LMFDB - Embedded newform 380.2.k.d.267.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, degree $2$, 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:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.7
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07073 - 0.923868i) q^{2} +(-1.14885 - 1.14885i) q^{3} +(0.292934 + 1.97843i) q^{4} +(1.95382 - 1.08746i) q^{5} +(0.168724 + 2.29149i) q^{6} +(-2.70883 + 2.70883i) q^{7} +(1.51416 - 2.38900i) q^{8} -0.360306i q^{9} +O(q^{10})$	\(q+(-1.07073 - 0.923868i) q^{2} +(-1.14885 - 1.14885i) q^{3} +(0.292934 + 1.97843i) q^{4} +(1.95382 - 1.08746i) q^{5} +(0.168724 + 2.29149i) q^{6} +(-2.70883 + 2.70883i) q^{7} +(1.51416 - 2.38900i) q^{8} -0.360306i q^{9} +(-3.09669 - 0.640694i) q^{10} -4.11798i q^{11} +(1.93638 - 2.60945i) q^{12} +(-1.95079 + 1.95079i) q^{13} +(5.40302 - 0.397828i) q^{14} +(-3.49397 - 0.995314i) q^{15} +(-3.82838 + 1.15910i) q^{16} +(-4.15549 - 4.15549i) q^{17} +(-0.332875 + 0.385791i) q^{18} -1.00000 q^{19} +(2.72381 + 3.54695i) q^{20} +6.22405 q^{21} +(-3.80447 + 4.40926i) q^{22} +(-3.01995 - 3.01995i) q^{23} +(-4.48413 + 1.00506i) q^{24} +(2.63485 - 4.24942i) q^{25} +(3.89106 - 0.286501i) q^{26} +(-3.86047 + 3.86047i) q^{27} +(-6.15273 - 4.56572i) q^{28} +2.35086i q^{29} +(2.82157 + 4.29368i) q^{30} +5.48110i q^{31} +(5.17002 + 2.29583i) q^{32} +(-4.73093 + 4.73093i) q^{33} +(0.610291 + 8.28855i) q^{34} +(-2.34682 + 8.23831i) q^{35} +(0.712840 - 0.105546i) q^{36} +(3.69981 + 3.69981i) q^{37} +(1.07073 + 0.923868i) q^{38} +4.48233 q^{39} +(0.360440 - 6.31428i) q^{40} -9.82744 q^{41} +(-6.66429 - 5.75020i) q^{42} +(-8.96408 - 8.96408i) q^{43} +(8.14714 - 1.20630i) q^{44} +(-0.391819 - 0.703974i) q^{45} +(0.443521 + 6.02359i) q^{46} +(-0.482563 + 0.482563i) q^{47} +(5.72985 + 3.06659i) q^{48} -7.67547i q^{49} +(-6.74712 + 2.11574i) q^{50} +9.54804i q^{51} +(-4.43097 - 3.28806i) q^{52} +(-2.71437 + 2.71437i) q^{53} +(7.70010 - 0.566964i) q^{54} +(-4.47815 - 8.04581i) q^{55} +(2.36981 + 10.5730i) q^{56} +(1.14885 + 1.14885i) q^{57} +(2.17189 - 2.51714i) q^{58} +9.02322 q^{59} +(0.945656 - 7.20414i) q^{60} -4.23945 q^{61} +(5.06381 - 5.86878i) q^{62} +(0.976005 + 0.976005i) q^{63} +(-3.41467 - 7.23464i) q^{64} +(-1.69009 + 5.93292i) q^{65} +(9.43631 - 0.694802i) q^{66} +(6.49679 - 6.49679i) q^{67} +(7.00407 - 9.43864i) q^{68} +6.93891i q^{69} +(10.1239 - 6.65288i) q^{70} -14.9562i q^{71} +(-0.860771 - 0.545559i) q^{72} +(7.29798 - 7.29798i) q^{73} +(-0.543368 - 7.37965i) q^{74} +(-7.90896 + 1.85490i) q^{75} +(-0.292934 - 1.97843i) q^{76} +(11.1549 + 11.1549i) q^{77} +(-4.79937 - 4.14108i) q^{78} +3.64828 q^{79} +(-6.21949 + 6.42790i) q^{80} +7.78926 q^{81} +(10.5226 + 9.07926i) q^{82} +(8.32940 + 8.32940i) q^{83} +(1.82324 + 12.3138i) q^{84} +(-12.6380 - 3.60015i) q^{85} +(1.31650 + 17.8798i) q^{86} +(2.70078 - 2.70078i) q^{87} +(-9.83787 - 6.23527i) q^{88} -9.76244i q^{89} +(-0.230846 + 1.11576i) q^{90} -10.5687i q^{91} +(5.09011 - 6.85941i) q^{92} +(6.29693 - 6.29693i) q^{93} +(0.962520 - 0.0708710i) q^{94} +(-1.95382 + 1.08746i) q^{95} +(-3.30201 - 8.57712i) q^{96} +(0.208633 + 0.208633i) q^{97} +(-7.09112 + 8.21837i) q^{98} -1.48373 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.07073	−	0.923868i	−0.757122	−	0.653274i
$2$	−1.07073	−	0.923868i	−0.757122	−	0.653274i
$3$	−1.14885	−	1.14885i	−0.663287	−	0.663287i	0.292867	−	0.956153i	$-0.405391\pi$
$3$	−1.14885	−	1.14885i	−0.663287	−	0.663287i	−0.956153	+	0.292867i	$0.905391\pi$
$4$	0.292934	+	1.97843i	0.146467	+	0.989216i
$5$	1.95382	−	1.08746i	0.873776	−	0.486328i
$5$	1.95382	−	1.08746i	0.873776	−	0.486328i
$6$	0.168724	+	2.29149i	0.0688812	+	0.935496i
$7$	−2.70883	+	2.70883i	−1.02384	+	1.02384i	−0.0241310	+	0.999709i	$0.507682\pi$
$7$	−2.70883	+	2.70883i	−1.02384	+	1.02384i	−0.999709	+	0.0241310i	$0.992318\pi$
$8$	1.51416	−	2.38900i	0.535335	−	0.844640i
$9$		−	0.360306i		−	0.120102i
$10$	−3.09669	−	0.640694i	−0.979261	−	0.202605i
$11$		−	4.11798i		−	1.24162i	−0.783962	−	0.620809i	$-0.786804\pi$
$11$		−	4.11798i		−	1.24162i	0.783962	−	0.620809i	$-0.213196\pi$
$12$	1.93638	−	2.60945i	0.558984	−	0.753283i
$13$	−1.95079	+	1.95079i	−0.541053	+	0.541053i	−0.923838	−	0.382785i	$-0.874965\pi$
$13$	−1.95079	+	1.95079i	−0.541053	+	0.541053i	0.382785	+	0.923838i	$0.374965\pi$
$14$	5.40302	−	0.397828i	1.44402	−	0.106324i
$15$	−3.49397	−	0.995314i	−0.902139	−	0.256989i
$16$	−3.82838	+	1.15910i	−0.957095	+	0.289775i
$17$	−4.15549	−	4.15549i	−1.00786	−	1.00786i	−0.999969	−	0.00788621i	$-0.997490\pi$
$17$	−4.15549	−	4.15549i	−1.00786	−	1.00786i	−0.00788621	−	0.999969i	$-0.502510\pi$
$18$	−0.332875	+	0.385791i	−0.0784594	+	0.0909318i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	2.72381	+	3.54695i	0.609063	+	0.793122i
$21$	6.22405			1.35820
$22$	−3.80447	+	4.40926i	−0.811117	+	0.940057i
$23$	−3.01995	−	3.01995i	−0.629703	−	0.629703i	0.318291	−	0.947993i	$-0.396891\pi$
$23$	−3.01995	−	3.01995i	−0.629703	−	0.629703i	−0.947993	+	0.318291i	$0.896891\pi$
$24$	−4.48413	+	1.00506i	−0.915319	+	0.205158i
$25$	2.63485	−	4.24942i	0.526970	−	0.849884i
$26$	3.89106	−	0.286501i	0.763099	−	0.0561875i
$27$	−3.86047	+	3.86047i	−0.742949	+	0.742949i
$28$	−6.15273	−	4.56572i	−1.16276	−	0.862839i
$29$			2.35086i			0.436544i	0.975888	+	0.218272i	$0.0700420\pi$
$29$			2.35086i			0.436544i	−0.975888	+	0.218272i	$0.929958\pi$
$30$	2.82157	+	4.29368i	0.515145	+	0.783916i
$31$			5.48110i			0.984434i	0.870473	+	0.492217i	$0.163813\pi$
$31$			5.48110i			0.984434i	−0.870473	+	0.492217i	$0.836187\pi$
$32$	5.17002	+	2.29583i	0.913940	+	0.405849i
$33$	−4.73093	+	4.73093i	−0.823549	+	0.823549i
$34$	0.610291	+	8.28855i	0.104664	+	1.42147i
$35$	−2.34682	+	8.23831i	−0.396685	+	1.39253i
$36$	0.712840	−	0.105546i	0.118807	−	0.0175910i
$37$	3.69981	+	3.69981i	0.608246	+	0.608246i	0.942487	−	0.334242i	$-0.108480\pi$
$37$	3.69981	+	3.69981i	0.608246	+	0.608246i	−0.334242	+	0.942487i	$0.608480\pi$
$38$	1.07073	+	0.923868i	0.173696	+	0.149871i
$39$	4.48233			0.717746
$40$	0.360440	−	6.31428i	0.0569905	−	0.998375i
$41$	−9.82744			−1.53479			−0.767394	−	0.641176i	$-0.778447\pi$
$41$	−9.82744			−1.53479			−0.767394	+	0.641176i	$0.778447\pi$
$42$	−6.66429	−	5.75020i	−1.02832	−	0.887275i
$43$	−8.96408	−	8.96408i	−1.36701	−	1.36701i	−0.864671	−	0.502339i	$-0.832473\pi$
$43$	−8.96408	−	8.96408i	−1.36701	−	1.36701i	−0.502339	−	0.864671i	$-0.667527\pi$
$44$	8.14714	−	1.20630i	1.22823	−	0.181856i
$45$	−0.391819	−	0.703974i	−0.0584090	−	0.104942i
$46$	0.443521	+	6.02359i	0.0653936	+	0.888130i
$47$	−0.482563	+	0.482563i	−0.0703891	+	0.0703891i	−0.741425	−	0.671036i	$-0.765850\pi$
$47$	−0.482563	+	0.482563i	−0.0703891	+	0.0703891i	0.671036	+	0.741425i	$0.265850\pi$
$48$	5.72985	+	3.06659i	0.827032	+	0.442624i
$49$		−	7.67547i		−	1.09650i
$50$	−6.74712	+	2.11574i	−0.954187	+	0.299211i
$51$			9.54804i			1.33699i
