LMFDB - Embedded newform 462.2.bc.b.95.12

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			95.12
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.b.107.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(0.882151 + 1.49057i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.35789 - 3.04988i) q^{5} +(-1.57462 + 0.721511i) q^{6} +(1.07443 - 2.41777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.44362 + 2.62982i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(0.882151 + 1.49057i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.35789 - 3.04988i) q^{5} +(-1.57462 + 0.721511i) q^{6} +(1.07443 - 2.41777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.44362 + 2.62982i) q^{9} +(2.89123 + 1.66925i) q^{10} +(0.617451 - 3.25864i) q^{11} +(-0.552966 - 1.64141i) q^{12} +(1.75434 - 2.41465i) q^{13} +(2.29221 + 1.32127i) q^{14} +(5.74393 - 0.666413i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.284826 - 2.70994i) q^{17} +(-2.46452 - 1.71060i) q^{18} +(1.31058 + 6.16579i) q^{19} +(-1.96232 + 2.70091i) q^{20} +(4.55167 - 0.531316i) q^{21} +(3.17625 + 0.954689i) q^{22} +(-0.928949 + 0.536329i) q^{23} +(1.69022 - 0.378363i) q^{24} +(-4.11222 - 4.56708i) q^{25} +(2.21804 + 1.99713i) q^{26} +(-5.19343 + 0.168079i) q^{27} +(-1.55363 + 2.14155i) q^{28} +(-0.535164 - 1.64707i) q^{29} +(0.0623578 + 5.78212i) q^{30} +(4.61371 - 2.05416i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.40193 - 1.95426i) q^{33} +2.72486 q^{34} +(-5.91492 - 6.55995i) q^{35} +(1.95884 - 2.27221i) q^{36} +(-6.72672 + 7.47078i) q^{37} +(-6.26901 + 0.658899i) q^{38} +(5.14681 + 0.484895i) q^{39} +(-2.48099 - 2.23390i) q^{40} +(-3.40181 + 10.4697i) q^{41} +(0.0526261 + 4.58227i) q^{42} +0.998721i q^{43} +(-1.28147 + 3.05906i) q^{44} +(6.06035 + 7.97387i) q^{45} +(-0.436290 - 0.979922i) q^{46} +(1.94346 + 9.14326i) q^{47} +(0.199614 + 1.72051i) q^{48} +(-4.69119 - 5.19545i) q^{49} +(4.97190 - 3.61230i) q^{50} +(3.78810 - 2.81513i) q^{51} +(-2.21804 + 1.99713i) q^{52} +(2.79637 + 6.28076i) q^{53} +(0.375703 - 5.18255i) q^{54} +(-9.10002 - 6.30803i) q^{55} +(-1.96742 - 1.76898i) q^{56} +(-8.03444 + 7.39267i) q^{57} +(1.69398 - 0.360067i) q^{58} +(-1.23972 + 5.83242i) q^{59} +(-5.75697 - 0.542380i) q^{60} +(4.16142 - 9.34670i) q^{61} +(1.56064 + 4.80315i) q^{62} +(4.80723 + 6.31590i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.98217 - 8.62936i) q^{65} +(1.37890 + 5.57662i) q^{66} +(1.86083 - 3.22305i) q^{67} +(-0.284826 + 2.70994i) q^{68} +(-1.61891 - 0.911544i) q^{69} +(7.14229 - 5.19682i) q^{70} +(-0.722902 - 0.994990i) q^{71} +(2.05501 + 2.18562i) q^{72} +(1.24396 - 5.85236i) q^{73} +(-6.72672 - 7.47078i) q^{74} +(3.17997 - 10.1584i) q^{75} -6.30354i q^{76} +(-7.21523 - 4.99404i) q^{77} +(-1.02023 + 5.06793i) q^{78} +(17.1227 + 1.79967i) q^{79} +(2.48099 - 2.23390i) q^{80} +(-4.83193 - 7.59292i) q^{81} +(-10.0568 - 4.47755i) q^{82} +(9.70645 - 7.05215i) q^{83} +(-4.56267 - 0.426640i) q^{84} +(-8.65173 - 2.81112i) q^{85} +(-0.993250 - 0.104395i) q^{86} +(1.98298 - 2.25066i) q^{87} +(-2.90835 - 1.59421i) q^{88} +(-11.7595 + 6.78938i) q^{89} +(-8.56367 + 5.19365i) q^{90} +(-3.95313 - 6.83597i) q^{91} +(1.02016 - 0.331470i) q^{92} +(7.13186 + 5.06500i) q^{93} +(-9.29632 + 0.977083i) q^{94} +(20.5845 + 4.37538i) q^{95} +(-1.73195 + 0.0186784i) q^{96} +(-2.77243 - 2.01429i) q^{97} +(5.65735 - 4.12242i) q^{98} +(7.67829 + 6.32803i) 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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

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
$3$	0.882151	+	1.49057i	0.509310	+	0.860583i
$3$	0.882151	+	1.49057i	0.509310	+	0.860583i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	1.35789	−	3.04988i	0.607268	−	1.36395i	−0.304213	−	0.952604i	$-0.598394\pi$
$5$	1.35789	−	3.04988i	0.607268	−	1.36395i	0.911481	−	0.411342i	$-0.134940\pi$
$6$	−1.57462	+	0.721511i	−0.642835	+	0.294556i
$7$	1.07443	−	2.41777i	0.406097	−	0.913830i
$7$	1.07443	−	2.41777i	0.406097	−	0.913830i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−1.44362	+	2.62982i	−0.481206	+	0.876607i
$10$	2.89123	+	1.66925i	0.914287	+	0.527864i
$11$	0.617451	−	3.25864i	0.186168	−	0.982518i
$11$	0.617451	−	3.25864i	0.186168	−	0.982518i
$12$	−0.552966	−	1.64141i	−0.159628	−	0.473834i
$13$	1.75434	−	2.41465i	0.486568	−	0.669703i	−0.493183	−	0.869926i	$-0.664167\pi$
$13$	1.75434	−	2.41465i	0.486568	−	0.669703i	0.979750	+	0.200223i	$0.0641666\pi$
$14$	2.29221	+	1.32127i	0.612620	+	0.353125i
$15$	5.74393	−	0.666413i	1.48308	−	0.172067i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.284826	−	2.70994i	−0.0690804	−	0.657256i	−0.973197	−	0.229971i	$-0.926137\pi$
$17$	−0.284826	−	2.70994i	−0.0690804	−	0.657256i	0.904117	−	0.427285i	$-0.140530\pi$
$18$	−2.46452	−	1.71060i	−0.580892	−	0.403193i
$19$	1.31058	+	6.16579i	0.300668	+	1.41453i	0.826018	+	0.563644i	$0.190601\pi$
$19$	1.31058	+	6.16579i	0.300668	+	1.41453i	−0.525350	+	0.850886i	$0.676066\pi$
$20$	−1.96232	+	2.70091i	−0.438789	+	0.603941i
$21$	4.55167	−	0.531316i	0.993256	−	0.115943i
$22$	3.17625	+	0.954689i	0.677179	+	0.203540i
$23$	−0.928949	+	0.536329i	−0.193699	+	0.111832i	−0.593713	−	0.804677i	$-0.702339\pi$
$23$	−0.928949	+	0.536329i	−0.193699	+	0.111832i	0.400014	+	0.916509i	$0.369005\pi$
$24$	1.69022	−	0.378363i	0.345015	−	0.0772330i
$25$	−4.11222	−	4.56708i	−0.822443	−	0.913416i
$26$	2.21804	+	1.99713i	0.434994	+	0.391670i
$27$	−5.19343	+	0.168079i	−0.999477	+	0.0323469i
$28$	−1.55363	+	2.14155i	−0.293609	+	0.404714i
$29$	−0.535164	−	1.64707i	−0.0993775	−	0.305852i	0.888992	−	0.457922i	$-0.151406\pi$
$29$	−0.535164	−	1.64707i	−0.0993775	−	0.305852i	−0.988370	+	0.152070i	$0.951406\pi$
$30$	0.0623578	+	5.78212i	0.0113849	+	1.05567i
$31$	4.61371	−	2.05416i	0.828647	−	0.368937i	0.0518236	−	0.998656i	$-0.483497\pi$
$31$	4.61371	−	2.05416i	0.828647	−	0.368937i	0.776823	+	0.629719i	$0.216830\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.40193	−	1.95426i	0.940356	−	0.340193i
$34$	2.72486			0.467310
$35$	−5.91492	−	6.55995i	−0.999805	−	1.10883i
$36$	1.95884	−	2.27221i	0.326474	−	0.378701i
$37$	−6.72672	+	7.47078i	−1.10587	+	1.22819i	−0.134422	+	0.990924i	$0.542918\pi$
$37$	−6.72672	+	7.47078i	−1.10587	+	1.22819i	−0.971445	+	0.237265i	$0.923749\pi$
$38$	−6.26901	+	0.658899i	−1.01697	+	0.106888i
$39$	5.14681	+	0.484895i	0.824149	+	0.0776454i
$40$	−2.48099	−	2.23390i	−0.392279	−	0.353210i
$41$	−3.40181	+	10.4697i	−0.531273	+	1.63509i	0.220293	+	0.975434i	$0.429299\pi$
$41$	−3.40181	+	10.4697i	−0.531273	+	1.63509i	−0.751567	+	0.659657i	$0.770701\pi$
$42$	0.0526261	+	4.58227i	0.00812038	+	0.707060i
$43$			0.998721i			0.152304i	0.997096	+	0.0761518i	$0.0242633\pi$
$43$			0.998721i			0.152304i	−0.997096	+	0.0761518i	$0.975737\pi$
$44$	−1.28147	+	3.05906i	−0.193189	+	0.461170i
$45$	6.06035	+	7.97387i	0.903424	+	1.18867i
$46$	−0.436290	−	0.979922i	−0.0643274	−	0.144482i
$47$	1.94346	+	9.14326i	0.283483	+	1.33368i	0.857350	+	0.514734i	$0.172109\pi$
$47$	1.94346	+	9.14326i	0.283483	+	1.33368i	−0.573867	+	0.818948i	$0.694558\pi$
$48$	0.199614	+	1.72051i	0.0288118	+	0.248334i
$49$	−4.69119	−	5.19545i	−0.670170	−	0.742207i
$50$	4.97190	−	3.61230i	0.703133	−	0.510856i
$51$	3.78810	−	2.81513i	0.530440	−	0.394196i
$52$	−2.21804	+	1.99713i	−0.307587	+	0.276953i
$53$	2.79637	+	6.28076i	0.384112	+	0.862729i	0.997345	+	0.0728266i	$0.0232020\pi$
$53$	2.79637	+	6.28076i	0.384112	+	0.862729i	−0.613233	+	0.789902i	$0.710131\pi$
$54$	0.375703	−	5.18255i	0.0511267	−	0.705256i
$55$	−9.10002	−	6.30803i	−1.22705	−	0.850575i
$56$	−1.96742	−	1.76898i	−0.262907	−	0.236389i
$57$	−8.03444	+	7.39267i	−1.06419	+	0.979184i
$58$	1.69398	−	0.360067i	0.222431	−	0.0472791i
$59$	−1.23972	+	5.83242i	−0.161398	+	0.759316i	0.820763	+	0.571270i	$0.193549\pi$
$59$	−1.23972	+	5.83242i	−0.161398	+	0.759316i	−0.982160	+	0.188046i	$0.939784\pi$
$60$	−5.75697	−	0.542380i	−0.743221	−	0.0700210i
$61$	4.16142	−	9.34670i	0.532815	−	1.19672i	−0.423904	−	0.905707i	$-0.639341\pi$
$61$	4.16142	−	9.34670i	0.532815	−	1.19672i	0.956719	−	0.291015i	$-0.0939928\pi$
$62$	1.56064	+	4.80315i	0.198201	+	0.610001i
$63$	4.80723	+	6.31590i	0.605654	+	0.795728i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−4.98217	−	8.62936i	−0.617962	−	1.07034i
$66$	1.37890	+	5.57662i	0.169731	+	0.686434i
$67$	1.86083	−	3.22305i	0.227336	−	0.393758i	−0.729681	−	0.683787i	$-0.760332\pi$
$67$	1.86083	−	3.22305i	0.227336	−	0.393758i	0.957018	+	0.290029i	$0.0936650\pi$
$68$	−0.284826	+	2.70994i	−0.0345402	+	0.328628i
$69$	−1.61891	−	0.911544i	−0.194894	−	0.109737i
$70$	7.14229	−	5.19682i	0.853667	−	0.621139i
$71$	−0.722902	−	0.994990i	−0.0857927	−	0.118084i	0.763963	−	0.645260i	$-0.223251\pi$
$71$	−0.722902	−	0.994990i	−0.0857927	−	0.118084i	−0.849756	+	0.527176i	$0.823251\pi$
$72$	2.05501	+	2.18562i	0.242185	+	0.257578i
$73$	1.24396	−	5.85236i	0.145594	−	0.684967i	−0.843433	−	0.537234i	$-0.819469\pi$
$73$	1.24396	−	5.85236i	0.145594	−	0.684967i	0.989027	−	0.147733i	$-0.0471975\pi$
$74$	−6.72672	−	7.47078i	−0.781966	−	0.868461i
$75$	3.17997	−	10.1584i	0.367191	−	1.17299i
$76$		−	6.30354i		−	0.723066i
$77$	−7.21523	−	4.99404i	−0.822252	−	0.569124i
$78$	−1.02023	+	5.06793i	−0.115518	+	0.573830i
$79$	17.1227	+	1.79967i	1.92645	+	0.202478i	0.989242	−	0.146290i	$-0.0467332\pi$
