LMFDB - Embedded newform 546.2.ch.a.401.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			401.20
Character	$\chi$	$=$	546.401
Dual form			546.2.ch.a.305.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.73205 + 0.00254284i) q^{3} -1.00000i q^{4} +(-0.852470 - 3.18146i) q^{5} +(-1.22295 + 1.22654i) q^{6} +(2.55679 + 0.680305i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99999 - 0.00880865i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.73205 + 0.00254284i) q^{3} -1.00000i q^{4} +(-0.852470 - 3.18146i) q^{5} +(-1.22295 + 1.22654i) q^{6} +(2.55679 + 0.680305i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99999 - 0.00880865i) q^{9} +(-2.85242 - 1.64685i) q^{10} +(4.19511 - 1.12408i) q^{11} +(0.00254284 + 1.73205i) q^{12} +(-3.59872 - 0.221835i) q^{13} +(2.28897 - 1.32688i) q^{14} +(1.48461 + 5.50828i) q^{15} -1.00000 q^{16} -5.29539 q^{17} +(2.11508 - 2.12754i) q^{18} +(1.57626 - 5.88267i) q^{19} +(-3.18146 + 0.852470i) q^{20} +(-4.43022 - 1.17182i) q^{21} +(2.17155 - 3.76124i) q^{22} -8.97313 q^{23} +(1.22654 + 1.22295i) q^{24} +(-5.06487 + 2.92420i) q^{25} +(-2.70154 + 2.38782i) q^{26} +(-5.19610 + 0.0228855i) q^{27} +(0.680305 - 2.55679i) q^{28} +(2.35873 - 1.36181i) q^{29} +(4.94472 + 2.84516i) q^{30} +(-0.298174 + 1.11280i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-7.26328 + 1.95762i) q^{33} +(-3.74441 + 3.74441i) q^{34} +(-0.0152231 - 8.71427i) q^{35} +(-0.00880865 - 2.99999i) q^{36} +(1.48834 - 1.48834i) q^{37} +(-3.04509 - 5.27425i) q^{38} +(6.23372 + 0.375078i) q^{39} +(-1.64685 + 2.85242i) q^{40} +(8.93434 + 2.39395i) q^{41} +(-3.96124 + 2.30404i) q^{42} +(-2.42543 - 1.40032i) q^{43} +(-1.12408 - 4.19511i) q^{44} +(-2.58542 - 9.53683i) q^{45} +(-6.34496 + 6.34496i) q^{46} +(4.19035 - 1.12280i) q^{47} +(1.73205 - 0.00254284i) q^{48} +(6.07437 + 3.47880i) q^{49} +(-1.51368 + 5.64912i) q^{50} +(9.17188 - 0.0134653i) q^{51} +(-0.221835 + 3.59872i) q^{52} +(-4.94841 + 2.85697i) q^{53} +(-3.65802 + 3.69038i) q^{54} +(-7.15242 - 12.3884i) q^{55} +(-1.32688 - 2.28897i) q^{56} +(-2.71519 + 10.1931i) q^{57} +(0.704925 - 2.63082i) q^{58} +(-0.571327 - 0.571327i) q^{59} +(5.50828 - 1.48461i) q^{60} +(1.18591 + 2.05406i) q^{61} +(0.576029 + 0.997711i) q^{62} +(7.67634 + 2.01839i) q^{63} +1.00000i q^{64} +(2.36204 + 11.6383i) q^{65} +(-3.75167 + 6.52017i) q^{66} +(9.45859 - 2.53442i) q^{67} +5.29539i q^{68} +(15.5419 - 0.0228172i) q^{69} +(-6.17269 - 6.15116i) q^{70} +(-2.23789 - 8.35193i) q^{71} +(-2.12754 - 2.11508i) q^{72} +(-1.45899 - 0.390935i) q^{73} -2.10482i q^{74} +(8.76516 - 5.07774i) q^{75} +(-5.88267 - 1.57626i) q^{76} +(11.4907 - 0.0200734i) q^{77} +(4.67313 - 4.14269i) q^{78} +(-0.257500 + 0.446002i) q^{79} +(0.852470 + 3.18146i) q^{80} +(8.99984 - 0.0528517i) q^{81} +(8.01031 - 4.62476i) q^{82} +(4.56024 - 4.56024i) q^{83} +(-1.17182 + 4.43022i) q^{84} +(4.51416 + 16.8471i) q^{85} +(-2.70522 + 0.724860i) q^{86} +(-4.08197 + 2.36472i) q^{87} +(-3.76124 - 2.17155i) q^{88} +(-1.56283 - 1.56283i) q^{89} +(-8.57173 - 4.91539i) q^{90} +(-9.05026 - 3.01542i) q^{91} +8.97313i q^{92} +(0.513623 - 1.92819i) q^{93} +(2.16909 - 3.75697i) q^{94} -20.0592 q^{95} +(1.22295 - 1.22654i) q^{96} +(2.82483 - 0.756910i) q^{97} +(6.75511 - 1.83535i) q^{98} +(12.5754 - 3.40917i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.73205	+	0.00254284i	−0.999999	+	0.00146811i
$3$	−1.73205	+	0.00254284i	−0.999999	+	0.00146811i
$4$		−	1.00000i		−	0.500000i
$5$	−0.852470	−	3.18146i	−0.381236	−	1.42279i	−0.844015	−	0.536319i	$-0.819814\pi$
$5$	−0.852470	−	3.18146i	−0.381236	−	1.42279i	0.462779	−	0.886474i	$-0.346852\pi$
$6$	−1.22295	+	1.22654i	−0.499265	+	0.500734i
$7$	2.55679	+	0.680305i	0.966376	+	0.257131i
$7$	2.55679	+	0.680305i	0.966376	+	0.257131i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.99999	−	0.00880865i	0.999996	−	0.00293622i
$10$	−2.85242	−	1.64685i	−0.902015	−	0.520778i
$11$	4.19511	−	1.12408i	1.26487	−	0.338922i	0.436809	−	0.899554i	$-0.356108\pi$
$11$	4.19511	−	1.12408i	1.26487	−	0.338922i	0.828065	+	0.560632i	$0.189442\pi$
$12$	0.00254284	+	1.73205i	0.000734055	+	0.499999i
$13$	−3.59872	−	0.221835i	−0.998105	−	0.0615260i
$13$	−3.59872	−	0.221835i	−0.998105	−	0.0615260i
$14$	2.28897	−	1.32688i	0.611754	−	0.354623i
$15$	1.48461	+	5.50828i	0.383325	+	1.42223i
$16$	−1.00000			−0.250000
$17$	−5.29539			−1.28432			−0.642161	−	0.766570i	$-0.721962\pi$
$17$	−5.29539			−1.28432			−0.642161	+	0.766570i	$0.721962\pi$
$18$	2.11508	−	2.12754i	0.498530	−	0.501466i
$19$	1.57626	−	5.88267i	0.361618	−	1.34958i	−0.510330	−	0.859978i	$-0.670477\pi$
$19$	1.57626	−	5.88267i	0.361618	−	1.34958i	0.871948	−	0.489598i	$-0.162856\pi$
$20$	−3.18146	+	0.852470i	−0.711396	+	0.190618i
$21$	−4.43022	−	1.17182i	−0.966753	−	0.255712i
$22$	2.17155	−	3.76124i	0.462976	−	0.801898i
$23$	−8.97313			−1.87103			−0.935513	−	0.353292i	$-0.885062\pi$
$23$	−8.97313			−1.87103			−0.935513	+	0.353292i	$0.885062\pi$
$24$	1.22654	+	1.22295i	0.250367	+	0.249633i
$25$	−5.06487	+	2.92420i	−1.01297	+	0.584840i
$26$	−2.70154	+	2.38782i	−0.529816	+	0.468290i
$27$	−5.19610	+	0.0228855i	−0.999990	+	0.00440432i
$28$	0.680305	−	2.55679i	0.128566	−	0.483188i
$29$	2.35873	−	1.36181i	0.438004	−	0.252882i	−0.264746	−	0.964318i	$-0.585288\pi$
$29$	2.35873	−	1.36181i	0.438004	−	0.252882i	0.702751	+	0.711436i	$0.251955\pi$
$30$	4.94472	+	2.84516i	0.902778	+	0.519454i
$31$	−0.298174	+	1.11280i	−0.0535537	+	0.199865i	−0.987519	−	0.157498i	$-0.949657\pi$
$31$	−0.298174	+	1.11280i	−0.0535537	+	0.199865i	0.933966	+	0.357363i	$0.116324\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−7.26328	+	1.95762i	−1.26438	+	0.340779i
$34$	−3.74441	+	3.74441i	−0.642161	+	0.642161i
$35$	−0.0152231	−	8.71427i	−0.00257318	−	1.47298i
$36$	−0.00880865	−	2.99999i	−0.00146811	−	0.499998i
$37$	1.48834	−	1.48834i	0.244681	−	0.244681i	−0.574103	−	0.818783i	$-0.694649\pi$
$37$	1.48834	−	1.48834i	0.244681	−	0.244681i	0.818783	+	0.574103i	$0.194649\pi$
$38$	−3.04509	−	5.27425i	−0.493979	−	0.855597i
$39$	6.23372	+	0.375078i	0.998195	+	0.0600606i
$40$	−1.64685	+	2.85242i	−0.260389	+	0.451007i
$41$	8.93434	+	2.39395i	1.39531	+	0.373872i	0.876658	−	0.481113i	$-0.159767\pi$
$41$	8.93434	+	2.39395i	1.39531	+	0.373872i	0.518652	+	0.854986i	$0.326434\pi$
$42$	−3.96124	+	2.30404i	−0.611233	+	0.355520i
$43$	−2.42543	−	1.40032i	−0.369875	−	0.213547i	0.303529	−	0.952822i	$-0.401835\pi$
$43$	−2.42543	−	1.40032i	−0.369875	−	0.213547i	−0.673404	+	0.739275i	$0.735168\pi$
$44$	−1.12408	−	4.19511i	−0.169461	−	0.632437i
$45$	−2.58542	−	9.53683i	−0.385412	−	1.42167i
$46$	−6.34496	+	6.34496i	−0.935513	+	0.935513i
$47$	4.19035	−	1.12280i	0.611226	−	0.163778i	0.0600900	−	0.998193i	$-0.480861\pi$
$47$	4.19035	−	1.12280i	0.611226	−	0.163778i	0.551136	+	0.834415i	$0.314195\pi$
$48$	1.73205	−	0.00254284i	0.250000	−	0.000367027i
$49$	6.07437	+	3.47880i	0.867767	+	0.496971i
$50$	−1.51368	+	5.64912i	−0.214066	+	0.798907i
$51$	9.17188	−	0.0134653i	1.28432	−	0.00188553i
$52$	−0.221835	+	3.59872i	−0.0307630	+	0.499053i
$53$	−4.94841	+	2.85697i	−0.679717	+	0.392435i	−0.799748	−	0.600335i	$-0.795034\pi$
$53$	−4.94841	+	2.85697i	−0.679717	+	0.392435i	0.120032	+	0.992770i	$0.461700\pi$
$54$	−3.65802	+	3.69038i	−0.497793	+	0.502197i
$55$	−7.15242	−	12.3884i	−0.964432	−	1.67044i
$56$	−1.32688	−	2.28897i	−0.177311	−	0.305877i
$57$	−2.71519	+	10.1931i	−0.359636	+	1.35011i
$58$	0.704925	−	2.63082i	0.0925612	−	0.345443i
$59$	−0.571327	−	0.571327i	−0.0743805	−	0.0743805i	0.668938	−	0.743318i	$-0.266749\pi$
$59$	−0.571327	−	0.571327i	−0.0743805	−	0.0743805i	−0.743318	+	0.668938i	$0.766749\pi$
$60$	5.50828	−	1.48461i	0.711116	−	0.191662i
$61$	1.18591	+	2.05406i	0.151840	+	0.262995i	0.931904	−	0.362705i	$-0.118147\pi$
$61$	1.18591	+	2.05406i	0.151840	+	0.262995i	−0.780064	+	0.625700i	$0.784813\pi$
$62$	0.576029	+	0.997711i	0.0731557	+	0.126709i
$63$	7.67634	+	2.01839i	0.967127	+	0.254293i
$64$			1.00000i			0.125000i
$65$	2.36204	+	11.6383i	0.292975	+	1.44355i
$66$	−3.75167	+	6.52017i	−0.461798	+	0.802577i
$67$	9.45859	−	2.53442i	1.15555	−	0.309629i	0.370364	−	0.928887i	$-0.379233\pi$
$67$	9.45859	−	2.53442i	1.15555	−	0.309629i	0.785188	+	0.619258i	$0.212566\pi$
$68$			5.29539i			0.642161i
$69$	15.5419	−	0.0228172i	1.87102	−	0.00274687i
$70$	−6.17269	−	6.15116i	−0.737777	−	0.735204i
$71$	−2.23789	−	8.35193i	−0.265589	−	0.991192i	−0.961889	−	0.273441i	$-0.911838\pi$
$71$	−2.23789	−	8.35193i	−0.265589	−	0.991192i	0.696300	−	0.717751i	$-0.254829\pi$
$72$	−2.12754	−	2.11508i	−0.250733	−	0.249265i
$73$	−1.45899	−	0.390935i	−0.170762	−	0.0457555i	0.172425	−	0.985023i	$-0.444840\pi$
$73$	−1.45899	−	0.390935i	−0.170762	−	0.0457555i	−0.343187	+	0.939267i	$0.611506\pi$
$74$		−	2.10482i		−	0.244681i
$75$	8.76516	−	5.07774i	1.01211	−	0.586327i
$76$	−5.88267	−	1.57626i	−0.674788	−	0.180809i
$77$	11.4907	−	0.0200734i	1.30949	−	0.00228758i
$78$	4.67313	−	4.14269i	0.529128	−	0.469067i
$79$	−0.257500	+	0.446002i	−0.0289710	+	0.0501792i	−0.880147	−	0.474701i	$-0.842556\pi$
$79$	−0.257500	+	0.446002i	−0.0289710	+	0.0501792i	0.851176	+	0.524880i	$0.175890\pi$
