LMFDB - Embedded newform 380.2.k.d.267.13

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			267.13
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00522099 + 1.41420i) q^{2} +(-0.212700 - 0.212700i) q^{3} +(-1.99995 + 0.0147671i) q^{4} +(2.19176 + 0.442915i) q^{5} +(0.299691 - 0.301912i) q^{6} +(2.65088 - 2.65088i) q^{7} +(-0.0313254 - 2.82825i) q^{8} -2.90952i q^{9} +O(q^{10})$	\(q+(0.00522099 + 1.41420i) 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} +(-0.0313254 - 2.82825i) q^{8} -2.90952i q^{9} +(-0.614930 + 3.10191i) q^{10} -2.04453i q^{11} +(0.428530 + 0.422248i) 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} +(4.11465 - 0.0151906i) q^{18} -1.00000 q^{19} +(-4.38995 - 0.853441i) q^{20} -1.12768 q^{21} +(2.89139 - 0.0106745i) 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} +(-5.26246 + 5.34075i) q^{28} +6.50979i q^{29} +(0.790574 - 0.528982i) q^{30} +5.78891i q^{31} +(0.104414 + 5.65589i) 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} +(-0.00522099 - 1.41420i) q^{38} +0.0962184 q^{39} +(1.18402 - 6.21274i) q^{40} +6.57779 q^{41} +(-0.00588763 - 1.59478i) 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} +(-0.863272 - 0.838145i) q^{48} -7.05428i q^{49} +(-2.72166 + 6.52630i) q^{50} +1.30273i q^{51} +(0.449014 - 0.455694i) 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} +(-9.20617 + 0.0339876i) q^{58} +4.42510 q^{59} +(0.752216 + 1.11527i) q^{60} +0.777701 q^{61} +(-8.18670 + 0.0302239i) 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} +(6.16975 + 6.07931i) q^{68} -2.29971i q^{69} +(6.59268 + 9.85289i) q^{70} +1.53345i q^{71} +(-8.22885 + 0.0911417i) 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} +(0.000502356 + 0.136072i) q^{78} +16.5071 q^{79} +(8.79226 + 1.64201i) q^{80} -8.19384 q^{81} +(0.0343426 + 9.30234i) 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} +(-5.78246 + 0.0640457i) q^{88} -8.74189i q^{89} +(9.02507 + 1.78915i) q^{90} +1.19917i q^{91} +(-10.8915 - 10.7319i) 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} +(9.97619 - 0.0368304i) 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} + 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 $

$2$	0.00522099	+	1.41420i	0.00369180	+	0.999993i
$2$	0.00522099	+	1.41420i	0.00369180	+	0.999993i
$3$	−0.212700	−	0.212700i	−0.122803	−	0.122803i	0.643035	−	0.765837i	$-0.277675\pi$
$3$	−0.212700	−	0.212700i	−0.122803	−	0.122803i	−0.765837	+	0.643035i	$0.777675\pi$
$4$	−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	0.00193869	−	0.999998i	$-0.499383\pi$
$7$	2.65088	−	2.65088i	1.00194	−	1.00194i	0.999998	−	0.00193869i	$-0.000617103\pi$
$8$	−0.0313254	−	2.82825i	−0.0110752	−	0.999939i
$9$		−	2.90952i		−	0.969839i
$10$	−0.614930	+	3.10191i	−0.194458	+	0.980911i
$11$		−	2.04453i		−	0.616450i	−0.951314	−	0.308225i	$-0.900265\pi$
$11$		−	2.04453i		−	0.616450i	0.951314	−	0.308225i	$-0.0997349\pi$
$12$	0.428530	+	0.422248i	0.123706	+	0.121893i
$13$	−0.226183	+	0.226183i	−0.0627319	+	0.0627319i	−0.737777	−	0.675045i	$-0.764124\pi$
$13$	−0.226183	+	0.226183i	−0.0627319	+	0.0627319i	0.675045	+	0.737777i	$0.264124\pi$
$14$	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	0.230374	−	0.973102i	$-0.426005\pi$
$17$	−3.06235	−	3.06235i	−0.742729	−	0.742729i	−0.973102	+	0.230374i	$0.926005\pi$
$18$	4.11465	−	0.0151906i	0.969832	−	0.00358045i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−4.38995	−	0.853441i	−0.981622	−	0.190835i
$21$	−1.12768			−0.246081
$22$	2.89139	−	0.0106745i	0.616445	−	0.00227581i
$23$	5.40599	+	5.40599i	1.12723	+	1.12723i	0.990626	+	0.136600i	$0.0436176\pi$
$23$	5.40599	+	5.40599i	1.12723	+	1.12723i	0.136600	+	0.990626i	$0.456382\pi$
$24$	−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
$28$	−5.26246	+	5.34075i	−0.994512	+	1.00931i
$29$			6.50979i			1.20884i	0.796667	+	0.604419i	$0.206595\pi$
$29$			6.50979i			1.20884i	−0.796667	+	0.604419i	$0.793405\pi$
$30$	0.790574	−	0.528982i	0.144338	−	0.0965785i
$31$			5.78891i			1.03972i	0.854252	+	0.519860i	$0.174016\pi$
$31$			5.78891i			1.03972i	−0.854252	+	0.519860i	$0.825984\pi$
$32$	0.104414	+	5.65589i	0.0184580	+	0.999830i
$33$	−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	−0.990275	−	0.139124i	$-0.955571\pi$
$37$	−6.86987	−	6.86987i	−1.12940	−	1.12940i	−0.139124	−	0.990275i	$-0.544429\pi$
$38$	−0.00522099	−	1.41420i	−0.000846957	−	0.229414i
$39$	0.0962184			0.0154073
$40$	1.18402	−	6.21274i	0.187210	−	0.982320i
$41$	6.57779			1.02728			0.513639	−	0.858006i	$-0.328297\pi$
$41$	6.57779			1.02728			0.513639	+	0.858006i	$0.328297\pi$
$42$	−0.00588763	−	1.59478i	−0.000908481	−	0.246079i
$43$	−3.72596	−	3.72596i	−0.568203	−	0.568203i	0.363422	−	0.931625i	$-0.381608\pi$
$43$	−3.72596	−	3.72596i	−0.568203	−	0.568203i	−0.931625	+	0.363422i	$0.881608\pi$
$44$	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	$-0.709141\pi$
$47$	1.24109	−	1.24109i	0.181032	−	0.181032i	0.791805	+	0.610773i	$0.209141\pi$
$48$	−0.863272	−	0.838145i	−0.124603	−	0.120976i
$49$		−	7.05428i		−	1.00775i
$50$	−2.72166	+	6.52630i	−0.384902	+	0.922958i
$51$			1.30273i			0.182418i
$52$	0.449014	−	0.455694i	0.0622670	−	0.0631933i