$79$	17.1227	+	1.79967i	1.92645	+	0.202478i	0.937209	+	0.348768i	$0.113400\pi$
$80$	2.48099	−	2.23390i	0.277383	−	0.249757i
$81$	−4.83193	−	7.59292i	−0.536881	−	0.843658i
$82$	−10.0568	−	4.47755i	−1.11058	−	0.494463i
$83$	9.70645	−	7.05215i	1.06542	−	0.774073i	0.0903372	−	0.995911i	$-0.471206\pi$
$83$	9.70645	−	7.05215i	1.06542	−	0.774073i	0.975084	+	0.221838i	$0.0712055\pi$
$84$	−4.56267	−	0.426640i	−0.497828	−	0.0465503i
$85$	−8.65173	−	2.81112i	−0.938412	−	0.304908i
$86$	−0.993250	−	0.104395i	−0.107105	−	0.0112572i
$87$	1.98298	−	2.25066i	0.212597	−	0.241296i
$88$	−2.90835	−	1.59421i	−0.310031	−	0.169943i
$89$	−11.7595	+	6.78938i	−1.24651	+	0.719673i	−0.970412	−	0.241457i	$-0.922375\pi$
$89$	−11.7595	+	6.78938i	−1.24651	+	0.719673i	−0.276098	+	0.961129i	$0.589041\pi$
$90$	−8.56367	+	5.19365i	−0.902690	+	0.547459i
$91$	−3.95313	−	6.83597i	−0.414401	−	0.716604i
$92$	1.02016	−	0.331470i	0.106359	−	0.0345581i
$93$	7.13186	+	5.06500i	0.739539	+	0.525216i
$94$	−9.29632	+	0.977083i	−0.958842	+	0.100778i
$95$	20.5845	+	4.37538i	2.11193	+	0.448904i
$96$	−1.73195	+	0.0186784i	−0.176766	+	0.00190635i
$97$	−2.77243	−	2.01429i	−0.281498	−	0.204520i	0.438073	−	0.898940i	$-0.355661\pi$
$97$	−2.77243	−	2.01429i	−0.281498	−	0.204520i	−0.719571	+	0.694419i	$0.755661\pi$
$98$	5.65735	−	4.12242i	0.571479	−	0.416427i
$99$	7.67829	+	6.32803i	0.771697	+	0.635990i
$100$	3.07280	+	5.32225i	0.307280	+	0.532225i
$101$	−8.16186	+	3.63389i	−0.812136	+	0.361586i	−0.770415	−	0.637543i	$-0.779951\pi$
$101$	−8.16186	+	3.63389i	−0.812136	+	0.361586i	−0.0417210	+	0.999129i	$0.513284\pi$
$102$	2.40374	+	4.06161i	0.238006	+	0.402159i
$103$	−6.97292	+	7.74421i	−0.687062	+	0.763060i	−0.981261	−	0.192684i	$-0.938281\pi$
$103$	−6.97292	+	7.74421i	−0.687062	+	0.763060i	0.294199	+	0.955744i	$0.404947\pi$
$104$	−1.75434	−	2.41465i	−0.172028	−	0.236776i
$105$	4.56023	−	14.6035i	0.445033	−	1.42516i
$106$	−6.53865	+	2.12454i	−0.635090	+	0.206353i
$107$	14.9358	−	3.17471i	1.44390	−	0.306911i	0.581670	−	0.813425i	$-0.302399\pi$
$107$	14.9358	−	3.17471i	1.44390	−	0.306911i	0.862232	+	0.506514i	$0.169066\pi$
$108$	5.11489	+	0.915369i	0.492181	+	0.0880814i
$109$	8.40092	+	4.85027i	0.804662	+	0.464572i	0.845099	−	0.534610i	$-0.179542\pi$
$109$	8.40092	+	4.85027i	0.804662	+	0.464572i	−0.0404368	+	0.999182i	$0.512875\pi$
$110$	7.22469	−	8.39080i	0.688847	−	0.800032i
$111$	−17.0697	−	3.43632i	−1.62019	−	0.326161i
$112$	1.96494	−	1.77173i	0.185669	−	0.167413i
$113$	−9.74475	−	3.16626i	−0.916709	−	0.297857i	−0.187593	−	0.982247i	$-0.560069\pi$
$113$	−9.74475	−	3.16626i	−0.916709	−	0.297857i	−0.729116	+	0.684390i	$0.760069\pi$
$114$	−6.51235	−	8.76317i	−0.609937	−	0.820746i
$115$	0.374324	+	3.56146i	0.0349059	+	0.332108i
$116$	0.181025	+	1.72234i	0.0168078	+	0.159915i
$117$	3.81749	+	8.09945i	0.352927	+	0.748794i
$118$	−5.67088	−	1.84258i	−0.522047	−	0.169623i
$119$	−6.85802	−	2.22300i	−0.628673	−	0.203782i
$120$	1.14118	−	5.66873i	0.104175	−	0.517482i
$121$	−10.2375	−	4.02410i	−0.930683	−	0.365828i
$122$	8.86051	+	5.11562i	0.802193	+	0.463146i
$123$	−18.6068	+	4.16520i	−1.67771	+	0.375564i
$124$	−4.93997	+	1.05002i	−0.443622	+	0.0942949i
$125$	−3.63743	+	1.18187i	−0.325342	+	0.105710i
$126$	−6.78379	+	4.12070i	−0.604348	+	0.367101i
$127$	−8.86744	−	12.2050i	−0.786858	−	1.08302i	−0.994492	−	0.104811i	$-0.966576\pi$
$127$	−8.86744	−	12.2050i	−0.786858	−	1.08302i	0.207634	−	0.978207i	$-0.433424\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−1.48867	+	0.881023i	−0.131070	+	0.0775697i
$130$	9.10287	−	4.05286i	0.798374	−	0.355459i
$131$	−1.43436	−	2.48439i	−0.125321	−	0.217062i	0.796537	−	0.604589i	$-0.206663\pi$
$131$	−1.43436	−	2.48439i	−0.125321	−	0.217062i	−0.921858	+	0.387527i	$0.873329\pi$
$132$	−5.69020	+	0.788429i	−0.495268	+	0.0686240i
$133$	16.3156	+	3.45605i	1.41474	+	0.299677i
$134$	3.01088	+	2.18753i	0.260101	+	0.188974i
$135$	−6.53950	+	16.0676i	−0.562831	+	1.38288i
$136$	−2.66532	−	0.566531i	−0.228549	−	0.0485796i
$137$	4.71796	−	0.495878i	0.403083	−	0.0423657i	0.0991818	−	0.995069i	$-0.468377\pi$
$137$	4.71796	−	0.495878i	0.403083	−	0.0423657i	0.303901	+	0.952704i	$0.401711\pi$
$138$	1.07577	−	1.51476i	0.0915759	−	0.128945i
$139$	−10.7864	+	3.50472i	−0.914891	+	0.297266i	−0.728369	−	0.685185i	$-0.759721\pi$
$139$	−10.7864	+	3.50472i	−0.914891	+	0.297266i	−0.186522	+	0.982451i	$0.559721\pi$
$140$	4.42178	+	7.64638i	0.373709	+	0.646237i
$141$	−11.9143	+	10.9626i	−1.00336	+	0.923218i
$142$	1.06510	−	0.614937i	0.0893815	−	0.0516044i
$143$	−6.78526	−	7.20771i	−0.567412	−	0.602739i
$144$	−2.38846	+	1.81529i	−0.199038	+	0.151274i
$145$	−5.75004	−	0.604353i	−0.477515	−	0.0501888i
$146$	5.69027	+	1.84888i	0.470930	+	0.153014i
$147$	3.60586	−	11.5757i	0.297406	−	0.954751i
$148$	8.13299	−	5.90896i	0.668528	−	0.485714i
$149$	4.69445	+	2.09010i	0.384584	+	0.171228i	0.589916	−	0.807464i	$-0.299161\pi$
$149$	4.69445	+	2.09010i	0.384584	+	0.171228i	−0.205332	+	0.978692i	$0.565827\pi$
$150$	9.77037	+	4.22439i	0.797747	+	0.344920i
$151$	6.38858	−	5.75230i	0.519895	−	0.468116i	−0.366912	−	0.930256i	$-0.619585\pi$
$151$	6.38858	−	5.75230i	0.519895	−	0.468116i	0.886807	+	0.462140i	$0.152918\pi$
$152$	6.26901	+	0.658899i	0.508484	+	0.0534438i
$153$	7.53783	+	3.16307i	0.609397	+	0.255719i
$154$	5.72088	−	6.65369i	0.461002	−	0.536169i
$155$		−	16.8606i		−	1.35427i
$156$	−4.93352	−	1.54438i	−0.394998	−	0.123649i
$157$	11.2607	+	12.5063i	0.898702	+	0.998109i	0.999995	+	0.00325285i	$0.00103542\pi$
$157$	11.2607	+	12.5063i	0.898702	+	0.998109i	−0.101293	+	0.994857i	$0.532298\pi$
$158$	−3.57961	+	16.8408i	−0.284779	+	1.33978i
$159$	−6.89511	+	9.70878i	−0.546818	+	0.769956i
$160$	1.96232	+	2.70091i	0.155135	+	0.213525i
$161$	0.298626	+	2.82223i	0.0235350	+	0.222423i
$162$	8.05640	−	4.01178i	0.632971	−	0.315195i
$163$	−0.645467	+	6.14121i	−0.0505569	+	0.481017i	0.939724	+	0.341934i	$0.111082\pi$
$163$	−0.645467	+	6.14121i	−0.0505569	+	0.481017i	−0.990281	+	0.139083i	$0.955585\pi$
$164$	5.50424	−	9.53363i	0.429809	−	0.744451i
$165$	1.37499	−	19.1289i	0.107043	−	1.48918i
$166$	5.99891	+	10.3904i	0.465606	+	0.806453i
$167$	0.650095	+	0.472322i	0.0503059	+	0.0365494i	0.612654	−	0.790351i	$-0.290102\pi$
$167$	0.650095	+	0.472322i	0.0503059	+	0.0365494i	−0.562348	+	0.826901i	$0.690102\pi$
$168$	0.901232	−	4.49308i	0.0695316	−	0.346649i
$169$	1.26442	+	3.89149i	0.0972631	+	0.299345i
$170$	3.70007	−	8.31049i	0.283782	−	0.637386i
$171$	−18.1069	−	5.45447i	−1.38467	−	0.417113i
$172$	0.207646	−	0.976897i	0.0158328	−	0.0744877i
$173$	−20.0964	+	4.27162i	−1.52790	+	0.324765i	−0.893792	−	0.448481i	$-0.851965\pi$
$173$	−20.0964	+	4.27162i	−1.52790	+	0.324765i	−0.634106	+	0.773246i	$0.718632\pi$
$174$	2.03105	+	2.20737i	0.153974	+	0.167340i
$175$	−15.4604	+	5.03536i	−1.16870	+	0.380638i
$176$	1.88948	−	2.72578i	0.142425	−	0.205463i
$177$	−9.78726	+	3.29718i	−0.735656	+	0.247831i
$178$	−5.52298	−	12.4048i	−0.413965	−	0.929780i
$179$	4.93620	−	4.44457i	0.368949	−	0.332203i	−0.463712	−	0.885986i	$-0.653483\pi$
$179$	4.93620	−	4.44457i	0.368949	−	0.332203i	0.832661	+	0.553783i	$0.186816\pi$
$180$	−4.27006	−	9.05964i	−0.318271	−	0.675266i
$181$	−9.87038	+	7.17125i	−0.733660	+	0.533035i	−0.890719	−	0.454554i	$-0.849799\pi$
$181$	−9.87038	+	7.17125i	−0.733660	+	0.533035i	0.157060	+	0.987589i	$0.449799\pi$
$182$	7.21174	−	3.21692i	0.534570	−	0.238454i
$183$	17.6029	−	2.04230i	1.30125	−	0.150971i
$184$	0.223018	+	1.04922i	0.0164411	+	0.0773494i
$185$	13.6508	+	30.6602i	1.00363	+	2.25418i
$186$	−5.78273	+	6.56335i	−0.424011	+	0.481248i
$187$	−9.00658	−	0.745106i	−0.658626	−	0.0544876i
$188$		−	9.34753i		−	0.681739i
$189$	−5.17361	+	12.7371i	−0.376325	+	0.926488i
$190$	−6.50307	+	20.0144i	−0.471783	+	1.45200i
$191$	−1.34358	−	1.20976i	−0.0972179	−	0.0875353i	0.619089	−	0.785321i	$-0.287502\pi$
$191$	−1.34358	−	1.20976i	−0.0972179	−	0.0875353i	−0.716307	+	0.697786i	$0.754169\pi$
$192$	0.162462	−	1.72441i	0.0117247	−	0.124449i
$193$	3.45738	−	0.363385i	0.248868	−	0.0261570i	0.0207268	−	0.999785i	$-0.493402\pi$
$193$	3.45738	−	0.363385i	0.248868	−	0.0261570i	0.228141	+	0.973628i	$0.426735\pi$
$194$	2.29305	−	2.54670i	0.164632	−	0.182842i
$195$	8.46768	−	15.0387i	0.606383	−	1.07694i
$196$	3.50848	+	6.05727i	0.250606	+	0.432662i
$197$	−2.52468			−0.179876			−0.0899379	−	0.995947i	$-0.528667\pi$
$197$	−2.52468			−0.179876			−0.0899379	+	0.995947i	$0.528667\pi$
$198$	−7.09596	+	6.97477i	−0.504288	+	0.495675i
$199$	−7.25141	+	12.5598i	−0.514039	+	0.890342i	0.485828	+	0.874054i	$0.338518\pi$
$199$	−7.25141	+	12.5598i	−0.514039	+	0.890342i	−0.999867	+	0.0162876i	$0.994815\pi$
$200$	−5.61429	+	2.49964i	−0.396991	+	0.176752i
$201$	6.44572	−	0.0695145i	0.454646	−	0.00490317i
$202$	−2.76084	−	8.49700i	−0.194252	−	0.597847i
$203$	−4.55722	−	0.475758i	−0.319854	−	0.0333916i
$204$	−4.29062	+	1.96602i	−0.300403	+	0.137649i
$205$	27.3120	+	24.5918i	1.90755	+	1.71757i
$206$	−6.97292	−	7.74421i	−0.485826	−	0.539565i
$207$	−0.0694010	−	3.21723i	−0.00482370	−	0.223613i
$208$	2.58480	−	1.49233i	0.179224	−	0.103475i
$209$	20.9013	−	0.463638i	1.44578	−	0.0320705i
$210$	14.0468	+	6.06173i	0.969323	+	0.418299i
$211$	1.03651	−	1.42663i	0.0713564	−	0.0982136i	−0.771847	−	0.635808i	$-0.780667\pi$
