LMFDB - Embedded newform 117.2.z.b.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(5,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("117.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	117.47
Dual form			117.2.z.b.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.120326 - 0.449064i) q^{2} +(-0.453962 + 1.67150i) q^{3} +(1.54487 - 0.891932i) q^{4} +(0.207401 + 0.0555730i) q^{5} +(0.805235 + 0.00273231i) q^{6} +(0.845006 + 3.15361i) q^{7} +(-1.24390 - 1.24390i) q^{8} +(-2.58784 - 1.51760i) q^{9} -0.0998232i q^{10} +(3.19743 - 0.856749i) q^{11} +(0.789553 + 2.98716i) q^{12} +(3.49708 + 0.877749i) q^{13} +(1.31449 - 0.758923i) q^{14} +(-0.187043 + 0.321443i) q^{15} +(1.37495 - 2.38148i) q^{16} -7.72994 q^{17} +(-0.370113 + 1.34471i) q^{18} +(-3.13690 - 3.13690i) q^{19} +(0.369975 - 0.0991346i) q^{20} +(-5.65486 - 0.0191880i) q^{21} +(-0.769470 - 1.33276i) q^{22} +(0.172481 + 0.298746i) q^{23} +(2.64386 - 1.51450i) q^{24} +(-4.29020 - 2.47695i) q^{25} +(-0.0266253 - 1.67603i) q^{26} +(3.71145 - 3.63664i) q^{27} +(4.11823 + 4.11823i) q^{28} +(-4.06978 - 2.34969i) q^{29} +(0.166855 + 0.0453159i) q^{30} +(-0.173532 + 0.647632i) q^{31} +(-4.63327 - 1.24148i) q^{32} +(-0.0194547 + 5.73344i) q^{33} +(0.930115 + 3.47124i) q^{34} +0.701021i q^{35} +(-5.35147 - 0.0363175i) q^{36} +(-1.04152 + 1.04152i) q^{37} +(-1.03122 + 1.78612i) q^{38} +(-3.05470 + 5.44691i) q^{39} +(-0.188859 - 0.327113i) q^{40} +(7.17396 + 1.92226i) q^{41} +(0.671811 + 2.54170i) q^{42} +(-3.27315 - 1.88976i) q^{43} +(4.17546 - 4.17546i) q^{44} +(-0.452383 - 0.458565i) q^{45} +(0.113402 - 0.113402i) q^{46} +(10.6369 - 2.85014i) q^{47} +(3.35647 + 3.37933i) q^{48} +(-3.16901 + 1.82963i) q^{49} +(-0.596084 + 2.22462i) q^{50} +(3.50910 - 12.9206i) q^{51} +(6.18543 - 1.76315i) q^{52} +1.94478i q^{53} +(-2.07967 - 1.22909i) q^{54} +0.710763 q^{55} +(2.87166 - 4.97386i) q^{56} +(6.66736 - 3.81930i) q^{57} +(-0.565458 + 2.11032i) q^{58} +(-2.48647 + 9.27964i) q^{59} +(-0.00225110 + 0.663418i) q^{60} +(-3.25198 + 5.63260i) q^{61} +0.311709 q^{62} +(2.59916 - 9.44339i) q^{63} -3.26977i q^{64} +(0.676519 + 0.376389i) q^{65} +(2.57702 - 0.681147i) q^{66} +(0.729983 - 2.72433i) q^{67} +(-11.9418 + 6.89458i) q^{68} +(-0.577654 + 0.152683i) q^{69} +(0.314803 - 0.0843512i) q^{70} +(2.22986 - 2.22986i) q^{71} +(1.33127 + 5.10674i) q^{72} +(-1.50413 + 1.50413i) q^{73} +(0.593032 + 0.342387i) q^{74} +(6.08781 - 6.04664i) q^{75} +(-7.64400 - 2.04820i) q^{76} +(5.40370 + 9.35947i) q^{77} +(2.81357 + 0.716349i) q^{78} +(3.82930 - 6.63255i) q^{79} +(0.417511 - 0.417511i) q^{80} +(4.39380 + 7.85459i) q^{81} -3.45286i q^{82} +(3.87333 + 14.4555i) q^{83} +(-8.75314 + 5.01410i) q^{84} +(-1.60320 - 0.429576i) q^{85} +(-0.454775 + 1.69724i) q^{86} +(5.77503 - 5.73597i) q^{87} +(-5.04298 - 2.91157i) q^{88} +(-1.95017 - 1.95017i) q^{89} +(-0.151491 + 0.258326i) q^{90} +(0.186980 + 11.7701i) q^{91} +(0.532922 + 0.307682i) q^{92} +(-1.00374 - 0.584060i) q^{93} +(-2.55979 - 4.43368i) q^{94} +(-0.476269 - 0.824922i) q^{95} +(4.17847 - 7.18093i) q^{96} +(-2.62010 + 0.702053i) q^{97} +(1.20294 + 1.20294i) q^{98} +(-9.57463 - 2.63528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.120326	−	0.449064i	−0.0850835	−	0.317536i	0.910246	−	0.414067i	$-0.135892\pi$
$2$	−0.120326	−	0.449064i	−0.0850835	−	0.317536i	−0.995330	+	0.0965308i	$0.969225\pi$
$3$	−0.453962	+	1.67150i	−0.262095	+	0.965042i
$3$	−0.453962	+	1.67150i	−0.262095	+	0.965042i
$4$	1.54487	−	0.891932i	0.772435	−	0.445966i
$5$	0.207401	+	0.0555730i	0.0927526	+	0.0248530i	0.304897	−	0.952385i	$-0.401378\pi$
$5$	0.207401	+	0.0555730i	0.0927526	+	0.0248530i	−0.212144	+	0.977238i	$0.568045\pi$
$6$	0.805235	+	0.00273231i	0.328736	+	0.00111546i
$7$	0.845006	+	3.15361i	0.319382	+	1.19195i	0.919840	+	0.392294i	$0.128318\pi$
$7$	0.845006	+	3.15361i	0.319382	+	1.19195i	−0.600458	+	0.799657i	$0.705015\pi$
$8$	−1.24390	−	1.24390i	−0.439784	−	0.439784i
$9$	−2.58784	−	1.51760i	−0.862612	−	0.505866i
$10$		−	0.0998232i		−	0.0315669i
$11$	3.19743	−	0.856749i	0.964062	−	0.258320i	0.257743	−	0.966214i	$-0.417021\pi$
$11$	3.19743	−	0.856749i	0.964062	−	0.258320i	0.706319	+	0.707894i	$0.250355\pi$
$12$	0.789553	+	2.98716i	0.227924	+	0.862318i
$13$	3.49708	+	0.877749i	0.969915	+	0.243444i
$13$	3.49708	+	0.877749i	0.969915	+	0.243444i
$14$	1.31449	−	0.758923i	0.351313	−	0.202831i
$15$	−0.187043	+	0.321443i	−0.0482942	+	0.0829963i
$16$	1.37495	−	2.38148i	0.343737	−	0.595370i
$17$	−7.72994			−1.87479			−0.937393	−	0.348274i	$-0.886768\pi$
$17$	−7.72994			−1.87479			−0.937393	+	0.348274i	$0.886768\pi$
$18$	−0.370113	+	1.34471i	−0.0872365	+	0.316951i
$19$	−3.13690	−	3.13690i	−0.719653	−	0.719653i	0.248881	−	0.968534i	$-0.419937\pi$
$19$	−3.13690	−	3.13690i	−0.719653	−	0.719653i	−0.968534	+	0.248881i	$0.919937\pi$
$20$	0.369975	−	0.0991346i	0.0827290	−	0.0221672i
$21$	−5.65486	−	0.0191880i	−1.23399	−	0.00418717i
$22$	−0.769470	−	1.33276i	−0.164052	−	0.284146i
$23$	0.172481	+	0.298746i	0.0359648	+	0.0622928i	0.883448	−	0.468530i	$-0.155216\pi$
$23$	0.172481	+	0.298746i	0.0359648	+	0.0622928i	−0.847483	+	0.530823i	$0.821883\pi$
$24$	2.64386	−	1.51450i	0.539676	−	0.309145i
$25$	−4.29020	−	2.47695i	−0.858040	−	0.495390i
$26$	−0.0266253	−	1.67603i	−0.00522165	−	0.328696i
$27$	3.71145	−	3.63664i	0.714268	−	0.699872i
$28$	4.11823	+	4.11823i	0.778271	+	0.778271i
$29$	−4.06978	−	2.34969i	−0.755739	−	0.436326i	0.0720248	−	0.997403i	$-0.477054\pi$
$29$	−4.06978	−	2.34969i	−0.755739	−	0.436326i	−0.827764	+	0.561077i	$0.810387\pi$
$30$	0.166855	+	0.0453159i	0.0304634	+	0.00827352i
$31$	−0.173532	+	0.647632i	−0.0311673	+	0.116318i	−0.979757	−	0.200190i	$-0.935844\pi$
$31$	−0.173532	+	0.647632i	−0.0311673	+	0.116318i	0.948590	+	0.316509i	$0.102511\pi$
$32$	−4.63327	−	1.24148i	−0.819054	−	0.219465i
$33$	−0.0194547	+	5.73344i	−0.00338662	+	0.998064i
$34$	0.930115	+	3.47124i	0.159513	+	0.595312i
$35$			0.701021i			0.118494i
$36$	−5.35147	−	0.0363175i	−0.891911	−	0.00605292i
$37$	−1.04152	+	1.04152i	−0.171225	+	0.171225i	−0.787517	−	0.616292i	$-0.788634\pi$
$37$	−1.04152	+	1.04152i	−0.171225	+	0.171225i	0.616292	+	0.787517i	$0.288634\pi$
$38$	−1.03122	+	1.78612i	−0.167285	+	0.289747i
$39$	−3.05470	+	5.44691i	−0.489143	+	0.872203i
$40$	−0.188859	−	0.327113i	−0.0298612	−	0.0517211i
$41$	7.17396	+	1.92226i	1.12038	+	0.300206i	0.771039	−	0.636788i	$-0.219737\pi$
$41$	7.17396	+	1.92226i	1.12038	+	0.300206i	0.349346	+	0.936994i	$0.386404\pi$
$42$	0.671811	+	2.54170i	0.103663	+	0.392193i
$43$	−3.27315	−	1.88976i	−0.499151	−	0.288185i	0.229212	−	0.973377i	$-0.426385\pi$
$43$	−3.27315	−	1.88976i	−0.499151	−	0.288185i	−0.728363	+	0.685191i	$0.759719\pi$
$44$	4.17546	−	4.17546i	0.629474	−	0.629474i
$45$	−0.452383	−	0.458565i	−0.0674373	−	0.0683588i
$46$	0.113402	−	0.113402i	0.0167202	−	0.0167202i
$47$	10.6369	−	2.85014i	1.55154	−	0.415735i	0.621570	−	0.783359i	$-0.286495\pi$
$47$	10.6369	−	2.85014i	1.55154	−	0.415735i	0.929975	+	0.367623i	$0.119828\pi$
$48$	3.35647	+	3.37933i	0.484465	+	0.487764i
$49$	−3.16901	+	1.82963i	−0.452716	+	0.261376i
$50$	−0.596084	+	2.22462i	−0.0842990	+	0.314608i
$51$	3.50910	−	12.9206i	0.491372	−	1.80925i
$52$	6.18543	−	1.76315i	0.857764	−	0.244504i
$53$			1.94478i			0.267136i	0.991040	+	0.133568i	$0.0426435\pi$
$53$			1.94478i			0.267136i	−0.991040	+	0.133568i	$0.957356\pi$
$54$	−2.07967	−	1.22909i	−0.283007	−	0.167258i
$55$	0.710763			0.0958392
$56$	2.87166	−	4.97386i	0.383742	−	0.664660i
$57$	6.66736	−	3.81930i	0.883113	−	0.505878i
$58$	−0.565458	+	2.11032i	−0.0742483	+	0.277099i
$59$	−2.48647	+	9.27964i	−0.323711	+	1.20811i	0.591890	+	0.806019i	$0.298382\pi$
$59$	−2.48647	+	9.27964i	−0.323711	+	1.20811i	−0.915601	+	0.402088i	$0.868285\pi$
$60$	−0.00225110	+	0.663418i	−0.000290616	+	0.0856468i
$61$	−3.25198	+	5.63260i	−0.416373	+	0.721180i	−0.995572	−	0.0940068i	$-0.970032\pi$
$61$	−3.25198	+	5.63260i	−0.416373	+	0.721180i	0.579198	+	0.815187i	$0.303366\pi$
$62$	0.311709			0.0395870
$63$	2.59916	−	9.44339i	0.327464	−	1.18976i
$64$		−	3.26977i		−	0.408722i
$65$	0.676519	+	0.376389i	0.0839118	+	0.0466853i
$66$	2.57702	−	0.681147i	0.317210	−	0.0838435i
$67$	0.729983	−	2.72433i	0.0891816	−	0.332830i	−0.906892	−	0.421364i	$-0.861551\pi$
$67$	0.729983	−	2.72433i	0.0891816	−	0.332830i	0.996073	+	0.0885338i	$0.0282181\pi$
$68$	−11.9418	+	6.89458i	−1.44815	+	0.836090i
$69$	−0.577654	+	0.152683i	−0.0695414	+	0.0183809i
$70$	0.314803	−	0.0843512i	0.0376262	−	0.0100819i
$71$	2.22986	−	2.22986i	0.264636	−	0.264636i	−0.562298	−	0.826935i	$-0.690083\pi$
$71$	2.22986	−	2.22986i	0.264636	−	0.264636i	0.826935	+	0.562298i	$0.190083\pi$
$72$	1.33127	+	5.10674i	0.156892	+	0.601835i
$73$	−1.50413	+	1.50413i	−0.176045	+	0.176045i	−0.789629	−	0.613584i	$-0.789727\pi$
$73$	−1.50413	+	1.50413i	−0.176045	+	0.176045i	0.613584	+	0.789629i	$0.289727\pi$
$74$	0.593032	+	0.342387i	0.0689386	+	0.0398017i
$75$	6.08781	−	6.04664i	0.702960	−	0.698206i
$76$	−7.64400	−	2.04820i	−0.876827	−	0.234945i
$77$	5.40370	+	9.35947i	0.615808	+	1.06661i
$78$	2.81357	+	0.716349i	0.318574	+	0.0811105i
