LMFDB - Embedded newform 462.2.bc.b.95.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.4
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.b.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(-1.29320 + 1.15223i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.572012 - 1.28476i) q^{5} +(-1.01074 - 1.40656i) q^{6} +(2.51605 + 0.818231i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.344742 - 2.98013i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(-1.29320 + 1.15223i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.572012 - 1.28476i) q^{5} +(-1.01074 - 1.40656i) q^{6} +(2.51605 + 0.818231i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.344742 - 2.98013i) q^{9} +(1.21793 + 0.703172i) q^{10} +(1.92213 + 2.70286i) q^{11} +(1.50450 - 0.858177i) q^{12} +(2.90286 - 3.99544i) q^{13} +(-1.07675 + 2.41674i) q^{14} +(0.740609 + 2.32054i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.333610 + 3.17409i) q^{17} +(2.92777 + 0.654361i) q^{18} +(0.221853 + 1.04374i) q^{19} +(-0.826629 + 1.13776i) q^{20} +(-4.19655 + 1.84092i) q^{21} +(-2.88897 + 1.62907i) q^{22} +(-2.41806 + 1.39607i) q^{23} +(0.696212 + 1.58597i) q^{24} +(2.02224 + 2.24593i) q^{25} +(3.67012 + 3.30459i) q^{26} +(2.98796 + 4.25113i) q^{27} +(-2.29095 - 1.32347i) q^{28} +(-0.161674 - 0.497582i) q^{29} +(-2.38524 + 0.493989i) q^{30} +(0.793258 - 0.353181i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.60000 - 1.28061i) q^{33} -3.19158 q^{34} +(2.49044 - 2.76448i) q^{35} +(-0.956812 + 2.84333i) q^{36} +(-3.96808 + 4.40700i) q^{37} +(-1.06121 + 0.111537i) q^{38} +(0.849678 + 8.51167i) q^{39} +(-1.04512 - 0.941028i) q^{40} +(3.44048 - 10.5887i) q^{41} +(-1.39218 - 4.36599i) q^{42} +6.81857i q^{43} +(-1.31817 - 3.04342i) q^{44} +(-3.63155 - 2.14758i) q^{45} +(-1.13567 - 2.55075i) q^{46} +(1.42258 + 6.69270i) q^{47} +(-1.65005 + 0.526620i) q^{48} +(5.66099 + 4.11742i) q^{49} +(-2.44501 + 1.77640i) q^{50} +(-4.08870 - 3.72035i) q^{51} +(-3.67012 + 3.30459i) q^{52} +(-0.170681 - 0.383356i) q^{53} +(-4.54017 + 2.52723i) q^{54} +(4.57200 - 0.923404i) q^{55} +(1.55569 - 2.14006i) q^{56} +(-1.48952 - 1.09414i) q^{57} +(0.511755 - 0.108777i) q^{58} +(2.03583 - 9.57781i) q^{59} +(-0.241957 - 2.42381i) q^{60} +(-3.13938 + 7.05115i) q^{61} +(0.268328 + 0.825830i) q^{62} +(3.30582 - 7.21606i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-3.47271 - 6.01492i) q^{65} +(1.85896 - 5.43547i) q^{66} +(3.24562 - 5.62158i) q^{67} +(0.333610 - 3.17409i) q^{68} +(1.51845 - 4.59156i) q^{69} +(2.48901 + 2.76576i) q^{70} +(1.01035 + 1.39063i) q^{71} +(-2.72774 - 1.24878i) q^{72} +(0.649602 - 3.05614i) q^{73} +(-3.96808 - 4.40700i) q^{74} +(-5.20299 - 0.574354i) q^{75} -1.06705i q^{76} +(2.62460 + 8.37326i) q^{77} +(-8.55386 - 0.0446884i) q^{78} +(7.75852 + 0.815454i) q^{79} +(1.04512 - 0.941028i) q^{80} +(-8.76231 - 2.05475i) q^{81} +(10.1711 + 4.52845i) q^{82} +(9.70225 - 7.04910i) q^{83} +(4.48759 - 0.928182i) q^{84} +(4.26878 + 1.38701i) q^{85} +(-6.78121 - 0.712734i) q^{86} +(0.782405 + 0.457188i) q^{87} +(3.16454 - 0.992822i) q^{88} +(-1.89178 + 1.09222i) q^{89} +(2.51541 - 3.38717i) q^{90} +(10.5729 - 7.67752i) q^{91} +(2.65548 - 0.862818i) q^{92} +(-0.618897 + 1.37075i) q^{93} +(-6.80474 + 0.715207i) q^{94} +(1.46785 + 0.312002i) q^{95} +(-0.351258 - 1.69606i) q^{96} +(-3.42729 - 2.49007i) q^{97} +(-4.68660 + 5.19960i) q^{98} +(8.71749 - 4.79639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	−1.29320	+	1.15223i	−0.746630	+	0.665239i
$3$	−1.29320	+	1.15223i	−0.746630	+	0.665239i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	0.572012	−	1.28476i	0.255812	−	0.574562i	−0.739294	−	0.673383i	$-0.764840\pi$
$5$	0.572012	−	1.28476i	0.255812	−	0.574562i	0.995105	+	0.0988210i	$0.0315071\pi$
$6$	−1.01074	−	1.40656i	−0.412633	−	0.574225i
$7$	2.51605	+	0.818231i	0.950977	+	0.309262i
$7$	2.51605	+	0.818231i	0.950977	+	0.309262i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.344742	−	2.98013i	0.114914	−	0.993375i
$10$	1.21793	+	0.703172i	0.385143	+	0.222363i
$11$	1.92213	+	2.70286i	0.579543	+	0.814942i
$11$	1.92213	+	2.70286i	0.579543	+	0.814942i
$12$	1.50450	−	0.858177i	0.434313	−	0.247734i
$13$	2.90286	−	3.99544i	0.805108	−	1.10814i	−0.186951	−	0.982369i	$-0.559861\pi$
$13$	2.90286	−	3.99544i	0.805108	−	1.10814i	0.992060	−	0.125767i	$-0.0401393\pi$
$14$	−1.07675	+	2.41674i	−0.287773	+	0.645900i
$15$	0.740609	+	2.32054i	0.191224	+	0.599161i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.333610	+	3.17409i	0.0809124	+	0.769830i	0.957470	+	0.288533i	$0.0931675\pi$
$17$	0.333610	+	3.17409i	0.0809124	+	0.769830i	−0.876557	+	0.481297i	$0.840166\pi$
$18$	2.92777	+	0.654361i	0.690081	+	0.154234i
$19$	0.221853	+	1.04374i	0.0508965	+	0.239449i	0.996241	−	0.0866237i	$-0.0276078\pi$
$19$	0.221853	+	1.04374i	0.0508965	+	0.239449i	−0.945345	+	0.326073i	$0.894274\pi$
$20$	−0.826629	+	1.13776i	−0.184840	+	0.254410i
$21$	−4.19655	+	1.84092i	−0.915762	+	0.401722i
$22$	−2.88897	+	1.62907i	−0.615930	+	0.347319i
$23$	−2.41806	+	1.39607i	−0.504201	+	0.291101i	−0.730447	−	0.682970i	$-0.760688\pi$
$23$	−2.41806	+	1.39607i	−0.504201	+	0.291101i	0.226246	+	0.974070i	$0.427355\pi$
$24$	0.696212	+	1.58597i	0.142114	+	0.323734i
$25$	2.02224	+	2.24593i	0.404449	+	0.449186i
$26$	3.67012	+	3.30459i	0.719771	+	0.648084i
$27$	2.98796	+	4.25113i	0.575034	+	0.818130i
$28$	−2.29095	−	1.32347i	−0.432948	−	0.250112i
$29$	−0.161674	−	0.497582i	−0.0300221	−	0.0923986i	0.934923	−	0.354851i	$-0.115469\pi$
$29$	−0.161674	−	0.497582i	−0.0300221	−	0.0923986i	−0.964945	+	0.262453i	$0.915469\pi$
$30$	−2.38524	+	0.493989i	−0.435484	+	0.0901897i
$31$	0.793258	−	0.353181i	0.142473	−	0.0634332i	−0.334261	−	0.942480i	$-0.608487\pi$
$31$	0.793258	−	0.353181i	0.142473	−	0.0634332i	0.476735	+	0.879047i	$0.341820\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−5.60000	−	1.28061i	−0.974835	−	0.222926i
$34$	−3.19158			−0.547351
$35$	2.49044	−	2.76448i	0.420961	−	0.467282i
$36$	−0.956812	+	2.84333i	−0.159469	+	0.473888i
$37$	−3.96808	+	4.40700i	−0.652348	+	0.724506i	−0.975048	−	0.221995i	$-0.928743\pi$
$37$	−3.96808	+	4.40700i	−0.652348	+	0.724506i	0.322699	+	0.946501i	$0.395410\pi$
$38$	−1.06121	+	0.111537i	−0.172151	+	0.0180938i
$39$	0.849678	+	8.51167i	0.136057	+	1.36296i
$40$	−1.04512	−	0.941028i	−0.165248	−	0.148790i
$41$	3.44048	−	10.5887i	0.537313	−	1.65368i	−0.201286	−	0.979533i	$-0.564512\pi$
$41$	3.44048	−	10.5887i	0.537313	−	1.65368i	0.738599	−	0.674146i	$-0.235488\pi$
$42$	−1.39218	−	4.36599i	−0.214818	−	0.673686i
$43$			6.81857i			1.03982i	0.854220	+	0.519911i	$0.174035\pi$
$43$			6.81857i			1.03982i	−0.854220	+	0.519911i	$0.825965\pi$
$44$	−1.31817	−	3.04342i	−0.198721	−	0.458814i
$45$	−3.63155	−	2.14758i	−0.541360	−	0.320142i
$46$	−1.13567	−	2.55075i	−0.167445	−	0.376087i
$47$	1.42258	+	6.69270i	0.207504	+	0.976231i	0.951405	+	0.307941i	$0.0996400\pi$
$47$	1.42258	+	6.69270i	0.207504	+	0.976231i	−0.743901	+	0.668290i	$0.767027\pi$
$48$	−1.65005	+	0.526620i	−0.238164	+	0.0760110i
$49$	5.66099	+	4.11742i	0.808714	+	0.588203i
$50$	−2.44501	+	1.77640i	−0.345776	+	0.251221i
$51$	−4.08870	−	3.72035i	−0.572533	−	0.520953i
$52$	−3.67012	+	3.30459i	−0.508955	+	0.458265i
$53$	−0.170681	−	0.383356i	−0.0234449	−	0.0526580i	0.901444	−	0.432897i	$-0.142509\pi$
$53$	−0.170681	−	0.383356i	−0.0234449	−	0.0526580i	−0.924888	+	0.380239i	$0.875842\pi$
$54$	−4.54017	+	2.52723i	−0.617838	+	0.343913i
$55$	4.57200	−	0.923404i	0.616488	−	0.124512i
$56$	1.55569	−	2.14006i	0.207887	−	0.285977i
$57$	−1.48952	−	1.09414i	−0.197292	−	0.144922i
$58$	0.511755	−	0.108777i	0.0671968	−	0.0142831i
$59$	2.03583	−	9.57781i	0.265042	−	1.24692i	−0.621182	−	0.783667i	$-0.713347\pi$
$59$	2.03583	−	9.57781i	0.265042	−	1.24692i	0.886224	−	0.463258i	$-0.153320\pi$
$60$	−0.241957	−	2.42381i	−0.0312366	−	0.312913i
$61$	−3.13938	+	7.05115i	−0.401956	+	0.902808i	0.593251	+	0.805017i	$0.297844\pi$
$61$	−3.13938	+	7.05115i	−0.401956	+	0.902808i	−0.995207	+	0.0977902i	$0.968823\pi$
$62$	0.268328	+	0.825830i	0.0340777	+	0.104881i
$63$	3.30582	−	7.21606i	0.416494	−	0.909138i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−3.47271	−	6.01492i	−0.430737	−	0.746059i
$66$	1.85896	−	5.43547i	0.228822	−	0.669060i
$67$	3.24562	−	5.62158i	0.396516	−	0.686786i	−0.596777	−	0.802407i	$-0.703552\pi$
$67$	3.24562	−	5.62158i	0.396516	−	0.686786i	0.993293	+	0.115621i	$0.0368858\pi$
$68$	0.333610	−	3.17409i	0.0404562	−	0.384915i
$69$	1.51845	−	4.59156i	0.182800	−	0.552759i
$70$	2.48901	+	2.76576i	0.297494	+	0.330572i
$71$	1.01035	+	1.39063i	0.119907	+	0.165038i	0.864751	−	0.502201i	$-0.167476\pi$
$71$	1.01035	+	1.39063i	0.119907	+	0.165038i	−0.744844	+	0.667239i	$0.767476\pi$
$72$	−2.72774	−	1.24878i	−0.321467	−	0.147170i
$73$	0.649602	−	3.05614i	0.0760301	−	0.357694i	−0.923643	−	0.383254i	$-0.874804\pi$
$73$	0.649602	−	3.05614i	0.0760301	−	0.357694i	0.999673	+	0.0255600i	$0.00813688\pi$
$74$	−3.96808	−	4.40700i	−0.461280	−	0.512303i
$75$	−5.20299	−	0.574354i	−0.600789	−	0.0663207i
$76$		−	1.06705i		−	0.122399i
$77$	2.62460	+	8.37326i	0.299101	+	0.954221i
$78$	−8.55386	−	0.0446884i	−0.968534	−	0.00505997i
$79$	7.75852	+	0.815454i	0.872902	+	0.0917457i	0.530376	−	0.847763i	$-0.322051\pi$
$79$	7.75852	+	0.815454i	0.872902	+	0.0917457i	0.342526	+	0.939508i	$0.388717\pi$
