LMFDB - Embedded newform 187.2.h.a.100.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(100,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("187.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.h (of order $8$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			100.5
Character	$\chi$	$=$	187.100
Dual form			187.2.h.a.144.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.746627 - 0.746627i) q^{2} +(-0.160212 - 0.386786i) q^{3} -0.885097i q^{4} +(1.10648 - 0.458319i) q^{5} +(-0.169166 + 0.408404i) q^{6} +(-3.06195 - 1.26830i) q^{7} +(-2.15409 + 2.15409i) q^{8} +(1.99738 - 1.99738i) q^{9} +O(q^{10})$	\(q+(-0.746627 - 0.746627i) q^{2} +(-0.160212 - 0.386786i) q^{3} -0.885097i q^{4} +(1.10648 - 0.458319i) q^{5} +(-0.169166 + 0.408404i) q^{6} +(-3.06195 - 1.26830i) q^{7} +(-2.15409 + 2.15409i) q^{8} +(1.99738 - 1.99738i) q^{9} +(-1.16832 - 0.483934i) q^{10} +(0.382683 - 0.923880i) q^{11} +(-0.342344 + 0.141803i) q^{12} -0.322834i q^{13} +(1.33919 + 3.23308i) q^{14} +(-0.354543 - 0.354543i) q^{15} +1.44641 q^{16} +(-3.71471 + 1.78912i) q^{17} -2.98260 q^{18} +(-2.34641 - 2.34641i) q^{19} +(-0.405657 - 0.979343i) q^{20} +1.38752i q^{21} +(-0.975515 + 0.404071i) q^{22} +(3.41265 - 8.23887i) q^{23} +(1.17828 + 0.488061i) q^{24} +(-2.52129 + 2.52129i) q^{25} +(-0.241036 + 0.241036i) q^{26} +(-2.25293 - 0.933193i) q^{27} +(-1.12257 + 2.71012i) q^{28} +(9.69711 - 4.01667i) q^{29} +0.529423i q^{30} +(1.88344 + 4.54703i) q^{31} +(3.22825 + 3.22825i) q^{32} -0.418655 q^{33} +(4.10930 + 1.43770i) q^{34} -3.96927 q^{35} +(-1.76788 - 1.76788i) q^{36} +(3.13777 + 7.57524i) q^{37} +3.50378i q^{38} +(-0.124868 + 0.0517219i) q^{39} +(-1.39620 + 3.37072i) q^{40} +(10.1995 + 4.22475i) q^{41} +(1.03596 - 1.03596i) q^{42} +(5.29629 - 5.29629i) q^{43} +(-0.817723 - 0.338712i) q^{44} +(1.29463 - 3.12551i) q^{45} +(-8.69934 + 3.60338i) q^{46} -0.500901i q^{47} +(-0.231732 - 0.559451i) q^{48} +(2.81720 + 2.81720i) q^{49} +3.76493 q^{50} +(1.28715 + 1.15016i) q^{51} -0.285739 q^{52} +(2.38321 + 2.38321i) q^{53} +(0.985348 + 2.37884i) q^{54} -1.19765i q^{55} +(9.32775 - 3.86368i) q^{56} +(-0.531635 + 1.28348i) q^{57} +(-10.2391 - 4.24116i) q^{58} +(3.24864 - 3.24864i) q^{59} +(-0.313805 + 0.313805i) q^{60} +(-10.4769 - 4.33967i) q^{61} +(1.98871 - 4.80116i) q^{62} +(-8.64918 + 3.58261i) q^{63} -7.71342i q^{64} +(-0.147961 - 0.357209i) q^{65} +(0.312579 + 0.312579i) q^{66} -3.61201 q^{67} +(1.58354 + 3.28788i) q^{68} -3.73343 q^{69} +(2.96357 + 2.96357i) q^{70} +(3.16055 + 7.63023i) q^{71} +8.60509i q^{72} +(7.28317 - 3.01679i) q^{73} +(3.31313 - 7.99862i) q^{74} +(1.37914 + 0.571260i) q^{75} +(-2.07680 + 2.07680i) q^{76} +(-2.34351 + 2.34351i) q^{77} +(0.131847 + 0.0546126i) q^{78} +(-3.32943 + 8.03795i) q^{79} +(1.60042 - 0.662916i) q^{80} -7.45327i q^{81} +(-4.46087 - 10.7695i) q^{82} +(2.95986 + 2.95986i) q^{83} +1.22809 q^{84} +(-3.29027 + 3.68214i) q^{85} -7.90870 q^{86} +(-3.10719 - 3.10719i) q^{87} +(1.16579 + 2.81445i) q^{88} -13.1996i q^{89} +(-3.30019 + 1.36698i) q^{90} +(-0.409450 + 0.988501i) q^{91} +(-7.29220 - 3.02053i) q^{92} +(1.45698 - 1.45698i) q^{93} +(-0.373986 + 0.373986i) q^{94} +(-3.67165 - 1.52085i) q^{95} +(0.731439 - 1.76585i) q^{96} +(4.46089 - 1.84776i) q^{97} -4.20679i q^{98} +(-1.08098 - 2.60971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 16 q^{6}+O(q^{10}) $ 56 * q - 16 * q^6	$ 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) $ 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.746627	−	0.746627i	−0.527945	−	0.527945i	0.392014	−	0.919959i	$-0.371778\pi$
$2$	−0.746627	−	0.746627i	−0.527945	−	0.527945i	−0.919959	+	0.392014i	$0.871778\pi$
$3$	−0.160212	−	0.386786i	−0.0924986	−	0.223311i	0.870858	−	0.491534i	$-0.163564\pi$
$3$	−0.160212	−	0.386786i	−0.0924986	−	0.223311i	−0.963357	+	0.268223i	$0.913564\pi$
$4$		−	0.885097i		−	0.442549i
$5$	1.10648	−	0.458319i	0.494833	−	0.204967i	−0.121289	−	0.992617i	$-0.538703\pi$
$5$	1.10648	−	0.458319i	0.494833	−	0.204967i	0.616122	+	0.787651i	$0.288703\pi$
$6$	−0.169166	+	0.408404i	−0.0690619	+	0.166730i
$7$	−3.06195	−	1.26830i	−1.15731	−	0.479373i	−0.280330	−	0.959904i	$-0.590444\pi$
$7$	−3.06195	−	1.26830i	−1.15731	−	0.479373i	−0.876978	+	0.480531i	$0.840444\pi$
$8$	−2.15409	+	2.15409i	−0.761586	+	0.761586i
$9$	1.99738	−	1.99738i	0.665795	−	0.665795i
$10$	−1.16832	−	0.483934i	−0.369455	−	0.153033i
$11$	0.382683	−	0.923880i	0.115383	−	0.278560i
$11$	0.382683	−	0.923880i	0.115383	−	0.278560i
$12$	−0.342344	+	0.141803i	−0.0988261	+	0.0409351i
$13$		−	0.322834i		−	0.0895380i	−0.998997	−	0.0447690i	$-0.985745\pi$
$13$		−	0.322834i		−	0.0895380i	0.998997	−	0.0447690i	$-0.0142552\pi$
$14$	1.33919	+	3.23308i	0.357912	+	0.864077i
$15$	−0.354543	−	0.354543i	−0.0915427	−	0.0915427i
$16$	1.44641			0.361602
$17$	−3.71471	+	1.78912i	−0.900949	+	0.433924i
$17$	−3.71471	+	1.78912i	−0.900949	+	0.433924i
$18$	−2.98260			−0.703006
$19$	−2.34641	−	2.34641i	−0.538302	−	0.538302i	0.384728	−	0.923030i	$-0.374295\pi$
$19$	−2.34641	−	2.34641i	−0.538302	−	0.538302i	−0.923030	+	0.384728i	$0.874295\pi$
$20$	−0.405657	−	0.979343i	−0.0907077	−	0.218988i
$21$			1.38752i			0.302781i
$22$	−0.975515	+	0.404071i	−0.207980	+	0.0861483i
$23$	3.41265	−	8.23887i	0.711587	−	1.71792i	0.0155905	−	0.999878i	$-0.495037\pi$
$23$	3.41265	−	8.23887i	0.711587	−	1.71792i	0.695997	−	0.718045i	$-0.254963\pi$
$24$	1.17828	+	0.488061i	0.240516	+	0.0996251i
$25$	−2.52129	+	2.52129i	−0.504258	+	0.504258i
$26$	−0.241036	+	0.241036i	−0.0472711	+	0.0472711i
$27$	−2.25293	−	0.933193i	−0.433576	−	0.179593i
$28$	−1.12257	+	2.71012i	−0.212146	+	0.512165i
$29$	9.69711	−	4.01667i	1.80071	−	0.745878i	0.814544	−	0.580101i	$-0.196987\pi$
$29$	9.69711	−	4.01667i	1.80071	−	0.745878i	0.986163	−	0.165776i	$-0.0530129\pi$
$30$			0.529423i			0.0966589i
$31$	1.88344	+	4.54703i	0.338276	+	0.816671i	0.997881	+	0.0650586i	$0.0207234\pi$
$31$	1.88344	+	4.54703i	0.338276	+	0.816671i	−0.659605	+	0.751612i	$0.729277\pi$
$32$	3.22825	+	3.22825i	0.570680	+	0.570680i
$33$	−0.418655			−0.0728784
$34$	4.10930	+	1.43770i	0.704740	+	0.246563i
$35$	−3.96927			−0.670930
$36$	−1.76788	−	1.76788i	−0.294647	−	0.294647i
$37$	3.13777	+	7.57524i	0.515846	+	1.24536i	0.940434	+	0.339975i	$0.110419\pi$
$37$	3.13777	+	7.57524i	0.515846	+	1.24536i	−0.424589	+	0.905386i	$0.639581\pi$
$38$			3.50378i			0.568388i
$39$	−0.124868	+	0.0517219i	−0.0199948	+	0.00828213i
$40$	−1.39620	+	3.37072i	−0.220758	+	0.532957i
$41$	10.1995	+	4.22475i	1.59289	+	0.659796i	0.990387	−	0.138323i	$-0.0441712\pi$
$41$	10.1995	+	4.22475i	1.59289	+	0.659796i	0.602500	+	0.798119i	$0.294171\pi$
$42$	1.03596	−	1.03596i	0.159852	−	0.159852i
$43$	5.29629	−	5.29629i	0.807676	−	0.807676i	−0.176605	−	0.984282i	$-0.556512\pi$
$43$	5.29629	−	5.29629i	0.807676	−	0.807676i	0.984282	+	0.176605i	$0.0565117\pi$
$44$	−0.817723	−	0.338712i	−0.123276	−	0.0510628i
$45$	1.29463	−	3.12551i	0.192992	−	0.465923i
$46$	−8.69934	+	3.60338i	−1.28265	+	0.531290i
$47$		−	0.500901i		−	0.0730640i	−0.999332	−	0.0365320i	$-0.988369\pi$
$47$		−	0.500901i		−	0.0730640i	0.999332	−	0.0365320i	$-0.0116311\pi$
$48$	−0.231732	−	0.559451i	−0.0334477	−	0.0807498i
$49$	2.81720	+	2.81720i	0.402457	+	0.402457i
$50$	3.76493			0.532441
$51$	1.28715	+	1.15016i	0.180237	+	0.161055i
$52$	−0.285739			−0.0396249
$53$	2.38321	+	2.38321i	0.327358	+	0.327358i	0.851581	−	0.524223i	$-0.175644\pi$
$53$	2.38321	+	2.38321i	0.327358	+	0.327358i	−0.524223	+	0.851581i	$0.675644\pi$
$54$	0.985348	+	2.37884i	0.134089	+	0.323719i
$55$		−	1.19765i		−	0.161490i
$56$	9.32775	−	3.86368i	1.24647	−	0.516306i
$57$	−0.531635	+	1.28348i	−0.0704168	+	0.170001i
$58$	−10.2391	−	4.24116i	−1.34446	−	0.556892i
$59$	3.24864	−	3.24864i	0.422937	−	0.422937i	−0.463277	−	0.886214i	$-0.653326\pi$
$59$	3.24864	−	3.24864i	0.422937	−	0.422937i	0.886214	+	0.463277i	$0.153326\pi$
$60$	−0.313805	+	0.313805i	−0.0405121	+	0.0405121i
$61$	−10.4769	−	4.33967i	−1.34143	−	0.555638i	−0.407535	−	0.913190i	$-0.633612\pi$
$61$	−10.4769	−	4.33967i	−1.34143	−	0.555638i	−0.933893	+	0.357552i	$0.883612\pi$
$62$	1.98871	−	4.80116i	0.252566	−	0.609748i
$63$	−8.64918	+	3.58261i	−1.08969	+	0.451366i
$64$		−	7.71342i		−	0.964177i
$65$	−0.147961	−	0.357209i	−0.0183523	−	0.0443063i
$66$	0.312579	+	0.312579i	0.0384758	+	0.0384758i
$67$	−3.61201			−0.441278			−0.220639	−	0.975356i	$-0.570814\pi$
$67$	−3.61201			−0.441278			−0.220639	+	0.975356i	$0.570814\pi$
$68$	1.58354	+	3.28788i	0.192033	+	0.398714i
$69$	−3.73343			−0.449452
$70$	2.96357	+	2.96357i	0.354214	+	0.354214i
$71$	3.16055	+	7.63023i	0.375088	+	0.905542i	0.992871	+	0.119194i	$0.0380309\pi$
$71$	3.16055	+	7.63023i	0.375088	+	0.905542i	−0.617783	+	0.786348i	$0.711969\pi$
$72$			8.60509i			1.01412i
