LMFDB - Embedded newform 546.2.bu.a.71.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.12
Character	$\chi$	$=$	546.71
Dual form			546.2.bu.a.323.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.563184 - 1.63793i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.58301 - 1.58301i) q^{5} +(0.120065 - 1.72788i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.36565 - 1.84491i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.563184 - 1.63793i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.58301 - 1.58301i) q^{5} +(0.120065 - 1.72788i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.36565 - 1.84491i) q^{9} +(-1.93879 - 1.11936i) q^{10} +(-1.28804 - 4.80702i) q^{11} +(-0.331235 - 1.70008i) q^{12} +(0.738744 + 3.52906i) q^{13} +1.00000i q^{14} +(-3.48440 + 1.70134i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.25294 - 2.17015i) q^{17} +(-2.76254 - 1.16978i) q^{18} +(1.54049 + 0.412774i) q^{19} +(-2.16244 - 0.579424i) q^{20} +(1.43636 + 0.967922i) q^{21} +(-2.48830 - 4.30986i) q^{22} +(0.566768 - 0.981671i) q^{23} +(-0.759962 - 1.55642i) q^{24} +0.0118705i q^{25} +(1.62696 + 3.21761i) q^{26} +(-4.35414 + 2.83575i) q^{27} +(0.258819 + 0.965926i) q^{28} +(5.50981 + 3.18109i) q^{29} +(-2.92533 + 2.54520i) q^{30} +(1.36926 - 1.36926i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-8.59898 - 0.597517i) q^{33} +(-1.77192 - 1.77192i) q^{34} +(1.93879 - 1.11936i) q^{35} +(-2.97117 - 0.414918i) q^{36} +(1.84621 - 0.494691i) q^{37} +1.59484 q^{38} +(6.19641 + 0.777496i) q^{39} -2.23872 q^{40} +(3.36855 - 0.902600i) q^{41} +(1.63793 + 0.563184i) q^{42} +(6.80079 - 3.92644i) q^{43} +(-3.51898 - 3.51898i) q^{44} +(0.824330 + 6.66538i) q^{45} +(0.293381 - 1.09491i) q^{46} +(-8.51745 + 8.51745i) q^{47} +(-1.13690 - 1.30670i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.00307230 + 0.0114660i) q^{50} +(-4.26020 + 0.830035i) q^{51} +(2.40430 + 2.68688i) q^{52} -1.61436i q^{53} +(-3.47183 + 3.86606i) q^{54} +(-5.57060 + 9.64856i) q^{55} +(0.500000 + 0.866025i) q^{56} +(1.54368 - 2.29076i) q^{57} +(6.14540 + 1.64665i) q^{58} +(5.35382 + 1.43455i) q^{59} +(-2.16691 + 3.21561i) q^{60} +(1.56891 + 2.71743i) q^{61} +(0.968212 - 1.67699i) q^{62} +(2.39433 - 1.80754i) q^{63} -1.00000i q^{64} +(4.41711 - 6.75599i) q^{65} +(-8.46062 + 1.64842i) q^{66} +(-3.18853 - 11.8997i) q^{67} +(-2.17015 - 1.25294i) q^{68} +(-1.28872 - 1.48119i) q^{69} +(1.58301 - 1.58301i) q^{70} +(0.709782 - 2.64894i) q^{71} +(-2.97732 + 0.368215i) q^{72} +(8.64213 + 8.64213i) q^{73} +(1.65527 - 0.955670i) q^{74} +(0.0194430 + 0.00668525i) q^{75} +(1.54049 - 0.412774i) q^{76} +4.97659 q^{77} +(6.18650 - 0.852745i) q^{78} +17.5434 q^{79} +(-2.16244 + 0.579424i) q^{80} +(2.19258 + 8.72884i) q^{81} +(3.02016 - 1.74369i) q^{82} +(4.87907 + 4.87907i) q^{83} +(1.72788 + 0.120065i) q^{84} +(-1.45197 + 5.41881i) q^{85} +(5.55282 - 5.55282i) q^{86} +(8.31346 - 7.23317i) q^{87} +(-4.30986 - 2.48830i) q^{88} +(-1.28335 - 4.78954i) q^{89} +(2.52137 + 6.22491i) q^{90} +(-3.60001 - 0.199816i) q^{91} -1.13354i q^{92} +(-1.47161 - 3.01390i) q^{93} +(-6.02275 + 10.4317i) q^{94} +(-1.78520 - 3.09205i) q^{95} +(-1.43636 - 0.967922i) q^{96} +(-15.8815 - 4.25543i) q^{97} +(-0.965926 - 0.258819i) q^{98} +(-5.82150 + 13.7480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.563184	−	1.63793i	0.325154	−	0.945661i
$3$	0.563184	−	1.63793i	0.325154	−	0.945661i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.58301	−	1.58301i	−0.707946	−	0.707946i	0.258157	−	0.966103i	$-0.416885\pi$
$5$	−1.58301	−	1.58301i	−0.707946	−	0.707946i	−0.966103	+	0.258157i	$0.916885\pi$
$6$	0.120065	−	1.72788i	0.0490165	−	0.705406i
$7$	−0.258819	+	0.965926i	−0.0978244	+	0.365086i
$7$	−0.258819	+	0.965926i	−0.0978244	+	0.365086i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.36565	−	1.84491i	−0.788549	−	0.614971i
$10$	−1.93879	−	1.11936i	−0.613099	−	0.353973i
$11$	−1.28804	−	4.80702i	−0.388358	−	1.44937i	−0.832805	−	0.553566i	$-0.813267\pi$
$11$	−1.28804	−	4.80702i	−0.388358	−	1.44937i	0.444447	−	0.895805i	$-0.353400\pi$
$12$	−0.331235	−	1.70008i	−0.0956193	−	0.490772i
$13$	0.738744	+	3.52906i	0.204891	+	0.978785i
$13$	0.738744	+	3.52906i	0.204891	+	0.978785i
$14$			1.00000i			0.267261i
$15$	−3.48440	+	1.70134i	−0.899668	+	0.439285i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.25294	−	2.17015i	−0.303882	−	0.526340i	0.673129	−	0.739525i	$-0.264950\pi$
$17$	−1.25294	−	2.17015i	−0.303882	−	0.526340i	−0.977012	+	0.213185i	$0.931616\pi$
$18$	−2.76254	−	1.16978i	−0.651137	−	0.275719i
$19$	1.54049	+	0.412774i	0.353414	+	0.0946969i	0.431158	−	0.902276i	$-0.358105\pi$
$19$	1.54049	+	0.412774i	0.353414	+	0.0946969i	−0.0777444	+	0.996973i	$0.524772\pi$
$20$	−2.16244	−	0.579424i	−0.483536	−	0.129563i
$21$	1.43636	+	0.967922i	0.313439	+	0.211218i
$22$	−2.48830	−	4.30986i	−0.530507	−	0.918864i
$23$	0.566768	−	0.981671i	0.118179	−	0.204692i	−0.800867	−	0.598842i	$-0.795628\pi$
$23$	0.566768	−	0.981671i	0.118179	−	0.204692i	0.919046	+	0.394150i	$0.128961\pi$
$24$	−0.759962	−	1.55642i	−0.155127	−	0.317704i
$25$			0.0118705i			0.00237409i
$26$	1.62696	+	3.21761i	0.319073	+	0.631025i
$27$	−4.35414	+	2.83575i	−0.837955	+	0.545740i
$28$	0.258819	+	0.965926i	0.0489122	+	0.182543i
$29$	5.50981	+	3.18109i	1.02315	+	0.590714i	0.915014	−	0.403422i	$-0.132179\pi$
$29$	5.50981	+	3.18109i	1.02315	+	0.590714i	0.108133	+	0.994136i	$0.465513\pi$
$30$	−2.92533	+	2.54520i	−0.534090	+	0.464688i
$31$	1.36926	−	1.36926i	0.245926	−	0.245926i	−0.573370	−	0.819296i	$-0.694364\pi$
$31$	1.36926	−	1.36926i	0.245926	−	0.245926i	0.819296	+	0.573370i	$0.194364\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−8.59898	−	0.597517i	−1.49689	−	0.104014i
$34$	−1.77192	−	1.77192i	−0.303882	−	0.303882i
$35$	1.93879	−	1.11936i	0.327715	−	0.189206i
$36$	−2.97117	−	0.414918i	−0.495195	−	0.0691531i
$37$	1.84621	−	0.494691i	0.303515	−	0.0813267i	−0.103847	−	0.994593i	$-0.533115\pi$
$37$	1.84621	−	0.494691i	0.303515	−	0.0813267i	0.407362	+	0.913267i	$0.366449\pi$
$38$	1.59484			0.258717
$39$	6.19641	+	0.777496i	0.992220	+	0.124499i
$40$	−2.23872			−0.353973
$41$	3.36855	−	0.902600i	0.526079	−	0.140963i	0.0140021	−	0.999902i	$-0.495543\pi$
$41$	3.36855	−	0.902600i	0.526079	−	0.140963i	0.512077	+	0.858939i	$0.328876\pi$
$42$	1.63793	+	0.563184i	0.252739	+	0.0869011i
$43$	6.80079	−	3.92644i	1.03711	−	0.598776i	0.118097	−	0.993002i	$-0.462320\pi$
$43$	6.80079	−	3.92644i	1.03711	−	0.598776i	0.919014	+	0.394226i	$0.128987\pi$
$44$	−3.51898	−	3.51898i	−0.530507	−	0.530507i
$45$	0.824330	+	6.66538i	0.122884	+	0.993616i
$46$	0.293381	−	1.09491i	0.0432566	−	0.161436i
$47$	−8.51745	+	8.51745i	−1.24240	+	1.24240i	−0.283394	+	0.959003i	$0.591460\pi$
$47$	−8.51745	+	8.51745i	−1.24240	+	1.24240i	−0.959003	+	0.283394i	$0.908540\pi$
$48$	−1.13690	−	1.30670i	−0.164097	−	0.188606i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	0.00307230	+	0.0114660i	0.000434489	+	0.00162153i
$51$	−4.26020	+	0.830035i	−0.596548	+	0.116228i
$52$	2.40430	+	2.68688i	0.333416	+	0.372604i
$53$		−	1.61436i		−	0.221750i	−0.993834	−	0.110875i	$-0.964635\pi$
$53$		−	1.61436i		−	0.221750i	0.993834	−	0.110875i	$-0.0353653\pi$
$54$	−3.47183	+	3.86606i	−0.472456	+	0.526104i
$55$	−5.57060	+	9.64856i	−0.751140	+	1.30101i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	1.54368	−	2.29076i	0.204465	−	0.303418i
$58$	6.14540	+	1.64665i	0.806931	+	0.216216i
$59$	5.35382	+	1.43455i	0.697007	+	0.186763i	0.589890	−	0.807484i	$-0.299171\pi$
$59$	5.35382	+	1.43455i	0.697007	+	0.186763i	0.107118	+	0.994246i	$0.465838\pi$
$60$	−2.16691	+	3.21561i	−0.279746	+	0.415133i
$61$	1.56891	+	2.71743i	0.200878	+	0.347931i	0.948812	−	0.315843i	$-0.102287\pi$
$61$	1.56891	+	2.71743i	0.200878	+	0.347931i	−0.747934	+	0.663774i	$0.768954\pi$
$62$	0.968212	−	1.67699i	0.122963	−	0.212978i
$63$	2.39433	−	1.80754i	0.301657	−	0.227729i
$64$		−	1.00000i		−	0.125000i
$65$	4.41711	−	6.75599i	0.547875	−	0.837978i
$66$	−8.46062	+	1.64842i	−1.04143	+	0.202907i
$67$	−3.18853	−	11.8997i	−0.389540	−	1.45378i	−0.830884	−	0.556446i	$-0.812165\pi$
$67$	−3.18853	−	11.8997i	−0.389540	−	1.45378i	0.441343	−	0.897338i	$-0.354502\pi$
$68$	−2.17015	−	1.25294i	−0.263170	−	0.151941i
$69$	−1.28872	−	1.48119i	−0.155143	−	0.178314i
$70$	1.58301	−	1.58301i	0.189206	−	0.189206i
$71$	0.709782	−	2.64894i	0.0842357	−	0.314372i	−0.910933	−	0.412555i	$-0.864636\pi$
$71$	0.709782	−	2.64894i	0.0842357	−	0.314372i	0.995168	+	0.0981832i	$0.0313031\pi$
$72$	−2.97732	+	0.368215i	−0.350880	+	0.0433945i
$73$	8.64213	+	8.64213i	1.01148	+	1.01148i	0.999933	+	0.0115511i	$0.00367692\pi$
$73$	8.64213	+	8.64213i	1.01148	+	1.01148i	0.0115511	+	0.999933i	$0.496323\pi$
$74$	1.65527	−	0.955670i	0.192421	−	0.111094i
$75$	0.0194430	+	0.00668525i	0.00224509	+	0.000771946i
$76$	1.54049	−	0.412774i	0.176707	−	0.0473485i
$77$	4.97659			0.567135
$78$	6.18650	−	0.852745i	0.700484	−	0.0965544i
$79$	17.5434			1.97379			0.986894	−	0.161370i	$-0.0515912\pi$
$79$	17.5434			1.97379			0.986894	+	0.161370i	$0.0515912\pi$
