LMFDB - Embedded newform 430.2.q.c.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	430.81
Dual form			430.2.q.c.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 - 0.974928i) q^{2} +(0.485771 + 0.149841i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(0.254178 - 0.440249i) q^{6} +(-2.29038 - 3.96705i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-2.26519 - 1.54438i) q^{9} +O(q^{10})$	\(q+(0.222521 - 0.974928i) q^{2} +(0.485771 + 0.149841i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(0.254178 - 0.440249i) q^{6} +(-2.29038 - 3.96705i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-2.26519 - 1.54438i) q^{9} +(0.988831 - 0.149042i) q^{10} +(2.13922 - 1.03019i) q^{11} +(-0.372652 - 0.345770i) q^{12} +(-2.32878 - 0.351007i) q^{13} +(-4.37724 + 1.35020i) q^{14} +(0.0379895 + 0.506935i) q^{15} +(0.623490 + 0.781831i) q^{16} +(1.59858 - 4.07313i) q^{17} +(-2.00972 + 1.86474i) q^{18} +(0.837255 - 0.570830i) q^{19} +(0.0747301 - 0.997204i) q^{20} +(-0.518174 - 2.27027i) q^{21} +(-0.528343 - 2.31482i) q^{22} +(0.109380 - 1.45957i) q^{23} +(-0.420024 + 0.286367i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-0.860407 + 2.19228i) q^{26} +(-1.81982 - 2.28198i) q^{27} +(0.342320 + 4.56794i) q^{28} +(8.24135 - 2.54212i) q^{29} +(0.502678 + 0.0757666i) q^{30} +(-2.25731 - 2.09448i) q^{31} +(0.900969 - 0.433884i) q^{32} +(1.19354 - 0.179897i) q^{33} +(-3.61529 - 2.46486i) q^{34} +(2.85605 - 3.58138i) q^{35} +(1.37079 + 2.37427i) q^{36} +(-3.06048 + 5.30091i) q^{37} +(-0.370212 - 0.943285i) q^{38} +(-1.07866 - 0.519454i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(-2.17018 + 9.50819i) q^{41} -2.32865 q^{42} +(6.39349 - 1.45714i) q^{43} -2.37435 q^{44} +(0.610058 - 2.67284i) q^{45} +(-1.39864 - 0.431423i) q^{46} +(0.199277 + 0.0959670i) q^{47} +(0.185723 + 0.473216i) q^{48} +(-6.99164 + 12.1099i) q^{49} +(0.500000 + 0.866025i) q^{50} +(1.38687 - 1.73908i) q^{51} +(1.94586 + 1.32666i) q^{52} +(-10.3947 + 1.56675i) q^{53} +(-2.62972 + 1.26640i) q^{54} +(1.74052 + 1.61497i) q^{55} +(4.52959 + 0.682725i) q^{56} +(0.492248 - 0.151838i) q^{57} +(-0.644511 - 8.60040i) q^{58} +(3.11608 + 3.90744i) q^{59} +(0.185723 - 0.473216i) q^{60} +(5.32325 - 4.93925i) q^{61} +(-2.54426 + 1.73465i) q^{62} +(-0.938495 + 12.5234i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.524055 - 2.29603i) q^{65} +(0.0902005 - 1.20364i) q^{66} +(8.06230 - 5.49678i) q^{67} +(-3.20754 + 2.97616i) q^{68} +(0.271837 - 0.692629i) q^{69} +(-2.85605 - 3.58138i) q^{70} +(-0.374677 - 4.99971i) q^{71} +(2.61977 - 0.808093i) q^{72} +(-3.62995 - 0.547126i) q^{73} +(4.48698 + 4.16331i) q^{74} +(-0.458013 + 0.220568i) q^{75} +(-1.00201 + 0.151029i) q^{76} +(-8.98644 - 6.12685i) q^{77} +(-0.746454 + 0.936024i) q^{78} +(7.44011 + 12.8866i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(2.46275 + 6.27497i) q^{81} +(8.78689 + 4.23154i) q^{82} +(10.5526 + 3.25506i) q^{83} +(-0.518174 + 2.27027i) q^{84} +4.37559 q^{85} +(0.00208142 - 6.55744i) q^{86} +4.38433 q^{87} +(-0.528343 + 2.31482i) q^{88} +(1.24084 + 0.382747i) q^{89} +(-2.47007 - 1.18952i) q^{90} +(3.94131 + 10.0423i) q^{91} +(-0.731833 + 1.26757i) q^{92} +(-0.782699 - 1.35567i) q^{93} +(0.137904 - 0.172926i) q^{94} +(0.837255 + 0.570830i) q^{95} +(0.502678 - 0.0757666i) q^{96} +(13.9599 - 6.72271i) q^{97} +(10.2505 + 9.51104i) q^{98} +(-6.43676 - 0.970185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{21}\right)$

Coefficient data

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

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

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

$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$3$	0.485771	+	0.149841i	0.280460	+	0.0865105i	0.431794	−	0.901972i	$-0.357881\pi$
$3$	0.485771	+	0.149841i	0.280460	+	0.0865105i	−0.151334	+	0.988483i	$0.548357\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	0.365341	+	0.930874i	0.163385	+	0.416299i
$5$	0.365341	+	0.930874i	0.163385	+	0.416299i
$6$	0.254178	−	0.440249i	0.103768	−	0.179731i
$7$	−2.29038	−	3.96705i	−0.865681	−	1.49940i	−0.866370	−	0.499403i	$-0.833553\pi$
$7$	−2.29038	−	3.96705i	−0.865681	−	1.49940i	0.000689300	−	1.00000i	$-0.499781\pi$
$8$	−0.623490	+	0.781831i	−0.220437	+	0.276419i
$9$	−2.26519	−	1.54438i	−0.755065	−	0.514795i
$10$	0.988831	−	0.149042i	0.312696	−	0.0471313i
$11$	2.13922	−	1.03019i	0.644999	−	0.310615i	−0.0826361	−	0.996580i	$-0.526334\pi$
$11$	2.13922	−	1.03019i	0.644999	−	0.310615i	0.727635	+	0.685965i	$0.240620\pi$
$12$	−0.372652	−	0.345770i	−0.107575	−	0.0998152i
$13$	−2.32878	−	0.351007i	−0.645886	−	0.0973517i	−0.182073	−	0.983285i	$-0.558281\pi$
$13$	−2.32878	−	0.351007i	−0.645886	−	0.0973517i	−0.463813	+	0.885933i	$0.653519\pi$
$14$	−4.37724	+	1.35020i	−1.16987	+	0.360856i
$15$	0.0379895	+	0.506935i	0.00980885	+	0.130890i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	1.59858	−	4.07313i	0.387714	−	0.987878i	−0.595162	−	0.803606i	$-0.702912\pi$
$17$	1.59858	−	4.07313i	0.387714	−	0.987878i	0.982875	−	0.184272i	$-0.0589928\pi$
$18$	−2.00972	+	1.86474i	−0.473695	+	0.439524i
$19$	0.837255	−	0.570830i	0.192079	−	0.130957i	−0.463462	−	0.886117i	$-0.653393\pi$
$19$	0.837255	−	0.570830i	0.192079	−	0.130957i	0.655541	+	0.755159i	$0.272441\pi$
$20$	0.0747301	−	0.997204i	0.0167102	−	0.222982i
$21$	−0.518174	−	2.27027i	−0.113075	−	0.495413i
$22$	−0.528343	−	2.31482i	−0.112643	−	0.493522i
$23$	0.109380	−	1.45957i	0.0228073	−	0.304342i	−0.974121	−	0.226026i	$-0.927427\pi$
$23$	0.109380	−	1.45957i	0.0228073	−	0.304342i	0.996929	−	0.0783161i	$-0.0249543\pi$
$24$	−0.420024	+	0.286367i	−0.0857370	+	0.0584545i
$25$	−0.733052	+	0.680173i	−0.146610	+	0.136035i
$26$	−0.860407	+	2.19228i	−0.168740	+	0.429942i
$27$	−1.81982	−	2.28198i	−0.350225	−	0.439168i
$28$	0.342320	+	4.56794i	0.0646924	+	0.863260i
$29$	8.24135	−	2.54212i	1.53038	−	0.472060i	0.588639	−	0.808396i	$-0.299664\pi$
$29$	8.24135	−	2.54212i	1.53038	−	0.472060i	0.941742	+	0.336336i	$0.109188\pi$
$30$	0.502678	+	0.0757666i	0.0917761	+	0.0138330i
$31$	−2.25731	−	2.09448i	−0.405425	−	0.376179i	0.450937	−	0.892556i	$-0.351090\pi$
$31$	−2.25731	−	2.09448i	−0.405425	−	0.376179i	−0.856362	+	0.516377i	$0.827281\pi$
$32$	0.900969	−	0.433884i	0.159270	−	0.0767005i
$33$	1.19354	−	0.179897i	0.207768	−	0.0313160i
$34$	−3.61529	−	2.46486i	−0.620016	−	0.422720i
$35$	2.85605	−	3.58138i	0.482761	−	0.605363i
$36$	1.37079	+	2.37427i	0.228464	+	0.395712i
$37$	−3.06048	+	5.30091i	−0.503140	+	0.871464i	0.496854	+	0.867834i	$0.334489\pi$
$37$	−3.06048	+	5.30091i	−0.503140	+	0.871464i	−0.999993	+	0.00362939i	$0.998845\pi$
$38$	−0.370212	−	0.943285i	−0.0600563	−	0.153021i
$39$	−1.07866	−	0.519454i	−0.172723	−	0.0831793i
$40$	−0.955573	−	0.294755i	−0.151089	−	0.0466049i
$41$	−2.17018	+	9.50819i	−0.338926	+	1.48493i	0.462383	+	0.886680i	$0.346994\pi$
$41$	−2.17018	+	9.50819i	−0.338926	+	1.48493i	−0.801309	+	0.598250i	$0.795863\pi$
$42$	−2.32865			−0.359319
$43$	6.39349	−	1.45714i	0.974998	−	0.222211i
$43$	6.39349	−	1.45714i	0.974998	−	0.222211i
$44$	−2.37435			−0.357947
$45$	0.610058	−	2.67284i	0.0909420	−	0.398443i
$46$	−1.39864	−	0.431423i	−0.206218	−	0.0636098i
$47$	0.199277	+	0.0959670i	0.0290676	+	0.0139982i	0.448361	−	0.893853i	$-0.352008\pi$
$47$	0.199277	+	0.0959670i	0.0290676	+	0.0139982i	−0.419293	+	0.907851i	$0.637722\pi$
$48$	0.185723	+	0.473216i	0.0268069	+	0.0683028i
$49$	−6.99164	+	12.1099i	−0.998806	+	1.72998i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	1.38687	−	1.73908i	0.194200	−	0.243519i
$52$	1.94586	+	1.32666i	0.269842	+	0.183975i
$53$	−10.3947	+	1.56675i	−1.42783	+	0.215210i	−0.817038	−	0.576584i	$-0.804385\pi$
$53$	−10.3947	+	1.56675i	−1.42783	+	0.215210i	−0.610788	+	0.791794i	$0.709147\pi$
$54$	−2.62972	+	1.26640i	−0.357859	+	0.172336i
$55$	1.74052	+	1.61497i	0.234692	+	0.217763i
$56$	4.52959	+	0.682725i	0.605292	+	0.0912330i
$57$	0.492248	−	0.151838i	0.0651998	−	0.0201115i
$58$	−0.644511	−	8.60040i	−0.0846284	−	1.12929i
$59$	3.11608	+	3.90744i	0.405679	+	0.508706i	0.942140	−	0.335220i	$-0.108811\pi$
$59$	3.11608	+	3.90744i	0.405679	+	0.508706i	−0.536461	+	0.843925i	$0.680239\pi$
$60$	0.185723	−	0.473216i	0.0239768	−	0.0610919i
$61$	5.32325	−	4.93925i	0.681572	−	0.632407i	−0.261419	−	0.965226i	$-0.584190\pi$
$61$	5.32325	−	4.93925i	0.681572	−	0.632407i	0.942991	+	0.332819i	$0.108000\pi$
$62$	−2.54426	+	1.73465i	−0.323122	+	0.220301i
$63$	−0.938495	+	12.5234i	−0.118239	+	1.57779i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−0.524055	−	2.29603i	−0.0650010	−	0.284788i
$66$	0.0902005	−	1.20364i	0.0111029	−	0.148158i
$67$	8.06230	−	5.49678i	0.984967	−	0.671539i	0.0401688	−	0.999193i	$-0.487210\pi$
$67$	8.06230	−	5.49678i	0.984967	−	0.671539i	0.944798	+	0.327654i	$0.106258\pi$
$68$	−3.20754	+	2.97616i	−0.388971	+	0.360912i
$69$	0.271837	−	0.692629i	0.0327253	−	0.0833827i
$70$	−2.85605	−	3.58138i	−0.341363	−	0.428056i
$71$	−0.374677	−	4.99971i	−0.0444659	−	0.593357i	−0.974282	−	0.225332i	$-0.927653\pi$
$71$	−0.374677	−	4.99971i	−0.0444659	−	0.593357i	0.929816	−	0.368025i	$-0.119966\pi$
$72$	2.61977	−	0.808093i	0.308743	−	0.0952347i
$73$	−3.62995	−	0.547126i	−0.424853	−	0.0640363i	−0.0668641	−	0.997762i	$-0.521299\pi$
$73$	−3.62995	−	0.547126i	−0.424853	−	0.0640363i	−0.357989	+	0.933726i	$0.616537\pi$
