LMFDB - Embedded newform 690.2.x.a.77.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.14
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(0.114573 - 1.72826i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(2.16257 - 0.568575i) q^{5} +(-1.45220 + 0.943986i) q^{6} +(0.773495 + 3.55570i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-2.97375 - 0.396023i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(0.114573 - 1.72826i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(2.16257 - 0.568575i) q^{5} +(-1.45220 + 0.943986i) q^{6} +(0.773495 + 3.55570i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-2.97375 - 0.396023i) q^{9} +(-1.75115 - 1.39049i) q^{10} +(0.333413 - 0.0479375i) q^{11} +(1.62597 + 0.596838i) q^{12} +(0.181512 - 0.834395i) q^{13} +(2.38294 - 2.75006i) q^{14} +(-0.734872 - 3.80263i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(3.10909 - 5.69387i) q^{17} +(1.46507 + 2.61793i) q^{18} +(0.569440 - 1.93934i) q^{19} +(-0.0637232 + 2.23516i) q^{20} +(6.23378 - 0.929411i) q^{21} +(-0.238183 - 0.238183i) q^{22} +(4.02180 + 2.61249i) q^{23} +(-0.496615 - 1.65933i) q^{24} +(4.35344 - 2.45917i) q^{25} +(-0.776743 + 0.354727i) q^{26} +(-1.02514 + 5.09402i) q^{27} +(-3.62959 - 0.259593i) q^{28} +(2.66785 - 0.783351i) q^{29} +(-2.60377 + 2.86712i) q^{30} +(3.91382 - 8.57008i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-0.0446483 - 0.581715i) q^{33} +(-6.42139 + 0.923256i) q^{34} +(3.69442 + 7.24967i) q^{35} +(1.21778 - 2.74172i) q^{36} +(-4.52001 + 0.323278i) q^{37} +(-1.89377 + 0.706340i) q^{38} +(-1.42125 - 0.409298i) q^{39} +(1.82753 - 1.28847i) q^{40} +(-1.70928 + 1.48110i) q^{41} +(-4.47980 - 4.43342i) q^{42} +(2.03119 + 0.757595i) q^{43} +(-0.0479375 + 0.333413i) q^{44} +(-6.65611 + 0.834370i) q^{45} +(-0.318773 - 4.78523i) q^{46} +(-2.51304 + 2.51304i) q^{47} +(-1.03075 + 1.39196i) q^{48} +(-5.67727 + 2.59272i) q^{49} +(-4.57759 - 2.01139i) q^{50} +(-9.48426 - 6.02567i) q^{51} +(0.749459 + 0.409235i) q^{52} +(-1.30411 - 5.99490i) q^{53} +(4.69232 - 2.23207i) q^{54} +(0.693773 - 0.293239i) q^{55} +(1.96731 + 3.06120i) q^{56} +(-3.28643 - 1.20633i) q^{57} +(-2.22589 - 1.66628i) q^{58} +(11.9246 - 7.66349i) q^{59} +(3.85563 + 0.366219i) q^{60} +(-2.89985 + 6.34979i) q^{61} +(-9.20617 + 2.00268i) q^{62} +(-0.892039 - 10.8801i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-0.0818845 - 1.90764i) q^{65} +(-0.438930 + 0.384352i) q^{66} +(-11.7648 + 8.80705i) q^{67} +(4.58730 + 4.58730i) q^{68} +(4.97584 - 6.65139i) q^{69} +(3.58967 - 7.30210i) q^{70} +(5.21223 + 0.749406i) q^{71} +(-2.92465 + 0.668164i) q^{72} +(-5.62775 + 3.07298i) q^{73} +(2.96754 + 3.42472i) q^{74} +(-3.75129 - 7.80563i) q^{75} +(1.70035 + 1.09275i) q^{76} +(0.428344 + 1.14844i) q^{77} +(0.524065 + 1.38305i) q^{78} +(2.03108 + 3.16043i) q^{79} +(-2.12667 - 0.690859i) q^{80} +(8.68633 + 2.35534i) q^{81} +(2.21001 + 0.480758i) q^{82} +(-8.72715 + 0.624178i) q^{83} +(-0.864496 + 6.24312i) q^{84} +(3.48624 - 14.0812i) q^{85} +(-0.610761 - 2.08006i) q^{86} +(-1.04817 - 4.70048i) q^{87} +(0.295638 - 0.161431i) q^{88} +(-2.49752 - 5.46881i) q^{89} +(4.65681 + 4.82847i) q^{90} +3.10725 q^{91} +(-3.63974 + 3.12287i) q^{92} +(-14.3629 - 7.74599i) q^{93} +(3.51780 + 0.505784i) q^{94} +(0.128798 - 4.51772i) q^{95} +(1.73203 - 0.00901144i) q^{96} +(-0.625347 + 8.74349i) q^{97} +(5.47784 + 2.99113i) q^{98} +(-1.01047 + 0.0105149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	0.114573	−	1.72826i	0.0661487	−	0.997810i
$3$	0.114573	−	1.72826i	0.0661487	−	0.997810i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	2.16257	−	0.568575i	0.967132	−	0.254275i
$5$	2.16257	−	0.568575i	0.967132	−	0.254275i
$6$	−1.45220	+	0.943986i	−0.592859	+	0.385381i
$7$	0.773495	+	3.55570i	0.292354	+	1.34393i	0.855600	+	0.517638i	$0.173189\pi$
$7$	0.773495	+	3.55570i	0.292354	+	1.34393i	−0.563246	+	0.826289i	$0.690448\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	−2.97375	−	0.396023i	−0.991249	−	0.132008i
$10$	−1.75115	−	1.39049i	−0.553762	−	0.439713i
$11$	0.333413	−	0.0479375i	0.100528	−	0.0144537i	−0.0918674	−	0.995771i	$-0.529284\pi$
$11$	0.333413	−	0.0479375i	0.100528	−	0.0144537i	0.192395	+	0.981318i	$0.438374\pi$
$12$	1.62597	+	0.596838i	0.469378	+	0.172292i
$13$	0.181512	−	0.834395i	0.0503422	−	0.231420i	−0.945101	−	0.326779i	$-0.894037\pi$
$13$	0.181512	−	0.834395i	0.0503422	−	0.231420i	0.995443	+	0.0953599i	$0.0304002\pi$
$14$	2.38294	−	2.75006i	0.636869	−	0.734986i
$15$	−0.734872	−	3.80263i	−0.189743	−	0.981834i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	3.10909	−	5.69387i	0.754065	−	1.38097i	−0.164773	−	0.986332i	$-0.552689\pi$
$17$	3.10909	−	5.69387i	0.754065	−	1.38097i	0.918838	−	0.394635i	$-0.129129\pi$
$18$	1.46507	+	2.61793i	0.345320	+	0.617053i
$19$	0.569440	−	1.93934i	0.130639	−	0.444914i	−0.868029	−	0.496513i	$-0.834614\pi$
$19$	0.569440	−	1.93934i	0.130639	−	0.444914i	0.998668	+	0.0515988i	$0.0164317\pi$
$20$	−0.0637232	+	2.23516i	−0.0142490	+	0.499797i
$21$	6.23378	−	0.929411i	1.36032	−	0.202814i
$22$	−0.238183	−	0.238183i	−0.0507807	−	0.0507807i
$23$	4.02180	+	2.61249i	0.838604	+	0.544741i
$23$	4.02180	+	2.61249i	0.838604	+	0.544741i
$24$	−0.496615	−	1.65933i	−0.101371	−	0.338709i
$25$	4.35344	−	2.45917i	0.870689	−	0.491834i
$26$	−0.776743	+	0.354727i	−0.152332	+	0.0695677i
$27$	−1.02514	+	5.09402i	−0.197288	+	0.980345i
$28$	−3.62959	−	0.259593i	−0.685927	−	0.0490585i
$29$	2.66785	−	0.783351i	0.495407	−	0.145465i	−0.0244787	−	0.999700i	$-0.507793\pi$
$29$	2.66785	−	0.783351i	0.495407	−	0.145465i	0.519886	+	0.854236i	$0.325974\pi$
$30$	−2.60377	+	2.86712i	−0.475381	+	0.523463i
$31$	3.91382	−	8.57008i	0.702943	−	1.53923i	−0.133422	−	0.991059i	$-0.542597\pi$
$31$	3.91382	−	8.57008i	0.702943	−	1.53923i	0.836366	−	0.548172i	$-0.184676\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	−0.0446483	−	0.581715i	−0.00777227	−	0.101264i
$34$	−6.42139	+	0.923256i	−1.10126	+	0.158337i
$35$	3.69442	+	7.24967i	0.624471	+	1.22542i
$36$	1.21778	−	2.74172i	0.202964	−	0.456953i
$37$	−4.52001	+	0.323278i	−0.743085	+	0.0531465i	−0.437748	−	0.899098i	$-0.644224\pi$
$37$	−4.52001	+	0.323278i	−0.743085	+	0.0531465i	−0.305337	+	0.952244i	$0.598769\pi$
$38$	−1.89377	+	0.706340i	−0.307210	+	0.114583i
$39$	−1.42125	−	0.409298i	−0.227583	−	0.0655401i
$40$	1.82753	−	1.28847i	0.288957	−	0.203725i
$41$	−1.70928	+	1.48110i	−0.266944	+	0.231308i	−0.778039	−	0.628216i	$-0.783785\pi$
$41$	−1.70928	+	1.48110i	−0.266944	+	0.231308i	0.511095	+	0.859524i	$0.329240\pi$
$42$	−4.47980	−	4.43342i	−0.691248	−	0.684092i
$43$	2.03119	+	0.757595i	0.309754	+	0.115532i	0.499534	−	0.866295i	$-0.333505\pi$
$43$	2.03119	+	0.757595i	0.309754	+	0.115532i	−0.189780	+	0.981827i	$0.560777\pi$
$44$	−0.0479375	+	0.333413i	−0.00722685	+	0.0502639i
$45$	−6.65611	+	0.834370i	−0.992235	+	0.124381i
$46$	−0.318773	−	4.78523i	−0.0470005	−	0.705543i
$47$	−2.51304	+	2.51304i	−0.366565	+	0.366565i	−0.866223	−	0.499658i	$-0.833459\pi$
$47$	−2.51304	+	2.51304i	−0.366565	+	0.366565i	0.499658	+	0.866223i	$0.333459\pi$
$48$	−1.03075	+	1.39196i	−0.148776	+	0.200912i
$49$	−5.67727	+	2.59272i	−0.811038	+	0.370389i
$50$	−4.57759	−	2.01139i	−0.647369	−	0.284453i
$51$	−9.48426	−	6.02567i	−1.32806	−	0.843762i
$52$	0.749459	+	0.409235i	0.103931	+	0.0567507i
$53$	−1.30411	−	5.99490i	−0.179133	−	0.823463i	−0.975734	−	0.218958i	$-0.929734\pi$
$53$	−1.30411	−	5.99490i	−0.179133	−	0.823463i	0.796601	−	0.604506i	$-0.206629\pi$
$54$	4.69232	−	2.23207i	0.638544	−	0.303746i
$55$	0.693773	−	0.293239i	0.0935484	−	0.0395403i
$56$	1.96731	+	3.06120i	0.262893	+	0.409070i
$57$	−3.28643	−	1.20633i	−0.435298	−	0.159783i
$58$	−2.22589	−	1.66628i	−0.292273	−	0.218793i
$59$	11.9246	−	7.66349i	1.55245	−	0.997702i	0.567804	−	0.823164i	$-0.307793\pi$
$59$	11.9246	−	7.66349i	1.55245	−	0.997702i	0.984650	−	0.174538i	$-0.0558431\pi$
$60$	3.85563	+	0.366219i	0.497760	+	0.0472787i
$61$	−2.89985	+	6.34979i	−0.371288	+	0.813008i	0.628103	+	0.778130i	$0.283832\pi$
$61$	−2.89985	+	6.34979i	−0.371288	+	0.813008i	−0.999392	+	0.0348779i	$0.988896\pi$
$62$	−9.20617	+	2.00268i	−1.16918	+	0.254340i
$63$	−0.892039	−	10.8801i	−0.112386	−	1.37076i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	−0.0818845	−	1.90764i	−0.0101565	−	0.236614i
$66$	−0.438930	+	0.384352i	−0.0540286	+	0.0473104i
$67$	−11.7648	+	8.80705i	−1.43730	+	1.07595i	−0.454615	+	0.890688i	$0.650223\pi$
$67$	−11.7648	+	8.80705i	−1.43730	+	1.07595i	−0.982689	+	0.185264i	$0.940686\pi$
$68$	4.58730	+	4.58730i	0.556292	+	0.556292i
$69$	4.97584	−	6.65139i	0.599021	−	0.800733i
$70$	3.58967	−	7.30210i	0.429048	−	0.872768i
$71$	5.21223	+	0.749406i	0.618578	+	0.0889381i	0.444478	−	0.895790i	$-0.353389\pi$
$71$	5.21223	+	0.749406i	0.618578	+	0.0889381i	0.174100	+	0.984728i	$0.444298\pi$
$72$	−2.92465	+	0.668164i	−0.344673	+	0.0787439i
$73$	−5.62775	+	3.07298i	−0.658678	+	0.359665i	−0.773568	−	0.633713i	$-0.781530\pi$
$73$	−5.62775	+	3.07298i	−0.658678	+	0.359665i	0.114891	+	0.993378i	$0.463348\pi$
$74$	2.96754	+	3.42472i	0.344969	+	0.398116i
$75$	−3.75129	−	7.80563i	−0.433162	−	0.901316i
$76$	1.70035	+	1.09275i	0.195043	+	0.125347i
$77$	0.428344	+	1.14844i	0.0488144	+	0.130876i
$78$	0.524065	+	1.38305i	0.0593387	+	0.156600i
$79$	2.03108	+	3.16043i	0.228515	+	0.355576i	0.936510	−	0.350642i	$-0.114036\pi$