$80$	−2.16244	+	0.579424i	−0.241768	+	0.0647815i
$81$	2.19258	+	8.72884i	0.243620	+	0.969871i
$82$	3.02016	−	1.74369i	0.333521	−	0.192558i
$83$	4.87907	+	4.87907i	0.535547	+	0.535547i	0.922218	−	0.386671i	$-0.126375\pi$
$83$	4.87907	+	4.87907i	0.535547	+	0.535547i	−0.386671	+	0.922218i	$0.626375\pi$
$84$	1.72788	+	0.120065i	0.188528	+	0.0131002i
$85$	−1.45197	+	5.41881i	−0.157488	+	0.587752i
$86$	5.55282	−	5.55282i	0.598776	−	0.598776i
$87$	8.31346	−	7.23317i	0.891296	−	0.775477i
$88$	−4.30986	−	2.48830i	−0.459432	−	0.265253i
$89$	−1.28335	−	4.78954i	−0.136035	−	0.507690i	−0.999991	−	0.00412321i	$-0.998688\pi$
$89$	−1.28335	−	4.78954i	−0.136035	−	0.507690i	0.863956	−	0.503567i	$-0.167979\pi$
$90$	2.52137	+	6.22491i	0.265776	+	0.656163i
$91$	−3.60001	−	0.199816i	−0.377384	−	0.0209464i
$92$		−	1.13354i		−	0.118179i
$93$	−1.47161	−	3.01390i	−0.152599	−	0.312527i
$94$	−6.02275	+	10.4317i	−0.621199	+	1.07595i
$95$	−1.78520	−	3.09205i	−0.183157	−	0.317238i
$96$	−1.43636	−	0.967922i	−0.146598	−	0.0987881i
$97$	−15.8815	−	4.25543i	−1.61252	−	0.432073i	−0.663727	−	0.747975i	$-0.731026\pi$
$97$	−15.8815	−	4.25543i	−1.61252	−	0.432073i	−0.948792	+	0.315902i	$0.897693\pi$
$98$	−0.965926	−	0.258819i	−0.0975732	−	0.0261447i
$99$	−5.82150	+	13.7480i	−0.585082	+	1.38173i
$100$	0.00593523	+	0.0102801i	0.000593523	+	0.00102801i
$101$	2.68778	−	4.65537i	0.267444	−	0.463226i	−0.700757	−	0.713400i	$-0.747154\pi$
$101$	2.68778	−	4.65537i	0.267444	−	0.463226i	0.968201	+	0.250174i	$0.0804877\pi$
$102$	−3.90021	+	1.90437i	−0.386178	+	0.188561i
$103$		−	10.5077i		−	1.03535i	−0.855577	−	0.517676i	$-0.826797\pi$
$103$		−	10.5077i		−	1.03535i	0.855577	−	0.517676i	$-0.173203\pi$
$104$	3.01779	+	1.97305i	0.295919	+	0.193474i
$105$	−0.741543	−	3.80601i	−0.0723672	−	0.371429i
$106$	−0.417828	−	1.55936i	−0.0405831	−	0.151458i
$107$	14.0696	+	8.12308i	1.36016	+	0.785288i	0.989645	−	0.143539i	$-0.0458483\pi$
$107$	14.0696	+	8.12308i	1.36016	+	0.785288i	0.370514	+	0.928827i	$0.379182\pi$
$108$	−2.35292	+	4.63290i	−0.226410	+	0.445801i
$109$	−8.50467	+	8.50467i	−0.814600	+	0.814600i	−0.985320	−	0.170720i	$-0.945391\pi$
$109$	−8.50467	+	8.50467i	−0.814600	+	0.814600i	0.170720	+	0.985320i	$0.445391\pi$
$110$	−2.88356	+	10.7616i	−0.274936	+	1.02608i
$111$	0.229486	−	3.30257i	0.0217818	−	0.313466i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−0.529726	+	0.305837i	−0.0498324	+	0.0287707i	−0.524709	−	0.851282i	$-0.675826\pi$
$113$	−0.529726	+	0.305837i	−0.0498324	+	0.0287707i	0.474877	+	0.880052i	$0.342493\pi$
$114$	0.898186	−	2.61224i	0.0841229	−	0.244658i
$115$	−2.45120	+	0.656797i	−0.228576	+	0.0612467i
$116$	6.36219			0.590714
$117$	4.76320	−	9.71143i	0.440358	−	0.897822i
$118$	5.54268			0.510245
$119$	2.42049	−	0.648569i	0.221886	−	0.0594542i
$120$	−1.26081	+	3.66687i	−0.115096	+	0.334738i
$121$	−11.9221	+	6.88324i	−1.08383	+	0.625749i
$122$	2.21877	+	2.21877i	0.200878	+	0.200878i
$123$	0.418714	−	6.02579i	0.0377542	−	0.543327i
$124$	0.501184	−	1.87044i	0.0450076	−	0.167971i
$125$	−7.89628	+	7.89628i	−0.706265	+	0.706265i
$126$	1.84491	−	2.36565i	0.164358	−	0.210749i
$127$	3.09276	+	1.78561i	0.274438	+	0.158447i	0.630903	−	0.775862i	$-0.282685\pi$
$127$	3.09276	+	1.78561i	0.274438	+	0.158447i	−0.356465	+	0.934309i	$0.616018\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−2.60115	−	13.3505i	−0.229018	−	1.17545i
$130$	2.51802	−	7.66902i	0.220845	−	0.672618i
$131$			21.9639i			1.91899i	0.281722	+	0.959496i	$0.409094\pi$
$131$			21.9639i			1.91899i	−0.281722	+	0.959496i	$0.590906\pi$
$132$	−7.74569	+	3.78202i	−0.674176	+	0.329183i
$133$	−0.797419	+	1.38117i	−0.0691450	+	0.119763i
$134$	−6.15976	−	10.6690i	−0.532122	−	0.921662i
$135$	11.3817	+	2.40364i	0.979581	+	0.206872i
$136$	−2.42049	−	0.648569i	−0.207556	−	0.0556143i
$137$	−3.85986	−	1.03425i	−0.329770	−	0.0883616i	0.0901352	−	0.995930i	$-0.471270\pi$
$137$	−3.85986	−	1.03425i	−0.329770	−	0.0883616i	−0.419905	+	0.907568i	$0.637937\pi$
$138$	−1.62816	−	1.09717i	−0.138599	−	0.0933976i
$139$	−5.62224	−	9.73800i	−0.476872	−	0.825966i	0.522777	−	0.852470i	$-0.324896\pi$
$139$	−5.62224	−	9.73800i	−0.476872	−	0.825966i	−0.999649	+	0.0265031i	$0.991563\pi$
$140$	1.11936	−	1.93879i	0.0946032	−	0.163858i
$141$	9.15412	+	18.7479i	0.770916	+	1.57886i
$142$		−	2.74239i		−	0.230136i
$143$	16.0127	−	8.09671i	1.33905	−	0.677081i
$144$	−2.78057	+	1.12625i	−0.231714	+	0.0938545i
$145$	−3.68640	−	13.7578i	−0.306139	−	1.14253i
$146$	10.5844	+	6.11091i	0.875971	+	0.505742i
$147$	−1.30670	+	1.13690i	−0.107775	+	0.0937699i
$148$	1.35152	−	1.35152i	0.111094	−	0.111094i
$149$	−1.48620	+	5.54659i	−0.121755	+	0.454394i	−0.999703	−	0.0243606i	$-0.992245\pi$
$149$	−1.48620	+	5.54659i	−0.121755	+	0.454394i	0.877949	+	0.478755i	$0.158912\pi$
$150$	0.0205108	+	0.00142523i	0.00167470	+	0.000116370i
$151$	4.76868	+	4.76868i	0.388070	+	0.388070i	0.873998	−	0.485929i	$-0.161519\pi$
$151$	4.76868	+	4.76868i	0.388070	+	0.388070i	−0.485929	+	0.873998i	$0.661519\pi$
$152$	1.38117	−	0.797419i	0.112028	−	0.0646792i
$153$	−1.03974	+	7.44539i	−0.0840576	+	0.601924i
$154$	4.80702	−	1.28804i	0.387361	−	0.103793i
$155$	−4.33511			−0.348205
$156$	5.75500	−	2.42487i	0.460768	−	0.194145i
$157$	−3.72232			−0.297074			−0.148537	−	0.988907i	$-0.547456\pi$
$157$	−3.72232			−0.297074			−0.148537	+	0.988907i	$0.547456\pi$
$158$	16.9456	−	4.54057i	1.34812	−	0.361228i
$159$	−2.64422	−	0.909183i	−0.209700	−	0.0721029i
$160$	−1.93879	+	1.11936i	−0.153275	+	0.0884932i
$161$	0.801531	+	0.801531i	0.0631695	+	0.0631695i
$162$	4.37706	+	7.86393i	0.343894	+	0.617848i
$163$	−0.0370686	+	0.138342i	−0.00290343	+	0.0108358i	−0.967362	−	0.253397i	$-0.918452\pi$
$163$	−0.0370686	+	0.138342i	−0.00290343	+	0.0108358i	0.964459	+	0.264233i	$0.0851187\pi$
$164$	2.46595	−	2.46595i	0.192558	−	0.192558i
$165$	12.6664	+	14.5582i	0.986080	+	1.13335i
$166$	5.97561	+	3.45002i	0.463798	+	0.267774i
$167$	−0.947784	−	3.53718i	−0.0733418	−	0.273715i	0.919510	−	0.393066i	$-0.128585\pi$
$167$	−0.947784	−	3.53718i	−0.0733418	−	0.273715i	−0.992852	+	0.119350i	$0.961919\pi$
$168$	1.70008	−	0.331235i	0.131164	−	0.0255553i
$169$	−11.9085	+	5.21414i	−0.916040	+	0.401088i
$170$			5.60996i			0.430264i
$171$	−2.88273	−	3.81856i	−0.220448	−	0.292012i
$172$	3.92644	−	6.80079i	0.299388	−	0.518556i
$173$	5.32718	+	9.22695i	0.405018	+	0.701512i	0.994324	−	0.106399i	$-0.0339319\pi$
$173$	5.32718	+	9.22695i	0.405018	+	0.701512i	−0.589306	+	0.807910i	$0.700599\pi$
$174$	6.15810	−	9.13838i	0.466844	−	0.692779i
$175$	−0.0114660	−	0.00307230i	−0.000866747	−	0.000232244i
$176$	−4.80702	−	1.28804i	−0.362343	−	0.0970894i
$177$	5.36488	−	7.96128i	0.403249	−	0.598406i
$178$	−2.47925	−	4.29418i	−0.185827	−	0.321862i
$179$	5.67227	−	9.82466i	0.423966	−	0.734330i	−0.572358	−	0.820004i	$-0.693971\pi$
$179$	5.67227	−	9.82466i	0.423966	−	0.734330i	0.996323	+	0.0856742i	$0.0273044\pi$
$180$	4.04658	+	5.36023i	0.301614	+	0.399528i
$181$			21.0789i			1.56678i	0.621528	+	0.783392i	$0.286512\pi$
$181$			21.0789i			1.56678i	−0.621528	+	0.783392i	$0.713488\pi$
$182$	−3.52906	+	0.738744i	−0.261591	+	0.0547593i
$183$	5.33455	−	1.03935i	0.394341	−	0.0768313i
$184$	−0.293381	−	1.09491i	−0.0216283	−	0.0807179i
$185$	−3.70568	−	2.13948i	−0.272447	−	0.157298i
$186$	−2.20152	−	2.53032i	−0.161423	−	0.185532i
$187$	−8.81814	+	8.81814i	−0.644847	+	0.644847i
$188$	−3.11760	+	11.6351i	−0.227375	+	0.848573i
$189$	−1.61219	−	4.93972i	−0.117269	−	0.359312i
$190$	−2.52465	−	2.52465i	−0.183157	−	0.183157i
$191$	12.3423	−	7.12581i	0.893055	−	0.515606i	0.0181148	−	0.999836i	$-0.494234\pi$
$191$	12.3423	−	7.12581i	0.893055	−	0.515606i	0.874941	+	0.484230i	$0.160900\pi$
$192$	−1.63793	−	0.563184i	−0.118208	−	0.0406443i
$193$	−23.8028	+	6.37795i	−1.71337	+	0.459095i	−0.976246	−	0.216667i	$-0.930482\pi$
$193$	−23.8028	+	6.37795i	−1.71337	+	0.459095i	−0.737120	+	0.675762i	$0.763815\pi$
$194$	−16.4417			−1.18045
$195$	−8.57822	−	11.0398i	−0.614299	−	0.790576i
$196$	−1.00000			−0.0714286
$197$	−12.8235	+	3.43606i	−0.913639	+	0.244809i	−0.684865	−	0.728670i	$-0.740139\pi$
$197$	−12.8235	+	3.43606i	−0.913639	+	0.244809i	−0.228775	+	0.973479i	$0.573472\pi$
$198$	−2.06488	+	14.7863i	−0.146745	+	1.05082i
$199$	10.9034	−	6.29510i	0.772924	−	0.446248i	−0.0609926	−	0.998138i	$-0.519427\pi$
$199$	10.9034	−	6.29510i	0.772924	−	0.446248i	0.833917	+	0.551890i	$0.186093\pi$
$200$	0.00839368	+	0.00839368i	0.000593523	+	0.000593523i
$201$	−21.2867	−	1.47915i	−1.50145	−	0.104331i
$202$	1.39130	−	5.19239i	0.0978912	−	0.365335i
$203$	−4.49875	+	4.49875i	−0.315750	+	0.315750i
$204$	−3.27443	+	2.84893i	−0.229256	+	0.199465i
$205$	−6.76130	−	3.90364i	−0.472229	−	0.272642i
$206$	−2.71958	−	10.1496i	−0.189482	−	0.707158i
$207$	−3.15187	+	1.27665i	−0.219070	+	0.0887333i
$208$	3.42563	+	1.12476i	0.237524	+	0.0779880i
$209$		−	7.93686i		−	0.549004i
$210$	−1.70134	−	3.48440i	−0.117404	−	0.240446i
$211$	−13.5521	+	23.4730i	−0.932967	+	1.61595i	−0.154748	+	0.987954i	$0.549456\pi$
$211$	−13.5521	+	23.4730i	−0.932967	+	1.61595i	−0.778219	+	0.627992i	$0.783877\pi$
