LMFDB - Embedded newform 845.2.t.e.418.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(188,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("845.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.t (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
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:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			418.5
Root			$-2.08794i$ of defining polynomial
Character	$\chi$	$=$	845.418
Dual form			845.2.t.e.657.5

$q$-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} +(0.713171 - 2.66159i) q^{3} +(1.17974 - 2.04338i) q^{4} +(-2.22760 - 0.194361i) q^{5} +(-1.48906 - 5.55724i) q^{6} +(1.45563 - 2.52122i) q^{7} -0.750585i q^{8} +(-3.97738 - 2.29634i) q^{9} +(-4.23088 + 1.97411i) q^{10} +(-0.00681908 + 0.0254491i) q^{11} +(-4.59727 - 4.59727i) q^{12} -6.07853i q^{14} +(-2.10597 + 5.79036i) q^{15} +(1.57590 + 2.72954i) q^{16} +(2.76664 - 0.741318i) q^{17} -9.58924 q^{18} +(-4.62320 + 1.23878i) q^{19} +(-3.02515 + 4.32254i) q^{20} +(-5.67236 - 5.67236i) q^{21} +(0.0142378 + 0.0531363i) q^{22} +(0.358680 + 0.0961080i) q^{23} +(-1.99775 - 0.535296i) q^{24} +(4.92445 + 0.865921i) q^{25} +(-3.10321 + 3.10321i) q^{27} +(-3.43454 - 5.94879i) q^{28} +(3.62262 - 2.09152i) q^{29} +(2.23692 + 12.6687i) 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} +(-3.73260 + 5.33337i) q^{35} +(-9.38457 + 5.41819i) q^{36} +(3.22588 + 5.58739i) q^{37} +(-7.06645 + 7.06645i) q^{38} +(-0.145885 + 1.67201i) q^{40} +(-7.57344 - 2.02930i) q^{41} +(-16.1786 - 4.33503i) q^{42} +(-1.79436 - 6.69664i) q^{43} +(0.0439574 + 0.0439574i) q^{44} +(8.41371 + 5.88839i) q^{45} +(0.748902 - 0.200668i) q^{46} -0.833377 q^{47} +(8.38880 - 2.24777i) q^{48} +(-0.737715 - 1.27776i) q^{49} +(9.80842 - 3.57521i) q^{50} -7.89234i q^{51} +(0.902268 + 0.902268i) q^{53} +(-2.37160 + 8.85092i) q^{54} +(0.0201365 - 0.0553653i) q^{55} +(-1.89239 - 1.09257i) q^{56} +13.1885i q^{57} +(4.36697 - 7.56381i) q^{58} +(-0.387581 - 1.44647i) q^{59} +(9.34737 + 11.1344i) q^{60} +(5.35090 - 9.26802i) q^{61} +(0.638351 - 2.38236i) q^{62} +(-11.5792 + 6.68524i) q^{63} +10.5710 q^{64} +0.151581 q^{66} +(10.6667 - 6.15845i) q^{67} +(1.74913 - 6.52784i) q^{68} +(0.511601 - 0.886118i) q^{69} +(-1.18143 + 13.5406i) q^{70} +(-0.957759 - 3.57441i) q^{71} +(-1.72360 + 2.98536i) q^{72} +15.0844i q^{73} +(11.6661 + 6.73544i) q^{74} +(5.81670 - 12.4893i) q^{75} +(-2.92289 + 10.9084i) q^{76} +(0.0542370 + 0.0542370i) q^{77} +4.25039i q^{79} +(-2.97996 - 6.38662i) q^{80} +(-0.842658 - 1.45953i) q^{81} +(-15.8129 + 4.23705i) q^{82} -1.31611 q^{83} +(-18.2827 + 4.89883i) q^{84} +(-6.30706 + 1.11364i) q^{85} +(-10.2357 - 10.2357i) q^{86} +(-2.98322 - 11.1335i) q^{87} +(0.0191018 + 0.00511830i) q^{88} +(-3.23688 - 0.867319i) q^{89} +(21.3610 + 1.86378i) q^{90} +(0.619535 - 0.619535i) q^{92} +(-1.62747 - 2.81886i) q^{93} +(-1.50692 + 0.870020i) q^{94} +(10.5394 - 1.86095i) 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} - 4 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{10} - 8 q^{11} - 24 q^{12} + 8 q^{15} - 2 q^{16} + 10 q^{17} - 16 q^{19} - 12 q^{20} - 4 q^{21} + 16 q^{22} + 2 q^{23} + 28 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 4 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^10 - 8 * q^11 - 24 * q^12 + 8 * q^15 - 2 * q^16 + 10 * q^17 - 16 * q^19 - 12 * q^20 - 4 * q^21 + 16 * q^22 + 2 * q^23 + 28 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 14 * q^30 + 48 * q^32 + 18 * q^33 - 2 * q^34 - 20 * q^35 - 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 28 * q^41 - 56 * q^42 + 22 * q^43 + 36 * q^44 - 6 * q^45 + 8 * q^46 + 40 * q^47 + 28 * q^48 + 18 * q^49 + 78 * q^50 - 10 * q^53 - 12 * q^54 + 26 * q^55 - 8 * q^59 - 28 * q^60 - 16 * q^61 + 40 * q^62 - 36 * q^63 + 20 * q^64 - 32 * q^66 + 18 * q^67 + 28 * q^68 - 16 * q^69 + 12 * q^70 - 56 * q^71 - 4 * q^72 - 18 * q^74 + 34 * q^75 - 80 * q^76 - 28 * q^77 + 110 * q^80 - 14 * q^81 - 22 * q^82 - 48 * q^83 - 32 * q^84 - 28 * q^85 - 60 * q^86 + 62 * q^87 - 50 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 + 48 * q^94 - 14 * q^95 - 56 * q^96 + 66 * q^97 - 30 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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	0.302006	−	0.953306i	$-0.402344\pi$
$2$	1.80821	−	1.04397i	1.27860	−	0.738198i	0.976590	+	0.215108i	$0.0690105\pi$
$3$	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
$5$	−2.22760	−	0.194361i	−0.996215	−	0.0869210i
$5$	−2.22760	−	0.194361i	−0.996215	−	0.0869210i
$6$	−1.48906	−	5.55724i	−0.607905	−	2.26873i
$7$	1.45563	−	2.52122i	0.550176	−	0.952933i	−0.448085	−	0.893991i	$-0.647894\pi$
$7$	1.45563	−	2.52122i	0.550176	−	0.952933i	0.998261	−	0.0589424i	$-0.0187728\pi$
$8$		−	0.750585i		−	0.265372i
$9$	−3.97738	−	2.29634i	−1.32579	−	0.765447i
$10$	−4.23088	+	1.97411i	−1.33792	+	0.624267i
$11$	−0.00681908	+	0.0254491i	−0.00205603	+	0.00767321i	−0.966946	−	0.254980i	$-0.917931\pi$
$11$	−0.00681908	+	0.0254491i	−0.00205603	+	0.00767321i	0.964890	+	0.262654i	$0.0845976\pi$
$12$	−4.59727	−	4.59727i	−1.32712	−	1.32712i
$13$		0			0
$13$		0			0
$14$		−	6.07853i		−	1.62456i
$15$	−2.10597	+	5.79036i	−0.543760	+	1.49506i
$16$	1.57590	+	2.72954i	0.393975	+	0.682384i
$17$	2.76664	−	0.741318i	0.671008	−	0.179796i	0.0927992	−	0.995685i	$-0.470419\pi$
$17$	2.76664	−	0.741318i	0.671008	−	0.179796i	0.578209	+	0.815889i	$0.303752\pi$
$18$	−9.58924			−2.26020
$19$	−4.62320	+	1.23878i	−1.06063	+	0.284196i	−0.746640	−	0.665229i	$-0.768334\pi$
$19$	−4.62320	+	1.23878i	−1.06063	+	0.284196i	−0.313995	+	0.949425i	$0.601667\pi$
$20$	−3.02515	+	4.32254i	−0.676445	+	0.966548i
$21$	−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	0.296020	−	0.955182i	$-0.404340\pi$
$23$	0.358680	+	0.0961080i	0.0747899	+	0.0200399i	−0.221230	+	0.975222i	$0.571007\pi$
$24$	−1.99775	−	0.535296i	−0.407789	−	0.109267i
$25$	4.92445	+	0.865921i	0.984889	+	0.173184i
$26$		0			0
$27$	−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	$-0.539700\pi$
$29$	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	$-0.716170\pi$
$31$	0.835277	−	0.835277i	0.150020	−	0.150020i	0.778127	+	0.628107i	$0.216170\pi$
$32$	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
$35$	−3.73260	+	5.33337i	−0.630924	+	0.901505i
$36$	−9.38457	+	5.41819i	−1.56410	+	0.903031i
$37$	3.22588	+	5.58739i	0.530332	+	0.918561i	0.999374	+	0.0353856i	$0.0112659\pi$
$37$	3.22588	+	5.58739i	0.530332	+	0.918561i	−0.469042	+	0.883176i	$0.655401\pi$
$38$	−7.06645	+	7.06645i	−1.14633	+	1.14633i
$39$		0			0
$40$	−0.145885	+	1.67201i	−0.0230664	+	0.264368i
$41$	−7.57344	−	2.02930i	−1.18277	−	0.316923i	−0.386747	−	0.922186i	$-0.626401\pi$
$41$	−7.57344	−	2.02930i	−1.18277	−	0.316923i	−0.796026	+	0.605263i	$0.793068\pi$
$42$	−16.1786	−	4.33503i	−2.49641	−	0.668910i
$43$	−1.79436	−	6.69664i	−0.273637	−	1.02123i	−0.956749	−	0.290915i	$-0.906040\pi$
$43$	−1.79436	−	6.69664i	−0.273637	−	1.02123i	0.683112	−	0.730314i	$-0.260626\pi$
$44$	0.0439574	+	0.0439574i	0.00662683	+	0.00662683i
$45$	8.41371	+	5.88839i	1.25424	+	0.877789i
$46$	0.748902	−	0.200668i	0.110420	−	0.0295868i
$47$	−0.833377			−0.121561			−0.0607803	−	0.998151i	$-0.519359\pi$
$47$	−0.833377			−0.121561			−0.0607803	+	0.998151i	$0.519359\pi$
$48$	8.38880	−	2.24777i	1.21082	−	0.324438i
$49$	−0.737715	−	1.27776i	−0.105388	−	0.182537i
$50$	9.80842	−	3.57521i	1.38712	−	0.505611i
$51$		−	7.89234i		−	1.10515i
$52$		0			0
$53$	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	$0.722069\pi$
$54$	−2.37160	+	8.85092i	−0.322733	+	1.20446i
$55$	0.0201365	−	0.0553653i	0.00271521	−	0.00746545i
