LMFDB - Embedded newform 570.2.v.c.83.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(83,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("570.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.v (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			83.19
Character	$\chi$	$=$	570.83
Dual form			570.2.v.c.467.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.71902 + 0.212096i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.72991 + 1.41683i) q^{5} +(-0.240045 + 1.71534i) q^{6} +(0.867998 - 0.867998i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91003 - 0.729192i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.71902 + 0.212096i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.72991 + 1.41683i) q^{5} +(-0.240045 + 1.71534i) q^{6} +(0.867998 - 0.867998i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91003 - 0.729192i) q^{9} +(0.920816 + 2.03767i) q^{10} +2.36135i q^{11} +(1.59476 + 0.675828i) q^{12} +(1.89385 - 0.507455i) q^{13} +(-0.613767 - 1.06308i) q^{14} +(2.67325 - 2.80246i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.528413 - 1.97206i) q^{17} +(0.0488262 - 2.99960i) q^{18} +(1.06065 - 4.22789i) q^{19} +(2.20656 - 0.362052i) q^{20} +(-1.30800 + 1.67620i) q^{21} +(2.28089 + 0.611163i) q^{22} +(-2.04907 - 7.64725i) q^{23} +(1.06555 - 1.36550i) q^{24} +(0.985200 - 4.90198i) q^{25} -1.96066i q^{26} +(-4.84773 + 1.87070i) q^{27} +(-1.18571 + 0.317709i) q^{28} +(-0.796320 + 1.37927i) q^{29} +(-2.01508 - 3.30749i) q^{30} +0.786684 q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.500833 - 4.05920i) q^{33} +(-1.76810 - 1.02081i) q^{34} +(-0.271758 + 2.73136i) q^{35} +(-2.88476 - 0.823517i) q^{36} +(5.39947 - 5.39947i) q^{37} +(-3.80931 - 2.11877i) q^{38} +(-3.14793 + 1.27400i) q^{39} +(0.221385 - 2.22508i) q^{40} +(10.4764 - 6.04853i) q^{41} +(1.28055 + 1.69727i) q^{42} +(0.191303 - 0.713953i) q^{43} +(1.18068 - 2.04499i) q^{44} +(-4.00096 + 5.38445i) q^{45} -7.91701 q^{46} +(9.65271 - 2.58643i) q^{47} +(-1.04319 - 1.38266i) q^{48} +5.49316i q^{49} +(-4.47996 - 2.22036i) q^{50} +(-0.490084 + 3.50208i) q^{51} +(-1.89385 - 0.507455i) q^{52} +(-0.493814 - 1.84294i) q^{53} +(0.552270 + 5.16672i) q^{54} +(-3.34563 - 4.08493i) q^{55} +1.22753i q^{56} +(-0.926561 + 7.49276i) q^{57} +(1.12617 + 1.12617i) q^{58} +(0.943147 + 1.63358i) q^{59} +(-3.71633 + 1.09038i) q^{60} +(-4.20476 + 7.28286i) q^{61} +(0.203609 - 0.759879i) q^{62} +(1.89296 - 3.15884i) q^{63} -1.00000i q^{64} +(-2.55722 + 3.56111i) q^{65} +(-4.05051 - 0.566832i) q^{66} +(-3.45309 - 12.8871i) q^{67} +(-1.44365 + 1.44365i) q^{68} +(5.14434 + 12.7111i) q^{69} +(2.56796 + 0.969427i) q^{70} +(5.79636 - 3.34653i) q^{71} +(-1.54209 + 2.57332i) q^{72} +(-1.43228 + 5.34533i) q^{73} +(-3.81800 - 6.61297i) q^{74} +(-0.653886 + 8.63553i) q^{75} +(-3.03249 + 3.13113i) q^{76} +(2.04965 + 2.04965i) q^{77} +(0.415847 + 3.37040i) q^{78} +(-7.19119 + 4.15183i) q^{79} +(-2.09197 - 0.789735i) q^{80} +(7.93656 - 4.24394i) q^{81} +(-3.13095 - 11.6849i) q^{82} +(-7.90145 + 7.90145i) q^{83} +(1.97086 - 0.797631i) q^{84} +(1.87997 + 4.16017i) q^{85} +(-0.640113 - 0.369569i) q^{86} +(1.07635 - 2.53988i) q^{87} +(-1.66973 - 1.66973i) q^{88} +(-3.33439 + 5.77534i) q^{89} +(4.16545 + 5.25823i) q^{90} +(1.20339 - 2.08433i) q^{91} +(-2.04907 + 7.64725i) q^{92} +(-1.35232 + 0.166852i) q^{93} -9.99322i q^{94} +(4.15535 + 8.81664i) q^{95} +(-1.60555 + 0.649783i) q^{96} +(12.7128 + 3.40638i) q^{97} +(5.30598 + 1.42173i) q^{98} +(1.72188 + 6.87161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) $ 144 * q - 4 * q^3 + 8 * q^6	$ 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) $ 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−1.71902	+	0.212096i	−0.992474	+	0.122454i
$3$	−1.71902	+	0.212096i	−0.992474	+	0.122454i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.72991	+	1.41683i	−0.773641	+	0.633625i
$5$	−1.72991	+	1.41683i	−0.773641	+	0.633625i
$6$	−0.240045	+	1.71534i	−0.0979981	+	0.700283i
$7$	0.867998	−	0.867998i	0.328072	−	0.328072i	−0.523781	−	0.851853i	$-0.675479\pi$
$7$	0.867998	−	0.867998i	0.328072	−	0.328072i	0.851853	+	0.523781i	$0.175479\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.91003	−	0.729192i	0.970010	−	0.243064i
$10$	0.920816	+	2.03767i	0.291188	+	0.644368i
$11$			2.36135i			0.711975i	0.934491	+	0.355987i	$0.115855\pi$
$11$			2.36135i			0.711975i	−0.934491	+	0.355987i	$0.884145\pi$
$12$	1.59476	+	0.675828i	0.460367	+	0.195095i
$13$	1.89385	−	0.507455i	0.525259	−	0.140743i	0.0135610	−	0.999908i	$-0.495683\pi$
$13$	1.89385	−	0.507455i	0.525259	−	0.140743i	0.511698	+	0.859165i	$0.329017\pi$
$14$	−0.613767	−	1.06308i	−0.164036	−	0.284119i
$15$	2.67325	−	2.80246i	0.690229	−	0.723591i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.528413	−	1.97206i	0.128159	−	0.478296i	−0.871774	−	0.489909i	$-0.837030\pi$
$17$	0.528413	−	1.97206i	0.128159	−	0.478296i	0.999933	+	0.0116133i	$0.00369671\pi$
$18$	0.0488262	−	2.99960i	0.0115084	−	0.707013i
$19$	1.06065	−	4.22789i	0.243330	−	0.969943i
$19$	1.06065	−	4.22789i	0.243330	−	0.969943i
$20$	2.20656	−	0.362052i	0.493402	−	0.0809573i
$21$	−1.30800	+	1.67620i	−0.285430	+	0.365777i
$22$	2.28089	+	0.611163i	0.486288	+	0.130300i
$23$	−2.04907	−	7.64725i	−0.427261	−	1.59456i	−0.758935	−	0.651167i	$-0.774280\pi$
$23$	−2.04907	−	7.64725i	−0.427261	−	1.59456i	0.331673	−	0.943394i	$-0.392387\pi$
$24$	1.06555	−	1.36550i	0.217505	−	0.278732i
$25$	0.985200	−	4.90198i	0.197040	−	0.980395i
$26$		−	1.96066i		−	0.384516i
$27$	−4.84773	+	1.87070i	−0.932946	+	0.360016i
$28$	−1.18571	+	0.317709i	−0.224078	+	0.0600414i
$29$	−0.796320	+	1.37927i	−0.147873	+	0.256123i	−0.930441	−	0.366442i	$-0.880576\pi$
$29$	−0.796320	+	1.37927i	−0.147873	+	0.256123i	0.782568	+	0.622565i	$0.213909\pi$
$30$	−2.01508	−	3.30749i	−0.367901	−	0.603861i
$31$	0.786684			0.141293			0.0706463	−	0.997501i	$-0.477494\pi$
$31$	0.786684			0.141293			0.0706463	+	0.997501i	$0.477494\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−0.500833	−	4.05920i	−0.0871838	−	0.706616i
$34$	−1.76810	−	1.02081i	−0.303227	−	0.175068i
$35$	−0.271758	+	2.73136i	−0.0459355	+	0.461685i
$36$	−2.88476	−	0.823517i	−0.480793	−	0.137253i
$37$	5.39947	−	5.39947i	0.887667	−	0.887667i	−0.106631	−	0.994299i	$-0.534006\pi$
$37$	5.39947	−	5.39947i	0.887667	−	0.887667i	0.994299	+	0.106631i	$0.0340064\pi$
$38$	−3.80931	−	2.11877i	−0.617951	−	0.343710i
$39$	−3.14793	+	1.27400i	−0.504072	+	0.204003i
$40$	0.221385	−	2.22508i	0.0350041	−	0.351816i
$41$	10.4764	−	6.04853i	1.63613	−	0.944622i	0.653987	−	0.756506i	$-0.273095\pi$
$41$	10.4764	−	6.04853i	1.63613	−	0.944622i	0.982147	−	0.188117i	$-0.0602384\pi$
$42$	1.28055	+	1.69727i	0.197593	+	0.261894i
$43$	0.191303	−	0.713953i	0.0291735	−	0.108877i	−0.949804	−	0.312846i	$-0.898718\pi$
$43$	0.191303	−	0.713953i	0.0291735	−	0.108877i	0.978977	+	0.203969i	$0.0653843\pi$
$44$	1.18068	−	2.04499i	0.177994	−	0.308294i
$45$	−4.00096	+	5.38445i	−0.596428	+	0.802666i
$46$	−7.91701			−1.16730
$47$	9.65271	−	2.58643i	1.40799	−	0.377270i	0.526784	−	0.849999i	$-0.323398\pi$
$47$	9.65271	−	2.58643i	1.40799	−	0.377270i	0.881208	+	0.472729i	$0.156731\pi$
$48$	−1.04319	−	1.38266i	−0.150571	−	0.199570i
$49$			5.49316i			0.784737i
$50$	−4.47996	−	2.22036i	−0.633562	−	0.314006i
$51$	−0.490084	+	3.50208i	−0.0686254	+	0.490390i
$52$	−1.89385	−	0.507455i	−0.262630	−	0.0703714i
$53$	−0.493814	−	1.84294i	−0.0678306	−	0.253147i	0.923682	−	0.383161i	$-0.125165\pi$
$53$	−0.493814	−	1.84294i	−0.0678306	−	0.253147i	−0.991512	+	0.130014i	$0.958498\pi$
$54$	0.552270	+	5.16672i	0.0751544	+	0.703102i
$55$	−3.34563	−	4.08493i	−0.451125	−	0.550813i
$56$			1.22753i			0.164036i
$57$	−0.926561	+	7.49276i	−0.122726	+	0.992441i
$58$	1.12617	+	1.12617i	0.147873	+	0.147873i
$59$	0.943147	+	1.63358i	0.122787	+	0.212674i	0.920866	−	0.389880i	$-0.127483\pi$
$59$	0.943147	+	1.63358i	0.122787	+	0.212674i	−0.798079	+	0.602553i	$0.794150\pi$
$60$	−3.71633	+	1.09038i	−0.479776	+	0.140767i
$61$	−4.20476	+	7.28286i	−0.538365	+	0.932475i	0.460628	+	0.887593i	$0.347624\pi$
$61$	−4.20476	+	7.28286i	−0.538365	+	0.932475i	−0.998992	+	0.0448813i	$0.985709\pi$
$62$	0.203609	−	0.759879i	0.0258584	−	0.0965047i
$63$	1.89296	−	3.15884i	0.238491	−	0.397976i
$64$		−	1.00000i		−	0.125000i
$65$	−2.55722	+	3.56111i	−0.317184	+	0.441701i
$66$	−4.05051	−	0.566832i	−0.498584	−	0.0697721i
$67$	−3.45309	−	12.8871i	−0.421862	−	1.57441i	−0.770682	−	0.637220i	$-0.780084\pi$
$67$	−3.45309	−	12.8871i	−0.421862	−	1.57441i	0.348820	−	0.937190i	$-0.386583\pi$
$68$	−1.44365	+	1.44365i	−0.175068	+	0.175068i
$69$	5.14434	+	12.7111i	0.619305	+	1.53024i
$70$	2.56796	+	0.969427i	0.306930	+	0.115869i
$71$	5.79636	−	3.34653i	0.687901	−	0.397160i	−0.114924	−	0.993374i	$-0.536663\pi$
$71$	5.79636	−	3.34653i	0.687901	−	0.397160i	0.802825	+	0.596214i	$0.203329\pi$
$72$	−1.54209	+	2.57332i	−0.181737	+	0.303269i
$73$	−1.43228	+	5.34533i	−0.167635	+	0.625624i	0.830054	+	0.557683i	$0.188310\pi$
$73$	−1.43228	+	5.34533i	−0.167635	+	0.625624i	−0.997689	+	0.0679408i	$0.978357\pi$
$74$	−3.81800	−	6.61297i	−0.443834	−	0.768742i
$75$	−0.653886	+	8.63553i	−0.0755042	+	0.997145i
$76$	−3.03249	+	3.13113i	−0.347851	+	0.359165i