$79$	2.03108	+	3.16043i	0.228515	+	0.355576i	−0.707995	+	0.706217i	$0.750400\pi$
$80$	−2.12667	−	0.690859i	−0.237769	−	0.0772404i
$81$	8.68633	+	2.35534i	0.965148	+	0.261705i
$82$	2.21001	+	0.480758i	0.244055	+	0.0530909i
$83$	−8.72715	+	0.624178i	−0.957929	+	0.0685125i	−0.541541	−	0.840674i	$-0.682159\pi$
$83$	−8.72715	+	0.624178i	−0.957929	+	0.0685125i	−0.416388	+	0.909187i	$0.636704\pi$
$84$	−0.864496	+	6.24312i	−0.0943242	+	0.681180i
$85$	3.48624	−	14.0812i	0.378136	−	1.52732i
$86$	−0.610761	−	2.08006i	−0.0658601	−	0.224299i
$87$	−1.04817	−	4.70048i	−0.112376	−	0.503945i
$88$	0.295638	−	0.161431i	0.0315152	−	0.0172086i
$89$	−2.49752	−	5.46881i	−0.264737	−	0.579693i	0.729849	−	0.683608i	$-0.239590\pi$
$89$	−2.49752	−	5.46881i	−0.264737	−	0.579693i	−0.994586	+	0.103915i	$0.966863\pi$
$90$	4.65681	+	4.82847i	0.490871	+	0.508966i
$91$	3.10725			0.325729
$92$	−3.63974	+	3.12287i	−0.379469	+	0.325582i
$93$	−14.3629	−	7.74599i	−1.48936	−	0.803222i
$94$	3.51780	+	0.505784i	0.362834	+	0.0521676i
$95$	0.128798	−	4.51772i	0.0132144	−	0.463509i
$96$	1.73203	−	0.00901144i	0.176774	−	0.000919726i
$97$	−0.625347	+	8.74349i	−0.0634943	+	0.887767i	0.861493	+	0.507769i	$0.169530\pi$
$97$	−0.625347	+	8.74349i	−0.0634943	+	0.887767i	−0.924988	+	0.379997i	$0.875925\pi$
$98$	5.47784	+	2.99113i	0.553346	+	0.302150i
$99$	−1.01047	+	0.0105149i	−0.101556	+	0.00105678i
$100$	1.13305	+	4.86993i	0.113305	+	0.486993i
$101$	−6.73141	−	5.83280i	−0.669800	−	0.580385i	0.252153	−	0.967687i	$-0.418861\pi$
$101$	−6.73141	−	5.83280i	−0.669800	−	0.580385i	−0.921953	+	0.387302i	$0.873407\pi$
$102$	0.859907	+	11.2036i	0.0851435	+	1.10932i
$103$	9.51996	+	7.12655i	0.938029	+	0.702200i	0.954671	−	0.297662i	$-0.0962067\pi$
$103$	9.51996	+	7.12655i	0.938029	+	0.702200i	−0.0166421	+	0.999862i	$0.505298\pi$
$104$	−0.121524	−	0.845218i	−0.0119164	−	0.0828804i
$105$	12.9526	−	5.55429i	1.26404	−	0.542044i
$106$	−4.01764	+	4.63661i	−0.390228	+	0.450347i
$107$	6.66441	+	17.8680i	0.644273	+	1.72736i	0.685358	+	0.728206i	$0.259646\pi$
$107$	6.66441	+	17.8680i	0.644273	+	1.72736i	−0.0410858	+	0.999156i	$0.513082\pi$
$108$	−4.59887	−	2.41877i	−0.442526	−	0.232746i
$109$	−1.09315	−	3.72294i	−0.104705	−	0.356593i	0.890429	−	0.455122i	$-0.150404\pi$
$109$	−1.09315	−	3.72294i	−0.104705	−	0.356593i	−0.995134	+	0.0985291i	$0.968586\pi$
$110$	−0.650512	−	0.379663i	−0.0620239	−	0.0361994i
$111$	0.0408359	+	7.84878i	0.00387597	+	0.744974i
$112$	1.27165	−	3.40943i	0.120160	−	0.322160i
$113$	−4.76365	+	3.56603i	−0.448127	+	0.335464i	−0.799389	−	0.600814i	$-0.794843\pi$
$113$	−4.76365	+	3.56603i	−0.448127	+	0.335464i	0.351262	+	0.936277i	$0.385753\pi$
$114$	1.00376	+	3.35385i	0.0940110	+	0.314117i
$115$	10.1828	+	3.36300i	0.949555	+	0.313601i
$116$			2.78048i			0.258161i
$117$	−0.870209	+	2.40940i	−0.0804508	+	0.222749i
$118$	−13.2811	−	4.95360i	−1.22262	−	0.456015i
$119$	22.6506	+	6.65080i	2.07637	+	0.609678i
$120$	−2.01742	−	3.30606i	−0.184164	−	0.301800i
$121$	−10.4456	+	3.06709i	−0.949596	+	0.278827i
$122$	6.82109	−	1.48384i	0.617552	−	0.134340i
$123$	2.36388	+	3.12376i	0.213144	+	0.281660i
$124$	7.12028	+	6.16975i	0.639420	+	0.554060i
$125$	8.01642	−	7.79340i	0.717010	−	0.697063i
$126$	−8.17536	+	7.23429i	−0.728319	+	0.644482i
$127$	−4.85196	+	6.48146i	−0.430542	+	0.575137i	−0.962379	−	0.271710i	$-0.912411\pi$
$127$	−4.85196	+	6.48146i	−0.430542	+	0.575137i	0.531837	+	0.846847i	$0.321502\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	1.54204	−	3.42362i	0.135769	−	0.301433i
$130$	−1.47808	+	1.20876i	−0.129636	+	0.106015i
$131$	5.21594	−	8.11616i	0.455719	−	0.709112i	−0.535028	−	0.844834i	$-0.679699\pi$
$131$	5.21594	−	8.11616i	0.455719	−	0.709112i	0.990747	+	0.135722i	$0.0433354\pi$
$132$	0.570731	+	0.121048i	0.0496757	+	0.0105359i
$133$	7.33615	+	0.524692i	0.636125	+	0.0454965i
$134$	14.1008	+	4.14037i	1.21812	+	0.357674i
$135$	0.679395	+	11.5991i	0.0584730	+	0.998289i
$136$	0.923256	−	6.42139i	0.0791686	−	0.550629i
$137$	−7.96084	+	7.96084i	−0.680141	+	0.680141i	−0.960032	−	0.279891i	$-0.909702\pi$
$137$	−7.96084	+	7.96084i	−0.680141	+	0.680141i	0.279891	+	0.960032i	$0.409702\pi$
$138$	−8.30662	+	0.00266478i	−0.707107	+	0.000226841i
$139$			10.2227i			0.867080i	0.901134	+	0.433540i	$0.142736\pi$
$139$			10.2227i			0.867080i	−0.901134	+	0.433540i	$0.857264\pi$
$140$	−7.99684	+	1.50230i	−0.675857	+	0.126968i
$141$	4.05526	+	4.63111i	0.341514	+	0.390010i
$142$	−2.52364	−	4.62171i	−0.211780	−	0.387845i
$143$	0.0205194	−	0.286899i	0.00171592	−	0.0239917i
$144$	2.28757	+	1.94088i	0.190631	+	0.161740i
$145$	5.32403	−	3.21093i	0.442136	−	0.266653i
$146$	5.83263	+	2.66367i	0.482712	+	0.220447i
$147$	3.83043	+	10.1088i	0.315928	+	0.833763i
$148$	0.963252	−	4.42800i	0.0791788	−	0.363979i
$149$	−1.91089	−	13.2905i	−0.156546	−	1.08880i	−0.904938	−	0.425544i	$-0.860083\pi$
$149$	−1.91089	−	13.2905i	−0.156546	−	1.08880i	0.748392	−	0.663257i	$-0.230826\pi$
$150$	−4.00066	+	7.68080i	−0.326652	+	0.627135i
$151$	−5.61328	+	3.60744i	−0.456803	+	0.293569i	−0.748735	−	0.662870i	$-0.769338\pi$
$151$	−5.61328	+	3.60744i	−0.456803	+	0.293569i	0.291932	+	0.956439i	$0.405702\pi$
$152$	−0.144191	−	2.01606i	−0.0116955	−	0.163524i
$153$	−11.5005	+	15.7009i	−0.929764	+	1.26934i
$154$	0.662673	−	1.03114i	0.0533997	−	0.0830915i
$155$	3.59119	−	20.7587i	0.288452	−	1.66738i
$156$	0.793132	−	1.24837i	0.0635013	−	0.0999496i
$157$	−0.981501	−	1.79749i	−0.0783323	−	0.143455i	0.835577	−	0.549373i	$-0.185134\pi$
$157$	−0.981501	−	1.79749i	−0.0783323	−	0.143455i	−0.913909	+	0.405918i	$0.866952\pi$
$158$	1.31287	−	3.51994i	0.104446	−	0.280031i
$159$	−10.5102	+	1.56699i	−0.833509	+	0.124270i
$160$	0.721403	+	2.11650i	0.0570319	+	0.167324i
$161$	−6.17837	+	16.3211i	−0.486924	+	1.28628i
$162$	−3.31997	−	8.36527i	−0.260842	−	0.657238i
$163$	−3.27075	−	4.36921i	−0.256185	−	0.342223i	0.653948	−	0.756540i	$-0.273112\pi$
$163$	−3.27075	−	4.36921i	−0.256185	−	0.342223i	−0.910133	+	0.414317i	$0.864021\pi$
$164$	−0.939543	−	2.05731i	−0.0733660	−	0.160649i
$165$	−0.427304	−	1.23262i	−0.0332656	−	0.0959590i
$166$	5.72967	+	6.61239i	0.444708	+	0.513221i
$167$	9.19655	−	16.8422i	0.711651	−	1.30329i	−0.232119	−	0.972687i	$-0.574566\pi$
$167$	9.19655	−	16.8422i	0.711651	−	1.30329i	0.943770	−	0.330603i	$-0.107252\pi$
$168$	5.51594	−	3.04929i	0.425564	−	0.235258i
$169$	11.1619	+	5.09749i	0.858611	+	0.392115i
$170$	−13.3618	+	5.64765i	−1.02480	+	0.433155i
$171$	−2.46139	+	5.54158i	−0.188227	+	0.423775i
$172$	−1.29916	+	1.73547i	−0.0990600	+	0.132329i
$173$	3.50003	−	4.67549i	0.266102	−	0.355471i	−0.647510	−	0.762057i	$-0.724190\pi$
$173$	3.50003	−	4.67549i	0.266102	−	0.355471i	0.913613	+	0.406586i	$0.133281\pi$
$174$	−3.13478	+	3.65600i	−0.237647	+	0.277160i
$175$	12.1114	+	13.5774i	0.915538	+	1.02635i
$176$	−0.306402	−	0.139929i	−0.0230959	−	0.0105475i
$177$	−11.8782	−	21.4869i	−0.892824	−	1.61505i
$178$	−2.88130	+	5.27671i	−0.215963	+	0.395506i
$179$	11.1123	+	12.8243i	0.830572	+	0.958531i	0.999633	−	0.0270744i	$-0.00861912\pi$
$179$	11.1123	+	12.8243i	0.830572	+	0.958531i	−0.169062	+	0.985605i	$0.554074\pi$
$180$	1.07467	−	6.62156i	0.0801013	−	0.493542i
$181$	−6.47314	−	14.1742i	−0.481145	−	1.05356i	−0.982147	−	0.188114i	$-0.939763\pi$
$181$	−6.47314	−	14.1742i	−0.481145	−	1.05356i	0.501002	−	0.865446i	$-0.332965\pi$
$182$	−1.86211	−	2.48749i	−0.138029	−	0.184385i
$183$	10.6418	+	5.73921i	0.786667	+	0.424254i
$184$	4.68120	+	1.04229i	0.345103	+	0.0768389i
$185$	−9.59105	+	3.26908i	−0.705148	+	0.240347i
$186$	2.40637	+	16.1401i	0.176443	+	1.18345i
$187$	0.763660	−	2.04745i	0.0558443	−	0.149724i
$188$	−1.70324	−	3.11925i	−0.124222	−	0.227495i
$189$	−18.9058	+	0.295111i	−1.37519	+	0.0214662i
$190$	−3.69381	+	2.60426i	−0.267977	+	0.188933i
$191$	−12.3894	+	19.2783i	−0.896464	+	1.39493i	0.0221434	+	0.999755i	$0.492951\pi$
$191$	−12.3894	+	19.2783i	−0.896464	+	1.39493i	−0.918608	+	0.395171i	$0.870685\pi$
$192$	−1.04518	−	1.38116i	−0.0754293	−	0.0996766i
$193$	1.10158	+	15.4021i	0.0792935	+	1.10867i	0.868878	+	0.495026i	$0.164842\pi$
$193$	1.10158	+	15.4021i	0.0792935	+	1.10867i	−0.789584	+	0.613642i	$0.789704\pi$
$194$	7.37428	−	4.73916i	0.529442	−	0.340252i
$195$	−3.30628	−	0.0770469i	−0.236768	−	0.00551744i
$196$	−0.888227	−	6.17775i	−0.0634448	−	0.441268i
$197$	−1.82006	+	8.36670i	−0.129674	+	0.596102i	0.865744	+	0.500487i	$0.166846\pi$
$197$	−1.82006	+	8.36670i	−0.129674	+	0.596102i	−0.995418	+	0.0956156i	$0.969518\pi$
$198$	0.613969	+	0.802621i	0.0436329	+	0.0570398i
$199$	18.6081	+	8.49803i	1.31909	+	0.602410i	0.945633	−	0.325237i	$-0.105444\pi$
$199$	18.6081	+	8.49803i	1.31909	+	0.602410i	0.373460	+	0.927646i	$0.378171\pi$
$200$	3.21957	−	3.82549i	0.227658	−	0.270503i
$201$	13.8729	+	21.3417i	0.978520	+	1.50533i
$202$	−0.635413	+	8.88423i	−0.0447075	+	0.625093i
$203$	4.84893	+	8.88015i	0.340328	+	0.623264i
$204$	8.45361	−	7.40245i	0.591871	−	0.518275i
$205$	−2.85432	+	4.17483i	−0.199354	+	0.291583i
$206$		−	11.8919i		−	0.828548i
$207$	−10.9252	−	9.36160i	−0.759355	−	0.650676i
$208$	−0.603805	+	0.603805i	−0.0418664	+	0.0418664i
$209$	0.0968917	−	0.673897i	0.00670214	−	0.0466144i
$210$	−12.2086	−	7.04050i	−0.842475	−	0.485841i
$211$	−23.4658	−	6.89017i	−1.61545	−	0.474339i	−0.655660	−	0.755056i	$-0.727610\pi$
$211$	−23.4658	−	6.89017i	−1.61545	−	0.474339i	−0.959791	+	0.280717i	$0.909428\pi$
$212$	6.11948	+	0.437674i	0.420287	+	0.0300596i