$212$	−0.807182	−	1.39808i	−0.0554375	−	0.0960205i
$213$	−3.93905	−	2.65442i	−0.269900	−	0.181878i
$214$	15.6926	+	4.20482i	1.07272	+	0.287435i
$215$	−16.9814	−	4.55014i	−1.15812	−	0.310317i
$216$	−1.07367	+	5.08402i	−0.0730537	+	0.345924i
$217$	0.968212	+	1.67699i	0.0657265	+	0.113842i
$218$	−6.01371	+	10.4161i	−0.407300	+	0.705464i
$219$	19.0223	−	9.28812i	1.28541	−	0.627633i
$220$			11.1412i			0.751140i
$221$	6.73300	−	6.02488i	0.452911	−	0.405278i
$222$	−0.633103	−	3.24944i	−0.0424911	−	0.218088i
$223$	−2.15953	−	8.05949i	−0.144613	−	0.539704i	−0.999772	−	0.0213380i	$-0.993207\pi$
$223$	−2.15953	−	8.05949i	−0.144613	−	0.539704i	0.855159	−	0.518365i	$-0.173459\pi$
$224$	0.866025	+	0.500000i	0.0578638	+	0.0334077i
$225$	0.0219000	−	0.0280813i	0.00146000	−	0.00187209i
$226$	−0.432519	+	0.432519i	−0.0287707	+	0.0287707i
$227$	−3.42193	+	12.7708i	−0.227121	+	0.847628i	0.754422	+	0.656389i	$0.227917\pi$
$227$	−3.42193	+	12.7708i	−0.227121	+	0.847628i	−0.981544	+	0.191239i	$0.938750\pi$
$228$	0.191485	−	2.75569i	0.0126814	−	0.182500i
$229$	−16.1525	−	16.1525i	−1.06739	−	1.06739i	−0.997559	−	0.0698266i	$-0.977755\pi$
$229$	−16.1525	−	16.1525i	−1.06739	−	1.06739i	−0.0698266	−	0.997559i	$-0.522245\pi$
$230$	−2.19769	+	1.26883i	−0.144911	+	0.0836645i
$231$	2.80274	−	8.15133i	0.184406	−	0.536318i
$232$	6.14540	−	1.64665i	0.403465	−	0.108108i
$233$	−2.62536			−0.171993			−0.0859967	−	0.996295i	$-0.527407\pi$
$233$	−2.62536			−0.171993			−0.0859967	+	0.996295i	$0.527407\pi$
$234$	2.08740	−	10.6133i	0.136457	−	0.693815i
$235$	26.9665			1.75910
$236$	5.35382	−	1.43455i	0.348504	−	0.0933813i
$237$	9.88016	−	28.7349i	0.641786	−	1.86653i
$238$	2.17015	−	1.25294i	0.140670	−	0.0812160i
$239$	−19.2179	−	19.2179i	−1.24310	−	1.24310i	−0.958708	−	0.284393i	$-0.908208\pi$
$239$	−19.2179	−	19.2179i	−1.24310	−	1.24310i	−0.284393	−	0.958708i	$-0.591792\pi$
$240$	−0.268793	+	3.86825i	−0.0173505	+	0.249694i
$241$	2.64967	−	9.88872i	0.170681	−	0.636988i	−0.826567	−	0.562839i	$-0.809709\pi$
$241$	2.64967	−	9.88872i	0.170681	−	0.636988i	0.997247	−	0.0741495i	$-0.0236242\pi$
$242$	−9.73437	+	9.73437i	−0.625749	+	0.625749i
$243$	15.5321	+	1.32463i	0.996383	+	0.0849753i
$244$	2.71743	+	1.56891i	0.173965	+	0.100439i
$245$	0.579424	+	2.16244i	0.0370180	+	0.138153i
$246$	−1.15514	−	5.92884i	−0.0736492	−	0.378009i
$247$	−0.318674	+	5.74143i	−0.0202768	+	0.365318i
$248$		−	1.93642i		−	0.122963i
$249$	10.7394	−	5.24377i	0.680582	−	0.332311i
$250$	−5.58351	+	9.67093i	−0.353132	+	0.611643i
$251$	−10.0300	−	17.3724i	−0.633087	−	1.09654i	−0.986917	−	0.161229i	$-0.948454\pi$
$251$	−10.0300	−	17.3724i	−0.633087	−	1.09654i	0.353830	−	0.935310i	$-0.384879\pi$
$252$	1.16978	−	2.76254i	0.0736889	−	0.174024i
$253$	−5.44893	−	1.46004i	−0.342571	−	0.0917917i
$254$	3.44953	+	0.924299i	0.216443	+	0.0579956i
$255$	8.05792	+	5.43001i	0.504607	+	0.340040i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.14621	+	15.8417i	−0.570525	+	0.988178i	0.425987	+	0.904729i	$0.359927\pi$
$257$	−9.14621	+	15.8417i	−0.570525	+	0.988178i	−0.996512	+	0.0834485i	$0.973407\pi$
$258$	−5.96789	−	12.2224i	−0.371545	−	0.760934i
$259$			1.91134i			0.118765i
$260$	0.447333	−	8.05942i	0.0277424	−	0.499824i
$261$	−7.16544	−	17.6905i	−0.443530	−	1.09501i
$262$	5.68467	+	21.2155i	0.351200	+	1.31070i
$263$	24.5608	+	14.1802i	1.51449	+	0.874389i	0.999856	+	0.0169770i	$0.00540421\pi$
$263$	24.5608	+	14.1802i	1.51449	+	0.874389i	0.514630	+	0.857412i	$0.327929\pi$
$264$	−6.50290	+	5.65789i	−0.400226	+	0.348219i
$265$	−2.55556	+	2.55556i	−0.156987	+	0.156987i
$266$	−0.412774	+	1.54049i	−0.0253088	+	0.0944538i
$267$	−8.56770	−	0.595344i	−0.524335	−	0.0364344i
$268$	−8.71121	−	8.71121i	−0.532122	−	0.532122i
$269$	7.67274	−	4.42986i	0.467815	−	0.270093i	−0.247510	−	0.968885i	$-0.579612\pi$
$269$	7.67274	−	4.42986i	0.467815	−	0.270093i	0.715325	+	0.698792i	$0.246279\pi$
$270$	11.6160	−	0.624064i	0.706926	−	0.0379793i
$271$	20.9937	−	5.62524i	1.27527	−	0.341709i	0.443225	−	0.896410i	$-0.353834\pi$
$271$	20.9937	−	5.62524i	1.27527	−	0.341709i	0.832049	+	0.554701i	$0.187168\pi$
$272$	−2.50588			−0.151941
$273$	−2.35475	+	5.78404i	−0.142516	+	0.350066i
$274$	−3.99602			−0.241408
$275$	0.0570615	−	0.0152896i	0.00344094	−	0.000921997i
$276$	−1.85666	−	0.638389i	−0.111758	−	0.0384265i
$277$	−5.24317	+	3.02715i	−0.315032	+	0.181884i	−0.649176	−	0.760638i	$-0.724886\pi$
$277$	−5.24317	+	3.02715i	−0.315032	+	0.181884i	0.334144	+	0.942522i	$0.391553\pi$
$278$	−7.95104	−	7.95104i	−0.476872	−	0.476872i
$279$	−5.76535	+	0.713020i	−0.345162	+	0.0426874i
$280$	0.579424	−	2.16244i	0.0346272	−	0.129230i
$281$	3.97123	−	3.97123i	0.236904	−	0.236904i	−0.578663	−	0.815567i	$-0.696425\pi$
$281$	3.97123	−	3.97123i	0.236904	−	0.236904i	0.815567	+	0.578663i	$0.196425\pi$
$282$	13.6945	+	15.7398i	0.815497	+	0.937293i
$283$	5.01459	+	2.89518i	0.298087	+	0.172100i	0.641583	−	0.767054i	$-0.278278\pi$
$283$	5.01459	+	2.89518i	0.298087	+	0.172100i	−0.343496	+	0.939154i	$0.611611\pi$
$284$	−0.709782	−	2.64894i	−0.0421178	−	0.157186i
$285$	−6.06997	+	1.18264i	−0.359554	+	0.0700535i
$286$	13.3715	−	11.9652i	0.790675	−	0.707519i
$287$			3.48738i			0.205854i
$288$	−2.39433	+	1.80754i	−0.141087	+	0.106510i
$289$	5.36029	−	9.28429i	0.315311	−	0.546135i
$290$	−7.12158	−	12.3349i	−0.418194	−	0.724332i
$291$	−15.9143	+	23.6162i	−0.932912	+	1.38441i
$292$	11.8054	+	3.16324i	0.690857	+	0.185114i
$293$	−25.7752	−	6.90644i	−1.50580	−	0.403478i	−0.590763	−	0.806845i	$-0.701173\pi$
$293$	−25.7752	−	6.90644i	−1.50580	−	0.403478i	−0.915038	+	0.403367i	$0.867840\pi$
$294$	−0.967922	+	1.43636i	−0.0564504	+	0.0837702i
$295$	−6.20425	−	10.7461i	−0.361226	−	0.625661i
$296$	0.955670	−	1.65527i	0.0555472	−	0.0962105i
$297$	19.2398	+	17.2779i	1.11641	+	1.00256i
$298$			5.74225i			0.332640i
$299$	3.88307	+	1.27495i	0.224564	+	0.0737325i
$300$	0.0201808	−	0.00393191i	0.00116514	−	0.000227009i
$301$	2.03247	+	7.58530i	0.117150	+	0.437209i
$302$	5.84042	+	3.37197i	0.336078	+	0.194035i
$303$	−6.11146	−	7.02422i	−0.351094	−	0.403531i
$304$	1.12772	−	1.12772i	0.0646792	−	0.0646792i
$305$	1.81812	−	6.78533i	0.104105	−	0.388527i
$306$	0.922701	+	7.46080i	0.0527473	+	0.426505i
$307$	11.6341	+	11.6341i	0.663995	+	0.663995i	0.956319	−	0.292324i	$-0.0944287\pi$
$307$	11.6341	+	11.6341i	0.663995	+	0.663995i	−0.292324	+	0.956319i	$0.594429\pi$
$308$	4.30986	−	2.48830i	0.245577	−	0.141784i
$309$	−17.2109	−	5.91775i	−0.979091	−	0.336649i
$310$	−4.18740	+	1.12201i	−0.237828	+	0.0637259i
$311$	−32.9657			−1.86931			−0.934656	−	0.355554i	$-0.884292\pi$
$311$	−32.9657			−1.86931			−0.934656	+	0.355554i	$0.884292\pi$
$312$	4.93130	−	3.83175i	0.279180	−	0.216930i
$313$	0.469408			0.0265325			0.0132663	−	0.999912i	$-0.495777\pi$
$313$	0.469408			0.0265325			0.0132663	+	0.999912i	$0.495777\pi$
$314$	−3.59549	+	0.963408i	−0.202905	+	0.0543682i
$315$	−6.65162	−	0.928887i	−0.374776	−	0.0523368i
$316$	15.1930	−	8.77171i	0.854675	−	0.493447i
$317$	−8.07451	−	8.07451i	−0.453510	−	0.453510i	0.443008	−	0.896518i	$-0.353911\pi$
$317$	−8.07451	−	8.07451i	−0.453510	−	0.453510i	−0.896518	+	0.443008i	$0.853911\pi$
$318$	−2.78943	−	0.193829i	−0.156424	−	0.0108694i
$319$	8.19473	−	30.5832i	0.458817	−	1.71233i
$320$	−1.58301	+	1.58301i	−0.0884932	+	0.0884932i
$321$	21.2288	−	18.4703i	1.18488	−	1.03091i
$322$	0.981671	+	0.566768i	0.0547064	+	0.0315847i
$323$	−1.03436	−	3.86029i	−0.0575535	−	0.214792i
$324$	6.26325	+	6.46310i	0.347958	+	0.359061i
$325$	−0.0418915	+	0.00876922i	−0.00232372	+	0.000486429i
$326$			0.143222i			0.00793233i
$327$	9.14039	+	18.7198i	0.505465	+	1.03521i
$328$	1.74369	−	3.02016i	0.0962792	−	0.166760i
$329$	−6.02275	−	10.4317i	−0.332045	−	0.575118i
$330$	16.0028	+	10.7838i	0.880923	+	0.593629i
$331$	−14.9180	−	3.99725i	−0.819965	−	0.219709i	−0.175634	−	0.984456i	$-0.556198\pi$
$331$	−14.9180	−	3.99725i	−0.819965	−	0.219709i	−0.644331	+	0.764747i	$0.722864\pi$
$332$	6.66493	+	1.78586i	0.365786	+	0.0980120i
$333$	−5.28015	−	2.23584i	−0.289350	−	0.122523i
$334$	−1.83098	−	3.17135i	−0.100187	−	0.173528i
$335$	−13.7900	+	23.8849i	−0.753427	+	1.30497i
$336$	1.55642	−	0.759962i	0.0849099	−	0.0414593i
$337$		−	21.9719i		−	1.19688i	−0.801166	−	0.598442i	$-0.795787\pi$
$337$		−	21.9719i		−	1.19688i	0.801166	−	0.598442i	$-0.204213\pi$
$338$	−10.1532	+	8.11862i	−0.552263	+	0.441595i
$339$	0.202608	+	1.03990i	0.0110042	+	0.0564795i
$340$	1.45197	+	5.41881i	0.0787439	+	0.293876i
$341$	−8.34571	−	4.81840i	−0.451946	−	0.260931i
$342$	−3.77282	−	2.94234i	−0.204011	−	0.159103i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	2.03247	−	7.58530i	0.109584	−	0.408972i
$345$	−0.304686	+	4.38480i	−0.0164038	+	0.236070i
$346$	7.53377	+	7.53377i	0.405018	+	0.405018i
$347$	−23.4175	+	13.5201i	−1.25712	+	0.725798i	−0.972514	−	0.232846i	$-0.925196\pi$
$347$	−23.4175	+	13.5201i	−1.25712	+	0.725798i	−0.284606	+	0.958645i	$0.591863\pi$
$348$	3.58308	−	10.4208i	0.192073	−	0.558615i
$349$	10.1686	−	2.72467i	0.544313	−	0.145848i	0.0238236	−	0.999716i	$-0.492416\pi$
