LMFDB - Embedded newform 279.2.bb.a.103.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [279,2,Mod(7,279)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(279, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 28]))

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

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

chi := DirichletCharacter("279.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.bb (of order $15$, degree $8$, 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:	$2.22782621639$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			103.18
Character	$\chi$	$=$	279.103
Dual form			279.2.bb.a.214.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0863656 - 0.821714i) q^{2} +(1.71910 + 0.211413i) q^{3} +(1.28854 + 0.273888i) q^{4} -1.91797 q^{5} +(0.322192 - 1.39435i) q^{6} +(0.517805 + 1.59364i) q^{7} +(0.846987 - 2.60676i) q^{8} +(2.91061 + 0.726880i) q^{9} +(-0.165647 + 1.57602i) q^{10} +(-2.69176 - 0.572151i) q^{11} +(2.15723 + 0.743254i) q^{12} +(4.78011 - 3.47295i) q^{13} +(1.35424 - 0.287852i) q^{14} +(-3.29718 - 0.405484i) q^{15} +(0.338017 + 0.150495i) q^{16} +(1.99882 + 2.21991i) q^{17} +(0.848664 - 2.32891i) q^{18} +(-5.46720 + 2.43415i) q^{19} +(-2.47138 - 0.525309i) q^{20} +(0.553242 + 2.84909i) q^{21} +(-0.702620 + 2.16244i) q^{22} +(-1.97584 - 2.19440i) q^{23} +(2.00716 - 4.30222i) q^{24} -1.32139 q^{25} +(-2.44094 - 4.22783i) q^{26} +(4.84996 + 1.86492i) q^{27} +(0.230734 + 2.19529i) q^{28} +(-0.788137 + 7.49862i) q^{29} +(-0.617955 + 2.67432i) q^{30} +(-4.78907 - 2.83987i) q^{31} +(2.89377 - 5.01215i) q^{32} +(-4.50644 - 1.55266i) q^{33} +(1.99676 - 1.45073i) q^{34} +(-0.993134 - 3.05655i) q^{35} +(3.55135 + 1.73379i) q^{36} +(-1.14441 + 1.98217i) q^{37} +(1.52800 + 4.70270i) q^{38} +(8.95171 - 4.95978i) q^{39} +(-1.62450 + 4.99969i) q^{40} +(-9.01317 - 6.54845i) q^{41} +(2.38892 - 0.208543i) q^{42} +(-4.37377 - 3.17773i) q^{43} +(-3.31174 - 1.47448i) q^{44} +(-5.58246 - 1.39413i) q^{45} +(-1.97381 + 1.43406i) q^{46} +(0.784681 + 0.349363i) q^{47} +(0.549268 + 0.330176i) q^{48} +(3.39156 - 2.46411i) q^{49} +(-0.114122 + 1.08580i) q^{50} +(2.96685 + 4.23882i) q^{51} +(7.11056 - 3.16583i) q^{52} +(-3.07734 + 0.654108i) q^{53} +(1.95130 - 3.82421i) q^{54} +(5.16272 + 1.09737i) q^{55} +4.59281 q^{56} +(-9.91327 + 3.02872i) q^{57} +(6.09366 + 1.29525i) q^{58} +(6.82682 + 3.03950i) q^{59} +(-4.13750 - 1.42554i) q^{60} +(3.24200 + 5.61530i) q^{61} +(-2.74717 + 3.68998i) q^{62} +(0.348743 + 5.01484i) q^{63} +(-3.26995 - 2.37576i) q^{64} +(-9.16811 + 6.66102i) q^{65} +(-1.66504 + 3.56891i) q^{66} -4.83641 q^{67} +(1.96755 + 3.40789i) q^{68} +(-2.93275 - 4.19010i) q^{69} +(-2.59738 + 0.552091i) q^{70} +(-3.20758 + 0.681791i) q^{71} +(4.36005 - 6.97160i) q^{72} +(-7.77780 + 8.63812i) q^{73} +(1.52994 + 1.11157i) q^{74} +(-2.27160 - 0.279358i) q^{75} +(-7.71139 + 1.63911i) q^{76} +(-0.482003 - 4.58596i) q^{77} +(-3.30240 - 7.78410i) q^{78} +(-0.988541 + 3.04242i) q^{79} +(-0.648306 - 0.288644i) q^{80} +(7.94329 + 4.23132i) q^{81} +(-6.15938 + 6.84068i) q^{82} +(3.82141 - 1.70140i) q^{83} +(-0.0674571 + 3.82270i) q^{84} +(-3.83367 - 4.25772i) q^{85} +(-2.98893 + 3.31954i) q^{86} +(-2.94019 + 12.7243i) q^{87} +(-3.77135 + 6.53217i) q^{88} +(-0.355098 - 1.09288i) q^{89} +(-1.62771 + 4.46678i) q^{90} +(8.00979 + 5.81946i) q^{91} +(-1.94494 - 3.36873i) q^{92} +(-7.63250 - 5.89448i) q^{93} +(0.354846 - 0.614611i) q^{94} +(10.4859 - 4.66864i) q^{95} +(6.03430 - 8.00461i) q^{96} +(-3.26035 + 3.62098i) q^{97} +(-1.73188 - 2.99970i) q^{98} +(-7.41878 - 3.62189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 3 q^{2} - 11 q^{3} + 25 q^{4} - 6 q^{5} - 8 q^{6} - 5 q^{7} - 29 q^{8} - 11 q^{9} - 30 q^{10} - 14 q^{11} - 8 q^{12} + q^{13} - 2 q^{14} - 26 q^{15} + 25 q^{16} - 26 q^{17} - 3 q^{18} - 20 q^{19}+ \cdots - 74 q^{99}+O(q^{100}) $ 240 * q - 3 * q^2 - 11 * q^3 + 25 * q^4 - 6 * q^5 - 8 * q^6 - 5 * q^7 - 29 * q^8 - 11 * q^9 - 30 * q^10 - 14 * q^11 - 8 * q^12 + q^13 - 2 * q^14 - 26 * q^15 + 25 * q^16 - 26 * q^17 - 3 * q^18 - 20 * q^19 - 84 * q^20 + q^21 - 11 * q^22 - 6 * q^23 + 14 * q^24 + 174 * q^25 + 22 * q^26 + 70 * q^27 - 60 * q^28 - 15 * q^29 - 6 * q^30 - 20 * q^31 - 24 * q^32 - 40 * q^33 + 25 * q^34 - 15 * q^35 - 8 * q^36 + 2 * q^37 + 37 * q^38 - q^39 + 6 * q^40 - 23 * q^41 - 134 * q^42 + 9 * q^43 - 77 * q^44 - 127 * q^45 - 2 * q^46 - 32 * q^47 + 26 * q^48 - 41 * q^49 - 37 * q^50 + 13 * q^51 + 3 * q^52 - 56 * q^53 - 29 * q^54 - 30 * q^55 - 62 * q^56 - 40 * q^57 + 76 * q^58 - 3 * q^59 + 41 * q^60 - q^61 - 51 * q^62 + 77 * q^63 - 51 * q^64 + 25 * q^65 - 130 * q^66 - 16 * q^67 + 87 * q^68 + 32 * q^69 - 90 * q^70 - 7 * q^71 + 112 * q^72 - 11 * q^73 - 9 * q^74 - 157 * q^75 + 12 * q^76 + 10 * q^77 + 50 * q^78 + 24 * q^79 + 142 * q^80 + 61 * q^81 - 2 * q^82 + 60 * q^83 + 132 * q^84 - 33 * q^85 - 152 * q^86 - 88 * q^87 + 2 * q^88 + 58 * q^89 + 96 * q^90 + 72 * q^92 + 31 * q^93 + 2 * q^94 - 63 * q^95 + 137 * q^96 - 30 * q^97 + 33 * q^98 - 74 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.0863656	−	0.821714i	0.0610697	−	0.581040i	−0.920608	−	0.390489i	$-0.872306\pi$
$2$	0.0863656	−	0.821714i	0.0610697	−	0.581040i	0.981677	−	0.190551i	$-0.0610273\pi$
$3$	1.71910	+	0.211413i	0.992523	+	0.122059i
$3$	1.71910	+	0.211413i	0.992523	+	0.122059i
$4$	1.28854	+	0.273888i	0.644270	+	0.136944i
$5$	−1.91797			−0.857743			−0.428871	−	0.903366i	$-0.641089\pi$
$5$	−1.91797			−0.857743			−0.428871	+	0.903366i	$0.641089\pi$
$6$	0.322192	−	1.39435i	0.131534	−	0.569241i
$7$	0.517805	+	1.59364i	0.195712	+	0.602339i	0.999968	+	0.00805554i	$0.00256419\pi$
$7$	0.517805	+	1.59364i	0.195712	+	0.602339i	−0.804256	+	0.594283i	$0.797436\pi$
$8$	0.846987	−	2.60676i	0.299455	−	0.921629i
$9$	2.91061	+	0.726880i	0.970203	+	0.242293i
$10$	−0.165647	+	1.57602i	−0.0523821	+	0.498382i
$11$	−2.69176	−	0.572151i	−0.811596	−	0.172510i	−0.216623	−	0.976255i	$-0.569504\pi$
$11$	−2.69176	−	0.572151i	−0.811596	−	0.172510i	−0.594973	+	0.803745i	$0.702837\pi$
$12$	2.15723	+	0.743254i	0.622738	+	0.214559i
$13$	4.78011	−	3.47295i	1.32576	−	0.963224i	0.325923	−	0.945396i	$-0.394325\pi$
$13$	4.78011	−	3.47295i	1.32576	−	0.963224i	0.999841	−	0.0178274i	$-0.00567494\pi$
$14$	1.35424	−	0.287852i	0.361935	−	0.0769316i
$15$	−3.29718	−	0.405484i	−0.851329	−	0.104695i
$16$	0.338017	+	0.150495i	0.0845041	+	0.0376237i
$17$	1.99882	+	2.21991i	0.484784	+	0.538407i	0.935063	−	0.354481i	$-0.115342\pi$
$17$	1.99882	+	2.21991i	0.484784	+	0.538407i	−0.450279	+	0.892888i	$0.648676\pi$
$18$	0.848664	−	2.32891i	0.200032	−	0.548930i
$19$	−5.46720	+	2.43415i	−1.25426	+	0.558433i	−0.922889	−	0.385067i	$-0.874178\pi$
$19$	−5.46720	+	2.43415i	−1.25426	+	0.558433i	−0.331373	+	0.943500i	$0.607512\pi$
$20$	−2.47138	−	0.525309i	−0.552618	−	0.117463i
$21$	0.553242	+	2.84909i	0.120727	+	0.621723i
$22$	−0.702620	+	2.16244i	−0.149799	+	0.461034i
$23$	−1.97584	−	2.19440i	−0.411992	−	0.457563i	0.501057	−	0.865414i	$-0.332945\pi$
$23$	−1.97584	−	2.19440i	−0.411992	−	0.457563i	−0.913048	+	0.407851i	$0.866278\pi$
$24$	2.00716	−	4.30222i	0.409710	−	0.878186i
$25$	−1.32139			−0.264277
$26$	−2.44094	−	4.22783i	−0.478707	−	0.829145i
$27$	4.84996	+	1.86492i	0.933375	+	0.358904i
$28$	0.230734	+	2.19529i	0.0436046	+	0.414870i
$29$	−0.788137	+	7.49862i	−0.146353	+	1.39246i	0.636991	+	0.770871i	$0.280179\pi$
$29$	−0.788137	+	7.49862i	−0.146353	+	1.39246i	−0.783344	+	0.621588i	$0.786488\pi$
$30$	−0.617955	+	2.67432i	−0.112823	+	0.488262i
$31$	−4.78907	−	2.83987i	−0.860142	−	0.510055i
$31$	−4.78907	−	2.83987i	−0.860142	−	0.510055i
$32$	2.89377	−	5.01215i	0.511550	−	0.886031i
$33$	−4.50644	−	1.55266i	−0.784471	−	0.270283i
$34$	1.99676	−	1.45073i	0.342441	−	0.248798i
$35$	−0.993134	−	3.05655i	−0.167870	−	0.516652i
$36$	3.55135	+	1.73379i	0.591892	+	0.288966i
$37$	−1.14441	+	1.98217i	−0.188139	+	0.325867i	−0.944630	−	0.328138i	$-0.893579\pi$
$37$	−1.14441	+	1.98217i	−0.188139	+	0.325867i	0.756491	+	0.654004i	$0.226912\pi$
$38$	1.52800	+	4.70270i	0.247874	+	0.762879i
$39$	8.95171	−	4.95978i	1.43342	−	0.794200i
$40$	−1.62450	+	4.99969i	−0.256856	+	0.790520i
$41$	−9.01317	−	6.54845i	−1.40762	−	1.02270i	−0.993663	−	0.112399i	$-0.964146\pi$
$41$	−9.01317	−	6.54845i	−1.40762	−	1.02270i	−0.413957	−	0.910297i	$-0.635854\pi$
$42$	2.38892	−	0.208543i	0.368619	−	0.0321789i
$43$	−4.37377	−	3.17773i	−0.666994	−	0.484600i	0.202023	−	0.979381i	$-0.435248\pi$
$43$	−4.37377	−	3.17773i	−0.666994	−	0.484600i	−0.869018	+	0.494781i	$0.835248\pi$
$44$	−3.31174	−	1.47448i	−0.499263	−	0.222286i
$45$	−5.58246	−	1.39413i	−0.832185	−	0.207825i
$46$	−1.97381	+	1.43406i	−0.291022	+	0.211440i
$47$	0.784681	+	0.349363i	0.114458	+	0.0509598i	0.463167	−	0.886271i	$-0.346713\pi$
$47$	0.784681	+	0.349363i	0.114458	+	0.0509598i	−0.348709	+	0.937231i	$0.613380\pi$
$48$	0.549268	+	0.330176i	0.0792800	+	0.0476569i
$49$	3.39156	−	2.46411i	0.484508	−	0.352016i
$50$	−0.114122	+	1.08580i	−0.0161393	+	0.153556i
$51$	2.96685	+	4.23882i	0.415441	+	0.593554i
$52$	7.11056	−	3.16583i	0.986058	−	0.439021i
$53$	−3.07734	+	0.654108i	−0.422705	+	0.0898487i	−0.414353	−	0.910116i	$-0.635992\pi$
$53$	−3.07734	+	0.654108i	−0.422705	+	0.0898487i	−0.00835222	+	0.999965i	$0.502659\pi$
$54$	1.95130	−	3.82421i	0.265538	−	0.520409i
$55$	5.16272	+	1.09737i	0.696141	+	0.147969i
$56$	4.59281			0.613740
$57$	−9.91327	+	3.02872i	−1.31305	+	0.401163i
$58$	6.09366	+	1.29525i	0.800136	+	0.170074i
$59$	6.82682	+	3.03950i	0.888776	+	0.395709i	0.799759	−	0.600321i	$-0.204961\pi$
$59$	6.82682	+	3.03950i	0.888776	+	0.395709i	0.0890174	+	0.996030i	$0.471627\pi$
$60$	−4.13750	−	1.42554i	−0.534149	−	0.184036i
