LMFDB - Embedded newform 690.2.w.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	690.37
Dual form			690.2.w.b.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(0.217321 - 2.22548i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.154967 + 0.415484i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(0.217321 - 2.22548i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.154967 + 0.415484i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-1.25730 + 1.84911i) q^{10} +(0.217319 - 0.740121i) q^{11} +(0.479249 + 0.877679i) q^{12} +(4.23690 + 1.58028i) q^{13} +(0.0631085 - 0.438929i) q^{14} +(0.375531 - 2.20431i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-1.50898 + 0.328258i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(3.34480 - 2.14957i) q^{19} +(1.98969 - 1.02036i) q^{20} +(0.124932 + 0.425480i) q^{21} +(-0.545439 + 0.545439i) q^{22} +(0.698428 - 4.74470i) q^{23} -1.00000i q^{24} +(-4.90554 - 0.967288i) q^{25} +(-2.96129 - 3.41751i) q^{26} +(0.977147 + 0.212565i) q^{27} +(-0.265746 + 0.354994i) q^{28} +(1.04783 - 1.63045i) q^{29} +(-1.38601 + 1.75470i) q^{30} +(0.0423632 - 0.0488897i) q^{31} +(0.800541 - 0.599278i) q^{32} +(0.269565 - 0.722732i) q^{33} +(1.48171 + 0.435070i) q^{34} +(0.958330 - 0.254584i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-1.25044 - 1.67039i) q^{37} +(-3.96584 + 0.283642i) q^{38} +(4.11337 + 1.87851i) q^{39} +(-2.23532 - 0.0580032i) q^{40} +(-0.905161 - 6.29553i) q^{41} +(0.0942606 - 0.433309i) q^{42} +(-0.391721 + 5.47698i) q^{43} +(0.740121 - 0.217319i) q^{44} +(0.531828 - 2.17190i) q^{45} +(-2.88689 + 3.82960i) q^{46} +(2.50355 + 2.50355i) q^{47} +(-0.479249 + 0.877679i) q^{48} +(5.14164 - 4.45525i) q^{49} +(3.84192 + 3.19995i) q^{50} +(-1.52855 + 0.219772i) q^{51} +(0.961223 + 4.41867i) q^{52} +(0.514249 - 0.191805i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-1.59990 - 0.644484i) q^{55} +(0.403370 - 0.184213i) q^{56} +(3.48963 - 1.90548i) q^{57} +(-1.70105 + 0.928842i) q^{58} +(6.40903 - 2.92691i) q^{59} +(2.05741 - 0.875822i) q^{60} +(-4.00167 - 3.46746i) q^{61} +(-0.0606116 + 0.0226070i) q^{62} +(0.0942606 + 0.433309i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(4.43766 - 9.08572i) q^{65} +(-0.582960 + 0.505138i) q^{66} +(-6.22762 + 11.4050i) q^{67} +(-1.09196 - 1.09196i) q^{68} +(1.03513 - 4.68279i) q^{69} +(-0.963115 - 0.235836i) q^{70} +(4.42946 - 1.30061i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(0.0554481 - 0.254891i) q^{73} +(0.296950 + 2.06534i) q^{74} +(-4.82404 - 1.31478i) q^{75} +(3.61667 + 1.65168i) q^{76} +(0.341186 - 0.0244021i) q^{77} +(-2.70994 - 3.62006i) q^{78} +(-0.951318 - 2.08310i) q^{79} +(1.93409 + 1.12218i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-2.22269 + 5.95926i) q^{82} +(1.14584 - 0.857764i) q^{83} +(-0.290393 + 0.335132i) q^{84} +(0.402599 + 3.42954i) q^{85} +(2.96864 - 4.61930i) q^{86} +(1.16147 - 1.55155i) q^{87} +(-0.753738 - 0.163966i) q^{88} +(0.0940165 + 0.108501i) q^{89} +(-1.50766 + 1.65135i) q^{90} +2.00526i q^{91} +(4.36910 - 1.97762i) q^{92} +(0.0457430 - 0.0457430i) q^{93} +(-0.997489 - 3.39714i) q^{94} +(-4.05694 - 7.91094i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-3.98889 - 2.98604i) q^{97} +(-6.64788 + 1.44616i) q^{98} +(0.320437 - 0.701660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$3$	0.997452	+	0.0713392i	0.575879	+	0.0411877i
$3$	0.997452	+	0.0713392i	0.575879	+	0.0411877i
$4$	0.540641	+	0.841254i	0.270320	+	0.420627i
$5$	0.217321	−	2.22548i	0.0971889	−	0.995266i
$5$	0.217321	−	2.22548i	0.0971889	−	0.995266i
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	0.154967	+	0.415484i	0.0585722	+	0.157038i	0.962940	−	0.269716i	$-0.0869298\pi$
$7$	0.154967	+	0.415484i	0.0585722	+	0.157038i	−0.904368	+	0.426754i	$0.859657\pi$
$8$	−0.0713392	−	0.997452i	−0.0252222	−	0.352653i
$9$	0.989821	+	0.142315i	0.329940	+	0.0474383i
$10$	−1.25730	+	1.84911i	−0.397593	+	0.584739i
$11$	0.217319	−	0.740121i	0.0655242	−	0.223155i	−0.920221	−	0.391399i	$-0.871991\pi$
$11$	0.217319	−	0.740121i	0.0655242	−	0.223155i	0.985745	+	0.168244i	$0.0538096\pi$
$12$	0.479249	+	0.877679i	0.138347	+	0.253364i
$13$	4.23690	+	1.58028i	1.17510	+	0.438291i	0.859766	−	0.510688i	$-0.170609\pi$
$13$	4.23690	+	1.58028i	1.17510	+	0.438291i	0.315338	+	0.948979i	$0.397882\pi$
$14$	0.0631085	−	0.438929i	0.0168665	−	0.117309i
$15$	0.375531	−	2.20431i	0.0969618	−	0.569150i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	−1.50898	+	0.328258i	−0.365981	+	0.0796142i	−0.391795	−	0.920053i	$-0.628146\pi$
$17$	−1.50898	+	0.328258i	−0.365981	+	0.0796142i	0.0258144	+	0.999667i	$0.491782\pi$
$18$	−0.800541	−	0.599278i	−0.188689	−	0.141251i
$19$	3.34480	−	2.14957i	0.767349	−	0.493146i	−0.0974639	−	0.995239i	$-0.531073\pi$
$19$	3.34480	−	2.14957i	0.767349	−	0.493146i	0.864813	+	0.502093i	$0.167437\pi$
$20$	1.98969	−	1.02036i	0.444908	−	0.228160i
$21$	0.124932	+	0.425480i	0.0272625	+	0.0928475i
$22$	−0.545439	+	0.545439i	−0.116288	+	0.116288i
$23$	0.698428	−	4.74470i	0.145632	−	0.989339i
$23$	0.698428	−	4.74470i	0.145632	−	0.989339i
$24$		−	1.00000i		−	0.204124i
$25$	−4.90554	−	0.967288i	−0.981109	−	0.193458i
$26$	−2.96129	−	3.41751i	−0.580757	−	0.670229i
$27$	0.977147	+	0.212565i	0.188052	+	0.0409082i
$28$	−0.265746	+	0.354994i	−0.0502212	+	0.0670876i
$29$	1.04783	−	1.63045i	0.194577	−	0.302767i	−0.730232	−	0.683199i	$-0.760588\pi$
$29$	1.04783	−	1.63045i	0.194577	−	0.302767i	0.924809	+	0.380432i	$0.124225\pi$
$30$	−1.38601	+	1.75470i	−0.253049	+	0.320363i
$31$	0.0423632	−	0.0488897i	0.00760865	−	0.00878085i	−0.751932	−	0.659240i	$-0.770878\pi$
$31$	0.0423632	−	0.0488897i	0.00760865	−	0.00878085i	0.759541	+	0.650459i	$0.225424\pi$
$32$	0.800541	−	0.599278i	0.141517	−	0.105938i
$33$	0.269565	−	0.722732i	0.0469252	−	0.125811i
$34$	1.48171	+	0.435070i	0.254112	+	0.0746140i
$35$	0.958330	−	0.254584i	0.161987	−	0.0430325i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−1.25044	−	1.67039i	−0.205571	−	0.274610i	0.685893	−	0.727702i	$-0.259412\pi$
$37$	−1.25044	−	1.67039i	−0.205571	−	0.274610i	−0.891464	+	0.453092i	$0.850321\pi$
$38$	−3.96584	+	0.283642i	−0.643344	+	0.0460129i
$39$	4.11337	+	1.87851i	0.658666	+	0.300803i
$40$	−2.23532	−	0.0580032i	−0.353434	−	0.00917112i
$41$	−0.905161	−	6.29553i	−0.141362	−	0.983197i	−0.929795	−	0.368077i	$-0.880016\pi$
$41$	−0.905161	−	6.29553i	−0.141362	−	0.983197i	0.788433	−	0.615121i	$-0.210893\pi$
$42$	0.0942606	−	0.433309i	0.0145447	−	0.0668610i
$43$	−0.391721	+	5.47698i	−0.0597369	+	0.835231i	0.875951	+	0.482401i	$0.160235\pi$
$43$	−0.391721	+	5.47698i	−0.0597369	+	0.835231i	−0.935687	+	0.352830i	$0.885219\pi$
$44$	0.740121	−	0.217319i	0.111577	−	0.0327621i
$45$	0.531828	−	2.17190i	0.0792803	−	0.323768i
$46$	−2.88689	+	3.82960i	−0.425649	+	0.564644i
$47$	2.50355	+	2.50355i	0.365180	+	0.365180i	0.865716	−	0.500536i	$-0.166864\pi$
$47$	2.50355	+	2.50355i	0.365180	+	0.365180i	−0.500536	+	0.865716i	$0.666864\pi$
$48$	−0.479249	+	0.877679i	−0.0691736	+	0.126682i
$49$	5.14164	−	4.45525i	0.734519	−	0.636465i
$50$	3.84192	+	3.19995i	0.543330	+	0.452541i
$51$	−1.52855	+	0.219772i	−0.214040	+	0.0307743i
$52$	0.961223	+	4.41867i	0.133298	+	0.612759i
$53$	0.514249	−	0.191805i	0.0706375	−	0.0263464i	−0.313897	−	0.949457i	$-0.601635\pi$
$53$	0.514249	−	0.191805i	0.0706375	−	0.0263464i	0.384535	+	0.923111i	$0.374362\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	−1.59990	−	0.644484i	−0.215730	−	0.0869022i
$56$	0.403370	−	0.184213i	0.0539026	−	0.0246165i
$57$	3.48963	−	1.90548i	0.462212	−	0.252387i
$58$	−1.70105	+	0.928842i	−0.223359	+	0.121963i
$59$	6.40903	−	2.92691i	0.834385	−	0.381051i	0.0480454	−	0.998845i	$-0.484701\pi$
$59$	6.40903	−	2.92691i	0.834385	−	0.381051i	0.786340	+	0.617794i	$0.211974\pi$
$60$	2.05741	−	0.875822i	0.265610	−	0.113068i
$61$	−4.00167	−	3.46746i	−0.512361	−	0.443963i	0.359910	−	0.932987i	$-0.382808\pi$
$61$	−4.00167	−	3.46746i	−0.512361	−	0.443963i	−0.872270	+	0.489024i	$0.837353\pi$
$62$	−0.0606116	+	0.0226070i	−0.00769768	+	0.00287109i
$63$	0.0942606	+	0.433309i	0.0118757	+	0.0545918i
$64$	−0.989821	+	0.142315i	−0.123728	+	0.0177894i
$65$	4.43766	−	9.08572i	0.550424	−	1.12694i
$66$	−0.582960	+	0.505138i	−0.0717574	+	0.0621782i
$67$	−6.22762	+	11.4050i	−0.760825	+	1.39335i	0.153409	+	0.988163i	$0.450975\pi$
$67$	−6.22762	+	11.4050i	−0.760825	+	1.39335i	−0.914235	+	0.405185i	$0.867207\pi$
$68$	−1.09196	−	1.09196i	−0.132420	−	0.132420i
$69$	1.03513	−	4.68279i	0.124615	−	0.563741i
$70$	−0.963115	−	0.235836i	−0.115114	−	0.0281877i
$71$	4.42946	−	1.30061i	0.525681	−	0.154354i	−0.00811539	−	0.999967i	$-0.502583\pi$
$71$	4.42946	−	1.30061i	0.525681	−	0.154354i	0.533796	+	0.845613i	$0.320765\pi$
$72$	0.0713392	−	0.997452i	0.00840740	−	0.117551i
$73$	0.0554481	−	0.254891i	0.00648971	−	0.0298327i	−0.973788	−	0.227457i	$-0.926959\pi$
$73$	0.0554481	−	0.254891i	0.00648971	−	0.0298327i	0.980278	+	0.197624i	$0.0633226\pi$
$74$	0.296950	+	2.06534i	0.0345198	+	0.240090i
$75$	−4.82404	−	1.31478i	−0.557032	−	0.151818i
$76$	3.61667	+	1.65168i	0.414860	+	0.189460i
$77$	0.341186	−	0.0244021i	0.0388817	−	0.00278087i
$78$	−2.70994	−	3.62006i	−0.306840	−	0.409891i
$79$	−0.951318	−	2.08310i	−0.107032	−	0.234367i	0.848537	−	0.529137i	$-0.177484\pi$
$79$	−0.951318	−	2.08310i	−0.107032	−	0.234367i	−0.955568	+	0.294770i	$0.904757\pi$
