LMFDB - Embedded newform 462.2.ba.b.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (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:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	462.19
Dual form			462.2.ba.b.73.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.994522 - 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.748568 - 1.68131i) q^{5} +(0.809017 + 0.587785i) q^{6} +(2.42705 + 1.05329i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.994522 - 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.748568 - 1.68131i) q^{5} +(0.809017 + 0.587785i) q^{6} +(2.42705 + 1.05329i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-0.920212 - 1.59385i) q^{10} +(-1.69354 - 2.85165i) q^{11} +(0.866025 + 0.500000i) q^{12} +(3.46658 - 2.51862i) q^{13} +(2.52386 + 0.793823i) q^{14} +(0.568722 - 1.75035i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.588150 + 5.59588i) q^{17} +(0.207912 + 0.978148i) q^{18} +(2.22128 + 0.472147i) q^{19} +(-1.08177 - 1.48893i) q^{20} +(1.09886 + 2.40676i) q^{21} +(-1.98235 - 2.65900i) q^{22} +(-1.63033 + 2.82382i) q^{23} +(0.913545 + 0.406737i) q^{24} +(1.07920 - 1.19857i) q^{25} +(3.18432 - 2.86718i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.59301 + 0.525660i) q^{28} +(-3.77204 - 1.22561i) q^{29} +(0.382646 - 1.80021i) q^{30} +(-2.55952 + 5.74878i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.649578 - 3.25239i) q^{33} +5.62670i q^{34} +(-0.0459068 - 4.86909i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-6.70769 - 7.44965i) q^{37} +(2.25846 + 0.237374i) q^{38} +(4.26146 + 0.447897i) q^{39} +(-1.23148 - 1.36770i) q^{40} +(-0.706454 - 2.17424i) q^{41} +(1.34442 + 2.27871i) q^{42} +2.46505i q^{43} +(-2.24943 - 2.43723i) q^{44} +(1.59385 - 0.920212i) q^{45} +(-1.32623 + 2.97876i) q^{46} +(-0.148237 + 0.697402i) q^{47} +(0.951057 + 0.309017i) q^{48} +(4.78116 + 5.11277i) q^{49} +(0.948004 - 1.30482i) q^{50} +(-4.18145 + 3.76500i) q^{51} +(2.86718 - 3.18432i) q^{52} +(-4.47546 - 1.99261i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.52678 + 4.98203i) q^{55} +(2.63375 + 0.251737i) q^{56} +(1.33480 + 1.83720i) q^{57} +(-3.87948 - 0.824610i) q^{58} +(2.01079 + 9.46001i) q^{59} +(0.192377 - 1.83034i) q^{60} +(-6.78428 + 3.02056i) q^{61} +(-1.94459 + 5.98483i) q^{62} +(-0.793823 + 2.52386i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-6.82955 - 3.94304i) q^{65} +(0.306052 - 3.30247i) q^{66} +(-2.00733 - 3.47679i) q^{67} +(0.588150 + 5.59588i) q^{68} +(-3.10108 + 1.00760i) q^{69} +(-0.554613 - 4.83761i) q^{70} +(-3.05019 - 2.21609i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-7.38458 + 1.56964i) q^{73} +(-7.44965 - 6.70769i) q^{74} +(1.60401 - 0.168588i) q^{75} +2.27090 q^{76} +(-1.10671 - 8.70489i) q^{77} +4.28493 q^{78} +(4.60579 - 0.484089i) q^{79} +(-1.36770 - 1.23148i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-0.929854 - 2.08849i) q^{82} +(-6.37882 - 4.63449i) q^{83} +(1.57524 + 2.12570i) q^{84} +(9.84867 - 3.20003i) q^{85} +(0.257668 + 2.45154i) q^{86} +(-1.98308 - 3.43479i) q^{87} +(-2.49186 - 2.18875i) q^{88} +(0.311206 + 0.179675i) q^{89} +(1.48893 - 1.08177i) q^{90} +(11.0664 - 2.46151i) q^{91} +(-1.00760 + 3.10108i) q^{92} +(-5.74878 + 2.55952i) q^{93} +(-0.0745269 + 0.709076i) q^{94} +(-0.868950 - 4.08809i) q^{95} +(0.978148 + 0.207912i) q^{96} +(2.60022 + 3.57889i) q^{97} +(5.28940 + 4.58500i) q^{98} +(2.65900 - 1.98235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.994522	−	0.104528i	0.703233	−	0.0739128i
$2$	0.994522	−	0.104528i	0.703233	−	0.0739128i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$4$	0.978148	−	0.207912i	0.489074	−	0.103956i
$5$	−0.748568	−	1.68131i	−0.334770	−	0.751905i	−0.999986	−	0.00525445i	$-0.998327\pi$
$5$	−0.748568	−	1.68131i	−0.334770	−	0.751905i	0.665217	−	0.746650i	$-0.268339\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	2.42705	+	1.05329i	0.917339	+	0.398106i
$7$	2.42705	+	1.05329i	0.917339	+	0.398106i
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	−0.920212	−	1.59385i	−0.290997	−	0.504021i
$11$	−1.69354	−	2.85165i	−0.510623	−	0.859805i
$11$	−1.69354	−	2.85165i	−0.510623	−	0.859805i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	3.46658	−	2.51862i	0.961456	−	0.698539i	0.00796792	−	0.999968i	$-0.497464\pi$
$13$	3.46658	−	2.51862i	0.961456	−	0.698539i	0.953489	+	0.301429i	$0.0974637\pi$
$14$	2.52386	+	0.793823i	0.674529	+	0.212158i
$15$	0.568722	−	1.75035i	0.146843	−	0.451938i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	−0.588150	+	5.59588i	−0.142647	+	1.35720i	0.655709	+	0.755014i	$0.272370\pi$
$17$	−0.588150	+	5.59588i	−0.142647	+	1.35720i	−0.798356	+	0.602185i	$0.794297\pi$
$18$	0.207912	+	0.978148i	0.0490053	+	0.230552i
$19$	2.22128	+	0.472147i	0.509596	+	0.108318i	0.455532	−	0.890220i	$-0.349449\pi$
$19$	2.22128	+	0.472147i	0.509596	+	0.108318i	0.0540640	+	0.998537i	$0.482782\pi$
$20$	−1.08177	−	1.48893i	−0.241892	−	0.332936i
$21$	1.09886	+	2.40676i	0.239792	+	0.525198i
$22$	−1.98235	−	2.65900i	−0.422637	−	0.566902i
$23$	−1.63033	+	2.82382i	−0.339948	+	0.588807i	−0.984423	−	0.175819i	$-0.943743\pi$
$23$	−1.63033	+	2.82382i	−0.339948	+	0.588807i	0.644475	+	0.764626i	$0.277076\pi$
$24$	0.913545	+	0.406737i	0.186477	+	0.0830248i
$25$	1.07920	−	1.19857i	0.215840	−	0.239715i
$26$	3.18432	−	2.86718i	0.624497	−	0.562300i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	2.59301	+	0.525660i	0.490032	+	0.0993403i
$29$	−3.77204	−	1.22561i	−0.700450	−	0.227590i	−0.0629231	−	0.998018i	$-0.520042\pi$
$29$	−3.77204	−	1.22561i	−0.700450	−	0.227590i	−0.637526	+	0.770429i	$0.720042\pi$
$30$	0.382646	−	1.80021i	0.0698612	−	0.328671i
$31$	−2.55952	+	5.74878i	−0.459704	+	1.03251i	0.523836	+	0.851819i	$0.324500\pi$
$31$	−2.55952	+	5.74878i	−0.459704	+	1.03251i	−0.983540	+	0.180692i	$0.942166\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.649578	−	3.25239i	0.113077	−	0.566169i
$34$			5.62670i			0.964971i
$35$	−0.0459068	−	4.86909i	−0.00775967	−	0.823026i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−6.70769	−	7.44965i	−1.10274	−	1.22471i	−0.972419	−	0.233243i	$-0.925066\pi$
$37$	−6.70769	−	7.44965i	−1.10274	−	1.22471i	−0.130320	−	0.991472i	$-0.541600\pi$
$38$	2.25846	+	0.237374i	0.366371	+	0.0385071i
$39$	4.26146	+	0.447897i	0.682379	+	0.0717209i
$40$	−1.23148	−	1.36770i	−0.194715	−	0.216253i
$41$	−0.706454	−	2.17424i	−0.110330	−	0.339559i	0.880615	−	0.473833i	$-0.157130\pi$
$41$	−0.706454	−	2.17424i	−0.110330	−	0.339559i	−0.990944	+	0.134274i	$0.957130\pi$
$42$	1.34442	+	2.27871i	0.207448	+	0.351613i
$43$			2.46505i			0.375916i	0.982177	+	0.187958i	$0.0601869\pi$
$43$			2.46505i			0.375916i	−0.982177	+	0.187958i	$0.939813\pi$
$44$	−2.24943	−	2.43723i	−0.339114	−	0.367426i
$45$	1.59385	−	0.920212i	0.237598	−	0.137177i
$46$	−1.32623	+	2.97876i	−0.195542	+	0.439195i
$47$	−0.148237	+	0.697402i	−0.0216226	+	0.101726i	−0.987636	−	0.156767i	$-0.949893\pi$
$47$	−0.148237	+	0.697402i	−0.0216226	+	0.101726i	0.966013	+	0.258494i	$0.0832261\pi$
$48$	0.951057	+	0.309017i	0.137273	+	0.0446028i
$49$	4.78116	+	5.11277i	0.683023	+	0.730396i
$50$	0.948004	−	1.30482i	0.134068	−	0.184529i
$51$	−4.18145	+	3.76500i	−0.585520	+	0.527205i
$52$	2.86718	−	3.18432i	0.397606	−	0.441586i
$53$	−4.47546	−	1.99261i	−0.614752	−	0.273705i	0.0756460	−	0.997135i	$-0.475898\pi$
$53$	−4.47546	−	1.99261i	−0.614752	−	0.273705i	−0.690398	+	0.723429i	$0.742565\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−3.52678	+	4.98203i	−0.475550	+	0.671776i
$56$	2.63375	+	0.251737i	0.351949	+	0.0336398i
$57$	1.33480	+	1.83720i	0.176799	+	0.243343i
$58$	−3.87948	−	0.824610i	−0.509401	−	0.108277i
$59$	2.01079	+	9.46001i	0.261782	+	1.23159i	0.890872	+	0.454255i	$0.150095\pi$
$59$	2.01079	+	9.46001i	0.261782	+	1.23159i	−0.629089	+	0.777333i	$0.716572\pi$
$60$	0.192377	−	1.83034i	0.0248357	−	0.236296i
$61$	−6.78428	+	3.02056i	−0.868638	+	0.386742i	−0.792149	−	0.610328i	$-0.791038\pi$
$61$	−6.78428	+	3.02056i	−0.868638	+	0.386742i	−0.0764889	+	0.997070i	$0.524371\pi$
$62$	−1.94459	+	5.98483i	−0.246963	+	0.760074i
$63$	−0.793823	+	2.52386i	−0.100012	+	0.317976i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−6.82955	−	3.94304i	−0.847101	−	0.489074i
$66$	0.306052	−	3.30247i	0.0376723	−	0.406506i
$67$	−2.00733	−	3.47679i	−0.245234	−	0.424758i	0.716963	−	0.697111i	$-0.245532\pi$
$67$	−2.00733	−	3.47679i	−0.245234	−	0.424758i	−0.962197	+	0.272353i	$0.912198\pi$
$68$	0.588150	+	5.59588i	0.0713237	+	0.678600i
$69$	−3.10108	+	1.00760i	−0.373326	+	0.121301i
$70$	−0.554613	−	4.83761i	−0.0662890	−	0.578206i
$71$	−3.05019	−	2.21609i	−0.361991	−	0.263002i	0.391891	−	0.920012i	$-0.371821\pi$
$71$	−3.05019	−	2.21609i	−0.361991	−	0.263002i	−0.753882	+	0.657010i	$0.771821\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	−7.38458	+	1.56964i	−0.864300	+	0.183713i	−0.618670	−	0.785651i	$-0.712328\pi$
$73$	−7.38458	+	1.56964i	−0.864300	+	0.183713i	−0.245630	+	0.969364i	$0.578995\pi$
$74$	−7.44965	−	6.70769i	−0.866004	−	0.779754i
$75$	1.60401	−	0.168588i	0.185215	−	0.0194668i
$76$	2.27090			0.260490
$77$	−1.10671	−	8.70489i	−0.126121	−	0.992015i
$78$	4.28493			0.485173
$79$	4.60579	−	0.484089i	0.518192	−	0.0544642i	0.158177	−	0.987411i	$-0.449438\pi$