$53$	−6.74839	+	6.74839i	−0.926962	+	0.926962i	−0.997509	−	0.0705463i	$-0.977526\pi$
$53$	−6.74839	+	6.74839i	−0.926962	+	0.926962i	0.0705463	+	0.997509i	$0.477526\pi$
$54$	−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
$58$	−9.20617	+	0.0339876i	−1.20883	+	0.00446279i
$59$	4.42510			0.576098			0.288049	−	0.957616i	$-0.406993\pi$
$59$	4.42510			0.576098			0.288049	+	0.957616i	$0.406993\pi$
$60$	0.752216	+	1.11527i	0.0971107	+	0.143981i
$61$	0.777701			0.0995745			0.0497872	−	0.998760i	$-0.484146\pi$
$61$	0.777701			0.0995745			0.0497872	+	0.998760i	$0.484146\pi$
$62$	−8.18670	+	0.0302239i	−1.03971	+	0.00383844i
$63$	−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	$-0.894891\pi$
$67$	−5.08912	+	5.08912i	−0.621734	+	0.621734i	0.324240	+	0.945975i	$0.394891\pi$
$68$	6.16975	+	6.07931i	0.748192	+	0.737224i
$69$		−	2.29971i		−	0.276853i
$70$	6.59268	+	9.85289i	0.787976	+	1.17765i
$71$			1.53345i			0.181986i	0.995852	+	0.0909932i	$0.0290042\pi$
$71$			1.53345i			0.181986i	−0.995852	+	0.0909932i	$0.970996\pi$
$72$	−8.22885	+	0.0911417i	−0.969780	+	0.0107412i
$73$	−7.28339	+	7.28339i	−0.852457	+	0.852457i	−0.990435	−	0.137979i	$-0.955939\pi$
$73$	−7.28339	+	7.28339i	−0.852457	+	0.852457i	0.137979	+	0.990435i	$0.455939\pi$
$74$	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
$78$	0.000502356		0.136072i	5.68806e−5		0.0154072i
$79$	16.5071			1.85720			0.928599	−	0.371086i	$-0.121014\pi$
$79$	16.5071			1.85720			0.928599	+	0.371086i	$0.121014\pi$
$80$	8.79226	+	1.64201i	0.983004	+	0.183582i
$81$	−8.19384			−0.910427
$82$	0.0343426	+	9.30234i	0.00379250	+	1.02727i
$83$	4.29909	+	4.29909i	0.471887	+	0.471887i	0.902525	−	0.430638i	$-0.141711\pi$
$83$	4.29909	+	4.29909i	0.471887	+	0.471887i	−0.430638	+	0.902525i	$0.641711\pi$
$84$	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
$88$	−5.78246	+	0.0640457i	−0.616412	+	0.00682730i
$89$		−	8.74189i		−	0.926639i	−0.886191	−	0.463319i	$-0.846658\pi$
$89$		−	8.74189i		−	0.926639i	0.886191	−	0.463319i	$-0.153342\pi$
$90$	9.02507	+	1.78915i	0.951326	+	0.188593i
$91$			1.19917i			0.125707i
$92$	−10.8915	−	10.7319i	−1.13552	−	1.11887i
$93$	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	0.562452	−	0.826830i	$-0.309858\pi$
$97$	−2.60382	−	2.60382i	−0.264377	−	0.264377i	−0.826830	+	0.562452i	$0.809858\pi$
$98$	9.97619	−	0.0368304i	1.00775	−	0.00372043i
$99$	−5.94860			−0.597857
$100$	−9.24372	−	3.81492i	−0.924372	−	0.381492i
$101$	13.0511			1.29864			0.649318	−	0.760517i	$-0.275054\pi$
$101$	13.0511			1.29864			0.649318	+	0.760517i	$0.275054\pi$
$102$	−1.84232	+	0.00680152i	−0.182417	+	0.000673451i
$103$	−12.4417	−	12.4417i	−1.22591	−	1.22591i	−0.965496	−	0.260419i	$-0.916139\pi$
$103$	−12.4417	−	12.4417i	−1.22591	−	1.22591i	−0.260419	−	0.965496i	$-0.583861\pi$
$104$	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	$-0.729716\pi$
$107$	0.931552	−	0.931552i	0.0900565	−	0.0900565i	0.750700	+	0.660643i	$0.229716\pi$
$108$	2.49528	−	2.53241i	0.240109	−	0.243681i
$109$			20.2411i			1.93874i	0.245597	+	0.969372i	$0.421016\pi$
$109$			20.2411i			1.93874i	−0.245597	+	0.969372i	$0.578984\pi$
$110$	6.34196	+	1.25724i	0.604682	+	0.119873i
$111$			2.92245i			0.277386i
$112$	10.4458	−	10.7589i	0.987032	−	1.01662i
$113$	3.01028	−	3.01028i	0.283183	−	0.283183i	−0.551194	−	0.834377i	$-0.685828\pi$
$113$	3.01028	−	3.01028i	0.283183	−	0.283183i	0.834377	+	0.551194i	$0.185828\pi$
$114$	−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
$118$	0.0231034	+	6.25799i	0.00212684	+	0.576094i
$119$	−16.2358			−1.48833
$120$	−1.57329	+	1.06961i	−0.143621	+	0.0976416i
$121$	6.81989			0.619990
$122$	0.00406037	+	1.09983i	0.000367609	+	0.0995738i
$123$	−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	$-0.624051\pi$
$127$	6.14286	−	6.14286i	0.545091	−	0.545091i	0.925017	+	0.379926i	$0.124051\pi$
$128$	−0.292344	−	11.3099i	−0.0258398	−	0.999666i
$129$			1.58503i			0.139554i
$130$	−0.562513	−	0.840686i	−0.0493357	−	0.0737331i
$131$			8.30018i			0.725190i	0.931947	+	0.362595i	$0.118109\pi$
$131$			8.30018i			0.725190i	−0.931947	+	0.362595i	$0.881891\pi$
$132$	0.863300	−	0.876144i	0.0751406	−	0.0762585i
$133$	−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	0.829146	−	0.559032i	$-0.188827\pi$
$137$	3.16161	+	3.16161i	0.270115	+	0.270115i	−0.559032	+	0.829146i	$0.688827\pi$
$138$	3.25226	−	0.0120068i	0.276851	−	0.00102208i
$139$	−16.9908			−1.44114			−0.720572	−	0.693380i	$-0.756121\pi$
$139$	−16.9908			−1.44114			−0.720572	+	0.693380i	$0.756121\pi$
$140$	−13.8996	+	9.37484i	−1.17473	+	0.792319i
$141$	−0.527962			−0.0444625
$142$	−2.16860	+	0.00800611i	−0.181985	+	0.000671857i
$143$	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
$148$	13.8408	+	13.6379i	1.13771	+	1.12103i
$149$		−	9.77519i		−	0.800815i	−0.916337	−	0.400407i	$-0.868869\pi$
$149$		−	9.77519i		−	0.800815i	0.916337	−	0.400407i	$-0.131131\pi$
$150$	1.96705	−	0.809247i	0.160609	−	0.0660747i
$151$			4.21919i			0.343353i	0.985153	+	0.171676i	$0.0549184\pi$
$151$			4.21919i			0.343353i	−0.985153	+	0.171676i	$0.945082\pi$
$152$	0.0313254	+	2.82825i	0.00254082	+	0.229402i
