LMFDB - Embedded newform 270.2.r.a.23.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(23,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 27]))

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

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

chi := DirichletCharacter("270.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.r (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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.13
Character	$\chi$	$=$	270.23
Dual form			270.2.r.a.47.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.422618 + 0.906308i) q^{2} +(-0.572880 - 1.63457i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-2.22872 + 0.181179i) q^{5} +(1.23931 - 1.21000i) q^{6} +(0.347359 - 3.97033i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.34362 + 1.87282i) q^{9} +(-1.10610 - 1.94333i) q^{10} +(-1.35885 + 0.239602i) q^{11} +(1.62039 + 0.611828i) q^{12} +(-6.29127 - 2.93367i) q^{13} +(3.74514 - 1.36312i) q^{14} +(1.57294 + 3.53919i) q^{15} +(-0.173648 - 0.984808i) q^{16} +(3.88494 - 1.04097i) q^{17} +(-2.68781 - 1.33255i) q^{18} +(3.21964 - 1.85886i) q^{19} +(1.29380 - 1.82375i) q^{20} +(-6.68877 + 1.70674i) q^{21} +(-0.791429 - 1.13028i) q^{22} +(-0.493571 + 0.0431819i) q^{23} +(0.130302 + 1.72714i) q^{24} +(4.93435 - 0.807592i) q^{25} -6.94165i q^{26} +(4.40386 + 2.75790i) q^{27} +(2.81817 + 2.81817i) q^{28} +(-5.74999 - 2.09283i) q^{29} +(-2.54285 + 2.92129i) q^{30} +(-1.18093 - 0.990920i) q^{31} +(0.819152 - 0.573576i) q^{32} +(1.17011 + 2.08387i) q^{33} +(2.58528 + 3.08102i) q^{34} +(-0.0548245 + 8.91168i) q^{35} +(0.0717843 - 2.99914i) q^{36} +(-0.520493 - 1.94251i) q^{37} +(3.04538 + 2.13240i) q^{38} +(-1.19113 + 11.9641i) q^{39} +(2.19967 + 0.401829i) q^{40} +(2.87157 + 7.88959i) q^{41} +(-4.37363 - 5.34078i) q^{42} +(-0.771633 + 1.10201i) q^{43} +(0.689907 - 1.19495i) q^{44} +(4.88394 - 4.59860i) q^{45} +(-0.247728 - 0.429078i) q^{46} +(8.00145 + 0.700036i) q^{47} +(-1.51025 + 0.848016i) q^{48} +(-8.74923 - 1.54272i) q^{49} +(2.81727 + 4.13074i) q^{50} +(-3.92714 - 5.75385i) q^{51} +(6.29127 - 2.93367i) q^{52} +(2.13282 - 2.13282i) q^{53} +(-0.638352 + 5.15679i) q^{54} +(2.98508 - 0.780201i) q^{55} +(-1.36312 + 3.74514i) q^{56} +(-4.88290 - 4.19782i) q^{57} +(-0.533307 - 6.09573i) q^{58} +(-0.447387 + 2.53726i) q^{59} +(-3.72224 - 1.07001i) q^{60} +(6.83565 - 5.73579i) q^{61} +(0.398995 - 1.48907i) q^{62} +(6.62164 + 9.95548i) q^{63} +(0.866025 + 0.500000i) q^{64} +(14.5530 + 5.39846i) q^{65} +(-1.39412 + 1.94116i) q^{66} +(-1.77666 + 3.81006i) q^{67} +(-1.69977 + 3.64516i) q^{68} +(0.353341 + 0.782037i) q^{69} +(-8.09989 + 3.71655i) q^{70} +(-10.9974 - 6.34938i) q^{71} +(2.74848 - 1.20243i) q^{72} +(2.06099 - 7.69172i) q^{73} +(1.54054 - 1.29267i) q^{74} +(-4.14685 - 7.60287i) q^{75} +(-0.645576 + 3.66124i) q^{76} +(0.479291 + 5.47832i) q^{77} +(-11.3466 + 3.97673i) q^{78} +(-1.30184 + 3.57678i) q^{79} +(0.565439 + 2.16340i) q^{80} +(1.98508 - 8.77835i) q^{81} +(-5.93681 + 5.93681i) q^{82} +(-1.01524 + 0.473413i) q^{83} +(2.99202 - 6.22097i) q^{84} +(-8.46983 + 3.02389i) q^{85} +(-1.32486 - 0.233609i) q^{86} +(-0.126809 + 10.5977i) q^{87} +(1.37456 + 0.120259i) q^{88} +(-3.93997 - 6.82423i) q^{89} +(6.23179 + 2.48290i) q^{90} +(-13.8330 + 23.9594i) q^{91} +(0.284182 - 0.405854i) q^{92} +(-0.943192 + 2.49799i) q^{93} +(2.74711 + 7.54763i) q^{94} +(-6.83889 + 4.72621i) q^{95} +(-1.40682 - 1.01037i) q^{96} +(-8.52287 - 5.96778i) q^{97} +(-2.29940 - 8.58148i) q^{98} +(2.73590 - 3.10642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100}) $ 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.422618	+	0.906308i	0.298836	+	0.640856i
$2$	0.422618	+	0.906308i	0.298836	+	0.640856i
$3$	−0.572880	−	1.63457i	−0.330752	−	0.943718i
$3$	−0.572880	−	1.63457i	−0.330752	−	0.943718i
$4$	−0.642788	+	0.766044i	−0.321394	+	0.383022i
$5$	−2.22872	+	0.181179i	−0.996712	+	0.0810256i
$5$	−2.22872	+	0.181179i	−0.996712	+	0.0810256i
$6$	1.23931	−	1.21000i	0.505947	−	0.493982i
$7$	0.347359	−	3.97033i	0.131289	−	1.50064i	−0.589657	−	0.807654i	$-0.700737\pi$
$7$	0.347359	−	3.97033i	0.131289	−	1.50064i	0.720946	−	0.692991i	$-0.243707\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−2.34362	+	1.87282i	−0.781206	+	0.624274i
$10$	−1.10610	−	1.94333i	−0.349779	−	0.614536i
$11$	−1.35885	+	0.239602i	−0.409709	+	0.0722428i	−0.374704	−	0.927144i	$-0.622256\pi$
$11$	−1.35885	+	0.239602i	−0.409709	+	0.0722428i	−0.0350050	+	0.999387i	$0.511145\pi$
$12$	1.62039	+	0.611828i	0.467767	+	0.176619i
$13$	−6.29127	−	2.93367i	−1.74488	−	0.813653i	−0.986891	−	0.161390i	$-0.948402\pi$
$13$	−6.29127	−	2.93367i	−1.74488	−	0.813653i	−0.757993	−	0.652263i	$-0.773820\pi$
$14$	3.74514	−	1.36312i	1.00093	−	0.364309i
$15$	1.57294	+	3.53919i	0.406130	+	0.913815i
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	3.88494	−	1.04097i	0.942237	−	0.252472i	0.245172	−	0.969480i	$-0.421156\pi$
$17$	3.88494	−	1.04097i	0.942237	−	0.252472i	0.697065	+	0.717008i	$0.254489\pi$
$18$	−2.68781	−	1.33255i	−0.633522	−	0.314085i
$19$	3.21964	−	1.85886i	0.738637	−	0.426452i	−0.0829365	−	0.996555i	$-0.526430\pi$
$19$	3.21964	−	1.85886i	0.738637	−	0.426452i	0.821574	+	0.570103i	$0.193097\pi$
$20$	1.29380	−	1.82375i	0.289302	−	0.407804i
$21$	−6.68877	+	1.70674i	−1.45961	+	0.372442i
$22$	−0.791429	−	1.13028i	−0.168733	−	0.240976i
$23$	−0.493571	+	0.0431819i	−0.102917	+	0.00900405i	−0.138498	−	0.990363i	$-0.544227\pi$
$23$	−0.493571	+	0.0431819i	−0.102917	+	0.00900405i	0.0355810	+	0.999367i	$0.488672\pi$
$24$	0.130302	+	1.72714i	0.0265979	+	0.352551i
$25$	4.93435	−	0.807592i	0.986870	−	0.161518i
$26$		−	6.94165i		−	1.36137i
$27$	4.40386	+	2.75790i	0.847524	+	0.530758i
$28$	2.81817	+	2.81817i	0.532585	+	0.532585i
$29$	−5.74999	−	2.09283i	−1.06775	−	0.388628i	−0.252413	−	0.967620i	$-0.581224\pi$
$29$	−5.74999	−	2.09283i	−1.06775	−	0.388628i	−0.815333	+	0.578992i	$0.803446\pi$
$30$	−2.54285	+	2.92129i	−0.464258	+	0.533352i
$31$	−1.18093	−	0.990920i	−0.212102	−	0.177974i	0.530547	−	0.847655i	$-0.321986\pi$
$31$	−1.18093	−	0.990920i	−0.212102	−	0.177974i	−0.742649	+	0.669681i	$0.766431\pi$
$32$	0.819152	−	0.573576i	0.144807	−	0.101395i
$33$	1.17011	+	2.08387i	0.203689	+	0.362755i
$34$	2.58528	+	3.08102i	0.443373	+	0.528391i
$35$	−0.0548245	+	8.91168i	−0.00926704	+	1.50635i
$36$	0.0717843	−	2.99914i	0.0119640	−	0.499857i
$37$	−0.520493	−	1.94251i	−0.0855685	−	0.319346i	0.909853	−	0.414931i	$-0.136194\pi$
$37$	−0.520493	−	1.94251i	−0.0855685	−	0.319346i	−0.995421	+	0.0955853i	$0.969528\pi$
$38$	3.04538	+	2.13240i	0.494026	+	0.345921i
$39$	−1.19113	+	11.9641i	−0.190734	+	1.91579i
$40$	2.19967	+	0.401829i	0.347798	+	0.0635347i
$41$	2.87157	+	7.88959i	0.448465	+	1.23215i	0.933793	+	0.357814i	$0.116478\pi$
$41$	2.87157	+	7.88959i	0.448465	+	1.23215i	−0.485328	+	0.874332i	$0.661300\pi$
$42$	−4.37363	−	5.34078i	−0.674866	−	0.824101i
$43$	−0.771633	+	1.10201i	−0.117673	+	0.168054i	−0.873667	−	0.486524i	$-0.838265\pi$
$43$	−0.771633	+	1.10201i	−0.117673	+	0.168054i	0.755995	+	0.654578i	$0.227154\pi$
$44$	0.689907	−	1.19495i	0.104007	−	0.180146i
$45$	4.88394	−	4.59860i	0.728055	−	0.685519i
$46$	−0.247728	−	0.429078i	−0.0365255	−	0.0632641i
$47$	8.00145	+	0.700036i	1.16713	+	0.102111i	0.654202	−	0.756320i	$-0.273005\pi$
$47$	8.00145	+	0.700036i	1.16713	+	0.102111i	0.512930	+	0.858431i	$0.328560\pi$
$48$	−1.51025	+	0.848016i	−0.217986	+	0.122401i
$49$	−8.74923	−	1.54272i	−1.24989	−	0.220389i
$50$	2.81727	+	4.13074i	0.398423	+	0.584174i
$51$	−3.92714	−	5.75385i	−0.549909	−	0.805700i
$52$	6.29127	−	2.93367i	0.872442	−	0.406826i
$53$	2.13282	−	2.13282i	0.292965	−	0.292965i	−0.545285	−	0.838251i	$-0.683579\pi$
$53$	2.13282	−	2.13282i	0.292965	−	0.292965i	0.838251	+	0.545285i	$0.183579\pi$
$54$	−0.638352	+	5.15679i	−0.0868687	+	0.701751i
$55$	2.98508	−	0.780201i	0.402509	−	0.105202i
$56$	−1.36312	+	3.74514i	−0.182155	+	0.500466i
$57$	−4.88290	−	4.19782i	−0.646757	−	0.556015i
$58$	−0.533307	−	6.09573i	−0.0700266	−	0.800408i
$59$	−0.447387	+	2.53726i	−0.0582449	+	0.330323i	−0.999982	−	0.00602718i	$-0.998081\pi$
$59$	−0.447387	+	2.53726i	−0.0582449	+	0.330323i	0.941737	+	0.336350i	$0.109193\pi$
$60$	−3.72224	−	1.07001i	−0.480539	−	0.138138i
$61$	6.83565	−	5.73579i	0.875215	−	0.734393i	−0.0899743	−	0.995944i	$-0.528678\pi$
$61$	6.83565	−	5.73579i	0.875215	−	0.734393i	0.965190	+	0.261551i	$0.0842340\pi$
$62$	0.398995	−	1.48907i	0.0506724	−	0.189112i
$63$	6.62164	+	9.95548i	0.834249	+	1.25427i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	14.5530	+	5.39846i	1.80507	+	0.669597i
$66$	−1.39412	+	1.94116i	−0.171604	+	0.238940i
$67$	−1.77666	+	3.81006i	−0.217054	+	0.465473i	−0.984442	−	0.175710i	$-0.943778\pi$
$67$	−1.77666	+	3.81006i	−0.217054	+	0.465473i	0.767388	+	0.641182i	$0.221556\pi$
$68$	−1.69977	+	3.64516i	−0.206127	+	0.442041i
$69$	0.353341	+	0.782037i	0.0425372	+	0.0941462i
$70$	−8.09989	+	3.71655i	−0.968122	+	0.444213i
$71$	−10.9974	−	6.34938i	−1.30516	−	0.753532i	−0.323873	−	0.946101i	$-0.604985\pi$
$71$	−10.9974	−	6.34938i	−1.30516	−	0.753532i	−0.981284	+	0.192568i	$0.938318\pi$
$72$	2.74848	−	1.20243i	0.323912	−	0.141708i
$73$	2.06099	−	7.69172i	0.241221	−	0.900248i	−0.734025	−	0.679123i	$-0.762360\pi$
$73$	2.06099	−	7.69172i	0.241221	−	0.900248i	0.975245	−	0.221125i	$-0.0709729\pi$
