LMFDB - Embedded newform 546.2.bu.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	546.71
Dual form			546.2.bu.a.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-1.68734 + 0.390990i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.95685 - 2.95685i) q^{5} +(1.52865 - 0.814384i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.69425 - 1.31947i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.68734 + 0.390990i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.95685 - 2.95685i) q^{5} +(1.52865 - 0.814384i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.69425 - 1.31947i) q^{9} +(3.62139 + 2.09081i) q^{10} +(-0.182104 - 0.679623i) q^{11} +(-1.26579 + 1.18228i) q^{12} +(1.11817 - 3.42778i) q^{13} +1.00000i q^{14} +(6.14532 + 3.83312i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.06039 + 3.56869i) q^{17} +(-2.26094 + 1.97183i) q^{18} +(-7.67233 - 2.05579i) q^{19} +(-4.03913 - 1.08228i) q^{20} +(-0.0590488 + 1.73104i) q^{21} +(0.351799 + 0.609333i) q^{22} +(-1.12597 + 1.95025i) q^{23} +(0.916660 - 1.46960i) q^{24} +12.4859i q^{25} +(-0.192896 + 3.60039i) q^{26} +(-4.03023 + 3.27983i) q^{27} +(-0.258819 - 0.965926i) q^{28} +(-1.72295 - 0.994745i) q^{29} +(-6.92801 - 2.11199i) q^{30} +(2.11439 - 2.11439i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.572999 + 1.07556i) q^{33} +(-2.91383 - 2.91383i) q^{34} +(-3.62139 + 2.09081i) q^{35} +(1.67356 - 2.48982i) q^{36} +(4.55669 - 1.22096i) q^{37} +7.94298 q^{38} +(-0.546510 + 6.22104i) q^{39} +4.18162 q^{40} +(-1.49512 + 0.400617i) q^{41} +(-0.390990 - 1.68734i) q^{42} +(-10.5411 + 6.08588i) q^{43} +(-0.497519 - 0.497519i) q^{44} +(-11.8680 - 4.06503i) q^{45} +(0.582847 - 2.17522i) q^{46} +(-3.65818 + 3.65818i) q^{47} +(-0.505064 + 1.65678i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-3.23160 - 12.0605i) q^{50} +(-4.87190 - 5.21602i) q^{51} +(-0.745526 - 3.52763i) q^{52} -0.161679i q^{53} +(3.04402 - 4.21117i) q^{54} +(-1.47109 + 2.54800i) q^{55} +(0.500000 + 0.866025i) q^{56} +(13.7497 + 0.469023i) q^{57} +(1.92170 + 0.514918i) q^{58} +(-5.46193 - 1.46352i) q^{59} +(7.23857 + 0.246920i) q^{60} +(0.568793 + 0.985179i) q^{61} +(-1.49510 + 2.58959i) q^{62} +(-0.577186 - 2.94395i) q^{63} -1.00000i q^{64} +(-13.4417 + 6.82918i) q^{65} +(-0.831849 - 0.890605i) q^{66} +(2.89331 + 10.7980i) q^{67} +(3.56869 + 2.06039i) q^{68} +(1.13738 - 3.73098i) q^{69} +(2.95685 - 2.95685i) q^{70} +(-0.345402 + 1.28906i) q^{71} +(-0.972118 + 2.83813i) q^{72} +(4.56529 + 4.56529i) q^{73} +(-4.08541 + 2.35871i) q^{74} +(-4.88189 - 21.0681i) q^{75} +(-7.67233 + 2.05579i) q^{76} -0.703598 q^{77} +(-1.08224 - 6.15051i) q^{78} +7.36643 q^{79} +(-4.03913 + 1.08228i) q^{80} +(5.51800 - 7.10997i) q^{81} +(1.34049 - 0.773933i) q^{82} +(10.3578 + 10.3578i) q^{83} +(0.814384 + 1.52865i) q^{84} +(4.45984 - 16.6443i) q^{85} +(8.60674 - 8.60674i) q^{86} +(3.29614 + 1.00482i) q^{87} +(0.609333 + 0.351799i) q^{88} +(-2.00418 - 7.47969i) q^{89} +(12.5157 + 0.854857i) q^{90} +(-3.02158 - 1.96725i) q^{91} +2.25195i q^{92} +(-2.74099 + 4.39441i) q^{93} +(2.58672 - 4.48033i) q^{94} +(16.6073 + 28.7646i) q^{95} +(0.0590488 - 1.73104i) q^{96} +(-16.1991 - 4.34053i) q^{97} +(0.965926 + 0.258819i) q^{98} +(-1.38738 - 1.59080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−1.68734	+	0.390990i	−0.974188	+	0.225738i
$3$	−1.68734	+	0.390990i	−0.974188	+	0.225738i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.95685	−	2.95685i	−1.32234	−	1.32234i	−0.911874	−	0.410471i	$-0.865364\pi$
$5$	−2.95685	−	2.95685i	−1.32234	−	1.32234i	−0.410471	−	0.911874i	$-0.634636\pi$
$6$	1.52865	−	0.814384i	0.624070	−	0.332471i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.69425	−	1.31947i	0.898084	−	0.439823i
$10$	3.62139	+	2.09081i	1.14518	+	0.661172i
$11$	−0.182104	−	0.679623i	−0.0549066	−	0.204914i	0.933023	−	0.359816i	$-0.117161\pi$
$11$	−0.182104	−	0.679623i	−0.0549066	−	0.204914i	−0.987930	+	0.154902i	$0.950494\pi$
$12$	−1.26579	+	1.18228i	−0.365401	+	0.341295i
$13$	1.11817	−	3.42778i	0.310125	−	0.950696i
$13$	1.11817	−	3.42778i	0.310125	−	0.950696i
$14$			1.00000i			0.267261i
$15$	6.14532	+	3.83312i	1.58672	+	0.989708i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.06039	+	3.56869i	0.499717	+	0.865535i	1.00000		0.000326888i	$-0.000104052\pi$
$17$	2.06039	+	3.56869i	0.499717	+	0.865535i	−0.500283	+	0.865862i	$0.666771\pi$
$18$	−2.26094	+	1.97183i	−0.532910	+	0.464766i
$19$	−7.67233	−	2.05579i	−1.76015	−	0.471632i	−0.773408	−	0.633908i	$-0.781450\pi$
$19$	−7.67233	−	2.05579i	−1.76015	−	0.471632i	−0.986745	+	0.162277i	$0.948116\pi$
$20$	−4.03913	−	1.08228i	−0.903178	−	0.242006i
$21$	−0.0590488	+	1.73104i	−0.0128855	+	0.377745i
$22$	0.351799	+	0.609333i	0.0750038	+	0.129910i
$23$	−1.12597	+	1.95025i	−0.234782	+	0.406654i	−0.959209	−	0.282697i	$-0.908771\pi$
$23$	−1.12597	+	1.95025i	−0.234782	+	0.406654i	0.724427	+	0.689351i	$0.242104\pi$
$24$	0.916660	−	1.46960i	0.187112	−	0.299982i
$25$			12.4859i			2.49719i
$26$	−0.192896	+	3.60039i	−0.0378300	+	0.706094i
$27$	−4.03023	+	3.27983i	−0.775618	+	0.631203i
$28$	−0.258819	−	0.965926i	−0.0489122	−	0.182543i
$29$	−1.72295	−	0.994745i	−0.319943	−	0.184719i	0.331424	−	0.943482i	$-0.392471\pi$
$29$	−1.72295	−	0.994745i	−0.319943	−	0.184719i	−0.651367	+	0.758763i	$0.725804\pi$
$30$	−6.92801	−	2.11199i	−1.26488	−	0.385594i
$31$	2.11439	−	2.11439i	0.379756	−	0.379756i	−0.491258	−	0.871014i	$-0.663463\pi$
$31$	2.11439	−	2.11439i	0.379756	−	0.379756i	0.871014	+	0.491258i	$0.163463\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.572999	+	1.07556i	0.0997463	+	0.187230i
$34$	−2.91383	−	2.91383i	−0.499717	−	0.499717i
$35$	−3.62139	+	2.09081i	−0.612127	+	0.353411i
$36$	1.67356	−	2.48982i	0.278926	−	0.414970i
$37$	4.55669	−	1.22096i	0.749115	−	0.200725i	0.135989	−	0.990710i	$-0.456579\pi$
$37$	4.55669	−	1.22096i	0.749115	−	0.200725i	0.613125	+	0.789986i	$0.289912\pi$
$38$	7.94298			1.28852
$39$	−0.546510	+	6.22104i	−0.0875116	+	0.996163i
$40$	4.18162			0.661172
$41$	−1.49512	+	0.400617i	−0.233499	+	0.0625659i	−0.373671	−	0.927561i	$-0.621901\pi$
$41$	−1.49512	+	0.400617i	−0.233499	+	0.0625659i	0.140172	+	0.990127i	$0.455234\pi$
$42$	−0.390990	−	1.68734i	−0.0603311	−	0.260363i
$43$	−10.5411	+	6.08588i	−1.60750	+	0.928088i	−0.617568	+	0.786517i	$0.711882\pi$
$43$	−10.5411	+	6.08588i	−1.60750	+	0.928088i	−0.989928	+	0.141571i	$0.954785\pi$
$44$	−0.497519	−	0.497519i	−0.0750038	−	0.0750038i
$45$	−11.8680	−	4.06503i	−1.76917	−	0.605979i
$46$	0.582847	−	2.17522i	0.0859362	−	0.320718i
$47$	−3.65818	+	3.65818i	−0.533600	+	0.533600i	−0.921642	−	0.388042i	$-0.873152\pi$
$47$	−3.65818	+	3.65818i	−0.533600	+	0.533600i	0.388042	+	0.921642i	$0.373152\pi$
$48$	−0.505064	+	1.65678i	−0.0728997	+	0.239135i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	−3.23160	−	12.0605i	−0.457017	−	1.70561i
$51$	−4.87190	−	5.21602i	−0.682203	−	0.730388i
$52$	−0.745526	−	3.52763i	−0.103386	−	0.489195i
$53$		−	0.161679i		−	0.0222083i	−0.999938	−	0.0111041i	$-0.996465\pi$
$53$		−	0.161679i		−	0.0222083i	0.999938	−	0.0111041i	$-0.00353463\pi$
$54$	3.04402	−	4.21117i	0.414239	−	0.573067i
$55$	−1.47109	+	2.54800i	−0.198362	+	0.343572i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	13.7497	+	0.469023i	1.82119	+	0.0621237i
$58$	1.92170	+	0.514918i	0.252331	+	0.0676120i
$59$	−5.46193	−	1.46352i	−0.711083	−	0.190534i	−0.114893	−	0.993378i	$-0.536653\pi$
$59$	−5.46193	−	1.46352i	−0.711083	−	0.190534i	−0.596189	+	0.802844i	$0.703319\pi$
$60$	7.23857	+	0.246920i	0.934495	+	0.0318772i
$61$	0.568793	+	0.985179i	0.0728265	+	0.126139i	0.900139	−	0.435603i	$-0.143465\pi$
$61$	0.568793	+	0.985179i	0.0728265	+	0.126139i	−0.827313	+	0.561742i	$0.810131\pi$
$62$	−1.49510	+	2.58959i	−0.189878	+	0.328878i
$63$	−0.577186	−	2.94395i	−0.0727186	−	0.370903i
$64$		−	1.00000i		−	0.125000i
$65$	−13.4417	+	6.82918i	−1.66724	+	0.847055i
$66$	−0.831849	−	0.890605i	−0.102394	−	0.109626i
$67$	2.89331	+	10.7980i	0.353475	+	1.31919i	0.882393	+	0.470513i	$0.155931\pi$
$67$	2.89331	+	10.7980i	0.353475	+	1.31919i	−0.528919	+	0.848672i	$0.677402\pi$
$68$	3.56869	+	2.06039i	0.432768	+	0.249858i
$69$	1.13738	−	3.73098i	0.136924	−	0.449157i
$70$	2.95685	−	2.95685i	0.353411	−	0.353411i
$71$	−0.345402	+	1.28906i	−0.0409916	+	0.152983i	−0.983388	−	0.181515i	$-0.941900\pi$
$71$	−0.345402	+	1.28906i	−0.0409916	+	0.152983i	0.942397	+	0.334498i	$0.108567\pi$
$72$	−0.972118	+	2.83813i	−0.114565	+	0.334477i
$73$	4.56529	+	4.56529i	0.534327	+	0.534327i	0.921857	−	0.387530i	$-0.126672\pi$
$73$	4.56529	+	4.56529i	0.534327	+	0.534327i	−0.387530	+	0.921857i	$0.626672\pi$
$74$	−4.08541	+	2.35871i	−0.474920	+	0.274195i
$75$	−4.88189	−	21.0681i	−0.563712	−	2.43273i
$76$	−7.67233	+	2.05579i	−0.880077	+	0.235816i
$77$	−0.703598			−0.0801824
$78$	−1.08224	−	6.15051i	−0.122539	−	0.696408i
$79$	7.36643			0.828788			0.414394	−	0.910098i	$-0.363994\pi$
$79$	7.36643			0.828788			0.414394	+	0.910098i	$0.363994\pi$
$80$	−4.03913	+	1.08228i	−0.451589	+	0.121003i
$81$	5.51800	−	7.10997i	0.613111	−	0.789997i
