LMFDB - Embedded newform 380.2.n.b.31.2

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			31.2
Character	$\chi$	$=$	380.31
Dual form			380.2.n.b.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33235 - 0.474182i) q^{2} +(-0.435478 - 0.754271i) q^{3} +(1.55030 + 1.26355i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.222547 + 1.21145i) q^{6} +3.15791i q^{7} +(-1.46639 - 2.41862i) q^{8} +(1.12072 - 1.94114i) q^{9} +O(q^{10})$	\(q+(-1.33235 - 0.474182i) q^{2} +(-0.435478 - 0.754271i) q^{3} +(1.55030 + 1.26355i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.222547 + 1.21145i) q^{6} +3.15791i q^{7} +(-1.46639 - 2.41862i) q^{8} +(1.12072 - 1.94114i) q^{9} +(0.255520 + 1.39094i) q^{10} +2.82746i q^{11} +(0.277936 - 1.71960i) q^{12} +(3.26520 + 1.88516i) q^{13} +(1.49742 - 4.20743i) q^{14} +(-0.435478 + 0.754271i) q^{15} +(0.806879 + 3.91777i) q^{16} +(-0.918627 - 1.59111i) q^{17} +(-2.41364 + 2.05485i) q^{18} +(4.35204 + 0.244409i) q^{19} +(0.319116 - 1.97438i) q^{20} +(2.38192 - 1.37520i) q^{21} +(1.34073 - 3.76716i) q^{22} +(-0.954851 - 0.551283i) q^{23} +(-1.18571 + 2.15931i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.45647 - 4.05999i) q^{26} -4.56506 q^{27} +(-3.99018 + 4.89571i) q^{28} +(4.92338 + 2.84252i) q^{29} +(0.937871 - 0.798455i) q^{30} +10.1528 q^{31} +(0.782694 - 5.60245i) q^{32} +(2.13267 - 1.23130i) q^{33} +(0.469456 + 2.55551i) q^{34} +(2.73483 - 1.57895i) q^{35} +(4.19018 - 1.59327i) q^{36} -10.8342i q^{37} +(-5.68254 - 2.38930i) q^{38} -3.28379i q^{39} +(-1.36139 + 2.47924i) q^{40} +(5.31936 - 3.07113i) q^{41} +(-3.82564 + 0.702784i) q^{42} +(-1.71337 + 0.989217i) q^{43} +(-3.57264 + 4.38342i) q^{44} -2.24143 q^{45} +(1.01079 + 1.18727i) q^{46} +(0.537802 + 0.310500i) q^{47} +(2.60368 - 2.31471i) q^{48} -2.97238 q^{49} +(1.07683 - 0.916756i) q^{50} +(-0.800085 + 1.38579i) q^{51} +(2.68004 + 7.04831i) q^{52} +(12.4169 + 7.16889i) q^{53} +(6.08225 + 2.16467i) q^{54} +(2.44865 - 1.41373i) q^{55} +(7.63776 - 4.63073i) q^{56} +(-1.71087 - 3.38905i) q^{57} +(-5.21179 - 6.12180i) q^{58} +(-3.49461 - 6.05284i) q^{59} +(-1.62818 + 0.619099i) q^{60} +(-5.91369 + 10.2428i) q^{61} +(-13.5271 - 4.81428i) q^{62} +(6.12994 + 3.53912i) q^{63} +(-3.69940 + 7.09327i) q^{64} -3.77032i q^{65} +(-3.42532 + 0.629244i) q^{66} +(-5.58251 + 9.66919i) q^{67} +(0.586297 - 3.62743i) q^{68} +0.960288i q^{69} +(-4.39246 + 0.806910i) q^{70} +(-4.66044 - 8.07212i) q^{71} +(-6.33828 + 0.135884i) q^{72} +(-0.0750974 - 0.130072i) q^{73} +(-5.13737 + 14.4349i) q^{74} +0.870957 q^{75} +(6.43816 + 5.87793i) q^{76} -8.92886 q^{77} +(-1.55711 + 4.37515i) q^{78} +(-1.12114 - 1.94187i) q^{79} +(2.98945 - 2.65766i) q^{80} +(-1.37416 - 2.38012i) q^{81} +(-8.54351 + 1.56947i) q^{82} +12.7672i q^{83} +(5.43033 + 0.877696i) q^{84} +(-0.918627 + 1.59111i) q^{85} +(2.75188 - 0.505530i) q^{86} -4.95142i q^{87} +(6.83854 - 4.14616i) q^{88} +(-7.77565 - 4.48928i) q^{89} +(2.98637 + 1.06285i) q^{90} +(-5.95317 + 10.3112i) q^{91} +(-0.783734 - 2.06116i) q^{92} +(-4.42133 - 7.65797i) q^{93} +(-0.569305 - 0.668710i) q^{94} +(-1.96436 - 3.89118i) q^{95} +(-4.56661 + 1.84938i) q^{96} +(-4.06833 + 2.34885i) q^{97} +(3.96025 + 1.40945i) q^{98} +(5.48849 + 3.16878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * 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 $

$2$	−1.33235	−	0.474182i	−0.942112	−	0.335297i
$2$	−1.33235	−	0.474182i	−0.942112	−	0.335297i
$3$	−0.435478	−	0.754271i	−0.251424	−	0.435478i	0.712494	−	0.701678i	$-0.247565\pi$
$3$	−0.435478	−	0.754271i	−0.251424	−	0.435478i	−0.963918	+	0.266199i	$0.914232\pi$
$4$	1.55030	+	1.26355i	0.775151	+	0.631775i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.222547	+	1.21145i	0.0908546	+	0.494571i
$7$			3.15791i			1.19358i	0.802399	+	0.596789i	$0.203557\pi$
$7$			3.15791i			1.19358i	−0.802399	+	0.596789i	$0.796443\pi$
$8$	−1.46639	−	2.41862i	−0.518447	−	0.855110i
$9$	1.12072	−	1.94114i	0.373572	−	0.647046i
$10$	0.255520	+	1.39094i	0.0808027	+	0.439853i
$11$			2.82746i			0.852511i	0.904603	+	0.426256i	$0.140168\pi$
$11$			2.82746i			0.852511i	−0.904603	+	0.426256i	$0.859832\pi$
$12$	0.277936	−	1.71960i	0.0802332	−	0.496405i
$13$	3.26520	+	1.88516i	0.905602	+	0.522850i	0.879014	−	0.476797i	$-0.158202\pi$
$13$	3.26520	+	1.88516i	0.905602	+	0.522850i	0.0265887	+	0.999646i	$0.491536\pi$
$14$	1.49742	−	4.20743i	0.400203	−	1.12448i
$15$	−0.435478	+	0.754271i	−0.112440	+	0.194752i
$16$	0.806879	+	3.91777i	0.201720	+	0.979443i
$17$	−0.918627	−	1.59111i	−0.222800	−	0.385901i	0.732857	−	0.680382i	$-0.238186\pi$
$17$	−0.918627	−	1.59111i	−0.222800	−	0.385901i	−0.955657	+	0.294482i	$0.904853\pi$
$18$	−2.41364	+	2.05485i	−0.568900	+	0.484333i
$19$	4.35204	+	0.244409i	0.998427	+	0.0560713i
$19$	4.35204	+	0.244409i	0.998427	+	0.0560713i
$20$	0.319116	−	1.97438i	0.0713564	−	0.441484i
$21$	2.38192	−	1.37520i	0.519777	−	0.300093i
$22$	1.34073	−	3.76716i	0.285845	−	0.803162i
$23$	−0.954851	−	0.551283i	−0.199100	−	0.114951i	0.397136	−	0.917760i	$-0.370004\pi$
$23$	−0.954851	−	0.551283i	−0.199100	−	0.114951i	−0.596236	+	0.802809i	$0.703338\pi$
$24$	−1.18571	+	2.15931i	−0.242032	+	0.440767i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−3.45647	−	4.05999i	−0.677869	−	0.796229i
$27$	−4.56506			−0.878547
$28$	−3.99018	+	4.89571i	−0.754073	+	0.925203i
$29$	4.92338	+	2.84252i	0.914249	+	0.527842i	0.881796	−	0.471631i	$-0.156335\pi$
$29$	4.92338	+	2.84252i	0.914249	+	0.527842i	0.0324533	+	0.999473i	$0.489668\pi$
$30$	0.937871	−	0.798455i	0.171231	−	0.145777i
$31$	10.1528			1.82350			0.911750	−	0.410746i	$-0.134732\pi$
$31$	10.1528			1.82350			0.911750	+	0.410746i	$0.134732\pi$
$32$	0.782694	−	5.60245i	0.138362	−	0.990382i
$33$	2.13267	−	1.23130i	0.371250	−	0.214342i
$34$	0.469456	+	2.55551i	0.0805111	+	0.438266i
$35$	2.73483	−	1.57895i	0.462270	−	0.266892i
$36$	4.19018	−	1.59327i	0.698363	−	0.265545i
$37$		−	10.8342i		−	1.78113i	−0.454860	−	0.890563i	$-0.650311\pi$
$37$		−	10.8342i		−	1.78113i	0.454860	−	0.890563i	$-0.349689\pi$
$38$	−5.68254	−	2.38930i	−0.921830	−	0.387595i
$39$		−	3.28379i		−	0.525827i
$40$	−1.36139	+	2.47924i	−0.215254	+	0.392002i
$41$	5.31936	−	3.07113i	0.830744	−	0.479630i	−0.0233635	−	0.999727i	$-0.507438\pi$
$41$	5.31936	−	3.07113i	0.830744	−	0.479630i	0.854107	+	0.520097i	$0.174104\pi$
$42$	−3.82564	+	0.702784i	−0.590309	+	0.108442i
$43$	−1.71337	+	0.989217i	−0.261287	+	0.150854i	−0.624922	−	0.780688i	$-0.714869\pi$
$43$	−1.71337	+	0.989217i	−0.261287	+	0.150854i	0.363634	+	0.931542i	$0.381536\pi$
$44$	−3.57264	+	4.38342i	−0.538596	+	0.660826i
$45$	−2.24143			−0.334133
$46$	1.01079	+	1.18727i	0.149032	+	0.175054i
$47$	0.537802	+	0.310500i	0.0784464	+	0.0452911i	0.538710	−	0.842491i	$-0.318912\pi$
$47$	0.537802	+	0.310500i	0.0784464	+	0.0452911i	−0.460264	+	0.887782i	$0.652245\pi$
$48$	2.60368	−	2.31471i	0.375809	−	0.334100i
$49$	−2.97238			−0.424626
$50$	1.07683	−	0.916756i	0.152286	−	0.129649i
$51$	−0.800085	+	1.38579i	−0.112034	+	0.194049i
$52$	2.68004	+	7.04831i	0.371655	+	0.977425i
$53$	12.4169	+	7.16889i	1.70559	+	0.984723i	0.939859	+	0.341563i	$0.110956\pi$
$53$	12.4169	+	7.16889i	1.70559	+	0.984723i	0.765732	+	0.643160i	$0.222377\pi$
$54$	6.08225	+	2.16467i	0.827690	+	0.294574i
$55$	2.44865	−	1.41373i	0.330176	−	0.190627i
$56$	7.63776	−	4.63073i	1.02064	−	0.618807i
$57$	−1.71087	−	3.38905i	−0.226610	−	0.448891i
$58$	−5.21179	−	6.12180i	−0.684342	−	0.803832i
$59$	−3.49461	−	6.05284i	−0.454959	−	0.788013i	0.543726	−	0.839262i	$-0.317013\pi$
$59$	−3.49461	−	6.05284i	−0.454959	−	0.788013i	−0.998686	+	0.0512497i	$0.983680\pi$
$60$	−1.62818	+	0.619099i	−0.210198	+	0.0799254i
$61$	−5.91369	+	10.2428i	−0.757171	+	1.31146i	0.187117	+	0.982338i	$0.440086\pi$
$61$	−5.91369	+	10.2428i	−0.757171	+	1.31146i	−0.944288	+	0.329121i	$0.893248\pi$
$62$	−13.5271	−	4.81428i	−1.71794	−	0.611414i
$63$	6.12994	+	3.53912i	0.772300	+	0.445887i
$64$	−3.69940	+	7.09327i	−0.462425	+	0.886658i
$65$		−	3.77032i		−	0.467651i
$66$	−3.42532	+	0.629244i	−0.421628	+	0.0774546i
$67$	−5.58251	+	9.66919i	−0.682012	+	1.18128i	0.292354	+	0.956310i	$0.405561\pi$
$67$	−5.58251	+	9.66919i	−0.682012	+	1.18128i	−0.974366	+	0.224969i	$0.927772\pi$
$68$	0.586297	−	3.62743i	0.0710989	−	0.439891i
$69$			0.960288i			0.115605i
$70$	−4.39246	+	0.806910i	−0.524999	+	0.0964442i
$71$	−4.66044	−	8.07212i	−0.553092	−	0.957984i	−0.998049	−	0.0624322i	$-0.980114\pi$
$71$	−4.66044	−	8.07212i	−0.553092	−	0.957984i	0.444957	−	0.895552i	$-0.353219\pi$
$72$	−6.33828	+	0.135884i	−0.746973	+	0.0160141i
$73$	−0.0750974	−	0.130072i	−0.00878948	−	0.0152238i	0.861597	−	0.507593i	$-0.169464\pi$
$73$	−0.0750974	−	0.130072i	−0.00878948	−	0.0152238i	−0.870387	+	0.492369i	$0.836131\pi$
$74$	−5.13737	+	14.4349i	−0.597207	+	1.67802i
$75$	0.870957			0.100569
$76$	6.43816	+	5.87793i	0.738508	+	0.674245i
