LMFDB - Embedded newform 71.2.g.a.12.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			12.5
Character	$\chi$	$=$	71.12
Dual form			71.2.g.a.6.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46643 + 1.53377i) q^{2} +(-0.822306 - 0.308617i) q^{3} +(-0.112290 + 2.50034i) q^{4} +(-0.577761 - 0.419768i) q^{5} +(-0.732509 - 1.71379i) q^{6} +(-0.0309991 + 0.228844i) q^{7} +(-0.803573 + 0.702060i) q^{8} +(-1.67827 - 1.46626i) q^{9} +O(q^{10})$	\(q+(1.46643 + 1.53377i) q^{2} +(-0.822306 - 0.308617i) q^{3} +(-0.112290 + 2.50034i) q^{4} +(-0.577761 - 0.419768i) q^{5} +(-0.732509 - 1.71379i) q^{6} +(-0.0309991 + 0.228844i) q^{7} +(-0.803573 + 0.702060i) q^{8} +(-1.67827 - 1.46626i) q^{9} +(-0.203420 - 1.50171i) q^{10} +(1.07787 - 0.644000i) q^{11} +(0.863983 - 2.02139i) q^{12} +(-2.30101 - 1.37479i) q^{13} +(-0.396452 + 0.288039i) q^{14} +(0.345549 + 0.523484i) q^{15} +(2.73038 + 0.245739i) q^{16} +(-0.509991 + 1.56959i) q^{17} +(-0.212166 - 4.72425i) q^{18} +(-3.60067 + 5.45478i) q^{19} +(1.11444 - 1.39746i) q^{20} +(0.0961159 - 0.178613i) q^{21} +(2.56837 + 0.708826i) q^{22} +(5.83841 + 2.81163i) q^{23} +(0.877450 - 0.329313i) q^{24} +(-1.38748 - 4.27023i) q^{25} +(-1.26567 - 5.54524i) q^{26} +(2.17615 + 4.04397i) q^{27} +(-0.568707 - 0.103205i) q^{28} +(0.799765 - 0.220721i) q^{29} +(-0.296179 + 1.29764i) q^{30} +(-7.67551 + 0.690808i) q^{31} +(4.95761 + 6.21665i) q^{32} +(-1.08509 + 0.196915i) q^{33} +(-3.15525 + 1.51949i) q^{34} +(0.113971 - 0.119205i) q^{35} +(3.85460 - 4.03160i) q^{36} +(-7.12068 + 3.42914i) q^{37} +(-13.6465 + 2.47647i) q^{38} +(1.46785 + 1.84063i) q^{39} +(0.758975 - 0.0683090i) q^{40} +(1.54883 - 6.78589i) q^{41} +(0.414898 - 0.114505i) q^{42} +(5.90700 + 1.07196i) q^{43} +(1.48918 + 2.76736i) q^{44} +(0.354150 + 1.55163i) q^{45} +(4.24924 + 13.0778i) q^{46} +(8.01087 - 3.00653i) q^{47} +(-2.16937 - 1.04471i) q^{48} +(6.69633 + 1.84807i) q^{49} +(4.51489 - 8.39007i) q^{50} +(0.903771 - 1.13329i) q^{51} +(3.69582 - 5.59892i) q^{52} +(-0.0866035 - 1.92838i) q^{53} +(-3.01133 + 9.26791i) q^{54} +(-0.893083 - 0.0803790i) q^{55} +(-0.135752 - 0.205656i) q^{56} +(4.64428 - 3.37427i) q^{57} +(1.51133 + 0.902980i) q^{58} +(-1.25123 + 2.92739i) q^{59} +(-1.34769 + 0.805207i) q^{60} +(-1.31136 - 9.68088i) q^{61} +(-12.3151 - 10.7594i) q^{62} +(0.387570 - 0.338610i) q^{63} +(-1.52891 + 11.2869i) q^{64} +(0.752341 + 1.76019i) q^{65} +(-1.89323 - 1.37551i) q^{66} +(0.161900 - 3.60499i) q^{67} +(-3.86724 - 1.45140i) q^{68} +(-3.93324 - 4.11385i) q^{69} +0.349964 q^{70} +(-3.31851 - 7.74516i) q^{71} +2.37802 q^{72} +(4.54650 + 4.75527i) q^{73} +(-15.7015 - 5.89286i) q^{74} +(-0.176929 + 3.93964i) q^{75} +(-13.2345 - 9.61540i) q^{76} +(0.113963 + 0.266629i) q^{77} +(-0.670590 + 4.95049i) q^{78} +(-4.26243 + 3.72397i) q^{79} +(-1.47435 - 1.28811i) q^{80} +(0.356016 + 2.62822i) q^{81} +(12.6792 - 7.57548i) q^{82} +(1.78766 - 4.18244i) q^{83} +(0.435800 + 0.260379i) q^{84} +(0.953516 - 0.692770i) q^{85} +(7.01807 + 10.6319i) q^{86} +(-0.725770 - 0.0653205i) q^{87} +(-0.414023 + 1.27423i) q^{88} +(-0.505464 - 11.2550i) q^{89} +(-1.86050 + 2.81854i) q^{90} +(0.385942 - 0.483956i) q^{91} +(-7.68562 + 14.2823i) q^{92} +(6.52481 + 1.80073i) q^{93} +(16.3587 + 7.87794i) q^{94} +(4.37006 - 1.64011i) q^{95} +(-2.15811 - 6.64199i) q^{96} +(-2.36055 - 10.3422i) q^{97} +(6.98520 + 12.9807i) q^{98} +(-2.75324 - 0.499639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{19}{35}\right)$

Coefficient data

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

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

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

$2$	1.46643	+	1.53377i	1.03692	+	1.08454i	0.996350	+	0.0853599i	$0.0272040\pi$
$2$	1.46643	+	1.53377i	1.03692	+	1.08454i	0.0405729	+	0.999177i	$0.487082\pi$
$3$	−0.822306	−	0.308617i	−0.474759	−	0.178180i	0.102514	−	0.994732i	$-0.467311\pi$
$3$	−0.822306	−	0.308617i	−0.474759	−	0.178180i	−0.577272	+	0.816552i	$0.695883\pi$
$4$	−0.112290	+	2.50034i	−0.0561451	+	1.25017i
$5$	−0.577761	−	0.419768i	−0.258382	−	0.187726i	0.451051	−	0.892498i	$-0.351049\pi$
$5$	−0.577761	−	0.419768i	−0.258382	−	0.187726i	−0.709434	+	0.704772i	$0.751049\pi$
$6$	−0.732509	−	1.71379i	−0.299046	−	0.699652i
$7$	−0.0309991	+	0.228844i	−0.0117165	+	0.0864950i	−0.995864	−	0.0908579i	$-0.971039\pi$
$7$	−0.0309991	+	0.228844i	−0.0117165	+	0.0864950i	0.984147	+	0.177353i	$0.0567534\pi$
$8$	−0.803573	+	0.702060i	−0.284106	+	0.248216i
$9$	−1.67827	−	1.46626i	−0.559424	−	0.488754i
$10$	−0.203420	−	1.50171i	−0.0643272	−	0.474882i
$11$	1.07787	−	0.644000i	0.324991	−	0.194173i	−0.341131	−	0.940016i	$-0.610810\pi$
$11$	1.07787	−	0.644000i	0.324991	−	0.194173i	0.666122	+	0.745843i	$0.267953\pi$
$12$	0.863983	−	2.02139i	0.249410	−	0.583525i
$13$	−2.30101	−	1.37479i	−0.638185	−	0.381298i	0.157057	−	0.987590i	$-0.449799\pi$
$13$	−2.30101	−	1.37479i	−0.638185	−	0.381298i	−0.795242	+	0.606292i	$0.792656\pi$
$14$	−0.396452	+	0.288039i	−0.105956	+	0.0769816i
$15$	0.345549	+	0.523484i	0.0892203	+	0.135163i
$16$	2.73038	+	0.245739i	0.682596	+	0.0614347i
$17$	−0.509991	+	1.56959i	−0.123691	+	0.380682i	−0.993660	−	0.112424i	$-0.964138\pi$
$17$	−0.509991	+	1.56959i	−0.123691	+	0.380682i	0.869969	+	0.493106i	$0.164138\pi$
$18$	−0.212166	−	4.72425i	−0.0500080	−	1.11352i
$19$	−3.60067	+	5.45478i	−0.826049	+	1.25141i	0.139248	+	0.990258i	$0.455532\pi$
$19$	−3.60067	+	5.45478i	−0.826049	+	1.25141i	−0.965297	+	0.261154i	$0.915897\pi$
$20$	1.11444	−	1.39746i	0.249196	−	0.312482i
$21$	0.0961159	−	0.178613i	0.0209742	−	0.0389766i
$22$	2.56837	+	0.708826i	0.547579	+	0.151122i
$23$	5.83841	+	2.81163i	1.21739	+	0.586265i	0.928584	−	0.371122i	$-0.121027\pi$
$23$	5.83841	+	2.81163i	1.21739	+	0.586265i	0.288808	+	0.957387i	$0.406741\pi$
$24$	0.877450	−	0.329313i	0.179109	−	0.0672207i
$25$	−1.38748	−	4.27023i	−0.277496	−	0.854046i
$26$	−1.26567	−	5.54524i	−0.248217	−	1.08751i
$27$	2.17615	+	4.04397i	0.418801	+	0.778263i
$28$	−0.568707	−	0.103205i	−0.107476	−	0.0195039i
$29$	0.799765	−	0.220721i	0.148513	−	0.0409869i	−0.190990	−	0.981592i	$-0.561170\pi$
$29$	0.799765	−	0.220721i	0.148513	−	0.0409869i	0.339503	+	0.940605i	$0.389741\pi$
$30$	−0.296179	+	1.29764i	−0.0540746	+	0.236916i
$31$	−7.67551	+	0.690808i	−1.37856	+	0.124073i	−0.753986	−	0.656891i	$-0.771871\pi$
$31$	−7.67551	+	0.690808i	−1.37856	+	0.124073i	−0.624577	+	0.780964i	$0.714728\pi$
$32$	4.95761	+	6.21665i	0.876391	+	1.09896i
$33$	−1.08509	+	0.196915i	−0.188890	+	0.0342785i
$34$	−3.15525	+	1.51949i	−0.541121	+	0.260590i
$35$	0.113971	−	0.119205i	0.0192647	−	0.0201493i
$36$	3.85460	−	4.03160i	0.642434	−	0.671933i
$37$	−7.12068	+	3.42914i	−1.17063	+	0.563747i	−0.915168	−	0.403072i	$-0.867943\pi$
$37$	−7.12068	+	3.42914i	−1.17063	+	0.563747i	−0.255464	+	0.966819i	$0.582228\pi$
$38$	−13.6465	+	2.47647i	−2.21375	+	0.401737i
$39$	1.46785	+	1.84063i	0.235044	+	0.294736i
$40$	0.758975	−	0.0683090i	0.120004	−	0.0108006i
$41$	1.54883	−	6.78589i	0.241887	−	1.05978i	−0.697410	−	0.716672i	$-0.745664\pi$
$41$	1.54883	−	6.78589i	0.241887	−	1.05978i	0.939297	−	0.343105i	$-0.111479\pi$
$42$	0.414898	−	0.114505i	0.0640202	−	0.0176684i
$43$	5.90700	+	1.07196i	0.900809	+	0.163473i	0.609155	−	0.793051i	$-0.291509\pi$
$43$	5.90700	+	1.07196i	0.900809	+	0.163473i	0.291654	+	0.956524i	$0.405794\pi$
$44$	1.48918	+	2.76736i	0.224503	+	0.417196i
$45$	0.354150	+	1.55163i	0.0527936	+	0.231304i
$46$	4.24924	+	13.0778i	0.626516	+	1.92822i
$47$	8.01087	−	3.00653i	1.16851	−	0.438548i	0.309693	−	0.950837i	$-0.399774\pi$
$47$	8.01087	−	3.00653i	1.16851	−	0.438548i	0.858813	+	0.512289i	$0.171202\pi$
$48$	−2.16937	−	1.04471i	−0.313122	−	0.150792i
$49$	6.69633	+	1.84807i	0.956619	+	0.264010i
$50$	4.51489	−	8.39007i	0.638502	−	1.18654i
$51$	0.903771	−	1.13329i	0.126553	−	0.158693i
$52$	3.69582	−	5.59892i	0.512518	−	0.776431i
$53$	−0.0866035	−	1.92838i	−0.0118959	−	0.264883i	−0.996123	−	0.0879727i	$-0.971961\pi$
$53$	−0.0866035	−	1.92838i	−0.0118959	−	0.264883i	0.984227	−	0.176910i	$-0.0566103\pi$
$54$	−3.01133	+	9.26791i	−0.409790	+	1.26120i
$55$	−0.893083	−	0.0803790i	−0.120423	−	0.0108383i
$56$	−0.135752	−	0.205656i	−0.0181407	−	0.0274820i
$57$	4.64428	−	3.37427i	0.615151	−	0.446933i
$58$	1.51133	+	0.902980i	0.198448	+	0.118567i
$59$	−1.25123	+	2.92739i	−0.162896	+	0.381114i	−0.981014	−	0.193936i	$-0.937875\pi$
$59$	−1.25123	+	2.92739i	−0.162896	+	0.381114i	0.818118	+	0.575050i	$0.195017\pi$
$60$	−1.34769	+	0.805207i	−0.173986	+	0.103952i
$61$	−1.31136	−	9.68088i	−0.167903	−	1.23951i	−0.857182	−	0.515014i	$-0.827787\pi$
$61$	−1.31136	−	9.68088i	−0.167903	−	1.23951i	0.689279	−	0.724496i	$-0.257927\pi$
$62$	−12.3151	−	10.7594i	−1.56402	−	1.36645i
$63$	0.387570	−	0.338610i	0.0488293	−	0.0426608i
$64$	−1.52891	+	11.2869i	−0.191114	+	1.41086i
$65$	0.752341	+	1.76019i	0.0933164	+	0.218325i
$66$	−1.89323	−	1.37551i	−0.233041	−	0.169314i
$67$	0.161900	−	3.60499i	0.0197792	−	0.440419i	−0.964531	−	0.263971i	$-0.914968\pi$
$67$	0.161900	−	3.60499i	0.0197792	−	0.440419i	0.984310	−	0.176448i	$-0.0564608\pi$
$68$	−3.86724	−	1.45140i	−0.468972	−	0.176008i
$69$	−3.93324	−	4.11385i	−0.473507	−	0.495249i
$70$	0.349964			0.0418286
$71$	−3.31851	−	7.74516i	−0.393834	−	0.919181i
$71$	−3.31851	−	7.74516i	−0.393834	−	0.919181i
$72$	2.37802			0.280252
$73$	4.54650	+	4.75527i	0.532128	+	0.556562i	0.933141	−	0.359510i	$-0.117056\pi$
