LMFDB - Embedded newform 546.2.ch.a.305.20

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			305.20
Character	$\chi$	$=$	546.305
Dual form			546.2.ch.a.401.20

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	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	0.462779	+	0.886474i	$0.346852\pi$
$5$	−0.852470	+	3.18146i	−0.381236	+	1.42279i	−0.844015	+	0.536319i	$0.819814\pi$
$6$	−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	0.828065	−	0.560632i	$-0.189442\pi$
$11$	4.19511	+	1.12408i	1.26487	+	0.338922i	0.436809	+	0.899554i	$0.356108\pi$
$12$	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	0.871948	+	0.489598i	$0.162856\pi$
$19$	1.57626	+	5.88267i	0.361618	+	1.34958i	−0.510330	+	0.859978i	$0.670477\pi$
$20$	−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	0.702751	−	0.711436i	$-0.251955\pi$
$29$	2.35873	+	1.36181i	0.438004	+	0.252882i	−0.264746	+	0.964318i	$0.585288\pi$
$30$	4.94472	−	2.84516i	0.902778	−	0.519454i
$31$	−0.298174	−	1.11280i	−0.0535537	−	0.199865i	0.933966	−	0.357363i	$-0.116324\pi$
$31$	−0.298174	−	1.11280i	−0.0535537	−	0.199865i	−0.987519	+	0.157498i	$0.949657\pi$
$32$	−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	0.818783	−	0.574103i	$-0.194649\pi$
$37$	1.48834	+	1.48834i	0.244681	+	0.244681i	−0.574103	+	0.818783i	$0.694649\pi$
$38$	−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	0.518652	−	0.854986i	$-0.326434\pi$
$41$	8.93434	−	2.39395i	1.39531	−	0.373872i	0.876658	+	0.481113i	$0.159767\pi$
$42$	−3.96124	−	2.30404i	−0.611233	−	0.355520i
$43$	−2.42543	+	1.40032i	−0.369875	+	0.213547i	−0.673404	−	0.739275i	$-0.735168\pi$
$43$	−2.42543	+	1.40032i	−0.369875	+	0.213547i	0.303529	+	0.952822i	$0.401835\pi$
$44$	−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	0.551136	−	0.834415i	$-0.314195\pi$
$47$	4.19035	+	1.12280i	0.611226	+	0.163778i	0.0600900	+	0.998193i	$0.480861\pi$
$48$	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	0.120032	−	0.992770i	$-0.461700\pi$
$53$	−4.94841	−	2.85697i	−0.679717	−	0.392435i	−0.799748	+	0.600335i	$0.795034\pi$
$54$	−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	−0.743318	−	0.668938i	$-0.766749\pi$
$59$	−0.571327	+	0.571327i	−0.0743805	+	0.0743805i	0.668938	+	0.743318i	$0.266749\pi$
$60$	5.50828	+	1.48461i	0.711116	+	0.191662i
$61$	1.18591	−	2.05406i	0.151840	−	0.262995i	−0.780064	−	0.625700i	$-0.784813\pi$
$61$	1.18591	−	2.05406i	0.151840	−	0.262995i	0.931904	+	0.362705i	$0.118147\pi$
$62$	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	0.785188	−	0.619258i	$-0.212566\pi$
$67$	9.45859	+	2.53442i	1.15555	+	0.309629i	0.370364	+	0.928887i	$0.379233\pi$
$68$		−	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	0.696300	+	0.717751i	$0.254829\pi$
$71$	−2.23789	+	8.35193i	−0.265589	+	0.991192i	−0.961889	+	0.273441i	$0.911838\pi$
$72$	−2.12754	+	2.11508i	−0.250733	+	0.249265i
$73$	−1.45899	+	0.390935i	−0.170762	+	0.0457555i	−0.343187	−	0.939267i	$-0.611506\pi$
$73$	−1.45899	+	0.390935i	−0.170762	+	0.0457555i	0.172425	+	0.985023i	$0.444840\pi$
$74$			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	0.851176	−	0.524880i	$-0.175890\pi$
$79$	−0.257500	−	0.446002i	−0.0289710	−	0.0501792i	−0.880147	+	0.474701i	$0.842556\pi$
$80$	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	0.911609	−	0.411058i	$-0.134841\pi$
$83$	4.56024	+	4.56024i	0.500551	+	0.500551i	−0.411058	+	0.911609i	$0.634841\pi$
$84$	−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	−0.785069	−	0.619409i	$-0.787372\pi$
$89$	−1.56283	+	1.56283i	−0.165660	+	0.165660i	0.619409	+	0.785069i	$0.287372\pi$
$90$	−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	0.399359	−	0.916794i	$-0.369233\pi$
