LMFDB - Embedded newform 380.2.k.c.267.1

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			267.1
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41374 + 0.0365245i) q^{2} +(-0.389264 - 0.389264i) q^{3} +(1.99733 - 0.103273i) q^{4} +(-1.49421 + 1.66354i) q^{5} +(0.564536 + 0.536101i) q^{6} +(-2.85353 + 2.85353i) q^{7} +(-2.81994 + 0.218952i) q^{8} -2.69695i q^{9} +O(q^{10})$	\(q+(-1.41374 + 0.0365245i) 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} +(-2.81994 + 0.218952i) q^{8} -2.69695i q^{9} +(2.05166 - 2.40638i) q^{10} -0.969790i q^{11} +(-0.817689 - 0.737288i) 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} +(0.0985048 + 3.81279i) q^{18} +1.00000 q^{19} +(-2.81263 + 3.47694i) q^{20} +2.22155 q^{21} +(0.0354211 + 1.37103i) 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} +(-5.40476 + 5.99414i) q^{28} -6.30270i q^{29} +(-1.73535 + 0.138081i) q^{30} -3.56684i q^{31} +(-5.60974 + 0.728543i) 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} +(-1.41374 + 0.0365245i) q^{38} -3.41864 q^{39} +(3.84933 - 5.01823i) q^{40} +1.73702 q^{41} +(-3.14070 + 0.0811412i) 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} +(-1.70934 - 1.38816i) q^{48} -9.28530i q^{49} +(0.937503 + 7.00864i) q^{50} +2.18138i q^{51} +(8.31712 - 9.22410i) 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} +(0.230203 + 8.91039i) q^{58} -12.9884 q^{59} +(2.44830 - 0.258594i) q^{60} -3.91061 q^{61} +(0.130277 + 5.04260i) 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} +(-5.88575 - 5.30702i) q^{68} +0.504566i q^{69} +(1.01222 + 12.7212i) q^{70} +5.91449i q^{71} +(0.590503 + 7.60523i) 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} +(4.83307 - 0.124864i) q^{78} +9.60097 q^{79} +(-5.25868 + 7.23508i) q^{80} -6.36437 q^{81} +(-2.45570 + 0.0634439i) 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} +(0.212338 + 2.73475i) q^{88} -2.69278i q^{89} +(-6.48989 - 5.53322i) q^{90} +25.0607i q^{91} +(-1.36141 - 1.22755i) 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} +(0.339141 + 13.1270i) 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} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.41374	+	0.0365245i	−0.999666	+	0.0258267i
$2$	−1.41374	+	0.0365245i	−0.999666	+	0.0258267i
$3$	−0.389264	−	0.389264i	−0.224741	−	0.224741i	0.585750	−	0.810492i	$-0.300800\pi$
$3$	−0.389264	−	0.389264i	−0.224741	−	0.224741i	−0.810492	+	0.585750i	$0.800800\pi$
$4$	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	$0.526097\pi$
$7$	−2.85353	+	2.85353i	−1.07853	+	1.07853i	−0.996641	+	0.0818930i	$0.973903\pi$
$8$	−2.81994	+	0.218952i	−0.996999	+	0.0774113i
$9$		−	2.69695i		−	0.898983i
$10$	2.05166	−	2.40638i	0.648792	−	0.760966i
$11$		−	0.969790i		−	0.292403i	−0.989255	−	0.146201i	$-0.953295\pi$
$11$		−	0.969790i		−	0.292403i	0.989255	−	0.146201i	$-0.0467047\pi$
$12$	−0.817689	−	0.737288i	−0.236046	−	0.212837i
$13$	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	$0.909555\pi$
$18$	0.0985048	+	3.81279i	0.0232178	+	0.898683i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−2.81263	+	3.47694i	−0.628922	+	0.777468i
$21$	2.22155			0.484783
$22$	0.0354211	+	1.37103i	0.00755181	+	0.292305i
$23$	−0.648103	−	0.648103i	−0.135139	−	0.135139i	0.636302	−	0.771440i	$-0.280463\pi$
$23$	−0.648103	−	0.648103i	−0.135139	−	0.135139i	−0.771440	+	0.636302i	$0.780463\pi$
$24$	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
$28$	−5.40476	+	5.99414i	−1.02140	+	1.13279i
$29$		−	6.30270i		−	1.17038i	−0.810895	−	0.585191i	$-0.801020\pi$
$29$		−	6.30270i		−	1.17038i	0.810895	−	0.585191i	$-0.198980\pi$
$30$	−1.73535	+	0.138081i	−0.316831	+	0.0252100i
$31$		−	3.56684i		−	0.640624i	−0.947312	−	0.320312i	$-0.896212\pi$
$31$		−	3.56684i		−	0.640624i	0.947312	−	0.320312i	$-0.103788\pi$
$32$	−5.60974	+	0.728543i	−0.991672	+	0.128789i
$33$	−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	$0.622951\pi$
$38$	−1.41374	+	0.0365245i	−0.229339	+	0.00592506i
$39$	−3.41864			−0.547420
$40$	3.84933	−	5.01823i	0.608633	−	0.793452i
$41$	1.73702			0.271277			0.135639	−	0.990758i	$-0.456691\pi$
$41$	1.73702			0.271277			0.135639	+	0.990758i	$0.456691\pi$
$42$	−3.14070	+	0.0811412i	−0.484621	+	0.0125204i
$43$	−6.20437	−	6.20437i	−0.946157	−	0.946157i	0.0524655	−	0.998623i	$-0.483292\pi$
$43$	−6.20437	−	6.20437i	−0.946157	−	0.946157i	−0.998623	+	0.0524655i	$0.983292\pi$
$44$	−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	$-0.454249\pi$
$47$	7.76694	−	7.76694i	1.13293	−	1.13293i	0.989688	−	0.143237i	$-0.0457510\pi$
$48$	−1.70934	−	1.38816i	−0.246722	−	0.200364i
$49$		−	9.28530i		−	1.32647i
$50$	0.937503	+	7.00864i	0.132583	+	0.991172i
$51$			2.18138i			0.305454i
$52$	8.31712	−	9.22410i	1.15338	−	1.27915i
$53$	−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
$58$	0.230203	+	8.91039i	0.0302272	+	1.16999i
$59$	−12.9884			−1.69095			−0.845475	−	0.534014i	$-0.820683\pi$
$59$	−12.9884			−1.69095			−0.845475	+	0.534014i	$0.820683\pi$
$60$	2.44830	−	0.258594i	0.316074	−	0.0333843i
$61$	−3.91061			−0.500702			−0.250351	−	0.968155i	$-0.580546\pi$
$61$	−3.91061			−0.500702			−0.250351	+	0.968155i	$0.580546\pi$
$62$	0.130277	+	5.04260i	0.0165452	+	0.640410i
$63$	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	−0.749296	−	0.662235i	$-0.769608\pi$
$67$	−0.712621	+	0.712621i	−0.0870606	+	0.0870606i	0.662235	+	0.749296i	$0.269608\pi$
$68$	−5.88575	−	5.30702i	−0.713751	−	0.643571i
$69$			0.504566i			0.0607426i
$70$	1.01222	+	12.7212i	0.120983	+	1.52047i
$71$			5.91449i			0.701921i	0.936390	+	0.350960i	$0.114145\pi$
$71$			5.91449i			0.701921i	−0.936390	+	0.350960i	$0.885855\pi$
$72$	0.590503	+	7.60523i	0.0695914	+	0.896285i
$73$	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
$78$	4.83307	−	0.124864i	0.547238	−	0.0141381i
$79$	9.60097			1.08019			0.540097	−	0.841603i	$-0.318388\pi$
$79$	9.60097			1.08019			0.540097	+	0.841603i	$0.318388\pi$
$80$	−5.25868	+	7.23508i	−0.587938	+	0.808906i
$81$	−6.36437			−0.707152
$82$	−2.45570	+	0.0634439i	−0.271187	+	0.00700621i
$83$	−10.3046	−	10.3046i	−1.13107	−	1.13107i	−0.989999	−	0.141073i	$-0.954945\pi$
$83$	−10.3046	−	10.3046i	−1.13107	−	1.13107i	−0.141073	−	0.989999i	$-0.545055\pi$
$84$	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
$88$	0.212338	+	2.73475i	0.0226353	+	0.291525i