$52$	−4.43097	−	3.28806i	−0.614465	−	0.455972i
$53$	−2.71437	+	2.71437i	−0.372848	+	0.372848i	−0.868513	−	0.495666i	$-0.834924\pi$
$53$	−2.71437	+	2.71437i	−0.372848	+	0.372848i	0.495666	+	0.868513i	$0.334924\pi$
$54$	7.70010	−	0.566964i	1.04785	−	0.0771540i
$55$	−4.47815	−	8.04581i	−0.603834	−	1.08490i
$56$	2.36981	+	10.5730i	0.316679	+	1.41287i
$57$	1.14885	+	1.14885i	0.152168	+	0.152168i
$58$	2.17189	−	2.51714i	0.285183	−	0.330517i
$59$	9.02322			1.17472			0.587361	−	0.809325i	$-0.300167\pi$
$59$	9.02322			1.17472			0.587361	+	0.809325i	$0.300167\pi$
$60$	0.945656	−	7.20414i	0.122084	−	0.930050i
$61$	−4.23945			−0.542806			−0.271403	−	0.962466i	$-0.587488\pi$
$61$	−4.23945			−0.542806			−0.271403	+	0.962466i	$0.587488\pi$
$62$	5.06381	−	5.86878i	0.643105	−	0.745336i
$63$	0.976005	+	0.976005i	0.122965	+	0.122965i
$64$	−3.41467	−	7.23464i	−0.426833	−	0.904330i
$65$	−1.69009	+	5.93292i	−0.209630	+	0.735889i
$66$	9.43631	−	0.694802i	1.16153	−	0.0855242i
$67$	6.49679	−	6.49679i	0.793710	−	0.793710i	−0.188386	−	0.982095i	$-0.560325\pi$
$67$	6.49679	−	6.49679i	0.793710	−	0.793710i	0.982095	+	0.188386i	$0.0603255\pi$
$68$	7.00407	−	9.43864i	0.849368	−	1.14460i
$69$			6.93891i			0.835347i
$70$	10.1239	−	6.65288i	1.21004	−	0.795171i
$71$		−	14.9562i		−	1.77497i	−0.460837	−	0.887485i	$-0.652451\pi$
$71$		−	14.9562i		−	1.77497i	0.460837	−	0.887485i	$-0.347549\pi$
$72$	−0.860771	−	0.545559i	−0.101443	−	0.0642947i
$73$	7.29798	−	7.29798i	0.854164	−	0.854164i	−0.136479	−	0.990643i	$-0.543579\pi$
$73$	7.29798	−	7.29798i	0.854164	−	0.854164i	0.990643	+	0.136479i	$0.0435785\pi$
$74$	−0.543368	−	7.37965i	−0.0631653	−	0.857867i
$75$	−7.90896	+	1.85490i	−0.913249	+	0.214185i
$76$	−0.292934	−	1.97843i	−0.0336019	−	0.226942i
$77$	11.1549	+	11.1549i	1.27122	+	1.27122i
$78$	−4.79937	−	4.14108i	−0.543422	−	0.468885i
$79$	3.64828			0.410464			0.205232	−	0.978713i	$-0.434205\pi$
$79$	3.64828			0.410464			0.205232	+	0.978713i	$0.434205\pi$
$80$	−6.21949	+	6.42790i	−0.695361	+	0.718661i
$81$	7.78926			0.865474
$82$	10.5226	+	9.07926i	1.16202	+	1.00264i
$83$	8.32940	+	8.32940i	0.914270	+	0.914270i	0.996605	−	0.0823347i	$-0.0262377\pi$
$83$	8.32940	+	8.32940i	0.914270	+	0.914270i	−0.0823347	+	0.996605i	$0.526238\pi$
$84$	1.82324	+	12.3138i	0.198932	+	1.34355i
$85$	−12.6380	−	3.60015i	−1.37079	−	0.390491i
$86$	1.31650	+	17.8798i	0.141962	+	1.92802i
$87$	2.70078	−	2.70078i	0.289554	−	0.289554i
$88$	−9.83787	−	6.23527i	−1.04872	−	0.664682i
$89$		−	9.76244i		−	1.03482i	−0.855739	−	0.517408i	$-0.826897\pi$
$89$		−	9.76244i		−	1.03482i	0.855739	−	0.517408i	$-0.173103\pi$
$90$	−0.230846	+	1.11576i	−0.0243333	+	0.117611i
$91$		−	10.5687i		−	1.10790i
$92$	5.09011	−	6.85941i	0.530681	−	0.715142i
$93$	6.29693	−	6.29693i	0.652962	−	0.652962i
$94$	0.962520	−	0.0708710i	0.0992764	−	0.00730979i
$95$	−1.95382	+	1.08746i	−0.200458	+	0.111571i
$96$	−3.30201	−	8.57712i	−0.337010	−	0.875399i
$97$	0.208633	+	0.208633i	0.0211835	+	0.0211835i	0.717619	−	0.696436i	$-0.245232\pi$
$97$	0.208633	+	0.208633i	0.0211835	+	0.0211835i	−0.696436	+	0.717619i	$0.745232\pi$
$98$	−7.09112	+	8.21837i	−0.716312	+	0.830181i
$99$	−1.48373			−0.149121
$100$	9.17902	+	3.96806i	0.917902	+	0.396806i
$101$	−18.7952			−1.87019			−0.935096	−	0.354394i	$-0.884687\pi$
$101$	−18.7952			−1.87019			−0.935096	+	0.354394i	$0.884687\pi$
$102$	8.82114	−	10.2234i	0.873423	−	1.01227i
$103$	−0.733254	−	0.733254i	−0.0722496	−	0.0722496i	0.670059	−	0.742308i	$-0.266269\pi$
$103$	−0.733254	−	0.733254i	−0.0722496	−	0.0722496i	−0.742308	+	0.670059i	$0.766269\pi$
$104$	1.70665	+	7.61426i	0.167350	+	0.746640i
$105$	12.1607	−	6.76842i	1.18676	−	0.660530i
$106$	5.41409	−	0.398643i	0.525863	−	0.0387196i
$107$	4.19542	−	4.19542i	0.405586	−	0.405586i	−0.474610	−	0.880196i	$-0.657411\pi$
$107$	4.19542	−	4.19542i	0.405586	−	0.405586i	0.880196	+	0.474610i	$0.157411\pi$
$108$	−8.76855	−	6.50682i	−0.843754	−	0.626119i
$109$			2.82743i			0.270819i	0.990790	+	0.135409i	$0.0432350\pi$
$109$			2.82743i			0.270819i	−0.990790	+	0.135409i	$0.956765\pi$
$110$	−2.63836	+	12.7521i	−0.251558	+	1.21587i
$111$		−	8.50103i		−	0.806882i
$112$	7.23061	−	13.5102i	0.683228	−	1.27660i
$113$	1.04439	−	1.04439i	0.0982483	−	0.0982483i	−0.656274	−	0.754522i	$-0.727869\pi$
$113$	1.04439	−	1.04439i	0.0982483	−	0.0982483i	0.754522	+	0.656274i	$0.227869\pi$
$114$	−0.168724	−	2.29149i	−0.0158024	−	0.214618i
$115$	−9.18453	−	2.61636i	−0.856461	−	0.243977i
$116$	−4.65102	+	0.688649i	−0.431836	+	0.0639394i
$117$	0.702883	+	0.702883i	0.0649815	+	0.0649815i
$118$	−9.66145	−	8.33627i	−0.889408	−	0.767415i
$119$	22.5130			2.06376
$120$	−7.66822	+	6.84004i	−0.700010	+	0.624407i
$121$	−5.95778			−0.541616
$122$	4.53931	+	3.91669i	0.410970	+	0.354601i
$123$	11.2902	+	11.2902i	1.01800	+	1.01800i
$124$	−10.8440	+	1.60560i	−0.973817	+	0.144187i
$125$	0.526938	−	11.1679i	0.0471308	−	0.998889i
$126$	−0.143340	−	1.94674i	−0.0127697	−	0.173429i
$127$	2.30575	−	2.30575i	0.204602	−	0.204602i	−0.597366	−	0.801969i	$-0.703786\pi$
$127$	2.30575	−	2.30575i	0.204602	−	0.204602i	0.801969	+	0.597366i	$0.203786\pi$
$128$	−3.02767	+	10.9011i	−0.267610	+	0.963527i
$129$			20.5967i			1.81344i
$130$	7.29087	−	4.79115i	0.639452	−	0.420212i
$131$			1.87892i			0.164162i	0.996626	+	0.0820810i	$0.0261566\pi$
$131$			1.87892i			0.164162i	−0.996626	+	0.0820810i	$0.973843\pi$
$132$	−10.7457	−	7.97396i	−0.935290	−	0.694044i
$133$	2.70883	−	2.70883i	0.234885	−	0.234885i
$134$	−12.9585	+	0.954143i	−1.11944	+	0.0824254i
$135$	−3.34456	+	11.7408i	−0.287854	+	1.01049i
$136$	−16.2195	+	3.63542i	−1.39081	+	0.311735i
$137$	4.38444	+	4.38444i	0.374588	+	0.374588i	0.869145	−	0.494557i	$-0.164670\pi$
$137$	4.38444	+	4.38444i	0.374588	+	0.374588i	−0.494557	+	0.869145i	$0.664670\pi$
$138$	6.41064	−	7.42971i	0.545710	−	0.632459i
$139$	5.70518			0.483907			0.241953	−	0.970288i	$-0.422212\pi$
$139$	5.70518			0.483907			0.241953	+	0.970288i	$0.422212\pi$
$140$	−16.9864	−	2.22973i	−1.43561	−	0.188447i
$141$	1.10878			0.0933762
$142$	−13.8175	+	16.0140i	−1.15954	+	1.34387i
$143$	8.03334	+	8.03334i	0.671781	+	0.671781i
$144$	0.417631	+	1.37939i	0.0348026	+	0.114949i
$145$	2.55648	+	4.59317i	0.212304	+	0.381442i
$146$	−14.5566	+	1.07181i	−1.20471	+	0.0887035i
$147$	−8.81793	+	8.81793i	−0.727291	+	0.727291i
$148$	−6.23602	+	8.40363i	−0.512598	+	0.690774i
$149$		−	3.91665i		−	0.320864i	−0.987047	−	0.160432i	$-0.948711\pi$
$149$		−	3.91665i		−	0.320864i	0.987047	−	0.160432i	$-0.0512888\pi$
$150$	10.1821	+	5.32075i	0.831362	+	0.434437i
$151$			4.24151i			0.345169i	0.984995	+	0.172584i	$0.0552118\pi$
$151$			4.24151i			0.345169i	−0.984995	+	0.172584i	$0.944788\pi$
$152$	−1.51416	+	2.38900i	−0.122814	+	0.193774i
$153$	−1.49725	+	1.49725i	−0.121045	+	0.121045i
$154$	−1.63825	−	22.2496i	−0.132014	−	1.79292i
$155$	5.96049	+	10.7091i	0.478758	+	0.860175i