$61$	3.24200	+	5.61530i	0.415095	+	0.718966i	0.995438	−	0.0954062i	$-0.0304150\pi$
$61$	3.24200	+	5.61530i	0.415095	+	0.718966i	−0.580343	+	0.814372i	$0.697082\pi$
$62$	−2.74717	+	3.68998i	−0.348891	+	0.468628i
$63$	0.348743	+	5.01484i	0.0439375	+	0.631811i
$64$	−3.26995	−	2.37576i	−0.408744	−	0.296970i
$65$	−9.16811	+	6.66102i	−1.13716	+	0.826198i
$66$	−1.66504	+	3.56891i	−0.204953	+	0.439303i
$67$	−4.83641			−0.590861			−0.295431	−	0.955364i	$-0.595463\pi$
$67$	−4.83641			−0.590861			−0.295431	+	0.955364i	$0.595463\pi$
$68$	1.96755	+	3.40789i	0.238600	+	0.413268i
$69$	−2.93275	−	4.19010i	−0.353061	−	0.504429i
$70$	−2.59738	+	0.552091i	−0.310447	+	0.0659875i
$71$	−3.20758	+	0.681791i	−0.380669	+	0.0809137i	−0.394272	−	0.918994i	$-0.629003\pi$
$71$	−3.20758	+	0.681791i	−0.380669	+	0.0809137i	0.0136029	+	0.999907i	$0.495670\pi$
$72$	4.36005	−	6.97160i	0.513837	−	0.821611i
$73$	−7.77780	+	8.63812i	−0.910323	+	1.01102i	0.0895644	+	0.995981i	$0.471453\pi$
$73$	−7.77780	+	8.63812i	−0.910323	+	1.01102i	−0.999887	+	0.0150346i	$0.995214\pi$
$74$	1.52994	+	1.11157i	0.177852	+	0.129217i
$75$	−2.27160	−	0.279358i	−0.262301	−	0.0322575i
$76$	−7.71139	+	1.63911i	−0.884557	+	0.188018i
$77$	−0.482003	−	4.58596i	−0.0549294	−	0.522618i
$78$	−3.30240	−	7.78410i	−0.373923	−	0.881376i
$79$	−0.988541	+	3.04242i	−0.111220	+	0.342299i	−0.991140	−	0.132823i	$-0.957596\pi$
$79$	−0.988541	+	3.04242i	−0.111220	+	0.342299i	0.879920	+	0.475121i	$0.157596\pi$
$80$	−0.648306	−	0.288644i	−0.0724828	−	0.0322714i
$81$	7.94329	+	4.23132i	0.882588	+	0.470147i
$82$	−6.15938	+	6.84068i	−0.680190	+	0.755427i
$83$	3.82141	−	1.70140i	0.419454	−	0.186753i	−0.186146	−	0.982522i	$-0.559600\pi$
$83$	3.82141	−	1.70140i	0.419454	−	0.186753i	0.605600	+	0.795769i	$0.292933\pi$
$84$	−0.0674571	+	3.82270i	−0.00736018	+	0.417091i
$85$	−3.83367	−	4.25772i	−0.415820	−	0.461815i
$86$	−2.98893	+	3.31954i	−0.322305	+	0.357956i
$87$	−2.94019	+	12.7243i	−0.315222	+	1.36418i
$88$	−3.77135	+	6.53217i	−0.402027	+	0.696331i
$89$	−0.355098	−	1.09288i	−0.0376403	−	0.115845i	0.930471	−	0.366366i	$-0.119398\pi$
$89$	−0.355098	−	1.09288i	−0.0376403	−	0.115845i	−0.968111	+	0.250521i	$0.919398\pi$
$90$	−1.62771	+	4.46678i	−0.171576	+	0.470840i
$91$	8.00979	+	5.81946i	0.839655	+	0.610045i
$92$	−1.94494	−	3.36873i	−0.202774	−	0.351214i
$93$	−7.63250	−	5.89448i	−0.791454	−	0.611229i
$94$	0.354846	−	0.614611i	0.0365995	−	0.0633922i
$95$	10.4859	−	4.66864i	1.07583	−	0.478992i
$96$	6.03430	−	8.00461i	0.615874	−	0.816967i
$97$	−3.26035	+	3.62098i	−0.331038	+	0.367655i	−0.885569	−	0.464508i	$-0.846231\pi$
$97$	−3.26035	+	3.62098i	−0.331038	+	0.367655i	0.554531	+	0.832163i	$0.312898\pi$
$98$	−1.73188	−	2.99970i	−0.174946	−	0.303016i
$99$	−7.41878	−	3.62189i	−0.745615	−	0.364014i
$100$	−1.70266	−	0.361912i	−0.170266	−	0.0361912i
$101$	14.3071	−	3.04107i	1.42361	−	0.302598i	0.569201	−	0.822199i	$-0.307253\pi$
$101$	14.3071	−	3.04107i	1.42361	−	0.302598i	0.854409	+	0.519601i	$0.173919\pi$
$102$	3.73933	−	2.07181i	0.370249	−	0.205140i
$103$	7.58276	+	5.50920i	0.747152	+	0.542837i	0.894943	−	0.446181i	$-0.147216\pi$
$103$	7.58276	+	5.50920i	0.747152	+	0.542837i	−0.147791	+	0.989019i	$0.547216\pi$
$104$	−5.00446	−	15.4021i	−0.490728	−	1.51030i
$105$	−1.06110	−	5.46448i	−0.103553	−	0.533279i
$106$	0.271714	+	2.58518i	0.0263912	+	0.251095i
$107$	−6.47578	−	7.19208i	−0.626037	−	0.695284i	0.343799	−	0.939043i	$-0.388286\pi$
$107$	−6.47578	−	7.19208i	−0.626037	−	0.695284i	−0.969836	+	0.243759i	$0.921619\pi$
$108$	5.73859	+	3.73137i	0.552196	+	0.359051i
$109$	16.7898	−	12.1985i	1.60817	−	1.16841i	0.739298	−	0.673378i	$-0.235157\pi$
$109$	16.7898	−	12.1985i	1.60817	−	1.16841i	0.868876	−	0.495029i	$-0.164843\pi$
$110$	1.34761	−	4.14750i	0.128489	−	0.395449i
$111$	−2.38640	+	3.16560i	−0.226507	+	0.300466i
$112$	−0.0648076	+	0.616603i	−0.00612374	+	0.0582635i
$113$	4.00610	+	12.3295i	0.376862	+	1.15986i	0.942214	+	0.335012i	$0.108741\pi$
$113$	4.00610	+	12.3295i	0.376862	+	1.15986i	−0.565351	+	0.824850i	$0.691259\pi$
$114$	1.63257	+	8.40745i	0.152905	+	0.787430i
$115$	3.78961	+	4.20879i	0.353383	+	0.392471i
$116$	−3.06933	+	9.44642i	−0.284980	+	0.877078i
$117$	16.4374	−	6.63384i	1.51964	−	0.613299i
$118$	3.08720	−	5.34719i	0.284200	−	0.492248i
$119$	−2.50274	+	4.33487i	−0.229426	+	0.397377i
$120$	−3.84967	+	8.25153i	−0.351425	+	0.753258i
$121$	−3.13079	−	1.39392i	−0.284617	−	0.126720i
$122$	4.89417	−	2.17902i	0.443097	−	0.197280i
$123$	−14.1101	−	13.1629i	−1.27227	−	1.18686i
$124$	−5.39310	−	4.97095i	−0.484315	−	0.446404i
$125$	12.1242			1.08442
$126$	4.15088	+	0.146543i	0.369790	+	0.0130550i
$127$	−1.78565	−	16.9893i	−0.158451	−	1.50756i	−0.727986	−	0.685592i	$-0.759543\pi$
$127$	−1.78565	−	16.9893i	−0.158451	−	1.50756i	0.569535	−	0.821967i	$-0.307123\pi$
$128$	5.51062	−	6.12017i	0.487075	−	0.540952i
$129$	−6.84714	−	6.38751i	−0.602857	−	0.562389i
$130$	4.68165	+	8.10885i	0.410608	+	0.711193i
$131$	8.65462	−	9.61193i	0.756158	−	0.839798i	−0.235068	−	0.971979i	$-0.575531\pi$
$131$	8.65462	−	9.61193i	0.756158	−	0.839798i	0.991226	+	0.132181i	$0.0421979\pi$
$132$	−5.38148	−	3.23492i	−0.468398	−	0.281564i
$133$	−6.71010	−	7.45232i	−0.581840	−	0.646198i
$134$	−0.417699	+	3.97414i	−0.0360837	+	0.343314i
$135$	−9.30208	−	3.57686i	−0.800595	−	0.307847i
$136$	7.47974	−	3.33019i	0.641382	−	0.285562i
$137$	0.765280	+	7.28115i	0.0653823	+	0.622071i	0.977324	+	0.211750i	$0.0679164\pi$
$137$	0.765280	+	7.28115i	0.0653823	+	0.622071i	−0.911941	+	0.410320i	$0.865417\pi$
$138$	−3.69636	+	2.04800i	−0.314655	+	0.174337i
$139$	−1.45849	−	13.8766i	−0.123707	−	1.17700i	−0.863567	−	0.504234i	$-0.831775\pi$
$139$	−1.45849	−	13.8766i	−0.123707	−	1.17700i	0.739860	−	0.672761i	$-0.234892\pi$
$140$	−0.442541	−	4.21050i	−0.0374016	−	0.355852i
$141$	1.27509	+	0.766481i	0.107382	+	0.0645493i
$142$	0.283213	+	2.69459i	0.0237667	+	0.226125i
$143$	−14.8540	+	6.61341i	−1.24215	+	0.553041i
$144$	0.874443	+	0.683729i	0.0728702	+	0.0569774i
$145$	1.51162	−	14.3821i	0.125534	−	1.19437i
$146$	6.42633	+	7.13716i	0.531847	+	0.590676i
$147$	6.35137	−	3.51903i	0.523852	−	0.290245i
$148$	−2.01750	+	2.24067i	−0.165838	+	0.184182i
$149$	7.48500	+	12.9644i	0.613195	+	1.06208i	0.990698	+	0.136077i	$0.0434493\pi$
$149$	7.48500	+	12.9644i	0.613195	+	1.06208i	−0.377503	+	0.926008i	$0.623217\pi$
$150$	−0.425740	+	1.84248i	−0.0347616	+	0.150438i
$151$	7.82409	−	8.68953i	0.636716	−	0.707144i	−0.335287	−	0.942116i	$-0.608833\pi$
$151$	7.82409	−	8.68953i	0.636716	−	0.707144i	0.972002	+	0.234972i	$0.0754998\pi$
$152$	1.71460	+	16.3134i	0.139073	+	1.32319i
$153$	4.20416	+	7.91419i	0.339886	+	0.639824i
$154$	−3.80997			−0.307016
$155$	9.18529	+	5.44678i	0.737780	+	0.437496i
$156$	12.8931	−	3.93911i	1.03227	−	0.315381i
$157$	19.2203	−	8.55743i	1.53395	−	0.682957i	0.546005	−	0.837782i	$-0.316148\pi$
$157$	19.2203	−	8.55743i	1.53395	−	0.682957i	0.987942	+	0.154824i	$0.0494812\pi$
$158$	2.41462	+	1.07506i	0.192097	+	0.0855271i
$159$	−5.42854	+	0.473889i	−0.430511	+	0.0375818i
$160$	−5.55016	+	9.61316i	−0.438779	+	0.759987i
$161$	2.47397	−	4.28505i	0.194976	−	0.337709i
$162$	4.16297	−	6.16167i	0.327073	−	0.484107i
$163$	−5.61696	+	17.2872i	−0.439954	+	1.35404i	0.447970	+	0.894049i	$0.352147\pi$
$163$	−5.61696	+	17.2872i	−0.439954	+	1.35404i	−0.887924	+	0.459990i	$0.847853\pi$
$164$	−9.82029	−	10.9065i	−0.766836	−	0.851657i
$165$	8.64323	+	2.97795i	0.672874	+	0.231833i
$166$	−1.06803	−	3.28705i	−0.0828949	−	0.255124i
$167$	0.660417	−	6.28345i	0.0511046	−	0.486228i	−0.938797	−	0.344471i	$-0.888058\pi$
$167$	0.660417	−	6.28345i	0.0511046	−	0.486228i	0.989902	−	0.141757i	$-0.0452750\pi$
$168$	7.89549	+	0.970978i	0.609151	+	0.0749126i
$169$	6.77082	−	20.8385i	0.520833	−	1.60296i
$170$	−3.82973	+	2.78246i	−0.293727	+	0.213405i
$171$	−17.6822	+	3.11088i	−1.35219	+	0.237895i
$172$	−4.76544	−	5.29256i	−0.363362	−	0.403554i
$173$	1.10458	+	10.5094i	0.0839799	+	0.799015i	0.952741	+	0.303784i	$0.0982500\pi$
$173$	1.10458	+	10.5094i	0.0839799	+	0.799015i	−0.868761	+	0.495231i	$0.835083\pi$
$174$	10.2018	+	3.51493i	0.773394	+	0.266467i
$175$	−0.684220	−	2.10581i	−0.0517222	−	0.159185i
$176$	−0.823754	−	0.598492i	−0.0620928	−	0.0451130i
$177$	11.0934	+	6.66847i	0.833831	+	0.501233i
$178$	−0.928703	+	0.197402i	−0.0696092	+	0.0147959i
$179$	−11.2525	−	2.39180i	−0.841054	−	0.178772i	−0.232811	−	0.972522i	$-0.574792\pi$
$179$	−11.2525	−	2.39180i	−0.841054	−	0.178772i	−0.608243	+	0.793751i	$0.708126\pi$
$180$	−6.81139	−	3.32537i	−0.507691	−	0.247858i
$181$	−3.37410	−	5.84411i	−0.250795	−	0.434389i	0.712950	−	0.701215i	$-0.247359\pi$
$181$	−3.37410	−	5.84411i	−0.250795	−	0.434389i	−0.963745	+	0.266826i	$0.914025\pi$
$182$	5.47370	−	6.07916i	0.405738	−	0.450617i
$183$	4.38617	+	10.3387i	0.324235	+	0.764256i
$184$	−7.39378	+	3.29192i	−0.545076	+	0.242684i
$185$	2.19494	−	3.80174i	0.161375	−	0.279510i
$186$	−5.50276	+	5.76265i	−0.403482	+	0.422538i
$187$	−4.11021	−	7.11909i	−0.300568	−	0.520599i
$188$	0.915407	+	0.665082i	0.0667629	+	0.0485061i
$189$	−0.460677	+	8.69474i	−0.0335093	+	0.632449i
$190$	−2.93066	−	9.01964i	−0.212612	−	0.654354i
$191$	−12.5410	+	21.7216i	−0.907432	+	1.57172i	−0.0898125	+	0.995959i	$0.528627\pi$
$191$	−12.5410	+	21.7216i	−0.907432	+	1.57172i	−0.817619	+	0.575759i	$0.804707\pi$
$192$	−5.11910	−	4.77547i	−0.369440	−	0.344640i
$193$	−10.1809	+	11.3070i	−0.732838	+	0.813899i	−0.988236	−	0.152937i	$-0.951127\pi$
$193$	−10.1809	+	11.3070i	−0.732838	+	0.813899i	0.255398	+	0.966836i	$0.417793\pi$
$194$	2.69383	+	2.99180i	0.193406	+	0.214799i
$195$	−17.1691	+	9.51271i	−1.22951	+	0.681219i
$196$	5.04505	−	2.24620i	0.360360	−	0.160443i
