LMFDB - Embedded newform 546.2.ch.a.305.12

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			305.12
Character	$\chi$	$=$	546.305
Dual form			546.2.ch.a.401.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.863822 - 1.50127i) q^{3} +1.00000i q^{4} +(0.852470 - 3.18146i) q^{5} +(-1.67237 + 0.450743i) q^{6} +(2.55679 - 0.680305i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.50762 - 2.59366i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.863822 - 1.50127i) q^{3} +1.00000i q^{4} +(0.852470 - 3.18146i) q^{5} +(-1.67237 + 0.450743i) q^{6} +(2.55679 - 0.680305i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.50762 - 2.59366i) q^{9} +(-2.85242 + 1.64685i) q^{10} +(-4.19511 - 1.12408i) q^{11} +(1.50127 + 0.863822i) q^{12} +(-3.59872 + 0.221835i) q^{13} +(-2.28897 - 1.32688i) q^{14} +(-4.03985 - 4.02801i) q^{15} -1.00000 q^{16} +5.29539 q^{17} +(-0.767945 + 2.90004i) q^{18} +(1.57626 + 5.88267i) q^{19} +(3.18146 + 0.852470i) q^{20} +(1.18729 - 4.42610i) q^{21} +(2.17155 + 3.76124i) q^{22} +8.97313 q^{23} +(-0.450743 - 1.67237i) 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} +(0.00837533 + 5.70483i) q^{30} +(-0.298174 - 1.11280i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.31138 + 5.32699i) q^{33} +(-3.74441 - 3.74441i) q^{34} +(0.0152231 - 8.71427i) q^{35} +(2.59366 - 1.50762i) q^{36} +(1.48834 + 1.48834i) q^{37} +(3.04509 - 5.27425i) q^{38} +(-2.77562 + 5.59428i) q^{39} +(-1.64685 - 2.85242i) q^{40} +(-8.93434 + 2.39395i) q^{41} +(-3.96927 + 2.29018i) q^{42} +(-2.42543 + 1.40032i) q^{43} +(1.12408 - 4.19511i) q^{44} +(-9.53683 + 2.58542i) q^{45} +(-6.34496 - 6.34496i) q^{46} +(-4.19035 - 1.12280i) q^{47} +(-0.863822 + 1.50127i) q^{48} +(6.07437 - 3.47880i) q^{49} +(1.51368 + 5.64912i) q^{50} +(4.57428 - 7.94981i) q^{51} +(-0.221835 - 3.59872i) q^{52} +(4.94841 + 2.85697i) q^{53} +(3.69038 + 3.65802i) q^{54} +(-7.15242 + 12.3884i) q^{55} +(1.32688 - 2.28897i) q^{56} +(10.1931 + 2.71519i) q^{57} +(0.704925 + 2.63082i) q^{58} +(0.571327 - 0.571327i) q^{59} +(4.02801 - 4.03985i) q^{60} +(1.18591 - 2.05406i) q^{61} +(-0.576029 + 0.997711i) q^{62} +(-5.61916 - 5.60581i) q^{63} -1.00000i q^{64} +(-2.36204 + 11.6383i) q^{65} +(7.52246 - 0.0110438i) q^{66} +(9.45859 + 2.53442i) q^{67} +5.29539i q^{68} +(7.75119 - 13.4711i) q^{69} +(-6.17269 + 6.15116i) q^{70} +(2.23789 - 8.35193i) q^{71} +(-2.90004 - 0.767945i) 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} +(5.91841 - 1.99309i) q^{78} +(-0.257500 - 0.446002i) q^{79} +(-0.852470 + 3.18146i) q^{80} +(-4.45415 + 7.82052i) q^{81} +(8.01031 + 4.62476i) q^{82} +(-4.56024 - 4.56024i) q^{83} +(4.42610 + 1.18729i) 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} +(-1.92819 - 0.513623i) q^{93} +(2.16909 + 3.75697i) q^{94} +20.0592 q^{95} +(1.67237 - 0.450743i) q^{96} +(2.82483 + 0.756910i) q^{97} +(-6.75511 - 1.83535i) q^{98} +(3.40917 + 12.5754i) 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
$3$	0.863822	−	1.50127i	0.498728	−	0.866759i
$3$	0.863822	−	1.50127i	0.498728	−	0.866759i
$4$			1.00000i			0.500000i
$5$	0.852470	−	3.18146i	0.381236	−	1.42279i	−0.462779	−	0.886474i	$-0.653148\pi$
$5$	0.852470	−	3.18146i	0.381236	−	1.42279i	0.844015	−	0.536319i	$-0.180186\pi$
$6$	−1.67237	+	0.450743i	−0.682743	+	0.184015i
$7$	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
$9$	−1.50762	−	2.59366i	−0.502541	−	0.864554i
$10$	−2.85242	+	1.64685i	−0.902015	+	0.520778i
$11$	−4.19511	−	1.12408i	−1.26487	−	0.338922i	−0.436809	−	0.899554i	$-0.643892\pi$
$11$	−4.19511	−	1.12408i	−1.26487	−	0.338922i	−0.828065	+	0.560632i	$0.810558\pi$
$12$	1.50127	+	0.863822i	0.433379	+	0.249364i
$13$	−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
$15$	−4.03985	−	4.02801i	−1.04308	−	1.04003i
$16$	−1.00000			−0.250000
$17$	5.29539			1.28432			0.642161	−	0.766570i	$-0.278038\pi$
$17$	5.29539			1.28432			0.642161	+	0.766570i	$0.278038\pi$
$18$	−0.767945	+	2.90004i	−0.181006	+	0.683547i
$19$	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
$21$	1.18729	−	4.42610i	0.259088	−	0.965854i
$22$	2.17155	+	3.76124i	0.462976	+	0.801898i
$23$	8.97313			1.87103			0.935513	−	0.353292i	$-0.114938\pi$
$23$	8.97313			1.87103			0.935513	+	0.353292i	$0.114938\pi$
$24$	−0.450743	−	1.67237i	−0.0920076	−	0.341372i
$25$	−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	$-0.414712\pi$
$29$	−2.35873	−	1.36181i	−0.438004	−	0.252882i	−0.702751	+	0.711436i	$0.748045\pi$
$30$	0.00837533	+	5.70483i	0.00152912	+	1.04156i
$31$	−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
$33$	−5.31138	+	5.32699i	−0.924592	+	0.927311i
$34$	−3.74441	−	3.74441i	−0.642161	−	0.642161i
$35$	0.0152231	−	8.71427i	0.00257318	−	1.47298i
$36$	2.59366	−	1.50762i	0.432277	−	0.251270i
$37$	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
$39$	−2.77562	+	5.59428i	−0.444455	+	0.895801i
$40$	−1.64685	−	2.85242i	−0.260389	−	0.451007i
$41$	−8.93434	+	2.39395i	−1.39531	+	0.373872i	−0.876658	−	0.481113i	$-0.840233\pi$
$41$	−8.93434	+	2.39395i	−1.39531	+	0.373872i	−0.518652	+	0.854986i	$0.673566\pi$
$42$	−3.96927	+	2.29018i	−0.612471	+	0.353383i
$43$	−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
$45$	−9.53683	+	2.58542i	−1.42167	+	0.385412i
$46$	−6.34496	−	6.34496i	−0.935513	−	0.935513i
$47$	−4.19035	−	1.12280i	−0.611226	−	0.163778i	−0.0600900	−	0.998193i	$-0.519139\pi$
$47$	−4.19035	−	1.12280i	−0.611226	−	0.163778i	−0.551136	+	0.834415i	$0.685805\pi$
$48$	−0.863822	+	1.50127i	−0.124682	+	0.216690i
$49$	6.07437	−	3.47880i	0.867767	−	0.496971i
$50$	1.51368	+	5.64912i	0.214066	+	0.798907i
$51$	4.57428	−	7.94981i	0.640527	−	1.11320i
$52$	−0.221835	−	3.59872i	−0.0307630	−	0.499053i
$53$	4.94841	+	2.85697i	0.679717	+	0.392435i	0.799748	−	0.600335i	$-0.204966\pi$
$53$	4.94841	+	2.85697i	0.679717	+	0.392435i	−0.120032	+	0.992770i	$0.538300\pi$
$54$	3.69038	+	3.65802i	0.502197	+	0.497793i
$55$	−7.15242	+	12.3884i	−0.964432	+	1.67044i
$56$	1.32688	−	2.28897i	0.177311	−	0.305877i
$57$	10.1931	+	2.71519i	1.35011	+	0.359636i
$58$	0.704925	+	2.63082i	0.0925612	+	0.345443i
$59$	0.571327	−	0.571327i	0.0743805	−	0.0743805i	−0.668938	−	0.743318i	$-0.733251\pi$
$59$	0.571327	−	0.571327i	0.0743805	−	0.0743805i	0.743318	+	0.668938i	$0.233251\pi$
$60$	4.02801	−	4.03985i	0.520013	−	0.521542i
$61$	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
$63$	−5.61916	−	5.60581i	−0.707947	−	0.706265i
$64$		−	1.00000i		−	0.125000i
$65$	−2.36204	+	11.6383i	−0.292975	+	1.44355i
$66$	7.52246	−	0.0110438i	0.925951	−	0.00135940i
$67$	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
$69$	7.75119	−	13.4711i	0.933133	−	1.62173i
$70$	−6.17269	+	6.15116i	−0.737777	+	0.735204i