$74$	1.54054	−	1.29267i	0.179084	−	0.150269i
$75$	−4.14685	−	7.60287i	−0.478837	−	0.877904i
$76$	−0.645576	+	3.66124i	−0.0740527	+	0.419974i
$77$	0.479291	+	5.47832i	0.0546203	+	0.624313i
$78$	−11.3466	+	3.97673i	−1.28475	+	0.450276i
$79$	−1.30184	+	3.57678i	−0.146469	+	0.402420i	−0.991132	−	0.132878i	$-0.957578\pi$
$79$	−1.30184	+	3.57678i	−0.146469	+	0.402420i	0.844664	+	0.535297i	$0.179800\pi$
$80$	0.565439	+	2.16340i	0.0632180	+	0.241875i
$81$	1.98508	−	8.77835i	0.220565	−	0.975372i
$82$	−5.93681	+	5.93681i	−0.655611	+	0.655611i
$83$	−1.01524	+	0.473413i	−0.111437	+	0.0519639i	−0.477537	−	0.878611i	$-0.658470\pi$
$83$	−1.01524	+	0.473413i	−0.111437	+	0.0519639i	0.366100	+	0.930575i	$0.380693\pi$
$84$	2.99202	−	6.22097i	0.326456	−	0.678763i
$85$	−8.46983	+	3.02389i	−0.918682	+	0.327987i
$86$	−1.32486	−	0.233609i	−0.142864	−	0.0251907i
$87$	−0.126809	+	10.5977i	−0.0135954	+	1.13619i
$88$	1.37456	+	0.120259i	0.146529	+	0.0128196i
$89$	−3.93997	−	6.82423i	−0.417636	−	0.723367i	0.578065	−	0.815991i	$-0.303808\pi$
$89$	−3.93997	−	6.82423i	−0.417636	−	0.723367i	−0.995701	+	0.0926237i	$0.970475\pi$
$90$	6.23179	+	2.48290i	0.656888	+	0.261721i
$91$	−13.8330	+	23.9594i	−1.45009	+	2.51163i
$92$	0.284182	−	0.405854i	0.0296280	−	0.0423132i
$93$	−0.943192	+	2.49799i	−0.0978045	+	0.259030i
$94$	2.74711	+	7.54763i	0.283343	+	0.778478i
$95$	−6.83889	+	4.72621i	−0.701655	+	0.484899i
$96$	−1.40682	−	1.01037i	−0.143583	−	0.103120i
$97$	−8.52287	−	5.96778i	−0.865366	−	0.605936i	0.0543491	−	0.998522i	$-0.482692\pi$
$97$	−8.52287	−	5.96778i	−0.865366	−	0.605936i	−0.919715	+	0.392586i	$0.871581\pi$
$98$	−2.29940	−	8.58148i	−0.232274	−	0.866860i
$99$	2.73590	−	3.10642i	0.274968	−	0.312207i
$100$	−2.55309	+	4.29904i	−0.255309	+	0.429904i
$101$	8.81667	+	10.5073i	0.877291	+	1.04552i	0.998600	+	0.0529004i	$0.0168466\pi$
$101$	8.81667	+	10.5073i	0.877291	+	1.04552i	−0.121308	+	0.992615i	$0.538709\pi$
$102$	3.55508	−	5.99088i	0.352005	−	0.593185i
$103$	15.4719	−	10.8335i	1.52449	−	1.06746i	0.552194	−	0.833716i	$-0.313791\pi$
$103$	15.4719	−	10.8335i	1.52449	−	1.06746i	0.972298	−	0.233745i	$-0.0750982\pi$
$104$	5.31761	+	4.46200i	0.521434	+	0.437535i
$105$	14.5981	−	5.01571i	1.42463	−	0.489483i
$106$	2.83436	+	1.03162i	0.275297	+	0.100200i
$107$	−9.84993	−	9.84993i	−0.952229	−	0.952229i	0.0466807	−	0.998910i	$-0.485136\pi$
$107$	−9.84993	−	9.84993i	−0.952229	−	0.952229i	−0.998910	+	0.0466807i	$0.985136\pi$
$108$	−4.94342	+	1.60081i	−0.475681	+	0.154038i
$109$		−	15.5323i		−	1.48772i	−0.668334	−	0.743861i	$-0.732992\pi$
$109$		−	15.5323i		−	1.48772i	0.668334	−	0.743861i	$-0.267008\pi$
$110$	1.96865	+	2.37568i	0.187704	+	0.226512i
$111$	−2.87698	+	1.96360i	−0.273070	+	0.186377i
$112$	−3.97033	+	0.347359i	−0.375161	+	0.0328223i
$113$	−6.50804	−	9.29445i	−0.612225	−	0.874348i	0.386628	−	0.922236i	$-0.373640\pi$
$113$	−6.50804	−	9.29445i	−0.612225	−	0.874348i	−0.998853	+	0.0478879i	$0.984751\pi$
$114$	1.74091	−	6.19949i	0.163051	−	0.580635i
$115$	1.09221	−	0.185665i	0.101849	−	0.0173133i
$116$	5.29922	−	3.05951i	0.492020	−	0.284068i
$117$	20.2386	−	4.90703i	1.87105	−	0.453655i
$118$	−2.48861	+	0.666822i	−0.229095	+	0.0613859i
$119$	−2.78352	−	15.7861i	−0.255165	−	1.44711i
$120$	−0.603329	−	3.82570i	−0.0550761	−	0.349237i
$121$	−8.54755	+	3.11105i	−0.777050	+	0.282823i
$122$	8.08726	+	3.77115i	0.732186	+	0.341424i
$123$	11.2510	−	9.21356i	1.01447	−	0.830759i
$124$	1.51818	−	0.267696i	0.136336	−	0.0240398i
$125$	−10.8509	+	2.69389i	−0.970538	+	0.240949i
$126$	−6.22430	+	10.2086i	−0.554505	+	0.909456i
$127$	14.0644	+	3.76854i	1.24801	+	0.334404i	0.821568	−	0.570110i	$-0.193100\pi$
$127$	14.0644	+	3.76854i	1.24801	+	0.334404i	0.426444	+	0.904514i	$0.359766\pi$
$128$	−0.0871557	+	0.996195i	−0.00770355	+	0.0880520i
$129$	2.24335	+	0.629968i	0.197516	+	0.0554656i
$130$	1.25768	+	15.4710i	0.110306	+	1.35689i
$131$	13.5155	−	16.1071i	1.18085	−	1.40728i	0.287586	−	0.957755i	$-0.407147\pi$
$131$	13.5155	−	16.1071i	1.18085	−	1.40728i	0.893266	−	0.449529i	$-0.148408\pi$
$132$	−2.34847	−	0.443134i	−0.204408	−	0.0385699i
$133$	−6.26193	−	13.4288i	−0.542978	−	1.16442i
$134$	−4.20394			−0.363165
$135$	−10.3146	−	5.34868i	−0.887742	−	0.460341i
$136$	−4.02199			−0.344883
$137$	0.0907604	+	0.194636i	0.00775418	+	0.0166289i	0.910147	−	0.414286i	$-0.135969\pi$
$137$	0.0907604	+	0.194636i	0.00775418	+	0.0166289i	−0.902393	+	0.430915i	$0.858191\pi$
$138$	−0.559438	+	0.650739i	−0.0476225	+	0.0553945i
$139$	5.37083	−	6.40070i	0.455548	−	0.542901i	−0.488563	−	0.872528i	$-0.662479\pi$
$139$	5.37083	−	6.40070i	0.455548	−	0.542901i	0.944111	+	0.329628i	$0.106923\pi$
$140$	−6.79150	−	5.77031i	−0.573987	−	0.487681i
$141$	−3.43961	−	13.4799i	−0.289668	−	1.13522i
$142$	1.10677	−	12.6504i	0.0928780	−	1.06160i
$143$	9.25182	+	2.47902i	0.773676	+	0.207306i
$144$	2.25133	+	1.98280i	0.187611	+	0.165233i
$145$	13.1943	+	3.62254i	1.09572	+	0.300835i
$146$	7.84208	−	1.38277i	0.649015	−	0.114439i
$147$	2.49057	+	15.1850i	0.205419	+	1.25244i
$148$	1.82261	+	0.849898i	0.149818	+	0.0698612i
$149$	−6.83147	+	2.48645i	−0.559655	+	0.203698i	−0.606331	−	0.795212i	$-0.707359\pi$
$149$	−6.83147	+	2.48645i	−0.559655	+	0.203698i	0.0466758	+	0.998910i	$0.485137\pi$
$150$	5.13800	−	6.97144i	0.419516	−	0.569215i
$151$	2.77651	+	15.7463i	0.225949	+	1.28142i	0.860863	+	0.508837i	$0.169924\pi$
$151$	2.77651	+	15.7463i	0.225949	+	1.28142i	−0.634914	+	0.772583i	$0.718965\pi$
$152$	−3.59105	+	0.962218i	−0.291272	+	0.0780462i
$153$	−7.15527	+	9.71543i	−0.578470	+	0.785446i
$154$	−4.76249	+	2.74963i	−0.383772	+	0.221571i
$155$	2.81150	+	1.99452i	0.225825	+	0.160204i
$156$	−8.39941	−	8.60286i	−0.672491	−	0.688780i
$157$	−7.89740	−	11.2787i	−0.630281	−	0.900135i	0.369293	−	0.929313i	$-0.379600\pi$
$157$	−7.89740	−	11.2787i	−0.630281	−	0.900135i	−0.999574	+	0.0291784i	$0.990711\pi$
$158$	−3.79185	+	0.331744i	−0.301663	+	0.0263921i
$159$	−4.70808	−	2.26439i	−0.373375	−	0.179578i
$160$	−1.72174	+	1.42675i	−0.136115	+	0.112795i
$161$			1.97464i			0.155624i
$162$	8.79482	−	1.91079i	0.690986	−	0.150126i
$163$	13.9177	+	13.9177i	1.09012	+	1.09012i	0.995515	+	0.0946021i	$0.0301579\pi$
$163$	13.9177	+	13.9177i	1.09012	+	1.09012i	0.0946021	+	0.995515i	$0.469842\pi$
$164$	−7.88959	−	2.87157i	−0.616073	−	0.224232i
$165$	−2.98539	−	4.43236i	−0.232412	−	0.345059i
$166$	−0.858116	−	0.720045i	−0.0666027	−	0.0558863i
$167$	−6.51381	+	4.56102i	−0.504053	+	0.352942i	−0.797781	−	0.602947i	$-0.793993\pi$
$167$	−6.51381	+	4.56102i	−0.504053	+	0.352942i	0.293728	+	0.955889i	$0.405104\pi$
$168$	6.90259	+	0.0825947i	0.532547	+	0.00637232i
$169$	22.6174	+	26.9544i	1.73980	+	2.07341i
$170$	−6.32008	−	6.39832i	−0.484728	−	0.490729i
$171$	−4.06430	+	10.3863i	−0.310805	+	0.794259i
$172$	−0.348189	−	1.29946i	−0.0265492	−	0.0990829i
$173$	−17.2309	−	12.0652i	−1.31004	−	0.917298i	−0.310590	−	0.950544i	$-0.600527\pi$
$173$	−17.2309	−	12.0652i	−1.31004	−	0.917298i	−0.999447	+	0.0332458i	$0.989416\pi$
$174$	−9.65835	+	4.36385i	−0.732198	+	0.330822i
$175$	−1.49242	−	19.8715i	−0.112816	−	1.50215i
$176$	0.471924	+	1.29660i	0.0355726	+	0.0977350i
$177$	4.40362	−	0.722260i	0.330996	−	0.0542884i
$178$	4.51975	−	6.45487i	0.338770	−	0.483813i
$179$	−5.88150	+	10.1870i	−0.439604	+	0.761416i	−0.997659	−	0.0683880i	$-0.978214\pi$
$179$	−5.88150	+	10.1870i	−0.439604	+	0.761416i	0.558055	+	0.829804i	$0.311548\pi$
$180$	0.383394	+	6.69724i	0.0285765	+	0.499183i
$181$	5.53321	+	9.58380i	0.411280	+	0.712358i	0.995030	−	0.0995756i	$-0.0317485\pi$
$181$	5.53321	+	9.58380i	0.411280	+	0.712358i	−0.583750	+	0.811933i	$0.698415\pi$
$182$	−27.5606	−	2.41124i	−2.04293	−	0.178733i
$183$	−13.2915	−	7.88741i	−0.982539	−	0.583054i
$184$	0.487929	+	0.0860351i	0.0359706	+	0.00634259i
$185$	1.51197	+	4.23499i	0.111162	+	0.311363i
$186$	−2.66256	+	0.200874i	−0.195228	+	0.0147288i
$187$	−5.02965	+	2.34536i	−0.367804	+	0.171510i
$188$	−5.67949	+	5.67949i	−0.414220	+	0.414220i
$189$	12.4795	−	16.5268i	0.907750	−	1.20215i
$190$	−7.17364	−	4.20075i	−0.520430	−	0.304755i
$191$	5.91305	−	16.2460i	0.427853	−	1.17552i	−0.519260	−	0.854617i	$-0.673792\pi$
$191$	5.91305	−	16.2460i	0.427853	−	1.17552i	0.947113	−	0.320901i	$-0.103986\pi$
$192$	0.321155	−	1.70202i	0.0231774	−	0.122832i
$193$	0.135785	+	1.55203i	0.00977402	+	0.111718i	0.999514	−	0.0311598i	$-0.00992008\pi$
$193$	0.135785	+	1.55203i	0.00977402	+	0.111718i	−0.989740	+	0.142877i	$0.954365\pi$
$194$	1.80672	−	10.2464i	0.129715	−	0.735651i
$195$	0.487049	−	26.8805i	0.0348783	−	1.92495i
$196$	6.80569	−	5.71065i	0.486121	−	0.407904i
$197$	−1.53697	+	5.73604i	−0.109504	+	0.408676i	−0.998817	−	0.0486235i	$-0.984517\pi$
$197$	−1.53697	+	5.73604i	−0.109504	+	0.408676i	0.889313	+	0.457299i	$0.151183\pi$
$198$	3.97162	+	1.16673i	0.282250	+	0.0829162i
$199$	1.77045	+	1.02217i	0.125504	+	0.0724599i	0.561438	−	0.827519i	$-0.310248\pi$
$199$	1.77045	+	1.02217i	0.125504	+	0.0724599i	−0.435934	+	0.899979i	$0.643582\pi$
$200$	−4.97523	−	0.497029i	−0.351802	−	0.0351453i
$201$	7.24561	+	0.721363i	0.511066	+	0.0508810i
$202$	−5.79676	+	12.4312i	−0.407859	+	0.874656i
$203$	−10.3065	+	22.1024i	−0.723376	+	1.55129i
$204$	6.93202	+	0.690142i	0.485338	+	0.0483196i
$205$	−7.82935	−	17.0634i	−0.546825	−	1.19176i
$206$	16.3572	+	9.44385i	1.13966	+	0.657984i
$207$	1.07587	−	1.02557i	0.0747781	−	0.0712822i