$73$	4.54650	+	4.75527i	0.532128	+	0.556562i	−0.401013	+	0.916072i	$0.631342\pi$
$74$	−15.7015	−	5.89286i	−1.82526	−	0.685031i
$75$	−0.176929	+	3.93964i	−0.0204300	+	0.454910i
$76$	−13.2345	−	9.61540i	−1.51810	−	1.10296i
$77$	0.113963	+	0.266629i	0.0129872	+	0.0303851i
$78$	−0.670590	+	4.95049i	−0.0759294	+	0.560533i
$79$	−4.26243	+	3.72397i	−0.479560	+	0.418979i	−0.863477	−	0.504389i	$-0.831718\pi$
$79$	−4.26243	+	3.72397i	−0.479560	+	0.418979i	0.383916	+	0.923368i	$0.374575\pi$
$80$	−1.47435	−	1.28811i	−0.164838	−	0.144015i
$81$	0.356016	+	2.62822i	0.0395574	+	0.292024i
$82$	12.6792	−	7.57548i	1.40019	−	0.836572i
$83$	1.78766	−	4.18244i	0.196221	−	0.459082i	−0.792306	−	0.610123i	$-0.791120\pi$
$83$	1.78766	−	4.18244i	0.196221	−	0.459082i	0.988527	+	0.151041i	$0.0482627\pi$
$84$	0.435800	+	0.260379i	0.0475497	+	0.0284096i
$85$	0.953516	−	0.692770i	0.103423	−	0.0751415i
$86$	7.01807	+	10.6319i	0.756778	+	1.14647i
$87$	−0.725770	−	0.0653205i	−0.0778107	−	0.00700309i
$88$	−0.414023	+	1.27423i	−0.0441350	+	0.135834i
$89$	−0.505464	−	11.2550i	−0.0535791	−	1.19303i	−0.828136	−	0.560527i	$-0.810599\pi$
$89$	−0.505464	−	11.2550i	−0.0535791	−	1.19303i	0.774557	−	0.632504i	$-0.217973\pi$
$90$	−1.86050	+	2.81854i	−0.196114	+	0.297101i
$91$	0.385942	−	0.483956i	0.0404577	−	0.0507323i
$92$	−7.68562	+	14.2823i	−0.801281	+	1.48903i
$93$	6.52481	+	1.80073i	0.676592	+	0.186727i
$94$	16.3587	+	7.87794i	1.68727	+	0.812547i
$95$	4.37006	−	1.64011i	0.448359	−	0.168272i
$96$	−2.15811	−	6.64199i	−0.220262	−	0.677896i
$97$	−2.36055	−	10.3422i	−0.239678	−	1.05010i	−0.941306	−	0.337553i	$-0.890401\pi$
$97$	−2.36055	−	10.3422i	−0.239678	−	1.05010i	0.701629	−	0.712543i	$-0.252456\pi$
$98$	6.98520	+	12.9807i	0.705612	+	1.31125i
$99$	−2.75324	−	0.499639i	−0.276711	−	0.0502156i
$100$	10.8328	−	2.98967i	1.08328	−	0.298967i
$101$	−1.97113	+	8.63607i	−0.196134	+	0.859321i	0.777076	+	0.629406i	$0.216702\pi$
$101$	−1.97113	+	8.63607i	−0.196134	+	0.859321i	−0.973211	+	0.229915i	$0.926155\pi$
$102$	3.06352	−	0.275722i	0.303334	−	0.0273006i
$103$	12.1974	+	15.2950i	1.20184	+	1.50706i	0.809368	+	0.587302i	$0.199810\pi$
$103$	12.1974	+	15.2950i	1.20184	+	1.50706i	0.392476	+	0.919762i	$0.371619\pi$
$104$	2.81421	−	0.510704i	0.275956	−	0.0500787i
$105$	−0.130508	+	0.0628494i	−0.0127363	+	0.00613347i
$106$	2.83068	−	2.96066i	0.274940	−	0.287565i
$107$	−5.86544	+	6.13477i	−0.567034	+	0.593071i	−0.942682	−	0.333691i	$-0.891706\pi$
$107$	−5.86544	+	6.13477i	−0.567034	+	0.593071i	0.375649	+	0.926762i	$0.377420\pi$
$108$	−10.3557	+	4.98702i	−0.996473	+	0.479876i
$109$	−16.0210	+	2.90738i	−1.53453	+	0.278476i	−0.879048	−	0.476733i	$-0.841821\pi$
$109$	−16.0210	+	2.90738i	−1.53453	+	0.278476i	−0.655484	+	0.755209i	$0.727535\pi$
$110$	−1.18636	−	1.48765i	−0.113115	−	0.141842i
$111$	6.91367	−	0.622241i	0.656216	−	0.0590605i
$112$	−0.140875	+	0.617215i	−0.0133115	+	0.0583213i
$113$	8.67249	−	2.39346i	0.815839	−	0.225157i	0.166877	−	0.985978i	$-0.446632\pi$
$113$	8.67249	−	2.39346i	0.815839	−	0.225157i	0.648962	+	0.760820i	$0.275203\pi$
$114$	11.9859	+	2.17511i	1.12258	+	0.203718i
$115$	−2.19297	−	4.07522i	−0.204496	−	0.380017i
$116$	0.462071	+	2.02447i	0.0429022	+	0.187967i
$117$	1.84592	+	5.68115i	0.170655	+	0.525222i
$118$	−6.32477	+	2.37373i	−0.582242	+	0.218519i
$119$	−0.343383	−	0.165364i	−0.0314778	−	0.0151589i
$120$	−0.645191	−	0.178061i	−0.0588976	−	0.0162547i
$121$	−4.46548	+	8.29825i	−0.405953	+	0.754386i
$122$	12.9252	−	16.2077i	1.17019	−	1.46737i
$123$	−3.36785	+	5.10208i	−0.303669	+	0.460039i
$124$	−0.865369	−	19.2689i	−0.0777124	−	1.73040i
$125$	−2.09430	+	6.44559i	−0.187320	+	0.576511i
$126$	1.08769	+	0.0978942i	0.0968994	+	0.00872111i
$127$	−5.57196	−	8.44116i	−0.494432	−	0.749032i	0.498606	−	0.866829i	$-0.333845\pi$
$127$	−5.57196	−	8.44116i	−0.494432	−	0.749032i	−0.993038	+	0.117797i	$0.962417\pi$
$128$	−6.68787	+	4.85902i	−0.591130	+	0.429481i
$129$	−4.52654	−	2.70448i	−0.398539	−	0.238116i
$130$	−1.59646	+	3.73511i	−0.140019	+	0.327591i
$131$	−9.59568	+	5.73315i	−0.838379	+	0.500908i	−0.866781	−	0.498689i	$-0.833815\pi$
$131$	−9.59568	+	5.73315i	−0.838379	+	0.500908i	0.0284026	+	0.999597i	$0.490958\pi$
$132$	−0.370509	−	2.73521i	−0.0322486	−	0.238069i
$133$	−1.13668	−	0.993085i	−0.0985624	−	0.0861114i
$134$	5.76662	−	5.03814i	0.498160	−	0.435229i
$135$	0.440232	−	3.24993i	0.0378892	−	0.279709i
$136$	−0.692133	−	1.61932i	−0.0593499	−	0.138856i
$137$	16.9888	+	12.3431i	1.45145	+	1.05454i	0.985490	+	0.169734i	$0.0542908\pi$
$137$	16.9888	+	12.3431i	1.45145	+	1.05454i	0.465960	+	0.884806i	$0.345709\pi$
$138$	0.541855	−	12.0653i	0.0461258	−	1.02707i
$139$	−12.2331	−	4.59116i	−1.03760	−	0.389417i	−0.226305	−	0.974056i	$-0.572665\pi$
$139$	−12.2331	−	4.59116i	−1.03760	−	0.389417i	−0.811293	+	0.584639i	$0.801236\pi$
$140$	0.285254	+	0.298353i	0.0241084	+	0.0252154i
$141$	−7.51526			−0.632899
$142$	7.01291	−	16.4476i	0.588510	−	1.38025i
$143$	−3.36556			−0.281442
$144$	−4.22201	−	4.41587i	−0.351834	−	0.367989i
$145$	−0.554724	−	0.208192i	−0.0460673	−	0.0172894i
$146$	−0.626340	+	13.9465i	−0.0518363	+	1.15422i
$147$	−4.93609	−	3.58628i	−0.407122	−	0.295791i
$148$	−7.77442	−	18.1892i	−0.639053	−	1.49514i
$149$	−1.84856	+	13.6466i	−0.151440	+	1.11797i	0.742519	+	0.669825i	$0.233631\pi$
$149$	−1.84856	+	13.6466i	−0.151440	+	1.11797i	−0.893959	+	0.448149i	$0.852084\pi$
$150$	−6.30194	+	5.50584i	−0.514551	+	0.449550i
$151$	−0.748254	−	0.653730i	−0.0608921	−	0.0531998i	0.626955	−	0.779056i	$-0.284301\pi$
$151$	−0.748254	−	0.653730i	−0.0608921	−	0.0531998i	−0.687847	+	0.725856i	$0.741444\pi$
$152$	−0.936185	−	6.91119i	−0.0759346	−	0.560572i
$153$	3.15733	−	1.88642i	0.255255	−	0.152508i
$154$	−0.241828	+	0.565784i	−0.0194870	+	0.0455922i
$155$	4.72459	+	2.82281i	0.379488	+	0.226734i
$156$	−4.76701	+	3.46344i	−0.381667	+	0.277297i
$157$	−4.73242	−	7.16931i	−0.377688	−	0.572173i	0.595163	−	0.803605i	$-0.297088\pi$
$157$	−4.73242	−	7.16931i	−0.377688	−	0.572173i	−0.972851	+	0.231432i	$0.925659\pi$
$158$	−11.9623	−	1.07662i	−0.951666	−	0.0856515i
$159$	−0.523915	+	1.61244i	−0.0415492	+	0.127875i
$160$	−0.254765	−	5.67278i	−0.0201409	−	0.448473i
$161$	−0.824410	+	1.24893i	−0.0649726	+	0.0984293i
$162$	−3.50900	+	4.40014i	−0.275693	+	0.345708i
$163$	0.238240	−	0.442723i	0.0186604	−	0.0346768i	−0.871095	−	0.491115i	$-0.836589\pi$
$163$	0.238240	−	0.442723i	0.0186604	−	0.0346768i	0.889755	+	0.456438i	$0.150875\pi$
$164$	16.7931	+	4.63460i	1.31132	+	0.361901i
$165$	0.709582	+	0.341717i	0.0552409	+	0.0266026i
$166$	9.03636	−	3.39140i	0.701357	−	0.263224i
$167$	−0.678626	−	2.08860i	−0.0525136	−	0.161620i	0.921360	−	0.388710i	$-0.127079\pi$
$167$	−0.678626	−	2.08860i	−0.0525136	−	0.161620i	−0.973874	+	0.227089i	$0.927079\pi$
$168$	0.0481612	+	0.211008i	0.00371571	+	0.0162796i
$169$	−2.75569	−	5.12094i	−0.211976	−	0.393918i
$170$	2.46081	+	0.446572i	0.188736	+	0.0342505i
$171$	14.0410	−	3.87508i	1.07374	−	0.296334i
$172$	−3.34357	+	14.6491i	−0.254945	+	1.11699i
$173$	−13.0378	+	1.17343i	−0.991247	+	0.0892139i	−0.573376	−	0.819292i	$-0.694367\pi$
$173$	−13.0378	+	1.17343i	−0.991247	+	0.0892139i	−0.417871	+	0.908506i	$0.637224\pi$
$174$	−0.964105	−	1.20895i	−0.0730886	−	0.0916502i
$175$	1.02023	−	0.185144i	0.0771220	−	0.0139956i
$176$	3.10126	−	1.49349i	0.233767	−	0.112576i
$177$	1.93233	−	2.02106i	0.145243	−	0.151912i
$178$	16.5214	−	17.2800i	1.23833	−	1.29519i
$179$	14.6079	−	7.03482i	1.09185	−	0.525807i	0.200762	−	0.979640i	$-0.435658\pi$
$179$	14.6079	−	7.03482i	1.09185	−	0.525807i	0.891087	+	0.453833i	$0.149944\pi$
$180$	−3.91937	+	0.711261i	−0.292133	+	0.0530143i
$181$	1.56282	+	1.95971i	0.116163	+	0.145664i	0.836513	−	0.547946i	$-0.184590\pi$
$181$	1.56282	+	1.95971i	0.116163	+	0.145664i	−0.720350	+	0.693611i	$0.756019\pi$
$182$	1.30823	−	0.117743i	0.0969726	−	0.00872769i
$183$	−1.90934	+	8.36536i	−0.141142	+	0.618385i
$184$	−6.66552	+	1.83957i	−0.491388	+	0.135615i
$185$	5.55349	+	1.00781i	0.408301	+	0.0740957i
$186$	6.80628	+	12.6482i	0.499061	+	0.927410i
$187$	0.461110	+	2.02025i	0.0337197	+	0.147736i
$188$	6.61780	+	20.3675i	0.482652	+	1.48545i
$189$	−0.992898	+	0.372641i	−0.0722227	+	0.0271056i
$190$	8.92394	+	4.29754i	0.647411	+	0.311777i
$191$	−9.60310	−	2.65029i	−0.694856	−	0.191768i	−0.0992712	−	0.995060i	$-0.531651\pi$
$191$	−9.60310	−	2.65029i	−0.694856	−	0.191768i	−0.595585	+	0.803292i	$0.703080\pi$
$192$	4.74056	−	8.80943i	0.342120	−	0.635766i
$193$	16.5856	−	20.7976i	1.19386	−	1.49705i	0.371156	−	0.928570i	$-0.378961\pi$
$193$	16.5856	−	20.7976i	1.19386	−	1.49705i	0.822699	−	0.568477i	$-0.192467\pi$
$194$	12.4010	−	18.7867i	0.890340	−	1.34881i
$195$	−0.0754309	−	1.67960i	−0.00540172	−	0.120279i
$196$	−5.37273	+	16.5356i	−0.383767	+	1.18111i
$197$	−2.90218	−	0.261201i	−0.206772	−	0.0186098i	−0.0142309	−	0.999899i	$-0.504530\pi$
$197$	−2.90218	−	0.261201i	−0.206772	−	0.0186098i	−0.192541	+	0.981289i	$0.561673\pi$
$198$	−3.27110	−	4.95551i	−0.232467	−	0.352172i
$199$	−9.57103	+	6.95376i	−0.678472	+	0.492939i	−0.872851	−	0.487988i	$-0.837731\pi$
$199$	−9.57103	+	6.95376i	−0.678472	+	0.492939i	0.194378	+	0.980927i	$0.437731\pi$
$200$	4.11290	+	2.45735i	0.290826	+	0.173761i
$201$	−1.24569	+	2.91444i	−0.0878642	+	0.205569i
$202$	−16.1362	+	9.64095i	−1.13534	+	0.678335i
$203$	0.0257188	+	0.189864i	0.00180511	+	0.0133258i
$204$	2.73213	+	2.38699i	0.191287	+	0.167123i
$205$	−3.74335	+	3.27047i	−0.261447	+	0.228419i