$97$	2.82483	+	0.756910i	0.286818	+	0.0768525i	−0.112542	+	0.993647i	$0.535899\pi$
$98$	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	0.518392	−	0.855143i	$-0.326531\pi$
$101$	−4.83780	−	8.37932i	−0.481379	−	0.833774i	−0.999772	+	0.0213693i	$0.993197\pi$
$102$	6.47598	+	6.49502i	0.641217	+	0.643103i
$103$	10.7642	−	6.21469i	1.06062	−	0.612351i	0.135019	−	0.990843i	$-0.456891\pi$
$103$	10.7642	−	6.21469i	1.06062	−	0.612351i	0.925605	+	0.378492i	$0.123557\pi$
$104$	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	$0.116329\pi$
$107$			7.39350i			0.714757i	−0.933960	+	0.357378i	$0.883671\pi$
$108$	0.0228855	−	5.19610i	0.00220216	−	0.499995i
$109$	−1.10760	−	4.13363i	−0.106089	−	0.395930i	0.892377	−	0.451290i	$-0.149036\pi$
$109$	−1.10760	−	4.13363i	−0.106089	−	0.395930i	−0.998466	+	0.0553599i	$0.982369\pi$
$110$	−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	−0.377986	−	0.925811i	$-0.623383\pi$
$113$	2.49592	−	1.44102i	0.234797	−	0.135560i	0.612783	+	0.790251i	$0.290050\pi$
$114$	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	0.818485	−	0.574528i	$-0.194814\pi$
$127$	8.22861	+	4.75079i	0.730171	+	0.421565i	−0.0883135	+	0.996093i	$0.528148\pi$
$128$	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	−0.690917	−	0.722934i	$-0.742793\pi$
$131$	−4.69605	+	2.71126i	−0.410295	+	0.236884i	0.280621	+	0.959819i	$0.409460\pi$
$132$	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	−0.774804	−	0.632202i	$-0.782151\pi$
$137$	−1.66912	+	1.66912i	−0.142602	+	0.142602i	0.632202	+	0.774804i	$0.282151\pi$
$138$	10.9736	+	11.0059i	0.934139	+	0.936886i
$139$	6.99492	+	12.1156i	0.593302	+	1.02763i	0.993784	+	0.111324i	$0.0355092\pi$
$139$	6.99492	+	12.1156i	0.593302	+	1.02763i	−0.400483	+	0.916304i	$0.631157\pi$
$140$	−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	0.587682	−	0.809092i	$-0.300041\pi$
$149$	18.3242	−	4.90995i	1.50118	−	0.402239i	0.913493	+	0.406853i	$0.133374\pi$
$150$	2.60740	+	9.78841i	0.212893	+	0.799220i
$151$	2.63524	−	0.706111i	0.214453	−	0.0574625i	−0.149993	−	0.988687i	$-0.547925\pi$
$151$	2.63524	−	0.706111i	0.214453	−	0.0574625i	0.364446	+	0.931225i	$0.381258\pi$
$152$	−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	−0.790158	−	0.612903i	$-0.790001\pi$
$157$	1.70045	−	2.94527i	0.135711	−	0.235058i	0.925869	+	0.377845i	$0.123335\pi$
$158$	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	0.927621	−	0.373522i	$-0.121850\pi$
$163$	24.4839	−	6.56044i	1.91773	−	0.513853i	0.990105	−	0.140331i	$-0.0448168\pi$
$164$	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	0.998789	−	0.0491979i	$-0.0156665\pi$
$167$	1.41135	+	5.26722i	0.109213	+	0.407590i	−0.889576	+	0.456788i	$0.849000\pi$
$168$	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	−0.475787	−	0.879560i	$-0.657837\pi$
$173$	6.88988	−	11.9336i	0.523828	−	0.907297i	0.999615	−	0.0277364i	$-0.00882989\pi$
$174$	−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	0.982976	−	0.183736i	$-0.0588190\pi$
$179$	4.44678	+	7.70206i	0.332368	+	0.575679i	−0.650607	+	0.759414i	$0.725486\pi$
$180$	−9.53683	−	2.58542i	−0.710834	−	0.192706i
$181$			20.2657i			1.50634i	0.657826	+	0.753170i	$0.271476\pi$
$181$			20.2657i			1.50634i	−0.657826	+	0.753170i	$0.728524\pi$
$182$	−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	−0.0987856	−	0.995109i	$-0.531496\pi$
$191$	−13.9580	−	8.05867i	−1.00997	−	0.583105i	−0.911182	+	0.412004i	$0.864829\pi$
$192$	−0.00254284	+	1.73205i	−0.000183514	+	0.125000i
$193$	−5.88842	+	21.9759i	−0.423857	+	1.58186i	0.342548	+	0.939500i	$0.388710\pi$
$193$	−5.88842	+	21.9759i	−0.423857	+	1.58186i	−0.766405	+	0.642357i	$0.777957\pi$
