LMFDB - Embedded newform 189.2.ba.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	189.5
Dual form			189.2.ba.a.38.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19961 + 0.211524i) q^{2} +(-0.0787989 + 1.73026i) q^{3} +(-0.485062 + 0.176548i) q^{4} +(-0.243175 + 1.37911i) q^{5} +(-0.271462 - 2.09230i) q^{6} +(2.41247 + 1.08628i) q^{7} +(2.65438 - 1.53251i) q^{8} +(-2.98758 - 0.272685i) q^{9} +O(q^{10})$	\(q+(-1.19961 + 0.211524i) q^{2} +(-0.0787989 + 1.73026i) q^{3} +(-0.485062 + 0.176548i) q^{4} +(-0.243175 + 1.37911i) q^{5} +(-0.271462 - 2.09230i) q^{6} +(2.41247 + 1.08628i) q^{7} +(2.65438 - 1.53251i) q^{8} +(-2.98758 - 0.272685i) q^{9} -1.70584i q^{10} +(-6.43190 + 1.13412i) q^{11} +(-0.267252 - 0.853194i) q^{12} +(-0.697759 + 0.831556i) q^{13} +(-3.12380 - 0.792815i) q^{14} +(-2.36706 - 0.529428i) q^{15} +(-2.06921 + 1.73627i) q^{16} -1.26001 q^{17} +(3.64161 - 0.304829i) q^{18} -3.25785i q^{19} +(-0.125525 - 0.711888i) q^{20} +(-2.06964 + 4.08859i) q^{21} +(7.47588 - 2.72100i) q^{22} +(-2.13769 + 2.54760i) q^{23} +(2.44247 + 4.71352i) q^{24} +(2.85565 + 1.03937i) q^{25} +(0.661145 - 1.14514i) q^{26} +(0.707233 - 5.14780i) q^{27} +(-1.36198 - 0.100995i) q^{28} +(1.95642 + 2.33157i) q^{29} +(2.95153 + 0.134418i) q^{30} +(1.14128 + 3.13563i) q^{31} +(-1.82533 + 2.17534i) q^{32} +(-1.45549 - 11.2182i) q^{33} +(1.51153 - 0.266523i) q^{34} +(-2.08475 + 3.06291i) q^{35} +(1.49731 - 0.395183i) q^{36} +(2.93451 + 5.08271i) q^{37} +(0.689112 + 3.90815i) q^{38} +(-1.38382 - 1.27283i) q^{39} +(1.46802 + 4.03336i) q^{40} +(1.04396 + 0.875988i) q^{41} +(1.61793 - 5.34250i) q^{42} +(-4.70788 - 1.71353i) q^{43} +(2.91965 - 1.68566i) q^{44} +(1.10257 - 4.05390i) q^{45} +(2.02552 - 3.50830i) q^{46} +(8.38019 + 3.05014i) q^{47} +(-2.84115 - 3.71708i) q^{48} +(4.64000 + 5.24122i) q^{49} +(-3.64551 - 0.642802i) q^{50} +(0.0992877 - 2.18015i) q^{51} +(0.191647 - 0.526545i) q^{52} +(7.98523 - 4.61027i) q^{53} +(0.240477 + 6.32495i) q^{54} -9.14610i q^{55} +(8.06834 - 0.813732i) q^{56} +(5.63692 + 0.256715i) q^{57} +(-2.84012 - 2.38314i) q^{58} +(0.516276 + 0.433207i) q^{59} +(1.24164 - 0.161095i) q^{60} +(-2.39061 + 6.56816i) q^{61} +(-2.03235 - 3.52013i) q^{62} +(-6.91123 - 3.90318i) q^{63} +(4.43070 - 7.67421i) q^{64} +(-0.977133 - 1.16450i) q^{65} +(4.11894 + 13.1496i) q^{66} +(-1.92589 + 10.9222i) q^{67} +(0.611185 - 0.222453i) q^{68} +(-4.23956 - 3.89950i) q^{69} +(1.85301 - 4.11527i) q^{70} +(1.73180 + 0.999853i) q^{71} +(-8.34807 + 3.85468i) q^{72} +(-12.1033 - 6.98783i) q^{73} +(-4.59538 - 5.47656i) q^{74} +(-2.02340 + 4.85910i) q^{75} +(0.575167 + 1.58026i) q^{76} +(-16.7487 - 4.25080i) q^{77} +(1.92928 + 1.23419i) q^{78} +(1.78424 + 10.1189i) q^{79} +(-1.89134 - 3.27589i) q^{80} +(8.85129 + 1.62934i) q^{81} +(-1.43764 - 0.830022i) q^{82} +(-7.80237 + 6.54697i) q^{83} +(0.282070 - 2.34861i) q^{84} +(0.306404 - 1.73770i) q^{85} +(6.01008 + 1.05974i) q^{86} +(-4.18838 + 3.20138i) q^{87} +(-15.3347 + 12.8673i) q^{88} +15.8461 q^{89} +(-0.465155 + 5.09632i) q^{90} +(-2.58662 + 1.24814i) q^{91} +(0.587139 - 1.61315i) q^{92} +(-5.51537 + 1.72762i) q^{93} +(-10.6981 - 1.88637i) q^{94} +(4.49294 + 0.792227i) q^{95} +(-3.62006 - 3.32970i) q^{96} +(6.09610 - 16.7489i) q^{97} +(-6.67484 - 5.30595i) q^{98} +(19.5251 - 1.63439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.19961	+	0.211524i	−0.848253	+	0.149570i	−0.580846	−	0.814014i	$-0.697278\pi$
$2$	−1.19961	+	0.211524i	−0.848253	+	0.149570i	−0.267407	+	0.963584i	$0.586167\pi$
$3$	−0.0787989	+	1.73026i	−0.0454946	+	0.998965i
$3$	−0.0787989	+	1.73026i	−0.0454946	+	0.998965i
$4$	−0.485062	+	0.176548i	−0.242531	+	0.0882741i
$5$	−0.243175	+	1.37911i	−0.108751	+	0.616758i	0.880904	+	0.473294i	$0.156935\pi$
$5$	−0.243175	+	1.37911i	−0.108751	+	0.616758i	−0.989656	+	0.143464i	$0.954176\pi$
$6$	−0.271462	−	2.09230i	−0.110824	−	0.854179i
$7$	2.41247	+	1.08628i	0.911827	+	0.410574i
$7$	2.41247	+	1.08628i	0.911827	+	0.410574i
$8$	2.65438	−	1.53251i	0.938465	−	0.541823i
$9$	−2.98758	−	0.272685i	−0.995860	−	0.0908949i
$10$		−	1.70584i		−	0.539432i
$11$	−6.43190	+	1.13412i	−1.93929	+	0.341949i	−0.999999	−	0.00117094i	$-0.999627\pi$
$11$	−6.43190	+	1.13412i	−1.93929	+	0.341949i	−0.939291	+	0.343120i	$0.888516\pi$
$12$	−0.267252	−	0.853194i	−0.0771489	−	0.246296i
$13$	−0.697759	+	0.831556i	−0.193523	+	0.230632i	−0.854077	−	0.520147i	$-0.825877\pi$
$13$	−0.697759	+	0.831556i	−0.193523	+	0.230632i	0.660553	+	0.750779i	$0.270322\pi$
$14$	−3.12380	−	0.792815i	−0.834869	−	0.211889i
$15$	−2.36706	−	0.529428i	−0.611172	−	0.136698i
$16$	−2.06921	+	1.73627i	−0.517302	+	0.434068i
$17$	−1.26001			−0.305598			−0.152799	−	0.988257i	$-0.548829\pi$
$17$	−1.26001			−0.305598			−0.152799	+	0.988257i	$0.548829\pi$
$18$	3.64161	−	0.304829i	0.858336	−	0.0718488i
$19$		−	3.25785i		−	0.747402i	−0.927549	−	0.373701i	$-0.878089\pi$
$19$		−	3.25785i		−	0.747402i	0.927549	−	0.373701i	$-0.121911\pi$
$20$	−0.125525	−	0.711888i	−0.0280682	−	0.159183i
$21$	−2.06964	+	4.08859i	−0.451632	+	0.892204i
$22$	7.47588	−	2.72100i	1.59386	−	0.580119i
$23$	−2.13769	+	2.54760i	−0.445739	+	0.531211i	−0.941394	−	0.337308i	$-0.890484\pi$
$23$	−2.13769	+	2.54760i	−0.445739	+	0.531211i	0.495655	+	0.868519i	$0.334928\pi$
$24$	2.44247	+	4.71352i	0.498567	+	0.962144i
$25$	2.85565	+	1.03937i	0.571129	+	0.207874i
$26$	0.661145	−	1.14514i	0.129661	−	0.224580i
$27$	0.707233	−	5.14780i	0.136107	−	0.990694i
$28$	−1.36198	−	0.100995i	−0.257390	−	0.0190863i
$29$	1.95642	+	2.33157i	0.363298	+	0.432961i	0.916469	−	0.400106i	$-0.131027\pi$
$29$	1.95642	+	2.33157i	0.363298	+	0.432961i	−0.553171	+	0.833068i	$0.686582\pi$
$30$	2.95153	+	0.134418i	0.538874	+	0.0245412i
$31$	1.14128	+	3.13563i	0.204979	+	0.563175i	0.999000	−	0.0447153i	$-0.0142381\pi$
$31$	1.14128	+	3.13563i	0.204979	+	0.563175i	−0.794021	+	0.607891i	$0.792016\pi$
$32$	−1.82533	+	2.17534i	−0.322675	+	0.384549i
$33$	−1.45549	−	11.2182i	−0.253368	−	1.95284i
$34$	1.51153	−	0.266523i	0.259225	−	0.0457083i
$35$	−2.08475	+	3.06291i	−0.352387	+	0.517726i
$36$	1.49731	−	0.395183i	0.249551	−	0.0658639i
$37$	2.93451	+	5.08271i	0.482430	+	0.835593i	0.999797	−	0.0201710i	$-0.00642107\pi$
$37$	2.93451	+	5.08271i	0.482430	+	0.835593i	−0.517367	+	0.855764i	$0.673088\pi$
$38$	0.689112	+	3.90815i	0.111789	+	0.633985i
$39$	−1.38382	−	1.27283i	−0.221589	−	0.203816i
$40$	1.46802	+	4.03336i	0.232115	+	0.637730i
$41$	1.04396	+	0.875988i	0.163039	+	0.136806i	0.720657	−	0.693291i	$-0.243840\pi$
$41$	1.04396	+	0.875988i	0.163039	+	0.136806i	−0.557618	+	0.830098i	$0.688285\pi$
$42$	1.61793	−	5.34250i	0.249651	−	0.824365i
$43$	−4.70788	−	1.71353i	−0.717946	−	0.261311i	−0.0428922	−	0.999080i	$-0.513657\pi$
$43$	−4.70788	−	1.71353i	−0.717946	−	0.261311i	−0.675053	+	0.737769i	$0.735879\pi$
$44$	2.91965	−	1.68566i	0.440153	−	0.254123i
$45$	1.10257	−	4.05390i	0.164361	−	0.604320i
$46$	2.02552	−	3.50830i	0.298646	−	0.517271i
$47$	8.38019	+	3.05014i	1.22238	+	0.444909i	0.870980	−	0.491318i	$-0.163485\pi$
$47$	8.38019	+	3.05014i	1.22238	+	0.444909i	0.351397	+	0.936227i	$0.385707\pi$
$48$	−2.84115	−	3.71708i	−0.410084	−	0.536514i
$49$	4.64000	+	5.24122i	0.662858	+	0.748745i
$50$	−3.64551	−	0.642802i	−0.515553	−	0.0909060i
$51$	0.0992877	−	2.18015i	0.0139031	−	0.305282i
$52$	0.191647	−	0.526545i	0.0265766	−	0.0730186i
$53$	7.98523	−	4.61027i	1.09686	−	0.633270i	0.161462	−	0.986879i	$-0.448379\pi$
$53$	7.98523	−	4.61027i	1.09686	−	0.633270i	0.935393	+	0.353609i	$0.115046\pi$
$54$	0.240477	+	6.32495i	0.0327248	+	0.860716i
$55$		−	9.14610i		−	1.23326i
$56$	8.06834	−	0.813732i	1.07818	−	0.108740i
$57$	5.63692	+	0.256715i	0.746628	+	0.0340027i
$58$	−2.84012	−	2.38314i	−0.372926	−	0.312922i
$59$	0.516276	+	0.433207i	0.0672134	+	0.0563987i	0.675775	−	0.737108i	$-0.263809\pi$
$59$	0.516276	+	0.433207i	0.0672134	+	0.0563987i	−0.608562	+	0.793506i	$0.708253\pi$
$60$	1.24164	−	0.161095i	0.160295	−	0.0207972i
$61$	−2.39061	+	6.56816i	−0.306087	+	0.840966i	0.687323	+	0.726352i	$0.258786\pi$
$61$	−2.39061	+	6.56816i	−0.306087	+	0.840966i	−0.993410	+	0.114615i	$0.963437\pi$
$62$	−2.03235	−	3.52013i	−0.258108	−	0.447056i
$63$	−6.91123	−	3.90318i	−0.870734	−	0.491755i
$64$	4.43070	−	7.67421i	0.553838	−	0.959276i
$65$	−0.977133	−	1.16450i	−0.121198	−	0.144439i
$66$	4.11894	+	13.1496i	0.507006	+	1.61861i
$67$	−1.92589	+	10.9222i	−0.235284	+	1.33436i	0.606729	+	0.794908i	$0.292481\pi$
$67$	−1.92589	+	10.9222i	−0.235284	+	1.33436i	−0.842014	+	0.539456i	$0.818630\pi$
$68$	0.611185	−	0.222453i	0.0741171	−	0.0269764i
$69$	−4.23956	−	3.89950i	−0.510383	−	0.469445i
$70$	1.85301	−	4.11527i	0.221477	−	0.491869i
$71$	1.73180	+	0.999853i	0.205526	+	0.118661i	0.599231	−	0.800576i	$-0.295473\pi$
$71$	1.73180	+	0.999853i	0.205526	+	0.118661i	−0.393704	+	0.919237i	$0.628807\pi$
$72$	−8.34807	+	3.85468i	−0.983830	+	0.454279i
$73$	−12.1033	−	6.98783i	−1.41658	−	0.817864i	−0.420585	−	0.907253i	$-0.638175\pi$
$73$	−12.1033	−	6.98783i	−1.41658	−	0.817864i	−0.995997	+	0.0893890i	$0.971509\pi$
$74$	−4.59538	−	5.47656i	−0.534202	−	0.636637i
$75$	−2.02340	+	4.85910i	−0.233642	+	0.561081i
$76$	0.575167	+	1.58026i	0.0659762	+	0.181268i
$77$	−16.7487	−	4.25080i	−1.90869	−	0.484424i
