LMFDB - Embedded newform 72.2.n.b.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,2,Mod(13,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("72.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	72.n (of order $6$, degree $2$, 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:	$0.574922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.2
Root			$-0.179748 - 1.40274i$ of defining polynomial
Character	$\chi$	$=$	72.13
Dual form			72.2.n.b.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12494 - 0.857038i) q^{2} +(-0.986088 + 1.42395i) q^{3} +(0.530970 + 1.92823i) q^{4} +(1.19115 + 0.687709i) q^{5} +(2.32967 - 0.756738i) q^{6} +(1.80469 + 3.12581i) q^{7} +(1.05526 - 2.62420i) q^{8} +(-1.05526 - 2.80828i) q^{9} +(-0.750573 - 1.79449i) q^{10} +(-1.83294 + 1.05825i) q^{11} +(-3.26928 - 1.14533i) q^{12} +(0.887751 + 0.512543i) q^{13} +(0.648778 - 5.06302i) q^{14} +(-2.15384 + 1.01799i) q^{15} +(-3.43614 + 2.04766i) q^{16} +0.808822 q^{17} +(-1.21970 + 4.06354i) q^{18} -7.43122i q^{19} +(-0.693598 + 2.66196i) q^{20} +(-6.23057 - 0.512543i) q^{21} +(2.96890 + 0.380437i) q^{22} +(-1.65498 + 2.86652i) q^{23} +(2.69615 + 4.09033i) q^{24} +(-1.55411 - 2.69180i) q^{25} +(-0.559395 - 1.33742i) q^{26} +(5.03942 + 1.26658i) q^{27} +(-5.06904 + 5.13956i) q^{28} +(7.71083 - 4.45185i) q^{29} +(3.29539 + 0.700747i) q^{30} +(3.26436 - 5.65403i) q^{31} +(5.62037 + 0.641410i) q^{32} +(0.300550 - 3.65354i) q^{33} +(-0.909875 - 0.693192i) q^{34} +4.96439i q^{35} +(4.85470 - 3.52589i) q^{36} +4.01531i q^{37} +(-6.36884 + 8.35966i) q^{38} +(-1.60524 + 0.758698i) q^{39} +(3.06165 - 2.40010i) q^{40} +(-3.45852 + 5.99034i) q^{41} +(6.56973 + 5.91642i) q^{42} +(0.245957 - 0.142003i) q^{43} +(-3.01378 - 2.97243i) q^{44} +(0.674310 - 4.07078i) q^{45} +(4.31847 - 1.80627i) q^{46} +(-3.61351 - 6.25878i) q^{47} +(0.472570 - 6.91207i) q^{48} +(-3.01378 + 5.22003i) q^{49} +(-0.558698 + 4.36005i) q^{50} +(-0.797570 + 1.15172i) q^{51} +(-0.516932 + 1.98393i) q^{52} +3.86330i q^{53} +(-4.58353 - 5.74380i) q^{54} -2.91107 q^{55} +(10.1072 - 1.43732i) q^{56} +(10.5817 + 7.32784i) q^{57} +(-12.4896 - 1.60042i) q^{58} +(-7.06904 - 4.08131i) q^{59} +(-3.10654 - 3.61257i) q^{60} +(-6.31237 + 3.64445i) q^{61} +(-8.51792 + 3.56275i) q^{62} +(6.87373 - 8.36660i) q^{63} +(-5.77286 - 5.53842i) q^{64} +(0.704961 + 1.22103i) q^{65} +(-3.46932 + 3.85242i) q^{66} +(2.43973 + 1.40858i) q^{67} +(0.429460 + 1.55960i) q^{68} +(-2.44981 - 5.18325i) q^{69} +(4.25468 - 5.58463i) q^{70} +4.69830 q^{71} +(-8.48306 - 0.194250i) q^{72} +0.409922 q^{73} +(3.44128 - 4.51698i) q^{74} +(5.36548 + 0.441379i) q^{75} +(14.3291 - 3.94576i) q^{76} +(-6.61576 - 3.81961i) q^{77} +(2.45602 + 0.522260i) q^{78} +(-0.0456121 - 0.0790024i) q^{79} +(-5.50115 + 0.0760042i) q^{80} +(-6.77286 + 5.92692i) q^{81} +(9.02458 - 3.77467i) q^{82} +(2.40891 - 1.39079i) q^{83} +(-2.31995 - 12.2861i) q^{84} +(0.963426 + 0.556234i) q^{85} +(-0.398389 - 0.0510497i) q^{86} +(-1.26436 + 15.3697i) q^{87} +(0.842830 + 5.92673i) q^{88} +8.91934 q^{89} +(-4.24737 + 4.00147i) q^{90} +3.69992i q^{91} +(-6.40605 - 1.66916i) q^{92} +(4.83210 + 10.2236i) q^{93} +(-1.29904 + 10.1377i) q^{94} +(5.11052 - 8.85168i) q^{95} +(-6.45552 + 7.37064i) q^{96} +(-2.76022 - 4.78084i) q^{97} +(7.86408 - 3.28928i) q^{98} +(4.90608 + 4.03068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26}+ \cdots + 66 q^{98}+O(q^{100}) $ 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^14 - 10 * q^15 - 9 * q^16 - 28 * q^17 + 4 * q^18 - 8 * q^20 + q^22 - 10 * q^23 + 7 * q^24 + 2 * q^25 + 28 * q^26 + 4 * q^28 + 22 * q^30 - 10 * q^31 + 11 * q^32 + q^34 + 27 * q^36 + 23 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^41 + 8 * q^42 + 18 * q^44 - 20 * q^46 + 6 * q^47 + 39 * q^48 + 18 * q^49 - 23 * q^50 - 8 * q^52 - 29 * q^54 - 4 * q^55 + 10 * q^56 + 10 * q^57 - 14 * q^58 + 6 * q^60 - 52 * q^62 + 2 * q^63 + 26 * q^64 - 14 * q^65 - 72 * q^66 - 39 * q^68 + 72 * q^71 - 77 * q^72 - 44 * q^73 - 38 * q^74 + 5 * q^76 + 10 * q^78 - 30 * q^79 - 96 * q^80 + 10 * q^81 + 38 * q^82 - 28 * q^84 + 7 * q^86 + 42 * q^87 + 31 * q^88 + 64 * q^89 + 64 * q^90 - 30 * q^92 - 12 * q^94 + 44 * q^95 - 26 * q^96 + 66 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.12494	−	0.857038i	−0.795451	−	0.606018i
$2$	−1.12494	−	0.857038i	−0.795451	−	0.606018i
$3$	−0.986088	+	1.42395i	−0.569318	+	0.822117i
$3$	−0.986088	+	1.42395i	−0.569318	+	0.822117i
$4$	0.530970	+	1.92823i	0.265485	+	0.964115i
$5$	1.19115	+	0.687709i	0.532697	+	0.307553i	0.742114	−	0.670274i	$-0.233823\pi$
$5$	1.19115	+	0.687709i	0.532697	+	0.307553i	−0.209417	+	0.977826i	$0.567157\pi$
$6$	2.32967	−	0.756738i	0.951083	−	0.308937i
$7$	1.80469	+	3.12581i	0.682107	+	1.18144i	0.974337	+	0.225096i	$0.0722696\pi$
$7$	1.80469	+	3.12581i	0.682107	+	1.18144i	−0.292229	+	0.956348i	$0.594397\pi$
$8$	1.05526	−	2.62420i	0.373090	−	0.927795i
$9$	−1.05526	−	2.80828i	−0.351753	−	0.936093i
$10$	−0.750573	−	1.79449i	−0.237352	−	0.567467i
$11$	−1.83294	+	1.05825i	−0.552652	+	0.319074i	−0.750191	−	0.661221i	$-0.770039\pi$
$11$	−1.83294	+	1.05825i	−0.552652	+	0.319074i	0.197539	+	0.980295i	$0.436705\pi$
$12$	−3.26928	−	1.14533i	−0.943761	−	0.330629i
$13$	0.887751	+	0.512543i	0.246218	+	0.142154i	0.618031	−	0.786154i	$-0.287931\pi$
$13$	0.887751	+	0.512543i	0.246218	+	0.142154i	−0.371813	+	0.928307i	$0.621264\pi$
$14$	0.648778	−	5.06302i	0.173393	−	1.35315i
$15$	−2.15384	+	1.01799i	−0.556119	+	0.262844i
$16$	−3.43614	+	2.04766i	−0.859035	+	0.511916i
$17$	0.808822			0.196168			0.0980841	−	0.995178i	$-0.468729\pi$
$17$	0.808822			0.196168			0.0980841	+	0.995178i	$0.468729\pi$
$18$	−1.21970	+	4.06354i	−0.287487	+	0.957785i
$19$		−	7.43122i		−	1.70484i	−0.522858	−	0.852420i	$-0.675134\pi$
$19$		−	7.43122i		−	1.70484i	0.522858	−	0.852420i	$-0.324866\pi$
$20$	−0.693598	+	2.66196i	−0.155093	+	0.595232i
$21$	−6.23057	−	0.512543i	−1.35962	−	0.111846i
$22$	2.96890	+	0.380437i	0.632972	+	0.0811093i
$23$	−1.65498	+	2.86652i	−0.345088	+	0.597710i	−0.985370	−	0.170430i	$-0.945484\pi$
$23$	−1.65498	+	2.86652i	−0.345088	+	0.597710i	0.640282	+	0.768140i	$0.278818\pi$
$24$	2.69615	+	4.09033i	0.550349	+	0.834935i
$25$	−1.55411	−	2.69180i	−0.310823	−	0.538361i
$26$	−0.559395	−	1.33742i	−0.109706	−	0.262289i
$27$	5.03942	+	1.26658i	0.969837	+	0.243753i
$28$	−5.06904	+	5.13956i	−0.957959	+	0.971286i
$29$	7.71083	−	4.45185i	1.43187	−	0.826688i	0.434603	−	0.900622i	$-0.356889\pi$
$29$	7.71083	−	4.45185i	1.43187	−	0.826688i	0.997263	+	0.0739344i	$0.0235555\pi$
$30$	3.29539	+	0.700747i	0.601653	+	0.127938i
$31$	3.26436	−	5.65403i	0.586296	−	1.01549i	−0.408417	−	0.912796i	$-0.633919\pi$
$31$	3.26436	−	5.65403i	0.586296	−	1.01549i	0.994713	−	0.102698i	$-0.0327476\pi$
$32$	5.62037	+	0.641410i	0.993551	+	0.113386i
$33$	0.300550	−	3.65354i	0.0523190	−	0.636000i
$34$	−0.909875	−	0.693192i	−0.156042	−	0.118881i
$35$			4.96439i			0.839136i
$36$	4.85470	−	3.52589i	0.809116	−	0.587649i
$37$			4.01531i			0.660113i	0.943961	+	0.330057i	$0.107068\pi$
$37$			4.01531i			0.660113i	−0.943961	+	0.330057i	$0.892932\pi$
$38$	−6.36884	+	8.35966i	−1.03316	+	1.35612i
$39$	−1.60524	+	0.758698i	−0.257043	+	0.121489i
$40$	3.06165	−	2.40010i	0.484090	−	0.379489i
$41$	−3.45852	+	5.99034i	−0.540131	+	0.935534i	0.458765	+	0.888557i	$0.348292\pi$
$41$	−3.45852	+	5.99034i	−0.540131	+	0.935534i	−0.998896	+	0.0469764i	$0.985041\pi$
$42$	6.56973	+	5.91642i	1.01373	+	0.912923i
$43$	0.245957	−	0.142003i	0.0375081	−	0.0216553i	−0.481129	−	0.876650i	$-0.659773\pi$
$43$	0.245957	−	0.142003i	0.0375081	−	0.0216553i	0.518637	+	0.854995i	$0.326440\pi$
$44$	−3.01378	−	2.97243i	−0.454345	−	0.448111i
$45$	0.674310	−	4.07078i	0.100520	−	0.606836i
$46$	4.31847	−	1.80627i	0.636724	−	0.266320i
$47$	−3.61351	−	6.25878i	−0.527084	−	0.912937i	−0.999502	−	0.0315619i	$-0.989952\pi$
$47$	−3.61351	−	6.25878i	−0.527084	−	0.912937i	0.472417	−	0.881375i	$-0.343381\pi$
$48$	0.472570	−	6.91207i	0.0682096	−	0.997671i
$49$	−3.01378	+	5.22003i	−0.430540	+	0.745718i
$50$	−0.558698	+	4.36005i	−0.0790118	+	0.616604i
$51$	−0.797570	+	1.15172i	−0.111682	+	0.161273i
$52$	−0.516932	+	1.98393i	−0.0716856	+	0.275122i
$53$			3.86330i			0.530666i	0.964157	+	0.265333i	$0.0854818\pi$
$53$			3.86330i			0.530666i	−0.964157	+	0.265333i	$0.914518\pi$
$54$	−4.58353	−	5.74380i	−0.623740	−	0.781632i
$55$	−2.91107			−0.392528
$56$	10.1072	−	1.43732i	1.35063	−	0.192070i
$57$	10.5817	+	7.32784i	1.40158	+	0.970597i
$58$	−12.4896	−	1.60042i	−1.63997	−	0.210146i
$59$	−7.06904	−	4.08131i	−0.920310	−	0.531341i	−0.0365764	−	0.999331i	$-0.511645\pi$
$59$	−7.06904	−	4.08131i	−0.920310	−	0.531341i	−0.883734	+	0.467989i	$0.844979\pi$
$60$	−3.10654	−	3.61257i	−0.401053	−	0.466381i
$61$	−6.31237	+	3.64445i	−0.808216	+	0.466624i	−0.846336	−	0.532650i	$-0.821196\pi$
$61$	−6.31237	+	3.64445i	−0.808216	+	0.466624i	0.0381201	+	0.999273i	$0.487863\pi$
$62$	−8.51792	+	3.56275i	−1.08178	+	0.452470i
$63$	6.87373	−	8.36660i	0.866008	−	1.05409i
$64$	−5.77286	−	5.53842i	−0.721607	−	0.692303i
$65$	0.704961	+	1.22103i	0.0874396	+	0.151450i
$66$	−3.46932	+	3.85242i	−0.427044	+	0.474200i
$67$	2.43973	+	1.40858i	0.298061	+	0.172085i	0.641571	−	0.767063i	$-0.278283\pi$
$67$	2.43973	+	1.40858i	0.298061	+	0.172085i	−0.343511	+	0.939149i	$0.611616\pi$