$208$	−1.79663	+	6.70511i	−0.124574	+	0.464916i
$209$	−3.92963	+	3.29735i	−0.271818	+	0.228083i
$210$	10.7152	+	11.1107i	0.739420	+	0.766710i
$211$	−1.44626	+	8.20212i	−0.0995643	+	0.564657i	0.893688	+	0.448688i	$0.148109\pi$
$211$	−1.44626	+	8.20212i	−0.0995643	+	0.564657i	−0.993253	+	0.115969i	$0.963003\pi$
$212$	0.262885	+	3.00478i	0.0180550	+	0.206369i
$213$	−4.07827	+	21.6135i	−0.279438	+	1.48093i
$214$	4.76431	−	13.0898i	0.325682	−	0.894803i
$215$	1.52009	−	2.59586i	0.103669	−	0.177036i
$216$	−3.54001	−	3.80373i	−0.240867	−	0.258811i
$217$	−4.34449	+	4.34449i	−0.294923	+	0.294923i
$218$	14.0770	−	6.56422i	0.953416	−	0.444585i
$219$	−13.7533	+	1.03761i	−0.929364	+	0.0701149i
$220$	−1.32111	+	2.78821i	−0.0890690	+	0.187981i
$221$	−27.4951	−	4.84812i	−1.84952	−	0.326120i
$222$	−2.99549	−	1.77757i	−0.201044	−	0.119303i
$223$	−11.2247	−	0.982038i	−0.751664	−	0.0657621i	−0.295117	−	0.955461i	$-0.595359\pi$
$223$	−11.2247	−	0.982038i	−0.751664	−	0.0657621i	−0.456547	+	0.889699i	$0.650914\pi$
$224$	−1.99275	−	3.45154i	−0.133146	−	0.230616i
$225$	−10.0517	+	11.1338i	−0.670117	+	0.742256i
$226$	5.67321	−	9.82629i	0.377376	−	0.653635i
$227$	−1.03065	+	1.47192i	−0.0684066	+	0.0976948i	−0.851898	−	0.523708i	$-0.824548\pi$
$227$	−1.03065	+	1.47192i	−0.0684066	+	0.0976948i	0.783491	+	0.621403i	$0.213437\pi$
$228$	6.35439	−	1.04222i	0.420830	−	0.0690224i
$229$	3.83749	+	10.5434i	0.253588	+	0.696728i	0.999528	+	0.0307150i	$0.00977844\pi$
$229$	3.83749	+	10.5434i	0.253588	+	0.696728i	−0.745940	+	0.666013i	$0.767999\pi$
$230$	0.629856	+	0.911410i	0.0415315	+	0.0600966i
$231$	8.68011	−	3.92185i	0.571109	−	0.258039i
$232$	5.01240	+	3.50972i	0.329080	+	0.230424i
$233$	2.08560	+	7.78355i	0.136632	+	0.509917i	0.999986	+	0.00531842i	$0.00169291\pi$
$233$	2.08560	+	7.78355i	0.136632	+	0.509917i	−0.863354	+	0.504599i	$0.831640\pi$
$234$	13.0005	+	16.2686i	0.849867	+	1.06351i
$235$	−17.9598	−	0.110488i	−1.17157	−	0.00720747i
$236$	−1.65608	−	1.97364i	−0.107802	−	0.128473i
$237$	6.59229	+	0.0788818i	0.428215	+	0.00512392i
$238$	13.1307	−	9.19422i	0.851137	−	0.595973i
$239$	7.43783	+	6.24108i	0.481113	+	0.403702i	0.850829	−	0.525443i	$-0.176100\pi$
$239$	7.43783	+	6.24108i	0.481113	+	0.403702i	−0.369715	+	0.929145i	$0.620545\pi$
$240$	3.21229	−	2.16361i	0.207352	−	0.139661i
$241$	6.66292	+	2.42510i	0.429196	+	0.156215i	0.547580	−	0.836753i	$-0.315549\pi$
$241$	6.66292	+	2.42510i	0.429196	+	0.156215i	−0.118384	+	0.992968i	$0.537771\pi$
$242$	−6.43192	−	6.43192i	−0.413460	−	0.413460i
$243$	−15.4860	+	1.78419i	−0.993428	+	0.114456i
$244$			8.92331i			0.571256i
$245$	19.7791	+	1.85312i	1.26364	+	0.118392i
$246$	13.1052	+	6.30304i	0.835557	+	0.401867i
$247$	−25.7089	+	2.24924i	−1.63582	+	0.143116i
$248$	0.884224	+	1.26280i	0.0561483	+	0.0801880i
$249$	1.35543	+	1.38827i	0.0858972	+	0.0879777i
$250$	−7.02730	−	8.69580i	−0.444446	−	0.549971i
$251$	4.18510	−	2.41627i	0.264161	−	0.152513i	−0.362070	−	0.932151i	$-0.617930\pi$
$251$	4.18510	−	2.41627i	0.264161	−	0.152513i	0.626231	+	0.779637i	$0.284597\pi$
$252$	−11.8827	−	1.32679i	−0.748537	−	0.0835797i
$253$	0.660344	−	0.176939i	0.0415155	−	0.0111240i
$254$	2.52841	+	14.3393i	0.158646	+	0.899728i
$255$	9.79495	+	12.1122i	0.613383	+	0.758494i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−4.31999	−	2.01444i	−0.269473	−	0.125657i	0.283185	−	0.959065i	$-0.408609\pi$
$257$	−4.31999	−	2.01444i	−0.269473	−	0.125657i	−0.552659	+	0.833408i	$0.686387\pi$
$258$	0.377137	+	2.29941i	0.0234796	+	0.143155i
$259$	−7.89319	+	1.39178i	−0.490459	+	0.0864812i
$260$	−13.4899	+	7.67815i	−0.836610	+	0.476179i
$261$	17.3953	−	5.86392i	1.07674	−	0.362968i
$262$	20.3099	+	5.44201i	1.25475	+	0.336209i
$263$	0.698450	−	7.98332i	0.0430683	−	0.492273i	−0.943775	−	0.330590i	$-0.892752\pi$
$263$	0.698450	−	7.98332i	0.0430683	−	0.492273i	0.986843	−	0.161683i	$-0.0516921\pi$
$264$	−0.590889	−	2.31571i	−0.0363667	−	0.142522i
$265$	−4.36703	+	5.13987i	−0.268264	+	0.315740i
$266$	9.52418	−	11.3505i	0.583965	−	0.695942i
$267$	−8.89753	+	10.3496i	−0.544520	+	0.633386i
$268$	−1.77666	−	3.81006i	−0.108527	−	0.232736i
$269$	−2.04232			−0.124522			−0.0622611	−	0.998060i	$-0.519831\pi$
$269$	−2.04232			−0.124522			−0.0622611	+	0.998060i	$0.519831\pi$
$270$	0.488403	−	11.6087i	0.0297233	−	0.706482i
$271$	20.6542			1.25465			0.627326	−	0.778757i	$-0.284149\pi$
$271$	20.6542			1.25465			0.627326	+	0.778757i	$0.284149\pi$
$272$	−1.69977	−	3.64516i	−0.103063	−	0.221020i
$273$	47.0878	+	8.88505i	2.84989	+	0.537747i
$274$	−0.138043	+	0.164514i	−0.00833951	+	0.00993864i
$275$	−6.51155	+	2.27968i	−0.392661	+	0.137470i
$276$	−0.826198	−	0.232009i	−0.0497313	−	0.0139653i
$277$	−1.57950	+	18.0538i	−0.0949032	+	1.08475i	0.788152	+	0.615480i	$0.211038\pi$
$277$	−1.57950	+	18.0538i	−0.0949032	+	1.08475i	−0.883056	+	0.469268i	$0.844518\pi$
$278$	8.07082	+	2.16257i	0.484055	+	0.129702i
$279$	4.62347	+	0.110662i	0.276800	+	0.00662519i
$280$	2.35947	−	8.59383i	0.141005	−	0.513580i
$281$	18.1038	−	3.19219i	1.07998	−	0.190430i	0.394776	−	0.918778i	$-0.370822\pi$
$281$	18.1038	−	3.19219i	1.07998	−	0.190430i	0.685208	+	0.728347i	$0.259711\pi$
$282$	10.7633	−	8.81422i	0.640947	−	0.524879i
$283$	22.8469	+	10.6537i	1.35811	+	0.633295i	0.958947	−	0.283586i	$-0.0915242\pi$
$283$	22.8469	+	10.6537i	1.35811	+	0.633295i	0.399159	+	0.916882i	$0.369302\pi$
$284$	11.9329	−	4.34323i	0.708089	−	0.257723i
$285$	11.6432	+	8.47107i	0.689681	+	0.501783i
$286$	1.66323	+	9.43267i	0.0983491	+	0.557766i
$287$	32.3217	−	8.66059i	1.90789	−	0.511218i
$288$	−0.845573	+	2.87837i	−0.0498259	+	0.169609i
$289$	−0.713261	+	0.411802i	−0.0419566	+	0.0242236i
$290$	2.29301	+	13.4890i	0.134650	+	0.792103i
$291$	−4.87215	+	17.3500i	−0.285610	+	1.01708i
$292$	4.56742	+	6.52295i	0.267288	+	0.381727i
$293$	−12.5077	+	1.09429i	−0.730711	+	0.0639289i	−0.446438	−	0.894815i	$-0.647308\pi$
$293$	−12.5077	+	1.09429i	−0.730711	+	0.0639289i	−0.284273	+	0.958743i	$0.591752\pi$
$294$	−12.7097	+	8.67468i	−0.741246	+	0.505917i
$295$	0.537402	−	5.73589i	0.0312887	−	0.333956i
$296$			2.01103i			0.116889i
$297$	−6.64500	−	2.69240i	−0.385582	−	0.156229i
$298$	−5.14059	−	5.14059i	−0.297786	−	0.297786i
$299$	3.23187	+	1.17630i	0.186904	+	0.0680274i
$300$	8.48968	+	1.71036i	0.490152	+	0.0987475i
$301$	4.10730	+	3.44643i	0.236741	+	0.198649i
$302$	−13.0976	+	9.17106i	−0.753684	+	0.527735i
$303$	12.1240	−	20.4309i	0.696505	−	1.17372i
$304$	−2.38971	−	2.84794i	−0.137059	−	0.163341i
$305$	−14.1955	+	14.0219i	−0.812833	+	0.802893i
$306$	−11.8291	−	2.37896i	−0.676226	−	0.135996i
$307$	−0.631788	−	2.35787i	−0.0360581	−	0.134571i	0.945550	−	0.325476i	$-0.105524\pi$
$307$	−0.631788	−	2.35787i	−0.0360581	−	0.134571i	−0.981609	+	0.190905i	$0.938858\pi$
$308$	−4.50472	−	3.15424i	−0.256680	−	0.179730i
$309$	−26.5717	−	19.0835i	−1.51161	−	1.08562i
$310$	−0.619458	+	3.39100i	−0.0351829	+	0.192596i
$311$	−0.679124	−	1.86588i	−0.0385096	−	0.105804i	0.918948	−	0.394380i	$-0.129041\pi$
$311$	−0.679124	−	1.86588i	−0.0385096	−	0.105804i	−0.957457	+	0.288576i	$0.906818\pi$
$312$	4.24709	−	11.2482i	0.240444	−	0.636803i
$313$	−10.5165	+	15.0191i	−0.594429	+	0.848932i	−0.997813	−	0.0660983i	$-0.978945\pi$
$313$	−10.5165	+	15.0191i	−0.594429	+	0.848932i	0.403384	+	0.915031i	$0.367834\pi$
$314$	6.88435	−	11.9240i	0.388506	−	0.672912i
$315$	−16.5615	−	20.9882i	−0.933134	−	1.18255i
$316$	−1.90317	−	3.29638i	−0.107062	−	0.185436i
$317$	2.27739	+	0.199246i	0.127911	+	0.0111907i	0.150931	−	0.988544i	$-0.451773\pi$
$317$	2.27739	+	0.199246i	0.127911	+	0.0111907i	−0.0230205	+	0.999735i	$0.507328\pi$
$318$	0.0625084	−	5.22394i	0.00350530	−	0.292944i
$319$	8.31483	+	1.46613i	0.465541	+	0.0820875i
$320$	−2.02071	−	0.957452i	−0.112961	−	0.0535232i
$321$	−10.4575	+	21.7432i	−0.583683	+	1.21359i
$322$	−1.78963	+	0.834520i	−0.0997323	+	0.0465060i
$323$	10.5731	−	10.5731i	0.588304	−	0.588304i
$324$	5.44862	+	7.16328i	0.302701	+	0.397960i
$325$	−33.4125	−	9.39495i	−1.85339	−	0.521138i
$326$	−6.73184	+	18.4956i	−0.372842	+	1.02438i
$327$	−25.3885	+	8.89813i	−1.40399	+	0.492068i
$328$	−0.731753	−	8.36397i	−0.0404043	−	0.461823i
$329$	5.55875	−	31.5253i	0.306464	−	1.73804i
$330$	2.75540	−	4.57887i	0.151680	−	0.252059i
$331$	−3.07159	+	2.57737i	−0.168830	+	0.141665i	−0.723288	−	0.690547i	$-0.757370\pi$
$331$	−3.07159	+	2.57737i	−0.168830	+	0.141665i	0.554458	+	0.832212i	$0.312926\pi$
$332$	0.289927	−	1.08202i	0.0159118	−	0.0593836i
$333$	4.85780	+	3.57770i	0.266206	+	0.196057i
$334$	−6.88654	−	3.97594i	−0.376815	−	0.217554i
$335$	3.26937	−	8.81343i	0.178625	−	0.481529i
$336$	2.84231	+	6.29078i	0.155060	+	0.343190i
$337$	10.3495	−	22.1947i	0.563775	−	1.20902i	−0.393361	−	0.919384i	$-0.628688\pi$
$337$	10.3495	−	22.1947i	0.563775	−	1.20902i	0.957137	−	0.289636i	$-0.0935343\pi$
$338$	−14.8704	+	31.8897i	−0.808845	+	1.73457i
$339$	−11.4641	+	15.9624i	−0.622643	+	0.866960i
$340$	3.12787	−	8.43199i	0.169633	−	0.457289i
$341$	1.84214	+	1.06356i	0.0997574	+	0.0575950i
$342$	−11.1308	+	0.705926i	−0.601885	+	0.0381721i
$343$	−1.94359	+	7.25359i	−0.104944	+	0.391657i
$344$	1.03056	−	0.864743i	0.0555641	−	0.0466238i
$345$	−0.929185	−	1.67892i	−0.0500256	−	0.0903900i
$346$	3.65269	−	20.7154i	0.196370	−	1.11367i
$347$	−0.127861	−	1.46146i	−0.00686396	−	0.0784554i	0.991990	−	0.126316i	$-0.0403153\pi$
