LMFDB - Embedded newform 289.2.i.a.128.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(2,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(136))

chi = DirichletCharacter(H, H._module([95]))

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

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

chi := DirichletCharacter("289.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.i (of order $136$, degree $64$, 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$1600$
Relative dimension:	$25$ over $\Q(\zeta_{136})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{136}]$

Embedding invariants

Embedding label			128.16
Character	$\chi$	$=$	289.128
Dual form			289.2.i.a.70.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.743476 + 0.103710i) q^{2} +(-2.33819 + 0.844243i) q^{3} +(-1.38165 - 0.393114i) q^{4} +(-0.407369 + 0.426638i) q^{5} +(-1.82595 + 0.385179i) q^{6} +(3.30312 - 1.02286i) q^{7} +(-2.35988 - 1.04199i) q^{8} +(2.44640 - 2.03147i) q^{9} +O(q^{10})$	\(q+(0.743476 + 0.103710i) q^{2} +(-2.33819 + 0.844243i) q^{3} +(-1.38165 - 0.393114i) q^{4} +(-0.407369 + 0.426638i) q^{5} +(-1.82595 + 0.385179i) q^{6} +(3.30312 - 1.02286i) q^{7} +(-2.35988 - 1.04199i) q^{8} +(2.44640 - 2.03147i) q^{9} +(-0.347116 + 0.274947i) q^{10} +(-0.359687 - 3.10032i) q^{11} +(3.56245 - 0.247273i) q^{12} +(-1.70762 - 4.40788i) q^{13} +(2.56187 - 0.417902i) q^{14} +(0.592322 - 1.34148i) q^{15} +(0.796205 + 0.492989i) q^{16} +(1.50037 - 3.84043i) q^{17} +(2.02952 - 1.25663i) q^{18} +(0.109461 + 0.784702i) q^{19} +(0.730559 - 0.429322i) q^{20} +(-6.85979 + 5.18027i) q^{21} +(0.0541170 - 2.34232i) q^{22} +(-1.77900 - 5.74492i) q^{23} +(6.39754 + 0.444060i) q^{24} +(0.214847 + 4.64707i) q^{25} +(-0.812433 - 3.45425i) q^{26} +(-0.226579 + 0.385559i) q^{27} +(-4.96585 + 0.114731i) q^{28} +(-1.18436 - 0.938118i) q^{29} +(0.579502 - 0.935928i) q^{30} +(1.05667 + 0.0244133i) q^{31} +(4.51011 + 3.74515i) q^{32} +(3.45844 + 6.94549i) q^{33} +(1.51378 - 2.69966i) q^{34} +(-0.909198 + 1.82592i) q^{35} +(-4.17867 + 1.84506i) q^{36} +(-7.12056 + 6.19622i) q^{37} +0.594759i q^{38} +(7.71408 + 8.86484i) q^{39} +(1.40589 - 0.582340i) q^{40} +(-8.75684 - 4.11078i) q^{41} +(-5.63734 + 3.13998i) q^{42} +(-1.78176 - 0.419067i) q^{43} +(-0.721816 + 4.42496i) q^{44} +(-0.129888 + 1.87128i) q^{45} +(-0.726833 - 4.45571i) q^{46} +(8.94259 - 0.828653i) q^{47} +(-2.27788 - 0.480514i) q^{48} +(4.08937 - 2.80128i) q^{49} +(-0.322216 + 3.47726i) q^{50} +(-0.265913 + 10.2463i) q^{51} +(0.626540 + 6.76145i) q^{52} +(1.69038 + 2.03565i) q^{53} +(-0.208442 + 0.263155i) q^{54} +(1.46924 + 1.10952i) q^{55} +(-8.86076 - 1.02799i) q^{56} +(-0.918421 - 1.74237i) q^{57} +(-0.783250 - 0.820299i) q^{58} +(-3.59016 - 2.45932i) q^{59} +(-1.34574 + 1.62061i) q^{60} +(-2.12602 - 10.0784i) q^{61} +(0.783074 + 0.127738i) q^{62} +(6.00285 - 9.21249i) q^{63} +(1.70295 + 1.86805i) q^{64} +(2.57620 + 1.06710i) q^{65} +(1.85095 + 5.52248i) q^{66} +(0.659599 - 0.873450i) q^{67} +(-3.58272 + 4.71631i) q^{68} +(9.00975 + 11.9308i) q^{69} +(-0.865333 + 1.26323i) q^{70} +(2.84010 - 5.38807i) q^{71} +(-7.88997 + 2.24489i) q^{72} +(-5.79294 + 4.16806i) q^{73} +(-5.93657 + 3.86827i) q^{74} +(-4.42561 - 10.6844i) q^{75} +(0.157240 - 1.12721i) q^{76} +(-4.35927 - 9.87281i) q^{77} +(4.81585 + 7.39082i) q^{78} +(2.98703 - 11.5013i) q^{79} +(-0.534677 + 0.138863i) q^{80} +(-1.54863 + 8.28445i) q^{81} +(-6.08417 - 3.96444i) q^{82} +(10.1743 - 0.470386i) q^{83} +(11.5143 - 4.46065i) q^{84} +(1.02727 + 2.20459i) q^{85} +(-1.28124 - 0.496354i) q^{86} +(3.56126 + 1.19361i) q^{87} +(-2.38168 + 7.69117i) q^{88} +(4.90374 - 12.6580i) q^{89} +(-0.290640 + 1.37778i) q^{90} +(-10.1491 - 12.8131i) q^{91} +(0.199546 + 8.63683i) q^{92} +(-2.49130 + 0.835000i) q^{93} +(6.73454 + 0.311357i) q^{94} +(-0.379375 - 0.272963i) q^{95} +(-13.7073 - 4.94925i) q^{96} +(14.1275 + 7.44674i) q^{97} +(3.33087 - 1.65858i) q^{98} +(-7.17813 - 6.85393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1600 q - 64 q^{2} - 64 q^{3} - 68 q^{4} - 68 q^{5} - 72 q^{6} - 64 q^{7} - 72 q^{8} - 76 q^{9}+O(q^{10}) $ 1600 * q - 64 * q^2 - 64 * q^3 - 68 * q^4 - 68 * q^5 - 72 * q^6 - 64 * q^7 - 72 * q^8 - 76 * q^9	\( 1600 q - 64 q^{2} - 64 q^{3} - 68 q^{4} - 68 q^{5} - 72 q^{6} - 64 q^{7} - 72 q^{8} - 76 q^{9} - 72 q^{10} - 64 q^{11} - 64 q^{12} - 68 q^{13} - 72 q^{14} - 60 q^{15} + 40 q^{16} - 68 q^{17} - 72 q^{18} - 76 q^{19} - 72 q^{20} - 68 q^{21} - 80 q^{22} - 72 q^{23} + 260 q^{24} - 64 q^{25} - 64 q^{26} - 76 q^{27} - 72 q^{28} - 64 q^{29} - 68 q^{30} - 56 q^{31} - 72 q^{32} - 44 q^{33} - 48 q^{34} - 92 q^{35} - 68 q^{36} - 68 q^{37} + 204 q^{39} - 60 q^{40} - 64 q^{41} - 60 q^{42} - 60 q^{43} - 48 q^{44} - 80 q^{45} - 88 q^{46} - 68 q^{47} - 80 q^{48} - 76 q^{49} - 32 q^{50} - 96 q^{51} - 116 q^{52} - 64 q^{53} + 484 q^{54} - 68 q^{55} - 48 q^{56} - 44 q^{57} - 68 q^{58} - 68 q^{59} - 60 q^{60} - 68 q^{61} + 352 q^{62} - 56 q^{63} - 68 q^{64} - 64 q^{65} - 76 q^{66} - 44 q^{67} - 80 q^{68} - 92 q^{69} - 60 q^{70} - 88 q^{71} - 68 q^{72} - 40 q^{73} - 88 q^{74} - 56 q^{75} + 60 q^{76} + 604 q^{77} - 60 q^{78} - 64 q^{79} - 68 q^{80} - 68 q^{81} - 72 q^{82} - 84 q^{83} - 4 q^{84} + 268 q^{85} - 132 q^{86} - 84 q^{87} - 80 q^{88} - 68 q^{89} - 72 q^{90} - 68 q^{91} + 232 q^{92} - 92 q^{93} - 44 q^{94} - 60 q^{95} - 48 q^{96} - 92 q^{97} - 68 q^{98} - 64 q^{99}+O(q^{100}) \) 1600 * q - 64 * q^2 - 64 * q^3 - 68 * q^4 - 68 * q^5 - 72 * q^6 - 64 * q^7 - 72 * q^8 - 76 * q^9 - 72 * q^10 - 64 * q^11 - 64 * q^12 - 68 * q^13 - 72 * q^14 - 60 * q^15 + 40 * q^16 - 68 * q^17 - 72 * q^18 - 76 * q^19 - 72 * q^20 - 68 * q^21 - 80 * q^22 - 72 * q^23 + 260 * q^24 - 64 * q^25 - 64 * q^26 - 76 * q^27 - 72 * q^28 - 64 * q^29 - 68 * q^30 - 56 * q^31 - 72 * q^32 - 44 * q^33 - 48 * q^34 - 92 * q^35 - 68 * q^36 - 68 * q^37 + 204 * q^39 - 60 * q^40 - 64 * q^41 - 60 * q^42 - 60 * q^43 - 48 * q^44 - 80 * q^45 - 88 * q^46 - 68 * q^47 - 80 * q^48 - 76 * q^49 - 32 * q^50 - 96 * q^51 - 116 * q^52 - 64 * q^53 + 484 * q^54 - 68 * q^55 - 48 * q^56 - 44 * q^57 - 68 * q^58 - 68 * q^59 - 60 * q^60 - 68 * q^61 + 352 * q^62 - 56 * q^63 - 68 * q^64 - 64 * q^65 - 76 * q^66 - 44 * q^67 - 80 * q^68 - 92 * q^69 - 60 * q^70 - 88 * q^71 - 68 * q^72 - 40 * q^73 - 88 * q^74 - 56 * q^75 + 60 * q^76 + 604 * q^77 - 60 * q^78 - 64 * q^79 - 68 * q^80 - 68 * q^81 - 72 * q^82 - 84 * q^83 - 4 * q^84 + 268 * q^85 - 132 * q^86 - 84 * q^87 - 80 * q^88 - 68 * q^89 - 72 * q^90 - 68 * q^91 + 232 * q^92 - 92 * q^93 - 44 * q^94 - 60 * q^95 - 48 * q^96 - 92 * q^97 - 68 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{121}{136}\right)$

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 $

$2$	0.743476	+	0.103710i	0.525717	+	0.0733344i	0.396060	−	0.918225i	$-0.370377\pi$
$2$	0.743476	+	0.103710i	0.525717	+	0.0733344i	0.129657	+	0.991559i	$0.458612\pi$
$3$	−2.33819	+	0.844243i	−1.34996	+	0.487424i	−0.911489	−	0.411323i	$-0.865067\pi$
$3$	−2.33819	+	0.844243i	−1.34996	+	0.487424i	−0.438467	+	0.898747i	$0.644478\pi$
$4$	−1.38165	−	0.393114i	−0.690825	−	0.196557i
$5$	−0.407369	+	0.426638i	−0.182181	+	0.190798i	−0.808022	−	0.589152i	$-0.799462\pi$
$5$	−0.407369	+	0.426638i	−0.182181	+	0.190798i	0.625841	+	0.779951i	$0.284756\pi$
$6$	−1.82595	+	0.385179i	−0.745440	+	0.157249i
$7$	3.30312	−	1.02286i	1.24846	−	0.386604i	0.400321	−	0.916375i	$-0.368899\pi$
$7$	3.30312	−	1.02286i	1.24846	−	0.386604i	0.848140	+	0.529771i	$0.177722\pi$
$8$	−2.35988	−	1.04199i	−0.834343	−	0.368399i
$9$	2.44640	−	2.03147i	0.815467	−	0.677155i
$10$	−0.347116	+	0.274947i	−0.109768	+	0.0869458i
$11$	−0.359687	−	3.10032i	−0.108450	−	0.934782i	−0.930732	−	0.365702i	$-0.880829\pi$
$11$	−0.359687	−	3.10032i	−0.108450	−	0.934782i	0.822282	−	0.569080i	$-0.192700\pi$
$12$	3.56245	−	0.247273i	1.02839	−	0.0713816i
$13$	−1.70762	−	4.40788i	−0.473610	−	1.22253i	−0.940979	−	0.338465i	$-0.890092\pi$
$13$	−1.70762	−	4.40788i	−0.473610	−	1.22253i	0.467369	−	0.884062i	$-0.345202\pi$
$14$	2.56187	−	0.417902i	0.684688	−	0.111689i
$15$	0.592322	−	1.34148i	0.152937	−	0.346369i
$16$	0.796205	+	0.492989i	0.199051	+	0.123247i
$17$	1.50037	−	3.84043i	0.363894	−	0.931440i
$17$	1.50037	−	3.84043i	0.363894	−	0.931440i
$18$	2.02952	−	1.25663i	0.478363	−	0.296190i
$19$	0.109461	+	0.784702i	0.0251121	+	0.180023i	0.998868	−	0.0475731i	$-0.0151487\pi$
$19$	0.109461	+	0.784702i	0.0251121	+	0.180023i	−0.973756	+	0.227596i	$0.926913\pi$
$20$	0.730559	−	0.429322i	0.163358	−	0.0959994i
$21$	−6.85979	+	5.18027i	−1.49693	+	1.13043i
$22$	0.0541170	−	2.34232i	0.0115378	−	0.499384i
$23$	−1.77900	−	5.74492i	−0.370947	−	1.19790i	−0.929622	−	0.368513i	$-0.879867\pi$
$23$	−1.77900	−	5.74492i	−0.370947	−	1.19790i	0.558676	−	0.829386i	$-0.311310\pi$
$24$	6.39754	+	0.444060i	1.30589	+	0.0906433i
$25$	0.214847	+	4.64707i	0.0429694	+	0.929413i
$26$	−0.812433	−	3.45425i	−0.159331	−	0.677435i
$27$	−0.226579	+	0.385559i	−0.0436051	+	0.0742008i
$28$	−4.96585	+	0.114731i	−0.938458	+	0.0216822i
$29$	−1.18436	−	0.938118i	−0.219930	−	0.174204i	0.504802	−	0.863235i	$-0.331566\pi$
$29$	−1.18436	−	0.938118i	−0.219930	−	0.174204i	−0.724732	+	0.689031i	$0.758036\pi$
$30$	0.579502	−	0.935928i	0.105802	−	0.170876i
$31$	1.05667	+	0.0244133i	0.189783	+	0.00438476i	0.117885	−	0.993027i	$-0.462389\pi$
$31$	1.05667	+	0.0244133i	0.189783	+	0.00438476i	0.0718979	+	0.997412i	$0.477094\pi$
$32$	4.51011	+	3.74515i	0.797282	+	0.662055i
$33$	3.45844	+	6.94549i	0.602037	+	1.20905i
$34$	1.51378	−	2.69966i	0.259612	−	0.462988i
$35$	−0.909198	+	1.82592i	−0.153683	+	0.308636i
$36$	−4.17867	+	1.84506i	−0.696445	+	0.307510i
$37$	−7.12056	+	6.19622i	−1.17061	+	1.01865i	−0.171170	+	0.985241i	$0.554755\pi$
$37$	−7.12056	+	6.19622i	−1.17061	+	1.01865i	−0.999442	+	0.0334116i	$0.989363\pi$
$38$			0.594759i			0.0964827i
$39$	7.71408	+	8.86484i	1.23524	+	1.41951i
$40$	1.40589	−	0.582340i	0.222291	−	0.0920761i
$41$	−8.75684	−	4.11078i	−1.36759	−	0.641995i	−0.405339	−	0.914166i	$-0.632847\pi$
$41$	−8.75684	−	4.11078i	−1.36759	−	0.641995i	−0.962249	+	0.272171i	$0.912258\pi$