$68$	0.429460	+	1.55960i	0.0520797	+	0.189129i
$69$	−2.44981	−	5.18325i	−0.294923	−	0.623990i
$70$	4.25468	−	5.58463i	0.508531	−	0.667492i
$71$	4.69830			0.557586			0.278793	−	0.960351i	$-0.410066\pi$
$71$	4.69830			0.557586			0.278793	+	0.960351i	$0.410066\pi$
$72$	−8.48306	−	0.194250i	−0.999738	−	0.0228926i
$73$	0.409922			0.0479777			0.0239889	−	0.999712i	$-0.492363\pi$
$73$	0.409922			0.0479777			0.0239889	+	0.999712i	$0.492363\pi$
$74$	3.44128	−	4.51698i	0.400040	−	0.525088i
$75$	5.36548	+	0.441379i	0.619552	+	0.0509660i
$76$	14.3291	−	3.94576i	1.64366	−	0.452609i
$77$	−6.61576	−	3.81961i	−0.753936	−	0.435285i
$78$	2.45602	+	0.522260i	0.278090	+	0.0591343i
$79$	−0.0456121	−	0.0790024i	−0.00513176	−	0.00888847i	0.863448	−	0.504438i	$-0.168300\pi$
$79$	−0.0456121	−	0.0790024i	−0.00513176	−	0.00888847i	−0.868580	+	0.495549i	$0.834967\pi$
$80$	−5.50115	+	0.0760042i	−0.615047	+	0.00849752i
$81$	−6.77286	+	5.92692i	−0.752540	+	0.658547i
$82$	9.02458	−	3.77467i	0.996598	−	0.416843i
$83$	2.40891	−	1.39079i	0.264412	−	0.152659i	−0.361933	−	0.932204i	$-0.617883\pi$
$83$	2.40891	−	1.39079i	0.264412	−	0.152659i	0.626346	+	0.779545i	$0.284550\pi$
$84$	−2.31995	−	12.2861i	−0.253127	−	1.34053i
$85$	0.963426	+	0.556234i	0.104498	+	0.0603321i
$86$	−0.398389	−	0.0510497i	−0.0429594	−	0.00550483i
$87$	−1.26436	+	15.3697i	−0.135553	+	1.64781i
$88$	0.842830	+	5.92673i	0.0898460	+	0.631791i
$89$	8.91934			0.945448			0.472724	−	0.881210i	$-0.343271\pi$
$89$	8.91934			0.945448			0.472724	+	0.881210i	$0.343271\pi$
$90$	−4.24737	+	4.00147i	−0.447713	+	0.421792i
$91$			3.69992i			0.387857i
$92$	−6.40605	−	1.66916i	−0.667877	−	0.174021i
$93$	4.83210	+	10.2236i	0.501066	+	1.06014i
$94$	−1.29904	+	10.1377i	−0.133986	+	1.04562i
$95$	5.11052	−	8.85168i	0.524328	−	0.908163i
$96$	−6.45552	+	7.37064i	−0.658864	+	0.752262i
$97$	−2.76022	−	4.78084i	−0.280258	−	0.485421i	0.691190	−	0.722673i	$-0.257087\pi$
$97$	−2.76022	−	4.78084i	−0.280258	−	0.485421i	−0.971448	+	0.237252i	$0.923753\pi$
$98$	7.86408	−	3.28928i	0.794392	−	0.332267i
$99$	4.90608	+	4.03068i	0.493080	+	0.405099i
$100$	4.36523	−	4.42595i	0.436523	−	0.442595i
$101$	−5.63193	+	3.25160i	−0.560398	+	0.323546i	−0.753305	−	0.657671i	$-0.771542\pi$
$101$	−5.63193	+	3.25160i	−0.560398	+	0.323546i	0.192907	+	0.981217i	$0.438208\pi$
$102$	1.88429	−	0.612066i	0.186572	−	0.0606036i
$103$	−1.50528	+	2.60723i	−0.148320	+	0.256898i	−0.930607	−	0.366021i	$-0.880720\pi$
$103$	−1.50528	+	2.60723i	−0.148320	+	0.256898i	0.782287	+	0.622918i	$0.214053\pi$
$104$	2.28182	−	1.78877i	0.223751	−	0.175403i
$105$	−7.06904	−	4.89533i	−0.689868	−	0.477735i
$106$	3.31100	−	4.34598i	0.321593	−	0.422119i
$107$			0.447393i			0.0432511i	0.999766	+	0.0216256i	$0.00688417\pi$
$107$			0.447393i			0.0432511i	−0.999766	+	0.0216256i	$0.993116\pi$
$108$	0.233532	+	10.3897i	0.0224716	+	0.999747i
$109$			9.36497i			0.897002i	0.893782	+	0.448501i	$0.148042\pi$
$109$			9.36497i			0.897002i	−0.893782	+	0.448501i	$0.851958\pi$
$110$	3.27477	+	2.49490i	0.312237	+	0.237879i
$111$	−5.71760	−	3.95945i	−0.542690	−	0.375815i
$112$	−12.6018	−	7.04533i	−1.19075	−	0.665721i
$113$	5.66349	−	9.80944i	0.532776	−	0.922795i	−0.466492	−	0.884526i	$-0.654482\pi$
$113$	5.66349	−	9.80944i	0.532776	−	0.922795i	0.999267	−	0.0382692i	$-0.0121844\pi$
$114$	−5.62349	−	17.3123i	−0.526688	−	1.62144i
$115$	−3.94266	+	2.27629i	−0.367655	+	0.212266i
$116$	12.6784	+	12.5045i	1.17716	+	1.16101i
$117$	0.502557	−	3.03392i	0.0464614	−	0.280486i
$118$	4.45439	+	10.6497i	0.410060	+	0.980381i
$119$	1.45967	+	2.52822i	0.133808	+	0.231762i
$120$	0.398552	+	6.72635i	0.0363827	+	0.614029i
$121$	−3.26022	+	5.64687i	−0.296384	+	0.513351i
$122$	10.2245	+	1.31017i	0.925678	+	0.118617i
$123$	−5.11952	−	10.8318i	−0.461612	−	0.976667i
$124$	12.6355	+	3.29231i	1.13471	+	0.295658i
$125$		−	11.1522i		−	0.997483i
$126$	−14.9030	+	3.52085i	−1.32767	+	0.313662i
$127$	−11.8341			−1.05011			−0.525053	−	0.851069i	$-0.675955\pi$
$127$	−11.8341			−1.05011			−0.525053	+	0.851069i	$0.675955\pi$
$128$	1.74746	+	11.1779i	0.154455	+	0.988000i
$129$	−0.0403299	+	0.490258i	−0.00355085	+	0.0431648i
$130$	0.253431	−	1.97776i	0.0222274	−	0.173461i
$131$	−2.40891	−	1.39079i	−0.210468	−	0.121514i	0.391061	−	0.920365i	$-0.372108\pi$
$131$	−2.40891	−	1.39079i	−0.210468	−	0.121514i	−0.601529	+	0.798851i	$0.705441\pi$
$132$	7.20445	−	1.36039i	0.627067	−	0.118407i
$133$	23.2286	−	13.4110i	2.01417	−	1.16288i
$134$	−1.53734	−	3.67551i	−0.132806	−	0.317516i
$135$	5.13166	+	4.97433i	0.441663	+	0.428123i
$136$	0.853517	−	2.12251i	0.0731885	−	0.182004i
$137$	−8.17841	−	14.1654i	−0.698729	−	1.21023i	−0.968907	−	0.247424i	$-0.920416\pi$
$137$	−8.17841	−	14.1654i	−0.698729	−	1.21023i	0.270178	−	0.962810i	$-0.412917\pi$
$138$	−1.68636	+	7.93042i	−0.143553	+	0.675082i
$139$	−1.22979	−	0.710017i	−0.104309	−	0.0602229i	0.446938	−	0.894565i	$-0.352514\pi$
$139$	−1.22979	−	0.710017i	−0.104309	−	0.0602229i	−0.551247	+	0.834342i	$0.685848\pi$
$140$	−9.57249	+	2.63594i	−0.809023	+	0.222778i
$141$	12.4754	+	1.02626i	1.05062	+	0.0864268i
$142$	−5.28530	−	4.02663i	−0.443533	−	0.337907i
$143$	−2.16959			−0.181430
$144$	9.37643	+	7.48883i	0.781369	+	0.624069i
$145$	12.2463			1.01700
$146$	−0.461137	−	0.351319i	−0.0381639	−	0.0290753i
$147$	−4.46119	−	9.43888i	−0.367953	−	0.778506i
$148$	−7.74245	+	2.13201i	−0.636425	+	0.175250i
$149$	4.91390	+	2.83704i	0.402563	+	0.232420i	0.687589	−	0.726100i	$-0.258669\pi$
$149$	4.91390	+	2.83704i	0.402563	+	0.232420i	−0.285027	+	0.958520i	$0.592002\pi$
$150$	−5.65755	−	5.09495i	−0.461937	−	0.416001i
$151$	7.07318	+	12.2511i	0.575607	+	0.996981i	0.995975	+	0.0896271i	$0.0285675\pi$
$151$	7.07318	+	12.2511i	0.575607	+	0.996981i	−0.420368	+	0.907354i	$0.638099\pi$
$152$	−19.5010	−	7.84186i	−1.58174	−	0.636059i
$153$	−0.853517	−	2.27140i	−0.0690027	−	0.183632i
$154$	4.16877	+	9.96679i	0.335929	+	0.803147i
$155$	7.77665	−	4.48985i	0.624636	−	0.360634i
$156$	−2.31528	−	2.69242i	−0.185371	−	0.215566i
$157$	−18.6713	−	10.7799i	−1.49013	−	0.860328i	−0.490196	−	0.871612i	$-0.663075\pi$
$157$	−18.6713	−	10.7799i	−1.49013	−	0.860328i	−0.999936	+	0.0112838i	$0.996408\pi$
$158$	−0.0163974	+	0.127964i	−0.00130451	+	0.0101803i
$159$	−5.50115	−	3.80956i	−0.436269	−	0.302118i
$160$	6.25359	+	4.62919i	0.494389	+	0.365970i
$161$	−11.9469			−0.941548
$162$	12.6986	−	0.862820i	0.997700	−	0.0677895i
$163$			14.9239i			1.16893i	0.811418	+	0.584466i	$0.198696\pi$
$163$			14.9239i			1.16893i	−0.811418	+	0.584466i	$0.801304\pi$
$164$	−13.3871	−	3.48814i	−1.04536	−	0.272378i
$165$	2.87057	−	4.14521i	0.223474	−	0.322704i
$166$	−3.90183	−	0.499983i	−0.302841	−	0.0388062i
$167$	−11.0234	+	19.0931i	−0.853019	+	1.47747i	0.0254524	+	0.999676i	$0.491897\pi$
$167$	−11.0234	+	19.0931i	−0.853019	+	1.47747i	−0.878471	+	0.477796i	$0.841436\pi$
$168$	−7.91988	+	15.8094i	−0.611032	+	1.21972i
$169$	−5.97460	−	10.3483i	−0.459585	−	0.796024i
$170$	−0.607080	−	1.45142i	−0.0465609	−	0.111319i
$171$	−20.8689	+	7.84186i	−1.59589	+	0.599682i
$172$	0.404411	+	0.398862i	0.0308361	+	0.0304130i
$173$	−10.9052	+	6.29612i	−0.829107	+	0.478685i	−0.853547	−	0.521016i	$-0.825553\pi$
$173$	−10.9052	+	6.29612i	−0.829107	+	0.478685i	0.0244397	+	0.999701i	$0.492220\pi$
$174$	14.5948	−	16.2064i	1.10643	−	1.22860i
$175$	5.60937	−	9.71572i	0.424029	−	0.734439i
$176$	4.13130	−	7.38954i	0.311409	−	0.557007i
$177$	12.7823	−	6.04141i	0.960775	−	0.454100i
$178$	−10.0337	−	7.64422i	−0.752058	−	0.572958i
$179$		−	12.1116i		−	0.905264i	−0.891697	−	0.452632i	$-0.850485\pi$
$179$		−	12.1116i		−	0.905264i	0.891697	−	0.452632i	$-0.149515\pi$
$180$	8.20744	−	0.861239i	0.611747	−	0.0641930i
$181$		−	17.6790i		−	1.31407i	−0.753862	−	0.657033i	$-0.771811\pi$
$181$		−	17.6790i		−	1.31407i	0.753862	−	0.657033i	$-0.228189\pi$
$182$	3.17097	−	4.16218i	0.235048	−	0.308521i
$183$	1.03505	−	12.5822i	0.0765129	−	0.930105i
$184$	5.77588	+	7.36793i	0.425803	+	0.543171i
$185$	−2.76137	+	4.78283i	−0.203020	+	0.351640i
$186$	3.32624	−	15.6423i	0.243892	−	1.14695i
$187$	−1.48252	+	0.855935i	−0.108413	+	0.0625922i
$188$	10.1497	−	10.2909i	0.740243	−	0.750541i
$189$	5.13550	+	18.0380i	0.373553	+	1.31207i
$190$	−13.3352	+	5.57768i	−0.967440	+	0.404647i
$191$	9.72173	+	16.8385i	0.703440	+	1.21839i	0.967252	+	0.253820i	$0.0816870\pi$
$191$	9.72173	+	16.8385i	0.703440	+	1.21839i	−0.263812	+	0.964574i	$0.584980\pi$
$192$	13.5790	−	2.75888i	0.979978	−	0.199105i
$193$	0.159120	−	0.275604i	0.0114537	−	0.0198384i	−0.860242	−	0.509886i	$-0.829687\pi$
$193$	0.159120	−	0.275604i	0.0114537	−	0.0198384i	0.871695	+	0.490048i	$0.163021\pi$
$194$	−0.992289	+	7.74376i	−0.0712422	+	0.555970i
$195$	−2.43384	−	0.200214i	−0.174291	−	0.0143376i
$196$	−11.6656	−	3.03959i	−0.833260	−	0.217114i
$197$			24.5066i			1.74602i	0.487701	+	0.873011i	$0.337836\pi$
$197$			24.5066i			1.74602i	−0.487701	+	0.873011i	$0.662164\pi$
$198$	−2.06459	−	8.73897i	−0.146724	−	0.621051i
$199$	−7.13579			−0.505843			−0.252921	−	0.967487i	$-0.581391\pi$
$199$	−7.13579			−0.505843			−0.252921	+	0.967487i	$0.581391\pi$
$200$	−8.70382	+	1.23776i	−0.615453	+	0.0875225i
$201$	−4.41154	+	2.08507i	−0.311166	+	0.147069i
$202$	9.12232	+	1.16894i	0.641844	+	0.0822462i
$203$	27.8313	+	16.0684i	1.95337	+	1.12778i
$204$	−2.64427	−	0.926369i	−0.185136	−	0.0648588i
$205$	−8.23922	+	4.75692i	−0.575452	+	0.332237i
