LMFDB - Embedded newform 637.2.bl.b.53.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.19
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.655312 + 0.446784i) q^{2} +(-1.79642 - 1.66683i) q^{3} +(-0.500865 - 1.27618i) q^{4} +(-0.752346 + 0.232068i) q^{5} +(-0.432499 - 1.89490i) q^{6} +(2.24469 + 1.40049i) q^{7} +(0.594930 - 2.60656i) q^{8} +(0.224596 + 2.99702i) q^{9} +O(q^{10})$	\(q+(0.655312 + 0.446784i) q^{2} +(-1.79642 - 1.66683i) q^{3} +(-0.500865 - 1.27618i) q^{4} +(-0.752346 + 0.232068i) q^{5} +(-0.432499 - 1.89490i) q^{6} +(2.24469 + 1.40049i) q^{7} +(0.594930 - 2.60656i) q^{8} +(0.224596 + 2.99702i) q^{9} +(-0.596706 - 0.184059i) q^{10} +(0.442507 - 5.90484i) q^{11} +(-1.22742 + 3.12741i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(0.845258 + 1.92065i) q^{14} +(1.73834 + 0.837142i) q^{15} +(-0.455524 + 0.422664i) q^{16} +(0.485721 - 0.0732106i) q^{17} +(-1.19184 + 2.06433i) q^{18} +(-1.19293 - 2.06621i) q^{19} +(0.672985 + 0.843896i) q^{20} +(-1.69803 - 6.25737i) q^{21} +(2.92817 - 3.67181i) q^{22} +(-8.06804 - 1.21606i) q^{23} +(-5.41343 + 3.69081i) q^{24} +(-3.61902 + 2.46741i) q^{25} +(-0.784268 - 0.118209i) q^{26} +(0.00829423 - 0.0104006i) q^{27} +(0.662989 - 3.56609i) q^{28} +(4.38780 + 5.50213i) q^{29} +(0.765136 + 1.32525i) q^{30} +(-4.15143 + 7.19048i) q^{31} +(-5.77481 + 0.870412i) q^{32} +(-10.6373 + 9.86997i) q^{33} +(0.351008 + 0.169036i) q^{34} +(-2.01379 - 0.532729i) q^{35} +(3.71226 - 1.78773i) q^{36} +(2.96544 - 7.55581i) q^{37} +(0.141411 - 1.88699i) q^{38} +(2.34172 + 0.722326i) q^{39} +(0.157306 + 2.09910i) q^{40} +(1.31278 - 5.75165i) q^{41} +(1.68296 - 4.85918i) q^{42} +(-1.44930 - 6.34981i) q^{43} +(-7.75729 + 2.39281i) q^{44} +(-0.864488 - 2.20268i) q^{45} +(-4.74376 - 4.40157i) q^{46} +(-3.93748 - 2.68453i) q^{47} +1.52282 q^{48} +(3.07728 + 6.28732i) q^{49} -3.47399 q^{50} +(-0.994586 - 0.678097i) q^{51} +(1.00498 + 0.932483i) q^{52} +(0.220113 + 0.560838i) q^{53} +(0.0100821 - 0.00310993i) q^{54} +(1.03741 + 4.54518i) q^{55} +(4.98588 - 5.01772i) q^{56} +(-1.30103 + 5.70018i) q^{57} +(0.417115 + 5.56601i) q^{58} +(-3.36363 - 1.03754i) q^{59} +(0.197671 - 2.63774i) q^{60} +(-1.88804 + 4.81064i) q^{61} +(-5.93307 + 2.85722i) q^{62} +(-3.69314 + 7.04194i) q^{63} +(-3.05345 - 1.47046i) q^{64} +(0.577150 - 0.535517i) q^{65} +(-11.3805 + 1.71533i) q^{66} +(4.20180 - 7.27773i) q^{67} +(-0.336710 - 0.583200i) q^{68} +(12.4666 + 15.6326i) q^{69} +(-1.08165 - 1.24883i) q^{70} +(9.63425 - 12.0810i) q^{71} +(7.94553 + 1.19760i) q^{72} +(-0.776867 + 0.529659i) q^{73} +(5.31910 - 3.62650i) q^{74} +(10.6140 + 1.59981i) q^{75} +(-2.03937 + 2.55728i) q^{76} +(9.26295 - 12.6348i) q^{77} +(1.21184 + 1.51959i) q^{78} +(-1.85108 - 3.20617i) q^{79} +(0.244625 - 0.423702i) q^{80} +(8.88334 - 1.33895i) q^{81} +(3.43002 - 3.18260i) q^{82} +(10.9153 + 5.25655i) q^{83} +(-7.13507 + 5.30109i) q^{84} +(-0.348440 + 0.167800i) q^{85} +(1.88725 - 4.80863i) q^{86} +(1.28880 - 17.1978i) q^{87} +(-15.1281 - 4.66639i) q^{88} +(0.0843959 + 1.12619i) q^{89} +(0.417613 - 1.82968i) q^{90} +(-2.63005 - 0.287859i) q^{91} +(2.48908 + 10.9054i) q^{92} +(19.4430 - 5.99737i) q^{93} +(-1.38087 - 3.51840i) q^{94} +(1.37700 + 1.27767i) q^{95} +(11.8248 + 8.06200i) q^{96} -8.77496 q^{97} +(-0.792497 + 5.49503i) q^{98} +17.7964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	0.655312	+	0.446784i	0.463375	+	0.315924i	0.772407	−	0.635128i	$-0.219053\pi$
$2$	0.655312	+	0.446784i	0.463375	+	0.315924i	−0.309032	+	0.951052i	$0.600005\pi$
$3$	−1.79642	−	1.66683i	−1.03716	−	0.962345i	−0.0378432	−	0.999284i	$-0.512049\pi$
$3$	−1.79642	−	1.66683i	−1.03716	−	0.962345i	−0.999318	+	0.0369391i	$0.988239\pi$
$4$	−0.500865	−	1.27618i	−0.250432	−	0.638091i
$5$	−0.752346	+	0.232068i	−0.336460	+	0.103784i	−0.458381	−	0.888756i	$-0.651571\pi$
$5$	−0.752346	+	0.232068i	−0.336460	+	0.103784i	0.121922	+	0.992540i	$0.461094\pi$
$6$	−0.432499	−	1.89490i	−0.176567	−	0.773591i
$7$	2.24469	+	1.40049i	0.848414	+	0.529334i
$7$	2.24469	+	1.40049i	0.848414	+	0.529334i
$8$	0.594930	−	2.60656i	0.210339	−	0.921557i
$9$	0.224596	+	2.99702i	0.0748653	+	0.999008i
$10$	−0.596706	−	0.184059i	−0.188695	−	0.0582047i
$11$	0.442507	−	5.90484i	0.133421	−	1.78038i	−0.382711	−	0.923868i	$-0.625009\pi$
$11$	0.442507	−	5.90484i	0.133421	−	1.78038i	0.516131	−	0.856509i	$-0.327372\pi$
$12$	−1.22742	+	3.12741i	−0.354325	+	0.902805i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	0.845258	+	1.92065i	0.225905	+	0.513314i
$15$	1.73834	+	0.837142i	0.448839	+	0.216149i
$16$	−0.455524	+	0.422664i	−0.113881	+	0.105666i
$17$	0.485721	−	0.0732106i	0.117805	−	0.0177562i	−0.0898753	−	0.995953i	$-0.528647\pi$
$17$	0.485721	−	0.0732106i	0.117805	−	0.0177562i	0.207680	+	0.978197i	$0.433409\pi$
$18$	−1.19184	+	2.06433i	−0.280920	+	0.486568i
$19$	−1.19293	−	2.06621i	−0.273676	−	0.474021i	0.696124	−	0.717922i	$-0.254906\pi$
$19$	−1.19293	−	2.06621i	−0.273676	−	0.474021i	−0.969800	+	0.243900i	$0.921573\pi$
$20$	0.672985	+	0.843896i	0.150484	+	0.188701i
$21$	−1.69803	−	6.25737i	−0.370539	−	1.36547i
$22$	2.92817	−	3.67181i	0.624288	−	0.782832i
$23$	−8.06804	−	1.21606i	−1.68230	−	0.253566i	−0.762795	−	0.646640i	$-0.776174\pi$
$23$	−8.06804	−	1.21606i	−1.68230	−	0.253566i	−0.919507	+	0.393074i	$0.871412\pi$
$24$	−5.41343	+	3.69081i	−1.10501	+	0.753384i
$25$	−3.61902	+	2.46741i	−0.723805	+	0.493482i
$26$	−0.784268	−	0.118209i	−0.153808	−	0.0231828i
$27$	0.00829423	−	0.0104006i	0.00159623	−	0.00200160i
$28$	0.662989	−	3.56609i	0.125293	−	0.673927i
$29$	4.38780	+	5.50213i	0.814795	+	1.02172i	0.999244	+	0.0388784i	$0.0123785\pi$
$29$	4.38780	+	5.50213i	0.814795	+	1.02172i	−0.184449	+	0.982842i	$0.559050\pi$
$30$	0.765136	+	1.32525i	0.139694	+	0.241957i
$31$	−4.15143	+	7.19048i	−0.745618	+	1.29145i	0.204287	+	0.978911i	$0.434512\pi$
$31$	−4.15143	+	7.19048i	−0.745618	+	1.29145i	−0.949905	+	0.312538i	$0.898821\pi$
$32$	−5.77481	+	0.870412i	−1.02085	+	0.153869i
$33$	−10.6373	+	9.86997i	−1.85172	+	1.71814i
$34$	0.351008	+	0.169036i	0.0601974	+	0.0289895i
$35$	−2.01379	−	0.532729i	−0.340393	−	0.0900477i
$36$	3.71226	−	1.78773i	0.618709	−	0.297955i
$37$	2.96544	−	7.55581i	0.487515	−	1.24217i	−0.449626	−	0.893217i	$-0.648443\pi$
$37$	2.96544	−	7.55581i	0.487515	−	1.24217i	0.937141	−	0.348951i	$-0.113462\pi$
$38$	0.141411	−	1.88699i	0.0229398	−	0.306111i
$39$	2.34172	+	0.722326i	0.374976	+	0.115665i
$40$	0.157306	+	2.09910i	0.0248722	+	0.331897i
$41$	1.31278	−	5.75165i	0.205021	−	0.898257i	−0.762803	−	0.646631i	$-0.776177\pi$
$41$	1.31278	−	5.75165i	0.205021	−	0.898257i	0.967824	−	0.251626i	$-0.0809654\pi$
$42$	1.68296	−	4.85918i	0.259686	−	0.749788i
$43$	−1.44930	−	6.34981i	−0.221017	−	0.968337i	−0.956715	−	0.291028i	$-0.906003\pi$
$43$	−1.44930	−	6.34981i	−0.221017	−	0.968337i	0.735698	−	0.677310i	$-0.236854\pi$
$44$	−7.75729	+	2.39281i	−1.16946	+	0.360729i
$45$	−0.864488	−	2.20268i	−0.128870	−	0.328356i
$46$	−4.74376	−	4.40157i	−0.699430	−	0.648976i
$47$	−3.93748	−	2.68453i	−0.574340	−	0.391579i	0.241031	−	0.970518i	$-0.422515\pi$
$47$	−3.93748	−	2.68453i	−0.574340	−	0.391579i	−0.815371	+	0.578939i	$0.803467\pi$
$48$	1.52282			0.219800
$49$	3.07728	+	6.28732i	0.439611	+	0.898188i
$50$	−3.47399			−0.491296
$51$	−0.994586	−	0.678097i	−0.139270	−	0.0949526i
$52$	1.00498	+	0.932483i	0.139365	+	0.129312i
$53$	0.220113	+	0.560838i	0.0302348	+	0.0770370i	0.945194	−	0.326510i	$-0.105873\pi$
$53$	0.220113	+	0.560838i	0.0302348	+	0.0770370i	−0.914959	+	0.403547i	$0.867777\pi$
$54$	0.0100821	−	0.00310993i	0.00137201	−	0.000423208i
$55$	1.03741	+	4.54518i	0.139884	+	0.612872i
$56$	4.98588	−	5.01772i	0.666266	−	0.670522i
$57$	−1.30103	+	5.70018i	−0.172325	+	0.755007i
$58$	0.417115	+	5.56601i	0.0547699	+	0.730853i
$59$	−3.36363	−	1.03754i	−0.437907	−	0.135076i	0.0679598	−	0.997688i	$-0.478351\pi$
$59$	−3.36363	−	1.03754i	−0.437907	−	0.135076i	−0.505867	+	0.862612i	$0.668827\pi$
$60$	0.197671	−	2.63774i	0.0255192	−	0.340531i
$61$	−1.88804	+	4.81064i	−0.241738	+	0.615939i	−0.999323	−	0.0367981i	$-0.988284\pi$
$61$	−1.88804	+	4.81064i	−0.241738	+	0.615939i	0.757584	+	0.652737i	$0.226379\pi$
$62$	−5.93307	+	2.85722i	−0.753501	+	0.362867i
$63$	−3.69314	+	7.04194i	−0.465292	+	0.887201i
$64$	−3.05345	−	1.47046i	−0.381681	−	0.183808i
$65$	0.577150	−	0.535517i	0.0715867	−	0.0664227i
$66$	−11.3805	+	1.71533i	−1.40084	+	0.211143i
$67$	4.20180	−	7.27773i	0.513332	−	0.889117i	−0.486549	−	0.873653i	$-0.661744\pi$
$67$	4.20180	−	7.27773i	0.513332	−	0.889117i	0.999880	−	0.0154632i	$-0.00492230\pi$
$68$	−0.336710	−	0.583200i	−0.0408321	−	0.0707233i
$69$	12.4666	+	15.6326i	1.50080	+	1.88194i
$70$	−1.08165	−	1.24883i	−0.129282	−	0.149264i
$71$	9.63425	−	12.0810i	1.14337	−	1.43375i	0.259673	−	0.965697i	$-0.416385\pi$
$71$	9.63425	−	12.0810i	1.14337	−	1.43375i	0.883702	−	0.468050i	$-0.155043\pi$
$72$	7.94553	+	1.19760i	0.936390	+	0.141138i
$73$	−0.776867	+	0.529659i	−0.0909254	+	0.0619919i	−0.607929	−	0.793991i	$-0.708000\pi$
$73$	−0.776867	+	0.529659i	−0.0909254	+	0.0619919i	0.517004	+	0.855983i	$0.327047\pi$
$74$	5.31910	−	3.62650i	0.618333	−	0.421572i
$75$	10.6140	+	1.59981i	1.22560	+	0.184730i
$76$	−2.03937	+	2.55728i	−0.233931	+	0.293341i
$77$	9.26295	−	12.6348i	1.05561	−	1.43987i