$211$	1.03651	−	1.42663i	0.0713564	−	0.0982136i	0.843203	+	0.537595i	$0.180667\pi$
$212$	−1.42942	−	6.72491i	−0.0981732	−	0.461869i
$213$	0.845396	−	1.95527i	0.0579256	−	0.133973i
$214$	1.59610	+	15.1859i	0.109107	+	1.03808i
$215$	3.04597	+	1.35616i	0.207734	+	0.0924890i
$216$	−1.44501	+	4.99119i	−0.0983202	+	0.339607i
$217$	−0.00935373	−	13.3619i	−0.000634972	−	0.907066i
$218$	−5.70184	+	7.84790i	−0.386177	+	0.531527i
$219$	9.82073	−	3.30845i	0.663623	−	0.223565i
$220$	7.58965	+	8.06219i	0.511694	+	0.543553i
$221$	−7.04322	−	4.06641i	−0.473778	−	0.273536i
$222$	5.20177	−	16.6170i	0.349120	−	1.11526i
$223$	4.13231	−	12.7179i	0.276720	−	0.851656i	−0.712040	−	0.702139i	$-0.752228\pi$
$223$	4.13231	−	12.7179i	0.276720	−	0.851656i	0.988759	−	0.149516i	$-0.0477716\pi$
$224$	1.55663	+	2.13937i	0.104007	+	0.142943i
$225$	17.9471	−	4.22127i	1.19647	−	0.281418i
$226$	4.16752	−	9.36040i	0.277219	−	0.622645i
$227$	−6.17656	−	1.31287i	−0.409953	−	0.0871381i	−0.00168099	−	0.999999i	$-0.500535\pi$
$227$	−6.17656	−	1.31287i	−0.409953	−	0.0871381i	−0.408272	+	0.912860i	$0.633868\pi$
$228$	9.39589	−	5.56067i	0.622258	−	0.368265i
$229$	1.02172	−	9.72100i	0.0675170	−	0.642382i	−0.907470	−	0.420118i	$-0.861989\pi$
$229$	1.02172	−	9.72100i	0.0675170	−	0.642382i	0.974987	−	0.222264i	$-0.0713446\pi$
$230$	−3.58107			−0.236129
$231$	1.07906	−	15.1603i	0.0709972	−	0.997477i
$232$	−1.73183			−0.113700
$233$	−0.0523197	+	0.497789i	−0.00342758	+	0.0326112i	−0.996102	−	0.0882088i	$-0.971886\pi$
$233$	−0.0523197	+	0.497789i	−0.00342758	+	0.0326112i	0.992674	+	0.120820i	$0.0385524\pi$
$234$	−8.45411	+	2.94995i	−0.552663	+	0.192845i
$235$	30.5248	+	6.48825i	1.99122	+	0.423247i
$236$	2.42526	−	5.44721i	0.157871	−	0.354583i
$237$	12.4222	+	27.1102i	0.806912	+	1.76100i
$238$	2.92768	−	6.58808i	0.189773	−	0.427042i
$239$	0.201722	−	0.620837i	0.0130483	−	0.0401586i	−0.944320	−	0.329027i	$-0.893279\pi$
$239$	0.201722	−	0.620837i	0.0130483	−	0.0401586i	0.957369	+	0.288869i	$0.0932791\pi$
$240$	5.51839	+	1.72747i	0.356211	+	0.111508i
$241$	−3.93195	−	2.27011i	−0.253279	−	0.146231i	0.367986	−	0.929831i	$-0.380047\pi$
$241$	−3.93195	−	2.27011i	−0.253279	−	0.146231i	−0.621265	+	0.783601i	$0.713381\pi$
$242$	5.07217	−	9.76079i	0.326051	−	0.627448i
$243$	7.05532	−	13.9004i	0.452599	−	0.891714i
$244$	−6.01377	+	8.27724i	−0.384992	+	0.529896i
$245$	−22.2156	+	7.25269i	−1.41930	+	0.463357i
$246$	−2.19745	−	18.9402i	−0.140104	−	1.20758i
$247$	17.1874	+	7.65234i	1.09361	+	0.486906i
$248$	−0.527904	−	5.02267i	−0.0335219	−	0.318940i
$249$	19.0743	+	8.24711i	1.20878	+	0.522640i
$250$	−0.795184	−	3.74105i	−0.0502918	−	0.236604i
$251$	−11.5950	+	15.9591i	−0.731869	+	1.00733i	0.267176	+	0.963648i	$0.413909\pi$
$251$	−11.5950	+	15.9591i	−0.731869	+	1.00733i	−0.999045	+	0.0436839i	$0.986091\pi$
$252$	−3.38903	−	7.17736i	−0.213489	−	0.452131i
$253$	1.17413	+	3.35827i	0.0738166	+	0.211133i
$254$	13.0650	−	7.54309i	0.819772	−	0.473296i
$255$	−3.44195	−	15.3759i	−0.215544	−	0.962874i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	3.34477	+	3.01164i	0.208641	+	0.187861i	0.766825	−	0.641856i	$-0.221835\pi$
$257$	3.34477	+	3.01164i	0.208641	+	0.187861i	−0.558185	+	0.829717i	$0.688502\pi$
$258$	−0.720588	−	1.57260i	−0.0448619	−	0.0979060i
$259$	10.8352	+	24.2905i	0.673267	+	1.50934i
$260$	3.07915	+	9.47664i	0.190961	+	0.587716i
$261$	5.10406	+	0.970349i	0.315933	+	0.0600631i
$262$	2.62071	−	1.16682i	0.161908	−	0.0720861i
$263$	9.14930	−	15.8471i	0.564170	−	0.977172i	−0.432956	−	0.901415i	$-0.642529\pi$
$263$	9.14930	−	15.8471i	0.564170	−	0.977172i	0.997126	−	0.0757566i	$-0.0241372\pi$
$264$	−0.189322	−	5.74144i	−0.0116520	−	0.353361i
$265$	22.9527			1.40997
$266$	−5.14256	+	15.8649i	−0.315310	+	0.972742i
$267$	−20.4938	−	11.5392i	−1.25420	−	0.706188i
$268$	−2.49027	+	2.76573i	−0.152118	+	0.168944i
$269$	−31.6670	+	3.32833i	−1.93077	+	0.202932i	−0.990502	−	0.137502i	$-0.956093\pi$
$269$	−31.6670	+	3.32833i	−1.93077	+	0.202932i	−0.940268	+	0.340434i	$0.889426\pi$
$270$	−15.2960	−	8.18319i	−0.930883	−	0.498013i
$271$	4.41742	+	3.97746i	0.268339	+	0.241614i	0.792304	−	0.610126i	$-0.208881\pi$
$271$	4.41742	+	3.97746i	0.268339	+	0.241614i	−0.523965	+	0.851740i	$0.675548\pi$
$272$	0.842029	−	2.59150i	0.0510555	−	0.157133i
$273$	6.70226	−	11.9228i	0.405639	−	0.721600i
$274$			4.74395i			0.286593i
$275$	−17.4216	+	10.5803i	−1.05056	+	0.638016i
$276$	1.39401	+	1.22822i	0.0839098	+	0.0739299i
$277$	−1.09009	−	2.44837i	−0.0654970	−	0.147109i	0.877831	−	0.478970i	$-0.158990\pi$
$277$	−1.09009	−	2.44837i	−0.0654970	−	0.147109i	−0.943328	+	0.331862i	$0.892323\pi$
$278$	−2.35803	−	11.0937i	−0.141425	−	0.665354i
$279$	−1.25838	+	15.0987i	−0.0753370	+	0.903933i
$280$	−8.06669	+	3.59829i	−0.482077	+	0.215039i
$281$	−15.7119	+	11.4154i	−0.937294	+	0.680984i	−0.947768	−	0.318961i	$-0.896666\pi$
$281$	−15.7119	+	11.4154i	−0.937294	+	0.680984i	0.0104735	+	0.999945i	$0.496666\pi$
$282$	−9.65717	−	12.9949i	−0.575076	−	0.773836i
$283$	−11.8718	+	10.6894i	−0.705706	+	0.635420i	−0.941747	−	0.336323i	$-0.890817\pi$
$283$	−11.8718	+	10.6894i	−0.705706	+	0.635420i	0.236041	+	0.971743i	$0.424150\pi$
$284$	0.500235	+	1.12355i	0.0296835	+	0.0666702i
$285$	11.6368	+	34.5425i	0.689307	+	2.04612i
$286$	7.87748	−	5.99467i	0.465805	−	0.354473i
$287$	21.6583	+	19.4737i	1.27845	+	1.14950i
$288$	−1.55568	−	2.56512i	−0.0916695	−	0.151151i
$289$	9.36588	−	1.99078i	0.550934	−	0.117105i
$290$	1.20209	−	5.65537i	0.0705889	−	0.332095i
$291$	0.556744	−	5.90943i	0.0326369	−	0.346417i
$292$	−2.43355	+	5.46584i	−0.142413	+	0.319864i
$293$	3.37442	+	10.3854i	0.197136	+	0.606722i	0.999945	+	0.0104858i	$0.00333781\pi$
$293$	3.37442	+	10.3854i	0.197136	+	0.606722i	−0.802809	+	0.596236i	$0.796662\pi$
$294$	11.1354	+	4.79610i	0.649430	+	0.279714i
$295$	16.1047	+	11.7008i	0.937654	+	0.681246i
$296$	5.02647	+	8.70609i	0.292157	+	0.506031i
$297$	−2.65898	+	17.0273i	−0.154290	+	0.988026i
$298$	−2.56936	+	4.45026i	−0.148839	+	0.257796i
$299$	−0.334651	+	3.18399i	−0.0193534	+	0.184135i
$300$	−5.22253	+	9.27527i	−0.301523	+	0.535508i
$301$	2.41467	+	1.07306i	0.139180	+	0.0618500i
$302$	5.05300	+	6.95486i	0.290768	+	0.400207i
$303$	−12.6166	−	8.96021i	−0.724804	−	0.514751i
$304$	−1.31058	+	6.16579i	−0.0751669	+	0.353632i
$305$	−22.8555	−	25.3836i	−1.30870	−	1.45346i
$306$	−3.93366	+	7.16590i	−0.224873	+	0.409647i
$307$		−	12.4401i		−	0.709997i	−0.934867	−	0.354998i	$-0.884481\pi$
$307$		−	12.4401i		−	0.709997i	0.934867	−	0.354998i	$-0.115519\pi$
$308$	6.01924	+	6.38504i	0.342978	+	0.363821i
$309$	−17.6945	−	3.56209i	−1.00660	−	0.202640i
$310$	16.7682	+	1.76241i	0.952369	+	0.100098i
$311$	2.77086	−	2.49490i	0.157121	−	0.141473i	−0.586821	−	0.809717i	$-0.699621\pi$
$311$	2.77086	−	2.49490i	0.157121	−	0.141473i	0.743942	+	0.668244i	$0.232954\pi$
$312$	2.05161	−	4.74506i	0.116150	−	0.268636i
$313$	−9.14380	−	4.07108i	−0.516838	−	0.230111i	0.131705	−	0.991289i	$-0.457955\pi$
$313$	−9.14380	−	4.07108i	−0.516838	−	0.230111i	−0.648543	+	0.761178i	$0.724621\pi$
$314$	−13.6148	+	9.89175i	−0.768329	+	0.558224i
$315$	25.7904	−	6.08513i	1.45312	−	0.342858i
$316$	−16.3743	−	5.32034i	−0.921128	−	0.299293i
$317$	21.7116	+	2.28198i	1.21944	+	0.128169i	0.692302	−	0.721608i	$-0.256597\pi$
$317$	21.7116	+	2.28198i	1.21944	+	0.128169i	0.527143	+	0.849777i	$0.323263\pi$
$318$	−8.93486	−	7.87218i	−0.501042	−	0.441450i
$319$	−5.69764	+	0.726927i	−0.319006	+	0.0407001i
$320$	−2.89123	+	1.66925i	−0.161625	+	0.0933140i
$321$	17.9078	+	19.4624i	0.999516	+	1.08628i
$322$	−2.83799	+	0.00198667i	−0.158155	+	0.000110713i
$323$	16.3356	−	5.30776i	0.908938	−	0.295332i
$324$	3.14768	+	8.43161i	0.174871	+	0.468423i
$325$	−18.2421	+	1.91733i	−1.01189	+	0.106354i
$326$	−6.04010	−	1.28386i	−0.334530	−	0.0711066i
$327$	0.181190	+	16.8009i	0.0100198	+	0.929090i
$328$	8.90605	+	6.47062i	0.491754	+	0.357280i
$329$	24.1944	+	5.12498i	1.33388	+	0.282549i
$330$	18.8804	+	3.36697i	1.03933	+	0.185346i
$331$	−11.7817	−	20.4066i	−0.647582	−	1.12165i	−0.983699	−	0.179825i	$-0.942447\pi$
$331$	−11.7817	−	20.4066i	−0.647582	−	1.12165i	0.336116	−	0.941821i	$-0.390887\pi$
$332$	−10.9606	+	4.87996i	−0.601539	+	0.267822i
$333$	−9.93600	−	28.4751i	−0.544490	−	1.56042i
$334$	−0.537688	+	0.597163i	−0.0294210	+	0.0326753i
$335$	−7.30309	−	10.0518i	−0.399011	−	0.549191i
$336$	4.37426	+	1.36595i	0.238636	+	0.0745187i
$337$	13.0031	−	4.22496i	0.708324	−	0.230148i	0.0673702	−	0.997728i	$-0.478539\pi$
$337$	13.0031	−	4.22496i	0.708324	−	0.230148i	0.640954	+	0.767580i	$0.278539\pi$
$338$	−4.00234	+	0.850723i	−0.217698	+	0.0462732i
$339$	−3.87680	−	17.3184i	−0.210559	−	0.940606i
$340$	7.87820	+	4.54848i	0.427256	+	0.246676i
$341$	−3.84502	−	16.3028i	−0.208220	−	0.882844i
$342$	7.31727	−	17.4376i	0.395673	−	0.942916i
$343$	−17.6018	+	5.76005i	−0.950405	+	0.311014i
$344$	0.949840	+	0.308622i	0.0512119	+	0.0166398i
$345$	−4.97840	+	3.69970i	−0.268028	+	0.199185i
$346$	−2.14757	−	20.4328i	−0.115454	−	1.09847i
$347$	−0.758453	−	7.21620i	−0.0407159	−	0.387386i	−0.995836	−	0.0911661i	$-0.970941\pi$
$347$	−0.758453	−	7.21620i	−0.0407159	−	0.387386i	0.955120	−	0.296220i	$-0.0957261\pi$
$348$	−2.40758	+	1.78920i	−0.129060	+	0.0959109i
$349$	−13.9076	−	4.51886i	−0.744458	−	0.241889i	−0.0878629	−	0.996133i	$-0.528004\pi$