$347$	−0.127861	−	1.46146i	−0.00686396	−	0.0784554i	−0.998854	+	0.0478605i	$0.984760\pi$
$348$	−8.03678	−	6.90920i	−0.430817	−	0.370372i
$349$	1.32197	−	3.63209i	0.0707637	−	0.194422i	−0.899269	−	0.437396i	$-0.855901\pi$
$349$	1.32197	−	3.63209i	0.0707637	−	0.194422i	0.970033	+	0.242974i	$0.0781231\pi$
$350$	17.3790	−	9.75066i	0.928946	−	0.521195i
$351$	−19.6151	−	30.2701i	−1.04698	−	1.61570i
$352$	−0.975676	+	0.975676i	−0.0520037	+	0.0520037i
$353$	1.52716	−	0.712125i	0.0812824	−	0.0379026i	−0.381552	−	0.924347i	$-0.624610\pi$
$353$	1.52716	−	0.712125i	0.0812824	−	0.0379026i	0.462834	+	0.886445i	$0.346832\pi$
$354$	2.51564	+	3.68579i	0.133705	+	0.195898i
$355$	25.6606	+	12.1585i	1.36192	+	0.645304i
$356$	7.76023	+	1.36834i	0.411291	+	0.0725217i
$357$	−24.2088	+	13.5934i	−1.28127	+	0.719438i
$358$	−11.7182	−	1.02521i	−0.619328	−	0.0541842i
$359$	−1.44240	−	2.49831i	−0.0761271	−	0.131856i	0.825449	−	0.564477i	$-0.190922\pi$
$359$	−1.44240	−	2.49831i	−0.0761271	−	0.131856i	−0.901576	+	0.432621i	$0.857589\pi$
$360$	−5.90773	+	3.17785i	−0.311365	+	0.167487i
$361$	−2.58926	+	4.48473i	−0.136277	+	0.236038i
$362$	−6.34743	+	9.06508i	−0.333614	+	0.476450i
$363$	9.98194	+	12.1893i	0.523916	+	0.639771i
$364$	−9.46230	−	25.9975i	−0.495959	−	1.36264i
$365$	−3.19979	+	17.5161i	−0.167484	+	0.916833i
$366$	1.53117	−	15.3796i	0.0800356	−	0.803904i
$367$	19.5523	+	13.6907i	1.02062	+	0.714647i	0.958987	−	0.283452i	$-0.0914796\pi$
$367$	19.5523	+	13.6907i	1.02062	+	0.714647i	0.0616352	+	0.998099i	$0.480368\pi$
$368$	0.128234	+	0.478574i	0.00668464	+	0.0249474i
$369$	−21.5057	−	13.1122i	−1.11954	−	0.682595i
$370$	−3.19922	+	3.16010i	−0.166319	+	0.164286i
$371$	−7.72715	−	9.20885i	−0.401173	−	0.478100i
$372$	−1.30730	−	2.32820i	−0.0677803	−	0.120712i
$373$	−19.7533	+	13.8314i	−1.02279	+	0.716162i	−0.959464	−	0.281831i	$-0.909058\pi$
$373$	−19.7533	+	13.8314i	−1.02279	+	0.716162i	−0.0633211	+	0.997993i	$0.520169\pi$
$374$	−4.25124	−	3.56721i	−0.219826	−	0.184456i
$375$	10.6196	+	16.1933i	0.548396	+	0.836219i
$376$	−7.54763	−	2.74711i	−0.389239	−	0.141671i
$377$	30.0351	+	30.0351i	1.54689	+	1.54689i
$378$	20.2524	+	4.32573i	1.04167	+	0.222491i
$379$		−	26.5732i		−	1.36497i	−0.730898	−	0.682487i	$-0.760899\pi$
$379$		−	26.5732i		−	1.36497i	0.730898	−	0.682487i	$-0.239101\pi$
$380$	0.775466	−	8.27684i	0.0397806	−	0.424593i
$381$	−1.89727	−	25.1481i	−0.0972001	−	1.28838i
$382$	17.2228	−	1.50680i	0.881196	−	0.0770946i
$383$	−10.6186	−	15.1649i	−0.542585	−	0.774892i	0.450438	−	0.892808i	$-0.351268\pi$
$383$	−10.6186	−	15.1649i	−0.542585	−	0.774892i	−0.993024	+	0.117915i	$0.962379\pi$
$384$	1.67828	−	0.428238i	0.0856442	−	0.0218534i
$385$	−2.06076	−	12.1228i	−0.105026	−	0.617835i
$386$	−1.34923	+	0.778980i	−0.0686741	+	0.0396490i
$387$	−0.255447	−	4.02781i	−0.0129851	−	0.204745i
$388$	10.0500	−	2.69288i	0.510210	−	0.136710i
$389$	1.17271	+	6.65076i	0.0594586	+	0.337207i	0.999997	−	0.00248101i	$-0.000789730\pi$
$389$	1.17271	+	6.65076i	0.0594586	+	0.337207i	−0.940538	+	0.339688i	$0.889679\pi$
$390$	24.5678	−	10.9188i	1.24404	−	0.552893i
$391$	−1.87255	+	0.681551i	−0.0946987	+	0.0344675i
$392$	8.05182	+	3.75462i	0.406678	+	0.189637i
$393$	−34.0709	−	12.8645i	−1.71865	−	0.648928i
$394$	−5.84817	+	1.03119i	−0.294626	+	0.0519506i
$395$	2.25340	−	8.20750i	0.113381	−	0.412964i
$396$	0.621057	+	4.09259i	0.0312093	+	0.205660i
$397$	−20.9576	−	5.61558i	−1.05183	−	0.281838i	−0.308824	−	0.951119i	$-0.599935\pi$
$397$	−20.9576	−	5.61558i	−1.05183	−	0.281838i	−0.743009	+	0.669281i	$0.766602\pi$
$398$	−0.178176	+	2.03657i	−0.00893118	+	0.102084i
$399$	−18.3629	+	17.9286i	−0.919293	+	0.897553i
$400$	−1.65216	−	4.71915i	−0.0826082	−	0.235957i
$401$	12.7195	−	15.1585i	0.635183	−	0.756982i	−0.348418	−	0.937339i	$-0.613281\pi$
$401$	12.7195	−	15.1585i	0.635183	−	0.756982i	0.983601	+	0.180358i	$0.0577255\pi$
$402$	2.40835	+	6.87161i	0.120118	+	0.342725i
$403$	4.52253	+	9.69860i	0.225283	+	0.483122i
$404$	−13.7163			−0.682412
$405$	−2.83374	+	19.9241i	−0.140810	+	0.990037i
$406$	−24.3873			−1.21032
$407$	1.17270	+	2.51487i	0.0581287	+	0.124657i
$408$	2.30412	+	6.57421i	0.114071	+	0.325472i
$409$	10.1988	−	12.1545i	0.504300	−	0.601002i	−0.452494	−	0.891767i	$-0.649466\pi$
$409$	10.1988	−	12.1545i	0.504300	−	0.601002i	0.956794	+	0.290766i	$0.0939101\pi$
$410$	12.1558	−	14.3071i	0.600334	−	0.706577i
$411$	0.266151	−	0.259857i	0.0131283	−	0.0128178i
$412$	−1.64617	+	18.8158i	−0.0811011	+	0.926990i
$413$	9.91836	+	2.65762i	0.488051	+	0.130773i
$414$	1.38417	+	0.541644i	0.0680281	+	0.0266203i
$415$	2.17690	−	1.23904i	0.106860	−	0.0608222i
$416$	−6.83619	+	1.20540i	−0.335172	+	0.0590998i
$417$	−13.5392	−	5.11214i	−0.663018	−	0.250343i
$418$	−4.64915	−	2.16794i	−0.227397	−	0.106037i
$419$	29.3155	−	10.6700i	1.43216	−	0.521262i	0.494607	−	0.869117i	$-0.335312\pi$
$419$	29.3155	−	10.6700i	1.43216	−	0.521262i	0.937548	+	0.347855i	$0.113090\pi$
$420$	−5.54125	+	14.4069i	−0.270385	+	0.702983i
$421$	−5.28257	−	29.9590i	−0.257457	−	1.46011i	−0.789687	−	0.613511i	$-0.789757\pi$
$421$	−5.28257	−	29.9590i	−0.257457	−	1.46011i	0.532230	−	0.846600i	$-0.321354\pi$
$422$	−8.04486	+	2.15561i	−0.391618	+	0.104934i
$423$	−20.0634	+	13.3447i	−0.975515	+	0.648840i
$424$	−2.61216	+	1.50813i	−0.126858	+	0.0732413i
$425$	18.3290	−	8.27395i	0.889086	−	0.401345i
$426$	−21.3120	+	5.43809i	−1.03257	+	0.263476i
$427$	−20.3986	−	29.1322i	−0.987156	−	1.40981i
$428$	13.8769	−	1.21407i	0.670765	−	0.0586844i
$429$	−1.24806	−	16.5429i	−0.0602569	−	0.798698i
$430$	2.99507	+	0.280611i	0.144435	+	0.0135323i
$431$			31.2636i			1.50592i	0.658069	+	0.752958i	$0.271373\pi$
$431$			31.2636i			1.50592i	−0.658069	+	0.752958i	$0.728627\pi$
$432$	1.95128	−	4.81586i	0.0938808	−	0.231703i
$433$	13.7999	+	13.7999i	0.663181	+	0.663181i	0.956129	−	0.292948i	$-0.0946361\pi$
$433$	13.7999	+	13.7999i	0.663181	+	0.663181i	−0.292948	+	0.956129i	$0.594636\pi$
$434$	−5.77350	−	2.10138i	−0.277137	−	0.100870i
$435$	−1.63745	−	23.6422i	−0.0785099	−	1.13356i
$436$	11.8984	+	9.98396i	0.569831	+	0.478145i
$437$	−1.50885	+	1.05651i	−0.0721783	+	0.0505398i
$438$	−6.75280	−	12.0262i	−0.322661	−	0.574636i
$439$	4.44322	+	5.29522i	0.212063	+	0.252727i	0.861582	−	0.507618i	$-0.169474\pi$
$439$	4.44322	+	5.29522i	0.212063	+	0.252727i	−0.649519	+	0.760346i	$0.725030\pi$
$440$	−3.08530	−	0.0189807i	−0.147086	−	0.000904871i
$441$	23.3941	−	12.7702i	1.11400	−	0.608104i
$442$	−7.22603	−	26.9679i	−0.343707	−	1.28273i
$443$	1.21988	+	0.854169i	0.0579583	+	0.0405828i	0.602197	−	0.798348i	$-0.294292\pi$
$443$	1.21988	+	0.854169i	0.0579583	+	0.0405828i	−0.544238	+	0.838931i	$0.683181\pi$
$444$	0.345077	−	3.46607i	0.0163766	−	0.164492i
$445$	10.0175	+	14.4954i	0.474874	+	0.687149i
$446$	−3.85375	−	10.5881i	−0.182480	−	0.501361i
$447$	7.97788	+	9.74205i	0.377341	+	0.460783i
$448$	2.28599	−	3.26473i	0.108003	−	0.154244i
$449$	−12.5295	+	21.7017i	−0.591304	+	1.02417i	0.402754	+	0.915308i	$0.368053\pi$
$449$	−12.5295	+	21.7017i	−0.591304	+	1.02417i	−0.994057	+	0.108859i	$0.965280\pi$
$450$	−14.3387	−	4.40462i	−0.675935	−	0.207636i
$451$	−5.79241	−	10.0327i	−0.272754	−	0.472424i
$452$	11.3032	+	0.988906i	0.531660	+	0.0465142i
$453$	24.1478	−	13.5591i	1.13456	−	0.637064i
$454$	−1.76958	−	0.312025i	−0.0830507	−	0.0146441i
$455$	26.4888	−	55.9049i	1.24181	−	2.62086i
$456$	3.63005	+	5.31857i	0.169993	+	0.249065i
$457$	−24.5331	+	11.4400i	−1.14761	+	0.535139i	−0.900933	−	0.433958i	$-0.857117\pi$
$457$	−24.5331	+	11.4400i	−1.14761	+	0.535139i	−0.246677	+	0.969098i	$0.579339\pi$
$458$	−7.93379	+	7.93379i	−0.370721	+	0.370721i
$459$	19.9796	+	6.13000i	0.932569	+	0.286124i
$460$	−0.559829	+	0.956022i	−0.0261022	+	0.0445747i
$461$	−3.95298	+	10.8607i	−0.184109	+	0.505835i	−0.997071	−	0.0764818i	$-0.975631\pi$
$461$	−3.95298	+	10.8607i	−0.184109	+	0.505835i	0.812962	+	0.582316i	$0.197854\pi$
$462$	7.22278	+	6.20940i	0.336034	+	0.288888i
$463$	−0.819693	−	9.36914i	−0.0380944	−	0.435421i	−0.991161	−	0.132661i	$-0.957648\pi$
$463$	−0.819693	−	9.36914i	−0.0380944	−	0.435421i	0.953067	−	0.302759i	$-0.0979078\pi$
$464$	−1.06256	+	6.02605i	−0.0493279	+	0.279752i
$465$	1.64952	−	5.73820i	0.0764949	−	0.266103i
$466$	−6.17288	+	5.17966i	−0.285953	+	0.239943i
$467$	2.20035	−	8.21181i	0.101820	−	0.379997i	−0.896145	−	0.443761i	$-0.853644\pi$
$467$	2.20035	−	8.21181i	0.101820	−	0.379997i	0.997965	+	0.0637641i	$0.0203105\pi$
$468$	−9.25009	+	18.6578i	−0.427586	+	0.862457i
$469$	14.5101	+	8.37739i	0.670012	+	0.386832i
$470$	−7.49000	−	16.3238i	−0.345488	−	0.752961i
$471$	−13.9115	+	19.3701i	−0.641006	+	0.892529i
$472$	1.08883	−	2.33501i	0.0501177	−	0.107478i
$473$	0.784492	−	1.68235i	0.0360710	−	0.0773544i
$474$	2.71453	+	6.00798i	0.124683	+	0.275956i
$475$	14.3856	−	11.7724i	0.660059	−	0.540156i
$476$	13.8821	+	8.01482i	0.636284	+	0.367358i
$477$	−1.00412	+	8.99290i	−0.0459757	+	0.411757i
$478$	−2.51298	+	9.37856i	−0.114941	+	0.428965i
$479$	−13.1222	+	11.0108i	−0.599566	+	0.503096i	−0.891306	−	0.453402i	$-0.850210\pi$
$479$	−13.1222	+	11.0108i	−0.599566	+	0.503096i	0.291740	+	0.956498i	$0.405766\pi$
$480$	3.31847	+	1.99694i	0.151467	+	0.0911473i
$481$	−2.42410	+	13.7478i	−0.110530	+	0.626845i
$482$	0.617981	+	7.06355i	0.0281482	+	0.321736i
$483$	3.22768	−	1.13123i	0.146865	−	0.0514729i
$484$	3.11105	−	8.54755i	0.141412	−	0.388525i
