LMFDB - Embedded newform 570.2.v.c.83.15

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			83.15
Character	$\chi$	$=$	570.83
Dual form			570.2.v.c.467.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.38266 + 1.04319i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.72991 - 1.41683i) q^{5} +(-1.36550 + 1.06555i) q^{6} +(0.867998 - 0.867998i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.823517 + 2.88476i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.38266 + 1.04319i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.72991 - 1.41683i) q^{5} +(-1.36550 + 1.06555i) q^{6} +(0.867998 - 0.867998i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.823517 + 2.88476i) q^{9} +(0.920816 + 2.03767i) q^{10} -2.36135i q^{11} +(-0.675828 - 1.59476i) q^{12} +(1.89385 - 0.507455i) q^{13} +(0.613767 + 1.06308i) q^{14} +(3.86991 - 0.154371i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.528413 + 1.97206i) q^{17} +(-2.99960 + 0.0488262i) q^{18} +(1.06065 - 4.22789i) q^{19} +(-2.20656 + 0.362052i) q^{20} +(2.10563 - 0.294664i) q^{21} +(2.28089 + 0.611163i) q^{22} +(2.04907 + 7.64725i) q^{23} +(1.71534 - 0.240045i) q^{24} +(0.985200 - 4.90198i) q^{25} +1.96066i q^{26} +(-1.87070 + 4.84773i) q^{27} +(-1.18571 + 0.317709i) q^{28} +(0.796320 - 1.37927i) q^{29} +(-0.852495 + 3.77800i) q^{30} +0.786684 q^{31} +(-0.965926 + 0.258819i) q^{32} +(2.46334 - 3.26496i) q^{33} +(-1.76810 - 1.02081i) q^{34} +(0.271758 - 2.73136i) q^{35} +(0.729192 - 2.91003i) 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} +(-0.260355 + 2.11015i) q^{42} +(0.191303 - 0.713953i) q^{43} +(-1.18068 + 2.04499i) q^{44} +(5.51181 + 3.82360i) q^{45} -7.91701 q^{46} +(-9.65271 + 2.58643i) q^{47} +(-0.212096 + 1.71902i) q^{48} +5.49316i q^{49} +(4.47996 + 2.22036i) q^{50} +(-2.78785 + 2.17547i) q^{51} +(-1.89385 - 0.507455i) q^{52} +(0.493814 + 1.84294i) q^{53} +(-4.19838 - 3.06164i) q^{54} +(-3.34563 - 4.08493i) q^{55} -1.22753i q^{56} +(5.87701 - 4.73928i) q^{57} +(1.12617 + 1.12617i) q^{58} +(-0.943147 - 1.63358i) q^{59} +(-3.42862 - 1.80126i) q^{60} +(-4.20476 + 7.28286i) q^{61} +(-0.203609 + 0.759879i) q^{62} +(3.21877 + 1.78915i) q^{63} -1.00000i q^{64} +(2.55722 - 3.56111i) q^{65} +(2.51615 + 3.22443i) 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} +(2.62215 + 1.45752i) q^{72} +(-1.43228 + 5.34533i) q^{73} +(3.81800 + 6.61297i) q^{74} +(6.47588 - 5.75004i) q^{75} +(-3.03249 + 3.13113i) q^{76} +(-2.04965 - 2.04965i) q^{77} +(-2.04533 + 2.71093i) q^{78} +(-7.19119 + 4.15183i) q^{79} +(2.09197 + 0.789735i) q^{80} +(-7.64364 + 4.75129i) 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} +(2.53988 - 1.07635i) q^{87} +(-1.66973 - 1.66973i) q^{88} +(3.33439 - 5.77534i) q^{89} +(-5.11987 + 4.33438i) q^{90} +(1.20339 - 2.08433i) q^{91} +(2.04907 - 7.64725i) q^{92} +(1.08772 + 0.820660i) 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} +(6.81193 - 1.94461i) 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
$3$	1.38266	+	1.04319i	0.798281	+	0.602285i
$3$	1.38266	+	1.04319i	0.798281	+	0.602285i
$4$	−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
$6$	−1.36550	+	1.06555i	−0.557464	+	0.435010i
$7$	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
$9$	0.823517	+	2.88476i	0.274506	+	0.961586i
$10$	0.920816	+	2.03767i	0.291188	+	0.644368i
$11$		−	2.36135i		−	0.711975i	−0.934491	−	0.355987i	$-0.884145\pi$
$11$		−	2.36135i		−	0.711975i	0.934491	−	0.355987i	$-0.115855\pi$
$12$	−0.675828	−	1.59476i	−0.195095	−	0.460367i
$13$	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
$15$	3.86991	−	0.154371i	0.999205	−	0.0398583i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.528413	+	1.97206i	−0.128159	+	0.478296i	−0.999933	−	0.0116133i	$-0.996303\pi$
$17$	−0.528413	+	1.97206i	−0.128159	+	0.478296i	0.871774	+	0.489909i	$0.162970\pi$
$18$	−2.99960	+	0.0488262i	−0.707013	+	0.0115084i
$19$	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
$21$	2.10563	−	0.294664i	0.459487	−	0.0643009i
$22$	2.28089	+	0.611163i	0.486288	+	0.130300i
$23$	2.04907	+	7.64725i	0.427261	+	1.59456i	0.758935	+	0.651167i	$0.225720\pi$
$23$	2.04907	+	7.64725i	0.427261	+	1.59456i	−0.331673	+	0.943394i	$0.607613\pi$
$24$	1.71534	−	0.240045i	0.350142	−	0.0489990i
$25$	0.985200	−	4.90198i	0.197040	−	0.980395i
$26$			1.96066i			0.384516i
$27$	−1.87070	+	4.84773i	−0.360016	+	0.932946i
$28$	−1.18571	+	0.317709i	−0.224078	+	0.0600414i
$29$	0.796320	−	1.37927i	0.147873	−	0.256123i	−0.782568	−	0.622565i	$-0.786091\pi$
$29$	0.796320	−	1.37927i	0.147873	−	0.256123i	0.930441	+	0.366442i	$0.119424\pi$
$30$	−0.852495	+	3.77800i	−0.155644	+	0.689765i
$31$	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
$33$	2.46334	−	3.26496i	0.428812	−	0.568356i
$34$	−1.76810	−	1.02081i	−0.303227	−	0.175068i
$35$	0.271758	−	2.73136i	0.0459355	−	0.461685i
$36$	0.729192	−	2.91003i	0.121532	−	0.485005i
$37$	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	$0.726905\pi$
$41$	−10.4764	+	6.04853i	−1.63613	+	0.944622i	−0.982147	+	0.188117i	$0.939762\pi$
$42$	−0.260355	+	2.11015i	−0.0401736	+	0.325603i
$43$	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
$45$	5.51181	+	3.82360i	0.821653	+	0.569988i
$46$	−7.91701			−1.16730
$47$	−9.65271	+	2.58643i	−1.40799	+	0.377270i	−0.881208	−	0.472729i	$-0.843269\pi$
$47$	−9.65271	+	2.58643i	−1.40799	+	0.377270i	−0.526784	+	0.849999i	$0.676602\pi$
$48$	−0.212096	+	1.71902i	−0.0306134	+	0.248119i
$49$			5.49316i			0.784737i
$50$	4.47996	+	2.22036i	0.633562	+	0.314006i
$51$	−2.78785	+	2.17547i	−0.390377	+	0.304626i
$52$	−1.89385	−	0.507455i	−0.262630	−	0.0703714i
$53$	0.493814	+	1.84294i	0.0678306	+	0.253147i	0.991512	−	0.130014i	$-0.0415022\pi$
$53$	0.493814	+	1.84294i	0.0678306	+	0.253147i	−0.923682	+	0.383161i	$0.874835\pi$
$54$	−4.19838	−	3.06164i	−0.571327	−	0.416636i
$55$	−3.34563	−	4.08493i	−0.451125	−	0.550813i
$56$		−	1.22753i		−	0.164036i
$57$	5.87701	−	4.73928i	0.778428	−	0.627733i
$58$	1.12617	+	1.12617i	0.147873	+	0.147873i
$59$	−0.943147	−	1.63358i	−0.122787	−	0.212674i	0.798079	−	0.602553i	$-0.205850\pi$
$59$	−0.943147	−	1.63358i	−0.122787	−	0.212674i	−0.920866	+	0.389880i	$0.872517\pi$
$60$	−3.42862	−	1.80126i	−0.442633	−	0.232542i
$61$	−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
$63$	3.21877	+	1.78915i	0.405527	+	0.225412i
$64$		−	1.00000i		−	0.125000i
$65$	2.55722	−	3.56111i	0.317184	−	0.441701i
$66$	2.51615	+	3.22443i	0.309716	+	0.396900i
$67$	−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	−0.802825	−	0.596214i	$-0.796671\pi$
$71$	−5.79636	+	3.34653i	−0.687901	+	0.397160i	0.114924	+	0.993374i	$0.463337\pi$
$72$	2.62215	+	1.45752i	0.309023	+	0.171770i
$73$	−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
