LMFDB - Embedded newform 546.2.bu.b.323.12

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			323.12
Character	$\chi$	$=$	546.323
Dual form			546.2.bu.b.71.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.505064 - 1.65678i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.95685 - 2.95685i) q^{5} +(0.916660 - 1.46960i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.48982 - 1.67356i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.505064 - 1.65678i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.95685 - 2.95685i) q^{5} +(0.916660 - 1.46960i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.48982 - 1.67356i) 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} +(-3.40545 - 6.39224i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.06039 + 3.56869i) q^{17} +(-1.97183 - 2.26094i) q^{18} +(-7.67233 + 2.05579i) q^{19} +(4.03913 - 1.08228i) q^{20} +(1.73104 + 0.0590488i) q^{21} +(0.351799 - 0.609333i) q^{22} +(1.12597 + 1.95025i) q^{23} +(1.52865 - 0.814384i) 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} +(-1.63497 - 7.05583i) q^{30} +(2.11439 + 2.11439i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.03401 - 0.644960i) q^{33} +(-2.91383 + 2.91383i) q^{34} +(3.62139 + 2.09081i) q^{35} +(-1.31947 - 2.69425i) q^{36} +(4.55669 + 1.22096i) q^{37} -7.94298 q^{38} +(6.24382 - 0.121313i) q^{39} +4.18162 q^{40} +(1.49512 + 0.400617i) q^{41} +(1.65678 + 0.505064i) q^{42} +(-10.5411 - 6.08588i) q^{43} +(0.497519 - 0.497519i) q^{44} +(-12.3105 + 2.41357i) q^{45} +(0.582847 + 2.17522i) q^{46} +(3.65818 + 3.65818i) q^{47} +(1.68734 - 0.390990i) 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} +(-4.74178 + 2.12497i) q^{54} +(-1.47109 - 2.54800i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-0.469023 + 13.7497i) q^{57} +(1.92170 - 0.514918i) q^{58} +(5.46193 - 1.46352i) q^{59} +(0.246920 - 7.23857i) q^{60} +(0.568793 - 0.985179i) q^{61} +(1.49510 + 2.58959i) q^{62} +(0.972118 - 2.83813i) 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} +(3.79981 - 0.880491i) q^{69} +(2.95685 + 2.95685i) q^{70} +(0.345402 + 1.28906i) q^{71} +(-0.577186 - 2.94395i) q^{72} +(4.56529 - 4.56529i) q^{73} +(4.08541 + 2.35871i) q^{74} +(-20.6864 - 6.30620i) q^{75} +(-7.67233 - 2.05579i) q^{76} +0.703598 q^{77} +(6.06246 + 1.49884i) q^{78} +7.36643 q^{79} +(4.03913 + 1.08228i) q^{80} +(3.39842 + 8.33371i) q^{81} +(1.34049 + 0.773933i) q^{82} +(-10.3578 + 10.3578i) q^{83} +(1.46960 + 0.916660i) q^{84} +(4.45984 + 16.6443i) q^{85} +(-8.60674 - 8.60674i) q^{86} +(-0.777871 - 3.35695i) 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} +(4.57097 - 2.43517i) q^{93} +(2.58672 + 4.48033i) q^{94} +(-16.6073 + 28.7646i) q^{95} +(1.73104 + 0.0590488i) q^{96} +(-16.1991 + 4.34053i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(-1.59080 + 1.38738i) 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^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 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} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 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^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 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 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{12}\right)$

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
$3$	0.505064	−	1.65678i	0.291599	−	0.956541i
$3$	0.505064	−	1.65678i	0.291599	−	0.956541i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	2.95685	−	2.95685i	1.32234	−	1.32234i	0.410471	−	0.911874i	$-0.365364\pi$
$5$	2.95685	−	2.95685i	1.32234	−	1.32234i	0.911874	−	0.410471i	$-0.134636\pi$
$6$	0.916660	−	1.46960i	0.374225	−	0.599963i
$7$	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
$9$	−2.48982	−	1.67356i	−0.829940	−	0.557852i
$10$	3.62139	−	2.09081i	1.14518	−	0.661172i
$11$	0.182104	−	0.679623i	0.0549066	−	0.204914i	−0.933023	−	0.359816i	$-0.882839\pi$
$11$	0.182104	−	0.679623i	0.0549066	−	0.204914i	0.987930	+	0.154902i	$0.0495061\pi$
$12$	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
$15$	−3.40545	−	6.39224i	−0.879282	−	1.65047i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.06039	+	3.56869i	−0.499717	+	0.865535i	−1.00000		0.000326888i	$-0.999896\pi$
$17$	−2.06039	+	3.56869i	−0.499717	+	0.865535i	0.500283	+	0.865862i	$0.333229\pi$
$18$	−1.97183	−	2.26094i	−0.464766	−	0.532910i
$19$	−7.67233	+	2.05579i	−1.76015	+	0.471632i	−0.986745	−	0.162277i	$-0.948116\pi$
$19$	−7.67233	+	2.05579i	−1.76015	+	0.471632i	−0.773408	+	0.633908i	$0.781450\pi$
$20$	4.03913	−	1.08228i	0.903178	−	0.242006i
$21$	1.73104	+	0.0590488i	0.377745	+	0.0128855i
$22$	0.351799	−	0.609333i	0.0750038	−	0.129910i
$23$	1.12597	+	1.95025i	0.234782	+	0.406654i	0.959209	−	0.282697i	$-0.0912291\pi$
$23$	1.12597	+	1.95025i	0.234782	+	0.406654i	−0.724427	+	0.689351i	$0.757896\pi$
$24$	1.52865	−	0.814384i	0.312035	−	0.166235i
$25$		−	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	$-0.607529\pi$
$29$	1.72295	−	0.994745i	0.319943	−	0.184719i	0.651367	+	0.758763i	$0.274196\pi$
$30$	−1.63497	−	7.05583i	−0.298504	−	1.28821i
$31$	2.11439	+	2.11439i	0.379756	+	0.379756i	0.871014	−	0.491258i	$-0.163463\pi$
$31$	2.11439	+	2.11439i	0.379756	+	0.379756i	−0.491258	+	0.871014i	$0.663463\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−1.03401	−	0.644960i	−0.179998	−	0.112273i
$34$	−2.91383	+	2.91383i	−0.499717	+	0.499717i
$35$	3.62139	+	2.09081i	0.612127	+	0.353411i
$36$	−1.31947	−	2.69425i	−0.219912	−	0.449042i
$37$	4.55669	+	1.22096i	0.749115	+	0.200725i	0.613125	−	0.789986i	$-0.289912\pi$
$37$	4.55669	+	1.22096i	0.749115	+	0.200725i	0.135989	+	0.990710i	$0.456579\pi$
$38$	−7.94298			−1.28852
$39$	6.24382	−	0.121313i	0.999811	−	0.0194256i
$40$	4.18162			0.661172
$41$	1.49512	+	0.400617i	0.233499	+	0.0625659i	0.373671	−	0.927561i	$-0.378099\pi$
$41$	1.49512	+	0.400617i	0.233499	+	0.0625659i	−0.140172	+	0.990127i	$0.544766\pi$
$42$	1.65678	+	0.505064i	0.255646	+	0.0779330i
$43$	−10.5411	−	6.08588i	−1.60750	−	0.928088i	−0.989928	−	0.141571i	$-0.954785\pi$
$43$	−10.5411	−	6.08588i	−1.60750	−	0.928088i	−0.617568	−	0.786517i	$-0.711882\pi$
$44$	0.497519	−	0.497519i	0.0750038	−	0.0750038i
$45$	−12.3105	+	2.41357i	−1.83514	+	0.359794i
$46$	0.582847	+	2.17522i	0.0859362	+	0.320718i
$47$	3.65818	+	3.65818i	0.533600	+	0.533600i	0.921642	−	0.388042i	$-0.126848\pi$
$47$	3.65818	+	3.65818i	0.533600	+	0.533600i	−0.388042	+	0.921642i	$0.626848\pi$
$48$	1.68734	−	0.390990i	0.243547	−	0.0564346i
$49$	−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	$-0.00353463\pi$
$54$	−4.74178	+	2.12497i	−0.645275	+	0.289172i
$55$	−1.47109	−	2.54800i	−0.198362	−	0.343572i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−0.469023	+	13.7497i	−0.0621237	+	1.82119i
$58$	1.92170	−	0.514918i	0.252331	−	0.0676120i
$59$	5.46193	−	1.46352i	0.711083	−	0.190534i	0.114893	−	0.993378i	$-0.463347\pi$
$59$	5.46193	−	1.46352i	0.711083	−	0.190534i	0.596189	+	0.802844i	$0.296681\pi$
$60$	0.246920	−	7.23857i	0.0318772	−	0.934495i
$61$	0.568793	−	0.985179i	0.0728265	−	0.126139i	−0.827313	−	0.561742i	$-0.810131\pi$
$61$	0.568793	−	0.985179i	0.0728265	−	0.126139i	0.900139	+	0.435603i	$0.143465\pi$
$62$	1.49510	+	2.58959i	0.189878	+	0.328878i
$63$	0.972118	−	2.83813i	0.122475	−	0.357571i
$64$			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	−0.528919	−	0.848672i	$-0.677402\pi$
$67$	2.89331	−	10.7980i	0.353475	−	1.31919i	0.882393	−	0.470513i	$-0.155931\pi$
$68$	−3.56869	+	2.06039i	−0.432768	+	0.249858i
$69$	3.79981	−	0.880491i	0.457444	−	0.105999i
$70$	2.95685	+	2.95685i	0.353411	+	0.353411i
$71$	0.345402	+	1.28906i	0.0409916	+	0.152983i	0.983388	−	0.181515i	$-0.0581000\pi$
$71$	0.345402	+	1.28906i	0.0409916	+	0.152983i	−0.942397	+	0.334498i	$0.891433\pi$
$72$	−0.577186	−	2.94395i	−0.0680220	−	0.346948i
$73$	4.56529	−	4.56529i	0.534327	−	0.534327i	−0.387530	−	0.921857i	$-0.626672\pi$
$73$	4.56529	−	4.56529i	0.534327	−	0.534327i	0.921857	+	0.387530i	$0.126672\pi$