$42$	−5.63734	+	3.13998i	−0.869860	+	0.484509i
$43$	−1.78176	−	0.419067i	−0.271716	−	0.0639071i	0.0908516	−	0.995864i	$-0.471041\pi$
$43$	−1.78176	−	0.419067i	−0.271716	−	0.0639071i	−0.362568	+	0.931957i	$0.618100\pi$
$44$	−0.721816	+	4.42496i	−0.108818	+	0.667087i
$45$	−0.129888	+	1.87128i	−0.0193625	+	0.278954i
$46$	−0.726833	−	4.45571i	−0.107166	−	0.656959i
$47$	8.94259	−	0.828653i	1.30441	−	0.120871i	0.582485	−	0.812842i	$-0.302081\pi$
$47$	8.94259	−	0.828653i	1.30441	−	0.120871i	0.721926	+	0.691970i	$0.243257\pi$
$48$	−2.27788	−	0.480514i	−0.328784	−	0.0693562i
$49$	4.08937	−	2.80128i	0.584195	−	0.400183i
$50$	−0.322216	+	3.47726i	−0.0455682	+	0.491759i
$51$	−0.265913	+	10.2463i	−0.0372353	+	1.43477i
$52$	0.626540	+	6.76145i	0.0868855	+	0.937644i
$53$	1.69038	+	2.03565i	0.232192	+	0.279618i	0.872620	−	0.488400i	$-0.162419\pi$
$53$	1.69038	+	2.03565i	0.232192	+	0.279618i	−0.640428	+	0.768018i	$0.721243\pi$
$54$	−0.208442	+	0.263155i	−0.0283654	+	0.0358109i
$55$	1.46924	+	1.10952i	0.198112	+	0.149607i
$56$	−8.86076	−	1.02799i	−1.18407	−	0.137371i
$57$	−0.918421	−	1.74237i	−0.121648	−	0.230783i
$58$	−0.783250	−	0.820299i	−0.102846	−	0.107710i
$59$	−3.59016	−	2.45932i	−0.467399	−	0.320176i	0.308289	−	0.951293i	$-0.400244\pi$
$59$	−3.59016	−	2.45932i	−0.467399	−	0.320176i	−0.775687	+	0.631117i	$0.782597\pi$
$60$	−1.34574	+	1.62061i	−0.173734	+	0.209220i
$61$	−2.12602	−	10.0784i	−0.272209	−	1.29041i	−0.871704	−	0.490033i	$-0.836985\pi$
$61$	−2.12602	−	10.0784i	−0.272209	−	1.29041i	0.599494	−	0.800379i	$-0.295368\pi$
$62$	0.783074	+	0.127738i	0.0994505	+	0.0162228i
$63$	6.00285	−	9.21249i	0.756288	−	1.16066i
$64$	1.70295	+	1.86805i	0.212869	+	0.233506i
$65$	2.57620	+	1.06710i	0.319539	+	0.132357i
$66$	1.85095	+	5.52248i	0.227836	+	0.679770i
$67$	0.659599	−	0.873450i	0.0805829	−	0.106709i	−0.755940	−	0.654641i	$-0.772820\pi$
$67$	0.659599	−	0.873450i	0.0805829	−	0.106709i	0.836523	+	0.547932i	$0.184585\pi$
$68$	−3.58272	+	4.71631i	−0.434468	+	0.571937i
$69$	9.00975	+	11.9308i	1.08465	+	1.43630i
$70$	−0.865333	+	1.26323i	−0.103427	+	0.150985i
$71$	2.84010	−	5.38807i	0.337058	−	0.639447i	−0.656301	−	0.754499i	$-0.727880\pi$
$71$	2.84010	−	5.38807i	0.337058	−	0.639447i	0.993359	+	0.115052i	$0.0367035\pi$
$72$	−7.88997	+	2.24489i	−0.929842	+	0.264563i
$73$	−5.79294	+	4.16806i	−0.678012	+	0.487835i	−0.869674	−	0.493626i	$-0.835671\pi$
$73$	−5.79294	+	4.16806i	−0.678012	+	0.487835i	0.191662	+	0.981461i	$0.438612\pi$
$74$	−5.93657	+	3.86827i	−0.690113	+	0.449677i
$75$	−4.42561	−	10.6844i	−0.511025	−	1.23372i
$76$	0.157240	−	1.12721i	0.0180366	−	0.129300i
$77$	−4.35927	−	9.87281i	−0.496785	−	1.12511i
$78$	4.81585	+	7.39082i	0.545288	+	0.836846i
$79$	2.98703	−	11.5013i	0.336067	−	1.29399i	−0.551832	−	0.833955i	$-0.686071\pi$
$79$	2.98703	−	11.5013i	0.336067	−	1.29399i	0.887899	−	0.460038i	$-0.152164\pi$
$80$	−0.534677	+	0.138863i	−0.0597787	+	0.0155253i
$81$	−1.54863	+	8.28445i	−0.172070	+	0.920495i
$82$	−6.08417	−	3.96444i	−0.671884	−	0.437799i
$83$	10.1743	−	0.470386i	1.11677	−	0.0516315i	0.520092	−	0.854110i	$-0.325898\pi$
$83$	10.1743	−	0.470386i	1.11677	−	0.0516315i	0.596681	+	0.802479i	$0.296486\pi$
$84$	11.5143	−	4.46065i	1.25631	−	0.486697i
$85$	1.02727	+	2.20459i	0.111423	+	0.239121i
$86$	−1.28124	−	0.496354i	−0.138159	−	0.0535232i
$87$	3.56126	+	1.19361i	0.381807	+	0.127969i
$88$	−2.38168	+	7.69117i	−0.253888	+	0.819881i
$89$	4.90374	−	12.6580i	0.519795	−	1.34175i	−0.387740	−	0.921769i	$-0.626744\pi$
$89$	4.90374	−	12.6580i	0.519795	−	1.34175i	0.907535	−	0.419977i	$-0.137962\pi$
$90$	−0.290640	+	1.37778i	−0.0306361	+	0.145231i
$91$	−10.1491	−	12.8131i	−1.06392	−	1.34318i
$92$	0.199546	+	8.63683i	0.0208041	+	0.900451i
$93$	−2.49130	+	0.835000i	−0.258336	+	0.0865855i
$94$	6.73454	+	0.311357i	0.694615	+	0.0321140i
$95$	−0.379375	−	0.272963i	−0.0389230	−	0.0280054i
$96$	−13.7073	−	4.94925i	−1.39900	−	0.505131i
$97$	14.1275	+	7.44674i	1.43443	+	0.756102i	0.990180	−	0.139799i	$-0.0446457\pi$
$97$	14.1275	+	7.44674i	1.43443	+	0.756102i	0.444253	+	0.895901i	$0.353469\pi$
$98$	3.33087	−	1.65858i	0.336469	−	0.167541i
$99$	−7.17813	−	6.85393i	−0.721429	−	0.688846i
$100$	1.52998	−	6.50508i	0.152998	−	0.650508i
$101$	1.30322	+	0.243614i	0.129675	+	0.0242405i	0.248187	−	0.968712i	$-0.420165\pi$
$101$	1.30322	+	0.243614i	0.129675	+	0.0242405i	−0.118512	+	0.992953i	$0.537812\pi$
$102$	−1.26035	+	7.59033i	−0.124794	+	0.751555i
$103$	1.40249	−	0.262171i	0.138191	−	0.0258324i	−0.114199	−	0.993458i	$-0.536430\pi$
$103$	1.40249	−	0.262171i	0.138191	−	0.0258324i	0.252391	+	0.967625i	$0.418783\pi$
$104$	−0.563180	+	12.1814i	−0.0552243	+	1.19448i
$105$	0.584365	−	5.03693i	0.0570282	−	0.491554i
$106$	1.04564	+	1.68877i	0.101562	+	0.164028i
$107$	4.09009	+	6.95993i	0.395404	+	0.672842i	0.991505	−	0.130068i	$-0.0415195\pi$
$107$	4.09009	+	6.95993i	0.395404	+	0.672842i	−0.596101	+	0.802909i	$0.703284\pi$
$108$	0.464621	−	0.443637i	0.0447082	−	0.0426890i
$109$	−4.46821	+	12.3751i	−0.427977	+	1.18532i	0.516370	+	0.856366i	$0.327283\pi$
$109$	−4.46821	+	12.3751i	−0.427977	+	1.18532i	−0.944347	+	0.328950i	$0.893305\pi$
$110$	0.977276	+	0.977276i	0.0931796	+	0.0931796i
$111$	11.4181	−	20.4994i	1.08376	−	1.94572i
$112$	3.13422	+	0.813998i	0.296156	+	0.0769156i
$113$	−3.33584	+	7.10605i	−0.313809	+	0.668481i	−0.998158	−	0.0606743i	$-0.980675\pi$
$113$	−3.33584	+	7.10605i	−0.313809	+	0.668481i	0.684349	+	0.729155i	$0.260087\pi$
$114$	−0.502121	−	1.39066i	−0.0470280	−	0.130247i
$115$	3.17571	+	1.58132i	0.296137	+	0.147459i
$116$	1.26758	+	1.76174i	0.117692	+	0.163573i
$117$	−13.1320	−	7.31447i	−1.21405	−	0.676223i
$118$	−2.41414	−	2.20078i	−0.222240	−	0.202598i
$119$	1.02770	−	14.2201i	0.0942095	−	1.30355i
$120$	−2.79561	+	2.54854i	−0.255204	+	0.232649i
$121$	1.22521	−	0.288166i	0.111383	−	0.0261969i
$122$	−0.535407	−	7.71357i	−0.0484734	−	0.698354i
$123$	23.9457	+	2.21889i	2.15911	+	0.200071i
$124$	−1.45035	−	0.449121i	−0.130245	−	0.0403322i
$125$	−4.29512	−	3.73756i	−0.384167	−	0.334298i
$126$	5.41841	−	6.22670i	0.482710	−	0.554719i
$127$	−5.71816	+	17.0607i	−0.507405	+	1.51389i	0.317299	+	0.948325i	$0.397224\pi$
$127$	−5.71816	+	17.0607i	−0.507405	+	1.51389i	−0.824704	+	0.565564i	$0.808658\pi$
$128$	−5.55369	−	8.10739i	−0.490882	−	0.716599i
$129$	4.51990	−	0.524381i	0.397955	−	0.0461692i
$130$	1.80468	+	1.06054i	0.158281	+	0.0930156i
$131$	0.127731	−	0.308370i	0.0111599	−	0.0269424i	−0.918201	−	0.396114i	$-0.870359\pi$
$131$	0.127731	−	0.308370i	0.0111599	−	0.0269424i	0.929361	+	0.369172i	$0.120359\pi$
$132$	−2.04799	−	10.9558i	−0.178255	−	0.953580i
$133$	1.16420	+	2.48000i	0.100949	+	0.215043i
$134$	0.580982	−	0.580982i	0.0501892	−	0.0501892i
$135$	−0.0721929	−	0.253732i	−0.00621338	−	0.0218378i
$136$	−7.54238	+	7.49957i	−0.646754	+	0.643083i
$137$	0.396591	−	1.39387i	0.0338830	−	0.119087i	−0.943039	−	0.332681i	$-0.892047\pi$
$137$	0.396591	−	1.39387i	0.0338830	−	0.119087i	0.976922	+	0.213595i	$0.0685172\pi$
$138$	5.46118	+	9.80470i	0.464886	+	0.834631i
$139$	0.464121	+	1.78705i	0.0393663	+	0.151576i	0.984601	−	0.174814i	$-0.0559324\pi$
$139$	0.464121	+	1.78705i	0.0393663	+	0.151576i	−0.945235	+	0.326390i	$0.894168\pi$
$140$	1.97399	−	2.16536i	0.166832	−	0.183006i
$141$	−20.2099	+	9.48727i	−1.70198	+	0.798972i
$142$	2.67035	−	3.71135i	0.224090	−	0.311450i
$143$	−13.0516	+	6.87964i	−1.09143	+	0.575304i
$144$	2.94933	−	0.411414i	0.245777	−	0.0342845i
$145$	0.882708	−	0.123133i	0.0733049	−	0.0102256i
$146$	−4.73918	+	2.49807i	−0.392218	+	0.206741i
$147$	−7.19677	+	10.0024i	−0.593580	+	0.824981i
$148$	12.2739	−	5.76183i	1.00891	−	0.473620i
$149$	−15.1941	+	16.6672i	−1.24475	+	1.36543i	−0.339470	+	0.940617i	$0.610248\pi$
$149$	−15.1941	+	16.6672i	−1.24475	+	1.36543i	−0.905282	+	0.424811i	$0.860341\pi$
$150$	−2.18225	−	8.40254i	−0.178180	−	0.686065i
$151$	10.3741	+	18.6251i	0.844231	+	1.51569i	0.856731	+	0.515763i	$0.172492\pi$
$151$	10.3741	+	18.6251i	0.844231	+	1.51569i	−0.0125001	+	0.999922i	$0.503979\pi$
$152$	0.559335	−	1.96586i	0.0453681	−	0.159452i
$153$	−4.13118	−	12.4432i	−0.333986	−	1.00597i
$154$	−2.21710	−	7.79230i	−0.178659	−	0.627922i
$155$	−0.440869	+	0.440869i	−0.0354114	+	0.0354114i
$156$	−7.17327	−	15.2806i	−0.574322	−	1.22343i
$157$	2.17044	+	11.6109i	0.173220	+	0.926647i	0.953540	+	0.301266i	$0.0974093\pi$
$157$	2.17044	+	11.6109i	0.173220	+	0.926647i	−0.780320	+	0.625381i	$0.784944\pi$
$158$	3.41359	−	8.24112i	0.271570	−	0.655629i
$159$	−5.67102	−	3.33265i	−0.449741	−	0.264296i
$160$	−3.43510	+	0.398527i	−0.271568	+	0.0315063i
$161$	−11.7525	−	17.1565i	−0.926225	−	1.35212i
$162$	−2.01056	+	5.99868i	−0.157964	+	0.471301i
$163$	14.7122	−	16.9069i	1.15234	−	1.32425i	0.214689	−	0.976682i	$-0.431126\pi$
$163$	14.7122	−	16.9069i	1.15234	−	1.32425i	0.937656	−	0.347565i	$-0.112992\pi$
$164$	10.4829	+	9.12209i	0.818576	+	0.712316i
$165$	−4.37207	−	1.35387i	−0.340365	−	0.105399i
$166$	7.61312	+	0.705460i	0.590893	+	0.0547543i
$167$	−1.10146	−	15.8687i	−0.0852336	−	1.22795i	−0.828897	−	0.559401i	$-0.811031\pi$
$167$	−1.10146	−	15.8687i	−0.0852336	−	1.22795i	0.743664	−	0.668554i	$-0.233086\pi$
$168$	21.5861	−	5.07699i	1.66540	−	0.391699i
$169$	−6.90635	+	6.29597i	−0.531258	+	0.484305i
$170$	0.535109	+	1.74560i	0.0410410	+	0.133881i
$171$	1.86188	+	1.69733i	0.142382	+	0.129798i
$172$	2.29703	+	1.27944i	0.175147	+	0.0975563i
$173$	−6.61096	−	9.18818i	−0.502622	−	0.698564i	0.481422	−	0.876489i	$-0.340120\pi$
$173$	−6.61096	−	9.18818i	−0.502622	−	0.698564i	−0.984044	+	0.177925i	$0.943062\pi$
$174$	2.52392	+	1.25676i	0.191338	+	0.0952750i
$175$	5.46295	+	15.1301i	0.412960	+	1.14372i
$176$	1.24204	−	2.64581i	0.0936223	−	0.199436i
$177$	10.4707	+	2.71939i	0.787029	+	0.204402i
$178$	4.95858	−	8.90235i	0.371661	−	0.667259i
$179$	−3.27872	−	3.27872i	−0.245063	−	0.245063i	0.573878	−	0.818941i	$-0.305438\pi$
$179$	−3.27872	−	3.27872i	−0.245063	−	0.245063i	−0.818941	+	0.573878i	$0.805438\pi$
$180$	0.915086	−	2.53440i	0.0682065	−	0.188903i
$181$	−2.77563	+	2.65027i	−0.206311	+	0.196993i	−0.786681	−	0.617360i	$-0.788202\pi$
$181$	−2.77563	+	2.65027i	−0.206311	+	0.196993i	0.580370	+	0.814353i	$0.302908\pi$