$194$	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	0.782286	−	0.622919i	$-0.214053\pi$
$197$	24.8603	−	6.66131i	1.77123	−	0.474598i	0.988939	+	0.148321i	$0.0473867\pi$
$198$	6.48149	+	11.3028i	0.460620	+	0.803254i
$199$		−	16.6668i		−	1.18148i	−0.806863	−	0.590739i	$-0.798836\pi$
$199$		−	16.6668i		−	1.18148i	0.806863	−	0.590739i	$-0.201164\pi$
$200$	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	−0.978697	−	0.205309i	$-0.934180\pi$
$211$	−4.52546	+	7.83833i	−0.311546	+	0.539613i	0.667152	+	0.744922i	$0.267513\pi$
$212$	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	0.999684	+	0.0251219i	$0.00799738\pi$
$223$	2.18761	+	8.16427i	0.146493	+	0.546720i	−0.853191	+	0.521598i	$0.825336\pi$
$224$	−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	0.992227	+	0.124442i	$0.0397142\pi$
$227$	16.8243	+	16.8243i	1.11667	+	1.11667i	0.124442	+	0.992227i	$0.460286\pi$
$228$	10.1931	−	2.71519i	0.675053	−	0.179818i
$229$	6.11927	−	22.8374i	0.404373	−	1.50914i	−0.400836	−	0.916150i	$-0.631280\pi$
$229$	6.11927	−	22.8374i	0.404373	−	1.50914i	0.805209	−	0.592991i	$-0.202053\pi$
$230$	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	−0.789460	−	0.613802i	$-0.789639\pi$
$233$	−14.1393	−	24.4900i	−0.926298	−	1.60440i	−0.136838	−	0.990593i	$-0.543694\pi$
$234$	−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	0.152569	−	0.988293i	$-0.451245\pi$
$239$	−12.9200	−	12.9200i	−0.835723	−	0.835723i	−0.988293	+	0.152569i	$0.951245\pi$
$240$	−1.48461	+	5.50828i	−0.0958312	+	0.355558i
$241$	−12.3866	−	12.3866i	−0.797893	−	0.797893i	0.184870	−	0.982763i	$-0.440814\pi$
$241$	−12.3866	−	12.3866i	−0.797893	−	0.797893i	−0.982763	+	0.184870i	$0.940814\pi$
$242$	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	0.533061	−	0.846077i	$-0.321042\pi$
$251$	−7.38589	−	12.7927i	−0.466193	−	0.807471i	−0.999255	+	0.0386062i	$0.987708\pi$
$252$	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	−0.525210	−	0.850973i	$-0.676013\pi$
$263$	−0.824649	+	0.476112i	−0.0508501	+	0.0293583i	0.474359	+	0.880331i	$0.342680\pi$
$264$	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	$-0.749510\pi$
$269$		−	23.2305i		−	1.41639i	0.706018	−	0.708194i	$-0.250490\pi$
$270$	14.8592	−	8.49190i	0.904299	−	0.516801i
$271$	19.0789	+	19.0789i	1.15896	+	1.15896i	0.984700	+	0.174259i	$0.0557530\pi$
$271$	19.0789	+	19.0789i	1.15896	+	1.15896i	0.174259	+	0.984700i	$0.444247\pi$
$272$	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	$-0.820497\pi$
$277$		−	17.7920i		−	1.06902i	0.845163	−	0.534508i	$-0.179503\pi$
$278$	−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	−0.0423209	+	0.999104i	$0.513475\pi$
$281$	−17.4575	+	17.4575i	−1.04142	+	1.04142i	−0.999104	+	0.0423209i	$0.986525\pi$
$282$	−3.74741	−	6.51277i	−0.223155	−	0.387830i
$283$	0.617271	−	0.356381i	0.0366929	−	0.0211847i	−0.481541	−	0.876423i	$-0.659923\pi$
$283$	0.617271	−	0.356381i	0.0366929	−	0.0211847i	0.518234	+	0.855239i	$0.326590\pi$
$284$	−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	0.237695	−	0.971340i	$-0.423608\pi$
$293$	−0.721061	−	0.193208i	−0.0421248	−	0.0112873i	−0.279820	+	0.960053i	$0.590275\pi$
$294$	−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	0.0116856	−	0.999932i	$-0.496280\pi$
$307$	−17.3155	−	17.3155i	−0.988246	−	0.988246i	−0.999932	+	0.0116856i	$0.996280\pi$
$308$	−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	−0.633125	−	0.774049i	$-0.718228\pi$
$311$	6.23904	−	10.8063i	0.353784	−	0.612771i	0.986909	+	0.161278i	$0.0515616\pi$
$312$	−4.14269	+	4.67313i	−0.234534	+	0.264564i
$313$	−6.77592	−	11.7362i	−0.382997	−	0.663371i	0.608492	−	0.793560i	$-0.291775\pi$