$153$	−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	0.960660	−	0.277727i	$-0.0895812\pi$
$157$	8.55712	+	8.55712i	0.682933	+	0.682933i	−0.277727	+	0.960660i	$0.589581\pi$
$158$	0.0861836	+	23.3444i	0.00685640	+	1.85718i
$159$	2.87077			0.227667
$160$	−2.27623	+	12.4426i	−0.179952	+	0.983675i
$161$	28.6612			2.25882
$162$	−0.0427800	−	11.5878i	−0.00336111	−	0.910421i
$163$	−11.5235	−	11.5235i	−0.902586	−	0.902586i	0.0930729	−	0.995659i	$-0.470331\pi$
$163$	−11.5235	−	11.5235i	−0.902586	−	0.902586i	−0.995659	+	0.0930729i	$0.970331\pi$
$164$	−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	$-0.813838\pi$
$167$	−3.64071	+	3.64071i	−0.281727	+	0.281727i	0.552071	+	0.833797i	$0.313838\pi$
$168$	0.0353252	+	3.18938i	0.00272539	+	0.246066i
$169$			12.8977i			0.992129i
$170$	11.3823	−	7.61601i	0.872980	−	0.584121i
$171$			2.90952i			0.222496i
$172$	7.50673	+	7.39669i	0.572383	+	0.563992i
$173$	1.45513	−	1.45513i	0.110632	−	0.110632i	−0.649624	−	0.760256i	$-0.725074\pi$
$173$	1.45513	−	1.45513i	0.110632	−	0.110632i	0.760256	+	0.649624i	$0.225074\pi$
$174$	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
$178$	12.3628	−	0.0456413i	0.926632	−	0.00342096i
$179$	−2.19695			−0.164208			−0.0821038	−	0.996624i	$-0.526164\pi$
$179$	−2.19695			−0.164208			−0.0821038	+	0.996624i	$0.526164\pi$
$180$	−2.48310	+	12.7726i	−0.185079	+	0.952015i
$181$	−4.48272			−0.333198			−0.166599	−	0.986025i	$-0.553279\pi$
$181$	−4.48272			−0.333198			−0.166599	+	0.986025i	$0.553279\pi$
$182$	−1.69587	+	0.00626084i	−0.125706	+	0.000464084i
$183$	−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
$188$	−2.46379	+	2.50045i	−0.179691	+	0.182364i
$189$			6.66407i			0.484740i
$190$	0.614930	−	3.10191i	0.0446117	−	0.225036i
$191$		−	6.36037i		−	0.460220i	−0.973165	−	0.230110i	$-0.926091\pi$
$191$		−	6.36037i		−	0.460220i	0.973165	−	0.230110i	$-0.0739087\pi$
$192$	1.73887	+	1.66350i	0.125492	+	0.120053i
$193$	−13.5977	+	13.5977i	−0.978787	+	0.978787i	−0.999780	−	0.0209930i	$-0.993317\pi$
$193$	−13.5977	+	13.5977i	−0.978787	+	0.978787i	0.0209930	+	0.999780i	$0.493317\pi$
$194$	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	0.917224	−	0.398373i	$-0.130425\pi$
$197$	7.28242	+	7.28242i	0.518851	+	0.518851i	−0.398373	+	0.917224i	$0.630425\pi$
$198$	−0.0310576	−	8.41253i	−0.00220717	−	0.597853i
$199$	−21.1117			−1.49657			−0.748284	−	0.663378i	$-0.769122\pi$
$199$	−21.1117			−1.49657			−0.748284	+	0.663378i	$0.769122\pi$
$200$	5.34681	−	13.0924i	0.378076	−	0.925774i
$201$	2.16491			0.152701
$202$	0.0681399	+	18.4570i	0.00479430	+	1.29863i
$203$	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
$208$	−0.891273	+	0.917993i	−0.0617987	+	0.0636514i
$209$			2.04453i			0.141423i
$210$	0.693447	−	3.49798i	0.0478524	−	0.241384i
$211$			13.4524i			0.926098i	0.886333	+	0.463049i	$0.153245\pi$
$211$			13.4524i			0.926098i	−0.886333	+	0.463049i	$0.846755\pi$
$212$	13.3968	−	13.5961i	0.920093	−	0.933781i
$213$	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
$218$	−28.6250	+	0.105679i	−1.93873	+	0.00715745i
$219$	3.09836			0.209368
$220$	−1.74489	+	8.97539i	−0.117640	+	0.605121i
$221$	1.38530			0.0931855
$222$	−4.13293	+	0.0152581i	−0.277384	+	0.00102405i
$223$	1.88885	+	1.88885i	0.126486	+	0.126486i	0.767516	−	0.641030i	$-0.221492\pi$
$223$	1.88885	+	1.88885i	0.126486	+	0.126486i	−0.641030	+	0.767516i	$0.721492\pi$
$224$	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	$-0.728105\pi$
$227$	1.46448	−	1.46448i	0.0972007	−	0.0972007i	0.754035	+	0.656834i	$0.228105\pi$
$228$	−0.428530	−	0.422248i	−0.0283801	−	0.0279641i
$229$			3.08873i			0.204109i	0.994779	+	0.102055i	$0.0325417\pi$
$229$			3.08873i			0.204109i	−0.994779	+	0.102055i	$0.967458\pi$
$230$	−20.0932	+	13.4446i	−1.32491	+	0.886511i
$231$			2.30559i			0.151697i
$232$	18.4113	−	0.203922i	1.20876	−	0.0133881i
$233$	0.275351	−	0.275351i	0.0180388	−	0.0180388i	−0.698030	−	0.716069i	$-0.745940\pi$
$233$	0.275351	−	0.275351i	0.0180388	−	0.0180388i	0.716069	+	0.698030i	$0.245940\pi$
$234$	−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
$238$	−0.0847670	−	22.9607i	−0.00549463	−	1.48832i
$239$	−2.55298			−0.165139			−0.0825693	−	0.996585i	$-0.526313\pi$
$239$	−2.55298			−0.165139			−0.0825693	+	0.996585i	$0.526313\pi$
$240$	−1.52086	−	2.21937i	−0.0981712	−	0.143260i
$241$	−10.8689			−0.700128			−0.350064	−	0.936726i	$-0.613840\pi$
$241$	−10.8689			−0.700128			−0.350064	+	0.936726i	$0.613840\pi$
$242$	0.0356066	+	9.64471i	0.00228888	+	0.619986i
$243$	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
$248$	16.3725	−	0.181340i	1.03966	−	0.0115151i
$249$		−	1.82884i		−	0.115898i
$250$	−8.85584	+	13.0986i	−0.560093	+	0.828430i
$251$			21.9355i			1.38456i	0.721630	+	0.692279i	$0.243393\pi$
$251$			21.9355i			1.38456i	−0.721630	+	0.692279i	$0.756607\pi$
$252$	15.5390	+	15.3112i	0.978866	+	0.964516i
$253$	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	0.372811	−	0.927907i	$-0.378394\pi$
$257$	−8.89886	−	8.89886i	−0.555096	−	0.555096i	−0.927907	+	0.372811i	$0.878394\pi$
$258$	−2.24155	+	0.00827541i	−0.139553	+	0.000515204i
$259$	−36.4223			−2.26317
$260$	1.18597	−	0.799898i	0.0735504	−	0.0496075i
