LMFDB - Embedded newform 354.2.e.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	354.289
Dual form			354.2.e.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.370138 - 0.928977i) q^{2} +(0.994138 - 0.108119i) q^{3} +(-0.725995 + 0.687699i) q^{4} +(-1.72394 - 2.02958i) q^{5} +(-0.468408 - 0.883512i) q^{6} +(-1.98744 + 1.19580i) q^{7} +(0.907575 + 0.419889i) q^{8} +(0.976621 - 0.214970i) q^{9} +O(q^{10})$	\(q+(-0.370138 - 0.928977i) q^{2} +(0.994138 - 0.108119i) q^{3} +(-0.725995 + 0.687699i) q^{4} +(-1.72394 - 2.02958i) q^{5} +(-0.468408 - 0.883512i) q^{6} +(-1.98744 + 1.19580i) q^{7} +(0.907575 + 0.419889i) q^{8} +(0.976621 - 0.214970i) q^{9} +(-1.24733 + 2.35272i) q^{10} +(-0.294458 - 5.43097i) q^{11} +(-0.647386 + 0.762162i) q^{12} +(-5.44454 - 1.19843i) q^{13} +(1.84650 + 1.40367i) q^{14} +(-1.93327 - 1.83129i) q^{15} +(0.0541389 - 0.998533i) q^{16} +(1.46494 + 0.881427i) q^{17} +(-0.561187 - 0.827689i) q^{18} +(-0.737921 - 2.65775i) q^{19} +(2.64731 + 0.287912i) q^{20} +(-1.84650 + 1.40367i) q^{21} +(-4.93625 + 2.28375i) q^{22} +(-3.56615 + 5.25967i) q^{23} +(0.947653 + 0.319302i) q^{24} +(-0.338311 + 2.06360i) q^{25} +(0.901915 + 5.50144i) q^{26} +(0.947653 - 0.319302i) q^{27} +(0.620518 - 2.23490i) q^{28} +(3.48345 - 8.74281i) q^{29} +(-0.985649 + 2.47379i) q^{30} +(0.106667 - 0.384178i) q^{31} +(-0.947653 + 0.319302i) q^{32} +(-0.879923 - 5.36729i) q^{33} +(0.276594 - 1.68715i) q^{34} +(5.85319 + 1.97217i) q^{35} +(-0.561187 + 0.827689i) q^{36} +(3.89511 - 1.80207i) q^{37} +(-2.19586 + 1.66925i) q^{38} +(-5.54220 - 0.602750i) q^{39} +(-0.712407 - 2.56586i) q^{40} +(3.92394 + 5.78738i) q^{41} +(1.98744 + 1.19580i) q^{42} +(-0.357175 + 6.58771i) q^{43} +(3.94865 + 3.74036i) q^{44} +(-2.11993 - 1.61153i) q^{45} +(6.20608 + 1.36606i) q^{46} +(1.07001 - 1.25972i) q^{47} +(-0.0541389 - 0.998533i) q^{48} +(-0.758898 + 1.43143i) q^{49} +(2.04226 - 0.449536i) q^{50} +(1.55165 + 0.717872i) q^{51} +(4.77687 - 2.87415i) q^{52} +(-3.61401 - 6.81675i) q^{53} +(-0.647386 - 0.762162i) q^{54} +(-10.5149 + 9.96028i) q^{55} +(-2.30585 + 0.250776i) q^{56} +(-1.02095 - 2.56239i) q^{57} -9.41122 q^{58} +(-0.551812 - 7.66130i) q^{59} +2.66292 q^{60} +(-1.64746 - 4.13481i) q^{61} +(-0.396374 + 0.0431083i) q^{62} +(-1.68391 + 1.59508i) q^{63} +(0.647386 + 0.762162i) q^{64} +(6.95374 + 13.1161i) q^{65} +(-4.66040 + 2.80407i) q^{66} +(11.2287 + 5.19495i) q^{67} +(-1.66970 + 0.367528i) q^{68} +(-2.97657 + 5.61441i) q^{69} +(-0.334389 - 6.16745i) q^{70} +(3.68066 - 4.33320i) q^{71} +(0.976621 + 0.214970i) q^{72} +(-6.01203 - 4.57023i) q^{73} +(-3.11581 - 2.95145i) q^{74} +(-0.113213 + 2.08808i) q^{75} +(2.36346 + 1.42205i) q^{76} +(7.07957 + 10.4416i) q^{77} +(1.49144 + 5.37167i) q^{78} +(6.70851 + 0.729595i) q^{79} +(-2.11993 + 1.61153i) q^{80} +(0.907575 - 0.419889i) q^{81} +(3.92394 - 5.78738i) q^{82} +(14.7151 + 4.95810i) q^{83} +(0.375245 - 2.28889i) q^{84} +(-0.736548 - 4.49274i) q^{85} +(6.25204 - 2.10656i) q^{86} +(2.51777 - 9.06818i) q^{87} +(2.01316 - 5.05265i) q^{88} +(2.82032 - 7.07847i) q^{89} +(-0.712407 + 2.56586i) q^{90} +(12.2538 - 4.12877i) q^{91} +(-1.02807 - 6.27093i) q^{92} +(0.0645043 - 0.393459i) q^{93} +(-1.56630 - 0.527749i) q^{94} +(-4.12198 + 6.07947i) q^{95} +(-0.907575 + 0.419889i) q^{96} +(4.94149 - 3.75643i) q^{97} +(1.61067 + 0.175170i) q^{98} +(-1.45507 - 5.24069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{11}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.370138	−	0.928977i	−0.261727	−	0.656886i
$2$	−0.370138	−	0.928977i	−0.261727	−	0.656886i
$3$	0.994138	−	0.108119i	0.573966	−	0.0624225i
$3$	0.994138	−	0.108119i	0.573966	−	0.0624225i
$4$	−0.725995	+	0.687699i	−0.362998	+	0.343850i
$5$	−1.72394	−	2.02958i	−0.770969	−	0.907655i	0.226832	−	0.973934i	$-0.427163\pi$
$5$	−1.72394	−	2.02958i	−0.770969	−	0.907655i	−0.997801	+	0.0662791i	$0.978887\pi$
$6$	−0.468408	−	0.883512i	−0.191227	−	0.360692i
$7$	−1.98744	+	1.19580i	−0.751180	+	0.451970i	−0.838976	−	0.544169i	$-0.816845\pi$
$7$	−1.98744	+	1.19580i	−0.751180	+	0.451970i	0.0877960	+	0.996138i	$0.472018\pi$
$8$	0.907575	+	0.419889i	0.320876	+	0.148453i
$9$	0.976621	−	0.214970i	0.325540	−	0.0716568i
$10$	−1.24733	+	2.35272i	−0.394442	+	0.743996i
$11$	−0.294458	−	5.43097i	−0.0887825	−	1.63750i	−0.615985	−	0.787758i	$-0.711242\pi$
$11$	−0.294458	−	5.43097i	−0.0887825	−	1.63750i	0.527202	−	0.849740i	$-0.323241\pi$
$12$	−0.647386	+	0.762162i	−0.186884	+	0.220017i
$13$	−5.44454	−	1.19843i	−1.51004	−	0.332386i	−0.618669	−	0.785652i	$-0.712328\pi$
$13$	−5.44454	−	1.19843i	−1.51004	−	0.332386i	−0.891375	+	0.453266i	$0.850259\pi$
$14$	1.84650	+	1.40367i	0.493497	+	0.375147i
$15$	−1.93327	−	1.83129i	−0.499168	−	0.472837i
$16$	0.0541389	−	0.998533i	0.0135347	−	0.249633i
$17$	1.46494	+	0.881427i	0.355301	+	0.213777i	0.682002	−	0.731350i	$-0.261109\pi$
$17$	1.46494	+	0.881427i	0.355301	+	0.213777i	−0.326701	+	0.945128i	$0.605937\pi$
$18$	−0.561187	−	0.827689i	−0.132273	−	0.195088i
$19$	−0.737921	−	2.65775i	−0.169291	−	0.609730i	−0.998695	−	0.0510806i	$-0.983733\pi$
$19$	−0.737921	−	2.65775i	−0.169291	−	0.609730i	0.829404	−	0.558650i	$-0.188680\pi$
$20$	2.64731	+	0.287912i	0.591957	+	0.0643792i
$21$	−1.84650	+	1.40367i	−0.402938	+	0.306306i
$22$	−4.93625	+	2.28375i	−1.05241	+	0.486898i
$23$	−3.56615	+	5.25967i	−0.743593	+	1.09672i	0.248181	+	0.968714i	$0.420167\pi$
$23$	−3.56615	+	5.25967i	−0.743593	+	1.09672i	−0.991774	+	0.128004i	$0.959143\pi$
$24$	0.947653	+	0.319302i	0.193439	+	0.0651772i
$25$	−0.338311	+	2.06360i	−0.0676621	+	0.412721i
$26$	0.901915	+	5.50144i	0.176880	+	1.07892i
$27$	0.947653	−	0.319302i	0.182376	−	0.0614496i
$28$	0.620518	−	2.23490i	0.117267	−	0.422357i
$29$	3.48345	−	8.74281i	0.646861	−	1.62350i	−0.128301	−	0.991735i	$-0.540952\pi$
$29$	3.48345	−	8.74281i	0.646861	−	1.62350i	0.775162	−	0.631763i	$-0.217668\pi$
$30$	−0.985649	+	2.47379i	−0.179954	+	0.451651i
$31$	0.106667	−	0.384178i	0.0191579	−	0.0690004i	−0.953353	−	0.301857i	$-0.902393\pi$
$31$	0.106667	−	0.384178i	0.0191579	−	0.0690004i	0.972511	+	0.232857i	$0.0748073\pi$
$32$	−0.947653	+	0.319302i	−0.167523	+	0.0564451i
$33$	−0.879923	−	5.36729i	−0.153175	−	0.934326i
$34$	0.276594	−	1.68715i	0.0474354	−	0.289343i
$35$	5.85319	+	1.97217i	0.989369	+	0.333357i
$36$	−0.561187	+	0.827689i	−0.0935312	+	0.137948i
$37$	3.89511	−	1.80207i	0.640353	−	0.296259i	−0.0727162	−	0.997353i	$-0.523167\pi$
$37$	3.89511	−	1.80207i	0.640353	−	0.296259i	0.713069	+	0.701094i	$0.247305\pi$
$38$	−2.19586	+	1.66925i	−0.356215	+	0.270788i
$39$	−5.54220	−	0.602750i	−0.887462	−	0.0965173i
$40$	−0.712407	−	2.56586i	−0.112641	−	0.405698i
$41$	3.92394	+	5.78738i	0.612817	+	0.903837i	0.999834	−	0.0182355i	$-0.00580486\pi$
$41$	3.92394	+	5.78738i	0.612817	+	0.903837i	−0.387017	+	0.922073i	$0.626495\pi$
$42$	1.98744	+	1.19580i	0.306668	+	0.184516i
$43$	−0.357175	+	6.58771i	−0.0544687	+	1.00462i	0.835758	+	0.549098i	$0.185029\pi$
$43$	−0.357175	+	6.58771i	−0.0544687	+	1.00462i	−0.890226	+	0.455518i	$0.849454\pi$
$44$	3.94865	+	3.74036i	0.595281	+	0.563880i
$45$	−2.11993	−	1.61153i	−0.316021	−	0.240233i
$46$	6.20608	+	1.36606i	0.915037	+	0.201415i
$47$	1.07001	−	1.25972i	0.156078	−	0.183749i	−0.678566	−	0.734540i	$-0.737398\pi$
$47$	1.07001	−	1.25972i	0.156078	−	0.183749i	0.834643	+	0.550791i	$0.185674\pi$
$48$	−0.0541389	−	0.998533i	−0.00781428	−	0.144126i
$49$	−0.758898	+	1.43143i	−0.108414	+	0.204491i
$50$	2.04226	−	0.449536i	0.288819	−	0.0635740i
$51$	1.55165	+	0.717872i	0.217275	+	0.100522i
$52$	4.77687	−	2.87415i	0.662433	−	0.398573i
$53$	−3.61401	−	6.81675i	−0.496423	−	0.936352i	−0.997481	−	0.0709387i	$-0.977401\pi$
$53$	−3.61401	−	6.81675i	−0.496423	−	0.936352i	0.501058	−	0.865414i	$-0.332944\pi$
$54$	−0.647386	−	0.762162i	−0.0880981	−	0.103717i
$55$	−10.5149	+	9.96028i	−1.41783	+	1.34304i
$56$	−2.30585	+	0.250776i	−0.308132	+	0.0335114i
$57$	−1.02095	−	2.56239i	−0.135228	−	0.339397i
$58$	−9.41122			−1.23575
$59$	−0.551812	−	7.66130i	−0.0718398	−	0.997416i
$59$	−0.551812	−	7.66130i	−0.0718398	−	0.997416i
$60$	2.66292			0.343782
$61$	−1.64746	−	4.13481i	−0.210935	−	0.529408i	0.784998	−	0.619498i	$-0.212664\pi$
$61$	−1.64746	−	4.13481i	−0.210935	−	0.529408i	−0.995934	+	0.0900903i	$0.971284\pi$
$62$	−0.396374	+	0.0431083i	−0.0503395	+	0.00547475i
$63$	−1.68391	+	1.59508i	−0.212153	+	0.200962i
$64$	0.647386	+	0.762162i	0.0809233	+	0.0952703i
$65$	6.95374	+	13.1161i	0.862505	+	1.62686i
$66$	−4.66040	+	2.80407i	−0.573655	+	0.345157i
$67$	11.2287	+	5.19495i	1.37180	+	0.634664i	0.960870	−	0.277001i	$-0.0893404\pi$
$67$	11.2287	+	5.19495i	1.37180	+	0.634664i	0.410935	+	0.911665i	$0.365202\pi$
$68$	−1.66970	+	0.367528i	−0.202481	+	0.0445694i
$69$	−2.97657	+	5.61441i	−0.358337	+	0.675895i
$70$	−0.334389	−	6.16745i	−0.0399672	−	0.737151i
$71$	3.68066	−	4.33320i	0.436813	−	0.514257i	−0.499072	−	0.866560i	$-0.666326\pi$
$71$	3.68066	−	4.33320i	0.436813	−	0.514257i	0.935886	+	0.352304i	$0.114602\pi$
$72$	0.976621	+	0.214970i	0.115096	+	0.0253345i
$73$	−6.01203	−	4.57023i	−0.703655	−	0.534905i	0.191040	−	0.981582i	$-0.438814\pi$
$73$	−6.01203	−	4.57023i	−0.703655	−	0.534905i	−0.894695	+	0.446677i	$0.852607\pi$
$74$	−3.11581	−	2.95145i	−0.362206	−	0.343100i
$75$	−0.113213	+	2.08808i	−0.0130727	+	0.241111i
$76$	2.36346	+	1.42205i	0.271108	+	0.163120i