$206$	−5.57239	+	41.1370i	−0.388247	+	2.86615i
$207$	−5.67585	−	13.2793i	−0.394499	−	0.922976i
$208$	−5.94480	−	4.31915i	−0.412198	−	0.299479i
$209$	−0.368190	+	8.19839i	−0.0254682	+	0.567094i
$210$	−0.287777	−	0.108005i	−0.0198585	−	0.00745303i
$211$	4.27204	+	4.46820i	0.294099	+	0.307604i	0.853291	−	0.521434i	$-0.174603\pi$
$211$	4.27204	+	4.46820i	0.294099	+	0.307604i	−0.559192	+	0.829038i	$0.688889\pi$
$212$	4.83132			0.331816
$213$	0.338543	+	7.39304i	0.0231966	+	0.506563i
$214$	−18.0106			−1.23118
$215$	−2.96286	−	3.09891i	−0.202065	−	0.211344i
$216$	−4.58781	−	1.72183i	−0.312161	−	0.117156i
$217$	0.0798461	−	1.77791i	0.00542030	−	0.120692i
$218$	−27.9529	−	20.3090i	−1.89321	−	1.37550i
$219$	−2.27106	−	5.31341i	−0.153464	−	0.359047i
$220$	0.301259	−	2.22398i	0.0203109	−	0.149941i
$221$	3.33135	−	2.91051i	0.224091	−	0.195782i
$222$	11.0928	+	9.69148i	0.744499	+	0.650449i
$223$	0.613996	+	4.53270i	0.0411162	+	0.303532i	0.999817	+	0.0191163i	$0.00608527\pi$
$223$	0.613996	+	4.53270i	0.0411162	+	0.303532i	−0.958701	+	0.284416i	$0.908200\pi$
$224$	−1.57633	+	0.941811i	−0.105323	+	0.0629274i
$225$	−3.93270	+	9.20102i	−0.262180	+	0.613401i
$226$	16.3886	+	9.79174i	1.09015	+	0.651337i
$227$	7.41208	−	5.38519i	0.491957	−	0.357428i	−0.313979	−	0.949430i	$-0.601662\pi$
$227$	7.41208	−	5.38519i	0.491957	−	0.357428i	0.805937	+	0.592002i	$0.201662\pi$
$228$	7.91531	+	11.9912i	0.524204	+	0.794135i
$229$	−0.219847	−	0.0197866i	−0.0145279	−	0.00130753i	0.0823730	−	0.996602i	$-0.473750\pi$
$229$	−0.219847	−	0.0197866i	−0.0145279	−	0.00130753i	−0.0969009	+	0.995294i	$0.530893\pi$
$230$	3.03460	−	9.33954i	0.200096	−	0.615831i
$231$	−0.0114261	−	0.254421i	−0.000751780	−	0.0167397i
$232$	−0.487710	+	0.738849i	−0.0320197	+	0.0485078i
$233$	−5.26172	+	6.59799i	−0.344707	+	0.432249i	−0.923719	−	0.383070i	$-0.874867\pi$
$233$	−5.26172	+	6.59799i	−0.344707	+	0.432249i	0.579013	+	0.815319i	$0.303438\pi$
$234$	−6.00665	+	11.1622i	−0.392667	+	0.729697i
$235$	−5.89041	−	1.62565i	−0.384248	−	0.106046i
$236$	−7.17896	−	3.45721i	−0.467311	−	0.225045i
$237$	4.65430	−	1.74679i	0.302329	−	0.113466i
$238$	−0.249917	−	0.769164i	−0.0161997	−	0.0498575i
$239$	−5.98005	−	26.2003i	−0.386817	−	1.69476i	−0.675523	−	0.737339i	$-0.736082\pi$
$239$	−5.98005	−	26.2003i	−0.386817	−	1.69476i	0.288705	−	0.957418i	$-0.406775\pi$
$240$	0.814841	+	1.51423i	0.0525977	+	0.0977430i
$241$	27.6008	+	5.00881i	1.77792	+	0.322646i	0.965496	−	0.260417i	$-0.0838601\pi$
$241$	27.6008	+	5.00881i	1.77792	+	0.322646i	0.812427	+	0.583063i	$0.198146\pi$
$242$	−19.2759	+	5.31981i	−1.23910	+	0.341970i
$243$	3.58402	−	15.7026i	0.229915	−	1.00732i
$244$	24.3527	−	2.19178i	1.55902	−	0.140315i
$245$	−3.09312	−	3.87865i	−0.197612	−	0.247798i
$246$	−12.7641	+	2.31635i	−0.813811	+	0.147685i
$247$	15.7843	−	7.60133i	1.00433	−	0.483661i
$248$	5.68284	−	5.94379i	0.360861	−	0.377431i
$249$	−2.76077	+	2.88754i	−0.174957	+	0.182990i
$250$	−12.9572	+	6.23984i	−0.819483	+	0.394642i
$251$	22.8170	−	4.14068i	1.44020	−	0.261357i	0.598420	−	0.801182i	$-0.295795\pi$
$251$	22.8170	−	4.14068i	1.44020	−	0.261357i	0.841777	+	0.539825i	$0.181510\pi$
$252$	0.803119	+	1.00708i	0.0505917	+	0.0634400i
$253$	8.10375	−	0.729351i	0.509479	−	0.0458539i
$254$	4.77587	−	20.9245i	0.299665	−	1.31292i
$255$	−0.997883	+	0.275398i	−0.0624899	+	0.0172461i
$256$	5.15397	+	0.935307i	0.322123	+	0.0584567i
$257$	−0.203108	−	0.377438i	−0.0126695	−	0.0235439i	0.874182	−	0.485598i	$-0.161398\pi$
$257$	−0.203108	−	0.377438i	−0.0126695	−	0.0235439i	−0.886852	+	0.462054i	$0.847112\pi$
$258$	−2.48981	−	10.9086i	−0.155009	−	0.679139i
$259$	−0.564004	−	1.73583i	−0.0350455	−	0.107859i
$260$	−4.48555	+	1.68345i	−0.278182	+	0.104403i
$261$	−1.66586	−	0.802234i	−0.103114	−	0.0496571i
$262$	−22.8647	−	6.31026i	−1.41259	−	0.389849i
$263$	−12.0042	+	22.3075i	−0.740210	+	1.37554i	0.179822	+	0.983699i	$0.442448\pi$
$263$	−12.0042	+	22.3075i	−0.740210	+	1.37554i	−0.920032	+	0.391842i	$0.871838\pi$
$264$	0.733703	−	0.920035i	0.0451563	−	0.0566242i
$265$	−0.759435	+	1.15049i	−0.0466517	+	0.0706743i
$266$	−0.143698	−	3.19969i	−0.00881069	−	0.196185i
$267$	−3.05784	+	9.41108i	−0.187137	+	0.575948i
$268$	8.99550	+	0.809610i	0.549488	+	0.0494548i
$269$	4.84856	+	7.34525i	0.295622	+	0.447848i	0.951783	−	0.306773i	$-0.0992493\pi$
$269$	4.84856	+	7.34525i	0.295622	+	0.447848i	−0.656161	+	0.754621i	$0.727821\pi$
$270$	5.63020	−	4.09058i	0.342643	−	0.248945i
$271$	−6.37705	−	3.81011i	−0.387378	−	0.231448i	0.305985	−	0.952036i	$-0.401014\pi$
$271$	−6.37705	−	3.81011i	−0.387378	−	0.231448i	−0.693363	+	0.720589i	$0.743872\pi$
$272$	−1.77818	+	4.16026i	−0.107818	+	0.252253i
$273$	−0.466719	+	0.278852i	−0.0282471	+	0.0168769i
$274$	5.98148	+	44.1571i	0.361355	+	2.66763i
$275$	−4.24556	−	3.70923i	−0.256017	−	0.223675i
$276$	10.7277	−	9.37249i	0.645730	−	0.564157i
$277$	2.34414	−	17.3051i	0.140846	−	1.03977i	−0.773202	−	0.634160i	$-0.781346\pi$
$277$	2.34414	−	17.3051i	0.140846	−	1.03977i	0.914048	−	0.405606i	$-0.132939\pi$
$278$	−10.8972	−	25.4953i	−0.653573	−	1.52911i
$279$	13.8945	+	10.0949i	0.831842	+	0.604368i
$280$	−0.00789539	+	0.175805i	−0.000471840	+	0.0105063i
$281$	−11.9245	−	4.47534i	−0.711357	−	0.266977i	−0.0306473	−	0.999530i	$-0.509757\pi$
$281$	−11.9245	−	4.47534i	−0.711357	−	0.266977i	−0.680709	+	0.732554i	$0.738328\pi$
$282$	−11.0206	−	11.5266i	−0.656267	−	0.686402i
$283$	−4.19397			−0.249306			−0.124653	−	0.992200i	$-0.539782\pi$
$283$	−4.19397			−0.249306			−0.124653	+	0.992200i	$0.539782\pi$
$284$	19.7382	−	7.42768i	1.17124	−	0.440752i
$285$	−4.09970			−0.242845
$286$	−4.93536	−	5.16198i	−0.291834	−	0.305234i
$287$	1.50490	+	0.564798i	0.0888313	+	0.0333390i
$288$	0.795015	−	17.7024i	0.0468467	−	1.04312i
$289$	11.5498	+	8.39139i	0.679398	+	0.493611i
$290$	−0.494148	−	1.15612i	−0.0290173	−	0.0678895i
$291$	−1.25069	+	9.23300i	−0.0733170	+	0.541248i
$292$	−12.4003	+	10.8338i	−0.725673	+	0.634001i
$293$	12.8220	+	11.2022i	0.749069	+	0.654442i	0.945332	−	0.326109i	$-0.105738\pi$
$293$	12.8220	+	11.2022i	0.749069	+	0.654442i	−0.196263	+	0.980551i	$0.562881\pi$
$294$	−1.73792	−	12.8298i	−0.101358	−	0.748251i
$295$	1.95173	−	1.16611i	0.113634	−	0.0678933i
$296$	3.31452	−	7.75471i	0.192653	−	0.450733i
$297$	4.94993	+	2.95745i	0.287224	+	0.171609i
$298$	−23.6415	+	17.1765i	−1.36951	+	0.995010i
$299$	−9.56883	−	14.4962i	−0.553380	−	0.838335i
$300$	−9.83056	−	0.884766i	−0.567568	−	0.0510820i
$301$	−0.428424	+	1.31855i	−0.0246939	+	0.0760001i
$302$	−0.0945939	−	2.10630i	−0.00544327	−	0.121204i
$303$	4.28610	−	6.49317i	0.246230	−	0.373023i
$304$	−11.1716	+	14.0088i	−0.640738	+	0.803460i
$305$	−3.30607	+	6.14370i	−0.189305	+	0.351787i
$306$	7.52334	+	2.07631i	0.430081	+	0.118695i
$307$	2.70505	+	1.30268i	0.154385	+	0.0743479i	0.509481	−	0.860482i	$-0.329837\pi$
$307$	2.70505	+	1.30268i	0.154385	+	0.0743479i	−0.355096	+	0.934830i	$0.615552\pi$
$308$	−0.679458	+	0.255005i	−0.0387157	+	0.0145303i
$309$	−5.30968	−	16.3415i	−0.302057	−	0.929636i
$310$	2.59875	+	11.3859i	0.147599	+	0.646674i
$311$	−7.27617	−	13.5214i	−0.412594	−	0.766727i	0.586471	−	0.809970i	$-0.300517\pi$
$311$	−7.27617	−	13.5214i	−0.412594	−	0.766727i	−0.999065	+	0.0432429i	$0.986231\pi$
$312$	−2.47176	−	0.448558i	−0.139936	−	0.0253946i
$313$	13.3078	−	3.67272i	0.752202	−	0.207595i	0.131148	−	0.991363i	$-0.458134\pi$
$313$	13.3078	−	3.67272i	0.752202	−	0.207595i	0.621053	+	0.783768i	$0.286705\pi$
$314$	4.05628	−	17.7717i	0.228909	−	1.00292i
$315$	−0.366060	+	0.0329460i	−0.0206252	+	0.00185630i
$316$	−8.83255	−	11.0757i	−0.496870	−	0.623055i
$317$	−33.7152	+	6.11840i	−1.89363	+	0.343644i	−0.995394	−	0.0958654i	$-0.969438\pi$
$317$	−33.7152	+	6.11840i	−1.89363	+	0.343644i	−0.898238	+	0.439509i	$0.855152\pi$
$318$	−3.24140	+	1.56097i	−0.181769	+	0.0875351i
$319$	0.719901	−	0.752958i	0.0403067	−	0.0421575i
$320$	5.62122	−	5.87933i	0.314236	−	0.328665i
$321$	6.71648	−	3.23449i	0.374877	−	0.180531i
$322$	−3.12450	+	0.567014i	−0.174122	+	0.0315984i
$323$	−6.72546	−	8.43346i	−0.374215	−	0.469250i
$324$	−6.61141	+	0.595038i	−0.367300	+	0.0330576i
$325$	−2.67806	+	11.7333i	−0.148552	+	0.650849i
$326$	1.02840	−	0.283819i	0.0569576	−	0.0157193i
$327$	14.0714	+	2.55359i	0.778151	+	0.141214i
$328$	3.51950	+	6.54033i	0.194332	+	0.361129i
$329$	0.439698	+	1.92644i	0.0242413	+	0.106208i
$330$	0.516439	+	1.58944i	0.0284290	+	0.0874956i
$331$	−18.9969	+	7.12966i	−1.04416	+	0.391881i	−0.813752	−	0.581212i	$-0.802579\pi$
$331$	−18.9969	+	7.12966i	−1.04416	+	0.391881i	−0.230412	+	0.973093i	$0.574007\pi$
$332$	10.2568	+	4.93940i	0.562913	+	0.271085i
$333$	16.9784	+	4.68575i	0.930413	+	0.256778i
$334$	2.20826	−	4.10363i	0.120831	−	0.224541i
$335$	−1.60680	+	2.01486i	−0.0877886	+	0.110083i
$336$	0.306325	−	0.464063i	0.0167114	−	0.0253167i
$337$	1.09992	+	24.4916i	0.0599165	+	1.33414i	0.773599	+	0.633675i	$0.218454\pi$
$337$	1.09992	+	24.4916i	0.0599165	+	1.33414i	−0.713683	+	0.700469i	$0.752974\pi$
$338$	3.81329	−	11.7361i	0.207415	−	0.638359i
$339$	−7.87010	−	0.708322i	−0.427445	−	0.0384708i
$340$	1.62509	+	2.46190i	0.0881328	+	0.133515i
$341$	−7.82835	+	5.68763i	−0.423929	+	0.308002i
$342$	26.5336	+	15.8531i	1.43478	+	0.857238i
$343$	−1.26584	+	2.96158i	−0.0683490	+	0.159910i
$344$	−5.49929	+	3.28567i	−0.296502	+	0.177152i
$345$	0.545612	+	4.02787i	0.0293748	+	0.216853i
$346$	−20.9188	−	18.2762i	−1.12460	−	0.982536i
