−69.3472	+	69.3472i	−2.34303	+	2.34303i
$877$	12.8573	−	7.42315i	0.434159	−	0.250662i	−0.266958	−	0.963708i	$-0.586018\pi$
$877$	12.8573	−	7.42315i	0.434159	−	0.250662i	0.701117	+	0.713046i	$0.252685\pi$
$878$	−43.1236	+	24.8974i	−1.45535	+	0.840248i
$879$	42.5790	−	42.5790i	1.43615	−	1.43615i
$880$	−0.0634663	+	0.174500i	−0.00213945	+	0.00588240i
$881$	−2.16038	−	1.24730i	−0.0727850	−	0.0420224i	0.463166	−	0.886272i	$-0.346713\pi$
$881$	−2.16038	−	1.24730i	−0.0727850	−	0.0420224i	−0.535951	+	0.844249i	$0.680047\pi$
$882$	−7.07412	+	12.2527i	−0.238198	+	0.412571i
$883$	2.64136	−	2.64136i	0.0888887	−	0.0888887i	−0.661264	−	0.750153i	$-0.729980\pi$
$883$	2.64136	−	2.64136i	0.0888887	−	0.0888887i	0.750153	+	0.661264i	$0.229980\pi$
$884$	22.3525	−	9.70083i	0.751794	−	0.326274i
$885$	9.19184	+	0.802000i	0.308980	+	0.0269589i
$886$	9.06411	+	33.8277i	0.304515	+	1.13646i
$887$	14.1781	+	52.9134i	0.476054	+	1.77666i	0.617348	+	0.786690i	$0.288207\pi$
$887$	14.1781	+	52.9134i	0.476054	+	1.77666i	−0.141294	+	0.989968i	$0.545126\pi$
$888$	12.8890	+	3.45360i	0.432527	+	0.115895i
$889$	30.9350	+	30.9350i	1.03753	+	1.03753i
$890$	5.34756	−	14.7031i	0.179251	−	0.492849i
$891$	0.0114923	−	0.0428898i	0.000385006	−	0.00143686i
$892$	−33.0893			−1.10791
$893$	−1.03237	+	3.85287i	−0.0345471	+	0.128931i
$894$	−16.8496	+	29.1843i	−0.563534	+	0.976070i
$895$	−8.41406	+	12.0225i	−0.281251	+	0.401869i
$896$		−	17.1988i		−	0.574572i
$897$	−2.29460	−	2.88878i	−0.0766143	−	0.0964536i
$898$	60.4125	+	60.4125i	2.01599	+	2.01599i
$899$	4.77289	−	1.27889i	0.159185	−	0.0426534i
$900$	41.5221	+	34.8079i	1.38407	+	1.16026i
$901$	−3.16512	+	1.82738i	−0.105445	+	0.0608789i
$902$			0.431317i			0.0143613i
$903$	27.8075	+	48.1640i	0.925375	+	1.60280i
$904$	6.30011	+	1.68811i	0.209539	+	0.0561457i
$905$	−0.304422	+	3.48903i	−0.0101193	+	0.115979i
$906$	11.8968	+	20.6059i	0.395245	+	0.684585i
$907$	46.4710	−	12.4519i	1.54304	−	0.413457i	0.615796	−	0.787906i	$-0.288835\pi$
$907$	46.4710	−	12.4519i	1.54304	−	0.413457i	0.927248	+	0.374448i	$0.122168\pi$
$908$	32.6760	+	18.8655i	1.08439	+	0.626074i
$909$	13.0810			0.433869
$910$	2.96964	+	48.9166i	0.0984425	+	1.62157i
$911$	28.6074			0.947806			0.473903	−	0.880577i	$-0.342845\pi$
$911$	28.6074			0.947806			0.473903	+	0.880577i	$0.342845\pi$
$912$	−35.9986	−	20.7838i	−1.19203	−	0.688220i
$913$	−0.0334940	+	0.00897469i	−0.00110849	+	0.000297019i
$914$	8.62738	+	14.9431i	0.285368	+	0.494272i
$915$	−42.3963	−	50.5018i	−1.40158	−	1.66954i
$916$	7.44744	+	1.99554i	0.246070	+	0.0659344i
$917$	−13.1653	−	22.8029i	−0.434755	−	0.753018i
$918$		−	26.2454i		−	0.866227i
$919$	−31.4065	+	18.1326i	−1.03600	+	0.598138i	−0.918699	−	0.394958i	$-0.870759\pi$
$919$	−31.4065	+	18.1326i	−1.03600	+	0.598138i	−0.117306	+	0.993096i	$0.537426\pi$