$349$	10.1686	−	2.72467i	0.544313	−	0.145848i	0.520490	+	0.853868i	$0.325749\pi$
$350$	−0.0118705			−0.000634503
$351$	−13.2241	−	13.2711i	−0.705851	−	0.708360i
$352$	−4.97659			−0.265253
$353$	24.4009	−	6.53820i	1.29873	−	0.347993i	0.457759	−	0.889076i	$-0.348652\pi$
$353$	24.4009	−	6.53820i	1.29873	−	0.347993i	0.840969	+	0.541083i	$0.181985\pi$
$354$	3.12155	−	9.07853i	0.165908	−	0.482519i
$355$	−5.31691	+	3.06972i	−0.282192	+	0.162924i
$356$	−3.50618	−	3.50618i	−0.185827	−	0.185827i
$357$	0.300869	−	4.32987i	0.0159237	−	0.229161i
$358$	2.93618	−	10.9580i	0.155182	−	0.579148i
$359$	10.0644	−	10.0644i	0.531180	−	0.531180i	−0.389744	−	0.920923i	$-0.627436\pi$
$359$	10.0644	−	10.0644i	0.531180	−	0.531180i	0.920923	+	0.389744i	$0.127436\pi$
$360$	5.29603	+	4.13025i	0.279125	+	0.217683i
$361$	−14.2517	−	8.22825i	−0.750092	−	0.433066i
$362$	5.45563	+	20.3607i	0.286741	+	1.07013i
$363$	4.55994	+	23.4042i	0.239335	+	1.22840i
$364$	−3.21761	+	1.62696i	−0.168649	+	0.0852758i
$365$		−	27.3612i		−	1.43215i
$366$	4.88377	−	2.38462i	0.255279	−	0.124646i
$367$	10.9933	−	19.0409i	0.573845	−	0.993929i	−0.422321	−	0.906446i	$-0.638784\pi$
$367$	10.9933	−	19.0409i	0.573845	−	0.993929i	0.996166	−	0.0874825i	$-0.0278822\pi$
$368$	−0.566768	−	0.981671i	−0.0295448	−	0.0511731i
$369$	−9.63403	−	4.07945i	−0.501527	−	0.212368i
$370$	−4.13315	−	1.10747i	−0.214872	−	0.0575749i
$371$	1.55936	+	0.417828i	0.0809577	+	0.0216926i
$372$	−2.78140	−	1.87431i	−0.144209	−	0.0971783i
$373$	4.13080	+	7.15475i	0.213885	+	0.370459i	0.952927	−	0.303200i	$-0.0980550\pi$
$373$	4.13080	+	7.15475i	0.213885	+	0.370459i	−0.739042	+	0.673659i	$0.764722\pi$
$374$	−6.23537	+	10.8000i	−0.322423	+	0.558453i
$375$	8.48652	+	17.3806i	0.438242	+	0.897532i
$376$			12.0455i			0.621199i
$377$	−7.15592	+	21.7945i	−0.368549	+	1.12247i
$378$	−2.83575	−	4.35414i	−0.145855	−	0.223953i
$379$	7.14022	+	26.6477i	0.366769	+	1.36880i	0.865007	+	0.501759i	$0.167314\pi$
$379$	7.14022	+	26.6477i	0.366769	+	1.36880i	−0.498239	+	0.867040i	$0.666020\pi$
$380$	−3.09205	−	1.78520i	−0.158619	−	0.0915787i
$381$	4.66650	−	4.06011i	0.239072	−	0.208006i
$382$	10.0774	−	10.0774i	0.515606	−	0.515606i
$383$	−8.42594	+	31.4460i	−0.430545	+	1.60682i	0.320962	+	0.947092i	$0.395994\pi$
$383$	−8.42594	+	31.4460i	−0.430545	+	1.60682i	−0.751507	+	0.659725i	$0.770673\pi$
$384$	−1.72788	−	0.120065i	−0.0881757	−	0.00612707i
$385$	−7.87802	−	7.87802i	−0.401501	−	0.401501i
$386$	−21.3410	+	12.3213i	−1.08623	+	0.627135i
$387$	−23.3322	−	3.25830i	−1.18604	−	0.165629i
$388$	−15.8815	+	4.25543i	−0.806260	+	0.216037i
$389$	8.73060			0.442659			0.221330	−	0.975199i	$-0.428960\pi$
$389$	8.73060			0.442659			0.221330	+	0.975199i	$0.428960\pi$
$390$	−11.1432	−	8.44342i	−0.564260	−	0.427549i
$391$	−2.84050			−0.143650
$392$	−0.965926	+	0.258819i	−0.0487866	+	0.0130723i
$393$	35.9753	+	12.3697i	1.81472	+	0.623968i
$394$	−11.4973	+	6.63795i	−0.579224	+	0.334415i
$395$	−27.7715	−	27.7715i	−1.39733	−	1.39733i
$396$	1.83245	+	14.8169i	0.0920843	+	0.744577i
$397$	−0.479393	+	1.78912i	−0.0240600	+	0.0897933i	−0.976912	−	0.213643i	$-0.931467\pi$
$397$	−0.479393	+	1.78912i	−0.0240600	+	0.0897933i	0.952852	+	0.303436i	$0.0981338\pi$
$398$	8.90262	−	8.90262i	0.446248	−	0.446248i
$399$	1.81317	+	2.08397i	0.0907720	+	0.104329i
$400$	0.0102801	+	0.00593523i	0.000514006	+	0.000296761i
$401$	−4.16963	−	15.5613i	−0.208221	−	0.777093i	−0.988443	−	0.151590i	$-0.951561\pi$
$401$	−4.16963	−	15.5613i	−0.208221	−	0.777093i	0.780222	−	0.625503i	$-0.215106\pi$
$402$	−20.9442	+	4.08066i	−1.04460	+	0.203525i
$403$	5.84373	+	3.82066i	0.291097	+	0.190321i
$404$		−	5.37555i		−	0.267444i
$405$	10.3470	−	17.2888i	0.514146	−	0.859086i
$406$	−3.18109	+	5.50981i	−0.157875	+	0.273448i
$407$	−4.75598	−	8.23760i	−0.235745	−	0.408323i
$408$	−2.42549	+	3.59934i	−0.120080	+	0.178194i
$409$	−4.38075	−	1.17382i	−0.216614	−	0.0580416i	0.148880	−	0.988855i	$-0.452433\pi$
$409$	−4.38075	−	1.17382i	−0.216614	−	0.0580416i	−0.365494	+	0.930814i	$0.619100\pi$
$410$	−7.54124	−	2.02067i	−0.372436	−	0.0997938i
$411$	−3.86784	+	5.73972i	−0.190786	+	0.283120i
$412$	−5.25383	−	9.09991i	−0.258838	−	0.448320i
$413$	−2.77134	+	4.80010i	−0.136369	+	0.236197i
$414$	−2.71405	+	2.04891i	−0.133388	+	0.100699i
$415$		−	15.4473i		−	0.758277i
$416$	3.60001	+	0.199816i	0.176505	+	0.00979679i
$417$	−19.1165	+	3.72456i	−0.936141	+	0.182393i
$418$	−2.05421	−	7.66641i	−0.100475	−	0.374977i
$419$	27.3709	+	15.8026i	1.33716	+	0.772008i	0.986385	−	0.164453i	$-0.0525860\pi$
$419$	27.3709	+	15.8026i	1.33716	+	0.772008i	0.350772	+	0.936461i	$0.385919\pi$
$420$	−2.54520	−	2.92533i	−0.124193	−	0.142742i
$421$	−7.48230	+	7.48230i	−0.364665	+	0.364665i	−0.865527	−	0.500862i	$-0.833016\pi$
$421$	−7.48230	+	7.48230i	−0.364665	+	0.364665i	0.500862	+	0.865527i	$0.333016\pi$
$422$	−7.01510	+	26.1807i	−0.341490	+	1.27446i
$423$	35.8633	−	4.43533i	1.74373	−	0.215653i
$424$	−1.14153	−	1.14153i	−0.0554375	−	0.0554375i
$425$	0.0257607	−	0.0148730i	0.00124958	−	0.000721445i
$426$	−4.49185	−	1.54447i	−0.217631	−	0.0748297i
$427$	−3.03090	+	0.812126i	−0.146675	+	0.0393015i
$428$	16.2462			0.785288
$429$	−4.24377	−	30.7877i	−0.204891	−	1.48644i
$430$	−17.5804			−0.847802
$431$	28.2946	−	7.58152i	1.36290	−	0.365189i	0.498021	−	0.867165i	$-0.334060\pi$
$431$	28.2946	−	7.58152i	1.36290	−	0.365189i	0.864882	+	0.501976i	$0.167393\pi$
$432$	0.278759	+	5.18867i	0.0134118	+	0.249640i
$433$	1.27868	−	0.738247i	0.0614495	−	0.0354779i	−0.468960	−	0.883219i	$-0.655371\pi$
$433$	1.27868	−	0.738247i	0.0614495	−	0.0354779i	0.530410	+	0.847741i	$0.322038\pi$
$434$	1.36926	+	1.36926i	0.0657265	+	0.0657265i
$435$	−24.6105	−	1.71011i	−1.17998	−	0.0819936i
$436$	−3.11293	+	11.6176i	−0.149082	+	0.556382i
$437$	1.27831	−	1.27831i	0.0611499	−	0.0611499i
$438$	15.9702	−	13.8950i	0.763086	−	0.663928i
$439$	4.51923	+	2.60918i	0.215691	+	0.124529i	0.603953	−	0.797020i	$-0.293591\pi$
$439$	4.51923	+	2.60918i	0.215691	+	0.124529i	−0.388263	+	0.921549i	$0.626925\pi$
$440$	2.88356	+	10.7616i	0.137468	+	0.513038i
$441$	1.12625	+	2.78057i	0.0536312	+	0.132408i
$442$	4.94423	−	7.56222i	0.235173	−	0.359698i
$443$			31.3186i			1.48799i	0.668184	+	0.743996i	$0.267072\pi$
$443$			31.3186i			1.48799i	−0.668184	+	0.743996i	$0.732928\pi$
$444$	−1.45255	−	2.97486i	−0.0689348	−	0.141180i
$445$	−5.55034	+	9.61347i	−0.263111	+	0.455722i
$446$	−4.17190	−	7.22594i	−0.197545	−	0.342158i
$447$	8.24793	+	5.55805i	0.390114	+	0.262887i
$448$	0.965926	+	0.258819i	0.0456357	+	0.0122281i
$449$	−14.3287	−	3.83936i	−0.676213	−	0.181191i	−0.0956610	−	0.995414i	$-0.530496\pi$
$449$	−14.3287	−	3.83936i	−0.676213	−	0.181191i	−0.580552	+	0.814223i	$0.697163\pi$
$450$	0.0138858	−	0.0327926i	0.000654581	−	0.00154586i
$451$	−8.67764	−	15.0301i	−0.408614	−	0.707740i
$452$	−0.305837	+	0.529726i	−0.0143854	+	0.0249162i
$453$	10.4964	−	5.12514i	0.493165	−	0.240800i
$454$			13.2213i			0.620507i
$455$	5.38256	+	6.01518i	0.252338	+	0.281996i
$456$	−0.528266	−	2.71136i	−0.0247383	−	0.126971i
$457$	9.76856	+	36.4568i	0.456954	+	1.70537i	0.682280	+	0.731091i	$0.260989\pi$
$457$	9.76856	+	36.4568i	0.456954	+	1.70537i	−0.225326	+	0.974283i	$0.572345\pi$
$458$	−19.7827	−	11.4215i	−0.924383	−	0.533693i
$459$	11.6095	+	5.89614i	0.541884	+	0.275208i
$460$	−1.79440	+	1.79440i	−0.0836645	+	0.0836645i
$461$	−5.51810	+	20.5938i	−0.257004	+	0.959150i	0.709961	+	0.704241i	$0.248712\pi$
$461$	−5.51810	+	20.5938i	−0.257004	+	0.959150i	−0.966965	+	0.254910i	$0.917954\pi$
$462$	0.597517	−	8.59898i	0.0277990	−	0.400061i
$463$	13.5636	+	13.5636i	0.630356	+	0.630356i	0.948157	−	0.317801i	$-0.102944\pi$
$463$	13.5636	+	13.5636i	0.630356	+	0.630356i	−0.317801	+	0.948157i	$0.602944\pi$
$464$	5.50981	−	3.18109i	0.255787	−	0.147679i
$465$	−2.44147	+	7.10063i	−0.113220	+	0.329284i
$466$	−2.53591	+	0.679494i	−0.117474	+	0.0314770i
$467$	17.4566			0.807796			0.403898	−	0.914804i	$-0.367655\pi$
$467$	17.4566			0.807796			0.403898	+	0.914804i	$0.367655\pi$
$468$	−0.730660	−	10.7919i	−0.0337748	−	0.498858i
$469$	12.3195			0.568862
$470$	26.0476	−	6.97944i	1.20149	−	0.321938i
$471$	−2.09635	+	6.09691i	−0.0965947	+	0.280931i
$472$	4.80010	−	2.77134i	0.220943	−	0.127561i
$473$	−27.6341	−	27.6341i	−1.27062	−	1.27062i
$474$	2.10636	−	30.3130i	0.0967482	−	1.39232i
$475$	−0.00489982	+	0.0182864i	−0.000224819	+	0.000839036i
$476$	1.77192	−	1.77192i	0.0812160	−	0.0812160i
$477$	−2.97836	+	3.81902i	−0.136370	+	0.174861i
$478$	−23.5370	−	13.5891i	−1.07656	−	0.621550i
$479$	2.23517	+	8.34178i	0.102128	+	0.381146i	0.998003	−	0.0631589i	$-0.0201175\pi$
$479$	2.23517	+	8.34178i	0.102128	+	0.381146i	−0.895876	+	0.444304i	$0.853451\pi$
$480$	0.741543	+	3.80601i	0.0338466	+	0.173720i
$481$	3.10967	+	6.14994i	0.141789	+	0.280413i
$482$		−	10.2376i		−	0.466308i
$483$	1.76426	−	0.861444i	0.0802767	−	0.0391971i
$484$	−6.88324	+	11.9221i	−0.312874	+	0.541915i
$485$	18.4042	+	31.8770i	0.835692	+	1.44746i
$486$	15.3457	−	2.74050i	0.696094	−	0.124312i
$487$	0.718108	+	0.192417i	0.0325406	+	0.00871922i	0.275053	−	0.961429i	$-0.411305\pi$