$56$	−1.89239	−	1.09257i	−0.252882	−	0.146001i
$57$			13.1885i			1.74686i
$58$	4.36697	−	7.56381i	0.573411	−	0.993176i
$59$	−0.387581	−	1.44647i	−0.0504588	−	0.188315i	0.936096	−	0.351744i	$-0.114411\pi$
$59$	−0.387581	−	1.44647i	−0.0504588	−	0.188315i	−0.986555	+	0.163429i	$0.947745\pi$
$60$	9.34737	+	11.1344i	1.20674	+	1.43745i
$61$	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
$63$	−11.5792	+	6.68524i	−1.45884	+	0.842262i
$64$	10.5710			1.32137
$65$		0			0
$66$	0.151581			0.0186583
$67$	10.6667	−	6.15845i	1.30315	−	0.752374i	0.322207	−	0.946669i	$-0.395575\pi$
$67$	10.6667	−	6.15845i	1.30315	−	0.752374i	0.980943	+	0.194295i	$0.0622419\pi$
$68$	1.74913	−	6.52784i	0.212113	−	0.791617i
$69$	0.511601	−	0.886118i	0.0615895	−	0.106676i
$70$	−1.18143	+	13.5406i	−0.141208	+	1.61841i
$71$	−0.957759	−	3.57441i	−0.113665	−	0.424204i	0.885518	−	0.464604i	$-0.153803\pi$
$71$	−0.957759	−	3.57441i	−0.113665	−	0.424204i	−0.999184	+	0.0404002i	$0.987137\pi$
$72$	−1.72360	+	2.98536i	−0.203128	+	0.351828i
$73$			15.0844i			1.76550i	0.469844	+	0.882750i	$0.344310\pi$
$73$			15.0844i			1.76550i	−0.469844	+	0.882750i	$0.655690\pi$
$74$	11.6661	+	6.73544i	1.35616	+	0.782979i
$75$	5.81670	−	12.4893i	0.671655	−	1.44214i
$76$	−2.92289	+	10.9084i	−0.335279	+	1.25128i
$77$	0.0542370	+	0.0542370i	0.00618088	+	0.00618088i
$78$		0			0
$79$			4.25039i			0.478207i	0.970994	+	0.239103i	$0.0768534\pi$
$79$			4.25039i			0.478207i	−0.970994	+	0.239103i	$0.923147\pi$
$80$	−2.97996	−	6.38662i	−0.333170	−	0.714046i
$81$	−0.842658	−	1.45953i	−0.0936286	−	0.162170i
$82$	−15.8129	+	4.23705i	−1.74624	+	0.467904i
$83$	−1.31611			−0.144462			−0.0722311	−	0.997388i	$-0.523012\pi$
$83$	−1.31611			−0.144462			−0.0722311	+	0.997388i	$0.523012\pi$
$84$	−18.2827	+	4.89883i	−1.99480	+	0.534506i
$85$	−6.30706	+	1.11364i	−0.684096	+	0.120791i
$86$	−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
$89$	−3.23688	−	0.867319i	−0.343109	−	0.0919357i	0.0831499	−	0.996537i	$-0.473502\pi$
$89$	−3.23688	−	0.867319i	−0.343109	−	0.0919357i	−0.426259	+	0.904601i	$0.640169\pi$
$90$	21.3610	+	1.86378i	2.25165	+	0.196459i
$91$		0			0
$92$	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
$95$	10.5394	−	1.86095i	1.08132	−	0.190929i
$96$	15.7470	−	15.7470i	1.60717	−	1.60717i
$97$	0.351145	+	0.202734i	0.0356534	+	0.0205845i	0.517721	−	0.855550i	$-0.326781\pi$
$97$	0.351145	+	0.202734i	0.0356534	+	0.0205845i	−0.482067	+	0.876134i	$0.660114\pi$
$98$	−2.66788	−	1.54030i	−0.269497	−	0.155594i
$99$	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	−0.617674	−	0.786434i	$-0.711925\pi$
$101$	−2.46663	+	1.42411i	−0.245439	+	0.141704i	0.372235	+	0.928139i	$0.378592\pi$
$102$	−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			0
$105$	11.5333	+	13.7383i	1.12553	+	1.34072i
$106$	2.57343	+	0.689548i	0.249953	+	0.0669748i
$107$	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	0.971414	−	0.237391i	$-0.0762921\pi$
$109$	7.66343	+	7.66343i	0.734024	+	0.734024i	−0.237391	+	0.971414i	$0.576292\pi$
$110$	−0.0213886	−	0.121134i	−0.00203932	−	0.0115497i
$111$	17.1720	−	4.60121i	1.62989	−	0.436728i
$112$	9.17570			0.867022
$113$	−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
$115$	−0.780318	−	0.283804i	−0.0727650	−	0.0264649i
$116$		−	9.86983i		−	0.916390i
$117$		0			0
$118$	−2.21090	−	2.21090i	−0.203530	−	0.203530i
$119$	2.15817	−	8.05440i	0.197839	−	0.738345i
$120$	4.34616	+	1.58071i	0.396748	+	0.144299i
$121$	9.52568	+	5.49965i	0.865971	+	0.499968i
$122$		−	22.3447i		−	2.02299i
$123$	−10.8023	+	18.7102i	−0.974012	+	1.68704i
$124$	−0.721372	−	2.69220i	−0.0647811	−	0.241766i
$125$	−10.8014	−	2.88605i	−0.966109	−	0.258136i
$126$	−13.9584	+	24.1766i	−1.24351	+	2.15382i
$127$	3.88938	−	14.5154i	0.345126	−	1.28803i	−0.547338	−	0.836912i	$-0.684359\pi$
$127$	3.88938	−	14.5154i	0.345126	−	1.28803i	0.892464	−	0.451118i	$-0.148975\pi$
$128$	5.11621	−	2.95384i	0.452213	−	0.261085i
$129$	−19.1034			−1.68196
$130$		0			0
$131$	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
$133$	−3.60642	+	13.4593i	−0.312716	+	1.16707i
$134$	12.8585	−	22.2715i	1.11080	−	1.92397i
$135$	7.51588	−	6.30959i	0.646864	−	0.543043i
$136$	−0.556423	−	2.07660i	−0.0477128	−	0.178067i
$137$	−7.28411	+	12.6164i	−0.622323	+	1.07790i	0.366729	+	0.930328i	$0.380478\pi$
$137$	−7.28411	+	12.6164i	−0.622323	+	1.07790i	−0.989052	+	0.147568i	$0.952856\pi$
$138$		−	2.13638i		−	0.181861i
$139$	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
$141$	−0.594341	+	2.21811i	−0.0500525	+	0.186799i
$142$	−5.46340	−	5.46340i	−0.458478	−	0.458478i
$143$		0			0
$144$		−	14.4752i		−	1.20627i
$145$	−8.47627	+	3.95498i	−0.703916	+	0.328443i
$146$	15.7477	+	27.2758i	1.30329	+	2.25736i
$147$	−3.92699	+	1.05223i	−0.323893	+	0.0867868i
$148$	15.2228			1.25131
$149$	5.65780	−	1.51600i	0.463505	−	0.124196i	−0.0195066	−	0.999810i	$-0.506210\pi$
$149$	5.65780	−	1.51600i	0.463505	−	0.124196i	0.483012	+	0.875614i	$0.339543\pi$
$150$	−2.52066	−	28.6557i	−0.205811	−	2.33973i
$151$	2.92436	+	2.92436i	0.237981	+	0.237981i	0.816014	−	0.578033i	$-0.196179\pi$
$151$	2.92436	+	2.92436i	0.237981	+	0.237981i	−0.578033	+	0.816014i	$0.696179\pi$
$152$	0.929812	+	3.47011i	0.0754177	+	0.281463i
$153$	−12.7063	−	3.40464i	−1.02724	−	0.275249i
$154$	0.154693	+	0.0414500i	0.0124655	+	0.00334013i
$155$	−2.02301	+	1.69832i	−0.162492	+	0.136412i
$156$		0			0
$157$	−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
$160$	−14.8059	−	10.3620i	−1.17051	−	0.819191i
$161$	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	0.630345	−	0.776315i	$-0.282914\pi$
$163$	3.48809	+	2.01385i	0.273208	+	0.157737i	−0.357137	+	0.934052i	$0.616247\pi$
$164$	−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
$167$	−11.9198	−	20.6458i	−0.922385	−	1.59762i	−0.795714	−	0.605672i	$-0.792904\pi$
$167$	−11.9198	−	20.6458i	−0.922385	−	1.59762i	−0.126670	−	0.991945i	$-0.540429\pi$
$168$	−4.25759	+	4.25759i	−0.328480	+	0.328480i
$169$		0			0
$170$	−10.2419	+	8.59806i	−0.785515	+	0.659441i
$171$	21.2329	+	5.68933i	1.62372	+	0.435074i
$172$	−15.8006	−	4.23377i	−1.20479	−	0.322822i
$173$	−0.210271	−	0.784743i	−0.0159866	−	0.0596629i	0.957472	−	0.288527i	$-0.0931655\pi$
$173$	−0.210271	−	0.784743i	−0.0159866	−	0.0596629i	−0.973458	+	0.228864i	$0.926499\pi$
$174$	−17.0174	−	17.0174i	−1.29008	−	1.29008i
$175$	9.35135	−	11.1552i	0.706896	−	0.843252i
$176$	−0.0802105	+	0.0214923i	−0.00604610	+	0.00162005i
$177$	−4.12633			−0.310154
$178$	−6.75841	+	1.81091i	−0.506564	+	0.135733i
$179$	−3.28130	−	5.68337i	−0.245256	−	0.424795i	0.716948	−	0.697127i	$-0.245539\pi$
$179$	−3.28130	−	5.68337i	−0.245256	−	0.424795i	−0.962203	+	0.272332i	$0.912205\pi$
$180$	21.9582	−	10.2456i	1.63667	−	0.763660i
$181$			1.56627i			0.116420i	0.998304	+	0.0582099i	$0.0185393\pi$
$181$			1.56627i			0.116420i	−0.998304	+	0.0582099i	$0.981461\pi$
$182$		0			0
$183$	−20.8516	−	20.8516i	−1.54139	−	1.54139i
$184$	0.0721373	−	0.269220i	0.00531803	−	0.0198472i
$185$	−6.10002	−	13.0735i	−0.448482	−	0.961182i
$186$	−5.88561	−	3.39806i	−0.431554	−	0.249158i
$187$			0.0754637i			0.00551845i
$188$	−0.983171	+	1.70290i	−0.0717051	+	0.124197i
$189$	3.30677	+	12.3410i	0.240532	+	0.897678i
$190$	17.1147	−	14.3678i	1.24163	−	1.04235i
$191$	−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
$193$	14.4037	−	8.31597i	1.03680	−	0.598597i	0.117875	−	0.993028i	$-0.462392\pi$
$193$	14.4037	−	8.31597i	1.03680	−	0.598597i	0.918925	+	0.394432i	$0.129058\pi$
$194$	0.846590			0.0607816
$195$		0			0
$196$	−3.48126			−0.248661
