LMFDB - Embedded newform 162.2.g.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	162.13
Dual form			162.2.g.a.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.893633 - 0.448799i) q^{2} +(0.647569 - 1.60644i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-0.750365 - 2.50640i) q^{5} +(-1.29966 + 1.14494i) q^{6} +(0.318489 + 0.738341i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-2.16131 - 2.08056i) q^{9} +O(q^{10})$	\(q+(-0.893633 - 0.448799i) q^{2} +(0.647569 - 1.60644i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-0.750365 - 2.50640i) q^{5} +(-1.29966 + 1.14494i) q^{6} +(0.318489 + 0.738341i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-2.16131 - 2.08056i) q^{9} +(-0.454317 + 2.57656i) q^{10} +(0.151352 - 0.0358710i) q^{11} +(1.67527 - 0.439871i) q^{12} +(-0.574171 - 0.377638i) q^{13} +(0.0467545 - 0.802743i) q^{14} +(-4.51229 - 0.417644i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(0.0626772 - 0.0228126i) q^{17} +(0.997663 + 2.82925i) q^{18} +(-0.221311 - 0.0805504i) q^{19} +(1.56235 - 2.09860i) q^{20} +(1.39235 - 0.0335080i) q^{21} +(-0.151352 - 0.0358710i) q^{22} +(3.45177 - 8.00209i) q^{23} +(-1.69449 - 0.358775i) q^{24} +(-1.54153 + 1.01388i) q^{25} +(0.343614 + 0.595158i) q^{26} +(-4.74190 + 2.12471i) q^{27} +(-0.402052 + 0.696374i) q^{28} +(0.585239 + 10.0482i) q^{29} +(3.84489 + 2.39833i) q^{30} +(7.28783 - 0.851825i) q^{31} +(0.686242 - 0.727374i) q^{32} +(0.0403859 - 0.266366i) q^{33} +(-0.0662487 - 0.00774336i) q^{34} +(1.61159 - 1.35229i) q^{35} +(0.378222 - 2.97606i) q^{36} +(6.12996 + 5.14365i) q^{37} +(0.161619 + 0.171306i) q^{38} +(-0.978469 + 0.677826i) q^{39} +(-2.33802 + 1.17420i) q^{40} +(-4.49262 + 2.25628i) q^{41} +(-1.25928 - 0.594940i) q^{42} +(2.28836 + 2.42552i) q^{43} +(0.119154 + 0.0999819i) q^{44} +(-3.59294 + 6.97828i) q^{45} +(-6.67595 + 5.60178i) q^{46} +(12.4934 + 1.46027i) q^{47} +(1.35323 + 1.08110i) q^{48} +(4.35998 - 4.62131i) q^{49} +(1.83259 - 0.214199i) q^{50} +(0.00394061 - 0.115460i) q^{51} +(-0.0399588 - 0.686066i) q^{52} +(-3.27068 + 5.66499i) q^{53} +(5.19108 + 0.229448i) q^{54} +(-0.203476 - 0.352430i) q^{55} +(0.671819 - 0.441862i) q^{56} +(-0.272713 + 0.303361i) q^{57} +(3.98662 - 9.24202i) q^{58} +(-7.05313 - 1.67162i) q^{59} +(-2.35955 - 3.86881i) q^{60} +(-3.70223 + 4.97296i) q^{61} +(-6.89494 - 2.50955i) q^{62} +(0.847811 - 2.25842i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(-0.515673 + 1.72247i) q^{65} +(-0.155635 + 0.219909i) q^{66} +(0.484143 - 8.31242i) q^{67} +(0.0557268 + 0.0366521i) q^{68} +(-10.6196 - 10.7270i) q^{69} +(-2.04708 + 0.485166i) q^{70} +(-0.683417 + 3.87585i) q^{71} +(-1.67365 + 2.48976i) q^{72} +(-1.74184 - 9.87849i) q^{73} +(-3.16947 - 7.34766i) q^{74} +(0.630493 + 3.13293i) q^{75} +(-0.0675461 - 0.225620i) q^{76} +(0.0746888 + 0.100325i) q^{77} +(1.17860 - 0.166591i) q^{78} +(-15.0576 - 7.56219i) q^{79} +2.61631 q^{80} +(0.342522 + 8.99348i) q^{81} +5.02737 q^{82} +(1.94848 + 0.978564i) q^{83} +(0.858329 + 1.09682i) q^{84} +(-0.104208 - 0.139976i) q^{85} +(-0.956381 - 3.19454i) q^{86} +(16.5208 + 5.56672i) q^{87} +(-0.0616079 - 0.142823i) q^{88} +(-0.587729 - 3.33317i) q^{89} +(6.34261 - 4.62351i) q^{90} +(0.0959586 - 0.544208i) q^{91} +(8.47992 - 2.00978i) q^{92} +(3.35096 - 12.2591i) q^{93} +(-10.5091 - 6.91197i) q^{94} +(-0.0358275 + 0.615134i) q^{95} +(-0.724095 - 1.57343i) q^{96} +(2.07475 - 6.93014i) q^{97} +(-5.97026 + 2.17300i) q^{98} +(-0.401749 - 0.237368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$3$	0.647569	−	1.60644i	0.373874	−	0.927480i
$3$	0.647569	−	1.60644i	0.373874	−	0.927480i
$4$	0.597159	+	0.802123i	0.298579	+	0.401062i
$5$	−0.750365	−	2.50640i	−0.335574	−	1.12089i	−0.944732	−	0.327845i	$-0.893678\pi$
$5$	−0.750365	−	2.50640i	−0.335574	−	1.12089i	0.609158	−	0.793049i	$-0.291508\pi$
$6$	−1.29966	+	1.14494i	−0.530583	+	0.467420i
$7$	0.318489	+	0.738341i	0.120378	+	0.279067i	0.967741	−	0.251947i	$-0.0810707\pi$
$7$	0.318489	+	0.738341i	0.120378	+	0.279067i	−0.847364	+	0.531013i	$0.821811\pi$
$8$	−0.173648	−	0.984808i	−0.0613939	−	0.348182i
$9$	−2.16131	−	2.08056i	−0.720437	−	0.693521i
$10$	−0.454317	+	2.57656i	−0.143668	+	0.814780i
$11$	0.151352	−	0.0358710i	0.0456342	−	0.0108155i	−0.207735	−	0.978185i	$-0.566609\pi$
$11$	0.151352	−	0.0358710i	0.0456342	−	0.0108155i	0.253370	+	0.967370i	$0.418461\pi$
$12$	1.67527	−	0.439871i	0.483607	−	0.126980i
$13$	−0.574171	−	0.377638i	−0.159246	−	0.104738i	0.467385	−	0.884054i	$-0.345196\pi$
$13$	−0.574171	−	0.377638i	−0.159246	−	0.104738i	−0.626631	+	0.779316i	$0.715567\pi$
$14$	0.0467545	−	0.802743i	0.0124957	−	0.214542i
$15$	−4.51229	−	0.417644i	−1.16507	−	0.107835i
$16$	−0.286803	+	0.957990i	−0.0717008	+	0.239497i
$17$	0.0626772	−	0.0228126i	0.0152015	−	0.00553288i	−0.334408	−	0.942428i	$-0.608536\pi$
$17$	0.0626772	−	0.0228126i	0.0152015	−	0.00553288i	0.349610	+	0.936895i	$0.386314\pi$
$18$	0.997663	+	2.82925i	0.235151	+	0.666861i
$19$	−0.221311	−	0.0805504i	−0.0507721	−	0.0184795i	0.316509	−	0.948589i	$-0.397489\pi$
$19$	−0.221311	−	0.0805504i	−0.0507721	−	0.0184795i	−0.367281	+	0.930110i	$0.619711\pi$
$20$	1.56235	−	2.09860i	0.349352	−	0.469261i
$21$	1.39235	−	0.0335080i	0.303835	−	0.00731204i
$22$	−0.151352	−	0.0358710i	−0.0322683	−	0.00764772i
$23$	3.45177	−	8.00209i	0.719743	−	1.66855i	−0.0236702	−	0.999720i	$-0.507535\pi$
$23$	3.45177	−	8.00209i	0.719743	−	1.66855i	0.743413	−	0.668832i	$-0.233206\pi$
$24$	−1.69449	−	0.358775i	−0.345885	−	0.0732346i
$25$	−1.54153	+	1.01388i	−0.308306	+	0.202776i
$26$	0.343614	+	0.595158i	0.0673883	+	0.116720i
$27$	−4.74190	+	2.12471i	−0.912579	+	0.408901i
$28$	−0.402052	+	0.696374i	−0.0759807	+	0.131602i
$29$	0.585239	+	10.0482i	0.108676	+	1.86590i	0.409622	+	0.912255i	$0.365661\pi$
$29$	0.585239	+	10.0482i	0.108676	+	1.86590i	−0.300946	+	0.953641i	$0.597302\pi$
$30$	3.84489	+	2.39833i	0.701978	+	0.437874i
$31$	7.28783	−	0.851825i	1.30893	−	0.152992i	0.567140	−	0.823621i	$-0.308050\pi$
$31$	7.28783	−	0.851825i	1.30893	−	0.152992i	0.741793	+	0.670629i	$0.233976\pi$
$32$	0.686242	−	0.727374i	0.121312	−	0.128583i
$33$	0.0403859	−	0.266366i	0.00703028	−	0.0463684i
$34$	−0.0662487	−	0.00774336i	−0.0113616	−	0.00132798i
$35$	1.61159	−	1.35229i	0.272409	−	0.228578i
$36$	0.378222	−	2.97606i	0.0630371	−	0.496010i
$37$	6.12996	+	5.14365i	1.00776	+	0.845611i	0.988040	−	0.154195i	$-0.0492783\pi$
$37$	6.12996	+	5.14365i	1.00776	+	0.845611i	0.0197193	+	0.999806i	$0.493723\pi$
$38$	0.161619	+	0.171306i	0.0262181	+	0.0277896i
$39$	−0.978469	+	0.677826i	−0.156681	+	0.108539i
$40$	−2.33802	+	1.17420i	−0.369673	+	0.185657i
$41$	−4.49262	+	2.25628i	−0.701630	+	0.352372i	−0.763585	−	0.645707i	$-0.776563\pi$
$41$	−4.49262	+	2.25628i	−0.701630	+	0.352372i	0.0619553	+	0.998079i	$0.480266\pi$
$42$	−1.25928	−	0.594940i	−0.194312	−	0.0918012i
$43$	2.28836	+	2.42552i	0.348971	+	0.369888i	0.877954	−	0.478744i	$-0.158908\pi$
$43$	2.28836	+	2.42552i	0.348971	+	0.369888i	−0.528983	+	0.848632i	$0.677426\pi$
$44$	0.119154	+	0.0999819i	0.0179631	+	0.0150728i
$45$	−3.59294	+	6.97828i	−0.535604	+	1.04026i
$46$	−6.67595	+	5.60178i	−0.984314	+	0.825938i
$47$	12.4934	+	1.46027i	1.82235	+	0.213002i	0.957382	−	0.288824i	$-0.0932643\pi$
$47$	12.4934	+	1.46027i	1.82235	+	0.213002i	0.864968	+	0.501827i	$0.167338\pi$
$48$	1.35323	+	1.08110i	0.195322	+	0.156043i
$49$	4.35998	−	4.62131i	0.622854	−	0.660187i
$50$	1.83259	−	0.214199i	0.259167	−	0.0302923i
$51$	0.00394061	−	0.115460i	0.000551796	−	0.0161676i
$52$	−0.0399588	−	0.686066i	−0.00554129	−	0.0951403i
$53$	−3.27068	+	5.66499i	−0.449263	+	0.778146i	−0.998338	−	0.0576268i	$-0.981647\pi$
$53$	−3.27068	+	5.66499i	−0.449263	+	0.778146i	0.549075	+	0.835773i	$0.314980\pi$
$54$	5.19108	+	0.229448i	0.706417	+	0.0312239i
$55$	−0.203476	−	0.352430i	−0.0274367	−	0.0475217i
$56$	0.671819	−	0.441862i	0.0897756	−	0.0590463i
$57$	−0.272713	+	0.303361i	−0.0361218	+	0.0401811i
$58$	3.98662	−	9.24202i	0.523469	−	1.21354i
$59$	−7.05313	−	1.67162i	−0.918239	−	0.217627i	−0.255789	−	0.966733i	$-0.582335\pi$
$59$	−7.05313	−	1.67162i	−0.918239	−	0.217627i	−0.662450	+	0.749106i	$0.730483\pi$
$60$	−2.35955	−	3.86881i	−0.304617	−	0.499462i
$61$	−3.70223	+	4.97296i	−0.474023	+	0.636723i	−0.973250	−	0.229748i	$-0.926210\pi$
$61$	−3.70223	+	4.97296i	−0.474023	+	0.636723i	0.499228	+	0.866471i	$0.333617\pi$
$62$	−6.89494	−	2.50955i	−0.875658	−	0.318714i
$63$	0.847811	−	2.25842i	0.106814	−	0.284534i
$64$	−0.939693	+	0.342020i	−0.117462	+	0.0427525i
$65$	−0.515673	+	1.72247i	−0.0639613	+	0.213646i
$66$	−0.155635	+	0.219909i	−0.0191574	+	0.0270689i
$67$	0.484143	−	8.31242i	0.0591475	−	1.01552i	−0.829959	−	0.557824i	$-0.811636\pi$
$67$	0.484143	−	8.31242i	0.0591475	−	1.01552i	0.889107	−	0.457700i	$-0.151326\pi$
$68$	0.0557268	+	0.0366521i	0.00675787	+	0.00444472i
$69$	−10.6196	−	10.7270i	−1.27845	−	1.29138i
$70$	−2.04708	+	0.485166i	−0.244672	+	0.0579884i
$71$	−0.683417	+	3.87585i	−0.0811066	+	0.459979i	0.917022	+	0.398836i	$0.130586\pi$
$71$	−0.683417	+	3.87585i	−0.0811066	+	0.459979i	−0.998129	+	0.0611428i	$0.980525\pi$
$72$	−1.67365	+	2.48976i	−0.197241	+	0.293421i
$73$	−1.74184	−	9.87849i	−0.203867	−	1.15619i	−0.899212	−	0.437513i	$-0.855859\pi$
$73$	−1.74184	−	9.87849i	−0.203867	−	1.15619i	0.695344	−	0.718677i	$-0.255252\pi$
$74$	−3.16947	−	7.34766i	−0.368443	−	0.854148i
$75$	0.630493	+	3.13293i	0.0728031	+	0.361760i
$76$	−0.0675461	−	0.225620i	−0.00774807	−	0.0258804i
