LMFDB - Embedded newform 429.2.bv.a.20.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(20,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 36, 55]))

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

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

chi := DirichletCharacter("429.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bv (of order $60$, degree $16$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$52$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			20.8
Character	$\chi$	$=$	429.20
Dual form			429.2.bv.a.236.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15849 - 0.113122i) q^{2} +(1.68832 - 0.386733i) q^{3} +(2.65724 + 0.279288i) q^{4} +(0.408417 + 0.208099i) q^{5} +(-3.68798 + 0.643774i) q^{6} +(2.50194 + 3.08964i) q^{7} +(-1.43436 - 0.227180i) q^{8} +(2.70088 - 1.30586i) q^{9} +O(q^{10})$	\(q+(-2.15849 - 0.113122i) q^{2} +(1.68832 - 0.386733i) q^{3} +(2.65724 + 0.279288i) q^{4} +(0.408417 + 0.208099i) q^{5} +(-3.68798 + 0.643774i) q^{6} +(2.50194 + 3.08964i) q^{7} +(-1.43436 - 0.227180i) q^{8} +(2.70088 - 1.30586i) q^{9} +(-0.858025 - 0.495381i) q^{10} +(-2.87989 + 1.64506i) q^{11} +(4.59430 - 0.556116i) q^{12} +(1.50821 + 3.27495i) q^{13} +(-5.05092 - 6.95200i) q^{14} +(0.770019 + 0.193390i) q^{15} +(-2.15663 - 0.458406i) q^{16} +(-1.79854 + 1.99749i) q^{17} +(-5.97754 + 2.51316i) q^{18} +(0.973486 + 2.53602i) q^{19} +(1.02715 + 0.667036i) q^{20} +(5.41896 + 4.24874i) q^{21} +(6.40231 - 3.22508i) q^{22} +(-1.32567 + 2.29613i) q^{23} +(-2.50952 + 0.171161i) q^{24} +(-2.81543 - 3.87510i) q^{25} +(-2.88498 - 7.23957i) q^{26} +(4.05493 - 3.24923i) q^{27} +(5.78538 + 8.90870i) q^{28} +(-2.03028 - 4.56009i) q^{29} +(-1.64020 - 0.504537i) q^{30} +(-5.21127 + 2.65528i) q^{31} +(7.40873 + 1.98516i) q^{32} +(-4.22599 + 3.89115i) q^{33} +(4.10810 - 4.10810i) q^{34} +(0.378886 + 1.78252i) q^{35} +(7.54160 - 2.71567i) q^{36} +(1.98804 - 5.17902i) q^{37} +(-1.81438 - 5.58409i) q^{38} +(3.81287 + 4.94591i) q^{39} +(-0.538542 - 0.391274i) q^{40} +(4.94252 + 4.00237i) q^{41} +(-11.2162 - 9.78386i) q^{42} +(1.06600 - 0.615457i) q^{43} +(-8.11202 + 3.56702i) q^{44} +(1.37483 + 0.0287131i) q^{45} +(3.12119 - 4.80621i) q^{46} +(4.36859 + 0.691916i) q^{47} +(-3.81837 + 0.0601026i) q^{48} +(-1.83079 + 8.61321i) q^{49} +(5.63872 + 8.68286i) q^{50} +(-2.26403 + 4.06796i) q^{51} +(3.09302 + 9.12357i) q^{52} +(10.0899 + 3.27842i) q^{53} +(-9.12010 + 6.55474i) q^{54} +(-1.51853 + 0.0725707i) q^{55} +(-2.88679 - 5.00006i) q^{56} +(2.62432 + 3.90514i) q^{57} +(3.86650 + 10.0726i) q^{58} +(3.36322 - 2.72348i) q^{59} +(1.99212 + 0.728942i) q^{60} +(7.60598 - 8.44729i) q^{61} +(11.5489 - 5.14188i) q^{62} +(10.7921 + 5.07755i) q^{63} +(-11.5733 - 3.76040i) q^{64} +(-0.0655370 + 1.65140i) q^{65} +(9.56193 - 7.92096i) q^{66} +(6.33247 - 1.69678i) q^{67} +(-5.33705 + 4.80550i) q^{68} +(-1.35017 + 4.38928i) q^{69} +(-0.616180 - 3.89041i) q^{70} +(0.123393 + 2.35448i) q^{71} +(-4.17070 + 1.25949i) q^{72} +(-6.77568 + 1.07316i) q^{73} +(-4.87702 + 10.9540i) q^{74} +(-6.25198 - 5.45361i) q^{75} +(1.87851 + 7.01070i) q^{76} +(-12.2880 - 4.78197i) q^{77} +(-7.67056 - 11.1070i) q^{78} +(0.194419 - 0.598360i) q^{79} +(-0.785412 - 0.636014i) q^{80} +(5.58945 - 7.05394i) q^{81} +(-10.2156 - 9.19819i) q^{82} +(-14.7188 - 7.49959i) q^{83} +(13.2129 + 12.8034i) q^{84} +(-1.15023 + 0.441533i) q^{85} +(-2.37058 + 1.20787i) q^{86} +(-5.19131 - 6.91373i) q^{87} +(4.50453 - 1.70536i) q^{88} +(13.8992 - 3.72429i) q^{89} +(-2.96432 - 0.217500i) q^{90} +(-6.34499 + 12.8536i) q^{91} +(-4.16391 + 5.73113i) q^{92} +(-7.77143 + 6.49834i) q^{93} +(-9.35129 - 1.98768i) q^{94} +(-0.130154 + 1.23833i) q^{95} +(13.2761 + 0.486398i) q^{96} +(-11.9112 - 7.73520i) q^{97} +(4.92609 - 18.3844i) q^{98} +(-5.63000 + 8.20385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.15849	−	0.113122i	−1.52628	−	0.0799891i	−0.729386	−	0.684103i	$-0.760194\pi$
$2$	−2.15849	−	0.113122i	−1.52628	−	0.0799891i	−0.796898	+	0.604114i	$0.793527\pi$
$3$	1.68832	−	0.386733i	0.974754	−	0.223280i
$3$	1.68832	−	0.386733i	0.974754	−	0.223280i
$4$	2.65724	+	0.279288i	1.32862	+	0.139644i
$5$	0.408417	+	0.208099i	0.182650	+	0.0930647i	0.542924	−	0.839782i	$-0.317317\pi$
$5$	0.408417	+	0.208099i	0.182650	+	0.0930647i	−0.360275	+	0.932846i	$0.617317\pi$
$6$	−3.68798	+	0.643774i	−1.50561	+	0.262820i
$7$	2.50194	+	3.08964i	0.945646	+	1.16778i	0.985688	+	0.168578i	$0.0539175\pi$
$7$	2.50194	+	3.08964i	0.945646	+	1.16778i	−0.0400420	+	0.999198i	$0.512749\pi$
$8$	−1.43436	−	0.227180i	−0.507123	−	0.0803204i
$9$	2.70088	−	1.30586i	0.900292	−	0.435287i
$10$	−0.858025	−	0.495381i	−0.271331	−	0.156653i
$11$	−2.87989	+	1.64506i	−0.868319	+	0.496006i
$11$	−2.87989	+	1.64506i	−0.868319	+	0.496006i
$12$	4.59430	−	0.556116i	1.32626	−	0.160537i
$13$	1.50821	+	3.27495i	0.418301	+	0.908308i
$13$	1.50821	+	3.27495i	0.418301	+	0.908308i
$14$	−5.05092	−	6.95200i	−1.34992	−	1.85800i
$15$	0.770019	+	0.193390i	0.198818	+	0.0499331i
$16$	−2.15663	−	0.458406i	−0.539158	−	0.114602i
$17$	−1.79854	+	1.99749i	−0.436211	+	0.484462i	−0.920664	−	0.390356i	$-0.872352\pi$
$17$	−1.79854	+	1.99749i	−0.436211	+	0.484462i	0.484453	+	0.874817i	$0.339019\pi$
$18$	−5.97754	+	2.51316i	−1.40892	+	0.592358i
$19$	0.973486	+	2.53602i	0.223333	+	0.581802i	0.998768	−	0.0496252i	$-0.0158027\pi$
$19$	0.973486	+	2.53602i	0.223333	+	0.581802i	−0.775435	+	0.631427i	$0.782469\pi$
$20$	1.02715	+	0.667036i	0.229677	+	0.149154i
$21$	5.41896	+	4.24874i	1.18251	+	0.927150i
$22$	6.40231	−	3.22508i	1.36498	−	0.687589i
$23$	−1.32567	+	2.29613i	−0.276421	+	0.478775i	−0.970493	−	0.241131i	$-0.922482\pi$
$23$	−1.32567	+	2.29613i	−0.276421	+	0.478775i	0.694072	+	0.719906i	$0.255815\pi$
$24$	−2.50952	+	0.171161i	−0.512254	+	0.0349380i
$25$	−2.81543	−	3.87510i	−0.563085	−	0.775021i
$26$	−2.88498	−	7.23957i	−0.565791	−	1.41980i
$27$	4.05493	−	3.24923i	0.780372	−	0.625315i
$28$	5.78538	+	8.90870i	1.09333	+	1.68359i
$29$	−2.03028	−	4.56009i	−0.377014	−	0.846788i	−0.998015	−	0.0629777i	$-0.979940\pi$
$29$	−2.03028	−	4.56009i	−0.377014	−	0.846788i	0.621001	−	0.783810i	$-0.286726\pi$
$30$	−1.64020	−	0.504537i	−0.299459	−	0.0921154i
$31$	−5.21127	+	2.65528i	−0.935972	+	0.476902i	−0.854313	−	0.519759i	$-0.826022\pi$
$31$	−5.21127	+	2.65528i	−0.935972	+	0.476902i	−0.0816591	+	0.996660i	$0.526022\pi$
$32$	7.40873	+	1.98516i	1.30969	+	0.350931i
$33$	−4.22599	+	3.89115i	−0.735650	+	0.677362i
$34$	4.10810	−	4.10810i	0.704534	−	0.704534i
$35$	0.378886	+	1.78252i	0.0640434	+	0.301300i
$36$	7.54160	−	2.71567i	1.25693	−	0.452612i
$37$	1.98804	−	5.17902i	0.326832	−	0.851425i	−0.667452	−	0.744653i	$-0.732615\pi$
$37$	1.98804	−	5.17902i	0.326832	−	0.851425i	0.994283	−	0.106772i	$-0.0340516\pi$
$38$	−1.81438	−	5.58409i	−0.294332	−	0.905860i
$39$	3.81287	+	4.94591i	0.610548	+	0.791979i
$40$	−0.538542	−	0.391274i	−0.0851509	−	0.0618658i
$41$	4.94252	+	4.00237i	0.771891	+	0.625065i	0.932176	−	0.362006i	$-0.117908\pi$
$41$	4.94252	+	4.00237i	0.771891	+	0.625065i	−0.160285	+	0.987071i	$0.551241\pi$
$42$	−11.2162	−	9.78386i	−1.73069	−	1.50968i
$43$	1.06600	−	0.615457i	0.162564	−	0.0938564i	−0.416511	−	0.909131i	$-0.636747\pi$
$43$	1.06600	−	0.615457i	0.162564	−	0.0938564i	0.579075	+	0.815274i	$0.303414\pi$
$44$	−8.11202	+	3.56702i	−1.22293	+	0.537749i
$45$	1.37483	+	0.0287131i	0.204948	+	0.00428030i
$46$	3.12119	−	4.80621i	0.460194	−	0.708636i
$47$	4.36859	+	0.691916i	0.637224	+	0.100926i	0.466684	−	0.884424i	$-0.345449\pi$
$47$	4.36859	+	0.691916i	0.637224	+	0.100926i	0.170540	+	0.985351i	$0.445449\pi$
$48$	−3.81837	+	0.0601026i	−0.551135	+	0.00867506i
$49$	−1.83079	+	8.61321i	−0.261542	+	1.23046i
$50$	5.63872	+	8.68286i	0.797435	+	1.22794i
$51$	−2.26403	+	4.06796i	−0.317028	+	0.569628i
$52$	3.09302	+	9.12357i	0.428924	+	1.26521i
$53$	10.0899	+	3.27842i	1.38596	+	0.450326i	0.904624	−	0.426210i	$-0.140152\pi$
$53$	10.0899	+	3.27842i	1.38596	+	0.450326i	0.481336	+	0.876536i	$0.340152\pi$
$54$	−9.12010	+	6.55474i	−1.24109	+	0.891988i
$55$	−1.51853	+	0.0725707i	−0.204759	+	0.00978543i
$56$	−2.88679	−	5.00006i	−0.385763	−	0.668161i
$57$	2.62432	+	3.90514i	0.347600	+	0.517248i
$58$	3.86650	+	10.0726i	0.507697	+	1.32260i
$59$	3.36322	−	2.72348i	0.437854	−	0.354567i	−0.384906	−	0.922956i	$-0.625766\pi$
$59$	3.36322	−	2.72348i	0.437854	−	0.354567i	0.822760	+	0.568388i	$0.192433\pi$
$60$	1.99212	+	0.728942i	0.257181	+	0.0941060i
$61$	7.60598	−	8.44729i	0.973845	−	1.08156i	−0.0228013	−	0.999740i	$-0.507259\pi$
$61$	7.60598	−	8.44729i	0.973845	−	1.08156i	0.996647	−	0.0818249i	$-0.0260748\pi$
$62$	11.5489	−	5.14188i	1.46671	−	0.653020i
$63$	10.7921	+	5.07755i	1.35968	+	0.639711i
$64$	−11.5733	−	3.76040i	−1.44666	−	0.470050i
$65$	−0.0655370	+	1.65140i	−0.00812886	+	0.204831i
$66$	9.56193	−	7.92096i	1.17699	−	0.975003i
$67$	6.33247	−	1.69678i	0.773635	−	0.207295i	0.149658	−	0.988738i	$-0.452183\pi$
$67$	6.33247	−	1.69678i	0.773635	−	0.207295i	0.623977	+	0.781443i	$0.285516\pi$
$68$	−5.33705	+	4.80550i	−0.647212	+	0.582752i
$69$	−1.35017	+	4.38928i	−0.162541	+	0.528408i
$70$	−0.616180	−	3.89041i	−0.0736476	−	0.464993i
$71$	0.123393	+	2.35448i	0.0146440	+	0.279425i	0.996130	+	0.0878913i	$0.0280128\pi$
$71$	0.123393	+	2.35448i	0.0146440	+	0.279425i	−0.981486	+	0.191534i	$0.938654\pi$
$72$	−4.17070	+	1.25949i	−0.491521	+	0.148432i
