LMFDB - Embedded newform 72.2.n.b.13.4

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			13.4
Root			$-1.12494 - 0.857038i$ of defining polynomial
Character	$\chi$	$=$	72.13
Dual form			72.2.n.b.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.179748 - 1.40274i) q^{2} +(0.986088 - 1.42395i) q^{3} +(-1.93538 + 0.504281i) q^{4} +(-1.19115 - 0.687709i) q^{5} +(-2.17468 - 1.12728i) 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} +(-1.19039 + 3.25315i) q^{12} +(-0.887751 - 0.512543i) q^{13} +(4.06032 - 3.09337i) q^{14} +(-2.15384 + 1.01799i) q^{15} +(3.49140 - 1.95195i) q^{16} +0.808822 q^{17} +(-3.74961 + 1.98504i) q^{18} +7.43122i q^{19} +(2.65212 + 0.730306i) q^{20} +(6.23057 + 0.512543i) q^{21} +(-1.81392 - 2.38093i) q^{22} +(-1.65498 + 2.86652i) q^{23} +(4.77731 + 1.08506i) 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} +(1.81513 + 2.83830i) q^{30} +(3.26436 - 5.65403i) q^{31} +(-3.36566 - 4.54668i) q^{32} +(0.300550 - 3.65354i) q^{33} +(-0.145384 - 1.13457i) q^{34} -4.96439i q^{35} +(3.45849 + 4.90294i) q^{36} -4.01531i q^{37} +(10.4241 - 1.33575i) q^{38} +(-1.60524 + 0.758698i) q^{39} +(0.547718 - 3.85152i) q^{40} +(-3.45852 + 5.99034i) q^{41} +(-0.400967 - 8.83202i) 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} +(0.663349 - 6.89637i) q^{48} +(-3.01378 + 5.22003i) q^{49} +(-3.49656 + 2.66387i) q^{50} +(0.797570 - 1.15172i) q^{51} +(1.97660 + 0.544290i) q^{52} -3.86330i q^{53} +(-0.870856 + 7.29668i) q^{54} -2.91107 q^{55} +(-6.29834 + 8.03439i) q^{56} +(10.5817 + 7.32784i) q^{57} +(7.63082 + 10.0161i) q^{58} +(7.06904 + 4.08131i) q^{59} +(3.65514 - 3.05634i) 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} +(-5.17900 + 0.235123i) q^{66} +(-2.43973 - 1.40858i) q^{67} +(-1.56538 + 0.407874i) q^{68} +(2.44981 + 5.18325i) q^{69} +(-6.96377 + 0.892341i) q^{70} +4.69830 q^{71} +(6.25591 - 5.73267i) q^{72} +0.409922 q^{73} +(-5.63245 + 0.721745i) q^{74} +(-5.36548 - 0.441379i) q^{75} +(-3.74743 - 14.3822i) q^{76} +(6.61576 + 3.81961i) q^{77} +(1.35280 + 2.11536i) 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} +(-12.3170 + 2.14999i) q^{84} +(-0.963426 - 0.556234i) q^{85} +(0.243405 + 0.319490i) q^{86} +(-1.26436 + 15.3697i) q^{87} +(4.71128 + 3.69328i) q^{88} +8.91934 q^{89} +(5.83147 + 0.214168i) q^{90} -3.69992i q^{91} +(1.75749 - 6.38238i) q^{92} +(-4.83210 - 10.2236i) q^{93} +(-8.12994 + 6.19383i) q^{94} +(5.11052 - 8.85168i) q^{95} +(-9.79308 + 0.309103i) 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 $

$2$	−0.179748	−	1.40274i	−0.127101	−	0.991890i
$2$	−0.179748	−	1.40274i	−0.127101	−	0.991890i
$3$	0.986088	−	1.42395i	0.569318	−	0.822117i
$3$	0.986088	−	1.42395i	0.569318	−	0.822117i
$4$	−1.93538	+	0.504281i	−0.967691	+	0.252141i
$5$	−1.19115	−	0.687709i	−0.532697	−	0.307553i	0.209417	−	0.977826i	$-0.432843\pi$
$5$	−1.19115	−	0.687709i	−0.532697	−	0.307553i	−0.742114	+	0.670274i	$0.766177\pi$
$6$	−2.17468	−	1.12728i	−0.887811	−	0.460209i
$7$	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	−0.197539	−	0.980295i	$-0.563295\pi$
$11$	1.83294	−	1.05825i	0.552652	−	0.319074i	0.750191	+	0.661221i	$0.229961\pi$
$12$	−1.19039	+	3.25315i	−0.343635	+	0.939103i
$13$	−0.887751	−	0.512543i	−0.246218	−	0.142154i	0.371813	−	0.928307i	$-0.378736\pi$
$13$	−0.887751	−	0.512543i	−0.246218	−	0.142154i	−0.618031	+	0.786154i	$0.712069\pi$
$14$	4.06032	−	3.09337i	1.08517	−	0.826738i
$15$	−2.15384	+	1.01799i	−0.556119	+	0.262844i
$16$	3.49140	−	1.95195i	0.872850	−	0.487988i
$17$	0.808822			0.196168			0.0980841	−	0.995178i	$-0.468729\pi$
$17$	0.808822			0.196168			0.0980841	+	0.995178i	$0.468729\pi$
$18$	−3.74961	+	1.98504i	−0.883793	+	0.467879i
$19$			7.43122i			1.70484i	0.522858	+	0.852420i	$0.324866\pi$
$19$			7.43122i			1.70484i	−0.522858	+	0.852420i	$0.675134\pi$
$20$	2.65212	+	0.730306i	0.593032	+	0.163301i
$21$	6.23057	+	0.512543i	1.35962	+	0.111846i
$22$	−1.81392	−	2.38093i	−0.386729	−	0.507615i
$23$	−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	$0.278818\pi$
$24$	4.77731	+	1.08506i	0.975163	+	0.221487i
$25$	−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	−0.997263	−	0.0739344i	$-0.976444\pi$
$29$	−7.71083	+	4.45185i	−1.43187	+	0.826688i	−0.434603	+	0.900622i	$0.643111\pi$
$30$	1.81513	+	2.83830i	0.331395	+	0.518201i
$31$	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	$-0.0327476\pi$
$32$	−3.36566	−	4.54668i	−0.594971	−	0.803747i
$33$	0.300550	−	3.65354i	0.0523190	−	0.636000i
$34$	−0.145384	−	1.13457i	−0.0249332	−	0.194577i
$35$		−	4.96439i		−	0.839136i
$36$	3.45849	+	4.90294i	0.576415	+	0.817157i
$37$		−	4.01531i		−	0.660113i	−0.943961	−	0.330057i	$-0.892932\pi$
$37$		−	4.01531i		−	0.660113i	0.943961	−	0.330057i	$-0.107068\pi$
$38$	10.4241	−	1.33575i	1.69101	−	0.216687i
$39$	−1.60524	+	0.758698i	−0.257043	+	0.121489i
$40$	0.547718	−	3.85152i	0.0866018	−	0.608979i
$41$	−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	$0.985041\pi$
$42$	−0.400967	−	8.83202i	−0.0618705	−	1.36281i
$43$	−0.245957	+	0.142003i	−0.0375081	+	0.0216553i	−0.518637	−	0.854995i	$-0.673560\pi$
$43$	−0.245957	+	0.142003i	−0.0375081	+	0.0216553i	0.481129	+	0.876650i	$0.340227\pi$
$44$	−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	$-0.343381\pi$
$48$	0.663349	−	6.89637i	0.0957461	−	0.995406i
$49$	−3.01378	+	5.22003i	−0.430540	+	0.745718i
$50$	−3.49656	+	2.66387i	−0.494488	+	0.376728i
$51$	0.797570	−	1.15172i	0.111682	−	0.161273i
$52$	1.97660	+	0.544290i	0.274105	+	0.0754795i
$53$		−	3.86330i		−	0.530666i	−0.964157	−	0.265333i	$-0.914518\pi$
$53$		−	3.86330i		−	0.530666i	0.964157	−	0.265333i	$-0.0854818\pi$
$54$	−0.870856	+	7.29668i	−0.118508	+	0.992953i
$55$	−2.91107			−0.392528
$56$	−6.29834	+	8.03439i	−0.841650	+	1.07364i
$57$	10.5817	+	7.32784i	1.40158	+	0.970597i
$58$	7.63082	+	10.0161i	1.00198	+	1.31518i
$59$	7.06904	+	4.08131i	0.920310	+	0.531341i	0.883734	−	0.467989i	$-0.155021\pi$
$59$	7.06904	+	4.08131i	0.920310	+	0.531341i	0.0365764	+	0.999331i	$0.488355\pi$
$60$	3.65514	−	3.05634i	0.471877	−	0.394572i
$61$	6.31237	−	3.64445i	0.808216	−	0.466624i	−0.0381201	−	0.999273i	$-0.512137\pi$
$61$	6.31237	−	3.64445i	0.808216	−	0.466624i	0.846336	+	0.532650i	$0.178804\pi$
$62$	−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
$66$	−5.17900	+	0.235123i	−0.637491	+	0.0289416i
$67$	−2.43973	−	1.40858i	−0.298061	−	0.172085i	0.343511	−	0.939149i	$-0.388384\pi$
$67$	−2.43973	−	1.40858i	−0.298061	−	0.172085i	−0.641571	+	0.767063i	$0.721717\pi$
$68$	−1.56538	+	0.407874i	−0.189830	+	0.0494620i
$69$	2.44981	+	5.18325i	0.294923	+	0.623990i
$70$	−6.96377	+	0.892341i	−0.832330	+	0.106655i
$71$	4.69830			0.557586			0.278793	−	0.960351i	$-0.410066\pi$
$71$	4.69830			0.557586			0.278793	+	0.960351i	$0.410066\pi$
$72$	6.25591	−	5.73267i	0.737267	−	0.675602i
$73$	0.409922			0.0479777			0.0239889	−	0.999712i	$-0.492363\pi$
$73$	0.409922			0.0479777			0.0239889	+	0.999712i	$0.492363\pi$
$74$	−5.63245	+	0.721745i	−0.654760	+	0.0839012i
$75$	−5.36548	−	0.441379i	−0.619552	−	0.0509660i
$76$	−3.74743	−	14.3822i	−0.429859	−	1.64976i