$79$	3.82930	−	6.63255i	0.430830	−	0.746220i	−0.566115	−	0.824327i	$-0.691554\pi$
$79$	3.82930	−	6.63255i	0.430830	−	0.746220i	0.996945	+	0.0781063i	$0.0248874\pi$
$80$	0.417511	−	0.417511i	0.0466792	−	0.0466792i
$81$	4.39380	+	7.85459i	0.488200	+	0.872732i
$82$		−	3.45286i		−	0.381305i
$83$	3.87333	+	14.4555i	0.425153	+	1.58669i	0.763588	+	0.645703i	$0.223436\pi$
$83$	3.87333	+	14.4555i	0.425153	+	1.58669i	−0.338435	+	0.940990i	$0.609898\pi$
$84$	−8.75314	+	5.01410i	−0.955046	+	0.547084i
$85$	−1.60320	−	0.429576i	−0.173891	−	0.0465940i
$86$	−0.454775	+	1.69724i	−0.0490396	+	0.183018i
$87$	5.77503	−	5.73597i	0.619149	−	0.614961i
$88$	−5.04298	−	2.91157i	−0.537584	−	0.310374i
$89$	−1.95017	−	1.95017i	−0.206718	−	0.206718i	0.596153	−	0.802871i	$-0.296695\pi$
$89$	−1.95017	−	1.95017i	−0.206718	−	0.206718i	−0.802871	+	0.596153i	$0.796695\pi$
$90$	−0.151491	+	0.258326i	−0.0159686	+	0.0272300i
$91$	0.186980	+	11.7701i	0.0196008	+	1.23384i
$92$	0.532922	+	0.307682i	0.0555609	+	0.0320781i
$93$	−1.00374	−	0.584060i	−0.104083	−	0.0605642i
$94$	−2.55979	−	4.43368i	−0.264022	−	0.457299i
$95$	−0.476269	−	0.824922i	−0.0488642	−	0.0846352i
$96$	4.17847	−	7.18093i	0.426463	−	0.732901i
$97$	−2.62010	+	0.702053i	−0.266031	+	0.0712827i	−0.389369	−	0.921082i	$-0.627307\pi$
$97$	−2.62010	+	0.702053i	−0.266031	+	0.0712827i	0.123338	+	0.992365i	$0.460640\pi$
$98$	1.20294	+	1.20294i	0.121515	+	0.121515i
$99$	−9.57463	−	2.63528i	−0.962286	−	0.264856i
$100$	−8.83707			−0.883707
$101$	−1.45348	+	2.51749i	−0.144626	+	0.250500i	−0.929233	−	0.369493i	$-0.879531\pi$
$101$	−1.45348	+	2.51749i	−0.144626	+	0.250500i	0.784607	+	0.619993i	$0.212865\pi$
$102$	−6.22441	−	0.0211206i	−0.616309	−	0.00209125i
$103$	−9.12195	+	5.26656i	−0.898813	+	0.518930i	−0.876815	−	0.480828i	$-0.840336\pi$
$103$	−9.12195	+	5.26656i	−0.898813	+	0.518930i	−0.0219980	+	0.999758i	$0.507003\pi$
$104$	−3.25818	−	5.44184i	−0.319491	−	0.533616i
$105$	−1.17176	−	0.318237i	−0.114352	−	0.0310567i
$106$	0.873331	−	0.234008i	0.0848254	−	0.0227289i
$107$			7.90628i			0.764329i	0.924094	+	0.382165i	$0.124821\pi$
$107$			7.90628i			0.764329i	−0.924094	+	0.382165i	$0.875179\pi$
$108$	2.49007	−	8.92850i	0.239607	−	0.859145i
$109$	−2.95134	−	2.95134i	−0.282687	−	0.282687i	0.551493	−	0.834180i	$-0.314058\pi$
$109$	−2.95134	−	2.95134i	−0.282687	−	0.282687i	−0.834180	+	0.551493i	$0.814058\pi$
$110$	−0.0855234	−	0.319178i	−0.00815434	−	0.0304324i
$111$	−1.26809	−	2.21372i	−0.120362	−	0.210117i
$112$	8.67208	+	2.32368i	0.819435	+	0.219567i
$113$	13.4508	−	7.76583i	1.26535	−	0.730548i	0.291242	−	0.956649i	$-0.405931\pi$
$113$	13.4508	−	7.76583i	1.26535	−	0.730548i	0.974104	+	0.226101i	$0.0725981\pi$
$114$	−2.51737	−	2.53451i	−0.235773	−	0.237378i
$115$	0.0191706	+	0.0715455i	0.00178766	+	0.00667165i
$116$	−8.38304			−0.778346
$117$	−7.71780	−	7.57863i	−0.713511	−	0.700644i
$118$	4.46634			0.411160
$119$	−6.53185	−	24.3772i	−0.598773	−	2.23465i
$120$	0.632504	−	0.167181i	0.0577395	−	0.0152615i
$121$	−0.0367377	+	0.0212105i	−0.00333979	+	0.00192823i
$122$	2.92069	+	0.782598i	0.264427	+	0.0708531i
$123$	−6.46976	+	11.1187i	−0.583359	+	1.00254i
$124$	0.309558	+	1.15529i	0.0277991	+	0.103748i
$125$	−1.51128	−	1.51128i	−0.135173	−	0.135173i
$126$	−4.55343	−	0.0309017i	−0.405652	−	0.00275294i
$127$		−	12.1339i		−	1.07671i	−0.842717	−	0.538356i	$-0.819045\pi$
$127$		−	12.1339i		−	1.07671i	0.842717	−	0.538356i	$-0.180955\pi$
$128$	−10.7349	+	2.87640i	−0.948838	+	0.254240i
$129$	4.64462	−	4.61321i	0.408936	−	0.406170i
$130$	0.0876197	−	0.349090i	0.00768475	−	0.0306172i
$131$	8.35287	−	4.82253i	0.729793	−	0.421346i	−0.0885533	−	0.996071i	$-0.528224\pi$
$131$	8.35287	−	4.82253i	0.729793	−	0.421346i	0.818347	+	0.574725i	$0.194891\pi$
$132$	5.08378	+	8.87478i	0.442487	+	0.772450i
$133$	7.24184	−	12.5432i	0.627947	−	1.08764i
$134$	−1.31124			−0.113273
$135$	0.971857	−	0.547988i	0.0836441	−	0.0471633i
$136$	9.61526	+	9.61526i	0.824501	+	0.824501i
$137$	−10.8376	+	2.90394i	−0.925922	+	0.248100i	−0.690115	−	0.723700i	$-0.742440\pi$
$137$	−10.8376	+	2.90394i	−0.925922	+	0.248100i	−0.235807	+	0.971800i	$0.575773\pi$
$138$	0.138071	+	0.241032i	0.0117534	+	0.0205180i
$139$	6.09520	+	10.5572i	0.516988	+	0.895449i	0.999805	+	0.0197282i	$0.00628008\pi$
$139$	6.09520	+	10.5572i	0.516988	+	0.895449i	−0.482818	+	0.875721i	$0.660387\pi$
$140$	0.625262	+	1.08299i	0.0528443	+	0.0915290i
$141$	−0.0647196	+	19.0734i	−0.00545037	+	1.60627i
$142$	−1.26966	−	0.733040i	−0.106548	−	0.0615154i
$143$	11.9337	−	0.189578i	0.997944	−	0.0158533i
$144$	−7.17226	+	4.07626i	−0.597689	+	0.339689i
$145$	−0.713498	−	0.713498i	−0.0592527	−	0.0592527i
$146$	0.856436	+	0.494464i	0.0708792	+	0.0409221i
$147$	−1.61962	−	6.12759i	−0.133584	−	0.505395i
$148$	−0.680051	+	2.53798i	−0.0558998	+	0.208621i
$149$	−13.8418	−	3.70889i	−1.13396	−	0.303845i	−0.357442	−	0.933935i	$-0.616351\pi$
$149$	−13.8418	−	3.70889i	−1.13396	−	0.303845i	−0.776521	+	0.630091i	$0.783018\pi$
$150$	−3.44785	−	2.00625i	−0.281516	−	0.163809i
$151$	5.32181	+	19.8613i	0.433083	+	1.61629i	0.745612	+	0.666380i	$0.232157\pi$
$151$	5.32181	+	19.8613i	0.433083	+	1.61629i	−0.312529	+	0.949908i	$0.601176\pi$
$152$			7.80396i			0.632984i
$153$	20.0038	+	11.7309i	1.61721	+	0.948390i
$154$	3.55279	−	3.55279i	0.286292	−	0.286292i
$155$	−0.0719816	+	0.124676i	−0.00578170	+	0.0100142i
$156$	0.139154	+	11.1394i	0.0111412	+	0.891862i
$157$	−1.84401	−	3.19392i	−0.147168	−	0.254903i	0.783012	−	0.622007i	$-0.213683\pi$
$157$	−1.84401	−	3.19392i	−0.147168	−	0.254903i	−0.930180	+	0.367104i	$0.880349\pi$
$158$	−3.43920	−	0.921532i	−0.273608	−	0.0733132i
$159$	−3.25071	−	0.882857i	−0.257798	−	0.0700151i
$160$	−0.891953	−	0.514969i	−0.0705150	−	0.0407119i
$161$	−0.796379	+	0.796379i	−0.0627634	+	0.0627634i
$162$	2.99852	−	2.91821i	0.235586	−	0.229276i
$163$	1.38274	−	1.38274i	0.108305	−	0.108305i	−0.650878	−	0.759183i	$-0.725599\pi$
$163$	1.38274	−	1.38274i	0.108305	−	0.108305i	0.759183	+	0.650878i	$0.225599\pi$
$164$	12.7974	−	3.42904i	0.999307	−	0.267763i
$165$	−0.322659	+	1.18804i	−0.0251190	+	0.0924889i
$166$	6.02536	−	3.47874i	0.467659	−	0.270003i
$167$	4.95130	−	18.4785i	0.383143	−	1.42991i	−0.457929	−	0.888989i	$-0.651409\pi$
$167$	4.95130	−	18.4785i	0.383143	−	1.42991i	0.841073	−	0.540922i	$-0.181925\pi$
$168$	7.01020	+	7.05793i	0.540848	+	0.544531i
$169$	11.4591	+	6.13911i	0.881470	+	0.472239i
$170$			0.771627i			0.0591811i
$171$	3.35723	+	12.8783i	0.256734	+	0.984830i
$172$	−6.74213			−0.514083
$173$	−5.34228	+	9.25309i	−0.406166	+	0.703500i	−0.994456	−	0.105150i	$-0.966468\pi$
$173$	−5.34228	+	9.25309i	−0.406166	+	0.703500i	0.588291	+	0.808650i	$0.299801\pi$
$174$	−3.27071	−	1.90317i	−0.247952	−	0.144279i
$175$	4.18607	−	15.6226i	0.316437	−	1.18096i
$176$	2.35597	−	8.79260i	0.177588	−	0.662767i
$177$	−14.3822	−	8.36875i	−1.08103	−	0.629034i
$178$	−0.641095	+	1.11041i	−0.0480521	+	0.0832287i
$179$	−2.19878			−0.164344			−0.0821722	−	0.996618i	$-0.526186\pi$
$179$	−2.19878			−0.164344			−0.0821722	+	0.996618i	$0.526186\pi$
$180$	−1.10788	−	0.304929i	−0.0825766	−	0.0227281i
$181$		−	15.8066i		−	1.17490i	−0.809262	−	0.587448i	$-0.800133\pi$
$181$		−	15.8066i		−	1.17490i	0.809262	−	0.587448i	$-0.199867\pi$
$182$	5.26303	−	1.50022i	0.390122	−	0.111204i
$183$	−7.93862	−	7.99268i	−0.586840	−	0.590836i
$184$	0.157061	−	0.586158i	0.0115787	−	0.0432121i
$185$	−0.273893	+	0.158132i	−0.0201370	+	0.0116261i
$186$	−0.141504	+	0.521021i	−0.0103756	+	0.0382031i
$187$	−24.7159	+	6.62262i	−1.80741	+	0.484294i
$188$	13.8904	−	13.8904i	1.01306	−	1.01306i
$189$	14.6047	+	8.63145i	1.06234	+	0.627846i
$190$	−0.313135	+	0.313135i	−0.0227172	+	0.0227172i
$191$	2.61567	+	1.51016i	0.189264	+	0.109271i	0.591638	−	0.806204i	$-0.298482\pi$
$191$	2.61567	+	1.51016i	0.189264	+	0.109271i	−0.402374	+	0.915475i	$0.631815\pi$
$192$	5.46543	+	1.48435i	0.394434	+	0.107124i
$193$	23.6950	+	6.34904i	1.70560	+	0.457014i	0.974339	−	0.225084i	$-0.0722656\pi$
$193$	23.6950	+	6.34904i	1.70560	+	0.457014i	0.731261	+	0.682098i	$0.238932\pi$
$194$	0.630534	+	1.09212i	0.0452697	+	0.0784094i
$195$	−0.936249	+	0.959936i	−0.0670462	+	0.0687425i
$196$	−3.26381	+	5.65308i	−0.233129	+	0.403792i
$197$	−14.6837	+	14.6837i	−1.04617	+	1.04617i	−0.0472909	+	0.998881i	$0.515059\pi$
$197$	−14.6837	+	14.6837i	−1.04617	+	1.04617i	−0.998881	+	0.0472909i	$0.984941\pi$
$198$	−0.0313311	+	4.61671i	−0.00222661	+	0.328095i
$199$			14.7267i			1.04395i	0.852962	+	0.521973i	$0.174804\pi$
$199$			14.7267i			1.04395i	−0.852962	+	0.521973i	$0.825196\pi$
$200$	2.25550	+	8.41764i	0.159488	+	0.595217i
$201$	4.22234	+	2.45691i	0.297821	+	0.173297i
$202$	1.30541	+	0.349783i	0.0918481	+	0.0246106i
$203$	3.97100	−	14.8200i	0.278710	−	1.04016i
$204$	−6.10319	−	23.0905i	−0.427309	−	1.61666i
$205$	1.38106	+	0.797357i	0.0964576	+	0.0556898i
$206$	3.46263	+	3.46263i	0.241253	+	0.241253i
$207$	0.00702304	−	1.03486i	0.000488135	−	0.0719279i
$208$	6.89864	−	7.12136i	0.478335	−	0.493777i
$209$	−12.7175	−	7.34247i	−0.879691	−	0.507890i
$210$	−0.00191541	+	0.564486i	−0.000132176	+	0.0389532i
$211$	4.42529	+	7.66483i	0.304650	+	0.527669i	0.977183	−	0.212398i	$-0.0681273\pi$
