LMFDB - Embedded newform 380.2.bj.a.347.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			347.8
Character	$\chi$	$=$	380.347
Dual form			380.2.bj.a.23.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31289 + 0.525665i) q^{2} +(1.78355 - 1.24886i) q^{3} +(1.44735 - 1.38028i) q^{4} +(-1.31769 - 1.80657i) q^{5} +(-1.68512 + 2.57716i) q^{6} +(-4.05211 - 1.08576i) q^{7} +(-1.17465 + 2.57297i) q^{8} +(0.595352 - 1.63572i) q^{9} +O(q^{10})$	\(q+(-1.31289 + 0.525665i) q^{2} +(1.78355 - 1.24886i) q^{3} +(1.44735 - 1.38028i) q^{4} +(-1.31769 - 1.80657i) q^{5} +(-1.68512 + 2.57716i) q^{6} +(-4.05211 - 1.08576i) q^{7} +(-1.17465 + 2.57297i) q^{8} +(0.595352 - 1.63572i) q^{9} +(2.67963 + 1.67916i) q^{10} +(0.636513 + 0.367491i) q^{11} +(0.857659 - 4.26933i) q^{12} +(-3.61545 - 2.53156i) q^{13} +(5.89071 - 0.704570i) q^{14} +(-4.60631 - 1.57650i) q^{15} +(0.189663 - 3.99550i) q^{16} +(-3.04089 - 1.41799i) q^{17} +(0.0782073 + 2.46047i) q^{18} +(-2.00344 + 3.87121i) q^{19} +(-4.40073 - 0.795965i) q^{20} +(-8.58310 + 3.12399i) q^{21} +(-1.02885 - 0.147882i) q^{22} +(7.79780 + 0.682219i) q^{23} +(1.11823 + 6.05600i) q^{24} +(-1.52739 + 4.76100i) q^{25} +(6.07743 + 1.42315i) q^{26} +(0.709658 + 2.64848i) q^{27} +(-7.36348 + 4.02156i) q^{28} +(2.65230 - 7.28713i) q^{29} +(6.87628 - 0.351602i) q^{30} +(-2.23860 + 1.29246i) q^{31} +(1.85129 + 5.34535i) q^{32} +(1.59420 - 0.139474i) q^{33} +(4.73774 + 0.263175i) q^{34} +(3.37793 + 8.75111i) q^{35} +(-1.39606 - 3.18921i) q^{36} +(-4.73432 - 4.73432i) q^{37} +(0.595338 - 6.13560i) q^{38} -9.60989 q^{39} +(6.19608 - 1.26830i) q^{40} +(1.21984 - 6.91803i) q^{41} +(9.62648 - 8.61329i) q^{42} +(-0.898247 - 10.2670i) q^{43} +(1.42850 - 0.346676i) q^{44} +(-3.73952 + 1.07982i) q^{45} +(-10.5963 + 3.20335i) q^{46} +(-1.71365 + 0.799087i) q^{47} +(-4.65153 - 7.36304i) q^{48} +(9.17854 + 5.29923i) q^{49} +(-0.497401 - 7.05355i) q^{50} +(-7.19444 + 1.26857i) q^{51} +(-8.72709 + 1.32626i) q^{52} +(0.729246 - 8.33532i) q^{53} +(-2.32391 - 3.10412i) q^{54} +(-0.174829 - 1.63414i) q^{55} +(7.55344 - 9.15059i) q^{56} +(1.26134 + 9.40650i) q^{57} +(0.348414 + 10.9614i) q^{58} +(5.52905 - 2.01241i) q^{59} +(-8.84297 + 4.07623i) q^{60} +(5.21429 - 4.37531i) q^{61} +(2.25963 - 2.87360i) q^{62} +(-4.18842 + 5.98169i) q^{63} +(-5.24039 - 6.04469i) q^{64} +(0.190595 + 9.86737i) q^{65} +(-2.01969 + 1.02113i) q^{66} +(3.86215 - 1.80095i) q^{67} +(-6.35846 + 2.14494i) q^{68} +(14.7598 - 8.52155i) q^{69} +(-9.03499 - 9.71358i) q^{70} +(1.55696 - 1.85551i) q^{71} +(3.50932 + 3.45322i) q^{72} +(-2.94518 - 4.20615i) q^{73} +(8.70430 + 3.72697i) q^{74} +(3.22163 + 10.3990i) q^{75} +(2.44366 + 8.36831i) q^{76} +(-2.18021 - 2.18021i) q^{77} +(12.6167 - 5.05158i) q^{78} +(-0.591642 + 3.35537i) q^{79} +(-7.46807 + 4.92219i) q^{80} +(8.57362 + 7.19412i) q^{81} +(2.03506 + 9.72383i) q^{82} +(0.616624 - 2.30127i) q^{83} +(-8.11080 + 16.3686i) q^{84} +(1.44525 + 7.36205i) q^{85} +(6.57630 + 13.0073i) q^{86} +(-4.37006 - 16.3093i) q^{87} +(-1.69323 + 1.20606i) q^{88} +(-2.79224 + 0.492347i) q^{89} +(4.34195 - 3.38342i) q^{90} +(11.9015 + 14.1837i) q^{91} +(12.2278 - 9.77572i) q^{92} +(-2.37857 + 5.10085i) q^{93} +(1.82978 - 1.94992i) q^{94} +(9.63351 - 1.48170i) q^{95} +(9.97743 + 7.22171i) q^{96} +(1.00171 + 0.467106i) q^{97} +(-14.8360 - 2.13247i) q^{98} +(0.980060 - 0.822368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.31289	+	0.525665i	−0.928352	+	0.371701i
$2$	−1.31289	+	0.525665i	−0.928352	+	0.371701i
$3$	1.78355	−	1.24886i	1.02973	−	0.721027i	0.0687501	−	0.997634i	$-0.478099\pi$
$3$	1.78355	−	1.24886i	1.02973	−	0.721027i	0.960983	+	0.276607i	$0.0892100\pi$
$4$	1.44735	−	1.38028i	0.723677	−	0.690139i
$5$	−1.31769	−	1.80657i	−0.589289	−	0.807922i
$5$	−1.31769	−	1.80657i	−0.589289	−	0.807922i
$6$	−1.68512	+	2.57716i	−0.687949	+	1.05212i
$7$	−4.05211	−	1.08576i	−1.53155	−	0.410378i	−0.608028	−	0.793916i	$-0.708039\pi$
$7$	−4.05211	−	1.08576i	−1.53155	−	0.410378i	−0.923525	+	0.383537i	$0.874706\pi$
$8$	−1.17465	+	2.57297i	−0.415302	+	0.909684i
$9$	0.595352	−	1.63572i	0.198451	−	0.545238i
$10$	2.67963	+	1.67916i	0.847373	+	0.530997i
$11$	0.636513	+	0.367491i	0.191916	+	0.110803i	0.592879	−	0.805291i	$-0.297991\pi$
$11$	0.636513	+	0.367491i	0.191916	+	0.110803i	−0.400963	+	0.916094i	$0.631324\pi$
$12$	0.857659	−	4.26933i	0.247585	−	1.23245i
$13$	−3.61545	−	2.53156i	−1.00274	−	0.702130i	−0.0477829	−	0.998858i	$-0.515216\pi$
$13$	−3.61545	−	2.53156i	−1.00274	−	0.702130i	−0.954962	+	0.296728i	$0.904104\pi$
$14$	5.89071	−	0.704570i	1.57436	−	0.188304i
$15$	−4.60631	−	1.57650i	−1.18934	−	0.407051i
$16$	0.189663	−	3.99550i	0.0474158	−	0.998875i
$17$	−3.04089	−	1.41799i	−0.737524	−	0.343913i	0.0172912	−	0.999850i	$-0.494496\pi$
$17$	−3.04089	−	1.41799i	−0.737524	−	0.343913i	−0.754815	+	0.655937i	$0.772274\pi$
$18$	0.0782073	+	2.46047i	0.0184336	+	0.579938i
$19$	−2.00344	+	3.87121i	−0.459621	+	0.888115i
$19$	−2.00344	+	3.87121i	−0.459621	+	0.888115i
$20$	−4.40073	−	0.795965i	−0.984034	−	0.177983i
$21$	−8.58310	+	3.12399i	−1.87299	+	0.681711i
$22$	−1.02885	−	0.147882i	−0.219351	−	0.0315286i
$23$	7.79780	+	0.682219i	1.62595	+	0.142252i	0.863347	−	0.504611i	$-0.168364\pi$
$23$	7.79780	+	0.682219i	1.62595	+	0.142252i	0.762606	+	0.646863i	$0.223920\pi$
$24$	1.11823	+	6.05600i	0.228257	+	1.23618i
$25$	−1.52739	+	4.76100i	−0.305477	+	0.952199i
$26$	6.07743	+	1.42315i	1.19188	+	0.279102i
$27$	0.709658	+	2.64848i	0.136574	+	0.509700i
$28$	−7.36348	+	4.02156i	−1.39157	+	0.760004i
$29$	2.65230	−	7.28713i	0.492519	−	1.35319i	−0.405848	−	0.913941i	$-0.633024\pi$
$29$	2.65230	−	7.28713i	0.492519	−	1.35319i	0.898367	−	0.439245i	$-0.144754\pi$
$30$	6.87628	−	0.351602i	1.25543	−	0.0641935i
$31$	−2.23860	+	1.29246i	−0.402064	+	0.232132i	−0.687374	−	0.726303i	$-0.741237\pi$
$31$	−2.23860	+	1.29246i	−0.402064	+	0.232132i	0.285310	+	0.958435i	$0.407903\pi$
$32$	1.85129	+	5.34535i	0.327264	+	0.944933i
$33$	1.59420	−	0.139474i	0.277514	−	0.0242793i
$34$	4.73774	+	0.263175i	0.812515	+	0.0451341i
$35$	3.37793	+	8.75111i	0.570974	+	1.47921i
$36$	−1.39606	−	3.18921i	−0.232676	−	0.531535i
$37$	−4.73432	−	4.73432i	−0.778318	−	0.778318i	0.201227	−	0.979545i	$-0.435507\pi$
$37$	−4.73432	−	4.73432i	−0.778318	−	0.778318i	−0.979545	+	0.201227i	$0.935507\pi$
$38$	0.595338	−	6.13560i	0.0965766	−	0.995326i
$39$	−9.60989			−1.53881
$40$	6.19608	−	1.26830i	0.979686	−	0.200535i
$41$	1.21984	−	6.91803i	0.190506	−	1.08041i	−0.728168	−	0.685399i	$-0.759628\pi$
$41$	1.21984	−	6.91803i	0.190506	−	1.08041i	0.918674	−	0.395016i	$-0.129261\pi$
$42$	9.62648	−	8.61329i	1.48540	−	1.32906i
$43$	−0.898247	−	10.2670i	−0.136981	−	1.56570i	−0.684564	−	0.728952i	$-0.740008\pi$
$43$	−0.898247	−	10.2670i	−0.136981	−	1.56570i	0.547583	−	0.836751i	$-0.315548\pi$
$44$	1.42850	−	0.346676i	0.215354	−	0.0522634i
$45$	−3.73952	+	1.07982i	−0.557455	+	0.160970i
$46$	−10.5963	+	3.20335i	−1.56233	+	0.472308i
$47$	−1.71365	+	0.799087i	−0.249961	+	0.116559i	−0.543561	−	0.839370i	$-0.682924\pi$
$47$	−1.71365	+	0.799087i	−0.249961	+	0.116559i	0.293600	+	0.955928i	$0.405147\pi$
$48$	−4.65153	−	7.36304i	−0.671390	−	1.06276i
$49$	9.17854	+	5.29923i	1.31122	+	0.757033i
$50$	−0.497401	−	7.05355i	−0.0703432	−	0.997523i
$51$	−7.19444	+	1.26857i	−1.00742	+	0.177636i
$52$	−8.72709	+	1.32626i	−1.21023	+	0.183919i
$53$	0.729246	−	8.33532i	0.100170	−	1.14494i	−0.765194	−	0.643800i	$-0.777357\pi$
$53$	0.729246	−	8.33532i	0.100170	−	1.14494i	0.865364	−	0.501144i	$-0.167087\pi$
$54$	−2.32391	−	3.10412i	−0.316245	−	0.422417i
$55$	−0.174829	−	1.63414i	−0.0235740	−	0.220348i
$56$	7.55344	−	9.15059i	1.00937	−	1.22280i
$57$	1.26134	+	9.40650i	0.167068	+	1.24592i
$58$	0.348414	+	10.9614i	0.0457490	+	1.43930i
$59$	5.52905	−	2.01241i	0.719821	−	0.261993i	0.0439710	−	0.999033i	$-0.485999\pi$
$59$	5.52905	−	2.01241i	0.719821	−	0.261993i	0.675850	+	0.737039i	$0.263777\pi$
$60$	−8.84297	+	4.07623i	−1.14162	+	0.526240i
$61$	5.21429	−	4.37531i	0.667621	−	0.560201i	−0.244739	−	0.969589i	$-0.578702\pi$
$61$	5.21429	−	4.37531i	0.667621	−	0.560201i	0.912360	+	0.409388i	$0.134258\pi$
$62$	2.25963	−	2.87360i	0.286974	−	0.364948i
$63$	−4.18842	+	5.98169i	−0.527692	+	0.753622i
$64$	−5.24039	−	6.04469i	−0.655049	−	0.755586i
$65$	0.190595	+	9.86737i	0.0236404	+	1.22390i
$66$	−2.01969	+	1.02113i	−0.248606	+	0.125692i
$67$	3.86215	−	1.80095i	0.471836	−	0.220021i	−0.172131	−	0.985074i	$-0.555065\pi$
$67$	3.86215	−	1.80095i	0.471836	−	0.220021i	0.643967	+	0.765053i	$0.277287\pi$
$68$	−6.35846	+	2.14494i	−0.771077	+	0.260112i
$69$	14.7598	−	8.52155i	1.77687	−	1.02587i
$70$	−9.03499	−	9.71358i	−1.07989	−	1.16099i
$71$	1.55696	−	1.85551i	0.184777	−	0.220208i	−0.665702	−	0.746218i	$-0.731868\pi$
$71$	1.55696	−	1.85551i	0.184777	−	0.220208i	0.850479	+	0.526009i	$0.176312\pi$
$72$	3.50932	+	3.45322i	0.413578	+	0.406966i
$73$	−2.94518	−	4.20615i	−0.344707	−	0.492293i	0.608941	−	0.793215i	$-0.291594\pi$
$73$	−2.94518	−	4.20615i	−0.344707	−	0.492293i	−0.953649	+	0.300922i	$0.902706\pi$
$74$	8.70430	+	3.72697i	1.01185	+	0.433252i
$75$	3.22163	+	10.3990i	0.372002	+	1.20077i
$76$	2.44366	+	8.36831i	0.280306	+	0.959911i
$77$	−2.18021	−	2.18021i	−0.248458	−	0.248458i
$78$	12.6167	−	5.05158i	1.42856	−	0.571979i
