LMFDB - Embedded newform 65.2.o.a.63.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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, 1]))

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

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

chi := DirichletCharacter("65.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.o (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			63.1
Root			$-2.08794i$ of defining polynomial
Character	$\chi$	$=$	65.63
Dual form			65.2.o.a.32.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04397 - 1.80821i) q^{2} +(0.713171 - 2.66159i) q^{3} +(-1.17974 + 2.04338i) q^{4} +(-0.194361 + 2.22760i) q^{5} +(-5.55724 + 1.48906i) q^{6} +(2.52122 + 1.45563i) q^{7} +0.750585 q^{8} +(-3.97738 - 2.29634i) q^{9} +O(q^{10})$	\(q+(-1.04397 - 1.80821i) q^{2} +(0.713171 - 2.66159i) q^{3} +(-1.17974 + 2.04338i) q^{4} +(-0.194361 + 2.22760i) q^{5} +(-5.55724 + 1.48906i) q^{6} +(2.52122 + 1.45563i) q^{7} +0.750585 q^{8} +(-3.97738 - 2.29634i) q^{9} +(4.23088 - 1.97411i) q^{10} +(-0.0254491 - 0.00681908i) q^{11} +(4.59727 + 4.59727i) q^{12} +(0.530479 - 3.56631i) q^{13} -6.07853i q^{14} +(5.79036 + 2.10597i) q^{15} +(1.57590 + 2.72954i) q^{16} +(-2.76664 + 0.741318i) q^{17} +9.58924i q^{18} +(1.23878 + 4.62320i) q^{19} +(-4.32254 - 3.02515i) q^{20} +(5.67236 - 5.67236i) q^{21} +(0.0142378 + 0.0531363i) q^{22} +(-0.358680 - 0.0961080i) 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} +(-5.94879 + 3.43454i) q^{28} +(3.62262 - 2.09152i) q^{29} +(-2.23692 - 12.6687i) q^{30} +(-0.835277 - 0.835277i) q^{31} +(4.04096 - 6.99915i) q^{32} +(-0.0362992 + 0.0628721i) q^{33} +(4.22874 + 4.22874i) q^{34} +(-3.73260 + 5.33337i) q^{35} +(9.38457 - 5.41819i) q^{36} +(-5.58739 + 3.22588i) 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} +(-16.1786 - 4.33503i) q^{42} +(1.79436 + 6.69664i) q^{43} +(0.0439574 - 0.0439574i) q^{44} +(5.88839 - 8.41371i) q^{45} +(0.200668 + 0.748902i) q^{46} -0.833377i q^{47} +(8.38880 - 2.24777i) q^{48} +(0.737715 + 1.27776i) q^{49} +(3.57521 + 9.80842i) q^{50} +7.89234i q^{51} +(6.66149 + 5.29130i) q^{52} +(0.902268 + 0.902268i) q^{53} +(8.85092 + 2.37160i) q^{54} +(0.0201365 - 0.0553653i) q^{55} +(1.89239 + 1.09257i) q^{56} +13.1885 q^{57} +(-7.56381 - 4.36697i) q^{58} +(1.44647 - 0.387581i) q^{59} +(-11.1344 + 9.34737i) q^{60} +(5.35090 - 9.26802i) q^{61} +(-0.638351 + 2.38236i) q^{62} +(-6.68524 - 11.5792i) q^{63} -10.5710 q^{64} +(7.84123 + 1.87485i) q^{65} +0.151581 q^{66} +(-6.15845 - 10.6667i) q^{67} +(1.74913 - 6.52784i) q^{68} +(-0.511601 + 0.886118i) q^{69} +(13.5406 + 1.18143i) q^{70} +(-3.57441 + 0.957759i) q^{71} +(-2.98536 - 1.72360i) q^{72} -15.0844 q^{73} +(11.6661 + 6.73544i) q^{74} +(-5.81670 + 12.4893i) q^{75} +(-10.9084 - 2.92289i) q^{76} +(-0.0542370 - 0.0542370i) q^{77} +(2.36245 + 20.6088i) q^{78} +4.25039i q^{79} +(-6.38662 + 2.97996i) q^{80} +(-0.842658 - 1.45953i) q^{81} +(15.8129 - 4.23705i) q^{82} +1.31611i q^{83} +(4.89883 + 18.2827i) q^{84} +(-1.11364 - 6.30706i) q^{85} +(10.2357 - 10.2357i) q^{86} +(-2.98322 - 11.1335i) q^{87} +(-0.0191018 - 0.00511830i) 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} +(-2.81886 + 1.62747i) q^{93} +(-1.50692 + 0.870020i) q^{94} +(-10.5394 + 1.86095i) q^{95} +(-15.7470 - 15.7470i) q^{96} +(0.202734 - 0.351145i) q^{97} +(1.54030 - 2.66788i) q^{98} +(0.0855620 + 0.0855620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−1.04397	−	1.80821i	−0.738198	−	1.27860i	−0.953306	−	0.302006i	$-0.902344\pi$
$2$	−1.04397	−	1.80821i	−0.738198	−	1.27860i	0.215108	−	0.976590i	$-0.430990\pi$
$3$	0.713171	−	2.66159i	0.411750	−	1.53667i	−0.379508	−	0.925188i	$-0.623907\pi$
$3$	0.713171	−	2.66159i	0.411750	−	1.53667i	0.791258	−	0.611482i	$-0.209426\pi$
$4$	−1.17974	+	2.04338i	−0.589872	+	1.02169i
$5$	−0.194361	+	2.22760i	−0.0869210	+	0.996215i
$5$	−0.194361	+	2.22760i	−0.0869210	+	0.996215i
$6$	−5.55724	+	1.48906i	−2.26873	+	0.607905i
$7$	2.52122	+	1.45563i	0.952933	+	0.550176i	0.893991	−	0.448085i	$-0.147894\pi$
$7$	2.52122	+	1.45563i	0.952933	+	0.550176i	0.0589424	+	0.998261i	$0.481227\pi$
$8$	0.750585			0.265372
$9$	−3.97738	−	2.29634i	−1.32579	−	0.765447i
$10$	4.23088	−	1.97411i	1.33792	−	0.624267i
$11$	−0.0254491	−	0.00681908i	−0.00767321	−	0.00205603i	0.254980	−	0.966946i	$-0.417931\pi$
$11$	−0.0254491	−	0.00681908i	−0.00767321	−	0.00205603i	−0.262654	+	0.964890i	$0.584598\pi$
$12$	4.59727	+	4.59727i	1.32712	+	1.32712i
$13$	0.530479	−	3.56631i	0.147129	−	0.989117i
$13$	0.530479	−	3.56631i	0.147129	−	0.989117i
$14$		−	6.07853i		−	1.62456i
$15$	5.79036	+	2.10597i	1.49506	+	0.543760i
$16$	1.57590	+	2.72954i	0.393975	+	0.682384i
$17$	−2.76664	+	0.741318i	−0.671008	+	0.179796i	−0.578209	−	0.815889i	$-0.696248\pi$
$17$	−2.76664	+	0.741318i	−0.671008	+	0.179796i	−0.0927992	+	0.995685i	$0.529581\pi$
$18$			9.58924i			2.26020i
$19$	1.23878	+	4.62320i	0.284196	+	1.06063i	0.949425	+	0.313995i	$0.101667\pi$
$19$	1.23878	+	4.62320i	0.284196	+	1.06063i	−0.665229	+	0.746640i	$0.731666\pi$
$20$	−4.32254	−	3.02515i	−0.966548	−	0.676445i
$21$	5.67236	−	5.67236i	1.23781	−	1.23781i
$22$	0.0142378	+	0.0531363i	0.00303551	+	0.0113287i
$23$	−0.358680	−	0.0961080i	−0.0747899	−	0.0200399i	0.221230	−	0.975222i	$-0.428993\pi$
$23$	−0.358680	−	0.0961080i	−0.0747899	−	0.0200399i	−0.296020	+	0.955182i	$0.595660\pi$
$24$	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
$28$	−5.94879	+	3.43454i	−1.12422	+	0.649067i
$29$	3.62262	−	2.09152i	0.672703	−	0.388386i	−0.124397	−	0.992233i	$-0.539700\pi$
$29$	3.62262	−	2.09152i	0.672703	−	0.388386i	0.797100	+	0.603847i	$0.206366\pi$
$30$	−2.23692	−	12.6687i	−0.408404	−	2.31299i
$31$	−0.835277	−	0.835277i	−0.150020	−	0.150020i	0.628107	−	0.778127i	$-0.283830\pi$
$31$	−0.835277	−	0.835277i	−0.150020	−	0.150020i	−0.778127	+	0.628107i	$0.783830\pi$
$32$	4.04096	−	6.99915i	0.714348	−	1.23729i
$33$	−0.0362992	+	0.0628721i	−0.00631888	+	0.0109446i
$34$	4.22874	+	4.22874i	0.725223	+	0.725223i
$35$	−3.73260	+	5.33337i	−0.630924	+	0.901505i
$36$	9.38457	−	5.41819i	1.56410	−	0.903031i
$37$	−5.58739	+	3.22588i	−0.918561	+	0.530332i	−0.883176	−	0.469042i	$-0.844599\pi$
$37$	−5.58739	+	3.22588i	−0.918561	+	0.530332i	−0.0353856	+	0.999374i	$0.511266\pi$
$38$	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	0.605263	+	0.796026i	$0.293068\pi$
$41$	−2.02930	+	7.57344i	−0.316923	+	1.18277i	−0.922186	+	0.386747i	$0.873599\pi$
$42$	−16.1786	−	4.33503i	−2.49641	−	0.668910i
$43$	1.79436	+	6.69664i	0.273637	+	1.02123i	0.956749	+	0.290915i	$0.0939595\pi$
$43$	1.79436	+	6.69664i	0.273637	+	1.02123i	−0.683112	+	0.730314i	$0.739374\pi$
$44$	0.0439574	−	0.0439574i	0.00662683	−	0.00662683i
$45$	5.88839	−	8.41371i	0.877789	−	1.25424i
$46$	0.200668	+	0.748902i	0.0295868	+	0.110420i
$47$		−	0.833377i		−	0.121561i	−0.998151	−	0.0607803i	$-0.980641\pi$
$47$		−	0.833377i		−	0.121561i	0.998151	−	0.0607803i	$-0.0193589\pi$
$48$	8.38880	−	2.24777i	1.21082	−	0.324438i
$49$	0.737715	+	1.27776i	0.105388	+	0.182537i
$50$	3.57521	+	9.80842i	0.505611	+	1.38712i
$51$			7.89234i			1.10515i
$52$	6.66149	+	5.29130i	0.923782	+	0.733772i
$53$	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
$55$	0.0201365	−	0.0553653i	0.00271521	−	0.00746545i
$56$	1.89239	+	1.09257i	0.252882	+	0.146001i
$57$	13.1885			1.74686
$58$	−7.56381	−	4.36697i	−0.993176	−	0.573411i
$59$	1.44647	−	0.387581i	0.188315	−	0.0504588i	−0.163429	−	0.986555i	$-0.552255\pi$
$59$	1.44647	−	0.387581i	0.188315	−	0.0504588i	0.351744	+	0.936096i	$0.385589\pi$
$60$	−11.1344	+	9.34737i	−1.43745	+	1.20674i
$61$	5.35090	−	9.26802i	0.685112	−	1.18665i	−0.288290	−	0.957543i	$-0.593087\pi$
$61$	5.35090	−	9.26802i	0.685112	−	1.18665i	0.973402	−	0.229105i	$-0.0735801\pi$
$62$	−0.638351	+	2.38236i	−0.0810706	+	0.302560i
$63$	−6.68524	−	11.5792i	−0.842262	−	1.45884i
$64$	−10.5710			−1.32137
$65$	7.84123	+	1.87485i	0.972585	+	0.232547i
$66$	0.151581			0.0186583
$67$	−6.15845	−	10.6667i	−0.752374	−	1.30315i	−0.946669	−	0.322207i	$-0.895575\pi$
$67$	−6.15845	−	10.6667i	−0.752374	−	1.30315i	0.194295	−	0.980943i	$-0.437758\pi$
$68$	1.74913	−	6.52784i	0.212113	−	0.791617i
$69$	−0.511601	+	0.886118i	−0.0615895	+	0.106676i
$70$	13.5406	+	1.18143i	1.61841	+	0.141208i
$71$	−3.57441	+	0.957759i	−0.424204	+	0.113665i	−0.464604	−	0.885518i	$-0.653803\pi$
$71$	−3.57441	+	0.957759i	−0.424204	+	0.113665i	0.0404002	+	0.999184i	$0.487137\pi$
$72$	−2.98536	−	1.72360i	−0.351828	−	0.203128i
$73$	−15.0844			−1.76550			−0.882750	−	0.469844i	$-0.844310\pi$
$73$	−15.0844			−1.76550			−0.882750	+	0.469844i	$0.844310\pi$
$74$	11.6661	+	6.73544i	1.35616	+	0.782979i
$75$	−5.81670	+	12.4893i	−0.671655	+	1.44214i
