LMFDB - Embedded newform 462.2.bf.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(5,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 25, 12]))

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

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

chi := DirichletCharacter("462.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bf (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$32$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	462.5
Dual form			462.2.bf.a.185.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207912 + 0.978148i) q^{2} +(1.70274 - 0.317274i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.03302 - 1.14729i) q^{5} +(-0.0436800 + 1.73150i) q^{6} +(-0.907001 + 2.48543i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.79867 - 1.08047i) q^{9} +O(q^{10})$	\(q+(-0.207912 + 0.978148i) q^{2} +(1.70274 - 0.317274i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.03302 - 1.14729i) q^{5} +(-0.0436800 + 1.73150i) q^{6} +(-0.907001 + 2.48543i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.79867 - 1.08047i) q^{9} +(1.33700 - 0.771915i) q^{10} +(3.30062 + 0.325408i) q^{11} +(-1.68458 - 0.402725i) q^{12} +(5.22383 - 1.69733i) q^{13} +(-2.24254 - 1.40393i) q^{14} +(-2.12298 - 1.62579i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-3.28117 + 0.697433i) q^{17} +(0.474983 + 2.96216i) q^{18} +(2.70867 + 6.08377i) q^{19} +(0.477070 + 1.46827i) q^{20} +(-0.755830 + 4.51981i) q^{21} +(-1.00453 + 3.16084i) q^{22} +(5.38329 + 3.10805i) q^{23} +(0.744168 - 1.56404i) q^{24} +(0.273508 - 2.60226i) q^{25} +(0.574139 + 5.46257i) q^{26} +(4.42262 - 2.72771i) q^{27} +(1.83950 - 1.90164i) q^{28} +(-1.75981 - 2.42217i) q^{29} +(2.03165 - 1.73857i) q^{30} +(-4.11689 - 3.70687i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(5.72336 - 0.493114i) q^{33} -3.35447i q^{34} +(3.78846 - 1.52691i) q^{35} +(-2.99618 - 0.151264i) q^{36} +(-0.343896 - 3.27196i) q^{37} +(-6.51399 + 1.38459i) q^{38} +(8.35633 - 4.54749i) q^{39} +(-1.53537 + 0.161374i) q^{40} +(2.69500 + 1.95803i) q^{41} +(-4.26390 - 1.67904i) q^{42} -3.13419 q^{43} +(-2.88291 - 1.63976i) q^{44} +(-4.13071 - 2.09474i) q^{45} +(-4.15938 + 4.61946i) q^{46} +(-10.1635 + 4.52509i) q^{47} +(1.37514 + 1.05309i) q^{48} +(-5.35470 - 4.50857i) q^{49} +(2.48853 + 0.808571i) q^{50} +(-5.36571 + 2.22858i) q^{51} +(-5.46257 - 0.574139i) q^{52} +(-0.749060 - 0.674456i) q^{53} +(1.74859 + 4.89310i) q^{54} +(-3.03628 - 4.12292i) q^{55} +(1.47763 + 2.19468i) q^{56} +(6.54239 + 9.49971i) q^{57} +(2.73513 - 1.21776i) q^{58} +(10.4568 + 4.65567i) q^{59} +(1.27817 + 2.34873i) q^{60} +(-3.24703 + 2.92364i) q^{61} +(4.48181 - 3.25623i) q^{62} +(0.147032 + 7.93589i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-7.34366 - 4.23987i) q^{65} +(-0.707615 + 5.70081i) q^{66} +(-5.28737 - 9.15800i) q^{67} +(3.28117 + 0.697433i) q^{68} +(10.1525 + 3.58423i) q^{69} +(0.705882 + 4.02313i) q^{70} +(-13.5346 - 4.39766i) q^{71} +(0.770900 - 2.89926i) q^{72} +(1.18946 - 2.67157i) q^{73} +(3.27196 + 0.343896i) q^{74} +(-0.359913 - 4.51775i) q^{75} -6.65951i q^{76} +(-3.80245 + 7.90831i) q^{77} +(2.71074 + 9.11920i) q^{78} +(-2.85521 - 0.606893i) q^{79} +(0.161374 - 1.53537i) q^{80} +(6.66516 - 6.04778i) q^{81} +(-2.47556 + 2.22901i) q^{82} +(-1.19899 + 3.69011i) q^{83} +(2.52886 - 3.82163i) q^{84} +(4.18968 + 3.04398i) q^{85} +(0.651634 - 3.06570i) q^{86} +(-3.76500 - 3.56600i) q^{87} +(2.20332 - 2.47899i) q^{88} +(-7.03694 + 12.1883i) q^{89} +(2.90778 - 3.60492i) q^{90} +(-0.519441 + 14.5229i) q^{91} +(-3.65373 - 5.02892i) q^{92} +(-8.18610 - 5.00566i) q^{93} +(-2.31309 - 10.8823i) q^{94} +(4.18172 - 9.39230i) q^{95} +(-1.31598 + 1.12614i) q^{96} +(-14.6249 + 4.75193i) q^{97} +(5.52335 - 4.30030i) q^{98} +(9.58896 - 2.65552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$3$	1.70274	−	0.317274i	0.983080	−	0.183178i
$3$	1.70274	−	0.317274i	0.983080	−	0.183178i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	−1.03302	−	1.14729i	−0.461982	−	0.513083i	0.466469	−	0.884538i	$-0.345526\pi$
$5$	−1.03302	−	1.14729i	−0.461982	−	0.513083i	−0.928451	+	0.371454i	$0.878859\pi$
$6$	−0.0436800	+	1.73150i	−0.0178323	+	0.706882i
$7$	−0.907001	+	2.48543i	−0.342814	+	0.939403i
$7$	−0.907001	+	2.48543i	−0.342814	+	0.939403i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	2.79867	−	1.08047i	0.932892	−	0.360157i
$10$	1.33700	−	0.771915i	0.422795	−	0.244101i
$11$	3.30062	+	0.325408i	0.995175	+	0.0981141i
$11$	3.30062	+	0.325408i	0.995175	+	0.0981141i
$12$	−1.68458	−	0.402725i	−0.486297	−	0.116257i
$13$	5.22383	−	1.69733i	1.44883	−	0.470753i	0.524192	−	0.851600i	$-0.324367\pi$
$13$	5.22383	−	1.69733i	1.44883	−	0.470753i	0.924638	+	0.380847i	$0.124367\pi$
$14$	−2.24254	−	1.40393i	−0.599344	−	0.375216i
$15$	−2.12298	−	1.62579i	−0.548151	−	0.419777i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−3.28117	+	0.697433i	−0.795800	+	0.169152i	−0.587832	−	0.808983i	$-0.700018\pi$
$17$	−3.28117	+	0.697433i	−0.795800	+	0.169152i	−0.207968	+	0.978136i	$0.566685\pi$
$18$	0.474983	+	2.96216i	0.111955	+	0.698188i
$19$	2.70867	+	6.08377i	0.621411	+	1.39571i	0.900250	+	0.435374i	$0.143384\pi$
$19$	2.70867	+	6.08377i	0.621411	+	1.39571i	−0.278839	+	0.960338i	$0.589949\pi$
$20$	0.477070	+	1.46827i	0.106676	+	0.328315i
$21$	−0.755830	+	4.51981i	−0.164936	+	0.986304i
$22$	−1.00453	+	3.16084i	−0.214168	+	0.673893i
$23$	5.38329	+	3.10805i	1.12249	+	0.648072i	0.942036	−	0.335511i	$-0.108909\pi$
$23$	5.38329	+	3.10805i	1.12249	+	0.648072i	0.180458	+	0.983583i	$0.442242\pi$
$24$	0.744168	−	1.56404i	0.151903	−	0.319258i
$25$	0.273508	−	2.60226i	0.0547016	−	0.520451i
$26$	0.574139	+	5.46257i	0.112598	+	1.07130i
$27$	4.42262	−	2.72771i	0.851134	−	0.524948i
$28$	1.83950	−	1.90164i	0.347633	−	0.359376i
$29$	−1.75981	−	2.42217i	−0.326789	−	0.449787i	0.613736	−	0.789511i	$-0.289666\pi$
$29$	−1.75981	−	2.42217i	−0.326789	−	0.449787i	−0.940525	+	0.339725i	$0.889666\pi$
$30$	2.03165	−	1.73857i	0.370927	−	0.317417i
$31$	−4.11689	−	3.70687i	−0.739415	−	0.665773i	0.210742	−	0.977542i	$-0.432412\pi$
$31$	−4.11689	−	3.70687i	−0.739415	−	0.665773i	−0.950158	+	0.311769i	$0.899079\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	5.72336	−	0.493114i	0.996309	−	0.0858401i
$34$		−	3.35447i		−	0.575287i
$35$	3.78846	−	1.52691i	0.640366	−	0.258095i
$36$	−2.99618	−	0.151264i	−0.499364	−	0.0252107i
$37$	−0.343896	−	3.27196i	−0.0565362	−	0.537906i	−0.985732	−	0.168320i	$-0.946166\pi$
$37$	−0.343896	−	3.27196i	−0.0565362	−	0.537906i	0.929196	−	0.369587i	$-0.120501\pi$
$38$	−6.51399	+	1.38459i	−1.05671	+	0.224610i
$39$	8.35633	−	4.54749i	1.33808	−	0.728182i
$40$	−1.53537	+	0.161374i	−0.242764	+	0.0255155i
$41$	2.69500	+	1.95803i	0.420888	+	0.305793i	0.777995	−	0.628271i	$-0.216237\pi$
$41$	2.69500	+	1.95803i	0.420888	+	0.305793i	−0.357107	+	0.934063i	$0.616237\pi$
$42$	−4.26390	−	1.67904i	−0.657934	−	0.259081i
$43$	−3.13419			−0.477959			−0.238980	−	0.971025i	$-0.576813\pi$
$43$	−3.13419			−0.477959			−0.238980	+	0.971025i	$0.576813\pi$
$44$	−2.88291	−	1.63976i	−0.434616	−	0.247203i
$45$	−4.13071	−	2.09474i	−0.615770	−	0.312265i
$46$	−4.15938	+	4.61946i	−0.613267	+	0.681102i
$47$	−10.1635	+	4.52509i	−1.48250	+	0.660053i	−0.978985	−	0.203932i	$-0.934628\pi$
$47$	−10.1635	+	4.52509i	−1.48250	+	0.660053i	−0.503518	+	0.863985i	$0.667961\pi$
$48$	1.37514	+	1.05309i	0.198484	+	0.152000i
$49$	−5.35470	−	4.50857i	−0.764957	−	0.644081i
$50$	2.48853	+	0.808571i	0.351931	+	0.114349i
$51$	−5.36571	+	2.22858i	−0.751350	+	0.312063i
$52$	−5.46257	−	0.574139i	−0.757522	−	0.0796188i
$53$	−0.749060	−	0.674456i	−0.102891	−	0.0926437i	0.616080	−	0.787684i	$-0.288720\pi$
$53$	−0.749060	−	0.674456i	−0.102891	−	0.0926437i	−0.718971	+	0.695040i	$0.755387\pi$
$54$	1.74859	+	4.89310i	0.237953	+	0.665867i
$55$	−3.03628	−	4.12292i	−0.409412	−	0.555935i
$56$	1.47763	+	2.19468i	0.197457	+	0.293276i
$57$	6.54239	+	9.49971i	0.866560	+	1.25827i
$58$	2.73513	−	1.21776i	0.359140	−	0.159899i
$59$	10.4568	+	4.65567i	1.36136	+	0.606117i	0.951956	−	0.306236i	$-0.0990696\pi$
$59$	10.4568	+	4.65567i	1.36136	+	0.606117i	0.409405	+	0.912353i	$0.365736\pi$
$60$	1.27817	+	2.34873i	0.165011	+	0.303219i
$61$	−3.24703	+	2.92364i	−0.415740	+	0.374334i	−0.850291	−	0.526313i	$-0.823574\pi$
$61$	−3.24703	+	2.92364i	−0.415740	+	0.374334i	0.434551	+	0.900647i	$0.356907\pi$
$62$	4.48181	−	3.25623i	0.569191	−	0.413541i
$63$	0.147032	+	7.93589i	0.0185243	+	0.999828i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−7.34366	−	4.23987i	−0.910869	−	0.525891i
$66$	−0.707615	+	5.70081i	−0.0871014	+	0.701722i
$67$	−5.28737	−	9.15800i	−0.645956	−	1.11883i	−0.984080	−	0.177726i	$-0.943126\pi$
$67$	−5.28737	−	9.15800i	−0.645956	−	1.11883i	0.338124	−	0.941101i	$-0.390208\pi$
$68$	3.28117	+	0.697433i	0.397900	+	0.0845762i
$69$	10.1525	+	3.58423i	1.22221	+	0.431490i
$70$	0.705882	+	4.02313i	0.0843690	+	0.480856i
$71$	−13.5346	−	4.39766i	−1.60626	−	0.521906i	−0.637616	−	0.770354i	$-0.720079\pi$
$71$	−13.5346	−	4.39766i	−1.60626	−	0.521906i	−0.968645	+	0.248448i	$0.920079\pi$
$72$	0.770900	−	2.89926i	0.0908515	−	0.341681i
$73$	1.18946	−	2.67157i	0.139216	−	0.312683i	−0.830460	−	0.557078i	$-0.811923\pi$
$73$	1.18946	−	2.67157i	0.139216	−	0.312683i	0.969676	+	0.244394i	$0.0785892\pi$
$74$	3.27196	+	0.343896i	0.380357	+	0.0399772i
