LMFDB - Embedded newform 73.2.k.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [73,2,Mod(6,73)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(73, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("73.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	73.k (of order $36$, degree $12$, 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:	$0.582907934755$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	73.19
Dual form			73.2.k.a.50.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.52218 + 0.917999i) q^{2} +(0.900019 + 0.519626i) q^{3} +(3.98659 - 3.34515i) q^{4} +(0.360692 - 0.168193i) q^{5} +(-2.74703 - 0.484375i) q^{6} +(1.15443 + 4.30840i) q^{7} +(-4.30002 + 7.44785i) q^{8} +(-0.959977 - 1.66273i) q^{9} +O(q^{10})$	\(q+(-2.52218 + 0.917999i) q^{2} +(0.900019 + 0.519626i) q^{3} +(3.98659 - 3.34515i) q^{4} +(0.360692 - 0.168193i) q^{5} +(-2.74703 - 0.484375i) q^{6} +(1.15443 + 4.30840i) q^{7} +(-4.30002 + 7.44785i) q^{8} +(-0.959977 - 1.66273i) q^{9} +(-0.755328 + 0.755328i) q^{10} +(1.40587 + 3.01491i) q^{11} +(5.32624 - 0.939159i) q^{12} +(1.79652 - 1.25794i) q^{13} +(-6.86680 - 9.80680i) q^{14} +(0.412027 + 0.0360477i) q^{15} +(2.20093 - 12.4821i) q^{16} +(-0.652760 - 0.174907i) q^{17} +(3.94762 + 3.31245i) q^{18} +(-1.11608 - 3.06640i) q^{19} +(0.875299 - 1.87708i) q^{20} +(-1.19975 + 4.47752i) q^{21} +(-6.31356 - 6.31356i) q^{22} +(2.00254 - 5.50193i) q^{23} +(-7.74020 + 4.46880i) q^{24} +(-3.11213 + 3.70889i) q^{25} +(-3.37636 + 4.82194i) q^{26} -5.11308i q^{27} +(19.0145 + 13.3141i) q^{28} +(1.84218 + 0.859024i) q^{29} +(-1.07230 + 0.287322i) q^{30} +(-0.277454 - 3.17131i) q^{31} +(2.92065 + 16.5639i) q^{32} +(-0.301311 + 3.44401i) q^{33} +(1.80694 - 0.158087i) q^{34} +(1.14104 + 1.35984i) q^{35} +(-9.38911 - 3.41736i) q^{36} +(-7.28626 - 2.65198i) q^{37} +(5.62990 + 6.70945i) q^{38} +(2.27056 - 0.198648i) q^{39} +(-0.298302 + 3.40961i) q^{40} +(-1.75580 - 9.95762i) q^{41} +(-1.08438 - 12.3945i) q^{42} +(-1.32796 + 0.355826i) q^{43} +(15.6900 + 7.31635i) q^{44} +(-0.625915 - 0.438271i) q^{45} +15.7152i q^{46} +(-1.29775 + 1.85338i) q^{47} +(8.46692 - 10.0905i) q^{48} +(-11.1674 + 6.44751i) q^{49} +(4.44460 - 12.2114i) q^{50} +(-0.496611 - 0.496611i) q^{51} +(2.95400 - 11.0245i) q^{52} +(0.602569 - 1.29221i) q^{53} +(4.69380 + 12.8961i) q^{54} +(1.01417 + 0.850993i) q^{55} +(-37.0524 - 9.92816i) q^{56} +(0.588889 - 3.33976i) q^{57} +(-5.43490 - 0.475492i) q^{58} +(4.24836 + 6.06729i) q^{59} +(1.76317 - 1.23458i) q^{60} +(4.95666 - 0.873994i) q^{61} +(3.61105 + 7.74392i) q^{62} +(6.05547 - 6.05547i) q^{63} +(-9.89736 - 17.1427i) q^{64} +(0.436412 - 0.755889i) q^{65} +(-2.40163 - 8.96301i) q^{66} +(2.87333 + 0.506646i) q^{67} +(-3.18738 + 1.48630i) q^{68} +(4.66127 - 3.91127i) q^{69} +(-4.12623 - 2.38228i) q^{70} +(9.93854 - 3.61733i) q^{71} +16.5117 q^{72} +(1.49673 + 8.41188i) q^{73} +20.8118 q^{74} +(-4.72821 + 1.72093i) q^{75} +(-14.7069 - 8.49102i) q^{76} +(-11.3664 + 9.53758i) q^{77} +(-5.54440 + 2.58540i) q^{78} +(-5.30933 - 0.936179i) q^{79} +(-1.30555 - 4.87237i) q^{80} +(-0.223041 + 0.386319i) q^{81} +(13.5695 + 23.5031i) q^{82} +(-11.7329 + 11.7329i) q^{83} +(10.1951 + 21.8634i) q^{84} +(-0.264863 + 0.0467025i) q^{85} +(3.02271 - 2.11653i) q^{86} +(1.21163 + 1.73038i) q^{87} +(-28.4999 - 2.49341i) q^{88} +(0.548981 - 3.11343i) q^{89} +(1.98100 + 0.530808i) q^{90} +(7.49365 + 6.28792i) q^{91} +(-10.4215 - 28.6327i) q^{92} +(1.39818 - 2.99841i) q^{93} +(1.57176 - 5.86590i) q^{94} +(-0.918306 - 0.918306i) q^{95} +(-5.97837 + 16.4254i) q^{96} +(-1.59802 + 0.922620i) q^{97} +(22.2475 - 26.5135i) q^{98} +(3.66337 - 5.23183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/73\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{31}{36}\right)$

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 $

$2$	−2.52218	+	0.917999i	−1.78345	+	0.649123i	−0.783849	+	0.620951i	$0.786746\pi$
$2$	−2.52218	+	0.917999i	−1.78345	+	0.649123i	−0.999603	+	0.0281720i	$0.991031\pi$
$3$	0.900019	+	0.519626i	0.519626	+	0.300006i	0.736782	−	0.676131i	$-0.236345\pi$
$3$	0.900019	+	0.519626i	0.519626	+	0.300006i	−0.217155	+	0.976137i	$0.569678\pi$
$4$	3.98659	−	3.34515i	1.99330	−	1.67257i
$5$	0.360692	−	0.168193i	0.161306	−	0.0752183i	−0.340288	−	0.940321i	$-0.610525\pi$
$5$	0.360692	−	0.168193i	0.161306	−	0.0752183i	0.501595	+	0.865103i	$0.332747\pi$
$6$	−2.74703	−	0.484375i	−1.12147	−	0.197745i
$7$	1.15443	+	4.30840i	0.436334	+	1.62842i	0.737853	+	0.674962i	$0.235840\pi$
$7$	1.15443	+	4.30840i	0.436334	+	1.62842i	−0.301518	+	0.953460i	$0.597493\pi$
$8$	−4.30002	+	7.44785i	−1.52029	+	2.63321i
$9$	−0.959977	−	1.66273i	−0.319992	−	0.554243i
$10$	−0.755328	+	0.755328i	−0.238856	+	0.238856i
$11$	1.40587	+	3.01491i	0.423887	+	0.909029i	0.996042	+	0.0888834i	$0.0283299\pi$
$11$	1.40587	+	3.01491i	0.423887	+	0.909029i	−0.572155	+	0.820146i	$0.693892\pi$
$12$	5.32624	−	0.939159i	1.53755	−	0.271112i
$13$	1.79652	−	1.25794i	0.498264	−	0.348888i	−0.297273	−	0.954792i	$-0.596077\pi$
$13$	1.79652	−	1.25794i	0.498264	−	0.348888i	0.795538	+	0.605904i	$0.207188\pi$
$14$	−6.86680	−	9.80680i	−1.83523	−	2.62098i
$15$	0.412027	+	0.0360477i	0.106385	+	0.00930747i
$16$	2.20093	−	12.4821i	0.550233	−	3.12053i
$17$	−0.652760	−	0.174907i	−0.158318	−	0.0424211i	0.178790	−	0.983887i	$-0.442782\pi$
$17$	−0.652760	−	0.174907i	−0.158318	−	0.0424211i	−0.337107	+	0.941466i	$0.609449\pi$
$18$	3.94762	+	3.31245i	0.930463	+	0.780751i
$19$	−1.11608	−	3.06640i	−0.256046	−	0.703479i	−0.999402	−	0.0345837i	$-0.988989\pi$
$19$	−1.11608	−	3.06640i	−0.256046	−	0.703479i	0.743356	−	0.668896i	$-0.233233\pi$
$20$	0.875299	−	1.87708i	0.195723	−	0.419729i
$21$	−1.19975	+	4.47752i	−0.261806	+	0.977074i
$22$	−6.31356	−	6.31356i	−1.34605	−	1.34605i
$23$	2.00254	−	5.50193i	0.417558	−	1.14723i	−0.535524	−	0.844520i	$-0.679886\pi$
$23$	2.00254	−	5.50193i	0.417558	−	1.14723i	0.953082	−	0.302712i	$-0.0978920\pi$
$24$	−7.74020	+	4.46880i	−1.57996	+	0.912191i
$25$	−3.11213	+	3.70889i	−0.622426	+	0.741778i
$26$	−3.37636	+	4.82194i	−0.662159	+	0.945661i
$27$		−	5.11308i		−	0.984012i
$28$	19.0145	+	13.3141i	3.59340	+	2.51613i
$29$	1.84218	+	0.859024i	0.342085	+	0.159517i	0.586066	−	0.810263i	$-0.300676\pi$
$29$	1.84218	+	0.859024i	0.342085	+	0.159517i	−0.243982	+	0.969780i	$0.578454\pi$
$30$	−1.07230	+	0.287322i	−0.195774	+	0.0524575i
$31$	−0.277454	−	3.17131i	−0.0498322	−	0.569584i	−0.979535	−	0.201274i	$-0.935492\pi$
$31$	−0.277454	−	3.17131i	−0.0498322	−	0.569584i	0.929703	−	0.368311i	$-0.120064\pi$
$32$	2.92065	+	16.5639i	0.516304	+	2.92810i
$33$	−0.301311	+	3.44401i	−0.0524516	+	0.599524i
$34$	1.80694	−	0.158087i	0.309888	−	0.0271117i
$35$	1.14104	+	1.35984i	0.192871	+	0.229854i
$36$	−9.38911	−	3.41736i	−1.56485	−	0.569559i
$37$	−7.28626	−	2.65198i	−1.19785	−	0.435983i	−0.335379	−	0.942083i	$-0.608864\pi$
$37$	−7.28626	−	2.65198i	−1.19785	−	0.435983i	−0.862475	+	0.506100i	$0.831086\pi$
$38$	5.62990	+	6.70945i	0.913290	+	1.08842i
$39$	2.27056	−	0.198648i	0.363580	−	0.0318091i
$40$	−0.298302	+	3.40961i	−0.0471657	+	0.539106i
$41$	−1.75580	−	9.95762i	−0.274209	−	1.55512i	−0.741462	−	0.670995i	$-0.765867\pi$
$41$	−1.75580	−	9.95762i	−0.274209	−	1.55512i	0.467253	−	0.884124i	$-0.345244\pi$
$42$	−1.08438	−	12.3945i	−0.167323	−	1.91251i
$43$	−1.32796	+	0.355826i	−0.202512	+	0.0542630i	−0.358649	−	0.933472i	$-0.616763\pi$
$43$	−1.32796	+	0.355826i	−0.202512	+	0.0542630i	0.156137	+	0.987735i	$0.450096\pi$
$44$	15.6900	+	7.31635i	2.36535	+	1.10298i
$45$	−0.625915	−	0.438271i	−0.0933059	−	0.0653335i
$46$			15.7152i			2.31708i
$47$	−1.29775	+	1.85338i	−0.189297	+	0.270344i	−0.902571	−	0.430542i	$-0.858323\pi$
$47$	−1.29775	+	1.85338i	−0.189297	+	0.270344i	0.713274	+	0.700885i	$0.247211\pi$
$48$	8.46692	−	10.0905i	1.22209	−	1.45644i
$49$	−11.1674	+	6.44751i	−1.59535	+	0.921073i
$50$	4.44460	−	12.2114i	0.628561	−	1.72696i
$51$	−0.496611	−	0.496611i	−0.0695394	−	0.0695394i
$52$	2.95400	−	11.0245i	0.409646	−	1.52882i
$53$	0.602569	−	1.29221i	0.0827693	−	0.177499i	−0.860567	−	0.509337i	$-0.829891\pi$
$53$	0.602569	−	1.29221i	0.0827693	−	0.177499i	0.943337	+	0.331837i	$0.107669\pi$
$54$	4.69380	+	12.8961i	0.638745	+	1.75494i
$55$	1.01417	+	0.850993i	0.136751	+	0.114748i
$56$	−37.0524	−	9.92816i	−4.95133	−	1.32671i
$57$	0.588889	−	3.33976i	0.0780003	−	0.442362i
$58$	−5.43490	−	0.475492i	−0.713638	−	0.0624352i
$59$	4.24836	+	6.06729i	0.553090	+	0.789894i	0.994199	−	0.107559i	$-0.0343036\pi$
$59$	4.24836	+	6.06729i	0.553090	+	0.789894i	−0.441109	+	0.897454i	$0.645415\pi$
$60$	1.76317	−	1.23458i	0.227624	−	0.159384i
$61$	4.95666	−	0.873994i	0.634636	−	0.111903i	0.152931	−	0.988237i	$-0.451129\pi$
$61$	4.95666	−	0.873994i	0.634636	−	0.111903i	0.481705	+	0.876333i	$0.340018\pi$
$62$	3.61105	+	7.74392i	0.458604	+	0.983479i
$63$	6.05547	−	6.05547i	0.762918	−	0.762918i
$64$	−9.89736	−	17.1427i	−1.23717	−	2.14284i
$65$	0.436412	−	0.755889i	0.0541303	−	0.0937564i
$66$	−2.40163	−	8.96301i	−0.295620	−	1.10327i
$67$	2.87333	+	0.506646i	0.351034	+	0.0618967i	0.346385	−	0.938093i	$-0.387409\pi$
$67$	2.87333	+	0.506646i	0.351034	+	0.0618967i	0.00464872	+	0.999989i	$0.498520\pi$
$68$	−3.18738	+	1.48630i	−0.386526	+	0.180240i
$69$	4.66127	−	3.91127i	0.561151	−	0.470862i
$70$	−4.12623	−	2.38228i	−0.493179	−	0.284737i