$77$	0.0746888	+	0.100325i	0.00851158	+	0.0114330i
$78$	1.17860	−	0.166591i	0.133450	−	0.0188627i
$79$	−15.0576	−	7.56219i	−1.69411	−	0.850812i	−0.990058	−	0.140661i	$-0.955077\pi$
$79$	−15.0576	−	7.56219i	−1.69411	−	0.850812i	−0.704049	−	0.710151i	$-0.748627\pi$
$80$	2.61631			0.292512
$81$	0.342522	+	8.99348i	0.0380580	+	0.999276i
$82$	5.02737			0.555180
$83$	1.94848	+	0.978564i	0.213874	+	0.107411i	0.552511	−	0.833506i	$-0.313670\pi$
$83$	1.94848	+	0.978564i	0.213874	+	0.107411i	−0.338637	+	0.940917i	$0.609966\pi$
$84$	0.858329	+	1.09682i	0.0936513	+	0.119673i
$85$	−0.104208	−	0.139976i	−0.0113030	−	0.0151825i
$86$	−0.956381	−	3.19454i	−0.103129	−	0.344476i
$87$	16.5208	+	5.56672i	1.77121	+	0.596815i
$88$	−0.0616079	−	0.142823i	−0.00656743	−	0.0152250i
$89$	−0.587729	−	3.33317i	−0.0622991	−	0.353316i	−0.999983	−	0.00582641i	$-0.998145\pi$
$89$	−0.587729	−	3.33317i	−0.0622991	−	0.353316i	0.937684	−	0.347489i	$-0.112966\pi$
$90$	6.34261	−	4.62351i	0.668570	−	0.487361i
$91$	0.0959586	−	0.544208i	0.0100592	−	0.0570485i
$92$	8.47992	−	2.00978i	0.884093	−	0.209534i
$93$	3.35096	−	12.2591i	0.347479	−	1.27121i
$94$	−10.5091	−	6.91197i	−1.08394	−	0.712916i
$95$	−0.0358275	+	0.615134i	−0.00367582	+	0.0631114i
$96$	−0.724095	−	1.57343i	−0.0739026	−	0.160588i
$97$	2.07475	−	6.93014i	0.210659	−	0.703649i	−0.785717	−	0.618586i	$-0.787706\pi$
$97$	2.07475	−	6.93014i	0.210659	−	0.703649i	0.996376	−	0.0850629i	$-0.0271091\pi$
$98$	−5.97026	+	2.17300i	−0.603087	+	0.219506i
$99$	−0.401749	−	0.237368i	−0.0403773	−	0.0238564i
$100$	−1.73379	−	0.631050i	−0.173379	−	0.0631050i
$101$	−4.13021	+	5.54784i	−0.410971	+	0.552030i	−0.958624	−	0.284676i	$-0.908114\pi$
$101$	−4.13021	+	5.54784i	−0.410971	+	0.552030i	0.547653	+	0.836706i	$0.315522\pi$
$102$	−0.0553398	+	0.101410i	−0.00547946	+	0.0100411i
$103$	12.1774	+	2.88610i	1.19988	+	0.284376i	0.781504	−	0.623900i	$-0.214453\pi$
$103$	12.1774	+	2.88610i	1.19988	+	0.284376i	0.418372	+	0.908276i	$0.362601\pi$
$104$	−0.272197	+	0.631025i	−0.0266912	+	0.0618771i
$105$	−1.12875	−	3.46463i	−0.110155	−	0.338113i
$106$	5.46523	−	3.59454i	0.530830	−	0.349133i
$107$	4.44410	+	7.69740i	0.429627	+	0.744136i	0.996840	−	0.0794354i	$-0.0253117\pi$
$107$	4.44410	+	7.69740i	0.429627	+	0.744136i	−0.567213	+	0.823571i	$0.691978\pi$
$108$	−4.53595	−	2.53480i	−0.436472	−	0.243911i
$109$	−5.81125	+	10.0654i	−0.556617	+	0.964089i	0.441158	+	0.897429i	$0.354568\pi$
$109$	−5.81125	+	10.0654i	−0.556617	+	0.964089i	−0.997776	+	0.0666601i	$0.978766\pi$
$110$	0.0236621	+	0.406263i	0.00225610	+	0.0387357i
$111$	12.2325	−	6.51656i	1.16106	−	0.618525i
$112$	−0.798667	+	0.0933508i	−0.0754669	+	0.00882082i
$113$	−8.52356	+	9.03445i	−0.801829	+	0.849889i	−0.991249	−	0.132007i	$-0.957858\pi$
$113$	−8.52356	+	9.03445i	−0.801829	+	0.849889i	0.189420	+	0.981896i	$0.439339\pi$
$114$	0.379853	−	0.148699i	0.0355765	−	0.0139270i
$115$	−22.6465	−	2.64700i	−2.11180	−	0.246834i
$116$	−7.71038	+	6.46978i	−0.715891	+	0.600704i
$117$	0.455262	+	2.01079i	0.0420890	+	0.185898i
$118$	5.55268	+	4.65925i	0.511166	+	0.428919i
$119$	0.0368055	+	0.0390116i	0.00337396	+	0.00357619i
$120$	0.372252	+	4.51626i	0.0339818	+	0.412276i
$121$	−9.80834	+	4.92593i	−0.891667	+	0.447812i
$122$	5.54030	−	2.78244i	0.501595	−	0.251911i
$123$	0.715301	+	8.67823i	0.0644965	+	0.782490i
$124$	5.03526	+	5.33706i	0.452180	+	0.479282i
$125$	−6.32314	−	5.30575i	−0.565559	−	0.474561i
$126$	−1.77121	+	1.63770i	−0.157792	+	0.145898i
$127$	−5.95411	+	4.99609i	−0.528342	+	0.443331i	−0.867528	−	0.497388i	$-0.834293\pi$
$127$	−5.95411	+	4.99609i	−0.528342	+	0.443331i	0.339187	+	0.940719i	$0.389848\pi$
$128$	0.993238	+	0.116093i	0.0877907	+	0.0102613i
$129$	5.37832	−	2.10542i	0.473535	−	0.185372i
$130$	1.23386	−	1.30782i	0.108217	−	0.114703i
$131$	9.32278	−	1.08968i	0.814535	−	0.0952055i	0.301383	−	0.953503i	$-0.402552\pi$
$131$	9.32278	−	1.08968i	0.814535	−	0.0952055i	0.513152	+	0.858298i	$0.328478\pi$
$132$	0.237775	−	0.126669i	0.0206957	−	0.0110251i
$133$	−0.0110113	−	0.189057i	−0.000954803	−	0.0163933i
$134$	−4.16325	+	7.21096i	−0.359650	+	0.622932i
$135$	8.88352	+	10.2908i	0.764572	+	0.885688i
$136$	−0.0333499	−	0.0577636i	−0.00285973	−	0.00495319i
$137$	−12.8062	+	8.42278i	−1.09411	+	0.719606i	−0.962388	−	0.271680i	$-0.912421\pi$
$137$	−12.8062	+	8.42278i	−1.09411	+	0.719606i	−0.131721	+	0.991287i	$0.542050\pi$
$138$	4.67581	+	14.3521i	0.398031	+	1.22173i
$139$	−1.56019	+	3.61692i	−0.132333	+	0.306783i	−0.971480	−	0.237122i	$-0.923796\pi$
$139$	−1.56019	+	3.61692i	−0.132333	+	0.306783i	0.839146	+	0.543906i	$0.183055\pi$
$140$	2.04708	+	0.485166i	0.173009	+	0.0410040i
$141$	10.4362	−	19.1243i	0.878884	−	1.61056i
$142$	2.35020	−	3.15687i	0.197224	−	0.264918i
$143$	−0.100448	−	0.0365601i	−0.00839988	−	0.00305731i
$144$	2.61303	−	1.47380i	0.217752	−	0.122817i
$145$	24.7455	−	9.00663i	2.05500	−	0.747960i
$146$	−2.87689	+	9.60948i	−0.238093	+	0.795286i
$147$	−4.60048	−	9.99667i	−0.379441	−	0.824511i
$148$	−0.465281	+	7.98856i	−0.0382458	+	0.656656i
$149$	−1.25658	−	0.826467i	−0.102943	−	0.0677068i	0.496994	−	0.867754i	$-0.334437\pi$
$149$	−1.25658	−	0.826467i	−0.102943	−	0.0677068i	−0.599937	+	0.800047i	$0.704808\pi$
$150$	0.842629	−	3.08266i	0.0688004	−	0.251698i
$151$	12.7162	−	3.01380i	1.03483	−	0.245259i	0.322106	−	0.946704i	$-0.395609\pi$
$151$	12.7162	−	3.01380i	1.03483	−	0.245259i	0.712724	+	0.701444i	$0.247461\pi$
$152$	−0.0408965	+	0.231936i	−0.00331715	+	0.0188125i
$153$	−0.182928	−	0.0810987i	−0.0147889	−	0.00655644i
$154$	−0.0217188	−	0.123174i	−0.00175015	−	0.00992561i
$155$	−7.60355	−	17.6270i	−0.610732	−	1.41583i
$156$	−1.12800	−	0.380083i	−0.0903124	−	0.0304310i
$157$	5.80940	+	19.4048i	0.463641	+	1.54867i	0.795869	+	0.605469i	$0.207014\pi$
$157$	5.80940	+	19.4048i	0.463641	+	1.54867i	−0.332228	+	0.943199i	$0.607800\pi$
$158$	10.0620	+	13.5156i	0.800491	+	1.07525i
$159$	6.98248	+	8.92263i	0.553747	+	0.707611i
$160$	−2.33802	−	1.17420i	−0.184837	−	0.0928284i
$161$	7.00763			0.552278
$162$	3.73018	−	8.19059i	0.293070	−	0.643514i
$163$	−1.85361			−0.145186			−0.0725930	−	0.997362i	$-0.523127\pi$
$163$	−1.85361			−0.145186			−0.0725930	+	0.997362i	$0.523127\pi$
$164$	−4.49262	−	2.25628i	−0.350815	−	0.176186i
$165$	−0.697923	+	0.0986492i	−0.0543333	+	0.00767983i
$166$	−1.30205	−	1.74895i	−0.101058	−	0.135745i
$167$	−3.60077	−	12.0274i	−0.278636	−	0.930709i	−0.976688	−	0.214662i	$-0.931135\pi$
$167$	−3.60077	−	12.0274i	−0.278636	−	0.930709i	0.698053	−	0.716047i	$-0.254050\pi$
$168$	−0.274777	−	1.36537i	−0.0211995	−	0.105341i
$169$	−4.96198	−	11.5032i	−0.381690	−	0.884858i
$170$	0.0303028	+	0.171856i	0.00232412	+	0.0131807i
$171$	0.310730	+	0.634545i	0.0237622	+	0.0485249i
$172$	−0.579051	+	3.28396i	−0.0441523	+	0.250400i
$173$	10.6230	−	2.51769i	0.807650	−	0.191416i	0.194007	−	0.981000i	$-0.437852\pi$
$173$	10.6230	−	2.51769i	0.807650	−	0.191416i	0.613643	+	0.789584i	$0.289703\pi$
$174$	−12.2652	−	12.3891i	−0.929819	−	0.939216i
$175$	−1.23955	−	0.815265i	−0.0937012	−	0.0616282i
$176$	−0.00904409	+	0.155281i	−0.000681724	+	0.0117048i
$177$	−7.25274	+	10.2479i	−0.545150	+	0.770283i
$178$	−0.970712	+	3.24241i	−0.0727580	+	0.243029i
$179$	−8.73770	+	3.18026i	−0.653087	+	0.237704i	−0.647249	−	0.762279i	$-0.724080\pi$
$179$	−8.73770	+	3.18026i	−0.653087	+	0.237704i	−0.00583785	+	0.999983i	$0.501858\pi$
$180$	−7.74299	+	1.28516i	−0.577129	+	0.0957902i
$181$	14.1384	+	5.14597i	1.05090	+	0.382497i	0.809003	−	0.587804i	$-0.200007\pi$
$181$	14.1384	+	5.14597i	1.05090	+	0.382497i	0.241899	+	0.970301i	$0.422230\pi$
$182$	−0.329992	+	0.443256i	−0.0244606	+	0.0328563i
$183$	5.59133	+	9.16776i	0.413323	+	0.677700i
$184$	−8.47992	−	2.00978i	−0.625148	−	0.148163i
$185$	8.29231	−	19.2237i	0.609663	−	1.41336i
$186$	−8.49640	+	9.45121i	−0.622986	+	0.692997i
$187$	0.00866798	−	0.00570102i	0.000633866	−	0.000416900i
$188$	6.28923	+	10.8933i	0.458689	+	0.794473i
$189$	−3.07901	−	2.82444i	−0.223965	−	0.205448i
$190$	0.308088	−	0.533624i	0.0223511	−	0.0387132i
$191$	0.434148	+	7.45404i	0.0314139	+	0.539355i	0.976901	+	0.213694i	$0.0685497\pi$
$191$	0.434148	+	7.45404i	0.0314139	+	0.539355i	−0.945487	+	0.325661i	$0.894413\pi$
$192$	−0.0590799	+	1.73104i	−0.00426373	+	0.124927i
$193$	−12.3408	+	1.44244i	−0.888313	+	0.103829i	−0.547995	−	0.836481i	$-0.684609\pi$
$193$	−12.3408	+	1.44244i	−0.888313	+	0.103829i	−0.340318	+	0.940310i	$0.610535\pi$
$194$	−4.96430	+	5.26186i	−0.356416	+	0.377779i
$195$	2.43311	+	1.94381i	0.174239	+	0.139199i
$196$	6.31046	+	0.737587i	0.450747	+	0.0526848i
$197$	15.5743	−	13.0684i	1.10962	−	0.931083i	0.111587	−	0.993755i	$-0.464407\pi$
$197$	15.5743	−	13.0684i	1.10962	−	0.931083i	0.998034	+	0.0626719i	$0.0199622\pi$
$198$	0.252486	+	0.392425i	0.0179434	+	0.0278884i
$199$	−17.7742	−	14.9143i	−1.25998	−	1.05725i	−0.995684	−	0.0928038i	$-0.970417\pi$
$199$	−17.7742	−	14.9143i	−1.25998	−	1.05725i	−0.264293	−	0.964443i	$-0.585139\pi$
$200$	1.26616	+	1.34205i	0.0895311	+	0.0948974i
$201$	−13.0399	−	6.16061i	−0.919764	−	0.434536i
$202$	6.18076	−	3.10409i	0.434876	−	0.218403i
$203$	−7.23258	+	3.63234i	−0.507627	+	0.254940i
$204$	0.0949664	−	0.0657871i	0.00664898	−	0.00460602i
$205$	9.02624	+	9.56725i	0.630420	+	0.668206i
$206$	−9.58685	−	8.04433i	−0.667948	−	0.560475i
$207$	−24.1092	+	10.1134i	−1.67570	+	0.702929i
$208$	0.526448	−	0.441742i	0.0365026	−	0.0306293i
$209$	−0.0363851	−	0.00425281i	−0.00251681	−	0.000294173i