$74$	4.48698	+	4.16331i	0.521601	+	0.483975i
$75$	−0.458013	+	0.220568i	−0.0528868	+	0.0254689i
$76$	−1.00201	+	0.151029i	−0.114939	+	0.0173243i
$77$	−8.98644	−	6.12685i	−1.02410	−	0.698219i
$78$	−0.746454	+	0.936024i	−0.0845193	+	0.105984i
$79$	7.44011	+	12.8866i	0.837078	+	1.44986i	0.892327	+	0.451389i	$0.149071\pi$
$79$	7.44011	+	12.8866i	0.837078	+	1.44986i	−0.0552495	+	0.998473i	$0.517595\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	2.46275	+	6.27497i	0.273638	+	0.697219i
$82$	8.78689	+	4.23154i	0.970350	+	0.467296i
$83$	10.5526	+	3.25506i	1.15830	+	0.357289i	0.813601	−	0.581424i	$-0.197504\pi$
$83$	10.5526	+	3.25506i	1.15830	+	0.357289i	0.344701	+	0.938712i	$0.387980\pi$
$84$	−0.518174	+	2.27027i	−0.0565374	+	0.247707i
$85$	4.37559			0.474600
$86$	0.00208142	−	6.55744i	0.000224446	−	0.707107i
$87$	4.38433			0.470049
$88$	−0.528343	+	2.31482i	−0.0563216	+	0.246761i
$89$	1.24084	+	0.382747i	0.131528	+	0.0405711i	0.359821	−	0.933022i	$-0.382838\pi$
$89$	1.24084	+	0.382747i	0.131528	+	0.0405711i	−0.228292	+	0.973593i	$0.573314\pi$
$90$	−2.47007	−	1.18952i	−0.260369	−	0.125387i
$91$	3.94131	+	10.0423i	0.413162	+	1.05272i
$92$	−0.731833	+	1.26757i	−0.0762988	+	0.132153i
$93$	−0.782699	−	1.35567i	−0.0811621	−	0.140577i
$94$	0.137904	−	0.172926i	0.0142237	−	0.0178360i
$95$	0.837255	+	0.570830i	0.0859005	+	0.0585660i
$96$	0.502678	−	0.0757666i	0.0513044	−	0.00773289i
$97$	13.9599	−	6.72271i	1.41741	−	0.682588i	0.440799	−	0.897606i	$-0.354695\pi$
$97$	13.9599	−	6.72271i	1.41741	−	0.682588i	0.976610	+	0.215018i	$0.0689809\pi$
$98$	10.2505	+	9.51104i	1.03545	+	0.960761i
$99$	−6.43676	−	0.970185i	−0.646919	−	0.0975073i
$100$	0.955573	−	0.294755i	0.0955573	−	0.0294755i
$101$	−1.37918	−	18.4039i	−0.137234	−	1.83126i	−0.463634	−	0.886027i	$-0.653455\pi$
$101$	−1.37918	−	18.4039i	−0.137234	−	1.83126i	0.326401	−	0.945232i	$-0.394164\pi$
$102$	−1.38687	−	1.73908i	−0.137320	−	0.172194i
$103$	3.26423	−	8.31711i	0.321634	−	0.819509i	−0.675022	−	0.737797i	$-0.735866\pi$
$103$	3.26423	−	8.31711i	0.321634	−	0.819509i	0.996656	−	0.0817120i	$-0.0260388\pi$
$104$	1.72640	−	1.60186i	0.169287	−	0.157075i
$105$	1.92402	−	1.31178i	0.187766	−	0.128016i
$106$	−0.785573	+	10.4827i	−0.0763016	+	1.01817i
$107$	−1.66677	−	7.30258i	−0.161132	−	0.705967i	−0.989349	−	0.145560i	$-0.953502\pi$
$107$	−1.66677	−	7.30258i	−0.161132	−	0.705967i	0.828217	−	0.560407i	$-0.189355\pi$
$108$	0.649486	+	2.84559i	0.0624969	+	0.273817i
$109$	−0.731213	+	9.75736i	−0.0700375	+	0.934586i	0.845920	+	0.533310i	$0.179052\pi$
$109$	−0.731213	+	9.75736i	−0.0700375	+	0.934586i	−0.915957	+	0.401276i	$0.868567\pi$
$110$	1.96178	−	1.33752i	0.187049	−	0.127528i
$111$	−2.28099	+	2.11645i	−0.216502	+	0.200884i
$112$	1.67354	−	4.26410i	0.158134	−	0.402920i
$113$	−8.33999	−	10.4580i	−0.784561	−	0.983808i	−0.999973	−	0.00728484i	$-0.997681\pi$
$113$	−8.33999	−	10.4580i	−0.784561	−	0.983808i	0.215413	−	0.976523i	$-0.430890\pi$
$114$	−0.0384960	−	0.513694i	−0.00360548	−	0.0481118i
$115$	1.39864	−	0.431423i	0.130424	−	0.0402304i
$116$	−8.52819	−	1.28542i	−0.791822	−	0.119348i
$117$	4.73304	+	4.39162i	0.437570	+	0.406006i
$118$	4.50287	−	2.16847i	0.414523	−	0.199624i
$119$	−19.8196	+	2.98733i	−1.81686	+	0.273848i
$120$	−0.420024	−	0.286367i	−0.0383427	−	0.0261416i
$121$	−3.34343	+	4.19253i	−0.303948	+	0.381139i
$122$	−3.63088	−	6.28887i	−0.328725	−	0.569368i
$123$	−2.47893	+	4.29363i	−0.223517	+	0.387143i
$124$	1.12501	+	2.86647i	0.101029	+	0.257417i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	12.0005	+	3.70167i	1.06909	+	0.329771i
$127$	0.272776	−	1.19511i	0.0242050	−	0.106049i	−0.961382	−	0.275216i	$-0.911251\pi$
$127$	0.272776	−	1.19511i	0.0242050	−	0.106049i	0.985587	+	0.169167i	$0.0541078\pi$
$128$	−1.00000			−0.0883883
$129$	3.32411	+	0.250169i	0.292672	+	0.0220262i
$130$	−2.35508			−0.206554
$131$	−0.485671	+	2.12786i	−0.0424332	+	0.185912i	−0.991703	−	0.128551i	$-0.958967\pi$
$131$	−0.485671	+	2.12786i	−0.0424332	+	0.185912i	0.949270	+	0.314463i	$0.101825\pi$
$132$	−1.15339	−	0.355775i	−0.100390	−	0.0309662i
$133$	−4.18214	−	2.01401i	−0.362637	−	0.174637i
$134$	−3.56494	−	9.08331i	−0.307964	−	0.784678i
$135$	1.45938	−	2.52772i	0.125604	−	0.217552i
$136$	2.18780	+	3.78938i	0.187602	+	0.324936i
$137$	5.49605	−	6.89182i	0.469559	−	0.588808i	−0.489504	−	0.872001i	$-0.662822\pi$
$137$	5.49605	−	6.89182i	0.469559	−	0.588808i	0.959063	+	0.283193i	$0.0913936\pi$
$138$	−0.614774	−	0.419146i	−0.0523330	−	0.0356801i
$139$	19.0512	−	2.87151i	1.61590	−	0.243558i	0.722025	−	0.691867i	$-0.243212\pi$
$139$	19.0512	−	2.87151i	1.61590	−	0.243558i	0.893879	+	0.448309i	$0.147973\pi$
$140$	−4.12711	+	1.98751i	−0.348805	+	0.167976i
$141$	0.0824235	+	0.0764779i	0.00694131	+	0.00644060i
$142$	−4.95773	−	0.747258i	−0.416044	−	0.0627085i
$143$	−5.34336	+	1.64821i	−0.446835	+	0.137830i
$144$	−0.204878	−	2.73391i	−0.0170732	−	0.227826i
$145$	5.37730	+	6.74292i	0.446560	+	0.559969i
$146$	−1.34115	+	3.41719i	−0.110994	+	0.282809i
$147$	−5.21089	+	4.83500i	−0.429787	+	0.398784i
$148$	5.05737	−	3.44806i	0.415714	−	0.283429i
$149$	−0.835347	+	11.1469i	−0.0684343	+	0.913192i	0.852313	+	0.523032i	$0.175199\pi$
$149$	−0.835347	+	11.1469i	−0.0684343	+	0.913192i	−0.920747	+	0.390160i	$0.872420\pi$
$150$	0.113120	+	0.495611i	0.00923620	+	0.0404664i
$151$	4.01132	+	17.5747i	0.326436	+	1.43021i	0.825871	+	0.563859i	$0.190684\pi$
$151$	4.01132	+	17.5747i	0.326436	+	1.43021i	−0.499434	+	0.866352i	$0.666459\pi$
$152$	−0.0757264	+	1.01050i	−0.00614222	+	0.0819623i
$153$	−9.91157	+	6.75760i	−0.801303	+	0.546319i
$154$	−7.97291	+	7.39778i	−0.642475	+	0.596130i
$155$	1.12501	−	2.86647i	0.0903627	−	0.230240i
$156$	0.746454	+	0.936024i	0.0597642	+	0.0749419i
$157$	−0.0640243	−	0.854345i	−0.00510970	−	0.0681842i	0.994066	−	0.108778i	$-0.0346939\pi$
$157$	−0.0640243	−	0.854345i	−0.00510970	−	0.0681842i	−0.999176	+	0.0405943i	$0.987075\pi$
$158$	14.2191	−	4.38602i	1.13121	−	0.348933i
$159$	−5.28422	−	0.796469i	−0.419066	−	0.0631641i
$160$	0.733052	+	0.680173i	0.0579528	+	0.0537724i
$161$	−6.04071	+	2.90905i	−0.476075	+	0.229266i
$162$	6.66566	−	1.00469i	0.523704	−	0.0789356i
$163$	15.7527	+	10.7400i	1.23385	+	0.841225i	0.991645	−	0.129000i	$-0.0411767\pi$
$163$	15.7527	+	10.7400i	1.23385	+	0.841225i	0.242206	+	0.970225i	$0.422129\pi$
$164$	6.08072	−	7.62498i	0.474824	−	0.595411i
$165$	0.603509	+	1.04531i	0.0469831	+	0.0813771i
$166$	5.52163	−	9.56374i	0.428561	−	0.742290i
$167$	−2.81054	−	7.16113i	−0.217486	−	0.554145i	0.779940	−	0.625855i	$-0.215250\pi$
$167$	−2.81054	−	7.16113i	−0.217486	−	0.554145i	−0.997426	+	0.0717096i	$0.977155\pi$
$168$	2.09804	+	1.01036i	0.161868	+	0.0779513i
$169$	−7.12245	−	2.19699i	−0.547881	−	0.168999i
$170$	0.973661	−	4.26589i	0.0746764	−	0.327179i
$171$	−2.77813			−0.212449
$172$	−6.39257	−	1.46120i	−0.487429	−	0.111415i
$173$	−9.28771			−0.706131			−0.353066	−	0.935599i	$-0.614861\pi$
$173$	−9.28771			−0.706131			−0.353066	+	0.935599i	$0.614861\pi$
$174$	0.975604	−	4.27440i	0.0739604	−	0.324042i
$175$	4.37724	+	1.35020i	0.330888	+	0.102066i
$176$	2.13922	+	1.03019i	0.161250	+	0.0776537i
$177$	0.928209	+	2.36504i	0.0697685	+	0.177767i
$178$	0.649263	−	1.12456i	0.0486643	−	0.0842891i
$179$	5.75584	+	9.96941i	0.430212	+	0.745149i	0.996891	−	0.0787895i	$-0.0251055\pi$
$179$	5.75584	+	9.96941i	0.430212	+	0.745149i	−0.566679	+	0.823938i	$0.691772\pi$
$180$	−1.70934	+	2.14345i	−0.127407	+	0.159763i
$181$	−13.8217	−	9.42347i	−1.02736	−	0.700441i	−0.0724588	−	0.997371i	$-0.523085\pi$
$181$	−13.8217	−	9.42347i	−1.02736	−	0.700441i	−0.954899	+	0.296931i	$0.904037\pi$
$182$	10.6675	−	1.60787i	0.790731	−	0.119184i
$183$	3.32598	−	1.60171i	0.245864	−	0.118402i
$184$	1.07294	+	0.995545i	0.0790984	+	0.0733926i
$185$	−6.05259	−	0.912282i	−0.444996	−	0.0670723i
$186$	−1.49585	+	0.461409i	−0.109681	+	0.0338322i
$187$	−0.776386	−	10.3602i	−0.0567750	−	0.757610i
$188$	−0.137904	−	0.172926i	−0.0100577	−	0.0126120i
$189$	−4.88466	+	12.4459i	−0.355307	+	0.905307i
$190$	0.742825	−	0.689241i	0.0538902	−	0.0500028i
$191$	−3.35306	+	2.28608i	−0.242619	+	0.165415i	−0.678525	−	0.734578i	$-0.737380\pi$
$191$	−3.35306	+	2.28608i	−0.242619	+	0.165415i	0.435906	+	0.899992i	$0.356428\pi$
$192$	0.0379895	−	0.506935i	0.00274166	−	0.0365849i
$193$	−2.91048	−	12.7516i	−0.209501	−	0.917882i	−0.964900	−	0.262618i	$-0.915414\pi$
$193$	−2.91048	−	12.7516i	−0.209501	−	0.917882i	0.755399	−	0.655265i	$-0.227443\pi$
$194$	−3.44780	−	15.1058i	−0.247538	−	1.08453i
$195$	0.0894684	−	1.19387i	0.00640696	−	0.0854950i
$196$	11.5535	−	7.87706i	0.825252	−	0.562647i
$197$	6.61009	−	6.13327i	0.470949	−	0.436977i	−0.408651	−	0.912691i	$-0.634001\pi$
$197$	6.61009	−	6.13327i	0.470949	−	0.436977i	0.879600	+	0.475714i	$0.157810\pi$
$198$	−2.37817	+	6.05949i	−0.169010	+	0.430629i
$199$	−1.99858	−	2.50613i	−0.141675	−	0.177655i	0.705931	−	0.708280i	$-0.250529\pi$
$199$	−1.99858	−	2.50613i	−0.141675	−	0.177655i	−0.847607	+	0.530625i	$0.821957\pi$
$200$	−0.0747301	−	0.997204i	−0.00528422	−	0.0705130i
$201$	4.74008	−	1.46212i	0.334339	−	0.103130i
$202$	−18.2494	−	2.75065i	−1.28402	−	0.193535i
$203$	−28.9605	−	26.8714i	−2.03263	−	1.88600i
$204$	−2.00408	+	0.965114i	−0.140314	+	0.0675715i
$205$	−9.64379	+	1.45357i	−0.673551	+	0.101522i
$206$	−7.38223	−	5.03312i	−0.514344	−	0.350674i