$89$		−	2.69278i		−	0.285435i	−0.989763	−	0.142717i	$-0.954416\pi$
$89$		−	2.69278i		−	0.285435i	0.989763	−	0.142717i	$-0.0455840\pi$
$90$	−6.48989	−	5.53322i	−0.684095	−	0.583253i
$91$			25.0607i			2.62707i
$92$	−1.36141	−	1.22755i	−0.141937	−	0.127981i
$93$	−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	$0.697988\pi$
$98$	0.339141	+	13.1270i	0.0342585	+	1.32603i
$99$	−2.61547			−0.262865
$100$	−1.58137	−	9.87417i	−0.158137	−	0.987417i
$101$	−0.419166			−0.0417086			−0.0208543	−	0.999783i	$-0.506639\pi$
$101$	−0.419166			−0.0417086			−0.0208543	+	0.999783i	$0.506639\pi$
$102$	−0.0796738	−	3.08391i	−0.00788888	−	0.305352i
$103$	2.41451	+	2.41451i	0.237909	+	0.237909i	0.815984	−	0.578075i	$-0.196196\pi$
$103$	2.41451	+	2.41451i	0.237909	+	0.237909i	−0.578075	+	0.815984i	$0.696196\pi$
$104$	−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	−0.138697	−	0.990335i	$-0.544291\pi$
$107$	8.80941	−	8.80941i	0.851638	−	0.851638i	0.990335	+	0.138697i	$0.0442914\pi$
$108$	−4.20029	+	4.65833i	−0.404173	+	0.448248i
$109$			8.13761i			0.779442i	0.920933	+	0.389721i	$0.127429\pi$
$109$			8.13761i			0.779442i	−0.920933	+	0.389721i	$0.872571\pi$
$110$	−2.33369	−	1.98968i	−0.222508	−	0.189709i
$111$		−	2.60265i		−	0.247033i
$112$	−10.1761	+	12.5305i	−0.961548	+	1.18402i
$113$	−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
$118$	18.3623	−	0.474397i	1.69039	−	0.0436718i
$119$	15.9908			1.46587
$120$	−3.45182	+	0.455008i	−0.315107	+	0.0415364i
$121$	10.0595			0.914501
$122$	5.52859	−	0.142833i	0.500535	−	0.0129315i
$123$	−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	−0.174206	−	0.984709i	$-0.555736\pi$
$127$	9.13391	−	9.13391i	0.810503	−	0.810503i	0.984709	+	0.174206i	$0.0557359\pi$
$128$	−11.1293	+	2.03447i	−0.983699	+	0.179824i
$129$			4.83027i			0.425281i
$130$	−1.55765	−	19.5760i	−0.136615	−	1.71693i
$131$			10.7793i			0.941795i	0.882188	+	0.470897i	$0.156070\pi$
$131$			10.7793i			0.941795i	−0.882188	+	0.470897i	$0.843930\pi$
$132$	−0.715015	+	0.792986i	−0.0622341	+	0.0690206i
$133$	−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	$0.662996\pi$
$138$	−0.0184290	−	0.713326i	−0.00156878	−	0.0607223i
$139$	−9.92662			−0.841965			−0.420982	−	0.907069i	$-0.638315\pi$
$139$	−9.92662			−0.841965			−0.420982	+	0.907069i	$0.638315\pi$
$140$	−1.89565	−	17.9475i	−0.160211	−	1.51684i
$141$	−6.04678			−0.509230
$142$	−0.216024	−	8.36156i	−0.0181283	−	0.701687i
$143$	−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
$148$	7.02242	+	6.33193i	0.577240	+	0.520482i
$149$			7.34543i			0.601761i	0.953662	+	0.300880i	$0.0972805\pi$
$149$			7.34543i			0.601761i	−0.953662	+	0.300880i	$0.902719\pi$
$150$	2.36327	−	3.09315i	0.192960	−	0.252554i
$151$		−	1.24659i		−	0.101446i	−0.998713	−	0.0507230i	$-0.983847\pi$
$151$		−	1.24659i		−	0.101446i	0.998713	−	0.0507230i	$-0.0161526\pi$
$152$	−2.81994	+	0.218952i	−0.228727	+	0.0177594i
$153$	−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	$0.992575\pi$
$158$	−13.5733	+	0.350671i	−1.07983	+	0.0278979i
$159$	5.92100			0.469566
$160$	7.17015	−	10.4206i	0.566850	−	0.823821i
$161$	3.69877			0.291504
$162$	8.99758	−	0.232456i	0.706916	−	0.0182634i
$163$	−10.0729	−	10.0729i	−0.788971	−	0.788971i	0.192355	−	0.981326i	$-0.438388\pi$
$163$	−10.0729	−	10.0729i	−0.788971	−	0.788971i	−0.981326	+	0.192355i	$0.938388\pi$
$164$	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	−0.916949	−	0.399005i	$-0.869356\pi$
$167$	−6.69330	+	6.69330i	−0.517943	+	0.517943i	0.399005	+	0.916949i	$0.369356\pi$
$168$	−6.26465	+	0.486414i	−0.483328	+	0.0375277i
$169$		−	25.5646i		−	1.96651i
$170$	−12.4911	+	0.993911i	−0.958026	+	0.0762295i
$171$		−	2.69695i		−	0.206241i
$172$	−13.0329	−	11.7514i	−0.993751	−	0.896039i
$173$	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
$178$	0.0983527	+	3.80690i	0.00737185	+	0.285339i
$179$	4.72583			0.353225			0.176613	−	0.984280i	$-0.443486\pi$
$179$	4.72583			0.353225			0.176613	+	0.984280i	$0.443486\pi$
$180$	9.37713	+	7.58551i	0.698930	+	0.565390i
$181$	−20.5190			−1.52517			−0.762584	−	0.646890i	$-0.776069\pi$
$181$	−20.5190			−1.52517			−0.762584	+	0.646890i	$0.776069\pi$
$182$	−0.915329	−	35.4293i	−0.0678487	−	2.62619i
$183$	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
$188$	14.7111	−	16.3153i	1.07291	−	1.18991i
$189$		−	12.6561i		−	0.920594i
$190$	2.05166	−	2.40638i	0.148843	−	0.174577i
$191$		−	8.89491i		−	0.643613i	−0.946805	−	0.321807i	$-0.895710\pi$
$191$		−	8.89491i		−	0.643613i	0.946805	−	0.321807i	$-0.104290\pi$
$192$	−3.55747	−	2.59610i	−0.256739	−	0.187357i
$193$	−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	$0.798800\pi$
$198$	3.69760	−	0.0955289i	0.262777	−	0.00678895i
$199$	−17.9178			−1.27016			−0.635080	−	0.772446i	$-0.719033\pi$
$199$	−17.9178			−1.27016			−0.635080	+	0.772446i	$0.719033\pi$
$200$	2.59631	+	13.9018i	0.183587	+	0.983004i
$201$	0.554795			0.0391322
$202$	0.592593	−	0.0153098i	0.0416947	−	0.00107720i
$203$	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
$208$	15.6595	−	19.2825i	1.08579	−	1.33700i
$209$		−	0.969790i		−	0.0670818i
$210$	4.55787	−	5.34591i	0.314523	−	0.368903i
$211$		−	3.02129i		−	0.207994i	−0.994578	−	0.103997i	$-0.966837\pi$
$211$		−	3.02129i		−	0.207994i	0.994578	−	0.103997i	$-0.0331633\pi$
$212$	−14.4050	+	15.9759i	−0.989343	+	1.09723i
$213$	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
$218$	−0.297223	−	11.5045i	−0.0201305	−	0.779182i
$219$	−2.02614			−0.136914
$220$	3.37190	+	2.72766i	0.227334	+	0.183899i
$221$	−24.6075			−1.65528
$222$	0.0950608	+	3.67948i	0.00638006	+	0.246951i
$223$	9.47805	+	9.47805i	0.634697	+	0.634697i	0.949242	−	0.314545i	$-0.101852\pi$
$223$	9.47805	+	9.47805i	0.634697	+	0.634697i	−0.314545	+	0.949242i	$0.601852\pi$
$224$	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	$-0.421917\pi$
$227$	18.2744	−	18.2744i	1.21292	−	1.21292i	0.970063	−	0.242853i	$-0.0780834\pi$
$228$	−0.817689	−	0.737288i	−0.0541528	−	0.0488281i
$229$			5.34676i			0.353324i	0.984272	+	0.176662i	$0.0565299\pi$
$229$			5.34676i			0.353324i	−0.984272	+	0.176662i	$0.943470\pi$
$230$	−2.88927	+	0.229898i	−0.190513	+	0.0151590i
$231$		−	2.15444i		−	0.141752i
$232$	1.37999	+	17.7732i	0.0906008	+	1.16687i
$233$	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
$238$	−22.6069	+	0.584056i	−1.46538	+	0.0378588i
