LMFDB - Embedded newform 380.2.bb.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.1
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41344 - 0.0466259i) q^{2} +(-1.17302 + 1.39795i) q^{3} +(1.99565 + 0.131806i) q^{4} +(-1.08439 - 1.95553i) q^{5} +(1.72317 - 1.92123i) q^{6} +(1.36812 + 2.36965i) q^{7} +(-2.81460 - 0.279350i) q^{8} +(-0.0573416 - 0.325200i) q^{9} +O(q^{10})$	\(q+(-1.41344 - 0.0466259i) q^{2} +(-1.17302 + 1.39795i) q^{3} +(1.99565 + 0.131806i) q^{4} +(-1.08439 - 1.95553i) q^{5} +(1.72317 - 1.92123i) q^{6} +(1.36812 + 2.36965i) q^{7} +(-2.81460 - 0.279350i) q^{8} +(-0.0573416 - 0.325200i) q^{9} +(1.44155 + 2.81459i) q^{10} +(-2.24016 - 1.29335i) q^{11} +(-2.52519 + 2.63520i) q^{12} +(-0.527993 + 0.443038i) q^{13} +(-1.82327 - 3.41316i) q^{14} +(4.00573 + 0.777939i) q^{15} +(3.96525 + 0.526079i) q^{16} +(0.544629 + 0.0960328i) q^{17} +(0.0658864 + 0.462326i) q^{18} +(-1.26967 + 4.16989i) q^{19} +(-1.90632 - 4.04548i) q^{20} +(-4.91747 - 0.867083i) q^{21} +(3.10603 + 1.93253i) q^{22} +(0.366941 + 0.133555i) q^{23} +(3.69208 - 3.60697i) q^{24} +(-2.64818 + 4.24113i) q^{25} +(0.766946 - 0.601592i) q^{26} +(-4.21932 - 2.43603i) q^{27} +(2.41796 + 4.90933i) q^{28} +(-8.63898 + 1.52328i) q^{29} +(-5.62561 - 1.28635i) q^{30} +(-4.91391 - 8.51114i) q^{31} +(-5.58014 - 0.928468i) q^{32} +(4.43578 - 1.61449i) q^{33} +(-0.765325 - 0.161131i) q^{34} +(3.15034 - 5.24504i) q^{35} +(-0.0715704 - 0.656544i) q^{36} -9.48947 q^{37} +(1.98903 - 5.83470i) q^{38} -1.25780i q^{39} +(2.50586 + 5.80695i) q^{40} +(-3.19809 + 3.81133i) q^{41} +(6.91015 + 1.45486i) q^{42} +(-2.46866 + 0.898519i) q^{43} +(-4.30010 - 2.87635i) q^{44} +(-0.573757 + 0.464779i) q^{45} +(-0.512423 - 0.205882i) q^{46} +(-0.347487 - 1.97070i) q^{47} +(-5.38673 + 4.92611i) q^{48} +(-0.243505 + 0.421764i) q^{49} +(3.94080 - 5.87113i) q^{50} +(-0.773107 + 0.648714i) q^{51} +(-1.11208 + 0.814558i) q^{52} +(9.32287 + 3.39325i) q^{53} +(5.85020 + 3.63992i) q^{54} +(-0.0999769 + 5.78319i) q^{55} +(-3.18875 - 7.05181i) q^{56} +(-4.33993 - 6.66626i) q^{57} +(12.2817 - 1.75028i) q^{58} +(-1.22506 + 6.94767i) q^{59} +(7.89151 + 2.08048i) q^{60} +(-1.23607 - 0.449894i) q^{61} +(6.54870 + 12.2591i) q^{62} +(0.692162 - 0.580793i) q^{63} +(7.84393 + 1.57252i) q^{64} +(1.43893 + 0.552076i) q^{65} +(-6.34500 + 2.07517i) q^{66} +(3.08193 - 0.543427i) q^{67} +(1.07423 + 0.263434i) q^{68} +(-0.617130 + 0.356300i) q^{69} +(-4.69739 + 7.26668i) q^{70} +(-3.62520 + 1.31947i) q^{71} +(0.0705488 + 0.931326i) q^{72} +(-5.31372 + 6.33264i) q^{73} +(13.4128 + 0.442455i) q^{74} +(-2.82251 - 8.67691i) q^{75} +(-3.08343 + 8.15429i) q^{76} -7.07786i q^{77} +(-0.0586459 + 1.77783i) q^{78} +(9.44434 + 7.92474i) q^{79} +(-3.27114 - 8.32464i) q^{80} +(9.28567 - 3.37971i) q^{81} +(4.69803 - 5.23799i) q^{82} +(-0.643215 - 1.11408i) q^{83} +(-9.69928 - 2.37855i) q^{84} +(-0.402798 - 1.16917i) q^{85} +(3.53121 - 1.15490i) q^{86} +(8.00419 - 13.8637i) q^{87} +(5.94384 + 4.26606i) q^{88} +(7.29789 + 8.69728i) q^{89} +(0.832645 - 0.630187i) q^{90} +(-1.77221 - 0.645030i) q^{91} +(0.714682 + 0.314895i) q^{92} +(17.6622 + 3.11432i) q^{93} +(0.399268 + 2.80167i) q^{94} +(9.53115 - 2.03894i) q^{95} +(7.84354 - 6.71162i) q^{96} +(1.36674 - 7.75117i) q^{97} +(0.363846 - 0.584786i) q^{98} +(-0.292145 + 0.802662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$

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 $

$2$	−1.41344	−	0.0466259i	−0.999456	−	0.0329695i
$2$	−1.41344	−	0.0466259i	−0.999456	−	0.0329695i
$3$	−1.17302	+	1.39795i	−0.677241	+	0.807104i	−0.989750	−	0.142811i	$-0.954386\pi$
$3$	−1.17302	+	1.39795i	−0.677241	+	0.807104i	0.312509	+	0.949915i	$0.398830\pi$
$4$	1.99565	+	0.131806i	0.997826	+	0.0659032i
$5$	−1.08439	−	1.95553i	−0.484956	−	0.874538i
$5$	−1.08439	−	1.95553i	−0.484956	−	0.874538i
$6$	1.72317	−	1.92123i	0.703482	−	0.784337i
$7$	1.36812	+	2.36965i	0.517101	+	0.895645i	0.999803	+	0.0198602i	$0.00632211\pi$
$7$	1.36812	+	2.36965i	0.517101	+	0.895645i	−0.482702	+	0.875785i	$0.660345\pi$
$8$	−2.81460	−	0.279350i	−0.995111	−	0.0987652i
$9$	−0.0573416	−	0.325200i	−0.0191139	−	0.108400i
$10$	1.44155	+	2.81459i	0.455859	+	0.890052i
$11$	−2.24016	−	1.29335i	−0.675433	−	0.389961i	0.122699	−	0.992444i	$-0.460845\pi$
$11$	−2.24016	−	1.29335i	−0.675433	−	0.389961i	−0.798132	+	0.602483i	$0.794178\pi$
$12$	−2.52519	+	2.63520i	−0.728959	+	0.760717i
$13$	−0.527993	+	0.443038i	−0.146439	+	0.122877i	−0.713064	−	0.701099i	$-0.752693\pi$
$13$	−0.527993	+	0.443038i	−0.146439	+	0.122877i	0.566625	+	0.823976i	$0.308249\pi$
$14$	−1.82327	−	3.41316i	−0.487291	−	0.912207i
$15$	4.00573	+	0.777939i	1.03428	+	0.200863i
$16$	3.96525	+	0.526079i	0.991314	+	0.131520i
$17$	0.544629	+	0.0960328i	0.132092	+	0.0232914i	0.239303	−	0.970945i	$-0.423081\pi$
$17$	0.544629	+	0.0960328i	0.132092	+	0.0232914i	−0.107211	+	0.994236i	$0.534192\pi$
$18$	0.0658864	+	0.462326i	0.0155296	+	0.108971i
$19$	−1.26967	+	4.16989i	−0.291281	+	0.956637i
$19$	−1.26967	+	4.16989i	−0.291281	+	0.956637i
$20$	−1.90632	−	4.04548i	−0.426267	−	0.904597i
$21$	−4.91747	−	0.867083i	−1.07308	−	0.189213i
$22$	3.10603	+	1.93253i	0.662208	+	0.412018i
$23$	0.366941	+	0.133555i	0.0765124	+	0.0278482i	0.379993	−	0.924989i	$-0.375926\pi$
$23$	0.366941	+	0.133555i	0.0765124	+	0.0278482i	−0.303480	+	0.952838i	$0.598149\pi$
$24$	3.69208	−	3.60697i	0.753643	−	0.736270i
$25$	−2.64818	+	4.24113i	−0.529635	+	0.848226i
$26$	0.766946	−	0.601592i	0.150410	−	0.117982i
$27$	−4.21932	−	2.43603i	−0.812009	−	0.468814i
$28$	2.41796	+	4.90933i	0.456951	+	0.927776i
$29$	−8.63898	+	1.52328i	−1.60422	+	0.282867i	−0.902857	−	0.429940i	$-0.858535\pi$
$29$	−8.63898	+	1.52328i	−1.60422	+	0.282867i	−0.701360	+	0.712807i	$0.747424\pi$
$30$	−5.62561	−	1.28635i	−1.02709	−	0.234853i
$31$	−4.91391	−	8.51114i	−0.882564	−	1.52865i	−0.848481	−	0.529226i	$-0.822482\pi$
$31$	−4.91391	−	8.51114i	−0.882564	−	1.52865i	−0.0340829	−	0.999419i	$-0.510851\pi$
$32$	−5.58014	−	0.928468i	−0.986438	−	0.164131i
$33$	4.43578	−	1.61449i	0.772170	−	0.281047i
$34$	−0.765325	−	0.161131i	−0.131252	−	0.0276337i
$35$	3.15034	−	5.24504i	0.532505	−	0.886573i
$36$	−0.0715704	−	0.656544i	−0.0119284	−	0.109424i
$37$	−9.48947			−1.56006			−0.780030	−	0.625743i	$-0.784796\pi$
$37$	−9.48947			−1.56006			−0.780030	+	0.625743i	$0.784796\pi$
$38$	1.98903	−	5.83470i	0.322663	−	0.946514i
$39$		−	1.25780i		−	0.201409i
$40$	2.50586	+	5.80695i	0.396211	+	0.918159i
$41$	−3.19809	+	3.81133i	−0.499457	+	0.595230i	−0.955596	−	0.294678i	$-0.904787\pi$
$41$	−3.19809	+	3.81133i	−0.499457	+	0.595230i	0.456139	+	0.889908i	$0.349232\pi$
$42$	6.91015	+	1.45486i	1.06626	+	0.224489i
$43$	−2.46866	+	0.898519i	−0.376467	+	0.137023i	−0.523322	−	0.852135i	$-0.675307\pi$
$43$	−2.46866	+	0.898519i	−0.376467	+	0.137023i	0.146854	+	0.989158i	$0.453085\pi$
$44$	−4.30010	−	2.87635i	−0.648264	−	0.433627i
$45$	−0.573757	+	0.464779i	−0.0855307	+	0.0692851i
$46$	−0.512423	−	0.205882i	−0.0755527	−	0.0303557i
$47$	−0.347487	−	1.97070i	−0.0506862	−	0.287456i	0.948920	−	0.315517i	$-0.102178\pi$
$47$	−0.347487	−	1.97070i	−0.0506862	−	0.287456i	−0.999606	+	0.0280610i	$0.991067\pi$
$48$	−5.38673	+	4.92611i	−0.777508	+	0.711023i
$49$	−0.243505	+	0.421764i	−0.0347865	+	0.0602519i
$50$	3.94080	−	5.87113i	0.557313	−	0.830303i
$51$	−0.773107	+	0.648714i	−0.108257	+	0.0908381i
$52$	−1.11208	+	0.814558i	−0.154218	+	0.112959i
$53$	9.32287	+	3.39325i	1.28059	+	0.466098i	0.890629	−	0.454731i	$-0.150265\pi$
$53$	9.32287	+	3.39325i	1.28059	+	0.466098i	0.389966	+	0.920829i	$0.372487\pi$
$54$	5.85020	+	3.63992i	0.796111	+	0.495330i
$55$	−0.0999769	+	5.78319i	−0.0134809	+	0.779806i
$56$	−3.18875	−	7.05181i	−0.426114	−	0.942337i
$57$	−4.33993	−	6.66626i	−0.574838	−	0.882968i
$58$	12.2817	−	1.75028i	1.61267	−	0.229823i
$59$	−1.22506	+	6.94767i	−0.159490	+	0.904510i	0.795076	+	0.606510i	$0.207431\pi$
$59$	−1.22506	+	6.94767i	−0.159490	+	0.904510i	−0.954566	+	0.298000i	$0.903680\pi$
$60$	7.89151	+	2.08048i	1.01879	+	0.268588i
$61$	−1.23607	−	0.449894i	−0.158263	−	0.0576031i	0.261674	−	0.965156i	$-0.415726\pi$
$61$	−1.23607	−	0.449894i	−0.158263	−	0.0576031i	−0.419937	+	0.907553i	$0.637948\pi$
$62$	6.54870	+	12.2591i	0.831685	+	1.55691i
$63$	0.692162	−	0.580793i	0.0872042	−	0.0731730i
$64$	7.84393	+	1.57252i	0.980491	+	0.196565i
$65$	1.43893	+	0.552076i	0.178477	+	0.0684765i
$66$	−6.34500	+	2.07517i	−0.781016	+	0.255436i
$67$	3.08193	−	0.543427i	0.376518	−	0.0663902i	0.0178130	−	0.999841i	$-0.494330\pi$
$67$	3.08193	−	0.543427i	0.376518	−	0.0663902i	0.358705	+	0.933451i	$0.383219\pi$
$68$	1.07423	+	0.263434i	0.130270	+	0.0319460i
$69$	−0.617130	+	0.356300i	−0.0742938	+	0.0428935i
$70$	−4.69739	+	7.26668i	−0.561445	+	0.868535i
$71$	−3.62520	+	1.31947i	−0.430233	+	0.156592i	−0.548054	−	0.836443i	$-0.684631\pi$
$71$	−3.62520	+	1.31947i	−0.430233	+	0.156592i	0.117821	+	0.993035i	$0.462409\pi$
$72$	0.0705488	+	0.931326i	0.00831425	+	0.109758i
$73$	−5.31372	+	6.33264i	−0.621924	+	0.741180i	−0.981400	−	0.191974i	$-0.938511\pi$
$73$	−5.31372	+	6.33264i	−0.621924	+	0.741180i	0.359476	+	0.933154i	$0.382955\pi$
$74$	13.4128	+	0.442455i	1.55921	+	0.0514344i
$75$	−2.82251	−	8.67691i	−0.325916	−	1.00192i
$76$	−3.08343	+	8.15429i	−0.353694	+	0.935361i
$77$		−	7.07786i		−	0.806597i
