LMFDB - Embedded newform 507.2.s.a.476.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.s (of order $52$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			476.11
Character	$\chi$	$=$	507.476
Dual form			507.2.s.a.278.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73173 - 0.779387i) q^{2} +(0.733520 + 1.56906i) q^{3} +(1.06519 + 1.20235i) q^{4} +(0.850485 + 0.666312i) q^{5} +(-0.0473518 - 3.28888i) q^{6} +(0.486647 - 0.151645i) q^{7} +(0.222416 + 0.713759i) q^{8} +(-1.92390 + 2.30187i) q^{9} +O(q^{10})$	\(q+(-1.73173 - 0.779387i) q^{2} +(0.733520 + 1.56906i) q^{3} +(1.06519 + 1.20235i) q^{4} +(0.850485 + 0.666312i) q^{5} +(-0.0473518 - 3.28888i) q^{6} +(0.486647 - 0.151645i) q^{7} +(0.222416 + 0.713759i) q^{8} +(-1.92390 + 2.30187i) q^{9} +(-0.953492 - 1.81673i) q^{10} +(-5.46788 + 2.46089i) q^{11} +(-1.10522 + 2.55329i) q^{12} +(2.26044 + 2.80899i) q^{13} +(-0.960931 - 0.116678i) q^{14} +(-0.421636 + 1.82321i) q^{15} +(0.558371 - 4.59860i) q^{16} +(-2.94188 - 1.54402i) q^{17} +(5.12571 - 2.48676i) q^{18} +(-0.193910 - 0.193910i) q^{19} +(0.104786 + 1.73233i) q^{20} +(0.594906 + 0.652344i) q^{21} +11.3869 q^{22} +2.68893 q^{23} +(-0.956784 + 0.872542i) q^{24} +(-0.917226 - 3.72133i) q^{25} +(-1.72517 - 6.62616i) q^{26} +(-5.02299 - 1.33024i) q^{27} +(0.700701 + 0.423589i) q^{28} +(-4.76353 + 1.80657i) q^{29} +(2.15115 - 2.82869i) q^{30} +(1.68900 + 2.79394i) q^{31} +(-3.77750 + 6.24875i) q^{32} +(-7.87209 - 6.77432i) q^{33} +(3.89114 + 4.96667i) q^{34} +(0.514929 + 0.195287i) q^{35} +(-4.81696 + 0.138734i) q^{36} +(-4.77670 + 2.88762i) q^{37} +(0.184668 + 0.486930i) q^{38} +(-2.74940 + 5.60721i) q^{39} +(-0.286425 + 0.755240i) q^{40} +(0.601451 + 3.28201i) q^{41} +(-0.521787 - 1.59334i) q^{42} +(-0.0628249 - 0.254891i) q^{43} +(-8.78317 - 3.95298i) q^{44} +(-3.17001 + 0.675793i) q^{45} +(-4.65650 - 2.09572i) q^{46} +(0.296967 + 4.90945i) q^{47} +(7.62506 - 2.49705i) q^{48} +(-5.54706 + 3.82886i) q^{49} +(-1.31197 + 7.15920i) q^{50} +(0.264728 - 5.74855i) q^{51} +(-0.969596 + 5.70993i) q^{52} +(2.85167 - 5.43340i) q^{53} +(7.66168 + 6.21846i) q^{54} +(-6.29007 - 1.55036i) q^{55} +(0.216477 + 0.313621i) q^{56} +(0.162020 - 0.446494i) q^{57} +(9.65715 + 0.584150i) q^{58} +(0.0837541 - 0.106904i) q^{59} +(-2.64126 + 1.43511i) q^{60} +(0.717187 - 0.376409i) q^{61} +(-0.747319 - 6.15472i) q^{62} +(-0.587190 + 1.41195i) q^{63} +(3.78705 - 2.61401i) q^{64} +(0.0508016 + 3.89516i) q^{65} +(8.35249 + 17.8667i) q^{66} +(0.304051 + 5.02657i) q^{67} +(-1.27721 - 5.18183i) q^{68} +(1.97239 + 4.21910i) q^{69} +(-0.739513 - 0.739513i) q^{70} +(2.67828 + 14.6149i) q^{71} +(-2.07089 - 0.861225i) q^{72} +(2.55083 + 5.66772i) q^{73} +(10.5225 - 1.27766i) q^{74} +(5.16619 - 4.16885i) q^{75} +(0.0265968 - 0.439698i) q^{76} +(-2.28775 + 2.02677i) q^{77} +(9.13139 - 7.56731i) q^{78} +(8.82755 + 7.82053i) q^{79} +(3.53899 - 3.53899i) q^{80} +(-1.59725 - 8.85713i) q^{81} +(1.51641 - 6.15231i) q^{82} +(-1.36810 - 0.250713i) q^{83} +(-0.150657 + 1.41015i) q^{84} +(-1.47322 - 3.27337i) q^{85} +(-0.0898629 + 0.490366i) q^{86} +(-6.32876 - 6.14911i) q^{87} +(-2.97263 - 3.35541i) q^{88} +(-11.5938 - 11.5938i) q^{89} +(6.01629 + 1.30038i) q^{90} +(1.52601 + 1.02420i) q^{91} +(2.86422 + 3.23303i) q^{92} +(-3.14495 + 4.69955i) q^{93} +(3.31209 - 8.73328i) q^{94} +(-0.0357129 - 0.294122i) q^{95} +(-12.5755 - 1.34354i) q^{96} +(-7.54824 + 5.91366i) q^{97} +(12.5901 - 2.30723i) q^{98} +(4.85497 - 17.3209i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9}+O(q^{10}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27} - 56 q^{28} + 78 q^{30} - 32 q^{31} - 10 q^{33} - 52 q^{34} - 26 q^{36} - 56 q^{37} + 70 q^{39} - 36 q^{40} - 10 q^{42} - 52 q^{43} - 140 q^{45} - 180 q^{46} - 2 q^{48} - 52 q^{49} - 26 q^{51} - 64 q^{52} - 22 q^{54} + 132 q^{55} - 22 q^{57} - 60 q^{58} - 18 q^{60} - 92 q^{61} + 108 q^{63} - 52 q^{64} - 124 q^{66} - 240 q^{67} - 104 q^{69} - 268 q^{70} - 2 q^{72} - 56 q^{73} + 104 q^{75} - 48 q^{76} - 22 q^{78} - 12 q^{79} + 2 q^{81} + 208 q^{82} - 22 q^{84} - 52 q^{85} - 26 q^{87} - 260 q^{88} - 26 q^{90} - 32 q^{91} - 176 q^{93} - 240 q^{94} + 292 q^{96} - 80 q^{97} - 58 q^{99}+O(q^{100}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{33}{52}\right)$

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 $

$2$	−1.73173	−	0.779387i	−1.22452	−	0.551110i	−0.308106	−	0.951352i	$-0.599695\pi$
$2$	−1.73173	−	0.779387i	−1.22452	−	0.551110i	−0.916409	+	0.400242i	$0.868926\pi$
$3$	0.733520	+	1.56906i	0.423498	+	0.905897i
$3$	0.733520	+	1.56906i	0.423498	+	0.905897i
$4$	1.06519	+	1.20235i	0.532594	+	0.601174i
$5$	0.850485	+	0.666312i	0.380348	+	0.297984i	0.788625	−	0.614874i	$-0.210793\pi$
$5$	0.850485	+	0.666312i	0.380348	+	0.297984i	−0.408277	+	0.912858i	$0.633870\pi$
$6$	−0.0473518	−	3.28888i	−0.0193313	−	1.34268i
$7$	0.486647	−	0.151645i	0.183935	−	0.0573166i	−0.204152	−	0.978939i	$-0.565444\pi$
$7$	0.486647	−	0.151645i	0.183935	−	0.0573166i	0.388087	+	0.921623i	$0.373136\pi$
$8$	0.222416	+	0.713759i	0.0786361	+	0.252352i
$9$	−1.92390	+	2.30187i	−0.641299	+	0.767291i
$10$	−0.953492	−	1.81673i	−0.301521	−	0.574499i
$11$	−5.46788	+	2.46089i	−1.64863	+	0.741987i	−0.999820	−	0.0189648i	$-0.993963\pi$
$11$	−5.46788	+	2.46089i	−1.64863	+	0.741987i	−0.648808	+	0.760952i	$0.724732\pi$
$12$	−1.10522	+	2.55329i	−0.319049	+	0.737071i
$13$	2.26044	+	2.80899i	0.626932	+	0.779074i
$13$	2.26044	+	2.80899i	0.626932	+	0.779074i
$14$	−0.960931	−	0.116678i	−0.256819	−	0.0311835i
$15$	−0.421636	+	1.82321i	−0.108866	+	0.470752i
$16$	0.558371	−	4.59860i	0.139593	−	1.14965i
$17$	−2.94188	−	1.54402i	−0.713510	−	0.374479i	0.0685789	−	0.997646i	$-0.478154\pi$
$17$	−2.94188	−	1.54402i	−0.713510	−	0.374479i	−0.782089	+	0.623167i	$0.785846\pi$
$18$	5.12571	−	2.48676i	1.20814	−	0.586134i
$19$	−0.193910	−	0.193910i	−0.0444861	−	0.0444861i	0.684514	−	0.729000i	$-0.260015\pi$
$19$	−0.193910	−	0.193910i	−0.0444861	−	0.0444861i	−0.729000	+	0.684514i	$0.760015\pi$
$20$	0.104786	+	1.73233i	0.0234309	+	0.387360i
$21$	0.594906	+	0.652344i	0.129819	+	0.142353i
$22$	11.3869			2.42769
$23$	2.68893			0.560682			0.280341	−	0.959901i	$-0.409553\pi$
$23$	2.68893			0.560682			0.280341	+	0.959901i	$0.409553\pi$
$24$	−0.956784	+	0.872542i	−0.195303	+	0.178107i
$25$	−0.917226	−	3.72133i	−0.183445	−	0.744267i
$26$	−1.72517	−	6.62616i	−0.338333	−	1.29950i
$27$	−5.02299	−	1.33024i	−0.966676	−	0.256004i
$28$	0.700701	+	0.423589i	0.132420	+	0.0800507i
$29$	−4.76353	+	1.80657i	−0.884566	+	0.335472i	−0.754708	−	0.656061i	$-0.772221\pi$
$29$	−4.76353	+	1.80657i	−0.884566	+	0.335472i	−0.129858	+	0.991533i	$0.541452\pi$
$30$	2.15115	−	2.82869i	0.392744	−	0.516446i
$31$	1.68900	+	2.79394i	0.303353	+	0.501807i	0.969851	−	0.243700i	$-0.0783613\pi$
$31$	1.68900	+	2.79394i	0.303353	+	0.501807i	−0.666498	+	0.745507i	$0.732207\pi$
$32$	−3.77750	+	6.24875i	−0.667774	+	1.10463i
$33$	−7.87209	−	6.77432i	−1.37035	−	1.17926i
$34$	3.89114	+	4.96667i	0.667325	+	0.851778i
$35$	0.514929	+	0.195287i	0.0870389	+	0.0330095i
$36$	−4.81696	+	0.138734i	−0.802827	+	0.0231223i
$37$	−4.77670	+	2.88762i	−0.785284	+	0.474721i	−0.852314	−	0.523030i	$-0.824802\pi$
$37$	−4.77670	+	2.88762i	−0.785284	+	0.474721i	0.0670298	+	0.997751i	$0.478648\pi$
$38$	0.184668	+	0.486930i	0.0299572	+	0.0789906i
$39$	−2.74940	+	5.60721i	−0.440256	+	0.897872i
$40$	−0.286425	+	0.755240i	−0.0452877	+	0.119414i
$41$	0.601451	+	3.28201i	0.0939309	+	0.512564i	0.996611	+	0.0822532i	$0.0262116\pi$
$41$	0.601451	+	3.28201i	0.0939309	+	0.512564i	−0.902681	+	0.430311i	$0.858404\pi$
$42$	−0.521787	−	1.59334i	−0.0805135	−	0.245858i
$43$	−0.0628249	−	0.254891i	−0.00958071	−	0.0388705i	0.965957	−	0.258703i	$-0.0832951\pi$
$43$	−0.0628249	−	0.254891i	−0.00958071	−	0.0388705i	−0.975538	+	0.219832i	$0.929449\pi$
$44$	−8.78317	−	3.95298i	−1.32411	−	0.595935i
$45$	−3.17001	+	0.675793i	−0.472557	+	0.100741i
$46$	−4.65650	−	2.09572i	−0.686563	−	0.308997i
$47$	0.296967	+	4.90945i	0.0433171	+	0.716117i	0.953403	+	0.301698i	$0.0975535\pi$
$47$	0.296967	+	4.90945i	0.0433171	+	0.716117i	−0.910086	+	0.414419i	$0.863985\pi$
$48$	7.62506	−	2.49705i	1.10058	−	0.360418i
$49$	−5.54706	+	3.82886i	−0.792437	+	0.546980i
$50$	−1.31197	+	7.15920i	−0.185541	+	1.01246i
$51$	0.264728	−	5.74855i	0.0370693	−	0.804958i
$52$	−0.969596	+	5.70993i	−0.134459	+	0.791825i
$53$	2.85167	−	5.43340i	0.391707	−	0.746335i	−0.607128	−	0.794604i	$-0.707678\pi$
$53$	2.85167	−	5.43340i	0.391707	−	0.746335i	0.998834	+	0.0482696i	$0.0153707\pi$
$54$	7.66168	+	6.21846i	1.04262	+	0.846226i
$55$	−6.29007	−	1.55036i	−0.848153	−	0.209051i
$56$	0.216477	+	0.313621i	0.0289279	+	0.0419093i
$57$	0.162020	−	0.446494i	0.0214600	−	0.0591395i
$58$	9.65715	+	0.584150i	1.26805	+	0.0767027i
$59$	0.0837541	−	0.106904i	0.0109039	−	0.0139177i	−0.781701	−	0.623654i	$-0.785648\pi$
$59$	0.0837541	−	0.106904i	0.0109039	−	0.0139177i	0.792605	+	0.609736i	$0.208724\pi$
$60$	−2.64126	+	1.43511i	−0.340985	+	0.185272i
$61$	0.717187	−	0.376409i	0.0918264	−	0.0481942i	−0.418185	−	0.908362i	$-0.637334\pi$
$61$	0.717187	−	0.376409i	0.0918264	−	0.0481942i	0.510011	+	0.860168i	$0.329641\pi$
$62$	−0.747319	−	6.15472i	−0.0949096	−	0.781651i
$63$	−0.587190	+	1.41195i	−0.0739790	+	0.177889i
$64$	3.78705	−	2.61401i	0.473381	−	0.326751i
$65$	0.0508016	+	3.89516i	0.00630116	+	0.483135i
$66$	8.35249	+	17.8667i	1.02812	+	2.19923i
$67$	0.304051	+	5.02657i	0.0371458	+	0.614093i	0.968350	+	0.249596i	$0.0802977\pi$
$67$	0.304051	+	5.02657i	0.0371458	+	0.614093i	−0.931204	+	0.364498i	$0.881241\pi$
