LMFDB - Embedded newform 288.2.bf.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26591 + 0.630463i) q^{2} +(-1.05404 - 1.37441i) q^{3} +(1.20503 - 1.59621i) q^{4} +(0.00886053 + 0.0673024i) q^{5} +(2.20083 + 1.07534i) q^{6} +(0.666754 + 2.48836i) q^{7} +(-0.519104 + 2.78038i) q^{8} +(-0.778009 + 2.89736i) q^{9} +O(q^{10})$	\(q+(-1.26591 + 0.630463i) q^{2} +(-1.05404 - 1.37441i) q^{3} +(1.20503 - 1.59621i) q^{4} +(0.00886053 + 0.0673024i) q^{5} +(2.20083 + 1.07534i) q^{6} +(0.666754 + 2.48836i) q^{7} +(-0.519104 + 2.78038i) q^{8} +(-0.778009 + 2.89736i) q^{9} +(-0.0536483 - 0.0796122i) q^{10} +(0.332332 - 0.255007i) q^{11} +(-3.46400 + 0.0262591i) q^{12} +(3.75972 - 4.89976i) q^{13} +(-2.41287 - 2.72966i) q^{14} +(0.0831618 - 0.0831173i) q^{15} +(-1.09579 - 3.84698i) q^{16} +3.64897 q^{17} +(-0.841793 - 4.15829i) q^{18} +(3.97733 - 1.64746i) q^{19} +(0.118106 + 0.0669583i) q^{20} +(2.71724 - 3.53922i) q^{21} +(-0.259928 + 0.532338i) q^{22} +(-8.77221 - 2.35051i) q^{23} +(4.36854 - 2.21717i) q^{24} +(4.82518 - 1.29290i) q^{25} +(-1.67033 + 8.57300i) q^{26} +(4.80221 - 1.98462i) q^{27} +(4.77541 + 1.93427i) q^{28} +(7.27433 + 0.957684i) q^{29} +(-0.0528726 + 0.157649i) q^{30} +(1.77380 - 1.02410i) q^{31} +(3.81255 + 4.17905i) q^{32} +(-0.700775 - 0.187973i) q^{33} +(-4.61925 + 2.30054i) q^{34} +(-0.161565 + 0.0669223i) q^{35} +(3.68728 + 4.73328i) q^{36} +(-3.36655 + 8.12758i) q^{37} +(-3.99625 + 4.59309i) q^{38} +(-10.6972 - 0.00286472i) q^{39} +(-0.191726 - 0.0103013i) q^{40} +(1.45472 - 5.42911i) q^{41} +(-1.20843 + 6.19344i) q^{42} +(-2.16028 - 2.81533i) q^{43} +(-0.00657510 - 0.837765i) q^{44} +(-0.201893 - 0.0266897i) q^{45} +(12.5867 - 2.55503i) q^{46} +(2.05961 + 1.18912i) q^{47} +(-4.13232 + 5.56093i) q^{48} +(0.314804 - 0.181752i) q^{49} +(-5.29309 + 4.67879i) q^{50} +(-3.84615 - 5.01518i) q^{51} +(-3.29048 - 11.9057i) q^{52} +(-0.0730018 + 0.176242i) q^{53} +(-4.82792 + 5.53997i) q^{54} +(0.0201073 + 0.0201073i) q^{55} +(-7.26471 + 0.562114i) q^{56} +(-6.45654 - 3.72999i) q^{57} +(-9.81240 + 3.37386i) q^{58} +(5.21160 - 0.686120i) q^{59} +(-0.0324602 - 0.232903i) q^{60} +(0.357730 - 2.71723i) q^{61} +(-1.59980 + 2.41473i) q^{62} +(-7.72842 - 0.00413936i) q^{63} +(-7.46106 - 2.88662i) q^{64} +(0.363079 + 0.209624i) q^{65} +(1.00563 - 0.203857i) q^{66} +(-0.969906 + 1.26401i) q^{67} +(4.39712 - 5.82453i) q^{68} +(6.01568 + 14.5341i) q^{69} +(0.162334 - 0.186578i) q^{70} +(7.18803 + 7.18803i) q^{71} +(-7.65191 - 3.66719i) q^{72} +(-6.62149 + 6.62149i) q^{73} +(-0.862401 - 12.4112i) q^{74} +(-6.86290 - 5.26901i) q^{75} +(2.16311 - 8.33390i) q^{76} +(0.856134 + 0.656935i) q^{77} +(13.5434 - 6.74054i) q^{78} +(-4.97251 + 8.61265i) q^{79} +(0.249202 - 0.107836i) q^{80} +(-7.78940 - 4.50835i) q^{81} +(1.58131 + 7.78988i) q^{82} +(-4.26191 - 0.561091i) q^{83} +(-2.37498 - 8.60218i) q^{84} +(0.0323318 + 0.245584i) q^{85} +(4.50967 + 2.20197i) q^{86} +(-6.35117 - 11.0074i) q^{87} +(0.536503 + 1.05639i) q^{88} +(2.46723 - 2.46723i) q^{89} +(0.272404 - 0.0934994i) q^{90} +(14.6992 + 6.08860i) q^{91} +(-14.3227 + 11.1699i) q^{92} +(-3.27719 - 1.35849i) q^{93} +(-3.35696 - 0.206801i) q^{94} +(0.146119 + 0.253086i) q^{95} +(1.72517 - 9.64488i) q^{96} +(-7.74713 + 13.4184i) q^{97} +(-0.283924 + 0.428554i) q^{98} +(0.480291 + 1.16128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.26591	+	0.630463i	−0.895130	+	0.445805i
$2$	−1.26591	+	0.630463i	−0.895130	+	0.445805i
$3$	−1.05404	−	1.37441i	−0.608549	−	0.793516i
$3$	−1.05404	−	1.37441i	−0.608549	−	0.793516i
$4$	1.20503	−	1.59621i	0.602516	−	0.798107i
$5$	0.00886053	+	0.0673024i	0.00396255	+	0.0300986i	0.993312	−	0.115462i	$-0.0368348\pi$
$5$	0.00886053	+	0.0673024i	0.00396255	+	0.0300986i	−0.989349	+	0.145560i	$0.953501\pi$
$6$	2.20083	+	1.07534i	0.898484	+	0.439006i
$7$	0.666754	+	2.48836i	0.252009	+	0.940512i	0.969730	+	0.244180i	$0.0785189\pi$
$7$	0.666754	+	2.48836i	0.252009	+	0.940512i	−0.717721	+	0.696331i	$0.754814\pi$
$8$	−0.519104	+	2.78038i	−0.183531	+	0.983014i
$9$	−0.778009	+	2.89736i	−0.259336	+	0.965787i
$10$	−0.0536483	−	0.0796122i	−0.0169651	−	0.0251756i
$11$	0.332332	−	0.255007i	0.100202	−	0.0768876i	−0.557445	−	0.830214i	$-0.688218\pi$
$11$	0.332332	−	0.255007i	0.100202	−	0.0768876i	0.657647	+	0.753326i	$0.271552\pi$
$12$	−3.46400	+	0.0262591i	−0.999971	+	0.00758034i
$13$	3.75972	−	4.89976i	1.04276	−	1.35895i	0.111838	−	0.993726i	$-0.464326\pi$
$13$	3.75972	−	4.89976i	1.04276	−	1.35895i	0.930920	−	0.365223i	$-0.119007\pi$
$14$	−2.41287	−	2.72966i	−0.644866	−	0.729533i
$15$	0.0831618	−	0.0831173i	0.0214723	−	0.0214608i
$16$	−1.09579	−	3.84698i	−0.273948	−	0.961744i
$17$	3.64897			0.885004			0.442502	−	0.896767i	$-0.354091\pi$
$17$	3.64897			0.885004			0.442502	+	0.896767i	$0.354091\pi$
$18$	−0.841793	−	4.15829i	−0.198413	−	0.980119i
$19$	3.97733	−	1.64746i	0.912461	−	0.377954i	0.123463	−	0.992349i	$-0.460600\pi$
$19$	3.97733	−	1.64746i	0.912461	−	0.377954i	0.788998	+	0.614395i	$0.210600\pi$
$20$	0.118106	+	0.0669583i	0.0264094	+	0.0149723i
$21$	2.71724	−	3.53922i	0.592951	−	0.772321i
$22$	−0.259928	+	0.532338i	−0.0554169	+	0.113495i
$23$	−8.77221	−	2.35051i	−1.82913	−	0.490114i	−0.831293	−	0.555834i	$-0.812399\pi$
$23$	−8.77221	−	2.35051i	−1.82913	−	0.490114i	−0.997838	+	0.0657198i	$0.979066\pi$
$24$	4.36854	−	2.21717i	0.891725	−	0.452577i
$25$	4.82518	−	1.29290i	0.965036	−	0.258581i
$26$	−1.67033	+	8.57300i	−0.327579	+	1.68130i
$27$	4.80221	−	1.98462i	0.924187	−	0.381941i
$28$	4.77541	+	1.93427i	0.902468	+	0.365543i
$29$	7.27433	+	0.957684i	1.35081	+	0.177837i	0.770959	−	0.636885i	$-0.219778\pi$
$29$	7.27433	+	0.957684i	1.35081	+	0.177837i	0.579851	+	0.814723i	$0.303111\pi$
$30$	−0.0528726	+	0.157649i	−0.00965317	+	0.0287826i
$31$	1.77380	−	1.02410i	0.318584	−	0.183935i	−0.332177	−	0.943217i	$-0.607783\pi$
$31$	1.77380	−	1.02410i	0.318584	−	0.183935i	0.650761	+	0.759282i	$0.274450\pi$
$32$	3.81255	+	4.17905i	0.673969	+	0.738759i
$33$	−0.700775	−	0.187973i	−0.121989	−	0.0327220i
$34$	−4.61925	+	2.30054i	−0.792194	+	0.394539i
$35$	−0.161565	+	0.0669223i	−0.0273094	+	0.0113119i
$36$	3.68728	+	4.73328i	0.614547	+	0.788881i
$37$	−3.36655	+	8.12758i	−0.553458	+	1.33617i	0.361408	+	0.932408i	$0.382296\pi$
$37$	−3.36655	+	8.12758i	−0.553458	+	1.33617i	−0.914866	+	0.403758i	$0.867704\pi$
$38$	−3.99625	+	4.59309i	−0.648278	+	0.745097i
$39$	−10.6972	−	0.00286472i	−1.71292	−	0.000458722i
$40$	−0.191726	−	0.0103013i	−0.0303145	−	0.00162877i
$41$	1.45472	−	5.42911i	0.227190	−	0.847884i	−0.754326	−	0.656501i	$-0.772036\pi$
$41$	1.45472	−	5.42911i	0.227190	−	0.847884i	0.981515	−	0.191383i	$-0.0612974\pi$
$42$	−1.20843	+	6.19344i	−0.186464	+	0.955668i
$43$	−2.16028	−	2.81533i	−0.329440	−	0.429334i	0.599039	−	0.800720i	$-0.295549\pi$
$43$	−2.16028	−	2.81533i	−0.329440	−	0.429334i	−0.928479	+	0.371386i	$0.878883\pi$
$44$	−0.00657510	−	0.837765i	−0.000991233	−	0.126298i
$45$	−0.201893	−	0.0266897i	−0.0300964	−	0.00397867i
$46$	12.5867	−	2.55503i	1.85581	−	0.376719i
$47$	2.05961	+	1.18912i	0.300425	+	0.173450i	0.642634	−	0.766173i	$-0.277842\pi$
$47$	2.05961	+	1.18912i	0.300425	+	0.173450i	−0.342209	+	0.939624i	$0.611175\pi$
$48$	−4.13232	+	5.56093i	−0.596449	+	0.802651i
$49$	0.314804	−	0.181752i	0.0449720	−	0.0259646i
$50$	−5.29309	+	4.67879i	−0.748556	+	0.661681i
$51$	−3.84615	−	5.01518i	−0.538568	−	0.702265i
$52$	−3.29048	−	11.9057i	−0.456307	−	1.65102i
$53$	−0.0730018	+	0.176242i	−0.0100276	+	0.0242087i	−0.928814	−	0.370546i	$-0.879171\pi$
$53$	−0.0730018	+	0.176242i	−0.0100276	+	0.0242087i	0.918786	+	0.394755i	$0.129171\pi$
$54$	−4.82792	+	5.53997i	−0.656996	+	0.753894i
$55$	0.0201073	+	0.0201073i	0.00271126	+	0.00271126i
$56$	−7.26471	+	0.562114i	−0.970788	+	0.0751157i
$57$	−6.45654	−	3.72999i	−0.855190	−	0.494049i
$58$	−9.81240	+	3.37386i	−1.28843	+	0.443009i
$59$	5.21160	−	0.686120i	0.678493	−	0.0893252i	0.216599	−	0.976261i	$-0.430504\pi$
$59$	5.21160	−	0.686120i	0.678493	−	0.0893252i	0.461893	+	0.886935i	$0.347170\pi$
$60$	−0.0324602	−	0.232903i	−0.00419059	−	0.0300676i
$61$	0.357730	−	2.71723i	0.0458026	−	0.347905i	−0.953164	−	0.302454i	$-0.902194\pi$
$61$	0.357730	−	2.71723i	0.0458026	−	0.347905i	0.998967	−	0.0454512i	$-0.0144725\pi$
$62$	−1.59980	+	2.41473i	−0.203175	+	0.306672i
$63$	−7.72842	−	0.00413936i	−0.973689	−	0.000521511i
$64$	−7.46106	−	2.88662i	−0.932633	−	0.360827i
$65$	0.363079	+	0.209624i	0.0450344	+	0.0260006i
$66$	1.00563	−	0.203857i	0.123784	−	0.0250930i
$67$	−0.969906	+	1.26401i	−0.118493	+	0.154423i	−0.848834	−	0.528660i	$-0.822695\pi$
$67$	−0.969906	+	1.26401i	−0.118493	+	0.154423i	0.730341	+	0.683083i	$0.239361\pi$
$68$	4.39712	−	5.82453i	0.533230	−	0.706328i
$69$	6.01568	+	14.5341i	0.724202	+	1.74970i
$70$	0.162334	−	0.186578i	0.0194026	−	0.0223003i
$71$	7.18803	+	7.18803i	0.853063	+	0.853063i	0.990509	−	0.137446i	$-0.0438895\pi$
$71$	7.18803	+	7.18803i	0.853063	+	0.853063i	−0.137446	+	0.990509i	$0.543889\pi$
$72$	−7.65191	−	3.66719i	−0.901786	−	0.432183i
$73$	−6.62149	+	6.62149i	−0.774986	+	0.774986i	−0.978974	−	0.203987i	$-0.934610\pi$
$73$	−6.62149	+	6.62149i	−0.774986	+	0.774986i	0.203987	+	0.978974i	$0.434610\pi$
$74$	−0.862401	−	12.4112i	−0.100252	−	1.44278i
$75$	−6.86290	−	5.26901i	−0.792459	−	0.608413i
$76$	2.16311	−	8.33390i	0.248125	−	0.955964i
$77$	0.856134	+	0.656935i	0.0975655	+	0.0748647i
$78$	13.5434	−	6.74054i	1.53349	−	0.763216i