$77$	6.61576	+	3.81961i	0.753936	+	0.435285i
$78$	1.35280	+	2.11536i	0.153174	+	0.239517i
$79$	−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	−0.626346	−	0.779545i	$-0.715450\pi$
$83$	−2.40891	+	1.39079i	−0.264412	+	0.152659i	0.361933	+	0.932204i	$0.382117\pi$
$84$	−12.3170	+	2.14999i	−1.34389	+	0.234584i
$85$	−0.963426	−	0.556234i	−0.104498	−	0.0603321i
$86$	0.243405	+	0.319490i	0.0262470	+	0.0344515i
$87$	−1.26436	+	15.3697i	−0.135553	+	1.64781i
$88$	4.71128	+	3.69328i	0.502224	+	0.393705i
$89$	8.91934			0.945448			0.472724	−	0.881210i	$-0.343271\pi$
$89$	8.91934			0.945448			0.472724	+	0.881210i	$0.343271\pi$
$90$	5.83147	+	0.214168i	0.614691	+	0.0225753i
$91$		−	3.69992i		−	0.387857i
$92$	1.75749	−	6.38238i	0.183231	−	0.665409i
$93$	−4.83210	−	10.2236i	−0.501066	−	1.06014i
$94$	−8.12994	+	6.19383i	−0.838540	+	0.638845i
$95$	5.11052	−	8.85168i	0.524328	−	0.908163i
$96$	−9.79308	+	0.309103i	−0.999502	+	0.0315476i
$97$	−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	−0.192907	−	0.981217i	$-0.561792\pi$
$101$	5.63193	−	3.25160i	0.560398	−	0.323546i	0.753305	+	0.657671i	$0.228458\pi$
$102$	−1.75893	−	0.911767i	−0.174160	−	0.0902784i
$103$	−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	$0.214053\pi$
$104$	0.408209	−	2.87050i	0.0400282	−	0.281476i
$105$	−7.06904	−	4.89533i	−0.689868	−	0.477735i
$106$	−5.41923	+	0.694422i	−0.526362	+	0.0674482i
$107$		−	0.447393i		−	0.0432511i	−0.999766	−	0.0216256i	$-0.993116\pi$
$107$		−	0.447393i		−	0.0432511i	0.999766	−	0.0216256i	$-0.00688417\pi$
$108$	10.3919	−	0.0899786i	0.999963	−	0.00865820i
$109$		−	9.36497i		−	0.897002i	−0.893782	−	0.448501i	$-0.851958\pi$
$109$		−	9.36497i		−	0.897002i	0.893782	−	0.448501i	$-0.148042\pi$
$110$	0.523259	+	4.08348i	0.0498908	+	0.389345i
$111$	−5.71760	−	3.95945i	−0.542690	−	0.375815i
$112$	12.4023	+	7.39078i	1.17191	+	0.698363i
$113$	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	$-0.0121844\pi$
$114$	8.37705	−	16.1606i	0.784583	−	1.51357i
$115$	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
$120$	−4.94427	−	4.57786i	−0.451348	−	0.417900i
$121$	−3.26022	+	5.64687i	−0.296384	+	0.513351i
$122$	−6.24686	−	8.19955i	−0.565564	−	0.742353i
$123$	5.11952	+	10.8318i	0.461612	+	0.976667i
$124$	−3.46655	+	12.5889i	−0.311305	+	1.13051i
$125$			11.1522i			0.997483i
$126$	−12.9717	−	8.13820i	−1.15561	−	0.725008i
$127$	−11.8341			−1.05011			−0.525053	−	0.851069i	$-0.675955\pi$
$127$	−11.8341			−1.05011			−0.525053	+	0.851069i	$0.675955\pi$
$128$	8.80665	+	7.10232i	0.778405	+	0.627762i
$129$	−0.0403299	+	0.490258i	−0.00355085	+	0.0431648i
$130$	1.58607	−	1.20836i	0.139108	−	0.105980i
$131$	2.40891	+	1.39079i	0.210468	+	0.121514i	0.601529	−	0.798851i	$-0.294559\pi$
$131$	2.40891	+	1.39079i	0.210468	+	0.121514i	−0.391061	+	0.920365i	$0.627892\pi$
$132$	1.26073	+	7.22255i	0.109733	+	0.628643i
$133$	−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	$-0.412917\pi$
$138$	6.83042	−	4.36814i	0.581444	−	0.371841i
$139$	1.22979	+	0.710017i	0.104309	+	0.0602229i	0.551247	−	0.834342i	$-0.314152\pi$
$139$	1.22979	+	0.710017i	0.104309	+	0.0602229i	−0.446938	+	0.894565i	$0.647486\pi$
$140$	2.50345	+	9.60800i	0.211580	+	0.812024i
$141$	−12.4754	−	1.02626i	−1.05062	−	0.0864268i
$142$	−0.844512	−	6.59052i	−0.0708699	−	0.553064i
$143$	−2.16959			−0.181430
$144$	−9.16596	−	7.74501i	−0.763830	−	0.645417i
$145$	12.2463			1.01700
$146$	−0.0736827	−	0.575015i	−0.00609802	−	0.0475886i
$147$	4.46119	+	9.43888i	0.367953	+	0.778506i
$148$	2.02485	+	7.77116i	0.166441	+	0.638785i
$149$	−4.91390	−	2.83704i	−0.402563	−	0.232420i	0.285027	−	0.958520i	$-0.407998\pi$
$149$	−4.91390	−	2.83704i	−0.402563	−	0.232420i	−0.687589	+	0.726100i	$0.741331\pi$
$150$	0.345294	+	7.60573i	0.0281932	+	0.621006i
$151$	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
$156$	2.72415	−	2.27786i	0.218106	−	0.182375i
$157$	18.6713	+	10.7799i	1.49013	+	0.860328i	0.999936	−	0.0112838i	$-0.00359181\pi$
$157$	18.6713	+	10.7799i	1.49013	+	0.860328i	0.490196	+	0.871612i	$0.336925\pi$
$158$	−0.102622	+	0.0781826i	−0.00816413	+	0.00621987i
$159$	−5.50115	−	3.80956i	−0.436269	−	0.302118i
$160$	0.882207	+	7.73036i	0.0697446	+	0.611139i
$161$	−11.9469			−0.941548
$162$	9.53136	+	8.43523i	0.748855	+	0.662734i
$163$		−	14.9239i		−	1.16893i	−0.811418	−	0.584466i	$-0.801304\pi$
$163$		−	14.9239i		−	1.16893i	0.811418	−	0.584466i	$-0.198696\pi$
$164$	3.67275	−	13.3377i	0.286793	−	1.04150i
$165$	−2.87057	+	4.14521i	−0.223474	+	0.322704i
$166$	2.38391	+	3.12910i	0.185028	+	0.242865i
$167$	−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	$0.841436\pi$
$168$	5.22985	+	16.8911i	0.403492	+	1.30318i
$169$	−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	−0.0244397	−	0.999701i	$-0.507780\pi$
$173$	10.9052	−	6.29612i	0.829107	−	0.478685i	0.853547	+	0.521016i	$0.174447\pi$
$174$	21.7871	−	0.989117i	1.65167	−	0.0749847i
$175$	5.60937	−	9.71572i	0.424029	−	0.734439i
$176$	4.33388	−	7.27258i	0.326678	−	0.548192i
$177$	12.7823	−	6.04141i	0.960775	−	0.454100i
$178$	−1.60324	−	12.5116i	−0.120168	−	0.937780i
$179$			12.1116i			0.905264i	0.891697	+	0.452632i	$0.149515\pi$
$179$			12.1116i			0.905264i	−0.891697	+	0.452632i	$0.850485\pi$
$180$	−0.747773	−	8.21856i	−0.0557357	−	0.612575i
$181$			17.6790i			1.31407i	0.753862	+	0.657033i	$0.228189\pi$
$181$			17.6790i			1.31407i	−0.753862	+	0.657033i	$0.771811\pi$
$182$	−5.19004	+	0.665054i	−0.384711	+	0.0492970i
$183$	1.03505	−	12.5822i	0.0765129	−	0.930105i
$184$	−9.26875	−	1.31809i	−0.683301	−	0.0971711i
$185$	−2.76137	+	4.78283i	−0.203020	+	0.351640i
$186$	−13.4726	+	8.61589i	−0.987859	+	0.631748i
$187$	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	$0.584980\pi$
$192$	2.19388	+	13.6816i	0.158330	+	0.987386i
$193$	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	$0.163021\pi$
$194$	−6.21015	+	4.73123i	−0.445863	+	0.339682i
$195$	2.43384	+	0.200214i	0.174291	+	0.0143376i
$196$	3.20046	−	11.6225i	0.228604	−	0.830181i
$197$		−	24.5066i		−	1.74602i	−0.487701	−	0.873011i	$-0.662164\pi$
$197$		−	24.5066i		−	1.74602i	0.487701	−	0.873011i	$-0.337836\pi$
$198$	−4.77215	+	7.60649i	−0.339142	+	0.540569i
$199$	−7.13579			−0.505843			−0.252921	−	0.967487i	$-0.581391\pi$
$199$	−7.13579			−0.505843			−0.252921	+	0.967487i	$0.581391\pi$
$200$	5.42384	−	6.91885i	0.383523	−	0.489237i
$201$	−4.41154	+	2.08507i	−0.311166	+	0.147069i
$202$	−5.57349	−	7.31569i	−0.392149	−	0.514730i
$203$	−27.8313	−	16.0684i	−1.95337	−	1.12778i
$204$	−0.962811	+	2.63122i	−0.0674102	+	0.184222i
$205$	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
$210$	−5.59625	+	10.7960i	−0.386178	+	0.744994i
$211$	−7.00175	−	4.04246i	−0.482020	−	0.278294i	0.239238	−	0.970961i	$-0.423102\pi$
$211$	−7.00175	−	4.04246i	−0.482020	−	0.278294i	−0.721258	+	0.692667i	$0.756436\pi$
$212$	1.94819	+	7.47697i	0.133802	+	0.513520i
$213$	4.63294	−	6.69014i	0.317444	−	0.458401i
$214$	−0.627578	+	0.0804181i	−0.0429003	+	0.00549727i
$215$	0.390628			0.0266406
$216$	−1.99415	−	14.5610i	−0.135684	−	0.990752i
$217$	23.5646			1.59967