$82$	1.34049	−	0.773933i	0.148032	−	0.0854666i
$83$	10.3578	+	10.3578i	1.13692	+	1.13692i	0.989000	+	0.147918i	$0.0472571\pi$
$83$	10.3578	+	10.3578i	1.13692	+	1.13692i	0.147918	+	0.989000i	$0.452743\pi$
$84$	0.814384	+	1.52865i	0.0888566	+	0.166790i
$85$	4.45984	−	16.6443i	0.483738	−	1.80533i
$86$	8.60674	−	8.60674i	0.928088	−	0.928088i
$87$	3.29614	+	1.00482i	0.353383	+	0.107728i
$88$	0.609333	+	0.351799i	0.0649552	+	0.0375019i
$89$	−2.00418	−	7.47969i	−0.212442	−	0.792845i	−0.987051	−	0.160405i	$-0.948720\pi$
$89$	−2.00418	−	7.47969i	−0.212442	−	0.792845i	0.774609	−	0.632440i	$-0.217947\pi$
$90$	12.5157	+	0.854857i	1.31927	+	0.0901099i
$91$	−3.02158	−	1.96725i	−0.316748	−	0.206223i
$92$			2.25195i			0.234782i
$93$	−2.74099	+	4.39441i	−0.284228	+	0.455679i
$94$	2.58672	−	4.48033i	0.266800	−	0.462111i
$95$	16.6073	+	28.7646i	1.70387	+	2.95119i
$96$	0.0590488	−	1.73104i	0.00602664	−	0.176674i
$97$	−16.1991	−	4.34053i	−1.64477	−	0.440714i	−0.686626	−	0.727011i	$-0.740909\pi$
$97$	−16.1991	−	4.34053i	−1.64477	−	0.440714i	−0.958141	+	0.286297i	$0.907575\pi$
$98$	0.965926	+	0.258819i	0.0975732	+	0.0261447i
$99$	−1.38738	−	1.59080i	−0.139437	−	0.159881i
$100$	6.24297	+	10.8131i	0.624297	+	1.08131i
$101$	−5.63189	+	9.75471i	−0.560394	+	0.970630i	0.437068	+	0.899428i	$0.356017\pi$
$101$	−5.63189	+	9.75471i	−0.560394	+	0.970630i	−0.997462	+	0.0712019i	$0.977317\pi$
$102$	6.05590	+	3.77734i	0.599623	+	0.374013i
$103$		−	1.77305i		−	0.174704i	−0.996178	−	0.0873520i	$-0.972160\pi$
$103$		−	1.77305i		−	0.174704i	0.996178	−	0.0873520i	$-0.0278405\pi$
$104$	1.63314	+	3.21448i	0.160143	+	0.315205i
$105$	5.29304	−	4.94384i	0.516548	−	0.482470i
$106$	0.0418456	+	0.156170i	0.00406440	+	0.0151686i
$107$	10.3779	+	5.99167i	1.00327	+	0.579237i	0.909213	−	0.416330i	$-0.136684\pi$
$107$	10.3779	+	5.99167i	1.00327	+	0.579237i	0.0940542	+	0.995567i	$0.470017\pi$
$108$	−1.85037	+	4.85553i	−0.178052	+	0.467223i
$109$	−7.89280	+	7.89280i	−0.755993	+	0.755993i	−0.975591	−	0.219597i	$-0.929526\pi$
$109$	−7.89280	+	7.89280i	−0.755993	+	0.755993i	0.219597	+	0.975591i	$0.429526\pi$
$110$	0.761492	−	2.84193i	0.0726054	−	0.270967i
$111$	−7.21131	+	3.84180i	−0.684467	+	0.364648i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	3.09181	−	1.78506i	0.290853	−	0.167924i	−0.347474	−	0.937690i	$-0.612960\pi$
$113$	3.09181	−	1.78506i	0.290853	−	0.167924i	0.638326	+	0.769766i	$0.279627\pi$
$114$	−13.4025	+	3.10563i	−1.25526	+	0.290869i
$115$	9.09593	−	2.43725i	0.848200	−	0.227274i
$116$	−1.98949			−0.184719
$117$	−1.51022	−	10.7107i	−0.139620	−	0.990205i
$118$	5.65460			0.520549
$119$	3.98036	−	1.06653i	0.364879	−	0.0977690i
$120$	−7.05583	+	1.63497i	−0.644106	+	0.149252i
$121$	9.09755	−	5.25248i	0.827050	−	0.477498i
$122$	−0.804395	−	0.804395i	−0.0728265	−	0.0728265i
$123$	2.36615	−	1.26056i	0.213348	−	0.113661i
$124$	0.773920	−	2.88831i	0.0695001	−	0.259378i
$125$	22.1348	−	22.1348i	1.97980	−	1.97980i
$126$	1.31947	+	2.69425i	0.117548	+	0.240023i
$127$	−8.56131	−	4.94287i	−0.759693	−	0.438609i	0.0694923	−	0.997582i	$-0.477862\pi$
$127$	−8.56131	−	4.94287i	−0.759693	−	0.438609i	−0.829186	+	0.558973i	$0.811195\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	15.4069	−	14.3904i	1.35650	−	1.26701i
$130$	11.2162	−	10.0754i	0.983724	−	0.883675i
$131$		−	11.2475i		−	0.982702i	−0.870962	−	0.491351i	$-0.836503\pi$
$131$		−	11.2475i		−	0.982702i	0.870962	−	0.491351i	$-0.163497\pi$
$132$	1.03401	+	0.644960i	0.0899990	+	0.0561365i
$133$	−3.97149	+	6.87882i	−0.344372	+	0.596470i
$134$	−5.58945	−	9.68122i	−0.482855	−	0.836330i
$135$	21.6147	+	2.21883i	1.86030	+	0.190967i
$136$	−3.98036	−	1.06653i	−0.341313	−	0.0914545i
$137$	−13.5656	−	3.63490i	−1.15899	−	0.310550i	−0.372428	−	0.928061i	$-0.621475\pi$
$137$	−13.5656	−	3.63490i	−1.15899	−	0.310550i	−0.786562	+	0.617511i	$0.788141\pi$
$138$	−0.132975	+	3.89822i	−0.0113196	+	0.331839i
$139$	−5.72868	−	9.92236i	−0.485900	−	0.841603i	0.513969	−	0.857809i	$-0.328175\pi$
$139$	−5.72868	−	9.92236i	−0.485900	−	0.841603i	−0.999869	+	0.0162056i	$0.994841\pi$
$140$	−2.09081	+	3.62139i	−0.176706	+	0.306063i
$141$	4.74228	−	7.60291i	0.399372	−	0.640280i
$142$		−	1.33453i		−	0.111991i
$143$	−2.53322	−	0.135721i	−0.211839	−	0.0113496i
$144$	0.204432	−	2.99303i	0.0170360	−	0.249419i
$145$	2.15319	+	8.03581i	0.178813	+	0.667338i
$146$	−5.59131	−	3.22815i	−0.462741	−	0.267163i
$147$	1.65678	+	0.505064i	0.136649	+	0.0416570i
$148$	3.33573	−	3.33573i	0.274195	−	0.274195i
$149$	4.04326	−	15.0897i	0.331237	−	1.23619i	−0.576654	−	0.816988i	$-0.695642\pi$
$149$	4.04326	−	15.0897i	0.331237	−	1.23619i	0.907891	−	0.419205i	$-0.137691\pi$
$150$	10.1684	+	19.0867i	0.830243	+	1.55842i
$151$	−7.41691	−	7.41691i	−0.603580	−	0.603580i	0.337681	−	0.941261i	$-0.390357\pi$
$151$	−7.41691	−	7.41691i	−0.603580	−	0.603580i	−0.941261	+	0.337681i	$0.890357\pi$
$152$	6.87882	−	3.97149i	0.557946	−	0.322130i
$153$	10.2600	+	6.89634i	0.829470	+	0.557536i
$154$	0.679623	−	0.182104i	0.0547656	−	0.0146744i
$155$	−12.5039			−1.00434
$156$	2.63723	+	5.66083i	0.211147	+	0.453229i
$157$	15.2580			1.21772			0.608861	−	0.793277i	$-0.291627\pi$
$157$	15.2580			1.21772			0.608861	+	0.793277i	$0.291627\pi$
$158$	−7.11542	+	1.90657i	−0.566073	+	0.151679i
$159$	0.0632149	+	0.272808i	0.00501327	+	0.0216351i
$160$	3.62139	−	2.09081i	0.286296	−	0.165293i
$161$	1.59237	+	1.59237i	0.125496	+	0.125496i
$162$	−3.48978	+	8.29587i	−0.274183	+	0.651785i
$163$	−0.301250	+	1.12428i	−0.0235957	+	0.0880604i	−0.976720	−	0.214520i	$-0.931181\pi$
$163$	−0.301250	+	1.12428i	−0.0235957	+	0.0880604i	0.953124	+	0.302580i	$0.0978480\pi$
$164$	−1.09451	+	1.09451i	−0.0854666	+	0.0854666i
$165$	1.48599	−	4.87453i	0.115684	−	0.379482i
$166$	−12.6857	−	7.32408i	−0.984599	−	0.568459i
$167$	6.17452	+	23.0436i	0.477798	+	1.78317i	0.610505	+	0.792012i	$0.290967\pi$
$167$	6.17452	+	23.0436i	0.477798	+	1.78317i	−0.132707	+	0.991155i	$0.542367\pi$
$168$	−1.18228	−	1.26579i	−0.0912148	−	0.0976576i
$169$	−10.4994	−	7.66570i	−0.807645	−	0.589669i
$170$			17.2315i			1.32160i
$171$	−23.3838	+	4.58458i	−1.78820	+	0.350591i
$172$	−6.08588	+	10.5411i	−0.464044	+	0.803748i
$173$	−7.02861	−	12.1739i	−0.534375	−	0.925565i	−0.999193	−	0.0401587i	$-0.987214\pi$
$173$	−7.02861	−	12.1739i	−0.534375	−	0.925565i	0.464818	−	0.885406i	$-0.346120\pi$
$174$	−3.44389	−	0.117477i	−0.261081	−	0.00890590i
$175$	12.0605	+	3.23160i	0.911688	+	0.244286i
$176$	−0.679623	−	0.182104i	−0.0512285	−	0.0137266i
$177$	9.78837	+	0.333897i	0.735739	+	0.0250973i
$178$	3.87177	+	6.70611i	0.290202	+	0.502644i
$179$	4.65902	−	8.06965i	0.348231	−	0.603154i	−0.637704	−	0.770281i	$-0.720116\pi$
$179$	4.65902	−	8.06965i	0.348231	−	0.603154i	0.985935	+	0.167127i	$0.0534491\pi$
$180$	−12.3105	+	2.41357i	−0.917570	+	0.179897i
$181$			19.6182i			1.45821i	0.684401	+	0.729105i	$0.260064\pi$
$181$			19.6182i			1.45821i	−0.684401	+	0.729105i	$0.739936\pi$
$182$	3.42778	+	1.11817i	0.254084	+	0.0828844i
$183$	−1.34495	−	1.43994i	−0.0994212	−	0.106444i
$184$	−0.582847	−	2.17522i	−0.0429681	−	0.160359i
$185$	−17.0836	−	9.86325i	−1.25601	−	0.725160i
$186$	1.51024	−	4.95409i	0.110736	−	0.363252i
$187$	2.05016	−	2.05016i	0.149923	−	0.149923i
$188$	−1.33899	+	4.99716i	−0.0976555	+	0.364455i
$189$	2.12497	+	4.74178i	0.154569	+	0.344914i
$190$	−23.4862	−	23.4862i	−1.70387	−	1.70387i
$191$	−13.7253	+	7.92432i	−0.993129	+	0.573383i	−0.906208	−	0.422832i	$-0.861036\pi$
$191$	−13.7253	+	7.92432i	−0.993129	+	0.573383i	−0.0869210	+	0.996215i	$0.527703\pi$
$192$	0.390990	+	1.68734i	0.0282173	+	0.121773i
$193$	−3.29073	+	0.881750i	−0.236872	+	0.0634697i	−0.375302	−	0.926902i	$-0.622461\pi$
$193$	−3.29073	+	0.881750i	−0.236872	+	0.0634697i	0.138430	+	0.990372i	$0.455794\pi$
$194$	16.7705			1.20405
$195$	20.0106	−	16.7787i	1.43299	−	1.20155i
$196$	−1.00000			−0.0714286
$197$	3.13569	−	0.840205i	0.223408	−	0.0598621i	−0.145378	−	0.989376i	$-0.546440\pi$
$197$	3.13569	−	0.840205i	0.223408	−	0.0598621i	0.368787	+	0.929514i	$0.379773\pi$
$198$	1.75183	+	1.17751i	0.124497	+	0.0836820i
$199$	−11.8560	+	6.84505i	−0.840447	+	0.485232i	−0.857416	−	0.514624i	$-0.827932\pi$
$199$	−11.8560	+	6.84505i	−0.840447	+	0.485232i	0.0169689	+	0.999856i	$0.494598\pi$
$200$	−8.82890	−	8.82890i	−0.624297	−	0.624297i
$201$	−9.10393	−	17.0887i	−0.642141	−	1.20534i
$202$	2.91528	−	10.8800i	0.205118	−	0.765512i
$203$	−1.40678	+	1.40678i	−0.0987367	+	0.0987367i
$204$	−6.82720	−	2.08125i	−0.478000	−	0.145717i
$205$	5.60542	+	3.23629i	0.391500	+	0.226032i
$206$	0.458900	+	1.71264i	0.0319730	+	0.119325i
$207$	−0.460371	+	6.74014i	−0.0319980	+	0.468472i
$208$	−2.40946	−	2.68226i	−0.167066	−	0.185981i
$209$			5.58866i			0.386576i
$210$	−3.83312	+	6.14532i	−0.264511	+	0.424068i
$211$	−10.3513	+	17.9290i	−0.712614	+	1.23428i	0.251259	+	0.967920i	$0.419156\pi$
$211$	−10.3513	+	17.9290i	−0.712614	+	1.23428i	−0.963873	+	0.266364i	$0.914178\pi$
$212$	−0.0808394	−	0.140018i	−0.00555207	−	0.00961648i
$213$	0.0788023	−	2.31013i	0.00539945	−	0.158287i
