LMFDB - Embedded newform 418.2.q.b.21.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (of order $18$, degree $6$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.9
Character	$\chi$	$=$	418.21
Dual form			418.2.q.b.219.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(1.60541 - 1.91325i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.62065 - 0.953840i) q^{5} +(-1.60541 - 1.91325i) q^{6} +(-0.240088 + 0.138615i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.562250 - 3.18868i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(1.60541 - 1.91325i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.62065 - 0.953840i) q^{5} +(-1.60541 - 1.91325i) q^{6} +(-0.240088 + 0.138615i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.562250 - 3.18868i) q^{9} +(-0.484277 - 2.74647i) q^{10} +(-3.26495 + 0.583175i) q^{11} +(-2.16296 + 1.24879i) q^{12} +(0.722503 - 0.606252i) q^{13} +(0.0948183 + 0.260511i) q^{14} +(2.38228 - 6.54527i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.42328 + 0.603616i) q^{17} -3.23787 q^{18} +(-0.610388 + 4.31595i) q^{19} -2.78884 q^{20} +(-0.120234 + 0.681883i) q^{21} +(0.00736239 + 3.31662i) q^{22} +(0.344115 + 0.125248i) q^{23} +(0.854220 + 2.34695i) q^{24} +(2.12779 - 1.78543i) q^{25} +(-0.471581 - 0.816802i) q^{26} +(-0.514502 - 0.297048i) q^{27} +(0.273018 - 0.0481405i) q^{28} +(0.197274 + 1.11880i) q^{29} +(-6.03216 - 3.48267i) q^{30} +(-5.30261 + 3.06146i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-4.12582 + 7.18291i) q^{33} +(1.18889 - 3.26645i) q^{34} +(-0.496972 + 0.592268i) q^{35} +(-0.562250 + 3.18868i) q^{36} -5.56473i q^{37} +(4.14439 + 1.35057i) q^{38} -2.35561i q^{39} +(-0.484277 + 2.74647i) q^{40} +(-2.43635 - 2.04434i) q^{41} +(0.650645 + 0.236816i) q^{42} +(-0.375037 - 1.03040i) q^{43} +(3.26751 + 0.568674i) q^{44} +(-4.51495 - 7.82013i) q^{45} +(0.183100 - 0.317138i) q^{46} +(0.877002 + 4.97372i) q^{47} +(2.45963 - 0.433699i) q^{48} +(-3.46157 + 5.99562i) q^{49} +(-1.38882 - 2.40550i) q^{50} +(6.65063 - 5.58054i) q^{51} +(-0.886282 + 0.322580i) q^{52} +(1.42082 - 3.90368i) q^{53} +(-0.381877 + 0.455104i) q^{54} +(-8.00005 + 4.64254i) q^{55} -0.277230i q^{56} +(7.27758 + 8.09669i) q^{57} +1.13606 q^{58} +(-1.46750 - 0.258760i) q^{59} +(-4.47723 + 5.33576i) q^{60} +(0.291694 - 0.801422i) q^{61} +(2.09416 + 5.75367i) q^{62} +(0.576989 + 0.687628i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.31516 - 2.27793i) q^{65} +(6.35734 + 5.31044i) q^{66} +(1.52399 - 0.268721i) q^{67} +(-3.01038 - 1.73804i) q^{68} +(0.792075 - 0.457305i) q^{69} +(0.496972 + 0.592268i) q^{70} +(5.27997 + 14.5066i) q^{71} +(3.04260 + 1.10742i) q^{72} +(9.32026 - 11.1075i) q^{73} +(-5.48019 - 0.966305i) q^{74} -6.93735i q^{75} +(2.04972 - 3.84690i) q^{76} +(0.703040 - 0.592585i) q^{77} +(-2.31983 - 0.409048i) q^{78} +(-7.99609 - 6.70952i) q^{79} +(2.62065 + 0.953840i) q^{80} +(7.73349 - 2.81476i) q^{81} +(-2.43635 + 2.04434i) q^{82} +(4.14067 - 2.39062i) q^{83} +(0.346201 - 0.599638i) q^{84} +(9.54698 - 1.68339i) q^{85} +(-1.07988 + 0.190411i) q^{86} +(2.45725 + 1.41869i) q^{87} +(1.12743 - 3.11912i) q^{88} +(-9.00683 - 10.7339i) q^{89} +(-8.48533 + 3.08841i) q^{90} +(-0.0894289 + 0.245704i) q^{91} +(-0.280525 - 0.235388i) q^{92} +(-2.65551 + 15.0601i) q^{93} +5.05045 q^{94} +(2.51711 + 11.8928i) q^{95} -2.49757i q^{96} +(-6.79598 - 1.19831i) q^{97} +(5.30344 + 4.45011i) q^{98} +(3.69528 + 10.0830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	1.60541	−	1.91325i	0.926883	−	1.10462i	−0.0673877	−	0.997727i	$-0.521466\pi$
$3$	1.60541	−	1.91325i	0.926883	−	1.10462i	0.994271	−	0.106889i	$-0.0340891\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	2.62065	−	0.953840i	1.17199	−	0.426570i	0.318625	−	0.947881i	$-0.396779\pi$
$5$	2.62065	−	0.953840i	1.17199	−	0.426570i	0.853367	+	0.521311i	$0.174557\pi$
$6$	−1.60541	−	1.91325i	−0.655405	−	0.781082i
$7$	−0.240088	+	0.138615i	−0.0907449	+	0.0523916i	−0.544686	−	0.838640i	$-0.683351\pi$
$7$	−0.240088	+	0.138615i	−0.0907449	+	0.0523916i	0.453941	+	0.891032i	$0.350018\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.562250	−	3.18868i	−0.187417	−	1.06289i
$10$	−0.484277	−	2.74647i	−0.153142	−	0.868511i
$11$	−3.26495	+	0.583175i	−0.984420	+	0.175834i
$11$	−3.26495	+	0.583175i	−0.984420	+	0.175834i
$12$	−2.16296	+	1.24879i	−0.624393	+	0.360494i
$13$	0.722503	−	0.606252i	0.200386	−	0.168144i	−0.537073	−	0.843536i	$-0.680470\pi$
$13$	0.722503	−	0.606252i	0.200386	−	0.168144i	0.737459	+	0.675392i	$0.236025\pi$
$14$	0.0948183	+	0.260511i	0.0253413	+	0.0696245i
$15$	2.38228	−	6.54527i	0.615103	−	1.68998i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	3.42328	+	0.603616i	0.830267	+	0.146398i	0.572600	−	0.819835i	$-0.305935\pi$
$17$	3.42328	+	0.603616i	0.830267	+	0.146398i	0.257667	+	0.966234i	$0.417046\pi$
$18$	−3.23787			−0.763173
$19$	−0.610388	+	4.31595i	−0.140033	+	0.990147i
$19$	−0.610388	+	4.31595i	−0.140033	+	0.990147i
$20$	−2.78884			−0.623604
$21$	−0.120234	+	0.681883i	−0.0262373	+	0.148799i
$22$	0.00736239	+	3.31662i	0.00156967	+	0.707105i
$23$	0.344115	+	0.125248i	0.0717529	+	0.0261159i	0.377647	−	0.925950i	$-0.376733\pi$
$23$	0.344115	+	0.125248i	0.0717529	+	0.0261159i	−0.305894	+	0.952065i	$0.598955\pi$
$24$	0.854220	+	2.34695i	0.174367	+	0.479069i
$25$	2.12779	−	1.78543i	0.425559	−	0.357086i
$26$	−0.471581	−	0.816802i	−0.0924846	−	0.160188i
$27$	−0.514502	−	0.297048i	−0.0990159	−	0.0571669i
$28$	0.273018	−	0.0481405i	0.0515956	−	0.00909770i
$29$	0.197274	+	1.11880i	0.0366329	+	0.207756i	0.997630	−	0.0688017i	$-0.0219176\pi$
$29$	0.197274	+	1.11880i	0.0366329	+	0.207756i	−0.960997	+	0.276557i	$0.910806\pi$
$30$	−6.03216	−	3.48267i	−1.10132	−	0.635845i
$31$	−5.30261	+	3.06146i	−0.952376	+	0.549855i	−0.893818	−	0.448429i	$-0.851984\pi$
$31$	−5.30261	+	3.06146i	−0.952376	+	0.549855i	−0.0585580	+	0.998284i	$0.518650\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−4.12582	+	7.18291i	−0.718213	+	1.25038i
$34$	1.18889	−	3.26645i	0.203893	−	0.560192i
$35$	−0.496972	+	0.592268i	−0.0840036	+	0.100112i
$36$	−0.562250	+	3.18868i	−0.0937083	+	0.531446i
$37$		−	5.56473i		−	0.914835i	−0.889252	−	0.457418i	$-0.848774\pi$
$37$		−	5.56473i		−	0.914835i	0.889252	−	0.457418i	$-0.151226\pi$
$38$	4.14439	+	1.35057i	0.672309	+	0.219092i
$39$		−	2.35561i		−	0.377200i
$40$	−0.484277	+	2.74647i	−0.0765710	+	0.434255i
$41$	−2.43635	−	2.04434i	−0.380494	−	0.319273i	0.432402	−	0.901681i	$-0.357666\pi$
$41$	−2.43635	−	2.04434i	−0.380494	−	0.319273i	−0.812896	+	0.582408i	$0.802111\pi$
$42$	0.650645	+	0.236816i	0.100397	+	0.0365414i
$43$	−0.375037	−	1.03040i	−0.0571926	−	0.157135i	0.907806	−	0.419390i	$-0.137756\pi$
$43$	−0.375037	−	1.03040i	−0.0571926	−	0.157135i	−0.964999	+	0.262255i	$0.915534\pi$
$44$	3.26751	+	0.568674i	0.492595	+	0.0857308i
$45$	−4.51495	−	7.82013i	−0.673049	−	1.16576i
$46$	0.183100	−	0.317138i	0.0269966	−	0.0467594i
$47$	0.877002	+	4.97372i	0.127924	+	0.725492i	0.979528	+	0.201307i	$0.0645189\pi$
$47$	0.877002	+	4.97372i	0.127924	+	0.725492i	−0.851604	+	0.524185i	$0.824370\pi$
$48$	2.45963	−	0.433699i	0.355017	−	0.0625991i
$49$	−3.46157	+	5.99562i	−0.494510	+	0.856517i
$50$	−1.38882	−	2.40550i	−0.196409	−	0.340190i
$51$	6.65063	−	5.58054i	0.931275	−	0.781432i
$52$	−0.886282	+	0.322580i	−0.122905	+	0.0447338i
$53$	1.42082	−	3.90368i	0.195165	−	0.536211i	−0.803051	−	0.595910i	$-0.796792\pi$
$53$	1.42082	−	3.90368i	0.195165	−	0.536211i	0.998216	+	0.0596982i	$0.0190138\pi$
$54$	−0.381877	+	0.455104i	−0.0519669	+	0.0619318i
$55$	−8.00005	+	4.64254i	−1.07873	+	0.626000i
$56$		−	0.277230i		−	0.0370464i
$57$	7.27758	+	8.09669i	0.963938	+	1.07243i
$58$	1.13606			0.149172
$59$	−1.46750	−	0.258760i	−0.191053	−	0.0336877i	0.0773030	−	0.997008i	$-0.475369\pi$
$59$	−1.46750	−	0.258760i	−0.191053	−	0.0336877i	−0.268356	+	0.963320i	$0.586480\pi$
$60$	−4.47723	+	5.33576i	−0.578008	+	0.688843i
$61$	0.291694	−	0.801422i	0.0373476	−	0.102612i	−0.919617	−	0.392816i	$-0.871501\pi$
$61$	0.291694	−	0.801422i	0.0373476	−	0.102612i	0.956965	+	0.290204i	$0.0937232\pi$
$62$	2.09416	+	5.75367i	0.265959	+	0.730716i
$63$	0.576989	+	0.687628i	0.0726937	+	0.0866330i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.31516	−	2.27793i	0.163126	−	0.282542i
$66$	6.35734	+	5.31044i	0.782535	+	0.653670i
$67$	1.52399	−	0.268721i	0.186186	−	0.0328295i	−0.0797778	−	0.996813i	$-0.525421\pi$
$67$	1.52399	−	0.268721i	0.186186	−	0.0328295i	0.265963	+	0.963983i	$0.414310\pi$
$68$	−3.01038	−	1.73804i	−0.365062	−	0.210769i
$69$	0.792075	−	0.457305i	0.0953546	−	0.0550530i
$70$	0.496972	+	0.592268i	0.0593995	+	0.0707896i
$71$	5.27997	+	14.5066i	0.626617	+	1.72162i	0.690180	+	0.723638i	$0.257531\pi$
$71$	5.27997	+	14.5066i	0.626617	+	1.72162i	−0.0635633	+	0.997978i	$0.520246\pi$
$72$	3.04260	+	1.10742i	0.358574	+	0.130510i
$73$	9.32026	−	11.1075i	1.09085	−	1.30003i	0.140081	−	0.990140i	$-0.455264\pi$
$73$	9.32026	−	11.1075i	1.09085	−	1.30003i	0.950773	−	0.309889i	$-0.100292\pi$
$74$	−5.48019	−	0.966305i	−0.637059	−	0.112331i
$75$		−	6.93735i		−	0.801056i
$76$	2.04972	−	3.84690i	0.235119	−	0.441270i
$77$	0.703040	−	0.592585i	0.0801188	−	0.0675313i