$73$	7.28317	−	3.01679i	0.852430	−	0.353088i	0.0866878	−	0.996236i	$-0.472372\pi$
$73$	7.28317	−	3.01679i	0.852430	−	0.353088i	0.765742	+	0.643147i	$0.222372\pi$
$74$	3.31313	−	7.99862i	0.385144	−	0.929820i
$75$	1.37914	+	0.571260i	0.159250	+	0.0659634i
$76$	−2.07680	+	2.07680i	−0.238225	+	0.238225i
$77$	−2.34351	+	2.34351i	−0.267068	+	0.267068i
$78$	0.131847	+	0.0546126i	0.0149287	+	0.00618366i
$79$	−3.32943	+	8.03795i	−0.374590	+	0.904340i	0.618370	+	0.785887i	$0.287793\pi$
$79$	−3.32943	+	8.03795i	−0.374590	+	0.904340i	−0.992960	+	0.118453i	$0.962207\pi$
$80$	1.60042	−	0.662916i	0.178933	−	0.0741163i
$81$		−	7.45327i		−	0.828142i
$82$	−4.46087	−	10.7695i	−0.492621	−	1.18929i
$83$	2.95986	+	2.95986i	0.324886	+	0.324886i	0.850638	−	0.525752i	$-0.176216\pi$
$83$	2.95986	+	2.95986i	0.324886	+	0.324886i	−0.525752	+	0.850638i	$0.676216\pi$
$84$	1.22809			0.133995
$85$	−3.29027	+	3.68214i	−0.356879	+	0.399385i
$86$	−7.90870			−0.852817
$87$	−3.10719	−	3.10719i	−0.333126	−	0.333126i
$88$	1.16579	+	2.81445i	0.124273	+	0.300022i
$89$		−	13.1996i		−	1.39916i	−0.714554	−	0.699580i	$-0.753370\pi$
$89$		−	13.1996i		−	1.39916i	0.714554	−	0.699580i	$-0.246630\pi$
$90$	−3.30019	+	1.36698i	−0.347870	+	0.144093i
$91$	−0.409450	+	0.988501i	−0.0429221	+	0.103623i
$92$	−7.29220	−	3.02053i	−0.760265	−	0.314912i
$93$	1.45698	−	1.45698i	0.151082	−	0.151082i
$94$	−0.373986	+	0.373986i	−0.0385737	+	0.0385737i
$95$	−3.67165	−	1.52085i	−0.376704	−	0.156036i
$96$	0.731439	−	1.76585i	0.0746522	−	0.180226i
$97$	4.46089	−	1.84776i	0.452935	−	0.187612i	−0.144541	−	0.989499i	$-0.546171\pi$
$97$	4.46089	−	1.84776i	0.452935	−	0.187612i	0.597475	+	0.801887i	$0.296171\pi$
$98$		−	4.20679i		−	0.424950i
$99$	−1.08098	−	2.60971i	−0.108642	−	0.262286i
$100$	2.23159	+	2.23159i	0.223159	+	0.223159i
$101$	−18.2550			−1.81644			−0.908221	−	0.418492i	$-0.862559\pi$
$101$	−18.2550			−1.81644			−0.908221	+	0.418492i	$0.862559\pi$
$102$	−0.102278	−	1.81976i	−0.0101270	−	0.180183i
$103$	−18.5779			−1.83053			−0.915265	−	0.402852i	$-0.868019\pi$
$103$	−18.5779			−1.83053			−0.915265	+	0.402852i	$0.868019\pi$
$104$	0.695413	+	0.695413i	0.0681909	+	0.0681909i
$105$	0.635926	+	1.53526i	0.0620600	+	0.149826i
$106$		−	3.55873i		−	0.345654i
$107$	2.91630	−	1.20797i	0.281930	−	0.116779i	−0.237238	−	0.971452i	$-0.576242\pi$
$107$	2.91630	−	1.20797i	0.281930	−	0.116779i	0.519167	+	0.854673i	$0.326242\pi$
$108$	−0.825966	+	1.99406i	−0.0794786	+	0.191878i
$109$	8.71401	+	3.60946i	0.834651	+	0.345724i	0.758742	−	0.651391i	$-0.225814\pi$
$109$	8.71401	+	3.60946i	0.834651	+	0.345724i	0.0759088	+	0.997115i	$0.475814\pi$
$110$	−0.894194	+	0.894194i	−0.0852581	+	0.0852581i
$111$	2.42729	−	2.42729i	0.230388	−	0.230388i
$112$	−4.42883	−	1.83448i	−0.418485	−	0.173342i
$113$	−3.19548	+	7.71458i	−0.300606	+	0.725726i	0.699335	+	0.714795i	$0.253480\pi$
$113$	−3.19548	+	7.71458i	−0.300606	+	0.725726i	−0.999940	+	0.0109318i	$0.996520\pi$
$114$	1.35521	−	0.561348i	0.126927	−	0.0525750i
$115$		−	10.6802i		−	0.995937i
$116$	−3.55515	−	8.58288i	−0.330087	−	0.796901i
$117$	−0.644823	−	0.644823i	−0.0596139	−	0.0596139i
$118$	−4.85104			−0.446575
$119$	13.6434	−	0.766814i	1.25069	−	0.0702937i
$120$	1.52744			0.139435
$121$	−0.707107	−	0.707107i	−0.0642824	−	0.0642824i
$122$	4.58221	+	11.0624i	0.414854	+	1.00155i
$123$		−	4.62187i		−	0.416740i
$124$	4.02456	−	1.66703i	0.361417	−	0.149704i
$125$	−3.92580	+	9.47772i	−0.351134	+	0.847713i
$126$	9.13257	+	3.78284i	0.813594	+	0.337002i
$127$	−4.87140	+	4.87140i	−0.432267	+	0.432267i	−0.889399	−	0.457132i	$-0.848877\pi$
$127$	−4.87140	+	4.87140i	−0.432267	+	0.432267i	0.457132	+	0.889399i	$0.348877\pi$
$128$	0.697466	−	0.697466i	0.0616479	−	0.0616479i
$129$	−2.89706	−	1.20000i	−0.255072	−	0.105654i
$130$	−0.156230	+	0.377173i	−0.0137023	+	0.0330803i
$131$	4.50013	−	1.86401i	0.393178	−	0.162860i	−0.177331	−	0.984151i	$-0.556746\pi$
$131$	4.50013	−	1.86401i	0.393178	−	0.162860i	0.570508	+	0.821292i	$0.306746\pi$
$132$			0.370550i			0.0322523i
$133$	4.20863	+	10.1605i	0.364934	+	0.881029i
$134$	2.69683	+	2.69683i	0.232970	+	0.232970i
$135$	−2.92052			−0.251358
$136$	4.14790	−	11.8557i	0.355680	−	1.01662i
$137$	12.3123			1.05191			0.525954	−	0.850513i	$-0.323708\pi$
$137$	12.3123			1.05191			0.525954	+	0.850513i	$0.323708\pi$
$138$	2.78748	+	2.78748i	0.237286	+	0.237286i
$139$	3.34055	+	8.06481i	0.283342	+	0.684048i	0.999909	−	0.0134699i	$-0.00428772\pi$
$139$	3.34055	+	8.06481i	0.283342	+	0.684048i	−0.716567	+	0.697518i	$0.754288\pi$
$140$			3.51319i			0.296919i
$141$	−0.193742	+	0.0802505i	−0.0163160	+	0.00675831i
$142$	3.33719	−	8.05668i	0.280051	−	0.676102i
$143$	−0.298260	−	0.123543i	−0.0249417	−	0.0103312i
$144$	2.88903	−	2.88903i	0.240753	−	0.240753i
$145$	8.88874	−	8.88874i	0.738170	−	0.738170i
$146$	−7.69022	−	3.18539i	−0.636447	−	0.263625i
$147$	0.638305	−	1.54101i	0.0526465	−	0.127100i
$148$	6.70482	−	2.77723i	0.551133	−	0.228287i
$149$			6.42254i			0.526155i	0.964775	+	0.263078i	$0.0847376\pi$
$149$			6.42254i			0.526155i	−0.964775	+	0.263078i	$0.915262\pi$
$150$	−0.603187	−	1.45622i	−0.0492500	−	0.118900i
$151$	−11.2675	−	11.2675i	−0.916934	−	0.916934i	0.0798714	−	0.996805i	$-0.474549\pi$
$151$	−11.2675	−	11.2675i	−0.916934	−	0.916934i	−0.996805	+	0.0798714i	$0.974549\pi$
$152$	10.1087			0.819927
$153$	−3.84615	+	10.9933i	−0.310943	+	0.888752i
$154$	3.49946			0.281995
$155$	4.16798	+	4.16798i	0.334780	+	0.334780i
$156$	0.0457789	+	0.110520i	0.00366525	+	0.00884869i
$157$			19.7763i			1.57832i	0.614190	+	0.789159i	$0.289483\pi$
$157$			19.7763i			1.57832i	−0.614190	+	0.789159i	$0.710517\pi$
$158$	8.48719	−	3.51551i	0.675204	−	0.279679i
$159$	0.539973	−	1.30361i	0.0428226	−	0.103383i
$160$	5.05157	+	2.09243i	0.399362	+	0.165421i
$161$	−20.8987	+	20.8987i	−1.64705	+	1.64705i
$162$	−5.56481	+	5.56481i	−0.437213	+	0.437213i
$163$	−3.02545	−	1.25318i	−0.236971	−	0.0981567i	0.261038	−	0.965329i	$-0.415935\pi$
$163$	−3.02545	−	1.25318i	−0.236971	−	0.0981567i	−0.498009	+	0.867172i	$0.665935\pi$
$164$	3.73932	−	9.02751i	0.291992	−	0.704930i
$165$	−0.463233	+	0.191877i	−0.0360626	+	0.0149376i
$166$		−	4.41981i		−	0.343044i
$167$	0.922820	+	2.22788i	0.0714100	+	0.172399i	0.955554	−	0.294815i	$-0.0952579\pi$
$167$	0.922820	+	2.22788i	0.0714100	+	0.172399i	−0.884144	+	0.467214i	$0.845258\pi$
$168$	−2.98884	−	2.98884i	−0.230594	−	0.230594i
$169$	12.8958			0.991983
$170$	5.20579	−	0.292586i	0.399266	−	0.0224403i
$171$	−9.37335			−0.716798
$172$	−4.68773	−	4.68773i	−0.357436	−	0.357436i
$173$	−2.23967	−	5.40704i	−0.170279	−	0.411090i	0.815585	−	0.578637i	$-0.196415\pi$
$173$	−2.23967	−	5.40704i	−0.170279	−	0.411090i	−0.985864	+	0.167547i	$0.946415\pi$
$174$			4.63982i			0.351744i
$175$	10.9178	−	4.52231i	0.825310	−	0.341855i
$176$	0.553516	−	1.33631i	0.0417229	−	0.100728i
$177$	−1.77700	−	0.736058i	−0.133568	−	0.0553255i
$178$	−9.85521	+	9.85521i	−0.738679	+	0.738679i
$179$	0.241812	−	0.241812i	0.0180739	−	0.0180739i	−0.698012	−	0.716086i	$-0.745932\pi$
$179$	0.241812	−	0.241812i	0.0180739	−	0.0180739i	0.716086	+	0.698012i	$0.245932\pi$
$180$	−2.76638	−	1.14587i	−0.206194	−	0.0854082i
$181$	5.68589	−	13.7270i	0.422629	−	1.02032i	−0.558940	−	0.829208i	$-0.688792\pi$
$181$	5.68589	−	13.7270i	0.422629	−	1.02032i	0.981569	−	0.191109i	$-0.0612083\pi$
$182$	1.04375	−	0.432334i	0.0773677	−	0.0320468i
$183$			4.74759i			0.350952i
$184$	10.3961	+	25.0984i	0.766412	+	1.85028i
$185$	6.94375	+	6.94375i	0.510515	+	0.510515i
$186$	−2.17564			−0.159526
$187$	0.231370	+	4.11661i	0.0169195	+	0.301036i
$188$	−0.443346			−0.0323344
$189$	5.71478	+	5.71478i	0.415689	+	0.415689i
$190$	1.60585	+	3.87686i	0.116500	+	0.281257i
$191$			13.9561i			1.00983i	0.863170	+	0.504913i	$0.168476\pi$
$191$			13.9561i			1.00983i	−0.863170	+	0.504913i	$0.831524\pi$
$192$	−2.98345	+	1.23578i	−0.215312	+	0.0891850i
$193$	5.18353	−	12.5141i	0.373118	−	0.900787i	−0.620100	−	0.784523i	$-0.712908\pi$
$193$	5.18353	−	12.5141i	0.373118	−	0.900787i	0.993218	−	0.116265i	$-0.0370920\pi$
$194$	−4.71020	−	1.95103i	−0.338173	−	0.140076i
$195$	−0.114459	+	0.114459i	−0.00819655	+	0.00819655i
$196$	2.49350	−	2.49350i	0.178107	−	0.178107i
$197$	−6.21978	−	2.57632i	−0.443141	−	0.183555i	0.149945	−	0.988694i	$-0.452090\pi$
$197$	−6.21978	−	2.57632i	−0.443141	−	0.183555i	−0.593086	+	0.805139i	$0.702090\pi$
$198$	−1.14139	+	2.75556i	−0.0811152	+	0.195829i
$199$	−4.01181	+	1.66175i	−0.284390	+	0.117798i	−0.520319	−	0.853972i	$-0.674187\pi$
$199$	−4.01181	+	1.66175i	−0.284390	+	0.117798i	0.235929	+	0.971770i	$0.424187\pi$
$200$		−	10.8622i		−	0.768072i
$201$	0.578689	+	1.39708i	0.0408176	+	0.0985423i
$202$	13.6297	+	13.6297i	0.958981	+	0.958981i
$203$	−34.7864			−2.44153
