LMFDB - Embedded newform 380.2.k.d.343.13

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			343.13
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.13

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	−0.765837	−	0.643035i	$-0.777675\pi$
$3$	−0.212700	+	0.212700i	−0.122803	+	0.122803i	0.643035	+	0.765837i	$0.277675\pi$
$4$	−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	$0.000617103\pi$
$7$	2.65088	+	2.65088i	1.00194	+	1.00194i	0.00193869	+	0.999998i	$0.499383\pi$
$8$	−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	$0.0997349\pi$
$11$			2.04453i			0.616450i	−0.951314	+	0.308225i	$0.900265\pi$
$12$	0.428530	−	0.422248i	0.123706	−	0.121893i
$13$	−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	$0.426005\pi$
$18$	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	0.136600	−	0.990626i	$-0.456382\pi$
$23$	5.40599	−	5.40599i	1.12723	−	1.12723i	0.990626	−	0.136600i	$-0.0436176\pi$
$24$	−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	$-0.793405\pi$
$29$		−	6.50979i		−	1.20884i	0.796667	−	0.604419i	$-0.206595\pi$
$30$	0.790574	+	0.528982i	0.144338	+	0.0965785i
$31$		−	5.78891i		−	1.03972i	−0.854252	−	0.519860i	$-0.825984\pi$
$31$		−	5.78891i		−	1.03972i	0.854252	−	0.519860i	$-0.174016\pi$
$32$	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	−0.139124	+	0.990275i	$0.544429\pi$
$37$	−6.86987	+	6.86987i	−1.12940	+	1.12940i	−0.990275	+	0.139124i	$0.955571\pi$
$38$	−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	−0.931625	−	0.363422i	$-0.881608\pi$
$43$	−3.72596	+	3.72596i	−0.568203	+	0.568203i	0.363422	+	0.931625i	$0.381608\pi$
$44$	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	0.791805	−	0.610773i	$-0.209141\pi$
$47$	1.24109	+	1.24109i	0.181032	+	0.181032i	−0.610773	+	0.791805i	$0.709141\pi$
$48$	−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	0.0705463	−	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
$58$	−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	0.324240	−	0.945975i	$-0.394891\pi$
$67$	−5.08912	−	5.08912i	−0.621734	−	0.621734i	−0.945975	+	0.324240i	$0.894891\pi$
$68$	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	$-0.970996\pi$
$71$		−	1.53345i		−	0.181986i	0.995852	−	0.0909932i	$-0.0290042\pi$
$72$	−8.22885	−	0.0911417i	−0.969780	−	0.0107412i
$73$	−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
$78$	0.000502356	−	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	−0.430638	−	0.902525i	$-0.641711\pi$
$83$	4.29909	−	4.29909i	0.471887	−	0.471887i	0.902525	+	0.430638i	$0.141711\pi$
$84$	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	$0.153342\pi$
$89$			8.74189i			0.926639i	−0.886191	+	0.463319i	$0.846658\pi$
$90$	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	−0.826830	−	0.562452i	$-0.809858\pi$
$97$	−2.60382	+	2.60382i	−0.264377	+	0.264377i	0.562452	+	0.826830i	$0.309858\pi$
$98$	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	−0.260419	+	0.965496i	$0.583861\pi$
$103$	−12.4417	+	12.4417i	−1.22591	+	1.22591i	−0.965496	+	0.260419i	$0.916139\pi$
$104$	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	0.750700	−	0.660643i	$-0.229716\pi$
$107$	0.931552	+	0.931552i	0.0900565	+	0.0900565i	−0.660643	+	0.750700i	$0.729716\pi$
$108$	2.49528	+	2.53241i	0.240109	+	0.243681i
$109$		−	20.2411i		−	1.93874i	−0.245597	−	0.969372i	$-0.578984\pi$
$109$		−	20.2411i		−	1.93874i	0.245597	−	0.969372i	$-0.421016\pi$
$110$	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	0.834377	−	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
$118$	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	0.925017	−	0.379926i	$-0.124051\pi$
$127$	6.14286	+	6.14286i	0.545091	+	0.545091i	−0.379926	+	0.925017i	$0.624051\pi$
$128$	−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	$-0.881891\pi$
$131$		−	8.30018i		−	0.725190i	0.931947	−	0.362595i	$-0.118109\pi$
$132$	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	−0.559032	−	0.829146i	$-0.688827\pi$