$313$	−6.77592	−	11.7362i	−0.382997	−	0.663371i	−0.991489	+	0.130189i	$0.958442\pi$
$314$	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	0.838625	+	0.544709i	$0.183360\pi$
$317$	−2.84872	+	10.6316i	−0.160000	+	0.597128i	−0.998625	+	0.0524189i	$0.983307\pi$
$318$	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	0.987476	−	0.157772i	$-0.0504310\pi$
$331$	0.971726	+	3.62653i	0.0534109	+	0.199332i	−0.934065	+	0.357104i	$0.883764\pi$
$332$	−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	$-0.903699\pi$
$337$		−	10.9390i		−	0.595886i	0.954584	−	0.297943i	$-0.0963006\pi$
$338$	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	$0.134005\pi$
$347$			15.2251i			0.817326i	−0.912685	+	0.408663i	$0.865995\pi$
$348$	2.36472	−	4.08197i	0.126762	−	0.218816i
$349$	−24.1050	+	6.45893i	−1.29031	+	0.345738i	−0.837779	−	0.546009i	$-0.816146\pi$
$349$	−24.1050	+	6.45893i	−1.29031	+	0.345738i	−0.452534	+	0.891747i	$0.649480\pi$
$350$	−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	−0.961544	−	0.274651i	$-0.911438\pi$
$353$	0.159758	−	0.596226i	0.00850308	−	0.0317339i	0.970047	+	0.242917i	$0.0781043\pi$
$354$	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	−0.607338	−	0.794444i	$-0.707763\pi$
$359$	−28.9994	−	7.77036i	−1.53053	−	0.410104i	−0.923192	+	0.384340i	$0.874429\pi$
$360$	−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	0.993875	−	0.110512i	$-0.0352491\pi$
$367$	7.68648	+	13.3134i	0.401231	+	0.694953i	−0.592644	+	0.805465i	$0.701916\pi$
$368$	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	−0.0160117	+	0.999872i	$0.505097\pi$
$373$	−16.8782	+	29.2339i	−0.873920	+	1.51367i	−0.857909	+	0.513802i	$0.828236\pi$
$374$	−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	0.995239	−	0.0974627i	$-0.0310727\pi$
$379$	1.64709	+	6.14703i	0.0846054	+	0.315752i	−0.910634	+	0.413214i	$0.864406\pi$
$380$		−	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	0.607437	−	0.794368i	$-0.292198\pi$
$383$	29.9559	−	8.02667i	1.53068	−	0.410144i	0.923240	+	0.384224i	$0.125531\pi$
$384$	−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	−0.836821	−	0.547476i	$-0.815589\pi$
$389$	1.09893	−	1.90340i	0.0557178	−	0.0965061i	0.892539	+	0.450970i	$0.148922\pi$
$390$	−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	−0.597641	−	0.801763i	$-0.703895\pi$
$397$	−14.2330	+	3.81371i	−0.714332	+	0.191405i	−0.116691	+	0.993168i	$0.537229\pi$
$398$	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	−0.738456	−	0.674302i	$-0.764445\pi$
$401$	−1.28469	+	1.28469i	−0.0641543	+	0.0641543i	0.674302	+	0.738456i	$0.264445\pi$
$402$	−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	−0.992406	−	0.123003i	$-0.960747\pi$
$409$	−17.5826	+	17.5826i	−0.869403	+	0.869403i	0.123003	+	0.992406i	$0.460747\pi$
$410$	−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	0.912242	−	0.409651i	$-0.134350\pi$
$419$	20.7478	+	11.9787i	1.01359	+	0.585199i	0.101352	+	0.994851i	$0.467683\pi$
$420$	15.0935	+	0.0485262i	0.736488	+	0.00236784i
$421$	−21.1259	+	21.1259i	−1.02961	+	1.02961i	−0.0300645	+	0.999548i	$0.509571\pi$
$421$	−21.1259	+	21.1259i	−1.02961	+	1.02961i	−0.999548	+	0.0300645i	$0.990429\pi$
$422$	−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	−0.684593	−	0.728925i	$-0.740020\pi$
$431$	5.66232	−	21.1321i	0.272744	−	1.01790i	0.957338	−	0.288971i	$-0.0933131\pi$
$432$	5.19610	+	0.0228855i	0.249998	+	0.00110108i
$433$	−9.26511	+	5.34922i	−0.445253	+	0.257067i	−0.705823	−	0.708388i	$-0.749423\pi$
$433$	−9.26511	+	5.34922i	−0.445253	+	0.257067i	0.260570	+	0.965455i	$0.416089\pi$
$434$	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	$-0.631957\pi$