$80$	0.852470	+	3.18146i	0.0953090	+	0.355698i
$81$	8.99984	−	0.0528517i	0.999983	−	0.00587241i
$82$	8.01031	−	4.62476i	0.884591	−	0.510719i
$83$	4.56024	−	4.56024i	0.500551	−	0.500551i	−0.411058	−	0.911609i	$-0.634841\pi$
$83$	4.56024	−	4.56024i	0.500551	−	0.500551i	0.911609	+	0.411058i	$0.134841\pi$
$84$	−1.17182	+	4.43022i	−0.127856	+	0.483376i
$85$	4.51416	+	16.8471i	0.489630	+	1.82732i
$86$	−2.70522	+	0.724860i	−0.291711	+	0.0781637i
$87$	−4.08197	+	2.36472i	−0.437633	+	0.253525i
$88$	−3.76124	−	2.17155i	−0.400949	−	0.231488i
$89$	−1.56283	−	1.56283i	−0.165660	−	0.165660i	0.619409	−	0.785069i	$-0.287372\pi$
$89$	−1.56283	−	1.56283i	−0.165660	−	0.165660i	−0.785069	+	0.619409i	$0.787372\pi$
$90$	−8.57173	−	4.91539i	−0.903540	−	0.518128i
$91$	−9.05026	−	3.01542i	−0.948725	−	0.316101i
$92$			8.97313i			0.935513i
$93$	0.513623	−	1.92819i	0.0532602	−	0.199943i
$94$	2.16909	−	3.75697i	0.223724	−	0.387502i
$95$	−20.0592			−2.05803
$96$	1.22295	−	1.22654i	0.124816	−	0.125183i
$97$	2.82483	−	0.756910i	0.286818	−	0.0768525i	−0.112542	−	0.993647i	$-0.535899\pi$
$97$	2.82483	−	0.756910i	0.286818	−	0.0768525i	0.399359	+	0.916794i	$0.369233\pi$
$98$	6.75511	−	1.83535i	0.682369	−	0.185398i
$99$	12.5754	−	3.40917i	1.26387	−	0.342635i
$100$	2.92420	+	5.06487i	0.292420	+	0.506487i
$101$	−4.83780	+	8.37932i	−0.481379	+	0.833774i	−0.999772	−	0.0213693i	$-0.993197\pi$
$101$	−4.83780	+	8.37932i	−0.481379	+	0.833774i	0.518392	+	0.855143i	$0.326531\pi$
$102$	6.47598	−	6.49502i	0.641217	−	0.643103i
$103$	10.7642	+	6.21469i	1.06062	+	0.612351i	0.925605	−	0.378492i	$-0.123557\pi$
$103$	10.7642	+	6.21469i	1.06062	+	0.612351i	0.135019	+	0.990843i	$0.456891\pi$
$104$	2.38782	+	2.70154i	0.234145	+	0.264908i
$105$	0.0485262	+	15.0935i	0.00473568	+	1.47298i
$106$	−1.47888	+	5.51924i	−0.143641	+	0.536076i
$107$		−	7.39350i		−	0.714757i	−0.933960	−	0.357378i	$-0.883671\pi$
$107$		−	7.39350i		−	0.714757i	0.933960	−	0.357378i	$-0.116329\pi$
$108$	0.0228855	+	5.19610i	0.00220216	+	0.499995i
$109$	−1.10760	+	4.13363i	−0.106089	+	0.395930i	−0.998466	−	0.0553599i	$-0.982369\pi$
$109$	−1.10760	+	4.13363i	−0.106089	+	0.395930i	0.892377	+	0.451290i	$0.149036\pi$
$110$	−13.8174	−	3.70236i	−1.31744	−	0.353007i
$111$	−2.57408	+	2.58165i	−0.244321	+	0.245040i
$112$	−2.55679	−	0.680305i	−0.241594	−	0.0642828i
$113$	2.49592	+	1.44102i	0.234797	+	0.135560i	0.612783	−	0.790251i	$-0.290050\pi$
$113$	2.49592	+	1.44102i	0.234797	+	0.135560i	−0.377986	+	0.925811i	$0.623383\pi$
$114$	5.28766	+	9.12752i	0.495235	+	0.854871i
$115$	7.64932	+	28.5477i	0.713303	+	2.66208i
$116$	−1.36181	−	2.35873i	−0.126441	−	0.219002i
$117$	−10.7981	−	0.633803i	−0.998282	−	0.0585951i
$118$	−0.807979			−0.0743805
$119$	−13.5392	−	3.60248i	−1.24114	−	0.330239i
$120$	2.84516	−	4.94472i	0.259727	−	0.451389i
$121$	6.80915	−	3.93126i	0.619014	−	0.357388i
$122$	2.29100	+	0.613873i	0.207418	+	0.0555774i
$123$	−15.4808	−	4.12372i	−1.39586	−	0.371823i
$124$	1.11280	+	0.298174i	0.0999325	+	0.0267768i
$125$	1.97592	+	1.97592i	0.176732	+	0.176732i
$126$	6.85520	−	4.00077i	0.610710	−	0.356417i
$127$	8.22861	−	4.75079i	0.730171	−	0.421565i	−0.0883135	−	0.996093i	$-0.528148\pi$
$127$	8.22861	−	4.75079i	0.730171	−	0.421565i	0.818485	+	0.574528i	$0.194814\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	4.20452	+	2.41926i	0.370188	+	0.213004i
$130$	9.89974	+	6.55930i	0.868264	+	0.575289i
$131$	−4.69605	−	2.71126i	−0.410295	−	0.236884i	0.280621	−	0.959819i	$-0.409460\pi$
$131$	−4.69605	−	2.71126i	−0.410295	−	0.236884i	−0.690917	+	0.722934i	$0.742793\pi$
$132$	1.95762	+	7.26328i	0.170389	+	0.632188i
$133$	8.03217	−	13.9684i	0.696477	−	1.21122i
$134$	4.89613	−	8.48034i	0.422961	−	0.732590i
$135$	4.50233	+	16.5117i	0.387499	+	1.42110i
$136$	3.74441	+	3.74441i	0.321080	+	0.321080i
$137$	−1.66912	−	1.66912i	−0.142602	−	0.142602i	0.632202	−	0.774804i	$-0.282151\pi$
$137$	−1.66912	−	1.66912i	−0.142602	−	0.142602i	−0.774804	+	0.632202i	$0.782151\pi$
$138$	10.9736	−	11.0059i	0.934139	−	0.936886i
$139$	6.99492	−	12.1156i	0.593302	−	1.02763i	−0.400483	−	0.916304i	$-0.631157\pi$
$139$	6.99492	−	12.1156i	0.593302	−	1.02763i	0.993784	−	0.111324i	$-0.0355092\pi$
$140$	−8.71427	+	0.0152231i	−0.736491	+	0.00128659i
$141$	−7.25504	+	1.95540i	−0.610985	+	0.164675i
$142$	−7.48814	−	4.32328i	−0.628391	−	0.362802i
$143$	−15.3464	+	3.11462i	−1.28333	+	0.260457i
$144$	−2.99999	+	0.00880865i	−0.249999	+	0.000734054i
$145$	−6.34329	−	6.34329i	−0.526782	−	0.526782i
$146$	−1.30809	+	0.755228i	−0.108259	+	0.0625031i
$147$	−10.5300	−	6.01000i	−0.868496	−	0.495697i
$148$	−1.48834	−	1.48834i	−0.122340	−	0.122340i
$149$	18.3242	+	4.90995i	1.50118	+	0.402239i	0.913493	−	0.406853i	$-0.133374\pi$
$149$	18.3242	+	4.90995i	1.50118	+	0.402239i	0.587682	+	0.809092i	$0.300041\pi$
$150$	2.60740	−	9.78841i	0.212893	−	0.799220i
$151$	2.63524	+	0.706111i	0.214453	+	0.0574625i	0.364446	−	0.931225i	$-0.381258\pi$
$151$	2.63524	+	0.706111i	0.214453	+	0.0574625i	−0.149993	+	0.988687i	$0.547925\pi$
$152$	−5.27425	+	3.04509i	−0.427799	+	0.246990i
$153$	−15.8861	+	0.0466453i	−1.28432	+	0.00377105i
$154$	8.11099	−	8.13938i	0.653602	−	0.655890i
$155$	3.79452			0.304783
$156$	0.375078	−	6.23372i	0.0300303	−	0.499097i
$157$	1.70045	+	2.94527i	0.135711	+	0.235058i	0.925869	−	0.377845i	$-0.123335\pi$
$157$	1.70045	+	2.94527i	0.135711	+	0.235058i	−0.790158	+	0.612903i	$0.790001\pi$
$158$	0.133292	+	0.497451i	0.0106041	+	0.0395751i
$159$	8.56363	−	4.96099i	0.679140	−	0.393432i
$160$	2.85242	+	1.64685i	0.225504	+	0.130195i
$161$	−22.9424	−	6.10447i	−1.80812	−	0.481099i
$162$	6.32648	−	6.40122i	0.497055	−	0.502928i
$163$	24.4839	+	6.56044i	1.91773	+	0.513853i	0.990105	+	0.140331i	$0.0448168\pi$
$163$	24.4839	+	6.56044i	1.91773	+	0.513853i	0.927621	+	0.373522i	$0.121850\pi$
$164$	2.39395	−	8.93434i	0.186936	−	0.697655i
$165$	12.4198	+	21.4390i	0.966883	+	1.66903i
$166$		−	6.44915i		−	0.500551i
$167$	1.41135	−	5.26722i	0.109213	−	0.407590i	−0.889576	−	0.456788i	$-0.849000\pi$
$167$	1.41135	−	5.26722i	0.109213	−	0.407590i	0.998789	+	0.0491979i	$0.0156665\pi$
$168$	2.30404	+	3.96124i	0.177760	+	0.305616i
$169$	12.9016	+	1.59665i	0.992429	+	0.122819i
$170$	15.1047	+	8.72070i	1.15848	+	0.668847i
$171$	4.67693	−	17.6618i	0.357654	−	1.35063i
$172$	−1.40032	+	2.42543i	−0.106774	+	0.184937i
$173$	6.88988	+	11.9336i	0.523828	+	0.907297i	0.999615	+	0.0277364i	$0.00882989\pi$
$173$	6.88988	+	11.9336i	0.523828	+	0.907297i	−0.475787	+	0.879560i	$0.657837\pi$
$174$	−1.21428	+	4.55850i	−0.0920540	+	0.345579i
$175$	−14.9392	+	4.03092i	−1.12929	+	0.304709i
$176$	−4.19511	+	1.12408i	−0.316219	+	0.0847305i
$177$	0.991019	+	0.988114i	0.0744896	+	0.0742712i
$178$	−2.21018			−0.165660
$179$	4.44678	−	7.70206i	0.332368	−	0.575679i	−0.650607	−	0.759414i	$-0.725486\pi$
$179$	4.44678	−	7.70206i	0.332368	−	0.575679i	0.982976	+	0.183736i	$0.0588190\pi$
$180$	−9.53683	+	2.58542i	−0.710834	+	0.192706i
$181$		−	20.2657i		−	1.50634i	−0.657826	−	0.753170i	$-0.728524\pi$
$181$		−	20.2657i		−	1.50634i	0.657826	−	0.753170i	$-0.271476\pi$
$182$	−8.53172	+	4.26728i	−0.632413	+	0.316312i
$183$	−2.05928	−	3.55471i	−0.152226	−	0.262772i
$184$	6.34496	+	6.34496i	0.467757	+	0.467757i
$185$	−6.00384	−	3.46632i	−0.441411	−	0.254849i
$186$	−1.00025	−	1.72662i	−0.0733416	−	0.126602i
$187$	−22.2148	+	5.95243i	−1.62451	+	0.435285i
$188$	−1.12280	−	4.19035i	−0.0818888	−	0.305613i
$189$	−13.3009	−	3.47642i	−0.967500	−	0.252873i
$190$	−14.1840	+	14.1840i	−1.02901	+	1.02901i
$191$	−13.9580	+	8.05867i	−1.00997	+	0.583105i	−0.911182	−	0.412004i	$-0.864829\pi$
$191$	−13.9580	+	8.05867i	−1.00997	+	0.583105i	−0.0987856	+	0.995109i	$0.531496\pi$
$192$	−0.00254284	−	1.73205i	−0.000183514	−	0.125000i
$193$	−5.88842	−	21.9759i	−0.423857	−	1.58186i	−0.766405	−	0.642357i	$-0.777957\pi$
$193$	−5.88842	−	21.9759i	−0.423857	−	1.58186i	0.342548	−	0.939500i	$-0.388710\pi$
$194$	1.46224	−	2.53267i	0.104983	−	0.181835i
$195$	−4.12077	−	20.1521i	−0.295094	−	1.44312i
$196$	3.47880	−	6.07437i	0.248486	−	0.433884i
$197$	24.8603	+	6.66131i	1.77123	+	0.474598i	0.988939	−	0.148321i	$-0.0473867\pi$
$197$	24.8603	+	6.66131i	1.77123	+	0.474598i	0.782286	+	0.622919i	$0.214053\pi$
$198$	6.48149	−	11.3028i	0.460620	−	0.803254i
$199$			16.6668i			1.18148i	0.806863	+	0.590739i	$0.201164\pi$
$199$			16.6668i			1.18148i	−0.806863	+	0.590739i	$0.798836\pi$
$200$	5.64912	+	1.51368i	0.399453	+	0.107033i
$201$	−16.3763	+	4.41380i	−1.15510	+	0.311325i
$202$	2.50423	+	9.34592i	0.176197	+	0.657577i
$203$	6.95722	−	1.87721i	0.488301	−	0.131755i
$204$	−0.0134653	−	9.17188i	−0.000942763	−	0.642160i
$205$		−	30.4650i		−	2.12777i
$206$	12.0059	−	3.21696i	0.836487	−	0.224136i
$207$	−26.9193	+	0.0790411i	−1.87102	+	0.00549374i
$208$	3.59872	+	0.221835i	0.249526	+	0.0153815i
$209$		−	26.4503i		−	1.82960i
$210$	10.7070	+	10.6384i	0.738856	+	0.734120i
$211$	−4.52546	−	7.83833i	−0.311546	−	0.539613i	0.667152	−	0.744922i	$-0.267513\pi$
$211$	−4.52546	−	7.83833i	−0.311546	−	0.539613i	−0.978697	+	0.205309i	$0.934180\pi$
$212$	2.85697	+	4.94841i	0.196217	+	0.339858i
$213$	3.89738	+	14.4603i	0.267044	+	0.990801i