$77$	7.07957	+	10.4416i	0.806791	+	1.18993i
$78$	1.49144	+	5.37167i	0.168872	+	0.608222i
$79$	6.70851	+	0.729595i	0.754767	+	0.0820858i	0.477409	−	0.878681i	$-0.341576\pi$
$79$	6.70851	+	0.729595i	0.754767	+	0.0820858i	0.277357	+	0.960767i	$0.410541\pi$
$80$	−2.11993	+	1.61153i	−0.237016	+	0.180175i
$81$	0.907575	−	0.419889i	0.100842	−	0.0466543i
$82$	3.92394	−	5.78738i	0.433327	−	0.639109i
$83$	14.7151	+	4.95810i	1.61519	+	0.544222i	0.974657	−	0.223705i	$-0.0718151\pi$
$83$	14.7151	+	4.95810i	1.61519	+	0.544222i	0.640537	+	0.767927i	$0.278712\pi$
$84$	0.375245	−	2.28889i	0.0409426	−	0.249739i
$85$	−0.736548	−	4.49274i	−0.0798898	−	0.487306i
$86$	6.25204	−	2.10656i	0.674174	−	0.227156i
$87$	2.51777	−	9.06818i	0.269933	−	0.972211i
$88$	2.01316	−	5.05265i	0.214604	−	0.538614i
$89$	2.82032	−	7.07847i	0.298953	−	0.750317i	−0.700379	−	0.713772i	$-0.746985\pi$
$89$	2.82032	−	7.07847i	0.298953	−	0.750317i	0.999332	−	0.0365451i	$-0.0116352\pi$
$90$	−0.712407	+	2.56586i	−0.0750943	+	0.270465i
$91$	12.2538	−	4.12877i	1.28454	−	0.432813i
$92$	−1.02807	−	6.27093i	−0.107183	−	0.653790i
$93$	0.0645043	−	0.393459i	0.00668878	−	0.0407998i
$94$	−1.56630	−	0.527749i	−0.161552	−	0.0544331i
$95$	−4.12198	+	6.07947i	−0.422907	+	0.623741i
$96$	−0.907575	+	0.419889i	−0.0926290	+	0.0428548i
$97$	4.94149	−	3.75643i	0.501733	−	0.381407i	−0.323475	−	0.946237i	$-0.604851\pi$
$97$	4.94149	−	3.75643i	0.501733	−	0.381407i	0.825208	+	0.564829i	$0.191058\pi$
$98$	1.61067	+	0.175170i	0.162702	+	0.0176949i
$99$	−1.45507	−	5.24069i	−0.146240	−	0.526709i
$100$	−1.17353	−	1.73082i	−0.117353	−	0.173082i
$101$	−4.28845	−	2.58027i	−0.426717	−	0.256747i	0.285957	−	0.958242i	$-0.407688\pi$
$101$	−4.28845	−	2.58027i	−0.426717	−	0.256747i	−0.712674	+	0.701496i	$0.752516\pi$
$102$	0.0925597	−	1.70716i	0.00916477	−	0.169034i
$103$	2.16721	+	2.05289i	0.213541	+	0.202277i	0.786992	−	0.616963i	$-0.211637\pi$
$103$	2.16721	+	2.05289i	0.213541	+	0.202277i	−0.573451	+	0.819240i	$0.694396\pi$
$104$	−4.43812	−	3.37377i	−0.435194	−	0.330826i
$105$	6.03210	+	1.32777i	0.588673	+	0.129577i
$106$	−4.99492	+	5.88047i	−0.485149	+	0.571162i
$107$	−0.794548	−	14.6546i	−0.0768119	−	1.41671i	−0.742182	−	0.670198i	$-0.766209\pi$
$107$	−0.794548	−	14.6546i	−0.0768119	−	1.41671i	0.665370	−	0.746514i	$-0.268274\pi$
$108$	−0.468408	+	0.883512i	−0.0450726	+	0.0850160i
$109$	−7.10337	+	1.56357i	−0.680379	+	0.149763i	−0.541697	−	0.840574i	$-0.682218\pi$
$109$	−7.10337	+	1.56357i	−0.680379	+	0.149763i	−0.138683	+	0.990337i	$0.544287\pi$
$110$	13.1448	+	6.08145i	1.25331	+	0.579844i
$111$	3.67744	−	2.21264i	0.349047	−	0.210015i
$112$	1.08645	+	2.04926i	0.102660	+	0.193637i
$113$	8.04279	+	9.46871i	0.756602	+	0.890741i	0.996796	−	0.0799838i	$-0.0254869\pi$
$113$	8.04279	+	9.46871i	0.756602	+	0.890741i	−0.240194	+	0.970725i	$0.577211\pi$
$114$	−2.00251	+	1.89688i	−0.187552	+	0.177659i
$115$	16.8227	−	1.82958i	1.56873	−	0.170609i
$116$	3.48345	+	8.74281i	0.323430	+	0.811749i
$117$	−5.57488			−0.515398
$118$	−6.91292	+	3.34836i	−0.636386	+	0.308241i
$119$	−3.96549			−0.363516
$120$	−0.985649	−	2.47379i	−0.0899770	−	0.225825i
$121$	−18.4732	+	2.00908i	−1.67938	+	0.182643i
$122$	−3.23135	+	3.06090i	−0.292553	+	0.277121i
$123$	4.52667	+	5.32920i	0.408156	+	0.480518i
$124$	0.186760	+	0.352266i	0.0167715	+	0.0316344i
$125$	−6.63725	+	3.99350i	−0.593653	+	0.357189i
$126$	2.10507	+	0.973911i	0.187535	+	0.0867629i
$127$	12.8311	−	2.82434i	1.13858	−	0.250620i	0.394619	−	0.918845i	$-0.370877\pi$
$127$	12.8311	−	2.82434i	1.13858	−	0.250620i	0.743959	+	0.668225i	$0.232946\pi$
$128$	0.468408	−	0.883512i	0.0414018	−	0.0780922i
$129$	0.357175	+	6.58771i	0.0314475	+	0.580016i
$130$	9.61075	−	11.3146i	0.842918	−	0.992360i
$131$	−16.9810	−	3.73781i	−1.48364	−	0.326574i	−0.601999	−	0.798497i	$-0.705629\pi$
$131$	−16.9810	−	3.73781i	−1.48364	−	0.326574i	−0.881640	+	0.471923i	$0.843560\pi$
$132$	4.32990	+	3.29151i	0.376870	+	0.286489i
$133$	4.64471	+	4.39970i	0.402747	+	0.381503i
$134$	0.669817	−	12.3541i	0.0578634	−	1.06723i
$135$	−2.28174	−	1.37288i	−0.196381	−	0.118159i
$136$	0.959445	+	1.41507i	0.0822717	+	0.121342i
$137$	−5.53699	−	19.9424i	−0.473057	−	1.70380i	−0.686749	−	0.726895i	$-0.740963\pi$
$137$	−5.53699	−	19.9424i	−0.473057	−	1.70380i	0.213692	−	0.976901i	$-0.431451\pi$
$138$	6.31740	+	0.687058i	0.537772	+	0.0584863i
$139$	−11.6125	+	8.82759i	−0.984959	+	0.748747i	−0.967959	−	0.251109i	$-0.919205\pi$
$139$	−11.6125	+	8.82759i	−0.984959	+	0.748747i	−0.0170006	+	0.999855i	$0.505412\pi$
$140$	−5.60565	+	2.59345i	−0.473764	+	0.219186i
$141$	0.927542	−	1.36802i	0.0781131	−	0.115208i
$142$	−5.38780	−	1.81536i	−0.452134	−	0.152342i
$143$	−4.90546	+	29.9220i	−0.410215	+	2.50220i
$144$	−0.161782	−	0.986827i	−0.0134818	−	0.0822355i
$145$	−23.7495	+	8.00213i	−1.97229	+	0.664540i
$146$	−2.02035	+	7.27665i	−0.167206	+	0.602220i
$147$	−0.599684	+	1.50509i	−0.0494611	+	0.124138i
$148$	−1.58855	+	3.98696i	−0.130578	+	0.327726i
$149$	1.75023	−	6.30376i	0.143384	−	0.516424i	−0.856615	−	0.515955i	$-0.827437\pi$
$149$	1.75023	−	6.30376i	0.143384	−	0.516424i	1.00000		0.000468725i	$-0.000149200\pi$
$150$	1.98169	−	0.667708i	0.161804	−	0.0545181i
$151$	2.77600	+	16.9328i	0.225907	+	1.37797i	0.819440	+	0.573164i	$0.194284\pi$
$151$	2.77600	+	16.9328i	0.225907	+	1.37797i	−0.593533	+	0.804810i	$0.702267\pi$
$152$	0.446242	−	2.72196i	0.0361950	−	0.220780i
$153$	1.62017	+	0.545900i	0.130983	+	0.0441334i
$154$	7.07957	−	10.4416i	0.570488	−	0.841406i
$155$	−0.963606	+	0.445812i	−0.0773987	+	0.0358084i
$156$	4.43812	−	3.37377i	0.355334	−	0.270118i
$157$	−11.8137	−	1.28482i	−0.942835	−	0.102540i	−0.376228	−	0.926527i	$-0.622779\pi$
$157$	−11.8137	−	1.28482i	−0.942835	−	0.102540i	−0.566608	+	0.823988i	$0.691744\pi$
$158$	−1.80530	−	6.50210i	−0.143622	−	0.517280i
$159$	−4.32985	−	6.38604i	−0.343379	−	0.506446i
$160$	2.28174	+	1.37288i	0.180388	+	0.108536i
$161$	0.797968	−	14.7177i	0.0628887	−	1.15991i
$162$	−0.725995	−	0.687699i	−0.0570396	−	0.0540308i
$163$	8.64744	+	6.57361i	0.677319	+	0.514885i	0.886345	−	0.463025i	$-0.153236\pi$
$163$	8.64744	+	6.57361i	0.677319	+	0.514885i	−0.209026	+	0.977910i	$0.567029\pi$
$164$	−6.82874	−	1.50312i	−0.533235	−	0.117374i
$165$	−9.37640	+	11.0388i	−0.729952	+	0.859366i
$166$	−0.840667	−	15.5052i	−0.0652484	−	1.20344i
$167$	−5.33573	+	10.0643i	−0.412891	+	0.778796i	−0.999517	−	0.0310621i	$-0.990111\pi$
$167$	−5.33573	+	10.0643i	−0.412891	+	0.778796i	0.586626	+	0.809858i	$0.300456\pi$
$168$	−2.26522	+	0.498613i	−0.174766	+	0.0384688i
$169$	16.4083	+	7.59128i	1.26218	+	0.583945i
$170$	−3.90103	+	2.34717i	−0.299195	+	0.180020i
$171$	−1.29201	−	2.43698i	−0.0988023	−	0.186361i
$172$	−4.27106	−	5.02828i	−0.325665	−	0.383403i
$173$	−2.43671	+	2.30818i	−0.185260	+	0.175488i	−0.774709	−	0.632318i	$-0.782104\pi$
$173$	−2.43671	+	2.30818i	−0.185260	+	0.175488i	0.589449	+	0.807806i	$0.299345\pi$
$174$	−9.35605	+	1.01753i	−0.709280	+	0.0771389i
$175$	−1.79529	−	4.50583i	−0.135711	−	0.340609i
$176$	−5.43894			−0.409976
$177$	−1.37691	−	7.55673i	−0.103495	−	0.567998i
$178$	−7.61965			−0.571117
$179$	1.75055	+	4.39354i	0.130842	+	0.328389i	0.979772	−	0.200116i	$-0.0641320\pi$
$179$	1.75055	+	4.39354i	0.130842	+	0.328389i	−0.848930	+	0.528505i	$0.822753\pi$
$180$	2.64731	−	0.287912i	0.197319	−	0.0214597i
$181$	−18.0220	+	17.0713i	−1.33956	+	1.26890i	−0.404446	+	0.914562i	$0.632536\pi$
$181$	−18.0220	+	17.0713i	−1.33956	+	1.26890i	−0.935117	+	0.354340i	$0.884706\pi$
$182$	−8.37112	−	9.85524i	−0.620508	−	0.730519i
$183$	−2.08485	−	3.93245i	−0.154117	−	0.290695i
$184$	−5.44503	+	3.27616i	−0.401413	+	0.241522i
$185$	−10.3724	−	4.79877i	−0.762593	−	0.352813i
$186$	−0.389389	+	0.0857111i	−0.0285514	+	0.00628464i
$187$	4.35563	−	8.21560i	0.318516	−	0.600784i
$188$	0.0894820	+	1.65040i	0.00652614	+	0.120368i
$189$	−1.50158	+	1.76779i	−0.109224	+	0.128588i
$190$	7.17339	+	1.57898i	0.520412	+	0.114551i
$191$	−9.85835	−	7.49412i	−0.713325	−	0.542256i	0.184378	−	0.982855i	$-0.440973\pi$
$191$	−9.85835	−	7.49412i	−0.713325	−	0.542256i	−0.897704	+	0.440600i	$0.854766\pi$
$192$	0.725995	+	0.687699i	0.0523942	+	0.0496304i
$193$	1.49827	−	27.6339i	0.107848	−	1.98913i	−0.0350100	−	0.999387i	$-0.511146\pi$
$193$	1.49827	−	27.6339i	0.107848	−	1.98913i	0.142858	−	0.989743i	$-0.454371\pi$
$194$	−5.31867	−	3.20014i	−0.381858	−	0.229756i
$195$	8.33108	+	12.2874i	0.596601	+	0.879921i
$196$	−0.433440	−	1.56111i	−0.0309600	−	0.111508i
$197$	−14.9738	−	1.62850i	−1.06684	−	0.116026i	−0.442184	−	0.896924i	$-0.645796\pi$
$197$	−14.9738	−	1.62850i	−1.06684	−	0.116026i	−0.624658	+	0.780898i	$0.714762\pi$
$198$	−4.32990	+	3.29151i	−0.307713	+	0.233917i
$199$	14.5743	−	6.74279i	1.03315	−	0.477984i	0.171334	−	0.985213i	$-0.445192\pi$
$199$	14.5743	−	6.74279i	1.03315	−	0.477984i	0.861811	+	0.507229i	$0.169330\pi$
$200$	−1.17353	+	1.73082i	−0.0829809	+	0.122388i
$201$	11.7246	+	3.95046i	0.826986	+	0.278644i
$202$	−0.809696	+	4.93893i	−0.0569700	+	0.347502i
$203$	3.53151	+	21.5413i	0.247864	+	1.51190i
$204$	−1.62017	+	0.545900i	−0.113435	+	0.0382207i
$205$	4.98130	−	17.9410i	0.347909	−	1.25306i
$206$	1.10492	−	2.77313i	0.0769833	−	0.193213i
$207$	−2.35210	+	5.90332i	−0.163482	+	0.410309i
$208$	−1.49144	+	5.37167i	−0.103413	+	0.372459i