$207$	−2.50191	+	3.13729i	−0.173895	+	0.218057i
$208$	−1.17754	−	2.03956i	−0.0816477	−	0.141418i
$209$	1.20300	−	2.08367i	0.0832136	−	0.144130i
$210$	−0.850753	−	2.16768i	−0.0587075	−	0.149584i
$211$	−2.77482	−	1.33628i	−0.191027	−	0.0919935i	0.335925	−	0.941889i	$-0.390951\pi$
$211$	−2.77482	−	1.33628i	−0.191027	−	0.0919935i	−0.526952	+	0.849895i	$0.676665\pi$
$212$	10.0451	+	3.09851i	0.689901	+	0.212806i
$213$	0.567153	−	2.48486i	0.0388607	−	0.170260i
$214$	−7.49038			−0.512032
$215$	3.69222	+	5.41918i	0.251807	+	0.369585i
$216$	2.91877			0.198597
$217$	−3.13880	+	13.7520i	−0.213076	+	0.933547i
$218$	9.35001	+	2.88410i	0.633263	+	0.195336i
$219$	−1.68134	−	0.809692i	−0.113615	−	0.0547139i
$220$	−0.867449	−	2.21022i	−0.0584834	−	0.149013i
$221$	−5.15244	+	8.92428i	−0.346590	+	0.600312i
$222$	1.55581	+	2.69475i	0.104419	+	0.180860i
$223$	6.99761	−	8.77473i	0.468595	−	0.587599i	−0.490232	−	0.871592i	$-0.663088\pi$
$223$	6.99761	−	8.77473i	0.468595	−	0.587599i	0.958826	+	0.283993i	$0.0916592\pi$
$224$	−3.78479	−	2.58043i	−0.252882	−	0.172412i
$225$	2.71095	−	0.408610i	0.180730	−	0.0272407i
$226$	−12.0516	+	5.80376i	−0.801663	+	0.386061i
$227$	−8.77417	−	8.14124i	−0.582362	−	0.540353i	0.333030	−	0.942916i	$-0.391929\pi$
$227$	−8.77417	−	8.14124i	−0.582362	−	0.540353i	−0.915392	+	0.402563i	$0.868119\pi$
$228$	−0.509380	−	0.0767767i	−0.0337345	−	0.00508466i
$229$	−9.78067	+	3.01694i	−0.646325	+	0.199365i	−0.600550	−	0.799587i	$-0.705052\pi$
$229$	−9.78067	+	3.01694i	−0.646325	+	0.199365i	−0.0457747	+	0.998952i	$0.514576\pi$
$230$	−0.109380	−	1.45957i	−0.00721229	−	0.0962414i
$231$	−3.44730	−	4.32278i	−0.226816	−	0.284418i
$232$	−3.15089	+	8.02833i	−0.206866	+	0.527086i
$233$	−17.4425	+	16.1843i	−1.14270	+	1.06027i	−0.145210	+	0.989401i	$0.546386\pi$
$233$	−17.4425	+	16.1843i	−1.14270	+	1.06027i	−0.997486	+	0.0708661i	$0.977424\pi$
$234$	5.33472	−	3.63715i	0.348741	−	0.237768i
$235$	−0.0165289	+	0.220563i	−0.00107823	+	0.0143879i
$236$	−1.11212	−	4.87250i	−0.0723926	−	0.317173i
$237$	1.68325	+	7.37480i	0.109339	+	0.479045i
$238$	−1.49785	+	19.9875i	−0.0970914	+	1.29559i
$239$	1.47889	−	1.00829i	0.0956613	−	0.0652208i	−0.514545	−	0.857464i	$-0.672039\pi$
$239$	1.47889	−	1.00829i	0.0956613	−	0.0652208i	0.610206	+	0.792243i	$0.291087\pi$
$240$	−0.372652	+	0.345770i	−0.0240546	+	0.0223194i
$241$	2.00890	−	5.11858i	0.129404	−	0.329717i	−0.851457	−	0.524424i	$-0.824281\pi$
$241$	2.00890	−	5.11858i	0.129404	−	0.329717i	0.980861	+	0.194707i	$0.0623758\pi$
$242$	3.34343	+	4.19253i	0.214924	+	0.269506i
$243$	0.910444	+	12.1490i	0.0584050	+	0.779361i
$244$	−6.93914	+	2.14044i	−0.444233	+	0.137028i
$245$	−13.8271	−	2.08410i	−0.883381	−	0.133148i
$246$	3.63436	+	3.37220i	0.231719	+	0.215003i
$247$	−2.15014	+	1.03545i	−0.136810	+	0.0658844i
$248$	3.04494	−	0.458951i	0.193354	−	0.0291434i
$249$	4.63843	+	3.16243i	0.293949	+	0.200411i
$250$	−0.623490	+	0.781831i	−0.0394330	+	0.0494474i
$251$	−8.36558	−	14.4896i	−0.528031	−	0.914576i	−0.999466	−	0.0326751i	$-0.989597\pi$
$251$	−8.36558	−	14.4896i	−0.528031	−	0.914576i	0.471436	−	0.881901i	$-0.343736\pi$
$252$	6.27923	−	10.8760i	0.395555	−	0.685121i
$253$	−1.26965	−	3.23503i	−0.0798225	−	0.203384i
$254$	−1.10445	−	0.531874i	−0.0692993	−	0.0333728i
$255$	2.12554	+	0.655642i	0.133106	+	0.0410579i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−3.42093			−0.213392			−0.106696	−	0.994292i	$-0.534027\pi$
$257$	−3.42093			−0.213392			−0.106696	+	0.994292i	$0.534027\pi$
$258$	0.983582	−	3.18510i	0.0612351	−	0.198296i
$259$	28.0386			1.74223
$260$	−0.524055	+	2.29603i	−0.0325005	+	0.142394i
$261$	−22.5943	−	6.96941i	−1.39855	−	0.431396i
$262$	1.96644	+	0.946987i	0.121487	+	0.0585051i
$263$	−4.69329	−	11.9583i	−0.289401	−	0.737381i	−0.999448	−	0.0332271i	$-0.989422\pi$
$263$	−4.69329	−	11.9583i	−0.289401	−	0.737381i	0.710047	−	0.704154i	$-0.248674\pi$
$264$	−0.603509	+	1.04531i	−0.0371434	+	0.0643342i
$265$	−5.25607	−	9.10378i	−0.322878	−	0.559241i
$266$	−2.89413	+	3.62912i	−0.177450	+	0.222516i
$267$	0.545412	+	0.371856i	0.0333787	+	0.0227572i
$268$	−9.64884	+	1.45433i	−0.589397	+	0.0888373i
$269$	25.0694	−	12.0728i	1.52851	−	0.736091i	0.534477	−	0.845183i	$-0.320509\pi$
$269$	25.0694	−	12.0728i	1.52851	−	0.736091i	0.994032	+	0.109092i	$0.0347944\pi$
$270$	−2.13961	−	1.98526i	−0.130212	−	0.120819i
$271$	−23.9713	−	3.61309i	−1.45615	−	0.219479i	−0.627225	−	0.778838i	$-0.715809\pi$
$271$	−23.9713	−	3.61309i	−1.45615	−	0.219479i	−0.828926	+	0.559359i	$0.811047\pi$
$272$	4.18120	−	1.28973i	0.253522	−	0.0782013i
$273$	0.409832	+	5.46883i	0.0248042	+	0.330989i
$274$	−5.49605	−	6.89182i	−0.332028	−	0.416350i
$275$	−0.867449	+	2.21022i	−0.0523091	+	0.133281i
$276$	−0.545437	+	0.506092i	−0.0328315	+	0.0304631i
$277$	−12.3819	+	8.44182i	−0.743955	+	0.507220i	−0.874980	−	0.484159i	$-0.839126\pi$
$277$	−12.3819	+	8.44182i	−0.743955	+	0.507220i	0.131025	+	0.991379i	$0.458173\pi$
$278$	1.43978	−	19.2125i	0.0863523	−	1.15229i
$279$	1.87857	+	8.23055i	0.112467	+	0.492750i
$280$	1.01931	+	4.46590i	0.0609156	+	0.266889i
$281$	1.30790	−	17.4527i	0.0780226	−	1.04114i	−0.811531	−	0.584309i	$-0.801366\pi$
$281$	1.30790	−	17.4527i	0.0780226	−	1.04114i	0.889554	−	0.456830i	$-0.151015\pi$
$282$	0.0929014	−	0.0633391i	0.00553220	−	0.00377179i
$283$	5.29152	−	4.90981i	0.314548	−	0.291858i	−0.507060	−	0.861911i	$-0.669268\pi$
$283$	5.29152	−	4.90981i	0.314548	−	0.291858i	0.821608	+	0.570053i	$0.193077\pi$
$284$	−1.83172	+	4.66715i	−0.108693	+	0.276944i
$285$	0.321181	+	0.402748i	0.0190251	+	0.0238567i
$286$	0.417875	+	5.57616i	0.0247095	+	0.329725i
$287$	42.6900	−	13.1681i	2.51991	−	0.777289i
$288$	−2.71095	−	0.408610i	−0.159744	−	0.0240776i
$289$	−1.57300	−	1.45953i	−0.0925295	−	0.0858549i
$290$	7.77042	−	3.74204i	0.456295	−	0.219740i
$291$	7.78864	−	1.17395i	0.456578	−	0.0688181i
$292$	3.03308	+	2.06792i	0.177498	+	0.121016i
$293$	−11.6381	+	14.5937i	−0.679904	+	0.852572i	−0.995345	−	0.0963727i	$-0.969276\pi$
$293$	−11.6381	+	14.5937i	−0.679904	+	0.852572i	0.315442	+	0.948945i	$0.397847\pi$
$294$	3.55424	+	6.15613i	0.207288	+	0.359033i
$295$	−2.49890	+	4.32823i	−0.145492	+	0.251999i
$296$	−2.23624	−	5.69784i	−0.129979	−	0.331180i
$297$	−6.24388	−	3.00689i	−0.362306	−	0.174478i
$298$	10.6816	+	3.29483i	0.618767	+	0.190864i
$299$	−0.767041	+	3.36062i	−0.0443591	+	0.194350i
$300$	0.508356			0.0293500
$301$	−20.4240	−	22.0259i	−1.17722	−	1.26955i
$302$	18.0267			1.03732
$303$	2.08769	−	9.14676i	0.119934	−	0.525467i
$304$	0.968313	+	0.298685i	0.0555366	+	0.0171308i
$305$	6.54262	+	3.15076i	0.374629	+	0.180412i
$306$	4.38264	+	11.1668i	0.250539	+	0.638362i
$307$	−9.82384	+	17.0154i	−0.560676	+	0.971120i	0.436761	+	0.899577i	$0.356125\pi$
$307$	−9.82384	+	17.0154i	−0.560676	+	0.971120i	−0.997438	+	0.0715423i	$0.977208\pi$
$308$	5.43816	+	9.41917i	0.309868	+	0.536707i
$309$	2.83191	−	3.55110i	0.161102	−	0.202015i
$310$	−2.54426	−	1.73465i	−0.144505	−	0.0985215i
$311$	20.2364	−	3.05014i	1.14750	−	0.172958i	0.452362	−	0.891834i	$-0.350581\pi$
$311$	20.2364	−	3.05014i	1.14750	−	0.172958i	0.695138	+	0.718876i	$0.255343\pi$
$312$	1.07866	−	0.519454i	0.0610670	−	0.0294083i
$313$	12.7156	+	11.7983i	0.718728	+	0.666882i	0.952198	−	0.305482i	$-0.0988176\pi$
$313$	12.7156	+	11.7983i	0.718728	+	0.666882i	−0.233470	+	0.972364i	$0.575008\pi$
$314$	−0.847172	−	0.127691i	−0.0478087	−	0.00720600i
$315$	−12.0005	+	3.70167i	−0.676153	+	0.208566i
$316$	−1.11200	−	14.8386i	−0.0625549	−	0.834737i
$317$	15.2815	+	19.1624i	0.858296	+	1.07627i	0.996309	+	0.0858388i	$0.0273570\pi$
$317$	15.2815	+	19.1624i	0.858296	+	1.07627i	−0.138013	+	0.990430i	$0.544072\pi$
$318$	−1.95235	+	4.97451i	−0.109482	+	0.278957i
$319$	15.0112	−	13.9283i	0.840464	−	0.779837i
$320$	0.826239	−	0.563320i	0.0461882	−	0.0314905i
$321$	0.284556	−	3.79713i	0.0158824	−	0.211935i
$322$	1.49193	+	6.53659i	0.0831422	+	0.364270i
$323$	−0.986643	−	4.32276i	−0.0548983	−	0.240525i
$324$	0.503752	−	6.72210i	0.0279862	−	0.373450i
$325$	1.94586	−	1.32666i	0.107937	−	0.0735901i
$326$	13.9761	−	12.9679i	0.774064	−	0.718226i
$327$	−1.81725	+	4.63028i	−0.100494	+	0.256055i
$328$	−6.08072	−	7.62498i	−0.335752	−	0.421019i
$329$	−0.0757148	−	1.01034i	−0.00417429	−	0.0557020i
$330$	1.15339	−	0.355775i	0.0634922	−	0.0195847i
$331$	8.01285	+	1.20774i	0.440426	+	0.0663835i	0.365512	−	0.930807i	$-0.380894\pi$
$331$	8.01285	+	1.20774i	0.440426	+	0.0663835i	0.0749136	+	0.997190i	$0.476132\pi$
$332$	−8.09528	−	7.51132i	−0.444286	−	0.412237i
$333$	15.1192	−	7.28103i	0.828528	−	0.398998i
$334$	−7.60699	+	1.14657i	−0.416236	+	0.0627375i
$335$	8.06230	+	5.49678i	0.440490	+	0.300321i
$336$	1.45189	−	1.82061i	0.0792072	−	0.0993227i
$337$	15.8579	+	27.4667i	0.863836	+	1.49621i	0.868199	+	0.496217i	$0.165278\pi$
$337$	15.8579	+	27.4667i	0.863836	+	1.49621i	−0.00436311	+	0.999990i	$0.501389\pi$
$338$	−3.72680	+	6.45500i	−0.202711	+	0.351106i
$339$	−2.48429	−	6.32988i	−0.134928	−	0.343792i
$340$	−3.94227	−	1.89850i	−0.213800	−	0.102961i
$341$	−6.98660	−	2.15508i	−0.378345	−	0.116704i
$342$	−0.618191	+	2.70847i	−0.0334279	+	0.146457i
$343$	31.9887			1.72723
$344$	−2.84704	+	5.90714i	−0.153502	+	0.318492i
$345$	0.744063			0.0400590
$346$	−2.06671	+	9.05485i	−0.111107	+	0.486792i