$77$	−8.92886			−1.01754
$78$	−1.55711	+	4.37515i	−0.176308	+	0.495388i
$79$	−1.12114	−	1.94187i	−0.126138	−	0.218478i	0.796039	−	0.605245i	$-0.206925\pi$
$79$	−1.12114	−	1.94187i	−0.126138	−	0.218478i	−0.922177	+	0.386767i	$0.873592\pi$
$80$	2.98945	−	2.65766i	0.334231	−	0.297136i
$81$	−1.37416	−	2.38012i	−0.152685	−	0.264458i
$82$	−8.54351	+	1.56947i	−0.943473	+	0.173319i
$83$			12.7672i			1.40139i	0.713462	+	0.700694i	$0.247126\pi$
$83$			12.7672i			1.40139i	−0.713462	+	0.700694i	$0.752874\pi$
$84$	5.43033	+	0.877696i	0.592498	+	0.0957645i
$85$	−0.918627	+	1.59111i	−0.0996391	+	0.172580i
$86$	2.75188	−	0.505530i	0.296743	−	0.0545128i
$87$		−	4.95142i		−	0.530848i
$88$	6.83854	−	4.14616i	0.728991	−	0.441982i
$89$	−7.77565	−	4.48928i	−0.824218	−	0.475862i	0.0276511	−	0.999618i	$-0.491197\pi$
$89$	−7.77565	−	4.48928i	−0.824218	−	0.475862i	−0.851869	+	0.523755i	$0.824531\pi$
$90$	2.98637	+	1.06285i	0.314791	+	0.112034i
$91$	−5.95317	+	10.3112i	−0.624061	+	1.08091i
$92$	−0.783734	−	2.06116i	−0.0817099	−	0.214891i
$93$	−4.42133	−	7.65797i	−0.458471	−	0.794095i
$94$	−0.569305	−	0.668710i	−0.0587194	−	0.0689721i
$95$	−1.96436	−	3.89118i	−0.201539	−	0.399227i
$96$	−4.56661	+	1.84938i	−0.466077	+	0.188752i
$97$	−4.06833	+	2.34885i	−0.413077	+	0.238490i	−0.692111	−	0.721791i	$-0.743319\pi$
$97$	−4.06833	+	2.34885i	−0.413077	+	0.238490i	0.279034	+	0.960281i	$0.409986\pi$
$98$	3.96025	+	1.40945i	0.400046	+	0.142376i
$99$	5.48849	+	3.16878i	0.551614	+	0.318475i
$100$	−1.86942	+	0.710826i	−0.186942	+	0.0710826i
$101$	−3.20334	+	5.54834i	−0.318744	+	0.552081i	−0.980226	−	0.197880i	$-0.936594\pi$
$101$	−3.20334	+	5.54834i	−0.318744	+	0.552081i	0.661482	+	0.749961i	$0.269928\pi$
$102$	1.72311	−	1.46697i	0.170613	−	0.145251i
$103$	4.17604			0.411478			0.205739	−	0.978607i	$-0.434040\pi$
$103$	4.17604			0.411478			0.205739	+	0.978607i	$0.434040\pi$
$104$	−0.228571	−	10.6616i	−0.0224132	−	1.04546i
$105$	−2.38192	−	1.37520i	−0.232451	−	0.134206i
$106$	−13.1443	−	15.4393i	−1.27668	−	1.49960i
$107$	0.141744			0.0137029			0.00685146	−	0.999977i	$-0.497819\pi$
$107$	0.141744			0.0137029			0.00685146	+	0.999977i	$0.497819\pi$
$108$	−7.07723	−	5.76819i	−0.681007	−	0.555044i
$109$	−15.8996	+	9.17965i	−1.52291	+	0.879251i	−0.523275	+	0.852164i	$0.675290\pi$
$109$	−15.8996	+	9.17965i	−1.52291	+	0.879251i	−0.999633	+	0.0270877i	$0.991377\pi$
$110$	−3.93282	+	0.722474i	−0.374980	+	0.0688852i
$111$	−8.17189	+	4.71805i	−0.775642	+	0.447817i
$112$	−12.3720	+	2.54805i	−1.16904	+	0.240768i
$113$			9.21056i			0.866457i	0.901284	+	0.433228i	$0.142626\pi$
$113$			9.21056i			0.866457i	−0.901284	+	0.433228i	$0.857374\pi$
$114$	0.672446	+	5.32666i	0.0629804	+	0.498888i
$115$			1.10257i			0.102815i
$116$	4.04107	+	10.6277i	0.375204	+	0.986758i
$117$	7.31872	−	4.22546i	0.676616	−	0.390644i
$118$	1.78589	+	9.72157i	0.164404	+	0.894943i
$119$	5.02458	−	2.90094i	0.460602	−	0.265929i
$120$	2.46287	−	0.0528006i	0.224828	−	0.00482001i
$121$	3.00547			0.273224
$122$	12.7361	−	10.8428i	1.15307	−	0.981664i
$123$	−4.63293	−	2.67482i	−0.417737	−	0.241181i
$124$	15.7399	+	12.8286i	1.41349	+	1.15204i
$125$	1.00000			0.0894427
$126$	−6.48902	−	7.62205i	−0.578088	−	0.679026i
$127$	8.48074	−	14.6891i	0.752544	−	1.30345i	−0.194041	−	0.980993i	$-0.562160\pi$
$127$	8.48074	−	14.6891i	0.752544	−	1.30345i	0.946586	−	0.322452i	$-0.104507\pi$
$128$	8.29239	−	7.69651i	0.732950	−	0.680282i
$129$	1.49228	+	0.861566i	0.131388	+	0.0758566i
$130$	−1.78782	+	5.02338i	−0.156802	+	0.440580i
$131$	−4.34129	+	2.50644i	−0.379300	+	0.218989i	−0.677514	−	0.735510i	$-0.736943\pi$
$131$	−4.34129	+	2.50644i	−0.379300	+	0.218989i	0.298214	+	0.954499i	$0.403609\pi$
$132$	4.86209	+	0.785853i	0.423191	+	0.0683997i
$133$	−0.771821	+	13.7433i	−0.0669254	+	1.19170i
$134$	12.0228	−	10.2356i	1.03861	−	0.884221i
$135$	2.28253	+	3.95346i	0.196449	+	0.340260i
$136$	−2.50121	+	4.55499i	−0.214477	+	0.390587i
$137$	−2.42918	+	4.20747i	−0.207539	+	0.359468i	−0.950939	−	0.309379i	$-0.899879\pi$
$137$	−2.42918	+	4.20747i	−0.207539	+	0.359468i	0.743400	+	0.668848i	$0.233212\pi$
$138$	0.455351	−	1.27944i	0.0387621	−	0.108913i
$139$	−1.52000	−	0.877574i	−0.128925	−	0.0744348i	0.434150	−	0.900840i	$-0.357049\pi$
$139$	−1.52000	−	0.877574i	−0.128925	−	0.0744348i	−0.563075	+	0.826406i	$0.690382\pi$
$140$	6.23490	+	1.00774i	0.526945	+	0.0851694i
$141$		−	0.540864i		−	0.0455490i
$142$	2.38168	+	12.9648i	0.199866	+	1.08798i
$143$	−5.33022	+	9.23221i	−0.445735	+	0.772036i
$144$	8.50922	+	2.82445i	0.709102	+	0.235371i
$145$		−	5.68503i		−	0.472116i
$146$	0.0383778	+	0.208912i	0.00317617	+	0.0172896i
$147$	1.29441	+	2.24198i	0.106761	+	0.184916i
$148$	13.6895	−	16.7962i	1.12527	−	1.38064i
$149$	−1.03406	−	1.79104i	−0.0847131	−	0.146727i	0.820556	−	0.571566i	$-0.193664\pi$
$149$	−1.03406	−	1.79104i	−0.0847131	−	0.146727i	−0.905269	+	0.424839i	$0.860331\pi$
$150$	−1.16042	−	0.412992i	−0.0947477	−	0.0337207i
$151$	−4.42900			−0.360427			−0.180213	−	0.983628i	$-0.557679\pi$
$151$	−4.42900			−0.360427			−0.180213	+	0.983628i	$0.557679\pi$
$152$	−5.79066	−	10.8843i	−0.469685	−	0.882834i
$153$	−4.11809			−0.332927
$154$	11.8964	+	4.23390i	0.958635	+	0.341178i
$155$	−5.07641	−	8.79260i	−0.407747	−	0.706238i
$156$	4.14923	−	5.09087i	0.332205	−	0.407596i
$157$	−3.40194	−	5.89234i	−0.271505	−	0.470260i	0.697743	−	0.716349i	$-0.254188\pi$
$157$	−3.40194	−	5.89234i	−0.271505	−	0.470260i	−0.969247	+	0.246089i	$0.920855\pi$
$158$	0.572949	+	3.11888i	0.0455814	+	0.248125i
$159$		−	12.4876i		−	0.990331i
$160$	−5.24321	+	2.12339i	−0.414512	+	0.167869i
$161$	1.74090	−	3.01533i	0.137202	−	0.237641i
$162$	0.702254	+	3.82276i	0.0551743	+	0.300344i
$163$		−	22.0360i		−	1.72599i	−0.505213	−	0.862995i	$-0.668586\pi$
$163$		−	22.0360i		−	1.72599i	0.505213	−	0.862995i	$-0.331414\pi$
$164$	12.1271	+	1.96009i	0.946971	+	0.153057i
$165$	−2.13267	−	1.23130i	−0.166028	−	0.0958564i
$166$	6.05400	−	17.0104i	0.469881	−	1.32026i
$167$	2.94610	−	5.10279i	0.227976	−	0.394866i	−0.729232	−	0.684266i	$-0.760123\pi$
$167$	2.94610	−	5.10279i	0.227976	−	0.394866i	0.957208	+	0.289400i	$0.0934559\pi$
$168$	−6.81890	−	3.74436i	−0.526090	−	0.288884i
$169$	0.607667	+	1.05251i	0.0467436	+	0.0809623i
$170$	1.97841	−	1.68431i	0.151737	−	0.129181i
$171$	5.35184	−	8.17400i	0.409265	−	0.625082i
$172$	−3.90618	−	0.631349i	−0.297843	−	0.0481399i
$173$	12.5503	−	7.24591i	0.954180	−	0.550896i	0.0598030	−	0.998210i	$-0.480953\pi$
$173$	12.5503	−	7.24591i	0.954180	−	0.550896i	0.894377	+	0.447314i	$0.147619\pi$
$174$	−2.34787	+	6.59701i	−0.177992	+	0.500118i
$175$	−2.73483	−	1.57895i	−0.206734	−	0.119358i
$176$	−11.0773	+	2.28142i	−0.834987	+	0.171968i
$177$	−3.04365	+	5.27176i	−0.228775	+	0.396250i
$178$	8.23114	+	9.66835i	0.616950	+	0.724674i
$179$	−8.16887			−0.610570			−0.305285	−	0.952261i	$-0.598752\pi$
$179$	−8.16887			−0.610570			−0.305285	+	0.952261i	$0.598752\pi$
$180$	−3.47490	−	2.83217i	−0.259004	−	0.211097i
$181$	8.92165	+	5.15092i	0.663141	+	0.382865i	0.793473	−	0.608606i	$-0.208271\pi$
$181$	8.92165	+	5.15092i	0.663141	+	0.382865i	−0.130331	+	0.991470i	$0.541604\pi$
$182$	12.8211	−	10.9152i	0.950361	−	0.809089i
$183$	10.3011			0.761482
$184$	0.0668416	+	3.11781i	0.00492763	+	0.229848i
$185$	−9.38266	+	5.41708i	−0.689827	+	0.398272i
$186$	2.25948	+	12.2996i	0.165673	+	0.901851i
$187$	4.49880	−	2.59738i	0.328985	−	0.189939i
$188$	0.441423	+	1.16091i	0.0321941	+	0.0846680i
$189$		−	14.4161i		−	1.04861i
$190$	0.772078	+	6.11587i	0.0560124	+	0.443692i
$191$		−	3.43763i		−	0.248738i	−0.992236	−	0.124369i	$-0.960309\pi$
$191$		−	3.43763i		−	0.248738i	0.992236	−	0.124369i	$-0.0396906\pi$
$192$	6.96125	−	0.298617i	0.502385	−	0.0215508i
$193$	12.1155	−	6.99487i	0.872091	−	0.503502i	0.00404862	−	0.999992i	$-0.498711\pi$
$193$	12.1155	−	6.99487i	0.872091	−	0.503502i	0.868043	+	0.496490i	$0.165378\pi$
$194$	6.53422	−	1.20036i	0.469130	−	0.0861808i
$195$	−2.84384	+	1.64189i	−0.203652	+	0.117578i
$196$	−4.60810	−	3.75576i	−0.329150	−	0.268268i
$197$	20.6076			1.46823			0.734117	−	0.679023i	$-0.237596\pi$
$197$	20.6076			1.46823			0.734117	+	0.679023i	$0.237596\pi$
$198$	−5.81000	−	6.82447i	−0.412899	−	0.484994i
$199$	−7.27679	−	4.20126i	−0.515838	−	0.297819i	0.219392	−	0.975637i	$-0.429593\pi$
$199$	−7.27679	−	4.20126i	−0.515838	−	0.297819i	−0.735230	+	0.677818i	$0.762926\pi$
$200$	2.82778	−	0.0606237i	0.199954	−	0.00428674i
$201$	9.72425			0.685895
$202$	6.89888	−	5.87336i	0.485404	−	0.413248i
$203$	−8.97641	+	15.5476i	−0.630020	+	1.09123i
$204$	−2.99139	+	1.13744i	−0.209439	+	0.0796369i
$205$	−5.31936	−	3.07113i	−0.371520	−	0.214497i
$206$	−5.56394	−	1.98020i	−0.387658	−	0.137967i
$207$	−2.14024	+	1.23567i	−0.148757	+	0.0858847i
$208$	−4.75102	+	14.3134i	−0.329424	+	0.992455i
$209$	−0.691057	+	12.3052i	−0.0478014	+	0.851170i