$261$	18.9404			1.17238
$262$	−11.7381	+	0.0433352i	−0.725185	+	0.00267725i
$263$	−16.0413	−	16.0413i	−0.989151	−	0.989151i	0.0107906	−	0.999942i	$-0.496565\pi$
$263$	−16.0413	−	16.0413i	−0.989151	−	0.989151i	−0.999942	+	0.0107906i	$0.996565\pi$
$264$	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
$268$	10.1028	−	10.2531i	0.617127	−	0.626308i
$269$		−	6.96525i		−	0.424679i	−0.977196	−	0.212339i	$-0.931892\pi$
$269$		−	6.96525i		−	0.424679i	0.977196	−	0.212339i	$-0.0681083\pi$
$270$	−3.12603	−	4.67191i	−0.190244	−	0.284323i
$271$		−	7.23572i		−	0.439539i	−0.975552	−	0.219769i	$-0.929470\pi$
$271$		−	7.23572i		−	0.439539i	0.975552	−	0.219769i	$-0.0705305\pi$
$272$	−12.4289	−	12.0672i	−0.753615	−	0.731680i
$273$	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	0.0878773	−	0.996131i	$-0.471992\pi$
$277$	−15.1164	−	15.1164i	−0.908254	−	0.908254i	−0.996131	+	0.0878773i	$0.971992\pi$
$278$	−0.0887090	−	24.0285i	−0.00532041	−	1.44113i
$279$	16.8429			1.00836
$280$	−13.3305	−	19.6079i	−0.796650	−	1.17179i
$281$	10.0095			0.597118			0.298559	−	0.954391i	$-0.403494\pi$
$281$	10.0095			0.597118			0.298559	+	0.954391i	$0.403494\pi$
$282$	−0.00275649	−	0.746646i	−0.000164146	−	0.0444622i
$283$	8.48356	+	8.48356i	0.504295	+	0.504295i	0.912770	−	0.408474i	$-0.133939\pi$
$283$	8.48356	+	8.48356i	0.504295	+	0.504295i	−0.408474	+	0.912770i	$0.633939\pi$
$284$	−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
$288$	16.4559	−	0.303795i	0.969674	−	0.0179013i
$289$			1.75596i			0.103292i
$290$	−20.1928	−	4.00306i	−1.18576	−	0.235068i
$291$			1.10767i			0.0649325i
$292$	14.4588	−	14.6739i	0.846139	−	0.858727i
$293$	10.3132	−	10.3132i	0.602501	−	0.602501i	−0.338475	−	0.940976i	$-0.609911\pi$
$293$	10.3132	−	10.3132i	0.602501	−	0.602501i	0.940976	+	0.338475i	$0.109911\pi$
$294$	−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
$298$	13.8241	−	0.0510362i	0.800809	−	0.00295645i
$299$	−2.44549			−0.141426
$300$	1.15471	+	2.77758i	0.0666672	+	0.160364i
$301$	−19.7541			−1.13861
$302$	−5.96680	+	0.0220284i	−0.343351	+	0.00126759i
$303$	−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	$-0.798712\pi$
$307$	−3.77726	+	3.77726i	−0.215579	+	0.215579i	0.591053	+	0.806633i	$0.298712\pi$
$308$	10.9193	+	10.7593i	0.622187	+	0.613066i
$309$			5.29270i			0.301091i
$310$	−17.9567	−	3.55977i	−1.01987	−	0.202182i
$311$		−	21.5006i		−	1.21919i	−0.792715	−	0.609593i	$-0.791333\pi$
$311$		−	21.5006i		−	1.21919i	0.792715	−	0.609593i	$-0.208667\pi$
$312$	−0.00301408	−	0.272130i	−0.000170639	−	0.0154063i
$313$	−12.1932	+	12.1932i	−0.689200	+	0.689200i	−0.962055	−	0.272855i	$-0.912032\pi$
$313$	−12.1932	+	12.1932i	−0.689200	+	0.689200i	0.272855	+	0.962055i	$0.412032\pi$
$314$	−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	0.713571	−	0.700583i	$-0.247077\pi$
$317$	0.231233	+	0.231233i	0.0129873	+	0.0129873i	−0.700583	+	0.713571i	$0.747077\pi$
$318$	0.0149883	+	4.05985i	0.000840500	+	0.227665i
$319$	13.3095			0.745188
$320$	−17.6083	−	3.15409i	−0.984333	−	0.176319i
$321$	−0.396283			−0.0221183
$322$	0.149640	+	40.5328i	0.00833911	+	2.25880i
$323$	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
$328$	−0.206052	−	18.6037i	−0.0113773	−	1.02722i
$329$		−	6.57997i		−	0.362766i
$330$	−1.08152	−	1.61635i	−0.0595358	−	0.0889773i
$331$		−	22.4492i		−	1.23392i	−0.786994	−	0.616960i	$-0.788364\pi$
$331$		−	22.4492i		−	1.23392i	0.786994	−	0.616960i	$-0.211636\pi$
$332$	−8.66143	−	8.53446i	−0.475358	−	0.468389i
$333$	−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	0.566451	−	0.824095i	$-0.308316\pi$
$337$	−4.72972	−	4.72972i	−0.257644	−	0.257644i	−0.824095	+	0.566451i	$0.808316\pi$
$338$	−18.2400	+	0.0673387i	−0.992123	+	0.00366274i
$339$	−1.28057			−0.0695512
$340$	10.8300	+	16.0571i	0.587340	+	0.870818i
$341$	11.8356			0.640935
$342$	−4.11465	+	0.0151906i	−0.222495	+	0.000821412i
$343$	−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	−0.527809	+	0.849363i	$0.676986\pi$
$347$	−25.6539	+	25.6539i	−1.37717	+	1.37717i	−0.849363	+	0.527809i	$0.823014\pi$
$348$	−2.74875	+	2.78964i	−0.147348	+	0.149541i
$349$		−	10.9773i		−	0.587600i	−0.955867	−	0.293800i	$-0.905080\pi$
$349$		−	10.9773i		−	0.587600i	0.955867	−	0.293800i	$-0.0949199\pi$
$350$	10.0856	+	24.5152i	0.539098	+	1.31039i
$351$		−	0.568604i		−	0.0303499i
$352$	11.5636	−	0.213478i	0.616345	−	0.0113784i
$353$	20.5889	−	20.5889i	1.09584	−	1.09584i	0.100947	−	0.994892i	$-0.467813\pi$
$353$	20.5889	−	20.5889i	1.09584	−	1.09584i	0.994892	−	0.100947i	$-0.0321874\pi$
$354$	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
$358$	−0.0114702	−	3.10693i	−0.000606221	−	0.164207i
$359$	21.8842			1.15500			0.577502	−	0.816390i	$-0.304028\pi$
$359$	21.8842			1.15500			0.577502	+	0.816390i	$0.304028\pi$
$360$	−18.0761	−	3.44492i	−0.952692	−	0.181563i
$361$	1.00000			0.0526316
$362$	−0.0234042	−	6.33948i	−0.00123010	−	0.333196i
$363$	−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	0.489195	−	0.872175i	$-0.337291\pi$
$367$	26.0801	−	26.0801i	1.36137	−	1.36137i	0.872175	−	0.489195i	$-0.162709\pi$
$368$	21.9409	+	21.3023i	1.14375	+	1.11046i
$369$		−	19.1382i		−	0.996294i