$213$	1.89235	−	8.92222i	0.129661	−	0.611340i
$214$	10.3102	−	16.0430i	0.704792	−	1.09668i
$215$	4.82335	+	0.483470i	0.328950	+	0.0329723i
$216$	0.819674	+	5.13109i	0.0557718	+	0.349127i
$217$	33.4999	+	7.28746i	2.27412	+	0.494705i
$218$	−2.32527	+	3.10619i	−0.157487	+	0.210378i
$219$	4.66612	+	10.0783i	0.315307	+	0.681027i
$220$	0.0859019	+	0.748285i	0.00579150	+	0.0504494i
$221$	−4.18660	−	3.62771i	−0.281621	−	0.244026i
$222$	6.25880	−	4.73629i	0.420063	−	0.317879i
$223$	25.1207	−	5.46467i	1.68220	−	0.365941i	0.732909	−	0.680327i	$-0.238162\pi$
$223$	25.1207	−	5.46467i	1.68220	−	0.365941i	0.949295	+	0.314386i	$0.101799\pi$
$224$	−3.49146	+	1.02518i	−0.233283	+	0.0684980i
$225$	−13.9199	+	5.58889i	−0.927995	+	0.372592i
$226$	5.70950	+	1.67646i	0.379790	+	0.111517i
$227$	−9.04315	−	3.37292i	−0.600215	−	0.223869i	0.0309453	−	0.999521i	$-0.490148\pi$
$227$	−9.04315	−	3.37292i	−0.600215	−	0.223869i	−0.631160	+	0.775652i	$0.717421\pi$
$228$	2.08336	−	2.81344i	0.137974	−	0.186325i
$229$		−	0.773974i		−	0.0511456i	−0.999673	−	0.0255728i	$-0.991859\pi$
$229$		−	0.773974i		−	0.0511456i	0.999673	−	0.0255728i	$-0.00814097\pi$
$230$	−3.41013	−	10.1672i	−0.224857	−	0.670402i
$231$	2.03387	−	0.608709i	0.133819	−	0.0400501i
$232$	2.22589	−	1.66628i	0.146137	−	0.109397i
$233$	2.97283	−	7.97046i	0.194756	−	0.522162i	−0.802462	−	0.596704i	$-0.796477\pi$
$233$	2.97283	−	7.97046i	0.194756	−	0.522162i	0.997218	+	0.0745419i	$0.0237495\pi$
$234$	2.45032	−	0.747259i	0.160182	−	0.0488499i
$235$	−4.00578	+	6.86349i	−0.261308	+	0.447725i
$236$	3.99351	+	13.6007i	0.259955	+	0.885327i
$237$	5.69474	−	3.14814i	0.369913	−	0.204493i
$238$	−8.24973	−	22.1184i	−0.534750	−	1.43372i
$239$	−9.17788	+	10.5918i	−0.593668	+	0.685129i	−0.970486	−	0.241158i	$-0.922473\pi$
$239$	−9.17788	+	10.5918i	−0.593668	+	0.685129i	0.376818	+	0.926287i	$0.377018\pi$
$240$	−1.43764	+	3.59627i	−0.0927993	+	0.232139i
$241$	2.54046	+	17.6693i	0.163646	+	1.13818i	0.891689	+	0.452649i	$0.149521\pi$
$241$	2.54046	+	17.6693i	0.163646	+	1.13818i	−0.728043	+	0.685532i	$0.759570\pi$
$242$	8.71512	+	6.52406i	0.560229	+	0.419382i
$243$	5.06586	−	14.7424i	0.324975	−	0.945723i
$244$	−5.27560	−	4.57133i	−0.337736	−	0.292650i
$245$	−10.8034	+	8.83491i	−0.690201	+	0.564441i
$246$	1.08408	−	3.76438i	0.0691185	−	0.240008i
$247$	−1.51481	−	0.827150i	−0.0963852	−	0.0526303i
$248$	0.672120	−	9.39747i	0.0426797	−	0.596740i
$249$	0.0788451	+	15.1543i	0.00499660	+	0.960363i
$250$	−11.0430	−	1.74706i	−0.698420	−	0.110494i
$251$	10.0737	+	1.44838i	0.635846	+	0.0914209i	0.452697	−	0.891664i	$-0.350462\pi$
$251$	10.0737	+	1.44838i	0.635846	+	0.0914209i	0.183149	+	0.983085i	$0.441371\pi$
$252$	10.6907	+	2.20936i	0.673448	+	0.139177i
$253$	1.46616	+	0.678241i	0.0921765	+	0.0426407i
$254$	8.09635			0.508010
$255$	−23.9364	−	7.63844i	−1.49896	−	0.478337i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−17.2803	+	9.43575i	−1.07791	+	0.588586i	−0.917205	−	0.398416i	$-0.869560\pi$
$257$	−17.2803	+	9.43575i	−1.07791	+	0.588586i	−0.160710	+	0.987002i	$0.551378\pi$
$258$	−3.66486	+	0.817234i	−0.228164	+	0.0508787i
$259$	−4.64568	−	15.8217i	−0.288669	−	0.983115i
$260$	1.85344	+	0.458878i	0.114945	+	0.0284584i
$261$	−8.24373	+	1.27296i	−0.510274	+	0.0787941i
$262$	−9.62312	+	0.688259i	−0.594518	+	0.0425208i
$263$	6.30015	+	1.37051i	0.388484	+	0.0845095i	0.402565	−	0.915391i	$-0.368119\pi$
$263$	6.30015	+	1.37051i	0.388484	+	0.0845095i	−0.0140812	+	0.999901i	$0.504482\pi$
$264$	−0.245122	−	0.529435i	−0.0150862	−	0.0325845i
$265$	−6.22879	−	12.2229i	−0.382632	−	0.750849i
$266$	−3.97635	−	6.18733i	−0.243806	−	0.379369i
$267$	−9.73766	+	3.68978i	−0.595935	+	0.225811i
$268$	−5.13576	−	13.7695i	−0.313717	−	0.841107i
$269$	−22.9394	−	14.7423i	−1.39864	−	0.898852i	−0.398806	−	0.917035i	$-0.630575\pi$
$269$	−22.9394	−	14.7423i	−1.39864	−	0.898852i	−0.999835	+	0.0181832i	$0.994212\pi$
$270$	8.87839	−	7.49495i	0.540321	−	0.456128i
$271$	−18.4693	−	21.3147i	−1.12193	−	1.29477i	−0.950897	−	0.309508i	$-0.899836\pi$
$271$	−18.4693	−	21.3147i	−1.12193	−	1.29477i	−0.171031	−	0.985266i	$-0.554710\pi$
$272$	−5.69387	+	3.10909i	−0.345242	+	0.188516i
$273$	0.356007	−	5.37014i	0.0215465	−	0.325015i
$274$	11.1437	+	1.60223i	0.673218	+	0.0967941i
$275$	1.33361	−	1.02861i	0.0804195	−	0.0620276i
$276$	4.98011	+	6.64820i	0.299767	+	0.400174i
$277$	2.96490	+	2.96490i	0.178144	+	0.178144i	0.790546	−	0.612403i	$-0.209797\pi$
$277$	2.96490	+	2.96490i	0.178144	+	0.178144i	−0.612403	+	0.790546i	$0.709797\pi$
$278$	8.18372	−	6.12625i	0.490827	−	0.367428i
$279$	−15.0327	+	23.9353i	−0.899982	+	1.43297i
$280$	5.99499	+	5.50151i	0.358269	+	0.328778i
$281$	9.24083	−	8.00722i	0.551261	−	0.477671i	−0.334124	−	0.942529i	$-0.608440\pi$
$281$	9.24083	−	8.00722i	0.551261	−	0.477671i	0.885385	+	0.464859i	$0.153895\pi$
$282$	1.27717	−	6.02172i	0.0760543	−	0.358588i
$283$	−28.1109	+	6.11515i	−1.67102	+	0.363508i	−0.945734	−	0.324941i	$-0.894655\pi$
$283$	−28.1109	+	6.11515i	−1.67102	+	0.363508i	−0.725285	+	0.688449i	$0.758292\pi$
$284$	−2.18751	+	4.78997i	−0.129805	+	0.284232i
$285$	−7.79303	−	0.740205i	−0.461619	−	0.0438460i
$286$	−0.241971	+	0.155506i	−0.0143081	+	0.00919524i
$287$	−6.58845	−	4.93205i	−0.388904	−	0.291130i
$288$	0.182869	−	2.99442i	0.0107757	−	0.176448i
$289$	−13.5628	−	21.1042i	−0.797814	−	1.24142i
$290$	−5.76105	−	2.33786i	−0.338301	−	0.137284i
$291$	15.0393	+	2.08253i	0.881622	+	0.122080i
$292$	−1.36299	−	6.26554i	−0.0797627	−	0.366663i
$293$	−0.982386	−	0.536423i	−0.0573916	−	0.0313382i	0.450297	−	0.892879i	$-0.351318\pi$
$293$	−0.982386	−	0.536423i	−0.0573916	−	0.0313382i	−0.507689	+	0.861541i	$0.669500\pi$
$294$	5.79705	−	9.12442i	0.338091	−	0.532147i
$295$	21.4306	−	23.3529i	1.24774	−	1.35966i
$296$	−4.12205	+	1.88248i	−0.239589	+	0.109417i
$297$	−0.0976000	+	1.74756i	−0.00566333	+	0.101403i
$298$	−9.49444	+	9.49444i	−0.549998	+	0.549998i
$299$	2.90985	−	2.88158i	0.168281	−	0.166646i
$300$	8.54630	−	1.40024i	0.493421	−	0.0808429i
$301$	−1.12266	+	7.80829i	−0.0647092	+	0.450063i
$302$	6.25182	+	2.33181i	0.359752	+	0.134180i
$303$	−10.8518	+	10.9653i	−0.623420	+	0.629941i
$304$	−1.52753	+	1.32361i	−0.0876097	+	0.0759143i
$305$	−2.66081	+	15.3807i	−0.152358	+	0.880695i
$306$	19.4612	−	0.202512i	1.11252	−	0.0115768i
$307$	22.3491	−	8.33579i	1.27553	−	0.475749i	0.381756	−	0.924263i	$-0.375319\pi$
$307$	22.3491	−	8.33579i	1.27553	−	0.475749i	0.893776	+	0.448514i	$0.148047\pi$
$308$	−1.22259	+	0.0874417i	−0.0696638	+	0.00498245i
$309$	13.4072	−	15.6364i	0.762711	−	0.889525i
$310$	−18.7703	+	9.56534i	−1.06608	+	0.543275i
$311$	−29.4225	+	4.23031i	−1.66840	+	0.239879i	−0.910801	−	0.412847i	$-0.864535\pi$
$311$	−29.4225	+	4.23031i	−1.66840	+	0.239879i	−0.757594	+	0.652726i	$0.773625\pi$
$312$	−1.47468	+	0.113186i	−0.0834872	+	0.00640787i
$313$	−0.862849	−	12.0642i	−0.0487711	−	0.681909i	−0.961755	−	0.273913i	$-0.911682\pi$
$313$	−0.862849	−	12.0642i	−0.0487711	−	0.681909i	0.912983	−	0.407997i	$-0.133772\pi$
$314$	−0.850769	+	1.86292i	−0.0480117	+	0.105131i
$315$	−8.11523	−	23.0217i	−0.457242	−	1.29713i
$316$	−3.60463	+	1.05842i	−0.202776	+	0.0595405i
$317$	19.3167	+	1.38156i	1.08493	+	0.0775961i	0.602334	−	0.798244i	$-0.294238\pi$
$317$	19.3167	+	1.38156i	1.08493	+	0.0775961i	0.482601	+	0.875840i	$0.339692\pi$
$318$	7.55294	+	7.47475i	0.423548	+	0.419163i
$319$	0.851943	−	0.389069i	0.0476997	−	0.0217837i
$320$	1.26203	−	1.84588i	0.0705494	−	0.103188i
$321$	31.6440	−	9.47062i	1.76620	−	0.528599i
$322$	16.7682	−	4.83481i	0.934458	−	0.269433i
$323$	−9.27189	−	9.27189i	−0.515902	−	0.515902i
$324$	−4.70716	+	7.67090i	−0.261509	+	0.426161i
$325$	−1.26172	−	4.07886i	−0.0699876	−	0.226254i
$326$	−1.53765	+	5.23674i	−0.0851623	+	0.290036i
$327$	−6.55945	+	1.46270i	−0.362738	+	0.0808877i
$328$	−1.08392	+	1.98504i	−0.0598492	+	0.109606i
$329$	−10.8794	−	6.99179i	−0.599803	−	0.385470i
$330$	−0.730686	+	1.08075i	−0.0402229	+	0.0594935i
$331$	4.46721	−	5.15543i	0.245540	−	0.283368i	−0.619580	−	0.784934i	$-0.712697\pi$
$331$	4.46721	−	5.15543i	0.245540	−	0.283368i	0.865120	+	0.501566i	$0.167242\pi$
$332$	1.85983	−	8.54949i	0.102071	−	0.469214i
$333$	13.5694	+	0.828683i	0.743598	+	0.0454116i
$334$	−18.9942	+	2.73095i	−1.03932	+	0.149431i
$335$	−20.4349	+	25.7351i	−1.11648	+	1.40606i
$336$	−5.74667	−	2.58837i	−0.313506	−	0.141207i
$337$	−22.1425	+	8.25873i	−1.20618	+	0.449882i	−0.870535	−	0.492107i	$-0.836227\pi$
$337$	−22.1425	+	8.25873i	−1.20618	+	0.449882i	−0.335645	+	0.941989i	$0.608954\pi$
$338$	−2.60835	−	11.9904i	−0.141876	−	0.652192i
$339$	5.61722	+	8.64139i	0.305086	+	0.469336i
$340$	12.5286	+	7.31214i	0.679458	+	0.396557i
$341$	0.894090	−	3.04499i	0.0484177	−	0.164896i
$342$	5.91132	−	1.35050i	0.319648	−	0.0730266i
$343$	1.65453	+	2.21019i	0.0893361	+	0.119339i
$344$	2.16788			0.116884
$345$	6.97880	−	17.2133i	0.375726	−	0.926731i
$346$	−5.84041			−0.313983
$347$	8.28096	+	11.0621i	0.444545	+	0.593843i	0.965713	−	0.259611i	$-0.0835945\pi$
$347$	8.28096	+	11.0621i	0.444545	+	0.593843i	−0.521168	+	0.853454i	$0.674504\pi$
$348$	4.80538	+	0.318568i	0.257596	+	0.0170770i
$349$	−4.39206	+	14.9580i	−0.235102	+	0.800683i	0.754432	+	0.656378i	$0.227913\pi$
$349$	−4.39206	+	14.9580i	−0.235102	+	0.800683i	−0.989533	+	0.144304i	$0.953906\pi$
$350$	3.61114	−	17.8323i	0.193023	−	0.953178i
$351$	4.06435	+	1.78000i	0.216939	+	0.0950092i