$182$	−6.21677	−	10.5788i	−0.460818	−	0.784153i
$183$	13.4797	+	21.7705i	0.996448	+	1.60932i
$184$	−1.78793	+	15.4110i	−0.131808	+	1.13612i
$185$	0.257149	−	5.56205i	0.0189060	−	0.408930i
$186$	−1.93882	+	0.362428i	−0.142161	+	0.0265745i
$187$	−12.4462	−	3.27029i	−0.910158	−	0.239147i
$188$	−12.6813	−	2.37054i	−0.924878	−	0.172890i
$189$	−0.354044	+	1.50530i	−0.0257529	+	0.109495i
$190$	−0.253747	−	0.242287i	−0.0184087	−	0.0175773i
$191$	2.29133	−	1.14095i	0.165795	−	0.0825559i	−0.360926	−	0.932595i	$-0.617539\pi$
$191$	2.29133	−	1.14095i	0.165795	−	0.0825559i	0.526720	+	0.850039i	$0.323422\pi$
$192$	−5.55891	−	2.93015i	−0.401180	−	0.211466i
$193$	22.2266	+	8.02529i	1.59991	+	0.577673i	0.978578	−	0.205876i	$-0.0660045\pi$
$193$	22.2266	+	8.02529i	1.59991	+	0.577673i	0.621330	+	0.783549i	$0.286593\pi$
$194$	9.73117	+	7.00165i	0.698657	+	0.502689i
$195$	−6.92455	−	0.320141i	−0.495878	−	0.0229258i
$196$	−6.75130	+	2.26281i	−0.482236	+	0.161629i
$197$	−0.547960	−	23.7170i	−0.0390405	−	1.68977i	−0.553970	−	0.832536i	$-0.686888\pi$
$197$	−0.547960	−	23.7170i	−0.0390405	−	1.68977i	0.514930	−	0.857232i	$-0.327818\pi$
$198$	−4.62594	−	5.84018i	−0.328751	−	0.415044i
$199$	4.57990	−	21.7111i	0.324660	−	1.53906i	−0.442006	−	0.897012i	$-0.645733\pi$
$199$	4.57990	−	21.7111i	0.324660	−	1.53906i	0.766666	−	0.642046i	$-0.221914\pi$
$200$	4.33518	−	11.1904i	0.306543	−	0.791280i
$201$	−0.804866	+	2.59916i	−0.0567709	+	0.183330i
$202$	0.943648	+	0.316279i	0.0663948	+	0.0222533i
$203$	−4.87164	−	1.88728i	−0.341922	−	0.132461i
$204$	4.39537	−	14.0523i	0.307738	−	0.983860i
$205$	5.32108	−	2.06140i	0.371640	−	0.143974i
$206$	1.06991	−	0.0494648i	0.0745439	−	0.00344637i
$207$	−16.0228	−	10.4404i	−1.11366	−	0.725659i
$208$	0.813422	−	4.35142i	0.0564006	−	0.301717i
$209$	2.39346	−	0.621612i	0.165559	−	0.0429978i
$210$	0.956843	−	3.68423i	0.0660285	−	0.254236i
$211$	2.79842	+	4.29470i	0.192651	+	0.295659i	0.921012	−	0.389535i	$-0.127364\pi$
$211$	2.79842	+	4.29470i	0.192651	+	0.295659i	−0.728360	+	0.685194i	$0.759717\pi$
$212$	−1.53528	−	3.47707i	−0.105443	−	0.238806i
$213$	−2.09187	+	14.9961i	−0.143332	+	1.02752i
$214$	2.31907	+	5.59872i	0.158528	+	0.382721i
$215$	0.904625	−	0.589453i	0.0616949	−	0.0402004i
$216$	0.936446	−	0.673780i	0.0637171	−	0.0458449i
$217$	3.51527	−	1.00018i	0.238632	−	0.0678966i
$218$	−4.60543	+	8.73715i	−0.311919	+	0.591755i
$219$	10.0262	−	14.6364i	0.677505	−	0.989035i
$220$	−1.59381	−	2.11054i	−0.107455	−	0.142293i
$221$	−19.4902	−	0.0554742i	−1.31105	−	0.00373160i
$222$	10.6151	−	14.0567i	0.712439	−	0.943422i
$223$	0.752738	+	2.24586i	0.0504070	+	0.150394i	0.970378	−	0.241593i	$-0.0776700\pi$
$223$	0.752738	+	2.24586i	0.0504070	+	0.150394i	−0.919971	+	0.391988i	$0.871788\pi$
$224$	18.7282	+	7.75746i	1.25133	+	0.518317i
$225$	9.96596	+	10.9321i	0.664397	+	0.728809i
$226$	−3.21708	+	4.93721i	−0.213997	+	0.328419i
$227$	8.30825	+	1.35527i	0.551438	+	0.0899527i	0.430305	−	0.902684i	$-0.358406\pi$
$227$	8.30825	+	1.35527i	0.551438	+	0.0899527i	0.121133	+	0.992636i	$0.461347\pi$
$228$	0.583986	+	2.76839i	0.0386754	+	0.183341i
$229$	−5.21167	+	6.27617i	−0.344397	+	0.414741i	−0.913057	−	0.407831i	$-0.866285\pi$
$229$	−5.21167	+	6.27617i	−0.344397	+	0.414741i	0.568661	+	0.822572i	$0.307462\pi$
$230$	2.19707	+	1.50502i	0.144870	+	0.0992384i
$231$	18.5279	+	19.4043i	1.21904	+	1.27671i
$232$	1.81744	+	3.44793i	0.119321	+	0.226368i
$233$	−1.43031	−	0.165939i	−0.0937026	−	0.0108710i	0.0682636	−	0.997667i	$-0.478254\pi$
$233$	−1.43031	−	0.165939i	−0.0937026	−	0.0108710i	−0.161966	+	0.986796i	$0.551784\pi$
$234$	−9.00473	−	6.80006i	−0.588658	−	0.444534i
$235$	−3.28940	+	4.15282i	−0.214577	+	0.270900i
$236$	3.99356	+	4.80926i	0.259958	+	0.313056i
$237$	2.72560	+	29.4140i	0.177047	+	1.91064i
$238$	2.23884	−	10.4657i	0.145123	−	0.678389i
$239$	2.02988	−	21.9059i	0.131302	−	1.41698i	−0.634014	−	0.773322i	$-0.718594\pi$
$239$	2.02988	−	21.9059i	0.131302	−	1.41698i	0.765316	−	0.643655i	$-0.222583\pi$
$240$	1.13295	−	0.776086i	0.0731313	−	0.0500961i
$241$	−19.7427	−	4.16468i	−1.27174	−	0.268270i	−0.478992	−	0.877819i	$-0.658998\pi$
$241$	−19.7427	−	4.16468i	−1.27174	−	0.268270i	−0.792748	+	0.609549i	$0.791351\pi$
$242$	0.940798	−	0.0871778i	0.0604768	−	0.00560400i
$243$	−3.58908	−	22.0022i	−0.230240	−	1.41144i
$244$	−1.02455	+	14.7607i	−0.0655902	+	0.944954i
$245$	−0.470748	+	2.88584i	−0.0300750	+	0.184369i
$246$	17.5729	+	4.13311i	1.12041	+	0.263517i
$247$	3.27196	−	1.82247i	0.208190	−	0.115961i
$248$	−2.46817	−	1.15865i	−0.156729	−	0.0735742i
$249$	−23.3923	+	9.68942i	−1.48243	+	0.614042i
$250$	−2.80569	−	3.22424i	−0.177448	−	0.203919i
$251$			4.14412i			0.261575i	0.991410	+	0.130787i	$0.0417505\pi$
$251$			4.14412i			0.261575i	−0.991410	+	0.130787i	$0.958249\pi$
$252$	−11.9154	+	10.3686i	−0.750599	+	0.653163i
$253$	−17.1712	+	7.58184i	−1.07955	+	0.476666i
$254$	−6.02068	+	12.0912i	−0.377771	+	0.758667i
$255$	−4.26315	−	4.28749i	−0.266969	−	0.268493i
$256$	−5.54167	−	11.1292i	−0.346354	−	0.695573i
$257$	2.27740	+	1.89113i	0.142061	+	0.117966i	0.707148	−	0.707065i	$-0.249981\pi$
$257$	2.27740	+	1.89113i	0.142061	+	0.117966i	−0.565088	+	0.825031i	$0.691158\pi$
$258$	3.41482	+	0.0788962i	0.212597	+	0.00491186i
$259$	−17.1822	+	27.7502i	−1.06765	+	1.72431i
$260$	−3.13992	−	2.48710i	−0.194730	−	0.154243i
$261$	−4.80317	+	0.110973i	−0.297309	+	0.00686904i
$262$	0.126946	−	0.216019i	0.00784275	−	0.0133457i
$263$	5.90141	+	25.0912i	0.363896	+	1.54719i	0.772821	+	0.634624i	$0.218845\pi$
$263$	5.90141	+	25.0912i	0.363896	+	1.54719i	−0.408925	+	0.912568i	$0.634096\pi$
$264$	−0.924386	−	19.9942i	−0.0568920	−	1.23056i
$265$	−1.55709	−	0.108079i	−0.0956516	−	0.00663927i
$266$	0.608354	+	1.96456i	0.0373006	+	0.120455i
$267$	−0.779457	+	33.7368i	−0.0477020	+	2.06466i
$268$	−1.25470	+	0.947506i	−0.0766431	+	0.0578782i
$269$	−12.9574	+	7.61456i	−0.790024	+	0.464268i	−0.845358	−	0.534200i	$-0.820613\pi$
$269$	−12.9574	+	7.61456i	−0.790024	+	0.464268i	0.0553342	+	0.998468i	$0.482378\pi$
$270$	−0.0273591	−	0.196131i	−0.00166502	−	0.0119361i
$271$	−5.05813	+	3.13186i	−0.307260	+	0.190247i	−0.671396	−	0.741098i	$-0.734305\pi$
$271$	−5.05813	+	3.13186i	−0.307260	+	0.190247i	0.364137	+	0.931345i	$0.381364\pi$
$272$	3.08790	−	2.31810i	0.187231	−	0.140555i
$273$	34.5480	+	21.3912i	2.09094	+	1.29465i
$274$	0.439415	−	0.995179i	0.0265460	−	0.0601210i
$275$	14.3301	−	2.33758i	0.864139	−	0.140962i
$276$	−7.75816	−	20.0261i	−0.466986	−	1.20543i
$277$	13.3663	−	0.927769i	0.803104	−	0.0557442i	0.338165	−	0.941087i	$-0.390194\pi$
$277$	13.3663	−	0.927769i	0.803104	−	0.0557442i	0.464939	+	0.885343i	$0.346076\pi$
$278$	0.159727	+	1.37677i	0.00957978	+	0.0825729i
$279$	2.63462	−	2.08686i	0.157731	−	0.124937i
$280$	4.04818	−	3.36157i	0.241925	−	0.200892i
$281$	23.7931	+	10.5057i	1.41938	+	0.626717i	0.964559	−	0.263866i	$-0.0849978\pi$
$281$	23.7931	+	10.5057i	1.41938	+	0.626717i	0.454820	+	0.890583i	$0.349704\pi$
$282$	−16.0095	+	4.95757i	−0.953353	+	0.295219i
$283$	4.63931	−	0.978652i	0.275779	−	0.0581748i	−0.0664560	−	0.997789i	$-0.521169\pi$
$283$	4.63931	−	0.978652i	0.275779	−	0.0581748i	0.342235	+	0.939615i	$0.388816\pi$
$284$	−6.04215	+	6.32795i	−0.358536	+	0.375495i
$285$	1.11750	+	0.317956i	0.0661949	+	0.0188341i
$286$	−10.4171	+	3.76125i	−0.615974	+	0.222408i
$287$	−33.1296	−	4.62138i	−1.95558	−	0.272792i
$288$	18.6417			1.09847
$289$	−12.4978	−	11.5242i	−0.735162	−	0.677892i
$290$	0.669042			0.0392875
$291$	−39.3197	−	5.48487i	−2.30496	−	0.321529i
$292$	9.64234	−	3.48152i	0.564275	−	0.203741i
$293$	12.0502	+	3.42859i	0.703983	+	0.200300i	0.606670	−	0.794953i	$-0.292505\pi$
$293$	12.0502	+	3.42859i	0.703983	+	0.200300i	0.0973126	+	0.995254i	$0.468975\pi$
$294$	−6.38797	+	6.69013i	−0.372554	+	0.390176i
$295$	2.51176	−	0.529849i	0.146240	−	0.0308490i
$296$	23.2600	−	7.20280i	1.35196	−	0.418654i
$297$	1.27685	+	0.563786i	0.0740905	+	0.0327142i
$298$	−13.0250	+	10.8158i	−0.754520	+	0.626545i
$299$	−22.2851	+	17.6518i	−1.28878	+	1.02083i
$300$	1.91448	+	16.5018i	0.110532	+	0.952733i
$301$	−6.31402	+	0.438262i	−0.363934	+	0.0252610i
$302$	5.78127	+	14.9232i	0.332675	+	0.858732i
$303$	−3.25285	+	0.530618i	−0.186871	+	0.0304832i
$304$	−0.299696	+	0.678747i	−0.0171888	+	0.0389288i
$305$	5.16592	+	3.19860i	0.295800	+	0.183152i
$306$	−1.78094	−	9.67965i	−0.101810	−	0.553349i
$307$	9.64918	−	5.97452i	0.550708	−	0.340984i	−0.222706	−	0.974886i	$-0.571489\pi$
$307$	9.64918	−	5.97452i	0.550708	−	0.340984i	0.773414	+	0.633902i	$0.218548\pi$
$308$	2.14186	+	15.3545i	0.122044	+	0.874902i
$309$	−3.05796	+	1.79705i	−0.173961	+	0.102230i
$310$	−0.373498	+	0.282053i	−0.0212133	+	0.0160195i
$311$	−0.182151	+	7.88396i	−0.0103289	+	0.447058i	0.969259	+	0.246042i	$0.0791302\pi$
$311$	−0.182151	+	7.88396i	−0.0103289	+	0.447058i	−0.979588	+	0.201016i	$0.935576\pi$
$312$	−8.96723	−	28.9579i	−0.507670	−	1.63942i
$313$	27.0351	+	1.87653i	1.52811	+	0.106068i	0.808579	−	0.588387i	$-0.200237\pi$
$313$	27.0351	+	1.87653i	1.52811	+	0.106068i	0.719536	+	0.694455i	$0.244355\pi$
$314$	0.409506	+	8.85749i	0.0231098	+	0.499857i
$315$	1.48502	+	6.31393i	0.0836715	+	0.355749i
$316$	−8.64833	+	14.7165i	−0.486507	+	0.827867i
$317$	−1.69932	+	0.0392611i	−0.0954432	+	0.00220513i	−0.0707932	−	0.997491i	$-0.522553\pi$
$317$	−1.69932	+	0.0392611i	−0.0954432	+	0.00220513i	−0.0246500	+	0.999696i	$0.507847\pi$
$318$	−3.87064	−	3.06589i	−0.217055	−	0.171927i
$319$	−2.48247	+	4.00932i	−0.138991	+	0.224479i
$320$	−1.49071	−	0.0344414i	−0.0833332	−	0.00192533i
$321$	−15.4393	−	12.8206i	−0.861737	−	0.715578i
$322$	−6.95837	−	13.9743i	−0.387775	−	0.778757i
$323$	3.17782	+	0.756969i	0.176819	+	0.0421189i
$324$	5.39640	−	10.8374i	0.299800	−	0.602080i
$325$	20.1169	−	8.88246i	1.11588	−	0.492710i
$326$	12.6916	−	11.0440i	0.702920	−	0.611673i
$327$		−	32.7075i		−	1.80873i
$328$	16.3817	+	18.8255i	0.904528	+	1.03946i
$329$	28.6908	−	11.8841i	1.58178	−	0.655194i
$330$	−3.11012	−	1.46000i	−0.171206	−	0.0803704i
$331$	−19.3075	+	10.7542i	−1.06124	+	0.591105i	−0.917184	−	0.398465i	$-0.869543\pi$