$79$	4.60579	−	0.484089i	0.518192	−	0.0544642i	0.360015	+	0.932947i	$0.382772\pi$
$80$	−1.36770	−	1.23148i	−0.152914	−	0.137684i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−0.929854	−	2.08849i	−0.102685	−	0.230635i
$83$	−6.37882	−	4.63449i	−0.700167	−	0.508701i	0.179820	−	0.983700i	$-0.442449\pi$
$83$	−6.37882	−	4.63449i	−0.700167	−	0.508701i	−0.879987	+	0.474999i	$0.842449\pi$
$84$	1.57524	+	2.12570i	0.171873	+	0.231933i
$85$	9.84867	−	3.20003i	1.06824	−	0.347092i
$86$	0.257668	+	2.45154i	0.0277850	+	0.264357i
$87$	−1.98308	−	3.43479i	−0.212608	−	0.368248i
$88$	−2.49186	−	2.18875i	−0.265634	−	0.233321i
$89$	0.311206	+	0.179675i	0.0329878	+	0.0190455i	0.516403	−	0.856346i	$-0.327271\pi$
$89$	0.311206	+	0.179675i	0.0329878	+	0.0190455i	−0.483415	+	0.875391i	$0.660604\pi$
$90$	1.48893	−	1.08177i	0.156947	−	0.114029i
$91$	11.0664	−	2.46151i	1.16007	−	0.258036i
$92$	−1.00760	+	3.10108i	−0.105050	+	0.323310i
$93$	−5.74878	+	2.55952i	−0.596121	+	0.265410i
$94$	−0.0745269	+	0.709076i	−0.00768686	+	0.0731356i
$95$	−0.868950	−	4.08809i	−0.0891524	−	0.419429i
$96$	0.978148	+	0.207912i	0.0998318	+	0.0212199i
$97$	2.60022	+	3.57889i	0.264012	+	0.363382i	0.920357	−	0.391080i	$-0.127898\pi$
$97$	2.60022	+	3.57889i	0.264012	+	0.363382i	−0.656345	+	0.754461i	$0.727898\pi$
$98$	5.28940	+	4.58500i	0.534310	+	0.463155i
$99$	2.65900	−	1.98235i	0.267240	−	0.199233i
$100$	0.806421	−	1.39676i	0.0806421	−	0.139676i
$101$	2.20536	+	0.981891i	0.219442	+	0.0977018i	0.513513	−	0.858082i	$-0.328344\pi$
$101$	2.20536	+	0.981891i	0.219442	+	0.0977018i	−0.294071	+	0.955783i	$0.595010\pi$
$102$	−3.76500	+	4.18145i	−0.372790	+	0.414025i
$103$	0.702810	−	0.632813i	0.0692499	−	0.0623529i	−0.633779	−	0.773514i	$-0.718497\pi$
$103$	0.702810	−	0.632813i	0.0692499	−	0.0623529i	0.703029	+	0.711161i	$0.251830\pi$
$104$	2.51862	−	3.46658i	0.246971	−	0.339926i
$105$	3.22394	−	3.64915i	0.314624	−	0.356121i
$106$	−4.65923	−	1.51388i	−0.452545	−	0.147041i
$107$	3.70460	−	17.4288i	0.358137	−	1.68490i	−0.317971	−	0.948100i	$-0.603002\pi$
$107$	3.70460	−	17.4288i	0.358137	−	1.68490i	0.676108	−	0.736802i	$-0.263665\pi$
$108$	−0.406737	+	0.913545i	−0.0391383	+	0.0879060i
$109$	−16.7081	+	9.64642i	−1.60034	+	0.923960i	−0.608927	+	0.793226i	$0.708400\pi$
$109$	−16.7081	+	9.64642i	−1.60034	+	0.923960i	−0.991418	+	0.130734i	$0.958267\pi$
$110$	−2.98669	+	5.32338i	−0.284770	+	0.507565i
$111$		−	10.0245i		−	0.951483i
$112$	2.64563	−	0.0249436i	0.249989	−	0.00235695i
$113$	0.133536	+	0.410983i	0.0125621	+	0.0386620i	0.957141	−	0.289622i	$-0.0935296\pi$
$113$	0.133536	+	0.410983i	0.0125621	+	0.0386620i	−0.944579	+	0.328284i	$0.893530\pi$
$114$	1.51953	+	1.68761i	0.142317	+	0.158059i
$115$	5.96813	+	0.627276i	0.556531	+	0.0584938i
$116$	−3.94443	−	0.414576i	−0.366231	−	0.0384924i
$117$	2.86718	+	3.18432i	0.265071	+	0.294391i
$118$	2.98861	+	9.19800i	0.275124	+	0.846745i
$119$	−7.32155	+	12.9620i	−0.671165	+	1.18822i
$120$		−	1.84042i		−	0.168007i
$121$	−5.26381	+	9.65879i	−0.478529	+	0.878072i
$122$	−6.43138	+	3.71316i	−0.582270	+	0.336174i
$123$	0.929854	−	2.08849i	0.0838421	−	0.188312i
$124$	−1.30835	+	6.15531i	−0.117493	+	0.552763i
$125$	−11.5748	−	3.76087i	−1.03528	−	0.336382i
$126$	−0.525660	+	2.59301i	−0.0468295	+	0.231003i
$127$	11.6166	−	15.9889i	1.03081	−	1.41879i	0.126471	−	0.991970i	$-0.459635\pi$
$127$	11.6166	−	15.9889i	1.03081	−	1.41879i	0.904338	−	0.426817i	$-0.140365\pi$
$128$	0.743145	−	0.669131i	0.0656853	−	0.0591433i
$129$	−1.64944	+	1.83189i	−0.145225	+	0.161289i
$130$	−7.20430	−	3.20756i	−0.631859	−	0.281322i
$131$	−3.79140	+	6.56690i	−0.331256	+	0.573753i	−0.982758	−	0.184894i	$-0.940806\pi$
$131$	−3.79140	+	6.56690i	−0.331256	+	0.573753i	0.651502	+	0.758647i	$0.274139\pi$
$132$	−0.0408275	−	3.31637i	−0.00355357	−	0.288653i
$133$	4.89385	+	3.48557i	0.424350	+	0.302237i
$134$	−2.35976	−	3.24792i	−0.203852	−	0.280578i
$135$	1.80021	+	0.382646i	0.154937	+	0.0329329i
$136$	1.16986	+	5.50374i	0.100314	+	0.471942i
$137$	−2.05869	+	19.5871i	−0.175886	+	1.67344i	0.449617	+	0.893221i	$0.351560\pi$
$137$	−2.05869	+	19.5871i	−0.175886	+	1.67344i	−0.625503	+	0.780222i	$0.715106\pi$
$138$	−2.97876	+	1.32623i	−0.253569	+	0.112896i
$139$	0.450654	−	1.38697i	0.0382239	−	0.117641i	−0.930124	−	0.367246i	$-0.880301\pi$
$139$	0.450654	−	1.38697i	0.0382239	−	0.117641i	0.968348	+	0.249605i	$0.0803007\pi$
$140$	−1.05724	−	4.75314i	−0.0893534	−	0.401714i
$141$	−0.576815	+	0.419080i	−0.0485765	+	0.0352929i
$142$	−3.26513	−	1.88512i	−0.274003	−	0.158196i
$143$	−13.0530	−	5.62008i	−1.09155	−	0.469975i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	0.762995	+	7.25942i	0.0633633	+	0.602862i
$146$	−7.18005	+	2.33294i	−0.594226	+	0.193076i
$147$	0.131983	+	6.99876i	0.0108858	+	0.577248i
$148$	−8.10998	−	5.89225i	−0.666637	−	0.484340i
$149$	−5.68878	−	12.7772i	−0.466043	−	1.04675i	−0.981783	−	0.190005i	$-0.939150\pi$
$149$	−5.68878	−	12.7772i	−0.466043	−	1.04675i	0.515740	−	0.856745i	$-0.327517\pi$
$150$	1.57760	−	0.335329i	0.128810	−	0.0273795i
$151$	7.66062	+	6.89765i	0.623412	+	0.561323i	0.919131	−	0.393952i	$-0.128892\pi$
$151$	7.66062	+	6.89765i	0.623412	+	0.561323i	−0.295719	+	0.955275i	$0.595559\pi$
$152$	2.25846	−	0.237374i	0.183185	−	0.0192536i
$153$	−5.62670			−0.454892
$154$	−2.01056	−	8.54153i	−0.162015	−	0.688296i
$155$	11.5815			0.930245
$156$	4.26146	−	0.447897i	0.341190	−	0.0358605i
$157$	16.6624	+	15.0029i	1.32980	+	1.19736i	0.963762	+	0.266763i	$0.0859541\pi$
$157$	16.6624	+	15.0029i	1.32980	+	1.19736i	0.366042	+	0.930598i	$0.380713\pi$
$158$	4.52996	−	0.962873i	0.360384	−	0.0766021i
$159$	−1.99261	−	4.47546i	−0.158024	−	0.354927i
$160$	−1.48893	−	1.08177i	−0.117711	−	0.0855217i
$161$	−6.93120	+	5.13634i	−0.546255	+	0.404801i
$162$	−0.951057	+	0.309017i	−0.0747221	+	0.0242787i
$163$	1.64059	+	15.6092i	0.128501	+	1.22260i	0.848714	+	0.528852i	$0.177377\pi$
$163$	1.64059	+	15.6092i	0.128501	+	1.22260i	−0.720213	+	0.693753i	$0.755956\pi$
$164$	−1.14307	−	1.97985i	−0.0892585	−	0.154600i
$165$	−5.95453	+	1.34249i	−0.463560	+	0.104513i
$166$	−6.82832	−	3.94233i	−0.529980	−	0.305984i
$167$	2.62658	−	1.90832i	0.203251	−	0.147670i	−0.481504	−	0.876444i	$-0.659909\pi$
$167$	2.62658	−	1.90832i	0.203251	−	0.147670i	0.684755	+	0.728774i	$0.259909\pi$
$168$	1.78881	+	1.94940i	0.138010	+	0.150399i
$169$	1.65652	−	5.09825i	0.127425	−	0.392173i
$170$	9.46023	−	4.21197i	0.725566	−	0.323043i
$171$	−0.237374	+	2.25846i	−0.0181524	+	0.172709i
$172$	0.512512	+	2.41118i	0.0390787	+	0.183851i
$173$	23.7296	+	5.04389i	1.80413	+	0.383480i	0.982458	−	0.186482i	$-0.0597085\pi$
$173$	23.7296	+	5.04389i	1.80413	+	0.383480i	0.821672	+	0.569961i	$0.193042\pi$
$174$	−2.33125	−	3.20869i	−0.176731	−	0.243250i
$175$	3.88172	−	1.77229i	0.293431	−	0.133973i
$176$	−2.70700	−	1.91629i	−0.204048	−	0.144445i
$177$	−4.83568	+	8.37564i	−0.363472	+	0.629551i
$178$	0.328282	+	0.146161i	0.0246058	+	0.0109552i
$179$	15.9984	−	17.7680i	1.19578	−	1.32805i	0.264215	−	0.964464i	$-0.414887\pi$
$179$	15.9984	−	17.7680i	1.19578	−	1.32805i	0.931562	−	0.363582i	$-0.118446\pi$
$180$	1.36770	−	1.23148i	0.101942	−	0.0917894i
$181$	13.2117	−	18.1843i	0.982015	−	1.35163i	0.0462787	−	0.998929i	$-0.485264\pi$
$181$	13.2117	−	18.1843i	0.982015	−	1.35163i	0.935737	−	0.352700i	$-0.114736\pi$
$182$	10.7485	−	3.60478i	0.796731	−	0.267204i
$183$	−7.06285	−	2.29486i	−0.522101	−	0.169641i
$184$	−0.677930	+	3.18941i	−0.0499777	+	0.235126i
$185$	−7.50401	+	16.8543i	−0.551706	+	1.23915i
$186$	−5.44974	+	3.14641i	−0.399595	+	0.230706i
$187$	16.9535	−	7.79967i	1.23977	−	0.570368i
$188$			0.712982i			0.0519996i
$189$	−2.27871	+	1.34442i	−0.165752	+	0.0977921i
$190$	−1.29151	−	3.97486i	−0.0936961	−	0.288367i
$191$	13.2897	+	14.7597i	0.961609	+	1.06797i	0.997643	+	0.0686243i	$0.0218610\pi$
$191$	13.2897	+	14.7597i	0.961609	+	1.06797i	−0.0360336	+	0.999351i	$0.511472\pi$
$192$	0.994522	+	0.104528i	0.0717734	+	0.00754369i
$193$	−24.7013	−	2.59621i	−1.77804	−	0.186879i	−0.842165	−	0.539220i	$-0.818719\pi$
$193$	−24.7013	−	2.59621i	−1.77804	−	0.186879i	−0.935872	+	0.352341i	$0.885386\pi$
$194$	2.96007	+	3.28749i	0.212521	+	0.236028i
$195$	−2.43693	−	7.50011i	−0.174512	−	0.537094i
$196$	5.73969	+	4.00699i	0.409978	+	0.286213i
$197$		−	21.6823i		−	1.54480i	−0.635138	−	0.772399i	$-0.719057\pi$
$197$		−	21.6823i		−	1.54480i	0.635138	−	0.772399i	$-0.280943\pi$
$198$	2.43723	−	2.24943i	0.173206	−	0.159860i
$199$	14.2822	−	8.24585i	1.01244	−	0.584533i	0.100535	−	0.994933i	$-0.467944\pi$
$199$	14.2822	−	8.24585i	1.01244	−	0.584533i	0.911905	+	0.410400i	$0.134611\pi$
$200$	0.656002	−	1.47340i	0.0463863	−	0.104185i
$201$	0.834694	−	3.92693i	0.0588748	−	0.276984i
$202$	2.29592	+	0.745989i	0.161540	+	0.0524876i
$203$	−7.86401	−	6.94766i	−0.551945	−	0.487630i
$204$	−3.30729	+	4.55210i	−0.231557	+	0.318710i
$205$	−3.12675	+	2.81533i	−0.218381	+	0.196631i
$206$	0.632813	−	0.702810i	0.0440902	−	0.0489671i
$207$	−2.97876	−	1.32623i	−0.207038	−	0.0921795i
$208$	2.14246	−	3.71086i	0.148553	−	0.257302i
$209$	−2.41543	−	7.13390i	−0.167079	−	0.493462i
$210$	2.82484	−	3.96616i	0.194932	−	0.273691i
$211$	2.19806	+	3.02537i	0.151320	+	0.208275i	0.877947	−	0.478758i	$-0.158913\pi$