$78$	−2.31983	−	0.409048i	−0.262669	−	0.0463156i
$79$	−7.99609	−	6.70952i	−0.899630	−	0.754880i	0.0704877	−	0.997513i	$-0.477544\pi$
$79$	−7.99609	−	6.70952i	−0.899630	−	0.754880i	−0.970118	+	0.242633i	$0.921989\pi$
$80$	2.62065	+	0.953840i	0.292998	+	0.106643i
$81$	7.73349	−	2.81476i	0.859277	−	0.312751i
$82$	−2.43635	+	2.04434i	−0.269050	+	0.225760i
$83$	4.14067	−	2.39062i	0.454498	−	0.262404i	−0.255230	−	0.966880i	$-0.582151\pi$
$83$	4.14067	−	2.39062i	0.454498	−	0.262404i	0.709728	+	0.704476i	$0.248818\pi$
$84$	0.346201	−	0.599638i	0.0377737	−	0.0654259i
$85$	9.54698	−	1.68339i	1.03552	−	0.182589i
$86$	−1.07988	+	0.190411i	−0.116446	+	0.0205326i
$87$	2.45725	+	1.41869i	0.263445	+	0.152100i
$88$	1.12743	−	3.11912i	0.120185	−	0.332499i
$89$	−9.00683	−	10.7339i	−0.954722	−	1.13779i	−0.990372	−	0.138429i	$-0.955795\pi$
$89$	−9.00683	−	10.7339i	−0.954722	−	1.13779i	0.0356501	−	0.999364i	$-0.488650\pi$
$90$	−8.48533	+	3.08841i	−0.894433	+	0.325547i
$91$	−0.0894289	+	0.245704i	−0.00937470	+	0.0257568i
$92$	−0.280525	−	0.235388i	−0.0292468	−	0.0245409i
$93$	−2.65551	+	15.0601i	−0.275363	+	1.56166i
$94$	5.05045			0.520914
$95$	2.51711	+	11.8928i	0.258250	+	1.22018i
$96$		−	2.49757i		−	0.254907i
$97$	−6.79598	−	1.19831i	−0.690027	−	0.121670i	−0.182370	−	0.983230i	$-0.558377\pi$
$97$	−6.79598	−	1.19831i	−0.690027	−	0.121670i	−0.507657	+	0.861560i	$0.669488\pi$
$98$	5.30344	+	4.45011i	0.535728	+	0.449529i
$99$	3.69528	+	10.0830i	0.371389	+	1.01338i
$100$	−2.61013	+	0.950008i	−0.261013	+	0.0950008i
$101$	10.5748	+	12.6025i	1.05223	+	1.25400i	0.966224	+	0.257705i	$0.0829662\pi$
$101$	10.5748	+	12.6025i	1.05223	+	1.25400i	0.0860068	+	0.996295i	$0.472589\pi$
$102$	−4.34089	−	7.51864i	−0.429812	−	0.744457i
$103$	5.50221	+	3.17670i	0.542149	+	0.313010i	0.745949	−	0.666003i	$-0.231996\pi$
$103$	5.50221	+	3.17670i	0.542149	+	0.313010i	−0.203801	+	0.979012i	$0.565329\pi$
$104$	0.163778	+	0.928833i	0.0160598	+	0.0910795i
$105$	0.335315	+	1.90166i	0.0327234	+	0.185583i
$106$	−3.59765	−	2.07710i	−0.349435	−	0.201746i
$107$	9.35985	+	16.2117i	0.904851	+	1.56725i	0.821118	+	0.570759i	$0.193351\pi$
$107$	9.35985	+	16.2117i	0.904851	+	1.56725i	0.0837330	+	0.996488i	$0.473316\pi$
$108$	0.381877	+	0.455104i	0.0367462	+	0.0437924i
$109$	−5.18310	+	1.88650i	−0.496451	+	0.180694i	−0.578097	−	0.815968i	$-0.696205\pi$
$109$	−5.18310	+	1.88650i	−0.496451	+	0.180694i	0.0816458	+	0.996661i	$0.473982\pi$
$110$	3.18282	+	8.68468i	0.303470	+	0.828052i
$111$	−10.6467	−	8.93366i	−1.01054	−	0.847946i
$112$	−0.273018	−	0.0481405i	−0.0257978	−	0.00454885i
$113$		−	12.9364i		−	1.21695i	−0.793573	−	0.608475i	$-0.791782\pi$
$113$		−	12.9364i		−	1.21695i	0.793573	−	0.608475i	$-0.208218\pi$
$114$	9.23742	−	5.76104i	0.865164	−	0.539571i
$115$	1.02127			0.0952341
$116$	0.197274	−	1.11880i	0.0183165	−	0.103878i
$117$	−2.33937	−	1.96297i	−0.216275	−	0.181476i
$118$	−0.509659	+	1.40028i	−0.0469179	+	0.128906i
$119$	−0.905560	+	0.329597i	−0.0830125	+	0.0302141i
$120$	4.47723	+	5.33576i	0.408713	+	0.487086i
$121$	10.3198	−	3.80808i	0.938165	−	0.346189i
$122$	−0.738595	−	0.426428i	−0.0668692	−	0.0386070i
$123$	−7.82268	+	1.37935i	−0.705347	+	0.124372i
$124$	6.02990	−	1.06323i	0.541501	−	0.0954813i
$125$	−3.09891	+	5.36747i	−0.277175	+	0.480081i
$126$	0.777375	−	0.448817i	0.0692540	−	0.0399838i
$127$	11.6285	−	9.75743i	1.03186	−	0.865832i	0.0407877	−	0.999168i	$-0.487013\pi$
$127$	11.6285	−	9.75743i	1.03186	−	0.865832i	0.991071	+	0.133336i	$0.0425688\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−2.57351	−	0.936681i	−0.226585	−	0.0824702i
$130$	−2.01495	−	1.69074i	−0.176723	−	0.148288i
$131$	−15.8740	−	2.79901i	−1.38692	−	0.244551i	−0.570161	−	0.821533i	$-0.693119\pi$
$131$	−15.8740	−	2.79901i	−1.38692	−	0.244551i	−0.816757	+	0.576982i	$0.804230\pi$
$132$	6.33370	−	5.33861i	0.551278	−	0.464666i
$133$	−0.451709	−	1.12082i	−0.0391681	−	0.0971873i
$134$		−	1.54750i		−	0.133684i
$135$	−1.63167	−	0.287707i	−0.140432	−	0.0247619i
$136$	−2.23439	+	2.66284i	−0.191597	+	0.228336i
$137$	−1.01329	−	0.368809i	−0.0865715	−	0.0315094i	0.298371	−	0.954450i	$-0.403557\pi$
$137$	−1.01329	−	0.368809i	−0.0865715	−	0.0315094i	−0.384943	+	0.922940i	$0.625779\pi$
$138$	−0.312815	−	0.859452i	−0.0266286	−	0.0731614i
$139$	−7.42638	−	8.85042i	−0.629898	−	0.750683i	0.352841	−	0.935683i	$-0.385216\pi$
$139$	−7.42638	−	8.85042i	−0.629898	−	0.750683i	−0.982738	+	0.185001i	$0.940771\pi$
$140$	0.669568	−	0.386575i	0.0565889	−	0.0326716i
$141$	10.9239	+	6.30694i	0.919961	+	0.531140i
$142$	15.2031	−	2.68071i	1.27581	−	0.224960i
$143$	−2.00539	+	2.40073i	−0.167699	+	0.200759i
$144$	1.61893	−	2.80408i	0.134911	−	0.233673i
$145$	1.58414	+	2.74381i	0.131556	+	0.227861i
$146$	−9.32026	−	11.1075i	−0.771350	−	0.919259i
$147$	5.91389	+	16.2483i	0.487769	+	1.34014i
$148$	−1.90325	+	5.22913i	−0.156446	+	0.429832i
$149$	−6.74587	+	8.03941i	−0.552643	+	0.658614i	−0.967972	−	0.251057i	$-0.919222\pi$
$149$	−6.74587	+	8.03941i	−0.552643	+	0.658614i	0.415329	+	0.909671i	$0.363666\pi$
$150$	−6.83196	−	1.20466i	−0.557827	−	0.0983600i
$151$	8.63960			0.703081			0.351540	−	0.936173i	$-0.385658\pi$
$151$	8.63960			0.703081			0.351540	+	0.936173i	$0.385658\pi$
$152$	−3.43253	−	2.68659i	−0.278415	−	0.217911i
$153$		−	11.2551i		−	0.909922i
$154$	−0.461501	−	0.795260i	−0.0371888	−	0.0640839i
$155$	−10.9762	+	13.0809i	−0.881626	+	1.05068i
$156$	−0.805667	+	2.21355i	−0.0645050	+	0.177226i
$157$	4.75145	−	1.72939i	0.379207	−	0.138020i	−0.145382	−	0.989376i	$-0.546441\pi$
$157$	4.75145	−	1.72939i	0.379207	−	0.138020i	0.524589	+	0.851355i	$0.324219\pi$
$158$	−7.99609	+	6.70952i	−0.636135	+	0.533780i
$159$	−5.18772	−	8.98539i	−0.411413	−	0.712588i
$160$	1.39442	−	2.41521i	0.110239	−	0.190939i
$161$	−0.0999792	+	0.0176290i	−0.00787946	+	0.00138936i
$162$	−1.42909	−	8.10478i	−0.112280	−	0.636772i
$163$	−7.02188	+	12.1623i	−0.549996	+	0.952621i	0.448278	+	0.893894i	$0.352037\pi$
$163$	−7.02188	+	12.1623i	−0.549996	+	0.952621i	−0.998274	+	0.0587269i	$0.981296\pi$
$164$	1.59022	+	2.75433i	0.124175	+	0.215077i
$165$	−3.96100	+	22.7593i	−0.308364	+	1.77181i
$166$	−1.63528	−	4.49289i	−0.126922	−	0.348716i
$167$	−21.3149	−	7.75799i	−1.64940	−	0.600331i	−0.660752	−	0.750604i	$-0.729763\pi$
$167$	−21.3149	−	7.75799i	−1.64940	−	0.600331i	−0.988645	+	0.150273i	$0.951985\pi$
$168$	−0.530411	−	0.445068i	−0.0409221	−	0.0343377i
$169$	−2.10296	+	11.9265i	−0.161766	+	0.917420i
$170$		−	9.69426i		−	0.743516i
$171$	14.1054	−	0.480311i	1.07866	−	0.0367303i
$172$			1.09653i			0.0836099i
$173$	−2.68039	+	15.2012i	−0.203786	+	1.15573i	0.695553	+	0.718475i	$0.255160\pi$
$173$	−2.68039	+	15.2012i	−0.203786	+	1.15573i	−0.899339	+	0.437253i	$0.855952\pi$
$174$	1.82384	−	2.17356i	0.138265	−	0.164777i
$175$	−0.263371	+	0.723606i	−0.0199090	+	0.0546994i
$176$	−2.87596	−	1.65193i	−0.216783	−	0.124519i
$177$	−2.85102	+	2.39229i	−0.214296	+	0.179815i
$178$	−12.1349	+	7.00607i	−0.909547	+	0.525127i
$179$	−7.15030	−	4.12823i	−0.534438	−	0.308558i	0.208384	−	0.978047i	$-0.433180\pi$
$179$	−7.15030	−	4.12823i	−0.534438	−	0.308558i	−0.742822	+	0.669489i	$0.766513\pi$
$180$	1.56803	+	8.89272i	0.116874	+	0.662824i
$181$	20.2499	−	3.57061i	1.50517	−	0.265401i	0.640582	−	0.767890i	$-0.278693\pi$
$181$	20.2499	−	3.57061i	1.50517	−	0.265401i	0.864584	+	0.502489i	$0.167582\pi$
$182$	0.226442	+	0.130736i	0.0167850	+	0.00969082i
$183$	−1.06503	−	1.84469i	−0.0787296	−	0.136364i
$184$	−0.280525	+	0.235388i	−0.0206806	+	0.0173531i
$185$	−5.30786	−	14.5832i	−0.390242	−	1.07218i
$186$	14.3702	+	5.23032i	1.05367	+	0.383506i
$187$	−11.5289	+	0.0255923i	−0.843073	+	0.00187150i
$188$	0.877002	−	4.97372i	0.0639619	−	0.362746i
$189$	0.164701			0.0119803
$190$	12.1492	−	0.413701i	0.881398	−	0.0300131i
$191$	−10.7029			−0.774432			−0.387216	−	0.921989i	$-0.626563\pi$
$191$	−10.7029			−0.774432			−0.387216	+	0.921989i	$0.626563\pi$
$192$	−2.45963	−	0.433699i	−0.177508	−	0.0312995i
$193$	−12.7500	−	10.6985i	−0.917762	−	0.770093i	0.0558181	−	0.998441i	$-0.482223\pi$
$193$	−12.7500	−	10.6985i	−0.917762	−	0.770093i	−0.973580	+	0.228348i	$0.926668\pi$
$194$	−2.36022	+	6.48465i	−0.169454	+	0.465571i
$195$	−2.24688	−	6.17325i	−0.160902	−	0.442076i
$196$	5.30344	−	4.45011i	0.378817	−	0.317865i
$197$	−2.68299	+	1.54902i	−0.191155	+	0.110363i	−0.592523	−	0.805553i	$-0.701868\pi$
$197$	−2.68299	+	1.54902i	−0.191155	+	0.110363i	0.401368	+	0.915917i	$0.368535\pi$
$198$	10.5715	−	1.88824i	0.751283	−	0.134192i
$199$	−1.75937	−	9.97791i	−0.124719	−	0.707315i	−0.981474	−	0.191593i	$-0.938635\pi$
$199$	−1.75937	−	9.97791i	−0.124719	−	0.707315i	0.856756	−	0.515722i	$-0.172476\pi$
$200$	0.482332	+	2.73544i	0.0341060	+	0.193425i
$201$	1.93250	−	3.34719i	0.136308	−	0.236093i
$202$	14.2474	−	8.22572i	1.00244	−	0.578760i
$203$	−0.202445	−	0.241265i	−0.0142089	−	0.0169335i
$204$	−8.15821	+	2.96934i	−0.571189	+	0.207896i
$205$	−8.33481	−	3.03362i	−0.582128	−	0.211877i
$206$	4.08389	−	4.86699i	0.284538	−	0.339099i
$207$	0.205896	−	1.16769i	0.0143107	−	0.0811602i
$208$	0.943161			0.0653965
$209$	−0.524066	−	14.4473i	−0.0362504	−	0.999343i
$210$	1.93100			0.133252