$137$	3.16161	−	3.16161i	0.270115	−	0.270115i	0.829146	+	0.559032i	$0.188827\pi$
$138$	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	$0.131131\pi$
$149$			9.77519i			0.800815i	−0.916337	+	0.400407i	$0.868869\pi$
$150$	1.96705	+	0.809247i	0.160609	+	0.0660747i
$151$		−	4.21919i		−	0.343353i	−0.985153	−	0.171676i	$-0.945082\pi$
$151$		−	4.21919i		−	0.343353i	0.985153	−	0.171676i	$-0.0549184\pi$
$152$	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	−0.277727	−	0.960660i	$-0.589581\pi$
$157$	8.55712	−	8.55712i	0.682933	−	0.682933i	0.960660	+	0.277727i	$0.0895812\pi$
$158$	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	−0.995659	−	0.0930729i	$-0.970331\pi$
$163$	−11.5235	+	11.5235i	−0.902586	+	0.902586i	0.0930729	+	0.995659i	$0.470331\pi$
$164$	−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	0.552071	−	0.833797i	$-0.313838\pi$
$167$	−3.64071	−	3.64071i	−0.281727	−	0.281727i	−0.833797	+	0.552071i	$0.813838\pi$
$168$	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	0.760256	−	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
$178$	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	$0.0739087\pi$
$191$			6.36037i			0.460220i	−0.973165	+	0.230110i	$0.926091\pi$
$192$	1.73887	−	1.66350i	0.125492	−	0.120053i
$193$	−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	$0.130425\pi$
$198$	−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	$-0.846755\pi$
$211$		−	13.4524i		−	0.926098i	0.886333	−	0.463049i	$-0.153245\pi$
$212$	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	−0.641030	−	0.767516i	$-0.721492\pi$
$223$	1.88885	−	1.88885i	0.126486	−	0.126486i	0.767516	+	0.641030i	$0.221492\pi$
$224$	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	0.754035	−	0.656834i	$-0.228105\pi$
$227$	1.46448	+	1.46448i	0.0972007	+	0.0972007i	−0.656834	+	0.754035i	$0.728105\pi$
$228$	−0.428530	+	0.422248i	−0.0283801	+	0.0279641i
$229$		−	3.08873i		−	0.204109i	−0.994779	−	0.102055i	$-0.967458\pi$
$229$		−	3.08873i		−	0.204109i	0.994779	−	0.102055i	$-0.0325417\pi$
$230$	−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	0.716069	−	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
$238$	−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	$-0.756607\pi$
$251$		−	21.9355i		−	1.38456i	0.721630	−	0.692279i	$-0.243393\pi$
$252$	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	−0.927907	−	0.372811i	$-0.878394\pi$
$257$	−8.89886	+	8.89886i	−0.555096	+	0.555096i	0.372811	+	0.927907i	$0.378394\pi$
$258$	−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	−0.999942	−	0.0107906i	$-0.996565\pi$
$263$	−16.0413	+	16.0413i	−0.989151	+	0.989151i	0.0107906	+	0.999942i	$0.496565\pi$
$264$	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	$0.0681083\pi$
$269$			6.96525i			0.424679i	−0.977196	+	0.212339i	$0.931892\pi$
$270$	−3.12603	+	4.67191i	−0.190244	+	0.284323i
$271$			7.23572i			0.439539i	0.975552	+	0.219769i	$0.0705305\pi$
$271$			7.23572i			0.439539i	−0.975552	+	0.219769i	$0.929470\pi$
$272$	−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	−0.996131	−	0.0878773i	$-0.971992\pi$
$277$	−15.1164	+	15.1164i	−0.908254	+	0.908254i	0.0878773	+	0.996131i	$0.471992\pi$
$278$	−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	−0.408474	−	0.912770i	$-0.633939\pi$
$283$	8.48356	−	8.48356i	0.504295	−	0.504295i	0.912770	+	0.408474i	$0.133939\pi$
$284$	−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	0.940976	−	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
$298$	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	0.591053	−	0.806633i	$-0.298712\pi$
$307$	−3.77726	−	3.77726i	−0.215579	−	0.215579i	−0.806633	+	0.591053i	$0.798712\pi$
$308$	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	$0.208667\pi$
$311$			21.5006i			1.21919i	−0.792715	+	0.609593i	$0.791333\pi$
$312$	−0.00301408	+	0.272130i	−0.000170639	+	0.0154063i