$80$	1.93409	+	1.12218i	0.216238	+	0.125464i
$81$	0.959493	+	0.281733i	0.106610	+	0.0313036i
$82$	−2.22269	+	5.95926i	−0.245455	+	0.658090i
$83$	1.14584	−	0.857764i	0.125772	−	0.0941518i	−0.534540	−	0.845143i	$-0.679515\pi$
$83$	1.14584	−	0.857764i	0.125772	−	0.0941518i	0.660312	+	0.750992i	$0.270424\pi$
$84$	−0.290393	+	0.335132i	−0.0316845	+	0.0365659i
$85$	0.402599	+	3.42954i	0.0436680	+	0.371986i
$86$	2.96864	−	4.61930i	0.320117	−	0.498111i
$87$	1.16147	−	1.55155i	0.124523	−	0.166343i
$88$	−0.753738	−	0.163966i	−0.0803488	−	0.0174788i
$89$	0.0940165	+	0.108501i	0.00996573	+	0.0115011i	0.760711	−	0.649091i	$-0.224851\pi$
$89$	0.0940165	+	0.108501i	0.00996573	+	0.0115011i	−0.750745	+	0.660592i	$0.770305\pi$
$90$	−1.50766	+	1.65135i	−0.158921	+	0.174068i
$91$			2.00526i			0.210208i
$92$	4.36910	−	1.97762i	0.455510	−	0.206182i
$93$	0.0457430	−	0.0457430i	0.00474333	−	0.00474333i
$94$	−0.997489	−	3.39714i	−0.102883	−	0.350388i
$95$	−4.05694	−	7.91094i	−0.416233	−	0.811645i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	−3.98889	−	2.98604i	−0.405010	−	0.303187i	0.377282	−	0.926098i	$-0.376859\pi$
$97$	−3.98889	−	2.98604i	−0.405010	−	0.303187i	−0.782292	+	0.622912i	$0.785950\pi$
$98$	−6.64788	+	1.44616i	−0.671537	+	0.146084i
$99$	0.320437	−	0.701660i	0.0322052	−	0.0705195i
$100$	−1.83840	−	4.64976i	−0.183840	−	0.464976i
$101$	−0.0549269	+	0.382025i	−0.00546543	+	0.0380129i	−0.992372	−	0.123282i	$-0.960658\pi$
$101$	−0.0549269	+	0.382025i	−0.00546543	+	0.0380129i	0.986906	+	0.161295i	$0.0515671\pi$
$102$	1.44690	+	0.539666i	0.143265	+	0.0534349i
$103$	−2.25315	−	4.12633i	−0.222009	−	0.406579i	0.742807	−	0.669506i	$-0.233494\pi$
$103$	−2.25315	−	4.12633i	−0.222009	−	0.406579i	−0.964816	+	0.262927i	$0.915312\pi$
$104$	1.27400	−	4.33884i	0.124926	−	0.425458i
$105$	0.974050	−	0.185569i	0.0950575	−	0.0181097i
$106$	−0.543268	−	0.0781101i	−0.0527668	−	0.00758672i
$107$	0.811651	+	11.3484i	0.0784652	+	1.09709i	0.872306	+	0.488961i	$0.162624\pi$
$107$	0.811651	+	11.3484i	0.0784652	+	1.09709i	−0.793840	+	0.608126i	$0.791921\pi$
$108$	0.349464	+	0.936950i	0.0336272	+	0.0901580i
$109$	3.50030	+	2.24951i	0.335268	+	0.215464i	0.697432	−	0.716651i	$-0.254326\pi$
$109$	3.50030	+	2.24951i	0.335268	+	0.215464i	−0.362164	+	0.932114i	$0.617962\pi$
$110$	1.09533	+	1.33240i	0.104435	+	0.127039i
$111$	−1.12809	−	1.75534i	−0.107073	−	0.166609i
$112$	−0.442313	−	0.0316349i	−0.0417947	−	0.00298921i
$113$	−12.1855	−	6.65376i	−1.14631	−	0.625933i	−0.210207	−	0.977657i	$-0.567414\pi$
$113$	−12.1855	−	6.65376i	−1.14631	−	0.625933i	−0.936104	+	0.351724i	$0.885596\pi$
$114$	−3.97597			−0.372384
$115$	−10.4075	−	2.58546i	−0.970501	−	0.241096i
$116$	1.93812			0.179950
$117$	3.96888	+	2.16717i	0.366923	+	0.200355i
$118$	−7.02779	−	0.502638i	−0.646961	−	0.0462715i
$119$	−0.370228	−	0.576086i	−0.0339387	−	0.0528097i
$120$	−2.22548	−	0.217321i	−0.203158	−	0.0198386i
$121$	8.75324	+	5.62536i	0.795749	+	0.511397i
$122$	1.85040	+	4.96111i	0.167527	+	0.449158i
$123$	−0.453737	−	6.34407i	−0.0409121	−	0.572025i
$124$	0.0640319	+	0.00920639i	0.00575023	+	0.000826759i
$125$	−3.21876	+	10.7070i	−0.287895	+	0.957662i
$126$	0.124932	−	0.425480i	0.0111299	−	0.0379048i
$127$	8.36914	+	15.3269i	0.742641	+	1.36005i	0.926198	+	0.377037i	$0.123057\pi$
$127$	8.36914	+	15.3269i	0.742641	+	1.36005i	−0.183557	+	0.983009i	$0.558761\pi$
$128$	0.936950	+	0.349464i	0.0828154	+	0.0308886i
$129$	−0.781446	+	5.43508i	−0.0688025	+	0.478532i
$130$	−8.24916	+	5.84760i	−0.723499	+	0.512868i
$131$	−3.23360	+	7.08059i	−0.282521	+	0.618634i	−0.996686	−	0.0813431i	$-0.974079\pi$
$131$	−3.23360	+	7.08059i	−0.282521	+	0.618634i	0.714166	+	0.699977i	$0.246806\pi$
$132$	0.753738	−	0.163966i	0.0656045	−	0.0142714i
$133$	1.41145	+	1.05660i	0.122388	+	0.0916185i
$134$	10.9317	−	7.02538i	0.944356	−	0.606901i
$135$	0.685415	−	2.12843i	0.0589911	−	0.183186i
$136$	0.435070	+	1.48171i	0.0373070	+	0.127056i
$137$	−15.7367	+	15.7367i	−1.34448	+	1.34448i	−0.452928	+	0.891547i	$0.649621\pi$
$137$	−15.7367	+	15.7367i	−1.34448	+	1.34448i	−0.891547	+	0.452928i	$0.850379\pi$
$138$	−3.15273	+	3.61390i	−0.268379	+	0.307635i
$139$		−	8.24745i		−	0.699540i	−0.936836	−	0.349770i	$-0.886260\pi$
$139$		−	8.24745i		−	0.699540i	0.936836	−	0.349770i	$-0.113740\pi$
$140$	0.732282	+	0.668560i	0.0618891	+	0.0565036i
$141$	2.31857	+	2.67577i	0.195259	+	0.225341i
$142$	−4.51096	−	0.981300i	−0.378551	−	0.0823488i
$143$	2.09036	−	2.79239i	0.174805	−	0.233512i
$144$	−0.540641	+	0.841254i	−0.0450534	+	0.0701045i
$145$	−3.40082	−	2.68625i	−0.282423	−	0.223081i
$146$	−0.170822	+	0.197139i	−0.0141373	+	0.0163153i
$147$	5.44637	−	4.07710i	0.449209	−	0.336274i
$148$	0.729183	−	1.95501i	0.0599385	−	0.160701i
$149$	−2.80231	−	0.822833i	−0.229574	−	0.0674091i	0.164922	−	0.986307i	$-0.447263\pi$
$149$	−2.80231	−	0.822833i	−0.229574	−	0.0674091i	−0.394496	+	0.918897i	$0.629081\pi$
$150$	3.60385	+	3.46587i	0.294253	+	0.282987i
$151$	5.96976	+	13.0719i	0.485812	+	1.06378i	0.980824	+	0.194894i	$0.0624362\pi$
$151$	5.96976	+	13.0719i	0.485812	+	1.06378i	−0.495012	+	0.868886i	$0.664837\pi$
$152$	−2.38271	−	3.18293i	−0.193263	−	0.258170i
$153$	−1.54033	+	0.110167i	−0.124529	+	0.00890646i
$154$	−0.311146	−	0.142096i	−0.0250729	−	0.0114504i
$155$	−0.0995967	−	0.104903i	−0.00799980	−	0.00842603i
$156$	0.643550	+	4.47599i	0.0515252	+	0.358366i
$157$	−0.257391	+	1.18321i	−0.0205421	+	0.0944303i	−0.986277	−	0.165102i	$-0.947205\pi$
$157$	−0.257391	+	1.18321i	−0.0205421	+	0.0944303i	0.965734	+	0.259532i	$0.0835684\pi$
$158$	−0.163370	+	2.28421i	−0.0129970	+	0.181722i
$159$	0.526622	−	0.154630i	0.0417638	−	0.0122630i
$160$	−1.15971	−	1.91183i	−0.0916829	−	0.151143i
$161$	2.07958	−	0.445089i	0.163894	−	0.0350779i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	1.14876	−	2.10379i	0.0899775	−	0.164782i	−0.828815	−	0.559523i	$-0.810984\pi$
$163$	1.14876	−	2.10379i	0.0899775	−	0.164782i	0.918792	+	0.394742i	$0.129166\pi$
$164$	4.80677	−	4.16509i	0.375346	−	0.325239i
$165$	−1.54984	−	0.756977i	−0.120655	−	0.0589306i
$166$	−1.41676	+	0.203699i	−0.109962	+	0.0158101i
$167$	4.51116	+	20.7375i	0.349084	+	1.60471i	0.732252	+	0.681034i	$0.238469\pi$
$167$	4.51116	+	20.7375i	0.349084	+	1.60471i	−0.383168	+	0.923679i	$0.625167\pi$
$168$	0.415484	−	0.154967i	0.0320553	−	0.0119560i
$169$	5.62928	+	4.87780i	0.433022	+	0.375215i
$170$	1.29025	−	3.20298i	0.0989576	−	0.245657i
$171$	3.61667	−	1.65168i	0.276574	−	0.126307i
$172$	−4.81931	+	2.63154i	−0.367469	+	0.200653i
$173$	−6.24580	+	3.41047i	−0.474860	+	0.259293i	−0.698810	−	0.715308i	$-0.746287\pi$
$173$	−6.24580	+	3.41047i	−0.474860	+	0.259293i	0.223950	+	0.974601i	$0.428105\pi$
$174$	−1.76298	+	0.805124i	−0.133651	+	0.0610363i
$175$	−0.358307	−	2.18807i	−0.0270855	−	0.165403i
$176$	0.582960	+	0.505138i	0.0439423	+	0.0380762i
$177$	6.60151	−	2.46224i	0.496200	−	0.185073i
$178$	−0.0305174	−	0.140286i	−0.00228738	−	0.0105149i
$179$	−9.73841	+	1.40017i	−0.727883	+	0.104654i	−0.496287	−	0.868158i	$-0.665304\pi$
$179$	−9.73841	+	1.40017i	−0.727883	+	0.104654i	−0.231596	+	0.972812i	$0.574395\pi$
$180$	2.11465	−	0.726817i	0.157617	−	0.0541737i
$181$	−14.1369	+	12.2497i	−1.05079	+	0.910513i	−0.996121	−	0.0879921i	$-0.971955\pi$
$181$	−14.1369	+	12.2497i	−1.05079	+	0.910513i	−0.0546663	+	0.998505i	$0.517410\pi$
$182$	0.961017	−	1.75997i	0.0712353	−	0.130458i
$183$	−3.74410	−	3.74410i	−0.276772	−	0.276772i
$184$	−4.78244	−	0.358166i	−0.352566	−	0.0264043i
$185$	−3.98917	+	2.41982i	−0.293289	+	0.177908i
$186$	−0.0620699	+	0.0182254i	−0.00455119	+	0.00133635i
$187$	−0.0849790	+	1.18816i	−0.00621428	+	0.0868870i
$188$	−0.752599	+	3.45964i	−0.0548889	+	0.252320i
$189$	0.0631085	+	0.438929i	0.00459047	+	0.0319274i
$190$	−0.230619	+	8.88755i	−0.0167309	+	0.644770i
$191$	23.4982	+	10.7312i	1.70027	+	0.776486i	0.997907	+	0.0646632i	$0.0205973\pi$
$191$	23.4982	+	10.7312i	1.70027	+	0.776486i	0.702359	+	0.711822i	$0.252130\pi$
$192$	−0.997452	+	0.0713392i	−0.0719849	+	0.00514846i
$193$	8.01574	+	10.7078i	0.576986	+	0.770763i	0.990168	−	0.139886i	$-0.0446735\pi$
$193$	8.01574	+	10.7078i	0.576986	+	0.770763i	−0.413182	+	0.910649i	$0.635583\pi$
$194$	2.06990	+	4.53246i	0.148610	+	0.325411i
$195$	5.07452	−	8.74599i	0.363394	−	0.626313i
$196$	6.52777	+	1.91673i	0.466270	+	0.136909i
$197$	−5.51283	+	14.7805i	−0.392773	+	1.05306i	0.578622	+	0.815596i	$0.303591\pi$
$197$	−5.51283	+	14.7805i	−0.392773	+	1.05306i	−0.971395	+	0.237469i	$0.923682\pi$
$198$	−0.617511	+	0.462263i	−0.0438846	+	0.0328516i
$199$	−13.7033	+	15.8144i	−0.971398	+	1.12105i	0.0212200	+	0.999775i	$0.493245\pi$
$199$	−13.7033	+	15.8144i	−0.971398	+	1.12105i	−0.992618	+	0.121279i	$0.961301\pi$
$200$	−0.614866	+	4.96205i	−0.0434776	+	0.350870i
$201$	−7.02538	+	10.9317i	−0.495532	+	0.771063i
$202$	0.231293	−	0.308972i	0.0162737	−	0.0217392i
$203$	0.839805	+	0.182688i	0.0589428	+	0.0128222i
$204$	−1.01128	−	1.16708i	−0.0708038	−	0.0817119i
$205$	−14.2073	+	0.646268i	−0.992282	+	0.0451373i
$206$			4.70141i			0.327563i
$207$	1.36656	−	4.59701i	0.0949825	−	0.319514i
$208$	−3.19755	+	3.19755i	−0.221710	+	0.221710i
$209$	−0.864054	−	2.94270i	−0.0597679	−	0.203551i
$210$	−0.943837	−	0.303942i	−0.0651309	−	0.0209740i
$211$	8.28752	−	5.32607i	0.570536	−	0.366661i	−0.223340	−	0.974741i	$-0.571696\pi$
$211$	8.28752	−	5.32607i	0.570536	−	0.366661i	0.793876	+	0.608079i	$0.208060\pi$