$214$	−11.5750	−	3.10152i	−0.791252	−	0.212015i
$215$	49.1634	+	13.1733i	3.35292	+	0.898411i
$216$	0.530615	−	5.16899i	0.0361038	−	0.351705i
$217$	−1.49510	−	2.58959i	−0.101494	−	0.175793i
$218$	5.58105	−	9.66667i	0.377997	−	0.654709i
$219$	−9.48819	−	5.91822i	−0.641153	−	0.399917i
$220$			2.94218i			0.198362i
$221$	14.5366	−	3.07214i	0.977835	−	0.206655i
$222$	5.97126	−	5.57732i	0.400765	−	0.374325i
$223$	0.772639	+	2.88353i	0.0517397	+	0.193095i	0.986958	−	0.160975i	$-0.0514639\pi$
$223$	0.772639	+	2.88353i	0.0517397	+	0.193095i	−0.935219	+	0.354071i	$0.884797\pi$
$224$	0.866025	+	0.500000i	0.0578638	+	0.0334077i
$225$	16.4748	+	33.6403i	1.09832	+	2.24269i
$226$	−2.52445	+	2.52445i	−0.167924	+	0.167924i
$227$	0.255531	−	0.953656i	0.0169602	−	0.0632963i	−0.956927	−	0.290328i	$-0.906236\pi$
$227$	0.255531	−	0.953656i	0.0169602	−	0.0632963i	0.973887	+	0.227032i	$0.0729022\pi$
$228$	12.1421	−	6.46864i	0.804127	−	0.428396i
$229$	−4.45709	−	4.45709i	−0.294533	−	0.294533i	0.544335	−	0.838868i	$-0.316782\pi$
$229$	−4.45709	−	4.45709i	−0.294533	−	0.294533i	−0.838868	+	0.544335i	$0.816782\pi$
$230$	−8.15519	+	4.70840i	−0.537737	+	0.310463i
$231$	1.18721	−	0.275100i	0.0781127	−	0.0181002i
$232$	1.92170	−	0.514918i	0.126166	−	0.0338060i
$233$	−26.6522			−1.74605			−0.873023	−	0.487679i	$-0.837844\pi$
$233$	−26.6522			−1.74605			−0.873023	+	0.487679i	$0.837844\pi$
$234$	4.23089	+	9.95488i	0.276582	+	0.650771i
$235$	21.6334			1.41121
$236$	−5.46193	+	1.46352i	−0.355541	+	0.0952670i
$237$	−12.4297	+	2.88020i	−0.807395	+	0.187089i
$238$	−3.56869	+	2.06039i	−0.231324	+	0.133555i
$239$	−9.69089	−	9.69089i	−0.626852	−	0.626852i	0.320423	−	0.947275i	$-0.396175\pi$
$239$	−9.69089	−	9.69089i	−0.626852	−	0.626852i	−0.947275	+	0.320423i	$0.896175\pi$
$240$	6.39224	−	3.40545i	0.412618	−	0.219821i
$241$	3.65471	−	13.6396i	0.235421	−	0.878601i	−0.742538	−	0.669804i	$-0.766378\pi$
$241$	3.65471	−	13.6396i	0.235421	−	0.878601i	0.977959	−	0.208798i	$-0.0669550\pi$
$242$	−7.42812	+	7.42812i	−0.477498	+	0.477498i
$243$	−6.53083	+	14.1544i	−0.418953	+	0.908008i
$244$	0.985179	+	0.568793i	0.0630696	+	0.0364133i
$245$	1.08228	+	4.03913i	0.0691445	+	0.258051i
$246$	−1.95927	+	1.83001i	−0.124918	+	0.116677i
$247$	−15.6258	+	24.0003i	−0.994246	+	1.52711i
$248$			2.99020i			0.189878i
$249$	−21.5270	−	13.4274i	−1.36422	−	0.850925i
$250$	−15.6517	+	27.1095i	−0.989900	+	1.71456i
$251$	−6.10097	−	10.5672i	−0.385090	−	0.666995i	0.606692	−	0.794937i	$-0.292496\pi$
$251$	−6.10097	−	10.5672i	−0.385090	−	0.666995i	−0.991782	+	0.127942i	$0.959163\pi$
$252$	−1.97183	−	2.26094i	−0.124214	−	0.142426i
$253$	1.53048	+	0.410090i	0.0962203	+	0.0257821i
$254$	9.54890	+	2.55862i	0.599151	+	0.160542i
$255$	−1.01750	+	29.8285i	−0.0637183	+	1.86793i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.98242	+	10.3619i	−0.373173	+	0.646355i	−0.990052	−	0.140703i	$-0.955064\pi$
$257$	−5.98242	+	10.3619i	−0.373173	+	0.646355i	0.616879	+	0.787058i	$0.288397\pi$
$258$	−11.1574	+	17.8877i	−0.694627	+	1.11364i
$259$		−	4.71743i		−	0.293127i
$260$	−8.22628	+	12.6351i	−0.510172	+	0.783595i
$261$	−5.95459	−	0.406715i	−0.368580	−	0.0251750i
$262$	2.91108	+	10.8643i	0.179847	+	0.671198i
$263$	−27.4691	−	15.8593i	−1.69381	−	0.977924i	−0.951387	−	0.307998i	$-0.900341\pi$
$263$	−27.4691	−	15.8593i	−1.69381	−	0.977924i	−0.742428	−	0.669926i	$-0.766326\pi$
$264$	−1.16570	−	0.355362i	−0.0717441	−	0.0218710i
$265$	−0.478060	+	0.478060i	−0.0293670	+	0.0293670i
$266$	2.05579	−	7.67233i	0.126049	−	0.470421i
$267$	6.30622	+	11.8372i	0.385934	+	0.724424i
$268$	7.90468	+	7.90468i	0.482855	+	0.482855i
$269$	−8.83825	+	5.10277i	−0.538878	+	0.311121i	−0.744624	−	0.667484i	$-0.767371\pi$
$269$	−8.83825	+	5.10277i	−0.538878	+	0.311121i	0.205746	+	0.978605i	$0.434038\pi$
$270$	−21.4525	+	3.45108i	−1.30556	+	0.210026i
$271$	2.64573	−	0.708922i	0.160717	−	0.0430639i	−0.177563	−	0.984109i	$-0.556822\pi$
$271$	2.64573	−	0.708922i	0.160717	−	0.0430639i	0.338280	+	0.941045i	$0.390155\pi$
$272$	4.12077			0.249858
$273$	5.86762	+	2.13801i	0.355124	+	0.129398i
$274$	14.0442			0.848440
$275$	8.48574	−	2.27375i	0.511709	−	0.137112i
$276$	−0.880491	−	3.79981i	−0.0529993	−	0.228722i
$277$	22.3808	−	12.9216i	1.34473	−	0.776382i	0.357236	−	0.934014i	$-0.383719\pi$
$277$	22.3808	−	12.9216i	1.34473	−	0.776382i	0.987498	+	0.157632i	$0.0503859\pi$
$278$	8.10157	+	8.10157i	0.485900	+	0.485900i
$279$	2.90683	−	8.48658i	0.174027	−	0.508078i
$280$	1.08228	−	4.03913i	0.0646788	−	0.241384i
$281$	10.3140	−	10.3140i	0.615281	−	0.615281i	−0.329036	−	0.944317i	$-0.606724\pi$
$281$	10.3140	−	10.3140i	0.615281	−	0.615281i	0.944317	+	0.329036i	$0.106724\pi$
$282$	−2.61292	+	8.57124i	−0.155597	+	0.510410i
$283$	−22.7040	−	13.1081i	−1.34961	−	0.779198i	−0.361416	−	0.932405i	$-0.617707\pi$
$283$	−22.7040	−	13.1081i	−1.34961	−	0.779198i	−0.988194	+	0.153207i	$0.951040\pi$
$284$	0.345402	+	1.28906i	0.0204958	+	0.0764914i
$285$	−39.2688	−	42.0425i	−2.32609	−	2.49038i
$286$	2.48203	−	0.524550i	0.146766	−	0.0310173i
$287$			1.54787i			0.0913676i
$288$	0.577186	+	2.94395i	0.0340110	+	0.173474i
$289$	0.00962336	−	0.0166681i	0.000566080	−	0.000980479i
$290$	−4.15964	−	7.20471i	−0.244263	−	0.423075i
$291$	29.0305	+	0.990278i	1.70180	+	0.0580511i
$292$	6.23630	+	1.67101i	0.364952	+	0.0977886i
$293$	−8.71015	−	2.33388i	−0.508853	−	0.136347i	−0.00474716	−	0.999989i	$-0.501511\pi$
$293$	−8.71015	−	2.33388i	−0.508853	−	0.136347i	−0.504106	+	0.863642i	$0.668178\pi$
$294$	−1.73104	−	0.0590488i	−0.100957	−	0.00344379i
$295$	11.8227	+	20.4775i	0.688344	+	1.19225i
$296$	−2.35871	+	4.08541i	−0.137098	+	0.237460i
$297$	2.96297	+	2.14177i	0.171929	+	0.124278i
$298$			15.6220i			0.904956i
$299$	5.42598	+	6.04031i	0.313793	+	0.349320i
$300$	−14.7619	−	15.8045i	−0.852277	−	0.912476i
$301$	3.15028	+	11.7570i	0.181579	+	0.677663i
$302$	9.08382	+	5.24455i	0.522715	+	0.301790i
$303$	5.68892	−	18.6616i	0.326820	−	1.07208i
$304$	−5.61654	+	5.61654i	−0.322130	+	0.322130i
$305$	1.23119	−	4.59487i	0.0704978	−	0.263101i
$306$	−11.6953	−	4.00588i	−0.668575	−	0.229001i
$307$	8.27001	+	8.27001i	0.471994	+	0.471994i	0.902559	−	0.430565i	$-0.141686\pi$
$307$	8.27001	+	8.27001i	0.471994	+	0.471994i	−0.430565	+	0.902559i	$0.641686\pi$
$308$	−0.609333	+	0.351799i	−0.0347200	+	0.0200456i
$309$	0.693246	+	2.99175i	0.0394374	+	0.170195i
$310$	12.0778	−	3.23624i	0.685974	−	0.183806i
$311$	11.0118			0.624422			0.312211	−	0.950013i	$-0.398930\pi$
$311$	11.0118			0.624422			0.312211	+	0.950013i	$0.398930\pi$
$312$	−4.01250	−	4.78538i	−0.227163	−	0.270919i
$313$	−19.0403			−1.07622			−0.538110	−	0.842874i	$-0.680862\pi$
$313$	−19.0403			−1.07622			−0.538110	+	0.842874i	$0.680862\pi$
$314$	−14.7381	+	3.94907i	−0.831720	+	0.222859i
$315$	−6.99818	+	10.4115i	−0.394303	+	0.586621i
$316$	6.37951	−	3.68321i	0.358876	−	0.207197i
$317$	−4.70491	−	4.70491i	−0.264254	−	0.264254i	0.562526	−	0.826780i	$-0.309830\pi$
$317$	−4.70491	−	4.70491i	−0.264254	−	0.264254i	−0.826780	+	0.562526i	$0.809830\pi$
$318$	−0.131669	−	0.247151i	−0.00738361	−	0.0138595i
$319$	−0.362295	+	1.35210i	−0.0202846	+	0.0757032i
$320$	−2.95685	+	2.95685i	−0.165293	+	0.165293i
$321$	−19.8537	−	6.05235i	−1.10813	−	0.337810i
$322$	−1.95025	−	1.12597i	−0.108683	−	0.0627481i
$323$	−8.47146	−	31.6159i	−0.471365	−	1.75916i
$324$	1.22374	−	8.91642i	0.0679856	−	0.495356i
$325$	42.7991	+	13.9614i	2.37407	+	0.774441i
$326$		−	1.16394i		−	0.0644647i
$327$	10.2319	−	16.4039i	0.565823	−	0.907136i
$328$	0.773933	−	1.34049i	0.0427333	−	0.0740162i
$329$	2.58672	+	4.48033i	0.142611	+	0.247009i
$330$	−0.173732	+	5.09304i	−0.00956363	+	0.280363i
$331$	−22.6950	−	6.08110i	−1.24743	−	0.334247i	−0.426085	−	0.904683i	$-0.640108\pi$
$331$	−22.6950	−	6.08110i	−1.24743	−	0.334247i	−0.821342	+	0.570436i	$0.806774\pi$
$332$	14.1490	+	3.79122i	0.776529	+	0.208070i
$333$	10.6658	−	9.30199i	0.584485	−	0.509746i
$334$	−11.9282	−	20.6603i	−0.652685	−	1.13048i
$335$	23.3730	−	40.4832i	1.27700	−	2.21183i
$336$	1.46960	+	0.916660i	0.0801735	+	0.0500079i
$337$			7.09525i			0.386503i	0.981149	+	0.193251i	$0.0619033\pi$
$337$			7.09525i			0.386503i	−0.981149	+	0.193251i	$0.938097\pi$
$338$	12.1257	+	4.68706i	0.659549	+	0.254942i
$339$	−4.51900	+	4.22087i	−0.245438	+	0.229246i
$340$	−4.45984	−	16.6443i	−0.241869	−	0.902667i
$341$	−1.82203	−	1.05195i	−0.0986684	−	0.0569662i
$342$	21.4004	−	10.4805i	1.15720	−	0.566722i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	3.15028	−	11.7570i	0.169852	−	0.633896i
$345$	−14.3950	+	7.66889i	−0.775001	+	0.412879i
$346$	9.93995	+	9.93995i	0.534375	+	0.534375i
$347$	−20.1321	+	11.6233i	−1.08075	+	0.623971i	−0.931099	−	0.364767i	$-0.881148\pi$
$347$	−20.1321	+	11.6233i	−1.08075	+	0.623971i	−0.149651	+	0.988739i	$0.547815\pi$
$348$	3.35695	−	0.777871i	0.179951	−	0.0416983i
$349$	−26.0797	+	6.98803i	−1.39601	+	0.374061i	−0.876912	−	0.480652i	$-0.840400\pi$
$349$	−26.0797	+	6.98803i	−1.39601	+	0.374061i	−0.519102	+	0.854712i	$0.673734\pi$
$350$	−12.4859			−0.667402