$211$	4.42529	+	7.66483i	0.304650	+	0.527669i	−0.672534	+	0.740067i	$0.734794\pi$
$212$	1.73461	+	3.00444i	0.119134	+	0.206346i
$213$	2.71495	+	4.73950i	0.186025	+	0.324745i
$214$	3.55043	−	0.951334i	0.242702	−	0.0650318i
$215$	−0.573836	−	0.573836i	−0.0391353	−	0.0391353i
$216$	−9.14027	−	0.0930469i	−0.621917	−	0.00633104i
$217$	−2.18901			−0.148600
$218$	−0.970216	+	1.68046i	−0.0657113	+	0.113815i
$219$	−1.83134	−	3.19697i	−0.123750	−	0.216031i
$220$	1.09804	−	0.633952i	0.0740296	−	0.0427410i
$221$	−27.0322	−	6.78494i	−1.81838	−	0.456405i
$222$	−0.841515	+	0.835824i	−0.0564788	+	0.0560968i
$223$	21.9597	−	5.88408i	1.47053	−	0.394027i	0.567416	−	0.823431i	$-0.307943\pi$
$223$	21.9597	−	5.88408i	1.47053	−	0.394027i	0.903113	+	0.429404i	$0.141276\pi$
$224$		−	15.6606i		−	1.04637i
$225$	7.34333	+	12.9207i	0.489555	+	0.861382i
$226$	−5.10584	−	5.10584i	−0.339635	−	0.339635i
$227$	1.66843	+	6.22667i	0.110738	+	0.413279i	0.998933	−	0.0461877i	$-0.0147072\pi$
$227$	1.66843	+	6.22667i	0.110738	+	0.413279i	−0.888195	+	0.459467i	$0.848041\pi$
$228$	6.89366	−	11.8471i	0.456544	−	0.784597i
$229$	−6.39707	−	1.71409i	−0.422730	−	0.113270i	0.0411814	−	0.999152i	$-0.486888\pi$
$229$	−6.39707	−	1.71409i	−0.422730	−	0.113270i	−0.463912	+	0.885881i	$0.653555\pi$
$230$	0.0298218	−	0.0172176i	0.00196639	−	0.00113529i
$231$	−18.0975	+	4.78344i	−1.19072	+	0.314727i
$232$	2.13962	+	7.98516i	0.140473	+	0.524252i
$233$	1.84502			0.120872			0.0604358	−	0.998172i	$-0.480751\pi$
$233$	1.84502			0.120872			0.0604358	+	0.998172i	$0.480751\pi$
$234$	−2.47463	+	4.37769i	−0.161772	+	0.286179i
$235$	2.36449			0.154242
$236$	4.43553	+	16.5536i	0.288728	+	1.07755i
$237$	9.34796	+	9.41162i	0.607215	+	0.611350i
$238$	−10.1610	+	5.86643i	−0.658637	+	0.380264i
$239$	6.75550	+	1.81013i	0.436977	+	0.117088i	0.470599	−	0.882347i	$-0.344038\pi$
$239$	6.75550	+	1.81013i	0.436977	+	0.117088i	−0.0336225	+	0.999435i	$0.510704\pi$
$240$	0.508337	+	0.887405i	0.0328130	+	0.0572818i
$241$	−7.22767	−	26.9740i	−0.465575	−	1.73755i	−0.654976	−	0.755650i	$-0.727321\pi$
$241$	−7.22767	−	26.9740i	−0.465575	−	1.73755i	0.189400	−	0.981900i	$-0.439346\pi$
$242$	0.0139454	+	0.0139454i	0.000896443	+	0.000896443i
$243$	−15.1236	+	3.77856i	−0.970178	+	0.242395i
$244$			11.6022i			0.742753i
$245$	−0.758934	+	0.203356i	−0.0484865	+	0.0129919i
$246$	5.77147	+	1.56747i	0.367975	+	0.0999382i
$247$	−8.21657	−	13.7234i	−0.522808	−	0.873198i
$248$	1.02144	−	0.589731i	0.0648618	−	0.0374480i
$249$	−25.9207	−	0.0879537i	−1.64266	−	0.00557384i
$250$	−0.496815	+	0.860509i	−0.0314213	+	0.0544233i
$251$	11.7155			0.739473			0.369737	−	0.929137i	$-0.379448\pi$
$251$	11.7155			0.739473			0.369737	+	0.929137i	$0.379448\pi$
$252$	−4.40749	−	16.9071i	−0.277646	−	1.06505i
$253$	0.807446	+	0.807446i	0.0507637	+	0.0507637i
$254$	−5.44891	+	1.46003i	−0.341895	+	0.0916105i
$255$	1.44583	−	2.48474i	0.0905412	−	0.155600i
$256$	−0.686397	−	1.18887i	−0.0428998	−	0.0743046i
$257$	7.37172	+	12.7682i	0.459835	+	0.796458i	0.998952	−	0.0457732i	$-0.0145752\pi$
$257$	7.37172	+	12.7682i	0.459835	+	0.796458i	−0.539117	+	0.842231i	$0.681242\pi$
$258$	−2.63049	−	1.53064i	−0.163767	−	0.0952935i
$259$	−4.16464	−	2.40446i	−0.258778	−	0.149406i
$260$	1.38085	−	0.0219361i	0.0856365	−	0.00136042i
$261$	6.96605	+	12.2569i	0.431187	+	0.758683i
$262$	−3.17069	−	3.17069i	−0.195886	−	0.195886i
$263$	−24.2747	−	14.0150i	−1.49684	−	0.864204i	−0.496851	−	0.867836i	$-0.665511\pi$
$263$	−24.2747	−	14.0150i	−1.49684	−	0.864204i	−0.999993	+	0.00363177i	$0.998844\pi$
$264$	7.15602	−	7.10762i	0.440422	−	0.437444i
$265$	−0.108077	+	0.403350i	−0.00663913	+	0.0247776i
$266$	−6.50409	−	1.74277i	−0.398792	−	0.106856i
$267$	4.14502	−	2.37441i	0.253671	−	0.145312i
$268$	−1.30219	−	4.85984i	−0.0795439	−	0.296862i
$269$		−	19.9944i		−	1.21908i	−0.792755	−	0.609541i	$-0.791354\pi$
$269$		−	19.9944i		−	1.21908i	0.792755	−	0.609541i	$-0.208646\pi$
$270$	−0.363021	−	0.370488i	−0.0220928	−	0.0225472i
$271$	−12.5200	+	12.5200i	−0.760537	+	0.760537i	−0.976419	−	0.215883i	$-0.930737\pi$
$271$	−12.5200	+	12.5200i	−0.760537	+	0.760537i	0.215883	+	0.976419i	$0.430737\pi$
$272$	−10.6283	+	18.4087i	−0.644433	+	1.11619i
$273$	−19.7586	−	5.03065i	−1.19585	−	0.304468i
$274$	2.60811	+	4.51737i	0.157561	+	0.272904i
$275$	−15.8397	−	4.24425i	−0.955172	−	0.255938i
$276$	−0.756218	+	0.751103i	−0.0455190	+	0.0452111i
$277$	−0.965871	−	0.557646i	−0.0580335	−	0.0335057i	0.470702	−	0.882292i	$-0.344001\pi$
$277$	−0.965871	−	0.557646i	−0.0580335	−	0.0335057i	−0.528736	+	0.848786i	$0.677334\pi$
$278$	4.00744	−	4.00744i	0.240350	−	0.240350i
$279$	1.43192	−	1.41261i	0.0857267	−	0.0845710i
$280$	0.871998	−	0.871998i	0.0521118	−	0.0521118i
$281$	8.07093	−	2.16260i	0.481471	−	0.129010i	−0.00991630	−	0.999951i	$-0.503157\pi$
$281$	8.07093	−	2.16260i	0.481471	−	0.129010i	0.491388	+	0.870941i	$0.336490\pi$
$282$	8.57295	−	2.26597i	0.510512	−	0.134936i
$283$	−10.6136	+	6.12777i	−0.630914	+	0.364258i	−0.781106	−	0.624399i	$-0.785344\pi$
$283$	−10.6136	+	6.12777i	−0.630914	+	0.364258i	0.150192	+	0.988657i	$0.452011\pi$
$284$	1.45597	−	5.43374i	0.0863957	−	0.322433i
$285$	1.59507	−	0.421601i	0.0944836	−	0.0249735i
$286$	−1.52107	−	5.33617i	−0.0899426	−	0.315534i
$287$			24.2482i			1.43132i
$288$	10.1061	+	10.2442i	0.595507	+	0.603644i
$289$	42.7520			2.51482
$290$	−0.234553	+	0.406258i	−0.0137735	+	0.0238563i
$291$	0.0159419	−	4.69821i	0.000934531	−	0.275414i
$292$	−0.982105	+	3.66527i	−0.0574734	+	0.214494i
$293$	3.24254	−	12.1013i	0.189431	−	0.706967i	−0.804207	−	0.594349i	$-0.797410\pi$
$293$	3.24254	−	12.1013i	0.189431	−	0.706967i	0.993638	−	0.112618i	$-0.0359236\pi$
$294$	−2.55680	+	1.46462i	−0.149115	+	0.0854185i
$295$	−1.03139	+	1.78643i	−0.0600501	+	0.104010i
$296$	2.59109			0.150604
$297$	8.75140	−	14.8077i	0.507808	−	0.859229i
$298$			6.66212i			0.385926i
$299$	0.340956	+	1.19613i	0.0197180	+	0.0691741i
$300$	4.01170	−	14.7712i	0.231615	−	0.852815i
$301$	3.19371	−	11.9191i	0.184082	−	0.687005i
$302$	8.27863	−	4.77967i	0.476382	−	0.275039i
$303$	−3.54817	−	3.57234i	−0.203837	−	0.205225i
$304$	−11.7835	+	3.15738i	−0.675831	+	0.181088i
$305$	−0.987484	+	0.987484i	−0.0565432	+	0.0565432i
$306$	2.86095	−	10.3945i	0.163550	−	0.594216i
$307$	−19.0486	+	19.0486i	−1.08716	+	1.08716i	−0.0913429	+	0.995820i	$0.529116\pi$
$307$	−19.0486	+	19.0486i	−1.08716	+	1.08716i	−0.995820	+	0.0913429i	$0.970884\pi$
$308$	16.6960	+	9.63945i	0.951344	+	0.549259i
$309$	−4.66205	−	17.6382i	−0.265215	−	1.00340i
$310$	0.0646487	+	0.0173226i	0.00367180	+	0.000983856i
$311$	7.87859	+	13.6461i	0.446754	+	0.773801i	0.998173	−	0.0604281i	$-0.0192466\pi$
$311$	7.87859	+	13.6461i	0.446754	+	0.773801i	−0.551419	+	0.834229i	$0.685913\pi$
$312$	10.5751	−	2.97566i	0.598699	−	0.168464i
$313$	−13.9012	+	24.0775i	−0.785740	+	1.36094i	0.142816	+	0.989749i	$0.454384\pi$
$313$	−13.9012	+	24.0775i	−0.785740	+	1.36094i	−0.928556	+	0.371193i	$0.878949\pi$
$314$	−1.21239	+	1.21239i	−0.0684192	+	0.0684192i
$315$	1.06387	−	1.81413i	0.0599421	−	0.102214i
$316$		−	13.6619i		−	0.768543i
$317$	−1.02375	−	3.82068i	−0.0574995	−	0.214591i	0.931198	−	0.364513i	$-0.118764\pi$
$317$	−1.02375	−	3.82068i	−0.0574995	−	0.214591i	−0.988698	+	0.149922i	$0.952098\pi$
$318$	−0.00531375	+	1.56601i	−0.000297980	+	0.0878172i
$319$	−15.0259	−	4.02619i	−0.841290	−	0.225423i
$320$	0.181711	−	0.678154i	0.0101579	−	0.0379100i
$321$	−13.2154	−	3.58915i	−0.737610	−	0.200327i
$322$	0.453450	+	0.261800i	0.0252698	+	0.0145895i
$323$	24.2480	+	24.2480i	1.34920	+	1.34920i
$324$	13.7936	+	8.21535i	0.766312	+	0.456408i
$325$	−12.8290	−	12.4278i	−0.711626	−	0.689370i
$326$	−0.787320	−	0.454559i	−0.0436056	−	0.0251757i
$327$	6.27297	−	3.59337i	0.346896	−	0.198714i
$328$	−6.53258	−	11.3148i	−0.360702	−	0.624754i
$329$	17.9764	+	31.1361i	0.991072	+	1.71659i
$330$	0.572331	+	0.00194203i	0.0315058	+	0.000106905i
$331$	16.5621	−	4.43780i	0.910336	−	0.243924i	0.226886	−	0.973921i	$-0.427145\pi$
$331$	16.5621	−	4.43780i	0.910336	−	0.243924i	0.683450	+	0.729997i	$0.260479\pi$
$332$	18.8771	+	18.8771i	1.03601	+	1.03601i
$333$	4.27590	−	1.11468i	0.234318	−	0.0610840i
$334$	−8.89381			−0.486647
$335$	0.302798	−	0.524462i	0.0165436	−	0.0286544i
$336$	−7.82083	+	13.4405i	−0.426661	+	0.733242i
$337$	−0.623289	+	0.359856i	−0.0339527	+	0.0196026i	−0.516880	−	0.856058i	$-0.672907\pi$
$337$	−0.623289	+	0.359856i	−0.0339527	+	0.0196026i	0.482928	+	0.875660i	$0.339573\pi$
$338$	1.37802	−	5.88457i	0.0749544	−	0.320078i
$339$	6.87444	+	26.0085i	0.373368	+	1.41259i
$340$	−2.85989	+	0.766304i	−0.155099	+	0.0415587i
$341$			2.21943i			0.120189i
$342$	5.37922	−	3.05721i	0.290875	−	0.165315i
$343$	7.71243	+	7.71243i	0.416432	+	0.416432i
$344$	1.72081	+	6.42213i	0.0927796	+	0.346258i
$345$	−0.128291		0.000435316i	−0.00690696		2.34366e-5i
$346$	4.79805	+	1.28563i	0.257945	+	0.0691160i
$347$	−20.2064	+	11.6662i	−1.08474	+	0.626274i	−0.932171	−	0.362019i	$-0.882088\pi$
$347$	−20.2064	+	11.6662i	−1.08474	+	0.626274i	−0.152568	+	0.988293i	$0.548754\pi$
$348$	3.80558	−	14.0123i	0.204001	−	0.751137i