$239$	−6.81283			−0.440686			−0.220343	−	0.975422i	$-0.570718\pi$
$239$	−6.81283			−0.440686			−0.220343	+	0.975422i	$0.570718\pi$
$240$	4.86336	−	0.769340i	0.313929	−	0.0496607i
$241$	−29.2936			−1.88696			−0.943482	−	0.331423i	$-0.892471\pi$
$241$	−29.2936			−1.88696			−0.943482	+	0.331423i	$0.892471\pi$
$242$	−14.2215	+	0.367419i	−0.914196	+	0.0236186i
$243$	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
$248$	0.780969	+	10.0583i	0.0495916	+	0.638702i
$249$			8.02238i			0.508398i
$250$	−13.0599	−	8.91278i	−0.825984	−	0.563694i
$251$			22.3421i			1.41022i	0.709097	+	0.705111i	$0.249103\pi$
$251$			22.3421i			1.41022i	−0.709097	+	0.705111i	$0.750897\pi$
$252$	16.1659	+	14.5764i	1.01836	+	0.918224i
$253$	−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	$0.714395\pi$
$258$	−0.176423	−	6.82875i	−0.0109836	−	0.425140i
$259$	−19.0790			−1.18551
$260$	2.91712	+	27.6185i	0.180912	+	1.71283i
$261$	−16.9981			−1.05215
$262$	−0.393710	−	15.2392i	−0.0243235	−	0.941480i
$263$	−16.4134	−	16.4134i	−1.01209	−	1.01209i	−0.999926	−	0.0121679i	$-0.996127\pi$
$263$	−16.4134	−	16.4134i	−1.01209	−	1.01209i	−0.0121679	−	0.999926i	$-0.503873\pi$
$264$	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
$268$	−1.34975	+	1.49694i	−0.0824489	+	0.0914399i
$269$			3.03533i			0.185067i	0.995710	+	0.0925337i	$0.0294966\pi$
$269$			3.03533i			0.185067i	−0.995710	+	0.0925337i	$0.970503\pi$
$270$	0.786641	+	9.88623i	0.0478734	+	0.601656i
$271$		−	28.9197i		−	1.75675i	−0.477977	−	0.878373i	$-0.658630\pi$
$271$		−	28.9197i		−	1.75675i	0.477977	−	0.878373i	$-0.341370\pi$
$272$	−12.3039	−	9.99205i	−0.746031	−	0.605857i
$273$	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	$0.438201\pi$
$278$	14.0337	−	0.362565i	0.841684	−	0.0217452i
$279$	−9.61959			−0.575910
$280$	3.33548	+	25.3039i	0.199333	+	1.51220i
$281$	22.9263			1.36767			0.683834	−	0.729637i	$-0.260311\pi$
$281$	22.9263			1.36767			0.683834	+	0.729637i	$0.260311\pi$
$282$	8.54858	−	0.220856i	0.509061	−	0.0131518i
$283$	−14.0869	−	14.0869i	−0.837380	−	0.837380i	0.151134	−	0.988513i	$-0.451708\pi$
$283$	−14.0869	−	14.0869i	−0.837380	−	0.837380i	−0.988513	+	0.151134i	$0.951708\pi$
$284$	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
$288$	1.96484	+	15.1292i	0.115779	+	0.891496i
$289$		−	1.29838i		−	0.0763755i
$290$	−15.1667	−	12.9310i	−0.890621	−	0.759335i
$291$		−	1.76398i		−	0.103406i
$292$	4.92935	−	5.46689i	0.288468	−	0.319926i
$293$	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
$298$	−0.268288	−	10.3845i	−0.0155415	−	0.601560i
$299$	−5.69185			−0.329168
$300$	−3.22808	+	4.45923i	−0.186373	+	0.257454i
$301$	35.4087			2.04093
$302$	0.0455311	+	1.76236i	0.00262002	+	0.101412i
$303$	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	−0.999978	−	0.00668634i	$-0.997872\pi$
$307$	−17.4039	+	17.4039i	−0.993291	+	0.993291i	0.00668634	+	0.999978i	$0.497872\pi$
$308$	5.81306	+	5.24148i	0.331230	+	0.298661i
$309$		−	1.87976i		−	0.106936i
$310$	−8.58320	−	7.31795i	−0.487493	−	0.415632i
$311$			5.65794i			0.320833i	0.987049	+	0.160416i	$0.0512837\pi$
$311$			5.65794i			0.320833i	−0.987049	+	0.160416i	$0.948716\pi$
$312$	9.64036	−	0.748519i	0.545778	−	0.0423765i
$313$	−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	$0.687785\pi$
$318$	−8.37076	+	0.216262i	−0.469409	+	0.0121274i
$319$	−6.11230			−0.342223
$320$	−9.75614	+	14.9939i	−0.545385	+	0.838186i
$321$	−6.85837			−0.382797
$322$	−5.22910	+	0.135096i	−0.291407	+	0.00752859i
$323$	−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
$328$	−4.89830	+	0.380325i	−0.270463	+	0.0209999i
$329$			44.3265i			2.44380i
$330$	0.133910	+	1.68293i	0.00737148	+	0.0926422i
$331$			10.7319i			0.589881i	0.955516	+	0.294941i	$0.0952999\pi$
$331$			10.7319i			0.589881i	−0.955516	+	0.294941i	$0.904700\pi$
$332$	−21.6458	−	19.5174i	−1.18797	−	1.07116i
$333$	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	$0.320077\pi$
$338$	0.933736	+	36.1418i	0.0507885	+	1.96585i
$339$	2.89379			0.157169
$340$	17.6229	−	1.86137i	0.955738	−	0.100947i
$341$	−3.45909			−0.187320
$342$	0.0985048	+	3.81279i	0.00532653	+	0.206172i
$343$	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	−0.163940	−	0.986470i	$-0.552420\pi$
$347$	15.3220	−	15.3220i	0.822531	−	0.822531i	0.986470	+	0.163940i	$0.0524202\pi$
$348$	−4.64691	+	5.15365i	−0.249100	+	0.276264i
$349$			13.6503i			0.730685i	0.930873	+	0.365342i	$0.119048\pi$
$349$			13.6503i			0.730685i	−0.930873	+	0.365342i	$0.880952\pi$
$350$	−22.6746	−	17.3242i	−1.21201	−	0.926017i
$351$			19.4758i			1.03954i
$352$	0.706534	+	5.44027i	0.0376584	+	0.289968i
$353$	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
$358$	−6.68110	+	0.172609i	−0.353107	+	0.00912266i
$359$	19.3739			1.02251			0.511257	−	0.859428i	$-0.329180\pi$
$359$	19.3739			1.02251			0.511257	+	0.859428i	$0.329180\pi$
$360$	−13.5339	−	10.3815i	−0.713299	−	0.547151i
$361$	1.00000			0.0526316
$362$	29.0086	−	0.749448i	1.52466	−	0.0393901i
$363$	−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	−0.999980	−	0.00632048i	$-0.997988\pi$
$367$	−19.0358	+	19.0358i	−0.993660	+	0.993660i	0.00632048	+	0.999980i	$0.497988\pi$
$368$	−2.84596	−	2.31122i	−0.148356	−	0.120481i
$369$		−	4.68466i		−	0.243874i
$370$	14.9035	−	1.18586i	0.774794	−	0.0616499i
$371$		−	43.4044i		−	2.25345i
$372$	−2.62979	+	2.91657i	−0.136348	+	0.151217i
$373$	−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
$378$	0.462257	+	17.8924i	0.0237759	+	0.920287i
$379$	0.191835			0.00985390			0.00492695	−	0.999988i	$-0.498432\pi$
$379$	0.191835			0.00985390			0.00492695	+	0.999988i	$0.498432\pi$
$380$	−2.81263	+	3.47694i	−0.144285	+	0.178363i
$381$	−7.11099			−0.364307
$382$	0.324883	+	12.5751i	0.0166224	+	0.643399i
$383$	19.0048	+	19.0048i	0.971099	+	0.971099i	0.999594	−	0.0284950i	$-0.00907147\pi$
$383$	19.0048	+	19.0048i	0.971099	+	0.971099i	−0.0284950	+	0.999594i	$0.509071\pi$
$384$	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
$388$	4.75952	+	4.29154i	0.241628	+	0.217870i
$389$		−	0.624834i		−	0.0316803i	−0.999875	−	0.0158402i	$-0.994958\pi$
$389$		−	0.624834i		−	0.0316803i	0.999875	−	0.0158402i	$-0.00504229\pi$
$390$	−7.01389	+	8.22656i	−0.355162	+	0.416568i
$391$			3.63188i			0.183672i
$392$	2.03304	+	26.1840i	0.102684	+	1.32249i
$393$	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	$0.569620\pi$