$218$	−13.1367	+	1.68334i	−0.889727	+	0.114010i
$219$	0.404219	−	0.583708i	0.0273146	−	0.0394433i
$220$	5.63403	−	1.46800i	0.379846	−	0.0989724i
$221$	−0.718032	−	0.414556i	−0.0483001	−	0.0278861i
$222$	−4.52637	+	8.73203i	−0.303790	+	0.586056i
$223$	−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	−0.463238	−	0.886234i	$-0.653312\pi$
$227$	1.09451	−	0.631913i	0.0726449	−	0.0419415i	0.535882	+	0.844293i	$0.319979\pi$
$228$	−24.1749	−	8.84603i	−1.60102	−	0.585842i
$229$	−6.29196	−	3.63267i	−0.415785	−	0.240053i	0.277487	−	0.960729i	$-0.410498\pi$
$229$	−6.29196	−	3.63267i	−0.415785	−	0.240053i	−0.693272	+	0.720676i	$0.743832\pi$
$230$	−3.90174	−	5.12138i	−0.257273	−	0.337694i
$231$	11.9627	−	5.65403i	0.787085	−	0.372008i
$232$	−19.8195	−	15.5369i	−1.30121	−	1.02005i
$233$	−5.91061			−0.387217			−0.193608	−	0.981079i	$-0.562019\pi$
$233$	−5.91061			−0.387217			−0.193608	+	0.981079i	$0.562019\pi$
$234$	4.34614	+	0.159618i	0.284116	+	0.0104345i
$235$			9.94017i			0.648425i
$236$	−15.7394	−	4.33411i	−1.02455	−	0.282126i
$237$	−0.157473	−	0.0129541i	−0.0102290	−	0.000841462i
$238$	3.28408	−	2.50199i	0.212875	−	0.162180i
$239$	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	$0.0406293\pi$
$240$	−5.53284	+	7.75840i	−0.357143	+	0.500803i
$241$	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
$246$	14.2740	−	9.12837i	0.910075	−	0.582004i
$247$	3.80882	−	6.59707i	0.242350	−	0.419762i
$248$	18.2821	+	2.59986i	1.16091	+	0.165091i
$249$	−0.394993	+	4.80161i	−0.0250316	+	0.304289i
$250$	15.6437	−	2.00459i	0.989393	−	0.126781i
$251$			0.641516i			0.0404922i	0.999795	+	0.0202461i	$0.00644497\pi$
$251$			0.641516i			0.0404922i	−0.999795	+	0.0202461i	$0.993555\pi$
$252$	−9.08416	+	19.6588i	−0.572249	+	1.23839i
$253$			7.00554i			0.440434i
$254$	2.12716	+	16.6002i	0.133470	+	1.04159i
$255$	−1.74207	+	0.823373i	−0.109093	+	0.0515616i
$256$	8.37976	−	13.6301i	0.523735	−	0.851881i
$257$	−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	$0.206459\pi$
$258$	0.694956	−	0.0315505i	0.0432661	−	0.00196425i
$259$	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	$0.946537\pi$
$264$	9.90478	−	3.06673i	0.609597	−	0.188744i
$265$	−2.65683	+	4.60176i	−0.163208	+	0.282684i
$266$	22.9875	+	30.1731i	1.40946	+	1.85003i
$267$	8.79526	−	12.7007i	0.538261	−	0.777269i
$268$	5.43213	+	1.49583i	0.331820	+	0.0913722i
$269$			24.2695i			1.47974i	0.672750	+	0.739870i	$0.265113\pi$
$269$			24.2695i			1.47974i	−0.672750	+	0.739870i	$0.734887\pi$
$270$	6.05531	−	8.09253i	0.368515	−	0.492496i
$271$	12.2330			0.743102			0.371551	−	0.928413i	$-0.378826\pi$
$271$	12.2330			0.743102			0.371551	+	0.928413i	$0.378826\pi$
$272$	2.82392	−	1.57878i	0.171225	−	0.0957278i
$273$	−5.26849	−	3.64845i	−0.318864	−	0.220814i
$274$	−18.4004	+	14.0184i	−1.11161	+	0.846884i
$275$	−5.69719	−	3.28928i	−0.343554	−	0.198351i
$276$	−7.35514	−	8.79617i	−0.442727	−	0.529467i
$277$	−10.9249	+	6.30750i	−0.656414	+	0.378981i	−0.790909	−	0.611933i	$-0.790392\pi$
$277$	−10.9249	+	6.30750i	−0.656414	+	0.378981i	0.134495	+	0.990914i	$0.457059\pi$
$278$	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	$0.640538\pi$
$282$	0.802853	+	17.6843i	0.0478092	+	1.05308i
$283$	−1.01045	−	0.583382i	−0.0600649	−	0.0346785i	0.469667	−	0.882844i	$-0.344374\pi$
$283$	−1.01045	−	0.583382i	−0.0600649	−	0.0346785i	−0.529732	+	0.848165i	$0.677707\pi$
$284$	−9.09301	+	2.36927i	−0.539571	+	0.140590i
$285$	−7.56491	−	16.0057i	−0.448107	−	0.948093i
$286$	0.389980	+	3.04338i	0.0230600	+	0.179959i
$287$	−24.9662			−1.47371
$288$	−9.21670	+	14.2496i	−0.543099	+	0.839669i
$289$	−16.3458			−0.961518
$290$	−2.20125	−	17.1784i	−0.129262	−	1.00875i
$291$	−9.52949	−	0.783921i	−0.558629	−	0.0459543i
$292$	−0.793355	+	0.206716i	−0.0464276	+	0.0120971i
$293$	2.11446	+	1.22079i	0.123528	+	0.0713191i	0.560491	−	0.828161i	$-0.310612\pi$
$293$	2.11446	+	1.22079i	0.123528	+	0.0713191i	−0.436963	+	0.899480i	$0.643946\pi$
$294$	12.4384	−	7.95453i	0.725425	−	0.463918i
$295$	−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
$300$	10.6068	−	1.85148i	0.612386	−	0.106895i
$301$	−0.887751	−	0.512543i	−0.0511691	−	0.0295425i
$302$	15.9138	−	12.1240i	0.915735	−	0.697656i
$303$	0.923476	−	11.2260i	0.0530523	−	0.644914i
$304$	14.5054	+	25.9454i	0.831942	+	1.48807i
$305$	−10.0253			−0.574046
$306$	−3.03277	+	1.60555i	−0.173372	+	0.0917829i
$307$			15.7452i			0.898626i	0.893374	+	0.449313i	$0.148331\pi$
$307$			15.7452i			0.898626i	−0.893374	+	0.449313i	$0.851669\pi$
$308$	−14.7302	−	4.05620i	−0.839330	−	0.231123i
$309$	2.22821	+	4.71440i	0.126759	+	0.268193i
$310$	7.69595	+	10.1016i	0.437101	+	0.573733i
$311$	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	$-0.0230900\pi$
$312$	−3.68492	−	3.41184i	−0.208617	−	0.193157i
$313$	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	−0.837218	−	0.546869i	$-0.815820\pi$
$317$	−13.9271	+	8.04083i	−0.782225	+	0.451618i	0.0549932	+	0.998487i	$0.482486\pi$
$318$	−4.35502	+	8.40146i	−0.244217	+	0.471131i
$319$	−9.42233	+	16.3200i	−0.527549	+	0.913742i
$320$	10.6851	−	2.62703i	0.597318	−	0.146855i
$321$	−0.637065	−	0.441169i	−0.0355575	−	0.0246237i
$322$	2.14743	+	16.7585i	0.119672	+	0.933912i
$323$			6.01054i			0.334435i
$324$	10.1192	−	14.8863i	0.562179	−	0.827016i
$325$			3.18620i			0.176739i
$326$	−20.9344	+	2.68255i	−1.15945	+	0.148573i
$327$	−13.3352	−	9.23469i	−0.737441	−	0.510680i
$328$	−19.3695	−	2.75450i	−1.06950	−	0.152092i
$329$	13.0425	−	22.5903i	0.719056	−	1.24544i
$330$	6.33065	+	3.28158i	0.348491	+	0.180645i
$331$	−17.7569	+	10.2520i	−0.976010	+	0.563499i	−0.901063	−	0.433688i	$-0.857212\pi$
$331$	−17.7569	+	10.2520i	−0.976010	+	0.563499i	−0.0749465	+	0.997188i	$0.523879\pi$
$332$	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
$336$	22.7539	−	10.3723i	1.24133	−	0.565855i
$337$	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	$0.0566815\pi$
$338$	−13.4421	+	10.2409i	−0.731154	+	0.557033i
$339$	−8.38345	−	17.7375i	−0.455326	−	0.963368i
$340$	2.14509	+	0.590687i	0.116334	+	0.0320345i
$341$		−	13.8180i		−	0.748287i
$342$	−14.7513	−	27.8642i	−0.797658	−	1.50672i
$343$	3.50988			0.189515
$344$	−0.632194	−	0.495590i	−0.0340856	−	0.0267204i
$345$	0.646483	−	7.85877i	0.0348055	−	0.423102i
$346$	−10.7920	−	14.1655i	−0.580183	−	0.761541i
$347$	24.1550	+	13.9459i	1.29671	+	0.748654i	0.979834	−	0.199814i	$-0.0640339\pi$
$347$	24.1550	+	13.9459i	1.29671	+	0.748654i	0.316873	+	0.948468i	$0.397367\pi$
$348$	−5.30367	−	30.3839i	−0.284306	−	1.62875i
$349$	26.0103	−	15.0171i	1.39230	−	0.803846i	0.398732	−	0.917068i	$-0.369450\pi$
$349$	26.0103	−	15.0171i	1.39230	−	0.803846i	0.993570	+	0.113222i	$0.0361171\pi$
$350$	−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	$-0.335018\pi$
$354$	−10.7721	−	16.8443i	−0.572533	−	0.895266i
$355$	−5.59637	−	3.23107i	−0.297024	−	0.171487i
$356$	−17.2623	+	4.49786i	−0.914901	+	0.238386i
$357$	5.03942	+	0.414556i	0.266715	+	0.0219406i
$358$	16.9895	−	2.17704i	0.897922	−	0.115060i
$359$	28.6420			1.51167			0.755833	−	0.654765i	$-0.227232\pi$
$359$	28.6420			1.51167			0.755833	+	0.654765i	$0.227232\pi$