$76$	−10.9084	−	2.92289i	−1.25128	−	0.335279i
$77$	−0.0542370	−	0.0542370i	−0.00618088	−	0.00618088i
$78$	2.36245	+	20.6088i	0.267494	+	2.33348i
$79$			4.25039i			0.478207i	0.970994	+	0.239103i	$0.0768534\pi$
$79$			4.25039i			0.478207i	−0.970994	+	0.239103i	$0.923147\pi$
$80$	−6.38662	+	2.97996i	−0.714046	+	0.333170i
$81$	−0.842658	−	1.45953i	−0.0936286	−	0.162170i
$82$	15.8129	−	4.23705i	1.74624	−	0.467904i
$83$			1.31611i			0.144462i	0.997388	+	0.0722311i	$0.0230119\pi$
$83$			1.31611i			0.144462i	−0.997388	+	0.0722311i	$0.976988\pi$
$84$	4.89883	+	18.2827i	0.534506	+	1.99480i
$85$	−1.11364	−	6.30706i	−0.120791	−	0.684096i
$86$	10.2357	−	10.2357i	1.10374	−	1.10374i
$87$	−2.98322	−	11.1335i	−0.319835	−	1.19364i
$88$	−0.0191018	−	0.00511830i	−0.00203625	−	0.000545613i
$89$	0.867319	−	3.23688i	0.0919357	−	0.343109i	−0.904601	−	0.426259i	$-0.859831\pi$
$89$	0.867319	−	3.23688i	0.0919357	−	0.343109i	0.996537	+	0.0831499i	$0.0264980\pi$
$90$	−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
$93$	−2.81886	+	1.62747i	−0.292302	+	0.168761i
$94$	−1.50692	+	0.870020i	−0.155427	+	0.0897357i
$95$	−10.5394	+	1.86095i	−1.08132	+	0.190929i
$96$	−15.7470	−	15.7470i	−1.60717	−	1.60717i
$97$	0.202734	−	0.351145i	0.0205845	−	0.0356534i	−0.855550	−	0.517721i	$-0.826781\pi$
$97$	0.202734	−	0.351145i	0.0205845	−	0.0356534i	0.876134	+	0.482067i	$0.160114\pi$
$98$	1.54030	−	2.66788i	0.155594	−	0.269497i
$99$	0.0855620	+	0.0855620i	0.00859930	+	0.00859930i
$100$	7.57898	−	9.04093i	0.757898	−	0.904093i
$101$	2.46663	−	1.42411i	0.245439	−	0.141704i	−0.372235	−	0.928139i	$-0.621408\pi$
$101$	2.46663	−	1.42411i	0.245439	−	0.141704i	0.617674	+	0.786434i	$0.288075\pi$
$102$	14.2710	−	8.23936i	1.41304	−	0.815819i
$103$	5.63497	−	5.63497i	0.555230	−	0.555230i	−0.372716	−	0.927946i	$-0.621573\pi$
$103$	5.63497	−	5.63497i	0.555230	−	0.555230i	0.927946	+	0.372716i	$0.121573\pi$
$104$	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
$107$	12.6223	+	3.38214i	1.22025	+	0.326964i	0.810774	−	0.585359i	$-0.199046\pi$
$107$	12.6223	+	3.38214i	1.22025	+	0.326964i	0.409472	+	0.912323i	$0.365713\pi$
$108$	−2.68004	−	10.0020i	−0.257887	−	0.962446i
$109$	7.66343	−	7.66343i	0.734024	−	0.734024i	−0.237391	−	0.971414i	$-0.576292\pi$
$109$	7.66343	−	7.66343i	0.734024	−	0.734024i	0.971414	+	0.237391i	$0.0762921\pi$
$110$	−0.121134	+	0.0213886i	−0.0115497	+	0.00203932i
$111$	4.60121	+	17.1720i	0.436728	+	1.62989i
$112$			9.17570i			0.867022i
$113$	−8.39360	+	2.24906i	−0.789604	+	0.211574i	−0.631014	−	0.775771i	$-0.717361\pi$
$113$	−8.39360	+	2.24906i	−0.789604	+	0.211574i	−0.158589	+	0.987345i	$0.550694\pi$
$114$	−13.7684	−	23.8476i	−1.28953	−	2.23353i
$115$	0.283804	−	0.780318i	0.0264649	−	0.0727650i
$116$			9.86983i			0.916390i
$117$	−10.2994	+	12.9664i	−0.952179	+	1.19875i
$118$	−2.21090	−	2.21090i	−0.203530	−	0.203530i
$119$	−8.05440	−	2.15817i	−0.738345	−	0.197839i
$120$	4.34616	+	1.58071i	0.396748	+	0.144299i
$121$	−9.52568	−	5.49965i	−0.865971	−	0.499968i
$122$	−22.3447			−2.02299
$123$	18.7102	+	10.8023i	1.68704	+	0.974012i
$124$	2.69220	−	0.721372i	0.241766	−	0.0647811i
$125$	2.88605	−	10.8014i	0.258136	−	0.966109i
$126$	−13.9584	+	24.1766i	−1.24351	+	2.15382i
$127$	−3.88938	+	14.5154i	−0.345126	+	1.28803i	0.547338	+	0.836912i	$0.315641\pi$
$127$	−3.88938	+	14.5154i	−0.345126	+	1.28803i	−0.892464	+	0.451118i	$0.851025\pi$
$128$	2.95384	+	5.11621i	0.261085	+	0.452213i
$129$	19.1034			1.68196
$130$	−4.79588	−	16.1359i	−0.420627	−	1.41521i
$131$	9.04438			0.790211			0.395105	−	0.918636i	$-0.370708\pi$
$131$	9.04438			0.790211			0.395105	+	0.918636i	$0.370708\pi$
$132$	−0.0856475	−	0.148346i	−0.00745466	−	0.0129118i
$133$	−3.60642	+	13.4593i	−0.312716	+	1.16707i
$134$	−12.8585	+	22.2715i	−1.11080	+	1.92397i
$135$	−6.30959	−	7.51588i	−0.543043	−	0.646864i
$136$	−2.07660	+	0.556423i	−0.178067	+	0.0477128i
$137$	−12.6164	−	7.28411i	−1.07790	−	0.622323i	−0.147568	−	0.989052i	$-0.547144\pi$
$137$	−12.6164	−	7.28411i	−1.07790	−	0.622323i	−0.930328	+	0.366729i	$0.880478\pi$
$138$	2.13638			0.181861
$139$	5.98819	+	3.45728i	0.507911	+	0.293243i	0.731975	−	0.681332i	$-0.238599\pi$
$139$	5.98819	+	3.45728i	0.507911	+	0.293243i	−0.224063	+	0.974575i	$0.571932\pi$
$140$	−6.49458	−	13.9191i	−0.548892	−	1.17638i
$141$	−2.21811	−	0.594341i	−0.186799	−	0.0500525i
$142$	5.46340	+	5.46340i	0.458478	+	0.458478i
$143$	−0.0378192	+	0.0871423i	−0.00316260	+	0.00728720i
$144$		−	14.4752i		−	1.20627i
$145$	3.95498	+	8.47627i	0.328443	+	0.703916i
$146$	15.7477	+	27.2758i	1.30329	+	2.25736i
$147$	3.92699	−	1.05223i	0.323893	−	0.0867868i
$148$		−	15.2228i		−	1.25131i
$149$	−1.51600	−	5.65780i	−0.124196	−	0.463505i	0.875614	−	0.483012i	$-0.160457\pi$
$149$	−1.51600	−	5.65780i	−0.124196	−	0.463505i	−0.999810	+	0.0195066i	$0.993790\pi$
$150$	28.6557	−	2.52066i	2.33973	−	0.205811i
$151$	−2.92436	+	2.92436i	−0.237981	+	0.237981i	−0.816014	−	0.578033i	$-0.803821\pi$
$151$	−2.92436	+	2.92436i	−0.237981	+	0.237981i	0.578033	+	0.816014i	$0.303821\pi$
$152$	0.929812	+	3.47011i	0.0754177	+	0.281463i
$153$	12.7063	+	3.40464i	1.02724	+	0.275249i
$154$	−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	$0.333562\pi$
$158$	7.68559	−	4.43728i	0.611433	−	0.353011i
$159$	3.04494	−	1.75800i	0.241480	−	0.139418i
$160$	14.8059	+	10.3620i	1.17051	+	0.819191i
$161$	−0.764415	−	0.764415i	−0.0602443	−	0.0602443i
$162$	−1.75942	+	3.04740i	−0.138233	+	0.239426i
$163$	−2.01385	+	3.48809i	−0.157737	+	0.273208i	−0.934052	−	0.357137i	$-0.883753\pi$
$163$	−2.01385	+	3.48809i	−0.157737	+	0.273208i	0.776315	+	0.630345i	$0.217086\pi$
$164$	−13.0813	−	13.0813i	−1.02148	−	1.02148i
$165$	−0.132999	−	0.0930802i	−0.0103540	−	0.00724628i
$166$	2.37981	−	1.37398i	0.184709	−	0.106642i
$167$	20.6458	−	11.9198i	1.59762	−	0.922385i	0.605672	−	0.795714i	$-0.292904\pi$
$167$	20.6458	−	11.9198i	1.59762	−	0.922385i	0.991945	−	0.126670i	$-0.0404289\pi$
$168$	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
$172$	−15.8006	−	4.23377i	−1.20479	−	0.322822i
$173$	0.210271	+	0.784743i	0.0159866	+	0.0596629i	0.973458	−	0.228864i	$-0.0735012\pi$
$173$	0.210271	+	0.784743i	0.0159866	+	0.0596629i	−0.957472	+	0.288527i	$0.906834\pi$
$174$	−17.0174	+	17.0174i	−1.29008	+	1.29008i
$175$	−11.1552	−	9.35135i	−0.843252	−	0.706896i
$176$	−0.0214923	−	0.0802105i	−0.00162005	−	0.00604610i
$177$		−	4.12633i		−	0.310154i
$178$	−6.75841	+	1.81091i	−0.506564	+	0.135733i
$179$	3.28130	+	5.68337i	0.245256	+	0.424795i	0.962203	−	0.272332i	$-0.0877948\pi$
$179$	3.28130	+	5.68337i	0.245256	+	0.424795i	−0.716948	+	0.697127i	$0.754461\pi$
$180$	10.2456	+	21.9582i	0.763660	+	1.63667i
$181$		−	1.56627i		−	0.116420i	−0.998304	−	0.0582099i	$-0.981461\pi$
$181$		−	1.56627i		−	0.116420i	0.998304	−	0.0582099i	$-0.0185393\pi$
$182$	−21.6779	−	3.22453i	−1.60688	−	0.239018i
$183$	−20.8516	−	20.8516i	−1.54139	−	1.54139i
$184$	−0.269220	−	0.0721373i	−0.0198472	−	0.00531803i
$185$	−6.10002	−	13.0735i	−0.448482	−	0.961182i
$186$	5.88561	+	3.39806i	0.431554	+	0.249158i
$187$	0.0754637			0.00551845
$188$	1.70290	+	0.983171i	0.124197	+	0.0717051i
$189$	−12.3410	+	3.30677i	−0.897678	+	0.240532i
$190$	14.3678	+	17.1147i	1.04235	+	1.24163i
$191$	−2.31024	+	4.00145i	−0.167163	+	0.289535i	−0.937421	−	0.348197i	$-0.886794\pi$
$191$	−2.31024	+	4.00145i	−0.167163	+	0.289535i	0.770258	+	0.637732i	$0.220127\pi$
$192$	−7.53891	+	28.1356i	−0.544074	+	2.03051i
$193$	8.31597	+	14.4037i	0.598597	+	1.03680i	0.993028	+	0.117875i	$0.0376082\pi$
$193$	8.31597	+	14.4037i	0.598597	+	1.03680i	−0.394432	+	0.918925i	$0.629058\pi$
$194$	−0.846590			−0.0607816
$195$	10.5822	−	19.5331i	0.757809	−	1.39879i
$196$	−3.48126			−0.248661
$197$	12.8646	+	22.2821i	0.916563	+	1.58753i	0.804597	+	0.593821i	$0.202381\pi$
$197$	12.8646	+	22.2821i	0.916563	+	1.58753i	0.111966	+	0.993712i	$0.464285\pi$
$198$	0.0653898	−	0.244038i	0.00464705	−	0.0173430i
$199$	13.8914	−	24.0606i	0.984736	−	1.70561i	0.341632	−	0.939834i	$-0.389020\pi$
$199$	13.8914	−	24.0606i	0.984736	−	1.70561i	0.643104	−	0.765779i	$-0.277646\pi$
$200$	−3.69622	−	0.649947i	−0.261362	−	0.0459582i
$201$	−32.7825	+	8.78406i	−2.31230	+	0.619580i
$202$	−5.15018	−	2.97346i	−0.362365	−	0.209212i
$203$	12.1779			0.854722
$204$	−16.1270	−	9.31094i	−1.12912	−	0.651896i
$205$	−16.4762	−	5.99246i	−1.15075	−	0.418531i
$206$	−16.0719	−	4.30646i	−1.11978	−	0.300045i
$207$	1.20591	+	1.20591i	0.0838165	+	0.0838165i
$208$	10.5704	−	4.17218i	0.732923	−	0.289289i
$209$		−	0.126104i		−	0.00872278i
$210$	12.8012	−	35.1969i	0.883369	−	2.42882i
$211$	−7.38830	−	12.7969i	−0.508632	−	0.880976i	−0.999950	−	0.00999576i	$-0.996818\pi$