$398$	25.3312	−	0.654440i	1.26974	−	0.0328041i
$399$	2.22155			0.111217
$400$	−4.17826	−	19.5587i	−0.208913	−	0.977934i
$401$	8.47122			0.423033			0.211516	−	0.977374i	$-0.432160\pi$
$401$	8.47122			0.423033			0.211516	+	0.977374i	$0.432160\pi$
$402$	−0.784337	+	0.0202636i	−0.0391192	+	0.00101066i
$403$	−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
$408$	−0.477618	−	6.15135i	−0.0236456	−	0.304537i
$409$		−	28.7680i		−	1.42249i	−0.702946	−	0.711243i	$-0.748133\pi$
$409$		−	28.7680i		−	1.42249i	0.702946	−	0.711243i	$-0.251867\pi$
$410$	3.56378	−	4.17995i	0.176003	−	0.206433i
$411$		−	3.47869i		−	0.171591i
$412$	5.07193	+	4.57323i	0.249876	+	0.225307i
$413$	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
$418$	0.0354211	+	1.37103i	0.00173250	+	0.0670594i
$419$	23.1003			1.12853			0.564263	−	0.825595i	$-0.309160\pi$
$419$	23.1003			1.12853			0.564263	+	0.825595i	$0.309160\pi$
$420$	−6.24840	+	7.72421i	−0.304891	+	0.376903i
$421$	9.20299			0.448526			0.224263	−	0.974529i	$-0.428002\pi$
$421$	9.20299			0.448526			0.224263	+	0.974529i	$0.428002\pi$
$422$	0.110351	+	4.27133i	0.00537182	+	0.207925i
$423$	−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
$428$	16.6856	−	18.5051i	0.806527	−	0.894477i
$429$			3.31536i			0.160067i
$430$	−27.6594	+	2.20084i	−1.33385	+	0.106134i
$431$			10.9176i			0.525881i	0.964812	+	0.262940i	$0.0846923\pi$
$431$			10.9176i			0.525881i	−0.964812	+	0.262940i	$0.915308\pi$
$432$	−7.90830	+	9.73801i	−0.380488	+	0.468520i
$433$	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
$438$	2.86444	−	0.0740039i	0.136868	−	0.00353604i
$439$	16.3970			0.782588			0.391294	−	0.920266i	$-0.372028\pi$
$439$	16.3970			0.782588			0.391294	+	0.920266i	$0.372028\pi$
$440$	−4.86663	−	3.73305i	−0.232007	−	0.177966i
$441$	−25.0420			−1.19248
$442$	34.7886	−	0.898776i	1.65472	−	0.0427504i
$443$	−23.3948	−	23.3948i	−1.11152	−	1.11152i	−0.992945	−	0.118573i	$-0.962168\pi$
$443$	−23.3948	−	23.3948i	−1.11152	−	1.11152i	−0.118573	−	0.992945i	$-0.537832\pi$
$444$	−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
$448$	−19.0309	+	26.0784i	−0.899127	+	1.23209i
$449$		−	11.4369i		−	0.539740i	−0.962897	−	0.269870i	$-0.913019\pi$
$449$		−	11.4369i		−	0.539740i	0.962897	−	0.269870i	$-0.0869808\pi$
$450$	18.9019	−	2.52840i	0.891046	−	0.119190i
$451$		−	1.68455i		−	0.0793222i
$452$	−7.04022	+	7.80795i	−0.331144	+	0.367255i
$453$	−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	$-0.554566\pi$
$458$	−0.195288	−	7.55894i	−0.00912520	−	0.353206i
$459$	12.4272			0.580052
$460$	4.07629	−	0.430545i	0.190058	−	0.0200743i
$461$	6.47208			0.301435			0.150717	−	0.988577i	$-0.451842\pi$
$461$	6.47208			0.301435			0.150717	+	0.988577i	$0.451842\pi$
$462$	0.0786899	+	3.04582i	0.00366099	+	0.141704i
$463$	23.7452	+	23.7452i	1.10353	+	1.10353i	0.993981	+	0.109552i	$0.0349418\pi$
$463$	23.7452	+	23.7452i	1.10353	+	1.10353i	0.109552	+	0.993981i	$0.465058\pi$
$464$	−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	−0.993269	−	0.115827i	$-0.963048\pi$
$467$	−18.9617	+	18.9617i	−0.877443	+	0.877443i	0.115827	+	0.993269i	$0.463048\pi$
$468$	−24.8769	−	22.4308i	−1.14994	−	1.03687i
$469$		−	4.06698i		−	0.187796i
$470$	−2.75512	−	34.6254i	−0.127084	−	1.59715i
$471$			9.52473i			0.438876i
$472$	36.6266	−	2.84385i	1.68588	−	0.130899i
$473$	−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
$478$	9.63159	−	0.248836i	0.440539	−	0.0113815i
$479$	9.99657			0.456755			0.228378	−	0.973573i	$-0.426658\pi$
$479$	9.99657			0.456755			0.228378	+	0.973573i	$0.426658\pi$
$480$	−6.84744	+	1.26528i	−0.312541	+	0.0577519i
$481$	29.3598			1.33869
$482$	41.4135	−	1.06993i	1.88633	−	0.0487341i
$483$	−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	−0.299462	−	0.954108i	$-0.596807\pi$
$487$	14.4468	−	14.4468i	0.654646	−	0.654646i	0.954108	+	0.299462i	$0.0968073\pi$
$488$	11.0277	−	0.856237i	0.499200	−	0.0387600i
$489$			7.84203i			0.354629i
$490$	−22.3440	−	19.0503i	−1.00940	−	0.860605i
$491$		−	11.3121i		−	0.510507i	−0.966874	−	0.255253i	$-0.917841\pi$
$491$		−	11.3121i		−	0.510507i	0.966874	−	0.255253i	$-0.0821589\pi$
$492$	−1.42034	−	1.28069i	−0.0640341	−	0.0577378i
$493$	−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
$498$	−0.293014	−	11.3416i	−0.0131303	−	0.508228i
$499$	−16.2447			−0.727212			−0.363606	−	0.931553i	$-0.618455\pi$
$499$	−16.2447			−0.727212			−0.363606	+	0.931553i	$0.618455\pi$
$500$	18.7889	+	12.1234i	0.840267	+	0.542173i
$501$	5.21092			0.232807
$502$	−0.816035	−	31.5860i	−0.0364214	−	1.40975i
$503$	−2.42975	−	2.42975i	−0.108337	−	0.108337i	0.650860	−	0.759198i	$-0.274408\pi$
$503$	−2.42975	−	2.42975i	−0.108337	−	0.108337i	−0.759198	+	0.650860i	$0.774408\pi$
$504$	−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
$508$	17.3002	−	19.1867i	0.767571	−	0.851273i
$509$		−	16.5994i		−	0.735757i	−0.929874	−	0.367878i	$-0.880084\pi$
$509$		−	16.5994i		−	0.735757i	0.929874	−	0.367878i	$-0.119916\pi$
$510$	5.24923	+	4.47545i	0.232440	+	0.198176i
$511$			14.8528i			0.657050i
$512$	−22.0188	+	5.21287i	−0.973101	+	0.230378i
$513$	−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
$518$	26.9728	−	0.696852i	1.18512	−	0.0306179i
$519$	−7.56447			−0.332043
$520$	−5.13281	−	38.9389i	−0.225089	−	1.70758i
$521$	−2.95077			−0.129276			−0.0646378	−	0.997909i	$-0.520589\pi$
$521$	−2.95077			−0.129276			−0.0646378	+	0.997909i	$0.520589\pi$
$522$	24.0309	−	0.620846i	1.05180	−	0.0271737i
$523$	−2.45025	−	2.45025i	−0.107142	−	0.107142i	0.651504	−	0.758646i	$-0.274139\pi$
$523$	−2.45025	−	2.45025i	−0.107142	−	0.107142i	−0.758646	+	0.651504i	$0.774139\pi$
$524$	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
$528$	−1.34623	+	1.65770i	−0.0585871	+	0.0721421i
$529$		−	22.1599i		−	0.963475i
$530$	2.69781	+	33.9051i	0.117185	+	1.47275i
$531$			35.0291i			1.52014i
$532$	−5.40476	+	5.99414i	−0.234326	+	0.259879i
$533$	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
$538$	−0.110864	−	4.29117i	−0.00477969	−	0.185006i
$539$	−9.00479			−0.387864
$540$	−1.47320	−	13.9478i	−0.0633963	−	0.600219i
$541$	−41.4423			−1.78174			−0.890871	−	0.454256i	$-0.849905\pi$
$541$	−41.4423			−1.78174			−0.890871	+	0.454256i	$0.849905\pi$
$542$	1.05628	+	40.8850i	0.0453710	+	1.75616i