$485$	20.0763	+	11.7563i	0.911617	+	0.533827i
$486$	−8.16170	−	13.2811i	−0.370222	−	0.602441i
$487$	24.7608	−	24.7608i	1.12202	−	1.12202i	0.130583	−	0.991437i	$-0.458315\pi$
$487$	24.7608	−	24.7608i	1.12202	−	1.12202i	0.991437	−	0.130583i	$-0.0416847\pi$
$488$	−8.08726	+	3.77115i	−0.366093	+	0.170712i
$489$	14.7762	−	30.7225i	0.668204	−	1.38932i
$490$	6.67949	+	18.7091i	0.301749	+	0.845190i
$491$	24.8545	+	4.38251i	1.12167	+	0.197780i	0.703572	−	0.710624i	$-0.251587\pi$
$491$	24.8545	+	4.38251i	1.12167	+	0.197780i	0.418094	+	0.908404i	$0.362698\pi$
$492$	−0.173996	+	14.5411i	−0.00784432	+	0.655564i
$493$	−24.5169	−	2.14496i	−1.10419	−	0.0966039i
$494$	−12.9036	−	22.3496i	−0.580559	−	1.00556i
$495$	−5.53472	+	7.41902i	−0.248767	+	0.333460i
$496$	−0.770799	+	1.33506i	−0.0346099	+	0.0599461i
$497$	−29.0292	+	41.4580i	−1.30214	+	1.85965i
$498$	−0.685364	+	1.81515i	−0.0307119	+	0.0813387i
$499$	−5.42986	−	14.9184i	−0.243074	−	0.667840i	−0.999899	−	0.0142224i	$-0.995473\pi$
$499$	−5.42986	−	14.9184i	−0.243074	−	0.667840i	0.756825	−	0.653618i	$-0.226750\pi$
$500$	4.91121	−	10.0439i	0.219636	−	0.449177i
$501$	11.1869	+	8.03434i	0.499794	+	0.358948i
$502$	3.95858	+	2.77183i	0.176680	+	0.123713i
$503$	−3.89277	−	14.5280i	−0.173570	−	0.647771i	−0.996791	−	0.0800503i	$-0.974492\pi$
$503$	−3.89277	−	14.5280i	−0.173570	−	0.647771i	0.823221	−	0.567721i	$-0.192175\pi$
$504$	−3.81935	−	11.3301i	−0.170127	−	0.504681i
$505$	−21.5536	−	21.8204i	−0.959120	−	0.970995i
$506$	0.439434	+	0.523697i	0.0195352	+	0.0232812i
$507$	31.1017	−	52.4113i	1.38127	−	2.32767i
$508$	−11.9273	+	8.35157i	−0.529187	+	0.370541i
$509$	33.2789	+	27.9243i	1.47506	+	1.23772i	0.911274	+	0.411801i	$0.135100\pi$
$509$	33.2789	+	27.9243i	1.47506	+	1.23772i	0.563786	+	0.825921i	$0.309344\pi$
$510$	−6.83784	+	13.9961i	−0.302785	+	0.619756i
$511$	−29.8228	−	10.8546i	−1.31928	−	0.480180i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	19.3054	+	0.693277i	0.852355	+	0.0306089i
$514$		−	4.76658i		−	0.210245i
$515$	−32.5197	+	26.9481i	−1.43299	+	1.18747i
$516$	−1.92458	+	1.31357i	−0.0847251	+	0.0578269i
$517$	−11.0405	+	0.965921i	−0.485562	+	0.0424811i
$518$	−4.59719	−	6.56547i	−0.201989	−	0.288470i
$519$	−9.85012	+	35.0769i	−0.432372	+	1.53970i
$520$	−12.6599	−	8.98110i	−0.555172	−	0.393847i
$521$	5.78678	−	3.34100i	0.253523	−	0.146372i	−0.367853	−	0.929884i	$-0.619907\pi$
$521$	5.78678	−	3.34100i	0.253523	−	0.146372i	0.621376	+	0.783512i	$0.286574\pi$
$522$	12.6661	+	13.2873i	0.554379	+	0.581568i
$523$	3.75281	−	1.00556i	0.164099	−	0.0439702i	−0.175834	−	0.984420i	$-0.556262\pi$
$523$	3.75281	−	1.00556i	0.164099	−	0.0439702i	0.339933	+	0.940450i	$0.389596\pi$
$524$	3.65118	+	20.7069i	0.159503	+	0.904585i
$525$	−31.6264	+	13.8235i	−1.38029	+	0.603305i
$526$	7.53052	−	2.74089i	0.328346	−	0.119508i
$527$	−5.61937	−	2.62035i	−0.244784	−	0.114144i
$528$	1.84903	−	1.51419i	0.0804685	−	0.0658966i
$529$	−22.4088	+	3.95128i	−0.974297	+	0.171795i
$530$	−6.50389	−	1.78567i	−0.282511	−	0.0775644i
$531$	−3.70333	−	6.78424i	−0.160711	−	0.294411i
$532$	14.3121	+	3.83492i	0.620509	+	0.166265i
$533$	5.07957	−	58.0597i	0.220021	−	2.51485i
$534$	−13.1402	−	3.68997i	−0.568632	−	0.159680i
$535$	23.7373	+	20.1681i	1.02625	+	0.871943i
$536$	2.70224	−	3.22040i	0.116719	−	0.139100i
$537$	20.0208	+	3.77774i	0.863961	+	0.163022i
$538$	−0.863121	−	1.85097i	−0.0372118	−	0.0798009i
$539$	12.2585			0.528013
$540$	10.7274	−	4.46340i	0.461636	−	0.192074i
$541$	20.8588			0.896788			0.448394	−	0.893836i	$-0.351996\pi$
$541$	20.8588			0.896788			0.448394	+	0.893836i	$0.351996\pi$
$542$	8.72883	+	18.7190i	0.374935	+	0.804051i
$543$	12.4955	−	14.5348i	0.536233	−	0.623746i
$544$	2.58528	−	3.08102i	0.110843	−	0.132098i
$545$	2.81412	+	34.6170i	0.120544	+	1.48283i
$546$	11.8476	+	46.4311i	0.507030	+	1.98707i
$547$	2.61574	−	29.8981i	0.111841	−	1.27835i	−0.708186	−	0.706026i	$-0.750486\pi$
$547$	2.61574	−	29.8981i	0.111841	−	1.27835i	0.820027	−	0.572324i	$-0.193958\pi$
$548$	−0.207440	−	0.0555833i	−0.00886139	−	0.00237440i
$549$	−5.27804	+	26.2444i	−0.225261	+	1.12009i
$550$	−4.81799	−	4.93803i	−0.205440	−	0.210558i
$551$	−22.4032	+	3.95029i	−0.954408	+	0.168288i
$552$	−0.138895	−	0.846841i	−0.00591175	−	0.0360440i
$553$	13.7488	+	6.41118i	0.584659	+	0.272631i
$554$	−17.0298	+	6.19835i	−0.723528	+	0.263343i
$555$	6.05620	−	4.89756i	0.257071	−	0.207890i
$556$	1.45092	+	8.22858i	0.0615328	+	0.348970i
$557$	17.6438	−	4.72765i	0.747594	−	0.200317i	0.135143	−	0.990826i	$-0.456851\pi$
$557$	17.6438	−	4.72765i	0.747594	−	0.200317i	0.612451	+	0.790509i	$0.290184\pi$
$558$	1.85367	+	4.23705i	0.0784720	+	0.179369i
$559$	8.08746	−	4.66930i	0.342063	−	0.197490i
$560$	8.78581	−	1.49350i	0.371268	−	0.0631121i
$561$	6.71503	+	6.87768i	0.283509	+	0.290376i
$562$	10.5441	+	15.0586i	0.444777	+	0.635207i
$563$	24.3545	−	2.13074i	1.02642	−	0.0898001i	0.438510	−	0.898727i	$-0.355507\pi$
$563$	24.3545	−	2.13074i	1.02642	−	0.0898001i	0.587910	+	0.808926i	$0.299951\pi$
$564$	12.5372	+	6.02984i	0.527910	+	0.253902i
$565$	16.1885	+	19.5356i	0.681057	+	0.821867i
$566$			25.2087i			1.05960i
$567$	−34.1634	−	10.9307i	−1.43473	−	0.459046i
$568$	8.97938	+	8.97938i	0.376766	+	0.376766i
$569$	6.28696	+	2.28827i	0.263563	+	0.0959291i	0.470422	−	0.882442i	$-0.344102\pi$
$569$	6.28696	+	2.28827i	0.263563	+	0.0959291i	−0.206859	+	0.978371i	$0.566324\pi$
$570$	−2.75678	+	14.1323i	−0.115469	+	0.591938i
$571$	18.3978	+	15.4376i	0.769924	+	0.646043i	0.940690	−	0.339269i	$-0.110180\pi$
$571$	18.3978	+	15.4376i	0.769924	+	0.646043i	−0.170765	+	0.985312i	$0.554624\pi$
$572$	−7.84599	+	5.49382i	−0.328057	+	0.229708i
$573$	−29.9426	−	0.358286i	−1.25087	−	0.0149676i
$574$	21.5089	+	25.6333i	0.897765	+	1.06991i
$575$	−2.40058	+	0.611679i	−0.100111	+	0.0255088i
$576$	−2.96604	+	0.450102i	−0.123585	+	0.0187542i
$577$	−0.846255	−	3.15827i	−0.0352301	−	0.131480i	0.946071	−	0.323959i	$-0.105014\pi$
$577$	−0.846255	−	3.15827i	−0.0352301	−	0.131480i	−0.981301	+	0.192479i	$0.938347\pi$
$578$	−0.674656	−	0.472399i	−0.0280620	−	0.0196492i
$579$	2.45911	−	1.11108i	0.102197	−	0.0461748i
$580$	−11.2561	+	7.77888i	−0.467386	+	0.323000i
$581$	1.52696	+	4.19528i	0.0633488	+	0.174049i
$582$	−17.7835	+	2.91677i	−0.737150	+	0.120904i
$583$	−2.38716	+	3.40921i	−0.0988660	+	0.141195i
$584$	−3.98153	+	6.89621i	−0.164757	+	0.285367i
$585$	−44.2169	+	14.6032i	−1.82815	+	0.603766i
$586$	−6.27776	−	10.8734i	−0.259332	−	0.449176i
$587$	−12.5047	−	1.09402i	−0.516124	−	0.0451550i	−0.173882	−	0.984767i	$-0.555631\pi$
$587$	−12.5047	−	1.09402i	−0.516124	−	0.0451550i	−0.342243	+	0.939612i	$0.611187\pi$
$588$	−13.2333	−	7.85284i	−0.545732	−	0.323846i
$589$	−5.64417	−	0.995219i	−0.232564	−	0.0410073i
$590$	5.42560	−	1.93704i	0.223368	−	0.0797467i
$591$	10.2564	−	0.773786i	0.421893	−	0.0318293i
$592$	−1.82261	+	0.849898i	−0.0749089	+	0.0349306i
$593$	−14.2960	+	14.2960i	−0.587065	+	0.587065i	−0.936835	−	0.349771i	$-0.886259\pi$
$593$	−14.2960	+	14.2960i	−0.587065	+	0.587065i	0.349771	+	0.936835i	$0.386259\pi$
$594$	−0.368153	−	7.16027i	−0.0151055	−	0.293789i
$595$	9.06377	+	34.6784i	0.371579	+	1.42168i
$596$	2.48645	−	6.83147i	0.101849	−	0.279828i
$597$	0.656551	−	3.47951i	0.0268709	−	0.142407i
$598$	0.299753	+	3.42620i	0.0122578	+	0.140108i
$599$	−1.75900	+	9.97576i	−0.0718706	+	0.407599i	0.927554	+	0.373689i	$0.121907\pi$
$599$	−1.75900	+	9.97576i	−0.0718706	+	0.407599i	−0.999425	+	0.0339101i	$0.989204\pi$
$600$	2.03778	+	8.41709i	0.0831922	+	0.343626i
$601$	19.0179	−	15.9580i	0.775758	−	0.650939i	−0.166418	−	0.986055i	$-0.553220\pi$
$601$	19.0179	−	15.9580i	0.775758	−	0.650939i	0.942177	+	0.335117i	$0.108776\pi$
$602$	−1.38771	+	5.17900i	−0.0565588	+	0.211080i
$603$	−2.97175	−	12.2567i	−0.121019	−	0.499131i
$604$	−13.8471	−	7.99463i	−0.563431	−	0.325297i
$605$	18.4864	−	8.48229i	0.751579	−	0.344854i
$606$	23.6405	+	2.35361i	0.960328	+	0.0956090i
$607$	8.72581	−	18.7126i	0.354170	−	0.759519i	−0.645823	−	0.763488i	$-0.723485\pi$
$607$	8.72581	−	18.7126i	0.354170	−	0.759519i	0.999992	+	0.00396842i	$0.00126319\pi$
$608$	1.57118	−	3.36940i	0.0637197	−	0.136647i
$609$	42.0323	+	4.18468i	1.70323	+	0.169572i
$610$	−18.7075	−	6.93959i	−0.757443	−	0.280976i
$611$	−48.2856	−	27.8777i	−1.95343	−	1.12781i
$612$	−2.84313	−	11.7262i	−0.114927	−	0.474004i
$613$	4.31596	−	16.1074i	0.174320	−	0.650570i	−0.822347	−	0.568987i	$-0.807336\pi$
$613$	4.31596	−	16.1074i	0.174320	−	0.650570i	0.996666	−	0.0815837i	$-0.0259978\pi$
$614$	1.86995	−	1.56907i	0.0754649	−	0.0633226i
$615$	−23.4060	+	22.5729i	−0.943819	+	0.910225i
$616$	0.954935	−	5.41570i	0.0384754	−	0.218205i
$617$	−3.76852	−	43.0744i	−0.151715	−	1.73411i	−0.566388	−	0.824139i	$-0.691659\pi$
$617$	−3.76852	−	43.0744i	−0.151715	−	1.73411i	0.414673	−	0.909971i	$-0.363896\pi$
$618$	6.06588	−	32.1472i	0.244005	−	1.29315i
$619$	−3.88899	+	10.6849i	−0.156312	+	0.429462i	−0.992985	−	0.118239i	$-0.962275\pi$
$619$	−3.88899	+	10.6849i	−0.156312	+	0.429462i	0.836674	+	0.547702i	$0.184497\pi$
$620$	−3.33508	+	0.871679i	−0.133940	+	0.0350075i
$621$	−2.29271	−	1.17105i	−0.0920033	−	0.0469927i
$622$	1.40405	−	1.40405i	0.0562973	−	0.0562973i
$623$	−28.4630	+	13.2725i	−1.14035	+	0.531753i
$624$	11.9892	−	0.904513i	0.479953	−	0.0362095i
$625$	23.6956	−	7.96988i	0.947824	−	0.318795i
$626$	−18.0564	−	3.18384i	−0.721681	−	0.127252i
