LMFDB - Embedded newform 462.2.bc.b.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	462.107
Dual form			462.2.bc.b.95.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 - 0.994522i) q^{2} +(-1.60606 - 0.648515i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.565716 - 1.27062i) q^{5} +(-0.477084 + 1.66505i) q^{6} +(0.339893 + 2.62383i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.15886 + 2.08311i) q^{9} +O(q^{10})$	\(q+(-0.104528 - 0.994522i) q^{2} +(-1.60606 - 0.648515i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.565716 - 1.27062i) q^{5} +(-0.477084 + 1.66505i) q^{6} +(0.339893 + 2.62383i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.15886 + 2.08311i) q^{9} +(-1.20453 + 0.695433i) q^{10} +(-2.19545 + 2.48596i) q^{11} +(1.70580 + 0.300425i) q^{12} +(0.0211702 + 0.0291382i) q^{13} +(2.57393 - 0.612296i) q^{14} +(0.0845576 + 2.40757i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.0282439 + 0.268723i) q^{17} +(1.84604 - 2.36477i) q^{18} +(-0.429111 + 2.01881i) q^{19} +(0.817530 + 1.12523i) q^{20} +(1.15570 - 4.43445i) q^{21} +(2.70183 + 1.92357i) q^{22} +(6.12090 + 3.53390i) q^{23} +(0.120475 - 1.72786i) q^{24} +(2.05121 - 2.27810i) q^{25} +(0.0267657 - 0.0241000i) q^{26} +(-2.11632 - 4.74565i) q^{27} +(-0.877990 - 2.49582i) q^{28} +(-0.0314788 + 0.0968816i) q^{29} +(2.38554 - 0.335754i) q^{30} +(5.54534 + 2.46894i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.13820 - 2.56882i) q^{33} +0.270203 q^{34} +(3.14160 - 1.91622i) q^{35} +(-2.54478 - 1.58874i) q^{36} +(1.90948 + 2.12070i) q^{37} +(2.05260 + 0.215737i) q^{38} +(-0.0151039 - 0.0605269i) q^{39} +(1.03361 - 0.930671i) q^{40} +(-0.326334 - 1.00435i) q^{41} +(-4.53096 - 0.685847i) q^{42} +6.49525i q^{43} +(1.63061 - 2.88810i) q^{44} +(1.42554 - 3.92153i) q^{45} +(2.87474 - 6.45677i) q^{46} +(-0.867439 + 4.08098i) q^{47} +(-1.73098 + 0.0607950i) q^{48} +(-6.76895 + 1.78364i) q^{49} +(-2.48004 - 1.80185i) q^{50} +(0.219632 - 0.413268i) q^{51} +(-0.0267657 - 0.0241000i) q^{52} +(-5.38668 + 12.0987i) q^{53} +(-4.49844 + 2.60078i) q^{54} +(4.40071 + 1.38323i) q^{55} +(-2.39038 + 1.13407i) q^{56} +(1.99841 - 2.96404i) q^{57} +(0.0996413 + 0.0211794i) q^{58} +(-0.697676 - 3.28231i) q^{59} +(-0.583271 - 2.33737i) q^{60} +(-2.99407 - 6.72479i) q^{61} +(1.87577 - 5.77303i) q^{62} +(-4.73194 + 6.37250i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0250473 - 0.0433832i) q^{65} +(-3.09184 - 4.84154i) q^{66} +(4.57840 + 7.93002i) q^{67} +(-0.0282439 - 0.268723i) q^{68} +(-7.53874 - 9.64516i) q^{69} +(-2.23411 - 2.92409i) q^{70} +(-2.58012 + 3.55124i) q^{71} +(-1.31403 + 2.69691i) q^{72} +(1.67822 + 7.89542i) q^{73} +(1.90948 - 2.12070i) q^{74} +(-4.77176 + 2.32853i) q^{75} -2.06391i q^{76} +(-7.26896 - 4.91551i) q^{77} +(-0.0586165 + 0.0213480i) q^{78} +(1.73217 - 0.182059i) q^{79} +(-1.03361 - 0.930671i) q^{80} +(0.321313 + 8.99426i) q^{81} +(-0.964741 + 0.429530i) q^{82} +(-13.4850 - 9.79746i) q^{83} +(-0.208475 + 4.57783i) q^{84} +(0.357422 - 0.116133i) q^{85} +(6.45967 - 0.678939i) q^{86} +(0.113386 - 0.135183i) q^{87} +(-3.04272 - 1.31979i) q^{88} +(4.76764 + 2.75260i) q^{89} +(-4.04906 - 1.00782i) q^{90} +(-0.0692581 + 0.0654507i) q^{91} +(-6.72189 - 2.18407i) q^{92} +(-7.30499 - 7.56151i) q^{93} +(4.14929 + 0.436108i) q^{94} +(2.80789 - 0.596836i) q^{95} +(0.241399 + 1.71515i) q^{96} +(14.5867 - 10.5979i) q^{97} +(2.48142 + 6.54542i) q^{98} +(-9.91818 + 0.793481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$3$	−1.60606	−	0.648515i	−0.927259	−	0.374421i
$3$	−1.60606	−	0.648515i	−0.927259	−	0.374421i
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	−0.565716	−	1.27062i	−0.252996	−	0.568238i	0.741743	−	0.670685i	$-0.234000\pi$
$5$	−0.565716	−	1.27062i	−0.252996	−	0.568238i	−0.994739	+	0.102447i	$0.967333\pi$
$6$	−0.477084	+	1.66505i	−0.194769	+	0.679754i
$7$	0.339893	+	2.62383i	0.128468	+	0.991714i
$7$	0.339893	+	2.62383i	0.128468	+	0.991714i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	2.15886	+	2.08311i	0.719618	+	0.694370i
$10$	−1.20453	+	0.695433i	−0.380904	+	0.219915i
$11$	−2.19545	+	2.48596i	−0.661952	+	0.749546i
$11$	−2.19545	+	2.48596i	−0.661952	+	0.749546i
$12$	1.70580	+	0.300425i	0.492421	+	0.0867253i
$13$	0.0211702	+	0.0291382i	0.00587154	+	0.00808149i	0.811943	−	0.583737i	$-0.198410\pi$
$13$	0.0211702	+	0.0291382i	0.00587154	+	0.00808149i	−0.806071	+	0.591819i	$0.798410\pi$
$14$	2.57393	−	0.612296i	0.687911	−	0.163643i
$15$	0.0845576	+	2.40757i	0.0218327	+	0.621631i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	−0.0282439	+	0.268723i	−0.00685015	+	0.0651748i	−0.997413	−	0.0718849i	$-0.977099\pi$
$17$	−0.0282439	+	0.268723i	−0.00685015	+	0.0651748i	0.990563	+	0.137060i	$0.0437652\pi$
$18$	1.84604	−	2.36477i	0.435115	−	0.557382i
$19$	−0.429111	+	2.01881i	−0.0984449	+	0.463147i	0.901118	+	0.433574i	$0.142748\pi$
$19$	−0.429111	+	2.01881i	−0.0984449	+	0.463147i	−0.999563	+	0.0295723i	$0.990585\pi$
$20$	0.817530	+	1.12523i	0.182805	+	0.251610i
$21$	1.15570	−	4.43445i	0.252195	−	0.967676i
$22$	2.70183	+	1.92357i	0.576032	+	0.410106i
$23$	6.12090	+	3.53390i	1.27630	+	0.736870i	0.976165	−	0.217028i	$-0.0696363\pi$
$23$	6.12090	+	3.53390i	1.27630	+	0.736870i	0.300131	+	0.953898i	$0.402970\pi$
$24$	0.120475	−	1.72786i	0.0245919	−	0.352697i
$25$	2.05121	−	2.27810i	0.410243	−	0.455621i
$26$	0.0267657	−	0.0241000i	0.00524919	−	0.00472639i
$27$	−2.11632	−	4.74565i	−0.407286	−	0.913300i
$28$	−0.877990	−	2.49582i	−0.165925	−	0.471666i
$29$	−0.0314788	+	0.0968816i	−0.00584546	+	0.0179905i	−0.953937	−	0.300008i	$-0.903011\pi$
$29$	−0.0314788	+	0.0968816i	−0.00584546	+	0.0179905i	0.948091	+	0.317998i	$0.103011\pi$
$30$	2.38554	−	0.335754i	0.435538	−	0.0612999i
$31$	5.54534	+	2.46894i	0.995972	+	0.443435i	0.838979	−	0.544164i	$-0.183153\pi$
$31$	5.54534	+	2.46894i	0.995972	+	0.443435i	0.156993	+	0.987600i	$0.449820\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	5.13820	−	2.56882i	0.894447	−	0.447175i
$34$	0.270203			0.0463394
$35$	3.14160	−	1.91622i	0.531028	−	0.323900i
$36$	−2.54478	−	1.58874i	−0.424130	−	0.264789i
$37$	1.90948	+	2.12070i	0.313917	+	0.348640i	0.879369	−	0.476141i	$-0.157965\pi$
$37$	1.90948	+	2.12070i	0.313917	+	0.348640i	−0.565452	+	0.824781i	$0.691298\pi$
$38$	2.05260	+	0.215737i	0.332976	+	0.0349972i
$39$	−0.0151039	−	0.0605269i	−0.00241857	−	0.00969206i
$40$	1.03361	−	0.930671i	0.163429	−	0.147152i
$41$	−0.326334	−	1.00435i	−0.0509649	−	0.156854i	0.922335	−	0.386391i	$-0.126279\pi$
$41$	−0.326334	−	1.00435i	−0.0509649	−	0.156854i	−0.973300	+	0.229538i	$0.926279\pi$
$42$	−4.53096	−	0.685847i	−0.699143	−	0.105828i
$43$			6.49525i			0.990516i	0.868746	+	0.495258i	$0.164927\pi$
$43$			6.49525i			0.990516i	−0.868746	+	0.495258i	$0.835073\pi$
$44$	1.63061	−	2.88810i	0.245824	−	0.435397i
$45$	1.42554	−	3.92153i	0.212507	−	0.584587i
$46$	2.87474	−	6.45677i	0.423857	−	0.951998i
$47$	−0.867439	+	4.08098i	−0.126529	+	0.595272i	0.868500	+	0.495689i	$0.165084\pi$
$47$	−0.867439	+	4.08098i	−0.126529	+	0.595272i	−0.995029	+	0.0995832i	$0.968249\pi$
$48$	−1.73098	+	0.0607950i	−0.249846	+	0.00877500i
$49$	−6.76895	+	1.78364i	−0.966992	+	0.254806i
$50$	−2.48004	−	1.80185i	−0.350730	−	0.254820i
$51$	0.219632	−	0.413268i	0.0307546	−	0.0578691i
$52$	−0.0267657	−	0.0241000i	−0.00371174	−	0.00334206i
$53$	−5.38668	+	12.0987i	−0.739917	+	1.66188i	0.00965146	+	0.999953i	$0.496928\pi$
$53$	−5.38668	+	12.0987i	−0.739917	+	1.66188i	−0.749568	+	0.661927i	$0.769739\pi$
$54$	−4.49844	+	2.60078i	−0.612160	+	0.353922i
$55$	4.40071	+	1.38323i	0.593392	+	0.186514i
$56$	−2.39038	+	1.13407i	−0.319427	+	0.151546i
$57$	1.99841	−	2.96404i	0.264696	−	0.392597i
$58$	0.0996413	+	0.0211794i	0.0130835	+	0.00278099i
$59$	−0.697676	−	3.28231i	−0.0908297	−	0.427320i	−0.999942	−	0.0107691i	$-0.996572\pi$
$59$	−0.697676	−	3.28231i	−0.0908297	−	0.427320i	0.909112	−	0.416551i	$-0.136761\pi$
$60$	−0.583271	−	2.33737i	−0.0753000	−	0.301754i
$61$	−2.99407	−	6.72479i	−0.383351	−	0.861021i	−0.997421	−	0.0717692i	$-0.977136\pi$
$61$	−2.99407	−	6.72479i	−0.383351	−	0.861021i	0.614070	−	0.789251i	$-0.289531\pi$
$62$	1.87577	−	5.77303i	0.238223	−	0.733176i
$63$	−4.73194	+	6.37250i	−0.596168	+	0.802859i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.0250473	−	0.0433832i	0.00310673	−	0.00538102i
$66$	−3.09184	−	4.84154i	−0.380579	−	0.595953i
$67$	4.57840	+	7.93002i	0.559340	+	0.968806i	0.997552	+	0.0699340i	$0.0222789\pi$
$67$	4.57840	+	7.93002i	0.559340	+	0.968806i	−0.438211	+	0.898872i	$0.644388\pi$
$68$	−0.0282439	−	0.268723i	−0.00342507	−	0.0325874i
$69$	−7.53874	−	9.64516i	−0.907558	−	1.16114i
$70$	−2.23411	−	2.92409i	−0.267027	−	0.349496i
$71$	−2.58012	+	3.55124i	−0.306204	+	0.421454i	−0.934193	−	0.356768i	$-0.883879\pi$
$71$	−2.58012	+	3.55124i	−0.306204	+	0.421454i	0.627988	+	0.778223i	$0.283879\pi$
$72$	−1.31403	+	2.69691i	−0.154860	+	0.317834i
$73$	1.67822	+	7.89542i	0.196421	+	0.924089i	0.960352	+	0.278791i	$0.0899336\pi$
$73$	1.67822	+	7.89542i	0.196421	+	0.924089i	−0.763931	+	0.645298i	$0.776733\pi$
$74$	1.90948	−	2.12070i	0.221973	−	0.246526i
$75$	−4.77176	+	2.32853i	−0.550995	+	0.268875i
$76$		−	2.06391i		−	0.236747i
$77$	−7.26896	−	4.91551i	−0.828375	−	0.560175i
$78$	−0.0586165	+	0.0213480i	−0.00663701	+	0.00241718i
$79$	1.73217	−	0.182059i	0.194885	−	0.0204832i	−0.00658316	−	0.999978i	$-0.502096\pi$
$79$	1.73217	−	0.182059i	0.194885	−	0.0204832i	0.201468	+	0.979495i	$0.435429\pi$