$78$	1.92928	+	1.23419i	0.218448	+	0.139744i
$79$	1.78424	+	10.1189i	0.200743	+	1.13847i	0.904000	+	0.427532i	$0.140617\pi$
$79$	1.78424	+	10.1189i	0.200743	+	1.13847i	−0.703258	+	0.710935i	$0.748272\pi$
$80$	−1.89134	−	3.27589i	−0.211458	−	0.366256i
$81$	8.85129	+	1.62934i	0.983476	+	0.181037i
$82$	−1.43764	−	0.830022i	−0.158761	−	0.0916606i
$83$	−7.80237	+	6.54697i	−0.856422	+	0.718623i	−0.961194	−	0.275873i	$-0.911033\pi$
$83$	−7.80237	+	6.54697i	−0.856422	+	0.718623i	0.104772	+	0.994496i	$0.466589\pi$
$84$	0.282070	−	2.34861i	0.0307763	−	0.256255i
$85$	0.306404	−	1.73770i	0.0332341	−	0.188480i
$86$	6.01008	+	1.05974i	0.648084	+	0.114275i
$87$	−4.18838	+	3.20138i	−0.449041	+	0.343224i
$88$	−15.3347	+	12.8673i	−1.63468	+	1.37166i
$89$	15.8461			1.67968			0.839842	−	0.542831i	$-0.182648\pi$
$89$	15.8461			1.67968			0.839842	+	0.542831i	$0.182648\pi$
$90$	−0.465155	+	5.09632i	−0.0490317	+	0.537199i
$91$	−2.58662	+	1.24814i	−0.271152	+	0.130841i
$92$	0.587139	−	1.61315i	0.0612134	−	0.168183i
$93$	−5.51537	+	1.72762i	−0.571918	+	0.179145i
$94$	−10.6981	−	1.88637i	−1.10343	−	0.194564i
$95$	4.49294	+	0.792227i	0.460966	+	0.0812807i
$96$	−3.62006	−	3.32970i	−0.369471	−	0.339836i
$97$	6.09610	−	16.7489i	0.618965	−	1.70059i	−0.0905410	−	0.995893i	$-0.528860\pi$
$97$	6.09610	−	16.7489i	0.618965	−	1.70059i	0.709506	−	0.704699i	$-0.248918\pi$
$98$	−6.67484	−	5.30595i	−0.674261	−	0.535982i
$99$	19.5251	−	1.63439i	1.96234	−	0.164262i
$100$	−1.56866			−0.156866
$101$	3.07014	−	2.57616i	0.305491	−	0.256337i	−0.477135	−	0.878830i	$-0.658325\pi$
$101$	3.07014	−	2.57616i	0.305491	−	0.256337i	0.782625	+	0.622493i	$0.213880\pi$
$102$	0.342047	+	2.63633i	0.0338677	+	0.261036i
$103$	−17.2239	−	3.03704i	−1.69712	−	0.299248i	−0.760434	−	0.649416i	$-0.775014\pi$
$103$	−17.2239	−	3.03704i	−1.69712	−	0.299248i	−0.936687	+	0.350167i	$0.886125\pi$
$104$	−0.577751	+	3.27659i	−0.0566531	+	0.321296i
$105$	−5.13535	−	3.84851i	−0.501159	−	0.375576i
$106$	−8.60398	+	7.21960i	−0.835692	+	0.701229i
$107$	5.14655	+	2.97136i	0.497535	+	0.287252i	0.727695	−	0.685901i	$-0.240592\pi$
$107$	5.14655	+	2.97136i	0.497535	+	0.287252i	−0.230160	+	0.973153i	$0.573925\pi$
$108$	0.565783	+	2.62186i	0.0544425	+	0.252289i
$109$	2.39857	+	4.15445i	0.229742	+	0.397924i	0.957731	−	0.287664i	$-0.0928786\pi$
$109$	2.39857	+	4.15445i	0.229742	+	0.397924i	−0.727990	+	0.685588i	$0.759545\pi$
$110$	1.93462	+	10.9718i	0.184459	+	1.04612i
$111$	−9.02564	+	4.67694i	−0.856675	+	0.443915i
$112$	−6.87797	+	1.94097i	−0.649907	+	0.183404i
$113$	3.57929	+	9.83401i	0.336711	+	0.925106i	0.986321	+	0.164838i	$0.0527101\pi$
$113$	3.57929	+	9.83401i	0.336711	+	0.925106i	−0.649610	+	0.760268i	$0.725068\pi$
$114$	−6.81640	+	0.884383i	−0.638415	+	0.0828301i
$115$	−2.99360	−	3.56763i	−0.279154	−	0.332683i
$116$	−1.36062	−	0.785553i	−0.126330	−	0.0729368i
$117$	2.31136	−	2.29407i	0.213686	−	0.212087i
$118$	−0.710964	−	0.410475i	−0.0654495	−	0.0377873i
$119$	−3.03974	−	1.36872i	−0.278653	−	0.125471i
$120$	−7.09443	+	2.22223i	−0.647630	+	0.202861i
$121$	29.7465	−	10.8268i	2.70423	−	0.984258i
$122$	1.47848	−	8.38490i	0.133856	−	0.759133i
$123$	−1.59795	+	1.73730i	−0.144082	+	0.156647i
$124$	−1.10718	−	1.31948i	−0.0994276	−	0.118493i
$125$	−5.62880	+	9.74936i	−0.503455	+	0.872010i
$126$	9.11640	+	3.22041i	0.812154	+	0.286897i
$127$	0.960162	+	1.66305i	0.0852006	+	0.147572i	0.905477	−	0.424396i	$-0.139514\pi$
$127$	0.960162	+	1.66305i	0.0852006	+	0.147572i	−0.820276	+	0.571968i	$0.806180\pi$
$128$	−1.74937	+	4.80636i	−0.154624	+	0.424826i
$129$	3.33582	−	8.01083i	0.293703	−	0.705314i
$130$	1.41850	+	1.19026i	0.124411	+	0.104393i
$131$	−8.86037	−	7.43473i	−0.774134	−	0.649576i	0.167630	−	0.985850i	$-0.446389\pi$
$131$	−8.86037	−	7.43473i	−0.774134	−	0.649576i	−0.941764	+	0.336274i	$0.890833\pi$
$132$	2.68656	+	5.18457i	0.233835	+	0.451259i
$133$	3.53893	−	7.85945i	0.306864	−	0.681501i
$134$		−	13.5098i		−	1.16707i
$135$	6.92741	+	2.22717i	0.596217	+	0.191684i
$136$	−3.34456	+	1.93098i	−0.286793	+	0.165580i
$137$	3.03544	−	8.33979i	0.259335	−	0.712517i	−0.739874	−	0.672746i	$-0.765115\pi$
$137$	3.03544	−	8.33979i	0.259335	−	0.712517i	0.999209	−	0.0397712i	$-0.0126629\pi$
$138$	5.91065	+	3.78112i	0.503148	+	0.321870i
$139$	3.10686	+	0.547823i	0.263520	+	0.0464657i	0.303847	−	0.952721i	$-0.401729\pi$
$139$	3.10686	+	0.547823i	0.263520	+	0.0464657i	−0.0403269	+	0.999187i	$0.512840\pi$
$140$	0.470482	−	1.85376i	0.0397630	−	0.156671i
$141$	−5.93788	+	14.2595i	−0.500060	+	1.20087i
$142$	−2.28897	−	0.833118i	−0.192086	−	0.0699137i
$143$	3.54483	−	6.13983i	0.296434	−	0.513438i
$144$	6.65539	−	4.62301i	0.554615	−	0.385251i
$145$	−3.69125	+	2.13114i	−0.306541	+	0.176982i
$146$	15.9973	+	5.82255i	1.32395	+	0.481877i
$147$	−9.43428	+	7.61540i	−0.778127	+	0.628108i
$148$	−2.32076	−	1.94735i	−0.190765	−	0.160071i
$149$	−5.54853	−	15.2445i	−0.454553	−	1.24887i	−0.929488	−	0.368853i	$-0.879750\pi$
$149$	−5.54853	−	15.2445i	−0.454553	−	1.24887i	0.474934	−	0.880021i	$-0.342472\pi$
$150$	1.39948	−	6.25702i	0.114267	−	0.510884i
$151$	−1.49133	−	8.45773i	−0.121362	−	0.688280i	−0.983402	−	0.181440i	$-0.941924\pi$
$151$	−1.49133	−	8.45773i	−0.121362	−	0.688280i	0.862040	−	0.506841i	$-0.169187\pi$
$152$	−4.99268	−	8.64757i	−0.404960	−	0.701411i
$153$	3.76439	+	0.343587i	0.304333	+	0.0277773i
$154$	20.9911	+	1.55656i	1.69151	+	0.125431i
$155$	−4.60191	+	0.811442i	−0.369635	+	0.0651766i
$156$	0.895956	+	0.373089i	0.0717339	+	0.0298710i
$157$	14.3459	−	17.0968i	1.14493	−	1.36447i	0.224070	−	0.974573i	$-0.428066\pi$
$157$	14.3459	−	17.0968i	1.14493	−	1.36447i	0.920858	−	0.389898i	$-0.127490\pi$
$158$	−4.28078	−	11.7614i	−0.340561	−	0.935683i
$159$	7.34773	+	14.1798i	0.582713	+	1.12453i
$160$	−2.55616	−	3.04632i	−0.202083	−	0.240833i
$161$	−7.92451	+	3.82388i	−0.624539	+	0.301364i
$162$	−10.9627	−	0.0823115i	−0.861314	−	0.00646701i
$163$	−3.71918	+	6.44181i	−0.291309	+	0.504561i	−0.974119	−	0.226034i	$-0.927424\pi$
$163$	−3.71918	+	6.44181i	−0.291309	+	0.504561i	0.682811	+	0.730595i	$0.260757\pi$
$164$	−0.661041	−	0.240599i	−0.0516186	−	0.0187876i
$165$	15.8251	+	0.720703i	1.23198	+	0.0561066i
$166$	7.97497	−	9.50420i	0.618978	−	0.737669i
$167$	19.7455	−	7.18677i	1.52795	−	0.556129i	0.564832	−	0.825206i	$-0.308941\pi$
$167$	19.7455	−	7.18677i	1.52795	−	0.556129i	0.963119	+	0.269077i	$0.0867187\pi$
$168$	0.772190	+	14.0244i	0.0595757	+	1.08201i
$169$	2.05281	+	11.6420i	0.157908	+	0.895542i
$170$			2.14938i			0.164850i
$171$	−0.888365	+	9.73309i	−0.0679350	+	0.744308i
$172$	2.58614			0.197191
$173$	1.97984	−	1.66128i	0.150524	−	0.126305i	−0.564416	−	0.825491i	$-0.690898\pi$
$173$	1.97984	−	1.66128i	0.150524	−	0.126305i	0.714940	+	0.699186i	$0.246454\pi$
$174$	4.34725	−	4.72635i	0.329564	−	0.358304i
$175$	5.76011	+	5.60947i	0.435423	+	0.424036i
$176$	11.3398	−	13.5143i	0.854770	−	1.01868i
$177$	−0.790242	+	0.859154i	−0.0593982	+	0.0645780i
$178$	−19.0091	+	3.35183i	−1.42480	+	0.251230i
$179$			6.63013i			0.495559i	0.968816	+	0.247779i	$0.0797008\pi$
$179$			6.63013i			0.495559i	−0.968816	+	0.247779i	$0.920299\pi$
$180$	0.180895	+	2.16105i	0.0134831	+	0.161075i
$181$	−5.39330	+	3.11382i	−0.400881	+	0.231449i	−0.686864	−	0.726786i	$-0.741013\pi$
$181$	−5.39330	+	3.11382i	−0.400881	+	0.231449i	0.285983	+	0.958235i	$0.407680\pi$
$182$	2.83893	−	2.04442i	0.210435	−	0.151542i
$183$	−11.1762	−	4.65394i	−0.826170	−	0.344029i
$184$	−1.77003	+	10.0383i	−0.130488	+	0.740035i
$185$	−7.72323	+	2.81103i	−0.567823	+	0.206671i
$186$	6.25087	−	3.23910i	0.458336	−	0.237502i
$187$	8.10428	−	1.42900i	0.592644	−	0.104499i
$188$	−4.60341			−0.335738
$189$	7.29811	−	11.6506i	0.530860	−	0.847460i
$190$	−5.55735			−0.403173
$191$	1.15411	−	0.203501i	0.0835084	−	0.0147248i	−0.131738	−	0.991285i	$-0.542056\pi$
$191$	1.15411	−	0.203501i	0.0835084	−	0.0147248i	0.215246	+	0.976560i	$0.430945\pi$
$192$	12.9292	+	8.27098i	0.933086	+	0.596906i
$193$	5.50708	−	2.00441i	0.396408	−	0.144281i	−0.136121	−	0.990692i	$-0.543464\pi$
$193$	5.50708	−	2.00441i	0.396408	−	0.144281i	0.532530	+	0.846411i	$0.321241\pi$
$194$	−3.77016	+	21.3816i	−0.270681	+	1.53511i
$195$	2.09188	−	1.59893i	0.149803	−	0.114502i
$196$	−3.17602	−	1.72313i	−0.226858	−	0.123081i
$197$	−10.6718	+	6.16136i	−0.760333	+	0.438979i	−0.829415	−	0.558632i	$-0.811326\pi$
$197$	−10.6718	+	6.16136i	−0.760333	+	0.438979i	0.0690821	+	0.997611i	$0.477993\pi$
$198$	−23.0768	+	6.09065i	−1.64000	+	0.432843i
$199$			4.92654i			0.349233i	0.984636	+	0.174617i	$0.0558686\pi$
$199$			4.92654i			0.349233i	−0.984636	+	0.174617i	$0.944131\pi$
$200$	9.17281	−	1.61741i	0.648616	−	0.114368i
$201$	−18.7465	−	4.19294i	−1.32228	−	0.295747i
$202$	−3.13806	+	3.73979i	−0.220793	+	0.263131i
$203$	2.18707	+	7.75004i	0.153502	+	0.543946i
$204$	0.336741	+	1.07504i	0.0235766	+	0.0752676i
$205$	−1.46195	+	1.22672i	−0.102107	+	0.0856780i
$206$	21.3044			1.48435
$207$	7.08121	−	7.02825i	0.492178	−	0.488497i
$208$		−	2.93216i		−	0.203309i
$209$	3.69478	+	20.9542i	0.255573	+	1.44943i
$210$	6.97447	+	3.53046i	0.481284	+	0.243625i
$211$	−12.9997	+	4.73151i	−0.894937	+	0.325730i	−0.748222	−	0.663448i	$-0.769092\pi$
$211$	−12.9997	+	4.73151i	−0.894937	+	0.325730i	−0.146715	+	0.989179i	$0.546870\pi$