$75$	−0.359913	−	4.51775i	−0.0415591	−	0.521665i
$76$		−	6.65951i		−	0.763898i
$77$	−3.80245	+	7.90831i	−0.433329	+	0.901236i
$78$	2.71074	+	9.11920i	0.306931	+	1.03255i
$79$	−2.85521	−	0.606893i	−0.321236	−	0.0682808i	0.0444716	−	0.999011i	$-0.485840\pi$
$79$	−2.85521	−	0.606893i	−0.321236	−	0.0682808i	−0.365707	+	0.930730i	$0.619173\pi$
$80$	0.161374	−	1.53537i	0.0180422	−	0.171660i
$81$	6.66516	−	6.04778i	0.740574	−	0.671975i
$82$	−2.47556	+	2.22901i	−0.273380	+	0.246153i
$83$	−1.19899	+	3.69011i	−0.131606	+	0.405042i	−0.995047	−	0.0994086i	$-0.968305\pi$
$83$	−1.19899	+	3.69011i	−0.131606	+	0.405042i	0.863441	+	0.504451i	$0.168305\pi$
$84$	2.52886	−	3.82163i	0.275921	−	0.416974i
$85$	4.18968	+	3.04398i	0.454435	+	0.330166i
$86$	0.651634	−	3.06570i	0.0702676	−	0.330583i
$87$	−3.76500	−	3.56600i	−0.403651	−	0.382315i
$88$	2.20332	−	2.47899i	0.234874	−	0.264261i
$89$	−7.03694	+	12.1883i	−0.745914	+	1.29196i	0.203853	+	0.979002i	$0.434654\pi$
$89$	−7.03694	+	12.1883i	−0.745914	+	1.29196i	−0.949767	+	0.312959i	$0.898680\pi$
$90$	2.90778	−	3.60492i	0.306507	−	0.379992i
$91$	−0.519441	+	14.5229i	−0.0544522	+	1.52242i
$92$	−3.65373	−	5.02892i	−0.380927	−	0.524301i
$93$	−8.18610	−	5.00566i	−0.848859	−	0.519063i
$94$	−2.31309	−	10.8823i	−0.238577	−	1.12242i
$95$	4.18172	−	9.39230i	0.429036	−	0.963630i
$96$	−1.31598	+	1.12614i	−0.134312	+	0.114936i
$97$	−14.6249	+	4.75193i	−1.48494	+	0.482485i	−0.935584	−	0.353105i	$-0.885126\pi$
$97$	−14.6249	+	4.75193i	−1.48494	+	0.482485i	−0.549354	+	0.835590i	$0.685126\pi$
$98$	5.52335	−	4.30030i	0.557943	−	0.434396i
$99$	9.58896	−	2.65552i	0.963727	−	0.266890i
$100$	−1.30830	+	2.26603i	−0.130830	+	0.226603i
$101$	5.80470	−	6.44678i	0.577590	−	0.641478i	−0.381571	−	0.924339i	$-0.624617\pi$
$101$	5.80470	−	6.44678i	0.577590	−	0.641478i	0.959161	+	0.282861i	$0.0912836\pi$
$102$	−1.06428	−	5.71180i	−0.105380	−	0.565553i
$103$	−0.603302	+	0.0634096i	−0.0594452	+	0.00624794i	−0.134204	−	0.990954i	$-0.542848\pi$
$103$	−0.603302	+	0.0634096i	−0.0594452	+	0.00624794i	0.0747592	+	0.997202i	$0.476181\pi$
$104$	1.69733	−	5.22383i	0.166436	−	0.512239i
$105$	5.96632	−	3.80192i	0.582254	−	0.371029i
$106$	0.815456	−	0.592463i	0.0792041	−	0.0575451i
$107$	2.31391	+	5.19713i	0.223694	+	0.502426i	0.990174	−	0.139843i	$-0.0446599\pi$
$107$	2.31391	+	5.19713i	0.223694	+	0.502426i	−0.766479	+	0.642269i	$0.777993\pi$
$108$	−5.14973	+	0.693046i	−0.495533	+	0.0666884i
$109$	−1.69064	−	2.92827i	−0.161934	−	0.280478i	0.773628	−	0.633640i	$-0.218440\pi$
$109$	−1.69064	−	2.92827i	−0.161934	−	0.280478i	−0.935562	+	0.353162i	$0.885106\pi$
$110$	4.66411	−	2.11273i	0.444705	−	0.201441i
$111$	−1.62367	−	5.46220i	−0.154112	−	0.518449i
$112$	−2.45393	+	0.989042i	−0.231875	+	0.0934557i
$113$	10.3035	−	14.1815i	0.969269	−	1.33408i	0.0268534	−	0.999639i	$-0.491451\pi$
$113$	10.3035	−	14.1815i	0.969269	−	1.33408i	0.942415	−	0.334445i	$-0.108549\pi$
$114$	−10.6524	+	4.42432i	−0.997685	+	0.414375i
$115$	−1.99524	−	9.38688i	−0.186057	−	0.875331i
$116$	0.622482	+	2.92855i	0.0577960	+	0.271909i
$117$	12.7859	−	10.3945i	1.18206	−	0.960968i
$118$	−6.72803	+	9.26034i	−0.619365	+	0.852483i
$119$	1.24260	−	8.78767i	0.113909	−	0.805565i
$120$	−2.56315	+	0.761912i	−0.233982	+	0.0695527i
$121$	10.7882	+	2.14810i	0.980747	+	0.195282i
$122$	−2.18466	−	3.78394i	−0.197790	−	0.342582i
$123$	5.21012	+	2.47897i	0.469781	+	0.223521i
$124$	2.25325	+	5.06088i	0.202348	+	0.454480i
$125$	−9.51300	+	6.91160i	−0.850869	+	0.618192i
$126$	−7.79304	−	1.50615i	−0.694259	−	0.134178i
$127$	1.17460	−	3.61504i	0.104229	−	0.320783i	−0.885320	−	0.464982i	$-0.846061\pi$
$127$	1.17460	−	3.61504i	0.104229	−	0.320783i	0.989549	+	0.144200i	$0.0460607\pi$
$128$	0.994522	−	0.104528i	0.0879041	−	0.00923910i
$129$	−5.33672	+	0.994395i	−0.469872	+	0.0875516i
$130$	5.67405	−	6.30167i	0.497647	−	0.552693i
$131$	7.60649	−	13.1748i	0.664582	−	1.15109i	−0.314817	−	0.949152i	$-0.601943\pi$
$131$	7.60649	−	13.1748i	0.664582	−	1.15109i	0.979399	−	0.201937i	$-0.0647236\pi$
$132$	−5.42912	−	1.87742i	−0.472544	−	0.163408i
$133$	−17.5775	+	1.21421i	−1.52416	+	0.105286i
$134$	10.0572	−	3.26778i	0.868808	−	0.282293i
$135$	−7.69815	−	2.25624i	−0.662551	−	0.194186i
$136$	−1.36439	+	3.06446i	−0.116995	+	0.262775i
$137$	−0.414629	−	1.95068i	−0.0354242	−	0.166658i	0.956880	−	0.290485i	$-0.0938165\pi$
$137$	−0.414629	−	1.95068i	−0.0354242	−	0.166658i	−0.992304	+	0.123827i	$0.960483\pi$
$138$	−5.61672	+	9.18541i	−0.478127	+	0.781914i
$139$	1.58886	+	2.18688i	0.134765	+	0.185488i	0.871066	−	0.491166i	$-0.163429\pi$
$139$	1.58886	+	2.18688i	0.134765	+	0.185488i	−0.736301	+	0.676654i	$0.763429\pi$
$140$	−4.08198	−	0.146000i	−0.344990	−	0.0123392i
$141$	−15.8702	+	10.9297i	−1.33651	+	0.920447i
$142$	7.11556	−	12.3245i	0.597124	−	1.03425i
$143$	17.7942	−	3.90236i	1.48803	−	0.326331i
$144$	2.67563	+	1.35684i	0.222969	+	0.113070i
$145$	−0.961006	+	4.52118i	−0.0798072	+	0.375463i
$146$	2.36589	+	1.71892i	0.195802	+	0.142259i
$147$	−10.5481	−	5.97804i	−0.869995	−	0.493060i
$148$	−1.01666	+	3.12896i	−0.0835689	+	0.257199i
$149$	−8.99650	+	8.10048i	−0.737022	+	0.663617i	−0.949578	−	0.313531i	$-0.898488\pi$
$149$	−8.99650	+	8.10048i	−0.737022	+	0.663617i	0.212556	+	0.977149i	$0.431821\pi$
$150$	4.49386	+	0.587246i	0.366922	+	0.0479484i
$151$	0.315591	−	3.00265i	0.0256825	−	0.244352i	−0.974148	−	0.225913i	$-0.927464\pi$
$151$	0.315591	−	3.00265i	0.0256825	−	0.244352i	0.999830	−	0.0184394i	$-0.00586979\pi$
$152$	6.51399	+	1.38459i	0.528354	+	0.112305i
$153$	−8.42936	+	5.49710i	−0.681473	+	0.444414i
$154$	−6.94492	−	5.36358i	−0.559638	−	0.432210i
$155$			8.55254i			0.686957i
$156$	−9.48352	+	0.755517i	−0.759289	+	0.0604898i
$157$	−21.0947	−	2.21714i	−1.68354	−	0.176947i	−0.786104	−	0.618094i	$-0.787905\pi$
$157$	−21.0947	−	2.21714i	−1.68354	−	0.176947i	−0.897435	+	0.441147i	$0.854572\pi$
$158$	1.18726	−	2.66663i	0.0944534	−	0.212146i
$159$	−1.48944	−	0.910770i	−0.118121	−	0.0722287i
$160$	1.46827	+	0.477070i	0.116077	+	0.0377157i
$161$	−12.6075	+	10.5608i	−0.993608	+	0.832306i
$162$	4.52985	+	7.77692i	0.355899	+	0.611012i
$163$	14.2270	+	3.02404i	1.11434	+	0.236861i	0.728057	−	0.685517i	$-0.240424\pi$
$163$	14.2270	+	3.02404i	1.11434	+	0.236861i	0.386288	+	0.922378i	$0.373757\pi$
$164$	−1.66560	−	2.88490i	−0.130061	−	0.225273i
$165$	−6.47811	−	6.05695i	−0.504320	−	0.471533i
$166$	−3.36019	−	1.94000i	−0.260801	−	0.150574i
$167$	−5.37819	−	16.5524i	−0.416177	−	1.28086i	−0.911194	−	0.411978i	$-0.864838\pi$
$167$	−5.37819	−	16.5524i	−0.416177	−	1.28086i	0.495017	−	0.868883i	$-0.335162\pi$
$168$	3.21234	+	3.26816i	0.247837	+	0.252144i
$169$	13.8903	−	10.0919i	1.06848	−	0.776298i
$170$	−3.84855	+	3.46525i	−0.295170	+	0.265772i
$171$	14.1540	+	14.0999i	1.08238	+	1.07824i
$172$	2.86322	+	1.27479i	0.218319	+	0.0972018i
$173$	−15.8454	+	7.05483i	−1.20470	+	0.536369i	−0.908149	−	0.418647i	$-0.862504\pi$
$173$	−15.8454	+	7.05483i	−1.20470	+	0.536369i	−0.296555	+	0.955016i	$0.595838\pi$
$174$	4.27086	−	2.94132i	0.323773	−	0.222981i
$175$	6.21965	+	3.04003i	0.470161	+	0.229805i
$176$	1.96672	+	2.67058i	0.148247	+	0.201303i
$177$	19.2824	+	4.60975i	1.44935	+	0.346490i
$178$	−10.4589	−	9.41726i	−0.783930	−	0.705853i
$179$	4.07983	+	0.428807i	0.304941	+	0.0320506i	0.255763	−	0.966739i	$-0.417673\pi$
$179$	4.07983	+	0.428807i	0.304941	+	0.0320506i	0.0491776	+	0.998790i	$0.484340\pi$
$180$	2.92159	+	3.59375i	0.217762	+	0.267862i
$181$	6.79407	+	2.20753i	0.504999	+	0.164084i	0.550427	−	0.834883i	$-0.314465\pi$
$181$	6.79407	+	2.20753i	0.504999	+	0.164084i	−0.0454274	+	0.998968i	$0.514465\pi$
$182$	−14.0976	−	3.52758i	−1.04498	−	0.261481i
$183$	−4.60127	+	6.00841i	−0.340136	+	0.444155i
$184$	5.67868	−	2.52831i	0.418638	−	0.186390i
$185$	−3.39863	+	3.77456i	−0.249872	+	0.277511i
$186$	6.59826	−	6.96648i	0.483808	−	0.510807i
$187$	−11.0568	+	1.23425i	−0.808556	+	0.0902571i
$188$	11.1254			0.811401
$189$	2.76821	+	13.4661i	0.201357	+	0.979518i
$190$	8.31763	+	6.04311i	0.603424	+	0.438413i
$191$	12.4041	−	1.30372i	0.897529	−	0.0943341i	0.355483	−	0.934683i	$-0.384316\pi$
$191$	12.4041	−	1.30372i	0.897529	−	0.0943341i	0.542046	+	0.840349i	$0.317650\pi$
$192$	−0.827922	−	1.52136i	−0.0597501	−	0.109795i
$193$	9.48296	−	2.01567i	0.682598	−	0.145091i	0.146455	−	0.989217i	$-0.453214\pi$
$193$	9.48296	−	2.01567i	0.682598	−	0.145091i	0.536144	+	0.844127i	$0.319880\pi$
$194$	−1.60739	−	15.2933i	−0.115404	−	1.09800i
$195$	−13.8496	−	4.88946i	−0.991789	−	0.350141i
$196$	3.05796	+	6.29674i	0.218426	+	0.449767i
$197$		−	3.83866i		−	0.273493i	−0.990606	−	0.136747i	$-0.956335\pi$
$197$		−	3.83866i		−	0.273493i	0.990606	−	0.136747i	$-0.0436646\pi$
$198$	0.603830	+	9.93154i	0.0429124	+	0.705803i
$199$	0.256695	−	0.148203i	0.0181967	−	0.0105058i	−0.490874	−	0.871231i	$-0.663322\pi$
$199$	0.256695	−	0.148203i	0.0181967	−	0.0105058i	0.509071	+	0.860725i	$0.329989\pi$
$200$	−1.94451	−	1.75084i	−0.137497	−	0.123803i
$201$	−11.9086	−	13.9162i	−0.839971	−	0.981572i
$202$	5.09903	+	7.01822i	0.358767	+	0.493800i
$203$	7.61629	−	2.17697i	0.534559	−	0.152793i
$204$	5.80826	+	0.146523i	0.406660	+	0.0102587i
$205$	−0.537569	−	5.11463i	−0.0375455	−	0.357221i
$206$	0.0634096	−	0.603302i	0.00441796	−	0.0420341i
$207$	18.4242	+	2.88192i	1.28057	+	0.200307i
$208$	4.75678	+	2.74633i	0.329824	+	0.190424i
$209$	6.96058	+	20.9616i	0.481474	+	1.44995i