$209$	−14.2169	+	4.79022i	−0.983402	+	0.331347i
$210$	−0.999248	−	6.09514i	−0.0689546	−	0.420605i
$211$	0.233347	−	1.42335i	0.0160643	−	0.0979876i	−0.977577	−	0.210576i	$-0.932466\pi$
$211$	0.233347	−	1.42335i	0.0160643	−	0.0979876i	0.993642	+	0.112589i	$0.0359142\pi$
$212$	7.31163	+	2.46357i	0.502165	+	0.169199i
$213$	3.19058	−	4.70575i	0.218615	−	0.322433i
$214$	−13.3197	+	6.16234i	−0.910514	+	0.421249i
$215$	13.9860	−	10.6319i	0.953839	−	0.725089i
$216$	0.994138	+	0.108119i	0.0676425	+	0.00735657i
$217$	0.247407	+	0.891081i	0.0167951	+	0.0604905i
$218$	4.08175	+	6.02013i	0.276451	+	0.407734i
$219$	−6.47092	−	3.89342i	−0.437264	−	0.263093i
$220$	0.784120	−	14.4622i	0.0528653	−	0.975044i
$221$	−6.91961	−	6.55460i	−0.465463	−	0.440910i
$222$	−3.41666	−	2.59727i	−0.229311	−	0.174318i
$223$	16.7358	+	3.68382i	1.12071	+	0.246687i	0.736420	−	0.676525i	$-0.236515\pi$
$223$	16.7358	+	3.68382i	1.12071	+	0.246687i	0.384291	+	0.923212i	$0.374446\pi$
$224$	1.50158	−	1.76779i	0.100328	−	0.118116i
$225$	0.113213	+	2.08808i	0.00754751	+	0.139206i
$226$	5.81926	−	10.9763i	0.387092	−	0.730132i
$227$	−9.43035	+	2.07578i	−0.625915	+	0.137774i	−0.516591	−	0.856232i	$-0.672799\pi$
$227$	−9.43035	+	2.07578i	−0.625915	+	0.137774i	−0.109323	+	0.994006i	$0.534868\pi$
$228$	2.50336	+	1.15818i	0.165789	+	0.0767021i
$229$	8.54584	−	5.14186i	0.564725	−	0.339784i	−0.204395	−	0.978889i	$-0.565523\pi$
$229$	8.54584	−	5.14186i	0.564725	−	0.339784i	0.769120	+	0.639105i	$0.220695\pi$
$230$	−7.92637	−	14.9507i	−0.522650	−	0.985822i
$231$	8.16700	+	9.61493i	0.537349	+	0.632616i
$232$	6.83250	−	6.47209i	0.448576	−	0.424914i
$233$	−16.1543	+	1.75689i	−1.05830	+	0.115098i	−0.620683	−	0.784062i	$-0.713145\pi$
$233$	−16.1543	+	1.75689i	−1.05830	+	0.115098i	−0.437622	+	0.899159i	$0.644179\pi$
$234$	2.06347	+	5.17893i	0.134894	+	0.338557i
$235$	−4.40133			−0.287111
$236$	5.66928	+	5.18259i	0.369039	+	0.337358i
$237$	6.74807			0.438334
$238$	1.46778	+	3.68385i	0.0951420	+	0.238788i
$239$	−8.28882	+	0.901464i	−0.536159	+	0.0583108i	−0.372193	−	0.928155i	$-0.621394\pi$
$239$	−8.28882	+	0.901464i	−0.536159	+	0.0583108i	−0.163966	+	0.986466i	$0.552429\pi$
$240$	−1.93327	+	1.83129i	−0.124792	+	0.118209i
$241$	−12.3975	−	14.5955i	−0.798593	−	0.940177i	0.200627	−	0.979668i	$-0.435702\pi$
$241$	−12.3975	−	14.5955i	−0.798593	−	0.940177i	−0.999220	+	0.0394912i	$0.987426\pi$
$242$	8.70401	+	16.4175i	0.559515	+	1.05536i
$243$	0.856857	−	0.515554i	0.0549674	−	0.0330728i
$244$	4.03955	+	1.86889i	0.258606	+	0.119644i
$245$	4.21350	−	0.927462i	0.269191	−	0.0592533i
$246$	3.27521	−	6.17771i	0.208820	−	0.393876i
$247$	0.832501	+	15.3546i	0.0529708	+	0.976989i
$248$	0.258120	−	0.303882i	0.0163906	−	0.0192966i
$249$	15.1649	+	3.33805i	0.961038	+	0.211540i
$250$	6.16657	+	4.68770i	0.390008	+	0.296476i
$251$	−0.197116	−	0.186718i	−0.0124419	−	0.0117855i	0.681453	−	0.731862i	$-0.261348\pi$
$251$	−0.197116	−	0.186718i	−0.0124419	−	0.0117855i	−0.693895	+	0.720076i	$0.744107\pi$
$252$	0.125572	−	2.31605i	0.00791031	−	0.145897i
$253$	29.6152	+	17.8189i	1.86189	+	1.12026i
$254$	−7.37304	−	10.8744i	−0.462626	−	0.682322i
$255$	−1.21798	−	4.38677i	−0.0762729	−	0.274710i
$256$	−0.994138	−	0.108119i	−0.0621336	−	0.00675744i
$257$	19.7104	−	14.9834i	1.22950	−	0.934640i	0.230239	−	0.973134i	$-0.426049\pi$
$257$	19.7104	−	14.9834i	1.22950	−	0.934640i	0.999259	+	0.0384937i	$0.0122559\pi$
$258$	5.98763	−	2.77017i	0.372773	−	0.172463i
$259$	−5.58637	+	8.23928i	−0.347120	+	0.511964i
$260$	−14.0683	−	4.74018i	−0.872482	−	0.293973i
$261$	1.52257	−	9.28724i	0.0942445	−	0.574866i
$262$	2.81299	+	17.1585i	0.173787	+	1.06005i
$263$	−20.1461	+	6.78800i	−1.24226	+	0.418566i	−0.862281	−	0.506430i	$-0.830965\pi$
$263$	−20.1461	+	6.78800i	−1.24226	+	0.418566i	−0.379978	+	0.924996i	$0.624068\pi$
$264$	1.45507	−	5.24069i	0.0895534	−	0.322542i
$265$	−7.60479	+	19.0866i	−0.467158	+	1.17248i
$266$	2.36804	−	5.94333i	0.145194	−	0.364409i
$267$	2.03847	−	7.34191i	0.124752	−	0.449318i
$268$	−11.7246	+	3.95046i	−0.716191	+	0.241313i
$269$	−1.03919	−	6.33876i	−0.0633603	−	0.386481i	−0.999402	−	0.0345906i	$-0.988987\pi$
$269$	−1.03919	−	6.33876i	−0.0633603	−	0.386481i	0.936041	−	0.351890i	$-0.114461\pi$
$270$	−0.430813	+	2.62784i	−0.0262184	+	0.159925i
$271$	13.1371	+	4.42639i	0.798020	+	0.268884i	0.688628	−	0.725115i	$-0.258213\pi$
$271$	13.1371	+	4.42639i	0.798020	+	0.268884i	0.109391	+	0.993999i	$0.465110\pi$
$272$	0.959445	−	1.41507i	0.0581749	−	0.0858015i
$273$	11.7355	−	5.42943i	0.710266	−	0.328604i
$274$	−16.4766	+	12.5252i	−0.995387	+	0.756674i
$275$	11.3070	+	1.22971i	0.681837	+	0.0741542i
$276$	−1.70005	−	6.12302i	−0.102331	−	0.368563i
$277$	1.13113	+	1.66829i	0.0679629	+	0.100238i	0.860152	−	0.510038i	$-0.170369\pi$
$277$	1.13113	+	1.66829i	0.0679629	+	0.100238i	−0.792189	+	0.610276i	$0.791058\pi$
$278$	12.4989	+	7.52031i	0.749632	+	0.451038i
$279$	0.0215858	−	0.398126i	0.00129231	−	0.0238352i
$280$	4.48412	+	4.24758i	0.267977	+	0.253841i
$281$	18.1645	+	13.8083i	1.08361	+	0.823735i	0.985200	−	0.171411i	$-0.0548326\pi$
$281$	18.1645	+	13.8083i	1.08361	+	0.823735i	0.0984057	+	0.995146i	$0.468626\pi$
$282$	−1.61418	−	0.355308i	−0.0961230	−	0.0211583i
$283$	−13.2387	+	15.5858i	−0.786958	+	0.926479i	−0.998707	−	0.0508453i	$-0.983808\pi$
$283$	−13.2387	+	15.5858i	−0.786958	+	0.926479i	0.211748	+	0.977324i	$0.432084\pi$
$284$	0.307802	+	5.67707i	0.0182647	+	0.336872i
$285$	−3.44051	+	6.48950i	−0.203798	+	0.384405i
$286$	29.6125	−	6.51821i	1.75103	−	0.385430i
$287$	−14.7191	−	6.80980i	−0.868843	−	0.401970i
$288$	−0.856857	+	0.515554i	−0.0504908	+	0.0303793i
$289$	−6.59380	−	12.4372i	−0.387871	−	0.731601i
$290$	16.2244	+	19.1008i	0.952728	+	1.12164i
$291$	4.50639	−	4.26868i	0.264169	−	0.250234i
$292$	7.50765	−	0.816506i	0.439352	−	0.0477824i
$293$	0.463065	+	1.16220i	0.0270525	+	0.0678967i	0.941882	−	0.335943i	$-0.109055\pi$
$293$	0.463065	+	1.16220i	0.0270525	+	0.0678967i	−0.914830	+	0.403839i	$0.867675\pi$
$294$	1.62016			0.0944898
$295$	−14.5979	+	14.3276i	−0.849923	+	0.834183i
$296$	4.29178			0.249455
$297$	−2.01316	−	5.05265i	−0.116815	−	0.293185i
$298$	−6.50387	+	0.707339i	−0.376759	+	0.0409750i
$299$	25.7194	−	24.3627i	1.48739	−	1.40893i
$300$	−1.35378	−	1.59380i	−0.0781607	−	0.0920179i
$301$	−7.16772	−	13.5198i	−0.413141	−	0.779266i
$302$	14.7027	−	8.84632i	0.846045	−	0.509049i
$303$	−4.54229	−	2.10149i	−0.260947	−	0.120727i
$304$	−2.69380	+	0.592951i	−0.154500	+	0.0340081i
$305$	−5.55179	+	10.4718i	−0.317895	+	0.599613i
$306$	−0.0925597	−	1.70716i	−0.00529128	−	0.0975920i
$307$	5.47426	−	6.44480i	0.312433	−	0.367824i	−0.583424	−	0.812168i	$-0.698287\pi$
$307$	5.47426	−	6.44480i	0.312433	−	0.367824i	0.895856	+	0.444344i	$0.146563\pi$
$308$	−12.3204	−	2.71193i	−0.702020	−	0.154526i
$309$	2.37646	+	1.80654i	0.135192	+	0.102770i
$310$	0.770816	+	0.730156i	0.0437794	+	0.0414701i
$311$	0.531326	−	9.79972i	0.0301287	−	0.555691i	−0.944035	−	0.329847i	$-0.893003\pi$
$311$	0.531326	−	9.79972i	0.0301287	−	0.555691i	0.974163	−	0.225845i	$-0.0725142\pi$
$312$	−4.77687	−	2.87415i	−0.270437	−	0.162717i
$313$	11.2649	+	16.6145i	0.636731	+	0.939107i	0.999973	+	0.00741253i	$0.00235950\pi$
$313$	11.2649	+	16.6145i	0.636731	+	0.939107i	−0.363242	+	0.931695i	$0.618330\pi$
$314$	3.17913	+	11.4502i	0.179409	+	0.646172i
$315$	6.14030	+	0.667798i	0.345967	+	0.0376261i
$316$	−5.37209	+	4.08376i	−0.302204	+	0.229729i
$317$	12.8334	−	5.93738i	0.720798	−	0.333477i	−0.0249646	−	0.999688i	$-0.507947\pi$
$317$	12.8334	−	5.93738i	0.720798	−	0.333477i	0.745763	+	0.666212i	$0.232085\pi$
$318$	−4.32985	+	6.38604i	−0.242806	+	0.358112i
$319$	−48.5076	−	16.3441i	−2.71590	−	0.915095i
$320$	0.430813	−	2.62784i	0.0240832	−	0.146901i
$321$	−2.37433	−	14.4828i	−0.132522	−	0.808349i
$322$	−13.9677	+	4.70627i	−0.778390	+	0.262270i
$323$	1.26160	−	4.54388i	0.0701974	−	0.252828i
$324$	−0.370138	+	0.928977i	−0.0205632	+	0.0516098i
$325$	4.31504	−	10.8299i	0.239355	−	0.600736i
$326$	2.90598	−	10.4664i	0.160948	−	0.579681i
$327$	−6.89267	+	2.32241i	−0.381166	+	0.128430i
$328$	1.13121	+	6.90011i	0.0624609	+	0.380995i
$329$	−0.620213	+	3.78313i	−0.0341934	+	0.208571i
$330$	13.7253	+	4.62460i	0.755554	+	0.254576i
$331$	9.92394	−	14.6367i	0.545469	−	0.804507i	−0.450634	−	0.892709i	$-0.648802\pi$
$331$	9.92394	−	14.6367i	0.545469	−	0.804507i	0.996103	+	0.0882024i	$0.0281122\pi$
$332$	−14.0928	+	6.52002i	−0.773443	+	0.357833i
$333$	3.41666	−	2.59727i	0.187232	−	0.142330i
$334$	11.3244	+	1.23161i	0.619645	+	0.0673904i
$335$	−8.81404	−	31.7453i	−0.481562	−	1.73443i
$336$	1.30164	+	1.91978i	0.0710105	+	0.104733i
$337$	13.6277	+	8.19952i	0.742349	+	0.446656i	0.835847	−	0.548963i	$-0.184977\pi$
$337$	13.6277	+	8.19952i	0.742349	+	0.446656i	−0.0934980	+	0.995619i	$0.529805\pi$
$338$	0.978791	−	18.0527i	0.0532392	−	0.981940i
$339$	9.01939	+	8.54362i	0.489866	+	0.464026i
$340$	3.62439	+	2.75519i	0.196560	+	0.149421i
$341$	−2.11787	−	0.466178i	−0.114689	−	0.0252449i
$342$	−1.78568	+	2.10227i	−0.0965585	+	0.113677i
$343$	−1.08245	−	19.9647i	−0.0584470	−	1.07799i
$344$	−3.09027	+	5.82887i	−0.166616	+	0.314272i
$345$	16.5263	−	3.63771i	0.889746	−	0.195848i
$346$	3.04616	+	1.40931i	0.163763	+	0.0757647i
$347$	28.9817	−	17.4377i	1.55582	−	0.936105i	0.561754	−	0.827304i	$-0.310127\pi$