$212$	−3.05940	+	3.64605i	−0.210120	+	0.250412i
$213$	−1.86647	+	2.91766i	−0.127888	+	0.199915i
$214$	−6.80236	−	2.47586i	−0.465000	−	0.169246i
$215$	3.50799	−	6.07602i	0.239243	−	0.414381i
$216$	−6.01177	−	14.7481i	−0.409049	−	1.00348i
$217$	−0.652871	+	8.80434i	−0.0443198	+	0.597678i
$218$	−3.75612	−	4.47636i	−0.254396	−	0.303178i
$219$	13.0445	−	20.3912i	0.881464	−	1.37791i
$220$	1.61473	+	4.43643i	0.108865	+	0.299104i
$221$	0.879186	−	1.04777i	0.0591404	−	0.0704808i
$222$	9.83796	−	7.51964i	0.660281	−	0.504685i
$223$	7.48235	−	1.31934i	0.501055	−	0.0883496i	0.0825923	−	0.996583i	$-0.473680\pi$
$223$	7.48235	−	1.31934i	0.501055	−	0.0883496i	0.418463	+	0.908234i	$0.362569\pi$
$224$	−6.76656	+	3.26513i	−0.452110	+	0.218160i
$225$	−8.24805	−	3.88389i	−0.549870	−	0.258926i
$226$	−6.37388	−	11.0399i	−0.423984	−	0.734362i
$227$	−2.67159	−	15.1514i	−0.177320	−	1.00563i	−0.935432	−	0.353507i	$-0.884989\pi$
$227$	−2.67159	−	15.1514i	−0.177320	−	1.00563i	0.758112	−	0.652124i	$-0.226122\pi$
$228$	−2.77958	+	0.870665i	−0.184082	+	0.0576612i
$229$	−6.65889	−	18.2952i	−0.440032	−	1.20898i	−0.939471	−	0.342629i	$-0.888683\pi$
$229$	−6.65889	−	18.2952i	−0.440032	−	1.20898i	0.499439	−	0.866349i	$-0.333540\pi$
$230$	4.34579	+	3.64655i	0.286553	+	0.240446i
$231$	8.67477	−	28.6446i	0.570758	−	1.88468i
$232$	8.76622	+	3.19064i	0.575531	+	0.209476i
$233$	5.56626	−	3.21368i	0.364658	−	0.210535i	−0.306464	−	0.951882i	$-0.599146\pi$
$233$	5.56626	−	3.21368i	0.364658	−	0.210535i	0.671122	+	0.741347i	$0.265813\pi$
$234$	−2.28748	+	3.24090i	−0.149538	+	0.211864i
$235$	−6.24434	+	10.8155i	−0.407336	+	0.705526i
$236$	−0.326908	−	0.118985i	−0.0212799	−	0.00774525i
$237$	−17.6489	+	2.28983i	−1.14642	+	0.148741i
$238$	3.93603	+	0.998959i	0.255135	+	0.0647529i
$239$	6.07613	+	1.07139i	0.393032	+	0.0693022i	0.366672	−	0.930350i	$-0.380497\pi$
$239$	6.07613	+	1.07139i	0.393032	+	0.0693022i	0.0263604	+	0.999653i	$0.491608\pi$
$240$	5.81717	−	3.01436i	0.375497	−	0.194576i
$241$	5.43413	−	14.9301i	0.350043	−	0.961735i	−0.632313	−	0.774713i	$-0.717894\pi$
$241$	5.43413	−	14.9301i	0.350043	−	0.961735i	0.982356	−	0.187022i	$-0.0598836\pi$
$242$	−33.3941	+	19.2801i	−2.14665	+	1.23937i
$243$	−3.51664	+	15.1866i	−0.225593	+	0.974222i
$244$		−	3.60802i		−	0.230980i
$245$	−8.35656	+	5.12456i	−0.533881	+	0.327396i
$246$	1.54944	−	2.42208i	0.0987884	−	0.154426i
$247$	2.70908	+	2.27319i	0.172375	+	0.144640i
$248$	7.83475	+	6.57414i	0.497507	+	0.417458i
$249$	−10.7131	−	14.0160i	−0.678917	−	0.888229i
$250$	4.69014	−	12.8861i	0.296631	−	0.814986i
$251$	−1.11938	−	1.93883i	−0.0706548	−	0.122378i	0.828534	−	0.559939i	$-0.189176\pi$
$251$	−1.11938	−	1.93883i	−0.0706548	−	0.122378i	−0.899188	+	0.437562i	$0.855842\pi$
$252$	4.04148	+	0.673122i	0.254589	+	0.0424027i
$253$	10.8601	−	18.8103i	0.682771	−	1.18259i
$254$	−1.50359	−	1.79191i	−0.0943439	−	0.112435i
$255$	2.98253	+	0.667086i	0.186773	+	0.0417746i
$256$	−1.99563	+	11.3178i	−0.124727	+	0.707361i
$257$	−2.72191	+	0.990695i	−0.169788	+	0.0617979i	−0.425516	−	0.904951i	$-0.639907\pi$
$257$	−2.72191	+	0.990695i	−0.169788	+	0.0617979i	0.255727	+	0.966749i	$0.417685\pi$
$258$	−2.30721	+	10.3155i	−0.143641	+	0.642214i
$259$	1.55817	+	15.4496i	0.0968197	+	0.959989i
$260$	0.679561	+	0.392345i	0.0421446	+	0.0243322i
$261$	−5.20917	−	7.49923i	−0.322440	−	0.464191i
$262$	12.2016	+	7.04460i	0.753818	+	0.435217i
$263$	−15.5785	−	18.5658i	−0.960614	−	1.14482i	−0.989398	−	0.145229i	$-0.953608\pi$
$263$	−15.5785	−	18.5658i	−0.960614	−	1.14482i	0.0287842	−	0.999586i	$-0.490836\pi$
$264$	−21.0554	−	27.5469i	−1.29587	−	1.69539i
$265$	4.41628	+	12.1336i	0.271290	+	0.745363i
$266$	−2.58287	+	10.1769i	−0.158366	+	0.623983i
$267$	−1.24866	+	27.4178i	−0.0764165	+	1.67794i
$268$	−0.994128	−	5.63798i	−0.0607260	−	0.344394i
$269$	8.17714	+	14.1632i	0.498569	+	0.863547i	0.999999	−	0.00165141i	$-0.000525660\pi$
$269$	8.17714	+	14.1632i	0.498569	+	0.863547i	−0.501429	+	0.865199i	$0.667192\pi$
$270$	−8.78129	−	1.20642i	−0.534413	−	0.0734206i
$271$	10.2571	+	5.92196i	0.623076	+	0.359733i	0.778066	−	0.628183i	$-0.216201\pi$
$271$	10.2571	+	5.92196i	0.623076	+	0.359733i	−0.154989	+	0.987916i	$0.549534\pi$
$272$	2.60723	−	2.18773i	0.158087	−	0.132650i
$273$	−1.95579	−	4.57387i	−0.118370	−	0.276823i
$274$	−1.87728	+	10.6466i	−0.113410	+	0.643183i
$275$	−19.5460	−	3.44649i	−1.17867	−	0.207831i
$276$	2.74490	+	1.14302i	0.165223	+	0.0688014i
$277$	1.76010	−	1.47690i	0.105754	−	0.0887385i	−0.588377	−	0.808587i	$-0.700233\pi$
$277$	1.76010	−	1.47690i	0.105754	−	0.0887385i	0.694132	+	0.719848i	$0.255789\pi$
$278$	−3.84289			−0.230481
$279$	−2.55461	−	9.67915i	−0.152941	−	0.579476i
$280$	−0.839788	+	11.3250i	−0.0501869	+	0.676800i
$281$	−9.16288	+	25.1748i	−0.546612	+	1.50180i	0.291645	+	0.956527i	$0.405798\pi$
$281$	−9.16288	+	25.1748i	−0.546612	+	1.50180i	−0.838256	+	0.545276i	$0.816425\pi$
$282$	4.10691	−	18.3619i	0.244563	−	1.09344i
$283$	−16.8040	−	2.96301i	−0.998897	−	0.176132i	−0.349789	−	0.936829i	$-0.613747\pi$
$283$	−16.8040	−	2.96301i	−0.998897	−	0.176132i	−0.649108	+	0.760696i	$0.724858\pi$
$284$	−1.01655	−	0.179245i	−0.0603212	−	0.0106363i
$285$	−1.72479	+	7.71152i	−0.102168	+	0.456791i
$286$	−2.95370	+	8.11522i	−0.174656	+	0.479863i
$287$	1.56696	+	3.24733i	0.0924947	+	0.191684i
$288$	6.04649	−	6.00126i	0.356293	−	0.353628i
$289$	−15.4124			−0.906610
$290$	3.97727	−	3.33733i	0.233553	−	0.195975i
$291$	28.4995	+	11.8676i	1.67067	+	0.695692i
$292$	7.10454	+	1.25272i	0.415761	+	0.0733100i
$293$	0.994906	−	5.64239i	0.0581230	−	0.329632i	−0.941857	−	0.336015i	$-0.890921\pi$
$293$	0.994906	−	5.64239i	0.0581230	−	0.329632i	0.999980	+	0.00638305i	$0.00203180\pi$
$294$	9.70663	−	11.1311i	0.566102	−	0.649178i
$295$	−0.722987	+	0.606658i	−0.0420939	+	0.0353210i
$296$	15.5786	+	8.99430i	0.905487	+	0.522783i
$297$	1.28936	+	33.9122i	0.0748160	+	1.96779i
$298$	9.88064	+	17.1138i	0.572370	+	0.991374i
$299$	−0.626881	−	3.55522i	−0.0362535	−	0.205604i
$300$	0.123609	−	2.71419i	0.00713657	−	0.156704i
$301$	−9.49625	−	9.24790i	−0.547355	−	0.533040i
$302$	3.57802	+	9.83053i	0.205892	+	0.565684i
$303$	4.21549	+	5.51514i	0.242174	+	0.316836i
$304$	5.65651	+	6.74117i	0.324423	+	0.386633i
$305$	−8.47689	−	4.89414i	−0.485385	−	0.280237i
$306$	−4.58848	+	0.384089i	−0.262306	+	0.0219569i
$307$	9.76278	+	5.63655i	0.557191	+	0.321695i	0.752017	−	0.659143i	$-0.229081\pi$
$307$	9.76278	+	5.63655i	0.557191	+	0.321695i	−0.194826	+	0.980838i	$0.562414\pi$
$308$	8.87464	−	0.895052i	0.505680	−	0.0510003i
$309$	6.61208	−	29.5625i	0.376148	−	1.68175i
$310$	5.34886	−	1.94683i	0.303795	−	0.110572i
$311$	4.30517	−	24.4158i	0.244124	−	1.38449i	−0.578395	−	0.815757i	$-0.696321\pi$
$311$	4.30517	−	24.4158i	0.244124	−	1.38449i	0.822519	−	0.568738i	$-0.192568\pi$
$312$	−5.62381	−	1.25785i	−0.318386	−	0.0712117i
$313$	11.6606	+	13.8966i	0.659096	+	0.785480i	0.987256	−	0.159142i	$-0.0508728\pi$
$313$	11.6606	+	13.8966i	0.659096	+	0.785480i	−0.328160	+	0.944622i	$0.606428\pi$
$314$	−13.5931	+	23.5440i	−0.767104	+	1.32866i
$315$	7.06357	−	8.58221i	0.397987	−	0.483553i
$316$	−2.65194	−	4.59330i	−0.149184	−	0.258393i
$317$	−1.13396	+	3.11552i	−0.0636893	+	0.174985i	−0.967455	−	0.253042i	$-0.918569\pi$
$317$	−1.13396	+	3.11552i	−0.0636893	+	0.174985i	0.903766	+	0.428027i	$0.140791\pi$
$318$	−11.8138	−	15.4560i	−0.662484	−	0.866729i
$319$	−15.2278	−	12.7776i	−0.852590	−	0.715408i
$320$	9.50616	+	7.97661i	0.531410	+	0.445906i
$321$	−5.54676	+	8.67071i	−0.309590	+	0.483952i
$322$	8.69748	−	6.26339i	0.484692	−	0.349045i
$323$			4.10493i			0.228405i
$324$	−4.58108	+	0.772350i	−0.254505	+	0.0429083i
$325$	−2.85685	+	1.64940i	−0.158469	+	0.0914923i
$326$	3.09897	−	8.51436i	0.171636	−	0.471567i
$327$	−7.37727	+	3.82278i	−0.407964	+	0.211400i
$328$	4.11353	+	0.725327i	0.227132	+	0.0400495i
$329$	16.9037	+	16.4616i	0.931928	+	0.907556i
$330$	−19.1364	+	2.48282i	−1.05343	+	0.136675i
$331$	−5.47613	−	1.99315i	−0.300995	−	0.109553i	0.187108	−	0.982339i	$-0.440089\pi$
$331$	−5.47613	−	1.99315i	−0.300995	−	0.109553i	−0.488103	+	0.872786i	$0.662311\pi$
$332$	2.62878	−	4.55318i	0.144273	−	0.249888i
$333$	−7.38109	−	15.9852i	−0.404482	−	0.875984i
$334$	−22.1667	+	12.7980i	−1.21291	+	0.700273i
$335$	−14.5947	−	5.31203i	−0.797392	−	0.290227i
$336$	−2.81640	−	12.0536i	−0.153647	−	0.657578i
$337$	−19.7317	−	16.5569i	−1.07485	−	0.901909i	−0.0793704	−	0.996845i	$-0.525291\pi$
$337$	−19.7317	−	16.5569i	−1.07485	−	0.901909i	−0.995483	+	0.0949358i	$0.969735\pi$
$338$	−4.92514	−	13.5317i	−0.267892	−	0.736028i
$339$	−17.2974	+	5.41818i	−0.939467	+	0.294275i
$340$	0.158163	+	0.896988i	0.00857761	+	0.0486460i
$341$	−10.8967	−	18.8737i	−0.590091	−	1.02207i
$342$	−0.993086	−	11.8638i	−0.0536999	−	0.641522i
$343$	5.50045	+	17.6846i	0.296996	+	0.954879i
$344$	−15.1225	+	2.66651i	−0.815352	+	0.143768i
$345$	6.40881	−	4.89856i	0.345039	−	0.263730i
$346$	−2.02363	+	2.41167i	−0.108791	+	0.129652i
$347$	4.20173	+	11.5442i	0.225561	+	0.619723i	0.999915	−	0.0130291i	$-0.00414741\pi$
$347$	4.20173	+	11.5442i	0.225561	+	0.619723i	−0.774354	+	0.632752i	$0.781925\pi$
$348$	1.46642	−	2.29232i	0.0786086	−	0.122881i
