LMFDB - Embedded newform 380.2.k.c.343.26

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			343.26
Character	$\chi$	$=$	380.343
Dual form			380.2.k.c.267.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41420 - 0.00522099i) q^{2} +(0.212700 - 0.212700i) q^{3} +(1.99995 - 0.0147671i) q^{4} +(2.19176 - 0.442915i) q^{5} +(0.299691 - 0.301912i) q^{6} +(-2.65088 - 2.65088i) q^{7} +(2.82825 - 0.0313254i) q^{8} +2.90952i q^{9} +O(q^{10})$	\(q+(1.41420 - 0.00522099i) q^{2} +(0.212700 - 0.212700i) q^{3} +(1.99995 - 0.0147671i) q^{4} +(2.19176 - 0.442915i) q^{5} +(0.299691 - 0.301912i) q^{6} +(-2.65088 - 2.65088i) q^{7} +(2.82825 - 0.0313254i) q^{8} +2.90952i q^{9} +(3.09729 - 0.637816i) q^{10} -2.04453i q^{11} +(0.422248 - 0.428530i) q^{12} +(-0.226183 - 0.226183i) q^{13} +(-3.76272 - 3.73504i) q^{14} +(0.371981 - 0.560397i) q^{15} +(3.99956 - 0.0590668i) q^{16} +(-3.06235 + 3.06235i) q^{17} +(0.0151906 + 4.11465i) q^{18} +1.00000 q^{19} +(4.37687 - 0.918173i) q^{20} -1.12768 q^{21} +(-0.0106745 - 2.89139i) q^{22} +(-5.40599 + 5.40599i) q^{23} +(0.594908 - 0.608234i) q^{24} +(4.60765 - 1.94153i) q^{25} +(-0.321050 - 0.318688i) q^{26} +(1.25696 + 1.25696i) q^{27} +(-5.34075 - 5.26246i) q^{28} -6.50979i q^{29} +(0.523131 - 0.794458i) q^{30} +5.78891i q^{31} +(5.65589 - 0.104414i) q^{32} +(-0.434873 - 0.434873i) q^{33} +(-4.31480 + 4.34677i) q^{34} +(-6.98421 - 4.63598i) q^{35} +(0.0429651 + 5.81888i) q^{36} +(-6.86987 + 6.86987i) q^{37} +(1.41420 - 0.00522099i) q^{38} -0.0962184 q^{39} +(6.18499 - 1.32133i) q^{40} +6.57779 q^{41} +(-1.59478 + 0.00588763i) q^{42} +(3.72596 - 3.72596i) q^{43} +(-0.0301918 - 4.08895i) q^{44} +(1.28867 + 6.37697i) q^{45} +(-7.61695 + 7.67340i) q^{46} +(-1.24109 - 1.24109i) q^{47} +(0.838145 - 0.863272i) q^{48} +7.05428i q^{49} +(6.50602 - 2.76978i) q^{50} +1.30273i q^{51} +(-0.455694 - 0.449014i) q^{52} +(-6.74839 - 6.74839i) q^{53} +(1.78416 + 1.77103i) q^{54} +(-0.905555 - 4.48113i) q^{55} +(-7.58039 - 7.41431i) q^{56} +(0.212700 - 0.212700i) q^{57} +(-0.0339876 - 9.20617i) q^{58} -4.42510 q^{59} +(0.735666 - 1.12626i) q^{60} +0.777701 q^{61} +(0.0302239 + 8.18670i) q^{62} +(7.71277 - 7.71277i) q^{63} +(7.99804 - 0.177192i) q^{64} +(-0.595919 - 0.395560i) q^{65} +(-0.617269 - 0.612728i) q^{66} +(5.08912 + 5.08912i) q^{67} +(-6.07931 + 6.16975i) q^{68} +2.29971i q^{69} +(-9.90129 - 6.51975i) q^{70} +1.53345i q^{71} +(0.0911417 + 8.22885i) q^{72} +(-7.28339 - 7.28339i) q^{73} +(-9.67952 + 9.75126i) q^{74} +(0.567085 - 1.39301i) q^{75} +(1.99995 - 0.0147671i) q^{76} +(-5.41980 + 5.41980i) q^{77} +(-0.136072 + 0.000502356i) q^{78} -16.5071 q^{79} +(8.73994 - 1.90093i) q^{80} -8.19384 q^{81} +(9.30234 - 0.0343426i) q^{82} +(-4.29909 + 4.29909i) q^{83} +(-2.25531 + 0.0166526i) q^{84} +(-5.35558 + 8.06830i) q^{85} +(5.24981 - 5.28872i) q^{86} +(-1.38464 - 1.38464i) q^{87} +(-0.0640457 - 5.78246i) q^{88} +8.74189i q^{89} +(1.85574 + 9.01161i) q^{90} +1.19917i q^{91} +(-10.7319 + 10.8915i) q^{92} +(1.23130 + 1.23130i) q^{93} +(-1.76164 - 1.74868i) q^{94} +(2.19176 - 0.442915i) q^{95} +(1.18080 - 1.22522i) q^{96} +(-2.60382 + 2.60382i) q^{97} +(0.0368304 + 9.97619i) q^{98} +5.94860 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} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 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 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.41420	−	0.00522099i	0.999993	−	0.00369180i
$2$	1.41420	−	0.00522099i	0.999993	−	0.00369180i
$3$	0.212700	−	0.212700i	0.122803	−	0.122803i	−0.643035	−	0.765837i	$-0.722325\pi$
$3$	0.212700	−	0.212700i	0.122803	−	0.122803i	0.765837	+	0.643035i	$0.222325\pi$
$4$	1.99995	−	0.0147671i	0.999973	−	0.00738355i
$5$	2.19176	−	0.442915i	0.980186	−	0.198078i
$5$	2.19176	−	0.442915i	0.980186	−	0.198078i
$6$	0.299691	−	0.301912i	0.122348	−	0.123255i
$7$	−2.65088	−	2.65088i	−1.00194	−	1.00194i	−0.999998	−	0.00193869i	$-0.999383\pi$
$7$	−2.65088	−	2.65088i	−1.00194	−	1.00194i	−0.00193869	−	0.999998i	$-0.500617\pi$
$8$	2.82825	−	0.0313254i	0.999939	−	0.0110752i
$9$			2.90952i			0.969839i
$10$	3.09729	−	0.637816i	0.979448	−	0.201695i
$11$		−	2.04453i		−	0.616450i	−0.951314	−	0.308225i	$-0.900265\pi$
$11$		−	2.04453i		−	0.616450i	0.951314	−	0.308225i	$-0.0997349\pi$
$12$	0.422248	−	0.428530i	0.121893	−	0.123706i
$13$	−0.226183	−	0.226183i	−0.0627319	−	0.0627319i	0.675045	−	0.737777i	$-0.264124\pi$
$13$	−0.226183	−	0.226183i	−0.0627319	−	0.0627319i	−0.737777	+	0.675045i	$0.764124\pi$
$14$	−3.76272	−	3.73504i	−1.00563	−	0.998231i
$15$	0.371981	−	0.560397i	0.0960450	−	0.144694i
$16$	3.99956	−	0.0590668i	0.999891	−	0.0147667i
$17$	−3.06235	+	3.06235i	−0.742729	+	0.742729i	−0.973102	−	0.230374i	$-0.926005\pi$
$17$	−3.06235	+	3.06235i	−0.742729	+	0.742729i	0.230374	+	0.973102i	$0.426005\pi$
$18$	0.0151906	+	4.11465i	0.00358045	+	0.969832i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	4.37687	−	0.918173i	0.978697	−	0.205310i
$21$	−1.12768			−0.246081
$22$	−0.0106745	−	2.89139i	−0.00227581	−	0.616445i
$23$	−5.40599	+	5.40599i	−1.12723	+	1.12723i	−0.136600	+	0.990626i	$0.543618\pi$
$23$	−5.40599	+	5.40599i	−1.12723	+	1.12723i	−0.990626	+	0.136600i	$0.956382\pi$
$24$	0.594908	−	0.608234i	0.121435	−	0.124155i
$25$	4.60765	−	1.94153i	0.921530	−	0.388306i
$26$	−0.321050	−	0.318688i	−0.0629630	−	0.0624999i
$27$	1.25696	+	1.25696i	0.241901	+	0.241901i
$28$	−5.34075	−	5.26246i	−1.00931	−	0.994512i
$29$		−	6.50979i		−	1.20884i	−0.796667	−	0.604419i	$-0.793405\pi$
$29$		−	6.50979i		−	1.20884i	0.796667	−	0.604419i	$-0.206595\pi$
$30$	0.523131	−	0.794458i	0.0955102	−	0.145048i
$31$			5.78891i			1.03972i	0.854252	+	0.519860i	$0.174016\pi$
$31$			5.78891i			1.03972i	−0.854252	+	0.519860i	$0.825984\pi$
$32$	5.65589	−	0.104414i	0.999830	−	0.0184580i
$33$	−0.434873	−	0.434873i	−0.0757016	−	0.0757016i
$34$	−4.31480	+	4.34677i	−0.739982	+	0.745466i
$35$	−6.98421	−	4.63598i	−1.18055	−	0.783623i
$36$	0.0429651	+	5.81888i	0.00716085	+	0.969813i
$37$	−6.86987	+	6.86987i	−1.12940	+	1.12940i	−0.139124	+	0.990275i	$0.544429\pi$
$37$	−6.86987	+	6.86987i	−1.12940	+	1.12940i	−0.990275	+	0.139124i	$0.955571\pi$
$38$	1.41420	−	0.00522099i	0.229414	−	0.000846957i
$39$	−0.0962184			−0.0154073
$40$	6.18499	−	1.32133i	0.977932	−	0.208921i
$41$	6.57779			1.02728			0.513639	−	0.858006i	$-0.328297\pi$
$41$	6.57779			1.02728			0.513639	+	0.858006i	$0.328297\pi$
$42$	−1.59478	+	0.00588763i	−0.246079	+	0.000908481i
$43$	3.72596	−	3.72596i	0.568203	−	0.568203i	−0.363422	−	0.931625i	$-0.618392\pi$
$43$	3.72596	−	3.72596i	0.568203	−	0.568203i	0.931625	+	0.363422i	$0.118392\pi$
$44$	−0.0301918	−	4.08895i	−0.00455158	−	0.616433i
$45$	1.28867	+	6.37697i	0.192104	+	0.950623i
$46$	−7.61695	+	7.67340i	−1.12306	+	1.13138i
$47$	−1.24109	−	1.24109i	−0.181032	−	0.181032i	0.610773	−	0.791805i	$-0.290859\pi$
$47$	−1.24109	−	1.24109i	−0.181032	−	0.181032i	−0.791805	+	0.610773i	$0.790859\pi$
$48$	0.838145	−	0.863272i	0.120976	−	0.124603i