$349$	−3.91392	−	14.6069i	−0.209507	−	0.781892i	−0.988028	−	0.154273i	$-0.950696\pi$
$349$	−3.91392	−	14.6069i	−0.209507	−	0.781892i	0.778521	−	0.627619i	$-0.215970\pi$
$350$	−7.51925			−0.401921
$351$	16.1713	−	9.45991i	0.863159	−	0.504933i
$352$	−15.8782			−0.846311
$353$	−8.51619	−	31.7828i	−0.453271	−	1.69163i	−0.693122	−	0.720820i	$-0.743765\pi$
$353$	−8.51619	−	31.7828i	−0.453271	−	1.69163i	0.239851	−	0.970810i	$-0.422901\pi$
$354$	−2.02755	+	7.46549i	−0.107763	+	0.396786i
$355$	0.586397	−	0.338556i	0.0311227	−	0.0179687i
$356$	−4.75219	−	1.27334i	−0.251865	−	0.0674871i
$357$	43.7117	+	0.148322i	2.31347	+	0.00785004i
$358$	0.264571	+	0.987392i	0.0139830	+	0.0521853i
$359$	12.6798	+	12.6798i	0.669217	+	0.669217i	0.957535	−	0.288318i	$-0.0930960\pi$
$359$	12.6798	+	12.6798i	0.669217	+	0.669217i	−0.288318	+	0.957535i	$0.593096\pi$
$360$	−0.00768991	+	1.13313i	−0.000405294	+	0.0597210i
$361$			0.680234i			0.0358018i
$362$	−7.09818	+	1.90195i	−0.373072	+	0.0999643i
$363$	−0.0187759	−	0.0710359i	−0.000985479	−	0.00372842i
$364$	10.7870	+	18.0165i	0.565392	+	0.944322i
$365$	−0.395547	+	0.228369i	−0.0207039	+	0.0119534i
$366$	−2.63400	+	4.52668i	−0.137681	+	0.236613i
$367$	11.1709	−	19.3485i	0.583114	−	1.00998i	−0.411994	−	0.911187i	$-0.635167\pi$
$367$	11.1709	−	19.3485i	0.583114	−	1.00998i	0.995108	−	0.0987961i	$-0.0314992\pi$
$368$	0.948609			0.0494497
$369$	−15.6478	−	15.8617i	−0.814594	−	0.825726i
$370$	0.103968	+	0.103968i	0.00540504	+	0.00540504i
$371$	−6.13307	+	1.64335i	−0.318413	+	0.0853186i
$372$	−2.07159	−	0.00702930i	−0.107407	−	0.000364452i
$373$	−0.438487	−	0.759482i	−0.0227040	−	0.0393245i	0.854450	−	0.519533i	$-0.173894\pi$
$373$	−0.438487	−	0.759482i	−0.0227040	−	0.0393245i	−0.877154	+	0.480209i	$0.840561\pi$
$374$	5.94796	+	10.3022i	0.307561	+	0.532712i
$375$	3.21217	−	1.84005i	0.165876	−	0.0950195i
$376$	−16.7764	−	9.68588i	−0.865179	−	0.499511i
$377$	−12.1699	−	11.7893i	−0.626782	−	0.607179i
$378$	2.11874	−	7.59705i	0.108976	−	0.390750i
$379$	3.65431	+	3.65431i	0.187709	+	0.187709i	0.794705	−	0.606996i	$-0.207626\pi$
$379$	3.65431	+	3.65431i	0.187709	+	0.187709i	−0.606996	+	0.794705i	$0.707626\pi$
$380$	−1.47155	−	0.849599i	−0.0754888	−	0.0435835i
$381$	20.2819	+	5.50835i	1.03907	+	0.282201i
$382$	0.363424	−	1.35632i	0.0185944	−	0.0693952i
$383$	1.84116	+	0.493339i	0.0940791	+	0.0252084i	0.305552	−	0.952176i	$-0.401159\pi$
$383$	1.84116	+	0.493339i	0.0940791	+	0.0252084i	−0.211472	+	0.977384i	$0.567826\pi$
$384$	0.0653160	−	19.2491i	0.00333314	−	0.982304i
$385$	0.600599	+	2.24146i	0.0306093	+	0.114236i
$386$		−	11.4045i		−	0.580474i
$387$	5.60250	+	9.85771i	0.284791	+	0.501096i
$388$	−3.42153	+	3.42153i	−0.173702	+	0.173702i
$389$	11.9704	−	20.7334i	0.606925	−	1.05122i	−0.384819	−	0.922992i	$-0.625736\pi$
$389$	11.9704	−	20.7334i	0.606925	−	1.05122i	0.991744	−	0.128232i	$-0.0409304\pi$
$390$	0.543728	+	0.304930i	0.0275327	+	0.0154407i
$391$	−1.33327	−	2.30929i	−0.0674262	−	0.116786i
$392$	6.21780	+	1.66605i	0.314046	+	0.0841485i
$393$	4.26898	+	16.1511i	0.215342	+	0.814714i
$394$	8.36077	+	4.82709i	0.421209	+	0.243185i
$395$	1.16279	−	1.16279i	0.0585064	−	0.0585064i
$396$	−17.1421	+	4.46874i	−0.861421	+	0.224563i
$397$	13.9863	−	13.9863i	0.701953	−	0.701953i	−0.262877	−	0.964829i	$-0.584671\pi$
$397$	13.9863	−	13.9863i	0.701953	−	0.701953i	0.964829	+	0.262877i	$0.0846713\pi$
$398$	6.61322	−	1.77201i	0.331491	−	0.0888227i
$399$	17.6785	+	17.7989i	0.885032	+	0.891059i
$400$	−11.7976	+	6.81135i	−0.589880	+	0.340567i
$401$	2.66203	−	9.93483i	0.132935	−	0.496121i	−0.867062	−	0.498199i	$-0.833995\pi$
$401$	2.66203	−	9.93483i	0.132935	−	0.496121i	0.999998	+	0.00207791i	$0.000661419\pi$
$402$	0.595251	−	2.19173i	0.0296884	−	0.109314i
$403$	−1.17531	+	2.11250i	−0.0585466	+	0.105231i
$404$			5.18561i			0.257994i
$405$	0.474776	+	1.87323i	0.0235918	+	0.0930814i
$406$	−7.13293			−0.354001
$407$	−2.43787	+	4.22252i	−0.120841	+	0.209302i
$408$	−20.4369	+	11.7070i	−1.01178	+	0.579581i
$409$	−1.10101	+	4.10902i	−0.0544413	+	0.203178i	−0.987789	−	0.155795i	$-0.950206\pi$
$409$	−1.10101	+	4.10902i	−0.0544413	+	0.203178i	0.933348	+	0.358973i	$0.116873\pi$
$410$	0.191886	−	0.716128i	0.00947657	−	0.0353670i
$411$	0.0659412	−	19.4334i	0.00325264	−	0.958579i
$412$	−9.39483	+	16.2723i	−0.462850	+	0.801680i
$413$	−31.3654			−1.54339
$414$	−0.465564	+	0.121367i	−0.0228812	+	0.00596488i
$415$			3.21333i			0.157736i
$416$	−15.1132	−	8.40840i	−0.740986	−	0.412256i
$417$	−20.4133	+	5.39557i	−0.999646	+	0.264222i
$418$	−1.76699	+	6.59448i	−0.0864261	+	0.322547i
$419$	7.63390	−	4.40744i	0.372941	−	0.215317i	−0.301802	−	0.953371i	$-0.597588\pi$
$419$	7.63390	−	4.40744i	0.372941	−	0.215317i	0.674742	+	0.738053i	$0.264255\pi$
$420$	−2.09406	+	0.553493i	−0.102180	+	0.0270077i
$421$	17.1986	−	4.60836i	0.838210	−	0.224598i	0.185918	−	0.982565i	$-0.440474\pi$
$421$	17.1986	−	4.60836i	0.838210	−	0.224598i	0.652292	+	0.757968i	$0.273808\pi$
$422$	2.90952	−	2.90952i	0.141633	−	0.141633i
$423$	−31.8518	−	8.76677i	−1.54869	−	0.426255i
$424$	2.41911	−	2.41911i	0.117482	−	0.117482i
$425$	33.1630	+	19.1467i	1.60864	+	0.928749i
$426$	1.80166	−	1.78947i	0.0872906	−	0.0867002i
$427$	−20.5109	−	5.49589i	−0.992593	−	0.265965i
$428$	7.05186	+	12.2142i	0.340865	+	0.590395i
$429$	−5.10056	+	20.0332i	−0.246257	+	0.967213i
$430$	−0.188642	+	0.326737i	−0.00909710	+	0.0157566i
$431$	7.53625	−	7.53625i	0.363008	−	0.363008i	−0.501911	−	0.864919i	$-0.667369\pi$
$431$	7.53625	−	7.53625i	0.363008	−	0.363008i	0.864919	+	0.501911i	$0.167369\pi$
$432$	−3.55755	−	13.8389i	−0.171162	−	0.665825i
$433$		−	6.91846i		−	0.332480i	−0.986085	−	0.166240i	$-0.946837\pi$
$433$		−	6.91846i		−	0.332480i	0.986085	−	0.166240i	$-0.0531626\pi$
$434$	0.263396	+	0.983006i	0.0126434	+	0.0471858i
$435$	1.51651	−	0.868712i	0.0727112	−	0.0416515i
$436$	−7.19183	−	1.92705i	−0.344426	−	0.0922888i
$437$	0.396080	−	1.47819i	0.0189471	−	0.0707114i
$438$	−1.21529	+	1.20707i	−0.0580687	+	0.0576759i
$439$	−4.58990	−	2.64998i	−0.219064	−	0.126477i	0.386453	−	0.922309i	$-0.373700\pi$
$439$	−4.58990	−	2.64998i	−0.219064	−	0.126477i	−0.605517	+	0.795832i	$0.707034\pi$
$440$	−0.884116	−	0.884116i	−0.0421486	−	0.0421486i
$441$	10.9775	+	0.0744985i	0.522739	+	0.00354755i
$442$	0.205812	+	12.9556i	0.00978948	+	0.616235i
$443$	−10.6504	−	6.14899i	−0.506014	−	0.292147i	0.225180	−	0.974317i	$-0.427703\pi$
$443$	−10.6504	−	6.14899i	−0.506014	−	0.292147i	−0.731194	+	0.682170i	$0.761036\pi$
$444$	−3.93353	−	2.28885i	−0.186677	−	0.108624i
$445$	−0.296091	−	0.512845i	−0.0140361	−	0.0243112i
$446$	−5.28465	−	9.15329i	−0.250236	−	0.433421i
$447$	12.4831	−	21.4529i	0.590429	−	1.01469i
$448$	10.3116	−	2.76298i	0.487176	−	0.130538i
$449$	−20.5476	−	20.5476i	−0.969701	−	0.969701i	0.0298537	−	0.999554i	$-0.490496\pi$
$449$	−20.5476	−	20.5476i	−0.969701	−	0.969701i	−0.999554	+	0.0298537i	$0.990496\pi$
$450$	4.91864	−	4.85233i	0.231867	−	0.228741i
$451$	24.5851			1.15767
$452$	13.8532	−	23.9944i	0.651599	−	1.12860i
$453$	−35.6141	−	0.120845i	−1.67330	−	0.00567781i
$454$	2.59542	−	1.49847i	0.121809	−	0.0703265i
$455$	−0.615320	+	2.45152i	−0.0288466	+	0.114929i
$456$	−13.0443	−	3.54270i	−0.610857	−	0.165902i
$457$	−24.4401	+	6.54871i	−1.14326	+	0.306336i	−0.780261	−	0.625454i	$-0.784914\pi$
$457$	−24.4401	+	6.54871i	−1.14326	+	0.306336i	−0.362999	+	0.931789i	$0.618247\pi$
$458$			3.07894i			0.143870i
$459$	−28.6893	+	28.1110i	−1.33910	+	1.31211i
$460$	0.0934297	+	0.0934297i	0.00435618	+	0.00435618i
$461$	4.71321	+	17.5899i	0.219516	+	0.819245i	0.984528	+	0.175229i	$0.0560665\pi$
$461$	4.71321	+	17.5899i	0.219516	+	0.819245i	−0.765012	+	0.644017i	$0.777267\pi$
$462$	4.32567	+	7.55134i	0.201248	+	0.351320i
$463$	22.9719	+	6.15531i	1.06760	+	0.286061i	0.749505	−	0.661999i	$-0.230292\pi$
$463$	22.9719	+	6.15531i	1.06760	+	0.286061i	0.318091	+	0.948060i	$0.396958\pi$
$464$	−11.1915	+	6.46140i	−0.519551	+	0.299963i
$465$	−0.175719	−	0.176916i	−0.00814877	−	0.00820426i
$466$	−0.222005	−	0.828534i	−0.0102842	−	0.0383811i
$467$	−10.0356			−0.464394			−0.232197	−	0.972669i	$-0.574591\pi$
$467$	−10.0356			−0.464394			−0.232197	+	0.972669i	$0.574591\pi$
$468$	−18.6826	−	4.82425i	−0.863604	−	0.223001i
$469$	9.20831			0.425200
$470$	−0.284510	−	1.06180i	−0.0131235	−	0.0489774i
$471$	6.17576	−	1.63235i	0.284564	−	0.0752147i
$472$	14.6358	−	8.45001i	0.673669	−	0.388943i
$473$	−12.0847	−	3.23809i	−0.555656	−	0.148888i
$474$	3.10161	−	5.33030i	0.142462	−	0.244829i
$475$	5.68798	+	21.2278i	0.260983	+	0.974000i
$476$	−31.8336	−	31.8336i	−1.45909	−	1.45909i
$477$	2.95139	−	5.03278i	0.135135	−	0.230435i
$478$		−	3.25146i		−	0.148718i
$479$	−17.1423	+	4.59327i	−0.783252	+	0.209872i	−0.628218	−	0.778037i	$-0.716215\pi$
$479$	−17.1423	+	4.59327i	−0.783252	+	0.209872i	−0.155034	+	0.987909i	$0.549549\pi$
$480$	1.26568	−	1.25712i	0.0577703	−	0.0573796i
$481$	−4.55648	+	2.72809i	−0.207758	+	0.124390i
$482$	−11.2434	+	6.49137i	−0.512122	+	0.295674i
$483$	−0.969623	−	1.69267i	−0.0441194	−	0.0770193i
$484$	−0.0378367	+	0.0655350i	−0.00171985	+	0.00297886i
$485$	−0.582427			−0.0264466