$212$	0.439380	+	0.328916i	0.0301768	+	0.0225900i
$213$	4.51096	−	0.981300i	0.309086	−	0.0672375i
$214$	4.72632	−	10.3492i	0.323085	−	0.707457i
$215$	12.1038	+	2.06203i	0.825471	+	0.140629i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	0.0268778	+	0.0100249i	0.00182458	+	0.000680534i
$218$	−1.99407	−	3.65186i	−0.135055	−	0.247335i
$219$	0.0734905	−	0.250286i	0.00496603	−	0.0169127i
$220$	−0.322796	−	1.69435i	−0.0217629	−	0.114233i
$221$	−6.91212	−	0.993813i	−0.464960	−	0.0668511i
$222$	0.148854	+	2.08126i	0.00999046	+	0.139685i
$223$	8.47870	+	22.7323i	0.567776	+	1.52227i	0.830286	+	0.557337i	$0.188177\pi$
$223$	8.47870	+	22.7323i	0.567776	+	1.52227i	−0.262510	+	0.964929i	$0.584550\pi$
$224$	0.373048	+	0.239743i	0.0249253	+	0.0160185i
$225$	−4.71795	−	1.65557i	−0.314530	−	0.110372i
$226$	7.50611	+	11.6797i	0.499299	+	0.776924i
$227$	−19.5364	−	1.39727i	−1.29667	−	0.0927400i	−0.594124	−	0.804374i	$-0.702501\pi$
$227$	−19.5364	−	1.39727i	−1.29667	−	0.0927400i	−0.702551	+	0.711634i	$0.747956\pi$
$228$	3.48963	+	1.90548i	0.231106	+	0.126193i
$229$	3.69813			0.244379			0.122190	−	0.992507i	$-0.461008\pi$
$229$	3.69813			0.244379			0.122190	+	0.992507i	$0.461008\pi$
$230$	7.89533	+	7.25698i	0.520603	+	0.478511i
$231$	0.342057			0.0225057
$232$	−1.70105	−	0.928842i	−0.111679	−	0.0609815i
$233$	−19.9721	−	1.42843i	−1.30841	−	0.0935796i	−0.600356	−	0.799733i	$-0.704974\pi$
$233$	−19.9721	−	1.42843i	−1.30841	−	0.0935796i	−0.708059	+	0.706153i	$0.750429\pi$
$234$	−2.44479	−	3.80416i	−0.159821	−	0.248686i
$235$	6.11568	−	5.02753i	0.398943	−	0.327960i
$236$	5.92726	+	3.80922i	0.385832	+	0.247959i
$237$	−0.800288	−	2.14566i	−0.0519843	−	0.139375i
$238$	0.0488527	+	0.683050i	0.00316665	+	0.0442756i
$239$	4.14563	+	0.596052i	0.268159	+	0.0385554i	0.275082	−	0.961421i	$-0.411295\pi$
$239$	4.14563	+	0.596052i	0.268159	+	0.0385554i	−0.00692388	+	0.999976i	$0.502204\pi$
$240$	1.84911	+	1.25730i	0.119359	+	0.0811583i
$241$	8.10265	−	27.5951i	0.521938	−	1.77756i	−0.100555	−	0.994931i	$-0.532062\pi$
$241$	8.10265	−	27.5951i	0.521938	−	1.77756i	0.622493	−	0.782625i	$-0.286120\pi$
$242$	−4.98658	−	9.13224i	−0.320550	−	0.587043i
$243$	0.936950	+	0.349464i	0.0601054	+	0.0224181i
$244$	0.753552	−	5.24107i	0.0482412	−	0.335525i
$245$	−8.79770	−	12.4108i	−0.562064	−	0.792899i
$246$	−2.64215	+	5.78551i	−0.168458	+	0.368870i
$247$	17.5685	−	3.82179i	1.11786	−	0.243175i
$248$	−0.0517873	−	0.0387675i	−0.00328850	−	0.00246174i
$249$	1.20411	−	0.773835i	0.0763074	−	0.0490398i
$250$	7.95635	−	7.85471i	0.503204	−	0.496775i
$251$	−2.23750	−	7.62024i	−0.141230	−	0.480985i	0.858250	−	0.513232i	$-0.171552\pi$
$251$	−2.23750	−	7.62024i	−0.141230	−	0.480985i	−0.999480	+	0.0322468i	$0.989734\pi$
$252$	−0.313562	+	0.313562i	−0.0197525	+	0.0197525i
$253$	−3.35987	−	1.54804i	−0.211233	−	0.0973242i
$254$		−	17.4630i		−	1.09573i
$255$	0.156913	+	3.44952i	0.00982629	+	0.216017i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−11.0831	−	2.41099i	−0.691346	−	0.150393i	−0.146853	−	0.989158i	$-0.546914\pi$
$257$	−11.0831	−	2.41099i	−0.691346	−	0.150393i	−0.544493	+	0.838765i	$0.683278\pi$
$258$	3.29061	−	4.39575i	0.204865	−	0.273667i
$259$	0.500242	−	0.778392i	0.0310835	−	0.0483669i
$260$	10.0426	−	1.17891i	0.622814	−	0.0731132i
$261$	1.26920	−	1.46473i	0.0785615	−	0.0906648i
$262$	6.23142	−	4.66478i	0.384979	−	0.288191i
$263$	1.46000	−	3.91442i	0.0900276	−	0.241373i	−0.884131	−	0.467240i	$-0.845249\pi$
$263$	1.46000	−	3.91442i	0.0900276	−	0.241373i	0.974158	+	0.225866i	$0.0725213\pi$
$264$	−0.740121	−	0.217319i	−0.0455513	−	0.0133751i
$265$	−0.315101	−	1.18613i	−0.0193565	−	0.0728637i
$266$	−0.732425	−	1.60379i	−0.0449079	−	0.0983345i
$267$	0.0860366	+	0.114931i	0.00526535	+	0.00703369i
$268$	−12.9614	+	0.927020i	−0.791746	+	0.0566268i
$269$	−1.91922	−	0.876478i	−0.117017	−	0.0534398i	0.356046	−	0.934468i	$-0.384125\pi$
$269$	−1.91922	−	0.876478i	−0.117017	−	0.0534398i	−0.473063	+	0.881028i	$0.656852\pi$
$270$	−1.62162	+	1.53959i	−0.0986887	+	0.0936966i
$271$	−2.17932	−	15.1575i	−0.132384	−	0.920752i	−0.942434	−	0.334392i	$-0.891469\pi$
$271$	−2.17932	−	15.1575i	−0.132384	−	0.920752i	0.810050	−	0.586361i	$-0.199440\pi$
$272$	0.328258	−	1.50898i	0.0199035	−	0.0914951i
$273$	−0.143053	+	2.00015i	−0.00865798	+	0.121054i
$274$	21.3535	−	6.26997i	1.29001	−	0.378782i
$275$	−1.78198	+	3.42048i	−0.107457	+	0.206263i
$276$	4.49905	−	1.66090i	0.270811	−	0.0999743i
$277$	−18.5544	−	18.5544i	−1.11482	−	1.11482i	−0.992489	−	0.122334i	$-0.960962\pi$
$277$	−18.5544	−	18.5544i	−1.11482	−	1.11482i	−0.122334	−	0.992489i	$-0.539038\pi$
$278$	−3.95258	+	7.23861i	−0.237060	+	0.434143i
$279$	0.0488897	−	0.0423632i	0.00292695	−	0.00253622i
$280$	−0.322302	−	0.937726i	−0.0192612	−	0.0560399i
$281$	5.51422	−	0.792825i	0.328951	−	0.0472960i	0.0241390	−	0.999709i	$-0.492316\pi$
$281$	5.51422	−	0.792825i	0.328951	−	0.0472960i	0.304812	+	0.952413i	$0.401406\pi$
$282$	−0.752599	−	3.45964i	−0.0448166	−	0.206019i
$283$	−4.20777	+	1.56942i	−0.250126	+	0.0932922i	−0.471400	−	0.881919i	$-0.656251\pi$
$283$	−4.20777	+	1.56942i	−0.250126	+	0.0932922i	0.221274	+	0.975212i	$0.428978\pi$
$284$	3.48889	+	3.02314i	0.207027	+	0.179390i
$285$	−3.48224	−	8.18020i	−0.206270	−	0.484553i
$286$	−3.17291	+	1.44902i	−0.187618	+	0.0856825i
$287$	2.47542	−	1.35168i	0.146120	−	0.0797873i
$288$	0.877679	−	0.479249i	0.0517177	−	0.0282400i
$289$	−13.2945	+	6.07139i	−0.782029	+	0.357141i
$290$	1.69745	+	3.98751i	0.0996776	+	0.234155i
$291$	−3.76570	−	3.26300i	−0.220749	−	0.191280i
$292$	0.244405	−	0.0911584i	0.0143027	−	0.00533464i
$293$	3.09717	+	14.2374i	0.180938	+	0.831761i	0.974697	+	0.223528i	$0.0717575\pi$
$293$	3.09717	+	14.2374i	0.180938	+	0.831761i	−0.793759	+	0.608232i	$0.791879\pi$
$294$	−6.73411	+	0.968219i	−0.392741	+	0.0564677i
$295$	−5.12096	−	14.8993i	−0.298154	−	0.867469i
$296$	−1.57693	+	1.36642i	−0.0916570	+	0.0794213i
$297$	0.369677	−	0.677012i	0.0214508	−	0.0392842i
$298$	2.06519	+	2.06519i	0.119633	+	0.119633i
$299$	10.4571	−	18.9991i	0.604752	−	1.09875i
$300$	−1.50201	−	4.76906i	−0.0867185	−	0.275342i
$301$	−2.33630	+	0.685999i	−0.134662	+	0.0395403i
$302$	1.02519	−	14.3340i	0.0589928	−	0.824827i
$303$	−0.0820404	+	0.377133i	−0.00471310	+	0.0216658i
$304$	0.565840	+	3.93550i	0.0324531	+	0.225716i
$305$	−8.58642	+	8.15208i	−0.491657	+	0.466787i
$306$	1.40472	+	0.641512i	0.0803022	+	0.0366728i
$307$	29.2590	−	2.09265i	1.66990	−	0.119434i	0.795922	−	0.605399i	$-0.206987\pi$
$307$	29.2590	−	2.09265i	1.66990	−	0.119434i	0.873978	+	0.485966i	$0.161532\pi$
$308$	0.204987	+	0.273831i	0.0116802	+	0.0156030i
$309$	−1.95304	−	4.27655i	−0.111104	−	0.243285i
$310$	0.0371392	+	0.139803i	0.00210936	+	0.00794028i
$311$	−16.7687	−	4.92374i	−0.950867	−	0.279200i	−0.230719	−	0.973020i	$-0.574108\pi$
$311$	−16.7687	−	4.92374i	−0.950867	−	0.279200i	−0.720148	+	0.693821i	$0.755926\pi$
$312$	1.58028	−	4.23690i	0.0894658	−	0.239867i
$313$	4.03374	−	3.01962i	0.228001	−	0.170679i	−0.479170	−	0.877722i	$-0.659062\pi$
$313$	4.03374	−	3.01962i	0.228001	−	0.170679i	0.707171	+	0.707043i	$0.249971\pi$
$314$	0.792958	−	0.915123i	0.0447492	−	0.0516434i
$315$	0.984806	−	0.115608i	0.0554875	−	0.00651378i
$316$	1.23809	−	1.92651i	0.0696481	−	0.108374i
$317$	−1.75404	+	2.34312i	−0.0985167	+	0.131603i	−0.847091	−	0.531448i	$-0.821648\pi$
$317$	−1.75404	+	2.34312i	−0.0985167	+	0.131603i	0.748574	+	0.663051i	$0.230739\pi$
$318$	−0.536311	−	0.116667i	−0.0300748	−	0.00654238i
$319$	−0.979018	−	1.12985i	−0.0548145	−	0.0632593i
$320$	0.101610	+	2.23376i	0.00568018	+	0.124871i
$321$			11.3773i			0.635022i
$322$	−2.03851	−	0.605992i	−0.113602	−	0.0337706i
$323$	−4.34161	+	4.34161i	−0.241574	+	0.241574i
$324$	0.281733	+	0.959493i	0.0156518	+	0.0533052i
$325$	−19.2557	−	11.8504i	−1.06811	−	0.657344i
$326$	−2.01648	+	1.29591i	−0.111682	+	0.0717739i
$327$	3.33090	+	2.49348i	0.184199	+	0.137890i
$328$	−6.21492	+	1.35197i	−0.343162	+	0.0746502i
$329$	−0.652216	+	1.42815i	−0.0359578	+	0.0787366i
$330$	0.997486	+	1.40714i	0.0549098	+	0.0774607i
$331$	2.64232	−	18.3778i	0.145235	−	1.01013i	−0.778649	−	0.627460i	$-0.784095\pi$
$331$	2.64232	−	18.3778i	0.145235	−	1.01013i	0.923884	−	0.382673i	$-0.124996\pi$
$332$	1.34108	+	0.500198i	0.0736015	+	0.0274520i
$333$	−0.999988	−	1.83134i	−0.0547990	−	0.100357i
$334$	5.97906	−	20.3628i	0.327159	−	1.11420i
$335$	24.0283	+	16.3380i	1.31281	+	0.892642i
$336$	−0.438929	−	0.0631085i	−0.0239456	−	0.00344285i
$337$	−2.01819	−	28.2180i	−0.109938	−	1.53713i	−0.690750	−	0.723094i	$-0.742719\pi$
$337$	−2.01819	−	28.2180i	−0.109938	−	1.53713i	0.580812	−	0.814038i	$-0.302735\pi$
$338$	−2.60302	−	6.97897i	−0.141586	−	0.379606i
$339$	−11.6797	−	7.50611i	−0.634356	−	0.407676i
$340$	−2.66745	+	2.19284i	−0.144663	+	0.118923i
$341$	−0.0269780	−	0.0419785i	−0.00146094	−	0.00227326i
$342$	−3.96584	−	0.283642i	−0.214448	−	0.0153376i
$343$	5.37228	+	2.93348i	0.290076	+	0.158393i
$344$	5.49097			0.296053
$345$	−10.1965	−	3.32134i	−0.548961	−	0.178815i
$346$	7.11627			0.382573
$347$	−8.05801	−	4.40000i	−0.432576	−	0.236205i	0.248181	−	0.968714i	$-0.420167\pi$
$347$	−8.05801	−	4.40000i	−0.432576	−	0.236205i	−0.680757	+	0.732509i	$0.738349\pi$
$348$	1.93318	+	0.138264i	0.103629	+	0.00741173i
$349$	15.1169	+	23.5224i	0.809189	+	1.25912i	0.962591	+	0.270959i	$0.0873409\pi$
$349$	15.1169	+	23.5224i	0.809189	+	1.25912i	−0.153401	+	0.988164i	$0.549023\pi$