$347$	−0.498924	+	0.435897i	−0.0267837	+	0.0234002i	−0.671227	−	0.741252i	$-0.734232\pi$
$347$	−0.498924	+	0.435897i	−0.0267837	+	0.0234002i	0.644443	+	0.764652i	$0.277089\pi$
$348$	0.244820	−	1.80733i	0.0131237	−	0.0968833i
$349$	7.43287	+	17.3901i	0.397872	+	0.930869i	0.991970	+	0.126476i	$0.0403666\pi$
$349$	7.43287	+	17.3901i	0.397872	+	0.930869i	−0.594097	+	0.804393i	$0.702491\pi$
$350$	1.78006	+	1.29329i	0.0951483	+	0.0691293i
$351$	0.552257	−	12.2970i	0.0294773	−	0.656364i
$352$	9.34720	+	3.50806i	0.498208	+	0.186980i
$353$	13.9962	+	14.6388i	0.744940	+	0.779146i	0.981293	−	0.192521i	$-0.0616663\pi$
$353$	13.9962	+	14.6388i	0.744940	+	0.779146i	−0.236353	+	0.971667i	$0.575952\pi$
$354$	5.93347			0.315360
$355$	−1.33387	+	5.86785i	−0.0707943	+	0.311433i
$356$	28.1981			1.49450
$357$	0.231331	+	0.241954i	0.0122434	+	0.0128055i
$358$	32.2113	+	12.0891i	1.70242	+	0.638929i
$359$	−0.509892	+	11.3536i	−0.0269111	+	0.599222i	0.939550	+	0.342410i	$0.111243\pi$
$359$	−0.509892	+	11.3536i	−0.0269111	+	0.599222i	−0.966462	+	0.256811i	$0.917328\pi$
$360$	−1.37392	−	0.998215i	−0.0724122	−	0.0526105i
$361$	−9.32231	−	21.8106i	−0.490648	−	1.14793i
$362$	−0.713976	+	5.27078i	−0.0375258	+	0.277026i
$363$	6.23297	−	5.44558i	0.327146	−	0.285819i
$364$	1.16671	+	1.01933i	0.0611525	+	0.0534273i
$365$	−0.630682	−	4.65588i	−0.0330114	−	0.243700i
$366$	−15.6304	+	9.33874i	−0.817015	+	0.488144i
$367$	−3.61396	+	8.45527i	−0.188647	+	0.441362i	−0.986978	−	0.160858i	$-0.948574\pi$
$367$	−3.61396	+	8.45527i	−0.188647	+	0.441362i	0.798331	+	0.602220i	$0.205717\pi$
$368$	15.2502	+	9.11155i	0.794970	+	0.474972i
$369$	−12.5492	+	9.11756i	−0.653288	+	0.474641i
$370$	6.59806	+	9.99564i	0.343017	+	0.519649i
$371$	0.443983	+	0.0399592i	0.0230504	+	0.00207458i
$372$	−5.23512	+	16.1120i	−0.271428	+	0.835370i
$373$	0.0567893	+	1.26451i	0.00294044	+	0.0654740i	0.999927	−	0.0121038i	$-0.00385284\pi$
$373$	0.0567893	+	1.26451i	0.00294044	+	0.0654740i	−0.996986	+	0.0775777i	$0.975281\pi$
$374$	−2.42241	+	3.66980i	−0.125260	+	0.189761i
$375$	3.71137	−	4.65391i	0.191654	−	0.240327i
$376$	−4.32655	+	8.04008i	−0.223125	+	0.414636i
$377$	−2.14371	−	0.591627i	−0.110407	−	0.0304703i
$378$	−2.02756	−	0.976422i	−0.104286	−	0.0502217i
$379$	5.66031	−	2.12435i	0.290751	−	0.109121i	−0.201738	−	0.979440i	$-0.564659\pi$
$379$	5.66031	−	2.12435i	0.290751	−	0.109121i	0.492488	+	0.870319i	$0.336087\pi$
$380$	3.61012	+	11.1108i	0.185195	+	0.569972i
$381$	1.97678	+	8.66082i	0.101273	+	0.443707i
$382$	−10.0174	−	18.6154i	−0.512533	−	0.952446i
$383$	−9.32352	−	1.69197i	−0.476410	−	0.0864556i	−0.0649595	−	0.997888i	$-0.520692\pi$
$383$	−9.32352	−	1.69197i	−0.476410	−	0.0864556i	−0.411450	+	0.911432i	$0.634978\pi$
$384$	6.99905	−	1.93162i	0.357169	−	0.0985723i
$385$	0.0460790	−	0.201885i	0.00234840	−	0.0102890i
$386$	56.2203	−	5.05992i	2.86154	−	0.257543i
$387$	−8.34177	−	10.4602i	−0.424036	−	0.531724i
$388$	26.1242	−	4.74084i	1.32625	−	0.240680i
$389$	29.2983	−	14.1093i	1.48548	−	0.715370i	0.497146	−	0.867667i	$-0.334381\pi$
$389$	29.2983	−	14.1093i	1.48548	−	0.715370i	0.988335	+	0.152297i	$0.0486670\pi$
$390$	2.46550	−	2.57871i	0.124845	−	0.130578i
$391$	−7.39064	+	7.73001i	−0.373761	+	0.390923i
$392$	−6.67845	+	3.21617i	−0.337312	+	0.162441i
$393$	9.65994	−	1.75302i	0.487279	−	0.0884282i
$394$	−3.85523	−	4.83430i	−0.194224	−	0.243549i
$395$	4.02586	−	0.362334i	0.202563	−	0.0182310i
$396$	1.55843	−	6.82791i	0.0783139	−	0.343116i
$397$	−24.7375	+	6.82711i	−1.24154	+	0.342643i	−0.824299	−	0.566154i	$-0.808431\pi$
$397$	−24.7375	+	6.82711i	−1.24154	+	0.342643i	−0.417239	+	0.908797i	$0.637002\pi$
$398$	−24.7007	−	4.48251i	−1.23813	−	0.224688i
$399$	0.628214	+	1.16742i	0.0314500	+	0.0584440i
$400$	−2.73900	−	12.0003i	−0.136950	−	0.600016i
$401$	−8.96953	−	27.6054i	−0.447917	−	1.37855i	−0.879253	−	0.476355i	$-0.841958\pi$
$401$	−8.96953	−	27.6054i	−0.447917	−	1.37855i	0.431336	−	0.902191i	$-0.358042\pi$
$402$	−6.29678	+	2.36322i	−0.314055	+	0.117867i
$403$	18.6111	+	8.96265i	0.927087	+	0.446461i
$404$	−21.3717	−	5.89823i	−1.06328	−	0.293448i
$405$	0.897549	−	1.66793i	0.0445996	−	0.0828799i
$406$	−0.253492	+	0.317869i	−0.0125806	+	0.0157756i
$407$	−5.46683	+	8.28189i	−0.270981	+	0.410518i
$408$	0.0693943	+	1.54518i	0.00343553	+	0.0764980i
$409$	5.57617	−	17.1617i	0.275724	−	0.848590i	−0.713303	−	0.700855i	$-0.752802\pi$
$409$	5.57617	−	17.1617i	0.275724	−	0.848590i	0.989027	−	0.147735i	$-0.0471982\pi$
$410$	−10.5055	−	0.945512i	−0.518830	−	0.0466955i
$411$	−10.1607	−	15.3928i	−0.501190	−	0.759271i
$412$	−39.6124	+	28.7801i	−1.95156	+	1.41789i
$413$	−0.631130	−	0.377082i	−0.0310559	−	0.0185550i
$414$	12.0441	−	28.1786i	0.591936	−	1.38490i
$415$	−2.78849	+	1.66605i	−0.136882	+	0.0817830i
$416$	−2.86093	−	21.1202i	−0.140269	−	1.03551i
$417$	8.64245	+	7.55068i	0.423223	+	0.369758i
$418$	−13.1143	+	11.4576i	−0.641443	+	0.560412i
$419$	1.65420	−	12.2118i	0.0808129	−	0.596585i	−0.904582	−	0.426300i	$-0.859817\pi$
$419$	1.65420	−	12.2118i	0.0808129	−	0.596585i	0.985395	−	0.170285i	$-0.0544688\pi$
$420$	−0.142490	−	0.333371i	−0.00695279	−	0.0162669i
$421$	−9.07450	−	6.59301i	−0.442264	−	0.321324i	0.344270	−	0.938871i	$-0.388126\pi$
$421$	−9.07450	−	6.59301i	−0.442264	−	0.321324i	−0.786534	+	0.617547i	$0.788126\pi$
$422$	−0.588529	+	13.1046i	−0.0286491	+	0.637923i
$423$	−17.8528	−	6.70026i	−0.868032	−	0.325778i
$424$	1.42343	+	1.48879i	0.0691279	+	0.0723021i
$425$	7.41012			0.359444
$426$	−10.8427	+	11.3606i	−0.525333	+	0.550424i
$427$	2.25606			0.109179
$428$	−14.6804	−	15.3545i	−0.709602	−	0.742186i
$429$	2.76752	+	1.03867i	0.133617	+	0.0501474i
$430$	0.408172	−	9.08866i	0.0196838	−	0.438294i
$431$	−0.576355	−	0.418746i	−0.0277620	−	0.0201703i	0.573818	−	0.818983i	$-0.305462\pi$
$431$	−0.576355	−	0.418746i	−0.0277620	−	0.0201703i	−0.601580	+	0.798813i	$0.705462\pi$
$432$	4.94797	+	11.5764i	0.238059	+	0.556968i
$433$	3.52239	−	26.0033i	0.169275	−	1.24964i	−0.684505	−	0.729008i	$-0.739982\pi$
$433$	3.52239	−	26.0033i	0.169275	−	1.24964i	0.853781	−	0.520633i	$-0.174304\pi$
$434$	2.84399	−	2.48472i	0.136516	−	0.119270i
$435$	0.391902	+	0.342394i	0.0187903	+	0.0164166i
$436$	−5.47043	−	40.3843i	−0.261986	−	1.93406i
$437$	−36.3590	+	21.7235i	−1.73928	+	1.03917i
$438$	4.81918	−	11.2750i	0.230269	−	0.538742i
$439$	−6.21964	−	3.71606i	−0.296847	−	0.177358i	0.356751	−	0.934199i	$-0.383884\pi$
$439$	−6.21964	−	3.71606i	−0.296847	−	0.177358i	−0.653598	+	0.756841i	$0.726741\pi$
$440$	0.774088	−	0.562408i	0.0369032	−	0.0268118i
$441$	−8.52851	−	12.9201i	−0.406119	−	0.615244i
$442$	9.34924	+	0.841447i	0.444698	+	0.0400235i
$443$	−11.0973	+	34.1540i	−0.527250	+	1.62271i	0.232575	+	0.972579i	$0.425285\pi$
$443$	−11.0973	+	34.1540i	−0.527250	+	1.62271i	−0.759824	+	0.650129i	$0.774715\pi$
$444$	0.779476	+	17.3564i	0.0369923	+	0.823697i
$445$	−4.43246	+	6.71489i	−0.210119	+	0.318316i
$446$	−6.05172	+	7.58861i	−0.286557	+	0.359331i
$447$	5.73165	−	10.6512i	0.271098	−	0.503784i
$448$	−2.53555	−	0.699766i	−0.119793	−	0.0330608i
$449$	−20.6258	−	9.93286i	−0.973392	−	0.468761i	−0.121564	−	0.992584i	$-0.538791\pi$
$449$	−20.6258	−	9.93286i	−0.973392	−	0.468761i	−0.851827	+	0.523823i	$0.824505\pi$
$450$	−19.8792	+	7.46081i	−0.937117	+	0.351706i
$451$	−2.70066	−	8.31178i	−0.127169	−	0.391386i
$452$	5.01061	+	21.9529i	0.235679	+	1.03258i
$453$	0.413542	+	0.768490i	0.0194299	+	0.0361068i
$454$	19.1289	+	3.47139i	0.897766	+	0.162920i
$455$	−0.426131	+	0.117605i	−0.0199773	+	0.00551339i
$456$	−1.36308	+	5.97204i	−0.0638320	+	0.279666i
$457$	−6.54033	+	0.588640i	−0.305944	+	0.0275354i	−0.241547	−	0.970389i	$-0.577655\pi$
$457$	−6.54033	+	0.588640i	−0.305944	+	0.0275354i	−0.0643961	+	0.997924i	$0.520512\pi$
$458$	−0.292042	−	0.366209i	−0.0136462	−	0.0171118i
$459$	−7.45720	+	1.35328i	−0.348072	+	0.0631658i
$460$	10.4357	−	5.02556i	0.486566	−	0.234318i
$461$	24.6674	−	25.8001i	1.14888	−	1.20163i	0.172627	−	0.984987i	$-0.444775\pi$
$461$	24.6674	−	25.8001i	1.14888	−	1.20163i	0.976251	−	0.216644i	$-0.0695112\pi$
$462$	0.373467	−	0.390616i	0.0173753	−	0.0181731i
$463$	3.48331	−	1.67747i	0.161883	−	0.0779588i	−0.351188	−	0.936305i	$-0.614222\pi$
$463$	3.48331	−	1.67747i	0.161883	−	0.0779588i	0.513071	+	0.858346i	$0.328508\pi$
$464$	2.23790	−	0.406120i	0.103892	−	0.0188536i
$465$	−3.01389	−	3.77930i	−0.139766	−	0.175261i
$466$	−17.8357	+	1.60524i	−0.826224	+	0.0743615i
$467$	7.18290	−	31.4704i	0.332385	−	1.45627i	−0.482113	−	0.876109i	$-0.660131\pi$
$467$	7.18290	−	31.4704i	0.332385	−	1.45627i	0.814498	−	0.580166i	$-0.197012\pi$
$468$	−14.4121	+	3.97748i	−0.666198	+	0.183859i
$469$	0.819961	+	0.148801i	0.0378623	+	0.00687099i
$470$	−6.14451	−	11.4184i	−0.283425	−	0.526692i
$471$	1.67893	+	7.35587i	0.0773610	+	0.338941i
$472$	−1.04975	−	3.23081i	−0.0483188	−	0.148710i
$473$	7.05734	−	2.64867i	0.324497	−	0.121786i
$474$	9.50437	+	4.57706i	0.436550	+	0.210231i
$475$	28.2890	+	7.80727i	1.29799	+	0.358222i
$476$	0.452025	−	0.840004i	0.0207185	−	0.0385015i
$477$	−2.68216	+	3.36332i	−0.122808	+	0.153996i
$478$	31.4158	−	47.5929i	1.43693	−	2.17685i
$479$	1.59367	+	35.4858i	0.0728167	+	1.62139i	0.620156	+	0.784479i	$0.287069\pi$
$479$	1.59367	+	35.4858i	0.0728167	+	1.62139i	−0.547339	+	0.836911i	$0.684359\pi$
$480$	−1.54122	+	4.74339i	−0.0703468	+	0.216505i
$481$	21.0991	+	1.89895i	0.962036	+	0.0865848i
$482$	32.7923	+	49.6782i	1.49365	+	2.26278i