$78$	1.21184	+	1.51959i	0.137213	+	0.172060i
$79$	−1.85108	−	3.20617i	−0.208263	−	0.360722i	0.742904	−	0.669398i	$-0.233448\pi$
$79$	−1.85108	−	3.20617i	−0.208263	−	0.360722i	−0.951167	+	0.308675i	$0.900114\pi$
$80$	0.244625	−	0.423702i	0.0273499	−	0.0473714i
$81$	8.88334	−	1.33895i	0.987038	−	0.148772i
$82$	3.43002	−	3.18260i	0.378783	−	0.351459i
$83$	10.9153	+	5.25655i	1.19811	+	0.576981i	0.923138	−	0.384469i	$-0.125616\pi$
$83$	10.9153	+	5.25655i	1.19811	+	0.576981i	0.274977	+	0.961451i	$0.411330\pi$
$84$	−7.13507	+	5.30109i	−0.778499	+	0.578396i
$85$	−0.348440	+	0.167800i	−0.0377937	+	0.0182005i
$86$	1.88725	−	4.80863i	0.203507	−	0.518528i
$87$	1.28880	−	17.1978i	0.138174	−	1.84380i
$88$	−15.1281	−	4.66639i	−1.61266	−	0.497439i
$89$	0.0843959	+	1.12619i	0.00894595	+	0.119375i	0.999889	−	0.0149084i	$-0.00474567\pi$
$89$	0.0843959	+	1.12619i	0.00894595	+	0.119375i	−0.990943	+	0.134284i	$0.957127\pi$
$90$	0.417613	−	1.82968i	0.0440202	−	0.192865i
$91$	−2.63005	−	0.287859i	−0.275704	−	0.0301759i
$92$	2.48908	+	10.9054i	0.259504	+	1.13696i
$93$	19.4430	−	5.99737i	2.01614	−	0.621898i
$94$	−1.38087	−	3.51840i	−0.142426	−	0.362896i
$95$	1.37700	+	1.27767i	0.141277	+	0.131086i
$96$	11.8248	+	8.06200i	1.20686	+	0.822824i
$97$	−8.77496			−0.890963			−0.445481	−	0.895291i	$-0.646967\pi$
$97$	−8.77496			−0.890963			−0.445481	+	0.895291i	$0.646967\pi$
$98$	−0.792497	+	5.49503i	−0.0800543	+	0.555082i
$99$	17.7964			1.78860
$100$	4.96150	+	3.38270i	0.496150	+	0.338270i
$101$	2.20820	+	2.04891i	0.219724	+	0.203874i	0.782353	−	0.622836i	$-0.214019\pi$
$101$	2.20820	+	2.04891i	0.219724	+	0.203874i	−0.562629	+	0.826710i	$0.690210\pi$
$102$	−0.348801	−	0.888730i	−0.0345364	−	0.0879974i
$103$	9.62551	−	2.96908i	0.948429	−	0.292552i	0.218316	−	0.975878i	$-0.429944\pi$
$103$	9.62551	−	2.96908i	0.948429	−	0.292552i	0.730113	+	0.683326i	$0.239467\pi$
$104$	0.594930	+	2.60656i	0.0583377	+	0.255594i
$105$	2.72964	+	4.31365i	0.266386	+	0.420969i
$106$	−0.106331	+	0.465866i	−0.0103278	+	0.0452490i
$107$	−0.757945	−	10.1141i	−0.0732733	−	0.977764i	−0.905780	−	0.423749i	$-0.860714\pi$
$107$	−0.757945	−	10.1141i	−0.0732733	−	0.977764i	0.832506	−	0.554015i	$-0.186905\pi$
$108$	−0.0174274	−	0.00537564i	−0.00167695	−	0.000517271i
$109$	−0.0290699	+	0.387911i	−0.00278440	+	0.0371552i	−0.998423	−	0.0561395i	$-0.982121\pi$
$109$	−0.0290699	+	0.387911i	−0.00278440	+	0.0371552i	0.995639	+	0.0932947i	$0.0297399\pi$
$110$	−1.35089	+	3.44201i	−0.128802	+	0.328182i
$111$	−17.9214	+	8.63049i	−1.70102	+	0.819170i
$112$	−1.61445	+	0.310796i	−0.152551	+	0.0293675i
$113$	−5.13845	−	2.47455i	−0.483385	−	0.232786i	0.176288	−	0.984339i	$-0.443591\pi$
$113$	−5.13845	−	2.47455i	−0.483385	−	0.232786i	−0.659673	+	0.751553i	$0.729305\pi$
$114$	−3.39933	+	3.15411i	−0.318376	+	0.295410i
$115$	6.35217	−	0.957435i	0.592343	−	0.0892813i
$116$	4.82403	−	8.35546i	0.447900	−	0.775785i
$117$	−1.50271	−	2.60278i	−0.138926	−	0.240627i
$118$	−1.74067	−	2.18273i	−0.160241	−	0.200936i
$119$	1.19282	+	0.515910i	0.109346	+	0.0472934i
$120$	3.21625	−	4.03305i	0.293602	−	0.368166i
$121$	−23.7942	−	3.58640i	−2.16311	−	0.326037i
$122$	−3.38657	+	2.30892i	−0.306605	+	0.209040i
$123$	−11.9453	+	8.14418i	−1.07707	+	0.734336i
$124$	11.2557	+	1.69652i	1.01079	+	0.152352i
$125$	4.60460	−	5.77398i	0.411848	−	0.516441i
$126$	−5.56638	+	2.96463i	−0.495893	+	0.264110i
$127$	−5.97739	−	7.49541i	−0.530407	−	0.665110i	0.442375	−	0.896830i	$-0.354136\pi$
$127$	−5.97739	−	7.49541i	−0.530407	−	0.665110i	−0.972782	+	0.231720i	$0.925565\pi$
$128$	4.49605	+	7.78739i	0.397399	+	0.688315i
$129$	−7.98051	+	13.8226i	−0.702644	+	1.21702i
$130$	0.617474	−	0.0930692i	0.0541560	−	0.00816271i
$131$	14.4222	−	13.3818i	1.26007	−	1.16918i	0.282343	−	0.959314i	$-0.408888\pi$
$131$	14.4222	−	13.3818i	1.26007	−	1.16918i	0.977731	−	0.209864i	$-0.0673021\pi$
$132$	17.9237	+	8.63161i	1.56006	+	0.751285i
$133$	0.215946	−	6.30868i	0.0187249	−	0.547032i
$134$	6.00506	−	2.89189i	0.518759	−	0.249821i
$135$	−0.00382648	+	0.00974971i	−0.000329331	+	0.000839121i
$136$	0.0981420	−	1.30961i	0.00841561	−	0.112298i
$137$	5.16496	+	1.59318i	0.441273	+	0.136115i	0.507427	−	0.861695i	$-0.330597\pi$
$137$	5.16496	+	1.59318i	0.441273	+	0.136115i	−0.0661542	+	0.997809i	$0.521073\pi$
$138$	1.18510	+	15.8141i	0.100883	+	1.34618i
$139$	−2.35940	+	10.3372i	−0.200122	+	0.876790i	0.770740	+	0.637150i	$0.219887\pi$
$139$	−2.35940	+	10.3372i	−0.200122	+	0.876790i	−0.970862	+	0.239641i	$0.922970\pi$
$140$	0.328778	+	2.83679i	0.0277868	+	0.239753i
$141$	2.59870	+	11.3856i	0.218850	+	0.958843i
$142$	11.7110	−	3.61237i	0.982767	−	0.303143i
$143$	2.16333	+	5.51208i	0.180907	+	0.460943i
$144$	−1.36904	−	1.27029i	−0.114087	−	0.105857i
$145$	−4.57802	−	3.12124i	−0.380184	−	0.259205i
$146$	−0.745733			−0.0617173
$147$	4.95182	−	16.4239i	0.408419	−	1.35462i
$148$	−11.1279			−0.914705
$149$	2.78616	+	1.89957i	0.228251	+	0.155619i	0.672046	−	0.740509i	$-0.265416\pi$
$149$	2.78616	+	1.89957i	0.228251	+	0.155619i	−0.443795	+	0.896128i	$0.646368\pi$
$150$	6.24072	+	5.79055i	0.509553	+	0.472796i
$151$	5.55922	+	14.1647i	0.452403	+	1.15270i	0.957190	+	0.289460i	$0.0934759\pi$
$151$	5.55922	+	14.1647i	0.452403	+	1.15270i	−0.504787	+	0.863244i	$0.668429\pi$
$152$	−6.09540	+	1.88018i	−0.494403	+	0.152503i
$153$	0.328505	+	1.43927i	0.0265581	+	0.116358i
$154$	11.7152	−	4.14122i	0.944034	−	0.333709i
$155$	1.45463	−	6.37315i	0.116839	−	0.511903i
$156$	−0.251067	−	3.35025i	−0.0201014	−	0.268235i
$157$	−20.8631	−	6.43541i	−1.66506	−	0.513602i	−0.687842	−	0.725860i	$-0.741442\pi$
$157$	−20.8631	−	6.43541i	−1.66506	−	0.513602i	−0.977214	+	0.212259i	$0.931918\pi$
$158$	0.219429	−	2.92807i	0.0174568	−	0.232945i
$159$	0.539408	−	1.37439i	0.0427778	−	0.108996i
$160$	4.14266	−	1.99500i	0.327506	−	0.157719i
$161$	−16.4072	−	14.0289i	−1.29307	−	1.10563i
$162$	6.41958	+	3.09151i	0.504370	+	0.242892i
$163$	−5.16698	+	4.79425i	−0.404709	+	0.375515i	−0.856099	−	0.516812i	$-0.827119\pi$
$163$	−5.16698	+	4.79425i	−0.404709	+	0.375515i	0.451390	+	0.892327i	$0.350928\pi$
$164$	−7.99768	+	1.20546i	−0.624514	+	0.0941303i
$165$	5.71243	−	9.89421i	0.444712	−	0.770263i
$166$	4.80441	+	8.32148i	0.372894	+	0.645872i
$167$	−2.60127	−	3.26189i	−0.201292	−	0.252412i	0.670932	−	0.741519i	$-0.265894\pi$
$167$	−2.60127	−	3.26189i	−0.201292	−	0.252412i	−0.872224	+	0.489107i	$0.837323\pi$
$168$	−17.3204	+	0.703303i	−1.33630	+	0.0542610i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	−0.303307	−	0.0457162i	−0.0232626	−	0.00350628i
$171$	5.92456	−	4.03929i	0.453062	−	0.308893i
$172$	−7.37761	+	5.02997i	−0.562538	+	0.383532i
$173$	3.77770	+	0.569397i	0.287213	+	0.0432904i	0.291069	−	0.956702i	$-0.405989\pi$
$173$	3.77770	+	0.569397i	0.287213	+	0.0432904i	−0.00385547	+	0.999993i	$0.501227\pi$
$174$	8.52828	−	10.6941i	0.646528	−	0.810720i
$175$	−11.5792	+	0.470178i	−0.875303	+	0.0355421i
$176$	2.29419	+	2.87683i	0.172931	+	0.216849i
$177$	4.31307	+	7.47045i	0.324190	+	0.561513i
$178$	−0.447856	+	0.775709i	−0.0335682	+	0.0581419i
$179$	−1.10396	+	0.166395i	−0.0825139	+	0.0124370i	−0.190169	−	0.981751i	$-0.560904\pi$
$179$	−1.10396	+	0.166395i	−0.0825139	+	0.0124370i	0.107656	+	0.994188i	$0.465666\pi$
$180$	−2.37803	+	2.20649i	−0.177248	+	0.164462i
$181$	−13.4668	−	6.48527i	−1.00098	−	0.482046i	−0.139709	−	0.990193i	$-0.544617\pi$
$181$	−13.4668	−	6.48527i	−1.00098	−	0.482046i	−0.861271	+	0.508146i	$0.830331\pi$
$182$	−1.59489	−	1.36370i	−0.118221	−	0.101084i
$183$	11.4102	−	5.49487i	0.843467	−	0.406192i
$184$	−7.96965	+	20.3063i	−0.587530	+	1.49700i
$185$	−0.477573	+	6.37277i	−0.0351119	+	0.468535i
$186$	15.4207	+	4.75667i	1.13070	+	0.348776i
$187$	−0.217363	−	2.90050i	−0.0158951	−	0.212106i
$188$	−1.45380	+	6.36952i	−0.106029	+	0.464545i
$189$	0.0331839	−	0.0117303i	0.00241378	−	0.000853251i
$190$	0.331521	+	1.45249i	0.0240511	+	0.105375i
$191$	14.8652	−	4.58529i	1.07561	−	0.331780i	0.294161	−	0.955756i	$-0.404960\pi$
$191$	14.8652	−	4.58529i	1.07561	−	0.331780i	0.781444	+	0.623976i	$0.214484\pi$
$192$	3.03425	+	7.73114i	0.218978	+	0.557947i
$193$	1.82972	+	1.69773i	0.131706	+	0.122205i	0.743276	−	0.668985i	$-0.233271\pi$
$193$	1.82972	+	1.69773i	0.131706	+	0.122205i	−0.611570	+	0.791191i	$0.709462\pi$
$194$	−5.75034	−	3.92051i	−0.412850	−	0.281476i
$195$	−1.92942			−0.138168
$196$	6.48246	−	7.07626i	0.463033	−	0.505447i
$197$	14.6834			1.04615			0.523075	−	0.852287i	$-0.324785\pi$
$197$	14.6834			1.04615			0.523075	+	0.852287i	$0.324785\pi$
$198$	11.6622	+	7.95112i	0.828793	+	0.565062i
$199$	−3.92738	−	3.64408i	−0.278405	−	0.258322i	0.528594	−	0.848875i	$-0.322719\pi$
$199$	−3.92738	−	3.64408i	−0.278405	−	0.258322i	−0.806999	+	0.590553i	$0.798910\pi$
$200$	4.27838	+	10.9011i	0.302527	+	0.770826i
$201$	−19.6789	+	6.07014i	−1.38804	+	0.428155i
$202$	0.531638	+	2.32926i	0.0374059	+	0.163886i
$203$	2.14360	+	18.4956i	0.150452	+	1.29814i
$204$	−0.367223	+	1.60891i	−0.0257107	+	0.112646i
$205$	0.347112	+	4.63189i	0.0242434	+	0.323505i
$206$	7.63424	+	2.35485i	0.531903	+	0.164070i
$207$	1.83252	−	24.4532i	0.127369	−	1.69962i
$208$	0.227026	−	0.578452i	0.0157414	−	0.0401084i
$209$	−12.7285	+	6.12974i	−0.880451	+	0.424003i
$210$	−0.138506	+	4.04635i	−0.00955785	+	0.279224i