$210$	−0.546231	+	3.60269i	−0.0376935	+	0.248609i
$211$	−12.8338	+	13.6031i	−0.883519	+	0.936475i	−0.998380	−	0.0569065i	$-0.981876\pi$
$211$	−12.8338	+	13.6031i	−0.883519	+	0.936475i	0.114861	+	0.993382i	$0.463358\pi$
$212$	−6.49714	+	0.759406i	−0.446225	+	0.0521562i
$213$	5.78376	+	3.60775i	0.396297	+	0.247199i
$214$	−0.516802	−	8.87315i	−0.0353279	−	0.606556i
$215$	4.36220	−	7.55556i	0.297500	−	0.515285i
$216$	2.91585	+	4.30091i	0.198399	+	0.292640i
$217$	2.95003	+	5.10961i	0.200261	+	0.346863i
$218$	9.71046	−	6.38667i	0.657676	−	0.432560i
$219$	−16.9972	−	3.59883i	−1.14856	−	0.243186i
$220$	0.161185	−	0.373670i	0.0108671	−	0.0251928i
$221$	−0.0446024	−	0.0105710i	−0.00300028	−	0.000711080i
$222$	−13.8560	+	0.333457i	−0.929956	+	0.0223802i
$223$	−5.57356	+	7.48658i	−0.373233	+	0.501339i	−0.948566	−	0.316581i	$-0.897465\pi$
$223$	−5.57356	+	7.48658i	−0.373233	+	0.501339i	0.575333	+	0.817919i	$0.304873\pi$
$224$	0.755610	+	0.275020i	0.0504863	+	0.0183755i
$225$	5.44116	+	1.01594i	0.362744	+	0.0677293i
$226$	11.6716	−	4.24811i	0.776382	−	0.282580i
$227$	6.03211	−	20.1487i	0.400365	−	1.33731i	−0.485851	−	0.874042i	$-0.661490\pi$
$227$	6.03211	−	20.1487i	0.400365	−	1.33731i	0.886216	−	0.463272i	$-0.153325\pi$
$228$	−0.406186	−	0.0375953i	−0.0269003	−	0.00248981i
$229$	0.524687	−	9.00853i	0.0346723	−	0.595301i	−0.935566	−	0.353151i	$-0.885110\pi$
$229$	0.524687	−	9.00853i	0.0346723	−	0.595301i	0.970239	−	0.242150i	$-0.0778526\pi$
$230$	19.0497	+	12.5292i	1.25610	+	0.826149i
$231$	0.209532	−	0.0550163i	0.0137862	−	0.00361980i
$232$	9.79388	−	2.32119i	0.643000	−	0.152394i
$233$	1.51248	−	8.57770i	0.0990858	−	0.561944i	−0.894333	−	0.447403i	$-0.852349\pi$
$233$	1.51248	−	8.57770i	0.0990858	−	0.561944i	0.993419	−	0.114541i	$-0.0365398\pi$
$234$	0.495605	−	2.00123i	0.0323987	−	0.130825i
$235$	−5.71461	−	32.4091i	−0.372780	−	2.11414i
$236$	−2.87099	−	6.65570i	−0.186885	−	0.433249i
$237$	−21.8990	+	19.2920i	−1.42249	+	1.25315i
$238$	−0.0153823	−	0.0513803i	−0.000997084	−	0.00333049i
$239$	14.8965	+	20.0094i	0.963572	+	1.29430i	0.955703	+	0.294332i	$0.0950972\pi$
$239$	14.8965	+	20.0094i	0.963572	+	1.29430i	0.00786849	+	0.999969i	$0.497495\pi$
$240$	1.69424	−	4.20295i	0.109363	−	0.271299i
$241$	17.6807	+	8.87956i	1.13891	+	0.571983i	0.915331	−	0.402703i	$-0.131929\pi$
$241$	17.6807	+	8.87956i	1.13891	+	0.571983i	0.223581	+	0.974685i	$0.428225\pi$
$242$	10.9758			0.705552
$243$	14.6693	+	5.27365i	0.941037	+	0.338305i
$244$	−6.19975			−0.396898
$245$	−14.8544	−	7.46016i	−0.949013	−	0.476612i
$246$	3.25557	−	8.07618i	0.207567	−	0.514918i
$247$	0.0966512	+	0.129825i	0.00614977	+	0.00826057i
$248$	−2.10440	−	7.02919i	−0.133630	−	0.446354i
$249$	2.83378	−	2.49643i	0.179584	−	0.158205i
$250$	3.26935	+	7.57921i	0.206772	+	0.479351i
$251$	−2.82742	−	16.0351i	−0.178465	−	1.01213i	−0.934068	−	0.357096i	$-0.883767\pi$
$251$	−2.82742	−	16.0351i	−0.178465	−	1.01213i	0.755602	−	0.655031i	$-0.227344\pi$
$252$	2.31781	−	0.668587i	0.146008	−	0.0421170i
$253$	0.235387	−	1.33495i	0.0147987	−	0.0839274i
$254$	7.56303	−	1.79247i	0.474546	−	0.112470i
$255$	−0.292345	+	0.0767605i	−0.0183074	+	0.00480693i
$256$	−0.835488	−	0.549509i	−0.0522180	−	0.0343443i
$257$	−0.122334	+	2.10039i	−0.00763099	+	0.131019i	0.992341	+	0.123529i	$0.0394212\pi$
$257$	−0.122334	+	2.10039i	−0.00763099	+	0.131019i	−0.999972	+	0.00748998i	$0.997616\pi$
$258$	−5.75116	−	0.532310i	−0.358051	−	0.0331402i
$259$	−1.84544	+	6.16420i	−0.114670	+	0.383025i
$260$	−1.68957	+	0.614953i	−0.104783	+	0.0381378i
$261$	19.6409	−	22.9348i	1.21574	−	1.41963i
$262$	−8.82019	−	3.21029i	−0.544913	−	0.198332i
$263$	3.53716	−	4.75123i	0.218111	−	0.292973i	−0.679579	−	0.733603i	$-0.737837\pi$
$263$	3.53716	−	4.75123i	0.218111	−	0.292973i	0.897689	+	0.440629i	$0.145245\pi$
$264$	−0.269333	+	0.00648172i	−0.0165763	+	0.000398922i
$265$	16.6529	+	3.94681i	1.02298	+	0.242451i
$266$	−0.0750086	+	0.173889i	−0.00459907	+	0.0106618i
$267$	−5.73514	−	1.21431i	−0.350985	−	0.0743144i
$268$	6.95669	−	4.57549i	0.424948	−	0.279492i
$269$	1.86000	+	3.22161i	0.113406	+	0.196425i	0.917141	−	0.398562i	$-0.130491\pi$
$269$	1.86000	+	3.22161i	0.113406	+	0.196425i	−0.803735	+	0.594987i	$0.797157\pi$
$270$	−3.32012	−	13.1831i	−0.202056	−	0.802297i
$271$	−9.85402	+	17.0677i	−0.598589	+	1.03679i	0.394441	+	0.918921i	$0.370938\pi$
$271$	−9.85402	+	17.0677i	−0.598589	+	1.03679i	−0.993030	+	0.117865i	$0.962395\pi$
$272$	0.00387824	+	0.0665869i	0.000235153	+	0.00403742i
$273$	−0.812099	−	0.506564i	−0.0491505	−	0.0306586i
$274$	15.2242	−	1.77945i	0.919727	−	0.107501i
$275$	−0.196944	+	0.208748i	−0.0118762	+	0.0125880i
$276$	2.26274	−	14.9240i	0.136201	−	0.898317i
$277$	−3.12717	−	0.365514i	−0.187893	−	0.0219616i	0.0216257	−	0.999766i	$-0.493116\pi$
$277$	−3.12717	−	0.365514i	−0.187893	−	0.0219616i	−0.209519	+	0.977805i	$0.567190\pi$
$278$	3.01751	−	2.53199i	0.180978	−	0.151859i
$279$	−17.5235	−	13.3217i	−1.04911	−	0.797551i
$280$	−1.61159	−	1.35229i	−0.0963110	−	0.0808145i
$281$	14.6740	+	15.5535i	0.875377	+	0.927845i	0.997910	−	0.0646194i	$-0.0205833\pi$
$281$	14.6740	+	15.5535i	0.875377	+	0.927845i	−0.122533	+	0.992464i	$0.539102\pi$
$282$	−17.9091	+	12.4064i	−1.06647	+	0.738788i
$283$	−9.73365	+	4.88842i	−0.578606	+	0.290587i	−0.713933	−	0.700214i	$-0.753088\pi$
$283$	−9.73365	+	4.88842i	−0.578606	+	0.290587i	0.135327	+	0.990801i	$0.456791\pi$
$284$	−3.51702	+	1.76631i	−0.208696	+	0.104811i
$285$	0.964976	+	0.455896i	0.0571602	+	0.0270050i
$286$	0.0733555	+	0.0777522i	0.00433760	+	0.00459759i
$287$	−3.09676	−	2.59849i	−0.182796	−	0.153384i
$288$	−2.99653	+	0.144312i	−0.176572	+	0.00850364i
$289$	−13.0193	+	10.9245i	−0.765844	+	0.642619i
$290$	−26.1556	−	3.05715i	−1.53591	−	0.179522i
$291$	−9.78933	−	7.82070i	−0.573860	−	0.458458i
$292$	6.88361	−	7.29620i	0.402833	−	0.426978i
$293$	−20.1441	+	2.35451i	−1.17683	+	0.137552i	−0.681943	−	0.731405i	$-0.738865\pi$
$293$	−20.1441	+	2.35451i	−1.17683	+	0.137552i	−0.494888	+	0.868957i	$0.664791\pi$
$294$	−0.375359	+	10.9980i	−0.0218914	+	0.641419i
$295$	1.10268	+	18.9322i	0.0642004	+	1.10228i
$296$	4.00105	−	6.93002i	0.232556	−	0.402799i
$297$	−0.641478	+	0.491675i	−0.0372223	+	0.0285299i
$298$	0.752005	+	1.30251i	0.0435625	+	0.0754524i
$299$	−5.00380	+	3.29105i	−0.289377	+	0.190327i
$300$	−2.13650	+	2.37659i	−0.123351	+	0.137213i
$301$	−1.06204	+	2.46209i	−0.0612151	+	0.141913i
$302$	−12.7162	−	3.01380i	−0.731735	−	0.173424i
$303$	6.23768	+	10.2275i	0.358345	+	0.587557i
$304$	0.140639	−	0.188911i	0.00806620	−	0.0108348i
$305$	15.2422	+	5.54772i	0.872768	+	0.317662i
$306$	0.127073	+	0.154570i	0.00726431	+	0.00883620i
$307$	4.98325	−	1.81375i	0.284409	−	0.103516i	−0.195877	−	0.980629i	$-0.562755\pi$
$307$	4.98325	−	1.81375i	0.284409	−	0.103516i	0.480286	+	0.877112i	$0.340533\pi$
$308$	−0.0358715	+	0.119819i	−0.00204397	+	0.00682734i
$309$	12.5221	−	17.6934i	0.712355	−	1.00654i
$310$	−1.11621	+	19.1645i	−0.0633963	+	1.08847i
$311$	3.54349	+	2.33059i	0.200933	+	0.132156i	0.645988	−	0.763347i	$-0.276446\pi$
$311$	3.54349	+	2.33059i	0.200933	+	0.132156i	−0.445055	+	0.895503i	$0.646816\pi$
$312$	0.837438	+	0.845901i	0.0474106	+	0.0478897i
$313$	4.47705	−	1.06108i	0.253058	−	0.0599758i	−0.102129	−	0.994771i	$-0.532565\pi$
$313$	4.47705	−	1.06108i	0.253058	−	0.0599758i	0.355187	+	0.934795i	$0.384417\pi$
$314$	3.51737	−	19.9480i	0.198496	−	1.12573i
$315$	−6.29666	−	0.430307i	−0.354777	−	0.0242451i
$316$	−2.92594	−	16.5938i	−0.164597	−	0.933476i
$317$	−2.50285	−	5.80226i	−0.140574	−	0.325887i	0.833356	−	0.552737i	$-0.186417\pi$
$317$	−2.50285	−	5.80226i	−0.140574	−	0.325887i	−0.973930	+	0.226850i	$0.927157\pi$
$318$	−2.23531	−	11.1073i	−0.125350	−	0.622866i
$319$	0.449014	+	1.49981i	0.0251400	+	0.0839733i
$320$	1.56235	+	2.09860i	0.0873381	+	0.117315i
$321$	15.2433	−	2.15459i	0.850797	−	0.120257i
$322$	−6.26224	−	3.14502i	−0.348981	−	0.175265i
$323$	−0.0157087			−0.000874055
$324$	−7.00934	+	5.64528i	−0.389408	+	0.313627i
$325$	1.26798			0.0703350
$326$	1.65645	+	0.831899i	0.0917421	+	0.0460746i
$327$	12.4063	+	15.8535i	0.686069	+	0.876699i
$328$	3.00214	+	4.03257i	0.165765	+	0.222661i
$329$	2.90084	+	9.68947i	0.159928	+	0.534198i
$330$	0.667961	+	0.225071i	0.0367700	+	0.0123898i
$331$	6.35611	+	14.7351i	0.349363	+	0.809915i	0.998775	+	0.0494782i	$0.0157558\pi$
$331$	6.35611	+	14.7351i	0.349363	+	0.809915i	−0.649412	+	0.760437i	$0.724985\pi$
$332$	0.378623	+	2.14728i	0.0207797	+	0.117847i
$333$	−2.54707	−	23.8708i	−0.139578	−	1.30811i
$334$	−2.18013	+	12.3641i	−0.119291	+	0.676534i
$335$	−21.1975	+	5.02390i	−1.15814	+	0.274485i
$336$	−0.367229	+	1.34346i	−0.0200340	+	0.0732919i
$337$	2.25984	+	1.48632i	0.123101	+	0.0809650i	0.609566	−	0.792735i	$-0.291344\pi$
$337$	2.25984	+	1.48632i	0.123101	+	0.0809650i	−0.486465	+	0.873700i	$0.661714\pi$
$338$	−0.728422	+	12.5065i	−0.0396209	+	0.680265i
$339$	8.99372	+	19.5430i	0.488472	+	1.06143i
$340$	0.0500492	−	0.167176i	0.00271430	−	0.00906638i
$341$	1.07247	−	0.390347i	0.0580774	−	0.0211385i
$342$	0.00710431	−	0.706505i	0.000384157	−	0.0382034i
$343$	10.0900	+	3.67245i	0.544808	+	0.198294i
$344$	1.99130	−	2.67478i	0.107364	−	0.144214i
$345$	−18.9174	+	34.6662i	−1.01848	+	1.86636i
$346$	−10.6230	−	2.51769i	−0.571095	−	0.135352i
$347$	3.72033	−	8.62470i	0.199718	−	0.462998i	−0.788696	−	0.614784i	$-0.789243\pi$
$347$	3.72033	−	8.62470i	0.199718	−	0.462998i	0.988413	+	0.151786i	$0.0485025\pi$