$543$	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	−0.284679	−	0.958623i	$-0.591887\pi$
$547$	15.7622	−	15.7622i	0.673944	−	0.673944i	0.958623	+	0.284679i	$0.0918869\pi$
$548$	9.38612	+	8.46321i	0.400955	+	0.361531i
$549$			10.5467i			0.450122i
$550$	6.79691	−	0.909181i	0.289821	−	0.0387676i
$551$		−	6.30270i		−	0.268504i
$552$	−0.110476	−	1.42285i	−0.00470217	−	0.0605603i
$553$	−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	$0.583736\pi$
$558$	13.5996	−	0.351351i	0.575718	−	0.0148739i
$559$	−54.4888			−2.30463
$560$	−5.63972	−	35.6513i	−0.238322	−	1.50654i
$561$	2.11548			0.0893156
$562$	−32.4119	+	0.837373i	−1.36721	+	0.0353224i
$563$	−6.23508	−	6.23508i	−0.262777	−	0.262777i	0.563404	−	0.826181i	$-0.309491\pi$
$563$	−6.23508	−	6.23508i	−0.262777	−	0.262777i	−0.826181	+	0.563404i	$0.809491\pi$
$564$	−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
$568$	−1.29499	−	16.6785i	−0.0543366	−	0.699814i
$569$			18.7909i			0.787754i	0.919163	+	0.393877i	$0.128866\pi$
$569$			18.7909i			0.787754i	−0.919163	+	0.393877i	$0.871134\pi$
$570$	−1.73535	+	0.138081i	−0.0726860	+	0.00578358i
$571$			14.2948i			0.598220i	0.954219	+	0.299110i	$0.0966897\pi$
$571$			14.2948i			0.598220i	−0.954219	+	0.299110i	$0.903310\pi$
$572$	−8.94544	−	8.06586i	−0.374028	−	0.337251i
$573$	−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	$0.642937\pi$
$578$	0.0474229	+	1.83558i	0.00197253	+	0.0763500i
$579$	2.49161			0.103548
$580$	21.9141	+	17.7271i	0.909935	+	0.736080i
$581$	58.8088			2.43980
$582$	0.0644284	+	2.49381i	0.00267064	+	0.103372i
$583$	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	−0.844372	−	0.535757i	$-0.820026\pi$
$587$	−7.47716	+	7.47716i	−0.308615	+	0.308615i	0.535757	+	0.844372i	$0.320026\pi$
$588$	−6.84595	+	7.59249i	−0.282322	+	0.313109i
$589$		−	3.56684i		−	0.146969i
$590$	−26.6479	+	31.2552i	−1.09708	+	1.28676i
$591$			2.35990i			0.0970732i
$592$	14.6800	+	11.9218i	0.603345	+	0.489981i
$593$	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
$598$	8.04681	−	0.207892i	0.329059	−	0.00850135i
$599$	20.7064			0.846041			0.423020	−	0.906120i	$-0.360970\pi$
$599$	20.7064			0.846041			0.423020	+	0.906120i	$0.360970\pi$
$600$	4.40081	−	6.42210i	0.179662	−	0.262181i
$601$	18.2704			0.745267			0.372634	−	0.927979i	$-0.378455\pi$
$601$	18.2704			0.745267			0.372634	+	0.927979i	$0.378455\pi$
$602$	−50.0588	+	1.29329i	−2.04025	+	0.0527105i
$603$	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	−0.359336	−	0.933208i	$-0.616997\pi$
$607$	14.1387	−	14.1387i	0.573872	−	0.573872i	0.933208	+	0.359336i	$0.116997\pi$
$608$	−5.60974	+	0.728543i	−0.227505	+	0.0295463i
$609$		−	14.0018i		−	0.567381i
$610$	−8.02324	+	9.41043i	−0.324852	+	0.381017i
$611$		−	68.2118i		−	2.75956i
$612$	−14.3128	+	15.8735i	−0.578559	+	0.641650i
$613$	−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	$0.531807\pi$
$618$	0.0686575	+	2.65750i	0.00276181	+	0.106900i
$619$	35.2546			1.41700			0.708501	−	0.705710i	$-0.249372\pi$
$619$	35.2546			1.41700			0.708501	+	0.705710i	$0.249372\pi$
$620$	12.4017	+	10.0322i	0.498065	+	0.402903i
$621$	2.87449			0.115349
$622$	−0.206654	−	7.99887i	−0.00828606	−	0.320726i
$623$	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
$628$	−25.6994	−	23.1725i	−1.02552	−	0.924683i
$629$		−	18.7340i		−	0.746973i
$630$	34.3084	−	2.72989i	1.36688	−	0.108762i
$631$		−	0.132174i		−	0.00526176i	−0.999997	−	0.00263088i	$-0.999163\pi$
$631$		−	0.132174i		−	0.00526176i	0.999997	−	0.00263088i	$-0.000837437\pi$
$632$	−27.0742	+	2.10215i	−1.07695	+	0.0836192i
$633$	−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
$638$	8.64121	−	0.223249i	0.342109	−	0.00883850i
$639$	15.9511			0.631015
$640$	13.2450	−	21.5539i	0.523555	−	0.851992i
$641$	2.21113			0.0873346			0.0436673	−	0.999046i	$-0.486096\pi$
$641$	2.21113			0.0873346			0.0436673	+	0.999046i	$0.486096\pi$
$642$	9.69596	−	0.250499i	0.382669	−	0.00988639i
$643$	−0.700269	−	0.700269i	−0.0276159	−	0.0276159i	0.693164	−	0.720780i	$-0.256216\pi$
$643$	−0.700269	−	0.700269i	−0.0276159	−	0.0276159i	−0.720780	+	0.693164i	$0.756216\pi$
$644$	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	−0.320241	−	0.947336i	$-0.603764\pi$
$647$	15.9509	−	15.9509i	0.627095	−	0.627095i	0.947336	+	0.320241i	$0.103764\pi$
$648$	17.9471	−	1.39349i	0.705030	−	0.0547416i
$649$			12.5961i			0.494439i
$650$	34.8928	+	26.6594i	1.36861	+	1.04567i
$651$		−	7.92393i		−	0.310563i
$652$	−21.1592	−	19.0787i	−0.828658	−	0.747179i
$653$	−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
$658$	−1.61900	−	62.6662i	−0.0631153	−	2.44298i
$659$	41.2766			1.60791			0.803954	−	0.594691i	$-0.202726\pi$
$659$	41.2766			1.60791			0.803954	+	0.594691i	$0.202726\pi$
$660$	−0.250782	−	2.37434i	−0.00976167	−	0.0924210i
$661$	8.97089			0.348927			0.174464	−	0.984664i	$-0.444181\pi$
$661$	8.97089			0.348927			0.174464	+	0.984664i	$0.444181\pi$
$662$	−0.391979	−	15.1722i	−0.0152347	−	0.589684i
$663$	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
$668$	−12.6775	+	14.0600i	−0.490508	+	0.543997i
$669$		−	7.37892i		−	0.285285i
$670$	0.252784	+	3.17690i	0.00976589	+	0.122734i
$671$			3.79247i			0.146407i
$672$	−12.4623	+	1.61850i	−0.480745	+	0.0624348i
$673$	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	$0.976421\pi$
$678$	−4.09107	+	0.105694i	−0.157117	+	0.00405916i
$679$	−12.9310			−0.496246
$680$	−24.8463	+	3.27516i	−0.952812	+	0.125597i
$681$	−14.2271			−0.545185
$682$	4.89026	−	0.126342i	0.187258	−	0.00483787i
$683$	35.7804	+	35.7804i	1.36910	+	1.36910i	0.861726	+	0.507374i	$0.169384\pi$
$683$	35.7804	+	35.7804i	1.36910	+	1.36910i	0.507374	+	0.861726i	$0.330616\pi$
$684$	−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
$688$	−27.2447	−	22.1256i	−1.03869	−	0.843530i
$689$			66.7930i			2.54461i
$690$	1.21418	+	1.03520i	0.0462230	+	0.0394093i
$691$		−	11.0617i		−	0.420808i	−0.977614	−	0.210404i	$-0.932522\pi$
$691$		−	11.0617i		−	0.420808i	0.977614	−	0.210404i	$-0.0674780\pi$
$692$	18.4034	−	20.4103i	0.699592	−	0.775882i
$693$	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
$698$	−0.498572	−	19.2980i	−0.0188712	−	0.730441i
$699$	−9.81610			−0.371279
$700$	32.6888	+	23.6638i	1.23552	+	0.894406i
$701$	−9.68706			−0.365875			−0.182938	−	0.983125i	$-0.558561\pi$
$701$	−9.68706			−0.365875			−0.182938	+	0.983125i	$0.558561\pi$