$360$	−11.3941	+	2.52621i	−0.600523	+	0.133143i
$361$	−36.2231			−1.90648
$362$	24.7990	−	3.17776i	1.30341	−	0.167019i
$363$	4.82598	+	10.2107i	0.253298	+	0.535923i
$364$	1.86580	+	7.16075i	0.0977945	+	0.375325i
$365$	−0.488277	−	0.281907i	−0.0255576	−	0.0147557i
$366$	−17.8357	+	0.809727i	−0.932287	+	0.0423251i
$367$	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
$372$	14.5076	+	17.3499i	0.752182	+	0.899551i
$373$	−19.4301	−	11.2180i	−1.00605	−	0.580846i	−0.0960206	−	0.995379i	$-0.530611\pi$
$373$	−19.4301	−	11.2180i	−1.00605	−	0.580846i	−0.910034	+	0.414533i	$0.863945\pi$
$374$	−1.46714	−	1.92575i	−0.0758639	−	0.0995780i
$375$	15.8802	+	10.9971i	0.820048	+	0.567885i
$376$	12.6111	−	16.0872i	0.650368	−	0.829634i
$377$	9.12706			0.470068
$378$	−24.3797	+	10.4461i	−1.25395	+	0.537289i
$379$		−	22.6668i		−	1.16431i	−0.813077	−	0.582157i	$-0.802209\pi$
$379$		−	22.6668i		−	1.16431i	0.813077	−	0.582157i	$-0.197791\pi$
$380$	−5.42706	+	19.7085i	−0.278403	+	1.01103i
$381$	−11.6695	+	16.8511i	−0.597845	+	0.863310i
$382$	21.8727	−	16.6638i	1.11910	−	0.852594i
$383$	−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	$0.198318\pi$
$384$	18.7975	−	5.53670i	0.959254	−	0.282544i
$385$	−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	−0.165579	−	0.986197i	$-0.552949\pi$
$389$	11.9463	−	6.89722i	0.605703	−	0.349703i	0.771282	+	0.636494i	$0.219616\pi$
$390$	−0.156629	−	3.45004i	−0.00793121	−	0.174699i
$391$	−1.33859	+	2.31850i	−0.0676953	+	0.117252i
$392$	−16.8787	−	2.40029i	−0.852504	−	0.121233i
$393$	4.35581	−	2.05873i	0.219721	−	0.103849i
$394$	−34.3765	+	4.40501i	−1.73186	+	0.221921i
$395$			0.125471i			0.00631315i
$396$	11.5277	+	5.32686i	0.579291	+	0.267685i
$397$		−	23.7680i		−	1.19288i	−0.802657	−	0.596441i	$-0.796581\pi$
$397$		−	23.7680i		−	1.19288i	0.802657	−	0.596441i	$-0.203419\pi$
$398$	1.28265	+	10.0097i	0.0642932	+	0.501740i
$399$	−3.80882	+	46.3008i	−0.190680	+	2.31794i
$400$	−10.6803	−	6.36461i	−0.534015	−	0.318230i
$401$	−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	$0.238451\pi$
$402$	3.71778	+	5.81347i	0.185426	+	0.289950i
$403$	−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
$408$	3.86399	+	0.877620i	0.191296	+	0.0434487i
$409$	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	$-0.00557480\pi$
$410$	−8.15372	−	10.7025i	−0.402683	−	0.528557i
$411$	−28.2355	−	2.32273i	−1.39275	−	0.114572i
$412$	1.59852	−	5.80506i	0.0787534	−	0.285995i
$413$			29.4619i			1.44973i
$414$	0.515400	−	14.0335i	0.0253305	−	0.689711i
$415$	3.82582			0.187802
$416$	0.657501	+	5.76137i	0.0322366	+	0.282474i
$417$	2.22371	−	1.05101i	0.108895	−	0.0514683i
$418$	17.6932	−	13.4796i	0.865403	−	0.659311i
$419$	8.74372	+	5.04819i	0.427159	+	0.246620i	0.698135	−	0.715966i	$-0.254013\pi$
$419$	8.74372	+	5.04819i	0.427159	+	0.246620i	−0.270977	+	0.962586i	$0.587347\pi$
$420$	16.1499	+	5.90955i	0.788035	+	0.288356i
$421$	20.2218	−	11.6751i	0.985551	−	0.569008i	0.0816096	−	0.996664i	$-0.473994\pi$
$421$	20.2218	−	11.6751i	0.985551	−	0.569008i	0.903941	+	0.427656i	$0.140661\pi$
$422$	−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
$426$	−10.2173	−	5.29629i	−0.495031	−	0.256606i
$427$	22.7837	+	13.1542i	1.10258	+	0.636575i
$428$	0.225612	+	0.865876i	0.0109054	+	0.0418537i
$429$	−2.13941	+	3.08939i	−0.103292	+	0.149157i
$430$	−0.0702147	−	0.547951i	−0.00338605	−	0.0264245i
$431$	−6.40348			−0.308445			−0.154222	−	0.988036i	$-0.549287\pi$
$431$	−6.40348			−0.308445			−0.154222	+	0.988036i	$0.549287\pi$
$432$	−20.0669	+	5.41459i	−0.965471	+	0.260510i
$433$	−9.82857			−0.472331			−0.236166	−	0.971713i	$-0.575891\pi$
$433$	−9.82857			−0.472331			−0.236166	+	0.971713i	$0.575891\pi$
$434$	−4.23569	−	33.0550i	−0.203319	−	1.58669i
$435$	12.0759	−	17.4381i	0.578997	−	0.836094i
$436$	4.72258	+	18.1248i	0.226171	+	0.868020i
$437$	−21.3017	−	12.2986i	−1.01900	−	0.588320i
$438$	−0.891450	−	0.462096i	−0.0425951	−	0.0220798i
$439$	−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	0.177840	−	0.984059i	$-0.443089\pi$
$443$	23.5518	−	13.5976i	1.11898	−	0.646044i	0.941140	+	0.338016i	$0.109756\pi$
$444$	13.0624	+	4.77977i	0.619915	+	0.226838i
$445$	−10.6242	−	6.13391i	−0.503637	−	0.290775i
$446$	−4.75255	+	3.62075i	−0.225040	+	0.171448i
$447$	−8.88535	+	4.19957i	−0.420262	+	0.198633i
$448$	−27.7302	−	8.04973i	−1.31013	−	0.380314i
$449$	32.6861			1.54255			0.771276	−	0.636501i	$-0.219619\pi$
$449$	32.6861			1.54255			0.771276	+	0.636501i	$0.219619\pi$
$450$	11.1707	+	7.00825i	0.526590	+	0.330372i
$451$			14.6399i			0.689367i
$452$	−6.01428	+	21.8410i	−0.282888	+	1.02731i
$453$	24.4197	+	2.00883i	1.14734	+	0.0943831i
$454$	−1.08315	−	1.42173i	−0.0508346	−	0.0667249i
$455$	−2.54447	+	4.40714i	−0.119286	+	0.206610i
$456$	−8.06332	+	35.5012i	−0.377599	+	1.66250i
$457$	−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	$0.671228\pi$
$461$	−32.4695	+	18.7463i	−1.51226	+	0.873101i	−0.999897	+	0.0143300i	$0.995438\pi$
$462$	−10.0814	−	15.7642i	−0.469030	−	0.733419i
$463$	−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	$0.287540\pi$
$464$	−18.2318	+	30.5944i	−0.846390	+	1.42031i
$465$	−1.27515	+	15.5009i	−0.0591336	+	0.718839i
$466$	1.06242	+	8.29107i	0.0492157	+	0.384077i
$467$		−	27.0476i		−	1.25161i	−0.779979	−	0.625806i	$-0.784770\pi$
$467$		−	27.0476i		−	1.25161i	0.779979	−	0.625806i	$-0.215230\pi$
$468$	−0.557309	−	6.12522i	−0.0257616	−	0.283138i
$469$		−	10.1682i		−	0.469523i
$470$	13.9435	−	1.78673i	0.643166	−	0.0824156i
$471$	33.7616	−	15.9571i	1.55565	−	0.735263i
$472$	−3.25051	+	22.8574i	−0.149617	+	1.05210i
$473$	−0.300550	+	0.520568i	−0.0138193	+	0.0239357i
$474$	0.0101341	+	0.223223i	0.000465476	+	0.0102530i
$475$	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	$0.618876\pi$
$480$	11.8776	+	6.36660i	0.542134	+	0.290594i
$481$	−2.05802	+	3.56460i	−0.0938377	+	0.162532i
$482$	4.05359	−	3.08825i	0.184636	−	0.140666i
$483$	−11.7807	+	17.0118i	−0.536041	+	0.774063i
$484$	3.46216	−	12.5729i	0.157371	−	0.571496i
$485$			7.59291i			0.344776i
$486$	21.4101	−	5.25429i	0.971182	−	0.238339i
$487$	19.1126			0.866073			0.433036	−	0.901376i	$-0.357442\pi$
$487$	19.1126			0.866073			0.433036	+	0.901376i	$0.357442\pi$
$488$	16.2249	+	12.7191i	0.734469	+	0.575766i
$489$	−21.2509	−	14.7163i	−0.960999	−	0.665494i
$490$	−7.10521	−	9.32621i	−0.320981	−	0.421315i
$491$	11.1131	+	6.41614i	0.501526	+	0.289556i	0.729344	−	0.684147i	$-0.239826\pi$
$491$	11.1131	+	6.41614i	0.501526	+	0.289556i	−0.227817	+	0.973704i	$0.573159\pi$
$492$	−15.3705	−	18.3819i	−0.692955	−	0.828721i
$493$	−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
$498$	6.80642	−	0.309006i	0.305003	−	0.0138469i
$499$	15.3846	+	8.88232i	0.688711	+	0.397627i	0.803129	−	0.595805i	$-0.203167\pi$
$499$	15.3846	+	8.88232i	0.688711	+	0.397627i	−0.114418	+	0.993433i	$0.536500\pi$
$500$	−5.62385	−	21.5838i	−0.251506	−	0.965255i
$501$	16.3176	+	34.5243i	0.729015	+	1.54243i
$502$	0.899883	−	0.115311i	0.0401638	−	0.00514660i
$503$	−24.0108			−1.07059			−0.535294	−	0.844666i	$-0.679799\pi$
