LMFDB - Embedded newform 380.2.k.d.267.14

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			267.14
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0365245 - 1.41374i) q^{2} +(0.389264 + 0.389264i) q^{3} +(-1.99733 - 0.103273i) q^{4} +(-1.49421 + 1.66354i) q^{5} +(0.564536 - 0.536101i) q^{6} +(2.85353 - 2.85353i) q^{7} +(-0.218952 + 2.81994i) q^{8} -2.69695i q^{9} +O(q^{10})$	\(q+(0.0365245 - 1.41374i) q^{2} +(0.389264 + 0.389264i) q^{3} +(-1.99733 - 0.103273i) q^{4} +(-1.49421 + 1.66354i) q^{5} +(0.564536 - 0.536101i) q^{6} +(2.85353 - 2.85353i) q^{7} +(-0.218952 + 2.81994i) q^{8} -2.69695i q^{9} +(2.29723 + 2.17318i) q^{10} +0.969790i q^{11} +(-0.737288 - 0.817689i) q^{12} +(4.39116 - 4.39116i) q^{13} +(-3.92994 - 4.13838i) q^{14} +(-1.22919 + 0.0659140i) q^{15} +(3.97867 + 0.412539i) q^{16} +(-2.80193 - 2.80193i) q^{17} +(-3.81279 - 0.0985048i) q^{18} -1.00000 q^{19} +(3.15622 - 3.16832i) q^{20} +2.22155 q^{21} +(1.37103 + 0.0354211i) q^{22} +(0.648103 + 0.648103i) q^{23} +(-1.18293 + 1.01247i) q^{24} +(-0.534700 - 4.97133i) q^{25} +(-6.04759 - 6.36836i) q^{26} +(2.21761 - 2.21761i) q^{27} +(-5.99414 + 5.40476i) q^{28} -6.30270i q^{29} +(0.0482896 + 1.74017i) q^{30} +3.56684i q^{31} +(0.728543 - 5.60974i) q^{32} +(-0.377504 + 0.377504i) q^{33} +(-4.06354 + 3.85887i) q^{34} +(0.483189 + 9.01072i) q^{35} +(-0.278521 + 5.38670i) q^{36} +(3.34305 + 3.34305i) q^{37} +(-0.0365245 + 1.41374i) q^{38} +3.41864 q^{39} +(-4.36391 - 4.57780i) q^{40} +1.73702 q^{41} +(0.0811412 - 3.14070i) q^{42} +(6.20437 + 6.20437i) q^{43} +(0.100153 - 1.93699i) q^{44} +(4.48647 + 4.02979i) q^{45} +(0.939922 - 0.892579i) q^{46} +(-7.76694 + 7.76694i) q^{47} +(1.38816 + 1.70934i) q^{48} -9.28530i q^{49} +(-7.04770 + 0.574352i) q^{50} -2.18138i q^{51} +(-9.22410 + 8.31712i) q^{52} +(-7.60538 + 7.60538i) q^{53} +(-3.05414 - 3.21613i) q^{54} +(-1.61328 - 1.44907i) q^{55} +(7.42200 + 8.67158i) q^{56} +(-0.389264 - 0.389264i) q^{57} +(-8.91039 - 0.230203i) q^{58} +12.9884 q^{59} +(2.46191 - 0.00471017i) q^{60} -3.91061 q^{61} +(5.04260 + 0.130277i) q^{62} +(-7.69583 - 7.69583i) q^{63} +(-7.90412 - 1.23486i) q^{64} +(0.743555 + 13.8662i) q^{65} +(0.519905 + 0.547481i) q^{66} +(0.712621 - 0.712621i) q^{67} +(5.30702 + 5.88575i) q^{68} +0.504566i q^{69} +(12.7565 - 0.353992i) q^{70} -5.91449i q^{71} +(7.60523 + 0.590503i) q^{72} +(2.60253 - 2.60253i) q^{73} +(4.84831 - 4.60411i) q^{74} +(1.72702 - 2.14330i) q^{75} +(1.99733 + 0.103273i) q^{76} +(2.76733 + 2.76733i) q^{77} +(0.124864 - 4.83307i) q^{78} -9.60097 q^{79} +(-6.63122 + 6.00224i) q^{80} -6.36437 q^{81} +(0.0634439 - 2.45570i) q^{82} +(10.3046 + 10.3046i) q^{83} +(-4.43718 - 0.229425i) q^{84} +(8.84777 - 0.474450i) q^{85} +(8.99799 - 8.54476i) q^{86} +(2.45341 - 2.45341i) q^{87} +(-2.73475 - 0.212338i) q^{88} -2.69278i q^{89} +(5.86095 - 6.19552i) q^{90} -25.0607i q^{91} +(-1.22755 - 1.36141i) q^{92} +(-1.38844 + 1.38844i) q^{93} +(10.6968 + 11.2641i) q^{94} +(1.49421 - 1.66354i) q^{95} +(2.46726 - 1.90007i) q^{96} +(2.26579 + 2.26579i) q^{97} +(-13.1270 - 0.339141i) q^{98} +2.61547 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 $

$2$	0.0365245	−	1.41374i	0.0258267	−	0.999666i
$2$	0.0365245	−	1.41374i	0.0258267	−	0.999666i
$3$	0.389264	+	0.389264i	0.224741	+	0.224741i	0.810492	−	0.585750i	$-0.199200\pi$
$3$	0.389264	+	0.389264i	0.224741	+	0.224741i	−0.585750	+	0.810492i	$0.699200\pi$
$4$	−1.99733	−	0.103273i	−0.998666	−	0.0516363i
$5$	−1.49421	+	1.66354i	−0.668229	+	0.743956i
$5$	−1.49421	+	1.66354i	−0.668229	+	0.743956i
$6$	0.564536	−	0.536101i	0.230471	−	0.218862i
$7$	2.85353	−	2.85353i	1.07853	−	1.07853i	0.0818930	−	0.996641i	$-0.473903\pi$
$7$	2.85353	−	2.85353i	1.07853	−	1.07853i	0.996641	−	0.0818930i	$-0.0260966\pi$
$8$	−0.218952	+	2.81994i	−0.0774113	+	0.996999i
$9$		−	2.69695i		−	0.898983i
$10$	2.29723	+	2.17318i	0.726449	+	0.687220i
$11$			0.969790i			0.292403i	0.989255	+	0.146201i	$0.0467047\pi$
$11$			0.969790i			0.292403i	−0.989255	+	0.146201i	$0.953295\pi$
$12$	−0.737288	−	0.817689i	−0.212837	−	0.236046i
$13$	4.39116	−	4.39116i	1.21789	−	1.21789i	0.249520	−	0.968370i	$-0.419727\pi$
$13$	4.39116	−	4.39116i	1.21789	−	1.21789i	0.968370	−	0.249520i	$-0.0802728\pi$
$14$	−3.92994	−	4.13838i	−1.05032	−	1.10603i
$15$	−1.22919	+	0.0659140i	−0.317376	+	0.0170189i
$16$	3.97867	+	0.412539i	0.994667	+	0.103135i
$17$	−2.80193	−	2.80193i	−0.679568	−	0.679568i	0.280335	−	0.959902i	$-0.409555\pi$
$17$	−2.80193	−	2.80193i	−0.679568	−	0.679568i	−0.959902	+	0.280335i	$0.909555\pi$
$18$	−3.81279	−	0.0985048i	−0.898683	−	0.0232178i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	3.15622	−	3.16832i	0.705753	−	0.708458i
$21$	2.22155			0.484783
$22$	1.37103	+	0.0354211i	0.292305	+	0.00755181i
$23$	0.648103	+	0.648103i	0.135139	+	0.135139i	0.771440	−	0.636302i	$-0.219537\pi$
$23$	0.648103	+	0.648103i	0.135139	+	0.135139i	−0.636302	+	0.771440i	$0.719537\pi$
$24$	−1.18293	+	1.01247i	−0.241465	+	0.206669i
$25$	−0.534700	−	4.97133i	−0.106940	−	0.994265i
$26$	−6.04759	−	6.36836i	−1.18603	−	1.24894i
$27$	2.21761	−	2.21761i	0.426780	−	0.426780i
$28$	−5.99414	+	5.40476i	−1.13279	+	1.02140i
$29$		−	6.30270i		−	1.17038i	−0.810895	−	0.585191i	$-0.801020\pi$
$29$		−	6.30270i		−	1.17038i	0.810895	−	0.585191i	$-0.198980\pi$
$30$	0.0482896	+	1.74017i	0.00881644	+	0.317710i
$31$			3.56684i			0.640624i	0.947312	+	0.320312i	$0.103788\pi$
$31$			3.56684i			0.640624i	−0.947312	+	0.320312i	$0.896212\pi$
$32$	0.728543	−	5.60974i	0.128789	−	0.991672i
$33$	−0.377504	+	0.377504i	−0.0657150	+	0.0657150i
$34$	−4.06354	+	3.85887i	−0.696892	+	0.661790i
$35$	0.483189	+	9.01072i	0.0816738	+	1.52309i
$36$	−0.278521	+	5.38670i	−0.0464201	+	0.897783i
$37$	3.34305	+	3.34305i	0.549594	+	0.549594i	0.926323	−	0.376729i	$-0.122951\pi$
$37$	3.34305	+	3.34305i	0.549594	+	0.549594i	−0.376729	+	0.926323i	$0.622951\pi$
$38$	−0.0365245	+	1.41374i	−0.00592506	+	0.229339i
$39$	3.41864			0.547420
$40$	−4.36391	−	4.57780i	−0.689995	−	0.723814i
$41$	1.73702			0.271277			0.135639	−	0.990758i	$-0.456691\pi$
$41$	1.73702			0.271277			0.135639	+	0.990758i	$0.456691\pi$
$42$	0.0811412	−	3.14070i	0.0125204	−	0.484621i
$43$	6.20437	+	6.20437i	0.946157	+	0.946157i	0.998623	−	0.0524655i	$-0.0167080\pi$
$43$	6.20437	+	6.20437i	0.946157	+	0.946157i	−0.0524655	+	0.998623i	$0.516708\pi$
$44$	0.100153	−	1.93699i	0.0150986	−	0.292013i
$45$	4.48647	+	4.02979i	0.668803	+	0.600726i
$46$	0.939922	−	0.892579i	0.138584	−	0.131604i
$47$	−7.76694	+	7.76694i	−1.13293	+	1.13293i	−0.143237	+	0.989688i	$0.545751\pi$
$47$	−7.76694	+	7.76694i	−1.13293	+	1.13293i	−0.989688	+	0.143237i	$0.954249\pi$
$48$	1.38816	+	1.70934i	0.200364	+	0.246722i
$49$		−	9.28530i		−	1.32647i
$50$	−7.04770	+	0.574352i	−0.996696	+	0.0812257i
$51$		−	2.18138i		−	0.305454i
$52$	−9.22410	+	8.31712i	−1.27915	+	1.15338i
$53$	−7.60538	+	7.60538i	−1.04468	+	1.04468i	−0.0457258	+	0.998954i	$0.514560\pi$