$71$	9.93854	−	3.61733i	1.17949	−	0.429298i	0.323466	−	0.946240i	$-0.395152\pi$
$71$	9.93854	−	3.61733i	1.17949	−	0.429298i	0.856021	+	0.516941i	$0.172930\pi$
$72$	16.5117			1.94592
$73$	1.49673	+	8.41188i	0.175179	+	0.984537i
$73$	1.49673	+	8.41188i	0.175179	+	0.984537i
$74$	20.8118			2.41932
$75$	−4.72821	+	1.72093i	−0.545967	+	0.198716i
$76$	−14.7069	−	8.49102i	−1.68700	−	0.973987i
$77$	−11.3664	+	9.53758i	−1.29533	+	1.08691i
$78$	−5.54440	+	2.58540i	−0.627780	+	0.292738i
$79$	−5.30933	−	0.936179i	−0.597347	−	0.105328i	−0.133204	−	0.991089i	$-0.542526\pi$
$79$	−5.30933	−	0.936179i	−0.597347	−	0.105328i	−0.464143	+	0.885760i	$0.653638\pi$
$80$	−1.30555	−	4.87237i	−0.145965	−	0.544748i
$81$	−0.223041	+	0.386319i	−0.0247824	+	0.0429244i
$82$	13.5695	+	23.5031i	1.49850	+	2.59548i
$83$	−11.7329	+	11.7329i	−1.28785	+	1.28785i	−0.351759	+	0.936090i	$0.614416\pi$
$83$	−11.7329	+	11.7329i	−1.28785	+	1.28785i	−0.936090	+	0.351759i	$0.885584\pi$
$84$	10.1951	+	21.8634i	1.11237	+	2.38549i
$85$	−0.264863	+	0.0467025i	−0.0287284	+	0.00506560i
$86$	3.02271	−	2.11653i	0.325947	−	0.228231i
$87$	1.21163	+	1.73038i	0.129900	+	0.185517i
$88$	−28.4999	−	2.49341i	−3.03810	−	0.265799i
$89$	0.548981	−	3.11343i	0.0581919	−	0.330023i	−0.941789	−	0.336205i	$-0.890857\pi$
$89$	0.548981	−	3.11343i	0.0581919	−	0.330023i	0.999981	+	0.00618185i	$0.00196776\pi$
$90$	1.98100	+	0.530808i	0.208816	+	0.0559521i
$91$	7.49365	+	6.28792i	0.785548	+	0.659153i
$92$	−10.4215	−	28.6327i	−1.08651	−	2.98517i
$93$	1.39818	−	2.99841i	0.144985	−	0.310921i
$94$	1.57176	−	5.86590i	0.162115	−	0.605022i
$95$	−0.918306	−	0.918306i	−0.0942162	−	0.0942162i
$96$	−5.97837	+	16.4254i	−0.610165	+	1.67641i
$97$	−1.59802	+	0.922620i	−0.162255	+	0.0936779i	−0.578929	−	0.815378i	$-0.696529\pi$
$97$	−1.59802	+	0.922620i	−0.162255	+	0.0936779i	0.416674	+	0.909056i	$0.363196\pi$
$98$	22.2475	−	26.5135i	2.24733	−	2.67827i
$99$	3.66337	−	5.23183i	0.368182	−	0.525819i
$100$			25.1964i			2.51964i
$101$	−9.11603	−	6.38311i	−0.907079	−	0.635144i	0.0240984	−	0.999710i	$-0.492328\pi$
$101$	−9.11603	−	6.38311i	−0.907079	−	0.635144i	−0.931178	+	0.364566i	$0.881217\pi$
$102$	1.70843	+	0.796654i	0.169160	+	0.0788805i
$103$	12.8422	−	3.44105i	1.26538	−	0.339057i	0.437119	−	0.899404i	$-0.355999\pi$
$103$	12.8422	−	3.44105i	1.26538	−	0.339057i	0.828258	+	0.560347i	$0.189332\pi$
$104$	1.64385	+	18.7893i	0.161193	+	1.84245i
$105$	0.320349	+	1.81679i	0.0312629	+	0.177301i
$106$	−0.333538	+	3.81236i	−0.0323961	+	0.370289i
$107$	−5.61036	+	0.490843i	−0.542374	+	0.0474515i	−0.355051	−	0.934847i	$-0.615537\pi$
$107$	−5.61036	+	0.490843i	−0.542374	+	0.0474515i	−0.187323	+	0.982298i	$0.559981\pi$
$108$	−17.1040	−	20.3837i	−1.64583	−	1.96143i
$109$	−1.75312	−	0.638084i	−0.167919	−	0.0611174i	0.256693	−	0.966493i	$-0.417367\pi$
$109$	−1.75312	−	0.638084i	−0.167919	−	0.0611174i	−0.424612	+	0.905376i	$0.639589\pi$
$110$	−3.33914	−	1.21535i	−0.318375	−	0.115879i
$111$	−5.17973	−	6.17297i	−0.491638	−	0.585912i
$112$	56.3188	−	4.92725i	5.32162	−	0.465582i
$113$	−0.221035	+	2.52644i	−0.0207932	+	0.237667i	0.978685	+	0.205367i	$0.0658388\pi$
$113$	−0.221035	+	2.52644i	−0.0207932	+	0.237667i	−0.999478	+	0.0323002i	$0.989717\pi$
$114$	1.58061	+	8.96408i	0.148038	+	0.839563i
$115$	−0.203089	−	2.32131i	−0.0189381	−	0.216464i
$116$	10.2176	−	2.73779i	0.948679	−	0.254198i
$117$	−3.81622	−	1.77953i	−0.352810	−	0.164518i
$118$	−16.2849	−	11.4028i	−1.49915	−	1.04971i
$119$		−	3.01427i		−	0.276318i
$120$	−2.04020	+	2.91371i	−0.186244	+	0.265984i
$121$	−0.0425247	+	0.0506789i	−0.00386588	+	0.00460718i
$122$	−11.6993	+	6.75458i	−1.05920	+	0.611531i
$123$	3.59399	−	9.87440i	0.324059	−	0.890345i
$124$	−11.7146	−	11.7146i	−1.05200	−	1.05200i
$125$	−1.01373	+	3.78330i	−0.0906709	+	0.338388i
$126$	−9.71408	+	20.8319i	−0.865399	+	1.85586i
$127$	−1.09535	−	3.00945i	−0.0971966	−	0.267045i	0.881560	−	0.472073i	$-0.156494\pi$
$127$	−1.09535	−	3.00945i	−0.0971966	−	0.267045i	−0.978756	+	0.205027i	$0.934272\pi$
$128$	14.9312	+	12.5287i	1.31974	+	1.10740i
$129$	−1.38009	−	0.369793i	−0.121510	−	0.0325585i
$130$	−0.406807	+	2.30712i	−0.0356793	+	0.202347i
$131$	2.78132	+	0.243334i	0.243005	+	0.0212602i	0.208008	−	0.978127i	$-0.433302\pi$
$131$	2.78132	+	0.243334i	0.243005	+	0.0212602i	0.0349974	+	0.999387i	$0.488858\pi$
$132$	10.3195	+	14.7378i	0.898197	+	1.28276i
$133$	11.9228	−	8.34845i	1.03384	−	0.723903i
$134$	−7.71217	+	1.35986i	−0.666230	+	0.117474i
$135$	−0.859985	−	1.84424i	−0.0740157	−	0.158727i
$136$	4.10956	−	4.10956i	0.352392	−	0.352392i
$137$	2.09503	+	3.62869i	0.178990	+	0.310020i	0.941535	−	0.336915i	$-0.109384\pi$
$137$	2.09503	+	3.62869i	0.178990	+	0.310020i	−0.762545	+	0.646935i	$0.776050\pi$
$138$	−8.16604	+	14.1440i	−0.695139	+	1.20402i
$139$	4.45115	+	16.6119i	0.377542	+	1.40900i	0.849596	+	0.527435i	$0.176846\pi$
$139$	4.45115	+	16.6119i	0.377542	+	1.40900i	−0.472054	+	0.881570i	$0.656487\pi$
$140$	9.09770	+	1.60417i	0.768896	+	0.135577i
$141$	−2.13107	+	0.993734i	−0.179468	+	0.0836875i
$142$	−21.7461	+	18.2471i	−1.82489	+	1.53127i
$143$	6.31824	+	3.64784i	0.528358	+	0.305047i
$144$	−22.8672	+	8.32298i	−1.90560	+	0.693582i
$145$	0.808942			0.0671789
$146$	−11.4971	−	19.8423i	−0.951509	−	1.64216i
$147$	−13.4012			−1.10531
$148$	−37.9186	+	13.8012i	−3.11689	+	1.13445i
$149$	5.42347	+	3.13124i	0.444308	+	0.256521i	0.705423	−	0.708786i	$-0.250757\pi$
$149$	5.42347	+	3.13124i	0.444308	+	0.256521i	−0.261116	+	0.965308i	$0.584090\pi$
$150$	10.3456	−	8.68099i	0.844715	−	0.708800i
$151$	9.83321	−	4.58530i	0.800216	−	0.373147i	0.0209026	−	0.999782i	$-0.493346\pi$
$151$	9.83321	−	4.58530i	0.800216	−	0.373147i	0.779313	+	0.626635i	$0.215568\pi$
$152$	27.6372	+	4.87318i	2.24167	+	0.395267i
$153$	0.335813	+	1.25327i	0.0271488	+	0.101321i
$154$	19.9128	−	34.4899i	1.60462	−	2.77928i
$155$	−0.633468	−	1.09720i	−0.0508814	−	0.0881292i
$156$	8.38728	−	8.38728i	0.671519	−	0.671519i
$157$	−2.75563	−	5.90947i	−0.219923	−	0.471627i	0.765130	−	0.643876i	$-0.222675\pi$
$157$	−2.75563	−	5.90947i	−0.219923	−	0.471627i	−0.985054	+	0.172249i	$0.944897\pi$
$158$	14.2505	−	2.51275i	1.13371	−	0.199904i
$159$	1.21379	−	0.849907i	0.0962600	−	0.0674020i
$160$	3.83938	+	5.48321i	0.303530	+	0.433486i
$161$	26.0163	+	2.27613i	2.05037	+	0.179384i
$162$	0.207911	−	1.17912i	0.0163350	−	0.0926403i
$163$	−16.9539	−	4.54277i	−1.32793	−	0.355817i	−0.475986	−	0.879453i	$-0.657909\pi$
$163$	−16.9539	−	4.54277i	−1.32793	−	0.355817i	−0.851942	+	0.523636i	$0.824575\pi$
$164$	−40.3093	−	33.8235i	−3.14763	−	2.64118i
$165$	0.470578	+	1.29290i	0.0366344	+	0.100652i
$166$	18.8217	−	40.3632i	1.46084	−	3.13279i
$167$	−0.167512	+	0.625164i	−0.0129625	+	0.0483766i	−0.972104	−	0.234550i	$-0.924638\pi$
$167$	−0.167512	+	0.625164i	−0.0129625	+	0.0483766i	0.959142	+	0.282926i	$0.0913051\pi$
$168$	−28.1889	−	28.1889i	−2.17482	−	2.17482i
$169$	−2.80119	+	7.69620i	−0.215476	+	0.592015i
$170$	0.625160	−	0.360936i	0.0479476	−	0.0276826i
$171$	−4.02718	+	4.79940i	−0.307966	+	0.367019i
$172$	−4.10375	+	5.86076i	−0.312908	+	0.446879i
$173$			13.5928i			1.03344i	0.856154	+	0.516721i	$0.172848\pi$
$173$			13.5928i			1.03344i	−0.856154	+	0.516721i	$0.827152\pi$
$174$	−4.64444	−	3.25207i	−0.352094	−	0.246539i
$175$	−19.5721	−	9.12663i	−1.47951	−	0.689909i
$176$	40.7267	−	10.9127i	3.06989	−	0.822574i
$177$	0.670884	+	7.66824i	0.0504268	+	0.576380i
$178$	1.47349	+	8.35660i	0.110443	+	0.626353i
$179$	−1.02121	+	11.6725i	−0.0763289	+	0.872444i	0.857444	+	0.514577i	$0.172051\pi$
$179$	−1.02121	+	11.6725i	−0.0763289	+	0.872444i	−0.933773	+	0.357866i	$0.883504\pi$
$180$	−3.96135	+	0.346573i	−0.295261	+	0.0258320i
$181$	−10.5374	−	12.5580i	−0.783239	−	0.933428i	0.215836	−	0.976430i	$-0.430752\pi$
$181$	−10.5374	−	12.5580i	−0.783239	−	0.933428i	−0.999075	+	0.0430014i	$0.986308\pi$
$182$	−24.6726	−	8.98011i	−1.82886	−	0.665650i
$183$	4.91524	+	1.78900i	0.363345	+	0.132247i
$184$	32.3666	+	38.5730i	2.38610	+	2.84364i
$185$	−3.07414	+	0.268952i	−0.226015	+	0.0197737i
$186$	−0.773932	+	8.84608i	−0.0567474	+	0.648626i
$187$	−0.390372	−	2.21391i	−0.0285468	−	0.161897i
$188$	1.02623	+	11.7299i	0.0748454	+	0.855487i
$189$	22.0292	−	5.90270i	1.60239	−	0.429358i
$190$	3.15914	+	1.47313i	0.229188	+	0.106872i
$191$	12.3466	+	8.64515i	0.893366	+	0.625541i	0.927478	−	0.373877i	$-0.121972\pi$
$191$	12.3466	+	8.64515i	0.893366	+	0.625541i	−0.0341129	+	0.999418i	$0.510861\pi$
$192$		−	20.5717i		−	1.48464i
$193$	1.57719	−	2.25246i	0.113529	−	0.162136i	−0.758366	−	0.651828i	$-0.774002\pi$
$193$	1.57719	−	2.25246i	0.113529	−	0.162136i	0.871895	+	0.489693i	$0.162891\pi$
$194$	3.18355	−	3.79400i	0.228565	−	0.272393i
$195$	0.785559	−	0.453543i	0.0562551	−	0.0324789i
$196$	−22.9521	+	63.0603i	−1.63943	+	4.50430i
$197$	−6.09766	−	6.09766i	−0.434440	−	0.434440i	0.455695	−	0.890136i	$-0.349391\pi$
$197$	−6.09766	−	6.09766i	−0.434440	−	0.434440i	−0.890136	+	0.455695i	$0.849391\pi$
$198$	−4.43686	+	16.5586i	−0.315314	+	1.17677i
$199$	8.03746	−	17.2364i	0.569760	−	1.22185i	−0.384569	−	0.923096i	$-0.625650\pi$
$199$	8.03746	−	17.2364i	0.569760	−	1.22185i	0.954329	−	0.298758i	$-0.0965724\pi$
$200$	−14.2410	−	39.1269i	−1.00699	−	2.76669i
$201$	2.32279	+	1.94905i	0.163837	+	0.137475i
$202$	28.8520	+	7.73087i	2.03002	+	0.543942i