$197$	3.75545	−	4.17085i	0.267565	−	0.297161i	−0.594358	−	0.804201i	$-0.702594\pi$
$197$	3.75545	−	4.17085i	0.267565	−	0.297161i	0.861923	+	0.507040i	$0.169260\pi$
$198$	−3.61689	+	5.78330i	−0.257041	+	0.411002i
$199$	1.48108	+	0.659419i	0.104991	+	0.0467450i	0.458560	−	0.888663i	$-0.348365\pi$
$199$	1.48108	+	0.659419i	0.104991	+	0.0467450i	−0.353569	+	0.935408i	$0.615032\pi$
$200$	−1.11920	+	3.44454i	−0.0791393	+	0.243566i
$201$	−8.31427	−	1.02248i	−0.586443	−	0.0721201i
$202$	−1.26325	−	12.0190i	−0.0888817	−	0.845653i
$203$	−12.3582	+	2.62682i	−0.867375	+	0.184366i
$204$	2.66194	+	6.27447i	0.186373	+	0.439301i
$205$	17.2870	+	12.5597i	1.20738	+	0.877210i
$206$	5.18188	−	5.75506i	0.361038	−	0.400974i
$207$	−4.15584	−	7.82323i	−0.288851	−	0.543752i
$208$	2.13842	−	0.454535i	0.148273	−	0.0315163i
$209$	16.1091	−	3.42409i	1.11429	−	0.236849i
$210$	−4.58188	+	0.399979i	−0.316180	+	0.0276012i
$211$	−2.84831	−	4.93342i	−0.196086	−	0.339631i	0.751170	−	0.660109i	$-0.229490\pi$
$211$	−2.84831	−	4.93342i	−0.196086	−	0.339631i	−0.947256	+	0.320478i	$0.896156\pi$
$212$	−4.14443			−0.284640
$213$	−5.65828	+	0.493945i	−0.387699	+	0.0338445i
$214$	−6.46912	+	4.70009i	−0.442220	+	0.321291i
$215$	8.38877	+	6.09480i	0.572109	+	0.415662i
$216$	8.96925	−	11.0631i	0.610280	−	0.752749i
$217$	2.04592	−	9.10254i	0.138886	−	0.617921i
$218$	−8.57364	−	14.8500i	−0.580680	−	1.00577i
$219$	−15.1970	+	13.2055i	−1.02692	+	0.892343i
$220$	6.35181	+	2.82801i	0.428239	+	0.190664i
$221$	17.2642	+	3.66962i	1.16132	+	0.246845i
$222$	2.39512	+	2.23434i	0.160750	+	0.149959i
$223$	6.78329			0.454243			0.227121	−	0.973866i	$-0.427069\pi$
$223$	6.78329			0.454243			0.227121	+	0.973866i	$0.427069\pi$
$224$	9.48596	+	2.01630i	0.633807	+	0.134720i
$225$	−3.84604	−	0.960489i	−0.256403	−	0.0640326i
$226$	10.4773	−	2.22702i	0.696941	−	0.148139i
$227$	21.4655	−	9.55707i	1.42472	−	0.634325i	0.457717	−	0.889098i	$-0.348667\pi$
$227$	21.4655	−	9.55707i	1.42472	−	0.634325i	0.967001	+	0.254773i	$0.0820008\pi$
$228$	−13.6032	+	1.18750i	−0.900893	+	0.0786442i
$229$	−0.0214960	+	0.204520i	−0.00142049	+	0.0135151i	−0.995209	−	0.0977685i	$-0.968830\pi$
$229$	−0.0214960	+	0.204520i	−0.00142049	+	0.0135151i	0.993789	+	0.111284i	$0.0354962\pi$
$230$	3.78571	−	2.75048i	0.249622	−	0.181361i
$231$	0.140918	−	7.98562i	0.00927172	−	0.525415i
$232$	18.8796	+	8.40572i	1.23950	+	0.551863i
$233$	−5.56452	+	4.04286i	−0.364544	+	0.264857i	−0.754945	−	0.655788i	$-0.772336\pi$
$233$	−5.56452	+	4.04286i	−0.364544	+	0.264857i	0.390401	+	0.920645i	$0.372336\pi$
$234$	−4.03149	−	14.0798i	−0.263547	−	0.920426i
$235$	−1.50500	−	0.670067i	−0.0981751	−	0.0437104i
$236$	7.96415	+	5.78630i	0.518422	+	0.376656i
$237$	−2.34261	+	5.02123i	−0.152169	+	0.326164i
$238$	3.34587	+	2.43092i	0.216881	+	0.157573i
$239$	−2.50946	+	7.72331i	−0.162323	+	0.499579i	−0.998829	−	0.0483786i	$-0.984595\pi$
$239$	−2.50946	+	7.72331i	−0.162323	+	0.499579i	0.836506	+	0.547958i	$0.184595\pi$
$240$	−1.05348	−	0.633269i	−0.0680018	−	0.0408773i
$241$	−6.56721	−	20.2118i	−0.423031	−	1.30196i	−0.904867	−	0.425694i	$-0.860030\pi$
$241$	−6.56721	−	20.2118i	−0.423031	−	1.30196i	0.481836	−	0.876262i	$-0.339970\pi$
$242$	−1.41579	+	2.45222i	−0.0910106	+	0.157635i
$243$	12.7608	+	8.95338i	0.818603	+	0.574360i
$244$	2.63948	+	8.12349i	0.168975	+	0.520053i
$245$	−6.50491	+	4.72609i	−0.415583	+	0.301939i
$246$	−12.0348	+	10.4576i	−0.767311	+	0.666755i
$247$	−17.6801	+	30.6228i	−1.12496	+	1.94849i
$248$	−11.4591	+	10.0786i	−0.727655	+	0.639993i
$249$	6.92908	−	2.11698i	0.439113	−	0.134158i
$250$	1.04712	−	9.96265i	0.0662255	−	0.630094i
$251$	−1.08065	−	10.2817i	−0.0682102	−	0.648977i	−0.974201	−	0.225680i	$-0.927540\pi$
$251$	−1.08065	−	10.2817i	−0.0682102	−	0.648977i	0.905991	−	0.423297i	$-0.139127\pi$
$252$	−0.924133	+	6.55734i	−0.0582149	+	0.413074i
$253$	4.06297	+	7.03727i	0.255437	+	0.442429i
$254$	−14.1146			−0.885628
$255$	−5.69032	−	8.12994i	−0.356342	−	0.509116i
$256$	−9.96219	−	11.0641i	−0.622637	−	0.691508i
$257$	−2.87770	+	8.85666i	−0.179506	+	0.552463i	−0.999811	−	0.0194641i	$-0.993804\pi$
$257$	−2.87770	+	8.85666i	−0.179506	+	0.552463i	0.820304	+	0.571927i	$0.193804\pi$
$258$	−5.84006	+	5.07473i	−0.363587	+	0.315939i
$259$	−3.75144	−	0.797393i	−0.233103	−	0.0495476i
$260$	−13.6379	+	6.07196i	−0.845784	+	0.376567i
$261$	−7.74455	+	21.2527i	−0.479376	+	1.31551i
$262$	−7.15080	−	7.94176i	−0.441778	−	0.490644i
$263$	−3.86957	−	1.72284i	−0.238608	−	0.106235i	0.283949	−	0.958839i	$-0.408355\pi$
$263$	−3.86957	−	1.72284i	−0.238608	−	0.106235i	−0.522557	+	0.852604i	$0.675022\pi$
$264$	−7.86431	+	10.4321i	−0.484015	+	0.642053i
$265$	5.90224	−	1.25456i	0.362572	−	0.0770671i
$266$	−6.70320	+	4.87016i	−0.411000	+	0.298609i
$267$	−0.379400	−	1.95384i	−0.0232189	−	0.119573i
$268$	−6.23190	−	1.32463i	−0.380674	−	0.0809148i
$269$	1.05736	−	10.0601i	0.0644686	−	0.613378i	−0.913818	−	0.406123i	$-0.866880\pi$
$269$	1.05736	−	10.0601i	0.0644686	−	0.613378i	0.978287	−	0.207255i	$-0.0664529\pi$
$270$	−3.74254	+	7.33473i	−0.227763	+	0.446377i
$271$	−0.0516160	+	0.158858i	−0.00313545	+	0.00964992i	−0.952612	−	0.304188i	$-0.901615\pi$
$271$	−0.0516160	+	0.158858i	−0.00313545	+	0.00964992i	0.949477	+	0.313838i	$0.101615\pi$
$272$	0.341548	+	1.05118i	0.0207094	+	0.0637370i
$273$	12.5393	+	11.6976i	0.758915	+	0.707971i
$274$	6.04912			0.365441
$275$	3.55686	+	0.756033i	0.214487	+	0.0455905i
$276$	−2.63135	−	6.20236i	−0.158388	−	0.373338i
$277$	−0.490162	+	4.66358i	−0.0294510	+	0.280207i	0.969878	+	0.243590i	$0.0783250\pi$
$277$	−0.490162	+	4.66358i	−0.0294510	+	0.280207i	−0.999329	+	0.0366177i	$0.988342\pi$
$278$	−11.5285			−0.691435
$279$	−11.8749	−	11.7468i	−0.710929	−	0.703263i
$280$	−8.80887			−0.526431
$281$	0.504247	−	4.79759i	0.0300809	−	0.286200i	−0.969132	−	0.246541i	$-0.920706\pi$
$281$	0.504247	−	4.79759i	0.0300809	−	0.286200i	0.999213	−	0.0396594i	$-0.0126273\pi$
$282$	0.739952	−	0.981558i	0.0440635	−	0.0584509i
$283$	−6.39199	−	1.35866i	−0.379965	−	0.0807640i	0.0139700	−	0.999902i	$-0.495553\pi$
$283$	−6.39199	−	1.35866i	−0.379965	−	0.0807640i	−0.393935	+	0.919138i	$0.628886\pi$
$284$	−4.31983			−0.256335
$285$	19.0134	−	5.80899i	1.12625	−	0.344095i
$286$	4.15146	+	12.7769i	0.245481	+	0.755513i
$287$	5.76880	−	17.7545i	0.340522	−	1.04802i
$288$	12.0658	−	12.4850i	0.710987	−	0.735685i
$289$	0.844249	−	8.03250i	0.0496617	−	0.472500i
$290$	−11.6875	−	2.48425i	−0.686311	−	0.145880i
$291$	−6.37039	+	5.53556i	−0.373439	+	0.324500i
$292$	−12.3879	+	9.00032i	−0.724946	+	0.526704i
$293$	28.3985	−	6.03628i	1.65906	−	0.352643i	0.719356	−	0.694642i	$-0.244437\pi$
$293$	28.3985	−	6.03628i	1.65906	−	0.352643i	0.939701	+	0.341998i	$0.111104\pi$
$294$	−2.34310	−	5.52293i	−0.136652	−	0.322104i
$295$	−13.0936	−	5.82967i	−0.762341	−	0.339416i
$296$	4.19774	+	4.66206i	0.243989	+	0.270977i
$297$	−11.9879	−	7.79482i	−0.695609	−	0.452301i
$298$	11.2995	−	5.03085i	0.654561	−	0.291429i
$299$	−17.0658	−	3.62744i	−0.986939	−	0.209780i
$300$	−2.85053	−	0.982127i	−0.164575	−	0.0567031i
$301$	2.79940	−	8.61566i	0.161355	−	0.496598i
$302$	−6.46458	−	7.17964i	−0.371995	−	0.413142i
$303$	25.2383	−	2.20319i	1.44990	−	0.126570i
$304$	−2.21433			−0.127001
$305$	−6.21805	−	10.7700i	−0.356045	−	0.616688i
$306$	6.86629	−	2.77111i	0.392520	−	0.158414i
$307$	2.90909	+	27.6781i	0.166030	+	1.57967i	0.687359	+	0.726318i	$0.258770\pi$
$307$	2.90909	+	27.6781i	0.166030	+	1.57967i	−0.521328	+	0.853356i	$0.674563\pi$
$308$	0.634956	−	6.04120i	0.0361800	−	0.344229i
$309$	11.8708	+	11.0740i	0.675307	+	0.629975i
$310$	5.26899	−	7.07727i	0.299258	−	0.401962i
$311$	−14.8722	+	25.7593i	−0.843323	+	1.46068i	0.0437472	+	0.999043i	$0.486070\pi$
$311$	−14.8722	+	25.7593i	−0.843323	+	1.46068i	−0.887070	+	0.461635i	$0.847263\pi$
$312$	−5.34696	−	27.5358i	−0.302712	−	1.55891i
$313$	−2.03709	+	1.48003i	−0.115143	+	0.0836563i	−0.643867	−	0.765138i	$-0.722671\pi$
$313$	−2.03709	+	1.48003i	−0.115143	+	0.0836563i	0.528724	+	0.848794i	$0.322671\pi$
$314$	−5.37179	−	16.5327i	−0.303147	−	0.932992i
$315$	−0.668880	−	9.61832i	−0.0376871	−	0.541931i
$316$	−2.10706	+	3.64953i	−0.118531	+	0.205302i
$317$	1.92331	+	5.91935i	0.108024	+	0.332464i	0.990428	−	0.138028i	$-0.0440765\pi$
$317$	1.92331	+	5.91935i	0.108024	+	0.332464i	−0.882404	+	0.470492i	$0.844076\pi$
$318$	−0.0794379	+	4.50163i	−0.00445466	+	0.252439i
$319$	6.41182	−	19.7336i	0.358993	−	1.10487i
$320$	6.27167	+	4.55663i	0.350597	+	0.254724i
$321$	−9.61201	−	13.7330i	−0.536490	−	0.766499i
$322$	−3.30742	−	2.40298i	−0.184315	−	0.133913i
$323$	−16.3315	−	7.27126i	−0.908710	−	0.404584i
$324$	9.07635	+	7.62780i	0.504241	+	0.423767i
$325$	−6.31638	+	4.58912i	−0.350369	+	0.254558i
$326$	13.7200	+	6.10855i	0.759882	+	0.338321i
$327$	31.4423	−	17.4209i	1.73876	−	0.963378i
$328$	−24.7043	+	17.9487i	−1.36406	+	0.991051i
$329$	−0.150446	+	1.43140i	−0.00829437	+	0.0789156i
$330$	3.19350	−	6.84507i	0.175797	−	0.376809i
$331$	−4.88037	+	2.17288i	−0.268249	+	0.119432i	−0.536454	−	0.843930i	$-0.680236\pi$
$331$	−4.88037	+	2.17288i	−0.268249	+	0.119432i	0.268204	+	0.963362i	$0.413570\pi$
$332$	5.39003	−	1.14569i	0.295816	−	0.0628777i
$333$	−4.77172	+	4.93747i	−0.261488	+	0.270572i
$334$	−5.10616	−	1.08535i	−0.279396	−	0.0593876i
$335$	9.27609			0.506807
$336$	−0.241769	+	1.04630i	−0.0131896	+	0.0570804i
$337$	4.79693	+	1.01962i	0.261306	+	0.0555422i	0.336701	−	0.941611i	$-0.390689\pi$
$337$	4.79693	+	1.01962i	0.261306	+	0.0555422i	−0.0753958	+	0.997154i	$0.524022\pi$
$338$	−16.5385	−	7.36341i	−0.899575	−	0.400517i
$339$	4.28027	+	22.0426i	0.232472	+	1.19719i
$340$	−3.77370	−	6.53624i	−0.204658	−	0.354477i