$206$	3.92784	−	1.64288i	0.273666	−	0.114465i
$207$	9.79641	+	1.62274i	0.680898	+	0.112788i
$208$	−4.09995	+	0.0566452i	−0.284281	+	0.00392764i
$209$	7.86408	+	13.6210i	0.543970	+	0.942183i
$210$	3.75674	+	11.5654i	0.259240	+	0.798087i
$211$	7.00175	+	4.04246i	0.482020	+	0.278294i	0.721258	−	0.692667i	$-0.243564\pi$
$211$	7.00175	+	4.04246i	0.482020	+	0.278294i	−0.239238	+	0.970961i	$0.576898\pi$
$212$	−7.44934	+	2.05130i	−0.511623	+	0.140884i
$213$	−4.63294	+	6.69014i	−0.317444	+	0.458401i
$214$	0.383433	−	0.503289i	0.0262109	−	0.0344042i
$215$	0.390628			0.0266406
$216$	8.64165	−	11.8879i	0.587990	−	0.808868i
$217$	23.5646			1.59967
$218$	8.02614	−	10.5350i	0.543599	−	0.713521i
$219$	−0.404219	+	0.583708i	−0.0273146	+	0.0394433i
$220$	−1.54569	−	5.61321i	−0.104210	−	0.378442i
$221$	0.718032	+	0.414556i	0.0483001	+	0.0278861i
$222$	3.03854	+	9.35434i	0.203933	+	0.627822i
$223$	−2.11236	−	3.65872i	−0.141454	−	0.245006i	0.786590	−	0.617475i	$-0.211844\pi$
$223$	−2.11236	−	3.65872i	−0.141454	−	0.245006i	−0.928044	+	0.372469i	$0.878511\pi$
$224$	8.13808	+	18.7257i	0.543749	+	1.25117i
$225$	−5.91934	+	7.20493i	−0.394623	+	0.480329i
$226$	−14.7781	+	6.18119i	−0.983027	+	0.411167i
$227$	−1.09451	+	0.631913i	−0.0726449	+	0.0419415i	−0.535882	−	0.844293i	$-0.680021\pi$
$227$	−1.09451	+	0.631913i	−0.0726449	+	0.0419415i	0.463238	+	0.886234i	$0.346688\pi$
$228$	−8.51121	+	24.2948i	−0.563669	+	1.60896i
$229$	6.29196	+	3.63267i	0.415785	+	0.240053i	0.693272	−	0.720676i	$-0.256168\pi$
$229$	6.29196	+	3.63267i	0.415785	+	0.240053i	−0.277487	+	0.960729i	$0.589502\pi$
$230$	6.38612	+	0.818320i	0.421088	+	0.0539584i
$231$	11.9627	−	5.65403i	0.787085	−	0.372008i
$232$	−3.54563	−	24.9326i	−0.232782	−	1.63691i
$233$	−5.91061			−0.387217			−0.193608	−	0.981079i	$-0.562019\pi$
$233$	−5.91061			−0.387217			−0.193608	+	0.981079i	$0.562019\pi$
$234$	−3.16553	+	2.98226i	−0.206937	+	0.194956i
$235$		−	9.94017i		−	0.648425i
$236$	4.11626	−	15.7978i	0.267946	−	1.02835i
$237$	0.157473	+	0.0129541i	0.0102290	+	0.000841462i
$238$	0.524746	−	4.09509i	0.0340142	−	0.265445i
$239$	5.96266	−	10.3276i	0.385692	−	0.668039i	−0.606173	−	0.795333i	$-0.707296\pi$
$239$	5.96266	−	10.3276i	0.385692	−	0.668039i	0.991865	+	0.127294i	$0.0406293\pi$
$240$	5.31639	−	7.90830i	0.343172	−	0.510478i
$241$	1.80170	+	3.12063i	0.116057	+	0.201017i	0.918202	−	0.396113i	$-0.129641\pi$
$241$	1.80170	+	3.12063i	0.116057	+	0.201017i	−0.802145	+	0.597130i	$0.796308\pi$
$242$	8.50713	−	3.55824i	0.546859	−	0.228732i
$243$	−1.76100	−	15.4887i	−0.112968	−	0.993599i
$244$	−10.3790	−	10.2366i	−0.664448	−	0.655331i
$245$	−7.17972	+	4.14521i	−0.458695	+	0.264828i
$246$	−3.52409	+	16.5727i	−0.224688	+	1.05664i
$247$	3.80882	−	6.59707i	0.242350	−	0.419762i
$248$	−11.3926	−	14.5328i	−0.723429	−	0.922833i
$249$	−0.394993	+	4.80161i	−0.0250316	+	0.304289i
$250$	−9.55786	+	12.5455i	−0.604492	+	0.793449i
$251$		−	0.641516i		−	0.0404922i	−0.999795	−	0.0202461i	$-0.993555\pi$
$251$		−	0.641516i		−	0.0404922i	0.999795	−	0.0202461i	$-0.00644497\pi$
$252$	19.7825	+	8.81172i	1.24618	+	0.555086i
$253$		−	7.00554i		−	0.440434i
$254$	13.3126	+	10.1423i	0.835308	+	0.636383i
$255$	−1.74207	+	0.823373i	−0.109093	+	0.0515616i
$256$	7.61414	−	14.0721i	0.475884	−	0.879508i
$257$	−1.99885	+	3.46212i	−0.124685	+	0.215961i	−0.921610	−	0.388118i	$-0.873125\pi$
$257$	−1.99885	+	3.46212i	−0.124685	+	0.215961i	0.796925	+	0.604079i	$0.206459\pi$
$258$	0.465539	−	0.516946i	0.0289832	−	0.0321836i
$259$	−12.5511	+	7.24638i	−0.779887	+	0.450268i
$260$	−1.98011	+	2.00766i	−0.122801	+	0.124510i
$261$	−20.6390	−	16.9563i	−1.27752	−	1.04957i
$262$	1.51792	+	3.62908i	0.0937774	+	0.224205i
$263$	−5.64671	−	9.78039i	−0.348191	−	0.603085i	0.637737	−	0.770254i	$-0.279871\pi$
$263$	−5.64671	−	9.78039i	−0.348191	−	0.603085i	−0.985928	+	0.167169i	$0.946537\pi$
$264$	−9.27046	−	4.64413i	−0.570558	−	0.285827i
$265$	−2.65683	+	4.60176i	−0.163208	+	0.282684i
$266$	−37.6245	−	4.82121i	−2.30690	−	0.295608i
$267$	−8.79526	+	12.7007i	−0.538261	+	0.777269i
$268$	−1.42064	+	5.45228i	−0.0867795	+	0.333051i
$269$		−	24.2695i		−	1.47974i	−0.672750	−	0.739870i	$-0.734887\pi$
$269$		−	24.2695i		−	1.47974i	0.672750	−	0.739870i	$-0.265113\pi$
$270$	−1.50960	−	9.99384i	−0.0918712	−	0.608206i
$271$	12.2330			0.743102			0.371551	−	0.928413i	$-0.378826\pi$
$271$	12.2330			0.743102			0.371551	+	0.928413i	$0.378826\pi$
$272$	−2.77923	+	1.65620i	−0.168515	+	0.100422i
$273$	−5.26849	−	3.64845i	−0.318864	−	0.220814i
$274$	−2.94011	+	22.9444i	−0.177619	+	1.38612i
$275$	5.69719	+	3.28928i	0.343554	+	0.198351i
$276$	8.69372	−	7.47595i	0.523301	−	0.449999i
$277$	10.9249	−	6.30750i	0.656414	−	0.378981i	−0.134495	−	0.990914i	$-0.542941\pi$
$277$	10.9249	−	6.30750i	0.656414	−	0.378981i	0.790909	+	0.611933i	$0.209608\pi$
$278$	0.774920	+	1.85270i	0.0464766	+	0.111117i
$279$	−19.3228	−	3.20075i	−1.15683	−	0.191624i
$280$	13.0276	+	5.23872i	0.778546	+	0.313073i
$281$	9.54364	+	16.5301i	0.569326	+	0.986101i	0.996633	+	0.0819947i	$0.0261291\pi$
$281$	9.54364	+	16.5301i	0.569326	+	0.986101i	−0.427307	+	0.904107i	$0.640538\pi$
$282$	−13.1545	−	11.8464i	−0.783341	−	0.705443i
$283$	1.01045	+	0.583382i	0.0600649	+	0.0346785i	0.529732	−	0.848165i	$-0.322293\pi$
$283$	1.01045	+	0.583382i	0.0600649	+	0.0346785i	−0.469667	+	0.882844i	$0.655626\pi$
$284$	2.49466	+	9.05941i	0.148031	+	0.537577i
$285$	7.56491	+	16.0057i	0.448107	+	0.948093i
$286$	2.44066	+	1.85942i	0.144319	+	0.109950i
$287$	−24.9662			−1.47371
$288$	−4.12969	−	16.4604i	−0.243344	−	0.969940i
$289$	−16.3458			−0.961518
$290$	−13.7763	−	10.4956i	−0.808974	−	0.616320i
$291$	9.52949	+	0.783921i	0.558629	+	0.0459543i
$292$	0.217656	+	0.790423i	0.0127374	+	0.0462560i
$293$	−2.11446	−	1.22079i	−0.123528	−	0.0713191i	0.436963	−	0.899480i	$-0.356054\pi$
$293$	−2.11446	−	1.22079i	−0.123528	−	0.0713191i	−0.560491	+	0.828161i	$0.689388\pi$
$294$	−3.07092	+	14.4416i	−0.179100	+	0.842249i
$295$	−5.61351	−	9.72288i	−0.326831	−	0.566088i
$296$	10.5370	+	4.23719i	0.612450	+	0.246282i
$297$	−10.5773	+	3.01140i	−0.613758	+	0.174739i
$298$	−3.09638	−	7.40290i	−0.179368	−	0.428839i
$299$	−2.93843	+	1.69650i	−0.169934	+	0.0981112i
$300$	1.99783	+	10.5802i	0.115345	+	0.610851i
$301$	0.887751	+	0.512543i	0.0511691	+	0.0295425i
$302$	2.54278	−	19.8437i	0.146321	−	1.14188i
$303$	0.923476	−	11.2260i	0.0530523	−	0.644914i
$304$	15.2167	+	25.5347i	0.872735	+	1.46452i
$305$	−10.0253			−0.574046
$306$	−0.986522	+	3.28668i	−0.0563957	+	0.187887i
$307$		−	15.7452i		−	0.898626i	−0.893374	−	0.449313i	$-0.851669\pi$
$307$		−	15.7452i		−	0.898626i	0.893374	−	0.449313i	$-0.148331\pi$
$308$	3.85232	−	14.7848i	0.219506	−	0.842443i
$309$	−2.22821	−	4.71440i	−0.126759	−	0.268193i
$310$	−12.5962	−	1.61409i	−0.715418	−	0.0916739i
$311$	9.90129	−	17.1495i	0.561451	−	0.972461i	−0.435919	−	0.899986i	$-0.643577\pi$
$311$	9.90129	−	17.1495i	0.561451	−	0.972461i	0.997370	−	0.0724757i	$-0.0230900\pi$
$312$	0.297037	+	5.01308i	0.0168164	+	0.283810i
$313$	16.2557	+	28.1557i	0.918828	+	1.59146i	0.801198	+	0.598399i	$0.204196\pi$
$313$	16.2557	+	28.1557i	0.918828	+	1.59146i	0.117630	+	0.993057i	$0.462470\pi$
$314$	11.7653	+	28.1287i	0.663953	+	1.58740i
$315$	13.9414	−	5.23872i	0.785509	−	0.295169i
$316$	0.128116	−	0.129899i	0.00720710	−	0.00730736i
$317$	13.9271	−	8.04083i	0.782225	−	0.451618i	−0.0549932	−	0.998487i	$-0.517514\pi$
$317$	13.9271	−	8.04083i	0.782225	−	0.451618i	0.837218	+	0.546869i	$0.184180\pi$
$318$	2.92351	+	9.00021i	0.163942	+	0.504707i
$319$	−9.42233	+	16.3200i	−0.527549	+	0.913742i
$320$	−3.06750	−	10.5671i	−0.171478	−	0.590720i
$321$	−0.637065	−	0.441169i	−0.0355575	−	0.0246237i
$322$	13.4395	+	10.2390i	0.748956	+	0.570595i
$323$		−	6.01054i		−	0.334435i
$324$	−15.0247	−	9.91261i	−0.834703	−	0.550700i
$325$		−	3.18620i		−	0.176739i
$326$	12.7904	−	16.7885i	0.708393	−	0.929828i
$327$	−13.3352	−	9.23469i	−0.737441	−	0.510680i
$328$	12.0702	+	15.3972i	0.666466	+	0.850169i
$329$	13.0425	−	22.5903i	0.719056	−	1.24544i
$330$	−6.78182	+	2.20291i	−0.373327	+	0.121266i
$331$	17.7569	−	10.2520i	0.976010	−	0.563499i	0.0749465	−	0.997188i	$-0.476121\pi$
$331$	17.7569	−	10.2520i	0.976010	−	0.563499i	0.901063	+	0.433688i	$0.142788\pi$
$332$	3.96082	+	3.90647i	0.217378	+	0.214395i
$333$	11.2761	−	4.23719i	0.617927	−	0.232197i
$334$	28.7642	−	12.0311i	1.57391	−	0.658312i
$335$	1.93739	+	3.35565i	0.105851	+	0.183339i
$336$	22.4586	−	10.9969i	1.22522	−	0.599933i
$337$	6.21760	−	10.7692i	0.338694	−	0.586635i	−0.645493	−	0.763766i	$-0.723348\pi$
$337$	6.21760	−	10.7692i	0.338694	−	0.586635i	0.984187	+	0.177131i	$0.0566815\pi$
$338$	−2.14785	+	16.7617i	−0.116827	+	0.911714i
$339$	8.38345	+	17.7375i	0.455326	+	0.963368i
$340$	−0.560997	+	2.15305i	−0.0304243	+	0.116766i
$341$			13.8180i			0.748287i
$342$	30.1970	+	9.06388i	1.63287	+	0.490118i
$343$	3.50988			0.189515
$344$	−0.113097	−	0.795291i	−0.00609778	−	0.0428792i
$345$	0.646483	−	7.85877i	0.0348055	−	0.423102i
$346$	17.6637	+	2.26343i	0.949606	+	0.121683i
$347$	−24.1550	−	13.9459i	−1.29671	−	0.748654i	−0.316873	−	0.948468i	$-0.602633\pi$
$347$	−24.1550	−	13.9459i	−1.29671	−	0.748654i	−0.979834	+	0.199814i	$0.935966\pi$
$348$	−30.3077	+	5.72291i	−1.62467	+	0.306780i
$349$	−26.0103	+	15.0171i	−1.39230	+	0.803846i	−0.993570	−	0.113222i	$-0.963883\pi$