$75$	6.47588	−	5.75004i	0.747771	−	0.663957i
$76$	−3.03249	+	3.13113i	−0.347851	+	0.359165i
$77$	−2.04965	−	2.04965i	−0.233579	−	0.233579i
$78$	−2.04533	+	2.71093i	−0.231588	+	0.306952i
$79$	−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
$81$	−7.64364	+	4.75129i	−0.849293	+	0.527921i
$82$	−3.13095	−	11.6849i	−0.345756	−	1.29038i
$83$	7.90145	−	7.90145i	0.867296	−	0.867296i	−0.124876	−	0.992172i	$-0.539853\pi$
$83$	7.90145	−	7.90145i	0.867296	−	0.867296i	0.992172	+	0.124876i	$0.0398533\pi$
$84$	−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
$87$	2.53988	−	1.07635i	0.272303	−	0.115397i
$88$	−1.66973	−	1.66973i	−0.177994	−	0.177994i
$89$	3.33439	−	5.77534i	0.353445	−	0.612185i	−0.633406	−	0.773820i	$-0.718344\pi$
$89$	3.33439	−	5.77534i	0.353445	−	0.612185i	0.986851	+	0.161635i	$0.0516769\pi$
$90$	−5.11987	+	4.33438i	−0.539682	+	0.456884i
$91$	1.20339	−	2.08433i	0.126149	−	0.218497i
$92$	2.04907	−	7.64725i	0.213631	−	0.797280i
$93$	1.08772	+	0.820660i	0.112791	+	0.0850985i
$94$		−	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
$99$	6.81193	−	1.94461i	0.684624	−	0.195441i
$100$	−3.30420	+	3.75264i	−0.330420	+	0.375264i
$101$	0.167917	+	0.0969467i	0.0167083	+	0.00964656i	0.508331	−	0.861162i	$-0.330263\pi$
$101$	0.167917	+	0.0969467i	0.0167083	+	0.00964656i	−0.491623	+	0.870808i	$0.663596\pi$
$102$	−1.37979	−	3.25591i	−0.136620	−	0.322383i
$103$	−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
$105$	3.22508	−	3.49306i	0.314735	−	0.340888i
$106$	−1.90795			−0.185317
$107$	−1.41333	−	1.41333i	−0.136632	−	0.136632i	0.635483	−	0.772115i	$-0.280801\pi$
$107$	−1.41333	−	1.41333i	−0.136632	−	0.136632i	−0.772115	+	0.635483i	$0.780801\pi$
$108$	4.04394	−	3.26291i	0.389128	−	0.313974i
$109$	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
$111$	13.0983	−	1.83299i	1.24324	−	0.173979i
$112$	1.18571	+	0.317709i	0.112039	+	0.0300207i
$113$	−10.7554	+	10.7554i	−1.01179	+	1.01179i	−0.0118556	+	0.999930i	$0.503774\pi$
$113$	−10.7554	+	10.7554i	−1.01179	+	1.01179i	−0.999930	+	0.0118556i	$0.996226\pi$
$114$	3.05672	+	6.90337i	0.286288	+	0.646560i
$115$	14.3795	+	10.3259i	1.34090	+	0.962894i
$116$	−1.37927	+	0.796320i	−0.128062	+	0.0739364i
$117$	3.02350	+	5.04539i	0.279523	+	0.466447i
$118$	1.82202	−	0.488209i	0.167731	−	0.0449433i
$119$	1.25309	+	2.17041i	0.114870	+	0.198961i
$120$	2.62728	−	2.84559i	0.239837	−	0.259766i
$121$	5.42401			0.493092
$122$	−5.94643	−	5.94643i	−0.538365	−	0.538365i
$123$	−20.7951	−	2.56574i	−1.87503	−	0.231345i
$124$	−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
$129$	1.00930	−	0.787592i	0.0888635	−	0.0693436i
$130$	2.77791	+	3.39177i	0.243639	+	0.297478i
$131$	−5.44362	+	3.14287i	−0.475611	+	0.274594i	−0.718586	−	0.695438i	$-0.755210\pi$
$131$	−5.44362	+	3.14287i	−0.475611	+	0.274594i	0.242975	+	0.970033i	$0.421877\pi$
$132$	−3.76579	+	1.59587i	−0.327770	+	0.138902i
$133$	−2.74915	−	4.59044i	−0.238382	−	0.398042i
$134$	13.3417			1.15255
$135$	3.63225	+	11.0366i	0.312615	+	0.949880i
$136$	1.02081	+	1.76810i	0.0875342	+	0.151614i
$137$	19.6714	−	5.27094i	1.68064	−	0.450327i	0.712694	−	0.701475i	$-0.247475\pi$
$137$	19.6714	−	5.27094i	1.68064	−	0.450327i	0.967949	+	0.251149i	$0.0808083\pi$
$138$	−10.9466	−	8.25893i	−0.931833	−	0.703047i
$139$	−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
$147$	−5.73040	+	7.59519i	−0.472635	+	0.626441i
$148$	−7.37581	+	1.97634i	−0.606288	+	0.162454i
$149$	−7.72513	−	13.3803i	−0.632867	−	1.09616i	−0.986963	−	0.160949i	$-0.948545\pi$
$149$	−7.72513	−	13.3803i	−0.632867	−	1.09616i	0.354096	−	0.935209i	$-0.384789\pi$
$150$	3.87803	+	7.74344i	0.316640	+	0.632249i
$151$	−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
$153$	−6.12408	+	0.0996850i	−0.495102	+	0.00805905i
$154$	2.51030	−	1.44932i	0.202286	−	0.116790i
$155$	1.36090	−	1.11460i	0.109310	−	0.0895265i
$156$	−2.08918	−	2.67728i	−0.167269	−	0.214354i
$157$	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
$162$	−2.61107	−	8.61291i	−0.205145	−	0.676694i
$163$	−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
$165$	−0.364523	−	9.13821i	−0.0283781	−	0.711409i
$166$	5.58717	+	9.67726i	0.433648	+	0.751101i
$167$	0.375997	−	0.100748i	0.0290955	−	0.00779613i	−0.244242	−	0.969714i	$-0.578539\pi$
$167$	0.375997	−	0.100748i	0.0290955	−	0.00779613i	0.273337	+	0.961918i	$0.411872\pi$
$168$	1.28055	−	1.69727i	0.0987965	−	0.130947i
$169$	−7.92918	+	4.57791i	−0.609937	+	0.352147i
$170$	−4.50498	+	0.739176i	−0.345517	+	0.0566922i
$171$	13.0699	−	0.422012i	0.999479	−	0.0322721i
$172$	−0.522650	+	0.522650i	−0.0398517	+	0.0398517i
$173$	−9.07003	−	2.43031i	−0.689581	−	0.184773i	−0.103022	−	0.994679i	$-0.532851\pi$
$173$	−9.07003	−	2.43031i	−0.689581	−	0.184773i	−0.586559	+	0.809906i	$0.699518\pi$
$174$	0.382306	+	2.73191i	0.0289825	+	0.207106i
$175$	−3.39976	−	5.11006i	−0.256997	−	0.386284i
$176$	2.04499	−	1.18068i	0.154147	−	0.0889968i
$177$	0.400075	−	3.24257i	0.0300715	−	0.243726i
$178$	4.71554	+	4.71554i	0.353445	+	0.353445i
$179$	2.41985			0.180868			0.0904340	−	0.995902i	$-0.471175\pi$
$179$	2.41985			0.180868			0.0904340	+	0.995902i	$0.471175\pi$
$180$	−2.86157	−	6.06724i	−0.213289	−	0.452225i
$181$	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
$183$	−13.4112	+	5.68339i	−0.991382	+	0.420128i
$184$	6.85633	+	3.95851i	0.505456	+	0.291825i
$185$	1.69050	−	16.9907i	0.124288	−	1.24918i
$186$	−1.07422	+	0.838254i	−0.0787656	+	0.0614638i
$187$	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	$0.274038\pi$
$191$			20.9637i			1.51688i	−0.651743	+	0.758440i	$0.725962\pi$
$192$	1.04319	−	1.38266i	0.0752856	−	0.0997851i
$193$	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
$195$	7.25068	−	2.25616i	0.519232	−	0.161567i
$196$	2.74658	−	4.75722i	0.196184	−	0.339801i
$197$	4.84435	+	4.84435i	0.345146	+	0.345146i	0.858298	−	0.513152i	$-0.171522\pi$
$197$	4.84435	+	4.84435i	0.345146	+	0.345146i	−0.513152	+	0.858298i	$0.671522\pi$
$198$	0.115296	+	7.08312i	0.00819371	+	0.503375i
$199$	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
$204$	3.50208	−	0.490084i	0.245195	−	0.0343127i
$205$	−9.55348	+	25.3066i	−0.667244	+	1.76749i
$206$	11.1777	−	6.45345i	0.778787	−	0.449633i
$207$	−20.3730	+	12.2087i	−1.41602	+	0.848564i
$208$	1.38639	+	1.38639i	0.0961291	+	0.0961291i
$209$	−9.98353	−	2.50457i	−0.690575	−	0.173245i
$210$	2.53933	+	4.01926i	0.175230	+	0.277355i
$211$	−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
$213$	−11.5055	−	1.41957i	−0.788342	−	0.0972672i
$214$	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
$219$	−7.55655	+	5.89666i	−0.510624	+	0.398459i
$220$	0.854932	+	5.21047i	0.0576395	+	0.351290i
$221$			4.00293i			0.269267i