$49$			7.05428i			1.00775i
$50$	6.50602	−	2.76978i	0.920091	−	0.391706i
$51$			1.30273i			0.182418i
$52$	−0.455694	−	0.449014i	−0.0631933	−	0.0622670i
$53$	−6.74839	−	6.74839i	−0.926962	−	0.926962i	0.0705463	−	0.997509i	$-0.477526\pi$
$53$	−6.74839	−	6.74839i	−0.926962	−	0.926962i	−0.997509	+	0.0705463i	$0.977526\pi$
$54$	1.78416	+	1.77103i	0.242793	+	0.241007i
$55$	−0.905555	−	4.48113i	−0.122105	−	0.604235i
$56$	−7.58039	−	7.41431i	−1.01297	−	0.990779i
$57$	0.212700	−	0.212700i	0.0281729	−	0.0281729i
$58$	−0.0339876	−	9.20617i	−0.00446279	−	1.20883i
$59$	−4.42510			−0.576098			−0.288049	−	0.957616i	$-0.593007\pi$
$59$	−4.42510			−0.576098			−0.288049	+	0.957616i	$0.593007\pi$
$60$	0.735666	−	1.12626i	0.0949740	−	0.145399i
$61$	0.777701			0.0995745			0.0497872	−	0.998760i	$-0.484146\pi$
$61$	0.777701			0.0995745			0.0497872	+	0.998760i	$0.484146\pi$
$62$	0.0302239	+	8.18670i	0.00383844	+	1.03971i
$63$	7.71277	−	7.71277i	0.971717	−	0.971717i
$64$	7.99804	−	0.177192i	0.999755	−	0.0221490i
$65$	−0.595919	−	0.395560i	−0.0739147	−	0.0490631i
$66$	−0.617269	−	0.612728i	−0.0759806	−	0.0754216i
$67$	5.08912	+	5.08912i	0.621734	+	0.621734i	0.945975	−	0.324240i	$-0.105109\pi$
$67$	5.08912	+	5.08912i	0.621734	+	0.621734i	−0.324240	+	0.945975i	$0.605109\pi$
$68$	−6.07931	+	6.16975i	−0.737224	+	0.748192i
$69$			2.29971i			0.276853i
$70$	−9.90129	−	6.51975i	−1.18343	−	0.779260i
$71$			1.53345i			0.181986i	0.995852	+	0.0909932i	$0.0290042\pi$
$71$			1.53345i			0.181986i	−0.995852	+	0.0909932i	$0.970996\pi$
$72$	0.0911417	+	8.22885i	0.0107412	+	0.969780i
$73$	−7.28339	−	7.28339i	−0.852457	−	0.852457i	0.137979	−	0.990435i	$-0.455939\pi$
$73$	−7.28339	−	7.28339i	−0.852457	−	0.852457i	−0.990435	+	0.137979i	$0.955939\pi$
$74$	−9.67952	+	9.75126i	−1.12522	+	1.13356i
$75$	0.567085	−	1.39301i	0.0654813	−	0.160851i
$76$	1.99995	−	0.0147671i	0.229409	−	0.00169390i
$77$	−5.41980	+	5.41980i	−0.617644	+	0.617644i
$78$	−0.136072		0.000502356i	−0.0154072		5.68806e-5i
$79$	−16.5071			−1.85720			−0.928599	−	0.371086i	$-0.878986\pi$
$79$	−16.5071			−1.85720			−0.928599	+	0.371086i	$0.878986\pi$
$80$	8.73994	−	1.90093i	0.977154	−	0.212530i
$81$	−8.19384			−0.910427
$82$	9.30234	−	0.0343426i	1.02727	−	0.00379250i
$83$	−4.29909	+	4.29909i	−0.471887	+	0.471887i	−0.902525	−	0.430638i	$-0.858289\pi$
$83$	−4.29909	+	4.29909i	−0.471887	+	0.471887i	0.430638	+	0.902525i	$0.358289\pi$
$84$	−2.25531	+	0.0166526i	−0.246074	+	0.00181695i
$85$	−5.35558	+	8.06830i	−0.580894	+	0.875131i
$86$	5.24981	−	5.28872i	0.566102	−	0.570297i
$87$	−1.38464	−	1.38464i	−0.148449	−	0.148449i
$88$	−0.0640457	−	5.78246i	−0.00682730	−	0.616412i
$89$			8.74189i			0.926639i	0.886191	+	0.463319i	$0.153342\pi$
$89$			8.74189i			0.926639i	−0.886191	+	0.463319i	$0.846658\pi$
$90$	1.85574	+	9.01161i	0.195612	+	0.949907i
$91$			1.19917i			0.125707i
$92$	−10.7319	+	10.8915i	−1.11887	+	1.13552i
$93$	1.23130	+	1.23130i	0.127680	+	0.127680i
$94$	−1.76164	−	1.74868i	−0.181699	−	0.180363i
$95$	2.19176	−	0.442915i	0.224870	−	0.0454422i
$96$	1.18080	−	1.22522i	0.120515	−	0.125048i
$97$	−2.60382	+	2.60382i	−0.264377	+	0.264377i	−0.826830	−	0.562452i	$-0.809858\pi$
$97$	−2.60382	+	2.60382i	−0.264377	+	0.264377i	0.562452	+	0.826830i	$0.309858\pi$
$98$	0.0368304	+	9.97619i	0.00372043	+	1.00775i
$99$	5.94860			0.597857
$100$	9.18638	−	3.95100i	0.918638	−	0.395100i
$101$	13.0511			1.29864			0.649318	−	0.760517i	$-0.275054\pi$
$101$	13.0511			1.29864			0.649318	+	0.760517i	$0.275054\pi$
$102$	0.00680152	+	1.84232i	0.000673451	+	0.182417i
$103$	12.4417	−	12.4417i	1.22591	−	1.22591i	0.260419	−	0.965496i	$-0.416139\pi$
$103$	12.4417	−	12.4417i	1.22591	−	1.22591i	0.965496	−	0.260419i	$-0.0838608\pi$
$104$	−0.646788	−	0.632618i	−0.0634228	−	0.0620333i
$105$	−2.47162	+	0.499469i	−0.241205	+	0.0487432i
$106$	−9.57883	−	9.50836i	−0.930378	−	0.923534i
$107$	−0.931552	−	0.931552i	−0.0900565	−	0.0900565i	0.660643	−	0.750700i	$-0.270284\pi$
$107$	−0.931552	−	0.931552i	−0.0900565	−	0.0900565i	−0.750700	+	0.660643i	$0.770284\pi$
$108$	2.53241	+	2.49528i	0.243681	+	0.240109i
$109$		−	20.2411i		−	1.93874i	−0.245597	−	0.969372i	$-0.578984\pi$
$109$		−	20.2411i		−	1.93874i	0.245597	−	0.969372i	$-0.421016\pi$
$110$	−1.30404	−	6.33250i	−0.124335	−	0.603781i
$111$			2.92245i			0.277386i
$112$	−10.7589	−	10.4458i	−1.01662	−	0.987032i
$113$	3.01028	+	3.01028i	0.283183	+	0.283183i	0.834377	−	0.551194i	$-0.185828\pi$
$113$	3.01028	+	3.01028i	0.283183	+	0.283183i	−0.551194	+	0.834377i	$0.685828\pi$
$114$	0.299691	−	0.301912i	0.0280687	−	0.0282767i
$115$	−9.45425	+	14.2430i	−0.881614	+	1.32817i
$116$	−0.0961307	−	13.0192i	−0.00892551	−	1.20881i
$117$	0.658083	−	0.658083i	0.0608398	−	0.0608398i
$118$	−6.25799	+	0.0231034i	−0.576094	+	0.00212684i
$119$	16.2358			1.48833
$120$	1.03450	−	1.59660i	0.0944366	−	0.145749i
$121$	6.81989			0.619990
$122$	1.09983	−	0.00406037i	0.0995738	−	0.000367609i
$123$	1.39910	−	1.39910i	0.126152	−	0.126152i
$124$	0.0854854	+	11.5775i	0.00767682	+	1.03969i
$125$	9.23895	−	6.29618i	0.826357	−	0.563147i
$126$	10.8672	−	10.9477i	0.968123	−	0.975298i
$127$	−6.14286	−	6.14286i	−0.545091	−	0.545091i	0.379926	−	0.925017i	$-0.375949\pi$
$127$	−6.14286	−	6.14286i	−0.545091	−	0.545091i	−0.925017	+	0.379926i	$0.875949\pi$
$128$	11.3099	−	0.292344i	0.999666	−	0.0258398i
$129$		−	1.58503i		−	0.139554i
$130$	−0.844817	−	0.556291i	−0.0740953	−	0.0487899i
$131$			8.30018i			0.725190i	0.931947	+	0.362595i	$0.118109\pi$
$131$			8.30018i			0.725190i	−0.931947	+	0.362595i	$0.881891\pi$
$132$	−0.876144	−	0.863300i	−0.0762585	−	0.0751406i
$133$	−2.65088	−	2.65088i	−0.229860	−	0.229860i
$134$	7.22362	+	7.17048i	0.624026	+	0.619435i
$135$	3.31168	+	2.19823i	0.285024	+	0.189193i
$136$	−8.56517	+	8.75703i	−0.734457	+	0.750909i
$137$	3.16161	−	3.16161i	0.270115	−	0.270115i	−0.559032	−	0.829146i	$-0.688827\pi$
$137$	3.16161	−	3.16161i	0.270115	−	0.270115i	0.829146	+	0.559032i	$0.188827\pi$
$138$	0.0120068	+	3.25226i	0.00102208	+	0.276851i
$139$	16.9908			1.44114			0.720572	−	0.693380i	$-0.243879\pi$
$139$	16.9908			1.44114			0.720572	+	0.693380i	$0.243879\pi$
$140$	−14.0365	−	9.16857i	−1.18630	−	0.774885i
$141$	−0.527962			−0.0444625
$142$	0.00800611	+	2.16860i	0.000671857	+	0.181985i
$143$	−0.462438	+	0.462438i	−0.0386710	+	0.0386710i
$144$	0.171856	+	11.6368i	0.0143213	+	0.969733i
$145$	−2.88329	−	14.2679i	−0.239444	−	1.18489i
$146$	−10.3382	−	10.2622i	−0.855598	−	0.849304i
$147$	1.50045	+	1.50045i	0.123755	+	0.123755i
$148$	−13.6379	+	13.8408i	−1.12103	+	1.13771i
$149$			9.77519i			0.800815i	0.916337	+	0.400407i	$0.131131\pi$
$149$			9.77519i			0.800815i	−0.916337	+	0.400407i	$0.868869\pi$
$150$	0.794701	−	1.97297i	0.0648870	−	0.161092i
$151$			4.21919i			0.343353i	0.985153	+	0.171676i	$0.0549184\pi$
$151$			4.21919i			0.343353i	−0.985153	+	0.171676i	$0.945082\pi$
$152$	2.82825	−	0.0313254i	0.229402	−	0.00254082i
$153$	−8.90996	−	8.90996i	−0.720327	−	0.720327i