$331$	−19.3075	+	10.7542i	−1.06124	+	0.591105i	−0.144054	+	0.989570i	$0.546014\pi$
$332$	−14.2422	−	3.34974i	−0.781644	−	0.183841i
$333$	−4.83232	+	29.6236i	−0.264809	+	1.62336i
$334$	0.826838	−	11.9122i	0.0452426	−	0.651807i
$335$	0.103947	+	0.637227i	0.00567922	+	0.0348154i
$336$	−8.01562	+	0.742756i	−0.437288	+	0.0405207i
$337$	−12.4917	−	2.63510i	−0.680468	−	0.143543i	−0.146709	−	0.989180i	$-0.546868\pi$
$337$	−12.4917	−	2.63510i	−0.680468	−	0.143543i	−0.533759	+	0.845637i	$0.679221\pi$
$338$	−5.78766	+	3.96464i	−0.314807	+	0.215648i
$339$	1.80060	−	19.4316i	0.0977952	−	1.05538i
$340$	−0.552669	−	3.44980i	−0.0299727	−	0.187092i
$341$	−0.304380	−	3.28479i	−0.0164831	−	0.177881i
$342$	1.20823	+	1.45502i	0.0653338	+	0.0786784i
$343$	−4.38672	+	5.53816i	−0.236861	+	0.299033i
$344$	3.76808	+	2.84552i	0.203161	+	0.153420i
$345$	−8.76044	−	1.01635i	−0.471646	−	0.0547186i
$346$	−3.96218	−	7.51681i	−0.213008	−	0.404106i
$347$	9.07070	+	9.49976i	0.486941	+	0.509974i	0.920282	−	0.391257i	$-0.127959\pi$
$347$	9.07070	+	9.49976i	0.486941	+	0.509974i	−0.433341	+	0.901230i	$0.642665\pi$
$348$	−4.45119	−	3.04914i	−0.238609	−	0.163451i
$349$	23.4287	−	28.2142i	1.25411	−	1.51027i	0.479930	−	0.877307i	$-0.340662\pi$
$349$	23.4287	−	28.2142i	1.25411	−	1.51027i	0.774182	−	0.632963i	$-0.218161\pi$
$350$	2.49243	+	11.8154i	0.133226	+	0.631559i
$351$	2.08641	+	0.340343i	0.111364	+	0.0181662i
$352$	9.98892	−	15.3299i	0.532411	−	0.817084i
$353$	0.774752	+	0.849863i	0.0412359	+	0.0452336i	0.759281	−	0.650763i	$-0.225551\pi$
$353$	0.774752	+	0.849863i	0.0412359	+	0.0452336i	−0.718045	+	0.695997i	$0.754963\pi$
$354$	7.50272	+	3.10773i	0.398765	+	0.165174i
$355$	1.14179	+	3.40663i	0.0605998	+	0.180805i
$356$	−11.7513	+	15.5612i	−0.622817	+	0.824743i
$357$	9.60220	+	34.1169i	0.508202	+	1.80566i
$358$	−2.09761	−	2.77769i	−0.110862	−	0.146805i
$359$	5.50408	−	8.03497i	0.290494	−	0.424069i	−0.652037	−	0.758187i	$-0.726085\pi$
$359$	5.50408	−	8.03497i	0.290494	−	0.424069i	0.942531	+	0.334118i	$0.108438\pi$
$360$	2.25637	−	4.28066i	0.118921	−	0.225611i
$361$	17.6709	−	5.02781i	0.930048	−	0.264621i
$362$	−2.33848	+	1.68255i	−0.122908	+	0.0884330i
$363$	−2.62149	+	1.70816i	−0.137593	+	0.0896552i
$364$	8.98553	+	21.6930i	0.470970	+	1.13702i
$365$	0.581610	−	4.16943i	0.0304429	−	0.218238i
$366$	7.76401	+	17.5838i	0.405831	+	0.919120i
$367$	10.8550	+	16.6590i	0.566627	+	0.869594i	0.999492	−	0.0318644i	$-0.0101445\pi$
$367$	10.8550	+	16.6590i	0.566627	+	0.869594i	−0.432865	+	0.901459i	$0.642497\pi$
$368$	1.41574	−	5.45117i	0.0738005	−	0.284162i
$369$	−29.7736	+	7.73261i	−1.54995	+	0.402543i
$370$	0.768027	−	4.10858i	0.0399278	−	0.213595i
$371$	7.66571	+	4.99497i	0.397984	+	0.259326i
$372$	3.77036	−	0.174314i	0.195484	−	0.00903777i
$373$	−7.74638	+	3.00096i	−0.401092	+	0.155384i	−0.553334	−	0.832959i	$-0.686645\pi$
$373$	−7.74638	+	3.00096i	−0.401092	+	0.155384i	0.152242	+	0.988343i	$0.451351\pi$
$374$	−8.91430	−	3.72218i	−0.460947	−	0.192470i
$375$	13.1982	+	5.11302i	0.681554	+	0.264035i
$376$	−21.9669	−	7.36256i	−1.13286	−	0.379695i
$377$	−2.11268	+	6.82247i	−0.108808	+	0.351375i
$378$	−0.419339	+	1.08244i	−0.0215685	+	0.0556747i
$379$	2.95181	−	13.9931i	0.151624	−	0.718777i	−0.834263	−	0.551367i	$-0.814106\pi$
$379$	2.95181	−	13.9931i	0.151624	−	0.718777i	0.985887	−	0.167411i	$-0.0535406\pi$
$380$	0.416858	+	0.526277i	0.0213844	+	0.0269974i
$381$	−1.03318	−	44.7187i	−0.0529315	−	2.29101i
$382$	1.82187	−	0.610631i	0.0932152	−	0.0312426i
$383$	−11.7169	−	0.541705i	−0.598706	−	0.0276799i	−0.255292	−	0.966864i	$-0.582172\pi$
$383$	−11.7169	−	0.541705i	−0.598706	−	0.0276799i	−0.343414	+	0.939184i	$0.611583\pi$
$384$	19.8302	+	14.2680i	1.01196	+	0.728110i
$385$	5.98795	+	2.16205i	0.305174	+	0.110188i
$386$	15.6927	+	8.27174i	0.798735	+	0.421020i
$387$	−5.21023	+	2.59438i	−0.264851	+	0.131880i
$388$	−16.5919	−	15.8425i	−0.842326	−	0.804282i
$389$	7.16198	−	30.4509i	0.363127	−	1.54392i	−0.411445	−	0.911435i	$-0.634976\pi$
$389$	7.16198	−	30.4509i	0.363127	−	1.54392i	0.774572	−	0.632486i	$-0.217966\pi$
$390$	−5.11504	−	0.956166i	−0.259010	−	0.0484173i
$391$	−24.7321	−	1.78743i	−1.25076	−	0.0903941i
$392$	−12.5693	+	2.34961i	−0.634846	+	0.118673i
$393$	−0.0383207	+	0.828864i	−0.00193302	+	0.0418107i
$394$	2.05231	−	17.6899i	0.103394	−	0.891203i
$395$	3.69005	+	5.95964i	0.185667	+	0.299862i
$396$	7.22330	+	12.2916i	0.362984	+	0.617674i
$397$	15.3989	−	14.7035i	0.772851	−	0.737946i	−0.197327	−	0.980338i	$-0.563226\pi$
$397$	15.3989	−	14.7035i	0.772851	−	0.737946i	0.970178	+	0.242392i	$0.0779320\pi$
$398$	5.65671	−	15.6667i	0.283545	−	0.785300i
$399$	−4.81585	−	4.81585i	−0.241094	−	0.241094i
$400$	−2.11989	+	3.80594i	−0.105995	+	0.190297i
$401$	4.56713	+	1.18614i	0.228071	+	0.0592332i	0.363659	−	0.931532i	$-0.381527\pi$
$401$	4.56713	+	1.18614i	0.228071	+	0.0592332i	−0.135587	+	0.990765i	$0.543292\pi$
$402$	−0.867958	+	1.84894i	−0.0432898	+	0.0922167i
$403$	−1.69678	−	4.69935i	−0.0845225	−	0.234091i
$404$	−1.70483	−	0.848903i	−0.0848184	−	0.0422345i
$405$	−2.90360	−	4.03554i	−0.144281	−	0.200527i
$406$	−3.42622	−	1.90839i	−0.170040	−	0.0947118i
$407$	21.7715	+	19.8473i	1.07917	+	0.983794i
$408$	11.3041	−	23.9030i	0.559636	−	1.18338i
$409$	1.42518	−	1.29923i	0.0704708	−	0.0642426i	−0.637694	−	0.770290i	$-0.720112\pi$
$409$	1.42518	−	1.29923i	0.0704708	−	0.0642426i	0.708165	+	0.706047i	$0.249523\pi$
$410$	4.16988	−	0.980747i	0.205936	−	0.0484357i
$411$	0.249460	+	3.59396i	0.0123050	+	0.177277i
$412$	−2.04081	−	0.189109i	−0.100544	−	0.00931674i
$413$	−14.3742	−	4.45119i	−0.707310	−	0.219029i
$414$	−10.8298	−	9.42392i	−0.532253	−	0.463161i
$415$	−3.94401	+	4.53236i	−0.193604	+	0.222485i
$416$	8.80660	−	26.2753i	0.431779	−	1.28825i
$417$	−2.59391	−	3.78664i	−0.127024	−	0.185433i
$418$	1.84394	−	0.213927i	0.0901903	−	0.0104635i
$419$	2.19250	+	1.28845i	0.107111	+	0.0629450i	0.559230	−	0.829012i	$-0.311097\pi$
$419$	2.19250	+	1.28845i	0.107111	+	0.0629450i	−0.452120	+	0.891957i	$0.649332\pi$
$420$	−2.78747	+	6.72955i	−0.136015	+	0.328369i
$421$	−4.23974	−	22.6806i	−0.206632	−	1.10538i	−0.916192	−	0.400740i	$-0.868753\pi$
$421$	−4.23974	−	22.6806i	−0.206632	−	1.10538i	0.709560	−	0.704645i	$-0.248894\pi$
$422$	1.63515	+	3.48323i	0.0795980	+	0.169561i
$423$	20.1938	−	20.1938i	0.981855	−	0.981855i
$424$	−1.86797	−	6.56525i	−0.0907168	−	0.318836i
$425$	18.1691	+	6.14724i	0.881329	+	0.298185i
$426$	−3.11050	+	10.9323i	−0.150704	+	0.529671i
$427$	−17.3313	−	31.1157i	−0.838721	−	1.50579i
$428$	−2.91504	−	11.2241i	−0.140904	−	0.542535i
$429$	24.7092	−	27.1047i	1.19297	−	1.30863i
$430$	0.733699	−	0.344425i	0.0353821	−	0.0166096i
$431$	−6.83575	+	9.50060i	−0.329267	+	0.457628i	−0.943440	−	0.331543i	$-0.892431\pi$
$431$	−6.83575	+	9.50060i	−0.329267	+	0.457628i	0.614173	+	0.789171i	$0.289490\pi$
$432$	−0.370480	+	0.195283i	−0.0178247	+	0.00939556i
$433$	9.42486	−	1.31471i	0.452930	−	0.0631810i	0.0919687	−	0.995762i	$-0.470684\pi$
$433$	9.42486	−	1.31471i	0.452930	−	0.0631810i	0.360961	+	0.932581i	$0.382449\pi$
$434$	2.71724	−	0.379039i	0.130432	−	0.0181945i
$435$	−1.95999	+	1.03313i	−0.0939743	+	0.0495347i
$436$	11.0383	−	15.3415i	0.528639	−	0.734724i
$437$	4.31332	−	2.02483i	0.206334	−	0.0968607i
$438$	8.97215	−	9.84198i	0.428706	−	0.470268i
$439$	−6.98900	−	26.9104i	−0.333567	−	1.28437i	−0.890947	−	0.454108i	$-0.849958\pi$
$439$	−6.98900	−	26.9104i	−0.333567	−	1.28437i	0.557380	−	0.830257i	$-0.311807\pi$
$440$	−2.31112	−	4.14926i	−0.110178	−	0.197808i
$441$	4.31352	−	15.1605i	0.205406	−	0.721927i
$442$	−14.4848	−	2.06258i	−0.688970	−	0.0981071i
$443$	−5.31038	−	18.6640i	−0.252304	−	0.886756i	−0.979688	−	0.200526i	$-0.935735\pi$
$443$	−5.31038	−	18.6640i	−0.252304	−	0.886756i	0.727385	−	0.686230i	$-0.240736\pi$
$444$	−23.8345	+	23.8345i	−1.13113	+	1.13113i
$445$	3.40275	+	7.24860i	0.161306	+	0.343617i
$446$	0.326723	+	1.74781i	0.0154708	+	0.0827613i
$447$	21.4557	−	51.7986i	1.01482	−	2.44999i
$448$	7.53579	+	4.42851i	0.356033	+	0.209227i
$449$	−26.3318	+	3.05491i	−1.24267	+	0.144170i	−0.711251	−	0.702938i	$-0.751871\pi$
$449$	−26.3318	+	3.05491i	−1.24267	+	0.144170i	−0.531421	+	0.847108i	$0.678342\pi$
$450$	6.27567	+	9.16135i	0.295838	+	0.431870i
$451$	−9.59500	+	28.6276i	−0.451811	+	1.34802i
$452$	7.40244	−	8.50671i	0.348182	−	0.400122i
$453$	−39.9807	−	34.7907i	−1.87846	−	1.63461i
$454$	6.03643	+	1.86927i	0.283304	+	0.0877290i
$455$	9.60099	+	0.889663i	0.450102	+	0.0417081i
$456$	0.351829	+	5.06877i	0.0164759	+	0.237367i
$457$	−10.0444	+	2.36242i	−0.469858	+	0.110510i	−0.457112	−	0.889409i	$-0.651116\pi$
$457$	−10.0444	+	2.36242i	−0.469858	+	0.110510i	−0.0127459	+	0.999919i	$0.504057\pi$
$458$	−4.52565	+	4.12568i	−0.211470	+	0.192780i
$459$	1.14076	+	1.44864i	0.0532460	+	0.0676168i
$460$	−3.76609	−	3.43324i	−0.175595	−	0.160076i
$461$	−11.9034	−	6.63016i	−0.554397	−	0.308797i	0.184261	−	0.982877i	$-0.441011\pi$
$461$	−11.9034	−	6.63016i	−0.554397	−	0.308797i	−0.738658	+	0.674080i	$0.764540\pi$
$462$	11.7626	+	16.3481i	0.547246	+	0.760584i
$463$	11.1339	+	5.54400i	0.517434	+	0.257652i	0.685433	−	0.728135i	$-0.259613\pi$
$463$	11.1339	+	5.54400i	0.517434	+	0.257652i	−0.167999	+	0.985787i	$0.553730\pi$
$464$	−0.480511	−	1.33081i	−0.0223072	−	0.0617814i
$465$	0.658636	−	1.40304i	0.0305435	−	0.0650643i
$466$	−1.04619	−	0.271709i	−0.0484638	−	0.0125867i
$467$	−10.3134	+	18.5160i	−0.477246	+	0.856820i	0.522745	+	0.852489i	$0.324908\pi$
$467$	−10.3134	+	18.5160i	−0.477246	+	0.856820i	−0.999991	+	0.00433109i	$0.998621\pi$
$468$	15.2684	+	15.2684i	0.705783	+	0.705783i
$469$	1.28532	−	3.55979i	0.0593505	−	0.164376i
$470$	−2.87628	+	2.74637i	−0.132673	+	0.126681i
$471$	−14.8773	−	25.3160i	−0.685510	−	1.16650i
$472$	5.90976	+	9.54459i	0.272019	+	0.439325i
$473$	−0.658364	+	5.67477i	−0.0302716	+	0.260926i
$474$	−1.02411	+	22.1512i	−0.0470391	+	1.01744i
$475$	−3.62305	+	0.677265i	−0.166237	+	0.0310750i
$476$	−7.01002	+	19.2431i	−0.321304	+	0.882008i
$477$	8.27070	+	1.54606i	0.378690	+	0.0707893i
$478$	3.78104	−	16.0760i	0.172941	−	0.735299i