$351$	6.73604	+	17.4822i	0.359543	+	0.933128i
$352$	0.703598			0.0375019
$353$	15.0133	−	4.02279i	0.799075	−	0.214112i	0.163897	−	0.986477i	$-0.447593\pi$
$353$	15.0133	−	4.02279i	0.799075	−	0.214112i	0.635178	+	0.772366i	$0.280927\pi$
$354$	−9.54126	+	2.21090i	−0.507112	+	0.117508i
$355$	4.83285	−	2.79025i	0.256501	−	0.148091i
$356$	−5.47551	−	5.47551i	−0.290202	−	0.290202i
$357$	−6.29923	+	3.35589i	−0.333390	+	0.177613i
$358$	−2.41168	+	9.00053i	−0.127461	+	0.475693i
$359$	0.0696043	−	0.0696043i	0.00367357	−	0.00367357i	−0.705268	−	0.708941i	$-0.749173\pi$
$359$	0.0696043	−	0.0696043i	0.00367357	−	0.00367357i	0.708941	+	0.705268i	$0.249173\pi$
$360$	11.2663	−	5.51752i	0.593788	−	0.290799i
$361$	38.1839	+	22.0455i	2.00968	+	1.16029i
$362$	−5.07757	−	18.9497i	−0.266871	−	0.995977i
$363$	−13.2970	+	12.4198i	−0.697913	+	0.651870i
$364$	−3.60039	−	0.192896i	−0.188712	−	0.0101105i
$365$		−	26.9978i		−	1.41313i
$366$	1.67180	+	1.04278i	0.0873865	+	0.0545070i
$367$	3.54542	−	6.14085i	0.185069	−	0.320550i	−0.758531	−	0.651638i	$-0.774082\pi$
$367$	3.54542	−	6.14085i	0.185069	−	0.320550i	0.943600	+	0.331088i	$0.107416\pi$
$368$	1.12597	+	1.95025i	0.0586955	+	0.101664i
$369$	−3.49964	+	3.05213i	−0.182184	+	0.158888i
$370$	19.0543	+	5.10559i	0.990588	+	0.265427i
$371$	−0.156170	−	0.0418456i	−0.00810793	−	0.00217251i
$372$	−0.176568	+	5.17617i	−0.00915460	+	0.268372i
$373$	−2.18505	−	3.78462i	−0.113138	−	0.195960i	0.803896	−	0.594770i	$-0.202757\pi$
$373$	−2.18505	−	3.78462i	−0.113138	−	0.195960i	−0.917034	+	0.398809i	$0.869423\pi$
$374$	−1.44968	+	2.51092i	−0.0749613	+	0.129837i
$375$	−28.6946	+	46.0036i	−1.48178	+	2.37561i
$376$		−	5.17344i		−	0.266800i
$377$	−5.33632	+	4.79360i	−0.274834	+	0.246883i
$378$	−3.27983	−	4.03023i	−0.168696	−	0.207293i
$379$	1.33638	+	4.98744i	0.0686452	+	0.256187i	0.991717	−	0.128439i	$-0.0409968\pi$
$379$	1.33638	+	4.98744i	0.0686452	+	0.256187i	−0.923072	+	0.384627i	$0.874330\pi$
$380$	28.7646	+	16.6073i	1.47559	+	0.851935i
$381$	16.3785	+	4.99293i	0.839095	+	0.255796i
$382$	11.2067	−	11.2067i	0.573383	−	0.573383i
$383$	1.23338	−	4.60305i	0.0630230	−	0.235205i	−0.927229	−	0.374496i	$-0.877816\pi$
$383$	1.23338	−	4.60305i	0.0630230	−	0.235205i	0.990251	+	0.139291i	$0.0444824\pi$
$384$	−0.814384	−	1.52865i	−0.0415589	−	0.0780087i
$385$	2.08043	+	2.08043i	0.106029	+	0.106029i
$386$	2.95039	−	1.70341i	0.150171	−	0.0867013i
$387$	−20.3701	+	30.3055i	−1.03547	+	1.54052i
$388$	−16.1991	+	4.34053i	−0.822383	+	0.220357i
$389$	23.4268			1.18779			0.593894	−	0.804543i	$-0.297590\pi$
$389$	23.4268			1.18779			0.593894	+	0.804543i	$0.297590\pi$
$390$	−14.9861	+	21.3862i	−0.758853	+	1.08293i
$391$	−9.27977			−0.469298
$392$	0.965926	−	0.258819i	0.0487866	−	0.0130723i
$393$	4.39768	+	18.9784i	0.221833	+	0.957336i
$394$	−2.81138	+	1.62315i	−0.141635	+	0.0817732i
$395$	−21.7814	−	21.7814i	−1.09594	−	1.09594i
$396$	−1.99690	−	0.683980i	−0.100348	−	0.0343713i
$397$	−2.12137	+	7.91705i	−0.106468	+	0.397345i	−0.998508	−	0.0546125i	$-0.982608\pi$
$397$	−2.12137	+	7.91705i	−0.106468	+	0.397345i	0.892039	+	0.451958i	$0.149274\pi$
$398$	9.68036	−	9.68036i	0.485232	−	0.485232i
$399$	4.01171	−	13.1597i	0.200837	−	0.658812i
$400$	10.8131	+	6.24297i	0.540657	+	0.312149i
$401$	−2.64602	−	9.87506i	−0.132136	−	0.493137i	0.867858	−	0.496813i	$-0.165497\pi$
$401$	−2.64602	−	9.87506i	−0.132136	−	0.493137i	−0.999993	+	0.00367599i	$0.998830\pi$
$402$	13.2166	+	14.1501i	0.659184	+	0.705743i
$403$	−4.88342	−	9.61192i	−0.243260	−	0.478804i
$404$			11.2638i			0.560394i
$405$	−37.3390	+	4.70723i	−1.85539	+	0.233904i
$406$	0.994745	−	1.72295i	0.0493683	−	0.0855085i
$407$	−1.65959	−	2.87449i	−0.0822626	−	0.142483i
$408$	7.13324	+	0.243326i	0.353148	+	0.0120465i
$409$	−31.7278	−	8.50144i	−1.56884	−	0.420369i	−0.633391	−	0.773832i	$-0.718338\pi$
$409$	−31.7278	−	8.50144i	−1.56884	−	0.420369i	−0.935449	+	0.353463i	$0.885004\pi$
$410$	−6.25204	−	1.67523i	−0.308766	−	0.0827336i
$411$	24.3111	+	0.829291i	1.19918	+	0.0409059i
$412$	−0.886526	−	1.53551i	−0.0436760	−	0.0756490i
$413$	−2.82730	+	4.89703i	−0.139122	+	0.240967i
$414$	−1.29979	−	6.62963i	−0.0638814	−	0.325829i
$415$		−	61.2530i		−	3.00679i
$416$	3.02158	+	1.96725i	0.148145	+	0.0964522i
$417$	13.5458	+	14.5026i	0.663340	+	0.710193i
$418$	−1.44645	−	5.39823i	−0.0707483	−	0.264036i
$419$	14.6566	+	8.46199i	0.716021	+	0.413395i	0.813287	−	0.581863i	$-0.197676\pi$
$419$	14.6566	+	8.46199i	0.716021	+	0.413395i	−0.0972651	+	0.995259i	$0.531009\pi$
$420$	2.11199	−	6.92801i	0.103054	−	0.338052i
$421$	−9.35311	+	9.35311i	−0.455843	+	0.455843i	−0.897288	−	0.441445i	$-0.854466\pi$
$421$	−9.35311	+	9.35311i	−0.455843	+	0.455843i	0.441445	+	0.897288i	$0.354466\pi$
$422$	5.35823	−	19.9972i	0.260835	−	0.973449i
$423$	−5.02920	+	14.6829i	−0.244528	+	0.713907i
$424$	0.114324	+	0.114324i	0.00555207	+	0.00555207i
$425$	−44.5585	+	25.7259i	−2.16140	+	1.24789i
$426$	0.521788	+	2.25181i	0.0252807	+	0.109100i
$427$	1.09882	−	0.294429i	0.0531758	−	0.0142484i
$428$	11.9833			0.579237
$429$	4.32748	−	0.761458i	0.208933	−	0.0367635i
$430$	−50.8977			−2.45450
$431$	33.4316	−	8.95798i	1.61034	−	0.431491i	0.662199	−	0.749328i	$-0.269623\pi$
$431$	33.4316	−	8.95798i	1.61034	−	0.431491i	0.948145	+	0.317837i	$0.102957\pi$
$432$	0.825298	+	5.13019i	0.0397072	+	0.246827i
$433$	10.2297	−	5.90611i	0.491607	−	0.283829i	−0.233634	−	0.972325i	$-0.575062\pi$
$433$	10.2297	−	5.90611i	0.491607	−	0.283829i	0.725241	+	0.688495i	$0.241728\pi$
$434$	2.11439	+	2.11439i	0.101494	+	0.101494i
$435$	−6.77510	−	12.7173i	−0.324841	−	0.609748i
$436$	−2.88897	+	10.7818i	−0.138356	+	0.516353i
$437$	12.6482	−	12.6482i	0.605043	−	0.605043i
$438$	10.6966	+	3.26084i	0.511105	+	0.155809i
$439$	9.96798	+	5.75502i	0.475746	+	0.274672i	0.718642	−	0.695380i	$-0.244764\pi$
$439$	9.96798	+	5.75502i	0.475746	+	0.274672i	−0.242896	+	0.970052i	$0.578097\pi$
$440$	−0.761492	−	2.84193i	−0.0363027	−	0.135483i
$441$	−2.99303	−	0.204432i	−0.142525	−	0.00973486i
$442$	−13.2461	+	6.72980i	−0.630053	+	0.320104i
$443$		−	24.7030i		−	1.17367i	−0.809706	−	0.586836i	$-0.800373\pi$
$443$		−	24.7030i		−	1.17367i	0.809706	−	0.586836i	$-0.199627\pi$
$444$	−4.32428	+	6.93275i	−0.205221	+	0.329014i
$445$	−16.1903	+	28.0424i	−0.767493	+	1.32934i
$446$	−1.49262	−	2.58530i	−0.0706778	−	0.122417i
$447$	−0.922458	+	27.0423i	−0.0436308	+	1.27906i
$448$	−0.965926	−	0.258819i	−0.0456357	−	0.0122281i
$449$	34.4014	+	9.21781i	1.62350	+	0.435016i	0.952027	−	0.306013i	$-0.0989953\pi$
$449$	34.4014	+	9.21781i	1.62350	+	0.435016i	0.671473	+	0.741029i	$0.265662\pi$
$450$	−24.6202	−	28.2300i	−1.16061	−	1.33078i
$451$	0.544537	+	0.943166i	0.0256413	+	0.0444120i
$452$	1.78506	−	3.09181i	0.0839620	−	0.145426i
$453$	15.4148	+	9.61493i	0.724251	+	0.451749i
$454$			0.987297i			0.0463361i
$455$	3.11750	+	14.7512i	0.146151	+	0.691548i
$456$	−10.0541	+	9.39082i	−0.470827	+	0.439765i
$457$	8.49655	+	31.7096i	0.397452	+	1.48331i	0.817564	+	0.575838i	$0.195324\pi$
$457$	8.49655	+	31.7096i	0.397452	+	1.48331i	−0.420112	+	0.907472i	$0.638009\pi$
$458$	5.45879	+	3.15164i	0.255073	+	0.147266i
$459$	−20.0085	−	7.62494i	−0.933917	−	0.355902i
$460$	6.65868	−	6.65868i	0.310463	−	0.310463i
$461$	−9.25958	+	34.5572i	−0.431261	+	1.60949i	0.318596	+	0.947890i	$0.396789\pi$
$461$	−9.25958	+	34.5572i	−0.431261	+	1.60949i	−0.749858	+	0.661599i	$0.769878\pi$
$462$	−1.07556	+	0.572999i	−0.0500394	+	0.0266583i
$463$	−12.6508	−	12.6508i	−0.587932	−	0.587932i	0.349139	−	0.937071i	$-0.386474\pi$
$463$	−12.6508	−	12.6508i	−0.587932	−	0.587932i	−0.937071	+	0.349139i	$0.886474\pi$
$464$	−1.72295	+	0.994745i	−0.0799859	+	0.0461799i
$465$	21.0983	−	4.88890i	0.978412	−	0.226717i
$466$	25.7441	−	6.89811i	1.19257	−	0.319549i
$467$	4.37635			0.202513			0.101257	−	0.994860i	$-0.467714\pi$
$467$	4.37635			0.202513			0.101257	+	0.994860i	$0.467714\pi$
$468$	−6.66324	−	8.52064i	−0.308008	−	0.393867i
$469$	11.1789			0.516194
$470$	−20.8962	+	5.59913i	−0.963871	+	0.258268i
$471$	−25.7455	+	5.96574i	−1.18629	+	0.274887i
$472$	4.89703	−	2.82730i	0.225404	−	0.130137i
$473$	6.05568	+	6.05568i	0.278440	+	0.278440i
$474$	11.2607	−	5.99910i	0.517221	−	0.275548i
$475$	25.6685	−	95.7963i	1.17775	−	4.39544i
$476$	2.91383	−	2.91383i	0.133555	−	0.133555i
$477$	−0.213330	−	0.435604i	−0.00976773	−	0.0199449i
$478$	11.8689	+	6.85249i	0.542869	+	0.313426i
$479$	−3.87231	−	14.4516i	−0.176930	−	0.660313i	−0.996215	−	0.0869256i	$-0.972296\pi$
$479$	−3.87231	−	14.4516i	−0.176930	−	0.660313i	0.819285	−	0.573387i	$-0.194371\pi$
$480$	−5.29304	+	4.94384i	−0.241593	+	0.225654i
$481$	0.909974	−	16.9846i	0.0414912	−	0.774430i
$482$			14.1207i			0.643181i
$483$	−3.30947	−	2.06427i	−0.150586	−	0.0939276i
$484$	5.25248	−	9.09755i	0.238749	−	0.413525i
$485$	35.0640	+	60.7326i	1.59217	+	2.75772i
$486$	2.64485	−	15.3624i	0.119973	−	0.696855i
$487$	−4.15885	−	1.11436i	−0.188456	−	0.0504965i	0.163357	−	0.986567i	$-0.447768\pi$
$487$	−4.15885	−	1.11436i	−0.188456	−	0.0504965i	−0.351812	+	0.936071i	$0.614434\pi$