$211$	−7.38830	−	12.7969i	−0.508632	−	0.880976i	0.491318	−	0.870980i	$-0.336515\pi$
$212$	−2.90812	+	0.779228i	−0.199730	+	0.0535176i
$213$			10.1967i			0.698663i
$214$	−7.06170	−	26.3546i	−0.482728	−	1.80157i
$215$	−15.2662	+	2.69556i	−1.04115	+	0.183835i
$216$	−2.32923	+	2.32923i	−0.158484	+	0.158484i
$217$	−0.890067	−	3.32178i	−0.0604217	−	0.225497i
$218$	−21.8575	−	5.85669i	−1.48037	−	0.396665i
$219$	−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
$223$	12.1451	−	7.01198i	0.813296	−	0.469557i	−0.0348032	−	0.999394i	$-0.511080\pi$
$223$	12.1451	−	7.01198i	0.813296	−	0.469557i	0.848099	+	0.529838i	$0.177747\pi$
$224$	20.3764	−	11.7643i	1.36145	−	0.786035i
$225$	17.5979	+	14.7523i	1.17320	+	0.983487i
$226$	12.8294	+	12.8294i	0.853401	+	0.853401i
$227$	7.99560	−	13.8488i	0.530687	−	0.919176i	−0.468672	−	0.883372i	$-0.655267\pi$
$227$	7.99560	−	13.8488i	0.530687	−	0.919176i	0.999359	−	0.0358042i	$-0.0113993\pi$
$228$	−15.5591	+	26.9491i	−1.03043	+	1.78475i
$229$	−2.31063	−	2.31063i	−0.152691	−	0.152691i	0.626628	−	0.779319i	$-0.284435\pi$
$229$	−2.31063	−	2.31063i	−0.152691	−	0.152691i	−0.779319	+	0.626628i	$0.784435\pi$
$230$	−1.70726	+	0.301451i	−0.112573	+	0.0198771i
$231$	−0.183037	+	0.105676i	−0.0120429	+	0.00695300i
$232$	2.71909	−	1.56986i	0.178517	−	0.103067i
$233$	17.8141	−	17.8141i	1.16704	−	1.16704i	0.184143	−	0.982899i	$-0.441049\pi$
$233$	17.8141	−	17.8141i	1.16704	−	1.16704i	0.982899	−	0.184143i	$-0.0589510\pi$
$234$	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
$237$	11.3128	+	3.03126i	0.734846	+	0.196901i
$238$	4.50612	+	16.8171i	0.292089	+	1.09009i
$239$	−4.31403	+	4.31403i	−0.279052	+	0.279052i	−0.832730	−	0.553679i	$-0.813224\pi$
$239$	−4.31403	+	4.31403i	−0.279052	+	0.279052i	0.553679	+	0.832730i	$0.313224\pi$
$240$	3.37669	+	19.1238i	0.217964	+	1.23444i
$241$	2.34253	+	8.74246i	0.150896	+	0.563151i	0.999422	+	0.0339976i	$0.0108239\pi$
$241$	2.34253	+	8.74246i	0.150896	+	0.563151i	−0.848526	+	0.529154i	$0.822509\pi$
$242$			22.9659i			1.47630i
$243$	−17.2028	+	4.60948i	−1.10356	+	0.295699i
$244$	12.6254	+	21.8678i	0.808256	+	1.39994i
$245$	−2.98973	+	1.39499i	−0.191007	+	0.0891227i
$246$		−	45.1091i		−	2.87605i
$247$	17.1449	−	1.96537i	1.09091	−	0.125054i
$248$	−0.626947	−	0.626947i	−0.0398112	−	0.0398112i
$249$	3.50296	+	0.938615i	0.221991	+	0.0594823i
$250$	−22.5442	+	6.05777i	−1.42582	+	0.383127i
$251$	0.503450	+	0.290667i	0.0317775	+	0.0183467i	0.515805	−	0.856706i	$-0.327493\pi$
$251$	0.503450	+	0.290667i	0.0317775	+	0.0183467i	−0.484027	+	0.875053i	$0.660826\pi$
$252$	31.5475			1.98730
$253$	0.00847273	+	0.00489173i	0.000532676	+	0.000307541i
$254$	30.3072	−	8.12078i	1.90164	−	0.509543i
$255$	−17.5810	−	1.53397i	−1.10097	−	0.0960607i
$256$	−4.40353	+	7.62714i	−0.275221	+	0.476696i
$257$	4.50394	−	16.8089i	0.280948	−	1.04851i	−0.670801	−	0.741637i	$-0.734050\pi$
$257$	4.50394	−	16.8089i	0.280948	−	1.04851i	0.951750	−	0.306876i	$-0.0992836\pi$
$258$	−19.9434	−	34.5429i	−1.24162	−	2.15055i
$259$	−18.7828			−1.16710
$260$	−13.0817	+	13.8107i	−0.811291	+	0.856505i
$261$	−19.2114			−1.18915
$262$	−9.44205	−	16.3541i	−0.583332	−	1.01036i
$263$	−7.13948	+	26.6449i	−0.440239	+	1.64299i	0.287970	+	0.957639i	$0.407020\pi$
$263$	−7.13948	+	26.6449i	−0.440239	+	1.64299i	−0.728209	+	0.685355i	$0.759647\pi$
$264$	−0.0272457	+	0.0471909i	−0.00167685	+	0.00290440i
$265$	−2.18526	+	1.83453i	−0.134240	+	0.112694i
$266$	28.1023	−	7.52998i	1.72306	−	0.461692i
$267$	−7.99671	−	4.61690i	−0.489390	−	0.282550i
$268$	29.0615			1.77522
$269$	15.9495	+	9.20844i	0.972457	+	0.561448i	0.899984	−	0.435922i	$-0.143578\pi$
$269$	15.9495	+	9.20844i	0.972457	+	0.561448i	0.0724726	+	0.997370i	$0.476911\pi$
$270$	−7.00326	+	19.2554i	−0.426205	+	1.17185i
$271$	25.0269	+	6.70594i	1.52028	+	0.407357i	0.919833	−	0.392310i	$-0.128324\pi$
$271$	25.0269	+	6.70594i	1.52028	+	0.407357i	0.600444	+	0.799667i	$0.294990\pi$
$272$	−6.38339	−	6.38339i	−0.387050	−	0.387050i
$273$	−17.2203	−	23.2385i	−1.04222	−	1.40646i
$274$			30.4175i			1.83759i
$275$	0.119418	+	0.0556171i	0.00720119	+	0.00335384i
$276$	−1.20711	−	2.09078i	−0.0726598	−	0.125850i
$277$	−22.6257	+	6.06254i	−1.35945	+	0.364263i	−0.863613	−	0.504155i	$-0.831804\pi$
$277$	−22.6257	+	6.06254i	−1.35945	+	0.364263i	−0.495833	+	0.868418i	$0.665137\pi$
$278$		−	14.4372i		−	0.865884i
$279$	1.40413	+	5.24030i	0.0840632	+	0.313728i
$280$	−2.80163	+	4.00315i	−0.167430	+	0.239234i
$281$	−9.93011	+	9.93011i	−0.592381	+	0.592381i	−0.938274	−	0.345893i	$-0.887576\pi$
$281$	−9.93011	+	9.93011i	−0.592381	+	0.592381i	0.345893	+	0.938274i	$0.387576\pi$
$282$	1.24095	+	4.63128i	0.0738973	+	0.275789i
$283$	3.97170	+	1.06421i	0.236093	+	0.0632610i	0.374926	−	0.927055i	$-0.377668\pi$
$283$	3.97170	+	1.06421i	0.236093	+	0.0632610i	−0.138832	+	0.990316i	$0.544335\pi$
$284$	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
$288$	−32.1449	+	18.5589i	−1.89416	+	1.09359i
$289$	−7.61770	+	4.39808i	−0.448100	+	0.258711i
$290$	11.1980	−	16.0004i	0.657568	−	0.939576i
$291$	−0.790020	−	0.790020i	−0.0463118	−	0.0463118i
$292$	17.7958	−	30.8232i	1.04142	−	1.80379i
$293$	10.9265	−	18.9253i	0.638336	−	1.10563i	−0.347462	−	0.937694i	$-0.612957\pi$
$293$	10.9265	−	18.9253i	0.638336	−	1.10563i	0.985798	−	0.167936i	$-0.0537101\pi$
$294$	−6.00232	−	6.00232i	−0.350062	−	0.350062i
$295$	0.582240	+	3.29750i	0.0338993	+	0.191988i
$296$	−4.19381	+	2.42130i	−0.243761	+	0.140735i
$297$	0.100135	−	0.0578131i	0.00581044	−	0.00335466i
$298$	−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
$302$	8.34078	+	2.23491i	0.479958	+	0.128604i
$303$	−2.03127	−	7.58081i	−0.116693	−	0.435506i
$304$	−10.6670	+	10.6670i	−0.611794	+	0.611794i
$305$	19.6055	+	13.7210i	1.12261	+	0.785664i
$306$	−7.10868	−	26.5299i	−0.406376	−	1.51662i
$307$			6.98281i			0.398530i	0.979946	+	0.199265i	$0.0638555\pi$
$307$			6.98281i			0.398530i	−0.979946	+	0.199265i	$0.936145\pi$
$308$	0.174812	−	0.0468408i	0.00996085	−	0.00266900i
$309$	−10.9793	−	19.0167i	−0.624590	−	1.08182i
$310$	−5.18288	−	1.88503i	−0.294368	−	0.107063i
$311$		−	21.2824i		−	1.20681i	−0.797434	−	0.603406i	$-0.793810\pi$
$311$		−	21.2824i		−	1.20681i	0.797434	−	0.603406i	$-0.206190\pi$
$312$	−6.84065	−	2.96880i	−0.387275	−	0.168075i
$313$	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
$315$	27.0932	−	12.6415i	1.52653	−	0.712270i
$316$	−8.68515	−	5.01437i	−0.488578	−	0.282080i
$317$	−15.6715			−0.880198			−0.440099	−	0.897949i	$-0.645057\pi$
$317$	−15.6715			−0.880198			−0.440099	+	0.897949i	$0.645057\pi$
$318$	−6.35765	−	3.67059i	−0.356519	−	0.205836i
$319$	−0.106455	+	0.0285245i	−0.00596032	+	0.00159706i
$320$	2.05459	−	23.5480i	0.114855	−	1.31637i
$321$	18.0038	−	31.1834i	1.00487	−	1.74049i
$322$	−0.584195	+	2.18025i	−0.0325559	+	0.121500i
$323$	−6.85452	−	11.8724i	−0.381396	−	0.660597i
$324$	3.97648			0.220915
$325$	−5.70046	+	17.1028i	−0.316205	+	0.948691i
$326$	8.40958			0.465763
$327$	−14.9316	−	25.8623i	−0.825719	−	1.43019i
$328$	−1.52316	+	5.68451i	−0.0841025	+	0.313875i
$329$	1.21309	−	2.10113i	0.0668797	−	0.115839i
$330$	−0.0294615	+	0.337663i	−0.00162180	+	0.0185877i
$331$	3.25207	−	0.871389i	0.178750	−	0.0478959i	−0.168334	−	0.985730i	$-0.553839\pi$
$331$	3.25207	−	0.871389i	0.178750	−	0.0478959i	0.347084	+	0.937834i	$0.387172\pi$
$332$	−2.68932	−	1.55268i	−0.147595	−	0.0852142i
$333$	29.6309			1.62376
$334$	−43.1071	−	24.8879i	−2.35871	−	1.36180i
$335$	24.9583	−	11.6454i	1.36362	−	0.636255i
$336$	24.4220	+	6.54384i	1.33233	+	0.356996i
$337$	−7.20813	−	7.20813i	−0.392652	−	0.392652i	0.482980	−	0.875631i	$-0.339554\pi$
$337$	−7.20813	−	7.20813i	−0.392652	−	0.392652i	−0.875631	+	0.482980i	$0.839554\pi$
$338$	6.14230	+	26.4391i	0.334097	+	1.43810i
$339$			23.9443i			1.30048i
$340$	14.2015	+	5.16513i	0.770184	+	0.280119i
$341$	0.0155613	+	0.0269529i	0.000842690	+	0.00145958i
$342$	−44.3330	+	11.8790i	−2.39725	+	0.642342i
$343$		−	16.0835i		−	0.868425i
$344$	1.34682	+	5.02640i	0.0726157	+	0.271005i
$345$	−1.87449	−	1.31187i	−0.100919	−	0.0706288i
$346$	1.19946	−	1.19946i	0.0644835	−	0.0644835i
$347$	5.07101	+	18.9253i	0.272226	+	1.01596i	0.957677	+	0.287844i	$0.0929384\pi$
$347$	5.07101	+	18.9253i	0.272226	+	1.01596i	−0.685451	+	0.728119i	$0.740395\pi$
$348$	26.2694	+	7.03888i	1.40819	+	0.377323i
$349$	2.15644	−	8.04794i	0.115432	−	0.430796i	−0.883887	−	0.467700i	$-0.845083\pi$
$349$	2.15644	−	8.04794i	0.115432	−	0.430796i	0.999319	+	0.0369035i	$0.0117494\pi$
$350$	−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
$353$	−4.47609	+	2.58427i	−0.238238	+	0.137547i	−0.614367	−	0.789021i	$-0.710588\pi$
$353$	−4.47609	+	2.58427i	−0.238238	+	0.137547i	0.376129	+	0.926567i	$0.377255\pi$