$211$	15.2492	+	7.34361i	1.04980	+	0.505555i	0.877543	−	0.479498i	$-0.159181\pi$
$211$	15.2492	+	7.34361i	1.04980	+	0.505555i	0.172253	+	0.985053i	$0.444895\pi$
$212$	0.605485	−	0.561808i	0.0415849	−	0.0385851i
$213$	−37.4440	+	5.64378i	−2.56562	+	0.386705i
$214$	4.02211	−	6.96651i	0.274946	−	0.476221i
$215$	2.56397	+	4.44092i	0.174861	+	0.302868i
$216$	−0.0221754	−	0.0278070i	−0.00150884	−	0.00189203i
$217$	−19.3888	+	10.3264i	−1.31620	+	0.701001i
$218$	−0.192362	+	0.241215i	−0.0130284	+	0.0163371i
$219$	2.27843	+	0.343418i	0.153962	+	0.0232060i
$220$	5.28088	−	3.60044i	0.356037	−	0.242742i
$221$	−0.405854	+	0.276707i	−0.0273007	+	0.0186133i
$222$	−15.6001	−	2.35133i	−1.04701	−	0.157811i
$223$	8.64745	−	10.8436i	0.579076	−	0.726138i	−0.402879	−	0.915253i	$-0.631990\pi$
$223$	8.64745	−	10.8436i	0.579076	−	0.726138i	0.981955	+	0.189115i	$0.0605619\pi$
$224$	−14.1817	−	6.13373i	−0.947552	−	0.409827i
$225$	−8.20770	−	10.2921i	−0.547180	−	0.686142i
$226$	−2.26170	−	3.91738i	−0.150446	−	0.260580i
$227$	−11.1483	+	19.3095i	−0.739940	+	1.28161i	0.212582	+	0.977143i	$0.431813\pi$
$227$	−11.1483	+	19.3095i	−0.739940	+	1.28161i	−0.952522	+	0.304470i	$0.901521\pi$
$228$	7.92610	−	1.19467i	0.524919	−	0.0791188i
$229$	19.8347	−	18.4039i	1.31071	−	1.21617i	0.350611	−	0.936521i	$-0.385974\pi$
$229$	19.8347	−	18.4039i	1.31071	−	1.21617i	0.960104	−	0.279644i	$-0.0902165\pi$
$230$	4.59042	+	2.21063i	0.302683	+	0.145765i
$231$	−37.7002	+	7.25764i	−2.48049	+	0.477518i
$232$	16.9521	−	8.16368i	1.11296	−	0.535972i
$233$	−2.52094	+	6.42325i	−0.165152	+	0.420801i	−0.989360	−	0.145486i	$-0.953525\pi$
$233$	−2.52094	+	6.42325i	−0.165152	+	0.420801i	0.824208	+	0.566287i	$0.191621\pi$
$234$	0.178133	−	2.37702i	0.0116449	−	0.155391i
$235$	3.58534	+	1.10593i	0.233882	+	0.0721430i
$236$	0.360630	+	4.81227i	0.0234750	+	0.313252i
$237$	−2.01883	+	8.84505i	−0.131137	+	0.574548i
$238$	0.551171	+	0.871016i	0.0357271	+	0.0564596i
$239$	−4.47436	−	19.6035i	−0.289423	−	1.26804i	−0.885320	−	0.464982i	$-0.846061\pi$
$239$	−4.47436	−	19.6035i	−0.289423	−	1.26804i	0.595897	−	0.803061i	$-0.296796\pi$
$240$	−1.14569	+	0.353398i	−0.0739538	+	0.0228117i
$241$	−3.70846	−	9.44899i	−0.238883	−	0.608663i	0.760279	−	0.649596i	$-0.225062\pi$
$241$	−3.70846	−	9.44899i	−0.238883	−	0.608663i	−0.999162	+	0.0409334i	$0.986967\pi$
$242$	−13.9903	−	12.9811i	−0.899330	−	0.834457i
$243$	−18.2229	−	12.4242i	−1.16900	−	0.797013i
$244$	7.08490			0.453564
$245$	−3.77426	−	4.01610i	−0.241129	−	0.256579i
$246$	−11.4666			−0.731083
$247$	1.97129	+	1.34400i	0.125430	+	0.0855167i
$248$	16.2726	+	15.0988i	1.03331	+	0.958772i
$249$	−10.8467	−	27.6370i	−0.687382	−	1.75142i
$250$	5.59717	−	1.72650i	0.353996	−	0.109193i
$251$	−4.11092	−	18.0111i	−0.259479	−	1.13685i	−0.921811	−	0.387641i	$-0.873290\pi$
$251$	−4.11092	−	18.0111i	−0.259479	−	1.13685i	0.662332	−	0.749211i	$-0.269567\pi$
$252$	10.8366	+	1.18607i	0.682639	+	0.0747151i
$253$	−10.7508	+	47.1024i	−0.675898	+	2.96130i
$254$	−0.568224	−	7.58243i	−0.0356536	−	0.475764i
$255$	0.905638	+	0.279352i	0.0567132	+	0.0174937i
$256$	−1.03950	+	13.8711i	−0.0649685	+	0.866945i
$257$	6.16480	−	15.7076i	0.384549	−	0.979816i	−0.599253	−	0.800560i	$-0.704536\pi$
$257$	6.16480	−	15.7076i	0.384549	−	0.979816i	0.983802	−	0.179256i	$-0.0573691\pi$
$258$	−11.4055	+	5.49258i	−0.710072	+	0.341953i
$259$	17.2383	−	12.8074i	1.07114	−	0.795814i
$260$	−0.972491	−	0.468327i	−0.0603113	−	0.0290444i
$261$	−15.5045	+	14.3861i	−0.959707	+	0.890478i
$262$	15.4298	−	2.32567i	0.953258	−	0.143681i
$263$	2.44777	−	4.23966i	0.150936	−	0.261429i	−0.780636	−	0.624986i	$-0.785105\pi$
$263$	2.44777	−	4.23966i	0.150936	−	0.261429i	0.931572	+	0.363557i	$0.118438\pi$
$264$	19.3982	+	33.5987i	1.19388	+	2.06785i
$265$	−0.295754	−	0.370863i	−0.0181680	−	0.0227819i
$266$	2.96013	−	4.03767i	0.181497	−	0.247566i
$267$	1.72555	−	2.16377i	0.105602	−	0.132421i
$268$	−11.3922	−	1.71710i	−0.695892	−	0.104889i
$269$	22.8048	−	15.5481i	1.39043	−	0.947982i	0.390813	−	0.920470i	$-0.372194\pi$
$269$	22.8048	−	15.5481i	1.39043	−	0.947982i	0.999621	−	0.0275121i	$-0.00875848\pi$
$270$	−0.00686355	+	0.00467949i	−0.000417702	+	0.000284785i
$271$	30.7160	+	4.62970i	1.86587	+	0.281234i	0.982334	−	0.187137i	$-0.0599210\pi$
$271$	30.7160	+	4.62970i	1.86587	+	0.281234i	0.883532	+	0.468371i	$0.155159\pi$
$272$	−0.190314	+	0.238646i	−0.0115395	+	0.0144700i
$273$	4.24484	+	4.90095i	0.256909	+	0.296619i
$274$	2.67285	+	3.35165i	0.161473	+	0.202481i
$275$	12.9682	+	22.4616i	0.782013	+	1.35449i
$276$	13.7060	−	23.7394i	0.825003	−	1.42895i
$277$	0.227370	−	0.0342705i	0.0136613	−	0.00205912i	−0.142208	−	0.989837i	$-0.545420\pi$
$277$	0.227370	−	0.0342705i	0.0136613	−	0.00205912i	0.155869	+	0.987778i	$0.450182\pi$
$278$	−6.16464	+	5.71995i	−0.369731	+	0.343060i
$279$	−22.4824	−	10.8270i	−1.34599	−	0.648194i
$280$	−2.58666	+	4.93213i	−0.154582	+	0.294751i
$281$	16.6688	−	8.02729i	0.994380	−	0.478868i	0.135352	−	0.990798i	$-0.456783\pi$
$281$	16.6688	−	8.02729i	0.994380	−	0.478868i	0.859027	+	0.511930i	$0.171069\pi$
$282$	−3.38396	+	8.62219i	−0.201512	+	0.513444i
$283$	0.490840	−	6.54980i	0.0291774	−	0.389345i	−0.963429	−	0.267965i	$-0.913649\pi$
$283$	0.490840	−	6.54980i	0.0291774	−	0.389345i	0.992606	−	0.121380i	$-0.0387321\pi$
$284$	−20.2430	−	6.24413i	−1.20120	−	0.370521i
$285$	−0.344006	−	4.59044i	−0.0203771	−	0.271914i
$286$	−1.04505	+	4.57867i	−0.0617952	+	0.270742i
$287$	11.0019	−	11.0722i	0.649421	−	0.653569i
$288$	−3.90564	−	17.1117i	−0.230142	−	1.00832i
$289$	−16.0142	+	4.93972i	−0.942010	+	0.290572i
$290$	−1.60551	−	4.09077i	−0.0942787	−	0.240218i
$291$	15.7635	+	14.6264i	0.924072	+	0.857413i
$292$	1.06505	+	0.726137i	0.0623271	+	0.0424939i
$293$	−32.4173			−1.89384			−0.946920	−	0.321470i	$-0.895823\pi$
$293$	−32.4173			−1.89384			−0.946920	+	0.321470i	$0.895823\pi$
$294$	10.5829	−	8.55040i	0.617209	−	0.498669i
$295$	2.77139			0.161357
$296$	−17.9304	−	12.2248i	−1.04218	−	0.710550i
$297$	−0.0577439	−	0.0535785i	−0.00335064	−	0.00310894i
$298$	0.977105	+	2.48962i	0.0566022	+	0.144220i
$299$	7.79668	−	2.40496i	0.450894	−	0.139082i
$300$	−3.27454	−	14.3467i	−0.189056	−	0.828308i
$301$	5.63959	−	16.2831i	0.325060	−	0.938542i
$302$	−2.68552	+	11.7660i	−0.154534	+	0.677060i
$303$	−0.551659	−	7.36138i	−0.0316920	−	0.422900i
$304$	1.41672	+	0.437000i	0.0812545	+	0.0250637i
$305$	0.304062	−	4.05742i	0.0174105	−	0.232327i
$306$	−0.427772	+	1.08994i	−0.0244541	+	0.0623080i
$307$	5.79117	−	2.78888i	0.330519	−	0.159170i	−0.261263	−	0.965268i	$-0.584139\pi$
$307$	5.79117	−	2.78888i	0.330519	−	0.159170i	0.591782	+	0.806098i	$0.298425\pi$
$308$	−20.7638	−	5.49287i	−1.18313	−	0.312985i
$309$	−22.2403	−	10.7104i	−1.26521	−	0.609293i
$310$	3.80065	−	3.52649i	0.215863	−	0.200291i
$311$	6.36618	−	0.959547i	0.360993	−	0.0544109i	0.0339581	−	0.999423i	$-0.489189\pi$
$311$	6.36618	−	0.959547i	0.360993	−	0.0544109i	0.327035	+	0.945012i	$0.393951\pi$
$312$	3.27595	−	5.67411i	0.185464	−	0.321233i
$313$	−6.77182	−	11.7291i	−0.382766	−	0.662970i	0.608690	−	0.793408i	$-0.291695\pi$
$313$	−6.77182	−	11.7291i	−0.382766	−	0.662970i	−0.991457	+	0.130437i	$0.958362\pi$
$314$	−10.7966	−	13.5385i	−0.609287	−	0.764021i
$315$	1.14431	−	6.15504i	0.0644748	−	0.346797i
$316$	−3.16451	+	3.96818i	−0.178018	+	0.223227i
$317$	19.6911	+	2.96795i	1.10596	+	0.166697i	0.676539	−	0.736407i	$-0.263479\pi$
$317$	19.6911	+	2.96795i	1.10596	+	0.166697i	0.429423	+	0.903104i	$0.358717\pi$
$318$	0.967535	−	0.659654i	0.0542566	−	0.0369916i
$319$	34.4309	−	23.4746i	1.92776	−	1.31432i
$320$	2.63850	+	0.397689i	0.147496	+	0.0222315i
$321$	−15.4968	+	19.4324i	−0.864950	+	1.08461i
$322$	−4.48395	−	16.5237i	−0.249881	−	0.920832i
$323$	−0.730698	−	0.916267i	−0.0406571	−	0.0509824i
$324$	−6.15809	−	10.6661i	−0.342116	−	0.592563i
$325$	2.19006	−	3.79329i	0.121483	−	0.210414i
$326$	−5.52798	+	0.833208i	−0.306166	+	0.0461471i
$327$	0.698804	−	0.648395i	0.0386439	−	0.0358563i
$328$	−14.2110	−	6.84366i	−0.784671	−	0.377878i
$329$	−5.07878	−	11.5403i	−0.280002	−	0.636239i
$330$	8.16399	−	3.93157i	0.449413	−	0.216426i
$331$	−3.17640	+	8.09334i	−0.174591	+	0.444850i	−0.991205	−	0.132333i	$-0.957753\pi$
$331$	−3.17640	+	8.09334i	−0.174591	+	0.444850i	0.816614	+	0.577184i	$0.195848\pi$
$332$	1.24121	−	16.5628i	0.0681202	−	0.909001i
$333$	23.3110	+	7.19048i	1.27743	+	0.394036i
$334$	−0.247283	−	3.29976i	−0.0135307	−	0.180555i
$335$	−1.47228	+	6.45048i	−0.0804393	+	0.352427i
$336$	3.41826	+	2.13269i	0.186481	+	0.116348i
$337$	8.15591	+	35.7334i	0.444281	+	1.94652i	0.279135	+	0.960252i	$0.409952\pi$
$337$	8.15591	+	35.7334i	0.444281	+	1.94652i	0.165145	+	0.986269i	$0.447191\pi$
$338$	0.757890	−	0.233778i	0.0412238	−	0.0127159i
$339$	5.10614	+	13.0102i	0.277328	+	0.706620i
$340$	0.388665	+	0.360628i	0.0210783	+	0.0195578i
$341$	40.6216	+	27.6954i	2.19979	+	1.49979i
$342$	5.68712			0.307524
$343$	−1.89777	+	18.4228i	−0.102470	+	0.994736i
$344$	−17.4134			−0.938867
$345$	−13.0070	−	8.86803i	−0.700274	−	0.477439i
$346$	2.22117	+	2.06095i	0.119411	+	0.110797i
$347$	1.03682	+	2.64178i	0.0556595	+	0.141818i	0.955999	−	0.293370i	$-0.0947769\pi$
$347$	1.03682	+	2.64178i	0.0556595	+	0.141818i	−0.900339	+	0.435189i	$0.856682\pi$
$348$	−22.5931	+	6.96904i	−1.21112	+	0.373580i