$73$	−6.77568	+	1.07316i	−0.793033	+	0.125604i	−0.539791	−	0.841799i	$-0.681497\pi$
$73$	−6.77568	+	1.07316i	−0.793033	+	0.125604i	−0.253242	+	0.967403i	$0.581497\pi$
$74$	−4.87702	+	10.9540i	−0.566943	+	1.27337i
$75$	−6.25198	−	5.45361i	−0.721917	−	0.629729i
$76$	1.87851	+	7.01070i	0.215480	+	0.804183i
$77$	−12.2880	−	4.78197i	−1.40035	−	0.544956i
$78$	−7.67056	−	11.1070i	−0.868520	−	1.25762i
$79$	0.194419	−	0.598360i	0.0218739	−	0.0673208i	−0.939524	−	0.342484i	$-0.888732\pi$
$79$	0.194419	−	0.598360i	0.0218739	−	0.0673208i	0.961398	+	0.275163i	$0.0887318\pi$
$80$	−0.785412	−	0.636014i	−0.0878117	−	0.0711085i
$81$	5.58945	−	7.05394i	0.621050	−	0.783771i
$82$	−10.2156	−	9.19819i	−1.12813	−	1.01577i
$83$	−14.7188	−	7.49959i	−1.61560	−	0.823187i	−0.999365	−	0.0356217i	$-0.988659\pi$
$83$	−14.7188	−	7.49959i	−1.61560	−	0.823187i	−0.616231	−	0.787566i	$-0.711341\pi$
$84$	13.2129	+	12.8034i	1.44164	+	1.39696i
$85$	−1.15023	+	0.441533i	−0.124760	+	0.0478909i
$86$	−2.37058	+	1.20787i	−0.255626	+	0.130248i
$87$	−5.19131	−	6.91373i	−0.556567	−	0.741230i
$88$	4.50453	−	1.70536i	0.480184	−	0.181792i
$89$	13.8992	−	3.72429i	1.47332	−	0.394774i	0.569249	−	0.822165i	$-0.307234\pi$
$89$	13.8992	−	3.72429i	1.47332	−	0.394774i	0.904067	+	0.427391i	$0.140567\pi$
$90$	−2.96432	−	0.217500i	−0.312466	−	0.0229266i
$91$	−6.34499	+	12.8536i	−0.665136	+	1.34742i
$92$	−4.16391	+	5.73113i	−0.434117	+	0.597511i
$93$	−7.77143	+	6.49834i	−0.805860	+	0.673846i
$94$	−9.35129	−	1.98768i	−0.964512	−	0.205013i
$95$	−0.130154	+	1.23833i	−0.0133535	+	0.127050i
$96$	13.2761	+	0.486398i	1.35498	+	0.0496428i
$97$	−11.9112	−	7.73520i	−1.20939	−	0.785390i	−0.227309	−	0.973823i	$-0.572993\pi$
$97$	−11.9112	−	7.73520i	−1.20939	−	0.785390i	−0.982086	+	0.188433i	$0.939659\pi$
$98$	4.92609	−	18.3844i	0.497611	−	1.85711i
$99$	−5.63000	+	8.20385i	−0.565836	+	0.824518i
$100$	−6.39901	−	11.0834i	−0.639901	−	1.10834i
$101$	−0.446852	−	0.496279i	−0.0444634	−	0.0493816i	0.720503	−	0.693452i	$-0.243911\pi$
$101$	−0.446852	−	0.496279i	−0.0444634	−	0.0493816i	−0.764966	+	0.644070i	$0.777244\pi$
$102$	5.34707	−	8.52455i	0.529439	−	0.844056i
$103$	10.2419	−	14.0967i	1.00916	−	1.38899i	0.0896310	−	0.995975i	$-0.471431\pi$
$103$	10.2419	−	14.0967i	1.00916	−	1.38899i	0.919531	−	0.393017i	$-0.128569\pi$
$104$	−1.41931	−	5.04010i	−0.139174	−	0.494222i
$105$	1.32904	+	2.86294i	0.129701	+	0.279394i
$106$	−21.4082	−	8.21784i	−2.07935	−	0.798187i
$107$	−6.53177	+	0.686517i	−0.631450	+	0.0663681i	−0.414846	−	0.909891i	$-0.636165\pi$
$107$	−6.53177	+	0.686517i	−0.631450	+	0.0663681i	−0.216604	+	0.976260i	$0.569498\pi$
$108$	11.6824	−	7.50152i	1.12414	−	0.721834i
$109$	−2.99471	−	2.99471i	−0.286841	−	0.286841i	0.548989	−	0.835830i	$-0.315013\pi$
$109$	−2.99471	−	2.99471i	−0.286841	−	0.286841i	−0.835830	+	0.548989i	$0.815013\pi$
$110$	3.28595	+	0.0151358i	0.313303	+	0.00144314i
$111$	1.35356	−	9.51270i	0.128474	−	0.902906i
$112$	−3.97946	−	7.81013i	−0.376024	−	0.737988i
$113$	−0.672006	+	1.50935i	−0.0632170	+	0.141988i	−0.942391	−	0.334513i	$-0.891428\pi$
$113$	−0.672006	+	1.50935i	−0.0632170	+	0.141988i	0.879174	+	0.476500i	$0.158095\pi$
$114$	−5.22282	−	8.72608i	−0.489162	−	0.817272i
$115$	−1.01925	+	0.661907i	−0.0950453	+	0.0617232i
$116$	−4.12138	−	12.6843i	−0.382661	−	1.17771i
$117$	8.35011	+	6.87573i	0.771968	+	0.635661i
$118$	−7.56757	+	5.49816i	−0.696651	+	0.506147i
$119$	−10.6714	−	0.559264i	−0.978244	−	0.0512676i
$120$	−1.06055	−	0.452325i	−0.0968147	−	0.0412914i
$121$	5.58753	−	9.47521i	0.507957	−	0.861383i
$122$	−17.3730	+	17.3730i	−1.57288	+	1.57288i
$123$	9.89242	+	4.84586i	0.891969	+	0.436937i
$124$	−14.5892	+	5.60027i	−1.31015	+	0.502919i
$125$	−0.701994	−	4.43222i	−0.0627883	−	0.396430i
$126$	−22.7202	−	12.1807i	−2.02408	−	1.08514i
$127$	1.32068	−	6.21331i	0.117191	−	0.551342i	−0.879902	−	0.475155i	$-0.842392\pi$
$127$	1.32068	−	6.21331i	0.117191	−	0.551342i	0.997094	−	0.0761871i	$-0.0242746\pi$
$128$	10.2342	+	3.92855i	0.904587	+	0.347238i
$129$	1.56174	−	1.45135i	0.137504	−	0.127784i
$130$	0.328271	−	3.55713i	0.0287912	−	0.311981i
$131$		−	21.5129i		−	1.87959i	−0.341734	−	0.939797i	$-0.611014\pi$
$131$		−	21.5129i		−	1.87959i	0.341734	−	0.939797i	$-0.388986\pi$
$132$	−12.3162	+	9.15947i	−1.07199	+	0.797230i
$133$	−5.39978	+	9.35270i	−0.468221	+	0.810982i
$134$	−13.8605	+	2.94615i	−1.19737	+	0.254508i
$135$	2.33227	−	0.483216i	0.200730	−	0.0415886i
$136$	3.03355	−	2.45652i	0.260125	−	0.210645i
$137$	−5.34200	+	0.279962i	−0.456398	+	0.0239188i	−0.279150	−	0.960247i	$-0.590053\pi$
$137$	−5.34200	+	0.279962i	−0.456398	+	0.0239188i	−0.177248	+	0.984166i	$0.556719\pi$
$138$	3.41086	−	9.32150i	0.290351	−	0.793499i
$139$	−2.40348	+	22.8676i	−0.203861	+	1.93961i	0.118423	+	0.992963i	$0.462216\pi$
$139$	−2.40348	+	22.8676i	−0.203861	+	1.93961i	−0.322284	+	0.946643i	$0.604451\pi$
$140$	0.508957	+	4.84240i	0.0430147	+	0.409258i
$141$	7.64318	−	0.521298i	0.643672	−	0.0439012i
$142$		−	5.09608i		−	0.427653i
$143$	−9.73097	−	6.95040i	−0.813745	−	0.581222i
$144$	−6.42341	+	1.57816i	−0.535284	+	0.131514i
$145$	0.119748	−	2.28492i	0.00994450	−	0.189752i
$146$	14.7466	−	1.54993i	1.22044	−	0.128274i
$147$	0.240039	+	15.2499i	0.0197981	+	1.25779i
$148$	6.72914	−	13.2067i	0.553132	−	1.08558i
$149$	0.795398	+	15.1771i	0.0651616	+	1.24336i	0.814103	+	0.580721i	$0.197229\pi$
$149$	0.795398	+	15.1771i	0.0651616	+	1.24336i	−0.748941	+	0.662636i	$0.769438\pi$
$150$	12.8779	+	12.4788i	1.05148	+	1.01889i
$151$	−0.741965	+	4.68458i	−0.0603803	+	0.381226i	0.938931	+	0.344107i	$0.111818\pi$
$151$	−0.741965	+	4.68458i	−0.0603803	+	0.381226i	−0.999311	+	0.0371193i	$0.988182\pi$
$152$	−0.820197	−	3.85872i	−0.0665267	−	0.312984i
$153$	−2.24920	+	7.74361i	−0.181837	+	0.626034i
$154$	25.9826	+	11.7119i	2.09374	+	0.943771i
$155$	−2.68093			−0.215338
$156$	8.75040	+	14.2074i	0.700593	+	1.13750i
$157$	19.2257	−	13.9683i	1.53438	−	1.11479i	0.580633	−	0.814165i	$-0.302805\pi$
$157$	19.2257	−	13.9683i	1.53438	−	1.11479i	0.953743	−	0.300624i	$-0.0971949\pi$
$158$	−0.487339	+	1.26956i	−0.0387706	+	0.101001i
$159$	18.3030	+	1.63292i	1.45152	+	0.129499i
$160$	2.61274	+	2.35252i	0.206555	+	0.185983i
$161$	−10.4110	+	1.64893i	−0.820499	+	0.129954i
$162$	−12.8627	+	14.5936i	−1.01059	+	1.14658i
$163$	1.85524	−	2.85682i	0.145314	−	0.223763i	−0.758517	−	0.651653i	$-0.774076\pi$
$163$	1.85524	−	2.85682i	0.145314	−	0.223763i	0.903831	+	0.427889i	$0.140743\pi$
$164$	12.0157	+	12.0157i	0.938265	+	0.938265i
$165$	−2.53571	+	0.709790i	−0.197405	+	0.0552571i
$166$	30.9220	+	17.8528i	2.40001	+	1.38565i
$167$	0.444689	−	8.48517i	0.0344110	−	0.656602i	−0.925917	−	0.377728i	$-0.876705\pi$
$167$	0.444689	−	8.48517i	0.0344110	−	0.656602i	0.960328	−	0.278874i	$-0.0899612\pi$
$168$	−6.80752	−	7.32530i	−0.525211	−	0.565159i
$169$	−8.45063	+	9.87861i	−0.650048	+	0.759893i
$170$	2.53271	−	0.822928i	0.194250	−	0.0631157i
$171$	5.94095	+	5.57823i	0.454316	+	0.426578i
$172$	3.00452	−	1.33770i	0.229093	−	0.101999i
$173$	−7.58216	−	3.37579i	−0.576461	−	0.256657i	0.0977314	−	0.995213i	$-0.468841\pi$
$173$	−7.58216	−	3.37579i	−0.576461	−	0.256657i	−0.674192	+	0.738556i	$0.735508\pi$
$174$	10.4233	+	15.5105i	0.790189	+	1.17585i
$175$	4.92865	−	18.3940i	0.372571	−	1.39045i
$176$	6.96497	−	2.22764i	0.525004	−	0.167915i
$177$	4.62495	−	5.89879i	0.347632	−	0.443380i
$178$	−30.4227	+	6.46654i	−2.28028	+	0.484688i
$179$	1.48006	+	14.0818i	0.110625	+	1.05252i	0.899185	+	0.437568i	$0.144160\pi$
$179$	1.48006	+	14.0818i	0.110625	+	1.05252i	−0.788561	+	0.614957i	$0.789173\pi$
$180$	3.64525	+	0.460272i	0.271701	+	0.0343066i
$181$	−22.3295	+	7.25528i	−1.65974	+	0.539281i	−0.980817	−	0.194933i	$-0.937551\pi$
$181$	−22.3295	+	7.25528i	−1.65974	+	0.539281i	−0.678919	+	0.734213i	$0.737551\pi$
$182$	15.1496	−	27.0266i	1.12297	−	2.00334i
$183$	9.57450	−	17.2032i	0.707768	−	1.27170i
$184$	2.42312	−	2.99231i	0.178635	−	0.220596i
$185$	1.88970	−	1.70149i	0.138933	−	0.125096i
$186$	17.5097	−	13.1475i	1.28387	−	0.964021i
$187$	1.89362	−	8.71126i	0.138475	−	0.637031i
$188$	11.4152	+	3.05868i	0.832536	+	0.223077i
$189$	20.1842	+	4.39889i	1.46818	+	0.319972i
$190$	0.421019	−	2.65821i	0.0305440	−	0.192847i
$191$	16.8797	+	1.77413i	1.22137	+	0.128371i	0.693186	−	0.720758i	$-0.256206\pi$
$191$	16.8797	+	1.77413i	1.22137	+	0.128371i	0.528185	+	0.849130i	$0.322873\pi$
$192$	−20.9938	−	1.87299i	−1.51509	−	0.135171i
$193$	−11.9693	+	7.77294i	−0.861567	+	0.559508i	−0.898084	−	0.439825i	$-0.855041\pi$
$193$	−11.9693	+	7.77294i	−0.861567	+	0.559508i	0.0365162	+	0.999333i	$0.488374\pi$
$194$	24.8351	+	18.0438i	1.78306	+	1.29547i
$195$	0.528005	+	2.81345i	0.0378112	+	0.201475i
$196$	−7.27043	+	22.3761i	−0.519316	+	1.59829i
$197$	−1.20947	−	4.51379i	−0.0861709	−	0.321594i	0.909362	−	0.416005i	$-0.136570\pi$
$197$	−1.20947	−	4.51379i	−0.0861709	−	0.321594i	−0.995533	+	0.0944106i	$0.969903\pi$
$198$	13.0803	−	17.0711i	0.929579	−	1.21319i
$199$	−7.28450	+	4.20571i	−0.516385	+	0.298135i	−0.735454	−	0.677574i	$-0.763031\pi$
$199$	−7.28450	+	4.20571i	−0.516385	+	0.298135i	0.219070	+	0.975709i	$0.429698\pi$
$200$	3.15799	+	6.19791i	0.223304	+	0.438258i
$201$	10.0351	−	5.31369i	0.707819	−	0.374799i
$202$	0.908385	+	1.12176i	0.0639138	+	0.0789269i
$203$	9.00940	−	17.6820i	0.632336	−	1.24103i
$204$	−7.15222	+	10.1773i	−0.500755	+	0.712550i
$205$	1.18572	+	2.66317i	0.0828143	+	0.186004i
$206$	−23.7016	+	29.2691i	−1.65137	+	2.03927i