$68$	−1.27721	−	5.18183i	−0.154884	−	0.628389i
$69$	1.97239	+	4.21910i	0.237448	+	0.507920i
$70$	−0.739513	−	0.739513i	−0.0883887	−	0.0883887i
$71$	2.67828	+	14.6149i	0.317853	+	1.73447i	0.623051	+	0.782181i	$0.285893\pi$
$71$	2.67828	+	14.6149i	0.317853	+	1.73447i	−0.305198	+	0.952289i	$0.598722\pi$
$72$	−2.07089	−	0.861225i	−0.244057	−	0.101496i
$73$	2.55083	+	5.66772i	0.298553	+	0.663357i	0.998718	−	0.0506242i	$-0.0161211\pi$
$73$	2.55083	+	5.66772i	0.298553	+	0.663357i	−0.700165	+	0.713981i	$0.746890\pi$
$74$	10.5225	−	1.27766i	1.22322	−	0.148525i
$75$	5.16619	−	4.16885i	0.596540	−	0.481378i
$76$	0.0265968	−	0.439698i	0.00305087	−	0.0504368i
$77$	−2.28775	+	2.02677i	−0.260713	+	0.230972i
$78$	9.13139	−	7.56731i	1.03393	−	0.856829i
$79$	8.82755	+	7.82053i	0.993177	+	0.879878i	0.992759	−	0.120122i	$-0.0383284\pi$
$79$	8.82755	+	7.82053i	0.993177	+	0.879878i	0.000418195		1.00000i	$0.499867\pi$
$80$	3.53899	−	3.53899i	0.395671	−	0.395671i
$81$	−1.59725	−	8.85713i	−0.177472	−	0.984126i
$82$	1.51641	−	6.15231i	0.167459	−	0.679409i
$83$	−1.36810	−	0.250713i	−0.150168	−	0.0275194i	0.104645	−	0.994510i	$-0.466629\pi$
$83$	−1.36810	−	0.250713i	−0.150168	−	0.0275194i	−0.254813	+	0.966990i	$0.582014\pi$
$84$	−0.150657	+	1.41015i	−0.0164381	+	0.153860i
$85$	−1.47322	−	3.27337i	−0.159794	−	0.355047i
$86$	−0.0898629	+	0.490366i	−0.00969017	+	0.0528775i
$87$	−6.32876	−	6.14911i	−0.678515	−	0.659254i
$88$	−2.97263	−	3.35541i	−0.316884	−	0.357688i
$89$	−11.5938	−	11.5938i	−1.22894	−	1.22894i	−0.964366	−	0.264571i	$-0.914770\pi$
$89$	−11.5938	−	11.5938i	−1.22894	−	1.22894i	−0.264571	−	0.964366i	$-0.585230\pi$
$90$	6.01629	+	1.30038i	0.634173	+	0.137072i
$91$	1.52601	+	1.02420i	0.159969	+	0.107366i
$92$	2.86422	+	3.23303i	0.298615	+	0.337067i
$93$	−3.14495	+	4.69955i	−0.326116	+	0.487320i
$94$	3.31209	−	8.73328i	0.341616	−	0.900769i
$95$	−0.0357129	−	0.294122i	−0.00366407	−	0.0301763i
$96$	−12.5755	−	1.34354i	−1.28348	−	0.137125i
$97$	−7.54824	+	5.91366i	−0.766407	+	0.600442i	−0.921915	−	0.387393i	$-0.873376\pi$
$97$	−7.54824	+	5.91366i	−0.766407	+	0.600442i	0.155507	+	0.987835i	$0.450299\pi$
$98$	12.5901	−	2.30723i	1.27180	−	0.233065i
$99$	4.85497	−	17.3209i	0.487943	−	1.74081i
$100$	3.49732	−	5.06674i	0.349732	−	0.506674i
$101$	18.7453	−	4.62031i	1.86523	−	0.459738i	0.866039	−	0.499976i	$-0.166658\pi$
$101$	18.7453	−	4.62031i	1.86523	−	0.459738i	0.999190	+	0.0402385i	$0.0128118\pi$
$102$	−4.93878	+	9.74859i	−0.489012	+	0.965254i
$103$	−4.72490	−	3.26136i	−0.465558	−	0.321351i	0.312089	−	0.950053i	$-0.398971\pi$
$103$	−4.72490	−	3.26136i	−0.465558	−	0.321351i	−0.777647	+	0.628701i	$0.783587\pi$
$104$	−1.50219	+	2.23817i	−0.147301	+	0.219471i
$105$	0.0712942	+	0.951202i	0.00695760	+	0.0928278i
$106$	−9.17303	+	7.18661i	−0.890963	+	0.698025i
$107$	1.06004	−	0.128712i	0.102478	−	0.0124431i	−0.0691369	−	0.997607i	$-0.522025\pi$
$107$	1.06004	−	0.128712i	0.102478	−	0.0124431i	0.171615	+	0.985164i	$0.445101\pi$
$108$	−3.75102	−	7.45634i	−0.360942	−	0.717486i
$109$	4.02511	+	2.43326i	0.385535	+	0.233064i	0.696810	−	0.717256i	$-0.254602\pi$
$109$	4.02511	+	2.43326i	0.385535	+	0.233064i	−0.311275	+	0.950320i	$0.600756\pi$
$110$	9.68435	+	7.58720i	0.923367	+	0.723412i
$111$	−8.03465	−	5.37680i	−0.762615	−	0.510343i
$112$	−0.425627	−	2.32257i	−0.0402180	−	0.219462i
$113$	6.60977	−	4.56240i	0.621795	−	0.429194i	−0.215074	−	0.976598i	$-0.568999\pi$
$113$	6.60977	−	4.56240i	0.621795	−	0.429194i	0.836869	+	0.547404i	$0.184384\pi$
$114$	−0.628565	+	0.646929i	−0.0588705	+	0.0605905i
$115$	2.28690	+	1.79167i	0.213254	+	0.167074i
$116$	−7.24618	−	3.80309i	−0.672791	−	0.353108i
$117$	−10.8148	−	0.200969i	−0.999827	−	0.0185796i
$118$	−0.228359	+	0.119852i	−0.0210221	+	0.0110333i
$119$	−1.66580	−	0.305269i	−0.152704	−	0.0279840i
$120$	−1.39512	+	0.104566i	−0.127356	+	0.00954555i
$121$	16.5474	−	18.6781i	1.50431	−	1.69801i
$122$	−1.53534	+	0.0928710i	−0.139003	+	0.00840814i
$123$	−4.70850	+	3.35114i	−0.424551	+	0.302162i
$124$	−1.56019	+	5.00683i	−0.140109	+	0.449627i
$125$	3.91656	−	8.70225i	0.350308	−	0.778352i
$126$	2.11731	−	1.98746i	0.188625	−	0.177057i
$127$	−8.50219	+	9.59699i	−0.754447	+	0.851595i	−0.992825	−	0.119578i	$-0.961846\pi$
$127$	−8.50219	+	9.59699i	−0.754447	+	0.851595i	0.238378	+	0.971173i	$0.423384\pi$
$128$	5.76895	−	1.05720i	0.509908	−	0.0934441i
$129$	0.353856	−	0.285544i	0.0311552	−	0.0251407i
$130$	2.94786	−	6.78494i	0.258545	−	0.595079i
$131$	15.3926	−	5.83766i	1.34486	−	0.510039i	0.426037	−	0.904706i	$-0.359909\pi$
$131$	15.3926	−	5.83766i	1.34486	−	0.510039i	0.918824	+	0.394667i	$0.129140\pi$
$132$	−0.240164	−	16.6809i	−0.0209036	−	1.45189i
$133$	−0.123771	−	0.0649603i	−0.0107323	−	0.00563277i
$134$	3.39111	−	8.94162i	0.292947	−	0.772438i
$135$	−3.38563	−	4.47823i	−0.291388	−	0.385425i
$136$	0.447734	−	2.44321i	0.0383929	−	0.209503i
$137$	−2.99972	−	1.81340i	−0.256284	−	0.154929i	0.383364	−	0.923598i	$-0.374766\pi$
$137$	−2.99972	−	1.81340i	−0.256284	−	0.154929i	−0.639647	+	0.768669i	$0.720919\pi$
$138$	−0.127326	−	8.84358i	−0.0108387	−	0.752815i
$139$	−0.444455	+	3.66042i	−0.0376982	+	0.310473i	0.961647	+	0.274290i	$0.0884428\pi$
$139$	−0.444455	+	3.66042i	−0.0376982	+	0.310473i	−0.999345	+	0.0361825i	$0.988480\pi$
$140$	0.313693	+	0.827141i	0.0265119	+	0.0699062i
$141$	−7.48539	+	4.06714i	−0.630383	+	0.342515i
$142$	6.75262	−	27.3964i	0.566667	−	2.29906i
$143$	−19.2724	−	9.79653i	−1.61164	−	0.819227i
$144$	9.51115	+	10.1325i	0.792596	+	0.844378i
$145$	−5.25505	−	1.63754i	−0.436408	−	0.135990i
$146$		−	11.8030i		−	0.976826i
$147$	−10.0766	−	5.89512i	−0.831103	−	0.486221i
$148$	−8.56000	−	2.66740i	−0.703627	−	0.219259i
$149$	18.2162	−	1.10188i	1.49233	−	0.0902694i	0.706060	−	0.708152i	$-0.250471\pi$
$149$	18.2162	−	1.10188i	1.49233	−	0.0902694i	0.786270	+	0.617883i	$0.212009\pi$
$150$	−12.1956	+	3.19286i	−0.995765	+	0.260696i
$151$	1.16774	−	19.3051i	0.0950297	−	1.57103i	−0.568376	−	0.822769i	$-0.692428\pi$
$151$	1.16774	−	19.3051i	0.0950297	−	1.57103i	0.663406	−	0.748260i	$-0.269110\pi$
$152$	0.0952764	−	0.181534i	0.00772794	−	0.0147244i
$153$	9.21400	−	3.80130i	0.744908	−	0.307317i
$154$	5.54139	−	1.72677i	0.446538	−	0.139147i
$155$	−0.425172	+	3.50160i	−0.0341506	+	0.281255i
$156$	−9.67044	+	2.66700i	−0.774255	+	0.213531i
$157$	0.916459	+	7.54772i	0.0731414	+	0.602374i	0.982487	+	0.186332i	$0.0596600\pi$
$157$	0.916459	+	7.54772i	0.0731414	+	0.602374i	−0.909345	+	0.416042i	$0.863417\pi$
$158$	−9.19169	−	20.4231i	−0.731252	−	1.62477i
$159$	10.6171	+	0.488929i	0.841989	+	0.0387746i
$160$	−7.37632	+	2.79747i	−0.583150	+	0.221159i
$161$	1.30856	−	0.407765i	0.103129	−	0.0321364i
$162$	−4.13714	+	16.5830i	−0.325045	+	1.30288i
$163$	14.1851	−	8.57520i	1.11106	−	0.671661i	0.162014	−	0.986788i	$-0.448201\pi$
$163$	14.1851	−	8.57520i	1.11106	−	0.671661i	0.949049	+	0.315127i	$0.102047\pi$
$164$	−3.30546	+	4.21911i	−0.258113	+	0.329457i
$165$	−2.18128	−	11.0067i	−0.169813	−	0.856872i
$166$	2.17377	+	1.50045i	0.168717	+	0.116457i
$167$	−7.22229	+	16.0473i	−0.558878	+	1.24178i	0.388438	+	0.921475i	$0.373015\pi$
$167$	−7.22229	+	16.0473i	−0.558878	+	1.24178i	−0.947316	+	0.320300i	$0.896216\pi$
$168$	−0.333300	+	0.569712i	−0.0257146	+	0.0439542i
$169$	−2.78086	+	12.6991i	−0.213912	+	0.976853i
$170$			6.81679i			0.522824i
$171$	0.819420	−	0.0732936i	0.0626626	−	0.00560491i
$172$	0.239547	−	0.347044i	0.0182653	−	0.0264618i
$173$	5.27980	−	4.67749i	0.401416	−	0.355623i	−0.438131	−	0.898911i	$-0.644359\pi$
$173$	5.27980	−	4.67749i	0.401416	−	0.355623i	0.839546	+	0.543288i	$0.182821\pi$
$174$	6.16715	+	15.5811i	0.467530	+	1.18120i
$175$	−1.01069	−	1.67188i	−0.0764009	−	0.126383i
$176$	8.26356	+	26.5187i	0.622889	+	1.99892i
$177$	0.229174	+	0.0529988i	0.0172258	+	0.00398363i
$178$	11.0412	+	29.1133i	0.827573	+	2.18213i
$179$	−11.9259	+	6.25918i	−0.891381	+	0.467833i	−0.847251	−	0.531193i	$-0.821744\pi$
$179$	−11.9259	+	6.25918i	−0.891381	+	0.467833i	−0.0441303	+	0.999026i	$0.514052\pi$
$180$	−4.18919	−	3.09161i	−0.312244	−	0.230435i
$181$	4.03211	−	0.489586i	0.299704	−	0.0363907i	0.0306966	−	0.999529i	$-0.490227\pi$
$181$	4.03211	−	0.489586i	0.299704	−	0.0363907i	0.269007	+	0.963138i	$0.413304\pi$
$182$	−1.84437	−	2.96299i	−0.136714	−	0.219631i
$183$	1.11668	+	0.849206i	0.0825473	+	0.0627751i
$184$	0.598063	+	1.91925i	0.0440898	+	0.141489i
$185$	−5.98656	−	0.726900i	−0.440141	−	0.0534428i
$186$	9.10895	−	5.68720i	0.667901	−	0.417006i
$187$	19.8855	+	1.20285i	1.45417	+	0.0879612i
$188$	−5.58654	+	5.58654i	−0.407440	+	0.407440i
$189$	−2.64615	+	0.114358i	−0.192479	+	0.00831829i
$190$	−0.167390	+	0.537174i	−0.0121438	+	0.0389707i
$191$			26.5527i			1.92128i	0.277789	+	0.960642i	$0.410398\pi$
$191$			26.5527i			1.92128i	−0.277789	+	0.960642i	$0.589602\pi$
$192$	6.87941	+	4.02467i	0.496479	+	0.290456i
$193$	6.07654	−	19.5003i	0.437399	−	1.40366i	−0.428544	−	0.903521i	$-0.640973\pi$
$193$	6.07654	−	19.5003i	0.437399	−	1.40366i	0.865943	−	0.500142i	$-0.166719\pi$
$194$	17.6805	−	4.35785i	1.26939	−	0.312876i
$195$	−6.07447	+	2.93689i	−0.435002	+	0.210315i
$196$	−10.5123	−	2.59104i	−0.750877	−	0.185074i
$197$	9.93085	−	16.4276i	0.707543	−	1.17042i	−0.270641	−	0.962680i	$-0.587236\pi$
$197$	9.93085	−	16.4276i	0.707543	−	1.17042i	0.978184	−	0.207739i	$-0.0666106\pi$
$198$	−21.9071	+	26.2111i	−1.55687	+	1.86274i
$199$	13.9149	+	1.68957i	0.986401	+	0.119771i	0.597809	−	0.801639i	$-0.296038\pi$
$199$	13.9149	+	1.68957i	0.986401	+	0.119771i	0.388593	+	0.921410i	$0.372961\pi$
$200$	2.45213	−	1.48236i	0.173392	−	0.104819i