$439$		−	38.3551i		−	1.83059i	0.402783	−	0.915295i	$-0.368043\pi$
$440$	−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	−0.658502	−	0.752579i	$-0.728810\pi$
$443$	−7.07201	+	4.08302i	−0.336001	+	0.193990i	0.322501	+	0.946569i	$0.395476\pi$
$444$	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	0.284905	−	0.958556i	$-0.408038\pi$
$449$	1.10954	+	0.297299i	0.0523622	+	0.0140304i	−0.232543	+	0.972586i	$0.574705\pi$
$450$	−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	−0.698652	−	0.715461i	$-0.746217\pi$
$457$	0.359340	−	0.359340i	0.0168092	−	0.0168092i	0.715461	+	0.698652i	$0.246217\pi$
$458$	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	−0.798680	−	0.601755i	$-0.794468\pi$
$461$	4.16267	−	15.5353i	0.193875	−	0.723551i	0.992555	−	0.121795i	$-0.0388651\pi$
$462$	−14.0279	−	14.1184i	−0.652639	−	0.656849i
$463$	12.3374	+	12.3374i	0.573369	+	0.573369i	0.933068	−	0.359699i	$-0.117121\pi$
$463$	12.3374	+	12.3374i	0.573369	+	0.573369i	−0.359699	+	0.933068i	$0.617121\pi$
$464$	−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	0.962032	+	0.272938i	$0.0879952\pi$
$467$	15.5029	+	26.8517i	0.717387	+	1.24255i	−0.244645	+	0.969613i	$0.578671\pi$
$468$	−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	0.699039	−	0.715083i	$-0.253611\pi$
$479$	20.7236	+	5.55286i	0.946883	+	0.253717i	0.247844	+	0.968800i	$0.420278\pi$
$480$	−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	−0.961439	−	0.275019i	$-0.911316\pi$
$487$	−15.1480	+	15.1480i	−0.686420	+	0.686420i	0.275019	+	0.961439i	$0.411316\pi$
$488$	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	−0.859874	−	0.510507i	$-0.829458\pi$
$491$	0.269785	−	0.467281i	0.0121752	−	0.0210881i	0.872049	+	0.489419i	$0.162791\pi$
$492$	−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	0.679891	−	0.733314i	$-0.262027\pi$
$499$	20.1500	+	5.39917i	0.902036	+	0.241700i	0.222146	+	0.975013i	$0.428694\pi$
$500$	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	0.308161	−	0.951334i	$-0.400286\pi$
$503$	28.8447	−	16.6535i	1.28612	−	0.742542i	0.977960	+	0.208792i	$0.0669532\pi$
$504$	−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	0.235081	−	0.971976i	$-0.424465\pi$
$509$	−16.6251	−	16.6251i	−0.736895	−	0.736895i	−0.971976	+	0.235081i	$0.924465\pi$
$510$	−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	0.913002	−	0.407956i	$-0.133758\pi$
$521$	23.1952	+	13.3918i	1.01620	+	0.586705i	0.103201	+	0.994661i	$0.467092\pi$
$522$	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	−0.807992	−	0.589193i	$-0.799446\pi$
$541$	4.33430	−	16.1758i	0.186346	−	0.695454i	0.994338	−	0.106260i	$-0.0338877\pi$
$542$			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	−0.114420	−	0.993432i	$-0.536501\pi$
$557$	−16.7620	−	4.49136i	−0.710227	−	0.190305i	−0.595807	+	0.803128i	$0.703168\pi$
$558$	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	0.284097	−	0.958796i	$-0.408306\pi$
$571$	−9.65851	−	5.57634i	−0.404196	−	0.233363i	−0.688293	+	0.725433i	$0.741640\pi$
$572$	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	0.906528	−	0.422146i	$-0.138723\pi$
$577$	−2.15277	−	8.03426i	−0.0896211	−	0.334470i	−0.996149	+	0.0876752i	$0.972056\pi$
$578$	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	−0.408701	−	0.912668i	$-0.634018\pi$
$587$	−7.42137	+	1.98855i	−0.306313	+	0.0820762i	0.102389	+	0.994744i	$0.467352\pi$
$588$	−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	−0.262149	−	0.965027i	$-0.584431\pi$
$593$	−23.6622	−	6.34027i	−0.971690	−	0.260364i	−0.709541	+	0.704664i	$0.751098\pi$
$594$	−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	−0.999951	−	0.00985856i	$-0.996862\pi$