$214$	−5.22799	−	5.22799i	−0.357378	−	0.357378i
$215$	−2.38747	+	8.91014i	−0.162824	+	0.607667i
$216$	3.69038	+	3.65802i	0.251099	+	0.248896i
$217$	−1.51941	+	2.64235i	−0.103145	+	0.179375i
$218$	2.13973	+	3.70611i	0.144921	+	0.251010i
$219$	2.52803	+	0.673408i	0.170829	+	0.0455047i
$220$	−12.3884	+	7.15242i	−0.835222	+	0.482216i
$221$	19.0566	+	1.17470i	1.28189	+	0.0790192i
$222$	0.00535223	+	3.64566i	0.000359218	+	0.244681i
$223$	2.18761	−	8.16427i	0.146493	−	0.546720i	−0.853191	−	0.521598i	$-0.825336\pi$
$223$	2.18761	−	8.16427i	0.146493	−	0.546720i	0.999684	−	0.0251219i	$-0.00799738\pi$
$224$	−2.28897	+	1.32688i	−0.152938	+	0.0886557i
$225$	−15.1688	+	8.81718i	−1.01125	+	0.587812i
$226$	2.78384	−	0.745928i	0.185178	−	0.0496184i
$227$	16.8243	−	16.8243i	1.11667	−	1.11667i	0.124442	−	0.992227i	$-0.460286\pi$
$227$	16.8243	−	16.8243i	1.11667	−	1.11667i	0.992227	−	0.124442i	$-0.0397142\pi$
$228$	10.1931	+	2.71519i	0.675053	+	0.179818i
$229$	6.11927	+	22.8374i	0.404373	+	1.50914i	0.805209	+	0.592991i	$0.202053\pi$
$229$	6.11927	+	22.8374i	0.404373	+	1.50914i	−0.400836	+	0.916150i	$0.631280\pi$
$230$	25.5951	+	14.7774i	1.68769	+	0.974390i
$231$	−19.9025	+	0.0639873i	−1.30949	+	0.00421006i
$232$	−2.63082	−	0.704925i	−0.172722	−	0.0462806i
$233$	−14.1393	+	24.4900i	−0.926298	+	1.60440i	−0.136838	+	0.990593i	$0.543694\pi$
$233$	−14.1393	+	24.4900i	−0.926298	+	1.60440i	−0.789460	+	0.613802i	$0.789639\pi$
$234$	−8.08355	+	7.18722i	−0.528438	+	0.469843i
$235$	−7.14430	−	12.3743i	−0.466043	−	0.807210i
$236$	−0.571327	+	0.571327i	−0.0371902	+	0.0371902i
$237$	0.444868	−	0.773153i	0.0288973	−	0.0502217i
$238$	−12.1210	+	7.02633i	−0.785689	+	0.455449i
$239$	−12.9200	+	12.9200i	−0.835723	+	0.835723i	−0.988293	−	0.152569i	$-0.951245\pi$
$239$	−12.9200	+	12.9200i	−0.835723	+	0.835723i	0.152569	+	0.988293i	$0.451245\pi$
$240$	−1.48461	−	5.50828i	−0.0958312	−	0.355558i
$241$	−12.3866	+	12.3866i	−0.797893	+	0.797893i	−0.982763	−	0.184870i	$-0.940814\pi$
$241$	−12.3866	+	12.3866i	−0.797893	+	0.797893i	0.184870	+	0.982763i	$0.440814\pi$
$242$	2.03497	−	7.59462i	0.130813	−	0.488201i
$243$	−15.5880	+	0.114427i	−0.999973	+	0.00734049i
$244$	2.05406	−	1.18591i	0.131498	−	0.0759202i
$245$	5.88945	−	22.2909i	0.376263	−	1.42412i
$246$	−13.8625	+	8.03067i	−0.883840	+	0.512017i
$247$	−6.97749	+	20.8204i	−0.443967	+	1.32477i
$248$	0.997711	−	0.576029i	0.0633547	−	0.0365779i
$249$	−7.88696	+	7.91015i	−0.499816	+	0.501286i
$250$	2.79438			0.176732
$251$	−7.38589	+	12.7927i	−0.466193	+	0.807471i	−0.999255	−	0.0386062i	$-0.987708\pi$
$251$	−7.38589	+	12.7927i	−0.466193	+	0.807471i	0.533061	+	0.846077i	$0.321042\pi$
$252$	2.01839	−	7.67634i	0.127146	−	0.483564i
$253$	−37.6433	+	10.0865i	−2.36661	+	0.634132i
$254$	2.45919	−	9.17783i	0.154303	−	0.575868i
$255$	−7.86159	−	29.1685i	−0.492312	−	1.82660i
$256$	1.00000			0.0625000
$257$	12.6694			0.790293			0.395147	−	0.918618i	$-0.370694\pi$
$257$	12.6694			0.790293			0.395147	+	0.918618i	$0.370694\pi$
$258$	4.68372	−	1.26237i	0.291596	−	0.0785919i
$259$	4.81789	−	2.79284i	0.299369	−	0.173539i
$260$	11.6383	−	2.36204i	0.721777	−	0.146488i
$261$	7.06415	−	4.10619i	0.437260	−	0.254167i
$262$	−5.23776	+	1.40345i	−0.323590	+	0.0867056i
$263$	−0.824649	−	0.476112i	−0.0508501	−	0.0293583i	0.474359	−	0.880331i	$-0.342680\pi$
$263$	−0.824649	−	0.476112i	−0.0508501	−	0.0293583i	−0.525210	+	0.850973i	$0.676013\pi$
$264$	6.52017	+	3.75167i	0.401289	+	0.230899i
$265$	13.3077	+	13.3077i	0.817486	+	0.817486i
$266$	−4.19756	−	15.5568i	−0.257369	−	0.953846i
$267$	2.71087	+	2.70292i	0.165903	+	0.165416i
$268$	−2.53442	−	9.45859i	−0.154815	−	0.577776i
$269$			23.2305i			1.41639i	0.706018	+	0.708194i	$0.250490\pi$
$269$			23.2305i			1.41639i	−0.706018	+	0.708194i	$0.749510\pi$
$270$	14.8592	+	8.49190i	0.904299	+	0.516801i
$271$	19.0789	−	19.0789i	1.15896	−	1.15896i	0.174259	−	0.984700i	$-0.444247\pi$
$271$	19.0789	−	19.0789i	1.15896	−	1.15896i	0.984700	−	0.174259i	$-0.0557530\pi$
$272$	5.29539			0.321080
$273$	15.6832	+	5.19983i	0.949188	+	0.314708i
$274$	−2.36049			−0.142602
$275$	−17.9607	+	17.9607i	−1.08307	+	1.08307i
$276$	−0.0228172	−	15.5419i	−0.00137344	−	0.935512i
$277$			17.7920i			1.06902i	0.845163	+	0.534508i	$0.179503\pi$
$277$			17.7920i			1.06902i	−0.845163	+	0.534508i	$0.820497\pi$
$278$	−3.62084	−	13.5132i	−0.217163	−	0.810465i
$279$	−0.884717	+	3.34102i	−0.0529666	+	0.200021i
$280$	−6.15116	+	6.17269i	−0.367602	+	0.368889i
$281$	−17.4575	−	17.4575i	−1.04142	−	1.04142i	−0.999104	−	0.0423209i	$-0.986525\pi$
$281$	−17.4575	−	17.4575i	−1.04142	−	1.04142i	−0.0423209	−	0.999104i	$-0.513475\pi$
$282$	−3.74741	+	6.51277i	−0.223155	+	0.387830i
$283$	0.617271	+	0.356381i	0.0366929	+	0.0211847i	0.518234	−	0.855239i	$-0.326590\pi$
$283$	0.617271	+	0.356381i	0.0366929	+	0.0211847i	−0.481541	+	0.876423i	$0.659923\pi$
$284$	−8.35193	+	2.23789i	−0.495596	+	0.132795i
$285$	34.7435	−	0.0510073i	2.05803	−	0.00302141i
$286$	−8.64918	+	13.0539i	−0.511437	+	0.771894i
$287$	21.2146	+	12.1989i	1.25226	+	0.720079i
$288$	−2.11508	+	2.12754i	−0.124632	+	0.125366i
$289$	11.0412			0.649482
$290$	−8.97077			−0.526782
$291$	−4.89081	+	1.31819i	−0.286704	+	0.0772735i
$292$	−0.390935	+	1.45899i	−0.0228777	+	0.0853809i
$293$	−0.721061	+	0.193208i	−0.0421248	+	0.0112873i	−0.279820	−	0.960053i	$-0.590275\pi$
$293$	−0.721061	+	0.193208i	−0.0421248	+	0.0112873i	0.237695	+	0.971340i	$0.423608\pi$
$294$	−11.6955	+	3.19609i	−0.682096	+	0.186400i
$295$	−1.33062	+	2.30469i	−0.0774715	+	0.134185i
$296$	−2.10482			−0.122340
$297$	−21.7725	+	5.93683i	−1.26337	+	0.344490i
$298$	16.4290	−	9.48529i	0.951707	−	0.549468i
$299$	32.2918	+	1.99055i	1.86748	+	0.115117i
$300$	−5.07774	−	8.76516i	−0.293163	−	0.506057i
$301$	−5.24867	−	5.23037i	−0.302528	−	0.301473i
$302$	2.36270	−	1.36410i	0.135958	−	0.0784953i
$303$	8.35801	−	14.5257i	0.480155	−	0.834480i
$304$	−1.57626	+	5.88267i	−0.0904045	+	0.337394i
$305$	5.52396	−	5.52396i	0.316301	−	0.316301i
$306$	−11.2002	+	11.2662i	−0.640272	+	0.644043i
$307$	−17.3155	+	17.3155i	−0.988246	+	0.988246i	−0.999932	−	0.0116856i	$-0.996280\pi$
$307$	−17.3155	+	17.3155i	−0.988246	+	0.988246i	0.0116856	+	0.999932i	$0.496280\pi$
$308$	−0.0200734	−	11.4907i	−0.00114379	−	0.654746i
$309$	−18.6598	−	10.7368i	−1.06152	−	0.610793i
$310$	2.68313	−	2.68313i	0.152392	−	0.152392i
$311$	6.23904	+	10.8063i	0.353784	+	0.612771i	0.986909	−	0.161278i	$-0.0515616\pi$
$311$	6.23904	+	10.8063i	0.353784	+	0.612771i	−0.633125	+	0.774049i	$0.718228\pi$
$312$	−4.14269	−	4.67313i	−0.234534	−	0.264564i
$313$	−6.77592	+	11.7362i	−0.382997	+	0.663371i	−0.991489	−	0.130189i	$-0.958442\pi$
$313$	−6.77592	+	11.7362i	−0.382997	+	0.663371i	0.608492	+	0.793560i	$0.291775\pi$
$314$	3.28502	+	0.880220i	0.185385	+	0.0496737i
$315$	−0.122430	−	26.1426i	−0.00689816	−	1.47297i
$316$	0.446002	+	0.257500i	0.0250896	+	0.0144855i
$317$	−2.84872	−	10.6316i	−0.160000	−	0.597128i	−0.998625	−	0.0524189i	$-0.983307\pi$
$317$	−2.84872	−	10.6316i	−0.160000	−	0.597128i	0.838625	−	0.544709i	$-0.183360\pi$
$318$	2.54745	−	9.56335i	0.142854	−	0.536286i
$319$	8.36434	−	8.36434i	0.468313	−	0.468313i
$320$	3.18146	−	0.852470i	0.177849	−	0.0476545i
$321$	0.0188005	+	12.8059i	0.00104934	+	0.714756i
$322$	−20.5392	+	11.9062i	−1.14461	+	0.663508i
$323$	−8.34689	+	31.1510i	−0.464434	+	1.73329i
$324$	−0.0528517	−	8.99984i	−0.00293620	−	0.499991i
$325$	18.8757	−	9.39982i	1.04704	−	0.521408i
$326$	21.9517	−	12.6738i	1.21579	−	0.701936i
$327$	1.90791	−	7.16247i	0.105508	−	0.396085i
$328$	−4.62476	−	8.01031i	−0.255359	−	0.442296i
$329$	11.4777	−	0.0200507i	0.632787	−	0.00110543i
$330$	23.9418	+	6.37754i	1.31796	+	0.351072i
$331$	0.971726	−	3.62653i	0.0534109	−	0.199332i	−0.934065	−	0.357104i	$-0.883764\pi$
$331$	0.971726	−	3.62653i	0.0534109	−	0.199332i	0.987476	+	0.157772i	$0.0504310\pi$
$332$	−4.56024	−	4.56024i	−0.250276	−	0.250276i
$333$	4.45188	−	4.47810i	0.243961	−	0.245398i
$334$	−2.72652	−	4.72246i	−0.149188	−	0.258402i
$335$	−16.1263	−	27.9316i	−0.881076	−	1.52607i
$336$	4.43022	+	1.17182i	0.241688	+	0.0639281i
$337$			10.9390i			0.595886i	0.954584	+	0.297943i	$0.0963006\pi$
$337$			10.9390i			0.595886i	−0.954584	+	0.297943i	$0.903699\pi$
$338$	10.2518	−	7.99379i	0.557624	−	0.434805i
$339$	−4.32673	−	2.48957i	−0.234996	−	0.135215i
$340$	16.8471	−	4.51416i	0.913662	−	0.244815i
$341$			5.00350i			0.270955i
$342$	−9.18170	−	15.7959i	−0.496489	−	0.854143i
$343$	13.1643	+	13.0270i	0.710803	+	0.703391i
$344$	0.724860	+	2.70522i	0.0390818	+	0.145855i
$345$	−13.3216	−	49.4265i	−0.717210	−	2.66103i
$346$	13.3102	+	3.56647i	0.715562	+	0.191734i
$347$		−	15.2251i		−	0.817326i	−0.912685	−	0.408663i	$-0.865995\pi$
$347$		−	15.2251i		−	0.817326i	0.912685	−	0.408663i	$-0.134005\pi$
$348$	2.36472	+	4.08197i	0.126762	+	0.218816i
$349$	−24.1050	−	6.45893i	−1.29031	−	0.345738i	−0.452534	−	0.891747i	$-0.649480\pi$
$349$	−24.1050	−	6.45893i	−1.29031	−	0.345738i	−0.837779	+	0.546009i	$0.816146\pi$
$350$	−7.71329	+	13.4139i	−0.412293	+	0.717001i
$351$	18.7044	+	1.07032i	0.998367	+	0.0571294i