$207$	−0.582044	+	7.93269i	−0.0404549	+	0.551360i
$208$	−1.75139	−	7.75424i	−0.121437	−	0.537660i
$209$	−6.97544	−	5.70200i	−0.482502	−	0.394416i
$210$	−2.54486	−	6.32997i	−0.175612	−	0.436809i
$211$	15.3375	+	17.0340i	1.05588	+	1.17267i	0.984529	+	0.175220i	$0.0560637\pi$
$211$	15.3375	+	17.0340i	1.05588	+	1.17267i	0.0713490	+	0.997451i	$0.477270\pi$
$212$	25.8958	+	11.5296i	1.77853	+	0.791854i
$213$	1.11888	+	3.92740i	0.0766645	+	0.269101i
$214$	14.1764	−	0.742955i	0.969081	−	0.0507874i
$215$	0.563450	−	0.0295292i	0.0384270	−	0.00201387i
$216$	−6.55440	+	3.73937i	−0.445970	+	0.254432i
$217$	−21.2422	−	9.45763i	−1.44201	−	0.642026i
$218$	6.12528	+	6.80282i	0.414857	+	0.460745i
$219$	−11.0245	+	4.43222i	−0.744968	+	0.299502i
$220$	−4.05538	−	0.231269i	−0.273414	−	0.0155922i
$221$	−9.25425	−	2.87753i	−0.622508	−	0.193563i
$222$	−3.99773	+	20.3800i	−0.268310	+	1.36781i
$223$	1.83717	−	2.26871i	0.123026	−	0.151924i	−0.711912	−	0.702269i	$-0.752170\pi$
$223$	1.83717	−	2.26871i	0.123026	−	0.151924i	0.834938	+	0.550345i	$0.185504\pi$
$224$	12.4028	+	27.8571i	0.828696	+	1.86128i
$225$	−12.6645	−	6.78961i	−0.844297	−	0.452641i
$226$	1.62126	−	3.18190i	0.107845	−	0.211657i
$227$	8.99805	+	11.1117i	0.597221	+	0.737507i	0.982699	−	0.185210i	$-0.0592966\pi$
$227$	8.99805	+	11.1117i	0.597221	+	0.737507i	−0.385478	+	0.922717i	$0.625963\pi$
$228$	5.88281	+	11.1099i	0.389598	+	0.735768i
$229$	−4.48615	−	8.80457i	−0.296453	−	0.581822i	0.693951	−	0.720022i	$-0.255868\pi$
$229$	−4.48615	−	8.80457i	−0.296453	−	0.581822i	−0.990404	+	0.138200i	$0.955868\pi$
$230$	2.27491	−	1.31342i	0.150003	−	0.0866045i
$231$	−22.5955	−	3.32135i	−1.48667	−	0.218529i
$232$	1.87620	+	7.00206i	0.123178	+	0.459708i
$233$	5.31236	−	16.3498i	0.348025	−	1.07111i	−0.611920	−	0.790920i	$-0.709603\pi$
$233$	5.31236	−	16.3498i	0.348025	−	1.07111i	0.959945	−	0.280190i	$-0.0903974\pi$
$234$	−17.2458	−	15.7858i	−1.12740	−	1.03195i
$235$	1.64022	+	1.19169i	0.106996	+	0.0777372i
$236$	9.69754	−	6.29765i	0.631256	−	0.409942i
$237$	0.0968366	−	1.08541i	0.00629022	−	0.0705052i
$238$	22.9708	+	2.41433i	1.48898	+	0.156498i
$239$	−1.16198	+	7.33646i	−0.0751623	+	0.474556i	0.921182	+	0.389131i	$0.127225\pi$
$239$	−1.16198	+	7.33646i	−0.0751623	+	0.474556i	−0.996345	+	0.0854248i	$0.972775\pi$
$240$	−1.57200	−	0.770053i	−0.101472	−	0.0497067i
$241$	−16.2374	−	4.35080i	−1.04594	−	0.280260i	−0.305369	−	0.952234i	$-0.598780\pi$
$241$	−16.2374	−	4.35080i	−1.04594	−	0.280260i	−0.740574	+	0.671974i	$0.765446\pi$
$242$	−13.1325	+	19.8201i	−0.844188	+	1.27408i
$243$	6.70882	−	14.0710i	0.430371	−	0.902652i
$244$	22.5702	−	20.3223i	1.44491	−	1.30100i
$245$	−2.54013	+	3.13680i	−0.162283	+	0.200403i
$246$	−20.8045	−	11.5788i	−1.32645	−	0.738237i
$247$	−6.83712	+	7.01296i	−0.435036	+	0.446224i
$248$	8.07807	−	2.62473i	0.512958	−	0.166670i
$249$	−27.7504	−	6.96950i	−1.75861	−	0.441674i
$250$	1.01387	+	9.64631i	0.0641227	+	0.610086i
$251$	−18.0178	+	3.82979i	−1.13727	+	0.241734i	−0.737805	−	0.675014i	$-0.764138\pi$
$251$	−18.0178	+	3.82979i	−1.13727	+	0.241734i	−0.399466	+	0.916748i	$0.630804\pi$
$252$	27.2591	+	16.5064i	1.71716	+	1.03981i
$253$	0.0405043	−	8.79340i	0.00254649	−	0.552836i
$254$	−3.55353	+	13.2620i	−0.222969	+	0.832130i
$255$	−1.77121	+	1.19028i	−0.110917	+	0.0745384i
$256$	0.587586	+	0.261610i	0.0367241	+	0.0163506i
$257$	10.5537	−	4.69881i	0.658322	−	0.293104i	−0.0502561	−	0.998736i	$-0.516004\pi$
$257$	10.5537	−	4.69881i	0.658322	−	0.293104i	0.708578	+	0.705633i	$0.249337\pi$
$258$	−3.53518	+	2.95606i	−0.220091	+	0.184036i
$259$	20.9753	−	6.81528i	1.30334	−	0.423481i
$260$	−0.635364	+	4.36988i	−0.0394036	+	0.271008i
$261$	−11.4384	−	9.66497i	−0.708018	−	0.598246i
$262$	−2.43358	+	46.4355i	−0.150347	+	2.86879i
$263$	−15.5243	−	8.96293i	−0.957267	−	0.552678i	−0.0619360	−	0.998080i	$-0.519727\pi$
$263$	−15.5243	−	8.96293i	−0.957267	−	0.552678i	−0.895331	+	0.445402i	$0.853061\pi$
$264$	6.94558	−	4.62125i	0.427471	−	0.284418i
$265$	3.43867	+	3.43867i	0.211236	+	0.211236i
$266$	12.7134	−	19.5769i	0.779507	−	1.20034i
$267$	22.0261	−	11.6631i	1.34798	−	0.713770i
$268$	17.3008	−	2.74018i	1.05682	−	0.167383i
$269$	0.264473	+	0.238133i	0.0161252	+	0.0145192i	0.677154	−	0.735841i	$-0.263213\pi$
$269$	0.264473	+	0.238133i	0.0161252	+	0.0145192i	−0.661029	+	0.750361i	$0.729880\pi$
$270$	−5.08884	+	0.779188i	−0.309697	+	0.0474199i
$271$	3.01258	−	7.84804i	0.183001	−	0.476734i	−0.811136	−	0.584857i	$-0.801151\pi$
$271$	3.01258	−	7.84804i	0.183001	−	0.476734i	0.994138	+	0.108123i	$0.0344839\pi$
$272$	4.79446	−	3.48338i	0.290707	−	0.211211i
$273$	−5.74150	+	24.1548i	−0.347491	+	1.46192i
$274$	11.5623			0.698506
$275$	14.4829	+	6.52831i	0.873352	+	0.393672i
$276$	−4.81361	+	11.2863i	−0.289745	+	0.679356i
$277$	−0.169866	−	0.799158i	−0.0102063	−	0.0480168i	0.972750	−	0.231857i	$-0.0744803\pi$
$277$	−0.169866	−	0.799158i	−0.0102063	−	0.0480168i	−0.982956	+	0.183841i	$0.941147\pi$
$278$	7.77472	−	49.0877i	0.466297	−	2.94408i
$279$	−10.6076	+	13.9768i	−0.635059	+	0.836767i
$280$	−0.138506	−	2.64285i	−0.00827730	−	0.157940i
$281$	5.00849	−	9.82971i	0.298781	−	0.586391i	−0.691995	−	0.721903i	$-0.743268\pi$
$281$	5.00849	−	9.82971i	0.298781	−	0.586391i	0.990776	+	0.135512i	$0.0432678\pi$
$282$	−16.5567	+	0.260608i	−0.985937	+	0.0155190i
$283$	21.2578	−	2.23428i	1.26364	−	0.132814i	0.551098	−	0.834440i	$-0.314209\pi$
$283$	21.2578	−	2.23428i	1.26364	−	0.132814i	0.712545	+	0.701626i	$0.247542\pi$
$284$	−0.329691	+	6.29088i	−0.0195636	+	0.373295i
$285$	0.259162	+	2.14105i	0.0153515	+	0.126825i
$286$	20.2180	+	16.1032i	1.19551	+	0.952201i
$287$			25.2843i			1.49249i
$288$	22.6024	−	4.31309i	1.33186	−	0.254152i
$289$	1.02180	+	9.72173i	0.0601056	+	0.571867i
$290$	−0.516948	+	4.91843i	−0.0303562	+	0.288820i
$291$	−23.1013	−	8.45308i	−1.35422	−	0.495528i
$292$	−18.3044	+	0.959291i	−1.07118	+	0.0561383i
$293$	−9.64568	+	7.81092i	−0.563506	+	0.456319i	−0.868258	−	0.496113i	$-0.834760\pi$
$293$	−9.64568	+	7.81092i	−0.563506	+	0.456319i	0.304751	+	0.952432i	$0.401427\pi$
$294$	1.20697	−	32.9440i	0.0703922	−	1.92133i
$295$	1.94035	−	0.412434i	0.112972	−	0.0240129i
$296$	−4.02814	+	6.97694i	−0.234131	+	0.405526i
$297$	−6.33256	+	16.0281i	−0.367452	+	0.930042i
$298$		−	32.8496i		−	1.90293i
$299$	−9.51909	−	0.878472i	−0.550503	−	0.0508034i
$300$	−15.0899	−	16.2377i	−0.871217	−	0.937483i
$301$	4.56863	+	1.75373i	0.263331	+	0.101083i
$302$	2.13145	−	10.0277i	0.122651	−	0.577029i
$303$	−0.946358	−	0.665067i	−0.0543668	−	0.0382071i
$304$	−0.936924	−	5.91551i	−0.0537363	−	0.339278i
$305$	4.86429	−	1.86722i	0.278528	−	0.106917i
$306$	5.73086	−	16.4601i	0.327611	−	0.940960i
$307$	−13.9701	+	13.9701i	−0.797317	+	0.797317i	−0.982672	−	0.185355i	$-0.940657\pi$
$307$	−13.9701	+	13.9701i	−0.797317	+	0.797317i	0.185355	+	0.982672i	$0.440657\pi$
$308$	−31.3166	−	16.1388i	−1.78443	−	0.919591i
$309$	11.8399	−	27.7607i	0.673550	−	1.57925i
$310$	5.78677	+	0.303272i	0.328667	+	0.0172247i
$311$	−10.5227	+	7.64520i	−0.596688	+	0.433520i	−0.844702	−	0.535237i	$-0.820222\pi$
$311$	−10.5227	+	7.64520i	−0.596688	+	0.433520i	0.248013	+	0.968757i	$0.420222\pi$
$312$	−4.34542	−	7.96043i	−0.246011	−	0.450670i
$313$	−0.0697866	−	0.214781i	−0.00394457	−	0.0121401i	0.949065	−	0.315081i	$-0.102032\pi$
$313$	−0.0697866	−	0.214781i	−0.00394457	−	0.0121401i	−0.953009	+	0.302941i	$0.902032\pi$
$314$	−43.0786	+	27.9755i	−2.43106	+	1.57875i
$315$	3.35104	+	4.31958i	0.188810	+	0.243381i
$316$	0.683734	−	1.53569i	0.0384630	−	0.0863894i
$317$	−1.89332	−	3.71586i	−0.106340	−	0.208703i	0.831705	−	0.555218i	$-0.187365\pi$
$317$	−1.89332	−	3.71586i	−0.106340	−	0.208703i	−0.938045	+	0.346515i	$0.887365\pi$
$318$	−39.3221	−	5.59511i	−2.20507	−	0.313758i
$319$	13.3486	+	9.79261i	0.747380	+	0.548281i
$320$	−3.94421	−	3.94421i	−0.220488	−	0.220488i
$321$	−10.7622	+	3.68512i	−0.600690	+	0.205683i
$322$	22.6585	−	2.38151i	1.26271	−	0.132716i
$323$	−6.81652	−	2.61662i	−0.379281	−	0.145592i
$324$	16.8226	−	17.1830i	0.934590	−	0.954609i
$325$	8.44453	−	15.0648i	0.468418	−	0.835647i
$326$	−4.32769	+	5.95656i	−0.239689	+	0.329903i
$327$	−6.21419	−	3.89788i	−0.343645	−	0.215553i
$328$	−6.18009	−	6.86369i	−0.341238	−	0.378984i
$329$	8.79219	+	15.2285i	0.484729	+	0.839576i
$330$	5.55360	−	1.24523i	0.305716	−	0.0685477i
$331$	−0.855470	+	3.19266i	−0.0470209	+	0.175484i	−0.985443	−	0.170007i	$-0.945621\pi$
$331$	−0.855470	+	3.19266i	−0.0470209	+	0.175484i	0.938422	+	0.345491i	$0.112288\pi$
$332$	−37.0169	−	24.0390i	−2.03156	−	1.31931i
$333$	−1.39363	−	16.5840i	−0.0763707	−	0.908797i
$334$	−1.91971	+	18.2649i	−0.105042	+	0.999408i
$335$	2.93939	+	0.624787i	0.160596	+	0.0341357i
$336$	−9.73906	−	11.6470i	−0.531309	−	0.635398i
$337$	6.78574	−	9.33977i	0.369643	−	0.508770i	−0.583161	−	0.812357i	$-0.698184\pi$
$337$	6.78574	−	9.33977i	0.369643	−	0.508770i	0.952804	+	0.303587i	$0.0981843\pi$
$338$	19.3581	−	20.3669i	1.05294	−	1.10782i
$339$	−0.550848	+	2.80816i	−0.0299180	+	0.152518i
$340$	−3.17976	+	0.852015i	−0.172447	+	0.0462070i
$341$	10.6398	−	16.2198i	0.576177	−	0.878350i
$342$	−12.1925	−	12.7126i	−0.659293	−	0.687419i
$343$	−6.39612	+	3.25898i	−0.345358	+	0.175969i
$344$	−1.66885	+	0.640613i	−0.0899786	+	0.0345395i
$345$	−1.46484	+	1.51169i	−0.0788643	+	0.0813867i
$346$	15.9841	+	8.14433i	0.859313	+	0.437842i
$347$	22.6200	+	20.3671i	1.21430	+	1.09336i	0.992994	+	0.118161i	$0.0377000\pi$