$201$	−7.66396	+	4.16417i	−0.540574	+	0.293718i
$202$	−36.0628	−	6.60875i	−2.53737	−	0.464990i
$203$	−2.04420	+	1.60153i	−0.143475	+	0.112405i
$204$	7.19374	−	5.80499i	0.503663	−	0.406430i
$205$	−1.67532	+	3.19206i	−0.117009	+	0.222943i
$206$	5.64037	+	9.33031i	0.392983	+	0.650073i
$207$	−5.17323	+	6.18959i	−0.359564	+	0.430206i
$208$	14.1796	−	8.82638i	0.983178	−	0.612000i
$209$	1.53747	+	0.583086i	0.106349	+	0.0403329i
$210$	0.617892	−	1.70279i	0.0426386	−	0.117503i
$211$	10.0706	+	8.92178i	0.693289	+	0.614200i	0.934370	−	0.356305i	$-0.115963\pi$
$211$	10.0706	+	8.92178i	0.693289	+	0.614200i	−0.241081	+	0.970505i	$0.577502\pi$
$212$	9.57039	−	2.35889i	0.657297	−	0.162009i
$213$	−20.9671	+	14.9227i	−1.43664	+	1.02249i
$214$	−1.93602	−	0.603288i	−0.132344	−	0.0412399i
$215$	0.116405	−	0.258642i	0.00793877	−	0.0176392i
$216$	−0.167727	−	3.88108i	−0.0114124	−	0.264074i
$217$	1.24563	+	1.10354i	0.0845591	+	0.0749129i
$218$	−5.07393	−	7.35086i	−0.343650	−	0.497863i
$219$	−7.02191	+	8.15980i	−0.474496	+	0.551388i
$220$	−4.83603	−	9.21428i	−0.326045	−	0.621227i
$221$	−2.31280	−	11.7539i	−0.155576	−	0.790650i
$222$	9.72320	+	15.5732i	0.652578	+	1.04521i
$223$	−12.6187	+	16.1066i	−0.845010	+	1.07858i	0.150929	+	0.988545i	$0.451774\pi$
$223$	−12.6187	+	16.1066i	−0.845010	+	1.07858i	−0.995939	+	0.0900311i	$0.971303\pi$
$224$	−0.890716	+	3.61378i	−0.0595135	+	0.241456i
$225$	10.3307	+	5.04812i	0.688712	+	0.336541i
$226$	−15.0022	+	2.74925i	−0.997931	+	0.182878i
$227$	−0.579030	+	9.57251i	−0.0384316	+	0.635350i	0.927060	+	0.374914i	$0.122328\pi$
$227$	−0.579030	+	9.57251i	−0.0384316	+	0.635350i	−0.965491	+	0.260436i	$0.916134\pi$
$228$	0.709422	−	0.280795i	0.0469826	−	0.0185961i
$229$	−10.3462	+	17.1147i	−0.683696	+	1.13097i	0.300482	+	0.953788i	$0.402853\pi$
$229$	−10.3462	+	17.1147i	−0.683696	+	1.13097i	−0.984178	+	0.177184i	$0.943301\pi$
$230$	−2.56388	−	4.88506i	−0.169057	−	0.322111i
$231$	−4.85823	−	2.10294i	−0.319648	−	0.138363i
$232$	−2.34894	−	2.99821i	−0.154216	−	0.196842i
$233$	−15.6021	−	22.6035i	−1.02213	−	1.48080i	−0.870377	−	0.492385i	$-0.836125\pi$
$233$	−15.6021	−	22.6035i	−1.02213	−	1.48080i	−0.151748	−	0.988419i	$-0.548490\pi$
$234$	18.5716	+	8.77692i	1.21406	+	0.573766i
$235$	−3.01866	+	4.37328i	−0.196916	+	0.285282i
$236$	0.217750	−	0.0131714i	0.0141743	−	0.000857388i
$237$	−5.79569	+	19.5875i	−0.376471	+	1.27234i
$238$	2.64679	+	1.82695i	0.171566	+	0.118423i
$239$	18.6510	−	18.6510i	1.20643	−	1.20643i	0.234259	−	0.972174i	$-0.424734\pi$
$239$	18.6510	−	18.6510i	1.20643	−	1.20643i	0.972174	−	0.234259i	$-0.0752664\pi$
$240$	8.14881	+	2.95697i	0.526003	+	0.190871i
$241$	10.7259	+	13.6906i	0.690914	+	0.881887i	0.997551	−	0.0699396i	$-0.0222807\pi$
$241$	10.7259	+	13.6906i	0.690914	+	0.881887i	−0.306637	+	0.951827i	$0.599204\pi$
$242$	−43.2130	+	19.4486i	−2.77784	+	1.25020i
$243$	12.7258	−	9.00306i	0.816358	−	0.577546i
$244$	1.21651	+	0.461363i	0.0778793	+	0.0295357i
$245$	−7.26890	−	0.439688i	−0.464393	−	0.0280906i
$246$	10.7657	−	2.13351i	0.686394	−	0.136028i
$247$	0.106370	−	0.983014i	0.00676818	−	0.0625477i
$248$	−1.61854	+	1.82696i	−0.102777	+	0.116012i
$249$	−0.610144	−	2.33053i	−0.0386663	−	0.147691i
$250$	−13.5648	+	12.0174i	−0.857915	+	0.760046i
$251$	14.7873	+	3.64473i	0.933363	+	0.230053i	0.676541	−	0.736405i	$-0.263478\pi$
$251$	14.7873	+	3.64473i	0.933363	+	0.230053i	0.256823	+	0.966459i	$0.417324\pi$
$252$	−2.32312	+	0.797985i	−0.146343	+	0.0502683i
$253$	−14.7028	+	6.61718i	−0.924356	+	0.416019i
$254$	22.2032	−	9.99286i	1.39315	−	0.627008i
$255$	4.05547	−	4.71266i	0.253964	−	0.295118i
$256$	−19.7500	−	4.86794i	−1.23437	−	0.304246i
$257$	−12.5289	+	11.0996i	−0.781531	+	0.692376i	−0.956350	−	0.292224i	$-0.905605\pi$
$257$	−12.5289	+	11.0996i	−0.781531	+	0.692376i	0.174819	+	0.984601i	$0.444066\pi$
$258$	−0.835330	+	0.218693i	−0.0520054	+	0.0136152i
$259$	−1.88667	+	2.12962i	−0.117232	+	0.132328i
$260$	−4.62922	+	4.21016i	−0.287092	+	0.261103i
$261$	5.00605	−	14.4407i	0.309867	−	0.893857i
$262$	−31.2056	−	1.88759i	−1.92789	−	0.116616i
$263$	1.14437	+	0.434001i	0.0705646	+	0.0267616i	0.389635	−	0.920970i	$-0.372601\pi$
$263$	1.14437	+	0.434001i	0.0705646	+	0.0267616i	−0.319070	+	0.947731i	$0.603371\pi$
$264$	3.08435	−	7.12550i	0.189829	−	0.438544i
$265$	6.04564	−	2.72092i	0.371381	−	0.167145i
$266$	0.163709	+	0.208959i	0.0100377	+	0.0128121i
$267$	9.68705	−	26.6956i	0.592838	−	1.63374i
$268$	−5.71981	+	5.71981i	−0.349393	+	0.349393i
$269$	3.15046	+	2.17461i	0.192087	+	0.132588i	0.660227	−	0.751066i	$-0.270460\pi$
$269$	3.15046	+	2.17461i	0.192087	+	0.132588i	−0.468140	+	0.883654i	$0.655076\pi$
$270$	2.37271	+	10.3938i	0.144398	+	0.632545i
$271$	−3.99765	+	0.241813i	−0.242840	+	0.0146891i	−0.181350	−	0.983419i	$-0.558047\pi$
$271$	−3.99765	+	0.241813i	−0.242840	+	0.0146891i	−0.0614898	+	0.998108i	$0.519585\pi$
$272$	−8.74298	+	12.6664i	−0.530121	+	0.768012i
$273$	−0.487680	+	3.14567i	−0.0295157	+	0.190384i
$274$	3.78136	+	5.47825i	0.228440	+	0.330953i
$275$	14.1731	+	18.0906i	0.854669	+	1.09090i
$276$	−2.97186	+	6.86563i	−0.178885	+	0.413262i
$277$	−8.77268	−	16.7149i	−0.527099	−	1.00430i	−0.992848	−	0.119386i	$-0.961907\pi$
$277$	−8.77268	−	16.7149i	−0.527099	−	1.00430i	0.465749	−	0.884917i	$-0.345785\pi$
$278$	3.62256	−	5.99244i	0.217266	−	0.359403i
$279$	−9.68075	−	1.48740i	−0.579572	−	0.0890481i
$280$	−0.0248591	+	0.410971i	−0.00148562	+	0.0245602i
$281$	12.1308	−	2.22304i	0.723660	−	0.132616i	0.194214	−	0.980959i	$-0.437784\pi$
$281$	12.1308	−	2.22304i	0.723660	−	0.132616i	0.529446	+	0.848344i	$0.322400\pi$
$282$	16.1325	−	1.20916i	0.960677	−	0.0720044i
$283$	−4.17480	+	16.9378i	−0.248166	+	1.00685i	0.706153	+	0.708060i	$0.250429\pi$
$283$	−4.17480	+	16.9378i	−0.248166	+	1.00685i	−0.954319	+	0.298790i	$0.903417\pi$
$284$	−14.7193	+	18.7878i	−0.873432	+	1.11485i
$285$	0.435299	−	0.271780i	0.0257849	−	0.0160989i
$286$	25.7393	+	31.9856i	1.52200	+	1.89135i
$287$	0.790397	+	1.50598i	0.0466557	+	0.0888950i
$288$	−7.11631	−	20.7173i	−0.419333	−	1.22078i
$289$	−3.38644	−	4.90611i	−0.199203	−	0.288595i
$290$	7.82403	+	6.93149i	0.459443	+	0.407031i
$291$	−14.8157	−	7.50584i	−0.868510	−	0.440000i
$292$	−4.09746	+	9.10418i	−0.239786	+	0.532782i
$293$	−6.75830	−	2.10597i	−0.394824	−	0.123032i	0.0936617	−	0.995604i	$-0.470143\pi$
$293$	−6.75830	−	2.10597i	−0.394824	−	0.123032i	−0.488486	+	0.872572i	$0.662450\pi$
$294$	12.8553	+	18.0623i	0.749737	+	1.05341i
$295$	0.142463	−	0.0351140i	0.00829453	−	0.00204442i
$296$	−3.12348	−	2.76716i	−0.181549	−	0.160838i
$297$	30.7387	−	5.08747i	1.78364	−	0.295205i
$298$	−32.4043	−	12.2893i	−1.87713	−	0.711902i
$299$	6.07817	+	7.55319i	0.351509	+	0.436812i
$300$	10.5154	+	1.77095i	0.607105	+	0.102246i
$301$	−0.0692266	−	0.114515i	−0.00399016	−	0.00660052i
$302$	−17.0684	+	32.5211i	−0.982175	+	1.87138i
$303$	20.9996	+	26.0234i	1.20640	+	1.49501i
$304$	−0.999990	+	0.783442i	−0.0573533	+	0.0449335i
$305$	0.860762	+	0.157741i	0.0492871	+	0.00903220i
$306$	−18.9188	−	0.598452i	−1.08152	−	0.0342112i
$307$	−7.96201	+	4.81320i	−0.454416	+	0.274704i	−0.725979	−	0.687717i	$-0.758613\pi$
$307$	−7.96201	+	4.81320i	−0.454416	+	0.274704i	0.271563	+	0.962421i	$0.412459\pi$
$308$	−4.87376	−	0.591781i	−0.277708	−	0.0337199i
$309$	1.65146	−	9.80592i	0.0939484	−	0.557839i
$310$	3.46538	−	5.73244i	0.196821	−	0.325581i
$311$	−8.71812	−	2.14882i	−0.494359	−	0.121849i	−0.0157488	−	0.999876i	$-0.505013\pi$
$311$	−8.71812	−	2.14882i	−0.494359	−	0.121849i	−0.478610	+	0.878027i	$0.658859\pi$
$312$	−4.61371	−	0.715273i	−0.261200	−	0.0404944i
$313$	26.9972	−	6.65422i	1.52597	−	0.376119i	0.614981	−	0.788542i	$-0.289164\pi$
$313$	26.9972	−	6.65422i	1.52597	−	0.376119i	0.910992	+	0.412424i	$0.135318\pi$
$314$	4.29554	−	13.7849i	0.242411	−	0.777925i
$315$	−1.44020	+	0.809590i	−0.0811459	+	0.0456153i
$316$			18.9441i			1.06569i
$317$	0.818926	−	2.62803i	0.0459955	−	0.147605i	−0.928866	−	0.370415i	$-0.879215\pi$
$317$	0.818926	−	2.62803i	0.0459955	−	0.147605i	0.974862	+	0.222811i	$0.0715231\pi$
$318$	−18.0048	−	9.12150i	−1.00966	−	0.511509i
$319$	21.6007	−	21.6007i	1.20940	−	1.20940i
$320$	4.96257	+	0.300180i	0.277416	+	0.0167806i
$321$	0.979520	+	1.56886i	0.0546715	+	0.0875651i
$322$	−2.58388	−	0.313740i	−0.143994	−	0.0174840i
$323$	0.271060	+	0.869861i	0.0150822	+	0.0484003i
$324$	8.94799	−	11.3549i	0.497111	−	0.630831i
$325$	8.37986	−	10.9883i	0.464831	−	0.609522i
$326$	−31.2481	+	3.79421i	−1.73067	+	0.210142i
$327$	−0.865436	+	8.10048i	−0.0478587	+	0.447957i
$328$	−2.20880	+	1.15927i	−0.121960	+	0.0640097i
$329$	0.889014	+	2.34414i	0.0490129	+	0.129236i
$330$	−4.80111	+	20.7607i	−0.264292	+	1.14284i
$331$	0.285172	+	0.915149i	0.0156745	+	0.0503012i	0.962227	−	0.272249i	$-0.0877675\pi$
$331$	0.285172	+	0.915149i	0.0156745	+	0.0503012i	−0.946552	+	0.322550i	$0.895460\pi$
$332$	−1.15584	−	1.91199i	−0.0634348	−	0.104934i
$333$	2.54295	−	16.5508i	0.139353	−	0.906980i
$334$	25.0141	−	22.1605i	1.36871	−	1.21257i
$335$	−3.09067	+	4.47761i	−0.168862	+	0.244638i
$336$	3.33205	−	2.37149i	0.181778	−	0.129375i
$337$			21.7754i			1.18618i	0.805135	+	0.593091i	$0.202093\pi$
$337$			21.7754i			1.18618i	−0.805135	+	0.593091i	$0.797907\pi$
$338$	14.7132	−	19.8240i	0.800292	−	1.07828i
$339$	12.0071	+	7.02452i	0.652135	+	0.381520i
$340$	2.36647	−	5.25808i	0.128340	−	0.285160i
$341$	−16.1108	−	11.1205i	−0.872450	−	0.602209i
$342$	−1.47614	−	0.511721i	−0.0798203	−	0.0276707i
$343$	−4.31934	+	5.51323i	−0.233223	+	0.297687i
$344$	0.167957	−	0.101534i	0.00905566	−	0.00547434i