$352$	−2.17155	+	3.76124i	−0.115744	+	0.200475i
$353$	0.159758	+	0.596226i	0.00850308	+	0.0317339i	0.970047	−	0.242917i	$-0.0781043\pi$
$353$	0.159758	+	0.596226i	0.00850308	+	0.0317339i	−0.961544	+	0.274651i	$0.911438\pi$
$354$	1.39946	−	0.00205456i	0.0743804	−	0.000109199i
$355$	−24.6636	+	14.2395i	−1.30901	+	0.755757i
$356$	−1.56283	+	1.56283i	−0.0828298	+	0.0828298i
$357$	23.4597	+	6.20525i	1.24162	+	0.328417i
$358$	−2.30182	−	8.59053i	−0.121655	−	0.454023i
$359$	−28.9994	+	7.77036i	−1.53053	+	0.410104i	−0.923192	−	0.384340i	$-0.874429\pi$
$359$	−28.9994	+	7.77036i	−1.53053	+	0.410104i	−0.607338	+	0.794444i	$0.707763\pi$
$360$	−4.91539	+	8.57173i	−0.259064	+	0.451770i
$361$	−15.6667	−	9.04518i	−0.824563	−	0.476062i
$362$	−14.3300	−	14.3300i	−0.753170	−	0.753170i
$363$	−11.7838	+	6.82646i	−0.618488	+	0.358296i
$364$	−3.01542	+	9.05026i	−0.158051	+	0.474363i
$365$			4.97498i			0.260402i
$366$	−3.96969	−	1.05743i	−0.207499	−	0.0552729i
$367$	7.68648	−	13.3134i	0.401231	−	0.694953i	−0.592644	−	0.805465i	$-0.701916\pi$
$367$	7.68648	−	13.3134i	0.401231	−	0.694953i	0.993875	+	0.110512i	$0.0352491\pi$
$368$	8.97313			0.467757
$369$	26.8240	+	7.10312i	1.39640	+	0.369774i
$370$	−6.69642	+	1.79430i	−0.348130	+	0.0932812i
$371$	−14.5957	+	3.93824i	−0.757770	+	0.204463i
$372$	−1.92819	−	0.513623i	−0.0999717	−	0.0266301i
$373$	−16.8782	−	29.2339i	−0.873920	−	1.51367i	−0.857909	−	0.513802i	$-0.828236\pi$
$373$	−16.8782	−	29.2339i	−0.873920	−	1.51367i	−0.0160117	−	0.999872i	$-0.505097\pi$
$374$	−11.4992	+	19.9172i	−0.594610	+	1.02990i
$375$	−3.42742	−	3.41737i	−0.176991	−	0.176472i
$376$	−3.75697	−	2.16909i	−0.193751	−	0.111862i
$377$	−8.79049	+	4.37753i	−0.452733	+	0.225454i
$378$	−11.8634	+	6.94697i	−0.610186	+	0.357314i
$379$	1.64709	−	6.14703i	0.0846054	−	0.315752i	−0.910634	−	0.413214i	$-0.864406\pi$
$379$	1.64709	−	6.14703i	0.0846054	−	0.315752i	0.995239	+	0.0974627i	$0.0310727\pi$
$380$			20.0592i			1.02901i
$381$	−14.2403	+	8.24953i	−0.729552	+	0.422636i
$382$	−4.17148	+	15.5682i	−0.213431	+	0.796537i
$383$	29.9559	+	8.02667i	1.53068	+	0.410144i	0.923240	−	0.384224i	$-0.125531\pi$
$383$	29.9559	+	8.02667i	1.53068	+	0.410144i	0.607437	+	0.794368i	$0.292198\pi$
$384$	−1.22654	−	1.22295i	−0.0625917	−	0.0624082i
$385$	−9.85938	−	36.5403i	−0.502481	−	1.86226i
$386$	−19.7030	−	11.3755i	−1.00286	−	0.579000i
$387$	−7.28859	−	4.17958i	−0.370500	−	0.212460i
$388$	−0.756910	−	2.82483i	−0.0384263	−	0.143409i
$389$	1.09893	+	1.90340i	0.0557178	+	0.0965061i	0.892539	−	0.450970i	$-0.148922\pi$
$389$	1.09893	+	1.90340i	0.0557178	+	0.0965061i	−0.836821	+	0.547476i	$0.815589\pi$
$390$	−17.1635	−	11.3359i	−0.869108	−	0.574014i
$391$	47.5162			2.40300
$392$	−1.83535	−	6.75511i	−0.0926990	−	0.341185i
$393$	8.14068	+	4.68410i	0.410643	+	0.236282i
$394$	22.2892	−	12.8687i	1.12291	−	0.648314i
$395$	1.63845	+	0.439021i	0.0824394	+	0.0220896i
$396$	−3.40917	−	12.5754i	−0.171317	−	0.631937i
$397$	−14.2330	−	3.81371i	−0.714332	−	0.191405i	−0.116691	−	0.993168i	$-0.537229\pi$
$397$	−14.2330	−	3.81371i	−0.714332	−	0.191405i	−0.597641	+	0.801763i	$0.703895\pi$
$398$	11.7852	+	11.7852i	0.590739	+	0.590739i
$399$	−13.8766	+	24.2144i	−0.694698	+	1.21224i
$400$	5.06487	−	2.92420i	0.253243	−	0.146210i
$401$	−1.28469	−	1.28469i	−0.0641543	−	0.0641543i	0.674302	−	0.738456i	$-0.264445\pi$
$401$	−1.28469	−	1.28469i	−0.0641543	−	0.0641543i	−0.738456	+	0.674302i	$0.764445\pi$
$402$	−8.45877	+	14.7008i	−0.421885	+	0.733210i
$403$	1.31990	−	3.93852i	0.0657491	−	0.196191i
$404$	8.37932	+	4.83780i	0.416887	+	0.240690i
$405$	−7.84024	−	28.5876i	−0.389585	−	1.42053i
$406$	3.59211	−	6.24689i	0.178273	−	0.310028i
$407$	4.57073	−	7.91674i	0.226563	−	0.392418i
$408$	−6.49502	−	6.47598i	−0.321551	−	0.320609i
$409$	−17.5826	−	17.5826i	−0.869403	−	0.869403i	0.123003	−	0.992406i	$-0.460747\pi$
$409$	−17.5826	−	17.5826i	−0.869403	−	0.869403i	−0.992406	+	0.123003i	$0.960747\pi$
$410$	−21.5420	−	21.5420i	−1.06389	−	1.06389i
$411$	2.89523	+	2.88675i	0.142811	+	0.142393i
$412$	6.21469	−	10.7642i	0.306176	−	0.530312i
$413$	−1.07209	−	1.84944i	−0.0527540	−	0.0910051i
$414$	−18.9789	+	19.0907i	−0.932762	+	0.938256i
$415$	−18.3957	−	10.6208i	−0.903009	−	0.521352i
$416$	2.70154	−	2.38782i	0.132454	−	0.117072i
$417$	−12.0847	+	21.0025i	−0.591792	+	1.02850i
$418$	−18.7032	−	18.7032i	−0.914802	−	0.914802i
$419$	20.7478	−	11.9787i	1.01359	−	0.585199i	0.101352	−	0.994851i	$-0.467683\pi$
$419$	20.7478	−	11.9787i	1.01359	−	0.585199i	0.912242	+	0.409651i	$0.134350\pi$
$420$	15.0935	−	0.0485262i	0.736488	−	0.00236784i
$421$	−21.1259	−	21.1259i	−1.02961	−	1.02961i	−0.999548	−	0.0300645i	$-0.990429\pi$
$421$	−21.1259	−	21.1259i	−1.02961	−	1.02961i	−0.0300645	−	0.999548i	$-0.509571\pi$
$422$	−8.74252	−	2.34255i	−0.425579	−	0.114034i
$423$	12.5611	−	3.40530i	0.610742	−	0.165571i
$424$	5.51924	+	1.47888i	0.268038	+	0.0718205i
$425$	26.8205	−	15.4848i	1.30098	−	0.751123i
$426$	12.9808	+	7.46909i	0.628923	+	0.361879i
$427$	1.63474	+	6.05858i	0.0791107	+	0.293195i
$428$	−7.39350			−0.357378
$429$	26.5728	−	5.43369i	1.28295	−	0.262341i
$430$	4.61223	+	7.98862i	0.222421	+	0.385245i
$431$	5.66232	+	21.1321i	0.272744	+	1.01790i	0.957338	+	0.288971i	$0.0933131\pi$
$431$	5.66232	+	21.1321i	0.272744	+	1.01790i	−0.684593	+	0.728925i	$0.740020\pi$
$432$	5.19610	−	0.0228855i	0.249998	−	0.00110108i
$433$	−9.26511	−	5.34922i	−0.445253	−	0.257067i	0.260570	−	0.965455i	$-0.416089\pi$
$433$	−9.26511	−	5.34922i	−0.445253	−	0.257067i	−0.705823	+	0.708388i	$0.749423\pi$
$434$	0.794037	+	2.94281i	0.0381150	+	0.141260i
$435$	11.0030	+	10.9708i	0.527555	+	0.526008i
$436$	4.13363	+	1.10760i	0.197965	+	0.0530446i
$437$	−14.1439	+	52.7859i	−0.676597	+	2.52509i
$438$	2.26376	−	1.31142i	0.108167	−	0.0626620i
$439$			38.3551i			1.83059i	0.402783	+	0.915295i	$0.368043\pi$
$439$			38.3551i			1.83059i	−0.402783	+	0.915295i	$0.631957\pi$
$440$	−3.70236	+	13.8174i	−0.176503	+	0.658719i
$441$	18.2537	+	10.3828i	0.869223	+	0.494421i
$442$	14.3057	−	12.6444i	0.680454	−	0.601435i
$443$	−7.07201	−	4.08302i	−0.336001	−	0.193990i	0.322501	−	0.946569i	$-0.395476\pi$
$443$	−7.07201	−	4.08302i	−0.336001	−	0.193990i	−0.658502	+	0.752579i	$0.728810\pi$
$444$	2.58165	+	2.57408i	0.122520	+	0.122161i
$445$	−3.63982	+	6.30435i	−0.172544	+	0.298855i
$446$	−4.22614	−	7.31989i	−0.200113	−	0.346607i
$447$	−31.7509	−	8.45768i	−1.50176	−	0.400034i
$448$	−0.680305	+	2.55679i	−0.0321414	+	0.120797i
$449$	1.10954	−	0.297299i	0.0523622	−	0.0140304i	−0.232543	−	0.972586i	$-0.574705\pi$
$449$	1.10954	−	0.297299i	0.0523622	−	0.0140304i	0.284905	+	0.958556i	$0.408038\pi$
$450$	−4.49125	+	16.9606i	−0.211720	+	0.799532i
$451$	40.1716			1.89161
$452$	1.44102	−	2.49592i	0.0677800	−	0.117398i
$453$	−4.56617	−	1.21632i	−0.214537	−	0.0571476i
$454$		−	23.7932i		−	1.11667i
$455$	−1.87835	+	31.3636i	−0.0880583	+	1.47035i
$456$	9.12752	−	5.28766i	0.427435	−	0.247617i
$457$	0.359340	+	0.359340i	0.0168092	+	0.0168092i	0.715461	−	0.698652i	$-0.246217\pi$
$457$	0.359340	+	0.359340i	0.0168092	+	0.0168092i	−0.698652	+	0.715461i	$0.746217\pi$
$458$	20.4755	+	11.8215i	0.956757	+	0.552384i
$459$	27.5154	−	0.121188i	1.28431	−	0.00565656i
$460$	28.5477	−	7.64932i	1.33104	−	0.356651i
$461$	4.16267	+	15.5353i	0.193875	+	0.723551i	0.992555	+	0.121795i	$0.0388651\pi$
$461$	4.16267	+	15.5353i	0.193875	+	0.723551i	−0.798680	+	0.601755i	$0.794468\pi$
$462$	−14.0279	+	14.1184i	−0.652639	+	0.656849i
$463$	12.3374	−	12.3374i	0.573369	−	0.573369i	−0.359699	−	0.933068i	$-0.617121\pi$
$463$	12.3374	−	12.3374i	0.573369	−	0.573369i	0.933068	+	0.359699i	$0.117121\pi$
$464$	−2.35873	+	1.36181i	−0.109501	+	0.0632205i
$465$	−6.57230	+	0.00964886i	−0.304783	+	0.000447455i
$466$	7.31905	+	27.3151i	0.339049	+	1.26535i
$467$	15.5029	−	26.8517i	0.717387	−	1.24255i	−0.244645	−	0.969613i	$-0.578671\pi$
$467$	15.5029	−	26.8517i	0.717387	−	1.24255i	0.962032	−	0.272938i	$-0.0879952\pi$
$468$	−0.633803	+	10.7981i	−0.0292975	+	0.499141i
$469$	25.9078	−	0.0452589i	1.19631	−	0.00208986i
$470$	−13.8017	−	3.69816i	−0.636627	−	0.170584i
$471$	−2.95276	−	5.09703i	−0.136056	−	0.234859i
$472$			0.807979i			0.0371902i
$473$	−11.7490	−	3.14814i	−0.540221	−	0.144752i
$474$	−0.232133	−	0.861271i	−0.0106622	−	0.0395595i
$475$	9.21858	+	34.4042i	0.422977	+	1.57857i
$476$	−3.60248	+	13.5392i	−0.165120	+	0.620569i
$477$	−14.8200	+	8.61445i	−0.678562	+	0.394429i
$478$			18.2716i			0.835723i
$479$	20.7236	−	5.55286i	0.946883	−	0.253717i	0.247844	−	0.968800i	$-0.420278\pi$
$479$	20.7236	−	5.55286i	0.946883	−	0.253717i	0.699039	+	0.715083i	$0.253611\pi$
$480$	−4.94472	−	2.84516i	−0.225695	−	0.129863i
$481$	−5.68627	+	5.02594i	−0.259271	+	0.229163i
$482$			17.5173i			0.797893i
$483$	39.7529	+	10.5149i	1.80882	+	0.478444i
$484$	−3.93126	−	6.80915i	−0.178694	−	0.309507i
$485$	−4.81616	−	8.34183i	−0.218690	−	0.378783i
$486$	−10.9415	+	11.1033i	−0.496316	+	0.503657i
$487$	−15.1480	−	15.1480i	−0.686420	−	0.686420i	0.275019	−	0.961439i	$-0.411316\pi$
$487$	−15.1480	−	15.1480i	−0.686420	−	0.686420i	−0.961439	+	0.275019i	$0.911316\pi$
$488$	0.613873	−	2.29100i	0.0277887	−	0.103709i