$74$	4.08541	+	2.35871i	0.474920	+	0.274195i
$75$	−20.6864	−	6.30620i	−2.38866	−	0.728177i
$76$	−7.67233	−	2.05579i	−0.880077	−	0.235816i
$77$	0.703598			0.0801824
$78$	6.06246	+	1.49884i	0.686439	+	0.169710i
$79$	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
$81$	3.39842	+	8.33371i	0.377602	+	0.925968i
$82$	1.34049	+	0.773933i	0.148032	+	0.0854666i
$83$	−10.3578	+	10.3578i	−1.13692	+	1.13692i	−0.147918	+	0.989000i	$0.547257\pi$
$83$	−10.3578	+	10.3578i	−1.13692	+	1.13692i	−0.989000	+	0.147918i	$0.952743\pi$
$84$	1.46960	+	0.916660i	0.160347	+	0.100016i
$85$	4.45984	+	16.6443i	0.483738	+	1.80533i
$86$	−8.60674	−	8.60674i	−0.928088	−	0.928088i
$87$	−0.777871	−	3.35695i	−0.0833965	−	0.359903i
$88$	0.609333	−	0.351799i	0.0649552	−	0.0375019i
$89$	2.00418	−	7.47969i	0.212442	−	0.792845i	−0.774609	−	0.632440i	$-0.782053\pi$
$89$	2.00418	−	7.47969i	0.212442	−	0.792845i	0.987051	−	0.160405i	$-0.0512800\pi$
$90$	−12.5157	−	0.854857i	−1.31927	−	0.0901099i
$91$	−3.02158	+	1.96725i	−0.316748	+	0.206223i
$92$			2.25195i			0.234782i
$93$	4.57097	−	2.43517i	0.473988	−	0.252515i
$94$	2.58672	+	4.48033i	0.266800	+	0.462111i
$95$	−16.6073	+	28.7646i	−1.70387	+	2.95119i
$96$	1.73104	+	0.0590488i	0.176674	+	0.00602664i
$97$	−16.1991	+	4.34053i	−1.64477	+	0.440714i	−0.958141	−	0.286297i	$-0.907575\pi$
$97$	−16.1991	+	4.34053i	−1.64477	+	0.440714i	−0.686626	+	0.727011i	$0.740909\pi$
$98$	−0.965926	+	0.258819i	−0.0975732	+	0.0261447i
$99$	−1.59080	+	1.38738i	−0.159881	+	0.139437i
$100$	6.24297	−	10.8131i	0.624297	−	1.08131i
$101$	5.63189	+	9.75471i	0.560394	+	0.970630i	0.997462	+	0.0712019i	$0.0226835\pi$
$101$	5.63189	+	9.75471i	0.560394	+	0.970630i	−0.437068	+	0.899428i	$0.643983\pi$
$102$	3.35589	+	6.29923i	0.332283	+	0.623716i
$103$			1.77305i			0.174704i	0.996178	+	0.0873520i	$0.0278405\pi$
$103$			1.77305i			0.174704i	−0.996178	+	0.0873520i	$0.972160\pi$
$104$	−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	$-0.863316\pi$
$107$	−10.3779	+	5.99167i	−1.00327	+	0.579237i	−0.0940542	+	0.995567i	$0.529983\pi$
$108$	−5.13019	+	0.825298i	−0.493653	+	0.0794143i
$109$	−7.89280	−	7.89280i	−0.755993	−	0.755993i	0.219597	−	0.975591i	$-0.429526\pi$
$109$	−7.89280	−	7.89280i	−0.755993	−	0.755993i	−0.975591	+	0.219597i	$0.929526\pi$
$110$	−0.761492	−	2.84193i	−0.0726054	−	0.270967i
$111$	4.32428	−	6.93275i	0.410442	−	0.658028i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	−3.09181	−	1.78506i	−0.290853	−	0.167924i	0.347474	−	0.937690i	$-0.387040\pi$
$113$	−3.09181	−	1.78506i	−0.290853	−	0.167924i	−0.638326	+	0.769766i	$0.720373\pi$
$114$	−4.01171	+	13.1597i	−0.375731	+	1.23252i
$115$	9.09593	+	2.43725i	0.848200	+	0.227274i
$116$	1.98949			0.184719
$117$	2.95254	−	10.4059i	0.272962	−	0.962025i
$118$	5.65460			0.520549
$119$	−3.98036	−	1.06653i	−0.364879	−	0.0977690i
$120$	2.11199	−	6.92801i	0.192797	−	0.632438i
$121$	9.09755	+	5.25248i	0.827050	+	0.477498i
$122$	0.804395	−	0.804395i	0.0728265	−	0.0728265i
$123$	1.41887	−	2.27475i	0.127935	−	0.205107i
$124$	0.773920	+	2.88831i	0.0695001	+	0.259378i
$125$	−22.1348	−	22.1348i	−1.97980	−	1.97980i
$126$	1.67356	−	2.48982i	0.149092	−	0.221811i
$127$	−8.56131	+	4.94287i	−0.759693	+	0.438609i	−0.829186	−	0.558973i	$-0.811195\pi$
$127$	−8.56131	+	4.94287i	−0.759693	+	0.438609i	0.0694923	+	0.997582i	$0.477862\pi$
$128$	−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	$-0.163497\pi$
$132$	−0.572999	−	1.07556i	−0.0498731	−	0.0936152i
$133$	−3.97149	−	6.87882i	−0.344372	−	0.596470i
$134$	5.58945	−	9.68122i	0.482855	−	0.836330i
$135$	−2.21883	+	21.6147i	−0.190967	+	1.86030i
$136$	−3.98036	+	1.06653i	−0.341313	+	0.0914545i
$137$	13.5656	−	3.63490i	1.15899	−	0.310550i	0.372428	−	0.928061i	$-0.378525\pi$
$137$	13.5656	−	3.63490i	1.15899	−	0.310550i	0.786562	+	0.617511i	$0.211859\pi$
$138$	3.89822	+	0.132975i	0.331839	+	0.0113196i
$139$	−5.72868	+	9.92236i	−0.485900	+	0.841603i	−0.999869	−	0.0162056i	$-0.994841\pi$
$139$	−5.72868	+	9.92236i	−0.485900	+	0.841603i	0.513969	+	0.857809i	$0.328175\pi$
$140$	2.09081	+	3.62139i	0.176706	+	0.306063i
$141$	7.90839	−	4.21317i	0.666007	−	0.354813i
$142$			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
$147$	0.390990	+	1.68734i	0.0322483	+	0.139170i
$148$	3.33573	+	3.33573i	0.274195	+	0.274195i
$149$	−4.04326	−	15.0897i	−0.331237	−	1.23619i	−0.907891	−	0.419205i	$-0.862309\pi$
$149$	−4.04326	−	15.0897i	−0.331237	−	1.23619i	0.576654	−	0.816988i	$-0.304358\pi$
$150$	−18.3494	−	11.4454i	−1.49822	−	0.934510i
$151$	−7.41691	+	7.41691i	−0.603580	+	0.603580i	−0.941261	−	0.337681i	$-0.890357\pi$
$151$	−7.41691	+	7.41691i	−0.603580	+	0.603580i	0.337681	+	0.941261i	$0.390357\pi$
$152$	−6.87882	−	3.97149i	−0.557946	−	0.322130i
$153$	11.1024	−	5.43723i	0.897576	−	0.439574i
$154$	0.679623	+	0.182104i	0.0547656	+	0.0146744i
$155$	12.5039			1.00434
$156$	5.46796	+	3.01685i	0.437787	+	0.241541i
$157$	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
$159$	−0.267866	−	0.0816582i	−0.0212431	−	0.00647591i
$160$	3.62139	+	2.09081i	0.286296	+	0.165293i
$161$	−1.59237	+	1.59237i	−0.125496	+	0.125496i
$162$	1.12569	+	8.92932i	0.0884429	+	0.701554i
$163$	−0.301250	−	1.12428i	−0.0235957	−	0.0880604i	0.953124	−	0.302580i	$-0.0978480\pi$
$163$	−0.301250	−	1.12428i	−0.0235957	−	0.0880604i	−0.976720	+	0.214520i	$0.931181\pi$
$164$	1.09451	+	1.09451i	0.0854666	+	0.0854666i
$165$	−4.96446	+	1.15036i	−0.386483	+	0.0895557i
$166$	−12.6857	+	7.32408i	−0.984599	+	0.568459i
$167$	−6.17452	+	23.0436i	−0.477798	+	1.78317i	0.132707	+	0.991155i	$0.457633\pi$
$167$	−6.17452	+	23.0436i	−0.477798	+	1.78317i	−0.610505	+	0.792012i	$0.709033\pi$
$168$	1.18228	+	1.26579i	0.0912148	+	0.0976576i
$169$	−10.4994	+	7.66570i	−0.807645	+	0.589669i
$170$			17.2315i			1.32160i
$171$	22.5432	+	7.72152i	1.72392	+	0.590479i
$172$	−6.08588	−	10.5411i	−0.464044	−	0.803748i
$173$	7.02861	−	12.1739i	0.534375	−	0.925565i	−0.464818	−	0.885406i	$-0.653880\pi$
$173$	7.02861	−	12.1739i	0.534375	−	0.925565i	0.999193	−	0.0401587i	$-0.0127863\pi$
$174$	0.117477	−	3.44389i	0.00890590	−	0.261081i
$175$	12.0605	−	3.23160i	0.911688	−	0.244286i
$176$	0.679623	−	0.182104i	0.0512285	−	0.0137266i
$177$	0.333897	−	9.78837i	0.0250973	−	0.735739i
$178$	3.87177	−	6.70611i	0.290202	−	0.502644i
$179$	−4.65902	−	8.06965i	−0.348231	−	0.603154i	0.637704	−	0.770281i	$-0.279884\pi$
$179$	−4.65902	−	8.06965i	−0.348231	−	0.603154i	−0.985935	+	0.167127i	$0.946551\pi$
$180$	−11.8680	−	4.06503i	−0.884587	−	0.302989i
$181$		−	19.6182i		−	1.45821i	−0.684401	−	0.729105i	$-0.739936\pi$
$181$		−	19.6182i		−	1.45821i	0.684401	−	0.729105i	$-0.260064\pi$
$182$	−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
$186$	5.04549	−	1.16914i	0.369953	−	0.0857254i
$187$	2.05016	+	2.05016i	0.149923	+	0.149923i
$188$	1.33899	+	4.99716i	0.0976555	+	0.364455i
$189$	−4.21117	−	3.04402i	−0.306317	−	0.221420i
$190$	−23.4862	+	23.4862i	−1.70387	+	1.70387i
$191$	13.7253	+	7.92432i	0.993129	+	0.573383i	0.906208	−	0.422832i	$-0.138964\pi$
$191$	13.7253	+	7.92432i	0.993129	+	0.573383i	0.0869210	+	0.996215i	$0.472297\pi$
$192$	1.65678	+	0.505064i	0.119568	+	0.0364498i
$193$	−3.29073	−	0.881750i	−0.236872	−	0.0634697i	0.138430	−	0.990372i	$-0.455794\pi$
$193$	−3.29073	−	0.881750i	−0.236872	−	0.0634697i	−0.375302	+	0.926902i	$0.622461\pi$
$194$	−16.7705			−1.20405
$195$	18.1033	−	18.8208i	1.29641	−	1.34778i
$196$	−1.00000			−0.0714286
$197$	−3.13569	−	0.840205i	−0.223408	−	0.0598621i	0.145378	−	0.989376i	$-0.453560\pi$
$197$	−3.13569	−	0.840205i	−0.223408	−	0.0598621i	−0.368787	+	0.929514i	$0.620227\pi$
$198$	−1.89567	+	0.928376i	−0.134719	+	0.0659768i
$199$	−11.8560	−	6.84505i	−0.840447	−	0.485232i	0.0169689	−	0.999856i	$-0.494598\pi$
$199$	−11.8560	−	6.84505i	−0.840447	−	0.485232i	−0.857416	+	0.514624i	$0.827932\pi$
$200$	8.82890	−	8.82890i	0.624297	−	0.624297i
$201$	−16.4286	−	10.2473i	−1.15878	−	0.722786i
$202$	2.91528	+	10.8800i	0.205118	+	0.765512i
$203$	1.40678	+	1.40678i	0.0987367	+	0.0987367i
$204$	1.61118	+	6.95315i	0.112805	+	0.486818i