$370$	25.5342	−	17.0852i	1.32746	−	0.888219i
$371$			35.7783i			1.85752i
$372$	−2.44436	+	2.48072i	−0.126734	+	0.128620i
$373$	−4.43315	+	4.43315i	−0.229540	+	0.229540i	−0.812500	−	0.582961i	$-0.801894\pi$
$373$	−4.43315	+	4.43315i	−0.229540	+	0.229540i	0.582961	+	0.812500i	$0.301894\pi$
$374$	−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
$378$	−9.42436	+	0.0347931i	−0.484737	+	0.00178956i
$379$	25.3291			1.30107			0.650534	−	0.759477i	$-0.274545\pi$
$379$	25.3291			1.30107			0.650534	+	0.759477i	$0.274545\pi$
$380$	4.38995	+	0.853441i	0.225200	+	0.0437806i
$381$	−2.61318			−0.133877
$382$	8.99486	−	0.0332075i	0.460217	−	0.00169904i
$383$	22.1823	+	22.1823i	1.13346	+	1.13346i	0.989597	+	0.143867i	$0.0459538\pi$
$383$	22.1823	+	22.1823i	1.13346	+	1.13346i	0.143867	+	0.989597i	$0.454046\pi$
$384$	−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
$388$	5.24594	+	5.16904i	0.266322	+	0.262418i
$389$			26.6415i			1.35078i	0.737462	+	0.675388i	$0.236024\pi$
$389$			26.6415i			1.35078i	−0.737462	+	0.675388i	$0.763976\pi$
$390$	−0.0591676	+	0.298461i	−0.00299607	+	0.0151132i
$391$		−	33.1100i		−	1.67445i
$392$	−19.9513	+	0.220978i	−1.00769	+	0.0111611i
$393$	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	−0.999763	−	0.0217671i	$-0.993071\pi$
$397$	−20.3538	−	20.3538i	−1.02153	−	1.02153i	−0.0217671	−	0.999763i	$-0.506929\pi$
$398$	−0.110224	−	29.8562i	−0.00552503	−	1.49656i
$399$	1.12768			0.0564548
$400$	18.5433	+	7.49312i	0.927164	+	0.374656i
$401$	−22.5998			−1.12858			−0.564289	−	0.825577i	$-0.690850\pi$
$401$	−22.5998			−1.12858			−0.564289	+	0.825577i	$0.690850\pi$
$402$	0.0113030	+	3.06163i	0.000563742	+	0.152700i
$403$	−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
$408$	3.68444	−	0.0408084i	0.182407	−	0.00202032i
$409$		−	3.50326i		−	0.173225i	−0.996242	−	0.0866126i	$-0.972396\pi$
$409$		−	3.50326i		−	0.173225i	0.996242	−	0.0866126i	$-0.0276042\pi$
$410$	−4.04488	+	20.4037i	−0.199762	+	1.00767i
$411$		−	1.34495i		−	0.0663416i
$412$	25.0664	+	24.6990i	1.23493	+	1.21683i
$413$	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
$418$	−2.89139	+	0.0106745i	−0.141422	+	0.000522106i
$419$	12.6029			0.615691			0.307846	−	0.951436i	$-0.400392\pi$
$419$	12.6029			0.615691			0.307846	+	0.951436i	$0.400392\pi$
$420$	4.95048	+	0.962412i	0.241559	+	0.0469609i
$421$	−38.3993			−1.87147			−0.935735	−	0.352704i	$-0.885262\pi$
$421$	−38.3993			−1.87147			−0.935735	+	0.352704i	$0.885262\pi$
$422$	−19.0244	+	0.0702346i	−0.926092	+	0.00341897i
$423$	−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
$428$	−1.84930	+	1.87681i	−0.0893891	+	0.0907190i
$429$		−	0.196722i		−	0.00949781i
$430$	13.8488	−	9.26639i	0.667848	−	0.446865i
$431$			22.0058i			1.05998i	0.848003	+	0.529992i	$0.177805\pi$
$431$			22.0058i			1.05998i	−0.848003	+	0.529992i	$0.822195\pi$
$432$	−4.95303	+	5.10152i	−0.238303	+	0.245447i
$433$	24.6830	−	24.6830i	1.18619	−	1.18619i	0.208077	−	0.978112i	$-0.433279\pi$
$433$	24.6830	−	24.6830i	1.18619	−	1.18619i	0.978112	−	0.208077i	$-0.0667205\pi$
$434$	−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
$438$	0.0161765	+	4.38171i	0.000772944	+	0.209366i
$439$	−14.9623			−0.714113			−0.357056	−	0.934083i	$-0.616220\pi$
$439$	−14.9623			−0.714113			−0.357056	+	0.934083i	$0.616220\pi$
$440$	−12.7021	−	2.42077i	−0.605551	−	0.115405i
$441$	−20.5246			−0.977360
$442$	0.00723265	+	1.95910i	0.000344022	+	0.0931849i
$443$	4.16446	+	4.16446i	0.197859	+	0.197859i	0.799082	−	0.601222i	$-0.205319\pi$
$443$	4.16446	+	4.16446i	0.197859	+	0.197859i	−0.601222	+	0.799082i	$0.705319\pi$
$444$	−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
$448$	−20.7321	+	21.6715i	−0.979499	+	1.02388i
$449$			4.32706i			0.204207i	0.994774	+	0.102103i	$0.0325572\pi$
$449$			4.32706i			0.204207i	−0.994774	+	0.102103i	$0.967443\pi$
$450$	18.9884	+	7.91873i	0.895120	+	0.373293i
$451$		−	13.4485i		−	0.633265i
$452$	−5.97593	+	6.06484i	−0.281084	+	0.285266i
$453$	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	0.918374	−	0.395714i	$-0.129503\pi$
$457$	11.1732	+	11.1732i	0.522659	+	0.522659i	−0.395714	+	0.918374i	$0.629503\pi$
$458$	−4.36810	+	0.0161263i	−0.204108	+	0.000753530i
$459$	7.69848			0.359334
$460$	−19.1183	−	28.3457i	−0.891396	−	1.32163i
$461$	−28.2155			−1.31413			−0.657064	−	0.753835i	$-0.728202\pi$
$461$	−28.2155			−1.31413			−0.657064	+	0.753835i	$0.728202\pi$
$462$	−3.26057	+	0.0120375i	−0.151695	+	0.000560033i
$463$	−23.1500	−	23.1500i	−1.07587	−	1.07587i	−0.996875	−	0.0789948i	$-0.974829\pi$
$463$	−23.1500	−	23.1500i	−1.07587	−	1.07587i	−0.0789948	−	0.996875i	$-0.525171\pi$
$464$	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	$-0.884128\pi$
$467$	−12.5001	+	12.5001i	−0.578435	+	0.578435i	0.356037	+	0.934472i	$0.384128\pi$
$468$	−1.32585	−	1.30641i	−0.0612874	−	0.0603889i
$469$			26.9812i			1.24588i
$470$	3.08658	+	4.61295i	0.142373	+	0.212780i
$471$		−	3.64021i		−	0.167732i
$472$	−0.138618	−	12.5153i	−0.00638040	−	0.576063i
$473$	−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
$478$	−0.0133291	−	3.61044i	−0.000609658	−	0.165137i
$479$	18.1663			0.830040			0.415020	−	0.909812i	$-0.363775\pi$