$347$	−5.55488	−	1.71345i	−0.298202	−	0.0919830i	0.142044	−	0.989860i	$-0.454632\pi$
$347$	−5.55488	−	1.71345i	−0.298202	−	0.0919830i	−0.440246	+	0.897877i	$0.645109\pi$
$348$	−3.95014	−	1.90229i	−0.211750	−	0.101973i
$349$	−3.03958	−	7.74472i	−0.162705	−	0.414565i	0.826150	−	0.563451i	$-0.190527\pi$
$349$	−3.03958	−	7.74472i	−0.162705	−	0.414565i	−0.988854	+	0.148886i	$0.952431\pi$
$350$	2.29038	−	3.96705i	0.122426	−	0.212048i
$351$	3.43696	+	5.95300i	0.183452	+	0.317747i
$352$	1.48039	−	1.85634i	0.0789048	−	0.0989435i
$353$	22.8154	+	15.5552i	1.21434	+	0.827922i	0.989224	−	0.146410i	$-0.0467720\pi$
$353$	22.8154	+	15.5552i	1.21434	+	0.827922i	0.225115	+	0.974332i	$0.427724\pi$
$354$	2.51229	−	0.378667i	0.133527	−	0.0201259i
$355$	4.51722	−	2.17538i	0.239749	−	0.115457i
$356$	−0.951887	−	0.883222i	−0.0504499	−	0.0468107i
$357$	−10.0754	−	1.51863i	−0.533249	−	0.0803743i
$358$	11.0003	−	3.39313i	0.581382	−	0.179332i
$359$	−0.738247	−	9.85123i	−0.0389632	−	0.519928i	−0.982204	−	0.187818i	$-0.939859\pi$
$359$	−0.738247	−	9.85123i	−0.0389632	−	0.519928i	0.943241	−	0.332110i	$-0.107761\pi$
$360$	1.70934	+	2.14345i	0.0900903	+	0.112970i
$361$	−6.56633	+	16.7307i	−0.345596	+	0.880565i
$362$	−12.2628	+	11.3782i	−0.644519	+	0.598026i
$363$	−2.25235	+	1.53563i	−0.118218	+	0.0805996i
$364$	0.806191	−	10.7579i	0.0422559	−	0.563866i
$365$	−0.816863	−	3.57891i	−0.0427565	−	0.187329i
$366$	−0.821450	−	3.59901i	−0.0429379	−	0.188123i
$367$	−0.544856	+	7.27060i	−0.0284412	+	0.379522i	0.964762	+	0.263126i	$0.0847534\pi$
$367$	−0.544856	+	7.27060i	−0.0284412	+	0.379522i	−0.993203	+	0.116396i	$0.962866\pi$
$368$	1.20934	−	0.824512i	0.0630410	−	0.0429807i
$369$	19.6002	−	18.1863i	1.02034	−	0.946742i
$370$	−2.23624	+	5.69784i	−0.116256	+	0.296217i
$371$	30.0232	+	37.6479i	1.55873	+	1.95458i
$372$	0.116982	+	1.56102i	0.00606525	+	0.0809352i
$373$	−0.627948	+	0.193696i	−0.0325139	+	0.0100292i	−0.310969	−	0.950420i	$-0.600654\pi$
$373$	−0.627948	+	0.193696i	−0.0325139	+	0.0100292i	0.278456	+	0.960449i	$0.410178\pi$
$374$	−10.2732	−	1.54843i	−0.531213	−	0.0800675i
$375$	−0.372652	−	0.345770i	−0.0192436	−	0.0178555i
$376$	−0.199277	+	0.0959670i	−0.0102769	+	0.00494912i
$377$	−20.0846	+	3.02726i	−1.03441	+	0.155912i
$378$	11.0469	+	7.53167i	0.568193	+	0.387387i
$379$	14.4588	−	18.1307i	0.742697	−	0.931313i	−0.256683	−	0.966496i	$-0.582630\pi$
$379$	14.4588	−	18.1307i	0.742697	−	0.931313i	0.999381	+	0.0351824i	$0.0112012\pi$
$380$	−0.506666	−	0.877572i	−0.0259914	−	0.0450185i
$381$	0.311583	−	0.539678i	0.0159629	−	0.0276485i
$382$	1.48263	+	3.77769i	0.0758581	+	0.193283i
$383$	−18.3127	−	8.81893i	−0.935735	−	0.450626i	−0.0970724	−	0.995277i	$-0.530948\pi$
$383$	−18.3127	−	8.81893i	−0.935735	−	0.450626i	−0.838663	+	0.544651i	$0.816662\pi$
$384$	−0.485771	−	0.149841i	−0.0247894	−	0.00764652i
$385$	2.42021	−	10.6036i	0.123345	−	0.540411i
$386$	−13.0796			−0.665732
$387$	−16.7329	−	6.57330i	−0.850580	−	0.334140i
$388$	−15.4943			−0.786603
$389$	−4.55016	+	19.9355i	−0.230702	+	1.01077i	0.718357	+	0.695675i	$0.244894\pi$
$389$	−4.55016	+	19.9355i	−0.230702	+	1.01077i	−0.949059	+	0.315098i	$0.897963\pi$
$390$	−1.14403	−	0.352887i	−0.0579303	−	0.0178691i
$391$	−5.77017	−	2.77877i	−0.291810	−	0.140528i
$392$	−5.10867	−	13.0167i	−0.258027	−	0.657441i
$393$	−0.554765	+	0.960881i	−0.0279842	+	0.0484700i
$394$	−4.50861	−	7.80914i	−0.227141	−	0.393419i
$395$	−9.27767	+	11.6338i	−0.466810	+	0.585361i
$396$	5.37837	+	3.66691i	0.270273	+	0.184269i
$397$	−28.9256	+	4.35983i	−1.45173	+	0.218814i	−0.827078	−	0.562087i	$-0.809999\pi$
$397$	−28.9256	+	4.35983i	−1.45173	+	0.218814i	−0.624655	+	0.780901i	$0.714760\pi$
$398$	−2.88803	+	1.39080i	−0.144764	+	0.0697145i
$399$	−1.72978	−	1.60500i	−0.0865975	−	0.0803507i
$400$	−0.988831	−	0.149042i	−0.0494415	−	0.00745211i
$401$	22.0166	−	6.79123i	1.09946	−	0.339138i	0.308634	−	0.951181i	$-0.400128\pi$
$401$	22.0166	−	6.79123i	1.09946	−	0.339138i	0.790825	+	0.612043i	$0.209652\pi$
$402$	−0.370695	−	4.94658i	−0.0184886	−	0.246713i
$403$	4.52160	+	5.66990i	0.225237	+	0.282438i
$404$	−6.74256	+	17.1798i	−0.335455	+	0.854725i
$405$	−4.94147	+	4.58501i	−0.245543	+	0.227831i
$406$	−32.6420	+	22.2549i	−1.62000	+	1.10449i
$407$	−1.08608	+	14.4927i	−0.0538348	+	0.718376i
$408$	0.494967	+	2.16859i	0.0245045	+	0.107361i
$409$	1.73242	+	7.59022i	0.0856626	+	0.375312i	0.999529	−	0.0307037i	$-0.00977484\pi$
$409$	1.73242	+	7.59022i	0.0856626	+	0.375312i	−0.913866	+	0.406016i	$0.866918\pi$
$410$	−0.728821	+	9.72544i	−0.0359939	+	0.480305i
$411$	3.70250	−	2.52432i	0.182631	−	0.124516i
$412$	−6.54963	+	6.07716i	−0.322677	+	0.299400i
$413$	8.36401	−	21.3111i	0.411566	−	1.04865i
$414$	2.50191	+	3.13729i	0.122962	+	0.154189i
$415$	0.825264	+	11.0124i	0.0405106	+	0.540576i
$416$	−2.25045	+	0.694172i	−0.110337	+	0.0340346i
$417$	9.68481	+	1.45975i	0.474267	+	0.0714843i
$418$	−1.76373	−	1.63650i	−0.0862668	−	0.0800439i
$419$	−0.856167	+	0.412308i	−0.0418265	+	0.0201426i	−0.454680	−	0.890655i	$-0.650246\pi$
$419$	−0.856167	+	0.412308i	−0.0418265	+	0.0201426i	0.412854	+	0.910797i	$0.364532\pi$
$420$	−2.30264	+	0.347068i	−0.112358	+	0.0169352i
$421$	10.6083	+	7.23265i	0.517019	+	0.352498i	0.793548	−	0.608508i	$-0.208232\pi$
$421$	10.6083	+	7.23265i	0.517019	+	0.352498i	−0.276529	+	0.961006i	$0.589184\pi$
$422$	−1.92024	+	2.40790i	−0.0934756	+	0.117215i
$423$	−0.303192	−	0.525145i	−0.0147417	−	0.0255334i
$424$	5.25607	−	9.10378i	0.255257	−	0.442119i
$425$	1.59858	+	4.07313i	0.0775427	+	0.197576i
$426$	−2.29636	−	1.10587i	−0.111259	−	0.0535794i
$427$	−31.7865	−	9.80483i	−1.53826	−	0.474489i
$428$	−1.66677	+	7.30258i	−0.0805662	+	0.352984i
$429$	−2.84262			−0.137243
$430$	6.10491	−	2.39376i	0.294405	−	0.115438i
$431$	27.8149			1.33979			0.669897	−	0.742454i	$-0.266338\pi$
$431$	27.8149			1.33979			0.669897	+	0.742454i	$0.266338\pi$
$432$	0.649486	−	2.84559i	0.0312484	−	0.136908i
$433$	29.4721	+	9.09094i	1.41634	+	0.436883i	0.906068	−	0.423131i	$-0.139069\pi$
$433$	29.4721	+	9.09094i	1.41634	+	0.436883i	0.510270	+	0.860014i	$0.329545\pi$
$434$	12.7088	+	6.12022i	0.610040	+	0.293780i
$435$	1.60177	+	4.08125i	0.0767992	+	0.195681i
$436$	4.89236	−	8.47382i	0.234302	−	0.405822i
$437$	−0.741590	−	1.28447i	−0.0354750	−	0.0614446i
$438$	−1.16353	+	1.45901i	−0.0555954	+	0.0697144i
$439$	−1.05347	−	0.718243i	−0.0502793	−	0.0342799i	0.537920	−	0.842996i	$-0.319210\pi$
$439$	−1.05347	−	0.718243i	−0.0502793	−	0.0342799i	−0.588199	+	0.808716i	$0.700163\pi$
$440$	−2.34783	+	0.353879i	−0.111929	+	0.0168705i
$441$	34.5397	−	16.6335i	1.64475	−	0.792069i
$442$	7.55401	+	7.00910i	0.359308	+	0.333389i
$443$	−35.3649	−	5.33040i	−1.68024	−	0.253255i	−0.761511	−	0.648152i	$-0.775542\pi$
$443$	−35.3649	−	5.33040i	−1.68024	−	0.253255i	−0.918725	+	0.394897i	$0.870780\pi$
$444$	2.97339	−	0.917169i	0.141111	−	0.0435269i
$445$	0.0970390	+	1.29490i	0.00460009	+	0.0613839i
$446$	−6.99761	−	8.77473i	−0.331347	−	0.415496i
$447$	−2.07605	+	5.28969i	−0.0981939	+	0.250194i
$448$	−3.35793	+	3.11570i	−0.158647	+	0.147203i
$449$	27.3284	−	18.6322i	1.28971	−	0.879308i	0.292670	−	0.956213i	$-0.405456\pi$
$449$	27.3284	−	18.6322i	1.28971	−	0.879308i	0.997038	+	0.0769052i	$0.0245039\pi$
$450$	0.204878	−	2.73391i	0.00965804	−	0.128878i
$451$	5.15278	+	22.5758i	0.242635	+	1.06305i
$452$	2.97651	+	13.0409i	0.140003	+	0.613394i
$453$	−0.684825	+	9.13836i	−0.0321759	+	0.429358i
$454$	−9.88956	+	6.74259i	−0.464140	+	0.316445i
$455$	−7.90819	+	7.33773i	−0.370742	+	0.343998i
$456$	−0.188200	+	0.479525i	−0.00881325	+	0.0224558i
$457$	13.2407	+	16.6033i	0.619372	+	0.776668i	0.988256	−	0.152808i	$-0.0488315\pi$
$457$	13.2407	+	16.6033i	0.619372	+	0.776668i	−0.368884	+	0.929475i	$0.620260\pi$
$458$	0.764893	+	10.2068i	0.0357411	+	0.476932i
$459$	−12.2039	+	3.76442i	−0.569631	+	0.175708i
$460$	−1.44732	−	0.218148i	−0.0674815	−	0.0101712i
$461$	0.732376	+	0.679545i	0.0341101	+	0.0316496i	0.697044	−	0.717029i	$-0.254498\pi$
$461$	0.732376	+	0.679545i	0.0341101	+	0.0316496i	−0.662934	+	0.748678i	$0.730689\pi$
$462$	−4.98150	+	2.39896i	−0.231760	+	0.111610i
$463$	−28.8761	+	4.35238i	−1.34199	+	0.202272i	−0.780470	−	0.625193i	$-0.785020\pi$
$463$	−28.8761	+	4.35238i	−1.34199	+	0.202272i	−0.561518	+	0.827465i	$0.689782\pi$
$464$	7.12591	+	4.85836i	0.330812	+	0.225544i
$465$	0.976010	−	1.22388i	0.0452614	−	0.0567560i
$466$	11.8972	+	20.6065i	0.551126	+	0.954578i
$467$	12.5438	−	21.7265i	0.580458	−	1.00538i	−0.414967	−	0.909836i	$-0.636207\pi$
$467$	12.5438	−	21.7265i	0.580458	−	1.00538i	0.995425	−	0.0955459i	$-0.0304597\pi$
$468$	−2.35887	−	6.01030i	−0.109039	−	0.277826i
$469$	−40.2717	−	19.3938i	−1.85957	−	0.895523i
$470$	0.211355	+	0.0651943i	0.00974907	+	0.00300719i
$471$	0.0969145	−	0.424610i	0.00446558	−	0.0195650i
$472$	−4.99781			−0.230043
$473$	12.1759	−	9.70367i	0.559850	−	0.446175i
$474$	7.56445			0.347447
$475$	−0.225488	+	0.987926i	−0.0103461	+	0.0453292i
$476$	19.1530	+	5.90793i	0.877878	+	0.270789i
$477$	25.9657	+	12.5044i	1.18889	+	0.572539i
$478$	−0.653926	−	1.66618i	−0.0299099	−	0.0762091i
$479$	20.3497	−	35.2467i	0.929801	−	1.61046i	0.146148	−	0.989263i	$-0.453312\pi$
$479$	20.3497	−	35.2467i	0.929801	−	1.61046i	0.783653	−	0.621199i	$-0.213354\pi$
$480$	0.254178	+	0.440249i	0.0116016	+	0.0200945i
$481$	8.98783	−	11.2704i	0.409810	−	0.513885i