$203$	−1.57434	+	8.92854i	−0.110497	+	0.626661i
$204$	−3.64102	−	0.318548i	−0.254922	−	0.0223028i
$205$	−2.30810	−	3.29631i	−0.161205	−	0.230225i
$206$	−29.2314	+	20.4681i	−2.03665	+	1.42608i
$207$	−11.0706	+	1.95205i	−0.769461	+	0.135677i
$208$	−11.7477	−	25.1930i	−0.814555	−	1.74682i
$209$	7.67584	−	7.67584i	0.530949	−	0.530949i
$210$	−2.47579	−	4.28820i	−0.170846	−	0.295914i
$211$	−10.2620	+	17.7743i	−0.706467	+	1.22364i	0.259693	+	0.965691i	$0.416379\pi$
$211$	−10.2620	+	17.7743i	−0.706467	+	1.22364i	−0.966160	+	0.257945i	$0.916955\pi$
$212$	−1.92045	−	7.16721i	−0.131897	−	0.492246i
$213$	10.8245	+	1.90866i	0.741685	+	0.130779i
$214$	13.6997	−	6.38830i	0.936495	−	0.436695i
$215$	−0.419137	+	0.351697i	−0.0285849	+	0.0239856i
$216$	38.0814	+	21.9863i	2.59111	+	1.49598i
$217$	13.3430	−	4.85645i	0.905780	−	0.329677i
$218$	5.00745			0.339147
$219$	−3.02395	+	8.34860i	−0.204340	+	0.564146i
$220$	6.88980			0.464510
$221$	−1.39272	+	0.506907i	−0.0936842	+	0.0340983i
$222$	18.7310	+	10.8144i	1.25714	+	0.725812i
$223$	8.55579	−	7.17916i	0.572938	−	0.480752i	−0.309681	−	0.950840i	$-0.600222\pi$
$223$	8.55579	−	7.17916i	0.572938	−	0.480752i	0.882619	+	0.470088i	$0.155778\pi$
$224$	−67.9920	+	31.7052i	−4.54291	+	2.11839i
$225$	9.15445	+	1.61418i	0.610297	+	0.107612i
$226$	−1.76178	−	6.57505i	−0.117192	−	0.437366i
$227$	1.97135	−	3.41448i	0.130843	−	0.226627i	−0.793159	−	0.609015i	$-0.791565\pi$
$227$	1.97135	−	3.41448i	0.130843	−	0.226627i	0.924002	+	0.382388i	$0.124898\pi$
$228$	−8.82432	−	15.2842i	−0.584405	−	1.01222i
$229$	2.81827	−	2.81827i	0.186236	−	0.186236i	−0.607831	−	0.794067i	$-0.707960\pi$
$229$	2.81827	−	2.81827i	0.186236	−	0.186236i	0.794067	+	0.607831i	$0.207960\pi$
$230$	2.64319	+	5.66834i	0.174287	+	0.373759i
$231$	−15.1860	+	2.67770i	−0.999165	+	0.176180i
$232$	−14.3193	+	10.0265i	−0.940108	+	0.658270i
$233$	−6.83915	−	9.76732i	−0.448048	−	0.639878i	0.530064	−	0.847957i	$-0.322168\pi$
$233$	−6.83915	−	9.76732i	−0.448048	−	0.639878i	−0.978112	+	0.208079i	$0.933279\pi$
$234$	11.2588	+	0.985018i	0.736012	+	0.0643927i
$235$	−0.156362	+	0.886772i	−0.0101999	+	0.0578467i
$236$	37.2325	+	9.97641i	2.42363	+	0.649409i
$237$	−4.29204	−	3.60145i	−0.278798	−	0.233939i
$238$	2.76710	+	7.60254i	0.179364	+	0.492799i
$239$	−10.7955	+	23.1510i	−0.698301	+	1.49751i	0.161495	+	0.986874i	$0.448368\pi$
$239$	−10.7955	+	23.1510i	−0.698301	+	1.49751i	−0.859796	+	0.510638i	$0.829409\pi$
$240$	1.35680	−	5.06363i	0.0875807	−	0.326856i
$241$	19.3901	+	19.3901i	1.24902	+	1.24902i	0.956152	+	0.292872i	$0.0946108\pi$
$241$	19.3901	+	19.3901i	1.24902	+	1.24902i	0.292872	+	0.956152i	$0.405389\pi$
$242$	0.0607318	−	0.166859i	0.00390399	−	0.0107261i
$243$	−13.6856	+	7.90141i	−0.877934	+	0.506876i
$244$	16.8366	−	20.0650i	1.07785	−	1.28453i
$245$	−2.94357	+	4.20385i	−0.188058	+	0.268574i
$246$			28.2043i			1.79824i
$247$	−5.86238	−	4.10488i	−0.373014	−	0.261187i
$248$	24.8125	+	11.5703i	1.57560	+	0.734712i
$249$	−16.6565	+	4.46310i	−1.05556	+	0.282838i
$250$	−0.916248	−	10.4728i	−0.0579486	−	0.662356i
$251$	2.30833	+	13.0912i	0.145701	+	0.826310i	0.966802	+	0.255527i	$0.0822490\pi$
$251$	2.30833	+	13.0912i	0.145701	+	0.826310i	−0.821101	+	0.570783i	$0.806640\pi$
$252$	3.88425	−	44.3971i	0.244685	−	2.79676i
$253$	19.4031	−	1.69756i	1.21987	−	0.106724i
$254$	5.52534	+	6.58485i	0.346691	+	0.413170i
$255$	−0.262650	−	0.0955967i	−0.0164478	−	0.00598650i
$256$	−11.9586	−	4.35258i	−0.747414	−	0.272036i
$257$	−10.2473	−	12.2123i	−0.639212	−	0.761783i	0.345033	−	0.938590i	$-0.387868\pi$
$257$	−10.2473	−	12.2123i	−0.639212	−	0.761783i	−0.984246	+	0.176807i	$0.943423\pi$
$258$	3.82030	−	0.334233i	0.237842	−	0.0208084i
$259$	3.01430	−	34.4536i	0.187300	−	2.14085i
$260$	−0.788760	−	4.47328i	−0.0489168	−	0.277421i
$261$	−0.340129	−	3.88769i	−0.0210535	−	0.240642i
$262$	−7.23837	+	1.93952i	−0.447188	+	0.119824i
$263$	−14.4812	−	6.75272i	−0.892952	−	0.416390i	−0.0786976	−	0.996899i	$-0.525076\pi$
$263$	−14.4812	−	6.75272i	−0.892952	−	0.416390i	−0.814254	+	0.580508i	$0.802854\pi$
$264$	−24.3548	−	17.0534i	−1.49893	−	1.04956i
$265$		−	0.567439i		−	0.0348575i
$266$	−22.4077	+	32.0015i	−1.37390	+	1.96214i
$267$	2.11191	−	2.51688i	0.129247	−	0.154031i
$268$	13.1496	−	7.59193i	0.803240	−	0.463751i
$269$	−2.64792	+	7.27510i	−0.161447	+	0.443571i	−0.993868	−	0.110572i	$-0.964732\pi$
$269$	−2.64792	+	7.27510i	−0.161447	+	0.443571i	0.832422	+	0.554143i	$0.186954\pi$
$270$	3.86205	+	3.86205i	0.235037	+	0.235037i
$271$	−2.37206	+	8.85265i	−0.144092	+	0.537760i	0.855702	+	0.517470i	$0.173126\pi$
$271$	−2.37206	+	8.85265i	−0.144092	+	0.537760i	−0.999794	+	0.0202909i	$0.993541\pi$
$272$	−3.61988	+	7.76287i	−0.219488	+	0.470693i
$273$	3.47706	+	9.55314i	0.210441	+	0.578182i
$274$	−8.61518	−	7.22899i	−0.520462	−	0.436719i
$275$	−15.5572	−	4.16855i	−0.938136	−	0.251373i
$276$	5.49881	−	31.1853i	0.330989	−	1.87713i
$277$	2.97698	+	0.260452i	0.178869	+	0.0156490i	0.176238	−	0.984348i	$-0.443607\pi$
$277$	2.97698	+	0.260452i	0.178869	+	0.0156490i	0.00263086	+	0.999997i	$0.499163\pi$
$278$	−26.4763	−	37.8121i	−1.58795	−	2.26782i
$279$	−5.00668	+	3.50572i	−0.299742	+	0.209882i
$280$	−15.0343	+	2.65096i	−0.898473	+	0.158425i
$281$	−12.4620	−	26.7249i	−0.743421	−	1.59427i	−0.802951	−	0.596045i	$-0.796738\pi$
$281$	−12.4620	−	26.7249i	−0.743421	−	1.59427i	0.0595300	−	0.998227i	$-0.481040\pi$
$282$	4.46270	−	4.46270i	0.265750	−	0.265750i
$283$	11.9623	+	20.7193i	0.711084	+	1.23163i	0.964450	+	0.264264i	$0.0851289\pi$
$283$	11.9623	+	20.7193i	0.711084	+	1.23163i	−0.253366	+	0.967370i	$0.581538\pi$
$284$	27.5204	−	47.6667i	1.63303	−	2.82850i
$285$	−0.349317	−	1.30367i	−0.0206918	−	0.0772227i
$286$	−19.2845	−	3.40037i	−1.14031	−	0.201068i
$287$	40.8744	−	19.0601i	2.41274	−	1.12508i
$288$	24.7374	−	20.7572i	1.45767	−	1.22313i
$289$	−14.3269	−	8.27166i	−0.842760	−	0.486568i
$290$	−2.04030	+	0.742608i	−0.119810	+	0.0436074i
$291$	−1.91767			−0.112416
$292$	34.1058	+	28.5280i	1.99589	+	1.66947i
$293$	−4.35388			−0.254356			−0.127178	−	0.991880i	$-0.540592\pi$
$293$	−4.35388			−0.254356			−0.127178	+	0.991880i	$0.540592\pi$
$294$	33.8002	−	12.3023i	1.97127	−	0.717484i
$295$	2.55283	+	1.47388i	0.148631	+	0.0858123i
$296$	51.0826	−	42.8634i	2.96911	−	2.49138i
$297$	15.4155	−	7.18834i	0.894495	−	0.417110i
$298$	−16.5534	−	2.91882i	−0.958915	−	0.169083i
$299$	−3.32348	−	12.4034i	−0.192202	−	0.717306i
$300$	−13.0927	+	22.6772i	−0.755907	+	1.30927i
$301$	−3.06608	−	5.31061i	−0.176726	−	0.306098i
$302$	−20.5919	+	20.5919i	−1.18493	+	1.18493i
$303$	−4.88777	−	10.4819i	−0.280795	−	0.602167i
$304$	−40.7315	+	7.18206i	−2.33611	+	0.411920i
$305$	1.64083	−	1.14892i	0.0939535	−	0.0657869i
$306$	−1.99748	−	2.85270i	−0.114188	−	0.163078i
$307$	−30.1375	−	2.63669i	−1.72004	−	0.150484i	−0.816034	−	0.578003i	$-0.803832\pi$
$307$	−30.1375	−	2.63669i	−1.72004	−	0.150484i	−0.904006	+	0.427519i	$0.859388\pi$
$308$	−13.4088	+	76.0449i	−0.764035	+	4.33306i
$309$	13.3463	+	3.57612i	0.759243	+	0.203438i
$310$	2.60495	+	2.18581i	0.147951	+	0.124146i
$311$	1.24050	+	3.40824i	0.0703422	+	0.193264i	0.969882	−	0.243575i	$-0.0783202\pi$
$311$	1.24050	+	3.40824i	0.0703422	+	0.193264i	−0.899540	+	0.436839i	$0.856098\pi$
$312$	−8.28393	+	17.7649i	−0.468985	+	1.00574i
$313$	6.74776	−	25.1830i	0.381406	−	1.42343i	−0.462349	−	0.886698i	$-0.652993\pi$
$313$	6.74776	−	25.1830i	0.381406	−	1.42343i	0.843755	−	0.536728i	$-0.180340\pi$
$314$	12.3751	+	12.3751i	0.698367	+	0.698367i
$315$	1.16567	−	3.20265i	0.0656780	−	0.180449i
$316$	−24.2978	+	14.0283i	−1.36686	+	0.789156i
$317$	−20.2662	+	24.1523i	−1.13826	+	1.35653i	−0.213068	+	0.977037i	$0.568346\pi$
$317$	−20.2662	+	24.1523i	−1.13826	+	1.35653i	−0.925195	+	0.379492i	$0.876099\pi$
$318$	−2.28119	+	3.25788i	−0.127923	+	0.182693i
$319$			6.76169i			0.378582i
$320$	−6.45319	−	4.51857i	−0.360744	−	0.252596i
$321$	−5.30448	−	2.47352i	−0.296067	−	0.138059i
$322$	−67.7074	+	18.1421i	−3.77319	+	1.01102i
$323$	0.192198	+	2.19683i	0.0106942	+	0.122235i
$324$	0.403119	+	2.28620i	0.0223955	+	0.127011i
$325$	−0.925450	+	10.5779i	−0.0513347	+	0.586759i
$326$	46.9310	−	4.10593i	2.59927	−	0.227406i
$327$	−1.24628	−	1.48526i	−0.0689193	−	0.0821348i
$328$	81.7128	+	29.7410i	4.51183	+	1.64217i
$329$	−9.48328	−	3.45163i	−0.522830	−	0.190295i
$330$	−2.37377	−	2.82894i	−0.130672	−	0.155728i
$331$	−20.3970	+	1.78451i	−1.12112	+	0.0980854i	−0.632609	−	0.774472i	$-0.718016\pi$
$331$	−20.3970	+	1.78451i	−1.12112	+	0.0980854i	−0.488512	+	0.872557i	$0.662460\pi$
$332$	−7.52598	+	86.0223i	−0.413042	+	4.72109i
$333$	2.58511	+	14.6609i	0.141663	+	0.803413i
$334$	−0.151404	−	1.73055i	−0.00828444	−	0.0946916i
$335$	1.12160	−	0.300532i	0.0612796	−	0.0164198i
$336$	53.2483	+	24.8301i	2.90493	+	1.35459i
$337$	−7.21288	−	5.05052i	−0.392911	−	0.275119i	0.360381	−	0.932805i	$-0.382647\pi$
$337$	−7.21288	−	5.05052i	−0.392911	−	0.275119i	−0.753292	+	0.657686i	$0.771535\pi$
$338$		−	21.9827i		−	1.19570i
$339$	−1.51174	+	2.15899i	−0.0821064	+	0.117260i
$340$	−0.899674	+	1.07219i	−0.0487917	+	0.0581477i
$341$	9.17115	−	5.29497i	0.496646	−	0.286738i
$342$	5.75142	−	15.8019i	0.311001	−	0.854469i
$343$	−18.5927	−	18.5927i	−1.00391	−	1.00391i
$344$	3.06012	−	11.4205i	0.164990	−	0.615753i
$345$	1.02343	−	2.19476i	0.0550997	−	0.118162i