$211$	2.19806	+	3.02537i	0.151320	+	0.208275i	−0.726626	+	0.687033i	$0.758913\pi$
$212$	−4.79195	−	1.01856i	−0.329113	−	0.0699550i
$213$	−0.783878	−	3.68786i	−0.0537104	−	0.252688i
$214$	1.86250	−	17.7205i	0.127318	−	1.21135i
$215$	4.14451	−	1.84525i	0.282653	−	0.125845i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	−12.2672	+	11.2567i	−0.832753	+	0.764153i
$218$	−15.6082	+	11.3400i	−1.05712	+	0.768045i
$219$	−6.53811	−	3.77478i	−0.441804	−	0.255076i
$220$	−2.41389	+	5.60642i	−0.162744	+	0.377984i
$221$	12.0550	+	20.8799i	0.810907	+	1.40453i
$222$	−1.04784	−	9.96958i	−0.0703267	−	0.669114i
$223$	9.62576	−	3.12760i	0.644588	−	0.209439i	0.0315618	−	0.999502i	$-0.489952\pi$
$223$	9.62576	−	3.12760i	0.644588	−	0.209439i	0.613026	+	0.790062i	$0.289952\pi$
$224$	2.62853	−	0.301351i	0.175626	−	0.0201349i
$225$	1.30482	+	0.948004i	0.0869877	+	0.0632003i
$226$	0.175764	+	0.394773i	0.0116917	+	0.0262599i
$227$	−6.49619	+	1.38081i	−0.431167	+	0.0916475i	−0.418383	−	0.908271i	$-0.637403\pi$
$227$	−6.49619	+	1.38081i	−0.431167	+	0.0916475i	−0.0127847	+	0.999918i	$0.504070\pi$
$228$	1.68761	+	1.51953i	0.111765	+	0.100633i
$229$	−9.23122	+	0.970240i	−0.610016	+	0.0641153i	−0.404499	−	0.914538i	$-0.632554\pi$
$229$	−9.23122	+	0.970240i	−0.610016	+	0.0641153i	−0.205517	+	0.978654i	$0.565887\pi$
$230$	6.00100			0.395694
$231$	5.00227	−	7.20953i	0.329125	−	0.474352i
$232$	−3.96615			−0.260391
$233$	3.34343	−	0.351409i	0.219036	−	0.0230216i	0.00562505	−	0.999984i	$-0.498209\pi$
$233$	3.34343	−	0.351409i	0.219036	−	0.0230216i	0.213411	+	0.976963i	$0.431543\pi$
$234$	3.18432	+	2.86718i	0.208166	+	0.187433i
$235$	1.28351	−	0.272819i	0.0837272	−	0.0177968i
$236$	3.93369	+	8.83522i	0.256062	+	0.575124i
$237$	3.74669	+	2.72213i	0.243374	+	0.176821i
$238$	−5.92654	+	13.6563i	−0.384161	+	0.885206i
$239$	13.5791	−	4.41212i	0.878359	−	0.285396i	0.165083	−	0.986280i	$-0.447211\pi$
$239$	13.5791	−	4.41212i	0.878359	−	0.285396i	0.713276	+	0.700883i	$0.247211\pi$
$240$	−0.192377	−	1.83034i	−0.0124179	−	0.118148i
$241$	−1.80853	−	3.13247i	−0.116498	−	0.201780i	0.801880	−	0.597486i	$-0.203834\pi$
$241$	−1.80853	−	3.13247i	−0.116498	−	0.201780i	−0.918378	+	0.395705i	$0.870500\pi$
$242$	−4.22536	+	10.1561i	−0.271616	+	0.652859i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−6.00802	+	4.36508i	−0.384624	+	0.279446i
$245$	5.01714	−	11.8659i	0.320533	−	0.758083i
$246$	0.706454	−	2.17424i	0.0450418	−	0.138625i
$247$	8.88939	−	3.95781i	0.565618	−	0.251830i
$248$	−0.657779	+	6.25835i	−0.0417690	+	0.397406i
$249$	−1.63931	−	7.71236i	−0.103887	−	0.488751i
$250$	−11.9045	−	2.53037i	−0.752905	−	0.160035i
$251$	11.5968	+	15.9617i	0.731986	+	1.00749i	0.999040	+	0.0438102i	$0.0139497\pi$
$251$	11.5968	+	15.9617i	0.731986	+	1.00749i	−0.267054	+	0.963681i	$0.586050\pi$
$252$	−0.251737	+	2.63375i	−0.0158579	+	0.165911i
$253$	10.8136	−	0.133125i	0.679844	−	0.00836948i
$254$	9.88170	−	17.1156i	0.620033	−	1.07393i
$255$	9.46023	+	4.21197i	0.592423	+	0.263763i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	13.8655	−	12.4846i	0.864907	−	0.778765i	−0.111713	−	0.993741i	$-0.535634\pi$
$257$	13.8655	−	12.4846i	0.864907	−	0.778765i	0.976620	+	0.214975i	$0.0689670\pi$
$258$	−1.44892	+	1.99426i	−0.0902057	+	0.124158i
$259$	−8.43329	−	25.1458i	−0.524019	−	1.56249i
$260$	−7.50011	−	2.43693i	−0.465137	−	0.151132i
$261$	0.824610	−	3.87948i	0.0510421	−	0.240134i
$262$	−3.08420	+	6.92724i	−0.190543	+	0.427966i
$263$	−8.27102	+	4.77528i	−0.510013	+	0.294456i	−0.732839	−	0.680402i	$-0.761805\pi$
$263$	−8.27102	+	4.77528i	−0.510013	+	0.294456i	0.222826	+	0.974858i	$0.428472\pi$
$264$	−0.387259	−	3.29394i	−0.0238342	−	0.202728i
$265$			9.01625i			0.553864i
$266$	5.23138	+	2.95493i	0.320756	+	0.181178i
$267$	0.111045	+	0.341762i	0.00679585	+	0.0209155i
$268$	−2.68633	−	2.98347i	−0.164094	−	0.182244i
$269$	28.5346	+	2.99911i	1.73978	+	0.182859i	0.920557	−	0.390609i	$-0.127736\pi$
$269$	28.5346	+	2.99911i	1.73978	+	0.182859i	0.819228	+	0.573468i	$0.194402\pi$
$270$	1.83034	+	0.192377i	0.111391	+	0.0117077i
$271$	−12.2474	−	13.6021i	−0.743977	−	0.826270i	0.245736	−	0.969337i	$-0.420970\pi$
$271$	−12.2474	−	13.6021i	−0.743977	−	0.826270i	−0.989713	+	0.143067i	$0.954304\pi$
$272$	1.73875	+	5.35131i	0.105427	+	0.324471i
$273$	9.87101	+	5.57561i	0.597421	+	0.337452i
$274$			19.6950i			1.18982i
$275$	−5.24559	−	1.04767i	−0.316321	−	0.0631766i
$276$	−2.82382	+	1.63033i	−0.169974	+	0.0981345i
$277$	2.86449	−	6.43376i	0.172111	−	0.386567i	−0.806809	−	0.590812i	$-0.798807\pi$
$277$	2.86449	−	6.43376i	0.172111	−	0.386567i	0.978920	+	0.204245i	$0.0654740\pi$
$278$	0.303207	−	1.42648i	0.0181852	−	0.0855544i
$279$	−5.98483	−	1.94459i	−0.358302	−	0.116419i
$280$	−1.54829	−	4.61659i	−0.0925281	−	0.275894i
$281$	3.37417	−	4.64415i	0.201286	−	0.277047i	−0.696426	−	0.717628i	$-0.745228\pi$
$281$	3.37417	−	4.64415i	0.201286	−	0.277047i	0.897713	+	0.440582i	$0.145228\pi$
$282$	−0.529849	+	0.477078i	−0.0315520	+	0.0284096i
$283$	−21.3141	+	23.6717i	−1.26699	+	1.40714i	−0.394213	+	0.919019i	$0.628983\pi$
$283$	−21.3141	+	23.6717i	−1.26699	+	1.40714i	−0.872778	+	0.488117i	$0.837684\pi$
$284$	−3.44429	−	1.53350i	−0.204381	−	0.0909963i
$285$	2.08971	−	3.61948i	0.123784	−	0.214400i
$286$	−13.5690	−	4.22488i	−0.802351	−	0.249823i
$287$	0.575504	−	6.02110i	0.0339709	−	0.355414i
$288$	0.587785	+	0.809017i	0.0346356	+	0.0476718i
$289$	−14.3394	−	3.04793i	−0.843494	−	0.179290i
$290$	1.51763	+	7.13989i	0.0891184	+	0.419269i
$291$	−0.462408	+	4.39952i	−0.0271069	+	0.257905i
$292$	−6.89686	+	3.07068i	−0.403608	+	0.179698i
$293$	−0.403280	+	1.24117i	−0.0235599	+	0.0725098i	−0.962145	−	0.272537i	$-0.912137\pi$
$293$	−0.403280	+	1.24117i	−0.0235599	+	0.0725098i	0.938585	+	0.345047i	$0.112137\pi$
$294$	0.862830	+	6.94662i	0.0503212	+	0.405135i
$295$	14.4000	−	10.4622i	0.838401	−	0.609134i
$296$	−8.68146	−	5.01225i	−0.504600	−	0.291331i
$297$	3.30247	+	0.306052i	0.191629	+	0.0177589i
$298$	−6.99320	−	12.1126i	−0.405105	−	0.701663i
$299$	1.46044	+	13.8952i	0.0844595	+	0.803579i
$300$	1.53390	−	0.498395i	0.0885599	−	0.0287749i
$301$	−2.59641	+	5.98280i	−0.149654	+	0.344843i
$302$	8.33966	+	6.05911i	0.479893	+	0.348663i
$303$	0.981891	+	2.20536i	0.0564082	+	0.126695i
$304$	2.22128	−	0.472147i	0.127399	−	0.0270795i
$305$	10.1570	+	9.14539i	0.581587	+	0.523663i
$306$	−5.59588	+	0.588150i	−0.319895	+	0.0336223i
$307$	28.4488			1.62366			0.811830	−	0.583894i	$-0.198472\pi$
$307$	28.4488			1.62366			0.811830	+	0.583894i	$0.198472\pi$
$308$	−2.89237	−	8.28457i	−0.164808	−	0.472057i
$309$	0.945724			0.0538003
$310$	11.5180	−	1.21059i	0.654179	−	0.0687570i
$311$	−4.42354	−	3.98298i	−0.250836	−	0.225854i	0.534115	−	0.845412i	$-0.320645\pi$
$311$	−4.42354	−	3.98298i	−0.250836	−	0.225854i	−0.784951	+	0.619558i	$0.787312\pi$
$312$	4.19129	−	0.890887i	0.237285	−	0.0504365i
$313$	−4.20244	−	9.43884i	−0.237536	−	0.533515i	0.754963	−	0.655767i	$-0.227655\pi$
$313$	−4.20244	−	9.43884i	−0.237536	−	0.533515i	−0.992499	+	0.122253i	$0.960988\pi$
$314$	18.1394	+	13.1790i	1.02366	+	0.743735i
$315$	4.83761	−	0.554613i	0.272569	−	0.0312489i
$316$	4.40450	−	1.43111i	0.247772	−	0.0805061i
$317$	2.02154	+	19.2337i	0.113541	+	1.08027i	0.891832	+	0.452367i	$0.149420\pi$
$317$	2.02154	+	19.2337i	0.113541	+	1.08027i	−0.778290	+	0.627904i	$0.783913\pi$
$318$	−2.44950	−	4.24266i	−0.137361	−	0.237917i
$319$	2.89310	+	12.8321i	0.161983	+	0.718462i
$320$	−1.59385	−	0.920212i	−0.0890991	−	0.0514414i
$321$	14.4152	−	10.4732i	0.804577	−	0.584559i
$322$	−6.35633	+	5.83271i	−0.354225	+	0.325044i
$323$	−3.94852	+	12.1523i	−0.219701	+	0.676172i
$324$	−0.913545	+	0.406737i	−0.0507525	+	0.0225965i
$325$	0.722387	−	6.87305i	0.0400708	−	0.381248i
$326$	3.26320	+	15.3522i	0.180732	+	0.850278i
$327$	−18.8712	−	4.01121i	−1.04358	−	0.221820i
$328$	−1.34375	−	1.84952i	−0.0741964	−	0.102123i
$329$	−1.09435	+	1.53649i	−0.0603332	+	0.0847096i
$330$	−5.78158	+	1.95756i	−0.318266	+	0.107760i
$331$	−2.87142	+	4.97344i	−0.157827	+	0.273365i	−0.934085	−	0.357051i	$-0.883782\pi$
$331$	−2.87142	+	4.97344i	−0.157827	+	0.273365i	0.776258	+	0.630416i	$0.217116\pi$
$332$	−7.20299	−	3.20698i	−0.395316	−	0.176006i
$333$	6.70769	−	7.44965i	0.367579	−	0.408238i
$334$	2.41271	−	2.17242i	0.132018	−	0.118869i
$335$	−4.34295	+	5.97756i	−0.237281	+	0.326589i
$336$	1.98278	+	1.75174i	0.108169	+	0.0955651i
$337$	−16.0177	−	5.20447i	−0.872541	−	0.283506i	−0.161684	−	0.986843i	$-0.551693\pi$
$337$	−16.0177	−	5.20447i	−0.872541	−	0.283506i	−0.710857	+	0.703337i	$0.751693\pi$
$338$	1.11454	−	5.24348i	0.0606227	−	0.285208i
$339$	−0.175764	+	0.394773i	−0.00954621	+	0.0214411i
$340$	8.96813	−	5.17775i	0.486365	−	0.280803i
$341$	20.7282	−	2.43695i	1.12249	−	0.131968i
$342$			2.27090i			0.122796i
$343$	6.21891	+	17.4449i	0.335789	+	0.941937i
$344$	0.761741	+	2.34440i	0.0410703	+	0.126402i
$345$	4.01545	+	4.45961i	0.216185	+	0.240098i
$346$	24.1269	+	2.53584i	1.29707	+	0.136327i
$347$	−6.25307	−	0.657224i	−0.335682	−	0.0352816i	−0.0648120	−	0.997897i	$-0.520645\pi$
$347$	−6.25307	−	0.657224i	−0.335682	−	0.0352816i	−0.270870	+	0.962616i	$0.587311\pi$
$348$	−2.65387	−	2.94743i	−0.142263	−	0.157999i
$349$	−10.0241	−	30.8510i	−0.536578	−	1.65142i	−0.740215	−	0.672370i	$-0.765276\pi$