$479$	18.1663			0.830040			0.415020	+	0.909812i	$0.363775\pi$
$480$	3.13071	−	2.16240i	0.142896	−	0.0986994i
$481$	3.10769			0.141699
$482$	−0.0567465	−	15.3709i	−0.00258473	−	0.700123i
$483$	−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	0.0646845	−	0.997906i	$-0.479396\pi$
$487$	23.4493	−	23.4493i	1.06259	−	1.06259i	0.997906	−	0.0646845i	$-0.0206041\pi$
$488$	−0.0243618	−	2.19954i	−0.00110281	−	0.0995684i
$489$			4.90209i			0.221680i
$490$	21.8818	+	4.33789i	0.988518	+	0.195966i
$491$		−	1.07295i		−	0.0484217i	−0.999707	−	0.0242108i	$-0.992293\pi$
$491$		−	1.07295i		−	0.0484217i	0.999707	−	0.0242108i	$-0.00770731\pi$
$492$	2.81878	+	2.77746i	0.127080	+	0.125218i
$493$	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
$498$	2.58635	−	0.00954834i	0.115897	−	0.000427871i
$499$	17.3943			0.778674			0.389337	−	0.921095i	$-0.372704\pi$
$499$	17.3943			0.778674			0.389337	+	0.921095i	$0.372704\pi$
$500$	−18.5704	−	12.4556i	−0.830492	−	0.557030i
$501$	1.54876			0.0691936
$502$	−31.0213	+	0.114525i	−1.38455	+	0.00511151i
$503$	−20.5398	−	20.5398i	−0.915826	−	0.915826i	0.0808962	−	0.996723i	$-0.474222\pi$
$503$	−20.5398	−	20.5398i	−0.915826	−	0.915826i	−0.996723	+	0.0808962i	$0.974222\pi$
$504$	−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
$508$	−12.1947	+	12.3761i	−0.541051	+	0.549101i
$509$		−	31.2945i		−	1.38710i	−0.720406	−	0.693552i	$-0.756045\pi$
$509$		−	31.2945i		−	1.38710i	0.720406	−	0.693552i	$-0.243955\pi$
$510$	−4.04094	−	0.801085i	−0.178936	−	0.0354726i
$511$			38.6147i			1.70822i
$512$	0.751686	+	22.6149i	0.0332201	+	0.999448i
$513$	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
$518$	−0.190161	−	51.5086i	−0.00835518	−	2.26316i
$519$	−0.619015			−0.0271717
$520$	1.13741	+	1.67302i	0.0498787	+	0.0733668i
$521$	17.9538			0.786572			0.393286	−	0.919416i	$-0.371338\pi$
$521$	17.9538			0.786572			0.393286	+	0.919416i	$0.371338\pi$
$522$	0.0988874	+	26.7855i	0.00432818	+	1.17237i
$523$	5.14238	+	5.14238i	0.224861	+	0.224861i	0.810542	−	0.585681i	$-0.199173\pi$
$523$	5.14238	+	5.14238i	0.224861	+	0.224861i	−0.585681	+	0.810542i	$0.699173\pi$
$524$	−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
$528$	−1.71362	+	1.76499i	−0.0745755	+	0.0768112i
$529$			35.4494i			1.54128i
$530$	−16.7831	−	25.0827i	−0.729012	−	1.08952i
$531$		−	12.8749i		−	0.558723i
$532$	5.26246	−	5.34075i	0.228157	−	0.231551i
$533$	−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
$538$	9.85029	−	0.0363655i	0.424676	−	0.00156783i
$539$	−14.4227			−0.621230
$540$	6.59071	−	4.44524i	0.283619	−	0.191292i
$541$	19.3237			0.830792			0.415396	−	0.909641i	$-0.363643\pi$
$541$	19.3237			0.830792			0.415396	+	0.909641i	$0.363643\pi$
$542$	10.2328	−	0.0377776i	0.439536	−	0.00162269i
$543$	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	$-0.562494\pi$
$547$	18.3764	−	18.3764i	0.785719	−	0.785719i	0.980789	+	0.195071i	$0.0624936\pi$
$548$	−6.36974	−	6.27636i	−0.272102	−	0.268113i
$549$		−	2.26274i		−	0.0965712i
$550$	13.3432	+	5.56453i	0.568957	+	0.237272i
$551$		−	6.50979i		−	0.277326i
$552$	−6.50417	+	0.0720394i	−0.276836	+	0.00306620i
$553$	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	0.998180	−	0.0603095i	$-0.0192088\pi$
$557$	22.1345	+	22.1345i	0.937870	+	0.937870i	−0.0603095	+	0.998180i	$0.519209\pi$
$558$	0.0879369	+	23.8194i	0.00372266	+	1.00835i
$559$	1.68550			0.0712889
$560$	27.6599	−	18.9544i	1.16885	−	0.800971i
$561$	2.66346			0.112452
$562$	0.0522597	+	14.1555i	0.00220444	+	0.597114i
$563$	−4.11064	−	4.11064i	−0.173243	−	0.173243i	0.615160	−	0.788403i	$-0.289092\pi$
$563$	−4.11064	−	4.11064i	−0.173243	−	0.173243i	−0.788403	+	0.615160i	$0.789092\pi$
$564$	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
$568$	4.33697	−	0.0480358i	0.181975	−	0.00201554i
$569$			21.3698i			0.895869i	0.894066	+	0.447934i	$0.147840\pi$
$569$			21.3698i			0.895869i	−0.894066	+	0.447934i	$0.852160\pi$
$570$	−0.790574	+	0.528982i	−0.0331135	+	0.0221566i
$571$		−	17.7556i		−	0.743049i	−0.928423	−	0.371524i	$-0.878835\pi$
$571$		−	17.7556i		−	0.743049i	0.928423	−	0.371524i	$-0.121165\pi$
$572$	−0.931680	−	0.918023i	−0.0389555	−	0.0383845i
$573$	−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	0.955128	−	0.296193i	$-0.0957170\pi$
$577$	15.8282	+	15.8282i	0.658936	+	0.658936i	−0.296193	+	0.955128i	$0.595717\pi$
$578$	−2.48329	+	0.00916785i	−0.103291	+	0.000381332i
$579$	5.78449			0.240395
$580$	5.55572	−	28.5776i	0.230689	−	1.18662i
$581$	22.7927			0.945601
$582$	−1.56646	+	0.00578311i	−0.0649320	+	0.000239718i
$583$	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	$-0.797294\pi$
$587$	−5.07211	+	5.07211i	−0.209348	+	0.209348i	0.594642	+	0.803991i	$0.297294\pi$
$588$	2.97866	−	3.02297i	0.122838	−	0.124665i
$589$		−	5.78891i		−	0.238528i
$590$	−2.72112	+	13.7263i	−0.112027	+	0.565101i
$591$		−	3.09795i		−	0.127433i
$592$	−27.8822	−	27.0707i	−1.14595	−	1.11260i
$593$	14.6665	−	14.6665i	0.602280	−	0.602280i	−0.338637	−	0.940917i	$-0.609966\pi$
$593$	14.6665	−	14.6665i	0.602280	−	0.602280i	0.940917	+	0.338637i	$0.109966\pi$
$594$	−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