$205$	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
$210$	6.39224	−	3.40545i	0.441107	−	0.234998i
$211$	−10.3513	−	17.9290i	−0.712614	−	1.23428i	−0.963873	−	0.266364i	$-0.914178\pi$
$211$	−10.3513	−	17.9290i	−0.712614	−	1.23428i	0.251259	−	0.967920i	$-0.419156\pi$
$212$	0.0808394	−	0.140018i	0.00555207	−	0.00961648i
$213$	2.31013	+	0.0788023i	0.158287	+	0.00539945i
$214$	−11.5750	+	3.10152i	−0.791252	+	0.212015i
$215$	−49.1634	+	13.1733i	−3.35292	+	0.898411i
$216$	−5.16899	−	0.530615i	−0.351705	−	0.0361038i
$217$	−1.49510	+	2.58959i	−0.101494	+	0.175793i
$218$	−5.58105	−	9.66667i	−0.377997	−	0.654709i
$219$	−5.25790	−	9.86943i	−0.355296	−	0.666914i
$220$		−	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	−0.935219	−	0.354071i	$-0.884797\pi$
$223$	0.772639	−	2.88353i	0.0517397	−	0.193095i	0.986958	+	0.160975i	$0.0514639\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	−20.8959	+	31.0878i	−1.39306	+	2.07252i
$226$	−2.52445	−	2.52445i	−0.167924	−	0.167924i
$227$	−0.255531	−	0.953656i	−0.0169602	−	0.0632963i	0.956927	−	0.290328i	$-0.0937645\pi$
$227$	−0.255531	−	0.953656i	−0.0169602	−	0.0632963i	−0.973887	+	0.227032i	$0.927098\pi$
$228$	−7.28101	+	11.6730i	−0.482197	+	0.773066i
$229$	−4.45709	+	4.45709i	−0.294533	+	0.294533i	−0.838868	−	0.544335i	$-0.816782\pi$
$229$	−4.45709	+	4.45709i	−0.294533	+	0.294533i	0.544335	+	0.838868i	$0.316782\pi$
$230$	8.15519	+	4.70840i	0.537737	+	0.310463i
$231$	0.355362	−	1.16570i	0.0233811	−	0.0766977i
$232$	1.92170	+	0.514918i	0.126166	+	0.0338060i
$233$	26.6522			1.74605			0.873023	−	0.487679i	$-0.162156\pi$
$233$	26.6522			1.74605			0.873023	+	0.487679i	$0.162156\pi$
$234$	5.54518	−	9.28714i	0.362499	−	0.607120i
$235$	21.6334			1.41121
$236$	5.46193	+	1.46352i	0.355541	+	0.0952670i
$237$	3.72052	−	12.2045i	0.241674	−	0.792769i
$238$	−3.56869	−	2.06039i	−0.231324	−	0.133555i
$239$	9.69089	−	9.69089i	0.626852	−	0.626852i	−0.320423	−	0.947275i	$-0.603825\pi$
$239$	9.69089	−	9.69089i	0.626852	−	0.626852i	0.947275	+	0.320423i	$0.103825\pi$
$240$	3.83312	−	6.14532i	0.247427	−	0.396679i
$241$	3.65471	+	13.6396i	0.235421	+	0.878601i	0.977959	+	0.208798i	$0.0669550\pi$
$241$	3.65471	+	13.6396i	0.235421	+	0.878601i	−0.742538	+	0.669804i	$0.766378\pi$
$242$	7.42812	+	7.42812i	0.477498	+	0.477498i
$243$	15.5235	−	1.42136i	0.995834	−	0.0911804i
$244$	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
$249$	11.9292	+	22.3919i	0.755984	+	1.41903i
$250$	−15.6517	−	27.1095i	−0.989900	−	1.71456i
$251$	6.10097	−	10.5672i	0.385090	−	0.666995i	−0.606692	−	0.794937i	$-0.707504\pi$
$251$	6.10097	−	10.5672i	0.385090	−	0.666995i	0.991782	+	0.127942i	$0.0408371\pi$
$252$	2.26094	−	1.97183i	0.142426	−	0.124214i
$253$	1.53048	−	0.410090i	0.0962203	−	0.0257821i
$254$	−9.54890	+	2.55862i	−0.599151	+	0.160542i
$255$	29.8285	+	1.01750i	1.86793	+	0.0637183i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.98242	+	10.3619i	0.373173	+	0.646355i	0.990052	−	0.140703i	$-0.0449364\pi$
$257$	5.98242	+	10.3619i	0.373173	+	0.646355i	−0.616879	+	0.787058i	$0.711603\pi$
$258$	−18.6064	+	9.91249i	−1.15838	+	0.617125i
$259$			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	0.742428	−	0.669926i	$-0.233674\pi$
$263$	27.4691	−	15.8593i	1.69381	−	0.977924i	0.951387	−	0.307998i	$-0.0996590\pi$
$264$	−0.275100	−	1.18721i	−0.0169312	−	0.0730678i
$265$	−0.478060	−	0.478060i	−0.0293670	−	0.0293670i
$266$	−2.05579	−	7.67233i	−0.126049	−	0.470421i
$267$	−11.3799	−	7.09819i	−0.696441	−	0.434402i
$268$	7.90468	−	7.90468i	0.482855	−	0.482855i
$269$	8.83825	+	5.10277i	0.538878	+	0.311121i	0.744624	−	0.667484i	$-0.232629\pi$
$269$	8.83825	+	5.10277i	0.538878	+	0.311121i	−0.205746	+	0.978605i	$0.565962\pi$
$270$	−7.73754	+	20.3040i	−0.470891	+	1.23566i
$271$	2.64573	+	0.708922i	0.160717	+	0.0430639i	0.338280	−	0.941045i	$-0.390155\pi$
$271$	2.64573	+	0.708922i	0.160717	+	0.0430639i	−0.177563	+	0.984109i	$0.556822\pi$
$272$	−4.12077			−0.249858
$273$	1.73320	+	5.99967i	0.104898	+	0.363116i
$274$	14.0442			0.848440
$275$	−8.48574	−	2.27375i	−0.511709	−	0.137112i
$276$	3.73098	+	1.13738i	0.224579	+	0.0684621i
$277$	22.3808	+	12.9216i	1.34473	+	0.776382i	0.987498	−	0.157632i	$-0.0503859\pi$
$277$	22.3808	+	12.9216i	1.34473	+	0.776382i	0.357236	+	0.934014i	$0.383719\pi$
$278$	−8.10157	+	8.10157i	−0.485900	+	0.485900i
$279$	−1.72590	−	8.80300i	−0.103327	−	0.527022i
$280$	1.08228	+	4.03913i	0.0646788	+	0.241384i
$281$	−10.3140	−	10.3140i	−0.615281	−	0.615281i	0.329036	−	0.944317i	$-0.393276\pi$
$281$	−10.3140	−	10.3140i	−0.615281	−	0.615281i	−0.944317	+	0.329036i	$0.893276\pi$
$282$	8.72937	−	2.02277i	0.519826	−	0.120454i
$283$	−22.7040	+	13.1081i	−1.34961	+	0.779198i	−0.988194	−	0.153207i	$-0.951040\pi$
$283$	−22.7040	+	13.1081i	−1.34961	+	0.779198i	−0.361416	+	0.932405i	$0.617707\pi$
$284$	−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
$288$	0.972118	−	2.83813i	0.0572826	−	0.167238i
$289$	0.00962336	+	0.0166681i	0.000566080	+	0.000980479i
$290$	4.15964	−	7.20471i	0.244263	−	0.423075i
$291$	−0.990278	+	29.0305i	−0.0580511	+	1.70180i
$292$	6.23630	−	1.67101i	0.364952	−	0.0977886i
$293$	8.71015	−	2.33388i	0.508853	−	0.136347i	0.00474716	−	0.999989i	$-0.498489\pi$
$293$	8.71015	−	2.33388i	0.508853	−	0.136347i	0.504106	+	0.863642i	$0.331822\pi$
$294$	−0.0590488	+	1.73104i	−0.00344379	+	0.100957i
$295$	11.8227	−	20.4775i	0.688344	−	1.19225i
$296$	2.35871	+	4.08541i	0.137098	+	0.237460i
$297$	1.49512	+	3.33631i	0.0867558	+	0.193592i
$298$		−	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
$303$	19.0058	−	4.40403i	1.09186	−	0.253005i
$304$	−5.61654	−	5.61654i	−0.322130	−	0.322130i
$305$	−1.23119	−	4.59487i	−0.0704978	−	0.263101i
$306$	12.1314	−	2.37845i	0.693503	−	0.135967i
$307$	8.27001	−	8.27001i	0.471994	−	0.471994i	−0.430565	−	0.902559i	$-0.641686\pi$
$307$	8.27001	−	8.27001i	0.471994	−	0.471994i	0.902559	+	0.430565i	$0.141686\pi$
$308$	0.609333	+	0.351799i	0.0347200	+	0.0200456i
$309$	2.93755	+	0.895504i	0.167111	+	0.0509435i
$310$	12.0778	+	3.23624i	0.685974	+	0.183806i
$311$	−11.0118			−0.624422			−0.312211	−	0.950013i	$-0.601070\pi$
$311$	−11.0118			−0.624422			−0.312211	+	0.950013i	$0.601070\pi$
$312$	4.50083	+	4.32927i	0.254809	+	0.245096i
$313$	−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
$315$	−5.51752	−	11.2663i	−0.310877	−	0.634786i
$316$	6.37951	+	3.68321i	0.358876	+	0.207197i
$317$	4.70491	−	4.70491i	0.264254	−	0.264254i	−0.562526	−	0.826780i	$-0.690170\pi$
$317$	4.70491	−	4.70491i	0.264254	−	0.264254i	0.826780	+	0.562526i	$0.190170\pi$
$318$	−0.237604	−	0.148204i	−0.0133242	−	0.00831090i
$319$	−0.362295	−	1.35210i	−0.0202846	−	0.0757032i
$320$	2.95685	+	2.95685i	0.165293	+	0.165293i
$321$	4.68537	+	20.2200i	0.261512	+	1.12857i
$322$	−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
$327$	−17.0630	+	9.09024i	−0.943585	+	0.502692i
$328$	0.773933	+	1.34049i	0.0427333	+	0.0740162i
$329$	−2.58672	+	4.48033i	−0.142611	+	0.247009i
$330$	−5.09304	−	0.173732i	−0.280363	−	0.00956363i
$331$	−22.6950	+	6.08110i	−1.24743	+	0.334247i	−0.821342	−	0.570436i	$-0.806774\pi$
$331$	−22.6950	+	6.08110i	−1.24743	+	0.334247i	−0.426085	+	0.904683i	$0.640108\pi$
$332$	−14.1490	+	3.79122i	−0.776529	+	0.208070i
$333$	−9.30199	−	10.6658i	−0.509746	−	0.584485i
$334$	−11.9282	+	20.6603i	−0.652685	+	1.13048i
$335$	−23.3730	−	40.4832i	−1.27700	−	2.21183i
$336$	0.814384	+	1.52865i	0.0444283	+	0.0833948i
$337$		−	7.09525i		−	0.386503i	−0.981149	−	0.193251i	$-0.938097\pi$
$337$		−	7.09525i		−	0.386503i	0.981149	−	0.193251i	$-0.0619033\pi$
$338$	−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
$342$	19.7766	+	13.2930i	1.06940	+	0.718805i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−3.15028	−	11.7570i	−0.169852	−	0.633896i
$345$	8.63200	−	13.8390i	0.464731	−	0.745065i
$346$	9.93995	−	9.93995i	0.534375	−	0.534375i
$347$	20.1321	+	11.6233i	1.08075	+	0.623971i	0.931099	−	0.364767i	$-0.118852\pi$
$347$	20.1321	+	11.6233i	1.08075	+	0.623971i	0.149651	+	0.988739i	$0.452185\pi$