$702$	−0.711345	−	27.5338i	−0.0268480	−	1.03920i
$703$	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
$708$	10.6205	+	9.57622i	0.399143	+	0.359897i
$709$		−	5.59192i		−	0.210009i	−0.994472	−	0.105005i	$-0.966514\pi$
$709$		−	5.59192i		−	0.210009i	0.994472	−	0.105005i	$-0.0334857\pi$
$710$	14.2325	+	12.1345i	0.534138	+	0.455401i
$711$		−	25.8933i		−	0.971075i
$712$	0.589591	+	7.59349i	0.0220959	+	0.284578i
$713$	−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
$718$	−27.3897	+	0.707622i	−1.02217	+	0.0264082i
$719$	−5.12019			−0.190951			−0.0954754	−	0.995432i	$-0.530437\pi$
$719$	−5.12019			−0.190951			−0.0954754	+	0.995432i	$0.530437\pi$
$720$	19.5126	+	14.1824i	0.727192	+	0.528546i
$721$	−13.7798			−0.513186
$722$	−1.41374	+	0.0365245i	−0.0526140	+	0.00135930i
$723$	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	−0.622951	−	0.782261i	$-0.714067\pi$
$727$	4.29545	−	4.29545i	0.159309	−	0.159309i	0.782261	+	0.622951i	$0.214067\pi$
$728$	−5.48709	−	70.6695i	−0.203365	−	2.61919i
$729$			11.9850i			0.443887i
$730$	−0.923180	−	11.6022i	−0.0341684	−	0.429417i
$731$			34.7684i			1.28596i
$732$	3.19766	+	2.88325i	0.118189	+	0.106568i
$733$	−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
$738$	0.171105	+	6.62290i	0.00629846	+	0.243792i
$739$	8.32614			0.306282			0.153141	−	0.988204i	$-0.451061\pi$
$739$	8.32614			0.306282			0.153141	+	0.988204i	$0.451061\pi$
$740$	−21.0263	+	2.22084i	−0.772944	+	0.0816397i
$741$	−3.41864			−0.125587
$742$	1.58533	+	61.3627i	0.0581992	+	2.25269i
$743$	12.6129	+	12.6129i	0.462722	+	0.462722i	0.899547	−	0.436825i	$-0.143897\pi$
$743$	12.6129	+	12.6129i	0.462722	+	0.462722i	−0.436825	+	0.899547i	$0.643897\pi$
$744$	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
$748$	−5.14670	+	5.70794i	−0.188182	+	0.208703i
$749$			50.2759i			1.83704i
$750$	1.61434	+	8.55318i	0.0589474	+	0.312318i
$751$			13.4816i			0.491952i	0.969276	+	0.245976i	$0.0791085\pi$
$751$			13.4816i			0.491952i	−0.969276	+	0.245976i	$0.920892\pi$
$752$	27.6979	−	34.1063i	1.01004	−	1.24373i
$753$	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	$0.560533\pi$
$758$	−0.271205	+	0.00700669i	−0.00985062	+	0.000254494i
$759$	0.489323			0.0177613
$760$	3.84933	−	5.01823i	0.139630	−	0.182030i
$761$	7.76971			0.281652			0.140826	−	0.990034i	$-0.455024\pi$
$761$	7.76971			0.281652			0.140826	+	0.990034i	$0.455024\pi$
$762$	10.0531	−	0.259726i	0.364186	−	0.00940887i
$763$	−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
$768$	−7.37356	−	4.81788i	−0.266070	−	0.173850i
$769$		−	9.32233i		−	0.336172i	−0.985772	−	0.168086i	$-0.946241\pi$
$769$		−	9.32233i		−	0.336172i	0.985772	−	0.168086i	$-0.0537586\pi$
$770$	12.3369	−	0.981637i	0.444590	−	0.0353757i
$771$		−	1.97018i		−	0.0709542i
$772$	−6.06177	+	6.72280i	−0.218168	+	0.241959i
$773$	−29.5041	+	29.5041i	−1.06119	+	1.06119i	−0.0631861	+	0.998002i	$0.520126\pi$
$773$	−29.5041	+	29.5041i	−1.06119	+	1.06119i	−0.998002	+	0.0631861i	$0.979874\pi$
$774$	23.0448	−	24.2671i	0.828327	−	0.872263i
$775$	−17.7319	+	1.90719i	−0.636950	+	0.0685083i
$776$	−6.88548	−	5.89328i	−0.247174	−	0.211557i
$777$	7.42676	+	7.42676i	0.266434	+	0.266434i
$778$	0.0228218	+	0.883354i	0.000818200	+	0.0316698i
$779$	1.73702			0.0622353
$780$	9.61536	−	11.8864i	0.344285	−	0.425602i
$781$	5.73581			0.205244
$782$	−0.132653	−	5.13454i	−0.00474365	−	0.183611i
$783$	13.9770	+	13.9770i	0.499496	+	0.499496i
$784$	−3.83055	−	36.9432i	−0.136805	−	1.31940i
$785$	38.6327	−	2.07163i	1.37886	−	0.0739397i
$786$	−5.77881	+	6.08532i	−0.206123	+	0.217056i
$787$	3.17153	−	3.17153i	0.113053	−	0.113053i	−0.648317	−	0.761370i	$-0.724527\pi$
$787$	3.17153	−	3.17153i	0.113053	−	0.113053i	0.761370	+	0.648317i	$0.224527\pi$
$788$	−6.36742	−	5.74134i	−0.226830	−	0.204527i
$789$			12.7783i			0.454919i
$790$	19.6979	−	23.1036i	0.700821	−	0.821990i
$791$		−	21.2132i		−	0.754254i
$792$	7.37548	−	0.572664i	0.262076	−	0.0203487i
$793$	−17.1721	+	17.1721i	−0.609800	+	0.609800i
$794$	−21.9381	−	20.8331i	−0.778555	−	0.739339i
$795$	−8.84719	+	9.84979i	−0.313777	+	0.349336i
$796$	−35.7878	+	1.85042i	−1.26847	+	0.0655863i
$797$	5.91374	+	5.91374i	0.209475	+	0.209475i	0.804045	−	0.594569i	$-0.202677\pi$
$797$	5.91374	+	5.91374i	0.209475	+	0.209475i	−0.594569	+	0.804045i	$0.702677\pi$
$798$	−3.14070	+	0.0811412i	−0.111180	+	0.00287237i
$799$	−43.5249			−1.53980
$800$	6.62135	+	27.4983i	0.234100	+	0.972212i
$801$	−7.26230			−0.256601
$802$	−11.9761	+	0.309407i	−0.422891	+	0.0109256i
$803$	−2.52391	−	2.52391i	−0.0890669	−	0.0890669i
$804$	1.10811	−	0.0572951i	0.0390800	−	0.00202064i
$805$	−5.52672	+	6.15303i	−0.194791	+	0.216866i
$806$	22.7149	+	21.5708i	0.800099	+	0.759799i
$807$	1.18154	−	1.18154i	0.0415923	−	0.0415923i
$808$	1.18202	−	0.0917774i	0.0415834	−	0.00322872i
$809$			24.3403i			0.855758i	0.903836	+	0.427879i	$0.140739\pi$
$809$			24.3403i			0.855758i	−0.903836	+	0.427879i	$0.859261\pi$
$810$	−13.0575	+	15.3151i	−0.458795	+	0.538119i
$811$		−	19.5303i		−	0.685802i	−0.939372	−	0.342901i	$-0.888591\pi$
$811$		−	19.5303i		−	0.685802i	0.939372	−	0.342901i	$-0.111409\pi$
$812$	37.7793	+	34.0646i	1.32579	+	1.19543i
$813$	−11.2574	+	11.2574i	−0.394813	+	0.394813i
$814$	−4.46502	+	4.70185i	−0.156499	+	0.164800i
$815$	31.8076	−	1.70564i	1.11417	−	0.0597461i
$816$	0.899904	+	8.67898i	0.0315029	+	0.303825i
$817$	−6.20437	−	6.20437i	−0.217063	−	0.217063i
$818$	1.05074	+	40.6705i	0.0367382	+	1.42201i
$819$	67.5873			2.36169
$820$	−4.88560	+	6.03953i	−0.170612	+	0.210909i
$821$	19.8217			0.691782			0.345891	−	0.938275i	$-0.387577\pi$
$821$	19.8217			0.691782			0.345891	+	0.938275i	$0.387577\pi$
$822$	0.127057	+	4.91797i	0.00443164	+	0.171534i
$823$	15.7710	+	15.7710i	0.549741	+	0.549741i	0.926366	−	0.376625i	$-0.122915\pi$
$823$	15.7710	+	15.7710i	0.549741	+	0.549741i	−0.376625	+	0.926366i	$0.622915\pi$
$824$	−7.33744	−	6.28012i	−0.255612	−	0.218778i
$825$	2.07855	+	1.67484i	0.0723657	+	0.0583106i
$826$	−51.0437	+	53.7511i	−1.77604	+	1.87024i
$827$	23.0810	−	23.0810i	0.802605	−	0.802605i	−0.180897	−	0.983502i	$-0.557900\pi$
$827$	23.0810	−	23.0810i	0.802605	−	0.802605i	0.983502	+	0.180897i	$0.0579001\pi$
$828$	−3.31063	+	3.67165i	−0.115052	+	0.127599i
$829$		−	5.05653i		−	0.175621i	−0.996137	−	0.0878103i	$-0.972013\pi$
$829$		−	5.05653i		−	0.175621i	0.996137	−	0.0878103i	$-0.0279869\pi$