$211$	4.78470	−	27.1354i	0.329392	−	1.86808i	−0.147424	−	0.989073i	$-0.547098\pi$
$211$	4.78470	−	27.1354i	0.329392	−	1.86808i	0.476816	−	0.879003i	$-0.341791\pi$
$212$	−2.67027	+	3.18231i	−0.183395	+	0.218562i
$213$	36.2313	+	13.1871i	2.48253	+	0.903565i
$214$	17.5908	−	6.40251i	1.20248	−	0.437667i
$215$	−1.96568	−	2.34261i	−0.134058	−	0.159765i
$216$	0.514502	−	0.297048i	0.0350074	−	0.0202115i
$217$	0.848729	−	1.47004i	0.0576155	−	0.0997930i
$218$	0.957799	+	5.43195i	0.0648703	+	0.367898i
$219$	−6.28852	−	35.6640i	−0.424939	−	2.40995i
$220$	9.10543	−	1.62638i	0.613888	−	0.109651i
$221$	2.83927	−	1.63926i	0.190990	−	0.110268i
$222$	−10.6467	+	8.93366i	−0.714561	+	0.599588i
$223$	−8.11033	−	22.2829i	−0.543108	−	1.49218i	−0.842846	−	0.538155i	$-0.819122\pi$
$223$	−8.11033	−	22.2829i	−0.543108	−	1.49218i	0.299738	−	0.954021i	$-0.403101\pi$
$224$	−0.0948183	+	0.260511i	−0.00633531	+	0.0174061i
$225$	−6.88952	−	5.78099i	−0.459301	−	0.385400i
$226$	−12.7398	−	2.24637i	−0.847441	−	0.149427i
$227$	−4.40417			−0.292315			−0.146157	−	0.989261i	$-0.546691\pi$
$227$	−4.40417			−0.292315			−0.146157	+	0.989261i	$0.546691\pi$
$228$	−4.06945	−	10.0975i	−0.269506	−	0.668722i
$229$	−6.58872			−0.435395			−0.217697	−	0.976016i	$-0.569855\pi$
$229$	−6.58872			−0.435395			−0.217697	+	0.976016i	$0.569855\pi$
$230$	0.177342	−	1.00576i	0.0116936	−	0.0663176i
$231$	−0.00509774	−	2.29643i	−0.000335406	−	0.151094i
$232$	−1.06754	−	0.388554i	−0.0700877	−	0.0255098i
$233$	6.74228	+	18.5243i	0.441701	+	1.21356i	0.938372	+	0.345626i	$0.112333\pi$
$233$	6.74228	+	18.5243i	0.441701	+	1.21356i	−0.496671	+	0.867939i	$0.665444\pi$
$234$	−2.33937	+	1.96297i	−0.152930	+	0.128323i
$235$	7.04246	+	12.1979i	0.459399	+	0.795703i
$236$	1.29050	+	0.745071i	0.0840045	+	0.0485000i
$237$	−25.6740	+	4.52702i	−1.66770	+	0.294061i
$238$	0.167341	+	0.949036i	0.0108471	+	0.0615169i
$239$	−15.8547	−	9.15371i	−1.02555	−	0.592104i	−0.109847	−	0.993949i	$-0.535036\pi$
$239$	−15.8547	−	9.15371i	−1.02555	−	0.592104i	−0.915708	+	0.401844i	$0.868369\pi$
$240$	6.03216	−	3.48267i	0.389374	−	0.224805i
$241$	−3.63626	+	3.05118i	−0.234232	+	0.196544i	−0.752347	−	0.658767i	$-0.771078\pi$
$241$	−3.63626	+	3.05118i	−0.234232	+	0.196544i	0.518115	+	0.855311i	$0.326634\pi$
$242$	−1.95821	−	10.8243i	−0.125878	−	0.695812i
$243$	7.63965	−	20.9898i	0.490084	−	1.34649i
$244$	−0.548205	+	0.653325i	−0.0350952	+	0.0418249i
$245$	−3.35272	+	19.0142i	−0.214197	+	1.21477i
$246$			7.94336i			0.506450i
$247$	2.17555	+	3.48834i	0.138427	+	0.221958i
$248$		−	6.12292i		−	0.388806i
$249$	2.07362	−	11.7601i	0.131410	−	0.745264i
$250$	4.74780	+	3.98388i	0.300277	+	0.251963i
$251$	−4.70974	−	1.71420i	−0.297276	−	0.108200i	0.189076	−	0.981962i	$-0.439451\pi$
$251$	−4.70974	−	1.71420i	−0.297276	−	0.108200i	−0.486352	+	0.873763i	$0.661673\pi$
$252$	−0.307009	−	0.843501i	−0.0193398	−	0.0531356i
$253$	−1.19656	−	0.208248i	−0.0752271	−	0.0130924i
$254$	−7.58994	−	13.1462i	−0.476235	−	0.824863i
$255$	12.1061	−	20.9683i	0.758111	−	1.31309i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−13.4550	+	2.37248i	−0.839301	+	0.147991i	−0.576744	−	0.816925i	$-0.695677\pi$
$257$	−13.4550	+	2.37248i	−0.839301	+	0.147991i	−0.262557	+	0.964916i	$0.584566\pi$
$258$	−1.36934	+	2.37176i	−0.0852512	+	0.147659i
$259$	0.771355	+	1.33603i	0.0479297	+	0.0830166i
$260$	−2.01495	+	1.69074i	−0.124962	+	0.104855i
$261$	3.45657	−	1.25809i	0.213956	−	0.0778737i
$262$	−5.51298	+	15.1468i	−0.340593	+	0.935772i
$263$	−15.6746	+	18.6803i	−0.966537	+	1.15187i	0.0218259	+	0.999762i	$0.493052\pi$
$263$	−15.6746	+	18.6803i	−0.966537	+	1.15187i	−0.988363	+	0.152113i	$0.951392\pi$
$264$	−4.15767	−	7.16452i	−0.255887	−	0.440946i
$265$		−	11.5854i		−	0.711687i
$266$	−1.18223	+	0.250218i	−0.0724871	+	0.0153419i
$267$	−34.9963			−2.14174
$268$	−1.52399	−	0.268721i	−0.0930928	−	0.0164148i
$269$	13.7049	−	16.3329i	0.835603	−	0.995833i	−0.164352	−	0.986402i	$-0.552553\pi$
$269$	13.7049	−	16.3329i	0.835603	−	0.995833i	0.999956	−	0.00943151i	$-0.00300219\pi$
$270$	−0.566672	+	1.55692i	−0.0344866	+	0.0947511i
$271$	6.66412	+	18.3095i	0.404817	+	1.11222i	0.959879	+	0.280415i	$0.0904722\pi$
$271$	6.66412	+	18.3095i	0.404817	+	1.11222i	−0.555062	+	0.831809i	$0.687306\pi$
$272$	2.23439	+	2.66284i	0.135480	+	0.161458i
$273$	0.326524	+	0.565555i	0.0197621	+	0.0342290i
$274$	−0.539162	+	0.933856i	−0.0325720	+	0.0564163i
$275$	−5.90593	+	7.07022i	−0.356141	+	0.426350i
$276$	−0.900715	+	0.158820i	−0.0542167	+	0.00955986i
$277$	−0.0206661	−	0.0119316i	−0.00124171	−	0.000716900i	0.499379	−	0.866384i	$-0.333562\pi$
$277$	−0.0206661	−	0.0119316i	−0.00124171	−	0.000716900i	−0.500621	+	0.865667i	$0.666895\pi$
$278$	−10.0055	+	5.77670i	−0.600092	+	0.346463i
$279$	12.7434	+	15.1870i	0.762928	+	0.909222i
$280$	−0.264433	−	0.726524i	−0.0158029	−	0.0434181i
$281$	15.9479	+	5.80455i	0.951370	+	0.346270i	0.770646	−	0.637264i	$-0.219934\pi$
$281$	15.9479	+	5.80455i	0.951370	+	0.346270i	0.180724	+	0.983534i	$0.442156\pi$
$282$	8.10804	−	9.66279i	0.482827	−	0.575411i
$283$	−19.9500	−	3.51773i	−1.18591	−	0.209107i	−0.454308	−	0.890844i	$-0.650114\pi$
$283$	−19.9500	−	3.51773i	−1.18591	−	0.209107i	−0.731597	+	0.681737i	$0.761225\pi$
$284$		−	15.4376i		−	0.916052i
$285$	26.7950	+	14.2770i	1.58720	+	0.845695i
$286$	2.01603	+	2.39180i	0.119210	+	0.141430i
$287$	0.868316	+	0.153108i	0.0512551	+	0.00903766i
$288$	−2.48035	−	2.08126i	−0.146156	−	0.122640i
$289$	−4.62029	−	1.68165i	−0.271782	−	0.0989205i
$290$	2.97721	−	1.08362i	0.174828	−	0.0636322i
$291$	−13.2030	+	11.0786i	−0.773974	+	0.649441i
$292$	−12.5571	+	7.24987i	−0.734852	+	0.424267i
$293$	−11.2599	+	19.5028i	−0.657812	+	1.13936i	0.323369	+	0.946273i	$0.395185\pi$
$293$	−11.2599	+	19.5028i	−0.657812	+	1.13936i	−0.981181	+	0.193091i	$0.938149\pi$
$294$	17.0284	−	3.00256i	0.993114	−	0.175113i
$295$	−4.09264	+	0.721642i	−0.238282	+	0.0420156i
$296$	4.81919	+	2.78236i	0.280110	+	0.161722i
$297$	1.85305	+	0.669802i	0.107525	+	0.0388659i
$298$	6.74587	+	8.03941i	0.390778	+	0.465711i
$299$	0.324556	−	0.118129i	0.0187695	−	0.00683156i
$300$	−2.37271	+	6.51898i	−0.136989	+	0.376373i
$301$	0.232872	+	0.195402i	0.0134225	+	0.0112628i
$302$	1.50025	−	8.50834i	0.0863297	−	0.489600i
$303$	41.0887			2.36048
$304$	−3.24182	+	2.91386i	−0.185931	+	0.167121i
$305$		−	2.37848i		−	0.136191i
$306$	−11.0841	−	1.95443i	−0.633637	−	0.111727i
$307$	−2.33404	−	1.95850i	−0.133211	−	0.111777i	0.573748	−	0.819032i	$-0.305489\pi$
$307$	−2.33404	−	1.95850i	−0.133211	−	0.111777i	−0.706959	+	0.707255i	$0.749933\pi$
$308$	−0.863317	+	0.316394i	−0.0491921	+	0.0180282i
$309$	14.9111	−	5.42720i	0.848264	−	0.308743i
$310$	10.9762	+	13.0809i	0.623404	+	0.742944i
$311$	10.8349	+	18.7666i	0.614392	+	1.06416i	0.990491	+	0.137579i	$0.0439321\pi$
$311$	10.8349	+	18.7666i	0.614392	+	1.06416i	−0.376098	+	0.926580i	$0.622735\pi$
$312$	2.04002	+	1.17781i	0.115493	+	0.0666802i
$313$	−2.43822	−	13.8278i	−0.137816	−	0.781596i	−0.972857	−	0.231407i	$-0.925667\pi$
$313$	−2.43822	−	13.8278i	−0.137816	−	0.781596i	0.835041	−	0.550188i	$-0.185444\pi$
$314$	−0.878033	−	4.97957i	−0.0495503	−	0.281014i
$315$	2.16797	+	1.25168i	0.122152	+	0.0705242i
$316$	5.21908	+	9.03971i	0.293596	+	0.508523i
$317$	1.36233	+	1.62356i	0.0765159	+	0.0911881i	0.802944	−	0.596054i	$-0.203266\pi$
$317$	1.36233	+	1.62356i	0.0765159	+	0.0911881i	−0.726428	+	0.687242i	$0.758821\pi$
$318$	−9.74972	+	3.54861i	−0.546737	+	0.198996i
$319$	−1.29655	−	3.53777i	−0.0725926	−	0.198077i
$320$	−2.13638	−	1.79263i	−0.119427	−	0.100211i
$321$	46.0435	+	8.11871i	2.56990	+	0.453142i
$322$			0.101522i			0.00565757i
$323$	−4.69471	+	14.4063i	−0.261221	+	0.801586i
$324$	−8.22981			−0.457212
$325$	0.454917	−	2.57996i	0.0252342	−	0.143110i
$326$	10.7581	+	9.02715i	0.595838	+	0.499968i
$327$	−4.71166	+	12.9452i	−0.260555	+	0.715870i
$328$	2.98863	−	1.08777i	0.165019	−	0.0600621i
$329$	−0.899991	−	1.07257i	−0.0496181	−	0.0591326i
$330$	21.7257	+	7.85294i	1.19596	+	0.432290i
$331$	−18.2206	−	10.5197i	−1.00150	−	0.578213i	−0.0928048	−	0.995684i	$-0.529583\pi$
$331$	−18.2206	−	10.5197i	−1.00150	−	0.578213i	−0.908690	+	0.417471i	$0.862917\pi$
$332$	−4.70860	+	0.830253i	−0.258418	+	0.0455660i
$333$	−17.7441	+	3.12877i	−0.972372	+	0.171455i
$334$	−11.3414	+	19.6439i	−0.620575	+	1.07487i
$335$	3.73754	−	2.15787i	0.204204	−	0.117897i
$336$	−0.530411	+	0.445068i	−0.0289363	+	0.0242804i
$337$	3.02401	−	1.10065i	0.164728	−	0.0599562i	−0.258340	−	0.966054i	$-0.583175\pi$
$337$	3.02401	−	1.10065i	0.164728	−	0.0599562i	0.423068	+	0.906098i	$0.360953\pi$
$338$	11.3801	+	4.14202i	0.618996	+	0.225296i
$339$	−24.7505	−	20.7681i	−1.34426	−	1.12797i
$340$	−9.54698	−	1.68339i	−0.517758	−	0.0912947i
$341$	15.5274	−	13.0879i	0.840855	−	0.708748i
$342$	1.97636	−	13.9745i	0.106869	−	0.755653i
$343$		−	3.85992i		−	0.208416i
$344$	1.07988	+	0.190411i	0.0582230	+	0.0102663i
$345$	1.63956	−	1.95395i	0.0882709	−	0.105197i
$346$	14.5048	+	5.27933i	0.779785	+	0.283818i
$347$	9.04491	+	24.8507i	0.485556	+	1.33405i	0.904667	+	0.426119i	$0.140120\pi$
$347$	9.04491	+	24.8507i	0.485556	+	1.33405i	−0.419111	+	0.907935i	$0.637658\pi$