$479$	−24.8305	−	23.7091i	−1.13454	−	1.08329i	−0.995668	−	0.0929841i	$-0.970359\pi$
$479$	−24.8305	−	23.7091i	−1.13454	−	1.08329i	−0.138868	−	0.990311i	$-0.544346\pi$
$480$	7.69547	−	3.83189i	0.351249	−	0.174901i
$481$	39.4715	+	20.8058i	1.79974	+	0.948661i
$482$	−14.2463	−	5.14386i	−0.648902	−	0.234297i
$483$	41.9638	+	30.1933i	1.90942	+	1.37384i
$484$	−1.80609	−	0.0835007i	−0.0820951	−	0.00379548i
$485$	−8.93218	+	2.99376i	−0.405589	+	0.135940i
$486$	−0.386538	−	16.7303i	−0.0175337	−	0.758903i
$487$	25.5395	+	32.2432i	1.15730	+	1.46108i	0.862884	+	0.505403i	$0.168656\pi$
$487$	25.5395	+	32.2432i	1.15730	+	1.46108i	0.294420	+	0.955676i	$0.404873\pi$
$488$	−5.48447	+	25.9992i	−0.248270	+	1.17693i
$489$	−20.1264	+	51.9521i	−0.910146	+	2.34936i
$490$	−0.649281	+	2.09673i	−0.0293315	+	0.0947205i
$491$	7.63520	+	2.55906i	0.344572	+	0.115489i	0.484787	−	0.874632i	$-0.338897\pi$
$491$	7.63520	+	2.55906i	0.344572	+	0.115489i	−0.140215	+	0.990121i	$0.544779\pi$
$492$	−32.2123	−	12.4791i	−1.45224	−	0.562602i
$493$	−5.37976	+	3.14092i	−0.242292	+	0.141460i
$494$	2.62163	−	1.01562i	0.117953	−	0.0456951i
$495$	5.84830	−	0.270383i	0.262861	−	0.0121528i
$496$	0.829288	+	0.540364i	0.0372361	+	0.0242630i
$497$	3.86996	−	20.7025i	0.173591	−	0.928632i
$498$	−18.3965	+	4.77782i	−0.824368	+	0.214099i
$499$	−5.89132	+	22.6839i	−0.263732	+	1.01547i	0.692158	+	0.721746i	$0.256660\pi$
$499$	−5.89132	+	22.6839i	−0.263732	+	1.01547i	−0.955889	+	0.293727i	$0.905104\pi$
$500$	4.46507	+	6.85248i	0.199684	+	0.306452i
$501$	15.9724	+	36.1741i	0.713596	+	1.61614i
$502$	−0.429789	+	3.08106i	−0.0191824	+	0.137514i
$503$	−1.92985	−	4.65906i	−0.0860476	−	0.207737i	0.874998	−	0.484126i	$-0.160862\pi$
$503$	−1.92985	−	4.65906i	−0.0860476	−	0.207737i	−0.961046	+	0.276389i	$0.910862\pi$
$504$	−23.7653	+	15.4855i	−1.05859	+	0.689777i
$505$	−0.634827	+	0.456763i	−0.0282494	+	0.0203257i
$506$	−13.5527	+	3.85608i	−0.602491	+	0.171424i
$507$	10.8331	−	20.5518i	0.481113	−	0.912739i
$508$	14.6073	−	21.3240i	0.648093	−	0.946100i
$509$	16.5226	+	21.8795i	0.732352	+	0.969790i	0.999980	+	0.00626832i	$0.00199528\pi$
$509$	16.5226	+	21.8795i	0.732352	+	0.969790i	−0.267629	+	0.963522i	$0.586240\pi$
$510$	−2.72489	−	3.62978i	−0.120660	−	0.160729i
$511$	−14.8714	+	19.6930i	−0.657873	+	0.871165i
$512$	3.28010	+	9.78648i	0.144961	+	0.432505i
$513$	−0.327350	−	0.135593i	−0.0144529	−	0.00598658i
$514$	1.49706	+	1.64220i	0.0660327	+	0.0724344i
$515$	−0.459479	+	0.705155i	−0.0202471	+	0.0310729i
$516$	−6.45107	−	1.05232i	−0.283992	−	0.0463259i
$517$	−5.78562	−	27.4268i	−0.254451	−	1.20623i
$518$	−15.6525	+	18.8496i	−0.687732	+	0.828204i
$519$	23.2148	+	15.9025i	1.01901	+	0.698041i
$520$	−4.96762	−	5.20260i	−0.217845	−	0.228149i
$521$	5.60496	+	10.6334i	0.245558	+	0.465858i	0.976191	−	0.216912i	$-0.0695985\pi$
$521$	5.60496	+	10.6334i	0.245558	+	0.465858i	−0.730633	+	0.682770i	$0.760775\pi$
$522$	−3.58255	−	0.415634i	−0.156804	−	0.0181918i
$523$	−25.9663	−	19.6088i	−1.13543	−	0.857434i	−0.144191	−	0.989550i	$-0.546058\pi$
$523$	−25.9663	−	19.6088i	−1.13543	−	0.857434i	−0.991234	+	0.132116i	$0.957823\pi$
$524$	−0.297704	+	0.375847i	−0.0130053	+	0.0164189i
$525$	−25.5469	−	30.7649i	−1.11496	−	1.34269i
$526$	1.78533	+	19.2668i	0.0778440	+	0.840071i
$527$	1.67915	−	4.02142i	0.0731451	−	0.175176i
$528$	−0.670422	+	7.23501i	−0.0291764	+	0.314863i
$529$	−10.8644	+	7.44227i	−0.472364	+	0.323577i
$530$	−1.14645	−	0.241841i	−0.0497988	−	0.0105049i
$531$	−13.7790	+	1.27681i	−0.597957	+	0.0554089i
$532$	−0.633599	−	3.88416i	−0.0274700	−	0.168400i
$533$	−3.16645	+	45.6188i	−0.137154	+	1.97597i
$534$	−4.07837	+	25.0017i	−0.176488	+	1.08193i
$535$	−4.63555	−	1.09027i	−0.200412	−	0.0471365i
$536$	−2.46670	+	1.37394i	−0.106545	+	0.0593453i
$537$	10.4343	+	4.89825i	0.450274	+	0.211375i
$538$	−10.4232	+	4.31743i	−0.449376	+	0.186137i
$539$	−10.1558	−	11.6708i	−0.437440	−	0.502695i
$540$			0.378949i			0.0163074i
$541$	7.84318	−	6.82505i	0.337205	−	0.293432i	−0.471238	−	0.882006i	$-0.656193\pi$
$541$	7.84318	−	6.82505i	0.337205	−	0.293432i	0.808443	+	0.588574i	$0.200311\pi$
$542$	−4.08541	+	1.80388i	−0.175483	+	0.0774834i
$543$	4.25249	−	8.54016i	0.182492	−	0.366493i
$544$	21.1498	−	11.7016i	0.906791	−	0.501703i
$545$	−3.45946	−	6.94752i	−0.148187	−	0.297599i
$546$	23.4671	+	19.4868i	1.00430	+	0.833959i
$547$	−20.4999	−	0.473630i	−0.876511	−	0.0202509i	−0.417495	−	0.908679i	$-0.637092\pi$
$547$	−20.4999	−	0.473630i	−0.876511	−	0.0202509i	−0.459016	+	0.888428i	$0.651798\pi$
$548$	−1.09590	+	1.76994i	−0.0468145	+	0.0756080i
$549$	−25.6751	−	20.3370i	−1.09579	−	0.867961i
$550$	10.8965	−	0.251754i	0.464630	−	0.0107348i
$551$	0.606502	−	1.03206i	0.0258378	−	0.0439671i
$552$	−8.83012	−	37.5434i	−0.375835	−	1.59795i
$553$	−1.89764	−	41.0453i	−0.0806959	−	1.74542i
$554$	10.0338	+	0.696453i	0.426293	+	0.0295894i
$555$	4.09446	+	13.2222i	0.173800	+	0.561253i
$556$	0.0612612	−	2.65154i	0.00259805	−	0.112450i
$557$	35.8175	−	27.0481i	1.51763	−	1.14606i	0.572263	−	0.820070i	$-0.306066\pi$
$557$	35.8175	−	27.0481i	1.51763	−	1.14606i	0.945372	−	0.325994i	$-0.105699\pi$
$558$	2.17521	−	1.27829i	0.0920839	−	0.0541143i
$559$	1.19538	+	8.56941i	0.0505593	+	0.362448i
$560$	−1.62407	+	1.00558i	−0.0686293	+	0.0424935i
$561$	31.8626	−	2.86106i	1.34524	−	0.120794i
$562$	16.6001	+	10.2783i	0.700232	+	0.433565i
$563$	15.2691	−	34.5812i	0.643515	−	1.45742i	−0.231260	−	0.972892i	$-0.574285\pi$
$563$	15.2691	−	34.5812i	0.643515	−	1.45742i	0.874775	−	0.484530i	$-0.161009\pi$
$564$	31.6526	−	5.16330i	1.33282	−	0.217414i
$565$	−1.67279	−	4.31798i	−0.0703749	−	0.181659i
$566$	3.55071	−	0.246459i	0.149248	−	0.0103594i
$567$	3.35850	+	28.9486i	0.141044	+	1.21573i
$568$	−12.3166	+	9.75585i	−0.516793	+	0.409346i
$569$	25.8651	−	21.4781i	1.08432	−	0.900409i	0.0889044	−	0.996040i	$-0.471663\pi$
$569$	25.8651	−	21.4781i	1.08432	−	0.900409i	0.995417	+	0.0956312i	$0.0304870\pi$
$570$	0.797858	+	0.352289i	0.0334186	+	0.0147558i
$571$	27.3789	−	8.47827i	1.14577	−	0.354805i	0.336180	−	0.941798i	$-0.390865\pi$
$571$	27.3789	−	8.47827i	1.14577	−	0.354805i	0.809592	+	0.586993i	$0.199688\pi$
$572$	20.7373	−	4.37448i	0.867070	−	0.182906i
$573$	−4.39433	+	4.60219i	−0.183576	+	0.192259i
$574$	−24.1518	−	6.87177i	−1.00808	−	0.286822i
$575$	26.3148	−	9.50140i	1.09740	−	0.396236i
$576$	7.96097	+	1.11051i	0.331707	+	0.0462712i
$577$	−27.2096			−1.13275			−0.566375	−	0.824147i	$-0.691655\pi$
$577$	−27.2096			−1.13275			−0.566375	+	0.824147i	$0.691655\pi$
$578$	−8.09660	−	9.86408i	−0.336774	−	0.410292i
$579$	−58.7454			−2.44138
$580$	−1.26800	−	0.176878i	−0.0526508	−	0.00734447i
$581$	33.1257	−	11.9606i	1.37429	−	0.496209i
$582$	−28.6644	−	8.15574i	−1.18818	−	0.338066i
$583$	5.70316	−	5.97292i	0.236201	−	0.247373i
$584$	18.0137	−	3.79995i	0.745413	−	0.157243i
$585$	8.47020	−	2.62292i	0.350200	−	0.108444i
$586$	8.60349	+	3.79881i	0.355407	+	0.156927i
$587$	−9.45911	+	7.85474i	−0.390419	+	0.324200i	−0.813149	−	0.582056i	$-0.802248\pi$
$587$	−9.45911	+	7.85474i	−0.390419	+	0.324200i	0.422730	+	0.906256i	$0.361072\pi$
$588$	13.8755	−	10.9906i	0.572215	−	0.453245i
$589$	0.0965069	+	0.831841i	0.00397650	+	0.0342754i
$590$	1.92238	−	0.133434i	0.0791432	−	0.00549341i
$591$	21.3042	+	54.9924i	0.876336	+	2.26208i
$592$	−8.72410	+	1.42311i	−0.358558	+	0.0584894i
$593$	−6.58542	+	14.9146i	−0.270431	+	0.612468i	−0.997230	−	0.0743827i	$-0.976301\pi$
$593$	−6.58542	+	14.9146i	−0.270431	+	0.612468i	0.726799	+	0.686850i	$0.241007\pi$
$594$	0.890839	+	0.551584i	0.0365516	+	0.0226318i
$595$	5.64816	+	6.23127i	0.231552	+	0.255457i
$596$	27.5451	−	17.0552i	1.12829	−	0.698608i
$597$	7.62074	+	54.6313i	0.311896	+	2.23591i
$598$	−18.3991	+	10.8125i	−0.752396	+	0.442155i
$599$	−22.1860	+	16.7541i	−0.906494	+	0.684553i	−0.949247	−	0.314533i	$-0.898152\pi$
$599$	−22.1860	+	16.7541i	−0.906494	+	0.684553i	0.0427523	+	0.999086i	$0.486387\pi$
$600$	−0.689084	+	29.8252i	−0.0281317	+	1.21761i
$601$	−8.08160	−	26.0980i	−0.329655	−	1.06456i	−0.958035	−	0.286651i	$-0.907458\pi$
$601$	−8.08160	−	26.0980i	−0.329655	−	1.06456i	0.628380	−	0.777907i	$-0.283718\pi$
$602$	−4.73977	−	0.328992i	−0.193179	−	0.0134087i
$603$	−0.160740	−	3.47676i	−0.00654586	−	0.141585i
$604$	−7.01160	−	29.8115i	−0.285298	−	1.21301i
$605$	−0.376169	+	0.640110i	−0.0152934	+	0.0260242i
$606$	−2.47345	+	0.0571467i	−0.100477	+	0.00232142i
$607$	4.69641	+	3.71998i	0.190621	+	0.150989i	0.711610	−	0.702574i	$-0.247966\pi$
$607$	4.69641	+	3.71998i	0.190621	+	0.150989i	−0.520989	+	0.853563i	$0.674437\pi$
$608$	−2.44514	+	3.94904i	−0.0991636	+	0.160155i
$609$	12.9842	+	0.299987i	0.526145	+	0.0121561i
$610$	3.50901	+	2.91384i	0.142076	+	0.117978i
$611$	−18.9232	−	38.0029i	−0.765550	−	1.53743i
$612$	0.816260	+	18.8162i	0.0329954	+	0.760598i
$613$	−12.4319	+	24.9666i	−0.502119	+	1.00839i	0.488605	+	0.872505i	$0.337506\pi$
$613$	−12.4319	+	24.9666i	−0.502119	+	1.00839i	−0.990724	+	0.135886i	$0.956612\pi$
$614$	7.79355	−	3.44119i	0.314522	−	0.138875i
$615$	−10.7014	+	9.31223i	−0.431522	+	0.375505i
$616$			27.8410i			1.12174i
$617$	−11.2174	−	12.8908i	−0.451597	−	0.518965i	0.482543	−	0.875872i	$-0.339713\pi$
$617$	−11.2174	−	12.8908i	−0.451597	−	0.518965i	−0.934140	+	0.356908i	$0.883831\pi$
$618$	−2.45989	+	1.01892i	−0.0989512	+	0.0409869i
$619$	−31.3923	−	14.7367i	−1.26176	−	0.592317i	−0.326141	−	0.945321i	$-0.605749\pi$
$619$	−31.3923	−	14.7367i	−1.26176	−	0.592317i	−0.935622	+	0.353004i	$0.885160\pi$
$620$	0.782438	−	0.435815i	0.0314235	−	0.0175028i
$621$	2.61809	+	0.615769i	0.105060	+	0.0247100i
$622$	−0.953074	+	5.84264i	−0.0382148	+	0.234269i
$623$	3.25029	−	46.8267i	0.130220	−	1.87607i
$624$	1.77172	+	10.8612i	0.0709255	+	0.434796i
$625$	−19.8166	+	1.83628i	−0.792666	+	0.0734513i
$626$	19.9053	+	4.19898i	0.795577	+	0.167825i
$627$	−5.07157	+	3.47411i	−0.202539	+	0.138742i
$628$	1.56559	−	16.8954i	0.0624737	−	0.674199i
$629$	13.1126	+	36.6426i	0.522835	+	1.46104i
$630$	0.449258	+	4.84826i	0.0178989	+	0.193159i
$631$	2.44090	+	2.93947i	0.0971708	+	0.117018i	0.815691	−	0.578487i	$-0.196357\pi$
$631$	2.44090	+	2.93947i	0.0971708	+	0.117018i	−0.718520	+	0.695506i	$0.755180\pi$