$920$	0.613736	−	0.108367i	0.0202343	−	0.00357277i
$921$	18.5854	−	4.97994i	0.612409	−	0.164095i
$922$	−28.0077	−	28.0077i	−0.922383	−	0.922383i
$923$	13.2555	+	1.51952i	0.436311	+	0.0500156i
$924$		−	0.498684i		−	0.0164055i
$925$	−20.7239	+	24.7215i	−0.681398	+	0.812836i
$926$	−26.0245	+	45.0757i	−0.855218	+	1.48128i
$927$	−9.47260	+	35.3522i	−0.311121	+	1.16112i
$928$	−33.8070			−1.10977
$929$	4.64847	−	17.3483i	0.152511	−	0.569180i	−0.846794	−	0.531921i	$-0.821470\pi$
$929$	4.64847	−	17.3483i	0.152511	−	0.569180i	0.999306	−	0.0372596i	$-0.0118629\pi$
$930$	13.7713	−	6.42560i	0.451578	−	0.210704i
$931$	−4.99347	−	4.99347i	−0.163654	−	0.163654i
$932$	−57.4171	−	15.3849i	−1.88076	−	0.503948i
$933$	−15.1780	−	56.6450i	−0.496905	−	1.85447i
$934$	−19.5690	−	73.0326i	−0.640318	−	2.38970i
$935$	0.0146672	−	0.168103i	0.000479669	−	0.00549756i
$936$	−7.73057	−	9.73241i	−0.252682	−	0.318114i
$937$	−31.2035	+	31.2035i	−1.01937	+	1.01937i	−0.0195653	+	0.999809i	$0.506228\pi$
$937$	−31.2035	+	31.2035i	−1.01937	+	1.01937i	−0.999809	+	0.0195653i	$0.993772\pi$
$938$	37.4343	−	64.8381i	1.22227	−	2.11704i
$939$	−59.6143	−	34.4183i	−1.94544	−	1.12320i
$940$	1.85914	+	3.98448i	0.0606384	+	0.129960i
$941$	−2.83451	+	2.83451i	−0.0924023	+	0.0924023i	−0.751797	−	0.659395i	$-0.770813\pi$
$941$	−2.83451	+	2.83451i	−0.0924023	+	0.0924023i	0.659395	+	0.751797i	$0.270813\pi$
$942$	32.4030	−	18.7079i	1.05575	−	0.609536i
$943$	−2.52141	+	1.45574i	−0.0821084	+	0.0474053i
$944$	−3.33741	+	3.33741i	−0.108624	+	0.108624i
$945$	26.8482	+	9.76480i	0.873373	+	0.317649i
$946$	−0.330287	−	0.190691i	−0.0107385	−	0.00619990i
$947$	−10.1283	+	17.5428i	−0.329127	+	0.570064i	−0.982339	−	0.187111i	$-0.940088\pi$
$947$	−10.1283	+	17.5428i	−0.329127	+	0.570064i	0.653212	+	0.757175i	$0.273421\pi$
$948$	19.5402	−	19.5402i	0.634636	−	0.634636i
$949$	8.00198	+	53.7958i	0.259755	+	1.74629i
$950$	−40.9174	+	28.6794i	−1.32753	+	0.930482i
$951$	−11.1764	−	41.7111i	−0.362421	−	1.35257i
$952$	1.61989	+	6.04551i	0.0525010	+	0.195936i
$953$	21.1724	+	5.67311i	0.685840	+	0.183770i	0.584879	−	0.811120i	$-0.301142\pi$
$953$	21.1724	+	5.67311i	0.685840	+	0.183770i	0.100960	+	0.994890i	$0.467808\pi$
$954$	8.65206	+	8.65206i	0.280121	+	0.280121i
$955$	−4.36858	−	9.36268i	−0.141364	−	0.302969i
$956$	−3.72574	+	13.9046i	−0.120499	+	0.449708i
$957$	−0.303682			−0.00981665
$958$	2.52183	−	9.41158i	0.0814765	−	0.304074i
$959$	21.2059	−	36.7297i	0.684775	−	1.18607i
$960$	−64.1403	+	11.3252i	−2.07012	+	0.365521i
$961$			29.6046i			0.954988i
$962$	38.0321	−	30.2093i	1.22620	−	0.973988i
$963$	−42.4372	−	42.4372i	−1.36752	−	1.36752i
$964$	20.6277	−	5.52718i	0.664374	−	0.178018i
$965$	30.4694	+	21.3242i	0.980846	+	0.686451i
$966$	5.38630	−	3.10978i	0.173301	−	0.100055i
$967$		−	18.3496i		−	0.590084i	−0.955484	−	0.295042i	$-0.904666\pi$