$348$	5.40032	+	16.5759i	0.289488	+	0.888562i
$349$	17.9125	−	11.7812i	0.958834	−	0.630635i	0.0293780	−	0.999568i	$-0.490647\pi$
$349$	17.9125	−	11.7812i	0.958834	−	0.630635i	0.929456	+	0.368933i	$0.120277\pi$
$350$	0.741812	+	1.28486i	0.0396515	+	0.0686785i
$351$	3.52504	+	0.570774i	0.188152	+	0.0304657i
$352$	0.0777721	−	0.134705i	0.00414527	−	0.00717981i
$353$	0.436688	+	7.49765i	0.0232426	+	0.399060i	0.989786	+	0.142558i	$0.0455328\pi$
$353$	0.436688	+	7.49765i	0.0232426	+	0.399060i	−0.966544	+	0.256501i	$0.917430\pi$
$354$	11.0806	−	5.90287i	0.588925	−	0.313734i
$355$	10.2272	−	1.19539i	0.542804	−	0.0634447i
$356$	2.32265	−	2.46186i	0.123100	−	0.130479i
$357$	0.0865040	−	0.0338633i	0.00457827	−	0.00179223i
$358$	9.23560	+	1.07949i	0.488116	+	0.0570526i
$359$	15.7373	−	13.2052i	0.830584	−	0.696943i	−0.124841	−	0.992177i	$-0.539842\pi$
$359$	15.7373	−	13.2052i	0.830584	−	0.696943i	0.955425	+	0.295234i	$0.0953975\pi$
$360$	7.49617	+	2.32659i	0.395083	+	0.122622i
$361$	−14.5124	−	12.1773i	−0.763808	−	0.640911i
$362$	−10.3251	−	10.9439i	−0.542673	−	0.575200i
$363$	1.56165	+	18.9464i	0.0819655	+	0.994428i
$364$	0.493824	−	0.248008i	0.0258834	−	0.0129991i
$365$	−23.4524	+	11.7782i	−1.22755	+	0.616501i
$366$	−0.882109	−	10.7020i	−0.0461086	−	0.559402i
$367$	10.6543	+	11.2929i	0.556149	+	0.589483i	0.943055	−	0.332636i	$-0.107938\pi$
$367$	10.6543	+	11.2929i	0.556149	+	0.589483i	−0.386907	+	0.922119i	$0.626456\pi$
$368$	6.67595	+	5.60178i	0.348008	+	0.292013i
$369$	14.4043	+	4.47066i	0.749857	+	0.232733i
$370$	−16.0379	+	13.4574i	−0.833769	+	0.699615i
$371$	−5.22437	−	0.610641i	−0.271236	−	0.0317029i
$372$	11.8344	−	4.63274i	0.613583	−	0.240196i
$373$	−12.2810	+	13.0171i	−0.635887	+	0.674001i	−0.962539	−	0.271144i	$-0.912598\pi$
$373$	−12.2810	+	13.0171i	−0.635887	+	0.674001i	0.326652	+	0.945145i	$0.394080\pi$
$374$	−0.0103046	+	0.00120444i	−0.000532839	+	6.22799e-5i
$375$	−12.6180	+	6.72193i	−0.651593	+	0.347119i
$376$	−0.731372	−	12.5572i	−0.0377176	−	0.647587i
$377$	3.45854	−	5.99038i	0.178124	−	0.308520i
$378$	1.48389	+	3.90587i	0.0763233	+	0.200896i
$379$	−2.29993	−	3.98360i	−0.118140	−	0.204624i	0.800891	−	0.598810i	$-0.204360\pi$
$379$	−2.29993	−	3.98360i	−0.118140	−	0.204624i	−0.919030	+	0.394187i	$0.871026\pi$
$380$	−0.514808	+	0.338594i	−0.0264091	+	0.0173695i
$381$	4.17023	+	12.8002i	0.213648	+	0.655776i
$382$	2.95740	−	6.85601i	0.151314	−	0.350784i
$383$	25.0504	+	5.93707i	1.28002	+	0.303370i	0.813720	−	0.581258i	$-0.197439\pi$
$383$	25.0504	+	5.93707i	1.28002	+	0.303370i	0.466298	+	0.884627i	$0.345587\pi$
$384$	0.829686	−	1.52040i	0.0423398	−	0.0775877i
$385$	0.195409	−	0.262480i	0.00995896	−	0.0133772i
$386$	11.6755	+	4.24955i	0.594270	+	0.216296i
$387$	0.100589	−	10.0034i	0.00511325	−	0.508500i
$388$	6.79778	−	2.47419i	0.345105	−	0.125608i
$389$	2.20453	−	7.36366i	0.111774	−	0.373352i	−0.883738	−	0.467981i	$-0.844981\pi$
$389$	2.20453	−	7.36366i	0.111774	−	0.373352i	0.995513	+	0.0946293i	$0.0301666\pi$
$390$	−1.30192	−	2.82903i	−0.0659255	−	0.143254i
$391$	0.0337982	−	0.580293i	0.00170925	−	0.0293467i
$392$	−5.30820	−	3.49126i	−0.268105	−	0.176335i
$393$	4.28664	−	15.6821i	0.216232	−	0.791059i
$394$	−19.7828	+	4.68860i	−0.996641	+	0.236208i
$395$	−7.65516	+	43.4146i	−0.385173	+	2.18442i
$396$	−0.0495097	−	0.463999i	−0.00248796	−	0.0233168i
$397$	−2.12664	−	12.0608i	−0.106733	−	0.605312i	−0.990514	−	0.137412i	$-0.956122\pi$
$397$	−2.12664	−	12.0608i	−0.106733	−	0.605312i	0.883781	−	0.467900i	$-0.154989\pi$
$398$	9.19005	+	21.3049i	0.460656	+	1.06792i
$399$	−0.310840	−	0.104738i	−0.0155615	−	0.00524348i
$400$	−0.529171	−	1.76755i	−0.0264585	−	0.0883777i
$401$	−14.2180	−	19.0981i	−0.710014	−	0.953714i	0.289981	−	0.957033i	$-0.406351\pi$
$401$	−14.2180	−	19.0981i	−0.710014	−	0.953714i	−0.999994	+	0.00331841i	$0.998944\pi$
$402$	8.88800	+	11.3576i	0.443293	+	0.566466i
$403$	−4.50615	−	2.26307i	−0.224467	−	0.112732i
$404$	−6.91644			−0.344106
$405$	22.2842	−	7.60689i	1.10731	−	0.377990i
$406$	8.09346			0.401672
$407$	1.11229	+	0.558612i	0.0551340	+	0.0276893i
$408$	−0.114390	+	0.0161687i	−0.00566316	+	0.000800469i
$409$	−18.3025	−	24.5846i	−0.905002	−	1.21563i	−0.975916	−	0.218146i	$-0.929999\pi$
$409$	−18.3025	−	24.5846i	−0.905002	−	1.21563i	0.0709147	−	0.997482i	$-0.477408\pi$
$410$	−3.77237	−	12.6006i	−0.186304	−	0.622298i
$411$	5.23780	+	26.0268i	0.258362	+	1.28381i
$412$	4.95684	+	11.4912i	0.244206	+	0.566133i
$413$	−1.01212	−	5.74001i	−0.0498031	−	0.282447i
$414$	26.0836	+	1.78253i	1.28194	+	0.0876065i
$415$	0.990595	−	5.61794i	0.0486264	−	0.275774i
$416$	−0.668705	+	0.158486i	−0.0327859	+	0.00777041i
$417$	4.80005	+	4.84856i	0.235059	+	0.237435i
$418$	0.0306063	+	0.0201301i	0.00149700	+	0.000984593i
$419$	−1.12397	+	19.2978i	−0.0549094	+	0.942759i	0.852557	+	0.522634i	$0.175051\pi$
$419$	−1.12397	+	19.2978i	−0.0549094	+	0.942759i	−0.907466	+	0.420125i	$0.861986\pi$
$420$	2.10501	−	2.97433i	0.102714	−	0.145132i
$421$	3.40157	−	11.3620i	0.165782	−	0.553752i	−0.834215	−	0.551440i	$-0.814079\pi$
$421$	3.40157	−	11.3620i	0.165782	−	0.553752i	0.999997	−	0.00231247i	$-0.000736082\pi$
$422$	17.5738	−	6.39634i	0.855479	−	0.311369i
$423$	−23.9639	−	29.1494i	−1.16517	−	1.41729i
$424$	6.14687	+	2.23728i	0.298519	+	0.108652i
$425$	−0.0734895	+	0.0987136i	−0.00356477	+	0.00478831i
$426$	−3.54941	−	5.81975i	−0.171969	−	0.281968i
$427$	−4.85087	−	1.14968i	−0.234750	−	0.0556367i
$428$	−3.52043	+	8.16128i	−0.170167	+	0.394490i
$429$	−0.123779	+	0.137689i	−0.00597609	+	0.00664767i
$430$	−7.28913	+	4.79414i	−0.351513	+	0.231194i
$431$	−9.72386	−	16.8422i	−0.468382	−	0.811261i	0.530965	−	0.847394i	$-0.321829\pi$
$431$	−9.72386	−	16.8422i	−0.468382	−	0.811261i	−0.999347	+	0.0361326i	$0.988496\pi$
$432$	−0.675460	−	5.15206i	−0.0324981	−	0.247879i
$433$	−2.82936	+	4.90059i	−0.135970	+	0.235507i	−0.925968	−	0.377603i	$-0.876748\pi$
$433$	−2.82936	+	4.90059i	−0.135970	+	0.235507i	0.789997	+	0.613110i	$0.210082\pi$
$434$	−0.343058	−	5.89008i	−0.0164673	−	0.282733i
$435$	1.55579	−	45.5847i	0.0745944	−	2.18562i
$436$	−11.5439	+	1.34929i	−0.552854	+	0.0646193i
$437$	−1.40848	+	1.49291i	−0.0673770	+	0.0714154i
$438$	13.5741	+	10.8444i	0.648595	+	0.518163i
$439$	12.2169	+	1.42795i	0.583079	+	0.0681521i	0.402519	−	0.915412i	$-0.368135\pi$
$439$	12.2169	+	1.42795i	0.583079	+	0.0681521i	0.180560	+	0.983564i	$0.442209\pi$
$440$	−0.311743	+	0.261583i	−0.0148618	+	0.0124705i
$441$	−19.0382	+	0.916871i	−0.906580	+	0.0436605i
$442$	0.0351139	+	0.0294641i	0.00167020	+	0.00140146i
$443$	−7.25165	−	7.68630i	−0.344536	−	0.365187i	0.531814	−	0.846861i	$-0.321510\pi$
$443$	−7.25165	−	7.68630i	−0.344536	−	0.365187i	−0.876351	+	0.481674i	$0.840029\pi$
$444$	12.5319	+	5.92059i	0.594736	+	0.280979i
$445$	−7.91324	+	3.97418i	−0.375124	+	0.188394i
$446$	8.34068	−	4.18885i	0.394943	−	0.198348i
$447$	−2.14139	+	1.48343i	−0.101284	+	0.0701639i
$448$	−0.551810	−	0.584884i	−0.0260705	−	0.0276332i
$449$	30.8275	+	25.8673i	1.45484	+	1.22075i	0.928952	+	0.370201i	$0.120711\pi$
$449$	30.8275	+	25.8673i	1.45484	+	1.22075i	0.525887	+	0.850554i	$0.323733\pi$
$450$	−4.40645	−	3.34987i	−0.207722	−	0.157914i
$451$	−0.599030	+	0.502646i	−0.0282072	+	0.0236687i
$452$	−12.3367	−	1.44195i	−0.580267	−	0.0678235i
$453$	3.39313	−	22.3795i	0.159423	−	1.05148i
$454$	−14.4332	+	15.2983i	−0.677384	+	0.717985i
$455$	−1.43600	+	0.167845i	−0.0673209	+	0.00786869i
$456$	0.346108	+	0.215892i	0.0162080	+	0.0101101i
$457$	−2.17275	−	37.3047i	−0.101637	−	1.74504i	−0.535924	−	0.844266i	$-0.680037\pi$
$457$	−2.17275	−	37.3047i	−0.101637	−	1.74504i	0.434287	−	0.900774i	$-0.357000\pi$
$458$	−4.51190	+	7.81484i	−0.210827	+	0.365164i
$459$	−0.248739	+	0.241346i	−0.0116101	+	0.0112651i
$460$	−11.4003	−	19.7460i	−0.531543	−	0.920660i
$461$	−31.2142	+	20.5299i	−1.45379	+	0.956173i	−0.455983	+	0.889988i	$0.650712\pi$
$461$	−31.2142	+	20.5299i	−1.45379	+	0.956173i	−0.997807	+	0.0661850i	$0.978917\pi$
$462$	−0.211936	−	0.0448733i	−0.00986014	−	0.00208769i
$463$	9.18807	−	21.3003i	0.427006	−	0.989911i	−0.559892	−	0.828566i	$-0.689157\pi$
$463$	9.18807	−	21.3003i	0.427006	−	0.989911i	0.986898	−	0.161345i	$-0.0515833\pi$
$464$	−9.79388	−	2.32119i	−0.454670	−	0.107759i
$465$	−33.2406	+	0.799963i	−1.54149	+	0.0370974i
$466$	−5.20127	+	6.98651i	−0.240944	+	0.323644i
$467$	0.406622	+	0.147998i	0.0188162	+	0.00684855i	0.351411	−	0.936221i	$-0.385702\pi$
$467$	0.406622	+	0.147998i	0.0188162	+	0.00684855i	−0.332595	+	0.943070i	$0.607924\pi$
$468$	−1.34104	+	1.56594i	−0.0619896	+	0.0723855i
$469$	6.29159	−	2.28995i	0.290519	−	0.105740i
$470$	−9.43844	+	31.5266i	−0.435363	+	1.45421i
$471$	34.9346	+	3.23344i	1.60970	+	0.148989i
$472$	−0.421463	+	7.23625i	−0.0193994	+	0.333075i
$473$	0.433352	+	0.285020i	0.0199256	+	0.0131052i
$474$	28.2279	−	7.41174i	1.29655	−	0.340433i
$475$	0.422825	−	0.100211i	0.0194006	−	0.00459802i
$476$	−0.00931336	+	0.0528187i	−0.000426877	+	0.00242094i
$477$	18.8553	−	5.43894i	0.863326	−	0.249032i
$478$	−4.33175	−	24.5666i	−0.198130	−	1.12365i
$479$	5.09110	+	11.8025i	0.232618	+	0.539270i	0.994044	−	0.108983i	$-0.0347593\pi$
$479$	5.09110	+	11.8025i	0.232618	+	0.539270i	−0.761425	+	0.648253i	$0.775500\pi$
$480$	−3.40031	+	2.99552i	−0.155202	+	0.136726i
$481$	−1.57721	−	5.26825i	−0.0719146	−	0.240211i
$482$	−11.8149	−	15.8701i	−0.538153	−	0.722865i
$483$	4.53792	−	11.2573i	0.206482	−	0.512227i
$484$	−9.80834	−	4.92593i	−0.445834	−	0.223906i