$341$	11.2662	+	10.3843i	0.610098	+	0.562342i
$342$	1.02911	+	14.7984i	0.0556481	+	0.800206i
$343$	15.1725	+	11.0234i	0.819237	+	0.595210i
$344$	−11.9881	+	8.70988i	−0.646356	+	0.469605i
$345$	5.62493	+	8.03650i	0.302836	+	0.432671i
$346$	8.73112			0.469388
$347$	−8.51576	−	14.7497i	−0.457150	−	0.791807i	0.541659	−	0.840598i	$-0.317796\pi$
$347$	−8.51576	−	14.7497i	−0.457150	−	0.791807i	−0.998809	+	0.0487913i	$0.984463\pi$
$348$	−7.27357	+	15.5904i	−0.389904	+	0.835735i
$349$	19.2864	−	4.09945i	1.03238	−	0.219438i	0.339584	−	0.940576i	$-0.389714\pi$
$349$	19.2864	−	4.09945i	1.03238	−	0.219438i	0.692792	+	0.721137i	$0.256380\pi$
$350$	−1.78947	+	0.380363i	−0.0956512	+	0.0203313i
$351$	29.6601	−	7.92915i	1.58314	−	0.423227i
$352$	−10.6570	+	11.8358i	−0.568022	+	0.630852i
$353$	−24.7830	−	18.0059i	−1.31907	−	0.958358i	−0.999943	−	0.0106443i	$-0.996612\pi$
$353$	−24.7830	−	18.0059i	−1.31907	−	0.958358i	−0.319123	−	0.947713i	$-0.603388\pi$
$354$	6.43767	−	8.53967i	0.342158	−	0.453878i
$355$	6.15204	−	1.30766i	0.326516	−	0.0694032i
$356$	−0.158232	−	1.50548i	−0.00838628	−	0.0797901i
$357$	−5.21890	+	6.92296i	−0.276214	+	0.366402i
$358$	−2.93721	+	9.03980i	−0.155236	+	0.477768i
$359$	22.2145	+	9.89054i	1.17244	+	0.522003i	0.898169	−	0.439650i	$-0.144898\pi$
$359$	22.2145	+	9.89054i	1.17244	+	0.522003i	0.274268	+	0.961653i	$0.411564\pi$
$360$	−8.36245	+	13.3713i	−0.440740	+	0.704731i
$361$	11.2517	−	12.4963i	0.592194	−	0.657698i
$362$	−5.09359	+	2.26781i	−0.267713	+	0.119194i
$363$	−5.08744	−	3.05817i	−0.267021	−	0.160512i
$364$	8.72707	+	9.69239i	0.457423	+	0.508019i
$365$	14.9176	−	16.5677i	0.780823	−	0.867191i
$366$	8.87424	−	2.71127i	0.463864	−	0.141720i
$367$	−13.5929	+	23.5436i	−0.709543	+	1.22896i	0.255484	+	0.966813i	$0.417765\pi$
$367$	−13.5929	+	23.5436i	−0.709543	+	1.22896i	−0.965027	+	0.262151i	$0.915568\pi$
$368$	−0.337623	−	1.03910i	−0.0175998	−	0.0541666i
$369$	−21.4739	−	25.6115i	−1.11788	−	1.33328i
$370$	−2.93438	−	2.13195i	−0.152551	−	0.110835i
$371$	−2.63587	−	4.56546i	−0.136848	−	0.237027i
$372$	−8.22036	−	9.68573i	−0.426206	−	0.502182i
$373$	−2.45986	+	4.26060i	−0.127367	+	0.220605i	−0.922656	−	0.385625i	$-0.873986\pi$
$373$	−2.45986	+	4.26060i	−0.127367	+	0.220605i	0.795289	+	0.606230i	$0.207319\pi$
$374$	−6.20483	+	2.76257i	−0.320844	+	0.142849i
$375$	20.8428	+	2.56322i	1.07632	+	0.132364i
$376$	1.57532	−	1.74957i	0.0812409	−	0.0902272i
$377$	22.2750	+	38.5814i	1.14722	+	1.98704i
$378$	7.10480	+	1.12947i	0.365432	+	0.0580937i
$379$	−8.90406	−	1.89262i	−0.457371	−	0.0972172i	−0.0265358	−	0.999648i	$-0.508448\pi$
$379$	−8.90406	−	1.89262i	−0.457371	−	0.0972172i	−0.430835	+	0.902431i	$0.641781\pi$
$380$	14.7902	−	3.14376i	0.758723	−	0.161271i
$381$	0.522051	−	29.5839i	0.0267455	−	1.51563i
$382$	16.7658	+	12.1811i	0.857814	+	0.623238i
$383$	−2.06163	−	6.34504i	−0.105344	−	0.324216i	0.884467	−	0.466603i	$-0.154522\pi$
$383$	−2.06163	−	6.34504i	−0.105344	−	0.324216i	−0.989811	+	0.142387i	$0.954522\pi$
$384$	10.7672	−	9.35616i	0.549461	−	0.477455i
$385$	0.924468	+	8.79573i	0.0471153	+	0.448272i
$386$	8.41187	+	9.34233i	0.428153	+	0.475512i
$387$	−10.4205	−	12.4283i	−0.529705	−	0.631768i
$388$	−5.19284	+	3.77282i	−0.263626	+	0.191536i
$389$	−8.88310	+	27.3394i	−0.450391	+	1.38616i	0.426071	+	0.904690i	$0.359897\pi$
$389$	−8.88310	+	27.3394i	−0.450391	+	1.38616i	−0.876462	+	0.481471i	$0.840103\pi$
$390$	6.33390	+	14.9297i	0.320730	+	0.755994i
$391$	0.922015	−	8.77238i	0.0466283	−	0.443638i
$392$	−3.55074	−	10.9280i	−0.179339	−	0.551949i
$393$	16.9102	−	14.6942i	0.853009	−	0.741223i
$394$	−3.10291	−	3.44613i	−0.156322	−	0.173613i
$395$	1.89599	−	5.83527i	0.0953978	−	0.293604i
$396$	−8.56740	−	6.69887i	−0.430528	−	0.336631i
$397$	0.0297614	−	0.0515483i	0.00149368	−	0.00258714i	−0.865278	−	0.501293i	$-0.832858\pi$
$397$	0.0297614	−	0.0515483i	0.00149368	−	0.00258714i	0.866771	+	0.498706i	$0.166191\pi$
$398$	0.669768	−	1.16007i	0.0335725	−	0.0581492i
$399$	−9.95982	−	14.2299i	−0.498615	−	0.712386i
$400$	−0.446651	−	0.198862i	−0.0223325	−	0.00994309i
$401$	−20.4581	+	9.10854i	−1.02163	+	0.454859i	−0.848025	−	0.529956i	$-0.822208\pi$
$401$	−20.4581	+	9.10854i	−1.02163	+	0.454859i	−0.173605	+	0.984815i	$0.555542\pi$
$402$	−1.55825	+	6.74364i	−0.0777185	+	0.336342i
$403$	−32.7550	+	3.05734i	−1.63164	+	0.152297i
$404$	19.2682			0.958628
$405$	−15.2350	−	8.11556i	−0.757033	−	0.403265i
$406$	1.09117	+	10.3818i	0.0541538	+	0.515239i
$407$	4.21457	−	4.68075i	0.208908	−	0.232016i
$408$	13.5625	−	4.14362i	0.671442	−	0.205140i
$409$	18.0386	+	31.2438i	0.891952	+	1.54491i	0.837532	+	0.546388i	$0.183998\pi$
$409$	18.0386	+	31.2438i	0.891952	+	1.54491i	0.0544197	+	0.998518i	$0.482669\pi$
$410$	11.8135	−	13.1202i	0.583428	−	0.647962i
$411$	−0.223736	+	12.6788i	−0.0110361	+	0.625400i
$412$	8.26179	+	9.17565i	0.407029	+	0.452052i
$413$	−1.30890	+	12.4533i	−0.0644067	+	0.612789i
$414$	−6.78738	+	2.73926i	−0.333581	+	0.134627i
$415$	−7.32935	+	3.26324i	−0.359784	+	0.160186i
$416$	−3.57444	−	34.0085i	−0.175251	−	1.66741i
$417$	0.426401	−	24.1635i	0.0208810	−	1.18329i
$418$	−1.42235	−	13.5328i	−0.0695696	−	0.661910i
$419$	1.58584	+	15.0882i	0.0774733	+	0.737109i	0.962447	+	0.271469i	$0.0875093\pi$
$419$	1.58584	+	15.0882i	0.0774733	+	0.737109i	−0.884974	+	0.465640i	$0.845824\pi$
$420$	0.129381	−	7.33183i	0.00631314	−	0.357757i
$421$	−1.49908	−	14.2628i	−0.0730609	−	0.695128i	−0.968342	−	0.249626i	$-0.919692\pi$
$421$	−1.49908	−	14.2628i	−0.0730609	−	0.695128i	0.895281	−	0.445501i	$-0.146974\pi$
$422$	−4.29986	+	1.91442i	−0.209314	+	0.0931925i
$423$	2.02996	+	1.58723i	0.0986998	+	0.0771736i
$424$	−0.901363	+	8.57590i	−0.0437741	+	0.416483i
$425$	−2.64121	−	2.93336i	−0.128117	−	0.142289i
$426$	−0.0827999	+	4.69215i	−0.00401167	+	0.227335i
$427$	−7.27004	+	8.07420i	−0.351822	+	0.390738i
$428$	−6.37448	−	11.0409i	−0.308122	−	0.533683i
$429$	−26.9336	+	8.22879i	−1.30037	+	0.397290i
$430$	5.73268	−	6.36679i	0.276455	−	0.307034i
$431$	−3.13047	−	29.7845i	−0.150790	−	1.43467i	−0.764239	−	0.644933i	$-0.776885\pi$
$431$	−3.13047	−	29.7845i	−0.150790	−	1.43467i	0.613449	−	0.789734i	$-0.289781\pi$
$432$	1.35871	+	1.36027i	0.0653707	+	0.0654458i
$433$	6.03904			0.290218			0.145109	−	0.989416i	$-0.453647\pi$
$433$	6.03904			0.290218			0.145109	+	0.989416i	$0.453647\pi$
$434$	−7.30299	−	2.46731i	−0.350555	−	0.118434i
$435$	5.63920	−	24.4048i	0.270379	−	1.17012i
$436$	24.9754	−	11.1198i	1.19611	−	0.532540i
$437$	16.1438	+	7.18769i	0.772264	+	0.343834i
$438$	9.53862	+	13.6281i	0.455773	+	0.651176i
$439$	2.66529	−	4.61642i	0.127208	−	0.220330i	−0.795386	−	0.606103i	$-0.792732\pi$
$439$	2.66529	−	4.61642i	0.127208	−	0.220330i	0.922594	+	0.385773i	$0.126065\pi$
$440$	7.23333	−	12.5285i	0.344836	−	0.597273i
$441$	11.6626	−	4.70681i	0.555362	−	0.224134i
$442$	4.50641	−	13.8693i	0.214348	−	0.659695i
$443$	6.13216	+	6.81045i	0.291348	+	0.323574i	0.870994	−	0.491294i	$-0.163476\pi$
$443$	6.13216	+	6.81045i	0.291348	+	0.323574i	−0.579646	+	0.814868i	$0.696809\pi$
$444$	−3.94200	+	3.42540i	−0.187079	+	0.162562i
$445$	0.681068	+	2.09611i	0.0322857	+	0.0993652i
$446$	0.585843	−	5.57393i	0.0277405	−	0.263933i
$447$	10.1266	+	23.8695i	0.478973	+	1.12899i
$448$	2.09290	−	6.44130i	0.0988804	−	0.304323i
$449$	11.2240	−	8.15473i	0.529695	−	0.384846i	−0.290549	−	0.956860i	$-0.593838\pi$
$449$	11.2240	−	8.15473i	0.529695	−	0.384846i	0.820244	+	0.572014i	$0.193838\pi$
$450$	−1.12141	+	3.07739i	−0.0528639	+	0.145070i
$451$	20.5146	+	22.7837i	0.965994	+	1.07284i
$452$	1.78512	+	16.9843i	0.0839650	+	0.798874i
$453$	15.2875	−	13.2841i	0.718268	−	0.624140i
$454$	−5.99929	−	18.4639i	−0.281561	−	0.866555i
$455$	−15.3626	−	11.1615i	−0.720208	−	0.523261i
$456$	−0.501280	+	28.4068i	−0.0234746	+	1.33027i
$457$	−21.9910	+	4.67434i	−1.02870	+	0.218656i	−0.691195	−	0.722668i	$-0.742915\pi$
$457$	−21.9910	+	4.67434i	−1.02870	+	0.218656i	−0.337502	+	0.941325i	$0.609582\pi$
$458$	0.166201	+	0.0353271i	0.00776605	+	0.00165073i
$459$	5.55422	+	14.4941i	0.259249	+	0.676526i
$460$	3.73033	+	6.46112i	0.173928	+	0.301251i
$461$	8.75034	−	9.71823i	0.407544	−	0.452623i	−0.504075	−	0.863660i	$-0.668166\pi$
$461$	8.75034	−	9.71823i	0.407544	−	0.452623i	0.911619	+	0.411037i	$0.134833\pi$
$462$	−6.54972	−	0.805477i	−0.304721	−	0.0374742i
$463$	−23.9602	+	10.6678i	−1.11352	+	0.495773i	−0.879232	−	0.476394i	$-0.841944\pi$
$463$	−23.9602	+	10.6678i	−1.11352	+	0.495773i	−0.234292	+	0.972166i	$0.575277\pi$
$464$	−1.39491	+	2.41605i	−0.0647569	+	0.112162i
$465$	14.6389	+	11.3054i	0.678863	+	0.524278i
$466$	2.84149	+	4.92161i	0.131630	+	0.227989i
$467$	−1.78749	−	1.29869i	−0.0827153	−	0.0600962i	0.545659	−	0.838007i	$-0.316279\pi$
$467$	−1.78749	−	1.29869i	−0.0827153	−	0.0600962i	−0.628374	+	0.777911i	$0.716279\pi$
$468$	22.9972	−	4.04596i	1.06305	−	0.187025i
$469$	−2.50431	−	7.70748i	−0.115638	−	0.355899i
$470$	−0.680584	+	1.17881i	−0.0313930	+	0.0543742i
$471$	34.8508	−	10.6477i	1.60584	−	0.490618i
$472$	13.7055	−	15.2215i	0.630845	−	0.700625i
$473$	9.95500	+	11.0562i	0.457732	+	0.508362i
$474$	3.92369	+	2.35861i	0.180221	+	0.108335i
$475$	7.22429	−	3.21646i	0.331473	−	0.147581i
$476$	−4.41215	+	4.90018i	−0.202230	+	0.224600i
$477$	−9.43238	−	0.333000i	−0.431879	−	0.0152470i
$478$	6.12962	+	2.72908i	0.280362	+	0.124825i
$479$	2.23120	−	6.86694i	0.101946	−	0.313759i	−0.887055	−	0.461663i	$-0.847253\pi$
$479$	2.23120	−	6.86694i	0.101946	−	0.313759i	0.989002	+	0.147905i	$0.0472529\pi$
$480$	−11.5736	+	15.3526i	−0.528261	+	0.700747i
$481$	1.41359	+	13.4495i	0.0644543	+	0.613242i
$482$	−17.1755	+	3.65076i	−0.782322	+	0.166288i
$483$	5.15892	−	6.84340i	0.234739	−	0.311385i