$210$	2.52145	+	2.96171i	0.173996	+	0.204377i
$211$	3.56073	+	6.16736i	0.245131	+	0.424579i	0.962168	−	0.272456i	$-0.0878358\pi$
$211$	3.56073	+	6.16736i	0.245131	+	0.424579i	−0.717038	+	0.697034i	$0.754502\pi$
$212$	10.1917	+	26.8033i	0.699967	+	1.84086i
$213$	−4.05904	+	7.03047i	−0.278121	+	0.481720i
$214$	−0.188853	−	0.0672125i	−0.0129097	−	0.00459455i
$215$	1.71337	+	0.989217i	0.116851	+	0.0674641i
$216$	6.69416	+	11.0411i	0.455480	+	0.751254i
$217$			32.0617i			2.17649i
$218$	25.5367	−	4.69118i	1.72956	−	0.317727i
$219$	−0.0654066	+	0.113288i	−0.00441977	+	0.00765526i
$220$	5.58247	+	0.902287i	0.376370	+	0.0608322i
$221$		−	6.92704i		−	0.465963i
$222$	13.1250	−	2.41111i	0.880894	−	0.161823i
$223$	−5.31223	−	9.20106i	−0.355734	−	0.616149i	0.631510	−	0.775368i	$-0.282436\pi$
$223$	−5.31223	−	9.20106i	−0.355734	−	0.616149i	−0.987243	+	0.159219i	$0.949102\pi$
$224$	17.6920	+	2.47168i	1.18210	+	0.165146i
$225$	1.12072	+	1.94114i	0.0747145	+	0.129409i
$226$	4.36748	−	12.2717i	0.290521	−	0.816300i
$227$	−22.8396			−1.51592			−0.757960	−	0.652301i	$-0.773804\pi$
$227$	−22.8396			−1.51592			−0.757960	+	0.652301i	$0.773804\pi$
$228$	1.62987	−	7.41583i	0.107941	−	0.491125i
$229$	−18.9611			−1.25299			−0.626494	−	0.779427i	$-0.715511\pi$
$229$	−18.9611			−1.25299			−0.626494	+	0.779427i	$0.715511\pi$
$230$	0.522817	−	1.46900i	0.0344736	−	0.0968632i
$231$	3.88833	+	6.73478i	0.255833	+	0.443116i
$232$	−0.344647	−	16.0760i	−0.0226272	−	1.05544i
$233$	9.45481	+	16.3762i	0.619405	+	1.07284i	0.989594	+	0.143885i	$0.0459594\pi$
$233$	9.45481	+	16.3762i	0.619405	+	1.07284i	−0.370190	+	0.928956i	$0.620707\pi$
$234$	−11.7547	+	2.15939i	−0.768430	+	0.141163i
$235$		−	0.621000i		−	0.0405096i
$236$	2.23037	−	13.7994i	0.145185	−	0.898261i
$237$	−0.976466	+	1.69129i	−0.0634283	+	0.109861i
$238$	−8.07006	+	1.48250i	−0.523104	+	0.0960962i
$239$		−	11.2560i		−	0.728087i	−0.931382	−	0.364044i	$-0.881396\pi$
$239$		−	11.2560i		−	0.728087i	0.931382	−	0.364044i	$-0.118604\pi$
$240$	−3.30644	−	1.09750i	−0.213430	−	0.0708434i
$241$	−4.26180	−	2.46055i	−0.274527	−	0.158498i	0.356416	−	0.934327i	$-0.383999\pi$
$241$	−4.26180	−	2.46055i	−0.274527	−	0.158498i	−0.630943	+	0.775829i	$0.717332\pi$
$242$	−4.00433	−	1.42514i	−0.257408	−	0.0916113i
$243$	−8.04443	+	13.9334i	−0.516051	+	0.893826i
$244$	−22.1103	+	8.40722i	−1.41547	+	0.538217i
$245$	1.48619	+	2.57416i	0.0949493	+	0.164457i
$246$	4.90432	+	5.76065i	0.312688	+	0.367285i
$247$	13.7495	+	9.00234i	0.874861	+	0.572805i
$248$	−14.8880	−	24.5558i	−0.945388	−	1.55929i
$249$	9.62996	−	5.55986i	0.610274	−	0.352342i
$250$	−1.33235	−	0.474182i	−0.0842651	−	0.0299899i
$251$	−18.3967	−	10.6214i	−1.16119	−	0.670414i	−0.209602	−	0.977787i	$-0.567217\pi$
$251$	−18.3967	−	10.6214i	−1.16119	−	0.670414i	−0.951589	+	0.307372i	$0.900550\pi$
$252$	5.03140	+	13.2322i	0.316949	+	0.833550i
$253$	1.55873	−	2.69980i	0.0979967	−	0.169735i
$254$	−18.2646	+	15.5496i	−1.14602	+	0.975666i
$255$	1.60017			0.100207
$256$	−14.6979	+	6.32234i	−0.918618	+	0.395146i
$257$	−7.37088	−	4.25558i	−0.459783	−	0.265456i	0.252170	−	0.967683i	$-0.418856\pi$
$257$	−7.37088	−	4.25558i	−0.459783	−	0.265456i	−0.711953	+	0.702227i	$0.752189\pi$
$258$	−1.57969	−	1.85552i	−0.0983473	−	0.115519i
$259$	34.2133			2.12591
$260$	4.76399	−	5.84514i	0.295450	−	0.362500i
$261$	11.0354	−	6.37131i	0.683076	−	0.394374i
$262$	6.97262	−	1.28090i	0.430770	−	0.0791340i
$263$	−5.97636	+	3.45045i	−0.368518	+	0.212764i	−0.672811	−	0.739815i	$-0.734913\pi$
$263$	−5.97636	+	3.45045i	−0.368518	+	0.212764i	0.304293	+	0.952579i	$0.401580\pi$
$264$	−6.10536	−	3.35255i	−0.375759	−	0.206335i
$265$		−	14.3378i		−	0.880763i
$266$	7.54518	−	17.9449i	0.462625	−	1.10027i
$267$			7.81993i			0.478572i
$268$	−20.8721	+	7.93639i	−1.27497	+	0.484792i
$269$	−20.7978	+	12.0076i	−1.26806	+	0.732116i	−0.974621	−	0.223861i	$-0.928134\pi$
$269$	−20.7978	+	12.0076i	−1.26806	+	0.732116i	−0.293441	+	0.955977i	$0.594801\pi$
$270$	−1.16647	−	6.34972i	−0.0709889	−	0.386432i
$271$	20.2531	−	11.6931i	1.23029	−	0.710308i	0.263199	−	0.964741i	$-0.415222\pi$
$271$	20.2531	−	11.6931i	1.23029	−	0.710308i	0.967090	+	0.254433i	$0.0818890\pi$
$272$	5.49238	−	4.88281i	0.333025	−	0.296064i
$273$	10.3699			0.627615
$274$	5.23163	−	4.45394i	0.316054	−	0.269072i
$275$	−2.44865	−	1.41373i	−0.147659	−	0.0852511i
$276$	−1.21337	+	1.48874i	−0.0730365	+	0.0896115i
$277$	−1.35344			−0.0813200			−0.0406600	−	0.999173i	$-0.512946\pi$
$277$	−1.35344			−0.0813200			−0.0406600	+	0.999173i	$0.512946\pi$
$278$	1.60904	+	1.88999i	0.0965040	+	0.113354i
$279$	11.3784	−	19.7080i	0.681209	−	1.17989i
$280$	−7.82921	−	4.29914i	−0.467885	−	0.256922i
$281$	−14.9007	−	8.60293i	−0.888902	−	0.513208i	−0.0153185	−	0.999883i	$-0.504876\pi$
$281$	−14.9007	−	8.60293i	−0.888902	−	0.513208i	−0.873583	+	0.486675i	$0.838210\pi$
$282$	−0.256468	+	0.720619i	−0.0152724	+	0.0429122i
$283$	−20.0795	+	11.5929i	−1.19360	+	0.689128i	−0.959122	−	0.282992i	$-0.908673\pi$
$283$	−20.0795	+	11.5929i	−1.19360	+	0.689128i	−0.234482	+	0.972120i	$0.575340\pi$
$284$	2.97444	−	18.4029i	0.176500	−	1.09201i
$285$	−2.07957	+	3.17618i	−0.123183	+	0.188141i
$286$	11.4795	−	9.77303i	0.678794	−	0.577891i
$287$	9.69835	+	16.7980i	0.572476	+	0.991557i
$288$	−9.99795	−	7.79807i	−0.589135	−	0.459506i
$289$	6.81225	−	11.7992i	0.400720	−	0.694068i
$290$	−2.69574	+	7.57444i	−0.158299	+	0.444787i
$291$	3.54334	+	2.04575i	0.207714	+	0.119924i
$292$	0.0479295	−	0.296541i	0.00280486	−	0.0173538i
$293$		−	15.3002i		−	0.893849i	−0.894572	−	0.446925i	$-0.852519\pi$
$293$		−	15.3002i		−	0.893849i	0.894572	−	0.446925i	$-0.147481\pi$
$294$	−0.661496	−	3.60089i	−0.0385792	−	0.210008i
$295$	−3.49461	+	6.05284i	−0.203464	+	0.352410i
$296$	−26.2037	+	15.8871i	−1.52306	+	0.923420i
$297$		−	12.9075i		−	0.748971i
$298$	0.528445	+	2.87661i	0.0306120	+	0.166638i
$299$	−2.07852	−	3.60010i	−0.120204	−	0.208199i
$300$	1.35025	+	1.10050i	0.0779566	+	0.0635373i
$301$	−3.12386	−	5.41068i	−0.180056	−	0.311866i
$302$	5.90097	+	2.10015i	0.339563	+	0.120850i
$303$	5.57994			0.320559
$304$	2.55403	+	17.2475i	0.146484	+	0.989213i
$305$	11.8274			0.677234
$306$	5.48672	+	1.95272i	0.313655	+	0.111630i
$307$	−6.98663	−	12.1012i	−0.398748	−	0.690652i	0.594824	−	0.803856i	$-0.297222\pi$
$307$	−6.98663	−	12.1012i	−0.398748	−	0.690652i	−0.993572	+	0.113204i	$0.963889\pi$
$308$	−13.8424	−	11.2821i	−0.788746	−	0.642856i
$309$	−1.81858	−	3.14987i	−0.103455	−	0.179190i
$310$	2.59425	+	14.1219i	0.147344	+	0.802072i
$311$			11.6867i			0.662695i	0.943509	+	0.331347i	$0.107503\pi$
$311$			11.6867i			0.662695i	−0.943509	+	0.331347i	$0.892497\pi$
$312$	−7.94222	+	4.81532i	−0.449640	+	0.272614i
$313$	0.441106	−	0.764018i	0.0249328	−	0.0431849i	−0.853290	−	0.521437i	$-0.825396\pi$
$313$	0.441106	−	0.764018i	0.0249328	−	0.0431849i	0.878223	+	0.478252i	$0.158729\pi$
$314$	1.73853	+	9.46379i	0.0981111	+	0.534073i
$315$		−	7.07824i		−	0.398814i
$316$	0.715548	−	4.42711i	0.0402527	−	0.249045i
$317$	−0.154226	−	0.0890423i	−0.00866219	−	0.00500111i	0.495663	−	0.868515i	$-0.334925\pi$
$317$	−0.154226	−	0.0890423i	−0.00866219	−	0.00500111i	−0.504325	+	0.863514i	$0.668259\pi$
$318$	−5.92139	+	16.6378i	−0.332055	+	0.933003i
$319$	−8.03710	+	13.9207i	−0.449991	+	0.779408i
$320$	7.99265	−	0.342860i	0.446803	−	0.0191665i
$321$	−0.0617265	−	0.106913i	−0.00344524	−	0.00596733i
$322$	−3.74930	+	3.19197i	−0.208941	+	0.177881i
$323$	−3.60902	−	7.14909i	−0.200811	−	0.397786i
$324$	0.877035	−	5.42624i	0.0487241	−	0.301458i
$325$	−3.26520	+	1.88516i	−0.181120	+	0.104570i
$326$	−10.4491	+	29.3596i	−0.578720	+	1.62608i
$327$	13.8479	+	7.99508i	0.765790	+	0.442129i
$328$	−15.2281	−	8.36200i	−0.840833	−	0.461714i
$329$	−0.980530	+	1.69833i	−0.0540584	+	0.0936319i
$330$	2.25760	+	2.65179i	0.124277	+	0.145976i
$331$	11.4931			0.631715			0.315858	−	0.948807i	$-0.397708\pi$
$331$	11.4931			0.631715			0.315858	+	0.948807i	$0.397708\pi$
$332$	−16.1321	+	19.7931i	−0.885362	+	1.08629i
$333$	−21.0306	−	12.1420i	−1.15247	−	0.665379i
$334$	−6.34488	+	5.40171i	−0.347176	+	0.295568i
$335$	11.1650			0.610010
$336$	7.30964	+	8.22219i	0.398774	+	0.448557i
$337$	9.24185	−	5.33579i	0.503436	−	0.290659i	−0.226695	−	0.973966i	$-0.572792\pi$
$337$	9.24185	−	5.33579i	0.503436	−	0.290659i	0.730131	+	0.683307i	$0.239459\pi$
$338$	−0.310543	−	1.69045i	−0.0168913	−	0.0919486i
$339$	6.94726	−	4.01100i	0.377323	−	0.217848i
$340$	−3.43460	+	1.30597i	−0.186267	+	0.0708261i
$341$			28.7067i			1.55455i
$342$	−11.0065	+	8.35287i	−0.595162	+	0.451672i
$343$			12.7188i			0.686753i
$344$	4.90501	+	2.69342i	0.264461	+	0.145219i
$345$	0.831634	−	0.480144i	0.0447737	−	0.0258501i
$346$	−20.1572	+	3.70295i	−1.08366	+	0.199072i
$347$	2.51658	−	1.45295i	0.135097	−	0.0779985i	−0.430928	−	0.902386i	$-0.641814\pi$
$347$	2.51658	−	1.45295i	0.135097	−	0.0779985i	0.566025	+	0.824388i	$0.308480\pi$