$488$	−1.09882	−	0.294429i	−0.0497414	−	0.0133282i
$489$	0.0687292	−	2.01483i	0.00310804	−	0.0911138i
$490$	−2.09081	−	3.62139i	−0.0944532	−	0.163598i
$491$	−2.76830	+	4.79484i	−0.124932	+	0.216388i	−0.921706	−	0.387889i	$-0.873204\pi$
$491$	−2.76830	+	4.79484i	−0.124932	+	0.216388i	0.796775	+	0.604277i	$0.206538\pi$
$492$	1.41887	−	2.27475i	0.0639674	−	0.102554i
$493$		−	8.19823i		−	0.369230i
$494$	8.88162	−	27.2268i	0.399603	−	1.22499i
$495$	−0.601476	+	8.80602i	−0.0270343	+	0.395801i
$496$	−0.773920	−	2.88831i	−0.0347501	−	0.129689i
$497$	1.15574	+	0.667265i	0.0518419	+	0.0299309i
$498$	24.2687	+	7.39825i	1.08751	+	0.331524i
$499$	0.246664	−	0.246664i	0.0110422	−	0.0110422i	−0.701564	−	0.712606i	$-0.747515\pi$
$499$	0.246664	−	0.246664i	0.0110422	−	0.0110422i	0.712606	+	0.701564i	$0.247515\pi$
$500$	8.10191	−	30.2368i	0.362329	−	1.35223i
$501$	−19.4284	−	36.4683i	−0.867995	−	1.62928i
$502$	8.62808	+	8.62808i	0.385090	+	0.385090i
$503$	−11.2647	+	6.50369i	−0.502269	+	0.289985i	−0.729650	−	0.683821i	$-0.760317\pi$
$503$	−11.2647	+	6.50369i	−0.502269	+	0.289985i	0.227381	+	0.973806i	$0.426984\pi$
$504$	2.48982	+	1.67356i	0.110905	+	0.0745461i
$505$	45.4959	−	12.1906i	2.02454	−	0.542474i
$506$	−1.58447			−0.0704381
$507$	20.7133	+	8.82951i	0.919909	+	0.392132i
$508$	−9.88575			−0.438609
$509$	24.3803	−	6.53269i	1.08064	−	0.289557i	0.325782	−	0.945445i	$-0.394372\pi$
$509$	24.3803	−	6.53269i	1.08064	−	0.289557i	0.754858	+	0.655888i	$0.227706\pi$
$510$	−6.73735	−	29.0754i	−0.298335	−	1.28748i
$511$	5.59131	−	3.22815i	0.247345	−	0.142805i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	37.6639	−	16.8786i	1.66290	−	0.745208i
$514$	3.09673	−	11.5572i	0.136591	−	0.509764i
$515$	−5.24265	+	5.24265i	−0.231019	+	0.231019i
$516$	6.14752	−	20.1659i	0.270629	−	0.887754i
$517$	3.15235	+	1.82001i	0.138640	+	0.0800440i
$518$	1.22096	+	4.55669i	0.0536459	+	0.200209i
$519$	16.6196	+	17.7934i	0.729517	+	0.781045i
$520$	4.67577	−	14.3337i	0.205046	−	0.628574i
$521$			24.4089i			1.06938i	0.845050	+	0.534688i	$0.179571\pi$
$521$			24.4089i			1.06938i	−0.845050	+	0.534688i	$0.820429\pi$
$522$	5.85696	−	1.14831i	0.256352	−	0.0502600i
$523$	7.91245	−	13.7048i	0.345987	−	0.599268i	−0.639545	−	0.768753i	$-0.720877\pi$
$523$	7.91245	−	13.7048i	0.345987	−	0.599268i	0.985533	+	0.169486i	$0.0542106\pi$
$524$	−5.62377	−	9.74065i	−0.245675	−	0.425522i
$525$	−21.6137	−	0.737280i	−0.943300	−	0.0321775i
$526$	30.6378	+	8.20936i	1.33587	+	0.357945i
$527$	11.9021	+	3.18915i	0.518462	+	0.138922i
$528$	1.21796	+	0.0415466i	0.0530048	+	0.00180808i
$529$	8.96436	+	15.5267i	0.389755	+	0.675075i
$530$	0.338040	−	0.585502i	0.0146835	−	0.0254326i
$531$	−16.6469	+	3.26376i	−0.722413	+	0.141635i
$532$			7.94298i			0.344372i
$533$	−0.298577	+	5.57292i	−0.0129328	+	0.241390i
$534$	−9.15503	−	9.80168i	−0.396177	−	0.424160i
$535$	−12.9694	−	48.4023i	−0.560715	−	2.09262i
$536$	−9.68122	−	5.58945i	−0.418165	−	0.241428i
$537$	−4.70620	+	15.4379i	−0.203088	+	0.666195i
$538$	7.21640	−	7.21640i	0.311121	−	0.311121i
$539$	−0.182104	+	0.679623i	−0.00784379	+	0.0292734i
$540$	19.8283	−	8.88581i	0.853276	−	0.382384i
$541$	−31.4485	−	31.4485i	−1.35208	−	1.35208i	−0.883335	−	0.468743i	$-0.844707\pi$
$541$	−31.4485	−	31.4485i	−1.35208	−	1.35208i	−0.468743	−	0.883335i	$-0.655293\pi$
$542$	−2.37210	+	1.36953i	−0.101890	+	0.0588264i
$543$	−7.67054	−	33.1027i	−0.329174	−	1.42057i
$544$	−3.98036	+	1.06653i	−0.170656	+	0.0457273i
$545$	46.6757			1.99937
$546$	−6.22104	−	0.546510i	−0.266236	−	0.0233885i
$547$	22.6058			0.966554			0.483277	−	0.875467i	$-0.339446\pi$
$547$	22.6058			0.966554			0.483277	+	0.875467i	$0.339446\pi$
$548$	−13.5656	+	3.63490i	−0.579495	+	0.155275i
$549$	2.83239	+	1.90382i	0.120883	+	0.0812529i
$550$	−7.60810	+	4.39254i	−0.324411	+	0.187299i
$551$	11.1740	+	11.1740i	0.476030	+	0.476030i
$552$	1.83395	+	3.44245i	0.0780582	+	0.146520i
$553$	1.90657	−	7.11542i	0.0810757	−	0.302579i
$554$	−18.2739	+	18.2739i	−0.776382	+	0.776382i
$555$	32.6824	+	9.96314i	1.38729	+	0.422912i
$556$	−9.92236	−	5.72868i	−0.420802	−	0.242950i
$557$	−9.86481	−	36.8160i	−0.417985	−	1.55994i	−0.778780	−	0.627297i	$-0.784161\pi$
$557$	−9.86481	−	36.8160i	−0.417985	−	1.55994i	0.360795	−	0.932645i	$-0.382505\pi$
$558$	−0.611293	+	8.94974i	−0.0258781	+	0.378873i
$559$	9.07436	+	42.9375i	0.383805	+	1.81606i
$560$			4.18162i			0.176706i
$561$	−2.65773	+	4.26092i	−0.112209	+	0.179896i
$562$	−7.29309	+	12.6320i	−0.307641	+	0.532849i
$563$	−9.25884	−	16.0368i	−0.390214	−	0.675870i	0.602264	−	0.798297i	$-0.294266\pi$
$563$	−9.25884	−	16.0368i	−0.390214	−	0.675870i	−0.992477	+	0.122427i	$0.960932\pi$
$564$	0.305485	−	8.95545i	0.0128633	−	0.377093i
$565$	−14.4202	−	3.86387i	−0.606661	−	0.162554i
$566$	25.3230	+	6.78527i	1.06440	+	0.285206i
$567$	−5.43954	−	7.17017i	−0.228439	−	0.301119i
$568$	−0.667265	−	1.15574i	−0.0279978	−	0.0484936i
$569$	−3.95174	+	6.84462i	−0.165666	+	0.286941i	−0.936891	−	0.349620i	$-0.886311\pi$
$569$	−3.95174	+	6.84462i	−0.165666	+	0.286941i	0.771226	+	0.636562i	$0.219644\pi$
$570$	48.8122	+	30.4464i	2.04452	+	1.27526i
$571$		−	0.428316i		−	0.0179245i	−0.999960	−	0.00896224i	$-0.997147\pi$
$571$		−	0.428316i		−	0.0179245i	0.999960	−	0.00896224i	$-0.00285281\pi$
$572$	−2.26170	+	1.14907i	−0.0945663	+	0.0480452i
$573$	20.0610	−	18.7375i	0.838060	−	0.782771i
$574$	−0.400617	−	1.49512i	−0.0167214	−	0.0624052i
$575$	−24.3507	−	14.0589i	−1.01549	−	0.586295i
$576$	−1.31947	−	2.69425i	−0.0549779	−	0.112261i
$577$	15.7496	−	15.7496i	0.655664	−	0.655664i	−0.298687	−	0.954351i	$-0.596549\pi$
$577$	15.7496	−	15.7496i	0.655664	−	0.655664i	0.954351	+	0.298687i	$0.0965486\pi$
$578$	−0.00498142	+	0.0185909i	−0.000207200	+	0.000773279i
$579$	5.20784	−	2.77446i	0.216431	−	0.115303i
$580$	5.88262	+	5.88262i	0.244263	+	0.244263i
$581$	12.6857	−	7.32408i	0.526291	−	0.303854i
$582$	−28.2976	+	6.55711i	−1.17297	+	0.271801i
$583$	−0.109881	+	0.0294424i	−0.00455079	+	0.00121938i
$584$	−6.45629			−0.267163
$585$	−27.2045	+	36.1355i	−1.12477	+	1.49402i
$586$	9.01742			0.372506
$587$	−38.7422	+	10.3809i	−1.59906	+	0.428467i	−0.944759	−	0.327766i	$-0.893704\pi$
$587$	−38.7422	+	10.3809i	−1.59906	+	0.428467i	−0.654303	+	0.756233i	$0.727038\pi$
$588$	1.68734	−	0.390990i	0.0695849	−	0.0161242i
$589$	−20.5691	+	11.8755i	−0.847533	+	0.489323i
$590$	−16.7198	−	16.7198i	−0.688344	−	0.688344i
$591$	−4.96247	+	2.64374i	−0.204129	+	0.108749i
$592$	1.22096	−	4.55669i	0.0501812	−	0.187279i
$593$	6.08567	−	6.08567i	0.249909	−	0.249909i	−0.571024	−	0.820933i	$-0.693454\pi$
$593$	6.08567	−	6.08567i	0.249909	−	0.249909i	0.820933	+	0.571024i	$0.193454\pi$
$594$	−3.41634	−	1.30191i	−0.140174	−	0.0534182i
$595$	−14.9229	−	8.61575i	−0.611780	−	0.353211i
$596$	−4.04326	−	15.0897i	−0.165619	−	0.618097i
$597$	17.3287	−	16.1855i	0.709218	−	0.662429i
$598$	−6.80444	−	4.43014i	−0.278254	−	0.181162i
$599$			18.8526i			0.770295i	0.922855	+	0.385147i	$0.125849\pi$
$599$			18.8526i			0.770295i	−0.922855	+	0.385147i	$0.874151\pi$
$600$	18.3494	+	11.4454i	0.749111	+	0.467255i
$601$	16.9224	−	29.3104i	0.690278	−	1.19560i	−0.281469	−	0.959570i	$-0.590822\pi$
$601$	16.9224	−	29.3104i	0.690278	−	1.19560i	0.971747	−	0.236025i	$-0.0758449\pi$
$602$	−6.08588	−	10.5411i	−0.248042	−	0.429621i
$603$	22.0429	+	25.2749i	0.897658	+	1.02927i
$604$	−10.1317	−	2.71478i	−0.412253	−	0.110463i
$605$	−42.4309	−	11.3693i	−1.72506	−	0.462229i
$606$	−0.665112	+	19.4981i	−0.0270183	+	0.792056i
$607$	22.6553	+	39.2401i	0.919549	+	1.59270i	0.800102	+	0.599864i	$0.204779\pi$
$607$	22.6553	+	39.2401i	0.919549	+	1.59270i	0.119447	+	0.992841i	$0.461888\pi$
$608$	3.97149	−	6.87882i	0.161065	−	0.278973i
$609$	1.82368	−	2.92376i	0.0738994	−	0.118477i
$610$			4.75696i			0.192604i
$611$	8.44896	+	16.6299i	0.341808	+	0.672774i
$612$	12.3336	+	0.842418i	0.498555	+	0.0340527i
$613$	−7.88320	−	29.4205i	−0.318400	−	1.18828i	−0.920783	−	0.390076i	$-0.872449\pi$
$613$	−7.88320	−	29.4205i	−0.318400	−	1.18828i	0.602383	−	0.798207i	$-0.294218\pi$
$614$	−10.1286	−	5.84778i	−0.408759	−	0.235997i
$615$	−10.7236	−	3.26907i	−0.432419	−	0.131822i
$616$	0.497519	−	0.497519i	0.0200456	−	0.0200456i
$617$	−4.94428	+	18.4523i	−0.199049	+	0.742861i	0.792132	+	0.610349i	$0.208971\pi$
$617$	−4.94428	+	18.4523i	−0.199049	+	0.742861i	−0.991181	+	0.132512i	$0.957696\pi$
$618$	−1.44395	−	2.71038i	−0.0580840	−	0.109027i
$619$	2.17589	+	2.17589i	0.0874563	+	0.0874563i	0.749482	−	0.662025i	$-0.230303\pi$
$619$	2.17589	+	2.17589i	0.0874563	+	0.0874563i	−0.662025	+	0.749482i	$0.730303\pi$
$620$	−10.8287	+	6.25194i	−0.434890	+	0.251084i
$621$	−1.85853	−	11.5529i	−0.0745802	−	0.463603i
$622$	−10.6366	+	2.85006i	−0.426488	+	0.114277i
$623$	−7.74354			−0.310239
$624$	5.11432	+	3.58381i	0.204737	+	0.143467i
$625$	−68.4691			−2.73877
$626$	18.3915	−	4.92799i	0.735072	−	0.196962i
$627$	−2.18511	−	9.42999i	−0.0872650	−	0.376598i
$628$	13.2138	−	7.62901i	0.527289	−	0.304431i
$629$	13.7458	+	13.7458i	0.548079	+	0.548079i
$630$	4.06503	−	11.8680i	0.161955	−	0.472832i