$346$	−12.4782	−	34.2836i	−0.670832	−	1.84310i
$347$	−6.02854	−	5.05855i	−0.323629	−	0.271557i	0.466469	−	0.884538i	$-0.345526\pi$
$347$	−6.02854	−	5.05855i	−0.323629	−	0.271557i	−0.790098	+	0.612981i	$0.789970\pi$
$348$	10.6187	+	2.84526i	0.569220	+	0.152522i
$349$	−4.17239	+	23.6628i	−0.223343	+	1.26664i	0.642485	+	0.766298i	$0.277904\pi$
$349$	−4.17239	+	23.6628i	−0.223343	+	1.26664i	−0.865828	+	0.500342i	$0.833208\pi$
$350$	57.7427	+	5.05183i	3.08648	+	0.270032i
$351$	−6.43192	−	9.18573i	−0.343310	−	0.490298i
$352$	−45.8324	+	32.0922i	−2.44288	+	1.71052i
$353$	9.94885	−	1.75425i	0.529524	−	0.0933693i	0.0975069	−	0.995235i	$-0.468913\pi$
$353$	9.94885	−	1.75425i	0.529524	−	0.0933693i	0.432017	+	0.901866i	$0.357802\pi$
$354$	−8.73153	−	18.7248i	−0.464076	−	0.995214i
$355$	2.97633	−	2.97633i	0.157967	−	0.157967i
$356$	−8.22631	−	14.2484i	−0.435994	−	0.755163i
$357$	1.56629	−	2.71290i	0.0828971	−	0.143582i
$358$	−8.13966	−	30.3776i	−0.430195	−	1.60551i
$359$	13.7862	+	2.43088i	0.727608	+	0.128297i	0.525169	−	0.850998i	$-0.324002\pi$
$359$	13.7862	+	2.43088i	0.727608	+	0.128297i	0.202439	+	0.979295i	$0.435113\pi$
$360$	5.95562	−	2.77715i	0.313889	−	0.146369i
$361$	6.39769	−	5.36830i	0.336721	−	0.282542i
$362$	38.1055	+	22.0002i	2.00278	+	1.15631i
$363$	−0.0646072	+	0.0235151i	−0.00339100	+	0.00123422i
$364$	50.9081			2.66831
$365$	1.95468	+	2.78236i	0.102313	+	0.145635i
$366$	−14.0394			−0.733853
$367$	30.9568	−	11.2674i	1.61593	−	0.588151i	0.633331	−	0.773881i	$-0.281687\pi$
$367$	30.9568	−	11.2674i	1.61593	−	0.588151i	0.982601	+	0.185730i	$0.0594649\pi$
$368$	−64.2683	−	37.1053i	−3.35022	−	1.93425i
$369$	−14.8713	+	12.4785i	−0.774168	+	0.649604i
$370$	7.50663	−	3.50040i	0.390251	−	0.181977i
$371$	6.26300	+	1.10434i	0.325159	+	0.0573343i
$372$	−4.45615	−	16.6306i	−0.231041	−	0.862256i
$373$	10.6983	−	18.5300i	0.553938	−	0.959448i	−0.444048	−	0.896003i	$-0.646458\pi$
$373$	10.6983	−	18.5300i	0.553938	−	0.959448i	0.997985	−	0.0634450i	$-0.0202087\pi$
$374$	3.01696	+	5.22552i	0.156003	+	0.270205i
$375$	−2.87828	+	2.87828i	−0.148634	+	0.148634i
$376$	−8.22335	−	17.6350i	−0.424087	−	0.909458i
$377$	4.39011	−	0.774095i	0.226102	−	0.0398679i
$378$	−50.1429	+	35.1104i	−2.57907	+	1.80589i
$379$	−3.34349	−	4.77500i	−0.171744	−	0.245275i	0.724048	−	0.689750i	$-0.242279\pi$
$379$	−3.34349	−	4.77500i	−0.171744	−	0.245275i	−0.895792	+	0.444474i	$0.853391\pi$
$380$	−6.73278	−	0.589042i	−0.345384	−	0.0302172i
$381$	0.577953	−	3.27774i	0.0296094	−	0.167923i
$382$	−39.0765	−	10.4705i	−1.99933	−	0.535718i
$383$	16.5926	+	13.9229i	0.847843	+	0.711425i	0.959314	−	0.282343i	$-0.0911115\pi$
$383$	16.5926	+	13.9229i	0.847843	+	0.711425i	−0.111470	+	0.993768i	$0.535556\pi$
$384$	6.92808	+	19.0348i	0.353547	+	0.971363i
$385$	−2.49562	+	5.35188i	−0.127189	+	0.272757i
$386$	−1.91020	+	7.12897i	−0.0972267	+	0.362855i
$387$	1.86645	+	1.86645i	0.0948772	+	0.0948772i
$388$	−3.28437	+	9.02374i	−0.166739	+	0.458111i
$389$	4.74688	−	2.74061i	0.240677	−	0.138955i	−0.374811	−	0.927101i	$-0.622292\pi$
$389$	4.74688	−	2.74061i	0.240677	−	0.138955i	0.615488	+	0.788147i	$0.288959\pi$
$390$	−1.56497	+	1.86506i	−0.0792454	+	0.0944410i
$391$	−2.26950	+	3.24119i	−0.114774	+	0.163914i
$392$		−	110.898i		−	5.60118i
$393$	2.37680	+	1.66425i	0.119894	+	0.0839504i
$394$	20.9771	+	9.78176i	1.05681	+	0.492798i
$395$	−2.07249	+	0.555322i	−0.104278	+	0.0279413i
$396$	−2.89690	−	33.1117i	−0.145574	−	1.66392i
$397$	6.75563	+	38.3131i	0.339055	+	1.92288i	0.382790	+	0.923836i	$0.374963\pi$
$397$	6.75563	+	38.3131i	0.339055	+	1.92288i	−0.0437342	+	0.999043i	$0.513925\pi$
$398$	−4.44894	+	50.8517i	−0.223005	+	2.54896i
$399$	15.0688	−	1.31835i	0.754386	−	0.0660002i
$400$	39.4452	+	47.0090i	1.97226	+	2.35045i
$401$	−31.2966	−	11.3910i	−1.56288	−	0.568840i	−0.591483	−	0.806318i	$-0.701457\pi$
$401$	−31.2966	−	11.3910i	−1.56288	−	0.568840i	−0.971393	+	0.237477i	$0.923679\pi$
$402$	−7.64772	−	2.78354i	−0.381434	−	0.138831i
$403$	−4.48776	−	5.34830i	−0.223551	−	0.266418i
$404$	−57.6944	+	5.04760i	−2.87040	+	0.251128i
$405$	−0.0154729	+	0.176856i	−0.000768855	+	0.00878805i
$406$	−4.22562	−	23.9647i	−0.209714	−	1.18935i
$407$	−2.24809	−	25.6957i	−0.111434	−	1.27369i
$408$	5.83411	−	1.56325i	0.288832	−	0.0773922i
$409$	8.31065	+	3.87532i	0.410935	+	0.191622i	0.617082	−	0.786899i	$-0.288315\pi$
$409$	8.31065	+	3.87532i	0.410935	+	0.191622i	−0.206147	+	0.978521i	$0.566092\pi$
$410$	8.84747	+	6.19507i	0.436946	+	0.305953i
$411$			4.35452i			0.214793i
$412$	39.6857	−	56.6770i	1.95517	−	2.79228i
$413$	−21.2359	+	25.3079i	−1.04495	+	1.24532i
$414$	26.1301	−	15.0862i	1.28423	−	0.741448i
$415$	−2.25856	+	6.20534i	−0.110868	+	0.304608i
$416$	26.0833	+	26.0833i	1.27884	+	1.27884i
$417$	−4.62587	+	17.2640i	−0.226530	+	0.845421i
$418$	−12.3134	+	26.4063i	−0.602270	+	1.29157i
$419$	9.34913	+	25.6865i	0.456735	+	1.25487i	0.927902	+	0.372825i	$0.121611\pi$
$419$	9.34913	+	25.6865i	0.456735	+	1.25487i	−0.471167	+	0.882044i	$0.656167\pi$
$420$	7.35454	+	6.17119i	0.358865	+	0.301123i
$421$	29.4626	+	7.89447i	1.43592	+	0.384753i	0.891102	−	0.453803i	$-0.149933\pi$
$421$	29.4626	+	7.89447i	1.43592	+	0.384753i	0.544815	+	0.838556i	$0.316600\pi$
$422$	9.56586	−	54.2507i	0.465659	−	2.64088i
$423$	4.32748	+	0.378606i	0.210409	+	0.0184084i
$424$	7.03316	+	10.0444i	0.341560	+	0.487799i
$425$	2.68018	−	1.87668i	0.130008	−	0.0910326i
$426$	−29.0536	+	5.12293i	−1.40765	+	0.248207i
$427$	9.48765	+	20.3463i	0.459139	+	0.984628i
$428$	−20.7243	+	20.7243i	−1.00174	+	1.00174i
$429$	3.79102	+	6.56625i	0.183032	+	0.317021i
$430$	0.734281	−	1.27181i	0.0354102	−	0.0613322i
$431$	2.24263	+	8.36960i	0.108024	+	0.403149i	0.998671	−	0.0515458i	$-0.0164148\pi$
$431$	2.24263	+	8.36960i	0.108024	+	0.403149i	−0.890647	+	0.454695i	$0.849748\pi$
$432$	−63.8220	−	11.2535i	−3.07064	−	0.541436i
$433$	11.3740	−	5.30379i	0.546600	−	0.254884i	−0.129645	−	0.991560i	$-0.541384\pi$
$433$	11.3740	−	5.30379i	0.546600	−	0.254884i	0.676245	+	0.736677i	$0.263606\pi$
$434$	−29.1952	+	24.4977i	−1.40141	+	1.17593i
$435$	0.728063	+	0.420347i	0.0349080	+	0.0201541i
$436$	−9.12346	+	3.32067i	−0.436935	+	0.159031i
$437$	−19.1061			−0.913968
$438$	−0.0370516	−	23.8327i	−0.00177039	−	1.13877i
$439$	−19.1503			−0.913992			−0.456996	−	0.889469i	$-0.651075\pi$
$439$	−19.1503			−0.913992			−0.456996	+	0.889469i	$0.651075\pi$
$440$	−10.6990	+	3.89413i	−0.510056	+	0.185645i
$441$	21.4409	+	12.3789i	1.02100	+	0.589473i
$442$	3.04734	−	2.55702i	0.144947	−	0.121625i
$443$	9.70745	−	4.52666i	0.461215	−	0.215068i	−0.178101	−	0.984012i	$-0.556995\pi$
$443$	9.70745	−	4.52666i	0.461215	−	0.215068i	0.639316	+	0.768944i	$0.279218\pi$
$444$	−41.2990	−	7.28212i	−1.95996	−	0.345594i
$445$	−0.325645	−	1.21532i	−0.0154370	−	0.0576118i
$446$	−14.9888	+	25.9613i	−0.709740	+	1.22931i
$447$	3.25415	+	5.63635i	0.153916	+	0.266590i
$448$	62.4319	−	62.4319i	2.94963	−	2.94963i
$449$	−14.3882	−	30.8556i	−0.679022	−	1.45617i	−0.879222	−	0.476413i	$-0.841937\pi$
$449$	−14.3882	−	30.8556i	−0.679022	−	1.45617i	0.200200	−	0.979755i	$-0.435841\pi$
$450$	−24.5710	+	4.33253i	−1.15829	+	0.204237i
$451$	27.5529	−	19.2927i	1.29741	−	0.908459i
$452$	7.57013	+	10.8113i	0.356069	+	0.508519i
$453$	11.2327	+	0.982736i	0.527760	+	0.0461730i
$454$	−1.83762	+	10.4216i	−0.0862437	+	0.489112i
$455$	3.76048	+	1.00762i	0.176294	+	0.0472378i
$456$	22.3418	+	18.7470i	1.04625	+	0.877907i
$457$	−1.21652	−	3.34237i	−0.0569066	−	0.156350i	0.907982	−	0.419009i	$-0.137623\pi$
$457$	−1.21652	−	3.34237i	−0.0569066	−	0.156350i	−0.964889	+	0.262660i	$0.915400\pi$
$458$	−4.52101	+	9.69535i	−0.211253	+	0.453034i
$459$	−0.894311	+	3.33761i	−0.0417428	+	0.155786i
$460$	−8.57477	−	8.57477i	−0.399801	−	0.399801i
$461$	9.07102	−	24.9224i	0.422480	−	1.16075i	−0.527804	−	0.849366i	$-0.676984\pi$
$461$	9.07102	−	24.9224i	0.422480	−	1.16075i	0.950283	−	0.311387i	$-0.100793\pi$
$462$	35.8437	−	20.6944i	1.66760	−	0.962790i
$463$	10.2456	−	12.2102i	0.476152	−	0.567456i	−0.473487	−	0.880801i	$-0.657005\pi$
$463$	10.2456	−	12.2102i	0.476152	−	0.567456i	0.949640	+	0.313345i	$0.101449\pi$
$464$	14.7770	−	21.1037i	0.686003	−	0.979713i
$465$		−	1.31667i		−	0.0610590i
$466$	26.2160	+	18.3566i	1.21443	+	0.850354i
$467$	25.0386	+	11.6757i	1.15865	+	0.540285i	0.904329	−	0.426835i	$-0.140372\pi$
$467$	25.0386	+	11.6757i	1.15865	+	0.540285i	0.254317	+	0.967121i	$0.418149\pi$
$468$	−21.1665	+	5.67155i	−0.978422	+	0.262167i
$469$	1.13423	+	12.9644i	0.0523741	+	0.598638i
$470$	−0.419683	−	2.38014i	−0.0193585	−	0.109788i
$471$	0.590595	−	6.75053i	0.0272132	−	0.311048i
$472$	−63.4563	+	5.55171i	−2.92081	+	0.255538i
$473$	−2.93973	−	3.50343i	−0.135169	−	0.161088i
$474$	14.1314	+	5.14342i	0.649078	+	0.236245i
$475$	14.8463	+	5.40361i	0.681195	+	0.247935i
$476$	−10.0832	−	12.0167i	−0.462162	−	0.550783i
$477$	−2.72705	+	0.238586i	−0.124863	+	0.0109241i
$478$	5.97558	−	68.3012i	0.273317	−	3.12402i
$479$	3.61001	+	20.4734i	0.164946	+	0.935453i	0.949121	+	0.314913i	$0.101975\pi$
$479$	3.61001	+	20.4734i	0.164946	+	0.935453i	−0.784175	+	0.620540i	$0.786914\pi$
$480$	0.606300	+	6.93004i	0.0276737	+	0.316312i
$481$	−16.4259	+	4.40131i	−0.748957	+	0.200682i
$482$	−66.7053	−	31.1052i	−3.03834	−	1.41680i
$483$	22.2325	+	15.5673i	1.01161	+	0.708338i