$78$	−0.0586459	+	1.77783i	−0.00664034	+	0.201299i
$79$	9.44434	+	7.92474i	1.06257	+	0.891603i	0.994359	−	0.106068i	$-0.0338260\pi$
$79$	9.44434	+	7.92474i	1.06257	+	0.891603i	0.0682124	+	0.997671i	$0.478270\pi$
$80$	−3.27114	−	8.32464i	−0.365724	−	0.930723i
$81$	9.28567	−	3.37971i	1.03174	−	0.375523i
$82$	4.69803	−	5.23799i	0.518810	−	0.578440i
$83$	−0.643215	−	1.11408i	−0.0706020	−	0.122286i	0.828563	−	0.559895i	$-0.189159\pi$
$83$	−0.643215	−	1.11408i	−0.0706020	−	0.122286i	−0.899165	+	0.437609i	$0.855825\pi$
$84$	−9.69928	−	2.37855i	−1.05828	−	0.259521i
$85$	−0.402798	−	1.16917i	−0.0436896	−	0.126815i
$86$	3.53121	−	1.15490i	0.380780	−	0.124536i
$87$	8.00419	−	13.8637i	0.858139	−	1.48634i
$88$	5.94384	+	4.26606i	0.633616	+	0.454764i
$89$	7.29789	+	8.69728i	0.773574	+	0.921910i	0.998624	−	0.0524373i	$-0.0166990\pi$
$89$	7.29789	+	8.69728i	0.773574	+	0.921910i	−0.225050	+	0.974347i	$0.572255\pi$
$90$	0.832645	−	0.630187i	0.0877685	−	0.0664275i
$91$	−1.77221	−	0.645030i	−0.185778	−	0.0676175i
$92$	0.714682	+	0.314895i	0.0745108	+	0.0328301i
$93$	17.6622	+	3.11432i	1.83148	+	0.322940i
$94$	0.399268	+	2.80167i	0.0411814	+	0.288971i
$95$	9.53115	−	2.03894i	0.977875	−	0.209190i
$96$	7.84354	−	6.71162i	0.800528	−	0.685002i
$97$	1.36674	−	7.75117i	0.138772	−	0.787012i	−0.833387	−	0.552689i	$-0.813602\pi$
$97$	1.36674	−	7.75117i	0.138772	−	0.787012i	0.972159	−	0.234323i	$-0.0752873\pi$
$98$	0.363846	−	0.584786i	0.0367540	−	0.0590723i
$99$	−0.292145	+	0.802662i	−0.0293617	+	0.0806706i
$100$	−5.84384	+	8.11477i	−0.584384	+	0.811477i
$101$	5.70389	−	4.78613i	0.567558	−	0.476238i	−0.313276	−	0.949662i	$-0.601427\pi$
$101$	5.70389	−	4.78613i	0.567558	−	0.476238i	0.880835	+	0.473424i	$0.156982\pi$
$102$	1.12299	−	0.880874i	0.111193	−	0.0872195i
$103$	9.76852	+	5.63986i	0.962521	+	0.555712i	0.896948	−	0.442136i	$-0.145779\pi$
$103$	9.76852	+	5.63986i	0.962521	+	0.555712i	0.0655730	+	0.997848i	$0.479112\pi$
$104$	1.60985	−	1.09948i	0.157859	−	0.107813i
$105$	3.63688	+	10.5565i	0.354923	+	1.03021i
$106$	−13.0192	−	5.23086i	−1.26453	−	0.508066i
$107$	−8.30629	+	4.79564i	−0.802999	+	0.463612i	−0.844519	−	0.535526i	$-0.820113\pi$
$107$	−8.30629	+	4.79564i	−0.802999	+	0.463612i	0.0415197	+	0.999138i	$0.486780\pi$
$108$	−8.09922	−	5.41760i	−0.779348	−	0.521309i
$109$	−4.54408	−	12.4848i	−0.435244	−	1.19582i	−0.942552	−	0.334059i	$-0.891582\pi$
$109$	−4.54408	−	12.4848i	−0.435244	−	1.19582i	0.507308	−	0.861765i	$-0.330641\pi$
$110$	0.410959	−	8.16956i	0.0391834	−	0.778937i
$111$	11.1313	−	13.2658i	1.05654	−	1.25913i
$112$	4.17832	+	10.1160i	0.394814	+	0.955874i
$113$	−16.7648			−1.57710			−0.788551	−	0.614970i	$-0.789168\pi$
$113$	−16.7648			−1.57710			−0.788551	+	0.614970i	$0.789168\pi$
$114$	5.82344	+	9.62475i	0.545415	+	0.901440i
$115$	−0.136737	−	0.862390i	−0.0127508	−	0.0804182i
$116$	−17.4412	+	1.90127i	−1.61937	+	0.176529i
$117$	0.174352	+	0.146299i	0.0161189	+	0.0135253i
$118$	2.05550	−	9.76303i	0.189224	−	0.898760i
$119$	0.517554	+	1.42197i	0.0474441	+	0.130351i
$120$	−11.0572	−	3.30859i	−1.00938	−	0.302031i
$121$	−2.15447	−	3.73165i	−0.195861	−	0.339241i
$122$	1.72615	+	0.693534i	0.156278	+	0.0627896i
$123$	−1.57663	−	8.94150i	−0.142160	−	0.806228i
$124$	−8.68463	−	17.6330i	−0.779902	−	1.58349i
$125$	11.1653	+	0.579522i	0.998656	+	0.0518340i
$126$	−1.00541	+	0.788646i	−0.0895693	+	0.0702581i
$127$	13.1642	+	15.6884i	1.16813	+	1.39212i	0.903944	+	0.427651i	$0.140659\pi$
$127$	13.1642	+	15.6884i	1.16813	+	1.39212i	0.264186	+	0.964472i	$0.414897\pi$
$128$	−11.0136	−	2.58840i	−0.973477	−	0.228784i
$129$	1.63970	−	4.50503i	0.144367	−	0.396646i
$130$	−2.00810	−	0.847420i	−0.176122	−	0.0743236i
$131$	−0.182318	−	0.0321476i	−0.0159292	−	0.00280875i	0.165678	−	0.986180i	$-0.447019\pi$
$131$	−0.182318	−	0.0321476i	−0.0159292	−	0.00280875i	−0.181607	+	0.983371i	$0.558130\pi$
$132$	9.06507	−	2.63730i	0.789013	−	0.229547i
$133$	−11.6182	+	2.69624i	−1.00743	+	0.233793i
$134$	−4.38147	+	0.624407i	−0.378502	+	0.0539405i
$135$	−0.188306	+	10.8926i	−0.0162068	+	0.937487i
$136$	−1.50609	−	0.422436i	−0.129146	−	0.0362236i
$137$	−0.245425	+	0.674299i	−0.0209681	+	0.0576092i	−0.949735	−	0.313055i	$-0.898648\pi$
$137$	−0.245425	+	0.674299i	−0.0209681	+	0.0576092i	0.928767	+	0.370664i	$0.120870\pi$
$138$	0.888893	−	0.474837i	0.0756676	−	0.0404208i
$139$	2.54609	+	3.03431i	0.215956	+	0.257367i	0.863137	−	0.504970i	$-0.168496\pi$
$139$	2.54609	+	3.03431i	0.215956	+	0.257367i	−0.647180	+	0.762337i	$0.724052\pi$
$140$	6.97831	−	10.0520i	0.589775	−	0.849552i
$141$	3.16254	+	1.82589i	0.266334	+	0.153768i
$142$	5.18555	−	1.69596i	0.435161	−	0.142322i
$143$	1.75579	−	0.309593i	0.146827	−	0.0258895i
$144$	−0.0562928	−	1.31967i	−0.00469107	−	0.109972i
$145$	12.3469	+	15.2419i	1.02535	+	1.26577i
$146$	7.80591	−	8.70309i	0.646022	−	0.720272i
$147$	−0.303967	−	0.835142i	−0.0250708	−	0.0688814i
$148$	−18.9377	−	1.25077i	−1.55667	−	0.102813i
$149$	10.7942	+	9.05743i	0.884297	+	0.742013i	0.967058	−	0.254556i	$-0.0819293\pi$
$149$	10.7942	+	9.05743i	0.884297	+	0.742013i	−0.0827608	+	0.996569i	$0.526374\pi$
$150$	3.58490	+	12.3959i	0.292706	+	1.01212i
$151$	−15.0663			−1.22608			−0.613038	−	0.790054i	$-0.710053\pi$
$151$	−15.0663			−1.22608			−0.613038	+	0.790054i	$0.710053\pi$
$152$	4.73846	−	11.3819i	0.384340	−	0.923192i
$153$		−	0.182620i		−	0.0147640i
$154$	−0.330012	+	10.0042i	−0.0265931	+	0.806158i
$155$	−11.3151	+	18.8387i	−0.908854	+	1.51316i
$156$	0.165786	−	2.51012i	0.0132735	−	0.200971i
$157$	−6.52871	−	17.9375i	−0.521048	−	1.43157i	−0.869355	−	0.494187i	$-0.835466\pi$
$157$	−6.52871	−	17.9375i	−0.521048	−	1.43157i	0.348307	−	0.937380i	$-0.386757\pi$
$158$	−12.9796	−	11.6415i	−1.03260	−	0.926151i
$159$	−15.6794	+	9.05253i	−1.24346	+	0.717913i
$160$	4.23543	+	11.9189i	0.334840	+	0.942275i
$161$	0.185539	+	1.05224i	0.0146225	+	0.0829283i
$162$	−13.2824	+	4.34408i	−1.04356	+	0.341303i
$163$	−7.60887	+	13.1789i	−0.595972	+	1.03225i	0.397437	+	0.917630i	$0.369900\pi$
$163$	−7.60887	+	13.1789i	−0.595972	+	1.03225i	−0.993409	+	0.114625i	$0.963433\pi$
$164$	−6.88463	+	7.18457i	−0.537599	+	0.561020i
$165$	−7.96732	−	6.92354i	−0.620255	−	0.538997i
$166$	0.857203	+	1.60468i	0.0665319	+	0.124547i
$167$	−1.44630	+	3.97367i	−0.111918	+	0.307492i	−0.982989	−	0.183665i	$-0.941204\pi$
$167$	−1.44630	+	3.97367i	−0.111918	+	0.307492i	0.871071	+	0.491157i	$0.163426\pi$
$168$	13.5985	+	3.81419i	1.04915	+	0.294271i
$169$	−2.17493	+	12.3347i	−0.167303	+	0.948820i
$170$	0.514819	+	1.67134i	0.0394848	+	0.128186i
$171$	1.42885	+	0.173788i	0.109267	+	0.0132899i
$172$	−5.04502	+	1.46775i	−0.384679	+	0.111915i
$173$	−0.635695	+	3.60521i	−0.0483310	+	0.274099i	−0.999390	−	0.0349091i	$-0.988886\pi$
$173$	−0.635695	+	3.60521i	−0.0483310	+	0.274099i	0.951060	+	0.309008i	$0.0999969\pi$
$174$	−11.9599	+	19.2223i	−0.906676	+	1.45724i
$175$	−13.6730	−	0.472886i	−1.03358	−	0.0357468i
$176$	−8.20238	−	6.30698i	−0.618278	−	0.475407i
$177$	−8.27545	−	9.86230i	−0.622021	−	0.741296i
$178$	−9.90964	−	12.6334i	−0.742759	−	0.946913i
$179$	10.1085	−	17.5085i	0.755546	−	1.30864i	−0.189556	−	0.981870i	$-0.560705\pi$
$179$	10.1085	−	17.5085i	0.755546	−	1.30864i	0.945102	−	0.326775i	$-0.105962\pi$
$180$	−1.20628	+	0.851911i	−0.0899108	+	0.0634977i
$181$	21.1624	−	3.73150i	1.57299	−	0.277360i	0.681987	−	0.731364i	$-0.261116\pi$
$181$	21.1624	−	3.73150i	1.57299	−	0.277360i	0.891000	+	0.454004i	$0.150005\pi$
$182$	2.47484	+	0.994345i	0.183447	+	0.0737057i
$183$	2.07886	−	1.20023i	0.153674	−	0.0887237i
$184$	−0.995482	−	0.478410i	−0.0733879	−	0.0352689i
$185$	10.2903	+	18.5569i	0.756560	+	1.36433i
$186$	−24.8193	−	5.22544i	−1.81984	−	0.383148i
$187$	−1.09585	−	0.919527i	−0.0801365	−	0.0672425i
$188$	−0.433713	−	3.97863i	−0.0316318	−	0.290171i
$189$		−	13.3311i		−	0.969696i
$190$	−13.5668	+	2.43752i	−0.984240	+	0.176837i
$191$		−	6.21850i		−	0.449955i	−0.974364	−	0.224977i	$-0.927769\pi$
$191$		−	6.21850i		−	0.449955i	0.974364	−	0.224977i	$-0.0722308\pi$
$192$	−11.3993	+	9.12080i	−0.822677	+	0.658237i
$193$	10.5116	+	8.82024i	0.756638	+	0.634895i	0.937249	−	0.348660i	$-0.113363\pi$
$193$	10.5116	+	8.82024i	0.756638	+	0.634895i	−0.180611	+	0.983555i	$0.557808\pi$
$194$	−2.29322	+	10.8921i	−0.164643	+	0.782009i
$195$	−2.45965	+	1.36395i	−0.176140	+	0.0976743i
$196$	−0.541543	+	0.809598i	−0.0386816	+	0.0578284i
$197$	−11.8514	+	6.84239i	−0.844375	+	0.487500i	−0.858749	−	0.512397i	$-0.828758\pi$
$197$	−11.8514	+	6.84239i	−0.844375	+	0.487500i	0.0143741	+	0.999897i	$0.495424\pi$
$198$	0.450356	−	1.12090i	0.0320054	−	0.0796587i
$199$	10.4631	−	1.84493i	0.741709	−	0.130783i	0.209990	−	0.977704i	$-0.432657\pi$
$199$	10.4631	−	1.84493i	0.741709	−	0.130783i	0.531720	+	0.846920i	$0.321546\pi$
$200$	8.63831	−	11.1973i	0.610821	−	0.791769i
$201$	−2.85547	+	4.94582i	−0.201409	+	0.348851i
$202$	−8.28529	+	6.49899i	−0.582951	+	0.457267i
$203$	−15.4288	−	18.3873i	−1.08289	−	1.29054i
$204$	−1.62836	+	1.19271i	−0.114008	+	0.0835062i
$205$	10.9212	+	2.12096i	0.762767	+	0.148134i
$206$	−13.5443	−	8.42710i	−0.943676	−	0.587144i
$207$	0.0223913	−	0.126987i	0.00155630	−	0.00882624i
$208$	−2.32670	+	1.47899i	−0.161328	+	0.102550i
$209$	8.23739	−	7.69907i	0.569792	−	0.532556i
$210$	−4.64832	−	15.0906i	−0.320764	−	1.04135i
$211$	−0.507885	+	2.88036i	−0.0349643	+	0.198292i	−0.997286	−	0.0736198i	$-0.976545\pi$