$71$	2.23789	−	8.35193i	0.265589	−	0.991192i	−0.696300	−	0.717751i	$-0.745171\pi$
$71$	2.23789	−	8.35193i	0.265589	−	0.991192i	0.961889	−	0.273441i	$-0.0881618\pi$
$72$	−2.90004	−	0.767945i	−0.341774	−	0.0905032i
$73$	−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
$78$	5.91841	−	1.99309i	0.670128	−	0.225673i
$79$	−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
$81$	−4.45415	+	7.82052i	−0.494906	+	0.868947i
$82$	8.01031	+	4.62476i	0.884591	+	0.510719i
$83$	−4.56024	−	4.56024i	−0.500551	−	0.500551i	0.411058	−	0.911609i	$-0.365159\pi$
$83$	−4.56024	−	4.56024i	−0.500551	−	0.500551i	−0.911609	+	0.411058i	$0.865159\pi$
$84$	4.42610	+	1.18729i	0.482927	+	0.129544i
$85$	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	$-0.712628\pi$
$89$	1.56283	−	1.56283i	0.165660	−	0.165660i	0.785069	+	0.619409i	$0.212628\pi$
$90$	8.57173	+	4.91539i	0.903540	+	0.518128i
$91$	−9.05026	+	3.01542i	−0.948725	+	0.316101i
$92$			8.97313i			0.935513i
$93$	−1.92819	−	0.513623i	−0.199943	−	0.0532602i
$94$	2.16909	+	3.75697i	0.223724	+	0.387502i
$95$	20.0592			2.05803
$96$	1.67237	−	0.450743i	0.170686	−	0.0460038i
$97$	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
$99$	3.40917	+	12.5754i	0.342635	+	1.26387i
$100$	2.92420	−	5.06487i	0.292420	−	0.506487i
$101$	4.83780	+	8.37932i	0.481379	+	0.833774i	0.999772	−	0.0213693i	$-0.00680258\pi$
$101$	4.83780	+	8.37932i	0.481379	+	0.833774i	−0.518392	+	0.855143i	$0.673469\pi$
$102$	−8.85587	+	2.38686i	−0.876862	+	0.236335i
$103$	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
$105$	−13.0693	−	7.55044i	−1.27544	−	0.736847i
$106$	−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	0.892377	−	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
$111$	3.52005	−	0.948736i	0.334108	−	0.0900500i
$112$	−2.55679	+	0.680305i	−0.241594	+	0.0642828i
$113$	−2.49592	+	1.44102i	−0.234797	+	0.135560i	−0.612783	−	0.790251i	$-0.709950\pi$
$113$	−2.49592	+	1.44102i	−0.234797	+	0.135560i	0.377986	+	0.925811i	$0.376617\pi$
$114$	−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
$117$	6.00088	+	8.99942i	0.554781	+	0.831996i
$118$	−0.807979			−0.0743805
$119$	13.5392	−	3.60248i	1.24114	−	0.330239i
$120$	−5.70483	+	0.00837533i	−0.520778	+	0.000764560i
$121$	6.80915	+	3.93126i	0.619014	+	0.357388i
$122$	−2.29100	+	0.613873i	−0.207418	+	0.0555774i
$123$	−4.12372	+	15.4808i	−0.371823	+	1.39586i
$124$	1.11280	−	0.298174i	0.0999325	−	0.0267768i
$125$	−1.97592	+	1.97592i	−0.176732	+	0.176732i
$126$	0.00943979	+	7.93725i	0.000840963	+	0.707106i
$127$	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
$129$	0.00712159	+	4.85085i	0.000627021	+	0.427094i
$130$	9.89974	−	6.55930i	0.868264	−	0.575289i
$131$	4.69605	−	2.71126i	0.410295	−	0.236884i	−0.280621	−	0.959819i	$-0.590540\pi$
$131$	4.69605	−	2.71126i	0.410295	−	0.236884i	0.690917	+	0.722934i	$0.257207\pi$
$132$	−5.32699	−	5.31138i	−0.463655	−	0.462296i
$133$	8.03217	+	13.9684i	0.696477	+	1.21122i
$134$	−4.89613	−	8.48034i	−0.422961	−	0.732590i
$135$	−4.35671	+	16.5507i	−0.374966	+	1.42446i
$136$	3.74441	−	3.74441i	0.321080	−	0.321080i
$137$	1.66912	−	1.66912i	0.142602	−	0.142602i	−0.632202	−	0.774804i	$-0.717849\pi$
$137$	1.66912	−	1.66912i	0.142602	−	0.142602i	0.774804	+	0.632202i	$0.217849\pi$
$138$	−15.0064	+	4.04458i	−1.27743	+	0.344297i
$139$	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
$141$	−5.30535	+	5.32095i	−0.446791	+	0.448105i
$142$	−7.48814	+	4.32328i	−0.628391	+	0.362802i
$143$	15.3464	+	3.11462i	1.28333	+	0.260457i
$144$	1.50762	+	2.59366i	0.125635	+	0.216138i
$145$	−6.34329	+	6.34329i	−0.526782	+	0.526782i
$146$	1.30809	+	0.755228i	0.108259	+	0.0625031i
$147$	0.0245606	−	12.1243i	0.00202573	−	0.999998i
$148$	−1.48834	+	1.48834i	−0.122340	+	0.122340i
$149$	−18.3242	+	4.90995i	−1.50118	+	0.402239i	−0.913493	−	0.406853i	$-0.866626\pi$
$149$	−18.3242	+	4.90995i	−1.50118	+	0.402239i	−0.587682	+	0.809092i	$0.699959\pi$
$150$	9.78841	+	2.60740i	0.799220	+	0.212893i
$151$	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
$153$	−7.98345	−	13.7345i	−0.645424	−	1.11036i
$154$	8.11099	+	8.13938i	0.653602	+	0.655890i
$155$	−3.79452			−0.304783
$156$	−5.59428	−	2.77562i	−0.447901	−	0.222228i
$157$	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
$162$	8.67950	−	2.38038i	0.681926	−	0.187020i
$163$	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	0.889576	−	0.456788i	$-0.151000\pi$
$167$	−1.41135	−	5.26722i	−0.109213	−	0.407590i	−0.998789	+	0.0491979i	$0.984334\pi$
$168$	−2.29018	−	3.96927i	−0.176691	−	0.306235i
$169$	12.9016	−	1.59665i	0.992429	−	0.122819i
$170$	−15.1047	+	8.72070i	−1.15848	+	0.668847i
$171$	12.8812	−	12.9571i	0.985053	−	0.990855i
$172$	−1.40032	−	2.42543i	−0.106774	−	0.184937i
$173$	−6.88988	+	11.9336i	−0.523828	+	0.907297i	0.475787	+	0.879560i	$0.342163\pi$
$173$	−6.88988	+	11.9336i	−0.523828	+	0.907297i	−0.999615	+	0.0277364i	$0.991170\pi$
$174$	4.55850	+	1.21428i	0.345579	+	0.0920540i
$175$	−14.9392	−	4.03092i	−1.12929	−	0.304709i
$176$	4.19511	+	1.12408i	0.316219	+	0.0847305i
$177$	−0.364191	−	1.35124i	−0.0273743	−	0.101566i
$178$	−2.21018			−0.165660
$179$	−4.44678	−	7.70206i	−0.332368	−	0.575679i	0.650607	−	0.759414i	$-0.274514\pi$
$179$	−4.44678	−	7.70206i	−0.332368	−	0.575679i	−0.982976	+	0.183736i	$0.941181\pi$
$180$	−2.58542	−	9.53683i	−0.192706	−	0.710834i
$181$			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
$189$	−13.2698	+	3.59345i	−0.965235	+	0.261385i
$190$	−14.1840	−	14.1840i	−1.02901	−	1.02901i
$191$	13.9580	+	8.05867i	1.00997	+	0.583105i	0.911182	−	0.412004i	$-0.135171\pi$
$191$	13.9580	+	8.05867i	1.00997	+	0.583105i	0.0987856	+	0.995109i	$0.468504\pi$
$192$	−1.50127	−	0.863822i	−0.108345	−	0.0623410i
$193$	−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
$195$	15.4318	+	13.5995i	1.10510	+	0.973879i
$196$	3.47880	+	6.07437i	0.248486	+	0.433884i
$197$	−24.8603	+	6.66131i	−1.77123	+	0.474598i	−0.988939	−	0.148321i	$-0.952613\pi$
$197$	−24.8603	+	6.66131i	−1.77123	+	0.474598i	−0.782286	+	0.622919i	$0.785947\pi$
$198$	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
$201$	11.9754	−	12.0106i	0.844679	−	0.847163i
$202$	2.50423	−	9.34592i	0.176197	−	0.657577i
$203$	−6.95722	−	1.87721i	−0.488301	−	0.131755i
$204$	7.94981	+	4.57428i	0.556598	+	0.320264i
$205$			30.4650i			2.12777i
$206$	−12.0059	−	3.21696i	−0.836487	−	0.224136i
$207$	−13.5281	−	23.2732i	−0.940267	−	1.61760i
$208$	3.59872	−	0.221835i	0.249526	−	0.0153815i
$209$		−	26.4503i		−	1.82960i
$210$	3.90244	+	14.5804i	0.269294	+	1.00614i
$211$	−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
$213$	−10.6054	−	10.5743i	−0.726668	−	0.724537i
$214$	−5.22799	+	5.22799i	−0.357378	+	0.357378i
$215$	2.38747	+	8.91014i	0.162824	+	0.607667i