$347$	22.6200	+	20.3671i	1.21430	+	1.09336i	0.221310	+	0.975203i	$0.428967\pi$
$348$	−11.8637	−	19.8213i	−0.635959	−	1.06254i
$349$	−3.20947	−	2.59898i	−0.171799	−	0.139120i	0.539565	−	0.841944i	$-0.318589\pi$
$349$	−3.20947	−	2.59898i	−0.171799	−	0.139120i	−0.711364	+	0.702824i	$0.751922\pi$
$350$	−12.7192	+	39.1457i	−0.679870	+	2.09242i
$351$	16.7568	+	8.37920i	0.894410	+	0.447248i
$352$	−24.6020	+	6.47079i	−1.31129	+	0.344894i
$353$	0.853150	+	3.18400i	0.0454086	+	0.169467i	0.984906	−	0.173088i	$-0.0553744\pi$
$353$	0.853150	+	3.18400i	0.0454086	+	0.169467i	−0.939498	+	0.342555i	$0.888708\pi$
$354$	−10.6502	+	12.2093i	−0.566051	+	0.648917i
$355$	−0.439569	+	0.987287i	−0.0233299	+	0.0523998i
$356$	37.9738	−	6.01446i	2.01261	−	0.318766i
$357$	−18.2330	+	3.18276i	−0.964995	+	0.168449i
$358$	−1.60173	−	30.5629i	−0.0846543	−	1.61530i
$359$	−4.72108	−	29.8077i	−0.249169	−	1.57319i	−0.721908	−	0.691989i	$-0.756735\pi$
$359$	−4.72108	−	29.8077i	−0.249169	−	1.57319i	0.472739	−	0.881202i	$-0.343265\pi$
$360$	−1.96548	−	0.353520i	−0.103590	−	0.0186321i
$361$	8.63604	−	7.77593i	0.454529	−	0.409259i
$362$	49.0187	−	13.1345i	2.57636	−	0.690335i
$363$	5.76918	−	18.1581i	0.302803	−	0.953053i
$364$	−20.4500	+	32.3830i	−1.07187	+	1.69733i
$365$	−2.99063	−	0.971714i	−0.156537	−	0.0508618i
$366$	−22.6125	+	36.0500i	−1.18198	+	1.88436i
$367$	−12.6089	+	5.61385i	−0.658180	+	0.293040i	−0.708519	−	0.705692i	$-0.750636\pi$
$367$	−12.6089	+	5.61385i	−0.658180	+	0.293040i	0.0503394	+	0.998732i	$0.483970\pi$
$368$	3.91154	−	4.34420i	0.203903	−	0.226457i
$369$	18.5757	+	4.35566i	0.967010	+	0.226747i
$370$	−4.27137	+	3.45889i	−0.222058	+	0.179819i
$371$	15.1153	+	39.3768i	0.784749	+	2.04434i
$372$	−22.4655	+	15.0972i	−1.16478	+	0.782754i
$373$	−7.54832	−	13.0741i	−0.390837	−	0.676950i	0.601723	−	0.798705i	$-0.294481\pi$
$373$	−7.54832	−	13.0741i	−0.390837	−	0.676950i	−0.992560	+	0.121755i	$0.961148\pi$
$374$	−5.07279	+	18.5890i	−0.262308	+	0.961213i
$375$	−2.89928	−	7.21153i	−0.149718	−	0.372402i
$376$	−6.10894	−	1.98492i	−0.315045	−	0.102364i
$377$	11.8720	−	13.5266i	0.611439	−	0.696657i
$378$	−43.0698	−	11.7782i	−2.21527	−	0.605808i
$379$	15.5414	+	23.9317i	0.798310	+	1.22929i	0.969751	+	0.244095i	$0.0784908\pi$
$379$	15.5414	+	23.9317i	0.798310	+	1.22929i	−0.171442	+	0.985194i	$0.554843\pi$
$380$	−0.691703	+	3.25421i	−0.0354836	+	0.166937i
$381$	−0.173157	−	11.0008i	−0.00887110	−	0.563589i
$382$	−36.2340	−	5.73889i	−1.85389	−	0.293627i
$383$	3.92016	−	6.03651i	0.200311	−	0.308451i	−0.724213	−	0.689577i	$-0.757797\pi$
$383$	3.92016	−	6.03651i	0.200311	−	0.308451i	0.924523	+	0.381125i	$0.124463\pi$
$384$	18.7980	+	2.67476i	0.959281	+	0.136496i
$385$	−4.02350	−	4.51016i	−0.205057	−	0.229859i
$386$	26.7149	−	15.4238i	1.35975	−	0.785053i
$387$	2.07544	−	3.05433i	0.105501	−	0.155260i
$388$	−29.4905	−	23.8809i	−1.49715	−	1.21237i
$389$	−16.4265	−	11.9345i	−0.832856	−	0.605105i	0.0875101	−	0.996164i	$-0.472109\pi$
$389$	−16.4265	−	11.9345i	−0.832856	−	0.605105i	−0.920366	+	0.391059i	$0.872109\pi$
$390$	−0.821431	−	6.13253i	−0.0415948	−	0.310533i
$391$	−2.20221	−	6.77769i	−0.111370	−	0.342763i
$392$	4.58277	−	11.9385i	0.231465	−	0.602987i
$393$	−8.31976	−	36.3208i	−0.419676	−	1.83214i
$394$	2.10001	+	9.87979i	0.105797	+	0.497737i
$395$	0.203922	−	0.203922i	0.0102604	−	0.0102604i
$396$	−17.2515	+	20.2272i	−0.866921	+	1.01646i
$397$	−12.2088	−	3.27135i	−0.612744	−	0.164184i	−0.0609172	−	0.998143i	$-0.519403\pi$
$397$	−12.2088	−	3.27135i	−0.612744	−	0.164184i	−0.551827	+	0.833958i	$0.686069\pi$
$398$	16.1993	−	8.25395i	0.811997	−	0.413733i
$399$	−5.49959	+	17.8787i	−0.275324	+	0.895053i
$400$	4.29547	+	9.64778i	0.214773	+	0.482389i
$401$	−17.3825	−	26.7668i	−0.868042	−	1.33667i	−0.940675	−	0.339309i	$-0.889807\pi$
$401$	−17.3825	−	26.7668i	−0.868042	−	1.33667i	0.0726326	−	0.997359i	$-0.476860\pi$
$402$	−22.2617	+	10.3344i	−1.11031	+	0.515432i
$403$	−16.5556	−	13.0620i	−0.824692	−	0.650663i
$404$	−1.04879	−	1.44353i	−0.0521792	−	0.0718185i
$405$	3.75075	−	1.71779i	0.186376	−	0.0853577i
$406$	−21.4469	+	37.1472i	−1.06439	+	1.84358i
$407$	2.79449	+	18.1855i	0.138518	+	0.901419i
$408$	4.17160	−	5.32058i	0.206525	−	0.263408i
$409$	−6.74449	−	4.37992i	−0.333493	−	0.216573i	0.367019	−	0.930213i	$-0.380378\pi$
$409$	−6.74449	−	4.37992i	−0.333493	−	0.216573i	−0.700512	+	0.713640i	$0.747045\pi$
$410$	−2.25810	−	5.88256i	−0.111520	−	0.290519i
$411$	−8.91076	+	2.53860i	−0.439535	+	0.125220i
$412$	31.1522	−	34.5980i	1.53476	−	1.70452i
$413$	16.8292	+	3.57715i	0.828110	+	0.176020i
$414$	2.15370	−	17.0568i	0.105848	−	0.838296i
$415$	−4.45075	−	6.12593i	−0.218479	−	0.300710i
$416$	4.67257	+	27.2573i	0.229092	+	1.33640i
$417$	4.78581	+	39.5375i	0.234362	+	1.93616i
$418$	14.4114	+	13.0968i	0.704885	+	0.640585i
$419$	6.92093	+	3.99580i	0.338110	+	0.195208i	0.659436	−	0.751761i	$-0.270795\pi$
$419$	6.92093	+	3.99580i	0.338110	+	0.195208i	−0.321326	+	0.946969i	$0.604129\pi$
$420$	2.73200	+	7.97871i	0.133308	+	0.389321i
$421$	11.3257	+	1.79381i	0.551978	+	0.0874248i	0.426192	−	0.904633i	$-0.359855\pi$
$421$	11.3257	+	1.79381i	0.551978	+	0.0874248i	0.125786	+	0.992057i	$0.459855\pi$
$422$	−31.1790	−	38.5028i	−1.51777	−	1.87429i
$423$	12.7026	−	3.83599i	0.617619	−	0.186512i
$424$	−13.7278	−	6.99468i	−0.666682	−	0.339692i
$425$	12.8041	+	1.34577i	0.621092	+	0.0652794i
$426$	−1.97082	−	8.60383i	−0.0954866	−	0.416857i
$427$	45.1289	+	2.36510i	2.18394	+	0.114455i
$428$	−17.5483			−0.848227
$429$	−19.1170	−	7.97125i	−0.922977	−	0.384855i
$430$	−1.21954			−0.0588116
$431$	−10.3012	−	0.539863i	−0.496191	−	0.0260043i	−0.197401	−	0.980323i	$-0.563250\pi$
$431$	−10.3012	−	0.539863i	−0.496191	−	0.0260043i	−0.298791	+	0.954319i	$0.596583\pi$
$432$	−10.2345	+	5.14860i	−0.492406	+	0.247712i
$433$	7.47599	+	0.785758i	0.359273	+	0.0377611i	0.282446	−	0.959283i	$-0.408854\pi$
$433$	7.47599	+	0.785758i	0.359273	+	0.0377611i	0.0768274	+	0.997044i	$0.475521\pi$
$434$	44.7812	+	22.8172i	2.14957	+	1.09526i
$435$	−0.681481	−	3.90400i	−0.0326745	−	0.187182i
$436$	−7.12129	−	8.79406i	−0.341048	−	0.421159i
$437$	−7.11354	−	1.12667i	−0.340287	−	0.0538961i
$438$	24.2977	−	8.31981i	1.16099	−	0.397536i
$439$	−6.52469	−	3.76703i	−0.311406	−	0.179791i	0.336149	−	0.941809i	$-0.390875\pi$
$439$	−6.52469	−	3.76703i	−0.311406	−	0.179791i	−0.647556	+	0.762018i	$0.724209\pi$
$440$	2.19461	+	0.240888i	0.104624	+	0.0114839i
$441$	6.30291	+	25.6540i	0.300139	+	1.22162i
$442$	19.6497	+	7.25798i	0.934641	+	0.345227i
$443$	12.6207	+	17.3709i	0.599627	+	0.825316i	0.995674	−	0.0929140i	$-0.0296182\pi$
$443$	12.6207	+	17.3709i	0.599627	+	0.825316i	−0.396047	+	0.918230i	$0.629618\pi$
$444$	6.25351	−	24.8995i	0.296778	−	1.18168i
$445$	6.45171	+	1.37135i	0.305840	+	0.0650084i
$446$	−4.22215	+	4.68917i	−0.199925	+	0.222039i
$447$	7.21238	+	25.3163i	0.341134	+	1.19742i
$448$	−17.3375	−	45.1657i	−0.819120	−	2.13388i
$449$	−9.94313	−	6.45715i	−0.469245	−	0.304732i	0.288270	−	0.957549i	$-0.406920\pi$
$449$	−9.94313	−	6.45715i	−0.469245	−	0.304732i	−0.757515	+	0.652818i	$0.773587\pi$
$450$	26.5681	+	16.0879i	1.25243	+	0.758393i
$451$	−20.8181	−	3.39563i	−0.980284	−	0.159894i
$452$	−2.20723	+	3.82303i	−0.103819	+	0.179820i
$453$	0.559006	+	8.19604i	0.0262644	+	0.385083i
$454$	−18.1652	−	25.0023i	−0.852537	−	1.17342i
$455$	−5.26622	+	3.92923i	−0.246884	+	0.184205i
$456$	−2.87705	−	6.19757i	−0.134730	−	0.290228i
$457$	−1.91773	−	2.95305i	−0.0897078	−	0.138138i	0.790968	−	0.611858i	$-0.209578\pi$
$457$	−1.91773	−	2.95305i	−0.0897078	−	0.138138i	−0.880676	+	0.473720i	$0.842911\pi$
$458$	8.68733	+	19.5121i	0.405932	+	0.911739i
$459$	−0.802676	+	13.9436i	−0.0374657	+	0.650830i
$460$	−2.89325	+	1.47419i	−0.134899	+	0.0687343i
$461$	−4.77225	−	1.27872i	−0.222266	−	0.0595559i	0.145967	−	0.989289i	$-0.453371\pi$
$461$	−4.77225	−	1.27872i	−0.222266	−	0.0595559i	−0.368233	+	0.929733i	$0.620037\pi$
$462$	48.3964	+	9.72514i	2.25160	+	0.452454i
$463$	−22.1389	+	22.1389i	−1.02888	+	1.02888i	−0.0293103	+	0.999570i	$0.509331\pi$
$463$	−22.1389	+	22.1389i	−1.02888	+	1.02888i	−0.999570	+	0.0293103i	$0.990669\pi$
$464$	2.28820	+	10.7651i	0.106227	+	0.499759i
$465$	−4.52629	+	1.03681i	−0.209901	+	0.0480807i
$466$	−13.3162	+	34.6899i	−0.616861	+	1.60698i
$467$	9.78402	+	30.1121i	0.452750	+	1.39342i	0.873756	+	0.486365i	$0.161677\pi$
$467$	9.78402	+	30.1121i	0.452750	+	1.39342i	−0.421005	+	0.907058i	$0.638323\pi$
$468$	20.2680	+	20.6026i	0.936888	+	0.952355i
$469$	21.0859	+	15.3198i	0.973659	+	0.707404i
$470$	−3.40559	−	2.75780i	−0.157088	−	0.127208i
$471$	27.0572	−	31.0182i	1.24673	−	1.42924i
$472$	−5.44280	+	3.14240i	−0.250525	+	0.144641i
$473$	−2.05750	+	3.52609i	−0.0946042	+	0.162130i
$474$	−0.331805	+	2.33190i	−0.0152403	+	0.107108i
$475$	7.08655	−	10.9123i	0.325153	−	0.500692i
$476$	−28.2003	−	4.46649i	−1.29256	−	0.204721i
$477$	31.5329	−	4.32146i	1.44379	−	0.197866i
$478$	3.33804	−	15.7042i	0.152678	−	0.718295i
$479$	−5.46937	−	8.42209i	−0.249902	−	0.384815i	0.691350	−	0.722520i	$-0.257016\pi$
$479$	−5.46937	−	8.42209i	−0.249902	−	0.384815i	−0.941252	+	0.337705i	$0.890349\pi$
$480$	5.32095	+	2.96139i	0.242867	+	0.135168i
$481$	19.9594	−	1.30029i	0.910071	−	0.0592883i
$482$	34.5561	+	11.2280i	1.57399	+	0.511420i
$483$	−16.9394	+	6.81020i	−0.770769	+	0.309875i
$484$	17.4937	−	23.6174i	0.795170	−	1.07352i