$77$	2.04965	+	2.04965i	0.233579	+	0.233579i
$78$	0.415847	+	3.37040i	0.0470854	+	0.381623i
$79$	−7.19119	+	4.15183i	−0.809072	+	0.467118i	−0.846633	−	0.532177i	$-0.821374\pi$
$79$	−7.19119	+	4.15183i	−0.809072	+	0.467118i	0.0375617	+	0.999294i	$0.488041\pi$
$80$	−2.09197	−	0.789735i	−0.233889	−	0.0882951i
$81$	7.93656	−	4.24394i	0.881840	−	0.471549i
$82$	−3.13095	−	11.6849i	−0.345756	−	1.29038i
$83$	−7.90145	+	7.90145i	−0.867296	+	0.867296i	−0.992172	−	0.124876i	$-0.960147\pi$
$83$	−7.90145	+	7.90145i	−0.867296	+	0.867296i	0.124876	+	0.992172i	$0.460147\pi$
$84$	1.97086	−	0.797631i	0.215039	−	0.0870287i
$85$	1.87997	+	4.16017i	0.203911	+	0.451234i
$86$	−0.640113	−	0.369569i	−0.0690252	−	0.0398517i
$87$	1.07635	−	2.53988i	0.115397	−	0.272303i
$88$	−1.66973	−	1.66973i	−0.177994	−	0.177994i
$89$	−3.33439	+	5.77534i	−0.353445	+	0.612185i	−0.986851	−	0.161635i	$-0.948323\pi$
$89$	−3.33439	+	5.77534i	−0.353445	+	0.612185i	0.633406	+	0.773820i	$0.281656\pi$
$90$	4.16545	+	5.25823i	0.439077	+	0.554266i
$91$	1.20339	−	2.08433i	0.126149	−	0.218497i
$92$	−2.04907	+	7.64725i	−0.213631	+	0.797280i
$93$	−1.35232	+	0.166852i	−0.140229	+	0.0173018i
$94$		−	9.99322i		−	1.03072i
$95$	4.15535	+	8.81664i	0.426330	+	0.904568i
$96$	−1.60555	+	0.649783i	−0.163865	+	0.0663182i
$97$	12.7128	+	3.40638i	1.29079	+	0.345865i	0.837959	−	0.545733i	$-0.183749\pi$
$97$	12.7128	+	3.40638i	1.29079	+	0.345865i	0.452827	+	0.891598i	$0.350416\pi$
$98$	5.30598	+	1.42173i	0.535985	+	0.143617i
$99$	1.72188	+	6.87161i	0.173055	+	0.690623i
$100$	−3.30420	+	3.75264i	−0.330420	+	0.375264i
$101$	−0.167917	−	0.0969467i	−0.0167083	−	0.00964656i	0.491623	−	0.870808i	$-0.336404\pi$
$101$	−0.167917	−	0.0969467i	−0.0167083	−	0.00964656i	−0.508331	+	0.861162i	$0.669737\pi$
$102$	3.25591	+	1.37979i	0.322383	+	0.136620i
$103$	−9.12655	−	9.12655i	−0.899266	−	0.899266i	0.0961053	−	0.995371i	$-0.469361\pi$
$103$	−9.12655	−	9.12655i	−0.899266	−	0.899266i	−0.995371	+	0.0961053i	$0.969361\pi$
$104$	−0.980328	+	1.69798i	−0.0961291	+	0.166500i
$105$	−0.112155	−	4.75290i	−0.0109452	−	0.463835i
$106$	−1.90795			−0.185317
$107$	1.41333	+	1.41333i	0.136632	+	0.136632i	0.772115	−	0.635483i	$-0.219199\pi$
$107$	1.41333	+	1.41333i	0.136632	+	0.136632i	−0.635483	+	0.772115i	$0.719199\pi$
$108$	5.13361	+	0.803794i	0.493982	+	0.0773451i
$109$	6.69466	−	3.86517i	0.641232	−	0.370216i	−0.143857	−	0.989599i	$-0.545950\pi$
$109$	6.69466	−	3.86517i	0.641232	−	0.370216i	0.785089	+	0.619383i	$0.212617\pi$
$110$	−4.81166	+	2.17437i	−0.458773	+	0.207318i
$111$	−8.13657	+	10.4270i	−0.772289	+	0.989685i
$112$	1.18571	+	0.317709i	0.112039	+	0.0300207i
$113$	10.7554	−	10.7554i	1.01179	−	1.01179i	0.0118556	−	0.999930i	$-0.496226\pi$
$113$	10.7554	−	10.7554i	1.01179	−	1.01179i	0.999930	−	0.0118556i	$-0.00377384\pi$
$114$	6.99764	+	2.83426i	0.655389	+	0.265453i
$115$	14.3795	+	10.3259i	1.34090	+	0.962894i
$116$	1.37927	−	0.796320i	0.128062	−	0.0739364i
$117$	5.14113	−	2.85769i	0.475297	−	0.264193i
$118$	1.82202	−	0.488209i	0.167731	−	0.0449433i
$119$	−1.25309	−	2.17041i	−0.114870	−	0.198961i
$120$	0.0913659	+	3.87191i	0.00834052	+	0.353455i
$121$	5.42401			0.493092
$122$	5.94643	+	5.94643i	0.538365	+	0.538365i
$123$	−16.7262	+	12.6195i	−1.50815	+	1.13786i
$124$	−0.681289	−	0.393342i	−0.0611815	−	0.0353232i
$125$	5.24095	+	9.87585i	0.468764	+	0.883323i
$126$	−2.56127	−	2.64603i	−0.228176	−	0.235727i
$127$	−4.07132	−	15.1944i	−0.361271	−	1.34828i	−0.872406	−	0.488782i	$-0.837442\pi$
$127$	−4.07132	−	15.1944i	−0.361271	−	1.34828i	0.511135	−	0.859500i	$-0.329225\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−0.177427	+	1.26787i	−0.0156216	+	0.111630i
$130$	2.77791	+	3.39177i	0.243639	+	0.297478i
$131$	5.44362	−	3.14287i	0.475611	−	0.274594i	−0.242975	−	0.970033i	$-0.578123\pi$
$131$	5.44362	−	3.14287i	0.475611	−	0.274594i	0.718586	+	0.695438i	$0.244790\pi$
$132$	−1.59587	+	3.76579i	−0.138902	+	0.327770i
$133$	−2.74915	−	4.59044i	−0.238382	−	0.398042i
$134$	−13.3417			−1.15255
$135$	5.73570	−	10.1045i	0.493650	−	0.869661i
$136$	1.02081	+	1.76810i	0.0875342	+	0.151614i
$137$	−19.6714	+	5.27094i	−1.68064	+	0.450327i	−0.967949	−	0.251149i	$-0.919192\pi$
$137$	−19.6714	+	5.27094i	−1.68064	+	0.450327i	−0.712694	+	0.701475i	$0.752525\pi$
$138$	13.6095	−	1.67916i	1.15851	−	0.142940i
$139$	−3.11754	−	1.79991i	−0.264426	−	0.152667i	0.361926	−	0.932207i	$-0.382119\pi$
$139$	−3.11754	−	1.79991i	−0.264426	−	0.152667i	−0.626352	+	0.779540i	$0.715453\pi$
$140$	1.60103	−	2.22955i	0.135312	−	0.188432i
$141$	−16.0446	+	6.49342i	−1.35120	+	0.546845i
$142$	−1.73229	−	6.46500i	−0.145371	−	0.542530i
$143$	1.19828	+	4.47204i	0.100205	+	0.373971i
$144$	2.08651	+	2.15556i	0.173876	+	0.179630i
$145$	−0.576618	−	3.51426i	−0.0478855	−	0.291843i
$146$	4.79249	+	2.76695i	0.396630	+	0.228994i
$147$	−1.16508	−	9.44283i	−0.0960938	−	0.778831i
$148$	−7.37581	+	1.97634i	−0.606288	+	0.162454i
$149$	7.72513	+	13.3803i	0.632867	+	1.09616i	0.986963	+	0.160949i	$0.0514553\pi$
$149$	7.72513	+	13.3803i	0.632867	+	1.09616i	−0.354096	+	0.935209i	$0.615211\pi$
$150$	8.17205	+	2.86665i	0.667245	+	0.234061i
$151$	−12.5694			−1.02288			−0.511440	−	0.859319i	$-0.670888\pi$
$151$	−12.5694			−1.02288			−0.511440	+	0.859319i	$0.670888\pi$
$152$	2.23957	+	3.73956i	0.181653	+	0.303318i
$153$	0.0996850	−	6.12408i	0.00805905	−	0.495102i
$154$	2.51030	−	1.44932i	0.202286	−	0.116790i
$155$	−1.36090	+	1.11460i	−0.109310	+	0.0895265i
$156$	3.36318	+	0.470646i	0.269270	+	0.0376819i
$157$	4.15417	+	1.11311i	0.331539	+	0.0888355i	0.420749	−	0.907177i	$-0.361767\pi$
$157$	4.15417	+	1.11311i	0.331539	+	0.0888355i	−0.0892098	+	0.996013i	$0.528434\pi$
$158$	2.14915	+	8.02073i	0.170977	+	0.638095i
$159$	1.23975	+	3.06331i	0.0983188	+	0.242936i
$160$	−1.30427	+	1.81628i	−0.103111	+	0.143590i
$161$	−8.41639	−	4.85920i	−0.663304	−	0.382959i
$162$	−2.04520	−	8.76454i	−0.160686	−	0.688607i
$163$	−2.20131	−	2.20131i	−0.172420	−	0.172420i	0.615622	−	0.788042i	$-0.288905\pi$
$163$	−2.20131	−	2.20131i	−0.172420	−	0.172420i	−0.788042	+	0.615622i	$0.788905\pi$
$164$	−12.0971			−0.944622
$165$	6.61759	+	6.31247i	0.515178	+	0.491425i
$166$	5.58717	+	9.67726i	0.433648	+	0.751101i
$167$	−0.375997	+	0.100748i	−0.0290955	+	0.00779613i	−0.273337	−	0.961918i	$-0.588128\pi$
$167$	−0.375997	+	0.100748i	−0.0290955	+	0.00779613i	0.244242	+	0.969714i	$0.421461\pi$
$168$	−0.260355	−	2.11015i	−0.0200868	−	0.162802i
$169$	−7.92918	+	4.57791i	−0.609937	+	0.352147i
$170$	4.50498	−	0.739176i	0.345517	−	0.0566922i
$171$	0.00359022	−	13.0767i	0.000274551	−	1.00000i
$172$	−0.522650	+	0.522650i	−0.0398517	+	0.0398517i
$173$	9.07003	+	2.43031i	0.689581	+	0.184773i	0.586559	−	0.809906i	$-0.300482\pi$
$173$	9.07003	+	2.43031i	0.689581	+	0.184773i	0.103022	+	0.994679i	$0.467149\pi$
$174$	−2.17475	−	1.69704i	−0.164868	−	0.128652i
$175$	−3.39976	−	5.11006i	−0.256997	−	0.386284i
$176$	−2.04499	+	1.18068i	−0.154147	+	0.0889968i
$177$	−1.96776	−	2.60811i	−0.147906	−	0.196038i
$178$	4.71554	+	4.71554i	0.353445	+	0.353445i
$179$	−2.41985			−0.180868			−0.0904340	−	0.995902i	$-0.528825\pi$
$179$	−2.41985			−0.180868			−0.0904340	+	0.995902i	$0.528825\pi$
$180$	6.15716	−	2.66259i	0.458928	−	0.198458i
$181$	1.02006	−	1.76680i	0.0758204	−	0.131325i	−0.825622	−	0.564223i	$-0.809176\pi$
$181$	1.02006	−	1.76680i	0.0758204	−	0.131325i	0.901443	+	0.432898i	$0.142509\pi$
$182$	−1.70185	−	1.70185i	−0.126149	−	0.126149i
$183$	5.68339	−	13.4112i	0.420128	−	0.991382i
$184$	6.85633	+	3.95851i	0.505456	+	0.291825i
$185$	−1.69050	+	16.9907i	−0.124288	+	1.24918i
$186$	−0.188840	+	1.34943i	−0.0138464	+	0.0989449i
$187$	4.65674	+	1.24777i	0.340534	+	0.0912459i
$188$	−9.65271	−	2.58643i	−0.703996	−	0.188635i
$189$	−2.58406	+	5.83158i	−0.187963	+	0.424185i
$190$	9.59170	−	1.73185i	0.695855	−	0.125641i
$191$		−	20.9637i		−	1.51688i	−0.651743	−	0.758440i	$-0.725962\pi$
$191$		−	20.9637i		−	1.51688i	0.651743	−	0.758440i	$-0.274038\pi$
$192$	0.212096	+	1.71902i	0.0153067	+	0.124059i
$193$	3.70667	−	13.8335i	0.266812	−	0.995754i	−0.694321	−	0.719666i	$-0.744295\pi$
$193$	3.70667	−	13.8335i	0.266812	−	0.995754i	0.961132	−	0.276089i	$-0.0890383\pi$
$194$	6.58061	−	11.3980i	0.472460	−	0.818325i
$195$	3.64060	−	6.66398i	0.260709	−	0.477218i
$196$	2.74658	−	4.75722i	0.196184	−	0.339801i
$197$	−4.84435	−	4.84435i	−0.345146	−	0.345146i	0.513152	−	0.858298i	$-0.328478\pi$
$197$	−4.84435	−	4.84435i	−0.345146	−	0.345146i	−0.858298	+	0.513152i	$0.828478\pi$
$198$	7.08312	+	0.115296i	0.503375	+	0.00819371i
$199$	0.668802	+	0.386133i	0.0474101	+	0.0273723i	0.523518	−	0.852015i	$-0.324619\pi$
$199$	0.668802	+	0.386133i	0.0474101	+	0.0273723i	−0.476108	+	0.879387i	$0.657953\pi$
$200$	2.76958	+	4.16286i	0.195839	+	0.294359i
$201$	8.66921	+	21.4207i	0.611479	+	1.51090i
$202$	−0.137103	+	0.137103i	−0.00964656	+	0.00964656i
$203$	0.505996	+	1.88840i	0.0355140	+	0.132540i
$204$	2.17547	−	2.78785i	0.152313	−	0.195189i
$205$	−9.55348	+	25.3066i	−0.667244	+	1.76749i
$206$	−11.1777	+	6.45345i	−0.778787	+	0.449633i
$207$	−11.5392	−	20.7596i	−0.802028	−	1.44289i
$208$	1.38639	+	1.38639i	0.0961291	+	0.0961291i
$209$	9.98353	+	2.50457i	0.690575	+	0.173245i