$503$	−24.0108			−1.07059			−0.535294	+	0.844666i	$0.679799\pi$
$504$	29.2092	+	9.20911i	1.30108	+	0.410207i
$505$	−8.94461			−0.398030
$506$	9.82698	−	1.25923i	0.436862	−	0.0559797i
$507$	−20.6269	−	1.69683i	−0.916075	−	0.0753587i
$508$	22.9035	−	5.96771i	1.01618	−	0.264775i
$509$	6.91916	+	3.99478i	0.306686	+	0.177065i	0.645443	−	0.763809i	$-0.276673\pi$
$509$	6.91916	+	3.99478i	0.306686	+	0.177065i	−0.338756	+	0.940874i	$0.610006\pi$
$510$	1.46812	+	2.29568i	0.0650092	+	0.101654i
$511$	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
$516$	−0.169174	−	0.969174i	−0.00744748	−	0.0426655i
$517$	−13.2467	−	7.64798i	−0.582589	−	0.336358i
$518$	−12.4208	−	16.3034i	−0.545741	−	0.716332i
$519$	1.78814	−	21.7370i	0.0784907	−	0.954147i
$520$	−2.46031	+	3.13846i	−0.107892	+	0.137631i
$521$	−36.9809			−1.62016			−0.810082	−	0.586317i	$-0.800577\pi$
$521$	−36.9809			−1.62016			−0.810082	+	0.586317i	$0.800577\pi$
$522$	20.0755	−	31.9990i	0.878683	−	1.40056i
$523$			18.4217i			0.805526i	0.915304	+	0.402763i	$0.131950\pi$
$523$			18.4217i			0.805526i	−0.915304	+	0.402763i	$0.868050\pi$
$524$	−5.36351	−	1.47693i	−0.234306	−	0.0645201i
$525$	−8.30334	−	17.5680i	−0.362388	−	0.766731i
$526$	−12.7044	+	9.67890i	−0.553938	+	0.422020i
$527$	2.64028	−	4.57311i	0.115013	−	0.199208i
$528$	−6.08220	−	13.3426i	−0.264694	−	0.580663i
$529$	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
$534$	−19.3967	−	10.0546i	−0.839379	−	0.435104i
$535$	−0.307676	+	0.532911i	−0.0133020	+	0.0230397i
$536$	1.12185	−	7.88876i	0.0484564	−	0.340743i
$537$	17.2463	+	11.9431i	0.744233	+	0.515384i
$538$	34.0439	−	4.36241i	1.46774	−	0.188077i
$539$			12.7573i			0.549497i
$540$	−12.4402	−	7.03943i	−0.535340	−	0.302929i
$541$		−	13.5032i		−	0.580549i	−0.956943	−	0.290275i	$-0.906253\pi$
$541$		−	13.5032i		−	0.580549i	0.956943	−	0.290275i	$-0.0937467\pi$
$542$	−2.19886	−	17.1598i	−0.0944491	−	0.737075i
$543$	25.1739	+	17.4330i	1.08032	+	0.748122i
$544$	−2.72222	−	3.67746i	−0.116714	−	0.157670i
$545$	−6.44038	+	11.1551i	−0.275875	+	0.477830i
$546$	−4.17083	+	8.04615i	−0.178495	+	0.344343i
$547$	−32.2252	+	18.6052i	−1.37785	+	0.795501i	−0.991900	−	0.127019i	$-0.959459\pi$
$547$	−32.2252	+	18.6052i	−1.37785	+	0.795501i	−0.385948	+	0.922520i	$0.626126\pi$
$548$	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
$552$	−11.0167	+	11.8985i	−0.468902	+	0.506432i
$553$	0.164631	−	0.285149i	0.00700082	−	0.0121258i
$554$	10.8115	+	14.1911i	0.459338	+	0.602922i
$555$	4.08755	+	8.64833i	0.173507	+	0.367101i
$556$	−2.73815	−	0.753996i	−0.116124	−	0.0319765i
$557$		−	16.9602i		−	0.718628i	−0.933217	−	0.359314i	$-0.883011\pi$
$557$		−	16.9602i		−	0.718628i	0.933217	−	0.359314i	$-0.116989\pi$
$558$	−1.01659	+	27.6803i	−0.0430359	+	1.17180i
$559$	0.291131			0.0123135
$560$	−9.69027	−	17.3327i	−0.409489	−	0.732440i
$561$	0.243091	−	2.95506i	0.0102633	−	0.124763i
$562$	21.4720	−	16.3585i	0.905742	−	0.690043i
$563$	−25.0083	−	14.4385i	−1.05397	−	0.608512i	−0.130214	−	0.991486i	$-0.541566\pi$
$563$	−25.0083	−	14.4385i	−1.05397	−	0.608512i	−0.923759	+	0.382974i	$0.874900\pi$
$564$	24.6622	−	4.30492i	1.03847	−	0.181270i
$565$	−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	$0.803926\pi$
$570$	−21.0921	+	13.4886i	−0.883449	+	0.564976i
$571$	−28.6730	−	16.5544i	−1.19993	−	0.692779i	−0.239390	−	0.970924i	$-0.576947\pi$
$571$	−28.6730	−	16.5544i	−1.19993	−	0.692779i	−0.960539	+	0.278144i	$0.910281\pi$
$572$	4.19899	−	1.09408i	0.175568	−	0.0457460i
$573$	33.5637	+	2.76104i	1.40214	+	0.115344i
$574$	4.48763	+	35.0212i	0.187310	+	1.46176i
$575$	10.2881			0.429045
$576$	21.6453	+	10.3673i	0.901887	+	0.431972i
$577$	11.4122			0.475097			0.237548	−	0.971376i	$-0.423656\pi$
$577$	11.4122			0.475097			0.237548	+	0.971376i	$0.423656\pi$
$578$	2.93813	+	22.9290i	0.122210	+	0.953720i
$579$	−0.235540	−	0.498349i	−0.00978870	−	0.0207107i
$580$	−23.7013	+	6.17559i	−0.984142	+	0.256427i
$581$	−8.69466	−	5.01986i	−0.360715	−	0.208259i
$582$	0.613268	+	13.5083i	0.0254208	+	0.559939i
$583$	−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	−0.887061	−	0.461653i	$-0.847257\pi$
$587$	−22.5512	+	13.0200i	−0.930788	+	0.537391i	−0.0437275	+	0.999043i	$0.513923\pi$
$588$	−13.3940	−	16.0181i	−0.552357	−	0.660577i
$589$	42.0164	+	24.2582i	1.73125	+	0.999540i
$590$	−12.6297	+	9.62199i	−0.519956	+	0.396131i
$591$	−34.8961	−	24.1657i	−1.43543	−	0.994042i
$592$	−7.83770	−	14.0191i	−0.322128	−	0.576180i
$593$	5.75114			0.236171			0.118086	−	0.993003i	$-0.462324\pi$
$593$	5.75114			0.236171			0.118086	+	0.993003i	$0.462324\pi$
$594$	6.12548	+	14.2960i	0.251331	+	0.586571i
$595$		−	4.01531i		−	0.164612i
$596$	10.9409	+	3.01277i	0.448158	+	0.123408i
$597$	−7.03652	+	10.1610i	−0.287986	+	0.415862i
$598$	−2.90793	−	3.81692i	−0.118914	−	0.156085i
$599$	−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	$0.274095\pi$
$600$	−4.50371	−	14.5459i	−0.183863	−	0.593833i
$601$	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
$606$	−15.9131	+	0.722444i	−0.646427	+	0.0293473i
$607$	−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	$0.216302\pi$
$608$	33.7874	−	25.0110i	1.37026	−	1.01433i
$609$	−50.3246	+	23.7854i	−2.03926	+	0.963834i
$610$	1.80203	+	14.0629i	0.0729619	+	0.569390i
$611$			7.40831i			0.299708i
$612$	2.79730	+	3.96561i	0.113074	+	0.160300i
$613$			27.6512i			1.11682i	0.829565	+	0.558410i	$0.188588\pi$
$613$			27.6512i			1.11682i	−0.829565	+	0.558410i	$0.811412\pi$
$614$	22.0865	−	2.83017i	0.891338	−	0.114216i
$615$	1.35100	−	16.4230i	0.0544774	−	0.662238i
$616$	−3.04209	+	21.3918i	−0.122569	+	0.861899i
$617$	−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	$0.995929\pi$
$618$	6.21258	−	3.97302i	0.249907	−	0.159818i
$619$	−19.8583	+	11.4652i	−0.798171	+	0.460824i	−0.842831	−	0.538178i	$-0.819113\pi$
$619$	−19.8583	+	11.4652i	−0.798171	+	0.460824i	0.0446605	+	0.999002i	$0.485779\pi$
$620$	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
$624$	−4.12358	+	5.78227i	−0.165075	+	0.231476i
$625$	−0.101100	+	0.175110i	−0.00404398	+	0.00700439i
$626$	36.5734	−	27.8636i	1.46177	−	1.11365i
$627$	27.1503	+	2.23345i	1.08428	+	0.0891955i
$628$	−41.5722	−	11.4476i	−1.65891	−	0.456809i
$629$		−	3.24767i		−	0.129493i
$630$	9.85453	+	18.6146i	0.392614	+	0.741622i
$631$	23.2785			0.926701			0.463350	−	0.886175i	$-0.346647\pi$
$631$	23.2785			0.926701			0.463350	+	0.886175i	$0.346647\pi$
$632$	0.159186	−	0.203063i	0.00633207	−	0.00807742i
$633$	−12.6606	+	5.98390i	−0.503214	+	0.237839i
$634$	13.7826	+	18.0909i	0.547377	+	0.718480i
$635$	14.0961	+	8.13841i	0.559388	+	0.322963i
$636$	12.5679	+	4.59882i	0.498350	+	0.182355i
$637$	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	$-0.408148\pi$
$642$	−0.504336	+	0.972938i	−0.0199046	+	0.0383988i
$643$	34.0047	+	19.6326i	1.34102	+	0.774236i	0.986956	−	0.160987i	$-0.0514678\pi$
$643$	34.0047	+	19.6326i	1.34102	+	0.774236i	0.354059	+	0.935223i	$0.384801\pi$
$644$	23.1218	−	6.02460i	0.911127	−	0.237403i
$645$	0.385194	−	0.556234i	0.0151670	−	0.0219017i
$646$	8.43125	−	1.08038i	0.331723	−	0.0425071i