$349$	−13.9076	−	4.51886i	−0.744458	−	0.241889i	−0.656595	+	0.754244i	$0.728004\pi$
$350$	−3.39173	−	15.9021i	−0.181295	−	0.850001i
$351$	−8.70522	+	12.8352i	−0.464650	+	0.685091i
$352$	2.51334	+	2.16405i	0.133962	+	0.115344i
$353$	−5.90086	−	3.40686i	−0.314071	−	0.181329i	0.334676	−	0.942333i	$-0.391373\pi$
$353$	−5.90086	−	3.40686i	−0.314071	−	0.181329i	−0.648747	+	0.761004i	$0.724707\pi$
$354$	−2.25607	−	10.0783i	−0.119909	−	0.535656i
$355$	−4.01622	+	0.853673i	−0.213159	+	0.0453083i
$356$	12.9142	−	4.19607i	0.684449	−	0.222391i
$357$	−2.73626	−	12.1834i	−0.144818	−	0.644814i
$358$	3.90425	+	5.37374i	0.206346	+	0.284011i
$359$	−4.75329	+	5.27907i	−0.250869	+	0.278618i	−0.855405	−	0.517959i	$-0.826692\pi$
$359$	−4.75329	+	5.27907i	−0.250869	+	0.278618i	0.604536	+	0.796578i	$0.293359\pi$
$360$	9.45635	−	3.29967i	0.498394	−	0.173908i
$361$	−18.9420	+	8.43353i	−0.996948	+	0.443870i
$362$	−6.10023	−	10.5659i	−0.320621	−	0.555332i
$363$	−3.03281	−	18.8096i	−0.159181	−	0.987249i
$364$	2.44547	+	7.50849i	0.128177	+	0.393552i
$365$	−16.1598	−	11.7408i	−0.845843	−	0.614541i
$366$	0.191103	+	17.7200i	0.00998910	+	0.926238i
$367$	8.58382	+	1.82455i	0.448072	+	0.0952405i	0.426420	−	0.904525i	$-0.359774\pi$
$367$	8.58382	+	1.82455i	0.448072	+	0.0952405i	0.0216510	+	0.999766i	$0.493108\pi$
$368$	−1.06678	+	0.112123i	−0.0556099	+	0.00584483i
$369$	−22.6225	−	24.0604i	−1.17768	−	1.25253i
$370$	−31.9191	+	10.3712i	−1.65940	+	0.539171i
$371$	18.1899	−	0.0127335i	0.944374	−	0.000661089i
$372$	−5.92294	−	6.43711i	−0.307090	−	0.333749i
$373$	−5.86734	+	3.38751i	−0.303799	+	0.175399i	−0.644148	−	0.764901i	$-0.722788\pi$
$373$	−5.86734	+	3.38751i	−0.303799	+	0.175399i	0.340349	+	0.940299i	$0.389455\pi$
$374$	1.68247	−	8.87935i	0.0869984	−	0.459140i
$375$	−4.97043	−	4.37927i	−0.256672	−	0.226145i
$376$	9.29632	+	0.977083i	0.479421	+	0.0503892i
$377$	−4.91595	−	1.59729i	−0.253184	−	0.0822645i
$378$	−12.1265	−	6.47666i	−0.623722	−	0.333124i
$379$	−25.4883	+	18.5184i	−1.30925	+	0.951224i	−0.309247	+	0.950982i	$0.600077\pi$
$379$	−25.4883	+	18.5184i	−1.30925	+	0.951224i	−1.00000		0.000242201i	$0.999923\pi$
$380$	−19.2250	−	8.55953i	−0.986222	−	0.439094i
$381$	10.3700	−	23.9842i	0.531271	−	1.22875i
$382$	1.34358	−	1.20976i	0.0687434	−	0.0618968i
$383$	27.8804	+	2.93035i	1.42462	+	0.149734i	0.785257	−	0.619170i	$-0.212531\pi$
$383$	27.8804	+	2.93035i	1.42462	+	0.149734i	0.639364	+	0.768904i	$0.279198\pi$
$384$	1.69799	+	0.341822i	0.0866500	+	0.0174436i
$385$	−25.0287	+	15.2242i	−1.27558	+	0.775896i
$386$			3.47642i			0.176945i
$387$	−2.62646	−	1.44177i	−0.133510	−	0.0732894i
$388$	2.29305	+	2.54670i	0.116412	+	0.129289i
$389$	−0.912422	+	4.29261i	−0.0462616	+	0.217644i	−0.995206	−	0.0977991i	$-0.968820\pi$
$389$	−0.912422	+	4.29261i	−0.0462616	+	0.217644i	0.948945	+	0.315443i	$0.102153\pi$
$390$	14.0712	+	9.99326i	0.712522	+	0.506029i
$391$	1.71801	+	2.36463i	0.0868833	+	0.119585i
$392$	−6.39083	+	2.85611i	−0.322785	+	0.144255i
$393$	2.43784	−	4.32963i	0.122973	−	0.218401i
$394$	0.263901	−	2.51085i	0.0132951	−	0.126495i
$395$	28.7395	−	49.7783i	1.44604	−	2.50462i
$396$	−6.19483	−	7.78615i	−0.311302	−	0.391269i
$397$	−18.5435	−	32.1184i	−0.930674	−	1.61197i	−0.782172	−	0.623062i	$-0.785888\pi$
$397$	−18.5435	−	32.1184i	−0.930674	−	1.61197i	−0.148502	−	0.988912i	$-0.547445\pi$
$398$	−11.7330	−	8.52455i	−0.588124	−	0.427297i
$399$	9.24131	+	27.3683i	0.462644	+	1.37013i
$400$	−1.89910	−	5.84482i	−0.0949549	−	0.292241i
$401$	11.4925	−	25.8125i	0.573906	−	1.28901i	−0.360486	−	0.932765i	$-0.617389\pi$
$401$	11.4925	−	25.8125i	0.573906	−	1.28901i	0.934391	−	0.356248i	$-0.115944\pi$
$402$	−0.604628	+	6.41768i	−0.0301561	+	0.320085i
$403$	3.13397	−	14.7442i	0.156114	−	0.734460i
$404$	8.73903	−	1.85754i	0.434783	−	0.0924160i
$405$	−29.7187	+	4.42640i	−1.47673	+	0.219950i
$406$	0.949510	−	4.48252i	0.0471234	−	0.222464i
$407$	20.1912	+	26.5328i	1.00084	+	1.31518i
$408$	−1.50676	−	4.47262i	−0.0745956	−	0.221428i
$409$	10.7656	+	24.1799i	0.532324	+	1.19562i	0.956951	+	0.290250i	$0.0937386\pi$
$409$	10.7656	+	24.1799i	0.532324	+	1.19562i	−0.424627	+	0.905368i	$0.639595\pi$
$410$	−27.3120	+	24.5918i	−1.34884	+	1.21450i
$411$	4.90110	+	6.59503i	0.241753	+	0.325309i
$412$	8.43066	−	6.12523i	0.415349	−	0.301768i
$413$	12.7694	+	9.26388i	0.628343	+	0.455846i
$414$	3.20686	+	0.267271i	0.157608	+	0.0131357i
$415$	−8.32786	−	39.1795i	−0.408799	−	1.92325i
$416$	1.21397	+	2.72663i	0.0595200	+	0.133684i
$417$	−14.7393	−	12.9862i	−0.721785	−	0.635939i
$418$	−1.72369	+	20.8353i	−0.0843082	+	1.01909i
$419$			33.9103i			1.65663i	0.560264	+	0.828314i	$0.310700\pi$
$419$			33.9103i			1.65663i	−0.560264	+	0.828314i	$0.689300\pi$
$420$	−7.49682	+	13.3362i	−0.365807	+	0.650742i
$421$	4.92289	−	15.1511i	0.239927	−	0.738420i	−0.756502	−	0.653991i	$-0.773093\pi$
$421$	4.92289	−	15.1511i	0.239927	−	0.738420i	0.996430	−	0.0844289i	$-0.0269066\pi$
$422$	1.31047	+	1.17996i	0.0637929	+	0.0574394i
$423$	−26.8508	−	8.08843i	−1.30553	−	0.393273i
$424$	6.83748	−	0.718649i	0.332058	−	0.0349007i
$425$	−11.2052	+	12.4447i	−0.543533	+	0.603655i
$426$	1.85619	+	1.04515i	0.0899328	+	0.0506375i
$427$	−18.1270	−	20.1037i	−0.877226	−	0.972887i
$428$	−15.2695			−0.738080
$429$	4.75800	−	16.4722i	0.229718	−	0.795286i
$430$	−1.66712	+	2.88753i	−0.0803955	+	0.139249i
$431$	−4.71976	+	2.10137i	−0.227343	+	0.101219i	−0.517247	−	0.855836i	$-0.673043\pi$
$431$	−4.71976	+	2.10137i	−0.227343	+	0.101219i	0.289904	+	0.957056i	$0.406376\pi$
$432$	−4.81280	−	1.95881i	−0.231556	−	0.0942434i
$433$	−0.666032	−	2.04984i	−0.0320074	−	0.0985088i	0.933777	−	0.357857i	$-0.116492\pi$
$433$	−0.666032	−	2.04984i	−0.0320074	−	0.0985088i	−0.965784	+	0.259348i	$0.916492\pi$
$434$	13.2897	+	1.38740i	0.637926	+	0.0665973i
$435$	−4.17157	−	9.10399i	−0.200011	−	0.436503i
$436$	−7.20891	−	6.49093i	−0.345244	−	0.310859i
$437$	−4.52436	−	5.02481i	−0.216429	−	0.240369i
$438$	2.26378	+	10.1128i	0.108168	+	0.483206i
$439$	18.5718	−	10.7224i	0.886383	−	0.511753i	0.0136252	−	0.999907i	$-0.495663\pi$
$439$	18.5718	−	10.7224i	0.886383	−	0.511753i	0.872758	+	0.488154i	$0.162330\pi$
$440$	−8.81136	+	6.70535i	−0.420065	+	0.319665i
$441$	20.4354	−	4.83675i	0.973115	−	0.230321i
$442$	4.78035	−	6.57958i	0.227378	−	0.312959i
$443$	2.57246	+	12.1025i	0.122221	+	0.575006i	0.996052	+	0.0887750i	$0.0282952\pi$
$443$	2.57246	+	12.1025i	0.122221	+	0.575006i	−0.873830	+	0.486231i	$0.838371\pi$
$444$	15.9823	+	6.91022i	0.758485	+	0.327945i
$445$	4.73856	+	45.0844i	0.224629	+	2.13721i
$446$	12.2163	+	5.43905i	0.578459	+	0.257547i
$447$	1.02576	+	8.84121i	0.0485168	+	0.418175i
$448$	−2.29036	+	1.32448i	−0.108209	+	0.0625758i
$449$	7.18781	−	9.89317i	0.339214	−	0.466887i	−0.604998	−	0.796227i	$-0.706826\pi$
$449$	7.18781	−	9.89317i	0.339214	−	0.466887i	0.944212	+	0.329340i	$0.106826\pi$
$450$	2.32217	+	18.2900i	0.109468	+	0.862199i
$451$	32.0165	+	17.5498i	1.50760	+	0.826388i
$452$	8.87350	+	5.12312i	0.417374	+	0.240971i
$453$	14.2099	+	4.44825i	0.667640	+	0.208997i
$454$	1.95130	−	6.00549i	0.0915792	−	0.281852i
$455$	−26.2168	+	2.77405i	−1.22906	+	0.130050i
$456$	4.54807	+	9.92567i	0.212983	+	0.464812i
$457$	6.54079	−	14.6909i	0.305965	−	0.687209i	−0.693481	−	0.720475i	$-0.743924\pi$
$457$	6.54079	−	14.6909i	0.305965	−	0.687209i	0.999447	+	0.0332653i	$0.0105906\pi$
$458$	9.56095	+	2.03224i	0.446754	+	0.0949604i
$459$	1.93471	+	14.0260i	0.0903044	+	0.654677i
$460$	0.374324	−	3.56146i	0.0174530	−	0.166054i
$461$	−17.8529			−0.831491			−0.415745	−	0.909481i	$-0.636479\pi$
$461$	−17.8529			−0.831491			−0.415745	+	0.909481i	$0.636479\pi$
$462$	14.9645	+	2.65784i	0.696211	+	0.123654i
$463$	−25.1200			−1.16742			−0.583712	−	0.811961i	$-0.698400\pi$
$463$	−25.1200			−1.16742			−0.583712	+	0.811961i	$0.698400\pi$
$464$	0.181025	−	1.72234i	0.00840388	−	0.0799576i
$465$	25.1319	−	14.8736i	1.16546	−	0.689745i
$466$	−0.489593	−	0.104066i	−0.0226800	−	0.00482077i
$467$	4.37854	−	9.83435i	0.202615	−	0.455080i	−0.783447	−	0.621458i	$-0.786541\pi$
$467$	4.37854	−	9.83435i	0.202615	−	0.455080i	0.986062	+	0.166378i	$0.0532073\pi$
$468$	−2.05010	−	8.71615i	−0.0947658	−	0.402904i
$469$	−5.79325	−	7.96199i	−0.267507	−	0.367651i
$470$	−9.64342	+	29.6794i	−0.444818	+	1.36901i
$471$	−8.70789	+	27.8173i	−0.401238	+	1.28175i
$472$	5.16386	+	2.98136i	0.237686	+	0.137228i
$473$	3.25448	+	0.616661i	0.149641	+	0.0283541i
$474$	−28.2601	+	9.52041i	−1.29803	+	0.437287i
$475$	22.7703	−	31.3406i	1.04477	−	1.43800i
$476$	6.24597	+	3.60028i	0.286283	+	0.165019i
$477$	−20.5542	−	1.71306i	−0.941111	−	0.0784356i
$478$	0.596351	+	0.265512i	0.0272764	+	0.0121443i
$479$	2.38882	+	22.7281i	0.109148	+	1.03847i	0.902788	+	0.430085i	$0.141516\pi$
$479$	2.38882	+	22.7281i	0.109148	+	1.03847i	−0.793641	+	0.608387i	$0.791817\pi$
$480$	−2.29483	+	5.30759i	−0.104744	+	0.242257i
$481$	6.23832	+	29.3490i	0.284443	+	1.33820i
$482$	2.66867	−	3.67312i	0.121555	−	0.167306i
$483$	−3.94331	+	2.93476i	−0.179427	+	0.133536i
$484$	9.17714	+	6.06466i	0.417143	+	0.275667i
$485$	−9.90800	+	5.72039i	−0.449899	+	0.259749i
$486$	13.0868	+	8.46966i	0.593630	+	0.384192i
$487$	8.88917	+	9.87243i	0.402807	+	0.447362i	0.910086	−	0.414419i	$-0.136015\pi$
$487$	8.88917	+	9.87243i	0.402807	+	0.447362i	−0.507279	+	0.861782i	$0.669349\pi$
$488$	−7.60329	−	6.84603i	−0.344185	−	0.309905i