$352$	0.0716008	+	0.329143i	0.00381633	+	0.0175434i
$353$	15.8739	−	5.92067i	0.844885	−	0.315126i	0.110514	−	0.993875i	$-0.464750\pi$
$353$	15.8739	−	5.92067i	0.844885	−	0.315126i	0.734370	+	0.678749i	$0.237478\pi$
$354$	−10.0827	+	22.3856i	−0.535892	+	1.18978i
$355$	11.6979	−	1.34290i	0.620862	−	0.0712738i
$356$	5.95092	−	0.855613i	0.315398	−	0.0453474i
$357$	14.0894	−	38.3840i	0.745692	−	2.03150i
$358$	3.60701	−	16.5811i	0.190636	−	0.876341i
$359$	−12.5253	+	14.4550i	−0.661061	+	0.762905i	−0.982950	−	0.183872i	$-0.941137\pi$
$359$	−12.5253	+	14.4550i	−0.661061	+	0.762905i	0.321889	+	0.946777i	$0.395682\pi$
$360$	−5.94486	+	3.10784i	−0.313322	+	0.163797i
$361$	12.5471	+	8.06350i	0.660371	+	0.424395i
$362$	−7.46782	+	13.6763i	−0.392500	+	0.718810i
$363$	4.10395	+	18.4040i	0.215401	+	0.965960i
$364$	−0.875415	+	2.98139i	−0.0458842	+	0.156267i
$365$	−10.4232	+	9.84534i	−0.545575	+	0.515329i
$366$	−1.78294	−	11.9586i	−0.0931958	−	0.625086i
$367$	−1.09615	−	1.09615i	−0.0572187	−	0.0572187i	0.677918	−	0.735137i	$-0.262882\pi$
$367$	−1.09615	−	1.09615i	−0.0572187	−	0.0572187i	−0.735137	+	0.677918i	$0.762882\pi$
$368$	−1.97094	−	4.37212i	−0.102742	−	0.227912i
$369$	5.66950	−	3.72749i	0.295142	−	0.194045i
$370$	8.36473	+	5.71894i	0.434862	+	0.297314i
$371$	20.3073	−	9.27405i	1.05430	−	0.481485i
$372$	11.4787	−	11.5988i	0.595144	−	0.601369i
$373$	17.1016	+	1.22313i	0.885486	+	0.0633312i	0.506669	−	0.862140i	$-0.330877\pi$
$373$	17.1016	+	1.22313i	0.885486	+	0.0633312i	0.378817	+	0.925472i	$0.376331\pi$
$374$	−2.09671	+	0.615651i	−0.108418	+	0.0318345i
$375$	−12.5505	−	14.7473i	−0.648107	−	0.761550i
$376$	−1.47638	+	3.23281i	−0.0761383	+	0.166720i
$377$	−0.169379	−	2.36823i	−0.00872346	−	0.121970i
$378$	11.5660	+	14.9580i	0.594893	+	0.769356i
$379$	−7.28220	+	1.04702i	−0.374062	+	0.0537819i	−0.326782	−	0.945100i	$-0.605964\pi$
$379$	−7.28220	+	1.04702i	−0.374062	+	0.0537819i	−0.0472796	+	0.998882i	$0.515055\pi$
$380$	4.29844	+	1.39637i	0.220505	+	0.0716323i
$381$	10.6457	+	9.12804i	0.545397	+	0.467644i
$382$	22.8577	−	1.63482i	1.16950	−	0.0836445i
$383$	−24.6335	+	9.18782i	−1.25871	+	0.469476i	−0.888245	−	0.459370i	$-0.848075\pi$
$383$	−24.6335	+	9.18782i	−1.25871	+	0.469476i	−0.370468	+	0.928845i	$0.620803\pi$
$384$	−0.479322	+	1.66441i	−0.0244603	+	0.0849364i
$385$	1.57930	+	2.24003i	0.0804885	+	0.114162i
$386$	11.6699	−	10.1120i	0.593981	−	0.514687i
$387$	−5.74022	−	3.05729i	−0.291792	−	0.155411i
$388$	−8.21313	−	3.06334i	−0.416959	−	0.155518i
$389$	4.02219	−	27.9749i	0.203933	−	1.41839i	−0.588535	−	0.808472i	$-0.700295\pi$
$389$	4.02219	−	27.9749i	0.203933	−	1.41839i	0.792468	−	0.609914i	$-0.208796\pi$
$390$	1.91970	+	2.69299i	0.0972078	+	0.136365i
$391$	27.3793	−	14.7772i	1.38463	−	0.747314i
$392$	−4.41325	+	4.41325i	−0.222903	+	0.222903i
$393$	−13.4292	−	9.94438i	−0.677414	−	0.501627i
$394$	7.78861	−	3.55694i	0.392384	−	0.179196i
$395$	6.18931	+	5.67983i	0.311418	+	0.285783i
$396$	0.274593	−	0.972500i	0.0137988	−	0.0488700i
$397$	−21.9399	−	11.9801i	−1.10113	−	0.601263i	−0.177337	−	0.984150i	$-0.556748\pi$
$397$	−21.9399	−	11.9801i	−1.10113	−	0.601263i	−0.923795	+	0.382887i	$0.874930\pi$
$398$	−4.34839	−	19.9892i	−0.217965	−	1.00197i
$399$	1.74733	−	12.6186i	0.0874757	−	0.631722i
$400$	−4.99188	−	0.284863i	−0.249594	−	0.0142432i
$401$	−15.1177	−	23.5236i	−0.754941	−	1.17471i	−0.979734	−	0.200305i	$-0.935807\pi$
$401$	−15.1177	−	23.5236i	−0.754941	−	1.17471i	0.224792	−	0.974407i	$-0.427830\pi$
$402$	8.77120	−	23.8955i	0.437468	−	1.19180i
$403$	−6.44043	−	4.82124i	−0.320820	−	0.240163i
$404$	7.49298	−	4.81545i	0.372790	−	0.239578i
$405$	20.1240	+	0.154770i	0.999970	+	0.00769057i
$406$	4.20307	−	9.20344i	0.208595	−	0.456759i
$407$	−1.49153	+	0.324463i	−0.0739325	+	0.0160830i
$408$	−10.9920	−	2.33134i	−0.544186	−	0.115419i
$409$	12.9532	−	11.2240i	0.640493	−	0.554990i	−0.272914	−	0.962038i	$-0.587987\pi$
$409$	12.9532	−	11.2240i	0.640493	−	0.554990i	0.913407	+	0.407048i	$0.133442\pi$
$410$	5.05265	−	0.216882i	0.249533	−	0.0107110i
$411$	12.8463	+	14.6705i	0.633661	+	0.723641i
$412$	−9.51996	+	7.12655i	−0.469015	+	0.351100i
$413$	36.4727	+	36.4727i	1.79470	+	1.79470i
$414$	−0.947109	+	14.3563i	−0.0465479	+	0.705573i
$415$	−18.5182	+	6.31187i	−0.909023	+	0.309838i
$416$	0.845218	+	0.121524i	0.0414402	+	0.00595820i
$417$	17.6675	+	1.17125i	0.865181	+	0.0573563i
$418$	−0.597547	+	0.326285i	−0.0292270	+	0.0159591i
$419$	−19.0605	−	21.9970i	−0.931166	−	1.07462i	−0.997047	−	0.0767955i	$-0.975531\pi$
$419$	−19.0605	−	21.9970i	−0.931166	−	1.07462i	0.0658808	−	0.997828i	$-0.479014\pi$
$420$	1.68015	+	13.9927i	0.0819827	+	0.682775i
$421$	−2.33979	−	1.50369i	−0.114034	−	0.0732855i	0.482380	−	0.875962i	$-0.339772\pi$
$421$	−2.33979	−	1.50369i	−0.114034	−	0.0732855i	−0.596415	+	0.802676i	$0.703409\pi$
$422$	8.54665	+	22.9145i	0.416044	+	1.11546i
$423$	8.46837	−	6.47793i	0.411746	−	0.314968i
$424$	−3.31689	−	5.16118i	−0.161082	−	0.250649i
$425$	−0.466958	−	32.4337i	−0.0226508	−	1.57327i
$426$	−8.27664	+	3.83198i	−0.401005	+	0.185660i
$427$	−24.8210	−	5.39947i	−1.20117	−	0.261299i
$428$	−19.0218	+	1.36046i	−0.919452	+	0.0657605i
$429$	−0.493485	−	0.0683337i	−0.0238257	−	0.00329918i
$430$	−2.50349	−	4.15102i	−0.120729	−	0.200180i
$431$	3.22967	+	10.9992i	0.155568	+	0.529815i	0.999983	−	0.00587474i	$-0.00187000\pi$
$431$	3.22967	+	10.9992i	0.155568	+	0.529815i	−0.844415	+	0.535689i	$0.820052\pi$
$432$	3.61644	−	3.73113i	0.173996	−	0.179514i
$433$	3.26685	−	1.78383i	0.156995	−	0.0857256i	−0.398831	−	0.917024i	$-0.630584\pi$
$433$	3.26685	−	1.78383i	0.156995	−	0.0857256i	0.555826	+	0.831299i	$0.312402\pi$
$434$	−14.2418	−	31.1853i	−0.683630	−	1.49694i
$435$	−4.93932	−	9.56917i	−0.236822	−	0.458807i
$436$	3.88011			0.185824
$437$	7.35667	−	6.31197i	0.351917	−	0.301943i
$438$	5.27177	−	9.77510i	0.251895	−	0.467072i
$439$	6.43638	+	0.925412i	0.307192	+	0.0441675i	0.294187	−	0.955748i	$-0.404951\pi$
$439$	6.43638	+	0.925412i	0.307192	+	0.0441675i	0.0130048	+	0.999915i	$0.495860\pi$
$440$	0.547554	−	0.517199i	0.0261036	−	0.0246565i
$441$	17.9095	−	5.46177i	0.852835	−	0.260084i
$442$	−0.395195	+	5.52556i	−0.0187975	+	0.262824i
$443$	−7.25550	−	3.96180i	−0.344719	−	0.188231i	0.297557	−	0.954704i	$-0.403828\pi$
$443$	−7.25550	−	3.96180i	−0.344719	−	0.188231i	−0.642276	+	0.766473i	$0.722010\pi$
$444$	−7.54236	−	2.17208i	−0.357944	−	0.103082i
$445$	−8.51051	−	10.4067i	−0.403437	−	0.493324i
$446$	−19.4289	−	16.8353i	−0.919987	−	0.797173i
$447$	−23.1883	+	1.77977i	−1.09677	+	0.0841802i
$448$	2.91306	+	2.18069i	0.137629	+	0.103028i
$449$	1.15965	+	8.06552i	0.0547271	+	0.380636i	0.998716	+	0.0506584i	$0.0161320\pi$
$449$	1.15965	+	8.06552i	0.0547271	+	0.380636i	−0.943989	+	0.329977i	$0.892959\pi$
$450$	12.8160	+	7.79418i	0.604154	+	0.367421i
$451$	−0.498894	+	0.575755i	−0.0234920	+	0.0271112i
$452$	−2.07950	−	5.57536i	−0.0978115	−	0.262243i
$453$	5.59145	+	10.1145i	0.262709	+	0.475221i
$454$	2.71920	+	9.26073i	0.127618	+	0.434628i
$455$	6.71967	−	1.76671i	0.315023	−	0.0828246i
$456$	−3.50079	+	0.0182140i	−0.163939	+	0.000852948i
$457$	−10.8669	+	29.1352i	−0.508331	+	1.36289i	0.388882	+	0.921288i	$0.372862\pi$
$457$	−10.8669	+	29.1352i	−0.508331	+	1.36289i	−0.897212	+	0.441600i	$0.854411\pi$
$458$	−0.619598	+	0.463825i	−0.0289519	+	0.0216731i
$459$	25.8175	+	21.6748i	1.20506	+	1.01169i
$460$	−6.09561	+	8.82290i	−0.284209	+	0.411370i
$461$		−	9.52574i		−	0.443658i	−0.975086	−	0.221829i	$-0.928797\pi$
$461$		−	9.52574i		−	0.443658i	0.975086	−	0.221829i	$-0.0712027\pi$
$462$	−1.70615	−	1.26341i	−0.0793772	−	0.0587791i
$463$	−14.4855	−	5.40283i	−0.673201	−	0.251091i	−0.0104660	−	0.999945i	$-0.503331\pi$
$463$	−14.4855	−	5.40283i	−0.673201	−	0.251091i	−0.662735	+	0.748854i	$0.730604\pi$
$464$	−2.66785	−	0.783351i	−0.123852	−	0.0363662i
$465$	−35.4649	−	8.58489i	−1.64465	−	0.398115i
$466$	−8.16223	+	2.39665i	−0.378108	+	0.111022i
$467$	−17.3746	+	3.77962i	−0.804001	+	0.174900i	−0.595744	−	0.803174i	$-0.703143\pi$
$467$	−17.3746	+	3.77962i	−0.804001	+	0.174900i	−0.208257	+	0.978074i	$0.566779\pi$
$468$	−2.06663	−	1.51376i	−0.0955301	−	0.0699738i
$469$	−40.4152	−	35.0200i	−1.86620	−	1.61707i
$470$	7.89508	−	0.906342i	0.364173	−	0.0418064i
$471$	−3.21897	+	1.49034i	−0.148322	+	0.0686714i
$472$	8.49466	−	11.3475i	0.390998	−	0.522313i
$473$	0.713542	+	0.155222i	0.0328087	+	0.00713709i
$474$	−5.93294	−	2.67227i	−0.272509	−	0.122741i
$475$	−2.29013	−	9.84314i	−0.105078	−	0.451634i
$476$	−12.7628	+	19.8593i	−0.584982	+	0.910249i
$477$	1.50398	+	18.3438i	0.0688623	+	0.839904i
$478$	13.9793	+	0.999820i	0.639399	+	0.0457307i
$479$	29.1753	+	8.56665i	1.33305	+	0.391420i	0.869187	−	0.494484i	$-0.164643\pi$
$479$	29.1753	+	8.56665i	1.33305	+	0.391420i	0.463868	+	0.885904i	$0.346461\pi$
$480$	3.74051	−	1.00428i	0.170730	−	0.0458387i
$481$	−0.550693	+	3.83015i	−0.0251094	+	0.174640i
$482$	12.6226	−	12.6226i	0.574943	−	0.574943i
$483$	27.4991	+	12.5478i	1.25125	+	0.570943i
$484$		−	10.8865i		−	0.494843i
$485$	3.61897	+	19.2640i	0.164329	+	0.874732i
$486$	−14.8377	+	4.77934i	−0.673053	+	0.216795i
$487$	9.20245	+	16.8530i	0.417003	+	0.763684i	0.998765	−	0.0496749i	$-0.0158185\pi$
$487$	9.20245	+	16.8530i	0.417003	+	0.763684i	−0.581763	+	0.813359i	$0.697637\pi$
$488$	−0.497992	+	6.96283i	−0.0225430	+	0.315193i
$489$	−7.92586	+	5.15210i	−0.358420	+	0.232986i