$80$	1.04512	−	0.941028i	0.116848	−	0.105210i
$81$	−8.76231	−	2.05475i	−0.973590	−	0.228305i
$82$	10.1711	+	4.52845i	1.12321	+	0.500084i
$83$	9.70225	−	7.04910i	1.06496	−	0.773739i	0.0899605	−	0.995945i	$-0.471326\pi$
$83$	9.70225	−	7.04910i	1.06496	−	0.773739i	0.975000	+	0.222207i	$0.0713259\pi$
$84$	4.48759	−	0.928182i	0.489636	−	0.101273i
$85$	4.26878	+	1.38701i	0.463014	+	0.150442i
$86$	−6.78121	−	0.712734i	−0.731237	−	0.0768561i
$87$	0.782405	+	0.457188i	0.0838826	+	0.0490157i
$88$	3.16454	−	0.992822i	0.337341	−	0.105835i
$89$	−1.89178	+	1.09222i	−0.200529	+	0.115775i	−0.596902	−	0.802314i	$-0.703602\pi$
$89$	−1.89178	+	1.09222i	−0.200529	+	0.115775i	0.396373	+	0.918089i	$0.370269\pi$
$90$	2.51541	−	3.38717i	0.265148	−	0.357039i
$91$	10.5729	−	7.67752i	1.10834	−	0.804822i
$92$	2.65548	−	0.862818i	0.276853	−	0.0899550i
$93$	−0.618897	+	1.37075i	−0.0641767	+	0.142140i
$94$	−6.80474	+	0.715207i	−0.701855	+	0.0737679i
$95$	1.46785	+	0.312002i	0.150598	+	0.0320107i
$96$	−0.351258	−	1.69606i	−0.0358501	−	0.173103i
$97$	−3.42729	−	2.49007i	−0.347988	−	0.252828i	0.400036	−	0.916499i	$-0.368998\pi$
$97$	−3.42729	−	2.49007i	−0.347988	−	0.252828i	−0.748025	+	0.663671i	$0.768998\pi$
$98$	−4.68660	+	5.19960i	−0.473418	+	0.525238i
$99$	8.71749	−	4.79639i	0.876141	−	0.482055i
$100$	−1.51110	−	2.61730i	−0.151110	−	0.261730i
$101$	1.20263	−	0.535443i	0.119666	−	0.0532786i	−0.346030	−	0.938223i	$-0.612471\pi$
$101$	1.20263	−	0.535443i	0.119666	−	0.0532786i	0.465696	+	0.884945i	$0.345804\pi$
$102$	4.12735	−	3.67742i	0.408669	−	0.364119i
$103$	9.54362	−	10.5993i	0.940361	−	1.04438i	−0.0585759	−	0.998283i	$-0.518656\pi$
$103$	9.54362	−	10.5993i	0.940361	−	1.04438i	0.998937	−	0.0460940i	$-0.0146774\pi$
$104$	−2.90286	−	3.99544i	−0.284649	−	0.391785i
$105$	−0.0353320	+	6.44458i	−0.00344805	+	0.628927i
$106$	0.399097	−	0.129675i	0.0387637	−	0.0125951i
$107$	−12.3254	+	2.61985i	−1.19154	+	0.253270i	−0.760668	−	0.649141i	$-0.775128\pi$
$107$	−12.3254	+	2.61985i	−1.19154	+	0.253270i	−0.430875	+	0.902412i	$0.641795\pi$
$108$	−2.03881	−	4.77946i	−0.196185	−	0.459904i
$109$	−8.70388	−	5.02518i	−0.833680	−	0.481325i	0.0214310	−	0.999770i	$-0.493178\pi$
$109$	−8.70388	−	5.02518i	−0.833680	−	0.481325i	−0.855111	+	0.518445i	$0.826511\pi$
$110$	0.440442	+	4.64348i	0.0419945	+	0.442738i
$111$	0.0536608	−	10.2713i	0.00509326	−	0.974906i
$112$	1.96572	+	1.77086i	0.185743	+	0.167331i
$113$	−4.42399	−	1.43744i	−0.416174	−	0.135223i	0.0934425	−	0.995625i	$-0.470213\pi$
$113$	−4.42399	−	1.43744i	−0.416174	−	0.135223i	−0.509617	+	0.860401i	$0.670213\pi$
$114$	1.24384	−	1.36699i	0.116496	−	0.128031i
$115$	0.410453	+	3.90520i	0.0382749	+	0.364162i
$116$	0.0546881	+	0.520322i	0.00507766	+	0.0483107i
$117$	−10.9062	−	10.0283i	−1.00828	−	0.927115i
$118$	9.31254	+	3.02583i	0.857288	+	0.278550i
$119$	−1.75776	+	8.25914i	−0.161134	+	0.757114i
$120$	2.43583	+	0.0127256i	0.222360	+	0.00116169i
$121$	−3.61086	+	10.3905i	−0.328260	+	0.944587i
$122$	−6.68437	−	3.85922i	−0.605175	−	0.349398i
$123$	7.75137	+	17.6576i	0.698917	+	1.59213i
$124$	−0.849354	+	0.180536i	−0.0762742	+	0.0162126i
$125$	10.7298	−	3.48632i	0.959702	−	0.311826i
$126$	6.83098	+	4.04199i	0.608552	+	0.360089i
$127$	10.6281	+	14.6284i	0.943095	+	1.29806i	0.954527	+	0.298125i	$0.0963611\pi$
$127$	10.6281	+	14.6284i	0.943095	+	1.29806i	−0.0114318	+	0.999935i	$0.503639\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−7.85654	−	8.81778i	−0.691730	−	0.776363i
$130$	6.34497	−	2.82496i	0.556490	−	0.247765i
$131$	−10.0367	−	17.3840i	−0.876908	−	1.51885i	−0.854717	−	0.519095i	$-0.826269\pi$
$131$	−10.0367	−	17.3840i	−0.876908	−	1.51885i	−0.0221908	−	0.999754i	$-0.507064\pi$
$132$	5.21138	+	2.41693i	0.453592	+	0.210367i
$133$	−0.295825	+	2.80762i	−0.0256513	+	0.243451i
$134$	5.25153	+	3.81546i	0.453663	+	0.329605i
$135$	7.17083	−	1.40712i	0.617167	−	0.121106i
$136$	3.12183	+	0.663566i	0.267695	+	0.0569003i
$137$	4.89003	−	0.513963i	0.417784	−	0.0439108i	0.106695	−	0.994292i	$-0.465973\pi$
$137$	4.89003	−	0.513963i	0.417784	−	0.0439108i	0.311088	+	0.950381i	$0.399306\pi$
$138$	4.40768	+	1.99008i	0.375207	+	0.169407i
$139$	−21.6082	+	7.02093i	−1.83278	+	0.595508i	−0.833724	+	0.552182i	$0.813795\pi$
$139$	−21.6082	+	7.02093i	−1.83278	+	0.595508i	−0.999061	+	0.0433258i	$0.986205\pi$
$140$	−3.01079	+	2.18628i	−0.254458	+	0.184774i
$141$	−9.55120	−	7.01588i	−0.804356	−	0.590844i
$142$	−1.48863	+	0.859459i	−0.124923	+	0.0721242i
$143$	16.3788	+	0.166266i	1.36966	+	0.0139038i
$144$	1.52706	−	2.58226i	0.127255	−	0.215188i
$145$	−0.731752	−	0.0769103i	−0.0607687	−	0.00638705i
$146$	2.97149	+	0.965496i	0.245922	+	0.0799050i
$147$	−12.0650	+	1.19810i	−0.995106	+	0.0988178i
$148$	4.79763	−	3.48569i	0.394363	−	0.286522i
$149$	−17.7071	−	7.88371i	−1.45062	−	0.645859i	−0.478023	−	0.878347i	$-0.658647\pi$
$149$	−17.7071	−	7.88371i	−1.45062	−	0.645859i	−0.972599	+	0.232488i	$0.925313\pi$
$150$	1.11507	−	5.11445i	0.0910449	−	0.417593i
$151$	−15.0418	+	13.5437i	−1.22408	+	1.10217i	−0.232513	+	0.972593i	$0.574695\pi$
$151$	−15.0418	+	13.5437i	−1.22408	+	1.10217i	−0.991570	+	0.129576i	$0.958639\pi$
$152$	1.06121	+	0.111537i	0.0860753	+	0.00904688i
$153$	9.57420	+	0.100041i	0.774029	+	0.00808782i
$154$	−8.60174	+	1.73498i	−0.693148	+	0.139808i
$155$		−	1.22117i		−	0.0980867i
$156$	0.938565	−	8.50233i	0.0751454	−	0.680731i
$157$	−9.71926	−	10.7943i	−0.775682	−	0.861482i	0.217739	−	0.976007i	$-0.430132\pi$
$157$	−9.71926	−	10.7943i	−0.775682	−	0.861482i	−0.993420	+	0.114525i	$0.963465\pi$
$158$	−1.62197	+	7.63078i	−0.129037	+	0.607073i
$159$	0.662439	+	0.299093i	0.0525348	+	0.0237196i
$160$	0.826629	+	1.13776i	0.0653507	+	0.0899476i
$161$	−7.22627	+	1.53404i	−0.569510	+	0.120899i
$162$	2.95940	−	8.49953i	0.232513	−	0.667786i
$163$	2.48171	−	23.6119i	0.194382	−	1.84942i	−0.268845	−	0.963184i	$-0.586642\pi$
$163$	2.48171	−	23.6119i	0.194382	−	1.84942i	0.463227	−	0.886240i	$-0.346692\pi$
$164$	−5.56681	+	9.64200i	−0.434695	+	0.752914i
$165$	−4.84855	+	6.46213i	−0.377459	+	0.503076i
$166$	5.99632	+	10.3859i	0.465405	+	0.806104i
$167$	−1.27598	−	0.927052i	−0.0987381	−	0.0717374i	0.537321	−	0.843378i	$-0.319436\pi$
$167$	−1.27598	−	0.927052i	−0.0987381	−	0.0717374i	−0.636059	+	0.771641i	$0.719436\pi$
$168$	0.454017	+	4.56003i	0.0350282	+	0.351814i
$169$	−3.51975	−	10.8327i	−0.270750	−	0.833283i
$170$	−1.82562	+	4.10041i	−0.140019	+	0.314487i
$171$	3.18695	−	0.301330i	0.243712	−	0.0230433i
$172$	1.41766	−	6.66957i	0.108096	−	0.508550i
$173$	17.6821	−	3.75844i	1.34434	−	0.285749i	0.521127	−	0.853479i	$-0.325512\pi$
$173$	17.6821	−	3.75844i	1.34434	−	0.285749i	0.823215	+	0.567730i	$0.192178\pi$
$174$	−0.536467	+	0.730329i	−0.0406695	+	0.0553661i
$175$	3.25037	+	7.30553i	0.245705	+	0.552246i
$176$	0.656599	+	3.25098i	0.0494930	+	0.245052i
$177$	8.40308	+	14.7318i	0.631614	+	1.10731i
$178$	−0.888493	−	1.99559i	−0.0665953	−	0.149576i
$179$	−14.1463	+	12.7374i	−1.05734	+	0.952035i	−0.998930	−	0.0462577i	$-0.985270\pi$
$179$	−14.1463	+	12.7374i	−1.05734	+	0.952035i	−0.0584123	+	0.998293i	$0.518604\pi$
$180$	3.10569	+	2.85569i	0.231484	+	0.212851i
$181$	−16.3703	+	11.8937i	−1.21679	+	0.884051i	−0.995830	−	0.0912314i	$-0.970920\pi$
$181$	−16.3703	+	11.8937i	−1.21679	+	0.884051i	−0.220962	+	0.975282i	$0.570920\pi$
$182$	6.53029	+	11.3175i	0.484057	+	0.838911i
$183$	−4.06469	−	12.7358i	−0.300470	−	0.941460i
$184$	0.580518	+	2.73112i	0.0427964	+	0.201341i
$185$	3.39215	+	7.61889i	0.249396	+	0.560152i
$186$	−1.29855	−	0.758789i	−0.0952141	−	0.0556371i
$187$	−7.93787	+	7.00271i	−0.580475	+	0.512089i
$188$		−	6.84222i		−	0.499020i
$189$	4.03946	+	13.1409i	0.293827	+	0.955859i
$190$	−0.463725	+	1.42720i	−0.0336421	+	0.103540i
$191$	−3.03287	−	2.73081i	−0.219451	−	0.197594i	0.552071	−	0.833797i	$-0.313838\pi$
$191$	−3.03287	−	2.73081i	−0.219451	−	0.197594i	−0.771522	+	0.636203i	$0.780504\pi$
$192$	1.72348	−	0.172047i	0.124382	−	0.0124164i
$193$	0.848255	−	0.0891552i	0.0610587	−	0.00641753i	−0.0739498	−	0.997262i	$-0.523560\pi$
$193$	0.848255	−	0.0891552i	0.0610587	−	0.00641753i	0.135009	+	0.990844i	$0.456894\pi$
$194$	2.83468	−	3.14823i	0.203518	−	0.226030i
$195$	11.4215	+	3.77714i	0.817909	+	0.270487i
$196$	−4.68123	−	5.20443i	−0.334373	−	0.371745i
$197$	0.565770			0.0403095			0.0201547	−	0.999797i	$-0.493584\pi$
$197$	0.565770			0.0403095			0.0201547	+	0.999797i	$0.493584\pi$
$198$	3.85889	+	9.17109i	0.274239	+	0.651761i
$199$	4.87809	−	8.44910i	0.345799	−	0.598941i	−0.639700	−	0.768625i	$-0.720941\pi$
$199$	4.87809	−	8.44910i	0.345799	−	0.598941i	0.985499	+	0.169684i	$0.0542747\pi$
$200$	2.76091	−	1.22924i	0.195226	−	0.0869202i
$201$	2.28010	+	11.0095i	0.160826	+	0.776553i
$202$	0.406801	+	1.25201i	0.0286225	+	0.0880908i
$203$	0.000357225	−	1.38423i	2.50723e−5	−	0.0971536i
$204$	3.22585	+	4.48914i	0.225855	+	0.314302i
$205$	−11.6359	−	10.4771i	−0.812690	−	0.731749i
$206$	9.54362	+	10.5993i	0.664936	+	0.738486i
$207$	3.32686	+	7.68742i	0.231232	+	0.534312i
$208$	4.27699	−	2.46932i	0.296556	−	0.171217i
$209$	−2.39464	+	2.60583i	−0.165641	+	0.180249i
$210$	−6.40559	−	0.708781i	−0.442028	−	0.0489105i
$211$	9.36900	−	12.8953i	0.644989	−	0.887751i	−0.353881	−	0.935291i	$-0.615138\pi$
$211$	9.36900	−	12.8953i	0.644989	−	0.887751i	0.998869	+	0.0475400i	$0.0151382\pi$
$212$	0.0872471	+	0.410466i	0.00599216	+	0.0281909i
