LMFDB - Embedded newform 115.2.l.a.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

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

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	115.17
Dual form			115.2.l.a.88.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79955 - 0.671199i) q^{2} +(0.756071 - 0.412846i) q^{3} +(1.27639 - 1.10600i) q^{4} +(-2.21107 - 0.333414i) q^{5} +(1.08349 - 1.25041i) q^{6} +(-0.0833334 - 0.111320i) q^{7} +(-0.286357 + 0.524424i) q^{8} +(-1.22072 + 1.89948i) q^{9} +O(q^{10})$	\(q+(1.79955 - 0.671199i) q^{2} +(0.756071 - 0.412846i) q^{3} +(1.27639 - 1.10600i) q^{4} +(-2.21107 - 0.333414i) q^{5} +(1.08349 - 1.25041i) q^{6} +(-0.0833334 - 0.111320i) q^{7} +(-0.286357 + 0.524424i) q^{8} +(-1.22072 + 1.89948i) q^{9} +(-4.20273 + 0.884071i) q^{10} +(1.28535 - 0.587001i) q^{11} +(0.508433 - 1.36316i) q^{12} +(2.01995 + 1.51212i) q^{13} +(-0.224681 - 0.144394i) q^{14} +(-1.80937 + 0.660746i) q^{15} +(-0.644034 + 4.47935i) q^{16} +(-0.207968 - 2.90778i) q^{17} +(-0.921825 + 4.23756i) q^{18} +(-3.45188 - 3.98368i) q^{19} +(-3.19094 + 2.01987i) q^{20} +(-0.108964 - 0.0497622i) q^{21} +(1.91907 - 1.91907i) q^{22} +(1.54448 - 4.54033i) q^{23} +0.514723i q^{24} +(4.77767 + 1.47441i) q^{25} +(4.64994 + 1.36535i) q^{26} +(-0.323123 + 4.51785i) q^{27} +(-0.229485 - 0.0499215i) q^{28} +(-4.48057 - 3.88244i) q^{29} +(-2.81257 + 2.40350i) q^{30} +(0.652073 - 0.191466i) q^{31} +(1.59354 + 7.32540i) q^{32} +(0.729477 - 0.974467i) q^{33} +(-2.32595 - 5.09311i) q^{34} +(0.147140 + 0.273922i) q^{35} +(0.542703 + 3.77458i) q^{36} +(-0.193425 + 0.0420771i) q^{37} +(-8.88569 - 4.85195i) q^{38} +(2.15150 + 0.309338i) q^{39} +(0.808006 - 1.06406i) q^{40} +(-1.97757 + 1.27090i) q^{41} +(-0.229487 - 0.0164132i) q^{42} +(4.95137 + 9.06775i) q^{43} +(0.991387 - 2.17083i) q^{44} +(3.33242 - 3.79288i) q^{45} +(-0.268088 - 9.20722i) q^{46} +(-0.690327 - 0.690327i) q^{47} +(1.36235 + 3.65259i) q^{48} +(1.96668 - 6.69790i) q^{49} +(9.58729 - 0.553495i) q^{50} +(-1.35770 - 2.11263i) q^{51} +(4.25063 - 0.304011i) q^{52} +(-6.23673 + 4.66876i) q^{53} +(2.45090 + 8.34700i) q^{54} +(-3.03772 + 0.869346i) q^{55} +(0.0822422 - 0.0118246i) q^{56} +(-4.25451 - 1.58685i) q^{57} +(-10.6689 - 3.97930i) q^{58} +(7.40914 - 1.06527i) q^{59} +(-1.57868 + 2.84453i) q^{60} +(-3.10490 - 10.5743i) q^{61} +(1.04493 - 0.782224i) q^{62} +(0.313178 - 0.0223989i) q^{63} +(2.89121 + 4.49882i) q^{64} +(-3.96209 - 4.01688i) q^{65} +(0.658671 - 2.24323i) q^{66} +(5.27969 + 14.1554i) q^{67} +(-3.48144 - 3.48144i) q^{68} +(-0.706719 - 4.07044i) q^{69} +(0.448643 + 0.394177i) q^{70} +(1.14559 - 2.50848i) q^{71} +(-0.646570 - 1.18411i) q^{72} +(13.0645 + 0.934391i) q^{73} +(-0.319837 + 0.205547i) q^{74} +(4.22096 - 0.857686i) q^{75} +(-8.81187 - 1.26695i) q^{76} +(-0.172458 - 0.0941692i) q^{77} +(4.07936 - 0.887410i) q^{78} +(1.12767 + 7.84310i) q^{79} +(2.91748 - 9.68944i) q^{80} +(-1.19304 - 2.61240i) q^{81} +(-2.70571 + 3.61440i) q^{82} +(-1.49191 - 6.85819i) q^{83} +(-0.194117 + 0.0569979i) q^{84} +(-0.509662 + 6.49864i) q^{85} +(14.9965 + 12.9946i) q^{86} +(-4.99047 - 1.08561i) q^{87} +(-0.0602326 + 0.842162i) q^{88} +(4.54179 + 1.33359i) q^{89} +(3.45109 - 9.06220i) q^{90} -0.350871i q^{91} +(-3.05023 - 7.50340i) q^{92} +(0.413967 - 0.413967i) q^{93} +(-1.70563 - 0.778934i) q^{94} +(6.30414 + 9.95911i) q^{95} +(4.22909 + 4.88063i) q^{96} +(-0.753650 + 3.46447i) q^{97} +(-0.956474 - 13.3733i) q^{98} +(-0.454061 + 3.15807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.79955	−	0.671199i	1.27248	−	0.474609i	0.379700	−	0.925110i	$-0.376027\pi$
$2$	1.79955	−	0.671199i	1.27248	−	0.474609i	0.892776	+	0.450500i	$0.148754\pi$
$3$	0.756071	−	0.412846i	0.436518	−	0.238357i	−0.245935	−	0.969286i	$-0.579095\pi$
$3$	0.756071	−	0.412846i	0.436518	−	0.238357i	0.682453	+	0.730930i	$0.260913\pi$
$4$	1.27639	−	1.10600i	0.638193	−	0.552998i
$5$	−2.21107	−	0.333414i	−0.988821	−	0.149107i
$5$	−2.21107	−	0.333414i	−0.988821	−	0.149107i
$6$	1.08349	−	1.25041i	0.442332	−	0.510478i
$7$	−0.0833334	−	0.111320i	−0.0314971	−	0.0420752i	0.784516	−	0.620108i	$-0.212911\pi$
$7$	−0.0833334	−	0.111320i	−0.0314971	−	0.0420752i	−0.816013	+	0.578033i	$0.803820\pi$
$8$	−0.286357	+	0.524424i	−0.101243	+	0.185412i
$9$	−1.22072	+	1.89948i	−0.406907	+	0.633160i
$10$	−4.20273	+	0.884071i	−1.32902	+	0.279568i
$11$	1.28535	−	0.587001i	0.387549	−	0.176987i	−0.212106	−	0.977247i	$-0.568032\pi$
$11$	1.28535	−	0.587001i	0.387549	−	0.176987i	0.599654	+	0.800259i	$0.295305\pi$
$12$	0.508433	−	1.36316i	0.146772	−	0.393511i
$13$	2.01995	+	1.51212i	0.560233	+	0.419386i	0.841510	−	0.540241i	$-0.181667\pi$
$13$	2.01995	+	1.51212i	0.560233	+	0.419386i	−0.281277	+	0.959627i	$0.590758\pi$
$14$	−0.224681	−	0.144394i	−0.0600485	−	0.0385908i
$15$	−1.80937	+	0.660746i	−0.467178	+	0.170604i
$16$	−0.644034	+	4.47935i	−0.161008	+	1.11984i
$17$	−0.207968	−	2.90778i	−0.0504397	−	0.705240i	−0.958263	−	0.285887i	$-0.907712\pi$
$17$	−0.207968	−	2.90778i	−0.0504397	−	0.705240i	0.907824	−	0.419352i	$-0.137743\pi$
$18$	−0.921825	+	4.23756i	−0.217276	+	0.998803i
$19$	−3.45188	−	3.98368i	−0.791916	−	0.913919i	0.205993	−	0.978553i	$-0.433957\pi$
$19$	−3.45188	−	3.98368i	−0.791916	−	0.913919i	−0.997909	+	0.0646340i	$0.979412\pi$
$20$	−3.19094	+	2.01987i	−0.713515	+	0.451656i
$21$	−0.108964	−	0.0497622i	−0.0237779	−	0.0108590i
$22$	1.91907	−	1.91907i	0.409147	−	0.409147i
$23$	1.54448	−	4.54033i	0.322046	−	0.946724i
$23$	1.54448	−	4.54033i	0.322046	−	0.946724i
$24$			0.514723i			0.105067i
$25$	4.77767	+	1.47441i	0.955534	+	0.294881i
$26$	4.64994	+	1.36535i	0.911928	+	0.267766i
$27$	−0.323123	+	4.51785i	−0.0621851	+	0.869462i
$28$	−0.229485	−	0.0499215i	−0.0433687	−	0.00943428i
$29$	−4.48057	−	3.88244i	−0.832021	−	0.720950i	0.130707	−	0.991421i	$-0.458275\pi$
$29$	−4.48057	−	3.88244i	−0.832021	−	0.720950i	−0.962728	+	0.270471i	$0.912821\pi$
$30$	−2.81257	+	2.40350i	−0.513503	+	0.438817i
$31$	0.652073	−	0.191466i	0.117116	−	0.0343883i	−0.222650	−	0.974899i	$-0.571471\pi$
$31$	0.652073	−	0.191466i	0.117116	−	0.0343883i	0.339765	+	0.940510i	$0.389652\pi$
$32$	1.59354	+	7.32540i	0.281701	+	1.29496i
$33$	0.729477	−	0.974467i	0.126986	−	0.169633i
$34$	−2.32595	−	5.09311i	−0.398897	−	0.873462i
$35$	0.147140	+	0.273922i	0.0248712	+	0.0463012i
$36$	0.542703	+	3.77458i	0.0904505	+	0.629097i
$37$	−0.193425	+	0.0420771i	−0.0317989	+	0.00691743i	−0.228437	−	0.973559i	$-0.573361\pi$
$37$	−0.193425	+	0.0420771i	−0.0317989	+	0.00691743i	0.196638	+	0.980476i	$0.436998\pi$
$38$	−8.88569	−	4.85195i	−1.44145	−	0.787091i
$39$	2.15150	+	0.309338i	0.344515	+	0.0495338i
$40$	0.808006	−	1.06406i	0.127757	−	0.168243i
$41$	−1.97757	+	1.27090i	−0.308844	+	0.198482i	−0.685876	−	0.727718i	$-0.740581\pi$
$41$	−1.97757	+	1.27090i	−0.308844	+	0.198482i	0.377032	+	0.926200i	$0.376945\pi$
$42$	−0.229487	−	0.0164132i	−0.0354106	−	0.00253262i
$43$	4.95137	+	9.06775i	0.755076	+	1.38282i	0.918161	+	0.396207i	$0.129674\pi$
$43$	4.95137	+	9.06775i	0.755076	+	1.38282i	−0.163085	+	0.986612i	$0.552144\pi$
$44$	0.991387	−	2.17083i	0.149457	−	0.327266i
$45$	3.33242	−	3.79288i	0.496767	−	0.565409i
$46$	−0.268088	−	9.20722i	−0.0395275	−	1.35753i
$47$	−0.690327	−	0.690327i	−0.100695	−	0.100695i	0.654965	−	0.755659i	$-0.272683\pi$
$47$	−0.690327	−	0.690327i	−0.100695	−	0.100695i	−0.755659	+	0.654965i	$0.772683\pi$
$48$	1.36235	+	3.65259i	0.196638	+	0.527206i
$49$	1.96668	−	6.69790i	0.280954	−	0.956842i
$50$	9.58729	−	0.553495i	1.35585	−	0.0782760i
$51$	−1.35770	−	2.11263i	−0.190116	−	0.295827i
$52$	4.25063	−	0.304011i	0.589456	−	0.0421587i
$53$	−6.23673	+	4.66876i	−0.856680	+	0.641303i	−0.934617	−	0.355655i	$-0.884258\pi$
$53$	−6.23673	+	4.66876i	−0.856680	+	0.641303i	0.0779368	+	0.996958i	$0.475167\pi$
$54$	2.45090	+	8.34700i	0.333525	+	1.13588i
$55$	−3.03772	+	0.869346i	−0.409606	+	0.117223i
$56$	0.0822422	−	0.0118246i	0.0109901	−	0.00158013i
$57$	−4.25451	−	1.58685i	−0.563524	−	0.210183i
$58$	−10.6689	−	3.97930i	−1.40090	−	0.522508i
$59$	7.40914	−	1.06527i	0.964588	−	0.138687i	0.358016	−	0.933715i	$-0.383453\pi$
$59$	7.40914	−	1.06527i	0.964588	−	0.138687i	0.606572	+	0.795029i	$0.292544\pi$
$60$	−1.57868	+	2.84453i	−0.203806	+	0.367227i
$61$	−3.10490	−	10.5743i	−0.397542	−	1.35390i	−0.878744	−	0.477294i	$-0.841618\pi$
$61$	−3.10490	−	10.5743i	−0.397542	−	1.35390i	0.481202	−	0.876610i	$-0.340200\pi$
$62$	1.04493	−	0.782224i	0.132706	−	0.0993425i
$63$	0.313178	−	0.0223989i	0.0394567	−	0.00282200i
$64$	2.89121	+	4.49882i	0.361402	+	0.562352i
$65$	−3.96209	−	4.01688i	−0.491437	−	0.498232i
$66$	0.658671	−	2.24323i	0.0810769	−	0.276122i
$67$	5.27969	+	14.1554i	0.645017	+	1.72936i	0.683348	+	0.730093i	$0.260523\pi$
$67$	5.27969	+	14.1554i	0.645017	+	1.72936i	−0.0383308	+	0.999265i	$0.512204\pi$
$68$	−3.48144	−	3.48144i	−0.422186	−	0.422186i
$69$	−0.706719	−	4.07044i	−0.0850790	−	0.490023i
$70$	0.448643	+	0.394177i	0.0536231	+	0.0471131i
$71$	1.14559	−	2.50848i	0.135956	−	0.297702i	−0.829392	−	0.558666i	$-0.811313\pi$
$71$	1.14559	−	2.50848i	0.135956	−	0.297702i	0.965348	+	0.260964i	$0.0840405\pi$
$72$	−0.646570	−	1.18411i	−0.0761990	−	0.139548i
$73$	13.0645	+	0.934391i	1.52908	+	0.109362i	0.810359	−	0.585934i	$-0.199272\pi$
$73$	13.0645	+	0.934391i	1.52908	+	0.109362i	0.718724	+	0.695296i	$0.244727\pi$
$74$	−0.319837	+	0.205547i	−0.0371803	+	0.0238943i
$75$	4.22096	−	0.857686i	0.487394	−	0.0990371i
