LMFDB - Embedded newform 380.2.n.a.31.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(31,380)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.n (of order $6$, 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:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.16
Character	$\chi$	$=$	380.31
Dual form			380.2.n.a.331.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05146 + 0.945743i) q^{2} +(0.256977 + 0.445098i) q^{3} +(0.211139 + 1.98882i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.150747 + 0.711038i) q^{6} +1.09058i q^{7} +(-1.65891 + 2.29085i) q^{8} +(1.36793 - 2.36932i) q^{9} +O(q^{10})$	\(q+(1.05146 + 0.945743i) q^{2} +(0.256977 + 0.445098i) q^{3} +(0.211139 + 1.98882i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.150747 + 0.711038i) q^{6} +1.09058i q^{7} +(-1.65891 + 2.29085i) q^{8} +(1.36793 - 2.36932i) q^{9} +(-0.293307 + 1.38346i) q^{10} +3.04025i q^{11} +(-0.830964 + 0.605061i) q^{12} +(-1.26840 - 0.732309i) q^{13} +(-1.03141 + 1.14670i) q^{14} +(-0.256977 + 0.445098i) q^{15} +(-3.91084 + 0.839838i) q^{16} +(-2.28580 - 3.95912i) q^{17} +(3.67908 - 1.19754i) q^{18} +(4.20179 + 1.15973i) q^{19} +(-1.61680 + 1.17726i) q^{20} +(-0.485415 + 0.280254i) q^{21} +(-2.87529 + 3.19670i) q^{22} +(0.879561 + 0.507815i) q^{23} +(-1.44596 - 0.149681i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.641093 - 1.96957i) q^{26} +2.94797 q^{27} +(-2.16897 + 0.230264i) q^{28} +(4.38585 + 2.53217i) q^{29} +(-0.691150 + 0.224968i) q^{30} -6.37354 q^{31} +(-4.90637 - 2.81559i) q^{32} +(-1.35321 + 0.781275i) q^{33} +(1.34088 - 6.32463i) q^{34} +(-0.944470 + 0.545290i) q^{35} +(5.00097 + 2.22031i) q^{36} -8.84448i q^{37} +(3.32121 + 5.19322i) q^{38} -0.752748i q^{39} +(-2.81339 - 0.291233i) q^{40} +(0.478536 - 0.276283i) q^{41} +(-0.775444 - 0.164401i) q^{42} +(7.50930 - 4.33550i) q^{43} +(-6.04651 + 0.641915i) q^{44} +2.73585 q^{45} +(0.444562 + 1.36579i) q^{46} +(0.0276817 + 0.0159821i) q^{47} +(-1.37881 - 1.52489i) q^{48} +5.81064 q^{49} +(-1.34477 + 0.437720i) q^{50} +(1.17480 - 2.03481i) q^{51} +(1.18863 - 2.67724i) q^{52} +(1.91837 + 1.10757i) q^{53} +(3.09967 + 2.78802i) q^{54} +(-2.63293 + 1.52012i) q^{55} +(-2.49836 - 1.80918i) q^{56} +(0.563571 + 2.16823i) q^{57} +(2.21677 + 6.81037i) q^{58} +(-2.46698 - 4.27294i) q^{59} +(-0.939480 - 0.417105i) q^{60} +(1.84959 - 3.20358i) q^{61} +(-6.70152 - 6.02773i) q^{62} +(2.58393 + 1.49183i) q^{63} +(-2.49602 - 7.60065i) q^{64} -1.46462i q^{65} +(-2.16173 - 0.458307i) q^{66} +(-3.70071 + 6.40982i) q^{67} +(7.39136 - 5.38197i) q^{68} +0.521988i q^{69} +(-1.50878 - 0.319875i) q^{70} +(0.153631 + 0.266097i) q^{71} +(3.15849 + 7.06420i) q^{72} +(-2.89297 - 5.01077i) q^{73} +(8.36461 - 9.29963i) q^{74} -0.513955 q^{75} +(-1.41934 + 8.60148i) q^{76} -3.31563 q^{77} +(0.711906 - 0.791485i) q^{78} +(0.197165 + 0.341500i) q^{79} +(-2.68274 - 2.96697i) q^{80} +(-3.34621 - 5.79581i) q^{81} +(0.764454 + 0.162072i) q^{82} -15.8208i q^{83} +(-0.659867 - 0.906232i) q^{84} +(2.28580 - 3.95912i) q^{85} +(11.9960 + 2.54327i) q^{86} +2.60285i q^{87} +(-6.96476 - 5.04350i) q^{88} +(12.0454 + 6.95441i) q^{89} +(2.87664 + 2.58741i) q^{90} +(0.798642 - 1.38329i) q^{91} +(-0.824245 + 1.85651i) q^{92} +(-1.63786 - 2.83685i) q^{93} +(0.0139913 + 0.0429843i) q^{94} +(1.09654 + 4.21872i) q^{95} +(-0.00760967 - 2.90736i) q^{96} +(0.00683827 - 0.00394808i) q^{97} +(6.10965 + 5.49537i) q^{98} +(7.20330 + 4.15883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	1.05146	+	0.945743i	0.743495	+	0.668741i
$2$	1.05146	+	0.945743i	0.743495	+	0.668741i
$3$	0.256977	+	0.445098i	0.148366	+	0.256977i	0.930624	−	0.365978i	$-0.119265\pi$
$3$	0.256977	+	0.445098i	0.148366	+	0.256977i	−0.782258	+	0.622955i	$0.785932\pi$
$4$	0.211139	+	1.98882i	0.105570	+	0.994412i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.150747	+	0.711038i	−0.0615421	+	0.290280i
$7$			1.09058i			0.412200i	0.978531	+	0.206100i	$0.0660773\pi$
$7$			1.09058i			0.412200i	−0.978531	+	0.206100i	$0.933923\pi$
$8$	−1.65891	+	2.29085i	−0.586514	+	0.809939i
$9$	1.36793	−	2.36932i	0.455975	−	0.789772i
$10$	−0.293307	+	1.38346i	−0.0927519	+	0.437490i
$11$			3.04025i			0.916669i	0.888780	+	0.458334i	$0.151554\pi$
$11$			3.04025i			0.916669i	−0.888780	+	0.458334i	$0.848446\pi$
$12$	−0.830964	+	0.605061i	−0.239879	+	0.174666i
$13$	−1.26840	−	0.732309i	−0.351790	−	0.203106i	0.313683	−	0.949528i	$-0.398437\pi$
$13$	−1.26840	−	0.732309i	−0.351790	−	0.203106i	−0.665473	+	0.746422i	$0.731770\pi$
$14$	−1.03141	+	1.14670i	−0.275656	+	0.306469i
$15$	−0.256977	+	0.445098i	−0.0663513	+	0.114924i
$16$	−3.91084	+	0.839838i	−0.977710	+	0.209959i
$17$	−2.28580	−	3.95912i	−0.554387	−	0.960227i	−0.997951	−	0.0639840i	$-0.979619\pi$
$17$	−2.28580	−	3.95912i	−0.554387	−	0.960227i	0.443564	−	0.896243i	$-0.353714\pi$
$18$	3.67908	−	1.19754i	0.867168	−	0.282262i
$19$	4.20179	+	1.15973i	0.963956	+	0.266061i
$19$	4.20179	+	1.15973i	0.963956	+	0.266061i
$20$	−1.61680	+	1.17726i	−0.361528	+	0.263244i
$21$	−0.485415	+	0.280254i	−0.105926	+	0.0611565i
$22$	−2.87529	+	3.19670i	−0.613014	+	0.681539i
$23$	0.879561	+	0.507815i	0.183401	+	0.105887i	0.588890	−	0.808213i	$-0.299565\pi$
$23$	0.879561	+	0.507815i	0.183401	+	0.105887i	−0.405488	+	0.914100i	$0.632899\pi$
$24$	−1.44596	−	0.149681i	−0.295155	−	0.0305535i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.641093	−	1.96957i	−0.125729	−	0.386265i
$27$	2.94797			0.567337
$28$	−2.16897	+	0.230264i	−0.409897	+	0.0435158i
$29$	4.38585	+	2.53217i	0.814432	+	0.470213i	0.848493	−	0.529207i	$-0.177511\pi$
$29$	4.38585	+	2.53217i	0.814432	+	0.470213i	−0.0340604	+	0.999420i	$0.510844\pi$
$30$	−0.691150	+	0.224968i	−0.126186	+	0.0410734i
$31$	−6.37354			−1.14472			−0.572361	−	0.820002i	$-0.693972\pi$
$31$	−6.37354			−1.14472			−0.572361	+	0.820002i	$0.693972\pi$
$32$	−4.90637	−	2.81559i	−0.867331	−	0.497732i
$33$	−1.35321	+	0.781275i	−0.235563	+	0.136002i
$34$	1.34088	−	6.32463i	0.229959	−	1.08467i
$35$	−0.944470	+	0.545290i	−0.159645	+	0.0921708i
$36$	5.00097	+	2.22031i	0.833496	+	0.370051i
$37$		−	8.84448i		−	1.45402i	−0.686625	−	0.727012i	$-0.740908\pi$
$37$		−	8.84448i		−	1.45402i	0.686625	−	0.727012i	$-0.259092\pi$
$38$	3.32121	+	5.19322i	0.538771	+	0.842452i
$39$		−	0.752748i		−	0.120536i
$40$	−2.81339	−	0.291233i	−0.444837	−	0.0460480i
$41$	0.478536	−	0.276283i	0.0747347	−	0.0431481i	−0.462167	−	0.886793i	$-0.652928\pi$
$41$	0.478536	−	0.276283i	0.0747347	−	0.0431481i	0.536902	+	0.843645i	$0.319595\pi$
$42$	−0.775444	−	0.164401i	−0.119654	−	0.0253677i
$43$	7.50930	−	4.33550i	1.14516	−	0.661157i	0.197455	−	0.980312i	$-0.436732\pi$
$43$	7.50930	−	4.33550i	1.14516	−	0.661157i	0.947703	+	0.319155i	$0.103399\pi$
$44$	−6.04651	+	0.641915i	−0.911546	+	0.0967724i
$45$	2.73585			0.407836
$46$	0.444562	+	1.36579i	0.0655470	+	0.201374i
$47$	0.0276817	+	0.0159821i	0.00403780	+	0.00233122i	0.502018	−	0.864857i	$-0.332591\pi$
$47$	0.0276817	+	0.0159821i	0.00403780	+	0.00233122i	−0.497980	+	0.867189i	$0.665925\pi$
$48$	−1.37881	−	1.52489i	−0.199014	−	0.220099i
$49$	5.81064			0.830091
$50$	−1.34477	+	0.437720i	−0.190179	+	0.0619030i
$51$	1.17480	−	2.03481i	0.164504	−	0.284930i
$52$	1.18863	−	2.67724i	0.164833	−	0.371266i
$53$	1.91837	+	1.10757i	0.263508	+	0.152136i	0.625934	−	0.779876i	$-0.284718\pi$
$53$	1.91837	+	1.10757i	0.263508	+	0.152136i	−0.362426	+	0.932013i	$0.618051\pi$
$54$	3.09967	+	2.78802i	0.421812	+	0.379402i
$55$	−2.63293	+	1.52012i	−0.355024	+	0.204973i
$56$	−2.49836	−	1.80918i	−0.333857	−	0.241761i
$57$	0.563571	+	2.16823i	0.0746468	+	0.287189i
$58$	2.21677	+	6.81037i	0.291076	+	0.894245i
$59$	−2.46698	−	4.27294i	−0.321174	−	0.556290i	0.659556	−	0.751655i	$-0.270744\pi$
$59$	−2.46698	−	4.27294i	−0.321174	−	0.556290i	−0.980731	+	0.195365i	$0.937411\pi$
$60$	−0.939480	−	0.417105i	−0.121286	−	0.0538481i
$61$	1.84959	−	3.20358i	0.236816	−	0.410177i	−0.722983	−	0.690866i	$-0.757230\pi$
$61$	1.84959	−	3.20358i	0.236816	−	0.410177i	0.959799	+	0.280689i	$0.0905629\pi$
$62$	−6.70152	−	6.02773i	−0.851094	−	0.765523i
$63$	2.58393	+	1.49183i	0.325544	+	0.187953i
$64$	−2.49602	−	7.60065i	−0.312003	−	0.950081i
$65$		−	1.46462i		−	0.181664i
$66$	−2.16173	−	0.458307i	−0.266091	−	0.0564137i
$67$	−3.70071	+	6.40982i	−0.452114	+	0.783085i	−0.998517	−	0.0544377i	$-0.982663\pi$
$67$	−3.70071	+	6.40982i	−0.452114	+	0.783085i	0.546403	+	0.837522i	$0.315997\pi$
$68$	7.39136	−	5.38197i	0.896335	−	0.652660i
$69$			0.521988i			0.0628400i
$70$	−1.50878	−	0.319875i	−0.180333	−	0.0382324i
$71$	0.153631	+	0.266097i	0.0182327	+	0.0315799i	0.874998	−	0.484127i	$-0.160863\pi$
$71$	0.153631	+	0.266097i	0.0182327	+	0.0315799i	−0.856765	+	0.515707i	$0.827529\pi$
$72$	3.15849	+	7.06420i	0.372231	+	0.832524i
$73$	−2.89297	−	5.01077i	−0.338597	−	0.586467i	0.645572	−	0.763699i	$-0.276619\pi$
$73$	−2.89297	−	5.01077i	−0.338597	−	0.586467i	−0.984169	+	0.177233i	$0.943286\pi$