$350$	−0.734153	+	2.09214i	−0.0392421	+	0.111830i
$351$	3.80416	+	2.44479i	0.203051	+	0.130493i
$352$	−0.269565	−	0.722732i	−0.0143679	−	0.0385217i
$353$	−2.52923	−	35.3632i	−0.134617	−	1.88220i	−0.397833	−	0.917458i	$-0.630238\pi$
$353$	−2.52923	−	35.3632i	−0.134617	−	1.88220i	0.263215	−	0.964737i	$-0.415217\pi$
$354$	−6.97403	−	1.00271i	−0.370665	−	0.0532936i
$355$	−1.93186	−	10.1403i	−0.102533	−	0.538193i
$356$	−0.0404475	+	0.137752i	−0.00214372	+	0.00730082i
$357$	−0.328187	−	0.601030i	−0.0173695	−	0.0318099i
$358$	9.21823	+	3.43822i	0.487199	+	0.181716i
$359$	−3.17183	+	22.0606i	−0.167403	+	1.16431i	0.716824	+	0.697254i	$0.245595\pi$
$359$	−3.17183	+	22.0606i	−0.167403	+	1.16431i	−0.884227	+	0.467058i	$0.845314\pi$
$360$	−2.20431	−	0.375531i	−0.116177	−	0.0197922i
$361$	−1.32586	+	2.90324i	−0.0697823	+	0.152802i
$362$	18.2783	−	3.97620i	0.960687	−	0.208985i
$363$	8.32963	+	6.23548i	0.437192	+	0.327278i
$364$	−1.68693	+	1.08412i	−0.0884191	+	0.0568235i
$365$	−0.555205	−	0.178792i	−0.0290607	−	0.00935839i
$366$	1.49176	+	5.08048i	0.0779757	+	0.265561i
$367$	16.5047	−	16.5047i	0.861539	−	0.861539i	−0.129978	−	0.991517i	$-0.541491\pi$
$367$	16.5047	−	16.5047i	0.861539	−	0.861539i	0.991517	+	0.129978i	$0.0414906\pi$
$368$	4.02580	+	2.60633i	0.209859	+	0.135865i
$369$		−	6.36027i		−	0.331103i
$370$	4.66090	−	0.212017i	0.242309	−	0.0110222i
$371$	0.159384	+	0.183939i	0.00827479	+	0.00954961i
$372$	0.0632120	+	0.0137509i	0.00327739	+	0.000712952i
$373$	21.2519	−	28.3892i	1.10038	−	1.46994i	0.232876	−	0.972506i	$-0.425186\pi$
$373$	21.2519	−	28.3892i	1.10038	−	1.46994i	0.867504	−	0.497430i	$-0.165723\pi$
$374$	0.644009	−	1.00210i	0.0333009	−	0.0518173i
$375$	−3.97439	+	10.4501i	−0.205236	+	0.539640i
$376$	2.31857	−	2.67577i	0.119571	−	0.137992i
$377$	7.01611	−	5.25219i	0.361348	−	0.270502i
$378$	0.154967	−	0.415484i	0.00797067	−	0.0213702i
$379$	−10.9030	−	3.20141i	−0.560049	−	0.164445i	−0.0105574	−	0.999944i	$-0.503361\pi$
$379$	−10.9030	−	3.20141i	−0.560049	−	0.164445i	−0.549492	+	0.835499i	$0.685179\pi$
$380$	4.46176	−	7.68989i	0.228883	−	0.394483i
$381$	7.25441	+	15.8849i	0.371655	+	0.813810i
$382$	−15.4809	−	20.6801i	−0.792071	−	1.05808i
$383$	16.6426	−	1.19030i	0.850397	−	0.0608216i	0.360666	−	0.932695i	$-0.382550\pi$
$383$	16.6426	−	1.19030i	0.850397	−	0.0608216i	0.489731	+	0.871874i	$0.337095\pi$
$384$	0.909632	+	0.415415i	0.0464195	+	0.0211991i
$385$	0.0198404	−	0.764606i	0.00101116	−	0.0389679i
$386$	−1.90356	−	13.2395i	−0.0968885	−	0.673874i
$387$	−1.16719	+	5.36548i	−0.0593315	+	0.272743i
$388$	0.355464	−	4.97004i	0.0180460	−	0.252316i
$389$	28.0805	−	8.24517i	1.42374	−	0.418047i	0.522970	−	0.852351i	$-0.324824\pi$
$389$	28.0805	−	8.24517i	1.42374	−	0.418047i	0.900766	+	0.434304i	$0.143006\pi$
$390$	−8.64530	+	5.24421i	−0.437772	+	0.265551i
$391$	0.503573	+	7.38891i	0.0254668	+	0.373673i
$392$	−4.81070	−	4.81070i	−0.242977	−	0.242977i
$393$	−3.73048	+	6.83186i	−0.188178	+	0.344622i
$394$	11.9220	−	10.3305i	0.600623	−	0.520442i
$395$	−4.84264	+	1.66444i	−0.243659	+	0.0837471i
$396$	0.763515	−	0.109777i	0.0383681	−	0.00551650i
$397$	4.28288	+	19.6881i	0.214952	+	0.988117i	0.950519	+	0.310666i	$0.100552\pi$
$397$	4.28288	+	19.6881i	0.214952	+	0.988117i	−0.735567	+	0.677452i	$0.763084\pi$
$398$	19.6061	−	7.31270i	0.982765	−	0.366552i
$399$	1.33247	+	1.15460i	0.0667072	+	0.0578021i
$400$	2.91771	−	4.06041i	0.145886	−	0.203021i
$401$	−25.4694	+	11.6315i	−1.27188	+	0.580849i	−0.932965	−	0.359967i	$-0.882788\pi$
$401$	−25.4694	+	11.6315i	−1.27188	+	0.580849i	−0.338917	+	0.940816i	$0.610061\pi$
$402$	11.4050	−	6.22762i	0.568832	−	0.310606i
$403$	0.256748	−	0.140195i	0.0127895	−	0.00698361i
$404$	−0.351076	+	0.160331i	−0.0174667	+	0.00797676i
$405$	0.835509	−	2.07411i	0.0415168	−	0.103063i
$406$	−0.649526	−	0.562818i	−0.0322354	−	0.0279322i
$407$	−1.50803	+	0.562467i	−0.0747504	+	0.0278805i
$408$	0.328258	+	1.50898i	0.0162512	+	0.0747055i
$409$	14.1672	−	2.03694i	0.700524	−	0.100720i	0.217156	−	0.976137i	$-0.430322\pi$
$409$	14.1672	−	2.03694i	0.700524	−	0.100720i	0.483369	+	0.875417i	$0.339413\pi$
$410$	12.7792	+	6.24162i	0.631119	+	0.308252i
$411$	−16.8192	+	14.5739i	−0.829631	+	0.718880i
$412$	2.25315	−	4.12633i	0.111004	−	0.203290i
$413$	2.20927	+	2.20927i	0.108711	+	0.108711i
$414$	−3.40251	+	3.37978i	−0.167224	+	0.166107i
$415$	−1.65992	−	2.73645i	−0.0814825	−	0.134327i
$416$	4.33884	−	1.27400i	0.212729	−	0.0624629i
$417$	0.588366	−	8.22644i	0.0288124	−	0.402850i
$418$	−0.651923	+	2.99684i	−0.0318866	+	0.146580i
$419$	0.377352	+	2.62454i	0.0184348	+	0.128217i	0.996961	−	0.0779075i	$-0.0248239\pi$
$419$	0.377352	+	2.62454i	0.0184348	+	0.128217i	−0.978526	+	0.206125i	$0.933915\pi$
$420$	0.682721	+	0.719097i	0.0333134	+	0.0350883i
$421$	−15.2862	−	6.98099i	−0.745006	−	0.340233i	0.00648261	−	0.999979i	$-0.497937\pi$
$421$	−15.2862	−	6.98099i	−0.745006	−	0.340233i	−0.751488	+	0.659746i	$0.770664\pi$
$422$	−9.82629	+	0.702790i	−0.478337	+	0.0342113i
$423$	2.12177	+	2.83436i	0.103164	+	0.137811i
$424$	−0.228002	−	0.499255i	−0.0110728	−	0.0242460i
$425$	7.71987	−	0.150667i	0.374469	−	0.00730843i
$426$	−4.42946	−	1.30061i	−0.214608	−	0.0630146i
$427$	0.820547	−	2.19997i	0.0397090	−	0.106464i
$428$	−9.10804	+	6.81819i	−0.440254	+	0.329570i
$429$	2.28424	−	2.63615i	0.110284	−	0.127275i
$430$	−9.63501	−	7.61053i	−0.464642	−	0.367012i
$431$	−8.96138	+	13.9442i	−0.431654	+	0.671667i	−0.987140	−	0.159859i	$-0.948896\pi$
$431$	−8.96138	+	13.9442i	−0.431654	+	0.671667i	0.555485	+	0.831526i	$0.312532\pi$
$432$	−0.599278	+	0.800541i	−0.0288328	+	0.0385161i
$433$	23.1208	+	5.02962i	1.11111	+	0.241708i	0.730424	−	0.682994i	$-0.239323\pi$
$433$	23.1208	+	5.02962i	1.11111	+	0.241708i	0.380690	+	0.924703i	$0.375686\pi$
$434$	−0.0187856	−	0.0216798i	−0.000901740	−	0.00104066i
$435$	−3.20052	−	2.92202i	−0.153453	−	0.140100i
$436$			4.16082i			0.199267i
$437$	−7.86298	−	17.3714i	−0.376137	−	0.830987i
$438$	−0.184450	+	0.184450i	−0.00881337	+	0.00881337i
$439$	−0.0953358	−	0.324684i	−0.00455013	−	0.0154963i	0.957187	−	0.289472i	$-0.0934796\pi$
$439$	−0.0953358	−	0.324684i	−0.00455013	−	0.0154963i	−0.961737	+	0.273975i	$0.911661\pi$
$440$	−0.528706	+	1.64180i	−0.0252051	+	0.0782697i
$441$	5.72335	−	3.67817i	0.272540	−	0.175151i
$442$	5.59034	+	4.18488i	0.265905	+	0.199054i
$443$	23.7054	−	5.15680i	1.12628	−	0.245007i	0.389424	−	0.921059i	$-0.372674\pi$
$443$	23.7054	−	5.15680i	1.12628	−	0.245007i	0.736854	+	0.676052i	$0.236310\pi$
$444$	0.866794	−	1.89801i	0.0411362	−	0.0900758i
$445$	0.261898	−	0.185653i	0.0124152	−	0.00880077i
$446$	3.45284	−	24.0151i	0.163497	−	1.13715i
$447$	−2.73647	−	1.02065i	−0.129431	−	0.0482752i
$448$	−0.212520	−	0.389201i	−0.0100406	−	0.0183880i
$449$	−10.0490	+	34.2239i	−0.474243	+	1.61512i	0.281020	+	0.959702i	$0.409327\pi$
$449$	−10.0490	+	34.2239i	−0.474243	+	1.61512i	−0.755263	+	0.655422i	$0.772491\pi$
$450$	3.34742	+	3.71414i	0.157799	+	0.175086i
$451$	−4.85616	−	0.698211i	−0.228668	−	0.0328775i
$452$	−0.990454	−	13.8484i	−0.0465870	−	0.651372i
$453$	5.02200	+	13.4645i	0.235954	+	0.632618i
$454$	16.4770	+	10.5891i	0.773305	+	0.496973i
$455$	4.46266	+	0.435784i	0.209213	+	0.0204299i
$456$	−2.14957	−	3.34480i	−0.100663	−	0.156635i
$457$	−5.81093	−	0.415606i	−0.271824	−	0.0194412i	−0.0652381	−	0.997870i	$-0.520781\pi$
$457$	−5.81093	−	0.415606i	−0.271824	−	0.0194412i	−0.206586	+	0.978429i	$0.566235\pi$
$458$	−3.24577	−	1.77233i	−0.151665	−	0.0828153i
$459$	−1.54427			−0.0720802
$460$	−3.45167	−	10.1531i	−0.160935	−	0.473392i
$461$	−5.60795			−0.261188			−0.130594	−	0.991436i	$-0.541688\pi$
$461$	−5.60795			−0.261188			−0.130594	+	0.991436i	$0.541688\pi$
$462$	−0.300216	−	0.163931i	−0.0139673	−	0.00762674i
$463$	−21.1047	−	1.50944i	−0.980819	−	0.0701496i	−0.428288	−	0.903642i	$-0.640883\pi$
$463$	−21.1047	−	1.50944i	−0.980819	−	0.0701496i	−0.552531	+	0.833493i	$0.686338\pi$
$464$	1.04783	+	1.63045i	0.0486442	+	0.0756918i
$465$	−0.0918593	−	0.111741i	−0.00425987	−	0.00518187i
$466$	16.8445	+	10.8253i	0.780306	+	0.501472i
$467$	14.6884	+	39.3812i	0.679699	+	1.82234i	0.558118	+	0.829762i	$0.311524\pi$
$467$	14.6884	+	39.3812i	0.679699	+	1.82234i	0.121581	+	0.992581i	$0.461203\pi$
$468$	0.322597	+	4.51049i	0.0149120	+	0.208498i
$469$	−5.70369	−	0.820067i	−0.263372	−	0.0378672i
$470$	−7.77704	+	1.48163i	−0.358728	+	0.0683423i
$471$	−0.341145	+	1.16183i	−0.0157191	+	0.0535344i
$472$	−3.37667	−	6.18390i	−0.155424	−	0.284637i
$473$	3.96850	+	1.48017i	0.182472	+	0.0680584i
$474$	−0.325907	+	2.26673i	−0.0149694	+	0.104115i
$475$	−18.4873	+	7.30943i	−0.848256	+	0.335380i
$476$	0.284474	−	0.622911i	0.0130388	−	0.0285511i
$477$	0.536311	−	0.116667i	0.0245560	−	0.00534183i
$478$	−3.35288	−	2.50993i	−0.153357	−	0.114802i
$479$	3.28814	−	2.11316i	0.150239	−	0.0965528i	−0.463362	−	0.886169i	$-0.653357\pi$
$479$	3.28814	−	2.11316i	0.150239	−	0.0965528i	0.613601	+	0.789617i	$0.289721\pi$
$480$	−1.02036	−	1.98969i	−0.0465731	−	0.0908164i
$481$	−2.65829	−	9.05331i	−0.121208	−	0.412795i
$482$	−20.3365	+	20.3365i	−0.926300	+	0.926300i
$483$	2.10603	−	0.295599i	0.0958279	−	0.0134502i
$484$			10.4050i			0.472954i
$485$	−7.51225	+	8.22827i	−0.341114	+	0.373626i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	27.0776	+	5.89037i	1.22700	+	0.266918i	0.778949	−	0.627088i	$-0.215753\pi$