$482$	−4.54323	−	3.09752i	−0.206938	−	0.141088i
$483$	−3.37030	+	0.507991i	−0.153354	+	0.0231144i
$484$	4.83140	−	2.32668i	0.219609	−	0.105758i
$485$	11.3581	+	10.5388i	0.515745	+	0.478542i
$486$	12.0470	+	1.81580i	0.546464	+	0.0823662i
$487$	5.56970	−	1.71803i	0.252387	−	0.0778512i	−0.165980	−	0.986129i	$-0.553079\pi$
$487$	5.56970	−	1.71803i	0.252387	−	0.0778512i	0.418367	+	0.908278i	$0.362603\pi$
$488$	0.542672	+	7.24146i	0.0245656	+	0.327805i
$489$	6.04294	+	7.57761i	0.273271	+	0.342671i
$490$	−5.10867	+	13.0167i	−0.230786	+	0.588033i
$491$	−28.8270	+	26.7476i	−1.30095	+	1.20710i	−0.336847	+	0.941559i	$0.609360\pi$
$491$	−28.8270	+	26.7476i	−1.30095	+	1.20710i	−0.964099	+	0.265542i	$0.914449\pi$
$492$	4.09637	−	2.79286i	0.184679	−	0.125912i
$493$	2.82012	−	37.6319i	0.127012	−	1.69485i
$494$	0.531042	+	2.32665i	0.0238927	+	0.104681i
$495$	−1.44849	−	6.34626i	−0.0651049	−	0.285243i
$496$	0.230119	−	3.07072i	0.0103326	−	0.137880i
$497$	−18.9759	+	12.9376i	−0.851187	+	0.580330i
$498$	4.11529	−	3.81843i	0.184410	−	0.171108i
$499$	3.74448	−	9.54079i	0.167626	−	0.427104i	−0.822234	−	0.569149i	$-0.807273\pi$
$499$	3.74448	−	9.54079i	0.167626	−	0.427104i	0.989860	+	0.142045i	$0.0453678\pi$
$500$	0.623490	+	0.781831i	0.0278833	+	0.0349646i
$501$	−0.292250	−	3.89981i	−0.0130568	−	0.174231i
$502$	−15.9878	+	4.93159i	−0.713572	+	0.220108i
$503$	−31.3192	−	4.72061i	−1.39645	−	0.210481i	−0.592690	−	0.805431i	$-0.701934\pi$
$503$	−31.3192	−	4.72061i	−1.39645	−	0.210481i	−0.803763	+	0.594949i	$0.797172\pi$
$504$	−9.20601	−	8.54193i	−0.410068	−	0.380488i
$505$	16.6279	−	8.00755i	0.739930	−	0.356331i
$506$	−3.43644	+	0.517960i	−0.152768	+	0.0230261i
$507$	−3.13069	−	2.13447i	−0.139039	−	0.0947950i
$508$	−0.764302	+	0.958405i	−0.0339104	+	0.0425223i
$509$	−2.14226	−	3.71050i	−0.0949540	−	0.164465i	0.814635	−	0.579973i	$-0.196937\pi$
$509$	−2.14226	−	3.71050i	−0.0949540	−	0.164465i	−0.909589	+	0.415508i	$0.863604\pi$
$510$	1.11218	−	1.92635i	0.0492482	−	0.0853004i
$511$	6.14346	+	15.6533i	0.271771	+	0.692461i
$512$	0.900969	+	0.433884i	0.0398176	+	0.0191751i
$513$	−2.82628	−	0.871791i	−0.124783	−	0.0384905i
$514$	−0.761228	+	3.33516i	−0.0335763	+	0.147108i
$515$	8.93474			0.393712
$516$	−2.88638	−	1.66767i	−0.127066	−	0.0734153i
$517$	0.525162			0.0230966
$518$	6.23917	−	27.3356i	0.274134	−	1.20106i
$519$	−4.51170	−	1.39168i	−0.198042	−	0.0610878i
$520$	2.12185	+	1.02183i	0.0930495	+	0.0448103i
$521$	12.7246	+	32.4216i	0.557473	+	1.42042i	0.880508	+	0.474031i	$0.157201\pi$
$521$	12.7246	+	32.4216i	0.557473	+	1.42042i	−0.323036	+	0.946387i	$0.604703\pi$
$522$	−11.8224	+	20.4769i	−0.517451	+	0.896252i
$523$	22.3922	+	38.7844i	0.979141	+	1.69592i	0.665529	+	0.746372i	$0.268206\pi$
$523$	22.3922	+	38.7844i	0.979141	+	1.69592i	0.313612	+	0.949551i	$0.398461\pi$
$524$	1.36082	−	1.70641i	0.0594476	−	0.0745450i
$525$	1.92402	+	1.31178i	0.0839713	+	0.0572507i
$526$	−12.7029	+	1.91465i	−0.553871	+	0.0834826i
$527$	−12.1396	+	5.84611i	−0.528808	+	0.254661i
$528$	0.884806	+	0.820980i	0.0385063	+	0.0357286i
$529$	20.6247	+	3.10868i	0.896727	+	0.135160i
$530$	−10.0451	+	3.09851i	−0.436332	+	0.134591i
$531$	−1.02394	−	13.6635i	−0.0444352	−	0.592947i
$532$	2.89413	+	3.62912i	0.125476	+	0.157342i
$533$	8.39131	−	21.3807i	0.363468	−	0.926101i
$534$	0.483898	−	0.448992i	0.0209403	−	0.0194298i
$535$	6.18884	−	4.21948i	0.267567	−	0.182424i
$536$	−0.729204	+	9.73055i	−0.0314968	+	0.420296i
$537$	1.30220	+	5.70532i	0.0561941	+	0.246203i
$538$	−6.19163	−	27.1273i	−0.266940	−	1.16954i
$539$	−2.48113	+	33.1084i	−0.106870	+	1.42608i
$540$	−2.41160	+	1.64420i	−0.103779	+	0.0707551i
$541$	−14.2507	+	13.2227i	−0.612684	+	0.568487i	−0.924274	−	0.381729i	$-0.875329\pi$
$541$	−14.2507	+	13.2227i	−0.612684	+	0.568487i	0.311591	+	0.950216i	$0.399138\pi$
$542$	−8.85661	+	22.5663i	−0.380424	+	0.969304i
$543$	−5.30216	−	6.64870i	−0.227538	−	0.285323i
$544$	−0.326989	−	4.36336i	−0.0140195	−	0.187077i
$545$	−9.35001	+	2.88410i	−0.400511	+	0.123541i
$546$	5.42291	+	0.817373i	0.232079	+	0.0349803i
$547$	−16.0378	−	14.8809i	−0.685725	−	0.636260i	0.258326	−	0.966058i	$-0.416829\pi$
$547$	−16.0378	−	14.8809i	−0.685725	−	0.636260i	−0.944052	+	0.329798i	$0.893020\pi$
$548$	−7.94202	+	3.82467i	−0.339266	+	0.163382i
$549$	−19.6863	+	2.96723i	−0.840191	+	0.126638i
$550$	1.96178	+	1.33752i	0.0836507	+	0.0570321i
$551$	5.44899	−	6.83282i	0.232135	−	0.291088i
$552$	0.372032	+	0.644378i	0.0158347	+	0.0274265i
$553$	34.0813	−	59.0305i	1.44928	−	2.51023i
$554$	5.47494	+	13.9499i	0.232608	+	0.592676i
$555$	−2.80348	−	1.35009i	−0.119001	−	0.0573079i
$556$	−18.4105	−	5.67888i	−0.780778	−	0.240838i
$557$	0.523530	−	2.29374i	0.0221827	−	0.0971888i	−0.962625	−	0.270839i	$-0.912699\pi$
$557$	0.523530	−	2.29374i	0.0221827	−	0.0971888i	0.984807	+	0.173650i	$0.0555561\pi$
$558$	8.44222			0.357388
$559$	−15.4005	+	1.14919i	−0.651371	+	0.0486056i
$560$	4.58075			0.193572
$561$	1.17523	−	5.14900i	0.0496181	−	0.217391i
$562$	−16.7241	−	5.15869i	−0.705462	−	0.217606i
$563$	7.39842	+	3.56289i	0.311806	+	0.150158i	0.583242	−	0.812299i	$-0.301784\pi$
$563$	7.39842	+	3.56289i	0.311806	+	0.150158i	−0.271436	+	0.962457i	$0.587498\pi$
$564$	−0.0410785	−	0.104666i	−0.00172972	−	0.00440725i
$565$	6.68816	−	11.5842i	0.281373	−	0.487352i
$566$	−3.60924	−	6.25138i	−0.151708	−	0.262765i
$567$	19.2525	−	24.1419i	0.808529	−	1.01386i
$568$	4.14254	+	2.82434i	0.173817	+	0.118506i
$569$	−22.6447	+	3.41314i	−0.949314	+	0.143086i	−0.605406	−	0.795917i	$-0.706989\pi$
$569$	−22.6447	+	3.41314i	−0.949314	+	0.143086i	−0.343909	+	0.939003i	$0.611751\pi$
$570$	0.464120	−	0.223508i	0.0194398	−	0.00936173i
$571$	26.0117	+	24.1353i	1.08856	+	1.01003i	0.999902	+	0.0139695i	$0.00444678\pi$
$571$	26.0117	+	24.1353i	1.08856	+	1.01003i	0.0886532	+	0.996063i	$0.471744\pi$
$572$	5.52934	+	0.833413i	0.231193	+	0.0348468i
$573$	−1.97137	+	0.608086i	−0.0823550	+	0.0254032i
$574$	−3.33855	−	44.5498i	−0.139348	−	1.85947i
$575$	0.912580	+	1.14434i	0.0380572	+	0.0477223i
$576$	−1.00161	+	2.55206i	−0.0417337	+	0.106336i
$577$	−7.79753	+	7.23505i	−0.324616	+	0.301199i	−0.825599	−	0.564258i	$-0.809162\pi$
$577$	−7.79753	+	7.23505i	−0.324616	+	0.301199i	0.500983	+	0.865457i	$0.332972\pi$
$578$	−1.77297	+	1.20879i	−0.0737456	+	0.0502789i
$579$	0.496886	−	6.63049i	0.0206499	−	0.275554i
$580$	−1.91913	−	8.40828i	−0.0796877	−	0.349135i
$581$	−11.2565	−	49.3181i	−0.467000	−	2.04606i
$582$	0.588620	−	7.85459i	0.0243991	−	0.325583i
$583$	−20.6225	+	14.0602i	−0.854098	+	0.582314i
$584$	2.69100	−	2.49688i	0.111354	−	0.103322i
$585$	−2.35887	+	6.01030i	−0.0975273	+	0.248495i
$586$	11.6381	+	14.5937i	0.480765	+	0.602860i
$587$	0.901931	+	12.0354i	0.0372267	+	0.496756i	0.984390	+	0.176003i	$0.0563168\pi$
$587$	0.901931	+	12.0354i	0.0372267	+	0.496756i	−0.947163	+	0.320753i	$0.896064\pi$
$588$	6.79268	−	2.09526i	0.280125	−	0.0864072i
$589$	−3.08554	−	0.465070i	−0.127137	−	0.0191629i
$590$	3.66365	+	3.39937i	0.150830	+	0.139950i
$591$	4.13001	−	1.98891i	0.169886	−	0.0818127i
$592$	−6.05259	+	0.912282i	−0.248760	+	0.0374946i
$593$	11.6913	+	7.97099i	0.480104	+	0.327329i	0.779073	−	0.626934i	$-0.215690\pi$
$593$	11.6913	+	7.97099i	0.480104	+	0.327329i	−0.298969	+	0.954263i	$0.596643\pi$
$594$	−4.32090	+	5.41823i	−0.177289	+	0.222313i
$595$	−10.0218	−	17.3582i	−0.410852	−	0.711616i
$596$	5.58909	−	9.68060i	0.228938	−	0.396533i
$597$	−0.595330	−	1.51688i	−0.0243652	−	0.0620816i
$598$	3.10568	+	1.49562i	0.127001	+	0.0611604i
$599$	−28.0301	−	8.64615i	−1.14528	−	0.353272i	−0.336673	−	0.941621i	$-0.609302\pi$
$599$	−28.0301	−	8.64615i	−1.14528	−	0.353272i	−0.808607	+	0.588349i	$0.799778\pi$
$600$	0.113120	−	0.495611i	0.00461810	−	0.0202332i
$601$	−32.4061			−1.32187			−0.660937	−	0.750441i	$-0.729841\pi$
$601$	−32.4061			−1.32187			−0.660937	+	0.750441i	$0.729841\pi$
$602$	−26.0184	+	15.0107i	−1.06043	+	0.611792i
$603$	−26.7518			−1.08942
$604$	4.01132	−	17.5747i	0.163218	−	0.715106i
$605$	−5.12421	−	1.58061i	−0.208329	−	0.0642609i
$606$	−8.45287	−	4.07069i	−0.343374	−	0.165360i
$607$	12.4041	+	31.6052i	0.503468	+	1.28282i	0.926361	+	0.376637i	$0.122919\pi$
$607$	12.4041	+	31.6052i	0.503468	+	1.28282i	−0.422893	+	0.906180i	$0.638985\pi$
$608$	0.506666	−	0.877572i	0.0205480	−	0.0355902i
$609$	−10.0418	−	17.3928i	−0.406912	−	0.704793i
$610$	4.52764	−	5.67748i	0.183319	−	0.229874i
$611$	−0.430387	−	0.293433i	−0.0174116	−	0.0118710i
$612$	11.8620	−	1.78791i	0.479494	−	0.0722721i
$613$	22.5071	−	10.8389i	0.909053	−	0.437777i	0.0799030	−	0.996803i	$-0.474539\pi$
$613$	22.5071	−	10.8389i	0.909053	−	0.437777i	0.829150	+	0.559026i	$0.188825\pi$
$614$	14.4028	+	13.3638i	0.581248	+	0.539320i
$615$	−4.90248	−	0.738930i	−0.197687	−	0.0297965i
$616$	10.3931	−	3.20585i	0.418751	−	0.129167i
$617$	−0.361211	−	4.82003i	−0.0145418	−	0.194047i	−0.999744	−	0.0226480i	$-0.992790\pi$
$617$	−0.361211	−	4.82003i	−0.0145418	−	0.194047i	0.985202	−	0.171399i	$-0.0548288\pi$
$618$	−2.83191	−	3.55110i	−0.113916	−	0.142846i
$619$	−6.47947	+	16.5094i	−0.260432	+	0.663570i	−0.999954	−	0.00956204i	$-0.996956\pi$
$619$	−6.47947	+	16.5094i	−0.260432	+	0.663570i	0.739522	+	0.673132i	$0.235051\pi$
$620$	−2.25731	+	2.09448i	−0.0906558	+	0.0841163i
$621$	−3.52977	+	2.40656i	−0.141645	+	0.0965718i
$622$	1.52935	−	20.4077i	0.0613213	−	0.818276i
