LMFDB - Embedded newform 930.2.bn.a.19.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.13
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.a.49.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.81096 - 1.31165i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.872484 - 0.785588i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.81096 - 1.31165i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.872484 - 0.785588i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(0.00330584 - 2.23607i) q^{10} +(5.06877 + 1.07740i) q^{11} +(0.994522 + 0.104528i) q^{12} +(-1.73101 + 0.181936i) q^{13} +(-1.14839 + 0.244097i) q^{14} +(0.461671 + 2.18789i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.891553 - 4.19443i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(0.274505 - 2.61174i) q^{19} +(-1.80707 - 1.31700i) q^{20} +(1.07254 - 0.477526i) q^{21} +(3.85099 - 3.46744i) q^{22} +(2.26058 + 0.734507i) q^{23} +(0.669131 - 0.743145i) q^{24} +(1.55914 - 4.75069i) q^{25} +(-0.870271 + 1.50735i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-0.477526 + 1.07254i) q^{28} +(0.936414 + 0.680345i) q^{29} +(2.04140 + 0.912510i) q^{30} +(4.04075 - 3.83045i) q^{31} +1.00000i q^{32} +(-3.04591 + 4.19234i) q^{33} +(-3.91741 - 1.74414i) q^{34} +(-2.61045 - 0.278272i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-6.06668 + 3.50260i) q^{37} +(-1.95159 - 1.75722i) q^{38} +(0.537857 - 1.65535i) q^{39} +(-2.12765 + 0.687838i) q^{40} +(1.25357 - 0.558126i) q^{41} +(0.244097 - 1.14839i) q^{42} +(-0.0593233 - 0.00623513i) q^{43} +(-0.541668 - 5.15363i) q^{44} +(-2.18651 - 0.468138i) q^{45} +(1.92296 - 1.39711i) q^{46} +(-0.567462 - 0.781045i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(-0.587620 - 5.59083i) q^{49} +(-2.92695 - 4.05376i) q^{50} +(4.19443 + 0.891553i) q^{51} +(0.707942 + 1.59006i) q^{52} +(4.48724 - 4.04033i) q^{53} +(0.309017 - 0.951057i) q^{54} +(10.5925 - 4.69734i) q^{55} +(0.587022 + 1.01675i) q^{56} +(2.27429 + 1.31306i) q^{57} +(1.10082 - 0.357678i) q^{58} +(-5.14789 - 2.29199i) q^{59} +(1.93814 - 1.11517i) q^{60} +4.17440 q^{61} +(-0.723811 - 5.52052i) q^{62} +1.17404i q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.89614 + 2.59996i) q^{65} +(1.60133 + 4.92839i) q^{66} +(6.91533 + 3.99257i) q^{67} +(-3.71363 + 2.14407i) q^{68} +(-1.59047 + 1.76639i) q^{69} +(-1.75951 + 1.94833i) q^{70} +(-6.33350 - 7.03406i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-2.03639 + 9.58045i) q^{73} +(-0.732242 + 6.96682i) q^{74} +(3.70582 + 3.35663i) q^{75} +(-2.56874 + 0.546002i) q^{76} +(-3.57603 - 4.92198i) q^{77} +(-1.02306 - 1.40813i) q^{78} +(14.4873 - 3.07936i) q^{79} +(-0.694126 + 2.12560i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(0.285298 - 1.34222i) q^{82} +(-0.659399 - 1.48103i) q^{83} +(-0.785588 - 0.872484i) q^{84} +(-7.11620 - 6.42653i) q^{85} +(-0.0399137 + 0.0443286i) q^{86} +(-1.00240 + 0.578736i) q^{87} +(-4.48775 - 2.59101i) q^{88} +(2.59788 + 7.99544i) q^{89} +(-1.66393 + 1.49376i) q^{90} +(1.65320 + 1.20112i) q^{91} -2.37691i q^{92} +(1.85577 + 5.24939i) q^{93} -0.965425 q^{94} +(-2.92857 - 5.08980i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(3.70048 - 1.20236i) q^{97} +(-4.86847 - 2.81081i) q^{98} +(-2.59101 - 4.48775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9}+O(q^{10}) $ 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9	$ 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} + 8 q^{14} + 8 q^{15} - 28 q^{16} + 16 q^{19} + 2 q^{20} + 28 q^{21} + 14 q^{24} + 14 q^{25} + 12 q^{26} + 16 q^{29} - 4 q^{30} + 10 q^{34} - 38 q^{35} - 56 q^{36} + 16 q^{39} - 6 q^{40} + 20 q^{41} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 38 q^{49} + 8 q^{50} - 10 q^{51} - 28 q^{54} - 46 q^{55} + 12 q^{56} + 60 q^{59} - 8 q^{60} + 88 q^{61} + 28 q^{64} - 28 q^{65} + 6 q^{66} + 46 q^{69} + 26 q^{70} + 116 q^{71} - 34 q^{74} + 8 q^{75} + 24 q^{76} - 40 q^{79} - 12 q^{80} + 14 q^{81} - 8 q^{84} + 18 q^{85} - 38 q^{86} - 60 q^{89} + 4 q^{90} - 92 q^{91} + 132 q^{94} + 132 q^{95} - 14 q^{96} + 2 q^{99}+O(q^{100}) $ 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 + 8 * q^14 + 8 * q^15 - 28 * q^16 + 16 * q^19 + 2 * q^20 + 28 * q^21 + 14 * q^24 + 14 * q^25 + 12 * q^26 + 16 * q^29 - 4 * q^30 + 10 * q^34 - 38 * q^35 - 56 * q^36 + 16 * q^39 - 6 * q^40 + 20 * q^41 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 38 * q^49 + 8 * q^50 - 10 * q^51 - 28 * q^54 - 46 * q^55 + 12 * q^56 + 60 * q^59 - 8 * q^60 + 88 * q^61 + 28 * q^64 - 28 * q^65 + 6 * q^66 + 46 * q^69 + 26 * q^70 + 116 * q^71 - 34 * q^74 + 8 * q^75 + 24 * q^76 - 40 * q^79 - 12 * q^80 + 14 * q^81 - 8 * q^84 + 18 * q^85 - 38 * q^86 - 60 * q^89 + 4 * q^90 - 92 * q^91 + 132 * q^94 + 132 * q^95 - 14 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.81096	−	1.31165i	0.809885	−	0.586589i
$5$	1.81096	−	1.31165i	0.809885	−	0.586589i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.872484	−	0.785588i	−0.329768	−	0.296924i	0.487569	−	0.873085i	$-0.337884\pi$
$7$	−0.872484	−	0.785588i	−0.329768	−	0.296924i	−0.817337	+	0.576160i	$0.804550\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	0.00330584	−	2.23607i	0.00104540	−	0.707106i
$11$	5.06877	+	1.07740i	1.52829	+	0.324849i	0.893937	−	0.448193i	$-0.147932\pi$
$11$	5.06877	+	1.07740i	1.52829	+	0.324849i	0.634356	+	0.773041i	$0.281265\pi$
$12$	0.994522	+	0.104528i	0.287094	+	0.0301748i
$13$	−1.73101	+	0.181936i	−0.480095	+	0.0504600i	−0.341485	−	0.939887i	$-0.610930\pi$
$13$	−1.73101	+	0.181936i	−0.480095	+	0.0504600i	−0.138610	+	0.990347i	$0.544263\pi$
$14$	−1.14839	+	0.244097i	−0.306920	+	0.0652378i
$15$	0.461671	+	2.18789i	0.119203	+	0.564911i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.891553	−	4.19443i	−0.216233	−	1.01730i	−0.943610	−	0.331060i	$-0.892594\pi$
$17$	−0.891553	−	4.19443i	−0.216233	−	1.01730i	0.727376	−	0.686239i	$-0.240739\pi$
$18$	−0.994522	+	0.104528i	−0.234411	+	0.0246376i
$19$	0.274505	−	2.61174i	0.0629757	−	0.599174i	−0.916838	−	0.399260i	$-0.869267\pi$
$19$	0.274505	−	2.61174i	0.0629757	−	0.599174i	0.979813	−	0.199914i	$-0.0640662\pi$
$20$	−1.80707	−	1.31700i	−0.404074	−	0.294490i
$21$	1.07254	−	0.477526i	0.234048	−	0.104205i
$22$	3.85099	−	3.46744i	0.821033	−	0.739261i
$23$	2.26058	+	0.734507i	0.471363	+	0.153155i	0.535060	−	0.844814i	$-0.320289\pi$
$23$	2.26058	+	0.734507i	0.471363	+	0.153155i	−0.0636967	+	0.997969i	$0.520289\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	1.55914	−	4.75069i	0.311828	−	0.950139i
$26$	−0.870271	+	1.50735i	−0.170674	+	0.295616i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−0.477526	+	1.07254i	−0.0902440	+	0.202691i
$29$	0.936414	+	0.680345i	0.173888	+	0.126337i	0.671325	−	0.741163i	$-0.265726\pi$
$29$	0.936414	+	0.680345i	0.173888	+	0.126337i	−0.497437	+	0.867500i	$0.665726\pi$
$30$	2.04140	+	0.912510i	0.372707	+	0.166601i
$31$	4.04075	−	3.83045i	0.725739	−	0.687970i
$31$	4.04075	−	3.83045i	0.725739	−	0.687970i
$32$			1.00000i			0.176777i
$33$	−3.04591	+	4.19234i	−0.530225	+	0.729792i
$34$	−3.91741	−	1.74414i	−0.671830	−	0.299118i
$35$	−2.61045	−	0.278272i	−0.441247	−	0.0470366i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−6.06668	+	3.50260i	−0.997355	+	0.575823i	−0.907465	−	0.420128i	$-0.861985\pi$
$37$	−6.06668	+	3.50260i	−0.997355	+	0.575823i	−0.0898906	+	0.995952i	$0.528652\pi$
$38$	−1.95159	−	1.75722i	−0.316590	−	0.285059i
$39$	0.537857	−	1.65535i	0.0861260	−	0.265069i
$40$	−2.12765	+	0.687838i	−0.336410	+	0.108757i
$41$	1.25357	−	0.558126i	0.195775	−	0.0871647i	−0.306507	−	0.951868i	$-0.599160\pi$
$41$	1.25357	−	0.558126i	0.195775	−	0.0871647i	0.502282	+	0.864704i	$0.332494\pi$
$42$	0.244097	−	1.14839i	0.0376650	−	0.177200i
$43$	−0.0593233	−	0.00623513i	−0.00904672	−	0.000950849i	0.100004	−	0.994987i	$-0.468114\pi$
$43$	−0.0593233	−	0.00623513i	−0.00904672	−	0.000950849i	−0.109051	+	0.994036i	$0.534781\pi$
$44$	−0.541668	−	5.15363i	−0.0816595	−	0.776938i
$45$	−2.18651	−	0.468138i	−0.325946	−	0.0697859i
$46$	1.92296	−	1.39711i	0.283525	−	0.205993i
$47$	−0.567462	−	0.781045i	−0.0827729	−	0.113927i	0.765623	−	0.643290i	$-0.222431\pi$
$47$	−0.567462	−	0.781045i	−0.0827729	−	0.113927i	−0.848396	+	0.529363i	$0.822431\pi$
$48$	−0.207912	−	0.978148i	−0.0300095	−	0.141183i
$49$	−0.587620	−	5.59083i	−0.0839456	−	0.798689i
$50$	−2.92695	−	4.05376i	−0.413934	−	0.573288i
$51$	4.19443	+	0.891553i	0.587338	+	0.124842i
$52$	0.707942	+	1.59006i	0.0981739	+	0.220502i
$53$	4.48724	−	4.04033i	0.616370	−	0.554982i	−0.300695	−	0.953720i	$-0.597219\pi$
$53$	4.48724	−	4.04033i	0.616370	−	0.554982i	0.917065	+	0.398739i	$0.130552\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	10.5925	−	4.69734i	1.42829	−	0.633389i
$56$	0.587022	+	1.01675i	0.0784441	+	0.135869i
$57$	2.27429	+	1.31306i	0.301237	+	0.173919i
$58$	1.10082	−	0.357678i	0.144545	−	0.0469655i
$59$	−5.14789	−	2.29199i	−0.670198	−	0.298391i	0.0432861	−	0.999063i	$-0.486217\pi$
$59$	−5.14789	−	2.29199i	−0.670198	−	0.298391i	−0.713484	+	0.700671i	$0.752884\pi$
$60$	1.93814	−	1.11517i	0.250213	−	0.143968i
$61$	4.17440			0.534478			0.267239	−	0.963630i	$-0.413889\pi$
$61$	4.17440			0.534478			0.267239	+	0.963630i	$0.413889\pi$
$62$	−0.723811	−	5.52052i	−0.0919241	−	0.701106i
$63$			1.17404i			0.147916i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−2.89614	+	2.59996i	−0.359222	+	0.322485i
$66$	1.60133	+	4.92839i	0.197110	+	0.606643i
$67$	6.91533	+	3.99257i	0.844842	+	0.487769i	0.858907	−	0.512132i	$-0.171144\pi$
$67$	6.91533	+	3.99257i	0.844842	+	0.487769i	−0.0140655	+	0.999901i	$0.504477\pi$