$204$	1.01800	−	1.13925i	0.0712746	−	0.0797635i
$205$	13.2218			0.923449
$206$	13.8707	+	13.8707i	0.966419	+	0.966419i
$207$	−9.63982	−	23.2726i	−0.670013	−	1.61756i
$208$		−	0.466949i		−	0.0323771i
$209$	−3.06573	+	1.26987i	−0.212061	+	0.0878384i
$210$	0.671468	−	1.62107i	0.0463357	−	0.111864i
$211$	7.41914	+	3.07311i	0.510755	+	0.211562i	0.623151	−	0.782102i	$-0.285852\pi$
$211$	7.41914	+	3.07311i	0.510755	+	0.211562i	−0.112396	+	0.993664i	$0.535852\pi$
$212$	2.10937	−	2.10937i	0.144872	−	0.144872i
$213$	2.44491	−	2.44491i	0.167523	−	0.167523i
$214$	−3.07929	−	1.27548i	−0.210496	−	0.0871903i
$215$	3.43285	−	8.28763i	0.234118	−	0.565211i
$216$	6.86319	−	2.84283i	0.466981	−	0.193430i
$217$		−	16.3116i		−	1.10730i
$218$	−3.81119	−	9.20103i	−0.258127	−	0.623173i
$219$	−2.33370	−	2.33370i	−0.157697	−	0.157697i
$220$	−1.06003			−0.0714674
$221$	0.577587	+	1.19923i	0.0388527	+	0.0806692i
$222$	−3.62456			−0.243265
$223$	−6.72514	−	6.72514i	−0.450349	−	0.450349i	0.445122	−	0.895470i	$-0.353160\pi$
$223$	−6.72514	−	6.72514i	−0.450349	−	0.450349i	−0.895470	+	0.445122i	$0.853160\pi$
$224$	−5.79035	−	13.9792i	−0.386884	−	0.934021i
$225$			10.0720i			0.671465i
$226$	8.14574	−	3.37408i	0.541847	−	0.224440i
$227$	−1.14522	+	2.76480i	−0.0760109	+	0.183506i	−0.957318	−	0.289038i	$-0.906664\pi$
$227$	−1.14522	+	2.76480i	−0.0760109	+	0.183506i	0.881307	+	0.472545i	$0.156664\pi$
$228$	1.13601	+	0.470549i	0.0752338	+	0.0311629i
$229$	−8.02441	+	8.02441i	−0.530268	+	0.530268i	−0.920652	−	0.390384i	$-0.872342\pi$
$229$	−8.02441	+	8.02441i	−0.530268	+	0.530268i	0.390384	+	0.920652i	$0.372342\pi$
$230$	−7.97414	+	7.97414i	−0.525800	+	0.525800i
$231$	1.28190	+	0.530980i	0.0843428	+	0.0349359i
$232$	−12.2362	+	29.5407i	−0.803344	+	1.93944i
$233$	5.37653	−	2.22703i	0.352228	−	0.145898i	−0.199552	−	0.979887i	$-0.563949\pi$
$233$	5.37653	−	2.22703i	0.352228	−	0.145898i	0.551780	+	0.833990i	$0.313949\pi$
$234$			0.962884i			0.0629457i
$235$	−0.229573	−	0.554237i	−0.0149757	−	0.0361545i
$236$	−2.87536	−	2.87536i	−0.187170	−	0.187170i
$237$	3.64239			0.236598
$238$	−10.7590	−	9.61400i	−0.697405	−	0.623183i
$239$	5.68959			0.368029			0.184015	−	0.982924i	$-0.441091\pi$
$239$	5.68959			0.368029			0.184015	+	0.982924i	$0.441091\pi$
$240$	−0.512814	−	0.512814i	−0.0331020	−	0.0331020i
$241$	1.98076	+	4.78198i	0.127592	+	0.308034i	0.974747	−	0.223311i	$-0.0716866\pi$
$241$	1.98076	+	4.78198i	0.127592	+	0.308034i	−0.847155	+	0.531345i	$0.821687\pi$
$242$			1.05589i			0.0678751i
$243$	−9.64160	+	3.99368i	−0.618509	+	0.256195i
$244$	−3.84103	+	9.27307i	−0.245897	+	0.593647i
$245$	4.40835	+	1.82600i	0.281639	+	0.116659i
$246$	−3.45081	+	3.45081i	−0.220016	+	0.220016i
$247$	−0.757499	+	0.757499i	−0.0481985	+	0.0481985i
$248$	−13.8518	−	5.73761i	−0.879591	−	0.364339i
$249$	0.670627	−	1.61904i	0.0424993	−	0.102602i
$250$	10.0074	−	4.14521i	0.632925	−	0.262166i
$251$			15.0997i			0.953082i	0.879152	+	0.476541i	$0.158110\pi$
$251$			15.0997i			0.953082i	−0.879152	+	0.476541i	$0.841890\pi$
$252$	3.17096	+	7.65536i	0.199751	+	0.482243i
$253$	−6.30576	−	6.30576i	−0.396440	−	0.396440i
$254$	7.27423			0.456426
$255$	1.95134	+	0.682706i	0.122198	+	0.0427527i
$256$	−16.4683			−1.02927
$257$	−4.41391	−	4.41391i	−0.275332	−	0.275332i	0.555910	−	0.831242i	$-0.312370\pi$
$257$	−4.41391	−	4.41391i	−0.275332	−	0.275332i	−0.831242	+	0.555910i	$0.812370\pi$
$258$	1.26707	+	3.05898i	0.0788843	+	0.190444i
$259$		−	27.1746i		−	1.68855i
$260$	−0.316165	+	0.130960i	−0.0196077	+	0.00812178i
$261$	11.3460	−	27.3917i	0.702300	−	1.69550i
$262$	−4.75164	−	1.96819i	−0.293557	−	0.121595i
$263$	10.4082	−	10.4082i	0.641794	−	0.641794i	−0.309202	−	0.950996i	$-0.600062\pi$
$263$	10.4082	−	10.4082i	0.641794	−	0.641794i	0.950996	+	0.309202i	$0.100062\pi$
$264$	0.901820	−	0.901820i	0.0555032	−	0.0555032i
$265$	3.72924	+	1.54470i	0.229085	+	0.0948902i
$266$	4.44384	−	10.7284i	0.272470	−	0.657800i
$267$	−5.10545	+	2.11474i	−0.312448	+	0.129420i
$268$			3.19698i			0.195287i
$269$	4.42833	+	10.6909i	0.270000	+	0.651837i	0.999483	−	0.0321618i	$-0.0102392\pi$
$269$	4.42833	+	10.6909i	0.270000	+	0.651837i	−0.729483	+	0.683999i	$0.760239\pi$
$270$	2.18054	+	2.18054i	0.132703	+	0.132703i
$271$	17.1350			1.04088			0.520439	−	0.853899i	$-0.325768\pi$
$271$	17.1350			1.04088			0.520439	+	0.853899i	$0.325768\pi$
$272$	−5.37298	+	2.58779i	−0.325785	+	0.156908i
$273$	0.447938			0.0271104
$274$	−9.19267	−	9.19267i	−0.555349	−	0.555349i
$275$	1.36451	+	3.29423i	0.0822833	+	0.198649i
$276$			3.30445i			0.198905i
$277$	−3.30968	+	1.37092i	−0.198860	+	0.0823703i	−0.479891	−	0.877328i	$-0.659324\pi$
$277$	−3.30968	+	1.37092i	−0.198860	+	0.0823703i	0.281031	+	0.959699i	$0.409324\pi$
$278$	3.52726	−	8.51555i	0.211551	−	0.510729i
$279$	12.8441	+	5.32021i	0.768958	+	0.318513i
$280$	8.55017	−	8.55017i	0.510971	−	0.510971i
$281$	−9.23446	+	9.23446i	−0.550882	+	0.550882i	−0.926695	−	0.375814i	$-0.877363\pi$
$281$	−9.23446	+	9.23446i	−0.550882	+	0.550882i	0.375814	+	0.926695i	$0.377363\pi$
$282$	0.204570	+	0.0847357i	0.0121820	+	0.00504594i
$283$	3.10776	−	7.50278i	0.184737	−	0.445994i	−0.804195	−	0.594366i	$-0.797403\pi$
$283$	3.10776	−	7.50278i	0.184737	−	0.445994i	0.988932	+	0.148372i	$0.0474031\pi$
$284$	6.75350	−	2.79739i	0.400746	−	0.165995i
$285$			1.66380i			0.0985553i
$286$	0.130448	+	0.314929i	0.00771355	+	0.0186221i
$287$	−25.8720	−	25.8720i	−1.52717	−	1.52717i
$288$	12.8961			0.759912
$289$	10.5981	−	13.2921i	0.623419	−	0.781888i
$290$	−13.2731			−0.779425
$291$	−1.42938	−	1.42938i	−0.0837916	−	0.0837916i
$292$	−2.67015	−	6.44631i	−0.156259	−	0.377242i
$293$			21.9369i			1.28157i	0.767721	+	0.640785i	$0.221391\pi$
$293$			21.9369i			1.28157i	−0.767721	+	0.640785i	$0.778609\pi$
$294$	−1.62713	+	0.673980i	−0.0948962	+	0.0393073i
$295$	2.10564	−	5.08347i	0.122595	−	0.295971i
$296$	−23.0768	−	9.55872i	−1.34131	−	0.555589i
$297$	−1.72432	+	1.72432i	−0.100055	+	0.100055i
$298$	4.79524	−	4.79524i	0.277781	−	0.277781i
$299$	−2.65979	−	1.10172i	−0.153819	−	0.0637141i
$300$	0.505621	−	1.22068i	0.0291920	−	0.0704758i
$301$	−22.9343	+	9.49968i	−1.32191	+	0.547552i
$302$			16.8252i			0.968181i
$303$	2.92467	+	7.06079i	0.168018	+	0.405632i
$304$	−3.39386	−	3.39386i	−0.194651	−	0.194651i
$305$	−13.5814			−0.777670
$306$	11.0795	−	5.33622i	0.633373	−	0.305051i
$307$	3.17581			0.181253			0.0906266	−	0.995885i	$-0.471113\pi$
$307$	3.17581			0.181253			0.0906266	+	0.995885i	$0.471113\pi$
$308$	2.07424	+	2.07424i	0.118191	+	0.118191i
$309$	2.97640	+	7.18566i	0.169321	+	0.408778i
$310$		−	6.22385i		−	0.353491i
$311$	4.46556	−	1.84970i	0.253219	−	0.104887i	−0.252464	−	0.967606i	$-0.581241\pi$
$311$	4.46556	−	1.84970i	0.253219	−	0.104887i	0.505682	+	0.862720i	$0.331241\pi$
$312$	0.157563	−	0.380390i	0.00892023	−	0.0215353i
$313$	−10.5713	−	4.37877i	−0.597524	−	0.247502i	0.0633600	−	0.997991i	$-0.479818\pi$
$313$	−10.5713	−	4.37877i	−0.597524	−	0.247502i	−0.660884	+	0.750488i	$0.729818\pi$
$314$	14.7655	−	14.7655i	0.833264	−	0.833264i
$315$	−7.92816	+	7.92816i	−0.446701	+	0.446701i
$316$	7.11437	+	2.94687i	0.400215	+	0.165774i
$317$	−2.71148	+	6.54608i	−0.152292	+	0.367665i	−0.981551	−	0.191199i	$-0.938762\pi$
$317$	−2.71148	+	6.54608i	−0.152292	+	0.367665i	0.829260	+	0.558864i	$0.188762\pi$
$318$	−1.37647	+	0.570152i	−0.0771885	+	0.0319725i
$319$		−	10.4961i		−	0.587667i
$320$	−3.53521	−	8.53474i	−0.197624	−	0.477107i
$321$	−0.934454	−	0.934454i	−0.0521562	−	0.0521562i
$322$	31.2071			1.73910
$323$	12.9142	+	4.51822i	0.718566	+	0.251401i
$324$	−6.59687			−0.366493
$325$	0.813958	+	0.813958i	0.0451503	+	0.0451503i
$326$	1.32322	+	3.19454i	0.0732864	+	0.176929i
$327$		−	3.94874i		−	0.218366i
$328$	−31.0711	+	12.8701i	−1.71561	+	0.710630i
$329$	−0.635294	+	1.53373i	−0.0350249	+	0.0845575i
$330$	0.489123	+	0.202601i	0.0269253	+	0.0111528i
$331$	−20.0465	+	20.0465i	−1.10185	+	1.10185i	−0.107667	+	0.994187i	$0.534338\pi$
$331$	−20.0465	+	20.0465i	−1.10185	+	1.10185i	−0.994187	+	0.107667i	$0.965662\pi$
$332$	2.61976	−	2.61976i	0.143778	−	0.143778i
$333$	21.3980	+	8.86334i	1.17260	+	0.485708i
$334$	0.974396	−	2.35240i	0.0533166	−	0.128718i
$335$	−3.99662	+	1.65545i	−0.218359	+	0.0904472i
$336$			2.00692i			0.109486i
$337$	−8.31378	−	20.0712i	−0.452880	−	1.09335i	−0.971222	−	0.238176i	$-0.923450\pi$
$337$	−8.31378	−	20.0712i	−0.452880	−	1.09335i	0.518342	−	0.855174i	$-0.326550\pi$
$338$	−9.62833	−	9.62833i	−0.523712	−	0.523712i
$339$	3.49585			0.189868
$340$	3.25906	+	2.91221i	0.176747	+	0.157937i
$341$	4.92167			0.266523
$342$	6.99839	+	6.99839i	0.378430	+	0.378430i
$343$	3.82504	+	9.23446i	0.206533	+	0.498614i
$344$			22.8174i			1.23023i
$345$	−4.13097	+	1.71110i	−0.222404	+	0.0921227i
$346$	−2.36485	+	5.70924i	−0.127135	+	0.306931i