$348$	1.00482	−	3.29614i	0.0538640	−	0.176692i
$349$	−26.0797	−	6.98803i	−1.39601	−	0.374061i	−0.519102	−	0.854712i	$-0.673734\pi$
$349$	−26.0797	−	6.98803i	−1.39601	−	0.374061i	−0.876912	+	0.480652i	$0.840400\pi$
$350$	12.4859			0.667402
$351$	−15.7490	−	10.1473i	−0.840620	−	0.541625i
$352$	0.703598			0.0375019
$353$	−15.0133	−	4.02279i	−0.799075	−	0.214112i	−0.163897	−	0.986477i	$-0.552407\pi$
$353$	−15.0133	−	4.02279i	−0.799075	−	0.214112i	−0.635178	+	0.772366i	$0.719073\pi$
$354$	2.85594	−	9.36842i	0.151791	−	0.497926i
$355$	4.83285	+	2.79025i	0.256501	+	0.148091i
$356$	5.47551	−	5.47551i	0.290202	−	0.290202i
$357$	−3.77734	+	6.05590i	−0.199918	+	0.320512i
$358$	−2.41168	−	9.00053i	−0.127461	−	0.475693i
$359$	−0.0696043	−	0.0696043i	−0.00367357	−	0.00367357i	0.705268	−	0.708941i	$-0.250827\pi$
$359$	−0.0696043	−	0.0696043i	−0.00367357	−	0.00367357i	−0.708941	+	0.705268i	$0.750827\pi$
$360$	−10.4115	−	6.99818i	−0.548733	−	0.368836i
$361$	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
$366$	−0.926433	−	1.73897i	−0.0484254	−	0.0908977i
$367$	3.54542	+	6.14085i	0.185069	+	0.320550i	0.943600	−	0.331088i	$-0.107416\pi$
$367$	3.54542	+	6.14085i	0.185069	+	0.320550i	−0.758531	+	0.651638i	$0.774082\pi$
$368$	−1.12597	+	1.95025i	−0.0586955	+	0.101664i
$369$	−3.05213	−	3.49964i	−0.158888	−	0.182184i
$370$	19.0543	−	5.10559i	0.990588	−	0.265427i
$371$	0.156170	−	0.0418456i	0.00810793	−	0.00217251i
$372$	5.17617	+	0.176568i	0.268372	+	0.00915460i
$373$	−2.18505	+	3.78462i	−0.113138	+	0.195960i	−0.917034	−	0.398809i	$-0.869423\pi$
$373$	−2.18505	+	3.78462i	−0.113138	+	0.195960i	0.803896	+	0.594770i	$0.202757\pi$
$374$	1.44968	+	2.51092i	0.0749613	+	0.129837i
$375$	−47.8520	+	25.4930i	−2.47107	+	1.31645i
$376$			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	−0.923072	−	0.384627i	$-0.874330\pi$
$379$	1.33638	−	4.98744i	0.0686452	−	0.256187i	0.991717	+	0.128439i	$0.0409968\pi$
$380$	−28.7646	+	16.6073i	−1.47559	+	0.851935i
$381$	3.86523	+	16.6806i	0.198022	+	0.854575i
$382$	11.2067	+	11.2067i	0.573383	+	0.573383i
$383$	−1.23338	−	4.60305i	−0.0630230	−	0.235205i	0.927229	−	0.374496i	$-0.122184\pi$
$383$	−1.23338	−	4.60305i	−0.0630230	−	0.235205i	−0.990251	+	0.139291i	$0.955518\pi$
$384$	1.46960	+	0.916660i	0.0749954	+	0.0467781i
$385$	2.08043	−	2.08043i	0.106029	−	0.106029i
$386$	−2.95039	−	1.70341i	−0.150171	−	0.0867013i
$387$	16.0603	+	32.7938i	0.816390	+	1.66700i
$388$	−16.1991	−	4.34053i	−0.822383	−	0.220357i
$389$	−23.4268			−1.18779			−0.593894	−	0.804543i	$-0.702410\pi$
$389$	−23.4268			−1.18779			−0.593894	+	0.804543i	$0.702410\pi$
$390$	22.3577	−	13.4940i	1.13212	−	0.683293i
$391$	−9.27977			−0.469298
$392$	−0.965926	−	0.258819i	−0.0487866	−	0.0130723i
$393$	−18.6347	−	5.68072i	−0.939994	−	0.286555i
$394$	−2.81138	−	1.62315i	−0.141635	−	0.0817732i
$395$	21.7814	−	21.7814i	1.09594	−	1.09594i
$396$	−2.07136	+	0.406107i	−0.104090	+	0.0204076i
$397$	−2.12137	−	7.91705i	−0.106468	−	0.397345i	0.892039	−	0.451958i	$-0.149274\pi$
$397$	−2.12137	−	7.91705i	−0.106468	−	0.397345i	−0.998508	+	0.0546125i	$0.982608\pi$
$398$	−9.68036	−	9.68036i	−0.485232	−	0.485232i
$399$	−13.4025	+	3.10563i	−0.670966	+	0.155476i
$400$	10.8131	−	6.24297i	0.540657	−	0.312149i
$401$	2.64602	−	9.87506i	0.132136	−	0.493137i	−0.867858	−	0.496813i	$-0.834503\pi$
$401$	2.64602	−	9.87506i	0.132136	−	0.493137i	0.999993	+	0.00367599i	$0.00117011\pi$
$402$	−13.2166	−	14.1501i	−0.659184	−	0.705743i
$403$	−4.88342	+	9.61192i	−0.243260	+	0.478804i
$404$			11.2638i			0.560394i
$405$	34.6902	+	14.5929i	1.72377	+	0.725129i
$406$	0.994745	+	1.72295i	0.0493683	+	0.0855085i
$407$	1.65959	−	2.87449i	0.0822626	−	0.142483i
$408$	−0.243326	+	7.13324i	−0.0120465	+	0.353148i
$409$	−31.7278	+	8.50144i	−1.56884	+	0.420369i	−0.935449	−	0.353463i	$-0.885004\pi$
$409$	−31.7278	+	8.50144i	−1.56884	+	0.420369i	−0.633391	+	0.773832i	$0.718338\pi$
$410$	6.25204	−	1.67523i	0.308766	−	0.0827336i
$411$	0.829291	−	24.3111i	0.0409059	−	1.19918i
$412$	−0.886526	+	1.53551i	−0.0436760	+	0.0756490i
$413$	2.82730	+	4.89703i	0.139122	+	0.240967i
$414$	2.18916	−	6.39133i	0.107591	−	0.314117i
$415$			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	$-0.802324\pi$
$419$	−14.6566	+	8.46199i	−0.716021	+	0.413395i	0.0972651	+	0.995259i	$0.468991\pi$
$420$	7.05583	−	1.63497i	0.344289	−	0.0797785i
$421$	−9.35311	−	9.35311i	−0.455843	−	0.455843i	0.441445	−	0.897288i	$-0.354466\pi$
$421$	−9.35311	−	9.35311i	−0.455843	−	0.455843i	−0.897288	+	0.441445i	$0.854466\pi$
$422$	−5.35823	−	19.9972i	−0.260835	−	0.973449i
$423$	−2.98604	−	15.2304i	−0.145186	−	0.740526i
$424$	0.114324	−	0.114324i	0.00555207	−	0.00555207i
$425$	44.5585	+	25.7259i	2.16140	+	1.24789i
$426$	2.21102	+	0.674023i	0.107124	+	0.0326565i
$427$	1.09882	+	0.294429i	0.0531758	+	0.0142484i
$428$	−11.9833			−0.579237
$429$	1.05458	−	4.26554i	0.0509156	−	0.205942i
$430$	−50.8977			−2.45450
$431$	−33.4316	−	8.95798i	−1.61034	−	0.431491i	−0.662199	−	0.749328i	$-0.730377\pi$
$431$	−33.4316	−	8.95798i	−1.61034	−	0.431491i	−0.948145	+	0.317837i	$0.897043\pi$
$432$	−4.85553	−	1.85037i	−0.233612	−	0.0890259i
$433$	10.2297	+	5.90611i	0.491607	+	0.283829i	0.725241	−	0.688495i	$-0.241728\pi$
$433$	10.2297	+	5.90611i	0.491607	+	0.283829i	−0.233634	+	0.972325i	$0.575062\pi$
$434$	−2.11439	+	2.11439i	−0.101494	+	0.101494i
$435$	−12.2261	−	7.62596i	−0.586194	−	0.365637i
$436$	−2.88897	−	10.7818i	−0.138356	−	0.516353i
$437$	−12.6482	−	12.6482i	−0.605043	−	0.605043i
$438$	−2.52435	−	10.8940i	−0.120618	−	0.520535i
$439$	9.96798	−	5.75502i	0.475746	−	0.274672i	−0.242896	−	0.970052i	$-0.578097\pi$
$439$	9.96798	−	5.75502i	0.475746	−	0.274672i	0.718642	+	0.695380i	$0.244764\pi$
$440$	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	$-0.199627\pi$
$444$	7.21131	−	3.84180i	0.342234	−	0.182324i
$445$	−16.1903	−	28.0424i	−0.767493	−	1.32934i
$446$	1.49262	−	2.58530i	0.0706778	−	0.122417i
$447$	−27.0423	−	0.922458i	−1.27906	−	0.0436308i
$448$	−0.965926	+	0.258819i	−0.0456357	+	0.0122281i
$449$	−34.4014	+	9.21781i	−1.62350	+	0.435016i	−0.952027	−	0.306013i	$-0.901005\pi$
$449$	−34.4014	+	9.21781i	−1.62350	+	0.435016i	−0.671473	+	0.741029i	$0.734338\pi$
$450$	−28.2300	+	24.6202i	−1.33078	+	1.16061i
$451$	0.544537	−	0.943166i	0.0256413	−	0.0444120i
$452$	−1.78506	−	3.09181i	−0.0839620	−	0.145426i
$453$	8.54215	+	16.0342i	0.401345	+	0.753352i
$454$		−	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	−0.420112	−	0.907472i	$-0.638009\pi$
$457$	8.49655	−	31.7096i	0.397452	−	1.48331i	0.817564	−	0.575838i	$-0.195324\pi$
$458$	−5.45879	+	3.15164i	−0.255073	+	0.147266i
$459$	−3.40086	−	21.1404i	−0.158739	−	0.986747i
$460$	6.65868	+	6.65868i	0.310463	+	0.310463i
$461$	9.25958	+	34.5572i	0.431261	+	1.60949i	0.749858	+	0.661599i	$0.230122\pi$
$461$	9.25958	+	34.5572i	0.431261	+	1.60949i	−0.318596	+	0.947890i	$0.603211\pi$
$462$	0.644960	−	1.03401i	0.0300062	−	0.0481065i
$463$	−12.6508	+	12.6508i	−0.587932	+	0.587932i	−0.937071	−	0.349139i	$-0.886474\pi$
$463$	−12.6508	+	12.6508i	−0.587932	+	0.587932i	0.349139	+	0.937071i	$0.386474\pi$
$464$	1.72295	+	0.994745i	0.0799859	+	0.0461799i
$465$	6.31526	−	20.7161i	0.292863	−	0.960688i
$466$	25.7441	+	6.89811i	1.19257	+	0.319549i
$467$	−4.37635			−0.202513			−0.101257	−	0.994860i	$-0.532286\pi$
$467$	−4.37635			−0.202513			−0.101257	+	0.994860i	$0.532286\pi$
$468$	7.75992	−	7.53549i	0.358702	−	0.348328i
$469$	11.1789			0.516194
$470$	20.8962	+	5.59913i	0.963871	+	0.258268i
$471$	7.70627	−	25.2791i	0.355086	−	1.16480i
$472$	4.89703	+	2.82730i	0.225404	+	0.130137i
$473$	−6.05568	+	6.05568i	−0.278440	+	0.278440i
$474$	6.75251	−	10.8257i	0.310153	−	0.497242i
$475$	25.6685	+	95.7963i	1.17775	+	4.39544i
$476$	−2.91383	−	2.91383i	−0.133555	−	0.133555i
$477$	−0.270579	+	0.402551i	−0.0123889	+	0.0184316i
$478$	11.8689	−	6.85249i	0.542869	−	0.313426i
$479$	3.87231	−	14.4516i	0.176930	−	0.660313i	−0.819285	−	0.573387i	$-0.805629\pi$