$599$	−36.9189	−	21.3151i	−1.50846	−	0.870913i	−0.508513	−	0.861054i	$-0.669805\pi$
$600$	−9.78841	+	2.60740i	−0.399610	+	0.106447i
$601$	15.8340	−	27.4254i	0.645884	−	1.11870i	−0.338213	−	0.941070i	$-0.609822\pi$
$601$	15.8340	−	27.4254i	0.645884	−	1.11870i	0.984097	−	0.177634i	$-0.0568443\pi$
$602$	−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	0.385118	+	0.922867i	$0.374161\pi$
$607$	−14.9467	+	25.8884i	−0.606668	+	1.05078i	−0.991786	+	0.127912i	$0.959172\pi$
$608$	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	0.394444	−	0.918920i	$-0.370937\pi$
$613$	6.84784	+	1.83487i	0.276582	+	0.0741098i	−0.117862	+	0.993030i	$0.537604\pi$
$614$		−	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	−0.926751	−	0.375677i	$-0.877410\pi$
$617$	1.58171	−	5.90302i	0.0636772	−	0.237647i	0.990428	+	0.138030i	$0.0440770\pi$
$618$	−20.7865	−	5.60246i	−0.836157	−	0.225364i
$619$	−17.8860	+	4.79255i	−0.718900	+	0.192629i	−0.599681	−	0.800239i	$-0.704706\pi$
$619$	−17.8860	+	4.79255i	−0.718900	+	0.192629i	−0.119219	+	0.992868i	$0.538039\pi$
$620$			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	0.639176	+	0.769060i	$0.279275\pi$
$631$	−7.50820	+	28.0210i	−0.298897	+	1.11550i	−0.938073	+	0.346438i	$0.887391\pi$
$632$	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	−0.446848	−	0.894610i	$-0.647454\pi$
$643$	−32.4863	−	8.70468i	−1.28114	−	0.343279i	−0.834287	+	0.551331i	$0.814120\pi$
$644$	−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	0.791147	−	0.611626i	$-0.209484\pi$
$647$	−3.41124	−	5.90844i	−0.134110	−	0.232285i	−0.925257	+	0.379341i	$0.876151\pi$
$648$	−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	$-0.776857\pi$
$653$		−	32.9646i		−	1.29000i	0.764181	−	0.645001i	$-0.223143\pi$
$654$	−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	−0.0679673	−	0.997688i	$-0.521651\pi$
$659$	19.5631	−	11.2948i	0.762072	−	0.439982i	0.830039	+	0.557705i	$0.188318\pi$
$660$	21.4390	+	12.4198i	0.834514	+	0.483442i
$661$	−2.91222	+	10.8686i	−0.113272	+	0.422738i	−0.999152	−	0.0411773i	$-0.986889\pi$
$661$	−2.91222	+	10.8686i	−0.113272	+	0.422738i	0.885880	+	0.463915i	$0.153556\pi$
$662$	−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	0.717660	−	0.696393i	$-0.245213\pi$
$673$	12.2810	+	7.09042i	0.473396	+	0.273315i	−0.244264	+	0.969709i	$0.578546\pi$
$674$	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	−0.799965	−	0.600047i	$-0.795148\pi$
$677$	−17.7006	+	10.2195i	−0.680291	+	0.392766i	0.119674	+	0.992813i	$0.461815\pi$
$678$	−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	−0.583046	−	0.812439i	$-0.698139\pi$
$683$	5.99503	−	5.99503i	0.229394	−	0.229394i	0.812439	+	0.583046i	$0.198139\pi$
$684$	−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	−0.595191	−	0.803584i	$-0.702924\pi$
$691$	5.47799	−	5.47799i	0.208392	−	0.208392i	0.803584	+	0.595191i	$0.202924\pi$
$692$	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	−0.0845242	−	0.996421i	$-0.526937\pi$
$709$	9.06615	−	2.42927i	0.340486	−	0.0912331i	0.425011	+	0.905188i	$0.360270\pi$
$710$	−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	−0.984425	−	0.175805i	$-0.943747\pi$
$719$	−9.11577	+	15.7890i	−0.339961	+	0.588829i	0.644464	+	0.764634i	$0.277080\pi$
$720$	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	$-0.987225\pi$
$727$		−	2.16371i		−	0.0802476i	0.999195	−	0.0401238i	$-0.0127752\pi$
$728$	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	0.483050	−	0.875593i	$-0.339529\pi$
$733$	12.5511	+	3.36306i	0.463586	+	0.124218i	−0.0194633	+	0.999811i	$0.506196\pi$
$734$	−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	0.220396	+	0.975410i	$0.429265\pi$