$213$	−2.90892	−	0.634211i	−0.199316	−	0.0434554i
$214$	−1.31714	−	12.5317i	−0.0900378	−	0.856653i
$215$	8.76022	+	3.90030i	0.597442	+	0.265998i
$216$	4.96639	−	1.52805i	0.337920	−	0.103971i
$217$	2.28486	−	0.239552i	0.155106	−	0.0162619i
$218$	5.90746	−	8.13092i	0.400104	−	0.550695i
$219$	2.68130	+	4.70069i	0.181185	+	0.317643i
$220$	−4.66408	−	0.0473464i	−0.314452	−	0.00319209i
$221$	13.6503	+	7.88102i	0.918220	+	0.530135i
$222$	10.2094	+	1.12701i	0.685210	+	0.0756398i
$223$	−3.77374	+	11.6144i	−0.252709	+	0.777757i	0.741564	+	0.670882i	$0.234084\pi$
$223$	−3.77374	+	11.6144i	−0.252709	+	0.777757i	−0.994272	+	0.106875i	$0.965916\pi$
$224$	−1.96663	+	1.76985i	−0.131401	+	0.118253i
$225$	7.39030	−	5.25227i	0.492687	−	0.350152i
$226$	1.89200	−	4.24951i	0.125854	−	0.282673i
$227$	−13.9907	−	2.97381i	−0.928595	−	0.197379i	−0.281301	−	0.959620i	$-0.590766\pi$
$227$	−13.9907	−	2.97381i	−0.928595	−	0.197379i	−0.647294	+	0.762241i	$0.724099\pi$
$228$	1.22949	+	1.37992i	0.0814249	+	0.0913871i
$229$	1.99267	−	18.9590i	0.131680	−	1.25285i	−0.706602	−	0.707611i	$-0.749773\pi$
$229$	1.99267	−	18.9590i	0.131680	−	1.25285i	0.838282	−	0.545237i	$-0.183560\pi$
$230$	−3.92671			−0.258920
$231$	−13.0420	−	7.80418i	−0.858103	−	0.513477i
$232$	−0.523188			−0.0343490
$233$	0.721428	−	6.86393i	0.0472623	−	0.449671i	−0.945143	−	0.326658i	$-0.894078\pi$
$233$	0.721428	−	6.86393i	0.0472623	−	0.449671i	0.992405	−	0.123013i	$-0.0392558\pi$
$234$	11.1134	−	9.79820i	0.726503	−	0.640529i
$235$	9.41224	+	2.00063i	0.613987	+	0.130507i
$236$	−3.98268	+	8.94524i	−0.259250	+	0.582285i
$237$	−10.9729	+	7.88504i	−0.712768	+	0.512189i
$238$	−8.03016	−	2.61145i	−0.520518	−	0.169275i
$239$	−8.84622	+	27.2259i	−0.572214	+	1.76109i	0.0732605	+	0.997313i	$0.476660\pi$
$239$	−8.84622	+	27.2259i	−0.572214	+	1.76109i	−0.645475	+	0.763782i	$0.723340\pi$
$240$	−0.267269	+	2.42115i	−0.0172522	+	0.156285i
$241$	−15.7349	−	9.08453i	−1.01357	−	0.585186i	−0.101336	−	0.994852i	$-0.532312\pi$
$241$	−15.7349	−	9.08453i	−1.01357	−	0.585186i	−0.912235	+	0.409666i	$0.865645\pi$
$242$	−9.95610	−	4.67718i	−0.640003	−	0.300661i
$243$	13.6990	−	7.43897i	0.878789	−	0.477210i
$244$	4.53679	−	6.24436i	0.290438	−	0.399754i
$245$	8.52805	−	4.91781i	0.544837	−	0.314187i
$246$	−18.3711	+	5.86319i	−1.17130	+	0.373823i
$247$	4.81419	+	2.14342i	0.306320	+	0.136382i
$248$	−0.0907651	−	0.863572i	−0.00576359	−	0.0548369i
$249$	−4.42480	+	20.2951i	−0.280410	+	1.28615i
$250$	2.34565	+	11.0354i	0.148352	+	0.697942i
$251$	7.31864	−	10.0732i	0.461948	−	0.635817i	−0.512963	−	0.858411i	$-0.671452\pi$
$251$	7.31864	−	10.0732i	0.461948	−	0.635817i	0.974911	+	0.222593i	$0.0714522\pi$
$252$	−4.73388	+	6.37106i	−0.298207	+	0.401339i
$253$	−8.42120	−	3.85226i	−0.529436	−	0.242189i
$254$	−15.6592	+	9.04084i	−0.982545	+	0.567273i
$255$	−7.11854	+	3.12492i	−0.445780	+	0.195690i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	10.3600	+	9.32820i	0.646240	+	0.581877i	0.925690	−	0.378283i	$-0.123485\pi$
$257$	10.3600	+	9.32820i	0.646240	+	0.581877i	−0.279450	+	0.960160i	$0.590152\pi$
$258$	9.59071	−	6.89180i	0.597092	−	0.429064i
$259$	−13.5898	+	7.84141i	−0.844431	+	0.487242i
$260$	2.14626	+	6.60550i	0.133105	+	0.409655i
$261$	−1.53859	+	0.310272i	−0.0952365	+	0.0192054i
$262$	18.3379	−	8.16456i	1.13292	−	0.504408i
$263$	−9.23084	+	15.9883i	−0.569198	+	0.985879i	0.427448	+	0.904040i	$0.359413\pi$
$263$	−9.23084	+	15.9883i	−0.569198	+	0.985879i	−0.996646	+	0.0818394i	$0.973921\pi$
$264$	−2.94843	+	4.93019i	−0.181463	+	0.303432i
$265$	−0.590152			−0.0362528
$266$	−2.76131	−	0.587680i	−0.169307	−	0.0360330i
$267$	1.18797	−	3.59223i	0.0727025	−	0.219841i
$268$	−4.34349	+	4.82394i	−0.265321	+	0.294669i
$269$	−7.68213	+	0.807425i	−0.468388	+	0.0492295i	−0.335783	−	0.941939i	$-0.609001\pi$
$269$	−7.68213	+	0.807425i	−0.468388	+	0.0492295i	−0.132605	+	0.991169i	$0.542334\pi$
$270$	0.649857	+	7.27863i	0.0395491	+	0.442963i
$271$	−13.9851	−	12.5923i	−0.849537	−	0.764926i	0.124283	−	0.992247i	$-0.460337\pi$
$271$	−13.9851	−	12.5923i	−0.849537	−	0.764926i	−0.973820	+	0.227321i	$0.927003\pi$
$272$	−0.986251	+	3.03537i	−0.0598003	+	0.184046i
$273$	−4.82669	+	22.1110i	−0.292124	+	1.33822i
$274$			4.91697i			0.297045i
$275$	−2.18341	+	9.78279i	−0.131665	+	0.589924i
$276$	−2.43991	+	4.17552i	−0.146865	+	0.251337i
$277$	1.51394	+	3.40038i	0.0909641	+	0.204309i	0.953298	−	0.302031i	$-0.0976647\pi$
$277$	1.51394	+	3.40038i	0.0909641	+	0.204309i	−0.862334	+	0.506340i	$0.830998\pi$
$278$	−4.72380	−	22.2237i	−0.283315	−	1.33289i
$279$	−0.779055	−	2.48577i	−0.0466408	−	0.148819i
$280$	−1.85959	−	3.22282i	−0.111132	−	0.192600i
$281$	11.5940	−	8.42355i	0.691642	−	0.502507i	−0.185558	−	0.982633i	$-0.559409\pi$
$281$	11.5940	−	8.42355i	0.691642	−	0.502507i	0.877199	+	0.480126i	$0.159409\pi$
$282$	7.97582	−	8.76551i	0.474953	−	0.521979i
$283$	−6.24565	+	5.62361i	−0.371266	+	0.334289i	−0.833551	−	0.552442i	$-0.813696\pi$
$283$	−6.24565	+	5.62361i	−0.371266	+	0.334289i	0.462286	+	0.886731i	$0.347029\pi$
$284$	−0.699147	−	1.57031i	−0.0414867	−	0.0931807i
$285$	−2.25773	+	1.28782i	−0.133736	+	0.0762838i
$286$	−1.87740	+	16.2717i	−0.111013	+	0.962164i
$287$	17.3204	−	23.8266i	1.02239	−	1.40644i
$288$	2.40849	+	1.78862i	0.141922	+	0.105395i
$289$	6.66495	−	1.41668i	0.392056	−	0.0833340i
$290$	0.152978	−	0.719705i	0.00898317	−	0.0422625i
$291$	7.30130	−	0.728853i	0.428010	−	0.0427261i
$292$	−1.27081	+	2.85429i	−0.0743687	+	0.167035i
$293$	0.953809	+	2.93552i	0.0557221	+	0.171495i	0.975044	−	0.222011i	$-0.0712621\pi$
$293$	0.953809	+	2.93552i	0.0557221	+	0.171495i	−0.919322	+	0.393506i	$0.871262\pi$
$294$	0.0695988	−	12.1242i	0.00405909	−	0.707095i
$295$	−11.1407	−	8.09417i	−0.648635	−	0.471261i
$296$	2.96510	+	5.13571i	0.172343	+	0.298507i
$297$	−5.74694	+	16.2472i	−0.333471	+	0.942760i
$298$	9.69142	−	16.7860i	0.561409	−	0.972389i
$299$	−1.44138	+	13.7138i	−0.0833572	+	0.793091i
$300$	4.96988	+	1.64357i	0.286936	+	0.0948913i
$301$	−5.57917	+	17.1558i	−0.321578	+	0.988846i
$302$	−11.8972	−	16.3751i	−0.684606	−	0.942280i
$303$	−0.938284	+	2.07813i	−0.0539030	+	0.119386i
$304$	−0.221853	+	1.04374i	−0.0127241	+	0.0598624i
$305$	7.26328	+	8.06669i	0.415894	+	0.461897i
$306$	−1.10027	+	9.51130i	−0.0628982	+	0.543725i
$307$			18.2478i			1.04146i	0.853722	+	0.520729i	$0.174340\pi$
$307$			18.2478i			1.04146i	−0.853722	+	0.520729i	$0.825660\pi$
$308$	−0.826347	−	8.73597i	−0.0470855	−	0.497778i
$309$	−0.129060	+	24.7034i	−0.00734194	+	1.40533i
$310$	1.21448	+	0.127647i	0.0689778	+	0.00724986i
$311$	8.89906	−	8.01275i	0.504619	−	0.454361i	−0.377075	−	0.926183i	$-0.623070\pi$
$311$	8.89906	−	8.01275i	0.504619	−	0.454361i	0.881694	+	0.471822i	$0.156403\pi$
$312$	8.35764	+	1.82216i	0.473158	+	0.103159i
$313$	26.2214	+	11.6745i	1.48212	+	0.659882i	0.978912	−	0.204283i	$-0.0654862\pi$
$313$	26.2214	+	11.6745i	1.48212	+	0.659882i	0.503208	+	0.864165i	$0.332153\pi$
$314$	11.7511	−	8.53770i	0.663155	−	0.481811i
$315$	−7.37994	−	8.37486i	−0.415812	−	0.471870i
$316$	−7.41944	−	2.41072i	−0.417376	−	0.135614i
$317$	12.2543	+	1.28798i	0.688271	+	0.0723402i	0.442206	−	0.896913i	$-0.354196\pi$
$317$	12.2543	+	1.28798i	0.688271	+	0.0723402i	0.246064	+	0.969253i	$0.420863\pi$
$318$	−0.366699	+	0.627546i	−0.0205634	+	0.0351910i
$319$	1.03413	−	1.39340i	0.0579004	−	0.0780152i
$320$	−1.21793	+	0.703172i	−0.0680844	+	0.0393085i
$321$	12.9206	−	17.5897i	0.721157	−	0.981760i
$322$	−0.770288	−	7.34704i	−0.0429265	−	0.409434i
$323$	−3.23890	+	1.05238i	−0.180217	+	0.0585561i
$324$	8.14362	+	3.83163i	0.452423	+	0.212869i
$325$	14.8438	−	1.56014i	0.823384	−	0.0865411i
$326$	23.2231	+	4.93622i	1.28621	+	0.273392i
$327$	17.0460	−	3.53027i	0.942647	−	0.195224i
$328$	−9.00729	−	6.54418i	−0.497344	−	0.361342i
$329$	−1.89691	+	18.0032i	−0.104580	+	0.992546i
$330$	−5.91992	−	5.49746i	−0.325881	−	0.302625i
$331$	−7.39402	−	12.8068i	−0.406412	−	0.703927i	0.588073	−	0.808808i	$-0.299887\pi$
$331$	−7.39402	−	12.8068i	−0.406412	−	0.703927i	−0.994485	+	0.104882i	$0.966554\pi$
$332$	−10.9558	+	4.87785i	−0.601279	+	0.267707i
$333$	11.7654	+	13.3447i	0.644743	+	0.731283i
$334$	1.05535	−	1.17208i	0.0577461	−	0.0641336i
$335$	−5.36585	−	7.38546i	−0.293168	−	0.403511i
$336$	−4.58251	−	0.0251233i	−0.249996	−	0.00137059i
$337$	4.99286	−	1.62228i	0.271978	−	0.0883711i	−0.169853	−	0.985469i	$-0.554329\pi$
$337$	4.99286	−	1.62228i	0.271978	−	0.0883711i	0.441831	+	0.897098i	$0.354329\pi$
$338$	11.1413	−	2.36815i	0.606004	−	0.128810i
$339$	7.37738	−	3.23855i	0.400684	−	0.175894i
$340$	−3.88712	−	2.24423i	−0.210809	−	0.121710i
$341$	2.47934	+	1.46520i	0.134264	+	0.0793452i
$342$	−0.0334471	+	3.20099i	−0.00180861	+	0.173089i
$343$	10.8743	+	14.9916i	0.587159	+	0.809472i
$344$	6.48484	+	2.10705i	0.349639	+	0.113605i
$345$	−5.03048	−	4.57728i	−0.270832	−	0.246432i
$346$	1.88957	+	17.9781i	0.101584	+	0.966506i
$347$	−3.50116	−	33.3113i	−0.187952	−	1.78825i	−0.529428	−	0.848355i	$-0.677594\pi$
$347$	−3.50116	−	33.3113i	−0.187952	−	1.78825i	0.341476	−	0.939890i	$-0.389073\pi$
$348$	−0.670253	−	0.609869i	−0.0359293	−	0.0326924i
$349$	−21.5358	−	6.99740i	−1.15278	−	0.374562i	−0.330593	−	0.943774i	$-0.607249\pi$
$349$	−21.5358	−	6.99740i	−1.15278	−	0.374562i	−0.822191	+	0.569211i	$0.807249\pi$
$350$	−7.60526	+	2.46893i	−0.406518	+	0.131970i