$349$	18.6013	+	22.1681i	0.995702	+	1.18663i	0.982413	+	0.186720i	$0.0597858\pi$
$349$	18.6013	+	22.1681i	0.995702	+	1.18663i	0.0132892	+	0.999912i	$0.495770\pi$
$350$	−8.09642	−	5.51078i	−0.432772	−	0.294563i
$351$	3.78721	+	4.18002i	0.202146	+	0.223113i
$352$	9.27322	−	16.0617i	0.494264	−	0.856091i
$353$	3.51751	+	1.28027i	0.187218	+	0.0681419i	0.433928	−	0.900948i	$-0.357127\pi$
$353$	3.51751	+	1.28027i	0.187218	+	0.0681419i	−0.246710	+	0.969089i	$0.579349\pi$
$354$	0.766251	−	1.19781i	0.0407258	−	0.0636626i
$355$	−1.80004	+	2.14520i	−0.0955361	+	0.113856i
$356$	−7.68635	+	2.79760i	−0.407376	+	0.148273i
$357$	2.60777	−	5.15169i	0.138018	−	0.272656i
$358$	−1.40243	−	7.95357i	−0.0741207	−	0.420359i
$359$			27.7719i			1.46574i	0.680366	+	0.732872i	$0.261821\pi$
$359$			27.7719i			1.46574i	−0.680366	+	0.732872i	$0.738179\pi$
$360$	−3.28600	−	12.4503i	−0.173187	−	0.656188i
$361$	8.38643			0.441391
$362$	5.81121	−	4.87619i	0.305431	−	0.256287i
$363$	16.3892	+	52.3222i	0.860211	+	2.74621i
$364$	1.03431	−	1.06209i	0.0542128	−	0.0556687i
$365$	12.5802	−	14.9925i	0.658479	−	0.784745i
$366$	14.3915	+	3.21888i	0.752258	+	0.168254i
$367$	−0.528883	+	0.0932564i	−0.0276075	+	0.00486795i	−0.187435	−	0.982277i	$-0.560017\pi$
$367$	−0.528883	+	0.0932564i	−0.0276075	+	0.00486795i	0.159827	+	0.987145i	$0.448906\pi$
$368$		−	8.98313i		−	0.468278i
$369$	−2.88005	−	2.90176i	−0.149930	−	0.151059i
$370$	8.67027	−	5.00578i	0.450746	−	0.260238i
$371$	24.2721	−	2.44797i	1.26015	−	0.127092i
$372$	2.37029	−	1.81173i	0.122894	−	0.0939339i
$373$	4.59769	−	26.0748i	0.238059	−	1.35010i	−0.598015	−	0.801485i	$-0.704044\pi$
$373$	4.59769	−	26.0748i	0.238059	−	1.35010i	0.836074	−	0.548616i	$-0.184845\pi$
$374$	−9.41972	+	3.42850i	−0.487082	+	0.177283i
$375$	−16.4254	−	10.5075i	−0.848202	−	0.542605i
$376$	26.9186	−	4.74647i	1.38822	−	0.244781i
$377$	−3.30394			−0.170161
$378$	−6.29050	+	15.5200i	−0.323549	+	0.798261i
$379$	2.24417			0.115275			0.0576375	−	0.998338i	$-0.481643\pi$
$379$	2.24417			0.115275			0.0576375	+	0.998338i	$0.481643\pi$
$380$	−2.31922	+	0.408941i	−0.118974	+	0.0209783i
$381$	−2.95316	+	1.53028i	−0.151295	+	0.0783986i
$382$	−1.34144	+	0.488243i	−0.0686338	+	0.0249807i
$383$	−0.800525	+	4.54000i	−0.0409049	+	0.231983i	−0.998406	−	0.0564478i	$-0.982023\pi$
$383$	−0.800525	+	4.54000i	−0.0409049	+	0.231983i	0.957501	+	0.288431i	$0.0931337\pi$
$384$	−8.17839	−	3.40560i	−0.417352	−	0.173791i
$385$	9.93520	−	22.0647i	0.506345	−	1.12452i
$386$	−6.18237	+	3.56939i	−0.314674	+	0.181677i
$387$	13.5979	+	6.40308i	0.691222	+	0.325487i
$388$			9.20051i			0.467085i
$389$	−21.7483	+	3.83480i	−1.10268	+	0.194432i	−0.695225	−	0.718793i	$-0.744695\pi$
$389$	−21.7483	+	3.83480i	−1.10268	+	0.194432i	−0.407456	+	0.913225i	$0.633584\pi$
$390$	−2.17123	+	2.36058i	−0.109945	+	0.119532i
$391$	2.69352	−	3.21001i	0.136217	−	0.162337i
$392$	20.3485	+	6.80135i	1.02776	+	0.343520i
$393$	13.5622	−	14.7449i	0.684122	−	0.743780i
$394$	11.4987	−	9.64857i	0.579297	−	0.486088i
$395$	−14.3890			−0.723990
$396$	−9.18233	+	4.23990i	−0.461430	+	0.213063i
$397$			32.2983i			1.62101i	0.585734	+	0.810503i	$0.300806\pi$
$397$			32.2983i			1.62101i	−0.585734	+	0.810503i	$0.699194\pi$
$398$	−1.04208	−	5.90993i	−0.0522348	−	0.296238i
$399$	13.3200	+	6.74257i	0.666835	+	0.337551i
$400$	−7.71356	+	2.80750i	−0.385678	+	0.140375i
$401$	−2.55228	+	3.04169i	−0.127455	+	0.151895i	−0.825998	−	0.563673i	$-0.809388\pi$
$401$	−2.55228	+	3.04169i	−0.127455	+	0.151895i	0.698543	+	0.715568i	$0.253832\pi$
$402$	23.3754	+	1.06456i	1.16586	+	0.0530953i
$403$	−3.40379	−	1.23888i	−0.169555	−	0.0617128i
$404$	−1.03439	+	1.79162i	−0.0514631	+	0.0891367i
$405$	−4.39945	+	11.8107i	−0.218610	+	0.586879i
$406$	−4.26294	−	8.83442i	−0.211566	−	0.438445i
$407$	−24.6388	−	29.3634i	−1.22130	−	1.45549i
$408$	−3.07755	−	5.93910i	−0.152361	−	0.294030i
$409$	5.76398	+	15.8364i	0.285011	+	0.783060i	0.996746	+	0.0806120i	$0.0256875\pi$
$409$	5.76398	+	15.8364i	0.285011	+	0.783060i	−0.711735	+	0.702448i	$0.752090\pi$
$410$	1.49429	−	1.78083i	0.0737978	−	0.0879488i
$411$	14.1908	+	5.90925i	0.699981	+	0.291482i
$412$	8.89085	−	1.56770i	0.438021	−	0.0772348i
$413$	0.774916	+	1.60592i	0.0381311	+	0.0790220i
$414$	−7.00806	+	9.92900i	−0.344427	+	0.487984i
$415$	−7.13167	−	12.3524i	−0.350080	−	0.606356i
$416$	−0.535280	−	3.03572i	−0.0262442	−	0.148839i
$417$	−1.19269	+	5.33249i	−0.0584063	+	0.261133i
$418$	−8.86460	−	24.3553i	−0.433582	−	1.19126i
$419$	3.67966	+	3.08760i	0.179763	+	0.150839i	0.728229	−	0.685334i	$-0.240344\pi$
$419$	3.67966	+	3.08760i	0.179763	+	0.150839i	−0.548466	+	0.836173i	$0.684788\pi$
$420$	3.17041	+	0.960130i	0.154700	+	0.0468495i
$421$	5.73851	+	2.08865i	0.279678	+	0.101794i	0.478051	−	0.878332i	$-0.341343\pi$
$421$	5.73851	+	2.08865i	0.279678	+	0.101794i	−0.198373	+	0.980127i	$0.563566\pi$
$422$	14.5938	−	8.42571i	0.710413	−	0.410157i
$423$	−24.2048	−	11.3977i	−1.17688	−	0.554175i
$424$	14.1306	−	24.4748i	0.686241	−	1.18860i
$425$	−3.59815	−	1.30962i	−0.174536	−	0.0635259i
$426$	1.62188	−	3.89486i	0.0785802	−	0.188707i
$427$	−12.9021	+	13.2486i	−0.624377	+	0.641145i
$428$	−3.02098	−	0.532681i	−0.146025	−	0.0257481i
$429$	10.3442	+	6.61728i	0.499420	+	0.319485i
$430$	−2.92300	+	8.03088i	−0.140960	+	0.387283i
$431$	5.79371	−	3.34500i	0.279073	−	0.161123i	−0.353931	−	0.935272i	$-0.615155\pi$
$431$	5.79371	−	3.34500i	0.279073	−	0.161123i	0.633004	+	0.774149i	$0.281822\pi$
$432$	7.47457	+	11.8798i	0.359620	+	0.571568i
$433$		−	26.0904i		−	1.25383i	−0.779089	−	0.626913i	$-0.784318\pi$
$433$		−	26.0904i		−	1.25383i	0.779089	−	0.626913i	$-0.215682\pi$
$434$	−1.07914	−	10.6999i	−0.0518002	−	0.513611i
$435$	−3.39656	−	6.55474i	−0.162852	−	0.314276i
$436$	−1.89692	−	1.59170i	−0.0908459	−	0.0762287i
$437$	8.29969	+	6.96427i	0.397028	+	0.333146i
$438$	−11.3351	+	27.2207i	−0.541611	+	1.30065i
$439$	10.5968	−	29.1143i	0.505755	−	1.38955i	−0.379822	−	0.925060i	$-0.624015\pi$
$439$	10.5968	−	29.1143i	0.505755	−	1.38955i	0.885577	−	0.464492i	$-0.153763\pi$
$440$	−14.0165	−	24.2772i	−0.668209	−	1.15737i
$441$	−12.4332	−	16.9238i	−0.592057	−	0.805896i
$442$	−0.833052	+	1.44289i	−0.0396242	+	0.0686312i
$443$	−14.0849	−	16.7857i	−0.669191	−	0.797511i	0.319482	−	0.947592i	$-0.396491\pi$
$443$	−14.0849	−	16.7857i	−0.669191	−	0.797511i	−0.988674	+	0.150081i	$0.952047\pi$
$444$	3.55229	−	3.86207i	0.168584	−	0.183286i
$445$	−3.85337	+	21.8536i	−0.182667	+	1.03596i
$446$	−8.69684	+	3.16539i	−0.411807	+	0.149886i
$447$	26.8141	−	8.39914i	1.26826	−	0.397265i
$448$	19.0252	−	13.7008i	0.898858	−	0.647302i
$449$	34.7658	+	20.0721i	1.64070	+	0.947259i	0.980585	+	0.196096i	$0.0628264\pi$
$449$	34.7658	+	20.0721i	1.64070	+	0.947259i	0.660116	+	0.751163i	$0.270507\pi$
$450$	10.7160	+	2.91450i	0.505156	+	0.137391i
$451$	−7.70813	−	4.45029i	−0.362962	−	0.209556i
$452$	−3.47235	−	4.13819i	−0.163326	−	0.194644i
$453$	14.7516	−	1.91392i	0.693089	−	0.0899237i
$454$	6.40975	+	17.6106i	0.300824	+	0.826508i
$455$	−1.09233	−	3.87076i	−0.0512092	−	0.181464i
$456$	15.3559	−	7.95720i	0.719108	−	0.372630i
$457$	4.01948	+	22.7956i	0.188023	+	1.06633i	0.922009	+	0.387169i	$0.126547\pi$
$457$	4.01948	+	22.7956i	0.188023	+	1.06633i	−0.733985	+	0.679165i	$0.762342\pi$
$458$	11.8579	+	20.5385i	0.554085	+	0.959703i
$459$	−0.891123	+	6.48630i	−0.0415941	+	0.302754i
$460$	2.08194	+	1.20201i	0.0970709	+	0.0560439i
$461$	19.1500	−	16.0688i	0.891905	−	0.748397i	−0.0766866	−	0.997055i	$-0.524434\pi$
$461$	19.1500	−	16.0688i	0.891905	−	0.748397i	0.968591	+	0.248658i	$0.0799896\pi$
$462$	−4.34732	+	36.1973i	−0.202256	+	1.68405i
$463$	−0.605828	+	3.43582i	−0.0281552	+	0.159676i	−0.995644	−	0.0932385i	$-0.970278\pi$
$463$	−0.605828	+	3.43582i	−0.0281552	+	0.159676i	0.967489	+	0.252915i	$0.0813892\pi$
$464$	−8.09647	−	1.42763i	−0.375869	−	0.0662759i
$465$	−1.04138	−	8.02644i	−0.0482927	−	0.372217i
$466$	−5.99758	+	5.03257i	−0.277832	+	0.233129i
$467$	15.1473			0.700932			0.350466	−	0.936575i	$-0.386023\pi$
$467$	15.1473			0.700932			0.350466	+	0.936575i	$0.386023\pi$
$468$	−0.716140	+	1.52084i	−0.0331036	+	0.0703007i
$469$	−16.5107	+	24.2575i	−0.762394	+	1.12011i
$470$	5.20304	−	14.2952i	0.239998	−	0.659390i
$471$	28.4514	+	26.1693i	1.31097	+	1.20582i
$472$	2.03429	+	0.358700i	0.0936356	+	0.0165105i
$473$	32.2240	+	5.68196i	1.48166	+	0.261257i
$474$	20.6875	−	6.48007i	0.950208	−	0.297640i
$475$	3.38611	−	9.30326i	0.155365	−	0.426863i
$476$	1.71611	+	0.127255i	0.0786578	+	0.00583274i
$477$	−25.1137	+	11.5961i	−1.14988	+	0.530950i
$478$	−7.51562			−0.343756
$479$	6.70132	−	5.62308i	0.306191	−	0.256925i	−0.476724	−	0.879053i	$-0.658176\pi$
$479$	6.70132	−	5.62308i	0.306191	−	0.256925i	0.782916	+	0.622128i	$0.213732\pi$
$480$	5.47234	−	4.18278i	0.249777	−	0.190917i
$481$	−6.27414	−	1.10630i	−0.286076	−	0.0504429i
$482$	−3.36076	+	19.0598i	−0.153078	+	0.868150i
$483$	−5.99185	−	14.0128i	−0.272639	−	0.637603i
$484$	−12.5174	+	10.5034i	−0.568975	+	0.477426i
$485$	21.6162	+	12.4801i	0.981541	+	0.566693i
$486$	1.00627	−	18.9619i	0.0456454	−	0.860128i
$487$	−12.1626	−	21.0663i	−0.551142	−	0.954606i	−0.998193	−	0.0600970i	$-0.980859\pi$
$487$	−12.1626	−	21.0663i	−0.551142	−	0.954606i	0.447051	−	0.894509i	$-0.352474\pi$