$345$	−1.13375	+	4.90250i	−0.0610391	+	0.263942i
$346$	−12.7887	+	3.98513i	−0.687527	+	0.214242i
$347$	9.56880	−	3.62897i	0.513680	−	0.194813i	−0.0841241	−	0.996455i	$-0.526809\pi$
$347$	9.56880	−	3.62897i	0.513680	−	0.194813i	0.597804	+	0.801642i	$0.296040\pi$
$348$	0.652054	−	14.1593i	0.0349538	−	0.759020i
$349$	3.93774	+	8.74930i	0.210782	+	0.468339i	0.986712	−	0.162481i	$-0.0519495\pi$
$349$	3.93774	+	8.74930i	0.210782	+	0.468339i	−0.775929	+	0.630820i	$0.782719\pi$
$350$	0.447193	+	3.68296i	0.0239035	+	0.196863i
$351$	−7.61753	−	17.1165i	−0.406594	−	0.913609i
$352$	5.27742	−	43.4634i	0.281287	−	2.31661i
$353$	−8.45004	+	2.63314i	−0.449750	+	0.140148i	−0.514008	−	0.857786i	$-0.671840\pi$
$353$	−8.45004	+	2.63314i	−0.449750	+	0.140148i	0.0642576	+	0.997933i	$0.479532\pi$
$354$	−0.355561	−	0.270395i	−0.0188978	−	0.0143713i
$355$	−7.46025	+	14.2143i	−0.395949	+	0.754418i
$356$	1.59021	−	26.2893i	0.0842809	−	1.39333i
$357$	−0.742912	−	2.83766i	−0.0393191	−	0.150185i
$358$	25.5307	−	1.54432i	1.34934	−	0.0816199i
$359$	−7.15179	−	2.22859i	−0.377457	−	0.117620i	0.102904	−	0.994691i	$-0.467187\pi$
$359$	−7.15179	−	2.22859i	−0.377457	−	0.117620i	−0.480361	+	0.877071i	$0.659494\pi$
$360$	−1.18742	−	2.11232i	−0.0625823	−	0.111329i
$361$		−	18.9248i		−	0.996042i
$362$	−7.36408	−	2.29474i	−0.387048	−	0.120609i
$363$	41.4449	+	12.2630i	2.17529	+	0.643643i
$364$	0.394034	+	2.92576i	0.0206530	+	0.153351i
$365$	−1.60703	+	6.51996i	−0.0841156	+	0.341270i
$366$	−1.27192	−	2.34092i	−0.0664845	−	0.122362i
$367$	−6.46819	−	17.0552i	−0.337637	−	0.890275i	−0.991076	−	0.133296i	$-0.957444\pi$
$367$	−6.46819	−	17.0552i	−0.337637	−	0.890275i	0.653440	−	0.756979i	$-0.273325\pi$
$368$	1.50142	−	12.3653i	0.0782671	−	0.644588i
$369$	−8.71191	−	4.92979i	−0.453524	−	0.256635i
$370$	9.80055	+	5.92464i	0.509506	+	0.308007i
$371$	0.563806	−	3.07659i	0.0292714	−	0.159729i
$372$	−9.00045	+	1.22458i	−0.466652	+	0.0634914i
$373$	4.48484	−	11.8256i	0.232216	−	0.612304i	−0.767366	−	0.641210i	$-0.778433\pi$
$373$	4.48484	−	11.8256i	0.232216	−	0.612304i	0.999582	+	0.0289053i	$0.00920214\pi$
$374$	−33.4988	−	17.5815i	−1.73218	−	0.909118i
$375$	16.5272	−	0.237952i	0.853462	−	0.0122878i
$376$	−3.43812	+	1.30391i	−0.177307	+	0.0672438i
$377$	−15.8423	−	9.29709i	−0.815920	−	0.478824i
$378$	4.67154	+	1.86434i	0.240278	+	0.0958913i
$379$	17.2741	−	3.16560i	0.887311	−	0.162606i	0.282778	−	0.959186i	$-0.408744\pi$
$379$	17.2741	−	3.16560i	0.887311	−	0.162606i	0.604534	+	0.796580i	$0.293360\pi$
$380$	0.315596	−	0.356235i	0.0161898	−	0.0182745i
$381$	−21.2948	−	6.30086i	−1.09096	−	0.322803i
$382$	20.6948	−	45.9820i	1.05884	−	2.35264i
$383$	−4.46822	+	14.3390i	−0.228316	+	0.732691i	0.767479	+	0.641074i	$0.221511\pi$
$383$	−4.46822	+	14.3390i	−0.228316	+	0.732691i	−0.995794	+	0.0916162i	$0.970797\pi$
$384$	5.89045	+	8.27635i	0.300596	+	0.422351i
$385$	−3.29615	+	0.199381i	−0.167987	+	0.0101614i
$386$	−25.7212	+	29.0332i	−1.30917	+	1.47775i
$387$	0.707595	+	0.345768i	0.0359691	+	0.0175764i
$388$	−15.1506	−	2.77644i	−0.769153	−	0.140953i
$389$	−1.46364	+	0.768180i	−0.0742097	+	0.0389483i	−0.501420	−	0.865204i	$-0.667189\pi$
$389$	−1.46364	+	0.768180i	−0.0742097	+	0.0389483i	0.427210	+	0.904152i	$0.359496\pi$
$390$	12.8083	−	0.351523i	0.648573	−	0.0178001i
$391$	−7.91052	−	4.15176i	−0.400052	−	0.209964i
$392$	−3.96664	−	3.10766i	−0.200346	−	0.156961i
$393$	20.4505	+	19.8699i	1.03159	+	1.00231i
$394$	−30.0010	+	20.7082i	−1.51143	+	1.04326i
$395$	2.29678	+	12.5331i	0.115564	+	0.630611i
$396$	25.9972	−	12.6126i	1.30641	−	0.633808i
$397$	−26.5189	−	20.7763i	−1.33095	−	1.04273i	−0.994898	−	0.100886i	$-0.967832\pi$
$397$	−26.5189	−	20.7763i	−1.33095	−	1.04273i	−0.336049	−	0.941844i	$-0.609091\pi$
$398$	−22.7800	−	13.7710i	−1.14186	−	0.690276i
$399$	0.0111377	−	0.241855i	0.000557582	−	0.0121079i
$400$	−17.6251	+	2.14007i	−0.881254	+	0.107004i
$401$	−20.7286	+	16.2398i	−1.03513	+	0.810976i	−0.982241	−	0.187624i	$-0.939921\pi$
$401$	−20.7286	+	16.2398i	−1.03513	+	0.810976i	−0.0528935	+	0.998600i	$0.516844\pi$
$402$	16.5174	−	1.23801i	0.823812	−	0.0617461i
$403$	−4.03029	+	11.0599i	−0.200763	+	0.550933i
$404$	25.5225	+	17.6169i	1.26979	+	0.876474i
$405$	4.54318	−	8.59712i	0.225753	−	0.427194i
$406$	4.78821	−	1.18019i	0.237635	−	0.0585718i
$407$	19.0123	−	27.5441i	0.942405	−	1.36531i
$408$	4.16196	−	1.08962i	0.206048	−	0.0539442i
$409$	−4.17101	+	0.764366i	−0.206243	+	0.0377955i	−0.282383	−	0.959302i	$-0.591125\pi$
$409$	−4.17101	+	0.764366i	−0.206243	+	0.0377955i	0.0761401	+	0.997097i	$0.475740\pi$
$410$	5.38904	−	4.22205i	0.266146	−	0.208512i
$411$	0.644969	−	6.03690i	0.0318140	−	0.297779i
$412$	−1.11161	−	9.15493i	−0.0547651	−	0.451031i
$413$	0.0245472	−	0.0647256i	0.00120789	−	0.00318494i
$414$	13.7827	−	6.68672i	0.677383	−	0.328635i
$415$	−0.996494	−	1.12481i	−0.0489160	−	0.0552147i
$416$	−26.0915	+	3.51393i	−1.27924	+	0.172285i
$417$	−6.06943	+	1.98761i	−0.297221	+	0.0973339i
$418$	−2.20803	−	2.20803i	−0.107998	−	0.107998i
$419$	15.0661	+	17.0061i	0.736025	+	0.830800i	0.990677	−	0.136232i	$-0.0434994\pi$
$419$	15.0661	+	17.0061i	0.736025	+	0.830800i	−0.254652	+	0.967033i	$0.581961\pi$
$420$	−1.06773	+	1.09893i	−0.0521001	+	0.0536222i
$421$	−5.09142	+	27.7830i	−0.248140	+	1.35406i	0.589470	+	0.807790i	$0.299337\pi$
$421$	−5.09142	+	27.7830i	−0.248140	+	1.35406i	−0.837610	+	0.546268i	$0.816048\pi$
$422$	−10.4860	−	23.2990i	−0.510451	−	1.13418i
$423$	−11.8723	−	8.76169i	−0.577249	−	0.426008i
$424$	4.51240	+	0.826927i	0.219141	+	0.0401591i
$425$	−3.04743	+	12.3639i	−0.147822	+	0.599738i
$426$	47.9398	−	9.50058i	2.32269	−	0.460305i
$427$	0.291937	−	0.291937i	0.0141278	−	0.0141278i
$428$	1.28390	+	1.13744i	0.0620597	+	0.0549801i
$429$	1.23464	−	37.4255i	0.0596088	−	1.80692i
$430$	−0.403164	+	0.357172i	−0.0194423	+	0.0172244i
$431$	1.27080	−	21.0088i	0.0612123	−	1.01196i	−0.829823	−	0.558027i	$-0.811559\pi$
$431$	1.27080	−	21.0088i	0.0612123	−	1.01196i	0.891035	−	0.453934i	$-0.149980\pi$
$432$	−8.92193	+	22.3560i	−0.429256	+	1.07560i
$433$	−29.7846	+	3.61651i	−1.43136	+	0.173798i	−0.799211	−	0.601050i	$-0.794749\pi$
$433$	−29.7846	+	3.61651i	−1.43136	+	0.173798i	−0.632147	+	0.774848i	$0.717826\pi$
$434$	−1.29702	−	2.88185i	−0.0622588	−	0.138333i
$435$	−1.28529	−	9.44666i	−0.0616248	−	0.452933i
$436$	1.36186	+	7.43145i	0.0652215	+	0.355902i
$437$	−0.521412	−	0.521412i	−0.0249425	−	0.0249425i
$438$	18.5197	−	8.65776i	0.884904	−	0.413684i
$439$	−9.45370	−	38.3552i	−0.451200	−	1.83059i	−0.549577	−	0.835443i	$-0.685211\pi$
$439$	−9.45370	−	38.3552i	−0.451200	−	1.83059i	0.0983767	−	0.995149i	$-0.468635\pi$
$440$	−0.292429	−	4.83442i	−0.0139410	−	0.230472i
$441$	1.85842	−	20.1350i	0.0884961	−	0.958807i
$442$	−5.15567	+	22.1570i	−0.245230	+	1.05390i
$443$	1.78705	−	1.23351i	0.0849052	−	0.0586058i	−0.524856	−	0.851191i	$-0.675881\pi$
$443$	1.78705	−	1.23351i	0.0849052	−	0.0586058i	0.609761	+	0.792585i	$0.291265\pi$
$444$	−2.09362	−	15.3877i	−0.0993586	−	0.730270i
$445$	−2.13525	−	17.5854i	−0.101221	−	0.833627i
$446$	34.4054	−	18.0573i	1.62914	−	0.855039i
$447$	15.0909	+	27.7741i	0.713774	+	1.31367i
$448$	1.44655	−	1.84639i	0.0683433	−	0.0872337i
$449$	−3.88636	−	0.235082i	−0.183409	−	0.0110942i	−0.0315812	−	0.999501i	$-0.510054\pi$
$449$	−3.88636	−	0.235082i	−0.183409	−	0.0110942i	−0.151828	+	0.988407i	$0.548516\pi$
$450$	−13.9555	−	16.7936i	−0.657868	−	0.791656i
$451$	−11.3654	−	16.4656i	−0.535174	−	0.775333i
$452$	12.5262	+	3.08744i	0.589185	+	0.145221i
$453$	31.1475	−	12.3284i	1.46344	−	0.579240i
$454$	8.46341	−	16.1257i	0.397208	−	0.756816i
$455$	0.615406	+	1.88787i	0.0288507	+	0.0885045i
$456$	0.354725	+	0.0163355i	0.0166115	+	0.000764980i
$457$	−3.43034	+	18.7187i	−0.160464	+	0.875626i	0.800579	+	0.599228i	$0.204526\pi$
$457$	−3.43034	+	18.7187i	−0.160464	+	0.875626i	−0.961043	+	0.276398i	$0.910859\pi$
$458$	31.2558	−	21.5743i	1.46049	−	1.00810i
$459$	12.7231	+	11.6690i	0.593865	+	0.544661i
$460$	0.281764	+	4.65811i	0.0131373	+	0.217186i
$461$	16.7600	+	7.54308i	0.780593	+	0.351316i	0.761218	−	0.648496i	$-0.224602\pi$
$461$	16.7600	+	7.54308i	0.780593	+	0.351316i	0.0193748	+	0.999812i	$0.493832\pi$
$462$	6.77412	+	7.42815i	0.315160	+	0.345589i
$463$	4.19282	+	1.88704i	0.194857	+	0.0876980i	0.505492	−	0.862831i	$-0.331311\pi$
$463$	4.19282	+	1.88704i	0.194857	+	0.0876980i	−0.310635	+	0.950529i	$0.600542\pi$
$464$	5.64787	+	22.9143i	0.262196	+	1.06377i
$465$	−5.80610	+	1.90138i	−0.269251	+	0.0881742i
$466$	9.40165	+	51.3031i	0.435523	+	2.37657i
$467$	−1.51588	+	3.99705i	−0.0701467	+	0.184962i	−0.965505	−	0.260385i	$-0.916150\pi$
$467$	−1.51588	+	3.99705i	−0.0701467	+	0.184962i	0.895358	+	0.445347i	$0.146920\pi$
$468$	−11.2781	−	13.2172i	−0.521332	−	0.610965i
$469$	0.910222	+	2.40006i	0.0420302	+	0.110824i
$470$	8.63597	−	5.22063i	0.398348	−	0.240810i
$471$	−11.1706	+	6.97439i	−0.514713	+	0.321363i
$472$	0.0949322	+	0.0360030i	0.00436961	+	0.00165717i
$473$	0.970778	+	1.23911i	0.0446364	+	0.0569742i
$474$	25.3028	−	29.4031i	1.16219	−	1.35053i
$475$	−0.543745	+	0.899464i	−0.0249487	+	0.0412702i
$476$	−1.40735	−	2.32804i	−0.0645057	−	0.106706i
$477$	7.02068	+	17.0175i	0.321455	+	0.779177i
$478$	−46.8348	+	17.7621i	−2.14217	+	0.812419i
$479$	2.30259	+	1.39197i	0.105208	+	0.0636005i	0.568964	−	0.822363i	$-0.307345\pi$
$479$	2.30259	+	1.39197i	0.105208	+	0.0636005i	−0.463755	+	0.885963i	$0.653498\pi$
$480$	−9.80008	−	9.52189i	−0.447310	−	0.434613i
$481$	−18.9087	−	6.89043i	−0.862163	−	0.314177i
$482$	−7.90403	−	32.0679i	−0.360019	−	1.46065i