$351$	25.6588	+	0.402181i	1.36956	+	0.0214668i
$352$	−3.30181	+	0.313182i	−0.175987	+	0.0166927i
$353$	−1.02529	−	0.591950i	−0.0545706	−	0.0315063i	0.472466	−	0.881349i	$-0.343364\pi$
$353$	−1.02529	−	0.591950i	−0.0545706	−	0.0315063i	−0.527037	+	0.849842i	$0.676697\pi$
$354$	−15.5294	+	6.81716i	−0.825380	+	0.362328i
$355$	2.36456	−	0.502604i	0.125498	−	0.0266754i
$356$	2.07753	−	0.675030i	0.110109	−	0.0357765i
$357$	−7.24327	−	12.7061i	−0.383354	−	0.672477i
$358$	−11.1889	−	15.4002i	−0.591351	−	0.813925i
$359$	−22.3727	+	24.8474i	−1.18079	+	1.31140i	−0.240646	+	0.970613i	$0.577359\pi$
$359$	−22.3727	+	24.8474i	−1.18079	+	1.31140i	−0.940141	+	0.340784i	$0.889307\pi$
$360$	−3.16468	+	2.79017i	−0.166793	+	0.147055i
$361$	16.3172	−	7.26488i	0.858800	−	0.382362i
$362$	−10.1174	−	17.5238i	−0.531758	−	0.921031i
$363$	−7.30260	−	17.5975i	−0.383287	−	0.923629i
$364$	−11.9381	+	5.31151i	−0.625728	+	0.278399i
$365$	−3.55482	−	2.58273i	−0.186068	−	0.135186i
$366$	13.0909	−	2.71116i	0.684275	−	0.141715i
$367$	22.4426	+	4.77032i	1.17149	+	0.249009i	0.752258	−	0.658868i	$-0.228965\pi$
$367$	22.4426	+	4.77032i	1.17149	+	0.249009i	0.419236	+	0.907877i	$0.362298\pi$
$368$	−2.77684	+	0.291858i	−0.144753	+	0.0152141i
$369$	−30.3696	−	13.9034i	−1.58098	−	0.723784i
$370$	−7.93172	+	2.57717i	−0.412351	+	0.133981i
$371$	−0.115768	−	1.10420i	−0.00601037	−	0.0573272i
$372$	0.890368	−	1.21212i	0.0461634	−	0.0628454i
$373$	−24.2117	+	13.9787i	−1.25364	+	0.723787i	−0.971830	−	0.235684i	$-0.924267\pi$
$373$	−24.2117	+	13.9787i	−1.25364	+	0.723787i	−0.281807	+	0.959471i	$0.590934\pi$
$374$	−6.13461	−	8.62637i	−0.317213	−	0.446059i
$375$	−9.85875	+	16.8717i	−0.509104	+	0.871250i
$376$	6.80474	+	0.715207i	0.350928	+	0.0368840i
$377$	−2.45738	−	0.798450i	−0.126561	−	0.0411223i
$378$	−13.4911	+	2.64373i	−0.693909	+	0.135979i
$379$	30.5843	−	22.2208i	1.57101	−	1.14141i	0.644831	−	0.764325i	$-0.276928\pi$
$379$	30.5843	−	22.2208i	1.57101	−	1.14141i	0.926180	−	0.377081i	$-0.123072\pi$
$380$	−1.37091	−	0.610367i	−0.0703261	−	0.0313112i
$381$	−30.5996	−	6.67141i	−1.56766	−	0.341787i
$382$	3.03287	−	2.73081i	0.155175	−	0.139720i
$383$	−17.2281	−	1.81074i	−0.880314	−	0.0925247i	−0.346423	−	0.938078i	$-0.612604\pi$
$383$	−17.2281	−	1.81074i	−0.880314	−	0.0925247i	−0.533890	+	0.845554i	$0.679271\pi$
$384$	−0.00904873	+	1.73203i	−0.000461766	+	0.0883871i
$385$	12.2589	+	1.41762i	0.624773	+	0.0722488i
$386$			0.852927i			0.0434128i
$387$	20.3202	+	2.35065i	1.03293	+	0.119490i
$388$	2.83468	+	3.14823i	0.143909	+	0.159827i
$389$	5.73185	−	26.9663i	0.290617	−	1.36724i	−0.554288	−	0.832325i	$-0.687009\pi$
$389$	5.73185	−	26.9663i	0.290617	−	1.36724i	0.844904	−	0.534918i	$-0.179657\pi$
$390$	−4.95032	+	10.9641i	−0.250669	+	0.555188i
$391$	−5.23794	−	7.20941i	−0.264894	−	0.364596i
$392$	5.66524	−	4.11157i	0.286138	−	0.207666i
$393$	33.0098	+	10.9165i	1.66512	+	0.550665i
$394$	−0.0591391	+	0.562671i	−0.00297939	+	0.0283470i
$395$	5.48563	−	9.50139i	0.276012	−	0.478067i
$396$	−9.52422	+	2.87911i	−0.478610	+	0.144681i
$397$	−12.5033	−	21.6563i	−0.627522	−	1.08690i	−0.988047	−	0.154150i	$-0.950736\pi$
$397$	−12.5033	−	21.6563i	−0.627522	−	1.08690i	0.360526	−	0.932749i	$-0.382597\pi$
$398$	7.89292	+	5.73454i	0.395636	+	0.287446i
$399$	−2.85245	−	3.97167i	−0.142801	−	0.198832i
$400$	0.933909	+	2.87428i	0.0466955	+	0.143714i
$401$	15.9632	−	35.8539i	0.797163	−	1.79046i	0.216564	−	0.976268i	$-0.430515\pi$
$401$	15.9632	−	35.8539i	0.797163	−	1.79046i	0.580599	−	0.814189i	$-0.302818\pi$
$402$	−11.1876	+	1.11680i	−0.557985	+	0.0557009i
$403$	0.891601	−	4.19465i	0.0444138	−	0.208951i
$404$	−1.28767	+	0.273703i	−0.0640640	+	0.0136172i
$405$	−7.65200	+	10.0821i	−0.380231	+	0.500985i
$406$	1.37661	+	0.145046i	0.0683198	+	0.00719853i
$407$	−19.5386	−	2.25434i	−0.968494	−	0.111744i
$408$	−4.80174	+	2.73894i	−0.237721	+	0.135598i
$409$	−8.30248	−	18.6477i	−0.410531	−	0.922068i	−0.993944	−	0.109892i	$-0.964950\pi$
$409$	−8.30248	−	18.6477i	−0.410531	−	0.922068i	0.583412	−	0.812176i	$-0.301717\pi$
$410$	11.6359	−	10.4771i	0.574659	−	0.517425i
$411$	−5.73159	+	6.29909i	−0.282719	+	0.310711i
$412$	−11.5388	+	8.38342i	−0.568475	+	0.413021i
$413$	12.9591	−	22.4324i	0.637675	−	1.10383i
$414$	−7.99306	+	2.50508i	−0.392837	+	0.123118i
$415$	−3.50659	−	16.4972i	−0.172132	−	0.809817i
$416$	2.00873	+	4.51167i	0.0984859	+	0.221203i
$417$	19.8541	−	33.9771i	0.972258	−	1.66386i
$418$	−2.34125	−	2.65390i	−0.114514	−	0.129807i
$419$			30.7965i			1.50451i	0.658872	+	0.752255i	$0.271034\pi$
$419$			30.7965i			1.50451i	−0.658872	+	0.752255i	$0.728966\pi$
$420$	1.37446	−	6.29641i	0.0670670	−	0.307233i
$421$	−1.54240	+	4.74702i	−0.0751721	+	0.231356i	−0.981581	−	0.191045i	$-0.938812\pi$
$421$	−1.54240	+	4.74702i	−0.0751721	+	0.231356i	0.906409	+	0.422401i	$0.138812\pi$
$422$	11.8454	+	10.6656i	0.576623	+	0.519193i
$423$	20.4355	−	1.93221i	0.993609	−	0.0939471i
$424$	−0.417337	+	0.0438639i	−0.0202677	+	0.00213022i
$425$	−6.45414	+	7.16805i	−0.313072	+	0.347701i
$426$	0.934802	−	2.82669i	0.0452913	−	0.136954i
$427$	−13.6683	+	15.1723i	−0.661455	+	0.734239i
$428$	12.6008			0.609081
$429$	−21.3726	+	18.6571i	−1.03188	+	0.900771i
$430$	−4.79463	+	8.30454i	−0.231218	+	0.400480i
$431$	−5.55420	+	2.47289i	−0.267536	+	0.119115i	−0.536121	−	0.844141i	$-0.680111\pi$
$431$	−5.55420	+	2.47289i	−0.267536	+	0.119115i	0.268584	+	0.963256i	$0.413444\pi$
$432$	1.00055	+	5.09891i	0.0481391	+	0.245321i
$433$	−5.61131	−	17.2698i	−0.269662	−	0.829935i	−0.990583	−	0.136917i	$-0.956281\pi$
$433$	−5.61131	−	17.2698i	−0.269662	−	0.829935i	0.720920	−	0.693018i	$-0.243719\pi$
$434$	−0.000592882		2.29738i	−2.84592e−5		0.110278i
$435$	1.03492	−	0.743685i	0.0496207	−	0.0356570i
$436$	7.46888	+	6.72501i	0.357694	+	0.322070i
$437$	−1.99358	−	2.21410i	−0.0953660	−	0.105915i
$438$	−4.95521	+	2.17525i	−0.236769	+	0.103938i
$439$	−3.36418	+	1.94231i	−0.160564	+	0.0927014i	−0.578129	−	0.815946i	$-0.696217\pi$
$439$	−3.36418	+	1.94231i	−0.160564	+	0.0927014i	0.417565	+	0.908647i	$0.362884\pi$
$440$	0.534616	−	4.63358i	0.0254868	−	0.220897i
$441$	14.2220	−	15.4510i	0.677239	−	0.735763i
$442$	−9.26470	+	12.7518i	−0.440677	+	0.606539i
$443$	−3.84129	−	18.0718i	−0.182505	−	0.858619i	−0.970153	−	0.242494i	$-0.922035\pi$
$443$	−3.84129	−	18.0718i	−0.182505	−	0.858619i	0.787648	−	0.616126i	$-0.211299\pi$
$444$	−2.18801	+	10.0357i	−0.103838	+	0.476271i
$445$	0.321120	+	3.05525i	0.0152225	+	0.144833i
$446$	−11.1563	−	4.96711i	−0.528266	−	0.235199i
$447$	31.9827	−	10.2074i	1.51273	−	0.482793i
$448$	−1.55458	−	2.14086i	−0.0734471	−	0.101146i
$449$	15.9011	−	21.8860i	0.750420	−	1.03286i	−0.247531	−	0.968880i	$-0.579619\pi$
$449$	15.9011	−	21.8860i	0.750420	−	1.03286i	0.997951	−	0.0639844i	$-0.0203808\pi$
$450$	4.45100	+	7.89883i	0.209822	+	0.372354i
$451$	35.2328	−	11.0537i	1.65905	−	0.520499i
$452$	4.02846	+	2.32583i	0.189483	+	0.109398i
$453$	3.84665	−	34.8463i	0.180731	−	1.63722i
$454$	4.41995	−	13.6032i	0.207438	−	0.638430i
$455$	−3.81592	−	17.9753i	−0.178893	−	0.842695i
$456$	−1.50087	+	1.07851i	−0.0702848	+	0.0505060i
$457$	−3.57017	+	8.01872i	−0.167005	+	0.375100i	−0.977589	−	0.210523i	$-0.932483\pi$
$457$	−3.57017	+	8.01872i	−0.167005	+	0.375100i	0.810584	+	0.585623i	$0.199150\pi$
$458$	18.6469	+	3.96352i	0.871311	+	0.185203i
$459$	−12.4966	+	10.9023i	−0.583294	+	0.508875i
$460$	0.410453	−	3.90520i	0.0191375	−	0.182081i
$461$	−16.4127			−0.764418			−0.382209	−	0.924076i	$-0.624837\pi$
$461$	−16.4127			−0.764418			−0.382209	+	0.924076i	$0.624837\pi$
$462$	9.12469	−	12.1548i	0.424519	−	0.565494i
$463$	−8.51812			−0.395871			−0.197935	−	0.980215i	$-0.563424\pi$
$463$	−8.51812			−0.395871			−0.197935	+	0.980215i	$0.563424\pi$
$464$	0.0546881	−	0.520322i	0.00253883	−	0.0241554i
$465$	1.40707	+	1.57922i	0.0652511	+	0.0732345i
$466$	6.75092	+	1.43495i	0.312730	+	0.0664729i
$467$	−14.2061	+	31.9075i	−0.657381	+	1.47650i	0.209409	+	0.977828i	$0.432846\pi$
$467$	−14.2061	+	31.9075i	−0.657381	+	1.47650i	−0.866790	+	0.498673i	$0.833821\pi$
$468$	8.58286	+	12.0767i	0.396743	+	0.558244i
$469$	12.7659	−	11.4885i	0.589475	−	0.530490i
$470$	−2.97352	+	9.15156i	−0.137158	+	0.422130i
$471$	25.0065	+	2.76045i	1.15224	+	0.127195i
$472$	−8.47993	−	4.89589i	−0.390320	−	0.225352i
$473$	−18.4296	+	13.1061i	−0.847394	+	0.602621i
$474$	−6.69486	−	11.7370i	−0.307505	−	0.539100i
$475$	−1.89552	+	2.60895i	−0.0869722	+	0.119707i
$476$	3.43652	−	7.71320i	0.157513	−	0.353534i
$477$	−1.20129	+	0.376493i	−0.0550033	+	0.0172384i
$478$	−26.1520	−	11.6436i	−1.19617	−	0.532567i
$479$	1.08697	+	10.3419i	0.0496651	+	0.472532i	0.990882	+	0.134730i	$0.0430168\pi$
$479$	1.08697	+	10.3419i	0.0496651	+	0.472532i	−0.941217	+	0.337802i	$0.890317\pi$
$480$	−2.37995	−	0.518885i	−0.108629	−	0.0236837i
$481$	6.08914	+	28.6471i	0.277641	+	1.30620i
$482$	10.6795	−	14.6991i	0.486438	−	0.669525i
$483$	7.57746	−	10.3101i	0.344786	−	0.469127i
$484$	5.69225	−	9.41266i	0.258739	−	0.427848i
$485$	−5.15959	+	2.97889i	−0.234285	+	0.135265i
$486$	5.96629	+	14.4015i	0.270636	+	0.653266i
$487$	−22.3574	−	24.8304i	−1.01311	−	1.12517i	−0.992107	−	0.125391i	$-0.959981\pi$
$487$	−22.3574	−	24.8304i	−1.01311	−	1.12517i	−0.0210011	−	0.999779i	$-0.506685\pi$
$488$	5.73592	+	5.16465i	0.259653	+	0.233793i
$489$	23.9969	+	33.3944i	1.08518	+	1.51015i