$210$	−4.61997	−	1.12181i	−0.318809	−	0.0774121i
$211$	−1.82783	−	3.16589i	−0.125833	−	0.217949i	0.796225	−	0.605000i	$-0.206827\pi$
$211$	−1.82783	−	3.16589i	−0.125833	−	0.217949i	−0.922058	+	0.387051i	$0.873494\pi$
$212$	−0.493814	+	1.84294i	−0.0339153	+	0.126574i
$213$	−9.25424	+	6.98212i	−0.634090	+	0.478407i
$214$	1.73097	−	0.999377i	0.118327	−	0.0683160i
$215$	0.680611	+	1.50612i	0.0464173	+	0.102717i
$216$	2.10508	−	4.75065i	0.143233	−	0.323241i
$217$	0.682841	−	0.682841i	0.0463542	−	0.0463542i
$218$	−2.00076	−	7.46693i	−0.135508	−	0.505724i
$219$	1.32839	−	9.49249i	0.0897640	−	0.641443i
$220$	0.854932	+	5.21047i	0.0576395	+	0.351290i
$221$		−	4.00293i		−	0.269267i
$222$	7.96579	+	10.5580i	0.534629	+	0.708608i
$223$	−1.24148	+	4.63326i	−0.0831355	+	0.310266i	−0.994955	−	0.100326i	$-0.968011\pi$
$223$	−1.24148	+	4.63326i	−0.0831355	+	0.310266i	0.911819	+	0.410592i	$0.134678\pi$
$224$	0.613767	−	1.06308i	0.0410091	−	0.0710298i
$225$	−0.707520	−	14.9833i	−0.0471680	−	0.998887i
$226$	−7.60523	−	13.1727i	−0.505893	−	0.876232i
$227$	18.0497	+	18.0497i	1.19800	+	1.19800i	0.974764	+	0.223238i	$0.0716626\pi$
$227$	18.0497	+	18.0497i	1.19800	+	1.19800i	0.223238	+	0.974764i	$0.428337\pi$
$228$	4.54881	−	6.02564i	0.301252	−	0.399058i
$229$			6.44942i			0.426190i	0.977032	+	0.213095i	$0.0683543\pi$
$229$			6.44942i			0.426190i	−0.977032	+	0.213095i	$0.931646\pi$
$230$	13.6957	−	11.2170i	0.903071	−	0.739630i
$231$	−3.95810	−	3.08866i	−0.260424	−	0.203219i
$232$	−0.412205	−	1.53837i	−0.0270626	−	0.100999i
$233$	−7.23764	−	1.93932i	−0.474154	−	0.127049i	0.0138253	−	0.999904i	$-0.495599\pi$
$233$	−7.23764	−	1.93932i	−0.474154	−	0.127049i	−0.487979	+	0.872855i	$0.662266\pi$
$234$	−1.42969	−	5.70557i	−0.0934621	−	0.372985i
$235$	−13.0338	+	18.1505i	−0.850232	+	1.18401i
$236$		−	1.88629i		−	0.122787i
$237$	11.4812	−	8.66229i	0.745783	−	0.562676i
$238$	−2.42078	+	0.648645i	−0.156916	+	0.0420454i
$239$	15.4669			1.00047			0.500236	−	0.865889i	$-0.333247\pi$
$239$	15.4669			1.00047			0.500236	+	0.865889i	$0.333247\pi$
$240$	3.76362	+	0.913870i	0.242941	+	0.0589901i
$241$	−8.92809	+	15.4639i	−0.575109	+	0.996118i	0.420921	+	0.907097i	$0.361707\pi$
$241$	−8.92809	+	15.4639i	−0.575109	+	0.996118i	−0.996030	+	0.0890207i	$0.971626\pi$
$242$	1.40384	−	5.23920i	0.0902421	−	0.336788i
$243$	−12.7429	+	8.97871i	−0.817460	+	0.575985i
$244$	7.28286	−	4.20476i	0.466237	−	0.269182i
$245$	−7.78286	−	9.50269i	−0.497229	−	0.607104i
$246$	7.86047	+	19.4224i	0.501165	+	1.23833i
$247$	−0.136748	−	8.54521i	−0.00870109	−	0.543719i
$248$	−0.556270	+	0.556270i	−0.0353232	+	0.0353232i
$249$	11.9068	−	15.2586i	0.754566	−	0.966973i
$250$	10.8958	−	2.50631i	0.689111	−	0.158513i
$251$	−4.37887	−	2.52814i	−0.276392	−	0.159575i	0.355397	−	0.934716i	$-0.384346\pi$
$251$	−4.37887	−	2.52814i	−0.276392	−	0.159575i	−0.631789	+	0.775140i	$0.717679\pi$
$252$	−3.21877	+	1.78915i	−0.202764	+	0.112706i
$253$	18.0578	−	4.83858i	1.13529	−	0.304199i
$254$	−15.7304			−0.987011
$255$	−4.11404	−	6.75266i	−0.257631	−	0.422868i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−17.6043	+	4.71705i	−1.09812	+	0.294242i	−0.762001	−	0.647576i	$-0.775783\pi$
$257$	−17.6043	+	4.71705i	−1.09812	+	0.294242i	−0.336124	+	0.941818i	$0.609116\pi$
$258$	1.17875	+	0.499530i	0.0733857	+	0.0310994i
$259$		−	9.37346i		−	0.582438i
$260$	3.99517	−	1.80540i	0.247770	−	0.111966i
$261$	−1.31156	+	4.59438i	−0.0811838	+	0.284385i
$262$	−1.62687	−	6.07157i	−0.100508	−	0.375103i
$263$	−30.5164	−	8.17686i	−1.88172	−	0.504207i	−0.999439	−	0.0334926i	$-0.989337\pi$
$263$	−30.5164	−	8.17686i	−1.88172	−	0.504207i	−0.882286	−	0.470714i	$-0.843996\pi$
$264$	3.22443	+	2.51615i	0.198450	+	0.154858i
$265$	3.46538	+	2.48848i	0.212877	+	0.152866i
$266$	−5.14556	+	1.46738i	−0.315494	+	0.0899711i
$267$	4.50695	−	10.6351i	0.275821	−	0.650858i
$268$	−3.45309	+	12.8871i	−0.210931	+	0.787205i
$269$	−8.79460	−	15.2327i	−0.536216	−	0.928754i	−0.999103	−	0.0423365i	$-0.986520\pi$
$269$	−8.79460	−	15.2327i	−0.536216	−	0.928754i	0.462887	−	0.886417i	$-0.346813\pi$
$270$	−8.27573	−	8.15551i	−0.503645	−	0.496328i
$271$	−4.98158	−	8.62835i	−0.302609	−	0.524135i	0.674117	−	0.738625i	$-0.264524\pi$
$271$	−4.98158	−	8.62835i	−0.302609	−	0.524135i	−0.976726	+	0.214490i	$0.931191\pi$
$272$	1.97206	−	0.528413i	0.119574	−	0.0320397i
$273$	−1.62656	+	3.83822i	−0.0984441	+	0.232300i
$274$			20.3653i			1.23032i
$275$	11.5753	+	2.32640i	0.698017	+	0.140287i
$276$	1.90044	−	13.5803i	0.114393	−	0.817440i
$277$	−21.2580	+	21.2580i	−1.27727	+	1.27727i	−0.335081	+	0.942189i	$0.608764\pi$
$277$	−21.2580	+	21.2580i	−1.27727	+	1.27727i	−0.942189	+	0.335081i	$0.891236\pi$
$278$	−2.54546	+	2.54546i	−0.152667	+	0.152667i
$279$	2.28928	−	0.573644i	0.137055	−	0.0343432i
$280$	−1.73920	−	2.12353i	−0.103937	−	0.126905i
$281$	−9.66800	−	5.58182i	−0.576744	−	0.332984i	0.183094	−	0.983095i	$-0.441389\pi$
$281$	−9.66800	−	5.58182i	−0.576744	−	0.332984i	−0.759839	+	0.650112i	$0.774722\pi$
$282$	2.11952	+	17.1785i	0.126215	+	1.02296i
$283$	−5.56328	+	20.7625i	−0.330703	+	1.23420i	0.577751	+	0.816213i	$0.303931\pi$
$283$	−5.56328	+	20.7625i	−0.330703	+	1.23420i	−0.908453	+	0.417986i	$0.862736\pi$
$284$	−6.69306			−0.397160
$285$	−9.01308	−	14.2746i	−0.533889	−	0.845555i
$286$	4.62980			0.273766
$287$	3.84335	−	14.3436i	0.226866	−	0.846675i
$288$	2.62215	−	1.45752i	0.154511	−	0.0858850i
$289$	11.1126	+	6.41587i	0.653683	+	0.377404i
$290$	−3.54375	−	0.352587i	−0.208096	−	0.0207046i
$291$	−22.5759	−	3.15929i	−1.32342	−	0.185201i
$292$	3.91305	−	3.91305i	0.228994	−	0.228994i
$293$	−7.13865	+	7.13865i	−0.417044	+	0.417044i	−0.884184	−	0.467139i	$-0.845285\pi$
$293$	−7.13865	+	7.13865i	−0.417044	+	0.417044i	0.467139	+	0.884184i	$0.345285\pi$
$294$	−9.42261	−	1.31861i	−0.549538	−	0.0769027i
$295$	−3.94606	−	1.48967i	−0.229749	−	0.0867321i
$296$			7.63600i			0.443834i
$297$	−4.41738	−	11.4472i	−0.256322	−	0.664234i
$298$	14.9238	−	3.99882i	0.864512	−	0.231645i
$299$	−7.76127	−	13.4429i	−0.448846	−	0.777424i
$300$	4.88405	−	7.15165i	0.281981	−	0.412901i
$301$	−0.453659	−	0.785761i	−0.0261485	−	0.0452905i
$302$	−3.25319	+	12.1411i	−0.187200	+	0.698640i
$303$	0.309213	+	0.131039i	0.0177638	+	0.00752797i
$304$	4.19178	−	1.19539i	0.240415	−	0.0685604i
$305$	−3.04468	−	18.5561i	−0.174338	−	1.06252i
$306$	−5.88961	−	1.68132i	−0.336686	−	0.0961145i
$307$	−1.92980	−	0.517089i	−0.110140	−	0.0295118i	0.203328	−	0.979111i	$-0.434824\pi$
$307$	−1.92980	−	0.517089i	−0.110140	−	0.0295118i	−0.313468	+	0.949599i	$0.601491\pi$
$308$	−0.750224	−	2.79987i	−0.0427480	−	0.159538i
$309$	17.6244	+	13.7530i	1.00262	+	0.782380i
$310$	0.724391	+	1.60300i	0.0411427	+	0.0910445i
$311$		−	21.8028i		−	1.23633i	−0.786050	−	0.618163i	$-0.787877\pi$
$311$		−	21.8028i		−	1.23633i	0.786050	−	0.618163i	$-0.212123\pi$
$312$	1.32507	−	3.12677i	0.0750171	−	0.177019i
$313$	1.28624	−	0.344648i	0.0727027	−	0.0194806i	−0.222284	−	0.974982i	$-0.571351\pi$
$313$	1.28624	−	0.344648i	0.0727027	−	0.0194806i	0.294987	+	0.955501i	$0.404685\pi$
$314$	2.15036	−	3.72453i	0.121352	−	0.210187i
$315$	1.20087	+	8.14652i	0.0676611	+	0.459004i
$316$	8.30367			0.467118
$317$	26.5113	−	7.10368i	1.48902	−	0.398982i	0.579616	−	0.814890i	$-0.303203\pi$
$317$	26.5113	−	7.10368i	1.48902	−	0.398982i	0.909407	+	0.415907i	$0.136536\pi$
$318$	3.27980	−	0.404668i	0.183922	−	0.0226927i
$319$	−3.25693	−	1.88039i	−0.182353	−	0.105282i
$320$	1.41683	+	1.72991i	0.0792031	+	0.0967051i
$321$	−2.72930	−	2.12978i	−0.152335	−	0.118873i
$322$	−6.87195	+	6.87195i	−0.382959	+	0.382959i
$323$	−7.77720	−	4.32574i	−0.432735	−	0.240691i
$324$	−8.99523	−	0.292918i	−0.499735	−	0.0162732i
$325$	−0.621715	−	9.78355i	−0.0344865	−	0.542694i
$326$	−2.69605	+	1.55656i	−0.149320	+	0.0862101i
$327$	−10.6884	+	8.06419i	−0.591072	+	0.445951i
$328$	−3.13095	+	11.6849i	−0.172878	+	0.645189i
$329$	6.13351	−	10.6235i	0.338151	−	0.585695i
$330$	7.81014	−	4.75831i	0.429934	−	0.261936i
$331$	11.4618			0.629999			0.314999	−	0.949092i	$-0.397996\pi$
$331$	11.4618			0.629999			0.314999	+	0.949092i	$0.397996\pi$
$332$	10.7936	−	2.89213i	0.592374	−	0.158726i
$333$	11.7754	−	19.6499i	0.645287	−	1.07681i
$334$			0.389261i			0.0212994i
$335$	24.2323	+	17.4011i	1.32395	+	0.950726i
$336$	−2.10563	−	0.294664i	−0.114872	−	0.0160752i
$337$	19.8716	+	5.32458i	1.08248	+	0.290049i	0.755610	−	0.655022i	$-0.227341\pi$
$337$	19.8716	+	5.32458i	1.08248	+	0.290049i	0.326866	+	0.945071i	$0.394007\pi$
$338$	2.36970	+	8.84385i	0.128895	+	0.481042i
$339$	−16.2076	+	20.7699i	−0.880274	+	1.12807i
$340$	0.451986	−	4.54279i	0.0245124	−	0.246368i
$341$			1.85764i			0.100597i
$342$	−12.6302	−	3.38797i	−0.682962	−	0.183200i
$343$	10.8440	+	10.8440i	0.585523	+	0.585523i
$344$	0.369569	+	0.640113i	0.0199258	+	0.0345126i
$345$	−26.9087	−	14.7005i	−1.44872	−	0.791450i
$346$	4.69499	−	8.13196i	0.252404	−	0.437177i
$347$	4.28124	−	15.9778i	0.229829	−	0.857733i	−0.750583	−	0.660776i	$-0.770227\pi$
$347$	4.28124	−	15.9778i	0.229829	−	0.857733i	0.980412	−	0.196957i	$-0.0631059\pi$
$348$	−2.20208	+	1.66142i	−0.118044	+	0.0890616i
$349$		−	6.91186i		−	0.369984i	−0.982740	−	0.184992i	$-0.940774\pi$
$349$		−	6.91186i		−	0.369984i	0.982740	−	0.184992i	$-0.0592259\pi$