$210$	2.47837	+	6.62641i	0.171024	+	0.457266i
$211$	5.81643	+	17.9011i	0.400420	+	1.23237i	0.924660	+	0.380795i	$0.124350\pi$
$211$	5.81643	+	17.9011i	0.400420	+	1.23237i	−0.524240	+	0.851571i	$0.675650\pi$
$212$	0.409974	+	0.920816i	0.0281571	+	0.0632419i
$213$	−24.4412	−	3.19392i	−1.67468	−	0.218843i
$214$	−5.56465	+	1.18280i	−0.380392	+	0.0808547i
$215$	3.23769	+	3.59582i	0.220809	+	0.245233i
$216$	0.392787	−	5.18129i	0.0267258	−	0.352542i
$217$	12.9472	−	6.87010i	0.878911	−	0.466373i
$218$	3.21579	−	1.04487i	0.217800	−	0.0707677i
$219$	1.17773	−	4.92638i	0.0795833	−	0.332894i
$220$	1.09684	+	5.00144i	0.0739490	+	0.337197i
$221$	−15.9565	+	9.21248i	−1.07335	+	0.619699i
$222$	5.68041	−	0.452538i	0.381244	−	0.0303723i
$223$	9.70766	−	13.3614i	0.650073	−	0.894749i	−0.349029	−	0.937112i	$-0.613489\pi$
$223$	9.70766	−	13.3614i	0.650073	−	0.894749i	0.999102	+	0.0423631i	$0.0134886\pi$
$224$	−0.457228	−	2.60594i	−0.0305498	−	0.174117i
$225$	−2.04620	−	7.57839i	−0.136414	−	0.505226i
$226$	11.7294	+	13.0268i	0.780228	+	0.866531i
$227$	0.983880	+	0.438052i	0.0653024	+	0.0290745i	0.439128	−	0.898425i	$-0.355287\pi$
$227$	0.983880	+	0.438052i	0.0653024	+	0.0290745i	−0.373826	+	0.927499i	$0.621954\pi$
$228$	−2.11289	−	11.3394i	−0.139929	−	0.750973i
$229$	−0.298937	+	1.40639i	−0.0197543	+	0.0929368i	−0.986920	−	0.161209i	$-0.948461\pi$
$229$	−0.298937	+	1.40639i	−0.0197543	+	0.0929368i	0.967166	+	0.254145i	$0.0817942\pi$
$230$	9.59658			0.632780
$231$	−3.96549	+	14.6722i	−0.260910	+	0.965363i
$232$	−2.99397			−0.196564
$233$	0.449739	−	2.11586i	0.0294634	−	0.138614i	−0.960957	−	0.276696i	$-0.910760\pi$
$233$	0.449739	−	2.11586i	0.0294634	−	0.138614i	0.990421	+	0.138082i	$0.0440937\pi$
$234$	7.50898	+	14.6676i	0.490877	+	0.958852i
$235$	15.6908	+	6.98597i	1.02355	+	0.455715i
$236$	−7.65914	−	8.50634i	−0.498567	−	0.553715i
$237$	−5.05424	−	0.127502i	−0.328308	−	0.00828213i
$238$	8.33729	+	3.04251i	0.540426	+	0.197216i
$239$	−17.6152	+	24.2452i	−1.13943	+	1.56829i	−0.370661	+	0.928768i	$0.620869\pi$
$239$	−17.6152	+	24.2452i	−1.13943	+	1.56829i	−0.768771	+	0.639524i	$0.779131\pi$
$240$	−0.212354	−	2.66555i	−0.0137074	−	0.172060i
$241$	−3.14193	+	1.81399i	−0.202389	+	0.116850i	−0.597769	−	0.801668i	$-0.703946\pi$
$241$	−3.14193	+	1.81399i	−0.202389	+	0.116850i	0.395380	+	0.918518i	$0.370613\pi$
$242$	−4.34415	+	10.1059i	−0.279253	+	0.649629i
$243$	9.43027	−	12.4125i	0.604952	−	0.796262i
$244$	4.15546	−	1.35019i	0.266026	−	0.0864372i
$245$	0.358897	+	10.8008i	0.0229291	+	0.690041i
$246$	−3.50805	+	4.58086i	−0.223665	+	0.292065i
$247$	24.4758	+	27.1831i	1.55736	+	1.72962i
$248$	−5.41876	+	1.15179i	−0.344092	+	0.0731390i
$249$	−0.870797	+	6.66372i	−0.0551845	+	0.422296i
$250$	−4.78270	−	10.7421i	−0.302485	−	0.679391i
$251$	1.51913	+	4.67539i	0.0958864	+	0.295108i	0.987484	−	0.157721i	$-0.0504148\pi$
$251$	1.51913	+	4.67539i	0.0958864	+	0.295108i	−0.891597	+	0.452829i	$0.850415\pi$
$252$	3.09350	−	7.30960i	0.194872	−	0.460462i
$253$	16.7568	+	12.0102i	1.05349	+	0.755078i
$254$	3.29183	+	1.90054i	0.206548	+	0.119250i
$255$	8.09973	+	3.85385i	0.507225	+	0.241337i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	0.374676	+	3.56481i	0.0233717	+	0.222367i	0.999973	+	0.00731007i	$0.00232689\pi$
$257$	0.374676	+	3.56481i	0.0233717	+	0.222367i	−0.976602	+	0.215056i	$0.931006\pi$
$258$	0.136901	−	5.42685i	0.00852311	−	0.337861i
$259$	8.44412	+	2.11294i	0.524692	+	0.131292i
$260$	4.98426	+	6.86025i	0.309111	+	0.425454i
$261$	−7.54223	−	4.87745i	−0.466853	−	0.301907i
$262$	11.3054	+	10.1795i	0.698453	+	0.628889i
$263$	−6.32889	+	3.65399i	−0.390256	+	0.225314i	−0.682271	−	0.731099i	$-0.739008\pi$
$263$	−6.32889	+	3.65399i	−0.390256	+	0.225314i	0.292015	+	0.956414i	$0.405674\pi$
$264$	2.96517	−	4.92014i	0.182493	−	0.302814i
$265$			1.55612i			0.0955915i
$266$	2.46689	−	17.4459i	0.151255	−	1.06967i
$267$	−8.11507	+	22.9862i	−0.496634	+	1.40674i
$268$	1.10536	+	10.5168i	0.0675207	+	0.642417i
$269$	−24.1577	+	5.13488i	−1.47292	+	0.313079i	−0.873292	−	0.487197i	$-0.838019\pi$
$269$	−24.1577	+	5.13488i	−1.47292	+	0.313079i	−0.599631	+	0.800277i	$0.704686\pi$
$270$	3.80747	−	7.06083i	0.231715	−	0.429708i
$271$	−2.06683	+	0.217233i	−0.125551	+	0.0131959i	−0.167096	−	0.985941i	$-0.553439\pi$
$271$	−2.06683	+	0.217233i	−0.125551	+	0.0131959i	0.0415445	+	0.999137i	$0.486772\pi$
$272$	−2.71382	−	1.97171i	−0.164550	−	0.119552i
$273$	3.72327	+	24.8936i	0.225342	+	1.50663i
$274$	1.99426			0.120477
$275$	1.74954	−	8.50006i	0.105501	−	0.512573i
$276$	−7.81690	−	7.40374i	−0.470522	−	0.445653i
$277$	15.6730	−	17.4066i	0.941698	−	1.04586i	−0.0571736	−	0.998364i	$-0.518209\pi$
$277$	15.6730	−	17.4066i	0.941698	−	1.04586i	0.998871	−	0.0474971i	$-0.0151245\pi$
$278$	−2.46943	+	1.09946i	−0.148107	+	0.0659413i
$279$	−15.5270	−	5.92613i	−0.929577	−	0.354788i
$280$	0.991501	−	3.96242i	0.0592535	−	0.236800i
$281$	6.52782	+	2.12102i	0.389417	+	0.126529i	0.497180	−	0.867647i	$-0.334369\pi$
$281$	6.52782	+	2.12102i	0.389417	+	0.126529i	−0.107763	+	0.994177i	$0.534369\pi$
$282$	−7.39126	−	17.7958i	−0.440143	−	1.05972i
$283$	−20.9060	−	2.19731i	−1.24273	−	0.130616i	−0.539750	−	0.841825i	$-0.681481\pi$
$283$	−20.9060	−	2.19731i	−1.24273	−	0.130616i	−0.702981	+	0.711209i	$0.748148\pi$
$284$	10.5758	+	9.52248i	0.627557	+	0.565055i
$285$	4.14047	−	17.3194i	0.245260	−	1.02591i
$286$	0.117454	+	18.2167i	0.00694521	+	1.07718i
$287$	−7.31090	+	4.92228i	−0.431549	+	0.290553i
$288$	−1.88349	+	2.33505i	−0.110986	+	0.137594i
$289$	−5.25063	+	2.33773i	−0.308861	+	0.137514i
$290$	−4.22257	−	1.88001i	−0.247958	−	0.110398i
$291$	−23.3949	+	12.7314i	−1.37143	+	0.746330i
$292$	−2.17325	+	1.95680i	−0.127180	+	0.114513i
$293$	−14.2793	+	10.3745i	−0.834204	+	0.606084i	−0.920745	−	0.390164i	$-0.872418\pi$
$293$	−14.2793	+	10.3745i	−0.834204	+	0.606084i	0.0865419	+	0.996248i	$0.472418\pi$
$294$	8.04048	−	9.07473i	0.468930	−	0.529249i
$295$	−5.46073	−	16.8064i	−0.317936	−	0.978507i
$296$	−2.84921	−	1.64499i	−0.165607	−	0.0956131i
$297$	15.4850	−	7.56399i	0.898532	−	0.438907i
$298$	−6.05299	−	10.4841i	−0.350640	−	0.607327i
$299$	33.3968	+	7.09870i	1.93139	+	0.410529i
$300$	−1.50874	+	4.27356i	−0.0871071	+	0.246734i
$301$	2.84271	−	7.78980i	0.163851	−	0.448996i
$302$	2.87142	+	0.932981i	0.165232	+	0.0536870i
$303$	7.83853	−	12.8189i	0.450312	−	0.736426i
$304$	−2.70867	+	6.08377i	−0.155353	+	0.348928i
$305$	6.70852	+	0.705094i	0.384129	+	0.0403736i
$306$	−3.62441	−	9.38807i	−0.207194	−	0.536680i
$307$			20.3672i			1.16242i	0.813754	+	0.581209i	$0.197420\pi$
$307$			20.3672i			1.16242i	−0.813754	+	0.581209i	$0.802580\pi$
$308$	6.69031	−	5.67801i	0.381216	−	0.323535i
$309$	−1.00715	+	0.299382i	−0.0572948	+	0.0170313i
$310$	−8.36565	−	1.77817i	−0.475137	−	0.100993i
$311$	0.672579	−	6.39916i	0.0381384	−	0.362863i	−0.958763	−	0.284206i	$-0.908270\pi$
$311$	0.672579	−	6.39916i	0.0381384	−	0.362863i	0.996902	−	0.0786572i	$-0.0250633\pi$
$312$	1.23273	−	9.43336i	0.0697895	−	0.534059i
$313$	−8.45581	+	7.61364i	−0.477950	+	0.430348i	−0.872565	−	0.488498i	$-0.837545\pi$
$313$	−8.45581	+	7.61364i	−0.477950	+	0.430348i	0.394614	+	0.918847i	$0.370878\pi$
$314$	6.55452	−	20.1727i	0.369893	−	1.13841i
$315$	8.95287	−	8.36665i	0.504437	−	0.471407i
$316$	2.36151	+	1.71574i	0.132846	+	0.0965180i
$317$	0.971741	−	4.57168i	0.0545784	−	0.256771i	−0.942396	−	0.334499i	$-0.891433\pi$
$317$	0.971741	−	4.57168i	0.0545784	−	0.256771i	0.996975	+	0.0777274i	$0.0247664\pi$
$318$	1.20054	−	1.26754i	0.0673229	−	0.0710799i
$319$	−5.02028	−	8.56734i	−0.281082	−	0.479679i
$320$	−0.771915	+	1.33700i	−0.0431513	+	0.0747403i
$321$	5.58891	+	8.11524i	0.311943	+	0.452949i
$322$	−7.70876	−	14.5277i	−0.429592	−	0.809596i
$323$	−13.1306	−	18.0727i	−0.730607	−	1.00559i
$324$	−8.54878	+	2.81395i	−0.474932	+	0.156331i
$325$	−2.98812	−	14.0580i	−0.165751	−	0.779796i
$326$	−5.91592	+	13.2874i	−0.327652	+	0.735919i
$327$	−3.80779	−	4.44970i	−0.210571	−	0.246069i
$328$	3.16816	−	1.02940i	0.174932	−	0.0568389i
$329$	−2.02846	−	29.3650i	−0.111833	−	1.61894i
$330$	7.27146	−	5.07724i	0.400281	−	0.279493i
$331$	−8.67369	+	15.0233i	−0.476749	+	0.825753i	−0.999645	−	0.0266432i	$-0.991518\pi$
$331$	−8.67369	+	15.0233i	−0.476749	+	0.825753i	0.522896	+	0.852396i	$0.324852\pi$
$332$	2.59623	−	2.88341i	0.142487	−	0.158248i
$333$	−4.49771	−	8.78557i	−0.246473	−	0.481446i
$334$	17.3089	−	1.81923i	0.947098	−	0.0995441i
$335$	−5.04489	+	15.5266i	−0.275632	+	0.848308i
$336$	−3.86463	+	2.46265i	−0.210833	+	0.134349i
$337$	−28.4771	+	20.6899i	−1.55125	+	1.12705i	−0.608495	+	0.793557i	$0.708227\pi$
$337$	−28.4771	+	20.6899i	−1.55125	+	1.12705i	−0.942753	+	0.333491i	$0.891773\pi$
$338$	6.98339	+	15.6850i	0.379846	+	0.853149i
$339$	13.0448	−	27.4165i	0.708494	−	1.48906i
$340$	−2.58936	−	4.48491i	−0.140428	−	0.243228i
$341$	−12.3821	−	13.5746i	−0.670526	−	0.735108i
$342$	−16.7345	+	10.9132i	−0.904899	+	0.590118i
$343$	16.0624	−	9.21944i	0.867290	−	0.497803i
$344$	−1.84223	+	2.53561i	−0.0993264	+	0.136711i
$345$	−6.37559	−	15.3504i	−0.343250	−	0.826438i
$346$	−3.60622	−	16.9659i	−0.193872	−	0.912094i
$347$	−4.79647	−	22.5656i	−0.257488	−	1.21139i	−0.896799	−	0.442438i	$-0.854114\pi$
$347$	−4.79647	−	22.5656i	−0.257488	−	1.21139i	0.639311	−	0.768948i	$-0.279220\pi$
$348$	1.98908	+	4.78907i	0.106626	+	0.256721i
$349$	2.17917	−	2.99936i	0.116648	−	0.160552i	−0.746700	−	0.665161i	$-0.768363\pi$