$490$	3.99944	+	8.99538i	0.180676	+	0.406370i
$491$	0.00146407	+	0.00450594i	6.60724e−5	+	0.000203350i	0.951090	−	0.308915i	$-0.0999660\pi$
$491$	0.00146407	+	0.00450594i	6.60724e−5	+	0.000203350i	−0.951023	+	0.309119i	$0.899966\pi$
$492$	−3.91077	−	18.8833i	−0.176311	−	0.851324i
$493$	1.52543	−	0.679167i	0.0687021	−	0.0305881i
$494$	−2.63490	+	4.56377i	−0.118550	+	0.205334i
$495$	−1.17570	−	13.9435i	−0.0528439	−	0.626713i
$496$	0.868329			0.0389891
$497$	1.40424	+	4.32560i	0.0629888	+	0.194030i
$498$	−19.7214	−	6.52198i	−0.883737	−	0.292257i
$499$	−11.6224	+	12.9080i	−0.520289	+	0.577840i	−0.944827	−	0.327571i	$-0.893770\pi$
$499$	−11.6224	+	12.9080i	−0.520289	+	0.577840i	0.424538	+	0.905410i	$0.360437\pi$
$500$	−11.2202	+	1.17929i	−0.501781	+	0.0527393i
$501$	2.71827	−	0.271352i	0.121443	−	0.0121231i
$502$	9.25305	+	8.33149i	0.412984	+	0.371852i
$503$	−4.15264	+	12.7805i	−0.185157	+	0.569855i	−0.999951	−	0.00989591i	$-0.996850\pi$
$503$	−4.15264	+	12.7805i	−0.185157	+	0.569855i	0.814794	+	0.579751i	$0.196850\pi$
$504$	−5.84133	−	5.37391i	−0.260193	−	0.239373i
$505$		−	1.85136i		−	0.0823846i
$506$	4.71141	−	7.97239i	0.209448	−	0.354416i
$507$	17.0335	+	9.95329i	0.756483	+	0.442041i
$508$	−7.35448	−	16.5184i	−0.326302	−	0.732887i
$509$	6.09622	+	28.6805i	0.270210	+	1.27124i	0.878584	+	0.477588i	$0.158489\pi$
$509$	6.09622	+	28.6805i	0.270210	+	1.27124i	−0.608374	+	0.793651i	$0.708178\pi$
$510$	−2.36371	−	7.40619i	−0.104667	−	0.327951i
$511$	4.13506	−	7.15786i	0.182924	−	0.316645i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−3.77416	+	4.06177i	−0.166633	+	0.179332i
$514$	−10.3600	+	9.32820i	−0.456961	+	0.411449i
$515$	−8.15845	−	18.3242i	−0.359504	−	0.807460i
$516$	5.85154	+	10.2586i	0.257600	+	0.451608i
$517$	−15.3550	+	16.7092i	−0.675314	+	0.734871i
$518$	−6.37793	−	14.3350i	−0.280230	−	0.629845i
$519$	−18.5359	+	25.2342i	−0.813635	+	1.10766i
$520$	−6.79366	+	1.44404i	−0.297921	+	0.0633252i
$521$	0.904642	−	4.25601i	0.0396331	−	0.186459i	−0.953878	−	0.300195i	$-0.902948\pi$
$521$	0.904642	−	4.25601i	0.0396331	−	0.186459i	0.993511	+	0.113736i	$0.0362817\pi$
$522$	−0.147746	−	1.56260i	−0.00646665	−	0.0683930i
$523$	−2.10387	+	4.72537i	−0.0919958	+	0.206626i	−0.953683	−	0.300814i	$-0.902742\pi$
$523$	−2.10387	+	4.72537i	−0.0919958	+	0.206626i	0.861687	+	0.507440i	$0.169408\pi$
$524$	6.20300	+	19.0909i	0.270979	+	0.833989i
$525$	−12.6210	−	5.70235i	−0.550826	−	0.248871i
$526$	−14.9358	−	10.8515i	−0.651232	−	0.473148i
$527$	1.38567	+	2.40005i	0.0603607	+	0.104548i
$528$	−4.59499	−	3.44762i	−0.199971	−	0.150039i
$529$	−7.60198	+	13.1670i	−0.330521	+	0.572479i
$530$	0.0616877	−	0.586919i	0.00267954	−	0.0254941i
$531$	−27.8412	−	9.36889i	−1.20821	−	0.406575i
$532$	0.873097	−	2.68476i	0.0378535	−	0.116399i
$533$	−32.3193	−	44.4838i	−1.39991	−	1.92681i
$534$	3.44837	+	1.55695i	0.149226	+	0.0673759i
$535$	−3.68441	+	17.3338i	−0.159291	+	0.749405i
$536$	−4.34349	−	4.82394i	−0.187610	−	0.208362i
$537$	3.61764	−	32.7717i	0.156113	−	1.41420i
$538$		−	7.72445i		−	0.333025i
$539$	−0.247646	+	23.2151i	−0.0106669	+	0.999943i
$540$	−7.30668	−	0.114527i	−0.314430	−	0.00492844i
$541$	−10.2016	−	1.07223i	−0.438599	−	0.0460987i	−0.117344	−	0.993091i	$-0.537438\pi$
$541$	−10.2016	−	1.07223i	−0.438599	−	0.0460987i	−0.321255	+	0.946993i	$0.604105\pi$
$542$	13.9851	−	12.5923i	0.600713	−	0.540884i
$543$	7.46581	−	34.2432i	0.320389	−	1.46952i
$544$	−2.91565	−	1.29813i	−0.125007	−	0.0556569i
$545$	−11.4349	+	8.30792i	−0.489816	+	0.355872i
$546$	−21.4854	−	7.11147i	−0.919488	−	0.304343i
$547$	28.9187	+	9.39625i	1.23647	+	0.401754i	0.853055	−	0.521821i	$-0.174747\pi$
$547$	28.9187	+	9.39625i	1.23647	+	0.401754i	0.383418	+	0.923575i	$0.374747\pi$
$548$	−4.89003	−	0.513963i	−0.208892	−	0.0219554i
$549$	19.9311	+	11.7866i	0.850637	+	0.503038i
$550$	−9.50097	−	3.19403i	−0.405123	−	0.136194i
$551$	0.483476	−	0.279135i	0.0205968	−	0.0118915i
$552$	−3.89760	−	2.86301i	−0.165893	−	0.121858i
$553$	18.8536	+	8.39999i	0.801736	+	0.357204i
$554$	−3.54000	+	1.15022i	−0.150400	+	0.0488680i
$555$	−13.1654	−	5.94423i	−0.558841	−	0.252319i
$556$	22.5958	−	2.37491i	0.958273	−	0.100719i
$557$	24.0837	+	5.11914i	1.02046	+	0.216905i	0.687614	−	0.726077i	$-0.258658\pi$
$557$	24.0837	+	5.11914i	1.02046	+	0.216905i	0.332845	+	0.942982i	$0.391992\pi$
$558$	2.55358	−	0.514954i	0.108102	−	0.0217998i
$559$	27.2432	+	19.7933i	1.15226	+	0.837169i
$560$	3.39955	−	1.51252i	0.143657	−	0.0639158i
$561$	2.19656	−	18.2021i	0.0927387	−	0.768495i
$562$	7.16550	+	12.4110i	0.302259	+	0.523527i
$563$	16.6707	−	7.42228i	0.702587	−	0.312812i	−0.0241687	−	0.999708i	$-0.507694\pi$
$563$	16.6707	−	7.42228i	0.702587	−	0.312812i	0.726756	+	0.686896i	$0.241027\pi$
$564$	7.88380	+	8.84837i	0.331968	+	0.372584i
$565$	−4.37735	+	4.86154i	−0.184156	+	0.204526i
$566$	−4.93996	−	6.79927i	−0.207642	−	0.285794i
$567$	−20.3651	−	12.3394i	−0.855255	−	0.518208i
$568$	1.63479	−	0.531175i	0.0685942	−	0.0222876i
$569$	3.56235	−	0.757202i	0.149342	−	0.0317435i	−0.132634	−	0.991165i	$-0.542344\pi$
$569$	3.56235	−	0.757202i	0.149342	−	0.0317435i	0.281976	+	0.959422i	$0.409010\pi$
$570$	−1.04477	−	2.37997i	−0.0437605	−	0.0996861i
$571$	−16.8149	−	9.70810i	−0.703683	−	0.406272i	0.105035	−	0.994469i	$-0.466505\pi$
$571$	−16.8149	−	9.70810i	−0.703683	−	0.406272i	−0.808718	+	0.588197i	$0.799838\pi$
$572$	−15.9863	−	3.56797i	−0.668420	−	0.149184i
$573$	7.06862	+	0.0369290i	0.295296	+	0.00154273i
$574$	21.8856	+	19.7161i	0.913487	+	0.822934i
$575$	−8.02538	−	2.60760i	−0.334682	−	0.108745i
$576$	−2.03058	+	2.20834i	−0.0846073	+	0.0920141i
$577$	3.02559	+	28.7866i	0.125957	+	1.19840i	0.856725	+	0.515774i	$0.172496\pi$
$577$	3.02559	+	28.7866i	0.125957	+	1.19840i	−0.730768	+	0.682626i	$0.760838\pi$
$578$	0.712241	+	6.77652i	0.0296253	+	0.281866i
$579$	−0.994237	+	1.09268i	−0.0413191	+	0.0454102i
$580$	0.699771	+	0.227370i	0.0290564	+	0.00944100i
$581$	30.1791	−	9.79718i	1.25204	−	0.406455i
$582$	−0.0383337	+	7.33749i	−0.00158898	+	0.304149i
$583$	0.708086	−	1.19819i	0.0293259	−	0.0496238i
$584$	−2.70582	−	1.56221i	−0.111968	−	0.0646445i
$585$	−19.1224	+	8.27553i	−0.790614	+	0.342151i
$586$	−3.01914	+	0.641738i	−0.124720	+	0.0265100i
$587$	−21.0052	+	6.82499i	−0.866976	+	0.281698i	−0.708539	−	0.705671i	$-0.750645\pi$
$587$	−21.0052	+	6.82499i	−0.866976	+	0.281698i	−0.158437	+	0.987369i	$0.550645\pi$
$588$	12.0505	+	1.33654i	0.496953	+	0.0551179i
$589$	0.544614	+	0.749597i	0.0224404	+	0.0308866i
$590$	9.21434	−	10.2336i	0.379348	−	0.421309i
$591$	−0.731655	+	0.651896i	−0.0300963	+	0.0268154i
$592$	−5.41751	+	2.41203i	−0.222658	+	0.0991338i
$593$	−9.11219	−	15.7828i	−0.374193	−	0.648121i	0.616013	−	0.787736i	$-0.288747\pi$
$593$	−9.11219	−	15.7828i	−0.374193	−	0.648121i	−0.990206	+	0.139615i	$0.955413\pi$
$594$	−15.5575	−	7.41375i	−0.638333	−	0.304190i
$595$	9.60555	+	6.98263i	0.393789	+	0.286260i
$596$	15.6810	+	11.3929i	0.642321	+	0.466673i
$597$	3.42693	+	16.5471i	0.140255	+	0.677226i
$598$	−13.4880	−	2.86697i	−0.551567	−	0.117239i
$599$	−25.7663	+	2.70814i	−1.05278	+	0.110652i	−0.615077	−	0.788467i	$-0.710875\pi$
$599$	−25.7663	+	2.70814i	−1.05278	+	0.110652i	−0.437704	+	0.899119i	$0.644208\pi$
$600$	−2.15405	+	4.77085i	−0.0879389	+	0.194769i
$601$	10.5842	−	3.43901i	0.431738	−	0.140280i	−0.0850828	−	0.996374i	$-0.527115\pi$
$601$	10.5842	−	3.43901i	0.431738	−	0.140280i	0.516820	+	0.856094i	$0.327115\pi$
$602$	−16.4787	−	7.34188i	−0.671621	−	0.299233i
$603$	−15.6341	−	11.6104i	−0.636671	−	0.472811i
$604$	17.5290	−	10.1204i	0.713244	−	0.411791i
$605$	11.2838	+	10.5826i	0.458751	+	0.430242i
$606$	−1.96867	−	1.15037i	−0.0799719	−	0.0467305i
$607$	−2.72283	−	0.286181i	−0.110516	−	0.0116157i	0.0491089	−	0.998793i	$-0.484362\pi$
$607$	−2.72283	−	0.286181i	−0.110516	−	0.0116157i	−0.159625	+	0.987178i	$0.551029\pi$
$608$	−1.01483	−	0.329738i	−0.0411567	−	0.0133726i
$609$	1.59448	+	1.79050i	0.0646117	+	0.0725545i
$610$	−8.78172	+	6.38029i	−0.355561	+	0.258330i
$611$	30.8698	+	13.7441i	1.24886	+	0.556028i
$612$	−9.34419	−	2.08844i	−0.377716	−	0.0844203i
$613$	28.8310	−	25.9595i	1.16447	−	1.04850i	0.166424	−	0.986054i	$-0.446778\pi$
$613$	28.8310	−	25.9595i	1.16447	−	1.04850i	0.998049	−	0.0624412i	$-0.0198886\pi$
$614$	−18.1478	−	1.90741i	−0.732387	−	0.0769770i
$615$	27.1196	+	0.141682i	1.09357	+	0.00571319i
$616$	8.77449	+	0.0913370i	0.353534	+	0.00368007i
$617$			19.4606i			0.783454i	0.920082	+	0.391727i	$0.128122\pi$
$617$			19.4606i			0.783454i	−0.920082	+	0.391727i	$0.871878\pi$
$618$	−24.5546	−	2.71056i	−0.987731	−	0.109035i
$619$	−8.70162	−	9.66413i	−0.349748	−	0.388434i	0.542443	−	0.840092i	$-0.317499\pi$
$619$	−8.70162	−	9.66413i	−0.349748	−	0.388434i	−0.892191	+	0.451658i	$0.850833\pi$
$620$	−0.253896	+	1.19448i	−0.0101967	+	0.0479716i
$621$	−13.1600	−	6.10809i	−0.528091	−	0.245109i
$622$	7.03865	+	9.68787i	0.282224	+	0.388448i
$623$	−5.65350	+	1.20016i	−0.226503	+	0.0480836i
$624$	−2.68579	+	8.12139i	−0.107518	+	0.325116i
$625$	0.0789576	−	0.751231i	0.00315830	−	0.0300493i
$626$	−14.3514	+	24.8574i	−0.573599	+	0.993502i
$627$	0.0942428	−	6.12903i	0.00376370	−	0.244770i
$628$	7.26261	+	12.5792i	0.289809	+	0.501965i
$629$	−15.3120	−	11.1248i	−0.610530	−	0.443576i
$630$	9.10039	−	6.46410i	0.362568	−	0.257536i