$967$		−	18.3496i		−	0.590084i	0.955484	−	0.295042i	$-0.0953337\pi$
$968$	−4.12796	−	7.14984i	−0.132678	−	0.229804i
$969$	36.4879	+	9.77690i	1.17216	+	0.314079i
$970$	1.88587	+	0.164544i	0.0605516	+	0.00528320i
$971$	24.5120	+	42.4560i	0.786627	+	1.36248i	0.928022	+	0.372525i	$0.121508\pi$
$971$	24.5120	+	42.4560i	0.786627	+	1.36248i	−0.141395	+	0.989953i	$0.545159\pi$
$972$	40.5898	−	10.8760i	1.30192	−	0.348848i
$973$	17.4332	+	10.0650i	0.558881	+	0.322670i
$974$	−30.5136			−0.977718
$975$	48.3052	−	11.5859i	1.54700	−	0.371047i
$976$	33.7299			1.07967
$977$	−2.28535	−	1.31945i	−0.0731149	−	0.0422129i	0.462997	−	0.886360i	$-0.346774\pi$
$977$	−2.28535	−	1.31945i	−0.0731149	−	0.0422129i	−0.536112	+	0.844147i	$0.680107\pi$
$978$	−22.3829	+	5.99747i	−0.715725	+	0.191778i
$979$	0.0441451	+	0.0764615i	0.00141088	+	0.00244372i
$980$	−7.75486	−	0.676622i	−0.247720	−	0.0216139i
$981$	−48.0782	−	12.8825i	−1.53502	−	0.411307i
$982$	−21.0765	−	36.5055i	−0.672577	−	1.16494i
$983$			36.6137i			1.16780i	0.811827	+	0.583898i	$0.198473\pi$
$983$			36.6137i			1.16780i	−0.811827	+	0.583898i	$0.801527\pi$
$984$	−14.0436	+	8.10806i	−0.447693	+	0.258476i
$985$	−47.1353	−	32.9880i	−1.50186	−	1.05108i
$986$	24.1636	−	6.47462i	0.769526	−	0.206194i
$987$	4.72721	+	4.72721i	0.150469	+	0.150469i
$988$	37.3522	−	16.2106i	1.18833	−	0.515728i
$989$		−	2.57440i		−	0.0818613i
$990$	−0.556329	+	0.0982310i	−0.0176813	+	0.00312199i
$991$	−1.39720	+	2.42002i	−0.0443834	+	0.0768744i	−0.887364	−	0.461070i	$-0.847466\pi$
$991$	−1.39720	+	2.42002i	−0.0443834	+	0.0768744i	0.842980	+	0.537944i	$0.180799\pi$
$992$	−2.47091	+	9.22156i	−0.0784514	+	0.292785i
$993$	−9.27712			−0.294401
$994$	−5.82177	+	21.7271i	−0.184655	+	0.689143i
$995$	−26.2681	−	56.2975i	−0.832755	−	1.78475i
$996$	−6.05053	−	6.05053i	−0.191718	−	0.191718i
$997$	38.5049	+	10.3174i	1.21946	+	0.326754i	0.810468	−	0.585783i	$-0.199213\pi$
$997$	38.5049	+	10.3174i	1.21946	+	0.326754i	0.408994	+	0.912537i	$0.365880\pi$
$998$	−0.396810	−	1.48092i	−0.0125608	−	0.0468776i
$999$	−7.32827	−	27.3495i	−0.231856	−	0.865299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.t.a.58.5	yes	20
3.2	odd	2		585.2.dp.a.253.1		20
5.2	odd	4		65.2.o.a.32.1	✓	20
5.3	odd	4		325.2.s.b.32.5		20
5.4	even	2		325.2.x.b.318.1		20
13.2	odd	12		845.2.o.g.258.5		20
13.3	even	3		845.2.t.f.418.1		20
13.4	even	6		845.2.f.d.408.9		20
13.5	odd	4		845.2.o.f.488.5		20
13.6	odd	12		845.2.k.d.268.2		20
13.7	odd	12		845.2.k.e.268.9		20
13.8	odd	4		845.2.o.e.488.1		20
13.9	even	3		845.2.f.e.408.2		20
13.10	even	6		845.2.t.e.418.5		20
13.11	odd	12		65.2.o.a.63.1	yes	20
13.12	even	2		845.2.t.g.188.1		20
15.2	even	4		585.2.cf.a.487.5		20
39.11	even	12		585.2.cf.a.388.5		20
65.2	even	12		845.2.t.g.427.1		20