$347$	28.9817	−	17.4377i	1.55582	−	0.936105i	0.994064	−	0.108800i	$-0.0347009\pi$
$348$	4.40830	+	8.31493i	0.236309	+	0.445727i
$349$	−1.35287	−	1.59272i	−0.0724174	−	0.0852564i	0.724760	−	0.689001i	$-0.241950\pi$
$349$	−1.35287	−	1.59272i	−0.0724174	−	0.0852564i	−0.797178	+	0.603745i	$0.793675\pi$
$350$	−3.52131	+	3.33556i	−0.188222	+	0.178293i
$351$	−5.54220	+	0.602750i	−0.295821	+	0.0321724i
$352$	2.01316	+	5.05265i	0.107302	+	0.269307i
$353$	−10.8124			−0.575486			−0.287743	−	0.957708i	$-0.592905\pi$
$353$	−10.8124			−0.575486			−0.287743	+	0.957708i	$0.592905\pi$
$354$	−6.51038	+	4.07615i	−0.346023	+	0.216645i
$355$	−15.1398			−0.803537
$356$	2.82032	+	7.07847i	0.149477	+	0.375158i
$357$	−3.94224	+	0.428745i	−0.208646	+	0.0226916i
$358$	3.43356	−	3.25244i	0.181469	−	0.171897i
$359$	12.2450	+	14.4159i	0.646265	+	0.760842i	0.983565	−	0.180556i	$-0.0577896\pi$
$359$	12.2450	+	14.4159i	0.646265	+	0.760842i	−0.337300	+	0.941397i	$0.609514\pi$
$360$	−1.24733	−	2.35272i	−0.0657403	−	0.123999i
$361$	9.76117	−	5.87310i	0.513746	−	0.309111i
$362$	22.5295	+	10.4232i	1.18412	+	0.547834i
$363$	−18.1477	+	3.99460i	−0.952505	+	0.209662i
$364$	−6.05682	+	11.4244i	−0.317464	+	0.598800i
$365$	1.08874	+	20.0807i	0.0569874	+	1.05107i
$366$	−2.88147	+	3.39233i	−0.150617	+	0.177320i
$367$	26.1584	+	5.75790i	1.36546	+	0.300560i	0.836444	−	0.548053i	$-0.184631\pi$
$367$	26.1584	+	5.75790i	1.36546	+	0.300560i	0.529014	+	0.848613i	$0.322562\pi$
$368$	5.05889	+	3.84567i	0.263713	+	0.200469i
$369$	5.07632	+	4.80854i	0.264263	+	0.250323i
$370$	−0.618736	+	11.4119i	−0.0321665	+	0.593277i
$371$	15.3341	+	9.22621i	0.796106	+	0.479001i
$372$	0.223752	+	0.330009i	0.0116010	+	0.0171102i
$373$	0.478448	+	1.72321i	0.0247731	+	0.0892246i	0.974903	−	0.222629i	$-0.0714639\pi$
$373$	0.478448	+	1.72321i	0.0247731	+	0.0892246i	−0.950130	+	0.311854i	$0.899050\pi$
$374$	−9.24429	−	1.00538i	−0.478011	−	0.0519868i
$375$	−6.16657	+	4.68770i	−0.318440	+	0.242072i
$376$	1.50006	−	0.694002i	0.0773597	−	0.0357904i
$377$	−29.4435	+	43.4259i	−1.51642	+	2.23655i
$378$	2.19803	+	0.740603i	0.113055	+	0.0380925i
$379$	−1.67058	+	10.1901i	−0.0858119	+	0.523429i	0.908583	+	0.417703i	$0.137165\pi$
$379$	−1.67058	+	10.1901i	−0.0858119	+	0.523429i	−0.994395	+	0.105726i	$0.966283\pi$
$380$	−1.18831	−	7.24835i	−0.0609589	−	0.371833i
$381$	12.4505	−	4.19508i	0.637861	−	0.214920i
$382$	−3.31291	+	11.9320i	−0.169503	+	0.610496i
$383$	−0.767703	+	1.92679i	−0.0392278	+	0.0984543i	−0.947285	−	0.320391i	$-0.896186\pi$
$383$	−0.767703	+	1.92679i	−0.0392278	+	0.0984543i	0.908058	+	0.418845i	$0.137565\pi$
$384$	0.370138	−	0.928977i	0.0188885	−	0.0474066i
$385$	8.98726	−	32.3692i	0.458033	−	1.64969i
$386$	−26.2258	+	8.83650i	−1.33486	+	0.449766i
$387$	1.06734	+	6.51048i	0.0542559	+	0.330946i
$388$	−1.00421	+	6.12541i	−0.0509810	+	0.310971i
$389$	16.2786	+	5.48491i	0.825360	+	0.278096i	0.700115	−	0.714030i	$-0.253132\pi$
$389$	16.2786	+	5.48491i	0.825360	+	0.278096i	0.125244	+	0.992126i	$0.460028\pi$
$390$	8.33108	−	12.2874i	0.421861	−	0.622198i
$391$	−9.86022	+	4.56182i	−0.498653	+	0.230701i
$392$	−1.28980	+	0.980481i	−0.0651448	+	0.0495218i
$393$	−17.2856	−	1.87992i	−0.871944	−	0.0948296i
$394$	4.02955	+	14.5131i	0.203006	+	0.731161i
$395$	−10.0843	−	14.8732i	−0.507396	−	0.748353i
$396$	4.66040	+	2.80407i	0.234194	+	0.140910i
$397$	−0.902865	+	16.6524i	−0.0453135	+	0.835759i	0.884231	+	0.467049i	$0.154683\pi$
$397$	−0.902865	+	16.6524i	−0.0453135	+	0.835759i	−0.929545	+	0.368709i	$0.879800\pi$
$398$	−11.6584	−	11.0434i	−0.584383	−	0.553557i
$399$	5.09317	+	3.87173i	0.254978	+	0.193829i
$400$	2.04226	+	0.449536i	0.102113	+	0.0224768i
$401$	−2.77454	+	3.26644i	−0.138554	+	0.163118i	−0.827063	−	0.562110i	$-0.809990\pi$
$401$	−2.77454	+	3.26644i	−0.138554	+	0.163118i	0.688509	+	0.725228i	$0.258266\pi$
$402$	−0.669817	−	12.3541i	−0.0334074	−	0.616164i
$403$	−1.04116	+	1.96384i	−0.0518640	+	0.0978258i
$404$	4.88785	−	1.07590i	0.243179	−	0.0535278i
$405$	−2.41680	−	1.11813i	−0.120092	−	0.0555604i
$406$	18.7042	−	11.2539i	0.928273	−	0.558524i
$407$	−10.9339	−	20.6236i	−0.541975	−	1.02227i
$408$	1.10682	+	1.30305i	0.0547956	+	0.0645104i
$409$	22.2977	−	21.1215i	1.10255	−	1.04439i	0.103789	−	0.994599i	$-0.466903\pi$
$409$	22.2977	−	21.1215i	1.10255	−	1.04439i	0.998760	−	0.0497905i	$-0.0158553\pi$
$410$	−18.5106	+	2.01315i	−0.914172	+	0.0994222i
$411$	−7.66068	−	19.2269i	−0.377874	−	0.948391i
$412$	−2.98515			−0.147068
$413$	10.2581	+	14.5665i	0.504767	+	0.716770i
$414$	6.35465			0.312314
$415$	−15.3051	−	38.4129i	−0.751299	−	1.88562i
$416$	5.54220	−	0.602750i	0.271729	−	0.0295523i
$417$	−10.5900	+	10.0314i	−0.518594	+	0.491239i
$418$	9.71221	+	11.4341i	0.475040	+	0.559260i
$419$	1.25151	+	2.36061i	0.0611405	+	0.115323i	0.912199	−	0.409748i	$-0.134383\pi$
$419$	1.25151	+	2.36061i	0.0611405	+	0.115323i	−0.851058	+	0.525071i	$0.824039\pi$
$420$	−5.29238	+	3.18432i	−0.258242	+	0.155379i
$421$	18.1396	+	8.39227i	0.884069	+	0.409014i	0.808755	−	0.588146i	$-0.200142\pi$
$421$	18.1396	+	8.39227i	0.884069	+	0.409014i	0.0753145	+	0.997160i	$0.476004\pi$
$422$	−1.40863	+	0.310063i	−0.0685711	+	0.0150936i
$423$	0.774196	−	1.46029i	0.0376427	−	0.0710016i
$424$	−0.417709	−	7.70420i	−0.0202858	−	0.374149i
$425$	−2.31452	+	2.72487i	−0.112271	+	0.132175i
$426$	−5.55249	−	1.22219i	−0.269019	−	0.0592155i
$427$	8.21862	+	6.24763i	0.397727	+	0.302344i
$428$	10.6548	+	10.0928i	0.515019	+	0.487851i
$429$	−1.64157	+	30.2770i	−0.0792557	+	1.46179i
$430$	−15.0535	−	9.05742i	−0.725946	−	0.436787i
$431$	5.25477	+	7.75021i	0.253114	+	0.373315i	0.932924	−	0.360073i	$-0.117248\pi$
$431$	5.25477	+	7.75021i	0.253114	+	0.373315i	−0.679810	+	0.733388i	$0.737938\pi$
$432$	−0.267528	−	0.963550i	−0.0128715	−	0.0463588i
$433$	−15.3095	−	1.66500i	−0.735725	−	0.0800150i	−0.267418	−	0.963581i	$-0.586170\pi$
$433$	−15.3095	−	1.66500i	−0.735725	−	0.0800150i	−0.468307	+	0.883566i	$0.655136\pi$
$434$	0.736219	−	0.559659i	0.0353396	−	0.0268645i
$435$	−22.7451	+	10.5230i	−1.09054	+	0.504539i
$436$	4.08175	−	6.02013i	0.195480	−	0.288312i
$437$	16.6104	+	5.59671i	0.794585	+	0.267727i
$438$	−1.22177	+	7.45244i	−0.0583782	+	0.356091i
$439$	−2.07899	−	12.6813i	−0.0992249	−	0.605245i	−0.988892	−	0.148635i	$-0.952512\pi$
$439$	−2.07899	−	12.6813i	−0.0992249	−	0.605245i	0.889667	−	0.456610i	$-0.150936\pi$
$440$	−13.7253	+	4.62460i	−0.654329	+	0.220469i
$441$	−0.433440	+	1.56111i	−0.0206400	+	0.0743385i
$442$	−3.52786	+	8.85426i	−0.167803	+	0.421154i
$443$	−9.09342	+	22.8228i	−0.432041	+	1.08434i	0.538332	+	0.842733i	$0.319055\pi$
$443$	−9.09342	+	22.8228i	−0.432041	+	1.08434i	−0.970374	+	0.241609i	$0.922325\pi$
$444$	−1.14817	+	4.13534i	−0.0544899	+	0.196255i
$445$	−19.2284	+	6.47879i	−0.911512	+	0.307124i
$446$	−2.77236	−	16.9107i	−0.131275	−	0.800744i
$447$	1.05841	−	6.45604i	0.0500613	−	0.305360i
$448$	−2.19803	−	0.740603i	−0.103847	−	0.0349902i
$449$	13.3714	−	19.7213i	0.631034	−	0.930706i	−0.368965	−	0.929443i	$-0.620288\pi$
$449$	13.3714	−	19.7213i	0.631034	−	0.930706i	0.999999	−	0.00126275i	$-0.000401946\pi$
$450$	1.89788	−	0.878052i	0.0894668	−	0.0413918i
$451$	30.2756	−	23.0149i	1.42562	−	1.08373i
$452$	−12.3507	−	1.34321i	−0.580926	−	0.0631795i
$453$	4.59048	+	16.5334i	0.215680	+	0.776808i
$454$	5.41888	+	7.99226i	0.254321	+	0.375095i
$455$	−29.5044	−	17.7522i	−1.38319	−	0.832236i
$456$	0.149331	−	2.75425i	0.00699306	−	0.128979i
$457$	−26.9020	−	25.4829i	−1.25842	−	1.19204i	−0.972271	−	0.233855i	$-0.924866\pi$
$457$	−26.9020	−	25.4829i	−1.25842	−	1.19204i	−0.286150	−	0.958185i	$-0.592376\pi$
$458$	−7.93981	−	6.03569i	−0.371003	−	0.282029i
$459$	1.66970	+	0.367528i	0.0779349	+	0.0171548i
$460$	−10.9550	+	12.8973i	−0.510781	+	0.601337i
$461$	−0.211159	−	3.89461i	−0.00983468	−	0.181390i	−0.999323	−	0.0367798i	$-0.988290\pi$
$461$	−0.211159	−	3.89461i	−0.00983468	−	0.181390i	0.989489	−	0.144610i	$-0.0461928\pi$
$462$	5.90913	−	11.1458i	0.274918	−	0.518550i
$463$	−5.28414	+	1.16313i	−0.245575	+	0.0540551i	−0.336052	−	0.941843i	$-0.609092\pi$
$463$	−5.28414	+	1.16313i	−0.245575	+	0.0540551i	0.0904771	+	0.995899i	$0.471161\pi$
$464$	−8.54139	−	3.95167i	−0.396524	−	0.183452i
$465$	−0.909757	+	0.547382i	−0.0421889	+	0.0253842i
$466$	7.61144	+	14.3567i	0.352593	+	0.665061i
$467$	13.4730	+	15.8616i	0.623455	+	0.733988i	0.979714	−	0.200399i	$-0.0642240\pi$
$467$	13.4730	+	15.8616i	0.623455	+	0.733988i	−0.356260	+	0.934387i	$0.615948\pi$
$468$	4.04734	−	3.83384i	0.187088	−	0.177219i
$469$	−28.5284	+	3.10266i	−1.31732	+	0.143267i
$470$	1.62910	+	4.08874i	0.0751449	+	0.188599i
$471$	−11.8834			−0.547556
$472$	2.71608	−	7.18491i	0.125018	−	0.330712i
$473$	35.8828			1.64989
$474$	−2.49772	−	6.26880i	−0.114724	−	0.287936i
$475$	5.73419	−	0.623631i	0.263103	−	0.0286142i
$476$	2.87893	−	2.72706i	0.131955	−	0.124995i
$477$	−4.99492	−	5.88047i	−0.228702	−	0.269248i
$478$	3.90545	+	7.36646i	0.178631	+	0.336934i
$479$	34.6558	−	20.8517i	1.58346	−	0.952738i	0.594580	−	0.804036i	$-0.297318\pi$
$479$	34.6558	−	20.8517i	1.58346	−	0.952738i	0.988882	−	0.148701i	$-0.0475093\pi$
$480$	2.41680	+	1.11813i	0.110311	+	0.0510355i
$481$	−23.3668	+	5.14341i	−1.06543	+	0.234519i
$482$	−8.97006	+	16.9193i	−0.408575	+	0.770654i
$483$	−0.797968	−	14.7177i	−0.0363088	−	0.669676i
$484$	12.0298	−	14.1626i	0.546809	−	0.643753i