$80$	−1.03361	−	0.930671i	−0.115562	−	0.104052i
$81$	0.321313	+	8.99426i	0.0357015	+	0.999362i
$82$	−0.964741	+	0.429530i	−0.106538	+	0.0474337i
$83$	−13.4850	−	9.79746i	−1.48018	−	1.07541i	−0.977500	−	0.210936i	$-0.932349\pi$
$83$	−13.4850	−	9.79746i	−1.48018	−	1.07541i	−0.502676	−	0.864475i	$-0.667651\pi$
$84$	−0.208475	+	4.57783i	−0.0227465	+	0.499482i
$85$	0.357422	−	0.116133i	0.0387679	−	0.0125964i
$86$	6.45967	−	0.678939i	0.696564	−	0.0732118i
$87$	0.113386	−	0.135183i	0.0121563	−	0.0144932i
$88$	−3.04272	−	1.31979i	−0.324355	−	0.140690i
$89$	4.76764	+	2.75260i	0.505369	+	0.291775i	0.730928	−	0.682455i	$-0.239088\pi$
$89$	4.76764	+	2.75260i	0.505369	+	0.291775i	−0.225559	+	0.974229i	$0.572421\pi$
$90$	−4.04906	−	1.00782i	−0.426808	−	0.106233i
$91$	−0.0692581	+	0.0654507i	−0.00726022	+	0.00686110i
$92$	−6.72189	−	2.18407i	−0.700805	−	0.227705i
$93$	−7.30499	−	7.56151i	−0.757493	−	0.784092i
$94$	4.14929	+	0.436108i	0.427967	+	0.0449812i
$95$	2.80789	−	0.596836i	0.288084	−	0.0612341i
$96$	0.241399	+	1.71515i	0.0246377	+	0.175051i
$97$	14.5867	−	10.5979i	1.48106	−	1.07605i	0.503843	−	0.863796i	$-0.331919\pi$
$97$	14.5867	−	10.5979i	1.48106	−	1.07605i	0.977214	−	0.212255i	$-0.0680808\pi$
$98$	2.48142	+	6.54542i	0.250661	+	0.661188i
$99$	−9.91818	+	0.793481i	−0.996815	+	0.0797478i
$100$	−1.53275	+	2.65479i	−0.153275	+	0.265479i
$101$	−1.71739	−	0.764632i	−0.170887	−	0.0760838i	0.319510	−	0.947583i	$-0.396482\pi$
$101$	−1.71739	−	0.764632i	−0.170887	−	0.0760838i	−0.490397	+	0.871499i	$0.663148\pi$
$102$	−0.433962	−	0.175231i	−0.0429686	−	0.0173504i
$103$	4.62294	+	5.13429i	0.455512	+	0.505897i	0.926527	−	0.376228i	$-0.122779\pi$
$103$	4.62294	+	5.13429i	0.455512	+	0.505897i	−0.471015	+	0.882125i	$0.656112\pi$
$104$	−0.0211702	+	0.0291382i	−0.00207590	+	0.00285724i
$105$	−6.28830	+	1.04018i	−0.613675	+	0.101511i
$106$	12.5955	+	4.09251i	1.22338	+	0.397500i
$107$	6.10284	+	1.29720i	0.589984	+	0.125405i	0.493223	−	0.869903i	$-0.335819\pi$
$107$	6.10284	+	1.29720i	0.589984	+	0.125405i	0.0967604	+	0.995308i	$0.469152\pi$
$108$	3.05675	+	4.20194i	0.294136	+	0.404332i
$109$	−10.4429	+	6.02923i	−1.00025	+	0.577496i	−0.908323	−	0.418270i	$-0.862637\pi$
$109$	−10.4429	+	6.02923i	−1.00025	+	0.577496i	−0.0919290	+	0.995766i	$0.529303\pi$
$110$	0.915650	−	4.52119i	0.0873038	−	0.431079i
$111$	−1.69144	−	4.64430i	−0.160544	−	0.440817i
$112$	1.37771	+	2.25874i	0.130182	+	0.213431i
$113$	−9.12194	+	2.96390i	−0.858120	+	0.278820i	−0.704843	−	0.709363i	$-0.748983\pi$
$113$	−9.12194	+	2.96390i	−0.858120	+	0.278820i	−0.153277	+	0.988183i	$0.548983\pi$
$114$	−3.15670	−	1.67763i	−0.295652	−	0.157125i
$115$	1.02755	−	9.77652i	0.0958199	−	0.911666i
$116$	0.0106480	−	0.101309i	0.000988646	−	0.00940634i
$117$	−0.0149948	+	0.107005i	−0.00138627	+	0.00989261i
$118$	−3.19140	+	1.03695i	−0.293792	+	0.0954589i
$119$	−0.714682	+	0.0172299i	−0.0655147	+	0.00157946i
$120$	−2.26360	+	0.824398i	−0.206638	+	0.0752569i
$121$	−1.36003	−	10.9156i	−0.123639	−	0.992327i
$122$	−6.37498	+	3.68060i	−0.577164	+	0.333226i
$123$	−0.127227	+	1.82468i	−0.0114716	+	0.164526i
$124$	−5.93748	−	1.26205i	−0.533201	−	0.113335i
$125$	−10.6690	−	3.46656i	−0.954262	−	0.310058i
$126$	6.83221	+	4.03991i	0.608662	+	0.359904i
$127$	−7.09279	+	9.76238i	−0.629383	+	0.866271i	−0.997994	−	0.0633125i	$-0.979834\pi$
$127$	−7.09279	+	9.76238i	−0.629383	+	0.866271i	0.368611	+	0.929584i	$0.379834\pi$
$128$	0.669131	+	0.743145i	0.0591433	+	0.0656853i
$129$	4.21227	−	10.4318i	0.370870	−	0.918465i
$130$	−0.0457637	−	0.0203753i	−0.00401374	−	0.00178703i
$131$	−10.4035	+	18.0194i	−0.908959	+	1.57436i	−0.0934464	+	0.995624i	$0.529788\pi$
$131$	−10.4035	+	18.0194i	−0.908959	+	1.57436i	−0.815513	+	0.578739i	$0.803545\pi$
$132$	−4.49183	+	3.58098i	−0.390964	+	0.311684i
$133$	−5.44286	−	0.439734i	−0.471956	−	0.0381298i
$134$	7.40800	−	5.38223i	0.639954	−	0.464954i
$135$	−4.83267	+	5.37373i	−0.415930	+	0.462497i
$136$	−0.264298	+	0.0561783i	−0.0226634	+	0.00481725i
$137$	0.763672	+	0.0802651i	0.0652449	+	0.00685751i	0.137095	−	0.990558i	$-0.456224\pi$
$137$	0.763672	+	0.0802651i	0.0652449	+	0.00685751i	−0.0718498	+	0.997415i	$0.522890\pi$
$138$	−8.80431	+	8.50564i	−0.749473	+	0.724048i
$139$	17.7480	+	5.76666i	1.50536	+	0.489122i	0.941577	−	0.336799i	$-0.109344\pi$
$139$	17.7480	+	5.76666i	1.50536	+	0.489122i	0.563786	+	0.825921i	$0.309344\pi$
$140$	−2.67455	+	2.52752i	−0.226041	+	0.213614i
$141$	4.03974	−	5.99175i	0.340207	−	0.504596i
$142$	3.80148	+	2.19478i	0.319013	+	0.184182i
$143$	−0.118914	−	0.0113432i	−0.00994413	−	0.000948564i
$144$	2.81949	+	1.02493i	0.234957	+	0.0854108i
$145$	0.140908	−	0.0148100i	0.0117017	−	0.00122990i
$146$	7.67675	−	2.49433i	0.635332	−	0.206432i
$147$	12.0280	+	1.52513i	0.992057	+	0.125791i
$148$	−2.30867	−	1.67735i	−0.189772	−	0.137877i
$149$	13.7881	−	6.13887i	1.12957	−	0.502916i	0.245091	−	0.969500i	$-0.421182\pi$
$149$	13.7881	−	6.13887i	1.12957	−	0.502916i	0.884477	+	0.466584i	$0.154516\pi$
$150$	2.81456	+	4.50222i	0.229808	+	0.367605i
$151$	−6.25365	−	5.63081i	−0.508915	−	0.458229i	0.374225	−	0.927338i	$-0.377909\pi$
$151$	−6.25365	−	5.63081i	−0.508915	−	0.458229i	−0.883141	+	0.469109i	$0.844575\pi$
$152$	−2.05260	+	0.215737i	−0.166488	+	0.0174986i
$153$	−0.620753	+	0.521298i	−0.0501849	+	0.0421444i
$154$	−4.12877	+	7.74295i	−0.332706	+	0.623945i
$155$		−	8.44273i		−	0.678137i
$156$	0.0273581	+	0.0560639i	0.00219040	+	0.00448871i
$157$	7.16210	−	7.95432i	0.571598	−	0.634824i	−0.386149	−	0.922436i	$-0.626195\pi$
$157$	7.16210	−	7.95432i	0.571598	−	0.634824i	0.957747	+	0.287613i	$0.0928616\pi$
$158$	−0.362123	−	1.70365i	−0.0288089	−	0.135535i
$159$	16.4975	−	15.9378i	1.30834	−	1.26395i
$160$	−0.817530	+	1.12523i	−0.0646315	+	0.0889576i
$161$	−7.19191	+	17.2613i	−0.566802	+	1.36038i
$162$	8.91140	−	1.25971i	0.700146	−	0.0989721i
$163$	0.666346	+	6.33986i	0.0521922	+	0.496576i	0.989126	+	0.147069i	$0.0469841\pi$
$163$	0.666346	+	6.33986i	0.0521922	+	0.496576i	−0.936934	+	0.349506i	$0.886349\pi$
$164$	0.528020	+	0.914558i	0.0412314	+	0.0714149i
$165$	−6.17076	−	5.07548i	−0.480393	−	0.395125i
$166$	−8.33422	+	14.4353i	−0.646861	+	1.12040i
$167$	−1.44791	+	1.05197i	−0.112043	+	0.0814037i	−0.642396	−	0.766373i	$-0.722059\pi$
$167$	−1.44791	+	1.05197i	−0.112043	+	0.0814037i	0.530353	+	0.847777i	$0.322059\pi$
$168$	4.57454	−	0.271180i	0.352934	−	0.0209220i
$169$	4.01682	−	12.3625i	0.308986	−	0.950962i
$170$	−0.152858	−	0.343325i	−0.0117237	−	0.0263318i
$171$	−5.13179	+	3.46443i	−0.392438	+	0.264932i
$172$	−1.35044	−	6.35331i	−0.102970	−	0.484436i
$173$	6.67440	+	1.41869i	0.507446	+	0.107861i	0.454518	−	0.890737i	$-0.349811\pi$
$173$	6.67440	+	1.41869i	0.507446	+	0.107861i	0.0529274	+	0.998598i	$0.483145\pi$
$174$	−0.146295	−	0.0986344i	−0.0110906	−	0.00747745i
$175$	6.67455	+	4.60772i	0.504548	+	0.348311i
$176$	−0.994508	+	3.16401i	−0.0749639	+	0.238496i
$177$	−1.00812	+	5.72404i	−0.0757748	+	0.430245i
$178$	2.23916	−	5.02925i	0.167832	−	0.376958i
$179$	6.77138	+	6.09698i	0.506117	+	0.455710i	0.882199	−	0.470877i	$-0.156062\pi$
$179$	6.77138	+	6.09698i	0.506117	+	0.455710i	−0.376082	+	0.926586i	$0.622729\pi$
$180$	−0.579055	+	4.13222i	−0.0431602	+	0.307998i
$181$	−14.4911	−	10.5284i	−1.07711	−	0.782567i	−0.0999346	−	0.994994i	$-0.531863\pi$
$181$	−14.4911	−	10.5284i	−1.07711	−	0.782567i	−0.977177	+	0.212427i	$0.931863\pi$
$182$	0.0723316	+	0.0620372i	0.00536158	+	0.00459850i
$183$	0.447524	+	12.7421i	0.0330819	+	0.941924i
$184$	−1.46948	+	6.91336i	−0.108332	+	0.509660i
$185$	1.61437	−	3.62594i	0.118691	−	0.266584i
$186$	−6.75650	+	8.05537i	−0.495411	+	0.590648i
$187$	−0.606026	−	0.660179i	−0.0443170	−	0.0482771i
$188$		−	4.17215i		−	0.304285i
$189$	11.7324	−	7.16588i	0.853410	−	0.521241i
$190$	−0.887071	−	2.73013i	−0.0643549	−	0.198064i
$191$	18.9382	−	17.0520i	1.37032	−	1.23384i	0.426035	−	0.904707i	$-0.359910\pi$
$191$	18.9382	−	17.0520i	1.37032	−	1.23384i	0.944284	−	0.329133i	$-0.106756\pi$
$192$	1.68052	−	0.419358i	0.121281	−	0.0302646i
$193$	−13.1750	−	1.38474i	−0.948354	−	0.0996761i	−0.382295	−	0.924040i	$-0.624866\pi$
$193$	−13.1750	−	1.38474i	−0.948354	−	0.0996761i	−0.566060	+	0.824364i	$0.691533\pi$
$194$	−12.0645	−	13.3990i	−0.866184	−	0.961994i
$195$	−0.0683621	+	0.0534324i	−0.00489551	+	0.00382637i
$196$	6.25019	−	3.15201i	0.446442	−	0.225143i
$197$	17.8744			1.27350			0.636749	−	0.771071i	$-0.280279\pi$
$197$	17.8744			1.27350			0.636749	+	0.771071i	$0.280279\pi$
$198$	1.82587	+	9.78091i	0.129759	+	0.695099i
$199$	−7.57275	−	13.1164i	−0.536818	−	0.929796i	−0.999073	−	0.0430486i	$-0.986293\pi$
$199$	−7.57275	−	13.1164i	−0.536818	−	0.929796i	0.462255	−	0.886747i	$-0.347040\pi$
$200$	2.80047	+	1.24685i	0.198023	+	0.0881655i
$201$	−2.21044	−	15.7052i	−0.155913	−	1.10776i
$202$	−0.580927	+	1.78791i	−0.0408739	+	0.125797i
$203$	−0.264900	−	0.0496654i	−0.0185923	−	0.00348583i
$204$	−0.128909	+	0.449901i	−0.00902546	+	0.0314994i
$205$	−1.09154	+	0.982826i	−0.0762364	+	0.0686435i
$206$	4.62294	−	5.13429i	0.322095	−	0.357723i
$207$	5.85263	+	20.3797i	0.406786	+	1.41649i
$208$	0.0311915	+	0.0180084i	0.00216274	+	0.00124866i
$209$	−4.07660	−	5.49894i	−0.281984	−	0.380370i
$210$	1.69179	+	6.14512i	0.116744	+	0.424054i
$211$	−14.8535	−	20.4441i	−1.02256	−	1.40743i	−0.910396	−	0.413738i	$-0.864223\pi$
$211$	−14.8535	−	20.4441i	−1.02256	−	1.40743i	−0.112160	−	0.993690i	$-0.535777\pi$