$76$	−8.81187	−	1.26695i	−1.01079	−	0.145330i
$77$	−0.172458	−	0.0941692i	−0.0196534	−	0.0107316i
$78$	4.07936	−	0.887410i	0.461896	−	0.100479i
$79$	1.12767	+	7.84310i	0.126873	+	0.882418i	0.949484	+	0.313815i	$0.101607\pi$
$79$	1.12767	+	7.84310i	0.126873	+	0.882418i	−0.822612	+	0.568604i	$0.807484\pi$
$80$	2.91748	−	9.68944i	0.326185	−	1.08331i
$81$	−1.19304	−	2.61240i	−0.132560	−	0.290267i
$82$	−2.70571	+	3.61440i	−0.298795	+	0.399144i
$83$	−1.49191	−	6.85819i	−0.163758	−	0.752785i	−0.983625	−	0.180230i	$-0.942316\pi$
$83$	−1.49191	−	6.85819i	−0.163758	−	0.752785i	0.819866	−	0.572555i	$-0.194048\pi$
$84$	−0.194117	+	0.0569979i	−0.0211799	+	0.00621898i
$85$	−0.509662	+	6.49864i	−0.0552806	+	0.704877i
$86$	14.9965	+	12.9946i	1.61712	+	1.40124i
$87$	−4.99047	−	1.08561i	−0.535035	−	0.116390i
$88$	−0.0602326	+	0.842162i	−0.00642082	+	0.0897748i
$89$	4.54179	+	1.33359i	0.481429	+	0.141360i	0.513437	−	0.858127i	$-0.328372\pi$
$89$	4.54179	+	1.33359i	0.481429	+	0.141360i	−0.0320080	+	0.999488i	$0.510190\pi$
$90$	3.45109	−	9.06220i	0.363776	−	0.955240i
$91$		−	0.350871i		−	0.0367813i
$92$	−3.05023	−	7.50340i	−0.318008	−	0.782284i
$93$	0.413967	−	0.413967i	0.0429264	−	0.0429264i
$94$	−1.70563	−	0.778934i	−0.175922	−	0.0803409i
$95$	6.30414	+	9.95911i	0.646791	+	1.02178i
$96$	4.22909	+	4.88063i	0.431630	+	0.498127i
$97$	−0.753650	+	3.46447i	−0.0765216	+	0.351764i	−0.999448	−	0.0332116i	$-0.989426\pi$
$97$	−0.753650	+	3.46447i	−0.0765216	+	0.351764i	0.922927	+	0.384976i	$0.125790\pi$
$98$	−0.956474	−	13.3733i	−0.0966185	−	1.35090i
$99$	−0.454061	+	3.15807i	−0.0456349	+	0.317398i
$100$	7.72884	−	3.40217i	0.772884	−	0.340217i
$101$	−15.7930	−	10.1496i	−1.57147	−	1.00992i	−0.978886	−	0.204407i	$-0.934473\pi$
$101$	−15.7930	−	10.1496i	−1.57147	−	1.00992i	−0.592579	−	0.805512i	$-0.701890\pi$
$102$	−3.86125	−	2.89050i	−0.382321	−	0.286202i
$103$	−2.72354	+	7.30210i	−0.268358	+	0.719497i	0.730954	+	0.682427i	$0.239075\pi$
$103$	−2.72354	+	7.30210i	−0.268358	+	0.719497i	−0.999313	+	0.0370703i	$0.988197\pi$
$104$	−1.37142	+	0.626305i	−0.134479	+	0.0614143i
$105$	0.224336	+	0.146358i	0.0218929	+	0.0142831i
$106$	−8.08966	+	12.5878i	−0.785737	+	1.22263i
$107$	0.698977	−	1.28008i	0.0675727	−	0.123750i	−0.841709	−	0.539932i	$-0.818450\pi$
$107$	0.698977	−	1.28008i	0.0675727	−	0.123750i	0.909282	+	0.416181i	$0.136632\pi$
$108$	4.58430	+	6.12390i	0.441124	+	0.589273i
$109$	−11.6505	+	13.4454i	−1.11592	+	1.28784i	−0.162328	+	0.986737i	$0.551900\pi$
$109$	−11.6505	+	13.4454i	−1.11592	+	1.28784i	−0.953592	+	0.301103i	$0.902645\pi$
$110$	−4.88304	+	3.60335i	−0.465579	+	0.343566i
$111$	−0.128872	+	0.111668i	−0.0122320	+	0.0105991i
$112$	0.552313	−	0.301586i	0.0521887	−	0.0284972i
$113$	−0.705951	+	0.263306i	−0.0664103	+	0.0247698i	−0.382450	−	0.923976i	$-0.624920\pi$
$113$	−0.705951	+	0.263306i	−0.0664103	+	0.0247698i	0.316040	+	0.948746i	$0.397647\pi$
$114$	−8.72131			−0.816826
$115$	−4.92877	+	9.52404i	−0.459610	+	0.888121i
$116$	−10.0129			−0.929674
$117$	−5.33803	+	1.99098i	−0.493501	+	0.184066i
$118$	12.6181	−	6.89002i	1.16159	−	0.634278i
$119$	−0.306364	+	0.265466i	−0.0280844	+	0.0243352i
$120$	0.171616	−	1.13809i	0.0156663	−	0.103893i
$121$	−5.89591	+	6.80424i	−0.535991	+	0.618567i
$122$	−12.6849	−	16.9451i	−1.14844	−	1.53413i
$123$	−0.970492	+	1.77732i	−0.0875063	+	0.160256i
$124$	0.620537	−	0.965574i	0.0557258	−	0.0867111i
$125$	−10.0722	−	4.85296i	−0.900883	−	0.434062i
$126$	0.548546	−	0.250513i	0.0488684	−	0.0223174i
$127$	−2.38994	+	6.40768i	−0.212073	+	0.568589i	−0.998814	−	0.0486941i	$-0.984494\pi$
$127$	−2.38994	+	6.40768i	−0.212073	+	0.568589i	0.786741	+	0.617283i	$0.211767\pi$
$128$	−3.78037	−	2.82995i	−0.334141	−	0.250135i
$129$	7.48716	+	4.81171i	0.659208	+	0.423647i
$130$	−9.82612	−	4.56923i	−0.861808	−	0.400748i
$131$	−2.86363	+	19.9170i	−0.250197	+	1.74016i	0.346825	+	0.937930i	$0.387260\pi$
$131$	−2.86363	+	19.9170i	−0.250197	+	1.74016i	−0.597021	+	0.802225i	$0.703649\pi$
$132$	−0.146661	−	2.05059i	−0.0127652	−	0.178481i
$133$	−0.155808	+	0.716238i	−0.0135103	+	0.0621057i
$134$	19.0022	+	21.9297i	1.64154	+	1.89444i
$135$	2.22077	−	9.88156i	0.191133	−	0.850470i
$136$	1.58446	+	0.723599i	0.135866	+	0.0620481i
$137$	11.0904	−	11.0904i	0.947517	−	0.947517i	−0.0511731	−	0.998690i	$-0.516296\pi$
$137$	11.0904	−	11.0904i	0.947517	−	0.947517i	0.998690	+	0.0511731i	$0.0162960\pi$
$138$	−4.00385	−	6.85063i	−0.340831	−	0.583164i
$139$		−	9.62085i		−	0.816030i	−0.912975	−	0.408015i	$-0.866221\pi$
$139$		−	9.62085i		−	0.816030i	0.912975	−	0.408015i	$-0.133779\pi$
$140$	0.490764	+	0.186894i	0.0414771	+	0.0157954i
$141$	−0.806934	−	0.236937i	−0.0679561	−	0.0199537i
$142$	0.377852	−	5.28306i	0.0317086	−	0.443345i
$143$	3.48396	+	0.757890i	0.291344	+	0.0633779i
$144$	−7.72225	−	6.69137i	−0.643521	−	0.557614i
$145$	8.61240	+	10.0782i	0.715221	+	0.836951i
$146$	24.1374	−	7.08738i	1.99763	−	0.586556i
$147$	−1.27825	−	5.87602i	−0.105428	−	0.484646i
$148$	−0.200348	+	0.267634i	−0.0164685	+	0.0219994i
$149$	−2.51894	−	5.51571i	−0.206359	−	0.451864i	0.777947	−	0.628329i	$-0.216261\pi$
$149$	−2.51894	−	5.51571i	−0.206359	−	0.451864i	−0.984307	+	0.176465i	$0.943534\pi$
$150$	7.02016	−	4.37655i	0.573194	−	0.357344i
$151$	1.65211	+	11.4906i	0.134446	+	0.935096i	0.939660	+	0.342110i	$0.111142\pi$
$151$	1.65211	+	11.4906i	0.134446	+	0.935096i	−0.805213	+	0.592985i	$0.797949\pi$
$152$	3.07761	−	0.669493i	0.249627	−	0.0543030i
$153$	5.77714	+	3.15456i	0.467054	+	0.255031i
$154$	−0.373554	−	0.0537089i	−0.0301018	−	0.00432799i
$155$	−1.50562	+	0.205934i	−0.120934	+	0.0165410i
$156$	3.08827	−	1.98471i	0.247259	−	0.158904i
$157$	−6.90113	−	0.493579i	−0.550770	−	0.0393919i	−0.206819	−	0.978379i	$-0.566311\pi$
$157$	−6.90113	−	0.493579i	−0.550770	−	0.0393919i	−0.343951	+	0.938987i	$0.611766\pi$
$158$	7.29358	+	13.3572i	0.580246	+	1.06264i
$159$	−2.78793	+	6.10471i	−0.221097	+	0.484135i
$160$	−1.08104	−	16.7283i	−0.0854640	−	1.32249i
$161$	−0.634138	+	0.206429i	−0.0499771	+	0.0162689i
$162$	−3.90039	−	3.90039i	−0.306443	−	0.306443i
$163$	−5.31244	−	14.2432i	−0.416102	−	1.11561i	−0.960864	−	0.277022i	$-0.910653\pi$
$163$	−5.31244	−	14.2432i	−0.416102	−	1.11561i	0.544761	−	0.838591i	$-0.316620\pi$
$164$	−1.11852	+	3.80934i	−0.0873421	+	0.297460i
$165$	−1.93783	+	1.91140i	−0.150860	+	0.148802i
$166$	−7.28798	−	11.3403i	−0.565657	−	0.880180i
$167$	7.62739	−	0.545522i	0.590225	−	0.0422137i	0.226967	−	0.973902i	$-0.427119\pi$
$167$	7.62739	−	0.545522i	0.590225	−	0.0422137i	0.363258	+	0.931689i	$0.381664\pi$
$168$	0.0572991	−	0.0428936i	0.00442072	−	0.00330931i
$169$	−1.86882	−	6.36461i	−0.143755	−	0.489585i
$170$	3.44472	+	12.0367i	0.264198	+	0.923176i
$171$	11.7807	−	1.69381i	0.900893	−	0.129529i
$172$	16.3487	+	6.09777i	1.24658	+	0.464950i
$173$	−0.505289	−	0.188463i	−0.0384164	−	0.0143286i	0.330183	−	0.943917i	$-0.392890\pi$
$173$	−0.505289	−	0.188463i	−0.0384164	−	0.0143286i	−0.368599	+	0.929589i	$0.620162\pi$
$174$	−9.70929	+	1.39598i	−0.736059	+	0.105829i
$175$	−0.234008	−	0.654719i	−0.0176893	−	0.0494921i
$176$	1.80157	+	6.13560i	0.135799	+	0.462488i
$177$	5.16204	−	3.86425i	0.388003	−	0.290455i
$178$	9.06830	−	0.648578i	0.679698	−	0.0486130i
$179$	5.46459	+	8.50307i	0.408442	+	0.635549i	0.983148	−	0.182811i	$-0.0585198\pi$
$179$	5.46459	+	8.50307i	0.408442	+	0.635549i	−0.574706	+	0.818360i	$0.694883\pi$
$180$	0.0585449	−	8.52681i	0.00436368	−	0.635551i
$181$	5.76861	−	19.6461i	0.428778	−	1.46028i	−0.408123	−	0.912927i	$-0.633816\pi$
$181$	5.76861	−	19.6461i	0.428778	−	1.46028i	0.836900	−	0.547355i	$-0.184365\pi$
$182$	−0.235504	−	0.631412i	−0.0174568	−	0.0468034i
$183$	−6.71309	−	6.71309i	−0.496246	−	0.496246i
$184$	1.93878	+	2.11012i	0.142929	+	0.155560i
$185$	0.441706	−	0.0285447i	0.0324749	−	0.00209865i
$186$	0.467102	−	1.02281i	0.0342496	−	0.0749961i
$187$	−1.97418	−	3.61544i	−0.144366	−	0.264387i
$188$	−1.64462	−	0.117626i	−0.119946	−	0.00857873i
$189$	0.529856	−	0.340518i	0.0385414	−	0.0247690i
$190$	18.0292	+	13.6906i	1.30797	+	0.993222i
$191$	−17.0448	−	2.45067i	−1.23332	−	0.177325i	−0.505338	−	0.862922i	$-0.668632\pi$
$191$	−17.0448	−	2.45067i	−1.23332	−	0.177325i	−0.727981	+	0.685597i	$0.759541\pi$
$192$	4.04328	+	2.20780i	0.291799	+	0.159334i
$193$	24.6562	−	5.36362i	1.77479	−	0.386082i	0.798405	−	0.602120i	$-0.205677\pi$
$193$	24.6562	−	5.36362i	1.77479	−	0.386082i	0.976385	+	0.216038i	$0.0693136\pi$
$194$	0.969117	+	6.74036i	0.0695785	+	0.483929i
$195$	−4.65397	−	1.40131i	−0.333278	−	0.100350i
$196$	−4.89760	−	10.7242i	−0.349828	−	0.766017i
$197$	11.5005	−	15.3629i	0.819377	−	1.09456i	−0.174564	−	0.984646i	$-0.555852\pi$
$197$	11.5005	−	15.3629i	0.819377	−	1.09456i	0.993941	−	0.109914i	$-0.0350575\pi$
$198$	1.30258	+	5.98788i	0.0925705	+	0.425540i
$199$	16.4112	−	4.81875i	1.16336	−	0.341592i	0.357620	−	0.933867i	$-0.383588\pi$
$199$	16.4112	−	4.81875i	1.16336	−	0.341592i	0.805736	+	0.592275i	$0.201770\pi$
$200$	−2.14133	+	2.08332i	−0.151415	+	0.147313i
$201$	9.83582	+	8.52279i	0.693765	+	0.601151i
$202$	−35.2328	−	7.66442i	−2.47897	−	0.539267i
$203$	−0.0588132	+	0.822316i	−0.00412788	+	0.0577152i
$204$	−4.06951	−	1.19492i	−0.284922	−	0.0836608i
$205$	4.79628	−	2.15071i	0.334987	−	0.150212i
$206$			14.9685i			1.04291i
$207$	6.73888	+	8.47618i	0.468385	+	0.589136i
$208$	−8.07422	+	8.07422i	−0.559846	+	0.559846i
$209$	−6.77531	−	3.09418i	−0.468658	−	0.214029i