$156$	1.31303	+	8.86797i	0.105126	+	0.710006i
$157$	−1.83855	−	1.83855i	−0.146733	−	0.146733i	0.629924	−	0.776657i	$-0.283086\pi$
$157$	−1.83855	−	1.83855i	−0.146733	−	0.146733i	−0.776657	+	0.629924i	$0.783086\pi$
$158$	−3.90633	−	3.37053i	−0.310771	−	0.268145i
$159$	6.23679			0.494610
$160$	12.5979	−	1.13656i	0.995955	−	0.0898532i
$161$	16.3610			1.28943
$162$	−8.34021	−	7.19625i	−0.655269	−	0.565391i
$163$	1.72096	+	1.72096i	0.134796	+	0.134796i	0.771285	−	0.636489i	$-0.219614\pi$
$163$	1.72096	+	1.72096i	0.134796	+	0.134796i	−0.636489	+	0.771285i	$0.719614\pi$
$164$	−2.87879	−	19.4429i	−0.224796	−	1.51824i
$165$	−4.09869	+	14.3881i	−0.319082	+	1.12011i
$166$	−1.22329	−	16.6138i	−0.0949454	−	1.28948i
$167$	9.53008	−	9.53008i	0.737460	−	0.737460i	−0.234626	−	0.972086i	$-0.575387\pi$
$167$	9.53008	−	9.53008i	0.737460	−	0.737460i	0.972086	+	0.234626i	$0.0753866\pi$
$168$	9.42417	−	14.8693i	0.727091	−	1.14719i
$169$			5.38880i			0.414523i
$170$	10.2059	+	15.5307i	0.782756	+	1.19115i
$171$			0.360306i			0.0275533i
$172$	15.1089	−	20.3607i	1.15205	−	1.55249i
$173$	1.38868	−	1.38868i	0.105579	−	0.105579i	−0.652344	−	0.757923i	$-0.726214\pi$
$173$	1.38868	−	1.38868i	0.105579	−	0.105579i	0.757923	+	0.652344i	$0.226214\pi$
$174$	−5.38697	+	0.396646i	−0.408386	+	0.0300697i
$175$	4.37360	+	18.6483i	0.330613	+	1.40968i
$176$	4.77316	+	15.7652i	0.359790	+	1.18835i
$177$	−10.3663	−	10.3663i	−0.779178	−	0.779178i
$178$	−9.01921	+	10.4530i	−0.676019	+	0.783483i
$179$	−20.9758			−1.56780			−0.783901	−	0.620886i	$-0.786773\pi$
$179$	−20.9758			−1.56780			−0.783901	+	0.620886i	$0.786773\pi$
$180$	1.27799	−	0.981405i	0.0952555	−	0.0731496i
$181$	15.9695			1.18701			0.593503	−	0.804832i	$-0.297744\pi$
$181$	15.9695			1.18701			0.593503	+	0.804832i	$0.297744\pi$
$182$	−9.76411	+	11.3163i	−0.723764	+	0.838818i
$183$	4.87047	+	4.87047i	0.360036	+	0.360036i
$184$	−11.7873	+	2.64199i	−0.868974	+	0.194770i
$185$	11.2522	+	3.20537i	0.827277	+	0.235663i
$186$	−12.5599	+	0.924791i	−0.920934	+	0.0678090i
$187$	−17.1122	+	17.1122i	−1.25137	+	1.25137i
$188$	−1.09608	−	0.813358i	−0.0799396	−	0.0593203i
$189$		−	20.9147i		−	1.52132i
$190$	3.09669	+	0.640694i	0.224658	+	0.0464808i
$191$			5.91787i			0.428202i	0.976811	+	0.214101i	$0.0686822\pi$
$191$			5.91787i			0.428202i	−0.976811	+	0.214101i	$0.931318\pi$
$192$	−4.38857	+	12.2344i	−0.316717	+	0.882943i
$193$	1.66414	−	1.66414i	0.119788	−	0.119788i	−0.644672	−	0.764460i	$-0.723006\pi$
$193$	1.66414	−	1.66414i	0.119788	−	0.119788i	0.764460	+	0.644672i	$0.223006\pi$
$194$	−0.0306406	−	0.416139i	−0.00219987	−	0.0298771i
$195$	8.75767	−	4.87436i	0.627150	−	0.349060i
$196$	15.1854	−	2.24841i	1.08467	−	0.160601i
$197$	−7.74801	−	7.74801i	−0.552023	−	0.552023i	0.375001	−	0.927024i	$-0.377642\pi$
$197$	−7.74801	−	7.74801i	−0.552023	−	0.552023i	−0.927024	+	0.375001i	$0.877642\pi$
$198$	1.58868	+	1.37077i	0.112903	+	0.0974167i
$199$	18.3552			1.30117			0.650583	−	0.759435i	$-0.274525\pi$
$199$	18.3552			1.30117			0.650583	+	0.759435i	$0.274525\pi$
$200$	−6.16231	−	12.7289i	−0.435741	−	0.900072i
$201$	−14.9276			−1.05291
$202$	20.1246	+	17.3643i	1.41596	+	1.22175i
$203$	−6.36808	−	6.36808i	−0.446951	−	0.446951i
$204$	−18.8901	+	2.79695i	−1.32257	+	0.195826i
$205$	−19.2011	+	10.6870i	−1.34106	+	0.746411i
$206$	0.107688	+	1.46255i	0.00750300	+	0.101901i
$207$	−1.08810	+	1.08810i	−0.0756285	+	0.0756285i
$208$	5.20721	−	9.72955i	0.361055	−	0.674623i
$209$			4.11798i			0.284847i
$210$	−19.2740	−	3.98771i	−1.33003	−	0.275178i
$211$		−	10.7675i		−	0.741266i	−0.928779	−	0.370633i	$-0.879141\pi$
$211$		−	10.7675i		−	0.741266i	0.928779	−	0.370633i	$-0.120859\pi$
$212$	−6.16533	−	4.57507i	−0.423437	−	0.314217i
$213$	−17.1823	+	17.1823i	−1.17731	+	1.17731i
$214$	−8.36818	+	0.616155i	−0.572037	+	0.0421195i
$215$	−27.2623	−	7.76612i	−1.85928	−	0.529645i
$216$	3.37732	+	15.0680i	0.229798	+	1.02525i
$217$	−14.8473	−	14.8473i	−1.00790	−	1.00790i
$218$	2.61217	−	3.02742i	0.176919	−	0.205043i
$219$	−16.7685			−1.13311
$220$	14.6063	−	11.2166i	0.984755	−	0.756224i
$221$	16.2130			1.09061
$222$	−7.85383	+	9.10233i	−0.527115	+	0.610908i
$223$	−2.60632	−	2.60632i	−0.174532	−	0.174532i	0.614435	−	0.788967i	$-0.289384\pi$
$223$	−2.60632	−	2.60632i	−0.174532	−	0.174532i	−0.788967	+	0.614435i	$0.789384\pi$
$224$	−20.2237	+	7.78569i	−1.35125	+	0.520203i
$225$	−1.53109	−	0.949351i	−0.102073	−	0.0632901i
$226$	−2.08315	+	0.153384i	−0.138569	+	0.0102029i
$227$	7.03256	−	7.03256i	0.466767	−	0.466767i	−0.434098	−	0.900866i	$-0.642933\pi$
$227$	7.03256	−	7.03256i	0.466767	−	0.466767i	0.900866	+	0.434098i	$0.142933\pi$
$228$	−1.93638	+	2.60945i	−0.128240	+	0.172815i
$229$		−	3.08487i		−	0.203854i	−0.994792	−	0.101927i	$-0.967499\pi$
$229$		−	3.08487i		−	0.203854i	0.994792	−	0.101927i	$-0.0325008\pi$
$230$	7.41699	+	11.2867i	0.489062	+	0.744224i
$231$		−	25.6305i		−	1.68636i
$232$	5.61622	+	3.55957i	0.368723	+	0.233697i
$233$	16.5824	−	16.5824i	1.08635	−	1.08635i	0.0904463	−	0.995901i	$-0.471171\pi$
$233$	16.5824	−	16.5824i	1.08635	−	1.08635i	0.995901	−	0.0904463i	$-0.0288294\pi$
$234$	−0.103228	−	1.40197i	−0.00674822	−	0.0916496i
$235$	−0.418073	+	1.46761i	−0.0272721	+	0.0957365i
$236$	2.64321	+	17.8518i	0.172058	+	1.16205i
$237$	−4.19132	−	4.19132i	−0.272255	−	0.272255i
$238$	−24.1054	−	20.7991i	−1.56252	−	1.34820i
$239$	9.09479			0.588293			0.294146	−	0.955760i	$-0.404965\pi$
$239$	9.09479			0.588293			0.294146	+	0.955760i	$0.404965\pi$
$240$	14.5299	−	0.239425i	0.937901	−	0.0154548i
$241$	0.806689			0.0519634			0.0259817	−	0.999662i	$-0.491729\pi$
$241$	0.806689			0.0519634			0.0259817	+	0.999662i	$0.491729\pi$
$242$	6.37919	+	5.50420i	0.410070	+	0.353824i
$243$	2.63276	+	2.63276i	0.168892	+	0.168892i
$244$	−1.24188	−	8.38745i	−0.0795032	−	0.536952i
$245$	−8.34679	−	14.9965i	−0.533257	−	0.958092i
$246$	−1.65812	−	22.5195i	−0.105718	−	1.43579i
$247$	1.95079	−	1.95079i	0.124126	−	0.124126i
$248$	13.0943	+	8.29923i	0.831492	+	0.527002i
$249$		−	19.1384i		−	1.21285i
$250$	−10.8819	+	11.4710i	−0.688231	+	0.725491i
$251$			2.39055i			0.150890i	0.997150	+	0.0754451i	$0.0240378\pi$
$251$			2.39055i			0.150890i	−0.997150	+	0.0754451i	$0.975962\pi$
$252$	−1.64505	+	2.21687i	−0.103629	+	0.139649i
$253$	−12.4361	+	12.4361i	−0.781850	+	0.781850i
$254$	−4.59906	+	0.338631i	−0.288570	+	0.0212476i
$255$	10.3831	+	18.6552i	0.650218	+	1.16823i
$256$	13.3130	−	8.87496i	0.832061	−	0.554685i
$257$	16.0798	+	16.0798i	1.00303	+	1.00303i	0.999995	+	0.00303293i	$0.000965412\pi$
$257$	16.0798	+	16.0798i	1.00303	+	1.00303i	0.00303293	+	0.999995i	$0.499035\pi$
$258$	19.0286	−	22.0535i	1.18467	−	1.37299i
$259$	−20.0443			−1.24549
$260$	−12.2330	−	1.60577i	−0.758656	−	0.0995856i
$261$	0.847029			0.0524298
$262$	1.73587	−	2.01182i	0.107243	−	0.124291i
$263$	−3.25350	−	3.25350i	−0.200619	−	0.200619i	0.599646	−	0.800265i	$-0.295308\pi$