$348$	6.25637	−	7.67620i	0.335377	−	0.411487i
$349$	6.79513			0.363735			0.181868	−	0.983323i	$-0.441786\pi$
$349$	6.79513			0.363735			0.181868	+	0.983323i	$0.441786\pi$
$350$	2.89503	+	3.40052i	0.154746	+	0.181766i
$351$	−14.9058	−	8.60588i	−0.795614	−	0.459348i
$352$	15.8407	+	2.21304i	0.844312	+	0.117955i
$353$	−28.4224			−1.51277			−0.756385	−	0.654127i	$-0.773036\pi$
$353$	−28.4224			−1.51277			−0.756385	+	0.654127i	$0.773036\pi$
$354$	6.55498	−	5.58058i	0.348393	−	0.296604i
$355$	−4.66044	+	8.07212i	−0.247350	+	0.428424i
$356$	−6.38219	−	16.7847i	−0.338255	−	0.889586i
$357$	−4.37619	−	2.52659i	−0.231613	−	0.133722i
$358$	10.8838	+	3.87353i	0.575226	+	0.204722i
$359$	−8.55880	+	4.94142i	−0.451716	+	0.260798i	−0.708555	−	0.705656i	$-0.750652\pi$
$359$	−8.55880	+	4.94142i	−0.451716	+	0.260798i	0.256839	+	0.966454i	$0.417319\pi$
$360$	3.28682	+	5.42117i	0.173230	+	0.285721i
$361$	18.8805	+	2.12736i	0.993712	+	0.111966i
$362$	−9.44428	−	11.0933i	−0.496380	−	0.583051i
$363$	−1.30882	−	2.26694i	−0.0686950	−	0.118983i
$364$	−22.2579	+	8.46334i	−1.16663	+	0.443599i
$365$	−0.0750974	+	0.130072i	−0.00393078	+	0.00680830i
$366$	−13.7247	−	4.88462i	−0.717402	−	0.255323i
$367$	0.270733	+	0.156308i	0.0141321	+	0.00815920i	0.507049	−	0.861917i	$-0.330736\pi$
$367$	0.270733	+	0.156308i	0.0141321	+	0.00815920i	−0.492917	+	0.870076i	$0.664069\pi$
$368$	1.38935	−	4.18571i	0.0724251	−	0.218195i
$369$		−	13.7675i		−	0.716706i
$370$	15.0697	−	2.76835i	0.783434	−	0.143920i
$371$	−22.6387	+	39.2114i	−1.17534	+	2.03575i
$372$	2.82183	−	17.4588i	0.146305	−	0.905194i
$373$		−	1.94496i		−	0.100706i	−0.998731	−	0.0503531i	$-0.983965\pi$
$373$		−	1.94496i		−	0.100706i	0.998731	−	0.0503531i	$-0.0160347\pi$
$374$	−7.22560	+	1.32737i	−0.373627	+	0.0686366i
$375$	−0.435478	−	0.754271i	−0.0224880	−	0.0389504i
$376$	−0.0376473	−	1.75605i	−0.00194151	−	0.0905613i
$377$	10.7172	+	18.5627i	0.551964	+	0.956030i
$378$	−6.83583	+	19.2072i	−0.351597	+	0.987912i
$379$	−10.1970			−0.523785			−0.261893	−	0.965097i	$-0.584347\pi$
$379$	−10.1970			−0.523785			−0.261893	+	0.965097i	$0.584347\pi$
$380$	1.87136	−	8.51458i	0.0959987	−	0.436789i
$381$	−14.7727			−0.756830
$382$	−1.63006	+	4.58011i	−0.0834011	+	0.234339i
$383$	−1.01670	−	1.76098i	−0.0519510	−	0.0899818i	0.838880	−	0.544316i	$-0.183211\pi$
$383$	−1.01670	−	1.76098i	−0.0519510	−	0.0899818i	−0.890831	+	0.454334i	$0.849877\pi$
$384$	−9.41641	−	2.90304i	−0.480529	−	0.148145i
$385$	4.46443	+	7.73262i	0.227528	+	0.394091i
$386$	−19.4589	+	3.57467i	−0.990431	+	0.181946i
$387$			4.43453i			0.225420i
$388$	−9.27504	−	1.49911i	−0.470869	−	0.0761058i
$389$	18.7988	−	32.5605i	0.953138	−	1.65088i	0.214566	−	0.976710i	$-0.431166\pi$
$389$	18.7988	−	32.5605i	0.953138	−	1.65088i	0.738572	−	0.674174i	$-0.235500\pi$
$390$	4.56755	−	0.839075i	0.231287	−	0.0424882i
$391$			2.02570i			0.102444i
$392$	4.35868	+	7.18905i	0.220146	+	0.363102i
$393$	3.78107	+	2.18300i	0.190730	+	0.110118i
$394$	−27.4566	−	9.77177i	−1.38324	−	0.492295i
$395$	−1.12114	+	1.94187i	−0.0564108	+	0.0977063i
$396$	4.50491	+	11.8476i	0.226380	+	0.595363i
$397$	11.5613	+	20.0248i	0.580247	+	1.00502i	0.995450	+	0.0952887i	$0.0303774\pi$
$397$	11.5613	+	20.0248i	0.580247	+	1.00502i	−0.415202	+	0.909729i	$0.636289\pi$
$398$	7.70306	+	9.04806i	0.386119	+	0.453538i
$399$	10.7023	−	5.40277i	0.535786	−	0.270477i
$400$	−3.79633	−	1.26011i	−0.189817	−	0.0630055i
$401$	−27.0198	+	15.5999i	−1.34931	+	0.779022i	−0.988151	−	0.153484i	$-0.950951\pi$
$401$	−27.0198	+	15.5999i	−1.34931	+	0.779022i	−0.361154	+	0.932506i	$0.617617\pi$
$402$	−12.9561	−	4.61106i	−0.646191	−	0.229979i
$403$	33.1509	+	19.1397i	1.65137	+	0.953416i
$404$	−11.9768	+	4.55403i	−0.595866	+	0.226572i
$405$	−1.37416	+	2.38012i	−0.0682828	+	0.118269i
$406$	19.3321	−	16.4584i	0.959435	−	0.816814i
$407$	30.6332			1.51843
$408$	4.52492	−	0.0970081i	0.224017	−	0.00480262i
$409$	−21.5213	−	12.4253i	−1.06416	−	0.614392i	−0.137578	−	0.990491i	$-0.543932\pi$
$409$	−21.5213	−	12.4253i	−1.06416	−	0.614392i	−0.926579	+	0.376099i	$0.877265\pi$
$410$	5.63096	+	6.61416i	0.278093	+	0.326650i
$411$	4.23143			0.208721
$412$	6.47413	+	5.27664i	0.318957	+	0.259961i
$413$	19.1143	−	11.0357i	0.940554	−	0.543029i
$414$	3.43747	−	0.631476i	0.168942	−	0.0310353i
$415$	11.0568	−	6.38362i	0.542755	−	0.313360i
$416$	13.1172	−	16.8176i	0.643122	−	0.824549i
$417$			1.52866i			0.0748587i
$418$	6.75564	−	16.0672i	0.330429	−	0.785870i
$419$			27.1890i			1.32827i	0.747613	+	0.664135i	$0.231200\pi$
$419$			27.1890i			1.32827i	−0.747613	+	0.664135i	$0.768800\pi$
$420$	−1.95506	−	5.14165i	−0.0953971	−	0.250887i
$421$	22.8012	−	13.1643i	1.11126	−	0.641588i	0.172107	−	0.985078i	$-0.444942\pi$
$421$	22.8012	−	13.1643i	1.11126	−	0.641588i	0.939156	+	0.343490i	$0.111609\pi$
$422$	−1.81968	−	9.90550i	−0.0885805	−	0.482192i
$423$	1.20545	−	0.695965i	0.0586108	−	0.0338390i
$424$	−0.869209	−	40.5441i	−0.0422125	−	1.96899i
$425$	1.83725			0.0891199
$426$	8.74178	−	7.44231i	0.423541	−	0.360581i
$427$	−32.3459	−	18.6749i	−1.56533	−	0.903742i
$428$	0.219746	+	0.179101i	0.0106218	+	0.00865717i
$429$	9.28478			0.448274
$430$	−1.81374	−	2.13043i	−0.0874664	−	0.102739i
$431$	19.3803	−	33.5677i	0.933518	−	1.61690i	0.156262	−	0.987716i	$-0.450056\pi$
$431$	19.3803	−	33.5677i	0.933518	−	1.61690i	0.777256	−	0.629184i	$-0.216611\pi$
$432$	−3.68345	−	17.8849i	−0.177220	−	0.860487i
$433$	−6.86500	−	3.96351i	−0.329911	−	0.190474i	0.325891	−	0.945407i	$-0.394336\pi$
$433$	−6.86500	−	3.96351i	−0.329911	−	0.190474i	−0.655801	+	0.754933i	$0.727669\pi$
$434$	15.2031	−	42.7173i	0.729770	−	2.05050i
$435$	−4.28805	+	2.47571i	−0.205596	+	0.118701i
$436$	−36.2482	−	5.85874i	−1.73597	−	0.280583i
$437$	−4.02081	−	2.63258i	−0.192342	−	0.125933i
$438$	0.140863	−	0.119924i	0.00673070	−	0.00573018i
$439$	0.161249	+	0.279291i	0.00769599	+	0.0133298i	0.869848	−	0.493320i	$-0.164217\pi$
$439$	0.161249	+	0.279291i	0.00769599	+	0.0133298i	−0.862152	+	0.506650i	$0.830884\pi$
$440$	−7.00995	−	3.84927i	−0.334186	−	0.183507i
$441$	−3.33120	+	5.76981i	−0.158629	+	0.274753i
$442$	−3.28468	+	9.22923i	−0.156236	+	0.438990i
$443$	18.6454	+	10.7649i	0.885869	+	0.511456i	0.872589	−	0.488455i	$-0.162439\pi$
$443$	18.6454	+	10.7649i	0.885869	+	0.511456i	0.0132796	+	0.999912i	$0.495773\pi$
$444$	−18.6304	−	3.01120i	−0.884160	−	0.142905i
$445$			8.97855i			0.425624i
$446$	2.71477	+	14.7780i	0.128548	+	0.699758i
$447$	−0.900618	+	1.55992i	−0.0425977	+	0.0737815i
$448$	−22.3999	−	11.6824i	−1.05830	−	0.551940i
$449$			12.6385i			0.596447i	0.954496	+	0.298224i	$0.0963941\pi$
$449$			12.6385i			0.596447i	−0.954496	+	0.298224i	$0.903606\pi$
$450$	−0.572732	−	3.11770i	−0.0269989	−	0.146970i
$451$	8.68350	+	15.0403i	0.408890	+	0.708219i
$452$	−11.6380	+	14.2792i	−0.547406	+	0.671635i
$453$	1.92873	+	3.34066i	0.0906198	+	0.156958i
$454$	30.4303	+	10.8301i	1.42817	+	0.508284i
$455$	11.9063			0.558178
$456$	−5.68801	+	9.10761i	−0.266366	+	0.426503i
$457$	2.11684			0.0990218			0.0495109	−	0.998774i	$-0.484234\pi$
$457$	2.11684			0.0990218			0.0495109	+	0.998774i	$0.484234\pi$
$458$	25.2628	+	8.99103i	1.18045	+	0.420123i
$459$	4.19359	+	7.26351i	0.195740	+	0.339032i
$460$	−1.39315	+	1.70931i	−0.0649559	+	0.0796971i
$461$	16.6840	+	28.8976i	0.777052	+	1.34589i	0.933634	+	0.358229i	$0.116619\pi$
$461$	16.6840	+	28.8976i	0.777052	+	1.34589i	−0.156581	+	0.987665i	$0.550047\pi$
$462$	−1.98709	−	10.8168i	−0.0924480	−	0.503245i
$463$		−	15.6036i		−	0.725159i	−0.931953	−	0.362579i	$-0.881896\pi$
$463$		−	15.6036i		−	0.725159i	0.931953	−	0.362579i	$-0.118104\pi$
$464$	−7.16376	+	21.5823i	−0.332569	+	1.00193i
$465$	−4.42133	+	7.65797i	−0.205034	+	0.355130i
$466$	−4.83179	−	26.3021i	−0.223828	−	1.21842i
$467$		−	10.7708i		−	0.498412i	−0.968450	−	0.249206i	$-0.919830\pi$
$467$		−	10.7708i		−	0.498412i	0.968450	−	0.249206i	$-0.0801697\pi$
$468$	16.6853	+	2.69682i	0.771279	+	0.124661i
$469$	−30.5344	−	17.6290i	−1.40995	−	0.814034i
$470$	−0.294467	+	0.827388i	−0.0135827	+	0.0381646i
$471$	−2.96295	+	5.13197i	−0.136525	+	0.236469i
$472$	−9.51503	+	17.3279i	−0.437965	+	0.797583i
$473$	−2.79697	−	4.84450i	−0.128605	−	0.222750i
$474$	2.10297	−	1.79036i	0.0965927	−	0.0822341i
$475$	−2.38769	+	3.64677i	−0.109555	+	0.167325i
$476$	11.4551	+	1.85147i	0.525044	+	0.0848620i
$477$	27.8316	−	16.0686i	1.27432	−	0.735731i
$478$	−5.33737	+	14.9969i	−0.244126	+	0.685940i
$479$	16.9919	+	9.81030i	0.776381	+	0.448244i	0.835146	−	0.550028i	$-0.185383\pi$
$479$	16.9919	+	9.81030i	0.776381	+	0.448244i	−0.0587650	+	0.998272i	$0.518716\pi$
$480$	3.88491	+	3.03011i	0.177321	+	0.138305i
$481$	20.4241	−	35.3757i	0.931261	−	1.61299i
$482$	4.51146	+	5.29918i	0.205491	+	0.241371i
$483$	−3.03250			−0.137984
$484$	4.65938	+	3.79756i	0.211790	+	0.172616i
$485$	4.06833	+	2.34885i	0.184733	+	0.106656i