$350$	−5.81586	+	1.96133i	−0.310871	+	0.104838i
$351$	−8.23157	+	6.00282i	−0.439369	+	0.320407i
$352$	0.611163	+	2.28089i	0.0325751	+	0.121572i
$353$	−16.2186	+	16.2186i	−0.863229	+	0.863229i	−0.991712	−	0.128483i	$-0.958989\pi$
$353$	−16.2186	+	16.2186i	−0.863229	+	0.863229i	0.128483	+	0.991712i	$0.458989\pi$
$354$	−3.02853	+	1.22568i	−0.160965	+	0.0651442i
$355$	−5.28574	+	14.0016i	−0.280538	+	0.743130i
$356$	5.77534	−	3.33439i	0.306092	−	0.176722i
$357$	2.61441	+	3.46519i	0.138369	+	0.183397i
$358$	−0.626303	+	2.33739i	−0.0331011	+	0.123535i
$359$	10.7713	+	18.6565i	0.568489	+	0.984651i	0.996716	+	0.0809799i	$0.0258050\pi$
$359$	10.7713	+	18.6565i	0.568489	+	0.984651i	−0.428227	+	0.903671i	$0.640862\pi$
$360$	−0.978274	−	6.63649i	−0.0515596	−	0.349774i
$361$	−16.7500	−	8.96863i	−0.881581	−	0.472033i
$362$	−1.44258	−	1.44258i	−0.0758204	−	0.0758204i
$363$	−9.32397	+	1.15041i	−0.489381	+	0.0603809i
$364$	−2.08433	+	1.20339i	−0.109248	+	0.0630746i
$365$	−5.09570	−	11.2763i	−0.266721	−	0.590226i
$366$	−11.4832	−	8.96080i	−0.600238	−	0.468388i
$367$	3.10681	+	11.5948i	0.162174	+	0.605241i	0.998384	+	0.0568318i	$0.0180999\pi$
$367$	3.10681	+	11.5948i	0.162174	+	0.605241i	−0.836210	+	0.548410i	$0.815233\pi$
$368$	5.59817	−	5.59817i	0.291825	−	0.291825i
$369$	26.0760	−	25.2407i	1.35746	−	1.31398i
$370$	15.9743	+	6.03042i	0.830462	+	0.313507i
$371$	−2.02830	−	1.17104i	−0.105304	−	0.0607972i
$372$	1.25457	+	0.531663i	0.0650465	+	0.0275654i
$373$	−6.98139	−	6.98139i	−0.361483	−	0.361483i	0.502876	−	0.864359i	$-0.332275\pi$
$373$	−6.98139	−	6.98139i	−0.361483	−	0.361483i	−0.864359	+	0.502876i	$0.832275\pi$
$374$	2.41050	−	4.17512i	0.124644	−	0.215890i
$375$	−11.1039	−	15.8652i	−0.573403	−	0.819274i
$376$	−4.99661	+	8.65438i	−0.257680	+	0.446316i
$377$	−0.808193	+	3.01622i	−0.0416241	+	0.155343i
$378$	4.96407	+	4.00533i	0.255324	+	0.206012i
$379$			8.88586i			0.456436i	0.973610	+	0.228218i	$0.0732899\pi$
$379$			8.88586i			0.456436i	−0.973610	+	0.228218i	$0.926710\pi$
$380$	0.809681	−	9.71311i	0.0415357	−	0.498272i
$381$	10.2213	+	25.2558i	0.523654	+	1.29390i
$382$	−20.2494	−	5.42581i	−1.03605	−	0.277608i
$383$	16.9509	+	4.54197i	0.866150	+	0.232084i	0.664422	−	0.747358i	$-0.268678\pi$
$383$	16.9509	+	4.54197i	0.866150	+	0.232084i	0.201728	+	0.979442i	$0.435344\pi$
$384$	1.71534	+	0.240045i	0.0875354	+	0.0122498i
$385$	−6.44971	−	0.641716i	−0.328708	−	0.0327049i
$386$	−12.4027	−	7.16073i	−0.631283	−	0.364471i
$387$	0.0360893	−	2.21712i	0.00183452	−	0.112703i
$388$	−9.30639	−	9.30639i	−0.472460	−	0.472460i
$389$	1.99002	−	3.44681i	0.100898	−	0.174760i	−0.811157	−	0.584829i	$-0.801162\pi$
$389$	1.99002	−	3.44681i	0.100898	−	0.174760i	0.912055	+	0.410068i	$0.134495\pi$
$390$	−5.49465	−	5.24132i	−0.278233	−	0.265404i
$391$	−16.1636			−0.817429
$392$	−3.88425	−	3.88425i	−0.196184	−	0.196184i
$393$	−8.69107	+	6.55722i	−0.438407	+	0.330768i
$394$	−5.93309	+	3.42547i	−0.298905	+	0.172573i
$395$	6.55770	−	17.3710i	0.329954	−	0.874029i
$396$	1.94461	−	6.81193i	0.0977205	−	0.342312i
$397$	28.5357	+	7.64611i	1.43217	+	0.383748i	0.889783	−	0.456384i	$-0.150856\pi$
$397$	28.5357	+	7.64611i	1.43217	+	0.383748i	0.542382	+	0.840132i	$0.317522\pi$
$398$	0.546075	−	0.546075i	0.0273723	−	0.0273723i
$399$	5.69945	+	7.30796i	0.285329	+	0.365855i
$400$	4.73784	−	1.59778i	0.236892	−	0.0798890i
$401$	33.2265	−	19.1833i	1.65925	−	0.957970i	0.686192	−	0.727420i	$-0.259281\pi$
$401$	33.2265	−	19.1833i	1.65925	−	0.957970i	0.973061	−	0.230550i	$-0.0740524\pi$
$402$	22.9346	−	2.82972i	1.14387	−	0.141134i
$403$	1.48986	−	0.399207i	0.0742153	−	0.0198859i
$404$	0.0969467	+	0.167917i	0.00482328	+	0.00835417i
$405$	−7.71663	+	18.5864i	−0.383442	+	0.923565i
$406$	1.95502			0.0970260
$407$	12.7501	+	12.7501i	0.631997	+	0.631997i
$408$	−2.12980	−	2.82289i	−0.105441	−	0.139754i
$409$	−4.45657	−	2.57300i	−0.220363	−	0.127227i	0.385755	−	0.922601i	$-0.373941\pi$
$409$	−4.45657	−	2.57300i	−0.220363	−	0.127227i	−0.606119	+	0.795374i	$0.707274\pi$
$410$	21.9717	+	15.7778i	1.08511	+	0.779210i
$411$	32.6975	−	13.2331i	1.61285	−	0.652738i
$412$	3.34055	+	12.4671i	0.164577	+	0.614210i
$413$	2.23659	+	0.599293i	0.110056	+	0.0294893i
$414$	−23.0387	+	5.77302i	−1.13229	+	0.283728i
$415$	2.47383	−	24.8638i	0.121436	−	1.22052i
$416$	1.69798	−	0.980328i	0.0832502	−	0.0480645i
$417$	5.74085	+	2.43286i	0.281131	+	0.119138i
$418$	5.00316	−	8.99512i	0.244713	−	0.439966i
$419$	2.33966			0.114300			0.0571499	−	0.998366i	$-0.481799\pi$
$419$	2.33966			0.114300			0.0571499	+	0.998366i	$0.481799\pi$
$420$	−2.27932	+	4.17221i	−0.111219	+	0.203583i
$421$	−8.45359	−	14.6420i	−0.412003	−	0.713610i	0.583106	−	0.812396i	$-0.301837\pi$
$421$	−8.45359	−	14.6420i	−0.412003	−	0.713610i	−0.995109	+	0.0987865i	$0.968504\pi$
$422$	−3.53109	+	0.946152i	−0.171891	+	0.0460580i
$423$	26.2037	−	14.5653i	1.27407	−	0.708188i
$424$	1.65233	+	0.953975i	0.0802444	+	0.0463291i
$425$	−9.14642	−	4.53314i	−0.443666	−	0.219890i
$426$	4.34903	+	10.7460i	0.210711	+	0.520646i
$427$	2.67178	+	9.97123i	0.129297	+	0.482542i
$428$	−0.517316	−	1.93065i	−0.0250054	−	0.0933214i
$429$	−3.00836	−	7.43336i	−0.145245	−	0.358886i
$430$	1.63096	−	0.267607i	0.0786517	−	0.0129051i
$431$	26.0164	+	15.0206i	1.25317	+	0.723517i	0.971737	−	0.236065i	$-0.0758579\pi$
$431$	26.0164	+	15.0206i	1.25317	+	0.723517i	0.281430	+	0.959582i	$0.409191\pi$
$432$	−4.04394	−	3.26291i	−0.194564	−	0.156987i
$433$	22.4286	−	6.00972i	1.07785	−	0.288809i	0.324134	−	0.946011i	$-0.394927\pi$
$433$	22.4286	−	6.00972i	1.07785	−	0.288809i	0.753714	+	0.657202i	$0.228260\pi$
$434$	−0.482841	−	0.836305i	−0.0231771	−	0.0401439i
$435$	1.73657	+	5.91877i	0.0832624	+	0.283783i
$436$	−7.73033			−0.370216
$437$	−34.5050	+	0.552181i	−1.65060	+	0.0264144i
$438$	−8.82523	−	3.73996i	−0.421686	−	0.178702i
$439$	15.2807	−	8.82229i	0.729306	−	0.421065i	−0.0888624	−	0.996044i	$-0.528323\pi$
$439$	15.2807	−	8.82229i	0.729306	−	0.421065i	0.818168	+	0.574979i	$0.194990\pi$
$440$	5.25420	+	0.522768i	0.250484	+	0.0249220i
$441$	4.00557	+	15.9853i	0.190741	+	0.761203i
$442$	−3.86654	−	1.03604i	−0.183912	−	0.0492792i
$443$	4.87575	+	18.1966i	0.231654	+	0.864545i	0.979629	+	0.200817i	$0.0643598\pi$
$443$	4.87575	+	18.1966i	0.231654	+	0.864545i	−0.747975	+	0.663727i	$0.768974\pi$
$444$	12.2600	−	4.96174i	0.581832	−	0.235474i
$445$	−2.41445	−	14.7151i	−0.114456	−	0.697562i
$446$	4.15406	+	2.39835i	0.196701	+	0.113565i
$447$	−16.1175	−	21.3625i	−0.762333	−	1.01041i
$448$	−0.867998	−	0.867998i	−0.0410091	−	0.0410091i
$449$	−24.3408			−1.14871			−0.574357	−	0.818605i	$-0.694748\pi$
$449$	−24.3408			−1.14871			−0.574357	+	0.818605i	$0.694748\pi$
$450$	−14.6559	−	3.19455i	−0.690885	−	0.150593i
$451$	14.2827	+	24.7384i	0.672547	+	1.16489i
$452$	−14.6922	+	3.93676i	−0.691062	+	0.185170i
$453$	21.6069	−	2.66591i	1.01518	−	0.125255i
$454$	22.1063	−	12.7631i	1.03750	−	0.599001i
$455$	0.871377	+	5.31070i	0.0408508	+	0.248969i
$456$	−4.64301	−	5.95336i	−0.217429	−	0.278792i
$457$	10.5377	−	10.5377i	0.492935	−	0.492935i	−0.416295	−	0.909230i	$-0.636672\pi$
$457$	10.5377	−	10.5377i	0.492935	−	0.492935i	0.909230	+	0.416295i	$0.136672\pi$
$458$	6.22966	+	1.66923i	0.291093	+	0.0779981i
$459$	1.12753	+	10.5485i	0.0526286	+	0.492363i
$460$	−7.29011	−	16.1323i	−0.339903	−	0.752170i
$461$	11.4957	−	6.63706i	0.535409	−	0.309119i	−0.207807	−	0.978170i	$-0.566633\pi$
$461$	11.4957	−	6.63706i	0.535409	−	0.309119i	0.743216	+	0.669051i	$0.233299\pi$
$462$	−4.00785	+	3.02383i	−0.186462	+	0.140681i
$463$	6.07381	+	6.07381i	0.282274	+	0.282274i	0.834015	−	0.551741i	$-0.186036\pi$
$463$	6.07381	+	6.07381i	0.282274	+	0.282274i	−0.551741	+	0.834015i	$0.686036\pi$
$464$	−1.59264			−0.0739364
$465$	2.10300	−	2.20465i	0.0975243	−	0.102238i
$466$	−3.74648	+	6.48909i	−0.173552	+	0.300601i
$467$	19.1091	+	19.1091i	0.884266	+	0.884266i	0.993965	−	0.109699i	$-0.0349887\pi$
$467$	19.1091	+	19.1091i	0.884266	+	0.884266i	−0.109699	+	0.993965i	$0.534989\pi$
$468$	−5.88119	−	0.0957313i	−0.271858	−	0.00442518i
$469$	−14.1833	−	8.18871i	−0.654922	−	0.378119i
$470$	14.1587	+	17.2874i	0.653090	+	0.797408i
$471$	−7.37717	−	1.03237i	−0.339922	−	0.0475689i
$472$	−1.82202	−	0.488209i	−0.0838653	−	0.0224716i
$473$	1.68590	+	0.451734i	0.0775175	+	0.0207708i
$474$	−5.39558	−	13.3319i	−0.247827	−	0.612356i
$475$	−19.6800	−	9.36460i	−0.902982	−	0.429678i
$476$			2.50617i			0.114870i
$477$	−2.78087	−	5.00292i	−0.127327	−	0.229068i
$478$	4.00313	−	14.9399i	0.183099	−	0.683335i
$479$	−21.2533	+	36.8118i	−0.971087	+	1.68197i	−0.278800	+	0.960349i	$0.589937\pi$
$479$	−21.2533	+	36.8118i	−0.971087	+	1.68197i	−0.692287	+	0.721623i	$0.743397\pi$
$480$	1.85683	−	3.39885i	0.0847522	−	0.155136i
$481$	7.48579	−	12.9658i	0.341323	−	0.591188i
$482$	12.6262	+	12.6262i	0.575109	+	0.575109i
$483$	15.4985	+	6.56797i	0.705207	+	0.298853i
$484$	−4.69733	−	2.71201i	−0.213515	−	0.123273i
$485$	−26.8182	+	12.1191i	−1.21775	+	0.550298i
$486$	5.37465	+	14.6326i	0.243799	+	0.663748i
$487$	−18.0297	+	18.0297i	−0.817005	+	0.817005i	−0.985673	−	0.168668i	$-0.946054\pi$
$487$	−18.0297	+	18.0297i	−0.817005	+	0.817005i	0.168668	+	0.985673i	$0.446054\pi$