$484$	−3.65237	−	2.65360i	−0.166017	−	0.120618i
$485$	6.25326	−	6.94494i	0.283946	−	0.315354i
$486$	8.45921	−	9.71243i	0.383718	−	0.440565i
$487$	8.66011	−	1.84076i	0.392427	−	0.0834129i	−0.00747220	−	0.999972i	$-0.502378\pi$
$487$	8.66011	−	1.84076i	0.392427	−	0.0834129i	0.399899	+	0.916559i	$0.369045\pi$
$488$	17.3837	−	3.69501i	0.786922	−	0.167265i
$489$	−13.3108	+	28.5309i	−0.601937	+	1.29021i
$490$	3.32170	+	5.75334i	0.150059	+	0.259910i
$491$	−10.7219			−0.483872			−0.241936	−	0.970292i	$-0.577782\pi$
$491$	−10.7219			−0.483872			−0.241936	+	0.970292i	$0.577782\pi$
$492$	−14.5763	−	20.8256i	−0.657149	−	0.938889i
$493$	−18.2216	+	13.2388i	−0.820660	+	0.596244i
$494$	23.6363	+	17.1728i	1.06345	+	0.772639i
$495$	14.2290	+	6.94669i	0.639546	+	0.312230i
$496$	−1.19140	−	1.68065i	−0.0534954	−	0.0754634i
$497$	−2.74743	−	4.75868i	−0.123239	−	0.213456i
$498$	−1.14112	−	5.87656i	−0.0511348	−	0.263335i
$499$	6.43799	+	2.86638i	0.288204	+	0.128317i	0.545747	−	0.837950i	$-0.316246\pi$
$499$	6.43799	+	2.86638i	0.288204	+	0.128317i	−0.257543	+	0.966267i	$0.582913\pi$
$500$	15.6226	+	3.32068i	0.698663	+	0.148505i
$501$	2.46372	−	10.6622i	0.110071	−	0.476354i
$502$	−8.54197			−0.381247
$503$	−25.3588	−	5.39019i	−1.13069	−	0.240337i	−0.395680	−	0.918388i	$-0.629491\pi$
$503$	−25.3588	−	5.39019i	−1.13069	−	0.240337i	−0.735014	+	0.678052i	$0.762825\pi$
$504$	13.3679	+	3.33842i	0.595452	+	0.148705i
$505$	−27.4406	+	5.83268i	−1.22109	+	0.259551i
$506$	6.13352	−	2.73082i	0.272668	−	0.121400i
$507$	16.0452	−	34.3919i	0.712594	−	1.52740i
$508$	2.35229	−	22.3805i	0.104366	−	0.992974i
$509$	12.7758	−	9.28220i	0.566279	−	0.411426i	−0.267472	−	0.963566i	$-0.586188\pi$
$509$	12.7758	−	9.28220i	0.566279	−	0.411426i	0.833752	+	0.552139i	$0.186188\pi$
$510$	−7.17193	+	3.97367i	−0.317578	+	0.175957i
$511$	−17.7934	−	7.92214i	−0.787135	−	0.350455i
$512$	3.37337	−	2.45090i	0.149083	−	0.108315i
$513$	−31.0552	+	1.60966i	−1.37112	+	0.0710681i
$514$	7.02910	+	3.12956i	0.310040	+	0.138039i
$515$	−14.5435	−	10.5665i	−0.640864	−	0.465615i
$516$	−7.07336	−	10.1059i	−0.311387	−	0.444888i
$517$	−1.91229	−	1.38936i	−0.0841022	−	0.0611038i
$518$	−0.979224	+	3.01374i	−0.0430246	+	0.132416i
$519$	−0.322934	+	18.3002i	−0.0141752	+	0.803291i
$520$	9.59841	+	29.5409i	0.420918	+	1.29545i
$521$	19.7889	−	34.2755i	0.866969	−	1.50164i	0.00189128	−	0.999998i	$-0.499398\pi$
$521$	19.7889	−	34.2755i	0.866969	−	1.50164i	0.865078	−	0.501637i	$-0.167269\pi$
$522$	16.7948	+	8.19931i	0.735087	+	0.358874i
$523$	0.187812	+	0.578025i	0.00821244	+	0.0252753i	0.955079	−	0.296352i	$-0.0957702\pi$
$523$	0.187812	+	0.578025i	0.00821244	+	0.0252753i	−0.946866	+	0.321627i	$0.895770\pi$
$524$	13.7844	−	10.0150i	0.602175	−	0.437506i
$525$	−0.731047	−	3.76476i	−0.0319055	−	0.164307i
$526$	−1.74988	+	3.03089i	−0.0762985	+	0.132153i
$527$	−3.26822	−	16.3077i	−0.142366	−	0.710373i
$528$	−1.28959	−	1.20302i	−0.0561220	−	0.0523547i
$529$	1.49274	−	14.2024i	0.0649016	−	0.617497i
$530$	−0.521139	−	4.95831i	−0.0226368	−	0.215375i
$531$	17.6609	+	13.8091i	0.766416	+	0.599262i
$532$	−6.60514	−	11.4404i	−0.286369	−	0.496006i
$533$	−65.8264			−2.85126
$534$	−1.63827	+	0.143014i	−0.0708947	+	0.00618881i
$535$	12.4204	+	13.7942i	0.536979	+	0.596375i
$536$	−4.09638	+	12.6073i	−0.176936	+	0.544554i
$537$	−18.8386	−	6.49068i	−0.812945	−	0.280093i
$538$	−8.17524	−	1.73770i	−0.352460	−	0.0749176i
$539$	−10.5391	+	4.69231i	−0.453951	+	0.202112i
$540$	−11.0064	−	7.15665i	−0.473642	−	0.307973i
$541$	17.8351	+	19.8079i	0.766792	+	0.851609i	0.992457	−	0.122596i	$-0.0391220\pi$
$541$	17.8351	+	19.8079i	0.766792	+	0.851609i	−0.225665	+	0.974205i	$0.572455\pi$
$542$	0.126078	+	0.0561334i	0.00541550	+	0.00241114i
$543$	−4.56489	−	10.7599i	−0.195898	−	0.461753i
$544$	16.9106	−	3.59446i	0.725037	−	0.154111i
$545$	−32.2024	+	23.3964i	−1.37940	+	1.00219i
$546$	10.6950	−	9.29347i	0.457706	−	0.397724i
$547$	36.8534	+	7.83342i	1.57574	+	0.334933i	0.911084	−	0.412220i	$-0.135247\pi$
$547$	36.8534	+	7.83342i	1.57574	+	0.334933i	0.664652	+	0.747153i	$0.268580\pi$
$548$	−1.00812	+	9.59166i	−0.0430649	+	0.409735i
$549$	5.35453	+	18.7005i	0.228526	+	0.798117i
$550$	0.928433	−	2.85742i	0.0395885	−	0.121841i
$551$	−13.9439	−	42.9149i	−0.594030	−	1.82824i
$552$	−13.4066	+	4.09600i	−0.570623	+	0.174337i
$553$	−5.36038			−0.227947
$554$	3.78980	+	0.805546i	0.161013	+	0.0342244i
$555$	4.57705	−	6.07154i	0.194285	−	0.257722i
$556$	1.92130	−	18.2800i	0.0814814	−	0.775244i
$557$	−3.41522			−0.144707			−0.0723537	−	0.997379i	$-0.523051\pi$
$557$	−3.41522			−0.144707			−0.0723537	+	0.997379i	$0.523051\pi$
$558$	−10.6781	+	8.74322i	−0.452040	+	0.370130i
$559$	−31.9432			−1.35105
$560$	0.124299	−	1.18263i	0.00525260	−	0.0499751i
$561$	−5.56079	−	13.1074i	−0.234777	−	0.553394i
$562$	−3.89870	−	0.828694i	−0.164457	−	0.0349563i
$563$	−21.8189			−0.919559			−0.459779	−	0.888033i	$-0.652072\pi$
$563$	−21.8189			−0.919559			−0.459779	+	0.888033i	$0.652072\pi$
$564$	1.43307	+	1.33687i	0.0603431	+	0.0562925i
$565$	−7.68358	−	23.6476i	−0.323251	−	0.994864i
$566$	−1.66848	+	5.13505i	−0.0701314	+	0.215842i
$567$	−2.63013	+	14.8497i	−0.110455	+	0.623630i
$568$	−0.939511	+	8.93885i	−0.0394210	+	0.375066i
$569$	−30.8204	−	6.55108i	−1.29206	−	0.274635i	−0.489916	−	0.871769i	$-0.662973\pi$
$569$	−30.8204	−	6.55108i	−1.29206	−	0.274635i	−0.802141	+	0.597134i	$0.796306\pi$
$570$	−3.13123	−	16.1252i	−0.131153	−	0.675412i
$571$	−32.8566	+	23.8717i	−1.37501	+	0.999000i	−0.377679	+	0.925937i	$0.623278\pi$
$571$	−32.8566	+	23.8717i	−1.37501	+	0.999000i	−0.997327	+	0.0730639i	$0.976722\pi$
$572$	−20.9513	+	4.45333i	−0.876016	+	0.186203i
$573$	−26.1514	+	34.6902i	−1.09249	+	1.44921i
$574$	−14.0909	−	6.27369i	−0.588144	−	0.261859i
$575$	2.61085	+	2.89965i	0.108880	+	0.120924i
$576$	−7.79066	−	9.29176i	−0.324611	−	0.387157i
$577$	2.97643	−	1.32519i	0.123911	−	0.0551685i	−0.343845	−	0.939026i	$-0.611729\pi$
$577$	2.97643	−	1.32519i	0.123911	−	0.0551685i	0.467755	+	0.883858i	$0.345063\pi$
$578$	−6.52750	−	1.38746i	−0.271508	−	0.0577109i
$579$	−19.8924	+	17.2856i	−0.826702	+	0.718363i
$580$	5.88688	−	18.1180i	0.244439	−	0.752307i
$581$	4.69016	+	5.20895i	0.194581	+	0.216104i
$582$	3.99846	+	5.71272i	0.165742	+	0.236800i
$583$	8.65770			0.358565
$584$	15.9298	+	27.5912i	0.659180	+	1.14173i
$585$	−31.5266	+	12.7235i	−1.30346	+	0.526053i
$586$	−2.50745	−	23.8567i	−0.103582	−	0.985513i
$587$	−3.03120	+	28.8399i	−0.125111	+	1.19035i	0.734213	+	0.678919i	$0.237551\pi$
$587$	−3.03120	+	28.8399i	−0.125111	+	1.19035i	−0.859324	+	0.511431i	$0.829115\pi$
$588$	9.14782	−	2.79485i	0.377250	−	0.115258i
$589$	33.0955	+	3.86878i	1.36367	+	0.159410i
$590$	−5.92116	+	10.2557i	−0.243770	+	0.422222i
$591$	7.33777	−	6.37616i	0.301836	−	0.262280i
$592$	−0.685134	+	0.497779i	−0.0281588	+	0.0204586i
$593$	−1.14215	−	3.51519i	−0.0469026	−	0.144351i	0.924863	−	0.380302i	$-0.124180\pi$
$593$	−1.14215	−	3.51519i	−0.0469026	−	0.144351i	−0.971765	+	0.235950i	$0.924180\pi$
$594$	−7.44046	+	9.17742i	−0.305286	+	0.376554i
$595$	4.80018	−	8.31415i	0.196788	−	0.340847i
$596$	6.09393	+	18.7552i	0.249617	+	0.768243i
$597$	2.40671	+	1.44673i	0.0985003	+	0.0592106i
$598$	−4.45462	+	13.7099i	−0.182163	+	0.560640i
$599$	−12.8017	−	9.30097i	−0.523063	−	0.380027i	0.294694	−	0.955592i	$-0.404782\pi$
$599$	−12.8017	−	9.30097i	−0.523063	−	0.380027i	−0.817756	+	0.575565i	$0.804782\pi$
$600$	−2.65223	+	5.68489i	−0.108277	+	0.232085i
$601$	36.8375	+	26.7640i	1.50263	+	1.09173i	0.969319	+	0.245807i	$0.0790529\pi$
$601$	36.8375	+	26.7640i	1.50263	+	1.09173i	0.533312	+	0.845918i	$0.320947\pi$
$602$	−6.83784	−	3.04440i	−0.278689	−	0.124081i
$603$	−14.0769	−	3.51548i	−0.573255	−	0.143162i
$604$	12.4616	−	9.05389i	0.507056	−	0.368398i
$605$	6.00476	+	2.67349i	0.244128	+	0.108693i
$606$	0.369321	−	20.9289i	0.0150026	−	0.850179i
$607$	−10.7523	+	7.81198i	−0.436421	+	0.317079i	−0.784211	−	0.620494i	$-0.786932\pi$
$607$	−10.7523	+	7.81198i	−0.436421	+	0.317079i	0.347790	+	0.937572i	$0.386932\pi$
$608$	−3.62045	+	34.4463i	−0.146829	+	1.39698i
$609$	−21.8003	+	1.90308i	−0.883393	+	0.0771166i
$610$	−9.38687	+	4.17931i	−0.380063	+	0.169215i
$611$	4.96418	−	1.05517i	0.200829	−	0.0426876i
$612$	3.24964	+	11.3492i	0.131359	+	0.458765i
$613$	−39.2635	−	8.34572i	−1.58584	−	0.337081i	−0.671177	−	0.741297i	$-0.734211\pi$
$613$	−39.2635	−	8.34572i	−1.58584	−	0.337081i	−0.914663	+	0.404217i	$0.867544\pi$
$614$	22.9947			0.927993
$615$	27.0628	+	25.2461i	1.09128	+	1.01802i
$616$	−12.3627	−	2.62778i	−0.498109	−	0.105876i
$617$	−10.0458	−	4.47267i	−0.404428	−	0.180063i	0.194433	−	0.980916i	$-0.437713\pi$
$617$	−10.0458	−	4.47267i	−0.404428	−	0.180063i	−0.598861	+	0.800853i	$0.704380\pi$
$618$	10.1249	−	8.79800i	0.407281	−	0.353908i
$619$	2.45723	+	4.25605i	0.0987646	+	0.171065i	0.911174	−	0.412023i	$-0.135178\pi$
$619$	2.45723	+	4.25605i	0.0987646	+	0.171065i	−0.812409	+	0.583088i	$0.801844\pi$
$620$	10.3438	+	9.53413i	0.415418	+	0.382900i
$621$	−5.49038	−	14.3275i	−0.220321	−	0.574943i
$622$	19.8824	+	14.4454i	0.797210	+	0.579207i
$623$	1.55778	−	1.13180i	0.0624113	−	0.0453444i
$624$	3.77225	−	0.329302i	0.151011	−	0.0131826i
$625$	−16.6470			−0.665880
$626$	1.04023	+	1.80173i	0.0415759	+	0.0720115i
$627$	28.4170	−	2.48069i	1.13487	−	0.0990692i
$628$	27.1099	−	5.76239i	1.08180	−	0.229944i
$629$	−6.68769	+	1.42151i	−0.266656	+	0.0566794i
$630$	−7.96128	−	0.281064i	−0.317185	−	0.0111979i
$631$	−25.1916	+	27.9781i	−1.00286	+	1.11379i	−0.00936129	+	0.999956i	$0.502980\pi$
$631$	−25.1916	+	27.9781i	−1.00286	+	1.11379i	−0.993500	+	0.113834i	$0.963687\pi$
$632$	7.09357	+	5.15378i	0.282167	+	0.205006i