$348$	−1.82384	−	2.17356i	−0.0977679	−	0.116515i
$349$	−10.8077	+	6.23985i	−0.578525	+	0.334012i	−0.760547	−	0.649283i	$-0.775069\pi$
$349$	−10.8077	+	6.23985i	−0.578525	+	0.334012i	0.182022	+	0.983294i	$0.441736\pi$
$350$	0.666879	+	0.385022i	0.0356462	+	0.0205803i
$351$	−0.551815	+	0.0972999i	−0.0294537	+	0.00519349i
$352$	−2.12624	+	2.54541i	−0.113329	+	0.135671i
$353$	−4.90508	+	8.49584i	−0.261071	+	0.452188i	−0.966527	−	0.256566i	$-0.917409\pi$
$353$	−4.90508	+	8.49584i	−0.261071	+	0.452188i	0.705456	+	0.708754i	$0.250742\pi$
$354$	1.86087	+	3.22312i	0.0989041	+	0.171307i
$355$	27.6739	+	32.9805i	1.46878	+	1.75042i
$356$	4.79243	+	13.1671i	0.253999	+	0.697855i
$357$	−0.823192	+	2.26170i	−0.0435679	+	0.119702i
$358$	−5.30714	+	6.32481i	−0.280491	+	0.334277i
$359$	26.0363	+	4.59089i	1.37414	+	0.242298i	0.811475	−	0.584387i	$-0.198665\pi$
$359$	26.0363	+	4.59089i	1.37414	+	0.242298i	0.562666	+	0.826685i	$0.309776\pi$
$360$	9.02990			0.475918
$361$	−18.2549	−	5.26881i	−0.960782	−	0.277306i
$362$		−	20.5623i		−	1.08073i
$363$	9.28171	−	25.8579i	0.487164	−	1.35719i
$364$	0.168071	−	0.200300i	0.00880934	−	0.0104986i
$365$	13.8304	−	37.9988i	0.723918	−	1.98895i
$366$	−2.00161	+	0.728527i	−0.104626	+	0.0380807i
$367$	−1.92602	+	1.61612i	−0.100537	+	0.0843609i	−0.691671	−	0.722213i	$-0.743125\pi$
$367$	−1.92602	+	1.61612i	−0.100537	+	0.0843609i	0.591133	+	0.806574i	$0.298681\pi$
$368$	0.183100	+	0.317138i	0.00954473	+	0.0165320i
$369$	−5.14891	+	8.91817i	−0.268042	+	0.464262i
$370$	−15.2834	+	2.69487i	−0.794545	+	0.140100i
$371$	0.199986	+	1.13418i	0.0103827	+	0.0588834i
$372$	7.64622	−	13.2436i	0.396438	−	0.686651i
$373$	19.0768	+	33.0420i	0.987761	+	1.71085i	0.628958	+	0.777439i	$0.283482\pi$
$373$	19.0768	+	33.0420i	0.987761	+	1.71085i	0.358803	+	0.933413i	$0.383185\pi$
$374$	−1.97676	+	11.3581i	−0.102216	+	0.587316i
$375$	5.29430	+	14.5460i	0.273396	+	0.751151i
$376$	−4.74587	−	1.72736i	−0.244750	−	0.0890816i
$377$	0.820805	+	0.688737i	0.0422736	+	0.0354718i
$378$	0.0286001	−	0.162199i	0.00147103	−	0.00834262i
$379$		−	9.58132i		−	0.492159i	−0.969250	−	0.246080i	$-0.920857\pi$
$379$		−	9.58132i		−	0.492159i	0.969250	−	0.246080i	$-0.0791425\pi$
$380$	1.70228	−	12.0365i	0.0873249	−	0.617460i
$381$		−	37.9128i		−	1.94233i
$382$	−1.85853	+	10.5403i	−0.0950908	+	0.539287i
$383$	21.4370	−	25.5476i	1.09538	−	1.30542i	0.146702	−	0.989181i	$-0.453134\pi$
$383$	21.4370	−	25.5476i	1.09538	−	1.30542i	0.948678	−	0.316242i	$-0.102421\pi$
$384$	−0.854220	+	2.34695i	−0.0435917	+	0.119767i
$385$	1.27719	−	2.22355i	0.0650918	−	0.113322i
$386$	−12.7500	+	10.6985i	−0.648955	+	0.544538i
$387$	−3.07477	+	1.77522i	−0.156299	+	0.0902393i
$388$	5.97628	+	3.45041i	0.303400	+	0.175168i
$389$	4.88347	+	27.6955i	0.247602	+	1.40422i	0.814372	+	0.580343i	$0.197082\pi$
$389$	4.88347	+	27.6955i	0.247602	+	1.40422i	−0.566770	+	0.823876i	$0.691807\pi$
$390$	−6.46963	+	1.14077i	−0.327602	+	0.0577651i
$391$	1.10240	+	0.636471i	0.0557507	+	0.0321877i
$392$	−3.46157	−	5.99562i	−0.174836	−	0.302824i
$393$	−30.8395	+	25.8774i	−1.55565	+	1.30534i
$394$	1.05960	+	2.91121i	0.0533816	+	0.146665i
$395$	−27.3548	−	9.95633i	−1.37637	−	0.500957i
$396$	−0.0238385	−	10.7388i	−0.00119793	−	0.539644i
$397$	−0.877985	+	4.97930i	−0.0440648	+	0.249904i	−0.998881	−	0.0472928i	$-0.984941\pi$
$397$	−0.877985	+	4.97930i	−0.0440648	+	0.249904i	0.954816	+	0.297197i	$0.0960517\pi$
$398$	−10.1318			−0.507863
$399$	−2.86958	−	0.935139i	−0.143659	−	0.0468155i
$400$	2.77764			0.138882
$401$	24.8533	+	4.38231i	1.24112	+	0.218842i	0.755394	−	0.655271i	$-0.227446\pi$
$401$	24.8533	+	4.38231i	1.24112	+	0.218842i	0.485722	+	0.874113i	$0.338557\pi$
$402$	−2.96077	−	2.48438i	−0.147670	−	0.123909i
$403$	−1.97513	+	5.42663i	−0.0983884	+	0.270320i
$404$	−5.62673	−	15.4593i	−0.279940	−	0.769129i
$405$	17.5820	−	14.7530i	0.873655	−	0.733084i
$406$	−0.272754	+	0.157475i	−0.0135366	+	0.00781533i
$407$	3.24521	+	18.1686i	0.160859	+	0.900582i
$408$	1.50758	+	8.54989i	0.0746361	+	0.423282i
$409$	1.45529	+	8.25336i	0.0719595	+	0.408102i	0.999416	+	0.0341714i	$0.0108792\pi$
$409$	1.45529	+	8.25336i	0.0719595	+	0.408102i	−0.927457	+	0.373931i	$0.878010\pi$
$410$	−4.43486	+	7.68140i	−0.219022	+	0.379357i
$411$	−2.33237	+	1.34660i	−0.115047	+	0.0664227i
$412$	−4.08389	−	4.86699i	−0.201199	−	0.239779i
$413$	0.388199	−	0.141293i	0.0191020	−	0.00695256i
$414$	−1.11420	−	0.405535i	−0.0547599	−	0.0199310i
$415$	8.57100	−	10.2145i	0.420734	−	0.501411i
$416$	0.163778	−	0.928833i	0.00802989	−	0.0455398i
$417$	−28.8555			−1.41306
$418$	−14.3188	−	1.99265i	−0.700358	−	0.0974636i
$419$	−22.8667			−1.11711			−0.558557	−	0.829466i	$-0.688645\pi$
$419$	−22.8667			−1.11711			−0.558557	+	0.829466i	$0.688645\pi$
$420$	0.335315	−	1.90166i	0.0163617	−	0.0927917i
$421$	20.0530	−	23.8982i	0.977323	−	1.16473i	−0.00900929	−	0.999959i	$-0.502868\pi$
$421$	20.0530	−	23.8982i	0.977323	−	1.16473i	0.986332	−	0.164769i	$-0.0526878\pi$
$422$	−25.8923	−	9.42402i	−1.26042	−	0.458754i
$423$	15.3665	−	5.59295i	0.747146	−	0.271939i
$424$	2.67027	+	3.18231i	0.129680	+	0.154547i
$425$	8.36175	−	4.82766i	0.405604	−	0.234176i
$426$	19.2783	−	33.3909i	0.934034	−	1.61779i
$427$	0.0410569	+	0.232845i	0.00198688	+	0.0112682i
$428$	−3.25064	−	18.4353i	−0.157126	−	0.891104i
$429$	1.37374	+	7.69096i	0.0663246	+	0.371323i
$430$	−2.64836	+	1.52903i	−0.127715	+	0.0737364i
$431$	4.59641	−	3.85685i	0.221401	−	0.185778i	−0.525340	−	0.850892i	$-0.676062\pi$
$431$	4.59641	−	3.85685i	0.221401	−	0.185778i	0.746741	+	0.665115i	$0.231617\pi$
$432$	−0.203193	−	0.558267i	−0.00977611	−	0.0268596i
$433$	0.223078	−	0.612900i	0.0107204	−	0.0294541i	−0.934217	−	0.356705i	$-0.883900\pi$
$433$	0.223078	−	0.612900i	0.0107204	−	0.0294541i	0.944937	+	0.327251i	$0.106122\pi$
$434$	−1.30033	−	1.09111i	−0.0624178	−	0.0523747i
$435$	7.79280	+	1.37408i	0.373636	+	0.0658821i
$436$	5.51574			0.264156
$437$	−0.750606	+	1.40873i	−0.0359064	+	0.0673888i
$438$	−36.2142			−1.73038
$439$	−3.05620	+	17.3326i	−0.145865	+	0.827239i	0.820804	+	0.571210i	$0.193526\pi$
$439$	−3.05620	+	17.3326i	−0.145865	+	0.827239i	−0.966669	+	0.256030i	$0.917585\pi$
$440$	−0.0205325	−	9.24952i	−0.000978850	−	0.440953i
$441$	21.0644	+	7.66680i	1.00307	+	0.365086i
$442$	−1.12132	−	3.08079i	−0.0533356	−	0.146538i
$443$	−0.136834	+	0.114817i	−0.00650117	+	0.00545513i	−0.646032	−	0.763310i	$-0.723573\pi$
$443$	−0.136834	+	0.114817i	−0.00650117	+	0.00545513i	0.639531	+	0.768765i	$0.279128\pi$
$444$	6.94915	+	12.0363i	0.329792	+	0.571217i
$445$	−33.8422	−	19.5388i	−1.60428	−	0.926229i
$446$	−23.3528	+	4.11772i	−1.10579	+	0.194980i
$447$	4.55154	+	25.8131i	0.215281	+	1.22092i
$448$	0.240088	+	0.138615i	0.0113431	+	0.00654895i
$449$	17.3585	−	10.0219i	0.819197	−	0.472963i	−0.0309427	−	0.999521i	$-0.509851\pi$
$449$	17.3585	−	10.0219i	0.819197	−	0.472963i	0.850139	+	0.526558i	$0.176518\pi$
$450$	−6.88952	+	5.78099i	−0.324775	+	0.272519i
$451$	9.14678	+	5.25386i	0.430705	+	0.247394i
$452$	−4.42449	+	12.1562i	−0.208111	+	0.571779i
$453$	13.8701	−	16.5297i	0.651674	−	0.776634i
$454$	−0.764776	+	4.33726i	−0.0358927	+	0.203558i
$455$			0.729206i			0.0341857i
$456$	−10.6507	+	2.25422i	−0.498766	+	0.105564i
$457$		−	29.7339i		−	1.39090i	−0.718577	−	0.695448i	$-0.755206\pi$
$457$		−	29.7339i		−	1.39090i	0.718577	−	0.695448i	$-0.244794\pi$
$458$	−1.14412	+	6.48862i	−0.0534612	+	0.303193i
$459$	−1.58198	−	1.32744i	−0.0738405	−	0.0619596i
$460$	−0.959682	−	0.349296i	−0.0447454	−	0.0162860i
$461$	4.63822	+	12.7434i	0.216023	+	0.593519i	0.999615	−	0.0277572i	$-0.00883653\pi$
$461$	4.63822	+	12.7434i	0.216023	+	0.593519i	−0.783591	+	0.621277i	$0.786614\pi$
$462$	−2.26243	−	0.393751i	−0.105258	−	0.0183190i
$463$	−3.16093	−	5.47489i	−0.146901	−	0.254440i	0.783180	−	0.621796i	$-0.213597\pi$
$463$	−3.16093	−	5.47489i	−0.146901	−	0.254440i	−0.930081	+	0.367356i	$0.880263\pi$
$464$	−0.568028	+	0.983854i	−0.0263701	+	0.0456743i
$465$	7.40578	+	42.0003i	0.343435	+	1.94772i
$466$	19.4136	−	3.42314i	0.899319	−	0.158574i
$467$	7.75787	−	13.4370i	0.358991	−	0.621791i	−0.628801	−	0.777566i	$-0.716454\pi$
$467$	7.75787	−	13.4370i	0.358991	−	0.621791i	0.987793	+	0.155775i	$0.0497875\pi$
$468$	1.52692	+	2.64470i	0.0705817	+	0.122251i
$469$	−0.328644	+	0.275765i	−0.0151754	+	0.0127337i
$470$	13.2355	−	4.81732i	0.610508	−	0.222207i
$471$	4.31927	−	11.8671i	0.199021	−	0.546807i
$472$	0.957845	−	1.14152i	0.0440884	−	0.0525425i
$473$	1.82538	+	3.14551i	0.0839312	+	0.144631i
$474$			26.0700i			1.19744i
$475$	6.40705	+	10.2733i	0.293976	+	0.471369i
$476$	0.963676			0.0441700
$477$	−13.2464	−	2.33570i	−0.606513	−	0.106945i
$478$	−11.7678	+	14.0243i	−0.538246	+	0.641456i
$479$	5.98436	−	16.4419i	0.273432	−	0.751249i	−0.724636	−	0.689131i	$-0.757992\pi$
$479$	5.98436	−	16.4419i	0.273432	−	0.751249i	0.998069	−	0.0621180i	$-0.0197855\pi$
$480$	−2.38228	−	6.54527i	−0.108736	−	0.298750i
$481$	−3.37363	−	4.02053i	−0.153824	−	0.183321i
$482$	2.37340	+	4.11085i	0.108105	+	0.187244i
$483$	−0.126779	+	0.219587i	−0.00576863	+	0.00999156i
$484$	−10.9999	+	0.0488364i	−0.499995	+	0.00221984i
$485$	−18.9529	+	3.34191i	−0.860607	+	0.151748i