$154$	−7.63641	+	7.69300i	−0.615359	+	0.619920i
$155$	2.56400	+	12.6879i	0.205945	+	1.01912i
$156$	−0.192432	+	0.00142087i	−0.0154069	+	0.000113760i
$157$	8.55712	−	8.55712i	0.682933	−	0.682933i	−0.277727	−	0.960660i	$-0.589581\pi$
$157$	8.55712	−	8.55712i	0.682933	−	0.682933i	0.960660	+	0.277727i	$0.0895812\pi$
$158$	−23.3444	+	0.0861836i	−1.85718	+	0.00685640i
$159$	−2.87077			−0.227667
$160$	12.3501	−	2.73393i	0.976363	−	0.216136i
$161$	28.6612			2.25882
$162$	−11.5878	+	0.0427800i	−0.910421	+	0.00336111i
$163$	11.5235	−	11.5235i	0.902586	−	0.902586i	−0.0930729	−	0.995659i	$-0.529669\pi$
$163$	11.5235	−	11.5235i	0.902586	−	0.902586i	0.995659	+	0.0930729i	$0.0296690\pi$
$164$	13.1552	−	0.0971348i	1.02725	−	0.00758496i
$165$	−1.14575	−	0.760526i	−0.0891965	−	0.0592069i
$166$	−6.05735	+	6.10224i	−0.470141	+	0.473625i
$167$	3.64071	+	3.64071i	0.281727	+	0.281727i	0.833797	−	0.552071i	$-0.186162\pi$
$167$	3.64071	+	3.64071i	0.281727	+	0.281727i	−0.552071	+	0.833797i	$0.686162\pi$
$168$	−3.18938	+	0.0353252i	−0.246066	+	0.00272539i
$169$		−	12.8977i		−	0.992129i
$170$	−7.53176	+	11.4382i	−0.577660	+	0.877269i
$171$			2.90952i			0.222496i
$172$	7.39669	−	7.50673i	0.563992	−	0.572383i
$173$	1.45513	+	1.45513i	0.110632	+	0.110632i	0.760256	−	0.649624i	$-0.225074\pi$
$173$	1.45513	+	1.45513i	0.110632	+	0.110632i	−0.649624	+	0.760256i	$0.725074\pi$
$174$	−1.96539	−	1.95093i	−0.148996	−	0.147899i
$175$	−17.3611	−	7.06755i	−1.31237	−	0.534257i
$176$	−0.120764	−	8.17724i	−0.00910292	−	0.616382i
$177$	−0.941220	+	0.941220i	−0.0707464	+	0.0707464i
$178$	0.0456413	+	12.3628i	0.00342096	+	0.926632i
$179$	2.19695			0.164208			0.0821038	−	0.996624i	$-0.473836\pi$
$179$	2.19695			0.164208			0.0821038	+	0.996624i	$0.473836\pi$
$180$	2.67144	+	12.7346i	0.199117	+	0.949179i
$181$	−4.48272			−0.333198			−0.166599	−	0.986025i	$-0.553279\pi$
$181$	−4.48272			−0.333198			−0.166599	+	0.986025i	$0.553279\pi$
$182$	0.00626084	+	1.69587i	0.000464084	+	0.125706i
$183$	0.165417	−	0.165417i	0.0122280	−	0.0122280i
$184$	−15.1202	+	15.4589i	−1.11467	+	1.13964i
$185$	−12.0143	+	18.0999i	−0.883312	+	1.33073i
$186$	1.74774	+	1.73489i	0.128151	+	0.127208i
$187$	6.26107	+	6.26107i	0.457855	+	0.457855i
$188$	−2.50045	−	2.46379i	−0.182364	−	0.179691i
$189$		−	6.66407i		−	0.484740i
$190$	3.09729	−	0.637816i	0.224701	−	0.0462720i
$191$		−	6.36037i		−	0.460220i	−0.973165	−	0.230110i	$-0.926091\pi$
$191$		−	6.36037i		−	0.460220i	0.973165	−	0.230110i	$-0.0739087\pi$
$192$	1.66350	−	1.73887i	0.120053	−	0.125492i
$193$	−13.5977	−	13.5977i	−0.978787	−	0.978787i	0.0209930	−	0.999780i	$-0.493317\pi$
$193$	−13.5977	−	13.5977i	−0.978787	−	0.978787i	−0.999780	+	0.0209930i	$0.993317\pi$
$194$	−3.66873	+	3.69592i	−0.263400	+	0.265352i
$195$	−0.210888	+	0.0426166i	−0.0151020	+	0.00305184i
$196$	0.104171	+	14.1082i	0.00744080	+	1.00773i
$197$	7.28242	−	7.28242i	0.518851	−	0.518851i	−0.398373	−	0.917224i	$-0.630425\pi$
$197$	7.28242	−	7.28242i	0.518851	−	0.518851i	0.917224	+	0.398373i	$0.130425\pi$
$198$	8.41253	−	0.0310576i	0.597853	−	0.00220717i
$199$	21.1117			1.49657			0.748284	−	0.663378i	$-0.230878\pi$
$199$	21.1117			1.49657			0.748284	+	0.663378i	$0.230878\pi$
$200$	12.9708	−	5.63548i	0.917173	−	0.398489i
$201$	2.16491			0.152701
$202$	18.4570	−	0.0681399i	1.29863	−	0.00479430i
$203$	−17.2566	+	17.2566i	−1.21118	+	1.21118i
$204$	0.0192375	+	2.60538i	0.00134689	+	0.182413i
$205$	14.4170	−	2.91340i	1.00692	−	0.203481i
$206$	17.5301	−	17.6600i	1.22138	−	1.23043i
$207$	−15.7288	−	15.7288i	−1.09323	−	1.09323i
$208$	−0.917993	−	0.891273i	−0.0636514	−	0.0617987i
$209$		−	2.04453i		−	0.141423i
$210$	−3.49276	+	0.719255i	−0.241024	+	0.0496333i
$211$			13.4524i			0.926098i	0.886333	+	0.463049i	$0.153245\pi$
$211$			13.4524i			0.926098i	−0.886333	+	0.463049i	$0.846755\pi$
$212$	−13.5961	−	13.3968i	−0.933781	−	0.920093i
$213$	0.326164	+	0.326164i	0.0223484	+	0.0223484i
$214$	−1.32227	−	1.31254i	−0.0903883	−	0.0897234i
$215$	6.51613	−	9.81670i	0.444397	−	0.669494i
$216$	3.59437	+	3.51562i	0.244566	+	0.239207i
$217$	15.3457	−	15.3457i	1.04173	−	1.04173i
$218$	−0.105679	−	28.6250i	−0.00715745	−	1.93873i
$219$	−3.09836			−0.209368
$220$	−1.87723	−	8.94864i	−0.126563	−	0.603317i
$221$	1.38530			0.0931855
$222$	0.0152581	+	4.13293i	0.00102405	+	0.277384i
$223$	−1.88885	+	1.88885i	−0.126486	+	0.126486i	−0.767516	−	0.641030i	$-0.778508\pi$
$223$	−1.88885	+	1.88885i	−0.126486	+	0.126486i	0.641030	+	0.767516i	$0.278508\pi$
$224$	−15.2699	−	14.7163i	−1.02026	−	0.983272i
$225$	5.64892	+	13.4060i	0.376595	+	0.893736i
$226$	4.27286	+	4.24143i	0.284226	+	0.282136i
$227$	−1.46448	−	1.46448i	−0.0972007	−	0.0972007i	0.656834	−	0.754035i	$-0.271895\pi$
$227$	−1.46448	−	1.46448i	−0.0972007	−	0.0972007i	−0.754035	+	0.656834i	$0.771895\pi$
$228$	0.422248	−	0.428530i	0.0279641	−	0.0283801i
$229$		−	3.08873i		−	0.204109i	−0.994779	−	0.102055i	$-0.967458\pi$
$229$		−	3.08873i		−	0.204109i	0.994779	−	0.102055i	$-0.0325417\pi$
$230$	−13.2959	+	20.1919i	−0.876704	+	1.33142i
$231$			2.30559i			0.151697i
$232$	−0.203922	−	18.4113i	−0.0133881	−	1.20876i
$233$	0.275351	+	0.275351i	0.0180388	+	0.0180388i	0.716069	−	0.698030i	$-0.245940\pi$
$233$	0.275351	+	0.275351i	0.0180388	+	0.0180388i	−0.698030	+	0.716069i	$0.745940\pi$
$234$	0.927228	−	0.934100i	0.0606148	−	0.0610640i
$235$	−3.26988	−	2.17048i	−0.213304	−	0.141587i
$236$	−8.84995	+	0.0653458i	−0.576083	+	0.00425365i
$237$	−3.51107	+	3.51107i	−0.228069	+	0.228069i
$238$	22.9607	−	0.0847670i	1.48832	−	0.00549463i
$239$	2.55298			0.165139			0.0825693	−	0.996585i	$-0.473687\pi$
$239$	2.55298			0.165139			0.0825693	+	0.996585i	$0.473687\pi$
$240$	1.45466	−	2.26332i	0.0938979	−	0.146096i
$241$	−10.8689			−0.700128			−0.350064	−	0.936726i	$-0.613840\pi$
$241$	−10.8689			−0.700128			−0.350064	+	0.936726i	$0.613840\pi$
$242$	9.64471	−	0.0356066i	0.619986	−	0.00228888i
$243$	−5.51370	+	5.51370i	−0.353704	+	0.353704i
$244$	1.55536	−	0.0114844i	0.0995718	−	0.000735213i
$245$	3.12445	+	15.4613i	0.199614	+	0.987787i
$246$	1.97131	−	1.98592i	0.125686	−	0.126617i
$247$	−0.226183	−	0.226183i	−0.0143917	−	0.0143917i
$248$	0.181340	+	16.3725i	0.0115151	+	1.03966i
$249$			1.82884i			0.115898i
$250$	13.0329	−	8.95231i	0.824272	−	0.566194i
$251$			21.9355i			1.38456i	0.721630	+	0.692279i	$0.243393\pi$
$251$			21.9355i			1.38456i	−0.721630	+	0.692279i	$0.756607\pi$
$252$	15.3112	−	15.5390i	0.964516	−	0.978866i
$253$	11.0527	+	11.0527i	0.694878	+	0.694878i
$254$	−8.71933	−	8.65519i	−0.547099	−	0.543075i
$255$	0.576997	+	2.85527i	0.0361330	+	0.178804i
$256$	15.9930	−	0.472483i	0.999564	−	0.0295302i
$257$	−8.89886	+	8.89886i	−0.555096	+	0.555096i	−0.927907	−	0.372811i	$-0.878394\pi$
$257$	−8.89886	+	8.89886i	−0.555096	+	0.555096i	0.372811	+	0.927907i	$0.378394\pi$
$258$	−0.00827541	−	2.24155i	−0.000515204	−	0.139553i
$259$	36.4223			2.26317
$260$	−1.19765	−	0.782298i	−0.0742750	−	0.0485160i
$261$	18.9404			1.17238
$262$	0.0433352	+	11.7381i	0.00267725	+	0.725185i