$74$	8.36461	−	9.29963i	0.972366	−	1.08106i
$75$	−0.513955			−0.0593464
$76$	−1.41934	+	8.60148i	−0.162809	+	0.986658i
$77$	−3.31563			−0.377851
$78$	0.711906	−	0.791485i	0.0806075	−	0.0896180i
$79$	0.197165	+	0.341500i	0.0221828	+	0.0384217i	0.876904	−	0.480666i	$-0.159605\pi$
$79$	0.197165	+	0.341500i	0.0221828	+	0.0384217i	−0.854721	+	0.519088i	$0.826272\pi$
$80$	−2.68274	−	2.96697i	−0.299940	−	0.331717i
$81$	−3.34621	−	5.79581i	−0.371802	−	0.643979i
$82$	0.764454	+	0.162072i	0.0844199	+	0.0178978i
$83$		−	15.8208i		−	1.73656i	−0.496079	−	0.868278i	$-0.665227\pi$
$83$		−	15.8208i		−	1.73656i	0.496079	−	0.868278i	$-0.334773\pi$
$84$	−0.659867	−	0.906232i	−0.0719974	−	0.0988780i
$85$	2.28580	−	3.95912i	0.247930	−	0.429426i
$86$	11.9960	+	2.54327i	1.29356	+	0.274247i
$87$			2.60285i			0.279054i
$88$	−6.96476	−	5.04350i	−0.742446	−	0.537639i
$89$	12.0454	+	6.95441i	1.27681	+	0.737166i	0.976260	−	0.216600i	$-0.0694967\pi$
$89$	12.0454	+	6.95441i	1.27681	+	0.737166i	0.300549	+	0.953766i	$0.402830\pi$
$90$	2.87664	+	2.58741i	0.303224	+	0.272737i
$91$	0.798642	−	1.38329i	0.0837204	−	0.145008i
$92$	−0.824245	+	1.85651i	−0.0859334	+	0.193555i
$93$	−1.63786	−	2.83685i	−0.169838	−	0.294168i
$94$	0.0139913	+	0.0429843i	0.00144310	+	0.00443349i
$95$	1.09654	+	4.21872i	0.112502	+	0.432832i
$96$	−0.00760967	−	2.90736i	−0.000776659	−	0.296731i
$97$	0.00683827	−	0.00394808i	0.000694321	−	0.000400866i	−0.499653	−	0.866226i	$-0.666539\pi$
$97$	0.00683827	−	0.00394808i	0.000694321	−	0.000400866i	0.500347	+	0.865825i	$0.333206\pi$
$98$	6.10965	+	5.49537i	0.617168	+	0.555116i
$99$	7.20330	+	4.15883i	0.723959	+	0.417978i
$100$	−1.82794	−	0.811560i	−0.182794	−	0.0811560i
$101$	−9.20365	+	15.9412i	−0.915798	+	1.58621i	−0.110068	+	0.993924i	$0.535107\pi$
$101$	−9.20365	+	15.9412i	−0.915798	+	1.58621i	−0.805729	+	0.592284i	$0.798226\pi$
$102$	3.15966	−	1.02846i	0.312853	−	0.101833i
$103$	−13.8051			−1.36026			−0.680129	−	0.733092i	$-0.738076\pi$
$103$	−13.8051			−1.36026			−0.680129	+	0.733092i	$0.738076\pi$
$104$	3.78177	−	1.69087i	0.370833	−	0.165804i
$105$	−0.485415	−	0.280254i	−0.0473716	−	0.0273500i
$106$	0.969611	+	2.97885i	0.0941769	+	0.289331i
$107$	−15.7181			−1.51953			−0.759765	−	0.650197i	$-0.774686\pi$
$107$	−15.7181			−1.51953			−0.759765	+	0.650197i	$0.774686\pi$
$108$	0.622432	+	5.86299i	0.0598935	+	0.564166i
$109$	8.81847	−	5.09134i	0.844656	−	0.487662i	−0.0141883	−	0.999899i	$-0.504516\pi$
$109$	8.81847	−	5.09134i	0.844656	−	0.487662i	0.858844	+	0.512237i	$0.171183\pi$
$110$	−4.20607	−	0.891727i	−0.401033	−	0.0850228i
$111$	3.93666	−	2.27283i	0.373651	−	0.215728i
$112$	−0.915910	−	4.26508i	−0.0865453	−	0.403013i
$113$		−	2.79601i		−	0.263026i	−0.991314	−	0.131513i	$-0.958016\pi$
$113$		−	2.79601i		−	0.263026i	0.991314	−	0.131513i	$-0.0419836\pi$
$114$	−1.45802	+	2.81280i	−0.136556	+	0.263443i
$115$			1.01563i			0.0947080i
$116$	−4.11002	+	9.25733i	−0.381606	+	0.859521i
$117$	−3.47014	+	2.00349i	−0.320815	+	0.185223i
$118$	1.44717	−	6.82597i	0.133223	−	0.628381i
$119$	4.31773	−	2.49284i	0.395806	−	0.228519i
$120$	−0.593351	−	1.32708i	−0.0541653	−	0.121145i
$121$	1.75690			0.159718
$122$	4.97454	−	1.61921i	0.450374	−	0.146596i
$123$	0.245946	+	0.141997i	0.0221762	+	0.0128034i
$124$	−1.34570	−	12.6758i	−0.120848	−	1.13832i
$125$	−1.00000			−0.0894427
$126$	1.30601	+	4.01234i	0.116349	+	0.357447i
$127$	0.904908	−	1.56735i	0.0802976	−	0.139080i	−0.823080	−	0.567925i	$-0.807746\pi$
$127$	0.904908	−	1.56735i	0.0802976	−	0.139080i	0.903378	+	0.428846i	$0.141080\pi$
$128$	4.56380	−	10.3524i	0.403386	−	0.915030i
$129$	3.85944	+	2.22825i	0.339805	+	0.196186i
$130$	1.38515	−	1.53999i	0.121486	−	0.135066i
$131$	8.28064	−	4.78083i	0.723483	−	0.417703i	−0.0925505	−	0.995708i	$-0.529502\pi$
$131$	8.28064	−	4.78083i	0.723483	−	0.417703i	0.816033	+	0.578005i	$0.196169\pi$
$132$	−1.83953	−	2.52633i	−0.160111	−	0.219889i
$133$	−1.26478	+	4.58239i	−0.109670	+	0.397343i
$134$	−9.95320	+	3.23975i	−0.859826	+	0.279872i
$135$	1.47398	+	2.55302i	0.126860	+	0.219729i
$136$	12.8617	+	1.33140i	1.10288	+	0.114167i
$137$	−9.95474	+	17.2421i	−0.850491	+	1.47309i	0.0302751	+	0.999542i	$0.490362\pi$
$137$	−9.95474	+	17.2421i	−0.850491	+	1.47309i	−0.880766	+	0.473552i	$0.842972\pi$
$138$	−0.493667	+	0.548850i	−0.0420237	+	0.0467212i
$139$	−2.07276	−	1.19671i	−0.175809	−	0.101503i	0.409513	−	0.912304i	$-0.365699\pi$
$139$	−2.07276	−	1.19671i	−0.175809	−	0.101503i	−0.585322	+	0.810801i	$0.699032\pi$
$140$	−1.28390	−	1.76325i	−0.108509	−	0.149022i
$141$			0.0164281i			0.00138350i
$142$	−0.0901224	+	0.425087i	−0.00756291	+	0.0356725i
$143$	2.22640	−	3.85624i	0.186181	−	0.322475i
$144$	−3.35990	+	10.4149i	−0.279991	+	0.867904i
$145$			5.06435i			0.420571i
$146$	1.69706	−	8.00464i	0.140450	−	0.662469i
$147$	1.49320	+	2.58630i	0.123157	+	0.213315i
$148$	17.5901	−	1.86742i	1.44590	−	0.153501i
$149$	10.2301	+	17.7191i	0.838082	+	1.45160i	0.891496	+	0.453029i	$0.149657\pi$
$149$	10.2301	+	17.7191i	0.838082	+	1.45160i	−0.0534133	+	0.998572i	$0.517010\pi$
$150$	−0.540403	−	0.486069i	−0.0441238	−	0.0396874i
$151$	−12.3419			−1.00437			−0.502186	−	0.864759i	$-0.667471\pi$
$151$	−12.3419			−1.00437			−0.502186	+	0.864759i	$0.667471\pi$
$152$	−9.62717	+	7.70179i	−0.780867	+	0.624698i
$153$	−12.5072			−1.01115
$154$	−3.48626	−	3.13574i	−0.280931	−	0.252685i
$155$	−3.18677	−	5.51965i	−0.255967	−	0.443349i
$156$	1.49708	−	0.158935i	0.119863	−	0.0127250i
$157$	−2.37511	−	4.11382i	−0.189555	−	0.328318i	0.755547	−	0.655094i	$-0.227371\pi$
$157$	−2.37511	−	4.11382i	−0.189555	−	0.328318i	−0.945102	+	0.326776i	$0.894038\pi$
$158$	−0.115660	+	0.545541i	−0.00920140	+	0.0434009i
$159$			1.13848i			0.0902875i
$160$	−0.0148061	−	5.65683i	−0.00117053	−	0.447212i
$161$	−0.553813	+	0.959232i	−0.0436466	+	0.0755981i
$162$	1.96294	−	9.25873i	0.154223	−	0.727434i
$163$			0.389301i			0.0304924i	0.999884	+	0.0152462i	$0.00485321\pi$
$163$			0.389301i			0.0304924i	−0.999884	+	0.0152462i	$0.995147\pi$
$164$	0.650516	+	0.893389i	0.0507967	+	0.0697620i
$165$	−1.35321	−	0.781275i	−0.105347	−	0.0608222i
$166$	14.9624	−	16.6349i	1.16131	−	1.29112i
$167$	−6.35714	+	11.0109i	−0.491930	+	0.852048i	−0.999957	−	0.00929337i	$-0.997042\pi$
$167$	−6.35714	+	11.0109i	−0.491930	+	0.852048i	0.508027	+	0.861341i	$0.330375\pi$
$168$	0.163239	−	1.57693i	0.0125941	−	0.121663i
$169$	−5.42745	−	9.40061i	−0.417496	−	0.723124i
$170$	6.14773	−	2.00108i	0.471510	−	0.153476i
$171$	8.49550	−	8.36894i	0.649667	−	0.639989i
$172$	10.2080	+	14.0193i	0.778356	+	1.06896i
$173$	−17.0866	+	9.86493i	−1.29907	+	0.750017i	−0.980243	−	0.197797i	$-0.936621\pi$
$173$	−17.0866	+	9.86493i	−1.29907	+	0.750017i	−0.318824	+	0.947814i	$0.603288\pi$
$174$	−2.46162	+	2.73679i	−0.186615	+	0.207476i
$175$	−0.944470	−	0.545290i	−0.0713952	−	0.0412200i
$176$	−2.55331	−	11.8899i	−0.192463	−	0.896236i
$177$	1.26792	−	2.19610i	0.0953026	−	0.165069i
$178$	6.08817	+	18.7041i	0.456328	+	1.40194i
$179$	0.466812			0.0348911			0.0174456	−	0.999848i	$-0.494447\pi$
$179$	0.466812			0.0348911			0.0174456	+	0.999848i	$0.494447\pi$
$180$	0.577645	+	5.44112i	0.0430551	+	0.405557i
$181$	−14.6748	−	8.47252i	−1.09077	−	0.629758i	−0.156990	−	0.987600i	$-0.550179\pi$
$181$	−14.6748	−	8.47252i	−1.09077	−	0.629758i	−0.933782	+	0.357842i	$0.883512\pi$
$182$	2.14798	−	0.699163i	0.159219	−	0.0518254i
$183$	1.90121			0.140542
$184$	−2.62244	+	1.17253i	−0.193329	+	0.0864398i
$185$	7.65955	−	4.42224i	0.563141	−	0.325130i
$186$	0.960790	−	4.53183i	0.0704486	−	0.332290i
$187$	12.0367	−	6.94939i	0.880210	−	0.508189i
$188$	−0.0259408	+	0.0584285i	−0.00189193	+	0.00426134i
$189$			3.21500i			0.233856i
$190$	−2.83686	+	5.47286i	−0.205808	+	0.397043i
$191$			16.9825i			1.22881i	0.788991	+	0.614405i	$0.210604\pi$
$191$			16.9825i			1.22881i	−0.788991	+	0.614405i	$0.789396\pi$
$192$	2.74161	−	3.06417i	0.197859	−	0.221137i
$193$	−15.3141	+	8.84158i	−1.10233	+	0.636431i	−0.936832	−	0.349779i	$-0.886257\pi$
$193$	−15.3141	+	8.84158i	−1.10233	+	0.636431i	−0.165499	+	0.986210i	$0.552923\pi$
$194$	0.0109240	+	0.00231600i	0.000784300	+	0.000166279i
$195$	0.651899	−	0.376374i	0.0466834	−	0.0269527i
$196$	1.22685	+	11.5563i	0.0876324	+	0.825452i
$197$	−7.62028			−0.542922			−0.271461	−	0.962449i	$-0.587507\pi$
$197$	−7.62028			−0.542922			−0.271461	+	0.962449i	$0.587507\pi$
$198$	3.64081	+	11.1853i	0.258741	+	0.794906i
$199$	−19.1120	−	11.0343i	−1.35481	−	0.782203i	−0.365895	−	0.930656i	$-0.619237\pi$
$199$	−19.1120	−	11.0343i	−1.35481	−	0.782203i	−0.988919	+	0.148453i	$0.952571\pi$
$200$	−1.15448	−	2.58209i	−0.0816342	−	0.182581i
$201$	−3.80400			−0.268313
$202$	−24.7536	+	8.05725i	−1.74165	+	0.566906i
$203$	−2.76154	+	4.78312i	−0.193822	+	0.335709i
$204$	4.29492	+	1.90684i	0.300705	+	0.133505i
$205$	0.478536	+	0.276283i	0.0334224	+	0.0192964i
$206$	−14.5155	−	13.0561i	−1.01135	−	0.909661i
$207$	2.40635	−	1.38931i	0.167253	−	0.0965634i