$53$	−7.60538	+	7.60538i	−1.04468	+	1.04468i	−0.998954	+	0.0457258i	$0.985440\pi$
$54$	−3.05414	−	3.21613i	−0.415615	−	0.437660i
$55$	−1.61328	−	1.44907i	−0.217535	−	0.195392i
$56$	7.42200	+	8.67158i	0.991807	+	1.15879i
$57$	−0.389264	−	0.389264i	−0.0515592	−	0.0515592i
$58$	−8.91039	−	0.230203i	−1.16999	−	0.0302272i
$59$	12.9884			1.69095			0.845475	−	0.534014i	$-0.179317\pi$
$59$	12.9884			1.69095			0.845475	+	0.534014i	$0.179317\pi$
$60$	2.46191	−	0.00471017i	0.317832	−	0.000608080i
$61$	−3.91061			−0.500702			−0.250351	−	0.968155i	$-0.580546\pi$
$61$	−3.91061			−0.500702			−0.250351	+	0.968155i	$0.580546\pi$
$62$	5.04260	+	0.130277i	0.640410	+	0.0165452i
$63$	−7.69583	−	7.69583i	−0.969583	−	0.969583i
$64$	−7.90412	−	1.23486i	−0.988015	−	0.154358i
$65$	0.743555	+	13.8662i	0.0922267	+	1.71988i
$66$	0.519905	+	0.547481i	0.0639959	+	0.0673903i
$67$	0.712621	−	0.712621i	0.0870606	−	0.0870606i	−0.662235	−	0.749296i	$-0.730392\pi$
$67$	0.712621	−	0.712621i	0.0870606	−	0.0870606i	0.749296	+	0.662235i	$0.230392\pi$
$68$	5.30702	+	5.88575i	0.643571	+	0.713751i
$69$			0.504566i			0.0607426i
$70$	12.7565	−	0.353992i	1.52469	−	0.0423101i
$71$		−	5.91449i		−	0.701921i	−0.936390	−	0.350960i	$-0.885855\pi$
$71$		−	5.91449i		−	0.701921i	0.936390	−	0.350960i	$-0.114145\pi$
$72$	7.60523	+	0.590503i	0.896285	+	0.0695914i
$73$	2.60253	−	2.60253i	0.304603	−	0.304603i	−0.538208	−	0.842812i	$-0.680899\pi$
$73$	2.60253	−	2.60253i	0.304603	−	0.304603i	0.842812	+	0.538208i	$0.180899\pi$
$74$	4.84831	−	4.60411i	0.563605	−	0.535216i
$75$	1.72702	−	2.14330i	0.199419	−	0.247486i
$76$	1.99733	+	0.103273i	0.229110	+	0.0118462i
$77$	2.76733	+	2.76733i	0.315366	+	0.315366i
$78$	0.124864	−	4.83307i	0.0141381	−	0.547238i
$79$	−9.60097			−1.08019			−0.540097	−	0.841603i	$-0.681612\pi$
$79$	−9.60097			−1.08019			−0.540097	+	0.841603i	$0.681612\pi$
$80$	−6.63122	+	6.00224i	−0.741393	+	0.671071i
$81$	−6.36437			−0.707152
$82$	0.0634439	−	2.45570i	0.00700621	−	0.271187i
$83$	10.3046	+	10.3046i	1.13107	+	1.13107i	0.989999	+	0.141073i	$0.0450552\pi$
$83$	10.3046	+	10.3046i	1.13107	+	1.13107i	0.141073	+	0.989999i	$0.454945\pi$
$84$	−4.43718	−	0.229425i	−0.484136	−	0.0250324i
$85$	8.84777	−	0.474450i	0.959675	−	0.0514614i
$86$	8.99799	−	8.54476i	0.970278	−	0.921405i
$87$	2.45341	−	2.45341i	0.263033	−	0.263033i
$88$	−2.73475	−	0.212338i	−0.291525	−	0.0226353i
$89$		−	2.69278i		−	0.285435i	−0.989763	−	0.142717i	$-0.954416\pi$
$89$		−	2.69278i		−	0.285435i	0.989763	−	0.142717i	$-0.0455840\pi$
$90$	5.86095	−	6.19552i	0.617799	−	0.653065i
$91$		−	25.0607i		−	2.62707i
$92$	−1.22755	−	1.36141i	−0.127981	−	0.141937i
$93$	−1.38844	+	1.38844i	−0.143975	+	0.143975i
$94$	10.6968	+	11.2641i	1.10329	+	1.16181i
$95$	1.49421	−	1.66354i	0.153302	−	0.170675i
$96$	2.46726	−	1.90007i	0.251814	−	0.193925i
$97$	2.26579	+	2.26579i	0.230056	+	0.230056i	0.812716	−	0.582660i	$-0.197988\pi$
$97$	2.26579	+	2.26579i	0.230056	+	0.230056i	−0.582660	+	0.812716i	$0.697988\pi$
$98$	−13.1270	−	0.339141i	−1.32603	−	0.0342585i
$99$	2.61547			0.262865
$100$	0.554572	+	9.98461i	0.0554572	+	0.998461i
$101$	−0.419166			−0.0417086			−0.0208543	−	0.999783i	$-0.506639\pi$
$101$	−0.419166			−0.0417086			−0.0208543	+	0.999783i	$0.506639\pi$
$102$	−3.08391	−	0.0796738i	−0.305352	−	0.00788888i
$103$	−2.41451	−	2.41451i	−0.237909	−	0.237909i	0.578075	−	0.815984i	$-0.303804\pi$
$103$	−2.41451	−	2.41451i	−0.237909	−	0.237909i	−0.815984	+	0.578075i	$0.803804\pi$
$104$	11.4214	+	13.3443i	1.11996	+	1.30851i
$105$	−3.31946	+	3.69563i	−0.323946	+	0.360657i
$106$	10.4743	+	11.0298i	1.01735	+	1.07131i
$107$	−8.80941	+	8.80941i	−0.851638	+	0.851638i	−0.990335	−	0.138697i	$-0.955709\pi$
$107$	−8.80941	+	8.80941i	−0.851638	+	0.851638i	0.138697	+	0.990335i	$0.455709\pi$
$108$	−4.65833	+	4.20029i	−0.448248	+	0.404173i
$109$			8.13761i			0.779442i	0.920933	+	0.389721i	$0.127429\pi$
$109$			8.13761i			0.779442i	−0.920933	+	0.389721i	$0.872571\pi$
$110$	−2.10753	+	2.22784i	−0.200945	+	0.212416i
$111$			2.60265i			0.247033i
$112$	12.5305	−	10.1761i	1.18402	−	0.961548i
$113$	−3.71700	+	3.71700i	−0.349666	+	0.349666i	−0.859985	−	0.510319i	$-0.829527\pi$
$113$	−3.71700	+	3.71700i	−0.349666	+	0.349666i	0.510319	+	0.859985i	$0.329527\pi$
$114$	−0.564536	+	0.536101i	−0.0528736	+	0.0502104i
$115$	−2.04654	+	0.109743i	−0.190841	+	0.0102336i
$116$	−0.650896	+	12.5886i	−0.0604342	+	1.16882i
$117$	−11.8427	−	11.8427i	−1.09486	−	1.09486i
$118$	0.474397	−	18.3623i	0.0436718	−	1.69039i
$119$	−15.9908			−1.46587
$120$	0.0832613	−	3.48068i	0.00760068	−	0.317741i
$121$	10.0595			0.914501
$122$	−0.142833	+	5.52859i	−0.0129315	+	0.500535i
$123$	0.676160	+	0.676160i	0.0609673	+	0.0609673i
$124$	0.368357	−	7.12417i	0.0330794	−	0.639769i
$125$	9.06893	+	6.53869i	0.811150	+	0.584838i
$126$	−11.1610	+	10.5988i	−0.994301	+	0.944219i
$127$	−9.13391	+	9.13391i	−0.810503	+	0.810503i	−0.984709	−	0.174206i	$-0.944264\pi$
$127$	−9.13391	+	9.13391i	−0.810503	+	0.810503i	0.174206	+	0.984709i	$0.444264\pi$
$128$	−2.03447	+	11.1293i	−0.179824	+	0.983699i
$129$			4.83027i			0.425281i
$130$	19.6303	−	0.544740i	1.72169	−	0.0477769i
$131$		−	10.7793i		−	0.941795i	−0.882188	−	0.470897i	$-0.843930\pi$
$131$		−	10.7793i		−	0.941795i	0.882188	−	0.470897i	$-0.156070\pi$
$132$	0.792986	−	0.715015i	0.0690206	−	0.0622341i
$133$	−2.85353	+	2.85353i	−0.247433	+	0.247433i
$134$	−0.981434	−	1.03349i	−0.0847830	−	0.0892800i
$135$	0.375508	+	7.00265i	0.0323186	+	0.602692i
$136$	8.51476	−	7.28778i	0.730135	−	0.624922i
$137$	4.46829	+	4.46829i	0.381752	+	0.381752i	0.871733	−	0.489981i	$-0.162996\pi$
$137$	4.46829	+	4.46829i	0.381752	+	0.381752i	−0.489981	+	0.871733i	$0.662996\pi$
$138$	0.713326	+	0.0184290i	0.0607223	+	0.00156878i
$139$	9.92662			0.841965			0.420982	−	0.907069i	$-0.361685\pi$
$139$	9.92662			0.841965			0.420982	+	0.907069i	$0.361685\pi$
$140$	−0.0345283	−	18.0473i	−0.00291817	−	1.52527i
$141$	−6.04678			−0.509230
$142$	−8.36156	−	0.216024i	−0.701687	−	0.0181283i
$143$	4.25851	+	4.25851i	0.356114	+	0.356114i
$144$	1.11260	−	10.7303i	0.0927163	−	0.894189i
$145$	10.4848	+	9.41753i	0.870712	+	0.782083i
$146$	−3.58425	−	3.77437i	−0.296635	−	0.312369i
$147$	3.61443	−	3.61443i	0.298113	−	0.298113i
$148$	−6.33193	−	7.02242i	−0.520482	−	0.577240i
$149$			7.34543i			0.601761i	0.953662	+	0.300880i	$0.0972805\pi$
$149$			7.34543i			0.601761i	−0.953662	+	0.300880i	$0.902719\pi$
$150$	−2.96699	−	2.51984i	−0.242254	−	0.205744i
$151$			1.24659i			0.101446i	0.998713	+	0.0507230i	$0.0161526\pi$
$151$			1.24659i			0.101446i	−0.998713	+	0.0507230i	$0.983847\pi$
$152$	0.218952	−	2.81994i	0.0177594	−	0.228727i
$153$	−7.55666	+	7.55666i	−0.610920	+	0.610920i
$154$	4.01336	−	3.81121i	0.323406	−	0.307116i
$155$	−5.93357	−	5.32960i	−0.476596	−	0.428084i
$156$	−6.82816	−	0.353052i	−0.546690	−	0.0282667i
$157$	−12.2343	−	12.2343i	−0.976403	−	0.976403i	0.0233249	−	0.999728i	$-0.492575\pi$