$211$	−0.507885	+	2.88036i	−0.0349643	+	0.198292i	0.962322	+	0.271912i	$0.0876560\pi$
$212$	18.1580	+	8.00056i	1.24709	+	0.549480i
$213$	2.40788	−	6.61559i	0.164985	−	0.453293i
$214$	11.9641	−	6.39108i	0.817848	−	0.436885i
$215$	4.43408	+	3.85318i	0.302402	+	0.262785i
$216$	11.1952	+	8.03511i	0.761737	+	0.546720i
$217$	13.4456	−	23.2885i	0.912749	−	1.58093i
$218$	5.84069	+	17.8584i	0.395582	+	1.20952i
$219$	−2.61962	−	14.8566i	−0.177017	−	1.00391i
$220$	−0.961781	+	11.5281i	−0.0648433	+	0.777222i
$221$	−0.330106	+	0.190587i	−0.0222054	+	0.0128203i
$222$	−16.3520	+	18.2314i	−1.09747	+	1.22361i
$223$	−0.702531	−	1.93019i	−0.0470450	−	0.129255i	0.913945	−	0.405838i	$-0.133020\pi$
$223$	−0.702531	−	1.93019i	−0.0470450	−	0.129255i	−0.960990	+	0.276583i	$0.910798\pi$
$224$	−5.43415	−	14.4933i	−0.363085	−	0.968371i
$225$	1.53107	+	0.617994i	0.102071	+	0.0411996i
$226$	23.6961	+	0.781675i	1.57624	+	0.0519963i
$227$		−	12.0059i		−	0.796857i	−0.917199	−	0.398428i	$-0.869556\pi$
$227$		−	12.0059i		−	0.796857i	0.917199	−	0.398428i	$-0.130444\pi$
$228$	−7.78234	−	13.8756i	−0.515398	−	0.918932i
$229$	14.3495			0.948243			0.474122	−	0.880459i	$-0.342766\pi$
$229$	14.3495			0.948243			0.474122	+	0.880459i	$0.342766\pi$
$230$	0.153061	+	1.22532i	0.0100925	+	0.0807949i
$231$	9.89446	+	8.30244i	0.651008	+	0.546260i
$232$	24.7408	−	1.87413i	1.62431	−	0.123043i
$233$	−3.31500	−	9.10788i	−0.217173	−	0.596677i	0.782490	−	0.622664i	$-0.213949\pi$
$233$	−3.31500	−	9.10788i	−0.217173	−	0.596677i	−0.999662	+	0.0259867i	$0.991727\pi$
$234$	−0.239616	−	0.214915i	−0.0156642	−	0.0140494i
$235$	−3.47694	+	2.81654i	−0.226811	+	0.183731i
$236$	−3.36055	+	13.7037i	−0.218753	+	0.892033i
$237$	−22.1567	+	3.90683i	−1.43923	+	0.253776i
$238$	−0.665233	−	2.03400i	−0.0431206	−	0.131845i
$239$	−7.14550	−	4.12545i	−0.462204	−	0.266853i	0.250767	−	0.968048i	$-0.419317\pi$
$239$	−7.14550	−	4.12545i	−0.462204	−	0.266853i	−0.712970	+	0.701194i	$0.752651\pi$
$240$	15.4745	+	5.19206i	0.998874	+	0.335146i
$241$	−9.16260	−	10.9196i	−0.590215	−	0.703391i	0.385432	−	0.922736i	$-0.374052\pi$
$241$	−9.16260	−	10.9196i	−0.590215	−	0.703391i	−0.975647	+	0.219345i	$0.929608\pi$
$242$	2.87123	+	5.37493i	0.184570	+	0.345514i
$243$	−1.16857	+	3.21061i	−0.0749636	+	0.205961i
$244$	−2.40748	−	1.06076i	−0.154123	−	0.0679079i
$245$	1.08883	+	0.0188231i	0.0695626	+	0.00120256i
$246$	1.81157	+	12.7118i	0.115502	+	0.810477i
$247$	−1.17705	−	2.76418i	−0.0748936	−	0.175881i
$248$	11.4531	+	25.3281i	0.727272	+	1.60834i
$249$	2.31192	+	0.407655i	0.146512	+	0.0258341i
$250$	−15.7545	−	1.33972i	−0.996404	−	0.0847311i
$251$	−4.54394	+	12.4844i	−0.286811	+	0.788007i	0.709697	+	0.704507i	$0.248832\pi$
$251$	−4.54394	+	12.4844i	−0.286811	+	0.788007i	−0.996508	+	0.0834994i	$0.973390\pi$
$252$	1.45787	−	1.06783i	0.0918369	−	0.0672669i
$253$	−0.649270	−	0.773770i	−0.0408192	−	0.0486465i
$254$	−17.8753	−	22.7885i	−1.12160	−	1.42988i
$255$	2.10693	+	0.808370i	0.131941	+	0.0506221i
$256$	15.4465	+	4.17208i	0.965405	+	0.260755i
$257$	0.0276182	+	0.156631i	0.00172278	+	0.00977034i	0.985657	−	0.168761i	$-0.0539766\pi$
$257$	0.0276182	+	0.156631i	0.00172278	+	0.00977034i	−0.983934	+	0.178531i	$0.942865\pi$
$258$	−2.52767	+	6.29116i	−0.157366	+	0.391670i
$259$	−12.9827	−	22.4868i	−0.806708	−	1.39726i
$260$	2.79883	+	1.29141i	0.173576	+	0.0800899i
$261$	0.990745	+	2.72205i	0.0613256	+	0.168491i
$262$	0.256198	+	0.0539396i	0.0158279	+	0.00333240i
$263$	5.37382	+	4.50917i	0.331364	+	0.278047i	0.793255	−	0.608889i	$-0.208385\pi$
$263$	5.37382	+	4.50917i	0.331364	+	0.278047i	−0.461891	+	0.886936i	$0.652829\pi$
$264$	−12.9359	+	3.30501i	−0.796152	+	0.203409i
$265$	−3.47409	−	21.9108i	−0.213411	−	1.34597i
$266$	16.5475	−	3.26927i	1.01459	−	0.200452i
$267$	−20.7189			−1.26797
$268$	6.22209	−	0.678274i	0.380074	−	0.0414322i
$269$	4.32068	−	5.14918i	0.263436	−	0.313951i	−0.618070	−	0.786123i	$-0.712085\pi$
$269$	4.32068	−	5.14918i	0.263436	−	0.313951i	0.881507	+	0.472172i	$0.156530\pi$
$270$	0.774039	−	15.3873i	0.0471065	−	0.936443i
$271$	5.61426	+	15.4251i	0.341042	+	0.937006i	0.985093	+	0.172023i	$0.0550303\pi$
$271$	5.61426	+	15.4251i	0.341042	+	0.937006i	−0.644051	+	0.764983i	$0.722747\pi$
$272$	2.10907	+	0.667313i	0.127881	+	0.0404618i
$273$	2.98054	−	1.72082i	0.180391	−	0.104149i
$274$	0.378334	−	0.941641i	0.0228560	−	0.0568866i
$275$	11.4176	−	6.07576i	0.688508	−	0.366382i
$276$	−1.27854	+	0.629710i	−0.0769591	+	0.0379041i
$277$	17.2303	+	9.94792i	1.03527	+	0.597713i	0.918490	−	0.395445i	$-0.129410\pi$
$277$	17.2303	+	9.94792i	1.03527	+	0.597713i	0.116779	+	0.993158i	$0.462743\pi$
$278$	−3.45728	−	4.40754i	−0.207354	−	0.264347i
$279$	−2.48605	+	2.08605i	−0.148836	+	0.124888i
$280$	−10.3321	+	13.8826i	−0.617464	+	0.829645i
$281$	−7.32284	+	20.1193i	−0.436844	+	1.20022i	0.504689	+	0.863301i	$0.331607\pi$
$281$	−7.32284	+	20.1193i	−0.436844	+	1.20022i	−0.941534	+	0.336919i	$0.890615\pi$
$282$	−4.38494	−	2.72825i	−0.261119	−	0.162465i
$283$	0.697814	−	3.95750i	0.0414808	−	0.235249i	−0.957018	−	0.290030i	$-0.906335\pi$
$283$	0.697814	−	3.95750i	0.0414808	−	0.235249i	0.998498	+	0.0547806i	$0.0174459\pi$
$284$	−7.40856	+	2.15537i	−0.439617	+	0.127898i
$285$	−8.32986	+	15.7157i	−0.493418	+	0.930919i
$286$	−2.49615	+	0.355728i	−0.147600	+	0.0210346i
$287$	−13.4069	−	2.36400i	−0.791385	−	0.139542i
$288$	0.0180360	+	1.86790i	0.00106278	+	0.110067i
$289$	−15.6874	−	5.70974i	−0.922787	−	0.335867i
$290$	−16.7410	−	22.1193i	−0.983064	−	1.29889i
$291$	9.23251	+	11.0029i	0.541219	+	0.645000i
$292$	−11.4390	+	11.9374i	−0.669418	+	0.698582i
$293$	12.0729	−	20.9108i	0.705305	−	1.22162i	−0.261277	−	0.965264i	$-0.584143\pi$
$293$	12.0729	−	20.9108i	0.705305	−	1.22162i	0.966581	−	0.256360i	$-0.0825232\pi$
$294$	0.390701	+	1.19460i	0.0227862	+	0.0696705i
$295$	14.9148	−	5.13838i	0.868374	−	0.299168i
$296$	26.7090	+	2.65088i	1.55243	+	0.154080i
$297$	6.30130	+	10.9142i	0.365638	+	0.633304i
$298$	−14.8347	−	13.3055i	−0.859353	−	0.770765i
$299$	−0.252912	+	0.0920525i	−0.0146263	+	0.00532353i
$300$	−4.48908	−	17.6881i	−0.259177	−	1.02122i
$301$	−5.50660	−	4.62059i	−0.317395	−	0.266326i
$302$	21.2953	+	0.702479i	1.22541	+	0.0404231i
$303$			13.5879i			0.780607i
$304$	−7.22824	+	15.8667i	−0.414568	+	0.910018i
$305$	0.460612	+	2.90504i	0.0263746	+	0.166342i
$306$	−0.00851484	+	0.258124i	−0.000486761	+	0.0147559i
$307$	−4.07184	+	4.85263i	−0.232392	+	0.276954i	−0.869620	−	0.493721i	$-0.835636\pi$
$307$	−4.07184	+	4.85263i	−0.232392	+	0.276954i	0.637228	+	0.770675i	$0.280081\pi$
$308$	0.932907	−	14.1249i	0.0531573	−	0.804843i
$309$	−19.3428	+	7.04022i	−1.10038	+	0.400504i
$310$	16.8717	−	26.0999i	0.958248	−	1.48237i
$311$	−24.9320	+	14.3945i	−1.41376	+	0.816236i	−0.995740	−	0.0922011i	$-0.970610\pi$
$311$	−24.9320	+	14.3945i	−1.41376	+	0.816236i	−0.418022	+	0.908437i	$0.637276\pi$
$312$	−0.351366	+	3.54019i	−0.0198922	+	0.200424i
$313$	−31.2411	+	5.50865i	−1.76585	+	0.311367i	−0.959844	−	0.280536i	$-0.909488\pi$
$313$	−31.2411	+	5.50865i	−1.76585	+	0.311367i	−0.806009	+	0.591903i	$0.798377\pi$
$314$	8.39162	+	25.6581i	0.473567	+	1.44797i
$315$	−1.88633	−	0.723733i	−0.106283	−	0.0407777i
$316$	17.8031	+	17.0599i	1.00150	+	0.959692i
$317$	−22.2893	+	18.7029i	−1.25189	+	1.05046i	−0.255392	+	0.966838i	$0.582204\pi$
$317$	−22.2893	+	18.7029i	−1.25189	+	1.05046i	−0.996498	+	0.0836220i	$0.973351\pi$
$318$	22.5841	−	12.0642i	1.26645	−	0.676526i
$319$	21.3228	+	7.76087i	1.19385	+	0.434525i
$320$	−5.43081	−	17.0442i	−0.303592	−	0.952802i
$321$	3.03936	−	17.2371i	0.169641	−	0.962081i
$322$	−0.213187	−	1.49594i	−0.0118804	−	0.0833653i
$323$	−1.09194	+	2.14911i	−0.0607573	+	0.119580i
$324$	18.9764	−	5.52081i	1.05425	−	0.306712i
$325$	−0.480766	−	3.41253i	−0.0266681	−	0.189293i
$326$	11.3692	−	18.2729i	0.629681	−	1.01204i
$327$	22.7833	+	8.29244i	1.25992	+	0.458573i
$328$	10.0660	−	9.83398i	0.555803	−	0.542991i
$329$	4.19447	−	3.51958i	0.231248	−	0.194040i
$330$	10.9385	+	10.1575i	0.602147	+	0.559153i
$331$	9.41823	−	16.3128i	0.517673	−	0.896635i	−0.482117	−	0.876107i	$-0.660132\pi$
$331$	9.41823	−	16.3128i	0.517673	−	0.896635i	0.999789	−	0.0205282i	$-0.00653480\pi$
$332$	−1.13679	−	2.30810i	−0.0623894	−	0.126673i
$333$	0.544141	+	3.08598i	0.0298187	+	0.169111i
$334$	2.22954	−	5.54913i	0.121995	−	0.303635i
$335$	−4.40472	−	5.43751i	−0.240655	−	0.297083i
$336$	−19.0429	−	6.02519i	−1.03887	−	0.328701i
$337$	11.2305	−	4.08757i	0.611764	−	0.222664i	−0.0175107	−	0.999847i	$-0.505574\pi$
$337$	11.2305	−	4.08757i	0.611764	−	0.222664i	0.629275	+	0.777183i	$0.283352\pi$
$338$	3.64926	−	17.3330i	0.198494	−	0.942788i
$339$	19.6654	−	23.4363i	1.06808	−	1.27289i
$340$	−0.649740	−	2.38636i	−0.0352371	−	0.129418i
$341$			25.4217i			1.37666i
$342$	−2.01150	−	0.312261i	−0.108770	−	0.0168852i
$343$	17.8211			0.962249
$344$	7.19929	−	1.83935i	0.388159	−	0.0991710i
$345$	1.36597	+	0.820445i	0.0735413	+	0.0441713i
$346$	1.06662	−	5.06612i	0.0573416	−	0.272356i
$347$	7.72163	−	2.81044i	0.414519	−	0.150872i	−0.126338	−	0.991987i	$-0.540322\pi$
$347$	7.72163	−	2.81044i	0.414519	−	0.150872i	0.540857	+	0.841115i	$0.318100\pi$
$348$	17.8009	−	26.6120i	0.954228	−	1.42655i
$349$	−1.88320	−	3.26180i	−0.100805	−	0.174600i	0.811211	−	0.584753i	$-0.198809\pi$