$263$	16.0413	−	16.0413i	0.989151	−	0.989151i	−0.0107906	−	0.999942i	$-0.503435\pi$
$263$	16.0413	−	16.0413i	0.989151	−	0.989151i	0.999942	+	0.0107906i	$0.00343481\pi$
$264$	−1.24355	−	1.21631i	−0.0765354	−	0.0748586i
$265$	−17.7798	−	11.8019i	−1.09221	−	0.724985i
$266$	−3.76272	−	3.73504i	−0.230707	−	0.229010i
$267$	1.85940	+	1.85940i	0.113794	+	0.113794i
$268$	10.2531	+	10.1028i	0.626308	+	0.617127i
$269$			6.96525i			0.424679i	0.977196	+	0.212339i	$0.0681083\pi$
$269$			6.96525i			0.424679i	−0.977196	+	0.212339i	$0.931892\pi$
$270$	4.69486	+	3.09145i	0.285720	+	0.188140i
$271$		−	7.23572i		−	0.439539i	−0.975552	−	0.219769i	$-0.929470\pi$
$271$		−	7.23572i		−	0.439539i	0.975552	−	0.219769i	$-0.0705305\pi$
$272$	−12.0672	+	12.4289i	−0.731680	+	0.753615i
$273$	0.255063	+	0.255063i	0.0154371	+	0.0154371i
$274$	4.45466	−	4.48767i	0.269116	−	0.271110i
$275$	−3.96952	−	9.42049i	−0.239371	−	0.568077i
$276$	0.0339601	+	4.59930i	0.00204416	+	0.276845i
$277$	−15.1164	+	15.1164i	−0.908254	+	0.908254i	−0.996131	−	0.0878773i	$-0.971992\pi$
$277$	−15.1164	+	15.1164i	−0.908254	+	0.908254i	0.0878773	+	0.996131i	$0.471992\pi$
$278$	24.0285	−	0.0887090i	1.44113	−	0.00532041i
$279$	−16.8429			−1.00836
$280$	−19.8983	−	12.8929i	−1.18915	−	0.770500i
$281$	10.0095			0.597118			0.298559	−	0.954391i	$-0.403494\pi$
$281$	10.0095			0.597118			0.298559	+	0.954391i	$0.403494\pi$
$282$	−0.746646	+	0.00275649i	−0.0444622	+	0.000164146i
$283$	−8.48356	+	8.48356i	−0.504295	+	0.504295i	−0.912770	−	0.408474i	$-0.866061\pi$
$283$	−8.48356	+	8.48356i	−0.504295	+	0.504295i	0.408474	+	0.912770i	$0.366061\pi$
$284$	0.0226445	+	3.06681i	0.00134371	+	0.181982i
$285$	0.371981	−	0.560397i	0.0220342	−	0.0331951i
$286$	−0.651568	+	0.656397i	−0.0385280	+	0.0388135i
$287$	−17.4369	−	17.4369i	−1.02927	−	1.02927i
$288$	0.303795	+	16.4559i	0.0179013	+	0.969674i
$289$		−	1.75596i		−	0.103292i
$290$	−4.15205	−	20.1627i	−0.243817	−	1.18399i
$291$			1.10767i			0.0649325i
$292$	−14.6739	−	14.4588i	−0.858727	−	0.846139i
$293$	10.3132	+	10.3132i	0.602501	+	0.602501i	0.940976	−	0.338475i	$-0.109911\pi$
$293$	10.3132	+	10.3132i	0.602501	+	0.602501i	−0.338475	+	0.940976i	$0.609911\pi$
$294$	2.12977	+	2.11411i	0.124211	+	0.123297i
$295$	−9.69876	+	1.95994i	−0.564684	+	0.114112i
$296$	−19.2145	+	19.6449i	−1.11682	+	1.14184i
$297$	2.56989	−	2.56989i	0.149120	−	0.149120i
$298$	0.0510362	+	13.8241i	0.00295645	+	0.800809i
$299$	2.44549			0.141426
$300$	1.11357	−	2.79433i	0.0642919	−	0.161330i
$301$	−19.7541			−1.13861
$302$	0.0220284	+	5.96680i	0.00126759	+	0.343351i
$303$	2.77598	−	2.77598i	0.159476	−	0.159476i
$304$	3.99956	−	0.0590668i	0.229391	−	0.00338771i
$305$	1.70454	−	0.344456i	0.0976015	−	0.0197235i
$306$	−12.6470	−	12.5540i	−0.722982	−	0.717663i
$307$	3.77726	+	3.77726i	0.215579	+	0.215579i	0.806633	−	0.591053i	$-0.201288\pi$
$307$	3.77726	+	3.77726i	0.215579	+	0.215579i	−0.591053	+	0.806633i	$0.701288\pi$
$308$	−10.7593	+	10.9193i	−0.613066	+	0.622187i
$309$		−	5.29270i		−	0.301091i
$310$	3.69226	+	17.9299i	0.209706	+	1.01835i
$311$		−	21.5006i		−	1.21919i	−0.792715	−	0.609593i	$-0.791333\pi$
$311$		−	21.5006i		−	1.21919i	0.792715	−	0.609593i	$-0.208667\pi$
$312$	−0.272130	+	0.00301408i	−0.0154063	+	0.000170639i
$313$	−12.1932	−	12.1932i	−0.689200	−	0.689200i	0.272855	−	0.962055i	$-0.412032\pi$
$313$	−12.1932	−	12.1932i	−0.689200	−	0.689200i	−0.962055	+	0.272855i	$0.912032\pi$
$314$	12.0568	−	12.1462i	0.680407	−	0.685449i
$315$	13.4885	−	20.3207i	0.759988	−	1.14494i
$316$	−33.0134	+	0.243762i	−1.85715	+	0.0137127i
$317$	0.231233	−	0.231233i	0.0129873	−	0.0129873i	−0.700583	−	0.713571i	$-0.747077\pi$
$317$	0.231233	−	0.231233i	0.0129873	−	0.0129873i	0.713571	+	0.700583i	$0.247077\pi$
$318$	−4.05985	+	0.0149883i	−0.227665	+	0.000840500i
$319$	−13.3095			−0.745188
$320$	17.4513	−	3.93082i	0.975559	−	0.219739i
$321$	−0.396283			−0.0221183
$322$	40.5328	−	0.149640i	2.25880	−	0.00833911i
$323$	−3.06235	+	3.06235i	−0.170394	+	0.170394i
$324$	−16.3872	+	0.120999i	−0.910402	+	0.00672218i
$325$	−1.48131	−	0.603031i	−0.0821685	−	0.0334501i
$326$	16.2363	−	16.3567i	0.899248	−	0.905912i
$327$	−4.30529	−	4.30529i	−0.238083	−	0.238083i
$328$	18.6037	−	0.206052i	1.02722	−	0.0113773i
$329$			6.57997i			0.362766i
$330$	−1.62429	−	1.06956i	−0.0894145	−	0.0588772i
$331$		−	22.4492i		−	1.23392i	−0.786994	−	0.616960i	$-0.788364\pi$
$331$		−	22.4492i		−	1.23392i	0.786994	−	0.616960i	$-0.211636\pi$
$332$	−8.53446	+	8.66143i	−0.468389	+	0.475358i
$333$	−19.9880	−	19.9880i	−1.09534	−	1.09534i
$334$	5.16772	+	5.12970i	0.282765	+	0.280685i
$335$	13.4082	+	8.90009i	0.732567	+	0.486264i
$336$	−4.51025	+	0.0666087i	−0.246054	+	0.00363380i
$337$	−4.72972	+	4.72972i	−0.257644	+	0.257644i	−0.824095	−	0.566451i	$-0.808316\pi$
$337$	−4.72972	+	4.72972i	−0.257644	+	0.257644i	0.566451	+	0.824095i	$0.308316\pi$
$338$	−0.0673387	−	18.2400i	−0.00366274	−	0.992123i
$339$	1.28057			0.0695512
$340$	−10.5917	+	16.2153i	−0.574417	+	0.879396i
$341$	11.8356			0.640935
$342$	0.0151906	+	4.11465i	0.000821412	+	0.222495i
$343$	0.143898	−	0.143898i	0.00776975	−	0.00776975i
$344$	10.4212	−	10.6547i	0.561875	−	0.574461i
$345$	1.01858	+	5.04042i	0.0548384	+	0.271367i
$346$	2.06545	+	2.05026i	0.111039	+	0.110223i
$347$	25.6539	+	25.6539i	1.37717	+	1.37717i	0.849363	+	0.527809i	$0.176986\pi$
$347$	25.6539	+	25.6539i	1.37717	+	1.37717i	0.527809	+	0.849363i	$0.323014\pi$
$348$	−2.78964	−	2.74875i	−0.149541	−	0.147348i
$349$			10.9773i			0.587600i	0.955867	+	0.293800i	$0.0949199\pi$
$349$			10.9773i			0.587600i	−0.955867	+	0.293800i	$0.905080\pi$
$350$	−24.5890	−	9.90432i	−1.31434	−	0.529408i
$351$		−	0.568604i		−	0.0303499i
$352$	−0.213478	−	11.5636i	−0.0113784	−	0.616345i
$353$	20.5889	+	20.5889i	1.09584	+	1.09584i	0.994892	+	0.100947i	$0.0321874\pi$
$353$	20.5889	+	20.5889i	1.09584	+	1.09584i	0.100947	+	0.994892i	$0.467813\pi$
$354$	−1.32616	+	1.33599i	−0.0704847	+	0.0710071i
$355$	0.679187	+	3.36095i	0.0360475	+	0.178381i
$356$	0.129092	+	17.4833i	0.00684188	+	0.926613i
$357$	3.45336	−	3.45336i	0.182771	−	0.182771i
$358$	3.10693	−	0.0114702i	0.164207	−	0.000606221i
$359$	−21.8842			−1.15500			−0.577502	−	0.816390i	$-0.695972\pi$
$359$	−21.8842			−1.15500			−0.577502	+	0.816390i	$0.695972\pi$
$360$	3.84445	+	17.9953i	0.202620	+	0.948437i
$361$	1.00000			0.0526316
$362$	−6.33948	+	0.0234042i	−0.333196	+	0.00123010i
$363$	1.45059	−	1.45059i	0.0761364	−	0.0761364i
$364$	0.0177082	+	2.39827i	0.000928162	+	0.125703i
$365$	−19.1894	−	12.7375i	−1.00442	−	0.666714i
$366$	0.233070	−	0.234798i	0.0121828	−	0.0122731i
$367$	−26.0801	−	26.0801i	−1.36137	−	1.36137i	−0.872175	−	0.489195i	$-0.837291\pi$
$367$	−26.0801	−	26.0801i	−1.36137	−	1.36137i	−0.489195	−	0.872175i	$-0.662709\pi$
$368$	−21.3023	+	21.9409i	−1.11046	+	1.14375i
$369$			19.1382i			0.996294i
$370$	−16.8962	+	25.6597i	−0.878394	+	1.33398i
$371$			35.7783i			1.85752i
$372$	2.48072	+	2.44436i	0.128620	+	0.126734i