$347$	11.3493	+	4.70102i	0.609261	+	0.252364i	0.665912	−	0.746030i	$-0.268042\pi$
$347$	11.3493	+	4.70102i	0.609261	+	0.252364i	−0.0566517	+	0.998394i	$0.518042\pi$
$348$	−2.75017	+	2.75017i	−0.147424	+	0.147424i
$349$	−7.42104	+	7.42104i	−0.397239	+	0.397239i	−0.877258	−	0.480019i	$-0.840630\pi$
$349$	−7.42104	+	7.42104i	−0.397239	+	0.397239i	0.480019	+	0.877258i	$0.340630\pi$
$350$	−11.5280	−	4.77506i	−0.616199	−	0.255238i
$351$	−0.301266	+	0.727321i	−0.0160804	+	0.0388215i
$352$	4.21792	−	1.74712i	0.224816	−	0.0931217i
$353$		−	18.0064i		−	0.958382i	−0.877711	−	0.479191i	$-0.840930\pi$
$353$		−	18.0064i		−	0.958382i	0.877711	−	0.479191i	$-0.159070\pi$
$354$	0.777196	+	1.87632i	0.0413075	+	0.0997252i
$355$	6.99416	+	6.99416i	0.371212	+	0.371212i
$356$	−11.6830			−0.619196
$357$	−2.48243	−	5.15423i	−0.131384	−	0.272791i
$358$	−0.361086			−0.0190840
$359$	4.88236	+	4.88236i	0.257681	+	0.257681i	0.824110	−	0.566429i	$-0.191676\pi$
$359$	4.88236	+	4.88236i	0.257681	+	0.257681i	−0.566429	+	0.824110i	$0.691676\pi$
$360$	3.94388	+	9.52137i	0.207861	+	0.501820i
$361$		−	7.98876i		−	0.420461i
$362$	−14.4942	+	6.00367i	−0.761796	+	0.315546i
$363$	−0.160212	+	0.386786i	−0.00840896	+	0.0203010i
$364$	0.874919	+	0.362404i	0.0458582	+	0.0189951i
$365$	6.67603	−	6.67603i	0.349439	−	0.349439i
$366$	3.54468	−	3.54468i	0.185283	−	0.185283i
$367$	16.5072	+	6.83749i	0.861667	+	0.356914i	0.769359	−	0.638817i	$-0.220576\pi$
$367$	16.5072	+	6.83749i	0.861667	+	0.356914i	0.0923075	+	0.995731i	$0.470576\pi$
$368$	4.93609	−	11.9168i	0.257311	−	0.621204i
$369$	28.8107	−	11.9338i	1.49982	−	0.621248i
$370$		−	10.3688i		−	0.539047i
$371$	−4.27463	−	10.3199i	−0.221928	−	0.535781i
$372$	−1.28957	−	1.28957i	−0.0668610	−	0.0668610i
$373$	−18.7990			−0.973376			−0.486688	−	0.873576i	$-0.661795\pi$
$373$	−18.7990			−0.973376			−0.486688	+	0.873576i	$0.661795\pi$
$374$	2.90082	−	3.24632i	0.149998	−	0.167863i
$375$	4.29481			0.221783
$376$	1.07899	+	1.07899i	0.0556445	+	0.0556445i
$377$	−1.29672	−	3.13055i	−0.0667844	−	0.161232i
$378$		−	8.53361i		−	0.438922i
$379$	7.68093	−	3.18155i	0.394543	−	0.163425i	−0.176586	−	0.984285i	$-0.556505\pi$
$379$	7.68093	−	3.18155i	0.394543	−	0.163425i	0.571129	+	0.820860i	$0.306505\pi$
$380$	−1.34610	+	3.24977i	−0.0690534	+	0.166710i
$381$	2.66465	+	1.10373i	0.136514	+	0.0565460i
$382$	10.4200	−	10.4200i	0.533133	−	0.533133i
$383$	−18.3797	+	18.3797i	−0.939158	+	0.939158i	−0.998252	−	0.0590943i	$-0.981179\pi$
$383$	−18.3797	+	18.3797i	−0.939158	+	0.939158i	0.0590943	+	0.998252i	$0.481179\pi$
$384$	−0.381513	−	0.158028i	−0.0194690	−	0.00806433i
$385$	−1.51898	+	3.66713i	−0.0774141	+	0.186894i
$386$	−13.2135	+	5.47323i	−0.672552	+	0.278580i
$387$		−	21.1574i		−	1.07549i
$388$	−1.63545	−	3.94832i	−0.0830273	−	0.200446i
$389$	−7.94242	−	7.94242i	−0.402697	−	0.402697i	0.476485	−	0.879182i	$-0.341910\pi$
$389$	−7.94242	−	7.94242i	−0.402697	−	0.402697i	−0.879182	+	0.476485i	$0.841910\pi$
$390$	0.170916			0.00865465
$391$	2.06329	+	36.7106i	0.104345	+	1.85654i
$392$	−12.1370			−0.613012
$393$	−1.44195	−	1.44195i	−0.0727368	−	0.0727368i
$394$	2.72031	+	6.56740i	0.137047	+	0.330861i
$395$			10.4198i			0.524276i
$396$	−2.30985	+	0.956770i	−0.116074	+	0.0480795i
$397$	−2.37354	+	5.73023i	−0.119124	+	0.287592i	−0.972183	−	0.234224i	$-0.924745\pi$
$397$	−2.37354	+	5.73023i	−0.119124	+	0.287592i	0.853058	+	0.521816i	$0.174745\pi$
$398$	4.23603	+	1.75462i	0.212333	+	0.0879512i
$399$	3.25568	−	3.25568i	0.162988	−	0.162988i
$400$	−3.64682	+	3.64682i	−0.182341	+	0.182341i
$401$	20.4917	+	8.48792i	1.02330	+	0.423867i	0.830291	−	0.557330i	$-0.188174\pi$
$401$	20.4917	+	8.48792i	1.02330	+	0.423867i	0.193013	+	0.981196i	$0.438174\pi$
$402$	0.611031	−	1.47516i	0.0304755	−	0.0735743i
$403$	1.46794	−	0.608039i	0.0731231	−	0.0302886i
$404$			16.1575i			0.803864i
$405$	−3.41598	−	8.24690i	−0.169741	−	0.409792i
$406$	25.9725	+	25.9725i	1.28899	+	1.28899i
$407$	8.19938			0.406428
$408$	−5.25018	+	0.295081i	−0.259923	+	0.0146087i
$409$	30.4544			1.50587			0.752936	−	0.658094i	$-0.228637\pi$
$409$	30.4544			1.50587			0.752936	+	0.658094i	$0.228637\pi$
$410$	−9.87173	−	9.87173i	−0.487530	−	0.487530i
$411$	−1.97258	−	4.76222i	−0.0973000	−	0.234903i
$412$			16.4432i			0.810099i
$413$	−14.0674	+	5.82692i	−0.692213	+	0.286724i
$414$	−10.1786	+	24.5733i	−0.500250	+	1.20771i
$415$	4.63158	+	1.91846i	0.227355	+	0.0941737i
$416$	1.04219	−	1.04219i	0.0510975	−	0.0510975i
$417$	2.58416	−	2.58416i	0.126547	−	0.126547i
$418$	3.23707	+	1.34084i	0.158330	+	0.0655825i
$419$	−9.09564	+	21.9588i	−0.444351	+	1.07276i	0.530055	+	0.847963i	$0.322171\pi$
$419$	−9.09564	+	21.9588i	−0.444351	+	1.07276i	−0.974406	+	0.224795i	$0.927829\pi$
$420$	1.35886	−	0.562856i	0.0663054	−	0.0274646i
$421$		−	4.48385i		−	0.218529i	−0.994013	−	0.109265i	$-0.965150\pi$
$421$		−	4.48385i		−	0.218529i	0.994013	−	0.109265i	$-0.0348496\pi$
$422$	−3.24486	−	7.83380i	−0.157958	−	0.381343i
$423$	−1.00049	−	1.00049i	−0.0486456	−	0.0486456i
$424$	−10.2673			−0.498623
$425$	4.85498	−	13.8768i	0.235501	−	0.673121i
$426$	−3.65087			−0.176885
$427$	26.5757	+	26.5757i	1.28609	+	1.28609i
$428$	−1.06917	−	2.58121i	−0.0516804	−	0.124768i
$429$			0.135156i			0.00652539i
$430$	−8.75082	+	3.62471i	−0.422002	+	0.174799i
$431$	9.09551	−	21.9585i	0.438115	−	1.05770i	−0.538484	−	0.842636i	$-0.681003\pi$
$431$	9.09551	−	21.9585i	0.438115	−	1.05770i	0.976599	−	0.215068i	$-0.0689973\pi$
$432$	−3.25865	−	1.34978i	−0.156782	−	0.0649412i
$433$	10.4523	−	10.4523i	0.502306	−	0.502306i	−0.409848	−	0.912154i	$-0.634418\pi$
$433$	10.4523	−	10.4523i	0.502306	−	0.502306i	0.912154	+	0.409848i	$0.134418\pi$
$434$	−12.1786	+	12.1786i	−0.584593	+	0.584593i
$435$	−4.86213	−	2.01396i	−0.233121	−	0.0965620i
$436$	3.19473	−	7.71275i	0.153000	−	0.369374i
$437$	−27.3392	+	11.3243i	−1.30781	+	0.541713i
$438$			3.48481i			0.166511i
$439$	2.96783	+	7.16497i	0.141647	+	0.341965i	0.978743	−	0.205090i	$-0.0657487\pi$
$439$	2.96783	+	7.16497i	0.141647	+	0.341965i	−0.837096	+	0.547055i	$0.815749\pi$
$440$	2.57984	+	2.57984i	0.122989	+	0.122989i
$441$	11.2541			0.535908
$442$	0.464138	−	1.32662i	0.0220768	−	0.0631010i
$443$	33.6384			1.59821			0.799105	−	0.601191i	$-0.205307\pi$
$443$	33.6384			1.59821			0.799105	+	0.601191i	$0.205307\pi$
$444$	−2.14839	−	2.14839i	−0.101958	−	0.101958i
$445$	−6.04965	−	14.6051i	−0.286781	−	0.692350i
$446$			10.0423i			0.475518i
$447$	2.48415	−	1.02897i	0.117496	−	0.0486686i
$448$	−9.78294	+	23.6181i	−0.462200	+	1.11585i
$449$	0.941145	+	0.389835i	0.0444154	+	0.0183975i	0.404781	−	0.914414i	$-0.367348\pi$
$449$	0.941145	+	0.389835i	0.0444154	+	0.0183975i	−0.360365	+	0.932811i	$0.617348\pi$
$450$	7.52001	−	7.52001i	0.354497	−	0.354497i
$451$	7.80633	−	7.80633i	0.367586	−	0.367586i
$452$	6.82815	+	2.82831i	0.321169	+	0.133033i
$453$	−2.55292	+	6.16329i	−0.119947	+	0.289577i
$454$	2.91933	−	1.20922i	0.137011	−	0.0567517i
$455$			1.28142i			0.0600737i
$456$	−1.61954	−	3.90992i	−0.0758421	−	0.183099i
$457$	11.7427	+	11.7427i	0.549298	+	0.549298i	0.926238	−	0.376939i	$-0.123024\pi$
$457$	11.7427	+	11.7427i	0.549298	+	0.549298i	−0.376939	+	0.926238i	$0.623024\pi$
$458$	11.9825			0.559905
$459$	10.0386	−	0.564207i	0.468560	−	0.0263349i
$460$	−9.45304			−0.440750
$461$	−6.37975	−	6.37975i	−0.297135	−	0.297135i	0.542756	−	0.839890i	$-0.317381\pi$
$461$	−6.37975	−	6.37975i	−0.297135	−	0.297135i	−0.839890	+	0.542756i	$0.817381\pi$
$462$	−0.560656	−	1.35354i	−0.0260841	−	0.0629726i
$463$		−	32.4882i		−	1.50986i	−0.655808	−	0.754928i	$-0.727672\pi$
$463$		−	32.4882i		−	1.50986i	0.655808	−	0.754928i	$-0.272328\pi$
$464$	14.0260	−	5.80975i	0.651139	−	0.269711i
$465$	0.944357	−	2.27988i	0.0437935	−	0.105727i
$466$	−5.67702	−	2.35150i	−0.262983	−	0.108931i
$467$	3.04942	−	3.04942i	0.141110	−	0.141110i	−0.633023	−	0.774133i	$-0.718186\pi$
$467$	3.04942	−	3.04942i	0.141110	−	0.141110i	0.774133	+	0.633023i	$0.218186\pi$
$468$	−0.570731	+	0.570731i	−0.0263821	+	0.0263821i
$469$	11.0598	+	4.58112i	0.510694	+	0.211537i
$470$	−0.242403	+	0.585213i	−0.0111812	+	0.0269939i
$471$	7.64919	−	3.16840i	0.352456	−	0.145992i
$472$			13.9957i			0.644206i
$473$	−2.86633	−	6.91993i	−0.131794	−	0.318179i
$474$	−2.71950	−	2.71950i	−0.124911	−	0.124911i
$475$	11.8319			0.542887
$476$	−0.678705	−	12.0757i	−0.0311084	−	0.553490i
$477$	9.52035			0.435907
$478$	−4.24800	−	4.24800i	−0.194299	−	0.194299i
$479$	−13.2844	−	32.0713i	−0.606978	−	1.46537i	−0.866271	−	0.499575i	$-0.833489\pi$
$479$	−13.2844	−	32.0713i	−0.606978	−	1.46537i	0.259293	−	0.965799i	$-0.416511\pi$
$480$		−	2.28911i		−	0.104483i
$481$	2.44554	−	1.01298i	0.111507	−	0.0461878i
$482$	2.09146	−	5.04924i	0.0952635	−	0.229987i
$483$	11.4316	+	4.73512i	0.520155	+	0.215455i