$632$	−19.0332	+	24.0291i	−0.757100	+	0.955828i
$633$	−10.1690	−	7.67929i	−0.404182	−	0.305224i
$634$	−1.26747	−	0.147047i	−0.0503378	−	0.00584000i
$635$	−4.94933	−	9.38957i	−0.196408	−	0.372614i
$636$	6.52526	+	6.83391i	0.258744	+	0.270982i
$637$	−19.3308	−	13.2419i	−0.765915	−	0.524664i
$638$	−2.26146	+	2.72338i	−0.0895322	+	0.107820i
$639$	−3.99766	−	18.9510i	−0.158145	−	0.749688i
$640$	5.72132	+	0.933284i	0.226155	+	0.0368913i
$641$	−14.8740	+	22.8269i	−0.587487	+	0.901608i	−0.999956	−	0.00936370i	$-0.997019\pi$
$641$	−14.8740	+	22.8269i	−0.587487	+	0.901608i	0.412469	+	0.910972i	$0.364666\pi$
$642$	−10.1491	−	11.1330i	−0.400553	−	0.439386i
$643$	39.6275	+	16.4142i	1.56276	+	0.647314i	0.985565	−	0.169295i	$-0.0541492\pi$
$643$	39.6275	+	16.4142i	1.56276	+	0.647314i	0.577190	+	0.816610i	$0.304149\pi$
$644$	9.49337	+	28.3244i	0.374091	+	1.11614i
$645$	−1.61755	+	2.14198i	−0.0636908	+	0.0843403i
$646$	2.28413	+	0.892362i	0.0898679	+	0.0351095i
$647$	−11.1118	−	14.7144i	−0.436849	−	0.578482i	0.525330	−	0.850898i	$-0.323942\pi$
$647$	−11.1118	−	14.7144i	−0.436849	−	0.578482i	−0.962179	+	0.272417i	$0.912177\pi$
$648$	12.2869	−	17.9366i	0.482675	−	0.704618i
$649$	−6.33333	+	12.0152i	−0.248605	+	0.471639i
$650$	15.8776	−	4.51757i	0.622771	−	0.177194i
$651$	−7.37498	+	5.30635i	−0.289048	+	0.207972i
$652$	−26.9734	+	17.5758i	−1.05636	+	0.688323i
$653$	13.8295	+	33.3873i	0.541189	+	1.30655i	0.923884	+	0.382672i	$0.124996\pi$
$653$	13.8295	+	33.3873i	0.541189	+	1.30655i	−0.382695	+	0.923875i	$0.625004\pi$
$654$	3.39211	−	24.3173i	0.132642	−	0.950880i
$655$	0.0795287	+	0.180115i	0.00310744	+	0.00703768i
$656$	−4.94567	−	7.59005i	−0.193096	−	0.296342i
$657$	−5.70458	+	21.9649i	−0.222557	+	0.856933i
$658$	22.5635	−	5.86003i	0.879615	−	0.228448i
$659$	−5.58938	+	29.9005i	−0.217731	+	1.16476i	0.683012	+	0.730407i	$0.260670\pi$
$659$	−5.58938	+	29.9005i	−0.217731	+	1.16476i	−0.900743	+	0.434352i	$0.856977\pi$
$660$	5.50845	+	3.58930i	0.214416	+	0.139713i
$661$	27.0970	−	1.25277i	1.05395	−	0.0487271i	0.487741	−	0.872988i	$-0.337821\pi$
$661$	27.0970	−	1.25277i	1.05395	−	0.0487271i	0.566210	+	0.824261i	$0.308409\pi$
$662$	−15.4700	+	5.99311i	−0.601259	+	0.232929i
$663$	45.6188	−	16.3248i	1.77169	−	0.634002i
$664$	−24.5002	−	9.49144i	−0.950793	−	0.368339i
$665$	−1.53232	−	0.513583i	−0.0594209	−	0.0199159i
$666$	−6.66499	+	21.5233i	−0.258263	+	0.834010i
$667$	−3.28244	+	8.47297i	−0.127097	+	0.328075i
$668$	−4.71636	+	22.3580i	−0.182481	+	0.865056i
$669$	−3.65610	−	4.61577i	−0.141353	−	0.178456i
$670$	0.0111949	+	0.484543i	0.000432497	+	0.0187195i
$671$	−30.4817	+	10.2164i	−1.17673	+	0.394401i
$672$	−50.3393	−	2.32732i	−1.94188	−	0.0897785i
$673$	−26.0708	−	18.7581i	−1.00496	−	0.723073i	−0.0437887	−	0.999041i	$-0.513943\pi$
$673$	−26.0708	−	18.7581i	−1.00496	−	0.723073i	−0.961167	+	0.275968i	$0.911002\pi$
$674$	−9.01401	−	3.25465i	−0.347207	−	0.125365i
$675$	−1.84040	−	0.970090i	−0.0708369	−	0.0373388i
$676$	12.0172	−	5.98385i	0.462200	−	0.230148i
$677$	6.62860	+	6.32923i	0.254758	+	0.243252i	0.807170	−	0.590319i	$-0.200998\pi$
$677$	6.62860	+	6.32923i	0.254758	+	0.243252i	−0.552412	+	0.833571i	$0.686292\pi$
$678$	3.35396	−	14.2602i	0.128808	−	0.547658i
$679$	54.2818	+	10.1470i	2.08315	+	0.389407i
$680$	−0.127068	−	6.27296i	−0.00487283	−	0.240557i
$681$	−20.5705	+	3.84529i	−0.788263	+	0.147352i
$682$	0.114367	−	2.47373i	0.00437935	−	0.0947239i
$683$	−3.98714	+	34.3672i	−0.152564	+	1.31502i	0.668297	+	0.743895i	$0.267024\pi$
$683$	−3.98714	+	34.3672i	−0.152564	+	1.31502i	−0.820861	+	0.571128i	$0.806506\pi$
$684$	−1.90523	−	3.07705i	−0.0728482	−	0.117654i
$685$	0.433120	+	0.737021i	0.0165487	+	0.0281601i
$686$	−3.83578	+	3.66254i	−0.146451	+	0.139837i
$687$	6.88727	−	19.0748i	0.262766	−	0.727749i
$688$	−1.21205	−	1.21205i	−0.0462091	−	0.0462091i
$689$	6.08637	−	10.9271i	0.231872	−	0.416291i
$690$	−6.40777	−	1.66418i	−0.243940	−	0.0633544i
$691$	2.53087	−	5.39129i	0.0962787	−	0.205094i	−0.851253	−	0.524755i	$-0.824157\pi$
$691$	2.53087	−	5.39129i	0.0962787	−	0.205094i	0.947532	+	0.319660i	$0.103569\pi$
$692$	5.52204	+	15.2937i	0.209917	+	0.581380i
$693$	−30.7208	−	15.2971i	−1.16699	−	0.581091i
$694$	5.75862	+	8.00357i	0.218594	+	0.303811i
$695$	−0.951493	−	0.529978i	−0.0360922	−	0.0201032i
$696$	−7.16041	−	6.52758i	−0.271415	−	0.247427i
$697$	−28.9257	+	27.4623i	−1.09564	+	1.04021i
$698$	20.3448	−	18.5467i	0.770062	−	0.702005i
$699$	3.48443	−	0.819530i	0.131793	−	0.0309975i
$700$	−1.60006	−	23.0520i	−0.0604767	−	0.871284i
$701$	3.48143	+	0.322602i	0.131492	+	0.0121845i	0.157813	−	0.987469i	$-0.449556\pi$
$701$	3.48143	+	0.322602i	0.131492	+	0.0121845i	−0.0263211	+	0.999654i	$0.508379\pi$
$702$	1.51590	+	0.469419i	0.0572139	+	0.0177171i
$703$	−5.64162	−	4.90927i	−0.212778	−	0.185157i
$704$	5.17902	−	5.95160i	0.195192	−	0.224309i
$705$	4.18527	−	12.4871i	0.157626	−	0.470293i
$706$	0.487870	+	0.712202i	0.0183612	+	0.0268041i
$707$	4.55387	−	0.528323i	0.171266	−	0.0198696i
$708$	−13.3979	−	7.87344i	−0.503523	−	0.295902i
$709$	1.48815	−	3.59271i	0.0558886	−	0.134927i	−0.893469	−	0.449125i	$-0.851736\pi$
$709$	1.48815	−	3.59271i	0.0558886	−	0.134927i	0.949357	+	0.314198i	$0.101736\pi$
$710$	0.495588	+	2.65116i	0.0185991	+	0.0994963i
$711$	−16.0569	−	34.2047i	−0.602182	−	1.28278i
$712$	−24.7617	+	24.7617i	−0.927985	+	0.927985i
$713$	−1.73955	−	6.11390i	−0.0651468	−	0.228967i
$714$	3.60073	+	26.3609i	0.134754	+	0.986532i
$715$	2.38172	−	8.37088i	0.0890713	−	0.313053i
$716$	3.24114	+	5.81896i	0.121127	+	0.217465i
$717$	13.7477	+	52.9340i	0.513416	+	1.97686i
$718$	4.92546	−	5.40297i	0.183817	−	0.201637i
$719$	−31.6921	+	14.8774i	−1.18192	+	0.554834i	−0.912853	−	0.408288i	$-0.866126\pi$
$719$	−31.6921	+	14.8774i	−1.18192	+	0.554834i	−0.269064	+	0.963122i	$0.586714\pi$
$720$	−1.02594	+	1.42589i	−0.0382345	+	0.0531399i
$721$	4.36442	−	2.30053i	0.162540	−	0.0856761i
$722$	13.6593	−	1.90540i	0.508348	−	0.0709115i
$723$	49.6783	−	6.92983i	1.84756	−	0.257723i
$724$	4.87681	−	2.57061i	0.181245	−	0.0955361i
$725$	4.10504	−	5.70535i	0.152457	−	0.211891i
$726$	−2.12617	+	0.998101i	−0.0789095	+	0.0370430i
$727$	17.9104	−	19.6468i	0.664260	−	0.728659i	−0.310830	−	0.950465i	$-0.600607\pi$
$727$	17.9104	−	19.6468i	0.664260	−	0.728659i	0.975091	+	0.221806i	$0.0711953\pi$
$728$	10.5996	+	40.8126i	0.392847	+	1.51262i
$729$	14.6639	+	26.3268i	0.543108	+	0.975066i
$730$	0.864826	−	3.03955i	0.0320087	−	0.112499i
$731$	−4.28271	+	6.21397i	−0.158402	+	0.229832i
$732$	−10.0660	−	35.3782i	−0.372049	−	1.30762i
$733$	14.0034	−	14.0034i	0.517228	−	0.517228i	−0.399504	−	0.916732i	$-0.630818\pi$
$733$	14.0034	−	14.0034i	0.517228	−	0.517228i	0.916732	+	0.399504i	$0.130818\pi$
$734$	6.34272	+	13.5114i	0.234114	+	0.498714i
$735$	−1.33564	−	7.14507i	−0.0492660	−	0.263550i
$736$	13.4921	−	32.5728i	0.497326	−	1.20065i
$737$	−2.94523	−	1.73080i	−0.108489	−	0.0637548i
$738$	−22.9379	+	2.66117i	−0.844357	+	0.0979590i
$739$	13.1869	+	19.2505i	0.485088	+	0.708141i	0.987698	−	0.156372i	$-0.0499798\pi$
$739$	13.1869	+	19.2505i	0.485088	+	0.708141i	−0.502610	+	0.864513i	$0.667627\pi$
$740$	−2.54181	+	7.58372i	−0.0934387	+	0.278783i
$741$	−6.11186	+	7.02361i	−0.224525	+	0.258019i
$742$	5.18124	+	4.50865i	0.190209	+	0.165518i
$743$	−19.7816	−	6.12567i	−0.725718	−	0.224729i	−0.0892251	−	0.996011i	$-0.528439\pi$
$743$	−19.7816	−	6.12567i	−0.725718	−	0.224729i	−0.636493	+	0.771283i	$0.719616\pi$
$744$	6.74923	+	0.625408i	0.247439	+	0.0229286i
$745$	−0.921228	−	13.2721i	−0.0337512	−	0.486252i
$746$	−6.07048	+	1.42776i	−0.222256	+	0.0522741i
$747$	23.9348	−	21.8195i	0.875729	−	0.798333i
$748$	15.9107	+	9.41117i	0.581754	+	0.344107i
$749$	20.6291	+	18.8059i	0.753770	+	0.687152i
$750$	9.28229	+	5.17020i	0.338941	+	0.188789i
$751$	−8.22271	−	11.4282i	−0.300051	−	0.417023i	0.634461	−	0.772955i	$-0.281222\pi$
$751$	−8.22271	−	11.4282i	−0.300051	−	0.417023i	−0.934512	+	0.355932i	$0.884163\pi$
$752$	7.52865	+	3.74882i	0.274542	+	0.136706i
$753$	−3.49865	−	9.68976i	−0.127498	−	0.353115i
$754$	−2.27828	+	4.85324i	−0.0829702	+	0.176744i
$755$	−12.1722	−	3.16129i	−0.442993	−	0.115051i
$756$	1.08092	−	1.94062i	0.0393127	−	0.0705798i
$757$	−22.9142	−	22.9142i	−0.832832	−	0.832832i	0.155072	−	0.987903i	$-0.450439\pi$
$757$	−22.9142	−	22.9142i	−0.832832	−	0.832832i	−0.987903	+	0.155072i	$0.950439\pi$
$758$	3.64583	−	10.0974i	0.132423	−	0.366754i
$759$	33.7487	−	32.2245i	1.22500	−	1.16967i
$760$	0.610854	+	1.03946i	0.0221580	+	0.0377053i
$761$	19.0093	+	30.7012i	0.689088	+	1.11292i	0.987369	+	0.158438i	$0.0506457\pi$
$761$	19.0093	+	30.7012i	0.689088	+	1.11292i	−0.298281	+	0.954478i	$0.596413\pi$
$762$	3.86965	−	33.3544i	0.140183	−	1.20830i
$763$	−2.10112	+	45.4466i	−0.0760658	+	1.64528i
$764$	−3.61433	+	0.675636i	−0.130762	+	0.0244437i
$765$	6.99165	+	3.30645i	0.252784	+	0.119545i
$766$	−8.65506	−	1.61791i	−0.312720	−	0.0584575i
$767$	−4.70974	+	20.0246i	−0.170059	+	0.723046i
$768$	22.3532	+	21.3436i	0.806602	+	0.770172i
$769$	2.23937	−	1.11507i	0.0807537	−	0.0402105i	−0.404908	−	0.914357i	$-0.632696\pi$
$769$	2.23937	−	1.11507i	0.0807537	−	0.0402105i	0.485662	+	0.874147i	$0.338579\pi$
$770$	4.22767	+	2.22844i	0.152355	+	0.0803075i
$771$	−6.92158	−	2.49915i	−0.249275	−	0.0900047i
$772$	−27.5546	−	19.8257i	−0.991711	−	0.713544i
$773$	−17.2472	−	0.797387i	−0.620339	−	0.0286800i	−0.266269	−	0.963899i	$-0.585791\pi$
$773$	−17.2472	−	0.797387i	−0.620339	−	0.0286800i	−0.354070	+	0.935219i	$0.615203\pi$
$774$	−4.14274	+	1.38851i	−0.148908	+	0.0499089i
$775$	0.113571	+	4.91565i	0.00407960	+	0.176575i
$776$	−25.5798	−	32.2941i	−0.918262	−	1.15929i
$777$	16.7474	−	79.3912i	0.600809	−	2.84814i
$778$	8.48284	−	21.8967i	0.304124	−	0.785036i
$779$	2.26720	−	7.32148i	0.0812309	−	0.262319i
$780$	9.44146	+	3.16446i	0.338059	+	0.113306i
$781$	−17.7263	−	6.86720i	−0.634297	−	0.245728i
$782$	−18.2024	−	3.89389i	−0.650915	−	0.139245i
$783$	0.630050	−	0.244083i	0.0225162	−	0.00872281i
$784$	4.63698	−	0.214380i	0.165606	−	0.00765644i
$785$	−5.83780	−	3.80391i	−0.208360	−	0.135767i
$786$	−0.114452	+	0.612266i	−0.00408238	+	0.0218388i