$484$			0.344288i			0.0156494i
$485$	−0.421216	+	0.601558i	−0.0191264	+	0.0273153i
$486$	27.2642	−	32.4922i	1.23673	−	1.47388i
$487$	−24.8230	+	14.3316i	−1.12484	+	0.649426i	−0.942632	−	0.333834i	$-0.891658\pi$
$487$	−24.8230	+	14.3316i	−1.12484	+	0.649426i	−0.182207	+	0.983260i	$0.558324\pi$
$488$	−14.8044	+	40.6747i	−0.670162	+	1.84126i
$489$	−12.8983	−	12.8983i	−0.583279	−	0.583279i
$490$	3.56508	−	13.3051i	0.161054	−	0.601061i
$491$	0.0576991	−	0.123736i	0.00260392	−	0.00558413i	−0.905002	−	0.425408i	$-0.860130\pi$
$491$	0.0576991	−	0.123736i	0.00260392	−	0.00558413i	0.907605	+	0.419824i	$0.137908\pi$
$492$	−18.7036	−	51.3876i	−0.843222	−	2.31673i
$493$	−1.05225	−	0.882946i	−0.0473912	−	0.0397659i
$494$	18.5543	+	4.97160i	0.834796	+	0.223683i
$495$	0.441387	−	2.50323i	0.0198389	−	0.112512i
$496$	−40.1953	−	3.51664i	−1.80482	−	0.157902i
$497$	27.0583	+	38.6432i	1.21373	+	1.73339i
$498$	37.9136	−	26.5474i	1.69895	−	1.18962i
$499$	−5.57052	+	0.982233i	−0.249371	+	0.0439708i	−0.296936	−	0.954897i	$-0.595965\pi$
$499$	−5.57052	+	0.982233i	−0.249371	+	0.0439708i	0.0475654	+	0.998868i	$0.484854\pi$
$500$	8.61435	+	18.4735i	0.385245	+	0.826161i
$501$	−0.475616	+	0.475616i	−0.0212489	+	0.0212489i
$502$	−17.8398	−	30.8994i	−0.796227	−	1.37911i
$503$	5.66330	−	9.80913i	0.252514	−	0.437367i	−0.711703	−	0.702480i	$-0.752076\pi$
$503$	5.66330	−	9.80913i	0.252514	−	0.437367i	0.964217	+	0.265113i	$0.0854093\pi$
$504$	19.0616	+	71.1389i	0.849071	+	3.16878i
$505$	−4.36167	−	0.769081i	−0.194092	−	0.0342236i
$506$	−47.3799	+	22.0936i	−2.10629	+	0.982181i
$507$	−6.52027	+	5.47116i	−0.289575	+	0.242983i
$508$	−14.4338	−	8.33334i	−0.640395	−	0.369732i
$509$	15.4991	−	5.64122i	0.686986	−	0.250043i	0.0251420	−	0.999684i	$-0.491996\pi$
$509$	15.4991	−	5.64122i	0.686986	−	0.250043i	0.661844	+	0.749641i	$0.269774\pi$
$510$	0.750208			0.0332198
$511$	−34.5139	+	16.1595i	−1.52680	+	0.714853i
$512$	−4.82505			−0.213239
$513$	−15.6787	+	5.70658i	−0.692232	+	0.251952i
$514$	37.0566	+	21.3946i	1.63450	+	0.943676i
$515$	4.05330	−	3.40112i	0.178610	−	0.149871i
$516$	−6.73886	+	3.14238i	−0.296662	+	0.138336i
$517$	−7.41226	−	1.30698i	−0.325991	−	0.0574809i
$518$	24.0258	+	89.6655i	1.05563	+	3.93968i
$519$	−7.06319	+	12.2338i	−0.310039	+	0.537004i
$520$	3.75316	+	6.50067i	0.164587	+	0.285073i
$521$	24.3323	−	24.3323i	1.06602	−	1.06602i	0.0683546	−	0.997661i	$-0.478225\pi$
$521$	24.3323	−	24.3323i	1.06602	−	1.06602i	0.997661	−	0.0683546i	$-0.0217749\pi$
$522$	4.42677	+	9.49323i	0.193754	+	0.415507i
$523$	8.44431	−	1.48896i	0.369244	−	0.0651077i	0.0140526	−	0.999901i	$-0.495527\pi$
$523$	8.44431	−	1.48896i	0.369244	−	0.0651077i	0.355191	+	0.934794i	$0.384416\pi$
$524$	11.9020	−	8.33385i	0.519940	−	0.364066i
$525$	−12.8729	−	18.3843i	−0.561817	−	0.802358i
$526$	42.7233	+	3.73781i	1.86283	+	0.162976i
$527$	−0.373572	+	2.11863i	−0.0162731	+	0.0922892i
$528$	42.3253	+	11.3410i	1.84197	+	0.493555i
$529$	−8.64208	−	7.25156i	−0.375742	−	0.315285i
$530$	0.520908	+	1.43118i	0.0226268	+	0.0621667i
$531$	6.00993	−	12.8883i	0.260809	−	0.559306i
$532$	19.6046	−	73.1655i	0.849968	−	3.17213i
$533$	−15.6804	−	15.6804i	−0.679192	−	0.679192i
$534$	−3.01614	+	8.28676i	−0.130521	+	0.358603i
$535$	−1.94105	+	1.12067i	−0.0839190	+	0.0484506i
$536$	−16.1288	+	19.2216i	−0.696658	+	0.830245i
$537$	−6.98445	+	9.97483i	−0.301401	+	0.430446i
$538$		−	20.7799i		−	0.895886i
$539$	−35.1387	−	24.6044i	−1.51353	−	1.05978i
$540$	−9.59767	−	4.47547i	−0.413018	−	0.192593i
$541$	−3.84083	+	1.02915i	−0.165130	+	0.0442465i	−0.340437	−	0.940267i	$-0.610575\pi$
$541$	−3.84083	+	1.02915i	−0.165130	+	0.0442465i	0.175307	+	0.984514i	$0.443908\pi$
$542$	−2.14396	−	24.5056i	−0.0920909	−	1.05260i
$543$	−2.95841	−	16.7780i	−0.126957	−	0.720011i
$544$	0.990640	−	11.3231i	0.0424733	−	0.485473i
$545$	−0.739657	+	0.0647116i	−0.0316834	+	0.00277194i
$546$	−17.5396	−	20.9028i	−0.750624	−	0.894558i
$547$	17.7724	+	6.46862i	0.759893	+	0.276578i	0.692762	−	0.721166i	$-0.256393\pi$
$547$	17.7724	+	6.46862i	0.759893	+	0.276578i	0.0671303	+	0.997744i	$0.478616\pi$
$548$	20.4905	+	7.45794i	0.875312	+	0.318587i
$549$	−6.21150	−	7.40257i	−0.265100	−	0.315934i
$550$	43.0649	−	3.76769i	1.83629	−	0.160655i
$551$	0.578090	−	6.60760i	0.0246275	−	0.281493i
$552$	9.08701	+	51.5350i	0.386769	+	2.19347i
$553$	−2.09583	−	23.9555i	−0.0891239	−	1.01869i
$554$	−7.74758	+	2.07596i	−0.329163	+	0.0881990i
$555$	−2.90654	−	1.35534i	−0.123376	−	0.0575310i
$556$	73.3142	+	51.3352i	3.10922	+	2.17710i
$557$		−	36.2506i		−	1.53599i	−0.640458	−	0.767994i	$-0.721255\pi$
$557$		−	36.2506i		−	1.53599i	0.640458	−	0.767994i	$-0.278745\pi$
$558$	9.40952	−	13.4382i	0.398337	−	0.568884i
$559$	−1.93810	+	2.30974i	−0.0819729	+	0.0976914i
$560$	19.4850	−	11.2497i	0.823390	−	0.475385i
$561$	0.799063	−	2.19541i	0.0337365	−	0.0926902i
$562$	55.9649	+	55.9649i	2.36073	+	2.36073i
$563$	5.60552	−	20.9201i	0.236244	−	0.881676i	−0.741340	−	0.671130i	$-0.765809\pi$
$563$	5.60552	−	20.9201i	0.236244	−	0.881676i	0.977584	−	0.210546i	$-0.0675242\pi$
$564$	−5.17151	+	11.0903i	−0.217760	+	0.466988i
$565$	0.345204	+	0.948441i	0.0145229	+	0.0399012i
$566$	−49.1914	−	41.2765i	−2.06767	−	1.73498i
$567$	−1.92190	−	0.514973i	−0.0807124	−	0.0216268i
$568$	−15.7945	+	89.5753i	−0.662724	+	3.75849i
$569$	−2.87802	−	0.251794i	−0.120653	−	0.0105558i	0.0266694	−	0.999644i	$-0.491510\pi$
$569$	−2.87802	−	0.251794i	−0.120653	−	0.0105558i	−0.147322	+	0.989089i	$0.547065\pi$
$570$	2.07781	+	2.96742i	0.0870299	+	0.124292i
$571$	−8.11090	+	5.67932i	−0.339431	+	0.237672i	−0.730846	−	0.682542i	$-0.760874\pi$
$571$	−8.11090	+	5.67932i	−0.339431	+	0.237672i	0.391416	+	0.920214i	$0.371986\pi$
$572$	37.3908	−	6.59300i	1.56339	−	0.275667i
$573$	6.61989	+	14.1964i	0.276550	+	0.593063i
$574$	−85.5957	+	85.5957i	−3.57269	+	3.57269i
$575$	14.1739	+	24.5499i	0.591093	+	1.02380i
$576$	−19.0025	+	32.9133i	−0.791770	+	1.37139i
$577$	11.8599	+	44.2619i	0.493736	+	1.84265i	0.536997	+	0.843584i	$0.319559\pi$
$577$	11.8599	+	44.2619i	0.493736	+	1.84265i	−0.0432607	+	0.999064i	$0.513775\pi$
$578$	43.7285	+	7.71051i	1.81887	+	0.320715i
$579$	2.58994	−	1.20771i	0.107634	−	0.0501906i
$580$	3.22492	−	2.70603i	0.133907	−	0.112362i
$581$	−64.0947	−	37.0051i	−2.65910	−	1.53523i
$582$	4.83672	−	1.76042i	0.200488	−	0.0729718i
$583$	4.74305			0.196437
$584$	−69.0864	−	25.0238i	−2.85882	−	1.03549i
$585$	−1.67578			−0.0692851
$586$	10.9813	−	3.99686i	0.453632	−	0.165109i
$587$	−24.0165	−	13.8659i	−0.991266	−	0.572308i	−0.0856136	−	0.996328i	$-0.527285\pi$
$587$	−24.0165	−	13.8659i	−0.991266	−	0.572308i	−0.905653	+	0.424021i	$0.860618\pi$
$588$	−53.4251	+	44.8290i	−2.20321	+	1.84872i
$589$	−9.41484	+	4.39021i	−0.387932	+	0.180895i
$590$	−7.79171	−	1.37389i	−0.320780	−	0.0565621i
$591$	−2.31951	−	8.65652i	−0.0954118	−	0.356082i
$592$	−49.1389	+	85.1110i	−2.01960	+	3.49804i
$593$	7.88446	+	13.6563i	0.323776	+	0.560797i	0.981264	−	0.192669i	$-0.0617142\pi$
$593$	7.88446	+	13.6563i	0.323776	+	0.560797i	−0.657488	+	0.753465i	$0.728381\pi$
$594$	−32.2817	+	32.2817i	−1.32453	+	1.32453i
$595$	−0.506980	−	1.08722i	−0.0207841	−	0.0445717i
$596$	32.0956	−	5.65932i	1.31469	−	0.231815i
$597$	16.1903	−	11.3366i	0.662627	−	0.463976i
$598$	19.7687	+	28.2326i	0.808403	+	1.15452i
$599$	1.36992	+	0.119852i	0.0559734	+	0.00489704i	0.115108	−	0.993353i	$-0.463279\pi$
$599$	1.36992	+	0.119852i	0.0559734	+	0.00489704i	−0.0591346	+	0.998250i	$0.518834\pi$
$600$	7.51418	−	42.6150i	0.306765	−	1.73975i
$601$	22.9779	+	6.15692i	0.937289	+	0.251146i	0.694960	−	0.719048i	$-0.255422\pi$
$601$	22.9779	+	6.15692i	0.937289	+	0.251146i	0.242329	+	0.970194i	$0.422089\pi$
$602$	12.6084	+	10.5797i	0.513878	+	0.431195i
$603$	−1.91592	−	5.26394i	−0.0780222	−	0.214364i
$604$	23.8625	−	51.1733i	0.970951	−	2.08221i
$605$	−0.00681444	+	0.0254318i	−0.000277046	+	0.00103395i
$606$	21.9502	+	21.9502i	0.891665	+	0.891665i
$607$	13.3297	−	36.6229i	0.541034	−	1.48648i	−0.304476	−	0.952520i	$-0.598481\pi$
$607$	13.3297	−	36.6229i	0.541034	−	1.48648i	0.845510	−	0.533959i	$-0.179296\pi$
$608$	47.5317	−	27.4424i	1.92766	−	1.11294i
$609$	−6.05645	+	7.21779i	−0.245420	+	0.292480i
$610$	−3.08376	+	4.40406i	−0.124858	+	0.178315i
$611$			4.96212i			0.200746i
$612$	5.53112	+	3.87293i	0.223582	+	0.156554i
$613$	−42.3218	−	19.7350i	−1.70936	−	0.797088i	−0.995282	−	0.0970224i	$-0.969068\pi$
$613$	−42.3218	−	19.7350i	−1.70936	−	0.797088i	−0.714079	−	0.700066i	$-0.753154\pi$
$614$	78.4329	−	21.0160i	3.16529	−	0.848138i
$615$	−0.364486	−	4.16610i	−0.0146975	−	0.167993i
$616$	−22.1585	−	125.667i	−0.892793	−	5.06328i
$617$	−3.71430	+	42.4547i	−0.149532	+	1.70916i	0.437187	+	0.899370i	$0.355975\pi$
$617$	−3.71430	+	42.4547i	−0.149532	+	1.70916i	−0.586720	+	0.809790i	$0.699581\pi$
$618$	−36.9446	+	3.23223i	−1.48613	+	0.130019i
$619$	−15.8257	−	18.8603i	−0.636088	−	0.758060i	0.347659	−	0.937621i	$-0.386977\pi$
$619$	−15.8257	−	18.8603i	−0.636088	−	0.758060i	−0.983747	+	0.179561i	$0.942532\pi$
$620$	−6.19567	−	2.25504i	−0.248824	−	0.0905646i
$621$	−28.1318	−	10.2391i	−1.12889	−	0.410882i
$622$	−6.25753	−	7.45743i	−0.250904	−	0.299016i
$623$	14.0477	−	1.22901i	0.562807	−	0.0492393i
$624$	2.51780	−	28.7786i	0.100793	−	1.15206i
$625$	−3.93301	−	22.3052i	−0.157320	−	0.892207i