$68$	−3.71363	+	2.14407i	−0.450344	+	0.260006i
$69$	−1.59047	+	1.76639i	−0.191470	+	0.212648i
$70$	−1.75951	+	1.94833i	−0.210302	+	0.232871i
$71$	−6.33350	−	7.03406i	−0.751648	−	0.834789i	0.239031	−	0.971012i	$-0.423170\pi$
$71$	−6.33350	−	7.03406i	−0.751648	−	0.834789i	−0.990678	+	0.136223i	$0.956504\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	−2.03639	+	9.58045i	−0.238341	+	1.12131i	0.682353	+	0.731023i	$0.260957\pi$
$73$	−2.03639	+	9.58045i	−0.238341	+	1.12131i	−0.920694	+	0.390284i	$0.872377\pi$
$74$	−0.732242	+	6.96682i	−0.0851214	+	0.809876i
$75$	3.70582	+	3.35663i	0.427911	+	0.387590i
$76$	−2.56874	+	0.546002i	−0.294654	+	0.0626307i
$77$	−3.57603	−	4.92198i	−0.407527	−	0.560912i
$78$	−1.02306	−	1.40813i	−0.115839	−	0.159439i
$79$	14.4873	−	3.07936i	1.62994	−	0.346455i	0.699996	−	0.714147i	$-0.253185\pi$
$79$	14.4873	−	3.07936i	1.62994	−	0.346455i	0.929948	+	0.367692i	$0.119852\pi$
$80$	−0.694126	+	2.12560i	−0.0776057	+	0.237650i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	0.285298	−	1.34222i	0.0315058	−	0.148223i
$83$	−0.659399	−	1.48103i	−0.0723785	−	0.162565i	0.873733	−	0.486406i	$-0.161692\pi$
$83$	−0.659399	−	1.48103i	−0.0723785	−	0.162565i	−0.946111	+	0.323841i	$0.895026\pi$
$84$	−0.785588	−	0.872484i	−0.0857147	−	0.0951958i
$85$	−7.11620	−	6.42653i	−0.771860	−	0.697055i
$86$	−0.0399137	+	0.0443286i	−0.00430400	+	0.00478008i
$87$	−1.00240	+	0.578736i	−0.107469	+	0.0620470i
$88$	−4.48775	−	2.59101i	−0.478396	−	0.276202i
$89$	2.59788	+	7.99544i	0.275374	+	0.847515i	0.989120	+	0.147110i	$0.0469972\pi$
$89$	2.59788	+	7.99544i	0.275374	+	0.847515i	−0.713746	+	0.700405i	$0.753003\pi$
$90$	−1.66393	+	1.49376i	−0.175394	+	0.157456i
$91$	1.65320	+	1.20112i	0.173303	+	0.125912i
$92$		−	2.37691i		−	0.247810i
$93$	1.85577	+	5.24939i	0.192435	+	0.544336i
$94$	−0.965425			−0.0995760
$95$	−2.92857	−	5.08980i	−0.300465	−	0.522203i
$96$	−0.913545	−	0.406737i	−0.0932383	−	0.0415124i
$97$	3.70048	−	1.20236i	0.375727	−	0.122081i	−0.115065	−	0.993358i	$-0.536708\pi$
$97$	3.70048	−	1.20236i	0.375727	−	0.122081i	0.490792	+	0.871277i	$0.336708\pi$
$98$	−4.86847	−	2.81081i	−0.491789	−	0.283935i
$99$	−2.59101	−	4.48775i	−0.260406	−	0.451036i
$100$	−4.99998	−	0.0147842i	−0.499998	−	0.00147842i
$101$	−6.03006	+	18.5586i	−0.600013	+	1.84665i	−0.0720184	+	0.997403i	$0.522944\pi$
$101$	−6.03006	+	18.5586i	−0.600013	+	1.84665i	−0.527995	+	0.849248i	$0.677056\pi$
$102$	3.18671	−	2.86932i	0.315531	−	0.284105i
$103$	−1.26547	−	2.84230i	−0.124691	−	0.280060i	0.840404	−	0.541960i	$-0.182318\pi$
$103$	−1.26547	−	2.84230i	−0.124691	−	0.280060i	−0.965095	+	0.261900i	$0.915651\pi$
$104$	1.70251	+	0.361879i	0.166945	+	0.0354852i
$105$	1.31598	−	2.27158i	0.128427	−	0.221684i
$106$	−0.631161	−	6.00510i	−0.0613038	−	0.583267i
$107$	−1.49980	−	7.05601i	−0.144991	−	0.682130i	−0.989255	−	0.146202i	$-0.953295\pi$
$107$	−1.49980	−	7.05601i	−0.144991	−	0.682130i	0.844264	−	0.535928i	$-0.180038\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$	−2.24438	+	1.63063i	−0.214972	+	0.156186i	−0.690061	−	0.723752i	$-0.742416\pi$
$109$	−2.24438	+	1.63063i	−0.214972	+	0.156186i	0.475088	+	0.879938i	$0.342416\pi$
$110$	2.42590	−	11.3305i	0.231300	−	1.08033i
$111$	−0.732242	−	6.96682i	−0.0695013	−	0.661261i
$112$	1.16761	+	0.122721i	0.110329	+	0.0115960i
$113$	−2.93281	+	13.7978i	−0.275896	+	1.29799i	0.593885	+	0.804550i	$0.297593\pi$
$113$	−2.93281	+	13.7978i	−0.275896	+	1.29799i	−0.869781	+	0.493438i	$0.835740\pi$
$114$	2.39908	−	1.06814i	0.224695	−	0.100041i
$115$	5.05723	−	1.63493i	0.471589	−	0.152458i
$116$	0.357678	−	1.10082i	0.0332096	−	0.102209i
$117$	1.29347	+	1.16465i	0.119582	+	0.107672i
$118$	−4.88011	+	2.81753i	−0.449251	+	0.259375i
$119$	−2.51723	+	4.35997i	−0.230754	+	0.399678i
$120$	0.237020	−	2.22347i	0.0216369	−	0.202974i
$121$	14.4827	+	6.44810i	1.31661	+	0.586191i
$122$	2.45365	−	3.37716i	0.222143	−	0.305754i
$123$			1.37221i			0.123728i
$124$	−4.89164	−	2.65930i	−0.439282	−	0.238812i
$125$	−3.40772	−	10.6484i	−0.304796	−	0.952418i
$126$	0.949821	+	0.690085i	0.0846168	+	0.0614777i
$127$	1.08727	−	2.44204i	0.0964794	−	0.216696i	−0.858858	−	0.512214i	$-0.828825\pi$
$127$	1.08727	−	2.44204i	0.0964794	−	0.216696i	0.955337	+	0.295518i	$0.0954921\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	0.0298250	−	0.0516585i	0.00262595	−	0.00454828i
$130$	0.401099	+	3.87125i	0.0351787	+	0.339531i
$131$	−5.08940	+	5.65235i	−0.444663	+	0.493848i	−0.923254	−	0.384190i	$-0.874481\pi$
$131$	−5.08940	+	5.65235i	−0.444663	+	0.493848i	0.478591	+	0.878038i	$0.341148\pi$
$132$	4.92839	+	1.60133i	0.428961	+	0.139378i
$133$	−2.29125	+	2.06305i	−0.198677	+	0.178889i
$134$	7.29478	−	3.24785i	0.630173	−	0.280571i
$135$	1.31700	−	1.80707i	0.113349	−	0.155528i
$136$	−0.448232	+	4.26464i	−0.0384356	+	0.365690i
$137$	−7.08465	+	0.744627i	−0.605283	+	0.0636178i	−0.402212	−	0.915546i	$-0.631759\pi$
$137$	−7.08465	+	0.744627i	−0.605283	+	0.0636178i	−0.203070	+	0.979164i	$0.565092\pi$
$138$	0.494188	+	2.32497i	0.0420681	+	0.197915i
$139$	−7.41649	+	5.38839i	−0.629058	+	0.457038i	−0.856074	−	0.516854i	$-0.827103\pi$
$139$	−7.41649	+	5.38839i	−0.629058	+	0.457038i	0.227016	+	0.973891i	$0.427103\pi$
$140$	0.542021	+	2.56868i	0.0458092	+	0.217093i
$141$	0.944328	−	0.200723i	0.0795268	−	0.0169039i
$142$	−9.41341	+	0.989389i	−0.789956	+	0.0830277i
$143$	−8.97010	−	0.942795i	−0.750117	−	0.0788405i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	2.58818	+	0.00382642i	0.214937	+	0.000317767i
$146$	6.55379	+	7.27872i	0.542396	+	0.602391i
$147$	5.34648	+	1.73718i	0.440970	+	0.143280i
$148$	5.20587	+	4.68739i	0.427920	+	0.385301i
$149$	2.25719	+	3.90957i	0.184916	+	0.320284i	0.943548	−	0.331235i	$-0.107465\pi$
$149$	2.25719	+	3.90957i	0.184916	+	0.320284i	−0.758632	+	0.651519i	$0.774132\pi$
$150$	4.89379	−	1.02509i	0.399576	−	0.0836985i
$151$	4.99185	+	15.3633i	0.406231	+	1.25025i	0.919863	+	0.392240i	$0.128300\pi$
$151$	4.99185	+	15.3633i	0.406231	+	1.25025i	−0.513632	+	0.858011i	$0.671700\pi$
$152$	−1.06814	+	2.39908i	−0.0866376	+	0.194591i
$153$	−2.52050	+	3.46917i	−0.203771	+	0.280466i
$154$	−6.08391			−0.490255
$155$	2.29340	−	12.2368i	0.184210	−	0.982887i
$156$	−1.74054			−0.139355
$157$	−13.6005	+	18.7194i	−1.08543	+	1.49397i	−0.232040	+	0.972706i	$0.574540\pi$
$157$	−13.6005	+	18.7194i	−1.08543	+	1.49397i	−0.853394	+	0.521266i	$0.825460\pi$
$158$	6.02414	−	13.5304i	0.479255	−	1.07642i
$159$	1.86590	+	5.74265i	0.147975	+	0.455421i
$160$	1.31165	+	1.81096i	0.103695	+	0.143169i
$161$	−1.39530	−	2.41673i	−0.109965	−	0.190465i
$162$	0.743145	+	0.669131i	0.0583870	+	0.0525719i
$163$	18.0277	+	5.85757i	1.41204	+	0.458800i	0.913065	−	0.407815i	$-0.133709\pi$
$163$	18.0277	+	5.85757i	1.41204	+	0.458800i	0.498977	+	0.866615i	$0.333709\pi$
$164$	−0.918185	−	1.01975i	−0.0716982	−	0.0796289i
$165$	−0.0171309	+	11.5873i	−0.00133364	+	0.902072i
$166$	−1.58577	−	0.337065i	−0.123079	−	0.0261613i
$167$	11.7619	+	1.23622i	0.910162	+	0.0956619i	0.548024	−	0.836463i	$-0.315380\pi$
$167$	11.7619	+	1.23622i	0.910162	+	0.0956619i	0.362138	+	0.932125i	$0.382047\pi$
$168$	−1.16761	+	0.122721i	−0.0900832	+	0.00946813i
$169$	−9.75264	+	2.07299i	−0.750203	+	0.159461i
$170$	−9.38197	+	1.97971i	−0.719564	+	0.151836i
$171$	−2.12458	+	1.54360i	−0.162471	+	0.118042i
$172$	0.0124019	+	0.0583466i	0.000945640	+	0.00444889i
$173$	−24.0549	+	2.52827i	−1.82886	+	0.192221i	−0.955527	−	0.294903i	$-0.904713\pi$
$173$	−24.0549	+	2.52827i	−1.82886	+	0.192221i	−0.873333	+	0.487124i	$0.838046\pi$
$174$	−0.120989	+	1.15113i	−0.00917213	+	0.0872670i
$175$	−5.09241	+	2.92006i	−0.384950	+	0.220736i
$176$	−4.73400	+	2.10771i	−0.356839	+	0.158875i
$177$	4.18767	−	3.77060i	0.314765	−	0.283415i
$178$	7.99544	+	2.59788i	0.599283	+	0.194719i
$179$	−4.09837	+	4.55170i	−0.306326	+	0.340210i	−0.876578	−	0.481260i	$-0.840179\pi$
$179$	−4.09837	+	4.55170i	−0.306326	+	0.340210i	0.570251	+	0.821470i	$0.306846\pi$
$180$	0.230445	+	2.22416i	0.0171763	+	0.165779i
$181$	−11.8049	+	20.4467i	−0.877452	+	1.51979i	−0.0233248	+	0.999728i	$0.507425\pi$
$181$	−11.8049	+	20.4467i	−0.877452	+	1.51979i	−0.854127	+	0.520064i	$0.825908\pi$
$182$	1.94346	−	0.631467i	0.144059	−	0.0468075i
$183$	−1.69788	+	3.81351i	−0.125511	+	0.281903i
$184$	−1.92296	−	1.39711i	−0.141763	−	0.102997i
$185$	−6.39231	+	14.3004i	−0.469972	+	1.05139i
$186$	5.33764	+	1.58416i	0.391375	+	0.116156i
$187$		−	22.2212i		−	1.62497i
$188$	−0.567462	+	0.781045i	−0.0413864	+	0.0569636i
$189$	−1.07254	−	0.477526i	−0.0780159	−	0.0347349i
$190$	−5.83911	−	0.622444i	−0.423613	−	0.0451569i
$191$	−8.82367	+	15.2830i	−0.638458	+	1.10584i	0.347313	+	0.937749i	$0.387094\pi$
$191$	−8.82367	+	15.2830i	−0.638458	+	1.10584i	−0.985771	+	0.168093i	$0.946239\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	15.4451	+	13.9068i	1.11176	+	1.00104i	0.999973	+	0.00730394i	$0.00232494\pi$
$193$	15.4451	+	13.9068i	1.11176	+	1.00104i	0.111790	+	0.993732i	$0.464342\pi$
$194$	1.20236	−	3.70048i	0.0863244	−	0.265679i
$195$	−1.19721	−	3.70326i	−0.0857341	−	0.265196i
$196$	−5.13561	+	2.28652i	−0.366829	+	0.163323i
$197$	0.00425777	−	0.0200312i	0.000303354	−	0.00142717i	−0.977996	−	0.208625i	$-0.933101\pi$
$197$	0.00425777	−	0.0200312i	0.000303354	−	0.00142717i	0.978299	+	0.207198i	$0.0664345\pi$
$198$	−5.15363	−	0.541668i	−0.366252	−	0.0384947i
$199$	0.387448	+	3.68632i	0.0274654	+	0.261316i	0.999634	+	0.0270356i	$0.00860676\pi$
$199$	0.387448	+	3.68632i	0.0274654	+	0.261316i	−0.972169	+	0.234281i	$0.924727\pi$
$200$	−2.95087	+	4.03638i	−0.208658	+	0.285415i
$201$	−6.46011	+	4.69354i	−0.455661	+	0.331057i