$212$	2.75351	−	12.9542i	0.189112	−	0.889701i
$213$	6.44687	−	4.03025i	0.441732	−	0.276148i
$214$	0.652172	−	6.20500i	0.0445815	−	0.424165i
$215$	8.25299	−	3.67447i	0.562849	−	0.250597i
$216$	3.85940	−	3.47923i	0.262599	−	0.236731i
$217$	−4.59326	+	15.3892i	−0.311811	+	1.04469i
$218$	7.08779	+	9.75550i	0.480045	+	0.660726i
$219$	2.42498	−	13.7689i	0.163865	−	0.930414i
$220$	−4.59214	−	0.438041i	−0.309602	−	0.0295327i
$221$	−0.00842802	+	0.00486592i	−0.000566930	+	0.000327317i
$222$	−4.44205	+	2.16764i	−0.298131	+	0.145482i
$223$	4.23205	+	13.0249i	0.283399	+	0.872213i	0.986874	+	0.161492i	$0.0516307\pi$
$223$	4.23205	+	13.0249i	0.283399	+	0.872213i	−0.703475	+	0.710720i	$0.748369\pi$
$224$	2.10235	−	1.60627i	0.140470	−	0.107323i
$225$	9.17382	−	0.645195i	0.611588	−	0.0430130i
$226$	3.90116	+	8.76216i	0.259501	+	0.582850i
$227$	−10.8818	+	2.31299i	−0.722249	+	0.153519i	−0.554348	−	0.832285i	$-0.687032\pi$
$227$	−10.8818	+	2.31299i	−0.722249	+	0.153519i	−0.167901	+	0.985804i	$0.553699\pi$
$228$	−1.33848	+	3.31476i	−0.0886429	+	0.219526i
$229$	−2.74827	−	26.1480i	−0.181611	−	1.72791i	−0.583406	−	0.812181i	$-0.698280\pi$
$229$	−2.74827	−	26.1480i	−0.181611	−	1.72791i	0.401795	−	0.915730i	$-0.368386\pi$
$230$	−9.83038			−0.648196
$231$	8.48659	+	12.6086i	0.558377	+	0.829587i
$232$	−0.101867			−0.00668792
$233$	−0.416357	−	3.96137i	−0.0272764	−	0.259518i	−0.999659	−	0.0261240i	$-0.991684\pi$
$233$	−0.416357	−	3.96137i	−0.0272764	−	0.259518i	0.972382	−	0.233394i	$-0.0749831\pi$
$234$	0.107986	+	0.00372758i	0.00705927	+	0.000243679i
$235$	5.67609	−	1.20649i	0.370268	−	0.0787028i
$236$	1.36486	+	3.06553i	0.0888449	+	0.199549i
$237$	−2.90004	−	0.830944i	−0.188378	−	0.0539756i
$238$	0.0918401	+	0.708965i	0.00595311	+	0.0459554i
$239$	−5.36063	−	16.4983i	−0.346750	−	1.06719i	−0.960640	−	0.277796i	$-0.910396\pi$
$239$	−5.36063	−	16.4983i	−0.346750	−	1.06719i	0.613890	−	0.789391i	$-0.289604\pi$
$240$	1.05649	+	2.16503i	0.0681963	+	0.139752i
$241$	−6.07195	+	3.50564i	−0.391129	+	0.225818i	−0.682649	−	0.730746i	$-0.739172\pi$
$241$	−6.07195	+	3.50564i	−0.391129	+	0.225818i	0.291520	+	0.956565i	$0.405839\pi$
$242$	−10.7136	+	2.49357i	−0.688699	+	0.160293i
$243$	5.31687	−	14.6537i	0.341077	−	0.940035i
$244$	4.32680	+	5.95533i	0.276995	+	0.381251i
$245$	6.09563	+	7.59172i	0.389436	+	0.485017i
$246$	1.82799	−	0.0642019i	0.116548	−	0.00409337i
$247$	−0.0679089	+	0.0302350i	−0.00432094	+	0.00192381i
$248$	−0.634501	+	6.03687i	−0.0402909	+	0.383342i
$249$	15.3040	+	24.4806i	0.969851	+	1.55139i
$250$	−2.33236	+	10.9729i	−0.147511	+	0.693986i
$251$	1.01915	+	1.40273i	0.0643279	+	0.0885397i	0.839969	−	0.542635i	$-0.182573\pi$
$251$	1.01915	+	1.40273i	0.0643279	+	0.0885397i	−0.775641	+	0.631174i	$0.782573\pi$
$252$	3.30362	−	7.21707i	0.208108	−	0.454633i
$253$	−22.2233	+	7.45784i	−1.39717	+	0.468870i
$254$	10.4503	+	6.03348i	0.655710	+	0.378574i
$255$	−0.649355	−	0.0452764i	−0.0406642	−	0.00283532i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	10.3606	−	9.32872i	0.646276	−	0.581910i	−0.279424	−	0.960168i	$-0.590143\pi$
$257$	10.3606	−	9.32872i	0.646276	−	0.581910i	0.925700	+	0.378258i	$0.123477\pi$
$258$	−10.8149	−	3.09878i	−0.673307	−	0.192922i
$259$	−4.91532	+	5.73097i	−0.305423	+	0.356105i
$260$	−0.0154801	+	0.0476428i	−0.000960033	+	0.00295468i
$261$	−0.269773	+	0.143580i	−0.0166985	+	0.00888736i
$262$	19.0082	+	8.46298i	1.17433	+	0.522845i
$263$	1.31498	+	2.27762i	0.0810853	+	0.140444i	0.903716	−	0.428132i	$-0.140828\pi$
$263$	1.31498	+	2.27762i	0.0810853	+	0.140444i	−0.822631	+	0.568576i	$0.807495\pi$
$264$	4.03089	+	4.09291i	0.248084	+	0.251901i
$265$	18.4201			1.13154
$266$	0.131608	+	5.45901i	0.00806943	+	0.334713i
$267$	−5.87201	−	7.51272i	−0.359361	−	0.459771i
$268$	−6.12709	−	6.80483i	−0.374272	−	0.415671i
$269$	29.8550	+	3.13789i	1.82029	+	0.191320i	0.952280	−	0.305226i	$-0.0987319\pi$
$269$	29.8550	+	3.13789i	1.82029	+	0.191320i	0.868011	+	0.496546i	$0.165399\pi$
$270$	5.84944	+	4.24449i	0.355986	+	0.258312i
$271$	−13.9317	+	12.5442i	−0.846293	+	0.762005i	−0.973212	−	0.229908i	$-0.926158\pi$
$271$	−13.9317	+	12.5442i	−0.846293	+	0.762005i	0.126920	+	0.991913i	$0.459491\pi$
$272$	0.0834972	+	0.256978i	0.00506276	+	0.0155816i
$273$	0.153678	−	0.0602028i	0.00930104	−	0.00364364i
$274$		−	0.767878i		−	0.0463892i
$275$	1.15995	+	10.1007i	0.0699478	+	0.609095i
$276$	9.37935	+	7.86700i	0.564570	+	0.473538i
$277$	8.61777	−	19.3558i	0.517792	−	1.16298i	−0.445686	−	0.895189i	$-0.647040\pi$
$277$	8.61777	−	19.3558i	0.517792	−	1.16298i	0.963477	−	0.267789i	$-0.0862931\pi$
$278$	3.87990	−	18.2535i	0.232701	−	1.09477i
$279$	6.82850	+	16.8816i	0.408812	+	1.01068i
$280$	2.79324	+	2.39570i	0.166928	+	0.143170i
$281$	21.0039	+	15.2602i	1.25299	+	0.910349i	0.998391	−	0.0566990i	$-0.0180575\pi$
$281$	21.0039	+	15.2602i	1.25299	+	0.910349i	0.254596	+	0.967048i	$0.418058\pi$
$282$	−6.38119	−	3.39130i	−0.379994	−	0.201949i
$283$	−14.9353	−	13.4478i	−0.887811	−	0.799389i	0.0927322	−	0.995691i	$-0.470440\pi$
$283$	−14.9353	−	13.4478i	−0.887811	−	0.799389i	−0.980543	+	0.196302i	$0.937107\pi$
$284$	1.78540	−	4.01007i	0.105944	−	0.237954i
$285$	−4.89670	−	0.862408i	−0.290056	−	0.0510846i
$286$	0.00114891	+	0.119449i	6.79366e−5	+	0.00706315i
$287$	2.52433	−	1.19762i	0.149007	−	0.0706932i
$288$	0.724598	−	2.91118i	0.0426973	−	0.171543i
$289$	16.5571	+	3.51932i	0.973947	+	0.207019i
$290$	−0.0294577	−	0.138588i	−0.00172982	−	0.00813815i
$291$	−30.3000	+	7.56110i	−1.77622	+	0.443240i
$292$	−3.28310	−	7.37397i	−0.192129	−	0.431529i
$293$	−7.53430	+	23.1882i	−0.440159	+	1.35467i	0.447548	+	0.894260i	$0.352297\pi$
$293$	−7.53430	+	23.1882i	−0.440159	+	1.35467i	−0.887707	+	0.460409i	$0.847703\pi$
$294$	0.259501	−	12.1216i	0.0151344	−	0.706945i
$295$	−3.77588	+	2.74334i	−0.219840	+	0.159723i
$296$	−1.42684	+	2.47136i	−0.0829334	+	0.143645i
$297$	16.4438	+	5.15772i	0.954165	+	0.299281i
$298$	−7.54649	−	13.0709i	−0.437157	−	0.757178i
$299$	0.0266088	+	0.253165i	0.00153882	+	0.0146409i
$300$	4.18336	−	3.26975i	0.241526	−	0.188779i
$301$	−17.0424	+	2.20769i	−0.982309	+	0.127249i
$302$	−4.94628	+	6.80798i	−0.284627	+	0.391755i
$303$	2.26236	+	2.34180i	0.129969	+	0.134533i
$304$	0.429111	+	2.01881i	0.0246112	+	0.115787i
$305$	−6.85085	+	7.60864i	−0.392278	+	0.435669i
$306$	0.583329	+	0.562862i	0.0333467	+	0.0321767i
$307$			28.0207i			1.59923i	0.600515	+	0.799613i	$0.294962\pi$
$307$			28.0207i			1.59923i	−0.600515	+	0.799613i	$0.705038\pi$
$308$	8.13211	+	3.29680i	0.463370	+	0.187852i
$309$	−4.09505	−	11.2440i	−0.232959	−	0.639650i
$310$	−8.39648	+	0.882506i	−0.476888	+	0.0501230i
$311$	−7.41490	−	6.67640i	−0.420460	−	0.378584i	0.431568	−	0.902081i	$-0.357961\pi$
$311$	−7.41490	−	6.67640i	−0.420460	−	0.378584i	−0.852028	+	0.523497i	$0.824627\pi$
$312$	0.0528971	−	0.0330685i	0.00299471	−	0.00187214i
$313$	2.39053	−	1.06433i	0.135121	−	0.0601597i	−0.338062	−	0.941124i	$-0.609771\pi$
$313$	2.39053	−	1.06433i	0.135121	−	0.0601597i	0.473183	+	0.880964i	$0.343105\pi$
$314$	−8.65939	−	6.29141i	−0.488678	−	0.355045i
$315$	10.7740	+	2.40747i	0.607044	+	0.135645i
$316$	−1.65647	+	0.538219i	−0.0931837	+	0.0302772i
$317$	1.14629	−	0.120480i	0.0643821	−	0.00676683i	−0.0722826	−	0.997384i	$-0.523028\pi$
$317$	1.14629	−	0.120480i	0.0643821	−	0.00676683i	0.136665	+	0.990617i	$0.456362\pi$
$318$	−17.5750	−	14.7412i	−0.985557	−	0.826643i
$319$	−0.171734	−	0.290953i	−0.00961527	−	0.0162903i
$320$	1.20453	+	0.695433i	0.0673350	+	0.0388759i
$321$	−8.96027	−	6.04116i	−0.500113	−	0.337185i
$322$	17.9185	+	5.34821i	0.998561	+	0.298044i
$323$	−0.530380	−	0.172331i	−0.0295111	−	0.00958875i
$324$	−2.18430	−	8.73091i	−0.121350	−	0.485051i
$325$	0.109804	+	0.0115409i	0.00609085	+	0.000640175i
$326$	6.23547	−	1.32539i	0.345351	−	0.0734066i
$327$	20.6820	−	2.91090i	1.14372	−	0.160973i
$328$	0.854354	−	0.620725i	0.0471738	−	0.0342738i
$329$	−11.0026	−	0.888913i	−0.606594	−	0.0490074i
$330$	−4.40265	+	6.66749i	−0.242358	+	0.367033i
$331$	14.9715	−	25.9314i	0.822909	−	1.42532i	−0.0805973	−	0.996747i	$-0.525683\pi$
$331$	14.9715	−	25.9314i	0.822909	−	1.42532i	0.903507	−	0.428574i	$-0.140984\pi$
$332$	15.2274	+	6.77966i	0.835711	+	0.372082i
$333$	−0.295343	+	8.55594i	−0.0161847	+	0.468863i
$334$	1.19755	+	1.33002i	0.0655272	+	0.0727753i
$335$	7.48596	−	10.3035i	0.409002	−	0.562943i
$336$	−0.747865	−	4.52114i	−0.0407994	−	0.246648i
$337$	−10.6256	−	3.45246i	−0.578813	−	0.188068i	0.00495597	−	0.999988i	$-0.498422\pi$
$337$	−10.6256	−	3.45246i	−0.578813	−	0.188068i	−0.583769	+	0.811920i	$0.698422\pi$
$338$	−12.7146	−	2.70258i	−0.691586	−	0.147001i
$339$	16.5725	+	1.15552i	0.900095	+	0.0627593i
$340$	−0.325466	+	0.187908i	−0.0176509	+	0.0101907i
$341$	−18.3122	+	8.36507i	−0.991661	+	0.452994i
$342$	3.98187	+	4.74155i	0.215315	+	0.256393i
$343$	−6.98069	−	17.1543i	−0.376922	−	0.926245i
$344$	−6.17735	+	2.00714i	−0.333060	+	0.108218i
$345$	−7.99054	+	15.0353i	−0.430196	+	0.809473i
$346$	0.713251	−	6.78613i	0.0383446	−	0.364825i
$347$	1.59268	−	15.1534i	0.0854996	−	0.813474i	−0.864796	−	0.502124i	$-0.832552\pi$
$347$	1.59268	−	15.1534i	0.0854996	−	0.813474i	0.950295	−	0.311350i	$-0.100781\pi$
$348$	−0.0828021	+	0.155803i	−0.00443866	+	0.00835194i
$349$	10.1717	−	3.30500i	0.544480	−	0.176912i	−0.0238460	−	0.999716i	$-0.507591\pi$
$349$	10.1717	−	3.30500i	0.544480	−	0.176912i	0.568326	+	0.822803i	$0.307591\pi$