$197$	−22.2821	+	12.8646i	−1.58753	+	0.916563i	−0.593821	+	0.804597i	$0.702381\pi$
$197$	−22.2821	+	12.8646i	−1.58753	+	0.916563i	−0.993712	+	0.111966i	$0.964285\pi$
$198$	0.0653898	−	0.244038i	0.00464705	−	0.0173430i
$199$	−13.8914	+	24.0606i	−0.984736	+	1.70561i	−0.341632	+	0.939834i	$0.610980\pi$
$199$	−13.8914	+	24.0606i	−0.984736	+	1.70561i	−0.643104	+	0.765779i	$0.722354\pi$
$200$	0.649947	−	3.69622i	0.0459582	−	0.261362i
$201$	−8.78406	−	32.7825i	−0.619580	−	2.31230i
$202$	−2.97346	+	5.15018i	−0.209212	+	0.362365i
$203$		−	12.1779i		−	0.854722i
$204$	−16.1270	−	9.31094i	−1.12912	−	0.651896i
$205$	16.4762	+	5.99246i	1.15075	+	0.418531i
$206$	−4.30646	+	16.0719i	−0.300045	+	1.11978i
$207$	−1.20591	−	1.20591i	−0.0838165	−	0.0838165i
$208$		0			0
$209$		−	0.126104i		−	0.00872278i
$210$	35.1969	+	12.8012i	2.42882	+	0.883369i
$211$	−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
$213$	−10.1967			−0.698663
$214$	26.3546	−	7.06170i	1.80157	−	0.482728i
$215$	2.69556	+	15.2662i	0.183835	+	1.04115i
$216$	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
$219$	40.1486	+	10.7578i	2.71299	+	0.726944i
$220$	−0.0893761	−	0.106463i	−0.00602573	−	0.00717776i
$221$		0			0
$222$	26.2469	−	26.2469i	1.76158	−	1.76158i
$223$	7.01198	+	12.1451i	0.469557	+	0.813296i	0.999394	−	0.0348032i	$-0.0110804\pi$
$223$	7.01198	+	12.1451i	0.469557	+	0.813296i	−0.529838	+	0.848099i	$0.677747\pi$
$224$	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
$227$	13.8488	+	7.99560i	0.919176	+	0.530687i	0.883372	−	0.468672i	$-0.155267\pi$
$227$	13.8488	+	7.99560i	0.919176	+	0.530687i	0.0358042	+	0.999359i	$0.488601\pi$
$228$	26.9491	+	15.5591i	1.78475	+	1.03043i
$229$	−2.31063	+	2.31063i	−0.152691	+	0.152691i	−0.779319	−	0.626628i	$-0.784435\pi$
$229$	−2.31063	+	2.31063i	−0.152691	+	0.152691i	0.626628	+	0.779319i	$0.284435\pi$
$230$	−1.70726	+	0.301451i	−0.112573	+	0.0198771i
$231$	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	$0.941049\pi$
$234$		0			0
$235$	1.85644	+	0.161976i	0.121100	+	0.0105662i
$236$	−3.41293	−	0.914493i	−0.222163	−	0.0595284i
$237$	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	0.553679	−	0.832730i	$-0.313224\pi$
$239$	−4.31403	−	4.31403i	−0.279052	−	0.279052i	−0.832730	+	0.553679i	$0.813224\pi$
$240$	−19.1238	+	3.37669i	−1.23444	+	0.217964i
$241$	8.74246	−	2.34253i	0.563151	−	0.150896i	0.0339976	−	0.999422i	$-0.489176\pi$
$241$	8.74246	−	2.34253i	0.563151	−	0.150896i	0.529154	+	0.848526i	$0.322509\pi$
$242$	22.9659			1.47630
$243$	−17.2028	+	4.60948i	−1.10356	+	0.295699i
$244$	−12.6254	−	21.8678i	−0.808256	−	1.39994i
$245$	1.39499	+	2.98973i	0.0891227	+	0.191007i
$246$			45.1091i			2.87605i
$247$		0			0
$248$	−0.626947	−	0.626947i	−0.0398112	−	0.0398112i
$249$	−0.938615	+	3.50296i	−0.0594823	+	0.221991i
$250$	−22.5442	+	6.05777i	−1.42582	+	0.383127i
$251$	−0.503450	−	0.290667i	−0.0317775	−	0.0183467i	0.484027	−	0.875053i	$-0.339174\pi$
$251$	−0.503450	−	0.290667i	−0.0317775	−	0.0183467i	−0.515805	+	0.856706i	$0.672507\pi$
$252$			31.5475i			1.98730i
$253$	−0.00489173	+	0.00847273i	−0.000307541	+	0.000532676i
$254$	−8.12078	−	30.3072i	−0.509543	−	1.90164i
$255$	−1.53397	+	17.5810i	−0.0960607	+	1.10097i
$256$	−4.40353	+	7.62714i	−0.275221	+	0.476696i
$257$	−4.50394	+	16.8089i	−0.280948	+	1.04851i	0.670801	+	0.741637i	$0.265950\pi$
$257$	−4.50394	+	16.8089i	−0.280948	+	1.04851i	−0.951750	+	0.306876i	$0.900716\pi$
$258$	−34.5429	+	19.9434i	−2.15055	+	1.24162i
$259$	18.7828			1.16710
$260$		0			0
$261$	−19.2114			−1.18915
$262$	16.3541	−	9.44205i	1.01036	−	0.583332i
$263$	−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
$265$	−1.83453	−	2.18526i	−0.112694	−	0.134240i
$266$	7.52998	+	28.1023i	0.461692	+	1.72306i
$267$	−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	$-0.143578\pi$
$269$	15.9495	+	9.20844i	0.972457	+	0.561448i	0.0724726	+	0.997370i	$0.476911\pi$
$270$	7.00326	−	19.2554i	0.426205	−	1.17185i
$271$	6.70594	−	25.0269i	0.407357	−	1.52028i	−0.392310	−	0.919833i	$-0.628324\pi$
$271$	6.70594	−	25.0269i	0.407357	−	1.52028i	0.799667	−	0.600444i	$-0.205010\pi$
$272$	6.38339	+	6.38339i	0.387050	+	0.387050i
$273$		0			0
$274$			30.4175i			1.83759i
$275$	−0.0556171	+	0.119418i	−0.00335384	+	0.00720119i
$276$	−1.20711	−	2.09078i	−0.0726598	−	0.125850i
$277$	22.6257	−	6.06254i	1.35945	−	0.364263i	0.495833	−	0.868418i	$-0.334863\pi$
$277$	22.6257	−	6.06254i	1.35945	−	0.364263i	0.863613	+	0.504155i	$0.168196\pi$
$278$	14.4372			0.865884
$279$	−5.24030	+	1.40413i	−0.313728	+	0.0840632i
$280$	4.00315	+	2.80163i	0.239234	+	0.167430i
$281$	9.93011	+	9.93011i	0.592381	+	0.592381i	0.938274	−	0.345893i	$-0.112424\pi$
$281$	9.93011	+	9.93011i	0.592381	+	0.592381i	−0.345893	+	0.938274i	$0.612424\pi$
$282$	1.24095	+	4.63128i	0.0738973	+	0.275789i
$283$	−3.97170	−	1.06421i	−0.236093	−	0.0632610i	0.138832	−	0.990316i	$-0.455665\pi$
$283$	−3.97170	−	1.06421i	−0.236093	−	0.0632610i	−0.374926	+	0.927055i	$0.622332\pi$
$284$	−8.43376	−	2.25982i	−0.500452	−	0.134096i
$285$	2.56334	−	29.3788i	0.151839	−	1.74025i
$286$		0			0
$287$	−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
$290$	−11.1980	+	16.0004i	−0.657568	+	0.939576i
$291$	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	−0.167936	−	0.985798i	$-0.553710\pi$
$293$	−18.9253	−	10.9265i	−1.10563	−	0.638336i	−0.937694	+	0.347462i	$0.887043\pi$
$294$	−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
$297$	−0.0578131	−	0.100135i	−0.00335466	−	0.00581044i
$298$	8.64782	−	8.64782i	0.500955	−	0.500955i
$299$		0			0
$300$	−18.6581	−	26.6199i	−1.07723	−	1.53690i
$301$	−19.4957	−	5.22385i	−1.12371	−	0.301098i
$302$	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
$305$	−13.7210	+	19.6055i	−0.785664	+	1.12261i
$306$	−26.5299	+	7.10868i	−1.51662	+	0.406376i
$307$	6.98281			0.398530			0.199265	−	0.979946i	$-0.436145\pi$
$307$	6.98281			0.398530			0.199265	+	0.979946i	$0.436145\pi$
$308$	0.174812	−	0.0468408i	0.00996085	−	0.00266900i
$309$	10.9793	+	19.0167i	0.624590	+	1.08182i
$310$	−1.88503	+	5.18288i	−0.107063	+	0.294368i
$311$			21.2824i			1.20681i	0.797434	+	0.603406i	$0.206190\pi$
$311$			21.2824i			1.20681i	−0.797434	+	0.603406i	$0.793810\pi$
$312$		0			0
$313$	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	$0.500487\pi$
$314$	−3.51442	+	13.1160i	−0.198330	+	0.740177i
$315$	27.0932	−	12.6415i	1.52653	−	0.712270i
$316$	8.68515	+	5.01437i	0.488578	+	0.282080i
$317$		−	15.6715i		−	0.880198i	−0.897949	−	0.440099i	$-0.854943\pi$
$317$		−	15.6715i		−	0.880198i	0.897949	−	0.440099i	$-0.145057\pi$
$318$	3.67059	−	6.35765i	0.205836	−	0.356519i
$319$	0.0285245	+	0.106455i	0.00159706	+	0.00596032i
$320$	−23.5480	−	2.05459i	−1.31637	−	0.114855i
$321$	18.0038	−	31.1834i	1.00487	−	1.74049i
$322$	0.584195	−	2.18025i	0.0325559	−	0.121500i
$323$	−11.8724	+	6.85452i	−0.660597	+	0.381396i
$324$	−3.97648			−0.220915
$325$		0			0
$326$	8.40958			0.465763
$327$	25.8623	−	14.9316i	1.43019	−	0.825719i
$328$	−1.52316	+	5.68451i	−0.0841025	+	0.313875i
$329$	−1.21309	+	2.10113i	−0.0668797	+	0.115839i
$330$	−0.337663	−	0.0294615i	−0.0185877	−	0.00162180i
$331$	0.871389	+	3.25207i	0.0478959	+	0.178750i	0.985730	−	0.168334i	$-0.0538387\pi$
$331$	0.871389	+	3.25207i	0.0478959	+	0.178750i	−0.937834	+	0.347084i	$0.887172\pi$
$332$	−1.55268	+	2.68932i	−0.0852142	+	0.147595i
$333$		−	29.6309i		−	1.62376i
$334$	−43.1071	−	24.8879i	−2.35871	−	1.36180i
$335$	−24.9583	+	11.6454i	−1.36362	+	0.636255i
$336$	6.54384	−	24.4220i	0.356996	−	1.33233i
$337$	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	$0.660446\pi$
$338$		0			0
$339$			23.9443i			1.30048i