$202$	11.4699	+	15.7869i	0.807016	+	1.11076i
$203$	−0.282536	−	1.32923i	−0.0198301	−	0.0932934i
$204$	−0.448232	−	4.26464i	−0.0313825	−	0.298585i
$205$	1.53810	−	2.65499i	0.107425	−	0.185433i
$206$	−3.04330	−	0.646873i	−0.212037	−	0.0450698i
$207$	−0.966778	−	2.17142i	−0.0671957	−	0.150924i
$208$	1.29347	−	1.16465i	0.0896863	−	0.0807539i
$209$	4.20529	−	12.9426i	0.290886	−	0.895255i
$210$	−1.06423	−	2.39985i	−0.0734392	−	0.165606i
$211$	4.82311	+	8.35388i	0.332037	+	0.575105i	0.982911	−	0.184081i	$-0.0589308\pi$
$211$	4.82311	+	8.35388i	0.332037	+	0.575105i	−0.650874	+	0.759186i	$0.725598\pi$
$212$	−5.22921	−	3.01909i	−0.359144	−	0.207352i
$213$	9.00200	−	2.92493i	0.616807	−	0.200413i
$214$	−6.58999	−	2.93405i	−0.450482	−	0.200568i
$215$	−0.115610	+	0.0665200i	−0.00788456	+	0.00453662i
$216$	−1.00000			−0.0680414
$217$	−6.53465	+	0.167647i	−0.443601	+	0.0113806i
$218$			2.77420i			0.187893i
$219$	−7.92390	−	5.75705i	−0.535448	−	0.389026i
$220$	−7.74070	−	8.62252i	−0.521878	−	0.581330i
$221$	2.30640	+	7.09838i	0.155145	+	0.477489i
$222$	−6.06668	−	3.50260i	−0.407169	−	0.235079i
$223$	21.7490	−	12.5568i	1.45642	−	0.840864i	0.457586	−	0.889165i	$-0.348714\pi$
$223$	21.7490	−	12.5568i	1.45642	−	0.840864i	0.998833	+	0.0483011i	$0.0153807\pi$
$224$	0.785588	−	0.872484i	0.0524893	−	0.0582953i
$225$	−4.57372	+	2.02017i	−0.304915	+	0.134678i
$226$	9.43879	+	10.4828i	0.627859	+	0.697308i
$227$	0.487813	+	1.09565i	0.0323773	+	0.0727205i	0.929010	−	0.370054i	$-0.120661\pi$
$227$	0.487813	+	1.09565i	0.0323773	+	0.0727205i	−0.896633	+	0.442775i	$0.853994\pi$
$228$	0.546002	−	2.56874i	0.0361599	−	0.170119i
$229$	2.06767	−	19.6725i	0.136635	−	1.30000i	−0.684395	−	0.729112i	$-0.739933\pi$
$229$	2.06767	−	19.6725i	0.136635	−	1.30000i	0.821030	−	0.570885i	$-0.193400\pi$
$230$	1.64988	−	5.05237i	0.108790	−	0.333144i
$231$	5.95096	−	1.26492i	0.391544	−	0.0832253i
$232$	−0.680345	−	0.936414i	−0.0446668	−	0.0614786i
$233$	−7.38391	−	10.1631i	−0.483736	−	0.665806i	0.495481	−	0.868619i	$-0.334992\pi$
$233$	−7.38391	−	10.1631i	−0.483736	−	0.665806i	−0.979218	+	0.202813i	$0.934992\pi$
$234$	1.70251	−	0.361879i	0.111296	−	0.0236568i
$235$	−2.05211	−	0.670127i	−0.133865	−	0.0437142i
$236$	−0.589025	+	5.60420i	−0.0383422	+	0.364802i
$237$	−3.07936	+	14.4873i	−0.200026	+	0.941048i
$238$	2.04770	+	4.59920i	0.132733	+	0.298122i
$239$	1.28891	+	1.43148i	0.0833725	+	0.0925946i	0.783388	−	0.621534i	$-0.213490\pi$
$239$	1.28891	+	1.43148i	0.0833725	+	0.0925946i	−0.700015	+	0.714128i	$0.746823\pi$
$240$	−1.65951	−	1.49868i	−0.107121	−	0.0967392i
$241$	16.5228	−	18.3505i	1.06433	−	1.18206i	0.0816659	−	0.996660i	$-0.473976\pi$
$241$	16.5228	−	18.3505i	1.06433	−	1.18206i	0.982664	−	0.185398i	$-0.0593574\pi$
$242$	13.7293	−	7.92663i	0.882554	−	0.509543i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−1.28996	−	3.97009i	−0.0825813	−	0.254159i
$245$	−8.39737	−	9.35400i	−0.536488	−	0.597605i
$246$	1.11014	+	0.806562i	0.0707798	+	0.0514245i
$247$			4.57088i			0.290838i
$248$	−5.02665	+	2.39432i	−0.319193	+	0.152039i
$249$	1.62119			0.102739
$250$	−10.6177	−	3.50204i	−0.671523	−	0.221489i
$251$	4.61807	+	2.05610i	0.291490	+	0.129780i	0.547272	−	0.836955i	$-0.315666\pi$
$251$	4.61807	+	2.05610i	0.291490	+	0.129780i	−0.255782	+	0.966734i	$0.582333\pi$
$252$	1.11658	−	0.362799i	0.0703380	−	0.0228542i
$253$	10.6670	+	6.15860i	0.670629	+	0.387188i
$254$	−1.33658	−	2.31502i	−0.0838642	−	0.145257i
$255$	8.76534	−	3.88706i	0.548907	−	0.243417i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	0.525913	−	0.473534i	0.0328055	−	0.0295382i	−0.652565	−	0.757733i	$-0.726307\pi$
$257$	0.525913	−	0.473534i	0.0328055	−	0.0295382i	0.685370	+	0.728195i	$0.259640\pi$
$258$	−0.0242619	−	0.0544931i	−0.00151048	−	0.00339259i
$259$	8.04468	+	1.70995i	0.499872	+	0.106251i
$260$	3.36766	+	1.95097i	0.208854	+	0.120994i
$261$	−0.120989	−	1.15113i	−0.00748901	−	0.0712532i
$262$	1.58137	+	7.43978i	0.0976976	+	0.459631i
$263$	5.88399	+	8.09862i	0.362822	+	0.499382i	0.950932	−	0.309399i	$-0.100128\pi$
$263$	5.88399	+	8.09862i	0.362822	+	0.499382i	−0.588110	+	0.808781i	$0.700128\pi$
$264$	4.19234	−	3.04591i	0.258020	−	0.187463i
$265$	2.82670	−	13.2026i	0.173643	−	0.811027i
$266$	0.322280	+	3.06629i	0.0197603	+	0.188006i
$267$	−8.36085	−	0.878761i	−0.511676	−	0.0537793i
$268$	1.66020	−	7.81064i	0.101413	−	0.477111i
$269$	5.95577	−	2.65168i	0.363130	−	0.161676i	−0.217058	−	0.976159i	$-0.569646\pi$
$269$	5.95577	−	2.65168i	0.363130	−	0.161676i	0.580187	+	0.814483i	$0.302979\pi$
$270$	−0.687838	−	2.12765i	−0.0418605	−	0.129484i
$271$	−3.95979	+	12.1870i	−0.240540	+	0.740306i	0.755798	+	0.654805i	$0.227249\pi$
$271$	−3.95979	+	12.1870i	−0.240540	+	0.740306i	−0.996338	+	0.0855012i	$0.972751\pi$
$272$	3.18671	+	2.86932i	0.193222	+	0.173978i
$273$	−1.76970	+	1.02174i	−0.107107	+	0.0618383i
$274$	−3.56184	+	6.16928i	−0.215178	+	0.372700i
$275$	13.0213	−	22.4004i	0.785215	−	1.35079i
$276$	2.17142	+	0.966778i	0.130704	+	0.0581932i
$277$	−2.85047	+	3.92333i	−0.171268	+	0.235730i	−0.886019	−	0.463649i	$-0.846540\pi$
$277$	−2.85047	+	3.92333i	−0.171268	+	0.235730i	0.714751	+	0.699379i	$0.246540\pi$
$278$			9.16728i			0.549817i
$279$	−5.55037	−	0.439786i	−0.332292	−	0.0263293i
$280$	2.39670	+	1.07133i	0.143230	+	0.0640240i
$281$	7.76550	+	5.64196i	0.463251	+	0.336571i	0.794805	−	0.606865i	$-0.207573\pi$
$281$	7.76550	+	5.64196i	0.463251	+	0.336571i	−0.331554	+	0.943436i	$0.607573\pi$
$282$	0.392674	−	0.881959i	0.0233834	−	0.0525199i
$283$	22.9554	−	7.45866i	1.36456	−	0.443371i	0.466995	−	0.884260i	$-0.345337\pi$
$283$	22.9554	−	7.45866i	1.36456	−	0.443371i	0.897562	+	0.440889i	$0.145337\pi$
$284$	−4.73263	+	8.19716i	−0.280830	+	0.486412i
$285$	5.84092	−	0.605176i	0.345986	−	0.0358476i
$286$	−6.03523	+	6.70280i	−0.356871	+	0.396345i
$287$	−1.53218	−	0.497835i	−0.0904417	−	0.0293863i
$288$	0.743145	−	0.669131i	0.0437902	−	0.0394289i
$289$	−1.26809	+	0.564592i	−0.0745938	+	0.0332113i
$290$	1.52439	−	2.09163i	0.0895153	−	0.122825i
$291$	−0.406712	+	3.86960i	−0.0238419	+	0.226840i
$292$	9.74083	−	1.02380i	0.570039	−	0.0599135i
$293$	−2.12270	−	9.98653i	−0.124010	−	0.583419i	−0.995642	−	0.0932590i	$-0.970272\pi$
$293$	−2.12270	−	9.98653i	−0.124010	−	0.583419i	0.871632	−	0.490160i	$-0.163062\pi$
$294$	4.54799	−	3.30431i	0.265244	−	0.192711i
$295$	−12.3289	+	2.60154i	−0.717816	+	0.151468i
$296$	6.85211	−	1.45646i	0.398271	−	0.0846551i
$297$	5.15363	−	0.541668i	0.299044	−	0.0314308i
$298$	4.48965	+	0.471881i	0.260078	+	0.0273353i
$299$	−4.04671	−	0.860155i	−0.234027	−	0.0497440i
$300$	2.04718	−	4.56169i	0.118194	−	0.263370i
$301$	0.0468604	+	0.0520438i	0.00270099	+	0.00299975i
$302$	15.3633	+	4.99185i	0.884061	+	0.287249i
$303$	−14.5015	−	13.0572i	−0.833089	−	0.750117i
$304$	1.31306	+	2.27429i	0.0753093	+	0.130439i
$305$	7.55967	−	5.47537i	0.432866	−	0.313519i
$306$	1.32511	+	4.07826i	0.0757513	+	0.233139i
$307$	0.321434	−	0.721953i	0.0183452	−	0.0412040i	−0.904141	−	0.427235i	$-0.859488\pi$
$307$	0.321434	−	0.721953i	0.0183452	−	0.0412040i	0.922486	+	0.386031i	$0.126154\pi$
$308$	−3.57603	+	4.92198i	−0.203763	+	0.280456i
$309$	3.11129			0.176995
$310$	−8.55179	−	9.04804i	−0.485709	−	0.513894i
$311$	−14.2068			−0.805593			−0.402796	−	0.915290i	$-0.631962\pi$
$311$	−14.2068			−0.805593			−0.402796	+	0.915290i	$0.631962\pi$
$312$	−1.02306	+	1.40813i	−0.0579196	+	0.0797195i
$313$	12.8256	−	28.8067i	0.724945	−	1.62825i	−0.0519716	−	0.998649i	$-0.516551\pi$
$313$	12.8256	−	28.8067i	0.724945	−	1.62825i	0.776916	−	0.629604i	$-0.216783\pi$
$314$	7.15018	+	22.0060i	0.403508	+	1.24187i
$315$	1.53994	+	2.12614i	0.0867656	+	0.119795i
$316$	−7.40545	−	12.8266i	−0.416589	−	0.721554i
$317$	−3.86502	−	3.48008i	−0.217081	−	0.195461i	0.553415	−	0.832906i	$-0.313325\pi$
$317$	−3.86502	−	3.48008i	−0.217081	−	0.195461i	−0.770496	+	0.637445i	$0.779991\pi$
$318$	5.74265	+	1.86590i	0.322032	+	0.104634i
$319$	4.01347	+	4.45741i	0.224711	+	0.249567i
$320$	2.23607	+	0.00330584i	0.125000	+	0.000184802i
$321$	7.05601	+	1.49980i	0.393828	+	0.0837107i
$322$	−2.77531	−	0.291697i	−0.154662	−	0.0162556i
$323$	−11.1995	+	1.17711i	−0.623156	+	0.0654963i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	−1.83456	+	8.50715i	−0.101763	+	0.471892i
$326$	15.3353	−	11.1418i	0.849345	−	0.617085i
$327$	−0.576789	−	2.71358i	−0.0318965	−	0.150061i
$328$	−1.36469	+	0.143435i	−0.0753523	+	0.00791985i
$329$	−0.118478	+	1.12724i	−0.00653189	+	0.0621468i
$330$	9.36427	+	6.82472i	0.515486	+	0.375688i
$331$	−19.1954	+	8.54634i	−1.05507	+	0.469749i	−0.859604	−	0.510960i	$-0.829290\pi$
$331$	−19.1954	+	8.54634i	−1.05507	+	0.469749i	−0.195470	+	0.980710i	$0.562623\pi$
$332$	−1.20478	+	1.08479i	−0.0661210	+	0.0595356i
$333$	6.66234	+	2.16472i	0.365094	+	0.118626i
$334$	7.91359	−	8.78893i	0.433012	−	0.480909i
$335$	17.7602	−	1.84013i	0.970345	−	0.100537i
$336$	−0.587022	+	1.01675i	−0.0320247	+	0.0554683i
$337$	−7.19847	+	2.33892i	−0.392126	+	0.127409i	−0.498442	−	0.866923i	$-0.666094\pi$
$337$	−7.19847	+	2.33892i	−0.392126	+	0.127409i	0.106316	+	0.994332i	$0.466094\pi$
$338$	−4.05537	+	9.10852i	−0.220583	+	0.495438i
$339$	−11.4120	−	8.29133i	−0.619817	−	0.450323i
$340$	−3.91297	+	8.75381i	−0.212210	+	0.474742i
$341$	24.6086	−	15.0622i	1.33263	−	0.815664i
$342$			2.62612i			0.142004i
$343$	−8.71000	+	11.9883i	−0.470296	+	0.647306i
$344$	0.0544931	+	0.0242619i	0.00293807	+	0.00130811i
$345$	−0.563377	+	5.28500i	−0.0303312	+	0.284535i
$346$	−12.0937	+	20.9469i	−0.650161	+	1.12611i
$347$	−2.61403	+	1.50921i	−0.140329	+	0.0810188i	−0.568521	−	0.822669i	$-0.692484\pi$