$490$	13.5469	+	3.35397i	0.611987	+	0.151517i
$491$	3.09320	+	1.41262i	0.139594	+	0.0637505i	0.483987	−	0.875075i	$-0.339188\pi$
$491$	3.09320	+	1.41262i	0.139594	+	0.0637505i	−0.344393	+	0.938825i	$0.611915\pi$
$492$	−3.66321	+	1.38806i	−0.165150	+	0.0625785i
$493$	3.83428	−	17.6259i	0.172687	−	0.793831i
$494$	0.245625	+	1.70836i	0.0110512	+	0.0768628i
$495$	−2.17923	+	0.597267i	−0.0979493	+	0.0268452i
$496$	−7.92585	+	5.09363i	−0.355881	+	0.228711i
$497$	1.36697	+	19.1128i	0.0613171	+	0.857326i
$498$	12.0844	−	9.14474i	0.541514	−	0.409786i
$499$	−7.38269	+	11.4877i	−0.330495	+	0.514260i	−0.966242	−	0.257638i	$-0.917056\pi$
$499$	−7.38269	+	11.4877i	−0.330495	+	0.514260i	0.635747	+	0.771898i	$0.280692\pi$
$500$	5.21922	+	9.88735i	0.233411	+	0.442176i
$501$	−28.0540	−	17.8237i	−1.25336	−	0.796303i
$502$	−4.87746	−	8.93239i	−0.217692	−	0.398672i
$503$	−6.27550	+	16.8253i	−0.279811	+	0.750201i	0.718683	+	0.695338i	$0.244745\pi$
$503$	−6.27550	+	16.8253i	−0.279811	+	0.750201i	−0.998494	+	0.0548635i	$0.982528\pi$
$504$	−4.63799	−	9.88234i	−0.206592	−	0.440194i
$505$	−17.8735	−	8.78654i	−0.795362	−	0.390996i
$506$	−0.335675	−	1.58017i	−0.0149226	−	0.0702473i
$507$	10.0886	−	18.7067i	0.448052	−	0.830793i
$508$	−4.85196	−	6.48146i	−0.215271	−	0.287568i
$509$	16.5019	+	36.1341i	0.731433	+	1.60161i	0.797154	+	0.603776i	$0.206338\pi$
$509$	16.5019	+	36.1341i	0.731433	+	1.60161i	−0.0657215	+	0.997838i	$0.520935\pi$
$510$	8.22969	+	23.7397i	0.364417	+	1.05121i
$511$	−15.2796	−	17.6336i	−0.675931	−	0.780066i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	9.29527	+	4.88883i	0.410396	+	0.215847i
$514$	17.9094	+	8.17895i	0.789950	+	0.360758i
$515$	24.6396	+	9.99887i	1.08575	+	0.440603i
$516$	2.85050	+	2.44412i	0.125486	+	0.107596i
$517$	−0.717411	+	0.958349i	−0.0315517	+	0.0421481i
$518$	−9.88190	+	13.2007i	−0.434186	+	0.580005i
$519$	−7.67944	−	6.58463i	−0.337090	−	0.289033i
$520$	−0.743375	−	1.75875i	−0.0325991	−	0.0771263i
$521$	−20.9571	−	9.57079i	−0.918148	−	0.419304i	−0.100444	−	0.994943i	$-0.532026\pi$
$521$	−20.9571	−	9.57079i	−0.918148	−	0.419304i	−0.817704	+	0.575639i	$0.804754\pi$
$522$	5.95934	+	5.83659i	0.260833	+	0.255461i
$523$	−18.5620	+	33.9937i	−0.811658	+	1.48644i	0.0610160	+	0.998137i	$0.480566\pi$
$523$	−18.5620	+	33.9937i	−0.811658	+	1.48644i	−0.872674	+	0.488304i	$0.837616\pi$
$524$	6.31790	+	7.29124i	0.275999	+	0.318519i
$525$	24.8528	−	19.3761i	1.08467	−	0.845641i
$526$	−2.67839	−	5.86485i	−0.116783	−	0.255720i
$527$	−36.6285	−	48.9299i	−1.59556	−	2.13142i
$528$	−0.276938	+	0.513509i	−0.0120522	+	0.0223476i
$529$	9.34982	+	21.0138i	0.406514	+	0.913645i
$530$	−6.05219	+	12.3113i	−0.262890	+	0.534770i
$531$	−38.4957	+	18.0669i	−1.67057	+	0.784035i
$532$	−2.57027	+	6.89116i	−0.111435	+	0.298770i
$533$	0.925566	+	1.69505i	0.0400907	+	0.0734207i
$534$	8.78939	+	5.58420i	0.380354	+	0.241652i
$535$	24.5716	+	34.8516i	1.06232	+	1.50676i
$536$	−7.94532	+	12.3632i	−0.343185	+	0.534007i
$537$	23.4368	−	17.7356i	1.01137	−	0.765347i
$538$	1.94529	+	27.1987i	0.0838673	+	1.17262i
$539$	−1.76858	+	1.13660i	−0.0761783	+	0.0489568i
$540$	−11.3206	−	2.61596i	−0.487163	−	0.112573i
$541$	−0.939881	−	6.53701i	−0.0404086	−	0.281048i	0.959591	−	0.281397i	$-0.0907979\pi$
$541$	−0.939881	−	6.53701i	−0.0404086	−	0.281048i	−1.00000		0.000349266i	$0.999889\pi$
$542$	−5.99505	+	27.5588i	−0.257510	+	1.18375i
$543$	−25.2383	+	9.56327i	−1.08308	+	0.410399i
$544$	5.90116	+	2.69497i	0.253010	+	0.115546i
$545$	−4.48080	−	7.42959i	−0.191936	−	0.318249i
$546$	−4.51236	+	2.93320i	−0.193111	+	0.125530i
$547$	−3.15688	+	44.1390i	−0.134979	+	1.88725i	0.255752	+	0.966742i	$0.417677\pi$
$547$	−3.15688	+	44.1390i	−0.134979	+	1.88725i	−0.390731	+	0.920505i	$0.627778\pi$
$548$	−5.39554	−	9.88120i	−0.230486	−	0.422104i
$549$	11.1381	−	17.7343i	0.475362	−	0.756880i
$550$	−1.62265	−	0.451183i	−0.0691899	−	0.0192385i
$551$		−	5.61993i		−	0.239417i
$552$	2.33769	−	7.97090i	0.0994987	−	0.339264i
$553$	−9.66649	+	9.66649i	−0.411061	+	0.411061i
$554$	0.596726	−	4.15032i	0.0253525	−	0.176330i
$555$	4.55093	+	16.9503i	0.193176	+	0.719502i
$556$	−9.80864	−	2.88008i	−0.415979	−	0.122142i
$557$	−19.0690	−	1.36384i	−0.807980	−	0.0577879i	−0.338764	−	0.940871i	$-0.610009\pi$
$557$	−19.0690	−	1.36384i	−0.807980	−	0.0577879i	−0.469216	+	0.883083i	$0.655463\pi$
$558$	28.1699	−	2.30960i	1.19253	−	0.0977734i
$559$	1.00082	−	1.55730i	0.0423301	−	0.0658669i
$560$	0.811521	−	8.09616i	0.0342930	−	0.342125i
$561$	−3.45103	−	1.55438i	−0.145702	−	0.0656261i
$562$	−11.9479	−	2.59911i	−0.503993	−	0.109637i
$563$	0.456731	−	0.610121i	0.0192489	−	0.0257135i	−0.790814	−	0.612057i	$-0.790342\pi$
$563$	0.456731	−	0.610121i	0.0192489	−	0.0257135i	0.810062	+	0.586344i	$0.199433\pi$
$564$	−5.58601	+	2.58626i	−0.235214	+	0.108901i
$565$	−8.27419	+	10.4203i	−0.348098	+	0.438385i
$566$	21.7417	+	18.8393i	0.913870	+	0.791873i
$567$	−1.65606	+	32.7078i	−0.0695480	+	1.37360i
$568$	5.14549	−	1.11933i	0.215900	−	0.0469662i
$569$	−31.0597	+	9.11996i	−1.30209	+	0.382329i	−0.857999	−	0.513652i	$-0.828292\pi$
$569$	−31.0597	+	9.11996i	−1.30209	+	0.382329i	−0.444093	+	0.895981i	$0.646474\pi$
$570$	4.07763	+	6.68223i	0.170793	+	0.279888i
$571$	−14.5366	−	4.26832i	−0.608337	−	0.178624i	−0.0369669	−	0.999316i	$-0.511770\pi$
$571$	−14.5366	−	4.26832i	−0.608337	−	0.178624i	−0.571370	+	0.820693i	$0.693588\pi$
$572$	0.269497	+	0.100517i	0.0112682	+	0.00420283i
$573$	31.8983	+	23.6208i	1.33257	+	0.986773i
$574$			8.22999i			0.343513i
$575$	23.9333	+	1.48302i	0.998086	+	0.0618460i
$576$	−2.50675	+	1.64810i	−0.104448	+	0.0686706i
$577$	2.55588	−	1.91331i	0.106403	−	0.0796519i	−0.544752	−	0.838597i	$-0.683376\pi$
$577$	2.55588	−	1.91331i	0.106403	−	0.0796519i	0.651154	+	0.758946i	$0.274285\pi$
$578$	−8.76687	+	23.5049i	−0.364654	+	0.977675i
$579$	26.7450	−	0.139150i	1.11149	−	0.00578286i
$580$	1.58091	+	6.01299i	0.0656438	+	0.249676i
$581$	−8.96980	−	30.5483i	−0.372130	−	1.26736i
$582$	−7.34560	−	13.2876i	−0.304485	−	0.550790i
$583$	−0.722188	−	1.93626i	−0.0299100	−	0.0801917i
$584$	−4.19902	+	4.84593i	−0.173757	+	0.200526i
$585$	−0.511967	+	5.70527i	−0.0211672	+	0.235884i
$586$	0.159293	+	1.10791i	0.00658033	+	0.0457672i
$587$	21.4595	+	16.0644i	0.885728	+	0.663047i	0.942089	−	0.335363i	$-0.108859\pi$
$587$	21.4595	+	16.0644i	0.885728	+	0.663047i	−0.0563613	+	0.998410i	$0.517950\pi$
$588$	−10.7785	+	0.827281i	−0.444498	+	0.0341165i
$589$	−14.3916	−	12.4704i	−0.592994	−	0.513832i
$590$	−31.5378	−	3.16121i	−1.29839	−	0.130145i
$591$	14.2513	+	4.10413i	0.586219	+	0.168822i
$592$	3.97725	+	2.17174i	0.163464	+	0.0892582i
$593$	0.172645	−	2.41389i	0.00708967	−	0.0991266i	−0.992675	−	0.120814i	$-0.961449\pi$
$593$	0.172645	−	2.41389i	0.00708967	−	0.0991266i	0.999765	+	0.0216878i	$0.00690398\pi$
$594$	1.45748	−	0.969138i	0.0598011	−	0.0397642i
$595$	52.7650	+	1.50430i	2.16315	+	0.0616703i
$596$	13.2905	+	1.91089i	0.544400	+	0.0782729i
$597$	16.8188	−	31.1859i	0.688346	−	1.27636i
$598$	−4.05063	−	0.602591i	−0.165643	−	0.0246418i
$599$	−35.5904			−1.45419			−0.727093	−	0.686539i	$-0.759129\pi$
$599$	−35.5904			−1.45419			−0.727093	+	0.686539i	$0.759129\pi$
$600$	−6.24256	−	6.00254i	−0.254851	−	0.245053i
$601$	5.09005	+	11.1457i	0.207628	+	0.454641i	0.984584	−	0.174914i	$-0.0559646\pi$
$601$	5.09005	+	11.1457i	0.207628	+	0.454641i	−0.776956	+	0.629555i	$0.783237\pi$
$602$	6.92365	−	3.78060i	0.282187	−	0.154086i
$603$	38.4734	−	21.5308i	1.56676	−	0.876801i
$604$	−1.87987	−	6.40224i	−0.0764907	−	0.260503i
$605$	−20.8454	+	12.5719i	−0.847486	+	0.511120i
$606$	15.2814	+	2.11605i	0.620766	+	0.0859586i
$607$	1.91282	−	0.136807i	0.0776389	−	0.00555284i	−0.0324657	−	0.999473i	$-0.510336\pi$
$607$	1.91282	−	0.136807i	0.0776389	−	0.00555284i	0.110105	+	0.993920i	$0.464881\pi$
$608$	1.97502	+	0.429639i	0.0800975	+	0.0174242i
$609$	15.9027	−	7.36277i	0.644412	−	0.298355i
$610$	13.9074	−	7.08721i	0.563095	−	0.286953i
$611$	1.64072	+	2.55302i	0.0663766	+	0.103284i
$612$	−11.8248	−	15.4581i	−0.477989	−	0.624858i
$613$	16.5802	+	44.4532i	0.669667	+	1.79545i	0.603102	+	0.797664i	$0.293931\pi$
$613$	16.5802	+	44.4532i	0.669667	+	1.79545i	0.0665647	+	0.997782i	$0.478796\pi$
$614$	−20.0665	−	12.8959i	−0.809817	−	0.520438i
$615$	6.88815	+	5.41132i	0.277757	+	0.218206i
$616$	0.802674	+	0.926335i	0.0323407	+	0.0373231i
$617$	20.9176	−	11.4219i	0.842112	−	0.459828i	0.000557097	−	1.00000i	$-0.499823\pi$
$617$	20.9176	−	11.4219i	0.842112	−	0.459828i	0.841555	+	0.540172i	$0.181641\pi$
$618$	−20.5523	−	1.36249i	−0.826733	−	0.0548074i
$619$	42.1126	+	6.05487i	1.69265	+	0.243366i	0.920126	−	0.391623i	$-0.128086\pi$
$619$	42.1126	+	6.05487i	1.69265	+	0.243366i	0.772522	+	0.634989i	$0.218995\pi$
$620$	18.9061	+	9.29413i	0.759287	+	0.373261i
$621$	−17.4310	+	17.8090i	−0.699482	+	0.714651i
$622$	21.0188	+	21.0188i	0.842776	+	0.842776i
$623$	17.5136	−	13.1105i	0.701669	−	0.525262i
$624$	0.974351	+	1.11271i	0.0390053	+	0.0445441i
$625$	12.9050	−	21.4117i	0.516198	−	0.856469i
$626$	−9.14081	+	7.92055i	−0.365340	+	0.316569i
$627$	−1.15357	−	0.244664i	−0.0460690	−	0.00977094i
$628$	2.00120	−	0.435333i	0.0798564	−	0.0173717i
$629$	−12.2124	+	26.7415i	−0.486941	+	1.06625i
$630$	−13.5666	+	20.2930i	−0.540505	+	0.808492i
$631$	1.07529	−	0.691046i	0.0428066	−	0.0275101i	−0.519063	−	0.854736i	$-0.673719\pi$