$208$	5.57552	+	1.79870i	0.386593	+	0.124717i
$209$	−3.52587	+	12.7745i	−0.243889	+	0.883629i
$210$	−0.245346	−	0.753754i	−0.0169305	−	0.0520140i
$211$	−6.31576	−	10.9392i	−0.434795	−	0.753087i	0.562484	−	0.826808i	$-0.309846\pi$
$211$	−6.31576	−	10.9392i	−0.434795	−	0.753087i	−0.997279	+	0.0737212i	$0.976513\pi$
$212$	−1.79772	+	4.04914i	−0.123468	+	0.278096i
$213$	−0.0789596	+	0.136762i	−0.00541022	+	0.00937078i
$214$	−16.5270	−	14.8653i	−1.12976	−	1.01617i
$215$	7.50930	+	4.33550i	0.512130	+	0.295678i
$216$	−4.89042	+	6.75336i	−0.332751	+	0.459508i
$217$		−	6.95085i		−	0.471855i
$218$	14.0874	+	2.98666i	0.954117	+	0.202282i
$219$	1.48686	−	2.57531i	0.100472	−	0.174023i
$220$	−3.57917	−	4.91548i	−0.241308	−	0.331401i
$221$			6.69564i			0.450398i
$222$	6.28876	+	1.33328i	0.422074	+	0.0894837i
$223$	11.8814	+	20.5791i	0.795636	+	1.37808i	0.922435	+	0.386153i	$0.126196\pi$
$223$	11.8814	+	20.5791i	0.795636	+	1.37808i	−0.126799	+	0.991928i	$0.540470\pi$
$224$	3.07063	−	5.35078i	0.205165	−	0.357514i
$225$	1.36793	+	2.36932i	0.0911950	+	0.157954i
$226$	2.64431	−	2.93989i	0.175897	−	0.195559i
$227$	−5.28315			−0.350655			−0.175327	−	0.984510i	$-0.556098\pi$
$227$	−5.28315			−0.350655			−0.175327	+	0.984510i	$0.556098\pi$
$228$	−4.19324	+	1.57864i	−0.277704	+	0.104548i
$229$	−0.824217			−0.0544658			−0.0272329	−	0.999629i	$-0.508670\pi$
$229$	−0.824217			−0.0544658			−0.0272329	+	0.999629i	$0.508670\pi$
$230$	−0.960525	+	1.06790i	−0.0633352	+	0.0704149i
$231$	−0.852043	−	1.47578i	−0.0560603	−	0.0970993i
$232$	−13.0766	+	5.84669i	−0.858520	+	0.383854i
$233$	−1.29089	−	2.23589i	−0.0845692	−	0.146478i	0.820638	−	0.571448i	$-0.193618\pi$
$233$	−1.29089	−	2.23589i	−0.0845692	−	0.146478i	−0.905208	+	0.424970i	$0.860285\pi$
$234$	−5.54351	−	1.17528i	−0.362390	−	0.0768302i
$235$			0.0319641i			0.00208511i
$236$	7.97725	−	5.80858i	0.519275	−	0.378107i
$237$	−0.101334	+	0.175515i	−0.00658234	+	0.0114010i
$238$	6.89752	+	1.46234i	0.447100	+	0.0947894i
$239$			25.9992i			1.68175i	0.541231	+	0.840874i	$0.317959\pi$
$239$			25.9992i			1.68175i	−0.541231	+	0.840874i	$0.682041\pi$
$240$	0.631188	−	1.95653i	0.0407430	−	0.126293i
$241$	−15.5627	−	8.98511i	−1.00248	−	0.578782i	−0.0934988	−	0.995619i	$-0.529805\pi$
$241$	−15.5627	−	8.98511i	−1.00248	−	0.578782i	−0.908981	+	0.416837i	$0.863138\pi$
$242$	1.84731	+	1.66158i	0.118750	+	0.106810i
$243$	6.14176	−	10.6378i	0.393994	−	0.682417i
$244$	6.76189	+	3.00211i	0.432885	+	0.192190i
$245$	2.90532	+	5.03216i	0.185614	+	0.321493i
$246$	0.124310	+	0.381906i	0.00792570	+	0.0243494i
$247$	−4.48025	−	4.54801i	−0.285072	−	0.289383i
$248$	10.5731	−	14.6008i	0.671395	−	0.927154i
$249$	7.04179	−	4.06558i	0.446256	−	0.257646i
$250$	−1.05146	−	0.945743i	−0.0665002	−	0.0598141i
$251$	17.8560	+	10.3092i	1.12706	+	0.650708i	0.943194	−	0.332243i	$-0.107805\pi$
$251$	17.8560	+	10.3092i	1.12706	+	0.650708i	0.183866	+	0.982951i	$0.441139\pi$
$252$	−2.42142	+	5.45396i	−0.152535	+	0.343567i
$253$	−1.54388	+	2.67408i	−0.0970631	+	0.168118i
$254$	2.43378	−	0.792193i	0.152709	−	0.0497066i
$255$	2.34959			0.147137
$256$	14.5893	−	6.56894i	0.911834	−	0.410559i
$257$	5.48172	+	3.16487i	0.341940	+	0.197419i	0.661130	−	0.750272i	$-0.270077\pi$
$257$	5.48172	+	3.16487i	0.341940	+	0.197419i	−0.319189	+	0.947691i	$0.603411\pi$
$258$	1.95070	+	5.99296i	0.121445	+	0.373105i
$259$	9.64561			0.599349
$260$	2.91287	−	0.309238i	0.180648	−	0.0191782i
$261$	11.9990	−	6.92765i	0.742722	−	0.428811i
$262$	13.2282	+	2.80450i	0.817241	+	0.173263i
$263$	−9.65283	+	5.57307i	−0.595219	+	0.343650i	−0.767159	−	0.641458i	$-0.778330\pi$
$263$	−9.65283	+	5.57307i	−0.595219	+	0.343650i	0.171939	+	0.985108i	$0.444997\pi$
$264$	0.455066	−	4.39607i	0.0280074	−	0.270559i
$265$			2.21514i			0.136075i
$266$	−5.66363	+	3.62204i	−0.347259	+	0.222082i
$267$			7.14851i			0.437482i
$268$	−13.5294	−	6.00670i	−0.826438	−	0.366918i
$269$	18.5068	−	10.6849i	1.12838	−	0.651471i	0.184853	−	0.982766i	$-0.440819\pi$
$269$	18.5068	−	10.6849i	1.12838	−	0.651471i	0.943527	+	0.331296i	$0.107486\pi$
$270$	−0.864661	+	4.07841i	−0.0526216	+	0.248204i
$271$	6.96748	−	4.02268i	0.423244	−	0.244360i	−0.273220	−	0.961952i	$-0.588089\pi$
$271$	6.96748	−	4.02268i	0.423244	−	0.244360i	0.696464	+	0.717591i	$0.254755\pi$
$272$	12.2644	+	13.5638i	0.743639	+	0.822425i
$273$	0.820932			0.0496850
$274$	−26.7736	+	8.71478i	−1.61745	+	0.526479i
$275$	−2.63293	−	1.52012i	−0.158772	−	0.0916669i
$276$	−1.03814	+	0.110212i	−0.0624888	+	0.00663399i
$277$	19.4937			1.17126			0.585632	−	0.810577i	$-0.300846\pi$
$277$	19.4937			1.17126			0.585632	+	0.810577i	$0.300846\pi$
$278$	−1.04765	−	3.21859i	−0.0628336	−	0.193038i
$279$	−8.71852	+	15.1009i	−0.521964	+	0.904069i
$280$	0.317613	−	3.06823i	0.0189810	−	0.183362i
$281$	1.17078	+	0.675950i	0.0698428	+	0.0403238i	0.534515	−	0.845159i	$-0.320494\pi$
$281$	1.17078	+	0.675950i	0.0698428	+	0.0403238i	−0.464672	+	0.885483i	$0.653828\pi$
$282$	−0.0155368	+	0.0172735i	−0.000925202	+	0.00102862i
$283$	−0.728870	+	0.420813i	−0.0433268	+	0.0250148i	−0.521507	−	0.853247i	$-0.674630\pi$
$283$	−0.728870	+	0.420813i	−0.0433268	+	0.0250148i	0.478180	+	0.878262i	$0.341297\pi$
$284$	−0.496783	+	0.361729i	−0.0294787	+	0.0214647i
$285$	−1.59596	+	1.57218i	−0.0945364	+	0.0931281i
$286$	5.98798	−	1.94908i	0.354077	−	0.115252i
$287$	0.301308	+	0.521882i	0.0177857	+	0.0308057i
$288$	−13.3826	+	7.77321i	−0.788576	+	0.458041i
$289$	−1.94974	+	3.37704i	−0.114690	+	0.198650i
$290$	−4.78957	+	5.32496i	−0.281253	+	0.312692i
$291$	0.00351456	+	0.00202913i	0.000206027	+	0.000118950i
$292$	9.35472	−	6.81158i	0.547444	−	0.398618i
$293$			4.65245i			0.271799i	0.990723	+	0.135900i	$0.0433925\pi$
$293$			4.65245i			0.271799i	−0.990723	+	0.135900i	$0.956608\pi$
$294$	−0.875935	+	4.13158i	−0.0510855	+	0.240959i
$295$	2.46698	−	4.27294i	0.143633	−	0.248780i
$296$	20.2614	+	14.6722i	1.17767	+	0.852805i
$297$			8.96255i			0.520060i
$298$	−6.00113	+	28.3059i	−0.347636	+	1.63972i
$299$	−0.743755	−	1.28822i	−0.0430125	−	0.0744998i
$300$	−0.108516	−	1.02217i	−0.00626518	−	0.0590148i
$301$	4.72820	+	8.18949i	0.272529	+	0.472034i
$302$	−12.9771	−	11.6723i	−0.746746	−	0.671666i
$303$	−9.46052			−0.543493
$304$	−17.4065	−	1.00670i	−0.998332	−	0.0577385i
$305$	3.69918			0.211814
$306$	−13.1508	−	11.8286i	−0.751783	−	0.676196i
$307$	−13.9647	−	24.1876i	−0.797009	−	1.38046i	−0.921556	−	0.388246i	$-0.873081\pi$
$307$	−13.9647	−	24.1876i	−0.797009	−	1.38046i	0.124547	−	0.992214i	$-0.460252\pi$
$308$	−0.700060	−	6.59421i	−0.0398896	−	0.375740i
$309$	−3.54760	−	6.14463i	−0.201816	−	0.349556i
$310$	1.86941	−	8.81756i	0.106175	−	0.500804i
$311$		−	21.5318i		−	1.22096i	−0.792033	−	0.610479i	$-0.790977\pi$
$311$		−	21.5318i		−	1.22096i	0.792033	−	0.610479i	$-0.209023\pi$
$312$	1.72444	+	1.24874i	0.0976269	+	0.0706961i
$313$	12.7440	−	22.0733i	0.720336	−	1.24766i	−0.240529	−	0.970642i	$-0.577321\pi$
$313$	12.7440	−	22.0733i	0.720336	−	1.24766i	0.960865	−	0.277016i	$-0.0893456\pi$
$314$	1.39328	−	6.57177i	0.0786272	−	0.370866i
$315$			2.98366i			0.168110i
$316$	−0.637553	+	0.464230i	−0.0358652	+	0.0261150i
$317$	9.32343	+	5.38289i	0.523656	+	0.302333i	0.738429	−	0.674331i	$-0.235568\pi$
$317$	9.32343	+	5.38289i	0.523656	+	0.302333i	−0.214773	+	0.976664i	$0.568901\pi$
$318$	−1.07671	+	1.19707i	−0.0603790	+	0.0671283i
$319$	−7.69843	+	13.3341i	−0.431029	+	0.746565i
$320$	5.33435	−	5.96194i	0.298199	−	0.333283i
$321$	−4.03921	−	6.99612i	−0.225447	−	0.390485i
$322$	−1.48950	+	0.484830i	−0.0830066	+	0.0270185i
$323$	−5.01292	−	19.2863i	−0.278927	−	1.07312i
$324$	10.8203	−	7.87875i	0.601130	−	0.437709i
$325$	1.26840	−	0.732309i	0.0703580	−	0.0406212i
$326$	−0.368179	+	0.409335i	−0.0203915	+	0.0226710i
$327$	4.53229	+	2.61672i	0.250636	+	0.144705i
$328$	−0.160925	+	1.55458i	−0.00888562	+	0.0858376i
$329$	−0.0174297	+	0.0301891i	−0.000960931	+	0.00166438i
$330$	−0.683959	−	2.10127i	−0.0376507	−	0.115671i
$331$	1.11431			0.0612478			0.0306239	−	0.999531i	$-0.490251\pi$
$331$	1.11431			0.0612478			0.0306239	+	0.999531i	$0.490251\pi$
$332$	31.4647	−	3.34039i	1.72685	−	0.183327i
$333$	−20.9554	−	12.0986i	−1.14835	−	0.662999i
$334$	−17.0978	+	5.56529i	−0.935547	+	0.304519i
$335$	−7.40143			−0.404383
$336$	1.66301	−	1.50370i	0.0907248	−	0.0820336i
$337$	3.53797	−	2.04265i	0.192726	−	0.111270i	−0.400532	−	0.916283i	$-0.631175\pi$
$337$	3.53797	−	2.04265i	0.192726	−	0.111270i	0.593258	+	0.805012i	$0.297841\pi$
$338$	3.18382	−	15.0173i	0.173177	−	0.816836i
$339$	1.24450	−	0.718511i	0.0675918	−	0.0390242i
$340$	8.35661	+	3.71012i	0.453201	+	0.201210i
$341$		−	19.3771i		−	1.04933i
$342$	16.8476	−	0.765046i	0.911011	−	0.0413689i
$343$			13.9710i			0.754364i
$344$	−2.52528	+	24.3949i	−0.136154	+	1.31529i
$345$	−0.452055	+	0.260994i	−0.0243378	+	0.0140514i
$346$	−27.2955	−	5.78691i	−1.46742	−	0.311106i
$347$	26.0983	−	15.0678i	1.40103	−	0.808884i	0.406530	−	0.913637i	$-0.366739\pi$