$350$	3.88480	−	7.11962i	0.207651	−	0.380560i
$351$	0.0934769	−	0.162132i	0.00498943	−	0.00865396i
$352$	3.25063	+	0.658331i	0.173259	+	0.0350892i
$353$	−29.8269	+	17.2206i	−1.58753	+	0.916559i	−0.593813	+	0.804603i	$0.702378\pi$
$353$	−29.8269	+	17.2206i	−1.58753	+	0.916559i	−0.993713	+	0.111956i	$0.964288\pi$
$354$	5.79806	+	0.404271i	0.308163	+	0.0214867i
$355$	5.97189	+	1.26936i	0.316955	+	0.0673708i
$356$	−5.23575	−	1.70120i	−0.277494	−	0.0901634i
$357$	1.15900	+	0.435810i	0.0613405	+	0.0230655i
$358$	5.35578	−	7.37159i	0.283062	−	0.389601i
$359$	−8.02146	−	8.90873i	−0.423356	−	0.470185i	0.493301	−	0.869859i	$-0.335790\pi$
$359$	−8.02146	−	8.90873i	−0.423356	−	0.470185i	−0.916657	+	0.399674i	$0.869123\pi$
$360$	4.17011	+	0.143948i	0.219784	+	0.00758674i
$361$	13.4659	+	5.99541i	0.708732	+	0.315548i
$362$	−8.95596	+	15.5122i	−0.470715	+	0.815302i
$363$	−4.89465	+	18.4131i	−0.256902	+	0.966437i
$364$	0.0541366	−	0.0784200i	0.00283753	−	0.00411033i
$365$	9.08268	−	6.59895i	0.475409	−	0.345405i
$366$	12.6255	−	1.77698i	0.659947	−	0.0928845i
$367$	3.76050	−	0.799320i	0.196297	−	0.0417241i	−0.108714	−	0.994073i	$-0.534673\pi$
$367$	3.76050	−	0.799320i	0.196297	−	0.0417241i	0.305011	+	0.952349i	$0.401340\pi$
$368$	7.02909	+	0.738787i	0.366417	+	0.0385119i
$369$	1.38767	−	2.84804i	0.0722392	−	0.148263i
$370$	−3.77482	−	1.22651i	−0.196244	−	0.0637635i
$371$	−33.5757	−	10.0215i	−1.74316	−	0.520288i
$372$	8.71749	+	5.87748i	0.451981	+	0.304733i
$373$	12.6504	+	7.30370i	0.655012	+	0.378171i	0.790374	−	0.612625i	$-0.209886\pi$
$373$	12.6504	+	7.30370i	0.655012	+	0.378171i	−0.135362	+	0.990796i	$0.543220\pi$
$374$	−0.593216	+	0.671714i	−0.0306745	+	0.0347335i
$375$	14.8869	+	12.4865i	0.768755	+	0.644800i
$376$	−4.14929	+	0.436108i	−0.213984	+	0.0224906i
$377$	−0.00348937	+	0.00113376i	−0.000179712	+	5.83918e-5i
$378$	−8.35300	−	10.9191i	−0.429632	−	0.561620i
$379$	−7.47992	−	5.43448i	−0.384218	−	0.279151i	0.378864	−	0.925452i	$-0.376315\pi$
$379$	−7.47992	−	5.43448i	−0.384218	−	0.279151i	−0.763082	+	0.646302i	$0.776315\pi$
$380$	−2.62245	+	1.16759i	−0.134529	+	0.0598960i
$381$	17.7225	−	11.0792i	0.907951	−	0.567604i
$382$	−18.9382	−	17.0520i	−0.968961	−	0.872457i
$383$	−21.4485	+	2.25433i	−1.09597	+	0.115191i	−0.635214	−	0.772336i	$-0.719088\pi$
$383$	−21.4485	+	2.25433i	−1.09597	+	0.115191i	−0.460755	+	0.887527i	$0.652421\pi$
$384$	−0.592723	−	1.62748i	−0.0302473	−	0.0830518i
$385$	−2.13358	+	12.0169i	−0.108737	+	0.612436i
$386$			13.2475i			0.674282i
$387$	−13.5303	+	14.0223i	−0.687785	+	0.712794i
$388$	−12.0645	+	13.3990i	−0.612484	+	0.680233i
$389$	1.17278	+	5.51749i	0.0594622	+	0.279748i	0.997826	−	0.0659011i	$-0.0209922\pi$
$389$	1.17278	+	5.51749i	0.0594622	+	0.279748i	−0.938364	+	0.345649i	$0.887659\pi$
$390$	0.0602855	+	0.0624024i	0.00305267	+	0.00315987i
$391$	−1.12252	+	1.54501i	−0.0567682	+	0.0781347i
$392$	−3.78806	−	5.88647i	−0.191326	−	0.297312i
$393$	28.3945	−	22.1934i	1.43231	−	1.11951i
$394$	−1.86838	−	17.7765i	−0.0941277	−	0.895566i
$395$	−1.21125	−	2.09794i	−0.0609444	−	0.105559i
$396$	9.53647	−	2.83825i	0.479226	−	0.142627i
$397$	−9.16739	+	15.8784i	−0.460098	+	0.796913i	−0.998965	−	0.0454775i	$-0.985519\pi$
$397$	−9.16739	+	15.8784i	−0.460098	+	0.796913i	0.538867	+	0.842391i	$0.318852\pi$
$398$	−12.2530	+	8.90230i	−0.614185	+	0.446232i
$399$	8.45639	+	4.23602i	0.423349	+	0.212066i
$400$	0.947289	−	2.91546i	0.0473645	−	0.145773i
$401$	6.91205	+	15.5247i	0.345171	+	0.775267i	0.999813	+	0.0193282i	$0.00615275\pi$
$401$	6.91205	+	15.5247i	0.345171	+	0.775267i	−0.654642	+	0.755939i	$0.727181\pi$
$402$	−15.3882	+	3.83998i	−0.767492	+	0.191521i
$403$	0.0454550	+	0.213849i	0.00226428	+	0.0106526i
$404$	1.83884	+	0.390857i	0.0914857	+	0.0194459i
$405$	11.2465	−	5.49647i	0.558844	−	0.273122i
$406$	−0.0217037	+	0.268640i	−0.00107714	+	0.0133324i
$407$	−9.46414	+	0.0910305i	−0.469120	+	0.00451221i
$408$	0.460911	+	0.0811757i	0.0228185	+	0.00401880i
$409$	−10.7955	+	24.2471i	−0.533803	+	1.19894i	0.422446	+	0.906388i	$0.361172\pi$
$409$	−10.7955	+	24.2471i	−0.533803	+	1.19894i	−0.956249	+	0.292553i	$0.905495\pi$
$410$	1.09154	+	0.982826i	0.0539072	+	0.0485383i
$411$	−1.17445	−	0.624163i	−0.0579313	−	0.0307877i
$412$	−5.58940	−	4.06093i	−0.275370	−	0.200068i
$413$	8.37508	−	2.94622i	0.412111	−	0.144974i
$414$	19.6563	−	7.95083i	0.966054	−	0.390762i
$415$	−4.82013	+	22.6769i	−0.236611	+	1.11317i
$416$	0.0146494	−	0.0329030i	0.000718244	−	0.00161320i
$417$	−24.7645	−	20.7714i	−1.21272	−	1.01718i
$418$	−5.04270	+	4.62906i	−0.246647	+	0.226415i
$419$		−	30.2025i		−	1.47549i	−0.675079	−	0.737745i	$-0.735890\pi$
$419$		−	30.2025i		−	1.47549i	0.675079	−	0.737745i	$-0.264110\pi$
$420$	5.93462	−	2.32486i	0.289580	−	0.113442i
$421$	−11.3748	−	35.0079i	−0.554372	−	1.70618i	−0.697596	−	0.716492i	$-0.745747\pi$
$421$	−11.3748	−	35.0079i	−0.554372	−	1.70618i	0.143223	−	0.989690i	$-0.454253\pi$
$422$	−18.7795	+	16.9091i	−0.914170	+	0.823122i
$423$	−10.3738	+	7.00327i	−0.504391	+	0.340511i
$424$	−13.1711	−	1.38434i	−0.639645	−	0.0672294i
$425$	0.554244	+	0.615550i	0.0268848	+	0.0298586i
$426$	−4.68205	−	5.99027i	−0.226846	−	0.290230i
$427$	16.6270	−	10.1416i	0.804638	−	0.490788i
$428$	−6.23918			−0.301582
$429$	0.183628	+	0.0953357i	0.00886562	+	0.00460285i
$430$	−4.51701	−	7.82369i	−0.217830	−	0.377292i
$431$	−9.32111	−	4.15003i	−0.448982	−	0.199900i	0.169774	−	0.985483i	$-0.445696\pi$
$431$	−9.32111	−	4.15003i	−0.448982	−	0.199900i	−0.618756	+	0.785583i	$0.712363\pi$
$432$	−3.86359	−	3.47458i	−0.185887	−	0.167171i
$433$	−2.20124	+	6.77473i	−0.105785	+	0.325573i	−0.989914	−	0.141670i	$-0.954753\pi$
$433$	−2.20124	+	6.77473i	−0.105785	+	0.325573i	0.884129	+	0.467243i	$0.154753\pi$
$434$	15.7850	+	2.95949i	0.757705	+	0.142060i
$435$	−0.235911	−	0.0675951i	−0.0113111	−	0.00324094i
$436$	8.96118	−	8.06869i	0.429163	−	0.386420i
$437$	−9.76083	+	10.8405i	−0.466924	+	0.518571i
$438$	−13.9469	−	0.972452i	−0.666410	−	0.0464656i
$439$	−19.2925	−	11.1385i	−0.920779	−	0.531612i	−0.0368957	−	0.999319i	$-0.511747\pi$
$439$	−19.2925	−	11.1385i	−0.920779	−	0.531612i	−0.883884	+	0.467707i	$0.845080\pi$
$440$	0.0443677	+	4.61277i	0.00211515	+	0.219905i
$441$	−18.3287	−	10.2498i	−0.872795	−	0.488087i
$442$	0.00572023	+	0.00787322i	0.000272084	+	0.000374491i
$443$	−5.91762	+	27.8402i	−0.281155	+	1.32273i	0.580096	+	0.814548i	$0.303015\pi$
$443$	−5.91762	+	27.8402i	−0.281155	+	1.32273i	−0.861250	+	0.508181i	$0.830318\pi$
$444$	2.62008	+	4.19114i	0.124344	+	0.198903i
$445$	0.800373	−	7.61504i	0.0379413	−	0.360988i
$446$	12.5112	−	5.57034i	0.592422	−	0.263763i
$447$	−26.1257	+	0.917578i	−1.23570	+	0.0433999i
$448$	−1.81723	−	1.92294i	−0.0858559	−	0.0908502i
$449$	−5.84081	−	8.03918i	−0.275645	−	0.379392i	0.648641	−	0.761095i	$-0.275338\pi$
$449$	−5.84081	−	8.03918i	−0.275645	−	0.379392i	−0.924285	+	0.381703i	$0.875338\pi$
$450$	−1.60059	−	9.05612i	−0.0754523	−	0.426910i
$451$	3.21324	+	1.39375i	0.151305	+	0.0656291i
$452$	8.30637	−	4.79569i	0.390699	−	0.225570i
$453$	6.39207	+	13.0990i	0.300326	+	0.615445i
$454$	3.43778	+	10.5804i	0.161343	+	0.496563i
$455$	0.122343	+	0.0509741i	0.00573554	+	0.00238970i
$456$	3.43652	+	0.984659i	0.160930	+	0.0461109i
$457$	6.00967	+	13.4979i	0.281120	+	0.631407i	0.997821	−	0.0659739i	$-0.0210154\pi$
$457$	6.00967	+	13.4979i	0.281120	+	0.631407i	−0.716701	+	0.697381i	$0.754349\pi$
$458$	−25.7175	+	5.46643i	−1.20170	+	0.255429i
$459$	1.33504	−	0.434668i	0.0623141	−	0.0202886i
$460$	1.02755	+	9.77652i	0.0479100	+	0.455833i
$461$	19.9169			0.927621			0.463810	−	0.885935i	$-0.346482\pi$
$461$	19.9169			0.927621			0.463810	+	0.885935i	$0.346482\pi$
$462$	11.6525	−	9.75806i	0.542122	−	0.453986i
$463$	11.6985			0.543673			0.271837	−	0.962343i	$-0.412369\pi$
$463$	11.6985			0.543673			0.271837	+	0.962343i	$0.412369\pi$
$464$	0.0106480	+	0.101309i	0.000494323	+	0.00470317i
$465$	−5.47524	+	13.5595i	−0.253908	+	0.628808i
$466$	−3.89615	+	0.828152i	−0.180486	+	0.0383634i
$467$	5.13763	+	11.5393i	0.237741	+	0.533975i	0.992531	−	0.121991i	$-0.0389280\pi$
$467$	5.13763	+	11.5393i	0.237741	+	0.533975i	−0.754790	+	0.655966i	$0.772261\pi$
$468$	−0.00758047	−	0.107784i	−0.000350407	−	0.00498233i
$469$	−19.2508	+	14.7083i	−0.888921	+	0.679166i
$470$	−1.79320	−	5.51889i	−0.0827139	−	0.254567i
$471$	−16.6613	+	8.13038i	−0.767710	+	0.374628i
$472$	2.90607	−	1.67782i	0.133763	−	0.0772279i
$473$	−16.1470	−	14.2600i	−0.742438	−	0.655674i
$474$	−0.523255	+	2.97101i	−0.0240339	+	0.136463i
$475$	3.71886	+	5.11857i	0.170633	+	0.234856i
$476$	0.695482	−	0.165444i	0.0318774	−	0.00758311i
$477$	−36.8319	+	14.8983i	−1.68642	+	0.682144i
$478$	−15.8476	+	7.05580i	−0.724852	+	0.322725i
$479$	2.21572	−	21.0811i	0.101239	−	0.963221i	−0.819510	−	0.573065i	$-0.805754\pi$
$479$	2.21572	−	21.0811i	0.101239	−	0.963221i	0.920749	−	0.390156i	$-0.127579\pi$
$480$	2.04273	−	1.27701i	0.0932376	−	0.0582874i
$481$	−0.0213693	+	0.100534i	−0.000974354	+	0.00458398i
$482$	4.12113	+	5.67225i	0.187712	+	0.258364i
$483$	22.7449	−	23.0587i	1.03493	−	1.04921i
$484$	3.59979	+	10.3943i	0.163627	+	0.472468i
$485$	−21.7178	−	12.5388i	−0.986154	−	0.569357i
$486$	−15.1292	−	3.75602i	−0.686274	−	0.170376i
$487$	12.7327	−	14.1411i	0.576976	−	0.640796i	−0.382041	−	0.924145i	$-0.624779\pi$
$487$	12.7327	−	14.1411i	0.576976	−	0.640796i	0.959017	+	0.283349i	$0.0914455\pi$
$488$	5.47043	−	4.92560i	0.247635	−	0.222971i
$489$	3.04130	−	10.6143i	0.137532	−	0.479996i