$483$	1.59966	+	1.75411i	0.0727873	+	0.0798148i
$484$	40.0837			1.82198
$485$	−10.3600			−0.470424
$486$	−29.0544	+	5.67255i	−1.31793	+	0.257312i
$487$	1.89756	+	31.3705i	0.0859868	+	1.42153i	0.743826	+	0.668373i	$0.233009\pi$
$487$	1.89756	+	31.3705i	0.0859868	+	1.42153i	−0.657839	+	0.753158i	$0.728529\pi$
$488$	0.428180	+	0.428180i	0.0193828	+	0.0193828i
$489$	23.8601	+	15.9672i	1.07899	+	0.722062i
$490$	12.2451	+	6.42670i	0.553176	+	0.290329i
$491$	−1.99156	+	16.4019i	−0.0898777	+	0.740209i	0.876198	+	0.481951i	$0.160072\pi$
$491$	−1.99156	+	16.4019i	−0.0898777	+	0.740209i	−0.966076	+	0.258258i	$0.916851\pi$
$492$	−9.04466	−	2.09167i	−0.407765	−	0.0942996i
$493$	16.8031	+	2.04027i	0.756774	+	0.0918890i
$494$	−0.950352	+	1.61941i	−0.0427584	+	0.0728606i
$495$	15.6702	−	11.4962i	0.704323	−	0.516716i
$496$	13.7913	−	6.20696i	0.619248	−	0.278701i
$497$	3.51966	+	6.70616i	0.157878	+	0.300812i
$498$	−0.759784	+	4.51138i	−0.0340467	+	0.202160i
$499$	−3.54424	−	11.3739i	−0.158662	−	0.509164i	0.840821	−	0.541313i	$-0.182073\pi$
$499$	−3.54424	−	11.3739i	−0.158662	−	0.509164i	−0.999483	+	0.0321490i	$0.989765\pi$
$500$	14.6350	−	4.56045i	0.654497	−	0.203950i
$501$	−30.4768	+	0.438792i	−1.36160	+	0.0196038i
$502$	−22.7668	−	17.8367i	−1.01613	−	0.796090i
$503$	16.0431	+	18.1089i	0.715327	+	0.807438i	0.987965	−	0.154679i	$-0.0494344\pi$
$503$	16.0431	+	18.1089i	0.715327	+	0.807438i	−0.272637	+	0.962117i	$0.587896\pi$
$504$	−1.13839	−	0.105072i	−0.0507081	−	0.00468026i
$505$	19.0212	+	8.56074i	0.846431	+	0.380948i
$506$	30.6185			1.36116
$507$	−21.9654	+	4.95171i	−0.975519	+	0.219913i
$508$	−20.5953			−0.913770
$509$	3.61940	+	1.62896i	0.160427	+	0.0722024i	0.489036	−	0.872264i	$-0.337349\pi$
$509$	3.61940	+	1.62896i	0.160427	+	0.0722024i	−0.328608	+	0.944466i	$0.606580\pi$
$510$	−10.6960	+	5.00026i	−0.473625	+	0.221415i
$511$	2.10084	+	2.37136i	0.0929357	+	0.104903i
$512$	21.1739	+	16.5887i	0.935762	+	0.733123i
$513$	0.716063	+	1.23196i	0.0316150	+	0.0543922i
$514$	30.3475	−	9.45667i	1.33857	−	0.417116i
$515$	−1.84537	−	5.92199i	−0.0813166	−	0.260954i
$516$	0.720245	+	0.121300i	0.0317070	+	0.00533993i
$517$	−13.7054	−	26.1135i	−0.602763	−	1.14847i
$518$	4.92700	−	2.21746i	0.216480	−	0.0974297i
$519$	11.2121	+	4.85328i	0.492157	+	0.213035i
$520$	−2.76891	+	0.902608i	−0.121425	+	0.0395820i
$521$	−11.2074	−	1.36083i	−0.491006	−	0.0596189i	−0.128710	−	0.991682i	$-0.541084\pi$
$521$	−11.2074	−	1.36083i	−0.491006	−	0.0596189i	−0.362295	+	0.932063i	$0.618007\pi$
$522$	−19.9240	+	21.1057i	−0.872050	+	0.923772i
$523$	−3.44389	+	28.3630i	−0.150591	+	1.24023i	0.699902	+	0.714239i	$0.253227\pi$
$523$	−3.44389	+	28.3630i	−0.150591	+	1.24023i	−0.850493	+	0.525987i	$0.823696\pi$
$524$	23.4149	+	12.2891i	1.02289	+	0.536852i
$525$	1.88192	−	2.81219i	0.0821339	−	0.122734i
$526$	−1.64347	−	1.64347i	−0.0716589	−	0.0716589i
$527$	−0.654929	−	10.8273i	−0.0285292	−	0.471643i
$528$	−35.5479	+	32.4180i	−1.54702	+	1.41081i
$529$	−15.7696			−0.685636
$530$	−12.5900			−0.546876
$531$	0.0849458	+	0.398464i	0.00368633	+	0.0172919i
$532$	−0.0537349	−	0.218011i	−0.00232971	−	0.00945199i
$533$	−7.85960	+	9.10825i	−0.340437	+	0.394522i
$534$	−37.5815	+	38.6795i	−1.62631	+	1.67382i
$535$	0.987313	+	0.596851i	0.0426852	+	0.0258041i
$536$	−3.52014	+	1.33501i	−0.152047	+	0.0576637i
$537$	−18.5689	−	14.1212i	−0.801307	−	0.609373i
$538$	−3.76088	−	6.22125i	−0.162143	−	0.268217i
$539$	20.9082	−	34.5865i	0.900582	−	1.48974i
$540$	1.77806	−	8.84085i	0.0765157	−	0.380450i
$541$	25.3134	+	32.3102i	1.08831	+	1.38912i	0.914616	+	0.404324i	$0.132493\pi$
$541$	25.3134	+	32.3102i	1.08831	+	1.38912i	0.173694	+	0.984800i	$0.444430\pi$
$542$	7.11130	+	2.69696i	0.305456	+	0.115844i
$543$	3.72582	+	5.96749i	0.159890	+	0.256090i
$544$	20.7611	−	12.5505i	0.890125	−	0.538100i
$545$	1.80198	+	4.75143i	0.0771883	+	0.203529i
$546$	3.29622	−	5.06735i	0.141065	−	0.216862i
$547$	3.76736	−	9.93372i	0.161081	−	0.424735i	−0.830039	−	0.557705i	$-0.811682\pi$
$547$	3.76736	−	9.93372i	0.161081	−	0.424735i	0.991120	+	0.132970i	$0.0424513\pi$
$548$	−1.01493	−	5.53831i	−0.0433558	−	0.236585i
$549$	−0.513348	+	2.37505i	−0.0219092	+	0.101364i
$550$	−10.4443	−	42.3743i	−0.445348	−	1.80685i
$551$	1.27401	+	0.573385i	0.0542747	+	0.0244270i
$552$	−2.57273	+	2.34621i	−0.109503	+	0.0998612i
$553$	5.48185	+	2.46718i	0.233112	+	0.104915i
$554$	2.16447	+	35.7830i	0.0919596	+	1.52027i
$555$	−3.25071	−	9.92647i	−0.137985	−	0.421355i
$556$	−4.87452	+	3.36464i	−0.206726	+	0.142693i
$557$	0.506258	−	2.76256i	0.0214508	−	0.117053i	−0.971152	−	0.238462i	$-0.923357\pi$
$557$	0.506258	−	2.76256i	0.0214508	−	0.117053i	0.992603	+	0.121409i	$0.0387412\pi$
$558$	15.6052	+	10.1208i	0.660619	+	0.428448i
$559$	0.573974	−	0.752639i	0.0242765	−	0.0318332i
$560$	1.18557	−	2.25891i	0.0500994	−	0.0954564i
$561$	12.6991	+	32.0838i	0.536155	+	1.35458i
$562$	−22.7398	−	5.60485i	−0.959219	−	0.236426i
$563$	17.4178	+	25.2340i	0.734072	+	1.06349i	0.995169	+	0.0981747i	$0.0313004\pi$
$563$	17.4178	+	25.2340i	0.734072	+	1.06349i	−0.261097	+	0.965313i	$0.584084\pi$
$564$	−12.8635	−	4.66778i	−0.541649	−	0.196549i
$565$	8.66149	+	0.523924i	0.364392	+	0.0220416i
$566$	20.4307	−	26.0779i	0.858768	−	1.09614i
$567$	−2.12044	−	4.06809i	−0.0890501	−	0.170844i
$568$	−9.83583	+	5.16224i	−0.412702	+	0.216603i
$569$	2.93520	+	24.1736i	0.123050	+	1.01341i	0.915177	+	0.403052i	$0.132051\pi$
$569$	2.93520	+	24.1736i	0.123050	+	1.01341i	−0.792127	+	0.610356i	$0.791026\pi$
$570$	−0.965641	+	0.131383i	−0.0404463	+	0.00550301i
$571$	−13.8886	+	9.58664i	−0.581222	+	0.401188i	−0.822080	−	0.569372i	$-0.807186\pi$
$571$	−13.8886	+	9.58664i	−0.581222	+	0.401188i	0.240858	+	0.970560i	$0.422571\pi$
$572$	−8.74990	−	33.6073i	−0.365852	−	1.40519i
$573$	−41.6627	+	19.4769i	−1.74049	+	0.813660i
$574$	−0.195014	−	3.22396i	−0.00813972	−	0.134566i
$575$	−2.46636	−	10.0064i	−0.102854	−	0.417297i
$576$	−1.26877	+	13.7464i	−0.0528653	+	0.572766i
$577$	−6.15944	−	6.15944i	−0.256421	−	0.256421i	0.567176	−	0.823597i	$-0.308036\pi$
$577$	−6.15944	−	6.15944i	−0.256421	−	0.256421i	−0.823597	+	0.567176i	$0.808036\pi$
$578$	2.04064	+	11.1354i	0.0848793	+	0.463171i
$579$	35.0544	−	4.76941i	1.45681	−	0.198210i
$580$	−3.62872	−	8.06269i	−0.150674	−	0.334785i
$581$	−0.703801	+	0.0854569i	−0.0291986	+	0.00354535i
$582$	19.8067	+	24.5452i	0.821016	+	1.01743i
$583$	−2.22156	+	36.7268i	−0.0920078	+	1.52107i
$584$	−3.47804	+	3.08128i	−0.143922	+	0.127504i
$585$	−9.06390	−	7.37694i	−0.374746	−	0.304999i
$586$	10.0622	+	8.91429i	0.415664	+	0.368246i
$587$	26.6538	−	26.6538i	1.10012	−	1.10012i	0.105725	−	0.994395i	$-0.466284\pi$
$587$	26.6538	−	26.6538i	1.10012	−	1.10012i	0.994395	−	0.105725i	$-0.0337163\pi$
$588$	−3.64546	−	18.3950i	−0.150336	−	0.758596i
$589$	0.214260	−	0.869287i	0.00882843	−	0.0358184i
$590$	−0.274075	−	0.0502260i	−0.0112835	−	0.00206777i
$591$	33.0604	+	3.53210i	1.35992	+	0.145291i
$592$	10.6118	+	23.5785i	0.436143	+	0.969070i
$593$	−6.07634	+	33.1575i	−0.249525	+	1.36162i	0.585173	+	0.810908i	$0.301027\pi$
$593$	−6.07634	+	33.1575i	−0.249525	+	1.36162i	−0.834698	+	0.550707i	$0.814358\pi$
$594$	−57.1961	−	15.1472i	−2.34679	−	0.621498i
$595$	−1.21333	−	1.36957i	−0.0497418	−	0.0561469i
$596$	20.7285	+	20.7285i	0.849073	+	0.849073i
$597$	7.55582	+	23.0726i	0.309239	+	0.944301i
$598$	−4.63886	−	17.8173i	−0.189697	−	0.728604i
$599$	−11.1949	−	12.6365i	−0.457412	−	0.516312i	0.473878	−	0.880591i	$-0.342854\pi$
$599$	−11.1949	−	12.6365i	−0.457412	−	0.516312i	−0.931290	+	0.364279i	$0.881315\pi$
$600$	4.12460	+	2.76019i	0.168386	+	0.112684i
$601$	8.18550	−	21.5834i	0.333894	−	0.880405i	−0.657964	−	0.753050i	$-0.728582\pi$
$601$	8.18550	−	21.5834i	0.333894	−	0.880405i	0.991857	−	0.127355i	$-0.0406488\pi$
$602$	0.0306302	+	0.252263i	0.00124840	+	0.0102815i
$603$	−12.1555	−	8.97071i	−0.495010	−	0.365316i
$604$	24.4553	−	19.1595i	0.995074	−	0.779590i
$605$	26.5188	−	4.85974i	1.07814	−	0.197577i
$606$	−16.0833	−	61.4323i	−0.653337	−	2.49552i
$607$	8.07740	−	11.7021i	0.327851	−	0.474975i	−0.624048	−	0.781386i	$-0.714513\pi$
$607$	8.07740	−	11.7021i	0.327851	−	0.474975i	0.951899	+	0.306411i	$0.0991283\pi$
$608$	1.94419	−	0.479200i	0.0788474	−	0.0194341i
$609$	−4.01236	−	2.03272i	−0.162589	−	0.0823700i
$610$	−1.36766	−	0.944030i	−0.0553751	−	0.0382227i
$611$	−13.1193	+	11.9317i	−0.530751	+	0.482704i
$612$	14.3851	+	7.02933i	0.581484	+	0.284144i
$613$	24.8706	−	19.4849i	1.00451	−	0.786986i	0.0273829	−	0.999625i	$-0.491283\pi$
$613$	24.8706	−	19.4849i	1.00451	−	0.786986i	0.977131	+	0.212639i	$0.0682058\pi$
$614$	17.5394	−	2.12967i	0.707832	−	0.0859463i
$615$	−6.23741	−	0.287240i	−0.251517	−	0.0115826i
$616$	−1.95546	−	1.18211i	−0.0787876	−	0.0476288i
$617$	−20.6581	−	16.1846i	−0.831662	−	0.651566i	0.107817	−	0.994171i	$-0.465614\pi$
$617$	−20.6581	−	16.1846i	−0.831662	−	0.651566i	−0.939480	+	0.342605i	$0.888691\pi$
$618$	−10.5025	+	15.6940i	−0.422472	+	0.631307i
$619$	4.60785	+	25.1442i	0.185205	+	1.01063i	0.936501	+	0.350666i	$0.114045\pi$
$619$	4.60785	+	25.1442i	0.185205	+	1.01063i	−0.751295	+	0.659966i	$0.770571\pi$
$620$	−4.66303	+	3.21866i	−0.187272	+	0.129264i
$621$	−13.5065	−	3.57692i	−0.541997	−	0.143537i
$622$	13.4226	+	10.5160i	0.538199	+	0.421652i
$623$	−7.40022	−	3.88393i	−0.296484	−	0.155607i
$624$	24.2501	+	15.7743i	0.970782	+	0.631477i
$625$	−7.83907	+	4.11426i	−0.313563	+	0.164570i
$626$	−51.9380	−	9.51799i	−2.07586	−	0.380415i
$627$	0.212869	+	2.84009i	0.00850118	+	0.113422i
$628$	−8.09879	+	9.14164i	−0.323177	+	0.364791i