$631$	−3.25192	−	10.0084i	−0.129457	−	0.398427i	0.865230	−	0.501375i	$-0.167172\pi$
$631$	−3.25192	−	10.0084i	−0.129457	−	0.398427i	−0.994687	+	0.102948i	$0.967172\pi$
$632$	3.17306	−	7.12681i	0.126217	−	0.283489i
$633$	2.74234	+	27.4715i	0.108998	+	1.09189i
$634$	−2.56185	+	12.0526i	−0.101744	+	0.478668i
$635$	24.8734	−	5.28700i	0.987070	−	0.209808i
$636$	−0.585778	−	0.430286i	−0.0232276	−	0.0170620i
$637$	32.8840	−	10.6659i	1.30291	−	0.422598i
$638$	1.27767	+	1.17412i	0.0505833	+	0.0464838i
$639$	4.49257	−	2.53157i	0.177724	−	0.100148i
$640$	−0.572012	−	1.28476i	−0.0226108	−	0.0507846i
$641$	−18.9939	+	17.1022i	−0.750215	+	0.675497i	−0.952742	−	0.303780i	$-0.901751\pi$
$641$	−18.9939	+	17.1022i	−0.750215	+	0.675497i	0.202527	+	0.979277i	$0.435085\pi$
$642$	16.1428	+	14.6884i	0.637104	+	0.579706i
$643$	−7.22615	+	5.25010i	−0.284971	+	0.207044i	−0.721083	−	0.692849i	$-0.756355\pi$
$643$	−7.22615	+	5.25010i	−0.284971	+	0.207044i	0.436111	+	0.899893i	$0.356355\pi$
$644$	7.38731	+	0.00190643i	0.291101	+	7.51239e-5i
$645$	−15.8228	+	5.04989i	−0.623021	+	0.198839i
$646$	−0.708060	−	3.33116i	−0.0278583	−	0.131063i
$647$	14.7259	+	33.0749i	0.578935	+	1.30031i	0.931234	+	0.364422i	$0.118733\pi$
$647$	14.7259	+	33.0749i	0.578935	+	1.30031i	−0.352299	+	0.935887i	$0.614600\pi$
$648$	−4.66188	+	7.69850i	−0.183136	+	0.302425i
$649$	29.8005	−	12.9072i	1.16977	−	0.506652i
$650$			14.9255i			0.585427i
$651$	−2.67877	+	2.94247i	−0.104989	+	0.115324i
$652$	−7.33666	+	22.5799i	−0.287326	+	0.884297i
$653$	28.5699	+	25.7245i	1.11803	+	1.00668i	0.999906	+	0.0136775i	$0.00435381\pi$
$653$	28.5699	+	25.7245i	1.11803	+	1.00668i	0.118121	+	0.992999i	$0.462313\pi$
$654$	1.72914	+	17.3217i	0.0676146	+	0.677330i
$655$	−28.0754	+	2.95084i	−1.09700	+	0.115299i
$656$	7.44985	−	8.27390i	0.290868	−	0.323041i
$657$	−8.88372	−	2.98947i	−0.346587	−	0.116630i
$658$	−17.7062	−	3.76836i	−0.690261	−	0.146906i
$659$	17.3596			0.676233			0.338117	−	0.941104i	$-0.390210\pi$
$659$	17.3596			0.676233			0.338117	+	0.941104i	$0.390210\pi$
$660$	6.08615	−	5.31285i	0.236903	−	0.206802i
$661$	−8.70627	+	15.0797i	−0.338635	+	0.586532i	−0.984176	−	0.177193i	$-0.943298\pi$
$661$	−8.70627	+	15.0797i	−0.338635	+	0.586532i	0.645542	+	0.763725i	$0.276632\pi$
$662$	13.5095	−	6.01484i	0.525064	−	0.233773i
$663$	−26.7334	+	5.53654i	−1.03824	+	0.215021i
$664$	−3.70593	−	11.4057i	−0.143818	−	0.442626i
$665$	3.43790	+	1.98605i	0.133316	+	0.0770159i
$666$	−14.5014	+	10.3061i	−0.561917	+	0.399353i
$667$	1.08560	+	0.977476i	0.0420345	+	0.0378480i
$668$	1.05535	+	1.17208i	0.0408327	+	0.0453493i
$669$	−8.50221	−	19.3680i	−0.328715	−	0.748809i
$670$	7.90589	−	4.56447i	0.305431	−	0.176341i
$671$	−25.0925	+	5.06792i	−0.968686	+	0.195645i
$672$	0.503988	−	4.55478i	0.0194418	−	0.175704i
$673$	−5.93002	+	8.16197i	−0.228585	+	0.314621i	−0.907868	−	0.419256i	$-0.862291\pi$
$673$	−5.93002	+	8.16197i	−0.228585	+	0.314621i	0.679283	+	0.733877i	$0.262291\pi$
$674$	1.09149	+	5.13508i	0.0420428	+	0.197796i
$675$	−3.50533	+	15.3076i	−0.134920	+	0.589188i
$676$	1.19060	+	11.3278i	0.0457921	+	0.435683i
$677$	−1.49502	−	0.665627i	−0.0574584	−	0.0255821i	0.377806	−	0.925885i	$-0.376679\pi$
$677$	−1.49502	−	0.665627i	−0.0574584	−	0.0255821i	−0.435265	+	0.900303i	$0.643345\pi$
$678$	2.44966	+	7.67549i	0.0940786	+	0.294775i
$679$	−6.58577	−	9.06945i	−0.252739	−	0.348054i
$680$	2.63825	−	3.63124i	0.101172	−	0.139252i
$681$	21.5193	−	12.2747i	0.824621	−	0.470368i
$682$	−1.71634	+	2.31260i	−0.0657220	+	0.0885541i
$683$	33.8117	+	19.5212i	1.29377	+	0.746957i	0.979320	−	0.202318i	$-0.0648474\pi$
$683$	33.8117	+	19.5212i	1.29377	+	0.746957i	0.314447	+	0.949275i	$0.398181\pi$
$684$	−3.17995	−	0.367858i	−0.121589	−	0.0140654i
$685$	2.13684	−	6.57651i	0.0816443	−	0.251275i
$686$	−16.0462	+	9.24771i	−0.612646	+	0.353079i
$687$	19.2682	+	26.8139i	0.735127	+	1.02301i
$688$	−2.77336	+	6.22907i	−0.105733	+	0.237481i
$689$	−2.02714	−	0.430882i	−0.0772279	−	0.0164153i
$690$	5.07803	−	4.52446i	0.193317	−	0.172243i
$691$	−4.60891	+	43.8508i	−0.175331	+	1.66816i	0.453981	+	0.891011i	$0.350003\pi$
$691$	−4.60891	+	43.8508i	−0.175331	+	1.66816i	−0.629312	+	0.777153i	$0.716663\pi$
$692$	−18.0771			−0.687188
$693$	25.8582	−	4.93503i	0.982271	−	0.187466i
$694$	33.4948			1.27145
$695$	−3.33994	+	31.7774i	−0.126691	+	1.20539i
$696$	0.676588	−	0.602832i	0.0256460	−	0.0228503i
$697$	34.7573	+	7.38789i	1.31653	+	0.279836i
$698$	9.21017	−	20.6864i	0.348610	−	0.782991i
$699$	6.97586	+	9.70770i	0.263851	+	0.367179i
$700$	−1.66044	−	7.82167i	−0.0627587	−	0.295631i
$701$	−13.3062	+	40.9524i	−0.502570	+	1.54675i	0.302249	+	0.953229i	$0.402263\pi$
$701$	−13.3062	+	40.9524i	−0.502570	+	1.54675i	−0.804818	+	0.593521i	$0.797737\pi$
$702$	−3.08205	+	25.4762i	−0.116324	+	0.961536i
$703$	−5.48007	−	3.16392i	−0.206685	−	0.119330i
$704$	0.0336663	−	3.31645i	0.00126885	−	0.124994i
$705$	−14.4771	+	8.25783i	−0.545240	+	0.311008i
$706$	0.695879	−	0.957796i	0.0261898	−	0.0360471i
$707$	3.46398	−	0.363175i	0.130276	−	0.0136586i
$708$	−5.15655	−	16.1569i	−0.193795	−	0.607215i
$709$	1.33042	+	0.592343i	0.0499651	+	0.0222459i	0.431567	−	0.902081i	$-0.357961\pi$
$709$	1.33042	+	0.592343i	0.0499651	+	0.0222459i	−0.381602	+	0.924327i	$0.624627\pi$
$710$	0.252686	+	2.40415i	0.00948314	+	0.0902261i
$711$	5.10484	−	22.8403i	0.191447	−	0.856577i
$712$	0.454171	+	2.13671i	0.0170208	+	0.0800765i
$713$	−1.42508	+	1.96146i	−0.0533698	+	0.0734572i
$714$	13.3936	−	5.87544i	0.501243	−	0.219883i
$715$	9.58246	−	20.9477i	0.358364	−	0.783399i
$716$	16.4854	−	9.51784i	0.616088	−	0.355698i
$717$	−19.9304	−	45.4014i	−0.744316	−	1.69555i
$718$	−22.3727	−	24.8474i	−0.834943	−	0.927298i
$719$	2.76180	+	2.48674i	0.102998	+	0.0927396i	0.719021	−	0.694988i	$-0.244591\pi$
$719$	2.76180	+	2.48674i	0.102998	+	0.0927396i	−0.616023	+	0.787728i	$0.711257\pi$
$720$	−2.44409	−	3.43900i	−0.0910858	−	0.128164i
$721$	32.6849	−	18.8594i	1.21725	−	0.702360i
$722$	5.51948	+	16.9872i	0.205414	+	0.632198i
$723$	30.8158	−	6.38202i	1.14605	−	0.237350i
$724$	18.4854	−	8.23022i	0.687003	−	0.305874i
$725$	0.790588	−	1.36934i	0.0293617	−	0.0508560i
$726$	18.2644	−	5.42316i	0.677857	−	0.201272i
$727$	8.32563			0.308781			0.154390	−	0.988010i	$-0.450659\pi$
$727$	8.32563			0.308781			0.154390	+	0.988010i	$0.450659\pi$
$728$	−4.03454	−	12.4279i	−0.149530	−	0.460610i
$729$	−9.14414	+	25.4044i	−0.338672	+	0.940905i
$730$	2.94016	−	3.26538i	0.108820	−	0.120857i
$731$	−21.6428	+	2.27475i	−0.800486	+	0.0841345i
$732$	1.32794	+	13.3026i	0.0490819	+	0.491679i
$733$	20.0749	+	18.0755i	0.741483	+	0.667634i	0.950657	−	0.310244i	$-0.100411\pi$
$733$	20.0749	+	18.0755i	0.741483	+	0.667634i	−0.209174	+	0.977878i	$0.567078\pi$
$734$	−7.09008	+	21.8210i	−0.261700	+	0.805429i
$735$	−5.36206	+	16.1860i	−0.197783	+	0.597029i
$736$		−	2.79214i		−	0.102920i
$737$	21.4328	−	2.03294i	0.789488	−	0.0748844i
$738$	17.0018	−	28.7499i	0.625843	−	1.05830i
$739$	−0.897769	−	2.01642i	−0.0330250	−	0.0741753i	0.896280	−	0.443489i	$-0.146259\pi$
$739$	−0.897769	−	2.01642i	−0.0330250	−	0.0741753i	−0.929305	+	0.369314i	$0.879593\pi$
$740$	−1.73396	−	8.15766i	−0.0637418	−	0.299882i
$741$	−8.69543	+	2.77518i	−0.319435	+	0.101949i
$742$	1.11025		0.000286521i	0.0407586		1.05185e-5i
$743$	−4.61210	+	3.35089i	−0.169202	+	0.122932i	−0.669163	−	0.743115i	$-0.733347\pi$
$743$	−4.61210	+	3.35089i	−0.169202	+	0.122932i	0.499962	+	0.866047i	$0.333347\pi$
$744$	1.11241	+	1.01219i	0.0407829	+	0.0371087i
$745$	−20.2574	+	18.2398i	−0.742172	+	0.668255i
$746$	−11.3713	−	25.5403i	−0.416332	−	0.935096i
$747$	−17.6624	−	31.3440i	−0.646234	−	1.14682i
$748$	9.22036	−	5.19930i	0.337130	−	0.190105i
$749$	−33.1550	−	3.49338i	−1.21146	−	0.127645i
$750$	−15.7487	−	11.5683i	−0.575063	−	0.422415i
$751$	34.6969	−	7.37505i	1.26611	−	0.269119i	0.474558	−	0.880224i	$-0.342608\pi$
$751$	34.6969	−	7.37505i	1.26611	−	0.269119i	0.791550	+	0.611105i	$0.209275\pi$
$752$	−1.42258	+	6.69270i	−0.0518761	+	0.244058i
$753$	2.14219	+	21.4595i	0.0780659	+	0.782027i
$754$	1.05094	−	2.36045i	0.0382730	−	0.0859627i
$755$	8.79630	+	27.0722i	0.320130	+	0.985259i
$756$	−1.21904	−	13.6936i	−0.0443361	−	0.498030i
$757$	17.6353	+	12.8128i	0.640966	+	0.465689i	0.860182	−	0.509988i	$-0.170350\pi$
$757$	17.6353	+	12.8128i	0.640966	+	0.465689i	−0.219216	+	0.975676i	$0.570350\pi$
$758$	18.9022	+	32.7395i	0.686557	+	1.18915i
$759$	15.3290	−	4.72139i	0.556407	−	0.171376i
$760$	0.750323	−	1.29960i	0.0272171	−	0.0471413i
$761$	−0.156380	+	1.48786i	−0.00566878	+	0.0539349i	−0.996991	−	0.0775226i	$-0.975299\pi$
$761$	−0.156380	+	1.48786i	−0.00566878	+	0.0539349i	0.991322	+	0.131457i	$0.0419657\pi$
$762$	9.83339	−	29.7346i	0.356226	−	1.07717i
$763$	−17.7876	−	19.7654i	−0.643954	−	0.715555i
$764$	2.39883	+	3.30170i	0.0867865	+	0.119451i
$765$	5.60509	−	12.2433i	0.202652	−	0.442658i
$766$	3.60165	−	16.9444i	0.130133	−	0.612227i
$767$	−32.3579	−	35.9370i	−1.16837	−	1.29761i
$768$	−1.72159	−	0.190045i	−0.0621226	−	0.00685767i
$769$		−	4.30792i		−	0.155348i	−0.996979	−	0.0776738i	$-0.975251\pi$
$769$		−	4.30792i		−	0.155348i	0.996979	−	0.0776738i	$-0.0247493\pi$
$770$	−2.69127	+	12.0436i	−0.0969865	+	0.434021i
$771$	−24.1458	−	0.126146i	−0.869590	−	0.00454305i
$772$	−0.848255	−	0.0891552i	−0.0305294	−	0.00320876i
$773$	−30.6426	+	27.5908i	−1.10214	+	0.992370i	−0.999997	−	0.00239950i	$-0.999236\pi$