$627$	7.64095	+	4.53426i	0.305150	+	0.181081i
$628$	13.7163	+	1.20002i	0.547340	+	0.0478860i
$629$	−4.04417	−	7.00471i	−0.161252	−	0.279296i
$630$	12.0226	−	23.8798i	0.478993	−	0.951395i
$631$	5.21919	−	9.03991i	0.207773	−	0.359873i	−0.743240	−	0.669025i	$-0.766712\pi$
$631$	5.21919	−	9.03991i	0.207773	−	0.359873i	0.951013	+	0.309152i	$0.100045\pi$
$632$	2.18322	−	3.11797i	0.0868440	−	0.124026i
$633$	14.2354	−	2.33483i	0.565808	−	0.0928011i
$634$	0.781888	+	2.14822i	0.0310527	+	0.0853167i
$635$	−32.0283	−	5.85084i	−1.27100	−	0.232183i
$636$	4.76092	−	2.15108i	0.188783	−	0.0852960i
$637$	50.5179	+	35.3730i	2.00159	+	1.40153i
$638$	2.18524	+	8.15541i	0.0865143	+	0.322876i
$639$	37.6650	−	5.71573i	1.49001	−	0.226111i
$640$	0.0137560	−	2.23603i	0.000543754	−	0.0883867i
$641$	−7.45071	−	8.87941i	−0.294285	−	0.350715i	0.598561	−	0.801077i	$-0.295739\pi$
$641$	−7.45071	−	8.87941i	−0.294285	−	0.350715i	−0.892846	+	0.450362i	$0.851295\pi$
$642$	−24.1256	−	0.288681i	−0.952161	−	0.0113933i
$643$	0.975543	−	0.683083i	0.0384717	−	0.0269382i	−0.554182	−	0.832395i	$-0.686969\pi$
$643$	0.975543	−	0.683083i	0.0384717	−	0.0269382i	0.592654	+	0.805457i	$0.298080\pi$
$644$	−1.51266	−	1.26928i	−0.0596073	−	0.0500164i
$645$	−5.11394	−	0.997572i	−0.201361	−	0.0392794i
$646$	14.0509	+	5.11411i	0.552825	+	0.201212i
$647$	−35.5625	−	35.5625i	−1.39811	−	1.39811i	−0.805472	−	0.592634i	$-0.798088\pi$
$647$	−35.5625	−	35.5625i	−1.39811	−	1.39811i	−0.592634	−	0.805472i	$-0.701912\pi$
$648$	−4.18945	+	7.96546i	−0.164577	+	0.312913i
$649$		−	3.55496i		−	0.139544i
$650$	−5.60602	−	34.2525i	−0.219886	−	1.34349i
$651$	9.59023	+	4.61249i	0.375871	+	0.180778i
$652$	−19.6077	+	1.71545i	−0.767896	+	0.0671822i
$653$	−11.0851	−	15.8312i	−0.433794	−	0.619523i	0.541429	−	0.840747i	$-0.317884\pi$
$653$	−11.0851	−	15.8312i	−0.433794	−	0.619523i	−0.975223	+	0.221224i	$0.928995\pi$
$654$	−18.7941	−	19.2493i	−0.734908	−	0.752708i
$655$	−27.2039	+	38.3469i	−1.06294	+	1.49834i
$656$	7.27108	−	4.19796i	0.283888	−	0.163903i
$657$	9.57504	+	21.8863i	0.373558	+	0.853867i
$658$	30.9208	−	8.28521i	1.20542	−	0.322991i
$659$	2.19147	+	12.4284i	0.0853676	+	0.484144i	0.997277	+	0.0737513i	$0.0234971\pi$
$659$	2.19147	+	12.4284i	0.0853676	+	0.484144i	−0.911909	+	0.410392i	$0.865392\pi$
$660$	5.31435	+	0.562128i	0.206861	+	0.0218808i
$661$	−20.0840	+	7.30999i	−0.781179	+	0.284326i	−0.701664	−	0.712508i	$-0.747559\pi$
$661$	−20.0840	+	7.30999i	−0.781179	+	0.284326i	−0.0795146	+	0.996834i	$0.525337\pi$
$662$	−3.63400	−	1.69456i	−0.141239	−	0.0658610i
$663$	7.82679	+	47.7199i	0.303967	+	1.85329i
$664$	1.10317	−	0.194519i	0.0428114	−	0.00754881i
$665$	16.3891	+	28.7943i	0.635541	+	1.11660i
$666$	−1.18950	+	5.91467i	−0.0460923	+	0.229189i
$667$	2.92840	+	0.784663i	0.113388	+	0.0303823i
$668$	0.693053	−	7.92163i	0.0268150	−	0.306497i
$669$	4.82522	+	18.9102i	0.186554	+	0.731110i
$670$	9.36938	−	0.761664i	0.361971	−	0.0294256i
$671$	−7.91433	+	9.43193i	−0.305529	+	0.364116i
$672$	−4.50017	+	5.23460i	−0.173598	+	0.201929i
$673$	11.8117	+	25.3302i	0.455307	+	0.976409i	0.991231	+	0.132142i	$0.0421856\pi$
$673$	11.8117	+	25.3302i	0.455307	+	0.976409i	−0.535924	+	0.844266i	$0.680037\pi$
$674$	24.4891			0.943285
$675$	23.9574	+	10.0519i	0.922123	+	0.386898i
$676$	−35.1864			−1.35332
$677$	−15.9845	−	34.2788i	−0.614333	−	1.31744i	−0.929646	−	0.368453i	$-0.879887\pi$
$677$	−15.9845	−	34.2788i	−0.614333	−	1.31744i	0.315313	−	0.948988i	$-0.397890\pi$
$678$	−19.3118	−	3.64396i	−0.741665	−	0.139945i
$679$	−26.6546	+	31.7657i	−1.02291	+	1.21905i
$680$	8.96387	−	0.728699i	0.343749	−	0.0279443i
$681$	2.99639	+	0.841432i	0.114822	+	0.0322438i
$682$	−0.185391	+	2.11902i	−0.00709897	+	0.0811416i
$683$	17.3808	+	4.65718i	0.665059	+	0.178202i	0.575528	−	0.817782i	$-0.304796\pi$
$683$	17.3808	+	4.65718i	0.665059	+	0.178202i	0.0895311	+	0.995984i	$0.471463\pi$
$684$	−5.34387	−	9.78960i	−0.204328	−	0.374315i
$685$	−0.237543	−	0.417345i	−0.00907606	−	0.0159459i
$686$	−7.39538	+	1.30401i	−0.282357	+	0.0497872i
$687$	15.0355	−	12.3127i	0.573640	−	0.469760i
$688$	1.21926	+	0.568549i	0.0464837	+	0.0216757i
$689$	−19.6751	+	7.16116i	−0.749562	+	0.272818i
$690$	1.12893	−	1.55167i	0.0429776	−	0.0590711i
$691$	3.48622	+	19.7713i	0.132622	+	0.752137i	0.976486	+	0.215580i	$0.0691642\pi$
$691$	3.48622	+	19.7713i	0.132622	+	0.752137i	−0.843864	+	0.536557i	$0.819725\pi$
$692$	20.3182	−	5.44426i	0.772383	−	0.206960i
$693$	−11.3832	−	11.9415i	−0.432412	−	0.453619i
$694$	1.27050	−	0.733522i	0.0482274	−	0.0278441i
$695$	−10.8104	+	15.2384i	−0.410061	+	0.578027i
$696$	2.86537	−	10.2038i	0.108612	−	0.386772i
$697$	19.3687	+	27.6614i	0.733642	+	1.04775i
$698$	3.85049	−	0.336874i	0.145743	−	0.0127509i
$699$	11.5279	−	7.86808i	0.436027	−	0.297598i
$700$	16.1818	+	11.6299i	0.611614	+	0.439569i
$701$			13.6300i			0.514800i	0.966305	+	0.257400i	$0.0828657\pi$
$701$			13.6300i			0.514800i	−0.966305	+	0.257400i	$0.917134\pi$
$702$	19.1443	−	30.5700i	0.722557	−	1.15379i
$703$	−5.28665	−	5.28665i	−0.199390	−	0.199390i
$704$	−1.29660	−	0.471924i	−0.0488675	−	0.0177863i
$705$	10.1082	+	29.4198i	0.380697	+	1.10801i
$706$	1.29081	+	1.08312i	0.0485802	+	0.0407637i
$707$	44.7800	−	31.3553i	1.68413	−	1.17924i
$708$	−2.27731	+	3.83763i	−0.0855865	+	0.144227i
$709$	7.94365	+	9.46687i	0.298330	+	0.355536i	0.894298	−	0.447473i	$-0.147676\pi$
$709$	7.94365	+	9.46687i	0.298330	+	0.355536i	−0.595968	+	0.803008i	$0.703231\pi$
$710$	−0.174684	+	28.3947i	−0.00655578	+	1.06564i
$711$	−3.64765	−	10.8207i	−0.136798	−	0.405809i
$712$	2.03948	+	7.61144i	0.0764327	+	0.285251i
$713$	0.625664	+	0.438095i	0.0234313	+	0.0164068i
$714$	−22.5509	−	16.1958i	−0.843946	−	0.606114i
$715$	−21.0688	−	3.84879i	−0.787929	−	0.143937i
$716$	−4.02318	−	11.0536i	−0.150353	−	0.413092i
$717$	5.94048	−	15.7330i	0.221851	−	0.587561i
$718$	1.65466	−	2.36309i	0.0617512	−	0.0881899i
$719$	13.8540	−	23.9958i	0.516666	−	0.894891i	−0.483147	−	0.875539i	$-0.660506\pi$
$719$	13.8540	−	23.9958i	0.516666	−	0.894891i	0.999813	−	0.0193519i	$-0.00616029\pi$
$720$	−5.37682	−	4.01121i	−0.200382	−	0.149489i
$721$	−37.6385	−	65.1917i	−1.40173	−	2.42787i
$722$	−5.15881	−	0.451338i	−0.191991	−	0.0167970i
$723$	0.146943	−	12.2803i	0.00546486	−	0.456709i
$724$	−10.8983	−	1.92166i	−0.405032	−	0.0714180i
$725$	−30.0626	−	5.68308i	−1.11650	−	0.211064i
$726$	−6.82869	+	14.1981i	−0.253436	+	0.526942i
$727$	−16.8057	+	7.83664i	−0.623290	+	0.290645i	−0.708492	−	0.705719i	$-0.750624\pi$
$727$	−16.8057	+	7.83664i	−0.623290	+	0.290645i	0.0852018	+	0.996364i	$0.472846\pi$
$728$	19.5628	−	19.5628i	0.725044	−	0.725044i
$729$	11.7880	+	24.2908i	0.436593	+	0.899659i
$730$	−17.2272	+	4.50262i	−0.637609	+	0.166649i
$731$	−1.85060	+	5.08447i	−0.0684468	+	0.188056i
$732$	14.5857	−	5.11198i	0.539105	−	0.188944i
$733$	−4.35514	−	49.7795i	−0.160861	−	1.83865i	−0.464160	−	0.885751i	$-0.653644\pi$
$733$	−4.35514	−	49.7795i	−0.160861	−	1.83865i	0.303299	−	0.952895i	$-0.401912\pi$
$734$	−4.14480	+	23.5063i	−0.152987	+	0.867634i
$735$	−8.30197	−	33.3918i	−0.306223	−	1.23167i
$736$	−0.379542	+	0.318473i	−0.0139901	+	0.0117391i
$737$	1.50132	−	5.60300i	0.0553018	−	0.206389i
$738$	2.79503	−	25.0322i	0.102887	−	0.921448i
$739$	−25.8007	−	14.8961i	−0.949095	−	0.547960i	−0.0562951	−	0.998414i	$-0.517929\pi$
$739$	−25.8007	−	14.8961i	−0.949095	−	0.547960i	−0.892800	+	0.450454i	$0.851262\pi$
$740$	−4.21607	−	1.56396i	−0.154986	−	0.0574924i
$741$	18.4047	+	40.7344i	0.676112	+	1.49642i
$742$	5.08042	−	10.8950i	0.186508	−	0.399968i
$743$	−10.8490	+	23.2658i	−0.398011	+	0.853538i	0.600533	+	0.799600i	$0.294955\pi$
$743$	−10.8490	+	23.2658i	−0.398011	+	0.853538i	−0.998544	+	0.0539380i	$0.982823\pi$
$744$	1.55758	−	2.16876i	0.0571037	−	0.0795105i
$745$	14.7749	−	6.77931i	0.541311	−	0.248375i
$746$	−20.8836	−	12.0571i	−0.764602	−	0.441443i
$747$	1.49271	−	3.01086i	0.0546154	−	0.110162i
$748$	1.43634	−	5.36050i	0.0525179	−	0.195999i
$749$	−42.5290	+	35.6861i	−1.55398	+	1.30394i
$750$	−10.1881	+	16.4682i	−0.372016	+	0.601335i
$751$	3.03368	−	17.2049i	0.110701	−	0.627814i	−0.878089	−	0.478498i	$-0.841182\pi$
$751$	3.03368	−	17.2049i	0.110701	−	0.627814i	0.988789	−	0.149317i	$-0.0477073\pi$
$752$	−0.700036	−	8.00145i	−0.0255277	−	0.291783i
$753$	−6.34711	−	5.45659i	−0.231301	−	0.198849i
$754$	−14.5277	+	39.9144i	−0.529066	+	1.45360i
$755$	−9.04095	−	34.5911i	−0.329034	−	1.25890i
$756$	4.63861	+	20.1831i	0.168705	+	0.734051i
$757$	0.867061	−	0.867061i	0.0315139	−	0.0315139i	−0.691174	−	0.722688i	$-0.742906\pi$
$757$	0.867061	−	0.867061i	0.0315139	−	0.0315139i	0.722688	+	0.691174i	$0.242906\pi$
$758$	24.0835	−	11.2303i	0.874752	−	0.407903i
$759$	−0.667516	−	0.978012i	−0.0242293	−	0.0354996i
$760$	7.82909	−	2.79513i	0.283991	−	0.101390i
$761$	−21.0273	−	3.70768i	−0.762239	−	0.134403i	−0.221002	−	0.975273i	$-0.570933\pi$
$761$	−21.0273	−	3.70768i	−0.762239	−	0.134403i	−0.541237	+	0.840870i	$0.682044\pi$
$762$	21.9901	−	12.3476i	0.796617	−	0.447305i
$763$	−61.6683	−	5.39528i	−2.23254	−	0.195322i
$764$	8.64430	+	14.9724i	0.312740	+	0.541681i
$765$	14.1868	−	22.9493i	0.512926	−	0.829734i
$766$	9.25649	−	16.0327i	0.334450	−	0.579285i
$767$	10.2581	−	14.6501i	0.370399	−	0.528984i
$768$	1.09739	+	1.34005i	0.0395985	+	0.0483550i
$769$	6.04624	+	16.6119i	0.218033	+	0.599041i	0.999696	−	0.0246605i	$-0.00785048\pi$