$488$	−2.17654	−	8.12298i	−0.0985275	−	0.367710i
$489$	4.25098	+	3.31720i	0.192236	+	0.150009i
$490$	−11.1932	+	5.05819i	−0.505659	+	0.228506i
$491$	−22.4012	+	12.9333i	−1.01095	+	0.583672i	−0.911470	−	0.411367i	$-0.865051\pi$
$491$	−22.4012	+	12.9333i	−1.01095	+	0.583672i	−0.0994805	+	0.995040i	$0.531718\pi$
$492$	20.7951	−	2.56574i	0.937513	−	0.115672i
$493$	2.29921	+	2.29921i	0.103551	+	0.103551i
$494$	−8.28943	−	2.07957i	−0.372959	−	0.0935645i
$495$	−12.7146	−	9.44768i	−0.571478	−	0.424642i
$496$	0.393342	+	0.681289i	0.0176616	+	0.0305908i
$497$	2.12645	−	7.93601i	0.0953841	−	0.355978i
$498$	−11.6569	−	15.4503i	−0.522360	−	0.692346i
$499$	−34.9516	+	20.1793i	−1.56465	+	0.903350i	−0.567872	+	0.823117i	$0.692233\pi$
$499$	−34.9516	+	20.1793i	−1.56465	+	0.903350i	−0.996776	+	0.0802332i	$0.974433\pi$
$500$	0.399135	−	11.1732i	0.0178498	−	0.499681i
$501$	0.624977	−	0.252935i	0.0279219	−	0.0113003i
$502$	−3.57534	+	3.57534i	−0.159575	+	0.159575i
$503$	3.40075	+	12.6918i	0.151632	+	0.565899i	0.999370	+	0.0354838i	$0.0112972\pi$
$503$	3.40075	+	12.6918i	0.151632	+	0.565899i	−0.847738	+	0.530415i	$0.822036\pi$
$504$	0.895108	+	3.57216i	0.0398713	+	0.159117i
$505$	0.427838	−	0.0701995i	0.0190385	−	0.00312384i
$506$		−	18.6949i		−	0.831088i
$507$	12.6594	−	9.55125i	0.562225	−	0.424186i
$508$	−4.07132	+	15.1944i	−0.180636	+	0.674141i
$509$	13.3964	−	23.2032i	0.593785	−	1.02847i	−0.399932	−	0.916545i	$-0.630966\pi$
$509$	13.3964	−	23.2032i	0.593785	−	1.02847i	0.993717	−	0.111921i	$-0.0357004\pi$
$510$	−7.58736	+	2.22614i	−0.335974	+	0.0985753i
$511$	3.39652	+	5.88295i	0.150253	+	0.260246i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.76734	+	22.4798i	0.122181	+	0.992508i
$514$			18.2253i			0.803883i
$515$	28.7189	+	2.85739i	1.26551	+	0.125912i
$516$	0.787592	−	1.00930i	0.0346718	−	0.0444318i
$517$	6.10748	+	22.7934i	0.268607	+	1.00245i
$518$	−9.05407	−	2.42603i	−0.397813	−	0.106594i
$519$	−16.1070	−	2.25402i	−0.707018	−	0.0989405i
$520$	−0.709859	−	4.32631i	−0.0311294	−	0.189721i
$521$			14.7508i			0.646243i	0.946357	+	0.323122i	$0.104732\pi$
$521$			14.7508i			0.646243i	−0.946357	+	0.323122i	$0.895268\pi$
$522$	4.09837	+	2.45599i	0.179381	+	0.107496i
$523$	31.4316	−	8.42208i	1.37441	−	0.368272i	0.505322	−	0.862931i	$-0.331374\pi$
$523$	31.4316	−	8.42208i	1.37441	−	0.368272i	0.869087	+	0.494659i	$0.164707\pi$
$524$	−6.28575			−0.274594
$525$	6.92805	+	8.06320i	0.302365	+	0.351907i
$526$	−15.7965	+	27.3603i	−0.688759	+	1.19297i
$527$	0.415694	−	1.55139i	0.0181079	−	0.0675797i
$528$	3.26496	−	2.46334i	0.142089	−	0.107203i
$529$	−34.3631	+	19.8395i	−1.49405	+	0.862588i
$530$	3.30059	−	2.70324i	0.143368	−	0.117421i
$531$	3.93578	+	4.06603i	0.170798	+	0.176451i
$532$	0.0856159	+	5.35001i	0.00371192	+	0.231953i
$533$	16.7713	−	16.7713i	0.726446	−	0.726446i
$534$	−9.10624	−	7.10595i	−0.394066	−	0.307504i
$535$	−4.44739	−	0.442494i	−0.192277	−	0.0191307i
$536$	11.5543	+	6.67086i	0.499068	+	0.288137i
$537$	4.15976	−	0.513240i	0.179507	−	0.0221479i
$538$	−16.9899	+	4.55242i	−0.732485	+	0.196269i
$539$	−12.9713			−0.558713
$540$	−10.0195	+	5.88294i	−0.431172	+	0.253161i
$541$	12.3716	−	21.4282i	0.531896	−	0.921270i	−0.467411	−	0.884040i	$-0.654813\pi$
$541$	12.3716	−	21.4282i	0.531896	−	0.921270i	0.999307	−	0.0372301i	$-0.0118534\pi$
$542$	−9.62367	+	2.57866i	−0.413372	+	0.110763i
$543$	−1.37877	+	3.25350i	−0.0591686	+	0.139621i
$544$		−	2.04163i		−	0.0875342i
$545$	−6.10491	+	16.1716i	−0.261506	+	0.692715i
$546$	3.28645	+	2.56455i	0.140647	+	0.109752i
$547$	1.88165	+	7.02240i	0.0804534	+	0.300256i	0.994414	−	0.105546i	$-0.0336589\pi$
$547$	1.88165	+	7.02240i	0.0804534	+	0.300256i	−0.913961	+	0.405802i	$0.866992\pi$
$548$	19.6714	+	5.27094i	0.840321	+	0.225163i
$549$	−6.92538	+	24.2594i	−0.295568	+	1.03537i
$550$	5.24304	−	10.5788i	0.223564	−	0.451080i
$551$	4.98676	+	4.82967i	0.212443	+	0.205751i
$552$	−12.6257	−	5.35053i	−0.537387	−	0.227734i
$553$	−2.63815	+	9.84572i	−0.112186	+	0.418683i
$554$	15.0317	+	26.0356i	0.638635	+	1.10615i
$555$	−0.697670	−	29.5659i	−0.0296144	−	1.25500i
$556$	1.79991	+	3.11754i	0.0763333	+	0.132213i
$557$	−19.2009	+	5.14486i	−0.813568	+	0.217995i	−0.641532	−	0.767096i	$-0.721701\pi$
$557$	−19.2009	+	5.14486i	−0.813568	+	0.217995i	−0.172035	+	0.985091i	$0.555034\pi$
$558$	0.0384108	−	2.35974i	0.00162606	−	0.0998958i
$559$		−	1.44920i		−	0.0612945i
$560$	−2.50131	+	1.13033i	−0.105700	+	0.0477653i
$561$	−8.26965	−	1.15726i	−0.349145	−	0.0488596i
$562$	−7.89389	+	7.89389i	−0.332984	+	0.332984i
$563$	−27.2681	+	27.2681i	−1.14921	+	1.14921i	−0.162505	+	0.986708i	$0.551957\pi$
$563$	−27.2681	+	27.2681i	−1.14921	+	1.14921i	−0.986708	+	0.162505i	$0.948043\pi$
$564$	17.1417	+	2.39882i	0.721797	+	0.101009i
$565$	−3.36737	+	33.8445i	−0.141666	+	1.42385i
$566$	18.6151	+	10.7474i	0.782451	+	0.451748i
$567$	3.20518	−	10.5726i	0.134605	−	0.444010i
$568$	−1.73229	+	6.46500i	−0.0726853	+	0.271265i
$569$	8.66956			0.363447			0.181723	−	0.983350i	$-0.441832\pi$
$569$	8.66956			0.363447			0.181723	+	0.983350i	$0.441832\pi$
$570$	−16.1210	+	5.01143i	−0.675233	+	0.209906i
$571$	25.5080			1.06748			0.533738	−	0.845650i	$-0.320787\pi$
$571$	25.5080			1.06748			0.533738	+	0.845650i	$0.320787\pi$
$572$	1.19828	−	4.47204i	0.0501026	−	0.186986i
$573$	4.44631	+	36.0369i	0.185747	+	1.50546i
$574$	−12.8601	−	7.42479i	−0.536770	−	0.309905i
$575$	−39.5054	+	2.51045i	−1.64749	+	0.104693i
$576$	−0.729192	−	2.91003i	−0.0303830	−	0.121251i
$577$	−22.5765	+	22.5765i	−0.939872	+	0.939872i	−0.998292	−	0.0584197i	$-0.981394\pi$
$577$	−22.5765	+	22.5765i	−0.939872	+	0.939872i	0.0584197	+	0.998292i	$0.481394\pi$
$578$	9.07342	−	9.07342i	0.377404	−	0.377404i
$579$	−3.43780	+	24.5661i	−0.142870	+	1.02093i
$580$	−1.25776	+	3.33175i	−0.0522258	+	0.138343i
$581$			13.7169i			0.569072i
$582$	−8.89472	+	20.9890i	−0.368698	+	0.870021i
$583$	4.35183	−	1.16607i	0.180234	−	0.0482936i
$584$	−2.76695	−	4.79249i	−0.114497	−	0.198315i
$585$	−4.84485	+	12.2276i	−0.200310	+	0.505551i
$586$	5.04779	+	8.74303i	0.208522	+	0.361171i
$587$	2.53325	−	9.45422i	0.104558	−	0.390218i	−0.893736	−	0.448593i	$-0.851925\pi$
$587$	2.53325	−	9.45422i	0.104558	−	0.390218i	0.998295	+	0.0583753i	$0.0185920\pi$
$588$	−3.71243	+	8.76027i	−0.153098	+	0.361267i
$589$	0.834398	−	3.32601i	0.0343808	−	0.137046i
$590$	−2.46023	+	3.42605i	−0.101286	+	0.141048i
$591$	9.35498	+	7.30005i	0.384812	+	0.300284i
$592$	7.37581	+	1.97634i	0.303144	+	0.0812272i
$593$	−5.02244	−	18.7440i	−0.206247	−	0.769724i	−0.989066	−	0.147474i	$-0.952886\pi$
$593$	−5.02244	−	18.7440i	−0.206247	−	0.769724i	0.782819	−	0.622249i	$-0.213781\pi$
$594$	−12.2004	+	1.30410i	−0.500590	+	0.0535080i
$595$	5.24282	+	1.97921i	0.214935	+	0.0811398i
$596$		−	15.4503i		−	0.632867i
$597$	−1.23158	−	0.521919i	−0.0504052	−	0.0213607i
$598$	−14.9936	+	4.01753i	−0.613135	+	0.164289i
$599$	−3.11272	+	5.39139i	−0.127182	+	0.220286i	−0.922584	−	0.385796i	$-0.873927\pi$
$599$	−3.11272	+	5.39139i	−0.127182	+	0.220286i	0.795401	+	0.606083i	$0.207260\pi$
$600$	−5.64388	−	6.56861i	−0.230410	−	0.268162i
$601$	45.4911			1.85562			0.927811	−	0.373051i	$-0.121688\pi$
$601$	45.4911			1.85562			0.927811	+	0.373051i	$0.121688\pi$
$602$	−0.876402	+	0.234831i	−0.0357195	+	0.00957101i
$603$	−19.4458	−	34.9839i	−0.791893	−	1.42465i
$604$	10.8854	+	6.28468i	0.442920	+	0.255720i
$605$	−9.38307	+	7.68489i	−0.381476	+	0.312435i
$606$	0.206604	−	0.264762i	0.00839271	−	0.0107552i
$607$	−24.3262	+	24.3262i	−0.987369	+	0.987369i	−0.999921	−	0.0125524i	$-0.996004\pi$
$607$	−24.3262	+	24.3262i	−0.987369	+	0.987369i	0.0125524	+	0.999921i	$0.496004\pi$
$608$	−0.0697462	−	4.35834i	−0.00282858	−	0.176754i
$609$	−1.27034	−	3.13888i	−0.0514767	−	0.127194i
$610$	−18.7119	−	1.86174i	−0.757622	−	0.0753798i
$611$	16.9683	−	9.79663i	0.686462	−	0.396329i
$612$	−3.14837	+	5.25377i	−0.127265	+	0.212371i
$613$	8.57274	−	31.9939i	0.346250	−	1.29222i	−0.544896	−	0.838504i	$-0.683431\pi$
$613$	8.57274	−	31.9939i	0.346250	−	1.29222i	0.891145	−	0.453718i	$-0.149903\pi$
$614$	−0.998940	+	1.73021i	−0.0403139	+	0.0698258i
$615$	11.0552	−	45.5288i	0.445787	−	1.83590i
$616$	−2.89864			−0.116790
$617$	−28.4968	+	7.63568i	−1.14724	+	0.307401i	−0.781857	−	0.623458i	$-0.785727\pi$
$617$	−28.4968	+	7.63568i	−1.14724	+	0.307401i	−0.365379	+	0.930859i	$0.619061\pi$
$618$	17.8459	−	13.4643i	0.717867	−	0.541614i
$619$		−	21.4960i		−	0.863995i	−0.901875	−	0.431998i	$-0.857809\pi$
$619$		−	21.4960i		−	0.863995i	0.901875	−	0.431998i	$-0.142191\pi$
$620$	1.73587	−	0.284821i	0.0697142	−	0.0114387i
$621$	24.2390	+	33.2386i	0.972679	+	1.33382i
$622$	−21.0599	−	5.64299i	−0.844426	−	0.226263i
$623$	2.11874	+	7.90723i	0.0848853	+	0.316796i
$624$	−2.67728	−	2.08918i	−0.107177	−	0.0836343i
$625$	−23.0588	−	9.65885i	−0.922351	−	0.386354i
$626$		−	1.33162i		−	0.0532221i
$627$	−17.6931	−	2.18794i	−0.706592	−	0.0873778i
$628$	−3.04106	−	3.04106i	−0.121352	−	0.121352i
$629$	−7.79495	−	13.5012i	−0.310805	−	0.538330i
$630$	8.17974	+	0.948528i	0.325889	+	0.0377902i
$631$	23.6744	−	41.0053i	0.942463	−	1.63239i	0.181710	−	0.983352i	$-0.441837\pi$
$631$	23.6744	−	41.0053i	0.942463	−	1.63239i	0.760753	−	0.649042i	$-0.224830\pi$