$340$	−5.16513	+	14.2015i	−0.280119	+	0.770184i
$341$	0.0155613	+	0.0269529i	0.000842690	+	0.00145958i
$342$	44.3330	−	11.8790i	2.39725	−	0.642342i
$343$	16.0835			0.868425
$344$	−5.02640	+	1.34682i	−0.271005	+	0.0726157i
$345$	−1.31187	+	1.87449i	−0.0706288	+	0.100919i
$346$	−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
$349$	−8.04794	−	2.15644i	−0.430796	−	0.115432i	0.0369035	−	0.999319i	$-0.488251\pi$
$349$	−8.04794	−	2.15644i	−0.430796	−	0.115432i	−0.467700	+	0.883887i	$0.654917\pi$
$350$	5.26352	−	29.9334i	0.281347	−	1.60001i
$351$		0			0
$352$	−0.150567	+	0.150567i	−0.00802524	+	0.00802524i
$353$	−2.58427	−	4.47609i	−0.137547	−	0.238238i	0.789021	−	0.614367i	$-0.210588\pi$
$353$	−2.58427	−	4.47609i	−0.137547	−	0.238238i	−0.926567	+	0.376129i	$0.877255\pi$
$354$	−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
$357$	−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	−0.938138	−	0.346261i	$-0.887451\pi$
$359$	−11.2145	+	11.2145i	−0.591877	+	0.591877i	0.346261	+	0.938138i	$0.387451\pi$
$360$	4.41974	−	6.31521i	0.232941	−	0.332841i
$361$	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
$364$		0			0
$365$	2.93183	−	33.6022i	0.153459	−	1.75882i
$366$	−59.4724	−	15.9356i	−3.10867	−	0.832966i
$367$	−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
$370$	−24.6784	−	17.2713i	−1.28297	−	0.897895i
$371$	3.58819	−	0.961452i	0.186289	−	0.0499161i
$372$	−7.67999			−0.398189
$373$	−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
$375$	−15.3848	+	26.6907i	−0.794465	+	1.37830i
$376$			0.625521i			0.0322588i
$377$		0			0
$378$	18.8630	+	18.8630i	0.970207	+	0.970207i
$379$	−4.01535	+	14.9855i	−0.206255	+	0.769754i	0.782809	+	0.622263i	$0.213786\pi$
$379$	−4.01535	+	14.9855i	−0.206255	+	0.769754i	−0.989063	+	0.147491i	$0.952880\pi$
$380$	8.63121	−	23.7315i	0.442772	−	1.21740i
$381$	−35.8602	−	20.7039i	−1.83717	−	1.06069i
$382$			9.64728i			0.493598i
$383$	11.2034	−	19.4048i	0.572465	−	0.991538i	−0.423847	−	0.905734i	$-0.639321\pi$
$383$	11.2034	−	19.4048i	0.572465	−	0.991538i	0.996312	−	0.0858043i	$-0.0273460\pi$
$384$	−4.21319	−	15.7238i	−0.215004	−	0.802404i
$385$	−0.110277	−	0.131360i	−0.00562023	−	0.00669473i
$386$	17.3632	−	30.0740i	0.883766	−	1.53073i
$387$	−8.24093	+	30.7556i	−0.418910	+	1.56339i
$388$	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	$0.560164\pi$
$390$		0			0
$391$	1.06358			0.0537878
$392$	−0.959068	+	0.553718i	−0.0484402	+	0.0279670i
$393$	6.45019	−	24.0724i	0.325369	−	1.21429i
$394$	−26.8604	+	46.5236i	−1.35321	+	2.34383i
$395$	0.826112	−	9.46820i	0.0415662	−	0.476397i
$396$	−0.0738941	−	0.275776i	−0.00371332	−	0.0138583i
$397$	8.77205	−	15.1936i	0.440257	−	0.762547i	−0.557452	−	0.830209i	$-0.688221\pi$
$397$	8.77205	−	15.1936i	0.440257	−	0.762547i	0.997708	+	0.0676626i	$0.0215541\pi$
$398$			58.0088i			2.90772i
$399$	33.2512	+	19.1976i	1.66464	+	0.961083i
$400$	5.39687	+	14.8061i	0.269843	+	0.740303i
$401$	−7.11268	+	26.5449i	−0.355190	+	1.32559i	0.525055	+	0.851068i	$0.324045\pi$
$401$	−7.11268	+	26.5449i	−0.355190	+	1.32559i	−0.880245	+	0.474520i	$0.842622\pi$
$402$	−50.1074	−	50.1074i	−2.49913	−	2.49913i
$403$		0			0
$404$			6.72034i			0.334350i
$405$	1.59343	+	3.41503i	0.0791783	+	0.169694i
$406$	−12.7134	−	22.0202i	−0.630954	−	1.09284i
$407$	−0.164192	+	0.0439951i	−0.00813869	+	0.00218076i
$408$	−5.92388			−0.293276
$409$	−16.1654	+	4.33151i	−0.799329	+	0.214179i	−0.635289	−	0.772274i	$-0.719119\pi$
$409$	−16.1654	+	4.33151i	−0.799329	+	0.214179i	−0.164039	+	0.986454i	$0.552452\pi$
$410$	36.0484	−	6.36505i	1.78030	−	0.314348i
$411$	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
$414$	−3.43947	−	0.921603i	−0.169041	−	0.0452943i
$415$	2.93178	+	0.255802i	0.143916	+	0.0125568i
$416$		0			0
$417$	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	$-0.914957\pi$
$419$	−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	$-0.844504\pi$
$421$	−8.48901	+	8.48901i	−0.413729	+	0.413729i	0.469306	+	0.883035i	$0.344504\pi$
$422$	−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
$425$	14.2661	−	1.25489i	0.692007	−	0.0608713i
$426$	−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			0
$430$	20.8116	+	24.7904i	1.00362	+	1.19550i
$431$	11.3625	+	3.04457i	0.547311	+	0.146652i	0.521870	−	0.853025i	$-0.325234\pi$
$431$	11.3625	+	3.04457i	0.547311	+	0.146652i	0.0254407	+	0.999676i	$0.491901\pi$
$432$	−13.3607	−	3.57999i	−0.642816	−	0.172242i
$433$	−5.01355	−	18.7108i	−0.240936	−	0.899184i	−0.975383	−	0.220518i	$-0.929225\pi$
$433$	−5.01355	−	18.7108i	−0.240936	−	0.899184i	0.734447	−	0.678666i	$-0.237442\pi$
$434$	−5.07726	−	5.07726i	−0.243716	−	0.243716i
$435$	4.48151	+	25.3810i	0.214872	+	1.21692i
$436$	24.7001	−	6.61838i	1.18292	−	0.316963i
$437$	−1.77731			−0.0850201
$438$	83.8278	−	22.4616i	4.00545	−	1.07326i
$439$	−11.9244	−	20.6537i	−0.569121	−	0.985747i	−0.996653	−	0.0817464i	$-0.973950\pi$
$439$	−11.9244	−	20.6537i	−0.569121	−	0.985747i	0.427532	−	0.904000i	$-0.359383\pi$
$440$	−0.0415564	−	0.0151142i	−0.00198112	−	0.000720541i
$441$			6.77618i			0.322675i
$442$		0			0
$443$	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	$0.619546\pi$
$444$	10.8565	−	40.5170i	0.515227	−	1.92285i
$445$	7.04192	+	2.56117i	0.333819	+	0.121411i
$446$	25.3582	+	14.6406i	1.20075	+	0.693251i
$447$		−	16.1399i		−	0.763392i
$448$	15.3874	−	26.6518i	0.726987	−	1.25918i
$449$	10.5906	+	39.5246i	0.499801	+	1.86528i	0.501284	+	0.865283i	$0.332861\pi$
$449$	10.5906	+	39.5246i	0.499801	+	1.86528i	−0.00148324	+	0.999999i	$0.500472\pi$
$450$	−47.2217	−	8.30352i	−2.22605	−	0.391432i
$451$	0.103288	−	0.178900i	0.00486363	−	0.00842405i
$452$	−5.30662	+	19.8046i	−0.249603	+	0.931529i
$453$	9.86901	−	5.69788i	0.463687	−	0.267710i
$454$	33.3886			1.56701
$455$		0			0
$456$	9.89912			0.463569
$457$	7.15685	−	4.13201i	0.334783	−	0.193287i	−0.323180	−	0.946338i	$-0.604752\pi$
$457$	7.15685	−	4.13201i	0.334783	−	0.193287i	0.657963	+	0.753051i	$0.271418\pi$
$458$	−1.76587	+	6.59033i	−0.0825139	+	0.307946i
$459$	−6.28500	+	10.8859i	−0.293359	+	0.508112i
$460$	−1.50049	+	1.25967i	−0.0699608	+	0.0587322i
$461$	−4.90987	−	18.3239i	−0.228676	−	0.853429i	−0.980899	−	0.194520i	$-0.937685\pi$
$461$	−4.90987	−	18.3239i	−0.228676	−	0.853429i	0.752223	−	0.658909i	$-0.228982\pi$
$462$	0.220646	−	0.382170i	0.0102654	−	0.0177801i
$463$		−	24.9284i		−	1.15852i	−0.815142	−	0.579261i	$-0.803341\pi$
$463$		−	24.9284i		−	1.15852i	0.815142	−	0.579261i	$-0.196659\pi$
$464$	11.4178	+	6.59205i	0.530056	+	0.306028i
$465$	3.07748	+	6.59563i	0.142715	+	0.305865i
$466$	−13.6142	+	50.8091i	−0.630668	+	2.35368i
$467$	−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	$-0.566188\pi$
$468$		0			0
$469$		−	35.8577i		−	1.65575i
$470$	3.52592	−	1.64517i	0.162639	−	0.0758862i
$471$	8.95998	+	15.5191i	0.412854	+	0.715084i
$472$	−1.08570	+	0.290913i	−0.0499735	+	0.0133904i
$473$	0.182660			0.00839870
$474$	23.6204	−	6.32908i	1.08492	−	0.290704i
$475$	−23.8394	+	2.09700i	−1.09383	+	0.0962167i
$476$	−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
$479$	−4.50760	−	1.20781i	−0.205957	−	0.0551861i	0.154365	−	0.988014i	$-0.450667\pi$
$479$	−4.50760	−	1.20781i	−0.205957	−	0.0551861i	−0.360323	+	0.932828i	$0.617333\pi$
$480$	−38.1387	+	32.0175i	−1.74078	+	1.46139i
$481$		0			0
$482$	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
$485$	−0.742808	−	0.519859i	−0.0337292	−	0.0236056i
$486$	−26.2941	+	26.2941i	−1.19273	+	1.19273i
$487$	−12.6563	−	7.30711i	−0.573511	−	0.331117i	0.185040	−	0.982731i	$-0.440759\pi$
$487$	−12.6563	−	7.30711i	−0.573511	−	0.331117i	−0.758550	+	0.651615i	$0.774092\pi$