$263$	−3.25350	−	3.25350i	−0.200619	−	0.200619i	−0.800265	+	0.599646i	$0.795308\pi$
$264$	4.13884	+	18.4656i	0.254728	+	1.13648i
$265$	−2.35162	+	8.25518i	−0.144459	+	0.507112i
$266$	−5.40302	+	0.397828i	−0.331281	+	0.0243924i
$267$	−11.2155	+	11.2155i	−0.686380	+	0.686380i
$268$	14.7566	+	10.9503i	0.901402	+	0.668897i
$269$			19.3588i			1.18033i	0.807284	+	0.590163i	$0.200936\pi$
$269$			19.3588i			1.18033i	−0.807284	+	0.590163i	$0.799064\pi$
$270$	14.4281	−	9.48132i	0.878065	−	0.577015i
$271$			2.77454i			0.168542i	0.996443	+	0.0842708i	$0.0268561\pi$
$271$			2.77454i			0.168542i	−0.996443	+	0.0842708i	$0.973144\pi$
$272$	20.7254	+	11.0922i	1.25666	+	0.672561i
$273$	−12.1418	+	12.1418i	−0.734857	+	0.734857i
$274$	−0.643915	−	8.74521i	−0.0389003	−	0.528317i
$275$	−17.4990	−	10.8503i	−1.05523	−	0.654295i
$276$	−13.7282	+	2.03265i	−0.826338	+	0.122351i
$277$	3.48594	+	3.48594i	0.209450	+	0.209450i	0.804034	−	0.594584i	$-0.202683\pi$
$277$	3.48594	+	3.48594i	0.209450	+	0.209450i	−0.594584	+	0.804034i	$0.702683\pi$
$278$	−6.10872	−	5.27083i	−0.366377	−	0.316124i
$279$	1.97487			0.118232
$280$	16.1279	+	18.0806i	0.963827	+	1.08052i
$281$	−27.6567			−1.64986			−0.824930	−	0.565235i	$-0.808786\pi$
$281$	−27.6567			−1.64986			−0.824930	+	0.565235i	$0.808786\pi$
$282$	−1.18721	−	1.02437i	−0.0706972	−	0.0610002i
$283$	6.97300	+	6.97300i	0.414502	+	0.414502i	0.883304	−	0.468802i	$-0.155314\pi$
$283$	6.97300	+	6.97300i	0.414502	+	0.414502i	−0.468802	+	0.883304i	$0.655314\pi$
$284$	29.5897	−	4.38117i	1.75583	−	0.259975i
$285$	3.49397	+	0.995314i	0.206965	+	0.0589573i
$286$	−1.17981	−	16.0233i	−0.0697634	−	0.947478i
$287$	26.6208	−	26.6208i	1.57138	−	1.57138i
$288$	0.827201	−	1.86279i	0.0487433	−	0.109766i
$289$			17.5362i			1.03154i
$290$	1.50618	−	7.27990i	0.0884461	−	0.427491i
$291$		−	0.479374i		−	0.0281014i
$292$	16.5764	+	12.3007i	0.970060	+	0.719846i
$293$	−4.11824	+	4.11824i	−0.240590	+	0.240590i	−0.817094	−	0.576504i	$-0.804416\pi$
$293$	−4.11824	+	4.11824i	−0.240590	+	0.240590i	0.576504	+	0.817094i	$0.304416\pi$
$294$	17.5883	−	1.29503i	1.02577	−	0.0755279i
$295$	17.6298	−	9.81242i	1.02644	−	0.571301i
$296$	14.4410	−	3.23677i	0.839363	−	0.188133i
$297$	15.8974	+	15.8974i	0.922459	+	0.922459i
$298$	−3.61847	+	4.19368i	−0.209612	+	0.242933i
$299$	11.7826			0.681405
$300$	−5.98659	−	15.1040i	−0.345636	−	0.872029i
$301$	48.5643			2.79920
$302$	3.91859	−	4.54152i	0.225490	−	0.261335i
$303$	21.5928	+	21.5928i	1.24047	+	1.24047i
$304$	3.82838	−	1.15910i	0.219573	−	0.0664790i
$305$	−8.28313	+	4.61024i	−0.474291	+	0.263982i
$306$	2.98641	−	0.219891i	0.170722	−	0.0125704i
$307$	−23.2710	+	23.2710i	−1.32814	+	1.32814i	−0.421155	+	0.906989i	$0.638375\pi$
$307$	−23.2710	+	23.2710i	−1.32814	+	1.32814i	−0.906989	+	0.421155i	$0.861625\pi$
$308$	−18.8015	+	25.3368i	−1.07132	+	1.44370i
$309$			1.68479i			0.0958444i
$310$	3.51170	−	16.9733i	0.199451	−	0.964017i
$311$		−	31.9359i		−	1.81092i	−0.424434	−	0.905459i	$-0.639527\pi$
$311$		−	31.9359i		−	1.81092i	0.424434	−	0.905459i	$-0.360473\pi$
$312$	6.78694	−	10.7083i	0.384235	−	0.606237i
$313$	3.53818	−	3.53818i	0.199990	−	0.199990i	−0.600006	−	0.799996i	$-0.704835\pi$
$313$	3.53818	−	3.53818i	0.199990	−	0.199990i	0.799996	+	0.600006i	$0.204835\pi$
$314$	0.270017	+	3.66718i	0.0152379	+	0.206951i
$315$	2.96831	+	0.845572i	0.167245	+	0.0476426i
$316$	1.06871	+	7.21788i	0.0601195	+	0.406037i
$317$	−7.96927	−	7.96927i	−0.447599	−	0.447599i	0.446957	−	0.894556i	$-0.352508\pi$
$317$	−7.96927	−	7.96927i	−0.447599	−	0.447599i	−0.894556	+	0.446957i	$0.852508\pi$
$318$	−6.67793	−	5.76197i	−0.374480	−	0.323115i
$319$	9.68081			0.542021
$320$	−14.5391	−	10.4219i	−0.812758	−	0.582601i
$321$	−9.63978			−0.538040
$322$	−17.5183	−	15.1154i	−0.976255	−	0.842350i
$323$	4.15549	+	4.15549i	0.231218	+	0.231218i
$324$	2.28174	+	15.4105i	0.126764	+	0.856140i
$325$	3.14970	+	13.4298i	0.174714	+	0.744951i
$326$	−0.252747	−	3.43263i	−0.0139983	−	0.190116i
$327$	3.24828	−	3.24828i	0.179630	−	0.179630i
$328$	−14.8803	+	23.4778i	−0.821625	+	1.29634i
$329$		−	2.61436i		−	0.144134i
$330$	17.6813	−	11.6192i	0.973324	−	0.639614i
$331$		−	0.243939i		−	0.0134081i	−0.999978	−	0.00670406i	$-0.997866\pi$
$331$		−	0.243939i		−	0.0134081i	0.999978	−	0.00670406i	$-0.00213398\pi$
$332$	−14.0392	+	18.9191i	−0.770500	+	1.03832i
$333$	1.33306	−	1.33306i	0.0730515	−	0.0730515i
$334$	−19.0087	+	1.39962i	−1.04011	+	0.0765840i
$335$	5.62856	−	19.7586i	0.307521	−	1.07953i
$336$	−23.8280	+	7.21430i	−1.29992	+	0.393572i
$337$	−21.6007	−	21.6007i	−1.17666	−	1.17666i	−0.980589	−	0.196075i	$-0.937180\pi$
$337$	−21.6007	−	21.6007i	−1.17666	−	1.17666i	−0.196075	−	0.980589i	$-0.562820\pi$
$338$	4.97854	−	5.76996i	0.270797	−	0.313845i
$339$	−2.39969			−0.130334
$340$	3.42053	−	26.0581i	0.185505	−	1.41320i
$341$	22.5711			1.22229
$342$	0.332875	−	0.385791i	0.0179998	−	0.0208612i
$343$	1.82973	+	1.82973i	0.0987963	+	0.0987963i
$344$	−34.9882	+	7.84220i	−1.88644	+	0.422823i
$345$	7.54581	+	13.5574i	0.406253	+	0.729906i
$346$	−2.76985	+	0.203946i	−0.148908	+	0.0109642i
$347$	−21.4891	+	21.4891i	−1.15360	+	1.15360i	−0.167770	+	0.985826i	$0.553657\pi$
$347$	−21.4891	+	21.4891i	−1.15360	+	1.15360i	−0.985826	+	0.167770i	$0.946343\pi$
$348$	6.13446	+	4.55215i	0.328841	+	0.244021i
$349$		−	16.9878i		−	0.909334i	−0.890661	−	0.454667i	$-0.849758\pi$
$349$		−	16.9878i		−	0.909334i	0.890661	−	0.454667i	$-0.150242\pi$
$350$	12.5456	−	24.0079i	0.670591	−	1.28328i
$351$		−	15.0620i		−	0.803949i
$352$	9.45419	−	21.2901i	0.503910	−	1.13476i
$353$	21.9390	−	21.9390i	1.16769	−	1.16769i	0.184946	−	0.982749i	$-0.440789\pi$
$353$	21.9390	−	21.9390i	1.16769	−	1.16769i	0.982749	−	0.184946i	$-0.0592110\pi$
$354$	1.52243	+	20.6766i	0.0809163	+	1.09895i
$355$	−16.2643	−	29.2217i	−0.863218	−	1.55093i
$356$	19.3143	−	2.85976i	1.02366	−	0.151567i
$357$	−25.8640	−	25.8640i	−1.36887	−	1.36887i
$358$	22.4594	+	19.3788i	1.18702	+	1.02420i
$359$	−9.38281			−0.495206			−0.247603	−	0.968862i	$-0.579643\pi$
$359$	−9.38281			−0.495206			−0.247603	+	0.968862i	$0.579643\pi$
$360$	−2.27507	−	0.129869i	−0.119907	−	0.00684467i
$361$	1.00000			0.0526316
$362$	−17.0991	−	14.7538i	−0.898709	−	0.775440i
$363$	6.84457	+	6.84457i	0.359247	+	0.359247i
$364$	20.9095	−	3.09594i	1.09596	−	0.162272i
$365$	6.32268	−	22.1953i	0.330944	−	1.16175i
$366$	−0.715296	−	9.71465i	−0.0373891	−	0.507793i
$367$	−8.72035	+	8.72035i	−0.455199	+	0.455199i	−0.897076	−	0.441877i	$-0.854313\pi$
$367$	−8.72035	+	8.72035i	−0.455199	+	0.455199i	0.441877	+	0.897076i	$0.354313\pi$
$368$	15.0619	+	8.06108i	0.785157	+	0.420213i
$369$			3.54088i			0.184331i
$370$	−9.08674	−	13.8276i	−0.472397	−	0.718864i
$371$		−	14.7055i		−	0.763473i
$372$	14.3026	+	10.6135i	0.741557	+	0.550282i
$373$	16.4931	−	16.4931i	0.853979	−	0.853979i	−0.136641	−	0.990621i	$-0.543631\pi$