$830$	−45.9382	+	3.65527i	−1.59454	+	0.126876i
$831$		−	15.2137i		−	0.527757i
$832$	29.2858	−	40.1308i	1.01530	−	1.39128i
$833$	−26.0168	+	26.0168i	−0.901427	+	0.901427i
$834$	−5.60393	−	5.32167i	−0.194048	−	0.184274i
$835$	−1.13338	−	21.1357i	−0.0392221	−	0.731432i
$836$	−0.100153	−	1.93699i	−0.00346385	−	0.0669923i
$837$	7.90988	+	7.90988i	0.273406	+	0.273406i
$838$	−32.6579	+	0.843729i	−1.12815	+	0.0291461i
$839$	25.7483			0.888929			0.444465	−	0.895796i	$-0.353394\pi$
$839$	25.7483			0.888929			0.444465	+	0.895796i	$0.353394\pi$
$840$	8.55150	−	11.1483i	0.295055	−	0.384652i
$841$	−10.7240			−0.369794
$842$	−13.0107	+	0.336135i	−0.448377	+	0.0115840i
$843$	−8.92438	−	8.92438i	−0.307372	−	0.307372i
$844$	−0.312017	−	6.03452i	−0.0107401	−	0.207717i
$845$	42.5277	+	38.1988i	1.46300	+	1.31408i
$846$	30.3788	+	28.8486i	1.04444	+	0.991836i
$847$	−28.7051	+	28.7051i	−0.986320	+	0.986320i
$848$	−27.1218	+	33.3968i	−0.931366	+	1.14685i
$849$			10.9670i			0.376388i
$850$	17.0109	−	22.2645i	0.583469	−	0.763668i
$851$		−	4.33328i		−	0.148543i
$852$	4.36068	−	4.83621i	0.149395	−	0.165686i
$853$	0.921427	−	0.921427i	0.0315491	−	0.0315491i	−0.691156	−	0.722705i	$-0.742898\pi$
$853$	0.921427	−	0.921427i	0.0315491	−	0.0315491i	0.722705	+	0.691156i	$0.242898\pi$
$854$	−15.3684	+	16.1836i	−0.525897	+	0.553791i
$855$	4.48647	+	4.02979i	0.153434	+	0.137816i
$856$	−22.9132	+	26.7709i	−0.783156	+	0.915009i
$857$	−10.4734	−	10.4734i	−0.357764	−	0.357764i	0.505224	−	0.862988i	$-0.331410\pi$
$857$	−10.4734	−	10.4734i	−0.357764	−	0.357764i	−0.862988	+	0.505224i	$0.831410\pi$
$858$	−0.121092	−	4.68707i	−0.00413402	−	0.160014i
$859$	−5.03701			−0.171861			−0.0859303	−	0.996301i	$-0.527386\pi$
$859$	−5.03701			−0.171861			−0.0859303	+	0.996301i	$0.527386\pi$
$860$	39.0228	−	4.12166i	1.33067	−	0.140547i
$861$	3.85889			0.131511
$862$	−0.398759	−	15.4346i	−0.0135818	−	0.525705i
$863$	14.1515	+	14.1515i	0.481724	+	0.481724i	0.905682	−	0.423958i	$-0.139360\pi$
$863$	14.1515	+	14.1515i	0.481724	+	0.481724i	−0.423958	+	0.905682i	$0.639360\pi$
$864$	10.8246	−	14.0559i	0.368261	−	0.478191i
$865$	1.64527	+	30.6818i	0.0559410	+	1.04321i
$866$	−7.40761	+	7.80051i	−0.251721	+	0.265072i
$867$	−0.505413	+	0.505413i	−0.0171647	+	0.0171647i
$868$	21.3802	+	19.2779i	0.725690	+	0.654336i
$869$		−	9.31092i		−	0.315851i
$870$	0.870283	+	10.9374i	0.0295054	+	0.370813i
$871$			6.25847i			0.212060i
$872$	−1.78175	−	22.9476i	−0.0603376	−	0.777103i
$873$	6.11071	−	6.11071i	0.206816	−	0.206816i
$874$	0.939922	+	0.892579i	0.0317933	+	0.0301919i
$875$	−44.5369	+	7.22012i	−1.50562	+	0.244085i
$876$	−4.04688	+	0.209245i	−0.136731	+	0.00706973i
$877$	−17.1018	−	17.1018i	−0.577488	−	0.577488i	0.356723	−	0.934210i	$-0.383894\pi$
$877$	−17.1018	−	17.1018i	−0.577488	−	0.577488i	−0.934210	+	0.356723i	$0.883894\pi$
$878$	−23.1812	+	0.598894i	−0.782327	+	0.0202117i
$879$	−12.1802			−0.410826
$880$	7.01650	+	5.09981i	0.236526	+	0.171915i
$881$	37.7891			1.27315			0.636573	−	0.771216i	$-0.280351\pi$
$881$	37.7891			1.27315			0.636573	+	0.771216i	$0.280351\pi$
$882$	35.4029	−	0.914647i	1.19208	−	0.0307978i
$883$	1.60062	+	1.60062i	0.0538653	+	0.0538653i	0.733526	−	0.679661i	$-0.237873\pi$
$883$	1.60062	+	1.60062i	0.0538653	+	0.0538653i	−0.679661	+	0.733526i	$0.737873\pi$
$884$	−49.1493	+	2.54127i	−1.65307	+	0.0854723i
$885$	−15.9653	+	0.856120i	−0.536668	+	0.0287781i
$886$	33.9286	+	32.2197i	1.13985	+	1.08244i
$887$	0.411294	−	0.411294i	0.0138099	−	0.0138099i	−0.700168	−	0.713978i	$-0.746892\pi$
$887$	0.411294	−	0.411294i	0.0138099	−	0.0138099i	0.713978	+	0.700168i	$0.246892\pi$
$888$	0.569857	+	7.33933i	0.0191232	+	0.246292i
$889$			52.1278i			1.74831i
$890$	−6.47988	−	5.52468i	−0.217206	−	0.185188i
$891$			6.17210i			0.206773i
$892$	19.9096	+	17.9520i	0.666624	+	0.601077i
$893$	7.76694	−	7.76694i	0.259911	−	0.259911i
$894$	−3.93789	+	4.14676i	−0.131703	+	0.138688i
$895$	−7.06136	+	7.86159i	−0.236035	+	0.262784i
$896$	25.9523	−	37.5632i	0.867007	−	1.25490i
$897$	2.21563	+	2.21563i	0.0739778	+	0.0739778i
$898$	0.417727	+	16.1688i	0.0139397	+	0.539560i
$899$	−22.4807			−0.749775
$900$	−26.6301	+	4.26489i	−0.887671	+	0.142163i
$901$	42.6195			1.41986
$902$	0.0615273	+	2.38152i	0.00204864	+	0.0792958i
$903$	−13.7833	−	13.7833i	−0.458681	−	0.458681i
$904$	9.66788	−	11.2956i	0.321549	−	0.375685i
$905$	30.6596	−	34.1341i	1.01916	−	1.13466i
$906$	0.668297	−	0.703745i	0.0222027	−	0.0233804i
$907$	30.2996	−	30.2996i	1.00608	−	1.00608i	0.00609989	−	0.999981i	$-0.498058\pi$
$907$	30.2996	−	30.2996i	1.00608	−	1.00608i	0.999981	−	0.00609989i	$-0.00194167\pi$
$908$	34.6129	−	38.3873i	1.14867	−	1.27393i
$909$			1.13047i			0.0374953i
$910$	60.3056	+	51.4160i	1.99911	+	1.70442i
$911$		−	13.8870i		−	0.460097i	−0.973179	−	0.230049i	$-0.926111\pi$
$911$		−	13.8870i		−	0.460097i	0.973179	−	0.230049i	$-0.0738885\pi$
$912$	−1.70934	−	1.38816i	−0.0566018	−	0.0459667i
$913$	−9.99326	+	9.99326i	−0.330729	+	0.330729i
$914$	35.8374	+	34.0323i	1.18540	+	1.12569i
$915$	−4.80689	+	0.257764i	−0.158911	+	0.00852141i
$916$	0.552173	+	10.6793i	0.0182443	+	0.352852i
$917$	−30.7592	−	30.7592i	−1.01576	−	1.01576i
$918$	−17.5688	+	0.453898i	−0.579858	+	0.0149809i
$919$	14.0392			0.463112			0.231556	−	0.972822i	$-0.425618\pi$
$919$	14.0392			0.463112			0.231556	+	0.972822i	$0.425618\pi$
$920$	−5.74710	+	0.757564i	−0.189476	+	0.0249762i
$921$	13.5494			0.446467
$922$	−9.14984	+	0.236390i	−0.301334	+	0.00778508i
$923$	25.9715	+	25.9715i	0.854862	+	0.854862i
$924$	−0.222494	−	4.30313i	−0.00731953	−	0.141563i
$925$	14.8319	−	18.4069i	0.487669	−	0.605216i
$926$	−34.4369	−	32.7023i	−1.13167	−	1.07466i
$927$	6.51181	−	6.51181i	0.213876	−	0.213876i
$928$	4.59179	+	35.3565i	0.150733	+	1.16064i
$929$		−	31.7859i		−	1.04286i	−0.853293	−	0.521431i	$-0.825398\pi$
$929$		−	31.7859i		−	1.04286i	0.853293	−	0.521431i	$-0.174602\pi$
$930$	0.492514	+	6.18974i	0.0161502	+	0.202970i
$931$		−	9.28530i		−	0.304314i
$932$	23.8813	−	26.4856i	0.782260	−	0.867564i
$933$	2.20243	−	2.20243i	0.0721044	−	0.0721044i
$934$	26.1144	−	27.4995i	0.854488	−	0.899811i
$935$	−0.460117	−	8.58048i	−0.0150474	−	0.280612i
$936$	35.9888	+	30.8028i	1.17633	+	1.00682i
$937$	−29.7753	−	29.7753i	−0.972718	−	0.972718i	0.0269194	−	0.999638i	$-0.491430\pi$