$216$	−3.65802	+	3.69038i	−0.248896	+	0.251099i
$217$	−1.51941	−	2.64235i	−0.103145	−	0.179375i
$218$	−2.13973	+	3.70611i	−0.144921	+	0.251010i
$219$	−0.673408	+	2.52803i	−0.0455047	+	0.170829i
$220$	−12.3884	−	7.15242i	−0.835222	−	0.482216i
$221$	−19.0566	+	1.17470i	−1.28189	+	0.0790192i
$222$	−3.15991	−	1.81819i	−0.212079	−	0.122029i
$223$	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
$225$	0.0515165	+	17.5451i	0.00343444	+	1.16968i
$226$	2.78384	+	0.745928i	0.185178	+	0.0496184i
$227$	−16.8243	−	16.8243i	−1.11667	−	1.11667i	−0.992227	−	0.124442i	$-0.960286\pi$
$227$	−16.8243	−	16.8243i	−1.11667	−	1.11667i	−0.124442	−	0.992227i	$-0.539714\pi$
$228$	−2.71519	+	10.1931i	−0.179818	+	0.675053i
$229$	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
$231$	−9.95610	+	17.2334i	−0.655063	+	1.13387i
$232$	−2.63082	+	0.704925i	−0.172722	+	0.0462806i
$233$	14.1393	+	24.4900i	0.926298	+	1.60440i	0.789460	+	0.613802i	$0.210361\pi$
$233$	14.1393	+	24.4900i	0.926298	+	1.60440i	0.136838	+	0.990593i	$0.456306\pi$
$234$	2.12029	−	10.6068i	0.138608	−	0.693389i
$235$	−7.14430	+	12.3743i	−0.466043	+	0.807210i
$236$	0.571327	+	0.571327i	0.0371902	+	0.0371902i
$237$	−0.892004	+	0.00130956i	−0.0579419	+	8.50651e-5i
$238$	−12.1210	−	7.02633i	−0.785689	−	0.455449i
$239$	12.9200	+	12.9200i	0.835723	+	0.835723i	0.988293	−	0.152569i	$-0.0487548\pi$
$239$	12.9200	+	12.9200i	0.835723	+	0.835723i	−0.152569	+	0.988293i	$0.548755\pi$
$240$	4.03985	+	4.02801i	0.260771	+	0.260007i
$241$	−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
$243$	7.89312	+	13.4424i	0.506344	+	0.862332i
$244$	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
$249$	−10.7854	+	2.90691i	−0.683496	+	0.184218i
$250$	2.79438			0.176732
$251$	7.38589	+	12.7927i	0.466193	+	0.807471i	0.999255	−	0.0386062i	$-0.0122918\pi$
$251$	7.38589	+	12.7927i	0.466193	+	0.807471i	−0.533061	+	0.846077i	$0.678958\pi$
$252$	5.60581	−	5.61916i	0.353133	−	0.353974i
$253$	−37.6433	−	10.0865i	−2.36661	−	0.634132i
$254$	−2.45919	−	9.17783i	−0.154303	−	0.575868i
$255$	−21.3926	−	21.3299i	−1.33966	−	1.33573i
$256$	1.00000			0.0625000
$257$	−12.6694			−0.790293			−0.395147	−	0.918618i	$-0.629306\pi$
$257$	−12.6694			−0.790293			−0.395147	+	0.918618i	$0.629306\pi$
$258$	3.42504	−	3.43511i	0.213233	−	0.213860i
$259$	4.81789	+	2.79284i	0.299369	+	0.173539i
$260$	−11.6383	−	2.36204i	−0.721777	−	0.146488i
$261$	0.0239914	+	8.17083i	0.00148503	+	0.505762i
$262$	−5.23776	−	1.40345i	−0.323590	−	0.0867056i
$263$	0.824649	−	0.476112i	0.0508501	−	0.0293583i	−0.474359	−	0.880331i	$-0.657320\pi$
$263$	0.824649	−	0.476112i	0.0508501	−	0.0293583i	0.525210	+	0.850973i	$0.323987\pi$
$264$	0.0110438	+	7.52246i	0.000679700	+	0.462976i
$265$	13.3077	−	13.3077i	0.817486	−	0.817486i
$266$	4.19756	−	15.5568i	0.257369	−	0.953846i
$267$	−0.996222	−	3.69624i	−0.0609678	−	0.226206i
$268$	−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	$0.749510\pi$
$270$	14.7838	−	8.62246i	0.899712	−	0.524746i
$271$	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
$273$	−3.29087	+	16.1917i	−0.199172	+	0.979964i
$274$	−2.36049			−0.142602
$275$	17.9607	+	17.9607i	1.08307	+	1.08307i
$276$	13.4711	+	7.75119i	0.810864	+	0.466567i
$277$		−	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
$279$	−2.43670	+	2.45105i	−0.145881	+	0.146740i
$280$	−6.15116	−	6.17269i	−0.367602	−	0.368889i
$281$	17.4575	−	17.4575i	1.04142	−	1.04142i	0.0423209	−	0.999104i	$-0.486525\pi$
$281$	17.4575	−	17.4575i	1.04142	−	1.04142i	0.999104	−	0.0423209i	$-0.0134752\pi$
$282$	7.51393	−	0.0110313i	0.447448	−	0.000656904i
$283$	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
$285$	17.3276	−	30.1143i	1.02640	−	1.78381i
$286$	−8.64918	−	13.0539i	−0.511437	−	0.771894i
$287$	−21.2146	+	12.1989i	−1.25226	+	0.720079i
$288$	0.767945	−	2.90004i	0.0452516	−	0.170887i
$289$	11.0412			0.649482
$290$	8.97077			0.526782
$291$	3.57647	−	3.58699i	0.209657	−	0.210273i
$292$	−0.390935	−	1.45899i	−0.0228777	−	0.0853809i
$293$	0.721061	+	0.193208i	0.0421248	+	0.0112873i	0.279820	−	0.960053i	$-0.409725\pi$
$293$	0.721061	+	0.193208i	0.0421248	+	0.0112873i	−0.237695	+	0.971340i	$0.576392\pi$
$294$	−8.59056	+	8.55583i	−0.501012	+	0.498986i
$295$	−1.33062	−	2.30469i	−0.0774715	−	0.134185i
$296$	2.10482			0.122340
$297$	21.8240	+	5.74481i	1.26635	+	0.333348i
$298$	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
$303$	16.7586	−	0.0246035i	0.962758	−	0.00141344i
$304$	−1.57626	−	5.88267i	−0.0904045	−	0.337394i
$305$	−5.52396	−	5.52396i	−0.316301	−	0.316301i
$306$	−4.06657	+	15.3569i	−0.232470	+	0.877894i
$307$	−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
$309$	−0.0316059	−	21.5283i	−0.00179800	−	1.22470i
$310$	2.68313	+	2.68313i	0.152392	+	0.152392i
$311$	−6.23904	+	10.8063i	−0.353784	+	0.612771i	−0.986909	−	0.161278i	$-0.948438\pi$
$311$	−6.23904	+	10.8063i	−0.353784	+	0.612771i	0.633125	+	0.774049i	$0.281772\pi$
$312$	1.99309	+	5.91841i	0.112837	+	0.335064i
$313$	−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
$315$	−22.6248	+	13.0983i	−1.27476	+	0.738008i
$316$	0.446002	−	0.257500i	0.0250896	−	0.0144855i
$317$	2.84872	−	10.6316i	0.160000	−	0.597128i	−0.838625	−	0.544709i	$-0.816640\pi$
$317$	2.84872	−	10.6316i	0.160000	−	0.597128i	0.998625	−	0.0524189i	$-0.0166931\pi$
$318$	−9.56335	−	2.54745i	−0.536286	−	0.142854i
$319$	8.36434	+	8.36434i	0.468313	+	0.468313i
$320$	−3.18146	−	0.852470i	−0.177849	−	0.0476545i
$321$	−11.0996	−	6.38667i	−0.619521	−	0.356469i
$322$	−20.5392	−	11.9062i	−1.14461	−	0.663508i
$323$	8.34689	+	31.1510i	0.464434	+	1.73329i
$324$	−7.82052	−	4.45415i	−0.434473	−	0.247453i
$325$	18.8757	+	9.39982i	1.04704	+	0.521408i
$326$	−21.9517	−	12.6738i	−1.21579	−	0.701936i
$327$	−7.16247	−	1.90791i	−0.396085	−	0.105508i
$328$	−4.62476	+	8.01031i	−0.255359	+	0.442296i
$329$	−11.4777	−	0.0200507i	−0.632787	−	0.00110543i
$330$	6.37754	−	23.9418i	0.351072	−	1.31796i
$331$	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
$333$	1.61639	−	6.10408i	0.0885776	−	0.334502i
$334$	−2.72652	+	4.72246i	−0.149188	+	0.258402i
$335$	16.1263	−	27.9316i	0.881076	−	1.52607i
$336$	−1.18729	+	4.42610i	−0.0647721	+	0.241463i
$337$		−	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
$339$	0.00732858	+	4.99184i	0.000398034	+	0.271120i
$340$	16.8471	+	4.51416i	0.913662	+	0.244815i
$341$			5.00350i			0.270955i
$342$	−18.2705	+	0.0536463i	−0.987954	+	0.00290086i
$343$	13.1643	−	13.0270i	0.710803	−	0.703391i
$344$	−0.724860	+	2.70522i	−0.0390818	+	0.145855i
$345$	−36.2501	−	36.1438i	−1.95164	−	1.94592i
$346$	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	−0.837779	−	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