$373$	16.4931	−	16.4931i	0.853979	−	0.853979i	0.990621	+	0.136641i	$0.0436308\pi$
$374$	34.1321	−	2.51317i	1.76493	−	0.129953i
$375$	−13.4356	+	12.2248i	−0.693811	+	0.631288i
$376$	0.422169	+	1.88352i	0.0217717	+	0.0971351i
$377$	−4.58605	−	4.58605i	−0.236194	−	0.236194i
$378$	−19.3224	+	22.3940i	−0.993839	+	1.15183i
$379$	−29.7168			−1.52645			−0.763224	−	0.646133i	$-0.776385\pi$
$379$	−29.7168			−1.52645			−0.763224	+	0.646133i	$0.776385\pi$
$380$	−2.72381	−	3.54695i	−0.139729	−	0.181955i
$381$	−5.29791			−0.271420
$382$	5.46734	−	6.33646i	0.279733	−	0.324201i
$383$	−8.57457	−	8.57457i	−0.438140	−	0.438140i	0.453246	−	0.891386i	$-0.350266\pi$
$383$	−8.57457	−	8.57457i	−0.438140	−	0.438140i	−0.891386	+	0.453246i	$0.850266\pi$
$384$	16.0020	−	9.04532i	0.816597	−	0.461592i
$385$	33.9252	+	9.66415i	1.72899	+	0.492531i
$386$	−3.31930	+	0.244402i	−0.168948	+	0.0124398i
$387$	−3.22981	+	3.22981i	−0.164180	+	0.164180i
$388$	−0.351650	+	0.473881i	−0.0178523	+	0.0240577i
$389$			9.66869i			0.490222i	0.969495	+	0.245111i	$0.0788244\pi$
$389$			9.66869i			0.490222i	−0.969495	+	0.245111i	$0.921176\pi$
$390$	−13.8804	−	2.87180i	−0.702861	−	0.145419i
$391$			25.0987i			1.26930i
$392$	−18.3367	−	11.6219i	−0.926144	−	0.586992i
$393$	2.15859	−	2.15859i	0.108886	−	0.108886i
$394$	1.13790	+	15.4542i	0.0573266	+	0.778570i
$395$	7.12810	−	3.96737i	0.358654	−	0.199620i
$396$	−0.434636	−	2.93546i	−0.0218413	−	0.147513i
$397$	19.0447	+	19.0447i	0.955827	+	0.955827i	0.999065	−	0.0432378i	$-0.0137673\pi$
$397$	19.0447	+	19.0447i	0.955827	+	0.955827i	−0.0432378	+	0.999065i	$0.513767\pi$
$398$	−19.6535	−	16.9578i	−0.985141	−	0.850017i
$399$	−6.22405			−0.311592
$400$	−5.16169	+	19.3224i	−0.258084	+	0.966122i
$401$	−0.178250			−0.00890139			−0.00445069	−	0.999990i	$-0.501417\pi$
$401$	−0.178250			−0.00890139			−0.00445069	+	0.999990i	$0.501417\pi$
$402$	15.9835	+	13.7912i	0.797184	+	0.687841i
$403$	−10.6925	−	10.6925i	−0.532631	−	0.532631i
$404$	−5.50576	−	37.1850i	−0.273922	−	1.85002i
$405$	15.2188	−	8.47054i	0.756230	−	0.420904i
$406$	0.935239	+	12.7018i	0.0464151	+	0.630378i
$407$	15.2358	−	15.2358i	0.755209	−	0.755209i
$408$	22.8103	+	14.4572i	1.12928	+	0.715739i
$409$			2.01061i			0.0994184i	0.998764	+	0.0497092i	$0.0158295\pi$
$409$			2.01061i			0.0994184i	−0.998764	+	0.0497092i	$0.984171\pi$
$410$	30.4326	+	6.29637i	1.50296	+	0.310956i
$411$		−	10.0741i		−	0.496918i
$412$	1.23590	−	1.66549i	0.0608882	−	0.0820526i
$413$	−24.4423	+	24.4423i	−1.20273	+	1.20273i
$414$	2.17033	−	0.159803i	0.106666	−	0.00785389i
$415$	25.3321	+	7.21625i	1.24350	+	0.354232i
$416$	−14.5644	+	5.60696i	−0.714076	+	0.274904i
$417$	−6.55437	−	6.55437i	−0.320969	−	0.320969i
$418$	3.80447	−	4.40926i	0.186083	−	0.215664i
$419$	−13.6641			−0.667536			−0.333768	−	0.942655i	$-0.608320\pi$
$419$	−13.6641			−0.667536			−0.333768	+	0.942655i	$0.608320\pi$
$420$	16.9531	+	22.0764i	0.827228	+	1.07722i
$421$	−13.8989			−0.677390			−0.338695	−	0.940896i	$-0.609985\pi$
$421$	−13.8989			−0.677390			−0.338695	+	0.940896i	$0.609985\pi$
$422$	−9.94776	+	11.5291i	−0.484249	+	0.561229i
$423$	0.173870	+	0.173870i	0.00845386	+	0.00845386i
$424$	2.37466	+	10.5946i	0.115324	+	0.514520i
$425$	−28.6075	+	6.70935i	−1.38767	+	0.325451i
$426$	34.2719	−	2.52346i	1.66048	−	0.122262i
$427$	11.4839	−	11.4839i	0.555746	−	0.555746i
$428$	9.52933	+	7.07136i	0.460618	+	0.341807i
$429$		−	18.4581i		−	0.891167i
$430$	22.0158	+	33.5022i	1.06170	+	1.61562i
$431$			20.3636i			0.980879i	0.871475	+	0.490440i	$0.163164\pi$
$431$			20.3636i			0.980879i	−0.871475	+	0.490440i	$0.836836\pi$
$432$	10.3047	−	19.2540i	0.495784	−	0.926360i
$433$	5.89872	−	5.89872i	0.283475	−	0.283475i	−0.551018	−	0.834493i	$-0.685761\pi$
$433$	5.89872	−	5.89872i	0.283475	−	0.283475i	0.834493	+	0.551018i	$0.185761\pi$
$434$	2.18053	+	29.6145i	0.104669	+	1.42154i
$435$	2.33985	−	8.21384i	0.112187	−	0.393824i
$436$	−5.59388	+	0.828252i	−0.267898	+	0.0396661i
$437$	3.01995	+	3.01995i	0.144464	+	0.144464i
$438$	17.9546	+	15.4919i	0.857903	+	0.740232i
$439$	−27.2435			−1.30026			−0.650131	−	0.759822i	$-0.725286\pi$
$439$	−27.2435			−1.30026			−0.650131	+	0.759822i	$0.725286\pi$
$440$	−26.0021	−	1.48428i	−1.23960	−	0.0707605i
$441$	−2.76552			−0.131691
$442$	−17.3598	−	14.9787i	−0.825722	−	0.712464i
$443$	20.1874	+	20.1874i	0.959131	+	0.959131i	0.999197	−	0.0400656i	$-0.0127567\pi$
$443$	20.1874	+	20.1874i	0.959131	+	0.959131i	−0.0400656	+	0.999197i	$0.512757\pi$
$444$	16.8187	−	2.49024i	0.798180	−	0.118182i
$445$	−10.6163	−	19.0741i	−0.503261	−	0.904198i
$446$	0.382774	+	5.19857i	0.0181249	+	0.246159i
$447$	−4.49963	+	4.49963i	−0.212825	+	0.212825i
$448$	28.8471	+	10.3477i	1.36290	+	0.488881i
$449$		−	4.84516i		−	0.228657i	−0.993443	−	0.114329i	$-0.963528\pi$
$449$		−	4.84516i		−	0.228657i	0.993443	−	0.114329i	$-0.0364717\pi$
$450$	0.762313	+	2.43103i	0.0359358	+	0.114600i
$451$			40.4692i			1.90562i
$452$	2.37220	+	1.76032i	0.111579	+	0.0827986i
$453$	4.87284	−	4.87284i	0.228946	−	0.228946i
$454$	−14.0271	+	1.03283i	−0.658326	+	0.0484730i
$455$	−11.4931	−	20.6494i	−0.538805	−	0.968060i
$456$	4.48413	−	1.00506i	0.209989	−	0.0470664i
$457$	−14.6913	−	14.6913i	−0.687230	−	0.687230i	0.274389	−	0.961619i	$-0.411524\pi$
$457$	−14.6913	−	14.6913i	−0.687230	−	0.687230i	−0.961619	+	0.274389i	$0.911524\pi$
$458$	−2.85002	+	3.30307i	−0.133172	+	0.154342i
$459$	32.0843			1.49757
$460$	2.48583	−	18.9374i	0.115902	−	0.882960i
$461$	24.5016			1.14115			0.570577	−	0.821244i	$-0.306720\pi$
$461$	24.5016			1.14115			0.570577	+	0.821244i	$0.306720\pi$
$462$	−23.6792	+	27.4434i	−1.10166	+	1.27678i
$463$	−25.8168	−	25.8168i	−1.19981	−	1.19981i	−0.974223	−	0.225586i	$-0.927570\pi$
$463$	−25.8168	−	25.8168i	−1.19981	−	1.19981i	−0.225586	−	0.974223i	$-0.572430\pi$
$464$	−2.72489	−	8.99999i	−0.126500	−	0.417814i
$465$	5.45541	−	19.1508i	0.252989	−	0.888096i
$466$	−33.0752	+	2.43535i	−1.53218	+	0.112815i
$467$	−6.04830	+	6.04830i	−0.279882	+	0.279882i	−0.833062	−	0.553180i	$-0.813414\pi$
$467$	−6.04830	+	6.04830i	−0.279882	+	0.279882i	0.553180	+	0.833062i	$0.313414\pi$
$468$	−1.18471	+	1.59650i	−0.0547631	+	0.0737984i
$469$			35.1974i			1.62526i
$470$	1.80352	−	1.18517i	0.0831904	−	0.0546680i
$471$			4.22443i			0.194651i
$472$	13.6626	−	21.5565i	0.628870	−	0.992218i
$473$	−36.9139	+	36.9139i	−1.69730	+	1.69730i
$474$	0.615552	+	8.36000i	0.0282733	+	0.383988i
$475$	−2.63485	+	4.24942i	−0.120895	+	0.194977i
$476$	6.59484	+	44.5404i	0.302274	+	2.04151i
$477$	0.978004	+	0.978004i	0.0447797	+	0.0447797i
$478$	−9.73808	−	8.40239i	−0.445409	−	0.384316i
$479$	−22.0969			−1.00963			−0.504816	−	0.863227i	$-0.668440\pi$
$479$	−22.0969			−1.00963			−0.504816	+	0.863227i	$0.668440\pi$
$480$	−15.7788	−	13.1674i	−0.720202	−	0.601005i
$481$	−14.4352			−0.658186
$482$	−0.863748	−	0.745275i	−0.0393427	−	0.0339463i
$483$	−18.7963	−	18.7963i	−0.855261	−	0.855261i