$79$	−4.97251	+	8.61265i	−0.559452	+	0.968999i	0.438091	+	0.898931i	$0.355655\pi$
$79$	−4.97251	+	8.61265i	−0.559452	+	0.968999i	−0.997542	+	0.0700678i	$0.977678\pi$
$80$	0.249202	−	0.107836i	0.0278616	−	0.0120564i
$81$	−7.78940	−	4.50835i	−0.865489	−	0.500927i
$82$	1.58131	+	7.78988i	0.174626	+	0.860249i
$83$	−4.26191	−	0.561091i	−0.467805	−	0.0615877i	−0.107061	−	0.994252i	$-0.534144\pi$
$83$	−4.26191	−	0.561091i	−0.467805	−	0.0615877i	−0.360744	+	0.932665i	$0.617477\pi$
$84$	−2.37498	−	8.60218i	−0.259131	−	0.938574i
$85$	0.0323318	+	0.245584i	0.00350687	+	0.0266373i
$86$	4.50967	+	2.20197i	0.486291	+	0.237444i
$87$	−6.35117	−	11.0074i	−0.680917	−	1.18011i
$88$	0.536503	+	1.05639i	0.0571915	+	0.112611i
$89$	2.46723	−	2.46723i	0.261526	−	0.261526i	−0.564148	−	0.825674i	$-0.690795\pi$
$89$	2.46723	−	2.46723i	0.261526	−	0.261526i	0.825674	+	0.564148i	$0.190795\pi$
$90$	0.272404	−	0.0934994i	0.0287139	−	0.00985570i
$91$	14.6992	+	6.08860i	1.54089	+	0.638259i
$92$	−14.3227	+	11.1699i	−1.49324	+	1.16454i
$93$	−3.27719	−	1.35849i	−0.339829	−	0.140868i
$94$	−3.35696	−	0.206801i	−0.346244	−	0.0213299i
$95$	0.146119	+	0.253086i	0.0149915	+	0.0259661i
$96$	1.72517	−	9.64488i	0.176074	−	0.984377i
$97$	−7.74713	+	13.4184i	−0.786602	+	1.36243i	0.141436	+	0.989947i	$0.454828\pi$
$97$	−7.74713	+	13.4184i	−0.786602	+	1.36243i	−0.928038	+	0.372486i	$0.878505\pi$
$98$	−0.283924	+	0.428554i	−0.0286807	+	0.0432905i
$99$	0.480291	+	1.16128i	0.0482711	+	0.116713i
$100$	3.75075	−	9.26000i	0.375075	−	0.926000i
$101$	−3.40929	+	2.61604i	−0.339237	+	0.260306i	−0.764304	−	0.644856i	$-0.776917\pi$
$101$	−3.40929	+	2.61604i	−0.339237	+	0.260306i	0.425067	+	0.905162i	$0.360251\pi$
$102$	8.03074	+	3.92389i	0.795162	+	0.388523i
$103$	−1.69436	−	0.454001i	−0.166950	−	0.0447341i	0.174376	−	0.984679i	$-0.444209\pi$
$103$	−1.69436	−	0.454001i	−0.166950	−	0.0447341i	−0.341326	+	0.939945i	$0.610876\pi$
$104$	11.6715	+	12.9969i	1.14449	+	1.27446i
$105$	0.262274	+	0.151518i	0.0255953	+	0.0147866i
$106$	−0.0187007	−	0.269131i	−0.00181637	−	0.0261403i
$107$	−6.52327	−	2.70203i	−0.630628	−	0.261215i	0.0443917	−	0.999014i	$-0.485865\pi$
$107$	−6.52327	−	2.70203i	−0.630628	−	0.261215i	−0.675020	+	0.737799i	$0.735865\pi$
$108$	2.61894	−	10.0569i	0.252008	−	0.967725i
$109$	−2.14998	−	5.19051i	−0.205931	−	0.497161i	0.786844	−	0.617152i	$-0.211713\pi$
$109$	−2.14998	−	5.19051i	−0.205931	−	0.497161i	−0.992775	+	0.119991i	$0.961713\pi$
$110$	−0.0381308	−	0.0127770i	−0.00363563	−	0.00121824i
$111$	14.7191	−	3.93975i	1.39708	−	0.373944i
$112$	8.84204	−	5.29171i	0.835494	−	0.500020i
$113$	−6.18560	−	10.7138i	−0.581893	−	1.00787i	−0.995255	−	0.0973009i	$-0.968979\pi$
$113$	−6.18560	−	10.7138i	−0.581893	−	1.00787i	0.413362	−	0.910567i	$-0.364354\pi$
$114$	10.5250	+	0.651205i	0.985756	+	0.0609910i
$115$	0.0804683	−	0.611217i	0.00750371	−	0.0569963i
$116$	10.2945	−	10.4573i	0.955818	−	0.970940i
$117$	11.2713	+	14.7053i	1.04203	+	1.35951i
$118$	−6.16482	+	4.15428i	−0.567518	+	0.382433i
$119$	2.43296	+	9.07994i	0.223029	+	0.832357i
$120$	0.187928	+	0.274368i	0.0171554	+	0.0250463i
$121$	−2.80159	+	10.4557i	−0.254690	+	0.950517i
$122$	1.26026	+	3.66529i	0.114098	+	0.331840i
$123$	−8.99516	+	3.72309i	−0.811066	+	0.335700i
$124$	0.502799	−	4.06544i	0.0451527	−	0.365087i
$125$	0.259658	+	0.626870i	0.0232245	+	0.0560689i
$126$	9.78606	−	4.86724i	0.871811	−	0.433608i
$127$			6.09879i			0.541180i	0.962695	+	0.270590i	$0.0872188\pi$
$127$			6.09879i			0.541180i	−0.962695	+	0.270590i	$0.912781\pi$
$128$	11.2649	−	1.04974i	0.995686	−	0.0927850i
$129$	−1.59241	+	5.93658i	−0.140204	+	0.522687i
$130$	−0.591783	−	0.0364559i	−0.0519028	−	0.00319740i
$131$	−10.9721	−	8.41920i	−0.958638	−	0.735589i	0.00577685	−	0.999983i	$-0.498161\pi$
$131$	−10.9721	−	8.41920i	−0.958638	−	0.735589i	−0.964415	+	0.264395i	$0.914828\pi$
$132$	−1.14450	+	0.892073i	−0.0996162	+	0.0776450i
$133$	6.75138	+	8.79856i	0.585419	+	0.762932i
$134$	0.430900	−	2.21160i	0.0372241	−	0.191053i
$135$	0.176120	+	0.305616i	0.0151580	+	0.0263032i
$136$	−1.89419	+	10.1455i	−0.162426	+	0.869972i
$137$	19.6939	−	5.27697i	1.68256	−	0.450842i	0.714110	−	0.700033i	$-0.246831\pi$
$137$	19.6939	−	5.27697i	1.68256	−	0.450842i	0.968454	+	0.249191i	$0.0801648\pi$
$138$	−16.7785	−	14.6062i	−1.42828	−	1.24336i
$139$	22.2105	−	2.92407i	1.88387	−	0.248017i	0.901206	−	0.433391i	$-0.142683\pi$
$139$	22.2105	−	2.92407i	1.88387	−	0.248017i	0.982668	+	0.185374i	$0.0593498\pi$
$140$	−0.0878686	+	0.338535i	−0.00742625	+	0.0286115i
$141$	−0.536572	−	4.08412i	−0.0451875	−	0.343945i
$142$	−13.6312	−	4.56758i	−1.14390	−	0.383303i
$143$		−	2.58710i		−	0.216345i
$144$	11.9986	−	0.181923i	0.999885	−	0.0151602i
$145$			0.498066i			0.0413621i
$146$	4.20757	−	12.5568i	0.348221	−	1.03921i
$147$	−0.581618	−	0.241097i	−0.0479710	−	0.0198853i
$148$	8.91654	+	15.1677i	0.732935	+	1.24678i
$149$	9.26048	−	1.21916i	0.758648	−	0.0998779i	0.258729	−	0.965950i	$-0.416696\pi$
$149$	9.26048	−	1.21916i	0.758648	−	0.0998779i	0.499919	+	0.866072i	$0.333363\pi$
$150$	12.0097	+	2.34326i	0.980587	+	0.191326i
$151$	−4.46253	+	1.19573i	−0.363155	+	0.0973071i	−0.435782	−	0.900052i	$-0.643528\pi$
$151$	−4.46253	+	1.19573i	−0.363155	+	0.0973071i	0.0726273	+	0.997359i	$0.476862\pi$
$152$	2.51593	+	11.9137i	0.204069	+	0.966328i
$153$	−2.83893	+	10.5724i	−0.229514	+	0.854726i
$154$	−1.49796	−	0.291856i	−0.120709	−	0.0235185i
$155$	0.0846415	+	0.110307i	0.00679857	+	0.00886007i
$156$	−12.8950	+	17.0715i	−1.03243	+	1.36681i
$157$	−3.89270	−	2.98697i	−0.310671	−	0.238386i	0.441643	−	0.897191i	$-0.354396\pi$
$157$	−3.89270	−	2.98697i	−0.310671	−	0.238386i	−0.752314	+	0.658804i	$0.771062\pi$
$158$	0.864777	−	14.0378i	0.0687979	−	1.11679i
$159$	0.319175	−	0.0854312i	0.0253123	−	0.00677513i
$160$	−0.247479	+	0.293622i	−0.0195649	+	0.0232129i
$161$		−	23.3956i		−	1.84383i
$162$	12.7030	+	0.796209i	0.998041	+	0.0625561i
$163$	−2.68046	−	6.47120i	−0.209950	−	0.506863i	0.783465	−	0.621436i	$-0.213450\pi$
$163$	−2.68046	−	6.47120i	−0.209950	−	0.506863i	−0.993415	+	0.114572i	$0.963450\pi$
$164$	−6.91302	−	8.86430i	−0.539816	−	0.692186i
$165$	0.00644182	−	0.0488294i	0.000501495	−	0.00380137i
$166$	5.74892	−	1.97669i	0.446203	−	0.153421i
$167$	−5.28563	+	19.7262i	−0.409014	+	1.52646i	0.387516	+	0.921863i	$0.373333\pi$
$167$	−5.28563	+	19.7262i	−0.409014	+	1.52646i	−0.796530	+	0.604599i	$0.793333\pi$
$168$	8.42985	+	9.39220i	0.650377	+	0.724624i
$169$	−6.50753	−	24.2864i	−0.500579	−	1.86819i
$170$	−0.195761	−	0.290502i	−0.0150142	−	0.0222805i
$171$	1.67890	+	12.8055i	0.128388	+	0.979260i
$172$	−7.09708	+	0.0557006i	−0.541147	+	0.00424713i
$173$	−1.17706	+	8.94067i	−0.0894903	+	0.679747i	0.886624	+	0.462490i	$0.153044\pi$
$173$	−1.17706	+	8.94067i	−0.0894903	+	0.679747i	−0.976115	+	0.217256i	$0.930289\pi$
$174$	14.9797	+	9.93009i	1.13561	+	0.752798i
$175$	6.43441	+	11.1447i	0.486396	+	0.842462i
$176$	−1.34517	−	0.999039i	−0.101396	−	0.0753054i
$177$	−6.43623	−	6.43968i	−0.483777	−	0.484036i
$178$	−1.56778	+	4.67878i	−0.117510	+	0.350690i
$179$	−3.79147	−	9.15342i	−0.283388	−	0.684159i	0.716522	−	0.697564i	$-0.245733\pi$
$179$	−3.79147	−	9.15342i	−0.283388	−	0.684159i	−0.999910	+	0.0134054i	$0.995733\pi$
$180$	−0.285890	+	0.290102i	−0.0213090	+	0.0216229i
$181$	−19.1915	−	7.94937i	−1.42649	−	0.590872i	−0.470009	−	0.882662i	$-0.655749\pi$
$181$	−19.1915	−	7.94937i	−1.42649	−	0.590872i	−0.956482	+	0.291790i	$0.905749\pi$
$182$	−22.4464	+	1.55970i	−1.66384	+	0.115613i
$183$	−4.11165	+	2.37239i	−0.303942	+	0.175372i
$184$	11.0890	−	23.1699i	0.817491	−	1.70811i
$185$	−0.576835	−	0.154563i	−0.0424098	−	0.0113637i
$186$	5.00509	−	0.346434i	0.366991	−	0.0254018i
$187$	1.21267	−	0.930513i	0.0886791	−	0.0680459i
$188$	4.37998	−	1.85465i	0.319443	−	0.135264i
$189$	8.14035	+	10.6264i	0.592124	+	0.772956i
$190$	−0.344535	−	0.228260i	−0.0249952	−	0.0165597i
$191$	4.73817	−	8.20675i	0.342842	−	0.593820i	−0.642117	−	0.766606i	$-0.721944\pi$
$191$	4.73817	−	8.20675i	0.342842	−	0.593820i	0.984959	+	0.172787i	$0.0552771\pi$
$192$	3.89685	+	13.2972i	0.281231	+	0.959640i
$193$	−8.97329	−	15.5422i	−0.645912	−	1.11875i	−0.984090	−	0.177670i	$-0.943144\pi$
$193$	−8.97329	−	15.5422i	−0.645912	−	1.11875i	0.338178	−	0.941082i	$-0.390189\pi$
$194$	1.34731	−	21.8707i	0.0967314	−	1.57023i
$195$	−0.0945898	−	0.719971i	−0.00677372	−	0.0515582i
$196$	0.0892340	−	0.721512i	0.00637386	−	0.0515366i
$197$	−4.82042	−	1.99668i	−0.343441	−	0.142258i	0.204295	−	0.978909i	$-0.434510\pi$
$197$	−4.82042	−	1.99668i	−0.343441	−	0.142258i	−0.547735	+	0.836652i	$0.684510\pi$
$198$	−1.34015	−	1.16727i	−0.0952403	−	0.0829543i
$199$	−14.2378	+	14.2378i	−1.00929	+	1.00929i	−0.00933576	+	0.999956i	$0.502972\pi$
$199$	−14.2378	+	14.2378i	−1.00929	+	1.00929i	−0.999956	+	0.00933576i	$0.997028\pi$
$200$	1.09000	+	14.0870i	0.0770743	+	0.996101i
$201$	2.75958		0.000739020i	0.194646		5.21264e-5i
$202$	2.66652	−	5.46109i	0.187616	−	0.384241i
$203$	2.46713	+	18.7397i	0.173158	+	1.31527i
$204$	−12.6400	+	0.0958185i	−0.884979	+	0.00670864i
$205$	0.378282	+	0.0498017i	0.0264203	+	0.00347830i
$206$	2.43113	−	0.493506i	0.169385	−	0.0343842i
$207$	13.6351	−	23.5875i	0.947706	−	1.63945i
$208$	−22.9691	−	9.09444i	−1.59262	−	0.630586i
$209$	0.901678	−	1.56175i	0.0623704	−	0.108029i
$210$	−0.427541	−	0.0264529i	−0.0295031	−	0.00182543i
$211$	5.21165	+	3.99904i	0.358785	+	0.275305i	0.772387	−	0.635153i	$-0.219063\pi$