$349$	−10.0241	−	30.8510i	−0.536578	−	1.65142i	0.203638	−	0.979046i	$-0.434724\pi$
$350$	3.67520	−	2.16833i	0.196448	−	0.115902i
$351$			4.28493i			0.228713i
$352$	−2.89248	−	1.62283i	−0.154170	−	0.0864971i
$353$	−27.8114	+	16.0569i	−1.48025	+	0.854622i	−0.999750	−	0.0223725i	$-0.992878\pi$
$353$	−27.8114	+	16.0569i	−1.48025	+	0.854622i	−0.480500	+	0.876995i	$0.659545\pi$
$354$	−3.93369	+	8.83522i	−0.209073	+	0.469587i
$355$	−1.44267	+	6.78722i	−0.0765688	+	0.360228i
$356$	0.341762	+	0.111045i	0.0181133	+	0.00588538i
$357$	−14.1142	+	4.73357i	−0.747004	+	0.250527i
$358$	14.0535	−	19.3430i	0.742751	−	1.02231i
$359$	24.9193	−	22.4374i	1.31519	−	1.18420i	0.345902	−	0.938271i	$-0.387573\pi$
$359$	24.9193	−	22.4374i	1.31519	−	1.18420i	0.969287	−	0.245931i	$-0.0790938\pi$
$360$	1.23148	−	1.36770i	0.0649049	−	0.0720842i
$361$	−12.6462	−	5.63046i	−0.665590	−	0.296340i
$362$	11.2385	−	19.4657i	0.590683	−	1.02309i
$363$	−10.3748	+	3.65570i	−0.544534	+	0.191875i
$364$	10.3128	−	4.70855i	0.540538	−	0.246795i
$365$	8.16691	+	11.2408i	0.427476	+	0.588370i
$366$	−7.26403	−	1.54402i	−0.379697	−	0.0807071i
$367$	−7.41780	−	34.8980i	−0.387206	−	1.82166i	−0.550199	−	0.835034i	$-0.685448\pi$
$367$	−7.41780	−	34.8980i	−0.387206	−	1.82166i	0.162993	−	0.986627i	$-0.447885\pi$
$368$	−0.340832	+	3.24280i	−0.0177671	+	0.169043i
$369$	2.08849	−	0.929854i	0.108722	−	0.0484062i
$370$	−5.70115	+	17.5463i	−0.296389	+	0.912191i
$371$	−8.76340	−	9.55012i	−0.454973	−	0.495817i
$372$	−5.09100	+	3.69883i	−0.263956	+	0.191775i
$373$	7.60376	+	4.39003i	0.393708	+	0.227307i	0.683765	−	0.729702i	$-0.260341\pi$
$373$	7.60376	+	4.39003i	0.393708	+	0.227307i	−0.290058	+	0.957009i	$0.593675\pi$
$374$	16.0454	−	9.52906i	0.829687	−	0.492736i
$375$	−6.08521	−	10.5399i	−0.314239	−	0.544278i
$376$	0.0745269	+	0.709076i	0.00384343	+	0.0365678i
$377$	−16.1629	+	5.25165i	−0.832432	+	0.270474i
$378$	−2.12570	+	1.57524i	−0.109334	+	0.0810218i
$379$	6.50305	+	4.72474i	0.334039	+	0.242694i	0.742143	−	0.670242i	$-0.233810\pi$
$379$	6.50305	+	4.72474i	0.334039	+	0.242694i	−0.408103	+	0.912936i	$0.633810\pi$
$380$	−1.69992	−	3.81809i	−0.0872042	−	0.195864i
$381$	19.3315	−	4.10904i	0.990383	−	0.210513i
$382$	14.7597	+	13.2897i	0.755172	+	0.679960i
$383$	20.4908	−	2.15367i	1.04703	−	0.110048i	0.434642	−	0.900603i	$-0.356875\pi$
$383$	20.4908	−	2.15367i	1.04703	−	0.110048i	0.612390	+	0.790556i	$0.290208\pi$
$384$	1.00000			0.0510310
$385$	−13.8072	+	8.37692i	−0.703679	+	0.426928i
$386$	−24.8373			−1.26419
$387$	−2.45154	+	0.257668i	−0.124619	+	0.0130980i
$388$	3.28749	+	2.96007i	0.166897	+	0.150275i
$389$	−22.2125	+	4.72140i	−1.12622	+	0.239385i	−0.733111	−	0.680109i	$-0.761932\pi$
$389$	−22.2125	+	4.72140i	−1.12622	+	0.239385i	−0.393105	+	0.919494i	$0.628599\pi$
$390$	−3.20756	−	7.20430i	−0.162421	−	0.364804i
$391$	−14.8429	−	10.7840i	−0.750635	−	0.545369i
$392$	6.12709	+	3.38508i	0.309465	+	0.170972i
$393$	−7.21167	+	2.34322i	−0.363781	+	0.118200i
$394$	−2.26641	−	21.5635i	−0.114180	−	1.08635i
$395$	−4.26165	−	7.38140i	−0.214427	−	0.371398i
$396$	2.18875	−	2.49186i	0.109989	−	0.125221i
$397$	−22.1317	−	12.7777i	−1.11076	−	0.641296i	−0.171732	−	0.985144i	$-0.554936\pi$
$397$	−22.1317	−	12.7777i	−1.11076	−	0.641296i	−0.939025	+	0.343848i	$0.888270\pi$
$398$	13.3421	−	9.69358i	0.668778	−	0.485895i
$399$	1.30453	+	5.86491i	0.0653084	+	0.293613i
$400$	0.498395	−	1.53390i	0.0249198	−	0.0766952i
$401$	18.5881	−	8.27596i	0.928246	−	0.413282i	0.113789	−	0.993505i	$-0.463701\pi$
$401$	18.5881	−	8.27596i	0.928246	−	0.413282i	0.814458	+	0.580223i	$0.197035\pi$
$402$	0.419646	−	3.99266i	0.0209300	−	0.199136i
$403$	5.60619	+	26.3751i	0.279264	+	1.31384i
$404$	2.36132	+	0.501914i	0.117480	+	0.0249711i
$405$	1.08177	+	1.48893i	0.0537538	+	0.0739857i
$406$	−8.54716	−	6.08759i	−0.424188	−	0.302122i
$407$	−9.88401	+	31.7443i	−0.489932	+	1.57351i
$408$	−2.81335	+	4.87286i	−0.139282	+	0.241243i
$409$	−4.57019	−	2.03478i	−0.225982	−	0.100613i	0.290623	−	0.956838i	$-0.406138\pi$
$409$	−4.57019	−	2.03478i	−0.225982	−	0.100613i	−0.516604	+	0.856224i	$0.672804\pi$
$410$	−2.81533	+	3.12675i	−0.139039	+	0.154419i
$411$	−14.6363	+	13.1786i	−0.721954	+	0.650050i
$412$	0.555883	−	0.765107i	0.0273864	−	0.0376941i
$413$	−5.08384	+	25.0779i	−0.250159	+	1.23400i
$414$	−3.10108	−	1.00760i	−0.152410	−	0.0495209i
$415$	−3.01703	+	14.1940i	−0.148100	+	0.696757i
$416$	1.74284	−	3.91448i	0.0854497	−	0.191923i
$417$	1.26296	−	0.729173i	0.0618476	−	0.0357078i
$418$	−3.14790	−	6.84234i	−0.153969	−	0.334670i
$419$			24.7866i			1.21091i	0.795881	+	0.605453i	$0.207008\pi$
$419$			24.7866i			1.21091i	−0.795881	+	0.605453i	$0.792992\pi$
$420$	2.39479	−	4.23971i	0.116854	−	0.206876i
$421$	−1.59910	−	4.92151i	−0.0779352	−	0.239860i	0.904497	−	0.426480i	$-0.140247\pi$
$421$	−1.59910	−	4.92151i	−0.0779352	−	0.239860i	−0.982432	+	0.186620i	$0.940247\pi$
$422$	2.50225	+	2.77903i	0.121808	+	0.135281i
$423$	−0.709076	−	0.0745269i	−0.0344765	−	0.00362362i
$424$	−4.87217	−	0.512086i	−0.236613	−	0.0248691i
$425$	6.07234	+	6.74402i	0.294552	+	0.327133i
$426$	−1.16507	−	3.58572i	−0.0564478	−	0.173729i
$427$	−19.6473	+	0.185239i	−0.950800	+	0.00896436i
$428$		−	17.8181i		−	0.861272i
$429$	−5.93972	−	12.9107i	−0.286772	−	0.623335i
$430$	3.92892	−	2.26837i	0.189470	−	0.109390i
$431$	2.93053	−	6.58208i	0.141159	−	0.317048i	−0.829107	−	0.559090i	$-0.811151\pi$
$431$	2.93053	−	6.58208i	0.141159	−	0.317048i	0.970266	+	0.242042i	$0.0778173\pi$
$432$	−0.207912	+	0.978148i	−0.0100032	+	0.0470611i
$433$	−36.5631	−	11.8801i	−1.75711	−	0.570920i	−0.760215	−	0.649671i	$-0.774907\pi$
$433$	−36.5631	−	11.8801i	−1.75711	−	0.570920i	−0.996894	+	0.0787517i	$0.974907\pi$
$434$	−11.0234	+	12.4773i	−0.529139	+	0.598929i
$435$	−4.29048	+	5.90534i	−0.205713	+	0.283139i
$436$	−14.3374	+	12.9094i	−0.686636	+	0.618250i
$437$	−4.95467	+	5.50272i	−0.237014	+	0.263231i
$438$	−6.89686	−	3.07068i	−0.329545	−	0.146723i
$439$	1.31427	−	2.27638i	0.0627265	−	0.108646i	−0.832957	−	0.553338i	$-0.813354\pi$
$439$	1.31427	−	2.27638i	0.0627265	−	0.108646i	0.895683	+	0.444693i	$0.146687\pi$
$440$	−1.81463	+	5.82802i	−0.0865092	+	0.277840i
$441$	−4.58500	+	5.28940i	−0.218333	+	0.251876i
$442$	14.1715	+	19.5054i	0.674070	+	0.927778i
$443$	12.9936	+	2.76186i	0.617342	+	0.131220i	0.505959	−	0.862557i	$-0.331139\pi$
$443$	12.9936	+	2.76186i	0.617342	+	0.131220i	0.111383	+	0.993778i	$0.464472\pi$
$444$	−2.08421	−	9.80543i	−0.0989122	−	0.465345i
$445$	0.0691305	−	0.657733i	0.00327710	−	0.0311795i
$446$	9.24610	−	4.11663i	0.437816	−	0.194928i
$447$	4.32204	−	13.3019i	0.204425	−	0.629156i
$448$	2.58263	−	0.574457i	0.122018	−	0.0271405i
$449$	−4.03254	+	2.92981i	−0.190307	+	0.138266i	−0.678859	−	0.734269i	$-0.737525\pi$
$449$	−4.03254	+	2.92981i	−0.190307	+	0.138266i	0.488552	+	0.872535i	$0.337525\pi$
$450$	1.39676	+	0.806421i	0.0658440	+	0.0380150i
$451$	−5.00376	+	5.69673i	−0.235618	+	0.268249i
$452$	0.216067	+	0.374238i	0.0101629	+	0.0176027i
$453$	1.07752	+	10.2519i	0.0506263	+	0.481677i
$454$	−6.31627	+	2.05228i	−0.296437	+	0.0963183i
$455$	−12.4225	−	16.7635i	−0.582376	−	0.785883i
$456$	1.83720	+	1.33480i	0.0860347	+	0.0625078i
$457$	3.86726	+	8.68600i	0.180903	+	0.406314i	0.981121	−	0.193395i	$-0.0619498\pi$
$457$	3.86726	+	8.68600i	0.180903	+	0.406314i	−0.800218	+	0.599709i	$0.795283\pi$
$458$	−9.07923	+	1.92985i	−0.424244	+	0.0901759i
$459$	−4.18145	−	3.76500i	−0.195173	−	0.175735i
$460$	5.96813	−	0.627276i	0.278265	−	0.0292469i
$461$	−31.8656			−1.48413			−0.742064	−	0.670329i	$-0.766153\pi$
$461$	−31.8656			−1.48413			−0.742064	+	0.670329i	$0.766153\pi$
$462$	4.22126	−	7.69292i	0.196391	−	0.357907i
$463$	−15.7767			−0.733207			−0.366603	−	0.930377i	$-0.619479\pi$
$463$	−15.7767			−0.733207			−0.366603	+	0.930377i	$0.619479\pi$
$464$	−3.94443	+	0.414576i	−0.183115	+	0.0192462i
$465$	8.60670	+	7.74951i	0.399126	+	0.359375i
$466$	3.28839	−	0.698968i	0.152331	−	0.0323791i
$467$	2.01437	+	4.52435i	0.0932140	+	0.209362i	0.954135	−	0.299377i	$-0.0967787\pi$
$467$	2.01437	+	4.52435i	0.0932140	+	0.209362i	−0.860921	+	0.508739i	$0.830112\pi$
$468$	3.46658	+	2.51862i	0.160243	+	0.116423i
$469$	−1.20982	−	10.5527i	−0.0558643	−	0.487276i
$470$	1.24797	−	0.405489i	0.0575644	−	0.0187038i
$471$	2.34368	+	22.2986i	0.107991	+	1.02747i
$472$	4.83568	+	8.37564i	0.222580	+	0.385520i
$473$	7.02945	−	4.17467i	0.323215	−	0.191951i
$474$	4.01071	+	2.31558i	0.184218	+	0.106358i
$475$	2.96311	−	2.15282i	0.135957	−	0.0987783i
$476$	−4.46660	+	14.2010i	−0.204726	+	0.650901i
$477$	1.51388	−	4.65923i	0.0693156	−	0.213332i
$478$	13.0435	−	5.80735i	0.596597	−	0.265622i
$479$	2.65122	−	25.2247i	0.121137	−	1.15254i	−0.749977	−	0.661464i	$-0.769936\pi$
$479$	2.65122	−	25.2247i	0.121137	−	1.15254i	0.871114	−	0.491080i	$-0.163398\pi$
$480$	−0.382646	−	1.80021i	−0.0174653	−	0.0821678i
$481$	−42.0156	−	8.93069i	−1.91575	−	0.407204i
$482$	−2.12606	−	2.92627i	−0.0968394	−	0.133288i
$483$	−8.58777	−	0.820830i	−0.390757	−	0.0373491i
$484$	−3.14061	+	10.5421i	−0.142755	+	0.479188i
$485$	4.07079	−	7.05082i	0.184845	−	0.320161i
$486$	−0.913545	−	0.406737i	−0.0414393	−	0.0184499i
$487$	−9.74269	+	10.8204i	−0.441484	+	0.490317i	−0.922284	−	0.386513i	$-0.873679\pi$