$479$	3.87231	−	14.4516i	0.176930	−	0.660313i	0.996215	−	0.0869256i	$-0.0277042\pi$
$480$	5.29304	−	4.94384i	0.241593	−	0.225654i
$481$	0.909974	+	16.9846i	0.0414912	+	0.774430i
$482$			14.1207i			0.643181i
$483$	1.83395	+	3.44245i	0.0834477	+	0.156637i
$484$	5.25248	+	9.09755i	0.238749	+	0.413525i
$485$	−35.0640	+	60.7326i	−1.59217	+	2.75772i
$486$	15.3624	+	2.64485i	0.696855	+	0.119973i
$487$	−4.15885	+	1.11436i	−0.188456	+	0.0504965i	−0.351812	−	0.936071i	$-0.614434\pi$
$487$	−4.15885	+	1.11436i	−0.188456	+	0.0504965i	0.163357	+	0.986567i	$0.447768\pi$
$488$	1.09882	−	0.294429i	0.0497414	−	0.0133282i
$489$	−2.01483	−	0.0687292i	−0.0911138	−	0.00310804i
$490$	−2.09081	+	3.62139i	−0.0944532	+	0.163598i
$491$	2.76830	+	4.79484i	0.124932	+	0.216388i	0.921706	−	0.387889i	$-0.126796\pi$
$491$	2.76830	+	4.79484i	0.124932	+	0.216388i	−0.796775	+	0.604277i	$0.793462\pi$
$492$	2.36615	−	1.26056i	0.106674	−	0.0568303i
$493$			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
$498$	5.72729	+	24.7165i	0.256646	+	1.10757i
$499$	0.246664	+	0.246664i	0.0110422	+	0.0110422i	0.712606	−	0.701564i	$-0.247515\pi$
$499$	0.246664	+	0.246664i	0.0110422	+	0.0110422i	−0.701564	+	0.712606i	$0.747515\pi$
$500$	−8.10191	−	30.2368i	−0.362329	−	1.35223i
$501$	35.0596	+	21.8683i	1.56635	+	0.977003i
$502$	8.62808	−	8.62808i	0.385090	−	0.385090i
$503$	11.2647	+	6.50369i	0.502269	+	0.289985i	0.729650	−	0.683821i	$-0.239683\pi$
$503$	11.2647	+	6.50369i	0.502269	+	0.289985i	−0.227381	+	0.973806i	$0.573016\pi$
$504$	2.69425	−	1.31947i	0.120012	−	0.0587739i
$505$	45.4959	+	12.1906i	2.02454	+	0.542474i
$506$	1.58447			0.0704381
$507$	7.39750	+	21.2668i	0.328535	+	0.944492i
$508$	−9.88575			−0.438609
$509$	−24.3803	−	6.53269i	−1.08064	−	0.289557i	−0.325782	−	0.945445i	$-0.605628\pi$
$509$	−24.3803	−	6.53269i	−1.08064	−	0.289557i	−0.754858	+	0.655888i	$0.772294\pi$
$510$	28.5488	+	8.70301i	1.26416	+	0.385376i
$511$	5.59131	+	3.22815i	0.247345	+	0.142805i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	24.1786	−	33.4492i	1.06751	−	1.47682i
$514$	3.09673	+	11.5572i	0.136591	+	0.509764i
$515$	5.24265	+	5.24265i	0.231019	+	0.231019i
$516$	−20.5379	+	4.75904i	−0.904133	+	0.209505i
$517$	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	$0.820429\pi$
$522$	−5.64643	−	1.93402i	−0.247138	−	0.0846497i
$523$	7.91245	+	13.7048i	0.345987	+	0.599268i	0.985533	−	0.169486i	$-0.0542106\pi$
$523$	7.91245	+	13.7048i	0.345987	+	0.599268i	−0.639545	+	0.768753i	$0.720877\pi$
$524$	5.62377	−	9.74065i	0.245675	−	0.425522i
$525$	0.737280	−	21.6137i	0.0321775	−	0.943300i
$526$	30.6378	−	8.20936i	1.33587	−	0.357945i
$527$	−11.9021	+	3.18915i	−0.518462	+	0.138922i
$528$	0.0415466	−	1.21796i	0.00180808	−	0.0530048i
$529$	8.96436	−	15.5267i	0.389755	−	0.675075i
$530$	−0.338040	−	0.585502i	−0.0146835	−	0.0254326i
$531$	−16.0485	−	5.49695i	−0.696446	−	0.238547i
$532$		−	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
$537$	−15.7227	+	3.64326i	−0.678485	+	0.157218i
$538$	7.21640	+	7.21640i	0.311121	+	0.311121i
$539$	0.182104	+	0.679623i	0.00784379	+	0.0292734i
$540$	−12.7289	+	17.6095i	−0.547766	+	0.757792i
$541$	−31.4485	+	31.4485i	−1.35208	+	1.35208i	−0.468743	+	0.883335i	$0.655293\pi$
$541$	−31.4485	+	31.4485i	−1.35208	+	1.35208i	−0.883335	+	0.468743i	$0.844707\pi$
$542$	2.37210	+	1.36953i	0.101890	+	0.0588264i
$543$	−32.5030	−	9.90846i	−1.39484	−	0.425213i
$544$	−3.98036	−	1.06653i	−0.170656	−	0.0457273i
$545$	−46.6757			−1.99937
$546$	0.121313	+	6.24382i	0.00519172	+	0.267211i
$547$	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
$549$	−3.06495	+	1.50101i	−0.130809	+	0.0640616i
$550$	−7.60810	−	4.39254i	−0.324411	−	0.187299i
$551$	−11.1740	+	11.1740i	−0.476030	+	0.476030i
$552$	3.30947	+	2.06427i	0.140861	+	0.0878612i
$553$	1.90657	+	7.11542i	0.0810757	+	0.302579i
$554$	18.2739	+	18.2739i	0.776382	+	0.776382i
$555$	−7.71287	−	33.2854i	−0.327393	−	1.41289i
$556$	−9.92236	+	5.72868i	−0.420802	+	0.242950i
$557$	9.86481	−	36.8160i	0.417985	−	1.55994i	−0.360795	−	0.932645i	$-0.617495\pi$
$557$	9.86481	−	36.8160i	0.417985	−	1.55994i	0.778780	−	0.627297i	$-0.215839\pi$
$558$	0.611293	−	8.94974i	0.0258781	−	0.378873i
$559$	9.07436	−	42.9375i	0.383805	−	1.81606i
$560$			4.18162i			0.176706i
$561$	4.43212	−	2.36120i	0.187124	−	0.0996898i
$562$	−7.29309	−	12.6320i	−0.307641	−	0.532849i
$563$	9.25884	−	16.0368i	0.390214	−	0.675870i	−0.602264	−	0.798297i	$-0.705734\pi$
$563$	9.25884	−	16.0368i	0.390214	−	0.675870i	0.992477	+	0.122427i	$0.0390678\pi$
$564$	8.95545	+	0.305485i	0.377093	+	0.0128633i
$565$	−14.4202	+	3.86387i	−0.606661	+	0.162554i
$566$	−25.3230	+	6.78527i	−1.06440	+	0.285206i
$567$	−7.17017	+	5.43954i	−0.301119	+	0.228439i
$568$	−0.667265	+	1.15574i	−0.0279978	+	0.0484936i
$569$	3.95174	+	6.84462i	0.165666	+	0.286941i	0.936891	−	0.349620i	$-0.113689\pi$
$569$	3.95174	+	6.84462i	0.165666	+	0.286941i	−0.771226	+	0.636562i	$0.780356\pi$
$570$	27.0494	+	50.7735i	1.13297	+	2.12667i
$571$			0.428316i			0.0179245i	0.999960	+	0.00896224i	$0.00285281\pi$
$571$			0.428316i			0.0179245i	−0.999960	+	0.00896224i	$0.997147\pi$
$572$	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
$576$	1.67356	−	2.48982i	0.0697315	−	0.103743i
$577$	15.7496	+	15.7496i	0.655664	+	0.655664i	0.954351	−	0.298687i	$-0.0965486\pi$
$577$	15.7496	+	15.7496i	0.655664	+	0.655664i	−0.298687	+	0.954351i	$0.596549\pi$
$578$	0.00498142	+	0.0185909i	0.000207200	+	0.000773279i
$579$	−3.12289	+	5.00667i	−0.129783	+	0.208070i
$580$	5.88262	−	5.88262i	0.244263	−	0.244263i
$581$	−12.6857	−	7.32408i	−0.526291	−	0.303854i
$582$	−8.47018	+	27.7850i	−0.351100	+	1.15173i
$583$	−0.109881	−	0.0294424i	−0.00455079	−	0.00121938i
$584$	6.45629			0.267163
$585$	−22.0385	−	39.4989i	−0.911178	−	1.63308i
$586$	9.01742			0.372506
$587$	38.7422	+	10.3809i	1.59906	+	0.428467i	0.944759	−	0.327766i	$-0.106296\pi$
$587$	38.7422	+	10.3809i	1.59906	+	0.428467i	0.654303	+	0.756233i	$0.272962\pi$
$588$	−0.505064	+	1.65678i	−0.0208285	+	0.0683243i
$589$	−20.5691	−	11.8755i	−0.847533	−	0.489323i
$590$	16.7198	−	16.7198i	0.688344	−	0.688344i
$591$	−2.97575	+	4.77078i	−0.122406	+	0.196244i
$592$	1.22096	+	4.55669i	0.0501812	+	0.187279i
$593$	−6.08567	−	6.08567i	−0.249909	−	0.249909i	0.571024	−	0.820933i	$-0.306546\pi$
$593$	−6.08567	−	6.08567i	−0.249909	−	0.249909i	−0.820933	+	0.571024i	$0.806546\pi$
$594$	0.580677	+	3.60959i	0.0238255	+	0.148103i
$595$	−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	$0.874151\pi$
$600$	−10.1684	−	19.0867i	−0.415122	−	0.779210i
$601$	16.9224	+	29.3104i	0.690278	+	1.19560i	0.971747	+	0.236025i	$0.0758449\pi$
$601$	16.9224	+	29.3104i	0.690278	+	1.19560i	−0.281469	+	0.959570i	$0.590822\pi$
$602$	6.08588	−	10.5411i	0.248042	−	0.429621i
$603$	−25.2749	+	22.0429i	−1.02927	+	0.897658i
$604$	−10.1317	+	2.71478i	−0.412253	+	0.110463i
$605$	42.4309	−	11.3693i	1.72506	−	0.462229i
$606$	19.4981	+	0.665112i	0.792056	+	0.0270183i
$607$	22.6553	−	39.2401i	0.919549	−	1.59270i	0.119447	−	0.992841i	$-0.461888\pi$
$607$	22.6553	−	39.2401i	0.919549	−	1.59270i	0.800102	−	0.599864i	$-0.204779\pi$
$608$	−3.97149	−	6.87882i	−0.161065	−	0.278973i
$609$	3.04124	−	1.62021i	0.123237	−	0.0656542i
$610$		−	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	0.602383	+	0.798207i	$0.294218\pi$
$613$	−7.88320	+	29.4205i	−0.318400	+	1.18828i	−0.920783	+	0.390076i	$0.872449\pi$
$614$	10.1286	−	5.84778i	0.408759	−	0.235997i
$615$	−2.53072	−	10.9215i	−0.102048	−	0.440396i
$616$	0.497519	+	0.497519i	0.0200456	+	0.0200456i
$617$	4.94428	+	18.4523i	0.199049	+	0.742861i	0.991181	+	0.132512i	$0.0423043\pi$
$617$	4.94428	+	18.4523i	0.199049	+	0.742861i	−0.792132	+	0.610349i	$0.791029\pi$
$618$	2.60568	+	1.62529i	0.104816	+	0.0653786i
$619$	2.17589	−	2.17589i	0.0874563	−	0.0874563i	−0.662025	−	0.749482i	$-0.730303\pi$
$619$	2.17589	−	2.17589i	0.0874563	−	0.0874563i	0.749482	+	0.662025i	$0.230303\pi$
$620$	10.8287	+	6.25194i	0.434890	+	0.251084i
$621$	−10.9344	−	4.16694i	−0.438782	−	0.167213i