$351$	18.6942	−	1.23504i	0.997825	−	0.0659214i
$352$	−2.17155	−	3.76124i	−0.115744	−	0.200475i
$353$	−0.159758	+	0.596226i	−0.00850308	+	0.0317339i	−0.970047	−	0.242917i	$-0.921896\pi$
$353$	−0.159758	+	0.596226i	−0.00850308	+	0.0317339i	0.961544	+	0.274651i	$0.0885623\pi$
$354$	−0.697950	+	1.21299i	−0.0370956	+	0.0644699i
$355$	−24.6636	−	14.2395i	−1.30901	−	0.755757i
$356$	1.56283	+	1.56283i	0.0828298	+	0.0828298i
$357$	6.28718	−	23.4379i	0.332753	−	1.24047i
$358$	−2.30182	+	8.59053i	−0.121655	+	0.454023i
$359$	28.9994	+	7.77036i	1.53053	+	0.410104i	0.923192	−	0.384340i	$-0.125571\pi$
$359$	28.9994	+	7.77036i	1.53053	+	0.410104i	0.607338	+	0.794444i	$0.292237\pi$
$360$	−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
$366$	−1.05743	+	3.96969i	−0.0552729	+	0.207499i
$367$	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
$369$	19.6787	+	19.5635i	1.02443	+	1.01843i
$370$	−6.69642	−	1.79430i	−0.348130	−	0.0932812i
$371$	14.5957	+	3.93824i	0.757770	+	0.204463i
$372$	0.513623	−	1.92819i	0.0266301	−	0.0999717i
$373$	−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
$375$	1.25955	+	4.67324i	0.0650427	+	0.241325i
$376$	−3.75697	+	2.16909i	−0.193751	+	0.111862i
$377$	8.79049	+	4.37753i	0.452733	+	0.225454i
$378$	11.9241	+	6.84220i	0.613310	+	0.351925i
$379$	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	−0.923240	−	0.384224i	$-0.874469\pi$
$383$	−29.9559	+	8.02667i	−1.53068	+	0.410144i	−0.607437	+	0.794368i	$0.707802\pi$
$384$	0.450743	+	1.67237i	0.0230019	+	0.0853429i
$385$	−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	$-0.851078\pi$
$389$	−1.09893	+	1.90340i	−0.0557178	+	0.0965061i	0.836821	+	0.547476i	$0.184411\pi$
$390$	−1.29567	−	20.5282i	−0.0656090	−	1.03949i
$391$	47.5162			2.40300
$392$	1.83535	−	6.75511i	0.0926990	−	0.341185i
$393$	−0.0137886	−	9.39208i	−0.000695544	−	0.473768i
$394$	22.2892	+	12.8687i	1.12291	+	0.648314i
$395$	−1.63845	+	0.439021i	−0.0824394	+	0.0220896i
$396$	−12.5754	+	3.40917i	−0.631937	+	0.171317i
$397$	−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
$399$	27.9087	+	0.00778119i	1.39718	+	0.000389547i
$400$	5.06487	+	2.92420i	0.253243	+	0.146210i
$401$	1.28469	−	1.28469i	0.0641543	−	0.0641543i	−0.674302	−	0.738456i	$-0.735555\pi$
$401$	1.28469	−	1.28469i	0.0641543	−	0.0641543i	0.738456	+	0.674302i	$0.235555\pi$
$402$	−16.9607	+	0.0249002i	−0.845921	+	0.00124191i
$403$	1.31990	+	3.93852i	0.0657491	+	0.196191i
$404$	−8.37932	+	4.83780i	−0.416887	+	0.240690i
$405$	21.0837	+	20.8375i	1.04766	+	1.03542i
$406$	3.59211	+	6.24689i	0.178273	+	0.310028i
$407$	−4.57073	−	7.91674i	−0.226563	−	0.392418i
$408$	−2.38686	−	8.85587i	−0.118167	−	0.438431i
$409$	−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
$411$	−1.06397	−	3.94761i	−0.0524819	−	0.194721i
$412$	6.21469	+	10.7642i	0.306176	+	0.530312i
$413$	1.07209	−	1.84944i	0.0527540	−	0.0910051i
$414$	−6.89087	+	26.0225i	−0.338668	+	1.27893i
$415$	−18.3957	+	10.6208i	−0.903009	+	0.521352i
$416$	−2.70154	−	2.38782i	−0.132454	−	0.117072i
$417$	24.2311	−	0.0355740i	1.18660	−	0.00174206i
$418$	−18.7032	+	18.7032i	−0.914802	+	0.914802i
$419$	−20.7478	−	11.9787i	−1.01359	−	0.585199i	−0.101352	−	0.994851i	$-0.532317\pi$
$419$	−20.7478	−	11.9787i	−1.01359	−	0.585199i	−0.912242	+	0.409651i	$0.865650\pi$
$420$	7.55044	−	13.0693i	0.368424	−	0.637718i
$421$	−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
$423$	3.40530	+	12.5611i	0.165571	+	0.610742i
$424$	5.51924	−	1.47888i	0.268038	−	0.0718205i
$425$	−26.8205	−	15.4848i	−1.30098	−	0.751123i
$426$	0.0219868	+	14.9763i	0.00106527	+	0.725602i
$427$	1.63474	−	6.05858i	0.0791107	−	0.293195i
$428$	7.39350			0.357378
$429$	17.9324	−	20.3486i	0.865787	−	0.982440i
$430$	4.61223	−	7.98862i	0.222421	−	0.385245i
$431$	−5.66232	+	21.1321i	−0.272744	+	1.01790i	0.684593	+	0.728925i	$0.259980\pi$
$431$	−5.66232	+	21.1321i	−0.272744	+	1.01790i	−0.957338	+	0.288971i	$0.906687\pi$
$432$	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
$435$	4.04352	+	15.0025i	0.193872	+	0.719314i
$436$	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
$441$	−18.1807	−	10.5101i	−0.865746	−	0.500483i
$442$	14.3057	+	12.6444i	0.680454	+	0.601435i
$443$	7.07201	−	4.08302i	0.336001	−	0.193990i	−0.322501	−	0.946569i	$-0.604524\pi$
$443$	7.07201	−	4.08302i	0.336001	−	0.193990i	0.658502	+	0.752579i	$0.271190\pi$
$444$	0.948736	+	3.52005i	0.0450250	+	0.167054i
$445$	−3.63982	−	6.30435i	−0.172544	−	0.298855i
$446$	4.22614	−	7.31989i	0.200113	−	0.346607i
$447$	−8.45768	+	31.7509i	−0.400034	+	1.50176i
$448$	−0.680305	−	2.55679i	−0.0321414	−	0.120797i
$449$	−1.10954	−	0.297299i	−0.0523622	−	0.0140304i	0.232543	−	0.972586i	$-0.425295\pi$
$449$	−1.10954	−	0.297299i	−0.0523622	−	0.0140304i	−0.284905	+	0.958556i	$0.591962\pi$
$450$	12.3699	−	12.4427i	0.583121	−	0.586555i
$451$	40.1716			1.89161
$452$	−1.44102	−	2.49592i	−0.0677800	−	0.117398i
$453$	1.21632	−	4.56617i	0.0571476	−	0.214537i
$454$			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	$0.205532\pi$
$461$	−4.16267	+	15.5353i	−0.193875	+	0.723551i	−0.992555	+	0.121795i	$0.961135\pi$
$462$	19.2259	−	5.14581i	0.894468	−	0.239405i
$463$	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
$465$	−3.27779	+	5.69660i	−0.152004	+	0.264173i
$466$	7.31905	−	27.3151i	0.339049	−	1.26535i
$467$	−15.5029	−	26.8517i	−0.717387	−	1.24255i	−0.962032	−	0.272938i	$-0.912005\pi$
$467$	−15.5029	−	26.8517i	−0.717387	−	1.24255i	0.244645	−	0.969613i	$-0.421329\pi$
$468$	−8.99942	+	6.00088i	−0.415998	+	0.277391i
$469$	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
$474$	0.631668	+	0.629816i	0.0290135	+	0.0289284i
$475$	9.21858	−	34.4042i	0.422977	−	1.57857i
$476$	3.60248	+	13.5392i	0.165120	+	0.620569i
$477$	−0.0503321	−	17.1417i	−0.00230455	−	0.784866i
$478$		−	18.2716i		−	0.835723i
$479$	−20.7236	−	5.55286i	−0.946883	−	0.253717i	−0.247844	−	0.968800i	$-0.579722\pi$
$479$	−20.7236	−	5.55286i	−0.946883	−	0.253717i	−0.699039	+	0.715083i	$0.746389\pi$
$480$	−0.00837533	−	5.70483i	−0.000382280	−	0.260389i
$481$	−5.68627	−	5.02594i	−0.259271	−	0.229163i
$482$			17.5173i			0.797893i
$483$	10.6537	−	39.7159i	0.484761	−	1.80714i
$484$	−3.93126	+	6.80915i	−0.178694	+	0.309507i
$485$	4.81616	−	8.34183i	0.218690	−	0.378783i
$486$	3.92395	−	15.0865i	0.177994	−	0.684338i
$487$	−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
$489$	11.3007	−	42.4240i	0.511037	−	1.91848i
$490$	−11.5976	+	19.9265i	−0.523927	+	0.900190i
$491$	−0.269785	+	0.467281i	−0.0121752	+	0.0210881i	−0.872049	−	0.489419i	$-0.837209\pi$
$491$	−0.269785	+	0.467281i	−0.0121752	+	0.0210881i	0.859874	+	0.510507i	$0.170542\pi$
$492$	−15.4808	−	4.12372i	−0.697929	−	0.185912i
$493$	−12.4904	−	7.21133i	−0.562539	−	0.324782i