$629$	18.5110	−	1.11971i	0.738081	−	0.0446457i
$630$	3.12501	−	0.279519i	0.124503	−	0.0111363i
$631$	4.32131	−	13.8676i	0.172029	−	0.552059i	−0.827933	−	0.560827i	$-0.810483\pi$
$631$	4.32131	−	13.8676i	0.172029	−	0.552059i	0.999962	+	0.00876792i	$0.00279095\pi$
$632$	−3.61858	+	8.04016i	−0.143940	+	0.319821i
$633$	−6.61181	+	22.3457i	−0.262796	+	0.888161i
$634$	−3.46640	+	3.91276i	−0.137668	+	0.155396i
$635$	−13.6256	+	2.49698i	−0.540714	+	0.0990896i
$636$	10.7213	+	13.2862i	0.425128	+	0.526833i
$637$	−23.2940	−	6.92675i	−0.922942	−	0.274448i
$638$	−54.2417	+	20.5712i	−2.14745	+	0.814420i
$639$	−38.7944	−	21.9525i	−1.53468	−	0.868428i
$640$	5.61083	+	2.94479i	0.221787	+	0.116403i
$641$	−14.1322	+	37.2636i	−0.558189	+	1.47182i	0.297698	+	0.954660i	$0.403781\pi$
$641$	−14.1322	+	37.2636i	−0.558189	+	1.47182i	−0.855887	+	0.517163i	$0.826988\pi$
$642$	−0.473515	−	3.48026i	−0.0186881	−	0.137355i
$643$	6.42100	−	35.0383i	0.253220	−	1.38177i	−0.573521	−	0.819191i	$-0.694423\pi$
$643$	6.42100	−	35.0383i	0.253220	−	1.38177i	0.826740	−	0.562584i	$-0.190193\pi$
$644$	1.88414	+	1.13900i	0.0742455	+	0.0448830i
$645$	0.491210	−	0.00707222i	0.0193414	−	0.000278468i
$646$	0.208557	−	1.71762i	0.00820556	−	0.0675789i
$647$	−8.26968	−	21.8053i	−0.325115	−	0.857257i	−0.993541	−	0.113478i	$-0.963801\pi$
$647$	−8.26968	−	21.8053i	−0.325115	−	0.857257i	0.668426	−	0.743779i	$-0.266968\pi$
$648$	5.96661	−	3.11002i	0.234391	−	0.122173i
$649$	−0.194878	+	0.790650i	−0.00764962	+	0.0310357i
$650$	−23.0758	+	12.4976i	−0.905106	+	0.490196i
$651$	−0.817815	+	2.76394i	−0.0320527	+	0.108327i
$652$	25.4202	+	7.92124i	0.995531	+	0.310220i
$653$		−	25.4711i		−	0.996760i	−0.866959	−	0.498380i	$-0.833928\pi$
$653$		−	25.4711i		−	0.996760i	0.866959	−	0.498380i	$-0.166072\pi$
$654$	7.81210	−	13.3533i	0.305477	−	0.522155i
$655$	16.9809	+	5.29147i	0.663499	+	0.206755i
$656$	15.4285	−	0.933253i	0.602382	−	0.0364374i
$657$	−17.9539	−	5.03241i	−0.700449	−	0.196333i
$658$	0.287461	−	4.75229i	0.0112064	−	0.185264i
$659$	−13.4950	+	25.7126i	−0.525692	+	1.00162i	0.467374	+	0.884060i	$0.345200\pi$
$659$	−13.4950	+	25.7126i	−0.525692	+	1.00162i	−0.993066	+	0.117562i	$0.962492\pi$
$660$	10.9104	−	14.3469i	0.424688	−	0.558451i
$661$	43.6306	−	13.5958i	1.69703	−	0.528817i	0.712149	−	0.702028i	$-0.247722\pi$
$661$	43.6306	−	13.5958i	1.69703	−	0.528817i	0.984885	+	0.173211i	$0.0554142\pi$
$662$	0.219415	−	1.80705i	0.00852782	−	0.0702329i
$663$	16.7460	−	12.2506i	0.650362	−	0.475774i
$664$	−0.125339	−	1.03226i	−0.00486408	−	0.0400593i
$665$	−0.0619819	−	0.137718i	−0.00240356	−	0.00534048i
$666$	−17.3032	+	26.6796i	−0.670485	+	1.03381i
$667$	−12.8088	+	4.85775i	−0.495960	+	0.188093i
$668$	−26.9875	+	8.40964i	−1.04418	+	0.325379i
$669$	−34.5282	−	7.98499i	−1.33494	−	0.308717i
$670$	8.84199	−	5.34517i	0.341596	−	0.206502i
$671$	−2.99519	+	3.82308i	−0.115628	+	0.147588i
$672$	−6.32359	+	1.25319i	−0.243938	+	0.0483429i
$673$	14.2183	+	9.81418i	0.548075	+	0.378309i	0.809685	−	0.586865i	$-0.199638\pi$
$673$	14.2183	+	9.81418i	0.548075	+	0.378309i	−0.261610	+	0.965174i	$0.584253\pi$
$674$	16.9715	−	37.7091i	0.653717	−	1.45250i
$675$	−0.343035	+	19.9124i	−0.0132034	+	0.766427i
$676$	−18.2309	+	10.1833i	−0.701187	+	0.391667i
$677$		−	45.7651i		−	1.75890i	−0.475995	−	0.879448i	$-0.657912\pi$
$677$		−	45.7651i		−	1.75890i	0.475995	−	0.879448i	$-0.342088\pi$
$678$	−15.3182	−	21.5227i	−0.588290	−	0.826574i
$679$	−2.77655	+	4.02252i	−0.106554	+	0.154370i
$680$	2.00873	−	1.77958i	0.0770313	−	0.0682438i
$681$	−15.4446	+	6.11310i	−0.591837	+	0.234254i
$682$	19.2324	+	31.8142i	0.736445	+	1.21823i
$683$	−12.9472	−	41.5489i	−0.495409	−	1.58982i	−0.776484	−	0.630137i	$-0.782999\pi$
$683$	−12.9472	−	41.5489i	−0.495409	−	1.58982i	0.281075	−	0.959686i	$-0.409309\pi$
$684$	0.960960	+	0.907156i	0.0367432	+	0.0346860i
$685$	−1.34293	−	3.54102i	−0.0513107	−	0.135295i
$686$	11.7769	−	6.18097i	0.449643	−	0.235991i
$687$	−34.4431	−	3.67982i	−1.31409	−	0.140394i
$688$	−1.20722	+	0.146583i	−0.0460249	+	0.00558843i
$689$	21.7084	−	4.27154i	0.827023	−	0.162733i
$690$	5.78429	−	7.60617i	0.220204	−	0.289562i
$691$	6.58894	+	21.1447i	0.250655	+	0.804381i	0.991200	+	0.132374i	$0.0422599\pi$
$691$	6.58894	+	21.1447i	0.250655	+	0.804381i	−0.740545	+	0.672007i	$0.765432\pi$
$692$	11.2479	+	1.36575i	0.427583	+	0.0519179i
$693$	−0.263973	−	9.16539i	−0.0100275	−	0.348165i
$694$	−19.3989	−	1.17342i	−0.736373	−	0.0445423i
$695$	−2.81698	+	2.81698i	−0.106854	+	0.106854i
$696$	2.98137	−	5.88488i	0.113008	−	0.223066i
$697$	3.29809	−	10.5839i	0.124924	−	0.400895i
$698$		−	18.2204i		−	0.689653i
$699$	24.0218	−	41.0607i	0.908588	−	1.55306i
$700$	0.933613	−	2.99607i	0.0352872	−	0.113241i
$701$	22.0980	−	5.44667i	0.834630	−	0.205718i	0.201231	−	0.979544i	$-0.435506\pi$
$701$	22.0980	−	5.44667i	0.834630	−	0.205718i	0.633398	+	0.773826i	$0.281660\pi$
$702$	−0.148862	+	35.5780i	−0.00561842	+	1.34281i
$703$	1.48619	+	0.366313i	0.0560527	+	0.0138157i
$704$	−14.2743	+	23.6126i	−0.537984	+	0.889934i
$705$	−9.07619	−	1.52857i	−0.341829	−	0.0575691i
$706$	16.6854	+	2.02597i	0.627963	+	0.0762485i
$707$	8.42171	−	5.09110i	0.316731	−	0.191471i
$708$	0.180391	+	0.332001i	0.00677950	+	0.0124774i
$709$	−20.5764	−	3.77077i	−0.772765	−	0.141614i	−0.220617	−	0.975361i	$-0.570807\pi$
$709$	−20.5764	−	3.77077i	−0.772765	−	0.141614i	−0.552148	+	0.833746i	$0.686192\pi$
$710$	23.9976	−	18.8009i	0.900613	−	0.705585i
$711$	−34.9852	+	5.27402i	−1.31205	+	0.197791i
$712$	5.69652	−	10.8538i	0.213486	−	0.406764i
$713$	4.54160	+	7.51273i	0.170084	+	0.281354i
$714$	−0.925114	+	5.49307i	−0.0346215	+	0.205573i
$715$	−9.86335	−	21.1733i	−0.368868	−	0.791835i
$716$	−20.2290	−	7.67184i	−0.755993	−	0.286710i
$717$	42.9454	+	15.5837i	1.60383	+	0.581982i
$718$	10.6480	+	9.43331i	0.397380	+	0.352048i
$719$	−28.7552	+	7.08753i	−1.07239	+	0.264320i	−0.735708	−	0.677298i	$-0.763151\pi$
$719$	−28.7552	+	7.08753i	−1.07239	+	0.264320i	−0.336681	+	0.941619i	$0.609304\pi$
$720$	1.33766	+	14.9550i	0.0498516	+	0.557338i
$721$	−2.79393	−	0.870624i	−0.104051	−	0.0324237i
$722$	−14.7497	+	32.7726i	−0.548928	+	1.21967i
$723$	−13.6137	+	26.8718i	−0.506298	+	0.999375i
$724$	4.88360	+	4.32649i	0.181498	+	0.160793i
$725$	11.0921	+	16.0697i	0.411950	+	0.596812i
$726$	−62.2136	−	53.5379i	−2.30896	−	1.98698i
$727$	9.52589	+	18.1501i	0.353296	+	0.673149i	0.995641	−	0.0932663i	$-0.0297308\pi$
$727$	9.52589	+	18.1501i	0.353296	+	0.673149i	−0.642345	+	0.766415i	$0.722038\pi$
$728$	−0.391626	+	1.31700i	−0.0145146	+	0.0488113i
$729$	23.4609	+	13.3636i	0.868924	+	0.494946i
$730$	7.86450	−	10.0383i	0.291078	−	0.371534i
$731$	−0.208732	+	0.846860i	−0.00772024	+	0.0313223i
$732$	0.168431	+	2.24720i	0.00622541	+	0.0830589i
$733$	−25.1657	+	4.61178i	−0.929515	+	0.170340i	−0.623622	−	0.781726i	$-0.714340\pi$
$733$	−25.1657	+	4.61178i	−0.929515	+	0.170340i	−0.305893	+	0.952066i	$0.598955\pi$
$734$	−2.09147	+	34.5762i	−0.0771977	+	1.27623i
$735$	−4.64199	−	11.7279i	−0.171222	−	0.432589i
$736$	−10.1575	+	16.8025i	−0.374409	+	0.619348i
$737$	−14.0324	−	26.7364i	−0.516889	−	0.984850i
$738$	11.2444	+	15.3270i	0.413913	+	0.564195i
$739$	22.3899	+	28.5786i	0.823627	+	1.05128i	0.997782	+	0.0665641i	$0.0212037\pi$
$739$	22.3899	+	28.5786i	0.823627	+	1.05128i	−0.174155	+	0.984718i	$0.555719\pi$
$740$	−5.50282	−	7.97221i	−0.202288	−	0.293064i
$741$	1.62043	−	0.554159i	0.0595280	−	0.0203575i
$742$	−3.37421	+	4.88839i	−0.123871	+	0.179458i
$743$	9.59301	−	0.580270i	0.351933	−	0.0212880i	0.116534	−	0.993187i	$-0.462822\pi$
$743$	9.59301	−	0.580270i	0.351933	−	0.0212880i	0.235400	+	0.971899i	$0.424360\pi$
$744$	−4.05383	−	1.19948i	−0.148621	−	0.0439750i
$745$	16.2268	+	11.2006i	0.594504	+	0.410357i
$746$	−16.9832	+	16.9832i	−0.621799	+	0.621799i
$747$	3.20919	−	2.66684i	0.117418	−	0.0975747i
$748$	19.7355	+	25.1905i	0.721603	+	0.921058i
$749$	0.496348	−	0.223388i	0.0181362	−	0.00816243i
$750$	−28.8061	−	12.4690i	−1.05185	−	0.455305i
$751$	20.7575	+	7.87228i	0.757452	+	0.287264i	0.702940	−	0.711249i	$-0.251870\pi$
$751$	20.7575	+	7.87228i	0.757452	+	0.287264i	0.0545123	+	0.998513i	$0.482640\pi$
$752$	22.7424	+	1.37566i	0.829331	+	0.0501653i
$753$	5.12795	+	25.8756i	0.186873	+	0.942958i
$754$	20.1885	+	28.4473i	0.735222	+	1.03599i
$755$	13.8564	−	15.6406i	0.504286	−	0.569221i
$756$	−2.95614	−	3.05978i	−0.107514	−	0.111283i
$757$	9.87814	−	8.75127i	0.359027	−	0.318070i	−0.464256	−	0.885701i	$-0.653678\pi$
$757$	9.87814	−	8.75127i	0.359027	−	0.318070i	0.823283	+	0.567631i	$0.192140\pi$
$758$	−32.3812	−	7.98126i	−1.17614	−	0.289892i
$759$	−21.1675	−	18.2157i	−0.768333	−	0.661188i
$760$	0.201989	−	0.0909081i	0.00732693	−	0.00329758i
$761$	−45.2088	+	20.3469i	−1.63882	+	0.737573i	−0.999508	−	0.0313748i	$-0.990011\pi$
$761$	−45.2088	+	20.3469i	−1.63882	+	0.737573i	−0.639312	+	0.768948i	$0.720781\pi$
$762$	31.9659	+	27.5082i	1.15800	+	0.996518i
$763$	2.32780	+	0.573751i	0.0842720	+	0.0207712i
$764$	−31.9256	+	28.2836i	−1.15503	+	1.02326i
$765$	10.3692	+	2.90645i	0.374900	+	0.105083i
$766$	18.9134	−	21.3488i	0.683369	−	0.771364i
$767$	0.489614	−	0.00638566i	0.0176789	−	0.000230573i
$768$	−6.84893	−	34.5596i	−0.247140	−	1.24706i
$769$	−29.8405	−	1.80501i	−1.07607	−	0.0650905i	−0.487181	−	0.873301i	$-0.661975\pi$
$769$	−29.8405	−	1.80501i	−1.07607	−	0.0650905i	−0.588893	+	0.808211i	$0.700436\pi$
$770$	5.86343	+	2.22371i	0.211303	+	0.0801368i
$771$	−26.6062	−	11.5168i	−0.958198	−	0.414767i
$772$	29.9188	−	13.4654i	1.07680	−	0.484629i
$773$	−10.1445	−	12.9486i	−0.364874	−	0.465727i	0.569516	−	0.821981i	$-0.307131\pi$