$210$	0.501940	+	0.112805i	0.0346371	+	0.00778429i
$211$	−3.71685	−	4.28948i	−0.255879	−	0.295300i	0.613247	−	0.789891i	$-0.289863\pi$
$211$	−3.71685	−	4.28948i	−0.255879	−	0.295300i	−0.869125	+	0.494592i	$0.835318\pi$
$212$	−2.79685	+	12.8569i	−0.192089	+	0.883017i
$213$	−0.169473	−	2.36954i	−0.0116121	−	0.162358i
$214$	0.398658	−	2.77273i	0.0272517	−	0.189540i
$215$	−7.92450	−	21.7003i	−0.540447	−	1.47995i
$216$	−2.27674	−	1.46317i	−0.154913	−	0.0995564i
$217$	−0.0756535	−	0.0566335i	−0.00513569	−	0.00384453i
$218$	−11.9412	+	32.0156i	−0.808761	+	2.16837i
$219$	10.2634	−	4.68715i	0.693539	−	0.316728i
$220$	−2.91581	+	4.46933i	−0.196584	+	0.301322i
$221$	3.97681	−	6.18804i	0.267509	−	0.416253i
$222$	−0.156960	+	0.287451i	−0.0105345	+	0.0192925i
$223$	−6.62942	−	8.85586i	−0.443938	−	0.593032i	0.521633	−	0.853170i	$-0.325323\pi$
$223$	−6.62942	−	8.85586i	−0.443938	−	0.593032i	−0.965572	+	0.260138i	$0.916232\pi$
$224$	0.682671	−	0.787844i	0.0456129	−	0.0526400i
$225$	−8.63281	+	7.27525i	−0.575520	+	0.485017i
$226$	−1.09367	+	0.947667i	−0.0727496	+	0.0630379i
$227$	−18.1249	+	9.89693i	−1.20299	+	0.656882i	−0.950502	−	0.310718i	$-0.899430\pi$
$227$	−18.1249	+	9.89693i	−1.20299	+	0.656882i	−0.252487	+	0.967600i	$0.581249\pi$
$228$	−7.18545	+	2.68003i	−0.475868	+	0.177490i
$229$	−7.35164			−0.485810			−0.242905	−	0.970050i	$-0.578100\pi$
$229$	−7.35164			−0.485810			−0.242905	+	0.970050i	$0.578100\pi$
$230$	−2.47706	+	20.4472i	−0.163332	+	1.34825i
$231$	−0.169268			−0.0111370
$232$	3.31909	−	1.23796i	0.217909	−	0.0812757i
$233$	−16.8869	+	9.22095i	−1.10630	+	0.604084i	−0.925238	−	0.379388i	$-0.876135\pi$
$233$	−16.8869	+	9.22095i	−1.10630	+	0.604084i	−0.181060	+	0.983472i	$0.557953\pi$
$234$	−8.26973	+	7.16576i	−0.540609	+	0.468440i
$235$	1.29620	+	1.75653i	0.0845546	+	0.114583i
$236$	8.27874	−	9.55417i	0.538900	−	0.621924i
$237$	4.09059	+	5.46439i	0.265712	+	0.354950i
$238$	−0.373138	+	0.683352i	−0.0241870	+	0.0442951i
$239$	14.7026	−	22.8777i	0.951034	−	1.47984i	0.0752334	−	0.997166i	$-0.476030\pi$
$239$	14.7026	−	22.8777i	0.951034	−	1.47984i	0.875801	−	0.482672i	$-0.160334\pi$
$240$	−1.79442	−	8.53037i	−0.115829	−	0.550633i
$241$	−18.8594	+	8.61278i	−1.21484	+	0.554798i	−0.916643	−	0.399707i	$-0.869112\pi$
$241$	−18.8594	+	8.61278i	−1.21484	+	0.554798i	−0.298195	+	0.954505i	$0.596385\pi$
$242$	−6.04300	+	16.2019i	−0.388459	+	1.04150i
$243$	−12.8584	−	9.62571i	−0.824870	−	0.617490i
$244$	−15.6582	−	10.0629i	−1.00241	−	0.644212i
$245$	−6.58164	+	14.1538i	−0.420486	+	0.904254i
$246$	−0.553515	+	3.84978i	−0.0352908	+	0.245453i
$247$	−0.948838	−	13.2665i	−0.0603731	−	0.844126i
$248$	−0.0863164	+	0.396790i	−0.00548110	+	0.0251962i
$249$	−3.95936	−	4.56935i	−0.250915	−	0.289571i
$250$	−21.3827	−	1.97272i	−1.35236	−	0.124766i
$251$	7.73322	+	3.53164i	0.488117	+	0.222915i	0.644242	−	0.764822i	$-0.277173\pi$
$251$	7.73322	+	3.53164i	0.488117	+	0.222915i	−0.156125	+	0.987737i	$0.549900\pi$
$252$	0.374963	−	0.374963i	0.0236204	−	0.0236204i
$253$	−0.679976	−	6.74254i	−0.0427497	−	0.423900i
$254$			13.1351i			0.824168i
$255$	2.29760	+	5.12384i	0.143881	+	0.320868i
$256$	−18.9647	−	5.56854i	−1.18529	−	0.348034i
$257$	−1.42951	+	19.9872i	−0.0891705	+	1.24677i	0.734070	+	0.679074i	$0.237618\pi$
$257$	−1.42951	+	19.9872i	−0.0891705	+	1.24677i	−0.823240	+	0.567693i	$0.807836\pi$
$258$	16.7032	+	3.63355i	1.03989	+	0.226215i
$259$	0.0208028	+	0.0180258i	0.00129262	+	0.00112007i
$260$	−9.49981	−	0.745031i	−0.589153	−	0.0462049i
$261$	12.8441	−	3.77138i	0.795032	−	0.233443i
$262$	8.21500	+	37.7638i	0.507524	+	2.33305i
$263$	−5.16773	+	6.90327i	−0.318656	+	0.425674i	−0.931057	−	0.364873i	$-0.881113\pi$
$263$	−5.16773	+	6.90327i	−0.318656	+	0.425674i	0.612402	+	0.790547i	$0.290203\pi$
$264$	0.302143	+	0.661601i	0.0185956	+	0.0407187i
$265$	15.3465	−	8.24354i	0.942726	−	0.506396i
$266$	0.200353	+	1.39349i	0.0122844	+	0.0854402i
$267$	3.98448	−	0.866771i	0.243846	−	0.0530455i
$268$	22.3947	+	12.2285i	1.36798	+	0.746972i
$269$	−13.2496	−	1.90500i	−0.807839	−	0.116150i	−0.273993	−	0.961732i	$-0.588345\pi$
$269$	−13.2496	−	1.90500i	−0.807839	−	0.116150i	−0.533846	+	0.845582i	$0.679254\pi$
$270$	−2.63611	−	19.2730i	−0.160428	−	1.17292i
$271$	14.5567	−	9.35499i	0.884254	−	0.568275i	−0.0178277	−	0.999841i	$-0.505675\pi$
$271$	14.5567	−	9.35499i	0.884254	−	0.568275i	0.902082	+	0.431566i	$0.142039\pi$
$272$	13.1589	+	0.941143i	0.797876	+	0.0570652i
$273$	−0.144856	−	0.265284i	−0.00876707	−	0.0160557i
$274$	12.5139	−	27.4016i	0.755993	−	1.65539i
$275$	7.00647	−	0.909366i	0.422506	−	0.0548368i
$276$	−5.40393	−	4.41383i	−0.325279	−	0.265681i
$277$	7.94440	+	7.94440i	0.477333	+	0.477333i	0.904278	−	0.426945i	$-0.140410\pi$
$277$	7.94440	+	7.94440i	0.477333	+	0.477333i	−0.426945	+	0.904278i	$0.640410\pi$
$278$	−6.45750	−	17.3132i	−0.387295	−	1.03838i
$279$	−0.432314	+	1.47233i	−0.0258820	+	0.0881458i
$280$	−0.185786	−	0.00127560i	−0.0111028	−	7.62318e-5i
$281$	−1.11664	−	1.73753i	−0.0666134	−	0.103652i	0.806349	−	0.591440i	$-0.201440\pi$
$281$	−1.11664	−	1.73753i	−0.0666134	−	0.103652i	−0.872962	+	0.487788i	$0.837804\pi$
$282$	−1.61115	+	0.115232i	−0.0959428	+	0.00686196i
$283$	13.5310	−	10.1292i	0.804333	−	0.602116i	−0.116001	−	0.993249i	$-0.537008\pi$
$283$	13.5310	−	10.1292i	0.804333	−	0.602116i	0.920334	+	0.391133i	$0.127917\pi$
$284$	−1.31216	−	4.46880i	−0.0778623	−	0.265175i
$285$	8.87795	+	4.92715i	0.525884	+	0.291859i
$286$	6.77827	−	0.974569i	0.400808	−	0.0576274i
$287$	0.306275	+	0.114235i	0.0180788	+	0.00674306i
$288$	−15.8597	−	5.91537i	−0.934542	−	0.348566i
$289$	8.41504	−	1.20990i	0.495003	−	0.0711706i
$290$	22.2630	+	12.3557i	1.30733	+	0.725551i
$291$	0.860481	+	2.93053i	0.0504423	+	0.171791i
$292$	17.7088	−	13.2566i	1.03633	−	0.775785i
$293$	3.76690	−	0.269414i	0.220065	−	0.0157393i	0.0391285	−	0.999234i	$-0.487542\pi$
$293$	3.76690	−	0.269414i	0.220065	−	0.0157393i	0.180936	+	0.983495i	$0.442087\pi$
$294$	−6.24426	−	9.71625i	−0.364172	−	0.566663i
$295$	−16.7373	−	0.114918i	−0.974484	−	0.00669079i
$296$	0.0333225	−	0.113486i	0.00193683	−	0.00659624i
$297$	2.23666	+	5.99671i	0.129784	+	0.347965i
$298$	−8.23510	−	8.23510i	−0.477047	−	0.477047i
$299$	9.98528	−	6.83581i	0.577463	−	0.395325i
$300$	4.43898	−	5.76310i	0.256284	−	0.332733i
$301$	0.596811	−	1.30683i	0.0343996	−	0.0753247i
$302$	10.6856	+	19.5691i	0.614885	+	1.12608i
$303$	−16.1308	−	1.15370i	−0.926693	−	0.0662784i
$304$	20.0674	−	12.8966i	1.15095	−	0.739669i
$305$	3.33953	+	24.4158i	0.191221	+	1.39804i
$306$	12.5136	+	1.79918i	0.715355	+	0.102853i
$307$	−13.5349	−	7.39059i	−0.772475	−	0.421803i	0.0441112	−	0.999027i	$-0.485954\pi$
$307$	−13.5349	−	7.39059i	−0.772475	−	0.421803i	−0.816586	+	0.577223i	$0.804136\pi$
$308$	−0.324274	+	0.0705414i	−0.0184772	+	0.00401947i
$309$	0.955450	+	6.64530i	0.0543537	+	0.378038i
$310$	−2.57122	+	1.38116i	−0.146035	+	0.0784445i
$311$	8.73484	+	19.1266i	0.495307	+	1.08457i	0.977966	+	0.208764i	$0.0669439\pi$
$311$	8.73484	+	19.1266i	0.495307	+	1.08457i	−0.482659	+	0.875809i	$0.660329\pi$
$312$	−0.778321	+	1.03971i	−0.0440637	+	0.0588622i
$313$	−3.77027	−	17.3316i	−0.213108	−	0.979642i	−0.952067	−	0.305891i	$-0.901046\pi$
$313$	−3.77027	−	17.3316i	−0.213108	−	0.979642i	0.738958	−	0.673751i	$-0.235318\pi$
$314$	−12.7502	+	3.74381i	−0.719538	+	0.211275i
$315$	−0.699926	−	0.0548923i	−0.0394364	−	0.00309283i
$316$	10.1138	+	8.76364i	0.568944	+	0.492993i
$317$	10.5528	+	2.29561i	0.592702	+	0.128934i	0.498905	−	0.866657i	$-0.333736\pi$
$317$	10.5528	+	2.29561i	0.592702	+	0.128934i	0.0937975	+	0.995591i	$0.470099\pi$
$318$	−0.919552	+	12.8570i	−0.0515659	+	0.720986i
$319$	−8.03811	−	2.36020i	−0.450048	−	0.132146i
$320$	−4.89271	−	10.9112i	−0.273511	−	0.609953i
$321$		−	1.25640i		−	0.0701255i
$322$	−1.00261	+	0.797112i	−0.0558733	+	0.0444213i
$323$	−10.8658	+	10.8658i	−0.604588	+	0.604588i
$324$	−4.41209	−	2.01493i	−0.245116	−	0.111941i
$325$	7.42118	+	10.2026i	0.411653	+	0.565939i
$326$	−19.1200	−	22.0657i	−1.05896	−	1.22211i
$327$	−3.25774	+	14.9756i	−0.180153	+	0.828151i
$328$	−0.100203	−	1.40102i	−0.00553276	−	0.0773582i
$329$	−0.0193202	+	0.134375i	−0.00106516	+	0.00740832i
$330$	−2.20429	+	4.74033i	−0.121342	+	0.260946i
$331$	−15.3802	−	9.88427i	−0.845374	−	0.543289i	0.0447548	−	0.998998i	$-0.485749\pi$
$331$	−15.3802	−	9.88427i	−0.845374	−	0.543289i	−0.890129	+	0.455709i	$0.849386\pi$
$332$	−9.48938	−	7.10366i	−0.520797	−	0.389864i
$333$	0.156194	−	0.418772i	0.00855937	−	0.0229486i
$334$	13.3597	−	6.10119i	0.731013	−	0.333842i
$335$	−6.95416	−	33.0589i	−0.379946	−	1.80620i
$336$	0.293079	−	0.456040i	0.0159888	−	0.0248790i
$337$	7.75569	−	14.2035i	0.422480	−	0.773714i	−0.576581	−	0.817040i	$-0.695614\pi$
$337$	7.75569	−	14.2035i	0.422480	−	0.773714i	0.999061	+	0.0433261i	$0.0137954\pi$
$338$	−7.63496	−	10.1991i	−0.415287	−	0.554758i
$339$	−0.425044	+	0.490527i	−0.0230852	+	0.0266418i
$340$	6.53694	+	8.85846i	0.354515	+	0.480418i
$341$	0.725753	−	0.628869i	0.0393017	−	0.0340551i
$342$	20.0631	−	10.9553i	1.08489	−	0.592395i
$343$	−1.82152	+	0.679394i	−0.0983531	+	0.0366838i
$344$	−6.17320			−0.332837
$345$	0.205464	+	9.23566i	0.0110618	+	0.497231i
$346$	−1.03579			−0.0556845
$347$	20.5676	−	7.67132i	1.10413	−	0.411818i	0.269704	−	0.962943i	$-0.413074\pi$
$347$	20.5676	−	7.67132i	1.10413	−	0.411818i	0.834423	+	0.551125i	$0.185801\pi$
$348$	−7.57045	+	4.13378i	−0.405819	+	0.221594i