$483$	1.06336	−	0.772574i	0.0483844	−	0.0351534i
$484$	−20.2470	−	12.0970i	−0.920318	−	0.549864i
$485$	−2.97751	+	6.96623i	−0.135202	+	0.316320i
$486$	29.3398	−	17.5297i	1.33088	−	0.795165i
$487$	0.0154445	+	0.114016i	0.000699857	+	0.00516655i	0.991296	−	0.131650i	$-0.0420274\pi$
$487$	0.0154445	+	0.114016i	0.000699857	+	0.00516655i	−0.990596	+	0.136816i	$0.956313\pi$
$488$	7.85034	+	6.85863i	0.355368	+	0.310476i
$489$	−0.332538	+	0.290529i	−0.0150379	+	0.0131382i
$490$	1.41309	−	10.4319i	0.0638371	−	0.471264i
$491$	14.4804	+	33.8786i	0.653492	+	1.52892i	0.837756	+	0.546045i	$0.183867\pi$
$491$	14.4804	+	33.8786i	0.653492	+	1.52892i	−0.184264	+	0.982877i	$0.558990\pi$
$492$	−12.3787	−	8.99368i	−0.558077	−	0.405467i
$493$	−0.0614311	+	1.36787i	−0.00276672	+	0.0616057i
$494$	34.8053	+	13.0626i	1.56596	+	0.587716i
$495$	1.38098	+	1.44439i	0.0620704	+	0.0649206i
$496$	−21.1268			−0.948623
$497$	1.87531	−	0.519328i	0.0841190	−	0.0232951i
$498$	−8.47729			−0.379877
$499$	2.90777	+	3.04128i	0.130169	+	0.136147i	0.784667	−	0.619918i	$-0.212834\pi$
$499$	2.90777	+	3.04128i	0.130169	+	0.136147i	−0.654497	+	0.756064i	$0.727120\pi$
$500$	−15.8810	−	5.96023i	−0.710218	−	0.266549i
$501$	−0.0865372	+	1.92690i	−0.00386620	+	0.0860876i
$502$	39.8104	+	28.9240i	1.77683	+	1.29094i
$503$	12.2874	+	28.7477i	0.547866	+	1.28180i	0.933312	+	0.359067i	$0.116905\pi$
$503$	12.2874	+	28.7477i	0.547866	+	1.28180i	−0.385446	+	0.922731i	$0.625952\pi$
$504$	−0.0737163	+	0.544195i	−0.00328358	+	0.0242404i
$505$	4.76398	−	4.16217i	0.211994	−	0.185214i
$506$	13.0022	+	11.3597i	0.578020	+	0.505001i
$507$	0.685617	+	5.06143i	0.0304493	+	0.224786i
$508$	21.7314	−	12.9839i	0.964177	−	0.576069i
$509$	4.67220	−	10.9311i	0.207091	−	0.484514i	−0.783496	−	0.621397i	$-0.786565\pi$
$509$	4.67220	−	10.9311i	0.207091	−	0.484514i	0.990587	+	0.136883i	$0.0437083\pi$
$510$	−1.88572	−	1.12667i	−0.0835012	−	0.0498896i
$511$	−1.22915	+	0.893032i	−0.0543745	+	0.0395054i
$512$	15.2315	+	23.0748i	0.673146	+	1.01977i
$513$	−29.8946	−	2.69056i	−1.31988	−	0.118791i
$514$	0.281058	−	0.865007i	0.0123969	−	0.0381538i
$515$	−0.626807	−	13.9569i	−0.0276204	−	0.615016i
$516$	7.27040	−	11.0142i	0.320061	−	0.484872i
$517$	6.69850	−	8.39966i	0.294600	−	0.369417i
$518$	1.83528	−	3.41052i	0.0806375	−	0.149850i
$519$	11.0832	+	3.05877i	0.486499	+	0.134265i
$520$	−1.84032	−	0.886251i	−0.0807033	−	0.0388647i
$521$	−36.6835	+	13.7675i	−1.60713	+	0.603166i	−0.983876	−	0.178852i	$-0.942762\pi$
$521$	−36.6835	+	13.7675i	−1.60713	+	0.603166i	−0.623255	+	0.782018i	$0.714190\pi$
$522$	−1.21242	−	3.73146i	−0.0530663	−	0.163321i
$523$	4.22083	+	18.4927i	0.184564	+	0.808627i	0.979421	+	0.201830i	$0.0646889\pi$
$523$	4.22083	+	18.4927i	0.184564	+	0.808627i	−0.794857	+	0.606797i	$0.792454\pi$
$524$	−13.2573	−	24.6362i	−0.579148	−	1.07624i
$525$	−0.896079	−	0.162614i	−0.0391081	−	0.00709707i
$526$	−51.8179	+	14.3008i	−2.25937	+	0.623545i
$527$	2.83015	−	12.3997i	0.123283	−	0.540140i
$528$	−3.01110	+	0.271004i	−0.131042	+	0.0117939i
$529$	11.8415	+	14.8487i	0.514847	+	0.645597i
$530$	−2.87825	+	0.522325i	−0.125023	+	0.0226883i
$531$	6.39222	−	3.07833i	0.277399	−	0.133588i
$532$	2.61068	−	2.73056i	0.113188	−	0.118385i
$533$	−12.8930	+	13.4851i	−0.558460	+	0.584103i
$534$	−18.9185	+	9.11067i	−0.818684	+	0.394257i
$535$	5.96400	−	1.08231i	0.257846	−	0.0467922i
$536$	2.40082	+	3.01053i	0.103700	+	0.130035i
$537$	−14.1833	+	1.27652i	−0.612053	+	0.0550858i
$538$	−4.15583	+	18.2079i	−0.179170	+	0.784997i
$539$	8.40796	−	2.32045i	0.362156	−	0.0999488i
$540$	8.07648	+	1.46566i	0.347556	+	0.0630722i
$541$	−21.2097	−	39.4142i	−0.911876	−	1.69455i	−0.695884	−	0.718154i	$-0.744987\pi$
$541$	−21.2097	−	39.4142i	−0.911876	−	1.69455i	−0.215992	−	0.976395i	$-0.569298\pi$
$542$	−3.50768	−	15.3682i	−0.150668	−	0.660119i
$543$	−0.680316	−	2.09380i	−0.0291952	−	0.0898534i
$544$	−12.2859	+	4.61099i	−0.526755	+	0.197695i
$545$	10.4767	+	5.04532i	0.448773	+	0.216118i
$546$	−1.11210	−	0.306921i	−0.0475937	−	0.0131350i
$547$	−17.1460	+	31.8626i	−0.733111	+	1.36235i	0.191522	+	0.981488i	$0.438658\pi$
$547$	−17.1460	+	31.8626i	−0.733111	+	1.36235i	−0.924633	+	0.380860i	$0.875628\pi$
$548$	−32.7695	+	41.0917i	−1.39984	+	1.75535i
$549$	−11.9939	+	18.1699i	−0.511886	+	0.775474i
$550$	−0.536721	−	11.9510i	−0.0228859	−	0.509593i
$551$	−1.67570	+	5.15728i	−0.0713873	+	0.219708i
$552$	6.04882	+	0.544403i	0.257455	+	0.0231713i
$553$	−0.720078	−	1.09087i	−0.0306208	−	0.0463886i
$554$	29.9796	−	21.7814i	1.27371	−	0.925404i
$555$	−4.25564	−	2.54263i	−0.180642	−	0.107929i
$556$	12.8531	−	30.0713i	0.545093	−	1.27531i
$557$	−17.3609	+	10.3726i	−0.735604	+	0.439503i	−0.831240	−	0.555914i	$-0.812369\pi$
$557$	−17.3609	+	10.3726i	−0.735604	+	0.439503i	0.0956363	+	0.995416i	$0.469511\pi$
$558$	4.89203	+	36.1144i	0.207096	+	1.52885i
$559$	−12.1183	−	10.5875i	−0.512551	−	0.447802i
$560$	0.340479	−	0.297468i	0.0143879	−	0.0125703i
$561$	0.244311	−	1.80357i	0.0103148	−	0.0761470i
$562$	−10.6223	−	24.8522i	−0.448076	−	1.04833i
$563$	6.01054	+	4.36691i	0.253314	+	0.184043i	0.707194	−	0.707019i	$-0.249961\pi$
$563$	6.01054	+	4.36691i	0.253314	+	0.184043i	−0.453880	+	0.891063i	$0.649961\pi$
$564$	0.843890	−	18.7907i	0.0355342	−	0.791230i
$565$	−6.01532	−	2.25759i	−0.253066	−	0.0949774i
$566$	−6.15016	−	6.43257i	−0.258511	−	0.270381i
$567$	−0.612489			−0.0257221
$568$	8.10423	+	3.89401i	0.340046	+	0.163389i
$569$	29.3544			1.23060			0.615299	−	0.788293i	$-0.289035\pi$
$569$	29.3544			1.23060			0.615299	+	0.788293i	$0.289035\pi$
$570$	−6.01192	−	6.28797i	−0.251812	−	0.263374i
$571$	34.0096	+	12.7640i	1.42326	+	0.534157i	0.939955	−	0.341298i	$-0.110866\pi$
$571$	34.0096	+	12.7640i	1.42326	+	0.534157i	0.483300	+	0.875455i	$0.339438\pi$
$572$	0.377920	−	8.41504i	0.0158016	−	0.351850i
$573$	7.07877	+	5.14303i	0.295720	+	0.214853i
$574$	1.34056	+	3.13640i	0.0559540	+	0.130911i
$575$	3.90562	−	28.8324i	0.162876	−	1.20240i
$576$	19.1155	−	16.7007i	0.796478	−	0.695862i
$577$	−14.8326	−	12.9589i	−0.617491	−	0.539486i	0.291356	−	0.956615i	$-0.405893\pi$
$577$	−14.8326	−	12.9589i	−0.617491	−	0.539486i	−0.908847	+	0.417129i	$0.863036\pi$
$578$	4.06649	+	30.0200i	0.169144	+	1.24867i
$579$	−20.0569	+	11.9835i	−0.833537	+	0.498015i
$580$	0.582839	−	1.36362i	0.0242011	−	0.0566212i
$581$	0.901711	+	0.538747i	0.0374093	+	0.0223510i
$582$	−15.9953	+	11.6213i	−0.663027	+	0.481717i
$583$	−1.33522	−	2.02277i	−0.0552992	−	0.0837748i
$584$	−6.99193	−	0.629285i	−0.289328	−	0.0260400i
$585$	1.31826	−	4.05720i	0.0545035	−	0.167745i
$586$	1.62095	+	36.0933i	0.0669608	+	1.49100i
$587$	0.570593	−	0.864412i	0.0235509	−	0.0356781i	−0.822607	−	0.568610i	$-0.807481\pi$
$587$	0.570593	−	0.864412i	0.0235509	−	0.0356781i	0.846158	+	0.532932i	$0.178910\pi$
$588$	9.52118	−	11.9392i	0.392647	−	0.492364i
$589$	23.8687	−	44.3556i	0.983494	−	1.82764i
$590$	4.65062	+	1.28349i	0.191463	+	0.0528404i
$591$	2.30587	+	1.11045i	0.0948509	+	0.0456778i
$592$	−20.2849	+	7.61303i	−0.833702	+	0.312894i
$593$	−7.73791	−	23.8149i	−0.317758	−	0.977959i	−0.974604	−	0.223934i	$-0.928110\pi$
$593$	−7.73791	−	23.8149i	−0.317758	−	0.977959i	0.656846	−	0.754025i	$-0.271890\pi$
$594$	2.72270	+	11.9289i	0.111714	+	0.489450i
$595$	0.128978	+	0.239682i	0.00528760	+	0.00982600i
$596$	−33.9135	−	6.15440i	−1.38915	−	0.252094i
$597$	10.0164	−	2.76434i	0.409942	−	0.113137i
$598$	8.20169	−	35.9340i	0.335392	−	1.46945i
$599$	17.9668	−	1.61704i	0.734105	−	0.0660706i	0.283723	−	0.958906i	$-0.408431\pi$
$599$	17.9668	−	1.61704i	0.734105	−	0.0660706i	0.450382	+	0.892836i	$0.351288\pi$
$600$	−2.62369	−	3.29000i	−0.107112	−	0.134314i
$601$	33.7013	−	6.11588i	1.37470	−	0.249472i	0.559588	−	0.828771i	$-0.310959\pi$
$601$	33.7013	−	6.11588i	1.37470	−	0.249472i	0.815115	+	0.579299i	$0.196674\pi$
$602$	−2.65061	+	1.27646i	−0.108031	+	0.0520248i
$603$	−5.55756	+	5.81275i	−0.226321	+	0.236714i
$604$	1.71857	−	1.79748i	0.0699275	−	0.0731384i
$605$	6.06332	−	2.91994i	0.246509	−	0.118712i
$606$	16.2443	−	2.94790i	0.659879	−	0.119750i
$607$	19.8626	+	24.9069i	0.806199	+	1.01094i	0.999555	+	0.0298129i	$0.00949115\pi$
$607$	19.8626	+	24.9069i	0.806199	+	1.01094i	−0.193357	+	0.981129i	$0.561937\pi$
$608$	−51.7612	+	4.65859i	−2.09919	+	0.188931i
$609$	0.0374464	−	0.164063i	0.00151740	−	0.00664818i
$610$	−14.2711	+	3.93858i	−0.577821	+	0.159468i
$611$	−22.5664	−	4.09520i	−0.912940	−	0.165674i
$612$	4.36215	+	8.10623i	0.176329	+	0.327675i
$613$	−2.61576	−	11.4604i	−0.105649	−	0.462880i	−0.999883	−	0.0152802i	$-0.995136\pi$
$613$	−2.61576	−	11.4604i	−0.105649	−	0.462880i	0.894234	−	0.447600i	$-0.147721\pi$
$614$	1.96875	+	6.05920i	0.0794524	+	0.244529i
$615$	4.08750	−	1.53407i	0.164824	−	0.0618595i
$616$	−0.278767	−	0.134247i	−0.0112318	−	0.00540896i
$617$	7.54428	+	2.08209i	0.303721	+	0.0838217i	0.414575	−	0.910015i	$-0.363930\pi$
$617$	7.54428	+	2.08209i	0.303721	+	0.0838217i	−0.110854	+	0.993837i	$0.535359\pi$
$618$	17.2778	−	32.1075i	0.695014	−	1.29155i
$619$	−16.3071	+	20.4485i	−0.655439	+	0.821895i	−0.992838	−	0.119467i	$-0.961881\pi$
$619$	−16.3071	+	20.4485i	−0.655439	+	0.821895i	0.337399	+	0.941362i	$0.390453\pi$
$620$	−7.58850	+	11.4961i	−0.304762	+	0.461694i
$621$	1.33513	+	29.7289i	0.0535767	+	1.19298i
$622$	10.0686	−	30.9881i	0.403716	−	1.24251i
$623$	2.59132	+	0.233223i	0.103819	+	0.00934388i
$624$	3.55548	+	5.38633i	0.142333	+	0.215626i