$622$	−10.6366	−	2.85006i	−0.426488	−	0.114277i
$623$	7.74354			0.310239
$624$	3.22697	+	5.34665i	0.129182	+	0.214037i
$625$	−68.4691			−2.73877
$626$	−18.3915	−	4.92799i	−0.735072	−	0.196962i
$627$	9.25917	+	2.82263i	0.369776	+	0.112725i
$628$	13.2138	+	7.62901i	0.527289	+	0.304431i
$629$	−13.7458	+	13.7458i	−0.548079	+	0.548079i
$630$	−2.41357	−	12.3105i	−0.0961590	−	0.490462i
$631$	3.35835	+	12.5335i	0.133694	+	0.498952i	1.00000		0.000561713i	$-0.000178799\pi$
$631$	3.35835	+	12.5335i	0.133694	+	0.498952i	−0.866306	+	0.499513i	$0.833512\pi$
$632$	5.20885	+	5.20885i	0.207197	+	0.207197i
$633$	−34.9324	+	8.09453i	−1.38844	+	0.321729i
$634$	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
$639$	1.29732	−	3.78757i	0.0513212	−	0.149834i
$640$	2.09081	+	3.62139i	0.0826465	+	0.143148i
$641$	6.89102	−	11.9356i	0.272179	−	0.471428i	−0.697241	−	0.716837i	$-0.745589\pi$
$641$	6.89102	−	11.9356i	0.272179	−	0.471428i	0.969419	+	0.245410i	$0.0789224\pi$
$642$	−0.707602	+	20.7437i	−0.0279268	+	0.818688i
$643$	−7.76316	+	2.08013i	−0.306149	+	0.0820325i	−0.408623	−	0.912703i	$-0.633991\pi$
$643$	−7.76316	+	2.08013i	−0.306149	+	0.0820325i	0.102474	+	0.994736i	$0.467324\pi$
$644$	−2.17522	+	0.582847i	−0.0857155	+	0.0229674i
$645$	−3.00545	+	88.1062i	−0.118339	+	3.46918i
$646$	16.3656	−	28.3461i	0.643896	−	1.11526i
$647$	−21.3142	−	36.9173i	−0.837948	−	1.45137i	−0.891607	−	0.452809i	$-0.850422\pi$
$647$	−21.3142	−	36.9173i	−0.837948	−	1.45137i	0.0536593	−	0.998559i	$-0.482912\pi$
$648$	−3.48978	+	8.29587i	−0.137092	+	0.325892i
$649$		−	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	$-0.759645\pi$
$653$	−12.7454	+	7.35857i	−0.498766	+	0.287963i	0.229438	+	0.973323i	$0.426311\pi$
$654$	−18.8343	+	4.36428i	−0.736480	+	0.170657i
$655$	−33.2573	−	33.2573i	−1.29947	−	1.29947i
$656$	0.400617	+	1.49512i	0.0156415	+	0.0583748i
$657$	−19.0070	+	3.72648i	−0.741535	+	0.145384i
$658$	−3.65818	+	3.65818i	−0.142611	+	0.142611i
$659$	24.2047	+	13.9746i	0.942881	+	0.544373i	0.890862	−	0.454273i	$-0.150101\pi$
$659$	24.2047	+	13.9746i	0.942881	+	0.544373i	0.0520190	+	0.998646i	$0.483434\pi$
$660$	−4.87453	−	1.48599i	−0.189741	−	0.0578420i
$661$	−5.53110	−	1.48206i	−0.215135	−	0.0576453i	0.149642	−	0.988740i	$-0.452188\pi$
$661$	−5.53110	−	1.48206i	−0.215135	−	0.0576453i	−0.364777	+	0.931095i	$0.618855\pi$
$662$	−23.4956			−0.913181
$663$	−12.4317	+	22.5322i	−0.482809	+	0.875079i
$664$	−14.6482			−0.568459
$665$	−32.0828	−	8.59655i	−1.24412	−	0.333360i
$666$	−6.22451	−	12.7099i	−0.241195	−	0.492500i
$667$	3.87999	+	2.24011i	0.150234	+	0.0867376i
$668$	−16.8691	+	16.8691i	−0.652685	+	0.652685i
$669$	−4.38713	−	2.73646i	−0.169616	−	0.105797i
$670$	−12.0987	−	45.1531i	−0.467415	−	1.74442i
$671$	−0.565971	−	0.565971i	−0.0218491	−	0.0218491i
$672$	0.390990	+	1.68734i	0.0150828	+	0.0650907i
$673$	−4.37077	+	2.52346i	−0.168481	+	0.0972723i	−0.581869	−	0.813282i	$-0.697678\pi$
$673$	−4.37077	+	2.52346i	−0.168481	+	0.0972723i	0.413389	+	0.910555i	$0.364345\pi$
$674$	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	$0.722962\pi$
$678$	−5.45746	+	2.90744i	−0.209593	+	0.111660i
$679$	−8.38526	−	14.5237i	−0.321797	−	0.557368i
$680$	−8.61575	+	14.9229i	−0.330399	+	0.572268i
$681$	−1.70905	−	0.0582987i	−0.0654911	−	0.00223401i
$682$	2.03221	−	0.544529i	0.0778173	−	0.0208511i
$683$	0.880806	−	0.236011i	0.0337031	−	0.00903072i	−0.241928	−	0.970294i	$-0.577780\pi$
$683$	0.880806	−	0.236011i	0.0337031	−	0.00903072i	0.275631	+	0.961263i	$0.411113\pi$
$684$	15.6622	+	17.9586i	0.598861	+	0.686666i
$685$	29.3637	−	50.8594i	1.12193	−	1.94324i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	5.13329	+	9.63551i	0.195847	+	0.367618i
$688$		−	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	−0.782157	−	0.623081i	$-0.785881\pi$
$691$	5.43485	−	20.2831i	0.206751	−	0.771607i	0.988909	−	0.148525i	$-0.0474527\pi$
$692$	12.1739	−	7.02861i	0.462782	−	0.267188i
$693$	−1.75183	−	1.17751i	−0.0665466	−	0.0447299i
$694$	16.4378	+	16.4378i	0.623971	+	0.623971i
$695$	12.4001	+	46.2778i	0.470362	+	1.75542i
$696$	1.82368	−	2.92376i	0.0691266	−	0.110825i
$697$	−4.51021	+	4.51021i	−0.170836	+	0.170836i
$698$	−23.3824	−	13.4998i	−0.885037	−	0.510976i
$699$	13.4611	−	44.1568i	0.509145	−	1.67016i
$700$	12.0605	+	3.23160i	0.455844	+	0.122143i
$701$	6.08878			0.229970			0.114985	−	0.993367i	$-0.463318\pi$
$701$	6.08878			0.229970			0.114985	+	0.993367i	$0.463318\pi$
$702$	−12.5861	−	13.8777i	−0.475030	−	0.523781i
$703$	−37.4705			−1.41322
$704$	0.679623	+	0.182104i	0.0256143	+	0.00686332i
$705$	10.9262	−	35.8417i	0.411506	−	1.34988i
$706$	−13.4605	−	7.77144i	−0.506593	−	0.292482i
$707$	−7.96469	+	7.96469i	−0.299543	+	0.299543i
$708$	5.18335	−	8.31003i	0.194802	−	0.312310i
$709$	−7.96160	−	29.7131i	−0.299004	−	1.11590i	−0.937985	−	0.346676i	$-0.887310\pi$
$709$	−7.96160	−	29.7131i	−0.299004	−	1.11590i	0.638981	−	0.769223i	$-0.279356\pi$
$710$	3.94601	+	3.94601i	0.148091	+	0.148091i
$711$	−18.3411	−	12.3281i	−0.687844	−	0.462341i
$712$	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
$717$	−11.1611	−	20.9502i	−0.416820	−	0.782398i
$718$	−0.0492176	−	0.0852475i	−0.00183679	−	0.00318141i
$719$	13.6742	−	23.6844i	0.509962	−	0.883281i	−0.489971	−	0.871739i	$-0.662993\pi$
$719$	13.6742	−	23.6844i	0.509962	−	0.883281i	0.999933	−	0.0115420i	$-0.00367400\pi$
$720$	−8.24546	−	9.45441i	−0.307290	−	0.352345i
$721$	−1.71264	+	0.458900i	−0.0637819	+	0.0170903i
$722$	42.5886	−	11.4116i	1.58498	−	0.424695i
$723$	24.4436	+	0.833811i	0.909066	+	0.0310098i
$724$	9.80911	−	16.9899i	0.364553	−	0.631424i
$725$	−12.4203	−	21.5126i	−0.461279	−	0.798959i
$726$	16.0584	−	8.55507i	0.595984	−	0.317508i
$727$			0.552818i			0.0205029i	0.999947	+	0.0102514i	$0.00326319\pi$
$727$			0.552818i			0.0205029i	−0.999947	+	0.0102514i	$0.996737\pi$
$728$	−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
$732$	−0.444786	−	1.91950i	−0.0164397	−	0.0709467i
$733$	−32.0572	−	32.0572i	−1.18406	−	1.18406i	−0.978683	−	0.205378i	$-0.934158\pi$
$733$	−32.0572	−	32.0572i	−1.18406	−	1.18406i	−0.205378	−	0.978683i	$-0.565842\pi$
$734$	1.83524	+	6.84923i	0.0677401	+	0.252810i
$735$	6.14532	+	3.83312i	0.226674	+	0.141387i
$736$	−1.59237	+	1.59237i	−0.0586955	+	0.0586955i
$737$	−6.81168	−	3.93273i	−0.250912	−	0.144864i
$738$	−2.04236	−	4.17034i	−0.0751804	−	0.153512i
$739$	14.1468	+	3.79062i	0.520398	+	0.139440i	0.509451	−	0.860500i	$-0.329849\pi$
$739$	14.1468	+	3.79062i	0.520398	+	0.139440i	0.0109472	+	0.999940i	$0.496515\pi$
$740$	19.7265			0.725160
$741$	−47.6553	+	13.7668i	−1.75066	+	0.505735i
$742$	0.161679			0.00593542
$743$	8.50232	+	2.27819i	0.311920	+	0.0835787i	0.411383	−	0.911463i	$-0.365046\pi$
$743$	8.50232	+	2.27819i	0.311920	+	0.0835787i	−0.0994631	+	0.995041i	$0.531713\pi$
$744$	4.95409	+	1.51024i	0.181626	+	0.0553681i
$745$	−56.5732	−	32.6626i	−2.07268	−	1.19666i
$746$	−3.09013	+	3.09013i	−0.113138	+	0.113138i
$747$	43.1235	−	8.45471i	1.57781	−	0.309342i
$748$	0.750411	+	2.80057i	0.0274377	+	0.102399i
$749$	−8.47350	−	8.47350i	−0.309615	−	0.309615i
$750$	−52.8196	+	12.2393i	−1.92870	+	0.446917i
$751$	1.83745	−	1.06085i	0.0670495	−	0.0387111i	−0.466100	−	0.884732i	$-0.654341\pi$
$751$	1.83745	−	1.06085i	0.0670495	−	0.0387111i	0.533150	+	0.846021i	$0.321008\pi$
$752$	−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
$756$	−2.12497	−	4.74178i	−0.0772843	−	0.172457i
$757$	12.5472	+	21.7324i	0.456035	+	0.789876i	0.998747	−	0.0500426i	$-0.0159357\pi$
$757$	12.5472	+	21.7324i	0.456035	+	0.789876i	−0.542712	+	0.839919i	$0.682602\pi$
$758$	2.58169	−	4.47161i	0.0937711	−	0.162416i
$759$	0.0935608	−	2.74278i	0.00339604	−	0.0995566i
$760$	−32.0828	+	8.59655i	−1.16376	+	0.311830i
$761$	42.5197	−	11.3931i	1.54134	−	0.413000i	0.614640	−	0.788808i	$-0.289301\pi$
$761$	42.5197	−	11.3931i	1.54134	−	0.413000i	0.926698	+	0.375808i	$0.122635\pi$
$762$	−0.583741	+	17.1127i	−0.0211467	+	0.619926i
$763$	5.58105	−	9.66667i	0.202048	−	0.349957i
$764$	7.92432	+	13.7253i	0.286692	+	0.496565i