$349$	−23.4259	+	20.2987i	−1.25396	+	1.08656i	−0.261348	+	0.965245i	$0.584167\pi$
$349$	−23.4259	+	20.2987i	−1.25396	+	1.08656i	−0.992614	+	0.121319i	$0.961288\pi$
$350$	−0.860557	−	1.02114i	−0.0459987	−	0.0545820i
$351$	−7.48421	+	8.63724i	−0.399478	+	0.461022i
$352$	6.34828	+	8.48031i	0.338364	+	0.452002i
$353$	−2.09891	+	3.84386i	−0.111714	+	0.204588i	−0.927554	−	0.373689i	$-0.878093\pi$
$353$	−2.09891	+	3.84386i	−0.111714	+	0.204588i	0.815841	+	0.578277i	$0.196275\pi$
$354$	6.69568	−	10.4187i	0.355872	−	0.553747i
$355$	−3.36933	+	5.16448i	−0.178826	+	0.274102i
$356$	7.27202	−	3.32102i	0.385417	−	0.176014i
$357$	−0.122036	+	0.327192i	−0.00645885	+	0.0173169i
$358$	15.5411	+	11.6339i	0.821371	+	0.614871i
$359$	3.20066	+	2.05694i	0.168924	+	0.108561i	0.622371	−	0.782722i	$-0.286169\pi$
$359$	3.20066	+	2.05694i	0.168924	+	0.108561i	−0.453447	+	0.891283i	$0.649806\pi$
$360$	1.03482	+	2.83372i	0.0545396	+	0.149350i
$361$	−1.25026	+	8.69578i	−0.0658034	+	0.457673i
$362$	−2.80551	−	39.2261i	−0.147454	−	2.06168i
$363$	−1.64862	+	7.57858i	−0.0865301	+	0.397772i
$364$	−0.388062	−	0.447848i	−0.0203400	−	0.0234736i
$365$	−28.5750	−	6.42189i	−1.49568	−	0.336137i
$366$	−16.5864	−	7.57475i	−0.866984	−	0.395938i
$367$	6.32386	−	6.32386i	0.330103	−	0.330103i	−0.522523	−	0.852625i	$-0.675009\pi$
$367$	6.32386	−	6.32386i	0.330103	−	0.330103i	0.852625	+	0.522523i	$0.175009\pi$
$368$	19.3430	+	9.84240i	1.00833	+	0.513070i
$369$		−	5.30777i		−	0.276311i
$370$	0.775715	−	0.347840i	0.0403275	−	0.0180834i
$371$	1.03946	+	0.305212i	0.0539658	+	0.0158458i
$372$	0.0705364	−	0.986228i	0.00365714	−	0.0511335i
$373$	−18.2148	−	3.96240i	−0.943129	−	0.205165i	−0.285390	−	0.958411i	$-0.592123\pi$
$373$	−18.2148	−	3.96240i	−0.943129	−	0.205165i	−0.657739	+	0.753246i	$0.728487\pi$
$374$	−5.97933	−	5.18112i	−0.309184	−	0.267909i
$375$	−9.61880	+	0.489077i	−0.496713	+	0.0252558i
$376$	0.559704	−	0.164344i	0.0288645	−	0.00847539i
$377$	−3.17984	−	14.6175i	−0.163770	−	0.752838i
$378$	0.724950	−	0.968419i	0.0372874	−	0.0498101i
$379$	11.8638	+	25.9780i	0.609400	+	1.33440i	0.922984	+	0.384839i	$0.125743\pi$
$379$	11.8638	+	25.9780i	0.609400	+	1.33440i	−0.313583	+	0.949561i	$0.601530\pi$
$380$	19.0612	+	5.73933i	0.977821	+	0.294421i
$381$	0.838419	+	5.83133i	0.0429535	+	0.298748i
$382$	−32.3179	+	7.03034i	−1.65353	+	0.359703i
$383$	24.7272	+	13.5021i	1.26350	+	0.689923i	0.964438	−	0.264310i	$-0.0851442\pi$
$383$	24.7272	+	13.5021i	1.26350	+	0.689923i	0.299063	+	0.954233i	$0.403326\pi$
$384$	−4.02656	−	0.578932i	−0.205480	−	0.0295435i
$385$	0.349920	+	0.265715i	0.0178336	+	0.0135421i
$386$	40.7701	−	26.2013i	2.07514	−	1.33361i
$387$	−23.2682	−	1.66418i	−1.18279	−	0.0845949i
$388$	2.86974	+	5.25554i	0.145689	+	0.266810i
$389$	−5.00903	+	10.9683i	−0.253968	+	0.556113i	−0.993076	−	0.117475i	$-0.962520\pi$
$389$	−5.00903	+	10.9683i	−0.253968	+	0.556113i	0.739108	+	0.673587i	$0.235247\pi$
$390$	−9.31563	+	0.602010i	−0.471715	+	0.0304840i
$391$	−13.5235	−	3.54676i	−0.683911	−	0.179367i
$392$	2.94936	+	2.94936i	0.148965	+	0.148965i
$393$	6.05754	+	16.2409i	0.305562	+	0.819244i
$394$	10.3842	−	35.3654i	0.523150	−	1.78169i
$395$	0.121649	−	17.7176i	0.00612082	−	0.891471i
$396$	2.91325	+	4.53310i	0.146396	+	0.227797i
$397$	−1.19393	+	0.0853917i	−0.0599217	+	0.00428569i	−0.101268	−	0.994859i	$-0.532290\pi$
$397$	−1.19393	+	0.0853917i	−0.0599217	+	0.00428569i	0.0413461	+	0.999145i	$0.486835\pi$
$398$	26.2984	−	19.6868i	1.31822	−	0.986808i
$399$	0.177894	+	0.605851i	0.00890584	+	0.0303305i
$400$	−9.68136	+	20.4513i	−0.484068	+	1.02257i
$401$	17.2836	−	2.48500i	0.863100	−	0.124095i	0.303473	−	0.952840i	$-0.401854\pi$
$401$	17.2836	−	2.48500i	0.863100	−	0.124095i	0.559627	+	0.828745i	$0.310945\pi$
$402$	23.4206	+	8.73542i	1.16811	+	0.435683i
$403$	1.60667	+	0.599258i	0.0800341	+	0.0298512i
$404$	−31.3834	+	4.51225i	−1.56138	+	0.224493i
$405$	1.76689	+	6.17398i	0.0877976	+	0.306788i
$406$	0.446100	+	1.51928i	0.0221396	+	0.0754004i
$407$	−0.223921	+	0.167625i	−0.0110993	+	0.00830885i
$408$	1.49670	−	0.107046i	0.0740977	−	0.00529957i
$409$	9.96356	+	15.5036i	0.492667	+	0.766604i	0.995190	−	0.0979592i	$-0.0312315\pi$
$409$	9.96356	+	15.5036i	0.492667	+	0.766604i	−0.502524	+	0.864563i	$0.667595\pi$
$410$	7.18760	−	7.08958i	0.354970	−	0.350129i
$411$	3.80650	−	12.9637i	0.187761	−	0.639454i
$412$	4.59979	+	12.3325i	0.226615	+	0.607580i
$413$	−0.736016	−	0.736016i	−0.0362170	−	0.0362170i
$414$	17.8162	+	10.7302i	0.875618	+	0.527362i
$415$	1.01210	+	15.6614i	0.0496819	+	0.768787i
$416$	−7.85797	+	17.2066i	−0.385269	+	0.843621i
$417$	−3.97193	−	7.27404i	−0.194506	−	0.356211i
$418$	−14.2693	−	1.02056i	−0.697936	−	0.0499174i
$419$	−2.58465	+	1.66106i	−0.126269	+	0.0811479i	−0.602250	−	0.798307i	$-0.705729\pi$
$419$	−2.58465	+	1.66106i	−0.126269	+	0.0811479i	0.475982	+	0.879455i	$0.342093\pi$
$420$	0.448210	−	0.0613050i	0.0218704	−	0.00299138i
$421$	34.3170	+	4.93405i	1.67251	+	0.240471i	0.912393	−	0.409315i	$-0.134232\pi$
$421$	34.3170	+	4.93405i	1.67251	+	0.240471i	0.760117	+	0.649786i	$0.225141\pi$
$422$	−9.56777	−	5.22440i	−0.465752	−	0.254320i
$423$	2.15396	−	0.468565i	0.104729	−	0.0227824i
$424$	−0.662476	−	4.60762i	−0.0321727	−	0.223766i
$425$	3.29364	−	14.1990i	0.159765	−	0.688754i
$426$	−1.89541	−	4.15036i	−0.0918328	−	0.201086i
$427$	−0.918396	+	1.22683i	−0.0444443	+	0.0593706i
$428$	−0.523599	−	2.40694i	−0.0253091	−	0.116344i
$429$	2.94701	−	0.865321i	0.142283	−	0.0417781i
$430$	−28.8258	−	33.7319i	−1.39010	−	1.62670i
$431$	14.6819	+	12.7220i	0.707203	+	0.612795i	0.932362	−	0.361527i	$-0.117744\pi$
$431$	14.6819	+	12.7220i	0.707203	+	0.612795i	−0.225158	+	0.974322i	$0.572290\pi$
$432$	−20.0290	−	4.35703i	−0.963644	−	0.209628i
$433$	−1.41164	+	19.7373i	−0.0678389	+	0.948512i	0.843572	+	0.537016i	$0.180448\pi$
$433$	−1.41164	+	19.7373i	−0.0678389	+	0.948512i	−0.911411	+	0.411497i	$0.865006\pi$
$434$	−0.174155	−	0.0511365i	−0.00835970	−	0.00245463i
$435$	10.6723	+	4.06426i	0.511699	+	0.194866i
$436$			30.0470i			1.43899i
$437$	−23.4186	+	9.51995i	−1.12026	+	0.455401i
$438$	15.3236	−	15.3236i	0.732189	−	0.732189i
$439$	−9.16613	−	4.18603i	−0.437476	−	0.199788i	0.184488	−	0.982835i	$-0.440937\pi$
$439$	−9.16613	−	4.18603i	−0.437476	−	0.199788i	−0.621963	+	0.783046i	$0.713665\pi$
$440$	0.413967	−	1.84200i	0.0197351	−	0.0878138i
$441$	10.3218	+	11.9119i	0.491512	+	0.567235i
$442$	3.00308	−	13.8049i	0.142842	−	0.656634i
$443$	−1.20033	−	16.7828i	−0.0570293	−	0.797374i	−0.942823	−	0.333294i	$-0.891840\pi$
$443$	−1.20033	−	16.7828i	−0.0570293	−	0.797374i	0.885794	−	0.464080i	$-0.153615\pi$
$444$	−0.0409859	+	0.285063i	−0.00194510	+	0.0135285i
$445$	−9.59758	−	4.46296i	−0.454969	−	0.211565i
$446$	−17.8740	−	11.4869i	−0.846360	−	0.543923i
$447$	−4.18163	−	3.13033i	−0.197784	−	0.148060i
$448$	0.259875	−	0.696753i	0.0122780	−	0.0329185i
$449$	−15.6687	+	7.15567i	−0.739453	+	0.337697i	−0.749279	−	0.662255i	$-0.769600\pi$
$449$	−15.6687	+	7.15567i	−0.739453	+	0.337697i	0.00982580	+	0.999952i	$0.496872\pi$
$450$	−10.6521	+	18.8865i	−0.502143	+	0.890320i
$451$	−1.79585	+	2.79439i	−0.0845632	+	0.131583i
$452$	−0.609851	+	1.11686i	−0.0286850	+	0.0525326i
$453$	5.99297	+	8.00567i	0.281574	+	0.376139i
$454$	−25.9739	+	29.9754i	−1.21901	+	1.40682i
$455$	−0.116986	+	0.775802i	−0.00548437	+	0.0363701i
$456$	2.05049	−	1.77676i	0.0960231	−	0.0832045i
$457$	20.7034	−	11.3049i	0.968466	−	0.528822i	0.0845250	−	0.996421i	$-0.473063\pi$
$457$	20.7034	−	11.3049i	0.968466	−	0.528822i	0.883941	+	0.467599i	$0.154881\pi$
$458$	−13.2297	+	4.93441i	−0.618182	+	0.230570i
$459$	13.2041			0.616315
$460$	4.24253	+	17.6075i	0.197809	+	0.820956i
$461$	4.41393			0.205577			0.102789	−	0.994703i	$-0.467223\pi$
$461$	4.41393			0.205577			0.102789	+	0.994703i	$0.467223\pi$
$462$	−0.304606	+	0.113612i	−0.0141716	+	0.00528572i
$463$	2.51550	−	1.37357i	0.116905	−	0.0638351i	−0.419732	−	0.907648i	$-0.637876\pi$
$463$	2.51550	−	1.37357i	0.116905	−	0.0638351i	0.536638	+	0.843813i	$0.319694\pi$
$464$	20.2764	−	17.5696i	0.941310	−	0.815650i
$465$	−1.05333	+	0.777288i	−0.0488472	+	0.0360459i
$466$	−24.1998	+	27.9281i	−1.12103	+	1.29374i
$467$	−11.4723	−	15.3252i	−0.530876	−	0.709168i	0.452292	−	0.891870i	$-0.350607\pi$
$467$	−11.4723	−	15.3252i	−0.530876	−	0.709168i	−0.983168	+	0.182702i	$0.941516\pi$
$468$	−4.61137	+	8.44510i	−0.213161	+	0.390375i
$469$	1.13581	−	1.76736i	0.0524469	−	0.0816089i
$470$	3.51155	+	2.29096i	0.161976	+	0.105674i
$471$	−5.42151	+	2.47592i	−0.249810	+	0.114084i
$472$	−1.56301	+	4.19058i	−0.0719432	+	0.192887i
$473$	11.6870	+	8.74880i	0.537370	+	0.402270i
$474$	11.0289	+	7.08786i	0.506575	+	0.325556i
$475$	−10.6184	−	24.1222i	−0.487205	−	1.10680i
$476$	−0.0974349	+	0.677675i	−0.00446592	+	0.0310612i
$477$	−1.25490	−	17.5458i	−0.0574579	−	0.803366i
$478$	11.1027	−	51.0381i	0.507824	−	2.33443i
$479$	−4.57944	−	5.28496i	−0.209240	−	0.241476i	0.641423	−	0.767188i	$-0.278345\pi$
$479$	−4.57944	−	5.28496i	−0.209240	−	0.241476i	−0.850663	+	0.525712i	$0.823799\pi$
$480$	−7.72354	−	12.2015i	−0.352530	−	0.556918i
$481$	−0.454335	−	0.207488i	−0.0207159	−	0.00946063i
$482$	−28.1575	+	28.1575i	−1.28254	+	1.28254i
$483$	−0.394230	+	0.417876i	−0.0179381	+	0.0190140i
$484$			15.2057i			0.691167i
$485$	2.82148	−	7.40892i	0.128117	−	0.336422i
$486$	−29.6002	−	8.69141i	−1.34269	−	0.394250i
$487$	0.834833	−	11.6725i	0.0378299	−	0.528931i	−0.942838	−	0.333251i	$-0.891854\pi$