$157$	−12.2343	−	12.2343i	−0.976403	−	0.976403i	−0.999728	+	0.0233249i	$0.992575\pi$
$158$	−0.350671	+	13.5733i	−0.0278979	+	1.07983i
$159$	−5.92100			−0.469566
$160$	8.24341	+	9.59407i	0.651699	+	0.758478i
$161$	3.69877			0.291504
$162$	−0.232456	+	8.99758i	−0.0182634	+	0.706916i
$163$	10.0729	+	10.0729i	0.788971	+	0.788971i	0.981326	−	0.192355i	$-0.0616124\pi$
$163$	10.0729	+	10.0729i	0.788971	+	0.788971i	−0.192355	+	0.981326i	$0.561612\pi$
$164$	−3.46941	−	0.179387i	−0.270915	−	0.0140078i
$165$	−0.0639227	−	1.19206i	−0.00497638	−	0.0928017i
$166$	14.9444	−	14.1916i	1.15991	−	1.10148i
$167$	6.69330	−	6.69330i	0.517943	−	0.517943i	−0.399005	−	0.916949i	$-0.630644\pi$
$167$	6.69330	−	6.69330i	0.517943	−	0.517943i	0.916949	+	0.399005i	$0.130644\pi$
$168$	−0.486414	+	6.26465i	−0.0375277	+	0.483328i
$169$		−	25.5646i		−	1.96651i
$170$	−0.347590	−	12.5258i	−0.0266589	−	0.960684i
$171$			2.69695i			0.206241i
$172$	−11.7514	−	13.0329i	−0.896039	−	0.993751i
$173$	9.71638	−	9.71638i	0.738723	−	0.738723i	−0.233608	−	0.972331i	$-0.575053\pi$
$173$	9.71638	−	9.71638i	0.738723	−	0.738723i	0.972331	+	0.233608i	$0.0750532\pi$
$174$	−3.37888	−	3.55810i	−0.256152	−	0.269739i
$175$	−15.7116	−	12.6601i	−1.18769	−	0.957011i
$176$	−0.400076	+	3.85847i	−0.0301569	+	0.290843i
$177$	5.05593	+	5.05593i	0.380027	+	0.380027i
$178$	−3.80690	−	0.0983527i	−0.285339	−	0.00737185i
$179$	−4.72583			−0.353225			−0.176613	−	0.984280i	$-0.556514\pi$
$179$	−4.72583			−0.353225			−0.176613	+	0.984280i	$0.556514\pi$
$180$	−8.54480	−	8.51217i	−0.636892	−	0.634459i
$181$	−20.5190			−1.52517			−0.762584	−	0.646890i	$-0.776069\pi$
$181$	−20.5190			−1.52517			−0.762584	+	0.646890i	$0.776069\pi$
$182$	−35.4293	−	0.915329i	−2.62619	−	0.0678487i
$183$	−1.52226	−	1.52226i	−0.112529	−	0.112529i
$184$	−1.96952	+	1.68571i	−0.145195	+	0.124272i
$185$	−10.5565	+	0.566078i	−0.776128	+	0.0416189i
$186$	1.91219	+	2.01361i	0.140208	+	0.147645i
$187$	2.71728	−	2.71728i	0.198707	−	0.198707i
$188$	16.3153	−	14.7111i	1.18991	−	1.07291i
$189$		−	12.6561i		−	0.920594i
$190$	−2.29723	−	2.17318i	−0.166659	−	0.157659i
$191$			8.89491i			0.643613i	0.946805	+	0.321807i	$0.104290\pi$
$191$			8.89491i			0.643613i	−0.946805	+	0.321807i	$0.895710\pi$
$192$	−2.59610	−	3.55747i	−0.187357	−	0.256739i
$193$	−3.20041	+	3.20041i	−0.230371	+	0.230371i	−0.812847	−	0.582477i	$-0.802084\pi$
$193$	−3.20041	+	3.20041i	−0.230371	+	0.230371i	0.582477	+	0.812847i	$0.302084\pi$
$194$	3.28600	−	3.12048i	0.235921	−	0.224038i
$195$	−5.10815	+	5.68703i	−0.365802	+	0.407257i
$196$	−0.958917	+	18.5458i	−0.0684941	+	1.32470i
$197$	−3.03123	−	3.03123i	−0.215967	−	0.215967i	0.590830	−	0.806796i	$-0.298800\pi$
$197$	−3.03123	−	3.03123i	−0.215967	−	0.215967i	−0.806796	+	0.590830i	$0.798800\pi$
$198$	0.0955289	−	3.69760i	0.00678895	−	0.262777i
$199$	17.9178			1.27016			0.635080	−	0.772446i	$-0.280967\pi$
$199$	17.9178			1.27016			0.635080	+	0.772446i	$0.280967\pi$
$200$	14.1359	−	0.419338i	0.999560	−	0.0296517i
$201$	0.554795			0.0391322
$202$	−0.0153098	+	0.592593i	−0.00107720	+	0.0416947i
$203$	−17.9850	−	17.9850i	−1.26230	−	1.26230i
$204$	−0.225276	+	4.35694i	−0.0157725	+	0.305047i
$205$	−2.59547	+	2.88960i	−0.181275	+	0.201818i
$206$	−3.50169	+	3.32531i	−0.243974	+	0.231685i
$207$	1.74790	−	1.74790i	0.121487	−	0.121487i
$208$	19.2825	−	15.6595i	1.33700	−	1.08579i
$209$		−	0.969790i		−	0.0670818i
$210$	5.10343	+	4.82784i	0.352170	+	0.333152i
$211$			3.02129i			0.207994i	0.994578	+	0.103997i	$0.0331633\pi$
$211$			3.02129i			0.207994i	−0.994578	+	0.103997i	$0.966837\pi$
$212$	15.9759	−	14.4050i	1.09723	−	0.989343i
$213$	2.30230	−	2.30230i	0.157751	−	0.157751i
$214$	12.1325	+	12.7760i	0.829359	+	0.873349i
$215$	−19.5918	+	1.05059i	−1.33615	+	0.0716493i
$216$	5.76799	+	6.73909i	0.392462	+	0.458537i
$217$	10.1781	+	10.1781i	0.690935	+	0.690935i
$218$	11.5045	+	0.297223i	0.779182	+	0.0201305i
$219$	2.02614			0.136914
$220$	3.07261	+	3.06087i	0.207155	+	0.206364i
$221$	−24.6075			−1.65528
$222$	3.67948	+	0.0950608i	0.246951	+	0.00638006i
$223$	−9.47805	−	9.47805i	−0.634697	−	0.634697i	0.314545	−	0.949242i	$-0.398148\pi$
$223$	−9.47805	−	9.47805i	−0.634697	−	0.634697i	−0.949242	+	0.314545i	$0.898148\pi$
$224$	−13.9287	−	18.0865i	−0.930648	−	1.20846i
$225$	−13.4074	+	1.44206i	−0.893827	+	0.0961372i
$226$	5.11912	+	5.39064i	0.340519	+	0.358580i
$227$	−18.2744	+	18.2744i	−1.21292	+	1.21292i	−0.242853	+	0.970063i	$0.578083\pi$
$227$	−18.2744	+	18.2744i	−1.21292	+	1.21292i	−0.970063	+	0.242853i	$0.921917\pi$
$228$	0.737288	+	0.817689i	0.0488281	+	0.0541528i
$229$			5.34676i			0.353324i	0.984272	+	0.176662i	$0.0565299\pi$
$229$			5.34676i			0.353324i	−0.984272	+	0.176662i	$0.943470\pi$
$230$	0.0803997	+	2.89729i	0.00530140	+	0.191042i
$231$			2.15444i			0.141752i
$232$	17.7732	+	1.37999i	1.16687	+	0.0906008i
$233$	12.6086	−	12.6086i	0.826014	−	0.826014i	−0.160949	−	0.986963i	$-0.551455\pi$
$233$	12.6086	−	12.6086i	0.826014	−	0.826014i	0.986963	+	0.160949i	$0.0514555\pi$
$234$	−17.1751	+	16.3100i	−1.12277	+	1.06622i
$235$	−1.31518	−	24.5260i	−0.0857926	−	1.59990i
$236$	−25.9422	−	1.34135i	−1.68870	−	0.0873144i
$237$	−3.73731	−	3.73731i	−0.242764	−	0.242764i
$238$	−0.584056	+	22.6069i	−0.0378588	+	1.46538i
$239$	6.81283			0.440686			0.220343	−	0.975422i	$-0.429282\pi$
$239$	6.81283			0.440686			0.220343	+	0.975422i	$0.429282\pi$
$240$	−4.91775	−	0.244840i	−0.317439	−	0.0158044i
$241$	−29.2936			−1.88696			−0.943482	−	0.331423i	$-0.892471\pi$
$241$	−29.2936			−1.88696			−0.943482	+	0.331423i	$0.892471\pi$
$242$	0.367419	−	14.2215i	0.0236186	−	0.914196i
$243$	−9.13026	−	9.13026i	−0.585706	−	0.585706i
$244$	7.81078	+	0.403858i	0.500034	+	0.0258544i
$245$	15.4464	+	13.8742i	0.986836	+	0.886387i
$246$	0.980612	−	0.931219i	0.0625215	−	0.0593723i
$247$	−4.39116	+	4.39116i	−0.279403	+	0.279403i
$248$	−10.0583	−	0.780969i	−0.638702	−	0.0495916i
$249$			8.02238i			0.508398i
$250$	9.57526	−	12.5823i	0.605593	−	0.795775i
$251$		−	22.3421i		−	1.41022i	−0.709097	−	0.705111i	$-0.750897\pi$
$251$		−	22.3421i		−	1.41022i	0.709097	−	0.705111i	$-0.249103\pi$
$252$	14.5764	+	16.1659i	0.918224	+	1.01836i
$253$	−0.628524	+	0.628524i	−0.0395150	+	0.0395150i
$254$	12.5794	+	13.2466i	0.789300	+	0.831165i
$255$	3.62880	+	3.25943i	0.227244	+	0.204113i
$256$	15.6596	+	3.28271i	0.978726	+	0.205170i
$257$	2.53065	+	2.53065i	0.157857	+	0.157857i	0.781617	−	0.623759i	$-0.214395\pi$
$257$	2.53065	+	2.53065i	0.157857	+	0.157857i	−0.623759	+	0.781617i	$0.714395\pi$
$258$	6.82875	+	0.176423i	0.425140	+	0.0109836i
$259$	19.0790			1.18551
$260$	−0.0531339	−	27.7721i	−0.00329523	−	1.72235i
$261$	−16.9981			−1.05215
$262$	−15.2392	−	0.393710i	−0.941480	−	0.0243235i
$263$	16.4134	+	16.4134i	1.01209	+	1.01209i	0.999926	+	0.0121679i	$0.00387326\pi$
$263$	16.4134	+	16.4134i	1.01209	+	1.01209i	0.0121679	+	0.999926i	$0.496127\pi$