$487$	27.0776	+	5.89037i	1.22700	+	0.266918i	0.448055	+	0.894006i	$0.352117\pi$
$488$	−3.17315	+	4.23884i	−0.143642	+	0.191883i
$489$	1.29591	−	2.01648i	0.0586032	−	0.0911883i
$490$	1.77367	+	15.1090i	0.0801264	+	0.682556i
$491$	24.1696	−	27.8932i	1.09076	−	1.25880i	0.127036	−	0.991898i	$-0.459453\pi$
$491$	24.1696	−	27.8932i	1.09076	−	1.25880i	0.963723	−	0.266905i	$-0.0860011\pi$
$492$	5.09166	−	3.81157i	0.229550	−	0.171839i
$493$	−1.04594	+	2.80427i	−0.0471067	+	0.126298i
$494$	−17.2511	−	5.06538i	−0.776164	−	0.227902i
$495$	−1.49189	−	0.865613i	−0.0670556	−	0.0389064i
$496$	0.0268733	+	0.0588444i	0.00120665	+	0.00264219i
$497$	1.22680	+	1.63882i	0.0550297	+	0.0735110i
$498$	−1.42768	+	0.102110i	−0.0639760	+	0.00457565i
$499$	−32.2946	−	14.7484i	−1.44570	−	0.660231i	−0.470675	−	0.882307i	$-0.655989\pi$
$499$	−32.2946	−	14.7484i	−1.44570	−	0.660231i	−0.975029	+	0.222076i	$0.928717\pi$
$500$	−10.7475	+	3.08084i	−0.480642	+	0.137779i
$501$	3.02027	+	21.0064i	0.134936	+	0.938498i
$502$	−1.68818	+	7.76044i	−0.0753472	+	0.346366i
$503$	−0.437781	+	6.12098i	−0.0195197	+	0.272921i	0.978314	+	0.207129i	$0.0664120\pi$
$503$	−0.437781	+	6.12098i	−0.0195197	+	0.272921i	−0.997833	+	0.0657921i	$0.979043\pi$
$504$	0.425480	−	0.124932i	0.0189524	−	0.00556493i
$505$	0.838254	+	0.205261i	0.0373018	+	0.00913400i
$506$	2.20699	+	2.96889i	0.0981128	+	0.131983i
$507$	5.26696	+	5.26696i	0.233914	+	0.233914i
$508$	−8.36914	+	15.3269i	−0.371321	+	0.680023i
$509$	−15.3218	+	13.2764i	−0.679128	+	0.588468i	−0.924602	−	0.380935i	$-0.875602\pi$
$509$	−15.3218	+	13.2764i	−0.679128	+	0.588468i	0.245473	+	0.969403i	$0.421057\pi$
$510$	1.51546	−	3.10277i	0.0671057	−	0.137393i
$511$	0.114496	−	0.0164620i	0.00506499	−	0.000728235i
$512$	0.212565	+	0.977147i	0.00939415	+	0.0431842i
$513$	3.72528	−	1.38946i	0.164475	−	0.0613461i
$514$	8.57196	+	7.42765i	0.378093	+	0.327620i
$515$	−9.67272	+	4.11760i	−0.426231	+	0.181443i
$516$	−4.99476	+	2.28103i	−0.219882	+	0.100417i
$517$	2.39700	−	1.30886i	0.105420	−	0.0575636i
$518$	−0.812096	+	0.443438i	−0.0356814	+	0.0194835i
$519$	−6.47319	+	2.95621i	−0.284141	+	0.129763i
$520$	−9.37915	−	3.77818i	−0.411303	−	0.165684i
$521$	−16.4466	−	14.2510i	−0.720537	−	0.624349i	0.215396	−	0.976527i	$-0.430896\pi$
$521$	−16.4466	−	14.2510i	−0.720537	−	0.624349i	−0.935933	+	0.352178i	$0.885441\pi$
$522$	−1.81592	+	0.677304i	−0.0794807	+	0.0296448i
$523$	0.432776	+	1.98944i	0.0189240	+	0.0869921i	0.985640	−	0.168859i	$-0.0540081\pi$
$523$	0.432776	+	1.98944i	0.0189240	+	0.0869921i	−0.966716	+	0.255851i	$0.917644\pi$
$524$	−7.70478	+	1.10778i	−0.336585	+	0.0483936i
$525$	−0.201299	−	2.20806i	−0.00878540	−	0.0963676i
$526$	−3.15739	+	2.73590i	−0.137669	+	0.119291i
$527$	−0.0478766	+	0.0876794i	−0.00208554	+	0.00381938i
$528$	0.545439	+	0.545439i	0.0237372	+	0.0237372i
$529$	−22.0244	−	6.62767i	−0.957582	−	0.288159i
$530$	−0.291896	+	1.19206i	−0.0126792	+	0.0517797i
$531$	6.76034	−	1.98502i	0.293374	−	0.0861423i
$532$	−0.125779	+	1.75862i	−0.00545322	+	0.0762460i
$533$	6.11364	−	28.1040i	0.264811	−	1.21732i
$534$	−0.0204317	−	0.142106i	−0.000884168	−	0.00614952i
$535$	25.4320	+	0.659923i	1.09952	+	0.0285310i
$536$	11.8203	+	5.39813i	0.510557	+	0.233164i
$537$	−9.81349	+	0.701874i	−0.423483	+	0.0302881i
$538$	1.26441	+	1.68905i	0.0545124	+	0.0728201i
$539$	−2.18005	−	4.77364i	−0.0939014	−	0.205615i
$540$	2.16111	−	0.574107i	0.0929994	−	0.0247057i
$541$	11.5020	+	3.37729i	0.494509	+	0.145201i	0.519472	−	0.854487i	$-0.326129\pi$
$541$	11.5020	+	3.37729i	0.494509	+	0.145201i	−0.0249629	+	0.999688i	$0.507947\pi$
$542$	−5.35147	+	14.3479i	−0.229865	+	0.616293i
$543$	−14.9748	+	11.2100i	−0.642629	+	0.481066i
$544$	−1.01128	+	1.16708i	−0.0433583	+	0.0500381i
$545$	5.76693	−	7.30099i	0.247028	−	0.312740i
$546$	1.08412	−	1.68693i	0.0463962	−	0.0721939i
$547$	6.66874	−	8.90839i	0.285135	−	0.380895i	−0.634990	−	0.772520i	$-0.718996\pi$
$547$	6.66874	−	8.90839i	0.285135	−	0.380895i	0.920125	+	0.391625i	$0.128087\pi$
$548$	−21.7464	−	4.73065i	−0.928961	−	0.202083i
$549$	−3.46746	−	4.00167i	−0.147988	−	0.170787i
$550$	3.20327	−	2.14808i	0.136588	−	0.0915943i
$551$		−	7.70591i		−	0.328283i
$552$	−4.74470	−	0.698428i	−0.201948	−	0.0297271i
$553$	0.718070	−	0.718070i	0.0305354	−	0.0305354i
$554$	7.39261	+	25.1769i	0.314082	+	1.06967i
$555$	−4.15163	+	2.12907i	−0.176227	+	0.0903738i
$556$	6.93820	−	4.45891i	0.294245	−	0.189100i
$557$	−22.0028	−	16.4711i	−0.932290	−	0.697904i	0.0210573	−	0.999778i	$-0.493297\pi$
$557$	−22.0028	−	16.4711i	−0.932290	−	0.697904i	−0.953348	+	0.301874i	$0.902388\pi$
$558$	−0.0632120	+	0.0137509i	−0.00267598	+	0.000582123i
$559$	−10.3148	+	22.5864i	−0.436272	+	0.955302i
$560$	−0.166527	+	0.977485i	−0.00703704	+	0.0413063i
$561$	−0.169525	+	1.17907i	−0.00715735	+	0.0497805i
$562$	−5.21967	−	1.94684i	−0.220179	−	0.0821224i
$563$	−4.36721	−	7.99794i	−0.184056	−	0.337073i	0.769317	−	0.638867i	$-0.220596\pi$
$563$	−4.36721	−	7.99794i	−0.184056	−	0.337073i	−0.953373	+	0.301794i	$0.902415\pi$
$564$	−0.997489	+	3.39714i	−0.0420019	+	0.143045i
$565$	−17.4560	+	25.6725i	−0.734379	+	1.08005i
$566$	4.44522	+	0.639126i	0.186846	+	0.0268645i
$567$	0.0316349	+	0.442313i	0.00132854	+	0.0185754i
$568$	−1.61329	−	4.32539i	−0.0676921	−	0.181489i
$569$	−4.88637	−	3.14028i	−0.204847	−	0.131647i	0.434195	−	0.900819i	$-0.357033\pi$
$569$	−4.88637	−	3.14028i	−0.204847	−	0.131647i	−0.639043	+	0.769171i	$0.720669\pi$
$570$	−0.864062	+	8.84845i	−0.0361916	+	0.370621i
$571$	−16.6126	−	25.8497i	−0.695215	−	1.08178i	−0.991927	−	0.126809i	$-0.959526\pi$
$571$	−16.6126	−	25.8497i	−0.695215	−	1.08178i	0.296712	−	0.954967i	$-0.404110\pi$
$572$	3.47924	+	0.248840i	0.145474	+	0.0104045i
$573$	22.6727	+	12.3802i	0.947167	+	0.517192i
$574$	−2.82042			−0.117722
$575$	−8.01566	+	22.5998i	−0.334276	+	0.942475i
$576$	−1.00000			−0.0416667
$577$	−22.4359	−	12.2509i	−0.934020	−	0.510014i	−0.0612379	−	0.998123i	$-0.519505\pi$
$577$	−22.4359	−	12.2509i	−0.934020	−	0.510014i	−0.872782	+	0.488110i	$0.837687\pi$
$578$	14.5780	+	1.04264i	0.606365	+	0.0433681i
$579$	7.23144	+	11.2523i	0.300528	+	0.467631i
$580$	0.421194	−	4.31325i	0.0174891	−	0.179098i
$581$	0.533955	+	0.343152i	0.0221522	+	0.0142363i
$582$	1.74129	+	4.66857i	0.0721787	+	0.193519i
$583$	−0.0302027	−	0.422289i	−0.00125087	−	0.0174894i
$584$	−0.258197	−	0.0371231i	−0.0106843	−	0.00153617i
$585$	5.68552	−	8.36169i	0.235067	−	0.345713i
$586$	4.10496	−	13.9802i	0.169574	−	0.577518i
$587$	10.7794	+	19.7410i	0.444913	+	0.814797i	0.999854	−	0.0170927i	$-0.00544104\pi$
$587$	10.7794	+	19.7410i	0.444913	+	0.814797i	−0.554941	+	0.831890i	$0.687259\pi$
$588$	6.37440	+	2.37753i	0.262876	+	0.0980477i
$589$	0.0366043	−	0.254589i	0.00150826	−	0.0104901i
$590$	−2.64590	+	15.5310i	−0.108930	+	0.639401i
$591$	−6.55321	+	14.3495i	−0.269563	+	0.590261i
$592$	2.03889	−	0.443533i	0.0837978	−	0.0182291i
$593$	−27.1654	−	20.3357i	−1.11555	−	0.835089i	−0.127901	−	0.991787i	$-0.540824\pi$
$593$	−27.1654	−	20.3357i	−1.11555	−	0.835089i	−0.987647	+	0.156698i	$0.949915\pi$
$594$	−0.648915	+	0.417032i	−0.0266253	+	0.0171110i
$595$	−1.36253	+	0.698740i	−0.0558582	+	0.0286456i
$596$	−0.822833	−	2.80231i	−0.0337046	−	0.114787i
$597$	−14.7965	+	14.7965i	−0.605582	+	0.605582i
$598$	−18.2833	+	11.6635i	−0.747660	+	0.476958i
$599$			20.9360i			0.855421i	0.903916	+	0.427710i	$0.140680\pi$
$599$			20.9360i			0.855421i	−0.903916	+	0.427710i	$0.859320\pi$
$600$	−0.967288	+	4.90554i	−0.0394894	+	0.200268i
$601$	8.00257	+	9.23546i	0.326432	+	0.376722i	0.895116	−	0.445834i	$-0.147093\pi$
$601$	8.00257	+	9.23546i	0.326432	+	0.376722i	−0.568684	+	0.822556i	$0.692547\pi$
$602$	2.37929	+	0.517582i	0.0969724	+	0.0210951i
$603$	−7.78734	+	10.4027i	−0.317125	+	0.423630i
$604$	−7.76932	+	12.0893i	−0.316129	+	0.491907i
$605$	14.4214	−	18.2577i	0.586314	−	0.742280i
$606$	0.252746	−	0.291684i	0.0102671	−	0.0118489i
$607$	23.6019	−	17.6681i	0.957970	−	0.717127i	−0.00118779	−	0.999999i	$-0.500378\pi$
$607$	23.6019	−	17.6681i	0.957970	−	0.717127i	0.959158	+	0.282872i	$0.0912872\pi$
$608$	1.38946	−	3.72528i	0.0563500	−	0.151080i
$609$	0.824633	+	0.242134i	0.0334158	+	0.00981176i
$610$	11.4430	−	3.03988i	0.463314	−	0.123081i
$611$	6.65097	+	14.5636i	0.269070	+	0.589180i
$612$	−0.925445	−	1.23625i	−0.0374089	−	0.0499724i
$613$	24.3694	−	1.74293i	0.984271	−	0.0703965i	0.430084	−	0.902789i	$-0.358484\pi$
$613$	24.3694	−	1.74293i	0.984271	−	0.0703965i	0.554187	+	0.832392i	$0.313029\pi$
$614$	−26.6829	−	12.1857i	−1.07683	−	0.491774i
$615$	−14.2172	−	0.368916i	−0.573293	−	0.0148761i
$616$	−0.0486798	−	0.338575i	−0.00196137	−	0.0136416i
$617$	−3.46216	+	15.9153i	−0.139381	+	0.640725i	0.853448	+	0.521179i	$0.174508\pi$
$617$	−3.46216	+	15.9153i	−0.139381	+	0.640725i	−0.992829	+	0.119546i	$0.961856\pi$
$618$	−0.335395	+	4.68943i	−0.0134916	+	0.188637i
$619$	−6.90268	+	2.02681i	−0.277442	+	0.0814644i	−0.417494	−	0.908680i	$-0.637091\pi$
$619$	−6.90268	+	2.02681i	−0.277442	+	0.0814644i	0.140051	+	0.990144i	$0.455273\pi$
$620$	0.0344041	−	0.140501i	0.00138170	−	0.00564266i
$621$	1.69103	−	4.48781i	0.0678585	−	0.180090i
$622$	12.3579	+	12.3579i	0.495505	+	0.495505i
$623$	−0.0305108	+	0.0558764i	−0.00122239	+	0.00223864i
$624$	−3.41751	+	2.96129i	−0.136810	+	0.118546i
$625$	23.1287	+	9.49015i	0.925148	+	0.379606i
$626$	−4.98748	+	0.717092i	−0.199340	+	0.0286608i
$627$	−0.651923	−	2.99684i	−0.0260353	−	0.119682i