$486$	17.3249	−	14.7496i	0.785875	−	0.669054i
$487$	−14.0309			−0.635801			−0.317901	−	0.948124i	$-0.602978\pi$
$487$	−14.0309			−0.635801			−0.317901	+	0.948124i	$0.602978\pi$
$488$	33.4452	−	0.717019i	1.51399	−	0.0324579i
$489$	−16.6211	+	9.59619i	−0.751631	+	0.433955i
$490$	−0.759505	−	4.13440i	−0.0343109	−	0.186773i
$491$	10.9976	−	6.34946i	0.496314	−	0.286547i	−0.230876	−	0.972983i	$-0.574159\pi$
$491$	10.9976	−	6.34946i	0.496314	−	0.286547i	0.727190	+	0.686436i	$0.240826\pi$
$492$	−3.80267	−	10.0007i	−0.171438	−	0.450868i
$493$		−	10.4449i		−	0.470413i
$494$	−14.0504	−	18.5140i	−0.632157	−	0.832985i
$495$		−	6.33757i		−	0.284852i
$496$	8.19209	+	39.7764i	0.367836	+	1.78601i
$497$	25.4910	−	14.7172i	1.14343	−	0.660159i
$498$	−15.4668	+	2.84132i	−0.693086	+	0.127322i
$499$	−38.5091	+	22.2332i	−1.72390	+	0.995296i	−0.813511	+	0.581549i	$0.802447\pi$
$499$	−38.5091	+	22.2332i	−1.72390	+	0.995296i	−0.910392	+	0.413747i	$0.864220\pi$
$500$	1.55030	+	1.26355i	0.0693317	+	0.0565077i
$501$	−5.13185			−0.229274
$502$	19.4744	+	22.8747i	0.869185	+	1.02095i
$503$	−31.4889	−	18.1801i	−1.40402	−	0.810612i	−0.409219	−	0.912436i	$-0.634199\pi$
$503$	−31.4889	−	18.1801i	−1.40402	−	0.810612i	−0.994802	+	0.101824i	$0.967532\pi$
$504$	−0.429109	−	20.0157i	−0.0191140	−	0.891570i
$505$	6.40667			0.285093
$506$	−3.35697	+	2.85796i	−0.149236	+	0.127052i
$507$	0.529252	−	0.916691i	0.0235049	−	0.0407117i
$508$	31.7081	−	12.0567i	1.40682	−	0.534928i
$509$	9.47098	+	5.46807i	0.419794	+	0.242368i	0.694989	−	0.719020i	$-0.255409\pi$
$509$	9.47098	+	5.46807i	0.419794	+	0.242368i	−0.275195	+	0.961388i	$0.588743\pi$
$510$	−2.13198	−	0.758772i	−0.0944058	−	0.0335990i
$511$	0.410757	−	0.237151i	0.0181708	−	0.0104909i
$512$	22.5806	−	1.45408i	0.997933	−	0.0642617i
$513$	−19.8673	−	1.11574i	−0.877165	−	0.0492612i
$514$	7.80266	+	9.16505i	0.344161	+	0.404253i
$515$	−2.08802	−	3.61656i	−0.0920092	−	0.159365i
$516$	1.22485	+	3.22125i	0.0539209	+	0.141808i
$517$	−0.877926	+	1.52061i	−0.0386111	+	0.0668765i
$518$	−45.5840	−	16.2233i	−2.00285	−	0.712812i
$519$	−10.9308	−	6.31087i	−0.479807	−	0.277017i
$520$	−9.11896	+	5.52876i	−0.399893	+	0.242452i
$521$			2.51624i			0.110238i	0.998480	+	0.0551191i	$0.0175539\pi$
$521$			2.51624i			0.110238i	−0.998480	+	0.0551191i	$0.982446\pi$
$522$	−17.7242	+	3.25600i	−0.775767	+	0.142511i
$523$	19.5521	−	33.8652i	0.854953	−	1.48082i	−0.0217365	−	0.999764i	$-0.506919\pi$
$523$	19.5521	−	33.8652i	0.854953	−	1.48082i	0.876689	−	0.481058i	$-0.159747\pi$
$524$	−9.89733	−	1.59969i	−0.432367	−	0.0698828i
$525$			2.75040i			0.120037i
$526$	9.59873	−	1.76332i	0.418525	−	0.0768845i
$527$	−9.32665	−	16.1542i	−0.406275	−	0.703690i
$528$	6.54475	+	7.36181i	0.284824	+	0.320382i
$529$	−10.8922	−	18.8658i	−0.473573	−	0.820252i
$530$	−6.79872	+	19.1029i	−0.295317	+	0.829778i
$531$	−15.6659			−0.679841
$532$	−18.5620	+	20.3311i	−0.804764	+	0.881466i
$533$	23.1583			1.00310
$534$	3.70807	−	10.4189i	0.160464	−	0.450869i
$535$	−0.0708721	−	0.122754i	−0.00306407	−	0.00530712i
$536$	31.5722	−	0.676864i	1.36371	−	0.0292361i
$537$	3.55737	+	6.16154i	0.153512	+	0.265890i
$538$	33.4037	−	6.13637i	1.44013	−	0.264558i
$539$		−	8.40430i		−	0.361999i
$540$	−1.45678	+	9.01316i	−0.0626900	+	0.387865i
$541$	19.4760	−	33.7335i	0.837339	−	1.45031i	−0.0547720	−	0.998499i	$-0.517443\pi$
$541$	19.4760	−	33.7335i	0.837339	−	1.45031i	0.892111	−	0.451815i	$-0.149223\pi$
$542$	−32.5289	+	5.97568i	−1.39724	+	0.256677i
$543$		−	8.97246i		−	0.385045i
$544$	−9.63311	+	3.90121i	−0.413016	+	0.167263i
$545$	15.8996	+	9.17965i	0.681065	+	0.393213i
$546$	−13.8163	−	4.91722i	−0.591284	−	0.210438i
$547$	−2.77657	+	4.80916i	−0.118717	+	0.205625i	−0.919260	−	0.393652i	$-0.871212\pi$
$547$	−2.77657	+	4.80916i	−0.118717	+	0.205625i	0.800542	+	0.599276i	$0.204545\pi$
$548$	−9.08233	+	3.45346i	−0.387978	+	0.147524i
$549$	13.2552	+	22.9586i	0.565716	+	0.979849i
$550$	2.59209	+	3.04469i	0.110527	+	0.129826i
$551$	20.7320	+	13.5741i	0.883214	+	0.578275i
$552$	2.32257	−	1.40816i	0.0988550	−	0.0599352i
$553$	6.13226	−	3.54046i	0.260770	−	0.150556i
$554$	1.80325	+	0.641774i	0.0766126	+	0.0272664i
$555$	8.17189	+	4.71805i	0.346878	+	0.200270i
$556$	−1.24761	−	3.28111i	−0.0529103	−	0.139150i
$557$	−19.7029	+	34.1263i	−0.834837	+	1.44598i	0.0593264	+	0.998239i	$0.481105\pi$
$557$	−19.7029	+	34.1263i	−0.834837	+	1.44598i	−0.894163	+	0.447741i	$0.852229\pi$
$558$	−24.5052	+	20.8625i	−1.03739	+	0.883180i
$559$	−7.45934			−0.315496
$560$	8.39266	+	9.44041i	0.354655	+	0.398930i
$561$	−3.91826	−	2.26221i	−0.165429	−	0.0955105i
$562$	15.7736	+	18.5277i	0.665368	+	0.781545i
$563$	22.5736			0.951363			0.475682	−	0.879617i	$-0.342201\pi$
$563$	22.5736			0.951363			0.475682	+	0.879617i	$0.342201\pi$
$564$	0.683409	−	0.838503i	0.0287767	−	0.0353074i
$565$	7.97658	−	4.60528i	0.335577	−	0.193746i
$566$	32.2501	−	5.92446i	1.35557	−	0.249024i
$567$	7.51621	−	4.33948i	0.315651	−	0.182241i
$568$	−12.6893	+	23.1087i	−0.532432	+	0.969619i
$569$		−	17.5498i		−	0.735725i	−0.929880	−	0.367863i	$-0.880090\pi$
$569$		−	17.5498i		−	0.735725i	0.929880	−	0.367863i	$-0.119910\pi$
$570$	4.27680	−	3.24569i	0.179135	−	0.135947i
$571$		−	36.5979i		−	1.53158i	−0.643093	−	0.765788i	$-0.722349\pi$
$571$		−	36.5979i		−	1.53158i	0.643093	−	0.765788i	$-0.277651\pi$
$572$	−19.9288	+	7.57772i	−0.833266	+	0.316840i
$573$	−2.59290	+	1.49701i	−0.108320	+	0.0625386i
$574$	−4.95625	−	26.9796i	−0.206870	−	1.12611i
$575$	0.954851	−	0.551283i	0.0398200	−	0.0229901i
$576$	9.62304	+	15.1306i	0.400960	+	0.630441i
$577$	−2.04416			−0.0850994			−0.0425497	−	0.999094i	$-0.513548\pi$
$577$	−2.04416			−0.0850994			−0.0425497	+	0.999094i	$0.513548\pi$
$578$	−14.6712	+	12.4903i	−0.610243	+	0.519530i
$579$	−10.5521	−	6.09223i	−0.438529	−	0.253185i
$580$	7.18333	−	8.81352i	0.298271	−	0.365962i
$581$	−40.3178			−1.67266
$582$	−3.75091	−	4.40584i	−0.155480	−	0.182628i
$583$	−20.2698	+	35.1083i	−0.839488	+	1.45404i
$584$	−0.204473	+	0.372369i	−0.00846116	+	0.0154087i
$585$	−7.31872	−	4.22546i	−0.302592	−	0.174701i
$586$	−7.25510	+	20.3852i	−0.299705	+	0.842107i
$587$	−18.7652	+	10.8341i	−0.774524	+	0.447172i	−0.834486	−	0.551029i	$-0.814235\pi$
$587$	−18.7652	+	10.8341i	−0.774524	+	0.447172i	0.0599621	+	0.998201i	$0.480902\pi$
$588$	−0.826133	+	5.11130i	−0.0340691	+	0.210787i
$589$	44.1855	+	2.48144i	1.82063	+	0.102246i
$590$	7.52618	−	6.40741i	0.309848	−	0.263789i
$591$	−8.97419	−	15.5437i	−0.369149	−	0.639384i
$592$	42.4458	−	8.74186i	1.74451	−	0.359288i
$593$	−5.09615	+	8.82679i	−0.209274	+	0.362473i	−0.951486	−	0.307692i	$-0.900443\pi$
$593$	−5.09615	+	8.82679i	−0.209274	+	0.362473i	0.742212	+	0.670165i	$0.233777\pi$
$594$	−6.12052	+	17.1973i	−0.251128	+	0.705615i
$595$	−5.02458	−	2.90094i	−0.205988	−	0.118927i
$596$	0.659966	−	4.08323i	0.0270333	−	0.167256i
$597$			7.31823i			0.299515i
$598$	1.06221	+	5.78218i	0.0434369	+	0.236451i
$599$	−19.2247	+	33.2982i	−0.785501	+	1.36053i	0.143198	+	0.989694i	$0.454262\pi$
$599$	−19.2247	+	33.2982i	−0.785501	+	1.36053i	−0.928699	+	0.370834i	$0.879072\pi$
$600$	−1.27716	−	2.10651i	−0.0521400	−	0.0859979i
$601$			17.9068i			0.730433i	0.930923	+	0.365216i	$0.119005\pi$
$601$			17.9068i			0.730433i	−0.930923	+	0.365216i	$0.880995\pi$
$602$	1.59642	+	8.69019i	0.0650652	+	0.354186i
$603$	12.5128	+	21.6728i	0.509561	+	0.882586i
$604$	−6.86629	−	5.59626i	−0.279385	−	0.227709i
$605$	−1.50273	−	2.60281i	−0.0610948	−	0.105819i
$606$	−7.43442	−	2.64591i	−0.302003	−	0.107483i
$607$	−15.4514			−0.627152			−0.313576	−	0.949563i	$-0.601527\pi$
$607$	−15.4514			−0.627152			−0.313576	+	0.949563i	$0.601527\pi$
$608$	4.77560	−	24.1908i	0.193676	−	0.981065i
$609$	15.6361			0.633608
$610$	−15.7582	−	5.60833i	−0.638031	−	0.227075i
$611$	1.17068	+	2.02769i	0.0473608	+	0.0820314i
$612$	−6.38428	−	5.20341i	−0.258069	−	0.210335i
$613$	−0.646381	−	1.11956i	−0.0261071	−	0.0452188i	0.852677	−	0.522439i	$-0.174978\pi$
$613$	−0.646381	−	1.11956i	−0.0261071	−	0.0452188i	−0.878784	+	0.477220i	$0.841644\pi$
$614$	3.57045	+	19.4359i	0.144092	+	0.784371i
$615$			5.34965i			0.215719i
$616$	13.0932	+	21.5955i	0.527540	+	0.870107i
$617$	8.14956	−	14.1154i	0.328089	−	0.568266i	−0.654044	−	0.756457i	$-0.726929\pi$
$617$	8.14956	−	14.1154i	0.328089	−	0.568266i	0.982133	+	0.188190i	$0.0602621\pi$
$618$	0.929367	+	5.05905i	0.0373846	+	0.203505i
$619$			26.6300i			1.07035i	0.844742	+	0.535174i	$0.179754\pi$
$619$			26.6300i			1.07035i	−0.844742	+	0.535174i	$0.820246\pi$
$620$	3.23992	−	20.0455i	0.130118	−	0.805046i
$621$	4.35895	+	2.51664i	0.174919	+	0.100989i
$622$	5.54164	−	15.5708i	0.222200	−	0.624333i
$623$	14.1767	−	24.5548i	0.567978	−	0.983767i
$624$	12.8651	−	2.64962i	0.515018	−	0.106070i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.949991	+	0.808774i	−0.0379693	+	0.0323251i