$739$	−12.4554	+	46.4840i	−0.458178	+	1.70994i	−0.678574	+	0.734532i	$0.737402\pi$
$740$	−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	−0.187620	−	0.982242i	$-0.560077\pi$
$743$	3.84387	−	1.02996i	0.141018	−	0.0377857i	0.328638	+	0.944456i	$0.393411\pi$
$744$	−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	$-0.918949\pi$
$751$		−	13.8056i		−	0.503772i	0.967757	−	0.251886i	$-0.0810508\pi$
$752$	−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	−0.997443	−	0.0714701i	$-0.977231\pi$
$757$	−12.0187	+	20.8170i	−0.436826	+	0.756606i	0.560616	+	0.828076i	$0.310564\pi$
$758$	−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	0.890184	−	0.455600i	$-0.150575\pi$
$761$	−2.99416	−	11.1743i	−0.108538	−	0.405070i	−0.998723	+	0.0505307i	$0.983909\pi$
$762$	−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	−0.986486	−	0.163848i	$-0.947609\pi$
$769$	−5.93685	−	22.1566i	−0.214088	−	0.798988i	0.772397	−	0.635140i	$-0.219057\pi$
$770$	−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	0.732120	−	0.681175i	$-0.238531\pi$
$773$	1.41642	+	1.41642i	0.0509449	+	0.0509449i	−0.681175	+	0.732120i	$0.738531\pi$
$774$	−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	0.414106	−	0.910229i	$-0.364094\pi$
$787$	−13.9180	−	13.9180i	−0.496123	−	0.496123i	−0.910229	+	0.414106i	$0.864094\pi$
$788$	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	0.824130	−	0.566401i	$-0.191665\pi$
$797$	−2.21480	−	3.83615i	−0.0784524	−	0.135883i	−0.902582	+	0.430517i	$0.858331\pi$
$798$	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	−0.628317	−	0.777957i	$-0.716256\pi$
$809$	−7.64391	+	4.41322i	−0.268746	+	0.155160i	0.359572	+	0.933117i	$0.382923\pi$
$810$	−25.7584	+	14.6706i	−0.905057	+	0.515472i
$811$	−18.3979	+	18.3979i	−0.646037	+	0.646037i	−0.952033	−	0.305996i	$-0.901011\pi$
$811$	−18.3979	+	18.3979i	−0.646037	+	0.646037i	0.305996	+	0.952033i	$0.401011\pi$
$812$	−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	0.781404	−	0.624025i	$-0.214504\pi$
$821$	4.50941	+	4.50941i	0.157379	+	0.157379i	−0.624025	+	0.781404i	$0.714504\pi$
$822$	4.08848	+	0.00600234i	0.142602	+	0.000209356i
$823$			6.90731i			0.240774i	0.992727	+	0.120387i	$0.0384135\pi$
$823$			6.90731i			0.240774i	−0.992727	+	0.120387i	$0.961586\pi$
$824$	−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	−0.826172	−	0.563418i	$-0.809486\pi$
$827$	−7.55620	+	7.55620i	−0.262755	+	0.262755i	0.563418	+	0.826172i	$0.309486\pi$
$828$	0.0790411	−	26.9193i	0.00274687	−	0.935509i
$829$	−29.0721	+	16.7848i	−1.00972	+	0.582959i	−0.911108	−	0.412167i	$-0.864772\pi$
$829$	−29.0721	+	16.7848i	−1.00972	+	0.582959i	−0.0986071	+	0.995126i	$0.531439\pi$
$830$	−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	0.788667	−	0.614821i	$-0.210772\pi$
$839$	33.7234	+	9.03616i	1.16426	+	0.311963i	0.375595	+	0.926784i	$0.377438\pi$
$840$	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	0.765630	−	0.643282i	$-0.222428\pi$
$853$	3.57332	+	3.57332i	0.122348	+	0.122348i	−0.643282	+	0.765630i	$0.722428\pi$
$854$	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	−0.566141	−	0.824308i	$-0.691564\pi$
$857$	12.6115	−	21.8438i	0.430802	−	0.746170i	0.996943	+	0.0781383i	$0.0248976\pi$
$858$	14.9476	+	22.6320i	0.510303	+	0.772644i
$859$	−24.5656	−	42.5489i	−0.838168	−	1.45175i	−0.891425	−	0.453169i	$-0.850294\pi$
$859$	−24.5656	−	42.5489i	−0.838168	−	1.45175i	0.0532569	−	0.998581i	$-0.483040\pi$
$860$	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	−0.930141	−	0.367202i	$-0.880316\pi$
$863$	1.73281	−	6.46693i	0.0589855	−	0.220137i	0.989127	+	0.147065i	$0.0469826\pi$
$864$	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	−0.981715	−	0.190359i	$-0.939035\pi$