$765$	16.7511	−	48.9052i	0.605636	−	1.76817i
$766$		−	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	−0.969616	−	0.244632i	$-0.921333\pi$
$769$	−0.210414	+	0.785274i	−0.00758771	+	0.0283177i	0.962028	+	0.272950i	$0.0879994\pi$
$770$	2.54800	−	1.47109i	0.0918236	−	0.0530144i
$771$	20.1888	−	4.67814i	0.727082	−	0.168479i
$772$	−2.40899	−	2.40899i	−0.0867013	−	0.0867013i
$773$	8.63524	+	32.2271i	0.310588	+	1.15913i	0.928028	+	0.372511i	$0.121503\pi$
$773$	8.63524	+	32.2271i	0.310588	+	1.15913i	−0.617440	+	0.786618i	$0.711830\pi$
$774$	7.02537	+	35.8331i	0.252522	+	1.28799i
$775$	26.4002	−	26.4002i	0.948322	−	0.948322i
$776$	−14.5237	−	8.38526i	−0.521370	−	0.301013i
$777$	7.81573	+	2.38260i	0.280388	+	0.0854754i
$778$	−22.6286	−	6.06331i	−0.811274	−	0.217380i
$779$	−12.2947			−0.440502
$780$	25.0883	−	7.24758i	0.898306	−	0.259505i
$781$	0.938972			0.0335990
$782$	−8.96357	−	2.40178i	−0.320537	−	0.0858875i
$783$	−3.68129	+	9.66002i	−0.131558	+	0.345221i
$784$	−0.866025	−	0.500000i	−0.0309295	−	0.0178571i
$785$	45.1157	−	45.1157i	1.61025	−	1.61025i
$786$	−16.5294	−	10.3102i	−0.589585	−	0.367751i
$787$	−8.11134	−	30.2719i	−0.289138	−	1.07908i	−0.945762	−	0.324860i	$-0.894683\pi$
$787$	−8.11134	−	30.2719i	−0.289138	−	1.07908i	0.656624	−	0.754218i	$-0.271984\pi$
$788$	−2.29548	−	2.29548i	−0.0817732	−	0.0817732i
$789$	−12.4016	−	53.5200i	−0.441510	−	1.90536i
$790$	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
$795$	−1.03349	+	0.550589i	−0.0366541	+	0.0195274i
$796$	−6.84505	−	11.8560i	−0.242616	−	0.420224i
$797$	0.223512	−	0.387133i	0.00791719	−	0.0137130i	−0.862040	−	0.506841i	$-0.830813\pi$
$797$	0.223512	−	0.387133i	0.00791719	−	0.0137130i	0.869957	+	0.493128i	$0.164147\pi$
$798$	−13.7497	−	0.469023i	−0.486732	−	0.0166032i
$799$	−20.5922	+	5.51765i	−0.728498	+	0.195200i
$800$	12.0605	−	3.23160i	0.426403	−	0.114254i
$801$	−17.5077	+	15.2690i	−0.618605	+	0.539503i
$802$	5.11171	−	8.85374i	0.180501	−	0.312636i
$803$	−2.27132	−	3.93404i	−0.0801530	−	0.138829i
$804$	−9.10393	−	17.0887i	−0.321071	−	0.602671i
$805$			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	$-0.514021\pi$
$809$	22.7298	−	13.1230i	0.799135	−	0.461381i	0.843169	+	0.537649i	$0.180687\pi$
$810$	29.7312	+	23.0742i	1.04465	+	0.810744i
$811$	−0.244577	−	0.244577i	−0.00858827	−	0.00858827i	0.702800	−	0.711388i	$-0.251933\pi$
$811$	−0.244577	−	0.244577i	−0.00858827	−	0.00858827i	−0.711388	+	0.702800i	$0.751933\pi$
$812$	0.514918	+	1.92170i	0.0180701	+	0.0674384i
$813$	2.51079	−	4.02534i	0.0880572	−	0.141175i
$814$	2.34701	−	2.34701i	0.0822626	−	0.0822626i
$815$	−4.21508	−	2.43358i	−0.147648	−	0.0852445i
$816$	−2.08125	+	6.82720i	−0.0728584	+	0.239000i
$817$	93.3858	+	25.0227i	3.26716	+	0.875432i
$818$	−32.8471			−1.14847
$819$	10.8155	+	0.158692i	0.377924	+	0.00554513i
$820$	6.47259			0.226032
$821$	3.01771	+	0.808593i	0.105319	+	0.0282201i	0.311094	−	0.950379i	$-0.399305\pi$
$821$	3.01771	+	0.808593i	0.105319	+	0.0282201i	−0.205775	+	0.978599i	$0.565971\pi$
$822$	7.09321	−	23.2681i	0.247404	−	0.811567i
$823$	26.7511	+	15.4448i	0.932484	+	0.538370i	0.887596	−	0.460622i	$-0.152374\pi$
$823$	26.7511	+	15.4448i	0.932484	+	0.538370i	0.0448880	+	0.998992i	$0.485707\pi$
$824$	−1.25374	+	1.25374i	−0.0436760	+	0.0436760i
$825$	−8.05293	+	12.9106i	−0.280367	+	0.449489i
$826$	1.46352	+	5.46193i	0.0509224	+	0.190045i
$827$	14.3490	+	14.3490i	0.498962	+	0.498962i	0.911115	−	0.412153i	$-0.135223\pi$
$827$	14.3490	+	14.3490i	0.498962	+	0.498962i	−0.412153	+	0.911115i	$0.635223\pi$
$828$	3.76876	−	5.60695i	0.130974	−	0.194855i
$829$	−19.5067	+	11.2622i	−0.677497	+	0.391153i	−0.798911	−	0.601449i	$-0.794590\pi$
$829$	−19.5067	+	11.2622i	−0.677497	+	0.391153i	0.121414	+	0.992602i	$0.461257\pi$
$830$	−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
$834$	9.33069	+	17.5143i	0.323095	+	0.606471i
$835$	49.8794	+	86.3937i	1.72615	+	2.98978i
$836$	−2.79433	+	4.83992i	−0.0966440	+	0.167392i
$837$	−15.4563	−	1.58665i	−0.534248	−	0.0548425i
$838$	−16.3473	+	4.38025i	−0.564708	+	0.151313i
$839$	38.3272	−	10.2697i	1.32320	−	0.354551i	0.473025	−	0.881049i	$-0.343162\pi$
$839$	38.3272	−	10.2697i	1.32320	−	0.354551i	0.850176	+	0.526498i	$0.176495\pi$
$840$	7.23857	+	0.246920i	0.249754	+	0.00851953i
$841$	−12.5210	+	21.6870i	−0.431757	+	0.747826i
$842$	−6.61365	−	11.4552i	−0.227921	−	0.394771i
$843$	−22.2972	+	11.8788i	−0.767957	+	0.409126i
$844$		−	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
$849$	10.2503	+	44.2359i	0.351790	+	1.51817i
$850$	36.3819	+	36.3819i	1.24789	+	1.24789i
$851$	2.74954	+	10.2614i	0.0942531	+	0.351757i
$852$	1.96123	+	1.22331i	0.0671906	+	0.0419099i
$853$	−0.903633	+	0.903633i	−0.0309398	+	0.0309398i	−0.722407	−	0.691468i	$-0.756964\pi$
$853$	−0.903633	+	0.903633i	−0.0309398	+	0.0309398i	0.691468	+	0.722407i	$0.256964\pi$
$854$	0.985179	+	0.568793i	0.0337121	+	0.0194637i
$855$	89.4884	−	43.8256i	3.06044	−	1.49880i
$856$	−11.5750	−	3.10152i	−0.395626	−	0.106008i
$857$	7.37918			0.252068			0.126034	−	0.992026i	$-0.459775\pi$
$857$	7.37918			0.252068			0.126034	+	0.992026i	$0.459775\pi$
$858$	2.12265	−	3.84725i	0.0724660	−	0.131343i
$859$	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
$861$	2.56447	+	0.781771i	0.0873968	+	0.0266427i
$862$	−29.9740	−	17.3055i	−1.02092	−	0.589427i
$863$	19.1821	−	19.1821i	0.652965	−	0.652965i	−0.300741	−	0.953706i	$-0.597234\pi$
$863$	19.1821	−	19.1821i	0.652965	−	0.652965i	0.953706	+	0.300741i	$0.0972339\pi$
$864$	−4.21117	−	3.04402i	−0.143267	−	0.103560i
$865$	−15.2139	−	56.7790i	−0.517288	−	1.93054i
$866$	8.35250	+	8.35250i	0.283829	+	0.283829i
$867$	0.0324758	−	0.00752528i	0.00110294	−	0.000255572i
$868$	−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
$873$	47.5969	+	16.3029i	1.61091	+	0.551770i
$874$	−8.94360	−	15.4908i	−0.302522	−	0.523983i
$875$	15.6517	−	27.1095i	0.529124	−	0.916469i
$876$	0.381236	−	11.1761i	0.0128808	−	0.377606i
$877$	17.6023	−	4.71653i	0.594389	−	0.159266i	0.0509307	−	0.998702i	$-0.483781\pi$
$877$	17.6023	−	4.71653i	0.594389	−	0.159266i	0.543458	+	0.839436i	$0.317115\pi$
$878$	11.1178	−	2.97901i	0.375209	−	0.100537i
$879$	0.532467	−	15.6095i	0.0179597	−	0.526497i
$880$	1.47109	−	2.54800i	0.0495904	−	0.0858931i
$881$	29.0407	+	50.2999i	0.978405	+	1.69465i	0.668208	+	0.743975i	$0.267062\pi$
$881$	29.0407	+	50.2999i	0.978405	+	1.69465i	0.310197	+	0.950672i	$0.399605\pi$
$882$	2.83813	+	0.972118i	0.0955648	+	0.0327329i
$883$			30.4291i			1.02402i	0.858979	+	0.512011i	$0.171099\pi$
$883$			30.4291i			1.02402i	−0.858979	+	0.512011i	$0.828901\pi$
$884$	−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	$-0.701169\pi$
$887$	−5.58052	+	3.22192i	−0.187376	+	0.108181i	0.403378	+	0.915034i	$0.367836\pi$
$888$	7.95992	−	1.84447i	0.267117	−	0.0618963i
$889$	−6.99028	−	6.99028i	−0.234446	−	0.234446i
$890$	−8.38071	−	31.2772i	−0.280922	−	1.04841i
$891$	6.28265	−	0.792036i	0.210477	−	0.0265342i
$892$	2.11089	−	2.11089i	0.0706778	−	0.0706778i
$893$	−35.5872	−	20.5463i	−1.19088	−	0.687555i
$894$	−25.8821	−	7.89009i	−0.865628	−	0.263884i
$895$	−37.6368	−	10.0847i	−1.25806	−	0.337096i
$896$	−1.00000			−0.0334077
$897$	7.26697	+	12.0404i	0.242637	+	0.402017i
$898$	−35.6149			−1.18848
$899$	5.74626	+	1.53971i	0.191649	+	0.0513521i
$900$	−33.6403	+	16.4748i	−1.12134	+	0.549161i
$901$	0.576982	+	0.333121i	0.0192221	+	0.0110979i
$902$	0.770092	−	0.770092i	0.0256413	−	0.0256413i
$903$	−17.8877	−	11.1574i	−0.595264	−	0.371294i
$904$	−0.924013	−	3.44846i	−0.0307322	−	0.114694i
$905$	−58.0082	−	58.0082i	−1.92826	−	1.92826i
$906$	4.10114	+	17.6987i	0.136251	+	0.588000i
$907$	−22.0310	+	12.7196i	−0.731529	+	0.422348i	−0.818981	−	0.573820i	$-0.805461\pi$
$907$	−22.0310	+	12.7196i	−0.731529	+	0.422348i	0.0874526	+	0.996169i	$0.472127\pi$
$908$	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	$-0.0787946\pi$
$912$	−12.1421	+	6.46864i	−0.402064	+	0.214198i
$913$	5.15320	+	8.92561i	0.170546	+	0.295395i
$914$	16.4141	−	28.4300i	0.542929	−	0.940381i