$633$	−3.85354	−	9.08321i	−0.153165	−	0.361025i
$634$	5.03012	−	1.06918i	0.199771	−	0.0424627i
$635$	3.42483	+	32.5850i	0.135910	+	1.29310i
$636$	−7.12468	−	0.876185i	−0.282512	−	0.0347430i
$637$	7.65427	−	23.5574i	0.303273	−	0.933379i
$638$	−15.6616	−	6.97298i	−0.620048	−	0.276063i
$639$	−9.83158	−	0.347093i	−0.388931	−	0.0137308i
$640$	−10.5692	+	11.7383i	−0.417785	+	0.463997i
$641$	−3.34979	+	1.49142i	−0.132309	+	0.0589076i	−0.471823	−	0.881693i	$-0.656404\pi$
$641$	−3.34979	+	1.49142i	−0.132309	+	0.0589076i	0.339514	+	0.940601i	$0.389737\pi$
$642$	−12.1147	+	6.71227i	−0.478130	+	0.264912i
$643$	−25.4043	−	28.2144i	−1.00185	−	1.11267i	−0.993629	−	0.112700i	$-0.964050\pi$
$643$	−25.4043	−	28.2144i	−1.00185	−	1.11267i	−0.00822017	−	0.999966i	$-0.502617\pi$
$644$	4.36144	−	4.84387i	0.171865	−	0.190875i
$645$	13.1326	+	12.2511i	0.517096	+	0.482385i
$646$	−7.38538	+	12.7919i	−0.290574	+	0.503289i
$647$	−2.50015	−	7.69466i	−0.0982910	−	0.302508i	0.889806	−	0.456338i	$-0.150839\pi$
$647$	−2.50015	−	7.69466i	−0.0982910	−	0.302508i	−0.988097	+	0.153830i	$0.950839\pi$
$648$	17.7579	−	17.1224i	0.697597	−	0.672630i
$649$	−16.6371	−	12.0876i	−0.653064	−	0.474478i
$650$	3.22542	+	5.58660i	0.126511	+	0.219124i
$651$	5.44153	−	15.2156i	0.213270	−	0.596348i
$652$	−11.9724	+	20.7369i	−0.468876	+	0.812118i
$653$	−9.22684	+	4.10805i	−0.361074	+	0.160761i	−0.579252	−	0.815148i	$-0.696655\pi$
$653$	−9.22684	+	4.10805i	−0.361074	+	0.160761i	0.218178	+	0.975909i	$0.429989\pi$
$654$	−11.5995	−	27.3412i	−0.453575	−	1.06912i
$655$	−16.5993	+	18.4354i	−0.648589	+	0.720331i
$656$	−2.06109	−	3.56992i	−0.0804722	−	0.139382i
$657$	−28.9170	+	19.4887i	−1.12816	+	0.760326i
$658$	1.16321	+	0.247247i	0.0453466	+	0.00963871i
$659$	21.8368	−	4.64155i	0.850640	−	0.180809i	0.238092	−	0.971243i	$-0.423478\pi$
$659$	21.8368	−	4.64155i	0.850640	−	0.180809i	0.612548	+	0.790434i	$0.290145\pi$
$660$	10.3215	+	6.20449i	0.401765	+	0.241509i
$661$	−0.438321	−	0.318459i	−0.0170487	−	0.0123866i	0.579228	−	0.815165i	$-0.303354\pi$
$661$	−0.438321	−	0.318459i	−0.0170487	−	0.0123866i	−0.596277	+	0.802779i	$0.703354\pi$
$662$	1.36399	+	4.19793i	0.0530130	+	0.163157i
$663$	28.9031	+	9.95831i	1.12250	+	0.386749i
$664$	−1.19846	−	11.4026i	−0.0465091	−	0.442505i
$665$	12.8698	+	14.2933i	0.499069	+	0.554272i
$666$	3.64508	+	4.34741i	0.141244	+	0.168459i
$667$	18.0122	−	13.0866i	0.697434	−	0.506716i
$668$	2.57193	−	7.91559i	0.0995110	−	0.306263i
$669$	11.6612	+	1.43408i	0.450846	+	0.0554446i
$670$	0.801135	−	7.62229i	0.0309505	−	0.294475i
$671$	−5.51387	−	16.9700i	−0.212861	−	0.655118i
$672$	15.8810	+	5.47168i	0.612624	+	0.211075i
$673$	33.4031	+	37.0979i	1.28759	+	1.43002i	0.846347	+	0.532632i	$0.178797\pi$
$673$	33.4031	+	37.0979i	1.28759	+	1.43002i	0.441247	+	0.897386i	$0.354536\pi$
$674$	1.25213	−	3.85365i	0.0482301	−	0.148437i
$675$	−6.40867	−	2.46428i	−0.246670	−	0.0948502i
$676$	14.4319	−	24.9967i	0.555072	−	0.961413i
$677$	18.9571	−	32.8347i	0.728581	−	1.26194i	−0.228902	−	0.973450i	$-0.573513\pi$
$677$	18.9571	−	32.8347i	0.728581	−	1.26194i	0.957483	−	0.288490i	$-0.0931532\pi$
$678$	18.4824	−	1.61344i	0.709811	−	0.0619636i
$679$	−7.45877	−	3.32086i	−0.286241	−	0.127443i
$680$	−14.3459	+	6.38722i	−0.550141	+	0.244939i
$681$	38.9219	−	11.8915i	1.49149	−	0.455682i
$682$	9.50594	−	8.36074i	0.364001	−	0.320149i
$683$	−8.26691			−0.316324			−0.158162	−	0.987413i	$-0.550557\pi$
$683$	−8.26691			−0.316324			−0.158162	+	0.987413i	$0.550557\pi$
$684$	−23.6363	−	0.834454i	−0.903756	−	0.0319061i
$685$	−1.46778	−	13.9650i	−0.0560812	−	0.533577i
$686$	10.3685	−	11.5154i	0.395871	−	0.439660i
$687$	−0.0801920	+	0.347047i	−0.00305951	+	0.0132407i
$688$	−1.00018	−	1.73236i	−0.0381314	−	0.0660455i
$689$	−12.4383	+	13.8142i	−0.473862	+	0.526277i
$690$	7.08950	−	3.92800i	0.269893	−	0.149536i
$691$	15.5229	+	17.2400i	0.590521	+	0.655840i	0.962143	−	0.272544i	$-0.0878651\pi$
$691$	15.5229	+	17.2400i	0.590521	+	0.655840i	−0.371623	+	0.928384i	$0.621198\pi$
$692$	−1.45510	+	13.8443i	−0.0553145	+	0.526282i
$693$	1.93051	−	13.6983i	0.0733342	−	0.520355i
$694$	−12.8555	+	5.72365i	−0.487989	+	0.217267i
$695$	2.79733	+	26.6149i	0.106109	+	1.00956i
$696$	30.6788	+	18.4417i	1.16288	+	0.699029i
$697$	−3.47869	−	33.0975i	−0.131765	−	1.25366i
$698$	−1.70289	−	16.2019i	−0.0644554	−	0.613252i
$699$	−10.4207	+	5.77367i	−0.394146	+	0.218380i
$700$	−0.304889	−	2.90083i	−0.0115237	−	0.109641i
$701$	35.7286	−	15.9074i	1.34945	−	0.600814i	0.400516	−	0.916290i	$-0.368831\pi$
$701$	35.7286	−	15.9074i	1.34945	−	0.600814i	0.948934	+	0.315476i	$0.102164\pi$
$702$	−3.95388	−	25.0569i	−0.149230	−	0.945713i
$703$	1.43179	−	13.6226i	0.0540010	−	0.513785i
$704$	7.44263	+	8.26587i	0.280505	+	0.311532i
$705$	−2.44558	−	1.47009i	−0.0921058	−	0.0553667i
$706$	−16.9361	+	18.8094i	−0.637399	+	0.707903i
$707$	12.2546	+	21.2257i	0.460883	+	0.798273i
$708$	12.4679	+	11.6309i	0.468572	+	0.437118i
$709$	2.22865	−	2.47517i	0.0836987	−	0.0929568i	−0.699841	−	0.714299i	$-0.746746\pi$
$709$	2.22865	−	2.47517i	0.0836987	−	0.0929568i	0.783539	+	0.621342i	$0.213412\pi$
$710$	−0.543195	−	5.16815i	−0.0203857	−	0.193957i
$711$	−5.08873	+	8.13674i	−0.190842	+	0.305151i
$712$	−3.14964			−0.118038
$713$	3.23066	+	16.1202i	0.120989	+	0.603708i
$714$	5.23796	+	4.88635i	0.196026	+	0.182867i
$715$	28.4895	−	12.6843i	1.06545	−	0.474367i
$716$	−13.8443	−	6.16386i	−0.517384	−	0.230354i
$717$	−5.94681	+	12.7466i	−0.222088	+	0.476031i
$718$	10.0458	−	17.3998i	0.374905	−	0.649354i
$719$	−7.54499	+	13.0683i	−0.281381	+	0.487366i	−0.971725	−	0.236115i	$-0.924126\pi$
$719$	−7.54499	+	13.0683i	−0.281381	+	0.487366i	0.690344	+	0.723481i	$0.257459\pi$
$720$	−1.67716	−	1.31137i	−0.0625039	−	0.0488719i
$721$	−4.85328	+	14.9369i	−0.180746	+	0.556278i
$722$	−9.29659	−	10.3249i	−0.345983	−	0.384253i
$723$	−7.01666	−	36.1345i	−0.260952	−	1.34386i
$724$	−2.74703	−	8.45449i	−0.102093	−	0.314209i
$725$	1.04143	−	9.90858i	0.0386779	−	0.367996i
$726$	−2.95232	+	3.91630i	−0.109571	+	0.145348i
$727$	4.85163	−	14.9318i	0.179937	−	0.553789i	−0.819888	−	0.572525i	$-0.805964\pi$
$727$	4.85163	−	14.9318i	0.179937	−	0.553789i	0.999824	+	0.0187357i	$0.00596411\pi$
$728$	21.9541	−	15.9506i	0.813674	−	0.591169i
$729$	20.0442	+	18.0896i	0.742376	+	0.669983i
$730$	−12.3255	−	13.6889i	−0.456188	−	0.506648i
$731$	−1.68809	−	16.0611i	−0.0624362	−	0.594040i
$732$	2.82012	+	14.5231i	0.104235	+	0.536789i
$733$	0.790916	+	2.43419i	0.0292132	+	0.0899088i	0.964600	−	0.263717i	$-0.0849486\pi$
$733$	0.790916	+	2.43419i	0.0292132	+	0.0899088i	−0.935387	+	0.353626i	$0.884949\pi$
$734$	18.1721	+	13.2028i	0.670745	+	0.487325i
$735$	−12.1817	+	6.74940i	−0.449330	+	0.248955i
$736$	−16.7163	+	3.55315i	−0.616170	+	0.130971i
$737$	13.0184	+	2.76716i	0.479541	+	0.101929i
$738$	−22.8999	+	15.4334i	−0.842957	+	0.568112i
$739$	−19.0062	−	32.9197i	−0.699155	−	1.21097i	−0.968760	−	0.248000i	$-0.920227\pi$
$739$	−19.0062	−	32.9197i	−0.699155	−	1.21097i	0.269605	−	0.962971i	$-0.413107\pi$
$740$	3.86952	−	4.29753i	0.142246	−	0.157980i
$741$	−36.8679	+	48.9059i	−1.35438	+	1.79660i
$742$	−3.97915	+	1.77163i	−0.146079	+	0.0650387i
$743$	8.39502	−	14.5406i	0.307983	−	0.533443i	−0.669938	−	0.742417i	$-0.733679\pi$
$743$	8.39502	−	14.5406i	0.307983	−	0.533443i	0.977921	+	0.208975i	$0.0670126\pi$
$744$	−21.8301	+	14.9035i	−0.800331	+	0.546390i
$745$	−14.3560	−	24.8653i	−0.525963	−	0.910995i
$746$	3.28854	+	2.38927i	0.120402	+	0.0874773i
$747$	12.3593	−	2.17441i	0.452205	−	0.0795574i
$748$	−3.34634	−	10.2990i	−0.122354	−	0.376567i
$749$	8.10839	−	14.0441i	0.296274	−	0.513162i
$750$	3.90633	−	16.9054i	0.142639	−	0.617299i
$751$	11.3705	−	12.6283i	0.414917	−	0.460812i	−0.499067	−	0.866564i	$-0.666324\pi$
$751$	11.3705	−	12.6283i	0.414917	−	0.460812i	0.913983	+	0.405752i	$0.132990\pi$
$752$	0.212658	+	0.236181i	0.00775484	+	0.00861262i
$753$	0.315938	−	17.9038i	0.0115134	−	0.652450i
$754$	33.6267	−	14.9716i	1.22461	−	0.545232i
$755$	−15.0064	+	16.6663i	−0.546138	+	0.606548i
$756$	−2.97498	+	11.0774i	−0.108199	+	0.402879i
$757$	22.1422	+	9.85836i	0.804773	+	0.358308i	0.767542	−	0.640999i	$-0.221480\pi$
$757$	22.1422	+	9.85836i	0.804773	+	0.358308i	0.0372312	+	0.999307i	$0.488146\pi$
$758$	−2.32419	+	7.15313i	−0.0844185	+	0.259813i
$759$	5.49688	+	12.9567i	0.199524	+	0.470299i
$760$	−3.28856	−	31.2886i	−0.119289	−	1.13496i
$761$	41.5211	−	8.82559i	1.50514	−	0.319927i	0.619758	−	0.784793i	$-0.287231\pi$
$761$	41.5211	−	8.82559i	1.50514	−	0.319927i	0.885381	+	0.464866i	$0.153897\pi$
$762$	−24.2644	−	2.98401i	−0.879006	−	0.108099i
$763$	28.1339	+	20.4405i	1.01852	+	0.739995i
$764$	−22.1088	+	24.5543i	−0.799868	+	0.888344i
$765$	−8.06346	−	15.1792i	−0.291535	−	0.548804i
$766$	−5.39186	+	1.14608i	−0.194816	+	0.0414094i
$767$	43.1890	−	9.18010i	1.55946	−	0.331474i
$768$	−14.7869	−	21.1265i	−0.533576	−	0.762336i
$769$	−22.1542	−	38.3722i	−0.798902	−	1.38374i	−0.920332	−	0.391139i	$-0.872081\pi$
$769$	−22.1542	−	38.3722i	−0.798902	−	1.38374i	0.121430	−	0.992600i	$-0.461252\pi$
$770$	7.30742			0.263341
$771$	−6.81947	+	14.6171i	−0.245597	+	0.526422i
$772$	−16.2154	+	11.7812i	−0.583604	+	0.424013i
$773$	−36.5408	−	26.5484i	−1.31428	−	0.954880i	−0.999985	−	0.00555508i	$-0.998232\pi$
$773$	−36.5408	−	26.5484i	−1.31428	−	0.954880i	−0.314295	−	0.949325i	$-0.601768\pi$
$774$	−11.1125	+	7.48930i	−0.399431	+	0.269197i
$775$	6.32821	+	3.75256i	0.227316	+	0.134796i
$776$	6.67756	+	11.5659i	0.239710	+	0.415191i
$777$	−6.28052	−	2.16390i	−0.225312	−	0.0776295i
$778$	21.6979	+	9.66054i	0.777909	+	0.346347i
$779$	65.2167	+	13.8622i	2.33663	+	0.496666i
$780$	−24.7285	+	7.55510i	−0.885423	+	0.270516i