$313$	−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	$0.247077\pi$
$318$	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	$0.211636\pi$
$331$			22.4492i			1.23392i	−0.786994	+	0.616960i	$0.788364\pi$
$332$	−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	−0.824095	−	0.566451i	$-0.808316\pi$
$337$	−4.72972	+	4.72972i	−0.257644	+	0.257644i	0.566451	+	0.824095i	$0.308316\pi$
$338$	−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	−0.849363	−	0.527809i	$-0.823014\pi$
$347$	−25.6539	−	25.6539i	−1.37717	−	1.37717i	−0.527809	−	0.849363i	$-0.676986\pi$
$348$	−2.74875	−	2.78964i	−0.147348	−	0.149541i
$349$			10.9773i			0.587600i	0.955867	+	0.293800i	$0.0949199\pi$
$349$			10.9773i			0.587600i	−0.955867	+	0.293800i	$0.905080\pi$
$350$	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	0.994892	+	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
$358$	−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	0.872175	+	0.489195i	$0.162709\pi$
$367$	26.0801	+	26.0801i	1.36137	+	1.36137i	0.489195	+	0.872175i	$0.337291\pi$
$368$	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	0.582961	−	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
$378$	−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	0.143867	−	0.989597i	$-0.454046\pi$
$383$	22.1823	−	22.1823i	1.13346	−	1.13346i	0.989597	−	0.143867i	$-0.0459538\pi$
$384$	−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	$-0.763976\pi$
$389$		−	26.6415i		−	1.35078i	0.737462	−	0.675388i	$-0.236024\pi$
$390$	−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	−0.0217671	+	0.999763i	$0.506929\pi$
$397$	−20.3538	+	20.3538i	−1.02153	+	1.02153i	−0.999763	+	0.0217671i	$0.993071\pi$
$398$	−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	$0.0276042\pi$
$409$			3.50326i			0.173225i	−0.996242	+	0.0866126i	$0.972396\pi$
$410$	−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	$-0.822195\pi$
$431$		−	22.0058i		−	1.05998i	0.848003	−	0.529992i	$-0.177805\pi$
$432$	−4.95303	−	5.10152i	−0.238303	−	0.245447i
$433$	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
$438$	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	−0.601222	−	0.799082i	$-0.705319\pi$
$443$	4.16446	−	4.16446i	0.197859	−	0.197859i	0.799082	+	0.601222i	$0.205319\pi$
$444$	−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	$-0.967443\pi$
$449$		−	4.32706i		−	0.204207i	0.994774	−	0.102103i	$-0.0325572\pi$
$450$	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	−0.395714	−	0.918374i	$-0.629503\pi$
$457$	11.1732	−	11.1732i	0.522659	−	0.522659i	0.918374	+	0.395714i	$0.129503\pi$
$458$	−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	−0.0789948	+	0.996875i	$0.525171\pi$
$463$	−23.1500	+	23.1500i	−1.07587	+	1.07587i	−0.996875	+	0.0789948i	$0.974829\pi$
$464$	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	0.356037	−	0.934472i	$-0.384128\pi$
$467$	−12.5001	−	12.5001i	−0.578435	−	0.578435i	−0.934472	+	0.356037i	$0.884128\pi$
$468$	−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	0.997906	+	0.0646845i	$0.0206041\pi$
$487$	23.4493	+	23.4493i	1.06259	+	1.06259i	0.0646845	+	0.997906i	$0.479396\pi$
$488$	−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	$0.00770731\pi$
$491$			1.07295i			0.0484217i	−0.999707	+	0.0242108i	$0.992293\pi$
$492$	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	−0.996723	−	0.0808962i	$-0.974222\pi$
$503$	−20.5398	+	20.5398i	−0.915826	+	0.915826i	0.0808962	+	0.996723i	$0.474222\pi$
$504$	−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	$0.243955\pi$
$509$			31.2945i			1.38710i	−0.720406	+	0.693552i	$0.756045\pi$
$510$	−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	−0.585681	−	0.810542i	$-0.699173\pi$
$523$	5.14238	−	5.14238i	0.224861	−	0.224861i	0.810542	+	0.585681i	$0.199173\pi$
$524$	−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	0.980789	−	0.195071i	$-0.0624936\pi$