$347$	−2.61403	+	1.50921i	−0.140329	+	0.0810188i	0.428192	+	0.903688i	$0.359151\pi$
$348$	0.860169	+	0.774500i	0.0461099	+	0.0415175i
$349$	−10.0877	+	31.0468i	−0.539983	+	1.66190i	0.192646	+	0.981268i	$0.438293\pi$
$349$	−10.0877	+	31.0468i	−0.539983	+	1.66190i	−0.732629	+	0.680628i	$0.761707\pi$
$350$	−0.630864	+	5.83622i	−0.0337211	+	0.311959i
$351$	−1.59006	+	0.707942i	−0.0848713	+	0.0377872i
$352$	−1.07740	+	5.06877i	−0.0574257	+	0.270167i
$353$	−11.3133	−	1.18908i	−0.602147	−	0.0632882i	−0.201450	−	0.979499i	$-0.564565\pi$
$353$	−11.3133	−	1.18908i	−0.602147	−	0.0632882i	−0.400697	+	0.916211i	$0.631232\pi$
$354$	−0.589025	−	5.60420i	−0.0313063	−	0.297860i
$355$	−20.6959	−	4.43105i	−1.09843	−	0.235176i
$356$	6.80133	−	4.94145i	0.360470	−	0.261896i
$357$	−2.95918	−	4.07296i	−0.156616	−	0.215564i
$358$	1.27344	+	5.99107i	0.0673035	+	0.316638i
$359$	1.41814	+	13.4927i	0.0748465	+	0.712117i	0.966022	+	0.258459i	$0.0832147\pi$
$359$	1.41814	+	13.4927i	0.0748465	+	0.712117i	−0.891176	+	0.453658i	$0.850119\pi$
$360$	1.93484	+	1.12090i	0.101975	+	0.0590764i
$361$	11.8390	+	2.51645i	0.623105	+	0.132445i
$362$	9.60298	+	21.5686i	0.504721	+	1.13362i
$363$	−11.7813	+	10.6079i	−0.618356	+	0.556770i
$364$	0.631467	−	1.94346i	0.0330979	−	0.101865i
$365$	8.87840	+	20.0208i	0.464717	+	1.04794i
$366$	2.08720	+	3.61514i	0.109100	+	0.188966i
$367$	−30.0042	−	17.3229i	−1.56621	−	0.904250i	−0.996605	−	0.0823285i	$-0.973764\pi$
$367$	−30.0042	−	17.3229i	−1.56621	−	0.904250i	−0.569601	−	0.821921i	$-0.692902\pi$
$368$	−2.26058	+	0.734507i	−0.117841	+	0.0382888i
$369$	−1.25357	−	0.558126i	−0.0652583	−	0.0290549i
$370$	7.81198	+	13.5771i	0.406126	+	0.705838i
$371$	−7.08908			−0.368047
$372$	4.41900	−	3.38710i	0.229115	−	0.175613i
$373$		−	19.4219i		−	1.00563i	−0.864395	−	0.502813i	$-0.832299\pi$
$373$		−	19.4219i		−	1.00563i	0.864395	−	0.502813i	$-0.167701\pi$
$374$	−17.9773	−	13.0613i	−0.929584	−	0.675383i
$375$	11.1138	+	1.21797i	0.573914	+	0.0628956i
$376$	0.298333	+	0.918173i	0.0153853	+	0.0473512i
$377$	−1.74472	−	1.00731i	−0.0898576	−	0.0518793i
$378$	−1.01675	+	0.587022i	−0.0522960	+	0.0301931i
$379$	17.2272	−	19.1327i	0.884902	−	0.982783i	−0.115042	−	0.993361i	$-0.536700\pi$
$379$	17.2272	−	19.1327i	0.884902	−	0.982783i	0.999944	+	0.0105774i	$0.00336695\pi$
$380$	−3.93571	+	4.35807i	−0.201898	+	0.223564i
$381$	1.78869	+	1.98654i	0.0916372	+	0.101773i
$382$	7.17782	+	16.1216i	0.367249	+	0.824855i
$383$	6.47721	−	30.4729i	0.330970	−	1.55709i	−0.426662	−	0.904411i	$-0.640311\pi$
$383$	6.47721	−	30.4729i	0.330970	−	1.55709i	0.757633	−	0.652681i	$-0.226356\pi$
$384$	−0.104528	+	0.994522i	−0.00533420	+	0.0507515i
$385$	−12.9320	−	4.22300i	−0.659074	−	0.215224i
$386$	20.3293	−	4.32112i	1.03473	−	0.219939i
$387$	0.0350614	+	0.0482579i	0.00178227	+	0.00245309i
$388$	−2.28702	−	3.14782i	−0.116106	−	0.159806i
$389$	−3.66293	+	0.778580i	−0.185718	+	0.0394756i	−0.299832	−	0.953992i	$-0.596931\pi$
$389$	−3.66293	+	0.778580i	−0.185718	+	0.0394756i	0.114114	+	0.993468i	$0.463597\pi$
$390$	−3.69970	−	1.20816i	−0.187342	−	0.0611773i
$391$	1.06541	−	10.1367i	0.0538800	−	0.512634i
$392$	−1.16880	+	5.49878i	−0.0590334	+	0.277730i
$393$	−3.09363	−	6.94842i	−0.156053	−	0.350501i
$394$	−0.0137030	−	0.0152187i	−0.000690345	−	0.000766706i
$395$	22.1968	−	24.5788i	1.11684	−	1.23670i
$396$	−3.46744	+	3.85099i	−0.174246	+	0.193519i
$397$	−6.68995	+	3.86244i	−0.335759	+	0.193850i	−0.658395	−	0.752673i	$-0.728764\pi$
$397$	−6.68995	+	3.86244i	−0.335759	+	0.193850i	0.322636	+	0.946523i	$0.395431\pi$
$398$	3.21003	+	1.85331i	0.160904	+	0.0928981i
$399$	−0.952756	−	2.93228i	−0.0476975	−	0.146798i
$400$	1.53102	+	4.75983i	0.0765509	+	0.237992i
$401$	−19.5462	−	14.2012i	−0.976092	−	0.709172i	−0.0192599	−	0.999815i	$-0.506131\pi$
$401$	−19.5462	−	14.2012i	−0.976092	−	0.709172i	−0.956832	+	0.290642i	$0.906131\pi$
$402$			7.98513i			0.398262i
$403$	−6.29766	+	7.36570i	−0.313709	+	0.366912i
$404$	19.5137			0.970842
$405$	1.11517	+	1.93814i	0.0554132	+	0.0963071i
$406$	−1.24144	−	0.552723i	−0.0616115	−	0.0274312i
$407$	−34.5243	+	11.2176i	−1.71131	+	0.556037i
$408$	−3.71363	−	2.14407i	−0.183852	−	0.106147i
$409$	−8.95879	−	15.5171i	−0.442984	−	0.767270i	0.554926	−	0.831900i	$-0.312747\pi$
$409$	−8.95879	−	15.5171i	−0.442984	−	0.767270i	−0.997909	+	0.0646297i	$0.979413\pi$
$410$	−1.24386	−	2.80491i	−0.0614300	−	0.138525i
$411$	2.20134	−	6.77502i	0.108584	−	0.334187i
$412$	−2.31214	+	2.08186i	−0.113911	+	0.102566i
$413$	2.69089	+	6.04384i	0.132410	+	0.297398i
$414$	−2.32497	−	0.494188i	−0.114266	−	0.0242880i
$415$	−3.13675	−	1.81719i	−0.153977	−	0.0892023i
$416$	−0.181936	−	1.73101i	−0.00892015	−	0.0848696i
$417$	−1.90599	−	8.96695i	−0.0933365	−	0.439114i
$418$	−7.99894	−	11.0096i	−0.391241	−	0.538497i
$419$	25.6248	−	18.6175i	1.25185	−	0.909523i	0.253523	−	0.967329i	$-0.418411\pi$
$419$	25.6248	−	18.6175i	1.25185	−	0.909523i	0.998328	+	0.0578062i	$0.0184106\pi$
$420$	−2.56706	−	0.549614i	−0.125260	−	0.0268184i
$421$	0.0704841	+	0.670612i	0.00343519	+	0.0326836i	0.996105	−	0.0881725i	$-0.0281027\pi$
$421$	0.0704841	+	0.670612i	0.00343519	+	0.0326836i	−0.992670	+	0.120856i	$0.961436\pi$
$422$	9.59338	+	1.00831i	0.466999	+	0.0490835i
$423$	−0.200723	+	0.944328i	−0.00975949	+	0.0459148i
$424$	−5.51615	+	2.45595i	−0.267888	+	0.119271i
$425$	−21.3165	−	2.30420i	−1.03400	−	0.111770i
$426$	2.92493	−	9.00200i	0.141713	−	0.436148i
$427$	−3.64210	−	3.27936i	−0.176254	−	0.158700i
$428$	−6.24720	+	3.60682i	−0.301970	+	0.174342i
$429$	4.50975	−	7.81112i	0.217733	−	0.377125i
$430$	−0.0141383	+	0.132630i	−0.000681808	+	0.00639600i
$431$	−0.398100	−	0.177246i	−0.0191758	−	0.00853762i	0.397126	−	0.917764i	$-0.370007\pi$
$431$	−0.398100	−	0.177246i	−0.0191758	−	0.00853762i	−0.416302	+	0.909226i	$0.636674\pi$
$432$	−0.587785	+	0.809017i	−0.0282798	+	0.0389238i
$433$		−	21.6779i		−	1.04177i	−0.853626	−	0.520886i	$-0.825601\pi$
$433$		−	21.6779i		−	1.04177i	0.853626	−	0.520886i	$-0.174399\pi$
$434$	−3.70534	+	5.38518i	−0.177862	+	0.258497i
$435$	−1.05620	+	2.36287i	−0.0506411	+	0.113291i
$436$	2.24438	+	1.63063i	0.107486	+	0.0780932i
$437$	2.53888	−	5.70241i	0.121451	−	0.272783i
$438$	−9.31511	+	3.02666i	−0.445093	+	0.144620i
$439$	1.85828	−	3.21864i	0.0886911	−	0.153617i	−0.818267	−	0.574838i	$-0.805065\pi$
$439$	1.85828	−	3.21864i	0.0886911	−	0.153617i	0.906958	+	0.421221i	$0.138398\pi$
$440$	−11.5256	+	1.19417i	−0.549463	+	0.0569297i
$441$	−3.76160	+	4.17768i	−0.179124	+	0.198937i
$442$	7.09838	+	2.30640i	0.337635	+	0.109704i
$443$	7.20216	−	6.48485i	0.342185	−	0.308105i	−0.480063	−	0.877234i	$-0.659386\pi$
$443$	7.20216	−	6.48485i	0.342185	−	0.308105i	0.822248	+	0.569129i	$0.192720\pi$
$444$	−6.39956	+	2.84927i	−0.303710	+	0.135220i
$445$	15.1919	+	11.0719i	0.720164	+	0.524858i
$446$	2.62508	−	24.9760i	0.124301	−	1.18265i
$447$	−4.48965	+	0.471881i	−0.212353	+	0.0223192i
$448$	−0.244097	−	1.14839i	−0.0115325	−	0.0542562i
$449$	2.94075	−	2.13658i	0.138782	−	0.100831i	−0.516228	−	0.856451i	$-0.672664\pi$
$449$	2.94075	−	2.13658i	0.138782	−	0.100831i	0.655010	+	0.755620i	$0.272664\pi$
$450$	−1.05401	+	4.88764i	−0.0496867	+	0.230406i
$451$	6.95540	−	1.47842i	0.327517	−	0.0696159i
$452$	14.0288	−	1.47448i	0.659858	−	0.0693539i
$453$	−16.0655	−	1.68855i	−0.754822	−	0.0793350i
$454$	1.17312	+	0.249355i	0.0550575	+	0.0117028i
$455$	4.56934	+	0.00675539i	0.214214	+	0.000316698i
$456$	−1.75722	−	1.95159i	−0.0822893	−	0.0913916i
$457$	−32.6762	−	10.6171i	−1.52853	−	0.496649i	−0.580344	−	0.814372i	$-0.697082\pi$
$457$	−32.6762	−	10.6171i	−1.52853	−	0.496649i	−0.948184	+	0.317723i	$0.897082\pi$
$458$	−14.7001	−	13.2360i	−0.686889	−	0.618478i
$459$	−2.14407	−	3.71363i	−0.100077	−	0.173338i
$460$	−3.11768	−	4.30449i	−0.145363	−	0.200698i
$461$	−3.21276	−	9.88785i	−0.149633	−	0.460523i	0.847945	−	0.530085i	$-0.177840\pi$
$461$	−3.21276	−	9.88785i	−0.149633	−	0.460523i	−0.997578	+	0.0695617i	$0.977840\pi$
$462$	2.47455	−	5.55793i	0.115126	−	0.258578i
$463$	−5.35229	+	7.36680i	−0.248742	+	0.342364i	−0.915070	−	0.403294i	$-0.867865\pi$
$463$	−5.35229	+	7.36680i	−0.248742	+	0.342364i	0.666328	+	0.745659i	$0.267865\pi$
$464$	−1.15747			−0.0537343
$465$	10.2461	+	7.07230i	0.475152	+	0.327970i
$466$	−12.5623			−0.581936
$467$	−12.1207	+	16.6826i	−0.560877	+	0.771981i	−0.991438	−	0.130581i	$-0.958316\pi$
$467$	−12.1207	+	16.6826i	−0.560877	+	0.771981i	0.430561	+	0.902562i	$0.358316\pi$
$468$	0.707942	−	1.59006i	0.0327246	−	0.0735007i
$469$	−2.89700	−	8.91605i	−0.133771	−	0.411705i
$470$	−1.74834	+	1.26630i	−0.0806451	+	0.0584101i
$471$	−11.5692	−	20.0385i	−0.533082	−	0.923326i
$472$	4.18767	+	3.77060i	0.192753	+	0.173556i
$473$	−0.293979	−	0.0955195i	−0.0135172	−	0.00439199i
$474$	9.91043	+	11.0067i	0.455201	+	0.505552i
$475$	−11.9796	−	5.37615i	−0.549660	−	0.246675i
$476$	4.92444	+	1.04672i	0.225711	+	0.0479764i
$477$	−6.00510	−	0.631161i	−0.274955	−	0.0288989i
$478$	1.91569	−	0.201347i	0.0876216	−	0.00920940i
$479$	−25.8630	+	5.49736i	−1.18171	+	0.251181i	−0.756550	−	0.653936i	$-0.773116\pi$
$479$	−25.8630	+	5.49736i	−1.18171	+	0.251181i	−0.425163	+	0.905117i	$0.639783\pi$
$480$	−2.18789	+	0.461671i	−0.0998630	+	0.0210723i
$481$	9.86421	−	7.16677i	0.449769	−	0.326776i
$482$	−5.13396	−	24.1534i	−0.233846	−	1.10016i
$483$	2.77531	−	0.291697i	0.126281	−	0.0132727i
$484$	1.65712	−	15.7664i	0.0753235	−	0.716655i
$485$	5.12434	−	7.03117i	0.232684	−	0.319269i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	−6.73032	+	6.06001i	−0.304980	+	0.274605i	−0.807382	−	0.590029i	$-0.799116\pi$