$485$	−3.25504	−	5.63789i	−0.147804	−	0.256003i
$486$	−16.0727	+	29.6131i	−0.729070	+	1.34328i
$487$	−1.87937	−	4.89594i	−0.0851626	−	0.221856i	0.884385	−	0.466757i	$-0.154578\pi$
$487$	−1.87937	−	4.89594i	−0.0851626	−	0.221856i	−0.969548	+	0.244901i	$0.921244\pi$
$488$	−12.8288	+	10.3885i	−0.580731	+	0.470267i
$489$	2.02742	−	5.54072i	0.0916831	−	0.250560i
$490$	5.83768	−	6.48341i	0.263720	−	0.292890i
$491$	18.9886	−	8.45426i	0.856943	−	0.381535i	0.0692466	−	0.997600i	$-0.477940\pi$
$491$	18.9886	−	8.45426i	0.856943	−	0.381535i	0.787696	+	0.616064i	$0.211274\pi$
$492$	24.9332	+	15.6395i	1.12407	+	0.705082i
$493$	12.7603	+	4.14606i	0.574694	+	0.186729i
$494$	15.5512	−	14.3640i	0.699681	−	0.646266i
$495$	−4.00660	+	2.17900i	−0.180083	+	0.0979387i
$496$	12.4560	−	3.33757i	0.559291	−	0.149861i
$497$	−6.96578	+	6.27201i	−0.312458	+	0.281338i
$498$	59.1106	+	18.1828i	2.64881	+	0.814790i
$499$	3.93099	+	24.8193i	0.175975	+	1.11106i	0.904635	+	0.426188i	$0.140144\pi$
$499$	3.93099	+	24.8193i	0.175975	+	1.11106i	−0.728659	+	0.684876i	$0.759856\pi$
$500$	−0.627507	−	11.9735i	−0.0280630	−	0.535473i
$501$	−2.53072	−	14.4977i	−0.113064	−	0.647709i
$502$	39.3244	−	6.22837i	1.75513	−	0.277986i
$503$	−5.84350	+	13.1247i	−0.260549	+	0.585202i	−0.995693	−	0.0927084i	$-0.970448\pi$
$503$	−5.84350	+	13.1247i	−0.260549	+	0.585202i	0.735145	+	0.677910i	$0.237114\pi$
$504$	−14.3262	−	9.73479i	−0.638141	−	0.433622i
$505$	−0.0792268	−	0.295678i	−0.00352554	−	0.0131575i
$506$	−1.08215	+	18.9759i	−0.0481076	+	0.843581i
$507$	−10.4470	+	19.9464i	−0.463968	+	0.885852i
$508$	5.24467	−	16.1414i	0.232695	−	0.716160i
$509$	−20.9639	−	16.9762i	−0.929208	−	0.752458i	0.0398716	−	0.999205i	$-0.487305\pi$
$509$	−20.9639	−	16.9762i	−0.929208	−	0.752458i	−0.969080	+	0.246747i	$0.920638\pi$
$510$	3.95779	−	2.36885i	0.175254	−	0.104895i
$511$	−20.2681	−	18.2495i	−0.896607	−	0.807308i
$512$	−20.7738	−	10.5848i	−0.918079	−	0.467784i
$513$	12.1875	+	7.12030i	0.538093	+	0.314369i
$514$	−23.3116	+	8.94849i	−1.02823	+	0.394701i
$515$	7.11648	−	3.62603i	0.313589	−	0.159782i
$516$	4.55527	−	3.42042i	0.200535	−	0.150575i
$517$	−13.7193	+	5.19397i	−0.603374	+	0.228430i
$518$	−46.0459	+	12.3380i	−2.02314	+	0.542099i
$519$	−14.1067	−	2.76716i	−0.619214	−	0.121465i
$520$	0.469170	−	2.35382i	0.0205745	−	0.103222i
$521$	−18.7646	+	25.8273i	−0.822093	+	1.13151i	0.167251	+	0.985914i	$0.446511\pi$
$521$	−18.7646	+	25.8273i	−0.822093	+	1.13151i	−0.989344	+	0.145599i	$0.953489\pi$
$522$	23.5963	+	22.1557i	1.03278	+	0.969728i
$523$	−21.5148	−	4.57310i	−0.940774	−	0.199968i	−0.288095	−	0.957602i	$-0.593022\pi$
$523$	−21.5148	−	4.57310i	−0.940774	−	0.199968i	−0.652680	+	0.757634i	$0.726355\pi$
$524$	6.00830	−	57.1651i	0.262474	−	2.49727i
$525$	1.20760	−	32.9610i	0.0527040	−	1.43854i
$526$	32.4951	+	21.1025i	1.41685	+	0.920115i
$527$	4.06883	−	15.1851i	0.177241	−	0.661472i
$528$	10.8976	−	6.45456i	0.474258	−	0.280899i
$529$	7.98520	+	13.8308i	0.347183	+	0.601338i
$530$	−7.03336	−	7.81133i	−0.305509	−	0.339303i
$531$	5.52715	−	11.7477i	0.239858	−	0.509806i
$532$	−16.9606	+	23.3443i	−0.735337	+	1.01210i
$533$	−5.65324	+	22.2229i	−0.244869	+	0.962581i
$534$	−48.8625	+	22.6831i	−2.11449	+	0.981592i
$535$	−2.81055	−	1.07887i	−0.121511	−	0.0466436i
$536$	−9.46853	+	0.995182i	−0.408978	+	0.0429853i
$537$	7.94472	+	23.2023i	0.342840	+	1.00125i
$538$	−0.543925	−	0.543925i	−0.0234503	−	0.0234503i
$539$	−8.89680	−	27.8169i	−0.383212	−	1.19816i
$540$	6.33236	−	0.632650i	0.272501	−	0.0272249i
$541$	−7.37191	−	14.4682i	−0.316943	−	0.622036i	0.676490	−	0.736452i	$-0.263500\pi$
$541$	−7.37191	−	14.4682i	−0.316943	−	0.622036i	−0.993433	+	0.114416i	$0.963500\pi$
$542$	−7.39041	+	16.5991i	−0.317445	+	0.712994i
$543$	−34.8935	+	20.8848i	−1.49742	+	0.896253i
$544$	−17.2903	+	11.2284i	−0.741314	+	0.481415i
$545$	−0.599895	−	1.84629i	−0.0256967	−	0.0790862i
$546$	15.1254	−	51.4885i	0.647308	−	2.20350i
$547$	−25.8183	+	18.7581i	−1.10391	+	0.802037i	−0.981694	−	0.190467i	$-0.939000\pi$
$547$	−25.8183	+	18.7581i	−1.10391	+	0.802037i	−0.122215	+	0.992504i	$0.539000\pi$
$548$	−14.2732	−	0.748026i	−0.609721	−	0.0319541i
$549$	9.51180	−	32.7474i	0.405954	−	1.39763i
$550$	−30.5227	−	15.7296i	−1.30149	−	0.670714i
$551$	9.58802	−	9.58802i	0.408463	−	0.408463i
$552$	2.93379	−	5.98909i	0.124870	−	0.254912i
$553$	2.33515	−	0.896379i	0.0993005	−	0.0381179i
$554$	0.276253	+	1.74419i	0.0117369	+	0.0741036i
$555$	2.53240	−	3.60348i	0.107494	−	0.152959i
$556$	−12.7733	+	60.0936i	−0.541708	+	2.54854i
$557$	−27.4817	−	10.5492i	−1.16444	−	0.446986i	−0.302079	−	0.953283i	$-0.597681\pi$
$557$	−27.4817	−	10.5492i	−1.16444	−	0.446986i	−0.862359	+	0.506297i	$0.831014\pi$
$558$	24.4774	−	28.9688i	1.03621	−	1.22635i
$559$	3.62335	+	2.56287i	0.153251	+	0.108398i
$560$		−	4.01792i		−	0.169788i
$561$	−0.171896	−	15.4398i	−0.00725745	−	0.651867i
$562$	−11.9227	+	20.6508i	−0.502930	+	0.871100i
$563$	−8.39703	+	1.78484i	−0.353893	+	0.0752222i	−0.381428	−	0.924399i	$-0.624568\pi$
$563$	−8.39703	+	1.78484i	−0.353893	+	0.0752222i	0.0275352	+	0.999621i	$0.491234\pi$
$564$	20.4554	+	0.749428i	0.861327	+	0.0315566i
$565$	−0.588553	+	0.476601i	−0.0247606	+	0.0200507i
$566$	−46.1375	+	2.41796i	−1.93930	+	0.101635i
$567$	35.7787	−	0.379137i	1.50256	−	0.0159223i
$568$	0.357901	−	3.40520i	0.0150172	−	0.142879i
$569$	3.90088	+	37.1144i	0.163533	+	1.55592i	0.701327	+	0.712840i	$0.252591\pi$
$569$	3.90088	+	37.1144i	0.163533	+	1.55592i	−0.537793	+	0.843077i	$0.680742\pi$
$570$	−0.317201	−	4.65074i	−0.0132861	−	0.194798i
$571$		−	5.31486i		−	0.222420i	−0.993797	−	0.111210i	$-0.964527\pi$
$571$		−	5.31486i		−	0.222420i	0.993797	−	0.111210i	$-0.0354726\pi$
$572$	−23.9164	−	21.1867i	−0.999996	−	0.885859i
$573$	29.1845	−	3.53263i	1.21920	−	0.147578i
$574$	2.86021	−	54.5760i	0.119383	−	2.27796i
$575$	12.6300	−	1.32747i	0.526709	−	0.0553594i
$576$	−36.1686	+	4.95678i	−1.50703	+	0.206532i
$577$	16.0536	−	31.5071i	0.668322	−	1.31166i	−0.268983	−	0.963145i	$-0.586687\pi$
$577$	16.0536	−	31.5071i	0.668322	−	1.31166i	0.937305	−	0.348511i	$-0.113313\pi$
$578$	−1.10580	−	21.0999i	−0.0459951	−	0.877639i
$579$	−17.2020	+	17.7522i	−0.714889	+	0.737754i
$580$	0.956349	−	6.03815i	0.0397102	−	0.250720i
$581$	−13.6545	−	64.2394i	−0.566484	−	2.66510i
$582$	48.9078	+	20.8592i	2.02729	+	0.864640i
$583$	−34.4511	+	7.15712i	−1.42682	+	0.296418i
$584$	9.96257			0.412254
$585$	1.97950	+	4.54582i	0.0818421	+	0.187946i
$586$	21.7037	−	15.7687i	0.896571	−	0.651397i
$587$	14.8443	−	38.6707i	0.612690	−	1.59611i	−0.178092	−	0.984014i	$-0.556993\pi$
$587$	14.8443	−	38.6707i	0.612690	−	1.59611i	0.790782	−	0.612098i	$-0.209674\pi$
$588$	−3.62127	+	40.5898i	−0.149339	+	1.67389i
$589$	−11.8069	−	10.6310i	−0.486496	−	0.438043i
$590$	−4.23489	+	0.670740i	−0.174348	+	0.0276139i
$591$	−3.78760	−	7.15300i	−0.155801	−	0.294235i
$592$	−6.66156	+	10.2579i	−0.273789	+	0.421597i
$593$	17.5342	+	17.5342i	0.720044	+	0.720044i	0.968614	−	0.248570i	$-0.0799607\pi$
$593$	17.5342	+	17.5342i	0.720044	+	0.720044i	−0.248570	+	0.968614i	$0.579961\pi$
$594$	15.4819	−	33.8801i	0.635230	−	1.39012i
$595$	−4.24200	−	2.44912i	−0.173905	−	0.100404i
$596$	−2.12521	+	40.5514i	−0.0870520	+	1.66105i
$597$	−10.6721	+	9.91776i	−0.436780	+	0.405907i
$598$	20.4475	+	2.97299i	0.836160	+	0.121575i
$599$	6.54849	−	2.12773i	0.267564	−	0.0869369i	−0.172162	−	0.985069i	$-0.555075\pi$
$599$	6.54849	−	2.12773i	0.267564	−	0.0869369i	0.439727	+	0.898132i	$0.355075\pi$
$600$	7.72865	+	9.24277i	0.315521	+	0.377335i
$601$	−9.18354	+	4.08877i	−0.374604	+	0.166785i	−0.585398	−	0.810746i	$-0.699062\pi$
$601$	−9.18354	+	4.08877i	−0.374604	+	0.166785i	0.210794	+	0.977531i	$0.432395\pi$
$602$	−9.66296	−	4.30223i	−0.393833	−	0.175346i
$603$	14.8875	−	12.8521i	0.606264	−	0.523379i
$604$	−3.27993	+	12.2409i	−0.133458	+	0.498074i
$605$	4.25382	−	2.70708i	0.172943	−	0.110058i
$606$	1.96747	+	1.54260i	0.0799231	+	0.0626637i
$607$	32.5863	−	6.92643i	1.32264	−	0.281135i	0.508126	−	0.861283i	$-0.330339\pi$
$607$	32.5863	−	6.92643i	1.32264	−	0.281135i	0.814511	+	0.580148i	$0.197005\pi$
$608$	2.17789	+	20.7212i	0.0883249	+	0.840355i
$609$	8.37260	−	33.3371i	0.339275	−	1.35089i
$610$	−10.7107	+	3.48013i	−0.433665	+	0.140906i
$611$	4.32274	+	15.3505i	0.174879	+	0.621014i
$612$	−8.13938	+	19.9485i	−0.329015	+	0.806370i
$613$	6.53698	−	8.07250i	0.264026	−	0.326045i	−0.627842	−	0.778341i	$-0.716062\pi$
$613$	6.53698	−	8.07250i	0.264026	−	0.326045i	0.891868	+	0.452296i	$0.149395\pi$
$614$	31.7347	−	28.5741i	1.28071	−	1.15316i
$615$	3.03181	+	4.03774i	0.122255	+	0.162817i
$616$	16.5390	+	9.65067i	0.666377	+	0.388836i
$617$	−30.4007	−	8.14585i	−1.22389	−	0.327940i	−0.411691	−	0.911323i	$-0.635062\pi$
$617$	−30.4007	−	8.14585i	−1.22389	−	0.327940i	−0.812197	+	0.583384i	$0.801728\pi$
$618$	−28.6967	+	58.5819i	−1.15435	+	2.35651i
$619$	−6.12174	+	38.6512i	−0.246054	+	1.55352i	0.487031	+	0.873384i	$0.338080\pi$
$619$	−6.12174	+	38.6512i	−0.246054	+	1.55352i	−0.733085	+	0.680137i	$0.761920\pi$
$620$	−7.12390	−	0.748752i	−0.286103	−	0.0300706i
$621$	2.08515	+	13.6180i	0.0836743	+	0.546473i
$622$	23.5780	−	15.3117i	0.945393	−	0.613945i
$623$	46.2818	+	33.6257i	1.85424	+	1.34719i
$624$	−5.95573	−	12.4143i	−0.238420	−	0.496972i
$625$	−6.76515	+	20.8210i	−0.270606	+	0.832840i
$626$	0.126337	+	0.471497i	0.00504946	+	0.0188448i
$627$	−13.9820	−	6.92919i	−0.558386	−	0.276725i