$373$	−4.43315	−	4.43315i	−0.229540	−	0.229540i	0.582961	−	0.812500i	$-0.301894\pi$
$373$	−4.43315	−	4.43315i	−0.229540	−	0.229540i	−0.812500	+	0.582961i	$0.801894\pi$
$374$	8.88712	+	8.82174i	0.459542	+	0.456161i
$375$	0.625929	−	3.30433i	0.0323228	−	0.170635i
$376$	−3.54901	−	3.47125i	−0.183026	−	0.179016i
$377$	−1.47240	+	1.47240i	−0.0758327	+	0.0758327i
$378$	−0.0347931	−	9.42436i	−0.00178956	−	0.484737i
$379$	−25.3291			−1.30107			−0.650534	−	0.759477i	$-0.725455\pi$
$379$	−25.3291			−1.30107			−0.650534	+	0.759477i	$0.725455\pi$
$380$	4.37687	−	0.918173i	0.224529	−	0.0471013i
$381$	−2.61318			−0.133877
$382$	−0.0332075	−	8.99486i	−0.00169904	−	0.460217i
$383$	−22.1823	+	22.1823i	−1.13346	+	1.13346i	−0.143867	+	0.989597i	$0.545954\pi$
$383$	−22.1823	+	22.1823i	−1.13346	+	1.13346i	−0.989597	+	0.143867i	$0.954046\pi$
$384$	2.34345	−	2.46781i	0.119588	−	0.125935i
$385$	−9.47841	+	14.2794i	−0.483064	+	0.727747i
$386$	−19.3010	−	19.1590i	−0.982393	−	0.975166i
$387$	10.8407	+	10.8407i	0.551066	+	0.551066i
$388$	−5.16904	+	5.24594i	−0.262418	+	0.266322i
$389$		−	26.6415i		−	1.35078i	−0.737462	−	0.675388i	$-0.763976\pi$
$389$		−	26.6415i		−	1.35078i	0.737462	−	0.675388i	$-0.236024\pi$
$390$	−0.298016	+	0.0613696i	−0.0150906	+	0.00310757i
$391$		−	33.1100i		−	1.67445i
$392$	0.220978	+	19.9513i	0.0111611	+	1.00769i
$393$	1.76545	+	1.76545i	0.0890552	+	0.0890552i
$394$	10.2608	−	10.3368i	0.516932	−	0.520763i
$395$	−36.1797	+	7.31126i	−1.82040	+	0.367870i
$396$	11.8969	−	0.0878435i	0.597841	−	0.00441430i
$397$	−20.3538	+	20.3538i	−1.02153	+	1.02153i	−0.0217671	+	0.999763i	$0.506929\pi$
$397$	−20.3538	+	20.3538i	−1.02153	+	1.02153i	−0.999763	+	0.0217671i	$0.993071\pi$
$398$	29.8562	−	0.110224i	1.49656	−	0.00552503i
$399$	−1.12768			−0.0564548
$400$	18.3139	−	8.03744i	0.915696	−	0.401872i
$401$	−22.5998			−1.12858			−0.564289	−	0.825577i	$-0.690850\pi$
$401$	−22.5998			−1.12858			−0.564289	+	0.825577i	$0.690850\pi$
$402$	3.06163	−	0.0113030i	0.152700	−	0.000563742i
$403$	1.30935	−	1.30935i	0.0652236	−	0.0652236i
$404$	26.1016	−	0.192727i	1.29860	−	0.00958854i
$405$	−17.9590	+	3.62918i	−0.892388	+	0.180335i
$406$	−24.3143	+	24.4945i	−1.20670	+	1.21564i
$407$	14.0457	+	14.0457i	0.696217	+	0.696217i
$408$	0.0408084	+	3.68444i	0.00202032	+	0.182407i
$409$			3.50326i			0.173225i	0.996242	+	0.0866126i	$0.0276042\pi$
$409$			3.50326i			0.173225i	−0.996242	+	0.0866126i	$0.972396\pi$
$410$	20.3733	−	4.19542i	1.00617	−	0.207197i
$411$		−	1.34495i		−	0.0663416i
$412$	24.6990	−	25.0664i	1.21683	−	1.23493i
$413$	11.7304	+	11.7304i	0.577214	+	0.577214i
$414$	−22.3259	−	22.1616i	−1.09726	−	1.08918i
$415$	−7.51846	+	11.3267i	−0.369066	+	0.556007i
$416$	−1.30288	−	1.25565i	−0.0638791	−	0.0615633i
$417$	3.61396	−	3.61396i	0.176976	−	0.176976i
$418$	−0.0106745	−	2.89139i	−0.000522106	−	0.141422i
$419$	−12.6029			−0.615691			−0.307846	−	0.951436i	$-0.599608\pi$
$419$	−12.6029			−0.615691			−0.307846	+	0.951436i	$0.599608\pi$
$420$	−4.93573	+	1.03541i	−0.240839	+	0.0505228i
$421$	−38.3993			−1.87147			−0.935735	−	0.352704i	$-0.885262\pi$
$421$	−38.3993			−1.87147			−0.935735	+	0.352704i	$0.885262\pi$
$422$	0.0702346	+	19.0244i	0.00341897	+	0.926092i
$423$	3.61098	−	3.61098i	0.175572	−	0.175572i
$424$	−19.2975	−	18.8748i	−0.937172	−	0.916639i
$425$	−8.16459	+	20.0559i	−0.396041	+	0.972853i
$426$	0.462966	+	0.459560i	0.0224308	+	0.0222658i
$427$	−2.06159	−	2.06159i	−0.0997673	−	0.0997673i
$428$	−1.87681	−	1.84930i	−0.0907190	−	0.0893891i
$429$			0.196722i			0.00949781i
$430$	9.16389	−	13.9168i	0.441922	−	0.671130i
$431$			22.0058i			1.05998i	0.848003	+	0.529992i	$0.177805\pi$
$431$			22.0058i			1.05998i	−0.848003	+	0.529992i	$0.822195\pi$
$432$	5.10152	+	4.95303i	0.245447	+	0.238303i
$433$	24.6830	+	24.6830i	1.18619	+	1.18619i	0.978112	+	0.208077i	$0.0667205\pi$
$433$	24.6830	+	24.6830i	1.18619	+	1.18619i	0.208077	+	0.978112i	$0.433279\pi$
$434$	21.6218	−	21.7821i	1.03788	−	1.04557i
$435$	−3.64807	−	2.42152i	−0.174912	−	0.116103i
$436$	−0.298902	−	40.4811i	−0.0143148	−	1.93869i
$437$	−5.40599	+	5.40599i	−0.258604	+	0.258604i
$438$	−4.38171	+	0.0161765i	−0.209366	+	0.000772944i
$439$	14.9623			0.714113			0.357056	−	0.934083i	$-0.383780\pi$
$439$	14.9623			0.714113			0.357056	+	0.934083i	$0.383780\pi$
$440$	−2.70151	−	12.6454i	−0.128790	−	0.602846i
$441$	−20.5246			−0.977360
$442$	1.95910	−	0.00723265i	0.0931849	−	0.000344022i
$443$	−4.16446	+	4.16446i	−0.197859	+	0.197859i	−0.799082	−	0.601222i	$-0.794681\pi$
$443$	−4.16446	+	4.16446i	−0.197859	+	0.197859i	0.601222	+	0.799082i	$0.294681\pi$
$444$	0.0431560	+	5.84473i	0.00204809	+	0.277379i
$445$	3.87192	+	19.1602i	0.183547	+	0.908279i
$446$	−2.66135	+	2.68107i	−0.126019	+	0.126953i
$447$	2.07919	+	2.07919i	0.0983422	+	0.0983422i
$448$	−21.6715	−	20.7321i	−1.02388	−	0.979499i
$449$		−	4.32706i		−	0.204207i	−0.994774	−	0.102103i	$-0.967443\pi$
$449$		−	4.32706i		−	0.204207i	0.994774	−	0.102103i	$-0.0325572\pi$
$450$	8.05872	+	18.9294i	0.379892	+	0.892340i
$451$		−	13.4485i		−	0.633265i
$452$	6.06484	+	5.97593i	0.285266	+	0.281084i
$453$	0.897424	+	0.897424i	0.0421646	+	0.0421646i
$454$	−2.07871	−	2.06342i	−0.0975589	−	0.0968412i
$455$	0.531129	+	2.62829i	0.0248997	+	0.123216i
$456$	0.594908	−	0.608234i	0.0278591	−	0.0284831i
$457$	11.1732	−	11.1732i	0.522659	−	0.522659i	−0.395714	−	0.918374i	$-0.629503\pi$
$457$	11.1732	−	11.1732i	0.522659	−	0.522659i	0.918374	+	0.395714i	$0.129503\pi$
$458$	−0.0161263	−	4.36810i	−0.000753530	−	0.204108i
$459$	−7.69848			−0.359334
$460$	−18.6977	+	28.6249i	−0.871783	+	1.33464i
$461$	−28.2155			−1.31413			−0.657064	−	0.753835i	$-0.728202\pi$
$461$	−28.2155			−1.31413			−0.657064	+	0.753835i	$0.728202\pi$
$462$	0.0120375	+	3.26057i	0.000560033	+	0.151695i
$463$	23.1500	−	23.1500i	1.07587	−	1.07587i	0.0789948	−	0.996875i	$-0.474829\pi$
$463$	23.1500	−	23.1500i	1.07587	−	1.07587i	0.996875	−	0.0789948i	$-0.0251710\pi$
$464$	−0.384512	−	26.0363i	−0.0178505	−	1.20871i
$465$	3.24409	+	2.15336i	0.150441	+	0.0998599i
$466$	0.390840	+	0.387964i	0.0181053	+	0.0179721i
$467$	12.5001	+	12.5001i	0.578435	+	0.578435i	0.934472	−	0.356037i	$-0.115872\pi$
$467$	12.5001	+	12.5001i	0.578435	+	0.578435i	−0.356037	+	0.934472i	$0.615872\pi$
$468$	1.30641	−	1.32585i	0.0603889	−	0.0612874i
$469$		−	26.9812i		−	1.24588i
$470$	−4.63561	−	3.05244i	−0.213825	−	0.140798i
$471$		−	3.64021i		−	0.167732i
$472$	−12.5153	+	0.138618i	−0.576063	+	0.00638040i
$473$	−7.61784	−	7.61784i	−0.350269	−	0.350269i
$474$	−4.94704	+	4.98370i	−0.227225	+	0.228909i
$475$	4.60765	−	1.94153i	0.211414	−	0.0890836i
$476$	32.4707	−	0.239756i	1.48829	−	0.0109892i
$477$	19.6345	−	19.6345i	0.899004	−	0.899004i
$478$	3.61044	−	0.0133291i	0.165137	−	0.000609658i
$479$	−18.1663			−0.830040			−0.415020	−	0.909812i	$-0.636225\pi$
$479$	−18.1663			−0.830040			−0.415020	+	0.909812i	$0.636225\pi$
$480$	2.04537	−	3.20839i	0.0933579	−	0.146442i
$481$	3.10769			0.141699