$222$	−1.61956	+	13.1264i	−0.108698	+	0.880987i
$223$	−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
$225$	14.9523	−	1.19480i	0.996823	−	0.0796532i
$226$	−7.60523	−	13.1727i	−0.505893	−	0.876232i
$227$	−18.0497	−	18.0497i	−1.19800	−	1.19800i	−0.974764	−	0.223238i	$-0.928337\pi$
$227$	−18.0497	−	18.0497i	−1.19800	−	1.19800i	−0.223238	−	0.974764i	$-0.571663\pi$
$228$	−7.45928	+	1.16584i	−0.494003	+	0.0772095i
$229$			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
$231$	−0.695805	−	4.97215i	−0.0457806	−	0.327143i
$232$	−0.412205	−	1.53837i	−0.0270626	−	0.100999i
$233$	7.23764	+	1.93932i	0.474154	+	0.127049i	0.487979	−	0.872855i	$-0.337734\pi$
$233$	7.23764	+	1.93932i	0.474154	+	0.127049i	−0.0138253	+	0.999904i	$0.504401\pi$
$234$	−5.65602	+	1.61463i	−0.369745	+	0.105552i
$235$	−13.0338	+	18.1505i	−0.850232	+	1.18401i
$236$			1.88629i			0.122787i
$237$	−14.2741	−	1.76117i	−0.927205	−	0.114400i
$238$	−2.42078	+	0.648645i	−0.156916	+	0.0420454i
$239$	−15.4669			−1.00047			−0.500236	−	0.865889i	$-0.666753\pi$
$239$	−15.4669			−1.00047			−0.500236	+	0.865889i	$0.666753\pi$
$240$	2.06864	+	3.27425i	0.133530	+	0.211352i
$241$	−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
$243$	−15.5251	−	1.40432i	−0.995934	−	0.0900871i
$244$	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
$249$	19.1677	−	2.68235i	1.21471	−	0.169987i
$250$	10.8958	−	2.50631i	0.689111	−	0.158513i
$251$	4.37887	+	2.52814i	0.276392	+	0.159575i	0.631789	−	0.775140i	$-0.282321\pi$
$251$	4.37887	+	2.52814i	0.276392	+	0.159575i	−0.355397	+	0.934716i	$0.615654\pi$
$252$	−1.89296	−	3.15884i	−0.119246	−	0.198988i
$253$	18.0578	−	4.83858i	1.13529	−	0.304199i
$254$	15.7304			0.987011
$255$	−1.74048	+	7.71327i	−0.108993	+	0.483024i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	17.6043	−	4.71705i	1.09812	−	0.294242i	0.336124	−	0.941818i	$-0.390884\pi$
$257$	17.6043	−	4.71705i	1.09812	−	0.294242i	0.762001	+	0.647576i	$0.224217\pi$
$258$	0.499530	+	1.17875i	0.0310994	+	0.0733857i
$259$		−	9.37346i		−	0.582438i
$260$	−3.99517	+	1.80540i	−0.247770	+	0.111966i
$261$	4.63463	+	1.16134i	0.286876	+	0.0718851i
$262$	−1.62687	−	6.07157i	−0.100508	−	0.375103i
$263$	30.5164	+	8.17686i	1.88172	+	0.504207i	0.999439	+	0.0334926i	$0.0106630\pi$
$263$	30.5164	+	8.17686i	1.88172	+	0.504207i	0.882286	+	0.470714i	$0.156004\pi$
$264$	−0.566832	−	4.05051i	−0.0348861	−	0.249292i
$265$	3.46538	+	2.48848i	0.212877	+	0.152866i
$266$	5.14556	−	1.46738i	0.315494	−	0.0899711i
$267$	10.6351	−	4.50695i	0.650858	−	0.275821i
$268$	−3.45309	+	12.8871i	−0.210931	+	0.787205i
$269$	8.79460	+	15.2327i	0.536216	+	0.928754i	0.999103	+	0.0423365i	$0.0134801\pi$
$269$	8.79460	+	15.2327i	0.536216	+	0.928754i	−0.462887	+	0.886417i	$0.653187\pi$
$270$	−11.6006	+	0.652003i	−0.705993	+	0.0396796i
$271$	−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
$273$	3.83822	−	1.62656i	0.232300	−	0.0984441i
$274$			20.3653i			1.23032i
$275$	−11.5753	−	2.32640i	−0.698017	−	0.140287i
$276$	10.8107	−	8.43600i	0.650727	−	0.507787i
$277$	−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
$279$	0.647848	+	2.26939i	0.0387856	+	0.135865i
$280$	−1.73920	−	2.12353i	−0.103937	−	0.126905i
$281$	9.66800	+	5.58182i	0.576744	+	0.332984i	0.759839	−	0.650112i	$-0.225278\pi$
$281$	9.66800	+	5.58182i	0.576744	+	0.332984i	−0.183094	+	0.983095i	$0.558611\pi$
$282$	10.4248	−	13.8173i	0.620788	−	0.822806i
$283$	−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
$285$	3.45196	−	16.5253i	0.204477	−	0.978871i
$286$	4.62980			0.273766
$287$	−3.84335	+	14.3436i	−0.226866	+	0.846675i
$288$	−1.54209	−	2.57332i	−0.0908683	−	0.151634i
$289$	11.1126	+	6.41587i	0.653683	+	0.377404i
$290$	3.54375	+	0.352587i	0.208096	+	0.0207046i
$291$	14.0240	+	17.9717i	0.822101	+	1.05352i
$292$	3.91305	−	3.91305i	0.228994	−	0.228994i
$293$	7.13865	−	7.13865i	0.417044	−	0.417044i	−0.467139	−	0.884184i	$-0.654715\pi$
$293$	7.13865	−	7.13865i	0.417044	−	0.417044i	0.884184	+	0.467139i	$0.154715\pi$
$294$	−5.85325	−	7.50092i	−0.341369	−	0.437463i
$295$	−3.94606	−	1.48967i	−0.229749	−	0.0867321i
$296$		−	7.63600i		−	0.443834i
$297$	11.4472	+	4.41738i	0.664234	+	0.256322i
$298$	14.9238	−	3.99882i	0.864512	−	0.231645i
$299$	7.76127	+	13.4429i	0.448846	+	0.777424i
$300$	−8.48330	+	1.74174i	−0.489783	+	0.100559i
$301$	−0.453659	−	0.785761i	−0.0261485	−	0.0452905i
$302$	3.25319	−	12.1411i	0.187200	−	0.698640i
$303$	0.131039	+	0.309213i	0.00752797	+	0.0177638i
$304$	4.19178	−	1.19539i	0.240415	−	0.0685604i
$305$	3.04468	+	18.5561i	0.174338	+	1.06252i
$306$	1.48874	−	5.94121i	0.0851056	−	0.339636i
$307$	−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
$309$	−3.09824	−	22.1397i	−0.176253	−	1.25948i
$310$	0.724391	+	1.60300i	0.0411427	+	0.0910445i
$311$			21.8028i			1.23633i	0.786050	+	0.618163i	$0.212123\pi$
$311$			21.8028i			1.23633i	−0.786050	+	0.618163i	$0.787877\pi$
$312$	3.12677	−	1.32507i	0.177019	−	0.0750171i
$313$	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
$315$	8.10312	−	1.46537i	0.456559	−	0.0825642i
$316$	8.30367			0.467118
$317$	−26.5113	+	7.10368i	−1.48902	+	0.398982i	−0.909407	−	0.415907i	$-0.863464\pi$
$317$	−26.5113	+	7.10368i	−1.48902	+	0.398982i	−0.579616	+	0.814890i	$0.696797\pi$
$318$	−2.63805	−	1.99035i	−0.147935	−	0.111613i
$319$	−3.25693	−	1.88039i	−0.182353	−	0.105282i
$320$	−1.41683	−	1.72991i	−0.0792031	−	0.0967051i
$321$	−0.479791	−	3.42853i	−0.0267793	−	0.191362i
$322$	−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
$327$	13.2886	+	1.63957i	0.734859	+	0.0906684i
$328$	−3.13095	+	11.6849i	−0.172878	+	0.645189i
$329$	−6.13351	+	10.6235i	−0.338151	+	0.585695i
$330$	8.92118	+	2.01304i	0.491095	+	0.110814i
$331$	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
$333$	20.0227	+	11.1296i	1.09724	+	0.609898i
$334$			0.389261i			0.0212994i
$335$	−24.2323	−	17.4011i	−1.32395	−	0.950726i
$336$	1.30800	+	1.67620i	0.0713574	+	0.0914443i
$337$	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
$339$	−26.0911	+	3.65120i	−1.41707	+	0.198306i
$340$	0.451986	−	4.54279i	0.0245124	−	0.246368i
$341$		−	1.85764i		−	0.100597i
$342$	−2.97510	+	12.7338i	−0.160875	+	0.688563i
$343$	10.8440	+	10.8440i	0.585523	+	0.585523i
$344$	−0.369569	−	0.640113i	−0.0199258	−	0.0345126i
$345$	9.11023	+	29.2778i	0.490478	+	1.57626i
$346$	4.69499	−	8.13196i	0.252404	−	0.437177i
$347$	−4.28124	+	15.9778i	−0.229829	+	0.857733i	0.750583	+	0.660776i	$0.229773\pi$
$347$	−4.28124	+	15.9778i	−0.229829	+	0.857733i	−0.980412	+	0.196957i	$0.936894\pi$
$348$	−2.73777	−	0.337792i	−0.146760	−	0.0181076i
$349$		−	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
$351$	−1.08281	+	10.1302i	−0.0577962	+	0.540708i
$352$	0.611163	+	2.28089i	0.0325751	+	0.121572i