$487$	−9.74269	+	10.8204i	−0.441484	+	0.490317i	0.480800	+	0.876830i	$0.340346\pi$
$488$	−5.51883	+	4.96918i	−0.249826	+	0.224944i
$489$	−9.22537	+	12.6976i	−0.417186	+	0.574207i
$490$	3.74933	−	12.3253i	0.169377	−	0.556801i
$491$	−8.02037	−	2.60598i	−0.361954	−	0.117606i	0.122393	−	0.992482i	$-0.460943\pi$
$491$	−8.02037	−	2.60598i	−0.361954	−	0.117606i	−0.484348	+	0.874876i	$0.660943\pi$
$492$	0.475314	−	2.23617i	0.0214288	−	0.100815i
$493$	9.07688	−	20.3870i	0.408802	−	0.918184i
$494$	8.42699	−	4.86532i	0.379148	−	0.218901i
$495$	−5.32338	−	2.98669i	−0.239268	−	0.134242i
$496$			6.29282i			0.282556i
$497$	−5.06879	−	8.59131i	−0.227366	−	0.385373i
$498$	−2.43649	−	7.49876i	−0.109182	−	0.336027i
$499$	19.2370	+	21.3648i	0.861165	+	0.956420i	0.999423	−	0.0339760i	$-0.0108170\pi$
$499$	19.2370	+	21.3648i	0.861165	+	0.956420i	−0.138258	+	0.990396i	$0.544150\pi$
$500$	−12.1038	−	1.27216i	−0.541297	−	0.0568926i
$501$	3.22884	+	0.339365i	0.144254	+	0.0151617i
$502$	13.2018	+	14.6620i	0.589223	+	0.654398i
$503$	−1.98460	−	6.10797i	−0.0884889	−	0.272341i	0.897013	−	0.442004i	$-0.145732\pi$
$503$	−1.98460	−	6.10797i	−0.0884889	−	0.272341i	−0.985502	+	0.169663i	$0.945732\pi$
$504$	0.0249436	+	2.64563i	0.00111108	+	0.117846i
$505$		−	4.44291i		−	0.197707i
$506$	10.7404	−	1.26272i	0.477470	−	0.0561349i
$507$	4.64243	−	2.68031i	0.206178	−	0.119037i
$508$	8.03850	−	18.0548i	0.356651	−	0.801050i
$509$	−2.07445	+	9.75953i	−0.0919485	+	0.432583i	0.907960	+	0.419057i	$0.137639\pi$
$509$	−2.07445	+	9.75953i	−0.0919485	+	0.432583i	−0.999909	+	0.0135267i	$0.995694\pi$
$510$	9.84867	+	3.20003i	0.436107	+	0.141700i
$511$	−19.5760	−	3.96850i	−0.865993	−	0.175556i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−1.68761	+	1.51953i	−0.0745097	+	0.0670889i
$514$	12.4846	−	13.8655i	0.550670	−	0.611581i
$515$	−1.59006	−	0.707938i	−0.0700662	−	0.0311955i
$516$	−1.23252	+	2.13479i	−0.0542588	+	0.0939790i
$517$	2.23979	−	0.758360i	0.0985059	−	0.0333526i
$518$	−11.0155	−	24.1266i	−0.483995	−	1.06006i
$519$	14.2595	+	19.6266i	0.625924	+	0.861510i
$520$	−7.71375	−	1.63961i	−0.338271	−	0.0719016i
$521$	0.852353	+	4.01001i	0.0373423	+	0.175682i	0.992867	−	0.119231i	$-0.0380429\pi$
$521$	0.852353	+	4.01001i	0.0373423	+	0.175682i	−0.955524	+	0.294912i	$0.904710\pi$
$522$	0.414576	−	3.94443i	0.0181455	−	0.172643i
$523$	−2.41769	+	1.07643i	−0.105718	+	0.0470689i	−0.458914	−	0.888480i	$-0.651762\pi$
$523$	−2.41769	+	1.07643i	−0.105718	+	0.0470689i	0.353196	+	0.935549i	$0.385095\pi$
$524$	−2.34322	+	7.21167i	−0.102364	+	0.315043i
$525$	4.07058	+	1.28031i	0.177655	+	0.0558773i
$526$	−7.72656	+	5.61368i	−0.336894	+	0.244768i
$527$	−30.6641	−	17.7039i	−1.33575	−	0.771194i
$528$	−0.729448	−	3.23541i	−0.0317452	−	0.140803i
$529$	6.18403	+	10.7111i	0.268871	+	0.465698i
$530$	0.942454	+	8.96685i	0.0409376	+	0.389495i
$531$	−9.19800	+	2.98861i	−0.399159	+	0.129695i
$532$	5.51159	+	2.39191i	0.238958	+	0.103703i
$533$	−7.92506	−	5.75789i	−0.343272	−	0.249402i
$534$	0.146161	+	0.328282i	0.00632499	+	0.0142062i
$535$	−32.0763	+	6.81803i	−1.38678	+	0.294769i
$536$	−2.98347	−	2.68633i	−0.128866	−	0.116032i
$537$	23.7783	−	2.49920i	1.02611	−	0.107848i
$538$	28.6918			1.23699
$539$	6.48273	−	22.2929i	0.279231	−	0.960224i
$540$	1.84042			0.0791992
$541$	−35.1778	+	3.69733i	−1.51241	+	0.158961i	−0.824095	−	0.566451i	$-0.808316\pi$
$541$	−35.1778	+	3.69733i	−1.51241	+	0.158961i	−0.688315	+	0.725412i	$0.741649\pi$
$542$	−13.6021	−	12.2474i	−0.584261	−	0.526071i
$543$	21.9858	−	4.67324i	0.943503	−	0.200548i
$544$	2.28858	+	5.14025i	0.0981223	+	0.220386i
$545$	28.7258	+	20.8705i	1.23048	+	0.893994i
$546$	10.3997	+	4.51327i	0.445068	+	0.193150i
$547$	27.2555	−	8.85585i	1.16536	−	0.378649i	0.338452	−	0.940984i	$-0.390097\pi$
$547$	27.2555	−	8.85585i	1.16536	−	0.378649i	0.826910	+	0.562335i	$0.190097\pi$
$548$	2.05869	+	19.5871i	0.0879430	+	0.836721i
$549$	−3.71316	−	6.43138i	−0.158474	−	0.274485i
$550$	−5.32637	−	0.493613i	−0.227117	−	0.0210477i
$551$	−7.80007	−	4.50337i	−0.332294	−	0.191850i
$552$	−2.63793	+	1.91657i	−0.112278	+	0.0815746i
$553$	11.6884	+	3.67633i	0.497041	+	0.156333i
$554$	2.17629	−	6.69794i	0.0924618	−	0.284568i
$555$	−16.8543	+	7.50401i	−0.715425	+	0.318528i
$556$	0.152439	−	1.45036i	0.00646484	−	0.0615088i
$557$	−4.45540	−	20.9610i	−0.188781	−	0.888146i	−0.965925	−	0.258823i	$-0.916665\pi$
$557$	−4.45540	−	20.9610i	−0.188781	−	0.888146i	0.777144	−	0.629323i	$-0.216668\pi$
$558$	−6.15531	−	1.30835i	−0.260575	−	0.0553869i
$559$	6.20851	+	8.54528i	0.262592	+	0.361427i
$560$	−2.02237	−	4.42946i	−0.0854609	−	0.187179i
$561$	17.8179	+	5.54785i	0.752274	+	0.234230i
$562$	2.87024	−	4.97140i	0.121074	−	0.209706i
$563$	−22.4107	−	9.97790i	−0.944499	−	0.420518i	−0.124075	−	0.992273i	$-0.539596\pi$
$563$	−22.4107	−	9.97790i	−0.944499	−	0.420518i	−0.820425	+	0.571755i	$0.806263\pi$
$564$	−0.477078	+	0.529849i	−0.0200886	+	0.0223107i
$565$	0.591029	−	0.532165i	0.0248648	−	0.0223883i
$566$	−18.7230	+	25.7699i	−0.786985	+	1.08319i
$567$	−2.59301	−	0.525660i	−0.108896	−	0.0220756i
$568$	−3.58572	−	1.16507i	−0.150453	−	0.0488852i
$569$	4.16835	−	19.6105i	0.174746	−	0.822117i	−0.800210	−	0.599720i	$-0.795279\pi$
$569$	4.16835	−	19.6105i	0.174746	−	0.822117i	0.974956	−	0.222397i	$-0.0713880\pi$
$570$	1.69992	−	3.81809i	0.0712019	−	0.159922i
$571$	30.5133	−	17.6169i	1.27694	−	0.737244i	0.300658	−	0.953732i	$-0.402794\pi$
$571$	30.5133	−	17.6169i	1.27694	−	0.737244i	0.976285	+	0.216488i	$0.0694603\pi$
$572$	−13.9363	−	2.78339i	−0.582705	−	0.116380i
$573$			19.8611i			0.829711i
$574$	−0.0570244	−	6.04827i	−0.00238015	−	0.252450i
$575$	1.62510	+	5.00154i	0.0677714	+	0.208579i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	33.2604	+	3.49581i	1.38465	+	0.145533i	0.767367	−	0.641209i	$-0.221567\pi$
$577$	33.2604	+	3.49581i	1.38465	+	0.145533i	0.617283	+	0.786741i	$0.288233\pi$
$578$	−14.5794	−	1.53236i	−0.606425	−	0.0637378i
$579$	−16.6194	−	18.4577i	−0.690680	−	0.767077i
$580$	2.25564	+	6.94214i	0.0936603	+	0.288257i
$581$	−10.6003	−	17.9669i	−0.439774	−	0.745392i
$582$			4.42376i			0.183371i
$583$	1.89719	+	16.1370i	0.0785734	+	0.668327i
$584$	−6.53811	+	3.77478i	−0.270549	+	0.156201i
$585$	3.20756	−	7.20430i	0.132616	−	0.297861i
$586$	−0.271333	+	1.27652i	−0.0112087	+	0.0527327i
$587$	−20.3720	−	6.61926i	−0.840841	−	0.273206i	−0.143236	−	0.989688i	$-0.545751\pi$
$587$	−20.3720	−	6.61926i	−0.840841	−	0.273206i	−0.697605	+	0.716483i	$0.745751\pi$
$588$	1.58422	+	6.81838i	0.0653322	+	0.281185i
$589$	−8.39967	+	11.5612i	−0.346102	+	0.476369i
$590$	13.2275	−	11.9101i	0.544568	−	0.490332i
$591$	14.5083	−	16.1131i	0.596790	−	0.662803i
$592$	−9.15783	−	4.07733i	−0.376384	−	0.167577i
$593$	−21.2473	+	36.8014i	−0.872523	+	1.51125i	−0.0131439	+	0.999914i	$0.504184\pi$
$593$	−21.2473	+	36.8014i	−0.872523	+	1.51125i	−0.859379	+	0.511340i	$0.829149\pi$
$594$	3.31637	−	0.0408275i	0.136072	−	0.00167517i
$595$	27.2738	+	2.60687i	1.11812	+	0.106871i
$596$	−8.22100	−	11.3152i	−0.336745	−	0.463490i
$597$	16.1313	+	3.42882i	0.660211	+	0.140332i
$598$	2.90488	+	13.6664i	0.118789	+	0.558861i
$599$	−1.02000	+	9.70469i	−0.0416762	+	0.396523i	0.953721	+	0.300692i	$0.0972175\pi$
$599$	−1.02000	+	9.70469i	−0.0416762	+	0.396523i	−0.995398	+	0.0958311i	$0.969449\pi$
$600$	1.47340	−	0.656002i	0.0601515	−	0.0267812i
$601$	−2.53121	+	7.79027i	−0.103250	+	0.317772i	−0.989316	−	0.145788i	$-0.953428\pi$
$601$	−2.53121	+	7.79027i	−0.103250	+	0.317772i	0.886066	+	0.463560i	$0.153428\pi$
$602$	−1.95681	+	6.22142i	−0.0797537	+	0.253566i
$603$	3.24792	−	2.35976i	0.132266	−	0.0960967i
$604$	8.92732	+	5.15419i	0.363247	+	0.209721i
$605$	20.1797	+	1.61985i	0.820423	+	0.0658562i
$606$	1.20704	+	2.09065i	0.0490325	+	0.0849267i
$607$	0.660865	+	6.28771i	0.0268237	+	0.255210i	0.999713	+	0.0239406i	$0.00762125\pi$
$607$	0.660865	+	6.28771i	0.0268237	+	0.255210i	−0.972890	+	0.231270i	$0.925712\pi$
$608$	2.15976	−	0.701747i	0.0875896	−	0.0284596i
$609$	−1.19520	−	10.4252i	−0.0484321	−	0.422449i
$610$	11.0573	+	8.03359i	0.447697	+	0.325271i
$611$	1.24261	+	2.79095i	0.0502707	+	0.112910i
$612$	−5.50374	+	1.16986i	−0.222476	+	0.0472886i
$613$	14.9748	+	13.4834i	0.604826	+	0.544588i	0.913634	−	0.406537i	$-0.133264\pi$
$613$	14.9748	+	13.4834i	0.604826	+	0.544588i	−0.308809	+	0.951124i	$0.599930\pi$
$614$	28.2930	−	2.97371i	1.14181	−	0.120009i
$615$	−4.20745			−0.169661
$616$	−3.74250	−	7.93686i	−0.150790	−	0.319785i
$617$	−15.2086			−0.612276			−0.306138	−	0.951987i	$-0.599037\pi$
$617$	−15.2086			−0.612276			−0.306138	+	0.951987i	$0.599037\pi$
$618$	0.940543	−	0.0988551i	0.0378342	−	0.00397653i
$619$	−20.5261	−	18.4818i	−0.825013	−	0.742845i	0.144073	−	0.989567i	$-0.453980\pi$
$619$	−20.5261	−	18.4818i	−0.825013	−	0.742845i	−0.969086	+	0.246722i	$0.920647\pi$
$620$	11.3284	−	2.40792i	0.454958	−	0.0967044i
$621$	−1.32623	−	2.97876i	−0.0532198	−	0.119534i
$622$	−4.81565	−	3.49877i	−0.193090	−	0.140288i
$623$	0.566064	+	0.763870i	0.0226789	+	0.0306038i
$624$	4.07521	−	1.32412i	0.163139	−	0.0530071i
$625$	1.49837	+	14.2560i	0.0599347	+	0.570240i
$626$	−5.16605	−	8.94786i	−0.206477	−	0.357628i
$627$	2.97850	−	6.91776i	0.118950	−	0.276269i
$628$	19.4176	+	11.2107i	0.774845	+	0.447357i