$486$	−19.3443	−	11.1684i	−0.877474	−	0.506610i
$487$	32.3710	−	18.6894i	1.46687	−	0.846897i	0.467555	−	0.883964i	$-0.345135\pi$
$487$	32.3710	−	18.6894i	1.46687	−	0.846897i	0.999313	+	0.0370672i	$0.0118016\pi$
$488$	0.548205	+	0.653325i	0.0248161	+	0.0295747i
$489$	11.9965	+	32.9600i	0.542499	+	1.49050i
$490$	18.1432	+	6.60357i	0.819625	+	0.298319i
$491$	27.2874	−	32.5198i	1.23146	−	1.46760i	0.395818	−	0.918329i	$-0.370461\pi$
$491$	27.2874	−	32.5198i	1.23146	−	1.46760i	0.835644	−	0.549271i	$-0.185095\pi$
$492$	7.82268	+	1.37935i	0.352674	+	0.0621859i
$493$			3.94903i			0.177856i
$494$	3.81312	−	1.53675i	0.171560	−	0.0691418i
$495$	19.3016	+	22.8993i	0.867542	+	1.02925i
$496$	−6.02990	−	1.06323i	−0.270751	−	0.0477406i
$497$	−3.27849	−	2.75098i	−0.147060	−	0.123398i
$498$	−11.2213	−	4.08423i	−0.502839	−	0.183019i
$499$	−33.2186	+	12.0906i	−1.48707	+	0.541248i	−0.952676	−	0.303988i	$-0.901682\pi$
$499$	−33.2186	+	12.0906i	−1.48707	+	0.541248i	−0.534392	+	0.845237i	$0.679459\pi$
$500$	4.74780	−	3.98388i	0.212328	−	0.178165i
$501$	−49.0621	+	28.3260i	−2.19193	+	1.26551i
$502$	−2.50600	+	4.34052i	−0.111848	+	0.193727i
$503$	−3.28937	+	0.580004i	−0.146666	+	0.0258611i	−0.246499	−	0.969143i	$-0.579280\pi$
$503$	−3.28937	+	0.580004i	−0.146666	+	0.0258611i	0.0998333	+	0.995004i	$0.468169\pi$
$504$	−0.883998	+	0.155873i	−0.0393764	+	0.00694312i
$505$	39.7337	+	22.9402i	1.76812	+	1.02083i
$506$	−0.412865	+	1.14222i	−0.0183541	+	0.0507778i
$507$	19.4422	+	23.1703i	0.863459	+	1.02903i
$508$	−14.2644	+	5.19182i	−0.632881	+	0.230350i
$509$	−4.16453	+	11.4420i	−0.184590	+	0.507156i	−0.997127	−	0.0757539i	$-0.975864\pi$
$509$	−4.16453	+	11.4420i	−0.184590	+	0.507156i	0.812537	+	0.582910i	$0.198086\pi$
$510$	−18.5476	−	15.5632i	−0.821300	−	0.689152i
$511$	−0.698025	+	3.95870i	−0.0308788	+	0.175122i
$512$	1.00000			0.0441942
$513$	1.59609	−	2.03925i	0.0704691	−	0.0900351i
$514$			13.6626i			0.602631i
$515$	17.4494	+	3.07681i	0.768915	+	0.135580i
$516$	2.09795	+	1.76039i	0.0923569	+	0.0774966i
$517$	−5.76392	−	15.7275i	−0.253497	−	0.691696i
$518$	1.44967	−	0.527638i	0.0636950	−	0.0231831i
$519$	24.7806	+	29.5324i	1.08775	+	1.29633i
$520$	1.31516	+	2.27793i	0.0576737	+	0.0998939i
$521$	−13.1619	−	7.59901i	−0.576632	−	0.332919i	0.183162	−	0.983083i	$-0.441367\pi$
$521$	−13.1619	−	7.59901i	−0.576632	−	0.332919i	−0.759794	+	0.650164i	$0.774700\pi$
$522$	−0.638748	−	3.62252i	−0.0279572	−	0.158553i
$523$	3.20115	+	18.1546i	0.139977	+	0.793847i	0.971264	+	0.238004i	$0.0764932\pi$
$523$	3.20115	+	18.1546i	0.139977	+	0.793847i	−0.831288	+	0.555843i	$0.812396\pi$
$524$	13.9594	+	8.05944i	0.609818	+	0.352078i
$525$	0.961622	+	1.66558i	0.0419686	+	0.0726918i
$526$	15.6746	+	18.6803i	0.683445	+	0.814498i
$527$	−20.0002	+	7.27950i	−0.871224	+	0.317100i
$528$	−7.77765	+	2.85040i	−0.338479	+	0.124048i
$529$	−17.5163	−	14.6979i	−0.761578	−	0.639040i
$530$	−11.4094	−	2.01179i	−0.495594	−	0.0873865i
$531$			4.82489i			0.209382i
$532$	0.0411248	+	1.20772i	0.00178299	+	0.0523612i
$533$	−2.99966			−0.129930
$534$	−6.07705	+	34.4647i	−0.262980	+	1.49143i
$535$	39.9923	+	33.5575i	1.72902	+	1.45082i
$536$	−0.529278	+	1.45418i	−0.0228613	+	0.0628109i
$537$	−19.3775	+	7.05283i	−0.836200	+	0.304352i
$538$	−13.7049	−	16.3329i	−0.590861	−	0.704160i
$539$	7.80537	−	21.5941i	0.336201	−	0.930124i
$540$	1.43486	+	0.828419i	0.0617467	+	0.0356495i
$541$	25.0653	−	4.41969i	1.07764	−	0.190017i	0.393469	−	0.919338i	$-0.371275\pi$
$541$	25.0653	−	4.41969i	1.07764	−	0.190017i	0.684172	+	0.729320i	$0.260164\pi$
$542$	19.1886	−	3.38346i	0.824220	−	0.145332i
$543$	25.6779	−	44.4755i	1.10195	−	1.90863i
$544$	3.01038	−	1.73804i	0.129069	−	0.0745180i
$545$	−11.7837	+	9.88771i	−0.504759	+	0.423543i
$546$	0.613664	−	0.223355i	0.0262624	−	0.00955872i
$547$	−25.9172	−	9.43309i	−1.10814	−	0.403330i	−0.277829	−	0.960631i	$-0.589615\pi$
$547$	−25.9172	−	9.43309i	−1.10814	−	0.403330i	−0.830311	+	0.557301i	$0.811837\pi$
$548$	0.826044	+	0.693133i	0.0352869	+	0.0296092i
$549$	−2.71948	−	0.479518i	−0.116065	−	0.0204653i
$550$	5.93726	+	7.04393i	0.253165	+	0.300354i
$551$	−4.94909	+	0.168525i	−0.210838	+	0.00717939i
$552$			0.914610i			0.0389284i
$553$	2.84981	+	0.502498i	0.121186	+	0.0213684i
$554$	−0.0153390	+	0.0182803i	−0.000651690	+	0.000776654i
$555$	−36.4227	−	13.2568i	−1.54606	−	0.562718i
$556$	3.95150	+	10.8566i	0.167581	+	0.460424i
$557$	−26.7545	−	31.8848i	−1.13363	−	1.35100i	−0.928091	−	0.372353i	$-0.878551\pi$
$557$	−26.7545	−	31.8848i	−1.13363	−	1.35100i	−0.205534	−	0.978650i	$-0.565893\pi$
$558$	17.1691	−	9.91261i	0.726828	−	0.419634i
$559$	−0.895651	−	0.517104i	−0.0378820	−	0.0218712i
$560$	−0.761405	+	0.134256i	−0.0321752	+	0.00567336i
$561$	−18.4596	+	22.0987i	−0.779363	+	0.933007i
$562$	8.48568	−	14.6976i	0.357947	−	0.619982i
$563$	9.08537	+	15.7363i	0.382903	+	0.663207i	0.991476	−	0.130291i	$-0.0415911\pi$
$563$	9.08537	+	15.7363i	0.382903	+	0.663207i	−0.608573	+	0.793498i	$0.708258\pi$
$564$	−8.10804	−	9.66279i	−0.341410	−	0.406877i
$565$	−12.3392	−	33.9017i	−0.519115	−	1.42626i
$566$	−6.92857	+	19.0361i	−0.291229	+	0.800146i
$567$	−1.46655	+	1.74777i	−0.0615894	+	0.0733994i
$568$	−15.2031	−	2.68071i	−0.637906	−	0.112480i
$569$	−9.56213			−0.400865			−0.200433	−	0.979707i	$-0.564235\pi$
$569$	−9.56213			−0.400865			−0.200433	+	0.979707i	$0.564235\pi$
$570$	18.7130	−	23.9087i	0.783800	−	1.00143i
$571$		−	11.8314i		−	0.495127i	−0.968872	−	0.247563i	$-0.920370\pi$
$571$		−	11.8314i		−	0.495127i	0.968872	−	0.247563i	$-0.0796298\pi$
$572$	2.70555	−	1.57007i	0.113125	−	0.0656477i
$573$	−17.1825	+	20.4773i	−0.717808	+	0.855450i
$574$	0.301563	−	0.828538i	0.0125870	−	0.0345825i
$575$	0.955827	−	0.347892i	0.0398607	−	0.0145081i
$576$	−2.48035	+	2.08126i	−0.103348	+	0.0867193i
$577$	−8.70361	−	15.0751i	−0.362336	−	0.627584i	0.626009	−	0.779816i	$-0.284687\pi$
$577$	−8.70361	−	15.0751i	−0.362336	−	0.627584i	−0.988345	+	0.152232i	$0.951354\pi$
$578$	−2.45841	+	4.25809i	−0.102256	+	0.177113i
$579$	−40.9378	+	7.21843i	−1.70132	+	0.299988i
$580$	−0.550167	−	3.12015i	−0.0228444	−	0.129557i
$581$	−0.662751	+	1.14792i	−0.0274956	+	0.0476237i
$582$	8.61765	+	14.9262i	0.357213	+	0.618711i
$583$	−2.36239	+	13.5739i	−0.0978402	+	0.562174i
$584$	4.95921	+	13.6253i	0.205213	+	0.563819i
$585$	−8.00304	−	2.91287i	−0.330885	−	0.120432i
$586$	17.2512	+	14.4755i	0.712641	+	0.597977i
$587$	6.72944	−	38.1646i	0.277754	−	1.57522i	−0.452322	−	0.891855i	$-0.649404\pi$
$587$	6.72944	−	38.1646i	0.277754	−	1.57522i	0.730076	−	0.683366i	$-0.239485\pi$
$588$		−	17.2911i		−	0.713071i
$589$	−9.97647	−	24.7545i	−0.411073	−	1.01999i
$590$			4.15577i			0.171090i
$591$	−1.34362	+	7.62005i	−0.0552692	+	0.313447i
$592$	3.57694	−	4.26283i	0.147011	−	0.175201i
$593$	6.76933	−	18.5986i	0.277983	−	0.763753i	−0.719608	−	0.694381i	$-0.755678\pi$
$593$	6.76933	−	18.5986i	0.277983	−	0.763753i	0.997591	−	0.0693717i	$-0.0220995\pi$
$594$	0.981406	−	1.70859i	0.0402676	−	0.0701044i
$595$	−2.05878	+	1.72752i	−0.0844016	+	0.0708213i
$596$	9.08868	−	5.24735i	0.372287	−	0.214940i
$597$	−21.9148	−	12.6525i	−0.896912	−	0.517832i
$598$	−0.0599755	−	0.340138i	−0.00245258	−	0.0139093i
$599$	22.0877	−	3.89466i	0.902481	−	0.159132i	0.296893	−	0.954911i	$-0.404049\pi$
$599$	22.0877	−	3.89466i	0.902481	−	0.159132i	0.605587	+	0.795779i	$0.292938\pi$
$600$	6.00792	+	3.46868i	0.245272	+	0.141608i
$601$	−14.6449	−	25.3658i	−0.597379	−	1.03469i	−0.993206	−	0.116366i	$-0.962875\pi$
$601$	−14.6449	−	25.3658i	−0.597379	−	1.03469i	0.395827	−	0.918325i	$-0.370458\pi$
$602$	0.232872	−	0.195402i	0.00949114	−	0.00796401i
$603$	−1.71373	−	4.70844i	−0.0697886	−	0.191742i
$604$	−8.11857	−	2.95492i	−0.330340	−	0.120234i
$605$	23.4124	−	19.8231i	0.951848	−	0.805924i
$606$	7.13497	−	40.4645i	0.289839	−	1.64376i
$607$	−3.29591			−0.133777			−0.0668884	−	0.997760i	$-0.521307\pi$
$607$	−3.29591			−0.133777			−0.0668884	+	0.997760i	$0.521307\pi$
$608$	2.30665	+	3.69856i	0.0935472	+	0.149996i
$609$	−0.786609			−0.0318750
$610$	−2.34235	−	0.413019i	−0.0948388	−	0.0167226i
$611$	3.64897	+	3.06185i	0.147621	+	0.123869i
$612$	−3.84948	+	10.5764i	−0.155606	+	0.427524i
$613$	−6.53052	−	17.9425i	−0.263765	−	0.724689i	−0.998905	−	0.0467741i	$-0.985106\pi$
$613$	−6.53052	−	17.9425i	−0.263765	−	0.724689i	0.735140	−	0.677915i	$-0.237116\pi$
$614$	−2.33404	+	1.95850i	−0.0941944	+	0.0790385i
$615$	−19.1849	+	11.0764i	−0.773608	+	0.446643i
$616$	0.161674	+	0.905143i	0.00651402	+	0.0364692i
$617$	1.11004	+	6.29537i	0.0446886	+	0.253442i	0.998965	−	0.0454837i	$-0.0144829\pi$
$617$	1.11004	+	6.29537i	0.0446886	+	0.253442i	−0.954276	+	0.298926i	$0.903372\pi$
$618$	−2.75546	−	15.6270i	−0.110841	−	0.628611i
$619$	1.05128	−	1.82087i	0.0422544	−	0.0731868i	−0.844125	−	0.536147i	$-0.819879\pi$
$619$	1.05128	−	1.82087i	0.0422544	−	0.0731868i	0.886379	+	0.462960i	$0.153213\pi$
$620$	14.7881	−	8.53793i	0.593906	−	0.342892i
$621$	−0.139843	−	0.166659i	−0.00561172	−	0.00668778i
$622$	20.3630	−	7.41153i	0.816482	−	0.297175i
$623$	3.65032	+	1.32861i	0.146247	+	0.0532295i
$624$	1.51416	−	1.80450i	0.0606149	−	0.0722380i
$625$	−5.41312	+	30.6993i	−0.216525	+	1.22797i