$487$	0.834833	−	11.6725i	0.0378299	−	0.528931i	0.980668	−	0.195680i	$-0.0626912\pi$
$488$	6.43454	+	1.39975i	0.291278	+	0.0633636i
$489$	−9.89682	−	8.57564i	−0.447550	−	0.387804i
$490$	−2.34400	+	29.8881i	−0.105891	+	1.35021i
$491$	−26.5407	+	7.79306i	−1.19777	+	0.351696i	−0.818998	−	0.573796i	$-0.805470\pi$
$491$	−26.5407	+	7.79306i	−1.19777	+	0.351696i	−0.378767	+	0.925492i	$0.623652\pi$
$492$	0.726988	+	3.34191i	0.0327752	+	0.150665i
$493$	−10.3574	+	13.8359i	−0.466476	+	0.623139i
$494$	−10.6119	−	23.2369i	−0.477453	−	1.04548i
$495$	2.05691	−	6.83132i	0.0924511	−	0.307045i
$496$	0.437686	+	3.04417i	0.0196527	+	0.136687i
$497$	−0.374711	+	0.0815133i	−0.0168081	+	0.00365637i
$498$	−10.1920	−	5.56527i	−0.456716	−	0.249386i
$499$	0.374786	+	0.0538861i	0.0167777	+	0.00241227i	0.150699	−	0.988580i	$-0.451848\pi$
$499$	0.374786	+	0.0538861i	0.0167777	+	0.00241227i	−0.133921	+	0.990992i	$0.542757\pi$
$500$	−18.2233	+	4.94553i	−0.814973	+	0.221171i
$501$	5.54163	−	3.56139i	0.247582	−	0.159111i
$502$	16.2868	+	1.16485i	0.726915	+	0.0519900i
$503$	13.2695	+	24.3012i	0.591657	+	1.08354i	0.986340	+	0.164721i	$0.0526725\pi$
$503$	13.2695	+	24.3012i	0.591657	+	1.08354i	−0.394683	+	0.918817i	$0.629146\pi$
$504$	−0.0779341	+	0.170652i	−0.00347146	+	0.00760144i
$505$	31.5355	+	27.7070i	1.40331	+	1.23295i
$506$	−5.74923	−	11.6772i	−0.255585	−	0.519113i
$507$	−4.04056	−	4.04056i	−0.179448	−	0.179448i
$508$	4.03637	+	10.8219i	0.179085	+	0.480146i
$509$	−7.61079	+	25.9200i	−0.337342	+	1.14888i	0.599862	+	0.800103i	$0.295222\pi$
$509$	−7.61079	+	25.9200i	−0.337342	+	1.14888i	−0.937205	+	0.348779i	$0.886596\pi$
$510$	7.57377	+	7.67849i	0.335372	+	0.340009i
$511$	−0.984691	−	1.53221i	−0.0435602	−	0.0677810i
$512$	−28.4451	+	2.03444i	−1.25711	+	0.0899102i
$513$	19.1131	−	14.3079i	0.843863	−	0.631708i
$514$	10.8429	+	36.9275i	0.478260	+	1.62880i
$515$	8.45656	−	15.2374i	0.372641	−	0.671439i
$516$	14.8782	−	2.13917i	0.654978	−	0.0941716i
$517$	−1.29254	−	0.482091i	−0.0568457	−	0.0212023i
$518$	0.0495347	+	0.0184755i	0.00217643	+	0.000811766i
$519$	−0.459841	+	0.0661151i	−0.0201848	+	0.00290213i
$520$	3.24112	−	0.927555i	0.142132	−	0.0406760i
$521$	−1.10896	−	3.77677i	−0.0485844	−	0.165463i	0.931627	−	0.363415i	$-0.118389\pi$
$521$	−1.10896	−	3.77677i	−0.0485844	−	0.165463i	−0.980212	+	0.197952i	$0.936571\pi$
$522$	20.5824	−	15.4078i	0.900866	−	0.674380i
$523$	−24.6407	+	1.76234i	−1.07746	+	0.0770615i	−0.598769	−	0.800922i	$-0.704343\pi$
$523$	−24.6407	+	1.76234i	−1.07746	+	0.0770615i	−0.478692	+	0.877983i	$0.658889\pi$
$524$	18.3730	+	28.5889i	0.802628	+	1.24891i
$525$	−0.447225	−	0.398405i	−0.0195185	−	0.0173878i
$526$	−4.66613	+	15.8914i	−0.203453	+	0.692897i
$527$	−0.692351	−	1.85626i	−0.0301593	−	0.0808601i
$528$	3.89517	+	3.89517i	0.169516	+	0.169516i
$529$	−18.2292	−	14.0249i	−0.792572	−	0.609778i
$530$	22.0838	−	25.1352i	0.959257	−	1.09180i
$531$	−7.02103	+	15.3739i	−0.304687	+	0.667171i
$532$	0.593285	+	1.08652i	0.0257222	+	0.0471066i
$533$	−5.91634	−	0.423145i	−0.256265	−	0.0183284i
$534$	6.58851	−	4.23418i	0.285113	−	0.183231i
$535$	−1.97229	+	2.59730i	−0.0852694	+	0.112291i
$536$	−8.93531	−	1.28470i	−0.385947	−	0.0554908i
$537$	7.64207	+	4.17288i	0.329780	+	0.180073i
$538$	−25.1219	+	5.46494i	−1.08308	+	0.235610i
$539$	−1.40379	−	9.76361i	−0.0604657	−	0.420548i
$540$	−8.09441	−	15.0689i	−0.348328	−	0.648460i
$541$	−11.3685	−	24.8934i	−0.488768	−	1.07025i	−0.979959	−	0.199200i	$-0.936166\pi$
$541$	−11.3685	−	24.8934i	−0.488768	−	1.07025i	0.491191	−	0.871052i	$-0.336562\pi$
$542$	19.9164	−	26.6052i	0.855484	−	1.14279i
$543$	−3.74933	−	17.2354i	−0.160899	−	0.739641i
$544$	20.9692	−	6.15712i	0.899048	−	0.263984i
$545$	30.2431	−	25.8444i	1.29547	−	1.10705i
$546$	−0.438734	−	0.380165i	−0.0187761	−	0.0162696i
$547$	0.503727	+	0.109579i	0.0215378	+	0.00468526i	0.223321	−	0.974745i	$-0.428310\pi$
$547$	0.503727	+	0.109579i	0.0215378	+	0.00468526i	−0.201783	+	0.979430i	$0.564674\pi$
$548$	1.88971	−	26.4216i	0.0807243	−	1.12867i
$549$	23.8759	+	7.01061i	1.01900	+	0.299205i
$550$	11.9982	−	6.33919i	0.511603	−	0.270304i
$551$			31.2509i			1.33133i
$552$	2.33701	+	0.794979i	0.0994698	+	0.0338366i
$553$	0.779125	−	0.779125i	0.0331318	−	0.0331318i
$554$	19.6286	+	8.96410i	0.833941	+	0.380848i
$555$	0.322176	−	0.203938i	0.0136756	−	0.00865670i
$556$	−10.6406	−	12.2799i	−0.451262	−	0.520784i
$557$	−3.90670	+	17.9588i	−0.165532	+	0.760939i	0.817267	+	0.576260i	$0.195488\pi$
$557$	−3.90670	+	17.9588i	−0.165532	+	0.760939i	−0.982799	+	0.184679i	$0.940875\pi$
$558$	0.210251	+	2.93970i	0.00890065	+	0.124447i
$559$	−3.70998	+	25.8034i	−0.156915	+	1.09137i
$560$	−1.32176	+	0.482678i	−0.0558544	+	0.0203969i
$561$	−2.98524	−	1.91850i	−0.126037	−	0.0809990i
$562$	−3.17569	−	2.37729i	−0.133958	−	0.100280i
$563$	10.3491	−	27.7470i	0.436162	−	1.16940i	−0.514041	−	0.857765i	$-0.671852\pi$
$563$	10.3491	−	27.7470i	0.436162	−	1.16940i	0.950203	−	0.311630i	$-0.100875\pi$
$564$	−1.29201	+	0.590042i	−0.0544035	+	0.0248452i
$565$	1.64870	−	0.346814i	0.0693612	−	0.0145906i
$566$	17.5510	−	27.3100i	0.737725	−	1.14792i
$567$	−0.191393	+	0.350510i	−0.00803775	+	0.0147200i
$568$	0.987461	+	1.31909i	0.0414330	+	0.0553480i
$569$	−11.4709	+	13.2382i	−0.480887	+	0.554973i	−0.943408	−	0.331635i	$-0.892400\pi$
$569$	−11.4709	+	13.2382i	−0.480887	+	0.554973i	0.462521	+	0.886608i	$0.346945\pi$
$570$	19.2834	+	2.90781i	0.807694	+	0.121795i
$571$	23.4718	−	20.3384i	0.982264	−	0.851136i	−0.00659742	−	0.999978i	$-0.502100\pi$
$571$	23.4718	−	20.3384i	0.982264	−	0.851136i	0.988861	+	0.148842i	$0.0475546\pi$
$572$	5.28511	−	2.88589i	0.220981	−	0.120665i
$573$	−13.8988	+	5.18399i	−0.580632	+	0.216564i
$574$	0.627832			0.0262052
$575$	14.0733	−	19.4150i	0.586897	−	0.809661i
$576$	−12.0748			−0.503116
$577$	−19.5893	+	7.30642i	−0.815513	+	0.304170i	−0.722391	−	0.691484i	$-0.756957\pi$
$577$	−19.5893	+	7.30642i	−0.815513	+	0.304170i	−0.0931211	+	0.995655i	$0.529684\pi$
$578$	14.3312	−	7.82545i	0.596101	−	0.325496i
$579$	16.4275	−	14.2345i	0.682702	−	0.591565i
$580$	22.1392	+	3.33844i	0.919281	+	0.138621i
$581$	−0.639131	+	0.737597i	−0.0265156	+	0.0306007i
$582$	3.51545	+	4.69609i	0.145720	+	0.194659i
$583$	−5.27583	+	9.66196i	−0.218503	+	0.400158i
$584$	−4.23113	+	6.58376i	−0.175085	+	0.272438i
$585$	12.4666	−	2.62243i	0.515430	−	0.108424i
$586$	6.59791	−	3.01316i	0.272557	−	0.124473i
$587$	−14.2334	+	38.1613i	−0.587477	+	1.57509i	0.213855	+	0.976865i	$0.431398\pi$
$587$	−14.2334	+	38.1613i	−0.587477	+	1.57509i	−0.801332	+	0.598220i	$0.795875\pi$
$588$	−8.13039	−	6.08633i	−0.335292	−	0.250996i
$589$	−3.01362	−	1.93673i	−0.124174	−	0.0798017i
$590$	−30.1968	+	11.0273i	−1.24318	+	0.453985i
$591$	2.35269	−	16.3634i	0.0967769	−	0.673098i
$592$	−0.0639058	−	0.893519i	−0.00262651	−	0.0367234i
$593$	1.59554	−	7.33459i	0.0655211	−	0.301196i	−0.932712	−	0.360623i	$-0.882564\pi$
$593$	1.59554	−	7.33459i	0.0655211	−	0.301196i	0.998233	+	0.0594278i	$0.0189276\pi$
$594$	8.04997	+	9.29016i	0.330294	+	0.381180i
$595$	0.765903	−	0.484818i	0.0313990	−	0.0198756i
$596$	−9.31548	−	4.25424i	−0.381577	−	0.174260i
$597$	10.4186	−	10.4186i	0.426405	−	0.426405i
$598$	13.3809	−	19.0035i	0.547184	−	0.777111i
$599$		−	43.9424i		−	1.79544i	−0.440567	−	0.897720i	$-0.645223\pi$
$599$		−	43.9424i		−	1.79544i	0.440567	−	0.897720i	$-0.354777\pi$
$600$	−0.758910	+	2.45918i	−0.0309824	+	0.100395i
$601$	−18.2861	−	5.36928i	−0.745905	−	0.219018i	−0.113374	−	0.993552i	$-0.536166\pi$
$601$	−18.2861	−	5.36928i	−0.745905	−	0.219018i	−0.632531	+	0.774535i	$0.717984\pi$
$602$	0.196848	−	2.75230i	0.00802293	−	0.112175i
$603$	−33.3329	−	7.25114i	−1.35742	−	0.295289i
$604$	14.8173	+	12.8393i	0.602908	+	0.522423i
$605$	15.3049	−	13.0789i	0.622233	−	0.531732i
$606$	−29.8027	+	8.75086i	−1.21065	+	0.355479i
$607$	−0.767026	−	3.52596i	−0.0311326	−	0.143114i	0.958957	−	0.283552i	$-0.0915128\pi$
$607$	−0.767026	−	3.52596i	−0.0311326	−	0.143114i	−0.990090	+	0.140437i	$0.955149\pi$
$608$	23.6813	−	31.6346i	0.960405	−	1.28295i
$609$	0.295023	+	0.646009i	0.0119549	+	0.0261776i
$610$	22.3975	+	41.6960i	0.906849	+	1.68822i
$611$	−0.350572	−	2.43828i	−0.0141826	−	0.0986423i
$612$	10.8628	−	2.36305i	0.439102	−	0.0955208i
$613$	−0.990353	−	0.540773i	−0.0400000	−	0.0218416i	0.459125	−	0.888372i	$-0.348163\pi$
$613$	−0.990353	−	0.540773i	−0.0400000	−	0.0218416i	−0.499125	+	0.866530i	$0.666345\pi$
$614$	−29.3173	−	4.21519i	−1.18315	−	0.170111i
$615$	2.73841	−	3.60621i	0.110423	−	0.145417i
$616$	0.0987692	−	0.0634751i	0.00397952	−	0.00255748i
$617$	22.2946	+	1.59454i	0.897549	+	0.0641940i	0.512485	−	0.858696i	$-0.328725\pi$
$617$	22.2946	+	1.59454i	0.897549	+	0.0641940i	0.385064	+	0.922890i	$0.374180\pi$
$618$	6.17970	+	11.3173i	0.248584	+	0.455248i
$619$	−6.05621	+	13.2612i	−0.243420	+	0.533014i	−0.991425	−	0.130678i	$-0.958284\pi$
$619$	−6.05621	+	13.2612i	−0.243420	+	0.533014i	0.748005	+	0.663693i	$0.231012\pi$
$620$	−1.69399	+	1.92806i	−0.0680321	+	0.0774326i
$621$	20.0135	+	8.44482i	0.803114	+	0.338879i
$622$	28.5566	+	28.5566i	1.14502	+	1.14502i
$623$	−0.230027	−	0.616727i	−0.00921584	−	0.0247086i
$624$	−2.77127	+	9.43808i	−0.110940	+	0.377826i
$625$	20.6523	+	14.0884i	0.826090	+	0.563538i
$626$	−18.4178	−	28.6586i	−0.736122	−	1.14543i
$627$	−6.40003	+	0.457739i	−0.255593	+	0.0182803i
$628$	−9.35440	+	7.00262i	−0.373281	+	0.279435i