$632$	2.14915	−	8.02073i	0.0854885	−	0.319047i
$633$	3.81353	+	5.05454i	0.151574	+	0.200900i
$634$		−	27.4465i		−	1.09004i
$635$	28.5708	+	20.5166i	1.13380	+	0.814176i
$636$	0.457995	−	3.27278i	0.0181607	−	0.129774i
$637$	2.78753	+	10.4032i	0.110446	+	0.412190i
$638$	−2.65927	+	2.65927i	−0.105282	+	0.105282i
$639$	14.4273	−	13.9652i	0.570736	−	0.552453i
$640$	2.03767	−	0.920816i	0.0805460	−	0.0363984i
$641$	15.5004	−	8.94915i	0.612228	−	0.353470i	−0.161609	−	0.986855i	$-0.551668\pi$
$641$	15.5004	−	8.94915i	0.612228	−	0.353470i	0.773837	+	0.633385i	$0.218335\pi$
$642$	−2.76360	+	2.08508i	−0.109071	+	0.0822914i
$643$	−12.3844	+	46.2193i	−0.488394	+	1.82271i	0.0758695	+	0.997118i	$0.475827\pi$
$643$	−12.3844	+	46.2193i	−0.488394	+	1.82271i	−0.564264	+	0.825595i	$0.690840\pi$
$644$	4.85920	+	8.41639i	0.191479	+	0.331652i
$645$	−1.48942	−	2.44469i	−0.0586459	−	0.0962596i
$646$	−6.19123	+	6.39261i	−0.243591	+	0.251514i
$647$	−6.35365	−	6.35365i	−0.249788	−	0.249788i	0.571096	−	0.820883i	$-0.306518\pi$
$647$	−6.35365	−	6.35365i	−0.249788	−	0.249788i	−0.820883	+	0.571096i	$0.806518\pi$
$648$	−2.61107	+	8.61291i	−0.102573	+	0.338347i
$649$	−3.85745	+	2.22710i	−0.151418	+	0.0874214i
$650$	−9.61109	−	1.93164i	−0.376978	−	0.0757651i
$651$	−1.02899	+	1.31864i	−0.0403291	+	0.0516816i
$652$	0.805737	+	3.00705i	0.0315551	+	0.117765i
$653$	−17.8662	+	17.8662i	−0.699158	+	0.699158i	−0.964229	−	0.265071i	$-0.914605\pi$
$653$	−17.8662	+	17.8662i	−0.699158	+	0.699158i	0.265071	+	0.964229i	$0.414605\pi$
$654$	5.02304	+	12.4114i	0.196416	+	0.485325i
$655$	−4.96408	+	13.1496i	−0.193962	+	0.513796i
$656$	10.4764	+	6.04853i	0.409033	+	0.236156i
$657$	−0.270199	+	16.5995i	−0.0105415	+	0.647608i
$658$	−8.67409	−	8.67409i	−0.338151	−	0.338151i
$659$	8.50138	−	14.7248i	0.331167	−	0.573598i	−0.651574	−	0.758585i	$-0.725891\pi$
$659$	8.50138	−	14.7248i	0.331167	−	0.573598i	0.982741	+	0.184987i	$0.0592244\pi$
$660$	−2.57476	−	8.77556i	−0.100222	−	0.341588i
$661$	12.5516	−	21.7401i	0.488202	−	0.845591i	−0.511706	−	0.859161i	$-0.670986\pi$
$661$	12.5516	−	21.7401i	0.488202	−	0.845591i	0.999908	+	0.0135699i	$0.00431957\pi$
$662$	2.96654	−	11.0713i	0.115298	−	0.430297i
$663$	0.849005	+	6.88111i	0.0329726	+	0.267240i
$664$		−	11.1743i		−	0.433648i
$665$	11.2597	+	4.04599i	0.436631	+	0.156897i
$666$	−15.9326	−	16.4599i	−0.617377	−	0.637808i
$667$	12.1793	+	3.26343i	0.471584	+	0.126361i
$668$	0.375997	+	0.100748i	0.0145478	+	0.00389806i
$669$	1.15143	−	8.22795i	0.0445167	−	0.318111i
$670$	23.0800	−	18.9029i	0.891658	−	0.730283i
$671$	−17.1974	−	9.92892i	−0.663898	−	0.383302i
$672$	−0.829602	+	1.95762i	−0.0320026	+	0.0755169i
$673$	33.6526	+	33.6526i	1.29721	+	1.29721i	0.930226	+	0.366988i	$0.119611\pi$
$673$	33.6526	+	33.6526i	1.29721	+	1.29721i	0.366988	+	0.930226i	$0.380389\pi$
$674$	10.2863	−	17.8164i	0.396214	−	0.686262i
$675$	4.39413	+	25.6065i	0.169130	+	0.985594i
$676$	9.15583			0.352147
$677$	−7.29937	−	7.29937i	−0.280537	−	0.280537i	0.552786	−	0.833323i	$-0.313565\pi$
$677$	−7.29937	−	7.29937i	−0.280537	−	0.280537i	−0.833323	+	0.552786i	$0.813565\pi$
$678$	15.8674	+	21.0310i	0.609383	+	0.807689i
$679$	13.9914	−	8.07793i	0.536940	−	0.310002i
$680$	−4.27102	−	1.61235i	−0.163786	−	0.0618307i
$681$	−34.8560	−	27.1995i	−1.33569	−	1.04229i
$682$	1.79434	+	0.480792i	0.0687089	+	0.0184105i
$683$	−12.8602	+	12.8602i	−0.492081	+	0.492081i	−0.908961	−	0.416880i	$-0.863123\pi$
$683$	−12.8602	+	12.8602i	−0.492081	+	0.492081i	0.416880	+	0.908961i	$0.363123\pi$
$684$	−6.54146	+	11.3230i	−0.250119	+	0.432944i
$685$	26.5618	−	36.9893i	1.01488	−	1.41329i
$686$	13.2812	−	7.66789i	0.507078	−	0.292761i
$687$	−1.36789	−	11.0867i	−0.0521884	−	0.422982i
$688$	0.713953	−	0.191303i	0.0272192	−	0.00729337i
$689$	−1.87042	−	3.23966i	−0.0712572	−	0.123421i
$690$	−21.1641	+	22.1871i	−0.805704	+	0.844648i
$691$	−3.08076			−0.117198			−0.0585989	−	0.998282i	$-0.518663\pi$
$691$	−3.08076			−0.117198			−0.0585989	+	0.998282i	$0.518663\pi$
$692$	−6.63972	−	6.63972i	−0.252404	−	0.252404i
$693$	7.45913	+	4.46995i	0.283349	+	0.169800i
$694$	−14.3253	−	8.27071i	−0.543781	−	0.313952i
$695$	7.94324	−	1.30332i	0.301304	−	0.0494379i
$696$	1.03487	+	2.55706i	0.0392266	+	0.0969250i
$697$	−6.39225	−	23.8562i	−0.242124	−	0.903617i
$698$	−6.67635	−	1.78892i	−0.252704	−	0.0677117i
$699$	12.8529	+	1.79865i	0.486143	+	0.0680312i
$700$	0.389245	+	6.12532i	0.0147121	+	0.231515i
$701$	−8.42794	+	4.86588i	−0.318319	+	0.183782i	−0.650643	−	0.759384i	$-0.725501\pi$
$701$	−8.42794	+	4.86588i	−0.318319	+	0.183782i	0.332324	+	0.943165i	$0.392167\pi$
$702$	3.66779	+	9.50473i	0.138432	+	0.358733i
$703$	−17.1014	−	28.5553i	−0.644991	−	1.07698i
$704$	2.36135			0.0889968
$705$	18.5557	−	33.9655i	0.698847	−	1.27921i
$706$	11.4683	+	19.8636i	0.431614	+	0.747578i
$707$	−0.229901	+	0.0616018i	−0.00864631	+	0.00231677i
$708$	0.400075	+	3.24257i	0.0150357	+	0.121863i
$709$	5.34691	+	3.08704i	0.200807	+	0.115936i	0.597032	−	0.802217i	$-0.296347\pi$
$709$	5.34691	+	3.08704i	0.200807	+	0.115936i	−0.396225	+	0.918154i	$0.629680\pi$
$710$	12.1565	+	8.72952i	0.456225	+	0.327613i
$711$	−17.8991	+	17.3257i	−0.671268	+	0.649765i
$712$	−1.72601	−	6.44155i	−0.0646849	−	0.241407i
$713$	−1.61197	−	6.01597i	−0.0603689	−	0.225300i
$714$	4.02378	−	1.62847i	0.150586	−	0.0609438i
$715$	−8.40904	−	6.03849i	−0.314480	−	0.225827i
$716$	2.09565	+	1.20992i	0.0783181	+	0.0452170i
$717$	−26.5879	+	3.28047i	−0.992942	+	0.122511i
$718$	20.8086	−	5.57565i	0.776570	−	0.208081i
$719$	0.857044	+	1.48444i	0.0319623	+	0.0553604i	0.881564	−	0.472064i	$-0.156491\pi$
$719$	0.857044	+	1.48444i	0.0319623	+	0.0553604i	−0.849602	+	0.527425i	$0.823158\pi$
$720$	−6.66355	−	0.772710i	−0.248336	−	0.0287972i
$721$	−15.8437			−0.590049
$722$	−12.9983	+	13.8580i	−0.483745	+	0.515743i
$723$	12.0677	−	28.4763i	0.448803	−	1.05905i
$724$	−1.76680	+	1.02006i	−0.0656624	+	0.0379102i
$725$	5.97660	+	5.26239i	0.221965	+	0.195440i
$726$	−1.30201	+	9.30401i	−0.0483221	+	0.345304i
$727$	37.1669	+	9.95883i	1.37844	+	0.369353i	0.870555	−	0.492071i	$-0.163760\pi$
$727$	37.1669	+	9.95883i	1.37844	+	0.369353i	0.507887	+	0.861424i	$0.330427\pi$
$728$	0.622919	+	2.32476i	0.0230869	+	0.0861615i
$729$	20.0010	−	18.1373i	0.740777	−	0.671751i
$730$	−12.2109	+	2.00356i	−0.451945	+	0.0741550i
$731$	−1.30687	−	0.754524i	−0.0483365	−	0.0279071i
$732$	−11.6275	+	8.77272i	−0.429766	+	0.324249i
$733$	−27.8884	−	27.8884i	−1.03008	−	1.03008i	−0.999533	−	0.0305469i	$-0.990275\pi$
$733$	−27.8884	−	27.8884i	−1.03008	−	1.03008i	−0.0305469	−	0.999533i	$-0.509725\pi$
$734$	12.0038			0.443067
$735$	15.3943	+	14.6846i	0.567829	+	0.541648i
$736$	−3.95851	−	6.85633i	−0.145912	−	0.252728i
$737$	30.4310	−	8.15396i	1.12094	−	0.300355i
$738$	−17.6317	−	31.7203i	−0.649031	−	1.16764i
$739$	27.9606	−	16.1431i	1.02855	−	0.593833i	0.111980	−	0.993710i	$-0.464281\pi$
$739$	27.9606	−	16.1431i	1.02855	−	0.593833i	0.916569	+	0.399878i	$0.130947\pi$
$740$	9.95938	−	13.8692i	0.366114	−	0.509840i
$741$	2.04747	+	14.6603i	0.0752159	+	0.538561i
$742$	−1.65610	+	1.65610i	−0.0607972	+	0.0607972i
$743$	−18.8424	−	5.04881i	−0.691262	−	0.185223i	−0.103948	−	0.994583i	$-0.533148\pi$
$743$	−18.8424	−	5.04881i	−0.691262	−	0.185223i	−0.587313	+	0.809360i	$0.699814\pi$
$744$	0.838254	−	1.07422i	0.0307319	−	0.0393828i
$745$	−32.3214	−	12.2016i	−1.18416	−	0.447032i
$746$	−8.55042	+	4.93659i	−0.313053	+	0.180741i
$747$	−17.2318	+	28.7551i	−0.630478	+	1.05209i
$748$	−3.40897	−	3.40897i	−0.124644	−	0.124644i
$749$	2.45354			0.0896504
$750$	−18.1985	+	6.61933i	−0.664514	+	0.241704i
$751$	−23.8760	+	41.3545i	−0.871248	+	1.50905i	−0.0105424	+	0.999944i	$0.503356\pi$
$751$	−23.8760	+	41.3545i	−0.871248	+	1.50905i	−0.860706	+	0.509102i	$0.829978\pi$
$752$	7.06627	+	7.06627i	0.257680	+	0.257680i
$753$	8.06356	+	3.41718i	0.293853	+	0.124529i
$754$	2.70427	+	1.56131i	0.0984836	+	0.0568595i
$755$	21.7439	−	17.8086i	0.791341	−	0.648122i
$756$	5.15365	−	3.75827i	0.187436	−	0.136687i
$757$	−49.6884	−	13.3140i	−1.80595	−	0.483904i	−0.811072	−	0.584946i	$-0.801116\pi$
$757$	−49.6884	−	13.3140i	−1.80595	−	0.483904i	−0.994882	+	0.101042i	$0.967782\pi$
$758$	8.58308	+	2.29983i	0.311752	+	0.0835336i
$759$	−30.0155	+	12.1476i	−1.08949	+	0.440930i
$760$	−9.17258	−	3.29603i	−0.332724	−	0.119560i
$761$			2.47955i			0.0898836i	0.998990	+	0.0449418i	$0.0143102\pi$
$761$			2.47955i			0.0898836i	−0.998990	+	0.0449418i	$0.985690\pi$
$762$	27.0407	−	3.33634i	0.979583	−	0.120863i
$763$	2.45600	−	9.16591i	0.0889131	−	0.331828i
$764$	−10.4819	+	18.1551i	−0.379220	+	0.656828i
$765$	8.50432	+	10.7354i	0.307474	+	0.388138i
$766$	8.77442	−	15.1977i	0.317033	−	0.549117i
$767$	2.61515	+	2.61515i	0.0944274	+	0.0944274i
$768$	0.675828	−	1.59476i	0.0243868	−	0.0575459i
$769$	12.0282	+	6.94451i	0.433749	+	0.250425i	0.700943	−	0.713218i	$-0.252763\pi$
$769$	12.0282	+	6.94451i	0.433749	+	0.250425i	−0.267193	+	0.963643i	$0.586096\pi$
$770$	−2.28916	+	6.06386i	−0.0824956	+	0.218526i
$771$	29.2616	−	11.8425i	1.05383	−	0.426496i
$772$	−10.1268	+	10.1268i	−0.364471	+	0.364471i
$773$	−10.5176	−	39.2522i	−0.378291	−	1.41180i	−0.848476	−	0.529234i	$-0.822479\pi$