$625$	−14.2467	+	10.3509i	−0.569869	+	0.414034i
$626$	25.1481	+	15.0253i	1.00512	+	0.600531i
$627$	2.83292	−	6.62795i	0.113136	−	0.264695i
$628$	18.4571	−	11.0276i	0.736518	−	0.440049i
$629$	−1.75086	−	12.9254i	−0.0698114	−	0.515369i
$630$	−0.587334	−	0.513138i	−0.0233999	−	0.0204439i
$631$	−26.1412	+	22.8389i	−1.04066	+	0.909202i	−0.995960	−	0.0897987i	$-0.971378\pi$
$631$	−26.1412	+	22.8389i	−1.04066	+	0.909202i	−0.0447050	+	0.999000i	$0.514235\pi$
$632$	0.810718	−	5.98496i	0.0322486	−	0.238069i
$633$	−2.13396	−	4.99265i	−0.0848174	−	0.198440i
$634$	−58.8252	−	42.7390i	−2.33625	−	1.69738i
$635$	−0.324067	+	7.21590i	−0.0128602	+	0.286354i
$636$	−3.97282	−	1.49103i	−0.157533	−	0.0591230i
$637$	−12.8676	−	13.4585i	−0.509833	−	0.533244i
$638$	2.21055			0.0875164
$639$	−5.78708	+	17.8643i	−0.228933	+	0.706700i
$640$	5.90365			0.233362
$641$	−1.38188	−	1.44533i	−0.0545809	−	0.0570872i	0.694941	−	0.719067i	$-0.255431\pi$
$641$	−1.38188	−	1.44533i	−0.0545809	−	0.0570872i	−0.749522	+	0.661980i	$0.769716\pi$
$642$	14.8102	+	5.55836i	0.584512	+	0.219371i
$643$	−1.05883	+	23.5768i	−0.0417563	+	0.929777i	0.863354	+	0.504599i	$0.168360\pi$
$643$	−1.05883	+	23.5768i	−0.0417563	+	0.929777i	−0.905110	+	0.425178i	$0.860212\pi$
$644$	−3.03017	−	2.20155i	−0.119405	−	0.0867531i
$645$	1.48000	+	3.46264i	0.0582750	+	0.136341i
$646$	3.07254	−	22.6824i	0.120887	−	0.892426i
$647$	33.1172	−	28.9337i	1.30197	−	1.13750i	0.320219	−	0.947344i	$-0.396243\pi$
$647$	33.1172	−	28.9337i	1.30197	−	1.13750i	0.981754	−	0.190156i	$-0.0608994\pi$
$648$	−2.13125	−	1.86202i	−0.0837235	−	0.0731470i
$649$	0.536574	+	3.96115i	0.0210624	+	0.155489i
$650$	−21.9234	+	13.0986i	−0.859906	+	0.513770i
$651$	−0.614351	+	1.43735i	−0.0240783	+	0.0563340i
$652$	1.08021	+	0.645393i	0.0423041	+	0.0252755i
$653$	37.4355	−	27.1985i	1.46496	−	1.06436i	0.482928	−	0.875660i	$-0.339573\pi$
$653$	37.4355	−	27.1985i	1.46496	−	1.06436i	0.982035	−	0.188698i	$-0.0604268\pi$
$654$	16.7182	+	25.3269i	0.653732	+	0.990361i
$655$	7.95060	+	0.715567i	0.310656	+	0.0279595i
$656$	5.89647	−	18.1475i	0.230218	−	0.708539i
$657$	−0.657797	−	14.6470i	−0.0256631	−	0.571434i
$658$	−2.30992	+	3.49939i	−0.0900502	+	0.136420i
$659$	12.6644	−	15.8807i	0.493336	−	0.618624i	−0.471376	−	0.881932i	$-0.656242\pi$
$659$	12.6644	−	15.8807i	0.493336	−	0.618624i	0.964712	+	0.263309i	$0.0848138\pi$
$660$	−0.934086	+	1.73582i	−0.0363592	+	0.0675668i
$661$	26.7315	+	7.37743i	1.03974	+	0.286949i	0.743901	−	0.668290i	$-0.232974\pi$
$661$	26.7315	+	7.37743i	1.03974	+	0.286949i	0.295835	+	0.955239i	$0.404402\pi$
$662$	−38.7929	−	18.6817i	−1.50773	−	0.726083i
$663$	−3.63762	+	1.36522i	−0.141274	+	0.0530209i
$664$	1.49981	+	4.61594i	0.0582039	+	0.179133i
$665$	0.239862	+	1.05091i	0.00930146	+	0.0407524i
$666$	17.7109	+	32.9123i	0.686282	+	1.27533i
$667$	5.28994	+	0.959982i	0.204827	+	0.0371707i
$668$	5.29840	−	1.46226i	0.205001	−	0.0565767i
$669$	0.893974	−	3.91675i	0.0345630	−	0.151430i
$670$	−5.44658	+	0.490201i	−0.210420	+	0.0189381i
$671$	−7.64797	−	9.59025i	−0.295246	−	0.370227i
$672$	1.58688	−	0.287977i	0.0612153	−	0.0111089i
$673$	−30.8060	+	14.8354i	−1.18748	+	0.571861i	−0.920083	−	0.391724i	$-0.871879\pi$
$673$	−30.8060	+	14.8354i	−1.18748	+	0.571861i	−0.267400	+	0.963586i	$0.586164\pi$
$674$	−35.9515	+	37.6023i	−1.38480	+	1.44839i
$675$	14.2493	−	14.9036i	0.548457	−	0.573641i
$676$	13.1135	−	6.31513i	0.504366	−	0.242890i
$677$	20.0114	−	3.63154i	0.769102	−	0.139572i	0.220196	−	0.975456i	$-0.429330\pi$
$677$	20.0114	−	3.63154i	0.769102	−	0.139572i	0.548906	+	0.835884i	$0.315044\pi$
$678$	−10.4546	−	13.1096i	−0.401505	−	0.503471i
$679$	2.43994	−	0.219598i	0.0936362	−	0.00842741i
$680$	−0.279853	+	1.22612i	−0.0107319	+	0.0470195i
$681$	−7.75696	+	2.14079i	−0.297248	+	0.0820351i
$682$	−20.2032	−	3.66634i	−0.773621	−	0.140392i
$683$	−16.4872	−	30.6383i	−0.630863	−	1.17234i	−0.972587	−	0.232540i	$-0.925296\pi$
$683$	−16.4872	−	30.6383i	−0.630863	−	1.17234i	0.341724	−	0.939801i	$-0.388989\pi$
$684$	8.11233	+	35.5424i	0.310183	+	1.35900i
$685$	−4.63423	−	14.2627i	−0.177065	−	0.544949i
$686$	−6.39864	+	2.40145i	−0.244301	+	0.0916878i
$687$	0.174675	+	0.0841191i	0.00666427	+	0.00320934i
$688$	15.8650	+	4.37845i	0.604846	+	0.166927i
$689$	−2.45184	+	4.55628i	−0.0934076	+	0.173580i
$690$	−5.37771	+	6.74343i	−0.204726	+	0.256718i
$691$	10.5948	−	16.0504i	0.403045	−	0.610587i	−0.575207	−	0.818008i	$-0.695079\pi$
$691$	10.5948	−	16.0504i	0.403045	−	0.610587i	0.978252	+	0.207421i	$0.0665071\pi$
$692$	−1.46994	−	32.7307i	−0.0558787	−	1.24424i
$693$	0.199687	−	0.614574i	0.00758549	−	0.0233457i
$694$	−1.40020	−	0.126021i	−0.0531510	−	0.00478367i
$695$	5.14059	+	7.78766i	0.194994	+	0.295403i
$696$	0.629068	−	0.457044i	0.0238448	−	0.0173242i
$697$	9.86117	+	5.89178i	0.373519	+	0.223167i
$698$	−15.7725	+	36.9016i	−0.596998	+	1.39675i
$699$	6.36299	−	3.80171i	0.240671	−	0.143794i
$700$	0.348361	+	2.57171i	0.0131668	+	0.0972013i
$701$	−3.61420	−	3.15763i	−0.136506	−	0.119262i	0.586978	−	0.809603i	$-0.300318\pi$
$701$	−3.61420	−	3.15763i	−0.136506	−	0.119262i	−0.723484	+	0.690341i	$0.757461\pi$
$702$	19.6705	−	17.1856i	0.742416	−	0.648629i
$703$	6.93401	−	51.1889i	0.261521	−	1.93063i
$704$	5.62078	+	13.1505i	0.211841	+	0.495627i
$705$	4.34202	+	3.15466i	0.163530	+	0.118811i
$706$	−1.92815	+	42.9337i	−0.0725670	+	1.61583i
$707$	−1.91521	−	0.718791i	−0.0720289	−	0.0270329i
$708$	4.83635	+	5.05843i	0.181761	+	0.190107i
$709$	4.23128			0.158909			0.0794545	−	0.996838i	$-0.474682\pi$
$709$	4.23128			0.158909			0.0794545	+	0.996838i	$0.474682\pi$
$710$	−10.9559	+	6.55896i	−0.411169	+	0.246153i
$711$	12.6138			0.473055
$712$	8.30789	+	8.68937i	0.311351	+	0.325648i
$713$	−46.7550	−	17.5475i	−1.75099	−	0.657158i
$714$	−0.0318689	+	0.709617i	−0.00119266	+	0.0265567i
$715$	1.94449	+	1.41275i	0.0727198	+	0.0528340i
$716$	15.9491	+	37.3147i	0.596045	+	1.39452i
$717$	−3.16842	+	23.3902i	−0.118327	+	0.873524i
$718$	−18.1615	+	15.8673i	−0.677782	+	0.592161i
$719$	2.33260	+	2.03793i	0.0869914	+	0.0760021i	0.700336	−	0.713813i	$-0.253033\pi$
$719$	2.33260	+	2.03793i	0.0869914	+	0.0760021i	−0.613345	+	0.789815i	$0.710176\pi$
$720$	0.585669	+	4.32358i	0.0218266	+	0.161130i
$721$	−3.87829	+	2.31717i	−0.144435	+	0.0862959i
$722$	19.7819	−	46.2820i	0.736205	−	1.72244i
$723$	−21.1505	−	12.6368i	−0.786596	−	0.469969i
$724$	−5.07544	+	3.68752i	−0.188627	+	0.137046i
$725$	−2.05219	−	3.10893i	−0.0762164	−	0.115463i
$726$	17.4925	+	1.57435i	0.649206	+	0.0584296i
$727$	−8.75848	+	26.9558i	−0.324834	+	0.999736i	0.646681	+	0.762760i	$0.276156\pi$
$727$	−8.75848	+	26.9558i	−0.324834	+	0.999736i	−0.971515	+	0.236976i	$0.923844\pi$
$728$	0.0296338	+	0.659848i	0.00109830	+	0.0244556i
$729$	−3.40994	+	5.16584i	−0.126294	+	0.191327i
$730$	6.21618	−	7.79485i	0.230071	−	0.288500i
$731$	−4.69506	+	8.72488i	−0.173653	+	0.322701i
$732$	−20.7018	−	5.71334i	−0.765161	−	0.211171i
$733$	20.4047	+	9.82640i	0.753666	+	0.362946i	0.770943	−	0.636904i	$-0.219785\pi$
$733$	20.4047	+	9.82640i	0.753666	+	0.362946i	−0.0172769	+	0.999851i	$0.505500\pi$
$734$	−18.2680	+	6.85611i	−0.674285	+	0.253064i
$735$	1.34647	+	4.14402i	0.0496655	+	0.152855i
$736$	11.4657	+	50.2343i	0.422630	+	1.85166i
$737$	−2.14710	−	3.98998i	−0.0790895	−	0.146973i
$738$	−32.3868	−	5.87734i	−1.19217	−	0.216348i
$739$	6.09652	−	1.68253i	0.224264	−	0.0618930i	−0.152099	−	0.988365i	$-0.548603\pi$
$739$	6.09652	−	1.68253i	0.224264	−	0.0618930i	0.376363	+	0.926472i	$0.377175\pi$
$740$	−3.14347	+	13.7724i	−0.115556	+	0.506285i
$741$	−15.3255	+	1.37932i	−0.562995	+	0.0506704i
$742$	0.589782	+	0.739563i	0.0216516	+	0.0271502i
$743$	−16.2154	+	2.94267i	−0.594887	+	0.107956i	−0.467646	−	0.883916i	$-0.654898\pi$
$743$	−16.2154	+	2.94267i	−0.594887	+	0.107956i	−0.127241	+	0.991872i	$0.540612\pi$
$744$	−6.50739	+	3.13379i	−0.238572	+	0.114890i
$745$	6.79643	−	7.10851i	0.249002	−	0.260436i
$746$	−1.85619	+	1.94142i	−0.0679599	+	0.0710805i
$747$	−9.13272	+	4.39809i	−0.334149	+	0.160918i
$748$	−5.10310	+	0.926075i	−0.186588	+	0.0338607i
$749$	−1.22208	−	1.53244i	−0.0446540	−	0.0559943i
$750$	12.5805	−	1.13226i	0.459374	−	0.0413444i
$751$	1.11606	−	4.88979i	0.0407257	−	0.178431i	−0.950474	−	0.310803i	$-0.899402\pi$
$751$	1.11606	−	4.88979i	0.0407257	−	0.178431i	0.991200	+	0.132372i	$0.0422593\pi$
$752$	22.6116	−	6.24040i	0.824559	−	0.227564i
$753$	−20.0405	−	3.63681i	−0.730315	−	0.132533i
$754$	−2.23619	−	4.15553i	−0.0814371	−	0.151336i
$755$	0.157897	+	0.691793i	0.00574647	+	0.0251769i
$756$	−0.820235	−	2.52442i	−0.0298317	−	0.0918124i
$757$	34.9023	−	13.0991i	1.26855	−	0.476093i	0.375820	−	0.926693i	$-0.377361\pi$
$757$	34.9023	−	13.0991i	1.26855	−	0.476093i	0.892726	+	0.450599i	$0.148790\pi$
$758$	11.5587	+	5.56638i	0.419831	+	0.202180i
$759$	−6.88886	−	1.90120i	−0.250050	−	0.0690093i
$760$	−2.36021	+	4.38600i	−0.0856137	+	0.159097i
$761$	−16.4537	+	20.6322i	−0.596445	+	0.747918i	−0.984819	−	0.173584i	$-0.944465\pi$
$761$	−16.4537	+	20.6322i	−0.596445	+	0.747918i	0.388375	+	0.921502i	$0.373037\pi$
$762$	−10.3849	+	15.7324i	−0.376204	+	0.569925i
$763$	−0.168702	−	3.75644i	−0.00610741	−	0.135992i
$764$	7.70495	−	23.7134i	0.278755	−	0.857921i
$765$	−2.61604	−	0.235448i	−0.0945832	−	0.00851264i
$766$	−11.0772	−	16.7813i	−0.400236	−	0.606331i
$767$	6.90363	−	5.01578i	0.249276	−	0.181109i
$768$	−3.94949	−	2.35971i	−0.142515	−	0.0851486i