$354$	−7.46127	+	4.30777i	−0.396562	+	0.228955i
$355$	−1.43878	−	8.14852i	−0.0763627	−	0.432478i
$356$	5.59095	+	5.59095i	0.296320	+	0.296320i
$357$	−11.4883	+	19.8984i	−0.608027	+	1.05313i
$358$	6.85114	−	11.8665i	0.362094	−	0.627166i
$359$	−11.2145	−	11.2145i	−0.591877	−	0.591877i	0.346261	−	0.938138i	$-0.387451\pi$
$359$	−11.2145	−	11.2145i	−0.591877	−	0.591877i	−0.938138	+	0.346261i	$0.887451\pi$
$360$	4.41974	−	6.31521i	0.232941	−	0.332841i
$361$	−3.38491	+	1.95428i	−0.178153	+	0.102857i
$362$	−2.83214	+	1.63513i	−0.148854	+	0.0859408i
$363$	−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
$367$	−11.7486	−	3.14803i	−0.613272	−	0.164326i	−0.0612047	−	0.998125i	$-0.519494\pi$
$367$	−11.7486	−	3.14803i	−0.613272	−	0.164326i	−0.552067	+	0.833799i	$0.686161\pi$
$368$	−0.302913	−	1.13049i	−0.0157904	−	0.0589307i
$369$	25.4625	−	25.4625i	1.32552	−	1.32552i
$370$	−17.2713	+	24.6784i	−0.897895	+	1.28297i
$371$	0.961452	+	3.58819i	0.0499161	+	0.186289i
$372$		−	7.67999i		−	0.398189i
$373$	−0.331070	+	0.0887099i	−0.0171421	+	0.00459322i	−0.267380	−	0.963591i	$-0.586158\pi$
$373$	−0.331070	+	0.0887099i	−0.0171421	+	0.00459322i	0.250238	+	0.968184i	$0.419491\pi$
$374$	−0.0787817	−	0.136454i	−0.00407371	−	0.00705587i
$375$	−26.6907	−	15.3848i	−1.37830	−	0.794465i
$376$		−	0.625521i		−	0.0322588i
$377$	−5.53729	−	14.0289i	−0.285185	−	0.722525i
$378$	18.8630	+	18.8630i	0.970207	+	0.970207i
$379$	14.9855	+	4.01535i	0.769754	+	0.206255i	0.622263	−	0.782809i	$-0.286214\pi$
$379$	14.9855	+	4.01535i	0.769754	+	0.206255i	0.147491	+	0.989063i	$0.452880\pi$
$380$	8.63121	−	23.7315i	0.442772	−	1.21740i
$381$	35.8602	+	20.7039i	1.83717	+	1.06069i
$382$	9.64728			0.493598
$383$	−19.4048	−	11.2034i	−0.991538	−	0.572465i	−0.0858043	−	0.996312i	$-0.527346\pi$
$383$	−19.4048	−	11.2034i	−0.991538	−	0.572465i	−0.905734	+	0.423847i	$0.860679\pi$
$384$	15.7238	−	4.21319i	0.802404	−	0.215004i
$385$	0.131360	−	0.110277i	0.00669473	−	0.00562023i
$386$	17.3632	−	30.0740i	0.883766	−	1.53073i
$387$	8.24093	−	30.7556i	0.418910	−	1.56339i
$388$	0.478347	+	0.828521i	0.0242844	+	0.0420618i
$389$	7.41149			0.375777			0.187889	−	0.982190i	$-0.439836\pi$
$389$	7.41149			0.375777			0.187889	+	0.982190i	$0.439836\pi$
$390$	−46.3674	+	1.25705i	−2.34790	+	0.0636530i
$391$	1.06358			0.0537878
$392$	0.553718	+	0.959068i	0.0279670	+	0.0484402i
$393$	6.45019	−	24.0724i	0.325369	−	1.21429i
$394$	26.8604	−	46.5236i	1.35321	−	2.34383i
$395$	−9.46820	−	0.826112i	−0.476397	−	0.0415662i
$396$	−0.275776	+	0.0738941i	−0.0138583	+	0.00371332i
$397$	15.1936	+	8.77205i	0.762547	+	0.440257i	0.830209	−	0.557452i	$-0.188221\pi$
$397$	15.1936	+	8.77205i	0.762547	+	0.440257i	−0.0676626	+	0.997708i	$0.521554\pi$
$398$	−58.0088			−2.90772
$399$	33.2512	+	19.1976i	1.66464	+	0.961083i
$400$	−5.39687	−	14.8061i	−0.269843	−	0.740303i
$401$	−26.5449	−	7.11268i	−1.32559	−	0.355190i	−0.474520	−	0.880245i	$-0.657378\pi$
$401$	−26.5449	−	7.11268i	−1.32559	−	0.355190i	−0.851068	+	0.525055i	$0.824045\pi$
$402$	50.1074	+	50.1074i	2.49913	+	2.49913i
$403$	−3.42196	+	2.53576i	−0.170460	+	0.126315i
$404$			6.72034i			0.334350i
$405$	3.41503	−	1.59343i	0.169694	−	0.0791783i
$406$	−12.7134	−	22.0202i	−0.630954	−	1.09284i
$407$	0.164192	−	0.0439951i	0.00813869	−	0.00218076i
$408$			5.92388i			0.293276i
$409$	4.33151	+	16.1654i	0.214179	+	0.799329i	0.986454	+	0.164039i	$0.0524524\pi$
$409$	4.33151	+	16.1654i	0.214179	+	0.799329i	−0.772274	+	0.635289i	$0.780881\pi$
$410$	6.36505	+	36.0484i	0.314348	+	1.78030i
$411$	−28.3850	+	28.3850i	−1.40013	+	1.40013i
$412$	4.86654	+	18.1622i	0.239757	+	0.894786i
$413$	4.21106	+	1.12835i	0.207213	+	0.0555225i
$414$	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
$418$	−0.228022	+	0.131649i	−0.0111529	+	0.00643914i
$419$	−24.9349	+	14.3962i	−1.21815	+	0.703299i	−0.964522	−	0.264003i	$-0.914957\pi$
$419$	−24.9349	+	14.3962i	−1.21815	+	0.703299i	−0.253627	+	0.967302i	$0.581624\pi$
$420$	−41.6787	+	7.35921i	−2.03371	+	0.359093i
$421$	8.48901	+	8.48901i	0.413729	+	0.413729i	0.883035	−	0.469306i	$-0.155496\pi$
$421$	8.48901	+	8.48901i	0.413729	+	0.413729i	−0.469306	+	0.883035i	$0.655496\pi$
$422$	−15.4263	+	26.7192i	−0.750941	+	1.30067i
$423$	−1.91372	+	3.31466i	−0.0930482	+	0.161164i
$424$	0.677229	+	0.677229i	0.0328892	+	0.0328892i
$425$	14.2661	−	1.25489i	0.692007	−	0.0608713i
$426$	18.4377	−	10.6450i	0.893308	−	0.515752i
$427$	26.9816	−	15.5778i	1.30573	−	0.753865i
$428$	−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	−0.853025	−	0.521870i	$-0.825234\pi$
$431$	3.04457	−	11.3625i	0.146652	−	0.547311i	0.999676	−	0.0254407i	$-0.00809891\pi$
$432$	−13.3607	−	3.57999i	−0.642816	−	0.172242i
$433$	5.01355	+	18.7108i	0.240936	+	0.899184i	0.975383	+	0.220518i	$0.0707749\pi$
$433$	5.01355	+	18.7108i	0.240936	+	0.899184i	−0.734447	+	0.678666i	$0.762558\pi$
$434$	−5.07726	+	5.07726i	−0.243716	+	0.243716i
$435$	25.3810	−	4.48151i	1.21692	−	0.214872i
$436$	6.61838	+	24.7001i	0.316963	+	1.18292i
$437$		−	1.77731i		−	0.0850201i
$438$	83.8278	−	22.4616i	4.00545	−	1.07326i
$439$	11.9244	+	20.6537i	0.569121	+	0.985747i	0.996653	+	0.0817464i	$0.0260498\pi$
$439$	11.9244	+	20.6537i	0.569121	+	0.985747i	−0.427532	+	0.904000i	$0.640617\pi$
$440$	0.0151142	−	0.0415564i	0.000720541	−	0.00198112i
$441$		−	6.77618i		−	0.322675i
$442$	17.3243	−	12.8378i	0.824032	−	0.610630i
$443$	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
$445$	7.04192	+	2.56117i	0.333819	+	0.121411i
$446$	−25.3582	−	14.6406i	−1.20075	−	0.693251i
$447$	−16.1399			−0.763392
$448$	−26.6518	−	15.3874i	−1.25918	−	0.726987i
$449$	−39.5246	+	10.5906i	−1.86528	+	0.499801i	−0.999999	−	0.00148324i	$-0.999528\pi$
$449$	−39.5246	+	10.5906i	−1.86528	+	0.499801i	−0.865283	+	0.501284i	$0.832861\pi$
$450$	8.30352	−	47.2217i	0.391432	−	2.22605i
$451$	0.103288	−	0.178900i	0.00486363	−	0.00842405i
$452$	5.30662	−	19.8046i	0.249603	−	0.931529i
$453$	5.69788	+	9.86901i	0.267710	+	0.463687i
$454$	−33.3886			−1.56701
$455$	17.0404	+	16.1409i	0.798867	+	0.756695i
$456$	9.89912			0.463569
$457$	−4.13201	−	7.15685i	−0.193287	−	0.334783i	0.753051	−	0.657963i	$-0.228582\pi$
$457$	−4.13201	−	7.15685i	−0.193287	−	0.334783i	−0.946338	+	0.323180i	$0.895248\pi$
$458$	−1.76587	+	6.59033i	−0.0825139	+	0.307946i
$459$	6.28500	−	10.8859i	0.293359	−	0.508112i
$460$	1.25967	+	1.50049i	0.0587322	+	0.0699608i
$461$	−18.3239	+	4.90987i	−0.853429	+	0.228676i	−0.658909	−	0.752223i	$-0.728982\pi$
$461$	−18.3239	+	4.90987i	−0.853429	+	0.228676i	−0.194520	+	0.980899i	$0.562315\pi$
$462$	0.382170	+	0.220646i	0.0177801	+	0.0102654i
$463$	24.9284			1.15852			0.579261	−	0.815142i	$-0.303341\pi$
$463$	24.9284			1.15852			0.579261	+	0.815142i	$0.303341\pi$
$464$	11.4178	+	6.59205i	0.530056	+	0.306028i
$465$	−3.07748	−	6.59563i	−0.142715	−	0.305865i
$466$	−50.8091	−	13.6142i	−2.35368	−	0.630668i
$467$	25.6059	+	25.6059i	1.18490	+	1.18490i	0.978459	+	0.206441i	$0.0661881\pi$
$467$	25.6059	+	25.6059i	1.18490	+	1.18490i	0.206441	+	0.978459i	$0.433812\pi$
$468$	−14.3446	−	36.3426i	−0.663081	−	1.67994i
$469$		−	35.8577i		−	1.65575i
$470$	−1.64517	−	3.52592i	−0.0758862	−	0.162639i
$471$	8.95998	+	15.5191i	0.412854	+	0.715084i
$472$	1.08570	−	0.290913i	0.0499735	−	0.0133904i
$473$		−	0.182660i		−	0.00839870i
$474$	−6.32908	−	23.6204i	−0.290704	−	1.08492i
$475$	−2.09700	−	23.8394i	−0.0962167	−	1.09383i
$476$	13.9121	−	13.9121i	0.637659	−	0.637659i
$477$	−1.51675	−	5.66058i	−0.0694471	−	0.259180i
$478$	12.3044	+	3.29695i	0.562789	+	0.150799i
$479$	1.20781	−	4.50760i	0.0551861	−	0.205957i	−0.932828	−	0.360323i	$-0.882667\pi$
$479$	1.20781	−	4.50760i	0.0551861	−	0.205957i	0.988014	+	0.154365i	$0.0493333\pi$
$480$	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
$483$	−2.57972	+	1.48940i	−0.117381	+	0.0677701i
$484$	22.4757	−	12.9764i	1.02162	−	0.589834i
$485$	0.742808	+	0.519859i	0.0337292	+	0.0236056i
$486$	26.2941	+	26.2941i	1.19273	+	1.19273i
$487$	−7.30711	+	12.6563i	−0.331117	+	0.573511i	−0.982731	−	0.185040i	$-0.940759\pi$
$487$	−7.30711	+	12.6563i	−0.331117	+	0.573511i	0.651615	+	0.758550i	$0.274092\pi$
$488$	4.01630	−	6.95644i	0.181810	−	0.314903i
$489$	7.84764	+	7.84764i	0.354883	+	0.354883i
$490$	5.64362	+	3.94972i	0.254953	+	0.178430i
$491$	−17.4840	+	10.0944i	−0.789042	+	0.455553i	−0.839625	−	0.543166i	$-0.817225\pi$
$491$	−17.4840	+	10.0944i	−0.789042	+	0.455553i	0.0505834	+	0.998720i	$0.483892\pi$
$492$	−44.1464	+	25.4879i	−1.99027	+	1.14908i
$493$	−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
$497$	−10.4060	−	2.78829i	−0.466774	−	0.125072i
$498$	−1.95977	−	7.31396i	−0.0878194	−	0.327746i