$781$	9.02411			0.322908
$782$	−7.12876	−	1.51526i	−0.254924	−	0.0541857i
$783$	−17.8068	+	34.8982i	−0.636361	+	1.24716i
$784$	1.51724	−	0.322499i	0.0541871	−	0.0115178i
$785$	−36.8640	+	16.4129i	−1.31573	+	0.585802i
$786$	−10.6139	−	15.1645i	−0.378587	−	0.540898i
$787$	1.39688	−	13.2904i	0.0497934	−	0.473752i	−0.941004	−	0.338396i	$-0.890116\pi$
$787$	1.39688	−	13.2904i	0.0497934	−	0.473752i	0.990797	−	0.135356i	$-0.0432178\pi$
$788$	5.98140	−	4.34574i	0.213079	−	0.154811i
$789$	−6.28795	−	3.77982i	−0.223857	−	0.134565i
$790$	−4.63117	−	2.06193i	−0.164770	−	0.0733602i
$791$	−17.5744	+	12.7686i	−0.624874	+	0.453997i
$792$	−15.7250	+	16.2713i	−0.558764	+	0.578174i
$793$	34.9988	+	15.5825i	1.24284	+	0.553349i
$794$	−0.0397876	−	0.0289074i	−0.00141201	−	0.00102589i
$795$	10.4118	−	0.908905i	0.369268	−	0.0322355i
$796$	1.72782	+	1.25534i	0.0612411	+	0.0444943i
$797$	2.51777	−	7.74889i	0.0891839	−	0.274480i	−0.896510	−	0.443023i	$-0.853906\pi$
$797$	2.51777	−	7.74889i	0.0891839	−	0.274480i	0.985694	+	0.168543i	$0.0539062\pi$
$798$	−12.5531	+	6.95515i	−0.444374	+	0.246210i
$799$	0.792880	+	2.44023i	0.0280501	+	0.0863292i
$800$	−3.82378	+	6.62299i	−0.135191	+	0.234158i
$801$	−0.239160	−	3.43906i	−0.00845030	−	0.121513i
$802$	5.71774	+	17.5974i	0.201900	+	0.621385i
$803$	25.8783	−	18.8017i	0.913225	−	0.663497i
$804$	−10.4332	−	3.59468i	−0.367951	−	0.126775i
$805$	−4.74501	+	8.21860i	−0.167240	+	0.289667i
$806$	−0.316647	+	27.1793i	−0.0111534	+	0.957349i
$807$	3.94456	−	17.0708i	0.138855	−	0.600922i
$808$	4.19060	−	39.8709i	0.147425	−	1.40265i
$809$	4.34157	+	41.3073i	0.152641	+	1.45229i	0.755872	+	0.654720i	$0.227213\pi$
$809$	4.34157	+	41.3073i	0.152641	+	1.45229i	−0.603230	+	0.797567i	$0.706120\pi$
$810$	−7.98445	+	11.8179i	−0.280545	+	0.415239i
$811$	0.553261	+	0.958276i	0.0194276	+	0.0336496i	0.875576	−	0.483081i	$-0.160482\pi$
$811$	0.553261	+	0.958276i	0.0194276	+	0.0336496i	−0.856148	+	0.516730i	$0.827149\pi$
$812$	−16.6435			−0.584072
$813$	−0.122318	+	0.262180i	−0.00428986	+	0.00919505i
$814$	−3.48224	−	3.86742i	−0.122053	−	0.135553i
$815$	10.7732	−	33.1564i	0.377367	−	1.16142i
$816$	0.364923	+	1.87929i	0.0127749	+	0.0657882i
$817$	31.6474	+	6.72686i	1.10720	+	0.235343i
$818$	27.2314	−	12.1242i	0.952123	−	0.423912i
$819$	19.0833	+	22.7603i	0.666826	+	0.795310i
$820$	18.8350	+	20.9184i	0.657748	+	0.730503i
$821$	−34.2798	−	15.2623i	−1.19637	−	0.532660i	−0.290773	−	0.956792i	$-0.593912\pi$
$821$	−34.2798	−	15.2623i	−1.19637	−	0.532660i	−0.905600	+	0.424132i	$0.860579\pi$
$822$	10.3990	+	1.27886i	0.362708	+	0.0446054i
$823$	34.1576	−	7.26043i	1.19066	−	0.253083i	0.430362	−	0.902657i	$-0.358386\pi$
$823$	34.1576	−	7.26043i	1.19066	−	0.253083i	0.760298	+	0.649574i	$0.225053\pi$
$824$	20.7837	−	15.1002i	0.724033	−	0.526041i
$825$	5.95476	+	2.05166i	0.207318	+	0.0714297i
$826$	10.1200	+	2.15108i	0.352121	+	0.0748457i
$827$	−4.30425	+	40.9522i	−0.149673	+	1.42405i	0.619495	+	0.785001i	$0.287338\pi$
$827$	−4.30425	+	40.9522i	−0.149673	+	1.42405i	−0.769168	+	0.639046i	$0.779329\pi$
$828$	−3.21229	−	11.2188i	−0.111635	−	0.389880i
$829$	−4.81299	+	14.8129i	−0.167162	+	0.514472i	−0.999189	−	0.0402632i	$-0.987180\pi$
$829$	−4.81299	+	14.8129i	−0.167162	+	0.514472i	0.832027	+	0.554735i	$0.187180\pi$
$830$	2.04844	+	6.30446i	0.0711025	+	0.218831i
$831$	−1.82858	+	7.91353i	−0.0634327	+	0.274517i
$832$	−23.8816			−0.827946
$833$	12.2492	+	2.60365i	0.424409	+	0.0902110i
$834$	−19.8187	−	2.43728i	−0.686265	−	0.0843961i
$835$	−1.26666	+	12.0515i	−0.0438346	+	0.417058i
$836$	21.6950			0.750338
$837$	−17.9307	−	22.7044i	−0.619774	−	0.784780i
$838$	12.5352			0.433021
$839$	−1.98657	+	18.9010i	−0.0685840	+	0.652533i	0.905189	+	0.425010i	$0.139729\pi$
$839$	−1.98657	+	18.9010i	−0.0685840	+	0.652533i	−0.973773	+	0.227523i	$0.926937\pi$
$840$	−15.1433	−	1.86231i	−0.522494	−	0.0642557i
$841$	−27.2419	−	5.79045i	−0.939376	−	0.199671i
$842$	−11.8494			−0.408358
$843$	1.88112	−	8.14093i	0.0647893	−	0.280389i
$844$	−2.31896	−	7.13703i	−0.0798219	−	0.245667i
$845$	−12.9862	+	39.9676i	−0.446740	+	1.37493i
$846$	1.47956	−	1.53096i	0.0508685	−	0.0526355i
$847$	0.600263	−	5.71112i	0.0206253	−	0.196236i
$848$	−1.13863	−	0.242023i	−0.0391007	−	0.00831112i
$849$	−10.7012	−	3.68702i	−0.367266	−	0.126538i
$850$	−2.63849	+	1.91698i	−0.0904995	+	0.0657518i
$851$	6.61083	−	1.40517i	0.226616	−	0.0481688i
$852$	−7.42621	−	0.913267i	−0.254418	−	0.0312880i
$853$	−41.6525	−	18.5449i	−1.42616	−	0.634966i	−0.458835	−	0.888521i	$-0.651733\pi$
$853$	−41.6525	−	18.5449i	−1.42616	−	0.634966i	−0.967321	+	0.253556i	$0.918400\pi$
$854$	6.00680	+	6.67123i	0.205548	+	0.228285i
$855$	33.9140	−	5.96657i	1.15983	−	0.204052i
$856$	−24.2329	+	10.7892i	−0.828264	+	0.368767i
$857$	11.0727	+	2.35358i	0.378237	+	0.0803967i	0.393107	−	0.919493i	$-0.371400\pi$
$857$	11.0727	+	2.35358i	0.378237	+	0.0803967i	−0.0148703	+	0.999889i	$0.504734\pi$
$858$	4.43558	+	22.8424i	0.151428	+	0.779827i
$859$	12.2575	−	37.7247i	0.418220	−	1.28715i	−0.491118	−	0.871093i	$-0.663412\pi$
$859$	12.2575	−	37.7247i	0.418220	−	1.28715i	0.909339	−	0.416057i	$-0.136588\pi$
$860$	9.13998	+	10.1510i	0.311671	+	0.346145i
$861$	13.6707	−	29.3022i	0.465896	−	0.998618i
$862$	−24.7447			−0.842807
$863$	−17.7897	−	30.8126i	−0.605568	−	1.04887i	−0.991961	−	0.126540i	$-0.959613\pi$
$863$	−17.7897	−	30.8126i	−0.605568	−	1.04887i	0.386394	−	0.922334i	$-0.373721\pi$
$864$	23.3819	−	18.9121i	0.795468	−	0.643402i
$865$	−2.11856	−	20.1567i	−0.0720331	−	0.685349i
$866$	0.521566	−	4.96237i	0.0177235	−	0.168628i
$867$	3.14952	−	13.6302i	0.106963	−	0.462905i
$868$	5.12932	−	11.1686i	0.174101	−	0.379088i
$869$	4.40164	−	7.62386i	0.149315	−	0.258622i
$870$	−19.5667	−	6.74154i	−0.663373	−	0.228560i
$871$	−23.1186	+	16.7966i	−0.783342	+	0.569131i
$872$	−17.5779	−	54.0991i	−0.595261	−	1.83203i
$873$	−12.1216	+	8.16939i	−0.410255	+	0.276492i
$874$	7.30050	−	12.6448i	0.246943	−	0.427718i
$875$	6.27799	+	19.3217i	0.212235	+	0.653191i
$876$	−23.1988	+	12.8535i	−0.783815	+	0.434280i
$877$	−13.7412	+	42.2911i	−0.464008	+	1.42807i	0.396218	+	0.918157i	$0.370323\pi$
$877$	−13.7412	+	42.2911i	−0.464008	+	1.42807i	−0.860226	+	0.509913i	$0.829677\pi$
$878$	−3.56319	−	2.58881i	−0.120252	−	0.0873681i
$879$	50.0960	−	4.37317i	1.68969	−	0.147503i
$880$	1.57994	+	1.14789i	0.0532596	+	0.0386954i
$881$	−8.41391	−	3.74612i	−0.283472	−	0.126210i	0.260075	−	0.965588i	$-0.416253\pi$
$881$	−8.41391	−	3.74612i	−0.283472	−	0.126210i	−0.543547	+	0.839378i	$0.682919\pi$
$882$	−2.86040	−	9.98983i	−0.0963147	−	0.336375i
$883$	21.9694	−	15.9617i	0.739331	−	0.537155i	−0.153171	−	0.988200i	$-0.548948\pi$
$883$	21.9694	−	15.9617i	0.739331	−	0.537155i	0.892501	+	0.451045i	$0.148948\pi$
$884$	21.2405	+	9.45690i	0.714397	+	0.318070i
$885$	−21.2768	−	12.7899i	−0.715212	−	0.429929i
$886$	6.12585	−	4.45069i	0.205802	−	0.149524i
$887$	5.01254	−	47.6911i	0.168305	−	1.60131i	−0.505784	−	0.862660i	$-0.668797\pi$
$887$	5.01254	−	47.6911i	0.168305	−	1.60131i	0.674088	−	0.738651i	$-0.264537\pi$
$888$	6.23071	+	8.90201i	0.209089	+	0.298732i
$889$	26.1502	−	11.6428i	0.877051	−	0.390488i
$890$	1.78122	−	0.378611i	0.0597068	−	0.0126911i
$891$	−18.9605	−	15.9345i	−0.635200	−	0.533825i
$892$	8.74055	+	1.85786i	0.292655	+	0.0622058i
$893$	−5.14041			−0.172017
$894$	20.4885	−	6.25968i	0.685238	−	0.209355i
$895$	21.5820	+	4.58740i	0.721408	+	0.153340i
$896$	12.6068	+	5.61289i	0.421162	+	0.187514i
$897$	−28.5709	−	9.84386i	−0.953954	−	0.328677i
$898$	−5.73149	−	9.92723i	−0.191262	−	0.331276i
$899$	25.0695	−	33.6732i	0.836115	−	1.12306i
$900$	−4.69271	−	2.29101i	−0.156424	−	0.0763671i
$901$	−7.60309	−	5.52397i	−0.253296	−	0.184030i
$902$	20.4935	−	14.8894i	0.682358	−	0.495762i
$903$	6.63390	−	14.2194i	0.220763	−	0.473190i
$904$	35.5332			1.18182
$905$	6.47142	+	11.2088i	0.215117	+	0.372594i
$906$	−9.59539	−	13.7092i	−0.318785	−	0.455458i
$907$	−47.7404	+	10.1475i	−1.58519	+	0.336943i	−0.914435	−	0.404732i	$-0.867365\pi$
$907$	−47.7404	+	10.1475i	−1.58519	+	0.336943i	−0.670759	+	0.741675i	$0.734031\pi$
$908$	30.2768	−	6.43553i	1.00477	−	0.213570i
$909$	43.8529	+	1.54818i	1.45451	+	0.0513498i
$910$	−10.4984	+	11.6597i	−0.348018	+	0.386514i
$911$	−38.6338	−	28.0691i	−1.28000	−	0.929971i	−0.280443	−	0.959871i	$-0.590481\pi$
$911$	−38.6338	−	28.0691i	−1.28000	−	0.929971i	−0.999553	+	0.0298992i	$0.990481\pi$
$912$	−3.80666	−	0.468138i	−0.126051	−	0.0155016i
$913$	−11.2598	+	2.39334i	−0.372644	+	0.0792079i
$914$	1.94170	+	18.4740i	0.0642258	+	0.611067i
$915$	−8.41254	−	19.8293i	−0.278110	−	0.655535i
$916$	−0.0837141	+	0.257645i	−0.00276599	+	0.00851284i
$917$	19.7993	+	8.81524i	0.653832	+	0.291105i
$918$	12.3897	−	3.31219i	0.408921	−	0.109318i
$919$	−0.110375	+	0.122584i	−0.00364093	+	0.00404366i	−0.744963	−	0.667106i	$-0.767533\pi$
$919$	−0.110375	+	0.122584i	−0.00364093	+	0.00404366i	0.741322	+	0.671150i	$0.234199\pi$
$920$	14.1810	−	6.31381i	0.467535	−	0.208160i
$921$	−0.850498	+	48.1965i	−0.0280248	+	1.58813i
$922$	−7.22988	−	8.02960i	−0.238103	−	0.264441i
$923$	−12.9647	+	14.3988i	−0.426739	+	0.473942i
$924$	2.36874	−	10.2512i	0.0779259	−	0.337240i
$925$	1.51220	−	2.61921i	0.0497209	−	0.0861192i
$926$	6.69651	+	20.6097i	0.220061	+	0.677278i
$927$	18.0659	+	21.5469i	0.593363	+	0.707692i
$928$	35.3035	+	25.6495i	1.15890	+	0.841987i
$929$	−18.7897	−	32.5447i	−0.616469	−	1.06776i	−0.990125	−	0.140188i	$-0.955229\pi$
$929$	−18.7897	−	32.5447i	−0.616469	−	1.06776i	0.373656	−	0.927567i	$-0.378104\pi$
$930$	10.5541	−	11.0526i	0.346084	−	0.362429i
$931$	−12.5443	+	21.7274i	−0.411123	+	0.712085i
$932$	−8.27740	+	3.68534i	−0.271135	+	0.120717i