$494$	−9.78842	+	19.6561i	−0.440402	+	0.884369i
$495$	42.9143	−	0.126006i	1.92886	−	0.00566356i
$496$	0.298174	+	1.11280i	0.0133884	+	0.0499663i
$497$	0.0399636	−	22.8766i	0.00179261	−	1.02616i
$498$	9.68192	+	5.57092i	0.433857	+	0.249639i
$499$	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
$501$	−9.12668	−	2.43113i	−0.407750	−	0.108615i
$502$	3.82322	−	14.2684i	0.170639	−	0.636832i
$503$	−28.8447	+	16.6535i	−1.28612	+	0.742542i	−0.977960	−	0.208792i	$-0.933047\pi$
$503$	−28.8447	+	16.6535i	−1.28612	+	0.742542i	−0.308161	+	0.951334i	$0.599714\pi$
$504$	−7.93725	+	0.00943979i	−0.353553	+	0.000420482i
$505$	30.7826	−	8.24817i	1.36981	−	0.367039i
$506$	19.4856	+	33.7500i	0.866241	+	1.50037i
$507$	8.74768	−	20.7480i	0.388498	−	0.921450i
$508$	−4.75079	+	8.22861i	−0.210782	+	0.365086i
$509$	16.6251	+	16.6251i	0.736895	+	0.736895i	0.971976	−	0.235081i	$-0.0755354\pi$
$509$	16.6251	+	16.6251i	0.736895	+	0.736895i	−0.235081	+	0.971976i	$0.575535\pi$
$510$	0.0443507	+	30.2093i	0.00196388	+	1.33769i
$511$	−3.46438	+	1.99210i	−0.153255	+	0.0881252i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−8.32501	−	30.5309i	−0.367558	−	1.34797i
$514$	8.95859	+	8.95859i	0.395147	+	0.395147i
$515$	−10.5957	−	39.5436i	−0.466901	−	1.74250i
$516$	−4.85085	+	0.00712159i	−0.213547	+	0.000313511i
$517$	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	$-0.532908\pi$
$521$	−23.1952	−	13.3918i	−1.01620	−	0.586705i	−0.913002	+	0.407956i	$0.866242\pi$
$522$	5.76069	−	5.79462i	0.252138	−	0.253623i
$523$	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
$525$	−18.9563	+	18.9457i	−0.827320	+	0.826858i
$526$	−0.919777	−	0.246453i	−0.0401042	−	0.0107459i
$527$	−1.57895	−	5.89272i	−0.0687802	−	0.256691i
$528$	5.31138	−	5.32699i	0.231148	−	0.231828i
$529$	57.5170			2.50074
$530$	−18.8199			−0.817486
$531$	−2.34317	−	0.620483i	−0.101685	−	0.0269267i
$532$	−13.9684	+	8.03217i	−0.605608	+	0.348239i
$533$	31.6211	−	10.5971i	1.36966	−	0.459012i
$534$	−1.90920	+	3.31807i	−0.0826191	+	0.143587i
$535$	−23.5221	−	6.30274i	−1.01695	−	0.272491i
$536$	8.48034	−	4.89613i	0.366295	−	0.211481i
$537$	−15.4041	+	0.0226149i	−0.664736	+	0.000975906i
$538$	16.4264	−	16.4264i	0.708194	−	0.708194i
$539$	−29.3931	+	7.76589i	−1.26605	+	0.334501i
$540$	−16.5507	−	4.35671i	−0.712229	−	0.187483i
$541$	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
$543$	30.4243	+	17.5060i	1.30563	+	0.751254i
$544$	3.74441	+	3.74441i	0.160540	+	0.160540i
$545$	−14.0952			−0.603772
$546$	13.7762	−	9.12224i	0.589568	−	0.390396i
$547$	−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
$549$	−7.11544	+	0.0208926i	−0.303679	+	0.000891673i
$550$		−	25.4002i		−	1.08307i
$551$	4.29313	−	16.0222i	0.182893	−	0.682567i
$552$	−4.04458	−	15.0064i	−0.172149	−	0.638715i
$553$	−0.961791	−	0.965157i	−0.0408995	−	0.0410427i
$554$	−12.5808	+	12.5808i	−0.534508	+	0.534508i
$555$	−0.0176286	−	12.0077i	−0.000748292	−	0.509697i
$556$	−12.1156	+	6.99492i	−0.513814	+	0.296651i
$557$	16.7620	+	4.49136i	0.710227	+	0.190305i	0.595807	−	0.803128i	$-0.296832\pi$
$557$	16.7620	+	4.49136i	0.710227	+	0.190305i	0.114420	+	0.993432i	$0.463499\pi$
$558$	3.45616	−	0.0101481i	0.146311	−	0.000429602i
$559$	8.41780	−	5.57741i	0.356035	−	0.235899i
$560$	−0.0152231	+	8.71427i	−0.000643295	+	0.368245i
$561$	−28.1258	+	28.2085i	−1.18747	+	1.19096i
$562$	−24.6886			−1.04142
$563$	4.16812			0.175665			0.0878327	−	0.996135i	$-0.472006\pi$
$563$	4.16812			0.175665			0.0878327	+	0.996135i	$0.472006\pi$
$564$	−5.32095	−	5.30535i	−0.224052	−	0.223396i
$565$	2.45686	+	9.16911i	0.103361	+	0.385748i
$566$	−0.688476	−	0.184477i	−0.0289388	−	0.00775413i
$567$	−6.06800	+	23.0256i	−0.254832	+	0.966985i
$568$	−4.32328	−	7.48814i	−0.181401	−	0.314195i
$569$	−33.3010			−1.39605			−0.698025	−	0.716073i	$-0.745938\pi$
$569$	−33.3010			−1.39605			−0.698025	+	0.716073i	$0.745938\pi$
$570$	−33.5464	+	9.04155i	−1.40511	+	0.378709i
$571$	−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
$576$	−2.59366	+	1.50762i	−0.108069	+	0.0628176i
$577$	−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
$579$	27.9052	+	27.8233i	1.15970	+	1.15630i
$580$	−6.34329	−	6.34329i	−0.263391	−	0.263391i
$581$	−14.7619	−	8.55723i	−0.612428	−	0.355014i
$582$	−5.06533	+	0.00743647i	−0.209965	+	0.000308252i
$583$	−17.5477	−	17.5477i	−0.726752	−	0.726752i
$584$	−0.755228	+	1.30809i	−0.0312516	+	0.0541293i
$585$	33.7469	−	11.4198i	1.39526	−	0.472152i
$586$	−0.373249	−	0.646486i	−0.0154188	−	0.0267061i
$587$	7.42137	−	1.98855i	0.306313	−	0.0820762i	−0.102389	−	0.994744i	$-0.532648\pi$
$587$	7.42137	−	1.98855i	0.306313	−	0.0820762i	0.408701	+	0.912668i	$0.365982\pi$
$588$	12.1243	+	0.0245606i	0.499999	+	0.00101286i
$589$	6.07624	−	3.50812i	0.250367	−	0.144550i
$590$	−0.688778	+	2.57055i	−0.0283565	+	0.105828i
$591$	−11.4745	+	43.0763i	−0.471998	+	1.77192i
$592$	−1.48834	−	1.48834i	−0.0611702	−	0.0611702i
$593$	23.6622	+	6.34027i	0.971690	+	0.260364i	0.709541	−	0.704664i	$-0.248902\pi$
$593$	23.6622	+	6.34027i	0.971690	+	0.260364i	0.262149	+	0.965027i	$0.415569\pi$
$594$	−11.3697	−	19.4941i	−0.466503	−	0.799851i
$595$	0.0806125	−	46.1455i	0.00330479	−	1.89178i
$596$	−4.90995	−	18.3242i	−0.201119	−	0.750588i
$597$	−25.0214	−	14.3971i	−1.02406	−	0.589236i
$598$	24.2413	+	21.4262i	0.991299	+	0.876182i
$599$	36.9189	+	21.3151i	1.50846	+	0.870913i	0.999951	+	0.00985856i	$0.00313813\pi$
$599$	36.9189	+	21.3151i	1.50846	+	0.870913i	0.508513	+	0.861054i	$0.330195\pi$
$600$	−2.60740	+	9.78841i	−0.106447	+	0.399610i
$601$	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
$603$	−7.68655	−	28.3533i	−0.313021	−	1.15464i
$604$	0.706111	+	2.63524i	0.0287313	+	0.107227i
$605$	18.3118	−	18.3118i	0.744479	−	0.744479i
$606$	−11.8675	−	11.8327i	−0.482086	−	0.480672i
$607$	−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
$609$	−8.82801	+	8.82308i	−0.357729	+	0.357529i
$610$			7.81205i			0.316301i
$611$	15.3290	+	3.11108i	0.620145	+	0.125861i
$612$	13.7345	−	7.98345i	0.555182	−	0.322712i
$613$	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
$615$	45.7363	+	26.3164i	1.84426	+	1.06118i
$616$	−8.13938	+	8.11099i	−0.327945	+	0.326801i
$617$	−1.58171	+	5.90302i	−0.0636772	+	0.237647i	−0.990428	−	0.138030i	$-0.955923\pi$
$617$	−1.58171	+	5.90302i	−0.0636772	+	0.237647i	0.926751	+	0.375677i	$0.122590\pi$
$618$	−15.2004	+	15.2451i	−0.611452	+	0.613250i
$619$	−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
$624$	2.77562	−	5.59428i	0.111114	−	0.223950i
$625$	−10.0191	−	17.3536i	−0.400764	−	0.694144i
$626$	−3.50747	+	13.0901i	−0.140187	+	0.523184i
$627$	−39.7090	−	22.8484i	−1.58583	−	0.912475i
$628$	2.94527	+	1.70045i	0.117529	+	0.0678555i