$499$	0.519223	−	0.519223i	0.0232436	−	0.0232436i	−0.695389	−	0.718633i	$-0.744768\pi$
$499$	0.519223	−	0.519223i	0.0232436	−	0.0232436i	0.718633	+	0.695389i	$0.244768\pi$
$500$	18.6666	+	18.6402i	0.834794	+	0.833615i
$501$	−17.0018	−	63.4515i	−0.759583	−	2.83480i
$502$		−	1.21379i		−	0.0541741i
$503$	−36.4639	+	9.77048i	−1.62585	+	0.435644i	−0.952712	−	0.303876i	$-0.901719\pi$
$503$	−36.4639	+	9.77048i	−1.62585	+	0.435644i	−0.673134	+	0.739520i	$0.735052\pi$
$504$	−5.01785	−	8.69117i	−0.223513	−	0.387135i
$505$	2.69294	+	5.77148i	0.119834	+	0.256827i
$506$		−	0.0204273i		−	0.000908103i
$507$	−18.9405	+	30.4043i	−0.841179	+	1.35030i
$508$	−25.0719	−	25.0719i	−1.11238	−	1.11238i
$509$	−39.8263	−	10.6714i	−1.76527	−	0.473003i	−0.777496	−	0.628887i	$-0.783511\pi$
$509$	−39.8263	−	10.6714i	−1.76527	−	0.473003i	−0.987775	+	0.155884i	$0.950177\pi$
$510$	15.5803	+	33.3916i	0.689908	+	1.47860i
$511$	−38.0312	−	21.9573i	−1.68240	−	0.971336i
$512$	30.2040			1.33484
$513$	−18.1910	−	10.5026i	−0.803152	−	0.463700i
$514$	−35.0960	+	9.40395i	−1.54802	+	0.414791i
$515$	11.4573	+	13.6477i	0.504867	+	0.601390i
$516$	−22.5371	+	39.0354i	−0.992142	+	1.71844i
$517$	−0.00568287	+	0.0212087i	−0.000249932	+	0.000932759i
$518$	19.6086	+	33.9631i	0.861553	+	1.49225i
$519$	2.23862			0.0982647
$520$	5.88552	+	1.40724i	0.258097	+	0.0617114i
$521$	2.07984			0.0911193			0.0455597	−	0.998962i	$-0.485493\pi$
$521$	2.07984			0.0911193			0.0455597	+	0.998962i	$0.485493\pi$
$522$	20.0561	+	34.7382i	0.877831	+	1.52045i
$523$	9.94861	−	37.1287i	0.435022	−	1.62353i	−0.305990	−	0.952035i	$-0.598987\pi$
$523$	9.94861	−	37.1287i	0.435022	−	1.62353i	0.741013	−	0.671491i	$-0.234346\pi$
$524$	−10.6700	+	18.4811i	−0.466123	+	0.807349i
$525$	−32.8450	+	23.0214i	−1.43347	+	1.00474i
$526$	55.6329	−	14.9068i	2.42571	−	0.649967i
$527$	2.93011	+	1.69170i	0.127638	+	0.0736917i
$528$	−0.228815			−0.00995791
$529$	−19.7992	−	11.4311i	−0.860833	−	0.497002i
$530$	5.59856	+	2.03622i	0.243186	+	0.0884475i
$531$	−6.64319	−	1.78004i	−0.288290	−	0.0772471i
$532$	−23.2478	−	23.2478i	−1.00792	−	1.00792i
$533$	25.9328	+	11.2547i	1.12327	+	0.487494i
$534$			19.2796i			0.834310i
$535$	−9.98736	+	27.4602i	−0.431791	+	1.18721i
$536$	−4.62244	−	8.00630i	−0.199659	−	0.345820i
$537$	17.4669	−	4.68025i	0.753754	−	0.201968i
$538$		−	38.4533i		−	1.65784i
$539$	−0.0100611	−	0.0375484i	−0.000433361	−	0.00161733i
$540$	22.8015	−	4.02605i	0.981219	−	0.173254i
$541$	17.3961	−	17.3961i	0.747916	−	0.747916i	−0.226171	−	0.974088i	$-0.572621\pi$
$541$	17.3961	−	17.3961i	0.747916	−	0.747916i	0.974088	+	0.226171i	$0.0726209\pi$
$542$	−14.0016	−	52.2547i	−0.601420	−	2.24453i
$543$	−4.16876	−	1.11702i	−0.178899	−	0.0479358i
$544$	−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	$0.376928\pi$
$548$	29.7683	−	17.1868i	1.27164	−	0.734182i
$549$	−42.5651	+	24.5750i	−1.81663	+	1.04883i
$550$	−0.0241016	−	0.273995i	−0.00102770	−	0.0116832i
$551$	14.1572	+	14.1572i	0.603115	+	0.603115i
$552$	−0.384000	+	0.665107i	−0.0163441	+	0.0283089i
$553$	−6.18700	+	10.7162i	−0.263098	+	0.455699i
$554$	34.5829	+	34.5829i	1.46928	+	1.46928i
$555$	−39.1466	+	6.91212i	−1.66168	+	0.293403i
$556$	−14.1290	+	8.15741i	−0.599205	+	0.345951i
$557$	26.1484	−	15.0968i	1.10794	−	0.639671i	0.169647	−	0.985505i	$-0.445737\pi$
$557$	26.1484	−	15.0968i	1.10794	−	0.639671i	0.938296	+	0.345834i	$0.112404\pi$
$558$	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
$562$	28.3224	+	7.58897i	1.19471	+	0.320122i
$563$	−7.36768	−	27.4966i	−0.310511	−	1.15884i	−0.928097	−	0.372339i	$-0.878556\pi$
$563$	−7.36768	−	27.4966i	−0.310511	−	1.15884i	0.617586	−	0.786503i	$-0.288111\pi$
$564$	3.83126	−	3.83126i	0.161325	−	0.161325i
$565$	−3.37862	−	19.1348i	−0.142140	−	0.805005i
$566$	−2.22201	−	8.29267i	−0.0933982	−	0.348567i
$567$		−	4.90639i		−	0.206049i
$568$	−2.68290	+	0.718880i	−0.112572	+	0.0301635i
$569$	16.3759	+	28.3638i	0.686512	+	1.18907i	0.972959	+	0.230978i	$0.0741926\pi$
$569$	16.3759	+	28.3638i	0.686512	+	1.18907i	−0.286447	+	0.958096i	$0.592474\pi$
$570$	55.7991	−	26.0355i	2.33717	−	1.09051i
$571$			7.81838i			0.327189i	0.986528	+	0.163594i	$0.0523088\pi$
$571$			7.81838i			0.327189i	−0.986528	+	0.163594i	$0.947691\pi$
$572$	−0.133447	−	0.180084i	−0.00557971	−	0.00752970i
$573$	9.00264	+	9.00264i	0.376091	+	0.376091i
$574$	46.0354	+	12.3351i	1.92148	+	0.514859i
$575$	1.68308	+	0.783867i	0.0701892	+	0.0326895i
$576$	42.0448	+	24.2746i	1.75187	+	1.01144i
$577$	14.7927			0.615830			0.307915	−	0.951414i	$-0.400369\pi$
$577$	14.7927			0.615830			0.307915	+	0.951414i	$0.400369\pi$
$578$	15.9053	+	9.18293i	0.661573	+	0.381959i
$579$	44.2675	−	11.8614i	1.83969	−	0.492944i
$580$	−21.9861	−	1.91831i	−0.912922	−	0.0796536i
$581$	−1.91577	+	3.31822i	−0.0794797	+	0.137663i
$582$	−0.603764	+	2.25328i	−0.0250268	+	0.0934014i
$583$	−0.0168093	−	0.0291146i	−0.000696171	−	0.00120580i
$584$	−11.3222			−0.468514
$585$	−26.8823	−	25.4631i	−1.11144	−	1.05277i
$586$	−45.6279			−1.88487
$587$	8.33757	+	14.4411i	0.344128	+	0.596048i	0.985195	−	0.171437i	$-0.0548411\pi$
$587$	8.33757	+	14.4411i	0.344128	+	0.596048i	−0.641067	+	0.767485i	$0.721508\pi$
$588$	−2.48273	+	9.26568i	−0.102386	+	0.382110i
$589$	2.82693	−	4.89638i	0.116481	−	0.201752i
$590$	5.35473	−	4.49530i	0.220451	−	0.185069i
$591$	68.4805	−	18.3493i	2.81691	−	0.754789i
$592$	−17.6103	−	10.1673i	−0.723780	−	0.417874i
$593$	−6.40700			−0.263104			−0.131552	−	0.991309i	$-0.541996\pi$
$593$	−6.40700			−0.263104			−0.131552	+	0.991309i	$0.541996\pi$
$594$	−0.209076	−	0.120710i	−0.00857850	−	0.00495280i
$595$	6.37301	−	17.5226i	0.261268	−	0.718355i
$596$	13.3495	+	3.57699i	0.546817	+	0.146519i
$597$	−54.1326	−	54.1326i	−2.21550	−	2.21550i
$598$	2.77727	−	0.318367i	0.113571	−	0.0130190i
$599$		−	37.0014i		−	1.51184i	−0.654667	−	0.755918i	$-0.727191\pi$
$599$		−	37.0014i		−	1.51184i	0.654667	−	0.755918i	$-0.272809\pi$
$600$	−4.36593	+	9.37430i	−0.178238	+	0.382704i
$601$	0.255112	+	0.441867i	0.0104062	+	0.0180241i	0.871182	−	0.490961i	$-0.163354\pi$
$601$	0.255112	+	0.441867i	0.0104062	+	0.0180241i	−0.860775	+	0.508985i	$0.830021\pi$
$602$	40.7057	−	10.9071i	1.65904	−	0.444539i
$603$			56.5676i			2.30361i
$604$	−2.52557	−	9.42555i	−0.102764	−	0.383520i
$605$	14.1025	−	20.1505i	0.573347	−	0.819235i
$606$	−11.5871	+	11.5871i	−0.470693	+	0.470693i
$607$	6.08093	+	22.6944i	0.246817	+	0.921135i	0.972461	+	0.233065i	$0.0748754\pi$
$607$	6.08093	+	22.6944i	0.246817	+	0.921135i	−0.725644	+	0.688071i	$0.758458\pi$
$608$	37.3644	+	10.0118i	1.51533	+	0.406030i
$609$	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
$613$	−10.7921	+	6.23084i	−0.435890	+	0.251661i	−0.701853	−	0.712322i	$-0.747644\pi$
$613$	−10.7921	+	6.23084i	−0.435890	+	0.251661i	0.265963	+	0.963983i	$0.414310\pi$
$614$	12.6264	−	7.28984i	0.509559	−	0.294194i
$615$	−27.6998	+	39.5793i	−1.11696	+	1.59599i
$616$	−0.0407095	−	0.0407095i	−0.00164023	−	0.00164023i
$617$	−13.9153	+	24.1020i	−0.560209	+	0.970311i	0.437268	+	0.899331i	$0.355946\pi$
$617$	−13.9153	+	24.1020i	−0.560209	+	0.970311i	−0.997478	+	0.0709800i	$0.977387\pi$
$618$	−22.9241	+	39.7057i	−0.922141	+	1.59720i
$619$	−9.96152	−	9.96152i	−0.400387	−	0.400387i	0.477982	−	0.878370i	$-0.341368\pi$
$619$	−9.96152	−	9.96152i	−0.400387	−	0.400387i	−0.878370	+	0.477982i	$0.841368\pi$
$620$	1.08367	+	6.13736i	0.0435213	+	0.246482i
$621$	1.41130	−	0.814817i	0.0566337	−	0.0326975i
$622$	−38.4830	+	22.2181i	−1.54303	+	0.890867i
$623$	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
$627$	−0.335637	−	0.0899336i	−0.0134040	−	0.00359160i
$628$	−3.97149	−	14.8218i	−0.158480	−	0.591454i
$629$	13.0669	−	13.0669i	0.521011	−	0.521011i
$630$	−51.1430	−	35.7928i	−2.03759	−	1.42602i
$631$	8.57363	+	31.9972i	0.341311	+	1.27379i	0.896863	+	0.442308i	$0.145840\pi$
$631$	8.57363	+	31.9972i	0.341311	+	1.27379i	−0.555552	+	0.831482i	$0.687493\pi$
$632$			3.19028i			0.126903i
$633$	−39.3293	+	10.5382i	−1.56320	+	0.418858i
$634$	16.3605	+	28.3373i	0.649760	+	1.12542i
$635$	−31.5785	−	11.4852i	−1.25316	−	0.455777i
$636$			8.29594i			0.328955i
$637$	4.94823	−	1.95310i	0.196056	−	0.0773845i
$638$	0.162714	+	0.162714i	0.00644190	+	0.00644190i
$639$	16.4161	+	4.39868i	0.649411	+	0.174009i
$640$	−11.9710	+	5.58560i	−0.473195	+	0.220790i
$641$	39.0498	+	22.5454i	1.54238	+	0.890491i	0.998688	+	0.0512035i	$0.0163057\pi$
$641$	39.0498	+	22.5454i	1.54238	+	0.890491i	0.543688	+	0.839288i	$0.317028\pi$
$642$	−75.1815			−2.96718
$643$	−15.0906	−	8.71256i	−0.595115	−	0.343590i	0.172003	−	0.985097i	$-0.444976\pi$
$643$	−15.0906	−	8.71256i	−0.595115	−	0.343590i	−0.767117	+	0.641507i	$0.778310\pi$