$347$	26.0983	−	15.0678i	1.40103	−	0.808884i	0.994498	+	0.104753i	$0.0334052\pi$
$348$	−5.17660	+	0.549563i	−0.277495	+	0.0294597i
$349$	3.12414			0.167231			0.0836157	−	0.996498i	$-0.473353\pi$
$349$	3.12414			0.167231			0.0836157	+	0.996498i	$0.473353\pi$
$350$	−0.477369	−	1.46658i	−0.0255164	−	0.0783918i
$351$	−3.73919	−	2.15882i	−0.199583	−	0.115230i
$352$	8.56010	−	14.9166i	0.456255	−	0.795055i
$353$	25.0027			1.33076			0.665380	−	0.746505i	$-0.268270\pi$
$353$	25.0027			1.33076			0.665380	+	0.746505i	$0.268270\pi$
$354$	3.41011	−	1.10999i	0.181246	−	0.0589952i
$355$	−0.153631	+	0.266097i	−0.00815391	+	0.0141230i
$356$	−11.2878	+	25.4245i	−0.598255	+	1.34750i
$357$	2.21912	+	1.28121i	0.117448	+	0.0678088i
$358$	0.490834	+	0.441484i	0.0259414	+	0.0233331i
$359$	−19.1267	+	11.0428i	−1.00947	+	0.582817i	−0.911036	−	0.412327i	$-0.864716\pi$
$359$	−19.1267	+	11.0428i	−1.00947	+	0.582817i	−0.0984328	+	0.995144i	$0.531383\pi$
$360$	−4.53854	+	6.26743i	−0.239202	+	0.330323i
$361$	16.3100	+	9.74589i	0.858424	+	0.512942i
$362$	−7.41719	−	22.7872i	−0.389839	−	1.19767i
$363$	0.451484	+	0.781994i	0.0236968	+	0.0410440i
$364$	2.91974	+	1.29629i	0.153036	+	0.0679441i
$365$	2.89297	−	5.01077i	0.151425	−	0.262276i
$366$	1.99905	+	1.79806i	0.104492	+	0.0939860i
$367$	1.95542	+	1.12896i	0.102072	+	0.0589312i	0.550167	−	0.835055i	$-0.314564\pi$
$367$	1.95542	+	1.12896i	0.102072	+	0.0589312i	−0.448095	+	0.893986i	$0.647897\pi$
$368$	−3.86631	−	1.24729i	−0.201545	−	0.0650197i
$369$		−	1.51174i		−	0.0786979i
$370$	12.2360	+	2.59415i	0.636120	+	0.134864i
$371$	−1.20789	+	2.09213i	−0.0627107	+	0.108618i
$372$	5.29618	−	3.85638i	0.274594	−	0.199944i
$373$		−	12.4460i		−	0.644427i	−0.946667	−	0.322214i	$-0.895573\pi$
$373$		−	12.4460i		−	0.644427i	0.946667	−	0.322214i	$-0.104427\pi$
$374$	19.2284	+	4.07661i	0.994279	+	0.210797i
$375$	−0.256977	−	0.445098i	−0.0132703	−	0.0229848i
$376$	−0.0825341	+	0.0369020i	−0.00425637	+	0.00190307i
$377$	−3.70867	−	6.42360i	−0.191006	−	0.330832i
$378$	−3.04056	+	3.38044i	−0.156390	+	0.173871i
$379$	24.4576			1.25630			0.628152	−	0.778090i	$-0.283811\pi$
$379$	24.4576			1.25630			0.628152	+	0.778090i	$0.283811\pi$
$380$	−8.15877	+	3.07156i	−0.418536	+	0.157568i
$381$	0.930164			0.0476537
$382$	−16.0611	+	17.8564i	−0.821756	+	0.913614i
$383$	−15.8501	−	27.4532i	−0.809902	−	1.40279i	−0.912931	−	0.408113i	$-0.866187\pi$
$383$	−15.8501	−	27.4532i	−0.809902	−	1.40279i	0.103030	−	0.994678i	$-0.467146\pi$
$384$	5.78062	−	0.628992i	0.294991	−	0.0320981i
$385$	−1.65782	−	2.87142i	−0.0844901	−	0.146341i
$386$	−24.4640	−	5.18660i	−1.24519	−	0.263991i
$387$		−	23.7225i		−	1.20588i
$388$	0.00929585	+	0.0127665i	0.000471926	+	0.000648122i
$389$	10.7295	−	18.5841i	0.544008	−	0.942249i	−0.454661	−	0.890665i	$-0.650239\pi$
$389$	10.7295	−	18.5841i	0.544008	−	0.942249i	0.998669	−	0.0515846i	$-0.0164272\pi$
$390$	1.04140	+	0.220787i	0.0527333	+	0.0111800i
$391$		−	4.64305i		−	0.234809i
$392$	−9.63933	+	13.3113i	−0.486860	+	0.672323i
$393$	4.25587	+	2.45713i	0.214680	+	0.123946i
$394$	−8.01242	−	7.20683i	−0.403660	−	0.363075i
$395$	−0.197165	+	0.341500i	−0.00992044	+	0.0171827i
$396$	−6.75028	+	15.2042i	−0.339214	+	0.764040i
$397$	−2.42666	−	4.20309i	−0.121790	−	0.210947i	0.798683	−	0.601751i	$-0.205530\pi$
$397$	−2.42666	−	4.20309i	−0.121790	−	0.210947i	−0.920474	+	0.390804i	$0.872197\pi$
$398$	−9.65989	−	29.6772i	−0.484207	−	1.48758i
$399$	−2.36463	+	0.614619i	−0.118380	+	0.0307694i
$400$	1.22810	−	3.80681i	0.0614050	−	0.190340i
$401$	7.18248	−	4.14681i	0.358676	−	0.207082i	−0.309824	−	0.950794i	$-0.600270\pi$
$401$	7.18248	−	4.14681i	0.358676	−	0.207082i	0.668500	+	0.743712i	$0.266937\pi$
$402$	−3.99976	−	3.59761i	−0.199490	−	0.179432i
$403$	8.08418	+	4.66740i	0.402701	+	0.232500i
$404$	−33.6475	−	14.9386i	−1.67402	−	0.743225i
$405$	3.34621	−	5.79581i	0.166275	−	0.287996i
$406$	−7.42725	+	2.41756i	−0.368608	+	0.119981i
$407$	26.8894			1.33286
$408$	2.71256	+	6.06685i	0.134292	+	0.300354i
$409$	−13.6056	−	7.85521i	−0.672755	−	0.388415i	0.124365	−	0.992237i	$-0.460311\pi$
$409$	−13.6056	−	7.85521i	−0.672755	−	0.388415i	−0.797120	+	0.603821i	$0.793644\pi$
$410$	0.241869	+	0.743073i	0.0119451	+	0.0366977i
$411$	−10.2326			−0.504736
$412$	−2.91480	−	27.4559i	−0.143602	−	1.35266i
$413$	4.65999	−	2.69044i	0.229303	−	0.132388i
$414$	3.84411	+	0.814987i	0.188928	+	0.0400544i
$415$	13.7012	−	7.91039i	0.672565	−	0.388306i
$416$	4.16133	+	7.16427i	0.204026	+	0.351257i
$417$		−	1.23011i		−	0.0602387i
$418$	−15.7887	+	10.0973i	−0.772250	+	0.493874i
$419$			15.1430i			0.739783i	0.929075	+	0.369892i	$0.120605\pi$
$419$			15.1430i			0.739783i	−0.929075	+	0.369892i	$0.879395\pi$
$420$	0.454887	−	1.02458i	0.0221962	−	0.0499943i
$421$	−4.82740	+	2.78710i	−0.235273	+	0.135835i	−0.613002	−	0.790081i	$-0.710038\pi$
$421$	−4.82740	+	2.78710i	−0.235273	+	0.135835i	0.377729	+	0.925916i	$0.376705\pi$
$422$	3.70492	−	17.4753i	0.180353	−	0.850682i
$423$	0.0757331	−	0.0437245i	0.00368227	−	0.00212596i
$424$	−5.71968	+	2.55734i	−0.277772	+	0.124195i
$425$	4.57159			0.221755
$426$	−0.212365	+	0.0691244i	−0.0102891	+	0.00334909i
$427$	3.49376	+	2.01713i	0.169075	+	0.0976156i
$428$	−3.31872	−	31.2606i	−0.160416	−	1.51104i
$429$	2.28854			0.110492
$430$	3.79547	+	11.6605i	0.183034	+	0.562318i
$431$	−15.6379	+	27.0856i	−0.753249	+	1.30467i	0.192991	+	0.981200i	$0.438181\pi$
$431$	−15.6379	+	27.0856i	−0.753249	+	1.30467i	−0.946240	+	0.323465i	$0.895152\pi$
$432$	−11.5290	+	2.47581i	−0.554691	+	0.119118i
$433$	−20.2800	−	11.7087i	−0.974594	−	0.562682i	−0.0739601	−	0.997261i	$-0.523564\pi$
$433$	−20.2800	−	11.7087i	−0.974594	−	0.562682i	−0.900634	+	0.434579i	$0.856897\pi$
$434$	6.57372	−	7.30855i	0.315549	−	0.350822i
$435$	−2.25413	+	1.30142i	−0.108077	+	0.0623984i
$436$	11.9877	+	16.4634i	0.574107	+	0.788454i
$437$	3.10680	+	3.15379i	0.148618	+	0.150866i
$438$	3.99895	−	1.30165i	0.191077	−	0.0621954i
$439$	−17.9994	−	31.1758i	−0.859063	−	1.48794i	−0.872824	−	0.488035i	$-0.837714\pi$
$439$	−17.9994	−	31.1758i	−0.859063	−	1.48794i	0.0137615	−	0.999905i	$-0.495619\pi$
$440$	0.885421	−	8.55341i	0.0422108	−	0.407768i
$441$	7.94851	−	13.7672i	0.378501	−	0.655582i
$442$	−6.33236	+	7.04020i	−0.301200	+	0.334868i
$443$	20.2644	+	11.6996i	0.962789	+	0.555866i	0.897030	−	0.441969i	$-0.145720\pi$
$443$	20.2644	+	11.6996i	0.962789	+	0.555866i	0.0657584	+	0.997836i	$0.479053\pi$
$444$	5.35145	+	7.34944i	0.253968	+	0.348789i
$445$			13.9088i			0.659342i
$446$	−6.96979	+	32.8749i	−0.330029	+	1.55667i
$447$	−5.25781	+	9.10679i	−0.248686	+	0.430737i
$448$	8.28912	−	2.72211i	0.391624	−	0.128608i
$449$			13.6131i			0.642443i	0.947004	+	0.321221i	$0.104093\pi$
$449$			13.6131i			0.642443i	−0.947004	+	0.321221i	$0.895907\pi$
$450$	−0.802445	+	3.78495i	−0.0378276	+	0.178424i
$451$	0.839968	+	1.45487i	0.0395525	+	0.0685070i
$452$	5.56077	−	0.590347i	0.261556	−	0.0277676i
$453$	−3.17160	−	5.49337i	−0.149015	−	0.258101i
$454$	−5.55502	−	4.99650i	−0.260710	−	0.234497i
$455$	1.59728			0.0748818
$456$	−5.90202	−	2.30585i	−0.276387	−	0.107981i
$457$	26.5111			1.24014			0.620069	−	0.784547i	$-0.287105\pi$
$457$	26.5111			1.24014			0.620069	+	0.784547i	$0.287105\pi$
$458$	−0.866632	−	0.779498i	−0.0404950	−	0.0364235i
$459$	−6.73846	−	11.6714i	−0.314524	−	0.544772i
$460$	−2.01991	+	0.214439i	−0.0941787	+	0.00999829i
$461$	4.25395	+	7.36806i	0.198126	+	0.343165i	0.947921	−	0.318506i	$-0.103181\pi$
$461$	4.25395	+	7.36806i	0.198126	+	0.343165i	−0.749795	+	0.661671i	$0.769848\pi$
$462$	0.499821	−	2.35754i	0.0232538	−	0.109683i
$463$			23.1254i			1.07473i	0.843351	+	0.537364i	$0.180580\pi$
$463$			23.1254i			1.07473i	−0.843351	+	0.537364i	$0.819420\pi$
$464$	−19.2790	−	6.21952i	−0.895004	−	0.288734i
$465$	1.63786	−	2.83685i	0.0759537	−	0.131556i
$466$	0.757256	−	3.57180i	0.0350792	−	0.165461i
$467$		−	20.2084i		−	0.935132i	−0.883958	−	0.467566i	$-0.845131\pi$
$467$		−	20.2084i		−	0.935132i	0.883958	−	0.467566i	$-0.154869\pi$
$468$	−4.71727	−	6.47849i	−0.218056	−	0.299468i
$469$	−6.99043	−	4.03592i	−0.322788	−	0.186362i
$470$	−0.0302298	+	0.0336090i	−0.00139440	+	0.00155027i
$471$	1.22070	−	2.11432i	0.0562470	−	0.0974226i
$472$	13.8812	+	1.43694i	0.638934	+	0.0661404i
$473$	13.1810	+	22.8301i	0.606062	+	1.04973i
$474$	−0.272541	+	0.0887117i	−0.0125182	+	0.00407467i
$475$	−3.10525	+	3.05899i	−0.142479	+	0.140356i
$476$	5.86947	+	8.06087i	0.269027	+	0.369469i
$477$	5.24836	−	3.03014i	0.240306	−	0.138741i
$478$	−24.5886	+	27.3371i	−1.12465	+	1.25037i
$479$	10.2257	+	5.90380i	0.467223	+	0.269751i	0.715077	−	0.699046i	$-0.246392\pi$
$479$	10.2257	+	5.90380i	0.467223	+	0.269751i	−0.247853	+	0.968798i	$0.579725\pi$
$480$	2.51404	−	1.46027i	0.114750	−	0.0666519i
$481$	−6.47690	+	11.2183i	−0.295321	+	0.511511i
$482$	−7.86593	−	24.1658i	−0.358283	−	1.10072i
$483$	−0.569270			−0.0259027
$484$	0.370951	+	3.49417i	0.0168614	+	0.158826i
$485$	0.00683827	+	0.00394808i	0.000310510	+	0.000179273i