$349$	−26.0103	+	15.0171i	−1.39230	+	0.803846i	−0.398732	+	0.917068i	$0.630550\pi$
$350$	−14.6369	+	6.12213i	−0.782377	+	0.327242i
$351$	3.82458	+	3.70733i	0.204141	+	0.197882i
$352$	−10.9806	+	4.77209i	−0.585267	+	0.254353i
$353$	−9.48011	−	16.4200i	−0.504575	−	0.873950i	−0.999986	−	0.00529122i	$-0.998316\pi$
$353$	−9.48011	−	16.4200i	−0.504575	−	0.873950i	0.495411	−	0.868659i	$-0.335018\pi$
$354$	−19.5570	−	4.15869i	−1.03944	−	0.221032i
$355$	5.59637	+	3.23107i	0.297024	+	0.171487i
$356$	4.73590	+	17.1985i	0.251002	+	0.911521i
$357$	−5.03942	−	0.414556i	−0.266715	−	0.0219406i
$358$	−10.3801	+	13.6248i	−0.548606	+	0.720093i
$359$	28.6420			1.51167			0.755833	−	0.654765i	$-0.227232\pi$
$359$	28.6420			1.51167			0.755833	+	0.654765i	$0.227232\pi$
$360$	−9.97098	−	6.06525i	−0.525517	−	0.319667i
$361$	−36.2231			−1.90648
$362$	−15.1515	+	19.8877i	−0.796348	+	1.04528i
$363$	−4.82598	−	10.2107i	−0.253298	−	0.535923i
$364$	−7.13429	+	1.96455i	−0.373938	+	0.102970i
$365$	0.488277	+	0.281907i	0.0255576	+	0.0147557i
$366$	−11.9478	+	13.2672i	−0.624523	+	0.693485i
$367$	5.77148	+	9.99650i	0.301269	+	0.521813i	0.976424	−	0.215863i	$-0.0692565\pi$
$367$	5.77148	+	9.99650i	0.301269	+	0.521813i	−0.675155	+	0.737676i	$0.735923\pi$
$368$	−0.182905	−	13.2386i	−0.00953461	−	0.690110i
$369$	20.4722	+	3.39114i	1.06574	+	0.176536i
$370$	7.20543	−	3.01378i	0.374593	−	0.156679i
$371$	−12.0759	+	6.97205i	−0.626952	+	0.361971i
$372$	−17.1478	+	14.7459i	−0.889074	+	0.764537i
$373$	19.4301	+	11.2180i	1.00605	+	0.580846i	0.910034	−	0.414533i	$-0.136055\pi$
$373$	19.4301	+	11.2180i	1.00605	+	0.580846i	0.0960206	+	0.995379i	$0.469389\pi$
$374$	2.40132	+	0.307706i	0.124169	+	0.0159111i
$375$	15.8802	+	10.9971i	0.820048	+	0.567885i
$376$	−20.2375	+	2.87794i	−1.04367	+	0.148418i
$377$	9.12706			0.470068
$378$	9.68218	−	24.6930i	0.497997	−	1.27007i
$379$			22.6668i			1.16431i	0.813077	+	0.582157i	$0.197791\pi$
$379$			22.6668i			1.16431i	−0.813077	+	0.582157i	$0.802209\pi$
$380$	19.7816	+	5.15428i	1.01477	+	0.264409i
$381$	11.6695	−	16.8511i	0.597845	−	0.863310i
$382$	3.49493	−	27.2742i	0.178816	−	1.39547i
$383$	−1.94277	+	3.36498i	−0.0992709	+	0.171942i	−0.911383	−	0.411559i	$-0.864984\pi$
$383$	−1.94277	+	3.36498i	−0.0992709	+	0.171942i	0.812112	+	0.583501i	$0.198318\pi$
$384$	−17.6400	−	8.53414i	−0.900186	−	0.435506i
$385$	−5.25356	−	9.09944i	−0.267746	−	0.463750i
$386$	−0.415204	+	0.173666i	−0.0211333	+	0.00883935i
$387$	−0.658334	−	0.540866i	−0.0334650	−	0.0274937i
$388$	7.75297	−	7.86082i	0.393597	−	0.399073i
$389$	−11.9463	+	6.89722i	−0.605703	+	0.349703i	−0.771282	−	0.636494i	$-0.780384\pi$
$389$	−11.9463	+	6.89722i	−0.605703	+	0.349703i	0.165579	+	0.986197i	$0.447051\pi$
$390$	2.56632	+	2.31112i	0.129951	+	0.117028i
$391$	−1.33859	+	2.31850i	−0.0676953	+	0.117252i
$392$	10.5181	+	13.4172i	0.531243	+	0.677673i
$393$	4.35581	−	2.05873i	0.219721	−	0.103849i
$394$	21.0031	−	27.5684i	1.05812	−	1.38887i
$395$		−	0.125471i		−	0.00631315i
$396$	−5.16710	+	11.6002i	−0.259656	+	0.582933i
$397$			23.7680i			1.19288i	0.802657	+	0.596441i	$0.203419\pi$
$397$			23.7680i			1.19288i	−0.802657	+	0.596441i	$0.796581\pi$
$398$	8.02732	+	6.11565i	0.402373	+	0.306550i
$399$	−3.80882	+	46.3008i	−0.190680	+	2.31794i
$400$	10.8521	+	6.06711i	0.542603	+	0.303356i
$401$	−4.47782	+	7.75581i	−0.223612	+	0.387307i	−0.955902	−	0.293686i	$-0.905118\pi$
$401$	−4.47782	+	7.75581i	−0.223612	+	0.387307i	0.732290	+	0.680992i	$0.238451\pi$
$402$	6.74969	+	1.43528i	0.336644	+	0.0715855i
$403$	5.79587	−	3.34625i	0.288713	−	0.166688i
$404$	−9.26022	−	9.13316i	−0.460713	−	0.454392i
$405$	−12.1435	+	2.40208i	−0.603414	+	0.119360i
$406$	−17.5372	−	41.9284i	−0.870357	−	2.08087i
$407$	−4.24920	−	7.35983i	−0.210625	−	0.364813i
$408$	2.18070	+	3.30835i	0.107961	+	0.163788i
$409$	10.4170	−	18.0429i	0.515090	−	0.892162i	−0.484757	−	0.874649i	$-0.661092\pi$
$409$	10.4170	−	18.0429i	0.515090	−	0.892162i	0.999847	−	0.0175128i	$-0.00557480\pi$
$410$	13.3455	+	1.71009i	0.659086	+	0.0844555i
$411$	28.2355	+	2.32273i	1.39275	+	0.114572i
$412$	−5.82659	−	1.51817i	−0.287055	−	0.0747949i
$413$		−	29.4619i		−	1.44973i
$414$	−9.62961	−	10.2214i	−0.473269	−	0.502354i
$415$	3.82582			0.187802
$416$	4.66074	+	3.45010i	0.228512	+	0.169155i
$417$	2.22371	−	1.05101i	0.108895	−	0.0514683i
$418$	2.82711	−	22.0626i	0.138278	−	1.07912i
$419$	−8.74372	−	5.04819i	−0.427159	−	0.246620i	0.270977	−	0.962586i	$-0.412653\pi$
$419$	−8.74372	−	5.04819i	−0.427159	−	0.246620i	−0.698135	+	0.715966i	$0.745987\pi$
$420$	5.68588	−	16.2300i	0.277442	−	0.791944i
$421$	−20.2218	+	11.6751i	−0.985551	+	0.569008i	−0.903941	−	0.427656i	$-0.859339\pi$
$421$	−20.2218	+	11.6751i	−0.985551	+	0.569008i	−0.0816096	+	0.996664i	$0.526006\pi$
$422$	−4.41199	−	10.5483i	−0.214772	−	0.513482i
$423$	−13.7632	+	16.7524i	−0.669190	+	0.814528i
$424$	10.1381	+	4.07679i	0.492349	+	0.197986i
$425$	−1.25700	−	2.17719i	−0.0609735	−	0.105609i
$426$	10.9455	−	3.55538i	0.530310	−	0.172259i
$427$	−22.7837	−	13.1542i	−1.10258	−	0.636575i
$428$	−0.862677	+	0.237552i	−0.0416991	+	0.0114825i
$429$	2.13941	−	3.08939i	0.103292	−	0.149157i
$430$	−0.439432	−	0.334783i	−0.0211913	−	0.0161447i
$431$	−6.40348			−0.308445			−0.154222	−	0.988036i	$-0.549287\pi$
$431$	−6.40348			−0.308445			−0.154222	+	0.988036i	$0.549287\pi$
$432$	−19.9097	+	5.96691i	−0.957906	+	0.287083i
$433$	−9.82857			−0.472331			−0.236166	−	0.971713i	$-0.575891\pi$
$433$	−9.82857			−0.472331			−0.236166	+	0.971713i	$0.575891\pi$
$434$	−26.5087	−	20.1957i	−1.27246	−	0.969426i
$435$	−12.0759	+	17.4381i	−0.578997	+	0.836094i
$436$	−18.0578	+	4.97252i	−0.864813	+	0.238141i
$437$	21.3017	+	12.2986i	1.01900	+	0.588320i
$438$	0.954981	−	0.310203i	0.0456308	−	0.0148221i
$439$	−12.3831	−	21.4482i	−0.591015	−	1.02367i	−0.994096	−	0.108504i	$-0.965394\pi$
$439$	−12.3831	−	21.4482i	−0.591015	−	1.02367i	0.403081	−	0.915164i	$-0.367939\pi$
$440$	−3.07193	+	7.63923i	−0.146449	+	0.364186i
$441$	17.8396	+	2.95506i	0.849505	+	0.140717i
$442$	−0.452451	−	1.08173i	−0.0215209	−	0.0514527i
$443$	−23.5518	+	13.5976i	−1.11898	+	0.646044i	−0.941140	−	0.338016i	$-0.890244\pi$
$443$	−23.5518	+	13.5976i	−1.11898	+	0.646044i	−0.177840	+	0.984059i	$0.556911\pi$
$444$	4.59886	−	13.1272i	0.218252	−	0.622989i
$445$	10.6242	+	6.13391i	0.503637	+	0.290775i
$446$	−0.759387	+	5.92621i	−0.0359580	+	0.280614i
$447$	−8.88535	+	4.19957i	−0.420262	+	0.198633i
$448$	6.89385	−	28.0400i	0.325704	−	1.32476i
$449$	32.6861			1.54255			0.771276	−	0.636501i	$-0.219619\pi$
$449$	32.6861			1.54255			0.771276	+	0.636501i	$0.219619\pi$
$450$	12.8338	−	3.03200i	0.604991	−	0.142930i
$451$		−	14.6399i		−	0.689367i
$452$	21.9220	+	5.71198i	1.03112	+	0.268669i
$453$	−24.4197	−	2.00883i	−1.14734	−	0.0943831i
$454$	1.77282	+	0.227170i	0.0832028	+	0.0106616i
$455$	−2.54447	+	4.40714i	−0.119286	+	0.206610i
$456$	30.3961	−	20.0357i	1.42343	−	0.938256i
$457$	−10.3779	−	17.9750i	−0.485456	−	0.840834i	0.514404	−	0.857548i	$-0.328013\pi$
$457$	−10.3779	−	17.9750i	−0.485456	−	0.840834i	−0.999860	+	0.0167133i	$0.994680\pi$
$458$	−3.96473	−	9.47898i	−0.185260	−	0.442924i
$459$	4.07600	+	1.02444i	0.190251	+	0.0478165i
$460$	−6.48265	−	6.39371i	−0.302255	−	0.298108i
$461$	32.4695	−	18.7463i	1.51226	−	0.873101i	0.512359	−	0.858771i	$-0.328772\pi$
$461$	32.4695	−	18.7463i	1.51226	−	0.873101i	0.999897	−	0.0143300i	$-0.00456153\pi$
$462$	−18.3030	−	3.89203i	−0.851531	−	0.181074i
$463$	−7.97597	+	13.8148i	−0.370675	+	0.642028i	−0.989670	−	0.143367i	$-0.954207\pi$
$463$	−7.97597	+	13.8148i	−0.370675	+	0.642028i	0.618995	+	0.785395i	$0.287540\pi$
$464$	−17.3796	+	31.0864i	−0.806828	+	1.44315i
$465$	−1.27515	+	15.5009i	−0.0591336	+	0.718839i
$466$	6.64907	+	5.06562i	0.308012	+	0.234660i
$467$			27.0476i			1.25161i	0.779979	+	0.625806i	$0.215230\pi$
$467$			27.0476i			1.25161i	−0.779979	+	0.625806i	$0.784770\pi$
$468$	6.11693	−	0.641874i	0.282755	−	0.0296706i
$469$			10.1682i			0.469523i
$470$	−8.51911	+	11.1821i	−0.392957	+	0.515790i
$471$	33.7616	−	15.9571i	1.55565	−	0.735263i
$472$	−18.1698	+	14.2437i	−0.836335	+	0.655621i
$473$	−0.300550	+	0.520568i	−0.0138193	+	0.0239357i
$474$	−0.166045	−	0.149533i	−0.00762670	−	0.00686828i
$475$	−20.0034	+	11.5490i	−0.917818	+	0.529903i
$476$	−4.09995	+	4.15699i	−0.187921	+	0.190535i
$477$	10.8492	−	4.07679i	0.496752	−	0.186663i
$478$	−15.5588	+	6.50771i	−0.711643	+	0.297656i
$479$	13.6550	+	23.6511i	0.623912	+	1.08065i	0.988750	+	0.149577i	$0.0477910\pi$
$479$	13.6550	+	23.6511i	0.623912	+	1.08065i	−0.364838	+	0.931071i	$0.618876\pi$
$480$	−12.7583	+	4.33999i	−0.582335	+	0.198093i
$481$	−2.05802	+	3.56460i	−0.0938377	+	0.162532i
$482$	0.647703	−	5.05464i	0.0295021	−	0.230232i
$483$	11.7807	−	17.0118i	0.536041	−	0.774063i
$484$	−12.6195	−	3.28814i	−0.573615	−	0.149461i
$485$		−	7.59291i		−	0.344776i
$486$	−11.2934	+	18.9330i	−0.512278	+	0.858820i
$487$	19.1126			0.866073			0.433036	−	0.901376i	$-0.357442\pi$
$487$	19.1126			0.866073			0.433036	+	0.901376i	$0.357442\pi$
$488$	2.90258	+	20.4108i	0.131394	+	0.923951i
$489$	−21.2509	−	14.7163i	−0.960999	−	0.665494i
$490$	11.6293	+	1.49019i	0.525360	+	0.0673198i
$491$	−11.1131	−	6.41614i	−0.501526	−	0.289556i	0.227817	−	0.973704i	$-0.426841\pi$
$491$	−11.1131	−	6.41614i	−0.501526	−	0.289556i	−0.729344	+	0.684147i	$0.760174\pi$