$488$	−6.95644	−	4.01630i	−0.314903	−	0.181810i
$489$	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	−0.0505834	−	0.998720i	$-0.516108\pi$
$491$	17.4840	−	10.0944i	0.789042	−	0.455553i	0.839625	+	0.543166i	$0.182775\pi$
$492$	25.4879	+	44.1464i	1.14908	+	1.99027i
$493$	8.47199	−	8.47199i	0.381559	−	0.381559i
$494$		0			0
$495$	−0.207228	+	0.173968i	−0.00931422	+	0.00781930i
$496$	3.59623	+	0.963607i	0.161476	+	0.0432672i
$497$	−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	0.718633	−	0.695389i	$-0.244768\pi$
$499$	0.519223	+	0.519223i	0.0232436	+	0.0232436i	−0.695389	+	0.718633i	$0.744768\pi$
$500$	−18.6402	+	18.6666i	−0.833615	+	0.834794i
$501$	−63.4515	+	17.0018i	−2.83480	+	0.759583i
$502$	−1.21379			−0.0541741
$503$	−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
$505$	5.77148	−	2.69294i	0.256827	−	0.119834i
$506$			0.0204273i			0.000908103i
$507$		0			0
$508$	−25.0719	−	25.0719i	−1.11238	−	1.11238i
$509$	10.6714	−	39.8263i	0.473003	−	1.76527i	−0.155884	−	0.987775i	$-0.549823\pi$
$509$	10.6714	−	39.8263i	0.473003	−	1.76527i	0.628887	−	0.777496i	$-0.283511\pi$
$510$	15.5803	+	33.3916i	0.689908	+	1.47860i
$511$	38.0312	+	21.9573i	1.68240	+	0.971336i
$512$			30.2040i			1.33484i
$513$	10.5026	−	18.1910i	0.463700	−	0.803152i
$514$	9.40395	+	35.0960i	0.414791	+	1.54802i
$515$	13.6477	−	11.4573i	0.601390	−	0.504867i
$516$	−22.5371	+	39.0354i	−0.992142	+	1.71844i
$517$	0.00568287	−	0.0212087i	0.000249932	−	0.000932759i
$518$	33.9631	−	19.6086i	1.49225	−	0.861553i
$519$	−2.23862			−0.0982647
$520$		0			0
$521$	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
$523$	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
$525$	−23.0214	−	32.8450i	−1.00474	−	1.43347i
$526$	14.9068	+	55.6329i	0.649967	+	2.42571i
$527$	1.69170	−	2.93011i	0.0736917	−	0.127638i
$528$			0.228815i			0.00995791i
$529$	−19.7992	−	11.4311i	−0.860833	−	0.497002i
$530$	−5.59856	−	2.03622i	−0.243186	−	0.0884475i
$531$	−1.78004	+	6.64319i	−0.0772471	+	0.288290i
$532$	23.2478	+	23.2478i	1.00792	+	1.00792i
$533$		0			0
$534$			19.2796i			0.834310i
$535$	−27.4602	−	9.98736i	−1.18721	−	0.431791i
$536$	−4.62244	−	8.00630i	−0.199659	−	0.345820i
$537$	−17.4669	+	4.68025i	−0.753754	+	0.201968i
$538$	38.4533			1.65784
$539$	0.0375484	−	0.0100611i	0.00161733	−	0.000433361i
$540$	−4.02605	−	22.8015i	−0.173254	−	0.981219i
$541$	−17.3961	−	17.3961i	−0.747916	−	0.747916i	0.226171	−	0.974088i	$-0.427379\pi$
$541$	−17.3961	−	17.3961i	−0.747916	−	0.747916i	−0.974088	+	0.226171i	$0.927379\pi$
$542$	−14.0016	−	52.2547i	−0.601420	−	2.24453i
$543$	4.16876	+	1.11702i	0.178899	+	0.0479358i
$544$	22.3598	+	5.99128i	0.958667	+	0.256874i
$545$	−15.5816	−	18.5606i	−0.667443	−	0.795048i
$546$		0			0
$547$	−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
$550$	0.0241016	+	0.273995i	0.00102770	+	0.0116832i
$551$	−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
$555$	−39.1466	+	6.91212i	−1.66168	+	0.293403i
$556$	14.1290	−	8.15741i	0.599205	−	0.345951i
$557$	−15.0968	−	26.1484i	−0.639671	−	1.10794i	−0.985505	−	0.169647i	$-0.945737\pi$
$557$	−15.0968	−	26.1484i	−0.639671	−	1.10794i	0.345834	−	0.938296i	$-0.387596\pi$
$558$	−8.00967	+	8.00967i	−0.339076	+	0.339076i
$559$		0			0
$560$	−20.4398	−	1.78340i	−0.863740	−	0.0753624i
$561$	0.200853	+	0.0538185i	0.00848004	+	0.00227222i
$562$	28.3224	+	7.58897i	1.19471	+	0.320122i
$563$	7.36768	+	27.4966i	0.310511	+	1.15884i	0.928097	+	0.372339i	$0.121444\pi$
$563$	7.36768	+	27.4966i	0.310511	+	1.15884i	−0.617586	+	0.786503i	$0.711889\pi$
$564$	3.83126	+	3.83126i	0.161325	+	0.161325i
$565$	19.1348	−	3.37862i	0.805005	−	0.142140i
$566$	−8.29267	+	2.22201i	−0.348567	+	0.0933982i
$567$	−4.90639			−0.206049
$568$	−2.68290	+	0.718880i	−0.112572	+	0.0301635i
$569$	−16.3759	−	28.3638i	−0.686512	−	1.18907i	−0.972959	−	0.230978i	$-0.925807\pi$
$569$	−16.3759	−	28.3638i	−0.686512	−	1.18907i	0.286447	−	0.958096i	$-0.407526\pi$
$570$	−26.0355	−	55.7991i	−1.09051	−	2.33717i
$571$		−	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			0
$573$	9.00264	+	9.00264i	0.376091	+	0.376091i
$574$	−12.3351	+	46.0354i	−0.514859	+	1.92148i
$575$	1.68308	+	0.783867i	0.0701892	+	0.0326895i
$576$	−42.0448	−	24.2746i	−1.75187	−	1.01144i
$577$			14.7927i			0.615830i	0.951414	+	0.307915i	$0.0996312\pi$
$577$			14.7927i			0.615830i	−0.951414	+	0.307915i	$0.900369\pi$
$578$	−9.18293	+	15.9053i	−0.381959	+	0.661573i
$579$	−11.8614	−	44.2675i	−0.492944	−	1.83969i
$580$	−1.91831	+	21.9861i	−0.0796536	+	0.912922i
$581$	−1.91577	+	3.31822i	−0.0794797	+	0.137663i
$582$	0.603764	−	2.25328i	0.0250268	−	0.0934014i
$583$	−0.0291146	+	0.0168093i	−0.00120580	+	0.000696171i
$584$	11.3222			0.468514
$585$		0			0
$586$	−45.6279			−1.88487
$587$	−14.4411	+	8.33757i	−0.596048	+	0.344128i	−0.767485	−	0.641067i	$-0.778492\pi$
$587$	−14.4411	+	8.33757i	−0.596048	+	0.344128i	0.171437	+	0.985195i	$0.445159\pi$
$588$	−2.48273	+	9.26568i	−0.102386	+	0.382110i
$589$	−2.82693	+	4.89638i	−0.116481	+	0.201752i
$590$	4.49530	+	5.35473i	0.185069	+	0.220451i
$591$	18.3493	+	68.4805i	0.754789	+	2.81691i
$592$	−10.1673	+	17.6103i	−0.417874	+	0.723780i
$593$			6.40700i			0.263104i	0.991309	+	0.131552i	$0.0419960\pi$
$593$			6.40700i			0.263104i	−0.991309	+	0.131552i	$0.958004\pi$
$594$	−0.209076	−	0.120710i	−0.00857850	−	0.00495280i
$595$	−6.37301	+	17.5226i	−0.261268	+	0.718355i
$596$	3.57699	−	13.3495i	0.146519	−	0.546817i
$597$	54.1326	+	54.1326i	2.21550	+	2.21550i
$598$		0			0
$599$		−	37.0014i		−	1.51184i	−0.654667	−	0.755918i	$-0.727191\pi$
$599$		−	37.0014i		−	1.51184i	0.654667	−	0.755918i	$-0.272809\pi$
$600$	−9.37430	−	4.36593i	−0.382704	−	0.178238i
$601$	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
$603$	−56.5676			−2.30361
$604$	9.42555	−	2.52557i	0.383520	−	0.102764i
$605$	−20.1505	−	14.1025i	−0.819235	−	0.573347i
$606$	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
$609$	−32.4126	−	8.68494i	−1.31343	−	0.351931i
$610$	−4.34294	+	49.7751i	−0.175841	+	2.01534i
$611$		0			0
$612$	−21.9471	+	21.9471i	−0.887159	+	0.887159i
$613$	−6.23084	−	10.7921i	−0.251661	−	0.435890i	0.712322	−	0.701853i	$-0.247644\pi$
$613$	−6.23084	−	10.7921i	−0.251661	−	0.435890i	−0.963983	+	0.265963i	$0.914310\pi$
$614$	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
$617$	−24.1020	−	13.9153i	−0.970311	−	0.560209i	−0.0709800	−	0.997478i	$-0.522613\pi$
$617$	−24.1020	−	13.9153i	−0.970311	−	0.560209i	−0.899331	+	0.437268i	$0.855946\pi$
$618$	39.7057	+	22.9241i	1.59720	+	0.922141i
$619$	−9.96152	+	9.96152i	−0.400387	+	0.400387i	−0.878370	−	0.477982i	$-0.841368\pi$
$619$	−9.96152	+	9.96152i	−0.400387	+	0.400387i	0.477982	+	0.878370i	$0.341368\pi$
$620$	1.08367	+	6.13736i	0.0435213	+	0.246482i
$621$	−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
$624$		0			0
$625$	23.5004	+	8.52836i	0.940015	+	0.341134i
$626$	50.3830	+	13.5001i	2.01371	+	0.539572i
$627$	−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
$630$	35.7928	−	51.1430i	1.42602	−	2.03759i
$631$	31.9972	−	8.57363i	1.27379	−	0.341311i	0.442308	−	0.896863i	$-0.354160\pi$
$631$	31.9972	−	8.57363i	1.27379	−	0.341311i	0.831482	+	0.555552i	$0.187493\pi$
$632$	3.19028			0.126903
$633$	−39.3293	+	10.5382i	−1.56320	+	0.418858i
$634$	−16.3605	−	28.3373i	−0.649760	−	1.12542i
$635$	−11.4852	+	31.5785i	−0.455777	+	1.25316i
$636$		−	8.29594i		−	0.328955i
$637$		0			0
$638$	0.162714	+	0.162714i	0.00644190	+	0.00644190i
$639$	−4.39868	+	16.4161i	−0.174009	+	0.649411i
$640$	−11.9710	+	5.58560i	−0.473195	+	0.220790i
$641$	−39.0498	−	22.5454i	−1.54238	−	0.890491i	−0.998688	−	0.0512035i	$-0.983694\pi$