$626$	6.09888	+	69.7105i	0.243760	+	2.78619i
$627$	10.8970	−	2.91983i	0.435183	−	0.116607i
$628$	−30.7536	−	14.3406i	−1.22720	−	0.572254i
$629$	4.29233	+	3.00552i	0.171146	+	0.119838i
$630$			9.14774i			0.364455i
$631$	−16.3263	+	23.3164i	−0.649939	+	0.928210i	−0.999964	−	0.00853099i	$-0.997284\pi$
$631$	−16.3263	+	23.3164i	−0.649939	+	0.928210i	0.350024	+	0.936741i	$0.386173\pi$
$632$	29.8027	−	35.5175i	1.18549	−	1.41281i
$633$	−18.4720	+	10.6648i	−0.734198	+	0.423889i
$634$	28.9432	−	79.5209i	1.14948	−	3.15818i
$635$	−0.901252	−	0.901252i	−0.0357651	−	0.0357651i
$636$	1.99583	−	7.44855i	0.0791399	−	0.295354i
$637$	−11.9519	+	25.6310i	−0.473552	+	1.01554i
$638$	−6.20723	−	17.0542i	−0.245746	−	0.675183i
$639$	−15.5554	−	13.0525i	−0.615362	−	0.516350i
$640$	7.49280	+	2.00769i	0.296179	+	0.0793609i
$641$	−0.795249	+	4.51008i	−0.0314105	+	0.178138i	−0.996477	−	0.0838677i	$-0.973273\pi$
$641$	−0.795249	+	4.51008i	−0.0314105	+	0.178138i	0.965066	+	0.262005i	$0.0843838\pi$
$642$	15.6496	+	1.36916i	0.617639	+	0.0540364i
$643$	12.3191	+	17.5935i	0.485819	+	0.693821i	0.984976	−	0.172690i	$-0.0552459\pi$
$643$	12.3191	+	17.5935i	0.485819	+	0.693821i	−0.499157	+	0.866511i	$0.666357\pi$
$644$	111.330	−	77.9544i	4.38703	−	3.07183i
$645$	−0.559982	+	0.0987400i	−0.0220493	+	0.00388788i
$646$	−2.50145	−	5.36437i	−0.0984181	−	0.211058i
$647$	18.0694	−	18.0694i	0.710382	−	0.710382i	−0.256233	−	0.966615i	$-0.582481\pi$
$647$	18.0694	−	18.0694i	0.710382	−	0.710382i	0.966615	+	0.256233i	$0.0824813\pi$
$648$	−1.91816	−	3.32236i	−0.0753526	−	0.130515i
$649$	−12.3197	+	21.3383i	−0.483589	+	0.837601i
$650$	−7.37639	−	27.5291i	−0.289326	−	1.07978i
$651$	14.5325	+	2.56247i	0.569573	+	0.100431i
$652$	−82.7843	+	38.6030i	−3.24208	+	1.51181i
$653$	22.9229	−	19.2346i	0.897041	−	0.752707i	−0.0725686	−	0.997363i	$-0.523120\pi$
$653$	22.9229	−	19.2346i	0.897041	−	0.752707i	0.969610	+	0.244656i	$0.0786752\pi$
$654$	4.50680	+	2.60200i	0.176230	+	0.101746i
$655$	1.04413	−	0.380031i	0.0407974	−	0.0148490i
$656$	−128.156			−5.00367
$657$	12.5499	−	10.5639i	0.489616	−	0.412136i
$658$	27.0872			1.05597
$659$	−31.0375	+	11.2967i	−1.20905	+	0.440058i	−0.866374	−	0.499395i	$-0.833555\pi$
$659$	−31.0375	+	11.2967i	−1.20905	+	0.440058i	−0.342676	+	0.939454i	$0.611333\pi$
$660$	6.20095	+	3.58012i	0.241372	+	0.139356i
$661$	−23.0857	+	19.3712i	−0.897931	+	0.753453i	−0.969785	−	0.243962i	$-0.921553\pi$
$661$	−23.0857	+	19.3712i	−0.897931	+	0.753453i	0.0718540	+	0.997415i	$0.477108\pi$
$662$	49.8068	−	23.2253i	1.93580	−	0.902677i
$663$	−1.51687	−	0.267466i	−0.0589105	−	0.0103875i
$664$	−36.9331	−	137.836i	−1.43328	−	5.34908i
$665$	2.89631	−	5.01655i	0.112314	−	0.194534i
$666$	−19.9788	−	34.6043i	−0.774164	−	1.34089i
$667$	8.41533	−	8.41533i	0.325843	−	0.325843i
$668$	1.42346	+	3.05262i	0.0550754	+	0.118110i
$669$	11.4309	−	2.01557i	0.441942	−	0.0779264i
$670$	−2.55299	+	1.78763i	−0.0986308	+	0.0690620i
$671$	9.60346	+	13.7152i	0.370737	+	0.529468i
$672$	−77.6690	−	6.79516i	−2.99615	−	0.262129i
$673$	−4.19823	+	23.8093i	−0.161830	+	0.917783i	0.790443	+	0.612535i	$0.209850\pi$
$673$	−4.19823	+	23.8093i	−0.161830	+	0.917783i	−0.952273	+	0.305247i	$0.901261\pi$
$674$	22.8286	+	6.11690i	0.879324	+	0.235614i
$675$	18.9638	+	15.9125i	0.729918	+	0.612474i
$676$	14.5777	+	40.0520i	0.560682	+	1.54046i
$677$	4.02407	−	8.62965i	0.154658	−	0.331664i	−0.813678	−	0.581316i	$-0.802538\pi$
$677$	4.02407	−	8.62965i	0.154658	−	0.331664i	0.968336	+	0.249651i	$0.0803159\pi$
$678$	1.83093	−	6.83314i	0.0703166	−	0.262425i
$679$	−5.81983	−	5.81983i	−0.223344	−	0.223344i
$680$	0.791083	−	2.17348i	0.0303366	−	0.0833492i
$681$	3.54851	−	2.04873i	0.135979	−	0.0785077i
$682$	−18.2705	+	21.7740i	−0.699615	+	0.833769i
$683$	6.98843	−	9.98051i	0.267405	−	0.381894i	−0.662884	−	0.748722i	$-0.730668\pi$
$683$	6.98843	−	9.98051i	0.267405	−	0.381894i	0.930288	+	0.366829i	$0.119557\pi$
$684$			32.6047i			1.24667i
$685$	1.36598	+	0.956469i	0.0521914	+	0.0365448i
$686$	63.9623	+	29.8261i	2.44209	+	1.13877i
$687$	4.00094	−	1.07205i	0.152645	−	0.0409012i
$688$	1.51871	+	17.3589i	0.0579002	+	0.661802i
$689$	−0.542995	−	3.07948i	−0.0206865	−	0.117319i
$690$	−0.566497	+	6.47509i	−0.0215662	+	0.246502i
$691$	27.4681	−	2.40315i	1.04494	−	0.0914200i	0.448261	−	0.893903i	$-0.352044\pi$
$691$	27.4681	−	2.40315i	1.04494	−	0.0914200i	0.596675	+	0.802483i	$0.296488\pi$
$692$	45.4700	+	54.1890i	1.72851	+	2.05996i
$693$	26.7699	+	9.74346i	1.01691	+	0.370123i
$694$	19.8488	+	7.22438i	0.753451	+	0.274234i
$695$	4.39950	+	5.24312i	0.166883	+	0.198883i
$696$	−18.0977	+	1.58334i	−0.685990	+	0.0600164i
$697$	−0.595538	+	6.80704i	−0.0225576	+	0.257835i
$698$	−11.1989	−	63.5121i	−0.423885	−	2.40397i
$699$	−1.08001	−	12.3446i	−0.0408497	−	0.466915i
$700$	−108.556	+	29.0875i	−4.10303	+	1.09940i
$701$	15.8665	+	7.39867i	0.599269	+	0.279444i	0.698488	−	0.715622i	$-0.253857\pi$
$701$	15.8665	+	7.39867i	0.599269	+	0.279444i	−0.0992187	+	0.995066i	$0.531634\pi$
$702$	24.6550	+	17.2636i	0.930542	+	0.651572i
$703$			25.3024i			0.954297i
$704$	37.7693	−	53.9402i	1.42348	−	2.03295i
$705$	−0.601519	+	0.716863i	−0.0226545	+	0.0269986i
$706$	−23.4824	+	13.5576i	−0.883772	+	0.510246i
$707$	16.9772	−	46.6444i	0.638492	−	1.75424i
$708$	28.3259	+	28.3259i	1.06455	+	1.06455i
$709$	8.97810	−	33.5067i	0.337180	−	1.25837i	−0.564307	−	0.825565i	$-0.690857\pi$
$709$	8.97810	−	33.5067i	0.337180	−	1.25837i	0.901487	−	0.432807i	$-0.142477\pi$
$710$	−4.77459	+	10.2391i	−0.179187	+	0.384268i
$711$	3.54023	+	9.72669i	0.132769	+	0.364779i
$712$	20.8277	+	17.4765i	0.780551	+	0.654960i
$713$	−18.0040	−	4.82415i	−0.674254	−	0.180666i
$714$	−1.46004	+	8.28029i	−0.0546406	+	0.309882i
$715$	2.89248	+	0.253059i	0.108172	+	0.00946387i
$716$	34.9751	+	49.9496i	1.30708	+	1.86670i
$717$	−21.7460	+	15.2267i	−0.812119	+	0.568652i
$718$	−37.0029	+	6.52461i	−1.38094	+	0.243496i
$719$	−0.00565396	−	0.0121250i	−0.000210857	−	0.000452185i	0.906202	−	0.422844i	$-0.138968\pi$
$719$	−0.00565396	−	0.0121250i	−0.000210857	−	0.000452185i	−0.906413	+	0.422392i	$0.861191\pi$
$720$	−6.84814	+	6.84814i	−0.255215	+	0.255215i
$721$	29.6508	+	51.3568i	1.10426	+	1.91263i
$722$	−11.2080	+	19.4129i	−0.417120	+	0.722473i
$723$	7.37584	+	27.5270i	0.274310	+	1.02374i
$724$	−84.0167	−	14.8144i	−3.12246	−	0.550573i
$725$	−8.91913	+	4.15906i	−0.331248	+	0.154464i
$726$	0.141364	−	0.118619i	0.00524652	−	0.00440235i
$727$	−6.97165	−	4.02508i	−0.258564	−	0.149282i	0.365115	−	0.930962i	$-0.381030\pi$
$727$	−6.97165	−	4.02508i	−0.258564	−	0.149282i	−0.623679	+	0.781680i	$0.714363\pi$
$728$	−79.0542	+	28.7734i	−2.92994	+	1.06641i
$729$	−15.0849			−0.558699
$730$	−7.48426	−	5.22321i	−0.277005	−	0.193320i
$731$	0.929076			0.0343631
$732$	25.5795	−	9.31019i	0.945447	−	0.344115i
$733$	−31.4106	−	18.1349i	−1.16018	−	0.669829i	−0.208831	−	0.977952i	$-0.566966\pi$
$733$	−31.4106	−	18.1349i	−1.16018	−	0.669829i	−0.951347	+	0.308123i	$0.900299\pi$
$734$	−67.7353	+	56.8366i	−2.50015	+	2.09788i
$735$	−4.83370	+	2.25399i	−0.178294	+	0.0831397i
$736$	96.9820	+	17.1005i	3.57480	+	0.630334i
$737$	2.51206	+	9.37512i	0.0925327	+	0.345337i
$738$	26.0529	−	45.1249i	0.959019	−	1.66107i
$739$	−6.94531	−	12.0296i	−0.255487	−	0.442517i	0.709540	−	0.704665i	$-0.248903\pi$
$739$	−6.94531	−	12.0296i	−0.255487	−	0.442517i	−0.965028	+	0.262148i	$0.915569\pi$
$740$	−11.3556	+	11.3556i	−0.417442	+	0.417442i
$741$	−3.14325	−	6.74072i	−0.115470	−	0.247627i
$742$	−16.8102	+	2.96409i	−0.617122	+	0.108815i
$743$	−11.0477	+	7.73567i	−0.405300	+	0.283794i	−0.758397	−	0.651792i	$-0.774017\pi$
$743$	−11.0477	+	7.73567i	−0.405300	+	0.283794i	0.353097	+	0.935587i	$0.385128\pi$
$744$	16.3195	+	23.3067i	0.598303	+	0.854465i
$745$	2.48285	+	0.217221i	0.0909646	+	0.00795837i
$746$	−9.97255	+	56.5571i	−0.365121	+	2.07070i
$747$	30.7719	+	8.24530i	1.12588	+	0.301680i
$748$	−8.96210	−	7.52010i	−0.327687	−	0.274962i
$749$	−8.59152	−	23.6050i	−0.313927	−	0.862509i
$750$	4.61728	−	9.90180i	0.168599	−	0.361563i
$751$	−10.2502	+	38.2541i	−0.374033	+	1.39591i	0.480719	+	0.876875i	$0.340376\pi$
$751$	−10.2502	+	38.2541i	−0.374033	+	1.39591i	−0.854752	+	0.519037i	$0.826291\pi$
$752$	20.2779	+	20.2779i	0.739458	+	0.739458i
$753$	−4.72499	+	12.9818i	−0.172188	+	0.473084i
$754$	−10.3620	+	5.98252i	−0.377363	+	0.217871i
$755$	2.77554	−	3.30776i	0.101012	−	0.120382i
$756$	68.0759	−	97.2225i	2.47590	−	3.53595i
$757$			11.3102i			0.411076i	0.978649	+	0.205538i	$0.0658945\pi$
$757$			11.3102i			0.411076i	−0.978649	+	0.205538i	$0.934106\pi$
$758$	12.8163	+	8.97410i	0.465511	+	0.325954i
$759$	18.3453	+	8.55455i	0.665892	+	0.310511i
$760$	10.7881	−	2.89067i	0.391327	−	0.104856i
$761$	−2.19438	−	25.0819i	−0.0795462	−	0.909217i	−0.926190	−	0.377057i	$-0.876936\pi$
$761$	−2.19438	−	25.0819i	−0.0795462	−	0.909217i	0.846644	−	0.532160i	$-0.178620\pi$
$762$	1.55126	+	8.79761i	0.0561961	+	0.318704i
$763$	0.725261	−	8.28977i	0.0262562	−	0.300110i
$764$	78.1400	−	6.83636i	2.82701	−	0.247331i
$765$	0.331916	+	0.395562i	0.0120005	+	0.0143016i
$766$	−54.6308	−	19.8840i	−1.97389	−	0.718438i
$767$	15.2645	+	5.55583i	0.551170	+	0.200609i
$768$	−8.50127	−	10.1314i	−0.306763	−	0.365586i
$769$	−0.939518	+	0.0821972i	−0.0338799	+	0.00296411i	−0.104083	−	0.994569i	$-0.533191\pi$