$485$	−16.1428	−	3.55330i	−0.733006	−	0.161347i
$486$	−0.796093	−	0.605174i	−0.0361115	−	0.0274513i
$487$	5.90926	+	5.59755i	0.267774	+	0.253649i	0.809791	−	0.586718i	$-0.199580\pi$
$487$	5.90926	+	5.59755i	0.267774	+	0.253649i	−0.542017	+	0.840368i	$0.682339\pi$
$488$	0.240968	−	4.44440i	0.0109081	−	0.201188i
$489$	9.30748	+	5.60012i	0.420899	+	0.253246i
$490$	−2.42117	−	3.57095i	−0.109377	−	0.161319i
$491$	5.46844	+	19.6955i	0.246787	+	0.888847i	0.978330	+	0.207052i	$0.0663869\pi$
$491$	5.46844	+	19.6955i	0.246787	+	0.888847i	−0.731543	+	0.681796i	$0.761199\pi$
$492$	−6.95123	−	0.755992i	−0.313386	−	0.0340827i
$493$	12.8092	−	9.73730i	0.576897	−	0.438546i
$494$	13.9559	−	6.45669i	0.627906	−	0.290500i
$495$	−8.12794	+	11.9878i	−0.365324	+	0.538812i
$496$	−0.377840	−	0.127309i	−0.0169655	−	0.00571635i
$497$	−2.13342	+	13.0133i	−0.0956970	+	0.583726i
$498$	−2.51214	−	15.3234i	−0.112572	−	0.686658i
$499$	0.383449	−	0.129199i	0.0171655	−	0.00578374i	−0.310706	−	0.950506i	$-0.600565\pi$
$499$	0.383449	−	0.129199i	0.0171655	−	0.00578374i	0.327871	+	0.944722i	$0.393669\pi$
$500$	2.07228	−	7.46369i	0.0926754	−	0.333786i
$501$	−4.21632	+	10.5822i	−0.188371	+	0.472776i
$502$	−0.100497	+	0.252228i	−0.00448539	+	0.0112575i
$503$	−4.31685	+	15.5479i	−0.192479	+	0.693246i	0.802805	+	0.596242i	$0.203340\pi$
$503$	−4.31685	+	15.5479i	−0.192479	+	0.693246i	−0.995284	+	0.0970047i	$0.969074\pi$
$504$	−2.19803	+	0.740603i	−0.0979081	+	0.0329891i
$505$	2.15616	+	13.1520i	0.0959477	+	0.585255i
$506$	5.59160	−	34.1073i	0.248577	−	1.51625i
$507$	17.1329	+	5.77273i	0.760897	+	0.256376i
$508$	−7.37304	+	10.8744i	−0.327126	+	0.482474i
$509$	14.0438	−	6.49734i	0.622479	−	0.287990i	−0.0831870	−	0.996534i	$-0.526510\pi$
$509$	14.0438	−	6.49734i	0.622479	−	0.287990i	0.705666	+	0.708544i	$0.250648\pi$
$510$	−3.62439	+	2.75519i	−0.160491	+	0.122002i
$511$	17.4136	+	1.89384i	0.770333	+	0.0837787i
$512$	0.267528	+	0.963550i	0.0118232	+	0.0425833i
$513$	−1.54792	−	2.28301i	−0.0683422	−	0.100797i
$514$	−21.2148	−	12.7645i	−0.935745	−	0.563019i
$515$	0.430362	−	7.93756i	0.0189640	−	0.349771i
$516$	−4.78967	−	4.53702i	−0.210854	−	0.199731i
$517$	−7.15656	−	5.44028i	−0.314745	−	0.239263i
$518$	9.72183	+	2.13994i	0.427152	+	0.0940234i
$519$	−2.17287	+	2.55810i	−0.0953785	+	0.112288i
$520$	0.803717	+	14.8237i	0.0352453	+	0.650062i
$521$	−9.59703	+	18.1019i	−0.420453	+	0.793059i	−0.999757	−	0.0220528i	$-0.992980\pi$
$521$	−9.59703	+	18.1019i	−0.420453	+	0.793059i	0.579303	+	0.815112i	$0.303325\pi$
$522$	−9.19119	+	2.02313i	−0.402288	+	0.0885502i
$523$	1.80457	+	0.834882i	0.0789082	+	0.0365068i	0.458946	−	0.888464i	$-0.348227\pi$
$523$	1.80457	+	0.834882i	0.0789082	+	0.0365068i	−0.380038	+	0.924971i	$0.624089\pi$
$524$	14.8986	−	8.96421i	0.650850	−	0.391603i
$525$	−2.27193	−	4.28531i	−0.0991551	−	0.187026i
$526$	13.7627	+	16.2027i	0.600083	+	0.706472i
$527$	0.494885	−	0.468780i	0.0215575	−	0.0204204i
$528$	−5.40706	+	0.588053i	−0.235312	+	0.0255917i
$529$	−6.43357	−	16.1471i	−0.279721	−	0.702046i
$530$	20.5458			0.892453
$531$	−2.18586	−	7.36356i	−0.0948584	−	0.319551i
$532$	−6.39771			−0.277376
$533$	−14.4283	−	36.2122i	−0.624957	−	1.56853i
$534$	−7.57498	+	0.823829i	−0.327801	+	0.0356506i
$535$	−28.3729	+	26.8762i	−1.22667	+	1.16196i
$536$	8.00959	+	9.42962i	0.345962	+	0.407298i
$537$	2.21531	+	4.17852i	0.0955978	+	0.180316i
$538$	−5.50392	+	3.31160i	−0.237291	+	0.142773i
$539$	7.99753	+	3.70005i	0.344478	+	0.159373i
$540$	2.60066	−	0.572449i	0.111915	−	0.0246343i
$541$	16.4482	−	31.0245i	0.707162	−	1.33385i	−0.225906	−	0.974149i	$-0.572534\pi$
$541$	16.4482	−	31.0245i	0.707162	−	1.33385i	0.933068	−	0.359700i	$-0.117121\pi$
$542$	−0.750513	−	13.8424i	−0.0322373	−	0.594582i
$543$	−16.0706	+	18.9198i	−0.689655	+	0.811925i
$544$	−1.66970	−	0.367528i	−0.0715877	−	0.0157577i
$545$	15.4192	+	11.7213i	0.660484	+	0.502087i
$546$	−9.38758	−	8.89239i	−0.401751	−	0.380559i
$547$	1.42702	−	26.3199i	0.0610151	−	1.12536i	−0.794393	−	0.607404i	$-0.792211\pi$
$547$	1.42702	−	26.3199i	0.0610151	−	1.12536i	0.855408	−	0.517954i	$-0.173306\pi$
$548$	17.7342	+	10.6703i	0.757568	+	0.455814i
$549$	−2.49780	−	3.68398i	−0.106604	−	0.157229i
$550$	−3.04277	−	10.9591i	−0.129744	−	0.467297i
$551$	−25.8067	−	2.80665i	−1.09940	−	0.119567i
$552$	−5.05889	+	3.84567i	−0.215321	+	0.163683i
$553$	−14.2052	+	6.57202i	−0.604066	+	0.279471i
$554$	1.13113	−	1.66829i	0.0480570	−	0.0708788i
$555$	−10.8304	−	3.64919i	−0.459726	−	0.154900i
$556$	2.35989	−	14.3947i	0.100082	−	0.610471i
$557$	0.299265	+	1.82544i	0.0126803	+	0.0773462i	0.992409	−	0.122985i	$-0.0392466\pi$
$557$	0.299265	+	1.82544i	0.0126803	+	0.0773462i	−0.979728	+	0.200331i	$0.935798\pi$
$558$	−0.377840	+	0.127309i	−0.0159952	+	0.00538942i
$559$	9.83959	−	35.4390i	0.416170	−	1.49891i
$560$	2.28616	−	5.73783i	0.0966079	−	0.242468i
$561$	3.44184	−	8.63836i	0.145315	−	0.364712i
$562$	6.10422	−	21.9854i	0.257491	−	0.927399i
$563$	−28.8114	+	9.70768i	−1.21425	+	0.409130i	−0.852294	−	0.523064i	$-0.824789\pi$
$563$	−28.8114	+	9.70768i	−1.21425	+	0.409130i	−0.361960	+	0.932193i	$0.617892\pi$
$564$	0.267397	+	1.63105i	0.0112594	+	0.0686795i
$565$	5.35220	−	32.6469i	0.225169	−	1.37347i
$566$	19.3790	+	6.52954i	0.814559	+	0.274457i
$567$	−1.30164	+	1.91978i	−0.0546639	+	0.0806232i
$568$	5.15994	−	2.38724i	0.216506	−	0.100166i
$569$	−24.5524	+	18.6642i	−1.02929	+	0.782445i	−0.976359	−	0.216153i	$-0.930649\pi$
$569$	−24.5524	+	18.6642i	−1.02929	+	0.782445i	−0.0529292	+	0.998598i	$0.516856\pi$
$570$	7.30206	+	0.794147i	0.305850	+	0.0332631i
$571$	−5.11009	−	18.4049i	−0.213851	−	0.770221i	−0.990169	−	0.139879i	$-0.955329\pi$
$571$	−5.11009	−	18.4049i	−0.213851	−	0.770221i	0.776318	−	0.630342i	$-0.217085\pi$
$572$	−17.0160	−	25.0967i	−0.711475	−	1.04935i
$573$	−10.6108	−	6.38432i	−0.443273	−	0.266709i
$574$	−0.878029	+	16.1943i	−0.0366482	+	0.675937i
$575$	−9.64741	−	9.13852i	−0.402325	−	0.381102i
$576$	0.796093	+	0.605174i	0.0331705	+	0.0252156i
$577$	−28.8023	−	6.33987i	−1.19906	−	0.263932i	−0.429831	−	0.902909i	$-0.641427\pi$
$577$	−28.8023	−	6.33987i	−1.19906	−	0.263932i	−0.769226	+	0.638977i	$0.779358\pi$
$578$	−9.11328	+	10.7290i	−0.379062	+	0.446267i
$579$	−1.49827	−	27.6339i	−0.0622658	−	1.14842i
$580$	11.7389	−	22.1420i	0.487433	−	0.919396i
$581$	−35.1743	+	7.74244i	−1.45927	+	0.321210i
$582$	−5.63348	−	2.60633i	−0.233515	−	0.108036i
$583$	−35.9573	+	21.6348i	−1.48920	+	0.896023i
$584$	−3.53738	−	6.67221i	−0.146378	−	0.276098i
$585$	9.61075	+	11.3146i	0.397356	+	0.467803i
$586$	0.908263	−	0.860353i	0.0375200	−	0.0355408i
$587$	−8.31959	+	0.904810i	−0.343386	+	0.0373455i	−0.278188	−	0.960527i	$-0.589734\pi$
$587$	−8.31959	+	0.904810i	−0.343386	+	0.0373455i	−0.0651988	+	0.997872i	$0.520768\pi$
$588$	−0.599684	−	1.50509i	−0.0247306	−	0.0620690i
$589$	−1.09976			−0.0453149
$590$	18.7132	+	8.25795i	0.770411	+	0.339974i
$591$	−15.0621			−0.619574
$592$	−1.58855	−	3.98696i	−0.0652891	−	0.163863i
$593$	9.57675	−	1.04153i	0.393270	−	0.0427707i	0.0906520	−	0.995883i	$-0.471105\pi$
$593$	9.57675	−	1.04153i	0.393270	−	0.0427707i	0.302618	+	0.953112i	$0.402139\pi$
$594$	−3.94865	+	3.74036i	−0.162015	+	0.153469i
$595$	6.83626	+	8.04827i	0.280259	+	0.329947i
$596$	3.06443	+	5.78013i	0.125524	+	0.236764i
$597$	13.7598	−	8.27903i	0.563153	−	0.338838i
$598$	−32.1521	−	14.8752i	−1.31480	−	0.608290i
$599$	45.7440	−	10.0690i	1.86905	−	0.411409i	0.872091	−	0.489344i	$-0.162764\pi$
$599$	45.7440	−	10.0690i	1.86905	−	0.411409i	0.996958	+	0.0779349i	$0.0248326\pi$
$600$	−0.979513	+	1.84756i	−0.0399885	+	0.0754262i
$601$	1.43869	+	26.5350i	0.0586852	+	1.08239i	0.868497	+	0.495695i	$0.165087\pi$
$601$	1.43869	+	26.5350i	0.0586852	+	1.08239i	−0.809811	+	0.586690i	$0.800431\pi$
$602$	−9.90650	+	11.6628i	−0.403759	+	0.475341i
$603$	12.0829	+	2.65966i	0.492055	+	0.108310i
$604$	−13.6601	−	10.3841i	−0.555820	−	0.422523i
$605$	35.9242	+	34.0292i	1.46053	+	1.38348i
$606$	−0.270958	+	4.99752i	−0.0110069	+	0.203010i
$607$	−12.6099	−	7.58710i	−0.511819	−	0.307951i	0.236114	−	0.971725i	$-0.424126\pi$
$607$	−12.6099	−	7.58710i	−0.511819	−	0.307951i	−0.747933	+	0.663774i	$0.768954\pi$
$608$	1.54792	+	2.28301i	0.0627763	+	0.0925882i
$609$	5.83983	+	21.0332i	0.236642	+	0.852307i
$610$	11.7830	+	1.28148i	0.477079	+	0.0518855i
$611$	−7.33542	+	5.57624i	−0.296759	+	0.225591i
$612$	−1.55165	+	0.717872i	−0.0627219	+	0.0290182i
$613$	−4.61311	+	6.80383i	−0.186322	+	0.274804i	−0.909365	−	0.415998i	$-0.863432\pi$
$613$	−4.61311	+	6.80383i	−0.186322	+	0.274804i	0.723044	+	0.690802i	$0.242743\pi$
$614$	−8.01330	−	2.70000i	−0.323391	−	0.108963i
$615$	3.01234	−	18.3744i	0.121469	−	0.740929i
$616$	2.04094	+	12.4492i	0.0822316	+	0.501591i
$617$	18.4620	−	6.22057i	0.743252	−	0.250431i	0.0779008	−	0.996961i	$-0.475178\pi$
$617$	18.4620	−	6.22057i	0.743252	−	0.250431i	0.665351	+	0.746530i	$0.268282\pi$
$618$	0.798612	−	2.87634i	0.0321249	−	0.115703i
$619$	−14.0379	+	35.2324i	−0.564229	+	1.41611i	0.319264	+	0.947666i	$0.396564\pi$
$619$	−14.0379	+	35.2324i	−0.564229	+	1.41611i	−0.883493	+	0.468443i	$0.844815\pi$
$620$	0.392989	−	0.986328i	0.0157828	−	0.0396119i
$621$	−1.70005	+	6.12302i	−0.0682206	+	0.245708i
$622$	−9.30038	+	3.13366i	−0.372911	+	0.125648i
$623$	2.85923	+	17.4405i	0.114553	+	0.698741i