65.7	even	12		845.2.f.e.437.9		20
65.12	odd	4		845.2.o.g.357.5		20
65.17	odd	12		845.2.k.d.577.2		20
65.22	odd	12		845.2.k.e.577.9		20
65.24	odd	12		325.2.s.b.193.5		20
65.32	even	12		845.2.f.d.437.2		20
65.37	even	12	inner	65.2.t.a.37.5	yes	20
65.42	odd	12		845.2.o.e.587.1		20
65.47	even	4		845.2.t.f.657.1		20
65.57	even	4		845.2.t.e.657.5		20
65.62	odd	12		845.2.o.f.587.5		20
65.63	even	12		325.2.x.b.232.1		20
195.167	odd	12		585.2.dp.a.37.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.1	✓	20	5.2	odd	4
65.2.o.a.63.1	yes	20	13.11	odd	12
65.2.t.a.37.5	yes	20	65.37	even	12	inner
65.2.t.a.58.5	yes	20	1.1	even	1	trivial
325.2.s.b.32.5		20	5.3	odd	4
325.2.s.b.193.5		20	65.24	odd	12
325.2.x.b.232.1		20	65.63	even	12
325.2.x.b.318.1		20	5.4	even	2
585.2.cf.a.388.5		20	39.11	even	12
585.2.cf.a.487.5		20	15.2	even	4
585.2.dp.a.37.1		20	195.167	odd	12
585.2.dp.a.253.1		20	3.2	odd	2
845.2.f.d.408.9		20	13.4	even	6
845.2.f.d.437.2		20	65.32	even	12
845.2.f.e.408.2		20	13.9	even	3
845.2.f.e.437.9		20	65.7	even	12
845.2.k.d.268.2		20	13.6	odd	12
845.2.k.d.577.2		20	65.17	odd	12
845.2.k.e.268.9		20	13.7	odd	12
845.2.k.e.577.9		20	65.22	odd	12
845.2.o.e.488.1		20	13.8	odd	4
845.2.o.e.587.1		20	65.42	odd	12
845.2.o.f.488.5		20	13.5	odd	4
845.2.o.f.587.5		20	65.62	odd	12
845.2.o.g.258.5		20	13.2	odd	12
845.2.o.g.357.5		20	65.12	odd	4
845.2.t.e.418.5		20	13.10	even	6
845.2.t.e.657.5		20	65.57	even	4
845.2.t.f.418.1		20	13.3	even	3
845.2.t.f.657.1		20	65.47	even	4
845.2.t.g.188.1		20	13.12	even	2
845.2.t.g.427.1		20	65.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80821 + 1.04397i) q^{2} +(-2.66159 + 0.713171i) q^{3} +(1.17974 + 2.04338i) q^{4} +(2.22760 + 0.194361i) q^{5} +(-5.55724 - 1.48906i) q^{6} +(-1.45563 - 2.52122i) q^{7} +0.750585i q^{8} +(3.97738 - 2.29634i) q^{9} +O(q^{10})\)	\(q+(1.80821 + 1.04397i) q^{2} +(-2.66159 + 0.713171i) q^{3} +(1.17974 + 2.04338i) q^{4} +(2.22760 + 0.194361i) q^{5} +(-5.55724 - 1.48906i) q^{6} +(-1.45563 - 2.52122i) q^{7} +0.750585i q^{8} +(3.97738 - 2.29634i) q^{9} +(3.82506 + 2.67700i) q^{10} +(-0.0254491 + 0.00681908i) q^{11} +(-4.59727 - 4.59727i) q^{12} +(-3.56631 + 0.530479i) q^{13} -6.07853i q^{14} +(-6.06759 + 1.07135i) q^{15} +(1.57590 - 2.72954i) q^{16} +(-0.741318 + 2.76664i) q^{17} +9.58924 q^{18} +(-1.23878 + 4.62320i) q^{19} +(2.23085 + 4.78113i) q^{20} +(5.67236 + 5.67236i) q^{21} +(-0.0531363 - 0.0142378i) q^{22} +(-0.0961080 - 0.358680i) q^{23} +(-0.535296 - 1.99775i) q^{24} +(4.92445 + 0.865921i) q^{25} +(-7.00244 - 2.76390i) q^{26} +(-3.10321 + 3.10321i) q^{27} +(3.43454 - 5.94879i) q^{28} +(-3.62262 - 2.09152i) q^{29} +(-12.0899 - 4.39714i) q^{30} +(-0.835277 + 0.835277i) q^{31} +(6.99915 - 4.04096i) q^{32} +(0.0628721 - 0.0362992i) q^{33} +(-4.22874 + 4.22874i) q^{34} +(-2.75254 - 