$628$	54.9885	−	31.7476i	2.19428	−	1.26687i
$629$	6.76944	+	13.2858i	0.269915	+	0.529739i
$630$	−6.74456	−	9.70286i	−0.268710	−	0.386571i
$631$	19.2900	+	23.8212i	0.767923	+	0.948306i	0.999701	−	0.0244627i	$-0.00778749\pi$
$631$	19.2900	+	23.8212i	0.767923	+	0.948306i	−0.231778	+	0.972769i	$0.574454\pi$
$632$	−0.414803	+	0.814097i	−0.0165000	+	0.0323830i
$633$	32.4823	+	22.8274i	1.29106	+	0.907310i
$634$	3.66638	+	8.23482i	0.145611	+	0.327047i
$635$	1.83237	−	2.26279i	0.0727154	−	0.0897961i
$636$	48.1794	+	9.45087i	1.91044	+	0.374751i
$637$	−30.9691	+	6.99473i	−1.22704	+	0.277141i
$638$	−27.7052	−	22.6473i	−1.09686	−	0.896615i
$639$	3.40789	+	6.19802i	0.134814	+	0.245190i
$640$	3.36231	+	3.73422i	0.132907	+	0.147608i
$641$	−17.2252	−	7.66916i	−0.680355	−	0.302914i	0.0373081	−	0.999304i	$-0.488122\pi$
$641$	−17.2252	−	7.66916i	−0.680355	−	0.302914i	−0.717663	+	0.696390i	$0.754788\pi$
$642$	23.6471	−	6.73684i	0.933276	−	0.265882i
$643$	30.4825	−	1.59752i	1.20211	−	0.0630001i	0.559262	−	0.828991i	$-0.311085\pi$
$643$	30.4825	−	1.59752i	1.20211	−	0.0630001i	0.642852	+	0.765991i	$0.277751\pi$
$644$	−28.1250	+	1.47397i	−1.10828	+	0.0580825i
$645$	0.939867	−	0.267760i	0.0370072	−	0.0105430i
$646$	14.4174	+	6.41904i	0.567245	+	0.252554i
$647$	−22.9025	−	25.4358i	−0.900389	−	0.999984i	−0.999988	−	0.00495584i	$-0.998423\pi$
$647$	−22.9025	−	25.4358i	−0.900389	−	0.999984i	0.0995985	−	0.995028i	$-0.468244\pi$
$648$	−9.61981	+	8.84808i	−0.377902	+	0.347585i
$649$	−5.20540	+	13.3760i	−0.204330	+	0.525056i
$650$	−19.9316	+	31.5621i	−0.781782	+	1.23797i
$651$	−39.5213	−	7.75249i	−1.54896	−	0.303844i
$652$	5.72770	−	7.07313i	0.224314	−	0.277005i
$653$	−7.28204	−	16.3557i	−0.284968	−	0.640049i	0.713173	−	0.700988i	$-0.247257\pi$
$653$	−7.28204	−	16.3557i	−0.284968	−	0.640049i	−0.998142	+	0.0609385i	$0.980591\pi$
$654$	12.9723	+	9.11651i	0.507259	+	0.356484i
$655$	4.47682	−	8.78625i	0.174924	−	0.343307i
$656$	−8.82448	−	10.8973i	−0.344538	−	0.425469i
$657$	−16.8989	+	11.7466i	−0.659287	+	0.458278i
$658$	−17.2552	−	33.8652i	−0.672677	−	1.32020i
$659$	12.8639	−	7.42695i	0.501105	−	0.289313i	−0.228065	−	0.973646i	$-0.573240\pi$
$659$	12.8639	−	7.42695i	0.501105	−	0.289313i	0.729170	+	0.684333i	$0.239907\pi$
$660$	−6.93624	+	1.17789i	−0.269993	+	0.0458494i
$661$	−2.70501	−	10.0952i	−0.105213	−	0.392659i	0.893157	−	0.449746i	$-0.148485\pi$
$661$	−2.70501	−	10.0952i	−0.105213	−	0.392659i	−0.998369	+	0.0570869i	$0.981819\pi$
$662$	2.20768	−	6.79455i	0.0858040	−	0.264078i
$663$	−16.7370	−	1.27928i	−0.650011	−	0.0496829i
$664$	19.4083	+	14.1009i	0.753188	+	0.547223i
$665$	−4.15165	+	2.69612i	−0.160994	+	0.104551i
$666$	1.13214	+	35.9540i	0.0438695	+	1.39319i
$667$	13.1620	+	1.38338i	0.509636	+	0.0535649i
$668$	3.55145	−	22.4230i	0.137410	−	0.867571i
$669$	2.22435	−	4.54082i	0.0859982	−	0.175558i
$670$	−6.27397	−	1.68111i	−0.242385	−	0.0649468i
$671$	−8.00803	+	36.8396i	−0.309146	+	1.42218i
$672$	31.7132	+	42.2353i	1.22336	+	1.62926i
$673$	−13.7883	+	12.4150i	−0.531499	+	0.478564i	−0.890633	−	0.454722i	$-0.849739\pi$
$673$	−13.7883	+	12.4150i	−0.531499	+	0.478564i	0.359135	+	0.933286i	$0.383072\pi$
$674$	−15.7035	+	19.3922i	−0.604876	+	0.746960i
$675$	−24.0075	−	6.56530i	−0.924048	−	0.252698i
$676$	−25.2144	+	23.8897i	−0.969783	+	0.918835i
$677$	29.3357	−	9.53176i	1.12746	−	0.366335i	0.314852	−	0.949141i	$-0.398045\pi$
$677$	29.3357	−	9.53176i	1.12746	−	0.366335i	0.812612	+	0.582805i	$0.198045\pi$
$678$	1.50666	−	5.99907i	0.0578631	−	0.230393i
$679$	−5.90205	−	56.1543i	−0.226500	−	2.15500i
$680$	1.75016	−	0.372007i	0.0671154	−	0.0142658i
$681$	19.4889	+	15.2802i	0.746815	+	0.585540i
$682$	−24.8007	+	33.8067i	−0.949668	+	1.29452i
$683$	7.91932	−	29.5553i	0.303025	−	1.13090i	−0.631608	−	0.775288i	$-0.717605\pi$
$683$	7.91932	−	29.5553i	0.303025	−	1.13090i	0.934633	−	0.355615i	$-0.115729\pi$
$684$	14.2286	+	16.4820i	0.544045	+	0.630203i
$685$	−2.24003	−	0.997324i	−0.0855870	−	0.0381058i
$686$	14.1746	−	6.31095i	0.541190	−	0.240953i
$687$	−10.9791	−	13.1300i	−0.418879	−	0.500941i
$688$	−2.58111	+	0.838652i	−0.0984038	+	0.0319733i
$689$	4.48104	+	37.9886i	0.170714	+	1.44725i
$690$	3.33285	−	3.09727i	0.126879	−	0.117911i
$691$	1.20548	−	23.0020i	0.0458588	−	0.875038i	−0.874756	−	0.484565i	$-0.838978\pi$
$691$	1.20548	−	23.0020i	0.0458588	−	0.875038i	0.920614	−	0.390473i	$-0.127689\pi$
$692$	−19.2048	−	11.0879i	−0.730058	−	0.421499i
$693$	−39.4329	+	3.13090i	−1.49793	+	0.118933i
$694$	−46.5211	−	46.5211i	−1.76592	−	1.76592i
$695$	−5.74035	+	8.83937i	−0.217744	+	0.335296i
$696$	5.87555	+	11.0962i	0.222712	+	0.420599i
$697$	−16.8840	+	2.67417i	−0.639528	+	0.101291i
$698$	6.63362	+	5.97294i	0.251086	+	0.226079i
$699$	2.64599	−	29.6582i	0.100081	−	1.12178i
$700$	18.2338	−	47.5007i	0.689174	−	1.79536i
$701$	29.0895	−	21.1348i	1.09870	−	0.798250i	0.117850	−	0.993031i	$-0.462400\pi$
$701$	29.0895	−	21.1348i	1.09870	−	0.798250i	0.980847	+	0.194781i	$0.0623998\pi$
$702$	−35.2215	−	19.9820i	−1.32935	−	0.754171i
$703$	15.0694			0.568353
$704$	39.5159	−	8.20932i	1.48931	−	0.309400i
$705$	3.23009	+	1.37763i	0.121652	+	0.0518846i
$706$	−1.48134	−	6.96915i	−0.0557509	−	0.262287i
$707$	0.415328	−	2.62228i	0.0156200	−	0.0986208i
$708$	13.9371	−	14.3828i	0.523787	−	0.540540i
$709$	1.17392	+	22.3997i	0.0440874	+	0.841238i	0.927770	+	0.373152i	$0.121723\pi$
$709$	1.17392	+	22.3997i	0.0440874	+	0.841238i	−0.883683	+	0.468086i	$0.844944\pi$
$710$	1.06049	−	2.08133i	0.0397994	−	0.0781108i
$711$	−0.256274	−	1.86998i	−0.00961103	−	0.0701298i
$712$	−20.7826	+	2.18434i	−0.778861	+	0.0818616i
$713$	0.811574	−	15.4858i	0.0303937	−	0.579946i
$714$	39.7159	−	4.80740i	1.48633	−	0.179913i
$715$	−2.52793	−	4.86367i	−0.0945391	−	0.181891i
$716$			37.8322i			1.41386i
$717$	0.875451	+	12.8357i	0.0326943	+	0.479358i
$718$	6.81851	+	64.8737i	0.254464	+	2.42107i
$719$	−0.660897	+	6.28801i	−0.0246473	+	0.234503i	0.975262	+	0.221051i	$0.0709488\pi$
$719$	−0.660897	+	6.28801i	−0.0246473	+	0.234503i	−0.999910	+	0.0134522i	$0.995718\pi$
$720$	−2.95185	−	0.692155i	−0.110009	−	0.0257951i
$721$	69.1785	−	3.62549i	2.57634	−	0.135020i
$722$	−19.5204	+	15.8073i	−0.726476	+	0.588289i
$723$	−29.0966	−	1.06602i	−1.08211	−	0.0396456i
$724$	−61.3611	+	13.0427i	−2.28047	+	0.484729i
$725$	−11.9547	+	20.7062i	−0.443987	+	0.769007i
$726$	−14.5068	+	38.5415i	−0.538398	+	1.43041i
$727$		−	46.9786i		−	1.74234i	−0.490983	−	0.871169i	$-0.663362\pi$
$727$		−	46.9786i		−	1.74234i	0.490983	−	0.871169i	$-0.336638\pi$
$728$	12.0211	−	16.9952i	0.445531	−	0.629884i
$729$	5.88495	−	26.3509i	0.217961	−	0.975957i
$730$	6.34532	+	2.43574i	0.234851	+	0.0901509i
$731$	−0.687887	+	3.23626i	−0.0254424	+	0.119697i
$732$	30.2465	−	43.0392i	1.11794	−	1.59077i
$733$	7.51026	+	47.4179i	0.277398	+	1.75142i	0.595491	+	0.803362i	$0.296958\pi$
$733$	7.51026	+	47.4179i	0.277398	+	1.75142i	−0.318093	+	0.948060i	$0.603042\pi$
$734$	27.8513	−	10.6911i	1.02801	−	0.394616i
$735$	−3.07546	+	6.27828i	−0.113440	+	0.231578i
$736$	−14.3797	+	14.3797i	−0.530043	+	0.530043i
$737$	−15.4455	+	15.3039i	−0.568942	+	0.563725i
$738$	−39.6027	−	11.5030i	−1.45779	−	0.423430i
$739$	39.8574	+	2.08884i	1.46618	+	0.0768391i	0.768628	−	0.639697i	$-0.220940\pi$
$739$	39.8574	+	2.08884i	1.46618	+	0.0768391i	0.697550	+	0.716536i	$0.254273\pi$
$740$	5.49660	−	3.99351i	0.202059	−	0.146804i
$741$	−8.83113	+	14.4843i	−0.324420	+	0.532093i
$742$	−28.1719	−	86.7043i	−1.03422	−	3.18302i
$743$	17.1353	−	11.1278i	0.628633	−	0.408239i	−0.190626	−	0.981663i	$-0.561052\pi$
$743$	17.1353	−	11.1278i	0.628633	−	0.408239i	0.819259	+	0.573424i	$0.194385\pi$
$744$	12.6233	−	7.55544i	0.462794	−	0.276996i
$745$	−2.83349	+	6.36411i	−0.103811	+	0.233163i
$746$	14.8140	+	29.0742i	0.542380	+	1.06448i
$747$	−49.5470	−	1.03478i	−1.81283	−	0.0378606i
$748$	7.46475	−	22.6191i	0.272938	−	0.827036i
$749$	−18.4632	−	18.4632i	−0.674632	−	0.674632i
$750$	5.44229	+	15.8940i	0.198724	+	0.580367i
$751$	−27.6072	+	2.90164i	−1.00740	+	0.105882i	−0.593831	−	0.804590i	$-0.702385\pi$
$751$	−27.6072	+	2.90164i	−1.00740	+	0.105882i	−0.413571	+	0.910472i	$0.635719\pi$
$752$	−9.10426	−	3.49480i	−0.331998	−	0.127442i
$753$	−28.9387	+	13.4340i	−1.05458	+	0.489562i
$754$	−27.1558	+	27.8541i	−0.988954	+	1.01439i
$755$	−1.27789	+	1.75886i	−0.0465071	+	0.0640116i
$756$	52.4058	+	17.3261i	1.90598	+	0.630145i
$757$	−15.9274	−	17.6892i	−0.578891	−	0.642923i	0.380574	−	0.924750i	$-0.375726\pi$
$757$	−15.9274	−	17.6892i	−0.578891	−	0.642923i	−0.959465	+	0.281827i	$0.909060\pi$
$758$	−30.8388	−	53.4144i	−1.12012	−	1.94010i
$759$	−3.33231	−	14.8618i	−0.120955	−	0.539448i
$760$	0.468014	−	1.74665i	0.0169766	−	0.0633577i
$761$	−1.70329	−	1.10613i	−0.0617444	−	0.0400973i	0.513398	−	0.858151i	$-0.328387\pi$
$761$	−1.70329	−	1.10613i	−0.0617444	−	0.0400973i	−0.575142	+	0.818054i	$0.695053\pi$
$762$	−0.870675	+	23.7648i	−0.0315412	+	0.860907i
$763$	1.75999	−	16.7452i	0.0637159	−	0.606216i
$764$	44.3580	+	9.42857i	1.60481	+	0.341114i
$765$	−2.53005	+	2.69457i	−0.0914742	+	0.0974223i
$766$	−9.14448	+	12.5863i	−0.330404	+	0.454762i
$767$	13.9917	+	6.90682i	0.505211	+	0.249391i
$768$	1.09321	+	0.214444i	0.0394478	+	0.00773807i
$769$	4.89353	−	1.31122i	0.176465	−	0.0472837i	−0.169504	−	0.985529i	$-0.554217\pi$
$769$	4.89353	−	1.31122i	0.176465	−	0.0472837i	0.345970	+	0.938246i	$0.387550\pi$
$770$	8.17450	+	10.1903i	0.294589	+	0.367232i