$629$	45.6324	−	33.1539i	1.81948	−	1.32193i
$630$	4.75314	−	1.05724i	0.189370	−	0.0421216i
$631$	−8.69646	+	26.7650i	−0.346201	+	1.06550i	0.614737	+	0.788732i	$0.289262\pi$
$631$	−8.69646	+	26.7650i	−0.346201	+	1.06550i	−0.960938	+	0.276764i	$0.910738\pi$
$632$	4.23078	−	1.88366i	0.168291	−	0.0749281i
$633$	−0.390890	+	3.71907i	−0.0155365	+	0.147820i
$634$	4.02094	+	18.9170i	0.159692	+	0.751291i
$635$	−35.5782	−	7.56237i	−1.41188	−	0.300104i
$636$	−2.87956	−	3.96338i	−0.114182	−	0.157158i
$637$	29.4514	+	5.68192i	1.16691	+	0.225126i
$638$	4.21858	+	12.4594i	0.167015	+	0.493274i
$639$	1.88512	−	3.26513i	0.0745743	−	0.129166i
$640$	−1.68131	−	0.748568i	−0.0664596	−	0.0295897i
$641$	25.9702	−	28.8428i	1.02576	−	1.13922i	0.0355872	−	0.999367i	$-0.488670\pi$
$641$	25.9702	−	28.8428i	1.02576	−	1.13922i	0.990172	−	0.139854i	$-0.0446635\pi$
$642$	13.2415	−	11.9227i	0.522599	−	0.470550i
$643$	−7.61578	+	10.4822i	−0.300337	+	0.413379i	−0.932337	−	0.361590i	$-0.882234\pi$
$643$	−7.61578	+	10.4822i	−0.300337	+	0.413379i	0.632000	+	0.774968i	$0.282234\pi$
$644$	−5.71183	+	6.46518i	−0.225078	+	0.254764i
$645$	4.31469	+	1.40193i	0.169891	+	0.0552008i
$646$	−2.65663	+	12.4985i	−0.104524	+	0.491745i
$647$	3.38991	−	7.61386i	0.133271	−	0.299332i	−0.834567	−	0.550907i	$-0.814282\pi$
$647$	3.38991	−	7.61386i	0.133271	−	0.299332i	0.967838	+	0.251575i	$0.0809486\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	23.5713	−	21.7550i	0.925254	−	0.853959i
$650$		−	6.91091i		−	0.271068i
$651$	−16.6485	+	0.156966i	−0.652506	+	0.00615198i
$652$	4.85007	+	14.9270i	0.189943	+	0.584585i
$653$	20.0361	+	22.2524i	0.784075	+	0.870803i	0.994275	−	0.106855i	$-0.0340782\pi$
$653$	20.0361	+	22.2524i	0.784075	+	0.870803i	−0.210200	+	0.977658i	$0.567412\pi$
$654$	−19.1872	−	2.01665i	−0.750277	−	0.0788573i
$655$	13.8791	+	1.45875i	0.542302	+	0.0569982i
$656$	−1.52972	−	1.69893i	−0.0597256	−	0.0663320i
$657$	−2.33294	−	7.18005i	−0.0910167	−	0.280121i
$658$	−0.927743	+	1.64247i	−0.0361672	+	0.0640300i
$659$			31.2237i			1.21630i	0.793822	+	0.608151i	$0.208088\pi$
$659$			31.2237i			1.21630i	−0.793822	+	0.608151i	$0.791912\pi$
$660$	−5.54529	+	2.55117i	−0.215850	+	0.0993043i
$661$	−20.2888	+	11.7137i	−0.789142	+	0.455611i	−0.839660	−	0.543112i	$-0.817246\pi$
$661$	−20.2888	+	11.7137i	−0.789142	+	0.455611i	0.0505185	+	0.998723i	$0.483913\pi$
$662$	−2.33582	+	5.24634i	−0.0907842	+	0.203905i
$663$	−5.01275	+	23.5831i	−0.194679	+	0.915894i
$664$	−7.49876	−	2.43649i	−0.291008	−	0.0945543i
$665$	2.19695	−	10.8373i	0.0851941	−	0.420251i
$666$	5.89225	−	8.10998i	0.228320	−	0.314256i
$667$	9.61057	−	8.65339i	0.372123	−	0.335061i
$668$	2.17242	−	2.41271i	0.0840533	−	0.0933507i
$669$	9.24610	+	4.11663i	0.357475	+	0.159158i
$670$	−3.69433	+	6.39877i	−0.142725	+	0.247206i
$671$	20.1030	+	14.2309i	0.776069	+	0.549379i
$672$	2.15502	+	1.53488i	0.0831319	+	0.0592095i
$673$	−11.8692	−	16.3366i	−0.457525	−	0.629730i	0.516468	−	0.856307i	$-0.327247\pi$
$673$	−11.8692	−	16.3366i	−0.457525	−	0.629730i	−0.973993	+	0.226577i	$0.927247\pi$
$674$	−16.4740	−	3.50166i	−0.634555	−	0.134879i
$675$	0.335329	+	1.57760i	0.0129068	+	0.0607217i
$676$	0.560337	−	5.33125i	0.0215514	−	0.205048i
$677$	10.1466	−	4.51755i	0.389965	−	0.173624i	−0.202382	−	0.979307i	$-0.564868\pi$
$677$	10.1466	−	4.51755i	0.389965	−	0.173624i	0.592347	+	0.805683i	$0.298202\pi$
$678$	−0.133536	+	0.410983i	−0.00512844	+	0.0157837i
$679$	2.54126	+	11.4249i	0.0975245	+	0.438449i
$680$	8.37778	−	6.08682i	0.321273	−	0.233419i
$681$	−5.75155	−	3.32066i	−0.220400	−	0.127248i
$682$	20.3599	−	4.59029i	0.779620	−	0.175771i
$683$	−1.73859	−	3.01132i	−0.0665252	−	0.115225i	0.830844	−	0.556505i	$-0.187858\pi$
$683$	−1.73859	−	3.01132i	−0.0665252	−	0.115225i	−0.897370	+	0.441280i	$0.854525\pi$
$684$	0.237374	+	2.25846i	0.00907621	+	0.0863544i
$685$	34.4731	−	11.2010i	1.31715	−	0.427968i
$686$	8.00833	+	16.6993i	0.305759	+	0.637582i
$687$	−7.50935	−	5.45586i	−0.286499	−	0.208154i
$688$	1.00262	+	2.25193i	0.0382247	+	0.0858541i
$689$	−20.5332	+	4.36446i	−0.782252	+	0.166273i
$690$	4.45961	+	4.01545i	0.169775	+	0.152866i
$691$	19.4132	−	2.04041i	0.738515	−	0.0776210i	0.272201	−	0.962240i	$-0.412248\pi$
$691$	19.4132	−	2.04041i	0.738515	−	0.0776210i	0.466314	+	0.884619i	$0.345582\pi$
$692$	24.2598			0.922218
$693$	8.54153	−	2.01056i	0.324466	−	0.0763747i
$694$	−6.28751			−0.238671
$695$	−2.66927	+	0.280552i	−0.101251	+	0.0106419i
$696$	−2.94743	−	2.65387i	−0.111722	−	0.100595i
$697$	12.5823	−	2.67445i	0.476588	−	0.101302i
$698$	−13.1940	−	29.6342i	−0.499400	−	1.12167i
$699$	2.71979	+	1.97605i	0.102872	+	0.0747409i
$700$	3.42842	−	2.54062i	0.129582	−	0.0960264i
$701$	17.3574	−	5.63977i	0.655581	−	0.213011i	0.0377075	−	0.999289i	$-0.487994\pi$
$701$	17.3574	−	5.63977i	0.655581	−	0.213011i	0.617873	+	0.786278i	$0.287994\pi$
$702$	0.447897	+	4.26146i	0.0169048	+	0.160838i
$703$	−11.3823	−	19.7147i	−0.429292	−	0.743556i
$704$	−3.04626	−	1.31159i	−0.114810	−	0.0494325i
$705$	1.13639	+	0.656094i	0.0427989	+	0.0247099i
$706$	−25.9806	+	18.8760i	−0.977793	+	0.710408i
$707$	4.31832	+	4.70599i	0.162407	+	0.176987i
$708$	−2.98861	+	9.19800i	−0.112319	+	0.345682i
$709$	45.2002	−	20.1244i	1.69753	−	0.755789i	0.698332	−	0.715774i	$-0.253926\pi$
$709$	45.2002	−	20.1244i	1.69753	−	0.755789i	0.999199	−	0.0400149i	$-0.0127405\pi$
$710$	−0.725307	+	6.90084i	−0.0272203	+	0.258984i
$711$	0.962873	+	4.52996i	0.0361106	+	0.169887i
$712$	0.351497	+	0.0747130i	0.0131729	+	0.00279999i
$713$	−12.0606	−	16.6000i	−0.451674	−	0.621676i
$714$	−13.5421	+	6.18297i	−0.506801	+	0.231392i
$715$	0.321969	+	26.1532i	0.0120410	+	0.978074i
$716$	11.9546	−	20.7060i	0.446765	−	0.773820i
$717$	13.0435	+	5.80735i	0.487119	+	0.216880i
$718$	22.4374	−	24.9193i	0.837357	−	0.929979i
$719$	−14.6045	+	13.1499i	−0.544655	+	0.490410i	−0.894911	−	0.446244i	$-0.852761\pi$
$719$	−14.6045	+	13.1499i	−0.544655	+	0.490410i	0.350256	+	0.936654i	$0.386095\pi$
$720$	1.08177	−	1.48893i	0.0403153	−	0.0554893i
$721$	2.37229	−	0.795608i	0.0883487	−	0.0296300i
$722$	−13.1655	−	4.27773i	−0.489969	−	0.159200i
$723$	0.752031	−	3.53803i	0.0279683	−	0.131581i
$724$	9.14223	−	20.5338i	0.339768	−	0.763132i
$725$	−5.53977	+	3.19839i	−0.205742	+	0.118785i
$726$	−9.93581	+	4.72013i	−0.368753	+	0.175181i
$727$		−	20.6608i		−	0.766266i	−0.923693	−	0.383133i	$-0.874845\pi$
$727$		−	20.6608i		−	0.766266i	0.923693	−	0.383133i	$-0.125155\pi$
$728$	9.76413	−	5.76074i	0.361883	−	0.213507i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	9.29716	+	10.3255i	0.344103	+	0.382165i
$731$	−13.7941	−	1.44982i	−0.510193	−	0.0536235i
$732$	−7.38563	−	0.776261i	−0.272981	−	0.0286914i
$733$	7.10655	+	7.89262i	0.262486	+	0.291521i	0.859953	−	0.510373i	$-0.170493\pi$
$733$	7.10655	+	7.89262i	0.262486	+	0.291521i	−0.597467	+	0.801894i	$0.703826\pi$
$734$	−11.0250	−	33.9315i	−0.406940	−	1.25243i
$735$	11.6683	−	5.46095i	0.430391	−	0.201430i
$736$			3.26066i			0.120190i
$737$	−6.51510	+	11.6123i	−0.239987	+	0.427745i
$738$	1.97985	−	1.14307i	0.0728792	−	0.0420768i
$739$	15.4290	−	34.6541i	0.567565	−	1.27477i	−0.370667	−	0.928766i	$-0.620871\pi$
$739$	15.4290	−	34.6541i	0.567565	−	1.27477i	0.938232	−	0.346007i	$-0.112463\pi$
$740$	−3.83583	+	18.0461i	−0.141008	+	0.663390i
$741$	9.25440	+	3.00694i	0.339969	+	0.110463i
$742$	−9.71365	−	8.58177i	−0.356599	−	0.315047i
$743$	−18.7334	+	25.7843i	−0.687263	+	0.945936i	−0.999992	−	0.00390627i	$-0.998757\pi$
$743$	−18.7334	+	25.7843i	−0.687263	+	0.945936i	0.312730	+	0.949842i	$0.398757\pi$
$744$	−4.67648	+	4.21072i	−0.171448	+	0.154372i
$745$	−17.2240	+	19.1292i	−0.631039	+	0.700840i
$746$	8.02099	+	3.57117i	0.293669	+	0.130750i
$747$	3.94233	−	6.82832i	0.144242	−	0.249835i
$748$	14.9614	−	11.1541i	0.547044	−	0.407833i
$749$	27.3488	−	38.3985i	0.999303	−	1.40305i
$750$	−7.15360	−	9.84608i	−0.261212	−	0.359528i
$751$	−7.43439	−	1.58023i	−0.271285	−	0.0576634i	0.0702605	−	0.997529i	$-0.477617\pi$
$751$	−7.43439	−	1.58023i	−0.271285	−	0.0576634i	−0.341545	+	0.939865i	$0.610950\pi$
$752$	0.148237	+	0.697402i	0.00540566	+	0.0254316i
$753$	−2.06232	+	19.6216i	−0.0751550	+	0.715052i
$754$	−15.5254	+	6.91236i	−0.565402	+	0.251733i
$755$	5.86260	−	18.0432i	0.213362	−	0.656661i
$756$	−1.94940	+	1.78881i	−0.0708989	+	0.0650584i
$757$	10.2587	−	7.45339i	0.372859	−	0.270898i	−0.385536	−	0.922693i	$-0.625984\pi$
$757$	10.2587	−	7.45339i	0.372859	−	0.270898i	0.758396	+	0.651795i	$0.225984\pi$
$758$	6.96129	+	4.01910i	0.252846	+	0.145980i
$759$	8.12513	+	7.13677i	0.294924	+	0.259048i
$760$	−2.08971	−	3.61948i	−0.0758017	−	0.131292i
$761$	0.998263	+	9.49784i	0.0361870	+	0.344296i	0.997603	+	0.0691976i	$0.0220439\pi$
$761$	0.998263	+	9.49784i	0.0361870	+	0.344296i	−0.961416	+	0.275099i	$0.911289\pi$
$762$	18.7961	−	6.10722i	0.680911	−	0.221241i
$763$	−50.7119	+	5.81392i	−1.83589	+	0.210478i
$764$	16.0680	+	11.6741i	0.581320	+	0.422354i
$765$	4.21197	+	9.46023i	0.152284	+	0.342035i
$766$	20.1535	−	4.28375i	0.728174	−	0.154778i
$767$	30.7967	+	27.7295i	1.11200	+	1.00125i
$768$	0.994522	−	0.104528i	0.0358867	−	0.00377185i
$769$	31.7614			1.14535			0.572673	−	0.819784i	$-0.305906\pi$
$769$	31.7614			1.14535			0.572673	+	0.819784i	$0.305906\pi$