$486$	16.5185	−	5.37674i	0.749293	−	0.243894i
$487$	22.8356			1.03478			0.517389	−	0.855750i	$-0.326904\pi$
$487$	22.8356			1.03478			0.517389	+	0.855750i	$0.326904\pi$
$488$	4.27064	+	9.55161i	0.193323	+	0.432381i
$489$	−0.173277	+	0.100042i	−0.00783586	+	0.00452404i
$490$	−1.70430	+	8.03880i	−0.0769925	+	0.363156i
$491$	−12.9081	+	7.45250i	−0.582535	+	0.336326i	−0.762140	−	0.647412i	$-0.775851\pi$
$491$	−12.9081	+	7.45250i	−0.582535	+	0.336326i	0.179605	+	0.983739i	$0.442518\pi$
$492$	−0.230478	+	0.519124i	−0.0103908	+	0.0234039i
$493$		−	23.1521i		−	1.04272i
$494$	−0.409562	−	9.01922i	−0.0184271	−	0.405794i
$495$			8.31766i			0.373851i
$496$	24.9259	−	5.35274i	1.11921	−	0.240345i
$497$	−0.290200	+	0.167547i	−0.0130173	+	0.00751552i
$498$	11.2492	+	2.38493i	0.504087	+	0.106871i
$499$	32.6901	−	18.8736i	1.46341	−	0.844899i	0.464241	−	0.885709i	$-0.346327\pi$
$499$	32.6901	−	18.8736i	1.46341	−	0.844899i	0.999167	+	0.0408096i	$0.0129937\pi$
$500$	−0.211139	−	1.98882i	−0.00944243	−	0.0889429i
$501$	−6.53456			−0.291943
$502$	9.02505	+	27.7269i	0.402808	+	1.23751i
$503$	−11.1960	−	6.46402i	−0.499206	−	0.288216i	0.229180	−	0.973384i	$-0.426396\pi$
$503$	−11.1960	−	6.46402i	−0.499206	−	0.288216i	−0.728385	+	0.685168i	$0.759729\pi$
$504$	−7.70408	+	3.44458i	−0.343167	+	0.153434i
$505$	−18.4073			−0.819114
$506$	−4.15233	+	1.35158i	−0.184594	+	0.0600849i
$507$	2.78946	−	4.83149i	0.123884	−	0.214574i
$508$	3.30824	+	1.46877i	0.146779	+	0.0651663i
$509$	−27.3794	−	15.8075i	−1.21357	−	0.700655i	−0.250035	−	0.968237i	$-0.580442\pi$
$509$	−27.3794	−	15.8075i	−1.21357	−	0.700655i	−0.963535	+	0.267582i	$0.913775\pi$
$510$	2.47051	+	2.22211i	0.109396	+	0.0983968i
$511$	5.46465	−	3.15502i	0.241742	−	0.139570i
$512$	21.5527	+	6.89079i	0.952502	+	0.304533i
$513$	12.3867	+	3.41885i	0.546888	+	0.150946i
$514$	2.77066	+	8.51204i	0.122208	+	0.375450i
$515$	−6.90256	−	11.9556i	−0.304163	−	0.526826i
$516$	−3.61672	+	8.14622i	−0.159217	+	0.358617i
$517$	−0.0485894	+	0.0841593i	−0.00213696	+	0.00370132i
$518$	10.1420	+	9.12228i	0.445613	+	0.400810i
$519$	−8.78172	−	5.07013i	−0.385475	−	0.222554i
$520$	3.35523	+	2.42967i	0.147136	+	0.106548i
$521$			0.154001i			0.00674692i	0.999994	+	0.00337346i	$0.00107381\pi$
$521$			0.154001i			0.00674692i	−0.999994	+	0.00337346i	$0.998926\pi$
$522$	19.1683	+	4.06386i	0.838973	+	0.177870i
$523$	−13.3132	+	23.0592i	−0.582147	+	1.00831i	0.413078	+	0.910696i	$0.364454\pi$
$523$	−13.3132	+	23.0592i	−0.582147	+	1.00831i	−0.995225	+	0.0976121i	$0.968880\pi$
$524$	11.2566	+	15.4593i	0.491747	+	0.675343i
$525$		−	0.560509i		−	0.0244626i
$526$	−15.4203	−	3.26924i	−0.672356	−	0.142546i
$527$	14.5686	+	25.2336i	0.634619	+	1.09919i
$528$	4.63604	−	4.19192i	0.201758	−	0.182430i
$529$	−10.9842	−	19.0253i	−0.477576	−	0.827186i
$530$	−2.09495	+	2.32913i	−0.0909989	+	0.101171i
$531$	−13.4986			−0.585789
$532$	−9.38060	−	1.54790i	−0.406701	−	0.0671101i
$533$	−0.809298			−0.0350546
$534$	−6.76066	+	7.51638i	−0.292562	+	0.325266i
$535$	−7.85907	−	13.6123i	−0.339777	−	0.588512i
$536$	−8.54481	−	19.1111i	−0.369080	−	0.825475i
$537$	0.119960	+	0.207777i	0.00517666	+	0.00896624i
$538$	29.5644	+	6.26793i	1.27461	+	0.270230i
$539$			17.6658i			0.760918i
$540$	−4.76628	+	3.47054i	−0.205108	+	0.149348i
$541$	−8.32908	+	14.4264i	−0.358095	+	0.620239i	−0.987643	−	0.156723i	$-0.949907\pi$
$541$	−8.32908	+	14.4264i	−0.358095	+	0.620239i	0.629547	+	0.776962i	$0.283240\pi$
$542$	11.1304	+	2.35976i	0.478094	+	0.101360i
$543$		−	8.70899i		−	0.373739i
$544$	0.0676875	+	25.8608i	0.00290208	+	1.10877i
$545$	8.81847	+	5.09134i	0.377742	+	0.218089i
$546$	0.863177	+	0.776391i	0.0369406	+	0.0332265i
$547$	−18.2416	+	31.5954i	−0.779954	+	1.35092i	0.152013	+	0.988378i	$0.451424\pi$
$547$	−18.2416	+	31.5954i	−0.779954	+	1.35092i	−0.931967	+	0.362542i	$0.881909\pi$
$548$	−36.3934	−	16.1577i	−1.55465	−	0.690224i
$549$	−5.06020	−	8.76453i	−0.215964	−	0.374061i
$550$	−1.33078	−	4.08843i	−0.0567445	−	0.174331i
$551$	15.4918	+	15.7261i	0.659972	+	0.669953i
$552$	−1.19580	−	0.865932i	−0.0508966	−	0.0368565i
$553$	−0.372433	+	0.215024i	−0.0158374	+	0.00914375i
$554$	20.4969	+	18.4361i	0.870829	+	0.783273i
$555$	3.93666	+	2.27283i	0.167102	+	0.0964764i
$556$	1.94240	−	4.37503i	0.0823761	−	0.185542i
$557$	−11.9243	+	20.6535i	−0.505248	+	0.875116i	0.494733	+	0.869045i	$0.335266\pi$
$557$	−11.9243	+	20.6535i	−0.505248	+	0.875116i	−0.999982	+	0.00607105i	$0.998068\pi$
$558$	−23.4488	+	7.63254i	−0.992666	+	0.323111i
$559$	−12.6997			−0.537140
$560$	3.23572	−	2.92574i	0.136734	−	0.123635i
$561$	6.18632	+	3.57167i	0.261186	+	0.150796i
$562$	0.591753	+	1.81799i	0.0249616	+	0.0766873i
$563$	21.8110			0.919225			0.459613	−	0.888119i	$-0.347988\pi$
$563$	21.8110			0.919225			0.459613	+	0.888119i	$0.347988\pi$
$564$	−0.0326726	+	0.00346862i	−0.00137577	+	0.000146055i
$565$	2.42141	−	1.39800i	0.101870	−	0.0588145i
$566$	−1.16436	−	0.246855i	−0.0489417	−	0.0103761i
$567$	6.32080	−	3.64931i	0.265449	−	0.153257i
$568$	−0.864451	−	0.0894851i	−0.0362716	−	0.00375471i
$569$			26.2300i			1.09962i	0.835291	+	0.549809i	$0.185299\pi$
$569$			26.2300i			1.09962i	−0.835291	+	0.549809i	$0.814701\pi$
$570$	−3.16497	+	0.143721i	−0.132566	+	0.00601981i
$571$			35.1315i			1.47021i	0.677955	+	0.735103i	$0.262866\pi$
$571$			35.1315i			1.47021i	−0.677955	+	0.735103i	$0.737134\pi$
$572$	8.13946	+	3.61372i	0.340328	+	0.151097i
$573$	−7.55888	+	4.36412i	−0.315777	+	0.182314i
$574$	−0.176752	+	0.833698i	−0.00737749	+	0.0347979i
$575$	−0.879561	+	0.507815i	−0.0366802	+	0.0211773i
$576$	−21.4227	−	4.48326i	−0.892613	−	0.186802i
$577$	−15.8057			−0.658000			−0.329000	−	0.944330i	$-0.606712\pi$
$577$	−15.8057			−0.658000			−0.329000	+	0.944330i	$0.606712\pi$
$578$	−5.24389	+	1.70688i	−0.218117	+	0.0709967i
$579$	−7.87074	−	4.54417i	−0.327097	−	0.188849i
$580$	−10.0721	+	1.06928i	−0.418221	+	0.0443995i
$581$	17.2538			0.715809
$582$	0.00177638	+	0.00545743i	7.36335e−5	+	0.000226218i
$583$	−3.36728	+	5.83231i	−0.139459	+	0.241549i
$584$	16.2781	+	1.68506i	0.673594	+	0.0697282i
$585$	−3.47014	−	2.00349i	−0.143473	−	0.0828341i
$586$	−4.40003	+	4.89187i	−0.181763	+	0.202081i
$587$	−9.98703	+	5.76601i	−0.412209	+	0.237989i	−0.691738	−	0.722148i	$-0.743155\pi$
$587$	−9.98703	+	5.76601i	−0.412209	+	0.237989i	0.279530	+	0.960137i	$0.409821\pi$
$588$	−4.82843	+	3.51579i	−0.199121	+	0.144989i
$589$	−26.7803	−	7.39159i	−1.10346	−	0.304565i
$590$	6.63505	−	2.15970i	0.273160	−	0.0889133i
$591$	−1.95824	−	3.39177i	−0.0805512	−	0.139519i
$592$	7.42793	+	34.5894i	0.305286	+	1.42161i
$593$	3.90557	−	6.76464i	0.160382	−	0.277791i	−0.774623	−	0.632423i	$-0.782061\pi$
$593$	3.90557	−	6.76464i	0.160382	−	0.277791i	0.935006	+	0.354632i	$0.115394\pi$
$594$	−8.47627	+	9.42377i	−0.347786	+	0.386662i
$595$	4.31773	+	2.49284i	0.177010	+	0.102197i
$596$	−33.0801	+	24.0871i	−1.35501	+	0.986644i
$597$		−	11.3423i		−	0.464209i
$598$	0.436298	−	2.05792i	0.0178415	−	0.0841545i
$599$	−0.720086	+	1.24723i	−0.0294219	+	0.0509603i	−0.880361	−	0.474303i	$-0.842700\pi$
$599$	−0.720086	+	1.24723i	−0.0294219	+	0.0509603i	0.850940	+	0.525264i	$0.176033\pi$
$600$	0.852606	−	1.17740i	0.0348075	−	0.0480670i
$601$			39.4287i			1.60833i	0.594406	+	0.804165i	$0.297387\pi$
$601$			39.4287i			1.60833i	−0.594406	+	0.804165i	$0.702613\pi$
$602$	−2.77363	+	13.0826i	−0.113045	+	0.533207i
$603$	10.1246	+	17.5363i	0.412306	+	0.714134i
$604$	−2.60587	−	24.5459i	−0.106031	−	0.998760i
$605$	0.878451	+	1.52152i	0.0357141	+	0.0618587i
$606$	−9.94737	−	8.94723i	−0.404084	−	0.363456i
$607$	−1.19357			−0.0484455			−0.0242228	−	0.999707i	$-0.507711\pi$
$607$	−1.19357			−0.0484455			−0.0242228	+	0.999707i	$0.507711\pi$
$608$	−17.3502	−	17.5206i	−0.703643	−	0.710554i
$609$	−2.83861			−0.115026
$610$	3.88954	+	3.49848i	0.157483	+	0.141649i
$611$	−0.0234076	−	0.0405432i	−0.000946971	−	0.00164020i
$612$	−2.64076	−	24.8746i	−0.106746	−	1.00550i
$613$	23.2609	+	40.2890i	0.939498	+	1.62726i	0.766411	+	0.642351i	$0.222041\pi$
$613$	23.2609	+	40.2890i	0.939498	+	1.62726i	0.173087	+	0.984907i	$0.444626\pi$
$614$	8.19191	−	38.6394i	0.330599	−	1.55936i
$615$			0.283994i			0.0114517i
$616$	5.50034	−	7.59563i	0.221615	−	0.306037i
$617$	11.3137	−	19.5958i	0.455471	−	0.788898i	−0.543245	−	0.839574i	$-0.682804\pi$
$617$	11.3137	−	19.5958i	0.455471	−	0.788898i	0.998715	+	0.0506764i	$0.0161377\pi$
$618$	2.08108	−	9.81596i	0.0837132	−	0.394856i
$619$			26.5008i			1.06516i	0.846380	+	0.532580i	$0.178777\pi$
$619$			26.5008i			1.06516i	−0.846380	+	0.532580i	$0.821223\pi$
$620$	10.3048	−	7.50334i	0.413849	−	0.301341i
$621$	2.59292	+	1.49702i	0.104050	+	0.0600734i
$622$	20.3636	−	22.6399i	0.816505	−	0.907776i
$623$	−7.58434	+	13.1365i	−0.303860	+	0.526302i
$624$	0.632186	+	2.94388i	0.0253077	+	0.117849i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	34.2756	−	11.1566i	1.36993	−	0.445909i