$353$	16.2186	−	16.2186i	0.863229	−	0.863229i	−0.128483	−	0.991712i	$-0.541011\pi$
$353$	16.2186	−	16.2186i	0.863229	−	0.863229i	0.991712	+	0.128483i	$0.0410108\pi$
$354$	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
$357$	−0.531548	+	4.30815i	−0.0281325	+	0.228011i
$358$	−0.626303	+	2.33739i	−0.0331011	+	0.123535i
$359$	−10.7713	−	18.6565i	−0.568489	−	0.984651i	−0.996716	−	0.0809799i	$-0.974195\pi$
$359$	−10.7713	−	18.6565i	−0.568489	−	0.984651i	0.428227	−	0.903671i	$-0.359138\pi$
$360$	6.60113	−	1.19375i	0.347910	−	0.0629161i
$361$	−16.7500	−	8.96863i	−0.881581	−	0.472033i
$362$	1.44258	+	1.44258i	0.0758204	+	0.0758204i
$363$	7.49959	+	5.65827i	0.393626	+	0.296982i
$364$	−2.08433	+	1.20339i	−0.109248	+	0.0630746i
$365$	5.09570	+	11.2763i	0.266721	+	0.590226i
$366$	−2.01867	−	14.4252i	−0.105517	−	0.754015i
$367$	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
$372$	−0.531663	−	1.25457i	−0.0275654	−	0.0650465i
$373$	−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
$375$	3.05591	−	19.1223i	0.157806	−	0.987470i
$376$	−4.99661	+	8.65438i	−0.257680	+	0.446316i
$377$	0.808193	−	3.01622i	0.0416241	−	0.155343i
$378$	−6.30168	+	0.986685i	−0.324123	+	0.0507496i
$379$			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	−0.201728	−	0.979442i	$-0.564656\pi$
$383$	−16.9509	−	4.54197i	−0.866150	−	0.232084i	−0.664422	+	0.747358i	$0.731322\pi$
$384$	1.06555	+	1.36550i	0.0543763	+	0.0696830i
$385$	−6.44971	−	0.641716i	−0.328708	−	0.0327049i
$386$	12.4027	+	7.16073i	0.631283	+	0.364471i
$387$	2.21712	−	0.0360893i	0.112703	−	0.00183452i
$388$	−9.30639	−	9.30639i	−0.472460	−	0.472460i
$389$	−1.99002	+	3.44681i	−0.100898	+	0.174760i	−0.912055	−	0.410068i	$-0.865505\pi$
$389$	−1.99002	+	3.44681i	−0.100898	+	0.174760i	0.811157	+	0.584829i	$0.198838\pi$
$390$	0.302668	+	7.58756i	0.0153262	+	0.384211i
$391$	−16.1636			−0.817429
$392$	3.88425	+	3.88425i	0.196184	+	0.196184i
$393$	−10.8053	−	1.33318i	−0.545055	−	0.0672500i
$394$	−5.93309	+	3.42547i	−0.298905	+	0.172573i
$395$	−6.55770	+	17.3710i	−0.329954	+	0.874029i
$396$	−6.87161	−	1.72188i	−0.345311	−	0.0865277i
$397$	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
$399$	0.987540	−	9.21492i	0.0494388	−	0.461323i
$400$	4.73784	−	1.59778i	0.236892	−	0.0798890i
$401$	−33.2265	+	19.1833i	−1.65925	+	0.957970i	−0.686192	+	0.727420i	$0.740719\pi$
$401$	−33.2265	+	19.1833i	−1.65925	+	0.957970i	−0.973061	+	0.230550i	$0.925948\pi$
$402$	18.4471	+	13.9179i	0.920058	+	0.694163i
$403$	1.48986	−	0.399207i	0.0742153	−	0.0198859i
$404$	−0.0969467	−	0.167917i	−0.00482328	−	0.00835417i
$405$	−6.49108	+	19.0490i	−0.322544	+	0.946554i
$406$	1.95502			0.0970260
$407$	−12.7501	−	12.7501i	−0.631997	−	0.631997i
$408$	−0.433021	+	3.50959i	−0.0214377	+	0.173751i
$409$	−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
$414$	−6.51979	−	22.8386i	−0.320430	−	1.12246i
$415$	2.47383	−	24.8638i	0.121436	−	1.22052i
$416$	−1.69798	+	0.980328i	−0.0832502	+	0.0480645i
$417$	−2.43286	−	5.74085i	−0.119138	−	0.281131i
$418$	5.00316	−	8.99512i	0.244713	−	0.439966i
$419$	−2.33966			−0.114300			−0.0571499	−	0.998366i	$-0.518201\pi$
$419$	−2.33966			−0.114300			−0.0571499	+	0.998366i	$0.518201\pi$
$420$	−4.53953	+	1.41254i	−0.221506	+	0.0689251i
$421$	−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
$423$	−15.4104	−	25.7157i	−0.749279	−	1.25034i
$424$	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	−0.281430	−	0.959582i	$-0.590809\pi$
$431$	−26.0164	−	15.0206i	−1.25317	−	0.723517i	−0.971737	+	0.236065i	$0.924142\pi$
$432$	−5.13361	+	0.803794i	−0.246991	+	0.0386725i
$433$	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
$435$	2.86876	−	5.46056i	0.137547	−	0.261814i
$436$	−7.73033			−0.370216
$437$	34.5050	−	0.552181i	1.65060	−	0.0264144i
$438$	−3.73996	−	8.82523i	−0.178702	−	0.421686i
$439$	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
$441$	−15.8464	+	4.52371i	−0.754592	+	0.215415i
$442$	−3.86654	−	1.03604i	−0.183912	−	0.0492792i
$443$	−4.87575	−	18.1966i	−0.231654	−	0.864545i	−0.979629	−	0.200817i	$-0.935640\pi$
$443$	−4.87575	−	18.1966i	−0.231654	−	0.864545i	0.747975	−	0.663727i	$-0.231026\pi$
$444$	−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
$447$	3.27693	−	26.5592i	0.154994	−	1.25621i
$448$	−0.867998	−	0.867998i	−0.0410091	−	0.0410091i
$449$	24.3408			1.14871			0.574357	−	0.818605i	$-0.305252\pi$
$449$	24.3408			1.14871			0.574357	+	0.818605i	$0.305252\pi$
$450$	−2.71586	+	14.7521i	−0.128027	+	0.695420i
$451$	14.2827	+	24.7384i	0.672547	+	1.16489i
$452$	14.6922	−	3.93676i	0.691062	−	0.185170i
$453$	−17.3792	−	13.1122i	−0.816546	−	0.616065i
$454$	22.1063	−	12.7631i	1.03750	−	0.599001i
$455$	−0.871377	−	5.31070i	−0.0408508	−	0.248969i
$456$	0.804491	−	7.50685i	0.0376737	−	0.351540i
$457$	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
$459$	−8.57153	−	6.25074i	−0.400085	−	0.291759i
$460$	−7.29011	−	16.1323i	−0.339903	−	0.752170i
$461$	−11.4957	+	6.63706i	−0.535409	+	0.309119i	−0.743216	−	0.669051i	$-0.766701\pi$
$461$	−11.4957	+	6.63706i	−0.535409	+	0.309119i	0.207807	+	0.978170i	$0.433367\pi$
$462$	4.98281	+	0.614790i	0.231821	+	0.0286026i
$463$	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
$465$	3.04439	−	0.121441i	0.141180	−	0.00563169i
$466$	−3.74648	+	6.48909i	−0.173552	+	0.300601i
$467$	−19.1091	−	19.1091i	−0.884266	−	0.884266i	0.109699	−	0.993965i	$-0.465011\pi$
$467$	−19.1091	−	19.1091i	−0.884266	−	0.884266i	−0.993965	+	0.109699i	$0.965011\pi$
$468$	−0.0957313	−	5.88119i	−0.00442518	−	0.271858i
$469$	−14.1833	−	8.18871i	−0.654922	−	0.378119i
$470$	−14.1587	−	17.2874i	−0.653090	−	0.797408i
$471$	4.58264	+	5.87263i	0.211157	+	0.270597i
$472$	−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
$477$	−4.90977	+	2.94222i	−0.224803	+	0.134715i
$478$	4.00313	−	14.9399i	0.183099	−	0.683335i
$479$	21.2533	−	36.8118i	0.971087	−	1.68197i	0.278800	−	0.960349i	$-0.410063\pi$
$479$	21.2533	−	36.8118i	0.971087	−	1.68197i	0.692287	−	0.721623i	$-0.256603\pi$
$480$	−3.69809	+	1.15072i	−0.168794	+	0.0525227i
$481$	7.48579	−	12.9658i	0.341323	−	0.591188i
$482$	−12.6262	−	12.6262i	−0.575109	−	0.575109i
$483$	6.56797	+	15.4985i	0.298853	+	0.705207i
$484$	−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
$489$	−0.747292	−	5.34006i	−0.0337937	−	0.241486i
$490$	−11.1932	+	5.05819i	−0.505659	+	0.228506i
$491$	22.4012	−	12.9333i	1.01095	−	0.583672i	0.0994805	−	0.995040i	$-0.468282\pi$
$491$	22.4012	−	12.9333i	1.01095	−	0.583672i	0.911470	+	0.411367i	$0.134949\pi$
$492$	16.7262	+	12.6195i	0.754074	+	0.568932i
$493$	2.29921	+	2.29921i	0.103551	+	0.103551i
$494$	8.28943	+	2.07957i	0.372959	+	0.0935645i
$495$	9.02886	−	13.0153i	0.405817	−	0.584996i