$773$	−30.6426	+	27.5908i	−1.10214	+	0.992370i	−0.102142	+	0.994770i	$0.532570\pi$
$774$	−4.46181	+	19.9632i	−0.160376	+	0.717561i
$775$	2.39738	+	1.06738i	0.0861164	+	0.0383415i
$776$	−3.42729	+	2.49007i	−0.123032	+	0.0893883i
$777$	8.53929	−	25.7991i	0.306345	−	0.925538i
$778$	26.2194	+	8.51919i	0.940010	+	0.305428i
$779$	11.8151	+	1.24182i	0.423320	+	0.0444927i
$780$	−10.3866	−	6.06926i	−0.371899	−	0.217315i
$781$	−1.81665	+	5.40382i	−0.0650050	+	0.193364i
$782$	7.71743	−	4.45566i	0.275975	−	0.159334i
$783$	1.63221	−	2.17405i	0.0583303	−	0.0776943i
$784$	3.49687	+	6.06398i	0.124888	+	0.216571i
$785$	−19.4277	+	6.31243i	−0.693403	+	0.225300i
$786$	−14.3072	+	31.6879i	−0.510320	+	1.13027i
$787$	−13.9269	+	1.46377i	−0.496439	+	0.0521778i	−0.349440	−	0.936959i	$-0.613628\pi$
$787$	−13.9269	+	1.46377i	−0.496439	+	0.0521778i	−0.146999	+	0.989137i	$0.546961\pi$
$788$	−0.553407	−	0.117630i	−0.0197143	−	0.00419041i
$789$	−6.48481	−	31.3121i	−0.230865	−	1.11474i
$790$	8.87594	+	6.44875i	0.315792	+	0.229436i
$791$	−9.95482	−	7.23653i	−0.353953	−	0.257301i
$792$	−1.86779	−	9.77299i	−0.0663689	−	0.347268i
$793$	19.0593	+	33.0117i	0.676816	+	1.17228i
$794$	22.8446	−	10.1711i	0.810725	−	0.360958i
$795$	0.763186	−	0.679990i	0.0270674	−	0.0241168i
$796$	−6.52816	+	7.25026i	−0.231384	+	0.256978i
$797$	−6.56467	−	9.03549i	−0.232533	−	0.320054i	0.676766	−	0.736198i	$-0.263381\pi$
$797$	−6.56467	−	9.03549i	−0.232533	−	0.320054i	−0.909298	+	0.416145i	$0.863381\pi$
$798$	4.24808	−	2.42167i	0.150380	−	0.0857263i
$799$	−20.7687	+	6.74815i	−0.734742	+	0.238732i
$800$	−2.95615	+	0.628350i	−0.104516	+	0.0222155i
$801$	2.60278	+	6.01428i	0.0919647	+	0.212504i
$802$	33.9889	+	19.6235i	1.20019	+	0.692929i
$803$	9.50891	−	4.11850i	0.335562	−	0.145339i
$804$	0.0587375	−	11.2430i	0.00207151	−	0.396511i
$805$	−2.16264	+	10.1615i	−0.0762230	+	0.358146i
$806$	4.07848	+	1.32518i	0.143658	+	0.0466774i
$807$	9.00421	−	9.89573i	0.316963	−	0.348346i
$808$	−0.137605	−	1.30923i	−0.00484093	−	0.0460584i
$809$	−0.764971	−	7.27821i	−0.0268950	−	0.255888i	−0.999705	−	0.0242843i	$-0.992269\pi$
$809$	−0.764971	−	7.27821i	−0.0268950	−	0.255888i	0.972810	−	0.231604i	$-0.0743974\pi$
$810$	−9.22704	−	8.66395i	−0.324205	−	0.304420i
$811$	−38.5510	−	12.5260i	−1.35371	−	0.439846i	−0.459770	−	0.888038i	$-0.652068\pi$
$811$	−38.5510	−	12.5260i	−1.35371	−	0.439846i	−0.893937	+	0.448192i	$0.852068\pi$
$812$	−0.288146	+	1.35390i	−0.0101119	+	0.0475127i
$813$	32.5948	+	0.170287i	1.14315	+	0.00597222i
$814$	4.28433	−	19.1960i	0.150166	−	0.672818i
$815$	−28.9160	−	16.6947i	−1.01288	−	0.584788i
$816$	−2.22201	−	5.06173i	−0.0777861	−	0.177196i
$817$	−7.11678	+	1.51272i	−0.248985	+	0.0529233i
$818$	19.4134	−	6.30778i	0.678772	−	0.220546i
$819$	−19.2350	−	34.1554i	−0.672127	−	1.19349i
$820$	9.20337	+	12.6674i	0.321396	+	0.442363i
$821$	24.3977	−	27.0964i	0.851487	−	0.945672i	−0.147572	−	0.989051i	$-0.547146\pi$
$821$	24.3977	−	27.0964i	0.851487	−	0.945672i	0.999059	+	0.0433795i	$0.0138125\pi$
$822$	−5.66547	−	6.35863i	−0.197606	−	0.221783i
$823$	−34.7537	+	15.4734i	−1.21144	+	0.539367i	−0.910195	−	0.414180i	$-0.864068\pi$
$823$	−34.7537	+	15.4734i	−1.21144	+	0.539367i	−0.301244	+	0.953547i	$0.597402\pi$
$824$	−7.13136	−	12.3519i	−0.248433	−	0.430298i
$825$	−8.44841	−	15.1669i	−0.294136	−	0.528044i
$826$	20.9550	+	15.2329i	0.729116	+	0.530022i
$827$	18.2864	+	13.2859i	0.635881	+	0.461994i	0.858432	−	0.512927i	$-0.171439\pi$
$827$	18.2864	+	13.2859i	0.635881	+	0.461994i	−0.222552	+	0.974921i	$0.571439\pi$
$828$	−1.65585	−	8.21112i	−0.0575448	−	0.285356i
$829$	−10.6662	−	2.26716i	−0.370451	−	0.0787419i	0.0189243	−	0.999821i	$-0.493976\pi$
$829$	−10.6662	−	2.26716i	−0.370451	−	0.0787419i	−0.389376	+	0.921079i	$0.627309\pi$
$830$	16.7734	−	1.76295i	0.582213	−	0.0611930i
$831$	−5.87584	−	2.65296i	−0.203831	−	0.0920302i
$832$	−4.69693	+	1.52612i	−0.162837	+	0.0529088i
$833$	−11.1805	+	19.3421i	−0.387381	+	0.670165i
$834$	31.7156	+	23.2969i	1.09822	+	0.806705i
$835$	−1.92091	+	1.10904i	−0.0664759	+	0.0383799i
$836$	2.88409	−	2.05101i	0.0997484	−	0.0709357i
$837$	3.87164	+	2.31695i	0.133824	+	0.0800854i
$838$	−30.6278	−	3.21911i	−1.05802	−	0.111202i
$839$	−21.5458	−	7.00065i	−0.743844	−	0.241689i	−0.0875135	−	0.996163i	$-0.527892\pi$
$839$	−21.5458	−	7.00065i	−0.743844	−	0.241689i	−0.656330	+	0.754474i	$0.727892\pi$
$840$	6.11825	+	2.02509i	0.211100	+	0.0698722i
$841$	23.2400	−	16.8849i	0.801381	−	0.582237i
$842$	−4.55980	−	2.03015i	−0.157141	−	0.0699636i
$843$	−5.28756	+	24.2523i	−0.182113	+	0.835294i
$844$	−11.8454	+	10.6656i	−0.407734	+	0.367125i
$845$	−15.9307	−	1.67439i	−0.548034	−	0.0576007i
$846$	−0.214471	+	20.5255i	−0.00737368	+	0.705683i
$847$	−17.5869	+	23.1884i	−0.604293	+	0.796762i
$848$		−	0.419636i		−	0.0144103i
$849$	1.59721	−	14.4689i	0.0548160	−	0.496571i
$850$	−6.45414	−	7.16805i	−0.221375	−	0.245862i
$851$	3.44259	−	16.1961i	0.118010	−	0.555196i
$852$	2.71349	+	1.22515i	0.0929627	+	0.0419730i
$853$	−24.4500	−	33.6525i	−0.837151	−	1.15224i	−0.986550	−	0.163463i	$-0.947734\pi$
$853$	−24.4500	−	33.6525i	−0.837151	−	1.15224i	0.149398	−	0.988777i	$-0.452266\pi$
$854$	−13.6605	−	15.1794i	−0.467451	−	0.519427i
$855$	1.43583	−	4.26683i	0.0491045	−	0.145922i
$856$	−1.31714	+	12.5317i	−0.0450189	+	0.428326i
$857$	−0.368855	+	0.638876i	−0.0125999	+	0.0218236i	−0.872257	−	0.489049i	$-0.837344\pi$
$857$	−0.368855	+	0.638876i	−0.0125999	+	0.0218236i	0.859657	+	0.510872i	$0.170677\pi$
$858$	−16.3208	−	23.2057i	−0.557183	−	0.792231i
$859$	−15.3932	−	26.6619i	−0.525210	−	0.909691i	−0.999569	−	0.0293590i	$-0.990653\pi$
$859$	−15.3932	−	26.6619i	−0.525210	−	0.909691i	0.474359	−	0.880332i	$-0.342680\pi$
$860$	−7.75787	−	5.63642i	−0.264541	−	0.192200i
$861$	5.05485	+	50.7697i	0.172269	+	1.73023i
$862$	−1.87877	−	5.78226i	−0.0639912	−	0.196945i
$863$	11.3230	−	25.4318i	0.385438	−	0.865708i	−0.611770	−	0.791036i	$-0.709542\pi$
$863$	11.3230	−	25.4318i	0.385438	−	0.865708i	0.997208	−	0.0746725i	$-0.0237911\pi$
$864$	−5.17557	+	0.462090i	−0.176076	+	0.0157206i
$865$	5.28566	−	24.8671i	0.179718	−	0.845506i
$866$	17.7618	−	3.77538i	0.603569	−	0.128293i
$867$	−6.98678	+	9.51159i	−0.237284	+	0.323030i
$868$	−2.28474	−	0.240731i	−0.0775490	−	0.00817096i
$869$	12.7088	+	22.5376i	0.431117	+	0.764535i
$870$	0.631432	+	1.10699i	0.0214076	+	0.0375304i
$871$	−13.0391	−	29.2864i	−0.441814	−	0.992331i
$872$	−7.46888	+	6.72501i	−0.252928	+	0.227738i
$873$	−8.60226	+	9.35532i	−0.291142	+	0.316630i
$874$	2.41035	−	1.75122i	0.0815314	−	0.0592361i
$875$	29.8493	+	0.00770316i	1.00909	+	0.000260414i
$876$	−1.64538	−	5.15544i	−0.0555922	−	0.174186i
$877$	−11.9476	−	56.2092i	−0.403443	−	1.89805i	−0.438627	−	0.898669i	$-0.644535\pi$
$877$	−11.9476	−	56.2092i	−0.403443	−	1.89805i	0.0351841	−	0.999381i	$-0.488798\pi$
$878$	−1.58002	−	3.54878i	−0.0533230	−	0.119765i
$879$	−4.61586	−	2.69722i	−0.155689	−	0.0909749i
$880$	4.55231	+	1.01603i	0.153458	+	0.0342503i
$881$			4.45958i			0.150247i	0.997174	+	0.0751236i	$0.0239351\pi$
$881$			4.45958i			0.150247i	−0.997174	+	0.0751236i	$0.976065\pi$
$882$	13.8798	+	15.7592i	0.467357	+	0.530639i
$883$	−17.0836	+	52.5780i	−0.574910	+	1.76939i	0.0615754	+	0.998102i	$0.480388\pi$
$883$	−17.0836	+	52.5780i	−0.574910	+	1.76939i	−0.636485	+	0.771289i	$0.719612\pi$
$884$	−11.7135	−	10.5469i	−0.393967	−	0.354729i
$885$	23.7335	−	2.36919i	0.797791	−	0.0796396i
$886$	18.3744	−	1.93122i	0.617299	−	0.0648808i
$887$	−11.1523	+	12.3859i	−0.374457	+	0.415876i	−0.900689	−	0.434465i	$-0.856938\pi$
$887$	−11.1523	+	12.3859i	−0.374457	+	0.415876i	0.526232	+	0.850341i	$0.323604\pi$
$888$	−9.75198	−	3.22503i	−0.327255	−	0.108225i
$889$	14.7715	+	45.5020i	0.495421	+	1.52609i
$890$	−3.07208			−0.102976
$891$	−11.2886	−	27.6327i	−0.378181	−	0.925732i
$892$	6.10605	−	10.5760i	0.204446	−	0.354110i
$893$	−6.66981	+	2.96959i	−0.223197	+	0.0993735i
$894$	6.80837	+	32.8744i	0.227706	+	1.09949i
$895$	8.27261	+	25.4605i	0.276523	+	0.851050i
$896$	2.29163	−	1.32228i	0.0765580	−	0.0441744i
$897$	−13.9375	−	19.3955i	−0.465358	−	0.647598i
$898$	20.1040	+	18.1017i	0.670879	+	0.604062i
$899$	−0.303986	−	0.337610i	−0.0101385	−	0.0112599i
$900$	−8.32081	+	3.60097i	−0.277360	+	0.120032i
$901$	1.15987	−	0.669649i	0.0386408	−	0.0223093i
$902$	7.31033	+	36.1952i	0.243407	+	1.20517i
$903$	−12.5525	−	28.6144i	−0.417719	−	0.952229i
$904$	−2.73418	+	3.76327i	−0.0909374	+	0.125165i
$905$	5.91655	+	27.8352i	0.196673	+	0.925273i
$906$	34.2533	+	7.46801i	1.13799	+	0.248108i
$907$	1.32831	+	12.6380i	0.0441058	+	0.419638i	0.994190	+	0.107644i	$0.0343305\pi$
$907$	1.32831	+	12.6380i	0.0441058	+	0.419638i	−0.950084	+	0.311995i	$0.899003\pi$
$908$	13.0667	+	5.81765i	0.433633	+	0.193066i
$909$	−1.18109	−	3.76856i	−0.0391744	−	0.124995i
$910$	18.2757	−	1.91609i	0.605834	−	0.0635176i
$911$	−3.64206	+	5.01287i	−0.120667	+	0.166084i	−0.865077	−	0.501639i	$-0.832731\pi$
$911$	−3.64206	+	5.01287i	−0.120667	+	0.166084i	0.744410	+	0.667723i	$0.232731\pi$
$912$	−0.915721	−	1.60539i	−0.0303225	−	0.0531596i
$913$	37.7016	+	12.6745i	1.24774	+	0.419466i
$914$	−7.60161	−	4.38879i	−0.251439	−	0.145168i
$915$	−18.6875	−	2.06290i	−0.617791	−	0.0681975i
$916$	−5.89093	+	18.1304i	−0.194642	+	0.599046i
$917$	−11.0286	−	51.9513i	−0.364196	−	1.71558i
$918$	−9.53631	−	13.5678i	−0.314745	−	0.447804i