$486$	3.51658	+	6.33679i	0.159515	+	0.287443i
$487$	−11.1554	−	11.1554i	−0.505498	−	0.505498i	0.407643	−	0.913141i	$-0.366351\pi$
$487$	−11.1554	−	11.1554i	−0.505498	−	0.505498i	−0.913141	+	0.407643i	$0.866351\pi$
$488$	11.0515	−	2.96124i	0.500278	−	0.134049i
$489$	1.68354	+	2.93897i	0.0761325	+	0.132905i
$490$	0.182640	+	0.316341i	0.00825081	+	0.0142908i
$491$	1.80111	+	3.11961i	0.0812829	+	0.140786i	0.903801	−	0.427952i	$-0.140765\pi$
$491$	1.80111	+	3.11961i	0.0812829	+	0.140786i	−0.822518	+	0.568739i	$0.807432\pi$
$492$	−0.0778651	+	22.9475i	−0.00351043	+	1.03455i
$493$	31.4591	+	18.1629i	1.41685	+	0.818018i
$494$	−5.17400	+	5.34105i	−0.232789	+	0.240305i
$495$	−1.83934	−	1.07865i	−0.0826721	−	0.0484818i
$496$	1.30372	+	1.30372i	0.0585389	+	0.0585389i
$497$	8.91636	+	5.14786i	0.399954	+	0.230913i
$498$	3.07944	+	11.6506i	0.137993	+	0.522077i
$499$	−2.31094	+	8.62453i	−0.103452	+	0.386087i	−0.998165	−	0.0605540i	$-0.980713\pi$
$499$	−2.31094	+	8.62453i	−0.103452	+	0.386087i	0.894713	+	0.446641i	$0.147380\pi$
$500$	−3.68269	−	0.986775i	−0.164695	−	0.0441299i
$501$	28.6392	+	16.6647i	1.27950	+	0.744522i
$502$	−1.40968	−	5.26099i	−0.0629170	−	0.234809i
$503$		−	26.0109i		−	1.15977i	−0.814700	−	0.579883i	$-0.803098\pi$
$503$		−	26.0109i		−	1.15977i	0.814700	−	0.579883i	$-0.196902\pi$
$504$	−14.9797	+	8.51352i	−0.667249	+	0.379222i
$505$	−0.441357	+	0.441357i	−0.0196401	+	0.0196401i
$506$	0.265438	−	0.459752i	0.0118001	−	0.0204385i
$507$	−15.4635	+	16.3670i	−0.686760	+	0.726884i
$508$	−10.8226	−	18.7454i	−0.480177	−	0.831691i
$509$	22.6540	+	6.07013i	1.00412	+	0.269054i	0.723172	−	0.690668i	$-0.242684\pi$
$509$	22.6540	+	6.07013i	1.00412	+	0.269054i	0.280951	+	0.959722i	$0.409350\pi$
$510$	−1.28978	−	0.350290i	−0.0571123	−	0.0155111i
$511$	−6.01443	−	3.47243i	−0.266063	−	0.153611i
$512$	−16.1682	+	16.1682i	−0.714542	+	0.714542i
$513$	−23.0502	−	0.234648i	−1.01769	−	0.0103600i
$514$	4.84672	−	4.84672i	0.213780	−	0.213780i
$515$	−2.18458	+	0.585357i	−0.0962642	+	0.0257939i
$516$	3.06067	−	11.2695i	0.134739	−	0.496112i
$517$	31.5688	−	18.2262i	1.38839	−	0.801589i
$518$	−0.578639	+	2.15951i	−0.0254239	+	0.0948834i
$519$	−13.0414	−	13.1302i	−0.572453	−	0.576351i
$520$	−0.373331	−	1.30971i	−0.0163716	−	0.0574346i
$521$		−	23.0464i		−	1.00968i	−0.863213	−	0.504840i	$-0.831552\pi$
$521$		−	23.0464i		−	1.00968i	0.863213	−	0.504840i	$-0.168448\pi$
$522$	4.66593	−	4.60303i	0.204222	−	0.201469i
$523$	−30.2009			−1.32059			−0.660297	−	0.751005i	$-0.729570\pi$
$523$	−30.2009			−1.32059			−0.660297	+	0.751005i	$0.729570\pi$
$524$	8.60273	−	14.9004i	0.375812	−	0.650926i
$525$	24.2129	+	14.0891i	1.05674	+	0.614899i
$526$	−3.37275	+	12.5873i	−0.147059	+	0.548832i
$527$	1.34140	−	5.00616i	0.0584321	−	0.218072i
$528$	13.6273	+	7.92951i	0.593053	+	0.345088i
$529$	11.4405	−	19.8155i	0.497413	−	0.861545i
$530$	0.194134			0.00843266
$531$	20.5173	−	20.2407i	0.890377	−	0.878373i
$532$		−	25.8369i		−	1.12017i
$533$	23.4007	+	13.0192i	1.01359	+	0.563925i
$534$	−1.56502	−	1.57568i	−0.0677250	−	0.0681861i
$535$	−0.439375	+	1.63977i	−0.0189959	+	0.0708935i
$536$	−4.29682	+	2.48077i	−0.185594	+	0.107153i
$537$	0.998162	−	3.67526i	0.0430739	−	0.158599i
$538$	−8.97877	+	2.40586i	−0.387102	+	0.103724i
$539$	−8.56516	+	8.56516i	−0.368928	+	0.368928i
$540$	1.01263	−	1.71340i	0.0435765	−	0.0737330i
$541$	6.91497	−	6.91497i	0.297298	−	0.297298i	−0.542657	−	0.839954i	$-0.682582\pi$
$541$	6.91497	−	6.91497i	0.297298	−	0.297298i	0.839954	+	0.542657i	$0.182582\pi$
$542$	7.12877	+	4.11580i	0.306207	+	0.176789i
$543$	26.4208	+	7.17560i	1.13382	+	0.307934i
$544$	35.8149	+	9.59657i	1.53555	+	0.411450i
$545$	−0.448097	−	0.776126i	−0.0191943	−	0.0332456i
$546$	0.118403	+	9.47821i	0.00506717	+	0.405630i
$547$	6.88394	−	11.9233i	0.294336	−	0.509805i	−0.680494	−	0.732754i	$-0.738235\pi$
$547$	6.88394	−	11.9233i	0.294336	−	0.509805i	0.974830	+	0.222948i	$0.0715681\pi$
$548$	−14.1526	+	14.1526i	−0.604571	+	0.604571i
$549$	16.9636	−	9.64104i	0.723989	−	0.411470i
$550$			7.62375i			0.325078i
$551$	5.39575	+	20.1372i	0.229867	+	0.857874i
$552$	0.908464	+	0.528620i	0.0386668	+	0.0224996i
$553$	24.1522	+	6.47157i	1.02706	+	0.275199i
$554$	−0.134199	+	0.500837i	−0.00570156	+	0.0212785i
$555$	−0.139981	−	0.529599i	−0.00594188	−	0.0224802i
$556$	18.8326	+	10.8730i	0.798679	+	0.461118i
$557$	6.79791	+	6.79791i	0.288037	+	0.288037i	0.836304	−	0.548267i	$-0.184712\pi$
$557$	6.79791	+	6.79791i	0.288037	+	0.288037i	−0.548267	+	0.836304i	$0.684712\pi$
$558$	−0.806651	−	0.473048i	−0.0341483	−	0.0200257i
$559$	−9.78775	−	9.48163i	−0.413978	−	0.401030i
$560$	1.66947	+	0.963866i	0.0705478	+	0.0407308i
$561$	0.150383	−	44.3192i	0.00634919	−	1.87116i
$562$	−1.94229	−	3.36415i	−0.0819306	−	0.141908i
$563$	−16.8374	−	29.1632i	−0.709611	−	1.22908i	−0.965002	−	0.262244i	$-0.915538\pi$
$563$	−16.8374	−	29.1632i	−0.709611	−	1.22908i	0.255391	−	0.966838i	$-0.417796\pi$
$564$	16.9122	+	29.5236i	0.712131	+	1.24317i
$565$	3.22128	−	0.863140i	0.135520	−	0.0363126i
$566$	4.02886	+	4.02886i	0.169345	+	0.169345i
$567$	−21.0575	+	20.4935i	−0.884331	+	0.860645i
$568$	−5.54745			−0.232766
$569$	14.6239	−	25.3293i	0.613065	−	1.06186i	−0.377655	−	0.925946i	$-0.623270\pi$
$569$	14.6239	−	25.3293i	0.613065	−	1.06186i	0.990721	−	0.135914i	$-0.0433971\pi$
$570$	−0.381254	−	0.665557i	−0.0159690	−	0.0278771i
$571$	−9.32626	+	5.38452i	−0.390292	+	0.225335i	−0.682287	−	0.731085i	$-0.739014\pi$
$571$	−9.32626	+	5.38452i	−0.390292	+	0.225335i	0.291995	+	0.956420i	$0.405681\pi$
$572$	18.2669	−	10.9369i	0.763777	−	0.457295i
$573$	−3.71165	+	3.68655i	−0.155057	+	0.154008i
$574$	10.8890	−	2.91769i	0.454497	−	0.121782i
$575$		−	1.70891i		−	0.0712663i
$576$	−4.96220	+	8.46164i	−0.206758	+	0.352568i
$577$	−7.56424	−	7.56424i	−0.314903	−	0.314903i	0.531902	−	0.846806i	$-0.321477\pi$
$577$	−7.56424	−	7.56424i	−0.314903	−	0.314903i	−0.846806	+	0.531902i	$0.821477\pi$
$578$	−5.14419	−	19.1984i	−0.213970	−	0.798547i
$579$	−21.3691	+	36.7239i	−0.888067	+	1.52619i
$580$	−1.73865	−	0.465871i	−0.0721936	−	0.0193442i
$581$	−42.3138	+	24.4299i	−1.75547	+	1.01352i
$582$	−2.11171	+	0.558159i	−0.0875333	+	0.0231364i
$583$	1.66619	+	6.21830i	0.0690065	+	0.257536i
$584$	3.74197			0.154844
$585$	−1.17951	−	2.00072i	−0.0487669	−	0.0827194i
$586$	−5.82443			−0.240605
$587$	2.60124	+	9.70796i	0.107365	+	0.400690i	0.998603	−	0.0528456i	$-0.0168291\pi$
$587$	2.60124	+	9.70796i	0.107365	+	0.400690i	−0.891238	+	0.453536i	$0.850162\pi$
$588$	−7.96749	−	8.02175i	−0.328574	−	0.330811i
$589$	2.57591	−	1.48720i	0.106138	−	0.0612790i
$590$	0.926323	+	0.248208i	0.0381361	+	0.0102185i
$591$	−17.8780	−	31.2097i	−0.735403	−	1.28380i
$592$	1.04832	+	3.91240i	0.0430859	+	0.160799i
$593$	−4.08098	−	4.08098i	−0.167586	−	0.167586i	0.618332	−	0.785917i	$-0.287809\pi$
$593$	−4.08098	−	4.08098i	−0.167586	−	0.167586i	−0.785917	+	0.618332i	$0.787809\pi$
$594$	−7.70262	−	2.14818i	−0.316042	−	0.0881410i
$595$		−	5.41885i		−	0.222151i
$596$	−24.6919	+	6.61616i	−1.01142	+	0.271009i
$597$	−24.6157	−	6.68535i	−1.00745	−	0.273613i
$598$	0.496114	−	0.297037i	0.0202876	−	0.0121467i
$599$	27.0004	−	15.5887i	1.10321	−	0.636936i	0.166144	−	0.986101i	$-0.446868\pi$
$599$	27.0004	−	15.5887i	1.10321	−	0.636936i	0.937061	+	0.349165i	$0.113535\pi$
$600$	−15.0940	−	0.0512168i	−0.616211	−	0.00209092i
$601$	−23.2036	+	40.1898i	−0.946494	+	1.63938i	−0.193763	+	0.981048i	$0.562069\pi$
$601$	−23.2036	+	40.1898i	−0.946494	+	1.63938i	−0.752731	+	0.658328i	$0.771264\pi$
$602$	−5.73672			−0.233811
$603$	−6.02352	+	5.94231i	−0.245297	+	0.241990i
$604$	25.9364	+	25.9364i	1.05534	+	1.05534i
$605$	−0.00879817	+	0.00235746i	−0.000357696	+	9.58445e-5i
$606$	−1.17727	+	2.02320i	−0.0478232	+	0.0821870i
$607$	3.68979	+	6.39090i	0.149764	+	0.259399i	0.931140	−	0.364662i	$-0.118815\pi$
$607$	3.68979	+	6.39090i	0.149764	+	0.259399i	−0.781376	+	0.624060i	$0.785482\pi$
$608$	10.6397	+	18.4285i	0.431496	+	0.747374i
$609$	22.9689	+	13.3652i	0.930748	+	0.541587i
$610$	0.562264	+	0.324623i	0.0227654	+	0.0131436i
$611$	39.6996	−	0.630667i	1.60607	−	0.0255140i
$612$	41.3665	+	0.280732i	1.67214	+	0.0113479i
$613$	9.22313	+	9.22313i	0.372519	+	0.372519i	0.868394	−	0.495875i	$-0.165153\pi$
$613$	9.22313	+	9.22313i	0.372519	+	0.372519i	−0.495875	+	0.868394i	$0.665153\pi$
$614$	10.8461	+	6.26200i	0.437713	+	0.252714i
$615$	−1.95973	+	1.94648i	−0.0790240	+	0.0784896i
$616$	4.92059	−	18.3639i	0.198256	−	0.739902i
$617$	11.8107	+	3.16466i	0.475480	+	0.127404i	0.488597	−	0.872510i	$-0.337509\pi$
$617$	11.8107	+	3.16466i	0.475480	+	0.127404i	−0.0131172	+	0.999914i	$0.504175\pi$
$618$	−7.35970	+	4.21589i	−0.296051	+	0.169588i
$619$	4.10240	+	15.3104i	0.164889	+	0.615375i	0.998054	+	0.0623509i	$0.0198598\pi$
$619$	4.10240	+	15.3104i	0.164889	+	0.615375i	−0.833165	+	0.553025i	$0.813474\pi$
$620$			0.256811i			0.0103138i
$621$	1.72659	+	0.481527i	0.0692855	+	0.0193230i
$622$	5.17998	−	5.17998i	0.207698	−	0.207698i
$623$	4.50217	−	7.79798i	0.180376	−	0.312420i
$624$	8.77165	+	14.7639i	0.351147	+	0.591030i
$625$	12.1553	+	21.0536i	0.486211	+	0.842143i