$641$	−39.0498	−	22.5454i	−1.54238	−	0.890491i	−0.543688	−	0.839288i	$-0.682972\pi$
$642$		−	75.1815i		−	2.96718i
$643$	8.71256	−	15.0906i	0.343590	−	0.595115i	−0.641507	−	0.767117i	$-0.721690\pi$
$643$	8.71256	−	15.0906i	0.343590	−	0.595115i	0.985097	+	0.172003i	$0.0550237\pi$
$644$	−0.660173	−	2.46380i	−0.0260145	−	0.0970873i
$645$	42.5549	+	3.71297i	1.67560	+	0.146198i
$646$	−14.3118	+	24.7888i	−0.563091	+	0.975302i
$647$	6.44377	−	24.0485i	0.253331	−	0.945442i	−0.715681	−	0.698427i	$-0.753884\pi$
$647$	6.44377	−	24.0485i	0.253331	−	0.945442i	0.969012	−	0.247015i	$-0.0794498\pi$
$648$	−1.09550	+	0.632487i	−0.0430353	+	0.0248464i
$649$	0.0394545			0.00154872
$650$		0			0
$651$	−9.47598			−0.371393
$652$	8.23009	−	4.75164i	0.322315	−	0.186089i
$653$	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
$655$	−20.1473	−	1.75788i	−0.787220	−	0.0686860i
$656$	−6.39593	−	23.8699i	−0.249719	−	0.931965i
$657$	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	$-0.520382\pi$
$659$	−24.6502	−	14.2318i	−0.960234	−	0.554391i	−0.896245	+	0.443559i	$0.853716\pi$
$660$	−0.347102	+	0.161956i	−0.0135109	+	0.00630413i
$661$	6.48898	−	24.2172i	0.252392	−	0.941941i	−0.717130	−	0.696939i	$-0.754545\pi$
$661$	6.48898	−	24.2172i	0.252392	−	0.941941i	0.969523	−	0.245002i	$-0.0787885\pi$
$662$	4.97071	+	4.97071i	0.193192	+	0.193192i
$663$		0			0
$664$			0.987856i			0.0383363i
$665$	10.6496	−	29.2811i	0.412976	−	1.13547i
$666$	−30.9337	−	53.5788i	−1.19866	−	2.07614i
$667$	1.50037	−	0.402024i	0.0580947	−	0.0155664i
$668$	−56.2494			−2.17635
$669$	37.3260	−	10.0015i	1.44311	−	0.386680i
$670$	−32.9723	+	47.1129i	−1.27383	+	1.82013i
$671$	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	0.745950	−	0.666002i	$-0.231996\pi$
$673$	27.4718	+	7.36105i	1.05896	+	0.283748i	0.313010	+	0.949750i	$0.398663\pi$
$674$	20.5588	+	5.50873i	0.791897	+	0.212188i
$675$	−17.9688	+	12.5945i	−0.691618	+	0.484762i
$676$		0			0
$677$	−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
$680$	0.835879	+	4.73399i	0.0320545	+	0.181540i
$681$	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	0.813018	−	0.582239i	$-0.197823\pi$
$683$	18.6936	+	10.7928i	0.715292	+	0.412974i	−0.0977251	+	0.995213i	$0.531157\pi$
$684$	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
$687$	4.50208	+	7.79784i	0.171765	+	0.297506i
$688$	15.4510	−	15.4510i	0.589064	−	0.589064i
$689$		0			0
$690$	−0.415230	+	4.75901i	−0.0158075	+	0.181172i
$691$	34.8910	+	9.34901i	1.32732	+	0.355653i	0.851713	−	0.524008i	$-0.175564\pi$
$691$	34.8910	+	9.34901i	1.32732	+	0.355653i	0.475602	+	0.879661i	$0.342230\pi$
$692$	−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
$695$	−12.6674	−	8.86533i	−0.480500	−	0.336281i
$696$	−8.35668	+	2.23916i	−0.316759	+	0.0848753i
$697$	−22.4573			−0.850631
$698$	−16.8036	+	4.50251i	−0.636026	+	0.170423i
$699$	34.7094	+	60.1185i	1.31283	+	2.27389i
$700$	−11.7620	−	32.2686i	−0.444563	−	1.21964i
$701$			16.0544i			0.606367i	0.952932	+	0.303184i	$0.0980496\pi$
$701$			16.0544i			0.606367i	−0.952932	+	0.303184i	$0.901950\pi$
$702$		0			0
$703$	−21.8355	−	21.8355i	−0.823540	−	0.823540i
$704$	−0.0720843	+	0.269022i	−0.00271678	+	0.0101392i
$705$	1.75507	−	4.82556i	0.0660998	−	0.181741i
$706$	−9.34579	−	5.39580i	−0.351734	−	0.203073i
$707$			8.29192i			0.311850i
$708$	−4.86801	+	8.43165i	−0.182951	+	0.316881i
$709$	−6.71639	−	25.0659i	−0.252239	−	0.941370i	−0.969605	−	0.244674i	$-0.921319\pi$
$709$	−6.71639	−	25.0659i	−0.252239	−	0.941370i	0.717366	−	0.696696i	$-0.245348\pi$
$710$	11.1084	+	13.2322i	0.416892	+	0.496594i
$711$	9.76035	−	16.9054i	0.366042	−	0.634003i
$712$	−0.650997	+	2.42956i	−0.0243972	+	0.0910514i
$713$	0.379874	−	0.219320i	0.0142264	−	0.00821361i
$714$	−47.9738			−1.79538
$715$		0			0
$716$	−15.4843			−0.578677
$717$	−14.5588	+	8.40555i	−0.543710	+	0.313911i
$718$	−8.57052	+	31.9856i	−0.319849	+	1.19369i
$719$	21.6867	−	37.5624i	0.808776	−	1.40084i	−0.104936	−	0.994479i	$-0.533464\pi$
$719$	21.6867	−	37.5624i	0.808776	−	1.40084i	0.913712	−	0.406362i	$-0.133203\pi$
$720$	−2.81342	+	32.2450i	−0.104850	+	1.20170i
$721$	6.00459	+	22.4094i	0.223623	+	0.834571i
$722$	4.08041	−	7.06747i	0.151857	−	0.263024i
$723$		−	24.9395i		−	0.927509i
$724$	3.20047	+	1.84779i	0.118945	+	0.0686727i
$725$	19.6505	−	7.16268i	0.729801	−	0.266015i
$726$	16.3786	−	61.1258i	0.607867	−	2.26859i
$727$	−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	$0.796239\pi$
$728$		0			0
$729$			44.0183i			1.63031i
$730$	−29.7783	−	63.8204i	−1.10214	−	2.36210i
$731$	−9.92869	−	17.1970i	−0.367226	−	0.636054i
$732$	−67.2071	+	18.0081i	−2.48405	+	0.665598i
$733$	−14.7183			−0.543633			−0.271817	−	0.962349i	$-0.587624\pi$
$733$	−14.7183			−0.543633			−0.271817	+	0.962349i	$0.587624\pi$
$734$	−24.5304	+	6.57289i	−0.905432	+	0.242610i
$735$	8.95230	−	1.58071i	0.330211	−	0.0583052i
$736$	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
$739$	32.4204	+	8.68701i	1.19260	+	0.319557i	0.799914	−	0.600115i	$-0.204878\pi$
$739$	32.4204	+	8.68701i	1.19260	+	0.319557i	0.392688	+	0.919672i	$0.371545\pi$
$740$	−33.9105	−	2.95873i	−1.24657	−	0.108765i
$741$		0			0
$742$	5.48446	−	5.48446i	0.201341	−	0.201341i
$743$	10.4647	+	18.1254i	0.383914	+	0.664958i	0.991618	−	0.129206i	$-0.0412427\pi$
$743$	10.4647	+	18.1254i	0.383914	+	0.664958i	−0.607704	+	0.794163i	$0.707909\pi$
$744$	−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
$747$	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
$750$	0.0454625	+	64.3236i	0.00166006	+	2.34876i
$751$	−28.8409	+	16.6513i	−1.05242	+	0.607614i	−0.923325	−	0.384019i	$-0.874540\pi$
$751$	−28.8409	+	16.6513i	−1.05242	+	0.607614i	−0.129093	+	0.991633i	$0.541207\pi$
$752$	−1.31332	−	2.27473i	−0.0478918	−	0.0829510i
$753$	−1.13268	+	1.13268i	−0.0412773	+	0.0412773i
$754$		0			0
$755$	−5.94593	−	7.08269i	−0.216395	−	0.257766i
$756$	29.1185	+	7.80228i	1.05903	+	0.283766i
$757$	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
$760$	−1.39680	−	7.91075i	−0.0506672	−	0.286953i
$761$	41.2764	−	11.0600i	1.49627	−	0.400924i	0.584421	−	0.811450i	$-0.301322\pi$
$761$	41.2764	−	11.0600i	1.49627	−	0.400924i	0.911849	+	0.410526i	$0.134655\pi$
$762$	−86.4568			−3.13200
$763$	30.4763	−	8.16611i	1.10332	−	0.295633i
$764$	5.45098	+	9.44138i	0.197210	+	0.341577i
$765$	27.6429	+	10.0538i	0.999429	+	0.363496i
$766$		−	46.7838i		−	1.69037i
$767$		0			0
$768$	17.1599	+	17.1599i	0.619203	+	0.619203i
$769$	−8.63611	+	32.2304i	−0.311426	+	1.16226i	0.615845	+	0.787867i	$0.288815\pi$
$769$	−8.63611	+	32.2304i	−0.311426	+	1.16226i	−0.927271	+	0.374391i	$0.877852\pi$
$770$	−0.336539	−	0.122401i	−0.0121280	−	0.00441101i
$771$	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	$-0.890614\pi$
$773$	−4.97625	+	8.61912i	−0.178983	+	0.310008i	0.762549	+	0.646930i	$0.223948\pi$
$774$	17.2065	+	64.2157i	0.618477	+	2.30819i
$775$	4.83656	−	3.38999i	0.173734	−	0.121772i
$776$	0.152169	−	0.263564i	0.00546254	−	0.00946140i
$777$	13.3953	−	49.9920i	0.480555	−	1.79345i
$778$	−13.4015	+	7.73737i	−0.480467	+	0.277398i
$779$	37.5274			1.34456
$780$		0			0
$781$	0.0974966			0.00348870
$782$	1.92318	−	1.11035i	0.0687728	−	0.0397060i
$783$	−4.75133	+	17.7322i	−0.169799	+	0.633697i
$784$	2.32513	−	4.02724i	0.0830403	−	0.143830i
$785$	11.1376	−	9.35004i	0.397519	−	0.333717i
$786$	−13.4676	−	50.2618i	−0.480373	−	1.79278i
$787$	−9.61957	+	16.6616i	−0.342901	+	0.593922i	−0.984970	−	0.172725i	$-0.944743\pi$
$787$	−9.61957	+	16.6616i	−0.342901	+	0.593922i	0.642069	+	0.766647i	$0.278076\pi$
$788$			60.7076i			2.16262i