$484$	−1.74524	−	11.7871i	−0.0793290	−	0.535775i
$485$	0.634512	+	0.180751i	0.0288117	+	0.00820748i
$486$	−0.386657	−	5.25130i	−0.0175391	−	0.238204i
$487$	−21.8223	+	21.8223i	−0.988864	+	0.988864i	−0.999939	−	0.0110744i	$-0.996475\pi$
$487$	−21.8223	+	21.8223i	−0.988864	+	0.988864i	0.0110744	+	0.999939i	$0.496475\pi$
$488$	−6.41918	+	10.1280i	−0.290583	+	0.458475i
$489$		−	3.95424i		−	0.178817i
$490$	−4.91762	+	23.7686i	−0.222156	+	1.07376i
$491$		−	29.1044i		−	1.31346i	−0.754124	−	0.656732i	$-0.771938\pi$
$491$		−	29.1044i		−	1.31346i	0.754124	−	0.656732i	$-0.228062\pi$
$492$	−19.0296	+	25.6442i	−0.857921	+	1.15613i
$493$	9.76899	−	9.76899i	0.439973	−	0.439973i
$494$	−3.89106	+	0.286501i	−0.175067	+	0.0128903i
$495$	−2.89895	+	1.61350i	−0.130298	+	0.0725216i
$496$	−6.35314	−	20.9837i	−0.285265	−	0.942196i
$497$	40.5136	+	40.5136i	1.81728	+	1.81728i
$498$	−17.6814	+	20.4921i	−0.792320	+	0.918272i
$499$	25.5652			1.14446			0.572228	−	0.820094i	$-0.306079\pi$
$499$	25.5652			1.14446			0.572228	+	0.820094i	$0.306079\pi$
$500$	22.2493	−	2.22896i	0.995019	−	0.0996820i
$501$	−21.8972			−0.978294
$502$	2.20855	−	2.55964i	0.0985726	−	0.114242i
$503$	−23.8295	−	23.8295i	−1.06250	−	1.06250i	−0.997912	−	0.0645931i	$-0.979425\pi$
$503$	−23.8295	−	23.8295i	−1.06250	−	1.06250i	−0.0645931	−	0.997912i	$-0.520575\pi$
$504$	3.80950	−	0.853855i	0.169689	−	0.0380337i
$505$	−36.7225	+	20.4391i	−1.63413	+	0.909527i
$506$	24.8050	−	1.82641i	1.10272	−	0.0811939i
$507$	6.19090	−	6.19090i	0.274948	−	0.274948i
$508$	5.23721	+	3.88634i	0.232363	+	0.172428i
$509$			0.373579i			0.0165586i	0.999966	+	0.00827931i	$0.00263542\pi$
$509$			0.373579i			0.0165586i	−0.999966	+	0.00827931i	$0.997365\pi$
$510$	6.11737	−	29.5674i	0.270882	−	1.30926i
$511$			39.5379i			1.74905i
$512$	−22.4539	−	2.79673i	−0.992332	−	0.123599i
$513$	3.86047	−	3.86047i	0.170444	−	0.170444i
$514$	−2.36153	−	32.0727i	−0.104163	−	1.41467i
$515$	−2.23003	−	0.635261i	−0.0982670	−	0.0279930i
$516$	−40.7491	+	6.03348i	−1.79388	+	0.265609i
$517$	1.98719	+	1.98719i	0.0873963	+	0.0873963i
$518$	21.4621	+	18.5183i	0.942989	+	0.813647i
$519$	−3.19075			−0.140058
$520$	11.6147	+	13.0210i	0.509339	+	0.571009i
$521$	−21.9839			−0.963131			−0.481566	−	0.876410i	$-0.659932\pi$
$521$	−21.9839			−0.963131			−0.481566	+	0.876410i	$0.659932\pi$
$522$	−0.906942	−	0.782544i	−0.0396958	−	0.0342510i
$523$	25.4734	+	25.4734i	1.11388	+	1.11388i	0.992621	+	0.121255i	$0.0386918\pi$
$523$	25.4734	+	25.4734i	1.11388	+	1.11388i	0.121255	+	0.992621i	$0.461308\pi$
$524$	−3.71731	+	0.550400i	−0.162392	+	0.0240443i
$525$	16.3994	−	26.4486i	0.715729	−	1.15431i
$526$	0.477821	+	6.48943i	0.0208340	+	0.282953i
$527$	22.7767	−	22.7767i	0.992167	−	0.992167i
$528$	12.6282	−	23.5954i	0.549570	−	1.02686i
$529$		−	4.75983i		−	0.206949i
$530$	10.1447	−	6.66650i	0.440656	−	0.289574i
$531$		−	3.25112i		−	0.141086i
$532$	6.15273	+	4.56572i	0.266755	+	0.197949i
$533$	19.1713	−	19.1713i	0.830402	−	0.830402i
$534$	22.3705	−	1.64716i	0.968067	−	0.0712794i
$535$	3.63474	−	12.7595i	0.157144	−	0.551640i
$536$	−5.68370	−	25.3580i	−0.245498	−	1.09530i
$537$	24.0979	+	24.0979i	1.03990	+	1.03990i
$538$	17.8850	−	20.7281i	0.771075	−	0.893650i
$539$	−31.6075			−1.36143
$540$	−24.2081	−	3.17769i	−1.04175	−	0.136746i
$541$	−11.3955			−0.489932			−0.244966	−	0.969532i	$-0.578777\pi$
$541$	−11.3955			−0.489932			−0.244966	+	0.969532i	$0.578777\pi$
$542$	2.56331	−	2.97079i	0.110104	−	0.127606i
$543$	−18.3465	−	18.3465i	−0.787326	−	0.787326i
$544$	−11.9437	−	31.0243i	−0.512082	−	1.33016i
$545$	3.07473	+	5.52430i	0.131707	+	0.236635i
$546$	24.2181	−	1.78320i	1.03644	−	0.0763137i
$547$	−20.7225	+	20.7225i	−0.886032	+	0.886032i	−0.994139	−	0.108107i	$-0.965521\pi$
$547$	−20.7225	+	20.7225i	−0.886032	+	0.886032i	0.108107	+	0.994139i	$0.465521\pi$
$548$	−7.38996	+	9.95867i	−0.315683	+	0.425413i
$549$			1.52750i			0.0651920i
$550$	8.71257	+	27.7845i	0.371505	+	1.18474i
$551$		−	2.35086i		−	0.100150i
$552$	16.5771	+	10.5066i	0.705567	+	0.447190i
$553$	−9.88257	+	9.88257i	−0.420249	+	0.420249i
$554$	−0.511958	−	6.95306i	−0.0217510	−	0.295407i
$555$	−9.24456	−	16.6095i	−0.392410	−	0.705034i
$556$	1.67124	+	11.2873i	0.0708765	+	0.478688i
$557$	12.2789	+	12.2789i	0.520272	+	0.520272i	0.917653	−	0.397382i	$-0.130081\pi$
$557$	12.2789	+	12.2789i	0.520272	+	0.520272i	−0.397382	+	0.917653i	$0.630081\pi$
$558$	−2.11456	−	1.82452i	−0.0895163	−	0.0772381i
$559$	34.9742			1.47925
$560$	−0.564532	−	34.2596i	−0.0238558	−	1.44773i
$561$	39.3187			1.66004
$562$	29.6129	+	25.5512i	1.24915	+	1.07781i
$563$	13.3587	+	13.3587i	0.563001	+	0.563001i	0.930159	−	0.367158i	$-0.119669\pi$
$563$	13.3587	+	13.3587i	0.563001	+	0.563001i	−0.367158	+	0.930159i	$0.619669\pi$
$564$	0.324800	+	2.19365i	0.0136766	+	0.0923692i
$565$	0.904821	−	3.17630i	0.0380661	−	0.133628i
$566$	−1.02408	−	13.9084i	−0.0430453	−	0.584612i
$567$	−21.0998	+	21.0998i	−0.886106	+	0.886106i
$568$	−35.7303	−	22.6459i	−1.49921	−	0.950203i
$569$			17.3531i			0.727478i	0.931501	+	0.363739i	$0.118500\pi$
$569$			17.3531i			0.727478i	−0.931501	+	0.363739i	$0.881500\pi$
$570$	−2.82157	−	4.29368i	−0.118182	−	0.179843i
$571$		−	19.3548i		−	0.809972i	−0.914323	−	0.404986i	$-0.867276\pi$
$571$		−	19.3548i		−	0.809972i	0.914323	−	0.404986i	$-0.132724\pi$
$572$	−13.5402	+	18.2466i	−0.566143	+	0.762931i
$573$	6.79873	−	6.79873i	0.284021	−	0.284021i
$574$	−53.0979	+	3.90963i	−2.21626	+	0.163185i
$575$	−20.7901	+	4.87593i	−0.867008	+	0.203340i
$576$	−2.60668	+	1.23032i	−0.108612	+	0.0512635i
$577$	3.22845	+	3.22845i	0.134402	+	0.134402i	0.771107	−	0.636705i	$-0.219703\pi$
$577$	3.22845	+	3.22845i	0.134402	+	0.134402i	−0.636705	+	0.771107i	$0.719703\pi$
$578$	16.2012	−	18.7766i	0.673880	−	0.781004i
$579$	−3.82369			−0.158907
$580$	−8.33839	+	6.40331i	−0.346233	+	0.265883i
$581$	−45.1258			−1.87213
$582$	−0.442878	+	0.513281i	−0.0183579	+	0.0212762i
$583$	11.1777	+	11.1777i	0.462935	+	0.462935i
$584$	−6.38462	−	28.4852i	−0.264197	−	1.17873i
$585$	2.13767	+	0.608949i	0.0883817	+	0.0251770i
$586$	8.21425	−	0.604820i	0.339327	−	0.0249849i
$587$	−19.7717	+	19.7717i	−0.816064	+	0.816064i	−0.985535	−	0.169471i	$-0.945794\pi$
$587$	−19.7717	+	19.7717i	−0.816064	+	0.816064i	0.169471	+	0.985535i	$0.445794\pi$
$588$	−20.0288	−	14.8626i	−0.825972	−	0.612923i
$589$		−	5.48110i		−	0.225845i
$590$	−27.9421	−	5.78112i	−1.15036	−	0.238005i
$591$			17.8025i			0.732298i
$592$	−18.4527	−	9.87583i	−0.758403	−	0.405894i
$593$	0.671001	−	0.671001i	0.0275547	−	0.0275547i	−0.693195	−	0.720750i	$-0.743798\pi$
$593$	0.671001	−	0.671001i	0.0275547	−	0.0275547i	0.720750	+	0.693195i	$0.243798\pi$
$594$	−2.33475	−	31.7089i	−0.0957958	−	1.30103i
$595$	43.9864	−	24.4821i	1.80327	−	1.00367i
$596$	7.74882	−	1.14732i	0.317404	−	0.0469961i
$597$	−21.0873	−	21.0873i	−0.863046	−	0.863046i
$598$	−12.6160	−	10.8856i	−0.515907	−	0.445144i