$631$	3.35835	−	12.5335i	0.133694	−	0.498952i	−0.866306	−	0.499513i	$-0.833512\pi$
$631$	3.35835	−	12.5335i	0.133694	−	0.498952i	1.00000		0.000561713i	$0.000178799\pi$
$632$	−5.20885	+	5.20885i	−0.207197	+	0.207197i
$633$	10.4562	−	34.2996i	0.415595	−	1.36329i
$634$	5.76231	+	3.32687i	0.228851	+	0.132127i
$635$	10.6992	+	39.9299i	0.424584	+	1.58457i
$636$	0.191150	+	0.204651i	0.00757957	+	0.00811494i
$637$	−2.68226	+	2.40946i	−0.106275	+	0.0954663i
$638$		−	1.39980i		−	0.0554186i
$639$	0.770272	+	3.92879i	0.0304715	+	0.155421i
$640$	2.09081	−	3.62139i	0.0826465	−	0.143148i
$641$	−6.89102	−	11.9356i	−0.272179	−	0.471428i	0.697241	−	0.716837i	$-0.254411\pi$
$641$	−6.89102	−	11.9356i	−0.272179	−	0.471428i	−0.969419	+	0.245410i	$0.921078\pi$
$642$	20.7437	+	0.707602i	0.818688	+	0.0279268i
$643$	−7.76316	−	2.08013i	−0.306149	−	0.0820325i	0.102474	−	0.994736i	$-0.467324\pi$
$643$	−7.76316	−	2.08013i	−0.306149	−	0.0820325i	−0.408623	+	0.912703i	$0.633991\pi$
$644$	2.17522	+	0.582847i	0.0857155	+	0.0229674i
$645$	−88.1062	−	3.00545i	−3.46918	−	0.118339i
$646$	16.3656	+	28.3461i	0.643896	+	1.11526i
$647$	21.3142	−	36.9173i	0.837948	−	1.45137i	−0.0536593	−	0.998559i	$-0.517088\pi$
$647$	21.3142	−	36.9173i	0.837948	−	1.45137i	0.891607	−	0.452809i	$-0.149578\pi$
$648$	1.12569	+	8.92932i	0.0442215	+	0.350777i
$649$			3.97857i			0.156172i
$650$	−44.9542	−	2.40849i	−1.76325	−	0.0944688i
$651$	3.53525	+	3.78495i	0.138557	+	0.148344i
$652$	0.301250	+	1.12428i	0.0117979	+	0.0440302i
$653$	12.7454	+	7.35857i	0.498766	+	0.287963i	0.728204	−	0.685360i	$-0.240355\pi$
$653$	12.7454	+	7.35857i	0.498766	+	0.287963i	−0.229438	+	0.973323i	$0.573689\pi$
$654$	−5.63758	+	18.4931i	−0.220447	+	0.723138i
$655$	−33.2573	+	33.2573i	−1.29947	+	1.29947i
$656$	−0.400617	+	1.49512i	−0.0156415	+	0.0583748i
$657$	18.3238	+	6.27628i	0.714880	+	0.244861i
$658$	−3.65818	−	3.65818i	−0.142611	−	0.142611i
$659$	−24.2047	+	13.9746i	−0.942881	+	0.544373i	−0.890862	−	0.454273i	$-0.849899\pi$
$659$	−24.2047	+	13.9746i	−0.942881	+	0.544373i	−0.0520190	+	0.998646i	$0.516566\pi$
$660$	−1.15036	−	4.96446i	−0.0447778	−	0.193241i
$661$	−5.53110	+	1.48206i	−0.215135	+	0.0576453i	−0.364777	−	0.931095i	$-0.618855\pi$
$661$	−5.53110	+	1.48206i	−0.215135	+	0.0576453i	0.149642	+	0.988740i	$0.452188\pi$
$662$	23.4956			0.913181
$663$	−23.3270	+	10.8674i	−0.905945	+	0.422055i
$664$	−14.6482			−0.568459
$665$	32.0828	−	8.59655i	1.24412	−	0.333360i
$666$	−7.89488	+	11.7456i	−0.305921	+	0.455131i
$667$	3.87999	−	2.24011i	0.150234	−	0.0867376i
$668$	16.8691	+	16.8691i	0.652685	+	0.652685i
$669$	−2.43114	−	4.56341i	−0.0939932	−	0.176431i
$670$	−12.0987	+	45.1531i	−0.467415	+	1.74442i
$671$	0.565971	−	0.565971i	0.0218491	−	0.0218491i
$672$	−1.65678	−	0.505064i	−0.0639116	−	0.0194833i
$673$	−4.37077	−	2.52346i	−0.168481	−	0.0972723i	0.413389	−	0.910555i	$-0.364345\pi$
$673$	−4.37077	−	2.52346i	−0.168481	−	0.0972723i	−0.581869	+	0.813282i	$0.697678\pi$
$674$	−1.83638	−	6.85348i	−0.0707349	−	0.263986i
$675$	−40.9517	−	50.3212i	−1.57623	−	1.93686i
$676$	−12.9256	−	1.38900i	−0.497138	−	0.0534231i
$677$			39.7859i			1.52910i	0.644567	+	0.764548i	$0.277038\pi$
$677$			39.7859i			1.52910i	−0.644567	+	0.764548i	$0.722962\pi$
$678$	3.27258	−	5.24665i	0.125683	−	0.201496i
$679$	−8.38526	+	14.5237i	−0.321797	+	0.557368i
$680$	8.61575	+	14.9229i	0.330399	+	0.572268i
$681$	−0.0582987	+	1.70905i	−0.00223401	+	0.0654911i
$682$	2.03221	+	0.544529i	0.0778173	+	0.0208511i
$683$	−0.880806	−	0.236011i	−0.0337031	−	0.00903072i	0.241928	−	0.970294i	$-0.422220\pi$
$683$	−0.880806	−	0.236011i	−0.0337031	−	0.00903072i	−0.275631	+	0.961263i	$0.588887\pi$
$684$	−17.9586	+	15.6622i	−0.686666	+	0.598861i
$685$	29.3637	+	50.8594i	1.12193	+	1.94324i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	9.26331	+	5.77796i	0.353417	+	0.220443i
$688$			12.1718i			0.464044i
$689$	−0.554200	−	0.180785i	−0.0211133	−	0.00688735i
$690$	11.9197	−	11.1333i	0.453774	−	0.423837i
$691$	5.43485	+	20.2831i	0.206751	+	0.771607i	0.988909	+	0.148525i	$0.0474527\pi$
$691$	5.43485	+	20.2831i	0.206751	+	0.771607i	−0.782157	+	0.623081i	$0.785881\pi$
$692$	−12.1739	−	7.02861i	−0.462782	−	0.267188i
$693$	−1.89567	+	0.928376i	−0.0720105	+	0.0352661i
$694$	16.4378	−	16.4378i	0.623971	−	0.623971i
$695$	−12.4001	+	46.2778i	−0.470362	+	1.75542i
$696$	−3.04124	+	1.62021i	−0.115278	+	0.0614138i
$697$	−4.51021	−	4.51021i	−0.170836	−	0.170836i
$698$	23.3824	−	13.4998i	0.885037	−	0.510976i
$699$	44.9715	−	10.4208i	1.70098	−	0.394150i
$700$	12.0605	−	3.23160i	0.455844	−	0.122143i
$701$	−6.08878			−0.229970			−0.114985	−	0.993367i	$-0.536682\pi$
$701$	−6.08878			−0.229970			−0.114985	+	0.993367i	$0.536682\pi$
$702$	−11.0312	−	15.1431i	−0.416347	−	0.571538i
$703$	−37.4705			−1.41322
$704$	−0.679623	+	0.182104i	−0.0256143	+	0.00686332i
$705$	−36.5029	+	8.45844i	−1.37478	+	0.318563i
$706$	−13.4605	+	7.77144i	−0.506593	+	0.292482i
$707$	7.96469	+	7.96469i	0.299543	+	0.299543i
$708$	8.64393	−	4.60502i	0.324859	−	0.173067i
$709$	−7.96160	+	29.7131i	−0.299004	+	1.11590i	0.638981	+	0.769223i	$0.279356\pi$
$709$	−7.96160	+	29.7131i	−0.299004	+	1.11590i	−0.937985	+	0.346676i	$0.887310\pi$
$710$	−3.94601	+	3.94601i	−0.148091	+	0.148091i
$711$	19.8470	−	9.71978i	0.744321	−	0.364520i
$712$	6.70611	+	3.87177i	0.251322	+	0.145101i
$713$	1.74283	+	6.50433i	0.0652695	+	0.243589i
$714$	5.21602	−	4.87190i	0.195205	−	0.182326i
$715$	7.08906	+	7.89168i	0.265116	+	0.295132i
$716$		−	9.31803i		−	0.348231i
$717$	20.1409	+	12.5628i	0.752176	+	0.469167i
$718$	−0.0492176	+	0.0852475i	−0.00183679	+	0.00318141i
$719$	−13.6742	−	23.6844i	−0.509962	−	0.883281i	−0.999933	−	0.0115420i	$-0.996326\pi$
$719$	−13.6742	−	23.6844i	−0.509962	−	0.883281i	0.489971	−	0.871739i	$-0.337007\pi$
$720$	−9.45441	+	8.24546i	−0.352345	+	0.307290i
$721$	−1.71264	−	0.458900i	−0.0637819	−	0.0170903i
$722$	−42.5886	−	11.4116i	−1.58498	−	0.424695i
$723$	−0.833811	+	24.4436i	−0.0310098	+	0.909066i
$724$	9.80911	+	16.9899i	0.364553	+	0.631424i
$725$	12.4203	−	21.5126i	0.461279	−	0.798959i
$726$	9.62946	−	15.4381i	0.357383	−	0.572962i
$727$		−	0.552818i		−	0.0205029i	−0.999947	−	0.0102514i	$-0.996737\pi$
$727$		−	0.552818i		−	0.0205029i	0.999947	−	0.0102514i	$-0.00326319\pi$
$728$	3.52763	−	0.745526i	0.130743	−	0.0276310i
$729$	5.48549	−	26.4369i	0.203166	−	0.979144i
$730$	6.98754	+	26.0778i	0.258620	+	0.965184i
$731$	−43.4373	−	25.0785i	−1.60659	−	0.927563i
$732$	−1.88473	−	0.574554i	−0.0696615	−	0.0212361i
$733$	−32.0572	+	32.0572i	−1.18406	+	1.18406i	−0.205378	+	0.978683i	$0.565842\pi$
$733$	−32.0572	+	32.0572i	−1.18406	+	1.18406i	−0.978683	+	0.205378i	$0.934158\pi$
$734$	−1.83524	+	6.84923i	−0.0677401	+	0.252810i
$735$	−3.40545	−	6.39224i	−0.125612	−	0.235781i
$736$	−1.59237	−	1.59237i	−0.0586955	−	0.0586955i
$737$	6.81168	−	3.93273i	0.250912	−	0.144864i
$738$	2.59044	−	3.85391i	0.0953554	−	0.141864i
$739$	14.1468	−	3.79062i	0.520398	−	0.139440i	0.0109472	−	0.999940i	$-0.496515\pi$
$739$	14.1468	−	3.79062i	0.520398	−	0.139440i	0.509451	+	0.860500i	$0.329849\pi$
$740$	−19.7265			−0.725160
$741$	16.9822	−	46.6064i	0.623856	−	1.71213i
$742$	0.161679			0.00593542
$743$	−8.50232	+	2.27819i	−0.311920	+	0.0835787i	−0.411383	−	0.911463i	$-0.634954\pi$
$743$	−8.50232	+	2.27819i	−0.311920	+	0.0835787i	0.0994631	+	0.995041i	$0.468287\pi$
$744$	−1.16914	−	5.04549i	−0.0428627	−	0.184977i
$745$	−56.5732	+	32.6626i	−2.07268	+	1.19666i
$746$	3.09013	+	3.09013i	0.113138	+	0.113138i
$747$	41.5734	+	14.2397i	1.52109	+	0.521005i
$748$	0.750411	−	2.80057i	0.0274377	−	0.102399i
$749$	8.47350	−	8.47350i	0.309615	−	0.309615i
$750$	15.8102	−	51.8627i	0.577307	−	1.89376i
$751$	1.83745	+	1.06085i	0.0670495	+	0.0387111i	0.533150	−	0.846021i	$-0.321008\pi$
$751$	1.83745	+	1.06085i	0.0670495	+	0.0387111i	−0.466100	+	0.884732i	$0.654341\pi$
$752$	1.33899	+	4.99716i	0.0488278	+	0.182228i
$753$	14.4261	+	15.4451i	0.525716	+	0.562849i
$754$	3.91382	−	6.01140i	0.142533	−	0.218922i
$755$			43.8614i			1.59628i
$756$	4.21117	+	3.04402i	0.153159	+	0.110710i
$757$	12.5472	−	21.7324i	0.456035	−	0.789876i	−0.542712	−	0.839919i	$-0.682602\pi$
$757$	12.5472	−	21.7324i	0.456035	−	0.789876i	0.998747	+	0.0500426i	$0.0159357\pi$
$758$	−2.58169	−	4.47161i	−0.0937711	−	0.162416i
$759$	−2.74278	−	0.0935608i	−0.0995566	−	0.00339604i
$760$	−32.0828	−	8.59655i	−1.16376	−	0.311830i
$761$	−42.5197	−	11.3931i	−1.54134	−	0.413000i	−0.614640	−	0.788808i	$-0.710699\pi$
$761$	−42.5197	−	11.3931i	−1.54134	−	0.413000i	−0.926698	+	0.375808i	$0.877365\pi$
$762$	−17.1127	−	0.583741i	−0.619926	−	0.0211467i
$763$	5.58105	+	9.66667i	0.202048	+	0.349957i
$764$	−7.92432	+	13.7253i	−0.286692	+	0.496565i
$765$	−9.94578	−	50.7287i	−0.359590	−	1.83410i
$766$			4.76543i			0.172182i
$767$	−11.1240	+	17.0858i	−0.401664	+	0.616934i
$768$	1.18228	+	1.26579i	0.0426618	+	0.0456751i
$769$	−0.210414	−	0.785274i	−0.00758771	−	0.0283177i	0.962028	−	0.272950i	$-0.0879994\pi$
$769$	−0.210414	−	0.785274i	−0.00758771	−	0.0283177i	−0.969616	+	0.244632i	$0.921333\pi$