$482$	−15.3709	+	0.0567465i	−0.700123	+	0.00258473i
$483$	6.09625	−	6.09625i	0.277389	−	0.277389i
$484$	13.6394	−	0.100710i	0.619973	−	0.00457772i
$485$	−4.55368	+	6.86022i	−0.206772	+	0.311506i
$486$	−7.76871	+	7.82629i	−0.352396	+	0.355008i
$487$	−23.4493	−	23.4493i	−1.06259	−	1.06259i	−0.997906	−	0.0646845i	$-0.979396\pi$
$487$	−23.4493	−	23.4493i	−1.06259	−	1.06259i	−0.0646845	−	0.997906i	$-0.520604\pi$
$488$	2.19954	−	0.0243618i	0.0995684	−	0.00110281i
$489$		−	4.90209i		−	0.221680i
$490$	4.49933	+	21.8491i	0.203259	+	0.987044i
$491$		−	1.07295i		−	0.0484217i	−0.999707	−	0.0242108i	$-0.992293\pi$
$491$		−	1.07295i		−	0.0484217i	0.999707	−	0.0242108i	$-0.00770731\pi$
$492$	2.77746	−	2.81878i	0.125218	−	0.127080i
$493$	19.9353	+	19.9353i	0.897839	+	0.897839i
$494$	−0.321050	−	0.318688i	−0.0144447	−	0.0143384i
$495$	13.0379	−	2.63473i	0.586011	−	0.118422i
$496$	0.341932	+	23.1531i	0.0153532	+	1.03961i
$497$	4.06497	−	4.06497i	0.182339	−	0.182339i
$498$	0.00954834	+	2.58635i	0.000427871	+	0.115897i
$499$	−17.3943			−0.778674			−0.389337	−	0.921095i	$-0.627296\pi$
$499$	−17.3943			−0.778674			−0.389337	+	0.921095i	$0.627296\pi$
$500$	18.3844	−	12.7284i	0.822176	−	0.569233i
$501$	1.54876			0.0691936
$502$	0.114525	+	31.0213i	0.00511151	+	1.38455i
$503$	20.5398	−	20.5398i	0.915826	−	0.915826i	−0.0808962	−	0.996723i	$-0.525778\pi$
$503$	20.5398	−	20.5398i	0.915826	−	0.915826i	0.996723	+	0.0808962i	$0.0257782\pi$
$504$	21.5721	−	22.0553i	0.960896	−	0.982420i
$505$	28.6050	−	5.78055i	1.27291	−	0.257231i
$506$	15.6885	+	15.5731i	0.697439	+	0.692308i
$507$	−2.74334	−	2.74334i	−0.121836	−	0.121836i
$508$	−12.3761	−	12.1947i	−0.549101	−	0.541051i
$509$			31.2945i			1.38710i	0.720406	+	0.693552i	$0.243955\pi$
$509$			31.2945i			1.38710i	−0.720406	+	0.693552i	$0.756045\pi$
$510$	0.830899	+	4.03492i	0.0367928	+	0.178669i
$511$			38.6147i			1.70822i
$512$	22.6149	−	0.751686i	0.999448	−	0.0332201i
$513$	1.25696	+	1.25696i	0.0554960	+	0.0554960i
$514$	−12.5383	+	12.6313i	−0.553043	+	0.557141i
$515$	21.7586	−	32.7798i	0.958799	−	1.44445i
$516$	−0.0234062	−	3.16996i	−0.00103040	−	0.139550i
$517$	−2.53746	+	2.53746i	−0.111597	+	0.111597i
$518$	51.5086	−	0.190161i	2.26316	−	0.00835518i
$519$	0.619015			0.0271717
$520$	−1.69780	−	1.10008i	−0.0744536	−	0.0482415i
$521$	17.9538			0.786572			0.393286	−	0.919416i	$-0.371338\pi$
$521$	17.9538			0.786572			0.393286	+	0.919416i	$0.371338\pi$
$522$	26.7855	−	0.0988874i	1.17237	−	0.00432818i
$523$	−5.14238	+	5.14238i	−0.224861	+	0.224861i	−0.810542	−	0.585681i	$-0.800827\pi$
$523$	−5.14238	+	5.14238i	−0.224861	+	0.224861i	0.585681	+	0.810542i	$0.300827\pi$
$524$	0.122569	+	16.5999i	0.00535447	+	0.725170i
$525$	−5.19598	+	2.18944i	−0.226771	+	0.0955548i
$526$	22.6020	−	22.7695i	0.985493	−	0.992796i
$527$	−17.7277	−	17.7277i	−0.772230	−	0.772230i
$528$	−1.76499	−	1.71362i	−0.0768112	−	0.0745755i
$529$		−	35.4494i		−	1.54128i
$530$	−25.2059	−	16.5975i	−1.09488	−	0.720948i
$531$		−	12.8749i		−	0.558723i
$532$	−5.34075	−	5.26246i	−0.231551	−	0.228157i
$533$	−1.48778	−	1.48778i	−0.0644431	−	0.0644431i
$534$	2.63928	+	2.61987i	0.114213	+	0.113373i
$535$	−2.45434	−	1.62914i	−0.106110	−	0.0704339i
$536$	14.5527	+	14.2339i	0.628582	+	0.614810i
$537$	0.467292	−	0.467292i	0.0201651	−	0.0201651i
$538$	0.0363655	+	9.85029i	0.00156783	+	0.424676i
$539$	14.4227			0.621230
$540$	6.65563	+	4.34743i	0.286413	+	0.187084i
$541$	19.3237			0.830792			0.415396	−	0.909641i	$-0.363643\pi$
$541$	19.3237			0.830792			0.415396	+	0.909641i	$0.363643\pi$
$542$	−0.0377776	−	10.2328i	−0.00162269	−	0.439536i
$543$	−0.953477	+	0.953477i	−0.0409176	+	0.0409176i
$544$	−17.0006	+	17.6401i	−0.728893	+	0.756311i
$545$	−8.96509	−	44.3637i	−0.384022	−	1.90033i
$546$	0.362043	+	0.359380i	0.0154940	+	0.0153800i
$547$	−18.3764	−	18.3764i	−0.785719	−	0.785719i	0.195071	−	0.980789i	$-0.437506\pi$
$547$	−18.3764	−	18.3764i	−0.785719	−	0.785719i	−0.980789	+	0.195071i	$0.937506\pi$
$548$	6.27636	−	6.36974i	0.268113	−	0.272102i
$549$			2.26274i			0.0965712i
$550$	−5.66290	−	13.3018i	−0.241467	−	0.567189i
$551$		−	6.50979i		−	0.277326i
$552$	0.0720394	+	6.50417i	0.00306620	+	0.276836i
$553$	43.7583	+	43.7583i	1.86079	+	1.86079i
$554$	−21.2987	+	21.4565i	−0.904895	+	0.911601i
$555$	1.29440	+	6.40531i	0.0549441	+	0.271890i
$556$	33.9808	−	0.250905i	1.44110	−	0.0106408i
$557$	22.1345	−	22.1345i	0.937870	−	0.937870i	−0.0603095	−	0.998180i	$-0.519209\pi$
$557$	22.1345	−	22.1345i	0.937870	−	0.937870i	0.998180	+	0.0603095i	$0.0192088\pi$
$558$	−23.8194	+	0.0879369i	−1.00835	+	0.00372266i
$559$	−1.68550			−0.0712889
$560$	−28.2076	−	18.1294i	−1.19199	−	0.766105i
$561$	2.66346			0.112452
$562$	14.1555	−	0.0522597i	0.597114	−	0.00220444i
$563$	4.11064	−	4.11064i	0.173243	−	0.173243i	−0.615160	−	0.788403i	$-0.710908\pi$
$563$	4.11064	−	4.11064i	0.173243	−	0.173243i	0.788403	+	0.615160i	$0.210908\pi$
$564$	−1.05590	+	0.00779647i	−0.0444612	+	0.000328291i
$565$	7.93111	+	5.26451i	0.333664	+	0.221480i
$566$	−11.9532	+	12.0418i	−0.502430	+	0.506154i
$567$	21.7209	+	21.7209i	0.912190	+	0.912190i
$568$	0.0480358	+	4.33697i	0.00201554	+	0.181975i
$569$		−	21.3698i		−	0.895869i	−0.894066	−	0.447934i	$-0.852160\pi$
$569$		−	21.3698i		−	0.895869i	0.894066	−	0.447934i	$-0.147840\pi$
$570$	0.523131	−	0.794458i	0.0219115	−	0.0332762i
$571$		−	17.7556i		−	0.743049i	−0.928423	−	0.371524i	$-0.878835\pi$
$571$		−	17.7556i		−	0.743049i	0.928423	−	0.371524i	$-0.121165\pi$
$572$	−0.918023	+	0.931680i	−0.0383845	+	0.0389555i
$573$	−1.35285	−	1.35285i	−0.0565163	−	0.0565163i
$574$	−24.7504	−	24.5683i	−1.03306	−	1.02546i
$575$	−14.4130	+	35.4048i	−0.601064	+	1.47648i
$576$	0.515544	+	23.2704i	0.0214810	+	0.969601i
$577$	15.8282	−	15.8282i	0.658936	−	0.658936i	−0.296193	−	0.955128i	$-0.595717\pi$
$577$	15.8282	−	15.8282i	0.658936	−	0.658936i	0.955128	+	0.296193i	$0.0957170\pi$
$578$	−0.00916785	−	2.48329i	−0.000381332	−	0.103291i
$579$	−5.78449			−0.240395
$580$	−5.97711	−	28.4925i	−0.248186	−	1.18309i
$581$	22.7927			0.945601
$582$	0.00578311	+	1.56646i	0.000239718	+	0.0649320i
$583$	−13.7973	+	13.7973i	−0.571425	+	0.571425i
$584$	−20.8274	−	20.3711i	−0.861845	−	0.842963i
$585$	1.15089	−	1.73384i	0.0475833	−	0.0716854i
$586$	14.6387	+	14.5311i	0.604721	+	0.600272i
$587$	5.07211	+	5.07211i	0.209348	+	0.209348i	0.803991	−	0.594642i	$-0.202706\pi$
$587$	5.07211	+	5.07211i	0.209348	+	0.209348i	−0.594642	+	0.803991i	$0.702706\pi$
$588$	3.02297	+	2.97866i	0.124665	+	0.122838i
$589$			5.78891i			0.238528i
$590$	−13.7058	+	2.82240i	−0.564259	+	0.116196i
$591$		−	3.09795i		−	0.127433i
$592$	−27.0707	+	27.8822i	−1.11260	+	1.14595i
$593$	14.6665	+	14.6665i	0.602280	+	0.602280i	0.940917	−	0.338637i	$-0.109966\pi$
$593$	14.6665	+	14.6665i	0.602280	+	0.602280i	−0.338637	+	0.940917i	$0.609966\pi$
$594$	3.62093	−	3.64776i	0.148569	−	0.149670i
$595$	35.5851	−	7.19109i	1.45884	−	0.294806i
$596$	0.144351	+	19.5498i	0.00591285	+	0.800793i
$597$	4.49047	−	4.49047i	0.183783	−	0.183783i