$489$	−42.4240	−	11.3007i	−1.91848	−	0.511037i
$490$	−11.5976	−	19.9265i	−0.523927	−	0.900190i
$491$	0.269785	+	0.467281i	0.0121752	+	0.0210881i	0.872049	−	0.489419i	$-0.162791\pi$
$491$	0.269785	+	0.467281i	0.0121752	+	0.0210881i	−0.859874	+	0.510507i	$0.829458\pi$
$492$	−4.12372	+	15.4808i	−0.185912	+	0.697929i
$493$	−12.4904	+	7.21133i	−0.562539	+	0.324782i
$494$	9.78842	+	19.6561i	0.440402	+	0.884369i
$495$	−21.5663	−	37.1019i	−0.969332	−	1.66761i
$496$	0.298174	−	1.11280i	0.0133884	−	0.0499663i
$497$	−0.0399636	−	22.8766i	−0.00179261	−	1.02616i
$498$	0.0163992	+	11.1702i	0.000734864	+	0.500551i
$499$	20.1500	−	5.39917i	0.902036	−	0.241700i	0.222146	−	0.975013i	$-0.428694\pi$
$499$	20.1500	−	5.39917i	0.902036	−	0.241700i	0.679891	+	0.733314i	$0.262027\pi$
$500$	1.97592	−	1.97592i	0.0883660	−	0.0883660i
$501$	−2.43113	+	9.12668i	−0.108615	+	0.407750i
$502$	3.82322	+	14.2684i	0.170639	+	0.636832i
$503$	28.8447	+	16.6535i	1.28612	+	0.742542i	0.977960	−	0.208792i	$-0.0669532\pi$
$503$	28.8447	+	16.6535i	1.28612	+	0.742542i	0.308161	+	0.951334i	$0.400286\pi$
$504$	−4.00077	−	6.85520i	−0.178209	−	0.305355i
$505$	30.7826	+	8.24817i	1.36981	+	0.367039i
$506$	−19.4856	+	33.7500i	−0.866241	+	1.50037i
$507$	−22.3502	−	2.73266i	−0.992608	−	0.121362i
$508$	−4.75079	−	8.22861i	−0.210782	−	0.365086i
$509$	−16.6251	+	16.6251i	−0.736895	+	0.736895i	−0.971976	−	0.235081i	$-0.924465\pi$
$509$	−16.6251	+	16.6251i	−0.736895	+	0.736895i	0.235081	+	0.971976i	$0.424465\pi$
$510$	−26.1842	−	15.0663i	−1.15946	−	0.667145i
$511$	−3.46438	−	1.99210i	−0.153255	−	0.0881252i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−8.05576	+	30.6030i	−0.355670	+	1.35116i
$514$	8.95859	−	8.95859i	0.395147	−	0.395147i
$515$	10.5957	−	39.5436i	0.466901	−	1.74250i
$516$	2.41926	−	4.20452i	0.106502	−	0.185094i
$517$	16.3169	−	9.42056i	0.717616	−	0.414316i
$518$	1.43192	−	5.38160i	0.0629151	−	0.236454i
$519$	−11.9640	−	20.6521i	−0.525159	−	0.906527i
$520$	6.55930	−	9.89974i	0.287645	−	0.434132i
$521$	23.1952	−	13.3918i	1.01620	−	0.586705i	0.103201	−	0.994661i	$-0.467092\pi$
$521$	23.1952	−	13.3918i	1.01620	−	0.586705i	0.913002	+	0.407956i	$0.133758\pi$
$522$	2.09159	−	7.89863i	0.0915465	−	0.345714i
$523$	30.5791			1.33713			0.668566	−	0.743653i	$-0.266908\pi$
$523$	30.5791			1.33713			0.668566	+	0.743653i	$0.266908\pi$
$524$	−2.71126	+	4.69605i	−0.118442	+	0.205148i
$525$	25.8651	−	7.01974i	1.12885	−	0.306366i
$526$	−0.919777	+	0.246453i	−0.0401042	+	0.0107459i
$527$	1.57895	−	5.89272i	0.0687802	−	0.256691i
$528$	7.26328	−	1.95762i	0.316094	−	0.0851947i
$529$	57.5170			2.50074
$530$	18.8199			0.817486
$531$	−1.71901	−	1.70894i	−0.0745985	−	0.0741617i
$532$	−13.9684	−	8.03217i	−0.605608	−	0.348239i
$533$	−31.6211	−	10.5971i	−1.36966	−	0.459012i
$534$	3.82813	−	0.00562013i	0.165659	−	0.000243207i
$535$	−23.5221	+	6.30274i	−1.01695	+	0.272491i
$536$	−8.48034	−	4.89613i	−0.366295	−	0.211481i
$537$	−7.68246	+	13.3516i	−0.331523	+	0.576166i
$538$	16.4264	+	16.4264i	0.708194	+	0.708194i
$539$	29.3931	+	7.76589i	1.26605	+	0.334501i
$540$	16.5117	−	4.50233i	0.710550	−	0.193749i
$541$	4.33430	+	16.1758i	0.186346	+	0.695454i	0.994338	+	0.106260i	$0.0338877\pi$
$541$	4.33430	+	16.1758i	0.186346	+	0.695454i	−0.807992	+	0.589193i	$0.799446\pi$
$542$		−	26.9816i		−	1.15896i
$543$	0.0515325	+	35.1012i	0.00221147	+	1.50634i
$544$	3.74441	−	3.74441i	0.160540	−	0.160540i
$545$	14.0952			0.603772
$546$	14.7665	−	7.41284i	0.631948	−	0.317240i
$547$	−9.21981			−0.394210			−0.197105	−	0.980382i	$-0.563154\pi$
$547$	−9.21981			−0.394210			−0.197105	+	0.980382i	$0.563154\pi$
$548$	−1.66912	+	1.66912i	−0.0713011	+	0.0713011i
$549$	3.57581	+	6.15170i	0.152612	+	0.262548i
$550$			25.4002i			1.08307i
$551$	−4.29313	−	16.0222i	−0.182893	−	0.682567i
$552$	−11.0059	−	10.9736i	−0.468443	−	0.467069i
$553$	−0.961791	+	0.965157i	−0.0408995	+	0.0410427i
$554$	12.5808	+	12.5808i	0.534508	+	0.534508i
$555$	10.4078	+	5.98857i	0.441785	+	0.254201i
$556$	−12.1156	−	6.99492i	−0.513814	−	0.296651i
$557$	−16.7620	+	4.49136i	−0.710227	+	0.190305i	−0.595807	−	0.803128i	$-0.703168\pi$
$557$	−16.7620	+	4.49136i	−0.710227	+	0.190305i	−0.114420	+	0.993432i	$0.536501\pi$
$558$	1.73687	+	2.98805i	0.0735274	+	0.126494i
$559$	8.41780	+	5.57741i	0.356035	+	0.235899i
$560$	0.0152231	+	8.71427i	0.000643295	+	0.368245i
$561$	38.4619	−	10.3664i	1.62386	−	0.437669i
$562$	−24.6886			−1.04142
$563$	−4.16812			−0.175665			−0.0878327	−	0.996135i	$-0.527994\pi$
$563$	−4.16812			−0.175665			−0.0878327	+	0.996135i	$0.527994\pi$
$564$	1.95540	+	7.25504i	0.0823373	+	0.305492i
$565$	2.45686	−	9.16911i	0.103361	−	0.385748i
$566$	0.688476	−	0.184477i	0.0289388	−	0.00775413i
$567$	23.0467	+	5.98751i	0.967870	+	0.251452i
$568$	−4.32328	+	7.48814i	−0.181401	+	0.314195i
$569$	33.3010			1.39605			0.698025	−	0.716073i	$-0.254062\pi$
$569$	33.3010			1.39605			0.698025	+	0.716073i	$0.254062\pi$
$570$	24.5313	−	24.6034i	1.02750	−	1.03052i
$571$	−9.65851	+	5.57634i	−0.404196	+	0.233363i	−0.688293	−	0.725433i	$-0.741640\pi$
$571$	−9.65851	+	5.57634i	−0.404196	+	0.233363i	0.284097	+	0.958796i	$0.408306\pi$
$572$	3.11462	+	15.3464i	0.130229	+	0.641665i
$573$	24.1555	−	13.9935i	1.00911	−	0.584587i
$574$	23.6270	−	6.37508i	0.986170	−	0.266091i
$575$	45.4477	−	26.2392i	1.89530	−	1.09425i
$576$	0.00880865	+	2.99999i	0.000367027	+	0.124999i
$577$	−2.15277	+	8.03426i	−0.0896211	+	0.334470i	−0.996149	−	0.0876752i	$-0.972056\pi$
$577$	−2.15277	+	8.03426i	−0.0896211	+	0.334470i	0.906528	+	0.422146i	$0.138723\pi$
$578$	7.80730	−	7.80730i	0.324741	−	0.324741i
$579$	10.2549	+	38.0483i	0.426179	+	1.58123i
$580$	−6.34329	+	6.34329i	−0.263391	+	0.263391i
$581$	14.7619	−	8.55723i	0.612428	−	0.355014i
$582$	−2.52623	+	4.39043i	−0.104715	+	0.181989i
$583$	−17.5477	+	17.5477i	−0.726752	+	0.726752i
$584$	0.755228	+	1.30809i	0.0312516	+	0.0541293i
$585$	7.18861	+	34.8939i	0.297213	+	1.44269i
$586$	−0.373249	+	0.646486i	−0.0154188	+	0.0267061i
$587$	−7.42137	−	1.98855i	−0.306313	−	0.0820762i	0.102389	−	0.994744i	$-0.467352\pi$
$587$	−7.42137	−	1.98855i	−0.306313	−	0.0820762i	−0.408701	+	0.912668i	$0.634018\pi$
$588$	−6.01000	+	10.5300i	−0.247848	+	0.434248i
$589$	6.07624	+	3.50812i	0.250367	+	0.144550i
$590$	0.688778	+	2.57055i	0.0283565	+	0.105828i
$591$	−43.0763	−	11.4745i	−1.77192	−	0.471998i
$592$	−1.48834	+	1.48834i	−0.0611702	+	0.0611702i
$593$	−23.6622	+	6.34027i	−0.971690	+	0.260364i	−0.709541	−	0.704664i	$-0.751098\pi$
$593$	−23.6622	+	6.34027i	−0.971690	+	0.260364i	−0.262149	+	0.965027i	$0.584431\pi$
$594$	−11.1975	+	19.5935i	−0.459440	+	0.803930i
$595$	0.0806125	+	46.1455i	0.00330479	+	1.89178i
$596$	4.90995	−	18.3242i	0.201119	−	0.750588i
$597$	−0.0423810	−	28.8677i	−0.00173454	−	1.18148i
$598$	24.2413	−	21.4262i	0.991299	−	0.876182i
$599$	−36.9189	+	21.3151i	−1.50846	+	0.870913i	−0.508513	+	0.861054i	$0.669805\pi$
$599$	−36.9189	+	21.3151i	−1.50846	+	0.870913i	−0.999951	+	0.00985856i	$0.996862\pi$
$600$	−9.78841	−	2.60740i	−0.399610	−	0.106447i
$601$	15.8340	+	27.4254i	0.645884	+	1.11870i	0.984097	+	0.177634i	$0.0568443\pi$
$601$	15.8340	+	27.4254i	0.645884	+	1.11870i	−0.338213	+	0.941070i	$0.609822\pi$
$602$	−7.40980	+	0.0129443i	−0.302001	+	0.000527571i
$603$	28.3533	−	7.68655i	1.15464	−	0.313021i
$604$	0.706111	−	2.63524i	0.0287313	−	0.107227i
$605$	−18.3118	−	18.3118i	−0.744479	−	0.744479i
$606$	−4.36122	−	16.1812i	−0.177162	−	0.657317i
$607$	−14.9467	−	25.8884i	−0.606668	−	1.05078i	−0.991786	−	0.127912i	$-0.959172\pi$
$607$	−14.9467	−	25.8884i	−0.606668	−	1.05078i	0.385118	−	0.922867i	$-0.374161\pi$
$608$	3.04509	+	5.27425i	0.123495	+	0.213899i
$609$	−12.0455	+	3.26912i	−0.488107	+	0.132471i
$610$		−	7.81205i		−	0.316301i
$611$	−15.3290	+	3.11108i	−0.620145	+	0.125861i
$612$	0.0466453	+	15.8861i	0.00188552	+	0.642158i
$613$	6.84784	−	1.83487i	0.276582	−	0.0741098i	−0.117862	−	0.993030i	$-0.537604\pi$
$613$	6.84784	−	1.83487i	0.276582	−	0.0741098i	0.394444	+	0.918920i	$0.370937\pi$
$614$			24.4878i			0.988246i
$615$	0.0774678	+	52.7669i	0.00312380	+	2.12777i
$616$	−8.13938	−	8.11099i	−0.327945	−	0.326801i
$617$	1.58171	+	5.90302i	0.0636772	+	0.237647i	0.990428	−	0.138030i	$-0.0440770\pi$
$617$	1.58171	+	5.90302i	0.0636772	+	0.237647i	−0.926751	+	0.375677i	$0.877410\pi$
$618$	−20.7865	+	5.60246i	−0.836157	+	0.225364i
$619$	−17.8860	−	4.79255i	−0.718900	−	0.192629i	−0.119219	−	0.992868i	$-0.538039\pi$
$619$	−17.8860	−	4.79255i	−0.718900	−	0.192629i	−0.599681	+	0.800239i	$0.704706\pi$
$620$		−	3.79452i		−	0.152392i
$621$	46.6253	−	0.205355i	1.87101	−	0.00824059i
$622$	12.0529	+	3.22956i	0.483277	+	0.129494i
$623$	−2.93263	−	5.05903i	−0.117493	−	0.202686i
$624$	−6.23372	−	0.375078i	−0.249549	−	0.0150152i
$625$	−10.0191	+	17.3536i	−0.400764	+	0.694144i
$626$	3.50747	+	13.0901i	0.140187	+	0.523184i
$627$	0.0672589	+	45.8132i	0.00268606	+	1.82960i
$628$	2.94527	−	1.70045i	0.117529	−	0.0678555i
$629$	−7.88132	+	7.88132i	−0.314249	+	0.314249i
$630$	−18.5722	−	18.3990i	−0.739933	−	0.733035i
$631$	−7.50820	−	28.0210i	−0.298897	−	1.11550i	−0.938073	−	0.346438i	$-0.887391\pi$