$773$	−10.5176	−	39.2522i	−0.378291	−	1.41180i	0.470185	−	0.882568i	$-0.344187\pi$
$774$	−2.13224	−	0.608693i	−0.0766416	−	0.0218790i
$775$	0.775041	−	3.85631i	0.0278403	−	0.138523i
$776$	−11.3980	+	6.58061i	−0.409163	+	0.236230i
$777$	1.98807	+	16.1131i	0.0713216	+	0.578055i
$778$	−2.81431	−	2.81431i	−0.100898	−	0.100898i
$779$	−14.4607	−	50.7083i	−0.518109	−	1.81681i
$780$	−6.48484	+	3.95088i	−0.232195	+	0.141464i
$781$	7.90233	+	13.6872i	0.282768	+	0.489768i
$782$	−4.18345	+	15.6128i	−0.149600	+	0.558314i
$783$	1.28015	−	8.17598i	0.0457490	−	0.292186i
$784$	−4.75722	+	2.74658i	−0.169901	+	0.0980921i
$785$	−8.76343	+	3.96016i	−0.312780	+	0.141344i
$786$	4.08437	+	10.0921i	0.145685	+	0.359972i
$787$	3.97421	−	3.97421i	0.141665	−	0.141665i	−0.632717	−	0.774383i	$-0.718061\pi$
$787$	3.97421	−	3.97421i	0.141665	−	0.141665i	0.774383	+	0.632717i	$0.218061\pi$
$788$	1.77315	+	6.61750i	0.0631660	+	0.235739i
$789$	54.1925	+	7.58374i	1.92931	+	0.269988i
$790$	−15.0818	−	10.8302i	−0.536587	−	0.385321i
$791$		−	18.6714i		−	0.663878i
$792$	−6.07651	−	3.64141i	−0.215919	−	0.129392i
$793$	−4.26746	+	15.9264i	−0.151542	+	0.565562i
$794$	14.7712	−	25.5844i	0.524209	−	0.907956i
$795$	−6.48484	−	3.54274i	−0.229994	−	0.125648i
$796$	−0.386133	−	0.668802i	−0.0136861	−	0.0237051i
$797$	−22.4735	−	22.4735i	−0.796051	−	0.796051i	0.186420	−	0.982470i	$-0.440312\pi$
$797$	−22.4735	−	22.4735i	−0.796051	−	0.796051i	−0.982470	+	0.186420i	$0.940312\pi$
$798$	8.53407	−	3.61381i	0.302103	−	0.127927i
$799$		−	20.4024i		−	0.721787i
$800$	−0.317095	−	4.98993i	−0.0112110	−	0.176421i
$801$	−5.49186	+	19.2378i	−0.194045	+	0.679735i
$802$	−9.93002	−	37.0594i	−0.350641	−	1.30861i
$803$	−12.6222	−	3.38211i	−0.445428	−	0.119352i
$804$	3.20261	−	22.8855i	0.112948	−	0.807110i
$805$	21.4443	−	3.51857i	0.755811	−	0.124013i
$806$		−	1.54242i		−	0.0543294i
$807$	18.3488	+	24.3199i	0.645910	+	0.856103i
$808$	0.187287	−	0.0501833i	0.00658872	−	0.00176544i
$809$	18.6603			0.656061			0.328030	−	0.944667i	$-0.393615\pi$
$809$	18.6603			0.656061			0.328030	+	0.944667i	$0.393615\pi$
$810$	15.9559	+	12.2642i	0.560632	+	0.430920i
$811$	18.5750	−	32.1728i	0.652255	−	1.12974i	−0.330319	−	0.943869i	$-0.607156\pi$
$811$	18.5750	−	32.1728i	0.652255	−	1.12974i	0.982574	−	0.185870i	$-0.0595102\pi$
$812$	0.505996	−	1.88840i	0.0177570	−	0.0662700i
$813$	10.3935	+	13.7757i	0.364514	+	0.483135i
$814$	15.6156	−	9.01565i	0.547325	−	0.315998i
$815$	6.92696	+	0.689200i	0.242641	+	0.0241416i
$816$	−3.27793	+	1.32662i	−0.114751	+	0.0464408i
$817$	−2.81561	−	1.56606i	−0.0985056	−	0.0547896i
$818$	−3.63878	+	3.63878i	−0.127227	+	0.127227i
$819$	1.98202	−	6.94296i	0.0692573	−	0.242607i
$820$	20.9269	−	17.1395i	0.730798	−	0.598536i
$821$	44.4304	+	25.6519i	1.55063	+	0.895258i	0.998090	+	0.0617728i	$0.0196754\pi$
$821$	44.4304	+	25.6519i	1.55063	+	0.895258i	0.552542	+	0.833485i	$0.313658\pi$
$822$	−4.31940	−	35.0084i	−0.150656	−	1.22106i
$823$	40.4211	−	10.8308i	1.40899	−	0.377538i	0.527426	−	0.849601i	$-0.323157\pi$
$823$	40.4211	−	10.8308i	1.40899	−	0.377538i	0.881565	+	0.472063i	$0.156490\pi$
$824$	12.9069			0.449633
$825$	−20.3915	−	1.54405i	−0.709942	−	0.0537571i
$826$	1.15775	−	2.00527i	0.0402831	−	0.0697724i
$827$	−36.8917	+	9.88510i	−1.28285	+	0.343738i	−0.834940	−	0.550341i	$-0.814498\pi$
$827$	−36.8917	+	9.88510i	−1.28285	+	0.343738i	−0.447909	+	0.894079i	$0.647831\pi$
$828$	−0.386557	+	23.7479i	−0.0134338	+	0.825296i
$829$			15.7241i			0.546122i	0.961997	+	0.273061i	$0.0880361\pi$
$829$			15.7241i			0.546122i	−0.961997	+	0.273061i	$0.911964\pi$
$830$	−23.3763	−	8.82476i	−0.811404	−	0.306312i
$831$	32.0341	−	41.0516i	1.11125	−	1.42406i
$832$	−0.507455	−	1.89385i	−0.0175928	−	0.0656574i
$833$	10.8329	+	2.90266i	0.375336	+	0.100571i
$834$	3.83580	−	4.91557i	0.132823	−	0.170212i
$835$	0.507700	−	0.707009i	0.0175697	−	0.0244670i
$836$	−7.39370	−	7.16079i	−0.255717	−	0.247661i
$837$	−3.81363	+	1.47165i	−0.131818	+	0.0508676i
$838$	0.605548	−	2.25994i	0.0209183	−	0.0780682i
$839$	−21.2535	−	36.8121i	−0.733751	−	1.27089i	−0.955269	−	0.295738i	$-0.904435\pi$
$839$	−21.2535	−	36.8121i	−0.733751	−	1.27089i	0.221518	−	0.975156i	$-0.428899\pi$
$840$	3.44011	+	3.28150i	0.118695	+	0.113223i
$841$	13.2318	+	22.9181i	0.456267	+	0.790278i
$842$	−16.3311	+	4.37590i	−0.562806	+	0.150803i
$843$	17.8033	+	7.54470i	0.613179	+	0.259853i
$844$			3.65565i			0.125833i
$845$	7.23068	−	19.1537i	0.248743	−	0.658906i
$846$	−7.28697	−	29.0806i	−0.250531	−	0.999810i
$847$	4.70803	−	4.70803i	0.161770	−	0.161770i
$848$	1.34912	−	1.34912i	0.0463291	−	0.0463291i
$849$	5.15974	−	36.8709i	0.177082	−	1.26541i
$850$	−6.74595	+	7.66150i	−0.231384	+	0.262787i
$851$	−52.3550	−	30.2272i	−1.79471	−	1.03617i
$852$	11.5055	−	1.41957i	0.394171	−	0.0486336i
$853$	0.499015	−	1.86235i	0.0170859	−	0.0637656i	−0.956857	−	0.290561i	$-0.906158\pi$
$853$	0.499015	−	1.86235i	0.0170859	−	0.0637656i	0.973942	+	0.226795i	$0.0728248\pi$
$854$	10.3230			0.353245
$855$	18.5212	+	22.6266i	0.633412	+	0.773815i
$856$	−1.99875			−0.0683160
$857$	−7.94044	+	29.6341i	−0.271240	+	1.01228i	0.687079	+	0.726583i	$0.258893\pi$
$857$	−7.94044	+	29.6341i	−0.271240	+	1.01228i	−0.958319	+	0.285700i	$0.907774\pi$
$858$	−7.95870	+	0.981961i	−0.271706	+	0.0335236i
$859$	36.3807	+	21.0044i	1.24129	+	0.716661i	0.969358	−	0.245654i	$-0.0790027\pi$
$859$	36.3807	+	21.0044i	1.24129	+	0.716661i	0.271936	+	0.962315i	$0.412336\pi$
$860$	0.163634	−	1.64464i	0.00557988	−	0.0560819i
$861$	−3.56457	+	25.4720i	−0.121480	+	0.868084i
$862$	21.2423	−	21.2423i	0.723517	−	0.723517i
$863$	−22.1606	+	22.1606i	−0.754357	+	0.754357i	−0.975289	−	0.220933i	$-0.929090\pi$
$863$	−22.1606	+	22.1606i	−0.754357	+	0.754357i	0.220933	+	0.975289i	$0.429090\pi$
$864$	−4.19838	+	3.06164i	−0.142832	+	0.104159i
$865$	−19.1337	+	8.64644i	−0.650565	+	0.293988i
$866$		−	23.2198i		−	0.789040i
$867$	−20.4635	−	8.67205i	−0.694978	−	0.294518i
$868$	−0.932777	+	0.249937i	−0.0316605	+	0.00848341i
$869$	−9.80394	−	16.9809i	−0.332576	−	0.576038i
$870$	6.16655	−	0.145513i	0.209066	−	0.00493335i
$871$	−13.0793	−	22.6539i	−0.443174	−	0.767599i
$872$	−2.00076	+	7.46693i	−0.0677542	+	0.252862i
$873$	39.4784	+	0.642612i	1.33614	+	0.0217491i
$874$	−8.39719	+	33.4722i	−0.284039	+	1.13221i
$875$	13.1214	+	4.02309i	0.443583	+	0.136005i
$876$	−5.89666	+	7.55655i	−0.199230	+	0.255312i
$877$	−17.3710	−	4.65454i	−0.586576	−	0.157173i	−0.0466882	−	0.998910i	$-0.514867\pi$
$877$	−17.3710	−	4.65454i	−0.586576	−	0.157173i	−0.539888	+	0.841737i	$0.681533\pi$
$878$	−4.56675	−	17.0434i	−0.154120	−	0.575185i
$879$	10.7574	−	13.7855i	0.362837	−	0.464974i
$880$	1.86484	−	4.93987i	0.0628638	−	0.166523i
$881$			34.9729i			1.17827i	0.808035	+	0.589134i	$0.200531\pi$
$881$			34.9729i			1.17827i	−0.808035	+	0.589134i	$0.799469\pi$
$882$	16.4773	+	0.268210i	0.554819	+	0.00903110i
$883$	−8.05541	+	2.15844i	−0.271086	+	0.0726374i	−0.391801	−	0.920050i	$-0.628148\pi$
$883$	−8.05541	+	2.15844i	−0.271086	+	0.0726374i	0.120715	+	0.992687i	$0.461481\pi$
$884$	−2.00147	+	3.46664i	−0.0673166	+	0.116596i
$885$	7.09929	+	1.72383i	0.238640	+	0.0579458i
$886$	18.8385			0.632891
$887$	32.0804	−	8.59591i	1.07715	−	0.288622i	0.323724	−	0.946152i	$-0.395065\pi$
$887$	32.0804	−	8.59591i	1.07715	−	0.288622i	0.753429	+	0.657529i	$0.228398\pi$
$888$	−1.61956	−	13.1264i	−0.0543490	−	0.440493i
$889$	−16.7226	−	9.65478i	−0.560857	−	0.323811i
$890$	−14.8386	−	1.47637i	−0.497391	−	0.0494880i
$891$	10.0214	+	18.7410i	0.335731	+	0.627848i
$892$	3.39178	−	3.39178i	0.113565	−	0.113565i
$893$	−0.696989	−	43.5538i	−0.0233238	−	1.45747i
$894$	−24.8061	+	10.0393i	−0.829640	+	0.335765i
$895$	4.18613	−	3.42851i	0.139927	−	0.114602i
$896$	−1.06308	+	0.613767i	−0.0355149	+	0.0205045i
$897$	16.1929	+	21.4624i	0.540666	+	0.716610i
$898$	−6.29986	+	23.5114i	−0.210229	+	0.784586i
$899$	−0.626452	+	1.08505i	−0.0208934	+	0.0361883i
$900$	−6.87892	+	13.3297i	−0.229297	+	0.444323i
$901$	−3.89533			−0.129772
$902$	27.5921	−	7.39328i	0.918716	−	0.246169i
$903$	0.946504	+	1.25452i	0.0314977	+	0.0417477i
$904$			15.2105i			0.505893i
$905$	0.738629	+	4.50165i	0.0245529	+	0.149640i
$906$	3.01721	−	21.5607i	0.100240	−	0.716305i
$907$	40.0341	+	10.7271i	1.32931	+	0.356187i	0.852458	−	0.522796i	$-0.175111\pi$
$907$	40.0341	+	10.7271i	1.32931	+	0.356187i	0.476852	+	0.878984i	$0.341778\pi$
$908$	−6.60665	−	24.6564i	−0.219250	−	0.818250i
$909$	−0.559335	−	0.159675i	−0.0185520	−	0.00529607i
$910$	5.35527	+	0.532824i	0.177525	+	0.0176629i
$911$			54.2849i			1.79854i	0.437396	+	0.899269i	$0.355901\pi$
$911$			54.2849i			1.79854i	−0.437396	+	0.899269i	$0.644099\pi$
$912$	−6.95220	+	2.94396i	−0.230210	+	0.0974841i
$913$	−18.6581	−	18.6581i	−0.617493	−	0.617493i
$914$	−7.45131	−	12.9060i	−0.246467	−	0.426894i
$915$	9.16954	+	31.2525i	0.303136	+	1.03318i
$916$	3.22471	−	5.58536i	0.106547	−	0.184546i
$917$	1.99704	−	7.45306i	0.0659481	−	0.246122i
$918$	10.4809	+	1.64105i	0.345922	+	0.0541627i
$919$		−	27.7373i		−	0.914970i	−0.889217	−	0.457485i	$-0.848750\pi$
$919$		−	27.7373i		−	0.914970i	0.889217	−	0.457485i	$-0.151250\pi$
$920$	−17.4694	+	2.86637i	−0.575948	+	0.0945014i
$921$	3.42703	+	0.479582i	0.112925	+	0.0158027i
$922$	−3.43559	−	12.8218i	−0.113145	−	0.422264i