$349$	3.86835	+	16.9483i	0.207068	+	0.907224i	0.966506	+	0.256644i	$0.0826169\pi$
$349$	3.86835	+	16.9483i	0.207068	+	0.907224i	−0.759438	+	0.650580i	$0.774526\pi$
$350$	−7.79803	−	4.86527i	−0.416822	−	0.260060i
$351$	−0.00296018	+	0.0129694i	−0.000158003	+	0.000692255i
$352$	2.58426	+	34.4845i	0.137741	+	1.83803i
$353$	−14.0869	−	4.34524i	−0.749770	−	0.231274i	−0.103760	−	0.994602i	$-0.533087\pi$
$353$	−14.0869	−	4.34524i	−0.749770	−	0.231274i	−0.646010	+	0.763329i	$0.723564\pi$
$354$	−0.511274	+	6.82248i	−0.0271739	+	0.362611i
$355$	−4.44468	+	11.3249i	−0.235899	+	0.601062i
$356$	1.39495	−	0.671771i	0.0739320	−	0.0356038i
$357$	−1.28287	−	2.91502i	−0.0678968	−	0.154279i
$358$	−0.797781	−	0.384191i	−0.0421640	−	0.0203051i
$359$	−17.7127	+	16.4350i	−0.934839	+	0.867404i	−0.991383	−	0.130996i	$-0.958182\pi$
$359$	−17.7127	+	16.4350i	−0.934839	+	0.867404i	0.0565439	+	0.998400i	$0.481992\pi$
$360$	−6.25572	+	0.942898i	−0.329705	+	0.0496951i
$361$	6.65385	−	11.5248i	0.350203	−	0.606569i
$362$	−5.92744	−	10.2666i	−0.311539	−	0.539602i
$363$	36.7664	+	46.1036i	1.92974	+	2.41981i
$364$	0.949935	+	3.50059i	0.0497901	+	0.183481i
$365$	0.461556	−	0.578773i	0.0241590	−	0.0302944i
$366$	9.93226	+	1.49705i	0.519168	+	0.0782519i
$367$	11.4912	−	7.83460i	0.599838	−	0.408963i	−0.224978	−	0.974364i	$-0.572231\pi$
$367$	11.4912	−	7.83460i	0.599838	−	0.408963i	0.824816	+	0.565401i	$0.191279\pi$
$368$	4.18917	−	2.85613i	0.218376	−	0.148886i
$369$	17.5327	+	2.64263i	0.912715	+	0.137570i
$370$	−3.16021	+	3.96278i	−0.164292	+	0.206015i
$371$	−0.291361	+	1.56717i	−0.0151267	+	0.0813636i
$372$	−17.3920	−	21.8089i	−0.901735	−	1.13074i
$373$	−1.92195	−	3.32892i	−0.0995148	−	0.172365i	0.811969	−	0.583700i	$-0.198396\pi$
$373$	−1.92195	−	3.32892i	−0.0995148	−	0.172365i	−0.911484	+	0.411336i	$0.865062\pi$
$374$	1.15346	−	1.99785i	0.0596439	−	0.103306i
$375$	−17.8960	+	2.69739i	−0.924146	+	0.139293i
$376$	−9.33990	+	8.66616i	−0.481668	+	0.446923i
$377$	−6.34056	−	3.05345i	−0.326556	−	0.157261i
$378$	0.0269867	+	0.00713907i	0.00138805	+	0.000367194i
$379$	−6.54108	+	3.15002i	−0.335993	+	0.161805i	−0.594271	−	0.804265i	$-0.702559\pi$
$379$	−6.54108	+	3.15002i	−0.335993	+	0.161805i	0.258278	+	0.966071i	$0.416845\pi$
$380$	0.940845	−	2.39723i	0.0482643	−	0.122976i
$381$	−1.75570	+	23.4281i	−0.0899471	+	1.20026i
$382$	11.7899	+	3.63672i	0.603226	+	0.186071i
$383$	−2.84747	−	37.9968i	−0.145499	−	1.94155i	−0.300813	−	0.953683i	$-0.597258\pi$
$383$	−2.84747	−	37.9968i	−0.145499	−	1.94155i	0.155314	−	0.987865i	$-0.450361\pi$
$384$	4.90348	−	21.4835i	0.250230	−	1.09633i
$385$	−4.03680	+	11.6554i	−0.205734	+	0.594014i
$386$	0.440517	+	1.93003i	0.0224217	+	0.0982360i
$387$	18.7050	−	5.76974i	0.950830	−	0.293292i
$388$	4.39507	+	11.1985i	0.223126	+	0.568515i
$389$	15.4126	+	14.3008i	0.781450	+	0.725080i	0.966225	−	0.257701i	$-0.0829649\pi$
$389$	15.4126	+	14.3008i	0.781450	+	0.725080i	−0.184774	+	0.982781i	$0.559155\pi$
$390$	−1.26437	−	0.862032i	−0.0640238	−	0.0436507i
$391$	−4.00784			−0.202685
$392$	18.2190	−	4.28059i	0.920199	−	0.216202i
$393$	−48.2135			−2.43205
$394$	9.62221	+	6.56031i	0.484760	+	0.330504i
$395$	2.13671	+	1.98257i	0.107509	+	0.0997541i
$396$	−8.91356	−	22.7114i	−0.447923	−	1.14129i
$397$	19.2475	−	5.93706i	0.966003	−	0.297972i	0.228672	−	0.973504i	$-0.426562\pi$
$397$	19.2475	−	5.93706i	0.966003	−	0.297972i	0.737331	+	0.675531i	$0.236086\pi$
$398$	−0.945543	−	4.14270i	−0.0473958	−	0.207655i
$399$	−10.9034	+	10.9731i	−0.545854	+	0.549340i
$400$	0.605666	−	2.65360i	0.0302833	−	0.132680i
$401$	−1.36609	−	18.2292i	−0.0682191	−	0.910320i	−0.921378	−	0.388669i	$-0.872935\pi$
$401$	−1.36609	−	18.2292i	−0.0682191	−	0.910320i	0.853159	−	0.521652i	$-0.174684\pi$
$402$	−15.6079	−	4.81439i	−0.778450	−	0.240120i
$403$	0.620473	−	8.27964i	0.0309080	−	0.412438i
$404$	1.50877	−	3.84429i	0.0750642	−	0.191260i
$405$	−6.37262	+	3.06889i	−0.316658	+	0.152495i
$406$	−6.85883	+	13.0781i	−0.340398	+	0.649057i
$407$	−43.3037	−	20.8539i	−2.14648	−	1.03369i
$408$	−2.35921	+	2.18902i	−0.116798	+	0.108373i
$409$	−30.0395	+	4.52773i	−1.48536	+	0.223882i	−0.841081	−	0.540909i	$-0.818080\pi$
$409$	−30.0395	+	4.52773i	−1.48536	+	0.223882i	−0.644279	+	0.764791i	$0.722842\pi$
$410$	−1.84199	+	3.19041i	−0.0909692	+	0.157563i
$411$	−6.62286	−	11.4711i	−0.326682	−	0.565829i
$412$	−8.61016	−	10.7968i	−0.424192	−	0.531920i
$413$	−6.09724	−	7.03967i	−0.300026	−	0.346400i
$414$	12.1262	−	15.2058i	0.595969	−	0.747322i
$415$	−9.43199	−	1.42164i	−0.462998	−	0.0697858i
$416$	4.82526	−	3.28981i	0.236578	−	0.161296i
$417$	21.4688	−	14.6372i	1.05133	−	0.716787i
$418$	−11.0798	−	1.67001i	−0.541932	−	0.0816831i
$419$	18.2040	−	22.8271i	0.889322	−	1.11517i	−0.103387	−	0.994641i	$-0.532968\pi$
$419$	18.2040	−	22.8271i	0.889322	−	1.11517i	0.992709	−	0.120534i	$-0.0384605\pi$
$420$	4.13783	−	5.64407i	0.201905	−	0.275403i
$421$	1.08021	+	1.35454i	0.0526464	+	0.0660165i	0.807458	−	0.589926i	$-0.200843\pi$
$421$	1.08021	+	1.35454i	0.0526464	+	0.0660165i	−0.754811	+	0.655942i	$0.772272\pi$
$422$	6.71195	+	11.6254i	0.326733	+	0.565918i
$423$	7.16125	−	12.4037i	0.348192	−	0.603086i
$424$	1.59281	−	0.240077i	0.0773536	−	0.0116592i
$425$	−1.57719	+	1.46342i	−0.0765052	+	0.0709864i
$426$	−27.0590	−	13.0310i	−1.31102	−	0.631352i
$427$	−10.9753	+	8.15423i	−0.531132	+	0.394611i
$428$	−12.5278	+	6.03305i	−0.605552	+	0.291619i
$429$	5.30145	−	13.5079i	0.255957	−	0.652167i
$430$	−0.303935	+	4.05573i	−0.0146570	+	0.195585i
$431$	0.889277	+	0.274305i	0.0428349	+	0.0132128i	0.316099	−	0.948726i	$-0.397627\pi$
$431$	0.889277	+	0.274305i	0.0428349	+	0.0132128i	−0.273264	+	0.961939i	$0.588103\pi$
$432$	0.000617758		0.00824341i	2.97219e−5		0.000396611i
$433$	−8.52598	+	37.3547i	−0.409732	+	1.79515i	0.175712	+	0.984442i	$0.443777\pi$
$433$	−8.52598	+	37.3547i	−0.409732	+	1.79515i	−0.585444	+	0.810713i	$0.699080\pi$
$434$	−17.3194	−	1.89562i	−0.831358	−	0.0909925i
$435$	3.02145	+	13.2378i	0.144867	+	0.634705i
$436$	0.509606	−	0.157193i	0.0244057	−	0.00752816i
$437$	7.11195	+	18.1209i	0.340210	+	0.866842i
$438$	1.33965	+	1.24301i	0.0640108	+	0.0593933i
$439$	9.24057	+	6.30012i	0.441029	+	0.300688i	0.763401	−	0.645925i	$-0.223528\pi$
$439$	9.24057	+	6.30012i	0.441029	+	0.300688i	−0.322373	+	0.946613i	$0.604480\pi$
$440$	12.4645			0.594220
$441$	−18.1521	+	10.6348i	−0.864386	+	0.506418i
$442$	−0.389589			−0.0185309
$443$	11.7656	+	8.02168i	0.559003	+	0.381122i	0.809611	−	0.586967i	$-0.199678\pi$
$443$	11.7656	+	8.02168i	0.559003	+	0.381122i	−0.250608	+	0.968089i	$0.580631\pi$
$444$	19.9903	+	18.5483i	0.948697	+	0.880262i
$445$	−0.324847	−	0.827696i	−0.0153992	−	0.0392365i
$446$	10.5115	−	3.24237i	0.497734	−	0.153531i
$447$	−1.83884	−	8.05647i	−0.0869740	−	0.381058i
$448$	−4.79468	−	7.57704i	−0.226527	−	0.357982i
$449$	0.252181	−	1.10488i	0.0119012	−	0.0521425i	−0.968629	−	0.248513i	$-0.920058\pi$
$449$	0.252181	−	1.10488i	0.0119012	−	0.0521425i	0.980530	+	0.196370i	$0.0629154\pi$
$450$	−0.780244	−	10.4116i	−0.0367810	−	0.490809i
$451$	−33.3817	−	10.2969i	−1.57188	−	0.484862i
$452$	−0.584306	+	7.79702i	−0.0274834	+	0.366741i
$453$	13.6234	−	34.7119i	0.640084	−	1.63091i
$454$	−15.9328	+	7.67282i	−0.747762	+	0.360103i
$455$	2.04551	−	0.393780i	0.0958949	−	0.0184607i
$456$	14.0838	+	6.78241i	0.659535	+	0.317615i
$457$	−24.7386	+	22.9541i	−1.15722	+	1.07375i	−0.160997	+	0.986955i	$0.551471\pi$
$457$	−24.7386	+	22.9541i	−1.15722	+	1.07375i	−0.996226	+	0.0867918i	$0.972339\pi$
$458$	21.2205	−	3.19848i	0.991569	−	0.149455i
$459$	0.00326724	−	0.00565903i	0.000152502	−	0.000264141i
$460$	−4.40344	−	7.62698i	−0.205311	−	0.355610i
$461$	11.6794	+	14.6456i	0.543966	+	0.682112i	0.975504	−	0.219983i	$-0.0706002\pi$
$461$	11.6794	+	14.6456i	0.543966	+	0.682112i	−0.431538	+	0.902095i	$0.642029\pi$
$462$	−27.9480	−	12.0878i	−1.30026	−	0.562377i
$463$	6.38434	−	8.00571i	0.296705	−	0.372057i	−0.611025	−	0.791612i	$-0.709242\pi$
$463$	6.38434	−	8.00571i	0.296705	−	0.372057i	0.907730	+	0.419555i	$0.137814\pi$
$464$	−4.32430	−	0.651784i	−0.200751	−	0.0302583i
$465$	−13.2361	+	9.02420i	−0.613808	+	0.418487i
$466$	−4.52181	+	3.08291i	−0.209469	+	0.142813i
$467$	−40.5479	−	6.11161i	−1.87633	−	0.282812i	−0.891071	−	0.453863i	$-0.850046\pi$
$467$	−40.5479	−	6.11161i	−1.87633	−	0.282812i	−0.985262	+	0.171051i	$0.945284\pi$
$468$	−2.56896	+	3.22138i	−0.118750	+	0.148908i
$469$	19.6241	−	10.4517i	0.906157	−	0.482615i
$470$	1.85540	+	2.32660i	0.0855834	+	0.107318i
$471$	26.7520	+	46.3359i	1.23267	+	2.13504i
$472$	−4.70553	+	8.15022i	−0.216590	+	0.375144i
$473$	−38.1360	+	5.74807i	−1.75349	+	0.264297i
$474$	−5.27479	+	4.89429i	−0.242279	+	0.224802i
$475$	9.41542	+	4.53423i	0.432009	+	0.208045i
$476$	0.0609520	−	1.78066i	0.00279373	−	0.0816165i
$477$	−1.63141	+	0.785645i	−0.0746971	+	0.0359722i
$478$	5.82641	−	14.8455i	0.266494	−	0.679015i
$479$	0.906074	−	12.0907i	0.0413996	−	0.552439i	−0.937485	−	0.348025i	$-0.886852\pi$
$479$	0.906074	−	12.0907i	0.0413996	−	0.552439i	0.978885	−	0.204413i	$-0.0655286\pi$
$480$	−10.7673	−	3.32126i	−0.491456	−	0.151594i
$481$	0.606577	+	8.09421i	0.0276575	+	0.369064i
$482$	1.79146	−	7.84891i	0.0815989	−	0.357508i
$483$	6.09039	+	52.5496i	0.277122	+	2.39109i
$484$	7.34079	+	32.1621i	0.333672	+	1.46191i