$264$	−0.981883	−	1.14719i	−0.0604307	−	0.0706049i
$265$	−1.28782	−	24.0158i	−0.0791101	−	1.47528i
$266$	3.92994	+	4.13838i	0.240960	+	0.253741i
$267$	1.04820	−	1.04820i	0.0641490	−	0.0641490i
$268$	−1.49694	+	1.34975i	−0.0914399	+	0.0824489i
$269$			3.03533i			0.185067i	0.995710	+	0.0925337i	$0.0294966\pi$
$269$			3.03533i			0.185067i	−0.995710	+	0.0925337i	$0.970503\pi$
$270$	9.91366	−	0.275103i	0.603326	−	0.0167423i
$271$			28.9197i			1.75675i	0.477977	+	0.878373i	$0.341370\pi$
$271$			28.9197i			1.75675i	−0.477977	+	0.878373i	$0.658630\pi$
$272$	−9.99205	−	12.3039i	−0.605857	−	0.746031i
$273$	9.75520	−	9.75520i	0.590412	−	0.590412i
$274$	6.48022	−	6.15381i	0.391484	−	0.371765i
$275$	4.82114	−	0.518547i	0.290726	−	0.0312695i
$276$	0.0521078	−	1.00779i	0.00313652	−	0.0606616i
$277$	19.5416	+	19.5416i	1.17414	+	1.17414i	0.981212	+	0.192931i	$0.0617992\pi$
$277$	19.5416	+	19.5416i	1.17414	+	1.17414i	0.192931	+	0.981212i	$0.438201\pi$
$278$	0.362565	−	14.0337i	0.0217452	−	0.841684i
$279$	9.61959			0.575910
$280$	−25.5155	−	0.610355i	−1.52484	−	0.0364757i
$281$	22.9263			1.36767			0.683834	−	0.729637i	$-0.260311\pi$
$281$	22.9263			1.36767			0.683834	+	0.729637i	$0.260311\pi$
$282$	−0.220856	+	8.54858i	−0.0131518	+	0.509061i
$283$	14.0869	+	14.0869i	0.837380	+	0.837380i	0.988513	−	0.151134i	$-0.0482923\pi$
$283$	14.0869	+	14.0869i	0.837380	+	0.837380i	−0.151134	+	0.988513i	$0.548292\pi$
$284$	−0.610804	+	11.8132i	−0.0362446	+	0.700984i
$285$	1.22919	−	0.0659140i	0.0728111	−	0.00390441i
$286$	6.17597	−	5.86489i	0.365193	−	0.346798i
$287$	4.95665	−	4.95665i	0.292582	−	0.292582i
$288$	−15.1292	−	1.96484i	−0.891496	−	0.115779i
$289$		−	1.29838i		−	0.0763755i
$290$	13.6969	−	14.4788i	0.804310	−	0.850223i
$291$			1.76398i			0.103406i
$292$	−5.46689	+	4.92935i	−0.319926	+	0.288468i
$293$	15.6451	−	15.6451i	0.913998	−	0.913998i	−0.0825860	−	0.996584i	$-0.526318\pi$
$293$	15.6451	−	15.6451i	0.913998	−	0.913998i	0.996584	+	0.0825860i	$0.0263179\pi$
$294$	−4.97786	−	5.24189i	−0.290314	−	0.305713i
$295$	−19.4074	+	21.6067i	−1.12994	+	1.25799i
$296$	−10.1592	+	8.69523i	−0.590490	+	0.505400i
$297$	2.15062	+	2.15062i	0.124792	+	0.124792i
$298$	10.3845	+	0.268288i	0.601560	+	0.0155415i
$299$	5.69185			0.329168
$300$	−3.67077	+	4.10252i	−0.211932	+	0.236859i
$301$	35.4087			2.04093
$302$	1.76236	+	0.0455311i	0.101412	+	0.00262002i
$303$	−0.163166	−	0.163166i	−0.00937365	−	0.00937365i
$304$	−3.97867	−	0.412539i	−0.228192	−	0.0236607i
$305$	5.84325	−	6.50544i	0.334584	−	0.372500i
$306$	10.4072	+	10.9592i	0.594938	+	0.626494i
$307$	17.4039	−	17.4039i	0.993291	−	0.993291i	−0.00668634	−	0.999978i	$-0.502128\pi$
$307$	17.4039	−	17.4039i	0.993291	−	0.993291i	0.999978	+	0.00668634i	$0.00212835\pi$
$308$	−5.24148	−	5.81306i	−0.298661	−	0.331230i
$309$		−	1.87976i		−	0.106936i
$310$	−7.75140	+	8.19388i	−0.440250	+	0.465381i
$311$		−	5.65794i		−	0.320833i	−0.987049	−	0.160416i	$-0.948716\pi$
$311$		−	5.65794i		−	0.320833i	0.987049	−	0.160416i	$-0.0512837\pi$
$312$	−0.748519	+	9.64036i	−0.0423765	+	0.545778i
$313$	−7.47780	+	7.47780i	−0.422670	+	0.422670i	−0.886122	−	0.463452i	$-0.846611\pi$
$313$	−7.47780	+	7.47780i	−0.422670	+	0.422670i	0.463452	+	0.886122i	$0.346611\pi$
$314$	−17.7430	+	16.8493i	−1.00129	+	0.950860i
$315$	24.3014	−	1.30313i	1.36923	−	0.0734233i
$316$	19.1763	+	0.991516i	1.07875	+	0.0557772i
$317$	4.89011	+	4.89011i	0.274656	+	0.274656i	0.830971	−	0.556315i	$-0.187785\pi$
$317$	4.89011	+	4.89011i	0.274656	+	0.274656i	−0.556315	+	0.830971i	$0.687785\pi$
$318$	−0.216262	+	8.37076i	−0.0121274	+	0.469409i
$319$	6.11230			0.342223
$320$	13.8646	−	11.3036i	0.775056	−	0.631893i
$321$	−6.85837			−0.382797
$322$	0.135096	−	5.22910i	0.00752859	−	0.291407i
$323$	2.80193	+	2.80193i	0.155904	+	0.155904i
$324$	12.7118	+	0.657265i	0.706209	+	0.0365147i
$325$	−24.1779	−	19.4820i	−1.34115	−	1.08066i
$326$	14.6084	−	13.8726i	0.809084	−	0.768331i
$327$	−3.16768	+	3.16768i	−0.175173	+	0.175173i
$328$	−0.380325	+	4.89830i	−0.0209999	+	0.270463i
$329$			44.3265i			2.44380i
$330$	−1.68760	+	0.0468308i	−0.0928993	+	0.00257795i
$331$		−	10.7319i		−	0.589881i	−0.955516	−	0.294941i	$-0.904700\pi$
$331$		−	10.7319i		−	0.589881i	0.955516	−	0.294941i	$-0.0952999\pi$
$332$	−19.5174	−	21.6458i	−1.07116	−	1.18797i
$333$	9.01603	−	9.01603i	0.494075	−	0.494075i
$334$	−9.21813	−	9.70707i	−0.504394	−	0.531147i
$335$	0.120668	+	2.25027i	0.00659280	+	0.122946i
$336$	8.83883	+	0.916477i	0.482197	+	0.0499979i
$337$	25.3349	+	25.3349i	1.38008	+	1.38008i	0.844457	+	0.535623i	$0.179923\pi$
$337$	25.3349	+	25.3349i	1.38008	+	1.38008i	0.535623	+	0.844457i	$0.320077\pi$
$338$	−36.1418	−	0.933736i	−1.96585	−	0.0507885i
$339$	−2.89379			−0.157169
$340$	−17.7209	+	0.0339039i	−0.961052	+	0.00183870i
$341$	−3.45909			−0.187320
$342$	3.81279	+	0.0985048i	0.206172	+	0.00532653i
$343$	−6.52119	−	6.52119i	−0.352111	−	0.352111i
$344$	−18.8544	+	16.1375i	−1.01656	+	0.870075i
$345$	−0.839363	−	0.753925i	−0.0451898	−	0.0405900i
$346$	−13.3816	−	14.0913i	−0.719398	−	0.757555i
$347$	−15.3220	+	15.3220i	−0.822531	+	0.822531i	−0.986470	−	0.163940i	$-0.947580\pi$
$347$	−15.3220	+	15.3220i	−0.822531	+	0.822531i	0.163940	+	0.986470i	$0.447580\pi$
$348$	−5.15365	+	4.64691i	−0.276264	+	0.249100i
$349$			13.6503i			0.730685i	0.930873	+	0.365342i	$0.119048\pi$
$349$			13.6503i			0.730685i	−0.930873	+	0.365342i	$0.880952\pi$
$350$	−18.4719	+	21.7498i	−0.987366	+	1.16258i
$351$		−	19.4758i		−	1.03954i
$352$	5.44027	+	0.706534i	0.289968	+	0.0376584i
$353$	1.81610	−	1.81610i	0.0966615	−	0.0966615i	−0.657122	−	0.753784i	$-0.728227\pi$
$353$	1.81610	−	1.81610i	0.0966615	−	0.0966615i	0.753784	+	0.657122i	$0.228227\pi$
$354$	7.33244	−	6.96311i	0.389715	−	0.370085i
$355$	9.83896	+	8.83746i	0.522198	+	0.469044i
$356$	−0.278091	+	5.37839i	−0.0147388	+	0.285054i
$357$	−6.22463	−	6.22463i	−0.329443	−	0.329443i
$358$	−0.172609	+	6.68110i	−0.00912266	+	0.353107i
$359$	−19.3739			−1.02251			−0.511257	−	0.859428i	$-0.670820\pi$
$359$	−19.3739			−1.02251			−0.511257	+	0.859428i	$0.670820\pi$
$360$	−12.3461	+	11.7692i	−0.650697	+	0.620293i
$361$	1.00000			0.0526316
$362$	−0.749448	+	29.0086i	−0.0393901	+	1.52466i
$363$	3.91580	+	3.91580i	0.205526	+	0.205526i
$364$	−2.58808	+	50.0545i	−0.135652	+	2.62357i
$365$	0.440687	+	8.21812i	0.0230666	+	0.430156i
$366$	−2.20768	+	2.09648i	−0.115397	+	0.109585i
$367$	19.0358	−	19.0358i	0.993660	−	0.993660i	−0.00632048	−	0.999980i	$-0.502012\pi$
$367$	19.0358	−	19.0358i	0.993660	−	0.993660i	0.999980	+	0.00632048i	$0.00201189\pi$
$368$	2.31122	+	2.84596i	0.120481	+	0.148356i
$369$		−	4.68466i		−	0.243874i
$370$	0.414718	+	14.9448i	0.0215602	+	0.776944i
$371$			43.4044i			2.25345i
$372$	2.91657	−	2.62979i	0.151217	−	0.136348i
$373$	−10.4041	+	10.4041i	−0.538702	+	0.538702i	−0.923148	−	0.384445i	$-0.874393\pi$
$373$	−10.4041	+	10.4041i	−0.538702	+	0.538702i	0.384445	+	0.923148i	$0.374393\pi$