$349$	2.17917	−	2.99936i	0.116648	−	0.160552i	0.863348	+	0.504608i	$0.168363\pi$
$350$	−4.26674	+	5.45167i	−0.228067	+	0.291404i
$351$	18.4732	−	21.7557i	0.986027	−	1.16124i
$352$	−3.02113	+	1.36850i	−0.161027	+	0.0729413i
$353$	5.05807	+	8.76084i	0.269214	+	0.466292i	0.968659	−	0.248394i	$-0.0799028\pi$
$353$	5.05807	+	8.76084i	0.269214	+	0.466292i	−0.699445	+	0.714686i	$0.746569\pi$
$354$	−8.51805	+	17.9026i	−0.452729	+	0.951513i
$355$	8.93618	+	20.0710i	0.474283	+	1.06526i
$356$	11.3860	−	8.27241i	0.603457	−	0.438437i
$357$	−0.672264	−	15.3574i	−0.0355800	−	0.812800i
$358$	−1.26768	+	3.90152i	−0.0669990	+	0.206202i
$359$	33.9907	−	3.57257i	1.79396	−	0.188553i	0.851835	−	0.523810i	$-0.175490\pi$
$359$	33.9907	−	3.57257i	1.79396	−	0.188553i	0.942127	+	0.335257i	$0.108823\pi$
$360$	−4.12265	+	2.11056i	−0.217283	+	0.111236i
$361$	−16.9619	+	18.8381i	−0.892730	+	0.991477i
$362$	−3.57186	+	6.18663i	−0.187733	+	0.325162i
$363$	19.0511	+	0.234842i	0.999924	+	0.0123260i
$364$	6.38154	−	13.0561i	0.334484	−	0.684324i
$365$	−4.29380	+	1.39514i	−0.224748	+	0.0730250i
$366$	−4.92045	−	5.74994i	−0.257196	−	0.300554i
$367$	0.959253	−	2.15452i	0.0500726	−	0.112465i	−0.886777	−	0.462198i	$-0.847061\pi$
$367$	0.959253	−	2.15452i	0.0500726	−	0.112465i	0.936849	+	0.349733i	$0.113728\pi$
$368$	1.29240	+	6.08025i	0.0673709	+	0.316955i
$369$	9.65801	+	2.56802i	0.502776	+	0.133686i
$370$	−2.98546	−	4.10913i	−0.155207	−	0.213624i
$371$	2.35571	−	1.25000i	0.122302	−	0.0648968i
$372$	5.44239	+	7.90249i	0.282175	+	0.409725i
$373$	−5.15858	+	8.93492i	−0.267101	+	0.462633i	−0.968112	−	0.250518i	$-0.919399\pi$
$373$	−5.15858	+	8.93492i	−0.267101	+	0.462633i	0.701011	+	0.713151i	$0.252732\pi$
$374$	1.09157	−	11.0718i	0.0564438	−	0.572511i
$375$	−14.0053	+	14.7869i	−0.723233	+	0.763593i
$376$	−2.31309	+	10.8823i	−0.119289	+	0.561209i
$377$	−13.3042	−	9.66605i	−0.685200	−	0.497827i
$378$	−13.7474	−	0.0920544i	−0.707091	−	0.00473477i
$379$	10.2708	−	31.6102i	0.527574	−	1.62370i	−0.231596	−	0.972812i	$-0.574395\pi$
$379$	10.2708	−	31.6102i	0.527574	−	1.62370i	0.759170	−	0.650893i	$-0.225605\pi$
$380$	−7.64039	+	6.87943i	−0.391943	+	0.352908i
$381$	0.853082	−	6.52815i	0.0437047	−	0.334447i
$382$	−1.30372	+	12.4041i	−0.0667043	+	0.634649i
$383$	0.00701042	+	0.00149011i	0.000358216	+	7.61411e-5i	0.208091	−	0.978110i	$-0.433275\pi$
$383$	0.00701042	+	0.00149011i	0.000358216	+	7.61411e-5i	−0.207733	+	0.978186i	$0.566608\pi$
$384$	1.66025	−	0.493521i	0.0847244	−	0.0251849i
$385$	13.0011	−	3.80697i	0.662599	−	0.194021i
$386$			9.69481i			0.493453i
$387$	−8.77158	+	3.38640i	−0.445884	+	0.172140i
$388$	15.2933	+	1.60739i	0.776401	+	0.0816031i
$389$	11.3779	−	25.5551i	0.576881	−	1.29570i	−0.355655	−	0.934617i	$-0.615742\pi$
$389$	11.3779	−	25.5551i	0.576881	−	1.29570i	0.932536	−	0.361078i	$-0.117591\pi$
$390$	7.66210	−	12.5304i	0.387985	−	0.634499i
$391$	−19.8311	−	6.44353i	−1.00290	−	0.325863i
$392$	−6.79492	+	1.68197i	−0.343195	+	0.0849523i
$393$	8.77188	−	24.8467i	0.442483	−	1.25335i
$394$	3.75478	+	0.798102i	0.189163	+	0.0402078i
$395$	2.25321	+	3.90268i	0.113371	+	0.196365i
$396$	−9.84005	−	1.47425i	−0.494481	−	0.0740837i
$397$	28.5378	+	16.4763i	1.43227	+	0.826922i	0.997294	−	0.0735198i	$-0.0234232\pi$
$397$	28.5378	+	16.4763i	1.43227	+	0.826922i	0.434977	+	0.900442i	$0.356757\pi$
$398$	0.0915946	+	0.281899i	0.00459122	+	0.0141303i
$399$	−29.5448	+	7.64438i	−1.47909	+	0.382698i
$400$	2.11687	−	1.53799i	0.105843	−	0.0768997i
$401$	6.25695	−	5.63379i	0.312457	−	0.281338i	−0.497949	−	0.867206i	$-0.665913\pi$
$401$	6.25695	−	5.63379i	0.312457	−	0.281338i	0.810406	+	0.585869i	$0.199247\pi$
$402$	16.0880	−	8.75507i	0.802398	−	0.436663i
$403$	−27.7977	−	12.3763i	−1.38470	−	0.616509i
$404$	−7.92500	+	3.52844i	−0.394283	+	0.175546i
$405$	−13.8238	−	1.39937i	−0.686911	−	0.0695354i
$406$	0.545884	+	7.90247i	0.0270918	+	0.392193i
$407$	−0.0703524	−	10.9114i	−0.00348724	−	0.540858i
$408$	−1.35093	+	5.65088i	−0.0668809	+	0.279760i
$409$	−8.27908	−	7.45452i	−0.409374	−	0.368602i	0.438562	−	0.898701i	$-0.355488\pi$
$409$	−8.27908	−	7.45452i	−0.409374	−	0.368602i	−0.847936	+	0.530099i	$0.822155\pi$
$410$	5.11463	+	0.537569i	0.252594	+	0.0265487i
$411$	−1.32491	−	3.18995i	−0.0653528	−	0.157349i
$412$	0.576935	+	0.187458i	0.0284236	+	0.00923537i
$413$	−21.0557	+	21.7669i	−1.03608	+	1.07108i
$414$	−6.64955	+	17.4224i	−0.326808	+	0.856266i
$415$	5.47220	−	2.43638i	0.268620	−	0.119597i
$416$	−3.67531	+	4.08184i	−0.180197	+	0.200129i
$417$	3.39926	+	3.21959i	0.166462	+	0.157664i
$418$	−21.9508	+	2.45031i	−1.07365	+	0.119849i
$419$	25.0492			1.22373			0.611867	−	0.790961i	$-0.290419\pi$
$419$	25.0492			1.22373			0.611867	+	0.790961i	$0.290419\pi$
$420$	−6.99689	+	1.04650i	−0.341413	+	0.0510641i
$421$	−5.39542	−	3.92000i	−0.262957	−	0.191049i	0.448493	−	0.893786i	$-0.351961\pi$
$421$	−5.39542	−	3.92000i	−0.262957	−	0.191049i	−0.711450	+	0.702737i	$0.751961\pi$
$422$	−18.7193	+	1.96747i	−0.911239	+	0.0957751i
$423$	−23.5552	+	23.6457i	−1.14529	+	1.14969i
$424$	−0.985933	+	0.209566i	−0.0478811	+	0.0101774i
$425$	0.917475	+	8.72919i	0.0445041	+	0.423428i
$426$	8.20574	−	23.2431i	0.397569	−	1.12613i
$427$	−4.32144	−	10.7220i	−0.209129	−	0.518874i
$428$		−	5.68897i		−	0.274987i
$429$	29.0609	−	12.2903i	1.40307	−	0.593384i
$430$	−4.19040	+	2.41933i	−0.202079	+	0.116670i
$431$	16.9362	+	15.2494i	0.815787	+	0.734538i	0.967223	−	0.253929i	$-0.0817231\pi$
$431$	16.9362	+	15.2494i	0.815787	+	0.734538i	−0.151436	+	0.988467i	$0.548390\pi$
$432$	4.98640	+	1.46145i	0.239908	+	0.0703142i
$433$	−17.2148	−	23.6941i	−0.827289	−	1.13867i	−0.988422	−	0.151732i	$-0.951515\pi$
$433$	−17.2148	−	23.6941i	−0.827289	−	1.13867i	0.161133	−	0.986933i	$-0.448485\pi$
$434$	4.02811	+	14.0926i	0.193355	+	0.676467i
$435$	−0.201897	+	8.00331i	−0.00968023	+	0.383729i
$436$	0.353440	+	3.36275i	0.0169267	+	0.161047i
$437$	−4.32707	+	41.1694i	−0.206992	+	1.96940i
$438$	4.57386	+	2.17624i	0.218548	+	0.103985i
$439$	5.32239	+	3.07289i	0.254024	+	0.146661i	0.621605	−	0.783331i	$-0.286481\pi$
$439$	5.32239	+	3.07289i	0.254024	+	0.146661i	−0.367581	+	0.929991i	$0.619814\pi$
$440$	−5.12020	+	0.0330130i	−0.244096	+	0.00157383i
$441$	−19.8574	−	6.83243i	−0.945592	−	0.325354i
$442$	−5.69363	−	17.5232i	−0.270818	−	0.833493i
$443$	−13.0574	−	29.3273i	−0.620374	−	1.39338i	−0.901107	−	0.433597i	$-0.857244\pi$
$443$	−13.0574	−	29.3273i	−0.620374	−	1.39338i	0.280733	−	0.959786i	$-0.409423\pi$
$444$	−0.738376	+	5.65037i	−0.0350418	+	0.268155i
$445$	21.2529	−	4.51743i	1.00748	−	0.214147i
$446$	11.0511	+	12.2735i	0.523286	+	0.581168i
$447$	−12.7487	+	16.6474i	−0.602991	+	0.787395i
$448$	2.64406	+	0.0945700i	0.124920	+	0.00446801i
$449$	18.6094	−	6.04656i	0.878232	−	0.285355i	0.165009	−	0.986292i	$-0.447235\pi$
$449$	18.6094	−	6.04656i	0.878232	−	0.285355i	0.713223	+	0.700937i	$0.247235\pi$
$450$	7.83821	−	0.425853i	0.369497	−	0.0200749i
$451$	8.25801	+	7.33969i	0.388854	+	0.345612i
$452$	−15.1808	+	8.76465i	−0.714046	+	0.412255i
$453$	−0.415290	−	5.21287i	−0.0195120	−	0.244922i
$454$	−0.633039	+	0.871304i	−0.0297100	+	0.0408923i
$455$	17.1986	−	14.4066i	0.806282	−	0.675391i
$456$	11.5309	+	0.290888i	0.539986	+	0.0136221i
$457$	14.5184	+	16.1243i	0.679143	+	0.754265i	0.979912	−	0.199432i	$-0.0639097\pi$
$457$	14.5184	+	16.1243i	0.679143	+	0.754265i	−0.300768	+	0.953697i	$0.597243\pi$
$458$	−1.31350	−	0.584809i	−0.0613760	−	0.0273263i
$459$	−12.6090	+	12.0346i	−0.588536	+	0.561725i
$460$	−1.99524	+	9.38688i	−0.0930286	+	0.437665i
$461$	6.48988			0.302264			0.151132	−	0.988514i	$-0.451708\pi$
$461$	6.48988			0.302264			0.151132	+	0.988514i	$0.451708\pi$
$462$	−13.5272	−	6.92937i	−0.629340	−	0.322383i
$463$	1.38903			0.0645536			0.0322768	−	0.999479i	$-0.489724\pi$
$463$	1.38903			0.0645536			0.0322768	+	0.999479i	$0.489724\pi$
$464$	0.622482	−	2.92855i	0.0288980	−	0.135954i
$465$	2.71350	+	14.5628i	0.125835	+	0.675333i
$466$	1.97611	+	0.879823i	0.0915417	+	0.0407570i
$467$	−18.2502	−	20.2689i	−0.844520	−	0.937935i	0.154224	−	0.988036i	$-0.450712\pi$
$467$	−18.2502	−	20.2689i	−0.844520	−	0.937935i	−0.998744	+	0.0501011i	$0.984046\pi$
$468$	−15.9083	+	4.29532i	−0.735362	+	0.198551i
$469$	27.5572	−	4.83507i	1.27247	−	0.223263i
$470$	−10.0956	+	13.8954i	−0.465676	+	0.640947i
$471$	−36.6223	+	2.91756i	−1.68747	+	0.134434i
$472$	9.91288	−	5.72320i	0.456277	−	0.263432i
$473$	−10.3448	−	1.01989i	−0.475653	−	0.0468946i
$474$	1.17555	−	4.91728i	0.0539948	−	0.225858i
$475$	16.5724	−	5.38469i	0.760392	−	0.247066i
$476$	−4.70944	+	7.52253i	−0.215857	+	0.344794i
$477$	−2.82510	−	1.07825i	−0.129353	−	0.0493695i
$478$	−20.0530	−	22.2711i	−0.917203	−	1.01866i
$479$	8.09317	−	1.72026i	0.369786	−	0.0786005i	−0.0192705	−	0.999814i	$-0.506134\pi$
$479$	8.09317	−	1.72026i	0.369786	−	0.0786005i	0.389057	+	0.921214i	$0.372801\pi$
$480$	2.65145	+	0.346484i	0.121021	+	0.0158148i
$481$	−7.35003	−	16.5084i	−0.335133	−	0.752720i
$482$	−1.12111	−	3.45042i	−0.0510651	−	0.157162i
$483$	−18.1166	+	21.9823i	−0.824336	+	1.00023i
$484$	−8.98182	−	6.35035i	−0.408265	−	0.288652i
$485$	20.5597	+	11.8702i	0.933570	+	0.538997i
$486$	10.1806	+	11.8049i	0.461801	+	0.535481i
$487$	−3.65182	+	34.7447i	−0.165480	+	1.57443i	0.525014	+	0.851094i	$0.324060\pi$
$487$	−3.65182	+	34.7447i	−0.165480	+	1.57443i	−0.690493	+	0.723339i	$0.742606\pi$