$489$	−9.72333	+	4.45536i	−0.439704	+	0.201478i
$490$	−4.89080	−	22.8520i	−0.220944	−	1.03235i
$491$	−7.50139	−	23.0869i	−0.338533	−	1.04190i	−0.964956	−	0.262413i	$-0.915482\pi$
$491$	−7.50139	−	23.0869i	−0.338533	−	1.04190i	0.626423	−	0.779484i	$-0.284518\pi$
$492$	19.0661	−	0.205621i	0.859568	−	0.00927009i
$493$	−4.31101	+	1.91939i	−0.194158	+	0.0864448i
$494$	−9.40699	+	16.2934i	−0.423240	+	0.733074i
$495$	29.7260	−	14.8250i	1.33608	−	0.666336i
$496$	5.05033			0.226767
$497$	−3.18236	+	0.678761i	−0.142748	+	0.0304466i
$498$	−10.1957	+	18.1077i	−0.456882	+	0.811427i
$499$	−26.1109	+	28.9991i	−1.16888	+	1.29818i	−0.222575	+	0.974916i	$0.571446\pi$
$499$	−26.1109	+	28.9991i	−1.16888	+	1.29818i	−0.946310	+	0.323262i	$0.895221\pi$
$500$	3.80367	−	0.399782i	0.170105	−	0.0178788i
$501$	−0.130548	+	1.38567i	−0.00583247	+	0.0619073i
$502$	−14.6597	−	13.1997i	−0.654295	−	0.589129i
$503$	13.1616	−	40.5071i	0.586845	−	1.80612i	−0.00488488	−	0.999988i	$-0.501555\pi$
$503$	13.1616	−	40.5071i	0.586845	−	1.80612i	0.591730	−	0.806136i	$-0.298445\pi$
$504$	7.49229	−	2.62022i	0.333733	−	0.116714i
$505$			29.8271i			1.32729i
$506$	−3.46260	+	0.816658i	−0.153932	+	0.0363049i
$507$	−4.68514	+	5.31759i	−0.208074	+	0.236162i
$508$	6.13611	+	13.7819i	0.272246	+	0.611474i
$509$	−7.43616	−	34.9844i	−0.329602	−	1.55066i	−0.761156	−	0.648569i	$-0.775368\pi$
$509$	−7.43616	−	34.9844i	−0.329602	−	1.55066i	0.431554	−	0.902087i	$-0.357965\pi$
$510$	15.6514	−	1.81588i	0.693056	−	0.0804086i
$511$	−12.8131	−	9.29556i	−0.566818	−	0.411211i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−7.84275	−	31.8013i	−0.346266	−	1.40406i
$514$	−3.34477	+	3.01164i	−0.147531	+	0.132838i
$515$	14.1504	+	31.7823i	0.623542	+	1.40050i
$516$	1.63931	−	0.552259i	0.0721666	−	0.0243118i
$517$	30.9946	−	0.687530i	1.36314	−	0.0302375i
$518$	−25.2900	+	8.23680i	−1.11118	+	0.361904i
$519$	−24.0952	−	26.1869i	−1.05766	−	1.14948i
$520$	−9.74659	+	2.07170i	−0.427416	+	0.0908501i
$521$	0.675410	−	3.17756i	0.0295903	−	0.139211i	−0.960873	−	0.276990i	$-0.910663\pi$
$521$	0.675410	−	3.17756i	0.0295903	−	0.139211i	0.990463	+	0.137779i	$0.0439964\pi$
$522$	−1.49855	+	4.97467i	−0.0655899	+	0.217735i
$523$	−5.26439	+	11.8240i	−0.230196	+	0.517028i	−0.991303	−	0.131598i	$-0.957989\pi$
$523$	−5.26439	+	11.8240i	−0.230196	+	0.517028i	0.761107	+	0.648626i	$0.224656\pi$
$524$	0.886485	+	2.72832i	0.0387263	+	0.119187i
$525$	−21.1440	−	18.6029i	−0.922800	−	0.811899i
$526$	14.8039	+	10.7557i	0.645480	+	0.468969i
$527$	−6.88073	−	11.9178i	−0.299729	−	0.519146i
$528$	5.72978	+	0.411859i	0.249357	+	0.0179239i
$529$	−10.9247	+	18.9221i	−0.474987	+	0.822702i
$530$	−2.39921	+	22.8270i	−0.104215	+	0.991540i
$531$	−13.5485	−	11.6800i	−0.587956	−	0.506870i
$532$	−15.2405	−	6.77272i	−0.660759	−	0.293635i
$533$	19.3127	+	26.5816i	0.836525	+	1.15138i
$534$	13.6182	−	19.1753i	0.589316	−	0.829797i
$535$	10.5988	−	49.8634i	0.458225	−	2.15578i
$536$	−2.49027	−	2.76573i	−0.107563	−	0.119461i
$537$	10.9794	+	3.43698i	0.473798	+	0.148317i
$538$		−	31.8414i		−	1.37278i
$539$	−19.8267	+	12.0790i	−0.853996	+	0.520279i
$540$	9.73723	−	14.3568i	0.419024	−	0.617818i
$541$	−36.8663	−	3.87481i	−1.58501	−	0.166591i	−0.729353	−	0.684138i	$-0.760179\pi$
$541$	−36.8663	−	3.87481i	−1.58501	−	0.166591i	−0.855655	+	0.517547i	$0.826845\pi$
$542$	−4.41742	+	3.97746i	−0.189744	+	0.170847i
$543$	−19.3964	−	8.38640i	−0.832381	−	0.359895i
$544$	2.48929	+	1.10830i	0.106727	+	0.0475180i
$545$	26.2003	−	19.0356i	1.12230	−	0.815396i
$546$	11.1569	+	7.91181i	0.477471	+	0.338594i
$547$	26.0099	+	8.45114i	1.11211	+	0.361345i	0.806750	−	0.590894i	$-0.201225\pi$
$547$	26.0099	+	8.45114i	1.11211	+	0.361345i	0.305356	+	0.952238i	$0.401225\pi$
$548$	−4.71796	−	0.495878i	−0.201541	−	0.0211829i
$549$	18.5726	+	24.4369i	0.792661	+	1.04294i
$550$	−8.70129	−	18.4321i	−0.371024	−	0.785946i
$551$	9.45409	−	5.45832i	0.402758	−	0.232532i
$552$	−1.36720	+	1.25799i	−0.0581920	+	0.0535438i
$553$	22.7483	−	39.4650i	0.967357	−	1.67822i
$554$	2.54891	−	0.828190i	0.108293	−	0.0351864i
$555$	−33.6592	+	47.3944i	−1.42875	+	2.01178i
$556$	11.2794	−	1.18551i	0.478352	−	0.0502768i
$557$	−36.3137	−	7.71872i	−1.53866	−	0.327053i	−0.640932	−	0.767598i	$-0.721452\pi$
$557$	−36.3137	−	7.71872i	−1.53866	−	0.327053i	−0.897731	+	0.440545i	$0.854785\pi$
$558$	−14.8844	−	2.82972i	−0.630107	−	0.119792i
$559$	2.41156	+	1.75210i	0.101998	+	0.0741060i
$560$	−2.73538	−	8.39863i	−0.115591	−	0.354907i
$561$	−6.83453	−	14.0823i	−0.288554	−	0.594554i
$562$	−9.71050	−	16.8191i	−0.409613	−	0.709470i
$563$	18.9959	−	8.45754i	0.800583	−	0.356443i	0.0346800	−	0.999398i	$-0.488959\pi$
$563$	18.9959	−	8.45754i	0.800583	−	0.356443i	0.765903	+	0.642956i	$0.222292\pi$
$564$	13.9332	−	8.24593i	0.586693	−	0.347216i
$565$	−22.8890	+	25.4208i	−0.962948	+	1.06946i
$566$	−9.38992	−	12.9241i	−0.394688	−	0.543241i
$567$	−23.5495	+	3.52439i	−0.988986	+	0.148011i
$568$	−1.16968	+	0.380052i	−0.0490787	+	0.0159466i
$569$	17.6574	−	3.75319i	0.740235	−	0.157342i	0.177665	−	0.984091i	$-0.443146\pi$
$569$	17.6574	−	3.75319i	0.740235	−	0.157342i	0.562571	+	0.826749i	$0.309812\pi$
$570$	−35.5696	+	7.96242i	−1.48985	+	0.333509i
$571$	−14.9901	−	8.65456i	−0.627317	−	0.362182i	0.152395	−	0.988320i	$-0.451301\pi$
$571$	−14.9901	−	8.65456i	−0.627317	−	0.362182i	−0.779712	+	0.626138i	$0.784635\pi$
$572$	5.13841	+	8.46094i	0.214848	+	0.353770i
$573$	0.618002	−	3.06989i	0.0258174	−	0.128247i
$574$	−21.6310	+	19.5041i	−0.902859	+	0.814083i
$575$	6.26950	+	2.03708i	0.261456	+	0.0849522i
$576$	2.71368	−	1.27903i	0.113070	−	0.0532930i
$577$	−1.15930	−	11.0300i	−0.0482623	−	0.459185i	−0.991789	−	0.127887i	$-0.959180\pi$
$577$	−1.15930	−	11.0300i	−0.0482623	−	0.459185i	0.943526	−	0.331297i	$-0.107486\pi$
$578$	1.00087	+	9.52267i	0.0416308	+	0.396091i
$579$	3.59158	+	4.83292i	0.149261	+	0.200849i
$580$	5.49873	+	1.78665i	0.228323	+	0.0741865i
$581$	−6.62153	−	31.0450i	−0.274707	−	1.28796i
$582$	5.81886	+	1.17140i	0.241199	+	0.0485560i
$583$	22.1934	−	5.23433i	0.919156	−	0.216784i
$584$	−5.18152	−	2.99155i	−0.214413	−	0.123791i
$585$	29.8860	−	0.644692i	1.23564	−	0.0266547i
$586$	−10.6812	+	2.27037i	−0.441238	+	0.0937880i
$587$	17.3402	−	5.63418i	0.715708	−	0.232548i	0.0715467	−	0.997437i	$-0.477206\pi$
$587$	17.3402	−	5.63418i	0.715708	−	0.232548i	0.644161	+	0.764890i	$0.277206\pi$
$588$	−5.93380	+	10.5731i	−0.244706	+	0.436027i
$589$	18.7121	+	25.7550i	0.771020	+	1.06122i
$590$	−13.3201	+	14.7935i	−0.548379	+	0.609037i
$591$	−2.22715	−	3.76322i	−0.0916126	−	0.154798i
$592$	−9.18381	+	4.08890i	−0.377452	+	0.168053i
$593$	6.16209	+	10.6730i	0.253047	+	0.438290i	0.964363	−	0.264582i	$-0.0852341\pi$
$593$	6.16209	+	10.6730i	0.253047	+	0.438290i	−0.711317	+	0.702872i	$0.751901\pi$
$594$	−16.6561	−	4.42425i	−0.683408	−	0.181529i
$595$	−16.0923	+	17.8975i	−0.659721	+	0.733726i
$596$	−4.15731	−	3.02046i	−0.170290	−	0.123723i
$597$	−25.1182	+	0.270889i	−1.02802	+	0.0110868i
$598$	−3.13157	−	0.665636i	−0.128059	−	0.0272199i
$599$	21.4437	−	2.25382i	0.876165	−	0.0920887i	0.344242	−	0.938881i	$-0.388136\pi$
$599$	21.4437	−	2.25382i	0.876165	−	0.0920887i	0.531924	+	0.846792i	$0.321469\pi$
$600$	−8.67856	−	6.16345i	−0.354301	−	0.251622i
$601$	17.0063	−	5.52569i	0.693702	−	0.225398i	0.0591179	−	0.998251i	$-0.481171\pi$
$601$	17.0063	−	5.52569i	0.693702	−	0.225398i	0.634585	+	0.772853i	$0.281171\pi$
$602$	−1.31958	+	2.28928i	−0.0537821	+	0.0933041i
$603$	5.78972	+	9.54650i	0.235776	+	0.388764i
$604$	−7.44494	+	4.29834i	−0.302930	+	0.174897i
$605$	−26.1744	+	25.7588i	−1.06414	+	1.04725i
$606$	10.2299	−	11.6109i	0.415562	−	0.471659i
$607$	20.0624	+	2.10864i	0.814308	+	0.0855872i	0.502521	−	0.864565i	$-0.332406\pi$
$607$	20.0624	+	2.10864i	0.814308	+	0.0855872i	0.311787	+	0.950152i	$0.399073\pi$
$608$	−5.99502	−	1.94790i	−0.243130	−	0.0789978i
$609$	−3.31100	−	7.21256i	−0.134169	−	0.292268i
$610$	27.6336	−	20.0770i	1.11885	−	0.812893i
$611$	25.4873	+	11.3477i	1.03110	+	0.459077i
$612$	−6.71547	−	4.66116i	−0.271457	−	0.188416i
$613$	7.99514	−	7.19885i	0.322921	−	0.290759i	−0.491686	−	0.870772i	$-0.663619\pi$
$613$	7.99514	−	7.19885i	0.322921	−	0.290759i	0.814607	+	0.580013i	$0.196953\pi$
$614$	12.3720	+	1.30035i	0.499293	+	0.0524778i
$615$	−12.5626	+	62.4042i	−0.506573	+	2.51638i
$616$	−6.97924	+	5.31885i	−0.281202	+	0.214303i
$617$		−	44.5484i		−	1.79345i	−0.442589	−	0.896725i	$-0.645940\pi$
$617$		−	44.5484i		−	1.79345i	0.442589	−	0.896725i	$-0.354060\pi$
$618$	5.39215	−	17.2252i	0.216904	−	0.692900i
$619$	10.5099	+	11.6725i	0.422430	+	0.469156i	0.916365	−	0.400343i	$-0.131109\pi$
$619$	10.5099	+	11.6725i	0.422430	+	0.469156i	−0.493936	+	0.869498i	$0.664442\pi$
$620$	−3.50551	+	16.4921i	−0.140785	+	0.662339i
$621$	4.73429	−	2.94153i	0.189981	−	0.118039i
$622$	2.19160	+	3.01647i	0.0878750	+	0.120950i
$623$	3.78030	+	35.7266i	0.151455	+	1.43135i
$624$	4.50462	+	2.53637i	0.180329	+	0.101536i
$625$	1.87728	−	17.8611i	0.0750913	−	0.714446i
$626$	5.00457	−	8.66816i	0.200023	−	0.346450i
$627$	19.1292	+	30.7460i	0.763947	+	1.22788i
$628$	−8.41443	−	14.5742i	−0.335772	−	0.581575i
$629$	22.1613	+	16.1011i	0.883628	+	0.641994i
$630$	3.35597	+	26.2852i	0.133705	+	1.04723i
$631$	−6.45028	−	19.8519i	−0.256782	−	0.790293i	−0.993473	−	0.114064i	$-0.963613\pi$