$771$	16.0009	−	12.0146i	0.576258	−	0.432694i
$772$	−33.9762	+	17.3117i	−1.22283	+	0.623063i
$773$	−0.141933	+	0.0544831i	−0.00510499	+	0.00195962i	−0.360919	−	0.932597i	$-0.617537\pi$
$773$	−0.141933	+	0.0544831i	−0.00510499	+	0.00195962i	0.355814	+	0.934557i	$0.384204\pi$
$774$	−4.82533	+	6.35796i	−0.173443	+	0.228532i
$775$	24.9614	+	12.7185i	0.896641	+	0.456861i
$776$	15.3276	+	13.8010i	0.550229	+	0.495429i
$777$	32.7774	−	19.6182i	1.17588	−	0.703801i
$778$	34.1064	+	27.6188i	1.22277	+	0.990182i
$779$	−5.33861	+	16.4306i	−0.191276	+	0.588686i
$780$	0.617276	+	7.62349i	0.0221020	+	0.272965i
$781$	−4.22863	−	6.57764i	−0.151312	−	0.235367i
$782$	3.98674	+	14.8787i	0.142565	+	0.532061i
$783$	−23.0495	−	11.8940i	−0.823721	−	0.425057i
$784$	7.89670	−	17.7363i	0.282025	−	0.633438i
$785$	10.7589	−	1.70404i	0.384001	−	0.0608198i
$786$	13.8495	+	79.3393i	0.493994	+	2.82994i
$787$	2.06199	+	39.3451i	0.0735020	+	1.40250i	0.747742	+	0.663990i	$0.231138\pi$
$787$	2.06199	+	39.3451i	0.0735020	+	1.40250i	−0.674240	+	0.738512i	$0.735529\pi$
$788$	−1.95320	−	12.3320i	−0.0695799	−	0.439310i
$789$	−29.6762	−	9.12859i	−1.05650	−	0.324986i
$790$	−0.463233	+	0.417097i	−0.0164811	+	0.0148396i
$791$	−6.34467	+	1.70005i	−0.225591	+	0.0604468i
$792$	9.93920	−	10.4883i	0.353174	−	0.372684i
$793$	39.1359	+	12.1690i	1.38976	+	0.432132i
$794$	25.9826	+	8.44227i	0.922089	+	0.299605i
$795$	7.13544	+	4.47574i	0.253068	+	0.158738i
$796$	−20.5313	+	9.14113i	−0.727713	+	0.323999i
$797$	−27.9905	+	31.0866i	−0.991474	+	1.10114i	0.00339739	+	0.999994i	$0.498919\pi$
$797$	−27.9905	+	31.0866i	−0.991474	+	1.10114i	−0.994871	+	0.101149i	$0.967748\pi$
$798$	13.8933	−	37.9688i	0.491817	−	1.34408i
$799$	−9.23919	+	7.48175i	−0.326859	+	0.264685i
$800$	−13.1660	−	34.2987i	−0.465489	−	1.21264i
$801$	32.6767	−	28.2093i	1.15457	−	0.996727i
$802$	34.4921	+	59.7422i	1.21796	+	2.10957i
$803$	17.7478	−	14.2370i	0.626306	−	0.502414i
$804$	28.1497	−	11.3171i	0.992762	−	0.399124i
$805$	−4.59516	−	1.49306i	−0.161958	−	0.0526234i
$806$	34.2575	+	30.0669i	1.20667	+	1.05906i
$807$	0.538610	+	0.299764i	0.0189600	+	0.0105522i
$808$	0.528202	+	0.813359i	0.0185821	+	0.0286139i
$809$	3.59497	−	16.9130i	0.126392	−	0.594629i	−0.868671	−	0.495389i	$-0.835026\pi$
$809$	3.59497	−	16.9130i	0.126392	−	0.594629i	0.995064	−	0.0992398i	$-0.0316411\pi$
$810$	−8.29027	+	3.28354i	−0.291290	+	0.115372i
$811$	27.5746	+	4.36739i	0.968276	+	0.153360i	0.620490	−	0.784214i	$-0.286934\pi$
$811$	27.5746	+	4.36739i	0.968276	+	0.153360i	0.347786	+	0.937574i	$0.386934\pi$
$812$	28.8785	−	44.4691i	1.01344	−	1.56056i
$813$	2.05111	−	14.4151i	0.0719357	−	0.505559i
$814$	−3.97471	−	39.5693i	−0.139313	−	1.38690i
$815$	1.35221	−	0.780701i	0.0473660	−	0.0273468i
$816$	6.74746	−	7.73525i	0.236208	−	0.270788i
$817$	2.59855	+	2.10426i	0.0909118	+	0.0736189i
$818$	14.0624	+	10.2170i	0.491682	+	0.357228i
$819$	−0.352049	+	43.0016i	−0.0123016	+	1.50260i
$820$	2.40696	+	7.40785i	0.0840546	+	0.258693i
$821$	−8.34681	+	21.7442i	−0.291306	+	0.758877i	0.707341	+	0.706872i	$0.249894\pi$
$821$	−8.34681	+	21.7442i	−0.291306	+	0.758877i	−0.998647	+	0.0520049i	$0.983439\pi$
$822$	19.5210	−	4.47154i	0.680872	−	0.155963i
$823$	7.95458	+	37.4234i	0.277279	+	1.30450i	0.867574	+	0.497309i	$0.165678\pi$
$823$	7.95458	+	37.4234i	0.277279	+	1.30450i	−0.590294	+	0.807188i	$0.700988\pi$
$824$	−17.8931	+	17.8931i	−0.623334	+	0.623334i
$825$	26.9766	+	5.42088i	0.939203	+	0.188731i
$826$	−35.9210	−	9.62500i	−1.24985	−	0.334897i
$827$	−14.3670	+	7.32035i	−0.499590	+	0.254554i	−0.685579	−	0.727998i	$-0.740451\pi$
$827$	−14.3670	+	7.32035i	−0.499590	+	0.254554i	0.185990	+	0.982552i	$0.440451\pi$
$828$	−3.76214	+	20.9165i	−0.130743	+	0.726900i
$829$	5.30273	+	11.9101i	0.184171	+	0.413656i	0.981910	−	0.189347i	$-0.0606372\pi$
$829$	5.30273	+	11.9101i	0.184171	+	0.413656i	−0.797739	+	0.603003i	$0.793971\pi$
$830$	8.91392	+	13.7262i	0.309407	+	0.476445i
$831$	−0.595850	−	1.28354i	−0.0206698	−	0.0445257i
$832$	−5.13982	−	43.5735i	−0.178191	−	1.51064i
$833$	−13.9120	−	19.1482i	−0.482022	−	0.663447i
$834$	−5.85757	−	85.8826i	−0.202831	−	2.97387i
$835$	1.94737	−	3.37295i	0.0673916	−	0.116726i
$836$	−16.9430	−	17.0998i	−0.585985	−	0.591408i
$837$	−12.5037	+	27.6996i	−0.432193	+	0.957439i
$838$	−14.4868	−	9.40781i	−0.500437	−	0.324987i
$839$	11.4302	+	29.7767i	0.394615	+	1.02801i	0.976649	+	0.214843i	$0.0689238\pi$
$839$	11.4302	+	29.7767i	0.394615	+	1.02801i	−0.582034	+	0.813165i	$0.697743\pi$
$840$	−1.25592	−	4.40842i	−0.0433333	−	0.152105i
$841$	2.73241	−	3.03465i	0.0942210	−	0.104643i
$842$	−24.2434	−	5.15309i	−0.835483	−	0.177587i
$843$	4.65447	−	18.5327i	0.160309	−	0.638299i
$844$	35.9981	+	49.5472i	1.23911	+	1.70548i
$845$	−5.50711	+	2.27603i	−0.189450	+	0.0782977i
$846$	−27.8523	+	6.84302i	−0.957582	+	0.235268i
$847$	43.2547	−	6.44298i	1.48625	−	0.221383i
$848$	−20.2575	−	11.6956i	−0.695644	−	0.401630i
$849$	35.0259	−	11.9933i	1.20209	−	0.411608i
$850$	−27.4854	−	4.35326i	−0.942741	−	0.149315i
$851$	9.25620	+	11.4305i	0.317298	+	0.391831i
$852$	1.87627	+	10.7486i	0.0642799	+	0.368239i
$853$	18.1929	+	9.26974i	0.622912	+	0.317390i	0.736807	−	0.676103i	$-0.236333\pi$
$853$	18.1929	+	9.26974i	0.622912	+	0.317390i	−0.113895	+	0.993493i	$0.536333\pi$
$854$	−97.1427	−	10.2101i	−3.32416	−	0.349383i
$855$	1.26556	+	3.51455i	0.0432813	+	0.120195i
$856$	9.52488	+	0.499178i	0.325554	+	0.0170616i
$857$	−52.3715			−1.78898			−0.894488	−	0.447092i	$-0.852460\pi$
$857$	−52.3715			−1.78898			−0.894488	+	0.447092i	$0.852460\pi$
$858$	40.3621	+	19.3684i	1.37794	+	0.661227i
$859$	−3.20350			−0.109302			−0.0546510	−	0.998506i	$-0.517405\pi$
$859$	−3.20350			−0.109302			−0.0546510	+	0.998506i	$0.517405\pi$
$860$	1.50547	+	0.0788985i	0.0513362	+	0.00269042i
$861$	9.77829	+	42.6881i	0.333243	+	1.45481i
$862$	22.1740	+	2.33058i	0.755249	+	0.0793799i
$863$	33.0177	+	16.8233i	1.12393	+	0.572673i	0.914272	−	0.405100i	$-0.132763\pi$
$863$	33.0177	+	16.8233i	1.12393	+	0.572673i	0.209663	+	0.977774i	$0.432763\pi$
$864$	36.4922	−	16.0230i	1.24149	−	0.545113i
$865$	−2.39418	−	2.95657i	−0.0814047	−	0.100526i
$866$	−16.0480	−	2.54175i	−0.545332	−	0.0863722i
$867$	5.48484	+	16.0183i	0.186275	+	0.544009i
$868$	−53.8043	−	31.0639i	−1.82624	−	1.05438i
$869$	0.424436	+	2.04304i	0.0143980	+	0.0693055i
$870$	1.02934	+	8.50383i	0.0348981	+	0.288307i
$871$	15.1075	+	18.1795i	0.511900	+	0.615987i
$872$	3.61515	+	4.97583i	0.122425	+	0.168503i
$873$	−42.2716	−	5.33748i	−1.43068	−	0.180646i
$874$	15.2271	+	3.23661i	0.515063	+	0.109480i
$875$	11.9376	−	13.2581i	0.403565	−	0.448205i
$876$	−30.5327	+	8.69849i	−1.03160	+	0.293895i
$877$	7.67407	+	19.9916i	0.259135	+	0.675070i	0.999994	+	0.00340946i	$0.00108527\pi$
$877$	7.67407	+	19.9916i	0.259135	+	0.675070i	−0.740859	+	0.671660i	$0.765581\pi$
$878$	13.6574	+	8.86919i	0.460913	+	0.299321i
$879$	−13.2643	+	16.9177i	−0.447393	+	0.570618i
$880$	3.30818	+	0.539597i	0.111519	+	0.0181898i
$881$	5.73934	−	9.94082i	0.193363	−	0.334915i	−0.753000	−	0.658021i	$-0.771394\pi$
$881$	5.73934	−	9.94082i	0.193363	−	0.334915i	0.946363	+	0.323106i	$0.104727\pi$
$882$	−10.7028	−	56.0869i	−0.360381	−	1.88854i
$883$	11.8657	+	16.3317i	0.399312	+	0.549605i	0.960571	−	0.278035i	$-0.0896830\pi$
$883$	11.8657	+	16.3317i	0.399312	+	0.549605i	−0.561259	+	0.827640i	$0.689683\pi$
$884$	−23.7871	−	10.2309i	−0.800048	−	0.344102i
$885$	3.11644	−	1.44672i	0.104758	−	0.0486310i
$886$	−25.2766	−	38.9226i	−0.849185	−	1.30763i
$887$	−16.6115	−	37.3100i	−0.557759	−	1.25275i	−0.943877	−	0.330297i	$-0.892851\pi$
$887$	−16.6115	−	37.3100i	−0.557759	−	1.25275i	0.386118	−	0.922449i	$-0.373816\pi$
$888$	−4.10259	+	13.3371i	−0.137674	+	0.447565i
$889$	22.5012	−	11.4649i	0.754665	−	0.384521i
$890$	−13.7708	−	3.68988i	−0.461599	−	0.123685i
$891$	−4.49282	+	29.5096i	−0.150515	+	0.988608i
$892$	5.51543	−	5.51543i	0.184670	−	0.184670i
$893$	2.49805	+	11.7524i	0.0835939	+	0.393279i
$894$	−12.7040	−	55.4608i	−0.424886	−	1.85489i
$895$	−2.32593	+	6.05926i	−0.0777473	+	0.202539i
$896$	13.4677	+	41.4492i	0.449923	+	1.38472i
$897$	−16.4110	+	2.19820i	−0.547948	+	0.0733957i
$898$	20.7317	+	15.0625i	0.691827	+	0.502641i
$899$	22.6887	+	18.3729i	0.756709	+	0.612771i
$900$	−31.7563	−	21.5787i	−1.05854	−	0.719290i
$901$	−24.6958	+	14.2581i	−0.822737	+	0.475008i
$902$	44.5515	+	9.68440i	1.48340	+	0.322455i
$903$	8.39155	+	1.19403i	0.279253	+	0.0397348i
$904$	1.30679	−	2.01229i	0.0434633	−	0.0669276i
$905$	−10.6296	−	1.68356i	−0.353338	−	0.0559633i
$906$	−0.279459	−	17.7543i	−0.00928441	−	0.589847i
$907$	10.6465	−	50.0880i	0.353513	−	1.66315i	−0.338277	−	0.941047i	$-0.609844\pi$
$907$	10.6465	−	50.0880i	0.353513	−	1.66315i	0.691789	−	0.722099i	$-0.256823\pi$
$908$	20.8067	+	32.0394i	0.690493	+	1.06327i
$909$	−1.85496	−	0.756861i	−0.0615252	−	0.0251035i
$910$	11.8116	−	7.88549i	0.391550	−	0.261402i
$911$	13.4446	+	4.36841i	0.445439	+	0.144732i	0.523143	−	0.852245i	$-0.324759\pi$
$911$	13.4446	+	4.36841i	0.445439	+	0.144732i	−0.0777049	+	0.996976i	$0.524759\pi$
$912$	−3.86955	−	9.62495i	−0.128134	−	0.318714i
$913$	54.7258	−	2.61535i	1.81116	−	0.0865553i
$914$	3.80536	+	6.59107i	0.125870	+	0.218013i
$915$	7.49037	−	5.03366i	0.247624	−	0.166408i
$916$	−9.46179	−	24.6488i	−0.312626	−	0.814420i
$917$	66.4673	−	53.8242i	2.19494	−	1.77743i
$918$	3.30989	−	30.0063i	0.109243	−	0.990354i