$631$	1.07529	−	0.691046i	0.0428066	−	0.0275101i	0.561869	+	0.827226i	$0.310082\pi$
$632$	3.00748	+	2.25137i	0.119631	+	0.0895547i
$633$	−14.5965	+	39.7655i	−0.580160	+	1.58054i
$634$	−10.4701	−	16.2918i	−0.415820	−	0.647028i
$635$	−6.80752	+	16.7753i	−0.270148	+	0.665709i
$636$	1.45754	−	10.5259i	0.0577952	−	0.417379i
$637$	1.13286	+	5.20769i	0.0448857	+	0.206336i
$638$	−0.822017	−	0.448855i	−0.0325439	−	0.0177703i
$639$	−15.2031	−	4.29271i	−0.601424	−	0.169817i
$640$	−2.23401	+	0.0958936i	−0.0883070	+	0.00379053i
$641$	39.2462	−	17.9231i	1.55013	−	0.707921i	0.557622	−	0.830095i	$-0.311714\pi$
$641$	39.2462	−	17.9231i	1.55013	−	0.707921i	0.992509	+	0.122175i	$0.0389868\pi$
$642$	−26.5452	−	19.6568i	−1.04765	−	0.775792i
$643$	−1.21940	+	1.21940i	−0.0480886	+	0.0480886i	−0.730742	−	0.682654i	$-0.760826\pi$
$643$	−1.21940	+	1.21940i	−0.0480886	+	0.0480886i	0.682654	+	0.730742i	$0.260826\pi$
$644$	−13.9193	−	10.5263i	−0.548497	−	0.414794i
$645$	1.38818	−	8.28059i	0.0546597	−	0.326048i
$646$	−1.86609	+	12.9790i	−0.0734205	+	0.510650i
$647$	−18.9939	−	7.08436i	−0.746728	−	0.278515i	−0.0528446	−	0.998603i	$-0.516829\pi$
$647$	−18.9939	−	7.08436i	−0.746728	−	0.278515i	−0.693883	+	0.720088i	$0.744102\pi$
$648$	8.96176	−	0.828723i	0.352051	−	0.0325553i
$649$	3.60845	−	3.12674i	0.141644	−	0.122735i
$650$	−2.50918	+	3.45443i	−0.0984180	+	0.135494i
$651$	16.4328	−	57.0615i	0.644052	−	2.23642i
$652$	5.11370	−	1.90731i	0.200268	−	0.0746961i
$653$	−40.6404	+	2.90666i	−1.59038	+	0.113746i	−0.838256	−	0.545276i	$-0.816425\pi$
$653$	−40.6404	+	2.90666i	−1.59038	+	0.113746i	−0.752123	+	0.659022i	$0.770970\pi$
$654$	5.10188	+	4.37454i	0.199499	+	0.171058i
$655$	6.66520	−	20.5174i	0.260431	−	0.801683i
$656$	2.23868	−	0.321873i	0.0874056	−	0.0125670i
$657$	17.9525	−	6.90955i	0.700392	−	0.269567i
$658$	0.922588	+	12.8995i	0.0359662	+	0.502874i
$659$	−6.68835	+	14.6454i	−0.260541	+	0.570506i	−0.994019	−	0.109208i	$-0.965169\pi$
$659$	−6.68835	+	14.6454i	−0.260541	+	0.570506i	0.733478	+	0.679713i	$0.237896\pi$
$660$	1.30307	−	0.0627272i	0.0507220	−	0.00244165i
$661$	32.1809	−	9.44918i	1.25169	−	0.367530i	0.412297	−	0.911050i	$-0.364727\pi$
$661$	32.1809	−	9.44918i	1.25169	−	0.367530i	0.839397	+	0.543519i	$0.182908\pi$
$662$	−6.80424	−	0.486649i	−0.264454	−	0.0189141i
$663$	−6.74929	+	6.81989i	−0.262121	+	0.264863i
$664$	−7.95877	+	3.63465i	−0.308860	+	0.141052i
$665$	16.1633	−	3.03647i	0.626785	−	0.117749i
$666$	−7.46844	−	11.3595i	−0.289396	−	0.440171i
$667$	12.7761	+	3.81924i	0.494691	+	0.147882i
$668$	13.5690	+	13.5690i	0.525002	+	0.525002i
$669$	−6.56620	−	44.0411i	−0.253864	−	1.70273i
$670$	32.8481	+	0.936484i	1.26903	+	0.0361795i
$671$	−0.662455	+	2.25611i	−0.0255738	+	0.0870963i
$672$	1.37176	+	6.15160i	0.0529166	+	0.237303i
$673$	−8.67412	+	15.8855i	−0.334363	+	0.612340i	−0.989726	−	0.142974i	$-0.954334\pi$
$673$	−8.67412	+	15.8855i	−0.334363	+	0.612340i	0.655364	+	0.755313i	$0.272515\pi$
$674$	19.8810	+	12.7767i	0.765786	+	0.492141i
$675$	8.06419	+	24.6975i	0.310391	+	0.950609i
$676$	−8.03569	+	9.27368i	−0.309065	+	0.356680i
$677$	9.10527	−	41.8562i	0.349944	−	1.60867i	−0.379883	−	0.925035i	$-0.624036\pi$
$677$	9.10527	−	41.8562i	0.349944	−	1.60867i	0.729827	−	0.683632i	$-0.239601\pi$
$678$	3.55151	−	9.67541i	0.136395	−	0.371582i
$679$	−31.5729	+	4.53950i	−1.21166	+	0.174210i
$680$	−1.65443	−	14.4117i	−0.0634446	−	0.552662i
$681$	−6.86537	+	15.2424i	−0.263082	+	0.584092i
$682$	−2.97345	+	1.10904i	−0.113859	+	0.0424673i
$683$	−10.2394	−	47.0700i	−0.391802	−	1.80108i	−0.575165	−	0.818038i	$-0.695062\pi$
$683$	−10.2394	−	47.0700i	−0.391802	−	1.80108i	0.183363	−	0.983045i	$-0.441302\pi$
$684$	−4.62365	−	3.92293i	−0.176790	−	0.149997i
$685$	−12.6896	+	21.7422i	−0.484843	+	0.830728i
$686$	0.777827	−	2.64904i	0.0296976	−	0.101141i
$687$	−1.33763	−	0.0886764i	−0.0510336	−	0.00338322i
$688$	−1.29916	−	1.73547i	−0.0495300	−	0.0661643i
$689$	−5.23883			−0.199583
$690$	−17.9622	+	4.72870i	−0.683808	+	0.180019i
$691$	20.3401			0.773775			0.386888	−	0.922127i	$-0.373550\pi$
$691$	20.3401			0.773775			0.386888	+	0.922127i	$0.373550\pi$
$692$	3.50003	+	4.67549i	0.133051	+	0.177736i
$693$	−0.818980	−	3.58479i	−0.0311105	−	0.136175i
$694$	3.89305	−	13.2585i	0.147778	−	0.503286i
$695$	5.81239	+	22.1074i	0.220477	+	0.838581i
$696$	−2.62473	−	4.03782i	−0.0994902	−	0.153053i
$697$	3.11888	+	14.3373i	0.118136	+	0.543062i
$698$	14.6065	−	5.44796i	0.552866	−	0.206208i
$699$	−13.4344	−	6.05101i	−0.508135	−	0.228870i
$700$	−16.4396	+	7.79565i	−0.621358	+	0.294648i
$701$	20.0004	−	2.87563i	0.755405	−	0.108611i	0.246156	−	0.969230i	$-0.420832\pi$
$701$	20.0004	−	2.87563i	0.755405	−	0.108611i	0.509249	+	0.860619i	$0.329923\pi$
$702$	−1.01072	−	4.32040i	−0.0381470	−	0.163063i
$703$	−1.94693	+	8.94991i	−0.0734300	+	0.337552i
$704$	0.220584	−	0.254568i	0.00831358	−	0.00959438i
$705$	11.4029	+	7.70939i	0.429459	+	0.290353i
$706$	−14.2526	−	9.15962i	−0.536405	−	0.344727i
$707$	15.5330	−	28.4465i	0.584177	−	1.06984i
$708$	23.9630	−	5.34355i	0.900584	−	0.200823i
$709$	−1.44203	+	4.91112i	−0.0541567	+	0.184441i	−0.982129	−	0.188208i	$-0.939732\pi$
$709$	−1.44203	+	4.91112i	−0.0541567	+	0.184441i	0.927972	+	0.372649i	$0.121550\pi$
$710$	−8.08536	−	8.55990i	−0.303438	−	0.321247i
$711$	−4.78833	−	10.2027i	−0.179576	−	0.382630i
$712$	−4.25121	−	4.25121i	−0.159321	−	0.159321i
$713$	38.1298	−	24.2424i	1.42797	−	0.907883i
$714$	−39.1714	+	11.7235i	−1.46595	+	0.438740i
$715$	−0.118749	−	0.632107i	−0.00444096	−	0.0236395i
$716$	−15.4355	+	7.04915i	−0.576851	+	0.263439i
$717$	17.2539	+	17.0753i	0.644358	+	0.637688i
$718$	19.0780	+	1.36448i	0.711983	+	0.0509220i
$719$	−10.1298	+	2.97439i	−0.377779	+	0.110926i	−0.465109	−	0.885254i	$-0.653985\pi$
$719$	−10.1298	+	2.97439i	−0.377779	+	0.110926i	0.0873298	+	0.996179i	$0.472167\pi$
$720$	6.05057	+	2.89665i	0.225492	+	0.107952i
$721$	−17.9762	+	39.3624i	−0.669470	+	1.46593i
$722$	−1.06400	−	14.8767i	−0.0395981	−	0.553654i
$723$	30.8282	−	2.36615i	1.14651	−	0.0879981i
$724$	15.4237	−	2.21760i	0.573219	−	0.0824164i
$725$	9.68794	−	9.97098i	0.359801	−	0.370313i
$726$	12.2738	−	14.3145i	0.455522	−	0.531261i
$727$	−16.0544	+	1.14824i	−0.595426	+	0.0425857i	−0.365800	−	0.930693i	$-0.619205\pi$
$727$	−16.0544	+	1.14824i	−0.595426	+	0.0425857i	−0.229625	+	0.973279i	$0.573750\pi$
$728$	2.91134	−	1.08587i	0.107902	−	0.0402452i
$729$	−24.8982	−	10.4442i	−0.922155	−	0.386822i
$730$	14.1280	+	2.44410i	0.522900	+	0.0904601i
$731$	10.6288	−	9.20991i	0.393120	−	0.340641i
$732$	−8.50488	+	8.59384i	−0.314349	+	0.317638i
$733$	−15.2221	−	5.67755i	−0.562241	−	0.209705i	0.0522430	−	0.998634i	$-0.483363\pi$
$733$	−15.2221	−	5.67755i	−0.562241	−	0.209705i	−0.614484	+	0.788929i	$0.710636\pi$
$734$	−0.220616	+	1.53442i	−0.00814308	+	0.0566363i
$735$	14.0312	+	19.6832i	0.517549	+	0.726026i
$736$	−2.31892	+	4.19793i	−0.0854765	+	0.154738i
$737$	−3.50036	+	3.50036i	−0.128937	+	0.128937i
$738$	−6.38162	−	2.30487i	−0.234911	−	0.0848434i
$739$	7.58290	−	3.46300i	0.278942	−	0.127388i	−0.271032	−	0.962570i	$-0.587365\pi$
$739$	7.58290	−	3.46300i	0.278942	−	0.127388i	0.549974	+	0.835182i	$0.314638\pi$
$740$	−0.434547	−	10.1236i	−0.0159743	−	0.372149i
$741$	−1.60308	+	2.52322i	−0.0588908	+	0.0926926i
$742$	−19.5940	−	10.6991i	−0.719318	−	0.392777i
$743$	2.71009	+	12.4581i	0.0994235	+	0.457042i	0.999761	+	0.0218506i	$0.00695581\pi$
$743$	2.71009	+	12.4581i	0.0994235	+	0.457042i	−0.900338	+	0.435192i	$0.856681\pi$
$744$	−16.1642	−	2.23829i	−0.592610	−	0.0820598i
$745$	−11.6891	−	27.6552i	−0.428255	−	1.01321i
$746$	−9.26943	−	14.4235i	−0.339378	−	0.528082i
$747$	26.1995	+	1.60001i	0.958590	+	0.0585411i
$748$	1.74937	+	1.30956i	0.0639632	+	0.0478822i
$749$	−58.3782	+	37.5174i	−2.13309	+	1.37086i
$750$	−4.28460	+	18.8850i	−0.156452	+	0.689582i
$751$	12.2731	−	26.8742i	0.447850	−	0.980655i	−0.542240	−	0.840223i	$-0.682424\pi$
$751$	12.2731	−	26.8742i	0.447850	−	0.980655i	0.990090	−	0.140431i	$-0.0448489\pi$
$752$	3.47276	−	0.755452i	0.126638	−	0.0275485i
$753$	3.65735	−	17.2440i	0.133281	−	0.628406i
$754$	−1.79436	+	1.55482i	−0.0653467	+	0.0566232i
$755$	−10.0880	+	10.9929i	−0.367141	+	0.400074i
$756$	5.04321	−	18.2231i	0.183420	−	0.662767i
$757$	10.3361	−	7.73747i	0.375670	−	0.281223i	−0.394713	−	0.918805i	$-0.629156\pi$
$757$	10.3361	−	7.73747i	0.375670	−	0.281223i	0.770383	+	0.637581i	$0.220065\pi$
$758$	5.20225	+	5.20225i	0.188954	+	0.188954i
$759$	1.34016	−	2.45619i	0.0486446	−	0.0891540i
$760$	−1.45811	−	4.27789i	−0.0528910	−	0.155175i
$761$	−1.29395	−	0.186043i	−0.0469058	−	0.00674404i	0.118822	−	0.992916i	$-0.462088\pi$
$761$	−1.29395	−	0.186043i	−0.0469058	−	0.00674404i	−0.165728	+	0.986172i	$0.552997\pi$
$762$	0.927623	−	13.9926i	0.0336042	−	0.506898i
$763$	12.3921	−	6.76660i	0.448624	−	0.244967i
$764$	−15.0069	−	17.3188i	−0.542929	−	0.626574i
$765$	−15.9437	+	40.4932i	−0.576444	+	1.46403i
$766$	22.1175	+	14.2141i	0.799139	+	0.513575i
$767$	−4.22992	−	11.3409i	−0.152734	−	0.409495i
$768$	1.61967	−	0.613725i	0.0584449	−	0.0221459i
$769$	6.68029	+	10.3947i	0.240897	+	0.374844i	0.940559	−	0.339631i	$-0.110302\pi$
$769$	6.68029	+	10.3947i	0.240897	+	0.374844i	−0.699661	+	0.714475i	$0.746666\pi$
$770$	0.846798	−	2.60669i	0.0305165	−	0.0939387i
$771$	14.3276	+	30.9459i	0.515994	+	1.11449i
$772$	−15.0886	−	3.28232i	−0.543050	−	0.118133i