$628$	−1.13453	+	0.423160i	−0.0452729	+	0.0168859i
$629$	2.43520	+	2.11011i	0.0970977	+	0.0841356i
$630$	−0.919749	−	0.370501i	−0.0366437	−	0.0147611i
$631$	−32.2381	+	14.7227i	−1.28338	+	0.586100i	−0.936124	−	0.351670i	$-0.885614\pi$
$631$	−32.2381	+	14.7227i	−1.28338	+	0.586100i	−0.347256	+	0.937770i	$0.612886\pi$
$632$	−2.00992	+	1.09750i	−0.0799504	+	0.0436562i
$633$	8.64636	−	4.72127i	0.343662	−	0.187654i
$634$	2.66242	−	1.21589i	0.105738	−	0.0482891i
$635$	35.9286	−	15.2945i	1.42578	−	0.606944i
$636$	0.414796	+	0.359423i	0.0164477	+	0.0142520i
$637$	28.8251	−	10.7512i	1.14209	−	0.425979i
$638$	0.317785	+	1.46084i	0.0125812	+	0.0578351i
$639$	4.56947	−	0.656991i	0.180766	−	0.0259902i
$640$	0.981345	−	2.00922i	0.0387911	−	0.0794214i
$641$	−7.93863	+	6.87886i	−0.313557	+	0.271699i	−0.797393	−	0.603460i	$-0.793788\pi$
$641$	−7.93863	+	6.87886i	−0.313557	+	0.271699i	0.483836	+	0.875158i	$0.339243\pi$
$642$	5.45258	−	9.98566i	0.215196	−	0.394103i
$643$	25.5325	+	25.5325i	1.00690	+	1.00690i	0.999976	+	0.00692632i	$0.00220474\pi$
$643$	25.5325	+	25.5325i	1.00690	+	1.00690i	0.00692632	+	0.999976i	$0.497795\pi$
$644$	1.49874	+	1.50882i	0.0590586	+	0.0594559i
$645$	11.9258	+	2.92025i	0.469580	+	0.114985i
$646$	5.89125	−	1.72983i	0.231788	−	0.0680591i
$647$	−1.92275	+	26.8836i	−0.0755912	+	1.05690i	0.808165	+	0.588956i	$0.200461\pi$
$647$	−1.92275	+	26.8836i	−0.0755912	+	1.05690i	−0.883756	+	0.467947i	$0.844994\pi$
$648$	0.212565	−	0.977147i	0.00835035	−	0.0383860i
$649$	−0.773460	−	5.37953i	−0.0303610	−	0.211165i
$650$	11.2210	+	19.6292i	0.440124	+	0.769919i
$651$	0.0260941	+	0.0119168i	0.00102271	+	0.000467056i
$652$	2.39089	−	0.170999i	0.0936343	−	0.00669686i
$653$	−1.49620	−	1.99869i	−0.0585508	−	0.0782147i	0.770310	−	0.637670i	$-0.220101\pi$
$653$	−1.49620	−	1.99869i	−0.0585508	−	0.0782147i	−0.828861	+	0.559455i	$0.811011\pi$
$654$	−1.72847	−	3.78481i	−0.0675883	−	0.147998i
$655$	15.0550	+	8.73507i	0.588247	+	0.341307i
$656$	6.10264	+	1.79190i	0.238268	+	0.0699618i
$657$	0.0911584	−	0.244405i	0.00355643	−	0.00953516i
$658$	1.25688	−	0.940886i	0.0489982	−	0.0366796i
$659$	28.2413	−	32.5922i	1.10013	−	1.26961i	0.139968	−	0.990156i	$-0.455300\pi$
$659$	28.2413	−	32.5922i	1.10013	−	1.26961i	0.960158	−	0.279457i	$-0.0901545\pi$
$660$	−0.201100	−	1.71306i	−0.00782779	−	0.0666810i
$661$	9.48267	−	14.7553i	0.368833	−	0.573915i	−0.606382	−	0.795173i	$-0.707380\pi$
$661$	9.48267	−	14.7553i	0.368833	−	0.573915i	0.975215	+	0.221258i	$0.0710163\pi$
$662$	−11.1266	+	14.8634i	−0.432449	+	0.577684i
$663$	−6.82361	−	1.48439i	−0.265007	−	0.0576488i
$664$	−0.937322	−	1.08173i	−0.0363751	−	0.0419791i
$665$	2.65817	−	2.91153i	0.103080	−	0.112904i
$666$			2.08657i			0.0808531i
$667$	−7.00417	−	6.11038i	−0.271203	−	0.236595i
$668$	−15.0065	+	15.0065i	−0.580620	+	0.580620i
$669$	6.83540	+	23.2792i	0.264272	+	0.900027i
$670$	−13.2592	−	25.8551i	−0.512247	−	0.998869i
$671$	−3.43598	+	2.20817i	−0.132645	+	0.0852455i
$672$	0.354994	+	0.265746i	0.0136942	+	0.0102514i
$673$	45.7996	−	9.96309i	1.76544	−	0.384049i	0.791560	−	0.611091i	$-0.209269\pi$
$673$	45.7996	−	9.96309i	1.76544	−	0.384049i	0.973885	+	0.227042i	$0.0729056\pi$
$674$	−11.7521	+	25.7336i	−0.452675	+	0.991219i
$675$	−4.58782	−	1.98793i	−0.176585	−	0.0765155i
$676$	−1.06005	+	7.37279i	−0.0407711	+	0.283569i
$677$	−35.7477	−	13.3332i	−1.37390	−	0.512436i	−0.449298	−	0.893382i	$-0.648326\pi$
$677$	−35.7477	−	13.3332i	−1.37390	−	0.512436i	−0.924597	+	0.380945i	$0.875599\pi$
$678$	6.65376	+	12.1855i	0.255536	+	0.467980i
$679$	0.622505	−	2.12006i	0.0238895	−	0.0813603i
$680$	3.39208	−	0.646234i	0.130080	−	0.0247819i
$681$	−19.3869	−	2.78742i	−0.742908	−	0.106814i
$682$	0.00355982	+	0.0497728i	0.000136313	+	0.00190590i
$683$	−6.54904	−	17.5586i	−0.250592	−	0.671863i	−0.999953	−	0.00970122i	$-0.996912\pi$
$683$	−6.54904	−	17.5586i	−0.250592	−	0.671863i	0.749361	−	0.662162i	$-0.230361\pi$
$684$	3.34480	+	2.14957i	0.127892	+	0.0821909i
$685$	31.6018	+	38.4416i	1.20744	+	1.46878i
$686$	−3.30926	−	5.14932i	−0.126348	−	0.196602i
$687$	3.68871	+	0.263822i	0.140733	+	0.0100654i
$688$	−4.81931	−	2.63154i	−0.183734	−	0.100327i
$689$	2.48193			0.0945538
$690$	7.35751	+	7.80173i	0.280096	+	0.297007i
$691$	13.4832			0.512927			0.256463	−	0.966554i	$-0.417443\pi$
$691$	13.4832			0.512927			0.256463	+	0.966554i	$0.417443\pi$
$692$	−6.24580	−	3.41047i	−0.237430	−	0.129646i
$693$	0.341186	+	0.0244021i	0.0129606	+	0.000926958i
$694$	4.96364	+	7.72358i	0.188417	+	0.293183i
$695$	−18.3546	−	1.79234i	−0.696228	−	0.0679875i
$696$	−1.63045	−	1.04783i	−0.0618021	−	0.0397178i
$697$	3.43242	+	9.20269i	0.130012	+	0.348577i
$698$	−1.99472	−	27.8898i	−0.0755013	−	1.05565i
$699$	−19.8193	−	2.84958i	−0.749634	−	0.107781i
$700$	1.64701	−	1.48439i	0.0622511	−	0.0561046i
$701$	8.53188	−	29.0569i	0.322245	−	1.09746i	−0.625973	−	0.779844i	$-0.715298\pi$
$701$	8.53188	−	29.0569i	0.322245	−	1.09746i	0.948218	−	0.317620i	$-0.102884\pi$
$702$	−2.16717	−	3.96888i	−0.0817946	−	0.149796i
$703$	−7.77308	−	2.89921i	−0.293167	−	0.109346i
$704$	−0.109777	+	0.763515i	−0.00413737	+	0.0287761i
$705$	6.45876	−	4.57843i	0.243251	−	0.172434i
$706$	−14.7279	+	32.2497i	−0.554293	+	1.21373i
$707$	−0.167237	+	0.0363802i	−0.00628960	+	0.00136822i
$708$	5.64041	+	4.22236i	0.211980	+	0.158686i
$709$	−35.0469	+	22.5233i	−1.31622	+	0.845880i	−0.994878	−	0.101084i	$-0.967769\pi$
$709$	−35.0469	+	22.5233i	−1.31622	+	0.845880i	−0.321338	+	0.946965i	$0.604132\pi$
$710$	−3.16419	+	9.82581i	−0.118750	+	0.368756i
$711$	−0.645180	−	2.19728i	−0.0241961	−	0.0824045i
$712$	0.101517	−	0.101517i	0.00380452	−	0.00380452i
$713$	−0.202379	−	0.235147i	−0.00757917	−	0.00880631i
$714$			0.684795i			0.0256278i
$715$	−5.76014	−	5.25890i	−0.215417	−	0.196672i
$716$	−6.44288	−	7.43548i	−0.240782	−	0.277877i
$717$	4.09255	+	0.890279i	0.152839	+	0.0332481i
$718$	13.3563	−	17.8420i	0.498454	−	0.665857i
$719$	4.89117	−	7.61081i	0.182410	−	0.283835i	−0.737992	−	0.674810i	$-0.764226\pi$
$719$	4.89117	−	7.61081i	0.182410	−	0.283835i	0.920401	+	0.390975i	$0.127862\pi$
$720$	1.75470	+	1.38601i	0.0653939	+	0.0516535i
$721$	1.36526	−	1.57559i	0.0508449	−	0.0586781i
$722$	2.55506	−	1.91269i	0.0950894	−	0.0711830i
$723$	10.0506	−	26.9468i	0.373787	−	1.00216i
$724$	−17.9481	−	5.27003i	−0.667035	−	0.195859i
$725$	−6.71728	+	6.98470i	−0.249473	+	0.259405i
$726$	−4.32239	−	9.46472i	−0.160419	−	0.351269i
$727$	−16.1846	−	21.6201i	−0.600254	−	0.801846i	0.392785	−	0.919630i	$-0.371512\pi$
$727$	−16.1846	−	21.6201i	−0.600254	−	0.801846i	−0.993039	+	0.117785i	$0.962421\pi$
$728$	2.00015	−	0.143053i	0.0741304	−	0.00530191i
$729$	0.909632	+	0.415415i	0.0336901	+	0.0153857i
$730$	0.401606	+	0.423003i	0.0148641	+	0.0156561i
$731$	−1.20676	−	8.39321i	−0.0446337	−	0.310434i
$732$	1.12553	−	5.17396i	0.0416006	−	0.191235i
$733$	−0.827583	+	11.5711i	−0.0305675	+	0.427389i	0.959008	+	0.283377i	$0.0914549\pi$
$733$	−0.827583	+	11.5711i	−0.0305675	+	0.427389i	−0.989576	+	0.144012i	$0.954000\pi$
$734$	−22.3957	+	6.57597i	−0.826641	+	0.242724i
$735$	−7.88990	−	13.0068i	−0.291024	−	0.479764i
$736$	−2.28427	−	4.21688i	−0.0841994	−	0.155436i
$737$	7.08773	+	7.08773i	0.261080	+	0.261080i
$738$	−3.04815	+	5.58228i	−0.112204	+	0.205486i
$739$	−21.3676	+	18.5151i	−0.786019	+	0.681090i	−0.952359	−	0.304979i	$-0.901351\pi$
$739$	−21.3676	+	18.5151i	−0.786019	+	0.681090i	0.166340	+	0.986068i	$0.446805\pi$
$740$	−4.19238	−	2.04765i	−0.154115	−	0.0752731i
$741$	17.7964	−	2.55873i	0.653767	−	0.0939974i
$742$	−0.0517353	−	0.237823i	−0.00189926	−	0.00873077i
$743$	15.6423	−	5.83428i	0.573861	−	0.214039i	−0.0457437	−	0.998953i	$-0.514566\pi$
$743$	15.6423	−	5.83428i	0.573861	−	0.214039i	0.619604	+	0.784914i	$0.287293\pi$
$744$	−0.0488897	−	0.0423632i	−0.00179238	−	0.00155311i
$745$	−2.44020	+	6.05768i	−0.0894021	+	0.221936i
$746$	−32.2578	+	14.7316i	−1.18104	+	0.539364i
$747$	1.25625	−	0.685963i	0.0459637	−	0.0250981i
$748$	−1.04549	+	0.570880i	−0.0382268	+	0.0208734i
$749$	−4.58928	+	2.09585i	−0.167689	+	0.0765808i
$750$	8.49643	−	7.26710i	0.310246	−	0.265357i
$751$	−9.84303	−	8.52904i	−0.359177	−	0.311229i	0.456514	−	0.889716i	$-0.349098\pi$
$751$	−9.84303	−	8.52904i	−0.359177	−	0.311229i	−0.815691	+	0.578487i	$0.803643\pi$
$752$	−3.31732	+	1.23730i	−0.120970	+	0.0451196i
$753$	−1.68818	−	7.76044i	−0.0615207	−	0.282806i
$754$	−8.67500	+	1.24728i	−0.315925	+	0.0454231i
$755$	30.3887	−	10.4448i	1.10596	−	0.380124i
$756$	−0.335132	+	0.290393i	−0.0121886	+	0.0105615i
$757$	−10.0009	+	18.3152i	−0.363487	+	0.665677i	−0.993864	−	0.110613i	$-0.964719\pi$
$757$	−10.0009	+	18.3152i	−0.363487	+	0.665677i	0.630376	+	0.776290i	$0.282901\pi$
$758$	8.03506	+	8.03506i	0.291847	+	0.291847i
$759$	−3.24087	−	1.78378i	−0.117636	−	0.0647472i
$760$	−7.60136	+	4.61096i	−0.275730	+	0.167257i
$761$	16.5681	−	4.86483i	0.600593	−	0.176350i	0.0327177	−	0.999465i	$-0.489584\pi$
$761$	16.5681	−	4.86483i	0.600593	−	0.176350i	0.567875	+	0.823115i	$0.307766\pi$
$762$	1.24580	−	17.4185i	0.0451305	−	0.631007i
$763$	−0.392201	+	1.80292i	−0.0141986	+	0.0652700i
$764$	3.67636	+	25.5697i	0.133006	+	0.925078i
$765$	−0.0895725	+	3.45193i	−0.00323850	+	0.124805i
$766$	−15.1773	−	6.93124i	−0.548378	−	0.250436i
$767$	31.7798	−	2.27293i	1.14750	−	0.0820709i
$768$	−0.599278	−	0.800541i	−0.0216246	−	0.0288870i