$485$	6.60181	−	2.03639i	0.299773	−	0.0924677i
$486$	−6.39078	−	16.2834i	−0.289892	−	0.738632i
$487$	−24.0774	−	22.3406i	−1.09105	−	1.01235i	−0.999864	−	0.0165146i	$-0.994743\pi$
$487$	−24.0774	−	22.3406i	−1.09105	−	1.01235i	−0.0911883	−	0.995834i	$-0.529067\pi$
$488$	11.4160	+	7.78327i	0.516776	+	0.352332i
$489$	17.2732			0.781123
$490$	−0.678989	−	4.31808i	−0.0306736	−	0.195071i
$491$	−7.14036			−0.322240			−0.161120	−	0.986935i	$-0.551511\pi$
$491$	−7.14036			−0.322240			−0.161120	+	0.986935i	$0.551511\pi$
$492$	16.3764	+	11.1653i	0.738307	+	0.503369i
$493$	2.53406	+	2.35127i	0.114128	+	0.105896i
$494$	0.691329	+	1.76148i	0.0311044	+	0.0792526i
$495$	−13.3890	+	4.12997i	−0.601792	+	0.185628i
$496$	−1.14809	−	5.03009i	−0.0515506	−	0.225858i
$497$	38.5451	−	13.6254i	1.72899	−	0.611183i
$498$	5.23978	−	22.9570i	0.234800	−	1.02873i
$499$	−1.91611	−	25.5687i	−0.0857769	−	1.14461i	−0.859516	−	0.511109i	$-0.829235\pi$
$499$	−1.91611	−	25.5687i	−0.0857769	−	1.14461i	0.773739	−	0.633505i	$-0.218384\pi$
$500$	−9.67493	−	2.98432i	−0.432676	−	0.133463i
$501$	−0.764052	+	10.1956i	−0.0341353	+	0.455504i
$502$	5.35314	−	13.6396i	0.238922	−	0.608764i
$503$	−1.48677	+	0.715990i	−0.0662917	+	0.0319244i	−0.466736	−	0.884397i	$-0.654570\pi$
$503$	−1.48677	+	0.715990i	−0.0662917	+	0.0319244i	0.400444	+	0.916321i	$0.368856\pi$
$504$	16.1581	+	13.8158i	0.719737	+	0.615407i
$505$	−2.13682	−	1.02904i	−0.0950870	−	0.0457915i
$506$	−28.0897	+	26.0635i	−1.24874	+	1.15866i
$507$	−2.42323	+	0.365243i	−0.107619	+	0.0162210i
$508$	−6.57164	+	11.3824i	−0.291569	+	0.505013i
$509$	−9.15322	−	15.8539i	−0.405710	−	0.702710i	0.588694	−	0.808356i	$-0.299642\pi$
$509$	−9.15322	−	15.8539i	−0.405710	−	0.702710i	−0.994404	+	0.105646i	$0.966309\pi$
$510$	0.468665	+	0.587687i	0.0207528	+	0.0260232i
$511$	−2.48561	+	0.100929i	−0.109957	+	0.00446485i
$512$	4.33439	−	5.43515i	0.191555	−	0.240202i
$513$	−0.0313843	−	0.00473043i	−0.00138565	−	0.000208853i
$514$	11.0578	−	7.53907i	0.487738	−	0.332534i
$515$	−6.55269	+	4.46755i	−0.288746	+	0.196864i
$516$	21.6374	+	3.26131i	0.952532	+	0.143571i
$517$	−17.5941	+	22.0623i	−0.773787	+	0.970298i
$518$	17.0186	−	0.691049i	0.747754	−	0.0303629i
$519$	−5.83723	−	7.31966i	−0.256226	−	0.321297i
$520$	−1.05249	−	1.82297i	−0.0461548	−	0.0799425i
$521$	−8.13652	+	14.0929i	−0.356468	+	0.617420i	−0.987368	−	0.158444i	$-0.949352\pi$
$521$	−8.13652	+	14.0929i	−0.356468	+	0.617420i	0.630900	+	0.775864i	$0.282686\pi$
$522$	−16.5878	+	2.50021i	−0.726028	+	0.109431i
$523$	−21.6489	+	20.0873i	−0.946642	+	0.878356i	−0.992703	−	0.120583i	$-0.961524\pi$
$523$	−21.6489	+	20.0873i	−0.946642	+	0.878356i	0.0460611	+	0.998939i	$0.485333\pi$
$524$	−24.3012	−	11.7029i	−1.06160	−	0.511242i
$525$	21.5847	+	18.4559i	0.942033	+	0.805480i
$526$	3.49826	−	1.68467i	0.152532	−	0.0734553i
$527$	−1.49001	+	3.79650i	−0.0649061	+	0.165378i
$528$	0.673858	−	8.99201i	0.0293259	−	0.391327i
$529$	41.6363	+	12.8431i	1.81027	+	0.558395i
$530$	−0.0281150	−	0.375169i	−0.00122124	−	0.0162963i
$531$	2.35408	−	10.3139i	0.102158	−	0.447585i
$532$	−8.15919	+	2.88421i	−0.353746	+	0.125046i
$533$	1.31278	+	5.75165i	0.0568627	+	0.249132i
$534$	2.09751	−	0.646996i	0.0907681	−	0.0279983i
$535$	2.91739	+	7.43339i	0.126130	+	0.321373i
$536$	−16.4701	−	15.2820i	−0.711398	−	0.660081i
$537$	2.26052	+	1.54120i	0.0975488	+	0.0665077i
$538$	21.8909			0.943783
$539$	38.4874	−	15.3887i	1.65777	−	0.662837i
$540$	0.0143590			0.000617911
$541$	9.91990	+	6.76327i	0.426490	+	0.290776i	0.757480	−	0.652858i	$-0.226430\pi$
$541$	9.91990	+	6.76327i	0.426490	+	0.290776i	−0.330990	+	0.943634i	$0.607383\pi$
$542$	18.0601	+	16.7573i	0.775747	+	0.719788i
$543$	13.3821	+	34.0971i	0.574282	+	1.46325i
$544$	−2.74122	+	0.845554i	−0.117529	+	0.0362528i
$545$	−0.0681512	−	0.298590i	−0.00291928	−	0.0127902i
$546$	0.592027	+	5.10818i	0.0253364	+	0.218610i
$547$	7.23844	−	31.7137i	0.309493	−	1.35598i	−0.545836	−	0.837892i	$-0.683788\pi$
$547$	7.23844	−	31.7137i	0.309493	−	1.35598i	0.855329	−	0.518086i	$-0.173355\pi$
$548$	−0.553759	−	7.38940i	−0.0236554	−	0.315660i
$549$	−14.8416	−	4.57804i	−0.633426	−	0.195386i
$550$	−1.53726	+	20.5134i	−0.0655491	+	0.874693i
$551$	6.13423	−	15.6298i	0.261327	−	0.665851i
$552$	48.1640	−	23.1946i	2.05000	−	0.987226i
$553$	0.335087	−	9.78928i	0.0142493	−	0.416282i
$554$	0.164310	+	0.0791274i	0.00698085	+	0.00336180i
$555$	11.4802	−	10.6521i	0.487309	−	0.452157i
$556$	14.3739	−	2.16652i	0.609589	−	0.0918808i
$557$	−21.6765	+	37.5449i	−0.918465	+	1.59083i	−0.116717	+	0.993165i	$0.537237\pi$
$557$	−21.6765	+	37.5449i	−0.918465	+	1.59083i	−0.801748	+	0.597662i	$0.796096\pi$
$558$	−9.89569	−	17.1398i	−0.418918	−	0.725587i
$559$	4.06086	+	5.09215i	0.171756	+	0.215375i
$560$	1.14250	−	0.608488i	0.0482793	−	0.0257133i
$561$	−4.44417	+	5.57281i	−0.187633	+	0.235284i
$562$	14.5098	+	2.18699i	0.612057	+	0.0922527i
$563$	7.86090	−	5.35947i	0.331297	−	0.225875i	−0.386234	−	0.922401i	$-0.626224\pi$
$563$	7.86090	−	5.35947i	0.331297	−	0.225875i	0.717531	+	0.696526i	$0.245272\pi$
$564$	13.2285	−	9.01907i	0.557022	−	0.379771i
$565$	4.44016	+	0.669247i	0.186799	+	0.0281554i
$566$	3.24800	−	4.07286i	0.136524	−	0.171195i
$567$	21.8155	+	9.43548i	0.916167	+	0.396253i
$568$	−25.7580	−	32.2995i	−1.08078	−	1.35526i
$569$	12.2018	+	21.1342i	0.511527	+	0.885991i	0.999911	+	0.0133619i	$0.00425337\pi$
$569$	12.2018	+	21.1342i	0.511527	+	0.885991i	−0.488384	+	0.872629i	$0.662413\pi$
$570$	1.82550	−	3.16186i	0.0764619	−	0.132436i
$571$	−18.4138	+	2.77544i	−0.770595	+	0.116149i	−0.522560	−	0.852603i	$-0.675023\pi$
$571$	−18.4138	+	2.77544i	−0.770595	+	0.116149i	−0.248035	+	0.968751i	$0.579785\pi$
$572$	5.95088	−	5.52161i	0.248819	−	0.230870i
$573$	−34.3469	−	16.5406i	−1.43486	−	0.690993i
$574$	12.1565	−	2.34025i	0.507404	−	0.0976800i
$575$	32.1990	−	15.5062i	1.34279	−	0.646653i
$576$	3.72122	−	9.48151i	0.155051	−	0.395063i
$577$	−0.517496	+	6.90551i	−0.0215437	+	0.287480i	0.976018	+	0.217690i	$0.0698521\pi$
$577$	−0.517496	+	6.90551i	−0.0215437	+	0.287480i	−0.997562	+	0.0697904i	$0.977767\pi$
$578$	−12.7013	−	3.91782i	−0.528303	−	0.162960i
$579$	−0.457106	−	6.09966i	−0.0189967	−	0.253493i
$580$	−1.69030	+	7.40570i	−0.0701860	+	0.307505i
$581$	17.1398	+	27.0861i	0.711080	+	1.12372i
$582$	3.79516	+	16.6277i	0.157315	+	0.689240i
$583$	3.40906	−	1.05156i	0.141189	−	0.0435510i
$584$	0.918405	+	2.34006i	0.0380039	+	0.0968323i
$585$	1.73458	+	1.60946i	0.0717162	+	0.0665429i
$586$	−21.2434	−	14.4835i	−0.877559	−	0.598309i
$587$	−2.96456			−0.122360			−0.0611802	−	0.998127i	$-0.519486\pi$
$587$	−2.96456			−0.122360			−0.0611802	+	0.998127i	$0.519486\pi$
$588$	−23.4401	+	1.90674i	−0.966654	+	0.0786326i
$589$	19.8094			0.816232
$590$	1.81613	+	1.23821i	0.0747687	+	0.0509765i
$591$	−26.3775	−	24.4747i	−1.08503	−	1.00676i
$592$	1.84274	+	4.69524i	0.0757363	+	0.192973i
$593$	−12.8684	+	3.96936i	−0.528440	+	0.163002i	−0.547483	−	0.836817i	$-0.684414\pi$
$593$	−12.8684	+	3.96936i	−0.528440	+	0.163002i	0.0190435	+	0.999819i	$0.493938\pi$
$594$	−0.0139022	−	0.0609097i	−0.000570416	−	0.00249915i
$595$	−1.01714	−	0.111327i	−0.0416988	−	0.00456395i
$596$	1.02871	−	4.50708i	0.0421376	−	0.184617i
$597$	0.981151	+	13.0925i	0.0401558	+	0.535842i
$598$	6.18375	+	1.90744i	0.252872	+	0.0780008i
$599$	−1.68190	+	22.4433i	−0.0687204	+	0.917010i	0.851184	+	0.524867i	$0.175885\pi$
$599$	−1.68190	+	22.4433i	−0.0687204	+	0.917010i	−0.919904	+	0.392143i	$0.871734\pi$
$600$	10.4846	−	26.7143i	0.428031	−	1.09061i
$601$	10.4661	−	5.04019i	0.426919	−	0.205594i	−0.208071	−	0.978114i	$-0.566718\pi$
$601$	10.4661	−	5.04019i	0.426919	−	0.205594i	0.634990	+	0.772520i	$0.281004\pi$
$602$	10.9707	−	8.15083i	0.447133	−	0.332203i
$603$	22.7553	+	10.9584i	0.926666	+	0.446259i
$604$	15.2923	−	14.1892i	0.622234	−	0.577349i
$605$	18.7338	−	2.82367i	0.761637	−	0.114798i
$606$	2.92744	−	5.07047i	0.118919	−	0.205974i
$607$	13.2690	+	22.9826i	0.538572	+	0.932834i	0.998981	+	0.0451275i	$0.0143694\pi$
$607$	13.2690	+	22.9826i	0.538572	+	0.932834i	−0.460409	+	0.887707i	$0.652297\pi$
$608$	8.68738	+	10.8936i	0.352320	+	0.441795i
$609$	26.9783	−	36.7989i	1.09322	−	1.49117i
$610$	2.01204	−	2.52302i	0.0814653	−	0.102154i
$611$	4.71232	+	0.710268i	0.190640	+	0.0287344i
$612$	1.67224	−	1.14011i	0.0675963	−	0.0460864i
$613$	0.0673131	−	0.0458933i	0.00271875	−	0.00185361i	−0.561960	−	0.827164i	$-0.689952\pi$
$613$	0.0673131	−	0.0458933i	0.00271875	−	0.00185361i	0.564679	+	0.825311i	$0.309000\pi$
$614$	5.04105	+	0.759815i	0.203440	+	0.0306637i
$615$	7.09701	−	8.89937i	0.286179	−	0.358857i
$616$	−27.4226	−	31.6612i	−1.10489	−	1.27567i
$617$	8.30494	+	10.4141i	0.334344	+	0.419255i	0.920377	−	0.391033i	$-0.127882\pi$
$617$	8.30494	+	10.4141i	0.334344	+	0.419255i	−0.586032	+	0.810288i	$0.699311\pi$
$618$	−9.78913	−	16.9553i	−0.393777	−	0.682041i
$619$	−7.71265	+	13.3587i	−0.309997	+	0.536931i	−0.978361	−	0.206903i	$-0.933662\pi$
$619$	−7.71265	+	13.3587i	−0.309997	+	0.536931i	0.668364	+	0.743834i	$0.266995\pi$
$620$	−8.86187	+	1.33571i	−0.355901	+	0.0536435i
$621$	−0.0795660	+	0.0738265i	−0.00319287	+	0.00296255i
$622$	4.60054	+	2.21550i	0.184465	+	0.0888336i
$623$	−1.38776	+	2.64613i	−0.0555996	+	0.106015i
$624$	−1.37201	+	0.660726i	−0.0549245	+	0.0264502i