$490$	6.91296	−	6.85579i	0.312296	−	0.309713i
$491$	−4.48973	+	13.8180i	−0.202619	+	0.623597i	0.797184	+	0.603736i	$0.206322\pi$
$491$	−4.48973	+	13.8180i	−0.202619	+	0.623597i	−0.999803	+	0.0198601i	$0.993678\pi$
$492$	−0.254927	−	1.81126i	−0.0114930	−	0.0816580i
$493$	−0.0251452	−	0.0111954i	−0.00113248	−	0.000504214i
$494$	0.0371678	+	0.0643764i	0.00167226	+	0.00289643i
$495$	6.61909	+	12.1534i	0.297506	+	0.546253i
$496$	6.07013			0.272557
$497$	−10.1948	−	5.56276i	−0.457299	−	0.249524i
$498$	22.7468	−	17.7791i	1.01931	−	0.796699i
$499$	−15.3267	−	17.0220i	−0.686115	−	0.762008i	0.294986	−	0.955502i	$-0.404685\pi$
$499$	−15.3267	−	17.0220i	−0.686115	−	0.762008i	−0.981102	+	0.193493i	$0.938018\pi$
$500$	11.1566	+	1.17260i	0.498937	+	0.0524404i
$501$	3.00765	−	0.750531i	0.134372	−	0.0335313i
$502$	1.28852	−	1.16019i	0.0575094	−	0.0517817i
$503$	3.42978	+	10.5558i	0.152926	+	0.470659i	0.997945	−	0.0640781i	$-0.0204107\pi$
$503$	3.42978	+	10.5558i	0.152926	+	0.470659i	−0.845019	+	0.534737i	$0.820411\pi$
$504$	−7.52286	−	2.53113i	−0.335095	−	0.112746i
$505$			2.61472i			0.116353i
$506$	9.73995	+	21.3220i	0.432994	+	0.947877i
$507$	−14.4685	+	17.2499i	−0.642570	+	0.766097i
$508$	4.90808	−	11.0237i	0.217761	−	0.489099i
$509$	−1.01337	+	4.76752i	−0.0449167	+	0.211316i	−0.994883	−	0.101037i	$-0.967784\pi$
$509$	−1.01337	+	4.76752i	−0.0449167	+	0.211316i	0.949966	+	0.312353i	$0.101117\pi$
$510$	0.0228477	+	0.650531i	0.00101171	+	0.0288060i
$511$	−20.1458	+	7.08697i	−0.891198	+	0.313509i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	10.4887	−	2.23604i	0.463087	−	0.0987236i
$514$	−10.3606	−	9.32872i	−0.456986	−	0.411472i
$515$	3.90846	−	8.77855i	0.172227	−	0.386829i
$516$	−1.95134	+	11.0796i	−0.0859028	+	0.487751i
$517$	−8.24075	−	11.1160i	−0.362428	−	0.488881i
$518$	6.21336	+	4.28935i	0.273000	+	0.188463i
$519$	−9.79945	−	6.60695i	−0.430148	−	0.290013i
$520$	0.0489999	+	0.0104152i	0.00214879	+	0.000456739i
$521$	1.03203	+	4.85534i	0.0452143	+	0.212716i	0.994955	−	0.100321i	$-0.0319869\pi$
$521$	1.03203	+	4.85534i	0.0452143	+	0.212716i	−0.949741	+	0.313037i	$0.898654\pi$
$522$	0.170992	+	0.253287i	0.00748412	+	0.0110861i
$523$	4.45842	+	10.0138i	0.194953	+	0.437871i	0.984399	−	0.175948i	$-0.0562990\pi$
$523$	4.45842	+	10.0138i	0.194953	+	0.437871i	−0.789447	+	0.613819i	$0.789632\pi$
$524$	6.42972	−	19.7887i	0.280884	−	0.864472i
$525$	−7.73154	−	11.7288i	−0.337432	−	0.511888i
$526$	2.12769	−	1.54586i	0.0927716	−	0.0674025i
$527$	−0.820082	+	1.42042i	−0.0357234	+	0.0618747i
$528$	3.64915	−	4.43663i	0.158809	−	0.193080i
$529$	13.4770	+	23.3428i	0.585955	+	1.01490i
$530$	−1.92543	−	18.3192i	−0.0836353	−	0.795736i
$531$	5.33122	−	8.53936i	0.231355	−	0.370577i
$532$	5.41535	−	0.701509i	0.234785	−	0.0304143i
$533$	0.0223565	−	0.0307711i	0.000968369	−	0.00133285i
$534$	−6.85778	+	6.62514i	−0.296765	+	0.286698i
$535$	−1.80423	−	8.48823i	−0.0780036	−	0.366978i
$536$	−6.12709	+	6.80483i	−0.264650	+	0.293924i
$537$	−6.92126	−	14.1835i	−0.298674	−	0.612061i
$538$		−	30.0194i		−	1.29423i
$539$	10.4268	−	20.7432i	0.449114	−	0.893475i
$540$	3.60981	−	6.26107i	0.155341	−	0.269434i
$541$	31.6270	−	3.32413i	1.35975	−	0.142916i	0.603586	−	0.797298i	$-0.293738\pi$
$541$	31.6270	−	3.32413i	1.35975	−	0.142916i	0.756164	+	0.654382i	$0.227071\pi$
$542$	13.9317	+	12.5442i	0.598419	+	0.538819i
$543$	16.4457	+	26.3069i	0.705752	+	1.12894i
$544$	0.246842	−	0.109901i	0.0105833	−	0.00471198i
$545$	13.5686	+	9.85816i	0.581215	+	0.422277i
$546$	−0.0759368	−	0.146544i	−0.00324979	−	0.00627149i
$547$	31.6493	−	10.2835i	1.35322	−	0.439689i	0.459449	−	0.888204i	$-0.348047\pi$
$547$	31.6493	−	10.2835i	1.35322	−	0.439689i	0.893775	+	0.448515i	$0.148047\pi$
$548$	−0.763672	+	0.0802651i	−0.0326224	+	0.00342876i
$549$	7.54470	−	20.7548i	0.322000	−	0.885794i
$550$	9.92412	−	2.20941i	0.423166	−	0.0942095i
$551$	−0.182078	−	0.105123i	−0.00775677	−	0.00447837i
$552$	6.84349	−	10.1503i	0.291278	−	0.432025i
$553$	1.06644	+	4.48304i	0.0453498	+	0.190638i
$554$	−20.1506	−	6.54732i	−0.856117	−	0.278169i
$555$	−4.94426	+	4.77653i	−0.209872	+	0.202752i
$556$	−18.5591	−	1.95064i	−0.787080	−	0.0827255i
$557$	15.2163	−	3.23433i	0.644737	−	0.137043i	0.126073	−	0.992021i	$-0.459763\pi$
$557$	15.2163	−	3.23433i	0.644737	−	0.137043i	0.518664	+	0.854978i	$0.326429\pi$
$558$	16.0754	−	8.55571i	0.680525	−	0.362192i
$559$	−0.189260	+	0.137505i	−0.00800484	+	0.00581586i
$560$	2.09060	−	3.02836i	0.0883440	−	0.127971i
$561$	0.545178	+	1.45330i	0.0230174	+	0.0613586i
$562$	12.9811	−	22.4840i	0.547576	−	0.948429i
$563$	−1.94895	−	0.867728i	−0.0821384	−	0.0365704i	0.365256	−	0.930907i	$-0.380981\pi$
$563$	−1.94895	−	0.867728i	−0.0821384	−	0.0365704i	−0.447395	+	0.894337i	$0.647648\pi$
$564$	−2.70570	+	6.70072i	−0.113931	+	0.282151i
$565$	8.92641	+	9.91378i	0.375537	+	0.417076i
$566$	−11.8130	+	16.2592i	−0.496536	+	0.683423i
$567$	−23.4902	+	3.90016i	−0.986495	+	0.163791i
$568$	−4.17473	−	1.35645i	−0.175168	−	0.0569154i
$569$	−36.4653	−	7.75094i	−1.52871	−	0.324936i	−0.634617	−	0.772827i	$-0.718842\pi$
$569$	−36.4653	−	7.75094i	−1.52871	−	0.324936i	−0.894089	+	0.447890i	$0.852176\pi$
$570$	−0.345839	+	4.96002i	−0.0144856	+	0.207753i
$571$	11.4948	−	6.63655i	0.481044	−	0.277731i	−0.239807	−	0.970821i	$-0.577084\pi$
$571$	11.4948	−	6.63655i	0.481044	−	0.277731i	0.720852	+	0.693089i	$0.243751\pi$
$572$	0.118674	−	0.0136284i	0.00496202	−	0.000569832i
$573$	−41.4743	+	15.1048i	−1.73261	+	0.631014i
$574$	−1.45492	−	2.38532i	−0.0607273	−	0.0995613i
$575$	20.6059	−	6.69526i	0.859325	−	0.279212i
$576$	−2.97097	−	0.416327i	−0.123790	−	0.0173470i
$577$	0.442689	−	4.21190i	0.0184294	−	0.175344i	−0.981435	−	0.191793i	$-0.938570\pi$
$577$	0.442689	−	4.21190i	0.0184294	−	0.175344i	0.999865	+	0.0164497i	$0.00523633\pi$
$578$	1.76935	−	16.8343i	0.0735954	−	0.700213i
$579$	20.2617	+	10.7681i	0.842049	+	0.447509i
$580$	−0.134749	+	0.0437827i	−0.00559516	+	0.00181798i
$581$	21.1234	−	38.7125i	0.876345	−	1.60607i
$582$	10.6869	+	29.3437i	0.442986	+	1.21633i
$583$	−18.2507	−	39.9531i	−0.755867	−	1.65469i
$584$	−6.99039	+	4.03591i	−0.289265	+	0.167007i
$585$	0.144445	−	0.0414818i	0.00597208	−	0.00171506i
$586$	23.8487	+	5.06920i	0.985182	+	0.209407i
$587$	37.5493	+	12.2005i	1.54983	+	0.503569i	0.954067	−	0.299594i	$-0.0968513\pi$
$587$	37.5493	+	12.2005i	1.54983	+	0.503569i	0.595759	+	0.803163i	$0.296851\pi$
$588$	−12.0823	+	1.00897i	−0.498266	+	0.0416092i
$589$	−7.36389	+	10.1355i	−0.303424	+	0.417627i
$590$	3.12299	+	3.46844i	0.128572	+	0.142793i
$591$	−28.7073	−	11.5918i	−1.18086	−	0.476824i
$592$	2.60697	+	1.16070i	0.107146	+	0.0477043i
$593$	−0.323227	+	0.559845i	−0.0132733	+	0.0229901i	−0.872586	−	0.488461i	$-0.837558\pi$
$593$	−0.323227	+	0.559845i	−0.0132733	+	0.0229901i	0.859312	+	0.511451i	$0.170892\pi$
$594$	3.41062	−	16.8928i	0.139939	−	0.693121i
$595$	0.426199	+	0.898341i	0.0174725	+	0.0368284i
$596$	−12.2105	+	8.87144i	−0.500161	+	0.363388i
$597$	3.65611	+	25.9767i	0.149634	+	1.06316i
$598$	0.248997	−	0.0529260i	0.0101823	−	0.00216430i
$599$	33.8159	+	3.55420i	1.38168	+	0.145221i	0.766033	−	0.642801i	$-0.222228\pi$
$599$	33.8159	+	3.55420i	1.38168	+	0.145221i	0.615648	+	0.788021i	$0.288894\pi$
$600$	−3.68912	−	3.81866i	−0.150608	−	0.155896i
$601$	36.4603	+	11.8467i	1.48725	+	0.483236i	0.936269	−	0.351284i	$-0.114255\pi$
$601$	36.4603	+	11.8467i	1.48725	+	0.483236i	0.550978	+	0.834520i	$0.314255\pi$
$602$	3.97701	+	16.7183i	0.162091	+	0.681387i
$603$	−6.63499	+	26.6571i	−0.270198	+	1.08556i
$604$	7.28771	+	4.20756i	0.296533	+	0.171203i
$605$	−13.1002	+	7.90321i	−0.532598	+	0.321311i
$606$	2.09249	−	2.49475i	0.0850016	−	0.101342i
$607$	−3.84714	+	0.404351i	−0.156151	+	0.0164121i	−0.182281	−	0.983246i	$-0.558348\pi$
$607$	−3.84714	+	0.404351i	−0.156151	+	0.0164121i	0.0261305	+	0.999659i	$0.491681\pi$
$608$	1.96290	−	0.637784i	0.0796060	−	0.0258655i
$609$	0.393237	+	0.251557i	0.0159348	+	0.0101936i
$610$	8.28307	+	6.01800i	0.335372	+	0.243662i
$611$	−0.137276	+	0.0611193i	−0.00555360	+	0.00247262i
$612$	0.498804	−	0.638968i	0.0201630	−	0.0258288i
$613$	−7.21288	−	6.49451i	−0.291326	−	0.262311i	0.510488	−	0.859885i	$-0.329465\pi$
$613$	−7.21288	−	6.49451i	−0.291326	−	0.262311i	−0.801814	+	0.597574i	$0.796131\pi$
$614$	27.8672	−	2.92896i	1.12463	−	0.118203i
$615$	2.39045	−	0.870597i	0.0963924	−	0.0351059i
$616$	2.42870	−	8.43217i	0.0978551	−	0.339742i
$617$		−	4.77106i		−	0.192076i	−0.995378	−	0.0960379i	$-0.969383\pi$
$617$		−	4.77106i		−	0.192076i	0.995378	−	0.0960379i	$-0.0306170\pi$
$618$	−10.7544	+	5.24793i	−0.432605	+	0.211103i
$619$	−27.7417	+	30.8103i	−1.11503	+	1.23837i	−0.146572	+	0.989200i	$0.546824\pi$
$619$	−27.7417	+	30.8103i	−1.11503	+	1.23837i	−0.968460	+	0.249169i	$0.919843\pi$
$620$	1.75534	+	8.25824i	0.0704963	+	0.331659i
$621$	3.81687	−	36.5265i	0.153166	−	1.46576i
$622$	−5.86476	+	8.07215i	−0.235155	+	0.323664i
$623$	−5.60185	+	13.4451i	−0.224434	+	0.538665i
$624$	−0.0384166	−	0.0491507i	−0.00153790	−	0.00196760i
$625$	0.0287763	+	0.273789i	0.00115105	+	0.0109515i
$626$	−1.30838	−	2.26619i	−0.0522935	−	0.0905750i
$627$	2.98111	+	11.4754i	0.119054	+	0.458282i
$628$	−5.35180	+	9.26958i	−0.213560	+	0.369897i
$629$	−0.623810	+	0.453225i	−0.0248729	+	0.0180713i
$630$	1.26809	−	10.9666i	0.0505221	−	0.436919i
$631$	−6.03045	+	18.5598i	−0.240069	+	0.738855i	0.756340	+	0.654179i	$0.226986\pi$