$769$	−0.939518	+	0.0821972i	−0.0338799	+	0.00296411i	0.0702032	+	0.997533i	$0.477635\pi$
$770$	1.38139	−	15.7894i	0.0497820	−	0.569011i
$771$	−2.87697	−	16.3161i	−0.103612	−	0.587610i
$772$	−1.24720	−	14.2556i	−0.0448877	−	0.513069i
$773$	42.9545	−	11.5096i	1.54497	−	0.413972i	0.617100	−	0.786885i	$-0.288308\pi$
$773$	42.9545	−	11.5096i	1.54497	−	0.413972i	0.927866	+	0.372913i	$0.121641\pi$
$774$	−6.42094	−	2.99413i	−0.230796	−	0.107622i
$775$	12.6255	+	8.84049i	0.453522	+	0.317560i
$776$		−	15.8691i		−	0.569668i
$777$	20.6160	−	29.4426i	0.739593	−	1.05625i
$778$	−9.45662	+	11.2700i	−0.339036	+	0.404048i
$779$	−28.5744	+	16.4974i	−1.02378	+	0.591082i
$780$	1.61454	−	4.43590i	0.0578097	−	0.158831i
$781$	24.8783	+	24.8783i	0.890214	+	0.890214i
$782$	2.74869	−	10.2583i	0.0982931	−	0.366835i
$783$	4.39225	−	9.41922i	0.156966	−	0.336615i
$784$	55.8998	+	153.584i	1.99642	+	5.48513i
$785$	−1.98786	−	1.66802i	−0.0709499	−	0.0595341i
$786$	−7.52250	−	2.01565i	−0.268319	−	0.0718958i
$787$	6.75284	−	38.2973i	0.240713	−	1.36515i	−0.589529	−	0.807747i	$-0.700687\pi$
$787$	6.75284	−	38.2973i	0.240713	−	1.36515i	0.830242	−	0.557403i	$-0.188202\pi$
$788$	−44.7065	−	3.91131i	−1.59260	−	0.139335i
$789$	−9.52451	−	13.6024i	−0.339082	−	0.484259i
$790$	4.71741	−	3.30317i	0.167838	−	0.117521i
$791$	−11.1401	+	1.96430i	−0.396096	+	0.0698423i
$792$	23.2133	+	49.7812i	0.824850	+	1.76890i
$793$	7.80531	−	7.80531i	0.277175	−	0.277175i
$794$	−52.2103	−	90.4309i	−1.85287	−	3.20927i
$795$	0.294856	−	0.510706i	0.0104575	−	0.0181129i
$796$	−25.6162	−	95.6009i	−0.907941	−	3.38848i
$797$	17.7764	+	3.13446i	0.629672	+	0.111028i	0.479371	−	0.877612i	$-0.340865\pi$
$797$	17.7764	+	3.13446i	0.629672	+	0.111028i	0.150301	+	0.988640i	$0.451976\pi$
$798$	−36.7961	+	17.1583i	−1.30257	+	0.607398i
$799$	1.17129	−	0.982829i	0.0414373	−	0.0347700i
$800$	−70.5230	−	40.7165i	−2.49336	−	1.43954i
$801$	−5.70380	+	2.07601i	−0.201534	+	0.0733523i
$802$	89.3926			3.15656
$803$	−23.2568	+	16.3386i	−0.820716	+	0.576575i
$804$	15.7799			0.556513
$805$	9.76670	−	3.55479i	0.344231	−	0.125290i
$806$	16.2287	+	9.36963i	0.571631	+	0.330031i
$807$	−6.16351	+	5.17180i	−0.216966	+	0.182056i
$808$	86.7396	−	40.4473i	3.05149	−	1.42293i
$809$	−34.0689	−	6.00727i	−1.19780	−	0.211204i	−0.461053	−	0.887373i	$-0.652528\pi$
$809$	−34.0689	−	6.00727i	−1.19780	−	0.211204i	−0.736747	+	0.676168i	$0.763639\pi$
$810$	−0.123328	−	0.460267i	−0.00433331	−	0.0161721i
$811$	−6.48921	+	11.2396i	−0.227867	+	0.394677i	−0.957176	−	0.289508i	$-0.906508\pi$
$811$	−6.48921	+	11.2396i	−0.227867	+	0.394677i	0.729309	+	0.684185i	$0.239842\pi$
$812$	23.5910	+	40.8609i	0.827883	+	1.43394i
$813$	−6.73497	+	6.73497i	−0.236206	+	0.236206i
$814$	29.2588	+	62.7456i	1.02552	+	2.19923i
$815$	−6.87917	+	1.21298i	−0.240967	+	0.0424890i
$816$	−7.29176	+	5.10574i	−0.255263	+	0.178737i
$817$	2.57321	+	3.67492i	0.0900252	+	0.128569i
$818$	−24.5185	−	2.14509i	−0.857269	−	0.0750014i
$819$	3.26137	−	18.4962i	0.113962	−	0.646308i
$820$	−20.2281	−	5.42011i	−0.706397	−	0.189278i
$821$	18.1365	+	15.2183i	0.632968	+	0.531123i	0.901850	−	0.432050i	$-0.142210\pi$
$821$	18.1365	+	15.2183i	0.632968	+	0.531123i	−0.268882	+	0.963173i	$0.586654\pi$
$822$	−3.99745	−	10.9829i	−0.139427	−	0.383073i
$823$	−9.35797	+	20.0682i	−0.326198	+	0.699535i	−0.999195	−	0.0401107i	$-0.987229\pi$
$823$	−9.35797	+	20.0682i	−0.326198	+	0.699535i	0.672997	+	0.739645i	$0.265007\pi$
$824$	−29.5931	+	110.443i	−1.03093	+	3.84747i
$825$	−11.8357	−	11.8357i	−0.412067	−	0.412067i
$826$	30.3281	−	83.3257i	1.05525	−	2.89927i
$827$	24.4938	−	14.1415i	0.851734	−	0.491749i	−0.00950144	−	0.999955i	$-0.503024\pi$
$827$	24.4938	−	14.1415i	0.851734	−	0.491749i	0.861236	+	0.508206i	$0.169691\pi$
$828$	−37.6041	+	44.8148i	−1.30683	+	1.55742i
$829$	−27.9677	+	39.9420i	−0.971359	+	1.38724i	−0.0499065	+	0.998754i	$0.515892\pi$
$829$	−27.9677	+	39.9420i	−0.971359	+	1.38724i	−0.921453	+	0.388491i	$0.872997\pi$
$830$		−	17.7243i		−	0.615221i
$831$	2.54400	+	1.78133i	0.0882504	+	0.0617936i
$832$	−39.3452	−	18.3470i	−1.36405	−	0.636067i
$833$	8.41736	−	2.25542i	0.291644	−	0.0781458i
$834$	−4.18103	−	47.7894i	−0.144777	−	1.65481i
$835$	0.0447281	+	0.253666i	0.00154788	+	0.00877846i
$836$	4.92362	−	56.2772i	0.170287	−	1.94639i
$837$	−16.2152	+	1.41864i	−0.560478	+	0.0490355i
$838$	−47.1604	−	56.2036i	−1.62913	−	1.94152i
$839$	42.7791	+	15.5703i	1.47690	+	0.537547i	0.949964	−	0.312360i	$-0.101119\pi$
$839$	42.7791	+	15.5703i	1.47690	+	0.537547i	0.526933	+	0.849907i	$0.323342\pi$
$840$	−14.9087	−	5.42632i	−0.514399	−	0.187226i
$841$	−15.9851	−	19.0503i	−0.551211	−	0.656908i
$842$	−81.5571	+	7.13532i	−2.81064	+	0.245899i
$843$	2.67090	−	30.5285i	0.0919905	−	1.05146i
$844$	18.5473	+	105.187i	0.638425	+	3.62069i
$845$	0.284084	+	3.24709i	0.00977278	+	0.111703i
$846$	−11.2623	+	3.01771i	−0.387205	+	0.103751i
$847$	−0.267437	−	0.124708i	−0.00918925	−	0.00428502i
$848$	−14.8034	−	10.3654i	−0.508349	−	0.355950i
$849$			24.8637i			0.853319i
$850$	−5.03711	+	7.19375i	−0.172772	+	0.246743i
$851$	−29.1820	+	34.7778i	−1.00035	+	1.19217i
$852$	49.5377	−	28.6006i	1.69713	−	0.979841i
$853$	5.66911	−	15.5758i	0.194107	−	0.533304i	−0.804012	−	0.594613i	$-0.797305\pi$
$853$	5.66911	−	15.5758i	0.194107	−	0.533304i	0.998119	+	0.0613091i	$0.0195276\pi$
$854$	−42.6075	−	42.6075i	−1.45800	−	1.45800i
$855$	−0.645341	+	2.40845i	−0.0220702	+	0.0823672i
$856$	20.4689	−	43.8957i	0.699613	−	1.50032i
$857$	−7.78278	−	21.3830i	−0.265855	−	0.730430i	−0.998745	−	0.0500830i	$-0.984051\pi$
$857$	−7.78278	−	21.3830i	−0.265855	−	0.730430i	0.732890	−	0.680347i	$-0.238171\pi$
$858$	−15.5895	−	13.0811i	−0.532215	−	0.446582i
$859$	20.7245	+	5.55310i	0.707110	+	0.189469i	0.594413	−	0.804160i	$-0.297384\pi$
$859$	20.7245	+	5.55310i	0.707110	+	0.189469i	0.112697	+	0.993629i	$0.464051\pi$
$860$	−0.494447	+	2.80415i	−0.0168605	+	0.0956207i
$861$	46.6919	+	4.08501i	1.59126	+	0.139217i
$862$	−13.3396	−	19.0509i	−0.454349	−	0.648877i
$863$	−39.3060	+	27.5224i	−1.33799	+	0.936872i	−0.999991	−	0.00427326i	$-0.998640\pi$
$863$	−39.3060	+	27.5224i	−1.33799	+	0.936872i	−0.338001	+	0.941146i	$0.609751\pi$
$864$	84.6923	−	14.9335i	2.88129	−	0.508049i
$865$	2.28622	+	4.90281i	0.0777338	+	0.166701i
$866$	−23.8185	+	23.8185i	−0.809384	+	0.809384i
$867$	−8.59634	−	14.8893i	−0.291947	−	0.505667i
$868$	36.9475	−	63.9949i	1.25408	−	2.17213i
$869$	−4.64177	−	17.3233i	−0.157461	−	0.587653i
$870$	−2.22219	−	0.391831i	−0.0753392	−	0.0132843i
$871$	5.79932	−	2.70427i	0.196503	−	0.0916306i
$872$	12.2908	−	10.3132i	0.416219	−	0.349249i
$873$	3.06813	+	1.77139i	0.103841	+	0.0599524i
$874$	48.1890	−	17.5394i	1.63002	−	0.593278i
$875$	−17.4702			−0.590602
$876$	15.8720	+	43.3980i	0.536266	+	1.46628i
$877$	2.96049			0.0999686			0.0499843	−	0.998750i	$-0.484083\pi$
$877$	2.96049			0.0999686			0.0499843	+	0.998750i	$0.484083\pi$
$878$	48.3004	−	17.5799i	1.63006	−	0.593294i
$879$	−3.91857	−	2.26239i	−0.132170	−	0.0763085i
$880$	12.8543	−	10.7861i	0.433319	−	0.363598i
$881$	0.125152	−	0.0583594i	0.00421649	−	0.00196618i	−0.420509	−	0.907288i	$-0.638148\pi$
$881$	0.125152	−	0.0583594i	0.00421649	−	0.00196618i	0.424725	+	0.905322i	$0.360371\pi$
$882$	−65.4418	−	11.5391i	−2.20354	−	0.388543i
$883$	1.53659	+	5.73462i	0.0517103	+	0.192985i	0.986949	−	0.161032i	$-0.0514821\pi$
$883$	1.53659	+	5.73462i	0.0517103	+	0.192985i	−0.935239	+	0.354017i	$0.884815\pi$
$884$	−3.85651	+	6.67967i	−0.129709	+	0.224662i
$885$	1.53173	+	2.65303i	0.0514885	+	0.0891807i
$886$	−20.3285	+	20.3285i	−0.682949	+	0.682949i
$887$	−5.95311	−	12.7665i	−0.199886	−	0.428657i	0.780657	−	0.624959i	$-0.214884\pi$
$887$	−5.95311	−	12.7665i	−0.199886	−	0.428657i	−0.980543	+	0.196302i	$0.937107\pi$
$888$	68.2482	−	12.0340i	2.29026	−	0.403835i
$889$	11.7014	−	8.19341i	0.392453	−	0.274798i
$890$	1.93700	+	2.76632i	0.0649284	+	0.0927273i
$891$	−1.47829	−	0.129333i	−0.0495244	−	0.00433283i
$892$	10.0931	−	57.2407i	0.337942	−	1.91656i
$893$	7.13160	+	1.91091i	0.238650	+	0.0639460i
$894$	−13.3817	−	11.2286i	−0.447552	−	0.375540i
$895$	1.59489	+	4.38193i	0.0533114	+	0.146472i
$896$	−36.7418	+	78.7931i	−1.22746	+	2.63229i
$897$	3.45393	−	12.8903i	0.115323	−	0.430393i
$898$	64.6152	+	64.6152i	2.15624	+	2.15624i
$899$	2.21311	−	6.08048i	0.0738114	−	0.202795i
$900$	41.8947	−	24.1879i	1.39649	−	0.806264i
$901$	−0.619350	+	0.738113i	−0.0206335	+	0.0245901i
$902$	−51.7826	+	73.9533i	−1.72417	+	2.46238i
$903$		−	6.37287i		−	0.212076i
$904$	−17.8661	−	12.5100i	−0.594217	−	0.416075i
$905$	−5.91292	−	2.75724i	−0.196552	−	0.0916538i
$906$	−29.2331	+	7.83299i	−0.971206	+	0.260234i
$907$	0.368796	+	4.21536i	0.0122457	+	0.139969i	0.999856	−	0.0169560i	$-0.00539752\pi$
$907$	0.368796	+	4.21536i	0.0122457	+	0.139969i	−0.987611	+	0.156925i	$0.949842\pi$
$908$	−3.56297	−	20.2066i	−0.118241	−	0.670580i
$909$	−1.86221	+	21.2851i	−0.0617655	+	0.705983i
$910$	−10.4096	+	0.910722i	−0.345075	+	0.0301902i
$911$	−0.851834	−	1.01518i	−0.0282225	−	0.0336343i	0.751749	−	0.659450i	$-0.229211\pi$
$911$	−0.851834	−	1.01518i	−0.0282225	−	0.0336343i	−0.779971	+	0.625816i	$0.784766\pi$
$912$	−40.3911	−	14.7012i	−1.33748	−	0.486804i
$913$	−51.8685	−	18.8786i	−1.71660	−	0.624790i
$914$	6.13659	+	7.31331i	0.202981	+	0.241903i
$915$	2.07378	−	0.181433i	0.0685572	−	0.00599798i