$488$	0.456718	+	4.34538i	0.0206746	+	0.196706i
$489$	25.1844	+	0.635319i	1.13888	+	0.0287301i
$490$	−10.6394	−	1.89457i	−0.480641	−	0.0855879i
$491$	−7.73557	−	10.6471i	−0.349101	−	0.480497i	0.597971	−	0.801518i	$-0.295974\pi$
$491$	−7.73557	−	10.6471i	−0.349101	−	0.480497i	−0.947072	+	0.321021i	$0.895974\pi$
$492$	−3.75139	−	4.38380i	−0.169126	−	0.197637i
$493$	7.46354	+	6.72021i	0.336141	+	0.302663i
$494$	−31.6779	+	18.2892i	−1.42525	+	0.822871i
$495$	−12.9523	−	8.25810i	−0.582161	−	0.371174i
$496$		−	5.53982i		−	0.248745i
$497$	23.2060	−	29.6506i	1.04093	−	1.33001i
$498$	−6.33705	−	2.23723i	−0.283970	−	0.100253i
$499$	−3.39026	−	32.2562i	−0.151769	−	1.44399i	−0.759843	−	0.650106i	$-0.774724\pi$
$499$	−3.39026	−	32.2562i	−0.151769	−	1.44399i	0.608074	−	0.793880i	$-0.291942\pi$
$500$	11.5018	−	2.44477i	0.514374	−	0.109334i
$501$	−14.4093	−	26.4781i	−0.643761	−	1.18295i
$502$	−4.88906	+	0.513861i	−0.218210	+	0.0229348i
$503$	2.90845	+	2.11312i	0.129682	+	0.0942192i	0.650735	−	0.759305i	$-0.274461\pi$
$503$	2.90845	+	2.11312i	0.129682	+	0.0942192i	−0.521054	+	0.853524i	$0.674461\pi$
$504$	6.50669	+	4.54565i	0.289831	+	0.202479i
$505$	−13.3927			−0.595968
$506$	−15.2317	+	13.8936i	−0.677133	+	0.617645i
$507$	20.4497	−	21.5909i	0.908203	−	0.958885i
$508$	−2.54342	+	2.82475i	−0.112846	+	0.125328i
$509$	3.18633	−	1.41865i	0.141232	−	0.0628804i	−0.334904	−	0.942252i	$-0.608704\pi$
$509$	3.18633	−	1.41865i	0.141232	−	0.0628804i	0.476136	+	0.879372i	$0.342037\pi$
$510$	−5.45366	+	7.12147i	−0.241492	+	0.315344i
$511$	5.56115	+	5.37943i	0.246011	+	0.237972i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	28.5742	+	19.5177i	1.26158	+	0.861729i
$514$	−3.56481	−	0.374676i	−0.157237	−	0.0165263i
$515$	0.695975	+	0.626659i	0.0306683	+	0.0276139i
$516$	5.27979	+	1.26221i	0.232430	+	0.0555659i
$517$	−35.0185	+	11.6283i	−1.54011	+	0.511414i
$518$	−3.82240	+	7.82030i	−0.167947	+	0.343604i
$519$	−24.7424	+	17.0399i	−1.08607	+	0.747968i
$520$	−7.74662	+	3.44902i	−0.339712	+	0.151249i
$521$	23.9942	+	10.6829i	1.05121	+	0.468027i	0.858277	−	0.513186i	$-0.171535\pi$
$521$	23.9942	+	10.6829i	1.05121	+	0.468027i	0.192928	+	0.981213i	$0.438202\pi$
$522$	6.33899	−	6.36334i	0.277450	−	0.278516i
$523$	−19.7801	+	17.8100i	−0.864921	+	0.778779i	−0.976622	−	0.214963i	$-0.931037\pi$
$523$	−19.7801	+	17.8100i	−0.864921	+	0.778779i	0.111701	+	0.993742i	$0.464370\pi$
$524$	−12.3076	+	8.94196i	−0.537658	+	0.390631i
$525$	11.5550	+	3.20307i	0.504301	+	0.139793i
$526$	−2.25829	−	6.95030i	−0.0984660	−	0.303047i
$527$	16.0935	+	9.29158i	0.701044	+	0.404748i
$528$	4.19613	+	3.92333i	0.182613	+	0.170741i
$529$	7.81989	+	13.5444i	0.339995	+	0.588889i
$530$	−1.52211	−	0.323535i	−0.0661163	−	0.0140535i
$531$	34.2955	+	1.73143i	1.48830	+	0.0751376i
$532$	16.5517	+	6.04019i	0.717609	+	0.261875i
$533$	17.4016	+	5.65413i	0.753748	+	0.244907i
$534$	−20.7967	−	12.7168i	−0.899962	−	0.550312i
$535$	3.57229	−	8.02348i	0.154443	−	0.346885i
$536$	−10.5168	−	1.10536i	−0.454257	−	0.0477444i
$537$	7.08295	−	0.564273i	0.305652	−	0.0243502i
$538$		−	24.6974i		−	1.06478i
$539$	−16.2067	−	16.6236i	−0.698073	−	0.716027i
$540$	6.11491	+	5.19229i	0.263144	+	0.223441i
$541$	19.3057	+	4.10355i	0.830016	+	0.176425i	0.603279	−	0.797530i	$-0.293861\pi$
$541$	19.3057	+	4.10355i	0.830016	+	0.176425i	0.226738	+	0.973956i	$0.427194\pi$
$542$	0.217233	−	2.06683i	0.00933094	−	0.0887780i
$543$	12.2690	+	1.60328i	0.526511	+	0.0688031i
$544$	2.49286	−	2.24458i	0.106880	−	0.0962355i
$545$	−1.61310	+	4.96462i	−0.0690978	+	0.212661i
$546$	−25.1238	−	1.53377i	−1.07520	−	0.0656395i
$547$	−29.4266	−	21.3797i	−1.25819	−	0.914129i	−0.259524	−	0.965737i	$-0.583566\pi$
$547$	−29.4266	−	21.3797i	−1.25819	−	0.914129i	−0.998667	+	0.0516075i	$0.983566\pi$
$548$	−0.414629	+	1.95068i	−0.0177121	+	0.0833288i
$549$	−5.92848	+	11.6906i	−0.253021	+	0.498945i
$550$	7.95057	+	3.47857i	0.339013	+	0.148327i
$551$	9.96920	−	17.2672i	0.424702	−	0.735606i
$552$	8.86717	−	6.10676i	0.377412	−	0.259921i
$553$	4.09806	−	6.54595i	0.174267	−	0.278362i
$554$	13.7676	+	18.9495i	0.584931	+	0.805088i
$555$	−4.58942	+	7.50540i	−0.194810	+	0.318586i
$556$	−0.562012	−	2.64406i	−0.0238346	−	0.112133i
$557$	5.92216	−	13.3014i	0.250930	−	0.563598i	−0.743531	−	0.668701i	$-0.766851\pi$
$557$	5.92216	−	13.3014i	0.250930	−	0.563598i	0.994461	+	0.105103i	$0.0335173\pi$
$558$	9.02487	−	13.9556i	0.382053	−	0.590787i
$559$	−16.3725	+	5.31974i	−0.692482	+	0.225001i
$560$	3.66969	+	1.79367i	0.155073	+	0.0757963i
$561$	−18.4354	+	5.60965i	−0.778342	+	0.236840i
$562$	−3.43188	+	5.94419i	−0.144765	+	0.250740i
$563$	−8.38578	+	9.31335i	−0.353418	+	0.392511i	−0.893471	−	0.449120i	$-0.851738\pi$
$563$	−8.38578	+	9.31335i	−0.353418	+	0.392511i	0.540053	+	0.841631i	$0.318404\pi$
$564$	18.9437	−	3.52978i	0.797672	−	0.148631i
$565$	−26.9140	+	2.82878i	−1.13228	+	0.119008i
$566$	6.49588	−	19.9923i	0.273042	−	0.840338i
$567$	8.98600	+	22.0511i	0.377376	+	0.926060i
$568$	−11.5132	+	8.36484i	−0.483084	+	0.350981i
$569$	−12.8425	−	28.8448i	−0.538387	−	1.20924i	−0.954031	−	0.299709i	$-0.903110\pi$
$569$	−12.8425	−	28.8448i	−0.538387	−	1.20924i	0.415644	−	0.909527i	$-0.363556\pi$
$570$	16.0801	+	7.65091i	0.673522	+	0.320461i
$571$	9.51246	+	16.4761i	0.398084	+	0.689502i	0.993490	−	0.113924i	$-0.0363419\pi$
$571$	9.51246	+	16.4761i	0.398084	+	0.689502i	−0.595405	+	0.803425i	$0.703009\pi$
$572$	−17.8431	−	3.67258i	−0.746056	−	0.153558i
$573$	20.7074	−	6.15540i	0.865063	−	0.257146i
$574$	−3.29470	−	8.17454i	−0.137518	−	0.341199i
$575$	9.56030	−	13.1586i	0.398692	−	0.548753i
$576$	−1.89243	−	2.32781i	−0.0788511	−	0.0969923i
$577$	4.34589	+	20.4458i	0.180922	+	0.851170i	0.971171	+	0.238384i	$0.0766177\pi$
$577$	4.34589	+	20.4458i	0.180922	+	0.851170i	−0.790249	+	0.612785i	$0.790049\pi$
$578$	−1.19498	−	5.62194i	−0.0497046	−	0.233842i
$579$	15.5075	−	6.44085i	0.644471	−	0.267673i
$580$	2.71685	−	3.73942i	0.112811	−	0.155271i
$581$	−8.08401	−	6.32693i	−0.335381	−	0.262485i
$582$	−7.58915	−	25.5306i	−0.314580	−	1.05828i
$583$	−2.25289	−	2.46988i	−0.0933052	−	0.102292i
$584$	−1.46220	−	2.53260i	−0.0605062	−	0.104800i
$585$	−25.1336	−	3.93139i	−1.03915	−	0.162543i
$586$	−7.17896	−	16.1242i	−0.296560	−	0.666085i
$587$	−1.93017	+	1.40235i	−0.0796666	+	0.0578812i	−0.626906	−	0.779095i	$-0.715679\pi$
$587$	−1.93017	+	1.40235i	−0.0796666	+	0.0578812i	0.547239	+	0.836976i	$0.315679\pi$
$588$	7.20471	+	9.75152i	0.297117	+	0.402146i
$589$	11.4004	−	35.0869i	0.469746	−	1.44573i
$590$	17.5745	−	1.84715i	0.723530	−	0.0760461i
$591$	−1.21791	−	6.53626i	−0.0500979	−	0.268866i
$592$	2.20143	−	2.44493i	0.0904780	−	0.100486i
$593$	4.07411	−	7.05656i	0.167303	−	0.289778i	−0.770167	−	0.637842i	$-0.779827\pi$
$593$	4.07411	−	7.05656i	0.167303	−	0.289778i	0.937471	+	0.348064i	$0.113161\pi$
$594$	4.17918	+	16.7193i	0.171474	+	0.686001i
$595$	−11.3656	+	7.65225i	−0.465946	+	0.313712i
$596$	11.5135	−	3.74095i	0.471610	−	0.153235i
$597$	0.390066	−	0.333795i	0.0159643	−	0.0136613i
$598$	−13.8872	+	31.1911i	−0.567888	+	1.27550i
$599$	1.91217	+	8.99604i	0.0781290	+	0.367568i	0.999791	−	0.0204247i	$-0.00650182\pi$
$599$	1.91217	+	8.99604i	0.0781290	+	0.367568i	−0.921662	+	0.387993i	$0.873168\pi$
$600$	−3.86649	−	2.36429i	−0.157849	−	0.0965219i
$601$	−2.69117	−	3.70408i	−0.109775	−	0.151092i	0.750594	−	0.660763i	$-0.229767\pi$
$601$	−2.69117	−	3.70408i	−0.109775	−	0.151092i	−0.860370	+	0.509671i	$0.829767\pi$
$602$	7.02854	+	4.40018i	0.286462	+	0.179338i
$603$	−24.6926	−	19.9174i	−1.00556	−	0.811100i
$604$	−1.50960	+	2.61470i	−0.0614246	+	0.106390i
$605$	−8.68000	−	14.5962i	−0.352892	−	0.593422i
$606$	10.9090	+	10.3324i	0.443150	+	0.419727i
$607$	0.637437	−	2.99890i	0.0258728	−	0.121722i	−0.963316	−	0.268370i	$-0.913515\pi$
$607$	0.637437	−	2.99890i	0.0258728	−	0.121722i	0.989189	+	0.146648i	$0.0468484\pi$
$608$	−5.38766	−	3.91436i	−0.218498	−	0.158748i
$609$	12.2779	−	6.12327i	0.497526	−	0.248128i
$610$	−2.08447	+	6.41533i	−0.0843976	+	0.259749i
$611$	−45.4120	+	40.8891i	−1.83717	+	1.65420i
$612$	9.93648	−	1.59332i	0.401658	−	0.0644060i
$613$	−3.46989	+	33.0138i	−0.140148	+	1.33342i	0.667879	+	0.744270i	$0.267202\pi$
$613$	−3.46989	+	33.0138i	−0.140148	+	1.33342i	−0.808026	+	0.589146i	$0.799464\pi$
$614$	−19.9221	−	4.23458i	−0.803992	−	0.170894i
$615$	−2.53808	−	8.53835i	−0.102345	−	0.344300i
$616$	4.16294	+	7.72463i	0.167730	+	0.311234i
$617$		−	9.84953i		−	0.396527i	−0.980149	−	0.198264i	$-0.936470\pi$
$617$		−	9.84953i		−	0.396527i	0.980149	−	0.198264i	$-0.0635302\pi$
$618$	−0.0834415	−	1.04739i	−0.00335651	−	0.0421321i
$619$	43.7903	+	4.60254i	1.76008	+	0.184992i	0.928730	−	0.370757i	$-0.120902\pi$
$619$	43.7903	+	4.60254i	1.76008	+	0.184992i	0.831350	+	0.555749i	$0.187569\pi$
$620$	3.47863	−	7.81314i	0.139705	−	0.313783i
$621$	32.2861	−	0.938359i	1.29560	−	0.0376551i
$622$	6.11949	+	1.98834i	0.245369	+	0.0797252i
$623$	−23.9107	−	28.5446i	−0.957962	−	1.14362i
$624$	8.97092	+	3.16710i	0.359124	+	0.126785i
$625$	4.95970	+	1.05422i	0.198388	+	0.0421687i
$626$	−5.68920	−	9.85399i	−0.227386	−	0.393845i
$627$	18.5027	+	33.4839i	0.738925	+	1.33722i
$628$	18.3692	+	10.6054i	0.733009	+	0.423203i
$629$	3.41035	+	10.4960i	0.135980	+	0.418502i
$630$	6.32241	+	10.4968i	0.251891	+	0.418201i
$631$	−19.1759	+	13.9321i	−0.763381	+	0.554629i	−0.899946	−	0.436002i	$-0.856394\pi$