$627$	−6.59196	+	1.71339i	−0.263258	+	0.0684264i
$628$	7.68018	−	5.59227i	0.306472	−	0.223156i
$629$	−35.0163	+	20.2167i	−1.39619	+	0.806092i
$630$	−2.82178	+	3.13720i	−0.112422	+	0.124989i
$631$	−11.7430	−	6.77981i	−0.467480	−	0.269900i	0.247704	−	0.968836i	$-0.420324\pi$
$631$	−11.7430	−	6.77981i	−0.467480	−	0.269900i	−0.715184	+	0.698936i	$0.753657\pi$
$632$	−1.10940	−	0.114842i	−0.0441298	−	0.00456817i
$633$	3.24602	−	5.62227i	0.129018	−	0.223465i
$634$	4.71239	+	14.4775i	0.187153	+	0.574974i
$635$	1.80982			0.0718204
$636$	−2.26424	+	0.240378i	−0.0897829	+	0.00953161i
$637$	−7.37019	−	4.25518i	−0.292018	−	0.168596i
$638$	−20.7052	+	6.73951i	−0.819727	+	0.266820i
$639$	0.840625			0.0332546
$640$	11.2473	−	1.22383i	0.444589	−	0.0483760i
$641$	−16.0531	+	9.26827i	−0.634060	+	0.366075i	−0.782323	−	0.622873i	$-0.785965\pi$
$641$	−16.0531	+	9.26827i	−0.634060	+	0.366075i	0.148263	+	0.988948i	$0.452632\pi$
$642$	2.36946	−	11.1762i	0.0935151	−	0.441089i
$643$	11.0587	−	6.38476i	0.436113	−	0.251790i	−0.265834	−	0.964019i	$-0.585647\pi$
$643$	11.0587	−	6.38476i	0.436113	−	0.251790i	0.701948	+	0.712229i	$0.252314\pi$
$644$	−2.02467	−	0.898905i	−0.0797834	−	0.0354218i
$645$			4.45650i			0.175474i
$646$	12.9690	−	25.0197i	0.510258	−	0.984387i
$647$		−	22.3445i		−	0.878454i	−0.898376	−	0.439227i	$-0.855252\pi$
$647$		−	22.3445i		−	0.878454i	0.898376	−	0.439227i	$-0.144748\pi$
$648$	18.8284	+	1.94906i	0.739651	+	0.0765662i
$649$	12.9908	−	7.50024i	0.509934	−	0.294410i
$650$	2.02625	+	0.429583i	0.0794759	+	0.0168496i
$651$	3.09381	−	1.78621i	0.121256	−	0.0700072i
$652$	−0.774251	+	0.0821967i	−0.0303220	+	0.00321907i
$653$	18.0339			0.705720			0.352860	−	0.935676i	$-0.385209\pi$
$653$	18.0339			0.705720			0.352860	+	0.935676i	$0.385209\pi$
$654$	2.29078	+	7.03777i	0.0895767	+	0.275198i
$655$	8.28064	+	4.78083i	0.323551	+	0.186802i
$656$	−1.63944	+	1.48239i	−0.0640096	+	0.0578776i
$657$	−15.8295			−0.617566
$658$	−0.0468778	+	0.0152587i	−0.00182749	+	0.000594845i
$659$	14.7320	−	25.5166i	0.573879	−	0.993987i	−0.422284	−	0.906464i	$-0.638771\pi$
$659$	14.7320	−	25.5166i	0.573879	−	0.993987i	0.996162	−	0.0875234i	$-0.0278953\pi$
$660$	1.26810	−	2.85625i	0.0493608	−	0.111179i
$661$	27.1476	+	15.6737i	1.05592	+	0.609635i	0.924301	−	0.381665i	$-0.124649\pi$
$661$	27.1476	+	15.6737i	1.05592	+	0.609635i	0.131618	+	0.991300i	$0.457983\pi$
$662$	1.17165	+	1.05385i	0.0455375	+	0.0409590i
$663$	−2.98022	+	1.72063i	−0.115742	+	0.0668237i
$664$	36.2431	+	26.2453i	1.40650	+	1.01851i
$665$	−4.60085	+	1.19586i	−0.178413	+	0.0463735i
$666$	−10.5916	−	32.5396i	−0.410416	−	1.26088i
$667$	2.57175	+	4.45440i	0.0995786	+	0.172475i
$668$	−23.2410	−	10.3184i	−0.899220	−	0.399231i
$669$	−6.10649	+	10.5768i	−0.236091	+	0.408921i
$670$	−7.78231	−	6.99985i	−0.300657	−	0.270428i
$671$	9.73969	+	5.62321i	0.375996	+	0.217082i
$672$	3.17071	−	0.00829895i	0.122313	−	0.000320139i
$673$			32.4305i			1.25010i	0.780584	+	0.625051i	$0.214922\pi$
$673$			32.4305i			1.25010i	−0.780584	+	0.625051i	$0.785078\pi$
$674$	5.65186	+	1.19825i	0.217702	+	0.0461548i
$675$	−1.47398	+	2.55302i	−0.0567337	+	0.0982656i
$676$	17.5502	−	12.7791i	0.675008	−	0.491503i
$677$			22.6533i			0.870638i	0.900276	+	0.435319i	$0.143364\pi$
$677$			22.6533i			0.870638i	−0.900276	+	0.435319i	$0.856636\pi$
$678$	1.98807	+	0.421489i	0.0763513	+	0.0161872i
$679$	0.00430569	+	0.00745768i	0.000165237	+	0.000286199i
$680$	5.27782	+	11.8043i	0.202395	+	0.452672i
$681$	−1.35765	−	2.35152i	−0.0520253	−	0.0901104i
$682$	18.3258	−	20.3743i	0.701731	−	0.780172i
$683$	−29.0727			−1.11243			−0.556217	−	0.831037i	$-0.687748\pi$
$683$	−29.0727			−1.11243			−0.556217	+	0.831037i	$0.687748\pi$
$684$	18.4381	+	15.1290i	0.704997	+	0.578473i
$685$	−19.9095			−0.760702
$686$	−13.2130	+	14.6900i	−0.504475	+	0.560866i
$687$	−0.211805	−	0.366857i	−0.00808087	−	0.0139965i
$688$	−25.7266	+	23.2620i	−0.980816	+	0.886856i
$689$	−1.62217	−	2.80968i	−0.0617996	−	0.107040i
$690$	−0.722151	−	0.153103i	−0.0274918	−	0.00582853i
$691$		−	32.1289i		−	1.22224i	−0.791538	−	0.611120i	$-0.790719\pi$
$691$		−	32.1289i		−	1.22224i	0.791538	−	0.611120i	$-0.209281\pi$
$692$	−23.2272	−	31.8993i	−0.882968	−	1.21263i
$693$	−4.53554	+	7.85578i	−0.172291	+	0.298416i
$694$	41.6916	+	8.83902i	1.58259	+	0.335525i
$695$		−	2.39342i		−	0.0907875i
$696$	−5.96274	−	4.31789i	−0.226017	−	0.163669i
$697$	−2.18767	−	1.26305i	−0.0828640	−	0.0478415i
$698$	3.28491	+	2.95463i	0.124336	+	0.111835i
$699$	0.663460	−	1.14915i	0.0250944	−	0.0434647i
$700$	0.885071	−	1.99352i	0.0334525	−	0.0753478i
$701$	−20.7234	−	35.8940i	−0.782713	−	1.35570i	−0.930356	−	0.366659i	$-0.880502\pi$
$701$	−20.7234	−	35.8940i	−0.782713	−	1.35570i	0.147642	−	0.989041i	$-0.452832\pi$
$702$	−1.88992	−	5.80624i	−0.0713305	−	0.219142i
$703$	10.2572	−	37.1626i	0.386858	−	1.40162i
$704$	23.1078	−	7.58852i	0.870910	−	0.286003i
$705$	−0.0142272	+	0.00821406i	−0.000535826	+	0.000309359i
$706$	26.2894	+	23.6461i	0.989413	+	0.889934i
$707$	−17.3851	−	10.0373i	−0.653836	−	0.377492i
$708$	4.63536	+	2.05798i	0.174208	+	0.0773438i
$709$	14.8415	−	25.7063i	0.557385	−	0.965419i	−0.440329	−	0.897837i	$-0.645138\pi$
$709$	14.8415	−	25.7063i	0.557385	−	0.965419i	0.997714	−	0.0675823i	$-0.0215285\pi$
$710$	−0.413197	+	0.134495i	−0.0155070	+	0.00504751i
$711$	1.07883			0.0404592
$712$	−35.9138	+	16.0575i	−1.34593	+	0.601780i
$713$	−5.60592	−	3.23658i	−0.209943	−	0.121211i
$714$	1.12162	+	3.44586i	0.0419757	+	0.128958i
$715$	4.45280			0.166525
$716$	0.0985622	+	0.928406i	0.00368344	+	0.0346962i
$717$	−11.5722	+	6.68121i	−0.432171	+	0.249514i
$718$	−30.5546	−	6.47787i	−1.14029	−	0.241752i
$719$	4.75822	−	2.74716i	0.177452	−	0.102452i	−0.408643	−	0.912694i	$-0.633998\pi$
$719$	4.75822	−	2.74716i	0.177452	−	0.102452i	0.586095	+	0.810242i	$0.300665\pi$
$720$	−10.6995	+	2.29767i	−0.398746	+	0.0856291i
$721$		−	15.0556i		−	0.560699i
$722$	7.93226	+	25.6725i	0.295208	+	0.955433i
$723$		−	9.23589i		−	0.343486i
$724$	13.7519	−	30.9746i	0.511086	−	1.15116i
$725$	−4.38585	+	2.53217i	−0.162886	+	0.0940425i
$726$	−0.264847	+	1.24922i	−0.00982941	+	0.0463630i
$727$	33.7864	−	19.5066i	1.25307	−	0.723460i	0.281352	−	0.959605i	$-0.409217\pi$
$727$	33.7864	−	19.5066i	1.25307	−	0.723460i	0.971718	+	0.236144i	$0.0758838\pi$
$728$	1.84403	+	4.12432i	0.0683444	+	0.152858i
$729$	−13.7641			−0.509782
$730$	7.78075	−	2.53262i	0.287978	−	0.0937366i
$731$	−34.3295	−	19.8201i	−1.26972	−	0.733074i
$732$	0.401420	+	3.78118i	0.0148369	+	0.139756i
$733$	23.0524			0.851460			0.425730	−	0.904850i	$-0.360017\pi$
$733$	23.0524			0.851460			0.425730	+	0.904850i	$0.360017\pi$
$734$	0.988337	+	3.03638i	0.0364802	+	0.112075i
$735$	−1.49320	+	2.58630i	−0.0550776	+	0.0953972i
$736$	−2.88565	−	4.96801i	−0.106366	−	0.183123i
$737$	−19.4874	−	11.2511i	−0.717829	−	0.414439i
$738$	1.42972	−	1.58953i	0.0526285	−	0.0585115i
$739$	16.4708	−	9.50944i	0.605889	−	0.349810i	−0.165466	−	0.986216i	$-0.552913\pi$
$739$	16.4708	−	9.50944i	0.605889	−	0.349810i	0.771355	+	0.636405i	$0.219579\pi$
$740$	10.4123	+	14.2998i	0.382763	+	0.525670i
$741$	0.872985	−	3.16289i	0.0320699	−	0.116192i
$742$	−3.24867	+	1.05744i	−0.119262	+	0.0388198i
$743$	−21.3413	−	36.9642i	−0.782936	−	1.35609i	−0.930224	−	0.366992i	$-0.880388\pi$
$743$	−21.3413	−	36.9642i	−0.782936	−	1.35609i	0.147288	−	0.989094i	$-0.452946\pi$
$744$	9.21586	+	0.953996i	0.337870	+	0.0349752i
$745$	−10.2301	+	17.7191i	−0.374802	+	0.649176i
$746$	11.7707	−	13.0864i	0.430955	−	0.479128i
$747$	−37.4844	−	21.6416i	−1.37148	−	0.791826i
$748$	16.3625	+	22.4716i	0.598273	+	0.821642i
$749$		−	17.1419i		−	0.626351i
$750$	0.150747	−	0.711038i	0.00550449	−	0.0259634i
$751$	−16.3180	+	28.2635i	−0.595451	+	1.03135i	0.398032	+	0.917371i	$0.369693\pi$
$751$	−16.3180	+	28.2635i	−0.595451	+	1.03135i	−0.993483	+	0.113979i	$0.963640\pi$
$752$	−0.121681	−	0.0392551i	−0.00443726	−	0.00143149i
$753$			10.5969i			0.386172i
$754$	2.17556	−	10.2616i	0.0792292	−	0.373706i
$755$	−6.17097	−	10.6884i	−0.224585	−	0.388992i
$756$	−6.39406	+	0.678812i	−0.232550	+	0.0246881i
$757$	−3.51582	−	6.08958i	−0.127785	−	0.221330i	0.795033	−	0.606566i	$-0.207453\pi$
$757$	−3.51582	−	6.08958i	−0.127785	−	0.221330i	−0.922818	+	0.385236i	$0.874120\pi$
$758$	25.7163	+	23.1307i	0.934056	+	0.840143i
$759$	−1.58697			−0.0576034
$760$	−11.4835	−	4.48648i	−0.416551	−	0.162742i
$761$	−4.70743			−0.170644			−0.0853220	−	0.996353i	$-0.527192\pi$
$761$	−4.70743			−0.170644			−0.0853220	+	0.996353i	$0.527192\pi$
$762$	0.978031	+	0.879696i	0.0354303	+	0.0318680i
$763$	5.55252	+	9.61724i	0.201015	+	0.348168i
$764$	−33.7752	+	3.58567i	−1.22194	+	0.129725i
$765$	−6.25360	−	10.8316i	−0.226099	−	0.391616i
$766$	9.29790	−	43.8560i	0.335947	−	1.58458i
$767$			7.22638i			0.260930i
$768$	6.67296	+	4.80562i	0.240790	+	0.173408i
$769$	−25.2251	+	43.6912i	−0.909642	+	1.57555i	−0.0950791	+	0.995470i	$0.530310\pi$