$485$	−18.9265			−0.859408
$486$	−10.7422	−	11.2963i	−0.487274	−	0.512410i
$487$	8.21477			0.372247			0.186123	−	0.982526i	$-0.440408\pi$
$487$	8.21477			0.372247			0.186123	+	0.982526i	$0.440408\pi$
$488$	5.54030	+	2.78244i	0.250798	+	0.125955i
$489$	−1.20034	+	2.97772i	−0.0542812	+	0.134657i
$490$	9.92626	+	13.3333i	0.448423	+	0.602337i
$491$	4.27347	+	14.2744i	0.192859	+	0.644194i	0.998648	+	0.0519904i	$0.0165565\pi$
$491$	4.27347	+	14.2744i	0.192859	+	0.644194i	−0.805789	+	0.592203i	$0.798258\pi$
$492$	−6.53386	+	5.75604i	−0.294569	+	0.259502i
$493$	0.265906	+	0.616440i	0.0119758	+	0.0277631i
$494$	−0.0281053	−	0.159393i	−0.00126452	−	0.00717143i
$495$	−0.293479	+	1.18506i	−0.0131909	+	0.0532643i
$496$	−1.27413	+	7.22597i	−0.0572103	+	0.324456i
$497$	−3.07936	+	0.729821i	−0.138128	+	0.0327370i
$498$	−3.65276	+	0.959096i	−0.163684	+	0.0429781i
$499$	−8.57019	−	5.63670i	−0.383654	−	0.252333i	0.343002	−	0.939335i	$-0.388556\pi$
$499$	−8.57019	−	5.63670i	−0.383654	−	0.252333i	−0.726656	+	0.687001i	$0.758927\pi$
$500$	0.479944	−	8.24031i	0.0214637	−	0.368518i
$501$	−21.6531	−	2.00414i	−0.967388	−	0.0895385i
$502$	−4.66987	+	15.5984i	−0.208426	+	0.696192i
$503$	−15.4431	+	5.62083i	−0.688574	+	0.250620i	−0.662524	−	0.749040i	$-0.730515\pi$
$503$	−15.4431	+	5.62083i	−0.688574	+	0.250620i	−0.0260494	+	0.999661i	$0.508293\pi$
$504$	−2.37133	−	0.442760i	−0.105627	−	0.0197221i
$505$	17.0042	+	6.18904i	0.756679	+	0.275409i
$506$	−0.809473	+	1.08731i	−0.0359855	+	0.0483369i
$507$	−21.6924	+	0.522045i	−0.963392	+	0.0231848i
$508$	−7.56303	−	1.79247i	−0.335555	−	0.0795280i
$509$	2.34085	−	5.42671i	0.103757	−	0.240535i	−0.858428	−	0.512935i	$-0.828558\pi$
$509$	2.34085	−	5.42671i	0.103757	−	0.240535i	0.962184	+	0.272400i	$0.0878175\pi$
$510$	0.295700	+	0.0626087i	0.0130938	+	0.00277236i
$511$	6.73894	−	4.43227i	0.298113	−	0.196072i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	1.22058	−	0.0882591i	0.0538899	−	0.00389674i
$514$	1.05198	−	1.82208i	0.0464007	−	0.0803684i
$515$	−1.90380	−	32.6870i	−0.0838916	−	1.44036i
$516$	4.90052	+	3.05680i	0.215733	+	0.134568i
$517$	1.94328	−	0.227137i	0.0854652	−	0.00998945i
$518$	4.41563	−	4.68030i	0.194012	−	0.205641i
$519$	2.83458	−	18.6956i	0.124424	−	0.820644i
$520$	1.78584	+	0.208735i	0.0783145	+	0.00915365i
$521$	−12.0595	+	10.1191i	−0.528335	+	0.443325i	−0.867526	−	0.497392i	$-0.834291\pi$
$521$	−12.0595	+	10.1191i	−0.528335	+	0.443325i	0.339191	+	0.940717i	$0.389847\pi$
$522$	−27.8449	+	11.6805i	−1.21874	+	0.511240i
$523$	−32.0731	−	26.9125i	−1.40246	−	1.17680i	−0.959996	−	0.280015i	$-0.909661\pi$
$523$	−32.0731	−	26.9125i	−1.40246	−	1.17680i	−0.442462	−	0.896787i	$-0.645895\pi$
$524$	6.44123	+	6.82731i	0.281387	+	0.298252i
$525$	−2.11237	+	1.46333i	−0.0921913	+	0.0638647i
$526$	−5.29327	+	2.65838i	−0.230797	+	0.115911i
$527$	0.437349	−	0.219645i	0.0190512	−	0.00956787i
$528$	0.243593	+	0.115084i	0.0106010	+	0.00500839i
$529$	−36.3353	−	38.5131i	−1.57979	−	1.67448i
$530$	−13.1103	−	11.0008i	−0.569473	−	0.477845i
$531$	11.7661	+	18.2874i	0.510604	+	0.793604i
$532$	0.145072	−	0.121730i	0.00628965	−	0.00527764i
$533$	3.43159	+	0.401096i	0.148639	+	0.0173734i
$534$	4.58013	+	3.65907i	0.198202	+	0.158344i
$535$	15.9580	−	16.9145i	0.689926	−	0.731279i
$536$	−8.27020	+	0.966648i	−0.357218	+	0.0417528i
$537$	−0.549353	+	16.0960i	−0.0237063	+	0.694596i
$538$	−0.216298	−	3.71370i	−0.00932528	−	0.160109i
$539$	0.494119	−	0.855839i	0.0212832	−	0.0368636i
$540$	−2.94958	+	13.2709i	−0.126930	+	0.571089i
$541$	−1.64686	−	2.85244i	−0.0708039	−	0.122636i	0.828450	−	0.560063i	$-0.189223\pi$
$541$	−1.64686	−	2.85244i	−0.0708039	−	0.122636i	−0.899254	+	0.437427i	$0.855890\pi$
$542$	16.4658	−	10.8297i	0.707268	−	0.465177i
$543$	17.4223	−	19.3802i	0.747663	−	0.831685i
$544$	0.0264184	−	0.0612448i	0.00113268	−	0.00262585i
$545$	29.5884	+	7.01258i	1.26743	+	0.300386i
$546$	0.498373	+	0.817151i	0.0213284	+	0.0349708i
$547$	4.94084	−	6.63669i	0.211255	−	0.283765i	−0.683848	−	0.729625i	$-0.739695\pi$
$547$	4.94084	−	6.63669i	0.211255	−	0.283765i	0.895103	+	0.445860i	$0.147102\pi$
$548$	−14.4034	−	5.24243i	−0.615285	−	0.223945i
$549$	18.3482	−	3.04539i	0.783084	−	0.129974i
$550$	0.269682	−	0.0981561i	0.0114993	−	0.00418539i
$551$	0.679864	−	2.27091i	0.0289632	−	0.0967438i
$552$	−8.71992	+	12.3210i	−0.371144	+	0.524418i
$553$	0.787805	−	13.5261i	0.0335009	−	0.575188i
$554$	2.63050	+	1.73011i	0.111759	+	0.0735052i
$555$	−25.5120	−	25.7698i	−1.08292	−	1.09387i
$556$	−3.83290	+	0.908413i	−0.162551	+	0.0385253i
$557$	1.30921	−	7.42492i	0.0554732	−	0.314604i	−0.944427	−	0.328721i	$-0.893383\pi$
$557$	1.30921	−	7.42492i	0.0554732	−	0.314604i	0.999900	+	0.0141167i	$0.00449362\pi$
$558$	9.68082	+	19.7693i	0.409822	+	0.836900i
$559$	−0.397941	−	2.25683i	−0.0168311	−	0.0954539i
$560$	0.833266	+	1.93173i	0.0352119	+	0.0816304i
$561$	−0.00354525	−	0.0176164i	−0.000149680	−	0.000743765i
$562$	−6.13275	−	20.4848i	−0.258694	−	0.864099i
$563$	17.9766	+	24.1468i	0.757625	+	1.01767i	0.998885	+	0.0472070i	$0.0150320\pi$
$563$	17.9766	+	24.1468i	0.757625	+	1.01767i	−0.241260	+	0.970461i	$0.577561\pi$
$564$	21.5721	−	3.04914i	0.908349	−	0.128392i
$565$	29.0397	+	14.5843i	1.22171	+	0.613565i
$566$	10.8922			0.457835
$567$	−6.53117	+	3.11722i	−0.274283	+	0.130911i
$568$	3.93564			0.165136
$569$	31.1284	+	15.6333i	1.30497	+	0.655381i	0.959144	−	0.282917i	$-0.0913021\pi$
$569$	31.1284	+	15.6333i	1.30497	+	0.655381i	0.345827	+	0.938298i	$0.387598\pi$
$570$	−0.657728	−	0.840484i	−0.0275492	−	0.0352040i
$571$	3.98459	+	5.35223i	0.166750	+	0.223984i	0.877642	−	0.479318i	$-0.159116\pi$
$571$	3.98459	+	5.35223i	0.166750	+	0.223984i	−0.710892	+	0.703302i	$0.751708\pi$
$572$	−0.0306577	−	0.102404i	−0.00128186	−	0.00428172i
$573$	12.2556	+	4.12957i	0.511986	+	0.172515i
$574$	1.60116	+	3.71191i	0.0668313	+	0.154932i
$575$	2.79216	+	15.8351i	0.116441	+	0.660371i
$576$	2.74256	+	1.21588i	0.114273	+	0.0506616i
$577$	−6.28429	+	35.6400i	−0.261619	+	1.48371i	0.516875	+	0.856061i	$0.327095\pi$
$577$	−6.28429	+	35.6400i	−0.261619	+	1.48371i	−0.778494	+	0.627652i	$0.784016\pi$
$578$	16.5374	−	3.91944i	0.687867	−	0.163027i
$579$	−5.67435	+	20.7589i	−0.235818	+	0.862711i
$580$	22.0014	+	14.4706i	0.913560	+	0.600858i
$581$	−0.101944	+	1.75031i	−0.00422934	+	0.0726149i
$582$	5.23814	+	11.3823i	0.217128	+	0.471811i
$583$	−0.291814	+	0.974727i	−0.0120857	+	0.0403691i
$584$	−9.42595	+	3.43076i	−0.390048	+	0.141966i
$585$	4.69823	−	2.64990i	0.194248	−	0.109560i
$586$	19.0581	+	6.93659i	0.787284	+	0.286548i
$587$	17.3965	−	23.3675i	0.718030	−	0.964482i	−0.281957	−	0.959427i	$-0.590984\pi$
$587$	17.3965	−	23.3675i	0.718030	−	0.964482i	0.999987	−	0.00505460i	$-0.00160894\pi$
$588$	5.27134	−	9.65974i	0.217387	−	0.398361i
$589$	−1.68149	−	0.398520i	−0.0692845	−	0.0164207i
$590$	7.51139	−	17.4134i	0.309239	−	0.716897i
$591$	−10.9082	−	33.4818i	−0.448702	−	1.37726i
$592$	−6.68566	+	4.39723i	−0.274779	+	0.180725i
$593$	−4.61527	−	7.99387i	−0.189526	−	0.328269i	0.755566	−	0.655072i	$-0.227362\pi$
$593$	−4.61527	−	7.99387i	−0.189526	−	0.328269i	−0.945092	+	0.326803i	$0.894029\pi$
$594$	0.793909	−	0.151482i	0.0325745	−	0.00621538i
$595$	0.0701609	−	0.121522i	0.00287631	−	0.00498192i
$596$	−0.0874504	−	1.50147i	−0.00358211	−	0.0615024i
$597$	−35.4689	+	18.8951i	−1.45165	+	0.773326i
$598$	5.94859	−	0.695290i	0.243256	−	0.0284325i
$599$	−0.807714	+	0.856127i	−0.0330023	+	0.0349804i	−0.743664	−	0.668553i	$-0.766914\pi$
$599$	−0.807714	+	0.856127i	−0.0330023	+	0.0349804i	0.710662	+	0.703533i	$0.248395\pi$
$600$	2.97585	−	1.16494i	0.121489	−	0.0475586i
$601$	16.3686	+	1.91321i	0.667688	+	0.0780416i	0.443183	−	0.896431i	$-0.353849\pi$
$601$	16.3686	+	1.91321i	0.667688	+	0.0780416i	0.224506	+	0.974473i	$0.427923\pi$
$602$	2.05406	−	1.72356i	0.0837172	−	0.0702471i
$603$	−18.3409	+	16.9584i	−0.746899	+	0.690600i
$604$	10.0110	+	8.40025i	0.407343	+	0.341801i
$605$	19.7062	+	20.8873i	0.801170	+	0.849190i
$606$	−0.984080	−	11.9391i	−0.0399755	−	0.484994i
$607$	32.1650	−	16.1539i	1.30554	−	0.655665i	0.346261	−	0.938138i	$-0.387451\pi$
$607$	32.1650	−	16.1539i	1.30554	−	0.655665i	0.959275	+	0.282473i	$0.0911548\pi$
$608$	−0.210463	+	0.105698i	−0.00853539	+	0.00428664i
$609$	1.15155	+	13.9709i	0.0466631	+	0.566130i
$610$	−11.1312	−	11.7983i	−0.450687	−	0.477700i
$611$	−6.62190	−	5.55643i	−0.267893	−	0.224789i
$612$	−0.0441859	−	0.195160i	−0.00178611	−	0.00788886i
$613$	−22.8633	+	19.1846i	−0.923441	+	0.774859i	−0.974628	−	0.223830i	$-0.928144\pi$
$613$	−22.8633	+	19.1846i	−0.923441	+	0.774859i	0.0511868	+	0.998689i	$0.483700\pi$
$614$	−5.26721	−	0.615648i	−0.212567	−	0.0248455i
$615$	21.2143	−	8.30467i	0.855445	−	0.334877i
$616$	0.0858308	−	0.0909753i	0.00345822	−	0.00366550i
$617$	−4.99903	+	0.584303i	−0.201253	+	0.0235231i	−0.216122	−	0.976366i	$-0.569341\pi$
$617$	−4.99903	+	0.584303i	−0.201253	+	0.0235231i	0.0148690	+	0.999889i	$0.495267\pi$
$618$	−19.1309	+	10.1915i	−0.769557	+	0.409961i
$619$	1.28092	+	21.9925i	0.0514844	+	0.883954i	0.920882	+	0.389841i	$0.127470\pi$
$619$	1.28092	+	21.9925i	0.0514844	+	0.883954i	−0.869398	+	0.494113i	$0.835493\pi$
$620$	9.59850	−	16.6251i	0.385485	−	0.667680i
$621$	0.634220	+	45.2791i	0.0254504	+	1.81699i
$622$	−2.12061	−	3.67301i	−0.0850288	−	0.147274i
$623$	2.27383	−	1.49552i	0.0910992	−	0.0599169i
$624$	−0.368722	−	1.13177i	−0.0147607	−	0.0453069i
$625$	−12.2076	+	28.3004i	−0.488304	+	1.13202i