$631$	−7.50820	−	28.0210i	−0.298897	−	1.11550i	0.639176	−	0.769060i	$-0.279275\pi$
$632$	0.497451	−	0.133292i	0.0197875	−	0.00530206i
$633$	7.85825	+	13.5649i	0.312338	+	0.539155i
$634$	−9.53199	−	5.50330i	−0.378564	−	0.218564i
$635$	−22.1291	−	22.1291i	−0.878167	−	0.878167i
$636$	−4.96099	−	8.56363i	−0.196716	−	0.339570i
$637$	−21.0882	−	13.8667i	−0.835546	−	0.549420i
$638$		−	11.8290i		−	0.468313i
$639$	−6.78722	−	25.0360i	−0.268498	−	0.990408i
$640$	1.64685	−	2.85242i	0.0650973	−	0.112752i
$641$	9.87085			0.389875			0.194938	−	0.980816i	$-0.437550\pi$
$641$	9.87085			0.389875			0.194938	+	0.980816i	$0.437550\pi$
$642$	9.06843	+	9.04185i	0.357903	+	0.356853i
$643$	−32.4863	+	8.70468i	−1.28114	+	0.343279i	−0.834287	−	0.551331i	$-0.814120\pi$
$643$	−32.4863	+	8.70468i	−1.28114	+	0.343279i	−0.446848	+	0.894610i	$0.647454\pi$
$644$	−6.10447	+	22.9424i	−0.240550	+	0.904058i
$645$	4.11255	−	15.4389i	0.161932	−	0.607905i
$646$	16.1250	+	27.9293i	0.634428	+	1.09886i
$647$	−3.41124	+	5.90844i	−0.134110	+	0.232285i	−0.925257	−	0.379341i	$-0.876151\pi$
$647$	−3.41124	+	5.90844i	−0.134110	+	0.232285i	0.791147	+	0.611626i	$0.209484\pi$
$648$	−6.40122	−	6.32648i	−0.251464	−	0.248528i
$649$	−3.03900	−	1.75457i	−0.119291	−	0.0688728i
$650$	6.70048	−	19.9938i	0.262814	−	0.784223i
$651$	2.62498	−	4.58055i	0.102881	−	0.179526i
$652$	6.56044	−	24.4839i	0.256927	−	0.958863i
$653$			32.9646i			1.29000i	0.764181	+	0.645001i	$0.223143\pi$
$653$			32.9646i			1.29000i	−0.764181	+	0.645001i	$0.776857\pi$
$654$	−3.71553	−	6.41373i	−0.145289	−	0.250797i
$655$	−4.62254	+	17.2516i	−0.180618	+	0.674074i
$656$	−8.93434	−	2.39395i	−0.348828	−	0.0934681i
$657$	−4.38039	−	1.15995i	−0.170895	−	0.0452539i
$658$	8.10179	−	8.13015i	0.315841	−	0.316946i
$659$	19.5631	+	11.2948i	0.762072	+	0.439982i	0.830039	−	0.557705i	$-0.188318\pi$
$659$	19.5631	+	11.2948i	0.762072	+	0.439982i	−0.0679673	+	0.997688i	$0.521651\pi$
$660$	21.4390	−	12.4198i	0.834514	−	0.483442i
$661$	−2.91222	−	10.8686i	−0.113272	−	0.422738i	0.885880	−	0.463915i	$-0.153556\pi$
$661$	−2.91222	−	10.8686i	−0.113272	−	0.422738i	−0.999152	+	0.0411773i	$0.986889\pi$
$662$	−1.87723	−	3.25146i	−0.0729606	−	0.126371i
$663$	−33.0100	−	1.98619i	−1.28200	−	0.0771371i
$664$	−6.44915			−0.250276
$665$	−51.2872	−	13.6464i	−1.98883	−	0.529184i
$666$	−0.0185407	−	6.31444i	−0.000718436	−	0.244680i
$667$	−21.1652	+	12.2197i	−0.819518	+	0.473149i
$668$	−5.26722	−	1.41135i	−0.203795	−	0.0546067i
$669$	−3.76829	+	14.1465i	−0.145690	+	0.546935i
$670$	−31.1537	−	8.34761i	−1.20357	−	0.322496i
$671$	7.28395	+	7.28395i	0.281194	+	0.281194i
$672$	3.96124	−	2.30404i	0.152808	−	0.0888801i
$673$	12.2810	−	7.09042i	0.473396	−	0.273315i	−0.244264	−	0.969709i	$-0.578546\pi$
$673$	12.2810	−	7.09042i	0.473396	−	0.273315i	0.717660	+	0.696393i	$0.245213\pi$
$674$	7.73506	+	7.73506i	0.297943	+	0.297943i
$675$	26.2506	−	15.3104i	1.01039	−	0.589296i
$676$	1.59665	−	12.9016i	0.0614094	−	0.496215i
$677$	−17.7006	−	10.2195i	−0.680291	−	0.392766i	0.119674	−	0.992813i	$-0.461815\pi$
$677$	−17.7006	−	10.2195i	−0.680291	−	0.392766i	−0.799965	+	0.600047i	$0.795148\pi$
$678$	−4.81985	+	1.29906i	−0.185105	+	0.0498902i
$679$	7.73742	−	0.0135167i	0.296935	−	0.000518722i
$680$	8.72070	−	15.1047i	0.334423	−	0.579238i
$681$	−29.0978	+	29.1833i	−1.11503	+	1.11831i
$682$	3.53801	+	3.53801i	0.135477	+	0.135477i
$683$	5.99503	+	5.99503i	0.229394	+	0.229394i	0.812439	−	0.583046i	$-0.198139\pi$
$683$	5.99503	+	5.99503i	0.229394	+	0.229394i	−0.583046	+	0.812439i	$0.698139\pi$
$684$	−17.6618	−	4.67693i	−0.675316	−	0.178827i
$685$	−3.88736	+	6.73310i	−0.148528	+	0.257258i
$686$	18.5200	−	0.0970597i	0.707097	−	0.00370576i
$687$	−10.6570	−	39.5400i	−0.406588	−	1.50854i
$688$	2.42543	+	1.40032i	0.0924686	+	0.0533868i
$689$	18.4417	−	9.18370i	0.702574	−	0.349871i
$690$	−44.3696	−	25.5300i	−1.68912	−	0.971911i
$691$	5.47799	+	5.47799i	0.208392	+	0.208392i	0.803584	−	0.595191i	$-0.202924\pi$
$691$	5.47799	+	5.47799i	0.208392	+	0.208392i	−0.595191	+	0.803584i	$0.702924\pi$
$692$	11.9336	−	6.88988i	0.453648	−	0.261914i
$693$	34.4719	−	0.161438i	1.30948	−	0.00613252i
$694$	−10.7658	−	10.7658i	−0.408663	−	0.408663i
$695$	−44.5082	−	11.9259i	−1.68829	−	0.452376i
$696$	4.55850	+	1.21428i	0.172789	+	0.0460270i
$697$	−47.3109	−	12.6769i	−1.79203	−	0.480172i
$698$	−21.6120	+	12.4777i	−0.818026	+	0.472287i
$699$	24.4277	−	42.4539i	0.923942	−	1.60575i
$700$	4.03092	+	14.9392i	0.152354	+	0.564647i
$701$	−27.6757			−1.04530			−0.522649	−	0.852548i	$-0.675056\pi$
$701$	−27.6757			−1.04530			−0.522649	+	0.852548i	$0.675056\pi$
$702$	13.9828	−	12.4692i	0.527748	−	0.470619i
$703$	−6.40938	−	11.1014i	−0.241734	−	0.418696i
$704$	1.12408	+	4.19511i	0.0423653	+	0.158109i
$705$	12.4057	+	21.4147i	0.467228	+	0.806525i
$706$	0.534562	+	0.308629i	0.0201185	+	0.0116154i
$707$	−18.0698	+	18.1330i	−0.679583	+	0.681962i
$708$	0.988114	−	0.991019i	0.0371356	−	0.0372448i
$709$	9.06615	+	2.42927i	0.340486	+	0.0912331i	0.425011	−	0.905188i	$-0.360270\pi$
$709$	9.06615	+	2.42927i	0.340486	+	0.0912331i	−0.0845242	+	0.996421i	$0.526937\pi$
$710$	−7.37093	+	27.5087i	−0.276626	+	1.03238i
$711$	−0.768567	+	1.34027i	−0.0288235	+	0.0502640i
$712$			2.21018i			0.0828298i
$713$	2.67556	−	9.98531i	0.100200	−	0.373953i
$714$	20.9763	−	12.2008i	0.785019	−	0.456602i
$715$	22.9914	+	46.1689i	0.859829	+	1.72662i
$716$	−7.70206	−	4.44678i	−0.287839	−	0.166184i
$717$	22.3452	−	22.4109i	0.834495	−	0.836949i
$718$	−15.0112	+	26.0001i	−0.560213	+	0.970317i
$719$	−9.11577	−	15.7890i	−0.339961	−	0.588829i	0.644464	−	0.764634i	$-0.277080\pi$
$719$	−9.11577	−	15.7890i	−0.339961	−	0.588829i	−0.984425	+	0.175805i	$0.943747\pi$
$720$	2.58542	+	9.53683i	0.0963530	+	0.355417i
$721$	23.2938	+	23.2126i	0.867507	+	0.864481i
$722$	−17.4739	+	4.68213i	−0.650313	+	0.174251i
$723$	21.4228	−	21.4858i	0.796721	−	0.799064i
$724$	−20.2657			−0.753170
$725$	−7.96442	+	13.7948i	−0.295791	+	0.512325i
$726$	−3.50536	+	13.1594i	−0.130096	+	0.488392i
$727$			2.16371i			0.0802476i	0.999195	+	0.0401238i	$0.0127752\pi$
$727$			2.16371i			0.0802476i	−0.999195	+	0.0401238i	$0.987225\pi$
$728$	4.26728	+	8.53172i	0.158156	+	0.316207i
$729$	26.9990	−	0.237831i	0.999961	−	0.00880855i
$730$	3.51784	+	3.51784i	0.130201	+	0.130201i
$731$	12.8436	+	7.41526i	0.475038	+	0.274263i
$732$	−3.55471	+	2.05928i	−0.131386	+	0.0761132i
$733$	12.5511	−	3.36306i	0.463586	−	0.124218i	−0.0194633	−	0.999811i	$-0.506196\pi$
$733$	12.5511	−	3.36306i	0.463586	−	0.124218i	0.483050	+	0.875593i	$0.339529\pi$
$734$	−3.97882	−	14.8491i	−0.146861	−	0.548092i
$735$	−10.1441	+	38.6240i	−0.374172	+	1.42467i
$736$	6.34496	−	6.34496i	0.233878	−	0.233878i
$737$	36.8310	−	21.2644i	1.35669	−	0.783284i
$738$	23.9901	−	13.9448i	0.883088	−	0.513314i
$739$	−12.4554	−	46.4840i	−0.458178	−	1.70994i	−0.678574	−	0.734532i	$-0.737402\pi$
$739$	−12.4554	−	46.4840i	−0.458178	−	1.70994i	0.220396	−	0.975410i	$-0.429265\pi$
$740$	−3.46632	+	6.00384i	−0.127424	+	0.220706i
$741$	12.0324	−	36.0797i	0.442021	−	1.32542i
$742$	−7.53594	+	13.1055i	−0.276653	+	0.481116i
$743$	3.84387	+	1.02996i	0.141018	+	0.0377857i	0.328638	−	0.944456i	$-0.393411\pi$
$743$	3.84387	+	1.02996i	0.141018	+	0.0377857i	−0.187620	+	0.982242i	$0.560077\pi$
$744$	−1.72662	+	1.00025i	−0.0633009	+	0.0366708i
$745$		−	62.4833i		−	2.28921i
$746$	−32.6062	−	8.73680i	−1.19380	−	0.319877i
$747$	13.6405	−	13.7208i	0.499079	−	0.502019i
$748$	5.95243	+	22.2148i	0.217642	+	0.812253i
$749$	5.02984	−	18.9036i	0.183786	−	0.690724i
$750$	−4.84000	+	0.00710566i	−0.176732	+	0.000259462i
$751$			13.8056i			0.503772i	0.967757	+	0.251886i	$0.0810508\pi$
$751$			13.8056i			0.503772i	−0.967757	+	0.251886i	$0.918949\pi$
$752$	−4.19035	+	1.12280i	−0.152806	+	0.0409444i
$753$	12.7602	−	22.1764i	0.465007	−	0.808154i
$754$	−3.12044	+	9.31120i	−0.113640	+	0.339094i
$755$		−	8.98587i		−	0.327029i
$756$	−3.47642	+	13.3009i	−0.126436	+	0.483750i
$757$	−12.0187	−	20.8170i	−0.436826	−	0.756606i	0.560616	−	0.828076i	$-0.310564\pi$
$757$	−12.0187	−	20.8170i	−0.436826	−	0.756606i	−0.997443	+	0.0714701i	$0.977231\pi$
$758$	−3.18194	−	5.51128i	−0.115573	−	0.200179i
$759$	65.1744	−	17.5660i	2.36568	−	0.637606i
$760$	14.1840	+	14.1840i	0.514507	+	0.514507i
$761$	−2.99416	+	11.1743i	−0.108538	+	0.405070i	−0.998723	−	0.0505307i	$-0.983909\pi$
$761$	−2.99416	+	11.1743i	−0.108538	+	0.405070i	0.890184	+	0.455600i	$0.150575\pi$
$762$	−4.23610	+	15.9027i	−0.153458	+	0.576094i
$763$	−5.64404	+	9.81533i	−0.204328	+	0.355339i
$764$	8.05867	+	13.9580i	0.291553	+	0.504984i
$765$	13.6908	+	50.5013i	0.494993	+	1.82588i
$766$	26.8578	−	15.5063i	0.970410	−	0.560267i
$767$	1.92931	+	2.18279i	0.0696632	+	0.0788159i
$768$	−1.73205	+	0.00254284i	−0.0624999	+	9.17569e-5i
$769$	−5.93685	+	22.1566i	−0.214088	+	0.798988i	0.772397	+	0.635140i	$0.219057\pi$
$769$	−5.93685	+	22.1566i	−0.214088	+	0.798988i	−0.986486	+	0.163848i	$0.947609\pi$
$770$	−32.8095	−	18.8662i	−1.18237	−	0.679892i
$771$	−21.9440	+	0.0322162i	−0.790292	+	0.00116024i
$772$	−21.9759	+	5.88842i	−0.790929	+	0.211929i