$770$	−2.54800	−	1.47109i	−0.0918236	−	0.0530144i
$771$	6.04301	−	19.8231i	0.217634	−	0.713911i
$772$	−2.40899	+	2.40899i	−0.0867013	+	0.0867013i
$773$	−8.63524	+	32.2271i	−0.310588	+	1.15913i	0.617440	+	0.786618i	$0.288170\pi$
$773$	−8.63524	+	32.2271i	−0.310588	+	1.15913i	−0.928028	+	0.372511i	$0.878497\pi$
$774$	11.8324	−	34.5451i	0.425307	−	1.24170i
$775$	26.4002	+	26.4002i	0.948322	+	0.948322i
$776$	14.5237	−	8.38526i	0.521370	−	0.301013i
$777$	1.84447	+	7.95992i	0.0661700	+	0.285561i
$778$	−22.6286	+	6.06331i	−0.811274	+	0.217380i
$779$	12.2947			0.440502
$780$	8.94035	−	24.5361i	0.320116	−	0.878535i
$781$	0.938972			0.0335990
$782$	8.96357	−	2.40178i	0.320537	−	0.0858875i
$783$	10.2065	−	1.64192i	0.364749	−	0.0586775i
$784$	−0.866025	+	0.500000i	−0.0309295	+	0.0178571i
$785$	−45.1157	−	45.1157i	−1.61025	−	1.61025i
$786$	−9.15981	−	17.1936i	−0.326720	−	0.613274i
$787$	−8.11134	+	30.2719i	−0.289138	+	1.07908i	0.656624	+	0.754218i	$0.271984\pi$
$787$	−8.11134	+	30.2719i	−0.289138	+	1.07908i	−0.945762	+	0.324860i	$0.894683\pi$
$788$	2.29548	−	2.29548i	0.0817732	−	0.0817732i
$789$	52.5505	+	16.0199i	1.87085	+	0.570323i
$790$	26.6767	+	15.4018i	0.949114	+	0.547971i
$791$	−0.924013	−	3.44846i	−0.0328541	−	0.122613i
$792$	2.10589	+	0.143838i	0.0748294	+	0.00511106i
$793$	4.01299	−	0.848100i	0.142505	−	0.0301169i
$794$		−	8.19634i		−	0.290877i
$795$	0.619735	−	0.993569i	0.0219797	−	0.0352383i
$796$	−6.84505	+	11.8560i	−0.242616	+	0.420224i
$797$	−0.223512	−	0.387133i	−0.00791719	−	0.0137130i	0.862040	−	0.506841i	$-0.169187\pi$
$797$	−0.223512	−	0.387133i	−0.00791719	−	0.0137130i	−0.869957	+	0.493128i	$0.835853\pi$
$798$	−0.469023	+	13.7497i	−0.0166032	+	0.486732i
$799$	−20.5922	−	5.51765i	−0.728498	−	0.195200i
$800$	−12.0605	−	3.23160i	−0.426403	−	0.114254i
$801$	−15.2690	−	17.5077i	−0.539503	−	0.618605i
$802$	5.11171	+	8.85374i	0.180501	+	0.312636i
$803$	2.27132	−	3.93404i	0.0801530	−	0.138829i
$804$	−16.4286	−	10.2473i	−0.579391	−	0.361393i
$805$		−	9.41680i		−	0.331899i
$806$	7.20477	+	8.02048i	0.253777	+	0.282509i
$807$	12.9180	−	12.0658i	0.454736	−	0.424736i
$808$	−2.91528	−	10.8800i	−0.102559	−	0.382756i
$809$	−22.7298	−	13.1230i	−0.799135	−	0.461381i	0.0440333	−	0.999030i	$-0.485979\pi$
$809$	−22.7298	−	13.1230i	−0.799135	−	0.461381i	−0.843169	+	0.537649i	$0.819313\pi$
$810$	34.8484	−	14.2109i	1.22445	−	0.499320i
$811$	−0.244577	+	0.244577i	−0.00858827	+	0.00858827i	−0.711388	−	0.702800i	$-0.751933\pi$
$811$	−0.244577	+	0.244577i	−0.00858827	+	0.00858827i	0.702800	+	0.711388i	$0.251933\pi$
$812$	−0.514918	+	1.92170i	−0.0180701	+	0.0674384i
$813$	−4.18707	+	2.23065i	−0.146847	+	0.0782323i
$814$	2.34701	+	2.34701i	0.0822626	+	0.0822626i
$815$	4.21508	−	2.43358i	0.147648	−	0.0852445i
$816$	−6.95315	+	1.61118i	−0.243409	+	0.0564026i
$817$	93.3858	−	25.0227i	3.26716	−	0.875432i
$818$	32.8471			1.14847
$819$	−10.7366	−	1.31338i	−0.375168	−	0.0458931i
$820$	6.47259			0.226032
$821$	−3.01771	+	0.808593i	−0.105319	+	0.0282201i	−0.311094	−	0.950379i	$-0.600695\pi$
$821$	−3.01771	+	0.808593i	−0.105319	+	0.0282201i	0.205775	+	0.978599i	$0.434029\pi$
$822$	−23.6973	+	5.49114i	−0.826540	+	0.191525i
$823$	26.7511	−	15.4448i	0.932484	−	0.538370i	0.0448880	−	0.998992i	$-0.485707\pi$
$823$	26.7511	−	15.4448i	0.932484	−	0.538370i	0.887596	+	0.460622i	$0.152374\pi$
$824$	1.25374	+	1.25374i	0.0436760	+	0.0436760i
$825$	−13.4293	+	7.15443i	−0.467550	+	0.249085i
$826$	1.46352	−	5.46193i	0.0509224	−	0.190045i
$827$	−14.3490	+	14.3490i	−0.498962	+	0.498962i	−0.911115	−	0.412153i	$-0.864777\pi$
$827$	−14.3490	+	14.3490i	−0.498962	+	0.498962i	0.412153	+	0.911115i	$0.364777\pi$
$828$	2.97138	+	6.06732i	0.103263	+	0.210854i
$829$	−19.5067	−	11.2622i	−0.677497	−	0.391153i	0.121414	−	0.992602i	$-0.461257\pi$
$829$	−19.5067	−	11.2622i	−0.677497	−	0.391153i	−0.798911	+	0.601449i	$0.794590\pi$
$830$	15.8535	+	59.1659i	0.550281	+	2.05368i
$831$	−32.7119	+	30.5538i	−1.13476	+	1.05990i
$832$	−3.42778	−	1.11817i	−0.118837	−	0.0387656i
$833$		−	4.12077i		−	0.142776i
$834$	−16.8378	−	10.5025i	−0.583044	−	0.363672i
$835$	49.8794	−	86.3937i	1.72615	−	2.98978i
$836$	2.79433	+	4.83992i	0.0966440	+	0.167392i
$837$	−1.58665	+	15.4563i	−0.0548425	+	0.534248i
$838$	−16.3473	−	4.38025i	−0.564708	−	0.151313i
$839$	−38.3272	−	10.2697i	−1.32320	−	0.354551i	−0.473025	−	0.881049i	$-0.656838\pi$
$839$	−38.3272	−	10.2697i	−1.32320	−	0.354551i	−0.850176	+	0.526498i	$0.823505\pi$
$840$	−0.246920	+	7.23857i	−0.00851953	+	0.249754i
$841$	−12.5210	−	21.6870i	−0.431757	−	0.747826i
$842$	6.61365	−	11.4552i	0.227921	−	0.394771i
$843$	−13.3706	+	21.4359i	−0.460507	+	0.738292i
$844$			20.7026i			0.712614i
$845$	8.37877	+	53.7115i	0.288239	+	1.84773i
$846$	1.05762	−	15.4842i	0.0363616	−	0.532359i
$847$	−2.71888	−	10.1470i	−0.0934219	−	0.348655i
$848$	−0.140018	−	0.0808394i	−0.00480824	−	0.00277604i
$849$	43.4345	+	13.2409i	1.49067	+	0.454426i
$850$	36.3819	−	36.3819i	1.24789	−	1.24789i
$851$	−2.74954	+	10.2614i	−0.0942531	+	0.351757i
$852$	−1.08682	−	2.04003i	−0.0372338	−	0.0698903i
$853$	−0.903633	−	0.903633i	−0.0309398	−	0.0309398i	0.691468	−	0.722407i	$-0.256964\pi$
$853$	−0.903633	−	0.903633i	−0.0309398	−	0.0309398i	−0.722407	+	0.691468i	$0.756964\pi$
$854$	−0.985179	+	0.568793i	−0.0337121	+	0.0194637i
$855$	82.6982	+	55.5864i	2.82822	+	1.90101i
$856$	−11.5750	+	3.10152i	−0.395626	+	0.106008i
$857$	−7.37918			−0.252068			−0.126034	−	0.992026i	$-0.540225\pi$
$857$	−7.37918			−0.252068			−0.126034	+	0.992026i	$0.540225\pi$
$858$	−3.98295	+	1.85555i	−0.135976	+	0.0633473i
$859$	16.0604			0.547972			0.273986	−	0.961734i	$-0.411658\pi$
$859$	16.0604			0.547972			0.273986	+	0.961734i	$0.411658\pi$
$860$	49.1634	−	13.1733i	1.67646	−	0.449206i
$861$	−0.605201	−	2.61178i	−0.0206252	−	0.0890092i
$862$	−29.9740	+	17.3055i	−1.02092	+	0.589427i
$863$	−19.1821	−	19.1821i	−0.652965	−	0.652965i	0.300741	−	0.953706i	$-0.402766\pi$
$863$	−19.1821	−	19.1821i	−0.652965	−	0.652965i	−0.953706	+	0.300741i	$0.902766\pi$
$864$	−2.12497	−	4.74178i	−0.0722929	−	0.161319i
$865$	−15.2139	+	56.7790i	−0.517288	+	1.93054i
$866$	−8.35250	+	8.35250i	−0.283829	+	0.283829i
$867$	−0.00972082	+	0.0318875i	−0.000330136	+	0.00108296i
$868$	−2.58959	−	1.49510i	−0.0878964	−	0.0507470i
$869$	−1.34146	−	5.00639i	−0.0455059	−	0.169830i
$870$	9.83572	+	10.5304i	0.333462	+	0.357015i
$871$	40.2484	+	2.15637i	1.36376	+	0.0730657i
$872$		−	11.1621i		−	0.377997i
$873$	−49.3716	+	9.67971i	−1.67098	+	0.327608i
$874$	−8.94360	+	15.4908i	−0.302522	+	0.523983i
$875$	−15.6517	−	27.1095i	−0.529124	−	0.916469i
$876$	−11.1761	−	0.381236i	−0.377606	−	0.0128808i
$877$	17.6023	+	4.71653i	0.594389	+	0.159266i	0.543458	−	0.839436i	$-0.317115\pi$
$877$	17.6023	+	4.71653i	0.594389	+	0.159266i	0.0509307	+	0.998702i	$0.483781\pi$
$878$	−11.1178	−	2.97901i	−0.375209	−	0.100537i
$879$	15.6095	+	0.532467i	0.526497	+	0.0179597i
$880$	1.47109	+	2.54800i	0.0495904	+	0.0858931i
$881$	−29.0407	+	50.2999i	−0.978405	+	1.69465i	−0.310197	+	0.950672i	$0.600395\pi$
$881$	−29.0407	+	50.2999i	−0.978405	+	1.69465i	−0.668208	+	0.743975i	$0.732938\pi$
$882$	2.94395	−	0.577186i	0.0991280	−	0.0194349i
$883$		−	30.4291i		−	1.02402i	−0.858979	−	0.512011i	$-0.828901\pi$
$883$		−	30.4291i		−	1.02402i	0.858979	−	0.512011i	$-0.171099\pi$
$884$	11.0530	−	9.92883i	0.371751	−	0.333943i
$885$	−27.9555	−	29.9300i	−0.939713	−	1.00609i
$886$	6.39359	+	23.8612i	0.214797	+	0.801633i
$887$	5.58052	+	3.22192i	0.187376	+	0.108181i	0.590753	−	0.806852i	$-0.298831\pi$
$887$	5.58052	+	3.22192i	0.187376	+	0.108181i	−0.403378	+	0.915034i	$0.632164\pi$
$888$	2.38260	−	7.81573i	0.0799549	−	0.262279i
$889$	−6.99028	+	6.99028i	−0.234446	+	0.234446i
$890$	8.38071	−	31.2772i	0.280922	−	1.04841i
$891$	−5.83695	−	2.45540i	−0.195545	−	0.0822591i
$892$	2.11089	+	2.11089i	0.0706778	+	0.0706778i
$893$	35.5872	−	20.5463i	1.19088	−	0.687555i
$894$	−6.10804	−	26.3596i	−0.204283	−	0.881598i
$895$	−37.6368	+	10.0847i	−1.25806	+	0.337096i
$896$	1.00000			0.0334077
$897$	−11.5172	−	8.07056i	−0.384548	−	0.269468i
$898$	−35.6149			−1.18848
$899$	−5.74626	+	1.53971i	−0.191649	+	0.0513521i
$900$	31.0878	+	20.8959i	1.03626	+	0.696531i
$901$	0.576982	−	0.333121i	0.0192221	−	0.0110979i
$902$	−0.770092	−	0.770092i	−0.0256413	−	0.0256413i
$903$	−9.91249	−	18.6064i	−0.329867	−	0.619182i
$904$	−0.924013	+	3.44846i	−0.0307322	+	0.114694i
$905$	58.0082	−	58.0082i	1.92826	−	1.92826i
$906$	−17.3781	−	5.29766i	−0.577348	−	0.176003i
$907$	−22.0310	−	12.7196i	−0.731529	−	0.422348i	0.0874526	−	0.996169i	$-0.472127\pi$
$907$	−22.0310	−	12.7196i	−0.731529	−	0.422348i	−0.818981	+	0.573820i	$0.805461\pi$
$908$	−0.255531	−	0.953656i	−0.00848010	−	0.0316482i
$909$	−2.30268	+	33.7128i	−0.0763749	+	1.11818i
$910$	−6.82918	−	13.4417i	−0.226385	−	0.445588i
$911$		−	14.7908i		−	0.490040i	−0.969518	−	0.245020i	$-0.921205\pi$
$911$		−	14.7908i		−	0.490040i	0.969518	−	0.245020i	$-0.0787946\pi$
$912$	7.28101	−	11.6730i	0.241098	−	0.386533i
$913$	5.15320	−	8.92561i	0.170546	−	0.295395i