$644$	2.46380	−	0.660173i	0.0970873	−	0.0260145i
$645$	−3.71297	+	42.5549i	−0.146198	+	1.67560i
$646$	−14.3118	+	24.7888i	−0.563091	+	0.975302i
$647$	−6.44377	+	24.0485i	−0.253331	+	0.945442i	0.715681	+	0.698427i	$0.246116\pi$
$647$	−6.44377	+	24.0485i	−0.253331	+	0.945442i	−0.969012	+	0.247015i	$0.920550\pi$
$648$	−0.632487	−	1.09550i	−0.0248464	−	0.0430353i
$649$	−0.0394545			−0.00154872
$650$	36.8765	−	7.54714i	1.44641	−	0.296023i
$651$	−9.47598			−0.371393
$652$	−4.75164	−	8.23009i	−0.186089	−	0.322315i
$653$	4.73226	−	17.6610i	0.185188	−	0.691129i	−0.809403	−	0.587254i	$-0.800209\pi$
$653$	4.73226	−	17.6610i	0.185188	−	0.691129i	0.994590	−	0.103875i	$-0.0331243\pi$
$654$	−31.1762	+	53.9988i	−1.21909	+	2.11152i
$655$	−1.75788	+	20.1473i	−0.0686860	+	0.787220i
$656$	−23.8699	+	6.39593i	−0.931965	+	0.249719i
$657$	59.9965	+	34.6390i	2.34069	+	1.35140i
$658$	−5.06571			−0.197482
$659$	−24.6502	−	14.2318i	−0.960234	−	0.554391i	−0.0639889	−	0.997951i	$-0.520382\pi$
$659$	−24.6502	−	14.2318i	−0.960234	−	0.554391i	−0.896245	+	0.443559i	$0.853716\pi$
$660$	0.347102	−	0.161956i	0.0135109	−	0.00630413i
$661$	24.2172	+	6.48898i	0.941941	+	0.252392i	0.696939	−	0.717130i	$-0.254545\pi$
$661$	24.2172	+	6.48898i	0.941941	+	0.252392i	0.245002	+	0.969523i	$0.421211\pi$
$662$	−4.97071	−	4.97071i	−0.193192	−	0.193192i
$663$	28.1466	+	4.18673i	1.09312	+	0.162599i
$664$			0.987856i			0.0383363i
$665$	−29.2811	−	10.6496i	−1.13547	−	0.412976i
$666$	−30.9337	−	53.5788i	−1.19866	−	2.07614i
$667$	−1.50037	+	0.402024i	−0.0580947	+	0.0155664i
$668$			56.2494i			2.17635i
$669$	−10.0015	−	37.3260i	−0.386680	−	1.44311i
$670$	−47.1129	−	32.9723i	−1.82013	−	1.27383i
$671$	−0.199375	+	0.199375i	−0.00769679	+	0.00769679i
$672$	−16.7799	−	62.6235i	−0.647299	−	2.41575i
$673$	−27.4718	−	7.36105i	−1.05896	−	0.283748i	−0.313010	−	0.949750i	$-0.601337\pi$
$673$	−27.4718	−	7.36105i	−1.05896	−	0.283748i	−0.745950	+	0.666002i	$0.768004\pi$
$674$	−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	$0.274940\pi$
$678$	43.2963	−	24.9971i	1.66278	−	0.960008i
$679$	1.02227	−	0.590210i	0.0392313	−	0.0226502i
$680$	−0.835879	−	4.73399i	−0.0320545	−	0.181540i
$681$	−31.1576	−	31.1576i	−1.19396	−	1.19396i
$682$	0.0324910	−	0.0562760i	0.00124414	−	0.00215492i
$683$	−10.7928	+	18.6936i	−0.412974	+	0.715292i	−0.995213	−	0.0977251i	$-0.968843\pi$
$683$	−10.7928	+	18.6936i	−0.412974	+	0.715292i	0.582239	+	0.813018i	$0.302177\pi$
$684$	36.6748	+	36.6748i	1.40230	+	1.40230i
$685$	18.6783	−	26.6887i	0.713660	−	1.01972i
$686$	−29.0822	+	16.7906i	−1.11036	+	0.641069i
$687$	−7.79784	+	4.50208i	−0.297506	+	0.171765i
$688$	−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	−0.524008	−	0.851713i	$-0.675564\pi$
$691$	9.34901	−	34.8910i	0.355653	−	1.32732i	0.879661	−	0.475602i	$-0.157770\pi$
$692$	−1.85159	−	0.496132i	−0.0703869	−	0.0188601i
$693$	0.0911744	+	0.340268i	0.00346343	+	0.0129257i
$694$	28.9269	−	28.9269i	1.09805	−	1.09805i
$695$	−8.86533	+	12.6674i	−0.336281	+	0.480500i
$696$	−2.23916	−	8.35668i	−0.0848753	−	0.316759i
$697$		−	22.4573i		−	0.850631i
$698$	−16.8036	+	4.50251i	−0.636026	+	0.170423i
$699$	−34.7094	−	60.1185i	−1.31283	−	2.27389i
$700$	32.2686	−	11.7620i	1.21964	−	0.444563i
$701$		−	16.0544i		−	0.606367i	−0.952932	−	0.303184i	$-0.901950\pi$
$701$		−	16.0544i		−	0.606367i	0.952932	−	0.303184i	$-0.0980496\pi$
$702$	13.1531	−	30.3071i	0.496431	−	1.14387i
$703$	−21.8355	−	21.8355i	−0.823540	−	0.823540i
$704$	0.269022	+	0.0720843i	0.0101392	+	0.00271678i
$705$	1.75507	−	4.82556i	0.0660998	−	0.181741i
$706$	9.34579	+	5.39580i	0.351734	+	0.203073i
$707$	8.29192			0.311850
$708$	8.43165	+	4.86801i	0.316881	+	0.182951i
$709$	25.0659	−	6.71639i	0.941370	−	0.252239i	0.244674	−	0.969605i	$-0.421319\pi$
$709$	25.0659	−	6.71639i	0.941370	−	0.252239i	0.696696	+	0.717366i	$0.254652\pi$
$710$	−13.2322	+	11.1084i	−0.496594	+	0.416892i
$711$	9.76035	−	16.9054i	0.366042	−	0.634003i
$712$	0.650997	−	2.42956i	0.0243972	−	0.0910514i
$713$	0.219320	+	0.379874i	0.00821361	+	0.0142264i
$714$	47.9738			1.79538
$715$	−0.186768	−	0.101183i	−0.00698472	−	0.00378404i
$716$	−15.4843			−0.578677
$717$	8.40555	+	14.5588i	0.313911	+	0.543710i
$718$	−8.57052	+	31.9856i	−0.319849	+	1.19369i
$719$	−21.6867	+	37.5624i	−0.808776	+	1.40084i	0.104936	+	0.994479i	$0.466536\pi$
$719$	−21.6867	+	37.5624i	−0.808776	+	1.40084i	−0.913712	+	0.406362i	$0.866797\pi$
$720$	32.2450	+	2.81342i	1.20170	+	0.104850i
$721$	22.4094	−	6.00459i	0.834571	−	0.223623i
$722$	7.06747	+	4.08041i	0.263024	+	0.151857i
$723$	24.9395			0.927509
$724$	3.20047	+	1.84779i	0.118945	+	0.0686727i
$725$	−19.6505	+	7.16268i	−0.729801	+	0.266015i
$726$	61.1258	+	16.3786i	2.26859	+	0.607867i
$727$	5.51970	+	5.51970i	0.204714	+	0.204714i	0.802016	−	0.597302i	$-0.203761\pi$
$727$	5.51970	+	5.51970i	0.204714	+	0.204714i	−0.597302	+	0.802016i	$0.703761\pi$
$728$	4.90034	−	6.16928i	0.181619	−	0.228649i
$729$			44.0183i			1.63031i
$730$	−63.8204	+	29.7783i	−2.36210	+	1.10214i
$731$	−9.92869	−	17.1970i	−0.367226	−	0.636054i
$732$	67.2071	−	18.0081i	2.48405	−	0.665598i
$733$			14.7183i			0.543633i	0.962349	+	0.271817i	$0.0876244\pi$
$733$			14.7183i			0.543633i	−0.962349	+	0.271817i	$0.912376\pi$
$734$	6.57289	+	24.5304i	0.242610	+	0.905432i
$735$	1.58071	+	8.95230i	0.0583052	+	0.330211i
$736$	−2.12209	+	2.12209i	−0.0782212	+	0.0782212i
$737$	0.0839899	+	0.313455i	0.00309381	+	0.0115462i
$738$	−72.6235	−	19.4594i	−2.67331	−	0.716311i
$739$	−8.68701	+	32.4204i	−0.319557	+	1.19260i	0.600115	+	0.799914i	$0.295122\pi$
$739$	−8.68701	+	32.4204i	−0.319557	+	1.19260i	−0.919672	+	0.392688i	$0.871545\pi$
$740$	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
$743$	18.1254	−	10.4647i	0.664958	−	0.383914i	−0.129206	−	0.991618i	$-0.541243\pi$
$743$	18.1254	−	10.4647i	0.664958	−	0.383914i	0.794163	+	0.607704i	$0.207909\pi$
$744$	−2.11580	+	1.22156i	−0.0775689	+	0.0447844i
$745$	12.8980	−	2.27740i	0.472546	−	0.0834374i
$746$	0.506032	+	0.506032i	0.0185272	+	0.0185272i
$747$	3.02225	−	5.23469i	0.110578	−	0.191527i
$748$	−0.0890277	+	0.154201i	−0.00325518	+	0.00563813i
$749$	26.9006	+	26.9006i	0.982925	+	0.982925i
$750$	0.0454625	+	64.3236i	0.00166006	+	2.34876i
$751$	28.8409	−	16.6513i	1.05242	−	0.607614i	0.129093	−	0.991633i	$-0.458793\pi$
$751$	28.8409	−	16.6513i	1.05242	−	0.607614i	0.923325	+	0.384019i	$0.125460\pi$
$752$	2.27473	−	1.31332i	0.0829510	−	0.0478918i
$753$	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
$757$	9.59581	+	2.57119i	0.348766	+	0.0934515i	0.428949	−	0.903329i	$-0.358884\pi$
$757$	9.59581	+	2.57119i	0.348766	+	0.0934515i	−0.0801834	+	0.996780i	$0.525551\pi$
$758$	−8.38381	−	31.2888i	−0.304514	−	1.13646i
$759$	0.0190623	−	0.0190623i	0.000691918	−	0.000691918i
$760$	−7.91075	+	1.39680i	−0.286953	+	0.0506672i
$761$	11.0600	+	41.2764i	0.400924	+	1.49627i	0.811450	+	0.584421i	$0.198678\pi$
$761$	11.0600	+	41.2764i	0.400924	+	1.49627i	−0.410526	+	0.911849i	$0.634655\pi$
$762$		−	86.4568i		−	3.13200i
$763$	30.4763	−	8.16611i	1.10332	−	0.295633i
$764$	−5.45098	−	9.44138i	−0.197210	−	0.341577i
$765$	−10.0538	+	27.6429i	−0.363496	+	0.999429i
$766$			46.7838i			1.69037i
$767$	−0.614912	−	5.36418i	−0.0222032	−	0.193689i
$768$	17.1599	+	17.1599i	0.619203	+	0.619203i
$769$	32.2304	+	8.63611i	1.16226	+	0.311426i	0.787867	−	0.615845i	$-0.211185\pi$
$769$	32.2304	+	8.63611i	1.16226	+	0.311426i	0.374391	+	0.927271i	$0.377852\pi$
$770$	−0.336539	−	0.122401i	−0.0121280	−	0.00441101i
$771$	−41.5264	−	23.9753i	−1.49554	−	0.863450i
$772$	−39.2429			−1.41238
$773$	8.61912	+	4.97625i	0.310008	+	0.178983i	0.646930	−	0.762549i	$-0.276052\pi$
$773$	8.61912	+	4.97625i	0.310008	+	0.178983i	−0.336922	+	0.941533i	$0.609386\pi$
$774$	−64.2157	+	17.2065i	−2.30819	+	0.618477i
$775$	3.38999	+	4.83656i	0.121772	+	0.173734i
$776$	0.152169	−	0.263564i	0.00546254	−	0.00946140i
$777$	−13.3953	+	49.9920i	−0.480555	+	1.79345i
$778$	−7.73737	−	13.4015i	−0.277398	−	0.480467i
$779$	−37.5274			−1.34456
$780$	27.4291	+	44.6675i	0.982118	+	1.59935i
$781$	0.0974966			0.00348870
$782$	−1.11035	−	1.92318i	−0.0397060	−	0.0687728i
$783$	−4.75133	+	17.7322i	−0.169799	+	0.633697i
$784$	−2.32513	+	4.02724i	−0.0830403	+	0.143830i
$785$	−9.35004	−	11.1376i	−0.333717	−	0.397519i
$786$	−50.2618	+	13.4676i	−1.79278	+	0.480373i
$787$	−16.6616	−	9.61957i	−0.593922	−	0.342901i	0.172725	−	0.984970i	$-0.444743\pi$
$787$	−16.6616	−	9.61957i	−0.593922	−	0.342901i	−0.766647	+	0.642069i	$0.778076\pi$
$788$	−60.7076			−2.16262
$789$	65.8262	+	38.0047i	2.34347	+	1.35300i
$790$	8.39072	+	17.9829i	0.298528	+	0.639803i
$791$	−24.4359	−	6.54759i	−0.868842	−	0.232806i