$79$	−0.591642	+	3.35537i	−0.0665649	+	0.377508i	0.933267	+	0.359183i	$0.116945\pi$
$79$	−0.591642	+	3.35537i	−0.0665649	+	0.377508i	−0.999832	+	0.0183254i	$0.994167\pi$
$80$	−7.46807	+	4.92219i	−0.834955	+	0.550318i
$81$	8.57362	+	7.19412i	0.952625	+	0.799347i
$82$	2.03506	+	9.72383i	0.224734	+	1.07382i
$83$	0.616624	−	2.30127i	0.0676832	−	0.252597i	−0.923792	−	0.382896i	$-0.874927\pi$
$83$	0.616624	−	2.30127i	0.0676832	−	0.252597i	0.991475	+	0.130298i	$0.0415935\pi$
$84$	−8.11080	+	16.3686i	−0.884960	+	1.78596i
$85$	1.44525	+	7.36205i	0.156760	+	0.798526i
$86$	6.57630	+	13.0073i	0.709141	+	1.40261i
$87$	−4.37006	−	16.3093i	−0.468520	−	1.74854i
$88$	−1.69323	+	1.20606i	−0.180498	+	0.128566i
$89$	−2.79224	+	0.492347i	−0.295977	+	0.0521887i	−0.319665	−	0.947531i	$-0.603570\pi$
$89$	−2.79224	+	0.492347i	−0.295977	+	0.0521887i	0.0236880	+	0.999719i	$0.492459\pi$
$90$	4.34195	−	3.38342i	0.457682	−	0.356644i
$91$	11.9015	+	14.1837i	1.24762	+	1.48685i
$92$	12.2278	−	9.77572i	1.27484	−	1.01919i
$93$	−2.37857	+	5.10085i	−0.246646	+	0.528933i
$94$	1.82978	−	1.94992i	0.188727	−	0.201118i
$95$	9.63351	−	1.48170i	0.988378	−	0.152019i
$96$	9.97743	+	7.22171i	1.01832	+	0.737062i
$97$	1.00171	+	0.467106i	0.101709	+	0.0474275i	0.472807	−	0.881166i	$-0.343241\pi$
$97$	1.00171	+	0.467106i	0.101709	+	0.0474275i	−0.371098	+	0.928594i	$0.621019\pi$
$98$	−14.8360	−	2.13247i	−1.49866	−	0.215412i
$99$	0.980060	−	0.822368i	0.0984997	−	0.0826511i
$100$	4.36084	+	8.99906i	0.436084	+	0.899906i
$101$	0.536895	+	3.04489i	0.0534231	+	0.302977i	0.999798	−	0.0200927i	$-0.00639613\pi$
$101$	0.536895	+	3.04489i	0.0534231	+	0.302977i	−0.946375	+	0.323070i	$0.895285\pi$
$102$	8.77866	−	5.44736i	0.869217	−	0.539369i
$103$	−10.7586	+	2.88275i	−1.06007	+	0.284046i	−0.746408	−	0.665488i	$-0.768223\pi$
$103$	−10.7586	+	2.88275i	−1.06007	+	0.284046i	−0.313665	+	0.949534i	$0.601557\pi$
$104$	10.7605	−	6.32875i	1.05516	−	0.620585i
$105$	16.9536	+	11.3895i	1.65450	+	1.11150i
$106$	3.42416	+	11.3267i	0.332584	+	1.10014i
$107$	−2.31153	−	0.619373i	−0.223464	−	0.0598770i	0.145350	−	0.989380i	$-0.453569\pi$
$107$	−2.31153	−	0.619373i	−0.223464	−	0.0598770i	−0.368814	+	0.929503i	$0.620236\pi$
$108$	4.68277	+	2.85376i	0.450599	+	0.274603i
$109$	−8.71555	+	10.3868i	−0.834798	+	0.994874i	0.165165	+	0.986266i	$0.447184\pi$
$109$	−8.71555	+	10.3868i	−0.834798	+	0.994874i	−0.999963	+	0.00860757i	$0.997260\pi$
$110$	1.08854	+	2.05355i	0.103789	+	0.195798i
$111$	−14.3564	−	2.53142i	−1.36265	−	0.240272i
$112$	−5.10669	+	15.9843i	−0.482537	+	1.51037i
$113$	−6.15406	+	6.15406i	−0.578926	+	0.578926i	−0.934607	−	0.355682i	$-0.884249\pi$
$113$	−6.15406	+	6.15406i	−0.578926	+	0.578926i	0.355682	+	0.934607i	$0.384249\pi$
$114$	−6.60066	−	11.6866i	−0.618209	−	1.09455i
$115$	−9.04261	−	14.9862i	−0.843227	−	1.39747i
$116$	−6.21945	−	14.2080i	−0.577462	−	1.31918i
$117$	−6.29338	+	4.40667i	−0.581823	+	0.407397i
$118$	−6.20117	+	5.54849i	−0.570864	+	0.510780i
$119$	10.7824	+	9.04753i	0.988423	+	0.829385i
$120$	9.46710	−	10.0001i	0.864224	−	0.912878i
$121$	−5.22990	−	9.05845i	−0.475446	−	0.823496i
$122$	−4.54583	+	8.48526i	−0.411560	+	0.768219i
$123$	−6.46398	−	13.8621i	−0.582838	−	1.24990i
$124$	−1.45610	+	4.96053i	−0.130761	+	0.445469i
$125$	10.6137	−	3.51419i	0.949317	−	0.314319i
$126$	2.35457	−	10.0550i	0.209762	−	0.895770i
$127$	7.95475	+	5.56998i	0.705870	+	0.494256i	0.870543	−	0.492093i	$-0.163768\pi$
$127$	7.95475	+	5.56998i	0.705870	+	0.494256i	−0.164673	+	0.986348i	$0.552657\pi$
$128$	10.0575	+	5.18131i	0.888969	+	0.457968i
$129$	−14.4241	−	17.1899i	−1.26997	−	1.51349i
$130$	−5.43716	−	12.8546i	−0.476870	−	1.12742i
$131$	6.53947	+	17.9670i	0.571356	+	1.56979i	0.802363	+	0.596836i	$0.203576\pi$
$131$	6.53947	+	17.9670i	0.571356	+	1.56979i	−0.231007	+	0.972952i	$0.574202\pi$
$132$	2.11485	−	2.40230i	0.184074	−	0.209094i
$133$	12.3214	−	13.5113i	1.06840	−	1.17158i
$134$	−4.12387	+	4.39464i	−0.356248	+	0.379639i
$135$	3.84955	−	4.77192i	0.331317	−	0.410702i
$136$	7.22043	−	6.15849i	0.619147	−	0.528086i
$137$	11.5266	+	1.00845i	0.984785	+	0.0861575i	0.568157	−	0.822920i	$-0.307656\pi$
$137$	11.5266	+	1.00845i	0.984785	+	0.0861575i	0.416627	+	0.909077i	$0.363212\pi$
$138$	−14.8984	+	18.9465i	−1.26824	+	1.61284i
$139$	−2.15897	−	12.2441i	−0.183122	−	1.03853i	−0.928345	−	0.371720i	$-0.878768\pi$
$139$	−2.15897	−	12.2441i	−0.183122	−	1.03853i	0.745223	−	0.666815i	$-0.232343\pi$
$140$	16.9680	+	8.00347i	1.43406	+	0.676417i
$141$	−2.05843	+	3.56531i	−0.173351	+	0.300253i
$142$	−1.06873	+	3.25451i	−0.0896862	+	0.273112i
$143$	−1.37095	−	2.94002i	−0.114645	−	0.245857i
$144$	−6.42259	−	2.68896i	−0.535215	−	0.224080i
$145$	−16.6596	+	4.81062i	−1.38351	+	0.399500i
$146$	6.07772	+	3.97403i	0.502996	+	0.328893i
$147$	22.9884	−	2.01122i	1.89605	−	0.165883i
$148$	−13.3869	−	0.317554i	−1.10040	−	0.0261028i
$149$	10.9446	+	1.92983i	0.896620	+	0.158098i	0.602922	−	0.797800i	$-0.294003\pi$
$149$	10.9446	+	1.92983i	0.896620	+	0.158098i	0.293698	+	0.955898i	$0.405114\pi$
$150$	−9.69601	−	11.9592i	−0.791676	−	0.976463i
$151$			7.10576i			0.578259i	0.957290	+	0.289129i	$0.0933658\pi$
$151$			7.10576i			0.578259i	−0.957290	+	0.289129i	$0.906634\pi$
$152$	−7.60717	−	9.70211i	−0.617023	−	0.786945i
$153$	−4.12983	+	4.12983i	−0.333877	+	0.333877i
$154$	4.00844	+	1.71632i	0.323009	+	0.138305i
$155$	5.28469	+	2.34113i	0.424477	+	0.188044i
$156$	−13.9089	+	13.2643i	−1.11360	+	1.06200i
$157$	0.367492	+	4.20045i	0.0293290	+	0.335232i	0.996657	+	0.0817031i	$0.0260359\pi$
$157$	0.367492	+	4.20045i	0.0293290	+	0.335232i	−0.967328	+	0.253529i	$0.918409\pi$
$158$	−0.987038	−	4.71623i	−0.0785246	−	0.375203i
$159$	−9.10896	−	15.7772i	−0.722388	−	1.25121i
$160$	7.21732	−	10.3880i	0.570579	−	0.821243i
$161$	−30.8568	−	11.2310i	−2.43186	−	0.885123i
$162$	−15.0379	−	4.93823i	−1.18149	−	0.387984i
$163$	10.3140	−	2.76363i	0.807856	−	0.216464i	0.168826	−	0.985646i	$-0.446002\pi$
$163$	10.3140	−	2.76363i	0.807856	−	0.216464i	0.639030	+	0.769182i	$0.279336\pi$
$164$	−7.78327	−	11.6965i	−0.607772	−	0.913347i
$165$	−2.35263	−	2.69624i	−0.183152	−	0.209902i
$166$	0.400139	+	3.34545i	0.0310568	+	0.259657i
$167$	−0.585922	+	6.69712i	−0.0453400	+	0.518239i	0.939235	+	0.343275i	$0.111536\pi$
$167$	−0.585922	+	6.69712i	−0.0453400	+	0.518239i	−0.984575	+	0.174964i	$0.944019\pi$
$168$	2.04419	−	25.7537i	0.157712	−	1.98694i
$169$	2.21639	+	6.08947i	0.170491	+	0.468421i
$170$	−5.76743	−	8.90583i	−0.442341	−	0.683046i
$171$	5.13944	+	5.58179i	0.393023	+	0.426850i
$172$	−15.4714	−	13.6202i	−1.17968	−	1.03853i
$173$	−10.5441	+	22.6120i	−0.801656	+	1.71916i	−0.113568	+	0.993530i	$0.536228\pi$
$173$	−10.5441	+	22.6120i	−0.801656	+	1.71916i	−0.688088	+	0.725627i	$0.741550\pi$
$174$	14.3106	+	19.1151i	1.08489	+	1.44911i
$175$	11.3584	−	17.6337i	0.858617	−	1.33298i
$176$	1.58903	−	2.47349i	0.119778	−	0.186446i
$177$	7.34813	−	10.4942i	0.552319	−	0.788793i
$178$	3.40709	−	2.11418i	0.255372	−	0.158464i
$179$	1.96648	−	3.40603i	0.146981	−	0.254579i	−0.783129	−	0.621859i	$-0.786378\pi$
$179$	1.96648	−	3.40603i	0.146981	−	0.254579i	0.930110	+	0.367280i	$0.119711\pi$
$180$	−3.92195	+	6.72447i	−0.292325	+	0.501212i
$181$	5.87245	+	2.13740i	0.436496	+	0.158872i	0.550916	−	0.834561i	$-0.314279\pi$
$181$	5.87245	+	2.13740i	0.436496	+	0.158872i	−0.114420	+	0.993433i	$0.536501\pi$
$182$	−23.0812	−	12.3654i	−1.71089	−	0.916583i
$183$	3.83582	−	14.3155i	0.283552	−	1.05823i
$184$	−10.9150	+	19.2622i	−0.804666	+	1.42003i
$185$	−2.31451	+	14.7912i	−0.170166	+	1.08747i
$186$	0.441455	−	7.94717i	0.0323690	−	0.582715i
$187$	−1.41447	−	2.02007i	−0.103436	−	0.147722i
$188$	−1.37729	+	3.52187i	−0.100449	+	0.256859i
$189$		−	11.5024i		−	0.836680i
$190$	−11.8689	+	7.00930i	−0.861057	+	0.508508i
$191$		−	20.3147i		−	1.46992i	−0.678108	−	0.734962i	$-0.737200\pi$
$191$		−	20.3147i		−	1.46992i	0.678108	−	0.734962i	$-0.262800\pi$
$192$	−16.8955	−	4.23651i	−1.21932	−	0.305744i
$193$	5.39360	+	7.70286i	0.388240	+	0.554464i	0.964933	−	0.262497i	$-0.0845460\pi$
$193$	5.39360	+	7.70286i	0.388240	+	0.554464i	−0.576693	+	0.816961i	$0.695657\pi$
$194$	−1.56068	−	0.0866936i	−0.112050	−	0.00622424i
$195$	12.6629	+	17.3609i	0.906806	+	1.24324i
$196$	20.5990	−	4.99908i	1.47136	−	0.357077i
$197$	3.39320	−	12.6636i	0.241755	−	0.902244i	−0.733231	−	0.679980i	$-0.761989\pi$
$197$	3.39320	−	12.6636i	0.241755	−	0.902244i	0.974986	−	0.222264i	$-0.0713447\pi$
$198$	−0.854420	+	1.59486i	−0.0607210	+	0.113342i
$199$	−7.27516	−	2.64794i	−0.515723	−	0.187708i	0.0710295	−	0.997474i	$-0.477372\pi$
$199$	−7.27516	−	2.64794i	−0.515723	−	0.187708i	−0.586752	+	0.809766i	$0.699594\pi$
$200$	−10.4558	−	9.52243i	−0.739335	−	0.673337i
$201$	4.63921	−	8.03535i	0.327225	−	0.566770i
$202$	−2.30547	−	3.71537i	−0.162213	−	0.261412i
$203$	−18.6595	+	26.6485i	−1.30964	+	1.87036i
$204$	−8.66192	+	11.7664i	−0.606456	+	0.823814i
$205$	−14.1053	+	6.91210i	−0.985154	+	0.482762i
$206$	12.6094	−	9.44013i	0.878541	−	0.657725i
$207$	5.75835	−	12.3488i	0.400233	−	0.858302i
$208$	−10.8006	+	13.9654i	−0.748886	+	0.968325i
$209$	−2.69785	+	1.72783i	−0.186614	+	0.119516i
$210$	−28.2452	−	6.04126i	−1.94910	−	0.416887i
$211$	−3.23927	−	8.89981i	−0.223000	−	0.612688i	0.776855	−	0.629679i	$-0.216814\pi$
$211$	−3.23927	−	8.89981i	−0.223000	−	0.612688i	−0.999856	+	0.0169908i	$0.994591\pi$