$599$	6.84669			0.279748			0.139874	−	0.990169i	$-0.455330\pi$
$599$	6.84669			0.279748			0.139874	+	0.990169i	$0.455330\pi$
$600$	−7.54405	+	21.7031i	−0.307985	+	0.886027i
$601$	−28.9163			−1.17952			−0.589761	−	0.807578i	$-0.700778\pi$
$601$	−28.9163			−1.17952			−0.589761	+	0.807578i	$0.700778\pi$
$602$	−51.9993	−	44.8670i	−2.11933	−	1.82864i
$603$	−2.34083	−	2.34083i	−0.0953261	−	0.0953261i
$604$	−8.39153	+	1.24248i	−0.341446	+	0.0505559i
$605$	−11.6404	+	6.47887i	−0.473251	+	0.263403i
$606$	−3.17120	−	43.0690i	−0.128821	−	1.74956i
$607$	5.48920	−	5.48920i	0.222800	−	0.222800i	−0.586877	−	0.809676i	$-0.699643\pi$
$607$	5.48920	−	5.48920i	0.222800	−	0.222800i	0.809676	+	0.586877i	$0.199643\pi$
$608$	−5.17002	−	2.29583i	−0.209672	−	0.0931083i
$609$			14.6319i			0.592914i
$610$	13.1283	+	2.71619i	0.531548	+	0.109975i
$611$		−	1.88276i		−	0.0761684i
$612$	−3.40080	−	2.52361i	−0.137469	−	0.102011i
$613$	8.13079	−	8.13079i	0.328399	−	0.328399i	−0.523578	−	0.851978i	$-0.675403\pi$
$613$	8.13079	−	8.13079i	0.328399	−	0.328399i	0.851978	+	0.523578i	$0.175403\pi$
$614$	46.4163	−	3.41766i	1.87321	−	0.137925i
$615$	34.3368	+	9.78138i	1.38459	+	0.394423i
$616$	43.5393	−	9.75883i	1.75425	−	0.393194i
$617$	−10.8891	−	10.8891i	−0.438379	−	0.438379i	0.453087	−	0.891466i	$-0.350323\pi$
$617$	−10.8891	−	10.8891i	−0.438379	−	0.438379i	−0.891466	+	0.453087i	$0.850323\pi$
$618$	1.55652	−	1.80396i	0.0626126	−	0.0725659i
$619$	−1.24466			−0.0500273			−0.0250136	−	0.999687i	$-0.507963\pi$
$619$	−1.24466			−0.0500273			−0.0250136	+	0.999687i	$0.507963\pi$
$620$	−19.4412	+	14.9295i	−0.780776	+	0.599582i
$621$	23.3169			0.935673
$622$	−29.5046	+	34.1948i	−1.18302	+	1.37109i
$623$	26.4448	+	26.4448i	1.05949	+	1.05949i
$624$	−17.1600	+	5.19547i	−0.686951	+	0.207985i
$625$	−11.1152	−	22.3932i	−0.444606	−	0.895726i
$626$	−7.05725	+	0.519630i	−0.282064	+	0.0207686i
$627$	4.73093	−	4.73093i	0.188935	−	0.188935i
$628$	3.09888	−	4.17603i	0.123659	−	0.166642i
$629$		−	30.7491i		−	1.22605i
$630$	−2.39707	−	3.64771i	−0.0955015	−	0.145328i
$631$		−	5.70526i		−	0.227123i	−0.993531	−	0.113561i	$-0.963774\pi$
$631$		−	5.70526i		−	0.227123i	0.993531	−	0.113561i	$-0.0362259\pi$
$632$	5.52407	−	8.71576i	0.219736	−	0.346694i
$633$	−12.3702	+	12.3702i	−0.491672	+	0.491672i
$634$	1.17040	+	15.8955i	0.0464824	+	0.631291i
$635$	1.99761	−	7.01245i	0.0792728	−	0.278281i
$636$	1.82697	+	12.3391i	0.0724441	+	0.489276i
$637$	14.9733	+	14.9733i	0.593262	+	0.593262i
$638$	−10.3656	−	8.94379i	−0.410376	−	0.354088i
$639$	−5.38879			−0.213177
$640$	5.93898	+	24.5912i	0.234759	+	0.972054i
$641$	−0.458904			−0.0181256			−0.00906280	−	0.999959i	$-0.502885\pi$
$641$	−0.458904			−0.0181256			−0.00906280	+	0.999959i	$0.502885\pi$
$642$	10.3216	+	8.90589i	0.407362	+	0.351487i
$643$	2.89559	+	2.89559i	0.114191	+	0.114191i	0.761893	−	0.647702i	$-0.224270\pi$
$643$	2.89559	+	2.89559i	0.114191	+	0.114191i	−0.647702	+	0.761893i	$0.724270\pi$
$644$	4.79271	+	32.3692i	0.188859	+	1.27552i
$645$	22.3981	+	40.2423i	0.881926	+	1.58454i
$646$	−0.610291	−	8.28855i	−0.0240116	−	0.326109i
$647$	26.0239	−	26.0239i	1.02311	−	1.02311i	0.0233789	−	0.999727i	$-0.492558\pi$
$647$	26.0239	−	26.0239i	1.02311	−	1.02311i	0.999727	−	0.0233789i	$-0.00744243\pi$
$648$	11.7942	−	18.6086i	0.463318	−	0.731014i
$649$		−	37.1575i		−	1.45856i
$650$	9.03488	−	17.2896i	0.354377	−	0.678155i
$651$			34.1146i			1.33706i
$652$	−2.90067	+	3.90893i	−0.113599	+	0.153086i
$653$	−19.7494	+	19.7494i	−0.772852	+	0.772852i	−0.978604	−	0.205752i	$-0.934036\pi$
$653$	−19.7494	+	19.7494i	−0.772852	+	0.772852i	0.205752	+	0.978604i	$0.434036\pi$
$654$	−6.47903	+	0.477055i	−0.253350	+	0.0186543i
$655$	2.04326	+	3.67108i	0.0798366	+	0.143441i
$656$	37.6231	−	11.3910i	1.46894	−	0.444744i
$657$	−2.62951	−	2.62951i	−0.102587	−	0.102587i
$658$	−2.41532	+	2.79928i	−0.0941591	+	0.109127i
$659$	−7.33213			−0.285619			−0.142810	−	0.989750i	$-0.545614\pi$
$659$	−7.33213			−0.285619			−0.142810	+	0.989750i	$0.545614\pi$
$660$	−29.6665	−	3.89420i	−1.15477	−	0.151581i
$661$	−32.0891			−1.24812			−0.624061	−	0.781376i	$-0.714518\pi$
$661$	−32.0891			−1.24812			−0.624061	+	0.781376i	$0.714518\pi$
$662$	−0.225368	+	0.261194i	−0.00875917	+	0.0101516i
$663$	−18.6263	−	18.6263i	−0.723384	−	0.723384i
$664$	32.5110	−	7.28695i	1.26167	−	0.282788i
$665$	2.34682	−	8.23831i	0.0910057	−	0.319468i
$666$	−2.65893	+	0.195779i	−0.103031	+	0.00758627i
$667$	7.09948	−	7.09948i	0.274893	−	0.274893i
$668$	21.6463	+	16.0629i	0.837520	+	0.621493i
$669$			5.98852i			0.231530i
$670$	−24.2810	+	15.9561i	−0.938058	+	0.616439i
$671$			17.4580i			0.673957i
$672$	32.1785	+	14.2894i	1.24131	+	0.551224i
$673$	24.8279	−	24.8279i	0.957047	−	0.957047i	−0.0420678	−	0.999115i	$-0.513395\pi$
$673$	24.8279	−	24.8279i	0.957047	−	0.957047i	0.999115	+	0.0420678i	$0.0133945\pi$
$674$	3.17236	+	43.0847i	0.122195	+	1.65956i
$675$	6.23302	+	26.5765i	0.239909	+	1.02293i
$676$	−10.6614	+	1.57857i	−0.410053	+	0.0607140i
$677$	−28.6500	−	28.6500i	−1.10111	−	1.10111i	−0.994277	−	0.106832i	$-0.965929\pi$
$677$	−28.6500	−	28.6500i	−1.10111	−	1.10111i	−0.106832	−	0.994277i	$-0.534071\pi$
$678$	2.56943	+	2.21700i	0.0986784	+	0.0851434i
$679$	−1.13030			−0.0433769
$680$	−27.7367	+	24.7411i	−1.06366	+	0.948779i
$681$	−16.1587			−0.619201
$682$	−24.1676	−	20.8527i	−0.925423	−	0.798490i
$683$	10.3844	+	10.3844i	0.397349	+	0.397349i	0.877297	−	0.479948i	$-0.159345\pi$
$683$	10.3844	+	10.3844i	0.397349	+	0.397349i	−0.479948	+	0.877297i	$0.659345\pi$
$684$	−0.712840	+	0.105546i	−0.0272561	+	0.00403565i
$685$	13.3343	+	3.79850i	0.509479	+	0.145133i
$686$	−0.268721	−	3.64959i	−0.0102598	−	0.139342i
$687$	−3.54404	+	3.54404i	−0.135214	+	0.135214i
$688$	44.7082	+	23.9276i	1.70448	+	0.912232i
$689$		−	10.5904i		−	0.403461i
$690$	4.44571	−	21.4877i	0.169245	−	0.818022i
$691$			4.95589i			0.188531i	0.995547	+	0.0942654i	$0.0300502\pi$
$691$			4.95589i			0.188531i	−0.995547	+	0.0942654i	$0.969950\pi$
$692$	3.15419	+	2.34061i	0.119904	+	0.0889766i
$693$	4.01917	−	4.01917i	0.152676	−	0.152676i
$694$	42.8622	−	3.15597i	1.62703	−	0.119799i
$695$	11.1469	−	6.20417i	0.422826	−	0.235338i
$696$	−2.36277	−	10.5416i	−0.0895605	−	0.399577i
$697$	40.8378	+	40.8378i	1.54684	+	1.54684i
$698$	−15.6945	+	18.1893i	−0.594044	+	0.688477i
$699$	−38.1012			−1.44112
$700$	−35.6132	+	14.1156i	−1.34605	+	0.533519i
$701$	50.5194			1.90809			0.954045	−	0.299662i	$-0.0968739\pi$
$701$	50.5194			1.90809			0.954045	+	0.299662i	$0.0968739\pi$
$702$	−13.9153	+	16.1273i	−0.525199	+	0.608688i
$703$	−3.69981	−	3.69981i	−0.139541	−	0.139541i
$704$	−29.7921	+	14.0615i	−1.12283	+	0.529964i
$705$	2.16636	−	1.20576i	0.0815899	−	0.0454115i
$706$	−43.7595	+	3.22204i	−1.64691	+	0.121263i
$707$	50.9129	−	50.9129i	1.91478	−	1.91478i
$708$	17.4723	−	23.5456i	0.656651	−	0.884899i