$789$	65.8262	+	38.0047i	2.34347	+	1.35300i
$790$	−8.39072	−	17.9829i	−0.298528	−	0.639803i
$791$	−6.54759	+	24.4359i	−0.232806	+	0.868842i
$792$	−0.0642216	−	0.0642216i	−0.00228201	−	0.00228201i
$793$		0			0
$794$		−	36.6310i		−	1.29999i
$795$	−7.12461	+	3.32430i	−0.252684	+	0.117901i
$796$	32.7766	+	56.7707i	1.16174	+	2.01219i
$797$	−19.5492	+	5.23820i	−0.692469	+	0.185546i	−0.587855	−	0.808966i	$-0.700027\pi$
$797$	−19.5492	+	5.23820i	−0.692469	+	0.185546i	−0.104614	+	0.994513i	$0.533361\pi$
$798$	80.1669			2.83788
$799$	−2.30565	+	0.617798i	−0.0815681	+	0.0218561i
$800$	30.9678	+	25.9602i	1.09488	+	0.917833i
$801$	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
$804$	−77.3500	−	20.7259i	−2.72792	−	0.730945i
$805$	−1.85139	+	1.55424i	−0.0652528	+	0.0547798i
$806$		0			0
$807$	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	$-0.659163\pi$
$809$	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	$-0.516847\pi$
$811$	26.9316	−	26.9316i	0.945697	−	0.945697i	0.998600	+	0.0529030i	$0.0168474\pi$
$812$	−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
$815$	−7.37866	−	5.16400i	−0.258463	−	0.180887i
$816$	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
$819$		0			0
$820$	31.6825	−	26.5975i	1.10640	−	0.928826i
$821$	−18.0461	−	4.83545i	−0.629815	−	0.168758i	−0.0702292	−	0.997531i	$-0.522373\pi$
$821$	−18.0461	−	4.83545i	−0.629815	−	0.168758i	−0.559586	+	0.828772i	$0.689040\pi$
$822$	80.9591	+	21.6929i	2.82377	+	0.756627i
$823$	0.647451	+	2.41632i	0.0225687	+	0.0842276i	0.976292	−	0.216459i	$-0.0694508\pi$
$823$	0.647451	+	2.41632i	0.0225687	+	0.0842276i	−0.953723	+	0.300687i	$0.902784\pi$
$824$	4.22953	+	4.22953i	0.147342	+	0.147342i
$825$	0.278178	+	0.233196i	0.00968491	+	0.00811883i
$826$	−8.79243	+	2.35593i	−0.305928	+	0.0819731i
$827$	−31.5605			−1.09747			−0.548733	−	0.835998i	$-0.684890\pi$
$827$	−31.5605			−1.09747			−0.548733	+	0.835998i	$0.684890\pi$
$828$	−3.88679	+	1.04146i	−0.135075	+	0.0361933i
$829$	−12.7105	−	22.0153i	−0.441455	−	0.764622i	0.556343	−	0.830953i	$-0.312204\pi$
$829$	−12.7105	−	22.0153i	−0.441455	−	0.764622i	−0.997798	+	0.0663305i	$0.978871\pi$
$830$	5.56832	−	2.59815i	0.193279	−	0.0901830i
$831$		−	64.5440i		−	2.23901i
$832$		0			0
$833$	−2.98822	−	2.98822i	−0.103536	−	0.103536i
$834$	10.2962	−	38.4259i	0.356528	−	1.33058i
$835$	22.5399	+	48.3074i	0.780027	+	1.67174i
$836$	−0.257677	−	0.148770i	−0.00891196	−	0.00514532i
$837$			5.18409i			0.179188i
$838$	−30.0583	+	52.0625i	−1.03835	+	1.79847i
$839$	−4.97501	−	18.5670i	−0.171757	−	0.641004i	−0.997081	−	0.0763459i	$-0.975675\pi$
$839$	−4.97501	−	18.5670i	−0.171757	−	0.641004i	0.825325	−	0.564658i	$-0.190992\pi$
$840$	10.3117	−	8.65671i	0.355789	−	0.298685i
$841$	−5.75109	+	9.96118i	−0.198313	+	0.343489i
$842$	−6.48763	+	24.2121i	−0.223578	+	0.834406i
$843$	33.5118	−	19.3480i	1.15421	−	0.666382i
$844$	−34.8652			−1.20011
$845$		0			0
$846$	7.99145			0.274752
$847$	27.7317	−	16.0109i	0.952873	−	0.550142i
$848$	−1.04089	+	3.88466i	−0.0357443	+	0.133400i
$849$	−5.66501	+	9.81208i	−0.194423	+	0.336750i
$850$	24.4860	−	17.1625i	0.839862	−	0.588667i
$851$	0.620066	+	2.31412i	0.0212556	+	0.0793270i
$852$	−12.0294	+	20.8356i	−0.412122	+	0.713816i
$853$			38.7388i			1.32639i	0.748445	+	0.663196i	$0.230801\pi$
$853$			38.7388i			1.32639i	−0.748445	+	0.663196i	$0.769199\pi$
$854$	−56.3359	−	32.5256i	−1.92778	−	1.11300i
$855$	−46.1927	−	16.8004i	−1.57976	−	0.574563i
$856$	2.53859	−	9.47413i	0.0867671	−	0.323819i
$857$	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			0
$859$		−	31.6153i		−	1.07870i	−0.842082	−	0.539350i	$-0.818670\pi$
$859$		−	31.6153i		−	1.07870i	0.842082	−	0.539350i	$-0.181330\pi$
$860$	34.3747	+	12.5022i	1.17217	+	0.426321i
$861$	31.4483	+	54.4701i	1.07176	+	1.85634i
$862$	23.7241	−	6.35687i	0.808048	−	0.216516i
$863$	9.51860			0.324017			0.162008	−	0.986789i	$-0.448203\pi$
$863$	9.51860			0.324017			0.162008	+	0.986789i	$0.448203\pi$
$864$	−34.2599	+	9.17990i	−1.16554	+	0.312307i
$865$	0.315878	+	1.78897i	0.0107402	+	0.0608267i
$866$	−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
$869$	−0.108169	−	0.0289838i	−0.00366938	−	0.000983207i
$870$	34.6004	+	41.2155i	1.17307	+	1.39734i
$871$		0			0
$872$	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
$875$	−22.9993	+	23.0318i	−0.777517	+	0.778616i
$876$	69.3472	−	69.3472i	2.34303	−	2.34303i
$877$	12.8573	+	7.42315i	0.434159	+	0.250662i	0.701117	−	0.713046i	$-0.252685\pi$
$877$	12.8573	+	7.42315i	0.434159	+	0.250662i	−0.266958	+	0.963708i	$0.586018\pi$
$878$	−43.1236	−	24.8974i	−1.45535	−	0.840248i
$879$	−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	−0.463166	−	0.886272i	$-0.653287\pi$
$881$	2.16038	−	1.24730i	0.0727850	−	0.0420224i	0.535951	+	0.844249i	$0.319953\pi$
$882$	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	$0.229980\pi$
$884$		0			0
$885$	9.19184	+	0.802000i	0.308980	+	0.0269589i
$886$	33.8277	+	9.06411i	1.13646	+	0.304515i
$887$	−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
$890$	15.4070	−	2.72042i	0.516445	−	0.0911886i
$891$	0.0428898	−	0.0114923i	0.00143686	−	0.000385006i
$892$	33.0893			1.10791
$893$	3.85287	−	1.03237i	0.128931	−	0.0345471i
$894$	−16.8496	−	29.1843i	−0.563534	−	0.976070i
$895$	6.20480	+	13.2981i	0.207404	+	0.444505i
$896$		−	17.1988i		−	0.574572i
$897$		0			0
$898$	60.4125	+	60.4125i	2.01599	+	2.01599i
$899$	1.27889	−	4.77289i	0.0426534	−	0.159185i
$900$	−50.9056	+	18.5553i	−1.69685	+	0.618509i
$901$	3.16512	+	1.82738i	0.105445	+	0.0608789i
$902$		−	0.431317i		−	0.0143613i
$903$	−27.8075	+	48.1640i	−0.925375	+	1.60280i
$904$	1.68811	+	6.30011i	0.0561457	+	0.209539i
$905$	0.304422	−	3.48903i	0.0101193	−	0.115979i
$906$	11.8968	−	20.6059i	0.395245	−	0.684585i
$907$	−12.4519	+	46.4710i	−0.413457	+	1.54304i	0.374448	+	0.927248i	$0.377832\pi$
$907$	−12.4519	+	46.4710i	−0.413457	+	1.54304i	−0.787906	+	0.615796i	$0.788835\pi$
$908$	32.6760	−	18.8655i	1.08439	−	0.626074i
$909$	13.0810			0.433869
$910$		0			0
$911$	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
$913$	0.00897469	−	0.0334940i	0.000297019	−	0.00110849i
$914$	8.62738	−	14.9431i	0.285368	−	0.494272i
$915$	42.3963	+	50.5018i	1.40158	+	1.66954i
$916$	1.99554	+	7.44744i	0.0659344	+	0.246070i
$917$	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	$-0.129241\pi$
$919$	31.4065	+	18.1326i	1.03600	+	0.598138i	0.117306	+	0.993096i	$0.462574\pi$
$920$	−0.213019	+	0.585695i	−0.00702304	+	0.0193098i
$921$	4.97994	−	18.5854i	0.164095	−	0.612409i
$922$	−28.0077	−	28.0077i	−0.922383	−	0.922383i
$923$		0			0
$924$		−	0.498684i		−	0.0164055i
$925$	11.0474	+	30.3082i	0.363238	+	0.996527i
$926$	−26.0245	−	45.0757i	−0.855218	−	1.48128i
$927$	35.3522	−	9.47260i	1.16112	−	0.311121i
$928$	33.8070			1.10977
$929$	17.3483	−	4.64847i	0.569180	−	0.152511i	0.0372596	−	0.999306i	$-0.488137\pi$
$929$	17.3483	−	4.64847i	0.569180	−	0.152511i	0.531921	+	0.846794i	$0.321470\pi$
$930$	12.4504	+	8.71347i	0.408263	+	0.285726i
$931$	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
$934$	−73.0326	−	19.5690i	−2.38970	−	0.640318i
$935$	0.0146672	−	0.168103i	0.000479669	−	0.00549756i
$936$		0			0
$937$	−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
$940$	2.52110	−	3.60230i	0.0822291	−	0.117494i
$941$	2.83451	−	2.83451i	0.0924023	−	0.0924023i	−0.659395	−	0.751797i	$-0.729187\pi$
$941$	2.83451	−	2.83451i	0.0924023	−	0.0924023i	0.751797	+	0.659395i	$0.229187\pi$
$942$	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
$945$	−4.96756	−	28.1337i	−0.161595	−	0.915188i
$946$	0.330287	−	0.190691i	0.0107385	−	0.00619990i