$631$	−6.03045	+	18.5598i	−0.240069	+	0.738855i	−0.996409	+	0.0846763i	$0.973014\pi$
$632$	0.708419	+	1.59114i	0.0281794	+	0.0632920i
$633$	10.5973	+	42.4671i	0.421204	+	1.68792i
$634$	−0.239640	−	1.12742i	−0.00951732	−	0.0447755i
$635$	16.4168	+	3.48949i	0.651480	+	0.138476i
$636$	−12.8233	+	19.0196i	−0.508478	+	0.754176i
$637$	−0.195272	−	0.159475i	−0.00773695	−	0.00631863i
$638$	−0.271408	+	0.201206i	−0.0107452	+	0.00796584i
$639$	−12.9677	+	2.29193i	−0.512995	+	0.0906672i
$640$	0.565716	−	1.27062i	0.0223619	−	0.0502256i
$641$	−24.4067	−	21.9759i	−0.964009	−	0.867997i	0.0272903	−	0.999628i	$-0.491312\pi$
$641$	−24.4067	−	21.9759i	−0.964009	−	0.867997i	−0.991299	+	0.131630i	$0.957979\pi$
$642$	−5.07147	+	9.54266i	−0.200155	+	0.376619i
$643$	7.46873	+	5.42635i	0.294538	+	0.213994i	0.725234	−	0.688503i	$-0.241732\pi$
$643$	7.46873	+	5.42635i	0.294538	+	0.213994i	−0.430696	+	0.902497i	$0.641732\pi$
$644$	3.44591	−	18.3794i	0.135788	−	0.724251i
$645$	−15.6377	+	0.549223i	−0.615735	+	0.0216256i
$646$	−0.115947	+	0.545488i	−0.00456188	+	0.0214619i
$647$	13.2674	−	29.7991i	0.521596	−	1.17152i	−0.440236	−	0.897882i	$-0.645105\pi$
$647$	13.2674	−	29.7991i	0.521596	−	1.17152i	0.961832	−	0.273642i	$-0.0882282\pi$
$648$	−8.45476	+	3.08497i	−0.332134	+	0.121189i
$649$	9.69141	+	5.47174i	0.380421	+	0.214784i
$650$		−	0.110409i		−	0.00433061i
$651$	17.3572	−	21.7372i	0.680281	−	0.851946i
$652$	−1.96991	−	6.06277i	−0.0771478	−	0.237437i
$653$	21.9500	−	19.7639i	0.858972	−	0.773422i	−0.116582	−	0.993181i	$-0.537194\pi$
$653$	21.9500	−	19.7639i	0.858972	−	0.773422i	0.975554	+	0.219759i	$0.0705272\pi$
$654$	−5.05681	−	20.2645i	−0.197737	−	0.792403i
$655$	28.7812	+	3.02503i	1.12458	+	0.118198i
$656$	−0.706629	−	0.784791i	−0.0275892	−	0.0306409i
$657$	−12.8240	+	20.5410i	−0.500311	+	0.801381i
$658$	0.266043	+	11.0353i	0.0103715	+	0.430199i
$659$	41.6105			1.62092			0.810458	−	0.585797i	$-0.199218\pi$
$659$	41.6105			1.62092			0.810458	+	0.585797i	$0.199218\pi$
$660$	7.09117	+	3.68159i	0.276023	+	0.143306i
$661$	0.0683175	+	0.118329i	0.00265724	+	0.00460248i	0.867351	−	0.497697i	$-0.165821\pi$
$661$	0.0683175	+	0.118329i	0.00265724	+	0.00460248i	−0.864694	+	0.502299i	$0.832488\pi$
$662$	−27.3543	−	12.1789i	−1.06316	−	0.473348i
$663$	0.0166915	−	0.00234926i	0.000648245	−	9.12376e-5i
$664$	5.15083	−	15.8526i	0.199891	−	0.615201i
$665$	2.52038	+	7.16457i	0.0977361	+	0.277830i
$666$	8.53994	−	0.600614i	0.330916	−	0.0232733i
$667$	−0.535049	+	0.481760i	−0.0207172	+	0.0186538i
$668$	1.19755	−	1.33002i	0.0463347	−	0.0514599i
$669$	1.64993	−	23.6633i	0.0637900	−	0.914877i
$670$	−11.0296	−	6.36794i	−0.426110	−	0.246015i
$671$	23.2909	+	7.32077i	0.899135	+	0.282615i
$672$	−4.41820	+	1.21636i	−0.170436	+	0.0469219i
$673$	26.2559	+	36.1381i	1.01209	+	1.39302i	0.917604	+	0.397495i	$0.130120\pi$
$673$	26.2559	+	36.1381i	1.01209	+	1.39302i	0.0944848	+	0.995526i	$0.469880\pi$
$674$	−2.32287	+	10.9283i	−0.0894737	+	0.420941i
$675$	−15.1521	−	4.91314i	−0.583205	−	0.189107i
$676$	−1.35873	+	12.9275i	−0.0522590	+	0.497211i
$677$	−3.85722	+	1.71734i	−0.148245	+	0.0660029i	−0.479518	−	0.877532i	$-0.659189\pi$
$677$	−3.85722	+	1.71734i	−0.148245	+	0.0660029i	0.331273	+	0.943535i	$0.392522\pi$
$678$	−0.583107	−	16.6025i	−0.0223941	−	0.637615i
$679$	32.7649	+	34.6709i	1.25740	+	1.33055i
$680$	0.220899	+	0.304041i	0.00847109	+	0.0116595i
$681$	18.9768	+	3.34220i	0.727193	+	0.128073i
$682$	10.2334	+	17.3375i	0.391857	+	0.663887i
$683$	24.2149	−	13.9805i	0.926559	−	0.534949i	0.0408374	−	0.999166i	$-0.486997\pi$
$683$	24.2149	−	13.9805i	0.926559	−	0.534949i	0.885722	+	0.464217i	$0.153664\pi$
$684$	4.29935	−	4.45569i	0.164390	−	0.170367i
$685$	−0.330035	−	1.01574i	−0.0126100	−	0.0388095i
$686$	−16.3306	+	8.73556i	−0.623507	+	0.333525i
$687$	−12.5435	+	43.7776i	−0.478565	+	1.67022i
$688$	2.64186	+	5.93371i	0.100720	+	0.226220i
$689$	−0.466570	+	0.0991726i	−0.0177749	+	0.00377818i
$690$	15.7882	+	6.37515i	0.601045	+	0.242698i
$691$	3.08560	+	29.3575i	0.117382	+	1.11681i	0.881647	+	0.471910i	$0.156435\pi$
$691$	3.08560	+	29.3575i	0.117382	+	1.11681i	−0.764265	+	0.644902i	$0.776898\pi$
$692$	−6.82351			−0.259391
$693$	−5.45308	−	25.7539i	−0.207145	−	0.978310i
$694$	−15.2368			−0.578382
$695$	−2.71308	−	25.8132i	−0.102913	−	0.979150i
$696$	0.163605	+	0.0660626i	0.00620143	+	0.00250410i
$697$	0.279109	−	0.0593265i	0.0105720	−	0.00224715i
$698$	−4.35013	−	9.77054i	−0.164655	−	0.369820i
$699$	−1.90032	+	6.63221i	−0.0718765	+	0.250853i
$700$	−7.48669	−	3.11932i	−0.282970	−	0.117899i
$701$	11.9775	+	36.8630i	0.452384	+	1.39229i	0.874179	+	0.485604i	$0.161400\pi$
$701$	11.9775	+	36.8630i	0.452384	+	1.39229i	−0.421795	+	0.906691i	$0.638600\pi$
$702$	−0.171015	−	0.0760174i	−0.00645454	−	0.00286909i
$703$	−5.10066	+	2.94487i	−0.192375	+	0.111068i
$704$	0.314941	−	3.30164i	0.0118698	−	0.124435i
$705$	−9.89857	−	1.74334i	−0.372802	−	0.0656579i
$706$	20.2440	+	27.8635i	0.761893	+	1.04866i
$707$	1.42253	−	4.76604i	0.0534999	−	0.179245i
$708$	−0.204006	−	5.80855i	−0.00766701	−	0.218299i
$709$	0.259766	−	0.115655i	0.00975571	−	0.00434352i	−0.401853	−	0.915704i	$-0.631634\pi$
$709$	0.259766	−	0.115655i	0.00975571	−	0.00434352i	0.411609	+	0.911361i	$0.364967\pi$
$710$	0.638178	−	6.07186i	0.0239504	−	0.227873i
$711$	4.11876	+	3.21527i	0.154466	+	0.120582i
$712$	−1.14459	+	5.38489i	−0.0428955	+	0.201807i
$713$	25.2175	+	34.7089i	0.944401	+	1.29986i
$714$	0.312274	−	1.19820i	0.0116866	−	0.0448415i
$715$	0.0528590	+	0.157512i	0.00197681	+	0.00589062i
$716$	−7.89104	−	4.55590i	−0.294902	−	0.170262i
$717$	−2.08992	+	29.9737i	−0.0780497	+	1.11939i
$718$	−8.02146	+	8.90873i	−0.299358	+	0.332471i
$719$	34.0908	−	30.6955i	1.27137	−	1.14475i	0.289099	−	0.957299i	$-0.406644\pi$
$719$	34.0908	−	30.6955i	1.27137	−	1.14475i	0.982274	−	0.187450i	$-0.0600223\pi$
$720$	−0.292736	−	4.16232i	−0.0109096	−	0.155120i
$721$	−11.9002	+	13.8749i	−0.443187	+	0.516729i
$722$	4.55499	−	14.0188i	0.169519	−	0.521727i
$723$	12.0254	−	1.69252i	0.447229	−	0.0629454i
$724$	16.3634	+	7.28544i	0.608140	+	0.270761i
$725$	0.156137	+	0.270437i	0.00579878	+	0.0100438i
$726$	18.8239	+	2.94314i	0.698619	+	0.109230i
$727$	10.8539			0.402550			0.201275	−	0.979535i	$-0.435492\pi$
$727$	10.8539			0.402550			0.201275	+	0.979535i	$0.435492\pi$
$728$	−0.0836492	−	0.0456430i	−0.00310025	−	0.00169164i
$729$	−18.0424	+	20.0866i	−0.668236	+	0.743950i
$730$	−7.51220	−	8.34314i	−0.278039	−	0.308794i
$731$	−1.74542	−	0.183451i	−0.0645567	−	0.00678518i
$732$	−3.08698	−	12.3706i	−0.114098	−	0.457231i
$733$	21.1651	−	19.0571i	0.781751	−	0.703891i	−0.178220	−	0.983991i	$-0.557034\pi$
$733$	21.1651	−	19.0571i	0.781751	−	0.703891i	0.959971	+	0.280099i	$0.0903674\pi$
$734$	−1.18802	−	3.65635i	−0.0438506	−	0.134958i
$735$	−4.86660	−	16.1459i	−0.179507	−	0.595549i
$736$		−	7.06781i		−	0.260523i
$737$	−29.7654	−	6.02820i	−1.09642	−	0.222052i
$738$	−2.97749	−	1.08237i	−0.109603	−	0.0398425i
$739$	−8.67634	+	19.4874i	−0.319164	+	0.716855i	−0.999877	−	0.0156959i	$-0.995004\pi$
$739$	−8.67634	+	19.4874i	−0.319164	+	0.716855i	0.680713	+	0.732551i	$0.261670\pi$
$740$	−0.825219	+	3.88235i	−0.0303357	+	0.142718i
$741$	0.128674	−	0.00451922i	0.00472694	−	0.000166018i
$742$	−6.45694	+	34.4393i	−0.237042	+	1.26431i
$743$	−7.61960	−	5.53596i	−0.279536	−	0.203095i	0.439179	−	0.898400i	$-0.355269\pi$
$743$	−7.61960	−	5.53596i	−0.279536	−	0.203095i	−0.718715	+	0.695305i	$0.755269\pi$
$744$	4.93405	−	9.28410i	0.180891	−	0.340372i
$745$	−15.6003	−	14.0466i	−0.571552	−	0.514628i
$746$	5.94137	−	13.3445i	0.217529	−	0.488578i
$747$	−8.70309	−	49.2421i	−0.318429	−	1.80168i
$748$	0.730042	+	0.519753i	0.0266930	+	0.0190040i
$749$	−1.32931	+	16.4537i	−0.0485720	+	0.601205i
$750$	10.8620	−	16.1105i	0.396624	−	0.588273i
$751$	−35.6351	−	7.57448i	−1.30034	−	0.276397i	−0.494839	−	0.868985i	$-0.664773\pi$
$751$	−35.6351	−	7.57448i	−1.30034	−	0.276397i	−0.805506	+	0.592588i	$0.798106\pi$
$752$	0.867439	+	4.08098i	0.0316322	+	0.148818i
$753$	−0.727114	−	2.91380i	−0.0264975	−	0.106185i
$754$	0.00149229	+	0.00335174i	5.43461e−5	+	0.000122063i
$755$	−3.61683	+	11.1315i	−0.131630	+	0.405115i
$756$	−9.98619	+	9.44860i	−0.363194	+	0.343642i
$757$	−35.4720	+	25.7719i	−1.28925	+	0.936695i	−0.999790	−	0.0204944i	$-0.993476\pi$
$757$	−35.4720	+	25.7719i	−1.28925	+	0.936695i	−0.289461	+	0.957190i	$0.593476\pi$
$758$	−4.62285	+	8.00700i	−0.167909	+	0.290827i
$759$	40.5284	+	2.43440i	1.47109	+	0.0883631i
$760$	1.43531	+	2.48603i	0.0520642	+	0.0901779i
$761$	3.91031	+	37.2041i	0.141748	+	1.34865i	0.801875	+	0.597492i	$0.203836\pi$
$761$	3.91031	+	37.2041i	0.141748	+	1.34865i	−0.660126	+	0.751155i	$0.729497\pi$
$762$	−12.8710	−	16.4673i	−0.466267	−	0.596548i
$763$	−19.3691	−	25.3512i	−0.701210	−	0.917774i
$764$	−14.9790	+	20.6168i	−0.541922	+	0.745891i
$765$	1.01354	+	0.493834i	0.0366447	+	0.0178546i
$766$	4.48396	+	21.0954i	0.162012	+	0.762207i
$767$	0.0808707	−	0.0898160i	0.00292007	−	0.00324307i
$768$	−1.55660	+	0.759593i	−0.0561691	+	0.0274095i
$769$			2.47310i			0.0891823i	0.999005	+	0.0445912i	$0.0141985\pi$
$769$			2.47310i			0.0891823i	−0.999005	+	0.0445912i	$0.985801\pi$
$770$	12.1741	+	0.865786i	0.438722	+	0.0312008i
$771$	−22.6896	+	8.26348i	−0.817145	+	0.297602i
$772$	13.1750	−	1.38474i	0.474177	−	0.0498380i
$773$	−9.16521	−	8.25239i	−0.329650	−	0.296818i	0.487640	−	0.873045i	$-0.337858\pi$
$773$	−9.16521	−	8.25239i	−0.329650	−	0.296818i	−0.817290	+	0.576227i	$0.804524\pi$