$487$	−6.73032	+	6.06001i	−0.304980	+	0.274605i	0.502402	+	0.864634i	$0.332450\pi$
$488$	−3.97009	−	1.28996i	−0.179718	−	0.0583938i
$489$	−12.6837	+	14.0867i	−0.573577	+	0.637022i
$490$	−12.5034	+	1.29547i	−0.564846	+	0.0585235i
$491$	−12.8911	+	22.3281i	−0.581769	+	1.00765i	0.413501	+	0.910504i	$0.364306\pi$
$491$	−12.8911	+	22.3281i	−0.581769	+	1.00765i	−0.995270	+	0.0971494i	$0.969028\pi$
$492$	1.30504	−	0.424035i	0.0588360	−	0.0191170i
$493$	2.01879	−	4.53429i	0.0909219	−	0.204214i
$494$	3.69792	+	2.68669i	0.166377	+	0.120880i
$495$	−10.5786	−	4.72864i	−0.475472	−	0.212536i
$496$	−1.01755	+	5.47399i	−0.0456893	+	0.245790i
$497$			11.1126i			0.498469i
$498$	0.952914	−	1.31157i	0.0427011	−	0.0587730i
$499$	34.9154	+	15.5454i	1.56303	+	0.695906i	0.992141	−	0.125122i	$-0.0399323\pi$
$499$	34.9154	+	15.5454i	1.56303	+	0.695906i	0.570888	+	0.821028i	$0.306599\pi$
$500$	−9.07414	+	6.53146i	−0.405808	+	0.292096i
$501$	−5.91334	+	10.2422i	−0.264188	+	0.457588i
$502$	4.37785	−	2.52755i	0.195393	−	0.112810i
$503$	24.9146	+	22.4332i	1.11089	+	1.00025i	0.999979	+	0.00641441i	$0.00204178\pi$
$503$	24.9146	+	22.4332i	1.11089	+	1.00025i	0.110906	+	0.993831i	$0.464625\pi$
$504$	0.362799	−	1.11658i	0.0161604	−	0.0497365i
$505$	13.4223	+	41.5182i	0.597282	+	1.84754i
$506$	11.2523	−	5.00985i	0.500227	−	0.222715i
$507$	2.07299	−	9.75264i	0.0920646	−	0.433130i
$508$	−2.65851	−	0.279420i	−0.117952	−	0.0123973i
$509$	2.42071	+	23.0315i	0.107296	+	1.02086i	0.907192	+	0.420717i	$0.138221\pi$
$509$	2.42071	+	23.0315i	0.107296	+	1.02086i	−0.799896	+	0.600139i	$0.795112\pi$
$510$	2.00744	−	9.37607i	0.0888908	−	0.415179i
$511$	9.30301	−	6.75903i	0.411541	−	0.299002i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−0.546002	−	2.56874i	−0.0241066	−	0.113412i
$514$	−0.0739733	−	0.703809i	−0.00326282	−	0.0310437i
$515$	−6.01983	−	3.48743i	−0.265266	−	0.153675i
$516$	−0.0583466	−	0.0124019i	−0.00256856	−	0.000545965i
$517$	−2.03484	−	4.57032i	−0.0894921	−	0.201003i
$518$	6.11192	−	5.50320i	0.268542	−	0.241797i
$519$	7.47432	−	23.0036i	0.328086	−	1.00975i
$520$	3.55783	−	1.57775i	0.156021	−	0.0691888i
$521$	9.48489	+	16.4283i	0.415540	+	0.719737i	0.995485	−	0.0949188i	$-0.0302591\pi$
$521$	9.48489	+	16.4283i	0.415540	+	0.719737i	−0.579945	+	0.814656i	$0.696926\pi$
$522$	−1.00240	−	0.578736i	−0.0438738	−	0.0253306i
$523$	17.8279	−	5.79263i	0.779559	−	0.253294i	0.107907	−	0.994161i	$-0.465585\pi$
$523$	17.8279	−	5.79263i	0.779559	−	0.253294i	0.671652	+	0.740867i	$0.265585\pi$
$524$	6.94842	+	3.09363i	0.303543	+	0.135146i
$525$	−0.596340	−	5.83985i	−0.0260264	−	0.254872i
$526$	10.0104			0.436476
$527$	−19.6691	−	13.5336i	−0.856800	−	0.589532i
$528$		−	5.18201i		−	0.225518i
$529$	−14.0367	−	10.1982i	−0.610290	−	0.443402i
$530$	−9.01960	−	10.0471i	−0.391787	−	0.436419i
$531$	1.74133	+	5.35927i	0.0755673	+	0.232572i
$532$	2.67011	+	1.54159i	0.115764	+	0.0668365i
$533$	−2.06840	+	1.19419i	−0.0895923	+	0.0517261i
$534$	−5.62532	+	6.24755i	−0.243431	+	0.270358i
$535$	−11.9711	−	10.8109i	−0.517556	−	0.467397i
$536$	−5.34310	−	5.93411i	−0.230787	−	0.256314i
$537$	−2.49123	−	5.59539i	−0.107504	−	0.241459i
$538$	1.35546	−	6.37694i	0.0584380	−	0.274929i
$539$	3.04505	−	28.9717i	0.131160	−	1.24790i
$540$	−2.12560	−	0.694126i	−0.0914714	−	0.0298704i
$541$	12.8196	−	2.72489i	0.551158	−	0.117152i	0.0760895	−	0.997101i	$-0.475757\pi$
$541$	12.8196	−	2.72489i	0.551158	−	0.117152i	0.475069	+	0.879949i	$0.342423\pi$
$542$	7.53196	+	10.3669i	0.323526	+	0.445295i
$543$	−13.8775	−	19.1007i	−0.595541	−	0.819692i
$544$	4.19443	−	0.891553i	0.179835	−	0.0382250i
$545$	−1.92565	+	5.89685i	−0.0824856	+	0.252593i
$546$	−0.213601	+	2.03228i	−0.00914128	+	0.0869734i
$547$	2.64664	−	12.4515i	0.113162	−	0.532386i	−0.884649	−	0.466258i	$-0.845602\pi$
$547$	2.64664	−	12.4515i	0.113162	−	0.532386i	0.997811	−	0.0661285i	$-0.0210647\pi$
$548$	2.89746	+	6.50780i	0.123773	+	0.277999i
$549$	−2.79322	−	3.10219i	−0.119212	−	0.132398i
$550$	−10.4685	−	23.7011i	−0.446380	−	1.01062i
$551$	2.03393	−	2.25891i	0.0866484	−	0.0962328i
$552$	2.05847	−	1.18846i	0.0876142	−	0.0505841i
$553$	−15.0590	−	8.69433i	−0.640374	−	0.369720i
$554$	1.49858	+	4.61215i	0.0636685	+	0.195952i
$555$	−10.4641	−	11.6562i	−0.444176	−	0.494777i
$556$	7.41649	+	5.38839i	0.314529	+	0.228519i
$557$			34.9064i			1.47903i	0.673139	+	0.739516i	$0.264946\pi$
$557$			34.9064i			1.47903i	−0.673139	+	0.739516i	$0.735054\pi$
$558$	−3.61822	+	4.23184i	−0.153171	+	0.179148i
$559$	0.103823			0.00439126
$560$	2.27546	−	1.30926i	0.0961559	−	0.0553262i
$561$	20.3001	+	9.03816i	0.857069	+	0.381592i
$562$	9.12889	−	2.96616i	0.385079	−	0.125120i
$563$	23.2380	+	13.4164i	0.979364	+	0.565436i	0.902078	−	0.431573i	$-0.142041\pi$
$563$	23.2380	+	13.4164i	0.979364	+	0.565436i	0.0772856	+	0.997009i	$0.475375\pi$
$564$	−0.482712	−	0.836082i	−0.0203259	−	0.0352054i
$565$	12.7867	+	28.8341i	0.537941	+	1.21306i
$566$	7.45866	−	22.9554i	0.313511	−	0.964887i
$567$	0.872484	−	0.785588i	0.0366409	−	0.0329916i
$568$	3.84987	+	8.64695i	0.161537	+	0.362818i
$569$	28.4411	+	6.04534i	1.19231	+	0.253434i	0.760990	−	0.648763i	$-0.224714\pi$
$569$	28.4411	+	6.04534i	1.19231	+	0.253434i	0.431323	+	0.902197i	$0.358047\pi$
$570$	2.94361	−	5.08112i	0.123294	−	0.212825i
$571$	−1.38304	−	13.1587i	−0.0578783	−	0.550675i	−0.984587	−	0.174895i	$-0.944041\pi$
$571$	−1.38304	−	13.1587i	−0.0578783	−	0.550675i	0.926709	−	0.375780i	$-0.122625\pi$
$572$	1.87526	+	8.82241i	0.0784086	+	0.368884i
$573$	−10.3728	−	14.2770i	−0.433332	−	0.596430i
$574$	−1.30335	+	0.946939i	−0.0544008	+	0.0395245i
$575$	7.01397	−	9.59412i	0.292503	−	0.400102i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−21.7274	−	2.28364i	−0.904523	−	0.0950692i	−0.359167	−	0.933273i	$-0.616939\pi$
$577$	−21.7274	−	2.28364i	−0.904523	−	0.0950692i	−0.545356	+	0.838204i	$0.683606\pi$
$578$	−0.288603	+	1.35777i	−0.0120043	+	0.0564757i
$579$	−18.9866	+	8.45339i	−0.789057	+	0.351311i
$580$	−0.796153	−	2.46269i	−0.0330585	−	0.102258i
$581$	−0.588168	+	1.81020i	−0.0244013	+	0.0750996i
$582$	2.89151	+	2.60353i	0.119857	+	0.107920i
$583$	27.0978	−	15.6450i	1.12228	−	0.647948i
$584$	4.89724	−	8.48227i	0.202649	−	0.350999i
$585$	3.87004	+	0.412544i	0.160007	+	0.0170566i
$586$	−9.32697	−	4.15263i	−0.385293	−	0.171544i
$587$	22.1134	−	30.4364i	0.912716	−	1.25625i	−0.0535143	−	0.998567i	$-0.517042\pi$
$587$	22.1134	−	30.4364i	0.912716	−	1.25625i	0.966231	−	0.257679i	$-0.0829577\pi$
$588$		−	5.62162i		−	0.231832i
$589$	−8.89493	−	11.6048i	−0.366509	−	0.478169i
$590$	−5.14205	+	11.5034i	−0.211695	+	0.473589i
$591$	0.0165677	+	0.0120371i	0.000681502	+	0.000495140i
$592$	2.84927	−	6.39956i	0.117104	−	0.263020i
$593$	−8.31203	+	2.70074i	−0.341334	+	0.110906i	−0.474668	−	0.880165i	$-0.657432\pi$
$593$	−8.31203	+	2.70074i	−0.341334	+	0.110906i	0.133334	+	0.991071i	$0.457432\pi$
$594$	2.59101	−	4.48775i	0.106310	−	0.184135i
$595$	1.16016	+	11.1974i	0.0475621	+	0.459050i
$596$	3.02071	−	3.35484i	0.123733	−	0.137420i
$597$	−3.52521	−	1.14541i	−0.144277	−	0.0468785i
$598$	−3.07448	+	2.76827i	−0.125725	+	0.113203i
$599$	−14.4081	+	6.41491i	−0.588700	+	0.262106i	−0.679395	−	0.733773i	$-0.737758\pi$
$599$	−14.4081	+	6.41491i	−0.588700	+	0.262106i	0.0906953	+	0.995879i	$0.471091\pi$
$600$	−2.48719	−	4.33750i	−0.101539	−	0.177078i
$601$	1.73585	−	16.5155i	0.0708067	−	0.673681i	−0.900338	−	0.435191i	$-0.856681\pi$
$601$	1.73585	−	16.5155i	0.0708067	−	0.673681i	0.971145	−	0.238490i	$-0.0766525\pi$
$602$	0.0696481	−	0.00732031i	0.00283865	−	0.000298354i
$603$	−1.66020	−	7.81064i	−0.0676087	−	0.318074i
$604$	13.0688	−	9.49506i	0.531763	−	0.386349i
$605$	34.6852	−	7.31898i	1.41015	−	0.297559i
$606$	−19.0873	+	4.05712i	−0.775367	+	0.164809i
$607$	7.33641	−	0.771088i	0.297776	−	0.0312975i	0.0455375	−	0.998963i	$-0.485500\pi$
$607$	7.33641	−	0.771088i	0.297776	−	0.0312975i	0.252238	+	0.967665i	$0.418833\pi$
$608$	2.61174	+	0.274505i	0.105920	+	0.0111326i
$609$	1.32923	+	0.282536i	0.0538629	+	0.0114489i
$610$	0.0137999	−	9.33424i	0.000558742	−	0.377932i
$611$	1.12438	+	1.24875i	0.0454876	+	0.0505191i
$612$	4.07826	+	1.32511i	0.164854	+	0.0535643i
$613$	18.8423	+	16.9656i	0.761032	+	0.685236i	0.955276	−	0.295717i	$-0.0955586\pi$
$613$	18.8423	+	16.9656i	0.761032	+	0.685236i	−0.194244	+	0.980953i	$0.562225\pi$
$614$	−0.395138	−	0.684399i	−0.0159465	−	0.0276201i
$615$	1.79986	+	2.48501i	0.0725772	+	0.100205i
$616$	1.88003	+	5.78614i	0.0757486	+	0.233130i
$617$	−4.71767	+	10.5961i	−0.189926	+	0.426581i	−0.983261	−	0.182205i	$-0.941677\pi$
$617$	−4.71767	+	10.5961i	−0.189926	+	0.426581i	0.793334	+	0.608786i	$0.208343\pi$
$618$	1.82877	−	2.51709i	0.0735639	−	0.101252i
$619$	−19.9021			−0.799933			−0.399967	−	0.916530i	$-0.630978\pi$
$619$	−19.9021			−0.799933			−0.399967	+	0.916530i	$0.630978\pi$
$620$	−12.3466	+	1.60024i	−0.495853	+	0.0642671i
$621$	2.37691			0.0953822
$622$	−8.35054	+	11.4935i	−0.334826	+	0.460849i
$623$	4.01452	−	9.01676i	0.160838	−	0.361249i
$624$	0.537857	+	1.65535i	0.0215315	+	0.0662672i
$625$	−20.1382	−	14.8140i	−0.805527	−	0.592559i
$626$	−15.7664	−	27.3083i	−0.630154	−	1.09146i
$627$	10.1132	+	9.10593i	0.403881	+	0.363656i
$628$	22.0060	+	7.15018i	0.878135	+	0.285323i
$629$	20.1002	+	22.3235i	0.801446	+	0.890096i
$630$	2.62524	+	0.00388120i	0.104592	+	0.000154631i
$631$	11.2736	+	2.39628i	0.448795	+	0.0953942i	0.426764	−	0.904363i	$-0.359654\pi$
$631$	11.2736	+	2.39628i	0.448795	+	0.0953942i	0.0220307	+	0.999757i	$0.492987\pi$
$632$	−14.7298	−	1.54816i	−0.585919	−	0.0615826i
$633$	−9.59338	+	1.00831i	−0.381303	+	0.0400765i