$484$	−0.625858	+	0.625858i	−0.0284481	+	0.0284481i
$485$	4.08902	−	4.08902i	0.185673	−	0.185673i
$486$	10.1805	+	4.21689i	0.461795	+	0.191282i
$487$	5.10341	−	12.3207i	0.231257	−	0.558305i	−0.765068	−	0.643949i	$-0.777295\pi$
$487$	5.10341	−	12.3207i	0.231257	−	0.558305i	0.996326	+	0.0856443i	$0.0272949\pi$
$488$	31.9162	−	13.2201i	1.44478	−	0.598447i
$489$			1.37098i			0.0619977i
$490$	−1.92805	−	4.65473i	−0.0871006	−	0.210279i
$491$	−4.78466	−	4.78466i	−0.215929	−	0.215929i	0.590852	−	0.806780i	$-0.298792\pi$
$491$	−4.78466	−	4.78466i	−0.215929	−	0.215929i	−0.806780	+	0.590852i	$0.798792\pi$
$492$	−4.09080			−0.184428
$493$	−28.8356	+	32.2700i	−1.29869	+	1.45337i
$494$	1.13114			0.0508923
$495$	−2.39216	−	2.39216i	−0.107520	−	0.107520i
$496$	2.72422	+	6.57686i	0.122321	+	0.295310i
$497$		−	27.3719i		−	1.22780i
$498$	−1.70952	+	0.708108i	−0.0766056	+	0.0317311i
$499$	−10.0212	+	24.1933i	−0.448610	+	1.08304i	0.524232	+	0.851575i	$0.324352\pi$
$499$	−10.0212	+	24.1933i	−0.448610	+	1.08304i	−0.972843	+	0.231466i	$0.925648\pi$
$500$	8.38870	+	3.47471i	0.375154	+	0.155394i
$501$	0.713869	−	0.713869i	0.0318933	−	0.0318933i
$502$	11.2738	−	11.2738i	0.503175	−	0.503175i
$503$	29.0732	+	12.0425i	1.29631	+	0.536949i	0.920860	−	0.389894i	$-0.127488\pi$
$503$	29.0732	+	12.0425i	1.29631	+	0.536949i	0.375450	+	0.926843i	$0.377488\pi$
$504$	10.9139	−	26.3484i	0.486142	−	1.17365i
$505$	−20.1988	+	8.36662i	−0.898835	+	0.372310i
$506$			9.41610i			0.418596i
$507$	−2.06606	−	4.98791i	−0.0917570	−	0.221521i
$508$	4.31166	+	4.31166i	0.191299	+	0.191299i
$509$	−26.5254			−1.17572			−0.587859	−	0.808964i	$-0.700029\pi$
$509$	−26.5254			−1.17572			−0.587859	+	0.808964i	$0.700029\pi$
$510$	−0.947199	−	1.96665i	−0.0419427	−	0.0870848i
$511$	−26.1269			−1.15579
$512$	10.9008	+	10.9008i	0.481750	+	0.481750i
$513$	3.09663	+	7.47593i	0.136720	+	0.330070i
$514$			6.59109i			0.290720i
$515$	−20.5560	+	8.51458i	−0.905807	+	0.375197i
$516$	−1.06212	+	2.56418i	−0.0467572	+	0.112882i
$517$	−0.462772	−	0.191687i	−0.0203527	−	0.00843037i
$518$	−20.2893	+	20.2893i	−0.891461	+	0.891461i
$519$	−1.73255	+	1.73255i	−0.0760505	+	0.0760505i
$520$	1.08818	+	0.450740i	0.0477199	+	0.0197662i
$521$	−4.43253	+	10.7011i	−0.194193	+	0.468822i	−0.990743	−	0.135750i	$-0.956656\pi$
$521$	−4.43253	+	10.7011i	−0.194193	+	0.468822i	0.796551	+	0.604572i	$0.206656\pi$
$522$	−28.9226	+	11.9801i	−1.26591	+	0.524356i
$523$			29.7080i			1.29904i	0.760344	+	0.649520i	$0.225030\pi$
$523$			29.7080i			1.29904i	−0.760344	+	0.649520i	$0.774970\pi$
$524$	−1.64983	−	3.98305i	−0.0720733	−	0.174000i
$525$	−3.49834	−	3.49834i	−0.152680	−	0.152680i
$526$	−15.5420			−0.677664
$527$	−15.1316	−	13.5212i	−0.659143	−	0.588993i
$528$	−0.605545			−0.0263530
$529$	−39.9693	−	39.9693i	−1.73780	−	1.73780i
$530$	−1.63103	−	3.93766i	−0.0708476	−	0.171041i
$531$		−	12.9776i		−	0.563178i
$532$	8.99305	−	3.72504i	0.389898	−	0.161501i
$533$	1.36389	−	3.29273i	0.0590768	−	0.142624i
$534$	5.39079	+	2.23294i	0.233282	+	0.0966286i
$535$	2.67319	−	2.67319i	0.115572	−	0.115572i
$536$	7.78061	−	7.78061i	0.336071	−	0.336071i
$537$	−0.132271	−	0.0547883i	−0.00570790	−	0.00236429i
$538$	4.67582	−	11.2884i	0.201589	−	0.486679i
$539$	3.68085	−	1.52466i	0.158545	−	0.0656717i
$540$			2.58494i			0.111238i
$541$	−2.27778	−	5.49904i	−0.0979293	−	0.236422i	0.867321	−	0.497749i	$-0.165840\pi$
$541$	−2.27778	−	5.49904i	−0.0979293	−	0.236422i	−0.965250	+	0.261327i	$0.915840\pi$
$542$	−12.7935	−	12.7935i	−0.549526	−	0.549526i
$543$	−6.22035			−0.266941
$544$	−17.7677	−	6.21630i	−0.761786	−	0.266522i
$545$	11.2962			0.483875
$546$	−0.334442	−	0.334442i	−0.0143128	−	0.0143128i
$547$	−6.89215	−	16.6391i	−0.294687	−	0.711437i	−0.999997	−	0.00253808i	$-0.999192\pi$
$547$	−6.89215	−	16.6391i	−0.294687	−	0.711437i	0.705310	−	0.708899i	$-0.250808\pi$
$548$		−	10.8976i		−	0.465520i
$549$	−29.5944	+	12.2584i	−1.26306	+	0.523175i
$550$	1.44078	−	3.47834i	0.0614349	−	0.148317i
$551$	−32.1781	−	13.3286i	−1.37083	−	0.567817i
$552$	8.04215	−	8.04215i	0.342297	−	0.342297i
$553$	20.3891	−	20.3891i	0.867032	−	0.867032i
$554$	3.49466	+	1.44753i	0.148474	+	0.0614999i
$555$	1.57328	−	3.79822i	0.0667818	−	0.161226i
$556$	7.13814	−	2.95671i	0.302725	−	0.125393i
$557$		−	4.05936i		−	0.172001i	−0.996295	−	0.0860003i	$-0.972591\pi$
$557$		−	4.05936i		−	0.172001i	0.996295	−	0.0860003i	$-0.0274086\pi$
$558$	−5.61755	−	13.5620i	−0.237810	−	0.574124i
$559$	−1.70982	−	1.70982i	−0.0723177	−	0.0723177i
$560$	−5.74119			−0.242609
$561$	1.55518	−	0.749022i	0.0656598	−	0.0316237i
$562$	13.7894			0.581670
$563$	13.4646	+	13.4646i	0.567467	+	0.567467i	0.931418	−	0.363951i	$-0.118572\pi$
$563$	13.4646	+	13.4646i	0.567467	+	0.567467i	−0.363951	+	0.931418i	$0.618572\pi$
$564$	0.0710295	+	0.171480i	0.00299088	+	0.00722063i
$565$			10.0006i			0.420727i
$566$	−7.92211	+	3.28145i	−0.332991	+	0.137929i
$567$	−9.45300	+	22.8216i	−0.396989	+	0.958415i
$568$	−23.2443	−	9.62811i	−0.975310	−	0.403987i
$569$	−2.45418	+	2.45418i	−0.102884	+	0.102884i	−0.756675	−	0.653791i	$-0.773178\pi$
$569$	−2.45418	+	2.45418i	−0.102884	+	0.102884i	0.653791	+	0.756675i	$0.273178\pi$
$570$	1.24224	−	1.24224i	0.0520317	−	0.0520317i
$571$	−22.2793	−	9.22837i	−0.932358	−	0.386195i	−0.135786	−	0.990738i	$-0.543356\pi$
$571$	−22.2793	−	9.22837i	−0.932358	−	0.386195i	−0.796573	+	0.604543i	$0.793356\pi$
$572$	−0.109348	+	0.263989i	−0.00457206	+	0.0110379i
$573$	5.39803	−	2.23594i	0.225506	−	0.0934075i
$574$			38.6334i			1.61253i
$575$	12.1683	+	29.3769i	0.507454	+	1.22510i
$576$	−15.4067	−	15.4067i	−0.641944	−	0.641944i
$577$	3.31891			0.138168			0.0690840	−	0.997611i	$-0.477992\pi$
$577$	3.31891			0.138168			0.0690840	+	0.997611i	$0.477992\pi$
$578$	−17.8371	+	2.01138i	−0.741924	+	0.0836626i
$579$	−5.67076			−0.235669
$580$	−7.86740	−	7.86740i	−0.326676	−	0.326676i
$581$	−5.30894	−	12.8169i	−0.220252	−	0.531735i
$582$			2.13442i			0.0884747i
$583$	3.11381	−	1.28978i	0.128961	−	0.0534173i
$584$	−9.19017	+	22.1870i	−0.380292	+	0.918106i
$585$	−1.00902	−	0.417949i	−0.0417178	−	0.0172801i
$586$	16.3787	−	16.3787i	0.676598	−	0.676598i
$587$	14.6744	−	14.6744i	0.605679	−	0.605679i	−0.336135	−	0.941814i	$-0.609120\pi$
$587$	14.6744	−	14.6744i	0.605679	−	0.605679i	0.941814	+	0.336135i	$0.109120\pi$
$588$	−1.36394	−	0.564962i	−0.0562479	−	0.0232987i
$589$	6.24986	−	15.0885i	0.257521	−	0.621711i
$590$	−5.36758	+	2.22333i	−0.220980	+	0.0915329i
$591$			2.81849i			0.115937i
$592$	4.53849	+	10.9569i	0.186531	+	0.450325i
$593$	−14.0852	−	14.0852i	−0.578411	−	0.578411i	0.356055	−	0.934465i	$-0.384122\pi$
$593$	−14.0852	−	14.0852i	−0.578411	−	0.578411i	−0.934465	+	0.356055i	$0.884122\pi$
$594$	2.57484			0.105647
$595$	14.7447	−	7.10149i	0.604474	−	0.291133i
$596$	5.68458			0.232849
$597$	1.28548	+	1.28548i	0.0526113	+	0.0526113i
$598$	1.16329	+	2.80844i	0.0475706	+	0.114846i
$599$			10.9441i			0.447162i	0.974685	+	0.223581i	$0.0717748\pi$
$599$			10.9441i			0.447162i	−0.974685	+	0.223581i	$0.928225\pi$
$600$	−4.20135	+	1.74025i	−0.171519	+	0.0710456i
$601$	4.20784	−	10.1586i	0.171641	−	0.414379i	−0.814527	−	0.580126i	$-0.803003\pi$
$601$	4.20784	−	10.1586i	0.171641	−	0.414379i	0.986168	+	0.165747i	$0.0530034\pi$
$602$	24.2160	+	10.0306i	0.986972	+	0.408817i
$603$	−7.21458	+	7.21458i	−0.293800	+	0.293800i
$604$	−9.97281	+	9.97281i	−0.405788	+	0.405788i
$605$	−1.10648	−	0.458319i	−0.0449848	−	0.0186333i
$606$	3.08813	−	7.45541i	0.125447	−	0.302855i
$607$	−13.4070	+	5.55336i	−0.544173	+	0.225404i	−0.637798	−	0.770204i	$-0.720155\pi$
$607$	−13.4070	+	5.55336i	−0.544173	+	0.225404i	0.0936249	+	0.995608i	$0.470155\pi$
$608$		−	15.1496i		−	0.614397i
$609$	5.57321	+	13.4549i	0.225838	+	0.545221i
$610$	10.1403	+	10.1403i	0.410567	+	0.410567i
$611$	−0.161708			−0.00654200
$612$	9.73010	+	3.40422i	0.393316	+	0.137607i
$613$	6.79186			0.274321			0.137160	−	0.990549i	$-0.456202\pi$
$613$	6.79186			0.274321			0.137160	+	0.990549i	$0.456202\pi$
$614$	−2.37115	−	2.37115i	−0.0956917	−	0.0956917i
$615$	−2.11829	−	5.11401i	−0.0854177	−	0.206217i
$616$		−	10.0963i		−	0.406791i
$617$	28.2236	−	11.6906i	1.13624	−	0.470646i	0.266342	−	0.963879i	$-0.414185\pi$
$617$	28.2236	−	11.6906i	1.13624	−	0.470646i	0.869897	+	0.493233i	$0.164185\pi$
$618$	3.14275	−	7.58726i	0.126420	−	0.305205i
$619$	−39.7202	−	16.4526i	−1.59649	−	0.661288i	−0.605576	−	0.795788i	$-0.707057\pi$
$619$	−39.7202	−	16.4526i	−1.59649	−	0.661288i	−0.990914	+	0.134500i	$0.957057\pi$
$620$	3.68907	−	3.68907i	0.148157	−	0.148157i
$621$	−15.3769	+	15.3769i	−0.617054	+	0.617054i
$622$	−4.71514	−	1.95308i	−0.189060	−	0.0783112i
$623$	−16.7411	+	40.4167i	−0.670719	+	1.61926i
$624$	−0.180610	+	0.0748110i	−0.00723017	+	0.00299484i