$374$	−3.74229	−	3.94078i	−0.193509	−	0.203773i
$375$	0.984930	+	6.07548i	0.0508616	+	0.313736i
$376$	−20.2017	−	23.6029i	−1.04182	−	1.21723i
$377$	−27.6762	−	27.6762i	−1.42540	−	1.42540i
$378$	−17.8924	−	0.462257i	−0.920287	−	0.0237759i
$379$	−0.191835			−0.00985390			−0.00492695	−	0.999988i	$-0.501568\pi$
$379$	−0.191835			−0.00985390			−0.00492695	+	0.999988i	$0.501568\pi$
$380$	−3.15622	+	3.16832i	−0.161911	+	0.162531i
$381$	−7.11099			−0.364307
$382$	12.5751	+	0.324883i	0.643399	+	0.0166224i
$383$	−19.0048	−	19.0048i	−0.971099	−	0.971099i	0.0284950	−	0.999594i	$-0.490929\pi$
$383$	−19.0048	−	19.0048i	−0.971099	−	0.971099i	−0.999594	+	0.0284950i	$0.990929\pi$
$384$	−5.12417	+	3.54028i	−0.261492	+	0.180664i
$385$	−8.73851	+	0.468591i	−0.445355	+	0.0238816i
$386$	4.40766	+	4.64145i	0.224344	+	0.236244i
$387$	16.7329	−	16.7329i	0.850579	−	0.850579i
$388$	−4.29154	−	4.75952i	−0.217870	−	0.241628i
$389$		−	0.624834i		−	0.0316803i	−0.999875	−	0.0158402i	$-0.994958\pi$
$389$		−	0.624834i		−	0.0316803i	0.999875	−	0.0158402i	$-0.00504229\pi$
$390$	7.85342	+	7.42932i	0.397673	+	0.376198i
$391$		−	3.63188i		−	0.183672i
$392$	26.1840	+	2.03304i	1.32249	+	0.102684i
$393$	4.19600	−	4.19600i	0.211660	−	0.211660i
$394$	−4.39610	+	4.17467i	−0.221472	+	0.210317i
$395$	14.3458	−	15.9716i	0.721817	−	0.803616i
$396$	−5.22397	−	0.270107i	−0.262514	−	0.0135734i
$397$	15.1270	+	15.1270i	0.759200	+	0.759200i	0.976177	−	0.216977i	$-0.0696196\pi$
$397$	15.1270	+	15.1270i	0.759200	+	0.759200i	−0.216977	+	0.976177i	$0.569620\pi$
$398$	0.654440	−	25.3312i	0.0328041	−	1.26974i
$399$	−2.22155			−0.111217
$400$	−0.0765282	−	19.9999i	−0.00382641	−	0.999993i
$401$	8.47122			0.423033			0.211516	−	0.977374i	$-0.432160\pi$
$401$	8.47122			0.423033			0.211516	+	0.977374i	$0.432160\pi$
$402$	0.0202636	−	0.784337i	0.00101066	−	0.0391192i
$403$	15.6626	+	15.6626i	0.780209	+	0.780209i
$404$	0.837214	+	0.0432883i	0.0416529	+	0.00215368i
$405$	9.50968	−	10.5874i	0.472540	−	0.526090i
$406$	−26.0830	+	24.7692i	−1.29448	+	1.22927i
$407$	−3.24206	+	3.24206i	−0.160703	+	0.160703i
$408$	6.15135	+	0.477618i	0.304537	+	0.0236456i
$409$		−	28.7680i		−	1.42249i	−0.702946	−	0.711243i	$-0.748133\pi$
$409$		−	28.7680i		−	1.42249i	0.702946	−	0.711243i	$-0.251867\pi$
$410$	3.99035	+	3.77486i	0.197069	+	0.186427i
$411$			3.47869i			0.171591i
$412$	4.57323	+	5.07193i	0.225307	+	0.249876i
$413$	37.0629	−	37.0629i	1.82375	−	1.82375i
$414$	−2.40724	−	2.53492i	−0.118309	−	0.124585i
$415$	−32.5391	+	1.74487i	−1.59728	+	0.0856523i
$416$	−21.4341	−	27.8324i	−1.05090	−	1.36460i
$417$	3.86407	+	3.86407i	0.189224	+	0.189224i
$418$	−1.37103	−	0.0354211i	−0.0670594	−	0.00173250i
$419$	−23.1003			−1.12853			−0.564263	−	0.825595i	$-0.690840\pi$
$419$	−23.1003			−1.12853			−0.564263	+	0.825595i	$0.690840\pi$
$420$	7.01171	−	7.03860i	0.342137	−	0.343448i
$421$	9.20299			0.448526			0.224263	−	0.974529i	$-0.428002\pi$
$421$	9.20299			0.448526			0.224263	+	0.974529i	$0.428002\pi$
$422$	4.27133	+	0.110351i	0.207925	+	0.00537182i
$423$	20.9470	+	20.9470i	1.01848	+	1.01848i
$424$	−19.7815	−	23.1119i	−0.960675	−	1.12242i
$425$	−12.4311	+	15.4275i	−0.602998	+	0.748344i
$426$	−3.17076	−	3.33894i	−0.153624	−	0.161772i
$427$	−11.1591	+	11.1591i	−0.540024	+	0.540024i
$428$	18.5051	−	16.6856i	0.894477	−	0.806527i
$429$			3.31536i			0.160067i
$430$	0.769675	+	27.7361i	0.0371170	+	1.33755i
$431$		−	10.9176i		−	0.525881i	−0.964812	−	0.262940i	$-0.915308\pi$
$431$		−	10.9176i		−	0.525881i	0.964812	−	0.262940i	$-0.0846923\pi$
$432$	9.73801	−	7.90830i	0.468520	−	0.380488i
$433$	5.37868	−	5.37868i	0.258483	−	0.258483i	−0.565954	−	0.824437i	$-0.691492\pi$
$433$	5.37868	−	5.37868i	0.258483	−	0.258483i	0.824437	+	0.565954i	$0.191492\pi$
$434$	14.7610	−	14.0175i	0.708549	−	0.672860i
$435$	0.415436	+	7.74724i	0.0199186	+	0.371452i
$436$	0.840392	−	16.2535i	0.0402475	−	0.778402i
$437$	−0.648103	−	0.648103i	−0.0310030	−	0.0310030i
$438$	0.0740039	−	2.86444i	0.00353604	−	0.136868i
$439$	−16.3970			−0.782588			−0.391294	−	0.920266i	$-0.627972\pi$
$439$	−16.3970			−0.782588			−0.391294	+	0.920266i	$0.627972\pi$
$440$	4.43951	−	4.23208i	0.211645	−	0.201756i
$441$	−25.0420			−1.19248
$442$	−0.898776	+	34.7886i	−0.0427504	+	1.65472i
$443$	23.3948	+	23.3948i	1.11152	+	1.11152i	0.992945	+	0.118573i	$0.0378320\pi$
$443$	23.3948	+	23.3948i	1.11152	+	1.11152i	0.118573	+	0.992945i	$0.462168\pi$
$444$	0.268783	−	5.19837i	0.0127559	−	0.246704i
$445$	4.47954	+	4.02357i	0.212351	+	0.190736i
$446$	−13.7457	+	13.0533i	−0.650878	+	0.618093i
$447$	−2.85931	+	2.85931i	−0.135241	+	0.135241i
$448$	−26.0784	+	19.0309i	−1.23209	+	0.899127i
$449$		−	11.4369i		−	0.539740i	−0.962897	−	0.269870i	$-0.913019\pi$
$449$		−	11.4369i		−	0.539740i	0.962897	−	0.269870i	$-0.0869808\pi$
$450$	1.54900	+	19.0073i	0.0730205	+	0.896012i
$451$			1.68455i			0.0793222i
$452$	7.80795	−	7.04022i	0.367255	−	0.331144i
$453$	−0.485252	+	0.485252i	−0.0227991	+	0.0227991i
$454$	25.1679	+	26.5028i	1.18119	+	1.24384i
$455$	41.6893	+	37.4458i	1.95442	+	1.75548i
$456$	1.18293	−	1.01247i	0.0553958	−	0.0474132i
$457$	−24.7109	−	24.7109i	−1.15593	−	1.15593i	−0.985343	−	0.170585i	$-0.945434\pi$
$457$	−24.7109	−	24.7109i	−1.15593	−	1.15593i	−0.170585	−	0.985343i	$-0.554566\pi$
$458$	7.55894	+	0.195288i	0.353206	+	0.00912520i
$459$	−12.4272			−0.580052
$460$	4.09896	−	0.00784218i	0.191115	−	0.000365643i
$461$	6.47208			0.301435			0.150717	−	0.988577i	$-0.451842\pi$
$461$	6.47208			0.301435			0.150717	+	0.988577i	$0.451842\pi$
$462$	3.04582	+	0.0786899i	0.141704	+	0.00366099i
$463$	−23.7452	−	23.7452i	−1.10353	−	1.10353i	−0.993981	−	0.109552i	$-0.965058\pi$
$463$	−23.7452	−	23.7452i	−1.10353	−	1.10353i	−0.109552	−	0.993981i	$-0.534942\pi$
$464$	2.60011	−	25.0764i	0.120707	−	1.16414i
$465$	−0.235105	−	4.38434i	−0.0109027	−	0.203319i
$466$	−17.3647	−	18.2858i	−0.804405	−	0.847071i
$467$	18.9617	−	18.9617i	0.877443	−	0.877443i	−0.115827	−	0.993269i	$-0.536952\pi$
$467$	18.9617	−	18.9617i	0.877443	−	0.877443i	0.993269	+	0.115827i	$0.0369518\pi$
$468$	22.4308	+	24.8769i	1.03687	+	1.14994i
$469$		−	4.06698i		−	0.187796i
$470$	−34.7215	+	0.963519i	−1.60158	+	0.0444438i
$471$		−	9.52473i		−	0.438876i
$472$	−2.84385	+	36.6266i	−0.130899	+	1.68588i
$473$	−6.01693	+	6.01693i	−0.276659	+	0.276659i
$474$	−5.42009	+	5.14708i	−0.248953	+	0.236413i
$475$	0.534700	+	4.97133i	0.0245337	+	0.228100i
$476$	31.9389	+	1.65141i	1.46392	+	0.0756923i
$477$	20.5113	+	20.5113i	0.939149	+	0.939149i
$478$	0.248836	−	9.63159i	0.0113815	−	0.440539i
$479$	−9.99657			−0.456755			−0.228378	−	0.973573i	$-0.573342\pi$
$479$	−9.99657			−0.456755			−0.228378	+	0.973573i	$0.573342\pi$
$480$	−0.525759	+	6.94348i	−0.0239975	+	0.316925i
$481$	29.3598			1.33869
$482$	−1.06993	+	41.4135i	−0.0487341	+	1.88633i
$483$	1.43980	+	1.43980i	0.0655130	+	0.0655130i
$484$	−20.0922	−	1.03887i	−0.913281	−	0.0472214i