$211$	5.21165	+	3.99904i	0.358785	+	0.275305i	−0.413602	+	0.910458i	$0.635729\pi$
$212$	0.193350	+	0.328904i	0.0132793	+	0.0225892i
$213$	2.30285	−	17.4558i	0.157789	−	1.19605i
$214$	9.96137	−	0.692171i	0.680945	−	0.0473158i
$215$	0.170337	−	0.170337i	0.0116169	−	0.0116169i
$216$	3.02517	+	14.3822i	0.205837	+	0.978586i
$217$	3.73103	+	3.73103i	0.253279	+	0.253279i
$218$	5.99410	+	5.21521i	0.405971	+	0.353219i
$219$	16.0799	+	2.12135i	1.08658	+	0.143347i
$220$	0.0563254	−	0.00786556i	0.00379745	−	0.000530296i
$221$	13.7191	−	17.8791i	0.922846	−	1.20268i
$222$	−16.1491	+	14.2672i	−1.08386	+	0.957552i
$223$	−2.03938	−	1.17744i	−0.136567	−	0.0788471i	0.430160	−	0.902753i	$-0.358457\pi$
$223$	−2.03938	−	1.17744i	−0.136567	−	0.0788471i	−0.566727	+	0.823906i	$0.691791\pi$
$224$	−7.85696	+	12.2734i	−0.524965	+	0.820050i
$225$	−0.00802664	+	14.9862i	−0.000535109	+	0.999078i
$226$	14.5850	+	9.66283i	0.970182	+	0.642762i
$227$	2.07726	−	15.7783i	0.137872	−	1.04725i	−0.772956	−	0.634460i	$-0.781223\pi$
$227$	2.07726	−	15.7783i	0.137872	−	1.04725i	0.910828	−	0.412786i	$-0.135444\pi$
$228$	−13.7342	+	5.81125i	−0.909570	+	0.384860i
$229$	−15.3299	+	2.01822i	−1.01303	+	0.133368i	−0.618720	−	0.785611i	$-0.712349\pi$
$229$	−15.3299	+	2.01822i	−1.01303	+	0.133368i	−0.394307	+	0.918979i	$0.629015\pi$
$230$	0.283485	+	0.824476i	0.0186924	+	0.0543643i
$231$	0.000500551	−	1.86911i	3.29339e−5	−	0.122979i
$232$	−6.43886	+	19.7283i	−0.422732	+	1.29523i
$233$	−5.49432	−	5.49432i	−0.359945	−	0.359945i	0.503848	−	0.863793i	$-0.331917\pi$
$233$	−5.49432	−	5.49432i	−0.359945	−	0.359945i	−0.863793	+	0.503848i	$0.831917\pi$
$234$	−23.5395	−	11.5094i	−1.53883	−	0.752394i
$235$	−0.0617812	+	0.149153i	−0.00403016	+	0.00972966i
$236$	5.18495	−	9.14562i	0.337512	−	0.595329i
$237$	17.0785	−	2.24378i	1.10937	−	0.145749i
$238$	−8.80447	−	9.96045i	−0.570709	−	0.645640i
$239$	−17.3751	+	10.0315i	−1.12390	+	0.648883i	−0.942393	−	0.334507i	$-0.891430\pi$
$239$	−17.3751	+	10.0315i	−1.12390	+	0.648883i	−0.181506	+	0.983390i	$0.558097\pi$
$240$	−0.410878	−	0.228842i	−0.0265221	−	0.0147717i
$241$	9.35807	+	5.40288i	0.602806	+	0.348030i	0.770145	−	0.637869i	$-0.220184\pi$
$241$	9.35807	+	5.40288i	0.602806	+	0.348030i	−0.167339	+	0.985899i	$0.553517\pi$
$242$	−3.04537	−	15.0022i	−0.195764	−	0.964379i
$243$	2.01401	+	15.4578i	0.129199	+	0.991619i
$244$	−3.90620	−	3.84536i	−0.250069	−	0.246174i
$245$	0.0150217	+	0.0195767i	0.000959701	+	0.00125071i
$246$	9.03974	−	10.3842i	0.576353	−	0.662072i
$247$	6.88146	−	25.6819i	0.437857	−	1.63410i
$248$	1.92662	+	5.46346i	0.122340	+	0.346930i
$249$	3.72104	+	6.44903i	0.235812	+	0.408690i
$250$	−0.723920	−	0.629853i	−0.0457847	−	0.0398354i
$251$	3.41749	−	8.25055i	0.215710	−	0.520770i	−0.778572	−	0.627555i	$-0.784056\pi$
$251$	3.41749	−	8.25055i	0.215710	−	0.520770i	0.994282	+	0.106785i	$0.0340557\pi$
$252$	−9.31960	+	12.3312i	−0.587080	+	0.776793i
$253$	−3.51468	+	1.45583i	−0.220966	+	0.0915272i
$254$	−3.84506	−	7.72050i	−0.241261	−	0.484427i
$255$	0.303455	−	0.303292i	0.0190031	−	0.0189929i
$256$	−13.5985	+	8.43098i	−0.849905	+	0.526936i
$257$	−23.7599	+	13.7178i	−1.48210	+	0.855692i	−0.999794	−	0.0203099i	$-0.993535\pi$
$257$	−23.7599	+	13.7178i	−1.48210	+	0.855692i	−0.482308	+	0.876002i	$0.660201\pi$
$258$	−1.72696	−	8.51910i	−0.107516	−	0.530376i
$259$	−22.4690	−	2.95810i	−1.39616	−	0.183807i
$260$	0.772126	−	0.326948i	0.0478852	−	0.0202764i
$261$	−8.43425	+	20.3313i	−0.522067	+	1.25847i
$262$	19.1976	+	3.74040i	1.18603	+	0.231082i
$263$	21.9440	−	5.87988i	1.35313	−	0.362569i	0.491838	−	0.870686i	$-0.336325\pi$
$263$	21.9440	−	5.87988i	1.35313	−	0.362569i	0.861288	+	0.508117i	$0.169658\pi$
$264$	0.886413	−	1.85085i	0.0545550	−	0.113912i
$265$	−0.0125083	−	0.00335160i	−0.000768381	−	0.000205887i
$266$	−14.0938	−	6.88166i	−0.864145	−	0.421941i
$267$	−5.99155	−	0.790435i	−0.366677	−	0.0483738i
$268$	0.848855	+	3.07135i	0.0518521	+	0.187612i
$269$	−26.9125	+	11.1475i	−1.64088	+	0.679677i	−0.996387	−	0.0849297i	$-0.972933\pi$
$269$	−26.9125	+	11.1475i	−1.64088	+	0.679677i	−0.644498	+	0.764606i	$0.722933\pi$
$270$	−0.415631	−	0.275843i	−0.0252945	−	0.0167873i
$271$	4.68410			0.284539			0.142269	−	0.989828i	$-0.454560\pi$
$271$	4.68410			0.284539			0.142269	+	0.989828i	$0.454560\pi$
$272$	−3.99851	−	14.0375i	−0.242445	−	0.851148i
$273$	−7.12525	−	26.6203i	−0.431240	−	1.61113i
$274$	−21.6037	+	19.0964i	−1.30513	+	1.15366i
$275$	1.27386	−	1.66013i	0.0768168	−	0.100110i
$276$	30.4487	+	7.91181i	1.83279	+	0.476235i
$277$	−9.86942	+	7.57307i	−0.592996	+	0.455022i	−0.861148	−	0.508355i	$-0.830254\pi$
$277$	−9.86942	+	7.57307i	−0.592996	+	0.455022i	0.268152	+	0.963377i	$0.413587\pi$
$278$	−26.2729	+	17.7045i	−1.57575	+	1.06185i
$279$	1.58717	+	5.93610i	0.0950212	+	0.355385i
$280$	−0.102201	−	0.483952i	−0.00610767	−	0.0289216i
$281$	3.14266	+	11.7286i	0.187475	+	0.699668i	0.994087	+	0.108586i	$0.0346323\pi$
$281$	3.14266	+	11.7286i	0.187475	+	0.699668i	−0.806612	+	0.591082i	$0.798701\pi$
$282$	3.25414	+	4.83182i	0.193781	+	0.287731i
$283$	−1.06070	−	8.05683i	−0.0630522	−	0.478929i	−0.993617	−	0.112803i	$-0.964017\pi$
$283$	−1.06070	−	8.05683i	−0.0630522	−	0.478929i	0.930565	−	0.366126i	$-0.119316\pi$
$284$	20.1355	−	2.81182i	1.19482	−	0.166851i
$285$	0.193829	−	0.467590i	0.0114814	−	0.0276977i
$286$	1.63107	+	3.27503i	0.0964474	+	0.193657i
$287$	14.4795			0.854699
$288$	−15.0744	+	7.79498i	−0.888269	+	0.459324i
$289$	−3.68505			−0.216767
$290$	−0.314012	−	0.630504i	−0.0184394	−	0.0370245i
$291$	26.6082	−	3.49578i	1.55980	−	0.204926i
$292$	2.59020	+	18.5484i	0.151580	+	1.08546i
$293$	1.06313	+	8.07531i	0.0621090	+	0.471764i	0.994030	+	0.109104i	$0.0347982\pi$
$293$	1.06313	+	8.07531i	0.0621090	+	0.471764i	−0.931921	+	0.362660i	$0.881869\pi$
$294$	0.888276	−	0.0614832i	0.0518053	−	0.00358577i
$295$	0.0923551	+	0.344674i	0.00537712	+	0.0200677i
$296$	−20.8502	−	13.5794i	−1.21189	−	0.789285i
$297$	1.08984	−	1.88415i	0.0632387	−	0.109330i
$298$	−10.9542	+	7.38173i	−0.634562	+	0.427612i
$299$	−44.4979	+	34.1445i	−2.57338	+	1.97463i
$300$	−16.6805	+	4.60532i	−0.963048	+	0.265888i
$301$	5.56519	−	7.25269i	0.320772	−	0.418038i
$302$	4.89527	−	4.32714i	0.281691	−	0.248999i
$303$	7.18904	+	1.92836i	0.412999	+	0.110781i
$304$	−10.6961	−	13.4954i	−0.613462	−	0.774015i
$305$	0.186046			0.0106529
$306$	−3.07168	−	15.1735i	−0.175596	−	0.867409i
$307$	30.9448	−	12.8178i	1.76611	−	0.731549i	0.770559	−	0.637368i	$-0.219977\pi$
$307$	30.9448	−	12.8178i	1.76611	−	0.731549i	0.995555	−	0.0941803i	$-0.0300230\pi$
$308$	2.08028	−	0.574944i	0.118535	−	0.0327605i
$309$	1.16193	+	2.80728i	0.0661000	+	0.159700i
$310$	−0.176693	−	0.0862748i	−0.0100355	−	0.00490008i
$311$	15.3848	+	4.12235i	0.872393	+	0.233757i	0.667122	−	0.744948i	$-0.267526\pi$
$311$	15.3848	+	4.12235i	0.872393	+	0.233757i	0.205270	+	0.978705i	$0.434193\pi$
$312$	5.56091	−	29.7407i	0.314824	−	1.68374i
$313$	26.6925	−	7.15224i	1.50875	−	0.404268i	0.592730	−	0.805401i	$-0.298050\pi$
$313$	26.6925	−	7.15224i	1.50875	−	0.404268i	0.916020	+	0.401132i	$0.131383\pi$
$314$	6.81096	+	1.32702i	0.384365	+	0.0748882i
$315$	−0.0681993	−	0.520178i	−0.00384259	−	0.0293087i
$316$	7.75558	+	18.3157i	0.436285	+	1.03034i
$317$	−0.823543	−	0.108422i	−0.0462548	−	0.00608956i	0.107363	−	0.994220i	$-0.465759\pi$
$317$	−0.823543	−	0.108422i	−0.0462548	−	0.00608956i	−0.153618	+	0.988130i	$0.549093\pi$
$318$	−0.350185	+	0.309376i	−0.0196374	+	0.0173490i
$319$	2.66171	−	1.53674i	0.149027	−	0.0860409i
$320$	0.128167	−	0.527724i	0.00716477	−	0.0295007i
$321$	3.16208	+	11.8137i	0.176490	+	0.659376i
$322$	14.7501	+	29.6166i	0.821989	+	1.65047i
$323$	14.5131	−	6.01153i	0.807532	−	0.334491i
$324$	−16.5828	+	7.00084i	−0.921265	+	0.388936i
$325$	11.8064	−	28.5032i	0.654901	−	1.58107i
$326$	7.47305	+	6.50199i	0.413894	+	0.360112i
$327$	−4.86773	+	8.42595i	−0.269186	+	0.465956i
$328$	14.3398	+	6.86296i	0.791785	+	0.378944i
$329$	−1.58570	+	5.91790i	−0.0874222	+	0.326264i
$330$	0.0226304	+	0.0658748i	0.00124576	+	0.00362629i
$331$	9.14211	+	11.9142i	0.502496	+	0.654866i	0.973880	−	0.227062i	$-0.0729121\pi$
$331$	9.14211	+	11.9142i	0.502496	+	0.654866i	−0.471384	+	0.881928i	$0.656245\pi$
$332$	−6.03136	+	6.12678i	−0.331014	+	0.336251i
$333$	−20.9293	−	16.0775i	−1.14692	−	0.881039i
$334$	−5.74556	−	28.3039i	−0.314383	−	1.54872i
$335$	−0.0936646	−	0.0540773i	−0.00511744	−	0.00295456i
$336$	−16.5928	−	6.57493i	−0.905213	−	0.358692i
$337$	−17.1129	+	9.88013i	−0.932198	+	0.538205i	−0.887506	−	0.460796i	$-0.847564\pi$
$337$	−17.1129	+	9.88013i	−0.932198	+	0.538205i	−0.0446921	+	0.999001i	$0.514231\pi$
$338$	23.5496	+	26.6416i	1.28093	+	1.44911i
$339$	−8.20527	+	19.7943i	−0.445649	+	1.07508i
$340$	0.430966	+	0.244329i	0.0233724	+	0.0132506i
$341$	0.328337	−	0.792675i	0.0177804	−	0.0429258i
$342$	−10.1987	−	15.1521i	−0.551483	−	0.819329i
$343$	13.4134	+	13.4134i	0.724256	+	0.724256i
$344$	8.94911	−	4.54496i	0.482504	−	0.245048i
$345$	−0.924880	+	0.533650i	−0.0497939	+	0.0287307i
$346$	−4.14671	−	12.0601i	−0.222929	−	0.648357i
$347$	−11.6853	+	1.53839i	−0.627298	+	0.0825853i	−0.437471	−	0.899232i	$-0.644126\pi$
$347$	−11.6853	+	1.53839i	−0.627298	+	0.0825853i	−0.189826	+	0.981818i	$0.560793\pi$
$348$	−25.2234	−	3.12640i	−1.35212	−	0.167593i
$349$	2.27090	−	17.2492i	0.121558	−	0.923327i	−0.816620	−	0.577176i	$-0.804155\pi$