$349$	−1.88320	−	3.26180i	−0.100805	−	0.174600i	−0.912017	+	0.410153i	$0.865475\pi$
$350$	19.3040	+	1.30592i	1.03184	+	0.0698041i
$351$	3.30703	−	0.583118i	0.176516	−	0.0311245i
$352$	11.2995	+	9.29701i	0.602268	+	0.495532i
$353$	15.3251	+	8.84794i	0.815672	+	0.470928i	0.848922	−	0.528519i	$-0.177252\pi$
$353$	15.3251	+	8.84794i	0.815672	+	0.470928i	−0.0332500	+	0.999447i	$0.510586\pi$
$354$	11.2371	+	14.3257i	0.597243	+	0.761400i
$355$	6.51141	+	5.65836i	0.345590	+	0.300315i
$356$	13.4177	+	18.3187i	0.711136	+	0.970887i
$357$	−2.59493	−	0.944477i	−0.137338	−	0.0499870i
$358$	−15.1042	+	24.2759i	−0.798281	+	1.28302i
$359$	−27.0391	−	4.76772i	−1.42707	−	0.251631i	−0.593850	−	0.804576i	$-0.702393\pi$
$359$	−27.0391	−	4.76772i	−1.42707	−	0.251631i	−0.833218	+	0.552945i	$0.813504\pi$
$360$	1.74473	−	1.14789i	0.0919554	−	0.0604989i
$361$	−15.7759	−	10.5887i	−0.830310	−	0.557301i
$362$	−30.0858	+	4.28755i	−1.58128	+	0.225349i
$363$	7.74386	+	1.36545i	0.406447	+	0.0716676i
$364$	−3.45169	−	1.52084i	−0.180917	−	0.0797138i
$365$	18.1458	+	3.52404i	0.949796	+	0.184457i
$366$	−2.99432	+	1.59953i	−0.156516	+	0.0836089i
$367$	19.3104	−	16.2034i	1.00800	−	0.845809i	0.0199242	−	0.999801i	$-0.493658\pi$
$367$	19.3104	−	16.2034i	1.00800	−	0.845809i	0.988072	+	0.153992i	$0.0492131\pi$
$368$	1.38475	+	0.722621i	0.0721852	+	0.0376692i
$369$	1.42283	+	0.821471i	0.0740695	+	0.0427641i
$370$	−13.6796	−	26.7090i	−0.711168	−	1.38853i
$371$	4.71399	+	26.7343i	0.244738	+	1.38798i
$372$	34.8371	+	8.54309i	1.80622	+	0.442939i
$373$	13.7616	+	23.8359i	0.712551	+	1.23417i	0.963897	+	0.266277i	$0.0857936\pi$
$373$	13.7616	+	23.8359i	0.712551	+	1.23417i	−0.251345	+	0.967897i	$0.580873\pi$
$374$	1.50605	+	1.35080i	0.0778759	+	0.0698480i
$375$	−13.9072	+	14.9287i	−0.718166	+	0.770915i
$376$	0.427522	+	5.64379i	0.0220478	+	0.291056i
$377$	3.88644	−	4.63168i	0.200162	−	0.238544i
$378$	−0.621576	+	18.8428i	−0.0319704	+	0.969169i
$379$	−10.8427			−0.556952			−0.278476	−	0.960443i	$-0.589829\pi$
$379$	−10.8427			−0.556952			−0.278476	+	0.960443i	$0.589829\pi$
$380$	19.2896	−	2.81274i	0.989535	−	0.144291i
$381$	−37.3733			−1.91469
$382$	−0.289943	+	8.78950i	−0.0148348	+	0.449710i
$383$	20.9261	−	24.9387i	1.06927	−	1.27431i	0.109361	−	0.994002i	$-0.465120\pi$
$383$	20.9261	−	24.9387i	1.06927	−	1.27431i	0.959911	−	0.280306i	$-0.0904359\pi$
$384$	16.5376	−	12.3602i	0.843931	−	0.630756i
$385$	−13.8409	+	7.67519i	−0.705400	+	0.391164i
$386$	−14.4462	−	12.9570i	−0.735295	−	0.659496i
$387$	0.433755	+	0.751286i	0.0220490	+	0.0381900i
$388$	3.74919	−	15.2885i	0.190336	−	0.776156i
$389$	5.36751	+	30.4407i	0.272144	+	1.54340i	0.747891	+	0.663821i	$0.231066\pi$
$389$	5.36751	+	30.4407i	0.272144	+	1.54340i	−0.475748	+	0.879582i	$0.657823\pi$
$390$	3.54018	−	1.81318i	0.179264	−	0.0918140i
$391$	0.187021	+	0.107977i	0.00945805	+	0.00546061i
$392$	0.803189	−	1.11907i	0.0405672	−	0.0565217i
$393$	0.258803	−	0.217161i	0.0130549	−	0.0109543i
$394$	17.0703	−	9.11876i	0.859988	−	0.459396i
$395$	5.25566	−	27.0622i	0.264441	−	1.36165i
$396$	−0.688816	+	1.56333i	−0.0346143	+	0.0785602i
$397$	3.15781	+	0.556807i	0.158486	+	0.0279453i	0.252328	−	0.967642i	$-0.418804\pi$
$397$	3.15781	+	0.556807i	0.158486	+	0.0279453i	−0.0938422	+	0.995587i	$0.529915\pi$
$398$	−14.8750	+	2.11985i	−0.745618	+	0.106258i
$399$	9.85919	−	19.4044i	0.493577	−	0.971435i
$400$	−12.7319	+	15.4240i	−0.636593	+	0.771200i
$401$	7.29685	+	1.28663i	0.364387	+	0.0642513i	0.352844	−	0.935682i	$-0.385215\pi$
$401$	7.29685	+	1.28663i	0.364387	+	0.0642513i	0.0115431	+	0.999933i	$0.496326\pi$
$402$	4.26665	−	6.85750i	0.212801	−	0.342021i
$403$	6.36527	+	2.31677i	0.317077	+	0.115406i
$404$	12.0138	−	8.79965i	0.597710	−	0.437799i
$405$	−16.6785	−	14.4935i	−0.828759	−	0.720185i
$406$	20.9505	+	26.7089i	1.03975	+	1.32554i
$407$	21.2579	+	12.2732i	1.05371	+	0.608362i
$408$	2.35720	−	1.60990i	0.116699	−	0.0797020i
$409$	−15.8416	+	2.79329i	−0.783315	+	0.138119i	−0.550982	−	0.834517i	$-0.685747\pi$
$409$	−15.8416	+	2.79329i	−0.783315	+	0.138119i	−0.232332	+	0.972636i	$0.574636\pi$
$410$	−15.3376	−	3.50707i	−0.757468	−	0.173202i
$411$	−0.654746	−	1.13405i	−0.0322962	−	0.0559387i
$412$	18.7512	+	12.5427i	0.923805	+	0.617937i
$413$	−18.1396	+	6.60228i	−0.892592	+	0.324877i
$414$	−0.0375698	+	0.178446i	−0.00184646	+	0.00877013i
$415$	−1.48112	+	2.46593i	−0.0727051	+	0.121048i
$416$	3.35762	−	1.98199i	0.164621	−	0.0971751i
$417$	−7.22840			−0.353976
$418$	−12.0021	+	10.4981i	−0.587041	+	0.513480i
$419$			33.7665i			1.64960i	0.565424	+	0.824801i	$0.308713\pi$
$419$			33.7665i			1.64960i	−0.565424	+	0.824801i	$0.691287\pi$
$420$	5.86653	+	21.5465i	0.286257	+	1.05136i
$421$	−23.2641	+	27.7250i	−1.13382	+	1.35124i	−0.205850	+	0.978584i	$0.565996\pi$
$421$	−23.2641	+	27.7250i	−1.13382	+	1.35124i	−0.927971	+	0.372652i	$0.878449\pi$
$422$	0.852167	−	4.04755i	0.0414829	−	0.197032i
$423$	−0.620946	+	0.226006i	−0.0301914	+	0.0109888i
$424$	−25.2922	−	12.1550i	−1.22830	−	0.590298i
$425$	−1.84956	+	2.05553i	−0.0897169	+	0.0997078i
$426$	−3.71186	+	9.23850i	−0.179840	+	0.447607i
$427$	−0.625005	−	3.54458i	−0.0302461	−	0.171534i
$428$	−17.2086	+	8.47560i	−0.831807	+	0.409684i
$429$	−1.62678	+	2.81766i	−0.0785415	+	0.136038i
$430$	−6.08767	−	5.65300i	−0.293573	−	0.272612i
$431$	18.8061	−	15.7802i	0.905858	−	0.760105i	−0.0654684	−	0.997855i	$-0.520854\pi$
$431$	18.8061	−	15.7802i	0.905858	−	0.760105i	0.971327	+	0.237749i	$0.0764097\pi$
$432$	−15.4491	−	11.8792i	−0.743297	−	0.571537i
$433$	−4.83707	−	1.76055i	−0.232455	−	0.0846067i	0.223166	−	0.974780i	$-0.428361\pi$
$433$	−4.83707	−	1.76055i	−0.232455	−	0.0846067i	−0.455621	+	0.890174i	$0.650583\pi$
$434$	−20.0905	+	32.2901i	−0.964375	+	1.54997i
$435$	−35.7905	−	0.618727i	−1.71602	−	0.0296657i
$436$	−7.42284	−	25.5142i	−0.355489	−	1.22191i
$437$	−1.02280	+	1.36053i	−0.0489273	+	0.0650830i
$438$	3.00998	+	21.1211i	0.143822	+	1.00921i
$439$	2.13084	−	12.0846i	0.101700	−	0.576767i	−0.890788	−	0.454419i	$-0.849847\pi$
$439$	2.13084	−	12.0846i	0.101700	−	0.576767i	0.992487	−	0.122347i	$-0.0390422\pi$
$440$	1.89693	−	16.2494i	0.0904326	−	0.774662i
$441$	0.151121	+	0.0550034i	0.00719622	+	0.00261921i
$442$	0.475473	−	0.253993i	0.0226160	−	0.0120812i
$443$	−20.1188	+	16.8817i	−0.955872	+	0.802072i	−0.980277	−	0.197631i	$-0.936675\pi$
$443$	−20.1188	+	16.8817i	−0.955872	+	0.802072i	0.0244049	+	0.999702i	$0.492231\pi$
$444$	23.9627	−	25.0067i	1.13722	−	1.18676i
$445$	9.09398	−	23.7025i	0.431096	−	1.12361i
$446$	0.902992	+	2.76097i	0.0427579	+	0.130736i
$447$	−25.3236	+	4.46523i	−1.19776	+	0.211198i
$448$	7.00511	+	20.7388i	0.330961	+	0.979815i
$449$	−20.9114	+	12.0732i	−0.986869	+	0.569769i	−0.904337	−	0.426820i	$-0.859634\pi$
$449$	−20.9114	+	12.0732i	−0.986869	+	0.569769i	−0.0825318	+	0.996588i	$0.526301\pi$
$450$	−2.13526	−	0.944888i	−0.100657	−	0.0445425i
$451$	12.0936	−	4.40172i	0.569466	−	0.207269i
$452$	−33.4567	−	2.20971i	−1.57367	−	0.103936i
$453$	17.6730	−	21.0618i	0.830349	−	0.989571i
$454$	−0.559784	+	16.9696i	−0.0262720	+	0.796423i
$455$	0.660396	+	4.16506i	0.0309599	+	0.195261i
$456$	10.3530	+	19.9752i	0.484821	+	0.935425i
$457$		−	24.6991i		−	1.15538i	−0.816257	−	0.577689i	$-0.803955\pi$
$457$		−	24.6991i		−	1.15538i	0.816257	−	0.577689i	$-0.196045\pi$
$458$	−20.2823	−	0.669060i	−0.947728	−	0.0312631i
$459$	−2.06403	−	1.73192i	−0.0963406	−	0.0808393i
$460$	−0.159211	−	1.73905i	−0.00742327	−	0.0810837i
$461$	18.0400	−	6.56603i	0.840207	−	0.305810i	0.114166	−	0.993462i	$-0.463580\pi$
$461$	18.0400	−	6.56603i	0.840207	−	0.305810i	0.726041	+	0.687651i	$0.241358\pi$
$462$	−13.5982	−	12.1964i	−0.632644	−	0.567427i
$463$	−12.5649	−	21.7630i	−0.583939	−	1.01141i	−0.995007	−	0.0998074i	$-0.968177\pi$
$463$	−12.5649	−	21.7630i	−0.583939	−	1.01141i	0.411068	−	0.911605i	$-0.365156\pi$
$464$	−35.0571	+	1.49542i	−1.62749	+	0.0694233i
$465$	−13.0627	−	37.9161i	−0.605766	−	1.75832i
$466$	4.26090	+	13.0280i	0.197382	+	0.603513i
$467$	0.475449	−	0.823502i	0.0220012	−	0.0381071i	−0.854815	−	0.518933i	$-0.826330\pi$
$467$	0.475449	−	0.823502i	0.0220012	−	0.0381071i	0.876816	+	0.480825i	$0.159663\pi$
$468$	0.328663	+	0.314942i	0.0151925	+	0.0145582i
$469$	5.50418	+	6.55963i	0.254160	+	0.302896i
$470$	5.04579	−	3.81890i	0.232745	−	0.176153i
$471$	32.7339	+	11.9142i	1.50830	+	0.548976i
$472$	5.38889	−	19.2127i	0.248044	−	0.884336i
$473$	6.69229	+	1.18003i	0.307712	+	0.0542579i
$474$	31.4995	−	4.48901i	1.44682	−	0.206187i
$475$	−14.3227	−	16.4274i	−0.657172	−	0.753741i
$476$	0.845432	+	2.90597i	0.0387503	+	0.133195i
$477$	0.568897	−	3.22637i	0.0260480	−	0.147726i
$478$	9.90741	+	6.16427i	0.453154	+	0.281947i
$479$	−8.95565	+	24.6055i	−0.409194	+	1.12425i	0.548421	+	0.836202i	$0.315229\pi$
$479$	−8.95565	+	24.6055i	−0.409194	+	1.12425i	−0.957615	+	0.288050i	$0.906993\pi$
$480$	−21.6303	−	8.06020i	−0.987281	−	0.367896i
$481$	5.01037	−	4.20420i	0.228453	−	0.191695i
$482$	12.4417	+	15.8614i	0.566704	+	0.722468i
$483$	−1.68862	−	0.974924i	−0.0768347	−	0.0443606i
$484$	−3.80771	−	7.73104i	−0.173078	−	0.351411i
$485$	−16.6397	+	5.73263i	−0.755571	+	0.260305i
$486$	1.80140	−	4.48354i	0.0817133	−	0.203377i
$487$	−6.80434	+	3.92849i	−0.308334	+	0.178017i	−0.646181	−	0.763184i	$-0.723635\pi$
$487$	−6.80434	+	3.92849i	−0.308334	+	0.178017i	0.337847	+	0.941201i	$0.390301\pi$