$212$	−10.4496	−	13.0707i	−0.717680	−	0.897700i
$213$	0.459648	−	5.25380i	0.0314946	−	0.359985i
$214$	3.36036	−	0.401922i	0.229710	−	0.0274748i
$215$	−17.3644	+	15.1515i	−1.18425	+	1.03332i
$216$	−7.64807	−	1.28511i	−0.520385	−	0.0874403i
$217$	10.4743	−	2.80659i	0.711045	−	0.190524i
$218$	5.98258	−	18.2181i	0.405191	−	1.23389i
$219$	−10.5058	−	3.82378i	−0.709913	−	0.258387i
$220$	−2.50861	−	2.12387i	−0.169131	−	0.143191i
$221$	7.40445	+	12.8249i	0.498077	+	0.862695i
$222$	20.1790	−	4.22317i	1.35433	−	0.283441i
$223$	0.151522	+	1.73191i	0.0101467	+	0.115977i	0.999579	−	0.0290195i	$-0.00923848\pi$
$223$	0.151522	+	1.73191i	0.0101467	+	0.115977i	−0.989432	+	0.144996i	$0.953683\pi$
$224$	−1.69786	−	23.6700i	−0.113443	−	1.58152i
$225$	6.87830	+	5.33284i	0.458554	+	0.355522i
$226$	4.84463	−	11.3146i	0.322260	−	0.752634i
$227$	−6.64263	+	6.64263i	−0.440887	+	0.440887i	−0.892310	−	0.451423i	$-0.850917\pi$
$227$	−6.64263	+	6.64263i	−0.440887	+	0.440887i	0.451423	+	0.892310i	$0.350917\pi$
$228$	14.8092	+	11.8735i	0.980762	+	0.786343i
$229$			5.07048i			0.335067i	0.985866	+	0.167533i	$0.0535802\pi$
$229$			5.07048i			0.335067i	−0.985866	+	0.167533i	$0.946420\pi$
$230$	19.7497	+	14.9219i	1.30225	+	0.983918i
$231$	−6.61129	−	1.16575i	−0.434991	−	0.0767007i
$232$	15.6341	+	15.3841i	1.02643	+	1.01002i
$233$	6.48452	−	0.567322i	0.424815	−	0.0371665i	0.127256	−	0.991870i	$-0.459383\pi$
$233$	6.48452	−	0.567322i	0.424815	−	0.0371665i	0.297559	+	0.954703i	$0.403828\pi$
$234$	5.94608	−	9.09368i	0.388707	−	0.594472i
$235$	3.70166	+	2.04287i	0.241470	+	0.133262i
$236$	5.22480	−	10.5443i	0.340106	−	0.686375i
$237$	3.13515	+	6.72334i	0.203650	+	0.436728i
$238$	−18.9121	−	6.21046i	−1.22589	−	0.402564i
$239$	4.37579	−	7.57908i	0.283046	−	0.490250i	−0.689087	−	0.724678i	$-0.741988\pi$
$239$	4.37579	−	7.57908i	0.283046	−	0.490250i	0.972133	+	0.234428i	$0.0753217\pi$
$240$	−7.17257	+	18.1055i	−0.462987	+	1.16871i
$241$	−4.07950	−	23.1360i	−0.262784	−	1.49032i	−0.775272	−	0.631627i	$-0.782387\pi$
$241$	−4.07950	−	23.1360i	−0.262784	−	1.49032i	0.512488	−	0.858694i	$-0.328724\pi$
$242$	11.6280	+	9.14357i	0.747475	+	0.587771i
$243$	16.0815	+	1.40695i	1.03163	+	0.0902557i
$244$	1.50777	−	13.5298i	0.0965254	−	0.866155i
$245$	−2.52104	−	23.5644i	−0.161063	−	1.50548i
$246$	15.7733	+	14.8014i	1.00567	+	0.943706i
$247$	17.0435	−	8.92430i	1.08445	−	0.567840i
$248$	−0.695885	−	7.27804i	−0.0441888	−	0.462156i
$249$	−1.77418	−	4.87451i	−0.112434	−	0.308909i
$250$	−12.0873	+	10.1930i	−0.764469	+	0.644661i
$251$	−11.7076	−	13.9525i	−0.738976	−	0.880677i	0.257351	−	0.966318i	$-0.417151\pi$
$251$	−11.7076	−	13.9525i	−0.738976	−	0.880677i	−0.996326	+	0.0856414i	$0.972706\pi$
$252$	2.19427	+	14.4388i	0.138226	+	0.909559i
$253$	4.71269	+	3.29986i	0.296284	+	0.207461i
$254$	−13.3716	−	3.13123i	−0.839012	−	0.196471i
$255$	11.7718	+	11.3257i	0.737180	+	0.709241i
$256$	−15.9281	−	1.51560i	−0.995503	−	0.0947249i
$257$	9.70661	+	20.8159i	0.605482	+	1.29846i	0.935113	+	0.354350i	$0.115298\pi$
$257$	9.70661	+	20.8159i	0.605482	+	1.29846i	−0.329631	+	0.944110i	$0.606924\pi$
$258$	27.9734	+	14.9863i	1.74154	+	0.933003i
$259$	14.0437	+	24.3243i	0.872630	+	1.51144i
$260$	13.8956	+	14.0185i	0.861767	+	0.869391i
$261$	−10.3406	−	8.67681i	−0.640068	−	0.537081i
$262$	−18.0302	−	20.1512i	−1.11391	−	1.24494i
$263$	−5.80453	+	4.06438i	−0.357923	+	0.250620i	−0.738682	−	0.674054i	$-0.764552\pi$
$263$	−5.80453	+	4.06438i	−0.357923	+	0.250620i	0.380759	+	0.924674i	$0.375663\pi$
$264$	−1.51376	+	4.26566i	−0.0931655	+	0.262533i
$265$	−16.0192	+	9.66593i	−0.984055	+	0.593774i
$266$	−9.07416	+	24.2157i	−0.556372	+	1.48476i
$267$	−4.36523	+	4.36523i	−0.267148	+	0.267148i
$268$	3.10408	−	7.93745i	0.189612	−	0.484857i
$269$	16.3726	+	2.88693i	0.998254	+	0.176019i	0.648820	−	0.760942i	$-0.275263\pi$
$269$	16.3726	+	2.88693i	0.998254	+	0.176019i	0.349434	+	0.936961i	$0.386374\pi$
$270$	−2.54560	+	8.28858i	−0.154920	+	0.504427i
$271$	−2.74990	+	3.27720i	−0.167045	+	0.199076i	−0.843072	−	0.537800i	$-0.819255\pi$
$271$	−2.74990	+	3.27720i	−0.167045	+	0.199076i	0.676028	+	0.736876i	$0.263700\pi$
$272$	−6.24233	+	11.8809i	−0.378497	+	0.720388i
$273$	38.9403	+	10.4340i	2.35678	+	0.631496i
$274$	−15.6633	+	4.73515i	−0.946252	+	0.286061i
$275$	−2.72182	+	2.46914i	−0.164132	+	0.148895i
$276$	9.60047	−	32.7063i	0.577880	−	1.96869i
$277$	−6.99734	+	1.87493i	−0.420429	+	0.112654i	−0.462830	−	0.886447i	$-0.653166\pi$
$277$	−6.99734	+	1.87493i	−0.420429	+	0.112654i	0.0424008	+	0.999101i	$0.486499\pi$
$278$	9.27080	+	14.9403i	0.556026	+	0.896060i
$279$	0.781336	+	4.43118i	0.0467774	+	0.265288i
$280$	−26.4843	−	1.58818i	−1.58274	−	0.0949118i
$281$	−4.26965	+	3.58266i	−0.254706	+	0.213724i	−0.761196	−	0.648522i	$-0.775387\pi$
$281$	−4.26965	+	3.58266i	−0.254706	+	0.213724i	0.506490	+	0.862246i	$0.330943\pi$
$282$	0.828335	−	5.76290i	0.0493266	−	0.343176i
$283$	5.99533	+	2.79567i	0.356385	+	0.166185i	0.592562	−	0.805525i	$-0.298117\pi$
$283$	5.99533	+	2.79567i	0.356385	+	0.166185i	−0.236177	+	0.971710i	$0.575894\pi$
$284$	−0.307652	−	4.83461i	−0.0182558	−	0.286881i
$285$	15.3314	−	14.6735i	0.908156	−	0.869186i
$286$	3.34537	+	3.13926i	0.197816	+	0.185628i
$287$	−12.4542	+	26.7082i	−0.735149	+	1.57653i
$288$	9.84563	+	0.154182i	0.580159	+	0.00908529i
$289$	−3.69107	−	4.39885i	−0.217122	−	0.258756i
$290$	19.3434	−	15.0732i	1.13589	−	0.885127i
$291$	2.36995	−	0.417887i	0.138929	−	0.0244970i
$292$	−10.0684	−	2.02262i	−0.589207	−	0.118365i
$293$	−7.61199	−	28.4083i	−0.444697	−	1.65963i	−0.716735	−	0.697346i	$-0.754364\pi$
$293$	−7.61199	−	28.4083i	−0.444697	−	1.65963i	0.272038	−	0.962287i	$-0.412302\pi$
$294$	−29.1239	+	14.7247i	−1.69854	+	0.858761i
$295$	−10.9211	−	7.33688i	−0.635853	−	0.427169i
$296$	17.7425	−	6.62012i	1.03126	−	0.384786i
$297$	−0.521586	+	1.94659i	−0.0302655	+	0.112952i
$298$	−15.3835	+	3.21955i	−0.891144	+	0.186504i
$299$	−26.4655	−	22.2072i	−1.53054	−	1.28427i
$300$	19.0163	+	10.6042i	1.09791	+	0.612235i
$301$	−7.50771	+	42.5783i	−0.432737	+	2.45417i
$302$	−3.73525	−	9.32908i	−0.214939	−	0.536828i
$303$	4.76020	+	4.76020i	0.273466	+	0.273466i
$304$	15.0874	+	8.73897i	0.865323	+	0.501214i
$305$	−14.7751	−	3.65467i	−0.846020	−	0.209266i
$306$	3.25110	−	7.59291i	0.185853	−	0.434058i
$307$	10.2539	+	14.6441i	0.585222	+	0.835783i	0.997151	−	0.0754327i	$-0.0240338\pi$
$307$	10.2539	+	14.6441i	0.585222	+	0.835783i	−0.411929	+	0.911216i	$0.635145\pi$
$308$	−6.16484	−	0.146238i	−0.351275	−	0.00833266i
$309$	−15.5883	+	18.5774i	−0.886788	+	1.05683i
$310$	−8.16886	−	0.295665i	−0.463960	−	0.0167927i
$311$	−17.1629	+	9.90903i	−0.973221	+	0.561889i	−0.900217	−	0.435442i	$-0.856592\pi$
$311$	−17.1629	+	9.90903i	−0.973221	+	0.561889i	−0.0730042	+	0.997332i	$0.523259\pi$
$312$	11.2883	−	24.7260i	0.639072	−	1.39983i
$313$	29.0795	−	13.5600i	1.64367	−	0.766455i	0.643670	−	0.765303i	$-0.277411\pi$
$313$	29.0795	−	13.5600i	1.64367	−	0.766455i	0.999999	−	0.00115199i	$-0.000366691\pi$
$314$	−2.69050	−	5.32155i	−0.151834	−	0.300312i
$315$	16.3254	−	0.315335i	0.919831	−	0.0177671i
$316$	3.77503	+	5.67303i	0.212362	+	0.319133i
$317$	−1.21393	+	1.73367i	−0.0681811	+	0.0973727i	−0.851794	−	0.523876i	$-0.824485\pi$
$317$	−1.21393	+	1.73367i	−0.0681811	+	0.0973727i	0.783613	+	0.621249i	$0.213374\pi$
$318$	20.2526	+	15.9254i	1.13571	+	0.893053i
$319$	4.36618	−	3.66366i	0.244459	−	0.205125i
$320$	−4.01493	+	17.4322i	−0.224442	+	0.974488i
$321$	−4.89624	+	1.78208i	−0.273281	+	0.0994662i
$322$	46.4153	−	1.47533i	2.58662	−	0.0822172i
$323$	11.5816	−	8.93105i	0.644416	−	0.496937i
$324$	22.3390	−	1.42155i	1.24105	−	0.0789749i
$325$	17.5750	−	13.3465i	0.974883	−	0.740329i
$326$	−12.0884	+	9.05005i	−0.669515	+	0.501236i
$327$	−2.57303	+	29.4098i	−0.142289	+	1.62637i
$328$	16.3670	+	11.2649i	0.903718	+	0.621998i
$329$	7.81150	−	1.37738i	0.430662	−	0.0759373i
$330$	4.50606	+	2.30317i	0.248050	+	0.126786i
$331$	7.33727	+	4.23618i	0.403293	+	0.232841i	0.687904	−	0.725802i	$-0.258531\pi$
$331$	7.33727	+	4.23618i	0.403293	+	0.232841i	−0.284611	+	0.958643i	$0.591864\pi$
$332$	−2.28392	−	4.18186i	−0.125347	−	0.229510i
$333$	−10.5626	+	4.92542i	−0.578826	+	0.269911i
$334$	−2.75119	−	9.10058i	−0.150538	−	0.497961i
$335$	−8.34265	−	4.60414i	−0.455808	−	0.251551i
$336$	10.8540	+	34.8863i	0.592135	+	1.90320i
$337$	−1.43205	−	16.3684i	−0.0780089	−	0.891646i	−0.929872	−	0.367882i	$-0.880083\pi$
$337$	−1.43205	−	16.3684i	−0.0780089	−	0.891646i	0.851863	−	0.523764i	$-0.175473\pi$
$338$	−6.11089	−	6.82972i	−0.332389	−	0.371488i
$339$	−3.29055	+	18.6616i	−0.178718	+	1.01356i
$340$	12.2535	+	8.66064i	0.664538	+	0.469689i
$341$	−1.89986			−0.102883
$342$	−9.68166	−	4.62664i	−0.523524	−	0.250180i
$343$	−10.6743	−	10.6743i	−0.576358	−	0.576358i
$344$	27.4719	+	9.74897i	1.48118	+	0.525629i
$345$	−34.8436	−	15.4358i	−1.87591	−	0.831033i
$346$	1.95696	−	35.2297i	0.105207	−	1.89396i
$347$	12.7689	−	1.11713i	0.685471	−	0.0599709i	0.260900	−	0.965366i	$-0.415981\pi$
$347$	12.7689	−	1.11713i	0.685471	−	0.0599709i	0.424570	+	0.905395i	$0.360425\pi$
$348$	−28.8364	−	17.5734i	−1.54579	−	0.942034i
$349$	−25.9505	+	14.9825i	−1.38910	+	0.801996i	−0.993214	−	0.116304i	$-0.962895\pi$
$349$	−25.9505	+	14.9825i	−1.38910	+	0.801996i	−0.395885	+	0.918300i	$0.629562\pi$