$487$	0.718108	+	0.192417i	0.0325406	+	0.00871922i	−0.242512	+	0.970148i	$0.577971\pi$
$488$	3.03090	+	0.812126i	0.137202	+	0.0367632i
$489$	0.205718	+	0.138628i	0.00930289	+	0.00626896i
$490$	1.11936	+	1.93879i	0.0505675	+	0.0875856i
$491$	17.7481	−	30.7405i	0.800959	−	1.38730i	−0.118027	−	0.993010i	$-0.537657\pi$
$491$	17.7481	−	30.7405i	0.800959	−	1.38730i	0.918986	−	0.394291i	$-0.129010\pi$
$492$	−2.65028	−	5.42784i	−0.119484	−	0.244706i
$493$		−	15.9429i		−	0.718031i
$494$	1.17818	+	5.62827i	0.0530086	+	0.253228i
$495$	30.9789	−	12.5478i	1.39240	−	0.563983i
$496$	−0.501184	−	1.87044i	−0.0225038	−	0.0839853i
$497$	2.37498	+	1.37119i	0.106532	+	0.0615065i
$498$	9.01627	−	7.84466i	0.404029	−	0.351528i
$499$	27.6348	−	27.6348i	1.23710	−	1.23710i	0.275921	−	0.961180i	$-0.411017\pi$
$499$	27.6348	−	27.6348i	1.23710	−	1.23710i	0.961180	−	0.275921i	$-0.0889829\pi$
$500$	−2.89024	+	10.7865i	−0.129255	+	0.482388i
$501$	−6.32744	−	0.439675i	−0.282689	−	0.0196432i
$502$	−14.1845	−	14.1845i	−0.633087	−	0.633087i
$503$	−11.4842	+	6.63042i	−0.512056	+	0.295636i	−0.733679	−	0.679497i	$-0.762198\pi$
$503$	−11.4842	+	6.63042i	−0.512056	+	0.295636i	0.221622	+	0.975133i	$0.428865\pi$
$504$	0.414918	−	2.97117i	0.0184819	−	0.132346i
$505$	−11.6243	+	3.11472i	−0.517275	+	0.138603i
$506$	−5.64114			−0.250779
$507$	1.83373	+	22.4419i	0.0814388	+	0.996678i
$508$	3.57122			0.158447
$509$	29.5365	−	7.91427i	1.30918	−	0.350794i	0.464267	−	0.885695i	$-0.346318\pi$
$509$	29.5365	−	7.91427i	1.30918	−	0.350794i	0.844914	+	0.534901i	$0.179651\pi$
$510$	9.18874	+	3.15944i	0.406884	+	0.139902i
$511$	−10.5844	+	6.11091i	−0.468226	+	0.270331i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−7.87805	+	2.57118i	−0.347825	+	0.113520i
$514$	−4.73442	+	17.6691i	−0.208826	+	0.779351i
$515$	−16.6338	+	16.6338i	−0.732972	+	0.732972i
$516$	−8.92793	−	10.2613i	−0.393030	−	0.451730i
$517$	51.9143	+	29.9728i	2.28319	+	1.31820i
$518$	0.494691	+	1.84621i	0.0217355	+	0.0811179i
$519$	18.1133	−	3.52910i	0.795086	−	0.154910i
$520$	−1.65384	−	7.90058i	−0.0725257	−	0.346463i
$521$			37.9878i			1.66428i	0.554568	+	0.832138i	$0.312883\pi$
$521$			37.9878i			1.66428i	−0.554568	+	0.832138i	$0.687117\pi$
$522$	−11.4999	−	15.2331i	−0.503338	−	0.666737i
$523$	−5.61192	+	9.72013i	−0.245392	+	0.425032i	−0.962242	−	0.272196i	$-0.912250\pi$
$523$	−5.61192	+	9.72013i	−0.245392	+	0.425032i	0.716850	+	0.697228i	$0.245583\pi$
$524$	10.9819	+	19.0213i	0.479748	+	0.830948i
$525$	−0.0114897	+	0.0170502i	−0.000501450	+	0.000744133i
$526$	27.3941	+	7.34022i	1.19444	+	0.320049i
$527$	−4.68710	−	1.25591i	−0.204173	−	0.0547081i
$528$	−4.81695	+	7.14817i	−0.209631	+	0.311084i
$529$	10.8575	+	18.8058i	0.472067	+	0.817645i
$530$	−1.80705	+	3.12991i	−0.0784934	+	0.135955i
$531$	−10.0186	−	13.2710i	−0.434771	−	0.575911i
$532$			1.59484i			0.0691450i
$533$	5.67383	+	11.2210i	0.245761	+	0.486037i
$534$	−8.42985	+	1.64243i	−0.364795	+	0.0710747i
$535$	−9.41341	−	35.1313i	−0.406977	−	1.51886i
$536$	−10.6690	−	6.15976i	−0.460831	−	0.266061i
$537$	−12.8976	−	14.8239i	−0.556573	−	0.639698i
$538$	6.26477	−	6.26477i	0.270093	−	0.270093i
$539$	−1.28804	+	4.80702i	−0.0554797	+	0.207053i
$540$	11.0587	−	3.60924i	0.475889	−	0.155317i
$541$	21.3151	+	21.3151i	0.916409	+	0.916409i	0.996766	−	0.0803571i	$-0.0256061\pi$
$541$	21.3151	+	21.3151i	0.916409	+	0.916409i	−0.0803571	+	0.996766i	$0.525606\pi$
$542$	18.8224	−	10.8671i	0.808492	−	0.466783i
$543$	34.5259	+	11.8713i	1.48165	+	0.509446i
$544$	−2.42049	+	0.648569i	−0.103778	+	0.0278072i
$545$	26.9260			1.15339
$546$	−0.777496	+	6.19641i	−0.0332738	+	0.265182i
$547$	−8.55508			−0.365789			−0.182894	−	0.983133i	$-0.558547\pi$
$547$	−8.55508			−0.365789			−0.182894	+	0.983133i	$0.558547\pi$
$548$	−3.85986	+	1.03425i	−0.164885	+	0.0441808i
$549$	1.30194	−	9.32298i	0.0555653	−	0.397895i
$550$	0.0511600	−	0.0295372i	0.00218147	−	0.00125947i
$551$	7.17477	+	7.17477i	0.305655	+	0.305655i
$552$	−1.95862	−	0.136098i	−0.0833643	−	0.00579274i
$553$	−4.54057	+	16.9456i	−0.193085	+	0.720602i
$554$	−4.28103	+	4.28103i	−0.181884	+	0.181884i
$555$	−5.59130	+	4.86474i	−0.237338	+	0.206497i
$556$	−9.73800	−	5.62224i	−0.412983	−	0.238436i
$557$	8.11955	+	30.3026i	0.344037	+	1.28396i	0.893734	+	0.448598i	$0.148076\pi$
$557$	8.11955	+	30.3026i	0.344037	+	1.28396i	−0.549697	+	0.835364i	$0.685257\pi$
$558$	−5.38436	+	2.18091i	−0.227938	+	0.0923251i
$559$	18.8807	+	21.0998i	0.798568	+	0.892425i
$560$		−	2.23872i		−	0.0946032i
$561$	9.47729	+	19.4098i	0.400132	+	0.819481i
$562$	2.80809	−	4.86375i	0.118452	−	0.205165i
$563$	−18.7355	−	32.4508i	−0.789605	−	1.36764i	−0.926209	−	0.377010i	$-0.876952\pi$
$563$	−18.7355	−	32.4508i	−0.789605	−	1.36764i	0.136604	−	0.990626i	$-0.456381\pi$
$564$	17.3017	+	11.6591i	0.728531	+	0.490937i
$565$	1.32271	+	0.354419i	0.0556467	+	0.0149105i
$566$	5.59305	+	1.49865i	0.235094	+	0.0629931i
$567$	−8.99889	−	0.141316i	−0.377918	−	0.00593473i
$568$	−1.37119	−	2.37498i	−0.0575340	−	0.0996519i
$569$	−15.1741	+	26.2824i	−0.636133	+	1.10181i	0.350141	+	0.936697i	$0.386134\pi$
$569$	−15.1741	+	26.2824i	−0.636133	+	1.10181i	−0.986274	+	0.165117i	$0.947200\pi$
$570$	−5.55705	+	2.71337i	−0.232759	+	0.113650i
$571$		−	23.8669i		−	0.998797i	−0.866372	−	0.499398i	$-0.833554\pi$
$571$		−	23.8669i		−	0.998797i	0.866372	−	0.499398i	$-0.166446\pi$
$572$	9.81907	−	15.0183i	0.410556	−	0.627948i
$573$	−4.72064	−	24.2290i	−0.197208	−	1.01218i
$574$	0.902600	+	3.36855i	0.0376738	+	0.140601i
$575$	0.0116529	+	0.00672779i	0.000485959	+	0.000280568i
$576$	−1.84491	+	2.36565i	−0.0768714	+	0.0985687i
$577$	4.27637	−	4.27637i	0.178027	−	0.178027i	−0.612468	−	0.790495i	$-0.709823\pi$
$577$	4.27637	−	4.27637i	0.178027	−	0.178027i	0.790495	+	0.612468i	$0.209823\pi$
$578$	2.77469	−	10.3553i	0.115412	−	0.430723i
$579$	−2.95871	+	42.5794i	−0.122960	+	1.76954i
$580$	−10.0714	−	10.0714i	−0.418194	−	0.418194i
$581$	−5.97561	+	3.45002i	−0.247910	+	0.143131i
$582$	−9.25970	+	26.9304i	−0.383827	+	1.11630i
$583$	−7.76028	+	2.07936i	−0.321398	+	0.0861183i
$584$	12.2218			0.505742
$585$	−22.9136	+	7.83312i	−0.947359	+	0.323859i
$586$	−26.6844			−1.10232
$587$	7.17007	−	1.92122i	0.295941	−	0.0792970i	−0.107794	−	0.994173i	$-0.534379\pi$
$587$	7.17007	−	1.92122i	0.295941	−	0.0792970i	0.403734	+	0.914876i	$0.367712\pi$
$588$	−0.563184	+	1.63793i	−0.0232253	+	0.0675472i
$589$	2.67453	−	1.54414i	0.110202	−	0.0636252i
$590$	−8.77414	−	8.77414i	−0.361226	−	0.361226i
$591$	−1.59398	+	22.9392i	−0.0655675	+	0.943594i
$592$	0.494691	−	1.84621i	0.0203317	−	0.0758788i
$593$	20.8143	−	20.8143i	0.854743	−	0.854743i	−0.135970	−	0.990713i	$-0.543415\pi$
$593$	20.8143	−	20.8143i	0.854743	−	0.854743i	0.990713	+	0.135970i	$0.0434151\pi$
$594$	23.0561	+	11.7095i	0.946001	+	0.480448i
$595$	−4.85837	−	2.80498i	−0.199174	−	0.114993i
$596$	1.48620	+	5.54659i	0.0608773	+	0.227197i
$597$	−4.17032	−	21.4044i	−0.170680	−	0.876024i
$598$	4.08074	+	0.226499i	0.166874	+	0.00926222i
$599$		−	26.0281i		−	1.06348i	−0.846908	−	0.531739i	$-0.821539\pi$
$599$		−	26.0281i		−	1.06348i	0.846908	−	0.531739i	$-0.178461\pi$
$600$	0.0184755	−	0.00902110i	0.000754258	−	0.000368285i
$601$	1.89419	−	3.28084i	0.0772657	−	0.133828i	−0.824804	−	0.565419i	$-0.808714\pi$
$601$	1.89419	−	3.28084i	0.0772657	−	0.133828i	0.902069	+	0.431591i	$0.142048\pi$
$602$	3.92644	+	6.80079i	0.160030	+	0.277180i
$603$	−14.4111	+	34.0332i	−0.586864	+	1.38594i
$604$	6.51414	+	1.74546i	0.265057	+	0.0710217i
$605$	29.7692	+	7.97662i	1.21029	+	0.324296i
$606$	−7.72122	−	5.20312i	−0.313653	−	0.211362i
$607$	−2.64461	−	4.58060i	−0.107341	−	0.185921i	0.807351	−	0.590071i	$-0.200900\pi$
$607$	−2.64461	−	4.58060i	−0.107341	−	0.185921i	−0.914692	+	0.404151i	$0.867567\pi$
$608$	0.797419	−	1.38117i	0.0323396	−	0.0560138i
$609$	4.83502	+	9.90226i	0.195925	+	0.401260i
$610$		−	7.02469i		−	0.284421i
$611$	−36.3508	−	23.7664i	−1.47060	−	0.961484i
$612$	2.82226	+	6.96776i	0.114083	+	0.281655i
$613$	8.05524	+	30.0626i	0.325348	+	1.21422i	0.913961	+	0.405801i	$0.133007\pi$
$613$	8.05524	+	30.0626i	0.325348	+	1.21422i	−0.588613	+	0.808415i	$0.700326\pi$
$614$	14.2488	+	8.22657i	0.575036	+	0.331997i
$615$	−10.2017	+	8.87608i	−0.411374	+	0.357918i
$616$	3.51898	−	3.51898i	0.141784	−	0.141784i
$617$	−5.64026	+	21.0497i	−0.227068	+	0.847430i	0.754497	+	0.656303i	$0.227881\pi$
$617$	−5.64026	+	21.0497i	−0.227068	+	0.847430i	−0.981565	+	0.191127i	$0.938786\pi$
$618$	−18.1560	−	1.26161i	−0.730343	−	0.0507493i
$619$	−3.03970	−	3.03970i	−0.122176	−	0.122176i	0.643375	−	0.765551i	$-0.277534\pi$
$619$	−3.03970	−	3.03970i	−0.122176	−	0.122176i	−0.765551	+	0.643375i	$0.777534\pi$
$620$	−3.75432	+	2.16756i	−0.150777	+	0.0870512i
$621$	0.315983	+	5.88154i	0.0126800	+	0.236018i
$622$	−31.8424	+	8.53214i	−1.27676	+	0.342108i
$623$	4.95849			0.198658
$624$	3.77154	−	4.97750i	0.150982	−	0.199259i
$625$	25.0592			1.00237
$626$	0.453414	−	0.121492i	0.0181221	−	0.00485579i
$627$	−13.0000	−	4.46991i	−0.519171	−	0.178511i
$628$	−3.22362	+	1.86116i	−0.128637	+	0.0742684i