$774$	15.3598	+	11.9905i	0.552096	+	0.430988i
$775$	16.9992	−	7.56853i	0.610629	−	0.271869i
$776$	14.5867	+	10.5979i	0.523633	+	0.380441i
$777$	11.6109	−	6.01661i	0.416540	−	0.215845i
$778$	5.36468	−	1.74309i	0.192333	−	0.0624928i
$779$	2.16763	−	0.227827i	0.0776635	−	0.00816276i
$780$	0.0557590	−	0.0664780i	0.00199649	−	0.00238030i
$781$	−3.16372	−	14.2106i	−0.113207	−	0.508497i
$782$	1.65388	+	0.954871i	0.0591428	+	0.0341461i
$783$	0.526385	−	0.0556457i	0.0188115	−	0.00198861i
$784$	−5.45827	+	4.38262i	−0.194938	+	0.156522i
$785$	−14.1586	−	4.60042i	−0.505343	−	0.164196i
$786$	−25.0399	−	25.9191i	−0.893143	−	0.924505i
$787$	39.1589	+	4.11577i	1.39587	+	0.146711i	0.772398	−	0.635138i	$-0.219057\pi$
$787$	39.1589	+	4.11577i	1.39587	+	0.146711i	0.623467	+	0.781850i	$0.285724\pi$
$788$	−17.4838	+	3.71629i	−0.622834	+	0.132388i
$789$	−0.634871	−	4.51078i	−0.0226020	−	0.160588i
$790$	−1.95984	+	1.42390i	−0.0697279	+	0.0506603i
$791$	−10.8772	−	22.9270i	−0.386750	−	0.815190i
$792$	−3.81953	−	9.18756i	−0.135721	−	0.326466i
$793$	0.132563	−	0.229607i	0.00470746	−	0.00815357i
$794$	16.7497	+	7.45742i	0.594423	+	0.264654i
$795$	−29.5838	−	11.9457i	−1.04923	−	0.423672i
$796$	10.1343	+	11.2553i	0.359201	+	0.398933i
$797$	20.7402	−	28.5464i	0.734654	−	1.01116i	−0.264254	−	0.964453i	$-0.585126\pi$
$797$	20.7402	−	28.5464i	0.734654	−	1.01116i	0.998908	−	0.0467117i	$-0.0148742\pi$
$798$	3.32888	−	8.85285i	0.117841	−	0.313387i
$799$	−1.07215	−	0.348363i	−0.0379300	−	0.0123242i
$800$	−2.99850	−	0.637352i	−0.106013	−	0.0225338i
$801$	4.55868	+	15.8740i	0.161073	+	0.560879i
$802$	14.7172	−	8.49696i	0.519681	−	0.300038i
$803$	−23.3122	−	13.1620i	−0.822669	−	0.464476i
$804$	5.42744	+	14.9025i	0.191411	+	0.525570i
$805$	26.0012	−	0.626849i	0.916421	−	0.0220935i
$806$	0.207926	−	0.0675593i	0.00732389	−	0.00237968i
$807$	−45.9139	−	24.4011i	−1.61625	−	0.858958i
$808$	0.196505	−	1.86962i	0.00691303	−	0.0657731i
$809$	−1.69295	+	16.1074i	−0.0595211	+	0.566306i	0.923601	+	0.383355i	$0.125231\pi$
$809$	−1.69295	+	16.1074i	−0.0595211	+	0.566306i	−0.983122	+	0.182950i	$0.941435\pi$
$810$	−6.64194	−	10.6104i	−0.233374	−	0.372810i
$811$	−31.1332	+	10.1158i	−1.09323	+	0.355213i	−0.799495	−	0.600673i	$-0.794899\pi$
$811$	−31.1332	+	10.1158i	−1.09323	+	0.355213i	−0.293738	+	0.955886i	$0.594899\pi$
$812$	0.269437	−	0.00649573i	0.00945540	−	0.000227955i
$813$	30.5103	−	11.1118i	1.07004	−	0.389707i
$814$	1.07980	+	9.40278i	0.0378471	+	0.329567i
$815$	7.67858	−	4.43323i	0.268969	−	0.155289i
$816$	0.0325527	−	0.466871i	0.00113957	−	0.0163438i
$817$	−13.1127	−	2.78719i	−0.458754	−	0.0975113i
$818$	25.2427	+	8.20185i	0.882590	+	0.286771i
$819$	−0.285859	−	0.00297348i	−0.00998873	−	0.000103902i
$820$	0.863345	−	1.18829i	0.0301493	−	0.0414970i
$821$	−23.6920	−	26.3126i	−0.826856	−	0.918317i	0.170899	−	0.985289i	$-0.445333\pi$
$821$	−23.6920	−	26.3126i	−0.826856	−	0.918317i	−0.997755	+	0.0669718i	$0.978666\pi$
$822$	−0.497981	+	1.23326i	−0.0173691	+	0.0430148i
$823$	−50.6186	−	22.5369i	−1.76445	−	0.785586i	−0.987813	−	0.155643i	$-0.950255\pi$
$823$	−50.6186	−	22.5369i	−1.76445	−	0.785586i	−0.776641	−	0.629943i	$-0.783078\pi$
$824$	−3.45444	+	5.98326i	−0.120341	+	0.208437i
$825$	4.68751	−	16.9746i	0.163198	−	0.590979i
$826$	−3.80551	−	8.02123i	−0.132411	−	0.279094i
$827$	17.3465	−	12.6030i	0.603197	−	0.438248i	−0.243815	−	0.969822i	$-0.578399\pi$
$827$	17.3465	−	12.6030i	0.603197	−	0.438248i	0.847012	+	0.531573i	$0.178399\pi$
$828$	−9.96192	−	18.7175i	−0.346201	−	0.650479i
$829$	46.0836	−	9.79537i	1.60055	−	0.340207i	0.680726	−	0.732539i	$-0.261665\pi$
$829$	46.0836	−	9.79537i	1.60055	−	0.340207i	0.919824	+	0.392331i	$0.128331\pi$
$830$	23.0566	+	2.42334i	0.800305	+	0.0841154i
$831$	−26.3932	+	25.4979i	−0.915570	+	0.884511i
$832$	−0.0342540	−	0.0111298i	−0.00118754	−	0.000385857i
$833$	−0.288124	−	1.86934i	−0.00998289	−	0.0647690i
$834$	−18.0690	+	26.8001i	−0.625680	+	0.928010i
$835$	2.15576	+	1.24463i	0.0746030	+	0.0430721i
$836$	5.13081	+	4.53121i	0.177453	+	0.156715i
$837$	−0.0189833	−	31.5413i	−0.000656158	−	1.09023i
$838$	−30.0371	+	3.15703i	−1.03761	+	0.109058i
$839$	−21.9358	+	7.12739i	−0.757309	+	0.246065i	−0.662123	−	0.749395i	$-0.730345\pi$
$839$	−21.9358	+	7.12739i	−0.757309	+	0.246065i	−0.0951860	+	0.995460i	$0.530345\pi$
$840$	−2.93246	−	5.65909i	−0.101180	−	0.195257i
$841$	23.4531	+	17.0397i	0.808728	+	0.587575i
$842$	−33.6272	+	14.9718i	−1.15887	+	0.515962i
$843$	−23.8370	−	38.1302i	−0.820990	−	1.31327i
$844$	18.7795	+	16.9091i	0.646416	+	0.582035i
$845$	−17.9804	+	1.88982i	−0.618545	+	0.0650117i
$846$	8.04927	+	9.58493i	0.276739	+	0.329537i
$847$	28.1784	−	7.27862i	0.968221	−	0.250096i
$848$			13.2436i			0.454789i
$849$	15.2659	+	31.2837i	0.523923	+	1.07366i
$850$	0.554244	−	0.615550i	0.0190104	−	0.0211132i
$851$	4.19343	+	19.7285i	0.143749	+	0.676285i
$852$	−5.46805	+	5.28256i	−0.187332	+	0.180977i
$853$	19.7681	−	27.2084i	0.676845	−	0.931598i	−0.323045	−	0.946383i	$-0.604707\pi$
$853$	19.7681	−	27.2084i	0.676845	−	0.931598i	0.999891	+	0.0147858i	$0.00470664\pi$
$854$	−11.8241	−	15.4758i	−0.404611	−	0.529572i
$855$	7.30511	+	4.56067i	0.249830	+	0.155971i
$856$	0.652172	+	6.20500i	0.0222908	+	0.212083i
$857$	5.79142	+	10.0310i	0.197831	+	0.342654i	0.947825	−	0.318791i	$-0.103277\pi$
$857$	5.79142	+	10.0310i	0.197831	+	0.342654i	−0.749994	+	0.661445i	$0.769944\pi$
$858$	0.0756191	−	0.192587i	0.00258159	−	0.00657481i
$859$	−4.26912	+	7.39433i	−0.145660	+	0.252291i	−0.929619	−	0.368522i	$-0.879864\pi$
$859$	−4.26912	+	7.39433i	−0.145660	+	0.252291i	0.783959	+	0.620813i	$0.213197\pi$
$860$	−7.30868	+	5.31006i	−0.249224	+	0.181072i
$861$	−4.83090	+	0.286377i	−0.164637	+	0.00975971i
$862$	−3.15297	+	9.70385i	−0.107391	+	0.330514i
$863$	14.0666	+	31.5941i	0.478833	+	1.07548i	0.977930	+	0.208931i	$0.0669985\pi$
$863$	14.0666	+	31.5941i	0.478833	+	1.07548i	−0.499097	+	0.866546i	$0.666335\pi$
$864$	−3.05169	+	4.20561i	−0.103821	+	0.143078i
$865$	−1.97321	−	9.28320i	−0.0670910	−	0.315638i
$866$	6.96771	+	1.48103i	0.236772	+	0.0503275i
$867$	−24.3094	−	16.3898i	−0.825589	−	0.556626i
$868$	1.29329	−	16.0079i	0.0438973	−	0.543343i
$869$	−3.35030	+	4.70582i	−0.113651	+	0.159634i
$870$	−0.0425654	+	0.241684i	−0.00144310	+	0.00819385i
$871$	−0.134141	+	0.301286i	−0.00454520	+	0.0102087i
$872$	−8.96118	−	8.06869i	−0.303464	−	0.273240i
$873$	53.5671	+	7.50645i	1.81297	+	0.254055i
$874$	11.8014	+	8.57422i	0.399188	+	0.290027i
$875$	5.46934	−	29.1718i	0.184898	−	0.986187i
$876$	0.490725	+	13.9722i	0.0165801	+	0.472076i
$877$	−4.53793	+	21.3493i	−0.153235	+	0.720913i	0.832692	+	0.553736i	$0.186798\pi$
$877$	−4.53793	+	21.3493i	−0.153235	+	0.720913i	−0.985927	+	0.167177i	$0.946535\pi$
$878$	−9.06088	+	20.3511i	−0.305790	+	0.686815i
$879$	27.1384	−	32.3555i	0.915357	−	1.09132i
$880$	4.58286	−	0.526290i	0.154488	−	0.0177412i
$881$		−	5.87061i		−	0.197786i	−0.995098	−	0.0988929i	$-0.968470\pi$
$881$		−	5.87061i		−	0.197786i	0.995098	−	0.0988929i	$-0.0315301\pi$
$882$	−8.27781	+	19.2997i	−0.278728	+	0.649854i
$883$	−10.4829	−	32.2632i	−0.352779	−	1.08574i	−0.957286	−	0.289143i	$-0.906630\pi$
$883$	−10.4829	−	32.2632i	−0.352779	−	1.08574i	0.604507	−	0.796600i	$-0.293370\pi$
$884$	0.00723217	−	0.00651187i	0.000243244	−	0.000219018i
$885$	7.84338	−	1.95725i	0.263652	−	0.0657921i
$886$	28.3063	+	2.97511i	0.950968	+	0.0999508i
$887$	−8.89023	−	9.87360i	−0.298505	−	0.331523i	0.575170	−	0.818034i	$-0.304936\pi$
$887$	−8.89023	−	9.87360i	−0.298505	−	0.331523i	−0.873674	+	0.486511i	$0.838269\pi$
$888$	3.89430	−	3.04382i	0.130684	−	0.102144i
$889$	−28.0256	−	15.2921i	−0.939948	−	0.512880i
$890$	−7.65699			−0.256663
$891$	−23.0648	−	18.9477i	−0.772701	−	0.634770i
$892$	−6.84760	−	11.8604i	−0.229275	−	0.397115i
$893$	−7.86649	−	3.50239i	−0.263242	−	0.117203i
$894$	3.64343	+	25.8867i	0.121855	+	0.865780i
$895$	3.91626	−	12.0530i	0.130906	−	0.402887i
$896$	−1.72245	+	2.00827i	−0.0575431	+	0.0670917i
$897$	0.121446	−	0.423855i	0.00405498	−	0.0141521i
$898$	−7.38461	+	6.64913i	−0.246428	+	0.221884i
$899$	−0.413756	+	0.459522i	−0.0137995	+	0.0153259i
$900$	−8.83920	+	2.53844i	−0.294640	+	0.0846146i
$901$	−3.09905	−	1.78923i	−0.103244	−	0.0596080i
$902$	1.05024	−	3.34132i	0.0349692	−	0.111254i
$903$	28.8029	+	7.50659i	0.958499	+	0.249804i
$904$	−5.63767	−	7.75958i	−0.187506	−	0.258080i
$905$	−5.17972	+	24.3687i	−0.172180	+	0.810042i
$906$	12.3591	−	7.72627i	0.410604	−	0.256688i
$907$	3.19945	−	30.4408i	0.106236	−	1.01077i	−0.803422	−	0.595410i	$-0.796989\pi$
$907$	3.19945	−	30.4408i	0.106236	−	1.01077i	0.909658	−	0.415359i	$-0.136344\pi$
$908$	10.1631	−	4.52490i	0.337274	−	0.150164i
$909$	−2.11479	−	5.22825i	−0.0701431	−	0.173410i
$910$	0.0379065	−	0.127001i	0.00125659	−	0.00421005i
$911$	−15.2440	−	20.9816i	−0.505057	−	0.695151i	0.478019	−	0.878349i	$-0.341355\pi$
$911$	−15.2440	−	20.9816i	−0.505057	−	0.695151i	−0.983076	+	0.183198i	$0.941355\pi$
$912$	0.620051	−	3.52061i	0.0205319	−	0.116579i
$913$	53.9618	−	12.0135i	1.78588	−	0.397590i
$914$	12.7958	−	7.38766i	0.423248	−	0.244362i
$915$	15.9372	−	7.77705i	0.526867	−	0.257101i
$916$	8.12469	+	25.0052i	0.268447	+	0.826196i
$917$	−50.8159	−	21.1724i	−1.67809	−	0.699173i
$918$	−0.571836	−	1.28229i	−0.0188734	−	0.0423218i
$919$	−21.2785	−	47.7922i	−0.701911	−	1.57652i	−0.812705	−	0.582675i	$-0.802006\pi$