$350$	−5.64294	+	29.1218i	−0.301628	+	1.55663i
$351$	4.13906	−	11.3720i	0.220927	−	0.606992i
$352$	−0.785999	+	4.08272i	−0.0418939	+	0.217609i
$353$	−8.20822	−	30.6335i	−0.436880	−	1.63046i	−0.736528	−	0.676407i	$-0.763536\pi$
$353$	−8.20822	−	30.6335i	−0.436880	−	1.63046i	0.299649	−	0.954050i	$-0.403131\pi$
$354$	−4.13084	+	17.6404i	−0.219551	+	0.937576i
$355$	−5.40369	−	0.367764i	−0.286798	−	0.0195189i
$356$	−3.36178	+	4.56667i	−0.178174	+	0.242033i
$357$	30.5300	+	2.67103i	1.61582	+	0.141366i
$358$	−0.791331	+	5.50545i	−0.0418231	+	0.290972i
$359$	11.1425	−	4.05555i	0.588080	−	0.214044i	−0.0308046	−	0.999525i	$-0.509807\pi$
$359$	11.1425	−	4.05555i	0.588080	−	0.214044i	0.618885	+	0.785482i	$0.287585\pi$
$360$	1.61428	−	10.8901i	0.0850798	−	0.573959i
$361$	−10.9725	−	15.5115i	−0.577498	−	0.816392i
$362$	−8.83343	+	0.280775i	−0.464275	+	0.0147572i
$363$	−20.6405	−	9.62482i	−1.08334	−	0.505172i
$364$	36.8031	+	4.10138i	1.92901	+	0.214971i
$365$	−3.71787	+	10.8631i	−0.194602	+	0.568600i
$366$	2.48913	+	20.8110i	0.130109	+	1.08781i
$367$	−17.4573	−	12.2237i	−0.911263	−	0.638073i	0.0210295	−	0.999779i	$-0.493306\pi$
$367$	−17.4573	−	12.2237i	−0.911263	−	0.638073i	−0.932292	+	0.361706i	$0.882195\pi$
$368$	4.20476	−	31.0267i	0.219188	−	1.61738i
$369$	−10.5897	−	6.11396i	−0.551278	−	0.318280i
$370$	−4.73654	−	20.6359i	−0.246241	−	1.07281i
$371$	−12.0051	+	32.9838i	−0.623275	+	1.71244i
$372$	3.59797	+	10.6658i	0.186546	+	0.552997i
$373$	12.3251	+	3.30251i	0.638170	+	0.170997i	0.563375	−	0.826202i	$-0.309503\pi$
$373$	12.3251	+	3.30251i	0.638170	+	0.170997i	0.0747959	+	0.997199i	$0.476169\pi$
$374$	2.91892	+	1.90859i	0.150934	+	0.0986909i
$375$	14.5413	−	19.5227i	0.750911	−	1.00815i
$376$	−0.0430940	−	5.34782i	−0.00222240	−	0.275793i
$377$	−28.0371	+	19.6318i	−1.44398	+	1.01109i
$378$	6.04643	+	15.1014i	0.310995	+	0.776734i
$379$	−7.74944			−0.398062			−0.199031	−	0.979993i	$-0.563779\pi$
$379$	−7.74944			−0.398062			−0.199031	+	0.979993i	$0.563779\pi$
$380$	11.8979	−	15.4415i	0.610352	−	0.792131i
$381$	21.1438			1.08323
$382$	10.6787	+	26.6710i	0.546372	+	1.36461i
$383$	1.05003	−	0.735241i	0.0536542	−	0.0375691i	−0.546442	−	0.837497i	$-0.684018\pi$
$383$	1.05003	−	0.735241i	0.0536542	−	0.0375691i	0.600096	+	0.799928i	$0.295129\pi$
$384$	24.4088	−	3.31927i	1.24561	−	0.169386i
$385$	−1.06586	+	6.81156i	−0.0543213	+	0.347149i
$386$	−11.1303	−	7.27777i	−0.566518	−	0.370429i
$387$	−17.3287	−	4.64320i	−0.880866	−	0.236027i
$388$	2.09457	−	0.706575i	0.106336	−	0.0358709i
$389$	−0.857234	+	2.35523i	−0.0434635	+	0.119415i	−0.959526	−	0.281622i	$-0.909128\pi$
$389$	−0.857234	+	2.35523i	−0.0434635	+	0.119415i	0.916062	+	0.401036i	$0.131350\pi$
$390$	−25.7510	−	16.1366i	−1.30395	−	0.817106i
$391$	−22.7449	−	13.1318i	−1.15026	−	0.664101i
$392$	−24.4164	+	17.3914i	−1.23321	+	0.878398i
$393$	34.1017	+	23.8783i	1.72020	+	1.20450i
$394$	2.20191	+	18.4096i	0.110931	+	0.927461i
$395$	6.84130	−	3.35249i	0.344223	−	0.168682i
$396$	0.283396	−	2.54301i	0.0142412	−	0.127791i
$397$	16.9632	+	7.91006i	0.851357	+	0.396994i	0.798781	−	0.601622i	$-0.205479\pi$
$397$	16.9632	+	7.91006i	0.851357	+	0.396994i	0.0525768	+	0.998617i	$0.483257\pi$
$398$	10.9434	−	0.347842i	0.548544	−	0.0174358i
$399$	5.10211	−	39.4857i	0.255425	−	1.97676i
$400$	18.7329	+	7.00565i	0.936644	+	0.350283i
$401$	−18.7831	+	6.83648i	−0.937982	+	0.341398i	−0.765369	−	0.643592i	$-0.777443\pi$
$401$	−18.7831	+	6.83648i	−0.937982	+	0.341398i	−0.172614	+	0.984990i	$0.555221\pi$
$402$	−1.86687	+	12.9882i	−0.0931109	+	0.647792i
$403$	11.3655	+	0.994351i	0.566155	+	0.0495321i
$404$	4.97987	+	3.66596i	0.247758	+	0.182388i
$405$	1.69930	−	24.9685i	0.0844391	−	1.24069i
$406$	10.4896	−	44.7951i	0.520592	−	2.22314i
$407$	−1.27364	−	4.75328i	−0.0631319	−	0.235611i
$408$	5.18695	−	20.0013i	0.256792	−	0.990210i
$409$	10.8218	−	29.7328i	0.535106	−	1.47019i	−0.317816	−	0.948152i	$-0.602949\pi$
$409$	10.8218	−	29.7328i	0.535106	−	1.47019i	0.852922	−	0.522039i	$-0.174828\pi$
$410$	14.8852	−	16.4895i	0.735127	−	0.814356i
$411$	21.8177	−	12.5965i	1.07619	−	0.621337i
$412$	−11.5924	+	19.0222i	−0.571119	+	0.937155i
$413$	−24.5893	+	2.15128i	−1.20996	+	0.105858i
$414$	−1.06873	+	19.2396i	−0.0525253	+	0.945574i
$415$	−4.96992	+	1.91839i	−0.243964	+	0.0941700i
$416$	6.83886	−	24.0125i	0.335302	−	1.17731i
$417$	−19.1418	−	19.1418i	−0.937378	−	0.937378i
$418$	2.63372	−	3.68661i	0.128819	−	0.180318i
$419$	4.91604			0.240164			0.120082	−	0.992764i	$-0.461684\pi$
$419$	4.91604			0.240164			0.120082	+	0.992764i	$0.461684\pi$
$420$	40.2585	−	6.91601i	1.96441	−	0.337467i
$421$	4.34038	−	24.6155i	0.211537	−	1.19969i	−0.675278	−	0.737563i	$-0.735976\pi$
$421$	4.34038	−	24.6155i	0.211537	−	1.19969i	0.886815	−	0.462124i	$-0.152912\pi$
$422$	8.93111	+	9.98169i	0.434760	+	0.485901i
$423$	0.286856	+	3.27878i	0.0139474	+	0.159420i
$424$	20.5900	+	11.6674i	0.999936	+	0.566620i
$425$	11.3957	−	12.3119i	0.552771	−	0.597212i
$426$	2.15827	+	7.13928i	0.104569	+	0.345899i
$427$	−25.8794	+	12.0678i	−1.25239	+	0.584000i
$428$	−4.20051	+	2.29410i	−0.203039	+	0.110890i
$429$	−6.11682	−	3.53155i	−0.295323	−	0.170505i
$430$	14.8330	−	29.0201i	0.715310	−	1.39947i
$431$	−21.5340	+	3.79702i	−1.03725	+	0.182896i	−0.666245	−	0.745733i	$-0.732100\pi$
$431$	−21.5340	+	3.79702i	−1.03725	+	0.182896i	−0.371010	+	0.928629i	$0.620988\pi$
$432$	10.7166	−	2.33312i	0.515603	−	0.112252i
$433$	−2.27997	+	26.0602i	−0.109568	+	1.25237i	0.720003	+	0.693971i	$0.244140\pi$
$433$	−2.27997	+	26.0602i	−0.109568	+	1.25237i	−0.829571	+	0.558401i	$0.811415\pi$
$434$	−12.2763	+	9.19074i	−0.589283	+	0.441170i
$435$	−23.7055	+	29.3854i	−1.13659	+	1.40892i
$436$	1.72218	+	27.0632i	0.0824774	+	1.29609i
$437$	−18.2634	+	28.8201i	−0.873658	+	1.37865i
$438$	15.8029	−	0.502304i	0.755093	−	0.0240010i
$439$	−12.9920	+	4.72872i	−0.620076	+	0.225689i	−0.632906	−	0.774228i	$-0.718138\pi$
$439$	−12.9920	+	4.72872i	−0.620076	+	0.225689i	0.0128299	+	0.999918i	$0.495916\pi$
$440$	4.40998	+	1.46972i	0.210237	+	0.0700660i
$441$	14.1325	−	11.8586i	0.672976	−	0.564694i
$442$	−16.4628	−	12.9454i	−0.783055	−	0.615749i
$443$	21.8012	−	31.1353i	1.03581	−	1.47928i	0.165852	−	0.986151i	$-0.446963\pi$
$443$	21.8012	−	31.1353i	1.03581	−	1.47928i	0.869954	−	0.493133i	$-0.164148\pi$
$444$	−24.2728	+	16.1520i	−1.15194	+	0.766538i
$445$	4.56877	+	4.39561i	0.216580	+	0.208372i
$446$	−1.10933	−	2.19415i	−0.0525285	−	0.103896i
$447$	21.9304	−	10.2263i	1.03727	−	0.483688i
$448$	14.6716	+	30.1835i	0.693167	+	1.42604i
$449$	−12.6885	+	7.32573i	−0.598809	+	0.345722i	−0.768573	−	0.639762i	$-0.779033\pi$
$449$	−12.6885	+	7.32573i	−0.598809	+	0.345722i	0.169764	+	0.985485i	$0.445699\pi$
$450$	−11.8337	−	3.38574i	−0.557847	−	0.159605i
$451$	3.31876	−	3.95514i	0.156274	−	0.186240i
$452$	−0.412783	+	17.4014i	−0.0194157	+	0.818494i
$453$	8.87407	+	12.6735i	0.416940	+	0.595452i
$454$	5.22924	−	12.2128i	0.245420	−	0.573177i
$455$	9.94129	−	40.1906i	0.466055	−	1.88417i
$456$	−25.6843	−	7.80395i	−1.20278	−	0.365453i
$457$	−9.42430	−	9.42430i	−0.440850	−	0.440850i	0.451447	−	0.892298i	$-0.350908\pi$
$457$	−9.42430	−	9.42430i	−0.440850	−	0.440850i	−0.892298	+	0.451447i	$0.850908\pi$
$458$	−2.66537	−	6.65698i	−0.124545	−	0.311060i
$459$	1.59753	−	9.06002i	0.0745662	−	0.422886i
$460$	−33.7730	−	9.20903i	−1.57467	−	0.429373i
$461$	−17.9103	−	15.0285i	−0.834165	−	0.699947i	0.122079	−	0.992520i	$-0.461044\pi$
$461$	−17.9103	−	15.0285i	−0.834165	−	0.699947i	−0.956243	+	0.292573i	$0.905488\pi$
$462$	9.29269	−	1.94482i	0.432335	−	0.0904814i
$463$	1.65700	−	6.18402i	0.0770074	−	0.287396i	−0.916674	−	0.399637i	$-0.869136\pi$
$463$	1.65700	−	6.18402i	0.0770074	−	0.287396i	0.993681	+	0.112241i	$0.0358029\pi$
$464$	−28.6127	−	11.9794i	−1.32831	−	0.556128i
$465$	12.3492	−	2.42430i	0.572683	−	0.112424i
$466$	−8.21523	+	4.15351i	−0.380563	+	0.192408i
$467$	2.68367	+	10.0156i	0.124185	+	0.463466i	0.999809	−	0.0195274i	$-0.00621616\pi$
$467$	2.68367	+	10.0156i	0.124185	+	0.463466i	−0.875624	+	0.482993i	$0.839549\pi$
$468$	−3.02631	+	15.0646i	−0.139891	+	0.696363i
$469$	−17.6052	+	3.10428i	−0.812934	+	0.143342i
$470$	−5.93374	−	0.736233i	−0.273703	−	0.0339599i
$471$	5.90120	+	7.03277i	0.271913	+	0.324053i
$472$	−1.31682	+	16.5900i	−0.0606116	+	0.763615i
$473$	3.20129	−	6.86518i	0.147195	−	0.315661i
$474$	−7.65032	−	7.17896i	−0.351391	−	0.329741i
$475$	−15.3708	−	15.4512i	−0.705259	−	0.708949i
$476$	28.0941	−	1.78778i	1.28769	−	0.0819426i
$477$	−13.2000	−	6.15528i	−0.604389	−	0.281831i
$478$	−1.76086	+	12.2507i	−0.0805400	+	0.560333i
$479$	−0.105633	+	0.0886370i	−0.00482652	+	0.00404993i	−0.645198	−	0.764016i	$-0.723225\pi$
$479$	−0.105633	+	0.0886370i	−0.00482652	+	0.00404993i	0.640371	+	0.768066i	$0.278781\pi$
$480$	−0.100649	−	27.5409i	−0.00459400	−	1.25706i
$481$	5.13146	+	29.1019i	0.233974	+	1.32693i
$482$	17.5177	+	28.2306i	0.797910	+	1.28587i
$483$	−69.0605	+	18.5047i	−3.14236	+	0.841993i
$484$	−20.0727	−	5.89206i	−0.912396	−	0.267821i
$485$	−0.476087	−	2.42516i	−0.0216180	−	0.110121i
$486$	−21.8528	+	6.60630i	−0.991262	+	0.299668i
$487$	−21.0712	−	5.64602i	−0.954829	−	0.255846i	−0.252419	−	0.967618i	$-0.581226\pi$
$487$	−21.0712	−	5.64602i	−0.954829	−	0.255846i	−0.702410	+	0.711772i	$0.747893\pi$