$488$	3.35338	+	1.61157i	0.151800	+	0.0729523i
$489$	−9.49812	−	26.0959i	−0.429520	−	1.18010i
$490$	−1.53812	−	0.0773729i	−0.0694851	−	0.00349535i
$491$	6.11989	−	7.29341i	0.276187	−	0.329147i	−0.610064	−	0.792352i	$-0.708856\pi$
$491$	6.11989	−	7.29341i	0.276187	−	0.329147i	0.886251	+	0.463205i	$0.153301\pi$
$492$	−1.96785	−	18.0519i	−0.0887177	−	0.813844i
$493$	−4.85132			−0.218493
$494$	1.53481	+	3.96190i	0.0690542	+	0.178254i
$495$	1.88643	−	0.299105i	0.0847887	−	0.0134438i
$496$	−15.0074	−	36.3339i	−0.673850	−	1.63144i
$497$	−8.08639	−	6.78529i	−0.362724	−	0.304362i
$498$	−3.24877	−	0.683993i	−0.145581	−	0.0306505i
$499$	3.92539	+	10.7849i	0.175724	+	0.482799i	0.996019	−	0.0891426i	$-0.0284127\pi$
$499$	3.92539	+	10.7849i	0.175724	+	0.482799i	−0.820294	+	0.571941i	$0.806190\pi$
$500$	22.2057	+	2.62818i	0.993069	+	0.117536i
$501$	−3.85844	−	6.68302i	−0.172383	−	0.298575i
$502$	7.00470	−	17.4341i	0.312635	−	0.778122i
$503$	3.92980	+	22.2870i	0.175221	+	0.993728i	0.937888	+	0.346937i	$0.112778\pi$
$503$	3.92980	+	22.2870i	0.175221	+	0.993728i	−0.762667	+	0.646791i	$0.776111\pi$
$504$	−2.11040	+	1.44134i	−0.0940048	+	0.0642025i
$505$	−15.5447	−	5.96406i	−0.691729	−	0.265397i
$506$	0.881629	+	1.12395i	0.0391932	+	0.0499658i
$507$	−14.6919	−	17.5092i	−0.652492	−	0.777610i
$508$	24.2032	+	33.0438i	1.07385	+	1.46608i
$509$	−3.07492	+	8.44829i	−0.136294	+	0.374464i	−0.988998	−	0.147930i	$-0.952739\pi$
$509$	−3.07492	+	8.44829i	−0.136294	+	0.374464i	0.852704	+	0.522394i	$0.174961\pi$
$510$	−2.94034	−	1.24082i	−0.130200	−	0.0549446i
$511$	−22.2760	−	3.92786i	−0.985431	−	0.173758i
$512$	−21.6382	−	6.61721i	−0.956283	−	0.292442i
$513$	15.5151	−	14.5012i	0.685008	−	0.640242i
$514$	−0.0317337	−	0.222676i	−0.00139972	−	0.00982183i
$515$	0.435963	−	25.2184i	0.0192108	−	1.11126i
$516$	3.86605	−	8.77435i	0.170194	−	0.386269i
$517$	−1.77039	+	4.86410i	−0.0778615	+	0.213923i
$518$	17.3019	+	32.3891i	0.760202	+	1.42310i
$519$	−4.29420	−	5.11763i	−0.188494	−	0.224639i
$520$	−3.89578	−	1.95584i	−0.170841	−	0.0857690i
$521$	28.9479	+	16.7131i	1.26823	+	0.732213i	0.974653	−	0.223722i	$-0.0718207\pi$
$521$	28.9479	+	16.7131i	1.26823	+	0.732213i	0.293578	+	0.955935i	$0.405154\pi$
$522$	−1.27345	−	3.89366i	−0.0557372	−	0.170421i
$523$	−35.3296	+	6.22956i	−1.54485	+	0.272399i	−0.880146	−	0.474704i	$-0.842555\pi$
$523$	−35.3296	+	6.22956i	−1.54485	+	0.272399i	−0.664708	+	0.747103i	$0.731444\pi$
$524$	−0.359606	−	0.0881861i	−0.0157095	−	0.00385243i
$525$	16.6997	−	18.5594i	0.728836	−	0.810000i
$526$	−7.38535	−	6.62402i	−0.322017	−	0.288821i
$527$	−1.85891	−	5.10731i	−0.0809753	−	0.222478i
$528$	18.4383	−	4.06830i	0.802426	−	0.177050i
$529$	−17.5022	−	14.6861i	−0.760966	−	0.638526i
$530$	3.88882	+	31.1316i	0.168919	+	1.35227i
$531$	2.32963			0.101097
$532$	−23.5413	+	3.84939i	−1.02065	+	0.166892i
$533$		−	3.42923i		−	0.148536i
$534$	29.2850	+	0.966036i	1.26728	+	0.0418045i
$535$	18.3853	+	11.0428i	0.794866	+	0.477422i
$536$	−8.82620	+	0.668592i	−0.381234	+	0.0288788i
$537$	12.6184	+	34.6689i	0.544526	+	1.49607i
$538$	−6.34713	+	7.07663i	−0.273644	+	0.305095i
$539$	1.09098	−	0.629878i	0.0469918	−	0.0271307i
$540$	−1.81151	+	21.7131i	−0.0779550	+	0.934381i
$541$	−0.791281	−	4.48758i	−0.0340198	−	0.192936i	0.963062	−	0.269281i	$-0.0867861\pi$
$541$	−0.791281	−	4.48758i	−0.0340198	−	0.192936i	−0.997081	+	0.0763450i	$0.975675\pi$
$542$	−7.21624	−	22.0642i	−0.309964	−	0.947740i
$543$	−19.6074	+	33.9610i	−0.841433	+	1.45740i
$544$	−2.94994	−	1.04155i	−0.126478	−	0.0446560i
$545$	−19.4867	+	22.4245i	−0.834719	+	0.960560i
$546$	−4.29306	+	2.29331i	−0.183726	+	0.0981445i
$547$	−11.2318	+	30.8590i	−0.480235	+	1.31944i	0.429057	+	0.903278i	$0.358846\pi$
$547$	−11.2318	+	30.8590i	−0.480235	+	1.31944i	−0.909292	+	0.416158i	$0.863376\pi$
$548$	−0.578659	+	1.31332i	−0.0247191	+	0.0561021i
$549$	−0.0754273	+	0.427769i	−0.00321916	+	0.0182568i
$550$	−16.4214	+	8.05539i	−0.700213	+	0.343483i
$551$	4.61669	−	37.9576i	0.196678	−	1.61705i
$552$	1.83651	−	0.830447i	0.0781669	−	0.0353462i
$553$	−5.85790	+	33.2218i	−0.249103	+	1.41274i
$554$	−23.8902	−	14.8642i	−1.01500	−	0.631520i
$555$	−38.0123	−	7.38223i	−1.61353	−	0.313358i
$556$	4.68117	+	6.39102i	0.198526	+	0.271040i
$557$	−1.32626	−	1.58057i	−0.0561953	−	0.0669710i	0.737215	−	0.675659i	$-0.236141\pi$
$557$	−1.32626	−	1.58057i	−0.0561953	−	0.0669710i	−0.793410	+	0.608688i	$0.791696\pi$
$558$	3.61116	−	2.83260i	0.152873	−	0.119913i
$559$	0.905356	−	1.56812i	0.0382925	−	0.0663245i
$560$	15.2512	−	19.1406i	0.644481	−	0.808837i
$561$	2.57090	−	0.453319i	0.108543	−	0.0191391i
$562$	11.2885	−	28.0962i	0.476177	−	1.18516i
$563$	26.4632	−	15.2786i	1.11529	−	0.643915i	0.175098	−	0.984551i	$-0.443976\pi$
$563$	26.4632	−	15.2786i	1.11529	−	0.643915i	0.940195	+	0.340636i	$0.110642\pi$
$564$	6.07066	+	4.06069i	0.255621	+	0.170986i
$565$	18.1797	+	32.7841i	0.764825	+	1.37924i
$566$	−1.17084	+	5.56117i	−0.0492143	+	0.233754i
$567$	20.7127	+	17.3800i	0.869850	+	0.729891i
$568$	10.5721	−	2.70107i	0.443595	−	0.113334i
$569$		−	7.97165i		−	0.334189i	−0.985941	−	0.167094i	$-0.946562\pi$
$569$		−	7.97165i		−	0.334189i	0.985941	−	0.167094i	$-0.0534385\pi$
$570$	12.5066	−	21.8249i	0.523842	−	0.914145i
$571$			42.2091i			1.76640i	0.468999	+	0.883199i	$0.344615\pi$
$571$			42.2091i			1.76640i	−0.468999	+	0.883199i	$0.655385\pi$
$572$	3.54476	−	0.386416i	0.148214	−	0.0161569i
$573$	8.69312	+	7.29439i	0.363160	+	0.304728i
$574$	18.8397	+	3.96649i	0.786354	+	0.165558i
$575$	−1.53815	+	1.20256i	−0.0641453	+	0.0501504i
$576$	0.0615998	−	2.64102i	0.00256666	−	0.110042i
$577$	16.5669	−	9.56489i	0.689688	−	0.398192i	−0.113807	−	0.993503i	$-0.536305\pi$
$577$	16.5669	−	9.56489i	0.689688	−	0.398192i	0.803495	+	0.595311i	$0.202971\pi$
$578$	21.9070	+	8.80184i	0.911212	+	0.366108i
$579$	−24.6604	+	4.34830i	−1.02485	+	0.180709i
$580$	22.6311	+	32.0450i	0.939706	+	1.33059i
$581$	1.75999	−	3.04839i	0.0730167	−	0.126469i
$582$	−12.5366	−	15.9824i	−0.519660	−	0.662493i
$583$	−16.4960	−	19.6592i	−0.683195	−	0.814200i
$584$	16.7250	−	16.3395i	0.692086	−	0.676132i
$585$	0.0970248	−	0.499596i	0.00401148	−	0.0206558i
$586$	−18.0393	+	28.9934i	−0.745198	+	1.19771i
$587$	3.85916	−	21.8864i	0.159285	−	0.903348i	−0.795479	−	0.605982i	$-0.792781\pi$
$587$	3.85916	−	21.8864i	0.159285	−	0.903348i	0.954763	−	0.297367i	$-0.0961084\pi$
$588$	−0.496535	−	1.70672i	−0.0204768	−	0.0703839i
$589$	41.7295	−	9.68413i	1.71943	−	0.399028i
$590$	−21.3209	+	6.56740i	−0.877766	+	0.270375i
$591$	4.33655	−	24.5938i	0.178382	−	1.01165i
$592$	−37.6282	−	4.99221i	−1.54651	−	0.205179i
$593$	6.68355	−	18.3629i	0.274461	−	0.754074i	−0.723505	−	0.690319i	$-0.757470\pi$
$593$	6.68355	−	18.3629i	0.274461	−	0.754074i	0.997966	−	0.0637551i	$-0.0203076\pi$
$594$	−8.39765	−	15.7204i	−0.344560	−	0.645015i
$595$	2.21946	−	2.55406i	0.0909891	−	0.104706i
$596$	20.3477	+	19.4982i	0.833474	+	0.798678i
$597$	−9.69427	+	16.7910i	−0.396760	+	0.687209i
$598$	0.361769	−	0.118319i	0.0147939	−	0.00483842i
$599$	3.71618	+	21.0755i	0.151839	+	0.861122i	0.961619	+	0.274388i	$0.0884753\pi$
$599$	3.71618	+	21.0755i	0.151839	+	0.861122i	−0.809780	+	0.586734i	$0.800414\pi$
$600$	5.52035	+	25.2105i	0.225367	+	1.02921i
$601$	−2.22870	+	1.28674i	−0.0909104	+	0.0524871i	−0.544766	−	0.838588i	$-0.683382\pi$
$601$	−2.22870	+	1.28674i	−0.0909104	+	0.0524871i	0.453856	+	0.891075i	$0.350048\pi$
$602$	7.56784	+	6.78769i	0.308442	+	0.276646i
$603$	−0.353445	−	0.971083i	−0.0143934	−	0.0395456i
$604$	−30.0670	−	1.98583i	−1.22341	−	0.0808023i
$605$	−4.96104	+	8.25970i	−0.201695	+	0.335804i
$606$	0.633550	−	19.2058i	0.0257362	−	0.780182i
$607$		−	41.1646i		−	1.67082i	−0.549629	−	0.835409i	$-0.685231\pi$
$607$		−	41.1646i		−	1.67082i	0.549629	−	0.835409i	$-0.314769\pi$
$608$	10.9565	−	22.0897i	0.444345	−	0.895856i
$609$	43.8027			1.77498
$610$	−0.515600	−	4.12759i	−0.0208760	−	0.167121i
$611$	1.05657	+	0.886564i	0.0427441	+	0.0358665i
$612$	0.0240705	−	0.364446i	0.000972992	−	0.0147319i
$613$	0.358494	+	0.984953i	0.0144794	+	0.0397819i	0.946722	−	0.322053i	$-0.104373\pi$
$613$	0.358494	+	0.984953i	0.0144794	+	0.0397819i	−0.932242	+	0.361834i	$0.882151\pi$
$614$	5.98158	−	6.66907i	0.241397	−	0.269142i
$615$	−15.7757	+	12.7793i	−0.636136	+	0.515310i
$616$	−1.97720	+	19.9213i	−0.0796637	+	0.802653i
$617$	23.3255	−	4.11292i	0.939050	−	0.165580i	0.316883	−	0.948465i	$-0.397364\pi$
$617$	23.3255	−	4.11292i	0.939050	−	0.165580i	0.622167	+	0.782885i	$0.286253\pi$
$618$	27.6683	−	9.04908i	1.11298	−	0.364007i
$619$	3.88344	+	2.24210i	0.156089	+	0.0901178i	0.576010	−	0.817443i	$-0.304609\pi$
$619$	3.88344	+	2.24210i	0.156089	+	0.0901178i	−0.419921	+	0.907561i	$0.637942\pi$
$620$	−25.0642	+	36.1041i	−1.00660	+	1.44998i
$621$	−1.22290	−	1.45739i	−0.0490732	−	0.0584831i
$622$	35.9111	−	19.1833i	1.43990	−	0.769181i
$623$	−10.6252	+	29.1924i	−0.425688	+	1.16957i
$624$	0.661700	−	4.98748i	0.0264892	−	0.199659i
$625$	−10.9743	−	22.4625i	−0.438973	−	0.898500i
$626$	44.4144	−	6.32953i	1.77516	−	0.252979i
$627$	1.10029	+	20.5466i	0.0439412	+	0.820550i
$628$	−10.6648	−	36.6575i	−0.425570	−	1.46279i
$629$	−5.16824	−	0.911300i	−0.206071	−	0.0363359i
$630$	2.63248	+	1.11091i	0.104881	+	0.0442596i
$631$	5.62826	−	15.4635i	0.224057	−	0.615592i	−0.775825	−	0.630948i	$-0.782666\pi$