$629$	7.88132	+	7.88132i	0.314249	+	0.314249i
$630$	25.2601	+	6.73623i	1.00639	+	0.268378i
$631$	−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
$639$	−25.0360	+	6.78722i	−0.990408	+	0.268498i
$640$	1.64685	+	2.85242i	0.0650973	+	0.112752i
$641$	−9.87085			−0.389875			−0.194938	−	0.980816i	$-0.562450\pi$
$641$	−9.87085			−0.389875			−0.194938	+	0.980816i	$0.562450\pi$
$642$	3.33257	+	12.3647i	0.131526	+	0.487995i
$643$	−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
$645$	15.4389	+	4.11255i	0.607905	+	0.161932i
$646$	16.1250	−	27.9293i	0.634428	−	1.09886i
$647$	3.41124	+	5.90844i	0.134110	+	0.232285i	0.925257	−	0.379341i	$-0.123849\pi$
$647$	3.41124	+	5.90844i	0.134110	+	0.232285i	−0.791147	+	0.611626i	$0.790516\pi$
$648$	2.38038	+	8.67950i	0.0935102	+	0.340963i
$649$	−3.03900	+	1.75457i	−0.119291	+	0.0688728i
$650$	−6.70048	−	19.9938i	−0.262814	−	0.784223i
$651$	−5.27939	−	0.00147194i	−0.206916	−	5.76898e-5i
$652$	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
$657$	3.21356	+	3.19474i	0.125373	+	0.124639i
$658$	8.10179	+	8.13015i	0.315841	+	0.316946i
$659$	−19.5631	+	11.2948i	−0.762072	+	0.439982i	−0.830039	−	0.557705i	$-0.811682\pi$
$659$	−19.5631	+	11.2948i	−0.762072	+	0.439982i	0.0679673	+	0.997688i	$0.478349\pi$
$660$	−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
$663$	−14.6980	+	29.6239i	−0.570823	+	1.15050i
$664$	−6.44915			−0.250276
$665$	51.2872	−	13.6464i	1.98883	−	0.529184i
$666$	−5.45920	+	3.17328i	−0.211540	+	0.122962i
$667$	−21.1652	−	12.2197i	−0.819518	−	0.473149i
$668$	5.26722	−	1.41135i	0.203795	−	0.0546067i
$669$	14.1465	+	3.76829i	0.546935	+	0.145690i
$670$	−31.1537	+	8.34761i	−1.20357	+	0.322496i
$671$	−7.28395	+	7.28395i	−0.281194	+	0.281194i
$672$	3.96927	−	2.29018i	0.153118	−	0.0883457i
$673$	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
$675$	26.3845	+	15.0785i	1.01554	+	0.580373i
$676$	1.59665	+	12.9016i	0.0614094	+	0.496215i
$677$	17.7006	−	10.2195i	0.680291	−	0.392766i	−0.119674	−	0.992813i	$-0.538185\pi$
$677$	17.7006	−	10.2195i	0.680291	−	0.392766i	0.799965	+	0.600047i	$0.204852\pi$
$678$	3.52458	−	3.53495i	0.135361	−	0.135759i
$679$	7.73742	+	0.0135167i	0.296935	+	0.000518722i
$680$	−8.72070	−	15.1047i	−0.334423	−	0.579238i
$681$	−39.7911	+	10.7246i	−1.52480	+	0.410968i
$682$	3.53801	−	3.53801i	0.135477	−	0.135477i
$683$	−5.99503	+	5.99503i	−0.229394	+	0.229394i	−0.812439	−	0.583046i	$-0.801861\pi$
$683$	−5.99503	+	5.99503i	−0.229394	+	0.229394i	0.583046	+	0.812439i	$0.301861\pi$
$684$	12.9571	+	12.8812i	0.495428	+	0.492527i
$685$	−3.88736	−	6.73310i	−0.148528	−	0.257258i
$686$	−18.5200	−	0.0970597i	−0.707097	−	0.00370576i
$687$	−28.9992	−	28.9142i	−1.10639	−	1.10314i
$688$	2.42543	−	1.40032i	0.0924686	−	0.0533868i
$689$	−18.4417	−	9.18370i	−0.702574	−	0.349871i
$690$	0.0751529	+	51.1902i	0.00286102	+	1.94878i
$691$	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
$693$	17.2716	+	29.8334i	0.656095	+	1.13328i
$694$	−10.7658	+	10.7658i	−0.408663	+	0.408663i
$695$	44.5082	−	11.9259i	1.68829	−	0.452376i
$696$	−1.21428	+	4.55850i	−0.0460270	+	0.172789i
$697$	−47.3109	+	12.6769i	−1.79203	+	0.480172i
$698$	21.6120	+	12.4777i	0.818026	+	0.472287i
$699$	48.9800	−	0.0719081i	1.85259	−	0.00271981i
$700$	4.03092	−	14.9392i	0.152354	−	0.564647i
$701$	27.6757			1.04530			0.522649	−	0.852548i	$-0.324944\pi$
$701$	27.6757			1.04530			0.522649	+	0.852548i	$0.324944\pi$
$702$	−14.0921	−	12.3455i	−0.531873	−	0.465952i
$703$	−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
$708$	1.35124	−	0.364191i	0.0507828	−	0.0136871i
$709$	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
$714$	−21.0188	+	12.1274i	−0.786610	+	0.453857i
$715$	22.9914	−	46.1689i	0.859829	−	1.72662i
$716$	7.70206	−	4.44678i	0.287839	−	0.166184i
$717$	30.5569	−	8.23580i	1.14117	−	0.307572i
$718$	−15.0112	−	26.0001i	−0.560213	−	0.970317i
$719$	9.11577	−	15.7890i	0.339961	−	0.588829i	−0.644464	−	0.764634i	$-0.722920\pi$
$719$	9.11577	−	15.7890i	0.339961	−	0.588829i	0.984425	+	0.175805i	$0.0562529\pi$
$720$	9.53683	−	2.58542i	0.355417	−	0.0963530i
$721$	23.2938	−	23.2126i	0.867507	−	0.864481i
$722$	17.4739	+	4.68213i	0.650313	+	0.174251i
$723$	−29.2955	+	7.89583i	−1.08951	+	0.293649i
$724$	−20.2657			−0.753170
$725$	7.96442	+	13.7948i	0.295791	+	0.512325i
$726$	−13.1594	−	3.50536i	−0.488392	−	0.130096i
$727$		−	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
$735$	−38.5522	−	10.4138i	−1.42202	−	0.384118i
$736$	6.34496	+	6.34496i	0.233878	+	0.233878i
$737$	−36.8310	−	21.2644i	−1.35669	−	0.783284i
$738$	−0.0814757	−	27.7484i	−0.00299916	−	1.02143i
$739$	−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
$741$	−37.2844	−	7.51004i	−1.36967	−	0.275888i
$742$	−7.53594	−	13.1055i	−0.276653	−	0.481116i
$743$	−3.84387	+	1.02996i	−0.141018	+	0.0377857i	−0.328638	−	0.944456i	$-0.606589\pi$
$743$	−3.84387	+	1.02996i	−0.141018	+	0.0377857i	0.187620	+	0.982242i	$0.439923\pi$
$744$	−1.72662	+	1.00025i	−0.0633009	+	0.0366708i
$745$			62.4833i			2.28921i
$746$	32.6062	−	8.73680i	1.19380	−	0.319877i
$747$	−4.95260	+	18.7028i	−0.181206	+	0.684301i
$748$	5.95243	−	22.2148i	0.217642	−	0.812253i
$749$	−5.02984	−	18.9036i	−0.183786	−	0.690724i
$750$	2.41385	−	4.19511i	0.0881412	−	0.153184i
$751$		−	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
$753$	25.5855	−	0.0375623i	0.932386	−	0.00136885i
$754$	−3.12044	−	9.31120i	−0.113640	−	0.339094i
$755$		−	8.98587i		−	0.327029i
$756$	−3.59345	−	13.2698i	−0.130692	−	0.482617i
$757$	−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
$759$	−47.6597	+	47.7998i	−1.72994	+	1.73502i
$760$	14.1840	−	14.1840i	0.514507	−	0.514507i
$761$	2.99416	+	11.1743i	0.108538	+	0.405070i	0.998723	−	0.0505307i	$-0.0160913\pi$
$761$	2.99416	+	11.1743i	0.108538	+	0.405070i	−0.890184	+	0.455600i	$0.849425\pi$
$762$	−15.9027	−	4.23610i	−0.576094	−	0.153458i
$763$	−5.64404	−	9.81533i	−0.204328	−	0.355339i
$764$	−8.05867	+	13.9580i	−0.291553	+	0.504984i
$765$	−50.5013	+	13.6908i	−1.82588	+	0.494993i
$766$	26.8578	+	15.5063i	0.970410	+	0.560267i
$767$	−1.92931	+	2.18279i	−0.0696632	+	0.0788159i
$768$	0.863822	−	1.50127i	0.0311705	−	0.0541724i
$769$	−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
$771$	−10.9441	+	19.0201i	−0.394141	+	0.684993i
$772$	−21.9759	−	5.88842i	−0.790929	−	0.211929i
$773$	−1.41642	−	1.41642i	−0.0509449	−	0.0509449i	0.681175	−	0.732120i	$-0.261469\pi$
$773$	−1.41642	−	1.41642i	−0.0509449	−	0.0509449i	−0.732120	+	0.681175i	$0.761469\pi$
$774$	−2.19840	−	8.10923i	−0.0790199	−	0.291480i
$775$	−1.74384	+	6.50811i	−0.0626407	+	0.233778i
$776$	2.53267	−	1.46224i	0.0909175	−	0.0524913i
$777$	8.35461	−	4.82043i	0.299720	−	0.172932i