$792$	0.0642216	+	0.0642216i	0.00228201	+	0.00228201i
$793$	−30.2141	−	23.9995i	−1.07294	−	0.852246i
$794$		−	36.6310i		−	1.29999i
$795$	3.32430	+	7.12461i	0.117901	+	0.252684i
$796$	32.7766	+	56.7707i	1.16174	+	2.01219i
$797$	19.5492	−	5.23820i	0.692469	−	0.185546i	0.104614	−	0.994513i	$-0.466639\pi$
$797$	19.5492	−	5.23820i	0.692469	−	0.185546i	0.587855	+	0.808966i	$0.299973\pi$
$798$		−	80.1669i		−	2.83788i
$799$	0.617798	+	2.30565i	0.0218561	+	0.0815681i
$800$	−25.9602	+	30.9678i	−0.917833	+	1.09488i
$801$	−10.8826	+	10.8826i	−0.384519	+	0.384519i
$802$	14.8508	+	55.4241i	0.524401	+	1.95709i
$803$	0.383886	+	0.102862i	0.0135470	+	0.00362992i
$804$	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
$808$	1.85142	−	1.06892i	0.0651327	−	0.0376044i
$809$	1.16125	−	0.670445i	0.0408272	−	0.0235716i	−0.479447	−	0.877571i	$-0.659163\pi$
$809$	1.16125	−	0.670445i	0.0408272	−	0.0235716i	0.520275	+	0.853999i	$0.325830\pi$
$810$	−6.44644	−	4.51158i	−0.226505	−	0.158521i
$811$	−26.9316	−	26.9316i	−0.945697	−	0.945697i	0.0529030	−	0.998600i	$-0.483153\pi$
$811$	−26.9316	−	26.9316i	−0.945697	−	0.945697i	−0.998600	+	0.0529030i	$0.983153\pi$
$812$	−14.3668	+	24.8840i	−0.504176	+	0.873259i
$813$	35.6970	−	61.8290i	1.25195	−	2.16844i
$814$	−0.250964	−	0.250964i	−0.00879627	−	0.00879627i
$815$	−7.37866	−	5.16400i	−0.258463	−	0.180887i
$816$	−21.5424	+	12.4375i	−0.754136	+	0.435401i
$817$	−28.7371	+	16.5914i	−1.00538	+	0.580459i
$818$	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	0.828772	+	0.559586i	$0.189040\pi$
$821$	−4.83545	+	18.0461i	−0.168758	+	0.629815i	−0.997531	+	0.0702292i	$0.977627\pi$
$822$	80.9591	+	21.6929i	2.82377	+	0.756627i
$823$	−0.647451	−	2.41632i	−0.0225687	−	0.0842276i	0.953723	−	0.300687i	$-0.0972159\pi$
$823$	−0.647451	−	2.41632i	−0.0225687	−	0.0842276i	−0.976292	+	0.216459i	$0.930549\pi$
$824$	4.22953	−	4.22953i	0.147342	−	0.147342i
$825$	0.233196	−	0.278178i	0.00811883	−	0.00968491i
$826$	−2.35593	−	8.79243i	−0.0819731	−	0.305928i
$827$		−	31.5605i		−	1.09747i	−0.835998	−	0.548733i	$-0.815110\pi$
$827$		−	31.5605i		−	1.09747i	0.835998	−	0.548733i	$-0.184890\pi$
$828$	−3.88679	+	1.04146i	−0.135075	+	0.0361933i
$829$	12.7105	+	22.0153i	0.441455	+	0.764622i	0.997798	−	0.0663305i	$-0.0211292\pi$
$829$	12.7105	+	22.0153i	0.441455	+	0.764622i	−0.556343	+	0.830953i	$0.687796\pi$
$830$	2.59815	+	5.56832i	0.0901830	+	0.193279i
$831$			64.5440i			2.23901i
$832$	−5.60768	+	37.6994i	−0.194411	+	1.30699i
$833$	−2.98822	−	2.98822i	−0.103536	−	0.103536i
$834$	−38.4259	−	10.2962i	−1.33058	−	0.356528i
$835$	22.5399	+	48.3074i	0.780027	+	1.67174i
$836$	0.257677	+	0.148770i	0.00891196	+	0.00514532i
$837$	5.18409			0.179188
$838$	52.0625	+	30.0583i	1.79847	+	1.03835i
$839$	18.5670	−	4.97501i	0.641004	−	0.171757i	0.0763459	−	0.997081i	$-0.475675\pi$
$839$	18.5670	−	4.97501i	0.641004	−	0.171757i	0.564658	+	0.825325i	$0.309008\pi$
$840$	8.65671	+	10.3117i	0.298685	+	0.355789i
$841$	−5.75109	+	9.96118i	−0.198313	+	0.343489i
$842$	6.48763	−	24.2121i	0.223578	−	0.834406i
$843$	19.3480	+	33.5118i	0.666382	+	1.15421i
$844$	34.8652			1.20011
$845$	10.8459	−	26.9697i	0.373111	−	0.927787i
$846$	7.99145			0.274752
$847$	−16.0109	−	27.7317i	−0.550142	−	0.952873i
$848$	−1.04089	+	3.88466i	−0.0357443	+	0.133400i
$849$	5.66501	−	9.81208i	0.194423	−	0.336750i
$850$	−17.1625	−	24.4860i	−0.588667	−	0.839862i
$851$	2.31412	−	0.620066i	0.0793270	−	0.0212556i
$852$	−20.8356	−	12.0294i	−0.713816	−	0.412122i
$853$	−38.7388			−1.32639			−0.663196	−	0.748445i	$-0.730801\pi$
$853$	−38.7388			−1.32639			−0.663196	+	0.748445i	$0.730801\pi$
$854$	−56.3359	−	32.5256i	−1.92778	−	1.11300i
$855$	46.1927	+	16.8004i	1.57976	+	0.574563i
$856$	9.47413	+	2.53859i	0.323819	+	0.0867671i
$857$	−28.3225	−	28.3225i	−0.967479	−	0.967479i	0.0320088	−	0.999488i	$-0.489810\pi$
$857$	−28.3225	−	28.3225i	−0.967479	−	0.967479i	−0.999488	+	0.0320088i	$0.989810\pi$
$858$	0.0804106	−	0.540585i	0.00274517	−	0.0184553i
$859$		−	31.6153i		−	1.07870i	−0.842082	−	0.539350i	$-0.818670\pi$
$859$		−	31.6153i		−	1.07870i	0.842082	−	0.539350i	$-0.181330\pi$
$860$	12.5022	−	34.3747i	0.426321	−	1.17217i
$861$	31.4483	+	54.4701i	1.07176	+	1.85634i
$862$	−23.7241	+	6.35687i	−0.808048	+	0.216516i
$863$		−	9.51860i		−	0.324017i	−0.986789	−	0.162008i	$-0.948203\pi$
$863$		−	9.51860i		−	0.324017i	0.986789	−	0.162008i	$-0.0517972\pi$
$864$	9.17990	+	34.2599i	0.312307	+	1.16554i
$865$	−1.78897	+	0.315878i	−0.0608267	+	0.0107402i
$866$	28.5991	−	28.5991i	0.971835	−	0.971835i
$867$	6.27317	+	23.4118i	0.213048	+	0.795107i
$868$	7.83768	+	2.10010i	0.266028	+	0.0712821i
$869$	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
$873$	−1.61270	+	0.931091i	−0.0545815	+	0.0315127i
$874$	−3.21374	+	1.85545i	−0.108706	+	0.0627616i
$875$	22.9993	−	23.0318i	0.777517	−	0.778616i
$876$	−69.3472	−	69.3472i	−2.34303	−	2.34303i
$877$	7.42315	−	12.8573i	0.250662	−	0.434159i	−0.713046	−	0.701117i	$-0.752685\pi$
$877$	7.42315	−	12.8573i	0.250662	−	0.434159i	0.963708	+	0.266958i	$0.0860184\pi$
$878$	24.8974	−	43.1236i	0.840248	−	1.45535i
$879$	−42.5790	−	42.5790i	−1.43615	−	1.43615i
$880$	0.182855	−	0.0322866i	0.00616403	−	0.00108838i
$881$	−2.16038	+	1.24730i	−0.0727850	+	0.0420224i	−0.535951	−	0.844249i	$-0.680047\pi$
$881$	−2.16038	+	1.24730i	−0.0727850	+	0.0420224i	0.463166	+	0.886272i	$0.346713\pi$
$882$	−12.2527	+	7.07412i	−0.412571	+	0.238198i
$883$	−2.64136	+	2.64136i	−0.0888887	+	0.0888887i	−0.750153	−	0.661264i	$-0.770020\pi$
$883$	−2.64136	+	2.64136i	−0.0888887	+	0.0888887i	0.661264	+	0.750153i	$0.270020\pi$
$884$	−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
$887$	−52.9134	−	14.1781i	−1.77666	−	0.476054i	−0.786690	−	0.617348i	$-0.788207\pi$
$887$	−52.9134	−	14.1781i	−1.77666	−	0.476054i	−0.989968	+	0.141294i	$0.954874\pi$
$888$	3.45360	+	12.8890i	0.115895	+	0.432527i
$889$	−30.9350	+	30.9350i	−1.03753	+	1.03753i
$890$	−2.72042	−	15.4070i	−0.0911886	−	0.516445i
$891$	0.0114923	+	0.0428898i	0.000385006	+	0.00143686i
$892$			33.0893i			1.10791i
$893$	3.85287	−	1.03237i	0.128931	−	0.0345471i
$894$	16.8496	+	29.1843i	0.563534	+	0.976070i
$895$	−13.2981	+	6.20480i	−0.444505	+	0.207404i
$896$			17.1988i			0.574572i
$897$	2.88878	+	2.29460i	0.0964536	+	0.0766143i
$898$	60.4125	+	60.4125i	2.01599	+	2.01599i
$899$	−4.77289	−	1.27889i	−0.159185	−	0.0426534i
$900$	−50.9056	+	18.5553i	−1.69685	+	0.618509i
$901$	−3.16512	−	1.82738i	−0.105445	−	0.0608789i
$902$	−0.431317			−0.0143613
$903$	48.1640	+	27.8075i	1.60280	+	0.925375i
$904$	−6.30011	+	1.68811i	−0.209539	+	0.0561457i
$905$	3.48903	+	0.304422i	0.115979	+	0.0101193i
$906$	11.8968	−	20.6059i	0.395245	−	0.684585i
$907$	12.4519	−	46.4710i	0.413457	−	1.54304i	−0.374448	−	0.927248i	$-0.622168\pi$
$907$	12.4519	−	46.4710i	0.413457	−	1.54304i	0.787906	−	0.615796i	$-0.211165\pi$
$908$	18.8655	+	32.6760i	0.626074	+	1.08439i
$909$	−13.0810			−0.433869
$910$	11.3963	−	47.6632i	0.377785	−	1.58002i
$911$	28.6074			0.947806			0.473903	−	0.880577i	$-0.342845\pi$
$911$	28.6074			0.947806			0.473903	+	0.880577i	$0.342845\pi$
$912$	20.7838	+	35.9986i	0.688220	+	1.19203i
$913$	0.00897469	−	0.0334940i	0.000297019	−	0.00110849i
$914$	−8.62738	+	14.9431i	−0.285368	+	0.494272i
$915$	50.5018	−	42.3963i	1.66954	−	1.40158i
$916$	7.44744	−	1.99554i	0.246070	−	0.0659344i
$917$	22.8029	+	13.1653i	0.753018	+	0.434755i
$918$	−26.2454			−0.866227
$919$	31.4065	+	18.1326i	1.03600	+	0.598138i	0.918699	−	0.394958i	$-0.129241\pi$
$919$	31.4065	+	18.1326i	1.03600	+	0.598138i	0.117306	+	0.993096i	$0.462574\pi$
$920$	0.213019	−	0.585695i	0.00702304	−	0.0193098i
$921$	18.5854	+	4.97994i	0.612409	+	0.164095i
$922$	28.0077	+	28.0077i	0.922383	+	0.922383i
$923$	1.51952	+	13.2555i	0.0500156	+	0.436311i
$924$		−	0.498684i		−	0.0164055i
$925$	30.3082	−	11.0474i	0.996527	−	0.363238i
$926$	−26.0245	−	45.0757i	−0.855218	−	1.48128i
$927$	−35.3522	+	9.47260i	−1.16112	+	0.311121i
$928$		−	33.8070i		−	1.10977i
$929$	−4.64847	−	17.3483i	−0.152511	−	0.569180i	−0.999306	−	0.0372596i	$-0.988137\pi$
$929$	−4.64847	−	17.3483i	−0.152511	−	0.569180i	0.846794	−	0.531921i	$-0.178530\pi$
$930$	−8.71347	+	12.4504i	−0.285726	+	0.408263i
$931$	−4.99347	+	4.99347i	−0.163654	+	0.163654i
$932$	15.3849	+	57.4171i	0.503948	+	1.88076i
$933$	−56.6450	−	15.1780i	−1.85447	−	0.496905i
$934$	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	$0.993772\pi$
$938$	−64.8381	+	37.4343i	−2.11704	+	1.22227i
$939$	59.6143	−	34.4183i	1.94544	−	1.12320i
$940$	−2.52110	+	3.60230i	−0.0822291	+	0.117494i
$941$	−2.83451	−	2.83451i	−0.0924023	−	0.0924023i	0.659395	−	0.751797i	$-0.270813\pi$
$941$	−2.83451	−	2.83451i	−0.0924023	−	0.0924023i	−0.751797	+	0.659395i	$0.770813\pi$