$933$	−31.0126	+	41.1387i	−1.01531	+	1.34682i
$934$	−1.22153	+	1.35665i	−0.0399696	+	0.0443908i
$935$	7.88326	+	13.6542i	0.257810	+	0.446540i
$936$	−3.37052	−	48.4673i	−0.110169	−	1.58420i
$937$	−43.8005	−	9.31009i	−1.43090	−	0.304147i	−0.573673	−	0.819085i	$-0.694482\pi$
$937$	−43.8005	−	9.31009i	−1.43090	−	0.304147i	−0.857228	+	0.514937i	$0.827815\pi$
$938$	−6.54963	+	1.39217i	−0.213853	+	0.0454559i
$939$	−3.81486	+	2.11366i	−0.124493	+	0.0689765i
$940$	−1.75572	−	1.27561i	−0.0572654	−	0.0416058i
$941$	16.9142	+	52.0565i	0.551386	+	1.69699i	0.705301	+	0.708908i	$0.250812\pi$
$941$	16.9142	+	52.0565i	0.551386	+	1.69699i	−0.153915	+	0.988084i	$0.549188\pi$
$942$	−5.73942	−	29.5570i	−0.187000	−	0.963018i
$943$	3.43871	+	32.7172i	0.111980	+	1.06542i
$944$	1.85015	+	2.05480i	0.0602173	+	0.0668780i
$945$	0.883565	−	16.6763i	0.0287424	−	0.542479i
$946$	9.94477	−	7.22529i	0.323332	−	0.234915i
$947$	−3.35777	+	10.3341i	−0.109113	+	0.335815i	−0.990674	−	0.136256i	$-0.956493\pi$
$947$	−3.35777	+	10.3341i	−0.109113	+	0.335815i	0.881561	+	0.472070i	$0.156493\pi$
$948$	−4.39380	+	5.82845i	−0.142704	+	0.189299i
$949$	−7.17894	+	68.3031i	−0.233038	+	2.21721i
$950$	−2.01908	−	6.21409i	−0.0655076	−	0.201612i
$951$	2.05494	+	10.5826i	0.0666360	+	0.343163i
$952$	9.18017	+	10.1956i	0.297531	+	0.330442i
$953$	11.3254	−	34.8561i	0.366867	−	1.12910i	−0.581937	−	0.813234i	$-0.697705\pi$
$953$	11.3254	−	34.8561i	0.366867	−	1.12910i	0.948804	−	0.315866i	$-0.102295\pi$
$954$	−1.08826	+	7.72196i	−0.0352339	+	0.250008i
$955$	24.0532	−	41.6613i	0.778343	−	1.34813i
$956$	−5.34885	+	9.26449i	−0.172994	+	0.299635i
$957$	15.1945	−	32.5684i	0.491168	−	1.05279i
$958$	−5.44996	−	2.42648i	−0.176080	−	0.0783960i
$959$	−11.2073	+	4.98979i	−0.361901	+	0.161129i
$960$	9.81830	+	9.15922i	0.316884	+	0.295613i
$961$	14.8703	+	27.2006i	0.479688	+	0.877439i
$962$	11.1737			0.360254
$963$	−13.6207	−	25.6404i	−0.438920	−	0.826252i
$964$	−2.92635	−	27.8424i	−0.0942515	−	0.896743i
$965$	19.5267	−	21.6866i	0.628586	−	0.698116i
$966$	−5.17776	−	4.83019i	−0.166592	−	0.155409i
$967$	−3.99182	−	6.91403i	−0.128368	−	0.222340i	0.794676	−	0.607033i	$-0.207641\pi$
$967$	−3.99182	−	6.91403i	−0.128368	−	0.222340i	−0.923044	+	0.384693i	$0.874307\pi$
$968$	−6.28534	+	6.98058i	−0.202018	+	0.224364i
$969$	−26.5383	−	15.9527i	−0.852532	−	0.512475i
$970$	−5.16669	−	5.73819i	−0.165892	−	0.184242i
$971$	1.74099	−	16.5645i	0.0558712	−	0.531579i	−0.930412	−	0.366516i	$-0.880551\pi$
$971$	1.74099	−	16.5645i	0.0558712	−	0.531579i	0.986283	−	0.165063i	$-0.0527828\pi$
$972$	13.9905	+	15.0318i	0.448746	+	0.482146i
$973$	21.3590	−	9.50965i	0.684739	−	0.304865i
$974$	−0.764645	−	7.27511i	−0.0245008	−	0.233110i
$975$	−11.8287	+	6.55379i	−0.378821	+	0.209889i
$976$	0.250775	+	2.38597i	0.00802712	+	0.0763730i
$977$	2.44066	+	23.2214i	0.0780838	+	0.742918i	0.961588	+	0.274495i	$0.0885107\pi$
$977$	2.44066	+	23.2214i	0.0780838	+	0.742918i	−0.883505	+	0.468422i	$0.844823\pi$
$978$	22.2947	+	13.4018i	0.712905	+	0.428542i
$979$	0.330546	+	3.14494i	0.0105643	+	0.100513i
$980$	−9.67625	+	4.30815i	−0.309097	+	0.137619i
$981$	57.7355	−	23.3010i	1.84335	−	0.743943i
$982$	−0.926002	+	8.81032i	−0.0295499	+	0.281149i
$983$	33.5935	+	37.3093i	1.07146	+	1.18998i	0.980985	+	0.194084i	$0.0621734\pi$
$983$	33.5935	+	37.3093i	1.07146	+	1.18998i	0.0904798	+	0.995898i	$0.471160\pi$
$984$	−46.2637	+	25.6328i	−1.47483	+	0.817144i
$985$	−7.20285	+	7.99958i	−0.229502	+	0.254888i
$986$	9.30476	+	16.1163i	0.296324	+	0.513248i
$987$	−0.561248	+	2.42891i	−0.0178647	+	0.0773132i
$988$	−31.1688	+	34.6164i	−0.991610	+	1.10129i
$989$	1.66869	+	15.8765i	0.0530611	+	0.504843i
$990$	6.93709	−	11.0922i	0.220475	−	0.352534i
$991$	−14.7877			−0.469746			−0.234873	−	0.972026i	$-0.575467\pi$
$991$	−14.7877			−0.469746			−0.234873	+	0.972026i	$0.575467\pi$
$992$	−28.0923	+	15.7856i	−0.891930	+	0.501194i
$993$	−8.84921	+	2.70362i	−0.280821	+	0.0857969i
$994$	−4.14756	+	1.84661i	−0.131553	+	0.0585710i
$995$	−2.84067	−	1.26475i	−0.0900553	−	0.0400952i
$996$	9.50822	−	0.830028i	0.301279	−	0.0263004i
$997$	11.0414	−	19.1243i	0.349686	−	0.605674i	−0.636508	−	0.771270i	$-0.719622\pi$
$997$	11.0414	−	19.1243i	0.349686	−	0.605674i	0.986194	+	0.165597i	$0.0529550\pi$
$998$	2.91136	−	5.04263i	0.0921576	−	0.159622i
$999$	−9.24690	+	7.47921i	−0.292559	+	0.236632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.bb.a.103.18	yes	240
3.2	odd	2		837.2.be.a.10.13		240
9.2	odd	6		837.2.bd.a.289.18		240
9.7	even	3		279.2.ba.a.196.13	yes	240
31.28	even	15		279.2.ba.a.121.13	✓	240
93.59	odd	30		837.2.bd.a.307.18		240
279.214	even	15	inner	279.2.bb.a.214.18	yes	240
279.245	odd	30		837.2.be.a.586.13		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
279.2.ba.a.121.13	✓	240	31.28	even	15
279.2.ba.a.196.13	yes	240	9.7	even	3
279.2.bb.a.103.18	yes	240	1.1	even	1	trivial
279.2.bb.a.214.18	yes	240	279.214	even	15	inner
837.2.bd.a.289.18		240	9.2	odd	6
837.2.bd.a.307.18		240	93.59	odd	30
837.2.be.a.10.13		240	3.2	odd	2
837.2.be.a.586.13		240	279.245	odd	30

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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.bb (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0863656 - 0.821714i) q^{2} +(1.71910 + 0.211413i) q^{3} +(1.28854 + 0.273888i) q^{4} -1.91797 q^{5} +(0.322192 - 1.39435i) q^{6} +(0.517805 + 1.59364i) q^{7} +(0.846987 - 2.60676i) q^{8} +(2.91061 + 0.726880i) q^{9} +(-0.165647 + 1.57602i) q^{10} +(-2.69176 - 0.572151i) q^{11} +(2.15723 + 0.743254i) q^{12} +(4.78011 - 3.47295i) q^{13} +(1.35424 - 0.287852i) q^{14} +(-3.29718 - 0.405484i) q^{15} +(0.338017 + 0.150495i) q^{16} +(1.99882 + 2.21991i) q^{17} +(0.848664 - 2.32891i) q^{18} +(-5.46720 + 2.43415i) q^{19} +(-2.47138 - 0.525309i) q^{20} +(0.553242 + 2.84909i) q^{21} +(-0.702620 + 2.16244i) q^{22} +(-1.97584 - 2.19440i) q^{23} +(2.00716 - 4.30222i) q^{24} -1.32139 q^{25} +(-2.44094 - 4.22783i) q^{26} +(4.84996 + 1.86492i) q^{27} +(0.230734 + 2.19529i) q^{28} +(-0.788137 + 7.49862i) q^{29} +(-0.617955 + 2.67432i) q^{30} +(-4.78907 - 2.83987i) q^{31} +(2.89377 - 5.01215i) q^{32} +(-4.50644 - 1.55266i) q^{33} +(1.99676 - 1.45073i) q^{34} +(-0.993134 - 3.05655i) q^{35} +(3.55135 + 1.73379i) q^{36} +(-1.14441 + 1.98217i) q^{37} +(1.52800 + 4.70270i) q^{38} +(8.95171 - 4.95978i) q^{39} +(-1.62450 + 4.99969i) q^{40} +(-9.01317 - 6.54845i) q^{41} +(2.38892 - 0.208543i) q^{42} +(-4.37377 - 3.17773i) q^{43} +(-3.31174 - 1.47448i) q^{44} +(-5.58246 - 1.39413i) q^{45} +(-1.97381 + 1.43406i) q^{46} +(0.784681 + 0.349363i) q^{47} +(0.549268 + 0.330176i) q^{48} +(3.39156 - 2.46411i) q^{49} +(-0.114122 + 1.08580i) q^{50} +(2.96685 + 4.23882i) q^{51} +(7.11056 - 3.16583i) q^{52} +(-3.07734 + 0.654108i) q^{53} +(1.95130 - 3.82421i) q^{54} +(5.16272 + 1.09737i) q^{55} +4.59281 q^{56} +(-9.91327 + 3.02872i) q^{57} +(6.09366 + 1.29525i) q^{58} +(6.82682 + 3.03950i) q^{59} +(-4.13750 - 1.42554i) q^{60} +(3.24200 + 5.61530i) q^{61} +(-2.74717 + 3.68998i) q^{62} +(0.348743 + 5.01484i) q^{63} +(-3.26995 - 2.37576i) q^{64} +(-9.16811 + 6.66102i) q^{65} +(-1.66504 + 3.56891i) q^{66} -4.83641 q^{67} +(1.96755 + 3.40789i) q^{68} +(-2.93275 - 4.19010i) q^{69} +(-2.59738 + 0.552091i) q^{70} +(-3.20758 + 0.681791i) q^{71} +(4.36005 - 6.97160i) q^{72} +(-7.77780 + 8.63812i) q^{73} +(1.52994 + 1.11157i) q^{74} +(-2.27160 - 0.279358i) q^{75} +(-7.71139 + 1.63911i) q^{76} +(-0.482003 - 4.58596i) q^{77} +(-3.30240 - 7.78410i) q^{78} +(-0.988541 + 3.04242i) q^{79} +(-0.648306 - 0.288644i) q^{80} +(7.94329 + 4.23132i) q^{81} +(-6.15938 + 6.84068i) q^{82} +(3.82141 - 1.70140i) q^{83} +(-0.0674571 + 3.82270i) q^{84} +(-3.83367 - 4.25772i) q^{85} +(-2.98893 + 3.31954i) q^{86} +(-2.94019 + 12.7243i) q^{87} +(-3.77135 + 6.53217i) q^{88} +(-0.355098 - 1.09288i) q^{89} +(-1.62771 + 4.46678i) q^{90} +(8.00979 + 5.81946i) q^{91} +(-1.94494 - 3.36873i) q^{92} +(-7.63250 - 5.89448i) q^{93} +(0.354846 - 0.614611i) q^{94} +(10.4859 - 4.66864i) q^{95} +(6.03430 - 8.00461i) q^{96} +(-3.26035 + 3.62098i) q^{97} +(-1.73188 - 2.99970i) q^{98} +(-7.41878 - 3.62189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 3 q^{2} - 11 q^{3} + 25 q^{4} - 6 q^{5} - 8 q^{6} - 5 q^{7} - 29 q^{8} - 11 q^{9} - 30 q^{10} - 14 q^{11} - 8 q^{12} + q^{13} - 2 q^{14} - 26 q^{15} + 25 q^{16} - 26 q^{17} - 3 q^{18} - 20 q^{19}+ \cdots - 74 q^{99}+O(q^{100}) \) 240 * q - 3 * q^2 - 11 * q^3 + 25 * q^4 - 6 * q^5 - 8 * q^6 - 5 * q^7 - 29 * q^8 - 11 * q^9 - 30 * q^10 - 14 * q^11 - 8 * q^12 + q^13 - 2 * q^14 - 26 * q^15 + 25 * q^16 - 26 * q^17 - 3 * q^18 - 20 * q^19 - 84 * q^20 + q^21 - 11 * q^22 - 6 * q^23 + 14 * q^24 + 174 * q^25 + 22 * q^26 + 70 * q^27 - 60 * q^28 - 15 * q^29 - 6 * q^30 - 20 * q^31 - 24 * q^32 - 40 * q^33 + 25 * q^34 - 15 * q^35 - 8 * q^36 + 2 * q^37 + 37 * q^38 - q^39 + 6 * q^40 - 23 * q^41 - 134 * q^42 + 9 * q^43 - 77 * q^44 - 127 * q^45 - 2 * q^46 - 32 * q^47 + 26 * q^48 - 41 * q^49 - 37 * q^50 + 13 * q^51 + 3 * q^52 - 56 * q^53 - 29 * q^54 - 30 * q^55 - 62 * q^56 - 40 * q^57 + 76 * q^58 - 3 * q^59 + 41 * q^60 - q^61 - 51 * q^62 + 77 * q^63 - 51 * q^64 + 25 * q^65 - 130 * q^66 - 16 * q^67 + 87 * q^68 + 32 * q^69 - 90 * q^70 - 7 * q^71 + 112 * q^72 - 11 * q^73 - 9 * q^74 - 157 * q^75 + 12 * q^76 + 10 * q^77 + 50 * q^78 + 24 * q^79 + 142 * q^80 + 61 * q^81 - 2 * q^82 + 60 * q^83 + 132 * q^84 - 33 * q^85 - 152 * q^86 - 88 * q^87 + 2 * q^88 + 58 * q^89 + 96 * q^90 + 72 * q^92 + 31 * q^93 + 2 * q^94 - 63 * q^95 + 137 * q^96 - 30 * q^97 + 33 * q^98 - 74 * q^99

Introduction

L-functions

Modular forms

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