$625$		−	5.54205i		−	0.221682i
$626$	4.62349	+	11.1621i	0.184792	+	0.446127i
$627$	0.982334	+	0.982334i	0.0392306	+	0.0392306i
$628$	17.5039			0.698482
$629$	−25.2089	−	22.5260i	−1.00514	−	0.898170i
$630$	11.8388			0.471667
$631$	6.24875	+	6.24875i	0.248759	+	0.248759i	0.820461	−	0.571702i	$-0.193717\pi$
$631$	6.24875	+	6.24875i	0.248759	+	0.248759i	−0.571702	+	0.820461i	$0.693717\pi$
$632$	−10.1426	−	24.4864i	−0.403450	−	0.974015i
$633$		−	3.36197i		−	0.133626i
$634$	6.91194	−	2.86302i	0.274508	−	0.113705i
$635$	−3.15745	+	7.62276i	−0.125300	+	0.302500i
$636$	−1.15382	−	0.477929i	−0.0457520	−	0.0189511i
$637$	0.909488	−	0.909488i	0.0360352	−	0.0360352i
$638$	−7.83665	+	7.83665i	−0.310256	+	0.310256i
$639$	21.5533	+	8.92768i	0.852637	+	0.353174i
$640$	0.452070	−	1.09139i	0.0178697	−	0.0431412i
$641$	−11.8960	+	4.92749i	−0.469864	+	0.194624i	−0.605036	−	0.796198i	$-0.706841\pi$
$641$	−11.8960	+	4.92749i	−0.469864	+	0.194624i	0.135172	+	0.990822i	$0.456841\pi$
$642$			1.39538i			0.0550711i
$643$	16.0485	+	38.7444i	0.632889	+	1.52793i	0.835974	+	0.548769i	$0.184903\pi$
$643$	16.0485	+	38.7444i	0.632889	+	1.52793i	−0.203085	+	0.979161i	$0.565097\pi$
$644$	18.4974	+	18.4974i	0.728900	+	0.728900i
$645$	−3.75553			−0.147874
$646$	−6.26866	−	13.0155i	−0.246637	−	0.512089i
$647$	37.1096			1.45893			0.729465	−	0.684018i	$-0.239769\pi$
$647$	37.1096			1.45893			0.729465	+	0.684018i	$0.239769\pi$
$648$	16.0550	+	16.0550i	0.630701	+	0.630701i
$649$	−1.75815	−	4.24455i	−0.0690135	−	0.166613i
$650$		−	1.21545i		−	0.0476737i
$651$	−6.30909	+	2.61331i	−0.247273	+	0.102424i
$652$	−1.10919	+	2.67781i	−0.0434391	+	0.104871i
$653$	−4.13384	−	1.71229i	−0.161770	−	0.0670072i	0.300329	−	0.953836i	$-0.402903\pi$
$653$	−4.13384	−	1.71229i	−0.161770	−	0.0670072i	−0.462099	+	0.886828i	$0.652903\pi$
$654$	−2.94824	+	2.94824i	−0.115285	+	0.115285i
$655$	4.12499	−	4.12499i	0.161177	−	0.161177i
$656$	14.7526	+	6.11072i	0.575991	+	0.238583i
$657$	8.52160	−	20.5730i	0.332459	−	0.802628i
$658$	1.61945	−	0.670800i	0.0631329	−	0.0261505i
$659$			20.8419i			0.811887i	0.913898	+	0.405943i	$0.133057\pi$
$659$			20.8419i			0.811887i	−0.913898	+	0.405943i	$0.866943\pi$
$660$	0.169830	+	0.410006i	0.00661063	+	0.0159595i
$661$	6.66370	+	6.66370i	0.259188	+	0.259188i	0.824724	−	0.565536i	$-0.191331\pi$
$661$	6.66370	+	6.66370i	0.259188	+	0.259188i	−0.565536	+	0.824724i	$0.691331\pi$
$662$	29.9345			1.16344
$663$	0.371311	−	0.415535i	0.0144205	−	0.0161380i
$664$	−12.7516			−0.494858
$665$	9.31352	+	9.31352i	0.361163	+	0.361163i
$666$	−9.35871	−	22.5939i	−0.362642	−	0.875496i
$667$		−	93.6007i		−	3.62423i
$668$	1.97189	−	0.816786i	0.0762949	−	0.0316024i
$669$	−1.52374	+	3.67864i	−0.0589113	+	0.142225i
$670$	4.21999	+	1.74798i	0.163032	+	0.0675303i
$671$	−8.01867	+	8.01867i	−0.309557	+	0.309557i
$672$	−4.47926	+	4.47926i	−0.172791	+	0.172791i
$673$	−4.03310	−	1.67056i	−0.155465	−	0.0643955i	0.303594	−	0.952801i	$-0.401813\pi$
$673$	−4.03310	−	1.67056i	−0.155465	−	0.0643955i	−0.459059	+	0.888406i	$0.651813\pi$
$674$	−8.77843	+	21.1930i	−0.338133	+	0.816324i
$675$	8.03314	−	3.32743i	0.309196	−	0.128073i
$676$		−	11.4140i		−	0.439001i
$677$	−15.7863	−	38.1116i	−0.606718	−	1.46475i	−0.866549	−	0.499092i	$-0.833667\pi$
$677$	−15.7863	−	38.1116i	−0.606718	−	1.46475i	0.259831	−	0.965654i	$-0.416333\pi$
$678$	−2.61009	−	2.61009i	−0.100240	−	0.100240i
$679$	−16.0025			−0.614121
$680$	−0.844140	−	15.0192i	−0.0323713	−	0.575960i
$681$	1.25287			0.0480100
$682$	−3.67465	−	3.67465i	−0.140710	−	0.140710i
$683$	9.32799	+	22.5198i	0.356926	+	0.861695i	0.995729	+	0.0923246i	$0.0294298\pi$
$683$	9.32799	+	22.5198i	0.356926	+	0.861695i	−0.638803	+	0.769370i	$0.720570\pi$
$684$			8.29633i			0.317218i
$685$	13.6233	−	5.64295i	0.520519	−	0.215606i
$686$	4.03882	−	9.75057i	0.154203	−	0.372278i
$687$	4.38934	+	1.81813i	0.167464	+	0.0693658i
$688$	7.66059	−	7.66059i	0.292057	−	0.292057i
$689$	0.769379	−	0.769379i	0.0293110	−	0.0293110i
$690$	4.36185	+	1.80674i	0.166053	+	0.0687813i
$691$	−8.94031	+	21.5838i	−0.340105	+	0.821087i	0.657599	+	0.753368i	$0.271572\pi$
$691$	−8.94031	+	21.5838i	−0.340105	+	0.821087i	−0.997704	+	0.0677187i	$0.978428\pi$
$692$	−4.78576	+	1.98233i	−0.181927	+	0.0753568i
$693$			9.36180i			0.355625i
$694$	−4.96376	−	11.9836i	−0.188422	−	0.454890i
$695$	7.39251	+	7.39251i	0.280414	+	0.280414i
$696$	13.3863			0.507408
$697$	−45.4466	+	2.55428i	−1.72141	+	0.0967503i
$698$	11.0815			0.419441
$699$	−1.72277	−	1.72277i	−0.0651611	−	0.0651611i
$700$	−4.00269	−	9.66334i	−0.151287	−	0.365240i
$701$			33.2360i			1.25531i	0.778492	+	0.627654i	$0.215985\pi$
$701$			33.2360i			1.25531i	−0.778492	+	0.627654i	$0.784015\pi$
$702$	0.767970	−	0.318104i	0.0289852	−	0.0120061i
$703$	10.4121	−	25.1371i	0.392700	−	0.948062i
$704$	−7.12627	−	2.95180i	−0.268581	−	0.111250i
$705$	−0.177591	+	0.177591i	−0.00668847	+	0.00668847i
$706$	−13.4440	+	13.4440i	−0.505973	+	0.505973i
$707$	55.8959	+	23.1528i	2.10218	+	0.870752i
$708$	−0.651483	+	1.57282i	−0.0244842	+	0.0591102i
$709$	−5.57955	+	2.31112i	−0.209544	+	0.0867961i	−0.484987	−	0.874521i	$-0.661176\pi$
$709$	−5.57955	+	2.31112i	−0.209544	+	0.0867961i	0.275443	+	0.961318i	$0.411176\pi$
$710$		−	10.4441i		−	0.391958i
$711$	9.40473	+	22.7050i	0.352705	+	0.851505i
$712$	28.4332	+	28.4332i	1.06558	+	1.06558i
$713$	43.8899			1.64369
$714$	−1.99483	+	5.70173i	−0.0746548	+	0.213382i
$715$	−0.386640			−0.0144595
$716$	−0.214027	−	0.214027i	−0.00799856	−	0.00799856i
$717$	−0.911542	−	2.20066i	−0.0340422	−	0.0821850i
$718$		−	7.29060i		−	0.272083i
$719$	29.3628	−	12.1625i	1.09505	−	0.453584i	0.239284	−	0.970950i	$-0.423087\pi$
$719$	29.3628	−	12.1625i	1.09505	−	0.453584i	0.855764	+	0.517366i	$0.173087\pi$
$720$	1.87256	−	4.52076i	0.0697861	−	0.168479i
$721$	56.8844	+	23.5623i	2.11849	+	0.877506i
$722$	−5.96462	+	5.96462i	−0.221980	+	0.221980i
$723$	1.53226	−	1.53226i	0.0569854	−	0.0569854i
$724$	−12.1497	−	5.03257i	−0.451540	−	0.187034i
$725$	−14.3220	+	34.5764i	−0.531907	+	1.28414i
$726$	0.408404	−	0.169166i	0.0151573	−	0.00627835i
$727$			42.9172i			1.59171i	0.605488	+	0.795855i	$0.292978\pi$
$727$			42.9172i			1.59171i	−0.605488	+	0.795855i	$0.707022\pi$
$728$	−1.24733	−	3.01131i	−0.0462290	−	0.111607i
$729$	−12.7214	−	12.7214i	−0.471162	−	0.471162i
$730$	−9.96900			−0.368969
$731$	−10.1985	+	29.1498i	−0.377205	+	1.07815i
$732$	4.20208			0.155313
$733$	18.1289	+	18.1289i	0.669606	+	0.669606i	0.957625	−	0.288019i	$-0.0929965\pi$
$733$	18.1289	+	18.1289i	0.669606	+	0.669606i	−0.288019	+	0.957625i	$0.592997\pi$
$734$	−7.21963	−	17.4297i	−0.266481	−	0.643343i
$735$		−	1.99764i		−	0.0736840i
$736$	37.6141	−	15.5803i	1.38647	−	0.574296i
$737$	−1.38226	+	3.33707i	−0.0509161	+	0.122922i
$738$	−30.4209	−	12.6008i	−1.11981	−	0.463840i
$739$	−2.79398	+	2.79398i	−0.102778	+	0.102778i	−0.756626	−	0.653848i	$-0.773154\pi$
$739$	−2.79398	+	2.79398i	−0.102778	+	0.102778i	0.653848	+	0.756626i	$0.273154\pi$
$740$	6.14590	−	6.14590i	0.225928	−	0.225928i
$741$	0.414351	+	0.171630i	0.0152216	+	0.00630498i
$742$	−4.51354	+	10.8966i	−0.165697	+	0.400029i
$743$	−6.48173	+	2.68482i	−0.237792	+	0.0984966i	−0.498397	−	0.866949i	$-0.666078\pi$
$743$	−6.48173	+	2.68482i	−0.237792	+	0.0984966i	0.260605	+	0.965445i	$0.416078\pi$
$744$			6.27693i			0.230123i
$745$	2.94357	+	7.10642i	0.107844	+	0.260359i
$746$	14.0358	+	14.0358i	0.513888	+	0.513888i
$747$	11.8239			0.432615
$748$	3.64360	−	0.204785i	0.133223	−	0.00748768i
$749$	−10.4616			−0.382260
$750$	−3.20662	−	3.20662i	−0.117089	−	0.117089i
$751$	20.5616	+	49.6400i	0.750303	+	1.81139i	0.557550	+	0.830143i	$0.311741\pi$
$751$	20.5616	+	49.6400i	0.750303	+	1.81139i	0.192753	+	0.981247i	$0.438259\pi$
$752$		−	0.724508i		−	0.0264201i
$753$	5.84035	−	2.41915i	0.212834	−	0.0881588i
$754$	−1.36919	+	3.30552i	−0.0498630	+	0.120380i
$755$	−17.6313	−	7.30314i	−0.641670	−	0.265788i
$756$	5.05813	−	5.05813i	0.183963	−	0.183963i
$757$	−0.809194	+	0.809194i	−0.0294107	+	0.0294107i	−0.721659	−	0.692249i	$-0.756620\pi$
$757$	−0.809194	+	0.809194i	−0.0294107	+	0.0294107i	0.692249	+	0.721659i	$0.256620\pi$
$758$	−8.11021	−	3.35936i	−0.294576	−	0.122017i
$759$	−1.42872	+	3.44924i	−0.0518594	+	0.125200i
$760$	11.1851	−	4.63303i	0.405727	−	0.168058i
$761$			21.3830i			0.775134i	0.921841	+	0.387567i	$0.126684\pi$
$761$			21.3830i			0.775134i	−0.921841	+	0.387567i	$0.873316\pi$
$762$	−1.16542	−	2.81357i	−0.0422187	−	0.101925i
$763$	−22.1040	−	22.1040i	−0.800218	−	0.800218i
$764$	12.3525			0.446898
$765$	0.782730	+	13.9266i	0.0282997	+	0.503517i
$766$	27.4455			0.991647
$767$	−1.04877	−	1.04877i	−0.0378689	−	0.0378689i
$768$	2.63843	+	6.36973i	0.0952060	+	0.229848i
$769$			5.48589i			0.197826i	0.995096	+	0.0989131i	$0.0315366\pi$