$349$	2.27090	−	17.2492i	0.121558	−	0.923327i	0.938178	−	0.346152i	$-0.112512\pi$
$350$	−15.1717	−	10.0515i	−0.810961	−	0.537276i
$351$	8.33080	−	30.9913i	0.444665	−	1.65420i
$352$	2.33272	+	0.416606i	0.124334	+	0.0222052i
$353$	−10.1154	−	5.84016i	−0.538391	−	0.310840i	0.206036	−	0.978544i	$-0.433944\pi$
$353$	−10.1154	−	5.84016i	−0.538391	−	0.310840i	−0.744427	+	0.667704i	$0.767277\pi$
$354$	12.2076	+	4.09422i	0.648829	+	0.217605i
$355$	−0.420082	+	0.547462i	−0.0222957	+	0.0290563i
$356$	−0.965133	−	6.91133i	−0.0511520	−	0.366300i
$357$	9.91513	−	12.9145i	0.524764	−	0.683507i
$358$	10.5705	+	9.19698i	0.558670	+	0.486076i
$359$	−5.22831	−	5.22831i	−0.275939	−	0.275939i	0.555546	−	0.831486i	$-0.312509\pi$
$359$	−5.22831	−	5.22831i	−0.275939	−	0.275939i	−0.831486	+	0.555546i	$0.812509\pi$
$360$	0.179011	−	0.547485i	0.00943471	−	0.0288550i
$361$	−0.330044	+	0.330044i	−0.0173707	+	0.0173707i
$362$	29.3064	−	2.03637i	1.54031	−	0.107029i
$363$	17.3234	−	7.17015i	0.909243	−	0.376335i
$364$	27.4317	−	16.1261i	1.43781	−	0.845235i
$365$	−0.504312	−	0.386972i	−0.0263969	−	0.0202550i
$366$	3.70925	−	5.59546i	0.193886	−	0.292480i
$367$	−0.612755	+	1.06132i	−0.0319855	+	0.0554006i	−0.881575	−	0.472044i	$-0.843516\pi$
$367$	−0.612755	+	1.06132i	−0.0319855	+	0.0554006i	0.849590	+	0.527444i	$0.176850\pi$
$368$	0.570175	+	36.3221i	0.0297224	+	1.89342i
$369$	14.5983	+	8.43876i	0.759957	+	0.439304i
$370$	0.827665	−	0.168012i	0.0430282	−	0.00873452i
$371$	−0.487228	−	0.0641447i	−0.0252956	−	0.00333023i
$372$	−6.11756	+	3.59408i	−0.317181	+	0.186344i
$373$	2.19784	+	16.6943i	0.113800	+	0.864396i	0.949182	+	0.314727i	$0.101913\pi$
$373$	2.19784	+	16.6943i	0.113800	+	0.864396i	−0.835382	+	0.549669i	$0.814754\pi$
$374$	−0.948469	+	1.94248i	−0.0490442	+	0.100443i
$375$	0.587887	−	1.01762i	0.0303584	−	0.0525497i
$376$	−4.37535	+	5.10923i	−0.225641	+	0.263488i
$377$	32.0419	−	32.0419i	1.65024	−	1.65024i
$378$	−17.0045	−	8.31980i	−0.874615	−	0.427924i
$379$	10.2546	+	4.24759i	0.526742	+	0.218184i	0.630176	−	0.776453i	$-0.282983\pi$
$379$	10.2546	+	4.24759i	0.526742	+	0.218184i	−0.103433	+	0.994636i	$0.532983\pi$
$380$	0.580058	+	0.0717395i	0.0297564	+	0.00368016i
$381$	8.38225	−	6.42836i	0.429436	−	0.329335i
$382$	−0.824021	+	13.3762i	−0.0421606	+	0.684387i
$383$	2.90214	+	5.02665i	0.148292	+	0.256850i	0.930596	−	0.366047i	$-0.119289\pi$
$383$	2.90214	+	5.02665i	0.148292	+	0.256850i	−0.782304	+	0.622897i	$0.785956\pi$
$384$	−13.3164	−	14.3761i	−0.679550	−	0.733629i
$385$	−0.0366275	+	0.0634407i	−0.00186671	+	0.00323324i
$386$	21.1581	+	14.0176i	1.07692	+	0.713478i
$387$	9.83775	−	4.06876i	0.500081	−	0.206827i
$388$	12.0831	+	28.5357i	0.613427	+	1.44868i
$389$	3.23589	−	2.48298i	0.164066	−	0.125892i	−0.523465	−	0.852047i	$-0.675361\pi$
$389$	3.23589	−	2.48298i	0.164066	−	0.125892i	0.687531	+	0.726155i	$0.258694\pi$
$390$	0.573657	+	0.851779i	0.0290482	+	0.0431315i
$391$	−32.0095	−	8.57692i	−1.61879	−	0.433753i
$392$	0.341925	+	0.969625i	0.0172698	+	0.0489734i
$393$	−0.00641500	+	23.9543i	−0.000323594	+	1.20834i
$394$	7.36103	−	0.511485i	0.370843	−	0.0257682i
$395$	−0.623711	−	0.258350i	−0.0313823	−	0.0129990i
$396$	2.43242	+	0.632738i	0.122234	+	0.0317963i
$397$	−10.8114	−	26.1011i	−0.542610	−	1.30998i	−0.922875	−	0.385099i	$-0.874167\pi$
$397$	−10.8114	−	26.1011i	−0.542610	−	1.30998i	0.380266	−	0.924877i	$-0.375833\pi$
$398$	9.04731	−	27.0001i	0.453501	−	1.35340i
$399$	4.97664	−	18.5532i	0.249143	−	0.928821i
$400$	−10.2612	−	17.1456i	−0.513058	−	0.857280i
$401$	13.2637	+	22.9733i	0.662355	+	1.14723i	0.979995	+	0.199022i	$0.0637764\pi$
$401$	13.2637	+	22.9733i	0.662355	+	1.14723i	−0.317640	+	0.948211i	$0.602890\pi$
$402$	−3.49384	+	1.73888i	−0.174257	+	0.0867274i
$403$	1.65113	−	12.5415i	0.0822484	−	0.624739i
$404$	0.0674519	+	8.59437i	0.00335586	+	0.427586i
$405$	0.234404	−	0.564192i	0.0116476	−	0.0280349i
$406$	−14.9378	−	22.1672i	−0.741352	−	1.10014i
$407$	0.953779	+	3.55955i	0.0472771	+	0.176440i
$408$	15.9407	−	8.09037i	0.789181	−	0.400533i
$409$	−7.12609	+	26.5949i	−0.352362	+	1.31503i	0.531409	+	0.847116i	$0.321663\pi$
$409$	−7.12609	+	26.5949i	−0.352362	+	1.31503i	−0.883771	+	0.467919i	$0.845004\pi$
$410$	−0.510267	+	0.175448i	−0.0252003	+	0.00866477i
$411$	−28.0108	−	21.5054i	−1.38167	−	1.06078i
$412$	−2.76644	+	2.15747i	−0.136293	+	0.106291i
$413$	5.18217	+	12.5109i	0.254998	+	0.615619i
$414$	−2.38970	+	38.4560i	−0.117447	+	1.89001i
$415$		−	0.291808i		−	0.0143243i
$416$	34.8105	−	2.96850i	1.70672	−	0.145543i
$417$	−27.4296	−	27.4443i	−1.34323	−	1.34395i
$418$	−0.156812	+	2.54550i	−0.00766992	+	0.124505i
$419$	−4.67711	−	3.58887i	−0.228492	−	0.175328i	0.488170	−	0.872748i	$-0.337664\pi$
$419$	−4.67711	−	3.58887i	−0.228492	−	0.175328i	−0.716662	+	0.697420i	$0.754331\pi$
$420$	0.557904	−	0.236062i	0.0272229	−	0.0115186i
$421$	−22.3387	−	29.1124i	−1.08872	−	1.41885i	−0.899502	−	0.436917i	$-0.856070\pi$
$421$	−22.3387	−	29.1124i	−1.08872	−	1.41885i	−0.189221	−	0.981935i	$-0.560596\pi$
$422$	−9.11870	−	1.77665i	−0.443892	−	0.0864861i
$423$	−5.04769	+	5.04229i	−0.245427	+	0.245165i
$424$	−0.452125	−	0.294461i	−0.0219571	−	0.0143003i
$425$	17.6069	−	4.71776i	0.854061	−	0.228845i
$426$	8.09003	+	23.5492i	0.391963	+	1.14096i
$427$	6.99996	−	0.921562i	0.338752	−	0.0445975i
$428$	−12.1738	+	7.15650i	−0.588441	+	0.345922i
$429$	−3.55574	+	2.72691i	−0.171673	+	0.131656i
$430$	−0.108240	+	0.323023i	−0.00521978	+	0.0155775i
$431$		−	5.39534i		−	0.259884i	−0.991522	−	0.129942i	$-0.958521\pi$
$431$		−	5.39534i		−	0.259884i	0.991522	−	0.129942i	$-0.0414792\pi$
$432$	−12.8970	−	16.2993i	−0.620509	−	0.784199i
$433$		−	1.07138i		−	0.0514873i	−0.999669	−	0.0257436i	$-0.991805\pi$
$433$		−	1.07138i		−	0.0514873i	0.999669	−	0.0257436i	$-0.00819536\pi$
$434$	−7.07540	−	2.37085i	−0.339630	−	0.113805i
$435$	0.684547	−	0.524980i	0.0328215	−	0.0251709i
$436$	−10.8760	−	2.82291i	−0.520864	−	0.135193i
$437$	−38.7623	+	5.10315i	−1.85425	+	0.244117i
$438$	−21.6931	+	7.45239i	−1.03654	+	0.356089i
$439$	−6.10948	+	1.63703i	−0.291589	+	0.0781312i	−0.401649	−	0.915794i	$-0.631563\pi$
$439$	−6.10948	+	1.63703i	−0.291589	+	0.0781312i	0.110059	+	0.993925i	$0.464896\pi$
$440$	−0.0663436	+	0.0454681i	−0.00316281	+	0.00216761i
$441$	0.281682	+	1.05351i	0.0134134	+	0.0501670i
$442$	−6.09498	+	31.2826i	−0.289909	+	1.48796i
$443$	12.2735	+	15.9952i	0.583133	+	0.759954i	0.988005	−	0.154419i	$-0.0493506\pi$
$443$	12.2735	+	15.9952i	0.583133	+	0.759954i	−0.404872	+	0.914373i	$0.632684\pi$
$444$	11.4483	−	28.2424i	0.543314	−	1.34032i
$445$	0.187912	+	0.144190i	0.00890787	+	0.00683525i
$446$	3.32400	+	0.204770i	0.157396	+	0.00969614i
$447$	−11.4365	−	11.4427i	−0.540929	−	0.541219i
$448$	2.20825	−	20.4905i	0.104330	−	0.968084i
$449$		−	2.03680i		−	0.0961223i	−0.998844	−	0.0480612i	$-0.984696\pi$
$449$		−	2.03680i		−	0.0961223i	0.998844	−	0.0480612i	$-0.0153042\pi$
$450$	−9.43807	−	18.9761i	−0.444915	−	0.894544i
$451$	−0.901011	−	2.17523i	−0.0424269	−	0.102428i
$452$	−24.5553	−	3.03691i	−1.15499	−	0.142844i
$453$	6.34709	+	4.87300i	0.298212	+	0.228953i
$454$	7.31805	+	21.2835i	0.343453	+	0.998885i
$455$	−0.279535	+	1.04324i	−0.0131048	+	0.0489078i
$456$	13.7224	−	16.0154i	0.642611	−	0.749990i
$457$	−2.86574	−	10.6951i	−0.134054	−	0.500295i	−1.00000		0.000158032i	$-0.999950\pi$
$457$	−2.86574	−	10.6951i	−0.134054	−	0.500295i	0.865946	−	0.500137i	$-0.166717\pi$
$458$	18.1338	−	12.2198i	0.847335	−	0.570994i
$459$	17.5231	−	7.24183i	0.817909	−	0.338019i
$460$	−0.878666	−	0.864981i	−0.0409680	−	0.0403300i
$461$	−3.77317	+	28.6601i	−0.175734	+	1.33483i	0.645289	+	0.763939i	$0.276737\pi$
$461$	−3.77317	+	28.6601i	−0.175734	+	1.33483i	−0.821023	+	0.570895i	$0.806596\pi$
$462$	1.17777	+	2.36644i	0.0547950	+	0.110097i
$463$	−3.25725	−	5.64172i	−0.151377	−	0.262193i	0.780357	−	0.625334i	$-0.215037\pi$
$463$	−3.25725	−	5.64172i	−0.151377	−	0.262193i	−0.931734	+	0.363142i	$0.881704\pi$
$464$	−4.28697	−	29.0336i	−0.199018	−	1.34785i
$465$	0.0623917	−	0.232600i	0.00289335	−	0.0107866i
$466$	10.4193	+	3.49132i	0.482663	+	0.161732i
$467$	8.14793	+	19.6708i	0.377041	+	0.910258i	0.992517	+	0.122103i	$0.0389638\pi$
$467$	8.14793	+	19.6708i	0.377041	+	0.910258i	−0.615476	+	0.788156i	$0.711036\pi$
$468$	37.0551	−	0.270974i	1.71287	−	0.0125258i
$469$	−3.79199	−	1.57069i	−0.175098	−	0.0725279i
$470$	−0.0158263	−	0.227764i	−0.000730013	−	0.0105060i
$471$	−0.00227592	+	8.49855i	−0.000104869	+	0.391592i
$472$	−0.797685	+	14.8464i	−0.0367164	+	0.683362i
$473$	−1.43586	−	0.384738i	−0.0660210	−	0.0176903i
$474$	−20.2052	+	13.6078i	−0.928055	+	0.625027i
$475$	17.0613	−	13.0916i	0.782826	−	0.600683i
$476$	17.4253	+	7.05810i	0.798688	+	0.323507i
$477$	−0.453841	−	0.348630i	−0.0207799	−	0.0159627i
$478$	15.6707	−	23.6533i	0.716761	−	1.08187i
$479$	0.238327	−	0.412794i	0.0108894	−	0.0188611i	−0.860529	−	0.509401i	$-0.829867\pi$
$479$	0.238327	−	0.412794i	0.0108894	−	0.0188611i	0.871419	+	0.490540i	$0.163200\pi$
$480$	0.664410	+	0.0306491i	0.0303260	+	0.00139893i
$481$	27.1659	+	47.0527i	1.23866	+	2.14542i
$482$	−15.2527	−	0.939622i	−0.694744	−	0.0427986i
$483$	−32.1552	+	24.6599i	−1.46311	+	1.12206i
$484$	13.3135	+	17.0714i	0.605159	+	0.775972i
$485$	−0.971735	−	0.402506i	−0.0441242	−	0.0182769i
$486$	−12.2951	−	18.2984i	−0.557718	−	0.830031i
$487$	19.6952	−	19.6952i	0.892476	−	0.892476i	−0.102280	−	0.994756i	$-0.532614\pi$