$769$	7.26785	−	17.0040i	0.262085	−	0.613179i	−0.735868	−	0.677125i	$-0.763226\pi$
$769$	7.26785	−	17.0040i	0.262085	−	0.613179i	0.997953	+	0.0639458i	$0.0203685\pi$
$770$	0.377217	−	0.225376i	0.0135939	−	0.00812200i
$771$	0.0505334	+	0.373052i	0.00181992	+	0.0134352i
$772$	50.1387	+	43.8049i	1.80453	+	1.57657i
$773$	19.7657	−	17.2688i	0.710923	−	0.621115i	−0.224571	−	0.974458i	$-0.572098\pi$
$773$	19.7657	−	17.2688i	0.710923	−	0.621115i	0.935494	+	0.353343i	$0.114955\pi$
$774$	3.81095	−	28.1336i	0.136982	−	1.01124i
$775$	13.5995	+	31.8177i	0.488510	+	1.14293i
$776$	9.15775	+	6.65350i	0.328744	+	0.238847i
$777$	−0.0719208	+	1.60144i	−0.00258015	+	0.0574514i
$778$	64.6042	+	24.2464i	2.31617	+	0.869275i
$779$	31.4387	+	32.8823i	1.12641	+	1.17813i
$780$	4.20803			0.150672
$781$	−8.56481	−	6.21119i	−0.306473	−	0.222254i
$782$	−22.6939			−0.811532
$783$	2.63300	+	2.75390i	0.0940958	+	0.0984165i
$784$	17.8294	+	6.69149i	0.636765	+	0.238982i
$785$	−0.275239	+	6.12866i	−0.00982368	+	0.218741i
$786$	16.8543	+	12.2454i	0.601175	+	0.436779i
$787$	−14.4213	−	33.7402i	−0.514062	−	1.20271i	−0.952664	−	0.304026i	$-0.901669\pi$
$787$	−14.4213	−	33.7402i	−0.514062	−	1.20271i	0.438601	−	0.898682i	$-0.355474\pi$
$788$	0.978978	−	7.22710i	0.0348746	−	0.257455i
$789$	16.7556	−	14.6389i	0.596515	−	0.521160i
$790$	6.45939	+	5.64340i	0.229815	+	0.200783i
$791$	0.278889	+	2.05884i	0.00991617	+	0.0732041i
$792$	2.56320	−	1.53144i	0.0910794	−	0.0544174i
$793$	−10.2917	+	24.0786i	−0.365469	+	0.855058i
$794$	−46.7470	−	27.9300i	−1.65899	−	0.991199i
$795$	0.979550	−	0.711684i	0.0347410	−	0.0252408i
$796$	−16.3120	−	24.7116i	−0.578164	−	0.875881i
$797$	1.46890	+	0.132203i	0.0520311	+	0.00468289i	0.115624	−	0.993293i	$-0.463113\pi$
$797$	1.46890	+	0.132203i	0.0520311	+	0.00468289i	−0.0635932	+	0.997976i	$0.520256\pi$
$798$	−0.869313	+	2.67547i	−0.0307733	+	0.0947106i
$799$	0.633550	+	14.1071i	0.0224134	+	0.499073i
$800$	19.6679	−	29.7957i	0.695367	−	1.05344i
$801$	−15.6545	+	19.6301i	−0.553125	+	0.693597i
$802$	29.1870	−	54.2385i	1.03063	−	1.91523i
$803$	7.96295	+	2.19763i	0.281006	+	0.0775528i
$804$	−7.14720	−	3.44191i	−0.252062	−	0.121387i
$805$	1.00057	−	0.375521i	0.0352655	−	0.0132354i
$806$	13.5453	+	41.6882i	0.477114	+	1.46841i
$807$	−1.72013	−	7.53639i	−0.0605515	−	0.265294i
$808$	−4.47910	−	8.32356i	−0.157574	−	0.292822i
$809$	−11.1013	−	2.01459i	−0.390301	−	0.0708292i	−0.0201408	−	0.999797i	$-0.506411\pi$
$809$	−11.1013	−	2.01459i	−0.390301	−	0.0708292i	−0.370160	+	0.928968i	$0.620697\pi$
$810$	3.87440	−	1.06927i	0.136133	−	0.0375702i
$811$	−6.19564	+	27.1449i	−0.217558	+	0.953186i	0.741717	+	0.670713i	$0.234012\pi$
$811$	−6.19564	+	27.1449i	−0.217558	+	0.953186i	−0.959275	+	0.282473i	$0.908845\pi$
$812$	−0.477611	+	0.0429858i	−0.0167609	+	0.00150851i
$813$	4.06802	+	5.10114i	0.142672	+	0.178905i
$814$	−20.7192	+	3.75998i	−0.726208	+	0.131787i
$815$	−0.323486	+	0.155783i	−0.0113312	+	0.00545683i
$816$	2.74613	−	2.87223i	0.0961339	−	0.100548i
$817$	−27.1164	+	28.3616i	−0.948684	+	0.992246i
$818$	34.4991	−	16.6139i	1.20623	−	0.580890i
$819$	−1.35732	+	0.246317i	−0.0474286	+	0.00860702i
$820$	−7.75693	−	9.72688i	−0.270884	−	0.339677i
$821$	37.3084	−	3.35782i	1.30207	−	0.117189i	0.583198	−	0.812330i	$-0.301801\pi$
$821$	37.3084	−	3.35782i	1.30207	−	0.117189i	0.718873	+	0.695141i	$0.244658\pi$
$822$	8.70900	−	38.1566i	0.303761	−	1.33087i
$823$	−19.7146	+	5.44088i	−0.687207	+	0.189657i	−0.592166	−	0.805816i	$-0.701727\pi$
$823$	−19.7146	+	5.44088i	−0.687207	+	0.189657i	−0.0950415	+	0.995473i	$0.530298\pi$
$824$	−20.5395	−	3.72737i	−0.715528	−	0.129849i
$825$	2.34642	+	4.36037i	0.0816918	+	0.151809i
$826$	−0.347152	−	1.52097i	−0.0120789	−	0.0529213i
$827$	−2.90406	−	8.93777i	−0.100984	−	0.310797i	0.887783	−	0.460262i	$-0.152245\pi$
$827$	−2.90406	−	8.93777i	−0.100984	−	0.310797i	−0.988767	+	0.149466i	$0.952245\pi$
$828$	33.8401	−	12.7004i	1.17602	−	0.441369i
$829$	9.31678	+	4.48673i	0.323585	+	0.155830i	0.588623	−	0.808408i	$-0.299670\pi$
$829$	9.31678	+	4.48673i	0.323585	+	0.155830i	−0.265038	+	0.964238i	$0.585384\pi$
$830$	−6.64445	−	1.83375i	−0.230632	−	0.0636505i
$831$	−7.26826	+	13.5067i	−0.252133	+	0.468542i
$832$	19.0351	−	23.8693i	0.659925	−	0.827519i
$833$	−6.31578	+	9.56800i	−0.218829	+	0.331512i
$834$	1.09257	+	24.3280i	0.0378327	+	0.842411i
$835$	−0.484642	+	1.49157i	−0.0167717	+	0.0516180i
$836$	−20.4574	−	1.84120i	−0.707534	−	0.0636792i
$837$	−19.4967	−	29.5362i	−0.673904	−	1.02092i
$838$	21.1558	−	15.3706i	0.730815	−	0.530968i
$839$	−18.1110	−	10.8208i	−0.625262	−	0.373577i	0.165046	−	0.986286i	$-0.447223\pi$
$839$	−18.1110	−	10.8208i	−0.625262	−	0.373577i	−0.790309	+	0.612709i	$0.790080\pi$
$840$	0.0607487	−	0.142129i	0.00209603	−	0.00490390i
$841$	−24.3041	+	14.5210i	−0.838073	+	0.500725i
$842$	−3.19499	−	23.5863i	−0.110107	−	0.812839i
$843$	8.42443	+	7.36020i	0.290153	+	0.253499i
$844$	−11.6517	+	10.1798i	−0.401069	+	0.350403i
$845$	−0.557473	+	4.11543i	−0.0191776	+	0.141575i
$846$	−15.9032	−	37.2074i	−0.546764	−	1.27922i
$847$	−1.76058	−	1.27914i	−0.0604943	−	0.0439517i
$848$	0.237417	−	5.28649i	0.00815292	−	0.181539i
$849$	3.44873	+	1.29433i	0.118360	+	0.0444213i
$850$	10.8664	+	11.3654i	0.372715	+	0.389830i
$851$	−51.2149			−1.75562
$852$	−18.5231	+	0.0163040i	−0.634591	+	0.000558565i
$853$	−18.7837			−0.643141			−0.321570	−	0.946886i	$-0.604211\pi$
$853$	−18.7837			−0.643141			−0.321570	+	0.946886i	$0.604211\pi$
$854$	3.30836	+	3.46028i	0.113210	+	0.118408i
$855$	−9.73898	−	3.65510i	−0.333066	−	0.125002i
$856$	0.406330	−	9.04763i	0.0138881	−	0.309242i
$857$	18.7882	+	13.6504i	0.641794	+	0.466290i	0.860466	−	0.509508i	$-0.170173\pi$
$857$	18.7882	+	13.6504i	0.641794	+	0.466290i	−0.218672	+	0.975798i	$0.570173\pi$
$858$	2.46530	+	5.76787i	0.0841641	+	0.196912i
$859$	0.984377	−	7.26697i	0.0335865	−	0.247946i	−0.966371	−	0.257151i	$-0.917216\pi$
$859$	0.984377	−	7.26697i	0.0335865	−	0.247946i	0.999958	+	0.00920583i	$0.00293035\pi$
$860$	8.08101	−	7.06017i	0.275560	−	0.240750i
$861$	−1.06318	−	0.928874i	−0.0362331	−	0.0316559i
$862$	−0.202926	−	1.49806i	−0.00691167	−	0.0510240i
$863$	5.35853	−	3.20157i	0.182406	−	0.108983i	−0.418793	−	0.908082i	$-0.637547\pi$
$863$	5.35853	−	3.20157i	0.182406	−	0.108983i	0.601200	+	0.799099i	$0.294690\pi$
$864$	−14.3514	+	33.5768i	−0.488245	+	1.14231i
$865$	8.02531	+	4.79490i	0.272869	+	0.163031i
$866$	45.0484	−	32.7296i	1.53081	−	1.11220i
$867$	−6.90772	−	10.4647i	−0.234598	−	0.355401i
$868$	4.43641	+	0.399284i	0.150582	+	0.0135526i
$869$	−2.19612	+	6.75897i	−0.0744983	+	0.229282i
$870$	0.0495440	+	1.10318i	0.00167970	+	0.0374014i
$871$	−5.32863	+	8.07253i	−0.180554	+	0.273527i
$872$	10.8329	−	13.5840i	0.366847	−	0.460012i
$873$	−11.2028	+	20.8183i	−0.379157	+	0.704592i
$874$	−86.6366	−	23.9102i	−2.93053	−	0.808774i
$875$	−1.41011	−	0.679075i	−0.0476705	−	0.0229569i
$876$	13.5403	−	5.08178i	0.457486	−	0.171697i
$877$	−6.41161	−	19.7329i	−0.216505	−	0.666333i	−0.999043	−	0.0437311i	$-0.986076\pi$
$877$	−6.41161	−	19.7329i	−0.216505	−	0.666333i	0.782539	−	0.622602i	$-0.213924\pi$
$878$	−3.42110	−	14.9888i	−0.115457	−	0.505848i
$879$	−7.08641	−	13.1688i	−0.239019	−	0.444171i
$880$	−2.41871	−	0.438931i	−0.0815346	−	0.0147964i
$881$	1.37834	−	0.380396i	0.0464373	−	0.0128159i	−0.242741	−	0.970091i	$-0.578047\pi$
$881$	1.37834	−	0.380396i	0.0464373	−	0.0128159i	0.289178	+	0.957275i	$0.406618\pi$
$882$	7.31000	−	32.0272i	0.246141	−	1.07841i
$883$	−35.4711	+	3.19246i	−1.19370	+	0.107435i	−0.668611	−	0.743613i	$-0.733111\pi$
$883$	−35.4711	+	3.19246i	−1.19370	+	0.107435i	−0.525089	+	0.851048i	$0.675968\pi$
$884$	6.90319	+	8.65632i	0.232179	+	0.291144i
$885$	−1.96480	+	0.356559i	−0.0660461	+	0.0119856i
$886$	−68.6578	+	33.0638i	−2.30660	+	1.11080i
$887$	−6.43003	+	6.72529i	−0.215899	+	0.225813i	−0.821872	−	0.569673i	$-0.807070\pi$
$887$	−6.43003	+	6.72529i	−0.215899	+	0.225813i	0.605972	+	0.795486i	$0.292784\pi$
$888$	−5.11878	+	5.35383i	−0.171775	+	0.179663i
$889$	2.10444	−	1.01344i	0.0705806	−	0.0339898i
$890$	−16.7990	+	3.04856i	−0.563103	+	0.102188i
$891$	2.07631	+	2.60361i	0.0695591	+	0.0872243i
$892$	−11.4022	+	1.02622i	−0.381775	+	0.0343603i
$893$	−12.4445	+	54.5230i	−0.416440	+	1.82454i
$894$	24.7415	−	6.82822i	0.827480	−	0.228370i
$895$	−11.3929	−	2.06750i	−0.380822	−	0.0691090i
$896$	−0.904641	−	1.68111i	−0.0302219	−	0.0561618i
$897$	3.39475	+	14.8734i	0.113348	+	0.496608i
$898$	−15.0116	−	46.2010i	−0.500944	−	1.54175i
$899$	−5.98613	+	2.24663i	−0.199649	+	0.0749293i
$900$	−22.5640	−	10.8663i	−0.752135	−	0.362209i
$901$	3.07093	+	0.847523i	0.102308	+	0.0282351i
$902$	8.78799	−	16.3308i	0.292608	−	0.543757i
$903$	0.759223	−	0.952036i	0.0252654	−	0.0316818i
$904$	−5.28863	+	8.01193i	−0.175897	+	0.266473i
$905$	−0.0803112	−	1.78827i	−0.00266963	−	0.0594440i
$906$	−0.572253	+	1.76121i	−0.0190118	+	0.0585124i
$907$	19.8811	+	1.78933i	0.660141	+	0.0594137i	0.414644	−	0.909984i	$-0.363906\pi$
$907$	19.8811	+	1.78933i	0.660141	+	0.0594137i	0.245497	+	0.969397i	$0.421049\pi$
$908$	12.6325	+	19.1374i	0.419224	+	0.635097i
$909$	15.9708	−	11.6035i	0.529719	−	0.384863i
$910$	−0.805269	−	0.481126i	−0.0266944	−	0.0159492i
$911$	6.14298	−	14.3722i	0.203526	−	0.476173i	−0.786407	−	0.617709i	$-0.788061\pi$
$911$	6.14298	−	14.3722i	0.203526	−	0.476173i	0.989933	+	0.141536i	$0.0452040\pi$
$912$	13.5099	−	8.07177i	0.447356	−	0.267283i
$913$	−0.766616	−	5.65939i	−0.0253713	−	0.187298i