$942$	18.7079	−	32.4030i	0.609536	−	1.05575i
$943$	1.45574	−	2.52141i	0.0474053	−	0.0821084i
$944$	3.33741	+	3.33741i	0.108624	+	0.108624i
$945$	−4.96756	−	28.1337i	−0.161595	−	0.915188i
$946$	−0.330287	+	0.190691i	−0.0107385	+	0.00619990i
$947$	−17.5428	+	10.1283i	−0.570064	+	0.329127i	−0.757175	−	0.653212i	$-0.773421\pi$
$947$	−17.5428	+	10.1283i	−0.570064	+	0.329127i	0.187111	+	0.982339i	$0.440088\pi$
$948$	−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
$952$	−6.04551	−	1.61989i	−0.195936	−	0.0525010i
$953$	5.67311	+	21.1724i	0.183770	+	0.685840i	0.994890	+	0.100960i	$0.0321915\pi$
$953$	5.67311	+	21.1724i	0.183770	+	0.685840i	−0.811120	+	0.584879i	$0.801142\pi$
$954$	−8.65206	+	8.65206i	−0.280121	+	0.280121i
$955$	−8.46464	−	5.92403i	−0.273909	−	0.191697i
$956$	−3.72574	−	13.9046i	−0.120499	−	0.449708i
$957$			0.303682i			0.00981665i
$958$	−9.41158	+	2.52183i	−0.304074	+	0.0814765i
$959$	−21.2059	−	36.7297i	−0.684775	−	1.18607i
$960$	−61.2098	−	22.2622i	−1.97554	−	0.718509i
$961$		−	29.6046i		−	0.954988i
$962$	30.2093	−	38.0321i	0.973988	−	1.22620i
$963$	−42.4372	−	42.4372i	−1.36752	−	1.36752i
$964$	−20.6277	−	5.52718i	−0.664374	−	0.178018i
$965$	−33.7020	+	15.7252i	−1.08491	+	0.506212i
$966$	5.38630	+	3.10978i	0.173301	+	0.100055i
$967$	18.3496			0.590084			0.295042	−	0.955484i	$-0.404666\pi$
$967$	18.3496			0.590084			0.295042	+	0.955484i	$0.404666\pi$
$968$	−7.14984	−	4.12796i	−0.229804	−	0.132678i
$969$	−36.4879	+	9.77690i	−1.17216	+	0.314079i
$970$	0.164544	−	1.88587i	0.00528320	−	0.0605516i
$971$	24.5120	−	42.4560i	0.786627	−	1.36248i	−0.141395	−	0.989953i	$-0.545159\pi$
$971$	24.5120	−	42.4560i	0.786627	−	1.36248i	0.928022	−	0.372525i	$-0.121508\pi$
$972$	10.8760	−	40.5898i	0.348848	−	1.30192i
$973$	10.0650	+	17.4332i	0.322670	+	0.558881i
$974$	30.5136			0.977718
$975$	41.4552	+	27.3695i	1.32763	+	0.876526i
$976$	33.7299			1.07967
$977$	1.31945	+	2.28535i	0.0422129	+	0.0731149i	0.886360	−	0.462997i	$-0.153226\pi$
$977$	1.31945	+	2.28535i	0.0422129	+	0.0731149i	−0.844147	+	0.536112i	$0.819893\pi$
$978$	5.99747	−	22.3829i	0.191778	−	0.715725i
$979$	−0.0441451	+	0.0764615i	−0.00141088	+	0.00244372i
$980$	0.676622	−	7.75486i	0.0216139	−	0.247720i
$981$	−48.0782	+	12.8825i	−1.53502	+	0.411307i
$982$	36.5055	+	21.0765i	1.16494	+	0.672577i
$983$	36.6137			1.16780			0.583898	−	0.811827i	$-0.301527\pi$
$983$	36.6137			1.16780			0.583898	+	0.811827i	$0.301527\pi$
$984$	14.0436	+	8.10806i	0.447693	+	0.258476i
$985$	−52.1361	+	24.3264i	−1.66119	+	0.775104i
$986$	24.1636	+	6.47462i	0.769526	+	0.206194i
$987$	−4.72721	−	4.72721i	−0.150469	−	0.150469i
$988$	−16.2106	+	37.3522i	−0.515728	+	1.18833i
$989$		−	2.57440i		−	0.0818613i
$990$	0.530911	+	0.193094i	0.0168735	+	0.00613693i
$991$	−1.39720	−	2.42002i	−0.0443834	−	0.0768744i	0.842980	−	0.537944i	$-0.180799\pi$
$991$	−1.39720	−	2.42002i	−0.0443834	−	0.0768744i	−0.887364	+	0.461070i	$0.847466\pi$
$992$	−9.22156	+	2.47091i	−0.292785	+	0.0784514i
$993$		−	9.27712i		−	0.294401i
$994$	5.82177	+	21.7271i	0.184655	+	0.689143i
$995$	50.8976	+	35.6210i	1.61356	+	1.12926i
$996$	−6.05053	+	6.05053i	−0.191718	+	0.191718i
$997$	−10.3174	−	38.5049i	−0.326754	−	1.21946i	−0.912537	−	0.408994i	$-0.865880\pi$
$997$	−10.3174	−	38.5049i	−0.326754	−	1.21946i	0.585783	−	0.810468i	$-0.300787\pi$
$998$	−1.48092	−	0.396810i	−0.0468776	−	0.0125608i
$999$	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.o.a.63.1	yes	20
3.2	odd	2		585.2.cf.a.388.5		20
5.2	odd	4		65.2.t.a.37.5	yes	20
5.3	odd	4		325.2.x.b.232.1		20
5.4	even	2		325.2.s.b.193.5		20
13.2	odd	12		845.2.f.e.408.2		20
13.3	even	3		845.2.k.e.268.9		20
13.4	even	6		845.2.o.f.488.5		20
13.5	odd	4		845.2.t.f.418.1		20
13.6	odd	12		65.2.t.a.58.5	yes	20
13.7	odd	12		845.2.t.g.188.1		20
13.8	odd	4		845.2.t.e.418.5		20
13.9	even	3		845.2.o.e.488.1		20
13.10	even	6		845.2.k.d.268.2		20
13.11	odd	12		845.2.f.d.408.9		20
13.12	even	2		845.2.o.g.258.5		20
15.2	even	4		585.2.dp.a.37.1		20
39.32	even	12		585.2.dp.a.253.1		20
65.2	even	12		845.2.k.e.577.9		20
65.7	even	12		845.2.o.g.357.5		20
65.12	odd	4		845.2.t.g.427.1		20
65.17	odd	12		845.2.t.e.657.5		20
65.19	odd	12		325.2.x.b.318.1		20
65.22	odd	12		845.2.t.f.657.1		20
65.32	even	12	inner	65.2.o.a.32.1	✓	20
65.37	even	12		845.2.k.d.577.2		20
65.42	odd	12		845.2.f.e.437.9		20
65.47	even	4		845.2.o.f.587.5		20
65.57	even	4		845.2.o.e.587.1		20
65.58	even	12		325.2.s.b.32.5		20
65.62	odd	12		845.2.f.d.437.2		20
195.32	odd	12		585.2.cf.a.487.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.1	✓	20	65.32	even	12	inner
65.2.o.a.63.1	yes	20	1.1	even	1	trivial
65.2.t.a.37.5	yes	20	5.2	odd	4
65.2.t.a.58.5	yes	20	13.6	odd	12
325.2.s.b.32.5		20	65.58	even	12
325.2.s.b.193.5		20	5.4	even	2
325.2.x.b.232.1		20	5.3	odd	4
325.2.x.b.318.1		20	65.19	odd	12
585.2.cf.a.388.5		20	3.2	odd	2
585.2.cf.a.487.5		20	195.32	odd	12
585.2.dp.a.37.1		20	15.2	even	4
585.2.dp.a.253.1		20	39.32	even	12
845.2.f.d.408.9		20	13.11	odd	12
845.2.f.d.437.2		20	65.62	odd	12
845.2.f.e.408.2		20	13.2	odd	12
845.2.f.e.437.9		20	65.42	odd	12
845.2.k.d.268.2		20	13.10	even	6
845.2.k.d.577.2		20	65.37	even	12
845.2.k.e.268.9		20	13.3	even	3
845.2.k.e.577.9		20	65.2	even	12
845.2.o.e.488.1		20	13.9	even	3
845.2.o.e.587.1		20	65.57	even	4
845.2.o.f.488.5		20	13.4	even	6
845.2.o.f.587.5		20	65.47	even	4
845.2.o.g.258.5		20	13.12	even	2
845.2.o.g.357.5		20	65.7	even	12
845.2.t.e.418.5		20	13.8	odd	4
845.2.t.e.657.5		20	65.17	odd	12
845.2.t.f.418.1		20	13.5	odd	4
845.2.t.f.657.1		20	65.22	odd	12
845.2.t.g.188.1		20	13.7	odd	12
845.2.t.g.427.1		20	65.12	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.04397 - 1.80821i) q^{2} +(0.713171 - 2.66159i) q^{3} +(-1.17974 + 2.04338i) q^{4} +(-0.194361 + 2.22760i) q^{5} +(-5.55724 + 1.48906i) q^{6} +(2.52122 + 1.45563i) q^{7} +0.750585 q^{8} +(-3.97738 - 2.29634i) q^{9} +O(q^{10})\)	\(q+(-1.04397 - 1.80821i) q^{2} +(0.713171 - 2.66159i) q^{3} +(-1.17974 + 2.04338i) q^{4} +(-0.194361 + 2.22760i) q^{5} +(-5.55724 + 1.48906i) q^{6} +(2.52122 + 1.45563i) q^{7} +0.750585 q^{8} +(-3.97738 - 2.29634i) q^{9} +(4.23088 - 1.97411i) q^{10} +(-0.0254491 - 0.00681908i) q^{11} +(4.59727 + 4.59727i) q^{12} +(0.530479 - 3.56631i) q^{13} -6.07853i q^{14} +(5.79036 + 2.10597i) q^{15} +(1.57590 + 2.72954i) q^{16} +(-2.76664 + 0.741318i) q^{17} +9.58924i q^{18} +(1.23878 + 4.62320i) q^{19} +(-4.32254 - 3.02515i) q^{20} +(5.67236 - 5.67236i) q^{21} +(0.0142378 + 0.0531363i) q^{22} +(-0.358680 - 0.0961080i) 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} +(-5.94879 + 3.43454i) q^{28} +(3.62262 - 2.09152i) q^{29} +(-2.23692 - 12.6687i) q^{30} +(-0.835277 - 0.835277i) q^{31} +(4.04096 - 6.99915i) q^{32} +(-0.0362992 + 0.0628721i) q^{33} +(4.22874 + 4.22874i) q^{34} +(-3.73260 + 5.33337i) q^{35} +(9.38457 - 5.41819i) q^{36} +(-5.58739 + 3.22588i) 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} +(-16.1786 - 4.33503i) q^{42} +(1.79436 + 6.69664i) q^{43} +(0.0439574 - 0.0439574i) q^{44} +(5.88839 - 8.41371i) q^{45} +(0.200668 + 0.748902i) q^{46} -0.833377i q^{47} +(8.38880 - 2.24777i) q^{48} +(0.737715 + 1.27776i) q^{49} +(3.57521 + 9.80842i) q^{50} +7.89234i q^{51} +(6.66149 + 5.29130i) q^{52} +(0.902268 + 0.902268i) q^{53} +(8.85092 + 2.37160i) q^{54} +(0.0201365 - 0.0553653i) q^{55} +(1.89239 + 1.09257i) q^{56} +13.1885 q^{57} +(-7.56381 - 4.36697i) q^{58} +(1.44647 - 0.387581i) q^{59} +(-11.1344 + 9.34737i) q^{60} +(5.35090 - 9.26802i) q^{61} +(-0.638351 + 2.38236i) q^{62} +(-6.68524 - 11.5792i) q^{63} -10.5710 q^{64} +(7.84123 + 1.87485i) q^{65} +0.151581 q^{66} +(-6.15845 - 10.6667i) q^{67} +(1.74913 - 6.52784i) q^{68} +(-0.511601 + 0.886118i) q^{69} +(13.5406 + 1.18143i) q^{70} +(-3.57441 + 0.957759i) q^{71} +(-2.98536 - 1.72360i) q^{72} -15.0844 q^{73} +(11.6661 + 6.73544i) q^{74} +(-5.81670 + 12.4893i) q^{75} +(-10.9084 - 2.92289i) q^{76} +(-0.0542370 - 0.0542370i) q^{77} +(2.36245 + 20.6088i) q^{78} +4.25039i q^{79} +(-6.38662 + 2.97996i) q^{80} +(-0.842658 - 1.45953i) q^{81} +(15.8129 - 4.23705i) q^{82} +1.31611i q^{83} +(4.89883 + 18.2827i) q^{84} +(-1.11364 - 6.30706i) q^{85} +(10.2357 - 10.2357i) q^{86} +(-2.98322 - 11.1335i) q^{87} +(-0.0191018 - 0.00511830i) 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} +(-2.81886 + 1.62747i) q^{93} +(-1.50692 + 0.870020i) q^{94} +(-10.5394 + 1.86095i) q^{95} +(-15.7470 - 15.7470i) q^{96} +(0.202734 - 0.351145i) q^{97} +(1.54030 - 2.66788i) q^{98} +(0.0855620 + 0.0855620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Introduction

L-functions

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