$647$	44.5092			1.74984			0.874918	−	0.484271i	$-0.160915\pi$
$647$	44.5092			1.74984			0.874918	+	0.484271i	$0.160915\pi$
$648$	−22.7006	−	11.5189i	−0.891762	−	0.452505i
$649$	17.2762			0.678149
$650$	4.46942	−	0.572714i	0.175305	−	0.0224637i
$651$	23.2367	−	33.5547i	0.910719	−	1.31511i
$652$	7.52586	+	28.8835i	0.294735	+	1.13116i
$653$	15.7763	+	9.10843i	0.617373	+	0.356440i	0.775845	−	0.630923i	$-0.217324\pi$
$653$	15.7763	+	9.10843i	0.617373	+	0.356440i	−0.158473	+	0.987363i	$0.550657\pi$
$654$	−10.5569	+	20.3659i	−0.412808	+	0.796368i
$655$	−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	−0.995434	−	0.0954566i	$-0.969569\pi$
$659$	−36.2085	+	20.9050i	−1.41048	+	0.814343i	−0.415049	+	0.909799i	$0.636236\pi$
$660$	3.46530	−	9.47014i	0.134886	−	0.368625i
$661$	9.78973	+	5.65210i	0.380776	+	0.219841i	0.678156	−	0.734918i	$-0.262779\pi$
$661$	9.78973	+	5.65210i	0.380776	+	0.219841i	−0.297380	+	0.954759i	$0.596113\pi$
$662$	17.5727	+	23.0657i	0.682981	+	0.896472i
$663$	−1.29835	+	0.613652i	−0.0504237	+	0.0238323i
$664$	−6.19173	−	4.85383i	−0.240286	−	0.188365i
$665$	36.8915			1.43059
$666$	7.97056	+	15.0559i	0.308853	+	0.583403i
$667$		−	29.4710i		−	1.14112i
$668$	11.7062	−	42.5114i	0.452927	−	1.64482i
$669$	−7.29280	−	0.599925i	−0.281956	−	0.0231945i
$670$	4.35888	−	3.32083i	0.168398	−	0.128295i
$671$	7.71346	−	13.3601i	0.297775	−	0.515761i
$672$	−18.6396	−	30.0535i	−0.719039	−	1.15934i
$673$	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	−0.797091	−	0.603859i	$-0.793629\pi$
$677$	−17.5026	+	10.1051i	−0.672679	+	0.388372i	0.124412	+	0.992231i	$0.460296\pi$
$678$	−23.3742	+	14.9481i	−0.897683	+	0.574079i
$679$	9.96266	−	17.2558i	0.382332	−	0.662218i
$680$	0.443006	−	3.11519i	0.0169885	−	0.119462i
$681$	0.179468	−	2.18164i	0.00687721	−	0.0836007i
$682$	−19.3831	+	2.48376i	−0.742218	+	0.0951081i
$683$		−	43.6659i		−	1.67083i	−0.549621	−	0.835414i	$-0.685228\pi$
$683$		−	43.6659i		−	1.67083i	0.549621	−	0.835414i	$-0.314772\pi$
$684$	−36.4349	+	25.7008i	−1.39312	+	0.982695i
$685$			22.4975i			0.859584i
$686$	−0.630894	−	4.92346i	−0.0240876	−	0.187978i
$687$	−11.3772	+	5.37730i	−0.434066	+	0.205157i
$688$	−0.581551	+	0.975888i	−0.0221714	+	0.0372054i
$689$	−1.98011	+	3.42965i	−0.0754362	+	0.130659i
$690$	−11.1400	+	0.505749i	−0.424094	+	0.0192535i
$691$	−7.91193	+	4.56796i	−0.300984	+	0.173773i	−0.642885	−	0.765963i	$-0.722263\pi$
$691$	−7.91193	+	4.56796i	−0.300984	+	0.173773i	0.341901	+	0.939736i	$0.388929\pi$
$692$	−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
$696$	−41.6675	+	12.9011i	−1.57940	+	0.489016i
$697$	−2.79733	+	4.84512i	−0.105956	+	0.183522i
$698$	−25.7404	−	33.7866i	−0.974290	−	1.27884i
$699$	−5.82839	+	8.41641i	−0.220450	+	0.318338i
$700$	−5.95682	+	21.6323i	−0.225147	+	0.817625i
$701$		−	44.8665i		−	1.69458i	−0.531127	−	0.847292i	$-0.678231\pi$
$701$		−	44.8665i		−	1.69458i	0.531127	−	0.847292i	$-0.321769\pi$
$702$	4.51297	−	6.03129i	0.170331	−	0.227636i
$703$	29.8387			1.12539
$704$	−4.72027	+	16.2607i	−0.177902	+	0.612849i
$705$	14.1543	+	9.80188i	0.533081	+	0.369160i
$706$	−21.3291	+	16.2496i	−0.802730	+	0.611563i
$707$	20.3277	+	11.7362i	0.764504	+	0.441386i
$708$	−21.6920	+	18.1383i	−0.815235	+	0.681679i
$709$	−23.1529	+	13.3673i	−0.869525	+	0.502021i	−0.867190	−	0.497977i	$-0.834077\pi$
$709$	−23.1529	+	13.3673i	−0.869525	+	0.502021i	−0.00233491	+	0.999997i	$0.500743\pi$
$710$	−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
$714$	−0.324311	−	7.14354i	−0.0121370	−	0.267340i
$715$	2.58430	+	1.49205i	0.0966474	+	0.0557994i
$716$	−6.10766	−	23.4406i	−0.228254	−	0.876016i
$717$	−8.82630	−	18.6745i	−0.329624	−	0.697411i
$718$	−5.14834	−	40.1774i	−0.192135	−	1.49941i
$719$	−37.4738			−1.39754			−0.698768	−	0.715348i	$-0.746268\pi$
$719$	−37.4738			−1.39754			−0.698768	+	0.715348i	$0.746268\pi$
$720$	5.59169	+	15.5290i	0.208390	+	0.578730i
$721$	−10.8662			−0.404680
$722$	6.51103	+	50.8117i	0.242316	+	1.89102i
$723$	6.22025	+	0.511694i	0.231333	+	0.0190301i
$724$	−8.91517	−	34.2155i	−0.331330	−	1.27161i
$725$	23.9670	+	13.8374i	0.890112	+	0.513907i
$726$	13.4555	−	8.60497i	0.499382	−	0.319360i
$727$	−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
$732$	4.34177	+	24.8734i	0.160477	+	0.919346i
$733$	−35.6508	−	20.5830i	−1.31679	−	0.760249i	−0.333580	−	0.942722i	$-0.608257\pi$
$733$	−35.6508	−	20.5830i	−1.31679	−	0.760249i	−0.983211	+	0.182472i	$0.941590\pi$
$734$	12.9851	−	9.89277i	0.479289	−	0.365149i
$735$	1.17727	−	14.3111i	0.0434242	−	0.527873i
$736$	18.6033	−	2.12305i	0.685725	−	0.0782565i
$737$	−5.96251			−0.219632
$738$	1.07706	−	29.3268i	0.0396472	−	1.07953i
$739$		−	45.1004i		−	1.65905i	−0.558473	−	0.829523i	$-0.688613\pi$
$739$		−	45.1004i		−	1.65905i	0.558473	−	0.829523i	$-0.311387\pi$
$740$	2.93241	−	10.6491i	0.107797	−	0.391469i
$741$	−5.63806	−	11.9289i	−0.207119	−	0.438218i
$742$	−11.9506	−	15.6862i	−0.438721	−	0.575860i
$743$	−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	$0.873142\pi$
$744$	21.7298	−	23.4690i	0.796653	−	0.860416i
$745$	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
$750$	12.5716	−	24.2525i	0.459051	−	0.885576i
$751$	−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	$0.977567\pi$
$752$	−24.8331	−	14.7985i	−0.905568	−	0.539646i
$753$	0.913486	+	0.632592i	0.0332893	+	0.0230529i
$754$	−1.64057	−	12.8029i	−0.0597461	−	0.466255i
$755$		−	19.4571i		−	0.708118i
$756$	19.0354	+	32.3207i	0.692311	+	1.17549i
$757$			2.84137i			0.103271i	0.998666	+	0.0516357i	$0.0164435\pi$
$757$			2.84137i			0.103271i	−0.998666	+	0.0516357i	$0.983557\pi$
$758$	−31.7957	+	4.07431i	−1.15487	+	0.147986i
$759$	9.97553	+	6.90808i	0.362089	+	0.250747i
$760$	28.6215	+	4.07021i	1.03821	+	0.147642i
$761$	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	$0.0906585\pi$
$762$	25.7354	+	13.3403i	0.932295	+	0.483268i
$763$	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
$768$	−11.1454	−	25.3728i	−0.402174	−	0.915563i
$769$	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	$0.00107067\pi$
$770$	−11.8199	+	9.00501i	−0.425958	+	0.324518i
$771$	2.95883	+	6.26022i	0.106560	+	0.225456i
$772$	−0.168976	+	0.613641i	−0.00608159	+	0.0220854i
$773$		−	15.7109i		−	0.565082i	−0.959255	−	0.282541i	$-0.908823\pi$
$773$		−	15.7109i		−	0.565082i	0.959255	−	0.282541i	$-0.0911774\pi$
$774$	0.640362	−	1.02069i	0.0230173	−	0.0366881i
$775$	−20.2927			−0.728936
$776$	9.63314	−	12.2884i	0.345810	−	0.441128i
$777$	2.05802	−	25.0177i	0.0738311	−	0.897504i
$778$	−11.8224	−	15.5179i	−0.423852	−	0.556343i
$779$	−44.5155	−	25.7011i	−1.59494	−	0.920836i
$780$	−4.81136	+	0.839848i	−0.172274	+	0.0300714i
$781$	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
$786$	−3.67082	−	5.74003i	−0.130934	−	0.204740i
$787$	−12.2138	−	7.05164i	−0.435375	−	0.251364i	0.266259	−	0.963902i	$-0.414212\pi$
$787$	−12.2138	−	7.05164i	−0.435375	−	0.251364i	−0.701634	+	0.712538i	$0.747546\pi$
$788$	12.3582	+	47.4296i	0.440243	+	1.68961i
$789$	−19.4949	−	1.60370i	−0.694038	−	0.0570934i
$790$	0.176004	−	0.0225532i	0.00626195	−	0.000802408i