$625$	5.87689	−	14.9741i	0.235076	−	0.598963i
$626$	0.802738	−	10.7118i	0.0320838	−	0.428129i
$627$	33.0830	+	10.2047i	1.32121	+	0.407538i
$628$	2.23683	+	29.8484i	0.0892591	+	1.19108i
$629$	0.887209	−	3.88712i	0.0353753	−	0.154989i
$630$	3.49985	−	3.52221i	0.139438	−	0.140328i
$631$	8.91452	+	39.0571i	0.354881	+	1.55484i	0.765748	+	0.643141i	$0.222369\pi$
$631$	8.91452	+	39.0571i	0.354881	+	1.55484i	−0.410866	+	0.911696i	$0.634774\pi$
$632$	−9.45833	+	2.91751i	−0.376232	+	0.116052i
$633$	−15.1533	−	38.6099i	−0.602289	−	1.53461i
$634$	11.5778	+	10.7426i	0.459812	+	0.426643i
$635$	6.23651	+	4.25198i	0.247488	+	0.168735i
$636$	−2.02414			−0.0802624
$637$	−5.50050	−	4.32950i	−0.217938	−	0.171541i
$638$	33.0510			1.30850
$639$	38.3708	+	26.1607i	1.51792	+	1.03490i
$640$	−5.18979	−	4.81543i	−0.205145	−	0.190346i
$641$	−5.35274	−	13.6386i	−0.211420	−	0.538690i	0.785345	−	0.619059i	$-0.212486\pi$
$641$	−5.35274	−	13.6386i	−0.211420	−	0.538690i	−0.996765	+	0.0803681i	$0.974390\pi$
$642$	−18.8374	+	5.81056i	−0.743452	+	0.229324i
$643$	−7.36489	−	32.2677i	−0.290443	−	1.27251i	−0.883911	−	0.467655i	$-0.845099\pi$
$643$	−7.36489	−	32.2677i	−0.290443	−	1.27251i	0.593468	−	0.804857i	$-0.297758\pi$
$644$	−9.68560	+	27.9651i	−0.381666	+	1.10198i
$645$	2.79631	−	12.2514i	0.110105	−	0.482400i
$646$	−0.0694619	−	0.926904i	−0.00273294	−	0.0364686i
$647$	11.8386	+	3.65172i	0.465423	+	0.143564i	0.518592	−	0.855022i	$-0.326456\pi$
$647$	11.8386	+	3.65172i	0.465423	+	0.143564i	−0.0531697	+	0.998585i	$0.516932\pi$
$648$	1.79492	−	23.9515i	0.0705111	−	0.940905i
$649$	−7.61495	+	19.4026i	−0.298913	+	0.761618i
$650$	3.12995	−	1.50731i	0.122767	−	0.0591214i
$651$	52.0427	+	13.7674i	2.03972	+	0.539587i
$652$	8.70630	+	4.19273i	0.340965	+	0.164200i
$653$	5.07529	−	4.70918i	0.198611	−	0.184285i	−0.574597	−	0.818437i	$-0.694841\pi$
$653$	5.07529	−	4.70918i	0.198611	−	0.184285i	0.773208	+	0.634152i	$0.218651\pi$
$654$	0.747627	−	0.112687i	0.0292345	−	0.00440640i
$655$	−7.74499	+	13.4147i	−0.302622	+	0.524156i
$656$	1.83302	+	3.17488i	0.0715673	+	0.123958i
$657$	−1.76188	−	2.20933i	−0.0687376	−	0.0861942i
$658$	1.82785	−	9.83162i	0.0712569	−	0.383277i
$659$	9.14870	−	11.4721i	0.356383	−	0.446890i	−0.571030	−	0.820929i	$-0.693456\pi$
$659$	9.14870	−	11.4721i	0.356383	−	0.446890i	0.927413	+	0.374039i	$0.122028\pi$
$660$	−15.4880	−	2.33444i	−0.602868	−	0.0908678i
$661$	3.12926	−	2.13349i	0.121714	−	0.0829832i	−0.500933	−	0.865486i	$-0.667010\pi$
$661$	3.12926	−	2.13349i	0.121714	−	0.0829832i	0.622647	+	0.782503i	$0.286057\pi$
$662$	−5.69751	+	3.88450i	−0.221440	+	0.150975i
$663$	1.19031	+	0.179410i	0.0462277	+	0.00696770i
$664$	20.1954	−	25.3242i	0.783732	−	0.982769i
$665$	1.30158	+	4.79643i	0.0504730	+	0.185998i
$666$	12.0634	+	15.1270i	0.467446	+	0.586158i
$667$	−28.7100	−	49.7273i	−1.11166	−	1.92545i
$668$	−2.85988	+	4.95345i	−0.110652	+	0.191655i
$669$	−33.6088	+	5.06571i	−1.29939	+	0.195852i
$670$	−3.84677	+	3.56928i	−0.148614	+	0.137893i
$671$	27.5706	+	13.2773i	1.06435	+	0.512565i
$672$	15.2523	+	34.6571i	0.588369	+	1.33693i
$673$	−21.9744	+	10.5823i	−0.847051	+	0.407918i	−0.806482	−	0.591259i	$-0.798631\pi$
$673$	−21.9744	+	10.5823i	−0.847051	+	0.407918i	−0.0405686	+	0.999177i	$0.512917\pi$
$674$	−10.6204	+	27.0604i	−0.409084	+	1.04233i
$675$	−0.00435440	+	0.0581054i	−0.000167601	+	0.00223648i
$676$	−1.31004	−	0.404095i	−0.0503863	−	0.0155421i
$677$	−2.41703	−	32.2531i	−0.0928941	−	1.23959i	−0.827646	−	0.561250i	$-0.810321\pi$
$677$	−2.41703	−	32.2531i	−0.0928941	−	1.23959i	0.734752	−	0.678336i	$-0.237298\pi$
$678$	−2.46665	+	10.8071i	−0.0947312	+	0.415045i
$679$	−19.6971	−	12.2892i	−0.755905	−	0.471617i
$680$	0.230083	+	1.00806i	0.00882328	+	0.0386573i
$681$	52.2126	−	16.1054i	2.00079	−	0.617162i
$682$	14.2460	+	36.2982i	0.545507	+	1.38993i
$683$	17.0203	+	15.7925i	0.651264	+	0.604285i	0.935013	−	0.354614i	$-0.115388\pi$
$683$	17.0203	+	15.7925i	0.651264	+	0.604285i	−0.283749	+	0.958899i	$0.591578\pi$
$684$	−8.12228	−	5.53767i	−0.310563	−	0.211738i
$685$	−4.25557			−0.162597
$686$	−9.47463	+	11.2248i	−0.361743	+	0.428564i
$687$	−66.3076			−2.52979
$688$	3.34403	+	2.27992i	0.127490	+	0.0869212i
$689$	−0.441653	−	0.409794i	−0.0168256	−	0.0156119i
$690$	−4.56155	−	11.6226i	−0.173655	−	0.442467i
$691$	−0.424408	+	0.130913i	−0.0161452	+	0.00498015i	−0.302817	−	0.953049i	$-0.597927\pi$
$691$	−0.424408	+	0.130913i	−0.0161452	+	0.00498015i	0.286672	+	0.958029i	$0.407451\pi$
$692$	−1.16546	−	5.10623i	−0.0443042	−	0.194110i
$693$	39.9473	+	24.9235i	1.51747	+	0.946767i
$694$	−0.500863	+	2.19442i	−0.0190125	+	0.0832992i
$695$	−0.623850	−	8.32470i	−0.0236640	−	0.315774i
$696$	−44.0604	−	13.5908i	−1.67011	−	0.515159i
$697$	0.216561	−	2.88981i	0.00820283	−	0.109459i
$698$	−5.03727	+	12.8348i	−0.190664	+	0.485803i
$699$	15.2351	−	7.33684i	0.576245	−	0.277505i
$700$	6.39963	+	14.5416i	0.241883	+	0.549622i
$701$	29.4364	+	14.1758i	1.11180	+	0.535413i	0.897349	−	0.441322i	$-0.145490\pi$
$701$	29.4364	+	14.1758i	1.11180	+	0.535413i	0.214448	+	0.976735i	$0.431205\pi$
$702$	−0.00773435	+	0.00717643i	−0.000291914	+	0.000270857i
$703$	−19.1494	+	2.88631i	−0.722235	+	0.108859i
$704$	−10.0340	+	17.3794i	−0.378171	+	0.655012i
$705$	−4.59736	−	7.96286i	−0.173147	−	0.299899i
$706$	−7.28993	−	9.14129i	−0.274360	−	0.344037i
$707$	2.08725	+	7.69171i	0.0784993	+	0.289277i
$708$	7.37339	−	9.24594i	0.277109	−	0.347484i
$709$	−12.5901	−	1.89765i	−0.472830	−	0.0712676i	−0.0916951	−	0.995787i	$-0.529229\pi$
$709$	−12.5901	−	1.89765i	−0.472830	−	0.0712676i	−0.381135	+	0.924519i	$0.624467\pi$
$710$	−7.97242	+	5.43551i	−0.299200	+	0.203991i
$711$	9.19322	−	6.26783i	0.344773	−	0.235062i
$712$	2.98568	+	0.450018i	0.111893	+	0.0168651i
$713$	42.2379	−	52.9647i	1.58182	−	1.98354i
$714$	0.461704	−	2.48342i	0.0172788	−	0.0929395i
$715$	−2.90675	−	3.64495i	−0.108706	−	0.136313i
$716$	0.765286	+	1.32551i	0.0286001	+	0.0495368i
$717$	−24.6378	+	42.6740i	−0.920116	+	1.59369i
$718$	−18.9502	+	2.85628i	−0.707215	+	0.106596i
$719$	−23.3455	+	21.6614i	−0.870640	+	0.807835i	−0.982572	−	0.185880i	$-0.940486\pi$
$719$	−23.3455	+	21.6614i	−0.870640	+	0.807835i	0.111933	+	0.993716i	$0.464296\pi$
$720$	1.32479	+	0.637984i	0.0493719	+	0.0237763i
$721$	25.7644	+	6.81573i	0.959518	+	0.253831i
$722$	9.50944	−	4.57951i	0.353905	−	0.170432i
$723$	−9.08793	+	23.1557i	−0.337984	+	0.861169i
$724$	−1.53134	+	20.4343i	−0.0569119	+	0.759436i
$725$	−29.4556	−	9.08584i	−1.09395	−	0.337440i
$726$	3.49510	+	46.6389i	0.129715	+	1.73093i
$727$	−3.47664	+	15.2321i	−0.128941	+	0.564929i	0.868642	+	0.495441i	$0.164994\pi$
$727$	−3.47664	+	15.2321i	−0.128941	+	0.564929i	−0.997583	+	0.0694876i	$0.977864\pi$
$728$	−2.31501	+	6.68411i	−0.0858001	+	0.247729i
$729$	6.02979	+	26.4182i	0.223325	+	0.978453i
$730$	0.561050	−	0.173061i	0.0207654	−	0.00640527i
$731$	−1.16883	−	2.97813i	−0.0432308	−	0.110150i
$732$	−12.7274	−	11.8093i	−0.470419	−	0.436485i
$733$	25.7228	+	17.5375i	0.950094	+	0.647763i	0.935949	−	0.352137i	$-0.114545\pi$
$733$	25.7228	+	17.5375i	0.950094	+	0.647763i	0.0141455	+	0.999900i	$0.495497\pi$
$734$	11.0307			0.407151
$735$	0.0859854	+	13.5056i	0.00317162	+	0.498163i
$736$	47.6498			1.75640
$737$	−41.1146	−	28.0314i	−1.51447	−	1.03255i
$738$	10.3087	+	9.56507i	0.379468	+	0.352095i
$739$	14.7366	+	37.5484i	0.542096	+	1.38124i	0.895204	+	0.445656i	$0.147030\pi$
$739$	14.7366	+	37.5484i	0.542096	+	1.38124i	−0.353108	+	0.935583i	$0.614875\pi$
$740$	8.37201	−	2.58242i	0.307761	−	0.0949318i
$741$	−1.30103	−	5.70018i	−0.0477945	−	0.209401i
$742$	−0.891120	+	0.896811i	−0.0327140	+	0.0329230i
$743$	−8.13649	+	35.6483i	−0.298499	+	1.30781i	0.573864	+	0.818950i	$0.305444\pi$
$743$	−8.13649	+	35.6483i	−0.298499	+	1.30781i	−0.872363	+	0.488858i	$0.837413\pi$
$744$	−4.06527	−	54.2473i	−0.149040	−	1.98880i
$745$	−2.53699	−	0.782557i	−0.0929480	−	0.0286707i
$746$	0.227830	−	3.04017i	0.00834143	−	0.111309i
$747$	−13.3025	+	33.8941i	−0.486712	+	1.24012i
$748$	−3.59270	+	1.73015i	−0.131362	+	0.0632607i
$749$	12.4633	−	23.7645i	0.455398	−	0.868334i
$750$	−12.9326	−	6.22802i	−0.472233	−	0.227415i
$751$	24.3003	−	22.5474i	0.886730	−	0.822765i	−0.0982983	−	0.995157i	$-0.531340\pi$
$751$	24.3003	−	22.5474i	0.886730	−	0.822765i	0.985028	+	0.172392i	$0.0551495\pi$
$752$	2.92827	−	0.441366i	0.106783	−	0.0160949i
$753$	−22.6365	+	39.2076i	−0.824921	+	1.42881i
$754$	−2.79081	−	4.83382i	−0.101635	−	0.176038i
$755$	−7.46963	−	9.36662i	−0.271848	−	0.340886i
$756$	−0.0315906	−	0.0364735i	−0.00114894	−	0.00132653i
$757$	10.9772	−	13.7650i	0.398975	−	0.500299i	−0.541246	−	0.840864i	$-0.682047\pi$
$757$	10.9772	−	13.7650i	0.398975	−	0.500299i	0.940221	+	0.340566i	$0.110619\pi$
$758$	−5.69382	−	0.858205i	−0.206809	−	0.0311714i
$759$	97.8246	−	66.6957i	3.55081	−	2.42090i
$760$	4.14952	−	2.82910i	0.150519	−	0.102622i
$761$	0.957697	+	0.144350i	0.0347165	+	0.00523267i	0.166378	−	0.986062i	$-0.446793\pi$
$761$	0.957697	+	0.144350i	0.0347165	+	0.00523267i	−0.131661	+	0.991295i	$0.542031\pi$
$762$	−11.6178	+	14.5683i	−0.420870	+	0.527755i
$763$	−0.608518	+	0.830029i	−0.0220298	+	0.0300491i
$764$	−13.2971	−	16.6740i	−0.481072	−	0.603245i
$765$	−0.581159	−	1.00660i	−0.0210119	−	0.0363936i
$766$	15.1104	−	26.1720i	0.545961	−	0.945632i