$626$	12.4850	+	3.34535i	0.499002	+	0.133707i
$627$	18.0462	−	17.9242i	0.720697	−	0.715823i
$628$	−5.69752	−	3.28946i	−0.227356	−	0.131264i
$629$	8.05090	−	8.05090i	0.321011	−	0.321011i
$630$	−0.942670	−	0.259457i	−0.0375569	−	0.0103370i
$631$	−5.24304	+	5.24304i	−0.208722	+	0.208722i	−0.803724	−	0.595002i	$-0.797151\pi$
$631$	−5.24304	+	5.24304i	−0.208722	+	0.208722i	0.595002	+	0.803724i	$0.297151\pi$
$632$	−13.0135	+	3.48695i	−0.517648	+	0.138703i
$633$	−14.8207	+	3.91734i	−0.589070	+	0.155700i
$634$	−1.59255	+	0.919457i	−0.0632481	+	0.0365163i
$635$	0.674319	−	2.51659i	0.0267595	−	0.0998679i
$636$	−5.80937	+	1.53551i	−0.230356	+	0.0608868i
$637$	−12.6882	+	3.61676i	−0.502726	+	0.143301i
$638$			7.23206i			0.286320i
$639$	−9.15456	+	2.38649i	−0.362149	+	0.0944081i
$640$	−2.38628			−0.0943258
$641$	8.32383	−	14.4173i	0.328772	−	0.569449i	−0.653497	−	0.756929i	$-0.726699\pi$
$641$	8.32383	−	14.4173i	0.328772	−	0.569449i	0.982268	+	0.187480i	$0.0600320\pi$
$642$	−0.0216024	+	6.36641i	−0.000852580	+	0.251262i
$643$	−1.51973	+	5.67171i	−0.0599323	+	0.223670i	−0.989396	−	0.145243i	$-0.953603\pi$
$643$	−1.51973	+	5.67171i	−0.0599323	+	0.223670i	0.929464	+	0.368914i	$0.120270\pi$
$644$	−0.519987	+	1.94062i	−0.0204904	+	0.0764710i
$645$	1.21967	−	0.698669i	0.0480244	−	0.0275101i
$646$	7.97123	−	13.8066i	0.313624	−	0.543213i
$647$	−46.1140			−1.81293			−0.906464	−	0.422283i	$-0.861229\pi$
$647$	−46.1140			−1.81293			−0.906464	+	0.422283i	$0.861229\pi$
$648$	4.30486	−	15.2357i	0.169111	−	0.598516i
$649$			31.8013i			1.24831i
$650$	−4.03721	+	7.25644i	−0.158352	+	0.284621i
$651$	0.993728	−	3.65894i	0.0389473	−	0.143405i
$652$	0.902847	−	3.36947i	0.0353582	−	0.131959i
$653$	−21.8245	+	12.6004i	−0.854059	+	0.493091i	−0.862018	−	0.506877i	$-0.830800\pi$
$653$	−21.8245	+	12.6004i	−0.854059	+	0.493091i	0.00795932	+	0.999968i	$0.497466\pi$
$654$	−2.36846	−	2.38459i	−0.0926140	−	0.0932447i
$655$	2.00040	−	0.536004i	0.0781619	−	0.0209434i
$656$	14.4416	−	14.4416i	0.563851	−	0.563851i
$657$	6.17510	−	1.60978i	0.240914	−	0.0628035i
$658$	11.8190	−	11.8190i	0.460754	−	0.460754i
$659$	−0.285017	−	0.164555i	−0.0111027	−	0.00641015i	0.494438	−	0.869213i	$-0.335374\pi$
$659$	−0.285017	−	0.164555i	−0.0111027	−	0.00641015i	−0.505541	+	0.862803i	$0.668707\pi$
$660$	0.561184	+	2.12316i	0.0218441	+	0.0826439i
$661$	−35.6548	−	9.55367i	−1.38681	−	0.371595i	−0.513220	−	0.858257i	$-0.671548\pi$
$661$	−35.6548	−	9.55367i	−1.38681	−	0.371595i	−0.873590	+	0.486662i	$0.838214\pi$
$662$	−3.98571	−	6.90346i	−0.154909	−	0.268311i
$663$	23.6126	−	42.1043i	0.917039	−	1.63519i
$664$	13.1631	−	22.7991i	0.510827	−	0.884778i
$665$	2.19903	−	2.19903i	0.0852747	−	0.0852747i
$666$	−1.01507	−	1.78603i	−0.0393330	−	0.0692071i
$667$		−	1.62111i		−	0.0627695i
$668$	−8.83245	−	32.9632i	−0.341738	−	1.27538i
$669$	−0.133613	+	39.3768i	−0.00516577	+	1.52239i
$670$	−0.271952	−	0.0728692i	−0.0105064	−	0.00281518i
$671$	−5.57226	+	20.7960i	−0.215115	+	0.802819i
$672$	26.1767	+	7.10930i	1.00979	+	0.274247i
$673$	−32.4557	−	18.7383i	−1.25107	−	0.722308i	−0.279752	−	0.960072i	$-0.590252\pi$
$673$	−32.4557	−	18.7383i	−1.25107	−	0.722308i	−0.971323	+	0.237764i	$0.923585\pi$
$674$	0.236597	+	0.236597i	0.00911336	+	0.00911336i
$675$	−24.9306	+	6.40887i	−0.959580	+	0.246677i
$676$	23.1785	−	0.736612i	0.891482	−	0.0283312i
$677$	10.2016	+	5.88988i	0.392078	+	0.226366i	0.683060	−	0.730362i	$-0.260649\pi$
$677$	10.2016	+	5.88988i	0.392078	+	0.226366i	−0.290982	+	0.956728i	$0.593982\pi$
$678$	10.8523	−	6.21656i	0.416779	−	0.238746i
$679$	−4.42800	−	7.66952i	−0.169931	−	0.294329i
$680$	1.45987	+	2.52856i	0.0559833	+	0.0969659i
$681$	−11.1653	−	0.0378860i	−0.427855	−	0.00145179i
$682$	0.996666	−	0.267056i	0.0381643	−	0.0102261i
$683$	−19.1452	−	19.1452i	−0.732572	−	0.732572i	0.238556	−	0.971129i	$-0.423326\pi$
$683$	−19.1452	−	19.1452i	−0.732572	−	0.732572i	−0.971129	+	0.238556i	$0.923326\pi$
$684$	16.6731	+	16.9009i	0.637511	+	0.646223i
$685$	−2.40912			−0.0920477
$686$	2.53537	−	4.39138i	0.0968007	−	0.167664i
$687$	5.76913	−	9.91458i	0.220106	−	0.378265i
$688$	−9.00083	+	5.19663i	−0.343153	+	0.198120i
$689$	−1.70703	+	6.80105i	−0.0650326	+	0.259100i
$690$	0.0152413	+	0.0576633i	0.000580227	+	0.00219520i
$691$	−24.1482	+	6.47049i	−0.918640	+	0.246149i	−0.687004	−	0.726654i	$-0.741075\pi$
$691$	−24.1482	+	6.47049i	−0.918640	+	0.246149i	−0.231636	+	0.972803i	$0.574408\pi$
$692$			19.0598i			0.724544i
$693$	0.220027	−	32.4214i	0.00835812	−	1.23159i
$694$	7.67023	+	7.67023i	0.291158	+	0.291158i
$695$	0.677456	+	2.52830i	0.0256974	+	0.0959039i
$696$	−14.3185	−	0.0485854i	−0.542742	−	0.00184163i
$697$	−55.4543	−	14.8589i	−2.10048	−	0.562822i
$698$	−6.08850	+	3.51520i	−0.230453	+	0.133052i
$699$	−0.837571	+	3.08396i	−0.0316798	+	0.116646i
$700$	−7.46738	−	27.8686i	−0.282240	−	1.05334i
$701$	30.1677			1.13942			0.569709	−	0.821846i	$-0.307056\pi$
$701$	30.1677			1.13942			0.569709	+	0.821846i	$0.307056\pi$
$702$	−6.19393	−	6.12366i	−0.233775	−	0.231123i
$703$	6.53429			0.246446
$704$	−2.80137	−	10.4549i	−0.105581	−	0.394033i
$705$	−1.07339	+	3.95224i	−0.0404261	+	0.148850i
$706$	−13.2478	+	7.64862i	−0.498588	+	0.287860i
$707$	−9.16738	−	2.45639i	−0.344775	−	0.0923821i
$708$	−29.6829	−	0.100720i	−1.11555	−	0.00378528i
$709$	1.84448	+	6.88371i	0.0692711	+	0.258523i	0.991873	−	0.127230i	$-0.0406085\pi$
$709$	1.84448	+	6.88371i	0.0692711	+	0.258523i	−0.922602	+	0.385753i	$0.873942\pi$
$710$	−0.222592	−	0.222592i	−0.00835374	−	0.00835374i
$711$	−19.9752	+	11.3526i	−0.749127	+	0.425756i
$712$			4.85163i			0.181823i
$713$	−0.223408	+	0.0598621i	−0.00836671	+	0.00224185i
$714$	−5.19306	−	19.6472i	−0.194345	−	0.735278i
$715$	2.48559	+	0.623871i	0.0929559	+	0.0233314i
$716$	−3.39683	+	1.96116i	−0.126945	+	0.0732920i
$717$	−6.09238	+	10.4701i	−0.227524	+	0.391013i
$718$	4.16834	−	7.21978i	0.155561	−	0.269440i
$719$	−10.5900			−0.394939			−0.197469	−	0.980309i	$-0.563272\pi$
$719$	−10.5900			−0.394939			−0.197469	+	0.980309i	$0.563272\pi$
$720$	−1.71407	+	0.446837i	−0.0638794	+	0.0166526i
$721$	−24.3168	−	24.3168i	−0.905604	−	0.905604i
$722$	0.305469	−	0.0818501i	0.0113684	−	0.00304614i
$723$	48.3682	+	0.164123i	1.79883	+	0.00610378i
$724$	−14.0984	−	24.4192i	−0.523963	−	0.907531i
$725$	11.6401	+	20.1613i	0.432303	+	0.748771i
$726$	−0.0296404	+	0.0169791i	−0.00110006	+	0.000630152i
$727$	−6.67295	−	3.85263i	−0.247486	−	0.142886i	0.371127	−	0.928582i	$-0.378972\pi$
$727$	−6.67295	−	3.85263i	−0.247486	−	0.142886i	−0.618613	+	0.785696i	$0.712305\pi$
$728$	14.4082	−	14.8734i	0.534004	−	0.551245i
$729$	0.549657	−	26.9944i	0.0203577	−	0.999793i
$730$	0.150147	+	0.150147i	0.00555719	+	0.00555719i
$731$	25.3013	+	14.6077i	0.935802	+	0.540285i
$732$	−19.3931	−	5.26695i	−0.716788	−	0.194672i
$733$	3.04971	−	11.3817i	0.112643	−	0.420391i	−0.886456	−	0.462812i	$-0.846840\pi$
$733$	3.04971	−	11.3817i	0.112643	−	0.420391i	0.999100	+	0.0424210i	$0.0135071\pi$
$734$	−10.0329	−	2.68829i	−0.370319	−	0.0992268i
$735$	0.00461771	−	1.36088i	0.000170327	−	0.0501967i
$736$	−0.428264	−	1.59830i	−0.0157860	−	0.0589142i
$737$		−	9.33628i		−	0.343906i
$738$	−5.24006	+	8.93545i	−0.192889	+	0.328919i
$739$	24.8595	−	24.8595i	0.914470	−	0.914470i	−0.0821501	−	0.996620i	$-0.526179\pi$
$739$	24.8595	−	24.8595i	0.914470	−	0.914470i	0.996620	+	0.0821501i	$0.0261787\pi$
$740$	−0.282087	+	0.488588i	−0.0103697	+	0.0179609i
$741$	26.6687	−	7.50411i	0.979698	−	0.275670i
$742$	1.47594	+	2.55640i	0.0541835	+	0.0938485i
$743$	27.9519	+	7.48970i	1.02546	+	0.274770i	0.732074	−	0.681225i	$-0.238552\pi$
$743$	27.9519	+	7.48970i	1.02546	+	0.274770i	0.293382	+	0.955995i	$0.405219\pi$
$744$	0.522040	+	1.97506i	0.0191389	+	0.0724093i
$745$	−2.66469	−	1.53846i	−0.0976266	−	0.0563647i
$746$	−0.288294	+	0.288294i	−0.0105552	+	0.0105552i
$747$	11.9140	−	43.2865i	0.435911	−	1.58377i
$748$	−32.2760	+	32.2760i	−1.18013	+	1.18013i
$749$	−24.9333	+	6.68086i	−0.911043	+	0.244113i
$750$	−1.21281	−	1.22107i	−0.0442854	−	0.0445870i
$751$	−5.93020	+	3.42380i	−0.216396	+	0.124936i	−0.604280	−	0.796772i	$-0.706539\pi$
$751$	−5.93020	+	3.42380i	−0.216396	+	0.124936i	0.387884	+	0.921708i	$0.373206\pi$
$752$	7.83758	−	29.2502i	0.285807	−	1.06665i
$753$	−5.31837	+	19.5824i	−0.193812	+	0.713623i
$754$	−3.82978	+	6.88362i	−0.139472	+	0.250687i
$755$			4.41500i			0.160678i
$756$	30.2611	+	0.308054i	1.10058	+	0.0112038i
$757$	−45.8994			−1.66824			−0.834120	−	0.551583i	$-0.814024\pi$
$757$	−45.8994			−1.66824			−0.834120	+	0.551583i	$0.814024\pi$
$758$	1.20131	−	2.08073i	0.0436335	−	0.0755754i
$759$	−1.71620	+	0.983097i	−0.0622940	+	0.0356842i
$760$	−0.433689	+	1.61855i	−0.0157316	+	0.0587109i
$761$	−9.36788	+	34.9614i	−0.339585	+	1.26735i	0.559226	+	0.829015i	$0.311098\pi$
$761$	−9.36788	+	34.9614i	−0.339585	+	1.26735i	−0.898812	+	0.438335i	$0.855568\pi$
$762$	0.0331537	−	9.77067i	0.00120103	−	0.353954i
$763$	6.81346	−	11.8013i	0.246664	−	0.427234i
$764$	5.38784			0.194925
$765$	3.49689	+	3.54468i	0.126430	+	0.128158i
$766$		−	0.886162i		−	0.0320183i
$767$	−16.8406	+	30.2691i	−0.608078	+	1.09295i
$768$	2.29880	−	0.607610i	0.0829509	−	0.0219252i