$485$	−7.15477	+	0.383666i	−0.324881	+	0.0174214i
$486$	−13.2413	+	12.5744i	−0.600638	+	0.570384i
$487$	−14.4468	+	14.4468i	−0.654646	+	0.654646i	−0.954108	−	0.299462i	$-0.903193\pi$
$487$	−14.4468	+	14.4468i	−0.654646	+	0.654646i	0.299462	+	0.954108i	$0.403193\pi$
$488$	0.856237	−	11.0277i	0.0387600	−	0.499200i
$489$			7.84203i			0.354629i
$490$	20.1786	−	21.3305i	0.911578	−	0.963615i
$491$			11.3121i			0.510507i	0.966874	+	0.255253i	$0.0821589\pi$
$491$			11.3121i			0.510507i	−0.966874	+	0.255253i	$0.917841\pi$
$492$	−1.28069	−	1.42034i	−0.0577378	−	0.0640341i
$493$	−17.6597	+	17.6597i	−0.795354	+	0.795354i
$494$	6.04759	+	6.36836i	0.272094	+	0.286526i
$495$	−3.90805	+	4.35093i	−0.175654	+	0.195560i
$496$	−1.47146	+	14.1913i	−0.0660706	+	0.637208i
$497$	−16.8772	−	16.8772i	−0.757045	−	0.757045i
$498$	11.3416	+	0.293014i	0.508228	+	0.0131303i
$499$	16.2447			0.727212			0.363606	−	0.931553i	$-0.381545\pi$
$499$	16.2447			0.727212			0.363606	+	0.931553i	$0.381545\pi$
$500$	−17.4384	−	13.9965i	−0.779869	−	0.625943i
$501$	5.21092			0.232807
$502$	−31.5860	−	0.816035i	−1.40975	−	0.0364214i
$503$	2.42975	+	2.42975i	0.108337	+	0.108337i	0.759198	−	0.650860i	$-0.225592\pi$
$503$	2.42975	+	2.42975i	0.108337	+	0.108337i	−0.650860	+	0.759198i	$0.725592\pi$
$504$	23.3868	−	20.0168i	1.04173	−	0.891617i
$505$	0.626320	−	0.697298i	0.0278709	−	0.0310293i
$506$	0.865614	+	0.911527i	0.0384812	+	0.0405223i
$507$	9.95138	−	9.95138i	0.441956	−	0.441956i
$508$	19.1867	−	17.3002i	0.851273	−	0.767571i
$509$		−	16.5994i		−	0.735757i	−0.929874	−	0.367878i	$-0.880084\pi$
$509$		−	16.5994i		−	0.735757i	0.929874	−	0.367878i	$-0.119916\pi$
$510$	4.74053	−	5.01114i	0.209914	−	0.221897i
$511$		−	14.8528i		−	0.657050i
$512$	5.21287	−	22.0188i	0.230378	−	0.973101i
$513$	−2.21761	+	2.21761i	−0.0979101	+	0.0979101i
$514$	3.67011	−	3.48525i	0.161882	−	0.153728i
$515$	7.62440	−	0.408849i	0.335971	−	0.0180160i
$516$	0.498834	−	9.64765i	0.0219599	−	0.424714i
$517$	−7.53231	−	7.53231i	−0.331270	−	0.331270i
$518$	0.696852	−	26.9728i	0.0306179	−	1.18512i
$519$	7.56447			0.332043
$520$	−39.2645	−	0.939245i	−1.72186	−	0.0411886i
$521$	−2.95077			−0.129276			−0.0646378	−	0.997909i	$-0.520589\pi$
$521$	−2.95077			−0.129276			−0.0646378	+	0.997909i	$0.520589\pi$
$522$	−0.620846	+	24.0309i	−0.0271737	+	1.05180i
$523$	2.45025	+	2.45025i	0.107142	+	0.107142i	0.758646	−	0.651504i	$-0.225861\pi$
$523$	2.45025	+	2.45025i	0.107142	+	0.107142i	−0.651504	+	0.758646i	$0.725861\pi$
$524$	−1.11321	+	21.5299i	−0.0486308	+	0.940538i
$525$	−1.18786	−	11.0441i	−0.0518427	−	0.482003i
$526$	23.8038	−	22.6048i	1.03790	−	0.985617i
$527$	9.99404	−	9.99404i	0.435347	−	0.435347i
$528$	−1.65770	+	1.34623i	−0.0721421	+	0.0585871i
$529$		−	22.1599i		−	0.963475i
$530$	−33.9992	+	0.943477i	−1.47683	+	0.0409820i
$531$		−	35.0291i		−	1.52014i
$532$	5.99414	−	5.40476i	0.259879	−	0.234326i
$533$	7.62755	−	7.62755i	0.330386	−	0.330386i
$534$	−1.44360	−	1.52017i	−0.0624708	−	0.0657843i
$535$	−1.49170	−	27.8178i	−0.0644917	−	1.20267i
$536$	1.85352	+	2.16558i	0.0800598	+	0.0935388i
$537$	−1.83959	−	1.83959i	−0.0793843	−	0.0793843i
$538$	4.29117	+	0.110864i	0.185006	+	0.00477969i
$539$	9.00479			0.387864
$540$	−0.0268336	−	14.0254i	−0.00115473	−	0.603557i
$541$	−41.4423			−1.78174			−0.890871	−	0.454256i	$-0.849905\pi$
$541$	−41.4423			−1.78174			−0.890871	+	0.454256i	$0.849905\pi$
$542$	40.8850	+	1.05628i	1.75616	+	0.0453710i
$543$	−7.98731	−	7.98731i	−0.342768	−	0.342768i
$544$	−17.7594	+	13.6768i	−0.761429	+	0.586387i
$545$	−13.5372	−	12.1593i	−0.579870	−	0.520846i
$546$	−13.4350	−	14.1476i	−0.574966	−	0.605463i
$547$	−15.7622	+	15.7622i	−0.673944	+	0.673944i	−0.958623	−	0.284679i	$-0.908113\pi$
$547$	−15.7622	+	15.7622i	−0.673944	+	0.673944i	0.284679	+	0.958623i	$0.408113\pi$
$548$	−8.46321	−	9.38612i	−0.361531	−	0.400955i
$549$			10.5467i			0.450122i
$550$	−0.557001	−	6.83479i	−0.0237506	−	0.291437i
$551$			6.30270i			0.268504i
$552$	−1.42285	−	0.110476i	−0.0605603	−	0.00470217i
$553$	−27.3967	+	27.3967i	−1.16503	+	1.16503i
$554$	28.3406	−	26.9131i	1.20408	−	1.14343i
$555$	−4.32961	−	3.88890i	−0.183782	−	0.165075i
$556$	−19.8268	−	1.02515i	−0.840842	−	0.0434759i
$557$	16.6517	+	16.6517i	0.705557	+	0.705557i	0.965598	−	0.260041i	$-0.0837360\pi$
$557$	16.6517	+	16.6517i	0.705557	+	0.705557i	−0.260041	+	0.965598i	$0.583736\pi$
$558$	0.351351	−	13.5996i	0.0148739	−	0.575718i
$559$	54.4888			2.30463
$560$	−1.79483	+	36.0500i	−0.0758452	+	1.52339i
$561$	2.11548			0.0893156
$562$	0.837373	−	32.4119i	0.0353224	−	1.36721i
$563$	6.23508	+	6.23508i	0.262777	+	0.262777i	0.826181	−	0.563404i	$-0.190509\pi$
$563$	6.23508	+	6.23508i	0.262777	+	0.262777i	−0.563404	+	0.826181i	$0.690509\pi$
$564$	12.0774	+	0.624466i	0.508551	+	0.0262948i
$565$	−0.629400	−	11.7373i	−0.0264790	−	0.493793i
$566$	20.4298	−	19.4007i	0.858727	−	0.815474i
$567$	−18.1609	+	18.1609i	−0.762688	+	0.762688i
$568$	16.6785	+	1.29499i	0.699814	+	0.0543366i
$569$			18.7909i			0.787754i	0.919163	+	0.393877i	$0.128866\pi$
$569$			18.7909i			0.787754i	−0.919163	+	0.393877i	$0.871134\pi$
$570$	−0.0482896	−	1.74017i	−0.00202263	−	0.0728877i
$571$		−	14.2948i		−	0.598220i	−0.954219	−	0.299110i	$-0.903310\pi$
$571$		−	14.2948i		−	0.598220i	0.954219	−	0.299110i	$-0.0966897\pi$
$572$	−8.06586	−	8.94544i	−0.337251	−	0.374028i
$573$	−3.46247	+	3.46247i	−0.144647	+	0.144647i
$574$	−6.82639	−	7.18847i	−0.284928	−	0.300041i
$575$	2.87539	−	3.56847i	0.119912	−	0.148816i
$576$	−3.33037	+	21.3170i	−0.138765	+	0.888208i
$577$	11.2118	+	11.2118i	0.466752	+	0.466752i	0.900860	−	0.434109i	$-0.142937\pi$
$577$	11.2118	+	11.2118i	0.466752	+	0.466752i	−0.434109	+	0.900860i	$0.642937\pi$
$578$	−1.83558	−	0.0474229i	−0.0763500	−	0.00197253i
$579$	−2.49161			−0.103548
$580$	−19.9690	−	19.8927i	−0.829167	−	0.826000i
$581$	58.8088			2.43980
$582$	2.49381	+	0.0644284i	0.103372	+	0.00267064i
$583$	−7.37563	−	7.37563i	−0.305467	−	0.305467i
$584$	6.76916	+	7.90882i	0.280110	+	0.327269i
$585$	37.3963	−	2.00533i	1.54615	−	0.0829102i
$586$	−21.5467	−	22.6896i	−0.890087	−	0.937299i
$587$	7.47716	−	7.47716i	0.308615	−	0.308615i	−0.535757	−	0.844372i	$-0.679974\pi$
$587$	7.47716	−	7.47716i	0.308615	−	0.308615i	0.844372	+	0.535757i	$0.179974\pi$
$588$	−7.59249	+	6.84595i	−0.313109	+	0.282322i
$589$		−	3.56684i		−	0.146969i
$590$	29.8375	+	28.2262i	1.22839	+	1.16206i
$591$		−	2.35990i		−	0.0970732i
$592$	11.9218	+	14.6800i	0.489981	+	0.603345i
$593$	0.925217	−	0.925217i	0.0379941	−	0.0379941i	−0.687855	−	0.725849i	$-0.741447\pi$
$593$	0.925217	−	0.925217i	0.0379941	−	0.0379941i	0.725849	+	0.687855i	$0.241447\pi$
$594$	3.11897	−	2.96187i	0.127973	−	0.121527i
$595$	23.8935	−	26.6013i	0.979539	−	1.09055i
$596$	0.758581	−	14.6713i	0.0310727	−	0.600958i
$597$	6.97475	+	6.97475i	0.285458	+	0.285458i
$598$	0.207892	−	8.04681i	0.00850135	−	0.329059i
$599$	−20.7064			−0.846041			−0.423020	−	0.906120i	$-0.639030\pi$