$627$	9.58241	−	4.83742i	0.382685	−	0.193188i
$628$	2.17123	−	13.4334i	0.0866414	−	0.536053i
$629$	−17.2383	+	9.95256i	−0.687338	+	0.396835i
$630$	−3.35637	+	9.43068i	−0.133721	+	0.375727i
$631$	33.6738	+	19.4416i	1.34053	+	0.773958i	0.986886	−	0.161420i	$-0.0516075\pi$
$631$	33.6738	+	19.4416i	1.34053	+	0.773958i	0.353649	+	0.935378i	$0.384941\pi$
$632$	−3.05262	+	5.55916i	−0.121427	+	0.221131i
$633$	3.10124	−	5.37151i	0.123263	−	0.213498i
$634$	0.163260	+	0.191766i	0.00648389	+	0.00761602i
$635$	−16.9615			−0.673096
$636$	15.7787	−	19.3596i	0.625667	−	0.767656i
$637$	−9.70542	−	5.60342i	−0.384543	−	0.222016i
$638$	17.3091	−	14.7361i	0.685276	−	0.583409i
$639$	−20.8921			−0.826480
$640$	−10.8116	−	3.33316i	−0.427365	−	0.131755i
$641$	−28.6990	+	16.5694i	−1.13354	+	0.654452i	−0.944824	−	0.327579i	$-0.893767\pi$
$641$	−28.6990	+	16.5694i	−1.13354	+	0.654452i	−0.188720	+	0.982031i	$0.560434\pi$
$642$	0.0315448	+	0.171716i	0.00124497	+	0.00677707i
$643$	5.25433	−	3.03359i	0.207210	−	0.119633i	−0.392804	−	0.919622i	$-0.628495\pi$
$643$	5.25433	−	3.03359i	0.207210	−	0.119633i	0.600014	+	0.799989i	$0.295162\pi$
$644$	6.50895	−	2.47496i	0.256489	−	0.0975270i
$645$		−	1.72313i		−	0.0678482i
$646$	1.41850	+	11.2364i	0.0558103	+	0.442091i
$647$			22.5653i			0.887134i	0.896241	+	0.443567i	$0.146287\pi$
$647$			22.5653i			0.887134i	−0.896241	+	0.443567i	$0.853713\pi$
$648$	−3.74154	+	6.81376i	−0.146982	+	0.267670i
$649$	17.1142	−	9.88087i	0.671790	−	0.387858i
$650$	5.24429	−	0.963395i	0.205698	−	0.0377874i
$651$	24.1832	−	13.9622i	0.947813	−	0.547220i
$652$	27.8436	−	34.1624i	1.09044	−	1.33790i
$653$	−14.0499			−0.549817			−0.274908	−	0.961470i	$-0.588648\pi$
$653$	−14.0499			−0.549817			−0.274908	+	0.961470i	$0.588648\pi$
$654$	−14.6591	−	17.2187i	−0.573216	−	0.673303i
$655$	4.34129	+	2.50644i	0.169628	+	0.0979349i
$656$	16.3241	+	18.3620i	0.637348	+	0.716916i
$657$	−0.336652			−0.0131340
$658$	2.11172	−	1.79781i	0.0823236	−	0.0700861i
$659$	0.456454	−	0.790601i	0.0177809	−	0.0307975i	−0.856998	−	0.515320i	$-0.827673\pi$
$659$	0.456454	−	0.790601i	0.0177809	−	0.0307975i	0.874779	+	0.484522i	$0.161007\pi$
$660$	−1.75048	−	4.60362i	−0.0681373	−	0.179196i
$661$	−36.3248	−	20.9722i	−1.41287	−	0.815723i	−0.417215	−	0.908808i	$-0.636994\pi$
$661$	−36.3248	−	20.9722i	−1.41287	−	0.815723i	−0.995658	+	0.0930854i	$0.970327\pi$
$662$	−15.3127	−	5.44980i	−0.595147	−	0.211812i
$663$	−5.22487	+	3.01658i	−0.202917	+	0.117154i
$664$	30.8791	−	18.7218i	1.19834	−	0.726546i
$665$	12.2880	−	6.20326i	0.476508	−	0.240552i
$666$	22.2626	+	26.1498i	0.862657	+	1.01328i
$667$	−3.13406	−	5.42836i	−0.121351	−	0.210187i
$668$	11.0150	−	4.18833i	0.426183	−	0.162051i
$669$	−4.62673	+	8.01373i	−0.178880	+	0.309829i
$670$	−14.8757	−	5.29425i	−0.574698	−	0.204535i
$671$	−28.9612	−	16.7207i	−1.11803	−	0.645497i
$672$	−5.84018	−	14.4209i	−0.225290	−	0.556299i
$673$		−	2.87304i		−	0.110747i	−0.998466	−	0.0553737i	$-0.982365\pi$
$673$		−	2.87304i		−	0.110747i	0.998466	−	0.0553737i	$-0.0176350\pi$
$674$	−14.8435	+	2.72680i	−0.571750	+	0.105033i
$675$	2.28253	−	3.95346i	0.0878547	−	0.152169i
$676$	−0.387832	+	2.39953i	−0.0149166	+	0.0922895i
$677$			21.7605i			0.836325i	0.908372	+	0.418162i	$0.137326\pi$
$677$			21.7605i			0.836325i	−0.908372	+	0.418162i	$0.862674\pi$
$678$	−11.1581	+	2.04979i	−0.428525	+	0.0787215i
$679$	−7.41746	−	12.8474i	−0.284656	−	0.493039i
$680$	5.19535	−	0.111381i	0.199232	−	0.00427127i
$681$	9.94617	+	17.2273i	0.381138	+	0.660150i
$682$	13.6122	−	38.2473i	0.521238	−	1.46456i
$683$	−8.42522			−0.322382			−0.161191	−	0.986923i	$-0.551534\pi$
$683$	−8.42522			−0.322382			−0.161191	+	0.986923i	$0.551534\pi$
$684$	18.6252	−	5.90986i	0.712154	−	0.225969i
$685$	4.85837			0.185629
$686$	6.03104	−	16.9459i	0.230266	−	0.646998i
$687$	8.25717	+	14.3018i	0.315031	+	0.545649i
$688$	−5.25801	−	5.91443i	−0.200460	−	0.225486i
$689$	27.0290	+	46.8157i	1.02972	+	1.78354i
$690$	−1.33570	+	0.245373i	−0.0508493	+	0.00934120i
$691$		−	14.9664i		−	0.569350i	−0.958624	−	0.284675i	$-0.908114\pi$
$691$		−	14.9664i		−	0.569350i	0.958624	−	0.284675i	$-0.0918857\pi$
$692$	28.6123	+	4.62456i	1.08768	+	0.175800i
$693$	−10.0067	+	17.3322i	−0.380124	+	0.658394i
$694$	−4.04193	+	0.742517i	−0.153430	+	0.0281856i
$695$			1.75515i			0.0665766i
$696$	−11.9756	+	7.26071i	−0.453933	+	0.275217i
$697$	−9.77301	−	5.64245i	−0.370179	−	0.213723i
$698$	−9.05348	−	3.22213i	−0.342679	−	0.121959i
$699$	8.23473	−	14.2630i	0.311466	−	0.539475i
$700$	−2.24472	−	5.90345i	−0.0848426	−	0.223130i
$701$	−12.7355	−	22.0585i	−0.481013	−	0.833139i	0.518750	−	0.854926i	$-0.326398\pi$
$701$	−12.7355	−	22.0585i	−0.481013	−	0.833139i	−0.999763	+	0.0217873i	$0.993064\pi$
$702$	15.7790	+	18.5341i	0.595540	+	0.699525i
$703$	2.64797	−	47.1507i	0.0998700	−	1.77832i
$704$	−20.0559	−	10.4599i	−0.755886	−	0.394222i
$705$	−0.468402	+	0.270432i	−0.0176410	+	0.0101851i
$706$	37.8685	+	13.4774i	1.42520	+	0.507228i
$707$	−17.5212	−	10.1158i	−0.658951	−	0.380446i
$708$	−11.3797	+	4.32702i	−0.427676	+	0.162619i
$709$	−10.0672	+	17.4369i	−0.378082	+	0.654857i	−0.990783	−	0.135457i	$-0.956750\pi$
$709$	−10.0672	+	17.4369i	−0.378082	+	0.654857i	0.612701	+	0.790315i	$0.290083\pi$
$710$	10.0370	−	8.54498i	0.376681	−	0.320687i
$711$	−5.02593			−0.188487
$712$	0.544313	+	25.3893i	0.0203990	+	0.951506i
$713$	−9.69442	−	5.59708i	−0.363059	−	0.209612i
$714$	4.63254	+	5.44141i	0.173369	+	0.203640i
$715$	10.6604			0.398678
$716$	−12.6642	−	10.3218i	−0.473284	−	0.385743i
$717$	−8.49004	+	4.90173i	−0.317066	+	0.183058i
$718$	13.7464	−	2.52527i	0.513012	−	0.0942422i
$719$	3.22817	−	1.86378i	0.120390	−	0.0695074i	−0.438596	−	0.898685i	$-0.644524\pi$
$719$	3.22817	−	1.86378i	0.120390	−	0.0695074i	0.558986	+	0.829177i	$0.311191\pi$
$720$	−1.80857	−	8.78143i	−0.0674013	−	0.327265i
$721$			13.1876i			0.491130i
$722$	−24.1467	−	11.7872i	−0.898646	−	0.438674i
$723$			4.28607i			0.159401i
$724$	7.32282	+	19.2585i	0.272150	+	0.715735i
$725$	−4.92338	+	2.84252i	−0.182850	+	0.105568i
$726$	0.668859	+	3.64096i	0.0248237	+	0.135129i
$727$	43.3983	−	25.0560i	1.60955	−	0.929276i	0.620083	−	0.784536i	$-0.287099\pi$
$727$	43.3983	−	25.0560i	1.60955	−	0.929276i	0.989470	−	0.144740i	$-0.0462344\pi$
$728$	33.6685	−	0.721805i	1.24784	−	0.0267519i
$729$	5.76772			0.213619
$730$	0.161734	−	0.137692i	0.00598604	−	0.00509621i
$731$	3.14791	+	1.81744i	0.116429	+	0.0672206i
$732$	15.9699	+	13.0160i	0.590264	+	0.481086i
$733$	−51.1557			−1.88948			−0.944740	−	0.327822i	$-0.893686\pi$
$733$	−51.1557			−1.88948			−0.944740	+	0.327822i	$0.893686\pi$
$734$	−0.286592	−	0.336633i	−0.0105783	−	0.0124253i
$735$	1.29441	−	2.24198i	0.0477450	−	0.0826968i
$736$	−3.83589	+	4.91801i	−0.141393	+	0.181280i
$737$	−27.3392	−	15.7843i	−1.00705	−	0.581423i
$738$	−6.52829	+	18.3431i	−0.240310	+	0.675218i
$739$	5.08608	−	2.93645i	0.187095	−	0.108019i	−0.403527	−	0.914968i	$-0.632216\pi$
$739$	5.08608	−	2.93645i	0.187095	−	0.108019i	0.590622	+	0.806949i	$0.298883\pi$
$740$	−21.3907	−	3.45735i	−0.786339	−	0.127095i
$741$	0.802588	−	14.2912i	0.0294838	−	0.525000i
$742$	48.7560	−	41.5084i	1.78989	−	1.52382i
$743$	−20.3235	−	35.2014i	−0.745598	−	1.29141i	−0.949915	−	0.312508i	$-0.898831\pi$
$743$	−20.3235	−	35.2014i	−0.745598	−	1.29141i	0.204317	−	0.978905i	$-0.434503\pi$
$744$	−12.0383	+	21.9231i	−0.441345	+	0.803739i
$745$	−1.03406	+	1.79104i	−0.0378849	+	0.0656185i
$746$	−0.922265	+	2.59136i	−0.0337665	+	0.0948766i
$747$	24.7830	+	14.3085i	0.906763	+	0.523520i
$748$	10.2564	+	1.65773i	0.375012	+	0.0606126i
$749$			0.447615i			0.0163555i
$750$	0.222547	+	1.21145i	0.00812628	+	0.0442358i
$751$	−21.4157	+	37.0931i	−0.781470	+	1.35355i	0.149616	+	0.988744i	$0.452196\pi$
$751$	−21.4157	+	37.0931i	−0.781470	+	1.35355i	−0.931086	+	0.364801i	$0.881137\pi$
$752$	−0.782527	+	2.35752i	−0.0285358	+	0.0859699i
$753$			18.5015i			0.674232i
$754$	−5.47693	−	29.8139i	−0.199458	−	1.08576i
$755$	2.21450	+	3.83563i	0.0805939	+	0.139593i
$756$	18.2154	−	22.3492i	0.662488	−	0.812834i
$757$	−6.48112	−	11.2256i	−0.235560	−	0.408002i	0.723875	−	0.689931i	$-0.242359\pi$
$757$	−6.48112	−	11.2256i	−0.235560	−	0.408002i	−0.959435	+	0.281929i	$0.909026\pi$
$758$	13.5860	+	4.83524i	0.493465	+	0.175624i
$759$	−2.71518			−0.0985547
$760$	−6.53076	+	10.4570i	−0.236896	+	0.379316i
$761$	−1.79225			−0.0649690			−0.0324845	−	0.999472i	$-0.510342\pi$
$761$	−1.79225			−0.0649690			−0.0324845	+	0.999472i	$0.510342\pi$
$762$	19.6824	+	7.00496i	0.713019	+	0.253763i
$763$	−28.9885	−	50.2096i	−1.04945	−	1.81771i
$764$	4.34361	−	5.32936i	0.157146	−	0.192809i
$765$	2.05904	+	3.56637i	0.0744448	+	0.128942i
$766$	0.519576	+	2.82834i	0.0187730	+	0.102192i
$767$		−	26.3516i		−	0.951502i
$768$	11.1694	+	8.33295i	0.403040	+	0.300689i
$769$	−15.9829	+	27.6832i	−0.576357	+	0.998280i	0.419535	+	0.907739i	$0.362193\pi$