$496$	0.393342	+	0.681289i	0.0176616	+	0.0305908i
$497$	−2.12645	+	7.93601i	−0.0953841	+	0.355978i
$498$	−2.37003	+	19.2089i	−0.106204	+	0.860769i
$499$	−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	$-0.988703\pi$
$503$	−3.40075	−	12.6918i	−0.151632	−	0.565899i	0.847738	−	0.530415i	$-0.177964\pi$
$504$	3.54114	−	1.01090i	0.157735	−	0.0450289i
$505$	0.427838	−	0.0701995i	0.0190385	−	0.00312384i
$506$			18.6949i			0.831088i
$507$	−15.7390	−	1.94191i	−0.698994	−	0.0862433i
$508$	−4.07132	+	15.1944i	−0.180636	+	0.674141i
$509$	−13.3964	+	23.2032i	−0.593785	+	1.02847i	0.399932	+	0.916545i	$0.369034\pi$
$509$	−13.3964	+	23.2032i	−0.593785	+	1.02847i	−0.993717	+	0.111921i	$0.964300\pi$
$510$	−6.99998	−	3.67751i	−0.309964	−	0.162843i
$511$	3.39652	+	5.88295i	0.150253	+	0.260246i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	18.5115	+	13.0508i	0.817302	+	0.576209i
$514$			18.2253i			0.803883i
$515$	−28.7189	−	2.85739i	−1.26551	−	0.125912i
$516$	−1.26787	+	0.177427i	−0.0558149	+	0.00781078i
$517$	6.10748	+	22.7934i	0.268607	+	1.00245i
$518$	9.05407	+	2.42603i	0.397813	+	0.106594i
$519$	−10.0055	−	12.8220i	−0.439194	−	0.562825i
$520$	−0.709859	−	4.32631i	−0.0311294	−	0.189721i
$521$		−	14.7508i		−	0.646243i	−0.946357	−	0.323122i	$-0.895268\pi$
$521$		−	14.7508i		−	0.646243i	0.946357	−	0.323122i	$-0.104732\pi$
$522$	−2.32130	+	4.17613i	−0.101600	+	0.182784i
$523$	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
$525$	0.630035	−	10.6121i	0.0274970	−	0.463149i
$526$	−15.7965	+	27.3603i	−0.688759	+	1.19297i
$527$	−0.415694	+	1.55139i	−0.0181079	+	0.0675797i
$528$	4.05920	+	0.500833i	0.176654	+	0.0217959i
$529$	−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
$534$	1.60081	+	11.4392i	0.0692738	+	0.495023i
$535$	−4.44739	−	0.442494i	−0.192277	−	0.0191307i
$536$	−11.5543	−	6.67086i	−0.499068	−	0.288137i
$537$	3.34584	+	2.52436i	0.144383	+	0.108934i
$538$	−16.9899	+	4.55242i	−0.732485	+	0.196269i
$539$	12.9713			0.558713
$540$	2.37268	−	11.3741i	0.102104	−	0.489464i
$541$	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
$543$	3.25350	−	1.37877i	0.139621	−	0.0591686i
$544$		−	2.04163i		−	0.0875342i
$545$	6.10491	−	16.1716i	0.261506	−	0.692715i
$546$	0.577735	+	4.12843i	0.0247248	+	0.176680i
$547$	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
$549$	−24.4720	−	6.13216i	−1.04444	−	0.261714i
$550$	5.24304	−	10.5788i	0.223564	−	0.451080i
$551$	−4.98676	−	4.82967i	−0.212443	−	0.205751i
$552$	5.35053	+	12.6257i	0.227734	+	0.537387i
$553$	−2.63815	+	9.84572i	−0.112186	+	0.418683i
$554$	−15.0317	−	26.0356i	−0.638635	−	1.10615i
$555$	20.0619	−	21.7290i	0.851581	−	0.922343i
$556$	1.79991	+	3.11754i	0.0763333	+	0.132213i
$557$	19.2009	−	5.14486i	0.813568	−	0.217995i	0.172035	−	0.985091i	$-0.444966\pi$
$557$	19.2009	−	5.14486i	0.813568	−	0.217995i	0.641532	+	0.767096i	$0.278299\pi$
$558$	−2.35974	+	0.0384108i	−0.0998958	+	0.00162606i
$559$		−	1.44920i		−	0.0612945i
$560$	2.50131	−	1.13033i	0.105700	−	0.0477653i
$561$	5.13704	+	6.58310i	0.216886	+	0.277939i
$562$	−7.89389	+	7.89389i	−0.332984	+	0.332984i
$563$	27.2681	−	27.2681i	1.14921	−	1.14921i	0.162505	−	0.986708i	$-0.448043\pi$
$563$	27.2681	−	27.2681i	1.14921	−	1.14921i	0.986708	−	0.162505i	$-0.0519573\pi$
$564$	10.6483	+	13.6458i	0.448375	+	0.574590i
$565$	−3.36737	+	33.8445i	−0.141666	+	1.42385i
$566$	−18.6151	−	10.7474i	−0.782451	−	0.451748i
$567$	−2.51055	+	10.7588i	−0.105433	+	0.451826i
$568$	−1.73229	+	6.46500i	−0.0726853	+	0.271265i
$569$	−8.66956			−0.363447			−0.181723	−	0.983350i	$-0.558168\pi$
$569$	−8.66956			−0.363447			−0.181723	+	0.983350i	$0.558168\pi$
$570$	15.0687	+	7.61139i	0.631160	+	0.318806i
$571$	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
$573$	−21.8691	+	28.9857i	−0.913594	+	1.21090i
$574$	−12.8601	−	7.42479i	−0.536770	−	0.309905i
$575$	39.5054	−	2.51045i	1.64749	−	0.104693i
$576$	2.88476	−	0.823517i	0.120198	−	0.0343132i
$577$	−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
$579$	19.5560	−	15.2603i	0.812719	−	0.634195i
$580$	−1.25776	+	3.33175i	−0.0522258	+	0.138343i
$581$		−	13.7169i		−	0.569072i
$582$	−20.9890	+	8.89472i	−0.870021	+	0.368698i
$583$	4.35183	−	1.16607i	0.180234	−	0.0482936i
$584$	2.76695	+	4.79249i	0.114497	+	0.198315i
$585$	12.3788	+	4.44432i	0.511802	+	0.183750i
$586$	5.04779	+	8.74303i	0.208522	+	0.361171i
$587$	−2.53325	+	9.45422i	−0.104558	+	0.390218i	−0.998295	−	0.0583753i	$-0.981408\pi$
$587$	−2.53325	+	9.45422i	−0.104558	+	0.390218i	0.893736	+	0.448593i	$0.148075\pi$
$588$	8.76027	−	3.71243i	0.361267	−	0.153098i
$589$	0.834398	−	3.32601i	0.0343808	−	0.137046i
$590$	2.46023	−	3.42605i	0.101286	−	0.141048i
$591$	1.64454	+	11.7517i	0.0676472	+	0.483399i
$592$	7.37581	+	1.97634i	0.303144	+	0.0812272i
$593$	5.02244	+	18.7440i	0.206247	+	0.769724i	0.989066	+	0.147474i	$0.0471144\pi$
$593$	5.02244	+	18.7440i	0.206247	+	0.769724i	−0.782819	+	0.622249i	$0.786219\pi$
$594$	−7.22961	+	9.91385i	−0.296635	+	0.406770i
$595$	5.24282	+	1.97921i	0.214935	+	0.0811398i
$596$			15.4503i			0.632867i
$597$	0.521919	+	1.23158i	0.0213607	+	0.0504052i
$598$	−14.9936	+	4.01753i	−0.613135	+	0.164289i
$599$	3.11272	−	5.39139i	0.127182	−	0.220286i	−0.795401	−	0.606083i	$-0.792740\pi$
$599$	3.11272	−	5.39139i	0.127182	−	0.220286i	0.922584	+	0.385796i	$0.126073\pi$
$600$	0.513252	−	8.64503i	0.0209534	−	0.352932i
$601$	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
$603$	34.3325	−	20.5741i	1.39813	−	0.837841i
$604$	10.8854	+	6.28468i	0.442920	+	0.255720i
$605$	9.38307	−	7.68489i	0.381476	−	0.312435i
$606$	−0.332592	+	0.0465432i	−0.0135106	+	0.00189069i
$607$	−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
$612$	5.35345	+	2.97571i	0.216400	+	0.120286i
$613$	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
$615$	−39.6088	+	25.0245i	−1.59718	+	1.00909i
$616$	−2.89864			−0.116790
$617$	28.4968	−	7.63568i	1.14724	−	0.307401i	0.365379	−	0.930859i	$-0.380939\pi$
$617$	28.4968	−	7.63568i	1.14724	−	0.307401i	0.781857	+	0.623458i	$0.214273\pi$
$618$	22.1872	+	2.73750i	0.892498	+	0.110118i
$619$		−	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
$621$	−40.9050	−	4.37233i	−1.64146	−	0.175455i
$622$	−21.0599	−	5.64299i	−0.844426	−	0.226263i
$623$	−2.11874	−	7.90723i	−0.0848853	−	0.316796i
$624$	0.470646	+	3.36318i	0.0188409	+	0.134635i
$625$	−23.0588	−	9.65885i	−0.922351	−	0.386354i
$626$			1.33162i			0.0532221i
$627$	−11.1911	−	13.8777i	−0.446930	−	0.554221i
$628$	−3.04106	−	3.04106i	−0.121352	−	0.121352i
$629$	7.79495	+	13.5012i	0.310805	+	0.538330i
$630$	−0.681804	+	8.20628i	−0.0271637	+	0.326946i
$631$	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
$633$	0.775348	−	6.28412i	0.0308173	−	0.249771i