$767$	3.48070	−	0.524630i	0.125681	−	0.0189433i
$768$	24.9882	−	23.1856i	0.901683	−	0.836639i
$769$	37.2241	+	17.9262i	1.34234	+	0.646435i	0.960625	−	0.277847i	$-0.0896209\pi$
$769$	37.2241	+	17.9262i	1.34234	+	0.646435i	0.381710	+	0.924282i	$0.375335\pi$
$770$	−7.85281	+	5.83434i	−0.282996	+	0.210255i
$771$	−37.2565	+	17.9418i	−1.34176	+	0.646158i
$772$	1.25017	−	3.18539i	0.0449947	−	0.114645i
$773$	0.383721	−	5.12040i	0.0138015	−	0.184168i	−0.986042	−	0.166495i	$-0.946755\pi$
$773$	0.383721	−	5.12040i	0.0138015	−	0.184168i	0.999844	−	0.0176733i	$-0.00562587\pi$
$774$	14.8355	+	4.57613i	0.533249	+	0.164486i
$775$	−2.71775	−	36.2658i	−0.0976243	−	1.30271i
$776$	−5.22049	+	22.8724i	−0.187405	+	0.821073i
$777$	−52.3149	−	5.72589i	−1.87679	−	0.205415i
$778$	3.71069	+	16.2576i	0.133035	+	0.582863i
$779$	−13.4502	+	4.14883i	−0.481902	+	0.148647i
$780$	0.966376	+	2.46229i	0.0346018	+	0.0881640i
$781$	−67.0730	−	62.2346i	−2.40006	−	2.22693i
$782$	−2.62639	−	1.79064i	−0.0939194	−	0.0640332i
$783$	0.0936192			0.00334568
$784$	−4.05920	−	1.56337i	−0.144971	−	0.0558346i
$785$	17.1897			0.613527
$786$	−31.5949	−	21.5410i	−1.12695	−	0.768343i
$787$	21.7436	+	20.1751i	0.775075	+	0.719165i	0.964890	−	0.262655i	$-0.0845982\pi$
$787$	21.7436	+	20.1751i	0.775075	+	0.719165i	−0.189814	+	0.981820i	$0.560789\pi$
$788$	−7.35440	−	18.7387i	−0.261990	−	0.667539i
$789$	−11.4640	+	3.53618i	−0.408129	+	0.125891i
$790$	0.514426	+	2.25385i	0.0183025	+	0.0801883i
$791$	−8.06867	−	12.7509i	−0.286889	−	0.453371i
$792$	10.5876	−	46.3872i	0.376213	−	1.64830i
$793$	−0.386196	−	5.15342i	−0.0137142	−	0.183003i
$794$	15.2657	+	4.70884i	0.541759	+	0.167110i
$795$	−0.0868697	+	1.15920i	−0.00308095	+	0.0411124i
$796$	−2.68342	+	6.83724i	−0.0951113	+	0.242340i
$797$	−30.4766	+	14.6767i	−1.07953	+	0.519877i	−0.887168	−	0.461446i	$-0.847331\pi$
$797$	−30.4766	+	14.6767i	−1.07953	+	0.519877i	−0.192367	+	0.981323i	$0.561616\pi$
$798$	−12.0477	+	2.31930i	−0.426485	+	0.0821024i
$799$	−2.10905	−	1.01567i	−0.0746129	−	0.0359317i
$800$	18.7515	−	17.3988i	0.662966	−	0.615142i
$801$	−3.35625	+	0.505873i	−0.118587	+	0.0178742i
$802$	7.24928	−	12.5561i	0.255981	−	0.443372i
$803$	2.78379	+	4.82166i	0.0982377	+	0.170153i
$804$	17.6031	+	22.0736i	0.620813	+	0.778475i
$805$	15.5995	+	6.74698i	0.549811	+	0.237800i
$806$	4.10581	−	5.14853i	0.144621	−	0.181349i
$807$	−66.8829	−	10.0810i	−2.35439	−	0.354867i
$808$	6.65432	−	4.53684i	0.234098	−	0.159605i
$809$	4.03436	−	2.75058i	0.141841	−	0.0967053i	−0.490321	−	0.871542i	$-0.663120\pi$
$809$	4.03436	−	2.75058i	0.141841	−	0.0967053i	0.632161	+	0.774837i	$0.282168\pi$
$810$	−5.54719	−	0.836104i	−0.194908	−	0.0293777i
$811$	−20.4857	+	25.6882i	−0.719349	+	0.902035i	−0.998301	−	0.0582703i	$-0.981441\pi$
$811$	−20.4857	+	25.6882i	−0.719349	+	0.902035i	0.278952	+	0.960305i	$0.410013\pi$
$812$	22.5302	−	11.9994i	0.790654	−	0.421098i
$813$	−47.4618	−	59.5152i	−1.66456	−	2.08729i
$814$	−19.0602	−	33.0132i	−0.668059	−	1.15711i
$815$	2.77476	−	4.80603i	0.0971957	−	0.168348i
$816$	0.739665	−	0.111487i	0.0258935	−	0.00390281i
$817$	−11.3911	+	10.5694i	−0.398525	+	0.369778i
$818$	−21.7082	−	10.4541i	−0.759009	−	0.365519i
$819$	0.272025	−	7.94696i	0.00950531	−	0.277689i
$820$	5.73727	−	2.76293i	0.200354	−	0.0964856i
$821$	20.2163	−	51.5103i	0.705553	−	1.79772i	0.110751	−	0.993848i	$-0.464674\pi$
$821$	20.2163	−	51.5103i	0.705553	−	1.79772i	0.594802	−	0.803872i	$-0.297230\pi$
$822$	0.785079	−	10.4762i	0.0273828	−	0.365398i
$823$	38.8780	+	11.9923i	1.35520	+	0.418024i	0.885434	−	0.464765i	$-0.153861\pi$
$823$	38.8780	+	11.9923i	1.35520	+	0.418024i	0.469768	+	0.882790i	$0.344338\pi$
$824$	−2.01257	−	26.8558i	−0.0701110	−	0.935567i
$825$	14.1434	−	61.9662i	0.492409	−	2.15739i
$826$	−0.850380	−	7.33733i	−0.0295885	−	0.255298i
$827$	8.18691	+	35.8692i	0.284687	+	1.24729i	0.891709	+	0.452610i	$0.149507\pi$
$827$	8.18691	+	35.8692i	0.284687	+	1.24729i	−0.607022	+	0.794685i	$0.707636\pi$
$828$	−32.1246	+	9.90913i	−1.11641	+	0.344366i
$829$	−0.832970	−	2.12237i	−0.0289302	−	0.0737131i	0.915679	−	0.401911i	$-0.131654\pi$
$829$	−0.832970	−	2.12237i	−0.0289302	−	0.0737131i	−0.944609	+	0.328198i	$0.893559\pi$
$830$	−5.54573	−	5.14568i	−0.192495	−	0.178609i
$831$	−0.465574	−	0.317423i	−0.0161506	−	0.0110113i
$832$	3.38907			0.117495
$833$	1.95500	+	2.82859i	0.0677366	+	0.0980049i
$834$	20.6084			0.713612
$835$	2.71403	+	1.85040i	0.0939230	+	0.0640356i
$836$	14.1979	+	13.1738i	0.491046	+	0.455624i
$837$	0.0403527	+	0.102817i	0.00139479	+	0.00355388i
$838$	22.1280	−	6.82560i	0.764400	−	0.235786i
$839$	9.49700	+	41.6091i	0.327873	+	1.43651i	0.823177	+	0.567785i	$0.192200\pi$
$839$	9.49700	+	41.6091i	0.327873	+	1.43651i	−0.495304	+	0.868720i	$0.664943\pi$
$840$	12.8677	−	4.54864i	0.443979	−	0.156943i
$841$	−4.56753	+	20.0117i	−0.157501	+	0.690057i
$842$	0.102688	+	1.37027i	0.00353885	+	0.0472227i
$843$	−43.3243	−	13.3638i	−1.49217	−	0.460273i
$844$	1.73402	−	23.1389i	0.0596874	−	0.796473i
$845$	−0.287642	+	0.732900i	−0.00989519	+	0.0252125i
$846$	10.2346	−	4.92873i	0.351873	−	0.169453i
$847$	−48.3880	−	41.3739i	−1.66263	−	1.42162i
$848$	−0.337313	−	0.162441i	−0.0115834	−	0.00557825i
$849$	−11.7992	+	10.9480i	−0.404946	+	0.375735i
$850$	−1.68739	+	0.254333i	−0.0578769	+	0.00872354i
$851$	−33.1136	+	57.3544i	−1.13512	+	1.96608i
$852$	25.9569	+	44.9586i	0.889268	+	1.54026i
$853$	8.19972	+	10.2821i	0.280753	+	0.352053i	0.902134	−	0.431455i	$-0.142000\pi$
$853$	8.19972	+	10.2821i	0.280753	+	0.352053i	−0.621381	+	0.783508i	$0.713428\pi$
$854$	−10.8354	+	0.439977i	−0.370780	+	0.0150557i
$855$	−3.51993	+	4.41385i	−0.120379	+	0.150950i
$856$	−26.8138	−	4.04153i	−0.916478	−	0.138137i
$857$	8.11223	−	5.53082i	0.277108	−	0.188929i	−0.416789	−	0.909003i	$-0.636845\pi$
$857$	8.11223	−	5.53082i	0.277108	−	0.188929i	0.693897	+	0.720074i	$0.255892\pi$
$858$	9.50921	−	6.48327i	0.324639	−	0.221335i
$859$	−28.9317	−	4.36076i	−0.987138	−	0.148787i	−0.364421	−	0.931234i	$-0.618733\pi$
$859$	−28.9317	−	4.36076i	−0.987138	−	0.148787i	−0.622717	+	0.782447i	$0.713971\pi$
$860$	4.38322	−	5.49639i	0.149467	−	0.187425i
$861$	−38.2194	+	1.55192i	−1.30251	+	0.0528891i
$862$	0.460198	+	0.577070i	0.0156744	+	0.0196551i
$863$	−8.56727	−	14.8389i	−0.291633	−	0.505124i	0.682563	−	0.730827i	$-0.260865\pi$
$863$	−8.56727	−	14.8389i	−0.291633	−	0.505124i	−0.974196	+	0.225703i	$0.927532\pi$
$864$	−0.0388447	+	0.0672811i	−0.00132152	+	0.00228895i
$865$	−2.97428	+	0.448300i	−0.101129	+	0.0152427i
$866$	−22.2767	+	20.6697i	−0.756992	+	0.702386i
$867$	37.0018	+	17.8191i	1.25665	+	0.605169i
$868$	22.8895	+	19.5716i	0.776922	+	0.664302i
$869$	−19.7511	+	9.51161i	−0.670009	+	0.322659i
$870$	−3.93446	+	10.0248i	−0.133391	+	0.339874i
$871$	−0.628002	+	8.38011i	−0.0212790	+	0.283949i
$872$	0.993819	+	0.306552i	0.0336549	+	0.0103812i
$873$	−1.97082	−	26.2988i	−0.0667022	−	0.890079i
$874$	−3.43560	+	15.0524i	−0.116211	+	0.509154i
$875$	18.4223	−	6.51213i	0.622787	−	0.220150i
$876$	−0.702920	−	3.07969i	−0.0237495	−	0.104053i
$877$	32.2405	−	9.94487i	1.08868	−	0.335814i	0.302086	−	0.953281i	$-0.402317\pi$
$877$	32.2405	−	9.94487i	1.08868	−	0.335814i	0.786597	+	0.617466i	$0.211841\pi$
$878$	3.24067	+	8.25708i	0.109367	+	0.278663i
$879$	58.2349	+	54.0341i	1.96422	+	1.82253i
$880$	−2.39365	−	1.63196i	−0.0806899	−	0.0550134i
$881$	−28.3224			−0.954205			−0.477102	−	0.878848i	$-0.658313\pi$
$881$	−28.3224			−0.954205			−0.477102	+	0.878848i	$0.658313\pi$
$882$	−16.6467	−	1.14097i	−0.560525	−	0.0384185i
$883$	−38.7990			−1.30569			−0.652846	−	0.757491i	$-0.726425\pi$
$883$	−38.7990			−1.30569			−0.652846	+	0.757491i	$0.726425\pi$
$884$	0.556406	+	0.379351i	0.0187140	+	0.0127590i
$885$	−4.97857	−	4.61944i	−0.167353	−	0.155281i
$886$	4.12621	+	10.5134i	0.138623	+	0.353205i
$887$	−23.3816	+	7.21227i	−0.785077	+	0.242164i	−0.661276	−	0.750143i	$-0.729985\pi$
$887$	−23.3816	+	7.21227i	−0.785077	+	0.242164i	−0.123801	+	0.992307i	$0.539509\pi$
$888$	11.8339	+	51.8477i	0.397120	+	1.73990i
$889$	−2.92017	−	25.1961i	−0.0979395	−	0.845051i
$890$	0.156925	−	0.687535i	0.00526015	−	0.0230462i
$891$	−3.97534	−	53.0473i	−0.133179	−	1.77715i
$892$	−18.1696	−	5.60456i	−0.608362	−	0.187655i
$893$	−0.849674	+	11.3381i	−0.0284332	+	0.379415i
$894$	2.39449	−	6.10107i	0.0800838	−	0.204050i
$895$	0.791946	−	0.381381i	0.0264718	−	0.0127482i
$896$	−0.813885	+	23.7770i	−0.0271900	+	0.794332i
$897$	−18.0147	−	8.67544i	−0.601494	−	0.289664i
$898$	0.658900	−	0.611370i	0.0219878	−	0.0204017i
$899$	−57.7786	+	8.70873i	−1.92703	+	0.290452i
$900$	−9.02369	+	15.6295i	−0.300790	+	0.520983i
$901$	0.147973	+	0.256296i	0.00492968	+	0.00853846i
$902$	−17.2749	−	21.6621i	−0.575192	−	0.721268i
$903$	−37.2722	+	19.8510i	−1.24034	+	0.660599i
$904$	−9.50707	+	11.9215i	−0.316201	+	0.396503i
$905$	11.6367	+	1.75395i	0.386818	+	0.0583034i
$906$	24.4363	−	16.6604i	0.811842	−	0.553504i
$907$	12.0856	−	8.23981i	0.401295	−	0.273598i	−0.345810	−	0.938305i	$-0.612396\pi$
$907$	12.0856	−	8.23981i	0.401295	−	0.273598i	0.747105	+	0.664706i	$0.231443\pi$
$908$	30.2262	+	4.55586i	1.00309	+	0.151192i
$909$	−5.64467	+	7.07820i	−0.187222	+	0.234769i
$910$	1.51638	+	0.655852i	0.0502675	+	0.0217413i
$911$	5.03369	+	6.31205i	0.166774	+	0.209127i	0.858194	−	0.513325i	$-0.171586\pi$