$626$	−14.0412			−0.561197
$627$	−28.4827	−	22.1912i	−1.13749	−	0.886231i
$628$	−5.05639			−0.201772
$629$	3.35896	−	19.0496i	0.133930	−	0.759558i
$630$	1.60913	−	1.91769i	0.0641093	−	0.0764025i
$631$	9.07413	+	3.30271i	0.361235	+	0.131479i	0.516261	−	0.856432i	$-0.327324\pi$
$631$	9.07413	+	3.30271i	0.361235	+	0.131479i	−0.155025	+	0.987911i	$0.549546\pi$
$632$	9.80866	−	3.57006i	0.390167	−	0.142009i
$633$	−44.2354	−	52.7177i	−1.75820	−	2.09534i
$634$	1.83546	−	1.05970i	0.0728954	−	0.0420862i
$635$	21.1671	−	36.6625i	0.839992	−	1.45491i
$636$	1.80168	+	10.2178i	0.0714411	+	0.405163i
$637$	1.13386	+	6.43044i	0.0449252	+	0.254783i
$638$	−3.70917	+	0.662520i	−0.146847	+	0.0262294i
$639$	43.2882	−	24.9924i	1.71245	−	0.988686i
$640$	−2.13638	+	1.79263i	−0.0844477	+	0.0708600i
$641$	3.55586	+	9.76965i	0.140448	+	0.385878i	0.989896	−	0.141794i	$-0.0452872\pi$
$641$	3.55586	+	9.76965i	0.140448	+	0.385878i	−0.849448	+	0.527672i	$0.823065\pi$
$642$	15.9907	−	43.9342i	0.631104	−	1.73394i
$643$	36.6930	+	30.7891i	1.44703	+	1.21420i	0.934710	+	0.355411i	$0.115659\pi$
$643$	36.6930	+	30.7891i	1.44703	+	1.21420i	0.512322	+	0.858794i	$0.328785\pi$
$644$	0.0999792	+	0.0176290i	0.00393973	+	0.000694681i
$645$	−7.63773			−0.300735
$646$	13.3722	+	7.12500i	0.526121	+	0.280330i
$647$	23.3234			0.916936			0.458468	−	0.888711i	$-0.348398\pi$
$647$	23.3234			0.916936			0.458468	+	0.888711i	$0.348398\pi$
$648$	−1.42909	+	8.10478i	−0.0561400	+	0.318386i
$649$	4.94223	−	0.0109710i	0.194000	−	0.000430650i
$650$	−2.46177	−	0.896011i	−0.0965585	−	0.0351444i
$651$	−1.45000	−	3.98385i	−0.0568301	−	0.156139i
$652$	10.7581	−	9.02715i	0.421321	−	0.353531i
$653$	−16.8689	−	29.2178i	−0.660132	−	1.14338i	−0.980581	−	0.196116i	$-0.937167\pi$
$653$	−16.8689	−	29.2178i	−0.660132	−	1.14338i	0.320449	−	0.947266i	$-0.396166\pi$
$654$	11.9303	+	6.88799i	0.466513	+	0.269342i
$655$	−44.2701	+	7.80601i	−1.72977	+	0.305006i
$656$	−0.552276	−	3.13211i	−0.0215628	−	0.122288i
$657$	−40.6584	−	23.4741i	−1.58624	−	0.915814i
$658$	−1.21255	+	0.700069i	−0.0472703	+	0.0272915i
$659$	15.1249	−	12.6913i	0.589183	−	0.494384i	−0.298765	−	0.954327i	$-0.596575\pi$
$659$	15.1249	−	12.6913i	0.589183	−	0.494384i	0.887948	+	0.459943i	$0.152130\pi$
$660$	11.5063	−	20.0320i	0.447881	−	0.779744i
$661$	−1.99156	+	5.47176i	−0.0774627	+	0.212827i	−0.972379	−	0.233407i	$-0.925013\pi$
$661$	−1.99156	+	5.47176i	−0.0774627	+	0.212827i	0.894917	+	0.446234i	$0.147235\pi$
$662$	−13.5238	+	16.1171i	−0.525619	+	0.626408i
$663$	1.42189	−	8.06392i	0.0552215	−	0.313177i
$664$			4.78123i			0.185548i
$665$	−2.25285	−	2.50642i	−0.0873619	−	0.0971948i
$666$			18.0179i			0.698178i
$667$	−0.0722417	+	0.409703i	−0.00279721	+	0.0158638i
$668$	17.3761	+	14.5803i	0.672300	+	0.564127i
$669$	−55.6533	−	20.2561i	−2.15168	−	0.783147i
$670$	−1.47607	−	4.05547i	−0.0570256	−	0.156677i
$671$	−0.484997	+	2.78671i	−0.0187231	+	0.107580i
$672$	0.346201	+	0.599638i	0.0133550	+	0.0231315i
$673$	20.5990	−	35.6785i	0.794032	−	1.37530i	−0.129419	−	0.991590i	$-0.541311\pi$
$673$	20.5990	−	35.6785i	0.794032	−	1.37530i	0.923452	−	0.383714i	$-0.125355\pi$
$674$	−0.558814	−	3.16919i	−0.0215247	−	0.122073i
$675$	−1.62511	+	0.286551i	−0.0625506	+	0.0110294i
$676$	6.05522	−	10.4880i	0.232893	−	0.403383i
$677$	−2.52520	−	4.37378i	−0.0970514	−	0.168098i	0.813411	−	0.581689i	$-0.197608\pi$
$677$	−2.52520	−	4.37378i	−0.0970514	−	0.168098i	−0.910463	+	0.413591i	$0.864274\pi$
$678$	−24.7505	+	20.7681i	−0.950537	+	0.797596i
$679$	1.79774	−	0.654324i	0.0689909	−	0.0251106i
$680$	−3.31563	+	9.10962i	−0.127149	+	0.349338i
$681$	−7.07049	+	8.42628i	−0.270942	+	0.322896i
$682$	−10.1927	−	17.5642i	−0.390300	−	0.672567i
$683$		−	22.9777i		−	0.879216i	−0.898190	−	0.439608i	$-0.855117\pi$
$683$		−	22.9777i		−	0.879216i	0.898190	−	0.439608i	$-0.144883\pi$
$684$	−13.4190	−	4.37298i	−0.513088	−	0.167205i
$685$	−3.00727			−0.114902
$686$	−3.80127	−	0.670267i	−0.145133	−	0.0255909i
$687$	−10.5776	+	12.6059i	−0.403560	+	0.480944i
$688$	0.375037	−	1.03040i	0.0142981	−	0.0392838i
$689$	−1.34007	−	3.68180i	−0.0510524	−	0.140265i
$690$	−1.63956	−	1.95395i	−0.0624170	−	0.0743856i
$691$	16.3056	+	28.2422i	0.620295	+	1.07438i	0.989431	+	0.145007i	$0.0463204\pi$
$691$	16.3056	+	28.2422i	0.620295	+	1.07438i	−0.369136	+	0.929375i	$0.620346\pi$
$692$	7.71786	−	13.3677i	0.293389	−	0.508165i
$693$	−2.28485	−	1.90859i	−0.0867942	−	0.0725012i
$694$	26.0438	−	4.59222i	0.988608	−	0.174318i
$695$	−27.9039	−	16.1103i	−1.05845	−	0.611099i
$696$	−2.45725	+	1.41869i	−0.0931417	+	0.0537754i
$697$	−7.10631	−	8.46897i	−0.269171	−	0.320785i
$698$	4.26831	+	11.7271i	0.161558	+	0.443877i
$699$	46.2657	+	16.8393i	1.74993	+	0.636922i
$700$	0.494975	−	0.589889i	0.0187083	−	0.0222957i
$701$	15.4435	+	2.72310i	0.583291	+	0.102850i	0.457505	−	0.889207i	$-0.348743\pi$
$701$	15.4435	+	2.72310i	0.583291	+	0.102850i	0.125787	+	0.992057i	$0.459854\pi$
$702$			0.560328i			0.0211482i
$703$	24.0171	+	3.39664i	0.905821	+	0.128107i
$704$	2.13752	+	2.53594i	0.0805608	+	0.0955770i
$705$	34.6437	+	6.10861i	1.30476	+	0.230064i
$706$	7.51501	+	6.30584i	0.282831	+	0.237324i
$707$	−4.28578	−	1.55990i	−0.161184	−	0.0586660i
$708$	3.49729	−	1.27291i	0.131436	−	0.0478389i
$709$	−36.6202	+	30.7280i	−1.37530	+	1.15402i	−0.404388	+	0.914587i	$0.632516\pi$
$709$	−36.6202	+	30.7280i	−1.37530	+	1.15402i	−0.970914	+	0.239428i	$0.923040\pi$
$710$	37.2850	−	21.5265i	1.39928	−	0.807875i
$711$	−16.8987	+	29.2694i	−0.633750	+	1.09769i
$712$	13.7993	−	2.43318i	0.517149	−	0.0911874i
$713$	−2.20815	+	0.389356i	−0.0826957	+	0.0145815i
$714$	2.08439	+	1.20343i	0.0780065	+	0.0450371i
$715$	−2.96551	+	8.20430i	−0.110904	+	0.306824i
$716$	5.30714	+	6.32481i	0.198337	+	0.236369i
$717$	−42.9666	+	15.6386i	−1.60462	+	0.584033i
$718$	9.04230	−	24.8435i	0.337455	−	0.927151i
$719$	21.0111	+	17.6304i	0.783583	+	0.657505i	0.944148	−	0.329521i	$-0.106887\pi$
$719$	21.0111	+	17.6304i	0.783583	+	0.657505i	−0.160565	+	0.987025i	$0.551332\pi$
$720$	1.56803	−	8.89272i	0.0584369	−	0.331412i
$721$	−1.76135			−0.0655963
$722$	−8.35869	+	17.0626i	−0.311078	+	0.635004i
$723$			11.8555i			0.440910i
$724$	−20.2499	−	3.57061i	−0.752583	−	0.132701i
$725$	2.41730	+	2.02835i	0.0897761	+	0.0753311i
$726$	−23.8533	−	13.6309i	−0.885280	−	0.505890i
$727$	38.5681	−	14.0376i	1.43041	−	0.520627i	0.493362	−	0.869824i	$-0.335768\pi$
$727$	38.5681	−	14.0376i	1.43041	−	0.520627i	0.937050	+	0.349197i	$0.113545\pi$
$728$	−0.168071	−	0.200300i	−0.00622914	−	0.00742360i
$729$	−15.5492	−	26.9320i	−0.575897	−	0.997483i
$730$	−35.0199	−	20.2187i	−1.29614	−	0.748329i
$731$	−0.661886	−	3.75374i	−0.0244807	−	0.138837i
$732$	0.369883	+	2.09771i	0.0136713	+	0.0775335i
$733$	−2.99042	−	1.72652i	−0.110454	−	0.0637705i	0.443755	−	0.896148i	$-0.353646\pi$
$733$	−2.99042	−	1.72652i	−0.110454	−	0.0637705i	−0.554209	+	0.832377i	$0.686979\pi$
$734$	1.25712	+	2.17740i	0.0464011	+	0.0803691i
$735$	30.9965	+	36.9402i	1.14332	+	1.36256i
$736$	0.344115	−	0.125248i	0.0126842	−	0.00461669i
$737$	−4.81906	+	1.76612i	−0.177512	+	0.0650558i
$738$	7.88859	+	6.61931i	0.290383	+	0.243660i
$739$	−5.63099	−	0.992896i	−0.207139	−	0.0365243i	0.0691155	−	0.997609i	$-0.477982\pi$
$739$	−5.63099	−	0.992896i	−0.207139	−	0.0365243i	−0.276255	+	0.961084i	$0.589093\pi$
$740$			15.5191i			0.570495i
$741$	10.1667	+	1.43784i	0.373484	+	0.0528204i
$742$	1.15167			0.0422792
$743$	−4.97846	+	28.2342i	−0.182642	+	1.03581i	0.746306	+	0.665603i	$0.231826\pi$
$743$	−4.97846	+	28.2342i	−0.182642	+	1.03581i	−0.928948	+	0.370211i	$0.879286\pi$
$744$	−11.7147	−	9.82979i	−0.429481	−	0.360378i
$745$	−10.0103	+	27.5030i	−0.366748	+	1.00763i
$746$	35.8527	−	13.0493i	1.31266	−	0.477770i
$747$	−9.95100	−	11.8591i	−0.364088	−	0.433903i
$748$	10.8423	+	3.91905i	0.396435	+	0.143295i
$749$	−4.49438	−	2.59483i	−0.164221	−	0.0948131i
$750$	15.2443	−	2.68799i	0.556644	−	0.0981514i
$751$	19.0923	−	3.36649i	0.696688	−	0.122845i	0.185922	−	0.982565i	$-0.440473\pi$
$751$	19.0923	−	3.36649i	0.696688	−	0.122845i	0.510766	+	0.859720i	$0.329362\pi$
$752$	−2.52523	+	4.37382i	−0.0920855	+	0.159497i
$753$	−10.8408	+	6.25892i	−0.395059	+	0.228088i
$754$	0.820805	−	0.688737i	0.0298920	−	0.0250823i
$755$	22.6414	−	8.24080i	0.824005	−	0.299913i
$756$	−0.154769	−	0.0563311i	−0.00562888	−	0.00204874i
$757$	33.4540	+	28.0712i	1.21591	+	1.02027i	0.999029	+	0.0440682i	$0.0140319\pi$
$757$	33.4540	+	28.0712i	1.21591	+	1.02027i	0.216878	+	0.976199i	$0.430413\pi$
$758$	−9.43576	−	1.66378i	−0.342722	−	0.0604312i
$759$	−2.31940	+	1.95500i	−0.0841888	+	0.0709619i
$760$	−11.5580	−	3.76653i	−0.419254	−	0.136626i
$761$		−	8.18244i		−	0.296613i	−0.988941	−	0.148307i	$-0.952618\pi$
$761$		−	8.18244i		−	0.296613i	0.988941	−	0.148307i	$-0.0473823\pi$
$762$	−37.3369	−	6.58349i	−1.35257	−	0.238495i
$763$	0.982906	−	1.17138i	0.0355836	−	0.0424069i
$764$	10.0574	+	3.66059i	0.363864	+	0.132436i
$765$	−10.7356	−	29.4958i	−0.388146	−	1.06642i
$766$	−21.4370	−	25.5476i	−0.774551	−	0.923074i
$767$	−1.21715	+	0.702722i	−0.0439488	+	0.0253738i
$768$	2.16296	+	1.24879i	0.0780491	+	0.0450617i
$769$	47.1508	−	8.31396i	1.70030	−	0.299809i	0.762501	−	0.646987i	$-0.223971\pi$