$634$		−	27.4465i		−	1.09004i
$635$	−28.5708	−	20.5166i	−1.13380	−	0.814176i
$636$	2.60531	−	2.03302i	0.103307	−	0.0806146i
$637$	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	−0.773837	−	0.633385i	$-0.781665\pi$
$641$	−15.5004	+	8.94915i	−0.612228	+	0.353470i	0.161609	+	0.986855i	$0.448332\pi$
$642$	3.43589	+	0.423927i	0.135604	+	0.0167311i
$643$	−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
$645$	0.630112	−	2.79246i	0.0248106	−	0.109953i
$646$	−6.19123	+	6.39261i	−0.243591	+	0.251514i
$647$	6.35365	+	6.35365i	0.249788	+	0.249788i	0.820883	−	0.571096i	$-0.193482\pi$
$647$	6.35365	+	6.35365i	0.249788	+	0.249788i	−0.571096	+	0.820883i	$0.693482\pi$
$648$	−2.04520	+	8.76454i	−0.0803430	+	0.344304i
$649$	−3.85745	+	2.22710i	−0.151418	+	0.0874214i
$650$	9.61109	+	1.93164i	0.376978	+	0.0757651i
$651$	1.65647	−	0.231807i	0.0649222	−	0.00908525i
$652$	0.805737	+	3.00705i	0.0315551	+	0.117765i
$653$	17.8662	−	17.8662i	0.699158	−	0.699158i	−0.265071	−	0.964229i	$-0.585395\pi$
$653$	17.8662	−	17.8662i	0.699158	−	0.699158i	0.964229	+	0.265071i	$0.0853953\pi$
$654$	−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
$657$	−16.5995	+	0.270199i	−0.647608	+	0.0105415i
$658$	−8.67409	−	8.67409i	−0.338151	−	0.338151i
$659$	−8.50138	+	14.7248i	−0.331167	+	0.573598i	−0.982741	−	0.184987i	$-0.940776\pi$
$659$	−8.50138	+	14.7248i	−0.331167	+	0.573598i	0.651574	+	0.758585i	$0.274109\pi$
$660$	−4.25342	+	8.09618i	−0.165564	+	0.315144i
$661$	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
$663$	−4.17581	+	5.53471i	−0.162175	+	0.214950i
$664$		−	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
$669$	−6.54990	+	5.11114i	−0.253234	+	0.197608i
$670$	23.0800	−	18.9029i	0.891658	−	0.730283i
$671$	17.1974	+	9.92892i	0.663898	+	0.383302i
$672$	−1.95762	+	0.829602i	−0.0755169	+	0.0320026i
$673$	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
$675$	21.9205	+	13.9461i	0.843719	+	0.536786i
$676$	9.15583			0.352147
$677$	7.29937	+	7.29937i	0.280537	+	0.280537i	0.833323	−	0.552786i	$-0.186435\pi$
$677$	7.29937	+	7.29937i	0.280537	+	0.280537i	−0.552786	+	0.833323i	$0.686435\pi$
$678$	3.22608	−	26.1470i	0.123897	−	1.00417i
$679$	13.9914	−	8.07793i	0.536940	−	0.310002i
$680$	4.27102	+	1.61235i	0.163786	+	0.0618307i
$681$	−6.12743	−	43.7859i	−0.234804	−	1.67788i
$682$	1.79434	+	0.480792i	0.0687089	+	0.0184105i
$683$	12.8602	−	12.8602i	0.492081	−	0.492081i	−0.416880	−	0.908961i	$-0.636877\pi$
$683$	12.8602	−	12.8602i	0.492081	−	0.492081i	0.908961	+	0.416880i	$0.136877\pi$
$684$	−11.5299	−	6.16947i	−0.440855	−	0.235896i
$685$	26.5618	−	36.9893i	1.01488	−	1.41329i
$686$	−13.2812	+	7.66789i	−0.507078	+	0.292761i
$687$	−6.72796	+	8.91738i	−0.256688	+	0.340219i
$688$	0.713953	−	0.191303i	0.0272192	−	0.00729337i
$689$	1.87042	+	3.23966i	0.0712572	+	0.123421i
$690$	−30.6381	+	1.22215i	−1.16637	+	0.0465266i
$691$	−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
$693$	4.22482	−	7.60066i	0.160488	−	0.288725i
$694$	−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
$699$	7.98415	+	10.2317i	0.301988	+	0.386997i
$700$	0.389245	+	6.12532i	0.0147121	+	0.231515i
$701$	8.42794	−	4.86588i	0.318319	−	0.183782i	−0.332324	−	0.943165i	$-0.607833\pi$
$701$	8.42794	−	4.86588i	0.318319	−	0.183782i	0.650643	+	0.759384i	$0.274499\pi$
$702$	−9.50473	−	3.66779i	−0.358733	−	0.138432i
$703$	−17.1014	−	28.5553i	−0.644991	−	1.07698i
$704$	−2.36135			−0.0889968
$705$	−36.9558	+	11.4994i	−1.39184	+	0.433091i
$706$	11.4683	+	19.8636i	0.431614	+	0.747578i
$707$	0.229901	−	0.0616018i	0.00864631	−	0.00231677i
$708$	−1.96776	+	2.60811i	−0.0739529	+	0.0980188i
$709$	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
$717$	−21.3855	−	16.1349i	−0.798658	−	0.602569i
$718$	20.8086	−	5.57565i	0.776570	−	0.208081i
$719$	−0.857044	−	1.48444i	−0.0319623	−	0.0553604i	0.849602	−	0.527425i	$-0.176842\pi$
$719$	−0.857044	−	1.48444i	−0.0319623	−	0.0553604i	−0.881564	+	0.472064i	$0.843509\pi$
$720$	−0.555425	+	6.68517i	−0.0206995	+	0.249142i
$721$	−15.8437			−0.590049
$722$	12.9983	−	13.8580i	0.483745	−	0.515743i
$723$	−28.4763	+	12.0677i	−1.05905	+	0.448803i
$724$	−1.76680	+	1.02006i	−0.0656624	+	0.0379102i
$725$	−5.97660	−	5.26239i	−0.221965	−	0.195440i
$726$	−7.40650	+	5.77958i	−0.274881	+	0.214500i
$727$	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
$732$	14.4561	+	1.78362i	0.534313	+	0.0659246i
$733$	−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
$735$	0.847982	+	21.2580i	0.0312783	+	0.784113i
$736$	−3.95851	−	6.85633i	−0.145912	−	0.252728i
$737$	−30.4310	+	8.15396i	−1.12094	+	0.300355i
$738$	31.1296	−	18.6547i	1.14590	−	0.686690i
$739$	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
$741$	8.72518	−	11.9578i	0.320528	−	0.439281i
$742$	−1.65610	+	1.65610i	−0.0607972	+	0.0607972i
$743$	18.8424	+	5.04881i	0.691262	+	0.185223i	0.587313	−	0.809360i	$-0.300186\pi$
$743$	18.8424	+	5.04881i	0.691262	+	0.185223i	0.103948	+	0.994583i	$0.466852\pi$
$744$	1.34943	−	0.188840i	0.0494724	−	0.00692321i
$745$	−32.3214	−	12.2016i	−1.18416	−	0.447032i
$746$	8.55042	−	4.93659i	0.313053	−	0.180741i
$747$	29.3007	+	16.2868i	1.07206	+	0.595902i
$748$	−3.40897	−	3.40897i	−0.124644	−	0.124644i
$749$	−2.45354			−0.0896504
$750$	17.6798	+	7.90099i	0.645574	+	0.288503i
$751$	−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
$753$	3.41718	+	8.06356i	0.124529	+	0.293853i
$754$	2.70427	+	1.56131i	0.0984836	+	0.0568595i
$755$	−21.7439	+	17.8086i	−0.791341	+	0.648122i
$756$	0.677930	−	6.34233i	0.0246561	−	0.230668i
$757$	−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	$-0.985690\pi$
$761$		−	2.47955i		−	0.0898836i	0.998990	−	0.0449418i	$-0.0143102\pi$
$762$	21.7498	+	16.4097i	0.787912	+	0.594462i
$763$	2.45600	−	9.16591i	0.0889131	−	0.331828i
$764$	10.4819	−	18.1551i	0.379220	−	0.656828i
$765$	−10.4529	+	8.84921i	−0.377925	+	0.319944i
$766$	8.77442	−	15.1977i	0.317033	−	0.549117i
$767$	−2.61515	−	2.61515i	−0.0944274	−	0.0944274i
$768$	−1.59476	+	0.675828i	−0.0575459	+	0.0243868i
$769$	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	$0.177521\pi$
$773$	10.5176	+	39.2522i	0.378291	+	1.41180i	−0.470185	+	0.882568i	$0.655813\pi$
$774$	−0.538974	+	2.15092i	−0.0193730	+	0.0773131i
$775$	0.775041	−	3.85631i	0.0278403	−	0.138523i
$776$	11.3980	−	6.58061i	0.409163	−	0.236230i
$777$	9.77828	−	12.9603i	0.350794	−	0.464950i
$778$	−2.81431	−	2.81431i	−0.100898	−	0.100898i
$779$	14.4607	+	50.7083i	0.518109	+	1.81681i
$780$	−7.40735	−	1.67145i	−0.265226	−	0.0598475i
$781$	7.90233	+	13.6872i	0.282768	+	0.489768i
$782$	4.18345	−	15.6128i	0.149600	−	0.558314i
$783$	5.19664	+	6.44053i	0.185713	+	0.230166i
$784$	−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