$769$	−8.38574	−	18.3622i	−0.302398	−	0.662158i	0.696042	−	0.718001i	$-0.254943\pi$
$769$	−8.38574	−	18.3622i	−0.302398	−	0.662158i	−0.998440	+	0.0558428i	$0.982215\pi$
$770$	−0.383850	+	0.661570i	−0.0138330	+	0.0238413i
$771$	−10.8829	−	3.19551i	−0.391938	−	0.115083i
$772$	−4.67432	+	12.5323i	−0.168232	+	0.451049i
$773$	18.9109	−	14.1565i	0.680179	−	0.509175i	−0.202422	−	0.979298i	$-0.564881\pi$
$773$	18.9109	−	14.1565i	0.680179	−	0.509175i	0.882601	+	0.470123i	$0.155790\pi$
$774$	3.59582	−	4.14980i	0.129249	−	0.149161i
$775$	−0.255105	+	0.198853i	−0.00916363	+	0.00714301i
$776$	−2.69387	+	4.19175i	−0.0967043	+	0.150475i
$777$	0.554498	−	0.740722i	0.0198925	−	0.0265733i
$778$	−28.5971	−	6.22092i	−1.02526	−	0.223031i
$779$	−16.5603	−	19.1116i	−0.593334	−	0.684744i
$780$	10.1011	−	0.459482i	0.361677	−	0.0164521i
$781$		−	3.56098i		−	0.127422i
$782$	3.09915	−	6.72643i	0.110825	−	0.240537i
$783$	1.37046	−	1.37046i	0.0489762	−	0.0489762i
$784$	1.91673	+	6.52777i	0.0684546	+	0.233135i
$785$	2.57727	+	0.829956i	0.0919868	+	0.0296224i
$786$	6.54833	−	4.20835i	0.233571	−	0.150107i
$787$	−3.45552	−	2.58677i	−0.123176	−	0.0922083i	0.535914	−	0.844273i	$-0.319967\pi$
$787$	−3.45552	−	2.58677i	−0.123176	−	0.0922083i	−0.659089	+	0.752065i	$0.729058\pi$
$788$	−15.4146	+	3.35324i	−0.549122	+	0.119454i
$789$	1.73553	−	3.80029i	0.0617866	−	0.135294i
$790$	5.04796	+	0.859983i	0.179598	+	0.0305968i
$791$	0.876181	−	6.09398i	0.0311534	−	0.216677i
$792$	−0.722732	−	0.269565i	−0.0256812	−	0.00957858i
$793$	−11.4751	−	21.0151i	−0.407492	−	0.746266i
$794$	5.67650	−	19.3324i	0.201452	−	0.686081i
$795$	−0.229681	−	1.20559i	−0.00814593	−	0.0427579i
$796$	−20.7125	−	2.97800i	−0.734134	−	0.105553i
$797$	−2.67733	−	37.4340i	−0.0948360	−	1.32598i	−0.792639	−	0.609691i	$-0.791294\pi$
$797$	−2.67733	−	37.4340i	−0.0948360	−	1.32598i	0.697803	−	0.716289i	$-0.254161\pi$
$798$	−0.616146	−	1.65195i	−0.0218113	−	0.0584784i
$799$	−4.59961	−	2.95599i	−0.162722	−	0.104575i
$800$	−4.50676	+	2.16543i	−0.159338	+	0.0765595i
$801$	0.0776183	+	0.120776i	0.00274251	+	0.00426742i
$802$	27.9284	+	1.99748i	0.986185	+	0.0705333i
$803$	−0.176600	−	0.0964309i	−0.00623208	−	0.00340297i
$804$	−12.9945			−0.458282
$805$	−0.538601	−	4.72480i	−0.0189832	−	0.166527i
$806$	−0.292531			−0.0103039
$807$	−1.85180	−	1.01116i	−0.0651865	−	0.0355945i
$808$	0.384970	+	0.0275336i	0.0135432	+	0.000968629i
$809$	23.3895	+	36.3948i	0.822332	+	1.27957i	0.957408	+	0.288738i	$0.0932356\pi$
$809$	23.3895	+	36.3948i	0.822332	+	1.27957i	−0.135076	+	0.990835i	$0.543128\pi$
$810$	−1.72732	+	1.41998i	−0.0606919	+	0.0498932i
$811$	4.20537	+	2.70263i	0.147671	+	0.0949021i	0.612390	−	0.790556i	$-0.290208\pi$
$811$	4.20537	+	2.70263i	0.147671	+	0.0949021i	−0.464719	+	0.885458i	$0.653845\pi$
$812$	0.300346	+	0.805258i	0.0105401	+	0.0282590i
$813$	−1.09244	−	15.2743i	−0.0383136	−	0.535695i
$814$	1.59313	+	0.229058i	0.0558392	+	0.00802847i
$815$	−4.43230	−	3.01373i	−0.155257	−	0.105567i
$816$	0.435070	−	1.48171i	0.0152305	−	0.0518704i
$817$	10.4629	+	19.1614i	0.366051	+	0.670373i
$818$	−13.4105	−	5.00185i	−0.468886	−	0.174886i
$819$	−0.285378	+	1.98484i	−0.00997190	+	0.0693561i
$820$	−8.22473	−	11.6026i	−0.287220	−	0.405179i
$821$	9.96499	−	21.8203i	0.347781	−	0.761533i	−0.652213	−	0.758036i	$-0.726159\pi$
$821$	9.96499	−	21.8203i	0.347781	−	0.761533i	0.999994	−	0.00349784i	$-0.00111340\pi$
$822$	21.7464	−	4.73065i	0.758494	−	0.165000i
$823$	−9.55879	−	7.15562i	−0.333199	−	0.249429i	0.419558	−	0.907729i	$-0.362185\pi$
$823$	−9.55879	−	7.15562i	−0.333199	−	0.249429i	−0.752756	+	0.658299i	$0.771276\pi$
$824$	−3.95508	+	2.54177i	−0.137782	+	0.0885469i
$825$	−2.02145	+	3.28464i	−0.0703779	+	0.114357i
$826$	−0.880241	−	2.99783i	−0.0306275	−	0.104308i
$827$	9.69107	−	9.69107i	0.336991	−	0.336991i	−0.518242	−	0.855234i	$-0.673413\pi$
$827$	9.69107	−	9.69107i	0.336991	−	0.336991i	0.855234	+	0.518242i	$0.173413\pi$
$828$	4.60607	−	1.33571i	0.160072	−	0.0464191i
$829$			37.5405i			1.30383i	0.758290	+	0.651917i	$0.226035\pi$
$829$			37.5405i			1.30383i	−0.758290	+	0.651917i	$0.773965\pi$
$830$	0.145438	+	3.19724i	0.00504821	+	0.110978i
$831$	−17.1834	−	19.8307i	−0.596087	−	0.687921i
$832$	−4.41867	−	0.961223i	−0.153190	−	0.0333244i
$833$	−6.29614	+	8.41065i	−0.218148	+	0.291412i
$834$	−4.45891	+	6.93820i	−0.154399	+	0.240250i
$835$	47.1312	−	5.53281i	1.63104	−	0.191471i
$836$	2.00841	−	2.31783i	0.0694624	−	0.0801639i
$837$	0.0517873	−	0.0387675i	0.00179003	−	0.00134000i
$838$	0.926614	−	2.48435i	0.0320093	−	0.0858204i
$839$	49.0805	+	14.4113i	1.69445	+	0.497534i	0.979466	−	0.201610i	$-0.0646175\pi$
$839$	49.0805	+	14.4113i	1.69445	+	0.497534i	0.714980	+	0.699145i	$0.246436\pi$
$840$	−0.254584	−	0.958330i	−0.00878398	−	0.0330655i
$841$	10.4866	+	22.9625i	0.361607	+	0.791809i
$842$	10.0708	+	13.4530i	0.347062	+	0.463621i
$843$	5.55673	−	0.397425i	0.191384	−	0.0136880i
$844$	8.96114	+	4.09242i	0.308455	+	0.140867i
$845$	12.0788	−	11.4678i	0.415524	−	0.394505i
$846$	−0.503873	−	3.50452i	−0.0173235	−	0.120488i
$847$	−0.980781	+	4.50858i	−0.0337000	+	0.154917i
$848$	−0.0391548	+	0.547456i	−0.00134458	+	0.0187997i
$849$	−4.30901	+	1.26524i	−0.147885	+	0.0434229i
$850$	−6.84777	−	3.56750i	−0.234877	−	0.122364i
$851$	−8.79884	+	4.76631i	−0.301620	+	0.163387i
$852$	3.26433	+	3.26433i	0.111834	+	0.111834i
$853$	−17.9910	+	32.9481i	−0.616002	+	1.12812i	0.364424	+	0.931233i	$0.381266\pi$
$853$	−17.9910	+	32.9481i	−0.616002	+	1.12812i	−0.980426	+	0.196890i	$0.936916\pi$
$854$	−1.77451	+	1.53762i	−0.0607225	+	0.0526164i
$855$	−2.88980	−	8.40778i	−0.0988291	−	0.287540i
$856$	11.2615	−	1.61917i	0.384912	−	0.0553419i
$857$	−4.23874	−	19.4852i	−0.144792	−	0.665600i	−0.991124	−	0.132943i	$-0.957557\pi$
$857$	−4.23874	−	19.4852i	−0.144792	−	0.665600i	0.846331	−	0.532657i	$-0.178806\pi$
$858$	−3.26820	+	1.21898i	−0.111575	+	0.0416152i
$859$	−15.5622	−	13.4847i	−0.530976	−	0.460093i	0.347636	−	0.937629i	$-0.386984\pi$
$859$	−15.5622	−	13.4847i	−0.530976	−	0.460093i	−0.878612	+	0.477536i	$0.841530\pi$
$860$	4.80911	+	11.2972i	0.163989	+	0.385230i
$861$	2.56554	−	1.17164i	0.0874335	−	0.0399295i
$862$	14.5479	−	7.94378i	0.495505	−	0.270566i
$863$	−42.8117	+	23.3769i	−1.45733	+	0.795760i	−0.995817	−	0.0913755i	$-0.970874\pi$
$863$	−42.8117	+	23.3769i	−1.45733	+	0.795760i	−0.461509	+	0.887135i	$0.652692\pi$
$864$	0.909632	−	0.415415i	0.0309463	−	0.0141327i
$865$	6.23259	+	14.6411i	0.211914	+	0.497812i
$866$	−17.8822	−	15.4950i	−0.607661	−	0.526542i
$867$	−13.6937	+	5.10750i	−0.465064	+	0.173460i
$868$	0.00609775	+	0.0280309i	0.000206971	+	0.000951431i
$869$	−1.74848	+	0.251394i	−0.0593132	+	0.00852795i
$870$	1.40866	+	4.09844i	0.0477580	+	0.138950i
$871$	−44.4090	+	38.4806i	−1.50474	+	1.30387i
$872$	1.99407	−	3.65186i	0.0675276	−	0.123668i
$873$	−3.52333	−	3.52333i	−0.119247	−	0.119247i
$874$	−1.42406	+	19.0148i	−0.0481694	+	0.643186i
$875$	−4.94738	+	0.321892i	−0.167252	+	0.0108819i
$876$	0.250286	−	0.0734905i	0.00845637	−	0.00248301i
$877$	2.24500	−	31.3893i	0.0758084	−	1.05994i	−0.807106	−	0.590406i	$-0.798968\pi$
$877$	2.24500	−	31.3893i	0.0758084	−	1.05994i	0.882915	−	0.469534i	$-0.155578\pi$
$878$	−0.0719302	+	0.330658i	−0.00242753	+	0.0111592i
$879$	2.07359	+	14.4221i	0.0699404	+	0.486446i
$880$	1.25086	−	1.18759i	0.0421666	−	0.0400337i
$881$	10.4929	+	4.79196i	0.353516	+	0.161445i	0.584255	−	0.811570i	$-0.301387\pi$
$881$	10.4929	+	4.79196i	0.353516	+	0.161445i	−0.230739	+	0.973016i	$0.574114\pi$
$882$	−6.78602	+	0.485346i	−0.228497	+	0.0163425i
$883$	−7.40544	−	9.89251i	−0.249213	−	0.332909i	0.658438	−	0.752635i	$-0.271217\pi$
$883$	−7.40544	−	9.89251i	−0.249213	−	0.332909i	−0.907651	+	0.419725i	$0.862126\pi$
$884$	−2.90093	−	6.35214i	−0.0975687	−	0.213646i
$885$	−4.04501	−	15.2266i	−0.135972	−	0.511838i
$886$	−23.2771	−	6.83478i	−0.782010	−	0.229619i
$887$	−4.55925	+	12.2238i	−0.153085	+	0.410436i	−0.990742	−	0.135761i	$-0.956652\pi$
$887$	−4.55925	+	12.2238i	−0.153085	+	0.410436i	0.837657	+	0.546197i	$0.183925\pi$
$888$	−1.67039	+	1.25044i	−0.0560546	+	0.0419619i
$889$	−5.07115	+	5.85242i	−0.170081	+	0.196284i
$890$	−0.318837	+	0.0374288i	−0.0106874	+	0.00125462i
$891$	0.417032	−	0.648915i	0.0139711	−	0.0217395i
$892$	−14.5397	+	19.4227i	−0.486825	+	0.650321i
$893$	13.7554	+	2.99231i	0.460308	+	0.100134i
$894$	1.91260	+	2.20726i	0.0639668	+	0.0738217i
$895$	0.999697	+	21.9770i	0.0334162	+	0.734608i
$896$			0.443443i			0.0148144i
$897$	11.7859	−	18.2047i	0.393519	−	0.607837i
$898$	25.2216	−	25.2216i	0.841655	−	0.841655i
$899$	−0.0353230	−	0.120299i	−0.00117809	−	0.00401220i
$900$	−1.15796	−	4.86407i	−0.0385987	−	0.162136i
$901$	−0.713028	+	0.458235i	−0.0237544	+	0.0152660i
$902$	3.92754	+	2.94012i	0.130773	+	0.0978952i
$903$	−2.37929	+	0.517582i	−0.0791777	+	0.0172240i
$904$	−5.76751	+	12.6291i	−0.191824	+	0.420037i
$905$	24.1892	+	34.1235i	0.804077	+	1.13430i
$906$	2.04515	−	14.2243i	0.0679455	−	0.472571i
$907$	−38.0986	−	14.2101i	−1.26504	−	0.471837i	−0.374709	−	0.927143i	$-0.622257\pi$
$907$	−38.0986	−	14.2101i	−1.26504	−	0.471837i	−0.890335	+	0.455305i	$0.849530\pi$
$908$	−9.38670	−	17.1905i	−0.311509	−	0.570485i
$909$	−0.108736	+	0.370320i	−0.00360654	+	0.0122827i
$910$	−3.70793	−	2.52120i	−0.122917	−	0.0835771i
$911$	−3.74754	−	0.538815i	−0.124162	−	0.0178517i	0.0799539	−	0.996799i	$-0.474523\pi$
$911$	−3.74754	−	0.538815i	−0.124162	−	0.0178517i	−0.204115	+	0.978947i	$0.565432\pi$