$914$	−16.4141	−	28.4300i	−0.542929	−	0.940381i
$915$	−0.280892	+	8.23450i	−0.00928602	+	0.272224i
$916$	−6.08849	−	1.63141i	−0.201169	−	0.0539032i
$917$	−10.8643	−	2.91108i	−0.358770	−	0.0961322i
$918$	21.3002	+	2.18654i	0.703012	+	0.0721667i
$919$	−12.2006	−	21.1320i	−0.402460	−	0.697081i	0.591562	−	0.806259i	$-0.298511\pi$
$919$	−12.2006	−	21.1320i	−0.402460	−	0.697081i	−0.994022	+	0.109179i	$0.965178\pi$
$920$	−4.70840	+	8.15519i	−0.155231	+	0.268869i
$921$	−17.1878	−	10.7208i	−0.566358	−	0.353264i
$922$		−	35.7763i		−	1.17823i
$923$	4.03239	+	2.62535i	0.132728	+	0.0864144i
$924$	0.890605	−	0.831849i	0.0292987	−	0.0273658i
$925$	15.2448	+	56.8945i	0.501248	+	1.87068i
$926$	15.4940	+	8.94545i	0.509164	+	0.293966i
$927$	−2.33949	−	4.77705i	−0.0768389	−	0.156899i
$928$	1.40678	−	1.40678i	0.0461799	−	0.0461799i
$929$	0.999322	−	3.72952i	0.0327867	−	0.122362i	−0.947593	−	0.319480i	$-0.896492\pi$
$929$	0.999322	−	3.72952i	0.0327867	−	0.122362i	0.980380	+	0.197119i	$0.0631584\pi$
$930$	−19.1141	+	10.1830i	−0.626775	+	0.333912i
$931$	5.61654	+	5.61654i	0.184075	+	0.184075i
$932$	−23.0815	+	13.3261i	−0.756060	+	0.436512i
$933$	−18.5807	+	4.30551i	−0.608304	+	0.140956i
$934$	−4.22723	+	1.13268i	−0.138319	+	0.0370625i
$935$	−12.1240			−0.396499
$936$	8.64150	+	6.50573i	0.282456	+	0.212646i
$937$	−14.0107			−0.457711			−0.228855	−	0.973460i	$-0.573498\pi$
$937$	−14.0107			−0.457711			−0.228855	+	0.973460i	$0.573498\pi$
$938$	−10.7980	+	2.89331i	−0.352567	+	0.0944701i
$939$	32.1275	−	7.44457i	1.04844	−	0.242944i
$940$	18.7350	−	10.8167i	0.611070	−	0.352801i
$941$	37.1412	+	37.1412i	1.21077	+	1.21077i	0.970774	+	0.239996i	$0.0771460\pi$
$941$	37.1412	+	37.1412i	1.21077	+	1.21077i	0.239996	+	0.970774i	$0.422854\pi$
$942$	23.3242	−	12.4259i	0.759944	−	0.404857i
$943$	0.902169	−	3.36694i	0.0293787	−	0.109643i
$944$	−3.99841	+	3.99841i	−0.130137	+	0.130137i
$945$	7.73754	−	20.3040i	0.251702	−	0.660488i
$946$	−7.41666	−	4.28201i	−0.241137	−	0.139220i
$947$	−6.44930	−	24.0691i	−0.209574	−	0.782141i	−0.988006	−	0.154413i	$-0.950651\pi$
$947$	−6.44930	−	24.0691i	−0.209574	−	0.782141i	0.778432	−	0.627729i	$-0.216015\pi$
$948$	−9.32433	+	8.70917i	−0.302840	+	0.282861i
$949$	20.7536	−	10.5440i	0.673690	−	0.342274i
$950$			99.1756i			3.21768i
$951$	9.77837	+	6.09922i	0.317085	+	0.197781i
$952$	−2.06039	+	3.56869i	−0.0667775	+	0.115662i
$953$	−3.36492	−	5.82821i	−0.109000	−	0.188794i	0.806365	−	0.591418i	$-0.201432\pi$
$953$	−3.36492	−	5.82821i	−0.109000	−	0.188794i	−0.915366	+	0.402624i	$0.868098\pi$
$954$	0.318804	+	0.365547i	0.0103217	+	0.0118350i
$955$	64.0148	+	17.1527i	2.07147	+	0.555048i
$956$	−13.2380	−	3.54711i	−0.428148	−	0.114722i
$957$	0.0826565	−	2.42311i	0.00267190	−	0.0783282i
$958$	7.48072	+	12.9570i	0.241691	+	0.418622i
$959$	−7.02209	+	12.1626i	−0.226755	+	0.392751i
$960$	3.83312	−	6.14532i	0.123714	−	0.198339i
$961$			22.0587i			0.711571i
$962$	3.51696	+	16.6414i	0.113391	+	0.536539i
$963$	35.8665	+	2.44978i	1.15578	+	0.0789431i
$964$	−3.65471	−	13.6396i	−0.117710	−	0.439301i
$965$	12.3374	+	7.12301i	0.397156	+	0.229298i
$966$	3.73098	+	1.13738i	0.120042	+	0.0365945i
$967$	2.12515	−	2.12515i	0.0683401	−	0.0683401i	−0.672111	−	0.740451i	$-0.734612\pi$
$967$	2.12515	−	2.12515i	0.0683401	−	0.0683401i	0.740451	+	0.672111i	$0.234612\pi$
$968$	−2.71888	+	10.1470i	−0.0873882	+	0.326137i
$969$	26.6558	+	50.0346i	0.856307	+	1.60734i
$970$	−49.5879	−	49.5879i	−1.59217	−	1.59217i
$971$	−14.7634	+	8.52365i	−0.473780	+	0.273537i	−0.717821	−	0.696228i	$-0.754860\pi$
$971$	−14.7634	+	8.52365i	−0.473780	+	0.273537i	0.244041	+	0.969765i	$0.421527\pi$
$972$	1.42136	+	15.5235i	0.0455902	+	0.497917i
$973$	−11.0670	+	2.96538i	−0.354790	+	0.0950657i
$974$	4.30556			0.137959
$975$	−77.6756	−	6.82370i	−2.48761	−	0.218533i
$976$	1.13759			0.0364133
$977$	−37.1574	+	9.95629i	−1.18877	+	0.318530i	−0.798399	−	0.602128i	$-0.794320\pi$
$977$	−37.1574	+	9.95629i	−1.18877	+	0.318530i	−0.390370	+	0.920658i	$0.627653\pi$
$978$	0.455089	+	1.96397i	0.0145522	+	0.0628007i
$979$	−4.71840	+	2.72417i	−0.150801	+	0.0870648i
$980$	2.95685	+	2.95685i	0.0944532	+	0.0944532i
$981$	−10.8509	+	31.6795i	−0.346442	+	1.01145i
$982$	1.43298	−	5.34795i	0.0457282	−	0.170660i
$983$	−13.9875	+	13.9875i	−0.446131	+	0.446131i	−0.894066	−	0.447935i	$-0.852160\pi$
$983$	−13.9875	+	13.9875i	−0.446131	+	0.446131i	0.447935	+	0.894066i	$0.352160\pi$
$984$	−0.781771	+	2.56447i	−0.0249219	+	0.0817523i
$985$	−11.7561	−	6.78740i	−0.374581	−	0.216265i
$986$	2.12186	+	7.91888i	0.0675737	+	0.252189i
$987$	−6.11645	−	6.54847i	−0.194689	−	0.208440i
$988$	−1.53217	+	28.5978i	−0.0487448	+	0.909818i
$989$		−	27.4102i		−	0.871594i
$990$	−1.69818	−	8.66163i	−0.0539718	−	0.275285i
$991$	6.67071	−	11.5540i	0.211902	−	0.367025i	−0.740408	−	0.672158i	$-0.765368\pi$
$991$	6.67071	−	11.5540i	0.211902	−	0.367025i	0.952310	+	0.305133i	$0.0987009\pi$
$992$	1.49510	+	2.58959i	0.0474695	+	0.0822195i
$993$	40.6718	+	1.38738i	1.29068	+	0.0440273i
$994$	−1.28906	−	0.345402i	−0.0408864	−	0.0109555i
$995$	55.2961	+	14.8166i	1.75301	+	0.469716i
$996$	−25.3566	−	0.864956i	−0.803455	−	0.0274072i
$997$	26.4382	+	45.7923i	0.837306	+	1.45026i	0.892139	+	0.451761i	$0.149204\pi$
$997$	26.4382	+	45.7923i	0.837306	+	1.45026i	−0.0548326	+	0.998496i	$0.517463\pi$
$998$	−0.174418	+	0.302101i	−0.00552110	+	0.00956283i
$999$	−14.3600	+	19.8659i	−0.454329	+	0.628529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.71.1	✓	56
3.2	odd	2		546.2.bu.b.71.12	yes	56
13.11	odd	12		546.2.bu.b.323.12	yes	56
39.11	even	12	inner	546.2.bu.a.323.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.1	✓	56	1.1	even	1	trivial
546.2.bu.a.323.1	yes	56	39.11	even	12	inner
546.2.bu.b.71.12	yes	56	3.2	odd	2
546.2.bu.b.323.12	yes	56	13.11	odd	12

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.68734 + 0.390990i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.95685 - 2.95685i) q^{5} +(1.52865 - 0.814384i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.69425 - 1.31947i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.68734 + 0.390990i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.95685 - 2.95685i) q^{5} +(1.52865 - 0.814384i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.69425 - 1.31947i) q^{9} +(3.62139 + 2.09081i) q^{10} +(-0.182104 - 0.679623i) q^{11} +(-1.26579 + 1.18228i) q^{12} +(1.11817 - 3.42778i) q^{13} +1.00000i q^{14} +(6.14532 + 3.83312i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.06039 + 3.56869i) q^{17} +(-2.26094 + 1.97183i) q^{18} +(-7.67233 - 2.05579i) q^{19} +(-4.03913 - 1.08228i) q^{20} +(-0.0590488 + 1.73104i) q^{21} +(0.351799 + 0.609333i) q^{22} +(-1.12597 + 1.95025i) q^{23} +(0.916660 - 1.46960i) q^{24} +12.4859i q^{25} +(-0.192896 + 3.60039i) q^{26} +(-4.03023 + 3.27983i) q^{27} +(-0.258819 - 0.965926i) q^{28} +(-1.72295 - 0.994745i) q^{29} +(-6.92801 - 2.11199i) q^{30} +(2.11439 - 2.11439i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.572999 + 1.07556i) q^{33} +(-2.91383 - 2.91383i) q^{34} +(-3.62139 + 2.09081i) q^{35} +(1.67356 - 2.48982i) q^{36} +(4.55669 - 1.22096i) q^{37} +7.94298 q^{38} +(-0.546510 + 6.22104i) q^{39} +4.18162 q^{40} +(-1.49512 + 0.400617i) q^{41} +(-0.390990 - 1.68734i) q^{42} +(-10.5411 + 6.08588i) q^{43} +(-0.497519 - 0.497519i) q^{44} +(-11.8680 - 4.06503i) q^{45} +(0.582847 - 2.17522i) q^{46} +(-3.65818 + 3.65818i) q^{47} +(-0.505064 + 1.65678i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-3.23160 - 12.0605i) q^{50} +(-4.87190 - 5.21602i) q^{51} +(-0.745526 - 3.52763i) q^{52} -0.161679i q^{53} +(3.04402 - 4.21117i) q^{54} +(-1.47109 + 2.54800i) q^{55} +(0.500000 + 0.866025i) q^{56} +(13.7497 + 0.469023i) q^{57} +(1.92170 + 0.514918i) q^{58} +(-5.46193 - 1.46352i) q^{59} +(7.23857 + 0.246920i) q^{60} +(0.568793 + 0.985179i) q^{61} +(-1.49510 + 2.58959i) q^{62} +(-0.577186 - 2.94395i) q^{63} -1.00000i q^{64} +(-13.4417 + 6.82918i) q^{65} +(-0.831849 - 0.890605i) q^{66} +(2.89331 + 10.7980i) q^{67} +(3.56869 + 2.06039i) q^{68} +(1.13738 - 3.73098i) q^{69} +(2.95685 - 2.95685i) q^{70} +(-0.345402 + 1.28906i) q^{71} +(-0.972118 + 2.83813i) q^{72} +(4.56529 + 4.56529i) q^{73} +(-4.08541 + 2.35871i) q^{74} +(-4.88189 - 21.0681i) q^{75} +(-7.67233 + 2.05579i) q^{76} -0.703598 q^{77} +(-1.08224 - 6.15051i) q^{78} +7.36643 q^{79} +(-4.03913 + 1.08228i) q^{80} +(5.51800 - 7.10997i) q^{81} +(1.34049 - 0.773933i) q^{82} +(10.3578 + 10.3578i) q^{83} +(0.814384 + 1.52865i) q^{84} +(4.45984 - 16.6443i) q^{85} +(8.60674 - 8.60674i) q^{86} +(3.29614 + 1.00482i) q^{87} +(0.609333 + 0.351799i) q^{88} +(-2.00418 - 7.47969i) q^{89} +(12.5157 + 0.854857i) q^{90} +(-3.02158 - 1.96725i) q^{91} +2.25195i q^{92} +(-2.74099 + 4.39441i) q^{93} +(2.58672 - 4.48033i) q^{94} +(16.6073 + 28.7646i) q^{95} +(0.0590488 - 1.73104i) q^{96} +(-16.1991 - 4.34053i) q^{97} +(0.965926 + 0.258819i) q^{98} +(-1.38738 - 1.59080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

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