5.89921i) q^{35} +(9.38457 + 5.41819i) q^{36} +(-3.22588 + 5.58739i) q^{37} +(-7.06645 + 7.06645i) q^{38} +(9.11375 - 3.95531i) q^{39} +(-0.145885 + 1.67201i) q^{40} +(-2.02930 - 7.57344i) q^{41} +(4.33503 + 16.1786i) q^{42} +(6.69664 + 1.79436i) q^{43} +(-0.0439574 - 0.0439574i) q^{44} +(9.30635 - 4.34229i) q^{45} +(0.200668 - 0.748902i) q^{46} +0.833377 q^{47} +(-2.24777 + 8.38880i) q^{48} +(-0.737715 + 1.27776i) q^{49} +(8.00043 + 6.70674i) q^{50} -7.89234i q^{51} +(-5.29130 - 6.66149i) q^{52} +(0.902268 + 0.902268i) q^{53} +(-8.85092 + 2.37160i) q^{54} +(-0.0580160 + 0.0102439i) q^{55} +(1.89239 - 1.09257i) q^{56} -13.1885i q^{57} +(-4.36697 - 7.56381i) q^{58} +(-1.44647 - 0.387581i) q^{59} +(-9.34737 - 11.1344i) q^{60} +(5.35090 + 9.26802i) q^{61} +(-2.38236 + 0.638351i) q^{62} +(-11.5792 - 6.68524i) q^{63} +10.5710 q^{64} +(-8.04744 + 0.488545i) q^{65} +0.151581 q^{66} +(10.6667 + 6.15845i) q^{67} +(-6.52784 + 1.74913i) q^{68} +(0.511601 + 0.886118i) q^{69} +(1.18143 - 13.5406i) q^{70} +(-3.57441 - 0.957759i) q^{71} +(1.72360 + 2.98536i) q^{72} -15.0844i q^{73} +(-11.6661 + 6.73544i) q^{74} +(-13.7244 + 1.20725i) q^{75} +(-10.9084 + 2.92289i) q^{76} +(0.0542370 + 0.0542370i) q^{77} +(20.6088 + 2.36245i) q^{78} +4.25039i q^{79} +(4.04100 - 5.77403i) q^{80} +(-0.842658 + 1.45953i) q^{81} +(4.23705 - 15.8129i) q^{82} +1.31611 q^{83} +(-4.89883 + 18.2827i) q^{84} +(-2.18909 + 6.01889i) q^{85} +(10.2357 + 10.2357i) q^{86} +(11.1335 + 2.98322i) q^{87} +(-0.00511830 - 0.0191018i) q^{88} +(-0.867319 - 3.23688i) q^{89} +(21.3610 + 1.86378i) q^{90} +(6.52869 + 8.21929i) q^{91} +(0.619535 - 0.619535i) q^{92} +(1.62747 - 2.81886i) q^{93} +(1.50692 + 0.870020i) q^{94} +(-3.65809 + 10.0579i) q^{95} +(-15.7470 + 15.7470i) q^{96} +(0.351145 - 0.202734i) q^{97} +(-2.66788 + 1.54030i) q^{98} +(-0.0855620 + 0.0855620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24} + 18 q^{25} - 24 q^{26} + 4 q^{27} + 18 q^{28} - 26 q^{30} + 48 q^{32} + 18 q^{33} + 2 q^{34} + 40 q^{35} + 36 q^{36} - 4 q^{37} - 8 q^{38} + 4 q^{39} - 16 q^{40} + 10 q^{41} + 40 q^{42} + 10 q^{43} - 36 q^{44} + 4 q^{46} - 40 q^{47} - 56 q^{48} + 18 q^{49} + 36 q^{50} - 30 q^{52} - 10 q^{53} - 48 q^{54} - 10 q^{55} - 16 q^{59} + 28 q^{60} - 16 q^{61} - 44 q^{62} - 36 q^{63} + 20 q^{64} - 14 q^{65} - 32 q^{66} + 18 q^{67} + 22 q^{68} - 16 q^{69} - 12 q^{70} - 16 q^{71} + 4 q^{72} + 18 q^{74} - 38 q^{75} - 64 q^{76} - 28 q^{77} + 68 q^{78} - 2 q^{80} - 14 q^{81} + 56 q^{82} + 48 q^{83} - 40 q^{84} - 26 q^{85} + 60 q^{86} - 34 q^{87} + 82 q^{88} - 6 q^{89} + 46 q^{90} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 48 q^{94} - 26 q^{95} + 56 q^{96} + 66 q^{97} - 30 q^{98} + 60 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

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