$769$	47.1508	−	8.31396i	1.70030	−	0.299809i	0.937799	+	0.347178i	$0.112860\pi$
$770$	−1.96798	−	1.64390i	−0.0709213	−	0.0592422i
$771$	−17.0617	+	29.5517i	−0.614461	+	1.06428i
$772$	8.32194	+	14.4140i	0.299513	+	0.518772i
$773$	0.372097	+	0.443448i	0.0133834	+	0.0159497i	0.772695	−	0.634778i	$-0.218908\pi$
$773$	0.372097	+	0.443448i	0.0133834	+	0.0159497i	−0.759311	+	0.650728i	$0.774464\pi$
$774$	1.21432	+	3.33632i	0.0436478	+	0.119921i
$775$	−5.81683	+	15.9816i	−0.208947	+	0.574076i
$776$	4.43576	−	5.28633i	0.159235	−	0.189768i
$777$	3.79449	+	0.669072i	0.136127	+	0.0240028i
$778$	28.1228			1.00825
$779$	10.3104	−	9.26733i	0.369408	−	0.332037i
$780$			6.56943i			0.235223i
$781$	−25.6987	−	44.2842i	−0.919572	−	1.58461i
$782$	0.818231	−	0.975130i	0.0292599	−	0.0348706i
$783$	0.230838	−	0.634223i	0.00824949	−	0.0226653i
$784$	−6.50563	+	2.36785i	−0.232344	+	0.0845662i
$785$	10.8024	−	9.06425i	0.385553	−	0.323517i
$786$	20.1290	+	34.8645i	0.717979	+	1.24358i
$787$	−15.5068	+	26.8585i	−0.552757	+	0.957403i	0.445318	+	0.895373i	$0.353091\pi$
$787$	−15.5068	+	26.8585i	−0.552757	+	0.957403i	−0.998074	+	0.0620300i	$0.980243\pi$
$788$	3.05098	−	0.537970i	0.108687	−	0.0191644i
$789$	10.5759	+	59.9789i	0.376512	+	2.13531i
$790$	−14.5552	+	25.2103i	−0.517850	+	0.896943i
$791$	1.79317	+	3.10587i	0.0637579	+	0.110432i
$792$	−10.5798	−	1.84129i	−0.375936	−	0.0654275i
$793$	−0.275114	−	0.755870i	−0.00976960	−	0.0268417i
$794$	4.75120	+	1.72929i	0.168614	+	0.0613703i
$795$	−22.1658	−	18.5993i	−0.786141	−	0.659651i
$796$	−1.75937	+	9.97791i	−0.0623594	+	0.353658i
$797$			23.1263i			0.819174i	0.912271	+	0.409587i	$0.134327\pi$
$797$			23.1263i			0.819174i	−0.912271	+	0.409587i	$0.865673\pi$
$798$	−1.41923	+	2.66360i	−0.0502402	+	0.0942906i
$799$			17.5558i			0.621080i
$800$	0.482332	−	2.73544i	0.0170530	−	0.0967124i
$801$	−29.1629	+	34.7550i	−1.03042	+	1.22801i
$802$	8.63147	−	23.7148i	0.304788	−	0.837397i
$803$	−23.9526	+	41.7006i	−0.845269	+	1.47158i
$804$	−2.96077	+	2.48438i	−0.104418	+	0.0876172i
$805$	−0.245196	+	0.141564i	−0.00864201	+	0.00498947i
$806$	5.00121	+	2.88745i	0.176160	+	0.101706i
$807$	−9.24692	−	52.4419i	−0.325507	−	1.84604i
$808$	−16.2015	+	2.85676i	−0.569967	+	0.100501i
$809$	4.20424	+	2.42732i	0.147813	+	0.0853400i	0.572083	−	0.820196i	$-0.306136\pi$
$809$	4.20424	+	2.42732i	0.147813	+	0.0853400i	−0.424269	+	0.905536i	$0.639469\pi$
$810$	−11.4758	−	19.8767i	−0.403219	−	0.698396i
$811$	24.7985	−	20.8084i	0.870793	−	0.730682i	−0.0934722	−	0.995622i	$-0.529797\pi$
$811$	24.7985	−	20.8084i	0.870793	−	0.730682i	0.964265	+	0.264940i	$0.0853522\pi$
$812$	0.107719	+	0.295955i	0.00378020	+	0.0103860i
$813$	45.7294	+	16.6441i	1.60380	+	0.583735i
$814$	18.4561	−	0.0409697i	0.646885	−	0.00143599i
$815$	−6.80107	+	38.5708i	−0.238231	+	1.35108i
$816$	8.68178			0.303923
$817$	4.67609	−	0.989692i	0.163596	−	0.0346250i
$818$	8.38068			0.293024
$819$	0.833753	+	0.147013i	0.0291337	+	0.00513705i
$820$	6.79460	+	5.70135i	0.237278	+	0.199100i
$821$	−6.86281	+	18.8554i	−0.239514	+	0.658059i	0.760449	+	0.649398i	$0.224979\pi$
$821$	−6.86281	+	18.8554i	−0.239514	+	0.658059i	−0.999962	+	0.00866061i	$0.997243\pi$
$822$	0.921126	+	2.53077i	0.0321280	+	0.0882708i
$823$	−25.9777	+	21.7979i	−0.905526	+	0.759826i	−0.971262	−	0.238011i	$-0.923505\pi$
$823$	−25.9777	+	21.7979i	−0.905526	+	0.759826i	0.0657370	+	0.997837i	$0.479060\pi$
$824$	−5.50221	+	3.17670i	−0.191679	+	0.110666i
$825$	4.04569	+	22.6501i	0.140853	+	0.788576i
$826$	−0.0717362	−	0.406836i	−0.00249602	−	0.0141556i
$827$	−7.94029	−	45.0316i	−0.276111	−	1.56590i	−0.735410	−	0.677622i	$-0.763011\pi$
$827$	−7.94029	−	45.0316i	−0.276111	−	1.56590i	0.459299	−	0.888282i	$-0.348101\pi$
$828$	−0.592853	+	1.02685i	−0.0206031	+	0.0356856i
$829$	−12.3436	+	7.12657i	−0.428710	+	0.247516i	−0.698797	−	0.715320i	$-0.746281\pi$
$829$	−12.3436	+	7.12657i	−0.428710	+	0.247516i	0.270087	+	0.962836i	$0.412948\pi$
$830$	−8.57100	−	10.2145i	−0.297504	−	0.354551i
$831$	−0.0560057	+	0.0203844i	−0.00194282	+	0.000707128i
$832$	−0.886282	−	0.322580i	−0.0307263	−	0.0111835i
$833$	−15.4690	+	18.4352i	−0.535968	+	0.638742i
$834$	−5.01070	+	28.4171i	−0.173506	+	0.984003i
$835$	−63.2589			−2.18916
$836$	−4.44882	+	13.7553i	−0.153866	+	0.475737i
$837$	3.63760			0.125734
$838$	−3.97077	+	22.5193i	−0.137168	+	0.777918i
$839$	0.627895	−	0.748296i	0.0216773	−	0.0258340i	−0.755097	−	0.655613i	$-0.772410\pi$
$839$	0.627895	−	0.748296i	0.0216773	−	0.0258340i	0.776774	+	0.629779i	$0.216855\pi$
$840$	−1.81455	−	0.660441i	−0.0626078	−	0.0227874i
$841$	26.0383	−	9.47716i	0.897872	−	0.326799i
$842$	−20.0530	−	23.8982i	−0.691072	−	0.823587i
$843$	36.7084	−	21.1936i	1.26430	−	0.729946i
$844$	−13.7770	+	23.8624i	−0.474224	+	0.821379i
$845$	5.86481	+	33.2610i	0.201756	+	1.14421i
$846$	−2.83962	−	16.1043i	−0.0976281	−	0.553676i
$847$	−1.94981	+	2.34476i	−0.0669963	+	0.0805668i
$848$	3.59765	−	2.07710i	0.123544	−	0.0713280i
$849$	−38.7582	+	32.5220i	−1.33018	+	1.11615i
$850$	−3.30231	−	9.07303i	−0.113268	−	0.311202i
$851$	0.696968	−	1.91491i	0.0238918	−	0.0656421i
$852$	−29.5360	−	24.7836i	−1.01189	−	0.849074i
$853$	−12.5216	−	2.20789i	−0.428730	−	0.0755967i	−0.0448806	−	0.998992i	$-0.514291\pi$
$853$	−12.5216	−	2.20789i	−0.428730	−	0.0755967i	−0.383849	+	0.923396i	$0.625402\pi$
$854$	0.236437			0.00809072
$855$	36.5072	−	14.7130i	1.24852	−	0.503174i
$856$	−18.7197			−0.639826
$857$	4.90569	−	27.8215i	0.167575	−	0.950365i	−0.778794	−	0.627279i	$-0.784169\pi$
$857$	4.90569	−	27.8215i	0.167575	−	0.950365i	0.946370	−	0.323086i	$-0.104720\pi$
$858$	7.81267	−	0.0173429i	0.266720	−	0.000592078i
$859$	−7.62025	−	2.77354i	−0.260000	−	0.0946321i	0.208732	−	0.977973i	$-0.433066\pi$
$859$	−7.62025	−	2.77354i	−0.260000	−	0.0946321i	−0.468731	+	0.883341i	$0.655289\pi$
$860$	1.04592	+	2.87364i	0.0356655	+	0.0979902i
$861$	1.68694	−	1.41551i	0.0574906	−	0.0482404i
$862$	−3.00009	−	5.19632i	−0.102184	−	0.176987i
$863$	−9.76427	−	5.63740i	−0.332379	−	0.191899i	0.324518	−	0.945880i	$-0.394798\pi$
$863$	−9.76427	−	5.63740i	−0.332379	−	0.191899i	−0.656897	+	0.753980i	$0.728131\pi$
$864$	−0.585070	+	0.103164i	−0.0199045	+	0.00350970i
$865$	7.47517	+	42.3938i	0.254163	+	1.44143i
$866$	−0.564852	−	0.326118i	−0.0191945	−	0.0110819i
$867$	−10.6349	+	6.14005i	−0.361179	+	0.208527i
$868$	−1.30033	+	1.09111i	−0.0441360	+	0.0370345i
$869$	30.0197	+	17.2431i	1.01835	+	0.584933i
$870$	2.70641	−	7.43580i	0.0917559	−	0.252097i
$871$	0.938178	−	1.11808i	0.0317890	−	0.0378846i
$872$	0.957799	−	5.43195i	0.0324352	−	0.183949i
$873$			22.3439i			0.756228i
$874$	1.25699	+	0.983827i	0.0425183	+	0.0332784i
$875$		−	1.71822i		−	0.0580865i
$876$	−6.28852	+	35.6640i	−0.212470	+	1.20497i
$877$	−17.8226	−	14.9550i	−0.601828	−	0.504993i	0.290205	−	0.956965i	$-0.406277\pi$
$877$	−17.8226	−	14.9550i	−0.601828	−	0.504993i	−0.892033	+	0.451971i	$0.850721\pi$
$878$	16.5386	+	6.01954i	0.558149	+	0.203150i
$879$	19.2369	+	52.8530i	0.648845	+	1.78269i
$880$	−9.11256	−	1.58594i	−0.307184	−	0.0534621i
$881$	9.15989	+	15.8654i	0.308604	+	0.534519i	0.978057	−	0.208336i	$-0.0668047\pi$
$881$	9.15989	+	15.8654i	0.308604	+	0.534519i	−0.669453	+	0.742855i	$0.733471\pi$
$882$	11.2081	−	19.4130i	0.377397	−	0.653671i
$883$	−6.12115	−	34.7148i	−0.205993	−	1.16824i	−0.895869	−	0.444317i	$-0.853446\pi$
$883$	−6.12115	−	34.7148i	−0.205993	−	1.16824i	0.689876	−	0.723927i	$-0.257665\pi$
$884$	−3.22870	+	0.569308i	−0.108593	+	0.0191479i
$885$	−5.18967	+	8.98877i	−0.174449	+	0.302154i
$886$	0.0893120	+	0.154693i	0.00300049	+	0.00519701i
$887$	7.75715	−	6.50902i	0.260459	−	0.218551i	−0.503201	−	0.864169i	$-0.667845\pi$
$887$	7.75715	−	6.50902i	0.260459	−	0.218551i	0.763661	+	0.645618i	$0.223400\pi$
$888$	13.0601	−	4.75350i	0.438270	−	0.159517i
$889$	−1.43933	+	3.95453i	−0.0482736	+	0.132631i
$890$	−25.1186	+	29.9352i	−0.841978	+	1.00343i
$891$	−23.6080	+	13.7000i	−0.790897	+	0.458968i
$892$			23.7130i			0.793970i
$893$	−22.0017	+	0.749192i	−0.736257	+	0.0250708i
$894$	26.2113			0.876637
$895$	−22.6761	−	3.99841i	−0.757979	−	0.133652i
$896$	0.178200	−	0.212371i	0.00595325	−	0.00709480i
$897$	0.295035	−	0.810602i	0.00985093	−	0.0270652i
$898$	−6.85539	−	18.8350i	−0.228767	−	0.628533i
$899$	−4.47122	−	5.32860i	−0.149124	−	0.177719i
$900$	4.49681	+	7.78871i	0.149894	+	0.259624i
$901$	7.22020	−	12.5057i	0.240540	−	0.416627i
$902$	6.76236	−	8.09550i	0.225162	−	0.269551i
$903$	0.747708	−	0.131841i	0.0248822	−	0.00438740i
$904$	11.2032	+	6.46818i	0.372613	+	0.215128i
$905$	49.6623	−	28.6725i	1.65083	−	0.953107i
$906$	−13.8701	−	16.5297i	−0.460803	−	0.549163i
$907$	−3.04366	−	8.36239i	−0.101063	−	0.277668i	0.878849	−	0.477101i	$-0.158312\pi$
$907$	−3.04366	−	8.36239i	−0.101063	−	0.277668i	−0.979912	+	0.199432i	$0.936090\pi$
$908$	4.13856	+	1.50631i	0.137343	+	0.0499888i
$909$	34.2398	−	40.8054i	1.13566	−	1.35343i
$910$	0.718128	+	0.126625i	0.0238057	+	0.00419759i
$911$			28.8999i			0.957495i	0.877953	+	0.478748i	$0.158909\pi$
$911$			28.8999i			0.957495i	−0.877953	+	0.478748i	$0.841091\pi$
$912$	0.370494	+	10.8804i	0.0122683	+	0.360285i