$631$	−19.1759	+	13.9321i	−0.763381	+	0.554629i	0.136564	+	0.990631i	$0.456394\pi$
$632$	−2.16923	+	1.95319i	−0.0862875	+	0.0776936i
$633$	15.5835	+	28.6357i	0.619387	+	1.13817i
$634$	4.26974	+	1.90101i	0.169573	+	0.0754988i
$635$	−5.36088	+	2.38682i	−0.212740	+	0.0947179i
$636$	0.990231	+	1.43784i	0.0392652	+	0.0570141i
$637$	−35.6245	−	14.4633i	−1.41150	−	0.573059i
$638$	9.42390	−	3.12933i	0.373096	−	0.123891i
$639$	−42.6305	+	2.31613i	−1.68644	+	0.0916247i
$640$	−1.14729	−	1.03302i	−0.0453506	−	0.0408338i
$641$	9.75273	+	1.02505i	0.385209	+	0.0404871i	0.295154	−	0.955450i	$-0.404629\pi$
$641$	9.75273	+	1.02505i	0.385209	+	0.0404871i	0.0900553	+	0.995937i	$0.471296\pi$
$642$	−9.09990	+	3.77953i	−0.359145	+	0.149166i
$643$	2.40815	+	0.782455i	0.0949681	+	0.0308570i	0.356116	−	0.934442i	$-0.384101\pi$
$643$	2.40815	+	0.782455i	0.0949681	+	0.0308570i	−0.261148	+	0.965299i	$0.584101\pi$
$644$	15.8130	−	4.51983i	0.623118	−	0.178106i
$645$	6.65382	+	5.09553i	0.261994	+	0.200636i
$646$	20.4078	−	9.08614i	0.802935	−	0.357490i
$647$	19.1887	−	21.3112i	0.754385	−	0.837829i	−0.236627	−	0.971600i	$-0.576042\pi$
$647$	19.1887	−	21.3112i	0.754385	−	0.837829i	0.991012	+	0.133771i	$0.0427088\pi$
$648$	−0.975069	−	8.94702i	−0.0383043	−	0.351472i
$649$	32.9990	+	18.7693i	1.29532	+	0.736761i
$650$	14.3720			0.563718
$651$	19.8660	−	15.8058i	0.778610	−	0.619479i
$652$	−11.7670	−	8.54924i	−0.460832	−	0.334814i
$653$	−18.2899	+	1.92234i	−0.715738	+	0.0752271i	−0.455395	−	0.890289i	$-0.650502\pi$
$653$	−18.2899	+	1.92234i	−0.715738	+	0.0752271i	−0.260342	+	0.965516i	$0.583835\pi$
$654$	5.14415	−	2.79943i	0.201152	−	0.109467i
$655$	−22.9730	+	4.88306i	−0.897630	+	0.190797i
$656$	0.348205	+	3.31295i	0.0135951	+	0.129349i
$657$	0.442356	−	8.76203i	0.0172579	−	0.341839i
$658$	29.1450	+	4.12119i	1.13619	+	0.160661i
$659$			23.7272i			0.924280i	0.886807	+	0.462140i	$0.152918\pi$
$659$			23.7272i			0.924280i	−0.886807	+	0.462140i	$0.847082\pi$
$660$	3.45446	+	8.16818i	0.134465	+	0.317946i
$661$	16.6159	−	9.59318i	0.646283	−	0.373131i	−0.140748	−	0.990045i	$-0.544951\pi$
$661$	16.6159	−	9.59318i	0.646283	−	0.373131i	0.787031	+	0.616914i	$0.211617\pi$
$662$	−12.8916	−	11.6077i	−0.501047	−	0.451144i
$663$	−24.2469	+	20.7491i	−0.941673	+	0.805827i
$664$	2.28061	+	3.13899i	0.0885049	+	0.121817i
$665$	19.5511	+	18.9122i	0.758157	+	0.733383i
$666$	9.52871	−	2.57280i	0.369230	−	0.0996940i
$667$	−1.94536	−	18.5088i	−0.0753246	−	0.716666i
$668$	−1.81923	+	17.3089i	−0.0703883	+	0.669700i
$669$	12.2904	−	25.8311i	0.475175	−	0.998688i
$670$	−14.1384	−	8.16281i	−0.546214	−	0.315357i
$671$	−11.6686	+	8.59323i	−0.450462	+	0.331738i
$672$	−1.60534	−	4.29219i	−0.0619273	−	0.165575i
$673$	6.57071	+	20.2226i	0.253282	+	0.779522i	0.994163	+	0.107886i	$0.0344082\pi$
$673$	6.57071	+	20.2226i	0.253282	+	0.779522i	−0.740881	+	0.671636i	$0.765592\pi$
$674$	−14.3170	−	32.1565i	−0.551470	−	1.23862i
$675$	−5.88858	−	12.2548i	−0.226652	−	0.471689i
$676$	−16.7941	+	3.56970i	−0.645928	+	0.137296i
$677$	2.49645	+	2.77259i	0.0959463	+	0.106559i	0.789206	−	0.614129i	$-0.210493\pi$
$677$	2.49645	+	2.77259i	0.0959463	+	0.106559i	−0.693259	+	0.720688i	$0.743826\pi$
$678$	24.1052	+	18.4599i	0.925756	+	0.708948i
$679$	1.45426	−	40.6592i	0.0558092	−	1.56036i
$680$	4.92526	−	1.60032i	0.188875	−	0.0613693i
$681$	1.81428	+	0.433731i	0.0695233	+	0.0166206i
$682$	15.8524	−	9.28916i	0.607019	−	0.355700i
$683$	−0.0973160	+	0.0561854i	−0.00372369	+	0.00214988i	−0.501861	−	0.864948i	$-0.667351\pi$
$683$	−0.0973160	+	0.0561854i	−0.00372369	+	0.00214988i	0.498137	+	0.867098i	$0.334018\pi$
$684$	−7.19541	−	18.6378i	−0.275123	−	0.712635i
$685$	−1.80967	+	2.49080i	−0.0691439	+	0.0951684i
$686$	5.67840	+	17.6283i	0.216802	+	0.673050i
$687$	−0.0628035	+	2.48956i	−0.00239610	+	0.0949828i
$688$	−2.09718	−	2.32916i	−0.0799543	−	0.0887982i
$689$	−5.05773	−	2.25185i	−0.192684	−	0.0857886i
$690$	16.3405	−	3.04474i	0.622073	−	0.115911i
$691$	7.01864	−	33.0201i	0.267001	−	1.25614i	−0.616365	−	0.787461i	$-0.711395\pi$
$691$	7.01864	−	33.0201i	0.267001	−	1.25614i	0.883367	−	0.468683i	$-0.155271\pi$
$692$	17.3450			0.659356
$693$	−2.09710	+	26.2412i	−0.0796624	+	0.996822i
$694$	23.0698			0.875716
$695$	0.867651	−	4.08197i	0.0329119	−	0.154838i
$696$	−5.09797	+	0.949908i	−0.193238	+	0.0360062i
$697$	−10.2083	−	4.54504i	−0.386668	−	0.172156i
$698$	2.48075	+	2.75515i	0.0938977	+	0.104284i
$699$	0.0944855	−	3.74545i	0.00357377	−	0.141666i
$700$	−4.44544	−	5.30697i	−0.168022	−	0.200585i
$701$	12.9624	−	17.8411i	0.489581	−	0.673851i	−0.490729	−	0.871312i	$-0.663270\pi$
$701$	12.9624	−	17.8411i	0.489581	−	0.673851i	0.980311	+	0.197461i	$0.0632697\pi$
$702$	17.4395	+	22.5928i	0.658212	+	0.852710i
$703$	18.9743	−	10.9548i	0.715630	−	0.413169i
$704$	−0.710467	−	3.23964i	−0.0267767	−	0.122098i
$705$	28.9338	+	6.91707i	1.08971	+	0.260512i
$706$	−9.62102	+	3.12606i	−0.362092	+	0.117651i
$707$	10.7581	+	20.2744i	0.404601	+	0.762497i
$708$	−15.7404	−	12.0541i	−0.591560	−	0.453020i
$709$	5.70434	+	6.33532i	0.214231	+	0.237928i	0.840677	−	0.541537i	$-0.182158\pi$
$709$	5.70434	+	6.33532i	0.214231	+	0.237928i	−0.626445	+	0.779465i	$0.715491\pi$
$710$	−21.4903	+	4.56791i	−0.806517	+	0.171431i
$711$	−8.64652	+	1.38647i	−0.324270	+	0.0519968i
$712$	5.72436	+	12.8571i	0.214529	+	0.481841i
$713$	−10.6413	−	32.7506i	−0.398521	−	1.22652i
$714$	15.1616	+	2.53541i	0.567408	+	0.0948853i
$715$	−22.8590	−	16.3839i	−0.854877	−	0.612722i
$716$	−3.55270	−	2.05115i	−0.132771	−	0.0766551i
$717$	−22.3018	+	46.8722i	−0.832875	+	1.75048i
$718$	−3.57257	+	33.9907i	−0.133327	+	1.26852i
$719$	5.39761	+	51.3548i	0.201297	+	1.91521i	0.369100	+	0.929390i	$0.379666\pi$
$719$	5.39761	+	51.3548i	0.201297	+	1.91521i	−0.167803	+	0.985821i	$0.553667\pi$
$720$	−1.20729	−	4.47137i	−0.0449931	−	0.166638i
$721$	0.389596	−	1.55698i	0.0145093	−	0.0579849i
$722$	−14.8998	−	20.5079i	−0.554514	−	0.763224i
$723$	−4.77437	+	4.08562i	−0.177561	+	0.151946i
$724$	−5.30881	−	4.78008i	−0.197300	−	0.177650i
$725$	−6.78444	+	3.91700i	−0.251968	+	0.145474i
$726$	−4.19066	+	18.5860i	−0.155530	+	0.689790i
$727$		−	13.5200i		−	0.501427i	−0.968061	−	0.250714i	$-0.919335\pi$
$727$		−	13.5200i		−	0.501427i	0.968061	−	0.250714i	$-0.0806653\pi$
$728$	11.4440	+	8.95660i	0.424142	+	0.331954i
$729$	12.1192	−	24.1273i	0.448858	−	0.893603i
$730$	−0.471922	−	4.49003i	−0.0174666	−	0.166184i
$731$	10.2838	−	2.18589i	0.380360	−	0.0808480i
$732$	6.64731	−	3.61745i	0.245692	−	0.133705i
$733$	−42.8819	+	4.50707i	−1.58388	+	0.166472i	−0.855169	−	0.518349i	$-0.826547\pi$
$733$	−42.8819	+	4.50707i	−1.58388	+	0.166472i	−0.728711	+	0.684822i	$0.759880\pi$
$734$	1.90800	+	1.38624i	0.0704254	+	0.0511671i
$735$	4.03793	+	18.2772i	0.148941	+	0.674165i
$736$	−6.21609			−0.229128
$737$	−14.4715	−	31.9477i	−0.533066	−	1.17681i
$738$	−4.51992	+	8.91304i	−0.166380	+	0.328094i
$739$	0.102776	−	0.114145i	0.00378069	−	0.00419888i	−0.741252	−	0.671227i	$-0.765767\pi$
$739$	0.102776	−	0.114145i	0.00378069	−	0.00419888i	0.745032	+	0.667028i	$0.232434\pi$
$740$	4.64005	−	2.06588i	0.170572	−	0.0759434i
$741$	50.3004	+	38.5203i	1.84783	+	1.41508i
$742$	0.732905	+	2.56412i	0.0269058	+	0.0941319i
$743$	−34.3417	−	11.1583i	−1.25988	−	0.409359i	−0.398426	−	0.917201i	$-0.630443\pi$
$743$	−34.3417	−	11.1583i	−1.25988	−	0.409359i	−0.861450	+	0.507842i	$0.830443\pi$
$744$	−8.86134	+	3.68044i	−0.324872	+	0.134932i
$745$	18.5872	+	1.95359i	0.680982	+	0.0715741i
$746$	−7.66714	−	6.90352i	−0.280714	−	0.252756i
$747$	0.631476	+	11.6229i	0.0231045	+	0.425259i
$748$	10.6029	+	3.36968i	0.387682	+	0.123208i
$749$	−15.0158	+	1.03726i	−0.548666	+	0.0379005i
$750$	−11.5519	−	16.7737i	−0.421816	−	0.612488i
$751$	36.9887	−	16.4684i	1.34974	−	0.600942i	0.400730	−	0.916196i	$-0.368756\pi$
$751$	36.9887	−	16.4684i	1.34974	−	0.600942i	0.949007	+	0.315254i	$0.102090\pi$
$752$	−10.1635	−	4.52509i	−0.370626	−	0.165013i
$753$	4.07006	+	7.47901i	0.148321	+	0.272550i
$754$	12.2209	−	11.0038i	0.445060	−	0.400734i
$755$	−3.77092	+	2.73973i	−0.137238	+	0.0997092i
$756$	2.94829	−	13.4279i	0.107228	−	0.488367i
$757$	−0.0148306	−	0.0456438i	−0.000539026	−	0.00165895i	0.950787	−	0.309846i	$-0.100278\pi$
$757$	−0.0148306	−	0.0456438i	−0.000539026	−	0.00165895i	−0.951326	+	0.308187i	$0.900278\pi$
$758$	28.7840	+	16.6184i	1.04548	+	0.603609i
$759$	32.3431	+	15.1339i	1.17398	+	0.549325i
$760$	−5.14058	−	8.90374i	−0.186468	−	0.322973i
$761$	35.2538	+	7.49343i	1.27795	+	0.271637i	0.796394	−	0.604778i	$-0.206738\pi$
$761$	35.2538	+	7.49343i	1.27795	+	0.271637i	0.481556	+	0.876415i	$0.340072\pi$
$762$	6.20813	+	2.19172i	0.224897	+	0.0793976i
$763$	8.81142	−	1.54601i	0.318995	−	0.0559694i
$764$	−11.8620	−	3.85419i	−0.429152	−	0.139440i
$765$	15.0145	+	3.99228i	0.542850	+	0.144341i
$766$	−0.00291510	+	0.00654742i	−0.000105327	+	0.000236568i
$767$	62.5268	+	6.57183i	2.25771	+	0.237295i
$768$	0.137550	+	1.72658i	0.00496342	+	0.0623026i
$769$			19.6766i			0.709555i	0.934951	+	0.354777i	$0.115443\pi$
$769$			19.6766i			0.709555i	−0.934951	+	0.354777i	$0.884557\pi$
$770$	1.02069	+	13.5085i	0.0367831	+	0.486814i
$771$	1.76900	+	5.95108i	0.0637089	+	0.214323i
$772$	−9.48296	−	2.01567i	−0.341299	−	0.0725454i
$773$	2.66800	−	25.3843i	0.0959611	−	0.913009i	−0.835579	−	0.549370i	$-0.814868\pi$
$773$	2.66800	−	25.3843i	0.0959611	−	0.913009i	0.931540	−	0.363639i	$-0.118466\pi$