$629$	−3.38675	−	3.38675i	−0.135038	−	0.135038i
$630$	−6.66538	+	0.824330i	−0.265555	+	0.0328421i
$631$	−8.03819	+	29.9989i	−0.319995	+	1.19424i	0.599253	+	0.800560i	$0.295464\pi$
$631$	−8.03819	+	29.9989i	−0.319995	+	1.19424i	−0.919248	+	0.393679i	$0.871202\pi$
$632$	12.4051	−	12.4051i	0.493447	−	0.493447i
$633$	30.8148	+	35.4171i	1.22478	+	1.40770i
$634$	−9.88922	−	5.70954i	−0.392751	−	0.226755i
$635$	−2.06925	−	7.72253i	−0.0821155	−	0.306459i
$636$	−2.74455	+	0.534734i	−0.108829	+	0.0212036i
$637$	1.12476	−	3.42563i	0.0445646	−	0.135728i
$638$		−	31.6620i		−	1.25351i
$639$	−6.56617	+	4.95698i	−0.259754	+	0.196095i
$640$	−1.11936	+	1.93879i	−0.0442466	+	0.0766374i
$641$	−17.8622	−	30.9382i	−0.705513	−	1.22198i	−0.966506	−	0.256643i	$-0.917383\pi$
$641$	−17.8622	−	30.9382i	−0.705513	−	1.22198i	0.260993	−	0.965341i	$-0.415950\pi$
$642$	15.7250	−	23.3353i	0.620617	−	0.920972i
$643$	3.75070	+	1.00500i	0.147913	+	0.0396332i	0.332016	−	0.943274i	$-0.392271\pi$
$643$	3.75070	+	1.00500i	0.147913	+	0.0396332i	−0.184103	+	0.982907i	$0.558938\pi$
$644$	1.09491	+	0.293381i	0.0431455	+	0.0115608i
$645$	−17.0165	+	25.2518i	−0.670022	+	0.994287i
$646$	−1.99823	−	3.46104i	−0.0786195	−	0.136173i
$647$	−3.36667	+	5.83124i	−0.132357	+	0.229250i	−0.924585	−	0.380976i	$-0.875588\pi$
$647$	−3.36667	+	5.83124i	−0.132357	+	0.229250i	0.792228	+	0.610226i	$0.208921\pi$
$648$	7.72261	+	4.62183i	0.303373	+	0.181563i
$649$		−	27.5837i		−	1.08275i
$650$	−0.0381945	+	0.0193127i	−0.00149811	+	0.000757508i
$651$	3.29208	−	0.641412i	0.129027	−	0.0251389i
$652$	0.0370686	+	0.138342i	0.00145172	+	0.00541788i
$653$	28.4810	+	16.4435i	1.11455	+	0.643486i	0.940004	−	0.341164i	$-0.110821\pi$
$653$	28.4810	+	16.4435i	1.11455	+	0.643486i	0.174546	+	0.984649i	$0.444154\pi$
$654$	13.6740	+	15.7162i	0.534695	+	0.614552i
$655$	34.7691	−	34.7691i	1.35854	−	1.35854i
$656$	0.902600	−	3.36855i	0.0352406	−	0.131520i
$657$	−4.50025	−	36.3882i	−0.175571	−	1.41964i
$658$	−8.51745	−	8.51745i	−0.332045	−	0.332045i
$659$	34.6566	−	20.0090i	1.35003	−	0.779441i	0.361778	−	0.932264i	$-0.382170\pi$
$659$	34.6566	−	20.0090i	1.35003	−	0.779441i	0.988254	+	0.152823i	$0.0488366\pi$
$660$	18.2485	+	6.27454i	0.710323	+	0.244236i
$661$	−41.2876	+	11.0630i	−1.60590	+	0.430300i	−0.946818	−	0.321769i	$-0.895722\pi$
$661$	−41.2876	+	11.0630i	−1.60590	+	0.430300i	−0.659084	+	0.752069i	$0.729056\pi$
$662$	−15.4442			−0.600256
$663$	−6.07644	−	14.4213i	−0.235989	−	0.560078i
$664$	6.90004			0.267774
$665$	3.44874	−	0.924086i	0.133736	−	0.0358345i
$666$	−5.67891	−	0.793050i	−0.220053	−	0.0307301i
$667$	6.24557	−	3.60588i	0.241829	−	0.139620i
$668$	−2.58940	−	2.58940i	−0.100187	−	0.100187i
$669$	−14.4171	−	1.00180i	−0.557398	−	0.0387319i
$670$	−7.13822	+	26.6402i	−0.275773	+	1.02920i
$671$	11.0419	−	11.0419i	0.426268	−	0.426268i
$672$	1.30670	−	1.13690i	0.0504070	−	0.0438569i
$673$	22.2799	+	12.8633i	0.858828	+	0.495845i	0.863620	−	0.504144i	$-0.168192\pi$
$673$	22.2799	+	12.8633i	0.858828	+	0.495845i	−0.00479162	+	0.999989i	$0.501525\pi$
$674$	−5.68674	−	21.2232i	−0.219045	−	0.817487i
$675$	−0.0336616	−	0.0516856i	−0.00129564	−	0.00198938i
$676$	−7.70601	+	10.4698i	−0.296385	+	0.402686i
$677$			29.2077i			1.12254i	0.827631	+	0.561272i	$0.189688\pi$
$677$			29.2077i			1.12254i	−0.827631	+	0.561272i	$0.810312\pi$
$678$	0.464850	+	0.952025i	0.0178524	+	0.0365623i
$679$	8.22085	−	14.2389i	0.315487	−	0.546440i
$680$	2.80498	+	4.85837i	0.107566	+	0.186310i
$681$	18.9905	+	12.7972i	0.727719	+	0.490389i
$682$	−9.30843	−	2.49419i	−0.356438	−	0.0955073i
$683$	−25.1156	−	6.72971i	−0.961022	−	0.257505i	−0.255989	−	0.966680i	$-0.582401\pi$
$683$	−25.1156	−	6.72971i	−0.961022	−	0.257505i	−0.705033	+	0.709174i	$0.749068\pi$
$684$	−4.40580	−	1.86560i	−0.168460	−	0.0713331i
$685$	4.47299	+	7.74744i	0.170904	+	0.296015i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−35.5535	+	17.3599i	−1.35645	+	0.662320i
$688$		−	7.85288i		−	0.299388i
$689$	5.69719	−	1.19260i	0.217045	−	0.0454345i
$690$	0.840565	+	4.31425i	0.0319998	+	0.164241i
$691$	−3.58545	−	13.3811i	−0.136397	−	0.509041i	−0.999988	−	0.00484814i	$-0.998457\pi$
$691$	−3.58545	−	13.3811i	−0.136397	−	0.509041i	0.863591	−	0.504193i	$-0.168210\pi$
$692$	9.22695	+	5.32718i	0.350756	+	0.202509i
$693$	−11.7729	−	9.18139i	−0.447214	−	0.348772i
$694$	−19.1203	+	19.1203i	−0.725798	+	0.725798i
$695$	−6.51531	+	24.3155i	−0.247140	+	0.922339i
$696$	0.763879	−	10.9931i	0.0289548	−	0.416693i
$697$	−6.17937	−	6.17937i	−0.234060	−	0.234060i
$698$	9.11693	−	5.26366i	0.345081	−	0.199233i
$699$	−1.47856	+	4.30017i	−0.0559244	+	0.162647i
$700$	−0.0114660	+	0.00307230i	−0.000433373	+	0.000116122i
$701$	20.7025			0.781924			0.390962	−	0.920407i	$-0.372142\pi$
$701$	20.7025			0.781924			0.390962	+	0.920407i	$0.372142\pi$
$702$	−16.2083	−	9.39627i	−0.611744	−	0.354639i
$703$	3.04827			0.114968
$704$	−4.80702	+	1.28804i	−0.181171	+	0.0485447i
$705$	15.1871	−	44.1693i	0.571979	−	1.66351i
$706$	21.8772	−	12.6308i	0.823361	−	0.475368i
$707$	3.80109	+	3.80109i	0.142955	+	0.142955i
$708$	0.665484	−	9.57711i	0.0250104	−	0.359930i
$709$	−4.80853	+	17.9457i	−0.180588	+	0.673964i	0.814944	+	0.579540i	$0.196768\pi$
$709$	−4.80853	+	17.9457i	−0.180588	+	0.673964i	−0.995532	+	0.0944240i	$0.969899\pi$
$710$	−4.34124	+	4.34124i	−0.162924	+	0.162924i
$711$	−41.5015	−	32.3661i	−1.55643	−	1.21382i
$712$	−4.29418	−	2.47925i	−0.160931	−	0.0929137i
$713$	−0.568109	−	2.12021i	−0.0212759	−	0.0794026i
$714$	−0.830035	−	4.26020i	−0.0310633	−	0.159434i
$715$	−38.1656	−	12.5312i	−1.42731	−	0.468639i
$716$		−	11.3445i		−	0.423966i
$717$	−42.3008	+	20.6544i	−1.57975	+	0.771352i
$718$	7.11662	−	12.3263i	0.265590	−	0.460015i
$719$	1.20412	+	2.08560i	0.0449063	+	0.0777799i	0.887605	−	0.460606i	$-0.152368\pi$
$719$	1.20412	+	2.08560i	0.0449063	+	0.0777799i	−0.842699	+	0.538386i	$0.819034\pi$
$720$	6.18455	+	2.61880i	0.230485	+	0.0975969i
$721$	10.1496	+	2.71958i	0.377992	+	0.101283i
$722$	−15.8958	−	4.25925i	−0.591579	−	0.158513i
$723$	−14.7048	−	9.90915i	−0.546878	−	0.368525i
$724$	10.5395	+	18.2549i	0.391696	+	0.678437i
$725$	−0.0377610	+	0.0654040i	−0.00140241	+	0.00242904i
$726$	10.4620	+	21.4265i	0.388281	+	0.795211i
$727$		−	19.3374i		−	0.717186i	−0.933494	−	0.358593i	$-0.883257\pi$
$727$		−	19.3374i		−	0.717186i	0.933494	−	0.358593i	$-0.116743\pi$
$728$	−2.68688	+	2.40430i	−0.0995825	+	0.0891093i
$729$	10.9171	−	24.6945i	0.404336	−	0.914610i
$730$	−7.08161	−	26.4289i	−0.262102	−	0.978178i
$731$	−17.0420	−	9.83918i	−0.630320	−	0.363915i
$732$	4.10018	−	3.56738i	0.151547	−	0.131854i
$733$	29.1374	−	29.1374i	1.07622	−	1.07622i	0.0793711	−	0.996845i	$-0.474709\pi$
$733$	29.1374	−	29.1374i	1.07622	−	1.07622i	0.996845	−	0.0793711i	$-0.0252912\pi$
$734$	5.69055	−	21.2374i	0.210042	−	0.783887i
$735$	3.86825	+	0.268793i	0.142683	+	0.00991458i
$736$	−0.801531	−	0.801531i	−0.0295448	−	0.0295448i
$737$	−53.0953	+	30.6546i	−1.95579	+	1.12918i
$738$	−10.3616	−	1.44698i	−0.381416	−	0.0532640i
$739$	−32.0414	+	8.58548i	−1.17866	+	0.315822i	−0.794396	−	0.607400i	$-0.792212\pi$
$739$	−32.0414	+	8.58548i	−1.17866	+	0.315822i	−0.384267	+	0.923222i	$0.625546\pi$
$740$	−4.27895			−0.157298
$741$	9.22461	+	3.75545i	0.338874	+	0.137960i
$742$	1.61436			0.0592652
$743$	−3.74703	+	1.00401i	−0.137465	+	0.0368337i	−0.326896	−	0.945060i	$-0.606003\pi$
$743$	−3.74703	+	1.00401i	−0.137465	+	0.0368337i	0.189430	+	0.981894i	$0.439336\pi$
$744$	−3.17173	−	1.09056i	−0.116281	−	0.0399820i
$745$	11.1330	−	6.42765i	0.407882	−	0.235491i
$746$	5.84183	+	5.84183i	0.213885	+	0.213885i
$747$	−2.54070	−	20.5436i	−0.0929592	−	0.751652i
$748$	−3.22766	+	12.0458i	−0.118015	+	0.440438i
$749$	−11.4878	+	11.4878i	−0.419754	+	0.419754i
$750$	12.6958	+	14.5919i	0.463585	+	0.532822i
$751$	−9.20781	−	5.31613i	−0.335998	−	0.193988i	0.322503	−	0.946568i	$-0.395476\pi$
$751$	−9.20781	−	5.31613i	−0.335998	−	0.193988i	−0.658501	+	0.752580i	$0.728809\pi$
$752$	3.11760	+	11.6351i	0.113687	+	0.424287i
$753$	−34.1036	+	6.64456i	−1.24280	+	0.242141i
$754$	−1.27127	+	22.9039i	−0.0462968	+	0.834112i
$755$		−	15.0978i		−	0.549465i
$756$	−3.86606	−	3.47183i	−0.140607	−	0.126269i
$757$	14.6540	−	25.3815i	0.532609	−	0.922506i	−0.466666	−	0.884434i	$-0.654545\pi$
$757$	14.6540	−	25.3815i	0.532609	−	0.922506i	0.999275	−	0.0380725i	$-0.0121218\pi$
$758$	13.7939	+	23.8917i	0.501015	+	0.867784i
$759$	−5.46019	+	8.10271i	−0.198192	+	0.294110i
$760$	−3.44874	−	0.924086i	−0.125099	−	0.0335201i
$761$	2.05863	+	0.551608i	0.0746252	+	0.0199958i	0.295938	−	0.955207i	$-0.404368\pi$
$761$	2.05863	+	0.551608i	0.0746252	+	0.0199958i	−0.221313	+	0.975203i	$0.571034\pi$
$762$	3.45666	−	5.12955i	0.125221	−	0.185824i
$763$	−6.01371	−	10.4161i	−0.217711	−	0.377087i
$764$	7.12581	−	12.3423i	0.257803	−	0.446528i
$765$	13.4321	−	10.1402i	0.485638	−	0.366621i
$766$			32.5553i			1.17627i
$767$	−1.10752	+	19.9537i	−0.0399901	+	0.720486i
$768$	−1.70008	+	0.331235i	−0.0613465	+	0.0119524i
$769$	−8.89775	−	33.2069i	−0.320861	−	1.19747i	−0.918408	−	0.395636i	$-0.870524\pi$