$915$	−8.23450	−	0.280892i	−0.272224	−	0.00928602i
$916$	−6.08849	+	1.63141i	−0.201169	+	0.0539032i
$917$	10.8643	−	2.91108i	0.358770	−	0.0961322i
$918$	2.18654	−	21.3002i	0.0721667	−	0.703012i
$919$	−12.2006	+	21.1320i	−0.402460	+	0.697081i	−0.994022	−	0.109179i	$-0.965178\pi$
$919$	−12.2006	+	21.1320i	−0.402460	+	0.697081i	0.591562	+	0.806259i	$0.298511\pi$
$920$	4.70840	+	8.15519i	0.155231	+	0.268869i
$921$	−9.52468	−	17.8784i	−0.313849	−	0.589115i
$922$			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
$927$	2.96730	−	4.41458i	0.0974590	−	0.144994i
$928$	1.40678	+	1.40678i	0.0461799	+	0.0461799i
$929$	−0.999322	−	3.72952i	−0.0327867	−	0.122362i	0.947593	−	0.319480i	$-0.103508\pi$
$929$	−0.999322	−	3.72952i	−0.0327867	−	0.122362i	−0.980380	+	0.197119i	$0.936842\pi$
$930$	11.4618	−	18.3757i	0.375847	−	0.602564i
$931$	5.61654	−	5.61654i	0.184075	−	0.184075i
$932$	23.0815	+	13.3261i	0.756060	+	0.436512i
$933$	−5.56166	+	18.2441i	−0.182081	+	0.597285i
$934$	−4.22723	−	1.13268i	−0.138319	−	0.0370625i
$935$	12.1240			0.396499
$936$	9.44583	−	5.27031i	0.308747	−	0.172266i
$937$	−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
$939$	−9.61656	+	31.5455i	−0.313825	+	1.02945i
$940$	18.7350	+	10.8167i	0.611070	+	0.352801i
$941$	−37.1412	+	37.1412i	−1.21077	+	1.21077i	−0.239996	+	0.970774i	$0.577146\pi$
$941$	−37.1412	+	37.1412i	−1.21077	+	1.21077i	−0.970774	+	0.239996i	$0.922854\pi$
$942$	13.9864	−	22.4232i	0.455702	−	0.730589i
$943$	0.902169	+	3.36694i	0.0293787	+	0.109643i
$944$	3.99841	+	3.99841i	0.130137	+	0.130137i
$945$	−21.4525	+	3.45108i	−0.697851	+	0.112264i
$946$	−7.41666	+	4.28201i	−0.241137	+	0.139220i
$947$	6.44930	−	24.0691i	0.209574	−	0.782141i	−0.778432	−	0.627729i	$-0.783985\pi$
$947$	6.44930	−	24.0691i	0.209574	−	0.782141i	0.988006	−	0.154413i	$-0.0493486\pi$
$948$	9.32433	−	8.70917i	0.302840	−	0.282861i
$949$	20.7536	+	10.5440i	0.673690	+	0.342274i
$950$			99.1756i			3.21768i
$951$	−5.41871	−	10.1713i	−0.175714	−	0.329826i
$952$	−2.06039	−	3.56869i	−0.0667775	−	0.115662i
$953$	3.36492	−	5.82821i	0.109000	−	0.188794i	−0.806365	−	0.591418i	$-0.798568\pi$
$953$	3.36492	−	5.82821i	0.109000	−	0.188794i	0.915366	+	0.402624i	$0.131902\pi$
$954$	−0.365547	+	0.318804i	−0.0118350	+	0.0103217i
$955$	64.0148	−	17.1527i	2.07147	−	0.555048i
$956$	13.2380	−	3.54711i	0.428148	−	0.114722i
$957$	−2.42311	−	0.0826565i	−0.0783282	−	0.00267190i
$958$	7.48072	−	12.9570i	0.241691	−	0.418622i
$959$	7.02209	+	12.1626i	0.226755	+	0.392751i
$960$	6.39224	−	3.40545i	0.206309	−	0.109910i
$961$		−	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
$966$	0.880491	+	3.79981i	0.0283293	+	0.122257i
$967$	2.12515	+	2.12515i	0.0683401	+	0.0683401i	0.740451	−	0.672111i	$-0.234612\pi$
$967$	2.12515	+	2.12515i	0.0683401	+	0.0683401i	−0.672111	+	0.740451i	$0.734612\pi$
$968$	2.71888	+	10.1470i	0.0873882	+	0.326137i
$969$	−48.1019	−	30.0034i	−1.54526	−	0.963847i
$970$	−49.5879	+	49.5879i	−1.59217	+	1.59217i
$971$	14.7634	+	8.52365i	0.473780	+	0.273537i	0.717821	−	0.696228i	$-0.245140\pi$
$971$	14.7634	+	8.52365i	0.473780	+	0.273537i	−0.244041	+	0.969765i	$0.578473\pi$
$972$	14.1544	+	6.53083i	0.454004	+	0.209476i
$973$	−11.0670	−	2.96538i	−0.354790	−	0.0950657i
$974$	−4.30556			−0.137959
$975$	−1.51471	−	77.9600i	−0.0485095	−	2.49672i
$976$	1.13759			0.0364133
$977$	37.1574	+	9.95629i	1.18877	+	0.318530i	0.798399	−	0.602128i	$-0.205680\pi$
$977$	37.1574	+	9.95629i	1.18877	+	0.318530i	0.390370	+	0.920658i	$0.372347\pi$
$978$	−1.92839	−	0.587864i	−0.0616631	−	0.0187978i
$979$	−4.71840	−	2.72417i	−0.150801	−	0.0870648i
$980$	−2.95685	+	2.95685i	−0.0944532	+	0.0944532i
$981$	6.44261	+	32.8607i	0.205697	+	1.04916i
$982$	1.43298	+	5.34795i	0.0457282	+	0.170660i
$983$	13.9875	+	13.9875i	0.446131	+	0.446131i	0.894066	−	0.447935i	$-0.147840\pi$
$983$	13.9875	+	13.9875i	0.446131	+	0.446131i	−0.447935	+	0.894066i	$0.647840\pi$
$984$	2.61178	−	0.605201i	0.0832605	−	0.0192931i
$985$	−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
$990$	−2.86015	+	8.35029i	−0.0909014	+	0.265389i
$991$	6.67071	+	11.5540i	0.211902	+	0.367025i	0.952310	−	0.305133i	$-0.0987009\pi$
$991$	6.67071	+	11.5540i	0.211902	+	0.367025i	−0.740408	+	0.672158i	$0.765368\pi$
$992$	−1.49510	+	2.58959i	−0.0474695	+	0.0822195i
$993$	−1.38738	+	40.6718i	−0.0440273	+	1.29068i
$994$	−1.28906	+	0.345402i	−0.0408864	+	0.0109555i
$995$	−55.2961	+	14.8166i	−1.75301	+	0.469716i
$996$	−0.864956	+	25.3566i	−0.0274072	+	0.803455i
$997$	26.4382	−	45.7923i	0.837306	−	1.45026i	−0.0548326	−	0.998496i	$-0.517463\pi$
$997$	26.4382	−	45.7923i	0.837306	−	1.45026i	0.892139	−	0.451761i	$-0.149204\pi$
$998$	0.174418	+	0.302101i	0.00552110	+	0.00956283i
$999$	−22.3690	+	10.0244i	−0.707725	+	0.317158i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.1	✓	56	13.6	odd	12
546.2.bu.a.323.1	yes	56	3.2	odd	2
546.2.bu.b.71.12	yes	56	39.32	even	12	inner
546.2.bu.b.323.12	yes	56	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.505064 - 1.65678i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.95685 - 2.95685i) q^{5} +(0.916660 - 1.46960i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.48982 - 1.67356i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.505064 - 1.65678i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.95685 - 2.95685i) q^{5} +(0.916660 - 1.46960i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.48982 - 1.67356i) 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} +(-3.40545 - 6.39224i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.06039 + 3.56869i) q^{17} +(-1.97183 - 2.26094i) q^{18} +(-7.67233 + 2.05579i) q^{19} +(4.03913 - 1.08228i) q^{20} +(1.73104 + 0.0590488i) q^{21} +(0.351799 - 0.609333i) q^{22} +(1.12597 + 1.95025i) q^{23} +(1.52865 - 0.814384i) 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} +(-1.63497 - 7.05583i) q^{30} +(2.11439 + 2.11439i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.03401 - 0.644960i) q^{33} +(-2.91383 + 2.91383i) q^{34} +(3.62139 + 2.09081i) q^{35} +(-1.31947 - 2.69425i) q^{36} +(4.55669 + 1.22096i) q^{37} -7.94298 q^{38} +(6.24382 - 0.121313i) q^{39} +4.18162 q^{40} +(1.49512 + 0.400617i) q^{41} +(1.65678 + 0.505064i) q^{42} +(-10.5411 - 6.08588i) q^{43} +(0.497519 - 0.497519i) q^{44} +(-12.3105 + 2.41357i) q^{45} +(0.582847 + 2.17522i) q^{46} +(3.65818 + 3.65818i) q^{47} +(1.68734 - 0.390990i) 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} +(-4.74178 + 2.12497i) q^{54} +(-1.47109 - 2.54800i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-0.469023 + 13.7497i) q^{57} +(1.92170 - 0.514918i) q^{58} +(5.46193 - 1.46352i) q^{59} +(0.246920 - 7.23857i) q^{60} +(0.568793 - 0.985179i) q^{61} +(1.49510 + 2.58959i) q^{62} +(0.972118 - 2.83813i) 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} +(3.79981 - 0.880491i) q^{69} +(2.95685 + 2.95685i) q^{70} +(0.345402 + 1.28906i) q^{71} +(-0.577186 - 2.94395i) q^{72} +(4.56529 - 4.56529i) q^{73} +(4.08541 + 2.35871i) q^{74} +(-20.6864 - 6.30620i) q^{75} +(-7.67233 - 2.05579i) q^{76} +0.703598 q^{77} +(6.06246 + 1.49884i) q^{78} +7.36643 q^{79} +(4.03913 + 1.08228i) q^{80} +(3.39842 + 8.33371i) q^{81} +(1.34049 + 0.773933i) q^{82} +(-10.3578 + 10.3578i) q^{83} +(1.46960 + 0.916660i) q^{84} +(4.45984 + 16.6443i) q^{85} +(-8.60674 - 8.60674i) q^{86} +(-0.777871 - 3.35695i) 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} +(4.57097 - 2.43517i) q^{93} +(2.58672 + 4.48033i) q^{94} +(-16.6073 + 28.7646i) q^{95} +(1.73104 + 0.0590488i) q^{96} +(-16.1991 + 4.34053i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(-1.59080 + 1.38738i) 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	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 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^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 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 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Introduction

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