$769$			5.48589i			0.197826i	−0.995096	+	0.0989131i	$0.968463\pi$
$770$	3.87208	−	1.60387i	0.139540	−	0.0577995i
$771$	−1.00008	+	2.41440i	−0.0360170	+	0.0869526i
$772$	−11.0762	−	4.58793i	−0.398642	−	0.165123i
$773$	8.25041	−	8.25041i	0.296747	−	0.296747i	−0.542992	−	0.839738i	$-0.682708\pi$
$773$	8.25041	−	8.25041i	0.296747	−	0.296747i	0.839738	+	0.542992i	$0.182708\pi$
$774$	−15.7967	+	15.7967i	−0.567801	+	0.567801i
$775$	−16.2131	−	6.71569i	−0.582392	−	0.241235i
$776$	−5.62891	+	13.5894i	−0.202066	+	0.487831i
$777$	−10.5108	+	4.35371i	−0.377072	+	0.156188i
$778$			11.8601i			0.425203i
$779$	−14.0191	−	33.8450i	−0.502286	−	1.21262i
$780$	0.101307	+	0.101307i	0.00362737	+	0.00362737i
$781$	8.25890			0.295527
$782$	25.8686	−	28.9496i	0.925061	−	1.03524i
$783$	−25.5952			−0.914698
$784$	4.07482	+	4.07482i	0.145529	+	0.145529i
$785$	9.06384	+	21.8820i	0.323502	+	0.781003i
$786$			2.15320i			0.0768020i
$787$	−35.6125	+	14.7512i	−1.26945	+	0.525823i	−0.912797	−	0.408414i	$-0.866082\pi$
$787$	−35.6125	+	14.7512i	−1.26945	+	0.525823i	−0.356653	+	0.934237i	$0.616082\pi$
$788$	−2.28029	+	5.50511i	−0.0812321	+	0.196112i
$789$	−5.69325	−	2.35822i	−0.202685	−	0.0839549i
$790$	7.77968	−	7.77968i	0.276789	−	0.276789i
$791$	19.5688	−	19.5688i	0.695787	−	0.695787i
$792$	7.95007	+	3.29303i	0.282493	+	0.117013i
$793$	−1.40099	+	3.38229i	−0.0497507	+	0.120109i
$794$	6.05049	−	2.50619i	0.214724	−	0.0889415i
$795$		−	1.68990i		−	0.0599345i
$796$	1.47081	+	3.55084i	0.0521314	+	0.125856i
$797$	−17.2326	−	17.2326i	−0.610410	−	0.610410i	0.332643	−	0.943053i	$-0.392060\pi$
$797$	−17.2326	−	17.2326i	−0.610410	−	0.610410i	−0.943053	+	0.332643i	$0.892060\pi$
$798$	−4.86155			−0.172097
$799$	0.896171	+	1.86070i	0.0317042	+	0.0658269i
$800$	−16.2787			−0.575541
$801$	−26.3648	−	26.3648i	−0.931553	−	0.931553i
$802$	−8.96231	−	21.6369i	−0.316470	−	0.764026i
$803$		−	7.88324i		−	0.278194i
$804$	1.23655	−	0.512196i	0.0436098	−	0.0180638i
$805$	−13.5457	+	32.7023i	−0.477425	+	1.15261i
$806$	−1.54998	−	0.642022i	−0.0545956	−	0.0226142i
$807$	3.42563	−	3.42563i	0.120588	−	0.120588i
$808$	39.3229	−	39.3229i	1.38338	−	1.38338i
$809$	−38.7874	−	16.0663i	−1.36369	−	0.564860i	−0.423621	−	0.905839i	$-0.639241\pi$
$809$	−38.7874	−	16.0663i	−1.36369	−	0.564860i	−0.940071	+	0.340980i	$0.889241\pi$
$810$	−3.60690	+	8.70782i	−0.126733	+	0.305961i
$811$	−18.6150	+	7.71059i	−0.653662	+	0.270756i	−0.684769	−	0.728761i	$-0.740097\pi$
$811$	−18.6150	+	7.71059i	−0.653662	+	0.270756i	0.0311070	+	0.999516i	$0.490097\pi$
$812$			30.7894i			1.08049i
$813$	−2.74524	−	6.62760i	−0.0962798	−	0.232440i
$814$	−6.12188	−	6.12188i	−0.214572	−	0.214572i
$815$	−3.92195			−0.137380
$816$	1.86174	+	1.66360i	0.0651740	+	0.0582377i
$817$	−24.8545			−0.869548
$818$	−22.7380	−	22.7380i	−0.795017	−	0.795017i
$819$	1.15659	+	2.79225i	0.0404144	+	0.0975690i
$820$		−	11.7026i		−	0.408671i
$821$	−39.0865	+	16.1902i	−1.36413	+	0.565041i	−0.940190	−	0.340650i	$-0.889353\pi$
$821$	−39.0865	+	16.1902i	−1.36413	+	0.565041i	−0.423939	+	0.905691i	$0.639353\pi$
$822$	−2.08282	+	5.02838i	−0.0726467	+	0.175385i
$823$	−8.59646	−	3.56077i	−0.299654	−	0.124121i	0.227791	−	0.973710i	$-0.426850\pi$
$823$	−8.59646	−	3.56077i	−0.299654	−	0.124121i	−0.527445	+	0.849589i	$0.676850\pi$
$824$	40.0184	−	40.0184i	1.39411	−	1.39411i
$825$	1.05555	−	1.05555i	0.0367496	−	0.0367496i
$826$	14.8536	+	6.15258i	0.516825	+	0.214076i
$827$	9.77011	−	23.5871i	0.339740	−	0.820205i	−0.658000	−	0.753018i	$-0.728597\pi$
$827$	9.77011	−	23.5871i	0.339740	−	0.820205i	0.997740	−	0.0671873i	$-0.0214025\pi$
$828$	−20.5985	+	8.53218i	−0.715847	+	0.296514i
$829$			24.3880i			0.847031i	0.905889	+	0.423516i	$0.139204\pi$
$829$			24.3880i			0.847031i	−0.905889	+	0.423516i	$0.860796\pi$
$830$	−2.02569	−	4.89044i	−0.0703126	−	0.169750i
$831$	1.06050	+	1.06050i	0.0367884	+	0.0367884i
$832$	−2.49015			−0.0863305
$833$	−15.5054	−	5.42478i	−0.537230	−	0.187958i
$834$	−3.85881			−0.133620
$835$	2.04216	+	2.04216i	0.0706720	+	0.0706720i
$836$	1.12395	+	2.71347i	0.0388728	+	0.0938472i
$837$		−	12.0017i		−	0.414841i
$838$	23.1861	−	9.60400i	0.800950	−	0.331765i
$839$	−10.9224	+	26.3691i	−0.377085	+	0.910363i	0.615425	+	0.788196i	$0.288984\pi$
$839$	−10.9224	+	26.3691i	−0.377085	+	0.910363i	−0.992510	+	0.122167i	$0.961016\pi$
$840$	−4.67693	−	1.93725i	−0.161370	−	0.0668415i
$841$	57.3941	−	57.3941i	1.97911	−	1.97911i
$842$	−3.34776	+	3.34776i	−0.115371	+	0.115371i
$843$	5.05124	+	2.09229i	0.173974	+	0.0720623i
$844$	2.72000	−	6.56667i	0.0936263	−	0.226034i
$845$	14.2689	−	5.91038i	0.490866	−	0.203323i
$846$			1.49399i			0.0513644i
$847$	1.26830	+	3.06195i	0.0435793	+	0.105210i
$848$	3.44709	+	3.44709i	0.118373	+	0.118373i
$849$	−3.39988			−0.116683
$850$	−13.9856	+	6.73589i	−0.479702	+	0.231039i
$851$	73.1195			2.50651
$852$	−2.16399	−	2.16399i	−0.0741369	−	0.0741369i
$853$	0.674515	+	1.62842i	0.0230950	+	0.0557562i	0.935006	−	0.354631i	$-0.115394\pi$
$853$	0.674515	+	1.62842i	0.0230950	+	0.0557562i	−0.911911	+	0.410387i	$0.865394\pi$
$854$		−	39.6843i		−	1.35797i
$855$	−10.3714	+	4.29598i	−0.354695	+	0.146920i
$856$	−3.67990	+	8.88406i	−0.125776	+	0.303651i
$857$	49.1356	+	20.3526i	1.67844	+	0.695233i	0.999250	−	0.0387289i	$-0.0123309\pi$
$857$	49.1356	+	20.3526i	1.67844	+	0.695233i	0.679191	+	0.733962i	$0.262331\pi$
$858$	0.100911	−	0.100911i	0.00344504	−	0.00344504i
$859$	−14.0214	+	14.0214i	−0.478403	+	0.478403i	−0.904621	−	0.426218i	$-0.859846\pi$
$859$	−14.0214	+	14.0214i	−0.478403	+	0.478403i	0.426218	+	0.904621i	$0.359846\pi$
$860$	−7.33536	−	3.03840i	−0.250134	−	0.103609i
$861$	−5.86192	+	14.1519i	−0.199774	+	0.482297i
$862$	−23.1857	+	9.60385i	−0.789710	+	0.327108i
$863$			15.4595i			0.526246i	0.964762	+	0.263123i	$0.0847525\pi$
$863$			15.4595i			0.526246i	−0.964762	+	0.263123i	$0.915248\pi$
$864$	−4.26044	−	10.2856i	−0.144943	−	0.349923i
$865$	−4.95630	−	4.95630i	−0.168519	−	0.168519i
$866$	−15.6080			−0.530380
$867$	−6.83915	−	1.96966i	−0.232270	−	0.0668931i
$868$	−14.4373			−0.490034
$869$	6.15198	+	6.15198i	0.208692	+	0.208692i
$870$	2.12652	+	5.13387i	0.0720957	+	0.174055i
$871$			1.16608i			0.0395111i
$872$	−26.5459	+	10.9957i	−0.898957	+	0.372360i
$873$	5.21942	−	12.6008i	0.176651	−	0.426472i
$874$	28.8672	+	11.9572i	0.976447	+	0.404457i
$875$	24.0412	−	24.0412i	0.812741	−	0.812741i
$876$	−2.06556	+	2.06556i	−0.0697887	+	0.0697887i
$877$	−42.4306	−	17.5753i	−1.43278	−	0.593477i	−0.474744	−	0.880124i	$-0.657459\pi$
$877$	−42.4306	−	17.5753i	−1.43278	−	0.593477i	−0.958036	+	0.286647i	$0.907459\pi$
$878$	3.13370	−	7.56542i	0.105757	−	0.255320i
$879$	8.48491	−	3.51456i	0.286189	−	0.118543i
$880$		−	1.73228i		−	0.0583953i
$881$	−4.41976	−	10.6702i	−0.148905	−	0.359490i	0.831773	−	0.555116i	$-0.187326\pi$
$881$	−4.41976	−	10.6702i	−0.148905	−	0.359490i	−0.980679	+	0.195626i	$0.937326\pi$
$882$	−8.40259	−	8.40259i	−0.282930	−	0.282930i
$883$	−45.0933			−1.51751			−0.758755	−	0.651376i	$-0.774192\pi$
$883$	−45.0933			−1.51751			−0.758755	+	0.651376i	$0.774192\pi$
$884$	1.06144	−	0.511221i	0.0357000	−	0.0171942i
$885$	−2.30357			−0.0774336
$886$	−25.1153	−	25.1153i	−0.843767	−	0.843767i
$887$	13.9880	+	33.7701i	0.469672	+	1.13389i	0.964307	+	0.264788i	$0.0853019\pi$
$887$	13.9880	+	33.7701i	0.469672	+	1.13389i	−0.494635	+	0.869101i	$0.664698\pi$
$888$			10.4572i			0.350921i
$889$	21.0944	−	8.73758i	0.707483	−	0.293049i
$890$	−6.38776	+	15.4214i	−0.214118	+	0.516927i
$891$	−6.88593	−	2.85224i	−0.230687	−	0.0955538i
$892$	−5.95240	+	5.95240i	−0.199301	+	0.199301i
$893$	−1.17532	+	1.17532i	−0.0393305	+	0.0393305i
$894$	−2.62299	−	1.08648i	−0.0877260	−	0.0363373i
$895$	0.156733	−	0.378387i	0.00523900	−	0.0126481i
$896$	−3.02020	+	1.25101i	−0.100898	+	0.0417933i
$897$			1.20528i			0.0402431i
$898$	−0.411623	−	0.993745i	−0.0137360	−	0.0331617i
$899$	36.5279	+	36.5279i	1.21827	+	1.21827i
$900$	8.91468			0.297156
$901$	−13.1167	−	4.58908i	−0.436982	−	0.152885i
$902$	−11.6568			−0.388130
$903$	7.34869	+	7.34869i	0.244549	+	0.244549i
$904$	−9.73454	−	23.5013i	−0.323766	−	0.781640i
$905$		−	17.7946i		−	0.591511i
$906$	6.50776	−	2.69560i	0.216206	−	0.0895553i
$907$	15.4866	−	37.3880i	0.514224	−	1.24145i	−0.427180	−	0.904167i	$-0.640493\pi$
$907$	15.4866	−	37.3880i	0.514224	−	1.24145i	0.941404	−	0.337281i	$-0.109507\pi$
$908$	2.44712	+	1.01363i	0.0812105	+	0.0336385i
$909$	−36.4623	+	36.4623i	−1.20938	+	1.20938i
$910$	0.956739	−	0.956739i	0.0317156	−	0.0317156i
$911$	−18.4420	−	7.63894i	−0.611012	−	0.253090i	0.0556491	−	0.998450i	$-0.482277\pi$
$911$	−18.4420	−	7.63894i	−0.611012	−	0.253090i	−0.666661	+	0.745361i	$0.732277\pi$
$912$	−0.768961	+	1.85644i	−0.0254628	+	0.0614728i
$913$	3.86724	−	1.60186i	0.127987	−	0.0530139i