$488$	5.13259	+	18.5557i	0.232341	+	0.839976i
$489$	14.9442	−	17.8098i	0.675800	−	0.805387i
$490$	15.6968	+	29.6122i	0.709110	+	1.33774i
$491$	19.0722	+	3.36295i	0.860717	+	0.151768i	0.586549	−	0.809914i	$-0.300486\pi$
$491$	19.0722	+	3.36295i	0.860717	+	0.151768i	0.274169	+	0.961682i	$0.411597\pi$
$492$	−28.4892	−	11.1412i	−1.28439	−	0.502284i
$493$	−18.3984	+	18.3984i	−0.828623	+	0.828623i
$494$	−17.6851	+	20.6758i	−0.795689	+	0.930248i
$495$	−2.77708	−	0.686920i	−0.124820	−	0.0308748i
$496$	4.73943	+	9.18946i	0.212807	+	0.412619i
$497$	−8.32359	+	5.82824i	−0.373364	+	0.261432i
$498$	4.89165	+	5.46706i	0.219200	+	0.244985i
$499$	24.8191	+	20.8257i	1.11106	+	0.932288i	0.998119	−	0.0613142i	$-0.0195292\pi$
$499$	24.8191	+	20.8257i	1.11106	+	0.932288i	0.112939	+	0.993602i	$0.463974\pi$
$500$	10.5112	−	19.7361i	0.470075	−	0.882626i
$501$	7.31872	+	12.6764i	0.326976	+	0.566339i
$502$	22.7051	+	12.1639i	1.01338	+	0.542900i
$503$	10.6427	+	22.8234i	0.474535	+	1.01764i	0.987264	+	0.159093i	$0.0508568\pi$
$503$	10.6427	+	22.8234i	0.474535	+	1.01764i	−0.512729	+	0.858551i	$0.671365\pi$
$504$	−10.4708	−	17.8031i	−0.466406	−	0.793013i
$505$	4.79333	−	4.98215i	0.213301	−	0.221703i
$506$	−7.92186	−	1.85506i	−0.352170	−	0.0824673i
$507$	11.5579	+	8.09294i	0.513305	+	0.359420i
$508$	19.2015	−	2.91805i	0.851927	−	0.129467i
$509$	6.23859	+	7.43486i	0.276521	+	0.329544i	0.886374	−	0.462970i	$-0.153216\pi$
$509$	6.23859	+	7.43486i	0.276521	+	0.329544i	−0.609853	+	0.792514i	$0.708772\pi$
$510$	−21.4086	−	8.68132i	−0.947988	−	0.384415i
$511$	7.36732	+	20.2416i	0.325911	+	0.895434i
$512$	21.7085	−	6.38301i	0.959387	−	0.282092i
$513$	−11.6746	−	2.55884i	−0.515445	−	0.112975i
$514$	−23.6859	−	22.2265i	−1.04474	−	0.980370i
$515$	19.3843	+	15.6375i	0.854176	+	0.689072i
$516$	−44.6036	−	4.97068i	−1.96357	−	0.218822i
$517$	−1.38442	−	0.121121i	−0.0608866	−	0.00532688i
$518$	−31.2242	−	24.5529i	−1.37191	−	1.07879i
$519$	9.43309	+	53.4977i	0.414067	+	2.34829i
$520$	−25.6124	−	11.1003i	−1.12318	−	0.486781i
$521$	9.94072	−	17.2178i	0.435511	−	0.754327i	−0.561826	−	0.827255i	$-0.689901\pi$
$521$	9.94072	−	17.2178i	0.435511	−	0.754327i	0.997337	+	0.0729284i	$0.0232345\pi$
$522$	18.1372	+	5.95599i	0.793842	+	0.260686i
$523$	10.6909	+	22.9267i	0.467481	+	1.00252i	0.988813	+	0.149162i	$0.0476577\pi$
$523$	10.6909	+	22.9267i	0.467481	+	1.00252i	−0.521331	+	0.853354i	$0.674564\pi$
$524$	34.2645	+	16.9784i	1.49685	+	0.741704i
$525$	−1.76362	−	45.6356i	−0.0769707	−	1.99170i
$526$	5.48420	−	8.38731i	0.239123	−	0.365704i
$527$	8.64003	−	0.755904i	0.376365	−	0.0329277i
$528$	−0.254909	−	6.39607i	−0.0110935	−	0.278353i
$529$	37.6896	+	6.64570i	1.63868	+	0.288943i
$530$	15.9505	−	21.1110i	0.692843	−	0.917005i
$531$		−	10.2420i		−	0.444467i
$532$	−0.815991	−	36.5625i	−0.0353777	−	1.58519i
$533$	−21.9237	+	21.9237i	−0.949620	+	0.949620i
$534$	3.43641	−	8.02571i	0.148708	−	0.347306i
$535$	1.92694	+	4.99208i	0.0833089	+	0.215826i
$536$	0.0971235	+	12.0527i	0.00419510	+	0.520597i
$537$	−0.746338	−	8.53068i	−0.0322068	−	0.368126i
$538$	−23.0129	+	4.81628i	−0.992159	+	0.207644i
$539$	3.89484	+	6.74606i	0.167763	+	0.290573i
$540$	−1.01492	−	12.2201i	−0.0436751	−	0.525870i
$541$	22.0102	+	8.01107i	0.946294	+	0.344423i	0.768648	−	0.639672i	$-0.220930\pi$
$541$	22.0102	+	8.01107i	0.946294	+	0.344423i	0.177646	+	0.984095i	$0.443152\pi$
$542$	1.88760	−	5.74813i	0.0810795	−	0.246903i
$543$	13.1431	−	3.52169i	0.564025	−	0.151130i
$544$	1.95009	−	18.8797i	0.0836094	−	0.809461i
$545$	30.2488	+	2.05868i	1.29572	+	0.0881840i
$546$	−56.6091	+	6.77084i	−2.42265	+	0.289765i
$547$	0.797963	−	9.12076i	0.0341184	−	0.389975i	−0.959866	−	0.280458i	$-0.909514\pi$
$547$	0.797963	−	9.12076i	0.0341184	−	0.389975i	0.993985	−	0.109518i	$-0.0349306\pi$
$548$	18.0750	−	14.4504i	0.772126	−	0.617288i
$549$	−4.05242	−	11.1339i	−0.172953	−	0.475185i
$550$	2.27551	−	4.67247i	0.0970283	−	0.199235i
$551$	22.8962	+	24.8669i	0.975413	+	1.05937i
$552$	4.58818	+	47.9863i	0.195286	+	2.04243i
$553$	6.04052	−	12.9539i	0.256869	−	0.550857i
$554$	8.20114	−	6.13983i	0.348433	−	0.260856i
$555$	14.3441	+	29.2714i	0.608872	+	1.24250i
$556$	−20.0251	−	14.7416i	−0.849254	−	0.625184i
$557$	4.72272	−	6.74474i	0.200108	−	0.285784i	−0.706539	−	0.707674i	$-0.749744\pi$
$557$	4.72272	−	6.74474i	0.200108	−	0.285784i	0.906647	+	0.421891i	$0.138633\pi$
$558$	−3.35512	−	5.40692i	−0.142034	−	0.228893i
$559$	−22.7440	+	39.3938i	−0.961970	+	1.66618i
$560$	35.6057	−	11.8367i	1.50462	−	0.500194i
$561$	−5.04555	−	1.83643i	−0.213023	−	0.0775341i
$562$	3.72229	−	6.94804i	0.157015	−	0.293085i
$563$	−1.68491	+	6.28819i	−0.0710107	+	0.265016i	−0.992299	−	0.123864i	$-0.960471\pi$
$563$	−1.68491	+	6.28819i	−0.0710107	+	0.265016i	0.921288	+	0.388880i	$0.127138\pi$
$564$	1.94184	+	8.00147i	0.0817662	+	0.336923i
$565$	19.2269	+	3.00859i	0.808882	+	0.126572i
$566$	−9.34078	−	0.518868i	−0.392622	−	0.0218096i
$567$	−26.9302	−	38.4603i	−1.13096	−	1.61518i
$568$	2.94529	+	6.18558i	0.123582	+	0.259541i
$569$		−	37.4721i		−	1.57091i	−0.618918	−	0.785455i	$-0.712429\pi$
$569$		−	37.4721i		−	1.57091i	0.618918	−	0.785455i	$-0.287571\pi$
$570$	−12.4151	+	27.3239i	−0.520011	+	1.14447i
$571$		−	7.53775i		−	0.315445i	−0.987483	−	0.157723i	$-0.949585\pi$
$571$		−	7.53775i		−	0.315445i	0.987483	−	0.157723i	$-0.0504152\pi$
$572$	−6.04230	−	2.36295i	−0.252641	−	0.0987999i
$573$	−25.3702	−	36.2324i	−1.05985	−	1.51363i
$574$	2.31147	−	41.6116i	0.0964788	−	1.73683i
$575$	−15.1583	+	36.0833i	−0.632144	+	1.50478i
$576$	−13.0073	+	4.97308i	−0.541970	+	0.207212i
$577$	1.42168	−	5.30580i	0.0591855	−	0.220883i	−0.929998	−	0.367563i	$-0.880192\pi$
$577$	1.42168	−	5.30580i	0.0591855	−	0.220883i	0.989184	+	0.146680i	$0.0468588\pi$
$578$	7.15829	+	3.83493i	0.297746	+	0.159512i
$579$	19.2395	+	7.00261i	0.799567	+	0.291018i
$580$	−17.4723	+	29.9576i	−0.725500	+	1.24392i
$581$	−4.99725	+	8.65550i	−0.207321	+	0.359090i
$582$	−2.89182	+	1.79444i	−0.119870	+	0.0743819i
$583$	3.52733	−	5.03755i	0.146087	−	0.208634i
$584$	14.2819	−	2.63712i	0.590989	−	0.109125i
$585$	16.2537	+	5.56280i	0.672007	+	0.229993i
$586$	24.9270	+	33.2956i	1.02972	+	1.37543i
$587$	17.0818	−	36.6320i	0.705041	−	1.51196i	−0.147364	−	0.989082i	$-0.547079\pi$
$587$	17.0818	−	36.6320i	0.705041	−	1.51196i	0.852405	−	0.522882i	$-0.175143\pi$
$588$	30.4962	−	34.6413i	1.25764	−	1.42858i
$589$	−0.518463	−	11.2554i	−0.0213629	−	0.463772i
$590$	18.1950	+	3.89165i	0.749075	+	0.160217i
$591$	−9.76306	−	26.8238i	−0.401598	−	1.10338i
$592$	−19.8139	+	18.0181i	−0.814347	+	0.740538i
$593$	0.200240	−	2.28875i	0.00822286	−	0.0939877i	−0.990974	−	0.134053i	$-0.957201\pi$
$593$	0.200240	−	2.28875i	0.00822286	−	0.0939877i	0.999197	+	0.0400649i	$0.0127565\pi$
$594$	−0.338467	−	2.82983i	−0.0138875	−	0.116109i
$595$	2.13709	−	31.4010i	0.0876122	−	1.28732i
$596$	18.5045	−	12.3135i	0.757973	−	0.504380i
$597$	−16.2825	+	4.36289i	−0.666399	+	0.178561i
$598$	46.4197	+	15.2436i	1.89824	+	0.623356i
$599$	−30.5487	−	11.1188i	−1.24819	−	0.454302i	−0.368397	−	0.929668i	$-0.620093\pi$
$599$	−30.5487	−	11.1188i	−1.24819	−	0.454302i	−0.879788	+	0.475366i	$0.842316\pi$
$600$	−30.5405	−	3.92597i	−1.24681	−	0.160277i
$601$	−4.90533	−	8.49628i	−0.200093	−	0.346571i	0.748465	−	0.663174i	$-0.230791\pi$
$601$	−4.90533	−	8.49628i	−0.200093	−	0.346571i	−0.948558	+	0.316603i	$0.897458\pi$
$602$	−12.5251	−	59.8471i	−0.510486	−	2.43919i
$603$	−0.646504	−	7.38957i	−0.0263277	−	0.300927i
$604$	9.80793	+	10.2846i	0.399079	+	0.418472i
$605$	−9.47334	+	21.3844i	−0.385146	+	0.869400i
$606$	−8.75189	−	3.74735i	−0.355521	−	0.152225i
$607$	−10.2565	+	10.2565i	−0.416297	+	0.416297i	−0.883925	−	0.467628i	$-0.845109\pi$
$607$	−10.2565	+	10.2565i	−0.416297	+	0.416297i	0.467628	+	0.883925i	$0.345109\pi$
$608$	−24.4019	−	3.54237i	−0.989627	−	0.143662i
$609$			70.8319i			2.87025i
$610$	21.3192	−	2.96857i	0.863189	−	0.120194i
$611$	8.21854	+	1.44915i	0.332487	+	0.0586264i
$612$	−0.277008	+	11.6776i	−0.0111974	+	0.472040i
$613$	44.7677	−	3.91667i	1.80815	−	0.158193i	0.867470	−	0.497489i	$-0.165744\pi$
$613$	44.7677	−	3.91667i	1.80815	−	0.158193i	0.940680	+	0.339296i	$0.110189\pi$
$614$	−21.1601	−	13.8360i	−0.853953	−	0.558374i
$615$	−16.5252	+	29.9435i	−0.666362	+	1.20744i
$616$	8.17062	−	3.04865i	0.329204	−	0.122833i
$617$	7.89633	+	16.9337i	0.317894	+	0.681727i	0.998713	−	0.0507257i	$-0.0161534\pi$
$617$	7.89633	+	16.9337i	0.317894	+	0.681727i	−0.680818	+	0.732452i	$0.738376\pi$
$618$	10.7002	−	32.5843i	0.430426	−	1.31073i
$619$	7.34363	−	12.7195i	0.295165	−	0.511241i	−0.679858	−	0.733344i	$-0.737959\pi$
$619$	7.34363	−	12.7195i	0.295165	−	0.511241i	0.975023	+	0.222102i	$0.0712920\pi$
$620$	10.8802	−	3.90591i	0.436960	−	0.156865i
$621$	3.72693	+	21.1364i	0.149556	+	0.848176i
$622$	17.3242	−	22.0314i	0.694637	−	0.883378i
$623$	11.8490	+	1.03666i	0.474721	+	0.0415327i
$624$	−1.82264	+	38.3963i	−0.0729640	+	1.53708i
$625$	−20.3342	−	14.5438i	−0.813368	−	0.581750i
$626$	−31.0501	+	33.0888i	−1.24101	+	1.32249i
$627$	−2.65394	+	6.45089i	−0.105988	+	0.257624i
$628$	6.32968	+	5.57230i	0.252582	+	0.222359i
$629$	7.68333	+	21.1098i	0.306354	+	0.841702i
$630$	−21.2676	+	8.99568i	−0.847323	+	0.358396i
$631$	−6.37634	−	7.59902i	−0.253838	−	0.302512i	0.624044	−	0.781389i	$-0.285489\pi$