$773$	1.41642	−	1.41642i	0.0509449	−	0.0509449i	−0.681175	−	0.732120i	$-0.738531\pi$
$773$	1.41642	−	1.41642i	0.0509449	−	0.0509449i	0.732120	+	0.681175i	$0.238531\pi$
$774$	−8.10923	+	2.19840i	−0.291480	+	0.0790199i
$775$	−1.74384	−	6.50811i	−0.0626407	−	0.233778i
$776$	−2.53267	−	1.46224i	−0.0909175	−	0.0524913i
$777$	−8.33771	+	4.84959i	−0.299114	+	0.173978i
$778$	2.12296	+	0.568847i	0.0761120	+	0.0203941i
$779$	28.1656	−	48.7843i	1.00914	−	1.74788i
$780$	−20.1521	+	4.12077i	−0.721561	+	0.147547i
$781$	−18.7764	−	32.5217i	−0.671874	−	1.16372i
$782$	33.5991	−	33.5991i	1.20150	−	1.20150i
$783$	−12.2250	+	7.13009i	−0.436886	+	0.254809i
$784$	−6.07437	−	3.47880i	−0.216942	−	0.124243i
$785$	7.92068	−	7.92068i	0.282701	−	0.282701i
$786$	9.06849	−	2.44417i	0.323462	−	0.0871806i
$787$	−13.9180	+	13.9180i	−0.496123	+	0.496123i	−0.910229	−	0.414106i	$-0.864094\pi$
$787$	−13.9180	+	13.9180i	−0.496123	+	0.496123i	0.414106	+	0.910229i	$0.364094\pi$
$788$	6.66131	−	24.8603i	0.237299	−	0.885613i
$789$	1.42954	+	0.822552i	0.0508931	+	0.0292836i
$790$	1.46899	−	0.848124i	0.0522645	−	0.0301749i
$791$	5.40122	+	5.38238i	0.192045	+	0.191376i
$792$	−11.3028	−	6.48149i	−0.401627	−	0.230310i
$793$	−3.81210	−	7.65506i	−0.135372	−	0.271839i
$794$	−12.7609	+	7.36753i	−0.452869	+	0.261464i
$795$	−23.0834	−	23.0158i	−0.818685	−	0.816285i
$796$	16.6668			0.590739
$797$	−2.21480	+	3.83615i	−0.0784524	+	0.135883i	−0.902582	−	0.430517i	$-0.858331\pi$
$797$	−2.21480	+	3.83615i	−0.0784524	+	0.135883i	0.824130	+	0.566401i	$0.191665\pi$
$798$	7.30994	+	26.9344i	0.258769	+	0.953468i
$799$	−22.1896	+	5.94568i	−0.785011	+	0.210343i
$800$	1.51368	−	5.64912i	0.0535166	−	0.199727i
$801$	−4.70224	−	4.67470i	−0.166145	−	0.165173i
$802$	−1.81682			−0.0641543
$803$	−6.56006			−0.231500
$804$	4.41380	+	16.3763i	0.155663	+	0.577548i
$805$	0.136599	+	78.1943i	0.00481449	+	2.75599i
$806$	−1.85164	−	3.71827i	−0.0652212	−	0.130970i
$807$	−0.0590714	−	40.2363i	−0.00207941	−	1.41639i
$808$	9.34592	−	2.50423i	0.328788	−	0.0880986i
$809$	−7.64391	−	4.41322i	−0.268746	−	0.155160i	0.359572	−	0.933117i	$-0.382923\pi$
$809$	−7.64391	−	4.41322i	−0.268746	−	0.155160i	−0.628317	+	0.777957i	$0.716256\pi$
$810$	−25.7584	−	14.6706i	−0.905057	−	0.515472i
$811$	−18.3979	−	18.3979i	−0.646037	−	0.646037i	0.305996	−	0.952033i	$-0.401011\pi$
$811$	−18.3979	−	18.3979i	−0.646037	−	0.646037i	−0.952033	+	0.305996i	$0.901011\pi$
$812$	−1.87721	−	6.95722i	−0.0658773	−	0.244151i
$813$	−32.9970	+	33.0941i	−1.15726	+	1.16066i
$814$	−2.36598	−	8.82998i	−0.0829277	−	0.309490i
$815$		−	83.4871i		−	2.92443i
$816$	−9.17188	+	0.0134653i	−0.321080	+	0.000471381i
$817$	−12.0607	+	12.0607i	−0.421951	+	0.421951i
$818$	−24.8655			−0.869403
$819$	−27.1772	−	8.96649i	−0.949649	−	0.313314i
$820$	−30.4650			−1.06389
$821$	4.50941	−	4.50941i	0.157379	−	0.157379i	−0.624025	−	0.781404i	$-0.714504\pi$
$821$	4.50941	−	4.50941i	0.157379	−	0.157379i	0.781404	+	0.624025i	$0.214504\pi$
$822$	4.08848	−	0.00600234i	0.142602	−	0.000209356i
$823$		−	6.90731i		−	0.240774i	−0.992727	−	0.120387i	$-0.961586\pi$
$823$		−	6.90731i		−	0.240774i	0.992727	−	0.120387i	$-0.0384135\pi$
$824$	−3.21696	−	12.0059i	−0.112068	−	0.418244i
$825$	31.0631	−	31.1544i	1.08148	−	1.08466i
$826$	−2.06583	−	0.549672i	−0.0718795	−	0.0191255i
$827$	−7.55620	−	7.55620i	−0.262755	−	0.262755i	0.563418	−	0.826172i	$-0.309486\pi$
$827$	−7.55620	−	7.55620i	−0.262755	−	0.262755i	−0.826172	+	0.563418i	$0.809486\pi$
$828$	0.0790411	+	26.9193i	0.00274687	+	0.935509i
$829$	−29.0721	−	16.7848i	−1.00972	−	0.582959i	−0.0986071	−	0.995126i	$-0.531439\pi$
$829$	−29.0721	−	16.7848i	−1.00972	−	0.582959i	−0.911108	+	0.412167i	$0.864772\pi$
$830$	−20.5177	+	5.49771i	−0.712181	+	0.190828i
$831$	−0.0452422	−	30.8166i	−0.00156943	−	1.06901i
$832$	0.221835	−	3.59872i	0.00769075	−	0.124763i
$833$	−32.1662	−	18.4216i	−1.11449	−	0.638271i
$834$	6.30583	+	23.3962i	0.218353	+	0.810145i
$835$	−17.9606			−0.621552
$836$	−26.4503			−0.914802
$837$	1.52388	−	5.78906i	0.0526729	−	0.200099i
$838$	6.20065	−	23.1411i	0.214198	−	0.799397i
$839$	33.7234	−	9.03616i	1.16426	−	0.311963i	0.375595	−	0.926784i	$-0.377438\pi$
$839$	33.7234	−	9.03616i	1.16426	−	0.311963i	0.788667	+	0.614821i	$0.210772\pi$
$840$	10.6384	−	10.7070i	0.367060	−	0.369428i
$841$	−10.7909	+	18.6905i	−0.372101	+	0.644498i
$842$	−29.8765			−1.02961
$843$	30.2816	+	30.1928i	1.04295	+	1.03989i
$844$	−7.83833	+	4.52546i	−0.269806	+	0.155773i
$845$	−5.91854	−	42.4070i	−0.203604	−	1.45884i
$846$	6.47414	−	11.2900i	0.222585	−	0.388157i
$847$	20.0840	−	5.41912i	0.690096	−	0.186203i
$848$	4.94841	−	2.85697i	0.169929	−	0.0981087i
$849$	−1.07005	−	0.615700i	−0.0367240	−	0.0211308i
$850$	8.01552	−	29.9143i	0.274930	−	1.02605i
$851$	−13.3550	+	13.3550i	−0.457804	+	0.457804i
$852$	14.4603	−	3.89738i	0.495401	−	0.133522i
$853$	3.57332	−	3.57332i	0.122348	−	0.122348i	−0.643282	−	0.765630i	$-0.722428\pi$
$853$	3.57332	−	3.57332i	0.122348	−	0.122348i	0.765630	+	0.643282i	$0.222428\pi$
$854$	5.44000	+	3.12813i	0.186153	+	0.107042i
$855$	−60.1773	+	0.176694i	−2.05802	+	0.00604282i
$856$	−5.22799	+	5.22799i	−0.178689	+	0.178689i
$857$	12.6115	+	21.8438i	0.430802	+	0.746170i	0.996943	−	0.0781383i	$-0.0248976\pi$
$857$	12.6115	+	21.8438i	0.430802	+	0.746170i	−0.566141	+	0.824308i	$0.691564\pi$
$858$	14.9476	−	22.6320i	0.510303	−	0.772644i
$859$	−24.5656	+	42.5489i	−0.838168	+	1.45175i	0.0532569	+	0.998581i	$0.483040\pi$
$859$	−24.5656	+	42.5489i	−0.838168	+	1.45175i	−0.891425	+	0.453169i	$0.850294\pi$
$860$	8.91014	+	2.38747i	0.303833	+	0.0814119i
$861$	−36.7758	−	21.0752i	−1.25332	−	0.718240i
$862$	18.9465	+	10.9388i	0.645320	+	0.372576i
$863$	1.73281	+	6.46693i	0.0589855	+	0.220137i	0.989127	−	0.147065i	$-0.0469826\pi$
$863$	1.73281	+	6.46693i	0.0589855	+	0.220137i	−0.930141	+	0.367202i	$0.880316\pi$
$864$	3.65802	−	3.69038i	0.124448	−	0.125549i
$865$	32.0930	−	32.0930i	1.09119	−	1.09119i
$866$	−10.3339	+	2.76896i	−0.351160	+	0.0940930i
$867$	−19.1239	+	0.0280760i	−0.649481	+	0.000953510i
$868$	2.64235	+	1.51941i	0.0896873	+	0.0515723i
$869$	−0.578899	+	2.16048i	−0.0196378	+	0.0732893i
$870$	15.5378	−	0.0228112i	0.526781	−	0.000773374i
$871$	−34.6011	+	7.02243i	−1.17241	+	0.237946i
$872$	3.70611	−	2.13973i	0.125505	−	0.0724603i
$873$	8.46777	−	2.29560i	0.286591	−	0.0776944i
$874$	27.3240	+	47.3266i	0.924248	+	1.60084i
$875$	3.70779	+	6.39626i	0.125346	+	0.216233i
$876$	0.673408	−	2.52803i	0.0227524	−	0.0854144i
$877$	−6.71366	+	25.0557i	−0.226704	+	0.846071i	0.755010	+	0.655713i	$0.227632\pi$
$877$	−6.71366	+	25.0557i	−0.226704	+	0.846071i	−0.981715	+	0.190359i	$0.939035\pi$
$878$	27.1212	+	27.1212i	0.915295	+	0.915295i
$879$	1.24842	−	0.336479i	0.0421082	−	0.0113492i
$880$	7.15242	+	12.3884i	0.241108	+	0.417611i
$881$	−0.0492472	−	0.0852986i	−0.00165918	−	0.00287378i	0.865195	−	0.501436i	$-0.167195\pi$
$881$	−0.0492472	−	0.0852986i	−0.00165918	−	0.00287378i	−0.866854	+	0.498562i	$0.833861\pi$
$882$	20.2491	−	5.56552i	0.681822	−	0.187401i
$883$			28.9269i			0.973469i	0.873550	+	0.486735i	$0.161812\pi$
$883$			28.9269i			0.973469i	−0.873550	+	0.486735i	$0.838188\pi$
$884$	1.17470	−	19.0566i	0.0395096	−	0.640944i
$885$	2.29883	−	3.99523i	0.0772744	−	0.134298i
$886$	−7.88780	+	2.11353i	−0.264996	+	0.0710054i
$887$			13.3735i			0.449038i	0.974470	+	0.224519i	$0.0720811\pi$
$887$			13.3735i			0.449038i	−0.974470	+	0.224519i	$0.927919\pi$
$888$	3.64566	−	0.00535223i	0.122340	−	0.000179609i
$889$	24.2708	−	6.54882i	0.814018	−	0.219640i
$890$	1.88411	+	7.03159i	0.0631555	+	0.235699i
$891$	37.6960	−	10.3382i	1.26286	−	0.346344i
$892$	−8.16427	−	2.18761i	−0.273360	−	0.0732466i
$893$		−	26.4203i		−	0.884121i
$894$	−28.4317	+	16.4708i	−0.950899	+	0.550865i
$895$	−28.2945	−	7.58150i	−0.945782	−	0.253422i
$896$	1.32688	+	2.28897i	0.0443278	+	0.0764692i
$897$	−55.9360	−	3.36563i	−1.86765	−	0.112375i
$898$	0.574338	−	0.994782i	0.0191659	−	0.0331963i
$899$	0.812114	+	3.03085i	0.0270855	+	0.101085i
$900$	8.81718	+	15.1688i	0.293906	+	0.505626i
$901$	26.2038	−	15.1288i	0.872975	−	0.504012i
$902$	28.4056	−	28.4056i	0.945803	−	0.945803i
$903$	9.10426	+	9.04590i	0.302971	+	0.301029i
$904$	−0.745928	−	2.78384i	−0.0248092	−	0.0925892i
$905$	−64.4746	+	17.2759i	−2.14321	+	0.574271i
$906$	−4.08883	+	2.36870i	−0.135842	+	0.0786948i
$907$	23.4037	+	13.5122i	0.777108	+	0.448664i	0.835404	−	0.549636i	$-0.185233\pi$
$907$	23.4037	+	13.5122i	0.777108	+	0.448664i	−0.0582963	+	0.998299i	$0.518567\pi$
$908$	−16.8243	−	16.8243i	−0.558335	−	0.558335i
$909$	−14.4395	+	25.1805i	−0.478929	+	0.835184i
$910$	20.8492	+	23.5056i	0.691145	+	0.779204i
$911$			27.3357i			0.905671i	0.891594	+	0.452836i	$0.149588\pi$
$911$			27.3357i			0.905671i	−0.891594	+	0.452836i	$0.850412\pi$
$912$	2.71519	−	10.1931i	0.0899090	−	0.337526i
$913$	14.0047	−	24.2568i	0.463487	−	0.802782i
$914$	0.508183			0.0168092
$915$	−9.55371	+	9.58181i	−0.315836	+	0.316765i
$916$	22.8374	−	6.11927i	0.754570	−	0.202186i
$917$	−10.1623	−	10.1269i	−0.335590	−	0.334419i
$918$	19.3706	−	19.5420i	0.639326	−	0.644983i
$919$	−23.7617	−	41.1565i	−0.783827	−	1.35763i	−0.929697	−	0.368324i	$-0.879932\pi$