$912$	0.283642	+	3.96584i	0.00939234	+	0.131322i
$913$	−0.385836	−	1.03447i	−0.0127693	−	0.0342359i
$914$	4.90095	+	3.14965i	0.162109	+	0.104181i
$915$	−9.14611	+	7.51876i	−0.302361	+	0.248563i
$916$	1.99936	+	3.11107i	0.0660607	+	0.102793i
$917$	−3.44297	−	0.246246i	−0.113697	−	0.00813176i
$918$	1.35537	+	0.740089i	0.0447339	+	0.0244266i
$919$	20.4472			0.674490			0.337245	−	0.941417i	$-0.390505\pi$
$919$	20.4472			0.674490			0.337245	+	0.941417i	$0.390505\pi$
$920$	−1.83642	+	10.5654i	−0.0605448	+	0.348331i
$921$	29.3337			0.966580
$922$	4.92198	+	2.68760i	0.162097	+	0.0885115i
$923$	20.8225	+	1.48926i	0.685381	+	0.0490194i
$924$	0.184930	+	0.287757i	0.00608375	+	0.00946650i
$925$	4.51833	+	9.40370i	0.148562	+	0.309192i
$926$	17.7998	+	11.4392i	0.584937	+	0.375916i
$927$	−1.64297	−	4.40498i	−0.0539623	−	0.144679i
$928$	−0.138264	−	1.93318i	−0.00453874	−	0.0634598i
$929$	11.9457	+	1.71753i	0.391926	+	0.0563504i	0.335461	−	0.942054i	$-0.391108\pi$
$929$	11.9457	+	1.71753i	0.391926	+	0.0563504i	0.0564651	+	0.998405i	$0.482017\pi$
$930$	0.0270711	+	0.142096i	0.000887698	+	0.00465952i
$931$	7.62085	−	25.9542i	0.249763	−	0.850616i
$932$	−9.59605	−	17.5739i	−0.314329	−	0.575651i
$933$	−16.3747	−	6.10746i	−0.536085	−	0.199949i
$934$	5.98167	−	41.6034i	0.195726	−	1.36131i
$935$	2.62576	+	0.447332i	0.0858717	+	0.0146293i
$936$	1.87851	−	4.11337i	0.0614011	−	0.134450i
$937$	−20.8117	+	4.52731i	−0.679888	+	0.147901i	−0.539231	−	0.842158i	$-0.681285\pi$
$937$	−20.8117	+	4.52731i	−0.679888	+	0.147901i	−0.140657	+	0.990058i	$0.544921\pi$
$938$	4.61299	+	3.45324i	0.150620	+	0.112752i
$939$	4.23888	−	2.72417i	0.138331	−	0.0888998i
$940$	7.53581	+	2.42675i	0.245791	+	0.0791518i
$941$	−6.02064	−	20.5044i	−0.196267	−	0.668425i	−0.997538	−	0.0701234i	$-0.977661\pi$
$941$	−6.02064	−	20.5044i	−0.196267	−	0.668425i	0.801271	−	0.598302i	$-0.204157\pi$
$942$	0.856222	−	0.856222i	0.0278972	−	0.0278972i
$943$	−30.5026	−	0.102259i	−0.993302	−	0.00333001i
$944$			7.04574i			0.229319i
$945$	0.990544	−	0.0450583i	0.0322224	−	0.00146575i
$946$	−2.77369	−	3.20101i	−0.0901806	−	0.104074i
$947$	−44.0541	−	9.58337i	−1.43156	−	0.311418i	−0.571080	−	0.820894i	$-0.693475\pi$
$947$	−44.0541	−	9.58337i	−1.43156	−	0.311418i	−0.860485	+	0.509477i	$0.829839\pi$
$948$	1.37237	−	1.83327i	0.0445726	−	0.0595420i
$949$	0.637727	−	0.992323i	0.0207015	−	0.0322122i
$950$	19.7290	+	2.44469i	0.640092	+	0.0793162i
$951$	−1.91673	+	2.21202i	−0.0621541	+	0.0717297i
$952$	−0.548206	+	0.410382i	−0.0177675	+	0.0133006i
$953$	−7.39182	+	19.8182i	−0.239445	+	0.641976i	−0.999973	−	0.00732870i	$-0.997667\pi$
$953$	−7.39182	+	19.8182i	−0.239445	+	0.641976i	0.760529	+	0.649304i	$0.224940\pi$
$954$	−0.526622	−	0.154630i	−0.0170500	−	0.00500633i
$955$	28.9888	−	49.9626i	0.938057	−	1.61675i
$956$	1.73987	+	3.80978i	0.0562713	+	0.123217i
$957$	−0.895921	−	1.19681i	−0.0289610	−	0.0386874i
$958$	−3.89866	+	0.278838i	−0.125960	+	0.00900884i
$959$	−8.97701	−	4.09966i	−0.289883	−	0.132385i
$960$	−0.0580032	+	2.23532i	−0.00187205	+	0.0721445i
$961$	4.41116	+	30.6803i	0.142296	+	0.989688i
$962$	−2.00566	+	9.21988i	−0.0646652	+	0.297261i
$963$	−0.811651	+	11.3484i	−0.0261551	+	0.365696i
$964$	27.5951	−	8.10265i	0.888778	−	0.260969i
$965$	25.5720	−	15.5119i	0.823191	−	0.499345i
$966$	−1.99009	−	0.749874i	−0.0640300	−	0.0241268i
$967$	−23.3542	−	23.3542i	−0.751021	−	0.751021i	0.223649	−	0.974670i	$-0.428203\pi$
$967$	−23.3542	−	23.3542i	−0.751021	−	0.751021i	−0.974670	+	0.223649i	$0.928203\pi$
$968$	4.98658	−	9.13224i	0.160275	−	0.293521i
$969$	−4.64027	+	4.02082i	−0.149067	+	0.129167i
$970$	10.5367	−	3.62154i	0.338314	−	0.116281i
$971$	−15.6975	+	2.25696i	−0.503757	+	0.0724293i	−0.389509	−	0.921023i	$-0.627355\pi$
$971$	−15.6975	+	2.25696i	−0.503757	+	0.0724293i	−0.114249	+	0.993452i	$0.536446\pi$
$972$	0.212565	+	0.977147i	0.00681803	+	0.0313420i
$973$	3.42668	−	1.27809i	0.109854	−	0.0409736i
$974$	−20.9425	−	18.1468i	−0.671041	−	0.581460i
$975$	−18.3612	−	13.1939i	−0.588030	−	0.422544i
$976$	4.81647	−	2.19961i	0.154171	−	0.0704077i
$977$	30.1824	−	16.4808i	0.965620	−	0.527268i	0.0825893	−	0.996584i	$-0.473681\pi$
$977$	30.1824	−	16.4808i	0.965620	−	0.527268i	0.883031	+	0.469315i	$0.155499\pi$
$978$	−2.10379	+	1.14876i	−0.0672718	+	0.0367332i
$979$	0.100735	−	0.0460043i	0.00321951	−	0.00147030i
$980$	5.68427	−	14.1109i	0.181577	−	0.450756i
$981$	3.14453	+	2.72475i	0.100397	+	0.0869947i
$982$	−34.5810	+	12.8980i	−1.10352	+	0.411593i
$983$	6.25716	+	28.7637i	0.199572	+	0.917420i	0.962573	+	0.271022i	$0.0873616\pi$
$983$	6.25716	+	28.7637i	0.199572	+	0.917420i	−0.763001	+	0.646398i	$0.776275\pi$
$984$	−6.29553	+	0.905161i	−0.200694	+	0.0288555i
$985$	31.6956	+	15.4808i	1.00991	+	0.493260i
$986$	2.26194	−	1.95998i	0.0720349	−	0.0624186i
$987$	−0.752437	+	1.37799i	−0.0239503	+	0.0438618i
$988$	12.7133	+	12.7133i	0.404466	+	0.404466i
$989$	25.7130	+	5.68388i	0.817627	+	0.180737i
$990$	0.894560	+	1.47472i	0.0284310	+	0.0468696i
$991$	−3.65555	+	1.07337i	−0.116122	+	0.0340966i	−0.339277	−	0.940686i	$-0.610183\pi$
$991$	−3.65555	+	1.07337i	−0.116122	+	0.0340966i	0.223155	+	0.974783i	$0.428364\pi$
$992$	0.00461496	−	0.0645255i	0.000146525	−	0.00204869i
$993$	3.94665	−	18.1424i	0.125243	−	0.575733i
$994$	−0.291338	−	2.02630i	−0.00924068	−	0.0642704i
$995$	32.2167	+	33.9332i	1.02134	+	1.07575i
$996$	1.30198	+	0.594596i	0.0412549	+	0.0188405i
$997$	37.4678	−	2.67975i	1.18662	−	0.0848685i	0.535962	−	0.844242i	$-0.319949\pi$
$997$	37.4678	−	2.67975i	1.18662	−	0.0848685i	0.650655	+	0.759374i	$0.274494\pi$
$998$	21.2761	+	28.4215i	0.673483	+	0.899668i
$999$	−0.866794	−	1.89801i	−0.0274242	−	0.0600505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.37.3	✓	240
5.3	odd	4	inner	690.2.w.b.313.4	yes	240
23.5	odd	22	inner	690.2.w.b.97.4	yes	240
115.28	even	44	inner	690.2.w.b.373.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.37.3	✓	240	1.1	even	1	trivial
690.2.w.b.97.4	yes	240	23.5	odd	22	inner
690.2.w.b.313.4	yes	240	5.3	odd	4	inner
690.2.w.b.373.3	yes	240	115.28	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(0.217321 - 2.22548i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.154967 + 0.415484i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(0.217321 - 2.22548i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.154967 + 0.415484i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-1.25730 + 1.84911i) q^{10} +(0.217319 - 0.740121i) q^{11} +(0.479249 + 0.877679i) q^{12} +(4.23690 + 1.58028i) q^{13} +(0.0631085 - 0.438929i) q^{14} +(0.375531 - 2.20431i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-1.50898 + 0.328258i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(3.34480 - 2.14957i) q^{19} +(1.98969 - 1.02036i) q^{20} +(0.124932 + 0.425480i) q^{21} +(-0.545439 + 0.545439i) q^{22} +(0.698428 - 4.74470i) q^{23} -1.00000i q^{24} +(-4.90554 - 0.967288i) q^{25} +(-2.96129 - 3.41751i) q^{26} +(0.977147 + 0.212565i) q^{27} +(-0.265746 + 0.354994i) q^{28} +(1.04783 - 1.63045i) q^{29} +(-1.38601 + 1.75470i) q^{30} +(0.0423632 - 0.0488897i) q^{31} +(0.800541 - 0.599278i) q^{32} +(0.269565 - 0.722732i) q^{33} +(1.48171 + 0.435070i) q^{34} +(0.958330 - 0.254584i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-1.25044 - 1.67039i) q^{37} +(-3.96584 + 0.283642i) q^{38} +(4.11337 + 1.87851i) q^{39} +(-2.23532 - 0.0580032i) q^{40} +(-0.905161 - 6.29553i) q^{41} +(0.0942606 - 0.433309i) q^{42} +(-0.391721 + 5.47698i) q^{43} +(0.740121 - 0.217319i) q^{44} +(0.531828 - 2.17190i) q^{45} +(-2.88689 + 3.82960i) q^{46} +(2.50355 + 2.50355i) q^{47} +(-0.479249 + 0.877679i) q^{48} +(5.14164 - 4.45525i) q^{49} +(3.84192 + 3.19995i) q^{50} +(-1.52855 + 0.219772i) q^{51} +(0.961223 + 4.41867i) q^{52} +(0.514249 - 0.191805i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-1.59990 - 0.644484i) q^{55} +(0.403370 - 0.184213i) q^{56} +(3.48963 - 1.90548i) q^{57} +(-1.70105 + 0.928842i) q^{58} +(6.40903 - 2.92691i) q^{59} +(2.05741 - 0.875822i) q^{60} +(-4.00167 - 3.46746i) q^{61} +(-0.0606116 + 0.0226070i) q^{62} +(0.0942606 + 0.433309i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(4.43766 - 9.08572i) q^{65} +(-0.582960 + 0.505138i) q^{66} +(-6.22762 + 11.4050i) q^{67} +(-1.09196 - 1.09196i) q^{68} +(1.03513 - 4.68279i) q^{69} +(-0.963115 - 0.235836i) q^{70} +(4.42946 - 1.30061i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(0.0554481 - 0.254891i) q^{73} +(0.296950 + 2.06534i) q^{74} +(-4.82404 - 1.31478i) q^{75} +(3.61667 + 1.65168i) q^{76} +(0.341186 - 0.0244021i) q^{77} +(-2.70994 - 3.62006i) q^{78} +(-0.951318 - 2.08310i) q^{79} +(1.93409 + 1.12218i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-2.22269 + 5.95926i) q^{82} +(1.14584 - 0.857764i) q^{83} +(-0.290393 + 0.335132i) q^{84} +(0.402599 + 3.42954i) q^{85} +(2.96864 - 4.61930i) q^{86} +(1.16147 - 1.55155i) q^{87} +(-0.753738 - 0.163966i) q^{88} +(0.0940165 + 0.108501i) q^{89} +(-1.50766 + 1.65135i) q^{90} +2.00526i q^{91} +(4.36910 - 1.97762i) q^{92} +(0.0457430 - 0.0457430i) q^{93} +(-0.997489 - 3.39714i) q^{94} +(-4.05694 - 7.91094i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-3.98889 - 2.98604i) q^{97} +(-6.64788 + 1.44616i) q^{98} +(0.320437 - 0.701660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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