$774$	−1.48869	−	9.28397i	−0.0535097	−	0.333705i
$775$	−10.7722	+	9.69935i	−0.386949	+	0.348411i
$776$	−4.75193	+	14.6249i	−0.170584	+	0.525005i
$777$	15.0486	+	0.918696i	0.539864	+	0.0329580i
$778$	22.6311	+	16.4424i	0.811363	+	0.589490i
$779$	−4.61235	+	21.6994i	−0.165254	+	0.777461i
$780$	10.6635	+	10.0999i	0.381814	+	0.361633i
$781$	−43.2416	−	18.9193i	−1.54730	−	0.676985i
$782$	10.4258	−	18.0581i	0.372827	−	0.645756i
$783$	−14.3900	−	5.91210i	−0.514256	−	0.211281i
$784$	−0.232472	−	6.99614i	−0.00830256	−	0.249862i
$785$	19.2476	+	26.4921i	0.686976	+	0.945542i
$786$	22.4799	+	13.7461i	0.801833	+	0.490307i
$787$	9.61836	+	45.2508i	0.342858	+	1.61302i	0.724887	+	0.688868i	$0.241892\pi$
$787$	9.61836	+	45.2508i	0.342858	+	1.61302i	−0.382029	+	0.924150i	$0.624775\pi$
$788$	−1.56132	+	3.50679i	−0.0556199	+	0.124924i
$789$	−9.61717	+	8.22979i	−0.342380	+	0.292988i
$790$	−4.28587	+	1.39256i	−0.152484	+	0.0495452i
$791$	25.9019	+	38.4712i	0.920964	+	1.36788i
$792$	3.48789	−	9.31851i	0.123937	−	0.331119i
$793$	−11.9996	+	20.7839i	−0.426118	+	0.738057i
$794$	−22.0496	+	24.4886i	−0.782511	+	0.869066i
$795$	0.493715	+	2.64967i	0.0175103	+	0.0939741i
$796$	−0.294783	+	0.0309829i	−0.0104483	+	0.00109816i
$797$	−0.194487	+	0.598570i	−0.00688909	+	0.0212024i	−0.954442	−	0.298397i	$-0.903548\pi$
$797$	−0.194487	+	0.598570i	−0.00688909	+	0.0212024i	0.947553	+	0.319599i	$0.103548\pi$
$798$	−1.33462	−	30.4885i	−0.0472452	−	1.07928i
$799$	30.1923	−	21.9360i	1.06813	−	0.776039i
$800$	1.06426	+	2.39037i	0.0376274	+	0.0845125i
$801$	−6.52495	+	41.7144i	−0.230548	+	1.47391i
$802$	4.20978	+	7.29155i	0.148653	+	0.257474i
$803$	4.79530	−	8.43078i	0.169223	−	0.297516i
$804$	5.21886	+	17.5568i	0.184055	+	0.619179i
$805$	25.1401	+	3.55488i	0.886071	+	0.125293i
$806$	17.8853	−	24.6171i	0.629984	−	0.867099i
$807$	−39.5053	+	16.4080i	−1.39065	+	0.577589i
$808$	−1.80363	−	8.48542i	−0.0634516	−	0.298516i
$809$	−5.89781	−	27.7470i	−0.207356	−	0.975533i	−0.951532	−	0.307550i	$-0.900491\pi$
$809$	−5.89781	−	27.7470i	−0.207356	−	0.975533i	0.744176	−	0.667984i	$-0.232842\pi$
$810$	4.24293	−	13.2308i	0.149081	−	0.464883i
$811$	3.54875	−	4.88443i	0.124613	−	0.171516i	−0.742152	−	0.670231i	$-0.766195\pi$
$811$	3.54875	−	4.88443i	0.124613	−	0.171516i	0.866766	+	0.498716i	$0.166195\pi$
$812$	−7.84328	−	1.10906i	−0.275245	−	0.0389204i
$813$	−3.45036	+	1.02564i	−0.121009	+	0.0359709i
$814$	10.6876	+	2.19979i	0.374600	+	0.0771027i
$815$	−11.2274	−	19.4464i	−0.393278	−	0.681177i
$816$	−5.24652	−	2.49629i	−0.183665	−	0.0873876i
$817$	−8.48948	−	19.0677i	−0.297009	−	0.667094i
$818$	9.01294	−	6.54828i	0.315130	−	0.228955i
$819$	14.2379	+	41.2062i	0.497511	+	1.43986i
$820$	−1.58921	+	4.89110i	−0.0554977	+	0.170804i
$821$	20.5343	−	2.15824i	0.716651	−	0.0753231i	0.260818	−	0.965388i	$-0.416008\pi$
$821$	20.5343	−	2.15824i	0.716651	−	0.0753231i	0.455834	+	0.890065i	$0.349341\pi$
$822$	3.39571	−	0.632725i	0.118439	−	0.0220688i
$823$	−12.1908	+	13.5392i	−0.424944	+	0.471948i	−0.917157	−	0.398527i	$-0.869521\pi$
$823$	−12.1908	+	13.5392i	−0.424944	+	0.471948i	0.492213	+	0.870475i	$0.336188\pi$
$824$	−0.303313	+	0.525353i	−0.0105664	+	0.0183015i
$825$	0.282176	−	15.0285i	0.00982411	−	0.523226i
$826$	−16.9136	−	25.1212i	−0.588498	−	0.874077i
$827$	−45.1197	+	14.6603i	−1.56897	+	0.509788i	−0.959185	−	0.282781i	$-0.908743\pi$
$827$	−45.1197	+	14.6603i	−1.56897	+	0.509788i	−0.609782	+	0.792569i	$0.708743\pi$
$828$	−15.6592	−	10.1266i	−0.544195	−	0.351923i
$829$	16.9878	−	38.1553i	0.590011	−	1.32519i	−0.333910	−	0.942605i	$-0.608368\pi$
$829$	16.9878	−	38.1553i	0.590011	−	1.32519i	0.923922	−	0.382582i	$-0.124965\pi$
$830$	1.24541	+	5.85917i	0.0432287	+	0.203375i
$831$	21.1644	−	34.6116i	0.734185	−	1.20066i
$832$	−3.22850	−	4.44366i	−0.111928	−	0.154056i
$833$	20.7141	+	11.0588i	0.717700	+	0.383166i
$834$	−3.85598	+	2.65559i	−0.133522	+	0.0919554i
$835$	−13.4346	+	23.2693i	−0.464922	+	0.805269i
$836$	2.16706	−	21.9805i	0.0749492	−	0.760213i
$837$	−28.3187	−	5.16437i	−0.978838	−	0.178507i
$838$	−5.20802	+	24.5018i	−0.179908	+	0.846401i
$839$	−2.14009	−	1.55487i	−0.0738841	−	0.0536800i	0.550230	−	0.835013i	$-0.314540\pi$
$839$	−2.14009	−	1.55487i	−0.0738841	−	0.0536800i	−0.624114	+	0.781333i	$0.714540\pi$
$840$	0.431100	−	7.06157i	0.0148744	−	0.243647i
$841$	6.19150	−	19.0555i	0.213500	−	0.657086i
$842$	4.95611	−	4.46250i	0.170799	−	0.153788i
$843$	11.7881	+	1.54044i	0.406005	+	0.0530557i
$844$	1.96747	−	18.7193i	0.0677232	−	0.644344i
$845$	−25.9273	−	5.51101i	−0.891925	−	0.189585i
$846$	−18.2316	−	27.9567i	−0.626814	−	0.961170i
$847$	−15.1239	+	24.8650i	−0.519662	+	0.854372i
$848$		−	1.00796i		−	0.0346135i
$849$	−36.2947	+	2.89146i	−1.24563	+	0.0992347i
$850$	−8.72919	−	0.917475i	−0.299409	−	0.0314691i
$851$	8.31809	−	18.6827i	0.285141	−	0.640436i
$852$	21.0291	+	12.8589i	0.720444	+	0.440540i
$853$	−18.8091	−	6.11145i	−0.644011	−	0.209252i	−0.0312396	−	0.999512i	$-0.509945\pi$
$853$	−18.8091	−	6.11145i	−0.644011	−	0.209252i	−0.612772	+	0.790260i	$0.709945\pi$
$854$	11.3862	−	1.99777i	0.389627	−	0.0683623i
$855$	1.55517	−	30.8042i	0.0531856	−	1.05348i
$856$	5.56465	+	1.18280i	0.190196	+	0.0404274i
$857$	10.0604	+	17.4251i	0.343657	+	0.595232i	0.985109	−	0.171932i	$-0.0550008\pi$
$857$	10.0604	+	17.4251i	0.343657	+	0.595232i	−0.641452	+	0.767163i	$0.721668\pi$
$858$	5.97968	+	30.9811i	0.204143	+	1.05768i
$859$	−39.1654	−	22.6122i	−1.33631	−	0.771518i	−0.350050	−	0.936731i	$-0.613835\pi$
$859$	−39.1654	−	22.6122i	−1.33631	−	0.771518i	−0.986258	+	0.165213i	$0.947169\pi$
$860$	−1.49523	−	4.60183i	−0.0509868	−	0.156921i
$861$	−10.8869	+	10.7009i	−0.371024	+	0.364687i
$862$	−18.4374	+	13.3955i	−0.627980	+	0.456254i
$863$	−18.2358	+	16.4196i	−0.620755	+	0.558930i	−0.918354	−	0.395761i	$-0.870481\pi$
$863$	−18.2358	+	16.4196i	−0.620755	+	0.558930i	0.297599	+	0.954691i	$0.403814\pi$
$864$	−2.46625	+	4.57358i	−0.0839034	+	0.155596i
$865$	24.4626	+	10.8915i	0.831753	+	0.370320i
$866$	26.7555	−	11.9123i	0.909188	−	0.404796i
$867$	−8.19878	+	5.64645i	−0.278445	+	0.191763i
$868$	−14.6222	+	1.01006i	−0.496308	+	0.0342838i
$869$	−9.22647	−	2.93223i	−0.312987	−	0.0994691i
$870$	−7.78644	−	1.86147i	−0.263985	−	0.0631096i
$871$	−43.1645	−	38.8655i	−1.46257	−	1.31691i
$872$	−3.36275	−	0.353440i	−0.113877	−	0.0119690i
$873$	−35.7961	+	29.1009i	−1.21152	+	0.984917i
$874$	−39.3701	−	12.7921i	−1.33171	−	0.432700i
$875$	−8.54998	−	29.9127i	−0.289042	−	1.01123i
$876$	−3.07965	+	4.02145i	−0.104052	+	0.135872i
$877$	−31.8448	+	14.1782i	−1.07532	+	0.478765i	−0.866494	−	0.499187i	$-0.833632\pi$
$877$	−31.8448	+	14.1782i	−1.07532	+	0.478765i	−0.208829	+	0.977952i	$0.566965\pi$
$878$	−4.11232	+	4.56720i	−0.138784	+	0.154135i
$879$	−21.0224	+	22.1955i	−0.709067	+	0.748637i
$880$	1.03226	−	5.01517i	0.0347974	−	0.169061i
$881$	0.407463			0.0137278			0.00686390	−	0.999976i	$-0.497815\pi$
$881$	0.407463			0.0137278			0.00686390	+	0.999976i	$0.497815\pi$
$882$	10.8117	−	18.0030i	0.364049	−	0.606191i
$883$	12.6323	+	9.17789i	0.425110	+	0.308860i	0.779691	−	0.626165i	$-0.215376\pi$
$883$	12.6323	+	9.17789i	0.425110	+	0.308860i	−0.354581	+	0.935025i	$0.615376\pi$
$884$	18.3240	−	1.92593i	0.616304	−	0.0647761i
$885$	−14.6305	−	26.8845i	−0.491797	−	0.903711i
$886$	31.4012	−	6.67454i	1.05494	−	0.224235i
$887$	1.78474	+	16.9807i	0.0599258	+	0.570156i	0.982751	+	0.184936i	$0.0592077\pi$
$887$	1.78474	+	16.9807i	0.0599258	+	0.570156i	−0.922825	+	0.385220i	$0.874126\pi$
$888$	−5.37338	−	1.89702i	−0.180319	−	0.0636598i
$889$	7.91955	+	6.19822i	0.265613	+	0.207882i
$890$			21.7277i			0.728313i
$891$	23.9672	−	17.7925i	0.802931	−	0.596072i
$892$	−14.3030	+	8.25783i	−0.478899	+	0.276493i
$893$	−55.0592	−	49.5756i	−1.84249	−	1.65898i
$894$	−13.6330	−	15.9313i	−0.455956	−	0.532821i
$895$	−3.72259	−	5.12371i	−0.124433	−	0.171267i
$896$	−0.642235	+	2.56662i	−0.0214555	+	0.0857447i
$897$	59.1184	+	1.49136i	1.97391	+	0.0497951i
$898$	2.04532	+	19.4599i	0.0682531	+	0.649385i
$899$	−1.73372	+	16.4952i	−0.0578227	+	0.550146i
$900$	−1.21311	+	7.75547i	−0.0404369	+	0.258516i
$901$	2.92818	+	1.69058i	0.0975517	+	0.0563215i
$902$	−8.89624	+	6.55154i	−0.296212	+	0.218143i
$903$	2.36891	−	14.1660i	0.0788325	−	0.471413i
$904$	−5.41685	−	16.6714i	−0.180162	−	0.554481i
$905$	−4.48576	−	10.0752i	−0.149112	−	0.334911i
$906$	5.18530	+	0.677602i	0.172270	+	0.0225118i
$907$	−12.2353	+	2.60069i	−0.406266	+	0.0863544i	−0.406512	−	0.913646i	$-0.633255\pi$
$907$	−12.2353	+	2.60069i	−0.406266	+	0.0863544i	0.000246085		1.00000i	$0.499922\pi$
$908$	−0.720648	−	0.800360i	−0.0239155	−	0.0265609i
$909$	9.27992	−	24.3142i	0.307796	−	0.806453i
$910$	10.5160	+	19.8181i	0.348601	+	0.656962i
$911$	31.5011	−	10.2353i	1.04368	−	0.339112i	0.263494	−	0.964661i	$-0.415125\pi$
$911$	31.5011	−	10.2353i	1.04368	−	0.339112i	0.780184	+	0.625550i	$0.215125\pi$
$912$	−2.68195	+	11.2185i	−0.0888082	+	0.371481i
$913$	−5.15820	+	11.7895i	−0.170711	+	0.390175i
$914$	−18.7905	+	10.8487i	−0.621536	+	0.358844i
$915$	11.6466	−	0.927842i	0.385025	−	0.0306735i
$916$	0.845122	−	1.16321i	0.0279236	−	0.0384336i
$917$	25.8460	+	30.8549i	0.853509	+	1.01892i
$918$	−9.15003	−	14.8356i	−0.301996	−	0.489646i
$919$	−22.0794	−	24.5217i	−0.728333	−	0.808896i	0.259280	−	0.965802i	$-0.416515\pi$
$919$	−22.0794	−	24.5217i	−0.728333	−	0.808896i	−0.987614	+	0.156906i	$0.949848\pi$