$778$	2.12296	−	0.568847i	0.0761120	−	0.0203941i
$779$	−28.1656	−	48.7843i	−1.00914	−	1.74788i
$780$	−13.5995	+	15.4318i	−0.486940	+	0.552549i
$781$	−18.7764	+	32.5217i	−0.671874	+	1.16372i
$782$	−33.5991	−	33.5991i	−1.20150	−	1.20150i
$783$	12.2873	+	7.02213i	0.439114	+	0.250950i
$784$	−6.07437	+	3.47880i	−0.216942	+	0.124243i
$785$	−7.92068	−	7.92068i	−0.282701	−	0.282701i
$786$	−6.63146	+	6.65096i	−0.236536	+	0.237232i
$787$	−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
$789$	−0.00242135	−	1.64930i	−8.62024e−5	−	0.0587165i
$790$	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
$795$	−8.48296	−	31.4740i	−0.300860	−	1.11627i
$796$	16.6668			0.590739
$797$	2.21480	+	3.83615i	0.0784524	+	0.135883i	0.902582	−	0.430517i	$-0.141669\pi$
$797$	2.21480	+	3.83615i	0.0784524	+	0.135883i	−0.824130	+	0.566401i	$0.808335\pi$
$798$	−19.7290	−	19.7400i	−0.698397	−	0.698787i
$799$	−22.1896	−	5.94568i	−0.785011	−	0.210343i
$800$	−1.51368	−	5.64912i	−0.0535166	−	0.199727i
$801$	−6.40961	−	1.69729i	−0.226472	−	0.0599709i
$802$	−1.81682			−0.0641543
$803$	6.56006			0.231500
$804$	12.0106	+	11.9754i	0.423582	+	0.422340i
$805$	0.136599	−	78.1943i	0.00481449	−	2.75599i
$806$	1.85164	−	3.71827i	0.0652212	−	0.130970i
$807$	34.8752	+	20.0670i	1.22767	+	0.706392i
$808$	9.34592	+	2.50423i	0.328788	+	0.0880986i
$809$	7.64391	−	4.41322i	0.268746	−	0.155160i	−0.359572	−	0.933117i	$-0.617077\pi$
$809$	7.64391	−	4.41322i	0.268746	−	0.155160i	0.628317	+	0.777957i	$0.283744\pi$
$810$	−0.174077	−	29.6427i	−0.00611645	−	1.04154i
$811$	−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
$813$	45.1233	−	12.1618i	1.58254	−	0.426532i
$814$	−2.36598	+	8.82998i	−0.0829277	+	0.309490i
$815$		−	83.4871i		−	2.92443i
$816$	−4.57428	+	7.94981i	−0.160132	+	0.278299i
$817$	−12.0607	−	12.0607i	−0.421951	−	0.421951i
$818$	24.8655			0.869403
$819$	21.4653	+	18.9272i	0.750060	+	0.661370i
$820$	−30.4650			−1.06389
$821$	−4.50941	−	4.50941i	−0.157379	−	0.157379i	0.624025	−	0.781404i	$-0.285496\pi$
$821$	−4.50941	−	4.50941i	−0.157379	−	0.157379i	−0.781404	+	0.624025i	$0.785496\pi$
$822$	−2.03904	+	3.54373i	−0.0711197	+	0.123602i
$823$			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
$825$	42.4786	−	11.4490i	1.47892	−	0.398602i
$826$	−2.06583	+	0.549672i	−0.0718795	+	0.0191255i
$827$	7.55620	−	7.55620i	0.262755	−	0.262755i	−0.563418	−	0.826172i	$-0.690514\pi$
$827$	7.55620	−	7.55620i	0.262755	−	0.262755i	0.826172	+	0.563418i	$0.190514\pi$
$828$	23.2732	−	13.5281i	0.808801	−	0.470133i
$829$	−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
$831$	−26.7105	−	15.3691i	−0.926579	−	0.533148i
$832$	0.221835	+	3.59872i	0.00769075	+	0.124763i
$833$	32.1662	−	18.4216i	1.11449	−	0.638271i
$834$	−17.1591	−	17.1088i	−0.594172	−	0.592430i
$835$	−17.9606			−0.621552
$836$	26.4503			0.914802
$837$	1.57481	+	5.77541i	0.0544334	+	0.199627i
$838$	6.20065	+	23.1411i	0.214198	+	0.799397i
$839$	−33.7234	−	9.03616i	−1.16426	−	0.311963i	−0.375595	−	0.926784i	$-0.622562\pi$
$839$	−33.7234	−	9.03616i	−1.16426	−	0.311963i	−0.788667	+	0.614821i	$0.789228\pi$
$840$	−14.5804	+	3.90244i	−0.503071	+	0.134647i
$841$	−10.7909	−	18.6905i	−0.372101	−	0.644498i
$842$	29.8765			1.02961
$843$	−11.1282	−	41.2885i	−0.383276	−	1.42205i
$844$	−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
$849$	−0.00181244	−	1.23454i	−6.22029e−5	−	0.0423693i
$850$	8.01552	+	29.9143i	0.274930	+	1.02605i
$851$	13.3550	+	13.3550i	0.457804	+	0.457804i
$852$	10.5743	−	10.6054i	0.362269	−	0.363334i
$853$	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
$855$	−30.2417	−	52.0267i	−1.03424	−	1.77928i
$856$	−5.22799	−	5.22799i	−0.178689	−	0.178689i
$857$	−12.6115	+	21.8438i	−0.430802	+	0.746170i	−0.996943	−	0.0781383i	$-0.975102\pi$
$857$	−12.6115	+	21.8438i	−0.430802	+	0.746170i	0.566141	+	0.824308i	$0.308436\pi$
$858$	−27.0688	+	1.70849i	−0.924113	+	0.0583269i
$859$	−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
$861$	−0.0118177	+	42.3866i	−0.000402747	+	1.44453i
$862$	18.9465	−	10.9388i	0.645320	−	0.372576i
$863$	−1.73281	+	6.46693i	−0.0589855	+	0.220137i	−0.989127	−	0.147065i	$-0.953017\pi$
$863$	−1.73281	+	6.46693i	−0.0589855	+	0.220137i	0.930141	+	0.367202i	$0.119684\pi$
$864$	−3.69038	−	3.65802i	−0.125549	−	0.124448i
$865$	32.0930	+	32.0930i	1.09119	+	1.09119i
$866$	10.3339	+	2.76896i	0.351160	+	0.0940930i
$867$	9.53762	−	16.5758i	0.323915	−	0.562944i
$868$	2.64235	−	1.51941i	0.0896873	−	0.0515723i
$869$	0.578899	+	2.16048i	0.0196378	+	0.0732893i
$870$	7.74915	−	13.4675i	0.262721	−	0.456593i
$871$	−34.6011	−	7.02243i	−1.17241	−	0.237946i
$872$	−3.70611	−	2.13973i	−0.125505	−	0.0724603i
$873$	−2.29560	−	8.46777i	−0.0776944	−	0.286591i
$874$	27.3240	−	47.3266i	0.924248	−	1.60084i
$875$	−3.70779	+	6.39626i	−0.125346	+	0.216233i
$876$	−2.52803	−	0.673408i	−0.0854144	−	0.0227524i
$877$	−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
$879$	0.912926	−	0.915610i	0.0307922	−	0.0308828i
$880$	7.15242	−	12.3884i	0.241108	−	0.417611i
$881$	0.0492472	−	0.0852986i	0.00165918	−	0.00287378i	−0.865195	−	0.501436i	$-0.832805\pi$
$881$	0.0492472	−	0.0852986i	0.00165918	−	0.00287378i	0.866854	+	0.498562i	$0.166139\pi$
$882$	5.42389	+	20.2875i	0.182632	+	0.683115i
$883$		−	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
$885$	−4.60938	+	0.00676709i	−0.154943	+	0.000227473i
$886$	−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	$0.927919\pi$
$888$	1.81819	−	3.15991i	0.0610146	−	0.106040i
$889$	24.2708	+	6.54882i	0.814018	+	0.219640i
$890$	−1.88411	+	7.03159i	−0.0631555	+	0.235699i
$891$	27.4765	−	27.8012i	0.920499	−	0.931374i
$892$	−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
$897$	−24.9060	+	50.1982i	−0.831587	+	1.67607i
$898$	0.574338	+	0.994782i	0.0191659	+	0.0331963i
$899$	−0.812114	+	3.03085i	−0.0270855	+	0.101085i
$900$	−17.5451	+	0.0515165i	−0.584838	+	0.00171722i
$901$	26.2038	+	15.1288i	0.872975	+	0.504012i
$902$	−28.4056	−	28.4056i	−0.945803	−	0.945803i
$903$	3.31827	+	12.3978i	0.110425	+	0.412572i
$904$	−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	$0.149588\pi$
$911$			27.3357i			0.905671i	−0.891594	+	0.452836i	$0.850412\pi$
$912$	−10.1931	−	2.71519i	−0.337526	−	0.0899090i
$913$	14.0047	+	24.2568i	0.463487	+	0.802782i
$914$	−0.508183			−0.0168092
$915$	−13.0647	+	3.52123i	−0.431904	+	0.116408i
$916$	22.8374	+	6.11927i	0.754570	+	0.202186i
$917$	10.1623	−	10.1269i	0.335590	−	0.334419i
$918$	19.5420	+	19.3706i	0.644983	+	0.639326i
$919$	−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
$921$	−40.9527	+	11.0377i	−1.34944	+	0.363705i
$922$	13.9286	−	8.04166i	0.458713	−	0.264838i
$923$	−6.20080	+	30.5527i	−0.204102	+	1.00566i
$924$	−17.2334	−	9.95610i	−0.566936	−	0.327532i