$947$	10.1283	+	17.5428i	0.329127	+	0.570064i	0.982339	−	0.187111i	$-0.0599123\pi$
$947$	10.1283	+	17.5428i	0.329127	+	0.570064i	−0.653212	+	0.757175i	$0.726579\pi$
$948$	19.5402	−	19.5402i	0.634636	−	0.634636i
$949$		0			0
$950$	−40.9174	+	28.6794i	−1.32753	+	0.930482i
$951$	−41.7111	−	11.1764i	−1.35257	−	0.362421i
$952$	−6.04551	−	1.61989i	−0.195936	−	0.0525010i
$953$	−5.67311	−	21.1724i	−0.183770	−	0.685840i	−0.994890	−	0.100960i	$-0.967808\pi$
$953$	−5.67311	−	21.1724i	−0.183770	−	0.685840i	0.811120	−	0.584879i	$-0.198858\pi$
$954$	−8.65206	−	8.65206i	−0.280121	−	0.280121i
$955$	5.92403	−	8.46464i	0.191697	−	0.273909i
$956$	−13.9046	+	3.72574i	−0.449708	+	0.120499i
$957$	0.303682			0.00981665
$958$	−9.41158	+	2.52183i	−0.304074	+	0.0814765i
$959$	21.2059	+	36.7297i	0.684775	+	1.18607i
$960$	−22.2622	+	61.2098i	−0.718509	+	1.97554i
$961$			29.6046i			0.954988i
$962$		0			0
$963$	−42.4372	−	42.4372i	−1.36752	−	1.36752i
$964$	5.52718	−	20.6277i	0.178018	−	0.664374i
$965$	−33.7020	+	15.7252i	−1.08491	+	0.506212i
$966$	−5.38630	−	3.10978i	−0.173301	−	0.100055i
$967$			18.3496i			0.590084i	0.955484	+	0.295042i	$0.0953337\pi$
$967$			18.3496i			0.590084i	−0.955484	+	0.295042i	$0.904666\pi$
$968$	4.12796	−	7.14984i	0.132678	−	0.229804i
$969$	9.77690	+	36.4879i	0.314079	+	1.17216i
$970$	−1.88587	−	0.164544i	−0.0605516	−	0.00528320i
$971$	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
$973$	17.4332	−	10.0650i	0.558881	−	0.322670i
$974$	−30.5136			−0.977718
$975$		0			0
$976$	33.7299			1.07967
$977$	−2.28535	+	1.31945i	−0.0731149	+	0.0422129i	−0.536112	−	0.844147i	$-0.680107\pi$
$977$	−2.28535	+	1.31945i	−0.0731149	+	0.0422129i	0.462997	+	0.886360i	$0.346774\pi$
$978$	5.99747	−	22.3829i	0.191778	−	0.715725i
$979$	0.0441451	−	0.0764615i	0.00141088	−	0.00244372i
$980$	7.75486	+	0.676622i	0.247720	+	0.0216139i
$981$	−12.8825	−	48.0782i	−0.411307	−	1.53502i
$982$	21.0765	−	36.5055i	0.672577	−	1.16494i
$983$		−	36.6137i		−	1.16780i	−0.811827	−	0.583898i	$-0.801527\pi$
$983$		−	36.6137i		−	1.16780i	0.811827	−	0.583898i	$-0.198473\pi$
$984$	14.0436	+	8.10806i	0.447693	+	0.258476i
$985$	52.1361	−	24.3264i	1.66119	−	0.775104i
$986$	6.47462	−	24.1636i	0.206194	−	0.769526i
$987$	4.72721	+	4.72721i	0.150469	+	0.150469i
$988$		0			0
$989$		−	2.57440i		−	0.0818613i
$990$	−0.193094	+	0.530911i	−0.00613693	+	0.0168735i
$991$	−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
$993$	9.27712			0.294401
$994$	−21.7271	+	5.82177i	−0.689143	+	0.184655i
$995$	35.6210	−	50.8976i	1.12926	−	1.61356i
$996$	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
$999$	−27.3495	−	7.32827i	−0.865299	−	0.231856i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.1	✓	20	65.17	odd	12
65.2.o.a.63.1	yes	20	13.5	odd	4
65.2.t.a.37.5	yes	20	65.57	even	4
65.2.t.a.58.5	yes	20	13.4	even	6
325.2.s.b.32.5		20	65.43	odd	12
325.2.s.b.193.5		20	65.44	odd	4
325.2.x.b.232.1		20	65.18	even	4
325.2.x.b.318.1		20	65.4	even	6
585.2.cf.a.388.5		20	39.5	even	4
585.2.cf.a.487.5		20	195.17	even	12
585.2.dp.a.37.1		20	195.122	odd	4
585.2.dp.a.253.1		20	39.17	odd	6
845.2.f.d.408.9		20	13.3	even	3
845.2.f.d.437.2		20	65.37	even	12
845.2.f.e.408.2		20	13.10	even	6
845.2.f.e.437.9		20	65.2	even	12
845.2.k.d.268.2		20	13.11	odd	12
845.2.k.d.577.2		20	65.42	odd	12
845.2.k.e.268.9		20	13.2	odd	12
845.2.k.e.577.9		20	65.62	odd	12
845.2.o.e.488.1		20	13.6	odd	12
845.2.o.e.587.1		20	65.12	odd	4
845.2.o.f.488.5		20	13.7	odd	12
845.2.o.f.587.5		20	5.2	odd	4
845.2.o.g.258.5		20	13.8	odd	4
845.2.o.g.357.5		20	65.22	odd	12
845.2.t.e.418.5		20	1.1	even	1	trivial
845.2.t.e.657.5		20	65.7	even	12	inner
845.2.t.f.418.1		20	13.12	even	2
845.2.t.f.657.1		20	65.32	even	12
845.2.t.g.188.1		20	13.9	even	3
845.2.t.g.427.1		20	65.47	even	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.t (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.80821 - 1.04397i) q^{2} +(0.713171 - 2.66159i) q^{3} +(1.17974 - 2.04338i) q^{4} +(-2.22760 - 0.194361i) q^{5} +(-1.48906 - 5.55724i) q^{6} +(1.45563 - 2.52122i) q^{7} -0.750585i q^{8} +(-3.97738 - 2.29634i) q^{9} +(-4.23088 + 1.97411i) q^{10} +(-0.00681908 + 0.0254491i) q^{11} +(-4.59727 - 4.59727i) q^{12} -6.07853i q^{14} +(-2.10597 + 5.79036i) q^{15} +(1.57590 + 2.72954i) q^{16} +(2.76664 - 0.741318i) q^{17} -9.58924 q^{18} +(-4.62320 + 1.23878i) q^{19} +(-3.02515 + 4.32254i) q^{20} +(-5.67236 - 5.67236i) q^{21} +(0.0142378 + 0.0531363i) q^{22} +(0.358680 + 0.0961080i) q^{23} +(-1.99775 - 0.535296i) q^{24} +(4.92445 + 0.865921i) q^{25} +(-3.10321 + 3.10321i) q^{27} +(-3.43454 - 5.94879i) q^{28} +(3.62262 - 2.09152i) q^{29} +(2.23692 + 12.6687i) 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} +(-3.73260 + 5.33337i) q^{35} +(-9.38457 + 5.41819i) q^{36} +(3.22588 + 5.58739i) q^{37} +(-7.06645 + 7.06645i) q^{38} +(-0.145885 + 1.67201i) q^{40} +(-7.57344 - 2.02930i) q^{41} +(-16.1786 - 4.33503i) q^{42} +(-1.79436 - 6.69664i) q^{43} +(0.0439574 + 0.0439574i) q^{44} +(8.41371 + 5.88839i) q^{45} +(0.748902 - 0.200668i) q^{46} -0.833377 q^{47} +(8.38880 - 2.24777i) q^{48} +(-0.737715 - 1.27776i) q^{49} +(9.80842 - 3.57521i) q^{50} -7.89234i q^{51} +(0.902268 + 0.902268i) q^{53} +(-2.37160 + 8.85092i) q^{54} +(0.0201365 - 0.0553653i) q^{55} +(-1.89239 - 1.09257i) q^{56} +13.1885i q^{57} +(4.36697 - 7.56381i) q^{58} +(-0.387581 - 1.44647i) q^{59} +(9.34737 + 11.1344i) q^{60} +(5.35090 - 9.26802i) q^{61} +(0.638351 - 2.38236i) q^{62} +(-11.5792 + 6.68524i) q^{63} +10.5710 q^{64} +0.151581 q^{66} +(10.6667 - 6.15845i) q^{67} +(1.74913 - 6.52784i) q^{68} +(0.511601 - 0.886118i) q^{69} +(-1.18143 + 13.5406i) q^{70} +(-0.957759 - 3.57441i) q^{71} +(-1.72360 + 2.98536i) q^{72} +15.0844i q^{73} +(11.6661 + 6.73544i) q^{74} +(5.81670 - 12.4893i) q^{75} +(-2.92289 + 10.9084i) q^{76} +(0.0542370 + 0.0542370i) q^{77} +4.25039i q^{79} +(-2.97996 - 6.38662i) q^{80} +(-0.842658 - 1.45953i) q^{81} +(-15.8129 + 4.23705i) q^{82} -1.31611 q^{83} +(-18.2827 + 4.89883i) q^{84} +(-6.30706 + 1.11364i) q^{85} +(-10.2357 - 10.2357i) q^{86} +(-2.98322 - 11.1335i) q^{87} +(0.0191018 + 0.00511830i) q^{88} +(-3.23688 - 0.867319i) q^{89} +(21.3610 + 1.86378i) q^{90} +(0.619535 - 0.619535i) q^{92} +(-1.62747 - 2.81886i) q^{93} +(-1.50692 + 0.870020i) q^{94} +(10.5394 - 1.86095i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 4 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{10} - 8 q^{11} - 24 q^{12} + 8 q^{15} - 2 q^{16} + 10 q^{17} - 16 q^{19} - 12 q^{20} - 4 q^{21} + 16 q^{22} + 2 q^{23} + 28 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 4 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^10 - 8 * q^11 - 24 * q^12 + 8 * q^15 - 2 * q^16 + 10 * q^17 - 16 * q^19 - 12 * q^20 - 4 * q^21 + 16 * q^22 + 2 * q^23 + 28 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 14 * q^30 + 48 * q^32 + 18 * q^33 - 2 * q^34 - 20 * q^35 - 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 28 * q^41 - 56 * q^42 + 22 * q^43 + 36 * q^44 - 6 * q^45 + 8 * q^46 + 40 * q^47 + 28 * q^48 + 18 * q^49 + 78 * q^50 - 10 * q^53 - 12 * q^54 + 26 * q^55 - 8 * q^59 - 28 * q^60 - 16 * q^61 + 40 * q^62 - 36 * q^63 + 20 * q^64 - 32 * q^66 + 18 * q^67 + 28 * q^68 - 16 * q^69 + 12 * q^70 - 56 * q^71 - 4 * q^72 - 18 * q^74 + 34 * q^75 - 80 * q^76 - 28 * q^77 + 110 * q^80 - 14 * q^81 - 22 * q^82 - 48 * q^83 - 32 * q^84 - 28 * q^85 - 60 * q^86 + 62 * q^87 - 50 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 + 48 * q^94 - 14 * q^95 - 56 * q^96 + 66 * q^97 - 30 * q^98 - 60 * q^99

Introduction

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