$769$	−11.2319	+	41.9181i	−0.405033	+	1.51160i	0.398961	+	0.916968i	$0.369371\pi$
$769$	−11.2319	+	41.9181i	−0.405033	+	1.51160i	−0.803994	+	0.594637i	$0.797296\pi$
$770$	0.934293	−	0.539414i	0.0336696	−	0.0194391i
$771$	−24.6885	+	6.52557i	−0.889136	+	0.235013i
$772$	42.2686	−	11.3258i	1.52128	−	0.407625i
$773$	−26.7611	+	26.7611i	−0.962528	+	0.962528i	−0.999323	−	0.0367944i	$-0.988285\pi$
$773$	−26.7611	+	26.7611i	−0.962528	+	0.962528i	0.0367944	+	0.999323i	$0.488285\pi$
$774$	3.75261	−	3.70202i	0.134885	−	0.133066i
$775$	2.34864	−	2.34864i	0.0843656	−	0.0843656i
$776$	4.13242	+	2.38585i	0.148345	+	0.0856471i
$777$	5.90964	−	5.86967i	0.212007	−	0.210573i
$778$	−10.7510	−	2.88071i	−0.385441	−	0.103279i
$779$	−16.4741	−	28.5339i	−0.590244	−	1.02233i
$780$	−0.590186	+	2.31805i	−0.0211321	+	0.0829994i
$781$	5.21940	−	9.04027i	0.186765	−	0.323486i
$782$	−0.876590	+	0.876590i	−0.0313468	+	0.0313468i
$783$	−23.6497	+	6.07959i	−0.845173	+	0.217267i
$784$			10.0626i			0.359378i
$785$	−0.204954	−	0.764900i	−0.00731513	−	0.0273004i
$786$	6.73919	−	3.86044i	0.240379	−	0.137698i
$787$	16.9135	+	4.53196i	0.602901	+	0.161547i	0.547343	−	0.836909i	$-0.315639\pi$
$787$	16.9135	+	4.53196i	0.602901	+	0.161547i	0.0555584	+	0.998455i	$0.482306\pi$
$788$	−9.58758	+	35.7813i	−0.341543	+	1.27466i
$789$	34.4460	−	34.2130i	1.22631	−	1.21801i
$790$	−0.662082	−	0.382253i	−0.0235558	−	0.0136000i
$791$	35.8564	+	35.8564i	1.27491	+	1.27491i
$792$	8.63183	+	15.1879i	0.306719	+	0.539678i
$793$	−16.3164	+	16.8432i	−0.579414	+	0.598120i
$794$	−7.96367	−	4.59782i	−0.282620	−	0.163171i
$795$	−0.625137	−	0.363757i	−0.0221713	−	0.0129011i
$796$	13.1352	+	22.7508i	0.465564	+	0.806381i
$797$	10.4651	+	18.1261i	0.370692	+	0.642058i	0.989672	−	0.143349i	$-0.0457871\pi$
$797$	10.4651	+	18.1261i	0.370692	+	0.642058i	−0.618980	+	0.785407i	$0.712454\pi$
$798$	5.86565	−	10.0805i	0.207642	−	0.356844i
$799$	−82.2222	+	22.0314i	−2.90881	+	0.779414i
$800$	16.8026	+	16.8026i	0.594061	+	0.594061i
$801$	2.08715	+	8.00631i	0.0737460	+	0.282889i
$802$	−4.78168			−0.168847
$803$	−3.52069	+	6.09801i	−0.124242	+	0.215194i
$804$	8.71437	+	0.0295695i	0.307332	+	0.00104284i
$805$	−0.209427	+	0.120913i	−0.00738133	+	0.00426161i
$806$	1.09007	+	0.273602i	0.0383961	+	0.00963721i
$807$	33.4207	+	9.07671i	1.17647	+	0.319515i
$808$	4.93948	−	1.32353i	0.173770	−	0.0465616i
$809$			9.55584i			0.335965i	0.985790	+	0.167983i	$0.0537253\pi$
$809$			9.55584i			0.335965i	−0.985790	+	0.167983i	$0.946275\pi$
$810$	0.784070	−	0.438603i	0.0275494	−	0.0154109i
$811$	11.1766	+	11.1766i	0.392464	+	0.392464i	0.875565	−	0.483101i	$-0.160490\pi$
$811$	11.1766	+	11.1766i	0.392464	+	0.392464i	−0.483101	+	0.875565i	$0.660490\pi$
$812$	−7.08372	−	26.4368i	−0.248590	−	0.927750i
$813$	−15.2436	−	26.6108i	−0.534617	−	0.933283i
$814$	2.18952	+	0.586680i	0.0767426	+	0.0205631i
$815$	0.363625	−	0.209939i	0.0127372	−	0.00735385i
$816$	−25.9453	−	26.1220i	−0.908268	−	0.914453i
$817$	4.33958	+	16.1955i	0.151823	+	0.566609i
$818$	1.97769			0.0691484
$819$	17.3784	−	30.7429i	0.607251	−	1.07424i
$820$	2.84475			0.0993430
$821$	8.73131	+	32.5857i	0.304725	+	1.13725i	0.933182	+	0.359405i	$0.117020\pi$
$821$	8.73131	+	32.5857i	0.304725	+	1.13725i	−0.628457	+	0.777844i	$0.716313\pi$
$822$	−8.73478	+	2.30874i	−0.304660	+	0.0805265i
$823$	31.5574	−	18.2197i	1.10002	−	0.635098i	0.163795	−	0.986494i	$-0.447626\pi$
$823$	31.5574	−	18.2197i	1.10002	−	0.635098i	0.936227	+	0.351396i	$0.114293\pi$
$824$	17.8978	+	4.79571i	0.623501	+	0.167067i
$825$	14.2849	−	24.5494i	0.497337	−	0.854701i
$826$	3.77408	+	14.0851i	0.131317	+	0.490082i
$827$	15.6509	+	15.6509i	0.544236	+	0.544236i	0.924768	−	0.380532i	$-0.124259\pi$
$827$	15.6509	+	15.6509i	0.544236	+	0.544236i	−0.380532	+	0.924768i	$0.624259\pi$
$828$	−0.912176	−	1.60499i	−0.0317003	−	0.0557773i
$829$			34.8622i			1.21081i	0.795916	+	0.605407i	$0.206990\pi$
$829$			34.8622i			1.21081i	−0.795916	+	0.605407i	$0.793010\pi$
$830$	1.44299	−	0.386648i	0.0500869	−	0.0134208i
$831$	1.37057	−	1.36130i	0.0475447	−	0.0472231i
$832$	2.87004	−	11.4347i	0.0995007	−	0.396425i
$833$	24.4963	−	14.1429i	0.848746	−	0.490023i
$834$	4.87922	+	8.51767i	0.168953	+	0.294943i
$835$	2.05381	−	3.55731i	0.0710751	−	0.123106i
$836$	−26.1959			−0.906006
$837$	1.71115	+	3.03473i	0.0591460	+	0.104895i
$838$	−2.89778	−	2.89778i	−0.100102	−	0.100102i
$839$	19.7987	−	5.30504i	0.683527	−	0.183150i	0.0996863	−	0.995019i	$-0.468216\pi$
$839$	19.7987	−	5.30504i	0.683527	−	0.183150i	0.583840	+	0.811868i	$0.301549\pi$
$840$	1.06169	+	1.85340i	0.0366319	+	0.0639484i
$841$	−3.45793	−	5.98931i	−0.119239	−	0.206528i
$842$	−4.13889	−	7.16877i	−0.142636	−	0.247052i
$843$	−0.0491073	+	14.4723i	−0.00169135	+	0.498453i
$844$	13.6730	+	7.89412i	0.470644	+	0.271727i
$845$	2.03546	+	1.91008i	0.0700221	+	0.0657086i
$846$	−0.104229	+	15.3584i	−0.00358346	+	0.528031i
$847$	−0.0979331	−	0.0979331i	−0.00336502	−	0.00336502i
$848$	4.63146	+	2.67397i	0.159045	+	0.0918246i
$849$	−5.42440	−	20.5224i	−0.186165	−	0.704329i
$850$	4.60769	−	17.1961i	0.158043	−	0.589823i
$851$	−0.490793	−	0.131508i	−0.0168242	−	0.00450802i
$852$	8.42155	+	4.90036i	0.288518	+	0.167884i
$853$	−13.2720	−	49.5319i	−0.454426	−	1.69594i	−0.689770	−	0.724029i	$-0.742288\pi$
$853$	−13.2720	−	49.5319i	−0.454426	−	1.69594i	0.235344	−	0.971912i	$-0.424378\pi$
$854$			9.87201i			0.337813i
$855$	−0.0193926	+	2.85755i	−0.000663214	+	0.0977261i
$856$	9.83461	−	9.83461i	0.336140	−	0.336140i
$857$	10.0868	−	17.4708i	0.344557	−	0.596791i	−0.640716	−	0.767778i	$-0.721362\pi$
$857$	10.0868	−	17.4708i	0.344557	−	0.596791i	0.985273	+	0.170987i	$0.0546957\pi$
$858$	9.60993	−	0.120048i	0.328077	−	0.00409838i
$859$	−3.53548	−	6.12362i	−0.120629	−	0.208935i	0.799387	−	0.600816i	$-0.205158\pi$
$859$	−3.53548	−	6.12362i	−0.120629	−	0.208935i	−0.920016	+	0.391881i	$0.871824\pi$
$860$	−1.39833	−	0.374680i	−0.0476825	−	0.0127765i
$861$	−40.5308	−	11.0077i	−1.38129	−	0.375143i
$862$	−4.29107	−	2.47745i	−0.146154	−	0.0843822i
$863$	29.7564	−	29.7564i	1.01292	−	1.01292i	0.0130054	−	0.999915i	$-0.495860\pi$
$863$	29.7564	−	29.7564i	1.01292	−	1.01292i	0.999915	−	0.0130054i	$-0.00413988\pi$
$864$	−21.7110	+	12.2419i	−0.738622	+	0.416477i
$865$	−1.62222	+	1.62222i	−0.0551570	+	0.0551570i
$866$	−3.10683	+	0.832472i	−0.105574	+	0.0282886i
$867$	−19.4078	+	71.4600i	−0.659122	+	2.42691i
$868$	−3.38174	+	1.95245i	−0.114784	+	0.0662704i
$869$	6.56151	−	24.4879i	0.222584	−	0.830694i
$870$	−0.572583	−	0.576482i	−0.0194124	−	0.0195446i
$871$	4.94409	−	8.88647i	0.167524	−	0.301106i
$872$			7.34233i			0.248643i
$873$	7.84582	+	2.15945i	0.265541	+	0.0730865i
$874$	−0.711460			−0.0240655
$875$	3.48894	−	6.04303i	0.117948	−	0.204292i
$876$	−5.68066	−	3.30548i	−0.191932	−	0.111682i
$877$	8.53829	−	31.8653i	0.288318	−	1.07602i	−0.658063	−	0.752963i	$-0.728624\pi$
$877$	8.53829	−	31.8653i	0.288318	−	1.07602i	0.946381	−	0.323053i	$-0.104709\pi$
$878$	−0.637725	+	2.38002i	−0.0215222	+	0.0803218i
$879$	18.7554	+	10.9135i	0.632604	+	0.368102i
$880$	0.977261	−	1.69267i	0.0329435	−	0.0570598i
$881$	9.86139			0.332239			0.166119	−	0.986106i	$-0.446876\pi$
$881$	9.86139			0.332239			0.166119	+	0.986106i	$0.446876\pi$
$882$	−1.28743	−	4.93857i	−0.0433500	−	0.166290i
$883$		−	9.88678i		−	0.332717i	−0.986065	−	0.166358i	$-0.946799\pi$
$883$		−	9.88678i		−	0.332717i	0.986065	−	0.166358i	$-0.0532008\pi$
$884$	−47.8130	+	13.6290i	−1.60812	+	0.458393i
$885$	−2.51780	−	2.53495i	−0.0846350	−	0.0852113i
$886$	−1.47977	+	5.52258i	−0.0497139	+	0.185535i
$887$	20.2670	−	11.7011i	0.680498	−	0.392886i	−0.119545	−	0.992829i	$-0.538144\pi$
$887$	20.2670	−	11.7011i	0.680498	−	0.392886i	0.800043	+	0.599943i	$0.204810\pi$
$888$	−1.17626	+	4.33102i	−0.0394726	+	0.145339i
$889$	38.2656	−	10.2532i	1.28339	−	0.343883i
$890$	−0.194673	+	0.194673i	−0.00652544	+	0.00652544i
$891$	20.7783	+	21.3501i	0.696098	+	0.715256i
$892$	28.6767	−	28.6767i	0.960166	−	0.960166i
$893$	−42.3073	−	24.4261i	−1.41576	−	0.817389i
$894$	−11.1357	−	3.02435i	−0.372435	−	0.101149i
$895$	−0.456029	−	0.122193i	−0.0152434	−	0.00408445i
$896$	−18.1421	−	31.4230i	−0.606084	−	1.04977i
$897$	−2.15412	+	0.0269095i	−0.0719239	+	0.000898481i
$898$	−6.75476	+	11.6996i	−0.225409	+	0.390420i
$899$	2.22797	−	2.22797i	0.0743070	−	0.0743070i
$900$	22.8689	+	13.4111i	0.762297	+	0.447037i
$901$		−	15.0330i		−	0.500823i
$902$	−2.95824	−	11.0403i	−0.0984986	−	0.367602i
$903$	18.4730	+	10.7491i	0.614742	+	0.357708i
$904$	−26.3913	−	7.07154i	−0.877763	−	0.235196i
$905$	0.878420	−	3.27831i	0.0291997	−	0.108975i
$906$	4.23104	+	16.0075i	0.140567	+	0.531815i
$907$	41.8979	+	24.1897i	1.39120	+	0.803207i	0.993448	−	0.114287i	$-0.0364584\pi$
$907$	41.8979	+	24.1897i	1.39120	+	0.803207i	0.397748	+	0.917495i	$0.369792\pi$
$908$	8.13128	+	8.13128i	0.269846	+	0.269846i
$909$	7.58190	−	4.30907i	0.251476	−	0.142923i
$910$	1.17493	−	0.0186649i	0.0389485	−	0.000618735i
$911$	−29.2362	−	16.8795i	−0.968638	−	0.559244i	−0.0698176	−	0.997560i	$-0.522242\pi$
$911$	−29.2362	−	16.8795i	−0.968638	−	0.559244i	−0.898821	+	0.438316i	$0.855575\pi$