$787$	−5.86009	+	1.52194i	−0.208890	+	0.0542514i	−0.354351	−	0.935113i	$-0.615298\pi$
$787$	−5.86009	+	1.52194i	−0.208890	+	0.0542514i	0.145461	+	0.989364i	$0.453533\pi$
$788$	−8.56640	+	32.9841i	−0.305165	+	1.17501i
$789$	−34.9817	−	53.6860i	−1.24538	−	1.91127i
$790$	2.12539	+	4.81354i	0.0756179	+	0.171258i
$791$	−3.75018	+	26.8842i	−0.133341	+	0.955892i
$792$	9.79780	+	23.6540i	0.348150	+	0.840508i
$793$	−40.7942	+	26.5814i	−1.44864	+	0.943935i
$794$	12.9736	−	9.33464i	0.460418	−	0.331274i
$795$	3.73203	−	1.06186i	0.132362	−	0.0376601i
$796$	−14.8627	+	28.1967i	−0.526796	+	0.999406i
$797$	−6.75065	+	9.85473i	−0.239120	+	0.349073i	−0.925884	−	0.377808i	$-0.876678\pi$
$797$	−6.75065	+	9.85473i	−0.239120	+	0.349073i	0.686764	+	0.726881i	$0.259031\pi$
$798$	−3.08101	−	4.07992i	−0.109067	−	0.144428i
$799$	10.2349	−	35.5867i	0.362083	−	1.25897i
$800$	−16.4350	+	21.7634i	−0.581064	+	0.769453i
$801$	−13.7178	−	40.9283i	−0.484694	−	1.44613i
$802$	3.27253	+	1.35553i	0.115557	+	0.0478653i
$803$	15.0060	+	16.4608i	0.529549	+	0.580888i
$804$	2.13381	−	3.27472i	0.0752536	−	0.115491i
$805$	12.1072	+	1.97497i	0.426723	+	0.0696087i
$806$	−0.774141	−	3.66983i	−0.0272680	−	0.129264i
$807$	23.8683	−	28.7435i	0.840203	−	1.01182i
$808$	−2.82160	−	1.93284i	−0.0992635	−	0.0679971i
$809$	−23.1805	−	24.2770i	−0.814983	−	0.853533i	0.176428	−	0.984314i	$-0.443546\pi$
$809$	−23.1805	−	24.2770i	−0.814983	−	0.853533i	−0.991411	+	0.130781i	$0.958252\pi$
$810$	−1.74023	−	3.30146i	−0.0611454	−	0.116001i
$811$	42.6927	+	4.95304i	1.49914	+	0.173925i	0.825193	−	0.564851i	$-0.191066\pi$
$811$	42.6927	+	4.95304i	1.49914	+	0.173925i	0.673951	+	0.738776i	$0.264596\pi$
$812$	5.98899	+	4.52267i	0.210172	+	0.158715i
$813$	9.18284	−	11.5932i	0.322056	−	0.406591i
$814$	14.1282	+	17.0139i	0.495192	+	0.596337i
$815$	1.21983	+	13.1641i	0.0427289	+	0.461118i
$816$	−5.26306	+	8.02710i	−0.184244	+	0.281005i
$817$	0.133809	−	1.44402i	0.00468137	−	0.0505200i
$818$	1.19433	−	0.818137i	0.0417589	−	0.0286055i
$819$	−50.8582	−	10.7284i	−1.77713	−	0.374881i
$820$	−8.16223	+	0.756342i	−0.285038	+	0.0264126i
$821$	2.33197	+	14.2957i	0.0813865	+	0.498924i	0.995601	+	0.0936940i	$0.0298675\pi$
$821$	2.33197	+	14.2957i	0.0813865	+	0.498924i	−0.914215	+	0.405230i	$0.867191\pi$
$822$	−0.187264	+	2.69789i	−0.00653157	+	0.0940999i
$823$	−3.23767	+	19.8479i	−0.112858	+	0.691856i	0.867916	+	0.496711i	$0.165459\pi$
$823$	−3.23767	+	19.8479i	−0.112858	+	0.691856i	−0.980774	+	0.195145i	$0.937482\pi$
$824$	−3.58288	−	0.842686i	−0.124816	−	0.0293564i
$825$	−31.5331	+	17.5638i	−1.09784	+	0.611494i
$826$	−10.2253	−	4.80011i	−0.355783	−	0.167017i
$827$	47.0302	−	19.4805i	1.63540	−	0.677405i	0.639578	−	0.768726i	$-0.279109\pi$
$827$	47.0302	−	19.4805i	1.63540	−	0.677405i	0.995822	+	0.0913209i	$0.0291089\pi$
$828$	18.0336	+	20.7238i	0.626710	+	0.720201i
$829$		−	7.67348i		−	0.266511i	−0.991082	−	0.133255i	$-0.957457\pi$
$829$		−	7.67348i		−	0.266511i	0.991082	−	0.133255i	$-0.0425431\pi$
$830$	−3.40233	+	2.96066i	−0.118096	+	0.102766i
$831$	−30.4698	+	13.4537i	−1.05698	+	0.466704i
$832$	5.32614	−	10.6963i	0.184651	−	0.370828i
$833$	−4.62254	−	19.9079i	−0.160161	−	0.689767i
$834$	−1.53580	−	3.08429i	−0.0531803	−	0.106800i
$835$	7.21888	+	5.99448i	0.249820	+	0.207448i
$836$	−3.55128	−	0.0820491i	−0.122824	−	0.00283773i
$837$	−0.248831	+	0.401876i	−0.00860085	+	0.0138909i
$838$	1.49645	+	1.18532i	0.0516939	+	0.0409461i
$839$	35.8927	−	0.829267i	1.23915	−	0.0286295i	0.601450	−	0.798911i	$-0.294590\pi$
$839$	35.8927	−	0.829267i	1.23915	−	0.0286295i	0.637704	+	0.770281i	$0.279884\pi$
$840$	−6.62745	+	11.2776i	−0.228669	+	0.389116i
$841$	−6.11692	−	26.0076i	−0.210928	−	0.896813i
$842$	−0.799928	−	17.3022i	−0.0275673	−	0.596273i
$843$	−64.5023	−	4.47717i	−2.22158	−	0.154202i
$844$	−2.17814	−	7.03387i	−0.0749746	−	0.242116i
$845$	0.127333	−	5.51129i	0.00438040	−	0.189594i
$846$	17.1079	−	12.9193i	0.588182	−	0.444174i
$847$	3.75225	−	2.20506i	0.128929	−	0.0757668i
$848$	0.342337	+	2.45414i	0.0117559	+	0.0842754i
$849$	−10.0214	+	6.20499i	−0.343933	+	0.212955i
$850$	12.8707	+	6.45464i	0.441462	+	0.221392i
$851$	48.2643	+	29.8840i	1.65448	+	1.02441i
$852$	8.78539	−	19.8970i	0.300983	−	0.681661i
$853$	50.6070	−	8.25521i	1.73275	−	0.282653i	0.789261	−	0.614057i	$-0.210464\pi$
$853$	50.6070	−	8.25521i	1.73275	−	0.282653i	0.943489	+	0.331404i	$0.107522\pi$
$854$	−9.65839	−	24.9312i	−0.330503	−	0.853128i
$855$	−1.48262	+	0.102910i	−0.0507045	+	0.00351945i
$856$	−2.39996	−	20.6864i	−0.0820288	−	0.707047i
$857$	−26.2621	+	20.8019i	−0.897096	+	0.710580i	−0.957757	−	0.287579i	$-0.907150\pi$
$857$	−26.2621	+	20.8019i	−0.897096	+	0.710580i	0.0606609	+	0.998158i	$0.480679\pi$
$858$	21.1817	−	17.5891i	0.723132	−	0.600481i
$859$	0.361031	+	0.159411i	0.0123182	+	0.00543902i	0.410071	−	0.912054i	$-0.365504\pi$
$859$	0.361031	+	0.159411i	0.0123182	+	0.00543902i	−0.397753	+	0.917493i	$0.630210\pi$
$860$	−1.48160	+	0.458798i	−0.0505221	+	0.0156449i
$861$	81.3650	−	17.1637i	2.77291	−	0.584939i
$862$	−6.06753	+	6.35453i	−0.206661	+	0.216436i
$863$	20.1360	+	5.72919i	0.685438	+	0.195024i	0.598420	−	0.801183i	$-0.295796\pi$
$863$	20.1360	+	5.72919i	0.685438	+	0.195024i	0.0870183	+	0.996207i	$0.472266\pi$
$864$	−2.46587	+	0.890342i	−0.0838906	+	0.0302900i
$865$	6.61313	+	0.922492i	0.224853	+	0.0313657i
$866$	7.14350			0.242746
$867$	38.9513	+	16.3946i	1.32286	+	0.556789i
$868$	−5.25005			−0.178198
$869$	−36.7320	−	5.12389i	−1.24605	−	0.173816i
$870$	−1.56435	+	0.564834i	−0.0530364	+	0.0191497i
$871$	−4.97642	−	1.41591i	−0.168619	−	0.0479764i
$872$	23.4391	−	24.5478i	0.793748	−	0.831293i
$873$	49.6894	−	10.4819i	1.68173	−	0.354757i
$874$	3.41685	−	1.05808i	0.115577	−	0.0357899i
$875$	−18.0103	−	7.95232i	−0.608859	−	0.268837i
$876$	−19.6064	+	16.2810i	−0.662439	+	0.550082i
$877$	−15.7876	+	12.5051i	−0.533108	+	0.422269i	−0.850461	−	0.526039i	$-0.823677\pi$
$877$	−15.7876	+	12.5051i	−0.533108	+	0.422269i	0.317353	+	0.948308i	$0.397206\pi$
$878$	−2.40526	−	20.7321i	−0.0811735	−	0.699674i
$879$	−31.0704	+	2.15663i	−1.04798	+	0.0727412i
$880$	0.622836	+	1.60772i	0.0209958	+	0.0541964i
$881$	16.9478	−	2.76458i	0.570984	−	0.0931412i	0.131379	−	0.991332i	$-0.458059\pi$
$881$	16.9478	−	2.76458i	0.570984	−	0.0931412i	0.439605	+	0.898191i	$0.355118\pi$
$882$	4.77930	−	10.8241i	0.160927	−	0.364466i
$883$	16.3867	+	10.1462i	0.551456	+	0.341447i	0.773708	−	0.633542i	$-0.218400\pi$
$883$	16.3867	+	10.1462i	0.551456	+	0.341447i	−0.222252	+	0.974989i	$0.571341\pi$
$884$	26.9069	+	7.73852i	0.904976	+	0.260275i
$885$	−5.42565	+	3.35942i	−0.182381	+	0.112926i
$886$	−2.01248	−	14.4270i	−0.0676107	−	0.484685i
$887$	49.3291	−	28.9889i	1.65631	−	0.973351i	0.687282	−	0.726391i	$-0.258804\pi$
$887$	49.3291	−	28.9889i	1.65631	−	0.973351i	0.969026	−	0.246960i	$-0.0794316\pi$
$888$	−48.3056	+	36.4787i	−1.62103	+	1.22414i
$889$	−1.43712	+	62.2023i	−0.0481996	+	2.08620i
$890$	1.77811	+	5.74206i	0.0596024	+	0.192474i
$891$	26.2415	+	1.82145i	0.879123	+	0.0610208i
$892$	−0.157141	−	3.39891i	−0.00526147	−	0.113804i
$893$	1.62911	+	6.92656i	0.0545162	+	0.231789i
$894$	21.3238	−	36.2858i	0.713176	−	1.21358i
$895$	2.73448	−	0.0631775i	0.0914035	−	0.00211179i
$896$	−26.6372	−	21.0990i	−0.889887	−	0.704869i
$897$	37.2045	−	60.0873i	1.24222	−	2.00626i
$898$	−19.8939	−	0.459629i	−0.663866	−	0.0153380i
$899$	−1.22857	−	1.02019i	−0.0409751	−	0.0340253i
$900$	−9.47190	−	19.0221i	−0.315730	−	0.634071i
$901$	10.3540	−	3.43755i	0.344941	−	0.114521i
$902$	−10.1026	+	20.2888i	−0.336381	+	0.675544i
$903$	14.3934	−	6.35531i	0.478982	−	0.211491i
$904$	15.2766	−	13.2935i	0.508092	−	0.442135i
$905$		−	2.26383i		−	0.0752523i
$906$	−26.1165	−	30.0125i	−0.867663	−	0.997098i
$907$	−45.2423	+	18.7400i	−1.50225	+	0.622250i	−0.973940	−	0.226805i	$-0.927172\pi$
$907$	−45.2423	+	18.7400i	−1.50225	+	0.622250i	−0.528305	+	0.849055i	$0.677172\pi$
$908$	−10.9463	−	5.13860i	−0.363267	−	0.170531i
$909$	3.68309	−	2.05147i	0.122161	−	0.0680430i
$910$	7.04584	+	1.65717i	0.233567	+	0.0549345i
$911$	7.64083	−	46.8407i	0.253152	−	1.55190i	−0.483327	−	0.875440i	$-0.660572\pi$
$911$	7.64083	−	46.8407i	0.253152	−	1.55190i	0.736479	−	0.676461i	$-0.236487\pi$
$912$	0.127720	−	1.84006i	0.00422924	−	0.0609304i
$913$	−5.11791	−	31.3744i	−0.169378	−	1.03834i
$914$	−7.71278	+	0.714695i	−0.255116	+	0.0236400i
$915$	−14.7793	−	3.11766i	−0.488589	−	0.103067i
$916$	9.66795	−	6.62270i	0.319438	−	0.218820i
$917$	0.106492	−	1.14923i	0.00351668	−	0.0379510i
$918$	0.697887	+	1.19534i	0.0230337	+	0.0394520i
$919$	−2.31111	−	24.9409i	−0.0762366	−	0.822724i	−0.944908	−	0.327335i	$-0.893849\pi$
$919$	−2.31111	−	24.9409i	−0.0762366	−	0.822724i	0.868672	−	0.495388i	$-0.164974\pi$
$920$	−5.84658	−	7.04077i	−0.192756	−	0.232127i
$921$	−17.5177	+	22.1158i	−0.577228	+	0.728742i
$922$	−8.16228	−	6.16387i	−0.268810	−	0.202996i
$923$	−28.5998	−	3.31804i	−0.941375	−	0.109215i
$924$	−17.9710	−	34.0935i	−0.591202	−	1.12159i
$925$	−30.3241	−	31.7585i	−0.997050	−	1.04421i
$926$	7.70279	+	5.27653i	0.253129	+	0.173398i
$927$	2.89846	−	3.49048i	0.0951979	−	0.114642i
$928$	−1.82820	−	8.66661i	−0.0600136	−	0.284495i
$929$	6.91672	+	1.12828i	0.226930	+	0.0370177i	0.273394	−	0.961902i	$-0.411854\pi$
$929$	6.91672	+	1.12828i	0.226930	+	0.0370177i	−0.0464632	+	0.998920i	$0.514795\pi$
$930$	0.635190	−	0.974817i	0.0208287	−	0.0319655i
$931$	2.64580	+	2.90230i	0.0867126	+	0.0951191i
$932$	1.91095	+	0.791542i	0.0625953	+	0.0259278i
$933$	−6.23007	−	18.5880i	−0.203963	−	0.608544i
$934$	−9.58805	+	12.6966i	−0.313730	+	0.415446i
$935$	6.46543	−	3.97781i	0.211442	−	0.130088i
$936$	23.3683	+	30.9447i	0.763817	+	1.01146i
$937$	−4.23344	+	6.18006i	−0.138300	+	0.201894i	−0.887948	−	0.459943i	$-0.847870\pi$
$937$	−4.23344	+	6.18006i	−0.138300	+	0.201894i	0.749648	+	0.661837i	$0.230223\pi$
$938$	1.32479	−	2.51331i	0.0432559	−	0.0820626i
$939$	−64.7976	+	18.4365i	−2.11459	+	0.601652i
$940$	6.17733	−	4.44463i	0.201482	−	0.144968i
$941$	13.2687	−	8.64586i	0.432546	−	0.281847i	−0.311155	−	0.950359i	$-0.600716\pi$