$769$	−15.9829	+	27.6832i	−0.576357	+	0.998280i	−0.995893	+	0.0905412i	$0.971140\pi$
$770$	−2.28151	−	12.4195i	−0.0822198	−	0.447568i
$771$			7.41285i			0.266967i
$772$	27.6210	+	4.46435i	0.994103	+	0.160675i
$773$	39.6004	+	22.8633i	1.42433	+	0.822337i	0.996665	−	0.0816013i	$-0.0260034\pi$
$773$	39.6004	+	22.8633i	1.42433	+	0.822337i	0.427664	+	0.903938i	$0.359337\pi$
$774$	2.10277	−	5.90834i	0.0755827	−	0.212371i
$775$	−5.07641	+	8.79260i	−0.182350	+	0.315839i
$776$	11.6467	+	6.39539i	0.418093	+	0.229581i
$777$	−14.8992	−	25.8061i	−0.534504	−	0.925788i
$778$	−40.4862	+	34.4679i	−1.45150	+	1.23573i
$779$	23.9007	−	12.0656i	0.856330	−	0.432295i
$780$	−6.48344	−	1.04791i	−0.232144	−	0.0375211i
$781$	22.8236	−	13.1772i	0.816693	−	0.471518i
$782$	0.960548	−	2.69893i	0.0343491	−	0.0965136i
$783$	−22.4756	−	12.9763i	−0.803211	−	0.463734i
$784$	−2.39835	−	11.6451i	−0.0856555	−	0.415897i
$785$	−3.40194	+	5.89234i	−0.121421	+	0.210307i
$786$	−4.00257	−	4.70144i	−0.142767	−	0.167695i
$787$	−32.7500			−1.16741			−0.583705	−	0.811966i	$-0.698398\pi$
$787$	−32.7500			−1.16741			−0.583705	+	0.811966i	$0.698398\pi$
$788$	31.9481	+	26.0388i	1.13810	+	0.927594i
$789$	5.20515	+	3.00519i	0.185308	+	0.106988i
$790$	2.41455	−	2.05563i	0.0859059	−	0.0731360i
$791$	−29.0861			−1.03418
$792$	−0.384206	−	17.9212i	−0.0136522	−	0.636803i
$793$	−38.6187	+	22.2965i	−1.37139	+	0.791773i
$794$	−5.90832	−	32.1622i	−0.209678	−	1.14140i
$795$	−10.8146	+	6.24380i	−0.383553	+	0.221445i
$796$	−5.97273	−	15.7078i	−0.211698	−	0.556749i
$797$		−	18.9032i		−	0.669585i	−0.942292	−	0.334793i	$-0.891334\pi$
$797$		−	18.9032i		−	0.669585i	0.942292	−	0.334793i	$-0.108666\pi$
$798$	−16.8211	+	2.12352i	−0.595461	+	0.0751719i
$799$		−	1.14093i		−	0.0403634i
$800$	4.46051	+	3.47906i	0.157703	+	0.123003i
$801$	−17.4286	+	10.0624i	−0.615810	+	0.355538i
$802$	43.3970	−	7.97219i	1.53240	−	0.281508i
$803$	0.367775	−	0.212335i	0.0129785	−	0.00749313i
$804$	15.0755	+	12.2871i	0.531673	+	0.433332i
$805$	−3.48180			−0.122718
$806$	−35.0929	−	41.2203i	−1.23609	−	1.45192i
$807$	18.1140	+	10.4581i	0.637642	+	0.368143i
$808$	18.1166	−	0.388396i	0.637341	−	0.0136637i
$809$	44.1186			1.55113			0.775563	−	0.631270i	$-0.217466\pi$
$809$	44.1186			1.55113			0.775563	+	0.631270i	$0.217466\pi$
$810$	2.95948	−	2.51955i	0.103985	−	0.0885279i
$811$	13.2655	−	22.9765i	0.465814	−	0.806814i	−0.533424	−	0.845848i	$-0.679095\pi$
$811$	13.2655	−	22.9765i	0.465814	−	0.806814i	0.999238	+	0.0390344i	$0.0124282\pi$
$812$	−33.5613	+	12.7613i	−1.17777	+	0.447835i
$813$	−17.6396	−	10.1842i	−0.618648	−	0.357176i
$814$	−40.8141	−	14.5257i	−1.43053	−	0.509125i
$815$	−19.0837	+	11.0180i	−0.668473	+	0.385943i
$816$	−6.07477	−	2.01639i	−0.212660	−	0.0705877i
$817$	−7.69845	+	3.88635i	−0.269335	+	0.135966i
$818$	22.7819	+	26.7598i	0.796552	+	0.935635i
$819$	13.3436	+	23.1118i	0.466264	+	0.807593i
$820$	−4.36608	−	11.4825i	−0.152470	−	0.400985i
$821$	−5.02456	+	8.70280i	−0.175359	+	0.303730i	−0.940285	−	0.340387i	$-0.889442\pi$
$821$	−5.02456	+	8.70280i	−0.175359	+	0.303730i	0.764927	+	0.644117i	$0.222775\pi$
$822$	−5.63774	−	2.00647i	−0.196639	−	0.0699836i
$823$	43.7981	+	25.2869i	1.52671	+	0.881445i	0.999497	+	0.0317093i	$0.0100951\pi$
$823$	43.7981	+	25.2869i	1.52671	+	0.881445i	0.527210	+	0.849735i	$0.323238\pi$
$824$	−6.12371	−	10.1002i	−0.213329	−	0.351858i
$825$			2.46260i			0.0857366i
$826$	−30.6998	+	5.63967i	−1.06818	+	0.196229i
$827$	−3.22074	+	5.57849i	−0.111996	+	0.193983i	−0.916575	−	0.399863i	$-0.869058\pi$
$827$	−3.22074	+	5.57849i	−0.111996	+	0.193983i	0.804579	+	0.593846i	$0.202391\pi$
$828$	−4.87934	−	0.788640i	−0.169569	−	0.0274071i
$829$			1.70936i			0.0593685i	0.999559	+	0.0296842i	$0.00945017\pi$
$829$			1.70936i			0.0593685i	−0.999559	+	0.0296842i	$0.990550\pi$
$830$	−17.7585	+	3.26229i	−0.616405	+	0.113236i
$831$	0.589392	+	1.02086i	0.0204458	+	0.0354131i
$832$	−25.4512	+	16.1869i	−0.882362	+	0.561181i
$833$	2.73051	+	4.72939i	0.0946067	+	0.163864i
$834$	0.724862	−	2.03670i	0.0250999	−	0.0705253i
$835$	−5.89220			−0.203908
$836$	−16.6196	+	18.2036i	−0.574802	+	0.629586i
$837$	−46.3482			−1.60203
$838$	12.8925	−	36.2252i	0.445365	−	1.25138i
$839$	−19.1956	−	33.2478i	−0.662707	−	1.14784i	−0.979902	−	0.199481i	$-0.936074\pi$
$839$	−19.1956	−	33.2478i	−0.662707	−	1.14784i	0.317195	−	0.948360i	$-0.397259\pi$
$840$	0.166739	+	7.77752i	0.00575306	+	0.268350i
$841$	1.65980	+	2.87485i	0.0572344	+	0.0991329i
$842$	−36.6214	+	6.72749i	−1.26206	+	0.231845i
$843$			14.9856i			0.516130i
$844$	−2.27257	+	14.0604i	−0.0782250	+	0.483980i
$845$	0.607667	−	1.05251i	0.0209044	−	0.0362074i
$846$	−1.93609	+	0.355667i	−0.0665641	+	0.0122281i
$847$			9.49099i			0.326114i
$848$	−18.0672	+	54.4310i	−0.620429	+	1.86917i
$849$	17.4884	+	10.0969i	0.600201	+	0.346526i
$850$	−2.44786	−	0.871193i	−0.0839610	−	0.0298817i
$851$	−5.97270	+	10.3450i	−0.204741	+	0.354622i
$852$	−15.1761	+	5.77055i	−0.519925	+	0.197696i
$853$	−11.4697	−	19.8660i	−0.392714	−	0.680200i	0.600093	−	0.799930i	$-0.295130\pi$
$853$	−11.4697	−	19.8660i	−0.392714	−	0.680200i	−0.992806	+	0.119730i	$0.961797\pi$
$854$	34.2407	+	40.2193i	1.17169	+	1.37628i
$855$	−9.75481	−	0.547827i	−0.333608	−	0.0187353i
$856$	−0.207852	−	0.342825i	−0.00710424	−	0.0117175i
$857$	−8.67523	+	5.00865i	−0.296340	+	0.171092i	−0.640798	−	0.767710i	$-0.721396\pi$
$857$	−8.67523	+	5.00865i	−0.296340	+	0.171092i	0.344457	+	0.938802i	$0.388063\pi$
$858$	−12.3706	−	4.40268i	−0.422324	−	0.150305i
$859$	19.1782	+	11.0725i	0.654351	+	0.377790i	0.790121	−	0.612951i	$-0.210018\pi$
$859$	19.1782	+	11.0725i	0.654351	+	0.377790i	−0.135770	+	0.990740i	$0.543351\pi$
$860$	1.40632	+	3.69852i	0.0479552	+	0.126119i
$861$	8.44685	−	14.6304i	0.287868	−	0.498602i
$862$	−41.7386	+	35.5341i	−1.42162	+	1.21030i
$863$	23.8546			0.812019			0.406009	−	0.913869i	$-0.366920\pi$
$863$	23.8546			0.812019			0.406009	+	0.913869i	$0.366920\pi$
$864$	−3.57305	+	25.5755i	−0.121558	+	0.870097i
$865$	−12.5503	−	7.24591i	−0.426722	−	0.246368i
$866$	7.26714	+	8.53603i	0.246947	+	0.290066i
$867$	−11.8663			−0.403002
$868$	−40.5115	+	49.7053i	−1.37505	+	1.68711i
$869$	5.49057	−	3.16998i	0.186255	−	0.107534i
$870$	6.88712	−	1.26519i	0.233495	−	0.0428939i
$871$	−36.4559	+	21.0479i	−1.23526	+	0.713179i
$872$	45.5171	+	24.9941i	1.54140	+	0.846408i
$873$			10.5296i			0.356373i
$874$	4.10880	+	5.41411i	0.138982	+	0.183135i
$875$			3.15791i			0.106757i
$876$	−0.244545	+	0.0929854i	−0.00826239	+	0.00314169i
$877$	−14.3601	+	8.29082i	−0.484907	+	0.279961i	−0.722459	−	0.691414i	$-0.756988\pi$
$877$	−14.3601	+	8.29082i	−0.484907	+	0.279961i	0.237552	+	0.971375i	$0.423655\pi$
$878$	−0.0824047	−	0.448574i	−0.00278103	−	0.0151386i
$879$	−11.5405	+	6.66292i	−0.389252	+	0.224735i
$880$	7.51444	+	8.45256i	0.253312	+	0.284936i
$881$	−23.4353			−0.789555			−0.394778	−	0.918777i	$-0.629178\pi$
$881$	−23.4353			−0.789555			−0.394778	+	0.918777i	$0.629178\pi$
$882$	7.17426	−	6.10780i	0.241570	−	0.205660i
$883$	31.3376	+	18.0928i	1.05460	+	0.608871i	0.923932	−	0.382556i	$-0.124956\pi$
$883$	31.3376	+	18.0928i	1.05460	+	0.608871i	0.130663	+	0.991427i	$0.458289\pi$
$884$	8.75267	−	10.7390i	0.294384	−	0.361192i
$885$	6.08731			0.204623
$886$	−19.7376	−	23.1839i	−0.663098	−	0.778879i
$887$	−28.0443	+	48.5741i	−0.941634	+	1.63096i	−0.179280	+	0.983798i	$0.557377\pi$
$887$	−28.0443	+	48.5741i	−0.941634	+	1.63096i	−0.762354	+	0.647160i	$0.775957\pi$
$888$	23.3943	+	12.8462i	0.785062	+	0.431089i
$889$	46.3868	+	26.7814i	1.55576	+	0.898220i
$890$	4.25747	−	11.9626i	0.142711	−	0.400986i
$891$	6.72970	−	3.88540i	0.225454	−	0.130166i
$892$	3.39043	−	20.9767i	0.113520	−	0.702352i
$893$	2.26465	+	1.48275i	0.0757835	+	0.0496184i
$894$	1.93962	−	1.65129i	0.0648706	−	0.0552275i
$895$	4.08444	+	7.07445i	0.136528	+	0.236473i
$896$	24.3049	+	26.1866i	0.811969	+	0.874833i
$897$	−1.81030	+	3.13553i	−0.0604441	+	0.104692i
$898$	5.99294	−	16.8389i	0.199987	−	0.561920i
$899$	49.9862	+	28.8595i	1.66713	+	0.962520i
$900$	−0.715277	+	4.42544i	−0.0238426	+	0.147515i
$901$		−	26.3422i		−	0.877585i
$902$	−4.43763	−	24.1564i	−0.147757	−	0.804321i
$903$	−2.72075	+	4.71247i	−0.0905407	+	0.156821i
$904$	22.2768	−	13.5063i	0.740915	−	0.449212i
$905$		−	10.3018i		−	0.342445i
$906$	−0.985662	−	5.36550i	−0.0327464	−	0.178257i
$907$	−8.73870	−	15.1359i	−0.290164	−	0.502578i	0.683684	−	0.729778i	$-0.260376\pi$
$907$	−8.73870	−	15.1359i	−0.290164	−	0.502578i	−0.973848	+	0.227199i	$0.927043\pi$
$908$	−35.4084	−	28.8590i	−1.17507	−	0.957721i
$909$	7.18007	+	12.4362i	0.238148	+	0.412484i
$910$	−15.8634	−	5.64577i	−0.525866	−	0.187155i
$911$	−18.3729			−0.608722			−0.304361	−	0.952557i	$-0.598443\pi$
$911$	−18.3729			−0.608722			−0.304361	+	0.952557i	$0.598443\pi$
$912$	11.8971	−	9.43735i	0.393952	−	0.312502i
$913$	−36.0989			−1.19470