$492$	18.1678	−	15.6230i	0.819069	−	0.704338i
$493$	6.23669	−	3.60076i	0.280886	−	0.162170i
$494$	−9.93863	+	4.15699i	−0.447160	+	0.187032i
$495$	3.07193	+	8.17509i	0.138073	+	0.367443i
$496$	0.360770	+	26.1124i	0.0161990	+	1.17248i
$497$	8.47896	+	14.6860i	0.380334	+	0.658757i
$498$	4.55950	−	5.06298i	0.204316	−	0.226878i
$499$	−15.3846	−	8.88232i	−0.688711	−	0.397627i	0.114418	−	0.993433i	$-0.463500\pi$
$499$	−15.3846	−	8.88232i	−0.688711	−	0.397627i	−0.803129	+	0.595805i	$0.796833\pi$
$500$	21.5040	−	5.92148i	0.961688	−	0.264817i
$501$	−16.3176	−	34.5243i	−0.729015	−	1.54243i
$502$	−0.549804	+	0.721666i	−0.0245390	+	0.0322095i
$503$	−24.0108			−1.07059			−0.535294	−	0.844666i	$-0.679799\pi$
$503$	−24.0108			−1.07059			−0.535294	+	0.844666i	$0.679799\pi$
$504$	−14.7021	−	26.8670i	−0.654882	−	1.19675i
$505$	−8.94461			−0.398030
$506$	−6.00402	+	7.88079i	−0.266911	+	0.350344i
$507$	20.6269	+	1.69683i	0.916075	+	0.0753587i
$508$	−6.28355	−	22.8189i	−0.278787	−	1.01242i
$509$	−6.91916	−	3.99478i	−0.306686	−	0.177065i	0.338756	−	0.940874i	$-0.389994\pi$
$509$	−6.91916	−	3.99478i	−0.306686	−	0.177065i	−0.645443	+	0.763809i	$0.723327\pi$
$510$	2.66538	+	0.566780i	0.118025	+	0.0250974i
$511$	0.739780	+	1.28134i	0.0327259	+	0.0566830i
$512$	−20.6258	+	9.30466i	−0.911540	+	0.411212i
$513$	9.41221	−	37.4491i	0.415559	−	1.65342i
$514$	5.21575	−	2.18157i	0.230057	−	0.0962250i
$515$	−3.58602	+	2.07039i	−0.158019	+	0.0912324i
$516$	−0.966745	+	0.182547i	−0.0425586	+	0.00803619i
$517$	13.2467	+	7.64798i	0.582589	+	0.336358i
$518$	20.3296	+	2.60505i	0.893232	+	0.114459i
$519$	1.78814	−	21.7370i	0.0784907	−	0.954147i
$520$	3.94814	−	0.561458i	0.173137	−	0.0246216i
$521$	−36.9809			−1.62016			−0.810082	−	0.586317i	$-0.800577\pi$
$521$	−36.9809			−1.62016			−0.810082	+	0.586317i	$0.800577\pi$
$522$	8.68534	+	36.7632i	0.380147	+	1.60908i
$523$		−	18.4217i		−	0.805526i	−0.915304	−	0.402763i	$-0.868050\pi$
$523$		−	18.4217i		−	0.805526i	0.915304	−	0.402763i	$-0.131950\pi$
$524$	1.40270	−	5.38340i	0.0612770	−	0.235175i
$525$	8.30334	+	17.5680i	0.362388	+	0.766731i
$526$	−2.02997	+	15.8418i	−0.0885110	+	0.690734i
$527$	2.64028	−	4.57311i	0.115013	−	0.199208i
$528$	6.44849	+	13.1695i	0.280635	+	0.573129i
$529$	6.02206	+	10.4305i	0.261828	+	0.453500i
$530$	6.93265	−	2.89969i	0.301135	−	0.125955i
$531$	−4.00179	+	24.1587i	−0.173663	+	1.04840i
$532$	38.1932	+	37.6692i	1.65589	+	1.63317i
$533$	−6.14061	+	3.54529i	−0.265980	+	0.153563i
$534$	20.7791	−	6.74960i	0.899199	−	0.292084i
$535$	−0.307676	+	0.532911i	−0.0133020	+	0.0230397i
$536$	6.27095	−	4.91593i	0.270864	−	0.212336i
$537$	17.2463	+	11.9431i	0.744233	+	0.515384i
$538$	−20.7999	+	27.3017i	−0.896748	+	1.17706i
$539$		−	12.7573i		−	0.549497i
$540$	−6.86691	+	12.5362i	−0.295505	+	0.539474i
$541$			13.5032i			0.580549i	0.956943	+	0.290275i	$0.0937467\pi$
$541$			13.5032i			0.580549i	−0.956943	+	0.290275i	$0.906253\pi$
$542$	−13.7614	−	10.4841i	−0.591101	−	0.450333i
$543$	25.1739	+	17.4330i	1.08032	+	0.748122i
$544$	4.54588	+	0.518787i	0.194903	+	0.0222428i
$545$	−6.44038	+	11.1551i	−0.275875	+	0.477830i
$546$	2.79987	+	8.61958i	0.119823	+	0.368884i
$547$	32.2252	−	18.6052i	1.37785	−	0.795501i	0.385948	−	0.922520i	$-0.373874\pi$
$547$	32.2252	−	18.6052i	1.37785	−	0.795501i	0.991900	+	0.127019i	$0.0405410\pi$
$548$	22.9717	−	23.2913i	0.981303	−	0.994954i
$549$	16.8958	+	13.8811i	0.721095	+	0.592429i
$550$	−3.58995	−	8.58294i	−0.153076	−	0.365978i
$551$	−33.0827	−	57.3009i	−1.40937	−	2.44110i
$552$	−16.1871	+	0.959124i	−0.688968	+	0.0408230i
$553$	0.164631	−	0.285149i	0.00700082	−	0.0121258i
$554$	−17.6956	−	2.26752i	−0.751815	−	0.0963378i
$555$	−4.08755	−	8.64833i	−0.173507	−	0.367101i
$556$	0.716097	−	2.74831i	0.0303693	−	0.116554i
$557$			16.9602i			0.718628i	0.933217	+	0.359314i	$0.116989\pi$
$557$			16.9602i			0.718628i	−0.933217	+	0.359314i	$0.883011\pi$
$558$	18.9938	+	20.1611i	0.804072	+	0.853486i
$559$	0.291131			0.0123135
$560$	−10.1654	−	17.0584i	−0.429567	−	0.720847i
$561$	0.243091	−	2.95506i	0.0102633	−	0.124763i
$562$	3.43090	−	26.7746i	0.144724	−	1.12942i
$563$	25.0083	+	14.4385i	1.05397	+	0.608512i	0.923759	−	0.382974i	$-0.125100\pi$
$563$	25.0083	+	14.4385i	1.05397	+	0.608512i	0.130214	+	0.991486i	$0.458434\pi$
$564$	4.64521	+	24.6004i	0.195599	+	1.03586i
$565$	13.4921	−	7.78966i	0.567616	−	0.327713i
$566$	−0.636710	−	1.52226i	−0.0267629	−	0.0639854i
$567$	−30.7493	−	10.4744i	−1.29135	−	0.439884i
$568$	4.95793	−	12.3293i	0.208030	−	0.517326i
$569$	2.20060	+	3.81154i	0.0922538	+	0.159788i	0.908459	−	0.417974i	$-0.137260\pi$
$569$	2.20060	+	3.81154i	0.0922538	+	0.159788i	−0.816205	+	0.577762i	$0.803926\pi$
$570$	5.20741	−	24.4888i	0.218114	−	1.02572i
$571$	28.6730	+	16.5544i	1.19993	+	0.692779i	0.960539	−	0.278144i	$-0.0897193\pi$
$571$	28.6730	+	16.5544i	1.19993	+	0.692779i	0.239390	+	0.970924i	$0.423053\pi$
$572$	−1.15199	−	4.18347i	−0.0481671	−	0.174920i
$573$	−33.5637	−	2.76104i	−1.40214	−	0.115344i
$574$	28.0854	+	21.3970i	1.17226	+	0.893093i
$575$	10.2881			0.429045
$576$	−9.46157	+	22.0563i	−0.394232	+	0.919011i
$577$	11.4122			0.475097			0.237548	−	0.971376i	$-0.423656\pi$
$577$	11.4122			0.475097			0.237548	+	0.971376i	$0.423656\pi$
$578$	18.3880	+	14.0090i	0.764841	+	0.582697i
$579$	0.235540	+	0.498349i	0.00978870	+	0.0207107i
$580$	6.50242	+	23.6137i	0.269998	+	0.980506i
$581$	8.69466	+	5.01986i	0.360715	+	0.208259i
$582$	−10.0482	−	9.04900i	−0.416513	−	0.375093i
$583$	−4.08834	−	7.08121i	−0.169322	−	0.293274i
$584$	0.432574	−	1.07572i	0.0179000	−	0.0445135i
$585$	2.68507	−	3.26823i	0.111014	−	0.135125i
$586$	1.33238	+	3.18548i	0.0550401	+	0.131591i
$587$	22.5512	−	13.0200i	0.930788	−	0.537391i	0.0437275	−	0.999043i	$-0.486077\pi$
$587$	22.5512	−	13.0200i	0.930788	−	0.537391i	0.887061	+	0.461653i	$0.152743\pi$
$588$	15.8316	−	13.6140i	0.652883	−	0.561430i
$589$	−42.0164	−	24.2582i	−1.73125	−	0.999540i
$590$	−2.01804	+	15.7486i	−0.0830812	+	0.648361i
$591$	−34.8961	−	24.1657i	−1.43543	−	0.994042i
$592$	−8.22201	−	13.7972i	−0.337923	−	0.567061i
$593$	5.75114			0.236171			0.118086	−	0.993003i	$-0.462324\pi$
$593$	5.75114			0.236171			0.118086	+	0.993003i	$0.462324\pi$
$594$	14.4797	+	5.67752i	0.594110	+	0.232952i
$595$			4.01531i			0.164612i
$596$	−2.86134	+	10.9815i	−0.117205	+	0.449821i
$597$	7.03652	−	10.1610i	0.287986	−	0.415862i
$598$	4.75951	+	0.609886i	0.194631	+	0.0249401i
$599$	−8.10409	+	14.0367i	−0.331124	+	0.573524i	−0.982733	−	0.185032i	$-0.940761\pi$
$599$	−8.10409	+	14.0367i	−0.331124	+	0.573524i	0.651608	+	0.758556i	$0.274095\pi$
$600$	6.82024	−	13.6143i	0.278435	−	0.555803i
$601$	9.78181	+	16.9426i	0.399008	+	0.691102i	0.993604	−	0.112922i	$-0.0360212\pi$
$601$	9.78181	+	16.9426i	0.399008	+	0.691102i	−0.594596	+	0.804025i	$0.702688\pi$
$602$	−0.559395	−	1.33742i	−0.0227992	−	0.0545090i
$603$	1.38114	−	8.33786i	0.0562442	−	0.339544i
$604$	−19.8673	+	20.1437i	−0.808389	+	0.819635i
$605$	−7.76680	+	4.48416i	−0.315765	+	0.182307i
$606$	−10.6599	+	11.8370i	−0.433030	+	0.480847i
$607$	−3.82627	+	6.62730i	−0.155304	+	0.268994i	−0.933170	−	0.359437i	$-0.882969\pi$
$607$	−3.82627	+	6.62730i	−0.155304	+	0.268994i	0.777866	+	0.628430i	$0.216302\pi$
$608$	4.76646	−	41.7662i	0.193306	−	1.69384i
$609$	−50.3246	+	23.7854i	−2.03926	+	0.963834i
$610$	11.2778	+	8.59205i	0.456625	+	0.347882i
$611$		−	7.40831i		−	0.299708i
$612$	3.92659	−	2.85182i	0.158723	−	0.115278i
$613$		−	27.6512i		−	1.11682i	−0.829565	−	0.558410i	$-0.811412\pi$
$613$		−	27.6512i		−	1.11682i	0.829565	−	0.558410i	$-0.188588\pi$
$614$	−13.4942	+	17.7124i	−0.544583	+	0.714813i
$615$	1.35100	−	16.4230i	0.0544774	−	0.662238i
$616$	−17.0048	+	13.3304i	−0.685142	+	0.537097i
$617$	−12.6938	+	21.9863i	−0.511034	+	0.885136i	0.488885	+	0.872348i	$0.337404\pi$
$617$	−12.6938	+	21.9863i	−0.511034	+	0.885136i	−0.999918	+	0.0127878i	$0.995929\pi$
$618$	−1.53382	+	7.21307i	−0.0616993	+	0.290152i
$619$	19.8583	−	11.4652i	0.798171	−	0.460824i	−0.0446605	−	0.999002i	$-0.514221\pi$
$619$	19.8583	−	11.4652i	0.798171	−	0.460824i	0.842831	+	0.538178i	$0.180887\pi$
$620$	12.7866	+	12.6112i	0.513524	+	0.506478i
$621$	−11.9708	+	12.3494i	−0.480373	+	0.495565i
$622$	−25.8362	+	10.8064i	−1.03594	+	0.433296i
$623$	16.0966	+	27.8801i	0.644897	+	1.11699i
$624$	3.96226	−	5.89398i	0.158617	−	0.235948i
$625$	−0.101100	+	0.175110i	−0.00404398	+	0.00700439i
$626$	5.84388	−	45.6052i	0.233568	−	1.82275i
$627$	−27.1503	−	2.23345i	−1.08428	−	0.0891955i
$628$	10.8722	−	41.7264i	0.433848	−	1.66506i
$629$			3.24767i			0.129493i
$630$	−20.1730	−	6.05508i	−0.803711	−	0.241240i
$631$	23.2785			0.926701			0.463350	−	0.886175i	$-0.346647\pi$
$631$	23.2785			0.926701			0.463350	+	0.886175i	$0.346647\pi$
$632$	−0.255451	+	0.0363272i	−0.0101613	+	0.00144502i
$633$	−12.6606	+	5.98390i	−0.503214	+	0.237839i
$634$	−22.5584	−	2.89065i	−0.895910	−	0.114802i
$635$	−14.0961	−	8.13841i	−0.559388	−	0.322963i
$636$	4.42476	−	12.6302i	0.175453	−	0.500821i
$637$	−5.35098	+	3.08939i	−0.212013	+	0.122406i
$638$	24.5864	−	10.2836i	0.973384	−	0.407133i
$639$	−4.95793	−	13.1941i	−0.196133	−	0.521952i
$640$	−5.60568	+	14.5163i	−0.221584	+	0.573808i
$641$	−17.4170	−	30.1672i	−0.687932	−	1.19153i	−0.972506	−	0.232879i	$-0.925185\pi$