$709$		−	28.2010i		−	1.05911i	−0.848276	−	0.529555i	$-0.822359\pi$
$709$		−	28.2010i		−	1.05911i	0.848276	−	0.529555i	$-0.177641\pi$
$710$	−9.58231	+	46.3146i	−0.359618	+	1.73816i
$711$		−	1.31450i		−	0.0492975i
$712$	−23.3225	−	14.7819i	−0.874048	−	0.553974i
$713$	16.5526	−	16.5526i	0.619901	−	0.619901i
$714$	3.79848	+	51.5883i	0.142155	+	1.93064i
$715$	24.4317	+	6.95976i	0.913693	+	0.260280i
$716$	−6.14452	−	41.4991i	−0.229632	−	1.55089i
$717$	−10.4485	−	10.4485i	−0.390207	−	0.390207i
$718$	10.0465	+	8.66848i	0.374931	+	0.323505i
$719$	7.39857			0.275920			0.137960	−	0.990438i	$-0.455945\pi$
$719$	7.39857			0.275920			0.137960	+	0.990438i	$0.455945\pi$
$720$	2.31601	+	2.24092i	0.0863126	+	0.0835142i
$721$	3.97251			0.147944
$722$	−1.07073	−	0.923868i	−0.0398485	−	0.0343828i
$723$	−0.926762	−	0.926762i	−0.0344666	−	0.0344666i
$724$	4.67803	+	31.5946i	0.173858	+	1.17421i
$725$	9.98980	+	6.19417i	0.371012	+	0.230046i
$726$	−1.00522	−	13.6522i	−0.0373072	−	0.506680i
$727$	−4.97602	+	4.97602i	−0.184550	+	0.184550i	−0.793335	−	0.608785i	$-0.791657\pi$
$727$	−4.97602	+	4.97602i	−0.184550	+	0.184550i	0.608785	+	0.793335i	$0.291657\pi$
$728$	−25.2487	−	16.0027i	−0.935779	−	0.593099i
$729$		−	29.4171i		−	1.08952i
$730$	−27.2754	+	17.9238i	−1.00951	+	0.663391i
$731$			74.5004i			2.75550i
$732$	−8.20916	+	11.0626i	−0.303419	+	0.408886i
$733$	−34.5680	+	34.5680i	−1.27680	+	1.27680i	−0.334348	+	0.942450i	$0.608516\pi$
$733$	−34.5680	+	34.5680i	−1.27680	+	1.27680i	−0.942450	+	0.334348i	$0.891484\pi$
$734$	17.3936	−	1.28070i	0.642010	−	0.0472716i
$735$	−7.63950	+	26.8179i	−0.281787	+	0.989192i
$736$	−8.67991	−	22.5465i	−0.319946	−	0.831075i
$737$	−26.7537	−	26.7537i	−0.985484	−	0.985484i
$738$	3.27131	−	3.79134i	0.120419	−	0.139561i
$739$	32.5879			1.19877			0.599383	−	0.800462i	$-0.295413\pi$
$739$	32.5879			1.19877			0.599383	+	0.800462i	$0.295413\pi$
$740$	−3.04545	+	23.2006i	−0.111953	+	0.852873i
$741$	−4.48233			−0.164662
$742$	−13.5860	+	15.7457i	−0.498756	+	0.578042i
$743$	−2.79042	−	2.79042i	−0.102371	−	0.102371i	0.654066	−	0.756437i	$-0.273062\pi$
$743$	−2.79042	−	2.79042i	−0.102371	−	0.102371i	−0.756437	+	0.654066i	$0.773062\pi$
$744$	−5.50885	−	24.5779i	−0.201964	−	0.901071i
$745$	−4.25921	−	7.65244i	−0.156045	−	0.280364i
$746$	−32.8971	+	2.42224i	−1.20445	+	0.0886843i
$747$	3.00113	−	3.00113i	0.109806	−	0.109806i
$748$	−38.8682	−	28.8426i	−1.42116	−	1.05459i
$749$			22.7293i			0.830511i
$750$	25.6801	−	0.676820i	0.937703	−	0.0247140i
$751$		−	10.9120i		−	0.398186i	−0.979981	−	0.199093i	$-0.936200\pi$
$751$		−	10.9120i		−	0.398186i	0.979981	−	0.199093i	$-0.0637996\pi$
$752$	1.28809	−	2.40677i	0.0469720	−	0.0877660i
$753$	2.74637	−	2.74637i	0.100083	−	0.100083i
$754$	0.673524	+	9.14734i	0.0245283	+	0.333126i
$755$	4.61248	+	8.28715i	0.167865	+	0.301600i
$756$	41.3783	−	6.12664i	1.50491	−	0.222824i
$757$	27.9482	+	27.9482i	1.01579	+	1.01579i	0.999873	+	0.0159213i	$0.00506814\pi$
$757$	27.9482	+	27.9482i	1.01579	+	1.01579i	0.0159213	+	0.999873i	$0.494932\pi$
$758$	31.8187	+	27.4544i	1.15571	+	0.997189i
$759$	28.5743			1.03718
$760$	−0.360440	+	6.31428i	−0.0130745	+	0.229043i
$761$	32.7705			1.18793			0.593964	−	0.804491i	$-0.297562\pi$
$761$	32.7705			1.18793			0.593964	+	0.804491i	$0.297562\pi$
$762$	5.67264	+	4.89457i	0.205498	+	0.177312i
$763$	−7.65902	−	7.65902i	−0.277275	−	0.277275i
$764$	−11.7081	+	1.73355i	−0.423584	+	0.0627176i
$765$	−1.29716	+	4.55356i	−0.0468988	+	0.164634i
$766$	1.25929	+	17.1028i	0.0455001	+	0.617951i
$767$	−17.6024	+	17.6024i	−0.635587	+	0.635587i
$768$	−25.4905	−	5.09859i	−0.919810	−	0.183980i
$769$			48.5580i			1.75104i	0.483178	+	0.875522i	$0.339482\pi$
$769$			48.5580i			1.75104i	−0.483178	+	0.875522i	$0.660518\pi$
$770$	−27.3964	−	41.6902i	−0.987299	−	1.50241i
$771$		−	36.9464i		−

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07073 - 0.923868i) q^{2} +(-1.14885 - 1.14885i) q^{3} +(0.292934 + 1.97843i) q^{4} +(1.95382 - 1.08746i) q^{5} +(0.168724 + 2.29149i) q^{6} +(-2.70883 + 2.70883i) q^{7} +(1.51416 - 2.38900i) q^{8} -0.360306i q^{9} +O(q^{10})\)	\(q+(-1.07073 - 0.923868i) q^{2} +(-1.14885 - 1.14885i) q^{3} +(0.292934 + 1.97843i) q^{4} +(1.95382 - 1.08746i) q^{5} +(0.168724 + 2.29149i) q^{6} +(-2.70883 + 2.70883i) q^{7} +(1.51416 - 2.38900i) q^{8} -0.360306i q^{9} +(-3.09669 - 0.640694i) q^{10} -4.11798i q^{11} +(1.93638 - 2.60945i) q^{12} +(-1.95079 + 1.95079i) q^{13} +(5.40302 - 0.397828i) q^{14} +(-3.49397 - 0.995314i) q^{15} +(-3.82838 + 1.15910i) q^{16} +(-4.15549 - 4.15549i) q^{17} +(-0.332875 + 0.385791i) q^{18} -1.00000 q^{19} +(2.72381 + 3.54695i) q^{20} +6.22405 q^{21} +(-3.80447 + 4.40926i) q^{22} +(-3.01995 - 3.01995i) q^{23} +(-4.48413 + 1.00506i) q^{24} +(2.63485 - 4.24942i) q^{25} +(3.89106 - 0.286501i) q^{26} +(-3.86047 + 3.86047i) q^{27} +(-6.15273 - 4.56572i) q^{28} +2.35086i q^{29} +(2.82157 + 4.29368i) q^{30} +5.48110i q^{31} +(5.17002 + 2.29583i) q^{32} +(-4.73093 + 4.73093i) q^{33} +(0.610291 + 8.28855i) q^{34} +(-2.34682 + 8.23831i) q^{35} +(0.712840 - 0.105546i) q^{36} +(3.69981 + 3.69981i) q^{37} +(1.07073 + 0.923868i) q^{38} +4.48233 q^{39} +(0.360440 - 6.31428i) q^{40} -9.82744 q^{41} +(-6.66429 - 5.75020i) q^{42} +(-8.96408 - 8.96408i) q^{43} +(8.14714 - 1.20630i) q^{44} +(-0.391819 - 0.703974i) q^{45} +(0.443521 + 6.02359i) q^{46} +(-0.482563 + 0.482563i) q^{47} +(5.72985 + 3.06659i) q^{48} -7.67547i q^{49} +(-6.74712 + 2.11574i) q^{50} +9.54804i q^{51} +(-4.43097 - 3.28806i) q^{52} +(-2.71437 + 2.71437i) q^{53} +(7.70010 - 0.566964i) q^{54} +(-4.47815 - 8.04581i) q^{55} +(2.36981 + 10.5730i) q^{56} +(1.14885 + 1.14885i) q^{57} +(2.17189 - 2.51714i) q^{58} +9.02322 q^{59} +(0.945656 - 7.20414i) q^{60} -4.23945 q^{61} +(5.06381 - 5.86878i) q^{62} +(0.976005 + 0.976005i) q^{63} +(-3.41467 - 7.23464i) q^{64} +(-1.69009 + 5.93292i) q^{65} +(9.43631 - 0.694802i) q^{66} +(6.49679 - 6.49679i) q^{67} +(7.00407 - 9.43864i) q^{68} +6.93891i q^{69} +(10.1239 - 6.65288i) q^{70} -14.9562i q^{71} +(-0.860771 - 0.545559i) q^{72} +(7.29798 - 7.29798i) q^{73} +(-0.543368 - 7.37965i) q^{74} +(-7.90896 + 1.85490i) q^{75} +(-0.292934 - 1.97843i) q^{76} +(11.1549 + 11.1549i) q^{77} +(-4.79937 - 4.14108i) q^{78} +3.64828 q^{79} +(-6.21949 + 6.42790i) q^{80} +7.78926 q^{81} +(10.5226 + 9.07926i) q^{82} +(8.32940 + 8.32940i) q^{83} +(1.82324 + 12.3138i) q^{84} +(-12.6380 - 3.60015i) q^{85} +(1.31650 + 17.8798i) q^{86} +(2.70078 - 2.70078i) q^{87} +(-9.83787 - 6.23527i) q^{88} -9.76244i q^{89} +(-0.230846 + 1.11576i) q^{90} -10.5687i q^{91} +(5.09011 - 6.85941i) q^{92} +(6.29693 - 6.29693i) q^{93} +(0.962520 - 0.0708710i) q^{94} +(-1.95382 + 1.08746i) q^{95} +(-3.30201 - 8.57712i) q^{96} +(0.208633 + 0.208633i) q^{97} +(-7.09112 + 8.21837i) q^{98} -1.48373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

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