$916$	1.80776	−	20.6628i	0.0597301	−	0.682718i
$917$	2.16247	+	12.2639i	0.0714109	+	0.404991i
$918$	−0.808311	−	9.23904i	−0.0266783	−	0.304934i
$919$	23.2675	−	6.23451i	0.767524	−	0.205658i	0.146247	−	0.989248i	$-0.453281\pi$
$919$	23.2675	−	6.23451i	0.767524	−	0.205658i	0.621278	+	0.783591i	$0.286614\pi$
$920$	18.1621	+	8.46912i	0.598786	+	0.279218i
$921$	−25.7543	−	18.0333i	−0.848632	−	0.594219i
$922$			71.1861i			2.34439i
$923$	13.3044	−	19.0006i	0.437919	−	0.625413i
$924$	−51.5831	+	61.4743i	−1.69696	+	2.02236i
$925$	32.5117	−	18.7706i	1.06898	−	0.617174i
$926$	−14.6323	+	40.2018i	−0.480846	+	1.32111i
$927$	−18.0497	−	18.0497i	−0.592831	−	0.592831i
$928$	−8.84837	+	33.0226i	−0.290462	+	1.08402i
$929$	−18.4582	+	39.5836i	−0.605592	+	1.29870i	0.329454	+	0.944172i	$0.393135\pi$
$929$	−18.4582	+	39.5836i	−0.605592	+	1.29870i	−0.935046	+	0.354525i	$0.884642\pi$
$930$	1.20870	+	3.32088i	0.0396348	+	0.108896i
$931$	32.2343	+	27.0478i	1.05644	+	0.886456i
$932$	−59.9380	−	16.0603i	−1.96333	−	0.526074i
$933$	−0.654540	+	3.71208i	−0.0214287	+	0.121528i
$934$	−73.8700	−	6.46279i	−2.41710	−	0.211469i
$935$	−0.513168	−	0.732880i	−0.0167824	−	0.0239677i
$936$	29.6635	−	20.7706i	0.969582	−	0.678908i
$937$	43.5550	−	7.67992i	1.42288	−	0.250892i	0.591369	−	0.806401i	$-0.298588\pi$
$937$	43.5550	−	7.67992i	1.42288	−	0.250892i	0.831511	+	0.555509i	$0.187477\pi$
$938$	−14.7620	−	31.6572i	−0.481997	−	1.03365i
$939$	19.1589	−	19.1589i	0.625226	−	0.625226i
$940$	2.34303	+	4.05825i	0.0764213	+	0.132366i
$941$	10.6908	−	18.5171i	0.348512	−	0.603640i	−0.637474	−	0.770472i	$-0.720020\pi$
$941$	10.6908	−	18.5171i	0.348512	−	0.603640i	0.985985	+	0.166832i	$0.0533538\pi$
$942$	4.70740	+	17.5682i	0.153375	+	0.572404i
$943$	−58.3022	−	10.2802i	−1.89858	−	0.334771i
$944$	85.0830	−	39.6749i	2.76922	−	1.29131i
$945$	6.95294	−	5.83421i	0.226179	−	0.189787i
$946$	10.6307	+	6.13763i	0.345633	+	0.199552i
$947$	29.2456	−	10.6445i	0.950354	−	0.345901i	0.180107	−	0.983647i	$-0.442355\pi$
$947$	29.2456	−	10.6445i	0.950354	−	0.345901i	0.770246	+	0.637746i	$0.220133\pi$
$948$	−29.1580			−0.947007
$949$	13.2705	+	13.2293i	0.430779	+	0.429442i
$950$	−42.4056			−1.37582
$951$	−30.7902	+	11.2067i	−0.998439	+	0.363402i
$952$	22.4498	+	12.9614i	0.727603	+	0.420082i
$953$	36.3340	−	30.4879i	1.17697	−	0.987599i	0.176980	−	0.984214i	$-0.443367\pi$
$953$	36.3340	−	30.4879i	1.17697	−	0.987599i	0.999994	−	0.00338449i	$-0.00107732\pi$
$954$	6.65911	−	3.10519i	0.215597	−	0.100534i
$955$	5.90735	+	1.04163i	0.191158	+	0.0337062i
$956$	34.4063	+	128.406i	1.11278	+	4.15294i
$957$	−3.51355	+	6.08565i	−0.113577	+	0.196721i
$958$	−27.8996	−	48.3236i	−0.901397	−	1.56126i
$959$	−13.2153	+	13.2153i	−0.426744	+	0.426744i
$960$	−3.46002	−	7.42005i	−0.111672	−	0.239481i
$961$	20.5488	−	3.62331i	0.662865	−	0.116881i
$962$	37.3887	−	26.1799i	1.20546	−	0.844073i
$963$	6.20195	+	8.85730i	0.199855	+	0.285423i
$964$	142.163	+	12.4376i	4.57876	+	0.400589i
$965$	0.190030	−	1.07772i	0.00611729	−	0.0346929i
$966$	−70.3651	−	18.8543i	−2.26396	−	0.606626i
$967$	−12.0689	−	10.1270i	−0.388111	−	0.325664i	0.427766	−	0.903890i	$-0.359301\pi$
$967$	−12.0689	−	10.1270i	−0.388111	−	0.325664i	−0.815877	+	0.578226i	$0.803745\pi$
$968$	−0.194592	−	0.534638i	−0.00625443	−	0.0171839i
$969$	−0.968549	+	2.07706i	−0.0311143	+	0.0667248i
$970$	0.510152	−	1.90391i	0.0163800	−	0.0611310i
$971$	−22.3542	−	22.3542i	−0.717380	−	0.717380i	0.250688	−	0.968068i	$-0.419343\pi$
$971$	−22.3542	−	22.3542i	−0.717380	−	0.717380i	−0.968068	+	0.250688i	$0.919343\pi$
$972$	−28.1277	+	77.2802i	−0.902196	+	2.47876i
$973$	−66.4322	+	38.3547i	−2.12972	+	1.22959i
$974$	49.4518	−	58.9344i	1.58454	−	1.88838i
$975$	−6.32950	+	9.03946i	−0.202706	+	0.289495i
$976$		−	63.7932i		−	2.04197i
$977$	13.1247	+	9.19001i	0.419896	+	0.294014i	0.764366	−	0.644783i	$-0.223052\pi$
$977$	13.1247	+	9.19001i	0.419896	+	0.294014i	−0.344470	+	0.938798i	$0.611941\pi$
$978$	44.3723	+	20.6912i	1.41887	+	0.661630i
$979$	10.1585	−	2.72196i	0.324667	−	0.0869943i
$980$	2.32770	+	26.6057i	0.0743555	+	0.849887i
$981$	0.621995	+	3.52751i	0.0198588	+	0.112625i
$982$	−0.0319380	+	0.365053i	−0.00101918	+	0.0116493i
$983$	−3.10902	+	0.272004i	−0.0991624	+	0.00867559i	−0.136629	−	0.990622i	$-0.543627\pi$
$983$	−3.10902	+	0.272004i	−0.0991624	+	0.00867559i	0.0374665	+	0.999298i	$0.488071\pi$
$984$	58.0888	+	69.2276i	1.85180	+	2.20689i
$985$	−3.22496	−	1.17379i	−0.102756	−	0.0374000i
$986$	3.46452	+	1.26098i	0.110333	+	0.0401579i
$987$	−6.74158	−	8.03430i	−0.214587	−	0.255735i
$988$	−37.1023	+	3.24603i	−1.18038	+	0.103270i
$989$	−0.701564	+	8.01891i	−0.0223084	+	0.254986i
$990$	1.18471	+	6.71880i	0.0376524	+	0.213537i
$991$	−4.29733	−	49.1187i	−0.136509	−	1.56031i	−0.687742	−	0.725955i	$-0.741398\pi$
$991$	−4.29733	−	49.1187i	−0.136509	−	1.56031i	0.551233	−	0.834352i	$-0.314158\pi$
$992$	51.7188	−	13.8580i	1.64207	−	0.439992i
$993$	−19.2850	−	8.99273i	−0.611990	−	0.285376i
$994$	−103.720	−	72.6258i	−3.28981	−	2.30355i
$995$		−	7.56886i		−	0.239949i
$996$	−51.4730	+	73.5111i	−1.63098	+	2.32929i
$997$	6.68653	−	7.96870i	0.211765	−	0.252371i	−0.649698	−	0.760193i	$-0.725105\pi$
$997$	6.68653	−	7.96870i	0.211765	−	0.252371i	0.861462	+	0.507821i	$0.169549\pi$
$998$	13.1482	−	7.59110i	0.416198	−	0.240292i
$999$	−13.5598	+	37.2552i	−0.429012	+	1.17870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	73.2.k.a.19.1	✓	72
3.2	odd	2		657.2.cc.d.19.6		72
73.14	odd	72		5329.2.a.o.1.69		72
73.50	even	36	inner	73.2.k.a.50.1	yes	72
73.59	odd	72		5329.2.a.o.1.70		72
219.50	odd	36		657.2.cc.d.415.6		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
73.2.k.a.19.1	✓	72	1.1	even	1	trivial
73.2.k.a.50.1	yes	72	73.50	even	36	inner
657.2.cc.d.19.6		72	3.2	odd	2
657.2.cc.d.415.6		72	219.50	odd	36
5329.2.a.o.1.69		72	73.14	odd	72
5329.2.a.o.1.70		72	73.59	odd	72

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:	\( N \)	\(=\)	\( 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	73.k (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.52218 + 0.917999i) q^{2} +(0.900019 + 0.519626i) q^{3} +(3.98659 - 3.34515i) q^{4} +(0.360692 - 0.168193i) q^{5} +(-2.74703 - 0.484375i) q^{6} +(1.15443 + 4.30840i) q^{7} +(-4.30002 + 7.44785i) q^{8} +(-0.959977 - 1.66273i) q^{9} +O(q^{10})\)	\(q+(-2.52218 + 0.917999i) q^{2} +(0.900019 + 0.519626i) q^{3} +(3.98659 - 3.34515i) q^{4} +(0.360692 - 0.168193i) q^{5} +(-2.74703 - 0.484375i) q^{6} +(1.15443 + 4.30840i) q^{7} +(-4.30002 + 7.44785i) q^{8} +(-0.959977 - 1.66273i) q^{9} +(-0.755328 + 0.755328i) q^{10} +(1.40587 + 3.01491i) q^{11} +(5.32624 - 0.939159i) q^{12} +(1.79652 - 1.25794i) q^{13} +(-6.86680 - 9.80680i) q^{14} +(0.412027 + 0.0360477i) q^{15} +(2.20093 - 12.4821i) q^{16} +(-0.652760 - 0.174907i) q^{17} +(3.94762 + 3.31245i) q^{18} +(-1.11608 - 3.06640i) q^{19} +(0.875299 - 1.87708i) q^{20} +(-1.19975 + 4.47752i) q^{21} +(-6.31356 - 6.31356i) q^{22} +(2.00254 - 5.50193i) q^{23} +(-7.74020 + 4.46880i) q^{24} +(-3.11213 + 3.70889i) q^{25} +(-3.37636 + 4.82194i) q^{26} -5.11308i q^{27} +(19.0145 + 13.3141i) q^{28} +(1.84218 + 0.859024i) q^{29} +(-1.07230 + 0.287322i) q^{30} +(-0.277454 - 3.17131i) q^{31} +(2.92065 + 16.5639i) q^{32} +(-0.301311 + 3.44401i) q^{33} +(1.80694 - 0.158087i) q^{34} +(1.14104 + 1.35984i) q^{35} +(-9.38911 - 3.41736i) q^{36} +(-7.28626 - 2.65198i) q^{37} +(5.62990 + 6.70945i) q^{38} +(2.27056 - 0.198648i) q^{39} +(-0.298302 + 3.40961i) q^{40} +(-1.75580 - 9.95762i) q^{41} +(-1.08438 - 12.3945i) q^{42} +(-1.32796 + 0.355826i) q^{43} +(15.6900 + 7.31635i) q^{44} +(-0.625915 - 0.438271i) q^{45} +15.7152i q^{46} +(-1.29775 + 1.85338i) q^{47} +(8.46692 - 10.0905i) q^{48} +(-11.1674 + 6.44751i) q^{49} +(4.44460 - 12.2114i) q^{50} +(-0.496611 - 0.496611i) q^{51} +(2.95400 - 11.0245i) q^{52} +(0.602569 - 1.29221i) q^{53} +(4.69380 + 12.8961i) q^{54} +(1.01417 + 0.850993i) q^{55} +(-37.0524 - 9.92816i) q^{56} +(0.588889 - 3.33976i) q^{57} +(-5.43490 - 0.475492i) q^{58} +(4.24836 + 6.06729i) q^{59} +(1.76317 - 1.23458i) q^{60} +(4.95666 - 0.873994i) q^{61} +(3.61105 + 7.74392i) q^{62} +(6.05547 - 6.05547i) q^{63} +(-9.89736 - 17.1427i) q^{64} +(0.436412 - 0.755889i) q^{65} +(-2.40163 - 8.96301i) q^{66} +(2.87333 + 0.506646i) q^{67} +(-3.18738 + 1.48630i) q^{68} +(4.66127 - 3.91127i) q^{69} +(-4.12623 - 2.38228i) q^{70} +(9.93854 - 3.61733i) q^{71} +16.5117 q^{72} +(1.49673 + 8.41188i) q^{73} +20.8118 q^{74} +(-4.72821 + 1.72093i) q^{75} +(-14.7069 - 8.49102i) q^{76} +(-11.3664 + 9.53758i) q^{77} +(-5.54440 + 2.58540i) q^{78} +(-5.30933 - 0.936179i) q^{79} +(-1.30555 - 4.87237i) q^{80} +(-0.223041 + 0.386319i) q^{81} +(13.5695 + 23.5031i) q^{82} +(-11.7329 + 11.7329i) q^{83} +(10.1951 + 21.8634i) q^{84} +(-0.264863 + 0.0467025i) q^{85} +(3.02271 - 2.11653i) q^{86} +(1.21163 + 1.73038i) q^{87} +(-28.4999 - 2.49341i) q^{88} +(0.548981 - 3.11343i) q^{89} +(1.98100 + 0.530808i) q^{90} +(7.49365 + 6.28792i) q^{91} +(-10.4215 - 28.6327i) q^{92} +(1.39818 - 2.99841i) q^{93} +(1.57176 - 5.86590i) q^{94} +(-0.918306 - 0.918306i) q^{95} +(-5.97837 + 16.4254i) q^{96} +(-1.59802 + 0.922620i) q^{97} +(22.2475 - 26.5135i) q^{98} +(3.66337 - 5.23183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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