$769$	−8.89775	−	33.2069i	−0.320861	−	1.19747i	0.597547	−	0.801834i	$-0.296142\pi$
$770$	−9.64856	−	5.57060i	−0.347710	−	0.200751i
$771$	20.7966	+	23.9027i	0.748972	+	0.860833i
$772$	−17.4249	+	17.4249i	−0.627135	+	0.627135i
$773$	9.33711	−	34.8466i	0.335833	−	1.25334i	−0.567131	−	0.823628i	$-0.691947\pi$
$773$	9.33711	−	34.8466i	0.335833	−	1.25334i	0.902964	−	0.429717i	$-0.141387\pi$
$774$	−23.3805	+	2.89154i	−0.840395	+	0.103934i
$775$	0.0162537	+	0.0162537i	0.000583851	+	0.000583851i
$776$	−14.2389	+	8.22085i	−0.511148	+	0.295111i
$777$	3.13065	+	1.07644i	0.112311	+	0.0386169i
$778$	8.43311	−	2.25965i	0.302342	−	0.0810122i
$779$	5.56180			0.199272
$780$	−12.9489	−	5.27163i	−0.463643	−	0.188755i
$781$	−13.6477			−0.488355
$782$	−2.74371	+	0.735176i	−0.0981150	+	0.0262898i
$783$	−33.0113	+	1.77352i	−1.17973	+	0.0633804i
$784$	−0.866025	+	0.500000i	−0.0309295	+	0.0178571i
$785$	5.89249	+	5.89249i	0.210312	+	0.210312i
$786$	37.9510	+	2.63710i	1.35367	+	0.0940623i
$787$	−11.3760	+	42.4560i	−0.405512	+	1.51339i	0.397597	+	0.917560i	$0.369844\pi$
$787$	−11.3760	+	42.4560i	−0.405512	+	1.51339i	−0.803109	+	0.595832i	$0.796822\pi$
$788$	−9.38748	+	9.38748i	−0.334415	+	0.334415i
$789$	37.0585	−	32.2429i	1.31932	−	1.14788i
$790$	−34.0130	−	19.6374i	−1.21013	−	0.698667i
$791$	−0.158313	−	0.590832i	−0.00562896	−	0.0210076i
$792$	5.60491	+	13.8377i	0.199162	+	0.491703i
$793$	−8.43094	+	7.54425i	−0.299392	+	0.267904i
$794$			1.85223i			0.0657333i
$795$	2.74659	+	5.62509i	0.0974114	+	0.199501i
$796$	6.29510	−	10.9034i	0.223124	−	0.386462i
$797$	12.7222	+	22.0354i	0.450642	+	0.780536i	0.998426	−	0.0560845i	$-0.0178616\pi$
$797$	12.7222	+	22.0354i	0.450642	+	0.780536i	−0.547784	+	0.836620i	$0.684528\pi$
$798$	2.29076	+	1.54368i	0.0810920	+	0.0546456i
$799$	29.1560	+	7.81233i	1.03147	+	0.276381i
$800$	0.0114660	+	0.00307230i	0.000405384	+	0.000108622i
$801$	−5.80032	+	13.6980i	−0.204944	+	0.483996i
$802$	−8.05510	−	13.9519i	−0.284436	−	0.492657i
$803$	30.4115	−	52.6743i	1.07320	−	1.85883i
$804$	−19.1744	+	9.36237i	−0.676229	+	0.330185i
$805$		−	2.53767i		−	0.0894411i
$806$	6.63347	+	2.17801i	0.233654	+	0.0767171i
$807$	−2.93465	−	15.0623i	−0.103305	−	0.530217i
$808$	−1.39130	−	5.19239i	−0.0489456	−	0.182667i
$809$	−19.5795	−	11.3042i	−0.688379	−	0.397436i	0.114626	−	0.993409i	$-0.463433\pi$
$809$	−19.5795	−	11.3042i	−0.688379	−	0.397436i	−0.803004	+	0.595973i	$0.796767\pi$
$810$	5.51976	−	19.3777i	0.193945	−	0.680862i
$811$	−25.7313	+	25.7313i	−0.903549	+	0.903549i	−0.995741	−	0.0921926i	$-0.970612\pi$
$811$	−25.7313	+	25.7313i	−0.903549	+	0.903549i	0.0921926	+	0.995741i	$0.470612\pi$
$812$	−1.64665	+	6.14540i	−0.0577863	+	0.215661i
$813$	2.60953	−	37.5543i	0.0915203	−	1.31709i
$814$	−6.72597	−	6.72597i	−0.235745	−	0.235745i
$815$	0.277677	−	0.160317i	0.00972660	−	0.00561566i
$816$	−1.41127	+	4.10446i	−0.0494043	+	0.143685i
$817$	12.0973	−	3.24147i	0.423231	−	0.113405i
$818$	−4.53529			−0.158573
$819$	8.14771	+	7.11440i	0.284704	+	0.248597i
$820$	−7.80727			−0.272642
$821$	−38.9072	+	10.4251i	−1.35787	+	0.363840i	−0.863033	−	0.505147i	$-0.831438\pi$
$821$	−38.9072	+	10.4251i	−1.35787	+	0.363840i	−0.494836	+	0.868987i	$0.664772\pi$
$822$	−2.25049	+	6.54522i	−0.0784950	+	0.228291i
$823$	6.92538	−	3.99837i	0.241403	−	0.139374i	−0.374418	−	0.927260i	$-0.622158\pi$
$823$	6.92538	−	3.99837i	0.241403	−	0.139374i	0.615822	+	0.787886i	$0.288824\pi$
$824$	−7.43004	−	7.43004i	−0.258838	−	0.258838i
$825$	0.00709280	−	0.102074i	0.000246940	−	0.00355375i
$826$	−1.43455	+	5.35382i	−0.0499144	+	0.186283i
$827$	24.8745	−	24.8745i	0.864972	−	0.864972i	−0.126939	−	0.991911i	$-0.540515\pi$
$827$	24.8745	−	24.8745i	0.864972	−	0.864972i	0.991911	+	0.126939i	$0.0405151\pi$
$828$	−2.09128	+	2.68155i	−0.0726769	+	0.0931902i
$829$	9.87941	+	5.70388i	0.343126	+	0.198104i	0.661654	−	0.749810i	$-0.269855\pi$
$829$	9.87941	+	5.70388i	0.343126	+	0.198104i	−0.318527	+	0.947914i	$0.603188\pi$
$830$	−3.99805	−	14.9209i	−0.138774	−	0.517913i
$831$	2.00539	+	10.2928i	0.0695664	+	0.357053i
$832$	3.52906	−	0.738744i	0.122348	−	0.0256113i
$833$			2.50588i			0.0868236i
$834$	−17.5012	+	8.54538i	−0.606016	+	0.295902i
$835$	−4.09905	+	7.09976i	−0.141853	+	0.245697i
$836$	−3.96843	−	6.87352i	−0.137251	−	0.237726i
$837$	−2.07907	+	9.84482i	−0.0718633	+	0.340287i
$838$	30.5283	+	8.18003i	1.05458	+	0.282574i
$839$	44.3216	+	11.8759i	1.53015	+	0.410003i	0.923069	−	0.384634i	$-0.125672\pi$
$839$	44.3216	+	11.8759i	1.53015	+	0.410003i	0.607084	+	0.794638i	$0.292339\pi$
$840$	−3.21561	−	2.16691i	−0.110949	−	0.0747654i
$841$	5.73871	+	9.93973i	0.197886	+	0.342749i
$842$	−5.29079	+	9.16391i	−0.182332	+	0.315809i
$843$	−4.26808	−	8.74115i	−0.147000	−	0.301061i
$844$			27.1043i			0.932967i
$845$	27.1054	+	10.5973i	0.932455	+	0.364558i
$846$	33.4933	−	13.5663i	1.15152	−	0.466419i
$847$	−3.56303	−	13.2974i	−0.122427	−	0.456904i
$848$	−1.39808	−	0.807182i	−0.0480103	−	0.0277187i
$849$	7.56624	−	6.58305i	0.259673	−	0.225930i
$850$	0.0210335	−	0.0210335i	0.000721445	−	0.000721445i
$851$	0.560750	−	2.09275i	0.0192223	−	0.0717384i
$852$	−4.73853	−	0.329266i	−0.162339	−	0.0112805i
$853$	−23.7588	−	23.7588i	−0.813485	−	0.813485i	0.171670	−	0.985155i	$-0.445084\pi$
$853$	−23.7588	−	23.7588i	−0.813485	−	0.813485i	−0.985155	+	0.171670i	$0.945084\pi$
$854$	−2.71743	+	1.56891i	−0.0929885	+	0.0536869i
$855$	−1.48142	+	10.6082i	−0.0506636	+	0.362794i
$856$	15.6926	−	4.20482i	0.536362	−	0.143718i
$857$	19.0007			0.649051			0.324525	−	0.945877i	$-0.394795\pi$
$857$	19.0007			0.649051			0.324525	+	0.945877i	$0.394795\pi$
$858$	−12.0676	−	28.6403i	−0.411981	−	0.977763i
$859$	−5.67989			−0.193795			−0.0968976	−	0.995294i	$-0.530892\pi$
$859$	−5.67989			−0.193795			−0.0968976	+	0.995294i	$0.530892\pi$
$860$	−16.9814	+	4.55014i	−0.579060	+	0.155159i
$861$	5.71210	+	1.96404i	0.194668	+	0.0669342i
$862$	25.3682	−	14.6464i	0.864046	−	0.498857i
$863$	−4.75015	−	4.75015i	−0.161697	−	0.161697i	0.621621	−	0.783318i	$-0.286474\pi$
$863$	−4.75015	−	4.75015i	−0.161697	−	0.161697i	−0.783318	+	0.621621i	$0.786474\pi$
$864$	1.61219	+	4.93972i	0.0548477	+	0.168053i
$865$	6.17339	−	23.0394i	0.209901	−	0.783363i
$866$	1.04404	−	1.04404i	0.0354779	−	0.0354779i
$867$	−12.1882	−	14.0085i	−0.413933	−	0.475755i
$868$	1.67699	+	0.968212i	0.0569208	+	0.0328633i
$869$	−22.5966	−	84.3315i	−0.766536	−	2.86075i
$870$	−24.2146	+	4.71783i	−0.820950	+	0.159950i
$871$	39.6394	−	20.0434i	1.34313	−	0.679143i
$872$			12.0274i			0.407300i
$873$	29.7191	+	39.3668i	1.00584	+	1.33236i
$874$	0.903902	−	1.56560i	0.0305750	−	0.0529574i
$875$	−5.58351	−	9.67093i	−0.188757	−	0.326937i
$876$	11.8298	−	17.5549i	0.399691	−	0.593125i
$877$	−5.82114	−	1.55977i	−0.196566	−	0.0526697i	0.159193	−	0.987248i	$-0.449111\pi$
$877$	−5.82114	−	1.55977i	−0.196566	−	0.0526697i	−0.355759	+	0.934578i	$0.615778\pi$
$878$	5.04054	+	1.35061i	0.170110	+	0.0455808i
$879$	−25.8284	+	38.3284i	−0.871172	+	1.29279i
$880$	5.57060	+	9.64856i	0.187785	+	0.325253i
$881$	9.99592	−	17.3134i	0.336771	−	0.583305i	−0.647052	−	0.762446i	$-0.723998\pi$
$881$	9.99592	−	17.3134i	0.336771	−	0.583305i	0.983823	+	0.179141i	$0.0573318\pi$
$882$	1.80754	+	2.39433i	0.0608631	+	0.0806211i
$883$		−	49.8542i		−	1.67773i	−0.544342	−	0.838863i	$-0.683221\pi$
$883$		−	49.8542i		−	1.67773i	0.544342	−	0.838863i	$-0.316779\pi$
$884$	2.81851	−	8.58420i	0.0947967	−	0.288718i
$885$	−21.0955	+	4.11013i	−0.709117	+	0.138161i
$886$	8.10586	+	30.2515i	0.272322	+	1.01632i
$887$	−48.5860	−	28.0511i	−1.63136	−	0.941865i	−0.983675	−	0.179954i	$-0.942405\pi$
$887$	−48.5860	−	28.0511i	−1.63136	−	0.941865i	−0.647682	−	0.761910i	$-0.724262\pi$
$888$	−2.17300	−	2.49754i	−0.0729211	−	0.0838121i
$889$	−2.52523	+	2.52523i	−0.0846935	+	0.0846935i
$890$	−2.87307	+	10.7224i	−0.0963054	+	0.359417i
$891$	39.1356	−	21.7829i	1.31109	−	0.729753i
$892$	−5.89996	−	5.89996i	−0.197545	−	0.197545i
$893$	−16.6369	+	9.60530i	−0.556732	+	0.321429i
$894$	9.40542	+	3.23394i	0.314564	+	0.108159i
$895$	−24.5319	+	6.57330i	−0.820010	+	0.219721i
$896$	1.00000			0.0334077
$897$	4.27517	−	5.64217i	0.142744	−	0.188387i
$898$	−14.8342			−0.495022
$899$	11.9001	−	3.18862i	0.396891	−	0.106347i
$900$	0.00492527	−	0.0352691i	0.000164176	−	0.00117564i
$901$	−3.50342	+	2.02270i	−0.116716	+	0.0673859i
$902$	−12.2720	−	12.2720i	−0.408614	−	0.408614i
$903$	13.5689	+	0.942859i	0.451544	+	0.0313764i
$904$	−0.158313	+	0.590832i	−0.00526541	+	0.0196508i
$905$	33.3682	−	33.3682i	1.10920	−	1.10920i
$906$	8.81228	−	7.66718i	0.292769	−	0.254725i
$907$	−15.4491	−	8.91954i	−0.512979	−	0.296169i	0.221078	−	0.975256i	$-0.429042\pi$
$907$	−15.4491	−	8.91954i	−0.512979	−	0.296169i	−0.734057	+	0.679087i	$0.762376\pi$
$908$	3.42193	+	12.7708i	0.113561	+	0.423814i
$909$	−14.9471	+	6.05424i	−0.495763	+	0.200806i
$910$	6.75599	+	4.41711i	0.223959	+	0.146426i
$911$			5.28604i			0.175134i	0.996159	+	0.0875671i	$0.0279092\pi$
$911$			5.28604i			0.175134i	−0.996159	+	0.0875671i	$0.972091\pi$
$912$	−1.21202	−	2.48224i	−0.0401339	−	0.0821953i