$911$	5.03369	+	6.31205i	0.166774	+	0.209127i	−0.691421	+	0.722452i	$0.743015\pi$
$912$	−1.81661	−	3.14646i	−0.0601540	−	0.104190i
$913$	35.8692	−	62.1273i	1.18710	−	2.05611i
$914$	−26.4670	+	3.98926i	−0.875451	+	0.131953i
$915$	−7.30925	+	6.78199i	−0.241636	+	0.224206i
$916$	−33.4213	−	16.0948i	−1.10427	−	0.531788i
$917$	51.1145	−	9.84002i	1.68795	−	0.324946i
$918$	0.00466943	−	0.00224868i	0.000154114	−	7.42174e-5i
$919$	−5.94923	+	15.1584i	−0.196247	+	0.500030i	−0.994794	−	0.101903i	$-0.967507\pi$
$919$	−5.94923	+	15.1584i	−0.196247	+	0.500030i	0.798547	+	0.601932i	$0.205602\pi$
$920$	1.28348	−	17.1269i	0.0423152	−	0.564657i
$921$	−15.0519	−	4.64290i	−0.495978	−	0.152989i
$922$	1.11028	+	14.8156i	0.0365650	+	0.487926i
$923$	−3.43842	+	15.0647i	−0.113177	+	0.495861i
$924$	28.1448	+	44.4772i	0.925895	+	1.46319i
$925$	7.91129	+	34.6616i	0.260121	+	1.13967i
$926$	7.76055	−	2.39381i	0.255028	−	0.0786656i
$927$	11.0602	+	28.1810i	0.363266	+	0.925587i
$928$	−30.1278	−	27.9545i	−0.988995	−	0.917653i
$929$	16.0226	+	10.9240i	0.525683	+	0.358405i	0.796898	−	0.604114i	$-0.206473\pi$
$929$	16.0226	+	10.9240i	0.525683	+	0.358405i	−0.271215	+	0.962519i	$0.587425\pi$
$930$	−12.7056			−0.416634
$931$	9.31996	−	13.8586i	0.305449	−	0.454198i
$932$	9.45988			0.309869
$933$	−13.0357	−	8.88759i	−0.426770	−	0.290967i
$934$	−23.8409	−	22.1212i	−0.780100	−	0.723827i
$935$	0.836646	+	2.13174i	0.0273613	+	0.0697153i
$936$	−7.67830	+	2.36844i	−0.250973	+	0.0774149i
$937$	3.86321	+	16.9258i	0.126205	+	0.552942i	0.998008	+	0.0630851i	$0.0200939\pi$
$937$	3.86321	+	16.9258i	0.126205	+	0.552942i	−0.871803	+	0.489857i	$0.837049\pi$
$938$	17.5296	+	1.91862i	0.572361	+	0.0626451i
$939$	−7.38548	+	32.3579i	−0.241016	+	1.05596i
$940$	−0.384401	−	5.12947i	−0.0125378	−	0.167305i
$941$	−40.0742	−	12.3613i	−1.30638	−	0.402966i	−0.438051	−	0.898950i	$-0.644331\pi$
$941$	−40.0742	−	12.3613i	−1.30638	−	0.402966i	−0.868331	+	0.495985i	$0.834807\pi$
$942$	−3.17121	+	42.3168i	−0.103324	+	1.37876i
$943$	−17.5859	+	44.8081i	−0.572676	+	1.45915i
$944$	1.97074	−	0.949060i	0.0641422	−	0.0308893i
$945$	−0.0222436	+	0.0165262i	−0.000723584	+	0.000537596i
$946$	−27.5591	−	13.2718i	−0.896024	−	0.431502i
$947$	15.3898	−	14.2797i	0.500103	−	0.464028i	−0.389327	−	0.921100i	$-0.627292\pi$
$947$	15.3898	−	14.2797i	0.500103	−	0.464028i	0.889430	+	0.457072i	$0.151102\pi$
$948$	12.2991	−	1.85378i	0.399455	−	0.0602081i
$949$	0.470123	−	0.814277i	0.0152608	−	0.0264325i
$950$	4.14421	+	7.17799i	0.134456	+	0.232885i
$951$	−30.4263	−	38.1534i	−0.986640	−	1.23721i
$952$	2.05440	−	2.80223i	0.0665833	−	0.0908209i
$953$	−19.6274	+	24.6120i	−0.635795	+	0.797261i	−0.990470	−	0.137728i	$-0.956020\pi$
$953$	−19.6274	+	24.6120i	−0.635795	+	0.797261i	0.354675	+	0.934990i	$0.384591\pi$
$954$	−1.42009	−	0.214045i	−0.0459773	−	0.00692996i
$955$	−10.1196	+	6.89946i	−0.327464	+	0.223261i
$956$	−22.7765	+	15.5288i	−0.736646	+	0.502237i
$957$	−100.980	−	15.2203i	−3.26423	−	0.492003i
$958$	5.99570	−	7.51836i	0.193712	−	0.242907i
$959$	9.36252	+	10.8097i	0.302332	+	0.349062i
$960$	−4.07695	−	5.11234i	−0.131583	−	0.165000i
$961$	−18.9687	−	32.8547i	−0.611893	−	1.05983i
$962$	−3.21886	+	5.57524i	−0.103780	+	0.179753i
$963$	30.1419	−	4.54316i	0.971309	−	0.146401i
$964$	−10.2012	+	9.46533i	−0.328558	+	0.304858i
$965$	−1.77057	−	0.852662i	−0.0569967	−	0.0274482i
$966$	−19.4872	+	37.1575i	−0.626991	+	1.19552i
$967$	−21.4416	+	10.3257i	−0.689516	+	0.332053i	−0.745620	−	0.666372i	$-0.767846\pi$
$967$	−21.4416	+	10.3257i	−0.689516	+	0.332053i	0.0561039	+	0.998425i	$0.482132\pi$
$968$	−23.5041	+	59.8874i	−0.755449	+	1.92485i
$969$	−0.214623	+	2.86394i	−0.00689468	+	0.0920031i
$970$	5.23607	+	1.61511i	0.168120	+	0.0518582i
$971$	0.143532	+	1.91530i	0.00460617	+	0.0614650i	0.999033	−	0.0439621i	$-0.0139981\pi$
$971$	0.143532	+	1.91530i	0.00460617	+	0.0614650i	−0.994427	+	0.105427i	$0.966379\pi$
$972$	−6.72831	+	29.4786i	−0.215811	+	0.945528i
$973$	−19.7732	+	19.8995i	−0.633901	+	0.637950i
$974$	−5.79680	−	25.3974i	−0.185741	−	0.813787i
$975$	−10.2570	+	3.16388i	−0.328488	+	0.101325i
$976$	−1.17324	−	2.98937i	−0.0375545	−	0.0956872i
$977$	−27.4097	−	25.4325i	−0.876914	−	0.813657i	0.106635	−	0.994298i	$-0.465992\pi$
$977$	−27.4097	−	25.4325i	−0.876914	−	0.813657i	−0.983549	+	0.180641i	$0.942183\pi$
$978$	11.3194	+	7.71741i	0.361953	+	0.246775i
$979$	6.68730			0.213727
$980$	−3.23488	+	6.82817i	−0.103335	+	0.218118i
$981$	−1.16911			−0.0373268
$982$	−4.67916	−	3.19020i	−0.149318	−	0.101803i
$983$	9.48462	+	8.80044i	0.302512	+	0.280691i	0.816792	−	0.576932i	$-0.195750\pi$
$983$	9.48462	+	8.80044i	0.302512	+	0.280691i	−0.514280	+	0.857622i	$0.671941\pi$
$984$	14.1216	+	35.9814i	0.450182	+	1.14704i
$985$	−11.0470	+	3.40755i	−0.351987	+	0.108574i
$986$	0.610093	+	2.67299i	0.0194293	+	0.0851254i
$987$	−10.1122	+	29.1967i	−0.321873	+	0.929340i
$988$	0.727841	−	3.18888i	0.0231557	−	0.101452i
$989$	3.97127	+	52.9930i	0.126279	+	1.68508i
$990$	−10.6192	−	3.27558i	−0.337500	−	0.104105i
$991$	0.0328285	−	0.438065i	0.00104283	−	0.0139156i	−0.996658	−	0.0816861i	$-0.973970\pi$
$991$	0.0328285	−	0.438065i	0.00104283	−	0.0139156i	0.997701	+	0.0677705i	$0.0215886\pi$
$992$	17.7150	−	45.1371i	0.562452	−	1.43310i
$993$	19.1964	−	9.24448i	0.609178	−	0.293365i
$994$	31.3467	+	8.29246i	0.994257	+	0.263021i
$995$	3.80042	+	1.83019i	0.120482	+	0.0580208i
$996$	−29.8371	+	27.6847i	−0.945424	+	0.877225i
$997$	50.0085	−	7.53756i	1.58378	−	0.238717i	0.702633	−	0.711552i	$-0.252008\pi$
$997$	50.0085	−	7.53756i	1.58378	−	0.238717i	0.881151	+	0.472835i	$0.156770\pi$
$998$	10.1680	−	17.6116i	0.321864	−	0.557485i
$999$	−0.0539892	−	0.0935121i	−0.00170814	−	0.00295859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.19	✓	348
49.37	even	21	inner	637.2.bl.b.625.19	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.19	✓	348	1.1	even	1	trivial
637.2.bl.b.625.19	yes	348	49.37	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.655312 + 0.446784i) q^{2} +(-1.79642 - 1.66683i) q^{3} +(-0.500865 - 1.27618i) q^{4} +(-0.752346 + 0.232068i) q^{5} +(-0.432499 - 1.89490i) q^{6} +(2.24469 + 1.40049i) q^{7} +(0.594930 - 2.60656i) q^{8} +(0.224596 + 2.99702i) q^{9} +O(q^{10})\)	\(q+(0.655312 + 0.446784i) q^{2} +(-1.79642 - 1.66683i) q^{3} +(-0.500865 - 1.27618i) q^{4} +(-0.752346 + 0.232068i) q^{5} +(-0.432499 - 1.89490i) q^{6} +(2.24469 + 1.40049i) q^{7} +(0.594930 - 2.60656i) q^{8} +(0.224596 + 2.99702i) q^{9} +(-0.596706 - 0.184059i) q^{10} +(0.442507 - 5.90484i) q^{11} +(-1.22742 + 3.12741i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(0.845258 + 1.92065i) q^{14} +(1.73834 + 0.837142i) q^{15} +(-0.455524 + 0.422664i) q^{16} +(0.485721 - 0.0732106i) q^{17} +(-1.19184 + 2.06433i) q^{18} +(-1.19293 - 2.06621i) q^{19} +(0.672985 + 0.843896i) q^{20} +(-1.69803 - 6.25737i) q^{21} +(2.92817 - 3.67181i) q^{22} +(-8.06804 - 1.21606i) q^{23} +(-5.41343 + 3.69081i) q^{24} +(-3.61902 + 2.46741i) q^{25} +(-0.784268 - 0.118209i) q^{26} +(0.00829423 - 0.0104006i) q^{27} +(0.662989 - 3.56609i) q^{28} +(4.38780 + 5.50213i) q^{29} +(0.765136 + 1.32525i) q^{30} +(-4.15143 + 7.19048i) q^{31} +(-5.77481 + 0.870412i) q^{32} +(-10.6373 + 9.86997i) q^{33} +(0.351008 + 0.169036i) q^{34} +(-2.01379 - 0.532729i) q^{35} +(3.71226 - 1.78773i) q^{36} +(2.96544 - 7.55581i) q^{37} +(0.141411 - 1.88699i) q^{38} +(2.34172 + 0.722326i) q^{39} +(0.157306 + 2.09910i) q^{40} +(1.31278 - 5.75165i) q^{41} +(1.68296 - 4.85918i) q^{42} +(-1.44930 - 6.34981i) q^{43} +(-7.75729 + 2.39281i) q^{44} +(-0.864488 - 2.20268i) q^{45} +(-4.74376 - 4.40157i) q^{46} +(-3.93748 - 2.68453i) q^{47} +1.52282 q^{48} +(3.07728 + 6.28732i) q^{49} -3.47399 q^{50} +(-0.994586 - 0.678097i) q^{51} +(1.00498 + 0.932483i) q^{52} +(0.220113 + 0.560838i) q^{53} +(0.0100821 - 0.00310993i) q^{54} +(1.03741 + 4.54518i) q^{55} +(4.98588 - 5.01772i) q^{56} +(-1.30103 + 5.70018i) q^{57} +(0.417115 + 5.56601i) q^{58} +(-3.36363 - 1.03754i) q^{59} +(0.197671 - 2.63774i) q^{60} +(-1.88804 + 4.81064i) q^{61} +(-5.93307 + 2.85722i) q^{62} +(-3.69314 + 7.04194i) q^{63} +(-3.05345 - 1.47046i) q^{64} +(0.577150 - 0.535517i) q^{65} +(-11.3805 + 1.71533i) q^{66} +(4.20180 - 7.27773i) q^{67} +(-0.336710 - 0.583200i) q^{68} +(12.4666 + 15.6326i) q^{69} +(-1.08165 - 1.24883i) q^{70} +(9.63425 - 12.0810i) q^{71} +(7.94553 + 1.19760i) q^{72} +(-0.776867 + 0.529659i) q^{73} +(5.31910 - 3.62650i) q^{74} +(10.6140 + 1.59981i) q^{75} +(-2.03937 + 2.55728i) q^{76} +(9.26295 - 12.6348i) q^{77} +(1.21184 + 1.51959i) q^{78} +(-1.85108 - 3.20617i) q^{79} +(0.244625 - 0.423702i) q^{80} +(8.88334 - 1.33895i) q^{81} +(3.43002 - 3.18260i) q^{82} +(10.9153 + 5.25655i) q^{83} +(-7.13507 + 5.30109i) q^{84} +(-0.348440 + 0.167800i) q^{85} +(1.88725 - 4.80863i) q^{86} +(1.28880 - 17.1978i) q^{87} +(-15.1281 - 4.66639i) q^{88} +(0.0843959 + 1.12619i) q^{89} +(0.417613 - 1.82968i) q^{90} +(-2.63005 - 0.287859i) q^{91} +(2.48908 + 10.9054i) q^{92} +(19.4430 - 5.99737i) q^{93} +(-1.38087 - 3.51840i) q^{94} +(1.37700 + 1.27767i) q^{95} +(11.8248 + 8.06200i) q^{96} -8.77496 q^{97} +(-0.792497 + 5.49503i) q^{98} +17.7964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

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