$791$	40.8832			1.45364
$792$	5.40013	−	17.1280i	0.191885	−	0.608616i
$793$	−7.47175			−0.265329
$794$	−33.3404	+	4.27226i	−1.18321	+	0.151617i
$795$	3.93280	+	8.32093i	0.139482	+	0.295113i
$796$	13.8105	−	3.59845i	0.489499	−	0.127544i
$797$	22.7555	+	13.1379i	0.806040	+	0.465367i	0.845579	−	0.533851i	$-0.179256\pi$
$797$	22.7555	+	13.1379i	0.806040	+	0.465367i	−0.0395390	+	0.999218i	$0.512589\pi$
$798$	65.6327	−	2.97967i	2.32337	−	0.105479i
$799$	−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
$804$	7.48655	−	6.26006i	0.264030	−	0.220775i
$805$	14.2305	+	8.21599i	0.501560	+	0.289576i
$806$	5.73572	+	7.52864i	0.202032	+	0.265185i
$807$	34.5586	+	23.9319i	1.21652	+	0.842443i
$808$	14.4760	+	11.3480i	0.509264	+	0.399223i
$809$	−37.5390			−1.31980			−0.659901	−	0.751353i	$-0.729402\pi$
$809$	−37.5390			−1.31980			−0.659901	+	0.751353i	$0.729402\pi$
$810$	−5.55227	−	16.6024i	−0.195087	−	0.583349i
$811$			37.7228i			1.32463i	0.749227	+	0.662314i	$0.230425\pi$
$811$			37.7228i			1.32463i	−0.749227	+	0.662314i	$0.769575\pi$
$812$	61.9671	+	17.0637i	2.17462	+	0.598817i
$813$	12.0628	−	17.4192i	0.423061	−	0.610917i
$814$	−9.56017	+	7.28345i	−0.335084	+	0.255285i
$815$	−10.2633	+	17.7766i	−0.359508	+	0.622686i
$816$	0.536531	−	5.57794i	0.0187823	−	0.195267i
$817$	−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	−0.481313	−	0.876549i	$-0.659840\pi$
$821$	1.06427	−	0.614456i	0.0371432	−	0.0214446i	0.518457	+	0.855104i	$0.326507\pi$
$822$	1.81709	+	40.0247i	0.0633782	+	1.39602i
$823$	−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	$0.957920\pi$
$824$	−8.43034	−	1.19886i	−0.293685	−	0.0417644i
$825$	−10.3017	+	4.86899i	−0.358659	+	0.169517i
$826$	41.3276	−	5.29573i	1.43797	−	0.184262i
$827$			48.7311i			1.69455i	0.531157	+	0.847273i	$0.321757\pi$
$827$			48.7311i			1.69455i	−0.531157	+	0.847273i	$0.678243\pi$
$828$	−19.7781	+	1.79953i	−0.687337	+	0.0625380i
$829$			28.9573i			1.00573i	0.864366	+	0.502863i	$0.167720\pi$
$829$			28.9573i			1.00573i	−0.864366	+	0.502863i	$0.832280\pi$
$830$	−0.687685	−	5.36665i	−0.0238699	−	0.186279i
$831$	−1.79137	+	21.7763i	−0.0621420	+	0.755410i
$832$	7.96354	−	1.95790i	0.276086	−	0.0678780i
$833$	−2.43761	+	4.22207i	−0.0844583	+	0.146286i
$834$	−1.87401	−	2.93037i	−0.0648916	−	0.101470i
$835$	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	$0.748138\pi$
$840$	5.38666	−	23.7164i	0.185858	−	0.818294i
$841$	25.1380	−	43.5402i	0.866826	−	1.50139i
$842$	−20.0120	−	26.2675i	−0.689658	−	0.905236i
$843$	32.9488	+	2.71046i	1.13482	+	0.0933532i
$844$	15.5896	+	4.29285i	0.536616	+	0.147766i
$845$			16.4351i			0.565386i
$846$	25.9732	+	16.2951i	0.892977	+	0.560235i
$847$	−23.5347			−0.808662
$848$	−7.54099	−	13.4883i	−0.258959	−	0.463192i
$849$	−1.82710	+	0.863559i	−0.0627058	+	0.0296373i
$850$	−2.82810	+	2.15460i	−0.0970029	+	0.0739021i
$851$	11.5100	+	6.64528i	0.394556	+	0.227797i
$852$	−5.59280	+	15.2843i	−0.191606	+	0.523631i
$853$	5.67204	−	3.27476i	0.194207	−	0.112126i	−0.399743	−	0.916627i	$-0.630901\pi$
$853$	5.67204	−	3.27476i	0.194207	−	0.112126i	0.593951	+	0.804502i	$0.297567\pi$
$854$	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	$0.906958\pi$
$858$	4.71817	+	2.44573i	0.161076	+	0.0834959i
$859$	−2.57865	−	1.48878i	−0.0879824	−	0.0507967i	0.455363	−	0.890306i	$-0.349509\pi$
$859$	−2.57865	−	1.48878i	−0.0879824	−	0.0507967i	−0.543346	+	0.839509i	$0.682843\pi$
$860$	−0.756014	+	0.196986i	−0.0257799	+	0.00671718i
$861$	−24.6189	+	35.5506i	−0.839009	+	1.21156i
$862$	1.15101	+	8.98245i	0.0392037	+	0.305943i
$863$	−24.3897			−0.830236			−0.415118	−	0.909768i	$-0.636260\pi$
$863$	−24.3897			−0.830236			−0.415118	+	0.909768i	$0.636260\pi$
$864$	11.2023	+	27.1755i	0.381109	+	0.924530i
$865$	−17.3196			−0.588884
$866$	1.76667	+	13.7870i	0.0600338	+	0.468500i
$867$	−16.1184	+	23.2756i	−0.547410	+	0.790480i
$868$	−45.6064	+	11.8832i	−1.54798	+	0.403341i
$869$	−0.167208	−	0.0965378i	−0.00567216	−	0.00327482i
$870$	−26.6318	−	13.8050i	−0.902904	−	0.468033i
$871$	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
$876$	−0.487965	+	1.33354i	−0.0164868	+	0.0450560i
$877$	4.38552	+	2.53198i	0.148088	+	0.0854988i	0.572213	−	0.820105i	$-0.306085\pi$
$877$	4.38552	+	2.53198i	0.148088	+	0.0854988i	−0.424125	+	0.905604i	$0.639418\pi$
$878$	−27.8605	+	21.2257i	−0.940248	+	0.716332i
$879$	3.82338	−	1.80708i	0.128960	−	0.0609514i
$880$	−10.1637	+	5.68227i	−0.342618	+	0.191549i
$881$	28.2318			0.951154			0.475577	−	0.879674i	$-0.342239\pi$
$881$	28.2318			0.951154			0.475577	+	0.879674i	$0.342239\pi$
$882$	0.938560	−	25.5556i	0.0316030	−	0.860501i
$883$		−	28.0994i		−	0.945619i	−0.881165	−	0.472809i	$-0.843240\pi$
$883$		−	28.0994i		−	0.945619i	0.881165	−	0.472809i	$-0.156760\pi$
$884$	1.59872	+	0.440234i	0.0537708	+	0.0148067i
$885$	−19.3803	−	1.59427i	−0.651462	−	0.0535910i
$886$	−23.3074	−	30.5930i	−0.783028	−	1.02779i
$887$	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	$0.159548\pi$
$888$	4.35685	−	19.1824i	0.146206	−	0.643718i
$889$	−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
$894$	7.48804	+	11.7090i	0.250438	+	0.391608i
$895$	8.32926	−	14.4267i	0.278417	−	0.482232i
$896$	−6.30725	+	40.3453i	−0.210710	+	1.34784i
$897$	0.481818	−	5.85707i	0.0160874	−	0.195562i
$898$	−5.87527	−	45.8502i	−0.196060	−	1.53004i
$899$			58.1297i			1.93873i
$900$	7.82287	−	16.9293i	0.260762	−	0.564310i
$901$		−	3.12473i		−	0.104100i
$902$	20.5360	−	2.63150i	0.683776	−	0.0876193i
$903$	−1.60524	+	0.758698i	−0.0534189	+	0.0252479i
$904$	31.7184	+	4.51062i	1.05494	+	0.150021i
$905$	12.1580	−	21.0582i	0.404145	−	0.699999i
$906$	−1.57153	−	34.6157i	−0.0522104	−	1.15003i
$907$	0.778677	−	0.449569i	0.0258555	−	0.0149277i	−0.487017	−	0.873393i	$-0.661915\pi$
$907$	0.778677	−	0.449569i	0.0258555	−	0.0149277i	0.512872	+	0.858465i	$0.328582\pi$
$908$	−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	$0.753031\pi$
$912$	51.2485	+	4.92949i	1.69701	+	0.163232i
$913$	−2.94360	+	5.09846i	−0.0974188	+	0.168734i
$914$	−23.3489	+	17.7885i	−0.772313	+	0.588390i
$915$	−9.88581	+	14.2755i	−0.326815	+	0.471933i
$916$	14.0092	+	3.85768i	0.462878	+	0.127461i
$917$			10.0397i			0.331541i
$918$	−0.704367	+	5.90172i	−0.0232476	+	0.194786i
$919$	−28.4761			−0.939339			−0.469670	−	0.882842i	$-0.655627\pi$
$919$	−28.4761			−0.939339			−0.469670	+	0.882842i	$0.655627\pi$
$920$	10.1340	+	7.94424i	0.334107	+	0.261914i
$921$	22.4204	+	15.5262i	0.738776	+	0.511604i
$922$	32.1326	+	42.1768i	1.05823	+	1.38902i
$923$	−4.17092	−	2.40808i	−0.137288	−	0.0792630i
$924$	−20.3011	+	16.9753i	−0.667857	+	0.558445i
$925$	−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	$0.811166\pi$
$930$	21.9731	−	0.997560i	0.720525	−	0.0327113i
$931$	−38.7912	−	22.3961i	−1.27133	−	0.734002i
$932$	11.4393	−	2.98061i	0.374706	−	0.0976332i
$933$	−14.6565	−	31.0099i	−0.479833	−	1.01522i
$934$	−37.9408	+	4.86175i	−1.24146	+	0.159081i
$935$	−2.35454			−0.0770016
$936$	−8.49193	+	1.88276i	−0.277568	+	0.0615399i
$937$	−15.1569			−0.495155			−0.247578	−	0.968868i	$-0.579634\pi$