$634$	−5.08725	+	1.08133i	−0.202040	+	0.0429450i
$635$	−1.23411	−	5.84856i	−0.0489744	−	0.232093i
$636$	4.88499	−	3.54915i	0.193702	−	0.140733i
$637$	2.03435	+	9.57085i	0.0806038	+	0.379211i
$638$	5.96517	−	0.626965i	0.236163	−	0.0248218i
$639$	−0.989389	+	9.41341i	−0.0391396	+	0.372389i
$640$	1.31700	−	1.80707i	0.0520590	−	0.0714308i
$641$	−10.1847	+	4.53450i	−0.402270	+	0.179102i	−0.597891	−	0.801577i	$-0.703994\pi$
$641$	−10.1847	+	4.53450i	−0.402270	+	0.179102i	0.195621	+	0.980680i	$0.437328\pi$
$642$	5.36078	−	4.82687i	0.211573	−	0.190501i
$643$	18.3037	+	5.94724i	0.721829	+	0.234536i	0.646816	−	0.762646i	$-0.276100\pi$
$643$	18.3037	+	5.94724i	0.721829	+	0.234536i	0.0750128	+	0.997183i	$0.476100\pi$
$644$	−1.86728	+	2.07382i	−0.0735810	+	0.0817199i
$645$	−0.0137460	−	0.132671i	−0.000541250	−	0.00522393i
$646$	−5.63059	+	9.75246i	−0.221532	+	0.383705i
$647$	6.92764	−	2.25093i	0.272354	−	0.0884931i	−0.169656	−	0.985503i	$-0.554266\pi$
$647$	6.92764	−	2.25093i	0.272354	−	0.0884931i	0.442010	+	0.897010i	$0.354266\pi$
$648$	0.406737	−	0.913545i	0.0159781	−	0.0358875i
$649$	−23.6241	−	17.1639i	−0.927327	−	0.673742i
$650$	5.80410	+	6.48456i	0.227656	+	0.254345i
$651$	2.50473	−	6.03788i	0.0981680	−	0.236643i
$652$		−	18.9555i		−	0.742354i
$653$	14.8153	−	20.3915i	0.579767	−	0.797981i	−0.413902	−	0.910321i	$-0.635835\pi$
$653$	14.8153	−	20.3915i	0.579767	−	0.797981i	0.993670	+	0.112340i	$0.0358345\pi$
$654$	−2.53436	−	1.12837i	−0.0991013	−	0.0441227i
$655$	−1.80277	+	16.9117i	−0.0704402	+	0.660794i
$656$	−0.686103	+	1.18836i	−0.0267878	+	0.0463978i
$657$	8.48227	−	4.89724i	0.330925	−	0.191060i
$658$	0.842318	+	0.758426i	0.0328370	+	0.0295665i
$659$	10.4960	−	32.3034i	0.408867	−	1.25836i	−0.508756	−	0.860911i	$-0.669894\pi$
$659$	10.4960	−	32.3034i	0.408867	−	1.25836i	0.917623	−	0.397453i	$-0.130106\pi$
$660$	11.0255	−	3.56439i	0.429167	−	0.138744i
$661$	19.6354	−	8.74226i	0.763730	−	0.340035i	0.0123671	−	0.999924i	$-0.496063\pi$
$661$	19.6354	−	8.74226i	0.763730	−	0.340035i	0.751363	+	0.659889i	$0.229397\pi$
$662$	−4.36864	+	20.5528i	−0.169792	+	0.798808i
$663$	−7.42279	−	0.780167i	−0.288277	−	0.0302992i
$664$	0.169461	+	1.61231i	0.00657636	+	0.0625699i
$665$	−1.44335	+	6.74142i	−0.0559709	+	0.261421i
$666$	5.66732	−	4.11755i	0.219604	−	0.159552i
$667$	1.61712	+	2.22577i	0.0626151	+	0.0861823i
$668$	−2.45890	−	11.5682i	−0.0951378	−	0.447588i
$669$	2.62508	+	24.9760i	0.101492	+	0.965627i
$670$	8.95050	−	15.4499i	0.345788	−	0.596883i
$671$	21.1591	+	4.49751i	0.816838	+	0.173624i
$672$	0.477526	+	1.07254i	0.0184210	+	0.0413742i
$673$	6.58600	−	5.93006i	0.253872	−	0.228587i	−0.532361	−	0.846517i	$-0.678695\pi$
$673$	6.58600	−	5.93006i	0.253872	−	0.228587i	0.786233	+	0.617930i	$0.212029\pi$
$674$	−2.33892	+	7.19847i	−0.0900920	+	0.277275i
$675$	0.0147842	−	4.99998i	0.000569042	−	0.192449i
$676$	4.98526	+	8.63472i	0.191741	+	0.332105i
$677$	18.9210	+	10.9241i	0.727194	+	0.419846i	0.817395	−	0.576078i	$-0.195417\pi$
$677$	18.9210	+	10.9241i	0.727194	+	0.419846i	−0.0902005	+	0.995924i	$0.528751\pi$
$678$	−13.4156	+	4.35901i	−0.515225	+	0.167407i
$679$	−4.17317	−	1.85802i	−0.160152	−	0.0713041i
$680$	4.78200	+	8.31102i	0.183381	+	0.318713i
$681$	−1.19933			−0.0459585
$682$	2.27898	−	28.7621i	0.0872665	−	1.10136i
$683$			8.19680i			0.313642i	0.987627	+	0.156821i	$0.0501245\pi$
$683$			8.19680i			0.313642i	−0.987627	+	0.156821i	$0.949875\pi$
$684$	2.12458	+	1.54360i	0.0812353	+	0.0590209i
$685$	−11.8533	+	10.6411i	−0.452892	+	0.406575i
$686$	4.57912	+	14.0931i	0.174831	+	0.538076i
$687$	17.1308	+	9.89044i	0.653579	+	0.377344i
$688$	0.0516585	−	0.0298250i	0.00196946	−	0.00113707i
$689$	−7.03236	+	7.81023i	−0.267912	+	0.297546i
$690$	3.94451	+	3.56222i	0.150165	+	0.135612i
$691$	−28.8218	−	32.0099i	−1.09643	−	1.21771i	−0.974313	−	0.225198i	$-0.927697\pi$
$691$	−28.8218	−	32.0099i	−1.09643	−	1.21771i	−0.122121	−	0.992515i	$-0.538970\pi$
$692$	9.83790	+	22.0963i	0.373981	+	0.839975i
$693$	−1.26492	+	5.95096i	−0.0480502	+	0.226058i
$694$	−0.315511	+	3.00189i	−0.0119766	+	0.113950i
$695$	−6.36325	+	19.4860i	−0.241372	+	0.739146i
$696$	1.13218	−	0.240652i	0.0429151	−	0.00912188i
$697$	−3.45865	−	4.76042i	−0.131006	−	0.180314i
$698$	19.1880	+	26.4100i	0.726275	+	0.999632i
$699$	12.2877	−	2.61184i	0.464765	−	0.0987889i
$700$	4.35079	+	3.94082i	0.164444	+	0.148949i
$701$	−3.87924	+	36.9085i	−0.146517	+	1.39402i	0.636145	+	0.771570i	$0.280528\pi$
$701$	−3.87924	+	36.9085i	−0.146517	+	1.39402i	−0.782662	+	0.622447i	$0.786139\pi$
$702$	−0.361879	+	1.70251i	−0.0136582	+	0.0642570i
$703$	7.48253	+	16.8060i	0.282209	+	0.633852i
$704$	3.46744	+	3.85099i	0.130684	+	0.145140i
$705$	1.44686	−	1.60213i	0.0544919	−	0.0603397i
$706$	−7.61178	+	8.45374i	−0.286473	+	0.318161i
$707$	19.8406	−	11.4550i	0.746181	−	0.430808i
$708$	−4.88011	−	2.81753i	−0.183406	−	0.105889i
$709$	−11.5905	−	35.6718i	−0.435289	−	1.33968i	−0.892790	−	0.450473i	$-0.851256\pi$
$709$	−11.5905	−	35.6718i	−0.435289	−	1.33968i	0.457501	−	0.889209i	$-0.348744\pi$
$710$	−15.7496	+	14.1389i	−0.591070	+	0.530622i
$711$	−11.9823	−	8.70563i	−0.449371	−	0.326487i
$712$		−	8.40690i		−	0.315062i
$713$	11.9479	−	5.69109i	0.447453	−	0.213133i
$714$	−5.03446			−0.188410
$715$	−17.4811	+	10.0583i	−0.653756	+	0.376159i
$716$	5.59539	+	2.49123i	0.209109	+	0.0931015i
$717$	−1.83197	+	0.595242i	−0.0684160	+	0.0222297i
$718$	11.7494	+	6.78351i	0.438483	+	0.253158i
$719$	−12.7023	−	22.0011i	−0.473717	−	0.820503i	0.525830	−	0.850590i	$-0.323755\pi$
$719$	−12.7023	−	22.0011i	−0.473717	−	0.820503i	−0.999547	+	0.0300870i	$0.990422\pi$
$720$	2.04409	−	0.906470i	0.0761788	−	0.0337821i
$721$	−1.12877	+	3.47401i	−0.0420377	+	0.129379i
$722$	8.99464	−	8.09881i	0.334746	−	0.301406i
$723$	10.0435	+	22.5582i	0.373523	+	0.838947i
$724$	23.0939	+	4.90876i	0.858278	+	0.182433i
$725$	4.69211	−	3.38786i	0.174261	−	0.125822i
$726$	1.65712	+	15.7664i	0.0615014	+	0.585146i
$727$	−9.22577	−	43.4038i	−0.342165	−	1.60976i	−0.726908	−	0.686735i	$-0.759043\pi$
$727$	−9.22577	−	43.4038i	−0.342165	−	1.60976i	0.384743	−	0.923024i	$-0.374290\pi$
$728$	−1.20112	−	1.65320i	−0.0445166	−	0.0612718i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	21.4158	+	4.58517i	0.792634	+	0.169705i
$731$	0.0267371	+	0.254386i	0.000988907	+	0.00940882i
$732$	4.15154	+	0.436344i	0.153445	+	0.0161277i
$733$	0.725606	−	3.41371i	0.0268009	−	0.126088i	−0.962713	−	0.270523i	$-0.912803\pi$
$733$	0.725606	−	3.41371i	0.0268009	−	0.126088i	0.989514	+	0.144435i	$0.0461366\pi$
$734$	−31.6506	+	14.0917i	−1.16824	+	0.520136i
$735$	11.9608	−	3.86677i	0.441182	−	0.142628i
$736$	−0.734507	+	2.26058i	−0.0270743	+	0.0833260i
$737$	30.7506	+	27.6880i	1.13271	+	1.01990i
$738$	−1.18836	+	0.686103i	−0.0437443	+	0.0252558i
$739$	−20.5919	+	35.6663i	−0.757486	+	1.31201i	0.186642	+	0.982428i	$0.440240\pi$
$739$	−20.5919	+	35.6663i	−0.757486	+	1.31201i	−0.944129	+	0.329577i	$0.893094\pi$
$740$	15.5758	+	1.66037i	0.572579	+	0.0610365i
$741$	−4.17570	−	1.85914i	−0.153398	−	0.0682973i
$742$	−4.16686	+	5.73519i	−0.152970	+	0.210545i
$743$			48.5141i			1.77981i	0.456145	+	0.889905i	$0.349230\pi$
$743$			48.5141i			1.77981i	−0.456145	+	0.889905i	$0.650770\pi$
$744$	−0.142795	−	5.56593i	−0.00523510	−	0.204057i
$745$	9.21567	+	4.11942i	0.337636	+	0.150924i
$746$	−15.7126	−	11.4159i	−0.575279	−	0.417965i
$747$	−0.659399	+	1.48103i	−0.0241262	+	0.0541882i
$748$	−21.1336	+	6.86672i	−0.772721	+	0.251072i
$749$	−4.23456	+	7.33448i	−0.154728	+	0.267996i
$750$	7.51788	−	8.27535i	0.274514	−	0.302173i
$751$	−29.9481	+	33.2607i	−1.09282	+	1.21370i	−0.117461	+	0.993078i	$0.537475\pi$
$751$	−29.9481	+	33.2607i	−1.09282	+	1.21370i	−0.975359	+	0.220622i	$0.929191\pi$
$752$	0.918173	+	0.298333i	0.0334823	+	0.0108791i
$753$	−3.75668	+	3.38253i	−0.136901	+	0.123266i
$754$	−1.84045	+	0.819423i	−0.0670254	+	0.0298416i
$755$	29.1914	+	21.2748i	1.06238	+	0.774269i
$756$	−0.122721	+	1.16761i	−0.00446332	+	0.0424656i
$757$	−14.9022	+	1.56629i	−0.541631	+	0.0569277i	−0.371394	−	0.928475i	$-0.621120\pi$
$757$	−14.9022	+	1.56629i	−0.541631	+	0.0569277i	−0.170237	+	0.985403i	$0.554453\pi$
$758$	−5.35282	−	25.1830i	−0.194423	−	0.914689i
$759$	−9.96482	+	7.23987i	−0.361700	+	0.262790i
$760$	1.21240	+	5.74567i	0.0439785	+	0.208417i
$761$	−28.8125	+	6.12429i	−1.04445	+	0.222005i	−0.698027	−	0.716072i	$-0.745938\pi$
$761$	−28.8125	+	6.12429i	−1.04445	+	0.222005i	−0.346427	+	0.938077i	$0.612605\pi$
$762$	2.65851	−	0.279420i	0.0963075	−	0.0101223i
$763$	3.23919	+	0.340453i	0.117267	+	0.0123252i
$764$	17.2617	+	3.66909i	0.624507	+	0.132743i
$765$	−0.0141759	+	9.58855i	−0.000512530	+	0.346675i
$766$	−20.8459	−	23.1517i	−0.753192	−	0.836505i
$767$	9.32803	+	3.03086i	0.336816	+	0.109438i
$768$	0.743145	+	0.669131i	0.0268159	+	0.0241452i
$769$	14.6087	+	25.3031i	0.526805	+	0.912452i	0.999512	+	0.0312329i	$0.00994336\pi$
$769$	14.6087	+	25.3031i	0.526805	+	0.912452i	−0.472708	+	0.881219i	$0.656723\pi$
$770$	−11.0177	+	7.97997i	−0.397050	+	0.287578i
$771$	0.218687	+	0.673049i	0.00787581	+	0.0242393i
$772$	8.45339	−	18.9866i	0.304244	−	0.683343i
$773$	27.9613	−	38.4854i	1.00570	−	1.38422i	0.0839322	−	0.996471i	$-0.473252\pi$
$773$	27.9613	−	38.4854i	1.00570	−	1.38422i	0.921764	−	0.387751i	$-0.126748\pi$
$774$	0.0596501			0.00214408
$775$	−11.8972	−	25.1686i	−0.427361	−	0.904081i
$776$	−3.89092			−0.139676
$777$	−4.83418	+	6.65368i	−0.173425	+	0.238699i
$778$	−1.52313	+	3.42101i	−0.0546069	+	0.122649i
$779$	−1.11357	−	3.42721i	−0.0398977	−	0.122792i
$780$	−3.15205	+	2.28298i	−0.112861	+	0.0817440i
$781$	−24.5246	−	42.4778i	−0.877557	−	1.51997i