$631$	5.62826	−	15.4635i	0.224057	−	0.615592i	0.999882	+	0.0153560i	$0.00488817\pi$
$632$	−24.3682	−	24.9432i	−0.969317	−	0.992189i
$633$	−3.43083	−	4.08870i	−0.136363	−	0.162511i
$634$	32.3767	−	25.3963i	1.28584	−	1.00861i
$635$	16.4040	−	42.7553i	0.650973	−	1.69669i
$636$	−32.4839	+	15.9991i	−1.28807	+	0.634404i
$637$	−0.0582885	−	0.330570i	−0.00230947	−	0.0130977i
$638$	−29.7767	−	11.9638i	−1.17887	−	0.473649i
$639$	0.636966	+	1.10326i	0.0251980	+	0.0436442i
$640$	6.88145	+	24.3443i	0.272013	+	0.962294i
$641$	−3.74903	−	10.3004i	−0.148078	−	0.406840i	0.843372	−	0.537330i	$-0.180567\pi$
$641$	−3.74903	−	10.3004i	−0.148078	−	0.406840i	−0.991450	+	0.130490i	$0.958345\pi$
$642$	−5.09967	+	24.2220i	−0.201268	+	0.955965i
$643$	−20.9035	−	17.5402i	−0.824356	−	0.691716i	0.129632	−	0.991562i	$-0.458620\pi$
$643$	−20.9035	−	17.5402i	−0.824356	−	0.691716i	−0.953988	+	0.299846i	$0.903065\pi$
$644$	0.231578	+	2.12436i	0.00912547	+	0.0837117i
$645$	−10.5878	+	1.67876i	−0.416894	+	0.0661010i
$646$	1.64361	−	2.98674i	0.0646668	−	0.117512i
$647$	−8.12098			−0.319269			−0.159634	−	0.987176i	$-0.551031\pi$
$647$	−8.12098			−0.319269			−0.159634	+	0.987176i	$0.551031\pi$
$648$	−27.0796	+	6.91857i	−1.06379	+	0.271787i
$649$	11.7301	−	13.9794i	0.460448	−	0.548741i
$650$	0.520423	+	4.84584i	0.0204127	+	0.190069i
$651$	16.7841	+	46.1140i	0.657822	+	1.80735i
$652$	−16.9217	+	25.2977i	−0.662706	+	0.990734i
$653$	8.02307	−	4.63212i	0.313967	−	0.181269i	−0.334733	−	0.942313i	$-0.608646\pi$
$653$	8.02307	−	4.63212i	0.313967	−	0.181269i	0.648700	+	0.761044i	$0.275313\pi$
$654$	−31.8163	−	12.7832i	−1.24412	−	0.499863i
$655$	0.134839	+	0.391389i	0.00526861	+	0.0152928i
$656$	−14.6863	+	13.4305i	−0.573403	+	0.524371i
$657$	2.36407	+	1.36490i	0.0922313	+	0.0532498i
$658$	−6.09275	+	4.77915i	−0.237520	+	0.186311i
$659$	−20.5268	+	17.2240i	−0.799610	+	0.670952i	−0.948104	−	0.317961i	$-0.897002\pi$
$659$	−20.5268	+	17.2240i	−0.799610	+	0.670952i	0.148494	+	0.988913i	$0.452557\pi$
$660$	−14.9874	−	14.8671i	−0.583385	−	0.578702i
$661$	13.9626	−	38.3620i	0.543083	−	1.49211i	−0.299795	−	0.954004i	$-0.596918\pi$
$661$	13.9626	−	38.3620i	0.543083	−	1.49211i	0.842878	−	0.538105i	$-0.180859\pi$
$662$	−14.0727	+	22.6182i	−0.546953	+	0.879080i
$663$	0.120790	−	0.685032i	0.00469108	−	0.0266044i
$664$	1.49917	+	3.31537i	0.0581792	+	0.128661i
$665$	17.8713	+	19.7960i	0.693020	+	0.767656i
$666$	−0.625227	−	4.38723i	−0.0242270	−	0.170002i
$667$	−3.37344	−	0.594828i	−0.130620	−	0.0230318i
$668$	−3.41006	+	7.73943i	−0.131939	+	0.299448i
$669$	3.52238	+	1.28204i	0.136183	+	0.0495666i
$670$	5.97229	+	7.89099i	0.230730	+	0.304856i
$671$	2.18713	+	2.60652i	0.0844331	+	0.100623i
$672$	26.6351	+	9.40416i	1.02747	+	0.362773i
$673$	−9.24882	+	16.0194i	−0.356516	+	0.617504i	−0.987376	−	0.158393i	$-0.949369\pi$
$673$	−9.24882	+	16.0194i	−0.356516	+	0.617504i	0.630860	+	0.775896i	$0.282702\pi$
$674$	−16.0643	+	5.25392i	−0.618773	+	0.202373i
$675$	21.5050	−	11.4437i	0.827728	−	0.440467i
$676$	−5.96620	+	24.3290i	−0.229469	+	0.935731i
$677$	10.2412	+	17.7383i	0.393602	+	0.681739i	0.992922	−	0.118771i	$-0.0378954\pi$
$677$	10.2412	+	17.7383i	0.393602	+	0.681739i	−0.599319	+	0.800510i	$0.704562\pi$
$678$	−28.8887	+	32.2090i	−1.10946	+	1.23698i
$679$	20.2375	−	7.36583i	0.776642	−	0.282675i
$680$	0.807106	+	3.40328i	0.0309511	+	0.130510i
$681$	16.7835	+	14.0831i	0.643146	+	0.539664i
$682$	1.18531	−	35.9322i	0.0453879	−	1.37591i
$683$			31.6147i			1.20970i	0.796338	+	0.604852i	$0.206768\pi$
$683$			31.6147i			1.20970i	−0.796338	+	0.604852i	$0.793232\pi$
$684$	2.82859	+	0.535152i	0.108154	+	0.0204621i
$685$	1.58475	−	0.251272i	0.0605501	−	0.00960059i
$686$	−25.1891	−	0.830926i	−0.961726	−	0.0317249i
$687$	−16.8322	+	20.0598i	−0.642189	+	0.765331i
$688$	−10.2616	+	2.26414i	−0.391218	+	0.0863197i
$689$	−6.42575	+	2.33878i	−0.244801	+	0.0891004i
$690$	−1.89247	−	1.22334i	−0.0720450	−	0.0465719i
$691$	−26.0592	+	15.0453i	−0.991340	+	0.572350i	−0.905675	−	0.423974i	$-0.860635\pi$
$691$	−26.0592	+	15.0453i	−0.991340	+	0.572350i	−0.0856655	+	0.996324i	$0.527302\pi$
$692$	−1.74381	+	7.11095i	−0.0662899	+	0.270318i
$693$	−2.30172	+	0.405856i	−0.0874352	+	0.0154172i
$694$	−11.0451	+	3.61238i	−0.419267	+	0.137124i
$695$	3.17271	−	8.26934i	0.120348	−	0.313674i
$696$	−26.4014	+	36.7846i	−1.00074	+	1.39432i
$697$	−2.10778	+	1.76864i	−0.0798380	+	0.0669921i
$698$	2.50972	+	4.69818i	0.0949942	+	0.177829i
$699$	16.6209	+	6.04950i	0.628659	+	0.228813i
$700$	−27.2243	−	2.74591i	−1.02898	−	0.103786i
$701$	−0.447131	+	2.53580i	−0.0168879	+	0.0957760i	−0.992087	−	0.125555i	$-0.959929\pi$
$701$	−0.447131	+	2.53580i	−0.0168879	+	0.0957760i	0.975199	+	0.221331i	$0.0710400\pi$
$702$	−4.70149	+	0.670012i	−0.177446	+	0.0252880i
$703$	12.0485	−	39.5700i	0.454416	−	1.49241i
$704$	−15.5378	−	13.6677i	−0.585603	−	0.515119i
$705$	0.141142	−	8.16441i	0.00531572	−	0.307490i
$706$	−21.2486	−	13.2206i	−0.799702	−	0.497564i
$707$	19.1451	+	6.96824i	0.720025	+	0.262068i
$708$	−15.2150	−	20.7725i	−0.571815	−	0.780677i
$709$	−6.24268	+	5.23823i	−0.234449	+	0.196726i	−0.752441	−	0.658659i	$-0.771124\pi$
$709$	−6.24268	+	5.23823i	−0.234449	+	0.196726i	0.517993	+	0.855385i	$0.326679\pi$
$710$	−8.93969	−	8.30138i	−0.335500	−	0.311545i
$711$	2.03557	−	3.52572i	0.0763400	−	0.132225i
$712$	−18.1110	−	26.5180i	−0.678740	−	0.993805i
$713$	−0.666403	−	3.77936i	−0.0249570	−	0.141538i
$714$	3.62375	+	1.45596i	0.135616	+	0.0544878i
$715$	−2.50939	−	3.09778i	−0.0938459	−	0.115850i
$716$	22.4808	−	33.6085i	0.840148	−	1.25601i
$717$	14.1489	−	5.14979i	0.528402	−	0.192322i
$718$	37.9959	+	7.99963i	1.41800	+	0.298544i
$719$	−19.6366	+	23.4020i	−0.732322	+	0.872748i	−0.995766	−	0.0919271i	$-0.970697\pi$
$719$	−19.6366	+	23.4020i	−0.732322	+	0.872748i	0.263443	+	0.964675i	$0.415142\pi$
$720$	−2.51960	+	1.54112i	−0.0939001	+	0.0574343i
$721$			30.8640i			1.14944i
$722$	21.8046	+	15.7021i	0.811485	+	0.584373i
$723$	26.0128			0.967427
$724$	42.7246	−	4.65744i	1.58785	−	0.173092i
$725$	16.4171	−	40.6729i	0.609715	−	1.51055i
$726$	−10.8819	−	2.29106i	−0.403863	−	0.0850290i
$727$	−17.9504	+	6.53342i	−0.665745	+	0.242311i	−0.652715	−	0.757604i	$-0.726370\pi$
$727$	−17.9504	+	6.53342i	−0.665745	+	0.242311i	−0.0130301	+	0.999915i	$0.504148\pi$
$728$	4.80786	+	2.31057i	0.178191	+	0.0856353i
$729$	11.7049	+	20.2735i	0.433515	+	0.750870i
$730$	−25.4838	−	5.82710i	−0.943198	−	0.215671i
$731$	−1.43079	+	0.252287i	−0.0529197	+	0.00933117i
$732$	4.30689	−	2.12124i	0.159187	−	0.0784032i
$733$	−25.3179	−	14.6173i	−0.935139	−	0.539903i	−0.0467061	−	0.998909i	$-0.514872\pi$
$733$	−25.3179	−	14.6173i	−0.935139	−	0.539903i	−0.888433	+	0.459006i	$0.848206\pi$
$734$	−28.0497	+	22.0022i	−1.03533	+	0.812116i
$735$	−1.30352	+	1.50004i	−0.0480812	+	0.0553298i
$736$	−1.92358	−	1.08595i	−0.0709040	−	0.0400287i
$737$	−7.60685	−	2.76867i	−0.280202	−	0.101985i
$738$	−1.97279	−	1.22744i	−0.0726194	−	0.0451829i
$739$	−18.1564	−	3.20146i	−0.667894	−	0.117768i	−0.170587	−	0.985343i	$-0.554567\pi$
$739$	−18.1564	−	3.20146i	−0.667894	−	0.117768i	−0.497307	+	0.867575i	$0.665678\pi$
$740$	18.0900	+	38.3895i	0.665002	+	1.41123i
$741$	5.24487	+	1.59698i	0.192675	+	0.0586666i
$742$	−5.41645	−	38.0073i	−0.198844	−	1.39529i
$743$	37.2186	+	6.56265i	1.36542	+	0.240760i	0.807859	−	0.589376i	$-0.200626\pi$
$743$	37.2186	+	6.56265i	1.36542	+	0.240760i	0.557560	+	0.830137i	$0.311738\pi$
$744$	−48.8420	−	13.6995i	−1.79063	−	0.502248i
$745$	6.00685	−	30.9302i	0.220074	−	1.13320i
$746$	−18.3400	−	34.3323i	−0.671474	−	1.25700i
$747$	−0.325416	+	0.273057i	−0.0119064	+	0.00999062i
$748$	−2.06574	−	1.97950i	−0.0755308	−	0.0723775i
$749$	−22.7280	−	13.1220i	−0.830463	−	0.479468i
$750$	20.3532	−	20.4525i	0.743192	−	0.746818i
$751$	−6.53721	−	37.0744i	−0.238546	−	1.35286i	−0.835015	−	0.550227i	$-0.814541\pi$
$751$	−6.53721	−	37.0744i	−0.238546	−	1.35286i	0.596469	−	0.802636i	$-0.296570\pi$
$752$	−0.341132	−	7.99712i	−0.0124398	−	0.291625i
$753$	−12.1224	−	20.9965i	−0.441763	−	0.765156i
$754$	−5.70923	+	6.36542i	−0.207918	+	0.231815i
$755$	16.3378	+	29.4625i	0.594593	+	1.07225i
$756$	1.75713	−	26.6043i	0.0639060	−	0.967588i
$757$	−19.4845	+	23.2207i	−0.708175	+	0.843970i	−0.993425	−	0.114483i	$-0.963479\pi$
$757$	−19.4845	+	23.2207i	−0.708175	+	0.843970i	0.285250	+	0.958453i	$0.407923\pi$
$758$	15.3255	+	0.505551i	0.556649	+	0.0183624i
$759$	1.84329			0.0669072
$760$	−27.3959	+	3.07626i	−0.993755	+	0.111588i
$761$	−27.9953			−1.01483			−0.507414	−	0.861702i	$-0.669399\pi$
$761$	−27.9953			−1.01483			−0.507414	+	0.861702i	$0.669399\pi$
$762$	52.8251	+	1.74257i	1.91365	+	0.0631265i
$763$	23.3677	−	27.8486i	0.845968	−	1.00819i
$764$	0.819638	−	12.4100i	0.0296535	−	0.448977i
$765$	−0.357119	+	0.198032i	−0.0129117	+	0.00715988i
$766$	−30.7406	+	34.2738i	−1.11070	+	1.23836i
$767$	−2.43126	−	4.21107i	−0.0877878	−	0.152053i
$768$	−23.9513	+	16.6994i	−0.864268	+	0.602589i
$769$	1.49615	+	8.48506i	0.0539524	+	0.305979i	0.999828	−	0.0185504i	$-0.00590512\pi$
$769$	1.49615	+	8.48506i	0.0539524	+	0.305979i	−0.945876	+	0.324530i	$0.894794\pi$
$770$	19.9213	−	10.2031i	0.717913	−	0.367695i
$771$	−0.251357	−	0.145121i	−0.00905242	−	0.00522642i
$772$	19.8148	+	18.9876i	0.713152	+	0.683379i