$629$	0.162577	+	0.553687i	0.00648238	+	0.0220770i
$630$	−1.29640	+	0.371008i	−0.0516497	+	0.0147813i
$631$	23.0554	−	3.31486i	0.917820	−	0.131963i	0.332815	−	0.942992i	$-0.392002\pi$
$631$	23.0554	−	3.31486i	0.917820	−	0.131963i	0.585005	+	0.811030i	$0.301093\pi$
$632$	−4.43603	−	1.65455i	−0.176456	−	0.0658146i
$633$	−4.58109	−	1.70866i	−0.182082	−	0.0679131i
$634$	20.5311	−	2.95192i	0.815393	−	0.117236i
$635$	7.42074	−	13.3710i	0.294483	−	0.530611i
$636$	3.19331	+	10.8754i	0.126623	+	0.431238i
$637$	14.1006	−	10.5556i	0.558686	−	0.418227i
$638$	−16.0492	+	1.14786i	−0.635393	+	0.0454442i
$639$	3.36637	+	5.23817i	0.133172	+	0.207219i
$640$	7.41512	+	7.51765i	0.293108	+	0.297161i
$641$	−6.56707	+	22.3654i	−0.259384	+	0.883380i	0.722092	+	0.691797i	$0.243181\pi$
$641$	−6.56707	+	22.3654i	−0.259384	+	0.883380i	−0.981476	+	0.191584i	$0.938638\pi$
$642$	−0.843295	−	2.26096i	−0.0332822	−	0.0892331i
$643$	19.2730	+	19.2730i	0.760052	+	0.760052i	0.976332	−	0.216279i	$-0.0693922\pi$
$643$	19.2730	+	19.2730i	0.760052	+	0.760052i	−0.216279	+	0.976332i	$0.569392\pi$
$644$	−0.581096	+	0.964836i	−0.0228984	+	0.0380199i
$645$	−14.9504	−	13.1354i	−0.588670	−	0.517204i
$646$	−12.2605	+	26.8467i	−0.482381	+	1.05627i
$647$	16.3870	+	30.0105i	0.644239	+	1.17984i	0.971979	+	0.235068i	$0.0755312\pi$
$647$	16.3870	+	30.0105i	0.644239	+	1.17984i	−0.327740	+	0.944768i	$0.606287\pi$
$648$	1.71164	+	0.122419i	0.0672396	+	0.00480907i
$649$	8.89805	−	5.71843i	0.349279	−	0.224468i
$650$	20.2028	+	13.3791i	0.792419	+	0.524770i
$651$	−0.0805803	−	0.0115857i	−0.00315819	−	0.000454079i
$652$	−22.5336	−	12.3043i	−0.882485	−	0.481873i
$653$	−7.48834	+	1.62899i	−0.293041	+	0.0637472i	−0.356683	−	0.934226i	$-0.616092\pi$
$653$	−7.48834	+	1.62899i	−0.293041	+	0.0637472i	0.0636414	+	0.997973i	$0.479729\pi$
$654$	4.18912	+	29.1360i	0.163807	+	1.13931i
$655$	12.9723	−	43.0831i	0.506870	−	1.68340i
$656$	−4.41921	−	9.67672i	−0.172541	−	0.377813i
$657$	−17.7230	+	23.6751i	−0.691438	+	0.923654i
$658$	0.0554245	+	0.254782i	0.00216067	+	0.00993245i
$659$	−29.7293	+	8.72931i	−1.15809	+	0.340046i	−0.803690	−	0.595048i	$-0.797133\pi$
$659$	−29.7293	+	8.72931i	−1.15809	+	0.340046i	−0.354400	+	0.935094i	$0.615315\pi$
$660$	−0.359419	+	4.58291i	−0.0139904	+	0.178389i
$661$	−12.2082	−	10.5784i	−0.474843	−	0.411454i	0.384285	−	0.923214i	$-0.374448\pi$
$661$	−12.2082	−	10.5784i	−0.474843	−	0.411454i	−0.859128	+	0.511761i	$0.828993\pi$
$662$	−34.3119	−	7.46409i	−1.33357	−	0.290100i
$663$	0.452044	−	6.32040i	0.0175559	−	0.245464i
$664$	4.02382	+	1.18150i	0.156155	+	0.0458511i
$665$	0.583307	−	1.53171i	0.0226197	−	0.0593970i
$666$		−	0.858440i		−	0.0332639i
$667$	−24.5477	+	14.3469i	−0.950490	+	0.555515i
$668$	9.13215	−	9.13215i	0.353334	−	0.353334i
$669$	−8.66841	−	3.95873i	−0.335140	−	0.153053i
$670$	−34.7035	−	54.8237i	−1.34071	−	2.11802i
$671$	−10.1980	−	11.7692i	−0.393691	−	0.454343i
$672$	0.190889	−	0.877503i	0.00736371	−	0.0338504i
$673$	−0.662155	−	9.25814i	−0.0255242	−	0.356875i	−0.994124	−	0.108249i	$-0.965476\pi$
$673$	−0.662155	−	9.25814i	−0.0255242	−	0.356875i	0.968600	−	0.248626i	$-0.0799790\pi$
$674$	4.42342	−	30.7656i	0.170384	−	1.18505i
$675$	−8.20493	+	21.1084i	−0.315808	+	0.812463i
$676$	−9.42456	−	6.05680i	−0.362483	−	0.232954i
$677$	−23.0020	−	17.2191i	−0.884037	−	0.661782i	0.0576262	−	0.998338i	$-0.481647\pi$
$677$	−23.0020	−	17.2191i	−0.884037	−	0.661782i	−0.941663	+	0.336556i	$0.890738\pi$
$678$	−0.435648	+	1.16802i	−0.0167310	+	0.0448575i
$679$	0.448471	−	0.204810i	0.0172107	−	0.00785988i
$680$	−3.26210	−	2.12821i	−0.125096	−	0.0816132i
$681$	−9.61777	+	14.9655i	−0.368554	+	0.573481i
$682$	0.883936	−	1.61881i	0.0338477	−	0.0619873i
$683$	28.4682	+	38.0291i	1.08931	+	1.45514i	0.878578	+	0.477598i	$0.158492\pi$
$683$	28.4682	+	38.0291i	1.08931	+	1.45514i	0.210728	+	0.977545i	$0.432417\pi$
$684$	13.1634	−	15.1914i	0.503315	−	0.580856i
$685$	−28.2194	+	20.8240i	−1.07821	+	0.795643i
$686$	−2.82192	+	2.44521i	−0.107742	+	0.0933586i
$687$	−5.55836	+	3.03509i	−0.212065	+	0.115796i
$688$	−43.8065	+	16.3390i	−1.67011	+	0.622918i
$689$	−19.6576			−0.748894
$690$	6.56871	+	16.4822i	0.250066	+	0.627465i
$691$	5.91511			0.225021			0.112511	−	0.993651i	$-0.464111\pi$
$691$	5.91511			0.225021			0.112511	+	0.993651i	$0.464111\pi$
$692$	−0.853384	+	0.318296i	−0.0324408	+	0.0120998i
$693$	0.389396	−	0.212626i	0.0147919	−	0.00807700i
$694$	31.8635	−	27.6099i	1.20952	−	1.04806i
$695$	−3.20773	+	21.2724i	−0.121676	+	0.806907i
$696$	1.99838	−	2.30625i	0.0757483	−	0.0874183i
$697$	4.10678	+	5.48602i	0.155555	+	0.207798i
$698$	−28.5318	+	52.2520i	−1.07994	+	1.97777i
$699$	−8.96086	+	13.9434i	−0.338931	+	0.527387i
$700$	−1.02280	−	0.576863i	−0.0386582	−	0.0218034i
$701$	7.94306	−	3.62747i	0.300005	−	0.137008i	−0.259725	−	0.965683i	$-0.583632\pi$
$701$	7.94306	−	3.62747i	0.300005	−	0.137008i	0.559730	+	0.828675i	$0.310905\pi$
$702$	−7.67094	+	20.5666i	−0.289521	+	0.776235i
$703$	0.835303	+	0.625300i	0.0315040	+	0.0235836i
$704$	6.35704	+	4.08542i	0.239590	+	0.153975i
$705$	1.70519	+	0.792929i	0.0642212	+	0.0298634i
$706$	−1.19710	+	8.32602i	−0.0450535	+	0.313354i
$707$	0.186233	+	2.60388i	0.00700403	+	0.0979291i
$708$	2.31491	−	10.6415i	0.0869997	−	0.399931i
$709$	−24.7165	−	28.5243i	−0.928246	−	1.07125i	−0.997285	−	0.0736393i	$-0.976539\pi$
$709$	−24.7165	−	28.5243i	−0.928246	−	1.07125i	0.0690387	−	0.997614i	$-0.478007\pi$
$710$	−2.59691	+	11.5552i	−0.0974602	+	0.433661i
$711$	−16.2744	−	7.43226i	−0.610337	−	0.278732i
$712$	−1.99994	+	1.99994i	−0.0749510	+	0.0749510i
$713$	0.137796	−	3.25634i	0.00516048	−	0.121951i
$714$			0.670711i			0.0251007i
$715$	−7.45060	−	2.83735i	−0.278637	−	0.106111i
$716$	16.3793	+	4.80939i	0.612122	+	0.179735i
$717$	1.67125	−	23.3671i	0.0624139	−	0.872661i
$718$	7.14037	+	1.55329i	0.266476	+	0.0579683i
$719$	31.2139	+	27.0470i	1.16408	+	1.00868i	0.999752	+	0.0222757i	$0.00709115\pi$
$719$	31.2139	+	27.0470i	1.16408	+	1.00868i	0.164328	+	0.986406i	$0.447454\pi$
$720$	14.8435	+	17.3698i	0.553183	+	0.647334i
$721$	1.03983	−	0.305323i	0.0387254	−	0.0113708i
$722$	3.58668	+	16.4877i	0.133482	+	0.613608i
$723$	−10.7033	+	14.2979i	−0.398058	+	0.531744i
$724$	−14.3655	−	31.4561i	−0.533890	−	1.16906i
$725$	−15.6824	−	25.1552i	−0.582430	−	0.934240i
$726$	2.11996	+	14.7446i	0.0786790	+	0.547224i
$727$	−25.5570	+	5.55959i	−0.947858	+	0.206194i	−0.659819	−	0.751425i	$-0.729367\pi$
$727$	−25.5570	+	5.55959i	−0.947858	+	0.206194i	−0.288039	+	0.957619i	$0.593003\pi$
$728$	0.184005	+	0.100475i	0.00681969	+	0.00372383i
$729$	−5.16773	−	0.743007i	−0.191397	−	0.0275188i
$730$	−55.7326	+	7.62295i	−2.06275	+	0.282138i
$731$	25.3373	−	16.2833i	0.937133	−	0.602259i
$732$	−15.9931	−	1.14385i	−0.591123	−	0.0422780i
$733$	−4.59186	−	8.40936i	−0.169604	−	0.310607i	0.779027	−	0.626990i	$-0.215713\pi$
$733$	−4.59186	−	8.40936i	−0.169604	−	0.310607i	−0.948632	+	0.316383i	$0.897532\pi$
$734$	7.13556	−	15.6247i	0.263378	−	0.576718i
$735$	0.867152	+	13.4185i	0.0319854	+	0.494948i
$736$	35.7209	+	4.07872i	1.31669	+	0.150344i
$737$	15.0955	+	15.0955i	0.556050	+	0.556050i
$738$	−3.56257	−	9.55161i	−0.131140	−	0.351600i
$739$	3.43836	−	11.7100i	0.126482	−	0.430759i	−0.871766	−	0.489922i	$-0.837025\pi$
$739$	3.43836	−	11.7100i	0.126482	−	0.430759i	0.998248	+	0.0591636i	$0.0188433\pi$
$740$	0.532217	−	0.524959i	0.0195647	−	0.0192979i
$741$	−6.19440	−	9.63867i	−0.227557	−	0.354086i
$742$	2.07541	−	0.148436i	0.0761908	−	0.00544927i
$743$	−20.9113	+	15.6540i	−0.767160	+	0.574289i	−0.909585	−	0.415517i	$-0.863601\pi$
$743$	−20.9113	+	15.6540i	−0.767160	+	0.574289i	0.142426	+	0.989806i	$0.454510\pi$
$744$	0.0985518	+	0.335637i	0.00361309	+	0.0123050i
$745$	3.73054	+	13.0355i	0.136676	+	0.477583i
$746$	−35.4381	+	5.09524i	−1.29748	+	0.186550i
$747$	14.8482	+	5.53809i	0.543267	+	0.202628i
$748$	−6.51848	−	2.43127i	−0.238339	−	0.0888960i
$749$	−0.200747	+	0.0288631i	−0.00733515	+	0.00105464i
$750$	−16.9813	+	7.33625i	−0.620069	+	0.267882i
$751$	2.89309	+	9.85296i	0.105570	+	0.359540i	0.995287	−	0.0969736i	$-0.0309162\pi$
$751$	2.89309	+	9.85296i	0.105570	+	0.359540i	−0.889717	+	0.456513i	$0.849098\pi$
$752$	3.53681	−	2.64762i	0.128974	−	0.0965489i
$753$	7.30489	−	0.522456i	0.266205	−	0.0190393i
$754$	−15.5335	−	24.1706i	−0.565697	−	0.880242i
$755$	0.178223	−	25.9575i	0.00648621	−	0.944689i
$756$	0.299690	−	1.02065i	0.0108996	−	0.0371207i
$757$	0.562344	+	1.50770i	0.0204387	+	0.0547984i	0.946768	−	0.321916i	$-0.104327\pi$
$757$	0.562344	+	1.50770i	0.0204387	+	0.0547984i	−0.926330	+	0.376714i	$0.877054\pi$
$758$	38.7859	+	38.7859i	1.40877	+	1.40877i
$759$	−3.29774	−	4.81711i	−0.119700	−	0.174850i
$760$	−7.02803	+	0.454177i	−0.254933	+	0.0164747i
$761$	9.78566	−	21.4276i	0.354730	−	0.776750i	−0.645189	−	0.764023i	$-0.723221\pi$
$761$	9.78566	−	21.4276i	0.354730	−	0.776750i	0.999919	−	0.0127270i	$-0.00405124\pi$
$762$	5.42276	+	9.93105i	0.196446	+	0.359764i
$763$	2.46763	+	0.176488i	0.0893343	+	0.00638931i
$764$	−24.4662	+	15.7235i	−0.885156	+	0.568855i
$765$	−11.7219	−	8.90113i	−0.423806	−	0.321821i
$766$	53.5605	+	7.70083i	1.93522	+	0.278242i
$767$	16.5769	+	9.05168i	0.598558	+	0.326837i
$768$	−16.6376	+	3.61929i	−0.600358	+	0.130600i
$769$	−3.08717	−	21.4717i	−0.111326	−	0.774291i	−0.966632	−	0.256168i	$-0.917540\pi$
$769$	−3.08717	−	21.4717i	−0.111326	−	0.774291i	0.855306	−	0.518123i	$-0.173369\pi$
$770$	0.808046	+	0.243302i	0.0291200	+	0.00876801i