$877$	−6.71366	−	25.0557i	−0.226704	−	0.846071i	0.755010	−	0.655713i	$-0.227632\pi$
$878$	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	−0.866854	−	0.498562i	$-0.833861\pi$
$881$	−0.0492472	+	0.0852986i	−0.00165918	+	0.00287378i	0.865195	+	0.501436i	$0.167195\pi$
$882$	20.2491	+	5.56552i	0.681822	+	0.187401i
$883$		−	28.9269i		−	0.973469i	−0.873550	−	0.486735i	$-0.838188\pi$
$883$		−	28.9269i		−	0.973469i	0.873550	−	0.486735i	$-0.161812\pi$
$884$	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	$-0.927919\pi$
$887$		−	13.3735i		−	0.449038i	0.974470	−	0.224519i	$-0.0720811\pi$
$888$	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	−0.0582963	−	0.998299i	$-0.518567\pi$
$907$	23.4037	−	13.5122i	0.777108	−	0.448664i	0.835404	+	0.549636i	$0.185233\pi$
$908$	−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	$-0.850412\pi$
$911$		−	27.3357i		−	0.905671i	0.891594	−	0.452836i	$-0.149588\pi$
$912$	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	0.145871	+	0.989304i	$0.453402\pi$
$919$	−23.7617	+	41.1565i	−0.783827	+	1.35763i	−0.929697	+	0.368324i	$0.879932\pi$
$920$	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	0.0711918	−	0.997463i	$-0.477320\pi$
$929$	19.2502	−	5.15806i	0.631577	−	0.169231i	0.560385	+	0.828232i	$0.310653\pi$
$930$	−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	−0.238361	−	0.971177i	$-0.576610\pi$
$941$	1.25159	−	0.335362i	0.0408006	−	0.0109325i	0.279162	+	0.960244i	$0.409943\pi$
$942$	−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	−0.308305	−	0.951288i	$-0.599762\pi$
$947$	19.7867	−	19.7867i	0.642983	−	0.642983i	0.951288	+	0.308305i	$0.0997617\pi$
$948$	−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	0.781383	−	0.624051i	$-0.214514\pi$
$953$	−4.62297	−	8.00722i	−0.149753	−	0.259379i	−0.931136	+	0.364672i	$0.881181\pi$
$954$	−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	0.0953471	−	0.995444i	$-0.469604\pi$
$967$	33.9199	−	33.9199i	1.09079	−	1.09079i	0.995444	−	0.0953471i	$-0.0303961\pi$
$968$	−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	0.440412	−	0.897796i	$-0.354832\pi$
$971$	−3.64259	−	2.10305i	−0.116896	−	0.0674901i	−0.557308	+	0.830306i	$0.688166\pi$
$972$	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	−0.888250	−	0.459360i	$-0.848079\pi$
$977$	3.45942	−	12.9107i	0.110677	−	0.413051i	0.998927	+	0.0463082i	$0.0147456\pi$
$978$	−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	−0.839811	−	0.542879i	$-0.817334\pi$
$983$	−12.0380	−	44.9265i	−0.383953	−	1.43293i	0.455858	−	0.890053i	$-0.349333\pi$
$984$	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	−0.974581	−	0.224037i	$-0.928076\pi$
$991$	−21.4478	−	37.1487i	−0.681312	−	1.18007i	0.293268	−	0.956030i	$-0.405257\pi$
$992$	−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.305.20	yes	152
3.2	odd	2	inner	546.2.ch.a.305.12	yes	152
7.2	even	3		546.2.bw.a.149.33	yes	152
13.11	odd	12		546.2.bw.a.11.14	✓	152
21.2	odd	6		546.2.bw.a.149.14	yes	152
39.11	even	12		546.2.bw.a.11.33	yes	152
91.37	odd	12	inner	546.2.ch.a.401.12	yes	152
273.128	even	12	inner	546.2.ch.a.401.20	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.14	✓	152	13.11	odd	12
546.2.bw.a.11.33	yes	152	39.11	even	12
546.2.bw.a.149.14	yes	152	21.2	odd	6
546.2.bw.a.149.33	yes	152	7.2	even	3
546.2.ch.a.305.12	yes	152	3.2	odd	2	inner
546.2.ch.a.305.20	yes	152	1.1	even	1	trivial
546.2.ch.a.401.12	yes	152	91.37	odd	12	inner
546.2.ch.a.401.20	yes	152	273.128	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
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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