$919$	−21.2785	−	47.7922i	−0.701911	−	1.57652i	0.110794	−	0.993843i	$-0.464661\pi$
$920$	9.61556	−	2.04385i	0.317016	−	0.0673837i
$921$	18.1719	−	45.0029i	0.598783	−	1.48290i
$922$	−2.08188	−	19.8078i	−0.0685630	−	0.652334i
$923$	−0.158098			−0.00520387
$924$	−10.9226	−	10.5686i	−0.359328	−	0.347683i
$925$	8.74793			0.287630
$926$	−1.22282	−	11.6344i	−0.0401844	−	0.382329i
$927$	−0.715037	+	20.7143i	−0.0234849	+	0.680346i
$928$	0.0996413	−	0.0211794i	0.00327089	−	0.000695248i
$929$	−1.60413	−	3.60293i	−0.0526298	−	0.118208i	0.885317	−	0.464989i	$-0.153942\pi$
$929$	−1.60413	−	3.60293i	−0.0526298	−	0.118208i	−0.937946	+	0.346780i	$0.887275\pi$
$930$	14.0576	+	4.02789i	0.460966	+	0.132080i
$931$	−0.696204	−	14.4306i	−0.0228172	−	0.472944i
$932$	1.23087	+	3.78824i	0.0403186	+	0.124088i
$933$	7.57902	+	15.5314i	0.248126	+	0.508474i
$934$	10.9391	−	6.31567i	0.357937	−	0.206655i
$935$	−0.495997	+	1.14350i	−0.0162209	+	0.0373965i
$936$	−0.106401	+	0.0188055i	−0.00347784	+	0.000614676i
$937$	8.32120	+	11.4531i	0.271842	+	0.374158i	0.923010	−	0.384775i	$-0.125721\pi$
$937$	8.32120	+	11.4531i	0.271842	+	0.374158i	−0.651169	+	0.758933i	$0.725721\pi$
$938$	16.6400	+	17.6079i	0.543315	+	0.574920i
$939$	−4.52958	+	0.159086i	−0.147817	+	0.00519158i
$940$	−5.30121	+	2.36025i	−0.172907	+	0.0769829i
$941$	−0.321745	+	3.06119i	−0.0104886	+	0.0997921i	−0.998514	−	0.0545008i	$-0.982643\pi$
$941$	−0.321745	+	3.06119i	−0.0104886	+	0.0997921i	0.988025	+	0.154293i	$0.0493099\pi$
$942$	9.82742	+	15.7201i	0.320194	+	0.512190i
$943$	1.55183	−	7.30079i	0.0505345	−	0.237746i
$944$	−1.97239	−	2.71477i	−0.0641960	−	0.0883582i
$945$	−15.7423	−	10.8536i	−0.512098	−	0.353068i
$946$	−12.4940	+	17.5491i	−0.406216	+	0.570570i
$947$	−8.41536	−	4.85861i	−0.273463	−	0.157884i	0.356998	−	0.934105i	$-0.383800\pi$
$947$	−8.41536	−	4.85861i	−0.273463	−	0.157884i	−0.630460	+	0.776222i	$0.717134\pi$
$948$	3.00943	+	0.209833i	0.0977418	+	0.00681507i
$949$	−0.194530	+	0.216048i	−0.00631472	+	0.00701321i
$950$	4.70181	−	4.23352i	0.152547	−	0.137354i
$951$	−1.91914	−	0.549889i	−0.0622325	−	0.0178314i
$952$	−0.237235	−	0.674378i	−0.00768884	−	0.0218567i
$953$	10.9114	−	33.5820i	0.353456	−	1.08783i	−0.603443	−	0.797406i	$-0.706205\pi$
$953$	10.9114	−	33.5820i	0.353456	−	1.08783i	0.956899	−	0.290421i	$-0.0937952\pi$
$954$	18.6666	+	35.0728i	0.604354	+	1.13553i
$955$	−32.3802	−	14.4166i	−1.04780	−	0.466511i
$956$	8.67368	+	15.0232i	0.280527	+	0.485887i
$957$	0.0871277	+	0.578661i	0.00281644	+	0.0187055i
$958$	−21.1972			−0.684852
$959$	0.0489649	+	2.03102i	0.00158116	+	0.0655852i
$960$	−1.48354	−	1.89806i	−0.0478811	−	0.0612596i
$961$	3.91204	+	4.34476i	0.126195	+	0.140153i
$962$	0.102217	+	0.0107435i	0.00329562	+	0.000346384i
$963$	10.4729	+	15.5133i	0.337486	+	0.499910i
$964$	5.21040	−	4.69147i	0.167816	−	0.151102i
$965$	5.69380	+	17.5237i	0.183290	+	0.564109i
$966$	−25.3099	−	20.2100i	−0.814331	−	0.650246i
$967$		−	6.69622i		−	0.215336i	−0.994187	−	0.107668i	$-0.965662\pi$
$967$		−	6.69622i		−	0.215336i	0.994187	−	0.107668i	$-0.0343383\pi$
$968$	9.96108	−	4.66657i	0.320161	−	0.149989i
$969$	0.740063	+	0.620733i	0.0237742	+	0.0199408i
$970$	−10.2000	+	22.9095i	−0.327501	+	0.735579i
$971$	−5.65624	+	26.6105i	−0.181517	+	0.853972i	0.789273	+	0.614043i	$0.210458\pi$
$971$	−5.65624	+	26.6105i	−0.181517	+	0.853972i	−0.970790	+	0.239930i	$0.922876\pi$
$972$	−2.15401	+	15.4389i	−0.0690899	+	0.495204i
$973$	−9.09832	+	48.5276i	−0.291679	+	1.55572i
$974$	−15.3946	−	11.1848i	−0.493275	−	0.358385i
$975$	−0.168868	−	0.0897453i	−0.00540810	−	0.00287415i
$976$	−5.47043	−	4.92560i	−0.175104	−	0.157665i
$977$	−4.97539	+	11.1749i	−0.159177	+	0.357517i	−0.975474	−	0.220115i	$-0.929357\pi$
$977$	−4.97539	+	11.1749i	−0.159177	+	0.357517i	0.816297	+	0.577633i	$0.196023\pi$
$978$	−10.8741	−	1.91514i	−0.347715	−	0.0612396i
$979$	−17.3100	+	5.80899i	−0.553229	+	0.185656i
$980$	−7.54083	−	6.15847i	−0.240883	−	0.196725i
$981$	−35.1043	−	8.73753i	−1.12080	−	0.278968i
$982$	14.2116	+	3.02077i	0.453510	+	0.0963965i
$983$	−1.93169	−	9.08789i	−0.0616113	−	0.289859i	0.936545	−	0.350546i	$-0.114004\pi$
$983$	−1.93169	−	9.08789i	−0.0616113	−	0.289859i	−0.998157	+	0.0606876i	$0.980671\pi$
$984$	−1.77469	+	0.442859i	−0.0565752	+	0.0141178i
$985$	−10.1118	−	22.7115i	−0.322190	−	0.723650i
$986$	−0.00850564	+	0.0261777i	−0.000270875	+	0.000833667i
$987$	17.0944	+	8.56302i	0.544121	+	0.272564i
$988$	0.0601387	−	0.0436933i	0.00191327	−	0.00139007i
$989$	−22.9536	+	39.7568i	−0.729882	+	1.26419i
$990$	11.3949	−	7.85320i	0.362153	−	0.249591i
$991$	7.35419	+	12.7378i	0.233614	+	0.404630i	0.958869	−	0.283850i	$-0.0916116\pi$
$991$	7.35419	+	12.7378i	0.233614	+	0.404630i	−0.725255	+	0.688480i	$0.758278\pi$
$992$	−0.634501	−	6.03687i	−0.0201454	−	0.191671i
$993$	−40.8621	+	31.9382i	−1.29672	+	1.01353i
$994$	−4.46664	+	10.7204i	−0.141673	+	0.340031i
$995$	−12.3819	+	17.0422i	−0.392533	+	0.540275i
$996$	−20.0594	−	20.7637i	−0.635605	−	0.657924i
$997$	−12.6884	−	59.6945i	−0.401847	−	1.89054i	−0.452390	−	0.891820i	$-0.649428\pi$
$997$	−12.6884	−	59.6945i	−0.401847	−	1.89054i	0.0505426	−	0.998722i	$-0.483905\pi$
$998$	−15.3267	+	17.0220i	−0.485157	+	0.538821i
$999$	6.02300	−	13.5498i	0.190559	−	0.428697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.107.3	yes	128
3.2	odd	2		462.2.bc.a.107.11	yes	128
7.4	even	3	inner	462.2.bc.b.305.9	yes	128
11.7	odd	10		462.2.bc.a.359.11	yes	128
21.11	odd	6		462.2.bc.a.305.11	yes	128
33.29	even	10	inner	462.2.bc.b.359.9	yes	128
77.18	odd	30		462.2.bc.a.95.11	✓	128
231.95	even	30	inner	462.2.bc.b.95.3	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.11	✓	128	77.18	odd	30
462.2.bc.a.107.11	yes	128	3.2	odd	2
462.2.bc.a.305.11	yes	128	21.11	odd	6
462.2.bc.a.359.11	yes	128	11.7	odd	10
462.2.bc.b.95.3	yes	128	231.95	even	30	inner
462.2.bc.b.107.3	yes	128	1.1	even	1	trivial
462.2.bc.b.305.9	yes	128	7.4	even	3	inner
462.2.bc.b.359.9	yes	128	33.29	even	10	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.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 - 0.994522i) q^{2} +(-1.60606 - 0.648515i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.565716 - 1.27062i) q^{5} +(-0.477084 + 1.66505i) q^{6} +(0.339893 + 2.62383i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.15886 + 2.08311i) q^{9} +O(q^{10})\)	\(q+(-0.104528 - 0.994522i) q^{2} +(-1.60606 - 0.648515i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.565716 - 1.27062i) q^{5} +(-0.477084 + 1.66505i) q^{6} +(0.339893 + 2.62383i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.15886 + 2.08311i) q^{9} +(-1.20453 + 0.695433i) q^{10} +(-2.19545 + 2.48596i) q^{11} +(1.70580 + 0.300425i) q^{12} +(0.0211702 + 0.0291382i) q^{13} +(2.57393 - 0.612296i) q^{14} +(0.0845576 + 2.40757i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.0282439 + 0.268723i) q^{17} +(1.84604 - 2.36477i) q^{18} +(-0.429111 + 2.01881i) q^{19} +(0.817530 + 1.12523i) q^{20} +(1.15570 - 4.43445i) q^{21} +(2.70183 + 1.92357i) q^{22} +(6.12090 + 3.53390i) q^{23} +(0.120475 - 1.72786i) q^{24} +(2.05121 - 2.27810i) q^{25} +(0.0267657 - 0.0241000i) q^{26} +(-2.11632 - 4.74565i) q^{27} +(-0.877990 - 2.49582i) q^{28} +(-0.0314788 + 0.0968816i) q^{29} +(2.38554 - 0.335754i) q^{30} +(5.54534 + 2.46894i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.13820 - 2.56882i) q^{33} +0.270203 q^{34} +(3.14160 - 1.91622i) q^{35} +(-2.54478 - 1.58874i) q^{36} +(1.90948 + 2.12070i) q^{37} +(2.05260 + 0.215737i) q^{38} +(-0.0151039 - 0.0605269i) q^{39} +(1.03361 - 0.930671i) q^{40} +(-0.326334 - 1.00435i) q^{41} +(-4.53096 - 0.685847i) q^{42} +6.49525i q^{43} +(1.63061 - 2.88810i) q^{44} +(1.42554 - 3.92153i) q^{45} +(2.87474 - 6.45677i) q^{46} +(-0.867439 + 4.08098i) q^{47} +(-1.73098 + 0.0607950i) q^{48} +(-6.76895 + 1.78364i) q^{49} +(-2.48004 - 1.80185i) q^{50} +(0.219632 - 0.413268i) q^{51} +(-0.0267657 - 0.0241000i) q^{52} +(-5.38668 + 12.0987i) q^{53} +(-4.49844 + 2.60078i) q^{54} +(4.40071 + 1.38323i) q^{55} +(-2.39038 + 1.13407i) q^{56} +(1.99841 - 2.96404i) q^{57} +(0.0996413 + 0.0211794i) q^{58} +(-0.697676 - 3.28231i) q^{59} +(-0.583271 - 2.33737i) q^{60} +(-2.99407 - 6.72479i) q^{61} +(1.87577 - 5.77303i) q^{62} +(-4.73194 + 6.37250i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0250473 - 0.0433832i) q^{65} +(-3.09184 - 4.84154i) q^{66} +(4.57840 + 7.93002i) q^{67} +(-0.0282439 - 0.268723i) q^{68} +(-7.53874 - 9.64516i) q^{69} +(-2.23411 - 2.92409i) q^{70} +(-2.58012 + 3.55124i) q^{71} +(-1.31403 + 2.69691i) q^{72} +(1.67822 + 7.89542i) q^{73} +(1.90948 - 2.12070i) q^{74} +(-4.77176 + 2.32853i) q^{75} -2.06391i q^{76} +(-7.26896 - 4.91551i) q^{77} +(-0.0586165 + 0.0213480i) q^{78} +(1.73217 - 0.182059i) q^{79} +(-1.03361 - 0.930671i) q^{80} +(0.321313 + 8.99426i) q^{81} +(-0.964741 + 0.429530i) q^{82} +(-13.4850 - 9.79746i) q^{83} +(-0.208475 + 4.57783i) q^{84} +(0.357422 - 0.116133i) q^{85} +(6.45967 - 0.678939i) q^{86} +(0.113386 - 0.135183i) q^{87} +(-3.04272 - 1.31979i) q^{88} +(4.76764 + 2.75260i) q^{89} +(-4.04906 - 1.00782i) q^{90} +(-0.0692581 + 0.0654507i) q^{91} +(-6.72189 - 2.18407i) q^{92} +(-7.30499 - 7.56151i) q^{93} +(4.14929 + 0.436108i) q^{94} +(2.80789 - 0.596836i) q^{95} +(0.241399 + 1.71515i) q^{96} +(14.5867 - 10.5979i) q^{97} +(2.48142 + 6.54542i) q^{98} +(-9.91818 + 0.793481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

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