$789$	33.6640	+	43.1402i	1.19847	+	1.53583i
$790$	−15.0818	−	10.8302i	−0.536587	−	0.385321i
$791$			18.6714i			0.663878i
$792$	3.44171	−	6.19181i	0.122296	−	0.220016i
$793$	−4.26746	+	15.9264i	−0.151542	+	0.565562i
$794$	−14.7712	+	25.5844i	−0.524209	+	0.907956i
$795$	2.19551	+	7.05577i	0.0778667	+	0.250242i
$796$	−0.386133	−	0.668802i	−0.0136861	−	0.0237051i
$797$	22.4735	+	22.4735i	0.796051	+	0.796051i	0.982470	−	0.186420i	$-0.0596884\pi$
$797$	22.4735	+	22.4735i	0.796051	+	0.796051i	−0.186420	+	0.982470i	$0.559688\pi$
$798$	8.64533	+	3.33889i	0.306041	+	0.118195i
$799$		−	20.4024i		−	0.721787i
$800$	0.317095	+	4.98993i	0.0112110	+	0.176421i
$801$	19.4064	+	4.86282i	0.685690	+	0.171819i
$802$	−9.93002	−	37.0594i	−0.350641	−	1.30861i
$803$	12.6222	+	3.38211i	0.445428	+	0.119352i
$804$	−18.2181	+	14.2163i	−0.642504	+	0.501370i
$805$	21.4443	−	3.51857i	0.755811	−	0.124013i
$806$			1.54242i			0.0543294i
$807$	−3.73059	+	30.2361i	−0.131323	+	1.06436i
$808$	0.187287	−	0.0501833i	0.00658872	−	0.00176544i
$809$	−18.6603			−0.656061			−0.328030	−	0.944667i	$-0.606385\pi$
$809$	−18.6603			−0.656061			−0.328030	+	0.944667i	$0.606385\pi$
$810$	−16.7199	−	11.2002i	−0.587479	−	0.393533i
$811$	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
$813$	2.11314	−	17.1268i	0.0741112	−	0.600664i
$814$	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
$819$	7.00379	+	1.75500i	0.244732	+	0.0613246i
$820$	20.9269	−	17.1395i	0.730798	−	0.598536i
$821$	−44.4304	−	25.6519i	−1.55063	−	0.895258i	−0.998090	−	0.0617728i	$-0.980325\pi$
$821$	−44.4304	−	25.6519i	−1.55063	−	0.895258i	−0.552542	−	0.833485i	$-0.686342\pi$
$822$	−21.2449	+	28.1584i	−0.741001	+	0.982138i
$823$	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
$825$	−13.5779	−	15.2918i	−0.472720	−	0.532394i
$826$	1.15775	−	2.00527i	0.0402831	−	0.0697724i
$827$	36.8917	−	9.88510i	1.28285	−	0.343738i	0.447909	−	0.894079i	$-0.352169\pi$
$827$	36.8917	−	9.88510i	1.28285	−	0.343738i	0.834940	+	0.550341i	$0.185502\pi$
$828$	23.7479	−	0.386557i	0.825296	−	0.0134338i
$829$			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
$831$	−51.5688	+	7.21657i	−1.78890	+	0.250340i
$832$	−0.507455	−	1.89385i	−0.0175928	−	0.0656574i
$833$	−10.8329	−	2.90266i	−0.375336	−	0.100571i
$834$	6.17491	−	0.864121i	0.213820	−	0.0299221i
$835$	0.507700	−	0.707009i	0.0175697	−	0.0244670i
$836$	7.39370	+	7.16079i	0.255717	+	0.247661i
$837$	−1.47165	+	3.81363i	−0.0508676	+	0.131818i
$838$	0.605548	−	2.25994i	0.0209183	−	0.0780682i
$839$	21.2535	+	36.8121i	0.733751	+	1.27089i	0.955269	+	0.295738i	$0.0955655\pi$
$839$	21.2535	+	36.8121i	0.733751	+	1.27089i	−0.221518	+	0.975156i	$0.571101\pi$
$840$	−0.189495	−	4.75044i	−0.00653820	−	0.163906i
$841$	13.2318	+	22.9181i	0.456267	+	0.790278i
$842$	16.3311	−	4.37590i	0.562806	−	0.150803i
$843$	7.54470	+	17.8033i	0.259853	+	0.613179i
$844$			3.65565i			0.125833i
$845$	−7.23068	+	19.1537i	−0.248743	+	0.658906i
$846$	28.8280	−	8.22958i	0.991127	−	0.282939i
$847$	4.70803	−	4.70803i	0.161770	−	0.161770i
$848$	−1.34912	+	1.34912i	−0.0463291	+	0.0463291i
$849$	−29.3513	+	22.9039i	−1.00733	+	0.786061i
$850$	−6.74595	+	7.66150i	−0.231384	+	0.262787i
$851$	52.3550	+	30.2272i	1.79471	+	1.03617i
$852$	9.25424	+	6.98212i	0.317045	+	0.239203i
$853$	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
$855$	22.0119	−	19.2478i	0.752789	−	0.658261i
$856$	−1.99875			−0.0683160
$857$	7.94044	−	29.6341i	0.271240	−	1.01228i	−0.687079	−	0.726583i	$-0.741107\pi$
$857$	7.94044	−	29.6341i	0.271240	−	1.01228i	0.958319	−	0.285700i	$-0.0922260\pi$
$858$	6.40146	+	4.82975i	0.218542	+	0.164885i
$859$	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
$861$	−20.2771	+	15.8230i	−0.691042	+	0.539247i
$862$	21.2423	−	21.2423i	0.723517	−	0.723517i
$863$	22.1606	−	22.1606i	0.754357	−	0.754357i	−0.220933	−	0.975289i	$-0.570910\pi$
$863$	22.1606	−	22.1606i	0.754357	−	0.754357i	0.975289	+	0.220933i	$0.0709101\pi$
$864$	0.552270	−	5.16672i	0.0187886	−	0.175775i
$865$	−19.1337	+	8.64644i	−0.650565	+	0.293988i
$866$			23.2198i			0.789040i
$867$	8.67205	+	20.4635i	0.294518	+	0.694978i
$868$	−0.932777	+	0.249937i	−0.0316605	+	0.00848341i
$869$	9.80394	+	16.9809i	0.332576	+	0.576038i
$870$	4.53200	+	4.18431i	0.153649	+	0.141861i
$871$	−13.0793	−	22.6539i	−0.443174	−	0.767599i
$872$	2.00076	−	7.46693i	0.0677542	−	0.252862i
$873$	0.642612	+	39.4784i	0.0217491	+	1.33614i
$874$	−8.39719	+	33.4722i	−0.284039	+	1.13221i
$875$	−13.1214	−	4.02309i	−0.443583	−	0.136005i
$876$	9.49249	−	1.32839i	0.320722	−	0.0448820i
$877$	−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
$879$	17.3173	−	2.42340i	0.584098	−	0.0817391i
$880$	1.86484	−	4.93987i	0.0628638	−	0.166523i
$881$		−	34.9729i		−	1.17827i	−0.808035	−	0.589134i	$-0.799469\pi$
$881$		−	34.9729i		−	1.17827i	0.808035	−	0.589134i	$-0.200531\pi$
$882$	−0.268210	−	16.4773i	−0.00903110	−	0.554819i
$883$	−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
$885$	−3.90207	−	6.17620i	−0.131167	−	0.207611i
$886$	18.8385			0.632891
$887$	−32.0804	+	8.59591i	−1.07715	+	0.288622i	−0.753429	−	0.657529i	$-0.771602\pi$
$887$	−32.0804	+	8.59591i	−1.07715	+	0.288622i	−0.323724	+	0.946152i	$0.604935\pi$
$888$	7.96579	−	10.5580i	0.267314	−	0.354304i
$889$	−16.7226	−	9.65478i	−0.560857	−	0.323811i
$890$	14.8386	+	1.47637i	0.497391	+	0.0494880i
$891$	11.2195	+	18.0493i	0.375866	+	0.604675i
$892$	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
$897$	−3.29226	+	26.6835i	−0.109926	+	0.890936i
$898$	−6.29986	+	23.5114i	−0.210229	+	0.784586i
$899$	0.626452	−	1.08505i	0.0208934	−	0.0361883i
$900$	−13.5465	−	6.44144i	−0.451550	−	0.214715i
$901$	−3.89533			−0.129772
$902$	−27.5921	+	7.39328i	−0.918716	+	0.246169i
$903$	0.192438	−	1.55969i	0.00640395	−	0.0519034i
$904$			15.2105i			0.505893i
$905$	−0.738629	−	4.50165i	−0.0245529	−	0.149640i
$906$	17.1635	−	13.3933i	0.570219	−	0.444963i
$907$	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
$909$	−0.141386	+	0.564236i	−0.00468946	+	0.0187145i
$910$	5.35527	+	0.532824i	0.177525	+	0.0176629i
$911$		−	54.2849i		−	1.79854i	−0.437396	−	0.899269i	$-0.644099\pi$
$911$		−	54.2849i		−	1.79854i	0.437396	−	0.899269i	$-0.355901\pi$
$912$	7.04284	+	2.71999i	0.233212	+	0.0900680i
$913$	−18.6581	−	18.6581i	−0.617493	−	0.617493i
$914$	7.45131	+	12.9060i	0.246467	+	0.426894i
$915$	−15.1478	+	28.8331i	−0.500770	+	0.953192i
$916$	3.22471	−	5.58536i	0.106547	−	0.184546i
$917$	−1.99704	+	7.45306i	−0.0659481	+	0.246122i
$918$	8.25622	−	6.66165i	0.272496	−	0.219867i
$919$		−	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
$921$	−2.12885	−	2.72811i	−0.0701479	−	0.0898942i
$922$	−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
$927$	18.8120	−	33.8437i	0.617868	−	1.11157i