$941$	13.2687	−	8.64586i	0.432546	−	0.281847i	0.743701	+	0.668512i	$0.233069\pi$
$942$	−8.43537	−	20.3648i	−0.274839	−	0.663521i
$943$	−8.03771	+	57.6204i	−0.261744	+	1.87638i
$944$	−1.64609	−	3.72803i	−0.0535756	−	0.121337i
$945$	−0.497993	−	0.764263i	−0.0161997	−	0.0248615i
$946$	−1.07801	+	4.15077i	−0.0350492	+	0.134953i
$947$	28.9444	−	7.51724i	0.940566	−	0.244278i	0.250577	−	0.968097i	$-0.419380\pi$
$947$	28.9444	−	7.51724i	0.940566	−	0.244278i	0.689990	+	0.723819i	$0.257615\pi$
$948$	7.79719	−	41.7113i	0.253241	−	1.35472i
$949$	28.2645	+	18.4171i	0.917504	+	0.597845i
$950$	−2.76389	+	0.127782i	−0.0896723	+	0.00414580i
$951$	3.94019	−	1.52644i	0.127769	−	0.0494981i
$952$	−17.2424	+	32.4867i	−0.558829	+	1.05290i
$953$	29.6823	+	11.4990i	0.961503	+	0.372488i	0.790281	−	0.612744i	$-0.209934\pi$
$953$	29.6823	+	11.4990i	0.961503	+	0.372488i	0.171222	+	0.985233i	$0.445229\pi$
$954$	5.98873	+	2.00722i	0.193892	+	0.0649861i
$955$	−0.446645	+	1.44235i	−0.0144531	+	0.0466734i
$956$	−11.4161	+	29.4684i	−0.369223	+	0.953075i
$957$	2.41965	−	11.4704i	0.0782161	−	0.370785i
$958$	−16.0020	−	20.2023i	−0.517002	−	0.652707i
$959$	−0.115746	−	5.00978i	−0.00373764	−	0.161774i
$960$	3.51464	−	1.17799i	0.113435	−	0.0380195i
$961$	−29.8510	−	1.38009i	−0.962935	−	0.0445192i
$962$	27.1883	+	19.5622i	0.876586	+	0.630710i
$963$	24.1449	+	8.71789i	0.778057	+	0.280930i
$964$	25.6404	+	13.5153i	0.825820	+	0.435297i
$965$	−12.4783	+	6.21347i	−0.401692	+	0.200019i
$966$	28.0677	+	26.8001i	0.903064	+	0.862278i
$967$	8.86158	−	37.6771i	0.284969	−	1.21162i	−0.619473	−	0.785018i	$-0.712653\pi$
$967$	8.86158	−	37.6771i	0.284969	−	1.21162i	0.904442	−	0.426597i	$-0.140288\pi$
$968$	−3.19161	−	0.596615i	−0.102582	−	0.0191759i
$969$	−8.06943	+	0.912915i	−0.259227	+	0.0293270i
$970$	−6.95134	+	1.29943i	−0.223194	+	0.0417222i
$971$	−1.31625	+	28.4701i	−0.0422405	+	0.913649i	0.867237	+	0.497896i	$0.165894\pi$
$971$	−1.31625	+	28.4701i	−0.0422405	+	0.913649i	−0.909477	+	0.415753i	$0.863518\pi$
$972$	−3.69050	+	31.8103i	−0.118373	+	1.02031i
$973$	3.36095	+	5.42812i	0.107747	+	0.174017i
$974$	15.6440	+	26.6207i	0.501267	+	0.852984i
$975$	−39.5381	+	37.7524i	−1.26623	+	1.20904i
$976$	3.27582	−	9.07262i	0.104856	−	0.290407i
$977$	−6.46125	−	6.46125i	−0.206714	−	0.206714i	0.596155	−	0.802869i	$-0.296694\pi$
$977$	−6.46125	−	6.46125i	−0.206714	−	0.206714i	−0.802869	+	0.596155i	$0.796694\pi$
$978$	−20.3515	+	36.5379i	−0.650768	+	1.16835i
$979$	−41.0077	−	10.6502i	−1.31061	−	0.340383i
$980$	1.78487	−	3.80216i	0.0570156	−	0.121456i
$981$	14.2084	+	39.3514i	0.453641	+	1.25639i
$982$	5.41118	+	2.69445i	0.172678	+	0.0859833i
$983$	3.29844	+	4.58430i	0.105204	+	0.146217i	0.861027	−	0.508559i	$-0.169822\pi$
$983$	3.29844	+	4.58430i	0.105204	+	0.146217i	−0.755823	+	0.654776i	$0.772763\pi$
$984$	−54.1968	−	30.1874i	−1.72773	−	0.962340i
$985$	10.3418	+	9.42780i	0.329517	+	0.300395i
$986$	−4.32546	+	1.77726i	−0.137751	+	0.0565995i
$987$	−57.0516	+	52.0094i	−1.81597	+	1.65548i
$988$	−5.23714	+	1.23176i	−0.166616	+	0.0391876i
$989$	0.762245	+	10.9816i	0.0242380	+	0.349195i
$990$	4.37611	+	0.405506i	0.139082	+	0.0128878i
$991$	−6.53796	−	2.02457i	−0.207685	−	0.0643127i	0.190211	−	0.981743i	$-0.439083\pi$
$991$	−6.53796	−	2.02457i	−0.207685	−	0.0643127i	−0.397896	+	0.917431i	$0.630259\pi$
$992$	4.67425	+	4.06748i	0.148408	+	0.129143i
$993$	36.0655	−	41.4457i	1.14451	−	1.31524i
$994$	5.02428	−	14.9904i	0.159361	−	0.475467i
$995$	7.39707	+	10.7984i	0.234503	+	0.342332i
$996$	36.1291	−	4.19155i	1.14479	−	0.132814i
$997$	29.5459	+	17.3630i	0.935728	+	0.549893i	0.893425	−	0.449212i	$-0.148295\pi$
$997$	29.5459	+	17.3630i	0.935728	+	0.549893i	0.0423028	+	0.999105i	$0.486531\pi$
$998$	−6.73262	+	16.2540i	−0.213117	+	0.514511i
$999$	−0.775643	−	4.14933i	−0.0245403	−	0.131279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.i.a.128.16	yes	1600
289.70	even	136	inner	289.2.i.a.70.16	✓	1600

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.i.a.70.16	✓	1600	289.70	even	136	inner
289.2.i.a.128.16	yes	1600	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.i (of order \(136\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(0.743476 + 0.103710i) q^{2} +(-2.33819 + 0.844243i) q^{3} +(-1.38165 - 0.393114i) q^{4} +(-0.407369 + 0.426638i) q^{5} +(-1.82595 + 0.385179i) q^{6} +(3.30312 - 1.02286i) q^{7} +(-2.35988 - 1.04199i) q^{8} +(2.44640 - 2.03147i) q^{9} +O(q^{10})\)	\(q+(0.743476 + 0.103710i) q^{2} +(-2.33819 + 0.844243i) q^{3} +(-1.38165 - 0.393114i) q^{4} +(-0.407369 + 0.426638i) q^{5} +(-1.82595 + 0.385179i) q^{6} +(3.30312 - 1.02286i) q^{7} +(-2.35988 - 1.04199i) q^{8} +(2.44640 - 2.03147i) q^{9} +(-0.347116 + 0.274947i) q^{10} +(-0.359687 - 3.10032i) q^{11} +(3.56245 - 0.247273i) q^{12} +(-1.70762 - 4.40788i) q^{13} +(2.56187 - 0.417902i) q^{14} +(0.592322 - 1.34148i) q^{15} +(0.796205 + 0.492989i) q^{16} +(1.50037 - 3.84043i) q^{17} +(2.02952 - 1.25663i) q^{18} +(0.109461 + 0.784702i) q^{19} +(0.730559 - 0.429322i) q^{20} +(-6.85979 + 5.18027i) q^{21} +(0.0541170 - 2.34232i) q^{22} +(-1.77900 - 5.74492i) q^{23} +(6.39754 + 0.444060i) q^{24} +(0.214847 + 4.64707i) q^{25} +(-0.812433 - 3.45425i) q^{26} +(-0.226579 + 0.385559i) q^{27} +(-4.96585 + 0.114731i) q^{28} +(-1.18436 - 0.938118i) q^{29} +(0.579502 - 0.935928i) q^{30} +(1.05667 + 0.0244133i) q^{31} +(4.51011 + 3.74515i) q^{32} +(3.45844 + 6.94549i) q^{33} +(1.51378 - 2.69966i) q^{34} +(-0.909198 + 1.82592i) q^{35} +(-4.17867 + 1.84506i) q^{36} +(-7.12056 + 6.19622i) q^{37} +0.594759i q^{38} +(7.71408 + 8.86484i) q^{39} +(1.40589 - 0.582340i) q^{40} +(-8.75684 - 4.11078i) q^{41} +(-5.63734 + 3.13998i) q^{42} +(-1.78176 - 0.419067i) q^{43} +(-0.721816 + 4.42496i) q^{44} +(-0.129888 + 1.87128i) q^{45} +(-0.726833 - 4.45571i) q^{46} +(8.94259 - 0.828653i) q^{47} +(-2.27788 - 0.480514i) q^{48} +(4.08937 - 2.80128i) q^{49} +(-0.322216 + 3.47726i) q^{50} +(-0.265913 + 10.2463i) q^{51} +(0.626540 + 6.76145i) q^{52} +(1.69038 + 2.03565i) q^{53} +(-0.208442 + 0.263155i) q^{54} +(1.46924 + 1.10952i) q^{55} +(-8.86076 - 1.02799i) q^{56} +(-0.918421 - 1.74237i) q^{57} +(-0.783250 - 0.820299i) q^{58} +(-3.59016 - 2.45932i) q^{59} +(-1.34574 + 1.62061i) q^{60} +(-2.12602 - 10.0784i) q^{61} +(0.783074 + 0.127738i) q^{62} +(6.00285 - 9.21249i) q^{63} +(1.70295 + 1.86805i) q^{64} +(2.57620 + 1.06710i) q^{65} +(1.85095 + 5.52248i) q^{66} +(0.659599 - 0.873450i) q^{67} +(-3.58272 + 4.71631i) q^{68} +(9.00975 + 11.9308i) q^{69} +(-0.865333 + 1.26323i) q^{70} +(2.84010 - 5.38807i) q^{71} +(-7.88997 + 2.24489i) q^{72} +(-5.79294 + 4.16806i) q^{73} +(-5.93657 + 3.86827i) q^{74} +(-4.42561 - 10.6844i) q^{75} +(0.157240 - 1.12721i) q^{76} +(-4.35927 - 9.87281i) q^{77} +(4.81585 + 7.39082i) q^{78} +(2.98703 - 11.5013i) q^{79} +(-0.534677 + 0.138863i) q^{80} +(-1.54863 + 8.28445i) q^{81} +(-6.08417 - 3.96444i) q^{82} +(10.1743 - 0.470386i) q^{83} +(11.5143 - 4.46065i) q^{84} +(1.02727 + 2.20459i) q^{85} +(-1.28124 - 0.496354i) q^{86} +(3.56126 + 1.19361i) q^{87} +(-2.38168 + 7.69117i) q^{88} +(4.90374 - 12.6580i) q^{89} +(-0.290640 + 1.37778i) q^{90} +(-10.1491 - 12.8131i) q^{91} +(0.199546 + 8.63683i) q^{92} +(-2.49130 + 0.835000i) q^{93} +(6.73454 + 0.311357i) q^{94} +(-0.379375 - 0.272963i) q^{95} +(-13.7073 - 4.94925i) q^{96} +(14.1275 + 7.44674i) q^{97} +(3.33087 - 1.65858i) q^{98} +(-7.17813 - 6.85393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1600 q - 64 q^{2} - 64 q^{3} - 68 q^{4} - 68 q^{5} - 72 q^{6} - 64 q^{7} - 72 q^{8} - 76 q^{9}+O(q^{10}) \) 1600 * q - 64 * q^2 - 64 * q^3 - 68 * q^4 - 68 * q^5 - 72 * q^6 - 64 * q^7 - 72 * q^8 - 76 * q^9	\( 1600 q - 64 q^{2} - 64 q^{3} - 68 q^{4} - 68 q^{5} - 72 q^{6} - 64 q^{7} - 72 q^{8} - 76 q^{9} - 72 q^{10} - 64 q^{11} - 64 q^{12} - 68 q^{13} - 72 q^{14} - 60 q^{15} + 40 q^{16} - 68 q^{17} - 72 q^{18} - 76 q^{19} - 72 q^{20} - 68 q^{21} - 80 q^{22} - 72 q^{23} + 260 q^{24} - 64 q^{25} - 64 q^{26} - 76 q^{27} - 72 q^{28} - 64 q^{29} - 68 q^{30} - 56 q^{31} - 72 q^{32} - 44 q^{33} - 48 q^{34} - 92 q^{35} - 68 q^{36} - 68 q^{37} + 204 q^{39} - 60 q^{40} - 64 q^{41} - 60 q^{42} - 60 q^{43} - 48 q^{44} - 80 q^{45} - 88 q^{46} - 68 q^{47} - 80 q^{48} - 76 q^{49} - 32 q^{50} - 96 q^{51} - 116 q^{52} - 64 q^{53} + 484 q^{54} - 68 q^{55} - 48 q^{56} - 44 q^{57} - 68 q^{58} - 68 q^{59} - 60 q^{60} - 68 q^{61} + 352 q^{62} - 56 q^{63} - 68 q^{64} - 64 q^{65} - 76 q^{66} - 44 q^{67} - 80 q^{68} - 92 q^{69} - 60 q^{70} - 88 q^{71} - 68 q^{72} - 40 q^{73} - 88 q^{74} - 56 q^{75} + 60 q^{76} + 604 q^{77} - 60 q^{78} - 64 q^{79} - 68 q^{80} - 68 q^{81} - 72 q^{82} - 84 q^{83} - 4 q^{84} + 268 q^{85} - 132 q^{86} - 84 q^{87} - 80 q^{88} - 68 q^{89} - 72 q^{90} - 68 q^{91} + 232 q^{92} - 92 q^{93} - 44 q^{94} - 60 q^{95} - 48 q^{96} - 92 q^{97} - 68 q^{98} - 64 q^{99}+O(q^{100}) \) 1600 * q - 64 * q^2 - 64 * q^3 - 68 * q^4 - 68 * q^5 - 72 * q^6 - 64 * q^7 - 72 * q^8 - 76 * q^9 - 72 * q^10 - 64 * q^11 - 64 * q^12 - 68 * q^13 - 72 * q^14 - 60 * q^15 + 40 * q^16 - 68 * q^17 - 72 * q^18 - 76 * q^19 - 72 * q^20 - 68 * q^21 - 80 * q^22 - 72 * q^23 + 260 * q^24 - 64 * q^25 - 64 * q^26 - 76 * q^27 - 72 * q^28 - 64 * q^29 - 68 * q^30 - 56 * q^31 - 72 * q^32 - 44 * q^33 - 48 * q^34 - 92 * q^35 - 68 * q^36 - 68 * q^37 + 204 * q^39 - 60 * q^40 - 64 * q^41 - 60 * q^42 - 60 * q^43 - 48 * q^44 - 80 * q^45 - 88 * q^46 - 68 * q^47 - 80 * q^48 - 76 * q^49 - 32 * q^50 - 96 * q^51 - 116 * q^52 - 64 * q^53 + 484 * q^54 - 68 * q^55 - 48 * q^56 - 44 * q^57 - 68 * q^58 - 68 * q^59 - 60 * q^60 - 68 * q^61 + 352 * q^62 - 56 * q^63 - 68 * q^64 - 64 * q^65 - 76 * q^66 - 44 * q^67 - 80 * q^68 - 92 * q^69 - 60 * q^70 - 88 * q^71 - 68 * q^72 - 40 * q^73 - 88 * q^74 - 56 * q^75 + 60 * q^76 + 604 * q^77 - 60 * q^78 - 64 * q^79 - 68 * q^80 - 68 * q^81 - 72 * q^82 - 84 * q^83 - 4 * q^84 + 268 * q^85 - 132 * q^86 - 84 * q^87 - 80 * q^88 - 68 * q^89 - 72 * q^90 - 68 * q^91 + 232 * q^92 - 92 * q^93 - 44 * q^94 - 60 * q^95 - 48 * q^96 - 92 * q^97 - 68 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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