$623$	−1.32360	−	5.79909i	−0.0530291	−	0.232336i
$624$	−0.266407	−	1.16720i	−0.0106648	−	0.0467255i
$625$	0.0747301	−	0.997204i	0.00298920	−	0.0398882i
$626$	14.3320	−	9.77141i	0.572823	−	0.390544i
$627$	0.896603	−	0.831926i	0.0358069	−	0.0332239i
$628$	−0.313003	+	0.797518i	−0.0124902	+	0.0318244i
$629$	16.6988	+	20.9397i	0.665826	+	0.834919i
$630$	0.938495	+	12.5234i	0.0373906	+	0.498942i
$631$	37.0727	−	11.4354i	1.47584	−	0.455236i	0.550648	−	0.834737i	$-0.314381\pi$
$631$	37.0727	−	11.4354i	1.47584	−	0.455236i	0.925191	+	0.379501i	$0.123904\pi$
$632$	−14.7140	−	2.21778i	−0.585292	−	0.0882186i
$633$	−1.14770	−	1.06491i	−0.0456170	−	0.0423263i
$634$	22.0824	−	10.6343i	0.877006	−	0.422344i
$635$	1.21215	−	0.182703i	0.0481029	−	0.00725034i
$636$	4.41535	+	3.01033i	0.175080	+	0.119367i
$637$	20.5326	−	25.7471i	0.813531	−	1.02014i
$638$	−10.2388	−	17.7342i	−0.405359	−	0.702102i
$639$	−6.87276	+	11.9040i	−0.271882	+	0.470914i
$640$	−0.365341	−	0.930874i	−0.0144414	−	0.0367960i
$641$	−18.3728	−	8.84786i	−0.725681	−	0.349469i	0.0343031	−	0.999411i	$-0.489079\pi$
$641$	−18.3728	−	8.84786i	−0.725681	−	0.349469i	−0.759984	+	0.649942i	$0.774793\pi$
$642$	−3.63861	−	1.12236i	−0.143605	−	0.0442961i
$643$	3.22631	−	14.1354i	0.127233	−	0.557446i	−0.870620	−	0.491956i	$-0.836282\pi$
$643$	3.22631	−	14.1354i	0.127233	−	0.557446i	0.997853	−	0.0654896i	$-0.0208609\pi$
$644$	6.70469			0.264202
$645$	0.981560	+	3.18573i	0.0386489	+	0.125438i
$646$	−4.43393			−0.174451
$647$	1.96599	−	8.61355i	0.0772909	−	0.338633i	−0.921467	−	0.388456i	$-0.873008\pi$
$647$	1.96599	−	8.61355i	0.0772909	−	0.338633i	0.998758	+	0.0498227i	$0.0158656\pi$
$648$	−6.44147	−	1.98693i	−0.253045	−	0.0780540i
$649$	10.6914	+	5.14871i	0.419674	+	0.202104i
$650$	−0.860407	−	2.19228i	−0.0337480	−	0.0859884i
$651$	−3.58535	+	6.21001i	−0.140521	+	0.243389i
$652$	−9.53281	−	16.5113i	−0.373334	−	0.646633i
$653$	−17.8818	+	22.4231i	−0.699770	+	0.877484i	−0.997006	−	0.0773198i	$-0.975364\pi$
$653$	−17.8818	+	22.4231i	−0.699770	+	0.877484i	0.297236	+	0.954804i	$0.403935\pi$
$654$	4.10981	+	2.80202i	0.160706	+	0.109568i
$655$	−2.15821	+	0.325297i	−0.0843281	+	0.0127104i
$656$	−8.78689	+	4.23154i	−0.343071	+	0.165214i
$657$	7.37756	+	6.84538i	0.287826	+	0.267064i
$658$	−1.00186	−	0.151006i	−0.0390566	−	0.00588683i
$659$	30.4078	−	9.37957i	1.18452	−	0.365376i	0.360948	−	0.932586i	$-0.382453\pi$
$659$	30.4078	−	9.37957i	1.18452	−	0.365376i	0.823573	+	0.567210i	$0.191977\pi$
$660$	−0.0902005	−	1.20364i	−0.00351105	−	0.0468517i
$661$	−25.9370	−	32.5239i	−1.00883	−	1.26503i	−0.963962	−	0.266041i	$-0.914284\pi$
$661$	−25.9370	−	32.5239i	−1.00883	−	1.26503i	−0.0448694	−	0.998993i	$-0.514287\pi$
$662$	2.96049	−	7.54320i	0.115063	−	0.293175i
$663$	−3.84013	+	3.56312i	−0.149138	+	0.138380i
$664$	−9.12437	+	6.22089i	−0.354094	+	0.241417i
$665$	0.346884	−	4.62884i	0.0134516	−	0.179499i
$666$	−3.73414	−	16.3603i	−0.144695	−	0.633950i
$667$	−2.80897	−	12.3069i	−0.108764	−	0.476525i
$668$	−0.574892	+	7.67141i	−0.0222433	+	0.296816i
$669$	4.71405	−	3.21399i	0.182256	−	0.124260i
$670$	7.15300	−	6.63701i	0.276344	−	0.256410i
$671$	6.29921	−	16.0501i	0.243178	−	0.619608i
$672$	−1.45189	−	1.82061i	−0.0560079	−	0.0702317i
$673$	3.37266	+	45.0051i	0.130007	+	1.73482i	0.556956	+	0.830542i	$0.311969\pi$
$673$	3.37266	+	45.0051i	0.130007	+	1.73482i	−0.426950	+	0.904275i	$0.640412\pi$
$674$	30.3068	−	9.34840i	1.16737	−	0.360087i
$675$	2.88617	+	0.435019i	0.111089	+	0.0167439i
$676$	5.46387	+	5.06973i	0.210149	+	0.194990i
$677$	−14.0732	+	6.77727i	−0.540875	+	0.260472i	−0.684314	−	0.729187i	$-0.739898\pi$
$677$	−14.0732	+	6.77727i	−0.540875	+	0.260472i	0.143439	+	0.989659i	$0.454184\pi$
$678$	−6.72398	+	1.01348i	−0.258233	+	0.0389224i
$679$	−58.6426	−	39.9819i	−2.25050	−	1.53436i
$680$	−2.72814	+	3.42098i	−0.104619	+	0.131188i
$681$	−3.04235	−	5.26951i	−0.116583	−	0.201928i
$682$	−3.65571	+	6.33188i	−0.139984	+	0.242460i
$683$	−13.3066	−	33.9046i	−0.509162	−	1.29732i	−0.922236	−	0.386626i	$-0.873640\pi$
$683$	−13.3066	−	33.9046i	−0.509162	−	1.29732i	0.413074	−	0.910697i	$-0.364455\pi$
$684$	2.50300	+	1.20538i	0.0957048	+	0.0460890i
$685$	8.42335	+	2.59826i	0.321840	+	0.0992744i
$686$	7.11815	−	31.1866i	0.271772	−	1.19071i
$687$	−5.20323			−0.198516
$688$	5.12551	+	4.09012i	0.195408	+	0.155934i
$689$	24.7569			0.943164
$690$	0.165570	−	0.725408i	0.00630313	−	0.0276158i
$691$	−30.2163	−	9.32049i	−1.14948	−	0.354568i	−0.339261	−	0.940692i	$-0.610177\pi$
$691$	−30.2163	−	9.32049i	−1.14948	−	0.354568i	−0.810221	+	0.586124i	$0.800653\pi$
$692$	8.36794	+	4.02979i	0.318101	+	0.153189i
$693$	10.8938	+	27.7570i	0.413822	+	1.05440i
$694$	−2.90657	+	5.03433i	−0.110332	+	0.191100i
$695$	9.63321	+	16.6852i	0.365408	+	0.632906i
$696$	−2.73358	+	3.42780i	−0.103616	+	0.129931i
$697$	35.2589	+	24.0391i	1.33552	+	0.910545i
$698$	−8.22691	+	1.24001i	−0.311393	+	0.0469350i
$699$	−10.8981	+	5.24826i	−0.412205	+	0.198508i
$700$	−3.35793	−	3.11570i	−0.126918	−	0.117762i
$701$	13.5820	+	2.04715i	0.512983	+	0.0773198i	0.400433	−	0.916326i	$-0.368860\pi$
$701$	13.5820	+	2.04715i	0.512983	+	0.0773198i	0.112551	+	0.993646i	$0.464098\pi$
$702$	6.56854	−	2.02613i	0.247913	−	0.0764712i
$703$	0.463518	+	6.18522i	0.0174819	+	0.233280i
$704$	−1.48039	−	1.85634i	−0.0557941	−	0.0699636i
$705$	−0.0410785	+	0.104666i	−0.00154711	+	0.00394197i
$706$	20.2421	−	18.7820i	0.761823	−	0.706868i
$707$	−69.8503	+	47.6232i	−2.62699	+	1.79105i
$708$	0.189864	−	2.53356i	0.00713553	−	0.0952171i
$709$	−4.39986	−	19.2771i	−0.165240	−	0.723965i	−0.987857	−	0.155368i	$-0.950344\pi$
$709$	−4.39986	−	19.2771i	−0.165240	−	0.723965i	0.822616	−	0.568597i	$-0.192514\pi$
$710$	−1.11566	−	4.88803i	−0.0418700	−	0.183444i
$711$	3.04863	−	40.6812i	0.114333	−	1.52566i
$712$	−1.07289	+	0.731486i	−0.0402084	+	0.0274136i
$713$	−3.30395	+	3.06561i	−0.123734	+	0.114808i
$714$	−3.72255	+	9.48490i	−0.139313	+	0.354963i
$715$	−3.48643	−	4.37184i	−0.130385	−	0.163498i
$716$	−0.860269	−	11.4795i	−0.0321498	−	0.429009i
$717$	0.869485	−	0.268200i	0.0324715	−	0.0100161i
$718$	−9.76851	−	1.47237i	−0.364558	−	0.0549482i
$719$	−2.11615	−	1.96350i	−0.0789191	−	0.0732262i	0.639727	−	0.768602i	$-0.279047\pi$
$719$	−2.11615	−	1.96350i	−0.0789191	−	0.0732262i	−0.718646	+	0.695376i	$0.755238\pi$
$720$	2.47007	−	1.18952i	0.0920542	−	0.0443310i
$721$	−40.4707	+	6.09997i	−1.50721	+	0.227175i
$722$	14.8501	+	10.1246i	0.552664	+	0.376800i
$723$	1.74284	−	2.18545i	0.0648168	−	0.0812777i
$724$	8.36422	+	14.4873i	0.310854	+	0.538415i
$725$	−4.31226	+	7.46905i	−0.160153	+	0.277393i
$726$	0.995932	+	2.53759i	0.0369625	+	0.0941789i
$727$	−35.6867	−	17.1858i	−1.32355	−	0.637386i	−0.367342	−	0.930086i	$-0.619732\pi$
$727$	−35.6867	−	17.1858i	−1.32355	−	0.637386i	−0.956205	+	0.292699i	$0.905446\pi$
$728$	−10.3088	−	3.17983i	−0.382068	−	0.117852i
$729$	3.12186	−	13.6777i	0.115624	−	0.506583i
$730$	−3.67095			−0.135868
$731$	4.28543	−	28.3709i	0.158502	−	1.04933i
$732$	−3.69156			−0.136444
$733$	−5.81389	+	25.4723i	−0.214741	+	0.940841i	0.746555	+	0.665324i	$0.231706\pi$
$733$	−5.81389	+	25.4723i	−0.214741	+	0.940841i	−0.961296	+	0.275518i	$0.911151\pi$
$734$	6.96706	+	2.14905i	0.257159	+	0.0793231i
$735$	−6.40453	−	3.08426i	−0.236235	−	0.113765i
$736$	−0.534737	−	1.36249i	−0.0197107	−	0.0502220i
$737$	11.5843	−	20.0645i	0.426712	−	0.739087i
$738$	−13.3689	−	23.1556i	−0.492116	−	0.852370i
$739$	−2.10358	+	2.63781i	−0.0773815	+	0.0970333i	−0.819015	−	0.573772i	$-0.805480\pi$
$739$	−2.10358	+	2.63781i	−0.0773815	+	0.0970333i	0.741634	+	0.670805i	$0.234051\pi$
$740$	5.05737	+	3.44806i	0.185913	+	0.126753i
$741$	−1.19963	+	0.180815i	−0.0440696	+	0.00664242i
$742$	43.3848	−	20.8930i	1.59271	−	0.767007i
$743$	30.4349	+	28.2395i	1.11655	+	1.03601i	0.999078	+	0.0429297i	$0.0136692\pi$
$743$	30.4349	+	28.2395i	1.11655	+	1.03601i	0.117471	+	0.993076i	$0.462521\pi$
$744$	1.54791	+	0.233311i	0.0567493	+	0.00855358i
$745$	−10.6816	+	3.29483i	−0.391343	+	0.120713i
$746$	0.0491084	+	0.655305i	0.00179798	+	0.0239924i
$747$	−18.8767	−	23.6707i	−0.690663	−	0.866064i
$748$	−3.79560	+	9.67104i	−0.138781	+	0.353608i
$749$	−25.1522	+	23.3378i	−0.919040	+	0.852744i
$750$	−0.420024	+	0.286367i	−0.0153371	+	0.0104567i
$751$	−3.40205	+	45.3972i	−0.124143	+	1.65657i	0.493231	+	0.869898i	$0.335816\pi$
$751$	−3.40205	+	45.3972i	−0.124143	+	1.65657i	−0.617373	+	0.786670i	$0.711803\pi$
$752$	0.0492175	+	0.215636i	0.00179478	+	0.00786343i
$753$	−1.89263	−	8.29214i	−0.0689712	−	0.302182i
$754$	−1.51787	+	20.2546i	−0.0552777	+	0.737630i
$755$	−14.8944	+	10.1548i	−0.542061	+	0.369571i
$756$	9.80100	−	9.09400i	0.356459	−	0.330746i
$757$	−7.74937	+	19.7451i	−0.281655	+	0.717646i	0.718109	+	0.695931i	$0.245008\pi$
$757$	−7.74937	+	19.7451i	−0.281655	+	0.717646i	−0.999764	+	0.0217155i	$0.993087\pi$
$758$	−14.4588	−	18.1307i	−0.525166	−	0.658538i
$759$	−0.132023	−	1.76173i	−0.00479214	−	0.0639467i
$760$	−0.968313	+	0.298685i	−0.0351244	+	0.0108344i
$761$	7.74224	+	1.16695i	0.280656	+	0.0423021i	0.287862	−	0.957672i	$-0.407056\pi$
$761$	7.74224	+	1.16695i	0.280656	+	0.0423021i	−0.00720591	+	0.999974i	$0.502294\pi$
$762$	−0.456813	−	0.423861i	−0.0165486	−	0.0153549i
$763$	40.3827	−	19.4473i	1.46195	−	0.704038i
$764$	4.01289	−	0.604846i	0.145181	−	0.0218826i