$769$	6.04624	+	16.6119i	0.218033	+	0.599041i	−0.781663	+	0.623701i	$0.785628\pi$
$770$	10.1161	−	6.99100i	0.364558	−	0.251938i
$771$	−0.817908	+	8.21534i	−0.0294562	+	0.295868i
$772$	−1.27621	−	0.893609i	−0.0459316	−	0.0321617i
$773$	9.71674	+	36.2634i	0.349487	+	1.30430i	0.887282	+	0.461227i	$0.152591\pi$
$773$	9.71674	+	36.2634i	0.349487	+	1.30430i	−0.537795	+	0.843075i	$0.680743\pi$
$774$	3.54248	−	1.93374i	0.127332	−	0.0695068i
$775$	−6.62739	−	3.93583i	−0.238063	−	0.141379i
$776$	6.68788	+	7.97031i	0.240081	+	0.286117i
$777$	6.79681	+	12.1046i	0.243834	+	0.434251i
$778$	−5.53202	+	3.87356i	−0.198333	+	0.138874i
$779$	23.9111	+	20.0638i	0.856704	+	0.718860i
$780$	20.2786	+	17.6515i	0.726089	+	0.632026i
$781$	16.4652	+	5.99285i	0.589172	+	0.214441i
$782$	−1.40907	−	1.40907i	−0.0503881	−	0.0503881i
$783$	−19.5504	−	25.0744i	−0.698673	−	0.896086i
$784$			8.88420i			0.317293i
$785$	19.6445	+	23.7061i	0.701143	+	0.846106i
$786$	−2.73978	−	36.3155i	−0.0977247	−	1.29533i
$787$	1.93066	−	0.168911i	0.0688205	−	0.00602102i	−0.0526935	−	0.998611i	$-0.516781\pi$
$787$	1.93066	−	0.168911i	0.0688205	−	0.00602102i	0.121514	+	0.992590i	$0.461225\pi$
$788$	−3.40612	−	4.86444i	−0.121338	−	0.173288i
$789$	−13.4494	+	3.43182i	−0.478811	+	0.122176i
$790$	8.39085	−	1.42637i	0.298533	−	0.0507478i
$791$	−39.1627	+	22.6106i	−1.39246	+	0.803940i
$792$	−3.44668	+	2.29247i	−0.122472	+	0.0814594i
$793$	−59.8318	+	16.0319i	−2.12469	+	0.569309i
$794$	−3.76763	−	21.3673i	−0.133708	−	0.758297i
$795$	10.9032	+	4.19367i	0.386698	+	0.148734i
$796$	−1.92106	+	0.699207i	−0.0680900	+	0.0247827i
$797$	44.4514	+	20.7280i	1.57455	+	0.734225i	0.996642	−	0.0818766i	$-0.0260913\pi$
$797$	44.4514	+	20.7280i	1.57455	+	0.734225i	0.577908	+	0.816102i	$0.303869\pi$
$798$	−24.0093	−	9.06545i	−0.849920	−	0.320913i
$799$	31.8139	−	5.60965i	1.12549	−	0.198455i
$800$	3.57877	−	3.49177i	0.126528	−	0.123453i
$801$	22.0143	+	8.61452i	0.777839	+	0.304379i
$802$	19.1138	+	5.12153i	0.674932	+	0.180848i
$803$	−0.957628	+	10.9457i	−0.0337939	+	0.386267i
$804$	−5.20998	+	5.08678i	−0.183742	+	0.179397i
$805$	−0.357763	−	4.40091i	−0.0126095	−	0.155112i
$806$	−6.87861	+	8.19761i	−0.242289	+	0.288749i
$807$	1.17000	+	3.33830i	0.0411860	+	0.117514i
$808$	−5.79676	−	12.4312i	−0.203929	−	0.437328i
$809$	−7.77851			−0.273478			−0.136739	−	0.990607i	$-0.543662\pi$
$809$	−7.77851			−0.273478			−0.136739	+	0.990607i	$0.543662\pi$
$810$	−19.2550	+	5.85205i	−0.676550	+	0.205620i
$811$	−23.3881			−0.821267			−0.410634	−	0.911800i	$-0.634692\pi$
$811$	−23.3881			−0.821267			−0.410634	+	0.911800i	$0.634692\pi$
$812$	−10.3065	−	22.1024i	−0.361688	−	0.775643i
$813$	−11.8324	−	33.7606i	−0.414979	−	1.18404i
$814$	−1.78364	+	2.12566i	−0.0625165	+	0.0745043i
$815$	−33.5402	−	28.4970i	−1.17486	−	0.998206i
$816$	−4.98450	+	4.86662i	−0.174492	+	0.170366i
$817$	−0.435906	+	4.98243i	−0.0152504	+	0.174313i
$818$	15.3259	+	4.10657i	0.535859	+	0.143583i
$819$	−12.4525	−	82.0583i	−0.435125	−	2.86735i
$820$	18.1039	+	4.97050i	0.632216	+	0.173577i
$821$	−1.35556	+	0.239021i	−0.0473093	+	0.00834190i	−0.197253	−	0.980353i	$-0.563202\pi$
$821$	−1.35556	+	0.239021i	−0.0473093	+	0.00834190i	0.149943	+	0.988695i	$0.452091\pi$
$822$	0.347991	+	0.131395i	0.0121376	+	0.00458291i
$823$	9.75163	+	4.54726i	0.339920	+	0.158507i	0.585081	−	0.810975i	$-0.301063\pi$
$823$	9.75163	+	4.54726i	0.339920	+	0.158507i	−0.245160	+	0.969483i	$0.578841\pi$
$824$	−17.7486	+	6.45998i	−0.618303	+	0.225044i
$825$	7.45663	+	9.33758i	0.259606	+	0.325093i
$826$	1.78306	+	10.1122i	0.0620406	+	0.351850i
$827$	20.8152	−	5.57741i	0.723815	−	0.193946i	0.121942	−	0.992537i	$-0.461088\pi$
$827$	20.8152	−	5.57741i	0.723815	−	0.193946i	0.601873	+	0.798592i	$0.294421\pi$
$828$	0.0940779	+	1.48339i	0.00326943	+	0.0515513i
$829$	33.7715	−	19.4980i	1.17293	−	0.677192i	0.218563	−	0.975823i	$-0.429863\pi$
$829$	33.7715	−	19.4980i	1.17293	−	0.677192i	0.954369	+	0.298631i	$0.0965298\pi$
$830$	2.04295	+	1.44930i	0.0709120	+	0.0503060i
$831$	30.4150	−	7.76086i	1.05509	−	0.269221i
$832$	−3.98156	−	5.68626i	−0.138036	−	0.197136i
$833$	−35.5962	+	3.11426i	−1.23333	+	0.107903i
$834$	−1.08874	−	14.4312i	−0.0377002	−	0.499711i
$835$	13.6911	−	11.3454i	0.473799	−	0.392623i
$836$		−	5.12977i		−	0.177417i
$837$	−2.46781	−	7.62076i	−0.0852999	−	0.263412i
$838$	22.0595	+	22.0595i	0.762034	+	0.762034i
$839$	−13.7227	−	4.99464i	−0.473759	−	0.172434i	0.0940957	−	0.995563i	$-0.470004\pi$
$839$	−13.7227	−	4.99464i	−0.473759	−	0.172434i	−0.567854	+	0.823129i	$0.692226\pi$
$840$	−15.3989	+	1.06652i	−0.531312	+	0.0367985i
$841$	6.46718	+	5.42661i	0.223006	+	0.187124i
$842$	24.9195	−	17.4488i	0.858784	−	0.601327i
$843$	−15.5892	−	27.7632i	−0.536920	−	0.956215i
$844$	−5.35355	−	6.38012i	−0.184277	−	0.219613i
$845$	−55.2913	−	55.9759i	−1.90208	−	1.92563i
$846$	−20.5735	−	12.5439i	−0.707333	−	0.431268i
$847$	9.38285	+	35.0173i	0.322398	+	1.20321i
$848$	−2.47078	−	1.73006i	−0.0848468	−	0.0594104i
$849$	4.32563	−	43.4480i	0.148455	−	1.49113i
$850$	15.2449	+	13.1150i	0.522896	+	0.449840i
$851$	0.340781	+	0.936289i	0.0116818	+	0.0320956i
$852$	−13.9354	−	17.0170i	−0.477420	−	0.582993i
$853$	−4.31796	+	6.16668i	−0.147844	+	0.211143i	−0.886243	−	0.463221i	$-0.846693\pi$
$853$	−4.31796	+	6.16668i	−0.147844	+	0.211143i	0.738399	+	0.674365i	$0.235582\pi$
$854$	17.7819	−	30.7992i	0.608485	−	1.05393i
$855$	7.17639	−	23.8844i	0.245427	−	0.816830i
$856$	6.96496	+	12.0637i	0.238057	+	0.412327i
$857$	−14.8296	−	1.29742i	−0.506568	−	0.0443190i	−0.168992	−	0.985617i	$-0.554051\pi$
$857$	−14.8296	−	1.29742i	−0.506568	−	0.0443190i	−0.337576	+	0.941298i	$0.609607\pi$
$858$	14.4655	−	8.12246i	0.493844	−	0.277296i
$859$	4.25194	+	0.749731i	0.145074	+	0.0255805i	0.245714	−	0.969342i	$-0.420978\pi$
$859$	4.25194	+	0.749731i	0.145074	+	0.0255805i	−0.100639	+	0.994923i	$0.532089\pi$
$860$	1.01145	+	2.83304i	0.0344902	+	0.0966060i
$861$	−32.6728	−	47.8706i	−1.11349	−	1.63142i
$862$	−28.3345	+	13.2126i	−0.965075	+	0.450022i
$863$	−8.34154	+	8.34154i	−0.283949	+	0.283949i	−0.834682	−	0.550733i	$-0.814348\pi$
$863$	−8.34154	+	8.34154i	−0.283949	+	0.283949i	0.550733	+	0.834682i	$0.314348\pi$
$864$	5.18930	−	0.266814i	0.176543	−	0.00907719i
$865$	40.5886	+	23.7680i	1.38005	+	0.808135i
$866$	−6.67487	+	18.3390i	−0.226821	+	0.623186i
$867$	1.08173	+	0.929961i	0.0367375	+	0.0315831i
$868$	−0.535488	−	6.12065i	−0.0181756	−	0.207749i
$869$	0.912007	−	5.17225i	0.0309377	−	0.175456i
$870$	20.7351	−	11.4757i	0.702985	−	0.389061i
$871$	22.3549	−	18.7580i	0.757466	−	0.635590i
$872$	−4.02005	+	15.0030i	−0.136136	+	0.508067i
$873$	31.1509	−	1.97562i	1.05430	−	0.0668646i
$874$	−1.59519	−	0.920986i	−0.0539582	−	0.0311528i
$875$	6.92648	+	44.0176i	0.234158	+	1.48807i
$876$	8.04562	−	11.2026i	0.271836	−	0.378502i
$877$	−6.00372	+	12.8750i	−0.202731	+	0.434759i	−0.981218	−	0.192903i	$-0.938210\pi$
$877$	−6.00372	+	12.8750i	−0.202731	+	0.434759i	0.778487	+	0.627661i	$0.215988\pi$
$878$	−2.92131	+	6.26478i	−0.0985896	+	0.211426i
$879$	8.95412	+	19.8179i	0.302015	+	0.668440i
$880$	−1.28670	−	2.80425i	−0.0433747	−	0.0945314i
$881$	17.1342	+	9.89241i	0.577264	+	0.333284i	0.760045	−	0.649870i	$-0.225177\pi$
$881$	17.1342	+	9.89241i	0.577264	+	0.333284i	−0.182781	+	0.983154i	$0.558510\pi$
$882$	21.4605	+	15.8053i	0.722612	+	0.532193i
$883$	−8.82448	+	32.9334i	−0.296967	+	1.10830i	0.642675	+	0.766139i	$0.277825\pi$
$883$	−8.82448	+	32.9334i	−0.296967	+	1.10830i	−0.939642	+	0.342158i	$0.888842\pi$
$884$	21.3874	−	17.9461i	0.719335	−	0.603594i
$885$	−9.68356	+	2.40756i	−0.325509	+	0.0809291i
$886$	−0.258597	+	1.46657i	−0.00868773	+	0.0492705i
$887$	3.43553	+	39.2682i	0.115354	+	1.31850i	0.804533	+	0.593908i	$0.202416\pi$
$887$	3.43553	+	39.2682i	0.115354	+	1.31850i	−0.689180	+	0.724591i	$0.742029\pi$
$888$	3.28716	−	1.15208i	0.110310	−	0.0386612i
$889$	19.8477	−	54.5312i	0.665672	−	1.82892i
$890$	−8.90375	+	15.2050i	−0.298454	+	0.509671i
$891$	−0.594124	+	12.4041i	−0.0199039	+	0.415553i
$892$	7.96741	−	7.96741i	0.266769	−	0.266769i
$893$	27.0631	−	12.6197i	0.905632	−	0.422303i
$894$	−5.45770	+	11.3476i	−0.182533	+	0.379520i
$895$	11.2625	−	23.7696i	0.376464	−	0.794531i
$896$	3.92495	+	0.692075i	0.131123	+	0.0231206i
$897$	0.0712751	−	5.95659i	0.00237981	−	0.198885i
$898$	−24.9636	−	2.18404i	−0.833047	−	0.0728822i
$899$	4.71653	+	8.16926i	0.157305	+	0.272460i
$900$	−2.06787	−	14.8568i	−0.0689291	−	0.495226i
$901$	6.06569	−	10.5061i	0.202077	−	0.350008i
$902$	6.64478	−	9.48973i	0.221247	−	0.315973i
$903$	3.28043	−	8.68804i	0.109166	−	0.289120i
$904$	3.88071	+	10.6622i	0.129070	+	0.354618i
$905$	−14.0683	−	20.3571i	−0.467647	−	0.676691i
$906$	22.4941	+	16.1550i	0.747316	+	0.536715i
$907$	−26.0320	−	18.2278i	−0.864378	−	0.605244i	0.0550582	−	0.998483i	$-0.482466\pi$
$907$	−26.0320	−	18.2278i	−0.864378	−	0.605244i	−0.919436	+	0.393239i	$0.871354\pi$
$908$	−0.465067	−	1.73566i	−0.0154338	−	0.0575997i
$909$	−40.3412	−	8.11304i	−1.33803	−	0.269093i
$910$	61.8617	+	0.380573i	2.05070	+	0.0126159i
$911$	22.3307	+	26.6127i	0.739850	+	0.881719i	0.996397	−	0.0848128i	$-0.0270292\pi$
$911$	22.3307	+	26.6127i	0.739850	+	0.881719i	−0.256547	+	0.966532i	$0.582585\pi$
$912$	−3.28614	+	5.53767i	−0.108815	+	0.183370i
$913$	1.26613	−	0.886552i	0.0419027	−	0.0293406i