$631$	−6.37634	−	7.59902i	−0.253838	−	0.302512i	−0.877882	+	0.478877i	$0.841044\pi$
$632$	−7.93830	−	5.46366i	−0.315769	−	0.217333i
$633$	−16.8920	−	11.8279i	−0.671396	−	0.470116i
$634$	0.682425	−	2.91424i	0.0271025	−	0.115739i
$635$	−0.419348	−	21.7103i	−0.0166413	−	0.861548i
$636$	−34.9608	−	10.2623i	−1.38629	−	0.406925i
$637$	−19.7692	−	42.3952i	−0.783284	−	1.67976i
$638$	−3.80645	+	7.10512i	−0.150699	+	0.281294i
$639$	−2.10815	−	3.65141i	−0.0833969	−	0.144448i
$640$	−3.89231	−	24.9970i	−0.153857	−	0.988093i
$641$	−1.53016	−	1.28396i	−0.0604379	−	0.0507134i	0.612068	−	0.790805i	$-0.290338\pi$
$641$	−1.53016	−	1.28396i	−0.0604379	−	0.0507134i	−0.672506	+	0.740091i	$0.734782\pi$
$642$	5.49143	−	4.91346i	0.216730	−	0.193919i
$643$	−38.0005	+	26.6082i	−1.49859	+	1.04933i	−0.517524	+	0.855669i	$0.673146\pi$
$643$	−38.0005	+	26.6082i	−1.49859	+	1.04933i	−0.981069	+	0.193657i	$0.937965\pi$
$644$	−60.1625	+	26.3358i	−2.37074	+	1.03778i
$645$	−12.0484	+	48.7091i	−0.474404	+	1.91792i
$646$	−10.5106	+	17.8135i	−0.413533	+	0.700863i
$647$	8.45933	−	8.45933i	0.332571	−	0.332571i	−0.520991	−	0.853562i	$-0.674438\pi$
$647$	8.45933	−	8.45933i	0.332571	−	0.332571i	0.853562	+	0.520991i	$0.174438\pi$
$648$	−28.5813	+	13.6091i	−1.12278	+	0.534617i
$649$	4.25885	+	0.750951i	0.167175	+	0.0294774i
$650$	−16.0582	+	26.7610i	−0.629854	+	1.04965i
$651$	15.1765	−	18.0866i	0.594814	−	0.708872i
$652$	11.1134	−	18.2362i	0.435236	−	0.714183i
$653$	13.0943	+	3.50860i	0.512419	+	0.137302i	0.505758	−	0.862676i	$-0.331213\pi$
$653$	13.0943	+	3.50860i	0.512419	+	0.137302i	0.00666129	+	0.999978i	$0.497880\pi$
$654$	−12.0816	−	39.9644i	−0.472428	−	1.56273i
$655$	23.8417	−	35.4890i	0.931573	−	1.38667i
$656$	−27.4096	−	6.18595i	−1.07017	−	0.241521i
$657$	−8.63349	+	2.31334i	−0.336825	+	0.0902519i
$658$	−9.53159	+	5.91457i	−0.371580	+	0.230574i
$659$	−2.39148	−	13.5628i	−0.0931589	−	0.528331i	−0.995296	−	0.0968810i	$-0.969113\pi$
$659$	−2.39148	−	13.5628i	−0.0931589	−	0.528331i	0.902137	−	0.431450i	$-0.141998\pi$
$660$	−7.12665	−	0.655136i	−0.277404	−	0.0255011i
$661$	7.08365	−	5.94389i	0.275522	−	0.231190i	−0.494547	−	0.869151i	$-0.664666\pi$
$661$	7.08365	−	5.94389i	0.275522	−	0.231190i	0.770069	+	0.637960i	$0.220222\pi$
$662$	−11.8598	−	1.70468i	−0.460946	−	0.0662544i
$663$	29.2226	+	13.6267i	1.13491	+	0.529218i
$664$	5.19679	+	4.28974i	0.201675	+	0.166474i
$665$	−40.6448	−	4.45569i	−1.57614	−	0.172784i
$666$	11.2784	−	12.0189i	0.437029	−	0.465723i
$667$	25.6535	−	55.0141i	0.993307	−	2.13015i
$668$	8.39586	+	10.5018i	0.324846	+	0.406328i
$669$	2.43315	+	2.89971i	0.0940709	+	0.112109i
$670$	13.3732	+	1.65929i	0.516652	+	0.0641040i
$671$	4.92685	−	0.868736i	0.190199	−	0.0335372i
$672$	−32.5886	−	40.0962i	−1.25713	−	1.54675i
$673$	4.04925	+	15.1120i	0.156087	+	0.582526i	0.999010	+	0.0444906i	$0.0141665\pi$
$673$	4.04925	+	15.1120i	0.156087	+	0.582526i	−0.842923	+	0.538035i	$0.819167\pi$
$674$	10.4844	+	20.7372i	0.403846	+	0.798766i
$675$	−13.6933	−	0.666569i	−0.527056	−	0.0256563i
$676$	11.6131	+	5.75439i	0.446656	+	0.221323i
$677$	−9.73875	+	36.3455i	−0.374291	+	1.39687i	0.480088	+	0.877221i	$0.340605\pi$
$677$	−9.73875	+	36.3455i	−0.374291	+	1.39687i	−0.854378	+	0.519651i	$0.826062\pi$
$678$	−5.48963	−	26.2304i	−0.210828	−	1.00737i
$679$	−3.55188	−	2.98039i	−0.136309	−	0.114377i
$680$	−20.6400	−	4.92923i	−0.791509	−	0.189027i
$681$	−3.55178	+	20.1432i	−0.136105	+	0.771887i
$682$	2.49431	−	0.998692i	0.0955121	−	0.0382419i
$683$	−9.06027	−	9.06027i	−0.346682	−	0.346682i	0.512190	−	0.858872i	$-0.328834\pi$
$683$	−9.06027	−	9.06027i	−0.346682	−	0.346682i	−0.858872	+	0.512190i	$0.828834\pi$
$684$	15.1430	+	0.984961i	0.579007	+	0.0376609i
$685$	−13.3667	−	22.1524i	−0.510714	−	0.846401i
$686$	19.6253	+	8.40307i	0.749297	+	0.320831i
$687$	6.33230	+	9.04346i	0.241592	+	0.345029i
$688$	−41.1922	+	1.64167i	−1.57044	+	0.0625882i
$689$	−23.7379	+	28.2898i	−0.904344	+	1.07775i
$690$	53.8597	+	1.94941i	2.05041	+	0.0742127i
$691$	18.1492	−	10.4785i	0.690429	−	0.398619i	−0.113344	−	0.993556i	$-0.536156\pi$
$691$	18.1492	−	10.4785i	0.690429	−	0.398619i	0.803773	+	0.594937i	$0.202823\pi$
$692$	15.9497	+	47.2814i	0.606318	+	1.79737i
$693$	−4.86420	+	2.26822i	−0.184776	+	0.0861624i
$694$	−16.1769	+	8.17883i	−0.614067	+	0.310464i
$695$	−19.2750	+	20.0343i	−0.731144	+	0.759945i
$696$	47.0967	+	7.91366i	1.78520	+	0.299966i
$697$	−13.5191	+	19.3072i	−0.512072	+	0.731314i
$698$	26.1943	−	33.3116i	0.991470	−	1.26086i
$699$	10.8570	−	9.11007i	0.410648	−	0.344575i
$700$	−7.89977	−	41.2000i	−0.298583	−	1.55721i
$701$	21.1527	−	7.69896i	0.798927	−	0.290786i	0.0898855	−	0.995952i	$-0.471350\pi$
$701$	21.1527	−	7.69896i	0.798927	−	0.290786i	0.709042	+	0.705166i	$0.249128\pi$
$702$	0.543721	+	17.1059i	0.0205214	+	0.645621i
$703$	27.8125	−	8.84260i	1.04897	−	0.333505i
$704$	−1.11421	−	5.77332i	−0.0419934	−	0.217590i
$705$	9.15335	−	0.979272i	0.344735	−	0.0368815i
$706$	26.8794	+	35.9036i	1.01162	+	1.35125i
$707$	1.13045	−	12.9211i	0.0425151	−	0.485950i
$708$	−3.84960	−	25.3313i	−0.144677	−	0.952008i
$709$	−22.8469	+	4.02852i	−0.858032	+	0.151294i	−0.585321	−	0.810802i	$-0.699032\pi$
$709$	−22.8469	+	4.02852i	−0.858032	+	0.151294i	−0.272711	+	0.962096i	$0.587920\pi$
$710$	7.28776	−	2.35769i	0.273505	−	0.0884827i
$711$	5.13619	+	2.96538i	0.192622	+	0.111210i
$712$	2.01311	−	7.76270i	0.0754444	−	0.290919i
$713$	−18.3379	+	8.55110i	−0.686759	+	0.320241i
$714$	−41.4866	+	12.5418i	−1.55260	+	0.469365i
$715$	−3.50486	+	6.35076i	−0.131074	+	0.237505i
$716$	−1.85509	−	7.64402i	−0.0693280	−	0.285670i
$717$	−1.66074	−	18.9824i	−0.0620217	−	0.708911i
$718$	−12.4970	+	11.1817i	−0.466386	+	0.417298i
$719$	−2.58088	+	14.6369i	−0.0962504	+	0.545863i	0.898107	+	0.439778i	$0.144943\pi$
$719$	−2.58088	+	14.6369i	−0.0962504	+	0.545863i	−0.994357	+	0.106085i	$0.966168\pi$
$720$	3.60518	+	15.1461i	0.134357	+	0.564461i
$721$	46.7249			1.74012
$722$	22.5594	+	14.5970i	0.839575	+	0.543243i
$723$	−36.1695	−	36.1695i	−1.34516	−	1.34516i
$724$	11.4497	−	5.01205i	0.425525	−	0.186271i
$725$	30.6429	+	23.7578i	1.13805	+	0.882344i
$726$	32.1581	+	1.78634i	1.19350	+	0.0662972i
$727$	−47.2506	+	4.13389i	−1.75243	+	0.153318i	−0.917682	−	0.397316i	$-0.869942\pi$
$727$	−47.2506	+	4.13389i	−1.75243	+	0.153318i	−0.834747	+	0.550634i	$0.814386\pi$
$728$	−50.4744	+	13.9614i	−1.87070	+	0.517446i
$729$	1.36136	−	0.785983i	0.0504208	−	0.0291105i
$730$	−0.829185	−	16.2164i	−0.0306895	−	0.600195i
$731$	−11.8270	+	32.4945i	−0.437439	+	1.20185i
$732$	−14.2075	−	26.0140i	−0.525126	−	0.961507i
$733$	−7.10733	−	26.5249i	−0.262515	−	0.979720i	−0.963754	−	0.266794i	$-0.914036\pi$
$733$	−7.10733	−	26.5249i	−0.262515	−	0.979720i	0.701238	−	0.712927i	$-0.252631\pi$
$734$	29.3451	+	6.87171i	1.08315	+	0.253639i
$735$	−33.9249	−	38.8799i	−1.25134	−	1.43411i
$736$	10.7893	+	42.9449i	0.397698	+	1.58297i
$737$	3.12014	+	0.272977i	0.114932	+	0.0100552i
$738$	17.1170	+	2.46032i	0.630085	+	0.0905658i
$739$	21.9164	−	7.97691i	0.806207	−	0.293435i	0.0941511	−	0.995558i	$-0.469986\pi$
$739$	21.9164	−	7.97691i	0.806207	−	0.293435i	0.712056	+	0.702122i	$0.247764\pi$
$740$	17.0661	+	24.6028i	0.627363	+	0.904418i
$741$	19.2528	−	37.2019i	0.707271	−	1.36664i
$742$	−1.57703	−	49.6148i	−0.0578947	−	1.82142i
$743$	11.2895	+	5.26438i	0.414171	+	0.193131i	0.618524	−	0.785766i	$-0.287731\pi$
$743$	11.2895	+	5.26438i	0.414171	+	0.193131i	−0.204352	+	0.978897i	$0.565509\pi$
$744$	−10.3304	−	12.1117i	−0.378730	−	0.444036i
$745$	−10.9353	−	22.3152i	−0.400637	−	0.817565i
$746$	−17.9175	+	2.14306i	−0.656007	+	0.0784629i
$747$	−3.39712	−	2.37869i	−0.124294	−	0.0870316i
$748$	−4.83549	−	0.971395i	−0.176803	−	0.0355177i
$749$	8.69408	+	5.01953i	0.317675	+	0.183410i
$750$	−8.82876	+	33.2750i	−0.322381	+	1.21503i
$751$	16.7952	−	46.1443i	0.612864	−	1.68383i	−0.110942	−	0.993827i	$-0.535387\pi$
$751$	16.7952	−	46.1443i	0.612864	−	1.68383i	0.723806	−	0.690004i	$-0.242391\pi$
$752$	2.86774	+	6.99844i	0.104576	+	0.255207i
$753$	−38.3058	−	10.2640i	−1.39594	−	0.374041i
$754$	26.4898	−	40.5124i	0.964703	−	1.47538i
$755$	12.8371	−	9.36320i	0.467188	−	0.340762i
$756$	−15.8766	−	16.6481i	−0.577426	−	0.605486i
$757$	41.6411	−	29.1574i	1.51347	−	1.05975i	0.537135	−	0.843496i	$-0.319507\pi$
$757$	41.6411	−	29.1574i	1.51347	−	1.05975i	0.976338	−	0.216249i	$-0.0693823\pi$
$758$	10.1741	−	4.07360i	0.369542	−	0.147960i
$759$	12.5264			0.454679
$760$	−7.50364	+	26.5273i	−0.272186	+	0.962245i
$761$	−8.74427			−0.316980			−0.158490	−	0.987361i	$-0.550662\pi$
$761$	−8.74427			−0.316980			−0.158490	+	0.987361i	$0.550662\pi$
$762$	−27.7594	+	11.1145i	−1.00562	+	0.402638i
$763$	46.5939	−	32.6254i	1.68681	−	1.18112i
$764$	−28.0400	−	29.4026i	−1.01445	−	1.06375i
$765$	12.9027	+	2.01899i	0.466496	+	0.0729966i
$766$	−0.992087	+	1.51726i	−0.0358455	+	0.0548207i
$767$	−25.0845	−	6.72138i	−0.905750	−	0.242695i
$768$	−30.3013	+	17.1887i	−1.09340	+	0.620244i
$769$	−1.74290	+	4.78858i	−0.0628506	+	0.172681i	−0.967143	−	0.254233i	$-0.918177\pi$
$769$	−1.74290	+	4.78858i	−0.0628506	+	0.172681i	0.904292	+	0.426914i	$0.140399\pi$
$770$	−2.18124	−	9.50310i	−0.0786063	−	0.342468i
$771$	43.3083	+	25.0040i	1.55971	+	0.900499i
$772$	18.4385	+	3.70409i	0.663617	+	0.133313i