$631$	−6.45028	−	19.8519i	−0.256782	−	0.790293i	0.736692	−	0.676229i	$-0.236387\pi$
$632$	7.00278	−	15.7285i	0.278556	−	0.625646i
$633$	3.04086	+	0.286488i	0.120863	+	0.0113869i
$634$	−4.53896	+	21.3541i	−0.180265	+	0.848080i
$635$	−49.2647	+	10.4715i	−1.95501	+	0.415550i
$636$	8.76300	−	8.06305i	0.347476	−	0.319721i
$637$	−20.7752	+	2.21297i	−0.823142	+	0.0876810i
$638$	−0.127379	−	5.74241i	−0.00504300	−	0.227344i
$639$	3.66024	−	0.464718i	0.144797	−	0.0183840i
$640$	−1.35789	−	3.04988i	−0.0536754	−	0.120557i
$641$	26.3759	−	23.7490i	1.04179	−	0.938029i	0.0436497	−	0.999047i	$-0.486101\pi$
$641$	26.3759	−	23.7490i	1.04179	−	0.938029i	0.998137	+	0.0610183i	$0.0194348\pi$
$642$	−21.2277	+	15.7753i	−0.837789	+	0.622603i
$643$	16.1761	−	11.7527i	0.637925	−	0.463480i	−0.221212	−	0.975226i	$-0.571001\pi$
$643$	16.1761	−	11.7527i	0.637925	−	0.463480i	0.859137	+	0.511746i	$0.171001\pi$
$644$	0.294675	−	2.82265i	0.0116118	−	0.111228i
$645$	0.665560	+	5.73658i	0.0262064	+	0.225878i
$646$	3.57115	+	16.8009i	0.140505	+	0.661024i
$647$	0.393180	+	0.883098i	0.0154575	+	0.0347181i	0.921109	−	0.389304i	$-0.127284\pi$
$647$	0.393180	+	0.883098i	0.0154575	+	0.0347181i	−0.905652	+	0.424022i	$0.860618\pi$
$648$	−8.71445	+	2.24909i	−0.342336	+	0.0883527i
$649$	18.2403	+	7.64103i	0.715994	+	0.299937i
$650$		−	18.3426i		−	0.719456i
$651$	19.9087	−	11.8012i	0.780283	−	0.462524i
$652$	1.90819	−	5.87281i	0.0747305	−	0.229997i
$653$	21.7712	+	19.6028i	0.851971	+	0.767118i	0.974272	−	0.225375i	$-0.0723607\pi$
$653$	21.7712	+	19.6028i	0.851971	+	0.767118i	−0.122301	+	0.992493i	$0.539027\pi$
$654$	−16.7278	−	1.57597i	−0.654107	−	0.0616253i
$655$	−9.52479	+	1.00110i	−0.372164	+	0.0391160i
$656$	−7.36611	+	8.18090i	−0.287598	+	0.319410i
$657$	13.5949	+	11.7200i	0.530386	+	0.457239i
$658$	−7.62590	+	23.5261i	−0.297289	+	0.917145i
$659$	−32.4424			−1.26378			−0.631888	−	0.775060i	$-0.717720\pi$
$659$	−32.4424			−1.26378			−0.631888	+	0.775060i	$0.717720\pi$
$660$	−5.32207	+	18.4250i	−0.207161	+	0.717192i
$661$	22.4002	−	38.7983i	0.871268	−	1.50908i	0.0105814	−	0.999944i	$-0.496632\pi$
$661$	22.4002	−	38.7983i	0.871268	−	1.50908i	0.860686	−	0.509136i	$-0.170035\pi$
$662$	21.5263	−	9.58412i	0.836643	−	0.372498i
$663$	−0.151908	−	14.0856i	−0.00589961	−	0.547040i
$664$	−3.70753	−	11.4106i	−0.143880	−	0.442818i
$665$	32.6953	−	45.0675i	1.26787	−	1.74764i
$666$	29.3577	−	6.90512i	1.13759	−	0.267568i
$667$	1.38051	+	1.24302i	0.0534535	+	0.0481298i
$668$	−0.537688	−	0.597163i	−0.0208038	−	0.0231049i
$669$	22.6023	−	5.05963i	0.873857	−	0.195617i
$670$	10.7602	−	6.21238i	0.415701	−	0.240005i
$671$	−27.8881	−	19.3317i	−1.07661	−	0.746292i
$672$	−1.81570	+	4.20752i	−0.0700422	+	0.162309i
$673$	−2.27193	+	3.12705i	−0.0875765	+	0.120539i	−0.850557	−	0.525883i	$-0.823735\pi$
$673$	−2.27193	+	3.12705i	−0.0875765	+	0.120539i	0.762981	+	0.646421i	$0.223735\pi$
$674$	2.84262	+	13.3735i	0.109494	+	0.515128i
$675$	22.1241	+	23.0276i	0.851559	+	0.886334i
$676$	−0.427704	−	4.06933i	−0.0164502	−	0.156513i
$677$	20.1480	+	8.97047i	0.774351	+	0.344763i	0.755577	−	0.655060i	$-0.227357\pi$
$677$	20.1480	+	8.97047i	0.774351	+	0.344763i	0.0187746	+	0.999824i	$0.494024\pi$
$678$	17.6288	−	2.04529i	0.677028	−	0.0785490i
$679$	−7.84888	+	4.53888i	−0.301212	+	0.174186i
$680$	−5.34706	+	7.35960i	−0.205050	+	0.282228i
$681$	−3.49173	−	10.3648i	−0.133803	−	0.397179i
$682$	16.6154	−	2.11985i	0.636236	−	0.0811734i
$683$	8.58069	+	4.95407i	0.328331	+	0.189562i	0.655100	−	0.755542i	$-0.272627\pi$
$683$	8.58069	+	4.95407i	0.328331	+	0.189562i	−0.326769	+	0.945104i	$0.605960\pi$
$684$	16.5772	+	9.09991i	0.633845	+	0.347944i
$685$	4.89412	−	15.0625i	0.186995	−	0.575510i
$686$	−3.88861	−	18.1074i	−0.148468	−	0.691345i
$687$	15.3912	−	7.05244i	0.587210	−	0.269067i
$688$	−0.406216	+	0.912377i	−0.0154869	+	0.0347840i
$689$	20.0716	+	4.26636i	0.764668	+	0.162535i
$690$	−3.15905	−	5.33786i	−0.120263	−	0.203209i
$691$	−4.34452	+	41.3354i	−0.165273	+	1.57247i	0.526385	+	0.850246i	$0.323547\pi$
$691$	−4.34452	+	41.3354i	−0.165273	+	1.57247i	−0.691658	+	0.722225i	$0.743120\pi$
$692$	20.5453			0.781017
$693$	23.5495	−	11.7653i	0.894571	−	0.446926i
$694$	7.25595			0.275432
$695$	−3.95783	+	37.6562i	−0.150129	+	1.42838i
$696$	−1.52773	−	2.58142i	−0.0579086	−	0.0978483i
$697$	29.3411	+	6.23664i	1.11137	+	0.236230i
$698$	5.94784	−	13.3591i	0.225129	−	0.505649i
$699$	−0.788145	+	0.361138i	−0.0298104	+	0.0136595i
$700$	16.1695	−	1.71093i	0.611149	−	0.0646670i
$701$	−13.0745	+	40.2391i	−0.493816	+	1.51981i	0.324978	+	0.945722i	$0.394643\pi$
$701$	−13.0745	+	40.2391i	−0.493816	+	1.51981i	−0.818794	+	0.574088i	$0.805357\pi$
$702$	−11.8549	−	9.99917i	−0.447435	−	0.377394i
$703$	−54.8792	−	31.6845i	−2.06981	−	1.19500i
$704$	−2.41491	+	2.27337i	−0.0910154	+	0.0856808i
$705$	17.2563	+	51.2231i	0.649909	+	1.92917i
$706$	4.00501	−	5.51242i	0.150730	−	0.207463i
$707$	0.0165472	+	23.6379i	0.000622320	+	0.888993i
$708$	10.2589	−	1.19024i	0.385554	−	0.0447320i
$709$	−3.70028	−	1.64747i	−0.138967	−	0.0618721i	0.336075	−	0.941835i	$-0.390900\pi$
$709$	−3.70028	−	1.64747i	−0.138967	−	0.0618721i	−0.475042	+	0.879963i	$0.657567\pi$
$710$	−0.429188	−	4.08345i	−0.0161071	−	0.153249i
$711$	−29.4514	+	42.4315i	−1.10451	+	1.59131i
$712$	2.82318	+	13.2820i	0.105803	+	0.497765i
$713$	−3.18420	+	4.38267i	−0.119249	+	0.164132i
$714$	12.4027	−	1.44776i	0.464159	−	0.0541811i
$715$	−31.1963	+	10.9069i	−1.16667	+	0.407895i
$716$	−5.75241	+	3.32116i	−0.214978	+	0.124117i
$717$	1.10335	−	0.246990i	0.0412055	−	0.00922402i
$718$	−4.75329	−	5.27907i	−0.177391	−	0.197013i
$719$	8.01069	+	7.21286i	0.298748	+	0.268994i	0.804848	−	0.593481i	$-0.202247\pi$
$719$	8.01069	+	7.21286i	0.298748	+	0.268994i	−0.506100	+	0.862475i	$0.668913\pi$
$720$	2.29314	+	9.74946i	0.0854602	+	0.363341i
$721$	11.2318	+	25.1795i	0.418293	+	0.937734i
$722$	−6.40735	−	19.7198i	−0.238457	−	0.733894i
$723$	−0.0848039	−	7.86343i	−0.00315389	−	0.292444i
$724$	11.1457	−	4.96237i	0.414226	−	0.184425i
$725$	−5.32157	+	9.21722i	−0.197638	+	0.342319i
$726$	19.0236	−	1.05005i	0.706032	−	0.0389711i
$727$	1.55296			0.0575962			0.0287981	−	0.999585i	$-0.490832\pi$
$727$	1.55296			0.0575962			0.0287981	+	0.999585i	$0.490832\pi$
$728$	−7.72298	+	1.64722i	−0.286233	+	0.0610501i
$729$	26.9435	−	1.74582i	0.997907	−	0.0646599i
$730$	13.3656	−	14.8440i	0.494684	−	0.549402i
$731$	2.70647	−	0.284461i	0.100102	−	0.0105212i
$732$	−17.6429	−	1.66219i	−0.652100	−	0.0614362i
$733$	−15.4000	−	13.8662i	−0.568810	−	0.512159i	0.333785	−	0.942649i	$-0.391674\pi$
$733$	−15.4000	−	13.8662i	−0.568810	−	0.512159i	−0.902595	+	0.430490i	$0.858341\pi$
$734$	−2.71180	+	8.34608i	−0.100095	+	0.308059i
$735$	−30.4082	−	26.7160i	−1.12162	−	0.985436i
$736$		−	1.07266i		−	0.0395387i
$737$	−9.35380	−	8.05385i	−0.344551	−	0.296667i
$738$	26.2933	−	19.9836i	0.967869	−	0.735606i
$739$	−8.16363	−	18.3358i	−0.300304	−	0.674494i	0.698865	−	0.715254i	$-0.253689\pi$
$739$	−8.16363	−	18.3358i	−0.300304	−	0.674494i	−0.999169	+	0.0407599i	$0.987022\pi$
$740$	−6.97788	−	32.8283i	−0.256512	−	1.20679i
$741$	3.75554	+	32.3696i	0.137963	+	1.18913i
$742$	−1.88870	+	18.0916i	−0.0693364	+	0.664164i
$743$	18.9719	−	13.7839i	0.696012	−	0.505683i	−0.182619	−	0.983184i	$-0.558457\pi$
$743$	18.9719	−	13.7839i	0.696012	−	0.505683i	0.878631	+	0.477501i	$0.158457\pi$
$744$	7.02096	−	5.21763i	0.257401	−	0.191288i
$745$	12.7491	−	11.4793i	0.467091	−	0.420571i
$746$	−2.75565	−	6.18929i	−0.100891	−	0.226606i
$747$	4.53347	+	35.7068i	0.165871	+	1.30644i
$748$	8.65485	+	2.60140i	0.316453	+	0.0951165i
$749$	8.37183	−	39.5224i	0.305900	−	1.44412i
$750$	4.87483	−	4.48545i	0.178004	−	0.163785i
$751$	40.1154	−	8.52678i	1.46383	−	0.311147i	0.593987	−	0.804475i	$-0.297553\pi$
$751$	40.1154	−	8.52678i	1.46383	−	0.311147i	0.869843	+	0.493328i	$0.164220\pi$
$752$	−1.94346	+	9.14326i	−0.0708707	+	0.333420i
$753$	−34.0168	−	3.20482i	−1.23964	−	0.116790i
$754$	2.10239	−	4.72205i	0.0765647	−	0.171967i
$755$	−8.86880	−	27.2954i	−0.322769	−	0.993380i
$756$	7.70875	−	11.3831i	0.280365	−	0.414000i
$757$	−15.5750	−	11.3159i	−0.566084	−	0.411284i	0.267597	−	0.963531i	$-0.413771\pi$
$757$	−15.5750	−	11.3159i	−0.566084	−	0.411284i	−0.833680	+	0.552247i	$0.813771\pi$
$758$	−15.7527	−	27.2844i	−0.572162	−	0.991014i
$759$	−3.97000	+	4.71262i	−0.144102	+	0.171057i
$760$	10.5222	−	18.2250i	0.381680	−	0.661089i
$761$	2.10959	−	20.0714i	0.0764724	−	0.727586i	−0.887360	−	0.461077i	$-0.847463\pi$
$761$	2.10959	−	20.0714i	0.0764724	−	0.727586i	0.963832	−	0.266509i	$-0.0858703\pi$
$762$	22.7689	+	12.8202i	0.824829	+	0.464428i
$763$	20.7530	−	15.1002i	0.751310	−	0.546663i
$764$	1.06269	+	1.46267i	0.0384469	+	0.0529176i
$765$	19.8825	−	18.6943i	0.718855	−	0.675895i
$766$	−5.82859	+	27.4213i	−0.210595	+	0.990773i
$767$	11.9083	+	13.2256i	0.429985	+	0.477547i
$768$	−0.517438	+	1.65295i	−0.0186714	+	0.0596459i
$769$		−	21.3254i		−	0.769014i	−0.923122	−	0.384507i	$-0.874371\pi$
$769$		−	21.3254i		−	0.769014i	0.923122	−	0.384507i	$-0.125629\pi$
$770$	−12.5246	−	26.4830i	−0.451354	−	0.954380i
$771$	−1.53848	+	7.64234i	−0.0554072	+	0.275232i
$772$	−3.45738	−	0.363385i	−0.124434	−	0.0130785i
$773$	−20.7084	+	18.6459i	−0.744828	+	0.670646i	−0.951460	−	0.307772i	$-0.900416\pi$