$641$	−17.4170	−	30.1672i	−0.687932	−	1.19153i	0.284574	−	0.958654i	$-0.408148\pi$
$642$	0.338559	+	1.04228i	0.0133619	+	0.0411354i
$643$	−34.0047	−	19.6326i	−1.34102	−	0.774236i	−0.354059	−	0.935223i	$-0.615199\pi$
$643$	−34.0047	−	19.6326i	−1.34102	−	0.774236i	−0.986956	+	0.160987i	$0.948532\pi$
$644$	−6.34345	−	23.0364i	−0.249967	−	0.907761i
$645$	−0.385194	+	0.556234i	−0.0151670	+	0.0219017i
$646$	−5.15126	+	6.76148i	−0.202674	+	0.266027i
$647$	44.5092			1.74984			0.874918	−	0.484271i	$-0.160915\pi$
$647$	44.5092			1.74984			0.874918	+	0.484271i	$0.160915\pi$
$648$	8.40631	+	24.0278i	0.330231	+	0.943900i
$649$	17.2762			0.678149
$650$	−2.73070	+	3.58428i	−0.107107	+	0.140587i
$651$	−23.2367	+	33.5547i	−0.910719	+	1.31511i
$652$	−28.7767	+	7.92415i	−1.12698	+	0.310334i
$653$	−15.7763	−	9.10843i	−0.617373	−	0.356440i	0.158473	−	0.987363i	$-0.449343\pi$
$653$	−15.7763	−	9.10843i	−0.617373	−	0.356440i	−0.775845	+	0.630923i	$0.782676\pi$
$654$	7.08683	+	21.8173i	0.277117	+	0.853123i
$655$	−1.91291	−	3.31326i	−0.0747437	−	0.129460i
$656$	−0.382229	−	27.6656i	−0.0149235	−	1.08016i
$657$	−0.432574	−	1.15117i	−0.0168763	−	0.0449116i
$658$	−34.0327	+	14.2347i	−1.32673	+	0.554927i
$659$	36.2085	−	20.9050i	1.41048	−	0.814343i	0.415049	−	0.909799i	$-0.363764\pi$
$659$	36.2085	−	20.9050i	1.41048	−	0.814343i	0.995434	+	0.0954566i	$0.0304311\pi$
$660$	9.51711	+	3.33414i	0.370453	+	0.129781i
$661$	−9.78973	−	5.65210i	−0.380776	−	0.219841i	0.297380	−	0.954759i	$-0.403887\pi$
$661$	−9.78973	−	5.65210i	−0.380776	−	0.219841i	−0.678156	+	0.734918i	$0.737221\pi$
$662$	−28.7618	−	3.68555i	−1.11786	−	0.143243i
$663$	−1.29835	+	0.613652i	−0.0504237	+	0.0238323i
$664$	−1.10768	−	7.78911i	−0.0429861	−	0.302276i
$665$	36.8915			1.43059
$666$	−16.3164	−	4.89748i	−0.632246	−	0.189774i
$667$			29.4710i			1.14112i
$668$	−42.6691	−	11.1178i	−1.65092	−	0.430161i
$669$	7.29280	+	0.599925i	0.281956	+	0.0231945i
$670$	0.696483	−	5.43531i	0.0269075	−	0.209984i
$671$	7.71346	−	13.3601i	0.297775	−	0.515761i
$672$	−34.6894	−	6.87703i	−1.33817	−	0.265287i
$673$	17.6390	+	30.5517i	0.679934	+	1.17768i	0.975000	+	0.222203i	$0.0713249\pi$
$673$	17.6390	+	30.5517i	0.679934	+	1.17768i	−0.295066	+	0.955477i	$0.595342\pi$
$674$	−16.2240	+	6.78595i	−0.624926	+	0.261385i
$675$	−4.42246	−	15.5335i	−0.170220	−	0.597886i
$676$	16.7816	−	17.0150i	0.645446	−	0.654425i
$677$	17.5026	−	10.1051i	0.672679	−	0.388372i	−0.124412	−	0.992231i	$-0.539704\pi$
$677$	17.5026	−	10.1051i	0.672679	−	0.388372i	0.797091	+	0.603859i	$0.206371\pi$
$678$	5.77086	−	27.1385i	0.221628	−	1.04225i
$679$	9.96266	−	17.2558i	0.382332	−	0.662218i
$680$	2.47633	−	1.94125i	0.0949631	−	0.0744436i
$681$	0.179468	−	2.18164i	0.00687721	−	0.0836007i
$682$	11.8426	−	15.5444i	0.453475	−	0.595226i
$683$			43.6659i			1.67083i	0.549621	+	0.835414i	$0.314772\pi$
$683$			43.6659i			1.67083i	−0.549621	+	0.835414i	$0.685228\pi$
$684$	−26.2017	−	36.0763i	−1.00185	−	1.37941i
$685$		−	22.4975i		−	0.859584i
$686$	−3.94839	−	3.00810i	−0.150750	−	0.114850i
$687$	−11.3772	+	5.37730i	−0.434066	+	0.205157i
$688$	−0.554368	+	0.991582i	−0.0211351	+	0.0378037i
$689$	−1.98011	+	3.42965i	−0.0754362	+	0.130659i
$690$	−7.46252	+	8.28657i	−0.284093	+	0.315464i
$691$	7.91193	−	4.56796i	0.300984	−	0.173773i	−0.341901	−	0.939736i	$-0.611071\pi$
$691$	7.91193	−	4.56796i	0.300984	−	0.173773i	0.642885	+	0.765963i	$0.277737\pi$
$692$	−17.9307	−	17.6847i	−0.681623	−	0.672271i
$693$	−3.74519	+	22.6096i	−0.142268	+	0.858867i
$694$	15.2207	+	36.3900i	0.577769	+	1.38134i
$695$	−0.976570	−	1.69147i	−0.0370434	−	0.0641611i
$696$	38.9991	+	19.5370i	1.47826	+	0.740548i
$697$	−2.79733	+	4.84512i	−0.105956	+	0.183522i
$698$	42.1302	+	5.39859i	1.59465	+	0.204339i
$699$	5.82839	−	8.41641i	0.220450	−	0.318338i
$700$	21.7125	+	5.65740i	0.820657	+	0.213830i
$701$			44.8665i			1.69458i	0.531127	+	0.847292i	$0.321769\pi$
$701$			44.8665i			1.69458i	−0.531127	+	0.847292i	$0.678231\pi$
$702$	−1.12509	−	7.44832i	−0.0424638	−	0.281119i
$703$	29.8387			1.12539
$704$	16.4423	+	4.04248i	0.619694	+	0.152357i
$705$	14.1543	+	9.80188i	0.533081	+	0.369160i
$706$	−3.40807	+	26.5963i	−0.128264	+	1.00097i
$707$	−20.3277	−	11.7362i	−0.764504	−	0.441386i
$708$	18.4362	+	21.4394i	0.692876	+	0.805740i
$709$	23.1529	−	13.3673i	0.869525	−	0.502021i	0.00233491	−	0.999997i	$-0.499257\pi$
$709$	23.1529	−	13.3673i	0.869525	−	0.502021i	0.867190	+	0.497977i	$0.165923\pi$
$710$	−3.52642	−	8.43105i	−0.132344	−	0.316412i
$711$	−0.173728	+	0.211459i	−0.00651532	+	0.00793035i
$712$	9.41221	−	23.4061i	0.352738	−	0.877182i
$713$	10.8049	+	18.7147i	0.404647	+	0.700870i
$714$	5.31375	+	4.78533i	0.198862	+	0.179086i
$715$	−2.58430	−	1.49205i	−0.0966474	−	0.0557994i
$716$	23.3540	−	6.43090i	0.872779	−	0.240334i
$717$	8.82630	+	18.6745i	0.329624	+	0.697411i
$718$	−32.2204	−	24.5473i	−1.20246	−	0.916096i
$719$	−37.4738			−1.39754			−0.698768	−	0.715348i	$-0.746268\pi$
$719$	−37.4738			−1.39754			−0.698768	+	0.715348i	$0.746268\pi$
$720$	6.01857	+	15.3685i	0.224299	+	0.572752i
$721$	−10.8662			−0.404680
$722$	40.7487	+	31.0446i	1.51651	+	1.15536i
$723$	−6.22025	−	0.511694i	−0.231333	−	0.0190301i
$724$	34.0891	−	9.38700i	1.26691	−	0.348865i
$725$	−23.9670	−	13.8374i	−0.890112	−	0.513907i
$726$	−3.32203	+	15.6224i	−0.123292	+	0.579803i
$727$	−9.18140	−	15.9027i	−0.340519	−	0.589797i	0.644010	−	0.765017i	$-0.277270\pi$
$727$	−9.18140	−	15.9027i	−0.340519	−	0.589797i	−0.984529	+	0.175220i	$0.943936\pi$
$728$	9.70933	+	3.90437i	0.359852	+	0.144706i
$729$	23.7916	+	12.7656i	0.881169	+	0.472801i
$730$	−0.307676	−	0.735600i	−0.0113876	−	0.0272258i
$731$	0.198936	−	0.114856i	0.00735790	−	0.00424808i
$732$	24.8110	−	4.68498i	0.917042	−	0.173162i
$733$	35.6508	+	20.5830i	1.31679	+	0.760249i	0.983211	−	0.182472i	$-0.0584100\pi$
$733$	35.6508	+	20.5830i	1.31679	+	0.760249i	0.333580	+	0.942722i	$0.391743\pi$
$734$	2.07483	−	16.1918i	0.0765833	−	0.597651i
$735$	1.17727	−	14.3111i	0.0434242	−	0.527873i
$736$	−11.1402	+	15.0494i	−0.410635	+	0.554727i
$737$	−5.96251			−0.219632
$738$	−20.1236	−	21.3603i	−0.740760	−	0.786282i
$739$			45.1004i			1.65905i	0.558473	+	0.829523i	$0.311387\pi$
$739$			45.1004i			1.65905i	−0.558473	+	0.829523i	$0.688613\pi$
$740$	−10.6886	−	2.78501i	−0.392920	−	0.102379i
$741$	5.63806	+	11.9289i	0.207119	+	0.438218i
$742$	19.5600	+	2.50643i	0.718070	+	0.0920138i
$743$	−21.7217	+	37.6231i	−0.796893	+	1.38026i	0.124737	+	0.992190i	$0.460191\pi$
$743$	−21.7217	+	37.6231i	−0.796893	+	1.38026i	−0.921630	+	0.388070i	$0.873142\pi$
$744$	31.9280	−	1.89181i	1.17054	−	0.0693573i
$745$	3.90212	+	6.75867i	0.142963	+	0.247618i
$746$	−12.2434	−	29.2719i	−0.448264	−	1.07172i
$747$	−6.44774	−	5.29726i	−0.235911	−	0.193817i
$748$	−2.43761	−	2.40417i	−0.0891280	−	0.0879051i
$749$	−1.39846	+	0.807404i	−0.0510988	+	0.0295019i
$750$	−8.43929	−	25.9809i	−0.308159	−	0.948689i
$751$	−15.3394	+	26.5686i	−0.559742	+	0.969501i	0.437776	+	0.899084i	$0.355766\pi$
$751$	−15.3394	+	26.5686i	−0.559742	+	0.969501i	−0.997518	+	0.0704172i	$0.977567\pi$
$752$	25.2324	+	14.1068i	0.920131	+	0.514422i
$753$	0.913486	+	0.632592i	0.0332893	+	0.0230529i
$754$	−10.2674	−	7.82224i	−0.373916	−	0.284869i
$755$			19.4571i			0.708118i
$756$	−32.0547	+	19.4801i	−1.16582	+	0.708484i
$757$		−	2.84137i		−	0.103271i	−0.998666	−	0.0516357i	$-0.983557\pi$
$757$		−	2.84137i		−	0.103271i	0.998666	−	0.0516357i	$-0.0164435\pi$
$758$	19.4263	−	25.4987i	0.705594	−	0.926154i
$759$	9.97553	+	6.90808i	0.362089	+	0.250747i
$760$	−17.8357	−	22.7518i	−0.646967	−	0.825296i
$761$	6.52480	−	11.3013i	0.236524	−	0.409672i	−0.723191	−	0.690649i	$-0.757325\pi$
$761$	6.52480	−	11.3013i	0.236524	−	0.409672i	0.959714	+	0.280977i	$0.0906585\pi$
$762$	−27.5695	+	8.95531i	−0.998738	+	0.324417i
$763$	−29.2731	+	16.9008i	−1.05976	+	0.611851i
$764$	−27.3066	+	27.6865i	−0.987919	+	1.00166i
$765$	0.545397	−	3.29254i	0.0197189	−	0.119042i
$766$	5.06941	−	2.12036i	0.183165	−	0.0766117i
$767$	−4.18370	−	7.24637i	−0.151065	−	0.261651i
$768$	12.5298	+	24.7185i	0.452129	+	0.891952i
$769$	13.7846	−	23.8756i	0.497084	−	0.860975i	−0.502910	−	0.864339i	$-0.667737\pi$
$769$	13.7846	−	23.8756i	0.497084	−	0.860975i	0.999994	+	0.00336360i	$0.00107067\pi$
$770$	−1.88864	+	14.7388i	−0.0680618	+	0.531150i
$771$	−2.95883	−	6.26022i	−0.106560	−	0.225456i
$772$	0.615917	+	0.160483i	0.0221673	+	0.00577590i
$773$			15.7109i			0.565082i	0.959255	+	0.282541i	$0.0911774\pi$
$773$			15.7109i			0.565082i	−0.959255	+	0.282541i	$0.908823\pi$
$774$	0.277042	+	1.17266i	0.00995805	+	0.0421503i
$775$	−20.2927			−0.728936
$776$	−15.4586	+	2.19835i	−0.554933	+	0.0789160i
$777$	2.05802	−	25.0177i	0.0738311	−	0.897504i
$778$	19.3501	+	2.47953i	0.693734	+	0.0888953i
$779$	44.5155	+	25.7011i	1.59494	+	0.920836i
$780$	−0.906236	−	4.79930i	−0.0324484	−	0.171843i
$781$	−8.61171	+	4.97197i	−0.308151	+	0.177911i
$782$	3.49287	−	1.46095i	0.124905	−	0.0522434i
$783$	44.4968	−	12.6684i	1.59018	−	0.452732i
$784$	−0.333077	−	24.1080i	−0.0118956	−	0.860999i
$785$	−14.8268	−	25.6808i	−0.529193	−	0.916589i
$786$	−6.66442	−	1.41715i	−0.237712	−	0.0505482i
$787$	12.2138	+	7.05164i	0.435375	+	0.251364i	0.701634	−	0.712538i	$-0.252454\pi$
$787$	12.2138	+	7.05164i	0.435375	+	0.251364i	−0.266259	+	0.963902i	$0.585788\pi$
$788$	−47.2543	+	13.0123i	−1.68337	+	0.463543i