$782$	−7.57452	−	6.82013i	−0.270864	−	0.243887i
$783$	1.10082	+	0.357678i	0.0393401	+	0.0127824i
$784$	3.76160	+	4.17768i	0.134343	+	0.149203i
$785$	−0.0764921	+	51.7391i	−0.00273012	+	1.84665i
$786$	−7.43978	−	1.58137i	−0.265368	−	0.0564057i
$787$	50.1129	+	5.26708i	1.78633	+	0.187751i	0.939140	−	0.343535i	$-0.111624\pi$
$787$	50.1129	+	5.26708i	1.78633	+	0.187751i	0.847193	+	0.531286i	$0.178291\pi$
$788$	−0.0203666	+	0.00214061i	−0.000725529	+	7.62562e-5i
$789$	−9.79169	+	2.08129i	−0.348593	+	0.0740958i
$790$	−6.83776	−	32.4046i	−0.243277	−	1.15291i
$791$	13.3982	−	9.73438i	0.476386	−	0.346115i
$792$	1.07740	+	5.06877i	0.0382838	+	0.180111i
$793$	−7.22592	+	0.759475i	−0.256600	+	0.0269697i
$794$	−0.807471	+	7.68257i	−0.0286561	+	0.272644i
$795$	10.9114	+	7.95228i	0.386988	+	0.282038i
$796$	3.38617	−	1.50762i	0.120020	−	0.0534362i
$797$	−13.8886	+	12.5053i	−0.491959	+	0.442961i	−0.877392	−	0.479774i	$-0.840719\pi$
$797$	−13.8886	+	12.5053i	−0.491959	+	0.442961i	0.385433	+	0.922736i	$0.374052\pi$
$798$	−2.93228	−	0.952756i	−0.103802	−	0.0337272i
$799$	−2.77011	+	3.07652i	−0.0979996	+	0.108840i
$800$	4.75069	+	1.55914i	0.167962	+	0.0551239i
$801$	4.20345	−	7.28059i	0.148522	−	0.257247i
$802$	−22.9780	+	7.46599i	−0.811380	+	0.263633i
$803$	−20.6440	+	46.3671i	−0.728510	+	1.63626i
$804$	6.46011	+	4.69354i	0.227830	+	0.165528i
$805$	−5.69674	−	2.54645i	−0.200784	−	0.0897505i
$806$	2.25730	+	9.42436i	0.0795101	+	0.331959i
$807$			6.51940i			0.229494i
$808$	11.4699	−	15.7869i	0.403508	−	0.555381i
$809$	−11.1879	−	4.98118i	−0.393346	−	0.175129i	0.200526	−	0.979688i	$-0.435735\pi$
$809$	−11.1879	−	4.98118i	−0.393346	−	0.175129i	−0.593872	+	0.804559i	$0.702402\pi$
$810$	2.22347	+	0.237020i	0.0781248	+	0.00832804i
$811$	12.3917	−	21.4630i	0.435130	−	0.753668i	−0.562176	−	0.827018i	$-0.690036\pi$
$811$	12.3917	−	21.4630i	0.435130	−	0.753668i	0.997306	+	0.0733497i	$0.0233689\pi$
$812$	−1.17686	+	0.679461i	−0.0412997	+	0.0238444i
$813$	−9.52276	−	8.57433i	−0.333978	−	0.300715i
$814$	−11.2176	+	34.5243i	−0.393178	+	1.21008i
$815$	40.3306	−	13.0383i	1.41272	−	0.456712i
$816$	−3.91741	+	1.74414i	−0.137137	+	0.0610572i
$817$	−0.0325690	+	0.153225i	−0.00113945	+	0.00536068i
$818$	−17.8194	−	1.87290i	−0.623042	−	0.0654843i
$819$	−0.213601	−	2.03228i	−0.00746382	−	0.0710135i
$820$	−3.00035	−	0.642381i	−0.104777	−	0.0224329i
$821$	15.4266	−	11.2081i	0.538391	−	0.391164i	−0.285096	−	0.958499i	$-0.592026\pi$
$821$	15.4266	−	11.2081i	0.538391	−	0.391164i	0.823487	+	0.567335i	$0.192026\pi$
$822$	−4.18719	−	5.76317i	−0.146045	−	0.201014i
$823$	0.685063	+	3.22297i	0.0238798	+	0.112346i	0.988473	−	0.151396i	$-0.0483768\pi$
$823$	0.685063	+	3.22297i	0.0238798	+	0.112346i	−0.964593	+	0.263741i	$0.915043\pi$
$824$	0.325218	+	3.09424i	0.0113295	+	0.107793i
$825$	15.1675	+	21.0066i	0.528065	+	0.731357i
$826$	6.47124	+	1.37550i	0.225163	+	0.0478599i
$827$	10.3921	+	23.3410i	0.361369	+	0.811647i	0.999142	+	0.0414229i	$0.0131891\pi$
$827$	10.3921	+	23.3410i	0.361369	+	0.811647i	−0.637773	+	0.770224i	$0.720144\pi$
$828$	−1.76639	+	1.59047i	−0.0613863	+	0.0552725i
$829$	−13.0761	+	40.2440i	−0.454150	+	1.39773i	0.417980	+	0.908456i	$0.362738\pi$
$829$	−13.0761	+	40.2440i	−0.454150	+	1.39773i	−0.872130	+	0.489274i	$0.837262\pi$
$830$	−3.31387	+	1.46956i	−0.115026	+	0.0510093i
$831$	−2.42475	−	4.19979i	−0.0841137	−	0.145689i
$832$	−1.50735	−	0.870271i	−0.0522581	−	0.0301712i
$833$	−22.9264	+	7.44925i	−0.794354	+	0.258101i
$834$	−8.37473	−	3.72867i	−0.289993	−	0.129113i
$835$	22.9218	−	13.1887i	0.793241	−	0.456415i
$836$	−13.6086			−0.470663
$837$	2.65930	−	4.89164i	0.0919189	−	0.169080i
$838$		−	31.6739i		−	1.09416i
$839$	−24.6063	−	17.8775i	−0.849505	−	0.617201i	0.0755048	−	0.997145i	$-0.475943\pi$
$839$	−24.6063	−	17.8775i	−0.849505	−	0.617201i	−0.925009	+	0.379944i	$0.875943\pi$
$840$	−1.95353	+	1.75374i	−0.0674032	+	0.0605099i
$841$	−8.54749	−	26.3065i	−0.294741	−	0.907120i
$842$	0.583966	+	0.337153i	0.0201248	+	0.0116191i
$843$	−8.31270	+	4.79934i	−0.286305	+	0.165298i
$844$	6.45459	−	7.16854i	0.222176	−	0.246751i
$845$	−14.9426	+	16.5462i	−0.514040	+	0.569205i
$846$	0.645995	+	0.717450i	0.0222098	+	0.0246665i
$847$	−7.57035	−	17.0033i	−0.260120	−	0.584240i
$848$	−1.25541	+	5.90623i	−0.0431109	+	0.202821i
$849$	−2.52298	+	24.0045i	−0.0865883	+	0.823833i
$850$	−14.3937	+	15.8910i	−0.493699	+	0.545058i
$851$	−16.2869	+	3.46188i	−0.558307	+	0.118672i
$852$	−5.56354	−	7.65756i	−0.190604	−	0.262344i
$853$	−28.5933	−	39.3553i	−0.979016	−	1.34750i	−0.937358	−	0.348368i	$-0.886736\pi$
$853$	−28.5933	−	39.3553i	−0.979016	−	1.34750i	−0.0416581	−	0.999132i	$-0.513264\pi$
$854$	−4.79383	+	1.01896i	−0.164042	+	0.0348681i
$855$	−1.82286	+	5.58210i	−0.0623405	+	0.190904i
$856$	−0.754031	+	7.17412i	−0.0257722	+	0.245207i
$857$	11.9149	−	56.0550i	0.407004	−	1.91480i	0.00311539	−	0.999995i	$-0.499008\pi$
$857$	11.9149	−	56.0550i	0.407004	−	1.91480i	0.403889	−	0.914808i	$-0.367658\pi$
$858$	−3.66857	−	8.23973i	−0.125243	−	0.281300i
$859$	3.03945	+	3.37565i	0.103705	+	0.115176i	0.792763	−	0.609531i	$-0.208642\pi$
$859$	3.03945	+	3.37565i	0.103705	+	0.115176i	−0.689058	+	0.724706i	$0.741975\pi$
$860$	0.0989898	+	0.0893962i	0.00337552	+	0.00304838i
$861$	1.07799	−	1.19723i	0.0367377	−	0.0408014i
$862$	−0.377392	+	0.217888i	−0.0128540	+	0.00742128i
$863$	−7.13184	−	4.11757i	−0.242771	−	0.140164i	0.373679	−	0.927558i	$-0.378096\pi$
$863$	−7.13184	−	4.11757i	−0.242771	−	0.140164i	−0.616450	+	0.787394i	$0.711430\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−40.2462	+	36.1303i	−1.36841	+	1.22847i
$866$	−17.5378	−	12.7419i	−0.595958	−	0.432989i
$867$		−	1.38810i		−	0.0471424i
$868$	2.17876	+	6.16301i	0.0739519	+	0.209186i
$869$	76.7503			2.60358
$870$	1.29078	+	2.24334i	0.0437614	+	0.0760565i
$871$	−12.6969	−	5.65301i	−0.430217	−	0.191545i
$872$	2.63842	−	0.857276i	0.0893483	−	0.0290310i
$873$	−3.36963	−	1.94546i	−0.114045	−	0.0658438i
$874$	−3.12103	−	5.40579i	−0.105571	−	0.182854i
$875$	−5.39204	+	11.9676i	−0.182284	+	0.404578i
$876$	−3.02666	+	9.31511i	−0.102261	+	0.314728i
$877$	−2.02424	+	1.82263i	−0.0683536	+	0.0615459i	−0.702599	−	0.711586i	$-0.747977\pi$
$877$	−2.02424	+	1.82263i	−0.0683536	+	0.0615459i	0.634246	+	0.773131i	$0.281311\pi$
$878$	−1.51167	−	3.39526i	−0.0510162	−	0.114584i
$879$	9.98653	+	2.12270i	0.336837	+	0.0715970i
$880$	−5.80850	+	10.0263i	−0.195804	+	0.337988i
$881$	−2.25919	−	21.4947i	−0.0761139	−	0.724176i	−0.964322	−	0.264734i	$-0.914716\pi$
$881$	−2.25919	−	21.4947i	−0.0761139	−	0.724176i	0.888208	−	0.459442i	$-0.151951\pi$
$882$	1.16880	+	5.49878i	0.0393556	+	0.185153i
$883$	20.7134	+	28.5096i	0.697063	+	0.959425i	0.999979	+	0.00640780i	$0.00203968\pi$
$883$	20.7134	+	28.5096i	0.697063	+	0.959425i	−0.302916	+	0.953017i	$0.597960\pi$
$884$	6.03824	−	4.38704i	0.203088	−	0.147552i
$885$	2.63799	−	12.3212i	0.0886750	−	0.414171i
$886$	−1.01303	−	9.63837i	−0.0340335	−	0.323807i
$887$	−49.7188	−	5.22565i	−1.66939	−	0.175460i	−0.777867	−	0.628429i	$-0.783698\pi$
$887$	−49.7188	−	5.22565i	−1.66939	−	0.175460i	−0.891526	+	0.452969i	$0.850365\pi$
$888$	−1.45646	+	6.85211i	−0.0488757	+	0.229942i
$889$	−2.86707	+	1.27650i	−0.0961583	+	0.0428124i
$890$	17.8869	−	5.78259i	0.599571	−	0.193833i
$891$	−1.60133	+	4.92839i	−0.0536466	+	0.165107i
$892$	−18.6630	−	16.8042i	−0.624884	−	0.562648i
$893$	−2.19566	+	1.26766i	−0.0734748	+	0.0424207i
$894$	−2.25719	+	3.90957i	−0.0754917	+	0.130756i
$895$	−1.45173	+	13.6186i	−0.0485259	+	0.455219i
$896$	−1.07254	−	0.477526i	−0.0358311	−	0.0159530i
$897$	2.43174	−	3.34700i	0.0811933	−	0.111753i
$898$		−	3.63496i		−	0.121300i
$899$	6.38984	−	0.837790i	0.213113	−	0.0279419i
$900$	3.33465	+	3.72560i	0.111155	+	0.124187i
$901$	−20.9475	−	15.2192i	−0.697862	−	0.507026i
$902$	2.89222	−	6.49603i	0.0963003	−	0.216294i
$903$	−0.0666042	+	0.0216410i	−0.00221645	+	0.000720168i
$904$	7.05302	−	12.2162i	0.234580	−	0.406305i
$905$	5.44076	+	52.5121i	0.180857	+	1.74556i
$906$	−10.8091	+	12.0047i	−0.359109	+	0.398831i
$907$	31.5069	+	10.2372i	1.04617	+	0.339921i	0.781165	−	0.624325i	$-0.214626\pi$
$907$	31.5069	+	10.2372i	1.04617	+	0.339921i	0.265006	+	0.964247i	$0.414626\pi$
$908$	0.891278	−	0.802511i	0.0295781	−	0.0266322i
$909$	17.8266	−	7.93693i	0.591272	−	0.263251i
$910$	2.69125	−	3.69270i	0.0892142	−	0.122412i
$911$	5.42652	−	51.6299i	0.179789	−	1.71057i	−0.417607	−	0.908628i	$-0.637131\pi$
$911$	5.42652	−	51.6299i	0.179789	−	1.71057i	0.597395	−	0.801947i	$-0.296202\pi$
$912$	−2.61174	+	0.274505i	−0.0864833	+	0.00908976i
$913$	−1.74668	−	8.21747i	−0.0578066	−	0.271958i
$914$	−27.7960	+	20.1950i	−0.919410	+	0.667991i
$915$	1.92720	+	9.13314i	0.0637113	+	0.301932i
$916$	−19.3486	+	4.11268i	−0.639297	+	0.135887i
$917$	8.88084	−	0.933414i	0.293271	−	0.0308240i
$918$	−4.26464	−	0.448232i	−0.140754	−	0.0147939i
$919$	41.0530	+	8.72609i	1.35421	+	0.287847i	0.827151	−	0.561979i	$-0.189960\pi$
$919$	41.0530	+	8.72609i	1.35421	+	0.287847i	0.527063	+	0.849826i	$0.323293\pi$
$920$	−5.31493	−	0.00785770i	−0.175228	−	0.000259061i
$921$	0.528798	+	0.587289i	0.0174245	+	0.0193518i
$922$	−9.88785	−	3.21276i	−0.325639	−	0.105807i
$923$	12.2431	+	11.0237i	0.402986	+	0.362850i
$924$	−3.04195	−	5.26882i	−0.100073	−	0.173331i
$925$	7.18097	+	34.2819i	0.236109	+	1.12718i
$926$	2.81387	+	8.66019i	0.0924694	+	0.284592i
$927$	−1.26547	+	2.84230i	−0.0415637	+	0.0933535i
$928$	−0.680345	+	0.936414i	−0.0223334	+	0.0307393i
$929$	−26.9712			−0.884898			−0.442449	−	0.896794i	$-0.645890\pi$
$929$	−26.9712			−0.884898			−0.442449	+	0.896794i	$0.645890\pi$