$626$	−4.47705	−	1.06108i	−0.178939	−	0.0424093i
$627$	−0.0303937	+	0.0556966i	−0.00121381	+	0.00222431i
$628$	−12.0959	+	16.2476i	−0.482678	+	0.648349i
$629$	0.501549	+	0.182549i	0.0199981	+	0.00727871i
$630$	5.43378	+	3.21047i	0.216487	+	0.127908i
$631$	−28.2782	+	10.2924i	−1.12574	+	0.409735i	−0.836743	−	0.547595i	$-0.815543\pi$
$631$	−28.2782	+	10.2924i	−1.12574	+	0.409735i	−0.288995	+	0.957331i	$0.593321\pi$
$632$	−4.83258	+	16.1420i	−0.192230	+	0.642092i
$633$	13.5418	+	29.4258i	0.538237	+	1.16957i
$634$	−0.367420	+	6.30836i	−0.0145921	+	0.250537i
$635$	16.9899	+	11.1745i	0.674225	+	0.443445i
$636$	−2.98740	+	10.9290i	−0.118458	+	0.433364i
$637$	−4.24856	+	1.00693i	−0.168334	+	0.0398959i
$638$	0.271861	−	1.54180i	0.0107631	−	0.0610404i
$639$	9.54102	−	6.95502i	0.377437	−	0.275136i
$640$	−0.454317	−	2.57656i	−0.0179585	−	0.101847i
$641$	11.6997	+	27.1229i	0.462109	+	1.07129i	0.976846	+	0.213942i	$0.0686303\pi$
$641$	11.6997	+	27.1229i	0.462109	+	1.07129i	−0.514737	+	0.857348i	$0.672110\pi$
$642$	−14.5889	−	4.91576i	−0.575777	−	0.194010i
$643$	1.81855	+	6.07439i	0.0717167	+	0.239550i	0.986331	−	0.164778i	$-0.0526906\pi$
$643$	1.81855	+	6.07439i	0.0717167	+	0.239550i	−0.914614	+	0.404328i	$0.867505\pi$
$644$	4.18466	+	5.62098i	0.164899	+	0.221498i
$645$	−9.31273	−	11.9004i	−0.366689	−	0.468576i
$646$	0.0140378	+	0.00705005i	0.000552310	+	0.000277381i
$647$	−34.8610			−1.37053			−0.685264	−	0.728295i	$-0.740313\pi$
$647$	−34.8610			−1.37053			−0.685264	+	0.728295i	$0.740313\pi$
$648$	8.79737	−	1.89902i	0.345593	−	0.0746005i
$649$	−1.12746			−0.0442568
$650$	−1.13311	−	0.569069i	−0.0444443	−	0.0223207i
$651$	10.1186	−	1.43024i	0.396581	−	0.0560553i
$652$	−1.10690	−	1.48682i	−0.0433495	−	0.0582285i
$653$	−4.91627	−	16.4215i	−0.192389	−	0.642623i	−0.998692	−	0.0511212i	$-0.983721\pi$
$653$	−4.91627	−	16.4215i	−0.192389	−	0.642623i	0.806304	−	0.591502i	$-0.201465\pi$
$654$	−3.97163	−	19.7351i	−0.155303	−	0.771704i
$655$	−9.72665	−	22.5489i	−0.380052	−	0.881059i
$656$	−0.872994	−	4.95099i	−0.0340847	−	0.193304i
$657$	−16.7881	+	24.9745i	−0.654968	+	0.974348i
$658$	1.75634	−	9.96072i	0.0684694	−	0.388309i
$659$	−24.3229	+	5.76463i	−0.947484	+	0.224558i	−0.675180	−	0.737653i	$-0.735934\pi$
$659$	−24.3229	+	5.76463i	−0.947484	+	0.224558i	−0.272305	+	0.962211i	$0.587786\pi$
$660$	−0.495900	−	0.500911i	−0.0193029	−	0.0194979i
$661$	−0.607381	−	0.399481i	−0.0236244	−	0.0155380i	0.537642	−	0.843173i	$-0.319315\pi$
$661$	−0.607381	−	0.399481i	−0.0236244	−	0.0155380i	−0.561266	+	0.827635i	$0.689686\pi$
$662$	0.933082	−	16.0204i	0.0362652	−	0.622650i
$663$	−0.0458647	+	0.0648057i	−0.00178124	+	0.00251685i
$664$	0.625347	−	2.08880i	0.0242682	−	0.0810613i
$665$	−0.465589	+	0.169461i	−0.0180548	+	0.00657140i
$666$	−8.43705	+	22.4748i	−0.326929	+	0.870882i
$667$	82.4265	+	30.0008i	3.19156	+	1.16163i
$668$	7.49723	−	10.0705i	0.290077	−	0.389640i
$669$	8.41750	+	13.8017i	0.325439	+	0.533603i
$670$	21.1975	+	5.02390i	0.818930	+	0.194090i
$671$	−0.381954	+	0.885468i	−0.0147452	+	0.0341831i
$672$	0.931113	−	1.03575i	0.0359185	−	0.0399549i
$673$	−37.1257	+	24.4179i	−1.43109	+	0.941242i	−0.431861	+	0.901940i	$0.642143\pi$
$673$	−37.1257	+	24.4179i	−1.43109	+	0.941242i	−0.999227	+	0.0393018i	$0.987487\pi$
$674$	−1.35241	−	2.34244i	−0.0520928	−	0.0902274i
$675$	5.15557	−	8.08302i	0.198438	−	0.311116i
$676$	6.26386	−	10.8493i	0.240918	−	0.417282i
$677$	−2.61091	−	44.8277i	−0.100346	−	1.72287i	−0.554703	−	0.832048i	$-0.687168\pi$
$677$	−2.61091	−	44.8277i	−0.100346	−	1.72287i	0.454358	−	0.890819i	$-0.349869\pi$
$678$	0.733810	−	21.5007i	0.0281818	−	0.825728i
$679$	5.77759	−	0.675304i	0.221724	−	0.0259158i
$680$	−0.119754	+	0.126932i	−0.00459235	+	0.00486761i
$681$	−28.4614	−	22.7379i	−1.09065	−	0.871317i
$682$	−1.13358	−	0.132497i	−0.0434070	−	0.00507355i
$683$	−16.4909	+	13.8375i	−0.631007	+	0.529478i	−0.901242	−	0.433317i	$-0.857343\pi$
$683$	−16.4909	+	13.8375i	−0.631007	+	0.529478i	0.270235	+	0.962795i	$0.412899\pi$
$684$	−0.323428	+	0.628168i	−0.0123666	+	0.0240186i
$685$	30.7201	+	25.7773i	1.17376	+	0.984899i
$686$	−7.36854	−	7.81020i	−0.281332	−	0.298195i
$687$	−14.1319	−	6.67652i	−0.539166	−	0.254725i
$688$	−2.97993	+	1.49658i	−0.113609	+	0.0570565i
$689$	4.01725	−	2.01754i	0.153045	−	0.0768621i
$690$	32.4634	−	22.4887i	1.23586	−	0.856130i
$691$	21.7759	+	23.0811i	0.828393	+	0.878045i	0.994137	−	0.108124i	$-0.0344842\pi$
$691$	21.7759	+	23.0811i	0.828393	+	0.878045i	−0.165745	+	0.986169i	$0.553003\pi$
$692$	8.36310	+	7.01747i	0.317917	+	0.266764i
$693$	0.0473057	−	0.372227i	0.00179699	−	0.0141397i
$694$	−7.19537	+	6.03763i	−0.273132	+	0.229185i
$695$	10.2361	+	1.19643i	0.388279	+	0.0453833i
$696$	2.61335	−	17.2364i	0.0990587	−	0.653345i
$697$	−0.230113	+	0.243906i	−0.00871617	+	0.00923860i
$698$	−21.2946	+	2.48898i	−0.806012	+	0.0942093i
$699$	−12.8001	−	7.98436i	−0.484146	−	0.301996i
$700$	−0.0862651	−	1.48111i	−0.00326051	−	0.0559809i
$701$	−11.1884	+	19.3789i	−0.422580	+	0.731929i	−0.996191	−	0.0871983i	$-0.972209\pi$
$701$	−11.1884	+	19.3789i	−0.422580	+	0.731929i	0.573611	+	0.819128i	$0.305542\pi$
$702$	−2.89392	−	2.09210i	−0.109224	−	0.0789611i
$703$	−0.942302	−	1.63212i	−0.0355396	−	0.0615564i
$704$	−0.129955	+	0.0854730i	−0.00489788	+	0.00322138i
$705$	−55.7640	−	11.8070i	−2.10019	−	0.444676i
$706$	2.97470	−	6.89613i	0.111954	−	0.259539i
$707$	−5.41162	−	1.28258i	−0.203525	−	0.0482363i
$708$	−12.5512	+	0.302054i	−0.471701	+	0.0113519i
$709$	2.37201	−	3.18616i	0.0890826	−	0.119659i	−0.755347	−	0.655324i	$-0.772532\pi$
$709$	2.37201	−	3.18616i	0.0890826	−	0.119659i	0.844430	+	0.535666i	$0.179939\pi$
$710$	−9.67587	−	3.52173i	−0.363129	−	0.132168i
$711$	16.8104	+	47.6724i	0.630441	+	1.78785i
$712$	−3.18048	+	1.15760i	−0.119193	+	0.0433829i
$713$	18.3395	−	61.2582i	0.686820	−	2.29414i
$714$	−0.0925006	−	0.00856158i	−0.00346175	−	0.000320409i
$715$	−0.0162613	+	0.279196i	−0.000608138	+	0.0104413i
$716$	−7.76876	−	5.10959i	−0.290332	−	0.190954i
$717$	41.7904	−	10.9728i	1.56069	−	0.409788i
$718$	−19.9899	+	4.73769i	−0.746015	+	0.176809i
$719$	−3.47213	+	19.6915i	−0.129489	+	0.734367i	0.849051	+	0.528310i	$0.177174\pi$
$719$	−3.47213	+	19.6915i	−0.129489	+	0.734367i	−0.978540	+	0.206057i	$0.933937\pi$
$720$	−5.65465	−	5.44339i	−0.210736	−	0.202863i
$721$	1.74745	+	9.91028i	0.0650784	+	0.369078i
$722$	7.50355	+	17.3952i	0.279253	+	0.647381i
$723$	25.7139	−	22.6528i	0.956312	−	0.842468i
$724$	4.31519	+	14.4137i	0.160373	+	0.535682i
$725$	−11.0898	−	14.8962i	−0.411865	−	0.553230i
$726$	7.10759	−	17.6320i	0.263787	−	0.654385i
$727$	0.370860	+	0.186253i	0.0137545	+	0.00690774i	0.455663	−	0.890152i	$-0.349402\pi$
$727$	0.370860	+	0.186253i	0.0137545	+	0.00690774i	−0.441909	+	0.897060i	$0.645698\pi$
$728$	−0.552603			−0.0204808
$729$	17.9712	−	20.1503i	0.665600	−	0.746309i
$730$	26.2439			0.971329
$731$	0.198760	+	0.0998212i	0.00735142	+	0.00369202i
$732$	−4.01476	+	9.95954i	−0.148390	+	0.368115i
$733$	−4.44910	−	5.97617i	−0.164331	−	0.220735i	0.712328	−	0.701846i	$-0.247641\pi$
$733$	−4.44910	−	5.97617i	−0.164331	−	0.220735i	−0.876660	+	0.481111i	$0.840233\pi$
$734$	−4.45278	−	14.8733i	−0.164355	−	0.548984i
$735$	−21.6036	+	19.0318i	−0.796859	+	0.701997i
$736$	−3.45177	−	8.00209i	−0.127234	−	0.294961i
$737$	−0.224899	−	1.27546i	−0.00828425	−	0.0469823i
$738$	−10.8657	−	10.4598i	−0.399972	−	0.385029i
$739$	−1.13092	+	6.41379i	−0.0416017	+	0.235935i	−0.998518	−	0.0544304i	$-0.982666\pi$
$739$	−1.13092	+	6.41379i	−0.0416017	+	0.235935i	0.956916	+	0.290365i	$0.0937768\pi$
$740$	20.3716	−	4.82816i	0.748876	−	0.177487i
$741$	0.271145	−	0.0711939i	0.00996075	−	0.00261537i
$742$	4.39461	+	2.89038i	0.161331	+	0.106109i
$743$	1.62467	−	27.8945i	0.0596033	−	1.02335i	−0.827408	−	0.561602i	$-0.810185\pi$
$743$	1.62467	−	27.8945i	0.0596033	−	1.02335i	0.887011	−	0.461748i	$-0.152778\pi$
$744$	−12.6547	−	1.17128i	−0.463945	−	0.0429414i
$745$	−1.12856	+	3.76964i	−0.0413471	+	0.138109i
$746$	16.8168	−	6.12081i	0.615706	−	0.224099i
$747$	−2.17531	−	6.16892i	−0.0795904	−	0.225709i
$748$	0.00974908	+	0.00354838i	0.000356462	+	0.000129741i
$749$	−4.26791	+	5.73280i	−0.155946	+	0.209472i
$750$	14.2927	−	0.343966i	0.521895	−	0.0125599i
$751$	−28.3649	−	6.72261i	−1.03505	−	0.245312i	−0.322233	−	0.946660i	$-0.604433\pi$
$751$	−28.3649	−	6.72261i	−1.03505	−	0.245312i	−0.712818	+	0.701349i	$0.752581\pi$
$752$	−4.98207	+	11.5497i	−0.181677	+	0.421176i
$753$	−27.5904	−	5.84174i	−1.00545	−	0.212885i
$754$	−5.77914	+	3.80100i	−0.210464	+	0.138424i
$755$	−17.0956	−	29.6104i	−0.622171	−	1.07763i
$756$	0.426894	−	4.15638i	0.0155260	−	0.151166i
$757$	−26.9567	+	46.6904i	−0.979758	+	1.69699i	−0.316511	+	0.948589i	$0.602512\pi$
$757$	−26.9567	+	46.6904i	−0.979758	+	1.69699i	−0.663246	+	0.748401i	$0.730822\pi$
$758$	0.267458	+	4.59208i	0.00971453	+	0.166792i
$759$	−1.99209	−	1.24261i	−0.0723081	−	0.0451037i
$760$	0.612010	−	0.0715337i	0.0221999	−	0.00259480i
$761$	13.9480	−	14.7840i	0.505614	−	0.535920i	−0.423410	−	0.905938i	$-0.639167\pi$
$761$	13.9480	−	14.7840i	0.505614	−	0.535920i	0.929025	+	0.370018i	$0.120649\pi$
$762$	2.01808	−	13.3103i	0.0731073	−	0.482182i
$763$	−9.28251	−	1.08497i	−0.336049	−	0.0392786i
$764$	−5.71980	+	4.79948i	−0.206935	+	0.173639i
$765$	−0.0660024	+	0.519344i	−0.00238632	+	0.0187769i
$766$	−19.7213	−	16.5482i	−0.712561	−	0.597910i
$767$	3.41843	+	3.62333i	0.123433	+	0.130831i