$925$	−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	$-0.689347\pi$
$929$	−19.2502	+	5.15806i	−0.631577	+	0.169231i	−0.0711918	+	0.997463i	$0.522680\pi$
$930$	6.34585	−	1.71036i	0.208089	−	0.0560848i
$931$	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
$936$	10.6068	+	2.12029i	0.346694	+	0.0693038i
$937$	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
$939$	−23.4724	+	0.0344602i	−0.765994	+	0.00112456i
$940$	−12.3743	−	7.14430i	−0.403605	−	0.233021i
$941$	−1.25159	+	0.335362i	−0.0408006	+	0.0109325i	−0.279162	−	0.960244i	$-0.590057\pi$
$941$	−1.25159	+	0.335362i	−0.0408006	+	0.0109325i	0.238361	+	0.971177i	$0.423390\pi$
$942$	−1.51623	+	5.69206i	−0.0494014	+	0.185457i
$943$	−80.1690	+	21.4812i	−2.61066	+	0.699525i
$944$	−0.571327	+	0.571327i	−0.0185951	+	0.0185951i
$945$	0.120330	+	45.2806i	0.00391432	+	1.47298i
$946$	−10.5339	−	6.08174i	−0.342486	−	0.197734i
$947$	−19.7867	+	19.7867i	−0.642983	+	0.642983i	−0.951288	−	0.308305i	$-0.900238\pi$
$947$	−19.7867	+	19.7867i	−0.642983	+	0.642983i	0.308305	+	0.951288i	$0.400238\pi$
$948$	−0.00130956	−	0.892004i	−4.25326e−5	−	0.0289709i
$949$	5.16377	−	1.73052i	0.167623	−	0.0561751i
$950$	−30.8460	+	17.8089i	−1.00078	+	0.577798i
$951$	−13.5000	−	13.4605i	−0.437769	−	0.436485i
$952$	7.02633	−	12.1210i	0.227725	−	0.392844i
$953$	4.62297	+	8.00722i	0.149753	+	0.259379i	0.931136	−	0.364672i	$-0.118819\pi$
$953$	4.62297	+	8.00722i	0.149753	+	0.259379i	−0.781383	+	0.624051i	$0.785486\pi$
$954$	−12.0854	+	12.1566i	−0.391281	+	0.393585i
$955$	37.5372	−	37.5372i	1.21467	−	1.21467i
$956$	−12.9200	+	12.9200i	−0.417862	+	0.417862i
$957$	19.7824	−	5.33183i	0.639476	−	0.172354i
$958$	10.7273	+	18.5802i	0.346583	+	0.600300i
$959$	3.13207	−	5.40309i	0.101140	−	0.174475i
$960$	−4.02801	+	4.03985i	−0.130003	+	0.130386i
$961$	25.6974	−	14.8364i	0.828947	−	0.478593i
$962$	0.466924	+	7.57467i	0.0150542	+	0.244217i
$963$	−19.1762	+	11.1466i	−0.617945	+	0.359194i
$964$	12.3866	−	12.3866i	0.398947	−	0.398947i
$965$	64.8957	+	37.4675i	2.08907	+	1.20612i
$966$	−35.6167	+	20.5501i	−1.14595	+	0.661188i
$967$	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
$969$	53.9763	+	14.3780i	1.73397	+	0.461888i
$970$	−9.30410	+	2.49303i	−0.298737	+	0.0800463i
$971$	3.64259	+	2.10305i	0.116896	+	0.0674901i	0.557308	−	0.830306i	$-0.311834\pi$
$971$	3.64259	+	2.10305i	0.116896	+	0.0674901i	−0.440412	+	0.897796i	$0.645168\pi$
$972$	−13.4424	+	7.89312i	−0.431166	+	0.253172i
$973$	26.1268	+	26.2183i	0.837588	+	0.840520i
$974$	21.4225			0.686420
$975$	30.4169	−	20.2178i	0.974122	−	0.647487i
$976$	−1.18591	+	2.05406i	−0.0379601	+	0.0657488i
$977$	−3.45942	+	12.9107i	−0.110677	+	0.413051i	−0.998927	−	0.0463082i	$-0.985254\pi$
$977$	−3.45942	+	12.9107i	−0.110677	+	0.413051i	0.888250	+	0.459360i	$0.151921\pi$
$978$	−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
$981$	−9.05139	+	9.10470i	−0.288989	+	0.290691i
$982$	0.521184	−	0.139651i	0.0166317	−	0.00445644i
$983$	12.0380	+	44.9265i	0.383953	+	1.43293i	0.839811	+	0.542879i	$0.182666\pi$
$983$	12.0380	+	44.9265i	0.383953	+	1.43293i	−0.455858	+	0.890053i	$0.650667\pi$
$984$	8.03067	+	13.8625i	0.256009	+	0.441920i
$985$			84.7708i			2.70102i
$986$	3.73286	+	13.9312i	0.118878	+	0.443660i
$987$	−9.94481	+	17.2138i	−0.316547	+	0.547922i
$988$	20.8204	−	6.97749i	0.662385	−	0.221983i
$989$	−21.7637	+	12.5653i	−0.692045	+	0.399552i
$990$	−30.4341	−	30.2559i	−0.967259	−	0.961596i
$991$	−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
$993$	6.28380	+	1.67385i	0.199410	+	0.0531182i
$994$	−16.2045	+	16.1479i	−0.513974	+	0.512182i
$995$	−53.0248	−	14.2079i	−1.68100	−	0.450422i
$996$	−2.90691	−	10.7854i	−0.0921090	−	0.341748i
$997$	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
$999$	−7.76760	−	7.69948i	−0.245756	−	0.243601i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.863822 - 1.50127i) q^{3} +1.00000i q^{4} +(0.852470 - 3.18146i) q^{5} +(-1.67237 + 0.450743i) q^{6} +(2.55679 - 0.680305i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.50762 - 2.59366i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.863822 - 1.50127i) q^{3} +1.00000i q^{4} +(0.852470 - 3.18146i) q^{5} +(-1.67237 + 0.450743i) q^{6} +(2.55679 - 0.680305i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.50762 - 2.59366i) q^{9} +(-2.85242 + 1.64685i) q^{10} +(-4.19511 - 1.12408i) q^{11} +(1.50127 + 0.863822i) q^{12} +(-3.59872 + 0.221835i) q^{13} +(-2.28897 - 1.32688i) q^{14} +(-4.03985 - 4.02801i) q^{15} -1.00000 q^{16} +5.29539 q^{17} +(-0.767945 + 2.90004i) q^{18} +(1.57626 + 5.88267i) q^{19} +(3.18146 + 0.852470i) q^{20} +(1.18729 - 4.42610i) q^{21} +(2.17155 + 3.76124i) q^{22} +8.97313 q^{23} +(-0.450743 - 1.67237i) 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} +(0.00837533 + 5.70483i) q^{30} +(-0.298174 - 1.11280i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.31138 + 5.32699i) q^{33} +(-3.74441 - 3.74441i) q^{34} +(0.0152231 - 8.71427i) q^{35} +(2.59366 - 1.50762i) q^{36} +(1.48834 + 1.48834i) q^{37} +(3.04509 - 5.27425i) q^{38} +(-2.77562 + 5.59428i) q^{39} +(-1.64685 - 2.85242i) q^{40} +(-8.93434 + 2.39395i) q^{41} +(-3.96927 + 2.29018i) q^{42} +(-2.42543 + 1.40032i) q^{43} +(1.12408 - 4.19511i) q^{44} +(-9.53683 + 2.58542i) q^{45} +(-6.34496 - 6.34496i) q^{46} +(-4.19035 - 1.12280i) q^{47} +(-0.863822 + 1.50127i) q^{48} +(6.07437 - 3.47880i) q^{49} +(1.51368 + 5.64912i) q^{50} +(4.57428 - 7.94981i) q^{51} +(-0.221835 - 3.59872i) q^{52} +(4.94841 + 2.85697i) q^{53} +(3.69038 + 3.65802i) q^{54} +(-7.15242 + 12.3884i) q^{55} +(1.32688 - 2.28897i) q^{56} +(10.1931 + 2.71519i) q^{57} +(0.704925 + 2.63082i) q^{58} +(0.571327 - 0.571327i) q^{59} +(4.02801 - 4.03985i) q^{60} +(1.18591 - 2.05406i) q^{61} +(-0.576029 + 0.997711i) q^{62} +(-5.61916 - 5.60581i) q^{63} -1.00000i q^{64} +(-2.36204 + 11.6383i) q^{65} +(7.52246 - 0.0110438i) q^{66} +(9.45859 + 2.53442i) q^{67} +5.29539i q^{68} +(7.75119 - 13.4711i) q^{69} +(-6.17269 + 6.15116i) q^{70} +(2.23789 - 8.35193i) q^{71} +(-2.90004 - 0.767945i) 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} +(5.91841 - 1.99309i) q^{78} +(-0.257500 - 0.446002i) q^{79} +(-0.852470 + 3.18146i) q^{80} +(-4.45415 + 7.82052i) q^{81} +(8.01031 + 4.62476i) q^{82} +(-4.56024 - 4.56024i) q^{83} +(4.42610 + 1.18729i) 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} +(-1.92819 - 0.513623i) q^{93} +(2.16909 + 3.75697i) q^{94} +20.0592 q^{95} +(1.67237 - 0.450743i) q^{96} +(2.82483 + 0.756910i) q^{97} +(-6.75511 - 1.83535i) q^{98} +(3.40917 + 12.5754i) 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

L-functions

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