$920$	−8.76692	−	3.90328i	−0.289037	−	0.128687i
$921$	6.46198	+	34.6802i	0.212929	+	1.14275i
$922$	−1.34932	+	6.34806i	−0.0444375	+	0.209062i
$923$	−78.1667			−2.57289
$924$	9.59040	−	11.7909i	0.315501	−	0.387891i
$925$	−8.60853			−0.283047
$926$	−0.288795	+	1.35867i	−0.00949040	+	0.0446488i
$927$	−1.61994	+	0.829314i	−0.0532057	+	0.0272382i
$928$	2.73513	+	1.21776i	0.0897850	+	0.0399749i
$929$	9.93803	+	11.0373i	0.326056	+	0.362122i	0.883779	−	0.467905i	$-0.154991\pi$
$929$	9.93803	+	11.0373i	0.326056	+	0.362122i	−0.557722	+	0.830028i	$0.688325\pi$
$930$	−14.8087	−	0.373575i	−0.485597	−	0.0122500i
$931$	12.9250	−	44.7890i	0.423600	−	1.46790i
$932$	−1.27145	+	1.75001i	−0.0416479	+	0.0573234i
$933$	−0.885055	−	11.1095i	−0.0289754	−	0.363709i
$934$	23.6205	−	13.6373i	0.772885	−	0.446225i
$935$	12.8380	+	11.4104i	0.419848	+	0.373160i
$936$	−0.893937	−	16.4537i	−0.0292192	−	0.537807i
$937$	19.1242	−	6.21383i	0.624760	−	0.202997i	0.0205077	−	0.999790i	$-0.493472\pi$
$937$	19.1242	−	6.21383i	0.624760	−	0.202997i	0.604253	+	0.796793i	$0.293472\pi$
$938$	−1.00005	+	27.9603i	−0.0326529	+	0.912935i
$939$	−11.9825	+	15.6469i	−0.391033	+	0.510617i
$940$	−11.4928	−	12.7640i	−0.374853	−	0.416316i
$941$	−6.13619	+	1.30429i	−0.200034	+	0.0425185i	−0.306839	−	0.951761i	$-0.599271\pi$
$941$	−6.13619	+	1.30429i	−0.200034	+	0.0425185i	0.106805	+	0.994280i	$0.465938\pi$
$942$	4.76040	−	36.4286i	0.155102	−	1.18691i
$943$	8.42231	+	18.9168i	0.274268	+	0.616016i
$944$	3.53713	+	10.8862i	0.115124	+	0.354315i
$945$	12.5899	−	17.0868i	0.409551	−	0.555833i
$946$	3.14840	−	9.90667i	0.102363	−	0.322094i
$947$	18.0678	+	10.4315i	0.587125	+	0.338977i	0.763960	−	0.645264i	$-0.223253\pi$
$947$	18.0678	+	10.4315i	0.587125	+	0.338977i	−0.176835	+	0.984241i	$0.556586\pi$
$948$	4.56541	+	2.17222i	0.148278	+	0.0705505i
$949$	1.67901	−	15.9747i	0.0545030	−	0.518561i
$950$	1.82143	+	17.3298i	0.0590950	+	0.562252i
$951$	0.204152	−	8.09271i	0.00662010	−	0.262424i
$952$	−6.37899	−	6.17055i	−0.206744	−	0.199989i
$953$	9.11370	+	12.5439i	0.295222	+	0.406338i	0.930701	−	0.365780i	$-0.119198\pi$
$953$	9.11370	+	12.5439i	0.295222	+	0.406338i	−0.635480	+	0.772118i	$0.719198\pi$
$954$	1.64206	−	2.53919i	0.0531635	−	0.0822093i
$955$	−14.3095	−	12.8843i	−0.463044	−	0.416927i
$956$	25.9537	−	14.9844i	0.839402	−	0.484629i
$957$	−11.2664	−	12.9952i	−0.364193	−	0.420075i
$958$			8.27397i			0.267320i
$959$	5.22434	+	0.738736i	0.168703	+	0.0238550i
$960$	−0.890180	+	2.52147i	−0.0287304	+	0.0813801i
$961$	−0.0324411	−	0.308657i	−0.00104649	−	0.00995667i
$962$	17.6759	−	3.75712i	0.569892	−	0.121134i
$963$	12.0912	+	12.0450i	0.389635	+	0.388144i
$964$	3.60811	−	0.379228i	0.116209	−	0.0122141i
$965$	−12.1087	−	8.79746i	−0.389792	−	0.283200i
$966$	−17.7353	−	22.2911i	−0.570624	−	0.717205i
$967$	−5.46149			−0.175630			−0.0878149	−	0.996137i	$-0.527988\pi$
$967$	−5.46149			−0.175630			−0.0878149	+	0.996137i	$0.527988\pi$
$968$	8.07900	−	7.46523i	0.259669	−	0.239942i
$969$	−28.0921	−	26.6073i	−0.902447	−	0.854748i
$970$	−15.8854	+	17.6425i	−0.510049	+	0.566467i
$971$	−41.5780	+	18.5117i	−1.33430	+	0.594070i	−0.945009	−	0.327044i	$-0.893948\pi$
$971$	−41.5780	+	18.5117i	−1.33430	+	0.594070i	−0.389294	+	0.921114i	$0.627281\pi$
$972$	−13.6636	+	7.50374i	−0.438260	+	0.240683i
$973$	−6.87642	+	1.96549i	−0.220448	+	0.0630108i
$974$	−33.2262	−	10.7958i	−1.06464	−	0.345921i
$975$	−9.54822	−	22.9891i	−0.305788	−	0.736240i
$976$	−4.34538	−	0.456718i	−0.139092	−	0.0146192i
$977$	6.49425	+	5.84745i	0.207769	+	0.187076i	0.766445	−	0.642310i	$-0.222024\pi$
$977$	6.49425	+	5.84745i	0.207769	+	0.187076i	−0.558676	+	0.829386i	$0.688690\pi$
$978$	−5.85756	+	24.5020i	−0.187304	+	0.783486i
$979$	−27.1924	+	37.9392i	−0.869074	+	1.21254i
$980$	4.06523	−	10.0130i	0.129859	−	0.319855i
$981$	−7.89546	−	6.36859i	−0.252083	−	0.203334i
$982$	12.0227	−	5.35287i	0.383661	−	0.170817i
$983$	25.7780	+	11.4771i	0.822191	+	0.366063i	0.774323	−	0.632791i	$-0.218091\pi$
$983$	25.7780	+	11.4771i	0.822191	+	0.366063i	0.0478678	+	0.998854i	$0.484757\pi$
$984$	5.06796	−	2.75797i	0.161561	−	0.0879210i
$985$	−4.40405	+	3.96543i	−0.140325	+	0.126349i
$986$	−8.12511	+	5.90324i	−0.258756	+	0.187997i
$987$	−12.7707	−	49.3575i	−0.406495	−	1.57107i
$988$	−11.3034	−	34.7882i	−0.359608	−	1.10676i
$989$	−16.8723	−	9.74120i	−0.536506	−	0.309752i
$990$	10.7706	−	10.9523i	0.342311	−	0.348086i
$991$	24.0035	+	41.5753i	0.762496	+	1.32068i	0.941560	+	0.336845i	$0.109360\pi$
$991$	24.0035	+	41.5753i	0.762496	+	1.32068i	−0.179064	+	0.983837i	$0.557307\pi$
$992$	5.41876	+	1.15179i	0.172046	+	0.0365695i
$993$	−10.0026	+	28.3327i	−0.317422	+	0.899111i
$994$	24.1779	+	28.8635i	0.766875	+	0.915496i
$995$	−0.435204	−	0.141406i	−0.0137969	−	0.00448289i
$996$	3.50589	−	5.73342i	0.111088	−	0.181670i
$997$	−6.42162	+	14.4232i	−0.203375	+	0.456787i	−0.986222	−	0.165427i	$-0.947100\pi$
$997$	−6.42162	+	14.4232i	−0.203375	+	0.456787i	0.782847	+	0.622214i	$0.213767\pi$
$998$	32.2562	+	3.39026i	1.02105	+	0.107317i
$999$	−10.4459	−	13.5326i	−0.330493	−	0.428152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bf.a.5.15	✓	256
3.2	odd	2	inner	462.2.bf.a.5.31	yes	256
7.3	odd	6	inner	462.2.bf.a.269.12	yes	256
11.9	even	5	inner	462.2.bf.a.383.24	yes	256
21.17	even	6	inner	462.2.bf.a.269.24	yes	256
33.20	odd	10	inner	462.2.bf.a.383.12	yes	256
77.31	odd	30	inner	462.2.bf.a.185.31	yes	256
231.185	even	30	inner	462.2.bf.a.185.15	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bf.a.5.15	✓	256	1.1	even	1	trivial
462.2.bf.a.5.31	yes	256	3.2	odd	2	inner
462.2.bf.a.185.15	yes	256	231.185	even	30	inner
462.2.bf.a.185.31	yes	256	77.31	odd	30	inner
462.2.bf.a.269.12	yes	256	7.3	odd	6	inner
462.2.bf.a.269.24	yes	256	21.17	even	6	inner
462.2.bf.a.383.12	yes	256	33.20	odd	10	inner
462.2.bf.a.383.24	yes	256	11.9	even	5	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bf (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207912 + 0.978148i) q^{2} +(1.70274 - 0.317274i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.03302 - 1.14729i) q^{5} +(-0.0436800 + 1.73150i) q^{6} +(-0.907001 + 2.48543i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.79867 - 1.08047i) q^{9} +O(q^{10})\)	\(q+(-0.207912 + 0.978148i) q^{2} +(1.70274 - 0.317274i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.03302 - 1.14729i) q^{5} +(-0.0436800 + 1.73150i) q^{6} +(-0.907001 + 2.48543i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.79867 - 1.08047i) q^{9} +(1.33700 - 0.771915i) q^{10} +(3.30062 + 0.325408i) q^{11} +(-1.68458 - 0.402725i) q^{12} +(5.22383 - 1.69733i) q^{13} +(-2.24254 - 1.40393i) q^{14} +(-2.12298 - 1.62579i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-3.28117 + 0.697433i) q^{17} +(0.474983 + 2.96216i) q^{18} +(2.70867 + 6.08377i) q^{19} +(0.477070 + 1.46827i) q^{20} +(-0.755830 + 4.51981i) q^{21} +(-1.00453 + 3.16084i) q^{22} +(5.38329 + 3.10805i) q^{23} +(0.744168 - 1.56404i) q^{24} +(0.273508 - 2.60226i) q^{25} +(0.574139 + 5.46257i) q^{26} +(4.42262 - 2.72771i) q^{27} +(1.83950 - 1.90164i) q^{28} +(-1.75981 - 2.42217i) q^{29} +(2.03165 - 1.73857i) q^{30} +(-4.11689 - 3.70687i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(5.72336 - 0.493114i) q^{33} -3.35447i q^{34} +(3.78846 - 1.52691i) q^{35} +(-2.99618 - 0.151264i) q^{36} +(-0.343896 - 3.27196i) q^{37} +(-6.51399 + 1.38459i) q^{38} +(8.35633 - 4.54749i) q^{39} +(-1.53537 + 0.161374i) q^{40} +(2.69500 + 1.95803i) q^{41} +(-4.26390 - 1.67904i) q^{42} -3.13419 q^{43} +(-2.88291 - 1.63976i) q^{44} +(-4.13071 - 2.09474i) q^{45} +(-4.15938 + 4.61946i) q^{46} +(-10.1635 + 4.52509i) q^{47} +(1.37514 + 1.05309i) q^{48} +(-5.35470 - 4.50857i) q^{49} +(2.48853 + 0.808571i) q^{50} +(-5.36571 + 2.22858i) q^{51} +(-5.46257 - 0.574139i) q^{52} +(-0.749060 - 0.674456i) q^{53} +(1.74859 + 4.89310i) q^{54} +(-3.03628 - 4.12292i) q^{55} +(1.47763 + 2.19468i) q^{56} +(6.54239 + 9.49971i) q^{57} +(2.73513 - 1.21776i) q^{58} +(10.4568 + 4.65567i) q^{59} +(1.27817 + 2.34873i) q^{60} +(-3.24703 + 2.92364i) q^{61} +(4.48181 - 3.25623i) q^{62} +(0.147032 + 7.93589i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-7.34366 - 4.23987i) q^{65} +(-0.707615 + 5.70081i) q^{66} +(-5.28737 - 9.15800i) q^{67} +(3.28117 + 0.697433i) q^{68} +(10.1525 + 3.58423i) q^{69} +(0.705882 + 4.02313i) q^{70} +(-13.5346 - 4.39766i) q^{71} +(0.770900 - 2.89926i) q^{72} +(1.18946 - 2.67157i) q^{73} +(3.27196 + 0.343896i) q^{74} +(-0.359913 - 4.51775i) q^{75} -6.65951i q^{76} +(-3.80245 + 7.90831i) q^{77} +(2.71074 + 9.11920i) q^{78} +(-2.85521 - 0.606893i) q^{79} +(0.161374 - 1.53537i) q^{80} +(6.66516 - 6.04778i) q^{81} +(-2.47556 + 2.22901i) q^{82} +(-1.19899 + 3.69011i) q^{83} +(2.52886 - 3.82163i) q^{84} +(4.18968 + 3.04398i) q^{85} +(0.651634 - 3.06570i) q^{86} +(-3.76500 - 3.56600i) q^{87} +(2.20332 - 2.47899i) q^{88} +(-7.03694 + 12.1883i) q^{89} +(2.90778 - 3.60492i) q^{90} +(-0.519441 + 14.5229i) q^{91} +(-3.65373 - 5.02892i) q^{92} +(-8.18610 - 5.00566i) q^{93} +(-2.31309 - 10.8823i) q^{94} +(4.18172 - 9.39230i) q^{95} +(-1.31598 + 1.12614i) q^{96} +(-14.6249 + 4.75193i) q^{97} +(5.52335 - 4.30030i) q^{98} +(9.58896 - 2.65552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Introduction

L-functions

Modular forms

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