$487$	19.6952	−	19.6952i	0.892476	−	0.892476i	0.994756	+	0.102280i	$0.0326138\pi$
$488$	7.36923	+	2.40515i	0.333589	+	0.108876i
$489$	−6.06878	+	10.5049i	−0.274440	+	0.475049i
$490$	−0.0313584	−	0.0153116i	−0.00141663	−	0.000691706i
$491$	−3.97996	−	30.2308i	−0.179613	−	1.36430i	−0.809277	−	0.587428i	$-0.800141\pi$
$491$	−3.97996	−	30.2308i	−0.179613	−	1.36430i	0.629664	−	0.776868i	$-0.283193\pi$
$492$	−4.89661	+	18.8446i	−0.220756	+	0.849582i
$493$	26.5438	+	3.49456i	1.19547	+	0.157387i
$494$	7.48024	+	36.8494i	0.336552	+	1.65793i
$495$	−0.0739016	+	0.0426143i	−0.00332163	+	0.00191537i
$496$	−5.88342	−	5.70157i	−0.264173	−	0.256008i
$497$	−13.0938	+	22.6791i	−0.587336	+	1.01730i
$498$	−8.77636	−	5.81787i	−0.393278	−	0.260705i
$499$	−26.8949	−	20.6372i	−1.20398	−	0.923846i	−0.205483	−	0.978661i	$-0.565877\pi$
$499$	−26.8949	−	20.6372i	−1.20398	−	0.923846i	−0.998497	+	0.0548147i	$0.982543\pi$
$500$	1.31351	+	0.340929i	0.0587421	+	0.0152468i
$501$	32.6832	−	13.5276i	1.46018	−	0.604367i
$502$	0.875448	+	12.5990i	0.0390732	+	0.562321i
$503$	−24.6072	+	24.6072i	−1.09718	+	1.09718i	−0.102441	+	0.994739i	$0.532665\pi$
$503$	−24.6072	+	24.6072i	−1.09718	+	1.09718i	−0.994739	+	0.102441i	$0.967335\pi$
$504$	4.02336	−	21.4858i	0.179215	−	0.957054i
$505$	−0.206274	−	0.206274i	−0.00917908	−	0.00917908i
$506$	3.53141	−	4.05882i	0.156990	−	0.180437i
$507$	−26.5203	+	34.5428i	−1.17781	+	1.53410i
$508$	9.73498	+	7.34925i	0.431920	+	0.326070i
$509$	−11.3991	+	14.8556i	−0.505258	+	0.658465i	−0.974443	−	0.224635i	$-0.927881\pi$
$509$	−11.3991	+	14.8556i	−0.505258	+	0.658465i	0.469185	+	0.883100i	$0.344548\pi$
$510$	−0.192930	+	0.575256i	−0.00854310	+	0.0254728i
$511$	−20.8915	−	12.0617i	−0.924188	−	0.533580i
$512$	11.8990	−	19.2462i	0.525865	−	0.850568i
$513$	15.8304	−	15.8050i	0.698928	−	0.697806i
$514$	21.4292	−	32.3452i	0.945203	−	1.42668i
$515$	0.0155425	−	0.118057i	0.000684884	−	0.00520221i
$516$	7.55715	+	9.69559i	0.332685	+	0.426825i
$517$	0.987708	−	0.130034i	0.0434393	−	0.00571890i
$518$	30.3086	−	10.4212i	1.33168	−	0.457881i
$519$	13.5288	−	7.80604i	0.593849	−	0.342647i
$520$	−0.771310	+	0.900682i	−0.0338242	+	0.0394975i
$521$	26.8438	+	26.8438i	1.17605	+	1.17605i	0.980743	+	0.195305i	$0.0625697\pi$
$521$	26.8438	+	26.8438i	1.17605	+	1.17605i	0.195305	+	0.980743i	$0.437430\pi$
$522$	−2.14115	−	31.0550i	−0.0937158	−	1.35924i
$523$	−8.96802	+	21.6507i	−0.392144	+	0.946720i	0.597328	+	0.801997i	$0.296229\pi$
$523$	−8.96802	+	21.6507i	−0.392144	+	0.946720i	−0.989472	+	0.144723i	$0.953771\pi$
$524$	−26.6606	+	7.36842i	−1.16467	+	0.321891i
$525$	8.53532	−	20.5905i	0.372512	−	0.898643i
$526$	−24.0720	+	21.2783i	−1.04959	+	0.927777i
$527$	6.47254	−	3.73692i	0.281948	−	0.162783i
$528$	0.0447751	+	2.90185i	0.00194859	+	0.126287i
$529$	51.5081	+	29.7382i	2.23948	+	1.29297i
$530$	0.0179474	−	0.00364324i	0.000779587	−	0.000158252i
$531$	−2.06673	+	15.6337i	−0.0896886	+	0.678445i
$532$	22.1800	−	0.174077i	0.961625	−	0.00754720i
$533$	−21.1320	−	27.5397i	−0.915327	−	1.19288i
$534$	8.08307	−	2.77683i	0.349789	−	0.120165i
$535$	0.124053	−	0.462973i	0.00536329	−	0.0200161i
$536$	−3.01094	−	3.35286i	−0.130053	−	0.144822i
$537$	−8.58421	+	14.8591i	−0.370436	+	0.641217i
$538$	27.0406	−	31.0791i	1.16580	−	1.33991i
$539$	0.0582714	−	0.140680i	0.00250993	−	0.00605950i
$540$	0.700058	+	0.0871518i	0.0301257	+	0.00375041i
$541$	−8.00916	+	3.31750i	−0.344341	+	0.142631i	−0.548150	−	0.836380i	$-0.684668\pi$
$541$	−8.00916	+	3.31750i	−0.344341	+	0.142631i	0.203809	+	0.979011i	$0.434668\pi$
$542$	−5.92963	+	2.95315i	−0.254699	+	0.126849i
$543$	9.30284	+	34.7559i	0.399223	+	1.49152i
$544$	13.9119	+	15.2492i	0.596466	+	0.653805i
$545$	0.330284	−	0.190689i	0.0141478	−	0.00816824i
$546$	25.8030	+	29.2066i	1.10427	+	1.24993i
$547$	−45.1314	−	5.94166i	−1.92968	−	0.254047i	−0.934803	−	0.355166i	$-0.884424\pi$
$547$	−45.1314	−	5.94166i	−1.92968	−	0.254047i	−0.994874	+	0.101119i	$0.967758\pi$
$548$	15.3086	−	37.7946i	0.653953	−	1.61451i
$549$	7.59447	+	3.15050i	0.324124	+	0.134460i
$550$	−0.565939	+	2.90469i	−0.0241317	+	0.123856i
$551$	30.5101	−	8.17516i	1.29978	−	0.348274i
$552$	−43.5332	+	9.18116i	−1.85290	+	0.390776i
$553$	−24.7468	−	6.63089i	−1.05234	−	0.281974i
$554$	7.71921	−	15.8091i	0.327958	−	0.671664i
$555$	0.395574	+	0.955723i	0.0167912	+	0.0405682i
$556$	22.0970	−	38.9764i	0.937121	−	1.65297i
$557$	−19.9105	+	8.24722i	−0.843637	+	0.349446i	−0.762286	−	0.647240i	$-0.775923\pi$
$557$	−19.9105	+	8.24722i	−0.843637	+	0.349446i	−0.0813502	+	0.996686i	$0.525923\pi$
$558$	−5.75170	−	6.51389i	−0.243489	−	0.275755i
$559$	−21.9165			−0.926970
$560$	0.434490	+	0.548203i	0.0183606	+	0.0231658i
$561$	−2.55711	−	0.685909i	−0.107961	−	0.0289591i
$562$	−11.3727	−	12.8659i	−0.479730	−	0.542717i
$563$	−4.05452	+	5.28396i	−0.170878	+	0.222692i	−0.870940	−	0.491390i	$-0.836489\pi$
$563$	−4.05452	+	5.28396i	−0.170878	+	0.222692i	0.700062	+	0.714082i	$0.253156\pi$
$564$	−7.16572	−	4.06502i	−0.301731	−	0.171168i
$565$	0.666255	−	0.511236i	0.0280296	−	0.0215078i
$566$	6.42228	+	9.53045i	0.269949	+	0.400595i
$567$	6.02477	−	22.3888i	0.253017	−	0.940241i
$568$	−23.7168	+	16.2542i	−0.995136	+	0.682009i
$569$	1.77871	+	6.63825i	0.0745676	+	0.278290i	0.993135	−	0.116975i	$-0.0373196\pi$
$569$	1.77871	+	6.63825i	0.0745676	+	0.278290i	−0.918567	+	0.395265i	$0.870653\pi$
$570$	0.0494293	+	0.714127i	0.00207037	+	0.0299115i
$571$	4.59351	+	34.8912i	0.192233	+	1.46015i	0.766901	+	0.641765i	$0.221798\pi$
$571$	4.59351	+	34.8912i	0.192233	+	1.46015i	−0.574669	+	0.818386i	$0.694869\pi$
$572$	−4.12957	−	3.11755i	−0.172666	−	0.130351i
$573$	−16.2737	+	2.13803i	−0.679842	+	0.0893177i
$574$	−18.3297	+	9.12880i	−0.765067	+	0.381029i
$575$	−45.3664			−1.89191
$576$	14.1683	−	19.3716i	0.590348	−	0.807149i
$577$	27.6999			1.15316			0.576580	−	0.817041i	$-0.304387\pi$
$577$	27.6999			1.15316			0.576580	+	0.817041i	$0.304387\pi$
$578$	4.66492	−	2.32328i	0.194035	−	0.0966359i
$579$	−11.9032	+	28.7151i	−0.494679	+	1.19336i
$580$	0.795019	+	0.600185i	0.0330114	+	0.0249213i
$581$	−1.44545	−	10.9793i	−0.0599673	−	0.455497i
$582$	−31.4795	+	21.2008i	−1.30487	+	0.878802i
$583$	0.0206822	+	0.0771869i	0.000856567	+	0.00319675i
$584$	−14.9730	−	21.8475i	−0.619588	−	0.904056i
$585$	−0.889834	+	0.888882i	−0.0367901	+	0.0367507i
$586$	−6.43701	−	9.55231i	−0.265910	−	0.394602i
$587$	−5.48578	+	4.20938i	−0.226422	+	0.173740i	−0.715743	−	0.698364i	$-0.753912\pi$
$587$	−5.48578	+	4.20938i	−0.226422	+	0.173740i	0.489320	+	0.872104i	$0.337245\pi$
$588$	−1.08571	+	0.637857i	−0.0447739	+	0.0263048i
$589$	5.36781	−	6.99546i	0.221177	−	0.288243i
$590$	−0.334217	−	0.378098i	−0.0137595	−	0.0155660i
$591$	2.33664	+	8.72982i	0.0961166	+	0.359097i
$592$	34.9557	+	4.04492i	1.43667	+	0.166245i
$593$	0.448752			0.0184280			0.00921401	−	0.999958i	$-0.497067\pi$
$593$	0.448752			0.0184280			0.00921401	+	0.999958i	$0.497067\pi$
$594$	−0.191740	+	3.07226i	−0.00786718	+	0.126056i
$595$	−0.589545	+	0.244197i	−0.0241690	+	0.0100111i
$596$	9.21313	−	16.2508i	0.377384	−	0.665660i
$597$	34.5758	+	4.56141i	1.41509	+	0.186686i
$598$	34.8034	−	71.2780i	1.42322	−	2.91477i
$599$	17.6744	+	4.73585i	0.722157	+	0.193501i	0.601134	−	0.799148i	$-0.294716\pi$
$599$	17.6744	+	4.73585i	0.722157	+	0.193501i	0.121023	+	0.992650i	$0.461382\pi$
$600$	18.2124	−	16.3463i	0.743519	−	0.667336i
$601$	−4.76933	+	1.27794i	−0.194545	+	0.0521282i	−0.354776	−	0.934951i	$-0.615443\pi$
$601$	−4.76933	+	1.27794i	−0.194545	+	0.0521282i	0.160231	+	0.987080i	$0.448776\pi$
$602$	−2.47244	+	12.6899i	−0.100769	+	0.517200i
$603$	−2.90769	−	3.79358i	−0.118410	−	0.154486i
$604$	−3.46885	+	8.56404i	−0.141145	+	0.348466i
$605$	−0.728517	−	0.0959110i	−0.0296184	−	0.00389934i
$606$	−10.3164	+	2.09130i	−0.419075	+	0.0849533i
$607$	11.1380	−	6.43050i	0.452075	−	0.261006i	−0.256631	−	0.966509i	$-0.582612\pi$
$607$	11.1380	−	6.43050i	0.452075	−	0.261006i	0.708706	+	0.705504i	$0.249279\pi$
$608$	22.0486	+	10.3404i	0.894188	+	0.419360i
$609$	23.1556	−	23.1432i	0.938312	−	0.937809i
$610$	−0.235516	+	0.117295i	−0.00953577	+	0.00474913i
$611$	13.5699	−	5.62085i	0.548981	−	0.227395i
$612$	13.4548	+	17.2716i	0.543876	+	0.698163i
$613$	1.29501	−	3.12642i	0.0523048	−	0.126275i	−0.895567	−	0.444926i	$-0.853230\pi$
$613$	1.29501	−	3.12642i	0.0523048	−	0.126275i	0.947872	+	0.318651i	$0.103230\pi$
$614$	−31.0921	+	35.7356i	−1.25477	+	1.44217i
$615$	−0.330275	−	0.572407i	−0.0133180	−	0.0230817i
$616$	−2.27095	+	2.03936i	−0.0914993	+	0.0821683i
$617$	3.73222	−	13.9289i	0.150254	−	0.560755i	−0.849211	−	0.528053i	$-0.822922\pi$
$617$	3.73222	−	13.9289i	0.150254	−	0.560755i	0.999465	−	0.0327016i	$-0.0104111\pi$
$618$	−3.24078	−	2.82119i	−0.130363	−	0.113485i
$619$	−2.66294	−	3.47042i	−0.107033	−	0.139488i	0.736765	−	0.676148i	$-0.236352\pi$
$619$	−2.66294	−	3.47042i	−0.107033	−	0.139488i	−0.843798	+	0.536661i	$0.819686\pi$
$620$	0.278069	−	0.00218239i	0.0111675	−	8.76469e-5i
$621$	−46.7909	+	6.12190i	−1.87765	+	0.245663i
$622$	−22.0747	+	4.48105i	−0.885115	+	0.179674i
$623$	7.78440	+	4.49433i	0.311875	+	0.180061i
$624$	11.7109	+	41.1549i	0.468810	+	1.64752i
$625$	21.5908	−	12.4654i	0.863632	−	0.498618i
$626$	−29.2810	+	25.8827i	−1.17030	+	1.03448i
$627$	−3.09689	+	0.406870i	−0.123678	+	0.0162488i
$628$	−9.45868	+	2.61418i	−0.377442	+	0.104317i
$629$	−12.2844	+	29.6573i	−0.489813	+	1.18251i
$630$	0.414287	+	0.615499i	0.0165056	+	0.0245221i