$914$	−10.4938	−	9.16813i	−0.347103	−	0.303255i
$915$	4.61465	−	4.03170i	0.152556	−	0.133284i
$916$	0.0741598	−	0.547470i	0.00245031	−	0.0180889i
$917$	−1.01454	−	2.37364i	−0.0335031	−	0.0783845i
$918$	−13.0111	−	9.45310i	−0.429430	−	0.311999i
$919$	0.752255	−	16.7503i	0.0248146	−	0.552540i	−0.947625	−	0.319385i	$-0.896524\pi$
$919$	0.752255	−	16.7503i	0.0248146	−	0.552540i	0.972440	−	0.233155i	$-0.0749049\pi$
$920$	4.62326	+	1.73514i	0.152425	+	0.0572059i
$921$	−1.82235	−	1.90602i	−0.0600484	−	0.0628057i
$922$	75.7445			2.49451
$923$	−3.01205	+	22.3839i	−0.0991428	+	0.736776i
$924$	0.637421			0.0209696
$925$	24.5230	+	25.6491i	0.806312	+	0.843337i
$926$	7.68088	+	2.88268i	0.252409	+	0.0947308i
$927$	1.95600	−	43.5538i	0.0642435	−	1.43049i
$928$	5.33707	+	3.87761i	0.175198	+	0.127289i
$929$	4.25867	+	9.96366i	0.139722	+	0.326897i	0.974746	−	0.223318i	$-0.0716887\pi$
$929$	4.25867	+	9.96366i	0.139722	+	0.326897i	−0.835023	+	0.550215i	$0.814546\pi$
$930$	1.37690	−	10.1647i	0.0451503	−	0.333313i
$931$	−34.1921	+	29.8727i	−1.12060	+	0.979038i
$932$	−15.9064	−	13.8970i	−0.521030	−	0.455210i
$933$	1.81031	+	13.3643i	0.0592670	+	0.437526i
$934$	58.8014	−	35.1322i	1.92404	−	1.14956i
$935$	0.581627	−	1.36078i	0.0190212	−	0.0445024i
$936$	−5.47184	−	3.26927i	−0.178853	−	0.106859i
$937$	−17.7915	+	12.9263i	−0.581222	+	0.422283i	−0.839164	−	0.543878i	$-0.816956\pi$
$937$	−17.7915	+	12.9263i	−0.581222	+	0.422283i	0.257942	+	0.966160i	$0.416956\pi$
$938$	0.974190	+	1.47584i	0.0318084	+	0.0481877i
$939$	−12.0766	−	1.08691i	−0.394104	−	0.0354700i
$940$	4.72611	−	14.5455i	0.154149	−	0.474421i
$941$	0.263736	+	5.87253i	0.00859753	+	0.191439i	0.998696	+	0.0510611i	$0.0162603\pi$
$941$	0.263736	+	5.87253i	0.00859753	+	0.191439i	−0.990098	+	0.140378i	$0.955168\pi$
$942$	−8.82015	+	13.3620i	−0.287376	+	0.435356i
$943$	28.1221	−	35.2640i	0.915782	−	1.14835i
$944$	−4.13570	+	7.68542i	−0.134606	+	0.250139i
$945$	0.730080	+	0.201489i	0.0237495	+	0.00655445i
$946$	14.4115	+	6.94023i	0.468559	+	0.225646i
$947$	28.1796	−	10.5760i	0.915715	−	0.343674i	0.151367	−	0.988478i	$-0.451632\pi$
$947$	28.1796	−	10.5760i	0.915715	−	0.343674i	0.764348	+	0.644804i	$0.223061\pi$
$948$	3.84493	+	11.8335i	0.124877	+	0.384333i
$949$	−3.92405	−	17.1924i	−0.127380	−	0.558089i
$950$	29.5094	+	54.8376i	0.957410	+	1.77917i
$951$	29.6124	+	5.37386i	0.960249	+	0.174259i
$952$	0.392029	−	0.108193i	0.0127057	−	0.00350656i
$953$	−0.645228	+	2.82693i	−0.0209010	+	0.0915732i	−0.984303	−	0.176489i	$-0.943526\pi$
$953$	−0.645228	+	2.82693i	−0.0209010	+	0.0915732i	0.963402	+	0.268062i	$0.0863832\pi$
$954$	−9.09176	+	0.818273i	−0.294356	+	0.0264926i
$955$	4.43579	+	5.56231i	0.143539	+	0.179992i
$956$	66.1811	−	12.0101i	2.14045	−	0.388434i
$957$	−0.824354	+	0.396988i	−0.0266476	+	0.0128328i
$958$	−52.0900	+	54.4818i	−1.68295	+	1.76023i
$959$	−3.35128	+	3.50516i	−0.108218	+	0.113188i
$960$	−6.43682	+	3.09981i	−0.207748	+	0.100046i
$961$	27.9344	−	5.06935i	0.901110	−	0.163527i
$962$	28.0278	+	35.1458i	0.903653	+	1.13314i
$963$	18.8390	−	1.69554i	0.607078	−	0.0546380i
$964$	−15.6230	+	68.4489i	−0.503183	+	2.20459i
$965$	−18.3127	+	5.05398i	−0.589506	+	0.162693i
$966$	2.74429	+	0.498015i	0.0882960	+	0.0160234i
$967$	10.0156	+	18.6121i	0.322081	+	0.598526i	0.989225	−	0.146402i	$-0.0467693\pi$
$967$	10.0156	+	18.6121i	0.322081	+	0.598526i	−0.667144	+	0.744928i	$0.732484\pi$
$968$	−2.23754	−	9.80328i	−0.0719171	−	0.315089i
$969$	2.92768	+	9.01047i	0.0940507	+	0.289458i
$970$	−15.0509	+	5.64869i	−0.483254	+	0.181368i
$971$	−27.2836	−	13.1391i	−0.875571	−	0.421653i	−0.0585661	−	0.998284i	$-0.518653\pi$
$971$	−27.2836	−	13.1391i	−0.875571	−	0.421653i	−0.817005	+	0.576631i	$0.804367\pi$
$972$	38.8593	+	10.7245i	1.24641	+	0.343988i
$973$	1.42988	−	2.65715i	0.0458397	−	0.0851844i
$974$	−0.152225	+	0.190885i	−0.00487761	+	0.00611634i
$975$	5.82329	−	8.82190i	0.186494	−	0.282527i
$976$	−1.20156	−	26.7548i	−0.0384609	−	0.856399i
$977$	3.59136	−	11.0531i	0.114898	−	0.353619i	−0.877028	−	0.480440i	$-0.840477\pi$
$977$	3.59136	−	11.0531i	0.114898	−	0.353619i	0.991926	+	0.126820i	$0.0404772\pi$
$978$	−0.933247	−	0.0839938i	−0.0298420	−	0.00268583i
$979$	−7.79306	−	11.8060i	−0.249067	−	0.377321i
$980$	10.0453	−	7.29830i	0.320884	−	0.233136i
$981$	31.1505	+	18.6116i	0.994560	+	0.594222i
$982$	−30.7274	+	71.8903i	−0.980550	+	2.29411i
$983$	24.1874	−	14.4513i	0.771458	−	0.460925i	−0.0724767	−	0.997370i	$-0.523090\pi$
$983$	24.1874	−	14.4513i	0.771458	−	0.460925i	0.843935	+	0.536445i	$0.180233\pi$
$984$	−0.875653	−	6.46433i	−0.0279148	−	0.206075i
$985$	1.56712	+	1.36915i	0.0499327	+	0.0436249i
$986$	−2.18808	+	1.91166i	−0.0696825	+	0.0608798i
$987$	0.232966	−	1.71982i	0.00741538	−	0.0547426i
$988$	17.2335	+	40.3197i	0.548270	+	1.28274i
$989$	31.4735	+	22.8668i	1.00080	+	0.727123i
$990$	−0.190248	+	4.23620i	−0.00604648	+	0.134635i
$991$	−44.8764	−	16.8424i	−1.42554	−	0.535016i	−0.484948	−	0.874543i	$-0.661162\pi$
$991$	−44.8764	−	16.8424i	−1.42554	−	0.535016i	−0.940596	+	0.339527i	$0.889733\pi$
$992$	−42.3467	−	44.2912i	−1.34451	−	1.40625i
$993$	17.8216			0.565551
$994$	3.54653	+	2.11472i	0.112489	+	0.0670749i
$995$	8.44873			0.267843
$996$	−6.90982	−	7.22710i	−0.218946	−	0.229000i
$997$	−0.0655510	−	0.0246017i	−0.00207602	−	0.000779144i	0.350337	−	0.936624i	$-0.386067\pi$
$997$	−0.0655510	−	0.0246017i	−0.00207602	−	0.000779144i	−0.352413	+	0.935845i	$0.614639\pi$
$998$	−0.400583	+	8.91967i	−0.0126802	+	0.282347i
$999$	−29.3630	−	21.3335i	−0.929005	−	0.674962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.12.5	yes	120
3.2	odd	2		639.2.v.a.154.1		120
71.6	even	35	inner	71.2.g.a.6.5	✓	120
71.19	even	35		5041.2.a.s.1.8		60
71.52	odd	70		5041.2.a.t.1.8		60
213.77	odd	70		639.2.v.a.361.1		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.6.5	✓	120	71.6	even	35	inner
71.2.g.a.12.5	yes	120	1.1	even	1	trivial
639.2.v.a.154.1		120	3.2	odd	2
639.2.v.a.361.1		120	213.77	odd	70
5041.2.a.s.1.8		60	71.19	even	35
5041.2.a.t.1.8		60	71.52	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46643 + 1.53377i) q^{2} +(-0.822306 - 0.308617i) q^{3} +(-0.112290 + 2.50034i) q^{4} +(-0.577761 - 0.419768i) q^{5} +(-0.732509 - 1.71379i) q^{6} +(-0.0309991 + 0.228844i) q^{7} +(-0.803573 + 0.702060i) q^{8} +(-1.67827 - 1.46626i) q^{9} +O(q^{10})\)	\(q+(1.46643 + 1.53377i) q^{2} +(-0.822306 - 0.308617i) q^{3} +(-0.112290 + 2.50034i) q^{4} +(-0.577761 - 0.419768i) q^{5} +(-0.732509 - 1.71379i) q^{6} +(-0.0309991 + 0.228844i) q^{7} +(-0.803573 + 0.702060i) q^{8} +(-1.67827 - 1.46626i) q^{9} +(-0.203420 - 1.50171i) q^{10} +(1.07787 - 0.644000i) q^{11} +(0.863983 - 2.02139i) q^{12} +(-2.30101 - 1.37479i) q^{13} +(-0.396452 + 0.288039i) q^{14} +(0.345549 + 0.523484i) q^{15} +(2.73038 + 0.245739i) q^{16} +(-0.509991 + 1.56959i) q^{17} +(-0.212166 - 4.72425i) q^{18} +(-3.60067 + 5.45478i) q^{19} +(1.11444 - 1.39746i) q^{20} +(0.0961159 - 0.178613i) q^{21} +(2.56837 + 0.708826i) q^{22} +(5.83841 + 2.81163i) q^{23} +(0.877450 - 0.329313i) q^{24} +(-1.38748 - 4.27023i) q^{25} +(-1.26567 - 5.54524i) q^{26} +(2.17615 + 4.04397i) q^{27} +(-0.568707 - 0.103205i) q^{28} +(0.799765 - 0.220721i) q^{29} +(-0.296179 + 1.29764i) q^{30} +(-7.67551 + 0.690808i) q^{31} +(4.95761 + 6.21665i) q^{32} +(-1.08509 + 0.196915i) q^{33} +(-3.15525 + 1.51949i) q^{34} +(0.113971 - 0.119205i) q^{35} +(3.85460 - 4.03160i) q^{36} +(-7.12068 + 3.42914i) q^{37} +(-13.6465 + 2.47647i) q^{38} +(1.46785 + 1.84063i) q^{39} +(0.758975 - 0.0683090i) q^{40} +(1.54883 - 6.78589i) q^{41} +(0.414898 - 0.114505i) q^{42} +(5.90700 + 1.07196i) q^{43} +(1.48918 + 2.76736i) q^{44} +(0.354150 + 1.55163i) q^{45} +(4.24924 + 13.0778i) q^{46} +(8.01087 - 3.00653i) q^{47} +(-2.16937 - 1.04471i) q^{48} +(6.69633 + 1.84807i) q^{49} +(4.51489 - 8.39007i) q^{50} +(0.903771 - 1.13329i) q^{51} +(3.69582 - 5.59892i) q^{52} +(-0.0866035 - 1.92838i) q^{53} +(-3.01133 + 9.26791i) q^{54} +(-0.893083 - 0.0803790i) q^{55} +(-0.135752 - 0.205656i) q^{56} +(4.64428 - 3.37427i) q^{57} +(1.51133 + 0.902980i) q^{58} +(-1.25123 + 2.92739i) q^{59} +(-1.34769 + 0.805207i) q^{60} +(-1.31136 - 9.68088i) q^{61} +(-12.3151 - 10.7594i) q^{62} +(0.387570 - 0.338610i) q^{63} +(-1.52891 + 11.2869i) q^{64} +(0.752341 + 1.76019i) q^{65} +(-1.89323 - 1.37551i) q^{66} +(0.161900 - 3.60499i) q^{67} +(-3.86724 - 1.45140i) q^{68} +(-3.93324 - 4.11385i) q^{69} +0.349964 q^{70} +(-3.31851 - 7.74516i) q^{71} +2.37802 q^{72} +(4.54650 + 4.75527i) q^{73} +(-15.7015 - 5.89286i) q^{74} +(-0.176929 + 3.93964i) q^{75} +(-13.2345 - 9.61540i) q^{76} +(0.113963 + 0.266629i) q^{77} +(-0.670590 + 4.95049i) q^{78} +(-4.26243 + 3.72397i) q^{79} +(-1.47435 - 1.28811i) q^{80} +(0.356016 + 2.62822i) q^{81} +(12.6792 - 7.57548i) q^{82} +(1.78766 - 4.18244i) q^{83} +(0.435800 + 0.260379i) q^{84} +(0.953516 - 0.692770i) q^{85} +(7.01807 + 10.6319i) q^{86} +(-0.725770 - 0.0653205i) q^{87} +(-0.414023 + 1.27423i) q^{88} +(-0.505464 - 11.2550i) q^{89} +(-1.86050 + 2.81854i) q^{90} +(0.385942 - 0.483956i) q^{91} +(-7.68562 + 14.2823i) q^{92} +(6.52481 + 1.80073i) q^{93} +(16.3587 + 7.87794i) q^{94} +(4.37006 - 1.64011i) q^{95} +(-2.15811 - 6.64199i) q^{96} +(-2.36055 - 10.3422i) q^{97} +(6.98520 + 12.9807i) q^{98} +(-2.75324 - 0.499639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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