$919$	11.3431	−	25.4769i	0.374173	−	0.840406i	−0.624082	−	0.781359i	$-0.714527\pi$
$919$	11.3431	−	25.4769i	0.374173	−	0.840406i	0.998255	−	0.0590477i	$-0.0188064\pi$
$920$	3.84090	+	0.816409i	0.126631	+	0.0269162i
$921$	−21.0256	−	23.5981i	−0.692818	−	0.777583i
$922$	1.71560	−	16.3228i	0.0565002	−	0.537564i
$923$	8.48911			0.279423
$924$	11.1345	+	10.3452i	0.366297	+	0.340333i
$925$	−17.9222			−0.589279
$926$	0.890386	−	8.47145i	0.0292599	−	0.278389i
$927$	−28.2971	−	32.0952i	−0.929398	−	1.05415i
$928$	0.511755	+	0.108777i	0.0167992	+	0.00357078i
$929$	7.37967	−	16.5750i	0.242119	−	0.543808i	−0.751083	−	0.660207i	$-0.770468\pi$
$929$	7.37967	−	16.5750i	0.242119	−	0.543808i	0.993203	+	0.116399i	$0.0371351\pi$
$930$	−1.71765	+	1.23428i	−0.0563238	+	0.0404738i
$931$	−3.04159	+	6.82204i	−0.0996841	+	0.223583i
$932$	−2.13275	+	6.56394i	−0.0698607	+	0.215009i
$933$	−2.27577	+	20.6158i	−0.0745052	+	0.674932i
$934$	−30.2477	−	17.4635i	−0.989736	−	0.571424i
$935$	4.45624	+	14.2039i	0.145735	+	0.464517i
$936$	−12.9077	+	7.27349i	−0.421900	+	0.237742i
$937$	−12.2132	+	16.8101i	−0.398989	+	0.549161i	−0.960490	−	0.278315i	$-0.910224\pi$
$937$	−12.2132	+	16.8101i	−0.398989	+	0.549161i	0.561501	+	0.827476i	$0.310224\pi$
$938$	10.0912	+	13.8968i	0.329488	+	0.453748i
$939$	−47.3612	+	15.1155i	−1.54558	+	0.493276i
$940$	−8.79061	−	3.91383i	−0.286718	−	0.127655i
$941$	−3.35309	−	31.9025i	−0.109307	−	1.03999i	−0.902403	−	0.430894i	$-0.858198\pi$
$941$	−3.35309	−	31.9025i	−0.109307	−	1.03999i	0.793095	−	0.609098i	$-0.208468\pi$
$942$	−5.35922	+	24.5810i	−0.174613	+	0.800891i
$943$	6.46327	+	30.4073i	0.210473	+	0.990198i
$944$	5.75546	−	7.92172i	0.187324	−	0.257830i
$945$	19.1935	+	2.32701i	0.624364	+	0.0756977i
$946$	−11.1079	−	19.6986i	−0.361150	−	0.640457i
$947$	3.17025	−	1.83034i	0.103019	−	0.0594781i	−0.447605	−	0.894231i	$-0.647723\pi$
$947$	3.17025	−	1.83034i	0.103019	−	0.0594781i	0.550624	+	0.834753i	$0.314390\pi$
$948$	12.3725	−	5.43134i	0.401841	−	0.176402i
$949$	−10.3249	−	11.4670i	−0.335161	−	0.372234i
$950$	−2.39653	−	2.15784i	−0.0777536	−	0.0700096i
$951$	−17.3313	+	12.4541i	−0.562007	+	0.403853i
$952$	7.31173	+	4.22394i	0.236974	+	0.136899i
$953$	−6.93199	−	21.3345i	−0.224549	−	0.691091i	−0.998337	−	0.0576463i	$-0.981640\pi$
$953$	−6.93199	−	21.3345i	−0.224549	−	0.691091i	0.773788	−	0.633445i	$-0.218360\pi$
$954$	−0.248861	−	1.23406i	−0.00805717	−	0.0399543i
$955$	−5.24327	+	2.33445i	−0.169668	+	0.0755412i
$956$	14.3135	−	24.7917i	0.462931	−	0.801820i
$957$	0.268167	+	2.99350i	0.00866860	+	0.0967661i
$958$	−10.3988			−0.335971
$959$	12.7241	+	2.70802i	0.410882	+	0.0874466i
$960$	0.764815	−	2.31268i	0.0246843	−	0.0746413i
$961$	−20.2385	+	22.4772i	−0.652856	+	0.725070i
$962$	−29.1267	+	3.06134i	−0.939082	+	0.0987015i
$963$	3.55839	+	37.6345i	0.114668	+	1.21275i
$964$	13.5022	+	12.1575i	0.434878	+	0.391566i
$965$	0.370669	−	1.14080i	0.0119323	−	0.0367237i
$966$	9.46160	+	8.61365i	0.304422	+	0.277140i
$967$			39.3163i			1.26433i	0.774835	+	0.632164i	$0.217833\pi$
$967$			39.3163i			1.26433i	−0.774835	+	0.632164i	$0.782167\pi$
$968$	8.76610	+	6.64496i	0.281753	+	0.213577i
$969$	2.97597	−	5.09290i	0.0956019	−	0.163607i
$970$	−2.42325	−	5.44271i	−0.0778059	−	0.174755i
$971$	1.23429	+	5.80686i	0.0396101	+	0.186351i	0.993505	−	0.113791i	$-0.0362993\pi$
$971$	1.23429	+	5.80686i	0.0396101	+	0.186351i	−0.953895	+	0.300142i	$0.902966\pi$
$972$	−14.9463	+	4.42823i	−0.479402	+	0.142036i
$973$	−60.1120	−	0.0155130i	−1.92710	−	0.000497325i
$974$	27.0313	−	19.6394i	0.866139	−	0.629287i
$975$	−17.3983	+	19.1210i	−0.557193	+	0.612361i
$976$	−5.73592	+	5.16465i	−0.183602	+	0.165316i
$977$	−2.39589	−	5.38126i	−0.0766513	−	0.172162i	0.871155	−	0.491008i	$-0.163371\pi$
$977$	−2.39589	−	5.38126i	−0.0766513	−	0.172162i	−0.947807	+	0.318846i	$0.896705\pi$
$978$	−35.7198	+	20.3748i	−1.14219	+	0.651513i
$979$	−6.58836	−	3.01383i	−0.210565	−	0.0963224i
$980$	−9.36416	+	3.03726i	−0.299127	+	0.0970217i
$981$	−17.9763	+	24.2063i	−0.573938	+	0.772846i
$982$	−0.00463429		0.000985049i	−0.000147886		3.14342e-5i
$983$	6.26921	−	29.4943i	0.199957	−	0.940723i	−0.757654	−	0.652657i	$-0.773654\pi$
$983$	6.26921	−	29.4943i	0.199957	−	0.940723i	0.957611	−	0.288066i	$-0.0930123\pi$
$984$	19.1886	−	1.91551i	0.611711	−	0.0610641i
$985$	0.323627	−	0.726879i	0.0103116	−	0.0231603i
$986$	0.515995	+	1.58807i	0.0164326	+	0.0505744i
$987$	−18.2907	−	25.4674i	−0.582198	−	0.810636i
$988$	−4.26335	−	3.09751i	−0.135635	−	0.0985448i
$989$	−9.51919	−	16.4877i	−0.302693	−	0.524279i
$990$	13.9900	+	0.288228i	0.444631	+	0.00916050i
$991$	10.6164	−	18.3881i	0.337241	−	0.584118i	−0.646672	−	0.762768i	$-0.723840\pi$
$991$	10.6164	−	18.3881i	0.337241	−	0.584118i	0.983913	+	0.178650i	$0.0571730\pi$
$992$	−0.0907651	+	0.863572i	−0.00288179	+	0.0274184i
$993$	24.3183	+	8.04221i	0.771719	+	0.255212i
$994$	−4.44869	+	0.944399i	−0.141104	+	0.0299545i
$995$	−8.06474	−	11.1002i	−0.255669	−	0.351899i
$996$	8.54770	−	18.9316i	0.270844	−	0.599872i
$997$	−0.0409410	+	0.192612i	−0.00129661	+	0.00610009i	−0.978791	−	0.204861i	$-0.934326\pi$
$997$	−0.0409410	+	0.192612i	−0.00129661	+	0.00610009i	0.977495	+	0.210961i	$0.0676592\pi$
$998$	−11.6224	−	12.9080i	−0.367900	−	0.408594i
$999$	−30.5912	−	3.70085i	−0.967862	−	0.117090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.95.4	yes	128
3.2	odd	2		462.2.bc.a.95.13	✓	128
7.2	even	3	inner	462.2.bc.b.359.8	yes	128
11.8	odd	10		462.2.bc.a.305.10	yes	128
21.2	odd	6		462.2.bc.a.359.10	yes	128
33.8	even	10	inner	462.2.bc.b.305.8	yes	128
77.30	odd	30		462.2.bc.a.107.13	yes	128
231.107	even	30	inner	462.2.bc.b.107.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.13	✓	128	3.2	odd	2
462.2.bc.a.107.13	yes	128	77.30	odd	30
462.2.bc.a.305.10	yes	128	11.8	odd	10
462.2.bc.a.359.10	yes	128	21.2	odd	6
462.2.bc.b.95.4	yes	128	1.1	even	1	trivial
462.2.bc.b.107.4	yes	128	231.107	even	30	inner
462.2.bc.b.305.8	yes	128	33.8	even	10	inner
462.2.bc.b.359.8	yes	128	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-1.29320 + 1.15223i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.572012 - 1.28476i) q^{5} +(-1.01074 - 1.40656i) q^{6} +(2.51605 + 0.818231i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.344742 - 2.98013i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-1.29320 + 1.15223i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.572012 - 1.28476i) q^{5} +(-1.01074 - 1.40656i) q^{6} +(2.51605 + 0.818231i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.344742 - 2.98013i) q^{9} +(1.21793 + 0.703172i) q^{10} +(1.92213 + 2.70286i) q^{11} +(1.50450 - 0.858177i) q^{12} +(2.90286 - 3.99544i) q^{13} +(-1.07675 + 2.41674i) q^{14} +(0.740609 + 2.32054i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.333610 + 3.17409i) q^{17} +(2.92777 + 0.654361i) q^{18} +(0.221853 + 1.04374i) q^{19} +(-0.826629 + 1.13776i) q^{20} +(-4.19655 + 1.84092i) q^{21} +(-2.88897 + 1.62907i) q^{22} +(-2.41806 + 1.39607i) q^{23} +(0.696212 + 1.58597i) q^{24} +(2.02224 + 2.24593i) q^{25} +(3.67012 + 3.30459i) q^{26} +(2.98796 + 4.25113i) q^{27} +(-2.29095 - 1.32347i) q^{28} +(-0.161674 - 0.497582i) q^{29} +(-2.38524 + 0.493989i) q^{30} +(0.793258 - 0.353181i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.60000 - 1.28061i) q^{33} -3.19158 q^{34} +(2.49044 - 2.76448i) q^{35} +(-0.956812 + 2.84333i) q^{36} +(-3.96808 + 4.40700i) q^{37} +(-1.06121 + 0.111537i) q^{38} +(0.849678 + 8.51167i) q^{39} +(-1.04512 - 0.941028i) q^{40} +(3.44048 - 10.5887i) q^{41} +(-1.39218 - 4.36599i) q^{42} +6.81857i q^{43} +(-1.31817 - 3.04342i) q^{44} +(-3.63155 - 2.14758i) q^{45} +(-1.13567 - 2.55075i) q^{46} +(1.42258 + 6.69270i) q^{47} +(-1.65005 + 0.526620i) q^{48} +(5.66099 + 4.11742i) q^{49} +(-2.44501 + 1.77640i) q^{50} +(-4.08870 - 3.72035i) q^{51} +(-3.67012 + 3.30459i) q^{52} +(-0.170681 - 0.383356i) q^{53} +(-4.54017 + 2.52723i) q^{54} +(4.57200 - 0.923404i) q^{55} +(1.55569 - 2.14006i) q^{56} +(-1.48952 - 1.09414i) q^{57} +(0.511755 - 0.108777i) q^{58} +(2.03583 - 9.57781i) q^{59} +(-0.241957 - 2.42381i) q^{60} +(-3.13938 + 7.05115i) q^{61} +(0.268328 + 0.825830i) q^{62} +(3.30582 - 7.21606i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-3.47271 - 6.01492i) q^{65} +(1.85896 - 5.43547i) q^{66} +(3.24562 - 5.62158i) q^{67} +(0.333610 - 3.17409i) q^{68} +(1.51845 - 4.59156i) q^{69} +(2.48901 + 2.76576i) q^{70} +(1.01035 + 1.39063i) q^{71} +(-2.72774 - 1.24878i) q^{72} +(0.649602 - 3.05614i) q^{73} +(-3.96808 - 4.40700i) q^{74} +(-5.20299 - 0.574354i) q^{75} -1.06705i q^{76} +(2.62460 + 8.37326i) q^{77} +(-8.55386 - 0.0446884i) q^{78} +(7.75852 + 0.815454i) q^{79} +(1.04512 - 0.941028i) q^{80} +(-8.76231 - 2.05475i) q^{81} +(10.1711 + 4.52845i) q^{82} +(9.70225 - 7.04910i) q^{83} +(4.48759 - 0.928182i) q^{84} +(4.26878 + 1.38701i) q^{85} +(-6.78121 - 0.712734i) q^{86} +(0.782405 + 0.457188i) q^{87} +(3.16454 - 0.992822i) q^{88} +(-1.89178 + 1.09222i) q^{89} +(2.51541 - 3.38717i) q^{90} +(10.5729 - 7.67752i) q^{91} +(2.65548 - 0.862818i) q^{92} +(-0.618897 + 1.37075i) q^{93} +(-6.80474 + 0.715207i) q^{94} +(1.46785 + 0.312002i) q^{95} +(-0.351258 - 1.69606i) q^{96} +(-3.42729 - 2.49007i) q^{97} +(-4.68660 + 5.19960i) q^{98} +(8.71749 - 4.79639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more