$624$	−0.901915	+	5.50144i	−0.0361055	+	0.220234i
$625$	29.4558	+	9.92480i	1.17823	+	0.396992i
$626$	11.2649	−	16.6145i	0.450237	−	0.664049i
$627$	−13.6156	+	6.29926i	−0.543755	+	0.251568i
$628$	9.46025	−	7.19150i	0.377505	−	0.286972i
$629$	7.29451	+	0.793326i	0.290851	+	0.0316320i
$630$	−1.65239	−	5.95137i	−0.0658328	−	0.237108i
$631$	−10.6068	−	15.6439i	−0.422250	−	0.622772i	0.555757	−	0.831345i	$-0.312428\pi$
$631$	−10.6068	−	15.6439i	−0.422250	−	0.622772i	−0.978007	+	0.208573i	$0.933118\pi$
$632$	5.78213	+	3.47899i	0.230001	+	0.138387i
$633$	0.0780874	−	1.44024i	0.00310370	−	0.0572443i
$634$	−10.2658	−	9.72432i	−0.407709	−	0.386202i
$635$	−27.8523	−	21.1728i	−1.10529	−	0.840216i
$636$	7.53513	+	1.65861i	0.298787	+	0.0657680i
$637$	5.84733	−	6.88401i	0.231680	−	0.272754i
$638$	2.77121	+	51.1120i	0.109713	+	2.02354i
$639$	2.66309	−	5.02313i	0.105350	−	0.198712i
$640$	−2.60066	+	0.572449i	−0.102800	+	0.0226281i
$641$	41.1466	+	19.0364i	1.62519	+	0.751894i	0.999601	−	0.0282577i	$-0.00899591\pi$
$641$	41.1466	+	19.0364i	1.62519	+	0.751894i	0.625591	+	0.780151i	$0.284858\pi$
$642$	−12.5753	+	7.56632i	−0.496309	+	0.298619i
$643$	−4.65126	−	8.77320i	−0.183428	−	0.345981i	0.774697	−	0.632333i	$-0.217902\pi$
$643$	−4.65126	−	8.77320i	−0.183428	−	0.345981i	−0.958125	+	0.286351i	$0.907558\pi$
$644$	9.54200	+	11.2337i	0.376008	+	0.442670i
$645$	12.7545	−	12.0817i	0.502209	−	0.475718i
$646$	−4.68812	+	0.509864i	−0.184452	+	0.0200603i
$647$	−10.0749	−	25.2861i	−0.396085	−	0.994099i	−0.982861	−	0.184350i	$-0.940982\pi$
$647$	−10.0749	−	25.2861i	−0.396085	−	0.994099i	0.586775	−	0.809750i	$-0.300397\pi$
$648$	1.00000			0.0392837
$649$	−41.4458	+	5.25281i	−1.62689	+	0.206191i
$650$	−11.6579			−0.457261
$651$	0.342300	+	0.859108i	0.0134158	+	0.0336711i
$652$	−10.7987	+	1.17443i	−0.422908	+	0.0459941i
$653$	2.06544	−	1.95649i	0.0808269	−	0.0765633i	−0.646220	−	0.763151i	$-0.723651\pi$
$653$	2.06544	−	1.95649i	0.0808269	−	0.0765633i	0.727047	+	0.686588i	$0.240892\pi$
$654$	4.70871	+	5.54352i	0.184125	+	0.216769i
$655$	21.6881	+	40.9081i	0.847423	+	1.59841i
$656$	5.99133	−	3.60486i	0.233922	−	0.140746i
$657$	−6.85394	−	3.17097i	−0.267398	−	0.123711i
$658$	3.74401	−	0.824118i	0.145957	−	0.0321275i
$659$	−11.3933	+	21.4900i	−0.443819	+	0.837131i	0.556163	+	0.831073i	$0.312273\pi$
$659$	−11.3933	+	21.4900i	−0.443819	+	0.837131i	−0.999982	+	0.00605781i	$0.998072\pi$
$660$	−0.784120	−	14.4622i	−0.0305218	−	0.562942i
$661$	2.70552	−	3.18519i	0.105233	−	0.123889i	−0.707024	−	0.707189i	$-0.749963\pi$
$661$	2.70552	−	3.18519i	0.105233	−	0.123889i	0.812257	+	0.583300i	$0.198239\pi$
$662$	−17.2704	−	3.80150i	−0.671233	−	0.147750i
$663$	−7.58772	−	5.76804i	−0.294683	−	0.224012i
$664$	11.2732	+	10.6786i	0.437486	+	0.414409i
$665$	0.922343	−	17.0116i	0.0357669	−	0.659682i
$666$	−3.67744	−	2.21264i	−0.142498	−	0.0857382i
$667$	33.5618	+	49.4999i	1.29952	+	1.91665i
$668$	−3.04747	−	10.9760i	−0.117910	−	0.424674i
$669$	17.0360	+	1.85277i	0.658648	+	0.0716323i
$670$	−26.2282	+	19.9382i	−1.01329	+	0.770279i
$671$	−21.9709	+	10.1648i	−0.848176	+	0.392408i
$672$	1.30164	−	1.91978i	0.0502120	−	0.0740572i
$673$	21.5878	+	7.27377i	0.832148	+	0.280383i	0.702953	−	0.711236i	$-0.251864\pi$
$673$	21.5878	+	7.27377i	0.832148	+	0.280383i	0.129195	+	0.991619i	$0.458761\pi$
$674$	2.57303	−	15.6948i	0.0991093	−	0.604540i
$675$	0.338311	+	2.06360i	0.0130216	+	0.0794281i
$676$	−17.1329	+	5.77273i	−0.658956	+	0.222028i
$677$	0.870925	−	3.13679i	0.0334724	−	0.120557i	−0.944926	−	0.327283i	$-0.893867\pi$
$677$	0.870925	−	3.13679i	0.0334724	−	0.120557i	0.978399	+	0.206726i	$0.0662809\pi$
$678$	4.59841	−	11.5411i	0.176601	−	0.443234i
$679$	−5.32896	+	13.3747i	−0.204507	+	0.513274i
$680$	1.21798	−	4.38677i	0.0467074	−	0.168225i
$681$	−9.15064	+	3.08321i	−0.350653	+	0.118149i
$682$	0.350835	+	2.14000i	0.0134342	+	0.0819448i
$683$	0.0934277	−	0.569884i	0.00357491	−	0.0218060i	−0.984979	−	0.172675i	$-0.944759\pi$
$683$	0.0934277	−	0.569884i	0.00357491	−	0.0218060i	0.988554	+	0.150869i	$0.0482072\pi$
$684$	2.61390	+	0.880727i	0.0999451	+	0.0336754i
$685$	−30.9293	+	45.6173i	−1.18175	+	1.74295i
$686$	−18.1461	+	8.39527i	−0.692820	+	0.320533i
$687$	7.93981	−	6.03569i	0.302923	−	0.230276i
$688$	6.55871	+	0.713303i	0.250049	+	0.0271944i
$689$	11.5072	+	41.4452i	0.438390	+	1.57894i
$690$	−9.49637	−	14.0061i	−0.361521	−	0.533203i
$691$	−4.68172	−	2.81690i	−0.178101	−	0.107160i	0.423712	−	0.905797i	$-0.360727\pi$
$691$	−4.68172	−	2.81690i	−0.178101	−	0.107160i	−0.601813	+	0.798637i	$0.705555\pi$
$692$	0.181711	−	3.35145i	0.00690760	−	0.127403i
$693$	9.15868	+	8.67556i	0.347910	+	0.329557i
$694$	−26.9264	−	20.4689i	−1.02211	−	0.776991i
$695$	37.9355	+	8.35024i	1.43898	+	0.316743i
$696$	6.09270	−	7.17288i	0.230943	−	0.271887i
$697$	0.647197	+	11.9369i	0.0245143	+	0.452140i
$698$	−0.978852	+	1.84631i	−0.0370501	+	0.0698839i
$699$	−15.8697	+	3.49318i	−0.600246	+	0.132124i
$700$	4.40203	+	2.03659i	0.166381	+	0.0769761i
$701$	39.4138	−	23.7145i	1.48864	−	0.895683i	0.488910	−	0.872334i	$-0.337395\pi$
$701$	39.4138	−	23.7145i	1.48864	−	0.895683i	0.999727	−	0.0233492i	$-0.00743295\pi$
$702$	2.61132	+	4.92547i	0.0985579	+	0.185900i
$703$	−7.66375	−	9.02246i	−0.289044	−	0.340288i
$704$	3.94865	−	3.74036i	0.148820	−	0.140970i
$705$	−4.37553	+	0.475868i	−0.164792	+	0.0179222i
$706$	4.00209	+	10.0445i	0.150620	+	0.378029i
$707$	11.6085			0.436583
$708$	6.19639	+	4.53925i	0.232874	+	0.170595i
$709$	31.4066			1.17950			0.589750	−	0.807586i	$-0.299226\pi$
$709$	31.4066			1.17950			0.589750	+	0.807586i	$0.299226\pi$
$710$	5.60382	+	14.0645i	0.210308	+	0.527832i
$711$	6.70851	−	0.729595i	0.251589	−	0.0273619i
$712$	5.53183	−	5.24003i	0.207314	−	0.196378i
$713$	1.64026	+	1.93107i	0.0614283	+	0.0723190i
$714$	1.85747	+	3.50356i	0.0695140	+	0.131117i
$715$	69.1857	−	41.6277i	2.58740	−	1.55679i
$716$	−4.29233	−	1.98584i	−0.160412	−	0.0742144i
$717$	−8.14277	+	1.79236i	−0.304097	+	0.0669369i
$718$	8.85970	−	16.7112i	0.330641	−	0.623655i
$719$	−1.75201	−	32.3139i	−0.0653389	−	1.20511i	−0.828910	−	0.559382i	$-0.811039\pi$
$719$	−1.75201	−	32.3139i	−0.0653389	−	1.20511i	0.763571	−	0.645724i	$-0.223444\pi$
$720$	−1.72394	+	2.02958i	−0.0642474	+	0.0756379i
$721$	−6.76202	−	1.48843i	−0.251831	−	0.0554322i
$722$	−9.06895	−	6.89404i	−0.337512	−	0.256570i
$723$	−13.9029	−	13.1695i	−0.517053	−	0.489779i
$724$	1.34393	−	24.7874i	0.0499469	−	0.921217i
$725$	16.8632	+	10.1462i	0.626283	+	0.376822i
$726$	10.4280	+	15.3802i	0.387020	+	0.570813i
$727$	7.54960	+	27.1912i	0.279999	+	1.00847i	0.961083	+	0.276260i	$0.0890952\pi$
$727$	7.54960	+	27.1912i	0.279999	+	1.00847i	−0.681084	+	0.732206i	$0.738491\pi$
$728$	12.8548	+	1.39805i	0.476432	+	0.0518151i
$729$	0.796093	−	0.605174i	0.0294849	−	0.0224139i
$730$	18.2515	−	8.44404i	0.675518	−	0.312528i
$731$	−6.32983	+	9.33580i	−0.234117	+	0.345297i
$732$	4.21793	+	1.42119i	0.155899	+	0.0525286i
$733$	−5.49652	+	33.5273i	−0.203018	+	1.23836i	0.666894	+	0.745152i	$0.267623\pi$
$733$	−5.49652	+	33.5273i	−0.203018	+	1.23836i	−0.869913	+	0.493205i	$0.835825\pi$
$734$	−4.33327	−	26.4318i	−0.159944	−	0.975615i
$735$	4.08852	−	1.37758i	0.150807	−	0.0508130i
$736$	1.70005	−	6.12302i	0.0626646	−	0.225698i
$737$	24.9072	−	62.5124i	0.917469	−	2.30267i
$738$	2.58809	−	6.49561i	0.0952688	−	0.239107i
$739$	−11.7846	+	42.4444i	−0.433505	+	1.56134i	0.348030	+	0.937483i	$0.386851\pi$
$739$	−11.7846	+	42.4444i	−0.433505	+	1.56134i	−0.781535	+	0.623861i	$0.785563\pi$
$740$	10.8304	−	3.64919i	0.398134	−	0.134147i
$741$	2.48774	+	15.1746i	0.0913896	+	0.557452i
$742$	2.89521	−	17.6600i	0.106286	−	0.648318i
$743$	−45.7683	−	15.4211i	−1.67908	−	0.565746i	−0.691429	−	0.722445i	$-0.743018\pi$
$743$	−45.7683	−	15.4211i	−1.67908	−	0.565746i	−0.987646	+	0.156699i	$0.949915\pi$
$744$	0.223752	−	0.330009i	0.00820313	−	0.0120987i
$745$	−15.8113	+	7.31507i	−0.579280	+	0.268003i
$746$	1.42373	−	1.08229i	0.0521266	−	0.0396256i
$747$	15.4369	+	1.67887i	0.564808	+	0.0614266i
$748$	2.48769	+	8.95985i	0.0909590	+	0.327605i
$749$	19.1031	+	28.1749i	0.698011	+	1.02949i
$750$	6.63725	+	3.99350i	0.242358	+	0.145822i
$751$	0.0830092	−	1.53101i	0.00302905	−	0.0558675i	−0.996628	−	0.0820515i	$-0.973853\pi$
$751$	0.0830092	−	1.53101i	0.00302905	−	0.0558675i	0.999657	+	0.0261840i	$0.00833557\pi$
$752$	−1.19994	−	1.13664i	−0.0437574	−	0.0414492i
$753$	−0.216148	−	0.164312i	−0.00787688	−	0.00598785i
$754$	51.2398	+	11.2787i	1.86604	+	0.410747i
$755$	29.5808	−	34.8253i	1.07656	−	1.26742i
$756$	−0.125572	−	2.31605i	−0.00456702	−	0.0842338i
$757$	19.4022	−	36.5965i	0.705186	−	1.33012i	−0.229031	−	0.973419i	$-0.573556\pi$
$757$	19.4022	−	36.5965i	0.705186	−	1.33012i	0.934218	−	0.356703i	$-0.116099\pi$
$758$	10.0847	−	2.21981i	0.366293	−	0.0806271i
$759$	31.3681	+	14.5124i	1.13859	+	0.526768i
$760$	−6.29371	+	3.78680i	−0.228297	+	0.137362i
$761$	−0.287296	−	0.541897i	−0.0104145	−	0.0196438i	0.878250	−	0.478201i	$-0.158711\pi$
$761$	−0.287296	−	0.541897i	−0.0104145	−	0.0196438i	−0.888665	+	0.458558i	$0.848366\pi$
$762$	−8.50555	−	10.0135i	−0.308124	−	0.362751i
$763$	12.2478	−	11.6017i	0.443399	−	0.420010i
$764$	12.3108	−	1.33888i	0.445390	−	0.0484391i
$765$	−1.68513	−	4.22937i	−0.0609262	−	0.152913i
$766$	2.07410			0.0749402
$767$	−6.17720	+	42.3736i	−0.223046	+	1.53002i