$598$	3.45842	−	0.0127679i	0.141425	−	0.000522117i
$599$	−10.7934			−0.441005			−0.220502	−	0.975386i	$-0.570770\pi$
$599$	−10.7934			−0.441005			−0.220502	+	0.975386i	$0.570770\pi$
$600$	1.56022	−	3.95756i	0.0636959	−	0.161567i
$601$	−8.15596			−0.332688			−0.166344	−	0.986068i	$-0.553196\pi$
$601$	−8.15596			−0.332688			−0.166344	+	0.986068i	$0.553196\pi$
$602$	−27.9363	+	0.103136i	−1.13860	+	0.00420351i
$603$	−14.8069	+	14.8069i	−0.602982	+	0.602982i
$604$	0.0623052	+	8.43815i	0.00253516	+	0.343344i
$605$	14.9476	−	3.02063i	0.607706	−	0.122806i
$606$	3.91131	−	3.94030i	0.158886	−	0.160064i
$607$	33.9049	+	33.9049i	1.37616	+	1.37616i	0.851011	+	0.525148i	$0.175990\pi$
$607$	33.9049	+	33.9049i	1.37616	+	1.37616i	0.525148	+	0.851011i	$0.324010\pi$
$608$	5.65589	−	0.104414i	0.229377	−	0.00423455i
$609$			7.34099i			0.297472i
$610$	2.40877	−	0.496030i	0.0975280	−	0.0200837i
$611$			0.561429i			0.0227130i
$612$	−17.9510	−	17.6879i	−0.725626	−	0.714989i
$613$	−8.50562	−	8.50562i	−0.343539	−	0.343539i	0.514157	−	0.857696i	$-0.328105\pi$
$613$	−8.50562	−	8.50562i	−0.343539	−	0.343539i	−0.857696	+	0.514157i	$0.828105\pi$
$614$	5.36153	+	5.32209i	0.216374	+	0.214782i
$615$	2.44681	−	3.68617i	0.0986649	−	0.148641i
$616$	−15.1588	+	15.4983i	−0.610765	+	0.624446i
$617$	−22.6320	+	22.6320i	−0.911129	+	0.911129i	−0.996361	−	0.0852322i	$-0.972837\pi$
$617$	−22.6320	+	22.6320i	−0.911129	+	0.911129i	0.0852322	+	0.996361i	$0.472837\pi$
$618$	−0.0276331	−	7.48496i	−0.00111157	−	0.301089i
$619$	14.5559			0.585051			0.292525	−	0.956258i	$-0.405504\pi$
$619$	14.5559			0.585051			0.292525	+	0.956258i	$0.405504\pi$
$620$	5.31522	+	25.3373i	0.213464	+	1.01757i
$621$	−13.5902			−0.545355
$622$	−0.112254	−	30.4062i	−0.00450099	−	1.21918i
$623$	23.1737	−	23.1737i	0.928433	−	0.928433i
$624$	−0.384832	+	0.00568331i	−0.0154056	+	0.000227515i
$625$	17.4609	−	17.8918i	0.698436	−	0.715672i
$626$	−17.3073	−	17.1800i	−0.691740	−	0.686651i
$627$	−0.434873	−	0.434873i	−0.0173671	−	0.0173671i
$628$	16.9874	−	17.2401i	0.677872	−	0.687956i
$629$		−	42.0758i		−	1.67767i
$630$	18.9693	−	28.8080i	0.755756	−	1.14774i
$631$			29.4769i			1.17346i	0.809784	+	0.586728i	$0.199584\pi$
$631$			29.4769i			1.17346i	−0.809784	+	0.586728i	$0.800416\pi$
$632$	−46.6864	+	0.517092i	−1.85708	+	0.0205688i
$633$	2.86132	+	2.86132i	0.113727	+	0.113727i
$634$	0.325803	−	0.328218i	0.0129393	−	0.0130352i
$635$	−16.1845	−	10.7429i	−0.642261	−	0.426320i
$636$	−5.74138	+	0.0423929i	−0.227661	+	0.00168099i
$637$	1.59556	−	1.59556i	0.0632183	−	0.0632183i
$638$	−18.8223	+	0.0694887i	−0.745183	+	0.00275108i
$639$	−4.46159			−0.176498
$640$	24.6592	−	5.65009i	0.974741	−	0.223339i
$641$	12.2729			0.484749			0.242374	−	0.970183i	$-0.422074\pi$
$641$	12.2729			0.484749			0.242374	+	0.970183i	$0.422074\pi$
$642$	−0.560425	+	0.00206899i	−0.0221182	+	8.16565e-5i
$643$	8.55592	−	8.55592i	0.337413	−	0.337413i	−0.517980	−	0.855393i	$-0.673316\pi$
$643$	8.55592	−	8.55592i	0.337413	−	0.337413i	0.855393	+	0.517980i	$0.173316\pi$
$644$	57.3209	−	0.423243i	2.25876	−	0.0166781i
$645$	−0.702032	−	3.47400i	−0.0276425	−	0.136789i
$646$	−4.31480	+	4.34677i	−0.169763	+	0.171022i
$647$	27.5524	+	27.5524i	1.08320	+	1.08320i	0.996209	+	0.0869883i	$0.0277243\pi$
$647$	27.5524	+	27.5524i	1.08320	+	1.08320i	0.0869883	+	0.996209i	$0.472276\pi$
$648$	−23.1743	+	0.256675i	−0.910371	+	0.0100832i
$649$			9.04725i			0.355136i
$650$	−2.09803	−	0.845075i	−0.0822914	−	0.0331466i
$651$		−	6.52807i		−	0.255855i
$652$	22.8761	−	23.2164i	0.895898	−	0.909226i
$653$	9.19195	+	9.19195i	0.359709	+	0.359709i	0.863706	−	0.503997i	$-0.168138\pi$
$653$	9.19195	+	9.19195i	0.359709	+	0.359709i	−0.503997	+	0.863706i	$0.668138\pi$
$654$	−6.11103	−	6.06608i	−0.238960	−	0.237202i
$655$	3.67628	+	18.1920i	0.143644	+	0.710821i
$656$	26.3083	−	0.388529i	1.02717	−	0.0151695i
$657$	21.1912	−	21.1912i	0.826746	−	0.826746i
$658$	0.0343540	+	9.30542i	0.00133926	+	0.362763i
$659$	1.02222			0.0398199			0.0199099	−	0.999802i	$-0.493662\pi$
$659$	1.02222			0.0398199			0.0199099	+	0.999802i	$0.493662\pi$
$660$	−2.30267	−	1.50409i	−0.0896312	−	0.0585467i
$661$	−8.72455			−0.339346			−0.169673	−	0.985500i	$-0.554271\pi$
$661$	−8.72455			−0.339346			−0.169673	+	0.985500i	$0.554271\pi$
$662$	−0.117207	−	31.7478i	−0.00455539	−	1.23391i
$663$	0.294654	−	0.294654i	0.0114434	−	0.0114434i
$664$	−12.0242	+	12.2936i	−0.466631	+	0.477084i
$665$	−6.98421	−	4.63598i	−0.270836	−	0.179776i
$666$	−28.3715	−	28.1627i	−1.09937	−	1.09128i
$667$	35.1919	+	35.1919i	1.36263	+	1.36263i
$668$	7.33499	+	7.22746i	0.283799	+	0.279639i
$669$			0.803516i			0.0310657i
$670$	19.0084	+	12.5165i	0.734358	+	0.483556i
$671$		−	1.59004i		−	0.0613826i
$672$	−6.37806	+	0.117746i	−0.246039	+	0.00454216i
$673$	−15.8449	−	15.8449i	−0.610777	−	0.610777i	0.332372	−	0.943148i	$-0.392151\pi$
$673$	−15.8449	−	15.8449i	−0.610777	−	0.610777i	−0.943148	+	0.332372i	$0.892151\pi$
$674$	−6.66409	+	6.71348i	−0.256691	+	0.258594i
$675$	8.23204	+	3.35120i	0.316851	+	0.128988i
$676$	−0.190461	−	25.7947i	−0.00732543	−	0.992102i
$677$	−19.7428	+	19.7428i	−0.758777	+	0.758777i	−0.976100	−	0.217323i	$-0.930268\pi$
$677$	−19.7428	+	19.7428i	−0.758777	+	0.758777i	0.217323	+	0.976100i	$0.430268\pi$
$678$	1.81099	−	0.00668587i	0.0695507	−	0.000256769i
$679$	13.8048			0.529779
$680$	−14.8942	+	22.9870i	−0.571167	+	0.881510i
$681$	−0.622990			−0.0238730
$682$	16.7380	−	0.0617937i	0.640930	−	0.00236620i
$683$	−25.7242	+	25.7242i	−0.984311	+	0.984311i	−0.999879	−	0.0155682i	$-0.995044\pi$
$683$	−25.7242	+	25.7242i	−0.984311	+	0.984311i	0.0155682	+	0.999879i	$0.495044\pi$
$684$	0.0429651	+	5.81888i	0.00164281	+	0.222490i
$685$	5.52918	−	8.32983i	0.211259	−	0.318266i
$686$	0.202749	−	0.204252i	0.00774101	−	0.00779838i
$687$	−0.656975	−	0.656975i	−0.0250652	−	0.0250652i
$688$	14.6821	−	15.1223i	0.559751	−	0.576532i
$689$			3.05274i			0.116300i
$690$	1.46679	+	7.12287i	0.0558399	+	0.271163i
$691$		−	28.0903i		−	1.06861i	−0.845293	−	0.534303i	$-0.820574\pi$
$691$		−	28.0903i		−	1.06861i	0.845293	−	0.534303i	$-0.179426\pi$
$692$	2.93167	+	2.88870i	0.111446	+	0.109812i
$693$	−15.7690	−	15.7690i	−0.599015	−	0.599015i
$694$	36.4137	+	36.1459i	1.38225	+	1.37208i
$695$	37.2399	−	7.52550i	1.41259	−	0.285459i
$696$	−3.95947	−	3.87273i	−0.150083	−	0.146795i
$697$	−20.1435	+	20.1435i	−0.762989	+	0.762989i
$698$	0.0573122	+	15.5241i	0.00216930	+	0.587596i
$699$	0.117134			0.00443043
$700$	−34.8256	−	13.8783i	−1.31628	−	0.524552i
$701$	17.5957			0.664579			0.332289	−	0.943177i	$-0.392179\pi$
$701$	17.5957			0.664579			0.332289	+	0.943177i	$0.392179\pi$
$702$	−0.00296868	−	0.804123i	−0.000112046	−	0.0303497i
$703$	−6.86987	+	6.86987i	−0.259102	+	0.259102i
$704$	−0.362275	−	16.3522i	−0.0136538	−	0.616298i
$705$	−1.15717	+	0.233843i	−0.0435815	+	0.00880702i
$706$	29.2245	+	29.0095i	1.09988	+	1.09179i
$707$	−34.5969	−	34.5969i	−1.30115	−	1.30115i
$708$	−1.86849	+	1.89629i	−0.0702221	+	0.0712668i