$631$	−10.5738	−	10.5738i	−0.420937	−	0.420937i	0.464589	−	0.885526i	$-0.346202\pi$
$631$	−10.5738	−	10.5738i	−0.420937	−	0.420937i	−0.885526	+	0.464589i	$0.846202\pi$
$632$	−21.3652	−	18.2964i	−0.849862	−	0.727790i
$633$	0.00304707	−	11.3781i	0.000121110	−	0.452238i
$634$	1.11088	−	0.381962i	0.0441188	−	0.0151697i
$635$	−0.410464	+	0.0540386i	−0.0162887	+	0.00214445i
$636$	0.248250	−	0.612419i	0.00984377	−	0.0242840i
$637$	0.293033	−	2.22580i	0.0116104	−	0.0881895i
$638$	−2.40062	+	3.62348i	−0.0950413	+	0.143455i
$639$	−26.4187	+	15.2340i	−1.04511	+	0.602647i
$640$	0.170463	+	0.748854i	0.00673815	+	0.0296010i
$641$	−25.9177	−	14.9636i	−1.02369	−	0.591027i	−0.108519	−	0.994094i	$-0.534611\pi$
$641$	−25.9177	−	14.9636i	−1.02369	−	0.591027i	−0.915170	+	0.403067i	$0.867944\pi$
$642$	−11.4510	−	12.9614i	−0.451934	−	0.511547i
$643$	3.48073	−	4.53618i	0.137267	−	0.178889i	−0.719662	−	0.694325i	$-0.755703\pi$
$643$	3.48073	−	4.53618i	0.137267	−	0.178889i	0.856928	+	0.515435i	$0.172370\pi$
$644$	−37.3444	−	28.1925i	−1.47157	−	1.11094i
$645$	−0.413656	−	0.0545715i	−0.0162877	−	0.00214875i
$646$	−14.5822	+	16.7600i	−0.573729	+	0.659414i
$647$	−5.34200	−	5.34200i	−0.210016	−	0.210016i	0.594258	−	0.804274i	$-0.297446\pi$
$647$	−5.34200	−	5.34200i	−0.210016	−	0.210016i	−0.804274	+	0.594258i	$0.797446\pi$
$648$	16.5784	−	19.3172i	0.651263	−	0.758852i
$649$	1.55702	−	1.55702i	0.0611182	−	0.0611182i
$650$	3.02441	+	43.5258i	0.118627	+	1.70722i
$651$	1.19532	−	9.06061i	0.0468483	−	0.355113i
$652$	−13.5594	−	3.51942i	−0.531029	−	0.137831i
$653$	30.0734	+	23.0761i	1.17686	+	0.903038i	0.996746	−	0.0806079i	$-0.0256862\pi$
$653$	30.0734	+	23.0761i	1.17686	+	0.903038i	0.180116	+	0.983645i	$0.442353\pi$
$654$	0.849840	−	13.7354i	0.0332314	−	0.537096i
$655$	0.469413	−	0.813048i	0.0183415	−	0.0317684i
$656$	−22.4797	+	0.352880i	−0.877686	+	0.0137777i
$657$	−14.0333	−	24.3364i	−0.547490	−	0.949454i
$658$	−1.72367	−	8.49122i	−0.0671958	−	0.331022i
$659$	−28.1151	−	3.70142i	−1.09521	−	0.144187i	−0.438795	−	0.898587i	$-0.644594\pi$
$659$	−28.1151	−	3.70142i	−1.09521	−	0.144187i	−0.656415	+	0.754400i	$0.727928\pi$
$660$	−0.0701796	−	0.0691236i	−0.00273174	−	0.00269063i
$661$	3.64650	+	27.6979i	0.141832	+	1.07732i	0.903266	+	0.429081i	$0.141163\pi$
$661$	3.64650	+	27.6979i	0.141832	+	1.07732i	−0.761434	+	0.648243i	$0.775504\pi$
$662$	−19.0845	−	9.31853i	−0.741742	−	0.362175i
$663$	−39.0336	−	0.0104533i	−1.51594	−	0.000405971i
$664$	3.77242	−	11.5585i	0.146398	−	0.448556i
$665$	−0.532344	+	0.532344i	−0.0206434	+	0.0206434i
$666$	36.6308	+	7.15737i	1.41941	+	0.277342i
$667$	−61.5609	−	25.4994i	−2.38365	−	0.987339i
$668$	25.1179	+	32.2077i	0.971841	+	1.24616i
$669$	0.531303	+	4.04402i	0.0205414	+	0.156351i
$670$	0.152664	+	0.00940465i	0.00589793	+	0.000363333i
$671$	−0.574028	−	0.994245i	−0.0221601	−	0.0383824i
$672$	25.1502	−	2.13793i	0.970190	−	0.0824724i
$673$	0.577904	−	1.00096i	0.0222766	−	0.0385841i	−0.854672	−	0.519168i	$-0.826242\pi$
$673$	0.577904	−	1.00096i	0.0222766	−	0.0385841i	0.876949	+	0.480584i	$0.159575\pi$
$674$	15.4342	−	23.2963i	0.594505	−	0.897342i
$675$	20.6056	−	15.7850i	0.793111	−	0.607563i
$676$	−46.6081	−	18.8785i	−1.79262	−	0.726097i
$677$	14.2749	−	10.9535i	0.548628	−	0.420977i	−0.296900	−	0.954909i	$-0.595953\pi$
$677$	14.2749	−	10.9535i	0.548628	−	0.420977i	0.845528	+	0.533932i	$0.179286\pi$
$678$	−2.09247	−	30.2308i	−0.0803607	−	1.16101i
$679$	−38.5553	−	10.3309i	−1.47962	−	0.396462i
$680$	−0.699602	−	0.0375890i	−0.0268285	−	0.00144147i
$681$	−23.8754	+	13.7760i	−0.914909	+	0.527896i
$682$	0.0841091	+	1.21046i	0.00322070	+	0.0463507i
$683$	−10.9938	−	4.55377i	−0.420665	−	0.174245i	0.162302	−	0.986741i	$-0.448108\pi$
$683$	−10.9938	−	4.55377i	−0.420665	−	0.174245i	−0.582967	+	0.812496i	$0.698108\pi$
$684$	22.4634	+	12.7512i	0.858910	+	0.487553i
$685$	0.529651	+	1.27869i	0.0202369	+	0.0488563i
$686$	−25.4368	−	8.52344i	−0.971180	−	0.325427i
$687$	18.9321	+	18.9423i	0.722306	+	0.722693i
$688$	−8.46330	+	11.3956i	−0.322660	+	0.434452i
$689$	0.589077	+	1.02031i	0.0224421	+	0.0388708i
$690$	0.834364	−	1.25865i	0.0317637	−	0.0479161i
$691$	−6.21944	+	47.2413i	−0.236599	+	1.79714i	0.300664	+	0.953730i	$0.402792\pi$
$691$	−6.21944	+	47.2413i	−0.236599	+	1.79714i	−0.537263	+	0.843415i	$0.680542\pi$
$692$	12.8528	+	12.6526i	0.488591	+	0.480981i
$693$	−2.56946	+	1.96943i	−0.0976056	+	0.0748124i
$694$	13.8225	−	9.31459i	0.524696	−	0.353577i
$695$	0.393594	+	1.46891i	0.0149299	+	0.0557191i
$696$	33.9016	−	11.9447i	1.28504	−	0.452763i
$697$	5.30824	−	19.8106i	0.201064	−	0.750381i
$698$	8.00023	+	23.2675i	0.302813	+	0.880690i
$699$	−1.76023	+	13.3427i	−0.0665781	+	0.504666i
$700$	25.5430	+	3.15907i	0.965436	+	0.119402i
$701$	−4.28366	−	10.3417i	−0.161792	−	0.390599i	0.822106	−	0.569335i	$-0.192799\pi$
$701$	−4.28366	−	10.3417i	−0.161792	−	0.390599i	−0.983897	+	0.178736i	$0.942799\pi$
$702$	8.99289	+	44.4844i	0.339415	+	1.67895i
$703$			37.8723i			1.42838i
$704$	−3.21566	+	0.943311i	−0.121195	+	0.0355524i
$705$	0.270117	−	0.0723001i	0.0101732	−	0.00272298i
$706$	16.4872	+	1.01567i	0.620504	+	0.0382252i
$707$	−8.78281	−	6.73929i	−0.330312	−	0.253457i
$708$	−18.0350	+	2.51357i	−0.677796	+	0.0944659i
$709$	22.2568	+	29.0056i	0.835872	+	1.08933i	0.994781	+	0.102036i	$0.0325356\pi$
$709$	22.2568	+	29.0056i	0.835872	+	1.08933i	−0.158909	+	0.987293i	$0.550798\pi$
$710$	0.186630	−	0.957881i	0.00700410	−	0.0359486i
$711$	−21.0853	−	21.1079i	−0.790760	−	0.791608i
$712$	5.57910	+	8.14060i	0.209086	+	0.305082i
$713$	−17.9673	+	4.81432i	−0.672881	+	0.180298i
$714$	−4.40951	+	22.5996i	−0.165022	+	0.845771i
$715$	0.174118	−	0.0229231i	0.00651166	−	0.000857276i
$716$	−19.1797	−	4.97818i	−0.716777	−	0.186043i
$717$	32.1014	+	13.3069i	1.19885	+	0.496955i
$718$	9.91480	+	3.32229i	0.370017	+	0.123987i
$719$		−	35.9890i		−	1.34216i	−0.741383	−	0.671082i	$-0.765830\pi$
$719$		−	35.9890i		−	1.34216i	0.741383	−	0.671082i	$-0.234170\pi$
$720$	0.118558	+	0.805924i	0.00441840	+	0.0300350i
$721$		−	4.51888i		−	0.168292i
$722$	0.209724	−	0.625885i	0.00780511	−	0.0232930i
$723$	−2.43798	−	18.5567i	−0.0906693	−	0.690130i
$724$	−35.8152	+	21.0544i	−1.33106	+	0.782482i
$725$	36.3381	−	4.78401i	1.34956	−	0.177674i
$726$	−17.4093	+	19.9985i	−0.646118	+	0.742214i
$727$	47.5511	−	12.7413i	1.76357	−	0.472548i	0.776137	−	0.630565i	$-0.217177\pi$
$727$	47.5511	−	12.7413i	1.76357	−	0.472548i	0.987436	+	0.158017i	$0.0505100\pi$
$728$	−24.5590	+	37.7087i	−0.910219	+	1.39758i
$729$	19.1225	−	19.0612i	0.708242	−	0.705970i
$730$	0.882383	+	0.171920i	0.0326585	+	0.00636305i
$731$	−7.88279	−	10.2731i	−0.291556	−	0.379963i
$732$	−1.16782	+	9.42187i	−0.0431640	+	0.348242i
$733$	9.72530	+	7.46248i	0.359212	+	0.275633i	0.772562	−	0.634939i	$-0.218975\pi$
$733$	9.72530	+	7.46248i	0.359212	+	0.275633i	−0.413350	+	0.910572i	$0.635641\pi$
$734$	0.106565	−	1.72985i	0.00393339	−	0.0638501i
$735$	0.0110729	−	0.0412805i	0.000408431	−	0.00152266i
$736$	−23.6216	−	45.6209i	−0.870702	−	1.68161i
$737$			0.667403i			0.0245841i
$738$	−23.8004	−	1.47898i	−0.876104	−	0.0544421i
$739$	15.0548	+	36.3454i	0.553798	+	1.33699i	0.914606	+	0.404347i	$0.132501\pi$
$739$	15.0548	+	36.3454i	0.553798	+	1.33699i	−0.360807	+	0.932640i	$0.617499\pi$
$740$	−0.941820	+	0.734499i	−0.0346220	+	0.0270007i
$741$	−42.5508	+	17.6118i	−1.56314	+	0.646985i
$742$	0.657225	−	0.225978i	0.0241275	−	0.00829591i
$743$	12.7934	−	47.7455i	0.469344	−	1.75161i	−0.172728	−	0.984969i	$-0.555258\pi$
$743$	12.7934	−	47.7455i	0.469344	−	1.75161i	0.642072	−	0.766644i	$-0.278075\pi$
$744$	5.47831	−	8.40665i	0.200845	−	0.308203i
$745$	0.164105	+	0.612450i	0.00601236	+	0.0224384i
$746$	−13.3074	−	19.7477i	−0.487217	−	0.723014i
$747$	4.94149	−	11.9118i	0.180800	−	0.435828i
$748$	−0.0239923	−	3.05698i	−0.000877246	−	0.111774i
$749$	2.37420	−	18.0338i	0.0867514	−	0.658942i
$750$	−0.102637	+	1.65885i	−0.00374778	+	0.0605727i
$751$	19.0194	+	32.9426i	0.694028	+	1.20209i	0.970507	+	0.241073i	$0.0774992\pi$
$751$	19.0194	+	32.9426i	0.694028	+	1.20209i	−0.276479	+	0.961020i	$0.589168\pi$
$752$	2.31760	−	9.22630i	0.0845141	−	0.336448i
$753$	−14.9418	+	3.99935i	−0.544509	+	0.145745i
$754$	−20.3608	+	60.7632i	−0.741495	+	2.21286i
$755$	−0.120016	−	0.289744i	−0.00436782	−	0.0105449i
$756$	26.7714	−	0.188602i	0.973665	−	0.00685940i
$757$	−13.4464	−	5.56969i	−0.488718	−	0.202434i	0.124696	−	0.992195i	$-0.460204\pi$
$757$	−13.4464	−	5.56969i	−0.488718	−	0.202434i	−0.613414	+	0.789761i	$0.710204\pi$
$758$	−15.6593	+	1.08809i	−0.568770	+	0.0395213i
$759$	5.70551	+	3.29612i	0.207097	+	0.119641i
$760$	−0.779528	+	0.274890i	−0.0282764	+	0.00997130i
$761$	−23.0675	−	6.18093i	−0.836197	−	0.224058i	−0.184782	−	0.982780i	$-0.559158\pi$
$761$	−23.0675	−	6.18093i	−0.836197	−	0.224058i	−0.651415	+	0.758721i	$0.725824\pi$
$762$	−6.55829	+	13.4224i	−0.237582	+	0.486242i
$763$	11.4823	−	8.81072i	0.415689	−	0.318969i
$764$	−7.39007	−	17.4525i	−0.267364	−	0.631410i
$765$	−0.736701	−	0.0973899i	−0.0266355	−	0.00352114i
$766$	−6.84295	−	4.53357i	−0.247246	−	0.163805i
$767$	16.2323	−	28.1152i	0.586115	−	1.01518i
$768$	25.9209	+	9.80332i	0.935341	+	0.353747i
$769$	−1.73319	−	3.00198i	−0.0625005	−	0.108254i	0.833082	−	0.553149i	$-0.186574\pi$
$769$	−1.73319	−	3.00198i	−0.0625005	−	0.108254i	−0.895583	+	0.444895i	$0.853241\pi$
$770$	0.00636993	−	0.103402i	0.000229556	−	0.00372636i
$771$	43.8977	+	18.1968i	1.58094	+	0.655342i