$768$	−1.00000			−0.0360844
$769$	9.62455	+	24.1558i	0.347070	+	0.871081i	0.994085	+	0.108603i	$0.0346378\pi$
$769$	9.62455	+	24.1558i	0.347070	+	0.871081i	−0.647015	+	0.762477i	$0.723983\pi$
$770$	−33.3967	+	3.63211i	−1.20353	+	0.130892i
$771$	17.9748	−	17.0267i	0.647347	−	0.613200i
$772$	17.9161	+	21.0924i	0.644813	+	0.759133i
$773$	−4.20034	−	7.92268i	−0.151076	−	0.284959i	0.796410	−	0.604757i	$-0.206730\pi$
$773$	−4.20034	−	7.92268i	−0.151076	−	0.284959i	−0.947486	+	0.319798i	$0.896385\pi$
$774$	5.65302	−	3.40131i	0.203194	−	0.122258i
$775$	0.756705	+	0.350089i	0.0271816	+	0.0125756i
$776$	6.06206	−	1.33436i	0.217615	−	0.0479007i
$777$	−4.66280	+	8.79497i	−0.167277	+	0.315518i
$778$	−0.929990	−	17.1526i	−0.0333417	−	0.614952i
$779$	12.4859	−	14.6995i	0.447353	−	0.526664i
$780$	−14.4984	−	3.19134i	−0.519125	−	0.114268i
$781$	−24.6173	−	18.7136i	−0.880875	−	0.669624i
$782$	7.88747	+	7.47141i	0.282055	+	0.267177i
$783$	0.509513	−	9.39742i	0.0182085	−	0.335836i
$784$	1.38825	+	0.835281i	0.0495803	+	0.0298315i
$785$	17.7584	+	26.1917i	0.633826	+	0.934824i
$786$	4.65166	+	16.7538i	0.165919	+	0.597587i
$787$	−38.3789	−	4.17396i	−1.36806	−	0.148786i	−0.605574	−	0.795789i	$-0.707056\pi$
$787$	−38.3789	−	4.17396i	−1.36806	−	0.148786i	−0.762487	+	0.647004i	$0.776022\pi$
$788$	11.9909	−	9.11522i	0.427157	−	0.324716i
$789$	−19.2940	+	8.92638i	−0.686886	+	0.317787i
$790$	−10.0843	+	14.8732i	−0.358783	+	0.529166i
$791$	−27.3072	−	9.20087i	−0.970933	−	0.327145i
$792$	0.879923	−	5.36729i	0.0312667	−	0.190718i
$793$	4.01436	+	24.4865i	0.142554	+	0.869540i
$794$	15.8038	−	5.32494i	0.560858	−	0.188975i
$795$	−5.49658	+	19.7969i	−0.194944	+	0.702124i
$796$	−5.94387	+	14.9180i	−0.210675	+	0.528754i
$797$	−13.5751	+	34.0708i	−0.480853	+	1.20685i	0.465885	+	0.884845i	$0.345736\pi$
$797$	−13.5751	+	34.0708i	−0.480853	+	1.20685i	−0.946738	+	0.322005i	$0.895643\pi$
$798$	1.71157	−	6.16452i	0.0605889	−	0.218222i
$799$	2.67786	−	0.902276i	0.0947358	−	0.0319202i
$800$	−0.338311	−	2.06360i	−0.0119611	−	0.0729594i
$801$	1.23272	−	7.51927i	0.0435561	−	0.265680i
$802$	4.06141	+	1.36845i	0.143413	+	0.0483216i
$803$	−23.0505	+	33.9969i	−0.813433	+	1.19972i
$804$	−11.2287	+	5.19495i	−0.396006	+	0.183212i
$805$	−31.2463	+	23.7528i	−1.10129	+	0.837176i
$806$	2.20974	+	0.240323i	0.0778346	+	0.00846502i
$807$	−1.71844	−	6.18925i	−0.0604918	−	0.217872i
$808$	−2.80866	−	4.14247i	−0.0988084	−	0.145731i
$809$	−33.3142	−	20.0445i	−1.17127	−	0.704727i	−0.209288	−	0.977854i	$-0.567115\pi$
$809$	−33.3142	−	20.0445i	−1.17127	−	0.704727i	−0.961978	+	0.273127i	$0.911942\pi$
$810$	−0.144168	+	2.65902i	−0.00506554	+	0.0934283i
$811$	−7.87209	−	7.45684i	−0.276426	−	0.261845i	0.536909	−	0.843640i	$-0.319592\pi$
$811$	−7.87209	−	7.45684i	−0.276426	−	0.261845i	−0.813335	+	0.581795i	$0.802351\pi$
$812$	−17.3778	−	13.2102i	−0.609841	−	0.463589i
$813$	13.5386	+	2.98008i	0.474820	+	0.104516i
$814$	−15.1118	+	17.7910i	−0.529667	+	0.623573i
$815$	−1.56600	−	28.8831i	−0.0548545	−	1.01173i
$816$	0.800824	−	1.51051i	0.0280344	−	0.0528786i
$817$	17.7721	−	3.91193i	0.621766	−	0.136861i
$818$	−27.8746	−	12.8962i	−0.974612	−	0.450903i
$819$	11.0797	−	6.66644i	0.387156	−	0.232944i
$820$	8.72164	+	16.4508i	0.304573	+	0.574485i
$821$	−10.7912	−	12.7043i	−0.376614	−	0.443385i	0.540900	−	0.841087i	$-0.318084\pi$
$821$	−10.7912	−	12.7043i	−0.376614	−	0.443385i	−0.917515	+	0.397702i	$0.869808\pi$
$822$	−15.0258	+	14.2332i	−0.524085	+	0.496440i
$823$	49.8947	−	5.42638i	1.73922	−	0.189152i	0.817216	−	0.576332i	$-0.195516\pi$
$823$	49.8947	−	5.42638i	1.73922	−	0.189152i	0.922004	+	0.387180i	$0.126551\pi$
$824$	1.10492	+	2.77313i	0.0384916	+	0.0966067i
$825$	11.3737			0.395980
$826$	9.73502	−	14.9211i	0.338725	−	0.519172i
$827$	−8.02228			−0.278962			−0.139481	−	0.990225i	$-0.544543\pi$
$827$	−8.02228			−0.278962			−0.139481	+	0.990225i	$0.544543\pi$
$828$	−2.35210	−	5.90332i	−0.0817410	−	0.205155i
$829$	38.6304	−	4.20131i	1.34169	−	0.145918i	0.591053	−	0.806633i	$-0.298712\pi$
$829$	38.6304	−	4.20131i	1.34169	−	0.145918i	0.750637	+	0.660715i	$0.229747\pi$
$830$	−30.0197	+	28.4362i	−1.04200	+	0.987035i
$831$	1.30487	+	1.53621i	0.0452655	+	0.0532906i
$832$	−2.61132	−	4.92547i	−0.0905312	−	0.170760i
$833$	−2.37345	+	1.42806i	−0.0822351	+	0.0494792i
$834$	13.2387	+	6.12486i	0.458418	+	0.212087i
$835$	29.6247	−	6.52088i	1.02520	−	0.225665i
$836$	7.02715	−	13.2546i	0.243039	−	0.458420i
$837$	−0.0215858	−	0.398126i	−0.000746114	−	0.0137613i
$838$	1.72972	−	2.03638i	0.0597520	−	0.0703455i
$839$	−25.2128	−	5.54976i	−0.870443	−	0.191599i	−0.242777	−	0.970082i	$-0.578058\pi$
$839$	−25.2128	−	5.54976i	−0.870443	−	0.191599i	−0.627666	+	0.778483i	$0.715989\pi$
$840$	4.91707	+	3.73786i	0.169655	+	0.128969i
$841$	−43.2483	−	40.9670i	−1.49132	−	1.41266i
$842$	1.08207	−	19.9576i	0.0372905	−	0.687783i
$843$	19.5510	+	11.7634i	0.673372	+	0.405155i
$844$	0.809430	+	1.19382i	0.0278617	+	0.0410930i
$845$	−12.8798	−	46.3888i	−0.443078	−	1.59582i
$846$	−1.64313	−	0.178701i	−0.0564921	−	0.00614388i
$847$	34.3118	−	26.0831i	1.17897	−	0.896227i
$848$	−7.00241	+	3.23966i	−0.240464	+	0.111250i
$849$	−11.4760	+	16.9258i	−0.393854	+	0.580891i
$850$	3.38803	+	1.14156i	0.116208	+	0.0391552i
$851$	−4.41224	+	26.9135i	−0.151250	+	0.922582i
$852$	0.919797	+	5.61051i	0.0315117	+	0.192213i
$853$	7.69724	−	2.59350i	0.263549	−	0.0887999i	−0.184425	−	0.982847i	$-0.559042\pi$
$853$	7.69724	−	2.59350i	0.263549	−	0.0887999i	0.447974	+	0.894047i	$0.352146\pi$
$854$	2.76188	−	9.94739i	0.0945095	−	0.340393i
$855$	−2.71871	+	6.82344i	−0.0929778	+	0.233357i
$856$	5.43219	−	13.6338i	0.185668	−	0.465992i
$857$	−10.2422	+	36.8891i	−0.349867	+	1.26011i	0.554081	+	0.832463i	$0.313070\pi$
$857$	−10.2422	+	36.8891i	−0.349867	+	1.26011i	−0.903948	+	0.427643i	$0.859344\pi$
$858$	28.7342	−	9.68168i	0.980970	−	0.330527i
$859$	−1.84489	−	11.2533i	−0.0629467	−	0.383958i	−0.999446	−	0.0332879i	$-0.989402\pi$
$859$	−1.84489	−	11.2533i	−0.0629467	−	0.383958i	0.936499	−	0.350670i	$-0.114046\pi$
$860$	−2.84224	+	17.3369i	−0.0969195	+	0.591183i
$861$	−15.3691	−	5.17846i	−0.523778	−	0.176481i
$862$	5.25477	−	7.75021i	0.178978	−	0.263973i
$863$	−17.5197	+	8.10546i	−0.596376	+	0.275913i	−0.694767	−	0.719235i	$-0.744493\pi$
$863$	−17.5197	+	8.10546i	−0.596376	+	0.275913i	0.0983909	+	0.995148i	$0.468630\pi$
$864$	−0.796093	+	0.605174i	−0.0270836	+	0.0205884i
$865$	8.88537	+	0.966343i	0.302112	+	0.0328566i
$866$	4.11986	+	14.8384i	0.139999	+	0.504230i
$867$	−7.89985	−	11.6514i	−0.268293	−	0.395702i
$868$	−0.792413	−	0.476779i	−0.0268962	−	0.0161829i
$869$	1.98703	−	36.6485i	0.0674052	−	1.24322i
$870$	18.1944	+	17.2347i	0.616849	+	0.584310i
$871$	−54.9093	−	41.7410i	−1.86053	−	1.41434i
$872$	−7.10337	−	1.56357i	−0.240550	−	0.0529491i
$873$	4.01844	−	4.73088i	0.136004	−	0.160116i
$874$	−0.948945	−	17.5023i	−0.0320986	−	0.592023i
$875$	8.41567	−	15.8736i	0.284502	−	0.536627i
$876$	7.37536	−	1.62344i	0.249190	−	0.0548510i
$877$	53.2906	+	24.6549i	1.79950	+	0.832535i	0.954776	+	0.297326i	$0.0960948\pi$
$877$	53.2906	+	24.6549i	1.79950	+	0.832535i	0.844719	+	0.535209i	$0.179767\pi$
$878$	−11.0111	+	6.62516i	−0.371607	+	0.223588i
$879$	0.586007	+	1.10533i	0.0197655	+	0.0372817i
$880$	9.37640	+	11.0388i	0.316079	+	0.372116i
$881$	13.2135	−	12.5165i	0.445175	−	0.421692i	−0.431992	−	0.901877i	$-0.642189\pi$
$881$	13.2135	−	12.5165i	0.445175	−	0.421692i	0.877167	+	0.480185i	$0.159431\pi$
$882$	1.61067	−	0.175170i	0.0542339	−	0.00589830i
$883$	−5.07422	−	12.7353i	−0.170761	−	0.428578i	0.818543	−	0.574445i	$-0.194782\pi$
$883$	−5.07422	−	12.7353i	−0.170761	−	0.428578i	−0.989304	+	0.145867i	$0.953403\pi$
$884$	9.53120			0.320569
$885$	−12.9633	+	15.8219i	−0.435755	+	0.531847i
$886$	24.5676			0.825366
$887$	6.79226	+	17.0473i	0.228062	+	0.572392i	0.997824	−	0.0659391i	$-0.0210043\pi$
$887$	6.79226	+	17.0473i	0.228062	+	0.572392i	−0.769762	+	0.638331i	$0.779625\pi$
$888$	4.26662	−	0.464023i	0.143178	−	0.0155716i
$889$	−22.1237	+	20.9567i	−0.742004	+	0.702864i
$890$	13.1358	+	15.4647i	0.440313	+	0.518377i
$891$	−2.54765	−	4.80537i	−0.0853494	−	0.160986i
$892$	−14.6835	+	8.83475i	−0.491639	+	0.295809i
$893$	−4.13760	−	1.91426i	−0.138460	−	0.0640583i
$894$	−6.38927	+	1.40638i	−0.213689	+	0.0470365i
$895$	5.89920	−	11.1271i	0.197189	−	0.371937i
$896$	0.125572	+	2.31605i	0.00419508	+	0.0773737i
$897$	22.9346	−	27.0006i	0.765762	−	0.901525i
$898$	−23.2699	−	5.12209i	−0.776526	−	0.170926i
$899$	−2.98723	−	2.27083i	−0.0996296	−	0.0757364i
$900$	−1.51817	−	1.43808i	−0.0506056	−	0.0479361i
$901$	0.714145	−	13.1716i	0.0237916	−	0.438811i
$902$	−32.5865	−	19.6066i	−1.08501	−	0.652830i
$903$	−8.58745	−	12.6655i	−0.285772	−	0.421483i
$904$	3.32363	+	11.9706i	0.110542	+	0.398138i
$905$	65.7164	+	7.14709i	2.18449	+	0.237577i
$906$	13.6601	−	10.3841i	0.453825	−	0.344989i
$907$	7.03951	−	3.25682i	0.233743	−	0.108141i	−0.299522	−	0.954090i	$-0.596827\pi$
$907$	7.03951	−	3.25682i	0.233743	−	0.108141i	0.533265	+	0.845948i	$0.320965\pi$
$908$	5.41888	−	7.99226i	0.179832	−	0.265232i
$909$	−4.74287	−	1.59806i	−0.157311	−	0.0530043i
$910$	−5.57068	+	33.9797i	−0.184666	+	1.12641i
$911$	2.74008	+	16.7138i	0.0907829	+	0.553751i	0.992580	+	0.121592i	$0.0388000\pi$
$911$	2.74008	+	16.7138i	0.0907829	+	0.553751i	−0.901797	+	0.432159i	$0.857752\pi$