$937$	−29.7753	−	29.7753i	−0.972718	−	0.972718i	−0.999638	+	0.0269194i	$0.991430\pi$
$938$	0.148544	+	5.74966i	0.00485015	+	0.187733i
$939$	5.82167			0.189983
$940$	5.15970	+	48.8507i	0.168291	+	1.59334i
$941$	−36.8483			−1.20122			−0.600609	−	0.799543i	$-0.705075\pi$
$941$	−36.8483			−1.20122			−0.600609	+	0.799543i	$0.705075\pi$
$942$	−0.347886	−	13.4655i	−0.0113347	−	0.438730i
$943$	−1.12577	−	1.12577i	−0.0366601	−	0.0366601i
$944$	−51.6767	+	5.35824i	−1.68193	+	0.174396i
$945$	21.0538	+	18.9108i	0.684881	+	0.615167i
$946$	8.28663	−	8.72616i	0.269421	−	0.283712i
$947$	−17.4545	+	17.4545i	−0.567194	+	0.567194i	−0.931341	−	0.364148i	$-0.881360\pi$
$947$	−17.4545	+	17.4545i	−0.567194	+	0.567194i	0.364148	+	0.931341i	$0.381360\pi$
$948$	−7.85060	−	7.07868i	−0.254976	−	0.229905i
$949$		−	22.8563i		−	0.741947i
$950$	0.937503	+	7.00864i	0.0304166	+	0.227390i
$951$		−	3.80708i		−	0.123453i
$952$	−45.0931	+	3.50122i	−1.46148	+	0.113475i
$953$	9.83058	−	9.83058i	0.318444	−	0.318444i	−0.529725	−	0.848169i	$-0.677705\pi$
$953$	9.83058	−	9.83058i	0.318444	−	0.318444i	0.848169	+	0.529725i	$0.177705\pi$
$954$	−29.7469	−	28.2485i	−0.963091	−	0.914581i
$955$	14.7970	+	13.2908i	0.478820	+	0.430081i
$956$	−13.6075	+	0.703579i	−0.440098	+	0.0227554i
$957$	2.37929	+	2.37929i	0.0769117	+	0.0769117i
$958$	−14.1326	+	0.365120i	−0.456603	+	0.0117965i
$959$	−25.5008			−0.823465
$960$	9.63430	−	2.03888i	0.310946	−	0.0658045i
$961$	18.2776			0.589601
$962$	−41.5071	+	1.07235i	−1.33824	+	0.0345740i
$963$	−23.7585	−	23.7585i	−0.765608	−	0.765608i
$964$	−58.5090	+	3.02522i	−1.88445	+	0.0974358i
$965$	−0.541926	−	10.1061i	−0.0174452	−	0.325326i
$966$	2.08809	+	1.98291i	0.0671831	+	0.0637991i
$967$	−30.3437	+	30.3437i	−0.975787	+	0.975787i	−0.999714	−	0.0239267i	$-0.992383\pi$
$967$	−30.3437	+	30.3437i	−0.975787	+	0.975787i	0.0239267	+	0.999714i	$0.492383\pi$
$968$	−28.3672	+	2.20255i	−0.911756	+	0.0707927i
$969$			2.18138i			0.0700760i
$970$	10.1010	−	0.803729i	0.324323	−	0.0258062i
$971$			21.8232i			0.700339i	0.936686	+	0.350170i	$0.113876\pi$
$971$			21.8232i			0.700339i	−0.936686	+	0.350170i	$0.886124\pi$
$972$	19.1791	+	17.2933i	0.615169	+	0.554681i
$973$	28.3259	−	28.3259i	0.908088	−	0.908088i
$974$	−19.8963	+	20.9517i	−0.637520	+	0.671335i
$975$	1.82795	+	16.9952i	0.0585411	+	0.544281i
$976$	−15.5590	+	1.61328i	−0.498032	+	0.0516398i
$977$	−29.7016	−	29.7016i	−0.950240	−	0.950240i	0.0485795	−	0.998819i	$-0.484531\pi$
$977$	−29.7016	−	29.7016i	−0.950240	−	0.950240i	−0.998819	+	0.0485795i	$0.984531\pi$
$978$	−0.286427	−	11.0866i	−0.00915891	−	0.354511i
$979$	−2.61144			−0.0834619
$980$	32.2845	+	26.1161i	1.03129	+	0.834248i
$981$	21.9467			0.700705
$982$	0.413168	+	15.9923i	0.0131847	+	0.510336i
$983$	1.01177	+	1.01177i	0.0322703	+	0.0322703i	0.723058	−	0.690788i	$-0.242736\pi$
$983$	1.01177	+	1.01177i	0.0322703	+	0.0322703i	−0.690788	+	0.723058i	$0.742736\pi$
$984$	2.05478	+	1.75868i	0.0655039	+	0.0560648i
$985$	9.57185	−	0.513279i	0.304985	−	0.0163544i
$986$	24.3213	−	25.6113i	0.774547	−	0.815630i
$987$	17.2547	−	17.2547i	0.549222	−	0.549222i
$988$	8.31712	−	9.22410i	0.264603	−	0.293458i
$989$			8.04214i			0.255725i
$990$	−5.36606	+	6.29383i	−0.170545	+	0.200031i
$991$		−	30.7559i		−	0.976994i	−0.872566	−	0.488497i	$-0.837545\pi$
$991$		−	30.7559i		−	0.976994i	0.872566	−	0.488497i	$-0.162455\pi$
$992$	2.59860	+	20.0091i	0.0825056	+	0.635289i
$993$	4.17756	−	4.17756i	0.132571	−	0.132571i
$994$	24.4764	+	23.2436i	0.776345	+	0.737241i
$995$	26.7729	−	29.8069i	0.848758	−	0.944943i
$996$	0.828491	+	16.0234i	0.0262518	+	0.507719i
$997$	20.1956	+	20.1956i	0.639600	+	0.639600i	0.950457	−	0.310857i	$-0.100616\pi$
$997$	20.1956	+	20.1956i	0.639600	+	0.639600i	−0.310857	+	0.950457i	$0.600616\pi$
$998$	22.9658	−	0.593330i	0.726970	−	0.0187815i
$999$	−14.8272			−0.469111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.c.267.1	✓	52
4.3	odd	2		380.2.k.d.267.14	yes	52
5.3	odd	4		380.2.k.d.343.14	yes	52
20.3	even	4	inner	380.2.k.c.343.1	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.1	✓	52	1.1	even	1	trivial
380.2.k.c.343.1	yes	52	20.3	even	4	inner
380.2.k.d.267.14	yes	52	4.3	odd	2
380.2.k.d.343.14	yes	52	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41374 + 0.0365245i) q^{2} +(-0.389264 - 0.389264i) q^{3} +(1.99733 - 0.103273i) q^{4} +(-1.49421 + 1.66354i) q^{5} +(0.564536 + 0.536101i) q^{6} +(-2.85353 + 2.85353i) q^{7} +(-2.81994 + 0.218952i) q^{8} -2.69695i q^{9} +O(q^{10})\)	\(q+(-1.41374 + 0.0365245i) 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} +(-2.81994 + 0.218952i) q^{8} -2.69695i q^{9} +(2.05166 - 2.40638i) q^{10} -0.969790i q^{11} +(-0.817689 - 0.737288i) 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} +(0.0985048 + 3.81279i) q^{18} +1.00000 q^{19} +(-2.81263 + 3.47694i) q^{20} +2.22155 q^{21} +(0.0354211 + 1.37103i) 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} +(-5.40476 + 5.99414i) q^{28} -6.30270i q^{29} +(-1.73535 + 0.138081i) q^{30} -3.56684i q^{31} +(-5.60974 + 0.728543i) 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} +(-1.41374 + 0.0365245i) q^{38} -3.41864 q^{39} +(3.84933 - 5.01823i) q^{40} +1.73702 q^{41} +(-3.14070 + 0.0811412i) 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} +(-1.70934 - 1.38816i) q^{48} -9.28530i q^{49} +(0.937503 + 7.00864i) q^{50} +2.18138i q^{51} +(8.31712 - 9.22410i) 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} +(0.230203 + 8.91039i) q^{58} -12.9884 q^{59} +(2.44830 - 0.258594i) q^{60} -3.91061 q^{61} +(0.130277 + 5.04260i) 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} +(-5.88575 - 5.30702i) q^{68} +0.504566i q^{69} +(1.01222 + 12.7212i) q^{70} +5.91449i q^{71} +(0.590503 + 7.60523i) 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} +(4.83307 - 0.124864i) q^{78} +9.60097 q^{79} +(-5.25868 + 7.23508i) q^{80} -6.36437 q^{81} +(-2.45570 + 0.0634439i) 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} +(0.212338 + 2.73475i) q^{88} -2.69278i q^{89} +(-6.48989 - 5.53322i) q^{90} +25.0607i q^{91} +(-1.36141 - 1.22755i) 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} +(0.339141 + 13.1270i) 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	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

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