$770$	−12.8559	+	9.77428i	−0.463295	+	0.352241i
$771$	18.6579			0.671947
$772$	−24.7013	+	2.59621i	−0.889018	+	0.0934396i
$773$	−12.5388	−	11.2900i	−0.450990	−	0.406073i	0.412088	−	0.911144i	$-0.364800\pi$
$773$	−12.5388	−	11.2900i	−0.450990	−	0.406073i	−0.863078	+	0.505071i	$0.831466\pi$
$774$	−2.41118	+	0.512512i	−0.0866681	+	0.0184219i
$775$	4.12810	+	9.27187i	0.148286	+	0.333055i
$776$	3.57889	+	2.60022i	0.128475	+	0.0933424i
$777$	10.5587	−	24.3300i	0.378791	−	0.872833i
$778$	−21.5972	+	7.01737i	−0.774299	+	0.251585i
$779$	−0.542668	−	5.16314i	−0.0194431	−	0.184989i
$780$	−3.94304	−	6.82955i	−0.141184	−	0.244537i
$781$	−1.15389	+	12.4511i	−0.0412894	+	0.445537i
$782$	−15.8888	−	9.17339i	−0.568181	−	0.328040i
$783$	3.20869	−	2.33125i	0.114669	−	0.0833120i
$784$	6.44736	+	2.72608i	0.230263	+	0.0973599i
$785$	12.7516	−	39.2454i	0.455124	−	1.40073i
$786$	−6.92724	+	3.08420i	−0.247086	+	0.110010i
$787$	2.95127	−	28.0795i	0.105201	−	1.00092i	−0.806824	−	0.590791i	$-0.798816\pi$
$787$	2.95127	−	28.0795i	0.105201	−	1.00092i	0.912026	−	0.410133i	$-0.134518\pi$
$788$	−4.50800	−	21.2085i	−0.160591	−	0.755520i
$789$	−9.34185	−	1.98567i	−0.332579	−	0.0706918i
$790$	−5.00987	−	6.89550i	−0.178243	−	0.245331i
$791$	−0.108784	+	1.13813i	−0.00386791	+	0.0404672i
$792$	1.91629	−	2.70700i	0.0680922	−	0.0961891i
$793$	−15.9106	+	27.5580i	−0.565003	+	0.978613i
$794$	−23.3461	−	10.3943i	−0.828521	−	0.368881i
$795$	−6.03305	+	6.70038i	−0.213970	+	0.237638i
$796$	12.2557	−	11.0351i	0.434393	−	0.391129i
$797$	−20.8013	+	28.6306i	−0.736820	+	1.01415i	0.261975	+	0.965075i	$0.415626\pi$
$797$	−20.8013	+	28.6306i	−0.736820	+	1.01415i	−0.998795	+	0.0490716i	$0.984374\pi$
$798$	1.91044	+	5.69642i	0.0676288	+	0.201651i
$799$	−3.81539	−	1.23969i	−0.134979	−	0.0438572i
$800$	0.335329	−	1.57760i	0.0118557	−	0.0557765i
$801$	−0.146161	+	0.328282i	−0.00516433	+	0.0115993i
$802$	17.6212	−	10.1736i	0.622227	−	0.359243i
$803$	16.9822	+	18.4000i	0.599288	+	0.649321i
$804$		−	4.01466i		−	0.141586i
$805$	13.8243	+	7.80860i	0.487241	+	0.275217i
$806$	8.33243	+	25.6446i	0.293497	+	0.903291i
$807$	19.1985	+	21.3221i	0.675821	+	0.750575i
$808$	2.40085	+	0.252339i	0.0844615	+	0.00887726i
$809$	33.6640	+	3.53823i	1.18356	+	0.124398i	0.675791	−	0.737093i	$-0.263802\pi$
$809$	33.6640	+	3.53823i	1.18356	+	0.124398i	0.507773	+	0.861491i	$0.330469\pi$
$810$	1.23148	+	1.36770i	0.0432699	+	0.0480561i
$811$	7.97308	+	24.5386i	0.279973	+	0.861668i	0.987861	+	0.155343i	$0.0496482\pi$
$811$	7.97308	+	24.5386i	0.279973	+	0.861668i	−0.707888	+	0.706325i	$0.750352\pi$
$812$	−9.13666	−	5.16082i	−0.320634	−	0.181109i
$813$		−	18.3035i		−	0.641930i
$814$	−6.51168	+	32.6036i	−0.228234	+	1.14275i
$815$	25.0158	−	14.4429i	0.876264	−	0.505911i
$816$	−2.28858	+	5.14025i	−0.0801165	+	0.179945i
$817$	−1.16386	+	5.47555i	−0.0407185	+	0.191565i
$818$	−4.75785	−	1.54592i	−0.166354	−	0.0540518i
$819$	3.60478	+	10.7485i	0.125961	+	0.375582i
$820$	−2.47308	+	3.40390i	−0.0863636	+	0.118869i
$821$	27.5177	−	24.7770i	0.960374	−	0.864724i	−0.0304976	−	0.999535i	$-0.509709\pi$
$821$	27.5177	−	24.7770i	0.960374	−	0.864724i	0.990871	+	0.134810i	$0.0430425\pi$
$822$	−13.1786	+	14.6363i	−0.459655	+	0.510498i
$823$	19.6691	+	8.75724i	0.685621	+	0.305258i	0.719824	−	0.694157i	$-0.244223\pi$
$823$	19.6691	+	8.75724i	0.685621	+	0.305258i	−0.0342028	+	0.999415i	$0.510889\pi$
$824$	0.472862	−	0.819021i	0.0164729	−	0.0285319i
$825$	−3.19721	−	4.28855i	−0.111313	−	0.149308i
$826$	−2.43464	+	25.4719i	−0.0847119	+	0.886281i
$827$	−15.7008	−	21.6102i	−0.545969	−	0.751462i	0.443489	−	0.896280i	$-0.353740\pi$
$827$	−15.7008	−	21.6102i	−0.545969	−	0.751462i	−0.989458	+	0.144818i	$0.953740\pi$
$828$	−3.18941	−	0.677930i	−0.110840	−	0.0235597i
$829$	−10.9274	−	51.4092i	−0.379523	−	1.78552i	−0.589456	−	0.807800i	$-0.700658\pi$
$829$	−10.9274	−	51.4092i	−0.379523	−	1.78552i	0.209933	−	0.977716i	$-0.432675\pi$
$830$	−1.51682	+	14.4316i	−0.0526497	+	0.500929i
$831$	6.43376	−	2.86449i	0.223185	−	0.0993682i
$832$	1.32412	−	4.07521i	0.0459055	−	0.141282i
$833$	−31.4225	+	23.7477i	−1.08872	+	0.822810i
$834$	1.17983	−	0.857194i	0.0408541	−	0.0296822i
$835$	−5.17465	−	2.98758i	−0.179076	−	0.103390i
$836$	−3.84587	−	6.47581i	−0.133012	−	0.223971i
$837$	−3.14641	−	5.44974i	−0.108756	−	0.188371i
$838$	2.59091	+	24.6509i	0.0895015	+	0.851550i
$839$	12.1771	−	3.95659i	0.420402	−	0.136597i	−0.0911740	−	0.995835i	$-0.529062\pi$
$839$	12.1771	−	3.95659i	0.420402	−	0.136597i	0.511576	+	0.859238i	$0.329062\pi$
$840$	1.93850	−	4.46680i	0.0668845	−	0.154119i
$841$	−10.7354	−	7.79969i	−0.370185	−	0.268955i
$842$	−2.10478	−	4.72740i	−0.0725353	−	0.162917i
$843$	5.61504	−	1.19351i	0.193392	−	0.0411068i
$844$	2.77903	+	2.50225i	0.0956583	+	0.0861311i
$845$	−9.81176	+	1.03126i	−0.337535	+	0.0354763i
$846$	−0.712982			−0.0245128
$847$	−22.9491	+	17.8981i	−0.788539	+	0.614985i
$848$	−4.89901			−0.168233
$849$	−31.6789	+	3.32959i	−1.08722	+	0.114271i
$850$	6.74402	+	6.07234i	0.231318	+	0.208280i
$851$	31.9722	−	6.79591i	1.09599	−	0.232961i
$852$	−1.53350	−	3.44429i	−0.0525367	−	0.117999i
$853$	15.1908	+	11.0368i	0.520123	+	0.377892i	0.816650	−	0.577133i	$-0.195828\pi$
$853$	15.1908	+	11.0368i	0.520123	+	0.377892i	−0.296527	+	0.955024i	$0.595828\pi$
$854$	−19.5203	+	2.23793i	−0.667972	+	0.0765803i
$855$	3.97486	−	1.29151i	0.135937	−	0.0441688i
$856$	−1.86250	−	17.7205i	−0.0636590	−	0.605675i
$857$	−0.300328	−	0.520183i	−0.0102590	−	0.0177691i	0.860850	−	0.508858i	$-0.169932\pi$
$857$	−0.300328	−	0.520183i	−0.0102590	−	0.0177691i	−0.871109	+	0.491089i	$0.836599\pi$
$858$	−7.25672	−	12.2191i	−0.247740	−	0.417154i
$859$	15.3642	+	8.87055i	0.524221	+	0.302659i	0.738660	−	0.674078i	$-0.235459\pi$
$859$	15.3642	+	8.87055i	0.524221	+	0.302659i	−0.214439	+	0.976737i	$0.568792\pi$
$860$	3.67029	−	2.66662i	0.125156	−	0.0909311i
$861$	4.45658	−	4.08946i	0.151880	−	0.139368i
$862$	2.22646	−	6.85235i	0.0758336	−	0.233392i
$863$	−25.7804	+	11.4782i	−0.877575	+	0.390721i	−0.795535	−	0.605908i	$-0.792810\pi$
$863$	−25.7804	+	11.4782i	−0.877575	+	0.390721i	−0.0820396	+	0.996629i	$0.526143\pi$
$864$	−0.104528	+	0.994522i	−0.00355613	+	0.0338343i
$865$	−9.28289	−	43.6726i	−0.315628	−	1.48491i
$866$	−37.6046	−	7.99310i	−1.27786	−	0.271617i
$867$	−8.61678	−	11.8600i	−0.292641	−	0.402786i
$868$	−9.65876	+	13.5612i	−0.327840	+	0.460297i
$869$	−9.18057	−	12.3143i	−0.311429	−	0.417734i
$870$	−3.64970	+	6.32147i	−0.123736	+	0.214318i
$871$	−15.7153	−	6.99689i	−0.532492	−	0.237081i
$872$	−12.9094	+	14.3374i	−0.437169	+	0.485525i
$873$	−3.28749	+	2.96007i	−0.111265	+	0.100183i
$874$	−4.35234	+	5.99048i	−0.147220	+	0.202631i
$875$	−24.1313	−	21.3194i	−0.815786	−	0.720727i
$876$	−7.18005	−	2.33294i	−0.242592	−	0.0788228i
$877$	3.97679	−	18.7093i	0.134287	−	0.631770i	−0.858594	−	0.512656i	$-0.828661\pi$
$877$	3.97679	−	18.7093i	0.134287	−	0.631770i	0.992881	−	0.119113i	$-0.0380052\pi$
$878$	1.06912	−	2.40128i	0.0360811	−	0.0810394i
$879$	−1.13020	+	0.652521i	−0.0381207	+	0.0220090i
$880$	−1.19550	+	5.98578i	−0.0403002	+	0.201781i
$881$		−	35.2030i		−	1.18602i	−0.805195	−	0.593010i	$-0.797940\pi$
$881$		−	35.2030i		−	1.18602i	0.805195	−	0.593010i	$-0.202060\pi$
$882$	−4.00699	+	5.73969i	−0.134922	+	0.193265i
$883$	−0.236841	−	0.728923i	−0.00797034	−	0.0245302i	0.946992	−	0.321256i	$-0.104105\pi$
$883$	−0.236841	−	0.728923i	−0.00797034	−	0.0245302i	−0.954963	+	0.296726i	$0.904105\pi$
$884$	16.1327	+	17.9172i	0.542603	+	0.602622i
$885$	17.7019	+	1.86054i	0.595042	+	0.0625414i
$886$	13.2111	+	1.38854i	0.443834	+	0.0466489i
$887$	12.2603	+	13.6165i	0.411661	+	0.457196i	0.912942	−	0.408088i	$-0.133804\pi$
$887$	12.2603	+	13.6165i	0.411661	+	0.457196i	−0.501281	+	0.865284i	$0.667138\pi$
$888$	−3.09774	−	9.53386i	−0.103953	−	0.319935i
$889$	45.0351	−	26.5703i	1.51043	−	0.891138i
$890$		−	0.661356i		−	0.0221687i
$891$	2.24943	+	2.43723i	0.0753587	+	0.0816502i
$892$	8.76515	−	5.06056i	0.293479	−	0.169440i
$893$	−0.658552	+	1.47913i	−0.0220376	+	0.0494973i
$894$	2.90794	−	13.6808i	0.0972559	−	0.457553i
$895$	−41.8495	−	13.5977i	−1.39887	−	0.454522i
$896$	2.50844	−	0.841269i	0.0838011	−	0.0281048i
$897$	−8.21237	+	11.3034i	−0.274203	+	0.377408i
$898$	−3.70420	+	3.33528i	−0.123611	+	0.111300i
$899$	16.7004	−	18.5476i	0.556988	−	0.618598i
$900$	1.47340	+	0.656002i	0.0491135	+	0.0218667i
$901$	13.7826	−	23.8722i	0.459166	−	0.795298i
$902$	−4.38088	+	6.18856i	−0.145867	+	0.206056i
$903$	−5.93278	+	2.70875i	−0.197431	+	0.0901415i
$904$	0.254001	+	0.349603i	0.00844796	+	0.0116276i
$905$	−40.4633	−	8.60073i	−1.34504	−	0.285898i
$906$	2.14323	+	10.0831i	0.0712041	+	0.334989i
$907$	−1.97811	+	18.8204i	−0.0656819	+	0.624922i	0.911321	+	0.411696i	$0.135064\pi$
$907$	−1.97811	+	18.8204i	−0.0656819	+	0.624922i	−0.977003	+	0.213225i	$0.931603\pi$
$908$	−6.06715	+	2.70127i	−0.201345	+	0.0896447i
$909$	−0.745989	+	2.29592i	−0.0247429	+	0.0761508i
$910$	−14.1067	−	15.3731i	−0.467633	−	0.509614i
$911$	−30.9452	+	22.4830i	−1.02526	+	0.744894i	−0.967354	−	0.253428i	$-0.918442\pi$
$911$	−30.9452	+	22.4830i	−1.02526	+	0.744894i	−0.0579044	+	0.998322i	$0.518442\pi$
$912$	1.96666	+	1.13545i	0.0651225	+	0.0375985i
$913$	−2.41311	+	26.0389i	−0.0798624	+	0.861761i