$919$	−23.7617	−	41.1565i	−0.783827	−	1.35763i	0.145871	−	0.989304i	$-0.453402\pi$
$920$	14.7774	−	25.5951i	0.487195	−	0.843846i
$921$	29.9472	−	30.0353i	0.986794	−	0.989696i
$922$	13.9286	+	8.04166i	0.458713	+	0.264838i
$923$	6.20080	+	30.5527i	0.204102	+	1.00566i
$924$	0.0639873	+	19.9025i	0.00210503	+	0.654744i
$925$	−3.18603	+	11.8904i	−0.104756	+	0.390954i
$926$		−	17.4478i		−	0.573369i
$927$	32.3471	+	18.5492i	1.06242	+	0.609234i
$928$	−0.704925	+	2.63082i	−0.0231403	+	0.0863608i
$929$	19.2502	+	5.15806i	0.631577	+	0.169231i	0.560385	−	0.828232i	$-0.310653\pi$
$929$	19.2502	+	5.15806i	0.631577	+	0.169231i	0.0711918	+	0.997463i	$0.477320\pi$
$930$	−4.64049	+	4.65414i	−0.152168	+	0.152615i
$931$	30.0394	−	30.2500i	0.984501	−	0.991404i
$932$	24.4900	+	14.1393i	0.802198	+	0.463149i
$933$	−10.8338	−	18.7012i	−0.354683	−	0.612251i
$934$	−8.02487	−	29.9492i	−0.262582	−	0.979969i
$935$	37.8749	+	65.6012i	1.23864	+	2.14539i
$936$	7.18722	+	8.08355i	0.234922	+	0.264219i
$937$	20.0256			0.654207			0.327103	−	0.944989i	$-0.393927\pi$
$937$	20.0256			0.654207			0.327103	+	0.944989i	$0.393927\pi$
$938$	18.2876	−	18.3516i	0.597111	−	0.599201i
$939$	11.7064	−	20.3450i	0.382023	−	0.663933i
$940$	−12.3743	+	7.14430i	−0.403605	+	0.233021i
$941$	1.25159	+	0.335362i	0.0408006	+	0.0109325i	0.279162	−	0.960244i	$-0.409943\pi$
$941$	1.25159	+	0.335362i	0.0408006	+	0.0109325i	−0.238361	+	0.971177i	$0.576610\pi$
$942$	−5.69206	−	1.51623i	−0.185457	−	0.0494014i
$943$	−80.1690	−	21.4812i	−2.61066	−	0.699525i
$944$	0.571327	+	0.571327i	0.0185951	+	0.0185951i
$945$	0.278532	+	45.2799i	0.00906063	+	1.47296i
$946$	−10.5339	+	6.08174i	−0.342486	+	0.197734i
$947$	19.7867	+	19.7867i	0.642983	+	0.642983i	0.951288	−	0.308305i	$-0.0997617\pi$
$947$	19.7867	+	19.7867i	0.642983	+	0.642983i	−0.308305	+	0.951288i	$0.599762\pi$
$948$	−0.773153	−	0.444868i	−0.0251108	−	0.0144486i
$949$	5.16377	+	1.73052i	0.167623	+	0.0561751i
$950$	30.8460	+	17.8089i	1.00078	+	0.577798i
$951$	4.96115	+	18.4071i	0.160876	+	0.596892i
$952$	7.02633	+	12.1210i	0.227725	+	0.392844i
$953$	−4.62297	+	8.00722i	−0.149753	+	0.259379i	−0.931136	−	0.364672i	$-0.881181\pi$
$953$	−4.62297	+	8.00722i	−0.149753	+	0.259379i	0.781383	+	0.624051i	$0.214514\pi$
$954$	−4.38799	+	16.5707i	−0.142066	+	0.536495i
$955$	37.5372	+	37.5372i	1.21467	+	1.21467i
$956$	12.9200	+	12.9200i	0.417862	+	0.417862i
$957$	−14.4662	+	14.5087i	−0.467625	+	0.469000i
$958$	10.7273	−	18.5802i	0.346583	−	0.600300i
$959$	−3.13207	−	5.40309i	−0.101140	−	0.174475i
$960$	−5.50828	+	1.48461i	−0.177779	+	0.0479156i
$961$	25.6974	+	14.8364i	0.828947	+	0.478593i
$962$	−0.466924	+	7.57467i	−0.0150542	+	0.244217i
$963$	−0.0651267	−	22.1804i	−0.00209868	−	0.714753i
$964$	12.3866	+	12.3866i	0.398947	+	0.398947i
$965$	−64.8957	+	37.4675i	−2.08907	+	1.20612i
$966$	35.5447	−	20.6744i	1.14363	−	0.665188i
$967$	33.9199	+	33.9199i	1.09079	+	1.09079i	0.995444	+	0.0953471i	$0.0303961\pi$
$967$	33.9199	+	33.9199i	1.09079	+	1.09079i	0.0953471	+	0.995444i	$0.469604\pi$
$968$	−7.59462	−	2.03497i	−0.244100	−	0.0654065i
$969$	14.3780	−	53.9763i	0.461888	−	1.73397i
$970$	−9.30410	−	2.49303i	−0.298737	−	0.0800463i
$971$	−3.64259	+	2.10305i	−0.116896	+	0.0674901i	−0.557308	−	0.830306i	$-0.688166\pi$
$971$	−3.64259	+	2.10305i	−0.116896	+	0.0674901i	0.440412	+	0.897796i	$0.354832\pi$
$972$	0.114427	+	15.5880i	0.00367024	+	0.499987i
$973$	26.1268	−	26.2183i	0.837588	−	0.840520i
$974$	−21.4225			−0.686420
$975$	−32.6698	+	16.3289i	−1.04627	+	0.522945i
$976$	−1.18591	−	2.05406i	−0.0379601	−	0.0657488i
$977$	3.45942	+	12.9107i	0.110677	+	0.413051i	0.998927	−	0.0463082i	$-0.0147456\pi$
$977$	3.45942	+	12.9107i	0.110677	+	0.413051i	−0.888250	+	0.459360i	$0.848079\pi$
$978$	−37.9891	+	22.0074i	−1.21476	+	0.703721i
$979$	−8.31299	−	4.79951i	−0.265684	−	0.153393i
$980$	−22.2909	−	5.88945i	−0.712058	−	0.188131i
$981$	−3.28638	+	12.4106i	−0.104926	+	0.396240i
$982$	0.521184	+	0.139651i	0.0166317	+	0.00445644i
$983$	−12.0380	+	44.9265i	−0.383953	+	1.43293i	0.455858	+	0.890053i	$0.349333\pi$
$983$	−12.0380	+	44.9265i	−0.383953	+	1.43293i	−0.839811	+	0.542879i	$0.817334\pi$
$984$	8.03067	+	13.8625i	0.256009	+	0.441920i
$985$		−	84.7708i		−	2.70102i
$986$	−3.73286	+	13.9312i	−0.118878	+	0.443660i
$987$	−19.8799	+	0.0639147i	−0.632784	+	0.00203443i
$988$	20.8204	+	6.97749i	0.662385	+	0.221983i
$989$	21.7637	+	12.5653i	0.692045	+	0.399552i
$990$	−41.4847	−	10.9853i	−1.31847	−	0.349137i
$991$	−21.4478	+	37.1487i	−0.681312	+	1.18007i	0.293268	+	0.956030i	$0.405257\pi$
$991$	−21.4478	+	37.1487i	−0.681312	+	1.18007i	−0.974581	+	0.224037i	$0.928076\pi$
$992$	−0.576029	−	0.997711i	−0.0182889	−	0.0316773i
$993$	−1.67385	+	6.28380i	−0.0531182	+	0.199410i
$994$	−16.2045	−	16.1479i	−0.513974	−	0.512182i
$995$	53.0248	−	14.2079i	1.68100	−	0.450422i
$996$	7.91015	+	7.88696i	0.250643	+	0.249908i
$997$	33.9859			1.07634			0.538172	−	0.842835i	$-0.319115\pi$
$997$	33.9859			1.07634			0.538172	+	0.842835i	$0.319115\pi$
$998$	10.4304	−	18.0660i	0.330168	−	0.571868i
$999$	−7.69948	+	7.76760i	−0.243601	+	0.245756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.401.20	yes	152
3.2	odd	2	inner	546.2.ch.a.401.12	yes	152
7.4	even	3		546.2.bw.a.11.33	yes	152
13.6	odd	12		546.2.bw.a.149.14	yes	152
21.11	odd	6		546.2.bw.a.11.14	✓	152
39.32	even	12		546.2.bw.a.149.33	yes	152
91.32	odd	12	inner	546.2.ch.a.305.12	yes	152
273.32	even	12	inner	546.2.ch.a.305.20	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.14	✓	152	21.11	odd	6
546.2.bw.a.11.33	yes	152	7.4	even	3
546.2.bw.a.149.14	yes	152	13.6	odd	12
546.2.bw.a.149.33	yes	152	39.32	even	12
546.2.ch.a.305.12	yes	152	91.32	odd	12	inner
546.2.ch.a.305.20	yes	152	273.32	even	12	inner
546.2.ch.a.401.12	yes	152	3.2	odd	2	inner
546.2.ch.a.401.20	yes	152	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.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.73205 + 0.00254284i) q^{3} -1.00000i q^{4} +(-0.852470 - 3.18146i) q^{5} +(-1.22295 + 1.22654i) q^{6} +(2.55679 + 0.680305i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99999 - 0.00880865i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.73205 + 0.00254284i) q^{3} -1.00000i q^{4} +(-0.852470 - 3.18146i) q^{5} +(-1.22295 + 1.22654i) q^{6} +(2.55679 + 0.680305i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99999 - 0.00880865i) q^{9} +(-2.85242 - 1.64685i) q^{10} +(4.19511 - 1.12408i) q^{11} +(0.00254284 + 1.73205i) q^{12} +(-3.59872 - 0.221835i) q^{13} +(2.28897 - 1.32688i) q^{14} +(1.48461 + 5.50828i) q^{15} -1.00000 q^{16} -5.29539 q^{17} +(2.11508 - 2.12754i) q^{18} +(1.57626 - 5.88267i) q^{19} +(-3.18146 + 0.852470i) q^{20} +(-4.43022 - 1.17182i) q^{21} +(2.17155 - 3.76124i) q^{22} -8.97313 q^{23} +(1.22654 + 1.22295i) q^{24} +(-5.06487 + 2.92420i) q^{25} +(-2.70154 + 2.38782i) q^{26} +(-5.19610 + 0.0228855i) q^{27} +(0.680305 - 2.55679i) q^{28} +(2.35873 - 1.36181i) q^{29} +(4.94472 + 2.84516i) q^{30} +(-0.298174 + 1.11280i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-7.26328 + 1.95762i) q^{33} +(-3.74441 + 3.74441i) q^{34} +(-0.0152231 - 8.71427i) q^{35} +(-0.00880865 - 2.99999i) q^{36} +(1.48834 - 1.48834i) q^{37} +(-3.04509 - 5.27425i) q^{38} +(6.23372 + 0.375078i) q^{39} +(-1.64685 + 2.85242i) q^{40} +(8.93434 + 2.39395i) q^{41} +(-3.96124 + 2.30404i) q^{42} +(-2.42543 - 1.40032i) q^{43} +(-1.12408 - 4.19511i) q^{44} +(-2.58542 - 9.53683i) q^{45} +(-6.34496 + 6.34496i) q^{46} +(4.19035 - 1.12280i) q^{47} +(1.73205 - 0.00254284i) q^{48} +(6.07437 + 3.47880i) q^{49} +(-1.51368 + 5.64912i) q^{50} +(9.17188 - 0.0134653i) q^{51} +(-0.221835 + 3.59872i) q^{52} +(-4.94841 + 2.85697i) q^{53} +(-3.65802 + 3.69038i) q^{54} +(-7.15242 - 12.3884i) q^{55} +(-1.32688 - 2.28897i) q^{56} +(-2.71519 + 10.1931i) q^{57} +(0.704925 - 2.63082i) q^{58} +(-0.571327 - 0.571327i) q^{59} +(5.50828 - 1.48461i) q^{60} +(1.18591 + 2.05406i) q^{61} +(0.576029 + 0.997711i) q^{62} +(7.67634 + 2.01839i) q^{63} +1.00000i q^{64} +(2.36204 + 11.6383i) q^{65} +(-3.75167 + 6.52017i) q^{66} +(9.45859 - 2.53442i) q^{67} +5.29539i q^{68} +(15.5419 - 0.0228172i) q^{69} +(-6.17269 - 6.15116i) q^{70} +(-2.23789 - 8.35193i) q^{71} +(-2.12754 - 2.11508i) q^{72} +(-1.45899 - 0.390935i) q^{73} -2.10482i q^{74} +(8.76516 - 5.07774i) q^{75} +(-5.88267 - 1.57626i) q^{76} +(11.4907 - 0.0200734i) q^{77} +(4.67313 - 4.14269i) q^{78} +(-0.257500 + 0.446002i) q^{79} +(0.852470 + 3.18146i) q^{80} +(8.99984 - 0.0528517i) q^{81} +(8.01031 - 4.62476i) q^{82} +(4.56024 - 4.56024i) q^{83} +(-1.17182 + 4.43022i) q^{84} +(4.51416 + 16.8471i) q^{85} +(-2.70522 + 0.724860i) q^{86} +(-4.08197 + 2.36472i) q^{87} +(-3.76124 - 2.17155i) q^{88} +(-1.56283 - 1.56283i) q^{89} +(-8.57173 - 4.91539i) q^{90} +(-9.05026 - 3.01542i) q^{91} +8.97313i q^{92} +(0.513623 - 1.92819i) q^{93} +(2.16909 - 3.75697i) q^{94} -20.0592 q^{95} +(1.22295 - 1.22654i) q^{96} +(2.82483 - 0.756910i) q^{97} +(6.75511 - 1.83535i) q^{98} +(12.5754 - 3.40917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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