$765$	−9.91157	−	6.75760i	−0.358354	−	0.244321i
$766$	−12.6728	+	15.8912i	−0.457886	+	0.574171i
$767$	−5.88512	−	10.1933i	−0.212499	−	0.368059i
$768$	−0.254178	+	0.440249i	−0.00917186	+	0.0158861i
$769$	−10.4776	−	26.6965i	−0.377833	−	0.962702i	−0.985677	−	0.168645i	$-0.946061\pi$
$769$	−10.4776	−	26.6965i	−0.377833	−	0.962702i	0.607844	−	0.794056i	$-0.292035\pi$
$770$	−9.79923	−	4.71906i	−0.353140	−	0.170063i
$771$	−1.66179	−	0.512594i	−0.0598479	−	0.0184606i
$772$	−2.91048	+	12.7516i	−0.104750	+	0.458941i
$773$	9.54292			0.343235			0.171617	−	0.985164i	$-0.445101\pi$
$773$	9.54292			0.343235			0.171617	+	0.985164i	$0.445101\pi$
$774$	−10.1319	+	14.8507i	−0.364184	+	0.533796i
$775$	3.07933			0.110613
$776$	−3.44780	+	15.1058i	−0.123769	+	0.542267i
$777$	13.6203	+	4.20132i	0.488627	+	0.150722i
$778$	18.4232	+	8.87215i	0.660504	+	0.318082i
$779$	3.61057	+	9.19959i	0.129362	+	0.329609i
$780$	−0.598610	+	1.03682i	−0.0214337	+	0.0371242i
$781$	−5.95218	−	10.3095i	−0.212986	−	0.368902i
$782$	−3.99308	+	5.00717i	−0.142792	+	0.179056i
$783$	−20.7989	−	14.1804i	−0.743290	−	0.506767i
$784$	−13.8271	+	2.08410i	−0.493825	+	0.0744321i
$785$	0.771897	−	0.371726i	0.0275502	−	0.0132675i
$786$	0.813343	+	0.754672i	0.0290110	+	0.0269183i
$787$	31.6079	+	4.76412i	1.12670	+	0.169823i	0.685839	−	0.727753i	$-0.259435\pi$
$787$	31.6079	+	4.76412i	1.12670	+	0.169823i	0.440860	+	0.897576i	$0.354674\pi$
$788$	−8.61661	+	2.65787i	−0.306954	+	0.0946828i
$789$	−0.488026	−	6.51226i	−0.0173742	−	0.231842i
$790$	9.27767	+	11.6338i	0.330085	+	0.413913i
$791$	−22.3857	+	57.0379i	−0.795945	+	2.02804i
$792$	4.77178	−	4.42756i	0.169558	−	0.157327i
$793$	−14.1304	+	9.63392i	−0.501784	+	0.342111i
$794$	−2.18603	+	29.1705i	−0.0775792	+	1.03522i
$795$	−1.18913	−	5.20993i	−0.0421742	−	0.184777i
$796$	0.713283	+	3.12510i	0.0252817	+	0.110766i
$797$	1.00893	−	13.4632i	0.0357380	−	0.476891i	−0.950407	−	0.311008i	$-0.899333\pi$
$797$	1.00893	−	13.4632i	0.0357380	−	0.476891i	0.986145	−	0.165883i	$-0.0530475\pi$
$798$	−1.94968	+	1.32927i	−0.0690178	+	0.0470555i
$799$	0.709447	−	0.658271i	0.0250984	−	0.0232879i
$800$	−0.365341	+	0.930874i	−0.0129168	+	0.0329114i
$801$	−2.21963	−	2.78333i	−0.0784267	−	0.0983440i
$802$	−1.72180	−	22.9758i	−0.0607989	−	0.811305i
$803$	−8.32889	+	2.56912i	−0.293920	+	0.0906624i
$804$	−4.90505	−	0.739317i	−0.172988	−	0.0260737i
$805$	−4.91488	−	4.56034i	−0.173227	−	0.160731i
$806$	6.53390	−	3.14656i	0.230147	−	0.110833i
$807$	13.9870	−	2.10820i	0.492366	−	0.0742122i
$808$	15.2487	+	10.3964i	0.536446	+	0.365743i
$809$	6.40959	−	8.03738i	0.225349	−	0.282579i	−0.656284	−	0.754514i	$-0.727873\pi$
$809$	6.40959	−	8.03738i	0.225349	−	0.282579i	0.881634	+	0.471935i	$0.156444\pi$
$810$	3.37047	+	5.83783i	0.118426	+	0.205121i
$811$	4.38655	−	7.59773i	0.154033	−	0.266792i	−0.778674	−	0.627429i	$-0.784107\pi$
$811$	4.38655	−	7.59773i	0.154033	−	0.266792i	0.932706	+	0.360637i	$0.117441\pi$
$812$	14.4334	+	36.7758i	0.506514	+	1.29058i
$813$	−11.1032	−	5.34700i	−0.389405	−	0.187528i
$814$	13.8876	+	4.28377i	0.486762	+	0.150146i
$815$	−4.24250	+	18.5876i	−0.148608	+	0.651095i
$816$	2.22436			0.0778682
$817$	4.52120	−	4.86960i	0.158177	−	0.170366i
$818$	7.78542			0.272211
$819$	6.58132	−	28.8347i	0.229970	−	1.00756i
$820$	9.31943	+	2.87466i	0.325449	+	0.100388i
$821$	20.0971	+	9.67824i	0.701393	+	0.337773i	0.750362	−	0.661027i	$-0.229879\pi$
$821$	20.0971	+	9.67824i	0.701393	+	0.337773i	−0.0489691	+	0.998800i	$0.515594\pi$
$822$	−1.63715	−	4.17138i	−0.0571021	−	0.145494i
$823$	1.81886	−	3.15036i	0.0634014	−	0.109815i	−0.832582	−	0.553901i	$-0.813138\pi$
$823$	1.81886	−	3.15036i	0.0634014	−	0.109815i	0.895984	+	0.444087i	$0.146472\pi$
$824$	4.46737	+	7.73771i	0.155628	+	0.269556i
$825$	−0.752563	+	0.943684i	−0.0262009	+	0.0328549i
$826$	−18.9157	−	12.8965i	−0.658160	−	0.448726i
$827$	32.8947	−	4.95808i	1.14386	−	0.172409i	0.450348	−	0.892853i	$-0.351300\pi$
$827$	32.8947	−	4.95808i	1.14386	−	0.172409i	0.693514	+	0.720443i	$0.256062\pi$
$828$	3.61536	−	1.74107i	0.125642	−	0.0605062i
$829$	19.0831	+	17.7065i	0.662784	+	0.614974i	0.938094	−	0.346382i	$-0.112590\pi$
$829$	19.0831	+	17.7065i	0.662784	+	0.614974i	−0.275309	+	0.961356i	$0.588780\pi$
$830$	10.9199	+	1.64591i	0.379036	+	0.0571304i
$831$	−7.27969	+	2.24549i	−0.252530	+	0.0778951i
$832$	0.175995	+	2.34850i	0.00610154	+	0.0814194i
$833$	38.1483	+	47.8365i	1.32176	+	1.65744i
$834$	3.57822	−	9.11717i	0.123904	−	0.315702i
$835$	5.63931	−	5.23251i	0.195156	−	0.181079i
$836$	−1.98794	+	1.35535i	−0.0687543	+	0.0468759i
$837$	−0.671663	+	8.96272i	−0.0232161	+	0.309797i
$838$	0.211456	+	0.926448i	0.00730462	+	0.0320036i
$839$	4.47197	+	19.5930i	0.154390	+	0.676425i	0.991578	+	0.129511i	$0.0413406\pi$
$839$	4.47197	+	19.5930i	0.154390	+	0.676425i	−0.837188	+	0.546915i	$0.815802\pi$
$840$	−0.174021	+	2.32214i	−0.00600428	+	0.0801215i
$841$	37.4966	−	25.5647i	1.29299	−	0.881542i
$842$	9.41189	−	8.73296i	0.324355	−	0.300958i
$843$	3.25046	−	8.28203i	0.111952	−	0.285248i
$844$	1.92024	+	2.40790i	0.0660972	+	0.0828833i
$845$	−0.557008	−	7.43275i	−0.0191617	−	0.255695i
$846$	−0.579445	+	0.178735i	−0.0199217	+	0.00614504i
$847$	24.2897	+	3.66108i	0.834603	+	0.125796i
$848$	−7.70594	−	7.15007i	−0.264623	−	0.245534i
$849$	3.30616	−	1.59216i	0.113467	−	0.0546428i
$850$	4.32672	−	0.652149i	0.148405	−	0.0223685i
$851$	7.40230	+	5.04681i	0.253748	+	0.173002i
$852$	−1.58913	+	1.99270i	−0.0544426	+	0.0682689i
$853$	14.9262	+	25.8530i	0.511064	+	0.885189i	0.999918	+	0.0128231i	$0.00408183\pi$
$853$	14.9262	+	25.8530i	0.511064	+	0.885189i	−0.488854	+	0.872366i	$0.662585\pi$
$854$	−16.6322	+	28.8078i	−0.569141	+	0.985781i
$855$	−1.01496	−	2.58608i	−0.0347110	−	0.0884422i
$856$	6.74860	+	3.24995i	0.230662	+	0.111081i
$857$	−12.6490	−	3.90169i	−0.432080	−	0.133279i	0.0710831	−	0.997470i	$-0.477354\pi$
$857$	−12.6490	−	3.90169i	−0.432080	−	0.133279i	−0.503163	+	0.864191i	$0.667831\pi$
$858$	−0.632543	+	2.77135i	−0.0215947	+	0.0946124i
$859$	−16.5515			−0.564728			−0.282364	−	0.959307i	$-0.591119\pi$
$859$	−16.5515			−0.564728			−0.282364	+	0.959307i	$0.591119\pi$
$860$	−0.975277	−	6.48451i	−0.0332567	−	0.221120i
$861$	22.7107			0.773978
$862$	6.18939	−	27.1175i	0.210811	−	0.923625i
$863$	45.7883	+	14.1238i	1.55865	+	0.480781i	0.949893	−	0.312574i	$-0.101191\pi$
$863$	45.7883	+	14.1238i	1.55865	+	0.480781i	0.608760	+	0.793355i	$0.291667\pi$
$864$	−2.62972	−	1.26640i	−0.0894648	−	0.0430840i
$865$	−3.39318	−	8.64568i	−0.115372	−	0.293962i
$866$	15.4212	−	26.7102i	0.524033	−	0.907651i
$867$	−0.545422	−	0.944699i	−0.0185235	−	0.0320837i
$868$	8.79473	−	11.0282i	0.298513	−	0.374323i
$869$	29.1918	+	19.9026i	0.990263	+	0.675150i
$870$	4.33536	−	0.653450i	0.146982	−	0.0221540i
$871$	−20.7047	+	9.97086i	−0.701552	+	0.337850i
$872$	−7.17271	−	6.65530i	−0.242899	−	0.225377i
$873$	−42.0042	−	6.33112i	−1.42163	−	0.214276i
$874$	−1.41729	+	0.437175i	−0.0479404	+	0.0147877i
$875$	0.342320	+	4.56794i	0.0115725	+	0.154425i
$876$	1.16353	+	1.45901i	0.0393119	+	0.0492955i
$877$	−13.6435	+	34.7630i	−0.460707	+	1.17386i	0.492168	+	0.870500i	$0.336204\pi$
$877$	−13.6435	+	34.7630i	−0.460707	+	1.17386i	−0.952875	+	0.303362i	$0.901891\pi$
$878$	−0.934654	+	0.867232i	−0.0315430	+	0.0292677i
$879$	−7.84017	+	5.34534i	−0.264442	+	0.180294i
$880$	−0.177436	+	2.36771i	−0.00598135	+	0.0798156i
$881$	6.99198	+	30.6339i	0.235566	+	1.03208i	0.944939	+	0.327248i	$0.106121\pi$
$881$	6.99198	+	30.6339i	0.235566	+	1.03208i	−0.709373	+	0.704834i	$0.751022\pi$
$882$	−8.53061	−	37.3750i	−0.287240	−	1.25848i
$883$	−2.19528	+	29.2939i	−0.0738770	+	0.985820i	0.829927	+	0.557872i	$0.188382\pi$
$883$	−2.19528	+	29.2939i	−0.0738770	+	0.985820i	−0.903804	+	0.427947i	$0.859237\pi$
$884$	8.51429	−	5.80494i	0.286367	−	0.195241i
$885$	−1.86244	+	1.72809i	−0.0626052	+	0.0580892i
$886$	−13.0662	+	33.2921i	−0.438967	+	1.11847i
$887$	−28.1643	−	35.3169i	−0.945664	−	1.18583i	−0.982455	−	0.186502i	$-0.940285\pi$
$887$	−28.1643	−	35.3169i	−0.945664	−	1.18583i	0.0367903	−	0.999323i	$-0.488287\pi$
$888$	−0.232532	−	3.10293i	−0.00780327	−	0.104127i
$889$	−5.36582	+	1.65514i	−0.179964	+	0.0555115i
$890$	1.28402	+	0.193535i	0.0430406	+	0.00648732i
$891$	11.7328	+	10.8864i	0.393063	+	0.364709i
$892$	−10.1118	+	4.86961i	−0.338570	+	0.163047i
$893$	0.221627	−	0.0334049i	0.00741646	−	0.00111785i
$894$	4.69510	+	3.20107i	0.157028	+	0.107060i
$895$	−7.17742	+	9.00020i	−0.239915	+	0.300843i
$896$	2.29038	+	3.96705i	0.0765161	+	0.132530i
$897$	−0.876165	+	1.51756i	−0.0292543	+	0.0506699i
$898$	−12.0839	−	30.7893i	−0.403245	−	1.02745i
$899$	−23.9277	−	11.5230i	−0.798034	−	0.384313i
$900$	−2.61977	−	0.808093i	−0.0873258	−	0.0269364i
$901$	−10.2353	+	44.8436i	−0.340986	+	1.49396i
$902$	23.1564			0.771023
$903$	−6.62104	−	13.7599i	−0.220334	−	0.457901i
$904$	13.3763			0.444890
$905$	3.72243	−	16.3090i	0.123738	−	0.542130i
$906$	8.75685	+	2.70113i	0.290927	+	0.0897391i
$907$	−38.1633	−	18.3785i	−1.26719	−	0.610248i	−0.325125	−	0.945671i	$-0.605407\pi$
$907$	−38.1633	−	18.3785i	−1.26719	−	0.610248i	−0.942068	+	0.335423i	$0.891121\pi$
$908$	4.37290	+	11.1420i	0.145120	+	0.369760i
$909$	−25.2986	+	43.8184i	−0.839101	+	1.45337i
$910$	5.39402	+	9.34271i	0.178810	+	0.309708i
$911$	5.36895	−	6.73245i	0.177881	−	0.223056i	−0.684895	−	0.728642i	$-0.740152\pi$