$930$	11.7441	−	4.13228i	0.385105	−	0.135503i
$931$	−14.7631			−0.483840
$932$	−7.38391	+	10.1631i	−0.241868	+	0.332903i
$933$	5.77842	−	12.9785i	0.189177	−	0.424898i
$934$	6.37220	+	19.6116i	0.208505	+	0.641712i
$935$	−29.1464	−	40.2416i	−0.953191	−	1.31604i
$936$	−0.870271	−	1.50735i	−0.0284457	−	0.0492694i
$937$	28.5586	+	25.7143i	0.932969	+	0.840049i	0.987364	−	0.158470i	$-0.0506562\pi$
$937$	28.5586	+	25.7143i	0.932969	+	0.840049i	−0.0543944	+	0.998520i	$0.517323\pi$
$938$	−8.91605	−	2.89700i	−0.291119	−	0.0945904i
$939$	21.0996	+	23.4335i	0.688560	+	0.764723i
$940$	−0.00319154	+	2.15875i	−0.000104097	+	0.0704108i
$941$	−21.7355	−	4.62002i	−0.708557	−	0.150608i	−0.160483	−	0.987039i	$-0.551305\pi$
$941$	−21.7355	−	4.62002i	−0.708557	−	0.150608i	−0.548073	+	0.836430i	$0.684639\pi$
$942$	−23.0117	−	2.41863i	−0.749762	−	0.0788032i
$943$	3.24375	−	0.340931i	0.105631	−	0.0111023i
$944$	5.51193	−	1.17160i	0.179398	−	0.0381322i
$945$	−2.56868	+	0.542021i	−0.0835591	+	0.0176320i
$946$	−0.250073	+	0.181689i	−0.00813058	+	0.00590721i
$947$	6.06375	+	28.5277i	0.197045	+	0.927026i	0.959875	+	0.280427i	$0.0904759\pi$
$947$	6.06375	+	28.5277i	0.197045	+	0.927026i	−0.762830	+	0.646599i	$0.776191\pi$
$948$	14.7298	−	1.54816i	0.478401	−	0.0502820i
$949$	1.78197	−	16.9543i	0.0578452	−	0.550361i
$950$	−11.3908	+	6.53166i	−0.369567	+	0.211915i
$951$	4.75126	−	2.11540i	0.154070	−	0.0685964i
$952$	3.74133	−	3.36871i	0.121257	−	0.109180i
$953$	−39.7756	−	12.9239i	−1.28846	−	0.418646i	−0.416907	−	0.908949i	$-0.636886\pi$
$953$	−39.7756	−	12.9239i	−1.28846	−	0.418646i	−0.871552	+	0.490304i	$0.836886\pi$
$954$	−4.04033	+	4.48724i	−0.130810	+	0.145280i
$955$	4.06674	+	39.2505i	0.131597	+	1.27012i
$956$	0.963121	−	1.66817i	0.0311496	−	0.0539526i
$957$	−5.70447	+	1.85349i	−0.184399	+	0.0599149i
$958$	−10.7545	+	24.1549i	−0.347461	+	0.780409i
$959$	6.76622	+	4.91594i	0.218493	+	0.158744i
$960$	−0.912510	+	2.04140i	−0.0294511	+	0.0658860i
$961$	1.65526	−	30.9558i	0.0533954	−	0.998573i
$962$		−	12.1928i		−	0.393113i
$963$	−4.24007	+	5.83596i	−0.136634	+	0.188061i
$964$	−22.5582	−	10.0435i	−0.726550	−	0.323481i
$965$	46.2114	+	4.92610i	1.48760	+	0.158577i
$966$	1.39530	−	2.41673i	0.0448930	−	0.0777570i
$967$	−2.99254	+	1.72774i	−0.0962335	+	0.0555605i	−0.547344	−	0.836907i	$-0.684361\pi$
$967$	−2.99254	+	1.72774i	−0.0962335	+	0.0555605i	0.451111	+	0.892468i	$0.351028\pi$
$968$	−11.7813	−	10.6079i	−0.378664	−	0.340951i
$969$	3.47989	−	10.7100i	0.111790	−	0.344055i
$970$	−2.67632	−	8.27849i	−0.0859315	−	0.265806i
$971$	−9.32891	+	4.15350i	−0.299379	+	0.133292i	−0.550929	−	0.834552i	$-0.685726\pi$
$971$	−9.32891	+	4.15350i	−0.299379	+	0.133292i	0.251550	+	0.967844i	$0.419060\pi$
$972$	−0.207912	+	0.978148i	−0.00666877	+	0.0313741i
$973$	10.7038	+	1.12502i	0.343149	+	0.0360664i
$974$	0.946666	+	9.00693i	0.0303331	+	0.288601i
$975$	−7.02548	−	5.13612i	−0.224996	−	0.164487i
$976$	−3.37716	+	2.45365i	−0.108100	+	0.0785395i
$977$	10.1058	+	13.9095i	0.323314	+	0.445003i	0.939475	−	0.342617i	$-0.111313\pi$
$977$	10.1058	+	13.9095i	0.323314	+	0.445003i	−0.616162	+	0.787620i	$0.711313\pi$
$978$	3.94107	+	18.5413i	0.126021	+	0.592884i
$979$	4.55375	+	43.3260i	0.145538	+	1.38471i
$980$	−6.30125	+	10.8769i	−0.201286	+	0.347450i
$981$	2.71358	+	0.576789i	0.0866379	+	0.0184155i
$982$	10.4866	+	23.5533i	0.334641	+	0.751615i
$983$	−36.8370	+	33.1682i	−1.17492	+	1.05790i	−0.177646	+	0.984094i	$0.556848\pi$
$983$	−36.8370	+	33.1682i	−1.17492	+	1.05790i	−0.997273	+	0.0738074i	$0.976485\pi$
$984$	0.424035	−	1.30504i	0.0135177	−	0.0416033i
$985$	−0.0185634	−	0.0418605i	−0.000591478	−	0.00133378i
$986$	−2.48170	−	4.29842i	−0.0790333	−	0.136890i
$987$	−0.981597	−	0.566725i	−0.0312446	−	0.0180391i
$988$	4.34716	−	1.41248i	0.138302	−	0.0449369i
$989$	−0.129525	−	0.0576684i	−0.00411866	−	0.00183375i
$990$	−10.0435	+	5.77882i	−0.319203	+	0.183663i
$991$	16.4334			0.522024			0.261012	−	0.965335i	$-0.415944\pi$
$991$	16.4334			0.522024			0.261012	+	0.965335i	$0.415944\pi$
$992$	3.83045	+	4.04075i	0.121617	+	0.128294i
$993$		−	21.0120i		−	0.666795i
$994$	8.99030	+	6.53184i	0.285155	+	0.207177i
$995$	5.53682	+	6.16757i	0.175529	+	0.195525i
$996$	−0.500977	−	1.54185i	−0.0158741	−	0.0488553i
$997$	−24.1496	−	13.9428i	−0.764826	−	0.441573i	0.0661995	−	0.997806i	$-0.478913\pi$
$997$	−24.1496	−	13.9428i	−0.764826	−	0.441573i	−0.831026	+	0.556234i	$0.812246\pi$
$998$	33.0992	−	19.1099i	1.04774	−	0.604912i
$999$	−4.68739	+	5.20587i	−0.148302	+	0.164707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.a.19.13	yes	112
5.4	even	2	inner	930.2.bn.a.19.5	✓	112
31.18	even	15	inner	930.2.bn.a.49.5	yes	112
155.49	even	30	inner	930.2.bn.a.49.13	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.a.19.5	✓	112	5.4	even	2	inner
930.2.bn.a.19.13	yes	112	1.1	even	1	trivial
930.2.bn.a.49.5	yes	112	31.18	even	15	inner
930.2.bn.a.49.13	yes	112	155.49	even	30	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.81096 - 1.31165i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.872484 - 0.785588i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.81096 - 1.31165i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.872484 - 0.785588i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(0.00330584 - 2.23607i) q^{10} +(5.06877 + 1.07740i) q^{11} +(0.994522 + 0.104528i) q^{12} +(-1.73101 + 0.181936i) q^{13} +(-1.14839 + 0.244097i) q^{14} +(0.461671 + 2.18789i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.891553 - 4.19443i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(0.274505 - 2.61174i) q^{19} +(-1.80707 - 1.31700i) q^{20} +(1.07254 - 0.477526i) q^{21} +(3.85099 - 3.46744i) q^{22} +(2.26058 + 0.734507i) q^{23} +(0.669131 - 0.743145i) q^{24} +(1.55914 - 4.75069i) q^{25} +(-0.870271 + 1.50735i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-0.477526 + 1.07254i) q^{28} +(0.936414 + 0.680345i) q^{29} +(2.04140 + 0.912510i) q^{30} +(4.04075 - 3.83045i) q^{31} +1.00000i q^{32} +(-3.04591 + 4.19234i) q^{33} +(-3.91741 - 1.74414i) q^{34} +(-2.61045 - 0.278272i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-6.06668 + 3.50260i) q^{37} +(-1.95159 - 1.75722i) q^{38} +(0.537857 - 1.65535i) q^{39} +(-2.12765 + 0.687838i) q^{40} +(1.25357 - 0.558126i) q^{41} +(0.244097 - 1.14839i) q^{42} +(-0.0593233 - 0.00623513i) q^{43} +(-0.541668 - 5.15363i) q^{44} +(-2.18651 - 0.468138i) q^{45} +(1.92296 - 1.39711i) q^{46} +(-0.567462 - 0.781045i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(-0.587620 - 5.59083i) q^{49} +(-2.92695 - 4.05376i) q^{50} +(4.19443 + 0.891553i) q^{51} +(0.707942 + 1.59006i) q^{52} +(4.48724 - 4.04033i) q^{53} +(0.309017 - 0.951057i) q^{54} +(10.5925 - 4.69734i) q^{55} +(0.587022 + 1.01675i) q^{56} +(2.27429 + 1.31306i) q^{57} +(1.10082 - 0.357678i) q^{58} +(-5.14789 - 2.29199i) q^{59} +(1.93814 - 1.11517i) q^{60} +4.17440 q^{61} +(-0.723811 - 5.52052i) q^{62} +1.17404i q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.89614 + 2.59996i) q^{65} +(1.60133 + 4.92839i) q^{66} +(6.91533 + 3.99257i) q^{67} +(-3.71363 + 2.14407i) q^{68} +(-1.59047 + 1.76639i) q^{69} +(-1.75951 + 1.94833i) q^{70} +(-6.33350 - 7.03406i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-2.03639 + 9.58045i) q^{73} +(-0.732242 + 6.96682i) q^{74} +(3.70582 + 3.35663i) q^{75} +(-2.56874 + 0.546002i) q^{76} +(-3.57603 - 4.92198i) q^{77} +(-1.02306 - 1.40813i) q^{78} +(14.4873 - 3.07936i) q^{79} +(-0.694126 + 2.12560i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(0.285298 - 1.34222i) q^{82} +(-0.659399 - 1.48103i) q^{83} +(-0.785588 - 0.872484i) q^{84} +(-7.11620 - 6.42653i) q^{85} +(-0.0399137 + 0.0443286i) q^{86} +(-1.00240 + 0.578736i) q^{87} +(-4.48775 - 2.59101i) q^{88} +(2.59788 + 7.99544i) q^{89} +(-1.66393 + 1.49376i) q^{90} +(1.65320 + 1.20112i) q^{91} -2.37691i q^{92} +(1.85577 + 5.24939i) q^{93} -0.965425 q^{94} +(-2.92857 - 5.08980i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(3.70048 - 1.20236i) q^{97} +(-4.86847 - 2.81081i) q^{98} +(-2.59101 - 4.48775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9}+O(q^{10}) \) 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9	\( 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} + 8 q^{14} + 8 q^{15} - 28 q^{16} + 16 q^{19} + 2 q^{20} + 28 q^{21} + 14 q^{24} + 14 q^{25} + 12 q^{26} + 16 q^{29} - 4 q^{30} + 10 q^{34} - 38 q^{35} - 56 q^{36} + 16 q^{39} - 6 q^{40} + 20 q^{41} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 38 q^{49} + 8 q^{50} - 10 q^{51} - 28 q^{54} - 46 q^{55} + 12 q^{56} + 60 q^{59} - 8 q^{60} + 88 q^{61} + 28 q^{64} - 28 q^{65} + 6 q^{66} + 46 q^{69} + 26 q^{70} + 116 q^{71} - 34 q^{74} + 8 q^{75} + 24 q^{76} - 40 q^{79} - 12 q^{80} + 14 q^{81} - 8 q^{84} + 18 q^{85} - 38 q^{86} - 60 q^{89} + 4 q^{90} - 92 q^{91} + 132 q^{94} + 132 q^{95} - 14 q^{96} + 2 q^{99}+O(q^{100}) \) 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 + 8 * q^14 + 8 * q^15 - 28 * q^16 + 16 * q^19 + 2 * q^20 + 28 * q^21 + 14 * q^24 + 14 * q^25 + 12 * q^26 + 16 * q^29 - 4 * q^30 + 10 * q^34 - 38 * q^35 - 56 * q^36 + 16 * q^39 - 6 * q^40 + 20 * q^41 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 38 * q^49 + 8 * q^50 - 10 * q^51 - 28 * q^54 - 46 * q^55 + 12 * q^56 + 60 * q^59 - 8 * q^60 + 88 * q^61 + 28 * q^64 - 28 * q^65 + 6 * q^66 + 46 * q^69 + 26 * q^70 + 116 * q^71 - 34 * q^74 + 8 * q^75 + 24 * q^76 - 40 * q^79 - 12 * q^80 + 14 * q^81 - 8 * q^84 + 18 * q^85 - 38 * q^86 - 60 * q^89 + 4 * q^90 - 92 * q^91 + 132 * q^94 + 132 * q^95 - 14 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more