$488$	3.72015	+	21.0980i	0.168403	+	0.955063i
$489$	−10.8529	−	6.94275i	−0.490786	−	0.313962i
$490$	8.94065	−	7.91508i	0.403898	−	0.357567i
$491$	4.07946	+	11.2082i	0.184103	+	0.505820i	0.997070	−	0.0764897i	$-0.0243712\pi$
$491$	4.07946	+	11.2082i	0.184103	+	0.505820i	−0.812967	+	0.582310i	$0.802149\pi$
$492$	0.468388	−	1.12481i	0.0211165	−	0.0507104i
$493$	−2.46511	−	2.93781i	−0.111023	−	0.132312i
$494$	−3.73068	−	2.15391i	−0.167851	−	0.0969089i
$495$	−2.49400	+	27.3247i	−0.112097	+	1.22816i
$496$	−7.80584	−	4.50670i	−0.350493	−	0.202357i
$497$	3.09178	+	4.29332i	0.138685	+	0.192582i
$498$	15.8163	+	14.5477i	0.708745	+	0.651897i
$499$	−3.92338	+	1.42799i	−0.175634	+	0.0639257i	−0.428341	−	0.903617i	$-0.640902\pi$
$499$	−3.92338	+	1.42799i	−0.175634	+	0.0639257i	0.252706	+	0.967543i	$0.418679\pi$
$500$	1.00908	−	5.72280i	0.0451276	−	0.255932i
$501$	10.8790	+	34.7311i	0.486039	+	1.55167i
$502$	1.75293	+	2.08906i	0.0782371	+	0.0932394i
$503$	5.52280	−	9.56576i	0.246249	−	0.426516i	−0.716233	−	0.697861i	$-0.754135\pi$
$503$	5.52280	−	9.56576i	0.246249	−	0.426516i	0.962482	+	0.271345i	$0.0874685\pi$
$504$	−24.3267	+	0.230978i	−1.08360	+	0.0102886i
$505$	2.80623	+	4.86053i	0.124876	+	0.216291i
$506$	−9.04910	+	24.8622i	−0.402282	+	1.10526i
$507$	−20.3055	+	2.63450i	−0.901799	+	0.117002i
$508$	−0.759346	−	0.637167i	−0.0336906	−	0.0282697i
$509$	−19.5610	−	16.4136i	−0.867026	−	0.727521i	0.0964436	−	0.995338i	$-0.469253\pi$
$509$	−19.5610	−	16.4136i	−0.867026	−	0.727521i	−0.963470	+	0.267817i	$0.913698\pi$
$510$	−3.71897	−	0.169368i	−0.164679	−	0.00749976i
$511$	−21.6081	−	30.0054i	−0.955884	−	1.32736i
$512$		−	24.2287i		−	1.07077i
$513$	−16.7707	−	2.30406i	−0.740446	−	0.101727i
$514$	3.05568	−	1.76420i	0.134780	−	0.0778154i
$515$	8.37683	−	23.0152i	0.369127	−	1.01417i
$516$	−0.203785	+	4.47468i	−0.00897113	+	0.196987i
$517$	−57.3598	−	10.1141i	−2.52268	−	0.444817i
$518$	−5.13714	−	18.2039i	−0.225713	−	0.799832i
$519$	2.71843	+	3.55653i	0.119326	+	0.156114i
$520$	−4.37829	−	1.59357i	−0.192001	−	0.0698825i
$521$	−1.17194	+	2.02986i	−0.0513436	+	0.0889298i	−0.890555	−	0.454876i	$-0.849684\pi$
$521$	−1.17194	+	2.02986i	−0.0513436	+	0.0889298i	0.839211	+	0.543805i	$0.183017\pi$
$522$	7.83524	+	7.89429i	0.342939	+	0.345524i
$523$	−22.8023	+	13.1649i	−0.997075	+	0.575662i	−0.907382	−	0.420308i	$-0.861922\pi$
$523$	−22.8023	+	13.1649i	−0.997075	+	0.575662i	−0.0896937	+	0.995969i	$0.528589\pi$
$524$	5.61042	+	2.04203i	0.245092	+	0.0892063i
$525$	−10.1597	+	9.52445i	−0.443406	+	0.415681i
$526$	22.6153	+	18.9765i	0.986073	+	0.827414i
$527$	−1.43802	−	3.95094i	−0.0626413	−	0.172105i
$528$	22.4896	+	20.6857i	0.978733	+	0.900229i
$529$	2.07336	+	11.7586i	0.0901462	+	0.511244i
$530$	−7.86437	−	13.6215i	−0.341606	−	0.591679i
$531$	−1.42429	−	1.43502i	−0.0618088	−	0.0622746i
$532$	−0.329027	+	4.43712i	−0.0142651	+	0.192373i
$533$	−1.45687	+	0.256885i	−0.0631039	+	0.0111269i
$534$	−4.30162	−	33.1548i	−0.186149	−	1.43475i
$535$	−5.34935	+	6.37511i	−0.231273	+	0.275620i
$536$	11.6264	+	31.9432i	0.502183	+	1.37974i
$537$	−11.4718	−	0.522447i	−0.495046	−	0.0225452i
$538$	−12.8052	−	15.2607i	−0.552073	−	0.657935i
$539$	−35.7882	−	28.4487i	−1.54151	−	1.22537i
$540$	−3.75343	+	0.142707i	−0.161522	+	0.00614113i
$541$	−7.55773	+	13.0904i	−0.324932	+	0.562799i	−0.981499	−	0.191469i	$-0.938675\pi$
$541$	−7.55773	+	13.0904i	−0.324932	+	0.562799i	0.656566	+	0.754268i	$0.272008\pi$
$542$	−13.5572	−	4.93442i	−0.582332	−	0.211951i
$543$	−4.96273	−	9.57716i	−0.212971	−	0.410995i
$544$	2.29994	−	2.74096i	0.0986090	−	0.117518i
$545$	−6.31272	+	2.29764i	−0.270407	+	0.0984203i
$546$	3.31366	+	5.07317i	0.141812	+	0.217112i
$547$	−0.705768	−	4.00261i	−0.0301764	−	0.171139i	0.965995	−	0.258561i	$-0.0832483\pi$
$547$	−0.705768	−	4.00261i	−0.0301764	−	0.171139i	−0.996171	+	0.0874219i	$0.972137\pi$
$548$			4.58122i			0.195700i
$549$	8.93319	−	18.9710i	0.381259	−	0.809663i
$550$	24.1766			1.03089
$551$	7.59589	−	6.37371i	0.323596	−	0.271529i
$552$	−17.2294	−	3.85361i	−0.733333	−	0.164021i
$553$	−6.68753	+	26.3497i	−0.284383	+	1.12051i
$554$	−1.79904	+	2.14401i	−0.0764339	+	0.0910904i
$555$	−4.25522	−	13.5847i	−0.180624	−	0.576638i
$556$	−1.60374	+	0.282782i	−0.0680135	+	0.0119926i
$557$		−	11.4174i		−	0.483772i	−0.970305	−	0.241886i	$-0.922234\pi$
$557$		−	11.4174i		−	0.483772i	0.970305	−	0.241886i	$-0.0777660\pi$
$558$	5.11191	+	11.0709i	0.216405	+	0.468666i
$559$	4.70986	−	2.71924i	0.199206	−	0.115012i
$560$	−1.00426	−	9.95749i	−0.0424379	−	0.420781i
$561$	1.83394	+	14.1351i	0.0774288	+	0.596785i
$562$	5.66682	−	32.1381i	0.239040	−	1.35567i
$563$	30.9865	−	11.2782i	1.30592	−	0.475318i	0.407003	−	0.913427i	$-0.366574\pi$
$563$	30.9865	−	11.2782i	1.30592	−	0.475318i	0.898922	+	0.438109i	$0.144352\pi$
$564$	0.362744	−	7.96509i	0.0152743	−	0.335391i
$565$	−14.4326	+	2.54486i	−0.607184	+	0.107063i
$566$	20.7850			0.873661
$567$	19.5835	+	13.5457i	0.822431	+	0.568865i
$568$	6.12913			0.257172
$569$	−30.8899	+	5.44673i	−1.29497	+	0.228339i	−0.778326	−	0.627860i	$-0.783931\pi$
$569$	−30.8899	+	5.44673i	−1.29497	+	0.228339i	−0.516647	+	0.856199i	$0.672820\pi$
$570$	0.437913	−	9.61565i	0.0183422	−	0.402755i
$571$	13.2797	−	4.83342i	0.555739	−	0.202272i	−0.0488555	−	0.998806i	$-0.515557\pi$
$571$	13.2797	−	4.83342i	0.555739	−	0.202272i	0.604595	+	0.796533i	$0.293335\pi$
$572$	−0.635488	+	3.60403i	−0.0265711	+	0.150692i
$573$	0.261166	+	2.01294i	0.0109104	+	0.0840918i
$574$	−2.56663	−	3.56408i	−0.107129	−	0.148762i
$575$	−8.75238	+	5.05319i	−0.365000	+	0.210733i
$576$	−15.3297	+	21.7191i	−0.638739	+	0.904964i
$577$		−	16.4989i		−	0.686860i	−0.939178	−	0.343430i	$-0.888411\pi$
$577$		−	16.4989i		−	0.686860i	0.939178	−	0.343430i	$-0.111589\pi$
$578$	18.4888	−	3.26008i	0.769034	−	0.135601i
$579$	3.03420	+	9.68661i	0.126097	+	0.402562i
$580$	1.41423	−	1.68542i	0.0587229	−	0.0699832i
$581$	−25.9348	+	7.31881i	−1.07596	+	0.303636i
$582$	−36.6986	−	8.20819i	−1.52121	−	0.340240i
$583$	−46.1316	+	38.7090i	−1.91058	+	1.60316i
$584$	−42.8356			−1.77255
$585$	2.60172	+	3.74549i	0.107568	+	0.154857i
$586$			6.97912i			0.288305i
$587$	−2.18078	−	12.3678i	−0.0900102	−	0.510473i	−0.996163	−	0.0875220i	$-0.972105\pi$
$587$	−2.18078	−	12.3678i	−0.0900102	−	0.510473i	0.906152	−	0.422951i	$-0.139006\pi$
$588$	3.23173	−	5.35955i	0.133274	−	0.221024i
$589$	10.2154	−	3.71810i	0.420918	−	0.153202i
$590$	0.738980	−	0.880682i	0.0304233	−	0.0362571i
$591$	−9.81981	−	18.9504i	−0.403933	−	0.779517i
$592$	−14.8971	−	5.42209i	−0.612266	−	0.222847i
$593$	0.438896	−	0.760190i	0.0180233	−	0.0312173i	−0.856873	−	0.515527i	$-0.827596\pi$
$593$	0.438896	−	0.760190i	0.0180233	−	0.0312173i	0.874896	+	0.484310i	$0.160929\pi$
$594$	−8.71996	−	40.4087i	−0.357784	−	1.65799i
$595$	2.62681	−	3.85931i	0.107689	−	0.158216i
$596$	5.38276	+	6.41493i	0.220487	+	0.262766i
$597$	−8.52419	−	0.388206i	−0.348872	−	0.0158882i
$598$	1.50403	+	4.13228i	0.0615042	+	0.168981i
$599$	11.1914	−	13.3374i	0.457267	−	0.544949i	−0.487315	−	0.873226i	$-0.662024\pi$
$599$	11.1914	−	13.3374i	0.457267	−	0.544949i	0.944581	+	0.328277i	$0.106468\pi$
$600$	2.07574	+	15.9988i	0.0847416	+	0.653147i
$601$	−4.00786	+	0.706693i	−0.163484	+	0.0288266i	−0.254791	−	0.966996i	$-0.582007\pi$
$601$	−4.00786	+	0.706693i	−0.163484	+	0.0288266i	0.0913070	+	0.995823i	$0.470896\pi$
$602$	13.3480	+	9.08520i	0.544022	+	0.370285i
$603$	8.73207	−	32.1059i	0.355597	−	1.30745i
$604$	2.21658	+	3.83924i	0.0901915	+	0.156216i
$605$	7.69783	+	43.6566i	0.312961	+	1.77489i
$606$	−6.22353	−	5.72434i	−0.252814	−	0.232535i
$607$	−10.9299	−	30.0296i	−0.443630	−	1.21886i	−0.937088	−	0.349094i	$-0.886490\pi$
$607$	−10.9299	−	30.0296i	−0.443630	−	1.21886i	0.493458	−	0.869770i	$-0.335733\pi$
$608$	7.08692	+	5.94663i	0.287413	+	0.241168i
$609$	−13.5819	+	3.17349i	−0.550367	+	0.128596i
$610$	11.2042	+	4.07799i	0.453645	+	0.165113i
$611$	−8.38372	+	4.84034i	−0.339169	+	0.195819i
$612$	−1.88663	+	0.497936i	−0.0762623	+	0.0201279i
$613$	6.60506	−	11.4403i	0.266776	−	0.462069i	−0.701252	−	0.712914i	$-0.747375\pi$
$613$	6.60506	−	11.4403i	0.266776	−	0.462069i	0.968027	+	0.250845i	$0.0807084\pi$
$614$	−12.9038	−	4.69660i	−0.520755	−	0.189539i
$615$	−2.00735	−	2.62622i	−0.0809440	−	0.105899i
$616$	−50.9719	+	14.3843i	−2.05372	+	0.579559i
$617$	19.4342	+	3.42678i	0.782393	+	0.137957i	0.550557	−	0.834798i	$-0.314415\pi$
$617$	19.4342	+	3.42678i	0.782393	+	0.137957i	0.231837	+	0.972755i	$0.425527\pi$
$618$	−1.67876	+	36.8620i	−0.0675297	+	1.48281i
$619$	−5.18243	+	14.2386i	−0.208299	+	0.572298i	−0.999215	−	0.0396279i	$-0.987383\pi$
$619$	−5.18243	+	14.2386i	−0.208299	+	0.572298i	0.790915	+	0.611926i	$0.209605\pi$
$620$	2.08896	−	1.20606i	0.0838945	−	0.0484365i
$621$	11.6027	+	12.8061i	0.465600	+	0.513893i
$622$			30.2001i			1.21092i
$623$	38.2282	+	17.2133i	1.53158	+	0.689635i
$624$	5.07340	+	0.231051i	0.203098	+	0.00924945i
$625$	−0.436975	−	0.366666i	−0.0174790	−	0.0146666i
$626$	−16.9276	−	14.2040i	−0.676564	−	0.567705i
$627$	−36.5472	+	4.74176i	−1.45956	+	0.189368i
$628$	−3.94025	+	10.8257i	−0.157233	+	0.431994i
$629$	−3.69752	−	6.40429i	−0.147430	−	0.255356i
$630$	−6.65819	+	11.7894i	−0.265269	+	0.469702i