$912$	−2.61390	+	0.880727i	−0.0865550	+	0.0291638i
$913$	22.5943	−	81.3773i	0.747762	−	2.69319i
$914$	−13.7156	+	34.4235i	−0.453671	+	1.13863i
$915$	−4.38705	+	11.0107i	−0.145031	+	0.364001i
$916$	−2.66819	+	9.60993i	−0.0881593	+	0.317521i
$917$	38.2184	−	12.8773i	1.26208	−	0.425245i
$918$	−0.276594	−	1.68715i	−0.00912896	−	0.0556842i
$919$	−6.54438	+	39.9189i	−0.215879	+	1.31680i	0.627134	+	0.778911i	$0.284228\pi$
$919$	−6.54438	+	39.9189i	−0.215879	+	1.31680i	−0.843013	+	0.537893i	$0.819220\pi$
$920$	16.0361	+	5.40320i	0.528695	+	0.178138i
$921$	4.74537	−	6.99889i	0.156365	−	0.230621i
$922$	−3.53984	+	1.63771i	−0.116578	+	0.0539349i
$923$	−25.2325	+	19.1813i	−0.830539	+	0.631359i
$924$	−12.5414	−	1.36396i	−0.412581	−	0.0448709i
$925$	2.40100	+	8.64763i	0.0789445	+	0.284332i
$926$	3.03638	+	4.47833i	0.0997817	+	0.147167i
$927$	2.55785	+	1.53901i	0.0840107	+	0.0505476i
$928$	−0.509513	+	9.39742i	−0.0167256	+	0.308485i
$929$	−39.4982	−	37.4147i	−1.29589	−	1.22754i	−0.958140	−	0.286300i	$-0.907574\pi$
$929$	−39.4982	−	37.4147i	−1.29589	−	1.22754i	−0.337753	−	0.941235i	$-0.609667\pi$
$930$	0.845241	+	0.642536i	0.0277165	+	0.0210696i
$931$	4.36440	+	0.960678i	0.143038	+	0.0314849i
$932$	10.5198	−	12.3848i	0.344586	−	0.405678i
$933$	−0.531326	−	9.79972i	−0.0173948	−	0.320829i
$934$	9.74820	−	18.3871i	0.318971	−	0.601643i
$935$	−24.1830	+	5.32309i	−0.790870	+	0.174084i
$936$	−5.05962	−	2.34083i	−0.165379	−	0.0765124i
$937$	−24.8409	+	14.9463i	−0.811517	+	0.488273i	−0.859843	−	0.510558i	$-0.829439\pi$
$937$	−24.8409	+	14.9463i	−0.811517	+	0.488273i	0.0483265	+	0.998832i	$0.484611\pi$
$938$	13.4418	+	25.3538i	0.438889	+	0.827832i
$939$	12.9952	+	15.2992i	0.424083	+	0.499269i
$940$	3.19535	−	3.02680i	0.104221	−	0.0987232i
$941$	−21.9911	+	2.39168i	−0.716890	+	0.0779665i	−0.459291	−	0.888286i	$-0.651897\pi$
$941$	−21.9911	+	2.39168i	−0.716890	+	0.0779665i	−0.257598	+	0.966252i	$0.582931\pi$
$942$	4.39848	+	11.0394i	0.143310	+	0.359682i
$943$	−44.4331			−1.44694
$944$	−7.67994	+	0.136228i	−0.249961	+	0.00443386i
$945$	6.17651			0.200922
$946$	−13.2816	−	33.3343i	−0.431822	−	1.08379i
$947$	38.8665	−	4.22699i	1.26299	−	0.137359i	0.547993	−	0.836483i	$-0.315392\pi$
$947$	38.8665	−	4.22699i	1.26299	−	0.137359i	0.715000	+	0.699124i	$0.246427\pi$
$948$	−4.89907	+	4.64064i	−0.159114	+	0.150721i
$949$	27.2556	+	32.0878i	0.884755	+	1.04161i
$950$	−2.70178	−	5.09610i	−0.0876574	−	0.165339i
$951$	12.1163	−	7.29012i	0.392897	−	0.236398i
$952$	−3.59898	−	1.66507i	−0.116644	−	0.0539651i
$953$	−6.30225	+	1.38723i	−0.204150	+	0.0449368i	−0.315868	−	0.948803i	$-0.602296\pi$
$953$	−6.30225	+	1.38723i	−0.204150	+	0.0449368i	0.111718	+	0.993740i	$0.464365\pi$
$954$	−3.61401	+	6.81675i	−0.117008	+	0.220700i
$955$	1.78529	+	32.9277i	0.0577706	+	1.06552i
$956$	5.39771	−	6.35468i	0.174574	−	0.205525i
$957$	−49.9904	−	11.0037i	−1.61596	−	0.355699i
$958$	−32.1981	−	24.4764i	−1.04027	−	0.790796i
$959$	34.8515	+	33.0131i	1.12542	+	1.06605i
$960$	0.144168	−	2.65902i	0.00465299	−	0.0858194i
$961$	26.4264	+	15.9002i	0.852463	+	0.512910i
$962$	13.4270	+	19.8034i	0.432905	+	0.638487i
$963$	−3.92627	−	14.1412i	−0.126522	−	0.455693i
$964$	19.0378	+	2.07049i	0.613167	+	0.0666859i
$965$	−58.6680	+	44.5983i	−1.88859	+	1.43567i
$966$	−13.3770	+	6.18886i	−0.430398	+	0.199123i
$967$	−33.2982	+	49.1112i	−1.07080	+	1.57931i	−0.287376	+	0.957818i	$0.592783\pi$
$967$	−33.2982	+	49.1112i	−1.07080	+	1.57931i	−0.783422	+	0.621490i	$0.786527\pi$
$968$	−17.6094	−	5.93329i	−0.565987	−	0.190703i
$969$	0.762926	−	4.65365i	0.0245087	−	0.149497i
$970$	2.67413	+	16.3115i	0.0858612	+	0.523730i
$971$	28.9747	−	9.76273i	0.929844	−	0.313301i	0.186688	−	0.982419i	$-0.440225\pi$
$971$	28.9747	−	9.76273i	0.929844	−	0.313301i	0.743156	+	0.669118i	$0.233328\pi$
$972$	−0.267528	+	0.963550i	−0.00858098	+	0.0309059i
$973$	12.5231	−	31.4305i	0.401471	−	1.00762i
$974$	3.01275	−	7.56143i	0.0965347	−	0.242284i
$975$	3.11882	−	11.2330i	0.0998822	−	0.359743i
$976$	−4.21793	+	1.42119i	−0.135013	+	0.0454911i
$977$	−2.59220	−	15.8117i	−0.0829319	−	0.505862i	−0.995328	−	0.0965535i	$-0.969218\pi$
$977$	−2.59220	−	15.8117i	−0.0829319	−	0.505862i	0.912396	−	0.409309i	$-0.134230\pi$
$978$	1.75733	−	10.7192i	0.0561933	−	0.342764i
$979$	−39.2734	−	13.2328i	−1.25518	−	0.422921i
$980$	−2.42117	+	3.57095i	−0.0773414	+	0.114070i
$981$	−6.60117	+	3.05403i	−0.210759	+	0.0975076i
$982$	16.2726	−	12.3701i	0.519280	−	0.394747i
$983$	29.6345	+	3.22295i	0.945194	+	0.102796i	0.567718	−	0.823223i	$-0.307826\pi$
$983$	29.6345	+	3.22295i	0.945194	+	0.102796i	0.377476	+	0.926019i	$0.376792\pi$
$984$	1.87062	+	6.73735i	0.0596331	+	0.214779i
$985$	22.5088	+	33.1980i	0.717191	+	1.05778i
$986$	−13.7869	−	8.29530i	−0.439064	−	0.264176i
$987$	−0.207549	+	3.82801i	−0.00660635	+	0.121847i
$988$	−11.1637	−	10.5748i	−0.355166	−	0.336431i
$989$	−33.3755	−	25.3714i	−1.06128	−	0.806763i
$990$	14.1449	+	3.11352i	0.449553	+	0.0989541i
$991$	−20.0416	+	23.5947i	−0.636641	+	0.749512i	−0.981984	−	0.188965i	$-0.939487\pi$
$991$	−20.0416	+	23.5947i	−0.636641	+	0.749512i	0.345343	+	0.938477i	$0.387763\pi$
$992$	0.0215858	+	0.398126i	0.000685349	+	0.0126405i
$993$	8.28326	−	15.6239i	0.262861	−	0.495809i
$994$	12.8787	−	2.83482i	0.408488	−	0.0899149i
$995$	−38.8102	−	17.9555i	−1.23037	−	0.569229i
$996$	−13.3052	+	8.00550i	−0.421593	+	0.253664i
$997$	23.2876	+	43.9250i	0.737525	+	1.39112i	0.913547	+	0.406733i	$0.133332\pi$
$997$	23.2876	+	43.9250i	0.737525	+	1.39112i	−0.176023	+	0.984386i	$0.556323\pi$
$998$	−0.261952	−	0.308393i	−0.00829194	−	0.00976202i
$999$	3.11581	−	2.95145i	0.0985799	−	0.0933799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.289.1	yes	84
59.49	even	29	inner	354.2.e.c.49.1	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.49.1	✓	84	59.49	even	29	inner
354.2.e.c.289.1	yes	84	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.370138 - 0.928977i) q^{2} +(0.994138 - 0.108119i) q^{3} +(-0.725995 + 0.687699i) q^{4} +(-1.72394 - 2.02958i) q^{5} +(-0.468408 - 0.883512i) q^{6} +(-1.98744 + 1.19580i) q^{7} +(0.907575 + 0.419889i) q^{8} +(0.976621 - 0.214970i) q^{9} +O(q^{10})\)	\(q+(-0.370138 - 0.928977i) q^{2} +(0.994138 - 0.108119i) q^{3} +(-0.725995 + 0.687699i) q^{4} +(-1.72394 - 2.02958i) q^{5} +(-0.468408 - 0.883512i) q^{6} +(-1.98744 + 1.19580i) q^{7} +(0.907575 + 0.419889i) q^{8} +(0.976621 - 0.214970i) q^{9} +(-1.24733 + 2.35272i) q^{10} +(-0.294458 - 5.43097i) q^{11} +(-0.647386 + 0.762162i) q^{12} +(-5.44454 - 1.19843i) q^{13} +(1.84650 + 1.40367i) q^{14} +(-1.93327 - 1.83129i) q^{15} +(0.0541389 - 0.998533i) q^{16} +(1.46494 + 0.881427i) q^{17} +(-0.561187 - 0.827689i) q^{18} +(-0.737921 - 2.65775i) q^{19} +(2.64731 + 0.287912i) q^{20} +(-1.84650 + 1.40367i) q^{21} +(-4.93625 + 2.28375i) q^{22} +(-3.56615 + 5.25967i) q^{23} +(0.947653 + 0.319302i) q^{24} +(-0.338311 + 2.06360i) q^{25} +(0.901915 + 5.50144i) q^{26} +(0.947653 - 0.319302i) q^{27} +(0.620518 - 2.23490i) q^{28} +(3.48345 - 8.74281i) q^{29} +(-0.985649 + 2.47379i) q^{30} +(0.106667 - 0.384178i) q^{31} +(-0.947653 + 0.319302i) q^{32} +(-0.879923 - 5.36729i) q^{33} +(0.276594 - 1.68715i) q^{34} +(5.85319 + 1.97217i) q^{35} +(-0.561187 + 0.827689i) q^{36} +(3.89511 - 1.80207i) q^{37} +(-2.19586 + 1.66925i) q^{38} +(-5.54220 - 0.602750i) q^{39} +(-0.712407 - 2.56586i) q^{40} +(3.92394 + 5.78738i) q^{41} +(1.98744 + 1.19580i) q^{42} +(-0.357175 + 6.58771i) q^{43} +(3.94865 + 3.74036i) q^{44} +(-2.11993 - 1.61153i) q^{45} +(6.20608 + 1.36606i) q^{46} +(1.07001 - 1.25972i) q^{47} +(-0.0541389 - 0.998533i) q^{48} +(-0.758898 + 1.43143i) q^{49} +(2.04226 - 0.449536i) q^{50} +(1.55165 + 0.717872i) q^{51} +(4.77687 - 2.87415i) q^{52} +(-3.61401 - 6.81675i) q^{53} +(-0.647386 - 0.762162i) q^{54} +(-10.5149 + 9.96028i) q^{55} +(-2.30585 + 0.250776i) q^{56} +(-1.02095 - 2.56239i) q^{57} -9.41122 q^{58} +(-0.551812 - 7.66130i) q^{59} +2.66292 q^{60} +(-1.64746 - 4.13481i) q^{61} +(-0.396374 + 0.0431083i) q^{62} +(-1.68391 + 1.59508i) q^{63} +(0.647386 + 0.762162i) q^{64} +(6.95374 + 13.1161i) q^{65} +(-4.66040 + 2.80407i) q^{66} +(11.2287 + 5.19495i) q^{67} +(-1.66970 + 0.367528i) q^{68} +(-2.97657 + 5.61441i) q^{69} +(-0.334389 - 6.16745i) q^{70} +(3.68066 - 4.33320i) q^{71} +(0.976621 + 0.214970i) q^{72} +(-6.01203 - 4.57023i) q^{73} +(-3.11581 - 2.95145i) q^{74} +(-0.113213 + 2.08808i) q^{75} +(2.36346 + 1.42205i) q^{76} +(7.07957 + 10.4416i) q^{77} +(1.49144 + 5.37167i) q^{78} +(6.70851 + 0.729595i) q^{79} +(-2.11993 + 1.61153i) q^{80} +(0.907575 - 0.419889i) q^{81} +(3.92394 - 5.78738i) q^{82} +(14.7151 + 4.95810i) q^{83} +(0.375245 - 2.28889i) q^{84} +(-0.736548 - 4.49274i) q^{85} +(6.25204 - 2.10656i) q^{86} +(2.51777 - 9.06818i) q^{87} +(2.01316 - 5.05265i) q^{88} +(2.82032 - 7.07847i) q^{89} +(-0.712407 + 2.56586i) q^{90} +(12.2538 - 4.12877i) q^{91} +(-1.02807 - 6.27093i) q^{92} +(0.0645043 - 0.393459i) q^{93} +(-1.56630 - 0.527749i) q^{94} +(-4.12198 + 6.07947i) q^{95} +(-0.907575 + 0.419889i) q^{96} +(4.94149 - 3.75643i) q^{97} +(1.61067 + 0.175170i) q^{98} +(-1.45507 - 5.24069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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Database

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