$789$	19.4949	+	1.60370i	0.694038	+	0.0570934i
$790$	−0.107534	+	0.141147i	−0.00382588	+	0.00502180i
$791$	40.8832			1.45364
$792$	15.7545	−	8.62114i	0.559812	−	0.306339i
$793$	−7.47175			−0.265329
$794$	20.3701	−	26.7375i	0.722907	−	0.948879i
$795$	−3.93280	−	8.32093i	−0.139482	−	0.295113i
$796$	−3.78889	−	13.7594i	−0.134294	−	0.487691i
$797$	−22.7555	−	13.1379i	−0.806040	−	0.465367i	0.0395390	−	0.999218i	$-0.487411\pi$
$797$	−22.7555	−	13.1379i	−0.806040	−	0.465367i	−0.845579	+	0.533851i	$0.820744\pi$
$798$	43.9662	−	48.8212i	1.55639	−	1.72825i
$799$	−2.92269	−	5.06224i	−0.103397	−	0.179089i
$800$	−7.00815	−	16.1258i	−0.247775	−	0.570132i
$801$	−9.41221	−	25.0480i	−0.332564	−	0.885027i
$802$	11.6843	−	4.88714i	0.412587	−	0.172571i
$803$	−0.751362	+	0.433799i	−0.0265150	+	0.0153084i
$804$	−6.36289	−	7.39935i	−0.224402	−	0.260955i
$805$	−14.2305	−	8.21599i	−0.501560	−	0.289576i
$806$	−9.38785	−	1.20296i	−0.330673	−	0.0423726i
$807$	34.5586	+	23.9319i	1.21652	+	0.842443i
$808$	2.58970	+	18.2106i	0.0911053	+	0.640647i
$809$	−37.5390			−1.31980			−0.659901	−	0.751353i	$-0.729402\pi$
$809$	−37.5390			−1.31980			−0.659901	+	0.751353i	$0.729402\pi$
$810$	15.7193	+	7.70522i	0.552320	+	0.270734i
$811$		−	37.7228i		−	1.32463i	−0.749227	−	0.662314i	$-0.769575\pi$
$811$		−	37.7228i		−	1.32463i	0.749227	−	0.662314i	$-0.230425\pi$
$812$	−16.2060	+	62.1969i	−0.568718	+	2.18268i
$813$	−12.0628	+	17.4192i	−0.423061	+	0.610917i
$814$	−1.52757	+	11.9211i	−0.0535414	+	0.417833i
$815$	−10.2633	+	17.7766i	−0.359508	+	0.622686i
$816$	0.382225	−	5.59063i	0.0133806	−	0.195711i
$817$	−1.05526	−	1.82776i	−0.0369188	−	0.0639453i
$818$	−27.1820	+	11.3693i	−0.950395	+	0.397518i
$819$	10.3904	−	3.90437i	0.363070	−	0.136430i
$820$	−13.5472	−	13.3613i	−0.473089	−	0.466598i
$821$	−1.06427	+	0.614456i	−0.0371432	+	0.0214446i	−0.518457	−	0.855104i	$-0.673493\pi$
$821$	−1.06427	+	0.614456i	−0.0371432	+	0.0214446i	0.481313	+	0.876549i	$0.340160\pi$
$822$	−29.7725	−	26.8118i	−1.03844	−	0.935169i
$823$	−17.4937	+	30.2999i	−0.609791	+	1.05619i	0.381484	+	0.924376i	$0.375413\pi$
$823$	−17.4937	+	30.2999i	−0.609791	+	1.05619i	−0.991275	+	0.131813i	$0.957920\pi$
$824$	5.25342	+	6.70146i	0.183012	+	0.233456i
$825$	−10.3017	+	4.86899i	−0.358659	+	0.169517i
$826$	−25.2500	+	33.1429i	−0.878561	+	1.15319i
$827$		−	48.7311i		−	1.69455i	−0.531157	−	0.847273i	$-0.678243\pi$
$827$		−	48.7311i		−	1.69455i	0.531157	−	0.847273i	$-0.321757\pi$
$828$	2.07259	+	19.7514i	0.0720274	+	0.686407i
$829$		−	28.9573i		−	1.00573i	−0.864366	−	0.502863i	$-0.832280\pi$
$829$		−	28.9573i		−	1.00573i	0.864366	−	0.502863i	$-0.167720\pi$
$830$	−4.30381	−	3.27888i	−0.149388	−	0.113812i
$831$	−1.79137	+	21.7763i	−0.0621420	+	0.755410i
$832$	−2.28618	−	7.87558i	−0.0792590	−	0.273036i
$833$	−2.43761	+	4.22207i	−0.0844583	+	0.146286i
$834$	−3.40229	−	0.723478i	−0.117812	−	0.0250520i
$835$	−26.2610	+	15.1618i	−0.908801	+	0.524696i
$836$	−22.0888	+	22.3961i	−0.763957	+	0.774585i
$837$	23.6117	−	24.3585i	0.816141	−	0.841953i
$838$	5.50965	+	13.1726i	0.190328	+	0.455040i
$839$	7.66037	+	13.2681i	0.264465	+	0.458067i	0.967423	−	0.253164i	$-0.0814712\pi$
$839$	7.66037	+	13.2681i	0.264465	+	0.458067i	−0.702958	+	0.711231i	$0.748138\pi$
$840$	−20.3060	+	13.3847i	−0.700624	+	0.461817i
$841$	25.1380	−	43.5402i	0.866826	−	1.50139i
$842$	32.7543	+	4.19715i	1.12879	+	0.144643i
$843$	−32.9488	−	2.71046i	−1.13482	−	0.0933532i
$844$	−4.07707	+	15.6474i	−0.140339	+	0.538606i
$845$		−	16.4351i		−	0.565386i
$846$	29.8402	−	7.04977i	1.02593	−	0.242376i
$847$	−23.5347			−0.808662
$848$	−7.91075	−	13.2749i	−0.271656	−	0.455861i
$849$	−1.82710	+	0.863559i	−0.0627058	+	0.0296373i
$850$	−0.451887	+	3.52650i	−0.0154996	+	0.120958i
$851$	−11.5100	−	6.64528i	−0.394556	−	0.227797i
$852$	−15.3601	−	5.38111i	−0.526228	−	0.184354i
$853$	−5.67204	+	3.27476i	−0.194207	+	0.112126i	−0.593951	−	0.804502i	$-0.702433\pi$
$853$	−5.67204	+	3.27476i	−0.194207	+	0.112126i	0.399743	+	0.916627i	$0.369099\pi$
$854$	14.3566	+	34.3241i	0.491273	+	1.17455i
$855$	−30.2509	−	5.01095i	−1.03456	−	0.171371i
$856$	1.17405	+	0.472116i	0.0401282	+	0.0161366i
$857$	−6.71094	−	11.6237i	−0.229241	−	0.397058i	0.728342	−	0.685214i	$-0.240291\pi$
$857$	−6.71094	−	11.6237i	−0.229241	−	0.397058i	−0.957583	+	0.288156i	$0.906958\pi$
$858$	−5.05443	+	1.64181i	−0.172555	+	0.0560505i
$859$	2.57865	+	1.48878i	0.0879824	+	0.0507967i	0.543346	−	0.839509i	$-0.317157\pi$
$859$	2.57865	+	1.48878i	0.0879824	+	0.0507967i	−0.455363	+	0.890306i	$0.650491\pi$
$860$	0.207412	+	0.753221i	0.00707268	+	0.0256846i
$861$	24.6189	−	35.5506i	0.839009	−	1.21156i
$862$	7.20352	+	5.48803i	0.245353	+	0.186923i
$863$	−24.3897			−0.830236			−0.415118	−	0.909768i	$-0.636260\pi$
$863$	−24.3897			−0.830236			−0.415118	+	0.909768i	$0.636260\pi$
$864$	27.5110	+	10.3510i	0.935945	+	0.352147i
$865$	−17.3196			−0.588884
$866$	11.0565	+	8.42347i	0.375716	+	0.286241i
$867$	16.1184	−	23.2756i	0.547410	−	0.790480i
$868$	12.5121	+	45.4379i	0.424687	+	1.54226i
$869$	0.167208	+	0.0965378i	0.00567216	+	0.00327482i
$870$	28.5298	−	9.26725i	0.967252	−	0.314189i
$871$	1.44392	+	2.50094i	0.0489252	+	0.0847410i
$872$	24.5756	+	9.88247i	0.832234	+	0.334663i
$873$	−10.5132	+	12.7965i	−0.355817	+	0.433096i
$874$	−13.4228	−	32.0915i	−0.454032	−	1.08551i
$875$	34.8596	−	20.1262i	1.17847	−	0.680390i
$876$	−1.34015	−	0.469496i	−0.0452795	−	0.0158628i
$877$	−4.38552	−	2.53198i	−0.148088	−	0.0854988i	0.424125	−	0.905604i	$-0.360582\pi$
$877$	−4.38552	−	2.53198i	−0.148088	−	0.0854988i	−0.572213	+	0.820105i	$0.693915\pi$
$878$	−4.45170	+	34.7408i	−0.150237	+	1.17244i
$879$	3.82338	−	1.80708i	0.128960	−	0.0609514i
$880$	10.0028	−	5.96089i	0.337196	−	0.200942i
$881$	28.2318			0.951154			0.475577	−	0.879674i	$-0.342239\pi$
$881$	28.2318			0.951154			0.475577	+	0.879674i	$0.342239\pi$
$882$	−17.5358	−	18.6135i	−0.590463	−	0.626749i
$883$			28.0994i			0.945619i	0.881165	+	0.472809i	$0.156760\pi$
$883$			28.0994i			0.945619i	−0.881165	+	0.472809i	$0.843240\pi$
$884$	−0.418106	+	1.60465i	−0.0140624	+	0.0539702i
$885$	19.3803	+	1.59427i	0.651462	+	0.0535910i
$886$	38.1480	+	4.88830i	1.28161	+	0.164226i
$887$	0.666005	−	1.15356i	0.0223623	−	0.0387326i	−0.854628	−	0.519241i	$-0.826215\pi$
$887$	0.666005	−	1.15356i	0.0223623	−	0.0387326i	0.876990	+	0.480509i	$0.159548\pi$
$888$	−16.4239	+	10.8259i	−0.551152	+	0.363293i
$889$	−21.3568	−	36.9911i	−0.716285	−	1.24064i
$890$	−6.69462	−	16.0057i	−0.224404	−	0.536511i
$891$	6.14209	−	18.0311i	0.205768	−	0.604063i
$892$	5.93325	−	6.01579i	0.198660	−	0.201424i
$893$	−46.5104	+	26.8528i	−1.55641	+	0.898594i
$894$	13.5947	+	2.89083i	0.454673	+	0.0966838i
$895$	8.32926	−	14.4267i	0.278417	−	0.482232i
$896$	−31.7865	+	25.6349i	−1.06191	+	0.856402i
$897$	0.481818	−	5.85707i	0.0160874	−	0.195562i
$898$	−36.7698	−	28.0132i	−1.22702	−	0.934814i
$899$		−	58.1297i		−	1.93873i
$900$	−17.0358	−	7.58825i	−0.567859	−	0.252942i
$901$			3.12473i			0.104100i
$902$	−12.5470	+	16.4690i	−0.417768	+	0.548357i
$903$	−1.60524	+	0.758698i	−0.0534189	+	0.0252479i
$904$	−19.7655	−	25.2136i	−0.657391	−	0.838593i
$905$	12.1580	−	21.0582i	0.404145	−	0.699999i
$906$	25.7490	+	23.1885i	0.855454	+	0.770385i
$907$	−0.778677	+	0.449569i	−0.0258555	+	0.0149277i	−0.512872	−	0.858465i	$-0.671418\pi$
$907$	−0.778677	+	0.449569i	−0.0258555	+	0.0149277i	0.487017	+	0.873393i	$0.338085\pi$
$908$	−1.79962	−	1.77493i	−0.0597226	−	0.0589032i
$909$	15.0745	+	12.3848i	0.499991	+	0.410777i
$910$	6.63946	−	2.77706i	0.220096	−	0.0920586i
$911$	7.53390	+	13.0491i	0.249609	+	0.432336i	0.963417	−	0.268005i	$-0.0863645\pi$
$911$	7.53390	+	13.0491i	0.249609	+	0.432336i	−0.713808	+	0.700341i	$0.753031\pi$
$912$	−51.3651	−	3.51178i	−1.70087	−	0.116286i
$913$	−2.94360	+	5.09846i	−0.0974188	+	0.168734i
$914$	−3.73080	+	29.1150i	−0.123404	+	0.963038i
$915$	9.88581	−	14.2755i	0.326815	−	0.471933i
$916$	−3.66377	+	14.0612i	−0.121054	+	0.464595i
$917$		−	10.0397i		−	0.331541i
$918$	−3.70726	−	4.64571i	−0.122358	−	0.153331i
$919$	−28.4761			−0.939339			−0.469670	−	0.882842i	$-0.655627\pi$
$919$	−28.4761			−0.939339			−0.469670	+	0.882842i	$0.655627\pi$
$920$	1.81293	+	12.7484i	0.0597705	+	0.420302i
$921$	22.4204	+	15.5262i	0.738776	+	0.511604i
$922$	−52.5925	−	6.73922i	−1.73204	−	0.221944i
$923$	4.17092	+	2.40808i	0.137288	+	0.0792630i
$924$	17.2541	+	20.0646i	0.567618	+	0.660078i
$925$	10.8084	−	6.24025i	0.355379	−	0.205178i
$926$	20.8123	−	8.70506i	0.683934	−	0.286066i
$927$	8.91028	+	1.47595i	0.292652	+	0.0484767i
$928$	46.1932	−	20.0753i	1.51637	−	0.659003i
$929$	2.12086	+	3.67344i	0.0695833	+	0.120522i	0.898718	−	0.438527i	$-0.144500\pi$
$929$	2.12086	+	3.67344i	0.0695833	+	0.120522i	−0.829135	+	0.559049i	$0.811166\pi$
$930$	14.7194	−	16.3448i	0.482667	−	0.535965i
$931$	38.7912	+	22.3961i	1.27133	+	0.734002i
$932$	−3.13836	−	11.3970i	−0.102800	−	0.373322i
$933$	14.6565	+	31.0099i	0.479833	+	1.01522i
$934$	23.1808	−	30.4268i	0.758499	−	0.995596i
$935$	−2.35454			−0.0770016
$936$	−7.43128	−	4.52038i	−0.242899	−	0.147753i
$937$	−15.1569			−0.495155			−0.247578	−	0.968868i	$-0.579634\pi$
$937$	−15.1569			−0.495155			−0.247578	+	0.968868i	$0.579634\pi$
$938$	8.71452	−	11.4386i	0.284539	−	0.373483i
$939$	−56.1219	−	4.61674i	−1.83147	−	0.150662i
$940$	19.1669	−	5.27793i	0.625156	−	0.172147i