$771$	7.17082	+	15.7019i	0.258251	+	0.565490i
$772$	25.5387	−	34.1157i	0.919157	−	1.22785i
$773$	2.61865	+	12.0378i	0.0941865	+	0.432968i	0.999958	+	0.00920114i	$0.00292886\pi$
$773$	2.61865	+	12.0378i	0.0941865	+	0.432968i	−0.905771	+	0.423767i	$0.860708\pi$
$774$	−42.9895	+	12.6228i	−1.54522	+	0.453719i
$775$	3.39769	+	0.0466591i	0.122049	+	0.00167604i
$776$	−1.60104	−	1.38731i	−0.0574740	−	0.0498015i
$777$	0.0231703	+	0.00504038i	0.000831228	+	0.000180823i
$778$	−1.65215	+	23.1000i	−0.0592323	+	0.828176i
$779$	11.8892	+	3.49098i	0.425975	+	0.125078i
$780$	−7.49011	+	3.35866i	−0.268189	+	0.120259i
$781$		−	3.89674i		−	0.139436i
$782$	−26.7168	+	2.69435i	−0.955390	+	0.0963498i
$783$	18.9881	−	18.9881i	0.678578	−	0.678578i
$784$	28.7356	+	13.1231i	1.02627	+	0.468683i
$785$	15.0943	+	3.39227i	0.538740	+	0.121075i
$786$	21.8017	+	25.1605i	0.777642	+	0.897446i
$787$	−0.467819	+	2.15053i	−0.0166759	+	0.0766581i	−0.984733	−	0.174073i	$-0.944307\pi$
$787$	−0.467819	+	2.15053i	−0.0166759	+	0.0766581i	0.968057	+	0.250731i	$0.0806709\pi$
$788$	−2.31218	−	32.3285i	−0.0823679	−	1.15165i
$789$	−1.05718	+	7.35284i	−0.0376365	+	0.261768i
$790$	−11.6731	−	31.9655i	−0.415312	−	1.13728i
$791$	0.0881406	+	0.0566445i	0.00313392	+	0.00201405i
$792$	−1.52614	−	1.14246i	−0.0542291	−	0.0405954i
$793$	9.71786	−	26.0546i	0.345091	−	0.925225i
$794$	−2.09123	+	0.955033i	−0.0742150	+	0.0338928i
$795$	8.19971	−	12.5684i	0.290814	−	0.445756i
$796$	15.6175	−	24.3012i	0.553546	−	0.861335i
$797$	−2.82017	+	5.16476i	−0.0998957	+	0.182945i	−0.922847	−	0.385166i	$-0.874144\pi$
$797$	−2.82017	+	5.16476i	−0.0998957	+	0.182945i	0.822951	+	0.568112i	$0.192326\pi$
$798$	0.726777	+	0.970860i	0.0257276	+	0.0343681i
$799$	−1.86375	+	2.15088i	−0.0659348	+	0.0760928i
$800$	−3.18718	+	37.3479i	−0.112684	+	1.32045i
$801$	−8.07739	+	6.99910i	−0.285401	+	0.247301i
$802$	29.4348	−	16.0726i	1.03938	−	0.567543i
$803$	17.3410	−	6.46785i	0.611949	−	0.228245i
$804$	21.9805			0.775191
$805$	1.47095	−	0.244998i	0.0518442	−	0.00863505i
$806$	3.29352			0.116009
$807$	−10.8041	+	4.02971i	−0.380321	+	0.141852i
$808$	9.84512	−	5.37584i	0.346350	−	0.189122i
$809$	−0.740956	+	0.642042i	−0.0260506	+	0.0225730i	−0.667789	−	0.744351i	$-0.732759\pi$
$809$	−0.740956	+	0.642042i	−0.0260506	+	0.0225730i	0.641738	+	0.766924i	$0.278214\pi$
$810$	7.32358	+	9.92447i	0.257325	+	0.348710i
$811$	25.1195	−	28.9895i	0.882065	−	1.01796i	−0.117625	−	0.993058i	$-0.537528\pi$
$811$	25.1195	−	28.9895i	0.882065	−	1.01796i	0.999690	−	0.0248997i	$-0.00792662\pi$
$812$	0.834409	+	1.11464i	0.0292820	+	0.0391162i
$813$	7.14369	−	13.0827i	0.250540	−	0.458830i
$814$	−0.290447	+	0.451945i	−0.0101802	+	0.0158407i
$815$	6.99729	+	33.2640i	0.245104	+	1.16519i
$816$	10.3376	−	4.72103i	0.361889	−	0.165269i
$817$	19.0315	−	51.0255i	0.665828	−	1.78515i
$818$	28.3360	+	21.2120i	0.990744	+	0.741662i
$819$	0.666473	+	0.428316i	0.0232885	+	0.0149666i
$820$	3.74323	−	8.04980i	0.130719	−	0.281111i
$821$	2.42647	−	16.8765i	0.0846843	−	0.588992i	−0.902654	−	0.430366i	$-0.858384\pi$
$821$	2.42647	−	16.8765i	0.0846843	−	0.588992i	0.987339	−	0.158626i	$-0.0507064\pi$
$822$	−1.85125	−	25.8839i	−0.0645698	−	0.902804i
$823$	3.66853	−	16.8640i	0.127877	−	0.587840i	−0.867956	−	0.496641i	$-0.834566\pi$
$823$	3.66853	−	16.8640i	0.127877	−	0.587840i	0.995833	−	0.0911990i	$-0.0290700\pi$
$824$	−3.04949	−	3.51930i	−0.106234	−	0.122601i
$825$	4.92196	−	3.58014i	0.171361	−	0.124644i
$826$	−1.81851	−	0.830487i	−0.0632741	−	0.0288963i
$827$	31.1192	−	31.1192i	1.08212	−	1.08212i	0.0858080	−	0.996312i	$-0.472653\pi$
$827$	31.1192	−	31.1192i	1.08212	−	1.08212i	0.996312	−	0.0858080i	$-0.0273472\pi$
$828$	17.9760	+	3.36572i	0.624710	+	0.116967i
$829$		−	21.1872i		−	0.735863i	−0.929853	−	0.367931i	$-0.880066\pi$
$829$		−	21.1872i		−	0.735863i	0.929853	−	0.367931i	$-0.119934\pi$
$830$	12.3332	+	27.5042i	0.428092	+	0.954684i
$831$	9.28633	+	2.72671i	0.322139	+	0.0945887i
$832$	−0.962624	+	13.4592i	−0.0333730	+	0.466615i
$833$	−19.8850	−	4.32572i	−0.688975	−	0.149877i
$834$	−12.0300	−	10.4241i	−0.416565	−	0.360956i
$835$	−17.0466	−	1.33689i	−0.589922	−	0.0462651i
$836$	−12.0701	+	3.54409i	−0.417452	+	0.122575i
$837$	0.654315	+	3.00784i	0.0226164	+	0.103966i
$838$	−3.53632	+	4.72397i	−0.122160	+	0.163187i
$839$	2.37472	+	5.19991i	0.0819844	+	0.179521i	0.946185	−	0.323627i	$-0.104902\pi$
$839$	2.37472	+	5.19991i	0.0819844	+	0.179521i	−0.864200	+	0.503148i	$0.832175\pi$
$840$	−0.140994	+	0.0757364i	−0.00486475	+	0.00261316i
$841$	0.875070	+	6.08624i	0.0301748	+	0.209870i
$842$	65.0671	−	14.1545i	2.24236	−	0.487796i
$843$	−1.56159	−	0.852695i	−0.0537841	−	0.0293684i
$844$	−9.48828	−	1.36421i	−0.326600	−	0.0469580i
$845$	2.01004	+	14.6957i	0.0691474	+	0.505547i
$846$	3.56166	−	2.28894i	0.122453	−	0.0786955i
$847$	1.24878	+	0.0893142i	0.0429085	+	0.00306887i
$848$	−16.8963	−	30.9433i	−0.580223	−	1.06260i
$849$	6.04859	−	13.2446i	0.207587	−	0.454552i
$850$	−3.60329	−	27.7626i	−0.123592	−	0.952250i
$851$	−0.107698	+	0.943202i	−0.00369183	+	0.0323325i
$852$	−2.83701	−	2.83701i	−0.0971944	−	0.0971944i
$853$	19.2723	+	51.6709i	0.659870	+	1.76918i	0.638765	+	0.769401i	$0.279445\pi$
$853$	19.2723	+	51.6709i	0.659870	+	1.76918i	0.0211041	+	0.999777i	$0.493282\pi$
$854$	−0.829254	+	2.82418i	−0.0283765	+	0.0966414i
$855$	−26.6127	−	0.182722i	−0.910136	−	0.00624897i
$856$	0.471148	+	0.733121i	0.0161035	+	0.0250576i
$857$	−9.76336	+	0.698289i	−0.333510	+	0.0238531i	−0.237090	−	0.971488i	$-0.576194\pi$
$857$	−9.76336	+	0.698289i	−0.333510	+	0.0238531i	−0.0964198	+	0.995341i	$0.530739\pi$
$858$	4.72251	−	3.53522i	0.161224	−	0.120691i
$859$	−0.869522	−	2.96132i	−0.0296677	−	0.101039i	0.943328	−	0.331861i	$-0.107677\pi$
$859$	−0.869522	−	2.96132i	−0.0296677	−	0.101039i	−0.972996	+	0.230822i	$0.925858\pi$
$860$	−34.1152	−	18.9335i	−1.16332	−	0.645627i
$861$	0.278727	−	0.0400749i	0.00949898	−	0.00136575i
$862$	34.9599	+	13.0394i	1.19074	+	0.444122i
$863$	−11.9616	−	4.46145i	−0.407178	−	0.151870i	0.137525	−	0.990498i	$-0.456085\pi$
$863$	−11.9616	−	4.46145i	−0.407178	−	0.151870i	−0.544704	+	0.838629i	$0.683358\pi$
$864$	−33.6100	+	4.83239i	−1.14343	+	0.164401i
$865$	1.05439	+	0.585176i	0.0358505	+	0.0198966i
$866$	10.7073	+	36.4658i	0.363849	+	1.23916i
$867$	5.86286	−	4.38888i	0.199113	−	0.149054i
$868$	−0.159199	+	0.0113862i	−0.00540358	+	0.000386472i
$869$	6.05336	+	9.41922i	0.205346	+	0.319525i
$870$	21.9334	+	0.150594i	0.743611	+	0.00510562i
$871$	−10.7399	+	36.5767i	−0.363907	+	1.23936i
$872$	−3.71490	−	9.96002i	−0.125802	−	0.337289i
$873$	−5.66070	−	5.66070i	−0.191586	−	0.191586i
$874$	−35.7532	+	32.8502i	−1.20937	+	1.11117i
$875$	0.299116	+	1.52565i	0.0101120	+	0.0515765i
$876$	7.91614	−	17.3339i	0.267462	−	0.585659i
$877$	−17.0569	−	31.2373i	−0.575969	−	1.05481i	−0.989529	−	0.144332i	$-0.953897\pi$
$877$	−17.0569	−	31.2373i	−0.575969	−	1.05481i	0.413560	−	0.910477i	$-0.364285\pi$
$878$	−19.3046	−	1.38069i	−0.651499	−	0.0465961i
$879$	2.73682	−	1.75884i	0.0923105	−	0.0593244i
$880$	−1.93771	−	14.1669i	−0.0653203	−	0.477567i
$881$	−4.84480	−	0.696578i	−0.163226	−	0.0234683i	0.0602175	−	0.998185i	$-0.480821\pi$
$881$	−4.84480	−	0.696578i	−0.163226	−	0.0234683i	−0.223443	+	0.974717i	$0.571730\pi$
$882$	26.5698	+	14.5082i	0.894652	+	0.488517i
$883$	−12.6305	+	2.74759i	−0.425049	+	0.0924638i	−0.420001	−	0.907523i	$-0.637970\pi$
$883$	−12.6305	+	2.74759i	−0.425049	+	0.0924638i	−0.00504789	+	0.999987i	$0.501607\pi$
$884$	−1.76799	−	12.2967i	−0.0594641	−	0.413582i
$885$	−12.7020	+	6.82304i	−0.426974	+	0.229354i
$886$	−13.4246	−	29.3959i	−0.451009	−	0.987573i
$887$	1.79157	−	2.39326i	0.0601551	−	0.0803578i	−0.769455	−	0.638701i	$-0.779472\pi$
$887$	1.79157	−	2.39326i	0.0601551	−	0.0803578i	0.829610	+	0.558343i	$0.188563\pi$
$888$	−0.0216580	−	0.0995604i	−0.000726796	−	0.00334103i
$889$	0.912467	−	0.267924i	0.0306032	−	0.00898590i
$890$	−20.2669	−	1.58945i	−0.679348	−	0.0532785i
$891$	−3.06696	−	2.65754i	−0.102747	−	0.0890309i
$892$	−18.2562	−	3.97140i	−0.611264	−	0.132972i
$893$	−0.367117	+	5.13297i	−0.0122851	+	0.171768i
$894$	−9.62614	−	2.82649i	−0.321946	−	0.0945320i
$895$	−9.24755	−	20.6229i	−0.309111	−	0.689346i
$896$			0.656662i			0.0219375i
$897$	4.72744	−	9.29073i	0.157845	−	0.310208i
$898$	−23.3938	+	23.3938i	−0.780662	+	0.780662i
$899$	−3.66501	−	1.67376i	−0.122235	−	0.0558229i
$900$	−2.97241	+	18.8339i	−0.0990803	+	0.627796i
$901$	14.8727	+	17.1641i	0.495483	+	0.571818i
$902$	−1.35613	+	6.23403i	−0.0451542	+	0.207571i
$903$	−0.0882896	−	1.23445i	−0.00293809	−	0.0410799i
$904$	0.0640701	−	0.445617i	0.00213094	−	0.0148210i
$905$	−19.3051	+	41.5156i	−0.641723	+	1.38002i
$906$	16.1581	+	10.3842i	0.536816	+	0.344991i
$907$	17.9222	+	13.4164i	0.595096	+	0.445484i	0.853893	−	0.520448i	$-0.174235\pi$
$907$	17.9222	+	13.4164i	0.595096	+	0.445484i	−0.258797	+	0.965932i	$0.583326\pi$
$908$	−12.1884	+	32.6783i	−0.404486	+	1.08447i
$909$	38.5578	−	17.6087i	1.27888	−	0.584045i
$910$	0.310195	+	1.47462i	0.0102829	+	0.0488831i
$911$	−19.1739	+	29.8351i	−0.635259	+	0.988483i	0.363130	+	0.931739i	$0.381708\pi$
$911$	−19.1739	+	29.8351i	−0.635259	+	0.988483i	−0.998389	+	0.0567439i	$0.981928\pi$
$912$	9.84811	−	18.0355i	0.326104	−	0.597214i
$913$	−5.94340	−	7.93945i	−0.196698	−	0.262757i
$914$	29.6691	−	34.2399i	0.981366	−	1.13256i
$915$	12.6049	+	17.0814i	0.416704	+	0.564692i
$916$	−9.38353	+	8.13088i	−0.310041	+	0.268652i