$598$	−0.0127679	−	3.45842i	−0.000522117	−	0.141425i
$599$	10.7934			0.441005			0.220502	−	0.975386i	$-0.429230\pi$
$599$	10.7934			0.441005			0.220502	+	0.975386i	$0.429230\pi$
$600$	−3.92203	+	1.64750i	−0.160116	+	0.0672588i
$601$	−8.15596			−0.332688			−0.166344	−	0.986068i	$-0.553196\pi$
$601$	−8.15596			−0.332688			−0.166344	+	0.986068i	$0.553196\pi$
$602$	−0.103136	−	27.9363i	−0.00420351	−	1.13860i
$603$	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	−0.525148	+	0.851011i	$0.675990\pi$
$607$	−33.9049	+	33.9049i	−1.37616	+	1.37616i	−0.851011	+	0.525148i	$0.824010\pi$
$608$	−0.104414	−	5.65589i	−0.00423455	−	0.229377i
$609$		−	7.34099i		−	0.297472i
$610$	−0.478232	+	2.41236i	−0.0193630	+	0.0976737i
$611$			0.561429i			0.0227130i
$612$	17.6879	−	17.9510i	0.714989	−	0.725626i
$613$	−8.50562	+	8.50562i	−0.343539	+	0.343539i	−0.857696	−	0.514157i	$-0.828105\pi$
$613$	−8.50562	+	8.50562i	−0.343539	+	0.343539i	0.514157	+	0.857696i	$0.328105\pi$
$614$	−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	0.0852322	−	0.996361i	$-0.472837\pi$
$617$	−22.6320	−	22.6320i	−0.911129	−	0.911129i	−0.996361	+	0.0852322i	$0.972837\pi$
$618$	−7.48496	+	0.0276331i	−0.301089	+	0.00111157i
$619$	−14.5559			−0.585051			−0.292525	−	0.956258i	$-0.594496\pi$
$619$	−14.5559			−0.585051			−0.292525	+	0.956258i	$0.594496\pi$
$620$	4.94049	−	25.4130i	0.198415	−	1.02061i
$621$	−13.5902			−0.545355
$622$	30.4062	−	0.112254i	1.21918	−	0.00450099i
$623$	−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
$628$	−17.2401	−	16.9874i	−0.687956	−	0.677872i
$629$			42.0758i			1.67767i
$630$	28.6671	−	19.1815i	1.14213	−	0.764210i
$631$			29.4769i			1.17346i	0.809784	+	0.586728i	$0.199584\pi$
$631$			29.4769i			1.17346i	−0.809784	+	0.586728i	$0.800416\pi$
$632$	−0.517092	−	46.6864i	−0.0205688	−	1.85708i
$633$	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
$638$	0.0694887	+	18.8223i	0.00275108	+	0.745183i
$639$	4.46159			0.176498
$640$	4.36859	−	24.9182i	0.172684	−	0.984977i
$641$	12.2729			0.484749			0.242374	−	0.970183i	$-0.422074\pi$
$641$	12.2729			0.484749			0.242374	+	0.970183i	$0.422074\pi$
$642$	−0.00206899	−	0.560425i	−8.16565e−5	−	0.0221182i
$643$	−8.55592	−	8.55592i	−0.337413	−	0.337413i	0.517980	−	0.855393i	$-0.326684\pi$
$643$	−8.55592	−	8.55592i	−0.337413	−	0.337413i	−0.855393	+	0.517980i	$0.826684\pi$
$644$	−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	−0.0869883	+	0.996209i	$0.527724\pi$
$647$	−27.5524	+	27.5524i	−1.08320	+	1.08320i	−0.996209	+	0.0869883i	$0.972276\pi$
$648$	0.256675	+	23.1743i	0.0100832	+	0.910371i
$649$		−	9.04725i		−	0.355136i
$650$	−0.860543	−	2.09173i	−0.0337533	−	0.0820445i
$651$		−	6.52807i		−	0.255855i
$652$	23.2164	+	22.8761i	0.909226	+	0.895898i
$653$	9.19195	−	9.19195i	0.359709	−	0.359709i	−0.503997	−	0.863706i	$-0.668138\pi$
$653$	9.19195	−	9.19195i	0.359709	−	0.359709i	0.863706	+	0.503997i	$0.168138\pi$
$654$	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
$658$	9.30542	−	0.0343540i	0.362763	−	0.00133926i
$659$	−1.02222			−0.0398199			−0.0199099	−	0.999802i	$-0.506338\pi$
$659$	−1.02222			−0.0398199			−0.0199099	+	0.999802i	$0.506338\pi$
$660$	2.28021	−	1.53793i	0.0887569	−	0.0598639i
$661$	−8.72455			−0.339346			−0.169673	−	0.985500i	$-0.554271\pi$
$661$	−8.72455			−0.339346			−0.169673	+	0.985500i	$0.554271\pi$
$662$	31.7478	−	0.117207i	1.23391	−	0.00455539i
$663$	−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
$668$	7.22746	−	7.33499i	0.279639	−	0.283799i
$669$		−	0.803516i		−	0.0310657i
$670$	−12.6565	−	18.9154i	−0.488965	−	0.730767i
$671$		−	1.59004i		−	0.0613826i
$672$	−0.117746	−	6.37806i	−0.00454216	−	0.246039i
$673$	−15.8449	+	15.8449i	−0.610777	+	0.610777i	−0.943148	−	0.332372i	$-0.892151\pi$
$673$	−15.8449	+	15.8449i	−0.610777	+	0.610777i	0.332372	+	0.943148i	$0.392151\pi$
$674$	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	0.217323	−	0.976100i	$-0.430268\pi$
$677$	−19.7428	−	19.7428i	−0.758777	−	0.758777i	−0.976100	+	0.217323i	$0.930268\pi$
$678$	−0.00668587	−	1.81099i	−0.000256769	−	0.0695507i
$679$	−13.8048			−0.529779
$680$	−22.6514	+	15.3997i	−0.868643	+	0.590551i
$681$	−0.622990			−0.0238730
$682$	0.0617937	+	16.7380i	0.00236620	+	0.640930i
$683$	25.7242	+	25.7242i	0.984311	+	0.984311i	0.999879	−	0.0155682i	$-0.00495571\pi$
$683$	25.7242	+	25.7242i	0.984311	+	0.984311i	−0.0155682	+	0.999879i	$0.504956\pi$
$684$	−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
$688$	−15.1223	−	14.6821i	−0.576532	−	0.559751i
$689$		−	3.05274i		−	0.116300i
$690$	7.13351	+	1.41416i	0.271568	+	0.0538362i
$691$		−	28.0903i		−	1.06861i	−0.845293	−	0.534303i	$-0.820574\pi$
$691$		−	28.0903i		−	1.06861i	0.845293	−	0.534303i	$-0.179426\pi$
$692$	−2.88870	+	2.93167i	−0.109812	+	0.111446i
$693$	−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
$698$	15.5241	−	0.0573122i	0.587596	−	0.00216930i
$699$	−0.117134			−0.00443043
$700$	−34.6168	+	14.3911i	−1.30839	+	0.543932i
$701$	17.5957			0.664579			0.332289	−	0.943177i	$-0.392179\pi$
$701$	17.5957			0.664579			0.332289	+	0.943177i	$0.392179\pi$
$702$	0.804123	−	0.00296868i	0.0303497	−	0.000112046i