$914$		−	17.5348i		−	0.579999i
$915$	2.17591	+	5.25311i	0.0719334	+	0.173663i
$916$	7.10239	+	7.10239i	0.234669	+	0.234669i
$917$	−16.1433			−0.533098
$918$	−7.91630	−	7.07380i	−0.261277	−	0.233470i
$919$	12.2595			0.404403			0.202201	−	0.979344i	$-0.435190\pi$
$919$	12.2595			0.404403			0.202201	+	0.979344i	$0.435190\pi$
$920$	23.0062	+	23.0062i	0.758491	+	0.758491i
$921$	−0.508804	−	1.22836i	−0.0167657	−	0.0404759i
$922$			9.52658i			0.313741i
$923$	2.46330	−	1.02033i	0.0810804	−	0.0335846i
$924$	0.469969	−	1.13461i	0.0154609	−	0.0373258i
$925$	−27.0106	−	11.1882i	−0.888104	−	0.367865i
$926$	−24.2566	+	24.2566i	−0.797120	+	0.797120i
$927$	−37.1071	+	37.1071i	−1.21876	+	1.21876i
$928$	44.2716	+	18.3379i	1.45329	+	0.601971i
$929$	−2.15834	+	5.21068i	−0.0708127	+	0.170957i	−0.955323	−	0.295564i	$-0.904493\pi$
$929$	−2.15834	+	5.21068i	−0.0708127	+	0.170957i	0.884510	+	0.466520i	$0.154493\pi$
$930$	−2.40730	+	0.997137i	−0.0789385	+	0.0326974i
$931$		−	13.2206i		−	0.433287i
$932$	−1.97114	−	4.75875i	−0.0645668	−	0.155878i
$933$	−1.43088	−	1.43088i	−0.0468448	−	0.0468448i
$934$	−4.55356			−0.148997
$935$	2.14273	+	4.44890i	0.0700747	+	0.145495i
$936$	2.77801			0.0908023
$937$	−39.8456	−	39.8456i	−1.30170	−	1.30170i	−0.927246	−	0.374454i	$-0.877830\pi$
$937$	−39.8456	−	39.8456i	−1.30170	−	1.30170i	−0.374454	−	0.927246i	$-0.622170\pi$
$938$	−4.83716	−	11.6779i	−0.157939	−	0.381298i
$939$			4.79036i			0.156327i
$940$	−0.490554	+	0.203194i	−0.0160001	+	0.00662746i
$941$	7.99970	−	19.3130i	0.260783	−	0.629585i	−0.738205	−	0.674577i	$-0.764326\pi$
$941$	7.99970	−	19.3130i	0.260783	−	0.629585i	0.998987	+	0.0449916i	$0.0143261\pi$
$942$	−8.07670	−	3.34548i	−0.263153	−	0.109002i
$943$	69.6144	−	69.6144i	2.26696	−	2.26696i
$944$	4.69886	−	4.69886i	0.152935	−	0.152935i
$945$	8.94248	+	3.70410i	0.290899	+	0.120494i
$946$	−3.02653	+	7.30668i	−0.0984009	+	0.237561i
$947$	38.7806	−	16.0635i	1.26020	−	0.521993i	0.350230	−	0.936664i	$-0.386103\pi$
$947$	38.7806	−	16.0635i	1.26020	−	0.521993i	0.909971	+	0.414671i	$0.136103\pi$
$948$		−	3.22387i		−	0.104706i
$949$	−0.973921	−	2.35125i	−0.0316148	−	0.0763249i
$950$	−8.83405	−	8.83405i	−0.286614	−	0.286614i
$951$	2.96635			0.0961904
$952$	−27.7373	+	31.0409i	−0.898971	+	1.00604i
$953$	10.0818			0.326582			0.163291	−	0.986578i	$-0.447789\pi$
$953$	10.0818			0.326582			0.163291	+	0.986578i	$0.447789\pi$
$954$	−7.10815	−	7.10815i	−0.230135	−	0.230135i
$955$	6.39634	+	15.4421i	0.206981	+	0.499696i
$956$		−	5.03584i		−	0.162871i
$957$	−4.05974	+	1.68160i	−0.131233	+	0.0543584i
$958$	−14.0268	+	33.8637i	−0.453186	+	1.09409i
$959$	−37.6995	−	15.6157i	−1.21738	−	0.504256i
$960$	−2.73474	+	2.73474i	−0.0882634	+	0.0882634i
$961$	4.79218	−	4.79218i	0.154586	−	0.154586i
$962$	−2.58222	−	1.06959i	−0.0832542	−	0.0344850i
$963$	3.41219	−	8.23776i	0.109956	−	0.265458i
$964$	4.23252	−	1.75317i	0.136320	−	0.0564657i
$965$		−	16.2224i		−	0.522216i
$966$	−4.99976	−	12.0705i	−0.160865	−	0.388362i
$967$	29.7935	+	29.7935i	0.958095	+	0.958095i	0.999157	−	0.0410616i	$-0.0130740\pi$
$967$	29.7935	+	29.7935i	0.958095	+	0.958095i	−0.0410616	+	0.999157i	$0.513074\pi$
$968$	3.04634			0.0979132
$969$	−0.321426	−	5.71891i	−0.0103257	−	0.183718i
$970$	−6.10594			−0.196050
$971$	−38.8876	−	38.8876i	−1.24796	−	1.24796i	−0.956618	−	0.291345i	$-0.905897\pi$
$971$	−38.8876	−	38.8876i	−1.24796	−	1.24796i	−0.291345	−	0.956618i	$-0.594103\pi$
$972$	3.53480	+	8.53376i	0.113379	+	0.273720i
$973$		−	28.9309i		−	0.927481i
$974$	−13.0093	+	5.38863i	−0.416845	+	0.172663i
$975$	0.184422	−	0.445234i	0.00590623	−	0.0142589i
$976$	−15.1539	−	6.27693i	−0.485063	−	0.200920i
$977$	−2.62108	+	2.62108i	−0.0838558	+	0.0838558i	−0.747791	−	0.663935i	$-0.768885\pi$
$977$	−2.62108	+	2.62108i	−0.0838558	+	0.0838558i	0.663935	+	0.747791i	$0.268885\pi$
$978$	1.02361	−	1.02361i	0.0327314	−	0.0327314i
$979$	−12.1949	−	5.05129i	−0.389750	−	0.161440i
$980$	1.61619	−	3.90182i	0.0516272	−	0.124639i
$981$	24.6147	−	10.1957i	0.785887	−	0.325525i
$982$			7.14470i			0.227997i
$983$	3.67988	+	8.88400i	0.117370	+	0.283356i	0.971637	−	0.236479i	$-0.0759935\pi$
$983$	3.67988	+	8.88400i	0.117370	+	0.283356i	−0.854267	+	0.519835i	$0.825993\pi$
$984$	9.95592	+	9.95592i	0.317383	+	0.317383i
$985$	−8.06284			−0.256904
$986$	45.6231	−	2.56420i	1.45294	−	0.0816609i
$987$	0.695010			0.0221224
$988$	0.670460	+	0.670460i	0.0213302	+	0.0213302i
$989$	−25.5610	−	61.7098i	−0.812794	−	1.96226i
$990$			3.57210i			0.113529i
$991$	14.2563	−	5.90514i	0.452865	−	0.187583i	−0.144579	−	0.989493i	$-0.546183\pi$
$991$	14.2563	−	5.90514i	0.452865	−	0.187583i	0.597445	+	0.801910i	$0.296183\pi$
$992$	−8.59874	+	20.7592i	−0.273010	+	0.659105i
$993$	10.9654	+	4.54201i	0.347976	+	0.144136i
$994$	−20.4366	+	20.4366i	−0.648210	+	0.648210i
$995$	−3.67738	+	3.67738i	−0.116581	+	0.116581i
$996$	−1.43301	−	0.593570i	−0.0454065	−	0.0188080i
$997$	−15.4478	+	37.2942i	−0.489236	+	1.18112i	0.465869	+	0.884854i	$0.345742\pi$
$997$	−15.4478	+	37.2942i	−0.489236	+	1.18112i	−0.955105	+	0.296267i	$0.904258\pi$
$998$	25.5455	−	10.5813i	0.808628	−	0.334945i
$999$		−	19.9946i		−	0.632601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.100.5	✓	56
17.5	odd	16		3179.2.a.bh.1.20		28
17.8	even	8	inner	187.2.h.a.144.5	yes	56
17.12	odd	16		3179.2.a.bi.1.20		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.100.5	✓	56	1.1	even	1	trivial
187.2.h.a.144.5	yes	56	17.8	even	8	inner
3179.2.a.bh.1.20		28	17.5	odd	16
3179.2.a.bi.1.20		28	17.12	odd	16

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.746627 - 0.746627i) q^{2} +(-0.160212 - 0.386786i) q^{3} -0.885097i q^{4} +(1.10648 - 0.458319i) q^{5} +(-0.169166 + 0.408404i) q^{6} +(-3.06195 - 1.26830i) q^{7} +(-2.15409 + 2.15409i) q^{8} +(1.99738 - 1.99738i) q^{9} +O(q^{10})\)	\(q+(-0.746627 - 0.746627i) q^{2} +(-0.160212 - 0.386786i) q^{3} -0.885097i q^{4} +(1.10648 - 0.458319i) q^{5} +(-0.169166 + 0.408404i) q^{6} +(-3.06195 - 1.26830i) q^{7} +(-2.15409 + 2.15409i) q^{8} +(1.99738 - 1.99738i) q^{9} +(-1.16832 - 0.483934i) q^{10} +(0.382683 - 0.923880i) q^{11} +(-0.342344 + 0.141803i) q^{12} -0.322834i q^{13} +(1.33919 + 3.23308i) q^{14} +(-0.354543 - 0.354543i) q^{15} +1.44641 q^{16} +(-3.71471 + 1.78912i) q^{17} -2.98260 q^{18} +(-2.34641 - 2.34641i) q^{19} +(-0.405657 - 0.979343i) q^{20} +1.38752i q^{21} +(-0.975515 + 0.404071i) q^{22} +(3.41265 - 8.23887i) q^{23} +(1.17828 + 0.488061i) q^{24} +(-2.52129 + 2.52129i) q^{25} +(-0.241036 + 0.241036i) q^{26} +(-2.25293 - 0.933193i) q^{27} +(-1.12257 + 2.71012i) q^{28} +(9.69711 - 4.01667i) q^{29} +0.529423i q^{30} +(1.88344 + 4.54703i) q^{31} +(3.22825 + 3.22825i) q^{32} -0.418655 q^{33} +(4.10930 + 1.43770i) q^{34} -3.96927 q^{35} +(-1.76788 - 1.76788i) q^{36} +(3.13777 + 7.57524i) q^{37} +3.50378i q^{38} +(-0.124868 + 0.0517219i) q^{39} +(-1.39620 + 3.37072i) q^{40} +(10.1995 + 4.22475i) q^{41} +(1.03596 - 1.03596i) q^{42} +(5.29629 - 5.29629i) q^{43} +(-0.817723 - 0.338712i) q^{44} +(1.29463 - 3.12551i) q^{45} +(-8.69934 + 3.60338i) q^{46} -0.500901i q^{47} +(-0.231732 - 0.559451i) q^{48} +(2.81720 + 2.81720i) q^{49} +3.76493 q^{50} +(1.28715 + 1.15016i) q^{51} -0.285739 q^{52} +(2.38321 + 2.38321i) q^{53} +(0.985348 + 2.37884i) q^{54} -1.19765i q^{55} +(9.32775 - 3.86368i) q^{56} +(-0.531635 + 1.28348i) q^{57} +(-10.2391 - 4.24116i) q^{58} +(3.24864 - 3.24864i) q^{59} +(-0.313805 + 0.313805i) q^{60} +(-10.4769 - 4.33967i) q^{61} +(1.98871 - 4.80116i) q^{62} +(-8.64918 + 3.58261i) q^{63} -7.71342i q^{64} +(-0.147961 - 0.357209i) q^{65} +(0.312579 + 0.312579i) q^{66} -3.61201 q^{67} +(1.58354 + 3.28788i) q^{68} -3.73343 q^{69} +(2.96357 + 2.96357i) q^{70} +(3.16055 + 7.63023i) q^{71} +8.60509i q^{72} +(7.28317 - 3.01679i) q^{73} +(3.31313 - 7.99862i) q^{74} +(1.37914 + 0.571260i) q^{75} +(-2.07680 + 2.07680i) q^{76} +(-2.34351 + 2.34351i) q^{77} +(0.131847 + 0.0546126i) q^{78} +(-3.32943 + 8.03795i) q^{79} +(1.60042 - 0.662916i) q^{80} -7.45327i q^{81} +(-4.46087 - 10.7695i) q^{82} +(2.95986 + 2.95986i) q^{83} +1.22809 q^{84} +(-3.29027 + 3.68214i) q^{85} -7.90870 q^{86} +(-3.10719 - 3.10719i) q^{87} +(1.16579 + 2.81445i) q^{88} -13.1996i q^{89} +(-3.30019 + 1.36698i) q^{90} +(-0.409450 + 0.988501i) q^{91} +(-7.29220 - 3.02053i) q^{92} +(1.45698 - 1.45698i) q^{93} +(-0.373986 + 0.373986i) q^{94} +(-3.67165 - 1.52085i) q^{95} +(0.731439 - 1.76585i) q^{96} +(4.46089 - 1.84776i) q^{97} -4.20679i q^{98} +(-1.08098 - 2.60971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 16 q^{6}+O(q^{10}) \) 56 * q - 16 * q^6	\( 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) \) 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

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