$631$	−7.62600	+	13.2086i	−0.303586	+	0.525827i	−0.976946	−	0.213489i	$-0.931517\pi$
$631$	−7.62600	+	13.2086i	−0.303586	+	0.525827i	0.673359	+	0.739315i	$0.264851\pi$
$632$	20.2434	+	24.1251i	0.805238	+	0.959645i
$633$	−7.16236	−	22.8657i	−0.284678	−	0.908829i
$634$	0.701300	−	3.97727i	0.0278522	−	0.157958i
$635$	−2.52702	+	0.919760i	−0.100282	+	0.0364995i
$636$	−6.06752	−	5.58085i	−0.240593	−	0.221295i
$637$	−7.59597	+	0.201320i	−0.300963	+	0.00797657i
$638$	20.9701	+	12.1071i	0.830216	+	0.479325i
$639$	−4.90124	−	3.45938i	−0.193890	−	0.136851i
$640$	−6.20311	−	3.58137i	−0.245199	−	0.141566i
$641$	1.47670	+	1.75987i	0.0583263	+	0.0695106i	0.794419	−	0.607370i	$-0.207776\pi$
$641$	1.47670	+	1.75987i	0.0583263	+	0.0695106i	−0.736092	+	0.676881i	$0.763331\pi$
$642$	4.81989	−	11.5747i	0.190226	−	0.456819i
$643$	3.12733	+	8.59228i	0.123330	+	0.338846i	0.985958	−	0.166992i	$-0.0534054\pi$
$643$	3.12733	+	8.59228i	0.123330	+	0.338846i	−0.862628	+	0.505838i	$0.831183\pi$
$644$	3.16878	−	3.25388i	0.124867	−	0.128221i
$645$	10.2366	+	6.54851i	0.403068	+	0.257847i
$646$	−0.868291	−	4.92432i	−0.0341624	−	0.193745i
$647$	−3.30310	−	5.72115i	−0.129858	−	0.224921i	0.793763	−	0.608227i	$-0.208119\pi$
$647$	−3.30310	−	5.72115i	−0.129858	−	0.224921i	−0.923622	+	0.383306i	$0.874786\pi$
$648$	25.9917	−	9.23979i	1.02105	−	0.362973i
$649$	−3.81194	−	2.20083i	−0.149632	−	0.0863900i
$650$	3.07821	−	2.58293i	0.120738	−	0.101311i
$651$	−15.1823	−	1.82341i	−0.595043	−	0.0714650i
$652$	0.666744	−	3.78129i	0.0261117	−	0.148087i
$653$	3.17671	+	0.560140i	0.124314	+	0.0219200i	0.235459	−	0.971884i	$-0.424341\pi$
$653$	3.17671	+	0.560140i	0.124314	+	0.0219200i	−0.111145	+	0.993804i	$0.535452\pi$
$654$	8.04124	−	6.14632i	0.314437	−	0.240340i
$655$	12.4080	−	10.4115i	0.484819	−	0.406811i
$656$	−3.68113			−0.143724
$657$	34.2541	+	24.1771i	1.33638	+	0.943239i
$658$	−23.7598	−	16.1720i	−0.926254	−	0.630449i
$659$	7.87606	−	21.6393i	0.306808	−	0.842948i	−0.686466	−	0.727162i	$-0.740839\pi$
$659$	7.87606	−	21.6393i	0.306808	−	0.842948i	0.993274	−	0.115786i	$-0.0369387\pi$
$660$	−7.80340	+	2.44431i	−0.303747	+	0.0951446i
$661$	37.0781	+	6.53786i	1.44217	+	0.254293i	0.839353	−	0.543586i	$-0.182934\pi$
$661$	37.0781	+	6.53786i	1.44217	+	0.254293i	0.602816	+	0.797880i	$0.294045\pi$
$662$	6.99082	+	1.23267i	0.271706	+	0.0479091i
$663$	1.74364	+	1.60378i	0.0677173	+	0.0622857i
$664$	−10.6772	+	29.3353i	−0.414355	+	1.13843i
$665$	9.97850	+	6.79180i	0.386949	+	0.263375i
$666$	12.2357	+	17.6147i	0.474123	+	0.682558i
$667$	−10.1221			−0.391930
$668$	−8.30898	+	6.97206i	−0.321484	+	0.269757i
$669$	1.69320	+	13.0504i	0.0654628	+	0.504556i
$670$	18.6315	+	3.28524i	0.719799	+	0.126920i
$671$	7.92713	−	44.9570i	0.306023	−	1.73554i
$672$	−5.11631	−	11.9652i	−0.197366	−	0.461567i
$673$	−3.99428	+	3.35160i	−0.153968	+	0.129195i	−0.716518	−	0.697569i	$-0.754265\pi$
$673$	−3.99428	+	3.35160i	−0.153968	+	0.129195i	0.562549	+	0.826764i	$0.309821\pi$
$674$	27.1725	+	15.6881i	1.04665	+	0.604281i
$675$	7.37007	−	13.9652i	0.283674	−	0.537521i
$676$	−3.05112	−	5.28470i	−0.117351	−	0.203258i
$677$	0.768000	+	4.35554i	0.0295166	+	0.167397i	0.996003	−	0.0893213i	$-0.0284698\pi$
$677$	0.768000	+	4.35554i	0.0295166	+	0.167397i	−0.966486	+	0.256718i	$0.917359\pi$
$678$	19.6041	−	10.1585i	0.752890	−	0.390136i
$679$	32.9006	−	33.7841i	1.26261	−	1.29652i
$680$	−1.84973	−	5.08209i	−0.0709339	−	0.194889i
$681$	26.4263	−	3.42864i	1.01266	−	0.131386i
$682$	17.0641	+	20.3362i	0.653417	+	0.778712i
$683$	42.6121	+	24.6021i	1.63051	+	0.941373i	0.983937	+	0.178517i	$0.0571301\pi$
$683$	42.6121	+	24.6021i	1.63051	+	0.941373i	0.646569	+	0.762856i	$0.276203\pi$
$684$	−1.28745	−	4.87799i	−0.0492268	−	0.186515i
$685$	10.7634	+	6.21424i	0.411247	+	0.237434i
$686$	−10.3391	−	20.0512i	−0.394749	−	0.765557i
$687$	32.1800	−	10.0800i	1.22775	−	0.384574i
$688$	12.7168	−	4.62852i	0.484822	−	0.176461i
$689$	−1.73806	+	9.85702i	−0.0662148	+	0.375523i
$690$	−6.65191	+	7.23198i	−0.253234	+	0.275317i
$691$	16.4941	+	19.6569i	0.627466	+	0.747785i	0.982335	−	0.187131i	$-0.0599189\pi$
$691$	16.4941	+	19.6569i	0.627466	+	0.747785i	−0.354869	+	0.934916i	$0.615474\pi$
$692$	−0.667048	+	1.15536i	−0.0253573	+	0.0439202i
$693$	48.8790	+	17.2667i	1.85676	+	0.655909i
$694$	−7.48230	−	12.9597i	−0.284024	−	0.491945i
$695$	−1.51102	+	4.15149i	−0.0573162	+	0.157475i
$696$	−6.21140	+	14.9164i	−0.235443	+	0.565405i
$697$	−1.31541	−	1.10376i	−0.0498246	−	0.0418078i
$698$	−27.0033	−	22.6585i	−1.02209	−	0.857637i
$699$	5.12188	+	9.88430i	0.193727	+	0.373859i
$700$	−3.78435	−	1.70400i	−0.143035	−	0.0644053i
$701$			7.17348i			0.270939i	0.990782	+	0.135469i	$0.0432542\pi$
$701$			7.17348i			0.270939i	−0.990782	+	0.135469i	$0.956746\pi$
$702$	−5.42735	−	4.21332i	−0.204842	−	0.159021i
$703$	16.5587	−	9.56017i	0.624523	−	0.360569i
$704$	−19.7944	+	54.3847i	−0.746029	+	2.04970i
$705$	−18.2216	−	11.6566i	−0.686264	−	0.439012i
$706$	−4.49045	−	0.791788i	−0.169000	−	0.0297993i
$707$	10.2050	−	2.87987i	0.383800	−	0.108309i
$708$	0.231634	−	0.556259i	0.00870535	−	0.0209055i
$709$	34.1456	+	12.4280i	1.28237	+	0.466743i	0.891214	−	0.453583i	$-0.149854\pi$
$709$	34.1456	+	12.4280i	1.28237	+	0.466743i	0.391152	+	0.920326i	$0.372077\pi$
$710$	1.70558	−	2.95416i	0.0640094	−	0.110868i
$711$	−2.57128	−	30.7176i	−0.0964307	−	1.15200i
$712$	42.0616	−	24.2843i	1.57632	−	0.910092i
$713$	−10.4280	−	3.79549i	−0.390532	−	0.142142i
$714$	−2.03861	+	6.73162i	−0.0762931	+	0.251925i
$715$	7.60550	+	6.38177i	0.284430	+	0.238665i
$716$	−1.17054	−	3.21602i	−0.0437450	−	0.120188i
$717$	−2.33257	+	10.4289i	−0.0871113	+	0.389473i
$718$	−5.87442	−	33.3155i	−0.219231	−	1.24332i
$719$	−13.9224	−	24.1144i	−0.519219	−	0.899314i	−0.999751	−	0.0223364i	$-0.992890\pi$
$719$	−13.9224	−	24.1144i	−0.519219	−	0.899314i	0.480531	−	0.876978i	$-0.340444\pi$
$720$	4.75723	+	10.3027i	0.177292	+	0.383960i
$721$	−38.2530	−	26.0367i	−1.42462	−	0.969657i
$722$	−10.0604	+	1.77393i	−0.374411	+	0.0660188i
$723$	25.4048	+	10.5789i	0.944814	+	0.393434i
$724$	2.06635	−	2.46258i	0.0767952	−	0.0915209i
$725$	3.16347	+	8.69157i	0.117488	+	0.322797i
$726$	−30.7281	−	59.2996i	−1.14043	−	2.20081i
$727$	−28.8118	−	34.3365i	−1.06857	−	1.27347i	−0.960186	−	0.279363i	$-0.909877\pi$
$727$	−28.8118	−	34.3365i	−1.06857	−	1.27347i	−0.108384	−	0.994109i	$-0.534568\pi$
$728$	−4.95309	+	7.27707i	−0.183574	+	0.269706i
$729$	−25.9996	−	7.28138i	−0.962950	−	0.269681i
$730$	−11.9201	+	20.6462i	−0.441182	+	0.764150i
$731$	5.93200	+	2.15907i	0.219403	+	0.0798562i
$732$	6.24281	+	0.284308i	0.230741	+	0.0105083i
$733$	−17.3125	+	20.6322i	−0.639451	+	0.762067i	−0.984283	−	0.176597i	$-0.943491\pi$
$733$	−17.3125	+	20.6322i	−0.639451	+	0.762067i	0.344833	+	0.938664i	$0.387936\pi$
$734$	0.614728	−	0.223743i	0.0226900	−	0.00825850i
$735$	−8.20831	−	14.8628i	−0.302768	−	0.548223i
$736$	−1.63991	−	9.30040i	−0.0604479	−	0.342817i
$737$		−	72.4349i		−	2.66818i
$738$	4.06873	+	2.87178i	0.149772	+	0.105712i
$739$	13.1981			0.485501			0.242750	−	0.970089i	$-0.421950\pi$
$739$	13.1981			0.485501			0.242750	+	0.970089i	$0.421950\pi$
$740$	3.24997	−	2.72705i	0.119471	−	0.100248i
$741$	−4.14668	+	4.50829i	−0.152332	+	0.165616i
$742$	−28.5993	+	8.07074i	−1.04991	+	0.296286i
$743$	−22.0972	+	26.3344i	−0.810667	+	0.966115i	−0.999875	−	0.0158221i	$-0.994963\pi$
$743$	−22.0972	+	26.3344i	−0.810667	+	0.966115i	0.189208	+	0.981937i	$0.439408\pi$
$744$	−11.9923	+	13.0381i	−0.439660	+	0.478000i
$745$	22.3731	−	3.94498i	0.819686	−	0.144533i
$746$			32.2521i			1.18083i
$747$	25.0955	−	17.4320i	0.918196	−	0.637804i
$748$	−3.67879	+	2.12395i	−0.134510	+	0.0776594i
$749$	9.18816	+	12.7589i	0.335728	+	0.466200i
$750$	21.9266	+	9.13056i	0.800647	+	0.333401i
$751$	−3.01307	+	17.0880i	−0.109949	+	0.623549i	0.879179	+	0.476491i	$0.158092\pi$
$751$	−3.01307	+	17.0880i	−0.109949	+	0.623549i	−0.989128	+	0.147058i	$0.953020\pi$
$752$	−22.6362	+	8.23892i	−0.825459	+	0.300443i
$753$	3.44288	−	1.78404i	0.125465	−	0.0650141i
$754$	3.96344	−	0.698861i	0.144340	−	0.0254510i
$755$	12.0268			0.437701
$756$	−1.48314	+	6.93976i	−0.0539412	+	0.252397i
$757$	27.2517			0.990478			0.495239	−	0.868757i	$-0.335080\pi$
$757$	27.2517			0.990478			0.495239	+	0.868757i	$0.335080\pi$
$758$	−2.69213	+	0.474694i	−0.0977824	+	0.0172417i
$759$	31.6909	+	20.2731i	1.15031	+	0.735865i
$760$	13.1401	−	4.78259i	0.476640	−	0.173483i
$761$	4.96087	−	28.1345i	0.179832	−	1.01988i	−0.752586	−	0.658494i	$-0.771194\pi$
$761$	4.96087	−	28.1345i	0.179832	−	1.01988i	0.932418	−	0.361382i	$-0.117695\pi$
$762$	3.21895	−	2.46040i	0.116610	−	0.0891310i
$763$	1.27360	+	12.6280i	0.0461073	+	0.457164i
$764$	−0.523887	+	0.302466i	−0.0189536	+	0.0109428i
$765$	−1.38925	+	5.10797i	−0.0502285	+	0.184679i
$766$		−	5.61557i		−	0.202899i
$767$	−0.720472	+	0.127039i	−0.0260147	+	0.00458710i
$768$	−19.4254	−	4.34478i	−0.700954	−	0.156779i
$769$	19.2125	−	22.8965i	0.692820	−	0.825671i	−0.298874	−	0.954293i	$-0.596611\pi$
$769$	19.2125	−	22.8965i	0.692820	−	0.825671i	0.991694	+	0.128622i	$0.0410554\pi$
$770$	−7.25117	+	28.5706i	−0.261314	+	1.02961i
$771$	−1.49967	−	4.78767i	−0.0540094	−	0.172424i
$772$	−2.31740	+	1.94453i	−0.0834051	+	0.0699852i