$773$	−20.7084	+	18.6459i	−0.744828	+	0.670646i	0.206632	+	0.978419i	$0.433750\pi$
$774$	1.70841	−	2.46136i	0.0614077	−	0.0884719i
$775$	−28.3541	−	12.6240i	−1.01851	−	0.453469i
$776$	−2.77243	+	2.01429i	−0.0995246	+	0.0723088i
$777$	−26.6485	+	37.5786i	−0.956009	+	1.34812i
$778$	−4.17372	−	1.35612i	−0.149635	−	0.0486194i
$779$	−69.0123	−	7.25348i	−2.47262	−	0.259883i
$780$	−11.4094	+	12.9495i	−0.408521	+	0.463667i
$781$	−3.68867	+	1.74132i	−0.131991	+	0.0623095i
$782$	−2.53126	+	1.46142i	−0.0905177	+	0.0522604i
$783$	3.05618	+	8.46397i	0.109219	+	0.302478i
$784$	−2.17244	−	6.65436i	−0.0775871	−	0.237656i
$785$	53.4334	−	17.3616i	1.90712	−	0.619661i
$786$	4.05109	+	2.87706i	0.144498	+	0.102621i
$787$	−7.13842	+	0.750278i	−0.254457	+	0.0267445i	−0.230898	−	0.972978i	$-0.574166\pi$
$787$	−7.13842	+	0.750278i	−0.254457	+	0.0267445i	−0.0235590	+	0.999722i	$0.507500\pi$
$788$	2.46951	+	0.524910i	0.0879726	+	0.0186991i
$789$	31.6923	−	0.341788i	1.12827	−	0.0121680i
$790$	46.5015	+	33.7853i	1.65445	+	1.20203i
$791$	−18.1254	+	20.1586i	−0.644463	+	0.716757i
$792$	8.39103	−	5.34702i	0.298162	−	0.189998i
$793$	−15.2684	−	26.4457i	−0.542198	−	0.939114i
$794$	33.8807	−	15.0847i	1.20238	−	0.535335i
$795$	20.2478	+	34.2127i	0.718114	+	1.21340i
$796$	9.70429	−	10.7777i	0.343959	−	0.382006i
$797$	−2.00296	−	2.75684i	−0.0709485	−	0.0976523i	0.772068	−	0.635540i	$-0.219222\pi$
$797$	−2.00296	−	2.75684i	−0.0709485	−	0.0976523i	−0.843017	+	0.537888i	$0.819222\pi$
$798$	−28.1844	+	6.32992i	−0.997716	+	0.224077i
$799$	24.2241	−	7.87089i	0.856987	−	0.278452i
$800$	6.01131	−	1.27774i	0.212532	−	0.0451751i
$801$	−0.878546	−	40.7268i	−0.0310419	−	1.43901i
$802$	24.4698	+	14.1276i	0.864058	+	0.498864i
$803$	−18.3027	−	7.66716i	−0.645887	−	0.270568i
$804$	−6.31932	−	1.27215i	−0.222865	−	0.0448651i
$805$	9.01296	+	2.92151i	0.317665	+	0.102970i
$806$	14.3358	+	4.65799i	0.504958	+	0.164071i
$807$	−32.8962	−	44.2659i	−1.15800	−	1.55823i
$808$	0.933886	+	8.88533i	0.0328540	+	0.312585i
$809$	−3.37616	−	32.1220i	−0.118699	−	1.12935i	−0.878017	−	0.478629i	$-0.841134\pi$
$809$	−3.37616	−	32.1220i	−0.118699	−	1.12935i	0.759318	−	0.650720i	$-0.225533\pi$
$810$	−1.29571	−	30.0186i	−0.0455265	−	1.05475i
$811$	38.3203	+	12.4510i	1.34561	+	0.437214i	0.891212	−	0.453586i	$-0.149856\pi$
$811$	38.3203	+	12.4510i	1.34561	+	0.437214i	0.454395	+	0.890800i	$0.349856\pi$
$812$	4.35872	+	1.41286i	0.152961	+	0.0495817i
$813$	−2.03187	+	10.0932i	−0.0712608	+	0.353984i
$814$	−28.4980	+	17.3072i	−0.998856	+	0.606615i
$815$	17.8535	+	10.3077i	0.625379	+	0.361063i
$816$	4.60562	−	1.03099i	0.161229	−	0.0360918i
$817$	−6.15791	+	1.30890i	−0.215438	+	0.0457927i
$818$	−25.1727	+	8.17912i	−0.880144	+	0.285976i
$819$	23.6842	−	0.527496i	0.827593	−	0.0184322i
$820$	−21.6022	−	29.7329i	−0.754382	−	1.03832i
$821$	5.31045	−	5.89786i	0.185336	−	0.205837i	−0.643316	−	0.765601i	$-0.722442\pi$
$821$	5.31045	−	5.89786i	0.185336	−	0.205837i	0.828652	+	0.559764i	$0.189108\pi$
$822$	−7.07121	+	4.18488i	−0.246637	+	0.145964i
$823$	7.00962	−	3.12088i	0.244340	−	0.108787i	−0.280913	−	0.959733i	$-0.590637\pi$
$823$	7.00962	−	3.12088i	0.244340	−	0.108787i	0.525253	+	0.850946i	$0.323971\pi$
$824$	5.21043	+	9.02473i	0.181514	+	0.314392i
$825$	−31.1392	−	16.6347i	−1.08413	−	0.579146i
$826$	−10.5479	+	11.7311i	−0.367009	+	0.408179i
$827$	27.4136	+	19.9172i	0.953265	+	0.692587i	0.951577	−	0.307411i	$-0.0994627\pi$
$827$	27.4136	+	19.9172i	0.953265	+	0.692587i	0.00168792	+	0.999999i	$0.499463\pi$
$828$	−0.601015	+	3.16135i	−0.0208867	+	0.109865i
$829$	−11.0901	−	2.35727i	−0.385175	−	0.0818715i	0.0112544	−	0.999937i	$-0.496418\pi$
$829$	−11.0901	−	2.35727i	−0.385175	−	0.0818715i	−0.396429	+	0.918065i	$0.629751\pi$
$830$	39.8354	−	4.18687i	1.38271	−	0.145328i
$831$	2.68786	−	3.78469i	0.0932409	−	0.131289i
$832$	−2.83859	+	0.922314i	−0.0984104	+	0.0319755i
$833$	−12.7432	+	14.1926i	−0.441524	+	0.491745i
$834$	14.4558	−	13.3011i	0.500563	−	0.460579i
$835$	2.32328	−	1.34135i	0.0804005	−	0.0464192i
$836$	−20.5410	−	3.89212i	−0.710425	−	0.134612i
$837$	−23.6157	+	11.4436i	−0.816279	+	0.395548i
$838$	−33.7246	−	3.54460i	−1.16500	−	0.122446i
$839$	33.7690	+	10.9722i	1.16584	+	0.378803i	0.827087	−	0.562074i	$-0.189996\pi$
$839$	33.7690	+	10.9722i	1.16584	+	0.378803i	0.338748	+	0.940877i	$0.389996\pi$
$840$	−12.4796	−	8.84976i	−0.430586	−	0.305346i
$841$	21.0351	−	15.2829i	0.725347	−	0.526996i
$842$	14.5535	+	6.47965i	0.501548	+	0.223303i
$843$	−30.8757	−	13.3497i	−1.06342	−	0.459788i
$844$	−1.31047	+	1.17996i	−0.0451084	+	0.0406158i
$845$	13.5855	+	1.42789i	0.467355	+	0.0491210i
$846$	10.8508	−	25.8582i	0.373058	−	0.889023i
$847$	−20.7288	+	20.4283i	−0.712252	+	0.701924i
$848$			6.87515i			0.236094i
$849$	−26.4061	−	8.26612i	−0.906255	−	0.283692i
$850$	−11.2052	−	12.4447i	−0.384336	−	0.426848i
$851$	2.24199	−	10.5477i	0.0768543	−	0.361571i
$852$	−1.23345	+	1.73678i	−0.0422572	+	0.0595009i
$853$	−17.7455	−	24.4246i	−0.607594	−	0.836281i	0.388783	−	0.921329i	$-0.372896\pi$
$853$	−17.7455	−	24.4246i	−0.607594	−	0.836281i	−0.996377	+	0.0850483i	$0.972896\pi$
$854$	21.8884	−	15.9263i	0.749005	−	0.544985i
$855$	−41.2227	+	47.8173i	−1.40979	+	1.63532i
$856$	1.59610	−	15.1859i	0.0545535	−	0.519042i
$857$	−5.38178	+	9.32152i	−0.183838	+	0.318417i	−0.943184	−	0.332270i	$-0.892186\pi$
$857$	−5.38178	+	9.32152i	−0.183838	+	0.318417i	0.759346	+	0.650687i	$0.225519\pi$
$858$	15.8846	+	6.45375i	0.542292	+	0.220327i
$859$	3.62893	+	6.28549i	0.123818	+	0.214458i	0.921270	−	0.388923i	$-0.127153\pi$
$859$	3.62893	+	6.28549i	0.123818	+	0.214458i	−0.797453	+	0.603382i	$0.793820\pi$
$860$	−2.69745	−	1.95981i	−0.0919823	−	0.0668291i
$861$	−9.92120	+	49.4620i	−0.338114	+	1.68566i
$862$	−1.59651	−	4.91355i	−0.0543773	−	0.167356i
$863$	19.9837	−	44.8841i	0.680253	−	1.52787i	−0.160839	−	0.986981i	$-0.551420\pi$
$863$	19.9837	−	44.8841i	0.680253	−	1.52787i	0.841092	−	0.540892i	$-0.181913\pi$
$864$	2.45116	−	4.58168i	0.0833900	−	0.155872i
$865$	−14.2608	+	67.0918i	−0.484882	+	2.28119i
$866$	2.10823	−	0.448117i	0.0716404	−	0.0152276i
$867$	11.2295	+	12.2044i	0.381375	+	0.414482i
$868$	−2.76895	+	13.0719i	−0.0939843	+	0.443688i
$869$	16.4369	−	54.6855i	0.557583	−	1.85508i
$870$	9.49016	−	3.19709i	0.321747	−	0.108392i
$871$	−4.51800	−	10.1476i	−0.153086	−	0.343838i
$872$	7.20891	−	6.49093i	0.244124	−	0.219811i
$873$	9.29957	−	4.38314i	0.314743	−	0.148347i
$874$	5.47020	−	3.97434i	0.185032	−	0.134434i
$875$	−1.05068	+	10.0643i	−0.0355194	+	0.340236i
$876$	−10.2940	+	1.19431i	−0.347802	+	0.0403521i
$877$	−3.79857	−	17.8709i	−0.128269	−	0.603456i	−0.994582	−	0.103955i	$-0.966850\pi$
$877$	−3.79857	−	17.8709i	−0.128269	−	0.603456i	0.866313	−	0.499501i	$-0.166483\pi$
$878$	8.72240	+	19.5908i	0.294367	+	0.661159i
$879$	−12.5035	+	14.1913i	−0.421731	+	0.478661i
$880$	−5.74758	−	9.46399i	−0.193751	−	0.319031i
$881$			40.1624i			1.35311i	0.736393	+	0.676554i	$0.236527\pi$
$881$			40.1624i			1.35311i	−0.736393	+	0.676554i	$0.763473\pi$
$882$	2.67417	+	20.8290i	0.0900440	+	0.701350i
$883$	−7.24539	+	22.2990i	−0.243827	+	0.750421i	0.752001	+	0.659163i	$0.229089\pi$
$883$	−7.24539	+	22.2990i	−0.243827	+	0.750421i	−0.995827	+	0.0912589i	$0.970911\pi$
$884$	6.04386	+	5.44191i	0.203277	+	0.183031i
$885$	−3.23406	+	34.3272i	−0.108712	+	1.15389i
$886$	−12.3051	+	1.29331i	−0.413397	+	0.0434498i
$887$	−12.4225	+	13.7966i	−0.417107	+	0.463245i	−0.914681	−	0.404177i	$-0.867558\pi$
$887$	−12.4225	+	13.7966i	−0.417107	+	0.463245i	0.497573	+	0.867422i	$0.334225\pi$
$888$	−8.54297	+	15.1724i	−0.286683	+	0.509153i
$889$	−39.0363	+	8.32598i	−1.30923	+	0.279244i
$890$	−45.3327			−1.51956
$891$	−27.7261	+	11.0573i	−0.928859	+	0.370432i
$892$	−6.68621	+	11.5809i	−0.223871	+	0.387756i
$893$	−53.8284	+	23.9659i	−1.80130	+	0.801990i
$894$	−8.90000	+	0.0959828i	−0.297660	+	0.00321015i
$895$	−6.85257	−	21.0900i	−0.229056	−	0.704962i
$896$	−1.07782	−	2.41626i	−0.0360073	−	0.0807216i
$897$	−5.04119	+	2.30994i	−0.168320	+	0.0771267i
$898$	9.08764	+	8.18255i	0.303259	+	0.273055i
$899$	−5.85242	−	6.49977i	−0.195189	−	0.216779i
$900$	−18.4325	+	0.397621i	−0.614418	+	0.0132540i
$901$	16.2240	−	9.36692i	0.540499	−	0.312057i
$902$	−20.8003	+	30.0067i	−0.692574	+	0.999113i
$903$	0.530636	+	4.54585i	0.0176585	+	0.151276i
$904$	−6.02259	+	8.28938i	−0.200308	+	0.275701i
$905$	8.46851	+	39.8412i	0.281503	+	1.32437i
$906$	−5.90922	+	13.6671i	−0.196321	+	0.454059i
$907$	−3.80738	−	36.2248i	−0.126422	−	1.20282i	−0.855282	−	0.518162i	$-0.826616\pi$
$907$	−3.80738	−	36.2248i	−0.126422	−	1.20282i	0.728860	−	0.684662i	$-0.240050\pi$
$908$	5.76863	+	2.56836i	0.191439	+	0.0852340i
$909$	2.22612	−	26.7102i	0.0738359	−	0.885922i
$910$	−0.0184549	−	26.3631i	−0.000611776	−	0.873929i
$911$	27.6833	−	38.1027i	0.917187	−	1.26240i	−0.0474648	−	0.998873i	$-0.515114\pi$
$911$	27.6833	−	38.1027i	0.917187	−	1.26240i	0.964652	−	0.263527i	$-0.0848858\pi$
$912$	−10.3467	+	3.48564i	−0.342613	+	0.115421i
$913$	−16.9872	−	35.9842i	−0.562193	−	1.19090i
$914$	13.9267	+	8.04057i	0.460654	+	0.265959i
$915$	17.6741	−	56.4600i	0.584289	−	1.86651i
$916$	−3.02050	+	9.29614i	−0.0998001	+	0.307153i
$917$	−7.54780	+	0.798648i	−0.249250	+	0.0263737i
$918$	−14.1514	+	0.457993i	−0.467066	+	0.0151160i
$919$	−16.5998	+	37.2838i	−0.547577	+	1.22988i	0.401796	+	0.915729i	$0.368386\pi$