$773$	−10.5454	−	7.38395i	−0.379291	−	0.265582i	0.368348	−	0.929688i	$-0.379924\pi$
$773$	−10.5454	−	7.38395i	−0.379291	−	0.265582i	−0.747639	+	0.664106i	$0.768812\pi$
$774$	25.1914	−	3.01306i	0.905486	−	0.108302i
$775$	−2.73418	−	12.6320i	−0.0982145	−	0.453757i
$776$	−2.37851	+	2.02869i	−0.0853837	+	0.0728259i
$777$	55.4251	+	25.8452i	1.98837	+	0.927190i
$778$	−0.112609	−	3.54277i	−0.00403723	−	0.127015i
$779$	24.3372	+	18.5821i	0.871972	+	0.665772i
$780$	42.2906	+	7.64913i	1.51424	+	0.273883i
$781$	1.67290	−	0.608888i	0.0598612	−	0.0217877i
$782$	36.7644	+	5.28436i	1.31469	+	0.188968i
$783$	21.1820	+	1.85319i	0.756984	+	0.0662275i
$784$	22.9139	−	35.6678i	0.818354	−	1.27385i
$785$	7.10417	−	6.19879i	0.253559	−	0.221244i
$786$	−57.3237	−	13.4235i	−2.04467	−	0.478799i
$787$	6.48699	+	24.2098i	0.231236	+	0.862985i	0.979810	+	0.199933i	$0.0640724\pi$
$787$	6.48699	+	24.2098i	0.231236	+	0.862985i	−0.748574	+	0.663052i	$0.769261\pi$
$788$	−12.5681	−	23.0123i	−0.447721	−	0.819778i
$789$	−5.27686	+	14.4980i	−0.187861	+	0.516144i
$790$	−7.21958	+	7.99768i	−0.256861	+	0.284545i
$791$	31.6188	−	18.2551i	1.12423	−	0.649077i
$792$	0.964704	+	3.48766i	0.0342793	+	0.123929i
$793$	−29.9284	+	2.61839i	−1.06279	+	0.0929818i
$794$	−26.4288	−	1.46808i	−0.937923	−	0.0521004i
$795$	−16.4998	+	37.2454i	−0.585187	+	1.32096i
$796$	−14.1846	+	6.20924i	−0.502761	+	0.220081i
$797$	39.4005	+	39.4005i	1.39564	+	1.39564i	0.812053	+	0.583584i	$0.198350\pi$
$797$	39.4005	+	39.4005i	1.39564	+	1.39564i	0.583584	+	0.812053i	$0.301650\pi$
$798$	14.0577	+	54.5223i	0.497638	+	1.93007i
$799$	6.34411			0.224438
$800$	−28.2768	+	0.649569i	−0.999736	+	0.0229657i
$801$	−0.857025	+	4.86043i	−0.0302815	+	0.171735i
$802$	21.0664	−	18.8491i	0.743880	−	0.665586i
$803$	−0.328922	−	3.75960i	−0.0116074	−	0.132673i
$804$	−4.37644	−	18.0334i	−0.154345	−	0.635988i
$805$	20.3702	+	70.5439i	0.717955	+	2.48634i
$806$	−15.4443	+	4.66896i	−0.544002	+	0.164457i
$807$	32.8067	−	15.2980i	1.15485	−	0.538516i
$808$	−8.46508	−	2.19526i	−0.297800	−	0.0772289i
$809$	34.3420	+	19.8274i	1.20740	+	0.697093i	0.962191	−	0.272377i	$-0.0878097\pi$
$809$	34.3420	+	19.8274i	1.20740	+	0.697093i	0.245210	+	0.969470i	$0.421143\pi$
$810$	10.8940	+	33.6741i	0.382778	+	1.18319i
$811$	34.2203	−	6.03397i	1.20164	−	0.211881i	0.463232	−	0.886237i	$-0.346690\pi$
$811$	34.2203	−	6.03397i	1.20164	−	0.211881i	0.738407	+	0.674356i	$0.235579\pi$
$812$	9.77548	+	64.3250i	0.343052	+	2.25737i
$813$	−0.811833	+	9.27929i	−0.0284722	+	0.325439i
$814$	4.17077	+	5.57102i	0.146186	+	0.195264i
$815$	−18.5834	−	14.9914i	−0.650947	−	0.525125i
$816$	3.70407	+	28.9860i	0.129668	+	1.01471i
$817$	41.5453	+	17.0920i	1.45349	+	0.597975i
$818$	1.42159	+	44.7245i	0.0497048	+	1.56375i
$819$	30.2861	−	11.0232i	1.05828	−	0.385183i
$820$	−10.8747	+	29.4734i	−0.379760	+	1.02926i
$821$	12.2159	−	10.2504i	0.426339	−	0.357741i	−0.404229	−	0.914658i	$-0.632460\pi$
$821$	12.2159	−	10.2504i	0.426339	−	0.357741i	0.830568	+	0.556917i	$0.188016\pi$
$822$	−22.0227	+	28.0065i	−0.768130	+	0.976840i
$823$	−26.3244	+	37.5952i	−0.917612	+	1.31049i	0.0327907	+	0.999462i	$0.489561\pi$
$823$	−26.3244	+	37.5952i	−0.917612	+	1.31049i	−0.950402	+	0.311023i	$0.899328\pi$
$824$	5.22031	−	31.0677i	0.181858	−	1.08230i
$825$	−1.77092	+	7.80300i	−0.0616554	+	0.271665i
$826$	31.1522	−	15.7501i	1.08392	−	0.548017i
$827$	−20.7610	+	9.68099i	−0.721929	+	0.336641i	−0.748617	−	0.663003i	$-0.769282\pi$
$827$	−20.7610	+	9.68099i	−0.721929	+	0.336641i	0.0266878	+	0.999644i	$0.491504\pi$
$828$	−8.71044	−	25.8212i	−0.302709	−	0.897350i
$829$	−26.5054	+	15.3029i	−0.920572	+	0.531493i	−0.883818	−	0.467832i	$-0.845035\pi$
$829$	−26.5054	+	15.3029i	−0.920572	+	0.531493i	−0.0367546	+	0.999324i	$0.511702\pi$
$830$	5.51653	−	5.13114i	0.191481	−	0.178105i
$831$	−10.1386	+	12.0827i	−0.351704	+	0.419144i
$832$	3.64386	+	35.1207i	0.126328	+	1.21759i
$833$	−20.3967	−	29.1295i	−0.706703	−	1.00928i
$834$	35.1932	+	15.0689i	1.21864	+	0.521793i
$835$	12.8709	−	7.76623i	0.445415	−	0.268761i
$836$	−1.51986	+	6.22456i	−0.0525654	+	0.215281i
$837$	−5.01169	−	5.01169i	−0.173229	−	0.173229i
$838$	−6.45421	+	2.58419i	−0.222957	+	0.0892693i
$839$	−0.332282	+	1.88447i	−0.0114717	+	0.0650590i	−0.990006	−	0.141024i	$-0.954961\pi$
$839$	−0.332282	+	1.88447i	−0.0114717	+	0.0650590i	0.978535	+	0.206083i	$0.0660717\pi$
$840$	−49.2194	+	30.2424i	−1.69823	+	1.04346i
$841$	−23.8523	−	20.0144i	−0.822492	−	0.690153i
$842$	7.24107	+	34.5990i	0.249544	+	1.19236i
$843$	−3.14091	+	11.7220i	−0.108179	+	0.403728i
$844$	−16.9726	−	8.41008i	−0.584220	−	0.289487i
$845$	8.08054	−	12.0281i	0.277979	−	0.413779i
$846$	−2.10015	−	4.15388i	−0.0722045	−	0.142813i
$847$	11.3568	+	42.3843i	0.390225	+	1.45634i
$848$	−33.1655	−	4.49460i	−1.13891	−	0.154345i
$849$	14.1843	−	2.50108i	0.486806	−	0.0858370i
$850$	−8.48932	+	22.1544i	−0.291181	+	0.759889i
$851$	−33.6874	−	40.1471i	−1.15479	−	1.37623i
$852$	−6.58644	−	8.23855i	−0.225648	−	0.282248i
$853$	9.10156	−	19.5184i	0.311631	−	0.668296i	−0.686644	−	0.726993i	$-0.740917\pi$
$853$	9.10156	−	19.5184i	0.311631	−	0.668296i	0.998276	+	0.0586977i	$0.0186948\pi$
$854$	27.6332	−	29.4475i	0.945587	−	1.00767i
$855$	3.31170	−	16.6398i	0.113258	−	0.569070i
$856$	4.30887	−	5.21996i	0.147274	−	0.178415i
$857$	−33.6867	−	15.7084i	−1.15072	−	0.536588i	−0.248824	−	0.968549i	$-0.580044\pi$
$857$	−33.6867	−	15.7084i	−1.15072	−	0.536588i	−0.901892	+	0.431961i	$0.857822\pi$
$858$	9.88712	+	1.42113i	0.337541	+	0.0485167i
$859$	−18.0015	+	15.1050i	−0.614203	+	0.515377i	−0.895975	−	0.444104i	$-0.853522\pi$
$859$	−18.0015	+	15.1050i	−0.614203	+	0.515377i	0.281773	+	0.959481i	$0.409078\pi$
$860$	−4.21923	+	45.8973i	−0.143875	+	1.56509i
$861$	11.1419	+	63.1889i	0.379715	+	2.15347i
$862$	26.2757	−	16.3047i	0.894956	−	0.555341i
$863$	24.1147	−	6.46152i	0.820875	−	0.219953i	0.176146	−	0.984364i	$-0.443637\pi$
$863$	24.1147	−	6.46152i	0.820875	−	0.219953i	0.644729	+	0.764411i	$0.276970\pi$
$864$	−12.8433	+	8.69646i	−0.436937	+	0.295860i
$865$	54.7440	−	10.7469i	1.86135	−	0.365404i
$866$	−10.7056	−	35.4126i	−0.363790	−	1.20337i
$867$	−12.0767	−	3.23595i	−0.410148	−	0.109899i
$868$	11.2862	−	18.5197i	0.383079	−	0.628598i
$869$	−1.60966	+	1.91831i	−0.0546038	+	0.0650743i
$870$	15.6758	−	51.0409i	0.531459	−	1.73045i
$871$	−18.5226	−	3.26604i	−0.627615	−	0.110665i
$872$	−16.4872	−	34.6257i	−0.558327	−	1.17257i
$873$	1.36042	−	1.36042i	0.0460434	−	0.0460434i
$874$	8.82815	−	47.4380i	0.298616	−	1.60461i
$875$	−46.8234	+	2.71597i	−1.58292	+	0.0918167i
$876$	−20.4834	+	8.96651i	−0.692071	+	0.302950i
$877$	19.0082	−	13.3097i	0.641861	−	0.449436i	−0.206792	−	0.978385i	$-0.566302\pi$
$877$	19.0082	−	13.3097i	0.641861	−	0.449436i	0.848654	+	0.528949i	$0.177414\pi$
$878$	14.5714	−	13.0377i	0.491761	−	0.440002i
$879$	−49.0543	−	41.1614i	−1.65456	−	1.38834i
$880$	−6.56238	+	0.388593i	−0.221218	+	0.0130995i
$881$	1.46272	+	2.53351i	0.0492803	+	0.0853560i	0.889613	−	0.456715i	$-0.150974\pi$
$881$	1.46272	+	2.53351i	0.0492803	+	0.0853560i	−0.840333	+	0.542070i	$0.817641\pi$
$882$	−12.3208	+	22.9979i	−0.414862	+	0.774381i
$883$	19.5377	+	41.8987i	0.657496	+	1.41000i	0.898279	+	0.439425i	$0.144818\pi$
$883$	19.5377	+	41.8987i	0.657496	+	1.41000i	−0.240784	+	0.970579i	$0.577404\pi$
$884$	28.4188	+	8.34193i	0.955826	+	0.280570i
$885$	−28.6411	+	0.553221i	−0.962759	+	0.0185963i
$886$	−12.2558	+	52.3373i	−0.411741	+	1.75831i
$887$	27.1700	+	19.0246i	0.912278	+	0.638784i	0.932562	−	0.361010i	$-0.117568\pi$
$887$	27.1700	+	19.0246i	0.912278	+	0.638784i	−0.0202840	+	0.999794i	$0.506457\pi$
$888$	23.3770	−	33.9651i	0.784481	−	1.13979i
$889$	−26.1859	−	31.2071i	−0.878246	−	1.04665i
$890$	−8.30890	−	3.36931i	−0.278515	−	0.112940i
$891$	2.81345	+	7.72988i	0.0942540	+	0.258961i
$892$	2.60982	+	2.29754i	0.0873832	+	0.0769272i
$893$	0.339760	−	8.23480i	0.0113696	−	0.275567i
$894$	−23.4166	+	24.9540i	−0.783167	+	0.834588i
$895$	−8.74444	+	0.935525i	−0.292295	+	0.0312712i
$896$	−35.1286	−	31.9153i	−1.17356	−	1.06622i
$897$	−74.9360	−	6.55605i	−2.50204	−	0.218900i
$898$	12.8078	−	16.2878i	0.427400	−	0.543530i
$899$	3.48086	+	19.7409i	0.116093	+	0.658397i
$900$	17.3161	−	1.77548i	0.577204	−	0.0591826i
$901$	−14.0370	+	24.3127i	−0.467639	+	0.809974i
$902$	−2.27808	+	6.93721i	−0.0758517	+	0.230984i
$903$	39.7838	+	85.3166i	1.32392	+	2.83916i
$904$	−8.60538	−	23.0631i	−0.286211	−	0.767068i
$905$	−3.87672	−	13.4254i	−0.128866	−	0.446276i
$906$	−18.3127	−	11.9741i	−0.608398	−	0.397813i
$907$	−44.8791	+	3.92641i	−1.49019	+	0.130374i	−0.802945	−	0.596054i	$-0.796735\pi$
$907$	−44.8791	+	3.92641i	−1.49019	+	0.130374i	−0.687242	+	0.726428i	$0.741179\pi$
$908$	−0.445554	+	18.7829i	−0.0147862	+	0.623333i
$909$	5.30021	+	0.934570i	0.175797	+	0.0309977i
$910$	8.07499	+	57.9916i	0.267683	+	1.92240i
$911$		−	44.2891i		−	1.46736i	−0.679493	−	0.733682i	$-0.737800\pi$
$911$		−	44.2891i		−	1.46736i	0.679493	−	0.733682i	$-0.262200\pi$
$912$	37.8229	−	3.25562i	1.25244	−	0.107804i
$913$	1.23819	−	1.23819i	0.0409780	−	0.0409780i
$914$	17.3271	+	7.41904i	0.573129	+	0.245400i
$915$	−30.9163	+	11.9337i	−1.02206	+	0.394515i
$916$	6.99867	+	7.33878i	0.231243	+	0.242480i
$917$	−6.99076	−	79.9047i	−0.230855	−	2.63869i
$918$	2.66516	+	12.7346i	0.0879634	+	0.420303i