$773$	9.40156			0.338151			0.169075	−	0.985603i	$-0.445922\pi$
$773$	9.40156			0.338151			0.169075	+	0.985603i	$0.445922\pi$
$774$	−17.6666	−	4.80491i	−0.635014	−	0.172709i
$775$			10.1404i			0.364256i
$776$	−9.48644	−	53.8003i	−0.340543	−	1.93132i
$777$	−26.8545	+	1.47862i	−0.963400	+	0.0530452i
$778$	25.2783	−	9.20054i	0.906270	−	0.329855i
$779$	2.85384	−	3.40107i	0.102249	−	0.121856i
$780$	−0.732406	+	1.14490i	−0.0262243	+	0.0409940i
$781$	−12.2727	−	4.46689i	−0.439151	−	0.159838i
$782$	−2.55218	+	4.42051i	−0.0912658	+	0.158077i
$783$	13.3861	−	8.42228i	0.478379	−	0.300988i
$784$	−18.7013	−	2.78886i	−0.667904	−	0.0996023i
$785$	20.0898	+	23.9421i	0.717037	+	0.854531i
$786$	−13.1505	+	20.5568i	−0.469061	+	0.733238i
$787$	6.87101	+	18.8779i	0.244925	+	0.672926i	0.999853	+	0.0171188i	$0.00544936\pi$
$787$	6.87101	+	18.8779i	0.244925	+	0.672926i	−0.754928	+	0.655807i	$0.772328\pi$
$788$	4.08870	−	4.87273i	0.145654	−	0.173584i
$789$	33.3511	−	25.4919i	1.18733	−	0.907536i
$790$	17.2612	−	3.04362i	0.614126	−	0.108287i
$791$	−2.04755	+	27.6123i	−0.0728023	+	0.981782i
$792$	49.3223	−	34.2606i	1.75259	−	1.21740i
$793$	−3.79372	−	6.57092i	−0.134719	−	0.233340i
$794$	−6.83186	−	38.7454i	−0.242454	−	1.37502i
$795$	−21.3423	+	6.68519i	−0.756934	+	0.237099i
$796$	−0.869772	−	2.38968i	−0.0308283	−	0.0846999i
$797$	−28.3691	−	23.8045i	−1.00489	−	0.843200i	−0.0172322	−	0.999852i	$-0.505485\pi$
$797$	−28.3691	−	23.8045i	−1.00489	−	0.843200i	−0.987654	+	0.156652i	$0.949930\pi$
$798$	−17.4050	−	5.27096i	−0.616132	−	0.186590i
$799$	−10.5592	−	3.84322i	−0.373556	−	0.135963i
$800$	−7.47346	+	4.31481i	−0.264227	+	0.152551i
$801$	−47.3415	−	4.32099i	−1.67273	−	0.152675i
$802$	2.41836	−	4.18871i	0.0853951	−	0.147909i
$803$	85.7721	+	31.2185i	3.02683	+	1.10168i
$804$	9.83349	−	1.27583i	0.346801	−	0.0449951i
$805$	−3.34652	−	11.8587i	−0.117949	−	0.417963i
$806$	4.34527	+	0.766188i	0.153056	+	0.0269878i
$807$	−25.1504	+	13.0325i	−0.885335	+	0.458766i
$808$	4.20135	−	11.5431i	0.147803	−	0.406085i
$809$	−26.7503	+	15.4443i	−0.940490	+	0.542992i	−0.890114	−	0.455738i	$-0.849375\pi$
$809$	−26.7503	+	15.4443i	−0.940490	+	0.542992i	−0.0503763	+	0.998730i	$0.516042\pi$
$810$	2.77938	−	15.0988i	0.0976574	−	0.530519i
$811$			18.0871i			0.635123i	0.948238	+	0.317562i	$0.102864\pi$
$811$			18.0871i			0.635123i	−0.948238	+	0.317562i	$0.897136\pi$
$812$	−2.42912	−	3.37313i	−0.0852454	−	0.118374i
$813$	−11.0548	+	17.2808i	−0.387707	+	0.606065i
$814$	35.7681	+	30.0130i	1.25367	+	1.05195i
$815$	−7.97957	−	6.69565i	−0.279512	−	0.234539i
$816$	3.57989	+	4.68357i	0.125321	+	0.163958i
$817$	−5.58242	+	15.3376i	−0.195304	+	0.536594i
$818$	−10.2643	−	17.7783i	−0.358883	−	0.621604i
$819$	8.06809	−	3.02360i	0.281922	−	0.105653i
$820$	0.492562	−	0.853142i	0.0172010	−	0.0297930i
$821$	11.1240	+	13.2571i	0.388231	+	0.462676i	0.924394	−	0.381439i	$-0.124571\pi$
$821$	11.1240	+	13.2571i	0.388231	+	0.462676i	−0.536163	+	0.844114i	$0.680127\pi$
$822$	−18.2734	−	4.08711i	−0.637357	−	0.142554i
$823$	−5.18109	+	29.3834i	−0.180602	+	1.02424i	0.750876	+	0.660443i	$0.229632\pi$
$823$	−5.18109	+	29.3834i	−0.180602	+	1.02424i	−0.931478	+	0.363799i	$0.881480\pi$
$824$	−50.3731	+	18.3343i	−1.75483	+	0.638705i
$825$	7.50351	−	33.5480i	0.261239	−	1.16799i
$826$	−1.26929	−	1.76256i	−0.0441642	−	0.0613274i
$827$	−4.28404	−	2.47339i	−0.148971	−	0.0860084i	0.423662	−	0.905820i	$-0.360745\pi$
$827$	−4.28404	−	2.47339i	−0.148971	−	0.0860084i	−0.572633	+	0.819812i	$0.694078\pi$
$828$	−2.19401	+	4.65931i	−0.0762470	+	0.161922i
$829$	12.9108	+	7.45405i	0.448410	+	0.258890i	0.707159	−	0.707055i	$-0.249977\pi$
$829$	12.9108	+	7.45405i	0.448410	+	0.258890i	−0.258748	+	0.965945i	$0.583310\pi$
$830$	11.1681	+	13.3096i	0.387649	+	0.461982i
$831$	2.41673	+	3.16181i	0.0838354	+	0.109682i
$832$	3.28997	+	9.03912i	0.114059	+	0.313375i
$833$	−5.84647	−	6.60401i	−0.202568	−	0.228815i
$834$	0.302816	−	6.64920i	0.0104857	−	0.230243i
$835$	5.10976	+	28.9789i	0.176830	+	1.00286i
$836$	−5.49162	−	9.51176i	−0.189932	−	0.328971i
$837$	16.9487	−	3.65743i	0.585834	−	0.126419i
$838$	−5.06726	−	2.92558i	−0.175045	−	0.101063i
$839$	−19.8789	+	16.6804i	−0.686296	+	0.575870i	−0.917838	−	0.396954i	$-0.870067\pi$
$839$	−19.8789	+	16.6804i	−0.686296	+	0.575870i	0.231543	+	0.972825i	$0.425623\pi$
$840$	−19.5290	−	2.34545i	−0.673816	−	0.0809257i
$841$	3.42716	−	19.4364i	0.118178	−	0.670220i
$842$	−7.32578	−	1.29173i	−0.252463	−	0.0445160i
$843$	−42.8369	−	17.8379i	−1.47538	−	0.614370i
$844$	5.47033	−	4.59015i	0.188297	−	0.158000i
$845$	−16.5549			−0.569506
$846$	31.4472	+	8.55291i	1.08118	+	0.294055i
$847$	83.5234	+	6.19354i	2.86990	+	0.212812i
$848$	−8.51841	+	23.4041i	−0.292524	+	0.803702i
$849$	6.45090	−	28.8418i	0.221394	−	0.989849i
$850$	4.59340	+	0.809940i	0.157552	+	0.0277807i
$851$	−19.2218	−	3.38932i	−0.658914	−	0.116184i
$852$	0.390244	−	1.74477i	0.0133695	−	0.0597749i
$853$	5.52056	−	15.1676i	0.189020	−	0.519329i	−0.808594	−	0.588368i	$-0.799771\pi$
$853$	5.52056	−	15.1676i	0.189020	−	0.519329i	0.997614	+	0.0690383i	$0.0219931\pi$
$854$	12.6751	−	18.6223i	0.433734	−	0.637241i
$855$	−13.2070	−	3.59200i	−0.451670	−	0.122844i
$856$	18.2145			0.622560
$857$	−35.6165	+	29.8858i	−1.21664	+	1.02088i	−0.217642	+	0.976029i	$0.569837\pi$
$857$	−35.6165	+	29.8858i	−1.21664	+	1.02088i	−0.998994	+	0.0448502i	$0.985719\pi$
$858$	−13.8087	−	5.75013i	−0.471420	−	0.196306i
$859$	48.2528	+	8.50828i	1.64637	+	0.290299i	0.918500	−	0.395421i	$-0.129401\pi$
$859$	48.2528	+	8.50828i	1.64637	+	0.290299i	0.727866	+	0.685720i	$0.240512\pi$
$860$	−0.628884	+	3.56658i	−0.0214448	+	0.121619i
$861$	−5.74218	+	2.45536i	−0.195693	+	0.0836783i
$862$	−6.24265	+	5.23820i	−0.212625	+	0.178414i
$863$	−41.6947	−	24.0725i	−1.41931	−	0.819436i	−0.423067	−	0.906098i	$-0.639047\pi$
$863$	−41.6947	−	24.0725i	−1.41931	−	0.819436i	−0.996238	+	0.0866620i	$0.972380\pi$
$864$	9.90727	+	10.9349i	0.337052	+	0.372012i
$865$	1.80965	+	3.13440i	0.0615298	+	0.106573i
$866$	5.51874	+	31.2984i	0.187535	+	1.06356i
$867$	1.21448	−	26.6674i	0.0412458	−	0.905671i
$868$	−1.23771	−	4.38592i	−0.0420105	−	0.148868i
$869$	−22.9521	−	63.0603i	−0.778596	−	2.13918i
$870$	5.46103	+	7.14468i	0.185146	+	0.242227i
$871$	−7.73866	−	9.22257i	−0.262214	−	0.312495i
$872$	12.7334	+	7.35166i	0.431209	+	0.248959i
$873$	−22.7798	+	48.3764i	−0.770978	+	1.63729i
$874$	−11.4295	−	6.59883i	−0.386609	−	0.223209i
$875$	−24.1698	+	17.4056i	−0.817089	+	0.588417i
$876$	−2.72736	+	12.1940i	−0.0921490	+	0.411996i
$877$	−16.2709	+	5.92211i	−0.549428	+	0.199975i	−0.601792	−	0.798653i	$-0.705546\pi$
$877$	−16.2709	+	5.92211i	−0.549428	+	0.199975i	0.0523645	+	0.998628i	$0.483324\pi$
$878$	−6.55360	+	37.1673i	−0.221173	+	1.25434i
$879$	9.68439	+	2.16606i	0.326646	+	0.0730593i
$880$	15.8801	+	18.9252i	0.535319	+	0.637968i
$881$	−29.5139	+	51.1195i	−0.994347	+	1.72226i	−0.405220	+	0.914219i	$0.632805\pi$
$881$	−29.5139	+	51.1195i	−0.994347	+	1.72226i	−0.589127	+	0.808040i	$0.700528\pi$
$882$	18.4948	+	17.6721i	0.622751	+	0.595050i
$883$	−10.2679	−	17.7846i	−0.345543	−	0.598498i	0.639909	−	0.768450i	$-0.278972\pi$
$883$	−10.2679	−	17.7846i	−0.345543	−	0.598498i	−0.985452	+	0.169953i	$0.945639\pi$
$884$	−0.241477	+	0.663454i	−0.00812176	+	0.0223144i
$885$	−0.992704	−	1.29876i	−0.0333694	−	0.0436572i
$886$	20.4469	+	17.1570i	0.686927	+	0.576400i
$887$	27.7930	+	23.3211i	0.933198	+	0.783046i	0.976389	−	0.216021i	$-0.0693080\pi$
$887$	27.7930	+	23.3211i	0.933198	+	0.783046i	−0.0431910	+	0.999067i	$0.513752\pi$
$888$	−16.7900	+	26.2462i	−0.563437	+	0.880766i
$889$	0.509827	+	5.05505i	0.0170991	+	0.169541i
$890$		−	27.0308i		−	0.906076i
$891$	−58.7784	−	0.441326i	−1.96915	−	0.0147850i
$892$	−3.39648	+	1.96096i	−0.113723	+	0.0656577i
$893$	9.93690	−	27.3014i	0.332526	−	0.913606i
$894$	−30.3898	+	15.7475i	−1.01639	+	0.526675i
$895$	−9.14369	−	1.61228i	−0.305640	−	0.0538926i
$896$	−9.44134	+	9.69489i	−0.315413	+	0.323883i
$897$	6.20084	−	0.804518i	0.207040	−	0.0268621i
$898$	−45.9512	−	16.7249i	−1.53341	−	0.558116i
$899$	−5.07812	+	8.79556i	−0.169365	+	0.293348i
$900$	4.68651	+	0.427751i	0.156217	+	0.0142584i
$901$	−10.0615	+	5.80901i	−0.335197	+	0.193526i
$902$	10.1881	+	3.70816i	0.339227	+	0.123468i
$903$	16.7495	−	15.7022i	0.557390	−	0.522538i
$904$	24.5715	+	20.6179i	0.817236	+	0.685742i
$905$	−2.98280	−	8.19517i	−0.0991516	−	0.272417i
$906$	−17.2913	+	5.41626i	−0.574465	+	0.179943i
$907$	−4.93442	−	27.9845i	−0.163845	−	0.929210i	−0.950247	−	0.311496i	$-0.899170\pi$
$907$	−4.93442	−	27.9845i	−0.163845	−	0.929210i	0.786403	−	0.617714i	$-0.211941\pi$
$908$	3.97084	+	6.87769i	0.131777	+	0.228244i
$909$	−9.87478	+	6.85930i	−0.327526	+	0.227508i
$910$	2.12913	+	4.41235i	0.0705799	+	0.146268i
$911$	−11.1214	+	1.96100i	−0.368468	+	0.0649708i	−0.354816	−	0.934936i	$-0.615457\pi$
$911$	−11.1214	+	1.96100i	−0.368468	+	0.0649708i	−0.0136513	+	0.999907i	$0.504345\pi$
$912$	−12.1097	+	9.25602i	−0.400992	+	0.306498i
$913$	42.7591	−	50.9583i	1.41512	−	1.68647i
$914$	−9.64363	−	26.4956i	−0.318983	−	0.876398i
$915$	9.13608	−	14.2816i	0.302030	−	0.472134i
$916$	6.45995	+	7.69867i	0.213443	+	0.254371i
$917$	−13.2992	−	27.5609i	−0.439177	−	0.910140i
$918$	−0.303005	−	7.96952i	−0.0100006	−	0.263033i