$769$	−25.2251	+	43.6912i	−0.909642	+	1.57555i	−0.814563	+	0.580076i	$0.803023\pi$
$770$	0.972499	−	4.58705i	0.0350464	−	0.165306i
$771$			3.25321i			0.117161i
$772$	−20.8177	−	28.5902i	−0.749247	−	1.02898i
$773$	23.6794	+	13.6713i	0.851690	+	0.491724i	0.861221	−	0.508231i	$-0.169700\pi$
$773$	23.6794	+	13.6713i	0.851690	+	0.491724i	−0.00953040	+	0.999955i	$0.503034\pi$
$774$	22.4354	−	24.9433i	0.806425	−	0.896569i
$775$	3.18677	−	5.51965i	0.114472	−	0.198272i
$776$	−0.00229962	+	0.0222150i	−8.25516e−5	+	0.000797471i
$777$	2.47871	+	4.29324i	0.0889231	+	0.154019i
$778$	28.8574	−	9.39305i	1.03459	−	0.336757i
$779$	2.33112	−	0.605909i	0.0835210	−	0.0217089i
$780$	0.886183	+	1.21704i	0.0317304	+	0.0435772i
$781$	−0.809001	+	0.467077i	−0.0289483	+	0.0167133i
$782$	4.39113	−	4.88198i	0.157027	−	0.174579i
$783$	12.9294	+	7.46477i	0.462057	+	0.266769i
$784$	−22.7245	+	4.87999i	−0.811588	+	0.174285i
$785$	2.37511	−	4.11382i	0.0847714	−	0.146828i
$786$	2.15107	+	6.60854i	0.0767261	+	0.235719i
$787$	−32.6075			−1.16233			−0.581166	−	0.813785i	$-0.697403\pi$
$787$	−32.6075			−1.16233			−0.581166	+	0.813785i	$0.697403\pi$
$788$	−1.60894	−	15.1554i	−0.0573161	−	0.539888i
$789$	−4.96112	−	2.86431i	−0.176621	−	0.101972i
$790$	−0.530282	+	0.172606i	−0.0188666	+	0.00614105i
$791$	3.04927			0.108420
$792$	−21.4769	+	9.60258i	−0.763149	+	0.341213i
$793$	−4.69203	+	2.70894i	−0.166619	+	0.0961974i
$794$	1.42351	−	6.71438i	0.0505186	−	0.238284i
$795$	−0.985954	+	0.569241i	−0.0349682	+	0.0201889i
$796$	17.9100	−	40.3402i	0.634804	−	1.42982i
$797$			33.3349i			1.18078i	0.807118	+	0.590391i	$0.201026\pi$
$797$			33.3349i			1.18078i	−0.807118	+	0.590391i	$0.798974\pi$
$798$	−3.06759	−	1.59009i	−0.108591	−	0.0562884i
$799$		−	0.146127i		−	0.00516960i
$800$	4.89156	−	2.84124i	0.172943	−	0.100453i
$801$	32.9544	−	19.0262i	1.16439	−	0.672259i
$802$	11.4739	+	2.43258i	0.405158	+	0.0858973i
$803$	15.2340	−	8.79534i	0.537596	−	0.310381i
$804$	−0.803174	−	7.56549i	−0.0283258	−	0.266814i
$805$	−1.10763			−0.0390387
$806$	4.08603	+	12.5531i	0.143924	+	0.442166i
$807$	9.51167	+	5.49156i	0.334827	+	0.193312i
$808$	−21.2509	−	47.5293i	−0.747604	−	1.67207i
$809$	−52.3383			−1.84012			−0.920059	−	0.391780i	$-0.871860\pi$
$809$	−52.3383			−1.84012			−0.920059	+	0.391780i	$0.871860\pi$
$810$	8.99976	−	2.92941i	0.316219	−	0.102929i
$811$	23.7664	−	41.1646i	0.834550	−	1.44548i	−0.0598461	−	0.998208i	$-0.519061\pi$
$811$	23.7664	−	41.1646i	0.834550	−	1.44548i	0.894396	−	0.447276i	$-0.147606\pi$
$812$	−10.0959	−	4.48231i	−0.354295	−	0.157298i
$813$	3.58097	+	2.06747i	0.125590	+	0.0725095i
$814$	28.2732	+	25.4305i	0.990974	+	0.891338i
$815$	−0.337145	+	0.194651i	−0.0118097	+	0.00681831i
$816$	−2.88553	+	8.94445i	−0.101014	+	0.313118i
$817$	36.5805	−	9.50807i	1.27979	−	0.332645i
$818$	−6.87677	−	21.1269i	−0.240441	−	0.738684i
$819$	−2.18496	−	3.78447i	−0.0763488	−	0.132240i
$820$	−0.448440	+	1.01006i	−0.0156602	+	0.0352727i
$821$	−0.827838	+	1.43386i	−0.0288917	+	0.0500420i	−0.880110	−	0.474770i	$-0.842531\pi$
$821$	−0.827838	+	1.43386i	−0.0288917	+	0.0500420i	0.851218	+	0.524812i	$0.175864\pi$
$822$	−10.7592	−	9.67739i	−0.375268	−	0.337538i
$823$	−4.08748	−	2.35991i	−0.142481	−	0.0822612i	0.427065	−	0.904221i	$-0.359548\pi$
$823$	−4.08748	−	2.35991i	−0.142481	−	0.0822612i	−0.569546	+	0.821960i	$0.692881\pi$
$824$	22.9015	−	31.6255i	0.797811	−	1.10173i
$825$		−	1.56255i		−	0.0544010i
$826$	7.44426	+	1.57825i	0.259019	+	0.0549145i
$827$	−26.0730	+	45.1597i	−0.906645	+	1.57036i	−0.0879523	+	0.996125i	$0.528032\pi$
$827$	−26.0730	+	45.1597i	−0.906645	+	1.57036i	−0.818693	+	0.574231i	$0.805301\pi$
$828$	3.27116	+	4.49247i	0.113681	+	0.156124i
$829$			19.0933i			0.663139i	0.943431	+	0.331569i	$0.107578\pi$
$829$			19.0933i			0.663139i	−0.943431	+	0.331569i	$0.892422\pi$
$830$	21.8875	+	4.64035i	0.759725	+	0.161069i
$831$	5.00945	+	8.67662i	0.173776	+	0.300988i
$832$	−2.40008	+	11.4685i	−0.0832079	+	0.397599i
$833$	−13.2819	−	23.0050i	−0.460192	−	0.797075i
$834$	1.16337	−	1.29341i	0.0402841	−	0.0447871i
$835$	−12.7143			−0.439996
$836$	−26.1506	−	4.31514i	−0.904438	−	0.149242i
$837$	−18.7890			−0.649442
$838$	−14.3214	+	15.9223i	−0.494724	+	0.550025i
$839$	−26.3494	−	45.6385i	−0.909683	−	1.57562i	−0.814505	−	0.580157i	$-0.802991\pi$
$839$	−26.3494	−	45.6385i	−0.909683	−	1.57562i	−0.0951779	−	0.995460i	$-0.530342\pi$
$840$	1.44728	−	0.647097i	0.0499360	−	0.0223270i
$841$	−1.67620	−	2.90326i	−0.0578000	−	0.100113i
$842$	−7.71171	−	1.63495i	−0.265763	−	0.0563443i
$843$			0.694815i			0.0239307i
$844$	20.4227	−	14.8706i	0.702978	−	0.511868i
$845$	5.42745	−	9.40061i	0.186710	−	0.323391i
$846$	0.120983	+	0.0256494i	0.00415946	+	0.000881846i
$847$			1.91604i			0.0658360i
$848$	−8.43260	−	2.72041i	−0.289577	−	0.0934193i
$849$	−0.374606	−	0.216279i	−0.0128565	−	0.00742268i
$850$	4.80685	+	4.32355i	0.164874	+	0.148297i
$851$	4.49136	−	7.77927i	0.153962	−	0.266670i
$852$	−0.288667	−	0.128161i	−0.00988957	−	0.00439072i
$853$	14.1745	+	24.5510i	0.485327	+	0.840611i	0.999858	−	0.0168609i	$-0.00536725\pi$
$853$	14.1745	+	24.5510i	0.485327	+	0.840611i	−0.514531	+	0.857472i	$0.672034\pi$
$854$	1.76587	+	5.42513i	0.0604269	+	0.185644i
$855$	11.4955	+	3.17285i	0.393137	+	0.108509i
$856$	26.0750	−	36.0080i	0.891226	−	1.23073i
$857$	3.81612	−	2.20324i	0.130356	−	0.0752611i	−0.433404	−	0.901200i	$-0.642688\pi$
$857$	3.81612	−	2.20324i	0.130356	−	0.0752611i	0.563760	+	0.825939i	$0.309354\pi$
$858$	2.40631	+	2.16437i	0.0821500	+	0.0738904i
$859$	11.0194	+	6.36206i	0.375978	+	0.217071i	0.676067	−	0.736840i	$-0.263683\pi$
$859$	11.0194	+	6.36206i	0.375978	+	0.217071i	−0.300089	+	0.953911i	$0.597016\pi$
$860$	−7.03703	+	15.8501i	−0.239961	+	0.540483i
$861$	−0.154859	+	0.268224i	−0.00527758	+	0.00914104i
$862$	−42.0586	+	13.6900i	−1.43252	+	0.466283i
$863$	3.83594			0.130577			0.0652884	−	0.997866i	$-0.479203\pi$
$863$	3.83594			0.130577			0.0652884	+	0.997866i	$0.479203\pi$
$864$	−14.4638	−	8.30029i	−0.492069	−	0.282381i
$865$	−17.0866	−	9.86493i	−0.580960	−	0.335418i
$866$	−10.2502	−	31.4908i	−0.348317	−	1.07010i
$867$	−2.00415			−0.0680646
$868$	13.8240	−	1.46760i	0.469218	−	0.0498135i
$869$	−1.03824	+	0.599430i	−0.0352200	+	0.0203343i
$870$	−3.60094	−	0.763434i	−0.122083	−	0.0258828i
$871$	9.38795	−	5.42013i	0.318098	−	0.183654i
$872$	−2.96554	+	28.6479i	−0.100426	+	0.970141i
$873$		−	0.0216027i		−	0.000731140i
$874$	0.284008	+	6.25432i	0.00960671	+	0.211555i
$875$		−	1.09058i		−	0.0368683i
$876$	5.43577	+	2.41335i	0.183658	+	0.0815394i
$877$	49.9252	−	28.8243i	1.68585	−	0.973327i	0.728216	−	0.685348i	$-0.240350\pi$
$877$	49.9252	−	28.8243i	1.68585	−	0.973327i	0.957636	−	0.287980i	$-0.0929836\pi$
$878$	10.5587	−	49.8029i	0.356339	−	1.68077i
$879$	−2.07080	+	1.19558i	−0.0698463	+	0.0403258i
$880$	9.02031	−	8.15619i	0.304075	−	0.274945i
$881$	−2.48182			−0.0836147			−0.0418074	−	0.999126i	$-0.513312\pi$
$881$	−2.48182			−0.0836147			−0.0418074	+	0.999126i	$0.513312\pi$
$882$	21.3778	−	6.95845i	0.719829	−	0.234303i
$883$	30.8740	+	17.8251i	1.03899	+	0.599863i	0.919548	−	0.392977i	$-0.128555\pi$
$883$	30.8740	+	17.8251i	1.03899	+	0.599863i	0.119446	+	0.992841i	$0.461888\pi$
$884$	−13.3165	+	1.41371i	−0.447881	+	0.0475483i
$885$	2.53584			0.0852413
$886$	10.2423	+	31.4666i	0.344098	+	1.05714i
$887$	5.16987	−	8.95448i	0.173587	−	0.300662i	−0.766084	−	0.642740i	$-0.777797\pi$
$887$	5.16987	−	8.95448i	0.173587	−	0.300662i	0.939672	+	0.342078i	$0.111131\pi$
$888$	−1.32385	+	12.7887i	−0.0444255	+	0.429162i
$889$	1.70932	+	0.986874i	0.0573286	+	0.0330987i
$890$	−13.1542	+	14.6246i	−0.440929	+	0.490217i
$891$	17.6207	−	10.1733i	0.590316	−	0.340819i
$892$	−38.4197	+	27.9750i	−1.28639	+	0.936673i
$893$	0.0977779	+	0.0992566i	0.00327201	+	0.00332149i
$894$	−14.1411	+	4.60290i	−0.472948	+	0.153944i
$895$	0.233406	+	0.404271i	0.00780189	+	0.0135133i
$896$	11.2901	+	4.97718i	0.377176	+	0.166276i
$897$	0.382257	−	0.662088i	0.0127632	−	0.0221065i
$898$	−12.8745	+	14.3137i	−0.429628	+	0.477653i
$899$	−27.9534	−	16.1389i	−0.932298	−	0.538262i
$900$	−4.42333	+	3.22082i	−0.147444	+	0.107361i
$901$		−	10.1267i		−	0.337370i
$902$	−0.492737	+	2.32413i	−0.0164064	+	0.0773850i
$903$	−2.43008	+	4.20903i	−0.0808681	+	0.140068i
$904$	6.40524	+	4.63833i	0.213035	+	0.154269i
$905$		−	16.9450i		−	0.563272i
$906$	1.86051	−	8.77559i	0.0618112	−	0.291549i
$907$	3.62675	+	6.28171i	0.120424	+	0.208581i	0.919935	−	0.392071i	$-0.128241\pi$
$907$	3.62675	+	6.28171i	0.120424	+	0.208581i	−0.799511	+	0.600652i	$0.794908\pi$
$908$	−1.11548	−	10.5073i	−0.0370185	−	0.348695i
$909$	25.1798	+	43.6127i	0.835162	+	1.44654i
$910$	1.67948	+	1.51062i	0.0556742	+	0.0500766i
$911$	−27.7796			−0.920378			−0.460189	−	0.887821i	$-0.652218\pi$
$911$	−27.7796			−0.920378			−0.460189	+	0.887821i	$0.652218\pi$
$912$	−4.02500	−	8.00630i	−0.133281	−	0.265115i
$913$	48.0990			1.59185
$914$	27.8754	+	25.0727i	0.922037	+	0.829332i