$919$	−16.5998	+	37.2838i	−0.547577	+	1.22988i	−0.949373	+	0.314150i	$0.898281\pi$
$920$	3.50282	+	0.744547i	0.115485	+	0.0245470i
$921$	18.5430	−	10.9741i	0.611011	−	0.361609i
$922$	1.86613	−	17.7551i	0.0614578	−	0.584732i
$923$	−3.67077			−0.120825
$924$	−4.20749	+	14.6047i	−0.138416	+	0.480459i
$925$	61.7814			2.03136
$926$	2.62575	−	24.9824i	0.0862876	−	0.820971i
$927$	−10.2997	−	29.5172i	−0.338285	−	0.969473i
$928$	1.69398	+	0.360067i	0.0556077	+	0.0118198i
$929$	−19.2139	+	43.1551i	−0.630387	+	1.41587i	0.262208	+	0.965011i	$0.415549\pi$
$929$	−19.2139	+	43.1551i	−0.630387	+	1.41587i	−0.892595	+	0.450860i	$0.851117\pi$
$930$	12.1651	+	26.5489i	0.398909	+	0.870574i
$931$	25.8859	−	35.7340i	0.848376	−	1.17113i
$932$	0.154672	−	0.476033i	0.00506647	−	0.0155930i
$933$	6.16315	+	1.92930i	0.201772	+	0.0631625i
$934$	9.32280	+	5.38252i	0.305051	+	0.176121i
$935$	−14.5024	+	26.4572i	−0.474281	+	0.865242i
$936$	8.88270	−	1.12778i	0.290340	−	0.0368627i
$937$	−15.0324	+	20.6903i	−0.491086	+	0.675921i	−0.980588	−	0.196081i	$-0.937179\pi$
$937$	−15.0324	+	20.6903i	−0.491086	+	0.675921i	0.489502	+	0.872002i	$0.337179\pi$
$938$	8.52394	−	4.92926i	0.278316	−	0.160946i
$939$	−1.99796	−	17.2208i	−0.0652011	−	0.561980i
$940$	−28.5088	−	12.6929i	−0.929854	−	0.413998i
$941$	5.77380	+	54.9340i	0.188220	+	1.79080i	0.526932	+	0.849908i	$0.323342\pi$
$941$	5.77380	+	54.9340i	0.188220	+	1.79080i	−0.338711	+	0.940890i	$0.609991\pi$
$942$	−26.7547	−	11.5679i	−0.871716	−	0.376902i
$943$	−2.45509	−	11.5503i	−0.0799488	−	0.376130i
$944$	−3.50480	+	4.82394i	−0.114071	+	0.157006i
$945$	31.8214	+	33.0745i	1.03515	+	1.07591i
$946$	−0.953468	+	3.17219i	−0.0309999	+	0.103137i
$947$	−43.5771	+	25.1592i	−1.41606	+	0.817565i	−0.995950	−	0.0899056i	$-0.971343\pi$
$947$	−43.5771	+	25.1592i	−1.41606	+	0.817565i	−0.420115	+	0.907471i	$0.638010\pi$
$948$	−6.51427	−	29.1005i	−0.211574	−	0.945140i
$949$	−11.9491	−	13.2708i	−0.387883	−	0.430788i
$950$	28.7888	+	25.9215i	0.934031	+	0.841005i
$951$	15.7514	+	34.3758i	0.510776	+	1.11471i
$952$	−4.23344	+	5.83542i	−0.137207	+	0.189127i
$953$	2.88825	+	8.88913i	0.0935597	+	0.287947i	0.986876	−	0.161482i	$-0.0516274\pi$
$953$	2.88825	+	8.88913i	0.0935597	+	0.287947i	−0.893316	+	0.449429i	$0.851627\pi$
$954$	3.85217	−	20.2625i	0.124719	−	0.656023i
$955$	−5.51406	+	2.45502i	−0.178431	+	0.0794425i
$956$	−0.326394	+	0.565330i	−0.0105563	+	0.0182841i
$957$	−6.10971	−	7.85149i	−0.197499	−	0.253802i
$958$	−22.8533			−0.738355
$959$	3.87021	−	11.9397i	0.124976	−	0.385554i
$960$	−5.03864	−	2.83706i	−0.162622	−	0.0915656i
$961$	−3.67630	+	4.08294i	−0.118590	+	0.131708i
$962$	−29.8403	+	3.13634i	−0.962090	+	0.101120i
$963$	−13.2127	+	43.8617i	−0.425775	+	1.41342i
$964$	3.37404	+	3.03800i	0.108671	+	0.0978474i
$965$	3.58647	−	11.0380i	0.115452	−	0.355326i
$966$	−2.50649	−	4.22848i	−0.0806451	−	0.136049i
$967$			10.5980i			0.340810i	0.985374	+	0.170405i	$0.0545076\pi$
$967$			10.5980i			0.340810i	−0.985374	+	0.170405i	$0.945492\pi$
$968$	−6.99071	+	8.49293i	−0.224690	+	0.272973i
$969$	22.3221	+	19.6672i	0.717089	+	0.631801i
$970$	−4.65338	−	10.4517i	−0.149411	−	0.335583i
$971$	−4.47327	−	21.0451i	−0.143554	−	0.675369i	−0.989787	−	0.142556i	$-0.954468\pi$
$971$	−4.47327	−	21.0451i	−0.143554	−	0.675369i	0.846233	−	0.532814i	$-0.178865\pi$
$972$	−9.79121	+	12.1298i	−0.314053	+	0.389064i
$973$	−3.11567	+	29.8446i	−0.0998839	+	0.956774i
$974$	−10.7475	+	7.80853i	−0.344373	+	0.250201i
$975$	−18.9502	−	25.4999i	−0.606893	−	0.816649i
$976$	7.60329	−	6.84603i	0.243375	−	0.219136i
$977$	−14.0953	−	31.6586i	−0.450950	−	1.01285i	−0.985803	−	0.167905i	$-0.946300\pi$
$977$	−14.0953	−	31.6586i	−0.450950	−	1.01285i	0.534854	−	0.844945i	$-0.320367\pi$
$978$	−3.41459	−	10.1358i	−0.109186	−	0.324106i
$979$	14.8632	+	42.5123i	0.475031	+	1.35870i
$980$	23.2381	−	2.47532i	0.742313	−	0.0790711i
$981$	−24.8831	+	15.0910i	−0.794455	+	0.481818i
$982$	23.7445	−	5.04706i	0.757718	−	0.161058i
$983$	−11.3325	+	53.3151i	−0.361450	+	1.70049i	0.302865	+	0.953034i	$0.402057\pi$
$983$	−11.3325	+	53.3151i	−0.361450	+	1.70049i	−0.664314	+	0.747453i	$0.731276\pi$
$984$	−1.78846	+	18.9832i	−0.0570140	+	0.605162i
$985$	−3.42824	+	7.69995i	−0.109233	+	0.245341i
$986$	−1.45825	−	4.48803i	−0.0464401	−	0.142928i
$987$	13.7040	+	40.5845i	0.436202	+	1.29182i
$988$	−15.2208	−	11.0586i	−0.484239	−	0.351820i
$989$	−0.535643	−	0.927761i	−0.0170325	−	0.0295011i
$990$	11.6366	+	31.1128i	0.369836	+	0.988829i
$991$	−25.1880	+	43.6270i	−0.800124	+	1.38586i	0.119410	+	0.992845i	$0.461900\pi$
$991$	−25.1880	+	43.6270i	−0.800124	+	1.38586i	−0.919534	+	0.393011i	$0.871434\pi$
$992$	−0.527904	+	5.02267i	−0.0167610	+	0.159470i
$993$	20.0242	−	35.5632i	0.635449	−	1.12856i
$994$	−0.342395	−	3.23588i	−0.0108601	−	0.102636i
$995$	28.4592	+	39.1708i	0.902219	+	1.24180i
$996$	−16.9428	−	12.0327i	−0.536853	−	0.381270i
$997$	−6.55914	+	30.8583i	−0.207730	+	0.977293i	0.743482	+	0.668756i	$0.233173\pi$
$997$	−6.55914	+	30.8583i	−0.207730	+	0.977293i	−0.951212	+	0.308537i	$0.900160\pi$
$998$	−26.1109	−	28.9991i	−0.826526	−	0.917950i
$999$	33.6791	−	39.9296i	1.06556	−	1.26332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.95.12	yes	128
3.2	odd	2		462.2.bc.a.95.14	✓	128
7.2	even	3	inner	462.2.bc.b.359.1	yes	128
11.8	odd	10		462.2.bc.a.305.3	yes	128
21.2	odd	6		462.2.bc.a.359.3	yes	128
33.8	even	10	inner	462.2.bc.b.305.1	yes	128
77.30	odd	30		462.2.bc.a.107.14	yes	128
231.107	even	30	inner	462.2.bc.b.107.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.14	✓	128	3.2	odd	2
462.2.bc.a.107.14	yes	128	77.30	odd	30
462.2.bc.a.305.3	yes	128	11.8	odd	10
462.2.bc.a.359.3	yes	128	21.2	odd	6
462.2.bc.b.95.12	yes	128	1.1	even	1	trivial
462.2.bc.b.107.12	yes	128	231.107	even	30	inner
462.2.bc.b.305.1	yes	128	33.8	even	10	inner
462.2.bc.b.359.1	yes	128	7.2	even	3	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)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.882151 + 1.49057i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.35789 - 3.04988i) q^{5} +(-1.57462 + 0.721511i) q^{6} +(1.07443 - 2.41777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.44362 + 2.62982i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.882151 + 1.49057i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.35789 - 3.04988i) q^{5} +(-1.57462 + 0.721511i) q^{6} +(1.07443 - 2.41777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.44362 + 2.62982i) q^{9} +(2.89123 + 1.66925i) q^{10} +(0.617451 - 3.25864i) q^{11} +(-0.552966 - 1.64141i) q^{12} +(1.75434 - 2.41465i) q^{13} +(2.29221 + 1.32127i) q^{14} +(5.74393 - 0.666413i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.284826 - 2.70994i) q^{17} +(-2.46452 - 1.71060i) q^{18} +(1.31058 + 6.16579i) q^{19} +(-1.96232 + 2.70091i) q^{20} +(4.55167 - 0.531316i) q^{21} +(3.17625 + 0.954689i) q^{22} +(-0.928949 + 0.536329i) q^{23} +(1.69022 - 0.378363i) q^{24} +(-4.11222 - 4.56708i) q^{25} +(2.21804 + 1.99713i) q^{26} +(-5.19343 + 0.168079i) q^{27} +(-1.55363 + 2.14155i) q^{28} +(-0.535164 - 1.64707i) q^{29} +(0.0623578 + 5.78212i) q^{30} +(4.61371 - 2.05416i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.40193 - 1.95426i) q^{33} +2.72486 q^{34} +(-5.91492 - 6.55995i) q^{35} +(1.95884 - 2.27221i) q^{36} +(-6.72672 + 7.47078i) q^{37} +(-6.26901 + 0.658899i) q^{38} +(5.14681 + 0.484895i) q^{39} +(-2.48099 - 2.23390i) q^{40} +(-3.40181 + 10.4697i) q^{41} +(0.0526261 + 4.58227i) q^{42} +0.998721i q^{43} +(-1.28147 + 3.05906i) q^{44} +(6.06035 + 7.97387i) q^{45} +(-0.436290 - 0.979922i) q^{46} +(1.94346 + 9.14326i) q^{47} +(0.199614 + 1.72051i) q^{48} +(-4.69119 - 5.19545i) q^{49} +(4.97190 - 3.61230i) q^{50} +(3.78810 - 2.81513i) q^{51} +(-2.21804 + 1.99713i) q^{52} +(2.79637 + 6.28076i) q^{53} +(0.375703 - 5.18255i) q^{54} +(-9.10002 - 6.30803i) q^{55} +(-1.96742 - 1.76898i) q^{56} +(-8.03444 + 7.39267i) q^{57} +(1.69398 - 0.360067i) q^{58} +(-1.23972 + 5.83242i) q^{59} +(-5.75697 - 0.542380i) q^{60} +(4.16142 - 9.34670i) q^{61} +(1.56064 + 4.80315i) q^{62} +(4.80723 + 6.31590i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.98217 - 8.62936i) q^{65} +(1.37890 + 5.57662i) q^{66} +(1.86083 - 3.22305i) q^{67} +(-0.284826 + 2.70994i) q^{68} +(-1.61891 - 0.911544i) q^{69} +(7.14229 - 5.19682i) q^{70} +(-0.722902 - 0.994990i) q^{71} +(2.05501 + 2.18562i) q^{72} +(1.24396 - 5.85236i) q^{73} +(-6.72672 - 7.47078i) q^{74} +(3.17997 - 10.1584i) q^{75} -6.30354i q^{76} +(-7.21523 - 4.99404i) q^{77} +(-1.02023 + 5.06793i) q^{78} +(17.1227 + 1.79967i) q^{79} +(2.48099 - 2.23390i) q^{80} +(-4.83193 - 7.59292i) q^{81} +(-10.0568 - 4.47755i) q^{82} +(9.70645 - 7.05215i) q^{83} +(-4.56267 - 0.426640i) q^{84} +(-8.65173 - 2.81112i) q^{85} +(-0.993250 - 0.104395i) q^{86} +(1.98298 - 2.25066i) q^{87} +(-2.90835 - 1.59421i) q^{88} +(-11.7595 + 6.78938i) q^{89} +(-8.56367 + 5.19365i) q^{90} +(-3.95313 - 6.83597i) q^{91} +(1.02016 - 0.331470i) q^{92} +(7.13186 + 5.06500i) q^{93} +(-9.29632 + 0.977083i) q^{94} +(20.5845 + 4.37538i) q^{95} +(-1.73195 + 0.0186784i) q^{96} +(-2.77243 - 2.01429i) q^{97} +(5.65735 - 4.12242i) q^{98} +(7.67829 + 6.32803i) 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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