$599$	−20.7064			−0.846041			−0.423020	+	0.906120i	$0.639030\pi$
$600$	5.66583	+	5.33936i	0.231307	+	0.217979i
$601$	18.2704			0.745267			0.372634	−	0.927979i	$-0.378455\pi$
$601$	18.2704			0.745267			0.372634	+	0.927979i	$0.378455\pi$
$602$	1.29329	−	50.0588i	0.0527105	−	2.04025i
$603$	−1.92190	−	1.92190i	−0.0782659	−	0.0782659i
$604$	0.128738	−	2.48985i	0.00523829	−	0.101311i
$605$	−15.0310	+	16.7343i	−0.611096	+	0.680348i
$606$	−0.236634	+	0.224715i	−0.00961261	+	0.00912843i
$607$	−14.1387	+	14.1387i	−0.573872	+	0.573872i	−0.933208	−	0.359336i	$-0.883003\pi$
$607$	−14.1387	+	14.1387i	−0.573872	+	0.573872i	0.359336	+	0.933208i	$0.383003\pi$
$608$	−0.728543	+	5.60974i	−0.0295463	+	0.227505i
$609$		−	14.0018i		−	0.567381i
$610$	−8.98358	−	8.49846i	−0.363735	−	0.344093i
$611$			68.2118i			2.75956i
$612$	15.8735	−	14.3128i	0.641650	−	0.578559i
$613$	−4.34947	+	4.34947i	−0.175673	+	0.175673i	−0.789467	−	0.613793i	$-0.789643\pi$
$613$	−4.34947	+	4.34947i	−0.175673	+	0.175673i	0.613793	+	0.789467i	$0.289643\pi$
$614$	−23.9689	−	25.2402i	−0.967306	−	1.01861i
$615$	−2.13514	+	0.114494i	−0.0860970	+	0.00461685i
$616$	−8.40961	+	7.19779i	−0.338833	+	0.290007i
$617$	22.2376	+	22.2376i	0.895253	+	0.895253i	0.995012	−	0.0997586i	$-0.0318071\pi$
$617$	22.2376	+	22.2376i	0.895253	+	0.895253i	−0.0997586	+	0.995012i	$0.531807\pi$
$618$	−2.65750	−	0.0686575i	−0.106900	−	0.00276181i
$619$	−35.2546			−1.41700			−0.708501	−	0.705710i	$-0.750628\pi$
$619$	−35.2546			−1.41700			−0.708501	+	0.705710i	$0.750628\pi$
$620$	11.3009	+	11.2577i	0.453855	+	0.452122i
$621$	2.87449			0.115349
$622$	−7.99887	−	0.206654i	−0.320726	−	0.00828606i
$623$	−7.68395	−	7.68395i	−0.307851	−	0.307851i
$624$	13.6016	+	1.41032i	0.544501	+	0.0564581i
$625$	−24.4282	+	5.31634i	−0.977128	+	0.212654i
$626$	10.2986	+	10.8448i	0.411613	+	0.433445i
$627$	0.377504	−	0.377504i	0.0150761	−	0.0150761i
$628$	23.1725	+	25.6994i	0.924683	+	1.02552i
$629$		−	18.7340i		−	0.746973i
$630$	−0.954697	−	34.4036i	−0.0380360	−	1.37067i
$631$			0.132174i			0.00526176i	0.999997	+	0.00263088i	$0.000837437\pi$
$631$			0.132174i			0.00526176i	−0.999997	+	0.00263088i	$0.999163\pi$
$632$	2.10215	−	27.0742i	0.0836192	−	1.07695i
$633$	−1.17608	+	1.17608i	−0.0467450	+	0.0467450i
$634$	7.09196	−	6.73474i	0.281658	−	0.267471i
$635$	−1.54664	−	28.8425i	−0.0613767	−	1.14458i
$636$	11.8262	+	0.611476i	0.468939	+	0.0242466i
$637$	−40.7733	−	40.7733i	−1.61550	−	1.61550i
$638$	0.223249	−	8.64121i	0.00883850	−	0.342109i
$639$	−15.9511			−0.631015
$640$	−15.4740	−	20.0139i	−0.611665	−	0.791117i
$641$	2.21113			0.0873346			0.0436673	−	0.999046i	$-0.486096\pi$
$641$	2.21113			0.0873346			0.0436673	+	0.999046i	$0.486096\pi$
$642$	−0.250499	+	9.69596i	−0.00988639	+	0.382669i
$643$	0.700269	+	0.700269i	0.0276159	+	0.0276159i	0.720780	−	0.693164i	$-0.243784\pi$
$643$	0.700269	+	0.700269i	0.0276159	+	0.0276159i	−0.693164	+	0.720780i	$0.743784\pi$
$644$	−7.38767	−	0.381981i	−0.291115	−	0.0150522i
$645$	−8.03532	−	7.21741i	−0.316391	−	0.284185i
$646$	4.06354	−	3.85887i	0.159878	−	0.151825i
$647$	−15.9509	+	15.9509i	−0.627095	+	0.627095i	−0.947336	−	0.320241i	$-0.896236\pi$
$647$	−15.9509	+	15.9509i	−0.627095	+	0.627095i	0.320241	+	0.947336i	$0.396236\pi$
$648$	1.39349	−	17.9471i	0.0547416	−	0.705030i
$649$			12.5961i			0.494439i
$650$	−28.4255	+	33.4697i	−1.11494	+	1.31279i
$651$			7.92393i			0.310563i
$652$	−19.0787	−	21.1592i	−0.747179	−	0.828658i
$653$	−6.14565	+	6.14565i	−0.240498	+	0.240498i	−0.817056	−	0.576558i	$-0.804395\pi$
$653$	−6.14565	+	6.14565i	−0.240498	+	0.240498i	0.576558	+	0.817056i	$0.304395\pi$
$654$	4.36258	+	4.59397i	0.170590	+	0.179639i
$655$	17.9318	+	16.1065i	0.700653	+	0.629334i
$656$	6.91104	+	0.716590i	0.269831	+	0.0279781i
$657$	−7.01890	−	7.01890i	−0.273833	−	0.273833i
$658$	62.6662	+	1.61900i	2.44298	+	0.0631153i
$659$	−41.2766			−1.60791			−0.803954	−	0.594691i	$-0.797274\pi$
$659$	−41.2766			−1.60791			−0.803954	+	0.594691i	$0.797274\pi$
$660$	0.00456787	+	2.38754i	0.000177804	+	0.0929349i
$661$	8.97089			0.348927			0.174464	−	0.984664i	$-0.444181\pi$
$661$	8.97089			0.348927			0.174464	+	0.984664i	$0.444181\pi$
$662$	−15.1722	−	0.391979i	−0.589684	−	0.0152347i
$663$	−9.57879	−	9.57879i	−0.372009	−	0.372009i
$664$	−31.3144	+	26.8020i	−1.21524	+	1.04012i
$665$	−0.483189	−	9.01072i	−0.0187372	−	0.349421i
$666$	−12.4170	−	13.0756i	−0.481150	−	0.506671i
$667$	4.08480	−	4.08480i	0.158164	−	0.158164i
$668$	−14.0600	+	12.6775i	−0.543997	+	0.490508i
$669$		−	7.37892i		−	0.285285i
$670$	3.18571	−	0.0884034i	0.123075	−	0.00341532i
$671$		−	3.79247i		−	0.146407i
$672$	1.61850	−	12.4623i	0.0624348	−	0.480745i
$673$	19.2041	−	19.2041i	0.740262	−	0.740262i	−0.232366	−	0.972628i	$-0.574647\pi$
$673$	19.2041	−	19.2041i	0.740262	−	0.740262i	0.972628	+	0.232366i	$0.0746467\pi$
$674$	36.7424	−	34.8917i	1.41526	−	1.34398i
$675$	−12.2102	−	9.83873i	−0.469973	−	0.378693i
$676$	−2.64012	+	51.0610i	−0.101543	+	1.96389i
$677$	−24.0223	−	24.0223i	−0.923251	−	0.923251i	0.0740063	−	0.997258i	$-0.476421\pi$
$677$	−24.0223	−	24.0223i	−0.923251	−	0.923251i	−0.997258	+	0.0740063i	$0.976421\pi$
$678$	−0.105694	+	4.09107i	−0.00405916	+	0.157117i
$679$	12.9310			0.496246
$680$	−0.599317	+	25.0541i	−0.0229828	+	0.960779i
$681$	−14.2271			−0.545185
$682$	−0.126342	+	4.89026i	−0.00483787	+	0.187258i
$683$	−35.7804	−	35.7804i	−1.36910	−	1.36910i	−0.861726	−	0.507374i	$-0.830616\pi$
$683$	−35.7804	−	35.7804i	−1.36910	−	1.36910i	−0.507374	−	0.861726i	$-0.669384\pi$
$684$	0.278521	−	5.38670i	0.0106495	−	0.205966i
$685$	−14.1097	+	0.756616i	−0.539104	+	0.0289088i
$686$	−9.45746	+	8.98109i	−0.361088	+	0.342900i
$687$	−2.08130	+	2.08130i	−0.0794065	+	0.0794065i
$688$	22.1256	+	27.2447i	0.843530	+	1.03869i
$689$			66.7930i			2.54461i
$690$	−1.09651	+	1.15911i	−0.0417435	+	0.0441264i
$691$			11.0617i			0.420808i	0.977614	+	0.210404i	$0.0674780\pi$
$691$			11.0617i			0.420808i	−0.977614	+	0.210404i	$0.932522\pi$
$692$	−20.4103	+	18.4034i	−0.775882	+	0.699592i
$693$	7.46334	−	7.46334i	0.283509	−	0.283509i
$694$	21.1018	+	22.2211i	0.801013	+	0.843500i
$695$	−14.8324	+	16.5133i	−0.562625	+	0.626385i
$696$	6.38129	+	7.45565i	0.241882	+	0.282606i
$697$	−4.86702	−	4.86702i	−0.184351	−	0.184351i
$698$	19.2980	+	0.498572i	0.730441	+	0.0188712i
$699$	9.81610			0.371279
$700$	30.0739	+	26.9089i	1.13669	+	1.01706i
$701$	−9.68706			−0.365875			−0.182938	−	0.983125i	$-0.558561\pi$
$701$	−9.68706			−0.365875			−0.182938	+	0.983125i	$0.558561\pi$
$702$	−27.5338	−	0.711345i	−1.03920	−	0.0268480i
$703$	−3.34305	−	3.34305i	−0.126086	−	0.126086i
$704$	1.19756	−	7.66534i	0.0451347	−	0.288898i
$705$	9.03513	−	10.0590i	0.340283	−	0.378845i
$706$	−2.50117	−	2.63383i	−0.0941328	−	0.0991257i
$707$	−1.19610	+	1.19610i	−0.0449841	+	0.0449841i
$708$	−9.57622	−	10.6205i	−0.359897	−	0.399143i