$911$	5.36895	−	6.73245i	0.177881	−	0.223056i	0.862777	+	0.505585i	$0.168723\pi$
$912$	0.425624	+	0.290185i	0.0140938	+	0.00960900i
$913$	25.9277	−	3.90798i	0.858083	−	0.129335i
$914$	19.1333	−	9.21411i	0.632873	−	0.304776i
$915$	2.70611	+	2.51090i	0.0894612	+	0.0830078i
$916$	10.1211	+	1.52551i	0.334410	+	0.0504042i
$917$	9.55369	−	2.94692i	0.315491	−	0.0973160i
$918$	0.954403	+	12.7356i	0.0315000	+	0.420338i
$919$	−1.39398	−	1.74800i	−0.0459832	−	0.0576611i	0.758308	−	0.651896i	$-0.226026\pi$
$919$	−1.39398	−	1.74800i	−0.0459832	−	0.0576611i	−0.804291	+	0.594235i	$0.797455\pi$
$920$	−0.534737	+	1.36249i	−0.0176298	+	0.0449199i
$921$	−7.32174	+	6.79358i	−0.241260	+	0.223856i
$922$	0.825477	−	0.562800i	0.0271856	−	0.0185348i
$923$	−0.882393	+	11.7747i	−0.0290443	+	0.387570i
$924$	1.23033	+	5.39042i	0.0404748	+	0.177332i
$925$	−1.36204	−	5.96750i	−0.0447837	−	0.196210i
$926$	−2.18229	+	29.1207i	−0.0717145	+	0.956964i
$927$	−20.2389	+	13.7987i	−0.664733	+	0.453207i
$928$	6.32222	−	5.86616i	0.207537	−	0.192566i
$929$	−17.0267	+	43.3833i	−0.558628	+	1.42336i	0.320717	+	0.947175i	$0.396076\pi$
$929$	−17.0267	+	43.3833i	−0.558628	+	1.42336i	−0.879345	+	0.476185i	$0.842019\pi$
$930$	−0.976010	−	1.22388i	−0.0320046	−	0.0401325i
$931$	1.05890	+	14.1301i	0.0347042	+	0.463095i
$932$	22.7372	−	7.01351i	0.744783	−	0.229735i
$933$	10.2873	+	1.55056i	0.336791	+	0.0507631i
$934$	−18.3905	−	17.0639i	−0.601756	−	0.558348i
$935$	9.36035	−	4.50771i	0.306116	−	0.147418i
$936$	−6.38451	+	0.962310i	−0.208684	+	0.0314541i
$937$	−25.5103	−	17.3926i	−0.833384	−	0.568192i	0.0697428	−	0.997565i	$-0.477782\pi$
$937$	−25.5103	−	17.3926i	−0.833384	−	0.568192i	−0.903127	+	0.429373i	$0.858735\pi$
$938$	−27.8689	+	34.9465i	−0.909951	+	1.14104i
$939$	4.40900	+	7.63661i	0.143882	+	0.249211i
$940$	0.110591	−	0.191549i	0.00360707	−	0.00624763i
$941$	2.06943	+	5.27283i	0.0674616	+	0.171889i	0.960629	−	0.277836i	$-0.0896172\pi$
$941$	2.06943	+	5.27283i	0.0674616	+	0.171889i	−0.893167	+	0.449725i	$0.851522\pi$
$942$	−0.392399	−	0.188969i	−0.0127850	−	0.00615695i
$943$	13.6405	+	4.20754i	0.444197	+	0.137017i
$944$	−1.11212	+	4.87250i	−0.0361963	+	0.158586i
$945$	−13.3701			−0.434931
$946$	−6.75098	−	14.0299i	−0.219493	−	0.456153i
$947$	49.9999			1.62478			0.812389	−	0.583116i	$-0.198167\pi$
$947$	49.9999			1.62478			0.812389	+	0.583116i	$0.198167\pi$
$948$	1.68325	−	7.37480i	0.0546694	−	0.239522i
$949$	8.26129	+	2.54827i	0.268173	+	0.0827203i
$950$	0.912981	+	0.439668i	0.0296210	+	0.0142647i
$951$	4.55202	+	11.5984i	0.147609	+	0.376102i
$952$	10.0218	−	17.3582i	0.324807	−	0.562582i
$953$	6.15936	+	10.6683i	0.199521	+	0.345581i	0.948373	−	0.317156i	$-0.102728\pi$
$953$	6.15936	+	10.6683i	0.199521	+	0.345581i	−0.748852	+	0.662737i	$0.769395\pi$
$954$	17.9689	−	22.5322i	0.581763	−	0.729508i
$955$	−3.35306	−	2.28608i	−0.108502	−	0.0739757i
$956$	−1.76991	+	0.266771i	−0.0572431	+	0.00862800i
$957$	9.37903	−	4.51670i	0.303181	−	0.146004i
$958$	−29.8347	−	27.6826i	−0.963917	−	0.894384i
$959$	−39.9282	−	6.01821i	−1.28935	−	0.194338i
$960$	0.485771	−	0.149841i	0.0156782	−	0.00483609i
$961$	−1.60802	−	21.4575i	−0.0518716	−	0.692179i
$962$	−8.98783	−	11.2704i	−0.289779	−	0.363372i
$963$	−7.50243	+	19.1159i	−0.241763	+	0.616001i
$964$	−4.03082	+	3.74006i	−0.129824	+	0.120459i
$965$	10.8068	−	7.36798i	0.347885	−	0.237184i
$966$	−0.254708	+	3.39884i	−0.00819509	+	0.109356i
$967$	2.53807	+	11.1200i	0.0816189	+	0.357596i	0.999202	−	0.0399489i	$-0.0127195\pi$
$967$	2.53807	+	11.1200i	0.0816189	+	0.357596i	−0.917583	+	0.397545i	$0.869862\pi$
$968$	−1.19326	−	5.22800i	−0.0383527	−	0.168034i
$969$	0.168443	−	2.24771i	0.00541117	−	0.0722070i
$970$	12.8020	−	8.72824i	0.411047	−	0.280247i
$971$	−23.4731	+	21.7799i	−0.753288	+	0.698949i	−0.960170	−	0.279417i	$-0.909859\pi$
$971$	−23.4731	+	21.7799i	−0.753288	+	0.698949i	0.206882	+	0.978366i	$0.433668\pi$
$972$	4.45099	−	11.3409i	0.142765	−	0.363760i
$973$	−55.0259	−	69.0003i	−1.76405	−	2.21205i
$974$	−0.435576	−	5.81235i	−0.0139567	−	0.186240i
$975$	1.14403	−	0.352887i	0.0366383	−	0.0113014i
$976$	7.18066	+	1.08231i	0.229847	+	0.0346439i
$977$	21.4449	+	19.8980i	0.686084	+	0.636593i	0.944143	−	0.329536i	$-0.106892\pi$
$977$	21.4449	+	19.8980i	0.686084	+	0.636593i	−0.258059	+	0.966129i	$0.583083\pi$
$978$	8.73230	−	4.20526i	0.279228	−	0.134469i
$979$	3.04872	−	0.459521i	0.0974377	−	0.0146864i
$980$	11.5535	+	7.87706i	0.369064	+	0.251623i
$981$	16.7254	−	20.9730i	0.534002	−	0.669618i
$982$	19.6623	+	34.0562i	0.627451	+	1.08678i
$983$	−19.9033	+	34.4734i	−0.634815	+	1.09953i	0.351739	+	0.936098i	$0.385590\pi$
$983$	−19.9033	+	34.4734i	−0.634815	+	1.09953i	−0.986554	+	0.163434i	$0.947743\pi$
$984$	−1.81131	−	4.61514i	−0.0577424	−	0.147125i
$985$	8.12424	+	3.91243i	0.258860	+	0.124660i
$986$	−36.0608	−	11.1233i	−1.14841	−	0.354238i
$987$	0.114610	−	0.502141i	0.00364809	−	0.0159833i
$988$	2.38648			0.0759240
$989$	−1.42748	−	9.49115i	−0.0453912	−	0.301801i
$990$	−6.50946			−0.206884
$991$	−4.62664	+	20.2706i	−0.146970	+	0.643917i	0.846747	+	0.531996i	$0.178558\pi$
$991$	−4.62664	+	20.2706i	−0.146970	+	0.643917i	−0.993717	+	0.111922i	$0.964299\pi$
$992$	−2.94253	−	0.907649i	−0.0934253	−	0.0288179i
$993$	3.71144	+	1.78734i	0.117779	+	0.0567194i
$994$	8.39066	+	21.3791i	0.266136	+	0.678102i
$995$	1.60273	−	2.77601i	0.0508101	−	0.0880056i
$996$	−2.80695	−	4.86179i	−0.0889418	−	0.154052i
$997$	21.3524	−	26.7751i	0.676238	−	0.847975i	−0.318764	−	0.947834i	$-0.603268\pi$
$997$	21.3524	−	26.7751i	0.676238	−	0.847975i	0.995002	+	0.0998588i	$0.0318391\pi$
$998$	−8.46836	−	5.77363i	−0.268061	−	0.182761i
$999$	17.6661	−	2.66274i	0.558931	−	0.0842453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.81.3	✓	48
43.17	even	21	inner	430.2.q.c.361.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.81.3	✓	48	1.1	even	1	trivial
430.2.q.c.361.3	yes	48	43.17	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(0.485771 + 0.149841i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(0.254178 - 0.440249i) q^{6} +(-2.29038 - 3.96705i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-2.26519 - 1.54438i) q^{9} +O(q^{10})\)	\(q+(0.222521 - 0.974928i) q^{2} +(0.485771 + 0.149841i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(0.254178 - 0.440249i) q^{6} +(-2.29038 - 3.96705i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-2.26519 - 1.54438i) q^{9} +(0.988831 - 0.149042i) q^{10} +(2.13922 - 1.03019i) q^{11} +(-0.372652 - 0.345770i) q^{12} +(-2.32878 - 0.351007i) q^{13} +(-4.37724 + 1.35020i) q^{14} +(0.0379895 + 0.506935i) q^{15} +(0.623490 + 0.781831i) q^{16} +(1.59858 - 4.07313i) q^{17} +(-2.00972 + 1.86474i) q^{18} +(0.837255 - 0.570830i) q^{19} +(0.0747301 - 0.997204i) q^{20} +(-0.518174 - 2.27027i) q^{21} +(-0.528343 - 2.31482i) q^{22} +(0.109380 - 1.45957i) q^{23} +(-0.420024 + 0.286367i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-0.860407 + 2.19228i) q^{26} +(-1.81982 - 2.28198i) q^{27} +(0.342320 + 4.56794i) q^{28} +(8.24135 - 2.54212i) q^{29} +(0.502678 + 0.0757666i) q^{30} +(-2.25731 - 2.09448i) q^{31} +(0.900969 - 0.433884i) q^{32} +(1.19354 - 0.179897i) q^{33} +(-3.61529 - 2.46486i) q^{34} +(2.85605 - 3.58138i) q^{35} +(1.37079 + 2.37427i) q^{36} +(-3.06048 + 5.30091i) q^{37} +(-0.370212 - 0.943285i) q^{38} +(-1.07866 - 0.519454i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(-2.17018 + 9.50819i) q^{41} -2.32865 q^{42} +(6.39349 - 1.45714i) q^{43} -2.37435 q^{44} +(0.610058 - 2.67284i) q^{45} +(-1.39864 - 0.431423i) q^{46} +(0.199277 + 0.0959670i) q^{47} +(0.185723 + 0.473216i) q^{48} +(-6.99164 + 12.1099i) q^{49} +(0.500000 + 0.866025i) q^{50} +(1.38687 - 1.73908i) q^{51} +(1.94586 + 1.32666i) q^{52} +(-10.3947 + 1.56675i) q^{53} +(-2.62972 + 1.26640i) q^{54} +(1.74052 + 1.61497i) q^{55} +(4.52959 + 0.682725i) q^{56} +(0.492248 - 0.151838i) q^{57} +(-0.644511 - 8.60040i) q^{58} +(3.11608 + 3.90744i) q^{59} +(0.185723 - 0.473216i) q^{60} +(5.32325 - 4.93925i) q^{61} +(-2.54426 + 1.73465i) q^{62} +(-0.938495 + 12.5234i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.524055 - 2.29603i) q^{65} +(0.0902005 - 1.20364i) q^{66} +(8.06230 - 5.49678i) q^{67} +(-3.20754 + 2.97616i) q^{68} +(0.271837 - 0.692629i) q^{69} +(-2.85605 - 3.58138i) q^{70} +(-0.374677 - 4.99971i) q^{71} +(2.61977 - 0.808093i) q^{72} +(-3.62995 - 0.547126i) q^{73} +(4.48698 + 4.16331i) q^{74} +(-0.458013 + 0.220568i) q^{75} +(-1.00201 + 0.151029i) q^{76} +(-8.98644 - 6.12685i) q^{77} +(-0.746454 + 0.936024i) q^{78} +(7.44011 + 12.8866i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(2.46275 + 6.27497i) q^{81} +(8.78689 + 4.23154i) q^{82} +(10.5526 + 3.25506i) q^{83} +(-0.518174 + 2.27027i) q^{84} +4.37559 q^{85} +(0.00208142 - 6.55744i) q^{86} +4.38433 q^{87} +(-0.528343 + 2.31482i) q^{88} +(1.24084 + 0.382747i) q^{89} +(-2.47007 - 1.18952i) q^{90} +(3.94131 + 10.0423i) q^{91} +(-0.731833 + 1.26757i) q^{92} +(-0.782699 - 1.35567i) q^{93} +(0.137904 - 0.172926i) q^{94} +(0.837255 + 0.570830i) q^{95} +(0.502678 - 0.0757666i) q^{96} +(13.9599 - 6.72271i) q^{97} +(10.2505 + 9.51104i) q^{98} +(-6.43676 - 0.970185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

L-functions

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