$773$	23.4774	−	1.67914i	0.844423	−	0.0603943i	0.357579	−	0.933883i	$-0.383602\pi$
$773$	23.4774	−	1.67914i	0.844423	−	0.0603943i	0.486844	+	0.873489i	$0.338148\pi$
$774$	0.992496	+	6.42745i	0.0356745	+	0.231030i
$775$	−4.03667	−	46.9341i	−0.145002	−	1.68592i
$776$	2.46962	+	8.41074i	0.0886541	+	0.301928i
$777$	−27.8763	+	6.21619i	−1.00006	+	0.223005i
$778$	−24.8055	+	13.5448i	−0.889320	+	0.485605i
$779$	1.89901	+	4.15826i	0.0680392	+	0.148985i
$780$	1.00541	−	3.15065i	0.0359995	−	0.112811i
$781$	1.77375			0.0634697
$782$	−28.2376	−	13.0626i	−1.00977	−	0.467119i
$783$	1.25549	+	14.3931i	0.0448676	+	0.514369i
$784$	6.17775	+	0.888227i	0.220634	+	0.0317224i
$785$	−3.14457	−	3.32914i	−0.112235	−	0.118822i
$786$	0.0869396	+	16.7101i	0.00310103	+	0.596029i
$787$	−0.806412	+	11.2751i	−0.0287455	+	0.401914i	0.962626	+	0.270834i	$0.0872993\pi$
$787$	−0.806412	+	11.2751i	−0.0287455	+	0.401914i	−0.991372	+	0.131081i	$0.958155\pi$
$788$	−7.51501	−	4.10351i	−0.267711	−	0.146181i
$789$	3.09043	−	10.7313i	0.110022	−	0.382043i
$790$	0.837826	−	8.35859i	0.0298085	−	0.297385i
$791$	−16.3644	−	14.1798i	−0.581850	−	0.504176i
$792$	−0.943084	+	0.362975i	−0.0335110	+	0.0128977i
$793$	4.77188	+	3.57218i	0.169454	+	0.126852i
$794$	3.55753	+	24.7432i	0.126252	+	0.878103i
$795$	−21.8380	+	9.36453i	−0.774515	+	0.332126i
$796$	−13.3963	+	15.4602i	−0.474820	+	0.547971i
$797$	6.69717	+	17.9558i	0.237226	+	0.636027i	0.999943	−	0.0107054i	$-0.00340769\pi$
$797$	6.69717	+	17.9558i	0.237226	+	0.636027i	−0.762717	+	0.646733i	$0.776135\pi$
$798$	−11.1489	+	6.16326i	−0.394666	+	0.218177i
$799$	6.49567	+	22.1222i	0.229800	+	0.782628i
$800$	2.76348	+	4.16692i	0.0977037	+	0.147323i
$801$	5.26122	+	17.2519i	0.185896	+	0.609567i
$802$	−9.77190	+	26.1995i	−0.345058	+	0.925136i
$803$	−1.72905	+	1.29435i	−0.0610169	+	0.0456767i
$804$	−24.3857	+	7.29831i	−0.860017	+	0.257391i
$805$	−4.08143	+	38.8084i	−0.143851	+	1.36782i
$806$			8.04509i			0.283376i
$807$	−28.1067	+	37.9561i	−0.989402	+	1.33612i
$808$	−8.34534	−	3.11265i	−0.293588	−	0.109503i
$809$	15.4750	+	4.54386i	0.544071	+	0.159754i	0.542208	−	0.840245i	$-0.317589\pi$
$809$	15.4750	+	4.54386i	0.544071	+	0.159754i	0.00186349	+	0.999998i	$0.499407\pi$
$810$	−11.9360	−	16.2029i	−0.419387	−	0.569310i
$811$	53.3838	−	15.6749i	1.87456	−	0.550420i	0.877006	−	0.480479i	$-0.159537\pi$
$811$	53.3838	−	15.6749i	1.87456	−	0.550420i	0.997551	−	0.0699406i	$-0.0222810\pi$
$812$	−9.88654	+	2.15069i	−0.346950	+	0.0754743i
$813$	−38.9533	+	29.4776i	−1.36615	+	1.03382i
$814$	1.15359	+	0.999590i	0.0404332	+	0.0350356i
$815$	−9.55746	−	7.58907i	−0.334783	−	0.265833i
$816$	4.72094	+	10.1967i	0.165266	+	0.356956i
$817$	2.62587	−	3.50775i	0.0918676	−	0.122721i
$818$	−16.7478	−	3.64326i	−0.585573	−	0.127384i
$819$	−9.24019	−	1.23054i	−0.322878	−	0.0429987i
$820$	−3.20157	−	3.91489i	−0.111804	−	0.136714i
$821$	−20.4625	+	31.8403i	−0.714148	+	1.11124i	0.274588	+	0.961562i	$0.411459\pi$
$821$	−20.4625	+	31.8403i	−0.714148	+	1.11124i	−0.988736	+	0.149673i	$0.952178\pi$
$822$	4.04583	−	19.0757i	0.141115	−	0.665341i
$823$	−34.0361	−	2.43431i	−1.18643	−	0.0848548i	−0.535861	−	0.844306i	$-0.680013\pi$
$823$	−34.0361	−	2.43431i	−1.18643	−	0.0848548i	−0.650564	+	0.759451i	$0.725467\pi$
$824$	11.4102	+	3.35034i	0.397493	+	0.116714i
$825$	−1.62491	−	2.42267i	−0.0565721	−	0.0843464i
$826$	7.34063	−	51.0552i	0.255413	−	1.77644i
$827$	14.3793	−	14.3793i	0.500018	−	0.500018i	−0.411426	−	0.911443i	$-0.634969\pi$
$827$	14.3793	−	14.3793i	0.500018	−	0.500018i	0.911443	+	0.411426i	$0.134969\pi$
$828$	12.0604	−	7.84520i	0.419127	−	0.272640i
$829$		−	15.7968i		−	0.548645i	−0.961638	−	0.274322i	$-0.911546\pi$
$829$		−	15.7968i		−	0.548645i	0.961638	−	0.274322i	$-0.0884535\pi$
$830$	16.1505	+	11.0420i	0.560591	+	0.383274i
$831$	5.46381	−	4.78441i	0.189537	−	0.165969i
$832$	−0.409235	−	0.749459i	−0.0141877	−	0.0259828i
$833$	−2.88851	+	40.3866i	−0.100081	+	1.39931i
$834$	−9.65011	−	14.8455i	−0.334156	−	0.514056i
$835$	10.3121	−	41.6515i	0.356866	−	1.44141i
$836$	0.619302	+	0.282826i	0.0214190	+	0.00978173i
$837$	39.6440	+	28.7226i	1.37030	+	0.992800i
$838$	−6.18696	+	28.4410i	−0.213725	+	0.982479i
$839$	−2.98752	−	20.7786i	−0.103141	−	0.717358i	−0.974119	−	0.226037i	$-0.927423\pi$
$839$	−2.98752	−	20.7786i	−0.103141	−	0.717358i	0.870978	−	0.491322i	$-0.163486\pi$
$840$	10.1949	−	9.73055i	0.351757	−	0.335736i
$841$	−17.8926	+	11.4989i	−0.616985	+	0.396512i
$842$	0.198417	+	2.77423i	0.00683789	+	0.0956063i
$843$	−12.7798	−	16.8879i	−0.440159	−	0.581651i
$844$	13.2221	−	20.5741i	0.455125	−	0.708189i
$845$	27.0368	+	4.67729i	0.930095	+	0.160904i
$846$	−10.2608	−	2.89720i	−0.352772	−	0.0996079i
$847$	−18.9852	−	34.7689i	−0.652340	−	1.19467i
$848$	−2.14400	+	5.74829i	−0.0736253	+	0.197397i
$849$	7.34780	+	49.2835i	0.252176	+	1.69140i
$850$	−25.6847	+	19.8106i	−0.880978	+	0.679499i
$851$	−19.0232	−	10.5083i	−0.652106	−	0.360220i
$852$	8.02767	+	4.32937i	0.275023	+	0.148322i
$853$	−19.2062	−	25.6565i	−0.657609	−	0.878463i	0.340480	−	0.940252i	$-0.389410\pi$
$853$	−19.2062	−	25.6565i	−0.657609	−	0.878463i	−0.998089	+	0.0617890i	$0.980319\pi$
$854$	10.5522	+	23.1060i	0.361087	+	0.790671i
$855$	−2.17214	+	13.3836i	−0.0742855	+	0.457708i
$856$	12.4884	+	14.4124i	0.426846	+	0.492606i
$857$	20.8234	−	38.1352i	0.711314	−	1.30267i	−0.232630	−	0.972565i	$-0.574733\pi$
$857$	20.8234	−	38.1352i	0.711314	−	1.30267i	0.943943	−	0.330108i	$-0.107085\pi$
$858$	0.241030	+	0.436006i	0.00822864	+	0.0148850i
$859$	7.31450	+	3.34042i	0.249568	+	0.113974i	0.536272	−	0.844046i	$-0.319832\pi$
$859$	7.31450	+	3.34042i	0.249568	+	0.113974i	−0.286704	+	0.958019i	$0.592560\pi$
$860$	−1.82278	+	4.49176i	−0.0621563	+	0.153168i
$861$	−9.27871	+	10.8215i	−0.316218	+	0.368794i
$862$	6.86988	−	9.17708i	0.233989	−	0.312573i
$863$	−2.41048	+	3.22003i	−0.0820537	+	0.109611i	−0.839690	−	0.543066i	$-0.817263\pi$
$863$	−2.41048	+	3.22003i	−0.0820537	+	0.109611i	0.757636	+	0.652677i	$0.226354\pi$
$864$	−5.15418	−	0.659125i	−0.175349	−	0.0224239i
$865$	4.91070	−	12.1011i	0.166969	−	0.411450i
$866$	−3.38578	−	1.54624i	−0.115054	−	0.0525432i
$867$	−38.0274	+	21.0221i	−1.29148	+	0.713948i
$868$	−16.4303	+	30.0898i	−0.557680	+	1.02132i
$869$	0.828692	+	0.956362i	0.0281115	+	0.0324424i
$870$	−4.70049	+	9.68872i	−0.159362	+	0.328478i
$871$	5.21310	+	11.4151i	0.176639	+	0.386786i
$872$	−2.32527	−	3.10619i	−0.0787434	−	0.105189i
$873$	5.32224	−	25.7533i	0.180131	−	0.871616i
$874$	−9.46168	−	2.10669i	−0.320046	−	0.0712599i
$875$	33.9116	+	22.4758i	1.14642	+	0.759821i
$876$	−10.9846	+	1.63773i	−0.371136	+	0.0553337i
$877$	13.2078	−	35.4116i	0.445997	−	1.19576i	−0.498397	−	0.866949i	$-0.666078\pi$
$877$	13.2078	−	35.4116i	0.445997	−	1.19576i	0.944394	−	0.328815i	$-0.106649\pi$
$878$	−3.11635	−	5.70717i	−0.105172	−	0.192608i
$879$	−1.03963	+	1.63636i	−0.0350659	+	0.0551929i
$880$	−0.742176	−	0.128394i	−0.0250187	−	0.00432817i
$881$	27.5218	−	42.8248i	0.927233	−	1.44280i	0.0308497	−	0.999524i	$-0.490179\pi$
$881$	27.5218	−	42.8248i	0.927233	−	1.44280i	0.896384	−	0.443279i	$-0.146185\pi$
$882$	−15.1052	−	11.0642i	−0.508617	−	0.372551i
$883$	−3.56568	−	49.8547i	−0.119995	−	1.67774i	−0.599632	−	0.800276i	$-0.704686\pi$
$883$	−3.56568	−	49.8547i	−0.119995	−	1.67774i	0.479637	−	0.877467i	$-0.340768\pi$
$884$	4.66027	−	2.99497i	0.156742	−	0.100732i
$885$	−37.9045	−	39.7132i	−1.27414	−	1.33494i
$886$	1.17647	+	8.18254i	0.0395244	+	0.274898i
$887$	11.6797	−	53.6908i	0.392167	−	1.80276i	−0.181182	−	0.983450i	$-0.557992\pi$
$887$	11.6797	−	53.6908i	0.392167	−	1.80276i	0.573348	−	0.819312i	$-0.305644\pi$
$888$	2.78113	+	7.33964i	0.0933286	+	0.246302i
$889$	−26.7991	−	12.2387i	−0.898813	−	0.410474i
$890$	−3.23082	+	13.0495i	−0.108297	+	0.437420i
$891$	3.00904	+	0.368900i	0.100807	+	0.0123586i
$892$	−1.83400	+	25.6427i	−0.0614069	+	0.858580i
$893$	3.44260	+	6.30466i	0.115202	+	0.210977i
$894$	15.3210	+	17.4966i	0.512412	+	0.585175i
$895$	31.3227	+	21.4152i	1.04700	+	0.715833i
$896$		−	3.63886i		−	0.121566i
$897$	−4.64672	−	5.35912i	−0.155149	−	0.178936i
$898$	5.76183	−	5.76183i	0.192275	−	0.192275i
$899$	3.72811	−	25.9296i	0.124339	−	0.864800i
$900$	−1.44080	−	14.9306i	−0.0480267	−	0.497688i
$901$	−38.1888	−	11.2132i	−1.27225	−	0.373567i
$902$	0.759892	+	0.0543485i	0.0253016	+	0.00180961i
$903$	13.3661	+	2.83487i	0.444796	+	0.0943386i
$904$	−3.21710	+	5.00591i	−0.106999	+	0.166494i
$905$	−22.0577	−	26.9723i	−0.733224	−	0.896589i
$906$	4.74625	−	10.5376i	0.157684	−	0.350088i
$907$	22.6493	+	4.92706i	0.752059	+	0.163600i	0.572225	−	0.820097i	$-0.306080\pi$
$907$	22.6493	+	4.92706i	0.752059	+	0.163600i	0.179834	+	0.983697i	$0.442444\pi$
$908$	5.78404	−	7.72658i	0.191950	−	0.256415i
$909$	17.7076	+	20.0110i	0.587323	+	0.663725i
$910$	−5.44127	−	4.32062i	−0.180376	−	0.143227i
$911$	14.9893	+	12.9883i	0.496617	+	0.430321i	0.866814	−	0.498632i	$-0.166164\pi$
$911$	14.9893	+	12.9883i	0.496617	+	0.430321i	−0.370196	+	0.928954i	$0.620710\pi$
$912$	2.11253	+	2.79161i	0.0699527	+	0.0924395i
$913$	−2.87982	+	0.626467i	−0.0953082	+	0.0207330i
$914$	29.8362	−	8.76070i	0.986894	−	0.289778i
$915$	26.2769	+	6.36077i	0.868688	+	0.210281i
$916$	0.742622	+	0.218054i	0.0245369	+	0.00720469i
$917$	32.8931	+	12.2685i	1.08623	+	0.405141i
$918$	1.87973	−	33.6572i	0.0620405	−	1.11085i
$919$		−	53.0169i		−	1.74887i	−0.485146	−	0.874433i	$-0.661233\pi$