$914$	−20.7363	−	17.3998i	−0.685895	−	0.575534i
$915$	31.0521	+	15.1706i	1.02655	+	0.501526i
$916$	−10.5434	−	3.83749i	−0.348364	−	0.126794i
$917$	−59.2558	−	59.2558i	−1.95680	−	1.95680i
$918$	2.88809	+	20.6983i	0.0953212	+	0.683147i
$919$			42.9427i			1.41655i	0.705937	+	0.708275i	$0.250526\pi$
$919$			42.9427i			1.41655i	−0.705937	+	0.708275i	$0.749474\pi$
$920$	−1.10304	−	0.103345i	−0.0363663	−	0.00340720i
$921$	−3.49215	+	2.38347i	−0.115070	+	0.0785381i
$922$	−11.5138	+	1.00732i	−0.379186	+	0.0331744i
$923$	50.5609	+	72.2085i	1.66423	+	2.37677i
$924$	−2.57515	+	9.17027i	−0.0847163	+	0.301680i
$925$	−4.13705	−	9.16466i	−0.136025	−	0.301332i
$926$	8.14491	−	4.70246i	0.267658	−	0.154533i
$927$	−15.9709	+	54.3658i	−0.524554	+	1.78561i
$928$	−5.91051	+	1.58372i	−0.194022	+	0.0519881i
$929$	−6.54454	−	37.1159i	−0.214719	−	1.21773i	−0.881393	−	0.472385i	$-0.843393\pi$
$929$	−6.54454	−	37.1159i	−0.214719	−	1.21773i	0.666673	−	0.745350i	$-0.267718\pi$
$930$	5.89769	−	0.930090i	0.193393	−	0.0304989i
$931$	−31.0371	+	11.2966i	−1.01720	+	0.370231i
$932$	−7.30314	−	3.40551i	−0.239222	−	0.111551i
$933$	−2.66085	+	2.17900i	−0.0871122	+	0.0713372i
$934$	8.37233	−	1.47627i	0.273951	−	0.0483050i
$935$	10.7847	−	6.13841i	0.352698	−	0.200748i
$936$	−20.8190	−	0.498301i	−0.680489	−	0.0162875i
$937$	−34.0800	−	9.13172i	−1.11335	−	0.298320i	−0.345158	−	0.938545i	$-0.612175\pi$
$937$	−34.0800	−	9.13172i	−1.11335	−	0.298320i	−0.768188	+	0.640224i	$0.778841\pi$
$938$	−1.46028	+	16.6910i	−0.0476797	+	0.544981i
$939$	30.5745	+	8.58579i	0.997761	+	0.280187i
$940$	11.6290	−	13.6870i	0.379295	−	0.446420i
$941$	−4.79884	+	5.71903i	−0.156438	+	0.186435i	−0.838570	−	0.544793i	$-0.816608\pi$
$941$	−4.79884	+	5.71903i	−0.156438	+	0.186435i	0.682133	+	0.731228i	$0.261053\pi$
$942$	−23.4345	−	4.42188i	−0.763539	−	0.144073i
$943$	−1.75801	−	3.77007i	−0.0572488	−	0.122770i
$944$	2.57640			0.0838547
$945$	−24.8189	+	39.0946i	−0.807360	+	1.27175i
$946$	1.85627			0.0603524
$947$	19.4134	+	41.6322i	0.630851	+	1.35286i	0.918611	+	0.395162i	$0.129312\pi$
$947$	19.4134	+	41.6322i	0.630851	+	1.35286i	−0.287760	+	0.957703i	$0.592911\pi$
$948$	−4.29787	+	4.99929i	−0.139588	+	0.162369i
$949$	−35.5312	+	42.3444i	−1.15339	+	1.37456i
$950$	16.7491	+	8.06258i	0.543412	+	0.261584i
$951$	−0.978989	−	3.83669i	−0.0317459	−	0.124413i
$952$	−1.39707	+	15.9686i	−0.0452794	+	0.517546i
$953$	54.0330	+	14.4781i	1.75030	+	0.468992i	0.984690	−	0.174312i	$-0.0557701\pi$
$953$	54.0330	+	14.4781i	1.75030	+	0.468992i	0.765611	+	0.643304i	$0.222437\pi$
$954$	−8.57470	+	2.89052i	−0.277616	+	0.0935840i
$955$	−10.2351	+	37.2790i	−0.331199	+	1.20632i
$956$	−9.56189	+	1.68602i	−0.309254	+	0.0545298i
$957$	−2.36691	−	14.4311i	−0.0765115	−	0.466490i
$958$	−15.5248	−	7.23935i	−0.501584	−	0.233893i
$959$	0.804297	−	0.292740i	0.0259721	−	0.00945308i
$960$	−0.407394	+	3.85150i	−0.0131486	+	0.124307i
$961$	−4.97041	−	28.1886i	−0.160336	−	0.909310i
$962$	−13.4842	+	3.61308i	−0.434748	+	0.116490i
$963$	41.5316	+	4.63732i	1.33834	+	0.149435i
$964$	−6.14058	+	3.54527i	−0.197775	+	0.114185i
$965$	−0.583821	−	3.43443i	−0.0187939	−	0.110558i
$966$	2.38932	+	2.44720i	0.0768752	+	0.0787372i
$967$	14.3690	+	20.5211i	0.462076	+	0.659914i	0.980797	−	0.195030i	$-0.0624805\pi$
$967$	14.3690	+	20.5211i	0.462076	+	0.659914i	−0.518721	+	0.854944i	$0.673592\pi$
$968$	9.06150	−	0.792778i	0.291248	−	0.0254809i
$969$	−23.3396	−	11.2253i	−0.749776	−	0.360610i
$970$	−2.17023	+	23.1637i	−0.0696820	+	0.743742i
$971$		−	23.4434i		−	0.752336i	−0.926551	−	0.376168i	$-0.877242\pi$
$971$		−	23.4434i		−	0.752336i	0.926551	−	0.376168i	$-0.122758\pi$
$972$	8.58745	−	13.0098i	0.275443	−	0.417290i
$973$	−23.5473	−	23.5473i	−0.754892	−	0.754892i
$974$	32.9053	+	11.9766i	1.05435	+	0.383753i
$975$	3.78468	+	59.9972i	0.121207	+	1.92145i
$976$	−6.83565	−	5.73579i	−0.218804	−	0.183598i
$977$	−27.4981	+	19.2543i	−0.879741	+	0.616001i	−0.923736	−	0.383031i	$-0.874880\pi$
$977$	−27.4981	+	19.2543i	−0.879741	+	0.616001i	0.0439949	+	0.999032i	$0.485991\pi$
$978$	34.0888	+	0.407898i	1.09004	+	0.0130431i
$979$	6.98894	+	8.32909i	0.223368	+	0.266199i
$980$	−14.1333	+	13.9605i	−0.451472	+	0.445951i
$981$	29.0892	+	36.4017i	0.928746	+	1.16222i
$982$	6.53205	+	24.3779i	0.208446	+	0.777931i
$983$	−11.1543	−	7.81033i	−0.355767	−	0.249111i	0.382006	−	0.924160i	$-0.375234\pi$
$983$	−11.1543	−	7.81033i	−0.355767	−	0.249111i	−0.737773	+	0.675049i	$0.764122\pi$
$984$	−13.2523	+	5.98765i	−0.422467	+	0.190879i
$985$	2.38621	−	13.0625i	0.0760311	−	0.416205i
$986$	−8.41732	−	23.1264i	−0.268062	−	0.736495i
$987$	−54.7146	+	8.97403i	−1.74159	+	0.285647i
$988$	14.8024	−	21.1400i	0.470926	−	0.672552i
$989$	0.333269	−	0.577239i	0.0105973	−	0.0183551i
$990$	−9.06299	−	1.88075i	−0.288041	−	0.0597741i
$991$	16.5679	+	28.6964i	0.526296	+	0.911571i	0.999531	+	0.0306346i	$0.00975283\pi$
$991$	16.5679	+	28.6964i	0.526296	+	0.911571i	−0.473235	+	0.880936i	$0.656914\pi$
$992$	−1.53573	−	0.134359i	−0.0487595	−	0.00426590i
$993$	5.97254	+	3.54420i	0.189533	+	0.112472i
$994$	−49.8420	−	8.78849i	−1.58089	−	0.278754i
$995$	−4.13104	−	1.95736i	−0.130963	−	0.0620526i
$996$	−1.93473	+	0.145964i	−0.0613043	+	0.00462503i
$997$	−7.54880	+	3.52006i	−0.239073	+	0.111481i	−0.538463	−	0.842649i	$-0.680995\pi$
$997$	−7.54880	+	3.52006i	−0.239073	+	0.111481i	0.299390	+	0.954131i	$0.403217\pi$
$998$	11.2259	−	11.2259i	0.355350	−	0.355350i
$999$	3.06505	−	9.98999i	0.0969740	−	0.316069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.r.a.23.13	✓	216
3.2	odd	2		810.2.s.a.503.9		216
5.2	odd	4	inner	270.2.r.a.77.1	yes	216
15.2	even	4		810.2.s.a.17.18		216
27.7	even	9		810.2.s.a.143.18		216
27.20	odd	18	inner	270.2.r.a.263.1	yes	216
135.7	odd	36		810.2.s.a.467.9		216
135.47	even	36	inner	270.2.r.a.47.13	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.23.13	✓	216	1.1	even	1	trivial
270.2.r.a.47.13	yes	216	135.47	even	36	inner
270.2.r.a.77.1	yes	216	5.2	odd	4	inner
270.2.r.a.263.1	yes	216	27.20	odd	18	inner
810.2.s.a.17.18		216	15.2	even	4
810.2.s.a.143.18		216	27.7	even	9
810.2.s.a.467.9		216	135.7	odd	36
810.2.s.a.503.9		216	3.2	odd	2

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.422618 + 0.906308i) q^{2} +(-0.572880 - 1.63457i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-2.22872 + 0.181179i) q^{5} +(1.23931 - 1.21000i) q^{6} +(0.347359 - 3.97033i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.34362 + 1.87282i) q^{9} +(-1.10610 - 1.94333i) q^{10} +(-1.35885 + 0.239602i) q^{11} +(1.62039 + 0.611828i) q^{12} +(-6.29127 - 2.93367i) q^{13} +(3.74514 - 1.36312i) q^{14} +(1.57294 + 3.53919i) q^{15} +(-0.173648 - 0.984808i) q^{16} +(3.88494 - 1.04097i) q^{17} +(-2.68781 - 1.33255i) q^{18} +(3.21964 - 1.85886i) q^{19} +(1.29380 - 1.82375i) q^{20} +(-6.68877 + 1.70674i) q^{21} +(-0.791429 - 1.13028i) q^{22} +(-0.493571 + 0.0431819i) q^{23} +(0.130302 + 1.72714i) q^{24} +(4.93435 - 0.807592i) q^{25} -6.94165i q^{26} +(4.40386 + 2.75790i) q^{27} +(2.81817 + 2.81817i) q^{28} +(-5.74999 - 2.09283i) q^{29} +(-2.54285 + 2.92129i) q^{30} +(-1.18093 - 0.990920i) q^{31} +(0.819152 - 0.573576i) q^{32} +(1.17011 + 2.08387i) q^{33} +(2.58528 + 3.08102i) q^{34} +(-0.0548245 + 8.91168i) q^{35} +(0.0717843 - 2.99914i) q^{36} +(-0.520493 - 1.94251i) q^{37} +(3.04538 + 2.13240i) q^{38} +(-1.19113 + 11.9641i) q^{39} +(2.19967 + 0.401829i) q^{40} +(2.87157 + 7.88959i) q^{41} +(-4.37363 - 5.34078i) q^{42} +(-0.771633 + 1.10201i) q^{43} +(0.689907 - 1.19495i) q^{44} +(4.88394 - 4.59860i) q^{45} +(-0.247728 - 0.429078i) q^{46} +(8.00145 + 0.700036i) q^{47} +(-1.51025 + 0.848016i) q^{48} +(-8.74923 - 1.54272i) q^{49} +(2.81727 + 4.13074i) q^{50} +(-3.92714 - 5.75385i) q^{51} +(6.29127 - 2.93367i) q^{52} +(2.13282 - 2.13282i) q^{53} +(-0.638352 + 5.15679i) q^{54} +(2.98508 - 0.780201i) q^{55} +(-1.36312 + 3.74514i) q^{56} +(-4.88290 - 4.19782i) q^{57} +(-0.533307 - 6.09573i) q^{58} +(-0.447387 + 2.53726i) q^{59} +(-3.72224 - 1.07001i) q^{60} +(6.83565 - 5.73579i) q^{61} +(0.398995 - 1.48907i) q^{62} +(6.62164 + 9.95548i) q^{63} +(0.866025 + 0.500000i) q^{64} +(14.5530 + 5.39846i) q^{65} +(-1.39412 + 1.94116i) q^{66} +(-1.77666 + 3.81006i) q^{67} +(-1.69977 + 3.64516i) q^{68} +(0.353341 + 0.782037i) q^{69} +(-8.09989 + 3.71655i) q^{70} +(-10.9974 - 6.34938i) q^{71} +(2.74848 - 1.20243i) q^{72} +(2.06099 - 7.69172i) q^{73} +(1.54054 - 1.29267i) q^{74} +(-4.14685 - 7.60287i) q^{75} +(-0.645576 + 3.66124i) q^{76} +(0.479291 + 5.47832i) q^{77} +(-11.3466 + 3.97673i) q^{78} +(-1.30184 + 3.57678i) q^{79} +(0.565439 + 2.16340i) q^{80} +(1.98508 - 8.77835i) q^{81} +(-5.93681 + 5.93681i) q^{82} +(-1.01524 + 0.473413i) q^{83} +(2.99202 - 6.22097i) q^{84} +(-8.46983 + 3.02389i) q^{85} +(-1.32486 - 0.233609i) q^{86} +(-0.126809 + 10.5977i) q^{87} +(1.37456 + 0.120259i) q^{88} +(-3.93997 - 6.82423i) q^{89} +(6.23179 + 2.48290i) q^{90} +(-13.8330 + 23.9594i) q^{91} +(0.284182 - 0.405854i) q^{92} +(-0.943192 + 2.49799i) q^{93} +(2.74711 + 7.54763i) q^{94} +(-6.83889 + 4.72621i) q^{95} +(-1.40682 - 1.01037i) q^{96} +(-8.52287 - 5.96778i) q^{97} +(-2.29940 - 8.58148i) q^{98} +(2.73590 - 3.10642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100}) \) 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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