$937$	−15.1569			−0.495155			−0.247578	+	0.968868i	$0.579634\pi$
$938$	−14.2634	+	1.82771i	−0.465715	+	0.0596769i
$939$	56.1219	+	4.61674i	1.83147	+	0.150662i
$940$	−5.01264	−	19.2380i	−0.163494	−	0.627475i
$941$	−36.9463	−	21.3310i	−1.20442	−	0.695370i	−0.242882	−	0.970056i	$-0.578093\pi$
$941$	−36.9463	−	21.3310i	−1.20442	−	0.695370i	−0.961534	+	0.274686i	$0.911426\pi$
$942$	−28.4522	−	44.4906i	−0.927024	−	1.44958i
$943$	−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	−0.0404213	−	0.999183i	$-0.512870\pi$
$947$	24.7629	−	14.2969i	0.804686	−	0.464585i	0.845107	+	0.534597i	$0.179537\pi$
$948$	0.311303	−	0.0543395i	0.0101106	−	0.00176486i
$949$	−0.363908	−	0.210103i	−0.0118130	−	0.00682022i
$950$	−19.7958	−	25.9837i	−0.642261	−	0.843023i
$951$	−2.28365	+	27.7605i	−0.0740524	+	0.900195i
$952$	−5.09423	+	6.49840i	−0.165105	+	0.210614i
$953$	−28.1424			−0.911622			−0.455811	−	0.890077i	$-0.650651\pi$
$953$	−28.1424			−0.911622			−0.455811	+	0.890077i	$0.650651\pi$
$954$	7.66882	+	14.4859i	0.248287	+	0.468998i
$955$		−	26.7429i		−	0.865380i
$956$	−6.33199	+	22.9948i	−0.204791	+	0.743704i
$957$	13.9475	+	29.5098i	0.450859	+	0.953917i
$958$	30.7220	−	23.4057i	0.992583	−	0.756204i
$959$	29.5189	−	51.1283i	0.953216	−	1.65102i
$960$	6.79574	−	17.8056i	0.219332	−	0.574672i
$961$	−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
$966$	25.9807	+	13.4675i	0.835916	+	0.433309i
$967$	−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	$0.238836\pi$
$968$	−18.2589	−	2.59656i	−0.586863	−	0.0834567i
$969$	8.55870	+	5.92692i	0.274945	+	0.190400i
$970$	10.6509	−	1.36481i	0.341980	−	0.0438215i
$971$		−	17.5426i		−	0.562969i	−0.959566	−	0.281484i	$-0.909173\pi$
$971$		−	17.5426i		−	0.562969i	0.959566	−	0.281484i	$-0.0908268\pi$
$972$	−11.2188	−	29.0884i	−0.359845	−	0.933012i
$973$			5.12543i			0.164314i
$974$	−3.43545	−	26.8100i	−0.110079	−	0.859049i
$975$	4.53698	+	3.14187i	0.145300	+	0.100621i
$976$	14.9252	−	25.0457i	0.477744	−	0.801692i
$977$	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	$-0.0926300\pi$
$978$	−16.8234	+	32.4548i	−0.537953	+	1.03779i
$979$	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	$0.884811\pi$
$984$	−23.0223	+	24.8650i	−0.733924	+	0.792666i
$985$	−16.8534	+	29.1909i	−0.536994	+	0.930100i
$986$	6.17197	+	8.10125i	0.196556	+	0.257996i
$987$	−19.3063	−	40.8478i	−0.614527	−	1.30020i
$988$	−4.04474	+	14.6886i	−0.128680	+	0.467306i
$989$		−	0.940054i		−	0.0298920i
$990$	10.9154	−	5.77859i	0.346914	−	0.183656i
$991$	−17.6057			−0.559263			−0.279631	−	0.960107i	$-0.590212\pi$
$991$	−17.6057			−0.559263			−0.279631	+	0.960107i	$0.590212\pi$
$992$	−36.6938	+	4.18758i	−1.16503	+	0.132956i
$993$	−2.91163	+	35.3943i	−0.0923978	+	1.12320i
$994$	19.0766	−	14.5336i	0.605073	−	0.460978i
$995$	8.49978	+	4.90735i	0.269461	+	0.155573i
$996$	−1.65690	−	9.49212i	−0.0525008	−	0.300769i
$997$	26.1168	−	15.0786i	0.827128	−	0.477543i	−0.0257404	−	0.999669i	$-0.508194\pi$
$997$	26.1168	−	15.0786i	0.827128	−	0.477543i	0.852868	+	0.522126i	$0.174861\pi$
$998$	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.13.4	yes	16
3.2	odd	2		216.2.n.b.37.5		16
4.3	odd	2		288.2.r.b.49.3		16
8.3	odd	2		288.2.r.b.49.6		16
8.5	even	2	inner	72.2.n.b.13.2	✓	16
9.2	odd	6		216.2.n.b.181.7		16
9.4	even	3		648.2.d.j.325.8		8
9.5	odd	6		648.2.d.k.325.1		8
9.7	even	3	inner	72.2.n.b.61.2	yes	16
12.11	even	2		864.2.r.b.145.6		16
24.5	odd	2		216.2.n.b.37.7		16
24.11	even	2		864.2.r.b.145.3		16
36.7	odd	6		288.2.r.b.241.6		16
36.11	even	6		864.2.r.b.721.3		16
36.23	even	6		2592.2.d.k.1297.3		8
36.31	odd	6		2592.2.d.j.1297.6		8
72.5	odd	6		648.2.d.k.325.2		8
72.11	even	6		864.2.r.b.721.6		16
72.13	even	6		648.2.d.j.325.7		8
72.29	odd	6		216.2.n.b.181.5		16
72.43	odd	6		288.2.r.b.241.3		16
72.59	even	6		2592.2.d.k.1297.6		8
72.61	even	6	inner	72.2.n.b.61.4	yes	16
72.67	odd	6		2592.2.d.j.1297.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.2	✓	16	8.5	even	2	inner
72.2.n.b.13.4	yes	16	1.1	even	1	trivial
72.2.n.b.61.2	yes	16	9.7	even	3	inner
72.2.n.b.61.4	yes	16	72.61	even	6	inner
216.2.n.b.37.5		16	3.2	odd	2
216.2.n.b.37.7		16	24.5	odd	2
216.2.n.b.181.5		16	72.29	odd	6
216.2.n.b.181.7		16	9.2	odd	6
288.2.r.b.49.3		16	4.3	odd	2
288.2.r.b.49.6		16	8.3	odd	2
288.2.r.b.241.3		16	72.43	odd	6
288.2.r.b.241.6		16	36.7	odd	6
648.2.d.j.325.7		8	72.13	even	6
648.2.d.j.325.8		8	9.4	even	3
648.2.d.k.325.1		8	9.5	odd	6
648.2.d.k.325.2		8	72.5	odd	6
864.2.r.b.145.3		16	24.11	even	2
864.2.r.b.145.6		16	12.11	even	2
864.2.r.b.721.3		16	36.11	even	6
864.2.r.b.721.6		16	72.11	even	6
2592.2.d.j.1297.3		8	72.67	odd	6
2592.2.d.j.1297.6		8	36.31	odd	6
2592.2.d.k.1297.3		8	36.23	even	6
2592.2.d.k.1297.6		8	72.59	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+(-0.179748 - 1.40274i) q^{2} +(0.986088 - 1.42395i) q^{3} +(-1.93538 + 0.504281i) q^{4} +(-1.19115 - 0.687709i) q^{5} +(-2.17468 - 1.12728i) 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} +(-1.19039 + 3.25315i) q^{12} +(-0.887751 - 0.512543i) q^{13} +(4.06032 - 3.09337i) q^{14} +(-2.15384 + 1.01799i) q^{15} +(3.49140 - 1.95195i) q^{16} +0.808822 q^{17} +(-3.74961 + 1.98504i) q^{18} +7.43122i q^{19} +(2.65212 + 0.730306i) q^{20} +(6.23057 + 0.512543i) q^{21} +(-1.81392 - 2.38093i) q^{22} +(-1.65498 + 2.86652i) q^{23} +(4.77731 + 1.08506i) 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} +(1.81513 + 2.83830i) q^{30} +(3.26436 - 5.65403i) q^{31} +(-3.36566 - 4.54668i) q^{32} +(0.300550 - 3.65354i) q^{33} +(-0.145384 - 1.13457i) q^{34} -4.96439i q^{35} +(3.45849 + 4.90294i) q^{36} -4.01531i q^{37} +(10.4241 - 1.33575i) q^{38} +(-1.60524 + 0.758698i) q^{39} +(0.547718 - 3.85152i) q^{40} +(-3.45852 + 5.99034i) q^{41} +(-0.400967 - 8.83202i) 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} +(0.663349 - 6.89637i) q^{48} +(-3.01378 + 5.22003i) q^{49} +(-3.49656 + 2.66387i) q^{50} +(0.797570 - 1.15172i) q^{51} +(1.97660 + 0.544290i) q^{52} -3.86330i q^{53} +(-0.870856 + 7.29668i) q^{54} -2.91107 q^{55} +(-6.29834 + 8.03439i) q^{56} +(10.5817 + 7.32784i) q^{57} +(7.63082 + 10.0161i) q^{58} +(7.06904 + 4.08131i) q^{59} +(3.65514 - 3.05634i) 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} +(-5.17900 + 0.235123i) q^{66} +(-2.43973 - 1.40858i) q^{67} +(-1.56538 + 0.407874i) q^{68} +(2.44981 + 5.18325i) q^{69} +(-6.96377 + 0.892341i) q^{70} +4.69830 q^{71} +(6.25591 - 5.73267i) q^{72} +0.409922 q^{73} +(-5.63245 + 0.721745i) q^{74} +(-5.36548 - 0.441379i) q^{75} +(-3.74743 - 14.3822i) q^{76} +(6.61576 + 3.81961i) q^{77} +(1.35280 + 2.11536i) 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} +(-12.3170 + 2.14999i) q^{84} +(-0.963426 - 0.556234i) q^{85} +(0.243405 + 0.319490i) q^{86} +(-1.26436 + 15.3697i) q^{87} +(4.71128 + 3.69328i) q^{88} +8.91934 q^{89} +(5.83147 + 0.214168i) q^{90} -3.69992i q^{91} +(1.75749 - 6.38238i) q^{92} +(-4.83210 - 10.2236i) q^{93} +(-8.12994 + 6.19383i) q^{94} +(5.11052 - 8.85168i) q^{95} +(-9.79308 + 0.309103i) 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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