$928$	−0.412205	+	1.53837i	−0.0135313	+	0.0504995i
$929$	−1.73605	−	3.00693i	−0.0569580	−	0.0986541i	0.836140	−	0.548515i	$-0.184807\pi$
$929$	−1.73605	−	3.00693i	−0.0569580	−	0.0986541i	−0.893098	+	0.449861i	$0.851473\pi$
$930$	−0.670644	+	2.97209i	−0.0219913	+	0.0974587i
$931$	23.2244	+	5.82633i	0.761151	+	0.190950i
$932$	−5.29832	−	5.29832i	−0.173552	−	0.173552i
$933$	−22.7445	+	30.1460i	−0.744620	+	0.986935i
$934$	23.4038	−	13.5122i	0.765797	−	0.442133i
$935$	9.82362	−	4.43926i	0.321267	−	0.145179i
$936$	5.70557	+	1.42969i	0.186492	+	0.0467310i
$937$	−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	0.968505	−	0.248993i	$-0.0800997\pi$
$941$	37.9497	+	21.9102i	1.23712	+	0.714254i	0.268618	+	0.963247i	$0.413433\pi$
$942$	−6.85860	+	2.90654i	−0.223465	+	0.0947002i
$943$	−67.7215	−	67.7215i	−2.20531	−	2.20531i
$944$	0.943147	−	1.63358i	0.0306968	−	0.0531684i
$945$	12.7325	+	6.42697i	0.414190	+	0.209069i
$946$	0.872684	−	1.51153i	0.0283734	−	0.0491442i
$947$	1.94456	−	7.25718i	0.0631896	−	0.235827i	−0.927107	−	0.374797i	$-0.877712\pi$
$947$	1.94456	−	7.25718i	0.0631896	−	0.235827i	0.990297	+	0.138970i	$0.0443792\pi$
$948$	11.4812	+	8.66229i	0.372891	+	0.281338i
$949$			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	0.172470	−	0.985015i	$-0.444825\pi$
$953$	−5.26882	−	1.41178i	−0.170674	−	0.0457319i	−0.343144	+	0.939283i	$0.611492\pi$
$954$	−1.57123	−	5.50397i	−0.0508704	−	0.178198i
$955$	29.7020	+	36.2654i	0.961133	+	1.17352i
$956$	13.3947	+	7.73346i	0.433217	+	0.250118i
$957$	−2.54164	−	5.99754i	−0.0821596	−	0.193873i
$958$	30.0567	+	30.0567i	0.971087	+	0.971087i
$959$	12.4996	−	21.6499i	0.403633	−	0.699112i
$960$	−0.154371	−	3.86991i	−0.00498229	−	0.124901i
$961$	−30.3811			−0.980036
$962$	10.5865	+	10.5865i	0.341323	+	0.341323i
$963$	2.91322	−	5.24102i	0.0938771	−	0.168890i
$964$	15.4639	−	8.92809i	0.498059	−	0.287555i
$965$	−13.1874	−	29.1824i	−0.424518	−	0.939415i
$966$	−16.6703	+	2.33286i	−0.536359	+	0.0750585i
$967$	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
$969$	6.24068	+	14.0941i	0.200480	+	0.452768i
$970$	4.76505	+	29.0411i	0.152996	+	0.932452i
$971$	25.2791	−	14.5949i	0.811244	−	0.468372i	−0.0361435	−	0.999347i	$-0.511507\pi$
$971$	25.2791	−	14.5949i	0.811244	−	0.468372i	0.847388	+	0.530974i	$0.178174\pi$
$972$	12.7429	+	8.97871i	0.408730	+	0.287992i
$973$	−4.26834	+	1.14370i	−0.136837	+	0.0366653i
$974$	−12.7489	−	22.0818i	−0.408503	−	0.707547i
$975$	9.34646	−	14.1759i	0.299326	−	0.453993i
$976$	−8.40952			−0.269182
$977$	−4.67807	−	4.67807i	−0.149665	−	0.149665i	0.628304	−	0.777968i	$-0.283750\pi$
$977$	−4.67807	−	4.67807i	−0.149665	−	0.149665i	−0.777968	+	0.628304i	$0.783750\pi$
$978$	5.35152	+	0.660281i	0.171123	+	0.0211135i
$979$	−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	−0.0350138	−	0.999387i	$-0.511148\pi$
$983$	−17.7153	−	4.74680i	−0.565030	−	0.151399i	−0.530016	+	0.847987i	$0.677814\pi$
$984$	−16.5186	+	12.8901i	−0.526593	+	0.410921i
$985$	15.2439	+	1.51670i	0.485711	+	0.0483260i
$986$	−2.81595	+	1.62579i	−0.0896781	+	0.0517757i
$987$	−19.5629	+	8.29039i	−0.622695	+	0.263886i
$988$	−4.15418	+	7.46874i	−0.132162	+	0.237612i
$989$	5.85177			0.186075
$990$	10.2350	+	12.0898i	0.325290	+	0.384240i
$991$	−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
$993$	15.8478	+	11.9568i	0.502916	+	0.379439i
$994$	−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.83.15	✓	144
3.2	odd	2	inner	570.2.v.c.83.19	yes	144
5.2	odd	4	inner	570.2.v.c.197.14	yes	144
15.2	even	4	inner	570.2.v.c.197.28	yes	144
19.11	even	3	inner	570.2.v.c.353.28	yes	144
57.11	odd	6	inner	570.2.v.c.353.14	yes	144
95.87	odd	12	inner	570.2.v.c.467.19	yes	144
285.182	even	12	inner	570.2.v.c.467.15	yes	144

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.38266 + 1.04319i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.72991 - 1.41683i) q^{5} +(-1.36550 + 1.06555i) q^{6} +(0.867998 - 0.867998i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.823517 + 2.88476i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.38266 + 1.04319i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.72991 - 1.41683i) q^{5} +(-1.36550 + 1.06555i) q^{6} +(0.867998 - 0.867998i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.823517 + 2.88476i) q^{9} +(0.920816 + 2.03767i) q^{10} -2.36135i q^{11} +(-0.675828 - 1.59476i) q^{12} +(1.89385 - 0.507455i) q^{13} +(0.613767 + 1.06308i) q^{14} +(3.86991 - 0.154371i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.528413 + 1.97206i) q^{17} +(-2.99960 + 0.0488262i) q^{18} +(1.06065 - 4.22789i) q^{19} +(-2.20656 + 0.362052i) q^{20} +(2.10563 - 0.294664i) q^{21} +(2.28089 + 0.611163i) q^{22} +(2.04907 + 7.64725i) q^{23} +(1.71534 - 0.240045i) q^{24} +(0.985200 - 4.90198i) q^{25} +1.96066i q^{26} +(-1.87070 + 4.84773i) q^{27} +(-1.18571 + 0.317709i) q^{28} +(0.796320 - 1.37927i) q^{29} +(-0.852495 + 3.77800i) q^{30} +0.786684 q^{31} +(-0.965926 + 0.258819i) q^{32} +(2.46334 - 3.26496i) q^{33} +(-1.76810 - 1.02081i) q^{34} +(0.271758 - 2.73136i) q^{35} +(0.729192 - 2.91003i) 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} +(-0.260355 + 2.11015i) q^{42} +(0.191303 - 0.713953i) q^{43} +(-1.18068 + 2.04499i) q^{44} +(5.51181 + 3.82360i) q^{45} -7.91701 q^{46} +(-9.65271 + 2.58643i) q^{47} +(-0.212096 + 1.71902i) q^{48} +5.49316i q^{49} +(4.47996 + 2.22036i) q^{50} +(-2.78785 + 2.17547i) q^{51} +(-1.89385 - 0.507455i) q^{52} +(0.493814 + 1.84294i) q^{53} +(-4.19838 - 3.06164i) q^{54} +(-3.34563 - 4.08493i) q^{55} -1.22753i q^{56} +(5.87701 - 4.73928i) q^{57} +(1.12617 + 1.12617i) q^{58} +(-0.943147 - 1.63358i) q^{59} +(-3.42862 - 1.80126i) q^{60} +(-4.20476 + 7.28286i) q^{61} +(-0.203609 + 0.759879i) q^{62} +(3.21877 + 1.78915i) q^{63} -1.00000i q^{64} +(2.55722 - 3.56111i) q^{65} +(2.51615 + 3.22443i) 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} +(2.62215 + 1.45752i) q^{72} +(-1.43228 + 5.34533i) q^{73} +(3.81800 + 6.61297i) q^{74} +(6.47588 - 5.75004i) q^{75} +(-3.03249 + 3.13113i) q^{76} +(-2.04965 - 2.04965i) q^{77} +(-2.04533 + 2.71093i) q^{78} +(-7.19119 + 4.15183i) q^{79} +(2.09197 + 0.789735i) q^{80} +(-7.64364 + 4.75129i) 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} +(2.53988 - 1.07635i) q^{87} +(-1.66973 - 1.66973i) q^{88} +(3.33439 - 5.77534i) q^{89} +(-5.11987 + 4.33438i) q^{90} +(1.20339 - 2.08433i) q^{91} +(2.04907 - 7.64725i) q^{92} +(1.08772 + 0.820660i) 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} +(6.81193 - 1.94461i) 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

Modular forms

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Database

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