$709$		−	5.59192i		−	0.210009i	−0.994472	−	0.105005i	$-0.966514\pi$
$709$		−	5.59192i		−	0.210009i	0.994472	−	0.105005i	$-0.0334857\pi$
$710$	12.8533	−	13.5870i	0.482374	−	0.509910i
$711$			25.8933i			0.971075i
$712$	7.59349	+	0.589591i	0.284578	+	0.0220959i
$713$	−2.31168	+	2.31168i	−0.0865732	+	0.0865732i
$714$	−9.02738	+	8.57267i	−0.337841	+	0.320824i
$715$	−13.4473	+	0.721093i	−0.502899	+	0.0269673i
$716$	9.43905	+	0.488048i	0.352754	+	0.0182392i
$717$	2.65199	+	2.65199i	0.0990403	+	0.0990403i
$718$	−0.707622	+	27.3897i	−0.0264082	+	1.02217i
$719$	5.12019			0.190951			0.0954754	−	0.995432i	$-0.469563\pi$
$719$	5.12019			0.190951			0.0954754	+	0.995432i	$0.469563\pi$
$720$	16.1877	+	17.8841i	0.603281	+	0.666500i
$721$	−13.7798			−0.513186
$722$	0.0365245	−	1.41374i	0.00135930	−	0.0526140i
$723$	−11.4029	−	11.4029i	−0.424079	−	0.424079i
$724$	40.9833	+	2.11905i	1.52313	+	0.0787539i
$725$	−31.3328	+	3.37005i	−1.16367	+	0.125161i
$726$	5.67895	−	5.39291i	0.210766	−	0.200150i
$727$	−4.29545	+	4.29545i	−0.159309	+	0.159309i	−0.782261	−	0.622951i	$-0.785933\pi$
$727$	−4.29545	+	4.29545i	−0.159309	+	0.159309i	0.622951	+	0.782261i	$0.285933\pi$
$728$	70.6695	+	5.48709i	2.61919	+	0.203365i
$729$			11.9850i			0.443887i
$730$	11.6344	−	0.322854i	0.430609	−	0.0119494i
$731$		−	34.7684i		−	1.28596i
$732$	2.88325	+	3.19766i	0.106568	+	0.118189i
$733$	−35.0078	+	35.0078i	−1.29304	+	1.29304i	−0.360149	+	0.932895i	$0.617274\pi$
$733$	−35.0078	+	35.0078i	−1.29304	+	1.29304i	−0.932895	+	0.360149i	$0.882726\pi$
$734$	−26.2164	−	27.6069i	−0.967665	−	1.01899i
$735$	0.612031	+	11.4134i	0.0225751	+	0.420991i
$736$	4.10786	−	3.16352i	0.151418	−	0.116609i
$737$	0.691093	+	0.691093i	0.0254567	+	0.0254567i
$738$	−6.62290	−	0.171105i	−0.243792	−	0.00629846i
$739$	−8.32614			−0.306282			−0.153141	−	0.988204i	$-0.548939\pi$
$739$	−8.32614			−0.306282			−0.153141	+	0.988204i	$0.548939\pi$
$740$	21.1433	−	0.0404516i	0.777242	−	0.00148703i
$741$	−3.41864			−0.125587
$742$	61.3627	+	1.58533i	2.25269	+	0.0581992i
$743$	−12.6129	−	12.6129i	−0.462722	−	0.462722i	0.436825	−	0.899547i	$-0.356103\pi$
$743$	−12.6129	−	12.6129i	−0.462722	−	0.462722i	−0.899547	+	0.436825i	$0.856103\pi$
$744$	−3.61132	−	4.21933i	−0.132397	−	0.154688i
$745$	−12.2194	−	10.9756i	−0.447683	−	0.402114i
$746$	14.3287	+	15.0887i	0.524610	+	0.552436i
$747$	27.7909	−	27.7909i	1.01681	−	1.01681i
$748$	−5.70794	+	5.14670i	−0.208703	+	0.188182i
$749$			50.2759i			1.83704i
$750$	8.62513	−	1.17053i	0.314945	−	0.0427418i
$751$		−	13.4816i		−	0.491952i	−0.969276	−	0.245976i	$-0.920892\pi$
$751$		−	13.4816i		−	0.491952i	0.969276	−	0.245976i	$-0.0791085\pi$
$752$	−34.1063	+	27.6979i	−1.24373	+	1.01004i
$753$	8.69697	−	8.69697i	0.316935	−	0.316935i
$754$	−40.1378	+	38.1161i	−1.46173	+	1.38811i
$755$	−2.07375	−	1.86266i	−0.0754714	−	0.0677892i
$756$	−1.30702	+	25.2784i	−0.0475360	+	0.919366i
$757$	21.8168	+	21.8168i	0.792946	+	0.792946i	0.981972	−	0.189026i	$-0.0605330\pi$
$757$	21.8168	+	21.8168i	0.792946	+	0.792946i	−0.189026	+	0.981972i	$0.560533\pi$
$758$	−0.00700669	+	0.271205i	−0.000254494	+	0.00985062i
$759$	−0.489323			−0.0177613
$760$	4.36391	+	4.57780i	0.158296	+	0.166054i
$761$	7.76971			0.281652			0.140826	−	0.990034i	$-0.455024\pi$
$761$	7.76971			0.281652			0.140826	+	0.990034i	$0.455024\pi$
$762$	−0.259726	+	10.0531i	−0.00940887	+	0.364186i
$763$	23.2210	+	23.2210i	0.840655	+	0.840655i
$764$	0.918600	−	17.7661i	0.0332338	−	0.642755i
$765$	−1.27957	−	23.8620i	−0.0462629	−	0.862731i
$766$	−27.5620	+	26.1737i	−0.995855	+	0.945695i
$767$	57.0344	−	57.0344i	2.05939	−	2.05939i
$768$	4.81788	+	7.37356i	0.173850	+	0.266070i
$769$		−	9.32233i		−	0.336172i	−0.985772	−	0.168086i	$-0.946241\pi$
$769$		−	9.32233i		−	0.336172i	0.985772	−	0.168086i	$-0.0537586\pi$
$770$	0.343298	+	12.3711i	0.0123716	+	0.445824i
$771$			1.97018i

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)

\(f(q)\)	\(=\)	\(q+(0.0365245 - 1.41374i) q^{2} +(0.389264 + 0.389264i) q^{3} +(-1.99733 - 0.103273i) q^{4} +(-1.49421 + 1.66354i) q^{5} +(0.564536 - 0.536101i) q^{6} +(2.85353 - 2.85353i) q^{7} +(-0.218952 + 2.81994i) q^{8} -2.69695i q^{9} +O(q^{10})\)	\(q+(0.0365245 - 1.41374i) q^{2} +(0.389264 + 0.389264i) q^{3} +(-1.99733 - 0.103273i) q^{4} +(-1.49421 + 1.66354i) q^{5} +(0.564536 - 0.536101i) q^{6} +(2.85353 - 2.85353i) q^{7} +(-0.218952 + 2.81994i) q^{8} -2.69695i q^{9} +(2.29723 + 2.17318i) q^{10} +0.969790i q^{11} +(-0.737288 - 0.817689i) q^{12} +(4.39116 - 4.39116i) q^{13} +(-3.92994 - 4.13838i) q^{14} +(-1.22919 + 0.0659140i) q^{15} +(3.97867 + 0.412539i) q^{16} +(-2.80193 - 2.80193i) q^{17} +(-3.81279 - 0.0985048i) q^{18} -1.00000 q^{19} +(3.15622 - 3.16832i) q^{20} +2.22155 q^{21} +(1.37103 + 0.0354211i) q^{22} +(0.648103 + 0.648103i) q^{23} +(-1.18293 + 1.01247i) q^{24} +(-0.534700 - 4.97133i) q^{25} +(-6.04759 - 6.36836i) q^{26} +(2.21761 - 2.21761i) q^{27} +(-5.99414 + 5.40476i) q^{28} -6.30270i q^{29} +(0.0482896 + 1.74017i) q^{30} +3.56684i q^{31} +(0.728543 - 5.60974i) q^{32} +(-0.377504 + 0.377504i) q^{33} +(-4.06354 + 3.85887i) q^{34} +(0.483189 + 9.01072i) q^{35} +(-0.278521 + 5.38670i) q^{36} +(3.34305 + 3.34305i) q^{37} +(-0.0365245 + 1.41374i) q^{38} +3.41864 q^{39} +(-4.36391 - 4.57780i) q^{40} +1.73702 q^{41} +(0.0811412 - 3.14070i) q^{42} +(6.20437 + 6.20437i) q^{43} +(0.100153 - 1.93699i) q^{44} +(4.48647 + 4.02979i) q^{45} +(0.939922 - 0.892579i) q^{46} +(-7.76694 + 7.76694i) q^{47} +(1.38816 + 1.70934i) q^{48} -9.28530i q^{49} +(-7.04770 + 0.574352i) q^{50} -2.18138i q^{51} +(-9.22410 + 8.31712i) q^{52} +(-7.60538 + 7.60538i) q^{53} +(-3.05414 - 3.21613i) q^{54} +(-1.61328 - 1.44907i) q^{55} +(7.42200 + 8.67158i) q^{56} +(-0.389264 - 0.389264i) q^{57} +(-8.91039 - 0.230203i) q^{58} +12.9884 q^{59} +(2.46191 - 0.00471017i) q^{60} -3.91061 q^{61} +(5.04260 + 0.130277i) q^{62} +(-7.69583 - 7.69583i) q^{63} +(-7.90412 - 1.23486i) q^{64} +(0.743555 + 13.8662i) q^{65} +(0.519905 + 0.547481i) q^{66} +(0.712621 - 0.712621i) q^{67} +(5.30702 + 5.88575i) q^{68} +0.504566i q^{69} +(12.7565 - 0.353992i) q^{70} -5.91449i q^{71} +(7.60523 + 0.590503i) q^{72} +(2.60253 - 2.60253i) q^{73} +(4.84831 - 4.60411i) q^{74} +(1.72702 - 2.14330i) q^{75} +(1.99733 + 0.103273i) q^{76} +(2.76733 + 2.76733i) q^{77} +(0.124864 - 4.83307i) q^{78} -9.60097 q^{79} +(-6.63122 + 6.00224i) q^{80} -6.36437 q^{81} +(0.0634439 - 2.45570i) q^{82} +(10.3046 + 10.3046i) q^{83} +(-4.43718 - 0.229425i) q^{84} +(8.84777 - 0.474450i) q^{85} +(8.99799 - 8.54476i) q^{86} +(2.45341 - 2.45341i) q^{87} +(-2.73475 - 0.212338i) q^{88} -2.69278i q^{89} +(5.86095 - 6.19552i) q^{90} -25.0607i q^{91} +(-1.22755 - 1.36141i) q^{92} +(-1.38844 + 1.38844i) q^{93} +(10.6968 + 11.2641i) q^{94} +(1.49421 - 1.66354i) q^{95} +(2.46726 - 1.90007i) q^{96} +(2.26579 + 2.26579i) q^{97} +(-13.1270 - 0.339141i) q^{98} +2.61547 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more