$915$	0.950606	+	1.64650i	0.0314261	+	0.0544315i
$916$	−0.174025	−	1.63922i	−0.00574993	−	0.0541614i
$917$	5.21388	+	9.03070i	0.172177	+	0.298220i
$918$	3.95288	−	18.6448i	0.130464	−	0.615371i
$919$		−	9.18433i		−	0.302963i	−0.988460	−	0.151482i	$-0.951596\pi$
$919$		−	9.18433i		−	0.302963i	0.988460	−	0.151482i	$-0.0484044\pi$
$920$	−2.32666	−	1.68484i	−0.0767077	−	0.0555476i
$921$	7.17724	−	12.4313i	0.236498	−	0.409627i
$922$	−2.49543	+	11.7704i	−0.0821826	+	0.387637i
$923$		−	0.450023i		−	0.0148127i
$924$	2.75517	−	2.00616i	0.0906384	−	0.0659977i
$925$	7.65955	+	4.42224i	0.251844	+	0.145402i
$926$	−21.8707	+	24.3154i	−0.718715	+	0.799054i
$927$	−18.8844	+	32.7087i	−0.620244	+	1.07429i
$928$	−14.3890	−	24.7726i	−0.472343	−	0.813199i
$929$	−12.4167	−	21.5064i	−0.407379	−	0.705601i	0.587216	−	0.809430i	$-0.300224\pi$
$929$	−12.4167	−	21.5064i	−0.407379	−	0.705601i	−0.994595	+	0.103829i	$0.966891\pi$
$930$	4.40507	−	1.43384i	0.144448	−	0.0470176i
$931$	24.4151	+	6.73878i	0.800171	+	0.220854i
$932$	4.17424	−	3.03944i	0.136732	−	0.0995602i
$933$	9.58377	−	5.53319i	0.313759	−	0.181149i
$934$	19.1119	−	21.2483i	0.625362	−	0.695266i
$935$	12.0367	+	6.94939i	0.393642	+	0.227269i
$936$	1.16697	−	11.2732i	0.0381434	−	0.368476i
$937$	4.87380	−	8.44167i	0.159220	−	0.275777i	−0.775368	−	0.631510i	$-0.782435\pi$
$937$	4.87380	−	8.44167i	0.159220	−	0.275777i	0.934588	+	0.355733i	$0.115769\pi$
$938$	−3.53321	−	10.8548i	−0.115363	−	0.354421i
$939$	13.0997			0.427493
$940$	−0.0635710	+	0.00674888i	−0.00207346	+	0.000220124i
$941$	29.7752	+	17.1907i	0.970642	+	0.560401i	0.899432	−	0.437061i	$-0.143980\pi$
$941$	29.7752	+	17.1907i	0.970642	+	0.560401i	0.0712104	+	0.997461i	$0.477314\pi$
$942$	3.28312	−	1.06865i	0.106970	−	0.0348185i
$943$	0.561202			0.0182753
$944$	13.2366	+	14.6389i	0.430813	+	0.476457i
$945$	−2.78427	+	1.60750i	−0.0905722	+	0.0522919i
$946$	−7.73216	+	36.4708i	−0.251394	+	1.18577i
$947$	−48.6216	+	28.0717i	−1.57999	+	0.912208i	−0.585132	+	0.810938i	$0.698957\pi$
$947$	−48.6216	+	28.0717i	−1.57999	+	0.912208i	−0.994859	+	0.101270i	$0.967709\pi$
$948$	−0.370465	−	0.164477i	−0.0120321	−	0.00534197i
$949$			8.47420i			0.275084i
$950$	−6.15807	+	0.279637i	−0.199794	+	0.00907263i
$951$			5.53312i			0.179424i
$952$	−1.45200	+	14.0267i	−0.0470595	+	0.454608i
$953$	−15.0683	+	8.69970i	−0.488111	+	0.281811i	−0.723790	−	0.690020i	$-0.757602\pi$
$953$	−15.0683	+	8.69970i	−0.488111	+	0.281811i	0.235680	+	0.971831i	$0.424268\pi$
$954$	8.38419	+	1.77753i	0.271448	+	0.0575496i
$955$	−14.7073	+	8.49125i	−0.475916	+	0.274770i
$956$	−51.7078	+	5.48945i	−1.67235	+	0.177542i
$957$	−7.91329			−0.255800
$958$	5.16842	+	15.8785i	0.166984	+	0.513010i
$959$	−18.8039	−	10.8564i	−0.607210	−	0.350573i
$960$	4.02446	+	0.842222i	0.129889	+	0.0271826i
$961$	9.62198			0.310387
$962$	−17.4198	+	5.67014i	−0.561638	+	0.182812i
$963$	−21.5012	+	37.2413i	−0.692868	+	1.20008i
$964$	14.5839	−	32.8485i	0.469716	−	1.05798i
$965$	−15.3141	−	8.84158i	−0.492977	−	0.284621i
$966$	−0.598565	−	0.538383i	−0.0192585	−	0.0173222i
$967$	5.77379	−	3.33350i	0.185673	−	0.107198i	−0.404282	−	0.914634i	$-0.632479\pi$
$967$	5.77379	−	3.33350i	0.185673	−	0.107198i	0.589955	+	0.807436i	$0.299145\pi$
$968$	−2.91455	+	4.02481i	−0.0936771	+	0.129362i
$969$	7.29608	−	7.18738i	0.234384	−	0.230892i
$970$	0.00345630	+	0.0106185i	0.000110975	+	0.000340939i
$971$	20.4837	+	35.4787i	0.657352	+	1.13857i	0.981299	+	0.192491i	$0.0616567\pi$
$971$	20.4837	+	35.4787i	0.657352	+	1.13857i	−0.323947	+	0.946075i	$0.605010\pi$
$972$	22.4535	+	9.96881i	0.720198	+	0.319750i
$973$	1.30511	−	2.26051i	0.0418398	−	0.0724686i
$974$	24.0107	+	21.5966i	0.769353	+	0.691999i
$975$	0.651899	+	0.376374i	0.0208775	+	0.0120536i
$976$	−4.54296	+	14.0821i	−0.145417	+	0.450756i
$977$			26.9207i			0.861270i	0.902526	+	0.430635i	$0.141710\pi$
$977$			26.9207i			0.861270i	−0.902526	+	0.430635i	$0.858290\pi$
$978$	−0.276808	−	0.0586859i	−0.00885134	−	0.00187657i
$979$	−21.1431	+	36.6210i	−0.675737	+	1.17041i
$980$	−9.39465	+	6.84065i	−0.300101	+	0.218517i
$981$		−	27.8583i		−	0.889447i
$982$	−20.6205	−	4.37174i	−0.658027	−	0.139508i
$983$	−2.02635	−	3.50974i	−0.0646306	−	0.111943i	0.831899	−	0.554926i	$-0.187254\pi$
$983$	−2.02635	−	3.50974i	−0.0646306	−	0.111943i	−0.896530	+	0.442983i	$0.853920\pi$
$984$	−0.733297	+	0.327866i	−0.0233766	+	0.0104520i
$985$	−3.81014	−	6.59935i	−0.121401	−	0.210273i
$986$	21.8960	−	24.3436i	0.697310	−	0.775257i
$987$	−0.0179162			−0.000570278
$988$	8.09923	−	9.87070i	0.257671	−	0.314029i
$989$	8.80652			0.280031
$990$	−7.86637	+	8.74569i	−0.250010	+	0.277956i
$991$	9.13364	+	15.8199i	0.290139	+	0.502536i	0.973843	−	0.227224i	$-0.0729650\pi$
$991$	9.13364	+	15.8199i	0.290139	+	0.502536i	−0.683703	+	0.729760i	$0.739632\pi$
$992$	31.2709	+	17.9453i	0.992852	+	0.569764i
$993$	0.286352	+	0.495976i	0.00908710	+	0.0157393i
$994$	−0.463591	−	0.0982857i	−0.0147042	−	0.00311743i
$995$		−	22.0687i		−	0.699623i
$996$	9.57252	+	13.1465i	0.303317	+	0.416562i
$997$	−15.4146	+	26.6988i	−0.488185	+	0.845561i	−0.999908	−	0.0135897i	$-0.995674\pi$
$997$	−15.4146	+	26.6988i	−0.488185	+	0.845561i	0.511723	+	0.859151i	$0.329007\pi$
$998$	52.2219	+	11.0715i	1.65306	+	0.350464i
$999$		−	26.0733i		−	0.824921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.a.31.16	yes	40
4.3	odd	2	inner	380.2.n.a.31.10	✓	40
19.8	odd	6	inner	380.2.n.a.331.10	yes	40
76.27	even	6	inner	380.2.n.a.331.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.a.31.10	✓	40	4.3	odd	2	inner
380.2.n.a.31.16	yes	40	1.1	even	1	trivial
380.2.n.a.331.10	yes	40	19.8	odd	6	inner
380.2.n.a.331.16	yes	40	76.27	even	6	inner

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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05146 + 0.945743i) q^{2} +(0.256977 + 0.445098i) q^{3} +(0.211139 + 1.98882i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.150747 + 0.711038i) q^{6} +1.09058i q^{7} +(-1.65891 + 2.29085i) q^{8} +(1.36793 - 2.36932i) q^{9} +O(q^{10})\)	\(q+(1.05146 + 0.945743i) q^{2} +(0.256977 + 0.445098i) q^{3} +(0.211139 + 1.98882i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.150747 + 0.711038i) q^{6} +1.09058i q^{7} +(-1.65891 + 2.29085i) q^{8} +(1.36793 - 2.36932i) q^{9} +(-0.293307 + 1.38346i) q^{10} +3.04025i q^{11} +(-0.830964 + 0.605061i) q^{12} +(-1.26840 - 0.732309i) q^{13} +(-1.03141 + 1.14670i) q^{14} +(-0.256977 + 0.445098i) q^{15} +(-3.91084 + 0.839838i) q^{16} +(-2.28580 - 3.95912i) q^{17} +(3.67908 - 1.19754i) q^{18} +(4.20179 + 1.15973i) q^{19} +(-1.61680 + 1.17726i) q^{20} +(-0.485415 + 0.280254i) q^{21} +(-2.87529 + 3.19670i) q^{22} +(0.879561 + 0.507815i) q^{23} +(-1.44596 - 0.149681i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.641093 - 1.96957i) q^{26} +2.94797 q^{27} +(-2.16897 + 0.230264i) q^{28} +(4.38585 + 2.53217i) q^{29} +(-0.691150 + 0.224968i) q^{30} -6.37354 q^{31} +(-4.90637 - 2.81559i) q^{32} +(-1.35321 + 0.781275i) q^{33} +(1.34088 - 6.32463i) q^{34} +(-0.944470 + 0.545290i) q^{35} +(5.00097 + 2.22031i) q^{36} -8.84448i q^{37} +(3.32121 + 5.19322i) q^{38} -0.752748i q^{39} +(-2.81339 - 0.291233i) q^{40} +(0.478536 - 0.276283i) q^{41} +(-0.775444 - 0.164401i) q^{42} +(7.50930 - 4.33550i) q^{43} +(-6.04651 + 0.641915i) q^{44} +2.73585 q^{45} +(0.444562 + 1.36579i) q^{46} +(0.0276817 + 0.0159821i) q^{47} +(-1.37881 - 1.52489i) q^{48} +5.81064 q^{49} +(-1.34477 + 0.437720i) q^{50} +(1.17480 - 2.03481i) q^{51} +(1.18863 - 2.67724i) q^{52} +(1.91837 + 1.10757i) q^{53} +(3.09967 + 2.78802i) q^{54} +(-2.63293 + 1.52012i) q^{55} +(-2.49836 - 1.80918i) q^{56} +(0.563571 + 2.16823i) q^{57} +(2.21677 + 6.81037i) q^{58} +(-2.46698 - 4.27294i) q^{59} +(-0.939480 - 0.417105i) q^{60} +(1.84959 - 3.20358i) q^{61} +(-6.70152 - 6.02773i) q^{62} +(2.58393 + 1.49183i) q^{63} +(-2.49602 - 7.60065i) q^{64} -1.46462i q^{65} +(-2.16173 - 0.458307i) q^{66} +(-3.70071 + 6.40982i) q^{67} +(7.39136 - 5.38197i) q^{68} +0.521988i q^{69} +(-1.50878 - 0.319875i) q^{70} +(0.153631 + 0.266097i) q^{71} +(3.15849 + 7.06420i) q^{72} +(-2.89297 - 5.01077i) q^{73} +(8.36461 - 9.29963i) q^{74} -0.513955 q^{75} +(-1.41934 + 8.60148i) q^{76} -3.31563 q^{77} +(0.711906 - 0.791485i) q^{78} +(0.197165 + 0.341500i) q^{79} +(-2.68274 - 2.96697i) q^{80} +(-3.34621 - 5.79581i) q^{81} +(0.764454 + 0.162072i) q^{82} -15.8208i q^{83} +(-0.659867 - 0.906232i) q^{84} +(2.28580 - 3.95912i) q^{85} +(11.9960 + 2.54327i) q^{86} +2.60285i q^{87} +(-6.96476 - 5.04350i) q^{88} +(12.0454 + 6.95441i) q^{89} +(2.87664 + 2.58741i) q^{90} +(0.798642 - 1.38329i) q^{91} +(-0.824245 + 1.85651i) q^{92} +(-1.63786 - 2.83685i) q^{93} +(0.0139913 + 0.0429843i) q^{94} +(1.09654 + 4.21872i) q^{95} +(-0.00760967 - 2.90736i) q^{96} +(0.00683827 - 0.00394808i) q^{97} +(6.10965 + 5.49537i) q^{98} +(7.20330 + 4.15883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

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