$547$	18.3764	+	18.3764i	0.785719	+	0.785719i	−0.195071	+	0.980789i	$0.562494\pi$
$548$	−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	−0.0603095	−	0.998180i	$-0.519209\pi$
$557$	22.1345	−	22.1345i	0.937870	−	0.937870i	0.998180	+	0.0603095i	$0.0192088\pi$
$558$	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	−0.788403	−	0.615160i	$-0.789092\pi$
$563$	−4.11064	+	4.11064i	−0.173243	+	0.173243i	0.615160	+	0.788403i	$0.289092\pi$
$564$	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	$-0.852160\pi$
$569$		−	21.3698i		−	0.895869i	0.894066	−	0.447934i	$-0.147840\pi$
$570$	−0.790574	−	0.528982i	−0.0331135	−	0.0221566i
$571$			17.7556i			0.743049i	0.928423	+	0.371524i	$0.121165\pi$
$571$			17.7556i			0.743049i	−0.928423	+	0.371524i	$0.878835\pi$
$572$	−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	−0.296193	−	0.955128i	$-0.595717\pi$
$577$	15.8282	−	15.8282i	0.658936	−	0.658936i	0.955128	+	0.296193i	$0.0957170\pi$
$578$	−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	0.594642	−	0.803991i	$-0.297294\pi$
$587$	−5.07211	−	5.07211i	−0.209348	−	0.209348i	−0.803991	+	0.594642i	$0.797294\pi$
$588$	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	0.940917	−	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
$598$	−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	−0.851011	−	0.525148i	$-0.824010\pi$
$607$	−33.9049	−	33.9049i	−1.37616	−	1.37616i	−0.525148	−	0.851011i	$-0.675990\pi$
$608$	−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	0.514157	−	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	$0.472837\pi$
$618$	−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	$-0.800416\pi$
$631$		−	29.4769i		−	1.17346i	0.809784	−	0.586728i	$-0.199584\pi$
$632$	−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	−0.855393	−	0.517980i	$-0.826684\pi$
$643$	−8.55592	+	8.55592i	−0.337413	+	0.337413i	0.517980	+	0.855393i	$0.326684\pi$
$644$	−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	$-0.972276\pi$
$647$	−27.5524	−	27.5524i	−1.08320	−	1.08320i	−0.0869883	−	0.996209i	$-0.527724\pi$
$648$	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	0.863706	−	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
$658$	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	0.332372	−	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	$0.430268\pi$
$678$	−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	−0.0155682	−	0.999879i	$-0.504956\pi$
$683$	25.7242	−	25.7242i	0.984311	−	0.984311i	0.999879	+	0.0155682i	$0.00495571\pi$
$684$	−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	$0.179426\pi$
$691$			28.0903i			1.06861i	−0.845293	+	0.534303i	$0.820574\pi$
$692$	−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	$0.279169\pi$
$709$			40.9442i			1.53769i	−0.639434	+	0.768846i	$0.720831\pi$
$710$	−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	0.920666	−	0.390352i	$-0.127647\pi$
$727$	14.2988	+	14.2988i	0.530314	+	0.530314i	−0.390352	+	0.920666i	$0.627647\pi$
$728$	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	0.754655	−	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
$738$	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	−0.732101	−	0.681196i	$-0.761460\pi$
$743$	−1.38756	+	1.38756i	−0.0509046	+	0.0509046i	0.681196	+	0.732101i	$0.261460\pi$
$744$	−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	$-0.920031\pi$
$751$		−	13.6253i		−	0.497193i	0.968607	−	0.248596i	$-0.0799693\pi$
$752$	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	−0.453424	−	0.891295i	$-0.649798\pi$
$757$	12.0474	−	12.0474i	0.437871	−	0.437871i	0.891295	+	0.453424i	$0.149798\pi$
$758$	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	$0.200770\pi$
$769$			32.7080i			1.17948i	−0.807593	+	0.589741i	$0.799230\pi$
$770$	20.1445	+	13.4790i	0.725959	+	0.485748i
$771$

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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