$941$	36.9463	+	21.3310i	1.20442	+	0.695370i	0.961534	−	0.274686i	$-0.0885738\pi$
$941$	36.9463	+	21.3310i	1.20442	+	0.695370i	0.242882	+	0.970056i	$0.421907\pi$
$942$	−51.6555	−	10.9843i	−1.68303	−	0.357886i
$943$	−11.4476	−	19.8278i	−0.372785	−	0.645683i
$944$	32.6474	−	0.451058i	1.06258	−	0.0146807i
$945$	−6.28779	+	25.0177i	−0.204542	+	0.813825i
$946$	0.784246	−	0.328023i	0.0254980	−	0.0106650i
$947$	−24.7629	+	14.2969i	−0.804686	+	0.464585i	−0.845107	−	0.534597i	$-0.820463\pi$
$947$	−24.7629	+	14.2969i	−0.804686	+	0.464585i	0.0404213	+	0.999183i	$0.487130\pi$
$948$	0.0586349	+	0.310522i	0.00190437	+	0.0100853i
$949$	0.363908	+	0.210103i	0.0118130	+	0.00682022i
$950$	32.4005	+	4.15181i	1.05121	+	0.134702i
$951$	−2.28365	+	27.7605i	−0.0740524	+	0.900195i
$952$	8.17489	−	1.16254i	0.264950	−	0.0376780i
$953$	−28.1424			−0.911622			−0.455811	−	0.890077i	$-0.650651\pi$
$953$	−28.1424			−0.911622			−0.455811	+	0.890077i	$0.650651\pi$
$954$	−15.6987	−	4.71208i	−0.508263	−	0.152559i
$955$			26.7429i			0.865380i
$956$	23.0800	+	6.01372i	0.746462	+	0.194498i
$957$	−13.9475	−	29.5098i	−0.450859	−	0.953917i
$958$	4.90892	−	38.3089i	0.158600	−	1.23770i
$959$	29.5189	−	51.1283i	0.953216	−	1.65102i
$960$	18.0719	+	6.05216i	0.583267	+	0.195332i
$961$	−5.81204	−	10.0668i	−0.187485	−	0.324734i
$962$	5.37014	−	2.24615i	0.173140	−	0.0724187i
$963$	1.25640	−	0.472116i	0.0404871	−	0.0152137i
$964$	−5.06064	+	5.13104i	−0.162992	+	0.165260i
$965$	0.379071	−	0.218857i	0.0122027	−	0.00704525i
$966$	−27.8323	+	9.04068i	−0.895490	+	0.290879i
$967$	−6.99023	+	12.1074i	−0.224791	+	0.389349i	−0.956257	−	0.292529i	$-0.905503\pi$
$967$	−6.99023	+	12.1074i	−0.224791	+	0.389349i	0.731466	+	0.681878i	$0.238836\pi$
$968$	11.3781	+	14.5144i	0.365707	+	0.466510i
$969$	8.55870	+	5.92692i	0.274945	+	0.190400i
$970$	−6.50742	+	8.54155i	−0.208941	+	0.274253i
$971$			17.5426i			0.562969i	0.959566	+	0.281484i	$0.0908268\pi$
$971$			17.5426i			0.562969i	−0.959566	+	0.281484i	$0.909173\pi$
$972$	28.9307	−	11.6196i	0.927952	−	0.372700i
$973$		−	5.12543i		−	0.164314i
$974$	−21.5004	−	16.3802i	−0.688918	−	0.524855i
$975$	4.53698	+	3.14187i	0.145300	+	0.100621i
$976$	14.2276	−	25.4484i	0.455414	−	0.814585i
$977$	22.7380	−	39.3834i	0.727454	−	1.25999i	−0.230502	−	0.973072i	$-0.574037\pi$
$977$	22.7380	−	39.3834i	0.727454	−	1.25999i	0.957956	−	0.286916i	$-0.0926300\pi$
$978$	11.2935	+	34.7678i	0.361126	+	1.11175i
$979$	−16.3486	+	9.43888i	−0.522504	+	0.301668i
$980$	−11.8051	−	11.6432i	−0.377101	−	0.371927i
$981$	26.2995	−	9.88247i	0.839677	−	0.315523i
$982$	7.00265	+	16.7421i	0.223463	+	0.534262i
$983$	−5.04836	−	8.74402i	−0.161018	−	0.278891i	0.774216	−	0.632921i	$-0.218144\pi$
$983$	−5.04836	−	8.74402i	−0.161018	−	0.278891i	−0.935234	+	0.354030i	$0.884811\pi$
$984$	−33.8271	+	2.00434i	−1.07837	+	0.0638961i
$985$	−16.8534	+	29.1909i	−0.536994	+	0.930100i
$986$	−10.1019	−	1.29446i	−0.321709	−	0.0412240i
$987$	19.3063	+	40.8478i	0.614527	+	1.30020i
$988$	14.7430	+	3.84144i	0.469039	+	0.122212i
$989$			0.940054i			0.0298920i
$990$	3.55064	−	11.8292i	0.112847	−	0.375958i
$991$	−17.6057			−0.559263			−0.279631	−	0.960107i	$-0.590212\pi$
$991$	−17.6057			−0.559263			−0.279631	+	0.960107i	$0.590212\pi$
$992$	21.9735	−	29.6840i	0.697658	−	0.942467i
$993$	−2.91163	+	35.3943i	−0.0923978	+	1.12320i
$994$	3.04816	−	23.7876i	0.0966817	−	0.754498i
$995$	−8.49978	−	4.90735i	−0.269461	−	0.155573i
$996$	−9.46833	+	1.78787i	−0.300015	+	0.0566509i
$997$	−26.1168	+	15.0786i	−0.827128	+	0.477543i	−0.852868	−	0.522126i	$-0.825139\pi$
$997$	−26.1168	+	15.0786i	−0.827128	+	0.477543i	0.0257404	+	0.999669i	$0.491806\pi$
$998$	9.69426	+	23.1773i	0.306866	+	0.733664i
$999$	−5.08570	+	20.2349i	−0.160904	+	0.640203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.2.n.b.13.2	✓	16
3.2	odd	2		216.2.n.b.37.7		16
4.3	odd	2		288.2.r.b.49.6		16
8.3	odd	2		288.2.r.b.49.3		16
8.5	even	2	inner	72.2.n.b.13.4	yes	16
9.2	odd	6		216.2.n.b.181.5		16
9.4	even	3		648.2.d.j.325.7		8
9.5	odd	6		648.2.d.k.325.2		8
9.7	even	3	inner	72.2.n.b.61.4	yes	16
12.11	even	2		864.2.r.b.145.3		16
24.5	odd	2		216.2.n.b.37.5		16
24.11	even	2		864.2.r.b.145.6		16
36.7	odd	6		288.2.r.b.241.3		16
36.11	even	6		864.2.r.b.721.6		16
36.23	even	6		2592.2.d.k.1297.6		8
36.31	odd	6		2592.2.d.j.1297.3		8
72.5	odd	6		648.2.d.k.325.1		8
72.11	even	6		864.2.r.b.721.3		16
72.13	even	6		648.2.d.j.325.8		8
72.29	odd	6		216.2.n.b.181.7		16
72.43	odd	6		288.2.r.b.241.6		16
72.59	even	6		2592.2.d.k.1297.3		8
72.61	even	6	inner	72.2.n.b.61.2	yes	16
72.67	odd	6		2592.2.d.j.1297.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.2	✓	16	1.1	even	1	trivial
72.2.n.b.13.4	yes	16	8.5	even	2	inner
72.2.n.b.61.2	yes	16	72.61	even	6	inner
72.2.n.b.61.4	yes	16	9.7	even	3	inner
216.2.n.b.37.5		16	24.5	odd	2
216.2.n.b.37.7		16	3.2	odd	2
216.2.n.b.181.5		16	9.2	odd	6
216.2.n.b.181.7		16	72.29	odd	6
288.2.r.b.49.3		16	8.3	odd	2
288.2.r.b.49.6		16	4.3	odd	2
288.2.r.b.241.3		16	36.7	odd	6
288.2.r.b.241.6		16	72.43	odd	6
648.2.d.j.325.7		8	9.4	even	3
648.2.d.j.325.8		8	72.13	even	6
648.2.d.k.325.1		8	72.5	odd	6
648.2.d.k.325.2		8	9.5	odd	6
864.2.r.b.145.3		16	12.11	even	2
864.2.r.b.145.6		16	24.11	even	2
864.2.r.b.721.3		16	72.11	even	6
864.2.r.b.721.6		16	36.11	even	6
2592.2.d.j.1297.3		8	36.31	odd	6
2592.2.d.j.1297.6		8	72.67	odd	6
2592.2.d.k.1297.3		8	72.59	even	6
2592.2.d.k.1297.6		8	36.23	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	72.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12494 - 0.857038i) q^{2} +(-0.986088 + 1.42395i) q^{3} +(0.530970 + 1.92823i) q^{4} +(1.19115 + 0.687709i) q^{5} +(2.32967 - 0.756738i) q^{6} +(1.80469 + 3.12581i) q^{7} +(1.05526 - 2.62420i) q^{8} +(-1.05526 - 2.80828i) q^{9} +(-0.750573 - 1.79449i) q^{10} +(-1.83294 + 1.05825i) q^{11} +(-3.26928 - 1.14533i) q^{12} +(0.887751 + 0.512543i) q^{13} +(0.648778 - 5.06302i) q^{14} +(-2.15384 + 1.01799i) q^{15} +(-3.43614 + 2.04766i) q^{16} +0.808822 q^{17} +(-1.21970 + 4.06354i) q^{18} -7.43122i q^{19} +(-0.693598 + 2.66196i) q^{20} +(-6.23057 - 0.512543i) q^{21} +(2.96890 + 0.380437i) q^{22} +(-1.65498 + 2.86652i) q^{23} +(2.69615 + 4.09033i) q^{24} +(-1.55411 - 2.69180i) q^{25} +(-0.559395 - 1.33742i) q^{26} +(5.03942 + 1.26658i) q^{27} +(-5.06904 + 5.13956i) q^{28} +(7.71083 - 4.45185i) q^{29} +(3.29539 + 0.700747i) q^{30} +(3.26436 - 5.65403i) q^{31} +(5.62037 + 0.641410i) q^{32} +(0.300550 - 3.65354i) q^{33} +(-0.909875 - 0.693192i) q^{34} +4.96439i q^{35} +(4.85470 - 3.52589i) q^{36} +4.01531i q^{37} +(-6.36884 + 8.35966i) q^{38} +(-1.60524 + 0.758698i) q^{39} +(3.06165 - 2.40010i) q^{40} +(-3.45852 + 5.99034i) q^{41} +(6.56973 + 5.91642i) q^{42} +(0.245957 - 0.142003i) q^{43} +(-3.01378 - 2.97243i) q^{44} +(0.674310 - 4.07078i) q^{45} +(4.31847 - 1.80627i) q^{46} +(-3.61351 - 6.25878i) q^{47} +(0.472570 - 6.91207i) q^{48} +(-3.01378 + 5.22003i) q^{49} +(-0.558698 + 4.36005i) q^{50} +(-0.797570 + 1.15172i) q^{51} +(-0.516932 + 1.98393i) q^{52} +3.86330i q^{53} +(-4.58353 - 5.74380i) q^{54} -2.91107 q^{55} +(10.1072 - 1.43732i) q^{56} +(10.5817 + 7.32784i) q^{57} +(-12.4896 - 1.60042i) q^{58} +(-7.06904 - 4.08131i) q^{59} +(-3.10654 - 3.61257i) q^{60} +(-6.31237 + 3.64445i) q^{61} +(-8.51792 + 3.56275i) q^{62} +(6.87373 - 8.36660i) q^{63} +(-5.77286 - 5.53842i) q^{64} +(0.704961 + 1.22103i) q^{65} +(-3.46932 + 3.85242i) q^{66} +(2.43973 + 1.40858i) q^{67} +(0.429460 + 1.55960i) q^{68} +(-2.44981 - 5.18325i) q^{69} +(4.25468 - 5.58463i) q^{70} +4.69830 q^{71} +(-8.48306 - 0.194250i) q^{72} +0.409922 q^{73} +(3.44128 - 4.51698i) q^{74} +(5.36548 + 0.441379i) q^{75} +(14.3291 - 3.94576i) q^{76} +(-6.61576 - 3.81961i) q^{77} +(2.45602 + 0.522260i) q^{78} +(-0.0456121 - 0.0790024i) q^{79} +(-5.50115 + 0.0760042i) q^{80} +(-6.77286 + 5.92692i) q^{81} +(9.02458 - 3.77467i) q^{82} +(2.40891 - 1.39079i) q^{83} +(-2.31995 - 12.2861i) q^{84} +(0.963426 + 0.556234i) q^{85} +(-0.398389 - 0.0510497i) q^{86} +(-1.26436 + 15.3697i) q^{87} +(0.842830 + 5.92673i) q^{88} +8.91934 q^{89} +(-4.24737 + 4.00147i) q^{90} +3.69992i q^{91} +(-6.40605 - 1.66916i) q^{92} +(4.83210 + 10.2236i) q^{93} +(-1.29904 + 10.1377i) q^{94} +(5.11052 - 8.85168i) q^{95} +(-6.45552 + 7.37064i) q^{96} +(-2.76022 - 4.78084i) q^{97} +(7.86408 - 3.28928i) q^{98} +(4.90608 + 4.03068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26}+ \cdots + 66 q^{98}+O(q^{100}) \) 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^14 - 10 * q^15 - 9 * q^16 - 28 * q^17 + 4 * q^18 - 8 * q^20 + q^22 - 10 * q^23 + 7 * q^24 + 2 * q^25 + 28 * q^26 + 4 * q^28 + 22 * q^30 - 10 * q^31 + 11 * q^32 + q^34 + 27 * q^36 + 23 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^41 + 8 * q^42 + 18 * q^44 - 20 * q^46 + 6 * q^47 + 39 * q^48 + 18 * q^49 - 23 * q^50 - 8 * q^52 - 29 * q^54 - 4 * q^55 + 10 * q^56 + 10 * q^57 - 14 * q^58 + 6 * q^60 - 52 * q^62 + 2 * q^63 + 26 * q^64 - 14 * q^65 - 72 * q^66 - 39 * q^68 + 72 * q^71 - 77 * q^72 - 44 * q^73 - 38 * q^74 + 5 * q^76 + 10 * q^78 - 30 * q^79 - 96 * q^80 + 10 * q^81 + 38 * q^82 - 28 * q^84 + 7 * q^86 + 42 * q^87 + 31 * q^88 + 64 * q^89 + 64 * q^90 - 30 * q^92 - 12 * q^94 + 44 * q^95 - 26 * q^96 + 66 * q^98

Introduction

L-functions

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