$773$	−10.1445	−	12.9486i	−0.364874	−	0.465727i	−0.934389	+	0.356254i	$0.884054\pi$
$774$	−0.955874	−	1.15027i	−0.0343582	−	0.0413455i
$775$	8.84799	−	8.84799i	0.317829	−	0.317829i
$776$	−5.89979	−	4.07233i	−0.211790	−	0.146188i
$777$	−4.72541	−	1.39819i	−0.169523	−	0.0501598i
$778$	3.13334	−	0.189532i	0.112336	−	0.00679506i
$779$	0.519788	−	0.753044i	0.0186234	−	0.0269806i
$780$	−10.0016	−	4.17529i	−0.358115	−	0.149499i
$781$	−50.6103	−	73.3216i	−1.81098	−	2.62365i
$782$	10.4630	+	13.3551i	0.374157	+	0.477576i
$783$	26.3304	−	2.73776i	0.940971	−	0.0978395i
$784$	14.5101	+	27.6466i	0.518217	+	0.987380i
$785$	−4.24970	+	7.02987i	−0.151678	+	0.250907i
$786$	−19.9282	−	50.3481i	−0.710816	−	1.79586i
$787$	−1.35072	+	22.3301i	−0.0481480	+	0.795981i	0.891327	+	0.453362i	$0.149775\pi$
$787$	−1.35072	+	22.3301i	−0.0481480	+	0.795981i	−0.939474	+	0.342619i	$0.888686\pi$
$788$	30.3299	−	5.55817i	1.08046	−	0.198001i
$789$	0.158442	+	2.11393i	0.00564070	+	0.0752578i
$790$	5.79077	−	23.4941i	0.206026	−	0.835881i
$791$	2.52476	−	3.22262i	0.0897702	−	0.114583i
$792$	13.4428	−	0.387166i	0.477668	−	0.0137574i
$793$	2.67848	+	1.16372i	0.0951158	+	0.0413250i
$794$	29.7308	+	56.6473i	1.05511	+	2.01034i
$795$	8.70389	+	7.49012i	0.308695	+	0.265647i
$796$	12.7905	+	18.5303i	0.453348	+	0.656788i
$797$	17.4315	+	15.4429i	0.617455	+	0.547017i	0.912817	−	0.408368i	$-0.133902\pi$
$797$	17.4315	+	15.4429i	0.617455	+	0.547017i	−0.295363	+	0.955385i	$0.595440\pi$
$798$	−0.207786	+	0.410145i	−0.00735553	+	0.0145190i
$799$	6.70663	−	14.9015i	0.237264	−	0.527178i
$800$	26.7185	+	8.32582i	0.944641	+	0.294362i
$801$	48.9926	−	4.38218i	1.73107	−	0.154837i
$802$	48.5532	−	11.9673i	1.71447	−	0.422580i
$803$	−27.8953	−	24.7131i	−0.984404	−	0.872106i
$804$	−13.1703	−	4.77913i	−0.464482	−	0.168547i
$805$	1.38461	+	0.525114i	0.0488011	+	0.0185078i
$806$	15.5993	−	16.0116i	0.549462	−	0.563983i
$807$	−1.10116	+	6.53838i	−0.0387627	+	0.230162i
$808$	7.46706	+	12.3520i	0.262690	+	0.434542i
$809$	9.21107	−	17.5502i	0.323844	−	0.617033i	−0.668048	−	0.744118i	$-0.732870\pi$
$809$	9.21107	−	17.5502i	0.323844	−	0.617033i	0.991892	+	0.127085i	$0.0405622\pi$
$810$	−14.5680	+	11.3470i	−0.511868	+	0.398692i
$811$	7.51336	−	5.88634i	0.263830	−	0.206697i	−0.476083	−	0.879400i	$-0.657944\pi$
$811$	7.51336	−	5.88634i	0.263830	−	0.206697i	0.739913	+	0.672703i	$0.234867\pi$
$812$	−4.10306	−	0.751913i	−0.143989	−	0.0263870i
$813$	−3.31177	−	6.09517i	−0.116149	−	0.213767i
$814$	−54.3916	+	32.8809i	−1.90643	+	1.15247i
$815$	17.7780	+	2.15864i	0.622735	+	0.0756138i
$816$	−26.2875	−	4.42720i	−0.920245	−	0.154983i
$817$	−0.0372435	+	0.0616083i	−0.00130299	+	0.00215540i
$818$	7.81879	+	1.92716i	0.273377	+	0.0673815i
$819$	−5.29346	+	1.54221i	−0.184969	+	0.0538893i
$820$	−5.62249	+	1.38582i	−0.196346	+	0.0483949i
$821$	8.87012	−	28.4652i	0.309569	−	0.993443i	−0.660543	−	0.750788i	$-0.729674\pi$
$821$	8.87012	−	28.4652i	0.309569	−	0.993443i	0.970113	−	0.242655i	$-0.0780183\pi$
$822$	−5.82199	+	9.95159i	−0.203065	+	0.347101i
$823$			7.12583i			0.248391i	0.992258	+	0.124195i	$0.0396349\pi$
$823$			7.12583i			0.248391i	−0.992258	+	0.124195i	$0.960365\pi$
$824$	1.27693	−	4.09782i	0.0444840	−	0.142754i
$825$	−17.9890	+	35.5082i	−0.626297	+	1.23624i
$826$	−0.0929553	+	0.0929553i	−0.00323433	+	0.00323433i
$827$	41.2960	+	2.49795i	1.43600	+	0.0868621i	0.759945	−	0.649987i	$-0.225226\pi$
$827$	41.2960	+	2.49795i	1.43600	+	0.0868621i	0.676057	+	0.736849i	$0.263687\pi$
$828$	−12.9525	+	0.373046i	−0.450130	+	0.0129642i
$829$	23.2010	+	2.81711i	0.805804	+	0.0978423i	0.513065	−	0.858350i	$-0.328510\pi$
$829$	23.2010	+	2.81711i	0.805804	+	0.0978423i	0.292739	+	0.956192i	$0.405433\pi$
$830$	0.848993	+	2.72452i	0.0294690	+	0.0945693i
$831$	19.7918	−	26.0256i	0.686570	−	0.902818i
$832$	15.9031	+	4.72898i	0.551341	+	0.163948i
$833$	22.2306	−	2.69928i	0.770244	−	0.0935246i
$834$	12.0597	+	1.28843i	0.417594	+	0.0446147i
$835$	−16.8349	+	8.83566i	−0.582597	+	0.305771i
$836$	0.936622	+	2.46967i	0.0323938	+	0.0854153i
$837$	−4.76721	−	16.2807i	−0.164779	−	0.562744i
$838$	−12.8360	−	41.1921i	−0.443412	−	1.42296i
$839$	−19.2270	−	31.8054i	−0.663791	−	1.09804i	−0.988353	−	0.152180i	$-0.951371\pi$
$839$	−19.2270	−	31.8054i	−0.663791	−	1.09804i	0.324562	−	0.945865i	$-0.394783\pi$
$840$	−0.663072	+	0.262450i	−0.0228782	+	0.00905538i
$841$	−2.27925	+	2.01924i	−0.0785948	+	0.0696290i
$842$	30.4706	−	44.1443i	1.05009	−	1.52131i
$843$	12.3862	+	17.4032i	0.426605	+	0.599399i
$844$			21.6117i			0.743906i
$845$	−10.8266	+	8.94746i	−0.372447	+	0.307802i
$846$	13.7308	+	24.4259i	0.472074	+	0.839781i
$847$	5.22029	−	11.5990i	0.179371	−	0.398546i
$848$	−23.3937	−	16.1475i	−0.803344	−	0.554509i
$849$	−29.6388	+	5.87373i	−1.01720	+	0.201586i
$850$	14.9136	−	19.0358i	0.511532	−	0.652922i
$851$	−12.8442	+	7.76461i	−0.440295	+	0.266167i
$852$	−40.2762	−	9.31425i	−1.37984	−	0.319101i
$853$	−7.22702	+	2.25203i	−0.247448	+	0.0771080i	−0.418719	−	0.908116i	$-0.637521\pi$
$853$	−7.22702	+	2.25203i	−0.247448	+	0.0771080i	0.171270	+	0.985224i	$0.445213\pi$
$854$	−0.733086	+	0.278023i	−0.0250857	+	0.00951374i
$855$	0.745741	+	0.483654i	0.0255038	+	0.0165406i
$856$	0.327641	+	0.727988i	0.0111985	+	0.0248821i
$857$	−0.185777	−	1.53001i	−0.00634601	−	0.0522641i	0.989192	−	0.146627i	$-0.0468417\pi$
$857$	−0.185777	−	1.53001i	−0.00634601	−	0.0522641i	−0.995538	+	0.0943629i	$0.969919\pi$
$858$	−31.3070	+	63.8485i	−1.06880	+	2.17975i
$859$	6.84713	−	56.3912i	0.233621	−	1.92404i	−0.128108	−	0.991760i	$-0.540890\pi$
$859$	6.84713	−	56.3912i	0.233621	−	1.92404i	0.361729	−	0.932283i	$-0.382186\pi$
$860$	0.434971	−	0.135542i	0.0148324	−	0.00462196i
$861$	−1.78319	+	2.34484i	−0.0607711	+	0.0799121i
$862$	−18.5747	+	35.3911i	−0.632657	+	1.20543i
$863$	1.15632	−	19.1163i	0.0393616	−	0.650725i	−0.923979	−	0.382444i	$-0.875083\pi$
$863$	1.15632	−	19.1163i	0.0393616	−	0.650725i	0.963340	−	0.268282i	$-0.0864558\pi$
$864$	27.2867	−	26.3625i	0.928312	−	0.896869i
$865$	7.60706	−	0.460142i	0.258648	−	0.0156453i
$866$	54.3975	+	16.9510i	1.84850	+	0.576017i
$867$	5.21396	−	8.91226i	0.177075	−	0.302676i
$868$			2.67316i			0.0907329i
$869$	−67.5135	−	21.0381i	−2.29024	−	0.713667i
$870$	−5.13683	+	17.3608i	−0.174155	+	0.588585i
$871$	−13.4323	+	12.2163i	−0.455136	+	0.413934i
$872$	−0.841513	+	3.41415i	−0.0284972	+	0.115618i
$873$	0.909514	−	28.7524i	0.0307824	−	0.973120i
$874$	0.496561	+	1.30932i	0.0167964	+	0.0442886i
$875$	0.586329	−	4.82885i	0.0198215	−	0.163245i
$876$	−17.2906	+	0.248942i	−0.584194	+	0.00841097i
$877$	−9.34276	−	5.64790i	−0.315483	−	0.190716i	0.350732	−	0.936476i	$-0.385933\pi$
$877$	−9.34276	−	5.64790i	−0.315483	−	0.190716i	−0.666215	+	0.745760i	$0.732087\pi$
$878$	−13.5223	+	73.7887i	−0.456355	+	2.49025i
$879$	−1.65295	−	12.1489i	−0.0557527	−	0.409774i
$880$	−10.6417	+	28.0599i	−0.358732	+	0.945897i
$881$	42.9969	+	22.5665i	1.44860	+	0.760285i	0.991620	−	0.129190i	$-0.0412377\pi$
$881$	42.9969	+	22.5665i	1.44860	+	0.760285i	0.456983	+	0.889475i	$0.348930\pi$
$882$	−18.9112	+	33.4198i	−0.636773	+	1.12530i
$883$	−53.8781	+	20.4333i	−1.81314	+	0.687634i	−0.819768	+	0.572695i	$0.805898\pi$
$883$	−53.8781	+	20.4333i	−1.81314	+	0.687634i	−0.993373	+	0.114938i	$0.963333\pi$
$884$	11.6687	−	15.3008i	0.392460	−	0.514623i
$885$	0.159596	+	0.197776i	0.00536475	+	0.00664818i
$886$	−4.05606	+	0.743300i	−0.136266	+	0.0249717i
$887$	−22.8652	+	25.8095i	−0.767738	+	0.866597i	−0.994214	−	0.107420i	$-0.965741\pi$
$887$	−22.8652	+	25.8095i	−0.767738	+	0.866597i	0.226476	+	0.974017i	$0.427280\pi$
$888$	2.05071	−	6.93069i	0.0688172	−	0.232579i
$889$	−2.68223	+	5.95967i	−0.0899591	+	0.199881i
$890$	−10.0081	+	32.1173i	−0.335474	+	1.07657i
$891$	30.5300	+	44.4991i	1.02279	+	1.49078i
$892$	−32.8070	+	1.98446i	−1.09846	+	0.0664445i
$893$	0.894407	−	1.00958i	0.0299302	−	0.0337842i
$894$	−4.48651	−	59.8587i	−0.150051	−	2.00198i
$895$	−14.3133	−	2.62302i	−0.478442	−	0.0876777i
$896$	2.64712	−	1.38932i	0.0884342	−	0.0464138i
$897$	−7.39295	+	15.0774i	−0.246844	+	0.503420i
$898$	6.54690	+	3.43608i	0.218473	+	0.114663i
$899$	−13.0930	−	10.2577i	−0.436677	−	0.342115i
$900$	4.93452	+	17.7983i	0.164484	+	0.593276i
$901$	−16.7785	+	11.5814i	−0.558973	+	0.385831i
$902$	6.84864	+	37.3718i	0.228035	+	1.24435i
$903$	0.128901	−	0.192620i	0.00428957	−	0.00640998i
$904$	4.72658	+	3.70304i	0.157204	+	0.123161i
$905$	3.75546	+	2.27026i	0.124836	+	0.0754658i
$906$	−63.5475	−	2.92644i	−2.11122	−	0.0972244i
$907$	40.4740	−	4.91443i	1.34392	−	0.163181i	0.583233	−	0.812305i	$-0.301787\pi$
$907$	40.4740	−	4.91443i	1.34392	−	0.163181i	0.760683	+	0.649124i	$0.224864\pi$
$908$	−12.1263	+	9.50032i	−0.402424	+	0.315279i
$909$	−25.4287	+	52.0384i	−0.843417	+	1.72600i
$910$	0.405663	−	3.74891i	0.0134476	−	0.124275i
$911$	3.63551	+	2.50941i	0.120450	+	0.0831406i	0.626767	−	0.779207i	$-0.284378\pi$
$911$	3.63551	+	2.50941i	0.120450	+	0.0831406i	−0.506317	+	0.862348i	$0.668993\pi$
$912$	−1.96278	−	0.994373i	−0.0649941	−	0.0329270i
$913$	8.09758	−	1.99587i	0.267991	−	0.0660538i
$914$	20.5296	−	29.7422i	0.679057	−	0.983784i
$915$	0.383882	+	1.46629i	0.0126908	+	0.0484742i
$916$	−31.5985	+	5.79063i	−1.04404	+	0.191328i
$917$	6.60554	−	5.17511i	0.218134	−	0.170897i
$918$	−12.9383	−	30.1237i	−0.427028	−	0.994231i
$919$	4.26329	+	35.1113i	0.140633	+	1.15822i	0.876607	+	0.481206i	$0.159801\pi$
$919$	4.26329	+	35.1113i	0.140633	+	1.15822i	−0.735975	+	0.677009i	$0.763276\pi$
$920$	−0.770178	+	2.03079i	−0.0253920	+	0.0669532i
$921$	−13.3925	−	8.96229i	−0.441298	−	0.295318i