$917$	2.45580	−	1.34097i	0.0810978	−	0.0442827i
$918$	23.7615	−	8.86259i	0.784247	−	0.292509i
$919$	−12.6364			−0.416838			−0.208419	−	0.978040i	$-0.566832\pi$
$919$	−12.6364			−0.416838			−0.208419	+	0.978040i	$0.566832\pi$
$920$	−3.58325	−	5.31204i	−0.118136	−	0.175133i
$921$	−13.2845			−0.437739
$922$	7.94311	−	2.96263i	0.261592	−	0.0975689i
$923$	6.10714	−	3.33475i	0.201019	−	0.109765i
$924$	−0.216051	+	0.187209i	−0.00710756	+	0.00615874i
$925$	−0.986161	−	0.0841568i	−0.0324248	−	0.00276706i
$926$	3.60484	−	4.16021i	0.118462	−	0.136713i
$927$	−10.5455	−	14.0871i	−0.346360	−	0.462682i
$928$	21.3004	−	39.0088i	0.699220	−	1.28053i
$929$	6.65636	−	10.3575i	0.218388	−	0.339818i	−0.714723	−	0.699408i	$-0.753447\pi$
$929$	6.65636	−	10.3575i	0.218388	−	0.339818i	0.933110	+	0.359590i	$0.117083\pi$
$930$	−1.37382	+	2.10577i	−0.0450492	+	0.0690509i
$931$	−33.4710	+	15.2857i	−1.09697	+	0.500969i
$932$	−11.3559	+	30.4463i	−0.371975	+	0.997302i
$933$	14.5005	+	10.8549i	0.474725	+	0.355375i
$934$	−30.9314	−	19.8784i	−1.01211	−	0.650441i
$935$	3.15961	+	8.65222i	0.103330	+	0.282958i
$936$	0.484464	−	3.36952i	0.0158352	−	0.110136i
$937$	−1.38896	−	19.4202i	−0.0453753	−	0.634430i	−0.968354	−	0.249580i	$-0.919708\pi$
$937$	−1.38896	−	19.4202i	−0.0453753	−	0.634430i	0.922979	−	0.384850i	$-0.125747\pi$
$938$	0.857705	−	3.94281i	0.0280051	−	0.128737i
$939$	−10.0059	−	11.5474i	−0.326530	−	0.376835i
$940$	3.59716	+	0.808419i	0.117326	+	0.0263677i
$941$	−31.0156	−	14.1644i	−1.01108	−	0.461745i	−0.160189	−	0.987086i	$-0.551210\pi$
$941$	−31.0156	−	14.1644i	−1.01108	−	0.461745i	−0.850892	+	0.525341i	$0.823938\pi$
$942$	−8.09447	+	8.09447i	−0.263732	+	0.263732i
$943$	2.71601	+	10.9417i	0.0884456	+	0.356310i
$944$			33.8742i			1.10251i
$945$	−1.28508	+	0.576248i	−0.0418038	+	0.0187453i
$946$	26.9036	+	7.89962i	0.874712	+	0.256839i
$947$	−2.26086	+	31.6110i	−0.0734682	+	1.02722i	0.818319	+	0.574765i	$0.194906\pi$
$947$	−2.26086	+	31.6110i	−0.0734682	+	1.02722i	−0.891787	+	0.452455i	$0.850548\pi$
$948$	11.2648	+	2.45050i	0.365862	+	0.0795885i
$949$	24.9767	+	21.6424i	0.810778	+	0.702543i
$950$	−35.2991	−	36.2821i	−1.14526	−	1.17715i
$951$	8.92637	−	2.62102i	0.289457	−	0.0849923i
$952$	−0.0514872	−	0.236683i	−0.00166871	−	0.00767094i
$953$	9.21604	−	12.3112i	0.298537	−	0.398798i	−0.626042	−	0.779789i	$-0.715326\pi$
$953$	9.21604	−	12.3112i	0.298537	−	0.398798i	0.924579	+	0.380991i	$0.124417\pi$
$954$	−14.0350	−	30.7323i	−0.454399	−	0.994995i
$955$	36.8702	+	11.1016i	1.19309	+	0.359239i
$956$	−6.53643	−	45.4619i	−0.211403	−	1.47034i
$957$	−7.05178	+	1.53402i	−0.227952	+	0.0495878i
$958$	−11.7882	−	6.43685i	−0.380860	−	0.207965i
$959$	−2.15879	−	0.310387i	−0.0697109	−	0.0100229i
$960$	−8.20387	−	6.22968i	−0.264779	−	0.201062i
$961$	−25.6903	+	16.5102i	−0.828720	+	0.532586i
$962$	−0.956866	−	0.0684364i	−0.0308506	−	0.00220648i
$963$	1.57823	+	2.89032i	0.0508578	+	0.0931391i
$964$	−14.5461	+	31.8516i	−0.468500	+	1.02587i
$965$	−56.3049	+	3.63863i	−1.81252	+	0.117132i
$966$	−0.428960	+	1.01660i	−0.0138015	+	0.0327085i
$967$	−0.252852	−	0.252852i	−0.00813118	−	0.00813118i	0.703030	−	0.711161i	$-0.251830\pi$
$967$	−0.252852	−	0.252852i	−0.00813118	−	0.00813118i	−0.711161	+	0.703030i	$0.751830\pi$
$968$	−1.87997	−	5.04040i	−0.0604245	−	0.162004i
$969$	−3.72941	+	12.7012i	−0.119806	+	0.408021i
$970$	0.104545	−	15.2265i	0.00335674	−	0.488894i
$971$	32.9812	+	51.3198i	1.05842	+	1.64693i	0.701290	+	0.712877i	$0.252608\pi$
$971$	32.9812	+	51.3198i	1.05842	+	1.64693i	0.357129	+	0.934055i	$0.383756\pi$
$972$	−27.0583	+	1.93525i	−0.867897	+	0.0620732i
$973$	−1.07100	+	0.801738i	−0.0343346	+	0.0257025i
$974$	−6.33223	−	21.5656i	−0.202898	−	0.691007i
$975$	9.82305	+	4.65009i	0.314589	+	0.148922i
$976$	49.3658	−	7.09773i	1.58016	−	0.227193i
$977$	28.8576	+	10.7633i	0.923237	+	0.344350i	0.765725	−	0.643168i	$-0.222380\pi$
$977$	28.8576	+	10.7633i	0.923237	+	0.344350i	0.157511	+	0.987517i	$0.449653\pi$
$978$	−23.5658	−	8.78959i	−0.753552	−	0.281060i
$979$	6.62062	−	0.951902i	0.211596	−	0.0304229i
$980$	7.25332	+	25.3450i	0.231699	+	0.809616i
$981$	−11.3173	−	38.5431i	−0.361333	−	1.23059i
$982$	−42.5307	+	31.8381i	−1.35721	+	1.01600i
$983$	28.2539	−	2.02076i	0.901159	−	0.0644522i	0.386934	−	0.922107i	$-0.373534\pi$
$983$	28.2539	−	2.02076i	0.901159	−	0.0644522i	0.514225	+	0.857655i	$0.328080\pi$
$984$	−0.654164	−	1.01790i	−0.0208540	−	0.0324494i
$985$	−30.5506	+	30.1340i	−0.973424	+	0.960148i
$986$	−9.35212	+	31.8504i	−0.297832	+	1.01432i
$987$	0.0408686	+	0.109573i	0.00130086	+	0.00348775i
$988$	−15.8837	−	15.8837i	−0.505329	−	0.505329i
$989$	48.8179	−	8.47587i	1.55232	−	0.269517i
$990$	−0.883659	−	13.6739i	−0.0280845	−	0.434586i
$991$	14.2894	−	31.2894i	0.453917	−	0.993940i	−0.534915	−	0.844906i	$-0.679656\pi$
$991$	14.2894	−	31.2894i	0.453917	−	0.993940i	0.988832	−	0.149034i	$-0.0476163\pi$
$992$	2.44167	+	4.47158i	0.0775231	+	0.141973i
$993$	−15.7092	−	1.12355i	−0.498517	−	0.0356546i
$994$	−0.619600	+	0.398193i	−0.0196525	+	0.0126299i
$995$	−37.8929	+	5.18289i	−1.20128	+	0.164309i
$996$	−10.1074	−	1.45322i	−0.320264	−	0.0460470i
$997$	9.24362	+	5.04740i	0.292748	+	0.159853i	0.618911	−	0.785461i	$-0.287574\pi$
$997$	9.24362	+	5.04740i	0.292748	+	0.159853i	−0.326163	+	0.945314i	$0.605756\pi$
$998$	0.710615	−	0.154585i	0.0224941	−	0.00489330i
$999$	−0.127598	−	0.887464i	−0.00403702	−	0.0280781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.17.9	✓	200
5.2	odd	4		575.2.r.b.293.9		200
5.3	odd	4	inner	115.2.l.a.63.2	yes	200
5.4	even	2		575.2.r.b.132.2		200
23.19	odd	22	inner	115.2.l.a.42.2	yes	200
115.19	odd	22		575.2.r.b.157.9		200
115.42	even	44		575.2.r.b.318.2		200
115.88	even	44	inner	115.2.l.a.88.9	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.17.9	✓	200	1.1	even	1	trivial
115.2.l.a.42.2	yes	200	23.19	odd	22	inner
115.2.l.a.63.2	yes	200	5.3	odd	4	inner
115.2.l.a.88.9	yes	200	115.88	even	44	inner
575.2.r.b.132.2		200	5.4	even	2
575.2.r.b.157.9		200	115.19	odd	22
575.2.r.b.293.9		200	5.2	odd	4
575.2.r.b.318.2		200	115.42	even	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.79955 - 0.671199i) q^{2} +(0.756071 - 0.412846i) q^{3} +(1.27639 - 1.10600i) q^{4} +(-2.21107 - 0.333414i) q^{5} +(1.08349 - 1.25041i) q^{6} +(-0.0833334 - 0.111320i) q^{7} +(-0.286357 + 0.524424i) q^{8} +(-1.22072 + 1.89948i) q^{9} +O(q^{10})\)	\(q+(1.79955 - 0.671199i) q^{2} +(0.756071 - 0.412846i) q^{3} +(1.27639 - 1.10600i) q^{4} +(-2.21107 - 0.333414i) q^{5} +(1.08349 - 1.25041i) q^{6} +(-0.0833334 - 0.111320i) q^{7} +(-0.286357 + 0.524424i) q^{8} +(-1.22072 + 1.89948i) q^{9} +(-4.20273 + 0.884071i) q^{10} +(1.28535 - 0.587001i) q^{11} +(0.508433 - 1.36316i) q^{12} +(2.01995 + 1.51212i) q^{13} +(-0.224681 - 0.144394i) q^{14} +(-1.80937 + 0.660746i) q^{15} +(-0.644034 + 4.47935i) q^{16} +(-0.207968 - 2.90778i) q^{17} +(-0.921825 + 4.23756i) q^{18} +(-3.45188 - 3.98368i) q^{19} +(-3.19094 + 2.01987i) q^{20} +(-0.108964 - 0.0497622i) q^{21} +(1.91907 - 1.91907i) q^{22} +(1.54448 - 4.54033i) q^{23} +0.514723i q^{24} +(4.77767 + 1.47441i) q^{25} +(4.64994 + 1.36535i) q^{26} +(-0.323123 + 4.51785i) q^{27} +(-0.229485 - 0.0499215i) q^{28} +(-4.48057 - 3.88244i) q^{29} +(-2.81257 + 2.40350i) q^{30} +(0.652073 - 0.191466i) q^{31} +(1.59354 + 7.32540i) q^{32} +(0.729477 - 0.974467i) q^{33} +(-2.32595 - 5.09311i) q^{34} +(0.147140 + 0.273922i) q^{35} +(0.542703 + 3.77458i) q^{36} +(-0.193425 + 0.0420771i) q^{37} +(-8.88569 - 4.85195i) q^{38} +(2.15150 + 0.309338i) q^{39} +(0.808006 - 1.06406i) q^{40} +(-1.97757 + 1.27090i) q^{41} +(-0.229487 - 0.0164132i) q^{42} +(4.95137 + 9.06775i) q^{43} +(0.991387 - 2.17083i) q^{44} +(3.33242 - 3.79288i) q^{45} +(-0.268088 - 9.20722i) q^{46} +(-0.690327 - 0.690327i) q^{47} +(1.36235 + 3.65259i) q^{48} +(1.96668 - 6.69790i) q^{49} +(9.58729 - 0.553495i) q^{50} +(-1.35770 - 2.11263i) q^{51} +(4.25063 - 0.304011i) q^{52} +(-6.23673 + 4.66876i) q^{53} +(2.45090 + 8.34700i) q^{54} +(-3.03772 + 0.869346i) q^{55} +(0.0822422 - 0.0118246i) q^{56} +(-4.25451 - 1.58685i) q^{57} +(-10.6689 - 3.97930i) q^{58} +(7.40914 - 1.06527i) q^{59} +(-1.57868 + 2.84453i) q^{60} +(-3.10490 - 10.5743i) q^{61} +(1.04493 - 0.782224i) q^{62} +(0.313178 - 0.0223989i) q^{63} +(2.89121 + 4.49882i) q^{64} +(-3.96209 - 4.01688i) q^{65} +(0.658671 - 2.24323i) q^{66} +(5.27969 + 14.1554i) q^{67} +(-3.48144 - 3.48144i) q^{68} +(-0.706719 - 4.07044i) q^{69} +(0.448643 + 0.394177i) q^{70} +(1.14559 - 2.50848i) q^{71} +(-0.646570 - 1.18411i) q^{72} +(13.0645 + 0.934391i) q^{73} +(-0.319837 + 0.205547i) q^{74} +(4.22096 - 0.857686i) q^{75} +(-8.81187 - 1.26695i) q^{76} +(-0.172458 - 0.0941692i) q^{77} +(4.07936 - 0.887410i) q^{78} +(1.12767 + 7.84310i) q^{79} +(2.91748 - 9.68944i) q^{80} +(-1.19304 - 2.61240i) q^{81} +(-2.70571 + 3.61440i) q^{82} +(-1.49191 - 6.85819i) q^{83} +(-0.194117 + 0.0569979i) q^{84} +(-0.509662 + 6.49864i) q^{85} +(14.9965 + 12.9946i) q^{86} +(-4.99047 - 1.08561i) q^{87} +(-0.0602326 + 0.842162i) q^{88} +(4.54179 + 1.33359i) q^{89} +(3.45109 - 9.06220i) q^{90} -0.350871i q^{91} +(-3.05023 - 7.50340i) q^{92} +(0.413967 - 0.413967i) q^{93} +(-1.70563 - 0.778934i) q^{94} +(6.30414 + 9.95911i) q^{95} +(4.22909 + 4.88063i) q^{96} +(-0.753650 + 3.46447i) q^{97} +(-0.956474 - 13.3733i) q^{98} +(-0.454061 + 3.15807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more