$913$	−12.1249	+	10.2200i	−0.401277	+	0.338232i
$914$	−29.2822	−	5.16325i	−0.968570	−	0.170785i
$915$	−4.55063	−	3.81843i	−0.150439	−	0.126233i
$916$	6.19137	+	2.25347i	0.204569	+	0.0744569i
$917$	4.19915	−	1.52837i	0.138668	−	0.0504711i
$918$	−1.58198	+	1.32744i	−0.0522131	+	0.0438120i
$919$	20.7765	−	11.9953i	0.685352	−	0.395688i	−0.116516	−	0.993189i	$-0.537173\pi$
$919$	20.7765	−	11.9953i	0.685352	−	0.395688i	0.801869	+	0.597500i	$0.203839\pi$
$920$	−0.510636	+	0.884448i	−0.0168352	+	0.0291594i
$921$	−7.49419	+	1.32143i	−0.246942	+	0.0435425i
$922$	13.3552	−	2.35489i	0.439831	−	0.0775540i
$923$	12.6094	+	7.28007i	0.415045	+	0.239626i
$924$	−0.780636	+	2.15969i	−0.0256810	+	0.0710484i
$925$	−9.93544	−	11.8406i	−0.326675	−	0.389316i
$926$	−5.94061	+	2.16220i	−0.195221	+	0.0710545i
$927$	7.03586	−	19.3309i	0.231088	−	0.634909i
$928$	0.870270	+	0.730243i	0.0285680	+	0.0239714i
$929$	1.20474	−	6.83242i	0.0395262	−	0.224164i	−0.958646	−	0.284602i	$-0.908139\pi$
$929$	1.20474	−	6.83242i	0.0395262	−	0.224164i	0.998172	+	0.0604377i	$0.0192497\pi$
$930$	42.6482			1.39849
$931$	−23.7639	−	18.5996i	−0.778830	−	0.609578i
$932$		−	19.7131i		−	0.645724i
$933$	53.2998	+	9.39819i	1.74496	+	0.307683i
$934$	−11.8857	−	9.97332i	−0.388913	−	0.326337i
$935$	−30.1887	+	11.0637i	−0.987277	+	0.361823i
$936$	2.86966	−	1.04447i	0.0937979	−	0.0341396i
$937$	31.2978	+	37.2993i	1.02246	+	1.21851i	0.975587	+	0.219614i	$0.0704797\pi$
$937$	31.2978	+	37.2993i	1.02246	+	1.21851i	0.0468683	+	0.998901i	$0.485076\pi$
$938$	0.214507	+	0.371538i	0.00700392	+	0.0121311i
$939$	−30.3705	−	17.5344i	−0.991103	−	0.572214i
$940$	−2.44582	−	13.8709i	−0.0797738	−	0.452420i
$941$	8.50977	+	48.2613i	0.277411	+	1.57327i	0.731199	+	0.682164i	$0.238961\pi$
$941$	8.50977	+	48.2613i	0.277411	+	1.57327i	−0.453789	+	0.891109i	$0.649928\pi$
$942$	−10.9368	−	6.31435i	−0.356339	−	0.205733i
$943$	−0.582336	−	1.00864i	−0.0189635	−	0.0328457i
$944$	−0.957845	−	1.14152i	−0.0311752	−	0.0371532i
$945$	0.431625	−	0.157099i	0.0140408	−	0.00511042i
$946$	3.41470	−	1.25144i	0.111021	−	0.0406878i
$947$	31.4759	+	26.4114i	1.02283	+	0.858256i	0.989981	−	0.141204i	$-0.0450973\pi$
$947$	31.4759	+	26.4114i	1.02283	+	0.858256i	0.0328496	+	0.999460i	$0.489542\pi$
$948$	25.6740	+	4.52702i	0.833852	+	0.147031i
$949$		−	13.6756i		−	0.443929i
$950$	11.2298	−	4.52578i	0.364341	−	0.146836i
$951$	5.29337			0.171649
$952$	0.167341	−	0.949036i	0.00542354	−	0.0307584i
$953$	37.0004	+	31.0470i	1.19856	+	1.00571i	0.999670	+	0.0256884i	$0.00817778\pi$
$953$	37.0004	+	31.0470i	1.19856	+	1.00571i	0.198889	+	0.980022i	$0.436267\pi$
$954$	−4.60044	+	12.6396i	−0.148945	+	0.409222i
$955$	−28.0485	+	10.2088i	−0.907628	+	0.330350i
$956$	11.7678	+	14.0243i	0.380597	+	0.453578i
$957$	−8.85014	−	3.19896i	−0.286084	−	0.103408i
$958$	−15.1529	−	8.74855i	−0.489569	−	0.282653i
$959$	0.294402	−	0.0519111i	0.00950675	−	0.00167630i
$960$	−6.85952	+	1.20952i	−0.221390	+	0.0390370i
$961$	3.24510	−	5.62067i	0.104680	−	0.181312i
$962$	−4.54528	+	2.62422i	−0.146546	+	0.0846082i
$963$	46.4314	−	38.9606i	1.49623	−	1.25549i
$964$	4.46053	−	1.62350i	0.143664	−	0.0522894i
$965$	−43.6178	−	15.8756i	−1.40411	−	0.511054i
$966$	0.194236	+	0.162984i	0.00624945	+	0.00524391i
$967$	−19.3523	−	3.41233i	−0.622327	−	0.109733i	−0.146411	−	0.989224i	$-0.546772\pi$
$967$	−19.3523	−	3.41233i	−0.622327	−	0.109733i	−0.475916	+	0.879491i	$0.657883\pi$
$968$	−1.86202	+	10.8413i	−0.0598475	+	0.348451i
$969$	20.0259	+	32.1101i	0.643324	+	1.03152i
$970$			19.2453i			0.617929i
$971$	−0.471059	−	0.0830604i	−0.0151170	−	0.00266553i	0.166085	−	0.986112i	$-0.446888\pi$
$971$	−0.471059	−	0.0830604i	−0.0151170	−	0.00266553i	−0.181202	+	0.983446i	$0.557999\pi$
$972$	−14.3578	+	17.1110i	−0.460528	+	0.548836i
$973$	3.00979	+	1.09547i	0.0964894	+	0.0351193i
$974$	−12.7843	−	35.1245i	−0.409635	−	1.12546i
$975$	−4.20579	−	5.01226i	−0.134693	−	0.160521i
$976$	0.738595	−	0.426428i	0.0236418	−	0.0136496i
$977$	22.1953	+	12.8145i	0.710091	+	0.409972i	0.811095	−	0.584915i	$-0.198872\pi$
$977$	22.1953	+	12.8145i	0.710091	+	0.409972i	−0.101003	+	0.994886i	$0.532205\pi$
$978$	34.5424	−	6.09076i	1.10455	−	0.194761i
$979$	35.6666	+	29.7932i	1.13991	+	0.952194i
$980$	9.65378	−	16.7208i	0.308379	−	0.534127i
$981$	8.92963	+	15.4666i	0.285101	+	0.493810i
$982$	−27.2874	−	32.5198i	−0.870776	−	1.03775i
$983$	−0.412426	−	1.13313i	−0.0131543	−	0.0361412i	0.932942	−	0.360028i	$-0.117233\pi$
$983$	−0.412426	−	1.13313i	−0.0131543	−	0.0361412i	−0.946096	+	0.323886i	$0.895010\pi$
$984$	2.71679	−	7.46432i	0.0866081	−	0.237954i
$985$	−5.55366	+	6.61860i	−0.176954	+	0.210886i
$986$	3.88904	+	0.685742i	0.123852	+	0.0218385i
$987$	−3.49695			−0.111309
$988$	−0.851264	−	4.02205i	−0.0270823	−	0.127958i
$989$		−	0.401550i		−	0.0127685i
$990$	25.9031	−	15.0319i	0.823255	−	0.477746i
$991$	−19.1725	+	22.8489i	−0.609034	+	0.725818i	−0.979143	−	0.203170i	$-0.934876\pi$
$991$	−19.1725	+	22.8489i	−0.609034	+	0.725818i	0.370110	+	0.928988i	$0.379320\pi$
$992$	−2.09416	+	5.75367i	−0.0664897	+	0.182679i
$993$	−49.3783	+	17.9722i	−1.56697	+	0.570332i
$994$	−3.27849	+	2.75098i	−0.103987	+	0.0872558i
$995$	−14.1280	−	24.4705i	−0.447889	−	0.775767i
$996$	−5.97074	+	10.3416i	−0.189190	+	0.327687i
$997$	−5.55662	+	0.979783i	−0.175980	+	0.0310300i	−0.260944	−	0.965354i	$-0.584034\pi$
$997$	−5.55662	+	0.979783i	−0.175980	+	0.0310300i	0.0849637	+	0.996384i	$0.472923\pi$
$998$	6.13854	+	34.8134i	0.194312	+	1.10200i
$999$	−1.65299	+	2.86306i	−0.0522983	+	0.0905833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.b.21.9	yes	60
11.10	odd	2		418.2.q.a.21.9	✓	60
19.10	odd	18		418.2.q.a.219.9	yes	60
209.10	even	18	inner	418.2.q.b.219.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.21.9	✓	60	11.10	odd	2
418.2.q.a.219.9	yes	60	19.10	odd	18
418.2.q.b.21.9	yes	60	1.1	even	1	trivial
418.2.q.b.219.9	yes	60	209.10	even	18	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(1.60541 - 1.91325i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.62065 - 0.953840i) q^{5} +(-1.60541 - 1.91325i) q^{6} +(-0.240088 + 0.138615i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.562250 - 3.18868i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(1.60541 - 1.91325i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.62065 - 0.953840i) q^{5} +(-1.60541 - 1.91325i) q^{6} +(-0.240088 + 0.138615i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.562250 - 3.18868i) q^{9} +(-0.484277 - 2.74647i) q^{10} +(-3.26495 + 0.583175i) q^{11} +(-2.16296 + 1.24879i) q^{12} +(0.722503 - 0.606252i) q^{13} +(0.0948183 + 0.260511i) q^{14} +(2.38228 - 6.54527i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.42328 + 0.603616i) q^{17} -3.23787 q^{18} +(-0.610388 + 4.31595i) q^{19} -2.78884 q^{20} +(-0.120234 + 0.681883i) q^{21} +(0.00736239 + 3.31662i) q^{22} +(0.344115 + 0.125248i) q^{23} +(0.854220 + 2.34695i) q^{24} +(2.12779 - 1.78543i) q^{25} +(-0.471581 - 0.816802i) q^{26} +(-0.514502 - 0.297048i) q^{27} +(0.273018 - 0.0481405i) q^{28} +(0.197274 + 1.11880i) q^{29} +(-6.03216 - 3.48267i) q^{30} +(-5.30261 + 3.06146i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-4.12582 + 7.18291i) q^{33} +(1.18889 - 3.26645i) q^{34} +(-0.496972 + 0.592268i) q^{35} +(-0.562250 + 3.18868i) q^{36} -5.56473i q^{37} +(4.14439 + 1.35057i) q^{38} -2.35561i q^{39} +(-0.484277 + 2.74647i) q^{40} +(-2.43635 - 2.04434i) q^{41} +(0.650645 + 0.236816i) q^{42} +(-0.375037 - 1.03040i) q^{43} +(3.26751 + 0.568674i) q^{44} +(-4.51495 - 7.82013i) q^{45} +(0.183100 - 0.317138i) q^{46} +(0.877002 + 4.97372i) q^{47} +(2.45963 - 0.433699i) q^{48} +(-3.46157 + 5.99562i) q^{49} +(-1.38882 - 2.40550i) q^{50} +(6.65063 - 5.58054i) q^{51} +(-0.886282 + 0.322580i) q^{52} +(1.42082 - 3.90368i) q^{53} +(-0.381877 + 0.455104i) q^{54} +(-8.00005 + 4.64254i) q^{55} -0.277230i q^{56} +(7.27758 + 8.09669i) q^{57} +1.13606 q^{58} +(-1.46750 - 0.258760i) q^{59} +(-4.47723 + 5.33576i) q^{60} +(0.291694 - 0.801422i) q^{61} +(2.09416 + 5.75367i) q^{62} +(0.576989 + 0.687628i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.31516 - 2.27793i) q^{65} +(6.35734 + 5.31044i) q^{66} +(1.52399 - 0.268721i) q^{67} +(-3.01038 - 1.73804i) q^{68} +(0.792075 - 0.457305i) q^{69} +(0.496972 + 0.592268i) q^{70} +(5.27997 + 14.5066i) q^{71} +(3.04260 + 1.10742i) q^{72} +(9.32026 - 11.1075i) q^{73} +(-5.48019 - 0.966305i) q^{74} -6.93735i q^{75} +(2.04972 - 3.84690i) q^{76} +(0.703040 - 0.592585i) q^{77} +(-2.31983 - 0.409048i) q^{78} +(-7.99609 - 6.70952i) q^{79} +(2.62065 + 0.953840i) q^{80} +(7.73349 - 2.81476i) q^{81} +(-2.43635 + 2.04434i) q^{82} +(4.14067 - 2.39062i) q^{83} +(0.346201 - 0.599638i) q^{84} +(9.54698 - 1.68339i) q^{85} +(-1.07988 + 0.190411i) q^{86} +(2.45725 + 1.41869i) q^{87} +(1.12743 - 3.11912i) q^{88} +(-9.00683 - 10.7339i) q^{89} +(-8.48533 + 3.08841i) q^{90} +(-0.0894289 + 0.245704i) q^{91} +(-0.280525 - 0.235388i) q^{92} +(-2.65551 + 15.0601i) q^{93} +5.05045 q^{94} +(2.51711 + 11.8928i) q^{95} -2.49757i q^{96} +(-6.79598 - 1.19831i) q^{97} +(5.30344 + 4.45011i) q^{98} +(3.69528 + 10.0830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more