$919$	25.6252	+	44.3841i	0.845297	+	1.46410i	0.885363	+	0.464899i	$0.153910\pi$
$919$	25.6252	+	44.3841i	0.845297	+	1.46410i	−0.0400670	+	0.999197i	$0.512757\pi$
$920$	49.1810	−	5.66283i	1.62145	−	0.186698i
$921$	36.5767	+	13.3128i	1.20524	+	0.438673i
$922$	31.4141	+	10.3160i	1.03457	+	0.339738i
$923$	−10.3264	+	2.76696i	−0.339898	+	0.0910755i
$924$	−11.1779	+	7.43818i	−0.367727	+	0.244698i
$925$	29.7712	−	15.3090i	0.978872	−	0.503355i
$926$	1.07526	+	8.98995i	0.0353352	+	0.295428i
$927$	−1.68977	+	19.3142i	−0.0554994	+	0.634362i
$928$	43.8624	+	0.686884i	1.43985	+	0.0225481i
$929$	5.70683	+	15.6794i	0.187235	+	0.514424i	0.997423	−	0.0717462i	$-0.0228572\pi$
$929$	5.70683	+	15.6794i	0.187235	+	0.514424i	−0.810188	+	0.586170i	$0.800635\pi$
$930$	−14.9388	+	9.67440i	−0.489863	+	0.317236i
$931$	−38.9031	+	24.9153i	−1.27500	+	0.816566i
$932$	8.60232	−	9.77155i	0.281779	−	0.320078i
$933$	−18.2360	+	39.1073i	−0.597020	+	1.28031i
$934$	−8.78820	−	11.7386i	−0.287559	−	0.384100i
$935$	−1.78556	+	5.21716i	−0.0583942	+	0.170619i
$936$	−3.94574	−	21.3690i	−0.128970	−	0.698468i
$937$	−9.81895	+	14.0229i	−0.320771	+	0.458109i	−0.946861	−	0.321642i	$-0.895765\pi$
$937$	−9.81895	+	14.0229i	−0.320771	+	0.458109i	0.626090	+	0.779751i	$0.284654\pi$
$938$	21.4819	−	13.3300i	0.701409	−	0.435241i
$939$	34.9302	−	60.5010i	1.13991	−	1.97437i
$940$	8.17735	−	2.15256i	0.266716	−	0.0702089i
$941$	41.6834	+	15.1715i	1.35884	+	0.494578i	0.915696	−	0.401872i	$-0.131640\pi$
$941$	41.6834	+	15.1715i	1.35884	+	0.494578i	0.443145	+	0.896450i	$0.353863\pi$
$942$	−11.4445	−	6.13120i	−0.372882	−	0.199765i
$943$	14.2316	−	53.1132i	0.463446	−	1.72960i
$944$	−6.99193	−	22.4730i	−0.227568	−	0.731434i
$945$	−20.7800	+	15.1567i	−0.675972	+	0.493046i
$946$	−0.594150	+	10.6960i	−0.0193175	+	0.347758i
$947$	−3.47946	−	4.96918i	−0.113067	−	0.161477i	0.758630	−	0.651522i	$-0.225869\pi$
$947$	−3.47946	−	4.96918i	−0.113067	−	0.161477i	−0.871697	+	0.490045i	$0.836980\pi$
$948$	13.8177	+	5.40368i	0.448780	+	0.175503i
$949$			22.6630i			0.735674i
$950$	28.3023	+	12.2058i	0.918247	+	0.396009i
$951$			4.60811i			0.149428i
$952$	−35.9446	+	17.1152i	−1.16497	+	0.554707i
$953$	9.70663	+	13.8625i	0.314429	+	0.449051i	0.944995	−	0.327085i	$-0.106066\pi$
$953$	9.70663	+	13.8625i	0.314429	+	0.449051i	−0.630566	+	0.776135i	$0.717177\pi$
$954$	20.5658	+	1.14240i	0.665843	+	0.0369867i
$955$	−36.7000	+	26.7685i	−1.18758	+	0.866210i
$956$	−4.12794	−	17.0094i	−0.133507	−	0.550124i
$957$	3.21192	−	11.9870i	0.103827	−	0.387486i
$958$	0.0920917	−	0.171898i	0.00297535	−	0.00555378i
$959$	−45.6122	−	16.6015i	−1.47289	−	0.536089i
$960$	14.6094	+	36.1052i	0.471517	+	1.16529i
$961$	−12.1591	+	21.0602i	−0.392229	+	0.679361i
$962$	−22.0349	−	35.5102i	−0.710433	−	1.14489i
$963$	−2.38929	+	3.41226i	−0.0769938	+	0.109959i
$964$	−37.8386	−	27.8551i	−1.21870	−	0.897154i
$965$	6.80865	−	19.8939i	0.219178	−	0.640407i
$966$	80.9415	−	60.5973i	2.60425	−	1.94969i
$967$	0.583075	−	1.25041i	0.0187504	−	0.0402104i	−0.896710	−	0.442619i	$-0.854049\pi$
$967$	0.583075	−	1.25041i	0.0187504	−	0.0402104i	0.915460	+	0.402409i	$0.131827\pi$
$968$	29.4505	−	2.81589i	0.946574	−	0.0905060i
$969$	9.50273	−	30.3927i	0.305272	−	0.976354i
$970$	1.89987	+	2.93371i	0.0610012	+	0.0941957i
$971$	−5.76500	−	15.8392i	−0.185008	−	0.508304i	0.812167	−	0.583425i	$-0.198288\pi$
$971$	−5.76500	−	15.8392i	−0.185008	−	0.508304i	−0.997174	+	0.0751212i	$0.976066\pi$
$972$	25.2176	−	20.1606i	0.808854	−	0.646651i
$973$	−4.54580	+	51.9587i	−0.145732	+	1.66572i
$974$	30.6321	−	3.66381i	0.981516	−	0.117396i
$975$	14.6780	−	45.7527i	0.470072	−	1.46526i
$976$	−16.4926	−	21.6635i	−0.527915	−	0.693432i
$977$	32.9295	−	8.82345i	1.05351	−	0.282287i	0.309808	−	0.950799i	$-0.399735\pi$
$977$	32.9295	−	8.82345i	1.05351	−	0.282287i	0.743701	+	0.668512i	$0.233068\pi$
$978$	−10.2581	+	31.2379i	−0.328017	+	0.998878i
$979$	−1.95823	−	0.712738i	−0.0625853	−	0.0227792i
$980$	−36.1743	−	30.6263i	−1.15555	−	0.978321i
$981$	11.8010	+	20.4399i	0.376777	+	0.652597i
$982$	−26.8075	+	5.61042i	−0.855461	+	0.179036i
$983$	4.57878	+	52.3356i	0.146040	+	1.66925i	0.616902	+	0.787040i	$0.288388\pi$
$983$	4.57878	+	52.3356i	0.146040	+	1.66925i	−0.470861	+	0.882207i	$0.656057\pi$
$984$	43.2596	−	0.348597i	1.37907	−	0.0111129i
$985$	−27.3488	+	10.5566i	−0.871407	+	0.336363i
$986$	14.4837	−	33.8265i	0.461254	−	1.07725i
$987$	12.2121	−	12.2121i	0.388714	−	0.388714i
$988$	12.3500	−	36.4414i	0.392906	−	1.15936i
$989$		−	80.6728i		−	2.56525i
$990$	4.00709	−	0.557963i	0.127354	−	0.0177332i
$991$	−3.52997	−	0.622429i	−0.112133	−	0.0197721i	0.117300	−	0.993097i	$-0.462576\pi$
$991$	−3.52997	−	0.622429i	−0.112133	−	0.0197721i	−0.229433	+	0.973324i	$0.573687\pi$
$992$	−11.0529	−	9.57339i	−0.350931	−	0.303955i
$993$	18.3768	−	1.60776i	0.583169	−	0.0510207i
$994$	7.86424	−	12.0272i	0.249439	−	0.381481i
$995$	4.80272	+	16.6323i	0.152256	+	0.527278i
$996$	−9.29603	−	4.60628i	−0.294556	−	0.145955i
$997$	−25.5604	−	54.8144i	−0.809505	−	1.73599i	−0.665480	−	0.746416i	$-0.731773\pi$
$997$	−25.5604	−	54.8144i	−0.809505	−	1.73599i	−0.144025	−	0.989574i	$-0.546005\pi$
$998$	−43.5321	−	14.2953i	−1.37799	−	0.452510i
$999$	9.17901	−	15.8985i	0.290411	−	0.503006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.347.8	yes	672
4.3	odd	2	inner	380.2.bj.a.347.24	yes	672
5.3	odd	4	inner	380.2.bj.a.43.36	yes	672
19.4	even	9	inner	380.2.bj.a.327.6	yes	672
20.3	even	4	inner	380.2.bj.a.43.6	yes	672
76.23	odd	18	inner	380.2.bj.a.327.36	yes	672
95.23	odd	36	inner	380.2.bj.a.23.24	yes	672
380.23	even	36	inner	380.2.bj.a.23.8	✓	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.8	✓	672	380.23	even	36	inner
380.2.bj.a.23.24	yes	672	95.23	odd	36	inner
380.2.bj.a.43.6	yes	672	20.3	even	4	inner
380.2.bj.a.43.36	yes	672	5.3	odd	4	inner
380.2.bj.a.327.6	yes	672	19.4	even	9	inner
380.2.bj.a.327.36	yes	672	76.23	odd	18	inner
380.2.bj.a.347.8	yes	672	1.1	even	1	trivial
380.2.bj.a.347.24	yes	672	4.3	odd	2	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31289 + 0.525665i) q^{2} +(1.78355 - 1.24886i) q^{3} +(1.44735 - 1.38028i) q^{4} +(-1.31769 - 1.80657i) q^{5} +(-1.68512 + 2.57716i) q^{6} +(-4.05211 - 1.08576i) q^{7} +(-1.17465 + 2.57297i) q^{8} +(0.595352 - 1.63572i) q^{9} +O(q^{10})\)	\(q+(-1.31289 + 0.525665i) q^{2} +(1.78355 - 1.24886i) q^{3} +(1.44735 - 1.38028i) q^{4} +(-1.31769 - 1.80657i) q^{5} +(-1.68512 + 2.57716i) q^{6} +(-4.05211 - 1.08576i) q^{7} +(-1.17465 + 2.57297i) q^{8} +(0.595352 - 1.63572i) q^{9} +(2.67963 + 1.67916i) q^{10} +(0.636513 + 0.367491i) q^{11} +(0.857659 - 4.26933i) q^{12} +(-3.61545 - 2.53156i) q^{13} +(5.89071 - 0.704570i) q^{14} +(-4.60631 - 1.57650i) q^{15} +(0.189663 - 3.99550i) q^{16} +(-3.04089 - 1.41799i) q^{17} +(0.0782073 + 2.46047i) q^{18} +(-2.00344 + 3.87121i) q^{19} +(-4.40073 - 0.795965i) q^{20} +(-8.58310 + 3.12399i) q^{21} +(-1.02885 - 0.147882i) q^{22} +(7.79780 + 0.682219i) q^{23} +(1.11823 + 6.05600i) q^{24} +(-1.52739 + 4.76100i) q^{25} +(6.07743 + 1.42315i) q^{26} +(0.709658 + 2.64848i) q^{27} +(-7.36348 + 4.02156i) q^{28} +(2.65230 - 7.28713i) q^{29} +(6.87628 - 0.351602i) q^{30} +(-2.23860 + 1.29246i) q^{31} +(1.85129 + 5.34535i) q^{32} +(1.59420 - 0.139474i) q^{33} +(4.73774 + 0.263175i) q^{34} +(3.37793 + 8.75111i) q^{35} +(-1.39606 - 3.18921i) q^{36} +(-4.73432 - 4.73432i) q^{37} +(0.595338 - 6.13560i) q^{38} -9.60989 q^{39} +(6.19608 - 1.26830i) q^{40} +(1.21984 - 6.91803i) q^{41} +(9.62648 - 8.61329i) q^{42} +(-0.898247 - 10.2670i) q^{43} +(1.42850 - 0.346676i) q^{44} +(-3.73952 + 1.07982i) q^{45} +(-10.5963 + 3.20335i) q^{46} +(-1.71365 + 0.799087i) q^{47} +(-4.65153 - 7.36304i) q^{48} +(9.17854 + 5.29923i) q^{49} +(-0.497401 - 7.05355i) q^{50} +(-7.19444 + 1.26857i) q^{51} +(-8.72709 + 1.32626i) q^{52} +(0.729246 - 8.33532i) q^{53} +(-2.32391 - 3.10412i) q^{54} +(-0.174829 - 1.63414i) q^{55} +(7.55344 - 9.15059i) q^{56} +(1.26134 + 9.40650i) q^{57} +(0.348414 + 10.9614i) q^{58} +(5.52905 - 2.01241i) q^{59} +(-8.84297 + 4.07623i) q^{60} +(5.21429 - 4.37531i) q^{61} +(2.25963 - 2.87360i) q^{62} +(-4.18842 + 5.98169i) q^{63} +(-5.24039 - 6.04469i) q^{64} +(0.190595 + 9.86737i) q^{65} +(-2.01969 + 1.02113i) q^{66} +(3.86215 - 1.80095i) q^{67} +(-6.35846 + 2.14494i) q^{68} +(14.7598 - 8.52155i) q^{69} +(-9.03499 - 9.71358i) q^{70} +(1.55696 - 1.85551i) q^{71} +(3.50932 + 3.45322i) q^{72} +(-2.94518 - 4.20615i) q^{73} +(8.70430 + 3.72697i) q^{74} +(3.22163 + 10.3990i) q^{75} +(2.44366 + 8.36831i) q^{76} +(-2.18021 - 2.18021i) q^{77} +(12.6167 - 5.05158i) q^{78} +(-0.591642 + 3.35537i) q^{79} +(-7.46807 + 4.92219i) q^{80} +(8.57362 + 7.19412i) q^{81} +(2.03506 + 9.72383i) q^{82} +(0.616624 - 2.30127i) q^{83} +(-8.11080 + 16.3686i) q^{84} +(1.44525 + 7.36205i) q^{85} +(6.57630 + 13.0073i) q^{86} +(-4.37006 - 16.3093i) q^{87} +(-1.69323 + 1.20606i) q^{88} +(-2.79224 + 0.492347i) q^{89} +(4.34195 - 3.38342i) q^{90} +(11.9015 + 14.1837i) q^{91} +(12.2278 - 9.77572i) q^{92} +(-2.37857 + 5.10085i) q^{93} +(1.82978 - 1.94992i) q^{94} +(9.63351 - 1.48170i) q^{95} +(9.97743 + 7.22171i) q^{96} +(1.00171 + 0.467106i) q^{97} +(-14.8360 - 2.13247i) q^{98} +(0.980060 - 0.822368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

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