$768$	−1.42379	+	0.986318i	−0.0513766	+	0.0355907i
$769$	35.7884	−	17.9736i	1.29056	−	0.648145i	0.334801	−	0.942289i	$-0.391331\pi$
$769$	35.7884	−	17.9736i	1.29056	−	0.648145i	0.955761	+	0.294144i	$0.0950346\pi$
$770$	−0.292425	+	0.146861i	−0.0105383	+	0.00529251i
$771$	3.29494	+	1.55667i	0.118664	+	0.0560622i
$772$	−8.52645	−	9.03751i	−0.306874	−	0.325267i
$773$	−15.5681	−	13.0632i	−0.559945	−	0.469850i	0.318347	−	0.947974i	$-0.396872\pi$
$773$	−15.5681	−	13.0632i	−0.559945	−	0.469850i	−0.878292	+	0.478124i	$0.841317\pi$
$774$	−4.57939	+	8.89419i	−0.164603	+	0.319695i
$775$	−10.3708	+	8.70210i	−0.372529	+	0.312589i
$776$	−7.18513	−	0.839822i	−0.257931	−	0.0301478i
$777$	8.70738	+	6.95634i	0.312376	+	0.249557i
$778$	−5.27485	+	5.59101i	−0.189112	+	0.200447i
$779$	1.17601	−	0.137456i	0.0421349	−	0.00492486i
$780$	−0.106226	+	3.11242i	−0.00380350	+	0.111442i
$781$	0.0355943	+	0.611130i	0.00127366	+	0.0218680i
$782$	−0.290638	+	0.503400i	−0.0103932	+	0.0180016i
$783$	−24.1246	−	46.4039i	−0.862143	−	1.65834i
$784$	3.17671	+	5.50222i	0.113454	+	0.196508i
$785$	44.2768	−	29.1213i	1.58031	−	1.03938i
$786$	−10.8688	+	12.0902i	−0.387678	+	0.431244i
$787$	−3.04443	+	7.05779i	−0.108522	+	0.251583i	−0.963820	−	0.266554i	$-0.914115\pi$
$787$	−3.04443	+	7.05779i	−0.108522	+	0.251583i	0.855298	+	0.518137i	$0.173374\pi$
$788$	19.7828	+	4.68860i	0.704731	+	0.167024i
$789$	−5.34202	−	8.75899i	−0.190181	−	0.311828i
$790$	26.3253	−	35.3611i	0.936613	−	1.25809i
$791$	−9.38516	−	3.41592i	−0.333698	−	0.121456i
$792$	−0.163999	+	0.436864i	−0.00582744	+	0.0155233i
$793$	4.00370	−	1.45723i	0.142176	−	0.0517477i
$794$	−3.51243	+	11.7323i	−0.124651	+	0.416365i
$795$	17.1242	−	24.1961i	0.607334	−	0.858147i
$796$	1.34911	−	23.1633i	0.0478178	−	0.821000i
$797$	−30.6284	−	20.1446i	−1.08492	−	0.713560i	−0.124525	−	0.992217i	$-0.539741\pi$
$797$	−30.6284	−	20.1446i	−1.08492	−	0.713560i	−0.960391	+	0.278656i	$0.910111\pi$
$798$	0.230770	+	0.233102i	0.00816917	+	0.00825173i
$799$	0.816365	−	0.193482i	0.0288809	−	0.00684490i
$800$	−0.320392	+	1.81703i	−0.0113276	+	0.0642419i
$801$	−5.66461	+	8.42683i	−0.200149	+	0.297747i
$802$	4.13447	+	23.4477i	0.145993	+	0.827968i
$803$	−0.617982	−	1.43264i	−0.0218081	−	0.0505569i
$804$	−2.84532	−	14.1385i	−0.100347	−	0.498625i
$805$	−5.25828	−	17.5639i	−0.185330	−	0.619045i
$806$	3.01117	+	4.04471i	0.106064	+	0.142469i
$807$	6.37980	−	0.901764i	0.224580	−	0.0317436i
$808$	6.18076	+	3.10409i	0.217438	+	0.109202i
$809$	32.5645			1.14491			0.572454	−	0.819937i	$-0.305992\pi$
$809$	32.5645			1.14491			0.572454	+	0.819937i	$0.305992\pi$
$810$	−23.3279	−	3.20336i	−0.819657	−	0.112555i
$811$	36.0860			1.26715			0.633575	−	0.773681i	$-0.281587\pi$
$811$	36.0860			1.26715			0.633575	+	0.773681i	$0.281587\pi$
$812$	−7.23258	−	3.63234i	−0.253814	−	0.127470i
$813$	21.0370	+	26.8824i	0.737801	+	0.942806i
$814$	−0.743272	−	0.998387i	−0.0260517	−	0.0349934i
$815$	1.39089	+	4.64588i	0.0487206	+	0.162738i
$816$	0.109479	+	0.0368894i	0.00383254	+	0.00129139i
$817$	−0.311061	−	0.721121i	−0.0108827	−	0.0252288i
$818$	5.32220	+	30.1837i	0.186086	+	1.05535i
$819$	−1.33965	+	0.976555i	−0.0468113	+	0.0341236i
$820$	−2.28402	+	12.9533i	−0.0797614	+	0.452350i
$821$	−28.4772	+	6.74923i	−0.993862	+	0.235550i	−0.695206	−	0.718811i	$-0.744687\pi$
$821$	−28.4772	+	6.74923i	−0.993862	+	0.235550i	−0.298657	+	0.954361i	$0.596539\pi$
$822$	7.00012	−	25.6091i	0.244157	−	0.893219i
$823$	25.8934	+	17.0304i	0.902588	+	0.593642i	0.913741	−	0.406296i	$-0.133180\pi$
$823$	25.8934	+	17.0304i	0.902588	+	0.593642i	−0.0111532	+	0.999938i	$0.503550\pi$
$824$	0.727668	−	12.4936i	0.0253495	−	0.435234i
$825$	0.207808	+	0.451558i	0.00723493	+	0.0157212i
$826$	−1.67165	+	5.58369i	−0.0581641	+	0.194282i
$827$	−7.43214	+	2.70508i	−0.258441	+	0.0940647i	−0.467991	−	0.883733i	$-0.655022\pi$
$827$	−7.43214	+	2.70508i	−0.258441	+	0.0940647i	0.209551	+	0.977798i	$0.432800\pi$
$828$	−22.5092	−	13.2992i	−0.782249	−	0.462181i
$829$	44.4988	+	16.1962i	1.54551	+	0.562518i	0.967358	−	0.253413i	$-0.0815532\pi$
$829$	44.4988	+	16.1962i	1.54551	+	0.562518i	0.578148	+	0.815932i	$0.303775\pi$
$830$	−3.40656	+	4.57580i	−0.118243	+	0.158828i
$831$	−2.61223	+	4.78692i	−0.0906174	+	0.166056i
$832$	0.668705	+	0.158486i	0.0231832	+	0.00549451i
$833$	0.167847	−	0.389113i	0.00581556	−	0.0134820i
$834$	−2.11345	−	6.48708i	−0.0731828	−	0.224629i
$835$	−27.4435	+	18.0499i	−0.949723	+	0.624643i
$836$	−0.0183164	−	0.0317249i	−0.000633486	−	0.00109723i
$837$	−32.7483	+	19.5238i	−1.13195	+	0.674842i
$838$	9.66525	−	16.7407i	0.333880	−	0.578298i
$839$	1.14559	+	19.6690i	0.0395502	+	0.679050i	0.958573	+	0.284846i	$0.0919425\pi$
$839$	1.14559	+	19.6690i	0.0395502	+	0.679050i	−0.919023	+	0.394204i	$0.871020\pi$
$840$	−3.21598	+	1.71323i	−0.110962	+	0.0591120i
$841$	−71.8191	+	8.39445i	−2.47652	+	0.289464i
$842$	−8.13903	+	8.62687i	−0.280490	+	0.297302i
$843$	34.4882	−	13.5009i	1.18784	−	0.464997i
$844$	−18.5752	−	2.17113i	−0.639385	−	0.0747333i
$845$	−25.1081	+	21.0682i	−0.863747	+	0.724769i
$846$	8.33273	+	36.8039i	0.286485	+	1.26534i
$847$	−6.76087	−	5.67304i	−0.232306	−	0.194928i
$848$	−4.48896	−	4.75802i	−0.154151	−	0.163391i
$849$	1.54976	+	18.8021i	0.0531877	+	0.645288i
$850$	0.109975	−	0.0552316i	0.00377212	−	0.00189443i
$851$	62.3192	−	31.2979i	2.13627	−	1.07288i
$852$	0.559968	+	6.79369i	0.0191842	+	0.232748i
$853$	−38.5735	−	40.8855i	−1.32073	−	1.39989i	−0.858221	−	0.513280i	$-0.828430\pi$
$853$	−38.5735	−	40.8855i	−1.32073	−	1.39989i	−0.462510	−	0.886614i	$-0.653051\pi$
$854$	3.81892	+	3.20445i	0.130681	+	0.109654i
$855$	1.35726	−	1.25495i	0.0464173	−	0.0429185i
$856$	6.80875	−	5.71322i	0.232718	−	0.195274i
$857$	11.5778	+	1.35325i	0.395491	+	0.0462262i	0.311514	−	0.950242i	$-0.399164\pi$
$857$	11.5778	+	1.35325i	0.395491	+	0.0462262i	0.0839765	+	0.996468i	$0.473238\pi$
$858$	0.172407	−	0.0674914i	0.00588588	−	0.00230412i
$859$	28.7098	−	30.4306i	0.979567	−	1.03828i	−0.0196927	−	0.999806i	$-0.506269\pi$
$859$	28.7098	−	30.4306i	0.979567	−	1.03828i	0.999260	−	0.0384741i	$-0.0122497\pi$
$860$	8.66541	−	1.01284i	0.295488	−	0.0345376i
$861$	−6.17968	+	3.29206i	−0.210603	+	0.112193i
$862$	1.13078	+	19.4148i	0.0385147	+	0.661271i
$863$	−3.21464	+	5.56792i	−0.109428	+	0.189534i	−0.915539	−	0.402230i	$-0.868235\pi$
$863$	−3.21464	+	5.56792i	−0.109428	+	0.189534i	0.806111	+	0.591765i	$0.201568\pi$
$864$	−1.70863	+	4.90720i	−0.0581287	+	0.166946i
$865$	−14.2814	−	24.7362i	−0.485584	−	0.841055i
$866$	4.72779	−	3.10951i	0.160657	−	0.105666i
$867$	9.11870	+	27.9892i	0.309687	+	0.950563i
$868$	−2.33690	+	5.41754i	−0.0793194	+	0.183883i
$869$	−2.55025	−	0.604420i	−0.0865112	−	0.0205035i
$870$	−21.8487	+	40.0377i	−0.740739	+	1.35740i
$871$	−3.41707	+	4.58992i	−0.115783	+	0.155524i
$872$	10.9216	+	3.97513i	0.369852	+	0.134615i
$873$	−18.9028	+	10.6615i	−0.639762	+	0.360839i
$874$	1.92868	−	0.701983i	0.0652387	−	0.0237449i
$875$	1.90360	−	6.35846i	0.0643534	−	0.214955i
$876$	−7.26331	−	15.7829i	−0.245405	−	0.533255i
$877$	−0.661751	+	11.3618i	−0.0223457	+	0.383662i	0.968531	+	0.248892i	$0.0800665\pi$
$877$	−0.661751	+	11.3618i	−0.0223457	+	0.383662i	−0.990877	+	0.134770i	$0.956971\pi$
$878$	−10.2765	−	6.75897i	−0.346816	−	0.228104i
$879$	−9.26231	+	33.8850i	−0.312410	+	1.14291i
$880$	0.395982	−	0.0938495i	0.0133486	−	0.00316367i
$881$	9.19564	−	52.1511i	0.309809	−	1.75701i	−0.290148	−	0.956982i	$-0.593705\pi$
$881$	9.19564	−	52.1511i	0.309809	−	1.75701i	0.599957	−	0.800032i	$-0.295184\pi$
$882$	17.4246	+	7.72498i	0.586718	+	0.260113i
$883$	−5.69410	−	32.2928i	−0.191622	−	1.08674i	−0.917148	−	0.398546i	$-0.869515\pi$
$883$	−5.69410	−	32.2928i	−0.191622	−	1.08674i	0.725526	−	0.688194i	$-0.241596\pi$
$884$	−0.0181555	−	0.0420892i	−0.000610635	−	0.00141561i
$885$	31.1276	+	10.4885i	1.04634	+	0.352568i
$886$	3.03071	+	10.1233i	0.101819	+	0.340098i
$887$	−18.9305	−	25.4280i	−0.635623	−	0.853789i	0.361278	−	0.932458i	$-0.382341\pi$
$887$	−18.9305	−	25.4280i	−0.635623	−	0.853789i	−0.996901	+	0.0786686i	$0.974933\pi$
$888$	−8.54172	−	10.9151i	−0.286641	−	0.366287i
$889$	−5.58514	−	2.80496i	−0.187320	−	0.0940754i
$890$	8.85514			0.296825
$891$	0.374446	+	1.34889i	0.0125444	+	0.0451895i
$892$	−9.33346			−0.312507
$893$	−2.64730	−	1.32952i	−0.0885884	−	0.0444908i
$894$	2.57938	−	0.364587i	0.0862675	−	0.0121936i
$895$	14.5275	+	19.5138i	0.485600	+	0.652274i
$896$	0.230620	+	0.770323i	0.00770446	+	0.0257347i
$897$	2.04658	+	10.1695i	0.0683333	+	0.339550i
$898$	−15.9392	−	36.9512i	−0.531898	−	1.23308i
$899$	12.8244	+	72.7308i	0.427718	+	2.42571i
$900$	2.43433	+	4.97116i	0.0811443	+	0.165705i
$901$	−0.0757640	+	0.429679i	−0.00252406	+	0.0143147i
$902$	0.760900	−	0.180337i	0.0253352	−	0.00600455i
$903$	3.26746	+	3.30048i	0.108734	+	0.109833i
$904$	10.3773	+	6.82525i	0.345144	+	0.227005i
$905$	2.28884	−	39.2979i	0.0760837	−	1.30631i
$906$	−13.0761	+	18.4762i	−0.434424	+	0.613831i
$907$	11.9961	−	40.0697i	0.398324	−	1.33049i	−0.490179	−	0.871622i	$-0.663069\pi$
$907$	11.9961	−	40.0697i	0.398324	−	1.33049i	0.888503	−	0.458872i	$-0.151746\pi$
$908$	19.7638	−	7.19345i	0.655886	−	0.238723i
$909$	20.4693	−	3.39743i	0.678923	−	0.112686i
$910$	1.35859	+	0.494486i	0.0450368	+	0.0163921i
$911$	−17.5501	+	23.5738i	−0.581460	+	0.781036i	−0.991370	−	0.131090i	$-0.958152\pi$
$911$	−17.5501	+	23.5738i	−0.581460	+	0.781036i	0.409911	+	0.912126i	$0.365560\pi$
$912$	−0.212401	−	0.348261i	−0.00703330	−	0.0115321i