$914$	−2.82037	−	1.00377i	−0.0932897	−	0.0332017i
$915$	−5.15057	−	8.92105i	−0.170273	−	0.294921i
$916$	−29.3955	−	23.9584i	−0.971255	−	0.791606i
$917$	−7.91512	−	13.7094i	−0.261380	−	0.452724i
$918$	−2.14310	−	11.6661i	−0.0707327	−	0.385037i
$919$		−	7.88498i		−	0.260101i	−0.991507	−	0.130051i	$-0.958486\pi$
$919$		−	7.88498i		−	0.260101i	0.991507	−	0.130051i	$-0.0415140\pi$
$920$	2.66668	−	1.61679i	0.0879180	−	0.0533041i
$921$	−6.08505	+	10.5396i	−0.200509	+	0.347292i
$922$	−8.52622	−	46.4129i	−0.280796	−	1.52853i
$923$		−	35.1427i		−	1.15674i
$924$	−2.48165	+	15.3540i	−0.0816403	+	0.505111i
$925$	9.38266	+	5.41708i	0.308500	+	0.178113i
$926$	−7.39892	+	20.7894i	−0.243144	+	0.683181i
$927$	4.68016	−	8.10628i	0.153717	−	0.266245i
$928$	19.7785	−	25.3582i	0.649262	−	0.832422i
$929$	−13.9850	−	24.2227i	−0.458832	−	0.794720i	0.540068	−	0.841622i	$-0.318399\pi$
$929$	−13.9850	−	24.2227i	−0.458832	−	0.794720i	−0.998900	+	0.0469015i	$0.985065\pi$
$930$	9.52203	−	8.10657i	0.312240	−	0.265825i
$931$	−12.9359	−	0.726478i	−0.423958	−	0.0238093i
$932$	−6.03435	+	37.3347i	−0.197662	+	1.22294i
$933$	8.81497	−	5.08933i	0.288589	−	0.166617i
$934$	−5.10731	+	14.3504i	−0.167116	+	0.469560i
$935$	−4.49880	−	2.59738i	−0.147126	−	0.0849435i
$936$	−20.9519	−	11.5050i	−0.684833	−	0.376052i
$937$	0.177446	−	0.307346i	0.00579691	−	0.0100405i	−0.863112	−	0.505012i	$-0.831488\pi$
$937$	0.177446	−	0.307346i	0.00579691	−	0.0100405i	0.868909	+	0.494971i	$0.164821\pi$
$938$	32.3231	+	37.9669i	1.05539	+	1.23966i
$939$	−0.768369			−0.0250748
$940$	0.784665	−	0.962738i	0.0255929	−	0.0314010i
$941$	−24.0269	−	13.8719i	−0.783254	−	0.452212i	0.0543280	−	0.998523i	$-0.482698\pi$
$941$	−24.0269	−	13.8719i	−0.783254	−	0.452212i	−0.837582	+	0.546311i	$0.816032\pi$
$942$	6.38117	−	5.43260i	0.207910	−	0.177004i
$943$	−6.77226			−0.220535
$944$	20.8939	−	18.5750i	0.680040	−	0.604565i
$945$	−12.4847	+	7.20803i	−0.406126	+	0.234477i
$946$	1.42937	+	7.78083i	0.0464727	+	0.252977i
$947$	5.23931	−	3.02492i	0.170255	−	0.0982967i	−0.412451	−	0.910980i	$-0.635327\pi$
$947$	5.23931	−	3.02492i	0.170255	−	0.0982967i	0.582706	+	0.812683i	$0.301994\pi$
$948$	−3.65085	+	1.38820i	−0.118574	+	0.0450865i
$949$		−	0.566283i		−	0.0183823i
$950$	4.91046	−	3.72658i	0.159316	−	0.120906i
$951$			0.155104i			0.00502959i
$952$	−14.3843	−	7.89861i	−0.466196	−	0.255995i
$953$	37.0716	−	21.4033i	1.20087	−	0.693321i	0.240119	−	0.970743i	$-0.422813\pi$
$953$	37.0716	−	21.4033i	1.20087	−	0.693321i	0.960748	+	0.277422i	$0.0894801\pi$
$954$	−44.7009	+	8.21171i	−1.44724	+	0.265864i
$955$	−2.97707	+	1.71881i	−0.0963357	+	0.0556195i
$956$	14.2225	−	17.4501i	0.459988	−	0.564378i
$957$	13.9999			0.452554
$958$	−17.9873	−	21.1280i	−0.581143	−	0.682615i
$959$	−13.2868	−	7.67114i	−0.429053	−	0.247714i
$960$	−3.73924	−	5.87931i	−0.120683	−	0.189754i
$961$	72.0797			2.32515
$962$	−43.9866	+	37.4479i	−1.41818	+	1.20737i
$963$	0.158855	−	0.275145i	0.00511903	−	0.00886643i
$964$	−3.49805	−	9.19961i	−0.112665	−	0.296299i
$965$	−12.1155	−	6.99487i	−0.390011	−	0.225173i
$966$	4.04035	+	1.43796i	0.129996	+	0.0462655i
$967$	31.2688	−	18.0531i	1.00554	−	0.580547i	0.0956553	−	0.995415i	$-0.469505\pi$
$967$	31.2688	−	18.0531i	1.00554	−	0.580547i	0.909882	+	0.414867i	$0.136172\pi$
$968$	−4.40719	−	7.26907i	−0.141652	−	0.233637i
$969$	−3.82070	+	5.83546i	−0.122739	+	0.187462i
$970$	−4.30665	−	5.05862i	−0.138278	−	0.162422i
$971$	−13.0907	−	22.6738i	−0.420101	−	0.727636i	0.575848	−	0.817557i	$-0.304672\pi$
$971$	−13.0907	−	22.6738i	−0.420101	−	0.727636i	−0.995949	+	0.0899206i	$0.971339\pi$
$972$	−30.0768	+	11.4364i	−0.964715	+	0.366822i
$973$	2.77130	−	4.80003i	0.0888437	−	0.153882i
$974$	18.6941	+	6.65320i	0.598996	+	0.213182i
$975$	2.84384	+	1.64189i	0.0910759	+	0.0525827i
$976$	−44.9007	−	14.9038i	−1.43724	−	0.477059i
$977$		−	37.5301i		−	1.20069i	−0.799740	−	0.600347i	$-0.795029\pi$
$977$		−	37.5301i		−	1.20069i	0.799740	−	0.600347i	$-0.204971\pi$
$978$	26.6954	−	4.90404i	0.853625	−	0.156814i
$979$	12.6933	−	21.9854i	0.405678	−	0.702655i
$980$	−0.948534	+	5.86861i	−0.0302998	+	0.187466i
$981$			41.1512i			1.31386i
$982$	−17.6634	+	3.24483i	−0.563662	+	0.103547i
$983$	8.30065	+	14.3771i	0.264749	+	0.458560i	0.967498	−	0.252879i	$-0.0813774\pi$
$983$	8.30065	+	14.3771i	0.264749	+	0.458560i	−0.702748	+	0.711438i	$0.748044\pi$
$984$	0.324315	+	15.1276i	0.0103388	+	0.482251i
$985$	−10.3038	−	17.8467i	−0.328307	−	0.568645i
$986$	−4.95276	+	13.9162i	−0.157728	+	0.443181i
$987$	1.70800			0.0543662
$988$	9.94100	+	31.3296i	0.316265	+	0.996726i
$989$	2.18136			0.0693631
$990$	−3.00516	+	8.44384i	−0.0955102	+	0.268363i
$991$	14.9607	+	25.9127i	0.475242	+	0.823143i	0.999598	−	0.0283560i	$-0.00902721\pi$
$991$	14.9607	+	25.9127i	0.475242	+	0.823143i	−0.524356	+	0.851499i	$0.675694\pi$
$992$	7.94655	−	56.8806i	0.252303	−	1.80596i
$993$	−5.00498	−	8.66887i	−0.158828	−	0.275098i
$994$	−40.9416	+	7.52111i	−1.29859	+	0.238555i
$995$			8.40252i			0.266378i
$996$	21.9545	+	3.54848i	0.695656	+	0.112438i
$997$	−7.19210	+	12.4571i	−0.227776	+	0.394520i	−0.957149	−	0.289597i	$-0.906479\pi$
$997$	−7.19210	+	12.4571i	−0.227776	+	0.394520i	0.729373	+	0.684117i	$0.239812\pi$
$998$	61.8501	−	11.3621i	1.95783	−	0.359661i
$999$			49.4586i			1.56480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.b.31.2	✓	40
4.3	odd	2	inner	380.2.n.b.31.8	yes	40
19.8	odd	6	inner	380.2.n.b.331.8	yes	40
76.27	even	6	inner	380.2.n.b.331.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.b.31.2	✓	40	1.1	even	1	trivial
380.2.n.b.31.8	yes	40	4.3	odd	2	inner
380.2.n.b.331.2	yes	40	76.27	even	6	inner
380.2.n.b.331.8	yes	40	19.8	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.33235 - 0.474182i) q^{2} +(-0.435478 - 0.754271i) q^{3} +(1.55030 + 1.26355i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.222547 + 1.21145i) q^{6} +3.15791i q^{7} +(-1.46639 - 2.41862i) q^{8} +(1.12072 - 1.94114i) q^{9} +O(q^{10})\)	\(q+(-1.33235 - 0.474182i) q^{2} +(-0.435478 - 0.754271i) q^{3} +(1.55030 + 1.26355i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.222547 + 1.21145i) q^{6} +3.15791i q^{7} +(-1.46639 - 2.41862i) q^{8} +(1.12072 - 1.94114i) q^{9} +(0.255520 + 1.39094i) q^{10} +2.82746i q^{11} +(0.277936 - 1.71960i) q^{12} +(3.26520 + 1.88516i) q^{13} +(1.49742 - 4.20743i) q^{14} +(-0.435478 + 0.754271i) q^{15} +(0.806879 + 3.91777i) q^{16} +(-0.918627 - 1.59111i) q^{17} +(-2.41364 + 2.05485i) q^{18} +(4.35204 + 0.244409i) q^{19} +(0.319116 - 1.97438i) q^{20} +(2.38192 - 1.37520i) q^{21} +(1.34073 - 3.76716i) q^{22} +(-0.954851 - 0.551283i) q^{23} +(-1.18571 + 2.15931i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.45647 - 4.05999i) q^{26} -4.56506 q^{27} +(-3.99018 + 4.89571i) q^{28} +(4.92338 + 2.84252i) q^{29} +(0.937871 - 0.798455i) q^{30} +10.1528 q^{31} +(0.782694 - 5.60245i) q^{32} +(2.13267 - 1.23130i) q^{33} +(0.469456 + 2.55551i) q^{34} +(2.73483 - 1.57895i) q^{35} +(4.19018 - 1.59327i) q^{36} -10.8342i q^{37} +(-5.68254 - 2.38930i) q^{38} -3.28379i q^{39} +(-1.36139 + 2.47924i) q^{40} +(5.31936 - 3.07113i) q^{41} +(-3.82564 + 0.702784i) q^{42} +(-1.71337 + 0.989217i) q^{43} +(-3.57264 + 4.38342i) q^{44} -2.24143 q^{45} +(1.01079 + 1.18727i) q^{46} +(0.537802 + 0.310500i) q^{47} +(2.60368 - 2.31471i) q^{48} -2.97238 q^{49} +(1.07683 - 0.916756i) q^{50} +(-0.800085 + 1.38579i) q^{51} +(2.68004 + 7.04831i) q^{52} +(12.4169 + 7.16889i) q^{53} +(6.08225 + 2.16467i) q^{54} +(2.44865 - 1.41373i) q^{55} +(7.63776 - 4.63073i) q^{56} +(-1.71087 - 3.38905i) q^{57} +(-5.21179 - 6.12180i) q^{58} +(-3.49461 - 6.05284i) q^{59} +(-1.62818 + 0.619099i) q^{60} +(-5.91369 + 10.2428i) q^{61} +(-13.5271 - 4.81428i) q^{62} +(6.12994 + 3.53912i) q^{63} +(-3.69940 + 7.09327i) q^{64} -3.77032i q^{65} +(-3.42532 + 0.629244i) q^{66} +(-5.58251 + 9.66919i) q^{67} +(0.586297 - 3.62743i) q^{68} +0.960288i q^{69} +(-4.39246 + 0.806910i) q^{70} +(-4.66044 - 8.07212i) q^{71} +(-6.33828 + 0.135884i) q^{72} +(-0.0750974 - 0.130072i) q^{73} +(-5.13737 + 14.4349i) q^{74} +0.870957 q^{75} +(6.43816 + 5.87793i) q^{76} -8.92886 q^{77} +(-1.55711 + 4.37515i) q^{78} +(-1.12114 - 1.94187i) q^{79} +(2.98945 - 2.65766i) q^{80} +(-1.37416 - 2.38012i) q^{81} +(-8.54351 + 1.56947i) q^{82} +12.7672i q^{83} +(5.43033 + 0.877696i) q^{84} +(-0.918627 + 1.59111i) q^{85} +(2.75188 - 0.505530i) q^{86} -4.95142i q^{87} +(6.83854 - 4.14616i) q^{88} +(-7.77565 - 4.48928i) q^{89} +(2.98637 + 1.06285i) q^{90} +(-5.95317 + 10.3112i) q^{91} +(-0.783734 - 2.06116i) q^{92} +(-4.42133 - 7.65797i) q^{93} +(-0.569305 - 0.668710i) q^{94} +(-1.96436 - 3.89118i) q^{95} +(-4.56661 + 1.84938i) q^{96} +(-4.06833 + 2.34885i) q^{97} +(3.96025 + 1.40945i) q^{98} +(5.48849 + 3.16878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * q^98

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