$919$	9.90735	−	17.1600i	0.326813	−	0.566057i	−0.655064	−	0.755573i	$-0.727359\pi$
$919$	9.90735	−	17.1600i	0.326813	−	0.566057i	0.981878	+	0.189516i	$0.0606919\pi$
$920$	−13.4136	−	4.88214i	−0.442232	−	0.160959i
$921$	−10.5220	+	16.4480i	−0.346711	+	0.541979i
$922$	−19.5736	+	23.3269i	−0.644623	+	0.768232i
$923$	−2.03981	+	0.742430i	−0.0671411	+	0.0244374i
$924$	0.849358	+	15.4259i	0.0279418	+	0.507476i
$925$	3.09709	+	17.5645i	0.101832	+	0.577516i
$926$		−	4.24980i		−	0.139657i
$927$	50.6296	+	13.7701i	1.66290	+	0.452269i
$928$	−8.64305			−0.283722
$929$	−30.9212	+	25.9459i	−1.01449	+	0.851259i	−0.988925	−	0.148414i	$-0.952583\pi$
$929$	−30.9212	+	25.9459i	−1.01449	+	0.851259i	−0.0255654	+	0.999673i	$0.508139\pi$
$930$	2.94703	+	9.40832i	0.0966369	+	0.308511i
$931$	17.0751	−	15.1164i	0.559614	−	0.495421i
$932$	−2.13261	+	2.54155i	−0.0698561	+	0.0832513i
$933$	41.9064	+	9.37299i	1.37196	+	0.306858i
$934$	−18.1708	+	3.20401i	−0.594567	+	0.104838i
$935$			11.5242i			0.376882i
$936$	2.61955	−	9.63153i	0.0856228	−	0.314816i
$937$	28.8945	−	16.6822i	0.943942	−	0.544985i	0.0527484	−	0.998608i	$-0.483202\pi$
$937$	28.8945	−	16.6822i	0.943942	−	0.544985i	0.891194	+	0.453622i	$0.149869\pi$
$938$	14.6754	−	32.5920i	0.479169	−	1.06417i
$939$	−24.9635	+	19.0808i	−0.814652	+	0.622679i
$940$	1.11943	−	6.34863i	0.0365119	−	0.207069i
$941$	−12.8888	+	4.69113i	−0.420162	+	0.152926i	−0.543444	−	0.839445i	$-0.682880\pi$
$941$	−12.8888	+	4.69113i	−0.420162	+	0.152926i	0.123283	+	0.992372i	$0.460658\pi$
$942$	−39.6660	−	25.3748i	−1.29239	−	0.826757i
$943$	−4.46333	+	0.787006i	−0.145346	+	0.0256284i
$944$	−1.82045			−0.0592505
$945$	14.2928	+	12.8981i	0.464946	+	0.419574i
$946$	−39.8581			−1.29590
$947$	13.7919	−	2.43188i	0.448176	−	0.0790255i	0.0549950	−	0.998487i	$-0.482486\pi$
$947$	13.7919	−	2.43188i	0.448176	−	0.0790255i	0.393181	+	0.919461i	$0.371375\pi$
$948$	8.15657	−	4.22660i	0.264913	−	0.137274i
$949$	14.2559	−	5.18874i	0.462768	−	0.168434i
$950$	−2.09415	+	11.8765i	−0.0679433	+	0.385325i
$951$	−5.30130	−	2.20754i	−0.171906	−	0.0715843i
$952$	−10.1662	+	1.02531i	−0.329489	+	0.0332306i
$953$	−15.7918	+	9.11739i	−0.511546	+	0.295341i	−0.733469	−	0.679723i	$-0.762100\pi$
$953$	−15.7918	+	9.11739i	−0.511546	+	0.295341i	0.221923	+	0.975064i	$0.428767\pi$
$954$	27.6738	−	19.2230i	0.895971	−	0.622366i
$955$			1.64113i			0.0531058i
$956$	−3.13645	+	0.553042i	−0.101440	+	0.0178866i
$957$	23.3085	−	25.3411i	0.753456	−	0.819160i
$958$	−6.84956	+	8.16299i	−0.221299	+	0.263734i
$959$	16.3822	−	16.8222i	0.529010	−	0.543216i
$960$	−14.5507	+	15.8196i	−0.469621	+	0.510574i
$961$	15.2177	−	12.7692i	0.490894	−	0.411909i
$962$	7.76053			0.250209
$963$	−14.5655	−	10.2806i	−0.469366	−	0.331287i
$964$			8.20144i			0.264150i
$965$	1.42513	+	8.08231i	0.0458765	+	0.260179i
$966$	10.1519	+	15.5424i	0.326633	+	0.500070i
$967$	14.9340	−	5.43554i	0.480246	−	0.174795i	−0.0905420	−	0.995893i	$-0.528860\pi$
$967$	14.9340	−	5.43554i	0.480246	−	0.174795i	0.570788	+	0.821097i	$0.306638\pi$
$968$	62.3663	−	74.3253i	2.00453	−	2.38891i
$969$	−7.10259	−	0.323464i	−0.228168	−	0.0103912i
$970$	−28.5708	−	10.3989i	−0.917355	−	0.333890i
$971$	0.384116	−	0.665309i	0.0123269	−	0.0213508i	−0.859796	−	0.510637i	$-0.829409\pi$
$971$	0.384116	−	0.665309i	0.0123269	−	0.0213508i	0.872123	+	0.489287i	$0.162743\pi$
$972$	−0.975379	−	7.98731i	−0.0312853	−	0.256193i
$973$	6.90010	+	4.69651i	0.221207	+	0.150563i
$974$	19.0465	+	22.6987i	0.610288	+	0.727313i
$975$	−2.62877	−	5.07305i	−0.0841881	−	0.162468i
$976$	−6.45743	−	17.7416i	−0.206697	−	0.567896i
$977$	−33.5996	+	40.0424i	−1.07495	+	1.28107i	−0.117308	+	0.993096i	$0.537426\pi$
$977$	−33.5996	+	40.0424i	−1.07495	+	1.28107i	−0.957638	+	0.287975i	$0.907018\pi$
$978$	14.4878	+	6.03294i	0.463270	+	0.192912i
$979$	−101.921	+	17.9713i	−3.25739	+	0.574367i
$980$	3.14872	−	3.96107i	0.100582	−	0.126532i
$981$	−6.03307	−	13.0658i	−0.192621	−	0.417159i
$982$	−7.26457	−	12.5826i	−0.231822	−	0.401527i
$983$	7.61431	+	43.1829i	0.242859	+	1.37732i	0.825414	+	0.564528i	$0.190942\pi$
$983$	7.61431	+	43.1829i	0.242859	+	1.37732i	−0.582555	+	0.812791i	$0.697947\pi$
$984$	−1.57914	+	7.06031i	−0.0503413	+	0.225075i
$985$	−5.90210	−	16.2159i	−0.188057	−	0.516681i
$986$	3.57859	+	3.00280i	0.113966	+	0.0956285i
$987$	−29.8148	+	27.9505i	−0.949014	+	0.889675i
$988$	−1.71540	−	0.624355i	−0.0545742	−	0.0198634i
$989$	14.4294	−	8.33081i	0.458828	−	0.264904i
$990$	−2.78800	−	33.3066i	−0.0886083	−	1.05855i
$991$	4.90359	−	8.49327i	0.155768	−	0.269798i	−0.777571	−	0.628796i	$-0.783548\pi$
$991$	4.90359	−	8.49327i	0.155768	−	0.269798i	0.933338	+	0.358998i	$0.116882\pi$
$992$	−8.90425	−	3.24088i	−0.282710	−	0.102898i
$993$	3.88017	−	9.31806i	0.123134	−	0.295700i
$994$	−4.61708	−	4.49633i	−0.146445	−	0.142615i
$995$	−6.79426	−	1.19801i	−0.215392	−	0.0379795i
$996$	7.67103	+	4.90725i	0.243066	+	0.155492i
$997$	−15.3662	+	42.2182i	−0.486651	+	1.33706i	0.417044	+	0.908886i	$0.363066\pi$
$997$	−15.3662	+	42.2182i	−0.486651	+	1.33706i	−0.903695	+	0.428177i	$0.859156\pi$
$998$	4.40447	−	2.54292i	0.139421	−	0.0804948i
$999$	28.2402	−	11.5116i	0.893479	−	0.364210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.5.9	✓	132
3.2	odd	2		567.2.ba.a.530.14		132
7.3	odd	6		189.2.bd.a.59.14	yes	132
21.17	even	6		567.2.bd.a.206.9		132
27.11	odd	18		189.2.bd.a.173.14	yes	132
27.16	even	9		567.2.bd.a.278.9		132
189.38	even	18	inner	189.2.ba.a.38.9	yes	132
189.178	odd	18		567.2.ba.a.521.14		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.9	✓	132	1.1	even	1	trivial
189.2.ba.a.38.9	yes	132	189.38	even	18	inner
189.2.bd.a.59.14	yes	132	7.3	odd	6
189.2.bd.a.173.14	yes	132	27.11	odd	18
567.2.ba.a.521.14		132	189.178	odd	18
567.2.ba.a.530.14		132	3.2	odd	2
567.2.bd.a.206.9		132	21.17	even	6
567.2.bd.a.278.9		132	27.16	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19961 + 0.211524i) q^{2} +(-0.0787989 + 1.73026i) q^{3} +(-0.485062 + 0.176548i) q^{4} +(-0.243175 + 1.37911i) q^{5} +(-0.271462 - 2.09230i) q^{6} +(2.41247 + 1.08628i) q^{7} +(2.65438 - 1.53251i) q^{8} +(-2.98758 - 0.272685i) q^{9} +O(q^{10})\)	\(q+(-1.19961 + 0.211524i) q^{2} +(-0.0787989 + 1.73026i) q^{3} +(-0.485062 + 0.176548i) q^{4} +(-0.243175 + 1.37911i) q^{5} +(-0.271462 - 2.09230i) q^{6} +(2.41247 + 1.08628i) q^{7} +(2.65438 - 1.53251i) q^{8} +(-2.98758 - 0.272685i) q^{9} -1.70584i q^{10} +(-6.43190 + 1.13412i) q^{11} +(-0.267252 - 0.853194i) q^{12} +(-0.697759 + 0.831556i) q^{13} +(-3.12380 - 0.792815i) q^{14} +(-2.36706 - 0.529428i) q^{15} +(-2.06921 + 1.73627i) q^{16} -1.26001 q^{17} +(3.64161 - 0.304829i) q^{18} -3.25785i q^{19} +(-0.125525 - 0.711888i) q^{20} +(-2.06964 + 4.08859i) q^{21} +(7.47588 - 2.72100i) q^{22} +(-2.13769 + 2.54760i) q^{23} +(2.44247 + 4.71352i) q^{24} +(2.85565 + 1.03937i) q^{25} +(0.661145 - 1.14514i) q^{26} +(0.707233 - 5.14780i) q^{27} +(-1.36198 - 0.100995i) q^{28} +(1.95642 + 2.33157i) q^{29} +(2.95153 + 0.134418i) q^{30} +(1.14128 + 3.13563i) q^{31} +(-1.82533 + 2.17534i) q^{32} +(-1.45549 - 11.2182i) q^{33} +(1.51153 - 0.266523i) q^{34} +(-2.08475 + 3.06291i) q^{35} +(1.49731 - 0.395183i) q^{36} +(2.93451 + 5.08271i) q^{37} +(0.689112 + 3.90815i) q^{38} +(-1.38382 - 1.27283i) q^{39} +(1.46802 + 4.03336i) q^{40} +(1.04396 + 0.875988i) q^{41} +(1.61793 - 5.34250i) q^{42} +(-4.70788 - 1.71353i) q^{43} +(2.91965 - 1.68566i) q^{44} +(1.10257 - 4.05390i) q^{45} +(2.02552 - 3.50830i) q^{46} +(8.38019 + 3.05014i) q^{47} +(-2.84115 - 3.71708i) q^{48} +(4.64000 + 5.24122i) q^{49} +(-3.64551 - 0.642802i) q^{50} +(0.0992877 - 2.18015i) q^{51} +(0.191647 - 0.526545i) q^{52} +(7.98523 - 4.61027i) q^{53} +(0.240477 + 6.32495i) q^{54} -9.14610i q^{55} +(8.06834 - 0.813732i) q^{56} +(5.63692 + 0.256715i) q^{57} +(-2.84012 - 2.38314i) q^{58} +(0.516276 + 0.433207i) q^{59} +(1.24164 - 0.161095i) q^{60} +(-2.39061 + 6.56816i) q^{61} +(-2.03235 - 3.52013i) q^{62} +(-6.91123 - 3.90318i) q^{63} +(4.43070 - 7.67421i) q^{64} +(-0.977133 - 1.16450i) q^{65} +(4.11894 + 13.1496i) q^{66} +(-1.92589 + 10.9222i) q^{67} +(0.611185 - 0.222453i) q^{68} +(-4.23956 - 3.89950i) q^{69} +(1.85301 - 4.11527i) q^{70} +(1.73180 + 0.999853i) q^{71} +(-8.34807 + 3.85468i) q^{72} +(-12.1033 - 6.98783i) q^{73} +(-4.59538 - 5.47656i) q^{74} +(-2.02340 + 4.85910i) q^{75} +(0.575167 + 1.58026i) q^{76} +(-16.7487 - 4.25080i) q^{77} +(1.92928 + 1.23419i) q^{78} +(1.78424 + 10.1189i) q^{79} +(-1.89134 - 3.27589i) q^{80} +(8.85129 + 1.62934i) q^{81} +(-1.43764 - 0.830022i) q^{82} +(-7.80237 + 6.54697i) q^{83} +(0.282070 - 2.34861i) q^{84} +(0.306404 - 1.73770i) q^{85} +(6.01008 + 1.05974i) q^{86} +(-4.18838 + 3.20138i) q^{87} +(-15.3347 + 12.8673i) q^{88} +15.8461 q^{89} +(-0.465155 + 5.09632i) q^{90} +(-2.58662 + 1.24814i) q^{91} +(0.587139 - 1.61315i) q^{92} +(-5.51537 + 1.72762i) q^{93} +(-10.6981 - 1.88637i) q^{94} +(4.49294 + 0.792227i) q^{95} +(-3.62006 - 3.32970i) q^{96} +(6.09610 - 16.7489i) q^{97} +(-6.67484 - 5.30595i) q^{98} +(19.5251 - 1.63439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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Database

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