$922$	−23.1448	−	26.1251i	−0.762234	−	0.860385i
$923$	−34.9991	+	40.5593i	−1.15201	+	1.33503i
$924$	−2.64646	−	8.08130i	−0.0870621	−	0.265855i
$925$	15.1271	+	15.1271i	0.497376	+	0.497376i
$926$	−5.79009	−	6.53566i	−0.190274	−	0.214775i
$927$	16.5975	−	4.60160i	0.545132	−	0.151136i
$928$	6.70545	−	36.5904i	0.220117	−	1.20114i
$929$	−4.69411	−	10.4299i	−0.154009	−	0.342193i	0.818701	−	0.574221i	$-0.194695\pi$
$929$	−4.69411	−	10.4299i	−0.154009	−	0.342193i	−0.972709	+	0.232027i	$0.925464\pi$
$930$	11.5365	+	1.23253i	0.378296	+	0.0404163i
$931$	1.81809	+	0.333177i	0.0595854	+	0.0109194i
$932$	10.5581	−	42.8361i	0.345844	−	1.40314i
$933$	−3.02328	−	15.2555i	−0.0989779	−	0.499441i
$934$	5.74034	−	5.74034i	0.187830	−	0.187830i
$935$	16.1108	+	14.2730i	0.526881	+	0.466776i
$936$	−2.26194	−	7.76385i	−0.0739339	−	0.253770i
$937$	37.5772	−	33.2905i	1.22759	−	1.08755i	0.234271	−	0.972171i	$-0.424730\pi$
$937$	37.5772	−	33.2905i	1.22759	−	1.08755i	0.993321	−	0.115381i	$-0.0368088\pi$
$938$	0.294318	−	4.86566i	0.00960983	−	0.158869i
$939$	30.2439	+	37.4792i	0.986971	+	1.22309i
$940$	−8.47365	+	1.02889i	−0.276380	+	0.0335586i
$941$	0.247803	+	0.550595i	0.00807814	+	0.0179489i	0.915895	−	0.401418i	$-0.131483\pi$
$941$	0.247803	+	0.550595i	0.00807814	+	0.0179489i	−0.907817	+	0.419367i	$0.862252\pi$
$942$	24.7801	−	3.37152i	0.807381	−	0.109850i
$943$	1.61726	+	8.82512i	0.0526653	+	0.287386i
$944$	−0.444844	−	0.444844i	−0.0144784	−	0.0144784i
$945$	−2.32671	−	1.66590i	−0.0756878	−	0.0541918i
$946$	−0.715379	−	2.90241i	−0.0232590	−	0.0943654i
$947$	−1.72488	−	28.5157i	−0.0560510	−	0.926634i	−0.912159	−	0.409837i	$-0.865586\pi$
$947$	−1.72488	−	28.5157i	−0.0560510	−	0.926634i	0.856108	−	0.516797i	$-0.172876\pi$
$948$	−29.7245	+	13.8959i	−0.965405	+	0.451318i
$949$	−10.1546	+	19.9768i	−0.329632	+	0.648474i
$950$	1.64265	−	1.13384i	0.0532945	−	0.0367866i
$951$	4.72423	−	0.642766i	0.153194	−	0.0208431i
$952$	−0.152613	−	1.25688i	−0.00494620	−	0.0407356i
$953$	−9.96532	+	5.23021i	−0.322808	+	0.169423i	−0.618341	−	0.785910i	$-0.712195\pi$
$953$	−9.96532	+	5.23021i	−0.322808	+	0.169423i	0.295533	+	0.955333i	$0.404503\pi$
$954$	1.10529	−	34.9414i	0.0357851	−	1.13127i
$955$	−17.6924	+	22.5826i	−0.572512	+	0.730757i
$956$	42.2918	+	2.55818i	1.36781	+	0.0827376i
$957$	49.7372	+	18.0482i	1.60778	+	0.583416i
$958$	−2.90258	−	4.20511i	−0.0937781	−	0.135861i
$959$	−1.73480	−	0.427590i	−0.0560196	−	0.0138076i
$960$	3.16915	+	8.00676i	0.102284	+	0.258417i
$961$	9.45302	−	18.0112i	0.304936	−	0.581007i
$962$	27.3744	+	26.6695i	0.882586	+	0.859861i
$963$	−1.74313	+	2.68771i	−0.0561717	+	0.0866104i
$964$	−5.03576	+	27.4792i	−0.162191	+	0.885047i
$965$	18.1613	−	12.5358i	0.584633	−	0.403543i
$966$	−1.40305	−	4.28440i	−0.0451424	−	0.137848i
$967$	1.53049	+	25.3020i	0.0492172	+	0.813657i	0.936116	+	0.351693i	$0.114394\pi$
$967$	1.53049	+	25.3020i	0.0492172	+	0.813657i	−0.886898	+	0.461965i	$0.847145\pi$
$968$	17.0121	+	7.65652i	0.546790	+	0.246090i
$969$	−1.16604	+	1.06337i	−0.0374585	+	0.0341603i
$970$	17.9407	+	8.07445i	0.576041	+	0.259255i
$971$	12.3162	+	49.9686i	0.395245	+	1.60357i	0.745225	+	0.666813i	$0.232342\pi$
$971$	12.3162	+	49.9686i	0.395245	+	1.60357i	−0.349981	+	0.936757i	$0.613812\pi$
$972$	24.3801	+	5.71085i	0.781993	+	0.183175i
$973$	0.338793	+	1.84873i	0.0108612	+	0.0592676i
$974$	21.1637	−	55.8040i	0.678127	−	1.78808i
$975$	23.3881	+	5.08835i	0.749019	+	0.162958i
$976$	−1.33050	−	3.50823i	−0.0425882	−	0.112296i
$977$	−24.4864	+	14.8025i	−0.783389	+	0.473575i	−0.851662	−	0.524092i	$-0.824405\pi$
$977$	−24.4864	+	14.8025i	−0.783389	+	0.473575i	0.0682729	+	0.997667i	$0.478251\pi$
$978$	−28.8745	−	46.2470i	−0.923304	−	1.47882i
$979$	91.9244	+	34.8623i	2.93792	+	1.11420i
$980$	−7.21408	−	9.20810i	−0.230445	−	0.294142i
$981$	−13.3449	+	4.58394i	−0.426071	+	0.146354i
$982$	16.2323	−	26.8515i	0.517993	−	0.856865i
$983$	0.396222	+	0.655431i	0.0126375	+	0.0209050i	0.862036	−	0.506847i	$-0.169189\pi$
$983$	0.396222	+	0.655431i	0.0126375	+	0.0209050i	−0.849399	+	0.527752i	$0.823035\pi$
$984$	−3.43915	−	2.61539i	−0.109636	−	0.0833755i
$985$	19.3920	−	7.35440i	0.617879	−	0.234331i
$986$	−27.5082	−	16.6293i	−0.876041	−	0.529585i
$987$	−3.02598	+	3.11439i	−0.0963180	+	0.0991320i
$988$	1.29523	−	0.919199i	0.0412067	−	0.0292436i
$989$	−0.168932	−	0.685385i	−0.00537173	−	0.0217940i
$990$	−36.0965	+	7.69516i	−1.14722	+	0.244568i
$991$	24.5311			0.779255			0.389627	−	0.920973i	$-0.372604\pi$
$991$	24.5311			0.779255			0.389627	+	0.920973i	$0.372604\pi$
$992$	−23.8388			−0.756883
$993$	−1.22674	+	1.11873i	−0.0389296	+	0.0355019i
$994$	−0.868403	−	14.3564i	−0.0275441	−	0.455358i
$995$	10.7086	+	10.7086i	0.339486	+	0.339486i
$996$	2.15219	−	3.21606i	0.0681948	−	0.101905i
$997$	18.3343	+	9.62256i	0.580652	+	0.304750i	0.729358	−	0.684132i	$-0.239819\pi$
$997$	18.3343	+	9.62256i	0.580652	+	0.304750i	−0.148707	+	0.988881i	$0.547511\pi$
$998$	−2.72699	+	22.4587i	−0.0863212	+	0.710919i
$999$	27.8345	−	8.15033i	0.880646	−	0.257865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.s.a.476.11	yes	1392
3.2	odd	2	inner	507.2.s.a.476.48	yes	1392
169.109	odd	52	inner	507.2.s.a.278.48	yes	1392
507.278	even	52	inner	507.2.s.a.278.11	✓	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.s.a.278.11	✓	1392	507.278	even	52	inner
507.2.s.a.278.48	yes	1392	169.109	odd	52	inner
507.2.s.a.476.11	yes	1392	1.1	even	1	trivial
507.2.s.a.476.48	yes	1392	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73173 - 0.779387i) q^{2} +(0.733520 + 1.56906i) q^{3} +(1.06519 + 1.20235i) q^{4} +(0.850485 + 0.666312i) q^{5} +(-0.0473518 - 3.28888i) q^{6} +(0.486647 - 0.151645i) q^{7} +(0.222416 + 0.713759i) q^{8} +(-1.92390 + 2.30187i) q^{9} +O(q^{10})\)	\(q+(-1.73173 - 0.779387i) q^{2} +(0.733520 + 1.56906i) q^{3} +(1.06519 + 1.20235i) q^{4} +(0.850485 + 0.666312i) q^{5} +(-0.0473518 - 3.28888i) q^{6} +(0.486647 - 0.151645i) q^{7} +(0.222416 + 0.713759i) q^{8} +(-1.92390 + 2.30187i) q^{9} +(-0.953492 - 1.81673i) q^{10} +(-5.46788 + 2.46089i) q^{11} +(-1.10522 + 2.55329i) q^{12} +(2.26044 + 2.80899i) q^{13} +(-0.960931 - 0.116678i) q^{14} +(-0.421636 + 1.82321i) q^{15} +(0.558371 - 4.59860i) q^{16} +(-2.94188 - 1.54402i) q^{17} +(5.12571 - 2.48676i) q^{18} +(-0.193910 - 0.193910i) q^{19} +(0.104786 + 1.73233i) q^{20} +(0.594906 + 0.652344i) q^{21} +11.3869 q^{22} +2.68893 q^{23} +(-0.956784 + 0.872542i) q^{24} +(-0.917226 - 3.72133i) q^{25} +(-1.72517 - 6.62616i) q^{26} +(-5.02299 - 1.33024i) q^{27} +(0.700701 + 0.423589i) q^{28} +(-4.76353 + 1.80657i) q^{29} +(2.15115 - 2.82869i) q^{30} +(1.68900 + 2.79394i) q^{31} +(-3.77750 + 6.24875i) q^{32} +(-7.87209 - 6.77432i) q^{33} +(3.89114 + 4.96667i) q^{34} +(0.514929 + 0.195287i) q^{35} +(-4.81696 + 0.138734i) q^{36} +(-4.77670 + 2.88762i) q^{37} +(0.184668 + 0.486930i) q^{38} +(-2.74940 + 5.60721i) q^{39} +(-0.286425 + 0.755240i) q^{40} +(0.601451 + 3.28201i) q^{41} +(-0.521787 - 1.59334i) q^{42} +(-0.0628249 - 0.254891i) q^{43} +(-8.78317 - 3.95298i) q^{44} +(-3.17001 + 0.675793i) q^{45} +(-4.65650 - 2.09572i) q^{46} +(0.296967 + 4.90945i) q^{47} +(7.62506 - 2.49705i) q^{48} +(-5.54706 + 3.82886i) q^{49} +(-1.31197 + 7.15920i) q^{50} +(0.264728 - 5.74855i) q^{51} +(-0.969596 + 5.70993i) q^{52} +(2.85167 - 5.43340i) q^{53} +(7.66168 + 6.21846i) q^{54} +(-6.29007 - 1.55036i) q^{55} +(0.216477 + 0.313621i) q^{56} +(0.162020 - 0.446494i) q^{57} +(9.65715 + 0.584150i) q^{58} +(0.0837541 - 0.106904i) q^{59} +(-2.64126 + 1.43511i) q^{60} +(0.717187 - 0.376409i) q^{61} +(-0.747319 - 6.15472i) q^{62} +(-0.587190 + 1.41195i) q^{63} +(3.78705 - 2.61401i) q^{64} +(0.0508016 + 3.89516i) q^{65} +(8.35249 + 17.8667i) q^{66} +(0.304051 + 5.02657i) q^{67} +(-1.27721 - 5.18183i) q^{68} +(1.97239 + 4.21910i) q^{69} +(-0.739513 - 0.739513i) q^{70} +(2.67828 + 14.6149i) q^{71} +(-2.07089 - 0.861225i) q^{72} +(2.55083 + 5.66772i) q^{73} +(10.5225 - 1.27766i) q^{74} +(5.16619 - 4.16885i) q^{75} +(0.0265968 - 0.439698i) q^{76} +(-2.28775 + 2.02677i) q^{77} +(9.13139 - 7.56731i) q^{78} +(8.82755 + 7.82053i) q^{79} +(3.53899 - 3.53899i) q^{80} +(-1.59725 - 8.85713i) q^{81} +(1.51641 - 6.15231i) q^{82} +(-1.36810 - 0.250713i) q^{83} +(-0.150657 + 1.41015i) q^{84} +(-1.47322 - 3.27337i) q^{85} +(-0.0898629 + 0.490366i) q^{86} +(-6.32876 - 6.14911i) q^{87} +(-2.97263 - 3.35541i) q^{88} +(-11.5938 - 11.5938i) q^{89} +(6.01629 + 1.30038i) q^{90} +(1.52601 + 1.02420i) q^{91} +(2.86422 + 3.23303i) q^{92} +(-3.14495 + 4.69955i) q^{93} +(3.31209 - 8.73328i) q^{94} +(-0.0357129 - 0.294122i) q^{95} +(-12.5755 - 1.34354i) q^{96} +(-7.54824 + 5.91366i) q^{97} +(12.5901 - 2.30723i) q^{98} +(4.85497 - 17.3209i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9}+O(q^{10}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27} - 56 q^{28} + 78 q^{30} - 32 q^{31} - 10 q^{33} - 52 q^{34} - 26 q^{36} - 56 q^{37} + 70 q^{39} - 36 q^{40} - 10 q^{42} - 52 q^{43} - 140 q^{45} - 180 q^{46} - 2 q^{48} - 52 q^{49} - 26 q^{51} - 64 q^{52} - 22 q^{54} + 132 q^{55} - 22 q^{57} - 60 q^{58} - 18 q^{60} - 92 q^{61} + 108 q^{63} - 52 q^{64} - 124 q^{66} - 240 q^{67} - 104 q^{69} - 268 q^{70} - 2 q^{72} - 56 q^{73} + 104 q^{75} - 48 q^{76} - 22 q^{78} - 12 q^{79} + 2 q^{81} + 208 q^{82} - 22 q^{84} - 52 q^{85} - 26 q^{87} - 260 q^{88} - 26 q^{90} - 32 q^{91} - 176 q^{93} - 240 q^{94} + 292 q^{96} - 80 q^{97} - 58 q^{99}+O(q^{100}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Introduction

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