$773$	−7.60795	+	6.38383i	−0.273639	+	0.229610i	−0.769272	−	0.638922i	$-0.779381\pi$
$773$	−7.60795	+	6.38383i	−0.273639	+	0.229610i	0.495633	+	0.868532i	$0.334936\pi$
$774$	−0.578060	−	1.08213i	−0.0207779	−	0.0388962i
$775$	49.1097	+	1.69847i	1.76407	+	0.0610110i
$776$	−6.01212	+	21.4346i	−0.215822	+	0.769459i
$777$	46.6642	+	8.22816i	1.67407	+	0.295184i
$778$	−6.16735	−	43.2765i	−0.221110	−	1.55154i
$779$	−11.8323	−	18.1748i	−0.423937	−	0.651179i
$780$	−5.08839	+	2.39777i	−0.182194	+	0.0858538i
$781$	9.82756	+	1.73286i	0.351658	+	0.0620068i
$782$	−0.259309	−	0.161339i	−0.00927288	−	0.00576947i
$783$	40.1614	+	14.6176i	1.43525	+	0.522389i
$784$	−1.18744	+	1.54430i	−0.0424086	+	0.0551535i
$785$	−27.9976	+	32.2184i	−0.999276	+	1.14992i
$786$	−0.375929	+	0.294878i	−0.0134089	+	0.0105180i
$787$	26.7401	+	15.4384i	0.953182	+	0.550320i	0.894068	−	0.447931i	$-0.147839\pi$
$787$	26.7401	+	15.4384i	0.953182	+	0.550320i	0.0591139	+	0.998251i	$0.481172\pi$
$788$	−24.5531	+	12.0929i	−0.874667	+	0.430793i
$789$	−12.6071	+	2.22298i	−0.448826	+	0.0791402i
$790$	−8.69038	+	38.0059i	−0.309190	+	1.35219i
$791$	−22.9363	−	39.7268i	−0.815520	−	1.41252i
$792$	1.04650	−	2.17756i	0.0371856	−	0.0773763i
$793$	0.851959	−	0.310088i	0.0302540	−	0.0110115i
$794$	−4.43742	−	0.934251i	−0.157478	−	0.0331553i
$795$	34.7052	+	20.8451i	1.23087	+	0.739298i
$796$	21.1239	−	2.30273i	0.748716	−	0.0816181i
$797$	43.7968			1.55136			0.775681	−	0.631125i	$-0.217407\pi$
$797$	43.7968			1.55136			0.775681	+	0.631125i	$0.217407\pi$
$798$	−14.8402	+	26.9673i	−0.525336	+	0.954634i
$799$		−	1.10667i		−	0.0391512i
$800$	18.7149	−	21.2073i	0.661673	−	0.749793i
$801$	2.40989	−	2.87199i	0.0851491	−	0.101477i
$802$	−10.2537	−	2.15881i	−0.362071	−	0.0762301i
$803$	20.0939	−	7.31359i	0.709099	−	0.258091i
$804$	−6.35041	+	9.49376i	−0.223962	+	0.334819i
$805$	1.85649	−	1.50387i	0.0654327	−	0.0530045i
$806$	−8.88893	−	3.57141i	−0.313099	−	0.125798i
$807$	2.13006	+	12.0801i	0.0749815	+	0.425241i
$808$	−17.3912	+	11.8777i	−0.611819	+	0.417855i
$809$	24.0224	−	41.6081i	0.844584	−	1.46286i	−0.0413975	−	0.999143i	$-0.513181\pi$
$809$	24.0224	−	41.6081i	0.844584	−	1.46286i	0.885982	−	0.463720i	$-0.153486\pi$
$810$	22.8983	+	21.2633i	0.804564	+	0.747118i
$811$	−16.4856	+	13.8330i	−0.578887	+	0.485744i	−0.884581	−	0.466386i	$-0.845556\pi$
$811$	−16.4856	+	13.8330i	−0.578887	+	0.485744i	0.305695	+	0.952130i	$0.401111\pi$
$812$	−28.3670	−	38.7284i	−0.995486	−	1.35910i
$813$	−28.1490	−	10.2454i	−0.987229	−	0.359322i
$814$	−29.4746	−	18.3387i	−1.03308	−	0.642772i
$815$	34.0228	+	0.588168i	1.19177	+	0.0206026i
$816$	−3.40684	+	2.16560i	−0.119263	+	0.0758111i
$817$	−0.612346	−	11.4348i	−0.0214233	−	0.400055i
$818$	22.5214	−	3.20954i	0.787442	−	0.112219i
$819$	−0.108143	+	0.613309i	−0.00377882	+	0.0214307i
$820$	21.5153	+	5.67217i	0.751346	+	0.198081i
$821$	7.61347	+	2.77108i	0.265712	+	0.0967113i	0.471441	−	0.881898i	$-0.343734\pi$
$821$	7.61347	+	2.77108i	0.265712	+	0.0967113i	−0.205729	+	0.978609i	$0.565956\pi$
$822$	0.872571	+	1.63345i	0.0304344	+	0.0569731i
$823$	−12.8774	+	10.8055i	−0.448879	+	0.376654i	−0.839020	−	0.544101i	$-0.816871\pi$
$823$	−12.8774	+	10.8055i	−0.448879	+	0.376654i	0.390140	+	0.920755i	$0.372426\pi$
$824$	−25.9190	−	18.6028i	−0.902930	−	0.648058i
$825$	−4.89945	+	23.0882i	−0.170577	+	0.803826i
$826$	25.9472	−	8.48618i	0.902818	−	0.295272i
$827$	−17.7356	+	3.12726i	−0.616726	+	0.108745i	−0.473279	−	0.880913i	$-0.656930\pi$
$827$	−17.7356	+	3.12726i	−0.616726	+	0.108745i	−0.143447	+	0.989658i	$0.545819\pi$
$828$	0.0614230	−	0.250472i	0.00213460	−	0.00870449i
$829$	21.5482	−	12.4409i	0.748399	−	0.432089i	−0.0767159	−	0.997053i	$-0.524443\pi$
$829$	21.5482	−	12.4409i	0.748399	−	0.432089i	0.825115	+	0.564964i	$0.191110\pi$
$830$	2.20845	−	3.41639i	0.0766565	−	0.118585i
$831$	−34.1181	+	12.4180i	−1.18354	+	0.430774i
$832$	−4.83822	+	2.64488i	−0.167735	+	0.0916948i
$833$	−0.173123	+	0.206320i	−0.00599836	+	0.00714857i
$834$	10.2169	+	0.337031i	0.353784	+	0.0116704i
$835$	9.33898	−	1.48075i	0.323189	−	0.0512436i
$836$	17.4538	−	14.2789i	0.603651	−	0.493847i
$837$			47.8817i			1.65503i
$838$	1.57439	−	47.7271i	0.0543866	−	1.64870i
$839$	9.21482	+	7.73215i	0.318131	+	0.266943i	0.787843	−	0.615876i	$-0.211198\pi$
$839$	9.21482	+	7.73215i	0.318131	+	0.266943i	−0.469712	+	0.882820i	$0.655642\pi$
$840$	−7.28739	−	30.7283i	−0.251439	−	1.06023i
$841$	45.0604	−	16.4007i	1.55381	−	0.565540i
$842$	34.1752	−	38.1031i	1.17775	−	1.31312i
$843$	−19.5359	−	33.8372i	−0.672854	−	1.16542i
$844$	−1.39321	+	5.68125i	−0.0479563	+	0.195557i
$845$	26.4793	−	9.12250i	0.910914	−	0.313824i
$846$	0.888210	−	0.290495i	0.0305373	−	0.00998741i
$847$	5.89514	−	10.2107i	0.202559	−	0.350843i
$848$	35.1824	+	18.3597i	1.20817	+	0.630473i
$849$	4.71382	+	5.61772i	0.161778	+	0.192800i
$850$	2.71009	−	2.81914i	0.0929554	−	0.0966957i
$851$	−3.48207	−	1.26737i	−0.119364	−	0.0434449i
$852$	5.67727	−	12.8850i	0.194500	−	0.441434i
$853$	−35.6551	−	6.28695i	−1.22081	−	0.215261i	−0.474134	−	0.880453i	$-0.657239\pi$
$853$	−35.6551	−	6.28695i	−1.22081	−	0.215261i	−0.746673	+	0.665192i	$0.768350\pi$
$854$	0.718141	+	5.03921i	0.0245743	+	0.172438i
$855$	−1.20959	−	2.98262i	−0.0413672	−	0.102003i
$856$	24.7185	−	11.1774i	0.844862	−	0.382037i
$857$	−7.03750	+	39.9116i	−0.240396	+	1.36336i	0.590549	+	0.807002i	$0.298911\pi$
$857$	−7.03750	+	39.9116i	−0.240396	+	1.36336i	−0.830946	+	0.556354i	$0.812200\pi$
$858$	2.43073	−	3.90676i	0.0829839	−	0.133374i
$859$	8.44644	−	23.2064i	0.288189	−	0.791793i	−0.708131	−	0.706081i	$-0.750461\pi$
$859$	8.44644	−	23.2064i	0.288189	−	0.791793i	0.996320	−	0.0857116i	$-0.0273164\pi$
$860$	8.34101	+	8.27405i	0.284426	+	0.282143i
$861$	19.0313	−	15.9691i	0.648583	−	0.544226i
$862$	−27.3172	+	21.4276i	−0.930426	+	0.729826i
$863$	−44.0512	−	25.4330i	−1.49952	−	0.865748i	−0.499520	−	0.866303i	$-0.666490\pi$
$863$	−44.0512	−	25.4330i	−1.49952	−	0.865748i	−1.00000		0.000554480i	$0.999824\pi$
$864$	21.2826	+	17.5109i	0.724050	+	0.595732i
$865$	7.73942	−	2.66635i	0.263148	−	0.0906585i
$866$	6.75485	+	2.71397i	0.229539	+	0.0922246i
$867$	26.3834	−	15.2325i	0.896029	−	0.517322i
$868$	29.9024	−	44.7036i	1.01495	−	1.51734i
$869$	−10.9073	−	29.9675i	−0.370005	−	1.01658i
$870$	50.5590	+	2.54330i	1.71411	+	0.0862259i
$871$	−1.38648	+	1.65234i	−0.0469790	+	0.0559874i
$872$	9.30214	+	36.4090i	0.315010	+	1.23296i
$873$	−2.59905			−0.0879647
$874$	1.50911	−	1.87534i	0.0510465	−	0.0634345i
$875$	13.9022	+	27.2508i	0.469981	+	0.921244i
$876$	−3.26965	−	29.9938i	−0.110471	−	1.01340i
$877$	43.4600	+	36.4673i	1.46754	+	1.23141i	0.918383	+	0.395693i	$0.129496\pi$
$877$	43.4600	+	36.4673i	1.46754	+	1.23141i	0.549157	+	0.835719i	$0.314949\pi$
$878$	−3.57528	+	16.9816i	−0.120660	+	0.573100i
$879$	15.0705	+	41.4060i	0.508316	+	1.39659i
$880$	−3.43885	+	22.8792i	−0.115924	+	0.771259i
$881$	−22.9221	−	39.7023i	−0.772267	−	1.33761i	−0.936318	−	0.351153i	$-0.885790\pi$
$881$	−22.9221	−	39.7023i	−0.772267	−	1.33761i	0.164051	−	0.986452i	$-0.447544\pi$
$882$	−0.211036	−	0.0847904i	−0.00710595	−	0.00285504i
$883$	4.60416	+	26.1115i	0.154942	+	0.878721i	0.958839	+	0.283952i	$0.0916455\pi$
$883$	4.60416	+	26.1115i	0.154942	+	0.878721i	−0.803896	+	0.594769i	$0.797243\pi$
$884$	−0.683898	+	0.336835i	−0.0230020	+	0.0113290i
$885$	−10.3121	+	26.8775i	−0.346639	+	0.903477i
$886$	29.2239	−	22.9232i	0.981796	−	0.770121i
$887$	6.63716	+	7.90985i	0.222854	+	0.265587i	0.865874	−	0.500263i	$-0.166763\pi$
$887$	6.63716	+	7.90985i	0.222854	+	0.265587i	−0.643020	+	0.765849i	$0.722319\pi$
$888$	−35.0359	+	34.2283i	−1.17573	+	1.14863i
$889$	−19.1660	+	52.6581i	−0.642807	+	1.76610i
$890$	−13.9590	+	33.0782i	−0.467907	+	1.10878i
$891$	−25.1725	−	4.43859i	−0.843311	−	0.148699i
$892$	−1.14760	−	3.94458i	−0.0384244	−	0.132074i
$893$	8.65878	+	1.05315i	0.289755	+	0.0352422i
$894$	36.0017	−	5.13062i	1.20408	−	0.171594i
$895$	−45.1999	−	0.781393i	−1.51087	−	0.0261191i
$896$	−8.93438	−	29.6397i	−0.298477	−	0.990194i
$897$	0.167986	−	0.461537i	0.00560887	−	0.0154103i
$898$	30.1200	−	16.0898i	1.00512	−	0.536923i
$899$	55.4160	+	66.0422i	1.84823	+	2.20263i
$900$	2.97402	+	1.43511i	0.0991340	+	0.0478369i
$901$	4.75164	+	2.74336i	0.158300	+	0.0913947i
$902$	−17.2989	+	5.65771i	−0.575990	+	0.188381i
$903$	12.9187	−	2.27791i	0.429906	−	0.0758040i
$904$	47.1862	+	4.68325i	1.56939	+	0.155763i
$905$	−30.2454	−	37.3372i	−1.00539	−	1.24113i
$906$	−25.9618	+	28.9457i	−0.862523	+	0.961657i
$907$	−17.0157	−	46.7503i	−0.564998	−	1.55232i	−0.812215	−	0.583359i	$-0.801738\pi$
$907$	−17.0157	−	46.7503i	−0.564998	−	1.55232i	0.247217	−	0.968960i	$-0.420484\pi$
$908$	1.58245	−	23.9595i	0.0525154	−	0.795124i
$909$	−1.88352	−	1.58046i	−0.0624725	−	0.0524206i
$910$	−0.739234	−	5.91788i	−0.0245054	−	0.196176i
$911$	−3.84133			−0.127269			−0.0636344	−	0.997973i	$-0.520269\pi$
$911$	−3.84133			−0.127269			−0.0636344	+	0.997973i	$0.520269\pi$
$912$	−13.7020	−	28.7166i	−0.453717	−	0.950901i
$913$			3.32762i			0.110128i
$914$	−1.15162	+	34.9109i	−0.0380922	+	1.15475i
$915$	−4.60140	−	2.76375i	−0.152117	−	0.0913667i
$916$	28.6367	+	1.89136i	0.946182	+	0.0624922i
$917$	−0.173254	−	0.476013i	−0.00572137	−	0.0157193i
$918$	2.83664	+	2.54422i	0.0936230	+	0.0839717i
$919$	−33.9448	+	19.5980i	−1.11974	+	0.646480i	−0.941333	−	0.337478i	$-0.890426\pi$