$772$	−35.6218	−	4.40557i	−1.28206	−	0.158560i
$773$	17.9811	+	7.44800i	0.646734	+	0.267886i	0.681844	−	0.731497i	$-0.261178\pi$
$773$	17.9811	+	7.44800i	0.646734	+	0.267886i	−0.0351102	+	0.999383i	$0.511178\pi$
$774$	−9.88846	+	11.3530i	−0.355433	+	0.408075i
$775$	7.23484	−	7.23484i	0.259883	−	0.259883i
$776$	−33.2868	−	28.5055i	−1.19493	−	1.02329i
$777$	19.6175	+	33.9996i	0.703775	+	1.21973i
$778$	−2.53090	+	5.18333i	−0.0907370	+	0.185831i
$779$	−3.15833	−	23.9899i	−0.113159	−	0.859528i
$780$	−1.26321	−	0.716603i	−0.0452302	−	0.0256585i
$781$	4.22182	+	0.555813i	0.151068	+	0.0198885i
$782$	45.9284	−	9.32323i	1.64240	−	0.333398i
$783$	36.8335	−	9.83781i	1.31632	−	0.351575i
$784$	−1.04416	−	1.01188i	−0.0372913	−	0.0361386i
$785$	0.166539	−	0.288454i	0.00594404	−	0.0102954i
$786$	−15.0942	−	30.3280i	−0.538392	−	1.08176i
$787$	−18.9960	−	14.5761i	−0.677133	−	0.519583i	0.211977	−	0.977275i	$-0.432010\pi$
$787$	−18.9960	−	14.5761i	−0.677133	−	0.519583i	−0.889111	+	0.457692i	$0.848676\pi$
$788$	−8.99590	+	5.28835i	−0.320466	+	0.188390i
$789$	−31.2112	−	23.9625i	−1.11115	−	0.853087i
$790$	0.952439	−	0.0661807i	0.0338863	−	0.00235460i
$791$	22.5355	−	22.5355i	0.801269	−	0.801269i
$792$	−3.47814	+	0.732566i	−0.123590	+	0.0260306i
$793$	−11.9688	−	11.9688i	−0.425025	−	0.425025i
$794$	30.1420	+	26.2253i	1.06970	+	0.930701i
$795$	0.00857779	+	0.0207243i	0.000304223	+	0.000735016i
$796$	5.56956	+	39.8836i	0.197408	+	1.41364i
$797$	−6.61805	+	8.62481i	−0.234423	+	0.305507i	−0.895721	−	0.444618i	$-0.853340\pi$
$797$	−6.61805	+	8.62481i	−0.234423	+	0.305507i	0.661297	+	0.750124i	$0.270006\pi$
$798$	5.39715	+	26.6242i	0.191057	+	0.942485i
$799$	7.51545	+	4.33904i	0.265877	+	0.153504i
$800$	23.7993	+	15.2354i	0.841433	+	0.538654i
$801$	5.22894	+	9.06799i	0.184755	+	0.320402i
$802$	−31.2744	−	20.7198i	−1.10434	−	0.731642i
$803$	−0.512005	+	3.88906i	−0.0180683	+	0.137242i
$804$	3.32657	−	4.40399i	0.117319	−	0.155317i
$805$	1.57458	−	0.207298i	0.0554967	−	0.00730628i
$806$	5.81681	+	16.9174i	0.204888	+	0.595889i
$807$	43.6881	+	25.2389i	1.53789	+	0.888452i
$808$	−5.50382	−	10.8371i	−0.193624	−	0.381249i
$809$	11.2197	+	11.2197i	0.394464	+	0.394464i	0.876275	−	0.481811i	$-0.160021\pi$
$809$	11.2197	+	11.2197i	0.394464	+	0.394464i	−0.481811	+	0.876275i	$0.660021\pi$
$810$	0.0589685	+	0.861997i	0.00207194	+	0.0302875i
$811$	15.3654	−	37.0955i	0.539554	−	1.30260i	−0.385481	−	0.922716i	$-0.625964\pi$
$811$	15.3654	−	37.0955i	0.539554	−	1.30260i	0.925035	−	0.379882i	$-0.124036\pi$
$812$	32.8855	+	18.6439i	1.15406	+	0.654272i
$813$	−4.93722	−	6.43788i	−0.173156	−	0.225786i
$814$	−3.45156	−	3.90473i	−0.120977	−	0.136861i
$815$	0.411777	−	0.237739i	0.0144239	−	0.00832765i
$816$	−15.0787	+	20.2916i	−0.527860	+	0.710350i
$817$	−13.2303	−	7.63851i	−0.462869	−	0.267238i
$818$	−7.74617	−	38.1594i	−0.270838	−	1.33421i
$819$	−29.0770	+	37.8518i	−1.01603	+	1.32265i
$820$	0.535336	−	0.543805i	0.0186947	−	0.0189905i
$821$	−14.6379	−	19.0765i	−0.510867	−	0.665774i	0.464703	−	0.885467i	$-0.346161\pi$
$821$	−14.6379	−	19.0765i	−0.510867	−	0.665774i	−0.975569	+	0.219693i	$0.929495\pi$
$822$	49.0174	+	9.56400i	1.70968	+	0.333583i
$823$	1.70474	−	6.36218i	0.0594236	−	0.221772i	−0.929828	−	0.367994i	$-0.880045\pi$
$823$	1.70474	−	6.36218i	0.0594236	−	0.221772i	0.989252	+	0.146222i	$0.0467114\pi$
$824$	2.14185	−	4.47529i	0.0746147	−	0.155904i
$825$	−3.62440		0.000970619i	−0.126185		3.37926e-5i
$826$	−14.4478	−	12.5704i	−0.502702	−	0.437380i
$827$	−12.8972	+	31.1365i	−0.448478	+	1.08272i	0.524414	+	0.851463i	$0.324284\pi$
$827$	−12.8972	+	31.1365i	−0.448478	+	1.08272i	−0.972892	+	0.231259i	$0.925716\pi$
$828$	−21.2200	−	50.1883i	−0.737445	−	1.74416i
$829$	21.8417	−	9.04712i	0.758593	−	0.314220i	0.0303508	−	0.999539i	$-0.490338\pi$
$829$	21.8417	−	9.04712i	0.758593	−	0.314220i	0.728242	+	0.685320i	$0.240338\pi$
$830$	0.183974	+	0.369402i	0.00638584	+	0.0128221i
$831$	20.8112	+	5.58233i	0.721934	+	0.193649i
$832$	−42.1952	+	25.7046i	−1.46286	+	0.891145i
$833$	1.14871	−	0.663208i	0.0398004	−	0.0229788i
$834$	52.0259	+	17.4486i	1.80151	+	0.604194i
$835$	−1.37446	−	0.180951i	−0.0475650	−	0.00626205i
$836$	−1.40634	−	3.32123i	−0.0486392	−	0.114867i
$837$	6.48571	−	8.43829i	0.224179	−	0.291670i
$838$	8.18343	+	1.59443i	0.282692	+	0.0550786i
$839$	28.6548	−	7.67802i	0.989272	−	0.265075i	0.272328	−	0.962205i	$-0.412207\pi$
$839$	28.6548	−	7.67802i	0.989272	−	0.265075i	0.716945	+	0.697130i	$0.245540\pi$
$840$	−0.557425	+	0.650569i	−0.0192330	+	0.0224468i
$841$	23.9869	+	6.42726i	0.827134	+	0.221630i
$842$	46.6330	+	22.7698i	1.60708	+	0.784699i
$843$	12.8074	−	16.6817i	0.441110	−	0.574547i
$844$	12.6635	−	3.49993i	0.435897	−	0.120473i
$845$	1.57687	−	0.653163i	0.0542461	−	0.0224695i
$846$	3.21093	−	9.56545i	0.110394	−	0.328867i
$847$	−27.8855			−0.958157
$848$	0.757994	+	0.0877117i	0.0260296	+	0.00301203i
$849$	−9.95537	+	9.95004i	−0.341667	+	0.341484i
$850$	−19.3143	+	17.0727i	−0.662475	+	0.585590i
$851$	48.6360	−	63.3837i	1.66722	−	2.17277i
$852$	−25.0881	−	24.7106i	−0.859505	−	0.846572i
$853$	−4.26787	+	3.27486i	−0.146129	+	0.112129i	−0.679239	−	0.733917i	$-0.737690\pi$
$853$	−4.26787	+	3.27486i	−0.146129	+	0.112129i	0.533110	+	0.846046i	$0.321023\pi$
$854$	−8.28027	+	5.57982i	−0.283345	+	0.190938i
$855$	−0.846964	+	0.226457i	−0.0289656	+	0.00774467i
$856$	10.8989	−	16.7346i	0.372518	−	0.571976i
$857$	−6.94395	−	25.9152i	−0.237201	−	0.885246i	−0.977144	−	0.212577i	$-0.931814\pi$
$857$	−6.94395	−	25.9152i	−0.237201	−	0.885246i	0.739943	−	0.672669i	$-0.234852\pi$
$858$	2.78202	−	5.69377i	0.0949767	−	0.194382i
$859$	−5.20582	−	39.5421i	−0.177620	−	1.34916i	−0.815381	−	0.578925i	$-0.803472\pi$
$859$	−5.20582	−	39.5421i	−0.177620	−	1.34916i	0.637760	−	0.770235i	$-0.279861\pi$
$860$	−0.0666327	−	0.477157i	−0.00227216	−	0.0162709i
$861$	−15.2620	−	19.9008i	−0.520126	−	0.678217i
$862$	3.40156	+	6.82999i	0.115858	+	0.232630i
$863$	31.8190			1.08313			0.541566	−	0.840658i	$-0.317831\pi$
$863$	31.8190			1.08313			0.541566	+	0.840658i	$0.317831\pi$
$864$	26.6025	+	12.5022i	0.905036	+	0.425335i
$865$	−0.612158			−0.0208140
$866$	0.675466	+	1.35627i	0.0229533	+	0.0460878i
$867$	3.88418	+	5.06477i	0.131914	+	0.172008i
$868$	10.4515	−	1.45951i	0.354748	−	0.0495388i
$869$	0.543763	+	4.13029i	0.0184459	+	0.140110i
$870$	−0.535591	+	1.09616i	−0.0181582	+	0.0371632i
$871$	2.54676	+	9.50462i	0.0862935	+	0.322052i
$872$	15.5477	−	3.28335i	0.526510	−	0.111188i
$873$	−32.8507	−	32.8859i	−1.11183	−	1.11302i
$874$	45.8520	−	30.8983i	1.55097	−	1.04515i
$875$	−1.38675	+	1.06409i	−0.0468807	+	0.0359728i
$876$	22.7630	−	23.1107i	0.769090	−	0.780839i
$877$	16.0161	−	20.8726i	0.540825	−	0.704817i	−0.440374	−	0.897814i	$-0.645154\pi$
$877$	16.0161	−	20.8726i	0.540825	−	0.704817i	0.981199	+	0.192998i	$0.0618209\pi$
$878$	6.70193	−	5.92412i	0.226179	−	0.199930i
$879$	9.97820	−	9.97286i	0.336556	−	0.336376i
$880$	0.0553188	−	0.0993855i	0.00186480	−	0.00335029i
$881$	28.0517			0.945086			0.472543	−	0.881308i	$-0.343336\pi$
$881$	28.0517			0.945086			0.472543	+	0.881308i	$0.343336\pi$
$882$	−1.02078	−	1.15605i	−0.0343714	−	0.0389262i
$883$	−19.5098	+	8.08123i	−0.656558	+	0.271955i	−0.685989	−	0.727612i	$-0.740630\pi$
$883$	−19.5098	+	8.08123i	−0.656558	+	0.271955i	0.0294315	+	0.999567i	$0.490630\pi$
$884$	−12.0068	−	43.4434i	−0.403834	−	1.46116i
$885$	0.376378	−	0.490233i	0.0126518	−	0.0164790i
$886$	−25.6215	−	12.5104i	−0.860772	−	0.420294i
$887$	−5.16774	−	1.38469i	−0.173516	−	0.0464934i	0.171015	−	0.985268i	$-0.445295\pi$
$887$	−5.16774	−	1.38469i	−0.173516	−	0.0464934i	−0.344531	+	0.938775i	$0.611962\pi$
$888$	3.31327	+	42.9699i	0.111186	+	1.44198i
$889$	−15.1760	+	4.06640i	−0.508987	+	0.136383i
$890$	−0.328785	−	0.0640592i	−0.0110209	−	0.00214727i
$891$	−3.73833	+	0.488087i	−0.125239	+	0.0163515i
$892$	−4.33697	+	1.83644i	−0.145212	+	0.0614885i
$893$	10.1508	+	1.33637i	0.339682	+	0.0447200i
$894$	21.6917	+	7.27501i	0.725480	+	0.243313i
$895$	0.582453	−	0.336279i	0.0194693	−	0.0112406i
$896$	10.1231	+	27.3312i	0.338188	+	0.913072i
$897$	93.8310	+	25.1689i	3.13293	+	0.840365i
$898$	1.28412	+	2.57839i	0.0428518	+	0.0860420i
$899$	13.8840	−	5.75093i	0.463057	−	0.191804i
$900$	23.9115	+	18.0716i	0.797048	+	0.602388i
$901$	−0.266381	+	0.643101i	−0.00887444	+	0.0214248i
$902$	2.51200	+	2.18558i	0.0836404	+	0.0727720i
$903$	−15.8341	−	0.00424039i	−0.526926	−	0.000141111i
$904$	32.9994	−	11.6368i	1.09754	−	0.387034i
$905$	0.364965	−	1.36207i	0.0121318	−	0.0452767i
$906$	−11.1071	−	2.16715i	−0.369008	−	0.0719986i
$907$	24.5568	+	32.0031i	0.815396	+	1.06264i	0.996855	+	0.0792463i	$0.0252514\pi$
$907$	24.5568	+	32.0031i	0.815396	+	1.06264i	−0.181459	+	0.983399i	$0.558082\pi$
$908$	−22.6824	−	22.3292i	−0.752743	−	0.741019i
$909$	−4.92716	−	11.9133i	−0.163424	−	0.395138i
$910$	−0.303859	−	1.49688i	−0.0100728	−	0.0496210i
$911$	−46.5326	−	26.8656i	−1.54169	−	0.890097i	−0.998732	−	0.0503391i	$-0.983970\pi$
$911$	−46.5326	−	26.8656i	−1.54169	−	0.890097i	−0.542961	−	0.839758i	$-0.682697\pi$
$912$	−7.27416	+	28.9255i	−0.240872	+	0.957818i
$913$	−1.55945	+	0.900350i	−0.0516103	+	0.0297972i
$914$	10.3706	+	11.7322i	0.343029	+	0.388067i
$915$	−0.196099	−	0.255703i	−0.00648283	−	0.00845328i
$916$	−15.2515	+	26.9018i	−0.503924	+	0.888860i
$917$	13.6343	−	32.9161i	0.450244	−	1.08699i
$918$	−17.6169	+	20.2151i	−0.581445	+	0.667199i