$703$	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
$708$	1.89629	+	1.86849i	0.0712668	+	0.0702221i
$709$		−	40.9442i		−	1.53769i	−0.639434	−	0.768846i	$-0.720831\pi$
$709$		−	40.9442i		−	1.53769i	0.639434	−	0.768846i	$-0.279169\pi$
$710$	−4.75661	−	0.942961i	−0.178513	−	0.0353887i
$711$		−	48.0278i		−	1.80118i
$712$	−24.7243	+	0.273843i	−0.926582	+	0.0102627i
$713$	−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
$718$	0.114257	+	30.9487i	0.00426404	+	1.15500i
$719$	18.4285			0.687266			0.343633	−	0.939104i	$-0.388342\pi$
$719$	18.4285			0.687266			0.343633	+	0.939104i	$0.388342\pi$
$720$	4.77745	−	25.5812i	0.178045	−	0.953356i
$721$	−65.9627			−2.45658
$722$	0.00522099	+	1.41420i	0.000194305	+	0.0526312i
$723$	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	$-0.627647\pi$
$727$	14.2988	−	14.2988i	0.530314	−	0.530314i	0.920666	+	0.390352i	$0.127647\pi$
$728$	3.39155	−	0.0375643i	0.125699	−	0.00139223i
$729$			22.2360i			0.823555i
$730$	−18.1137	−	27.0712i	−0.670417	−	1.00195i
$731$			22.8204i			0.844042i
$732$	0.333269	+	0.328383i	0.0123180	+	0.0121374i
$733$	2.66770	−	2.66770i	0.0985337	−	0.0985337i	−0.656122	−	0.754655i	$-0.727804\pi$
$733$	2.66770	−	2.66770i	0.0985337	−	0.0985337i	0.754655	+	0.656122i	$0.227804\pi$
$734$	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
$738$	27.0653	−	0.0999203i	0.996288	−	0.00367812i
$739$	−38.6731			−1.42261			−0.711307	−	0.702882i	$-0.751896\pi$
$739$	−38.6731			−1.42261			−0.711307	+	0.702882i	$0.751896\pi$
$740$	24.2953	+	36.0214i	0.893114	+	1.32417i
$741$	−0.0962184			−0.00353467
$742$	−50.5978	+	0.186798i	−1.85750	+	0.00685757i
$743$	−1.38756	−	1.38756i	−0.0509046	−	0.0509046i	0.681196	−	0.732101i	$-0.261460\pi$
$743$	−1.38756	−	1.38756i	−0.0509046	−	0.0509046i	−0.732101	+	0.681196i	$0.761460\pi$
$744$	−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
$748$	12.4293	−	12.6143i	0.454462	−	0.461223i
$749$		−	4.93885i		−	0.180462i
$750$	4.66972	−	0.902442i	0.170514	−	0.0329525i
$751$			13.6253i			0.497193i	0.968607	+	0.248596i	$0.0799693\pi$
$751$			13.6253i			0.497193i	−0.968607	+	0.248596i	$0.920031\pi$
$752$	4.89053	−	5.03714i	0.178339	−	0.183686i
$753$	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	0.891295	−	0.453424i	$-0.149798\pi$
$757$	12.0474	+	12.0474i	0.437871	+	0.437871i	−0.453424	+	0.891295i	$0.649798\pi$
$758$	0.132243	+	35.8205i	0.00480328	+	1.30106i
$759$	−4.70184			−0.170666
$760$	−1.18402	+	6.21274i	−0.0429489	+	0.225360i
$761$	−9.84572			−0.356907			−0.178454	−	0.983948i	$-0.557109\pi$
$761$	−9.84572			−0.356907			−0.178454	+	0.983948i	$0.557109\pi$
$762$	−0.0136434	−	3.69557i	−0.000494248	−	0.133876i
$763$	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
$768$	−3.50222	−	3.30123i	−0.126375	−	0.119123i
$769$		−	32.7080i		−	1.17948i	−0.807593	−	0.589741i	$-0.799230\pi$
$769$		−	32.7080i		−	1.17948i	0.807593	−	0.589741i	$-0.200770\pi$
$770$	20.1445	−	13.4790i	0.725959	−	0.485748i

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)

\(f(q)\)	\(=\)	\(q+(0.00522099 + 1.41420i) q^{2} +(-0.212700 - 0.212700i) q^{3} +(-1.99995 + 0.0147671i) q^{4} +(2.19176 + 0.442915i) q^{5} +(0.299691 - 0.301912i) q^{6} +(2.65088 - 2.65088i) q^{7} +(-0.0313254 - 2.82825i) q^{8} -2.90952i q^{9} +O(q^{10})\)	\(q+(0.00522099 + 1.41420i) 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} +(-0.0313254 - 2.82825i) q^{8} -2.90952i q^{9} +(-0.614930 + 3.10191i) q^{10} -2.04453i q^{11} +(0.428530 + 0.422248i) 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} +(4.11465 - 0.0151906i) q^{18} -1.00000 q^{19} +(-4.38995 - 0.853441i) q^{20} -1.12768 q^{21} +(2.89139 - 0.0106745i) 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} +(-5.26246 + 5.34075i) q^{28} +6.50979i q^{29} +(0.790574 - 0.528982i) q^{30} +5.78891i q^{31} +(0.104414 + 5.65589i) 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} +(-0.00522099 - 1.41420i) q^{38} +0.0962184 q^{39} +(1.18402 - 6.21274i) q^{40} +6.57779 q^{41} +(-0.00588763 - 1.59478i) 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} +(-0.863272 - 0.838145i) q^{48} -7.05428i q^{49} +(-2.72166 + 6.52630i) q^{50} +1.30273i q^{51} +(0.449014 - 0.455694i) 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} +(-9.20617 + 0.0339876i) q^{58} +4.42510 q^{59} +(0.752216 + 1.11527i) q^{60} +0.777701 q^{61} +(-8.18670 + 0.0302239i) 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} +(6.16975 + 6.07931i) q^{68} -2.29971i q^{69} +(6.59268 + 9.85289i) q^{70} +1.53345i q^{71} +(-8.22885 + 0.0911417i) 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} +(0.000502356 + 0.136072i) q^{78} +16.5071 q^{79} +(8.79226 + 1.64201i) q^{80} -8.19384 q^{81} +(0.0343426 + 9.30234i) 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} +(-5.78246 + 0.0640457i) q^{88} -8.74189i q^{89} +(9.02507 + 1.78915i) q^{90} +1.19917i q^{91} +(-10.8915 - 10.7319i) 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} +(9.97619 - 0.0368304i) 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	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 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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