$912$	0.0716964	−	21.1295i	0.00237411	−	0.699668i
$913$	24.7694	+	42.9019i	0.819747	+	1.41984i
$914$	5.88158	+	10.1872i	0.194545	+	0.336962i
$915$	−1.20230	−	2.09886i	−0.0397469	−	0.0693862i
$916$	−11.4115	+	3.05770i	−0.377047	+	0.101029i
$917$	22.2666	+	22.2666i	0.735307	+	0.735307i
$918$	16.0757	+	9.50081i	0.530578	+	0.313573i
$919$	18.9562			0.625306			0.312653	−	0.949867i	$-0.398782\pi$
$919$	18.9562			0.625306			0.312653	+	0.949867i	$0.398782\pi$
$920$	0.0651490	−	0.112841i	0.00214790	−	0.00372027i
$921$	−23.1925	−	40.4872i	−0.764217	−	1.33410i
$922$	7.33188	−	4.23307i	0.241463	−	0.139409i
$923$	9.75527	−	5.84075i	0.321099	−	0.192251i
$924$	−23.6917	+	23.5315i	−0.779401	+	0.774129i
$925$	7.04813	−	1.88854i	0.231741	−	0.0620949i
$926$		−	11.0565i		−	0.363339i
$927$	31.5986	+	0.214443i	1.03784	+	0.00704323i
$928$	15.9393	+	15.9393i	0.523233	+	0.523233i
$929$	14.5530	+	54.3124i	0.477467	+	1.78193i	0.611819	+	0.790998i	$0.290438\pi$
$929$	14.5530	+	54.3124i	0.477467	+	1.78193i	−0.134351	+	0.990934i	$0.542895\pi$
$930$	−0.0583028	+	0.100197i	−0.00191182	+	0.00328558i
$931$	15.6802	+	4.20150i	0.513898	+	0.137699i
$932$	2.85032	−	1.64564i	0.0933655	−	0.0539046i
$933$	−26.3861	+	6.97426i	−0.863842	+	0.228327i
$934$	1.20755	+	4.50664i	0.0395123	+	0.147462i
$935$	−5.49415			−0.179678
$936$	0.173119	+	19.0272i	0.00565859	+	0.621923i
$937$	14.8067			0.483715			0.241858	−	0.970312i	$-0.422243\pi$
$937$	14.8067			0.483715			0.241858	+	0.970312i	$0.422243\pi$
$938$	−1.10800	−	4.13512i	−0.0361775	−	0.135016i
$939$	−33.9350	−	34.1661i	−1.10743	−	1.11497i
$940$	3.65283	−	2.10896i	0.119142	−	0.0687867i
$941$	−56.4212	−	15.1180i	−1.83928	−	0.492833i	−0.840481	−	0.541841i	$-0.817727\pi$
$941$	−56.4212	−	15.1180i	−1.83928	−	0.492833i	−0.998798	+	0.0490079i	$0.984394\pi$
$942$	−1.47613	−	2.57689i	−0.0480951	−	0.0839597i
$943$	0.663106	+	2.47474i	0.0215937	+	0.0805887i
$944$	18.6805	+	18.6805i	0.607998	+	0.607998i
$945$	2.54936	+	2.60180i	0.0829307	+	0.0846366i
$946$			5.81644i			0.189109i
$947$	−26.8408	+	7.19197i	−0.872209	+	0.233708i	−0.667043	−	0.745019i	$-0.732440\pi$
$947$	−26.8408	+	7.19197i	−0.872209	+	0.233708i	−0.205166	+	0.978727i	$0.565773\pi$
$948$	22.8359	+	6.20199i	0.741676	+	0.201431i
$949$	−6.58031	+	3.93981i	−0.213606	+	0.127892i
$950$	8.84824	−	5.10853i	0.287075	−	0.165743i
$951$	6.85102	+	0.0232468i	0.222160	+	0.000753829i
$952$	−22.1978	+	38.4477i	−0.719434	+	1.24610i
$953$	−3.20152			−0.103707			−0.0518536	−	0.998655i	$-0.516513\pi$
$953$	−3.20152			−0.103707			−0.0518536	+	0.998655i	$0.516513\pi$
$954$	−2.61517	−	0.719789i	−0.0846692	−	0.0233040i
$955$	0.458570	+	0.458570i	0.0148390	+	0.0148390i
$956$	12.0509	−	3.22903i	0.389754	−	0.104434i
$957$	13.5510	−	23.2881i	0.438041	−	0.752798i
$958$	4.12534	+	7.14530i	0.133284	+	0.230854i
$959$	−18.3157	−	31.7238i	−0.591446	−	1.02441i
$960$	1.05105	+	0.611587i	0.0339224	+	0.0197389i
$961$	26.4575	+	15.2752i	0.853467	+	0.492749i
$962$	1.77335	+	1.71789i	0.0571751	+	0.0553870i
$963$	11.9985	−	20.4602i	0.386648	−	0.659320i
$964$	−35.2248	−	35.2248i	−1.13451	−	1.13451i
$965$	4.56152	+	2.63360i	0.146841	+	0.0847785i
$966$	−0.643448	+	0.639096i	−0.0207026	+	0.0205626i
$967$	−7.87586	+	29.3931i	−0.253270	+	0.945218i	0.715774	+	0.698332i	$0.246074\pi$
$967$	−7.87586	+	29.3931i	−0.253270	+	0.945218i	−0.969044	+	0.246886i	$0.920593\pi$
$968$	0.0720816	+	0.0193142i	0.00231679	+	0.000620782i
$969$	−51.5383	+	29.5229i	−1.65565	+	0.948413i
$970$	0.0700812	+	0.261547i	0.00225017	+	0.00839776i
$971$		−	42.2849i		−	1.35699i	−0.734607	−	0.678493i	$-0.762633\pi$
$971$		−	42.2849i		−	1.35699i	0.734607	−	0.678493i	$-0.237367\pi$
$972$	−19.9938	+	19.3266i	−0.641300	+	0.619900i
$973$	−28.1427	+	28.1427i	−0.902214	+	0.902214i
$974$	−3.66719	+	6.35176i	−0.117504	+	0.203524i
$975$	26.5970	−	15.8020i	0.851785	−	0.506069i
$976$	8.94260	+	15.4890i	0.286246	+	0.495792i
$977$	27.9693	+	7.49435i	0.894817	+	0.239766i	0.676789	−	0.736177i	$-0.263371\pi$
$977$	27.9693	+	7.49435i	0.894817	+	0.239766i	0.218028	+	0.975943i	$0.430038\pi$
$978$	1.11721	−	1.10965i	0.0357244	−	0.0354828i
$979$	−7.90635	−	4.56473i	−0.252688	−	0.145890i
$980$	−0.991076	+	0.991076i	−0.0316588	+	0.0316588i
$981$	3.15864	+	12.1165i	0.100848	+	0.386851i
$982$	1.18418	−	1.18418i	0.0377888	−	0.0377888i
$983$	−13.2183	+	3.54183i	−0.421598	+	0.112967i	−0.463380	−	0.886160i	$-0.653363\pi$
$983$	−13.2183	+	3.54183i	−0.421598	+	0.112967i	0.0417814	+	0.999127i	$0.486697\pi$
$984$	21.8782	−	5.78275i	0.697452	−	0.184347i
$985$	−3.86144	+	2.22940i	−0.123036	+	0.0710347i
$986$	4.37096	−	16.3126i	0.139200	−	0.519500i
$987$	−60.2046	+	15.9130i	−1.91633	+	0.506517i
$988$	−24.9338	−	13.8722i	−0.793251	−	0.441335i
$989$		−	1.30379i		−	0.0414580i
$990$	−0.263062	+	0.955770i	−0.00836067	+	0.0303764i
$991$	30.2905			0.962210			0.481105	−	0.876663i	$-0.340236\pi$
$991$	30.2905			0.962210			0.481105	+	0.876663i	$0.340236\pi$
$992$	1.60805	−	2.78522i	0.0510555	−	0.0884307i
$993$	−0.100772	+	29.6982i	−0.00319789	+	0.942444i
$994$	1.23885	−	4.62344i	0.0392938	−	0.146647i
$995$	−0.818405	+	3.05433i	−0.0259452	+	0.0968287i
$996$	−40.1225	+	22.9836i	−1.27133	+	0.728263i
$997$	−3.40788	+	5.90262i	−0.107929	+	0.186938i	−0.914931	−	0.403610i	$-0.867755\pi$
$997$	−3.40788	+	5.90262i	−0.107929	+	0.186938i	0.807002	+	0.590548i	$0.201088\pi$
$998$	4.15103			0.131399
$999$	−0.0779086	+	7.65320i	−0.00246492	+	0.242136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.z.b.47.6	yes	44
3.2	odd	2		351.2.bc.b.8.6		44
9.4	even	3		351.2.bc.b.125.6		44
9.5	odd	6	inner	117.2.z.b.86.6	yes	44
13.5	odd	4	inner	117.2.z.b.83.6	yes	44
39.5	even	4		351.2.bc.b.278.6		44
117.5	even	12	inner	117.2.z.b.5.6	✓	44
117.31	odd	12		351.2.bc.b.44.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.z.b.5.6	✓	44	117.5	even	12	inner
117.2.z.b.47.6	yes	44	1.1	even	1	trivial
117.2.z.b.83.6	yes	44	13.5	odd	4	inner
117.2.z.b.86.6	yes	44	9.5	odd	6	inner
351.2.bc.b.8.6		44	3.2	odd	2
351.2.bc.b.44.6		44	117.31	odd	12
351.2.bc.b.125.6		44	9.4	even	3
351.2.bc.b.278.6		44	39.5	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.120326 - 0.449064i) q^{2} +(-0.453962 + 1.67150i) q^{3} +(1.54487 - 0.891932i) q^{4} +(0.207401 + 0.0555730i) q^{5} +(0.805235 + 0.00273231i) q^{6} +(0.845006 + 3.15361i) q^{7} +(-1.24390 - 1.24390i) q^{8} +(-2.58784 - 1.51760i) q^{9} -0.0998232i q^{10} +(3.19743 - 0.856749i) q^{11} +(0.789553 + 2.98716i) q^{12} +(3.49708 + 0.877749i) q^{13} +(1.31449 - 0.758923i) q^{14} +(-0.187043 + 0.321443i) q^{15} +(1.37495 - 2.38148i) q^{16} -7.72994 q^{17} +(-0.370113 + 1.34471i) q^{18} +(-3.13690 - 3.13690i) q^{19} +(0.369975 - 0.0991346i) q^{20} +(-5.65486 - 0.0191880i) q^{21} +(-0.769470 - 1.33276i) q^{22} +(0.172481 + 0.298746i) q^{23} +(2.64386 - 1.51450i) q^{24} +(-4.29020 - 2.47695i) q^{25} +(-0.0266253 - 1.67603i) q^{26} +(3.71145 - 3.63664i) q^{27} +(4.11823 + 4.11823i) q^{28} +(-4.06978 - 2.34969i) q^{29} +(0.166855 + 0.0453159i) q^{30} +(-0.173532 + 0.647632i) q^{31} +(-4.63327 - 1.24148i) q^{32} +(-0.0194547 + 5.73344i) q^{33} +(0.930115 + 3.47124i) q^{34} +0.701021i q^{35} +(-5.35147 - 0.0363175i) q^{36} +(-1.04152 + 1.04152i) q^{37} +(-1.03122 + 1.78612i) q^{38} +(-3.05470 + 5.44691i) q^{39} +(-0.188859 - 0.327113i) q^{40} +(7.17396 + 1.92226i) q^{41} +(0.671811 + 2.54170i) q^{42} +(-3.27315 - 1.88976i) q^{43} +(4.17546 - 4.17546i) q^{44} +(-0.452383 - 0.458565i) q^{45} +(0.113402 - 0.113402i) q^{46} +(10.6369 - 2.85014i) q^{47} +(3.35647 + 3.37933i) q^{48} +(-3.16901 + 1.82963i) q^{49} +(-0.596084 + 2.22462i) q^{50} +(3.50910 - 12.9206i) q^{51} +(6.18543 - 1.76315i) q^{52} +1.94478i q^{53} +(-2.07967 - 1.22909i) q^{54} +0.710763 q^{55} +(2.87166 - 4.97386i) q^{56} +(6.66736 - 3.81930i) q^{57} +(-0.565458 + 2.11032i) q^{58} +(-2.48647 + 9.27964i) q^{59} +(-0.00225110 + 0.663418i) q^{60} +(-3.25198 + 5.63260i) q^{61} +0.311709 q^{62} +(2.59916 - 9.44339i) q^{63} -3.26977i q^{64} +(0.676519 + 0.376389i) q^{65} +(2.57702 - 0.681147i) q^{66} +(0.729983 - 2.72433i) q^{67} +(-11.9418 + 6.89458i) q^{68} +(-0.577654 + 0.152683i) q^{69} +(0.314803 - 0.0843512i) q^{70} +(2.22986 - 2.22986i) q^{71} +(1.33127 + 5.10674i) q^{72} +(-1.50413 + 1.50413i) q^{73} +(0.593032 + 0.342387i) q^{74} +(6.08781 - 6.04664i) q^{75} +(-7.64400 - 2.04820i) q^{76} +(5.40370 + 9.35947i) q^{77} +(2.81357 + 0.716349i) q^{78} +(3.82930 - 6.63255i) q^{79} +(0.417511 - 0.417511i) q^{80} +(4.39380 + 7.85459i) q^{81} -3.45286i q^{82} +(3.87333 + 14.4555i) q^{83} +(-8.75314 + 5.01410i) q^{84} +(-1.60320 - 0.429576i) q^{85} +(-0.454775 + 1.69724i) q^{86} +(5.77503 - 5.73597i) q^{87} +(-5.04298 - 2.91157i) q^{88} +(-1.95017 - 1.95017i) q^{89} +(-0.151491 + 0.258326i) q^{90} +(0.186980 + 11.7701i) q^{91} +(0.532922 + 0.307682i) q^{92} +(-1.00374 - 0.584060i) q^{93} +(-2.55979 - 4.43368i) q^{94} +(-0.476269 - 0.824922i) q^{95} +(4.17847 - 7.18093i) q^{96} +(-2.62010 + 0.702053i) q^{97} +(1.20294 + 1.20294i) q^{98} +(-9.57463 - 2.63528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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