$709$			40.9442i			1.53769i	0.639434	+	0.768846i	$0.279169\pi$
$709$			40.9442i			1.53769i	−0.639434	+	0.768846i	$0.720831\pi$
$710$	0.978056	+	4.74952i	0.0367058	+	0.178246i
$711$		−	48.0278i		−	1.80118i
$712$	0.273843	+	24.7243i	0.0102627	+	0.926582i
$713$	−31.2948	−	31.2948i	−1.17200	−	1.17200i
$714$	4.86573	−	4.90179i	0.182095	−	0.183445i
$715$	−0.808734	+	1.21838i	−0.0302449	+	0.0455647i
$716$	4.39378	−	0.0324425i	0.164203	−	0.00121243i
$717$	0.543020	−	0.543020i	0.0202795	−	0.0202795i
$718$	−30.9487	+	0.114257i	−1.15500	+	0.00426404i
$719$	−18.4285			−0.687266			−0.343633	−	0.939104i	$-0.611658\pi$
$719$	−18.4285			−0.687266			−0.343633	+	0.939104i	$0.611658\pi$
$720$	5.53078	+	25.4290i	0.206120	+	0.947683i
$721$	−65.9627			−2.45658
$722$	1.41420	−	0.00522099i	0.0526312	−	0.000194305i
$723$	−2.31182	+	2.31182i	−0.0859775	+	0.0859775i
$724$	−8.96520	+	0.0661968i	−0.333189	+	0.00246018i
$725$	−12.6390	−	29.9949i	−0.469399	−	1.11398i
$726$	2.04386	−	2.05901i	0.0758548	−	0.0764170i
$727$	−14.2988	−	14.2988i	−0.530314	−	0.530314i	0.390352	−	0.920666i	$-0.372353\pi$
$727$	−14.2988	−	14.2988i	−0.530314	−	0.530314i	−0.920666	+	0.390352i	$0.872353\pi$
$728$	0.0375643	+	3.39155i	0.00139223	+	0.125699i
$729$		−	22.2360i		−	0.823555i
$730$	−27.2042	−	17.9133i	−1.00687	−	0.663001i
$731$			22.8204i			0.844042i
$732$	0.328383	−	0.333269i	0.0121374	−	0.0123180i
$733$	2.66770	+	2.66770i	0.0985337	+	0.0985337i	0.754655	−	0.656122i	$-0.227804\pi$
$733$	2.66770	+	2.66770i	0.0985337	+	0.0985337i	−0.656122	+	0.754655i	$0.727804\pi$
$734$	−37.0187	−	36.7464i	−1.36639	−	1.35633i
$735$	3.95320	+	2.62406i	0.145816	+	0.0967898i
$736$	−30.0112	+	31.1401i	−1.10623	+	1.14784i
$737$	10.4049	−	10.4049i	0.383268	−	0.383268i
$738$	0.0999203	+	27.0653i	0.00367812	+	0.996288i
$739$	38.6731			1.42261			0.711307	−	0.702882i	$-0.248104\pi$
$739$	38.6731			1.42261			0.711307	+	0.702882i	$0.248104\pi$
$740$	−23.7608	+	36.3762i	−0.873463	+	1.33722i
$741$	−0.0962184			−0.00353467
$742$	0.186798	+	50.5978i	0.00685757	+	1.85750i
$743$	1.38756	−	1.38756i	0.0509046	−	0.0509046i	−0.681196	−	0.732101i	$-0.738540\pi$
$743$	1.38756	−	1.38756i	0.0509046	−	0.0509046i	0.732101	+	0.681196i	$0.238540\pi$
$744$	3.52101	+	3.44387i	0.129087	+	0.126258i
$745$	4.32958	+	21.4249i	0.158624	+	0.784948i
$746$	−6.29252	−	6.24623i	−0.230385	−	0.228691i
$747$	−12.5083	−	12.5083i	−0.457654	−	0.457654i
$748$	12.6143	+	12.4293i	0.461223	+	0.454462i
$749$			4.93885i			0.180462i
$750$	0.867939	−	4.67626i	0.0316926	−	0.170753i
$751$			13.6253i			0.497193i	0.968607	+	0.248596i	$0.0799693\pi$
$751$			13.6253i			0.497193i	−0.968607	+	0.248596i	$0.920031\pi$
$752$	−5.03714	−	4.89053i	−0.183686	−	0.178339i
$753$	4.66569	+	4.66569i	0.170027	+	0.170027i
$754$	−2.07459	+	2.08997i	−0.0755522	+	0.0761121i
$755$	1.86874	+	9.24747i	0.0680106	+	0.336550i
$756$	−0.0984090	−	13.3278i	−0.00357910	−	0.484727i
$757$	12.0474	−	12.0474i	0.437871	−	0.437871i	−0.453424	−	0.891295i	$-0.649798\pi$
$757$	12.0474	−	12.0474i	0.437871	−	0.437871i	0.891295	+	0.453424i	$0.149798\pi$
$758$	−35.8205	+	0.132243i	−1.30106	+	0.00480328i
$759$	4.70184			0.170666
$760$	6.18499	−	1.32133i	0.224353	−	0.0479299i
$761$	−9.84572			−0.356907			−0.178454	−	0.983948i	$-0.557109\pi$
$761$	−9.84572			−0.356907			−0.178454	+	0.983948i	$0.557109\pi$
$762$	−3.69557	+	0.0136434i	−0.133876	+	0.000494248i
$763$	−53.6566	+	53.6566i	−1.94250	+	1.94250i
$764$	−0.0939242	−	12.7204i	−0.00339806	−	0.460208i
$765$	−23.4749	−	15.5822i	−0.848736	−	0.563374i
$766$	−31.2545	+	31.4862i	−1.12927	+	1.13764i
$767$	1.00088	+	1.00088i	0.0361397	+	0.0361397i
$768$	3.30123	−	3.50222i	0.119123	−	0.126375i
$769$			32.7080i			1.17948i	0.807593	+	0.589741i	$0.200770\pi$

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)

\(f(q)\)	\(=\)	\(q+(1.41420 - 0.00522099i) q^{2} +(0.212700 - 0.212700i) q^{3} +(1.99995 - 0.0147671i) q^{4} +(2.19176 - 0.442915i) q^{5} +(0.299691 - 0.301912i) q^{6} +(-2.65088 - 2.65088i) q^{7} +(2.82825 - 0.0313254i) q^{8} +2.90952i q^{9} +O(q^{10})\)	\(q+(1.41420 - 0.00522099i) q^{2} +(0.212700 - 0.212700i) q^{3} +(1.99995 - 0.0147671i) q^{4} +(2.19176 - 0.442915i) q^{5} +(0.299691 - 0.301912i) q^{6} +(-2.65088 - 2.65088i) q^{7} +(2.82825 - 0.0313254i) q^{8} +2.90952i q^{9} +(3.09729 - 0.637816i) q^{10} -2.04453i q^{11} +(0.422248 - 0.428530i) q^{12} +(-0.226183 - 0.226183i) q^{13} +(-3.76272 - 3.73504i) q^{14} +(0.371981 - 0.560397i) q^{15} +(3.99956 - 0.0590668i) q^{16} +(-3.06235 + 3.06235i) q^{17} +(0.0151906 + 4.11465i) q^{18} +1.00000 q^{19} +(4.37687 - 0.918173i) q^{20} -1.12768 q^{21} +(-0.0106745 - 2.89139i) q^{22} +(-5.40599 + 5.40599i) q^{23} +(0.594908 - 0.608234i) q^{24} +(4.60765 - 1.94153i) q^{25} +(-0.321050 - 0.318688i) q^{26} +(1.25696 + 1.25696i) q^{27} +(-5.34075 - 5.26246i) q^{28} -6.50979i q^{29} +(0.523131 - 0.794458i) q^{30} +5.78891i q^{31} +(5.65589 - 0.104414i) q^{32} +(-0.434873 - 0.434873i) q^{33} +(-4.31480 + 4.34677i) q^{34} +(-6.98421 - 4.63598i) q^{35} +(0.0429651 + 5.81888i) q^{36} +(-6.86987 + 6.86987i) q^{37} +(1.41420 - 0.00522099i) q^{38} -0.0962184 q^{39} +(6.18499 - 1.32133i) q^{40} +6.57779 q^{41} +(-1.59478 + 0.00588763i) q^{42} +(3.72596 - 3.72596i) q^{43} +(-0.0301918 - 4.08895i) q^{44} +(1.28867 + 6.37697i) q^{45} +(-7.61695 + 7.67340i) q^{46} +(-1.24109 - 1.24109i) q^{47} +(0.838145 - 0.863272i) q^{48} +7.05428i q^{49} +(6.50602 - 2.76978i) q^{50} +1.30273i q^{51} +(-0.455694 - 0.449014i) q^{52} +(-6.74839 - 6.74839i) q^{53} +(1.78416 + 1.77103i) q^{54} +(-0.905555 - 4.48113i) q^{55} +(-7.58039 - 7.41431i) q^{56} +(0.212700 - 0.212700i) q^{57} +(-0.0339876 - 9.20617i) q^{58} -4.42510 q^{59} +(0.735666 - 1.12626i) q^{60} +0.777701 q^{61} +(0.0302239 + 8.18670i) q^{62} +(7.71277 - 7.71277i) q^{63} +(7.99804 - 0.177192i) q^{64} +(-0.595919 - 0.395560i) q^{65} +(-0.617269 - 0.612728i) q^{66} +(5.08912 + 5.08912i) q^{67} +(-6.07931 + 6.16975i) q^{68} +2.29971i q^{69} +(-9.90129 - 6.51975i) q^{70} +1.53345i q^{71} +(0.0911417 + 8.22885i) q^{72} +(-7.28339 - 7.28339i) q^{73} +(-9.67952 + 9.75126i) q^{74} +(0.567085 - 1.39301i) q^{75} +(1.99995 - 0.0147671i) q^{76} +(-5.41980 + 5.41980i) q^{77} +(-0.136072 + 0.000502356i) q^{78} -16.5071 q^{79} +(8.73994 - 1.90093i) q^{80} -8.19384 q^{81} +(9.30234 - 0.0343426i) q^{82} +(-4.29909 + 4.29909i) q^{83} +(-2.25531 + 0.0166526i) q^{84} +(-5.35558 + 8.06830i) q^{85} +(5.24981 - 5.28872i) q^{86} +(-1.38464 - 1.38464i) q^{87} +(-0.0640457 - 5.78246i) q^{88} +8.74189i q^{89} +(1.85574 + 9.01161i) q^{90} +1.19917i q^{91} +(-10.7319 + 10.8915i) q^{92} +(1.23130 + 1.23130i) q^{93} +(-1.76164 - 1.74868i) q^{94} +(2.19176 - 0.442915i) q^{95} +(1.18080 - 1.22522i) q^{96} +(-2.60382 + 2.60382i) q^{97} +(0.0368304 + 9.97619i) q^{98} +5.94860 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	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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