$913$	0.330008	+	0.0782132i	0.0109217	+	0.00258848i
$914$	−14.8007	+	34.3118i	−0.489563	+	1.13493i
$915$	18.7825	−	20.8932i	0.620930	−	0.690709i
$916$	7.53928	−	4.95866i	0.249105	−	0.163839i
$917$	3.77376	+	6.53634i	0.124620	+	0.215849i
$918$	0.330597	−	0.104041i	0.0109113	−	0.00343387i
$919$	−5.37872	+	9.31622i	−0.177428	+	0.307314i	−0.940999	−	0.338410i	$-0.890111\pi$
$919$	−5.37872	+	9.31622i	−0.177428	+	0.307314i	0.763571	+	0.645724i	$0.223444\pi$
$920$	1.32574	+	22.7621i	0.0437084	+	0.750444i
$921$	0.313305	−	9.17983i	0.0103237	−	0.302486i
$922$	37.1078	−	4.33729i	1.22208	−	0.142841i
$923$	1.85607	−	1.96732i	0.0610932	−	0.0647550i
$924$	0.169253	+	0.135217i	0.00556803	+	0.00444831i
$925$	−14.6646	−	1.71404i	−0.482168	−	0.0563574i
$926$	−17.7703	+	14.9111i	−0.583970	+	0.490009i
$927$	−20.3145	−	31.5736i	−0.667214	−	1.03701i
$928$	7.71038	+	6.46978i	0.253106	+	0.212381i
$929$	−1.32318	−	1.40249i	−0.0434121	−	0.0460141i	0.705304	−	0.708905i	$-0.250811\pi$
$929$	−1.32318	−	1.40249i	−0.0434121	−	0.0460141i	−0.748716	+	0.662891i	$0.769329\pi$
$930$	30.0639	+	14.2035i	0.985834	+	0.465750i
$931$	−1.33716	+	0.671546i	−0.0438236	+	0.0220090i
$932$	7.78356	−	3.90905i	0.254959	−	0.128045i
$933$	6.03861	−	4.18319i	0.197695	−	0.136952i
$934$	−0.296949	−	0.314748i	−0.00971647	−	0.0102989i
$935$	−0.0207932	−	0.0174475i	−0.000680009	−	0.000570596i
$936$	1.90119	−	0.797516i	0.0621423	−	0.0260676i
$937$	−24.5880	+	20.6318i	−0.803255	+	0.674011i	−0.948988	−	0.315313i	$-0.897891\pi$
$937$	−24.5880	+	20.6318i	−0.803255	+	0.674011i	0.145732	+	0.989324i	$0.453446\pi$
$938$	−6.65010	−	0.777286i	−0.217134	−	0.0253793i
$939$	1.19463	−	7.87924i	0.0389854	−	0.257129i
$940$	22.5836	−	23.9372i	0.736596	−	0.780746i
$941$	31.3900	−	3.66897i	1.02328	−	0.119605i	0.412137	−	0.911122i	$-0.364782\pi$
$941$	31.3900	−	3.66897i	1.02328	−	0.119605i	0.611147	+	0.791517i	$0.290708\pi$
$942$	−29.7675	−	18.5681i	−0.969878	−	0.604982i
$943$	2.54748	+	43.7385i	0.0829574	+	1.42432i
$944$	3.62426	−	6.27739i	0.117959	−	0.204312i
$945$	−4.76878	+	9.83657i	−0.155129	+	0.319984i
$946$	−0.259341	−	0.449191i	−0.00843190	−	0.0146045i
$947$	23.3956	−	15.3875i	0.760256	−	0.500028i	−0.109211	−	0.994019i	$-0.534833\pi$
$947$	23.3956	−	15.3875i	0.760256	−	0.500028i	0.869467	+	0.493990i	$0.164462\pi$
$948$	−28.5518	−	6.04529i	−0.927319	−	0.196342i
$949$	−2.73038	+	6.32973i	−0.0886319	+	0.205472i
$950$	−0.422825	−	0.100211i	−0.0137183	−	0.00325129i
$951$	−10.9418	+	0.263323i	−0.354811	+	0.00853882i
$952$	0.0320277	−	0.0430207i	0.00103802	−	0.00139431i
$953$	−20.1844	−	7.34651i	−0.653836	−	0.237977i	−0.00626309	−	0.999980i	$-0.501994\pi$
$953$	−20.1844	−	7.34651i	−0.653836	−	0.237977i	−0.647573	+	0.762004i	$0.724216\pi$
$954$	−19.2907	−	3.60184i	−0.624560	−	0.116614i
$955$	18.3570	−	6.68140i	0.594018	−	0.216205i
$956$	−7.15447	+	23.8976i	−0.231392	+	0.772903i
$957$	2.70013	+	0.249916i	0.0872827	+	0.00807863i
$958$	0.747378	−	12.8320i	0.0241467	−	0.414583i
$959$	−10.2975	−	6.77279i	−0.332524	−	0.218705i
$960$	4.38301	−	1.15084i	0.141461	−	0.0371431i
$961$	22.2225	−	5.26682i	0.716854	−	0.169897i
$962$	−0.954939	+	5.41573i	−0.0307885	+	0.174610i
$963$	6.40985	−	25.8827i	0.206555	−	0.834058i
$964$	3.43566	+	19.4846i	0.110655	+	0.627556i
$965$	12.8755	+	29.8487i	0.414476	+	0.960863i
$966$	−9.10752	+	8.02332i	−0.293030	+	0.258146i
$967$	−11.4223	−	38.1531i	−0.367316	−	1.22692i	−0.919464	−	0.393174i	$-0.871377\pi$
$967$	−11.4223	−	38.1531i	−0.367316	−	1.22692i	0.552148	−	0.833746i	$-0.313808\pi$
$968$	6.55430	+	8.80395i	0.210663	+	0.282970i
$969$	−0.0101725	+	0.0252351i	−0.000326786	+	0.000810669i
$970$	16.9133	+	8.49419i	0.543054	+	0.272732i
$971$	−33.1226			−1.06295			−0.531477	−	0.847073i	$-0.678363\pi$
$971$	−33.1226			−1.06295			−0.531477	+	0.847073i	$0.678363\pi$
$972$	4.52978	+	14.9158i	0.145293	+	0.478424i
$973$	−3.16743			−0.101543
$974$	−7.34099	−	3.68678i	−0.235220	−	0.118132i
$975$	0.821106	−	2.03694i	0.0262964	−	0.0652343i
$976$	−3.70223	−	4.97296i	−0.118506	−	0.159181i
$977$	15.6736	+	52.3535i	0.501444	+	1.67494i	0.715898	+	0.698204i	$0.246017\pi$
$977$	15.6736	+	52.3535i	0.501444	+	1.67494i	−0.214455	+	0.976734i	$0.568797\pi$
$978$	2.40906	−	2.12227i	0.0770332	−	0.0678628i
$979$	−0.208518	−	0.483399i	−0.00666426	−	0.0154495i
$980$	−2.88647	−	16.3700i	−0.0922048	−	0.522919i
$981$	33.5016	−	9.66375i	1.06962	−	0.308540i
$982$	2.58742	−	14.6740i	0.0825678	−	0.468265i
$983$	−21.2682	+	5.04066i	−0.678351	+	0.160772i	−0.555328	−	0.831632i	$-0.687407\pi$
$983$	−21.2682	+	5.04066i	−0.678351	+	0.160772i	−0.123023	+	0.992404i	$0.539259\pi$
$984$	8.42218	−	2.21139i	0.268489	−	0.0704966i
$985$	−44.4409	−	29.2292i	−1.41600	−	0.931321i
$986$	0.0390353	−	0.670210i	0.00124314	−	0.0213438i
$987$	17.4441	+	1.61457i	0.555251	+	0.0513924i
$988$	−0.0464196	+	0.155052i	−0.00147681	+	0.00493287i
$989$	27.3081	−	9.93934i	0.868347	−	0.316053i
$990$	0.794114	−	0.927291i	0.0252386	−	0.0294712i
$991$	−40.5755	−	14.7683i	−1.28892	−	0.469130i	−0.395550	−	0.918444i	$-0.629446\pi$
$991$	−40.5755	−	14.7683i	−1.28892	−	0.469130i	−0.893374	+	0.449315i	$0.851668\pi$
$992$	4.38162	−	5.88553i	0.139116	−	0.186866i
$993$	27.7871	−	0.668721i	0.881797	−	0.0212212i
$994$	3.07936	+	0.729821i	0.0976713	+	0.0231485i
$995$	−24.0440	+	55.7403i	−0.762246	+	1.76708i
$996$	3.69466	+	0.782274i	0.117070	+	0.0247873i
$997$	4.06161	−	2.67136i	0.128633	−	0.0846029i	−0.483562	−	0.875310i	$-0.660657\pi$
$997$	4.06161	−	2.67136i	0.128633	−	0.0846029i	0.612195	+	0.790707i	$0.290287\pi$
$998$	5.12885	+	8.88343i	0.162351	+	0.281200i
$999$	−39.9964	−	11.3663i	−1.26543	−	0.359612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.13.3	✓	72
3.2	odd	2		486.2.g.a.253.4		72
81.25	even	27	inner	162.2.g.a.25.3	yes	72
81.56	odd	54		486.2.g.a.73.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.13.3	✓	72	1.1	even	1	trivial
162.2.g.a.25.3	yes	72	81.25	even	27	inner
486.2.g.a.73.4		72	81.56	odd	54
486.2.g.a.253.4		72	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.893633 - 0.448799i) q^{2} +(0.647569 - 1.60644i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-0.750365 - 2.50640i) q^{5} +(-1.29966 + 1.14494i) q^{6} +(0.318489 + 0.738341i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-2.16131 - 2.08056i) q^{9} +O(q^{10})\)	\(q+(-0.893633 - 0.448799i) q^{2} +(0.647569 - 1.60644i) q^{3} +(0.597159 + 0.802123i) q^{4} +(-0.750365 - 2.50640i) q^{5} +(-1.29966 + 1.14494i) q^{6} +(0.318489 + 0.738341i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-2.16131 - 2.08056i) q^{9} +(-0.454317 + 2.57656i) q^{10} +(0.151352 - 0.0358710i) q^{11} +(1.67527 - 0.439871i) q^{12} +(-0.574171 - 0.377638i) q^{13} +(0.0467545 - 0.802743i) q^{14} +(-4.51229 - 0.417644i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(0.0626772 - 0.0228126i) q^{17} +(0.997663 + 2.82925i) q^{18} +(-0.221311 - 0.0805504i) q^{19} +(1.56235 - 2.09860i) q^{20} +(1.39235 - 0.0335080i) q^{21} +(-0.151352 - 0.0358710i) q^{22} +(3.45177 - 8.00209i) q^{23} +(-1.69449 - 0.358775i) q^{24} +(-1.54153 + 1.01388i) q^{25} +(0.343614 + 0.595158i) q^{26} +(-4.74190 + 2.12471i) q^{27} +(-0.402052 + 0.696374i) q^{28} +(0.585239 + 10.0482i) q^{29} +(3.84489 + 2.39833i) q^{30} +(7.28783 - 0.851825i) q^{31} +(0.686242 - 0.727374i) q^{32} +(0.0403859 - 0.266366i) q^{33} +(-0.0662487 - 0.00774336i) q^{34} +(1.61159 - 1.35229i) q^{35} +(0.378222 - 2.97606i) q^{36} +(6.12996 + 5.14365i) q^{37} +(0.161619 + 0.171306i) q^{38} +(-0.978469 + 0.677826i) q^{39} +(-2.33802 + 1.17420i) q^{40} +(-4.49262 + 2.25628i) q^{41} +(-1.25928 - 0.594940i) q^{42} +(2.28836 + 2.42552i) q^{43} +(0.119154 + 0.0999819i) q^{44} +(-3.59294 + 6.97828i) q^{45} +(-6.67595 + 5.60178i) q^{46} +(12.4934 + 1.46027i) q^{47} +(1.35323 + 1.08110i) q^{48} +(4.35998 - 4.62131i) q^{49} +(1.83259 - 0.214199i) q^{50} +(0.00394061 - 0.115460i) q^{51} +(-0.0399588 - 0.686066i) q^{52} +(-3.27068 + 5.66499i) q^{53} +(5.19108 + 0.229448i) q^{54} +(-0.203476 - 0.352430i) q^{55} +(0.671819 - 0.441862i) q^{56} +(-0.272713 + 0.303361i) q^{57} +(3.98662 - 9.24202i) q^{58} +(-7.05313 - 1.67162i) q^{59} +(-2.35955 - 3.86881i) q^{60} +(-3.70223 + 4.97296i) q^{61} +(-6.89494 - 2.50955i) q^{62} +(0.847811 - 2.25842i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(-0.515673 + 1.72247i) q^{65} +(-0.155635 + 0.219909i) q^{66} +(0.484143 - 8.31242i) q^{67} +(0.0557268 + 0.0366521i) q^{68} +(-10.6196 - 10.7270i) q^{69} +(-2.04708 + 0.485166i) q^{70} +(-0.683417 + 3.87585i) q^{71} +(-1.67365 + 2.48976i) q^{72} +(-1.74184 - 9.87849i) q^{73} +(-3.16947 - 7.34766i) q^{74} +(0.630493 + 3.13293i) q^{75} +(-0.0675461 - 0.225620i) q^{76} +(0.0746888 + 0.100325i) q^{77} +(1.17860 - 0.166591i) q^{78} +(-15.0576 - 7.56219i) q^{79} +2.61631 q^{80} +(0.342522 + 8.99348i) q^{81} +5.02737 q^{82} +(1.94848 + 0.978564i) q^{83} +(0.858329 + 1.09682i) q^{84} +(-0.104208 - 0.139976i) q^{85} +(-0.956381 - 3.19454i) q^{86} +(16.5208 + 5.56672i) q^{87} +(-0.0616079 - 0.142823i) q^{88} +(-0.587729 - 3.33317i) q^{89} +(6.34261 - 4.62351i) q^{90} +(0.0959586 - 0.544208i) q^{91} +(8.47992 - 2.00978i) q^{92} +(3.35096 - 12.2591i) q^{93} +(-10.5091 - 6.91197i) q^{94} +(-0.0358275 + 0.615134i) q^{95} +(-0.724095 - 1.57343i) q^{96} +(2.07475 - 6.93014i) q^{97} +(-5.97026 + 2.17300i) q^{98} +(-0.401749 - 0.237368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

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