$923$	9.27921	−	9.27921i	0.305429	−	0.305429i
$924$	1.88349	+	4.65391i	0.0619622	+	0.153102i
$925$	−21.1485	−	31.7876i	−0.695359	−	1.04517i
$926$	7.43887	−	4.29484i	0.244457	−	0.141137i
$927$	−33.2136	−	19.9035i	−1.09088	−	0.653718i
$928$	−0.412205	+	1.53837i	−0.0135313	+	0.0504995i
$929$	1.73605	+	3.00693i	0.0569580	+	0.0986541i	0.893098	−	0.449861i	$-0.148527\pi$
$929$	1.73605	+	3.00693i	0.0569580	+	0.0986541i	−0.836140	+	0.548515i	$0.815193\pi$
$930$	−1.58523	−	2.60195i	−0.0519818	−	0.0853212i
$931$	23.2244	+	5.82633i	0.761151	+	0.190950i
$932$	5.29832	+	5.29832i	0.173552	+	0.173552i
$933$	4.62429	+	37.4794i	0.151392	+	1.22702i
$934$	23.4038	−	13.5122i	0.765797	−	0.442133i
$935$	−9.82362	+	4.43926i	−0.321267	+	0.145179i
$936$	−1.61463	+	5.65602i	−0.0527759	+	0.184873i
$937$	−6.72511	−	25.0985i	−0.219700	−	0.819931i	−0.984459	−	0.175615i	$-0.943809\pi$
$937$	−6.72511	−	25.0985i	−0.219700	−	0.819931i	0.764759	−	0.644316i	$-0.222858\pi$
$938$	−11.5806	+	11.5806i	−0.378119	+	0.378119i
$939$	−2.13797	+	0.865261i	−0.0697701	+	0.0282367i
$940$	20.3629	−	9.20191i	0.664164	−	0.300133i
$941$	−37.9497	−	21.9102i	−1.23712	−	0.714254i	−0.268618	−	0.963247i	$-0.586567\pi$
$941$	−37.9497	−	21.9102i	−1.23712	−	0.714254i	−0.968505	+	0.248993i	$0.919900\pi$
$942$	−2.90654	+	6.85860i	−0.0947002	+	0.223465i
$943$	−67.7215	−	67.7215i	−2.20531	−	2.20531i
$944$	−0.943147	+	1.63358i	−0.0306968	+	0.0531684i
$945$	−3.79215	−	13.7493i	−0.123359	−	0.447265i
$946$	0.872684	−	1.51153i	0.0283734	−	0.0491442i
$947$	−1.94456	+	7.25718i	−0.0631896	+	0.235827i	−0.990297	−	0.138970i	$-0.955621\pi$
$947$	−1.94456	+	7.25718i	−0.0631896	+	0.235827i	0.927107	+	0.374797i	$0.122288\pi$
$948$	−14.2741	+	1.76117i	−0.463602	+	0.0572002i
$949$			10.8501i			0.352208i
$950$	−14.1391	+	16.5857i	−0.458732	+	0.538112i
$951$	−44.0667	+	17.8343i	−1.42896	+	0.578316i
$952$	2.42078	+	0.648645i	0.0784578	+	0.0210227i
$953$	5.26882	+	1.41178i	0.170674	+	0.0457319i	0.343144	−	0.939283i	$-0.388508\pi$
$953$	5.26882	+	1.41178i	0.170674	+	0.0457319i	−0.172470	+	0.985015i	$0.555175\pi$
$954$	−5.55220	+	1.39126i	−0.179759	+	0.0450438i
$955$	29.7020	+	36.2654i	0.961133	+	1.17352i
$956$	−13.3947	−	7.73346i	−0.433217	−	0.250118i
$957$	5.99754	+	2.54164i	0.193873	+	0.0821596i
$958$	30.0567	+	30.0567i	0.971087	+	0.971087i
$959$	−12.4996	+	21.6499i	−0.403633	+	0.699112i
$960$	−2.80246	−	2.67325i	−0.0904489	−	0.0862786i
$961$	−30.3811			−0.980036
$962$	−10.5865	−	10.5865i	−0.341323	−	0.341323i
$963$	5.14343	+	3.08225i	0.165745	+	0.0993241i
$964$	15.4639	−	8.92809i	0.498059	−	0.287555i
$965$	13.1874	+	29.1824i	0.424518	+	0.939415i
$966$	10.3555	−	13.2705i	0.333182	−	0.426971i
$967$	23.7851	+	6.37320i	0.764877	+	0.204948i	0.620107	−	0.784517i	$-0.287089\pi$
$967$	23.7851	+	6.37320i	0.764877	+	0.204948i	0.144770	+	0.989465i	$0.453756\pi$
$968$	−3.83536	+	3.83536i	−0.123273	+	0.123273i
$969$	14.2866	+	5.78651i	0.458951	+	0.185889i
$970$	4.76505	+	29.0411i	0.152996	+	0.932452i
$971$	−25.2791	+	14.5949i	−0.811244	+	0.468372i	−0.847388	−	0.530974i	$-0.821826\pi$
$971$	−25.2791	+	14.5949i	−0.811244	+	0.468372i	0.0361435	+	0.999347i	$0.488493\pi$
$972$	15.5251	−	1.40432i	0.497967	−	0.0450436i
$973$	−4.26834	+	1.14370i	−0.136837	+	0.0366653i
$974$	12.7489	+	22.0818i	0.408503	+	0.707547i
$975$	3.14379	+	16.6862i	0.100682	+	0.534386i
$976$	−8.40952			−0.269182
$977$	4.67807	+	4.67807i	0.149665	+	0.149665i	0.777968	−	0.628304i	$-0.216250\pi$
$977$	4.67807	+	4.67807i	0.149665	+	0.149665i	−0.628304	+	0.777968i	$0.716250\pi$
$978$	4.30441	−	3.24758i	0.137640	−	0.103846i
$979$	−13.6376	−	7.87368i	−0.435860	−	0.251644i
$980$	1.98881	+	12.1210i	0.0635302	+	0.387191i
$981$	16.6632	−	16.1294i	0.532016	−	0.514974i
$982$	6.69478	+	24.9852i	0.213639	+	0.797311i
$983$	17.7153	+	4.74680i	0.565030	+	0.151399i	0.530016	−	0.847987i	$-0.322186\pi$
$983$	17.7153	+	4.74680i	0.565030	+	0.151399i	0.0350138	+	0.999387i	$0.488852\pi$
$984$	2.90384	−	20.7505i	0.0925712	−	0.661503i
$985$	15.2439	+	1.51670i	0.485711	+	0.0483260i
$986$	2.81595	−	1.62579i	0.0896781	−	0.0517757i
$987$	−8.29039	+	19.5629i	−0.263886	+	0.622695i
$988$	−4.15418	+	7.46874i	−0.132162	+	0.237612i
$989$	−5.85177			−0.186075
$990$	−12.4165	+	9.83611i	−0.394623	+	0.312612i
$991$	−5.78732	−	10.0239i	−0.183840	−	0.318421i	0.759345	−	0.650688i	$-0.225520\pi$
$991$	−5.78732	−	10.0239i	−0.183840	−	0.318421i	−0.943185	+	0.332268i	$0.892186\pi$
$992$	0.759879	−	0.203609i	0.0241262	−	0.00646459i
$993$	−19.7031	+	2.43100i	−0.625257	+	0.0771456i
$994$	−7.11523	−	4.10798i	−0.225681	−	0.130297i
$995$	−1.70405	+	0.279601i	−0.0540222	+	0.00886394i
$996$	−17.9409	+	7.26089i	−0.568480	+	0.230070i
$997$	−0.218803	−	0.816584i	−0.00692956	−	0.0258615i	0.962374	−	0.271727i	$-0.0875946\pi$
$997$	−0.218803	−	0.816584i	−0.00692956	−	0.0258615i	−0.969304	+	0.245865i	$0.920928\pi$
$998$	10.4456	+	38.9834i	0.330649	+	1.23400i
$999$	−16.0744	+	36.2759i	−0.508571	+	1.14772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.v.c.83.19	yes	144
3.2	odd	2	inner	570.2.v.c.83.15	✓	144
5.2	odd	4	inner	570.2.v.c.197.28	yes	144
15.2	even	4	inner	570.2.v.c.197.14	yes	144
19.11	even	3	inner	570.2.v.c.353.14	yes	144
57.11	odd	6	inner	570.2.v.c.353.28	yes	144
95.87	odd	12	inner	570.2.v.c.467.15	yes	144
285.182	even	12	inner	570.2.v.c.467.19	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.v.c.83.15	✓	144	3.2	odd	2	inner
570.2.v.c.83.19	yes	144	1.1	even	1	trivial
570.2.v.c.197.14	yes	144	15.2	even	4	inner
570.2.v.c.197.28	yes	144	5.2	odd	4	inner
570.2.v.c.353.14	yes	144	19.11	even	3	inner
570.2.v.c.353.28	yes	144	57.11	odd	6	inner
570.2.v.c.467.15	yes	144	95.87	odd	12	inner
570.2.v.c.467.19	yes	144	285.182	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.71902 + 0.212096i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.72991 + 1.41683i) q^{5} +(-0.240045 + 1.71534i) q^{6} +(0.867998 - 0.867998i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91003 - 0.729192i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.71902 + 0.212096i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.72991 + 1.41683i) q^{5} +(-0.240045 + 1.71534i) q^{6} +(0.867998 - 0.867998i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91003 - 0.729192i) q^{9} +(0.920816 + 2.03767i) q^{10} +2.36135i q^{11} +(1.59476 + 0.675828i) q^{12} +(1.89385 - 0.507455i) q^{13} +(-0.613767 - 1.06308i) q^{14} +(2.67325 - 2.80246i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.528413 - 1.97206i) q^{17} +(0.0488262 - 2.99960i) q^{18} +(1.06065 - 4.22789i) q^{19} +(2.20656 - 0.362052i) q^{20} +(-1.30800 + 1.67620i) q^{21} +(2.28089 + 0.611163i) q^{22} +(-2.04907 - 7.64725i) q^{23} +(1.06555 - 1.36550i) q^{24} +(0.985200 - 4.90198i) q^{25} -1.96066i q^{26} +(-4.84773 + 1.87070i) q^{27} +(-1.18571 + 0.317709i) q^{28} +(-0.796320 + 1.37927i) q^{29} +(-2.01508 - 3.30749i) q^{30} +0.786684 q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.500833 - 4.05920i) q^{33} +(-1.76810 - 1.02081i) q^{34} +(-0.271758 + 2.73136i) q^{35} +(-2.88476 - 0.823517i) q^{36} +(5.39947 - 5.39947i) q^{37} +(-3.80931 - 2.11877i) q^{38} +(-3.14793 + 1.27400i) q^{39} +(0.221385 - 2.22508i) q^{40} +(10.4764 - 6.04853i) q^{41} +(1.28055 + 1.69727i) q^{42} +(0.191303 - 0.713953i) q^{43} +(1.18068 - 2.04499i) q^{44} +(-4.00096 + 5.38445i) q^{45} -7.91701 q^{46} +(9.65271 - 2.58643i) q^{47} +(-1.04319 - 1.38266i) q^{48} +5.49316i q^{49} +(-4.47996 - 2.22036i) q^{50} +(-0.490084 + 3.50208i) q^{51} +(-1.89385 - 0.507455i) q^{52} +(-0.493814 - 1.84294i) q^{53} +(0.552270 + 5.16672i) q^{54} +(-3.34563 - 4.08493i) q^{55} +1.22753i q^{56} +(-0.926561 + 7.49276i) q^{57} +(1.12617 + 1.12617i) q^{58} +(0.943147 + 1.63358i) q^{59} +(-3.71633 + 1.09038i) q^{60} +(-4.20476 + 7.28286i) q^{61} +(0.203609 - 0.759879i) q^{62} +(1.89296 - 3.15884i) q^{63} -1.00000i q^{64} +(-2.55722 + 3.56111i) q^{65} +(-4.05051 - 0.566832i) q^{66} +(-3.45309 - 12.8871i) q^{67} +(-1.44365 + 1.44365i) q^{68} +(5.14434 + 12.7111i) q^{69} +(2.56796 + 0.969427i) q^{70} +(5.79636 - 3.34653i) q^{71} +(-1.54209 + 2.57332i) q^{72} +(-1.43228 + 5.34533i) q^{73} +(-3.81800 - 6.61297i) q^{74} +(-0.653886 + 8.63553i) q^{75} +(-3.03249 + 3.13113i) q^{76} +(2.04965 + 2.04965i) q^{77} +(0.415847 + 3.37040i) q^{78} +(-7.19119 + 4.15183i) q^{79} +(-2.09197 - 0.789735i) q^{80} +(7.93656 - 4.24394i) q^{81} +(-3.13095 - 11.6849i) q^{82} +(-7.90145 + 7.90145i) q^{83} +(1.97086 - 0.797631i) q^{84} +(1.87997 + 4.16017i) q^{85} +(-0.640113 - 0.369569i) q^{86} +(1.07635 - 2.53988i) q^{87} +(-1.66973 - 1.66973i) q^{88} +(-3.33439 + 5.77534i) q^{89} +(4.16545 + 5.25823i) q^{90} +(1.20339 - 2.08433i) q^{91} +(-2.04907 + 7.64725i) q^{92} +(-1.35232 + 0.166852i) q^{93} -9.99322i q^{94} +(4.15535 + 8.81664i) q^{95} +(-1.60555 + 0.649783i) q^{96} +(12.7128 + 3.40638i) q^{97} +(5.30598 + 1.42173i) q^{98} +(1.72188 + 6.87161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) \) 144 * q - 4 * q^3 + 8 * q^6	\( 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) \) 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Introduction

L-functions

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