$919$	−18.7622	−	18.7622i	−0.618909	−	0.618909i	0.326343	−	0.945252i	$-0.394184\pi$
$919$	−18.7622	−	18.7622i	−0.618909	−	0.618909i	−0.945252	+	0.326343i	$0.894184\pi$
$920$	1.65765	+	0.541018i	0.0546510	+	0.0178368i
$921$	−50.2339	−	29.0205i	−1.65526	−	0.956258i
$922$	−13.2926	−	38.6598i	−0.437770	−	1.27319i
$923$	62.2447	−	8.19466i	2.04881	−	0.269731i
$924$	−2.98290	−	2.25314i	−0.0981302	−	0.0741229i
$925$	−5.73605	+	43.5697i	−0.188600	+	1.43256i
$926$	7.68026	+	5.08831i	0.252389	+	0.167212i
$927$	2.63363	−	4.55595i	0.0864998	−	0.149637i
$928$	23.7315	+	34.0510i	0.779025	+	1.11778i
$929$	38.2126	+	22.0621i	1.25371	+	0.723832i	0.971845	−	0.235620i	$-0.0757122\pi$
$929$	38.2126	+	22.0621i	1.25371	+	0.723832i	0.281869	+	0.959453i	$0.409046\pi$
$930$	0.0676636	+	0.333785i	0.00221878	+	0.0109452i
$931$	0.952649	−	1.24152i	0.0312218	−	0.0406890i
$932$	−15.3909	+	2.14927i	−0.504147	+	0.0704017i
$933$	−10.5504	−	25.4902i	−0.345404	−	0.834510i
$934$	−22.7163	−	19.7645i	−0.743299	−	0.646713i
$935$	0.0733707	+	0.0733707i	0.00239948	+	0.00239948i
$936$	−46.7374	+	23.7049i	−1.52766	+	0.774819i
$937$	−17.0883	+	17.0883i	−0.558251	+	0.558251i	−0.928809	−	0.370558i	$-0.879166\pi$
$937$	−17.0883	+	17.0883i	−0.558251	+	0.558251i	0.370558	+	0.928809i	$0.379166\pi$
$938$	5.79057	−	0.402360i	0.189069	−	0.0131375i
$939$	−37.9650	−	29.1478i	−1.23894	−	0.951201i
$940$	0.163631	+	0.278350i	0.00533707	+	0.00907878i
$941$	−7.02586	−	5.39113i	−0.229037	−	0.175746i	0.487868	−	0.872918i	$-0.337775\pi$
$941$	−7.02586	−	5.39113i	−0.229037	−	0.175746i	−0.716904	+	0.697172i	$0.754442\pi$
$942$	−5.35514	−	10.7598i	−0.174480	−	0.350573i
$943$	−25.5223	+	44.2059i	−0.831120	+	1.43954i
$944$	−8.35032	−	19.2971i	−0.271780	−	0.628066i
$945$	−0.643053	+	0.642021i	−0.0209185	+	0.0208849i
$946$	2.06023	−	0.418216i	0.0669838	−	0.0135974i
$947$	44.1003	+	5.80592i	1.43307	+	0.188667i	0.806747	−	0.590897i	$-0.201226\pi$
$947$	44.1003	+	5.80592i	1.43307	+	0.188667i	0.626322	+	0.779565i	$0.284560\pi$
$948$	16.9986	−	29.9648i	0.552090	−	0.973212i
$949$	7.54878	+	57.3386i	0.245044	+	1.86129i
$950$	−13.3442	+	27.3292i	−0.432944	+	0.886677i
$951$	0.719030	+	1.24617i	0.0233161	+	0.0404097i
$952$	−26.5087	+	2.05114i	−0.859151	+	0.0664777i
$953$	−31.3869	+	31.3869i	−1.01672	+	1.01672i	−0.0168649	+	0.999858i	$0.505369\pi$
$953$	−31.3869	+	31.3869i	−1.01672	+	1.01672i	−0.999858	+	0.0168649i	$0.994631\pi$
$954$	0.794318	+	0.155203i	0.0257170	+	0.00502490i
$955$	0.594317	+	0.246174i	0.0192316	+	0.00796601i
$956$	−4.92511	+	39.8226i	−0.159289	+	1.28795i
$957$	−4.91765	−	2.03850i	−0.158965	−	0.0658954i
$958$	−0.0414477	+	0.672815i	−0.00133912	+	0.0217377i
$959$	26.2620	+	45.4871i	0.848044	+	1.46886i
$960$	−0.860403	+	0.380087i	−0.0277694	+	0.0122673i
$961$	−13.4024	+	23.2137i	−0.432336	+	0.748828i
$962$	−64.0545	−	42.4372i	−2.06520	−	1.36823i
$963$	12.9039	−	16.7981i	0.415823	−	0.541310i
$964$	19.9009	−	8.42682i	0.640966	−	0.271410i
$965$	0.966519	−	0.741636i	0.0311134	−	0.0238741i
$966$	25.1583	−	51.4897i	0.809455	−	1.65665i
$967$	3.02217	+	0.809787i	0.0971863	+	0.0260410i	0.307084	−	0.951682i	$-0.400647\pi$
$967$	3.02217	+	0.809787i	0.0971863	+	0.0260410i	−0.209898	+	0.977723i	$0.567313\pi$
$968$	−27.6165	−	13.2171i	−0.887628	−	0.424813i
$969$	−23.5597	−	13.6106i	−0.756847	−	0.437236i
$970$	1.48389	−	0.103109i	0.0476448	−	0.00331062i
$971$	38.1764	+	15.8132i	1.22514	+	0.507470i	0.899040	−	0.437866i	$-0.144265\pi$
$971$	38.1764	+	15.8132i	1.22514	+	0.507470i	0.326100	+	0.945335i	$0.394265\pi$
$972$	27.1009	+	15.4124i	0.869262	+	0.494352i
$973$	22.0851	+	53.3182i	0.708016	+	1.70930i
$974$	−12.5152	+	37.3494i	−0.401012	+	1.19675i
$975$	−51.6195	+	13.8166i	−1.65315	+	0.442485i
$976$	−10.8451	+	1.60134i	−0.347143	+	0.0512576i
$977$	−15.1894	−	26.3088i	−0.485951	−	0.841692i	0.513919	−	0.857839i	$-0.328193\pi$
$977$	−15.1894	−	26.3088i	−0.485951	−	0.841692i	−0.999870	+	0.0161471i	$0.994860\pi$
$978$	1.05953	−	17.1244i	0.0338799	−	0.547578i
$979$	0.190778	−	1.44910i	0.00609729	−	0.0463135i
$980$	0.0493502		0.000387319i	0.00157643		1.23724e-5i
$981$	16.7115	−	2.19100i	0.533557	−	0.0699534i
$982$	24.0976	+	35.7601i	0.768986	+	1.14115i
$983$	9.55477	+	35.6589i	0.304750	+	1.13734i	0.933161	+	0.359460i	$0.117039\pi$
$983$	9.55477	+	35.6589i	0.304750	+	1.13734i	−0.628411	+	0.777882i	$0.716294\pi$
$984$	−5.68221	−	26.9427i	−0.181142	−	0.858900i
$985$	0.0916701	−	0.342118i	0.00292085	−	0.0109008i
$986$	−35.8051	+	12.3111i	−1.14027	+	0.392065i
$987$	9.80500	−	4.05829i	0.312097	−	0.129177i
$988$	−32.7015	−	41.9318i	−1.04037	−	1.33403i
$989$	12.3330	+	29.7744i	0.392166	+	0.946772i
$990$	0.0666857	−	0.100538i	0.00211941	−	0.00319531i
$991$			43.6720i			1.38729i	0.720319	+	0.693643i	$0.243995\pi$
$991$			43.6720i			1.38729i	−0.720319	+	0.693643i	$0.756005\pi$
$992$	11.0425	+	3.50836i	0.350599	+	0.111391i
$993$	6.73892	−	25.1231i	0.213853	−	0.797257i
$994$	2.27715	−	36.9647i	0.0722269	−	1.17245i
$995$	−1.08439	−	0.832085i	−0.0343776	−	0.0263789i
$996$	14.7780	+	1.83171i	0.468259	+	0.0580399i
$997$	−1.33100	−	1.73459i	−0.0421532	−	0.0549352i	0.771801	−	0.635864i	$-0.219356\pi$
$997$	−1.33100	−	1.73459i	−0.0421532	−	0.0549352i	−0.813954	+	0.580929i	$0.802689\pi$
$998$	47.0573	+	9.16847i	1.48957	+	0.290223i
$999$	−0.0367250	+	45.7117i	−0.00116193	+	1.44626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.8	✓	368
3.2	odd	2		864.2.bn.a.683.39		368
9.4	even	3		864.2.bn.a.395.23		368
9.5	odd	6	inner	288.2.bf.a.203.24	yes	368
32.3	odd	8	inner	288.2.bf.a.227.24	yes	368
96.35	even	8		864.2.bn.a.35.23		368
288.67	odd	24		864.2.bn.a.611.39		368
288.131	even	24	inner	288.2.bf.a.131.8	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.8	✓	368	1.1	even	1	trivial
288.2.bf.a.131.8	yes	368	288.131	even	24	inner
288.2.bf.a.203.24	yes	368	9.5	odd	6	inner
288.2.bf.a.227.24	yes	368	32.3	odd	8	inner
864.2.bn.a.35.23		368	96.35	even	8
864.2.bn.a.395.23		368	9.4	even	3
864.2.bn.a.611.39		368	288.67	odd	24
864.2.bn.a.683.39		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26591 + 0.630463i) q^{2} +(-1.05404 - 1.37441i) q^{3} +(1.20503 - 1.59621i) q^{4} +(0.00886053 + 0.0673024i) q^{5} +(2.20083 + 1.07534i) q^{6} +(0.666754 + 2.48836i) q^{7} +(-0.519104 + 2.78038i) q^{8} +(-0.778009 + 2.89736i) q^{9} +O(q^{10})\)	\(q+(-1.26591 + 0.630463i) q^{2} +(-1.05404 - 1.37441i) q^{3} +(1.20503 - 1.59621i) q^{4} +(0.00886053 + 0.0673024i) q^{5} +(2.20083 + 1.07534i) q^{6} +(0.666754 + 2.48836i) q^{7} +(-0.519104 + 2.78038i) q^{8} +(-0.778009 + 2.89736i) q^{9} +(-0.0536483 - 0.0796122i) q^{10} +(0.332332 - 0.255007i) q^{11} +(-3.46400 + 0.0262591i) q^{12} +(3.75972 - 4.89976i) q^{13} +(-2.41287 - 2.72966i) q^{14} +(0.0831618 - 0.0831173i) q^{15} +(-1.09579 - 3.84698i) q^{16} +3.64897 q^{17} +(-0.841793 - 4.15829i) q^{18} +(3.97733 - 1.64746i) q^{19} +(0.118106 + 0.0669583i) q^{20} +(2.71724 - 3.53922i) q^{21} +(-0.259928 + 0.532338i) q^{22} +(-8.77221 - 2.35051i) q^{23} +(4.36854 - 2.21717i) q^{24} +(4.82518 - 1.29290i) q^{25} +(-1.67033 + 8.57300i) q^{26} +(4.80221 - 1.98462i) q^{27} +(4.77541 + 1.93427i) q^{28} +(7.27433 + 0.957684i) q^{29} +(-0.0528726 + 0.157649i) q^{30} +(1.77380 - 1.02410i) q^{31} +(3.81255 + 4.17905i) q^{32} +(-0.700775 - 0.187973i) q^{33} +(-4.61925 + 2.30054i) q^{34} +(-0.161565 + 0.0669223i) q^{35} +(3.68728 + 4.73328i) q^{36} +(-3.36655 + 8.12758i) q^{37} +(-3.99625 + 4.59309i) q^{38} +(-10.6972 - 0.00286472i) q^{39} +(-0.191726 - 0.0103013i) q^{40} +(1.45472 - 5.42911i) q^{41} +(-1.20843 + 6.19344i) q^{42} +(-2.16028 - 2.81533i) q^{43} +(-0.00657510 - 0.837765i) q^{44} +(-0.201893 - 0.0266897i) q^{45} +(12.5867 - 2.55503i) q^{46} +(2.05961 + 1.18912i) q^{47} +(-4.13232 + 5.56093i) q^{48} +(0.314804 - 0.181752i) q^{49} +(-5.29309 + 4.67879i) q^{50} +(-3.84615 - 5.01518i) q^{51} +(-3.29048 - 11.9057i) q^{52} +(-0.0730018 + 0.176242i) q^{53} +(-4.82792 + 5.53997i) q^{54} +(0.0201073 + 0.0201073i) q^{55} +(-7.26471 + 0.562114i) q^{56} +(-6.45654 - 3.72999i) q^{57} +(-9.81240 + 3.37386i) q^{58} +(5.21160 - 0.686120i) q^{59} +(-0.0324602 - 0.232903i) q^{60} +(0.357730 - 2.71723i) q^{61} +(-1.59980 + 2.41473i) q^{62} +(-7.72842 - 0.00413936i) q^{63} +(-7.46106 - 2.88662i) q^{64} +(0.363079 + 0.209624i) q^{65} +(1.00563 - 0.203857i) q^{66} +(-0.969906 + 1.26401i) q^{67} +(4.39712 - 5.82453i) q^{68} +(6.01568 + 14.5341i) q^{69} +(0.162334 - 0.186578i) q^{70} +(7.18803 + 7.18803i) q^{71} +(-7.65191 - 3.66719i) q^{72} +(-6.62149 + 6.62149i) q^{73} +(-0.862401 - 12.4112i) q^{74} +(-6.86290 - 5.26901i) q^{75} +(2.16311 - 8.33390i) q^{76} +(0.856134 + 0.656935i) q^{77} +(13.5434 - 6.74054i) q^{78} +(-4.97251 + 8.61265i) q^{79} +(0.249202 - 0.107836i) q^{80} +(-7.78940 - 4.50835i) q^{81} +(1.58131 + 7.78988i) q^{82} +(-4.26191 - 0.561091i) q^{83} +(-2.37498 - 8.60218i) q^{84} +(0.0323318 + 0.245584i) q^{85} +(4.50967 + 2.20197i) q^{86} +(-6.35117 - 11.0074i) q^{87} +(0.536503 + 1.05639i) q^{88} +(2.46723 - 2.46723i) q^{89} +(0.272404 - 0.0934994i) q^{90} +(14.6992 + 6.08860i) q^{91} +(-14.3227 + 11.1699i) q^{92} +(-3.27719 - 1.35849i) q^{93} +(-3.35696 - 0.206801i) q^{94} +(0.146119 + 0.253086i) q^{95} +(1.72517 - 9.64488i) q^{96} +(-7.74713 + 13.4184i) q^{97} +(-0.283924 + 0.428554i) q^{98} +(0.480291 + 1.16128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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