$919$		−	53.0169i		−	1.74887i	0.485146	−	0.874433i	$-0.338767\pi$
$920$	10.7161	−	0.407579i	0.353298	−	0.0134375i
$921$	−11.8458	−	39.5801i	−0.390332	−	1.30421i
$922$	−7.62575	+	5.70856i	−0.251141	+	0.188002i
$923$	1.57138	−	4.21304i	0.0517226	−	0.138674i
$924$	0.0110455	+	2.12298i	0.000363369	+	0.0698408i
$925$	−18.8826	+	12.5229i	−0.620857	+	0.411749i
$926$	4.35568	+	14.8341i	0.143136	+	0.487478i
$927$	−25.4877	−	24.9627i	−0.837125	−	0.819882i
$928$	0.971678	+	2.60517i	0.0318969	+	0.0855189i
$929$	−14.6371	+	16.8921i	−0.480228	+	0.554213i	−0.943228	−	0.332145i	$-0.892228\pi$
$929$	−14.6371	+	16.8921i	−0.480228	+	0.554213i	0.463000	+	0.886358i	$0.346773\pi$
$930$	14.3808	+	33.5359i	0.471565	+	1.09969i
$931$	1.79529	+	12.4865i	0.0588383	+	0.409229i
$932$	6.81005	+	5.09794i	0.223071	+	0.166989i
$933$	3.94005	+	51.3343i	0.128991	+	1.68061i
$934$	13.4380	+	11.6441i	0.439703	+	0.381005i
$935$	0.487340	−	4.86196i	0.0159377	−	0.159003i
$936$	0.0266557	+	2.56159i	0.000871270	+	0.0837282i
$937$	32.6432	+	17.8246i	1.06641	+	0.582303i	0.913875	−	0.405995i	$-0.133075\pi$
$937$	32.6432	+	17.8246i	1.06641	+	0.582303i	0.152533	+	0.988298i	$0.451257\pi$
$938$	−3.81501	+	53.3408i	−0.124564	+	1.74164i
$939$	−20.9489	+	0.108994i	−0.683642	+	0.00355687i
$940$	−5.45691	−	5.77719i	−0.177985	−	0.188431i
$941$	8.96640	+	1.28917i	0.292296	+	0.0420258i	0.286903	−	0.957960i	$-0.407374\pi$
$941$	8.96640	+	1.28917i	0.292296	+	0.0420258i	0.00539308	+	0.999985i	$0.498283\pi$
$942$	3.12214	+	1.68379i	0.101725	+	0.0548608i
$943$	−10.7437	+	1.49122i	−0.349864	+	0.0485607i
$944$	−14.1748			−0.461351
$945$	−40.7173	+	11.3875i	−1.32453	+	0.370437i
$946$	−0.303348	−	0.664240i	−0.00986271	−	0.0215963i
$947$	17.1639	−	9.37220i	0.557752	−	0.304556i	−0.175537	−	0.984473i	$-0.556166\pi$
$947$	17.1639	−	9.37220i	0.557752	−	0.304556i	0.733289	+	0.679917i	$0.237984\pi$
$948$	1.41622	+	6.35100i	0.0459967	+	0.206271i
$949$	1.54258	+	5.25355i	0.0500743	+	0.170537i
$950$	−6.50742	+	7.73212i	−0.211128	+	0.250863i
$951$	4.60086	−	33.2260i	0.149193	−	1.07743i
$952$	23.5466	−	1.68409i	0.763151	−	0.0545816i
$953$	42.5238	+	9.25048i	1.37748	+	0.299653i	0.839525	−	0.543321i	$-0.182833\pi$
$953$	42.5238	+	9.25048i	1.37748	+	0.299653i	0.537955	+	0.842973i	$0.319197\pi$
$954$	13.7837	−	12.1970i	0.446262	−	0.394893i
$955$	−15.8318	+	48.7349i	−0.512305	+	1.57703i
$956$	−7.57709	−	11.7902i	−0.245061	−	0.381322i
$957$	−0.574802	−	1.51695i	−0.0185807	−	0.0490361i
$958$	−10.6262	−	28.4899i	−0.343316	−	0.920465i
$959$	−34.4640	−	22.1487i	−1.11290	−	0.715218i
$960$	−3.04557	−	2.39259i	−0.0982953	−	0.0772206i
$961$	−37.8275	−	43.6553i	−1.22024	−	1.40823i
$962$	3.39621	−	1.85447i	0.109498	−	0.0597906i
$963$	−12.7421	−	55.7741i	−0.410609	−	1.79729i
$964$	−17.6693	−	2.54046i	−0.569090	−	0.0818229i
$965$	11.1395	+	32.6819i	0.358594	+	1.05207i
$966$	−6.43460	−	29.5338i	−0.207030	−	0.950234i
$967$	4.95994	+	4.95994i	0.159501	+	0.159501i	0.782345	−	0.622845i	$-0.214023\pi$
$967$	4.95994	+	4.95994i	0.159501	+	0.159501i	−0.622845	+	0.782345i	$0.714023\pi$
$968$	−8.71512	+	6.52406i	−0.280115	+	0.209691i
$969$	−17.0865	+	14.9619i	−0.548898	+	0.480645i
$970$	13.2528	−	14.4416i	0.425523	−	0.463692i
$971$	8.36547	−	7.24872i	0.268461	−	0.232623i	−0.510218	−	0.860045i	$-0.670435\pi$
$971$	8.36547	−	7.24872i	0.268461	−	0.232623i	0.778679	+	0.627422i	$0.215890\pi$
$972$	12.7180	+	9.01406i	0.407929	+	0.289126i
$973$	−36.3489	+	7.90723i	−1.16529	+	0.253494i
$974$	7.97672	−	17.4666i	0.255591	−	0.559666i
$975$	−7.19388	+	1.71325i	−0.230389	+	0.0548679i
$976$	5.87247	−	3.77401i	0.187973	−	0.120803i
$977$	−13.2957	−	9.95300i	−0.425366	−	0.318425i	0.365059	−	0.930985i	$-0.381049\pi$
$977$	−13.2957	−	9.95300i	−0.425366	−	0.318425i	−0.790424	+	0.612560i	$0.790140\pi$
$978$	8.87426	+	3.25744i	0.283768	+	0.104161i
$979$	−1.09487	−	1.70365i	−0.0349921	−	0.0544488i
$980$	−5.43337	−	12.8548i	−0.173563	−	0.410632i
$981$	1.77639	+	11.5040i	0.0567158	+	0.367294i
$982$	−0.722827	−	3.32278i	−0.0230664	−	0.106034i
$983$	−10.2417	−	5.59242i	−0.326661	−	0.178370i	0.307547	−	0.951533i	$-0.400492\pi$
$983$	−10.2417	−	5.59242i	−0.326661	−	0.178370i	−0.634208	+	0.773163i	$0.718674\pi$
$984$	3.30648	+	2.10072i	0.105407	+	0.0669684i
$985$	0.821077	+	19.1284i	0.0261617	+	0.609483i
$986$	−16.4081	+	7.49331i	−0.522539	+	0.238636i
$987$	−13.3301	+	18.0014i	−0.424302	+	0.572991i
$988$	1.22042	−	1.22042i	0.0388266	−	0.0388266i
$989$	6.18984	+	8.35336i	0.196826	+	0.265621i
$990$	1.78410	+	1.38664i	0.0567025	+	0.0440703i
$991$	7.20586	−	50.1179i	0.228902	−	1.59205i	−0.473846	−	0.880608i	$-0.657135\pi$
$991$	7.20586	−	50.1179i	0.228902	−	1.59205i	0.702748	−	0.711439i	$-0.251956\pi$
$992$	8.82745	+	3.29247i	0.280272	+	0.104536i
$993$	−8.39809	−	8.31116i	−0.266505	−	0.263747i
$994$	14.4814	−	12.5482i	0.459321	−	0.398004i
$995$	45.0731	+	7.79751i	1.42891	+	0.247198i
$996$	−14.5626	−	4.19380i	−0.461435	−	0.132886i
$997$	−32.5371	+	12.1357i	−1.03046	+	0.384342i	−0.807113	−	0.590397i	$-0.798971\pi$
$997$	−32.5371	+	12.1357i	−1.03046	+	0.384342i	−0.223348	+	0.974739i	$0.571698\pi$
$998$	13.6207	−	0.974168i	0.431154	−	0.0308368i
$999$	2.98686	−	23.3565i	0.0945002	−	0.738966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.14	✓	960
3.2	odd	2	inner	690.2.x.a.77.33	yes	960
5.3	odd	4	inner	690.2.x.a.353.24	yes	960
15.8	even	4	inner	690.2.x.a.353.29	yes	960
23.3	even	11	inner	690.2.x.a.647.29	yes	960
69.26	odd	22	inner	690.2.x.a.647.24	yes	960
115.3	odd	44	inner	690.2.x.a.233.33	yes	960
345.233	even	44	inner	690.2.x.a.233.14	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.14	✓	960	1.1	even	1	trivial
690.2.x.a.77.33	yes	960	3.2	odd	2	inner
690.2.x.a.233.14	yes	960	345.233	even	44	inner
690.2.x.a.233.33	yes	960	115.3	odd	44	inner
690.2.x.a.353.24	yes	960	5.3	odd	4	inner
690.2.x.a.353.29	yes	960	15.8	even	4	inner
690.2.x.a.647.24	yes	960	69.26	odd	22	inner
690.2.x.a.647.29	yes	960	23.3	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(0.114573 - 1.72826i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(2.16257 - 0.568575i) q^{5} +(-1.45220 + 0.943986i) q^{6} +(0.773495 + 3.55570i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-2.97375 - 0.396023i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(0.114573 - 1.72826i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(2.16257 - 0.568575i) q^{5} +(-1.45220 + 0.943986i) q^{6} +(0.773495 + 3.55570i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-2.97375 - 0.396023i) q^{9} +(-1.75115 - 1.39049i) q^{10} +(0.333413 - 0.0479375i) q^{11} +(1.62597 + 0.596838i) q^{12} +(0.181512 - 0.834395i) q^{13} +(2.38294 - 2.75006i) q^{14} +(-0.734872 - 3.80263i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(3.10909 - 5.69387i) q^{17} +(1.46507 + 2.61793i) q^{18} +(0.569440 - 1.93934i) q^{19} +(-0.0637232 + 2.23516i) q^{20} +(6.23378 - 0.929411i) q^{21} +(-0.238183 - 0.238183i) q^{22} +(4.02180 + 2.61249i) q^{23} +(-0.496615 - 1.65933i) q^{24} +(4.35344 - 2.45917i) q^{25} +(-0.776743 + 0.354727i) q^{26} +(-1.02514 + 5.09402i) q^{27} +(-3.62959 - 0.259593i) q^{28} +(2.66785 - 0.783351i) q^{29} +(-2.60377 + 2.86712i) q^{30} +(3.91382 - 8.57008i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-0.0446483 - 0.581715i) q^{33} +(-6.42139 + 0.923256i) q^{34} +(3.69442 + 7.24967i) q^{35} +(1.21778 - 2.74172i) q^{36} +(-4.52001 + 0.323278i) q^{37} +(-1.89377 + 0.706340i) q^{38} +(-1.42125 - 0.409298i) q^{39} +(1.82753 - 1.28847i) q^{40} +(-1.70928 + 1.48110i) q^{41} +(-4.47980 - 4.43342i) q^{42} +(2.03119 + 0.757595i) q^{43} +(-0.0479375 + 0.333413i) q^{44} +(-6.65611 + 0.834370i) q^{45} +(-0.318773 - 4.78523i) q^{46} +(-2.51304 + 2.51304i) q^{47} +(-1.03075 + 1.39196i) q^{48} +(-5.67727 + 2.59272i) q^{49} +(-4.57759 - 2.01139i) q^{50} +(-9.48426 - 6.02567i) q^{51} +(0.749459 + 0.409235i) q^{52} +(-1.30411 - 5.99490i) q^{53} +(4.69232 - 2.23207i) q^{54} +(0.693773 - 0.293239i) q^{55} +(1.96731 + 3.06120i) q^{56} +(-3.28643 - 1.20633i) q^{57} +(-2.22589 - 1.66628i) q^{58} +(11.9246 - 7.66349i) q^{59} +(3.85563 + 0.366219i) q^{60} +(-2.89985 + 6.34979i) q^{61} +(-9.20617 + 2.00268i) q^{62} +(-0.892039 - 10.8801i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-0.0818845 - 1.90764i) q^{65} +(-0.438930 + 0.384352i) q^{66} +(-11.7648 + 8.80705i) q^{67} +(4.58730 + 4.58730i) q^{68} +(4.97584 - 6.65139i) q^{69} +(3.58967 - 7.30210i) q^{70} +(5.21223 + 0.749406i) q^{71} +(-2.92465 + 0.668164i) q^{72} +(-5.62775 + 3.07298i) q^{73} +(2.96754 + 3.42472i) q^{74} +(-3.75129 - 7.80563i) q^{75} +(1.70035 + 1.09275i) q^{76} +(0.428344 + 1.14844i) q^{77} +(0.524065 + 1.38305i) q^{78} +(2.03108 + 3.16043i) q^{79} +(-2.12667 - 0.690859i) q^{80} +(8.68633 + 2.35534i) q^{81} +(2.21001 + 0.480758i) q^{82} +(-8.72715 + 0.624178i) q^{83} +(-0.864496 + 6.24312i) q^{84} +(3.48624 - 14.0812i) q^{85} +(-0.610761 - 2.08006i) q^{86} +(-1.04817 - 4.70048i) q^{87} +(0.295638 - 0.161431i) q^{88} +(-2.49752 - 5.46881i) q^{89} +(4.65681 + 4.82847i) q^{90} +3.10725 q^{91} +(-3.63974 + 3.12287i) q^{92} +(-14.3629 - 7.74599i) q^{93} +(3.51780 + 0.505784i) q^{94} +(0.128798 - 4.51772i) q^{95} +(1.73203 - 0.00901144i) q^{96} +(-0.625347 + 8.74349i) q^{97} +(5.47784 + 2.99113i) q^{98} +(-1.01047 + 0.0105149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

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