$919$	−25.7337	+	28.5801i	−0.848875	+	0.942771i	−0.998946	−	0.0459039i	$-0.985383\pi$
$919$	−25.7337	+	28.5801i	−0.848875	+	0.942771i	0.150071	+	0.988675i	$0.452050\pi$
$920$	1.61234	−	0.717861i	0.0531573	−	0.0236672i
$921$	−18.1834	+	28.9888i	−0.599163	+	0.955213i
$922$	10.1562	+	3.29995i	0.334477	+	0.108678i
$923$	−7.52470	+	3.95514i	−0.247679	+	0.130185i
$924$	−59.1140	−	15.1363i	−1.94471	−	0.497947i
$925$	−25.6664	+	6.87729i	−0.843906	+	0.226124i
$926$	50.2910	−	45.2822i	1.65266	−	1.48806i
$927$	9.25365	−	51.4480i	0.303930	−	1.68977i
$928$	−5.98930	−	37.8149i	−0.196608	−	1.24134i
$929$	−1.75715	−	33.5285i	−0.0576503	−	1.10003i	−0.862337	−	0.506335i	$-0.831000\pi$
$929$	−1.75715	−	33.5285i	−0.0576503	−	1.10003i	0.804687	−	0.593700i	$-0.202333\pi$
$930$	9.88723	−	1.72592i	0.324215	−	0.0565950i
$931$	−23.6255	+	3.74191i	−0.774294	+	0.122636i
$932$	18.6825	−	41.9617i	0.611967	−	1.37450i
$933$	−14.8091	+	16.9771i	−0.484828	+	0.555804i
$934$	−17.7124	−	66.1035i	−0.579567	−	2.16297i
$935$	2.58619	−	3.16377i	0.0845775	−	0.103466i
$936$	−10.4150	−	11.7593i	−0.340426	−	0.384363i
$937$	10.4657	−	32.2100i	0.341898	−	1.05225i	−0.621325	−	0.783553i	$-0.713405\pi$
$937$	10.4657	−	32.2100i	0.341898	−	1.05225i	0.963223	−	0.268702i	$-0.0865945\pi$
$938$	−43.7808	−	35.4530i	−1.42949	−	1.15758i
$939$	−0.200885	−	0.335631i	−0.00655564	−	0.0109529i
$940$	4.02564	+	3.62470i	0.131302	+	0.118225i
$941$	−3.06106	−	1.55969i	−0.0997876	−	0.0508443i	0.403384	−	0.915031i	$-0.367834\pi$
$941$	−3.06106	−	1.55969i	−0.0997876	−	0.0508443i	−0.503172	+	0.864186i	$0.667834\pi$
$942$	−61.9115	+	63.8917i	−2.01719	+	2.08170i
$943$	−15.7421	+	6.04282i	−0.512633	+	0.196781i
$944$	−8.50169	+	4.33183i	−0.276706	+	0.140989i
$945$	7.32817	+	5.99690i	0.238385	+	0.195079i
$946$	4.83998	−	7.37829i	0.157361	−	0.239889i
$947$	49.1661	−	13.1740i	1.59769	−	0.428098i	0.653343	−	0.757062i	$-0.273366\pi$
$947$	49.1661	−	13.1740i	1.59769	−	0.428098i	0.944343	+	0.328964i	$0.106699\pi$
$948$	0.560462	−	2.85717i	0.0182029	−	0.0927965i
$949$	−13.7337	−	20.5715i	−0.445814	−	0.667779i
$950$	−16.5307	+	22.7525i	−0.536326	+	0.738189i
$951$	−4.63359	−	5.54136i	−0.150254	−	0.179691i
$952$	15.1796	+	3.22652i	0.491972	+	0.104572i
$953$	−4.18297	+	39.7983i	−0.135500	+	1.28919i	0.689594	+	0.724196i	$0.257789\pi$
$953$	−4.18297	+	39.7983i	−0.135500	+	1.28919i	−0.825093	+	0.564996i	$0.808878\pi$
$954$	−68.5522	+	5.76079i	−2.21946	+	0.186512i
$955$	6.52476	+	4.23723i	0.211136	+	0.137114i
$956$	−5.13665	+	19.1702i	−0.166131	+	0.620010i
$957$	26.3239	+	11.3707i	0.850932	+	0.367564i
$958$	10.8529	+	18.7977i	0.350640	+	0.607326i
$959$	−14.2304	−	15.8044i	−0.459523	−	0.510352i
$960$	−8.18445	−	5.13374i	−0.264152	−	0.165691i
$961$	1.88553	−	2.59521i	0.0608237	−	0.0837166i
$962$	−43.2293	+	0.548828i	−1.39377	+	0.0176949i
$963$	−16.7450	+	10.3838i	−0.539600	+	0.334613i
$964$	−41.9316	−	16.0960i	−1.35053	−	0.518419i
$965$	−6.50600	+	0.683808i	−0.209436	+	0.0220126i
$966$	37.3339	−	12.7835i	1.20120	−	0.411304i
$967$	−42.0979	−	42.0979i	−1.35378	−	1.35378i	−0.881394	−	0.472381i	$-0.843395\pi$
$967$	−42.0979	−	42.0979i	−1.35378	−	1.35378i	−0.472381	−	0.881394i	$-0.656605\pi$
$968$	−10.1671	+	12.3215i	−0.326783	+	0.396028i
$969$	−12.5204	−	1.78152i	−0.402214	−	0.0572308i
$970$	6.38820	+	12.5375i	0.205113	+	0.402556i
$971$	−12.3518	+	27.7426i	−0.396387	+	0.890301i	0.599557	+	0.800332i	$0.295343\pi$
$971$	−12.3518	+	27.7426i	−0.396387	+	0.890301i	−0.995945	+	0.0899689i	$0.971323\pi$
$972$	21.7568	−	35.5163i	0.697850	−	1.13919i
$973$	−76.6662	+	49.7876i	−2.45781	+	1.59612i
$974$	3.50278	+	10.7804i	0.112236	+	0.345427i
$975$	8.43104	−	28.7001i	0.270009	−	0.919139i
$976$	−20.2756	+	14.7311i	−0.649006	+	0.471530i
$977$	−60.1647	−	3.15310i	−1.92484	−	0.100877i	−0.948455	−	0.316913i	$-0.897354\pi$
$977$	−60.1647	−	3.15310i	−1.92484	−	0.100877i	−0.976385	+	0.216036i	$0.930687\pi$
$978$	−5.00295	+	11.7303i	−0.159977	+	0.375092i
$979$	−33.9016	+	33.5907i	−1.08350	+	1.07356i
$980$	−7.62581	+	7.62581i	−0.243598	+	0.243598i
$981$	−11.9990	−	4.17766i	−0.383099	−	0.133382i
$982$	−41.9430	+	16.1004i	−1.33846	+	0.513785i
$983$	7.09499	+	44.7960i	0.226295	+	1.42877i	0.795190	+	0.606361i	$0.207371\pi$
$983$	7.09499	+	44.7960i	0.226295	+	1.42877i	−0.568895	+	0.822410i	$0.692629\pi$
$984$	−13.0884	−	9.19808i	−0.417243	−	0.293224i
$985$	0.445348	−	2.09520i	0.0141900	−	0.0667586i
$986$	−27.0739	−	10.3927i	−0.862210	−	0.330971i
$987$	20.7334	+	22.3104i	0.659953	+	0.710149i
$988$	−20.1265	+	16.7256i	−0.640310	+	0.532113i
$989$			3.26357i			0.103776i
$990$	8.89470	−	4.25011i	0.282692	−	0.135077i
$991$	20.4977	−	35.5031i	0.651132	−	1.12779i	−0.331717	−	0.943379i	$-0.607628\pi$
$991$	20.4977	−	35.5031i	0.651132	−	1.12779i	0.982849	−	0.184414i	$-0.0590389\pi$
$992$	−43.8801	+	9.32700i	−1.39319	+	0.296132i
$993$	−0.209604	+	5.72108i	−0.00665159	+	0.181553i
$994$	15.7451	−	12.7501i	0.499403	−	0.404409i
$995$	−3.85032	+	0.201787i	−0.122063	+	0.00639707i
$996$	−71.7931	−	26.2700i	−2.27485	−	0.832398i
$997$	3.19404	−	30.3893i	0.101156	−	0.962439i	−0.819767	−	0.572696i	$-0.805897\pi$
$997$	3.19404	−	30.3893i	0.101156	−	0.962439i	0.920924	−	0.389742i	$-0.127436\pi$
$998$	−5.67741	−	54.0169i	−0.179715	−	1.70988i
$999$	−8.76648	−	27.4602i	−0.277359	−	0.868801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bv.a.20.8	✓	832
3.2	odd	2	inner	429.2.bv.a.20.45	yes	832
11.5	even	5	inner	429.2.bv.a.137.45	yes	832
13.2	odd	12	inner	429.2.bv.a.119.8	yes	832
33.5	odd	10	inner	429.2.bv.a.137.8	yes	832
39.2	even	12	inner	429.2.bv.a.119.45	yes	832
143.93	odd	60	inner	429.2.bv.a.236.45	yes	832
429.236	even	60	inner	429.2.bv.a.236.8	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bv.a.20.8	✓	832	1.1	even	1	trivial
429.2.bv.a.20.45	yes	832	3.2	odd	2	inner
429.2.bv.a.119.8	yes	832	13.2	odd	12	inner
429.2.bv.a.119.45	yes	832	39.2	even	12	inner
429.2.bv.a.137.8	yes	832	33.5	odd	10	inner
429.2.bv.a.137.45	yes	832	11.5	even	5	inner
429.2.bv.a.236.8	yes	832	429.236	even	60	inner
429.2.bv.a.236.45	yes	832	143.93	odd	60	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15849 - 0.113122i) q^{2} +(1.68832 - 0.386733i) q^{3} +(2.65724 + 0.279288i) q^{4} +(0.408417 + 0.208099i) q^{5} +(-3.68798 + 0.643774i) q^{6} +(2.50194 + 3.08964i) q^{7} +(-1.43436 - 0.227180i) q^{8} +(2.70088 - 1.30586i) q^{9} +O(q^{10})\)	\(q+(-2.15849 - 0.113122i) q^{2} +(1.68832 - 0.386733i) q^{3} +(2.65724 + 0.279288i) q^{4} +(0.408417 + 0.208099i) q^{5} +(-3.68798 + 0.643774i) q^{6} +(2.50194 + 3.08964i) q^{7} +(-1.43436 - 0.227180i) q^{8} +(2.70088 - 1.30586i) q^{9} +(-0.858025 - 0.495381i) q^{10} +(-2.87989 + 1.64506i) q^{11} +(4.59430 - 0.556116i) q^{12} +(1.50821 + 3.27495i) q^{13} +(-5.05092 - 6.95200i) q^{14} +(0.770019 + 0.193390i) q^{15} +(-2.15663 - 0.458406i) q^{16} +(-1.79854 + 1.99749i) q^{17} +(-5.97754 + 2.51316i) q^{18} +(0.973486 + 2.53602i) q^{19} +(1.02715 + 0.667036i) q^{20} +(5.41896 + 4.24874i) q^{21} +(6.40231 - 3.22508i) q^{22} +(-1.32567 + 2.29613i) q^{23} +(-2.50952 + 0.171161i) q^{24} +(-2.81543 - 3.87510i) q^{25} +(-2.88498 - 7.23957i) q^{26} +(4.05493 - 3.24923i) q^{27} +(5.78538 + 8.90870i) q^{28} +(-2.03028 - 4.56009i) q^{29} +(-1.64020 - 0.504537i) q^{30} +(-5.21127 + 2.65528i) q^{31} +(7.40873 + 1.98516i) q^{32} +(-4.22599 + 3.89115i) q^{33} +(4.10810 - 4.10810i) q^{34} +(0.378886 + 1.78252i) q^{35} +(7.54160 - 2.71567i) q^{36} +(1.98804 - 5.17902i) q^{37} +(-1.81438 - 5.58409i) q^{38} +(3.81287 + 4.94591i) q^{39} +(-0.538542 - 0.391274i) q^{40} +(4.94252 + 4.00237i) q^{41} +(-11.2162 - 9.78386i) q^{42} +(1.06600 - 0.615457i) q^{43} +(-8.11202 + 3.56702i) q^{44} +(1.37483 + 0.0287131i) q^{45} +(3.12119 - 4.80621i) q^{46} +(4.36859 + 0.691916i) q^{47} +(-3.81837 + 0.0601026i) q^{48} +(-1.83079 + 8.61321i) q^{49} +(5.63872 + 8.68286i) q^{50} +(-2.26403 + 4.06796i) q^{51} +(3.09302 + 9.12357i) q^{52} +(10.0899 + 3.27842i) q^{53} +(-9.12010 + 6.55474i) q^{54} +(-1.51853 + 0.0725707i) q^{55} +(-2.88679 - 5.00006i) q^{56} +(2.62432 + 3.90514i) q^{57} +(3.86650 + 10.0726i) q^{58} +(3.36322 - 2.72348i) q^{59} +(1.99212 + 0.728942i) q^{60} +(7.60598 - 8.44729i) q^{61} +(11.5489 - 5.14188i) q^{62} +(10.7921 + 5.07755i) q^{63} +(-11.5733 - 3.76040i) q^{64} +(-0.0655370 + 1.65140i) q^{65} +(9.56193 - 7.92096i) q^{66} +(6.33247 - 1.69678i) q^{67} +(-5.33705 + 4.80550i) q^{68} +(-1.35017 + 4.38928i) q^{69} +(-0.616180 - 3.89041i) q^{70} +(0.123393 + 2.35448i) q^{71} +(-4.17070 + 1.25949i) q^{72} +(-6.77568 + 1.07316i) q^{73} +(-4.87702 + 10.9540i) q^{74} +(-6.25198 - 5.45361i) q^{75} +(1.87851 + 7.01070i) q^{76} +(-12.2880 - 4.78197i) q^{77} +(-7.67056 - 11.1070i) q^{78} +(0.194419 - 0.598360i) q^{79} +(-0.785412 - 0.636014i) q^{80} +(5.58945 - 7.05394i) q^{81} +(-10.2156 - 9.19819i) q^{82} +(-14.7188 - 7.49959i) q^{83} +(13.2129 + 12.8034i) q^{84} +(-1.15023 + 0.441533i) q^{85} +(-2.37058 + 1.20787i) q^{86} +(-5.19131 - 6.91373i) q^{87} +(4.50453 - 1.70536i) q^{88} +(13.8992 - 3.72429i) q^{89} +(-2.96432 - 0.217500i) q^{90} +(-6.34499 + 12.8536i) q^{91} +(-4.16391 + 5.73113i) q^{92} +(-7.77143 + 6.49834i) q^{93} +(-9.35129 - 1.98768i) q^{94} +(-0.130154 + 1.23833i) q^{95} +(13.2761 + 0.486398i) q^{96} +(-11.9112 - 7.73520i) q^{97} +(4.92609 - 18.3844i) q^{98} +(-5.63000 + 8.20385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

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