$919$	−33.9448	+	19.5980i	−1.11974	+	0.646480i	−0.178402	+	0.983958i	$0.557093\pi$
$920$	0.143952	+	2.46548i	0.00474594	+	0.0812844i
$921$	−2.00738	−	11.3844i	−0.0661454	−	0.375129i
$922$	−25.8047	+	8.43958i	−0.849833	+	0.277943i
$923$	1.32951	−	2.30277i	0.0437613	−	0.0757967i
$924$	18.6516	+	17.8729i	0.613592	+	0.587976i
$925$	25.1298	−	40.2461i	0.826262	−	1.32328i
$926$	16.7450	+	31.3466i	0.550276	+	1.03011i
$927$	1.27394	−	3.50012i	0.0418417	−	0.114959i
$928$	49.6210	−	0.479129i	1.62889	−	0.0157282i
$929$	−5.98718	+	33.9550i	−0.196433	+	1.11403i	0.713931	+	0.700217i	$0.246913\pi$
$929$	−5.98718	+	33.9550i	−0.196433	+	1.11403i	−0.910363	+	0.413810i	$0.864198\pi$
$930$	16.6955	+	54.2013i	0.547466	+	1.77733i
$931$	−1.44954	−	1.55089i	−0.0475066	−	0.0508283i
$932$	−5.41510	−	18.6131i	−0.177378	−	0.609692i
$933$	9.12289	−	51.7385i	0.298670	−	1.69384i
$934$	−0.710418	+	1.14181i	−0.0232456	+	0.0373611i
$935$	−0.609827	+	3.14009i	−0.0199435	+	0.102692i
$936$	−0.449863	−	0.460478i	−0.0147042	−	0.0150512i
$937$	21.2716	+	25.3505i	0.694911	+	0.828163i	0.991940	−	0.126705i	$-0.0404402\pi$
$937$	21.2716	+	25.3505i	0.694911	+	0.828163i	−0.297029	+	0.954868i	$0.595996\pi$
$938$	−7.47401	−	9.52831i	−0.244035	−	0.311110i
$939$	28.9455	−	50.1351i	0.944601	−	1.63610i
$940$	−7.31000	+	5.16254i	−0.238426	+	0.168384i
$941$	38.2758	−	6.74905i	1.24775	−	0.220013i	0.489519	−	0.871993i	$-0.337172\pi$
$941$	38.2758	−	6.74905i	1.24775	−	0.220013i	0.758236	+	0.651980i	$0.226061\pi$
$942$	−45.7121	−	18.3663i	−1.48938	−	0.598406i
$943$	−1.68253	+	0.971411i	−0.0547908	+	0.0316335i
$944$	−8.51271	+	26.9048i	−0.277065	+	0.875677i
$945$	−26.0694	+	14.4562i	−0.848036	+	0.470260i
$946$	−9.40416	−	1.97994i	−0.305756	−	0.0643735i
$947$	−12.4334	−	10.4329i	−0.404033	−	0.339024i	0.418017	−	0.908439i	$-0.362725\pi$
$947$	−12.4334	−	10.4329i	−0.404033	−	0.339024i	−0.822050	+	0.569415i	$0.807170\pi$
$948$	−44.7320	+	4.87627i	−1.45283	+	0.158374i
$949$		−	5.69777i		−	0.184957i
$950$	19.4784	+	23.8870i	0.631964	+	0.774998i
$951$		−	53.0980i		−	1.72182i
$952$	−1.05948	−	4.14684i	−0.0343379	−	0.134400i
$953$	−13.2500	−	11.1181i	−0.429210	−	0.360150i	0.402443	−	0.915445i	$-0.368161\pi$
$953$	−13.2500	−	11.1181i	−0.429210	−	0.360150i	−0.831654	+	0.555295i	$0.812605\pi$
$954$	−0.954537	+	4.53378i	−0.0309043	+	0.146786i
$955$	−12.1604	+	6.74331i	−0.393503	+	0.218208i
$956$	−13.7162	−	9.17479i	−0.443612	−	0.296734i
$957$	−35.8612	+	20.7045i	−1.15923	+	0.669282i
$958$	13.8056	−	34.3609i	0.446038	−	1.11015i
$959$	−1.93363	+	0.340950i	−0.0624400	+	0.0110099i
$960$	30.1974	+	12.4012i	0.974615	+	0.400246i
$961$	−32.7930	+	56.7991i	−1.05784	+	1.83223i
$962$	−7.27791	+	5.70879i	−0.234649	+	0.184059i
$963$	2.03584	+	2.42622i	0.0656040	+	0.0781837i
$964$	−16.8461	−	22.9993i	−0.542576	−	0.740759i
$965$	5.84955	−	30.1203i	0.188304	−	0.969605i
$966$	2.34131	+	1.45673i	0.0753304	+	0.0468696i
$967$	0.493186	−	2.79699i	0.0158598	−	0.0899453i	−0.975850	−	0.218440i	$-0.929903\pi$
$967$	0.493186	−	2.79699i	0.0158598	−	0.0899453i	0.991710	+	0.128494i	$0.0410144\pi$
$968$	5.02152	+	11.1049i	0.161398	+	0.356926i
$969$	−1.72347	−	4.04742i	−0.0553660	−	0.130022i
$970$	23.7866	−	7.32692i	0.763742	−	0.235253i
$971$	2.47794	−	14.0531i	0.0795208	−	0.450985i	−0.918884	−	0.394527i	$-0.870908\pi$
$971$	2.47794	−	14.0531i	0.0795208	−	0.450985i	0.998405	−	0.0564574i	$-0.0179805\pi$
$972$	−2.75523	+	6.25324i	−0.0883741	+	0.200573i
$973$	−3.70691	+	10.1846i	−0.118838	+	0.326505i
$974$	9.80073	−	5.23544i	0.314036	−	0.167754i
$975$	5.33447	+	3.33086i	0.170840	+	0.106673i
$976$	−4.66467	−	2.43422i	−0.149312	−	0.0779175i
$977$	−26.4111	+	45.7454i	−0.844966	+	1.46352i	0.0406851	+	0.999172i	$0.487046\pi$
$977$	−26.4111	+	45.7454i	−0.844966	+	1.46352i	−0.885651	+	0.464352i	$0.846287\pi$
$978$	12.2083	+	37.3279i	0.390379	+	1.19362i
$979$	−5.09973	−	28.9220i	−0.162988	−	0.924352i
$980$	2.17044	+	0.181079i	0.0693321	+	0.00578434i
$981$	−3.79948	+	2.19363i	−0.121308	+	0.0700373i
$982$	−8.99019	+	10.0235i	−0.286889	+	0.319862i
$983$	−6.10489	−	16.7730i	−0.194716	−	0.534977i	0.803460	−	0.595359i	$-0.202990\pi$
$983$	−6.10489	−	16.7730i	−0.194716	−	0.534977i	−0.998175	+	0.0603823i	$0.980768\pi$
$984$	1.93976	+	25.6072i	0.0618374	+	0.816327i
$985$	26.2320	+	15.7558i	0.835822	+	0.502022i
$986$	6.85708	+	0.226197i	0.218374	+	0.00720360i
$987$			9.99215i			0.318054i
$988$	−1.98464	−	5.67148i	−0.0631397	−	0.180434i
$989$	−1.02585			−0.0326203
$990$	−2.68031	+	0.334812i	−0.0851858	+	0.0106410i
$991$	−13.6667	−	11.4677i	−0.434137	−	0.364285i	0.399373	−	0.916789i	$-0.369228\pi$
$991$	−13.6667	−	11.4677i	−0.434137	−	0.364285i	−0.833510	+	0.552504i	$0.813672\pi$
$992$	19.5180	+	52.0557i	0.619696	+	1.65277i
$993$	11.7567	+	32.3014i	0.373089	+	1.02505i
$994$	11.1133	+	9.96767i	0.352492	+	0.316155i
$995$	−14.9539	−	18.4602i	−0.474072	−	0.585229i
$996$	4.56006	+	1.11826i	0.144491	+	0.0354335i
$997$	31.9997	−	5.64242i	1.01344	−	0.178697i	0.357823	−	0.933789i	$-0.383519\pi$
$997$	31.9997	−	5.64242i	1.01344	−	0.178697i	0.655619	+	0.755092i	$0.272408\pi$
$998$	−5.04546	−	15.4269i	−0.159711	−	0.488330i
$999$	40.0391	+	23.1166i	1.26678	+	0.731377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.59.1	✓	336
4.3	odd	2	inner	380.2.bb.a.59.52	yes	336
5.4	even	2	inner	380.2.bb.a.59.56	yes	336
19.10	odd	18	inner	380.2.bb.a.219.5	yes	336
20.19	odd	2	inner	380.2.bb.a.59.5	yes	336
76.67	even	18	inner	380.2.bb.a.219.56	yes	336
95.29	odd	18	inner	380.2.bb.a.219.52	yes	336
380.219	even	18	inner	380.2.bb.a.219.1	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.1	✓	336	1.1	even	1	trivial
380.2.bb.a.59.5	yes	336	20.19	odd	2	inner
380.2.bb.a.59.52	yes	336	4.3	odd	2	inner
380.2.bb.a.59.56	yes	336	5.4	even	2	inner
380.2.bb.a.219.1	yes	336	380.219	even	18	inner
380.2.bb.a.219.5	yes	336	19.10	odd	18	inner
380.2.bb.a.219.52	yes	336	95.29	odd	18	inner
380.2.bb.a.219.56	yes	336	76.67	even	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41344 - 0.0466259i) q^{2} +(-1.17302 + 1.39795i) q^{3} +(1.99565 + 0.131806i) q^{4} +(-1.08439 - 1.95553i) q^{5} +(1.72317 - 1.92123i) q^{6} +(1.36812 + 2.36965i) q^{7} +(-2.81460 - 0.279350i) q^{8} +(-0.0573416 - 0.325200i) q^{9} +O(q^{10})\)	\(q+(-1.41344 - 0.0466259i) q^{2} +(-1.17302 + 1.39795i) q^{3} +(1.99565 + 0.131806i) q^{4} +(-1.08439 - 1.95553i) q^{5} +(1.72317 - 1.92123i) q^{6} +(1.36812 + 2.36965i) q^{7} +(-2.81460 - 0.279350i) q^{8} +(-0.0573416 - 0.325200i) q^{9} +(1.44155 + 2.81459i) q^{10} +(-2.24016 - 1.29335i) q^{11} +(-2.52519 + 2.63520i) q^{12} +(-0.527993 + 0.443038i) q^{13} +(-1.82327 - 3.41316i) q^{14} +(4.00573 + 0.777939i) q^{15} +(3.96525 + 0.526079i) q^{16} +(0.544629 + 0.0960328i) q^{17} +(0.0658864 + 0.462326i) q^{18} +(-1.26967 + 4.16989i) q^{19} +(-1.90632 - 4.04548i) q^{20} +(-4.91747 - 0.867083i) q^{21} +(3.10603 + 1.93253i) q^{22} +(0.366941 + 0.133555i) q^{23} +(3.69208 - 3.60697i) q^{24} +(-2.64818 + 4.24113i) q^{25} +(0.766946 - 0.601592i) q^{26} +(-4.21932 - 2.43603i) q^{27} +(2.41796 + 4.90933i) q^{28} +(-8.63898 + 1.52328i) q^{29} +(-5.62561 - 1.28635i) q^{30} +(-4.91391 - 8.51114i) q^{31} +(-5.58014 - 0.928468i) q^{32} +(4.43578 - 1.61449i) q^{33} +(-0.765325 - 0.161131i) q^{34} +(3.15034 - 5.24504i) q^{35} +(-0.0715704 - 0.656544i) q^{36} -9.48947 q^{37} +(1.98903 - 5.83470i) q^{38} -1.25780i q^{39} +(2.50586 + 5.80695i) q^{40} +(-3.19809 + 3.81133i) q^{41} +(6.91015 + 1.45486i) q^{42} +(-2.46866 + 0.898519i) q^{43} +(-4.30010 - 2.87635i) q^{44} +(-0.573757 + 0.464779i) q^{45} +(-0.512423 - 0.205882i) q^{46} +(-0.347487 - 1.97070i) q^{47} +(-5.38673 + 4.92611i) q^{48} +(-0.243505 + 0.421764i) q^{49} +(3.94080 - 5.87113i) q^{50} +(-0.773107 + 0.648714i) q^{51} +(-1.11208 + 0.814558i) q^{52} +(9.32287 + 3.39325i) q^{53} +(5.85020 + 3.63992i) q^{54} +(-0.0999769 + 5.78319i) q^{55} +(-3.18875 - 7.05181i) q^{56} +(-4.33993 - 6.66626i) q^{57} +(12.2817 - 1.75028i) q^{58} +(-1.22506 + 6.94767i) q^{59} +(7.89151 + 2.08048i) q^{60} +(-1.23607 - 0.449894i) q^{61} +(6.54870 + 12.2591i) q^{62} +(0.692162 - 0.580793i) q^{63} +(7.84393 + 1.57252i) q^{64} +(1.43893 + 0.552076i) q^{65} +(-6.34500 + 2.07517i) q^{66} +(3.08193 - 0.543427i) q^{67} +(1.07423 + 0.263434i) q^{68} +(-0.617130 + 0.356300i) q^{69} +(-4.69739 + 7.26668i) q^{70} +(-3.62520 + 1.31947i) q^{71} +(0.0705488 + 0.931326i) q^{72} +(-5.31372 + 6.33264i) q^{73} +(13.4128 + 0.442455i) q^{74} +(-2.82251 - 8.67691i) q^{75} +(-3.08343 + 8.15429i) q^{76} -7.07786i q^{77} +(-0.0586459 + 1.77783i) q^{78} +(9.44434 + 7.92474i) q^{79} +(-3.27114 - 8.32464i) q^{80} +(9.28567 - 3.37971i) q^{81} +(4.69803 - 5.23799i) q^{82} +(-0.643215 - 1.11408i) q^{83} +(-9.69928 - 2.37855i) q^{84} +(-0.402798 - 1.16917i) q^{85} +(3.53121 - 1.15490i) q^{86} +(8.00419 - 13.8637i) q^{87} +(5.94384 + 4.26606i) q^{88} +(7.29789 + 8.69728i) q^{89} +(0.832645 - 0.630187i) q^{90} +(-1.77221 - 0.645030i) q^{91} +(0.714682 + 0.314895i) q^{92} +(17.6622 + 3.11432i) q^{93} +(0.399268 + 2.80167i) q^{94} +(9.53115 - 2.03894i) q^{95} +(7.84354 - 6.71162i) q^{96} +(1.36674 - 7.75117i) q^{97} +(0.363846 - 0.584786i) q^{98} +(-0.292145 + 0.802662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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