$914$	4.75401	+	8.23418i	0.157249	+	0.272363i
$915$	1.42865	+	13.5927i	0.0472297	+	0.449361i
$916$	−8.82777	+	2.86832i	−0.291678	+	0.0947718i
$917$	−16.1188	+	11.9448i	−0.532289	+	0.394451i
$918$	−4.55210	−	3.30729i	−0.150242	−	0.109157i
$919$	−12.3292	−	27.6917i	−0.406701	−	0.913466i	−0.994527	−	0.104478i	$-0.966683\pi$
$919$	−12.3292	−	27.6917i	−0.406701	−	0.913466i	0.587826	−	0.808987i	$-0.299984\pi$
$920$	5.86987	−	1.24768i	0.193524	−	0.0411347i
$921$	21.1416	+	19.0360i	0.696639	+	0.627257i
$922$	−31.6910	+	3.33086i	−1.04369	+	0.109696i
$923$	−16.1552			−0.531756
$924$	3.39401	−	8.09201i	0.111655	−	0.266208i
$925$	−16.1679			−0.531598
$926$	−15.6903	+	1.64912i	−0.515615	+	0.0541933i
$927$	0.702810	+	0.632813i	0.0230833	+	0.0207843i
$928$	−3.87948	+	0.824610i	−0.127350	+	0.0270691i
$929$	−7.98906	−	17.9437i	−0.262113	−	0.588715i	0.733767	−	0.679401i	$-0.237760\pi$
$929$	−7.98906	−	17.9437i	−0.262113	−	0.588715i	−0.995879	+	0.0906867i	$0.971094\pi$
$930$	9.36960	+	6.80741i	0.307241	+	0.223224i
$931$	8.20631	+	13.6143i	0.268951	+	0.446191i
$932$	3.19731	−	1.03887i	0.104731	−	0.0340293i
$933$	−0.622202	−	5.91986i	−0.0203700	−	0.193807i
$934$	2.47626	+	4.28901i	0.0810257	+	0.140341i
$935$	−25.8045	−	22.6656i	−0.843898	−	0.741244i
$936$	3.71086	+	2.14246i	0.121293	+	0.0700286i
$937$	−20.0924	+	14.5980i	−0.656391	+	0.476896i	−0.865442	−	0.501009i	$-0.832962\pi$
$937$	−20.0924	+	14.5980i	−0.656391	+	0.476896i	0.209051	+	0.977905i	$0.432962\pi$
$938$	−2.30625	−	10.3684i	−0.0753016	−	0.338540i
$939$	3.19279	−	9.82641i	0.104193	−	0.320673i
$940$	1.19874	−	0.533715i	0.0390987	−	0.0174079i
$941$	−5.06054	+	48.1478i	−0.164969	+	1.56957i	0.528402	+	0.848994i	$0.322791\pi$
$941$	−5.06054	+	48.1478i	−0.164969	+	1.56957i	−0.693371	+	0.720581i	$0.743875\pi$
$942$	4.66169	+	21.9315i	0.151886	+	0.714567i
$943$	7.29141	+	1.54984i	0.237441	+	0.0504697i
$944$	5.68468	+	7.82429i	0.185021	+	0.254659i
$945$	3.96616	+	2.82484i	0.129019	+	0.0918920i
$946$	6.55457	−	4.88658i	0.213108	−	0.158876i
$947$	−18.9870	+	32.8864i	−0.616994	+	1.06867i	0.373037	+	0.927817i	$0.378317\pi$
$947$	−18.9870	+	32.8864i	−0.616994	+	1.06867i	−0.990031	+	0.140849i	$0.955017\pi$
$948$	4.23078	+	1.88366i	0.137409	+	0.0611786i
$949$	−21.6459	+	24.0402i	−0.702656	+	0.780379i
$950$	2.72184	−	2.45076i	0.0883083	−	0.0795131i
$951$	−11.3676	+	15.6461i	−0.368618	+	0.507359i
$952$	−2.95773	+	14.5901i	−0.0958605	+	0.472867i
$953$	50.0939	+	16.2765i	1.62270	+	0.527248i	0.972577	−	0.232580i	$-0.0747167\pi$
$953$	50.0939	+	16.2765i	1.62270	+	0.527248i	0.650125	+	0.759828i	$0.274717\pi$
$954$	1.01856	−	4.79195i	0.0329771	−	0.155145i
$955$	14.8674	−	33.3928i	0.481098	−	1.08056i
$956$	12.3650	−	7.13896i	0.399914	−	0.230890i
$957$	−6.43639	+	11.4720i	−0.208059	+	0.370837i
$958$		−	25.3636i		−	0.819461i
$959$	−25.6275	+	45.3706i	−0.827554	+	1.46509i
$960$	−0.568722	−	1.75035i	−0.0183554	−	0.0564922i
$961$	−5.75426	−	6.39075i	−0.185621	−	0.206153i
$962$	−42.7189	−	4.48994i	−1.37731	−	0.144761i
$963$	17.7205	+	1.86250i	0.571036	+	0.0600183i
$964$	−2.42029	−	2.68801i	−0.0779524	−	0.0865749i
$965$	14.1255	+	43.4740i	0.454717	+	1.39948i
$966$	−8.62652	+	0.0813328i	−0.277554	+	0.00261684i
$967$			26.6917i			0.858347i	0.903222	+	0.429173i	$0.141195\pi$
$967$			26.6917i			0.858347i	−0.903222	+	0.429173i	$0.858805\pi$
$968$	−2.02145	+	10.8127i	−0.0649720	+	0.347532i
$969$	−11.0658	+	6.38884i	−0.355484	+	0.205239i
$970$	3.31148	−	7.43771i	0.106325	−	0.238810i
$971$	−9.16827	+	43.1333i	−0.294224	+	1.38421i	0.544090	+	0.839027i	$0.316875\pi$
$971$	−9.16827	+	43.1333i	−0.294224	+	1.38421i	−0.838314	+	0.545188i	$0.816458\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	2.55464	−	2.89158i	0.0818980	−	0.0926998i
$974$	−8.55829	+	11.7795i	−0.274225	+	0.377439i
$975$	5.13581	−	4.62430i	0.164477	−	0.148096i
$976$	−4.96918	+	5.51883i	−0.159059	+	0.176653i
$977$	−16.9791	−	7.55960i	−0.543211	−	0.241853i	0.116739	−	0.993163i	$-0.462756\pi$
$977$	−16.9791	−	7.55960i	−0.543211	−	0.241853i	−0.659950	+	0.751310i	$0.729423\pi$
$978$	−7.84757	+	13.5924i	−0.250938	+	0.434637i
$979$	−0.0146713	−	1.19174i	−0.000468898	−	0.0380881i
$980$	2.44045	−	12.6497i	0.0779572	−	0.404080i
$981$	−11.3400	−	15.6082i	−0.362060	−	0.498333i
$982$	−8.24883	−	1.75334i	−0.263231	−	0.0559514i
$983$	11.3345	+	53.3248i	0.361515	+	1.70080i	0.664076	+	0.747665i	$0.268825\pi$
$983$	11.3345	+	53.3248i	0.361515	+	1.70080i	−0.302560	+	0.953130i	$0.597841\pi$
$984$	0.238966	−	2.27361i	0.00761795	−	0.0724800i
$985$	−36.4546	+	16.2306i	−1.16154	+	0.517151i
$986$	6.89613	−	21.2241i	0.219618	−	0.675913i
$987$	−1.84137	+	0.409577i	−0.0586115	+	0.0130370i
$988$	7.87226	−	5.71953i	0.250450	−	0.181963i
$989$	−6.96084	−	4.01885i	−0.221342	−	0.127792i
$990$	−5.60642	−	2.41389i	−0.178184	−	0.0767183i
$991$	−5.97688	−	10.3523i	−0.189862	−	0.328850i	0.755342	−	0.655331i	$-0.227471\pi$
$991$	−5.97688	−	10.3523i	−0.189862	−	0.328850i	−0.945204	+	0.326480i	$0.894137\pi$
$992$	0.657779	+	6.25835i	0.0208845	+	0.198703i
$993$	−5.46176	+	1.77463i	−0.173324	+	0.0563163i
$994$	−5.93906	−	8.01441i	−0.188375	−	0.254202i
$995$	−24.5551	−	17.8403i	−0.778448	−	0.565575i
$996$	−3.20698	−	7.20299i	−0.101617	−	0.228236i
$997$	56.4620	−	12.0014i	1.78817	−	0.380087i	0.809759	−	0.586763i	$-0.199598\pi$
$997$	56.4620	−	12.0014i	1.78817	−	0.380087i	0.978410	+	0.206676i	$0.0662645\pi$
$998$	21.3648	+	19.2370i	0.676291	+	0.608935i
$999$	9.96958	−	1.04784i	0.315423	−	0.0331523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.b.19.6	yes	64
7.3	odd	6		462.2.ba.a.283.2	yes	64
11.7	odd	10		462.2.ba.a.271.2	✓	64
77.73	even	30	inner	462.2.ba.b.73.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.271.2	✓	64	11.7	odd	10
462.2.ba.a.283.2	yes	64	7.3	odd	6
462.2.ba.b.19.6	yes	64	1.1	even	1	trivial
462.2.ba.b.73.6	yes	64	77.73	even	30	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.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.994522 - 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.748568 - 1.68131i) q^{5} +(0.809017 + 0.587785i) q^{6} +(2.42705 + 1.05329i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.994522 - 0.104528i) q^{2} +(0.743145 + 0.669131i) q^{3} +(0.978148 - 0.207912i) q^{4} +(-0.748568 - 1.68131i) q^{5} +(0.809017 + 0.587785i) q^{6} +(2.42705 + 1.05329i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-0.920212 - 1.59385i) q^{10} +(-1.69354 - 2.85165i) q^{11} +(0.866025 + 0.500000i) q^{12} +(3.46658 - 2.51862i) q^{13} +(2.52386 + 0.793823i) q^{14} +(0.568722 - 1.75035i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.588150 + 5.59588i) q^{17} +(0.207912 + 0.978148i) q^{18} +(2.22128 + 0.472147i) q^{19} +(-1.08177 - 1.48893i) q^{20} +(1.09886 + 2.40676i) q^{21} +(-1.98235 - 2.65900i) q^{22} +(-1.63033 + 2.82382i) q^{23} +(0.913545 + 0.406737i) q^{24} +(1.07920 - 1.19857i) q^{25} +(3.18432 - 2.86718i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.59301 + 0.525660i) q^{28} +(-3.77204 - 1.22561i) q^{29} +(0.382646 - 1.80021i) q^{30} +(-2.55952 + 5.74878i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.649578 - 3.25239i) q^{33} +5.62670i q^{34} +(-0.0459068 - 4.86909i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-6.70769 - 7.44965i) q^{37} +(2.25846 + 0.237374i) q^{38} +(4.26146 + 0.447897i) q^{39} +(-1.23148 - 1.36770i) q^{40} +(-0.706454 - 2.17424i) q^{41} +(1.34442 + 2.27871i) q^{42} +2.46505i q^{43} +(-2.24943 - 2.43723i) q^{44} +(1.59385 - 0.920212i) q^{45} +(-1.32623 + 2.97876i) q^{46} +(-0.148237 + 0.697402i) q^{47} +(0.951057 + 0.309017i) q^{48} +(4.78116 + 5.11277i) q^{49} +(0.948004 - 1.30482i) q^{50} +(-4.18145 + 3.76500i) q^{51} +(2.86718 - 3.18432i) q^{52} +(-4.47546 - 1.99261i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.52678 + 4.98203i) q^{55} +(2.63375 + 0.251737i) q^{56} +(1.33480 + 1.83720i) q^{57} +(-3.87948 - 0.824610i) q^{58} +(2.01079 + 9.46001i) q^{59} +(0.192377 - 1.83034i) q^{60} +(-6.78428 + 3.02056i) q^{61} +(-1.94459 + 5.98483i) q^{62} +(-0.793823 + 2.52386i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-6.82955 - 3.94304i) q^{65} +(0.306052 - 3.30247i) q^{66} +(-2.00733 - 3.47679i) q^{67} +(0.588150 + 5.59588i) q^{68} +(-3.10108 + 1.00760i) q^{69} +(-0.554613 - 4.83761i) q^{70} +(-3.05019 - 2.21609i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-7.38458 + 1.56964i) q^{73} +(-7.44965 - 6.70769i) q^{74} +(1.60401 - 0.168588i) q^{75} +2.27090 q^{76} +(-1.10671 - 8.70489i) q^{77} +4.28493 q^{78} +(4.60579 - 0.484089i) q^{79} +(-1.36770 - 1.23148i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-0.929854 - 2.08849i) q^{82} +(-6.37882 - 4.63449i) q^{83} +(1.57524 + 2.12570i) q^{84} +(9.84867 - 3.20003i) q^{85} +(0.257668 + 2.45154i) q^{86} +(-1.98308 - 3.43479i) q^{87} +(-2.49186 - 2.18875i) q^{88} +(0.311206 + 0.179675i) q^{89} +(1.48893 - 1.08177i) q^{90} +(11.0664 - 2.46151i) q^{91} +(-1.00760 + 3.10108i) q^{92} +(-5.74878 + 2.55952i) q^{93} +(-0.0745269 + 0.709076i) q^{94} +(-0.868950 - 4.08809i) q^{95} +(0.978148 + 0.207912i) q^{96} +(2.60022 + 3.57889i) q^{97} +(5.28940 + 4.58500i) q^{98} +(2.65900 - 1.98235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

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