$913$	17.1694	−	29.7382i	0.568223	−	0.984191i
$914$	18.8714	+	32.6862i	0.624211	+	1.08116i
$915$	−10.0900	−	6.79935i	−0.333564	−	0.224780i
$916$	−22.0647	−	5.91222i	−0.729038	−	0.195345i
$917$	−21.2155	−	5.68467i	−0.700596	−	0.187724i
$918$	12.7399	+	2.69048i	0.420480	+	0.0887990i
$919$	−21.8919	−	37.9178i	−0.722146	−	1.25079i	−0.960138	−	0.279527i	$-0.909822\pi$
$919$	−21.8919	−	37.9178i	−0.722146	−	1.25079i	0.237992	−	0.971267i	$-0.423511\pi$
$920$	−1.26883	+	2.19769i	−0.0418322	+	0.0724556i
$921$	25.6081	−	12.5038i	0.843815	−	0.412013i
$922$			21.3203i			0.702147i
$923$	9.87263	+	0.547973i	0.324961	+	0.0180368i
$924$	−1.64842	−	8.46062i	−0.0542291	−	0.278334i
$925$	0.00587221	+	0.0219154i	0.000193077	+	0.000720573i
$926$	16.6120	+	9.59095i	0.545904	+	0.315178i
$927$	−19.3857	+	24.8574i	−0.636711	+	0.816425i
$928$	4.49875	−	4.49875i	0.147679	−	0.147679i
$929$	10.3476	−	38.6176i	0.339492	−	1.26700i	−0.559424	−	0.828882i	$-0.688978\pi$
$929$	10.3476	−	38.6176i	0.339492	−	1.26700i	0.898916	−	0.438121i	$-0.144356\pi$
$930$	−0.520497	+	7.49058i	−0.0170678	+	0.245626i
$931$	−1.12772	−	1.12772i	−0.0369595	−	0.0369595i
$932$	−2.27363	+	1.31268i	−0.0744753	+	0.0429983i
$933$	−18.5657	+	53.9956i	−0.607815	+	1.76774i
$934$	16.8618	−	4.51811i	0.551735	−	0.147837i
$935$	27.9185			0.913033
$936$	−3.49893	−	10.2351i	−0.114366	−	0.334545i
$937$	−6.59358			−0.215403			−0.107701	−	0.994183i	$-0.534349\pi$
$937$	−6.59358			−0.215403			−0.107701	+	0.994183i	$0.534349\pi$
$938$	11.8997	−	3.18853i	0.388540	−	0.104109i
$939$	0.264363	−	0.768859i	0.00862716	−	0.0250908i
$940$	23.3537	−	13.4832i	0.761713	−	0.439775i
$941$	−35.0177	−	35.0177i	−1.14155	−	1.14155i	−0.988168	−	0.153377i	$-0.950985\pi$
$941$	−35.0177	−	35.0177i	−1.14155	−	1.14155i	−0.153377	−	0.988168i	$-0.549015\pi$
$942$	−0.446922	+	6.43174i	−0.0145615	+	0.209557i
$943$	1.02313	−	3.81837i	0.0333177	−	0.124343i
$944$	3.91927	−	3.91927i	0.127561	−	0.127561i
$945$	−5.26754	+	10.3718i	−0.171353	+	0.337394i
$946$	−33.8448	−	19.5403i	−1.10039	−	0.635310i
$947$	0.602447	+	2.24836i	0.0195769	+	0.0730619i	0.975023	−	0.222103i	$-0.0712921\pi$
$947$	0.602447	+	2.24836i	0.0195769	+	0.0730619i	−0.955446	+	0.295165i	$0.904625\pi$
$948$	−5.81099	−	29.8253i	−0.188732	−	0.968679i
$949$	−24.1143	+	36.8829i	−0.782782	+	1.19727i
$950$			0.0189314i			0.000614217i
$951$	−17.7729	+	8.67808i	−0.576327	+	0.281406i
$952$	1.25294	−	2.17015i	0.0406080	−	0.0703351i
$953$	−1.78680	−	3.09483i	−0.0578801	−	0.100251i	0.835634	−	0.549287i	$-0.185101\pi$
$953$	−1.78680	−	3.09483i	−0.0578801	−	0.100251i	−0.893514	+	0.449036i	$0.851767\pi$
$954$	−1.88844	+	4.45974i	−0.0611406	+	0.144390i
$955$	−30.8183	−	8.25773i	−0.997256	−	0.267214i
$956$	−26.2521	−	7.03423i	−0.849054	−	0.227503i
$957$	−45.4780	−	30.6464i	−1.47010	−	0.990656i
$958$	4.31802	+	7.47903i	0.139509	+	0.241637i
$959$	1.99801	−	3.46066i	0.0645191	−	0.111750i
$960$	1.70134	+	3.48440i	0.0549106	+	0.112459i
$961$			27.2503i			0.879041i
$962$	4.59543	+	5.13554i	0.148163	+	0.165577i
$963$	−18.2973	−	45.1735i	−0.589623	−	1.45570i
$964$	−2.64967	−	9.88872i	−0.0853403	−	0.318494i
$965$	47.7766	+	27.5839i	1.53798	+	0.887956i
$966$	1.48119	−	1.28872i	0.0476565	−	0.0414638i
$967$	−24.9932	+	24.9932i	−0.803729	+	0.803729i	−0.983676	−	0.179948i	$-0.942407\pi$
$967$	−24.9932	+	24.9932i	−0.803729	+	0.803729i	0.179948	+	0.983676i	$0.442407\pi$
$968$	−3.56303	+	13.2974i	−0.114520	+	0.427395i
$969$	−6.90544	−	0.479838i	−0.221835	−	0.0154146i
$970$	26.0275	+	26.0275i	0.835692	+	0.835692i
$971$	13.1700	−	7.60373i	0.422647	−	0.244015i	−0.273562	−	0.961854i	$-0.588202\pi$
$971$	13.1700	−	7.60373i	0.422647	−	0.244015i	0.696209	+	0.717839i	$0.254869\pi$
$972$	14.1135	−	6.61887i	0.452690	−	0.212300i
$973$	10.8613	−	2.91028i	0.348198	−	0.0932994i
$974$	0.743440			0.0238214
$975$	−0.00922923	+	0.0735542i	−0.000295572	+	0.00235562i
$976$	3.13782			0.100439
$977$	−28.9604	+	7.75992i	−0.926526	+	0.248262i	−0.690373	−	0.723454i	$-0.742553\pi$
$977$	−28.9604	+	7.75992i	−0.926526	+	0.248262i	−0.236153	+	0.971716i	$0.575887\pi$
$978$	0.234588	+	0.0806602i	0.00750129	+	0.00257923i
$979$	−21.3704	+	12.3382i	−0.683001	+	0.394331i
$980$	1.58301	+	1.58301i	0.0505675	+	0.0505675i
$981$	35.8095	−	4.42867i	1.14331	−	0.141397i
$982$	9.18707	−	34.2866i	0.293171	−	1.09413i
$983$	7.07354	−	7.07354i	0.225611	−	0.225611i	−0.585245	−	0.810856i	$-0.699002\pi$
$983$	7.07354	−	7.07354i	0.225611	−	0.225611i	0.810856	+	0.585245i	$0.199002\pi$
$984$	−3.96480	−	4.55695i	−0.126393	−	0.145270i
$985$	25.7392	+	14.8605i	0.820118	+	0.473496i
$986$	−4.12632	−	15.3996i	−0.131409	−	0.490424i
$987$	−20.4783	+	3.98989i	−0.651833	+	0.127000i
$988$	2.59474	+	5.13156i	0.0825495	+	0.163257i
$989$		−	8.90152i		−	0.283052i
$990$	26.6757	−	20.1382i	0.847808	−	0.640034i
$991$	−8.69196	+	15.0549i	−0.276109	+	0.478235i	−0.970414	−	0.241446i	$-0.922378\pi$
$991$	−8.69196	+	15.0549i	−0.276109	+	0.478235i	0.694305	+	0.719681i	$0.255712\pi$
$992$	−0.968212	−	1.67699i	−0.0307408	−	0.0532446i
$993$	−14.9488	+	22.1834i	−0.474385	+	0.703970i
$994$	2.64894	+	0.709782i	0.0840194	+	0.0225129i
$995$	−27.2255	−	7.29506i	−0.863108	−	0.231269i
$996$	6.67870	−	9.91094i	0.211623	−	0.314040i
$997$	20.3712	+	35.2839i	0.645162	+	1.11745i	0.984264	+	0.176704i	$0.0565435\pi$
$997$	20.3712	+	35.2839i	0.645162	+	1.11745i	−0.339102	+	0.940750i	$0.610123\pi$
$998$	19.5407	−	33.8455i	0.618551	−	1.07136i
$999$	−6.63585	+	7.38934i	−0.209949	+	0.233789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.71.12	✓	56
3.2	odd	2		546.2.bu.b.71.6	yes	56
13.11	odd	12		546.2.bu.b.323.6	yes	56
39.11	even	12	inner	546.2.bu.a.323.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.12	✓	56	1.1	even	1	trivial
546.2.bu.a.323.12	yes	56	39.11	even	12	inner
546.2.bu.b.71.6	yes	56	3.2	odd	2
546.2.bu.b.323.6	yes	56	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.563184 - 1.63793i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.58301 - 1.58301i) q^{5} +(0.120065 - 1.72788i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.36565 - 1.84491i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.563184 - 1.63793i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.58301 - 1.58301i) q^{5} +(0.120065 - 1.72788i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.36565 - 1.84491i) q^{9} +(-1.93879 - 1.11936i) q^{10} +(-1.28804 - 4.80702i) q^{11} +(-0.331235 - 1.70008i) q^{12} +(0.738744 + 3.52906i) q^{13} +1.00000i q^{14} +(-3.48440 + 1.70134i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.25294 - 2.17015i) q^{17} +(-2.76254 - 1.16978i) q^{18} +(1.54049 + 0.412774i) q^{19} +(-2.16244 - 0.579424i) q^{20} +(1.43636 + 0.967922i) q^{21} +(-2.48830 - 4.30986i) q^{22} +(0.566768 - 0.981671i) q^{23} +(-0.759962 - 1.55642i) q^{24} +0.0118705i q^{25} +(1.62696 + 3.21761i) q^{26} +(-4.35414 + 2.83575i) q^{27} +(0.258819 + 0.965926i) q^{28} +(5.50981 + 3.18109i) q^{29} +(-2.92533 + 2.54520i) q^{30} +(1.36926 - 1.36926i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-8.59898 - 0.597517i) q^{33} +(-1.77192 - 1.77192i) q^{34} +(1.93879 - 1.11936i) q^{35} +(-2.97117 - 0.414918i) q^{36} +(1.84621 - 0.494691i) q^{37} +1.59484 q^{38} +(6.19641 + 0.777496i) q^{39} -2.23872 q^{40} +(3.36855 - 0.902600i) q^{41} +(1.63793 + 0.563184i) q^{42} +(6.80079 - 3.92644i) q^{43} +(-3.51898 - 3.51898i) q^{44} +(0.824330 + 6.66538i) q^{45} +(0.293381 - 1.09491i) q^{46} +(-8.51745 + 8.51745i) q^{47} +(-1.13690 - 1.30670i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.00307230 + 0.0114660i) q^{50} +(-4.26020 + 0.830035i) q^{51} +(2.40430 + 2.68688i) q^{52} -1.61436i q^{53} +(-3.47183 + 3.86606i) q^{54} +(-5.57060 + 9.64856i) q^{55} +(0.500000 + 0.866025i) q^{56} +(1.54368 - 2.29076i) q^{57} +(6.14540 + 1.64665i) q^{58} +(5.35382 + 1.43455i) q^{59} +(-2.16691 + 3.21561i) q^{60} +(1.56891 + 2.71743i) q^{61} +(0.968212 - 1.67699i) q^{62} +(2.39433 - 1.80754i) q^{63} -1.00000i q^{64} +(4.41711 - 6.75599i) q^{65} +(-8.46062 + 1.64842i) q^{66} +(-3.18853 - 11.8997i) q^{67} +(-2.17015 - 1.25294i) q^{68} +(-1.28872 - 1.48119i) q^{69} +(1.58301 - 1.58301i) q^{70} +(0.709782 - 2.64894i) q^{71} +(-2.97732 + 0.368215i) q^{72} +(8.64213 + 8.64213i) q^{73} +(1.65527 - 0.955670i) q^{74} +(0.0194430 + 0.00668525i) q^{75} +(1.54049 - 0.412774i) q^{76} +4.97659 q^{77} +(6.18650 - 0.852745i) q^{78} +17.5434 q^{79} +(-2.16244 + 0.579424i) q^{80} +(2.19258 + 8.72884i) q^{81} +(3.02016 - 1.74369i) q^{82} +(4.87907 + 4.87907i) q^{83} +(1.72788 + 0.120065i) q^{84} +(-1.45197 + 5.41881i) q^{85} +(5.55282 - 5.55282i) q^{86} +(8.31346 - 7.23317i) q^{87} +(-4.30986 - 2.48830i) q^{88} +(-1.28335 - 4.78954i) q^{89} +(2.52137 + 6.22491i) q^{90} +(-3.60001 - 0.199816i) q^{91} -1.13354i q^{92} +(-1.47161 - 3.01390i) q^{93} +(-6.02275 + 10.4317i) q^{94} +(-1.78520 - 3.09205i) q^{95} +(-1.43636 - 0.967922i) q^{96} +(-15.8815 - 4.25543i) q^{97} +(-0.965926 - 0.258819i) q^{98} +(-5.82150 + 13.7480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

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