LMFDB - Embedded newform 560.2.bb.d.29.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.10
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.d.309.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866818 + 1.11742i) q^{2} +(0.969878 - 0.969878i) q^{3} +(-0.497254 - 1.93720i) q^{4} +(1.42081 + 1.72664i) q^{5} +(0.243053 + 1.92447i) q^{6} +1.00000 q^{7} +(2.59569 + 1.12356i) q^{8} +1.11867i q^{9} +O(q^{10})$	\(q+(-0.866818 + 1.11742i) q^{2} +(0.969878 - 0.969878i) q^{3} +(-0.497254 - 1.93720i) q^{4} +(1.42081 + 1.72664i) q^{5} +(0.243053 + 1.92447i) q^{6} +1.00000 q^{7} +(2.59569 + 1.12356i) q^{8} +1.11867i q^{9} +(-3.16097 + 0.0909610i) q^{10} +(-3.66206 + 3.66206i) q^{11} +(-2.36112 - 1.39657i) q^{12} +(-3.00277 + 3.00277i) q^{13} +(-0.866818 + 1.11742i) q^{14} +(3.05265 + 0.296616i) q^{15} +(-3.50548 + 1.92656i) q^{16} -5.78965i q^{17} +(-1.25003 - 0.969687i) q^{18} +(4.80124 + 4.80124i) q^{19} +(2.63834 - 3.61098i) q^{20} +(0.969878 - 0.969878i) q^{21} +(-0.917719 - 7.26639i) q^{22} +7.46391 q^{23} +(3.60722 - 1.42779i) q^{24} +(-0.962581 + 4.90647i) q^{25} +(-0.752500 - 5.95820i) q^{26} +(3.99461 + 3.99461i) q^{27} +(-0.497254 - 1.93720i) q^{28} +(-4.64612 - 4.64612i) q^{29} +(-2.97753 + 3.15397i) q^{30} -3.48917 q^{31} +(0.885835 - 5.58707i) q^{32} +7.10349i q^{33} +(6.46947 + 5.01857i) q^{34} +(1.42081 + 1.72664i) q^{35} +(2.16709 - 0.556265i) q^{36} +(3.30077 + 3.30077i) q^{37} +(-9.52679 + 1.20320i) q^{38} +5.82464i q^{39} +(1.74801 + 6.07819i) q^{40} -0.955310i q^{41} +(0.243053 + 1.92447i) q^{42} +(3.96822 + 3.96822i) q^{43} +(8.91510 + 5.27316i) q^{44} +(-1.93155 + 1.58943i) q^{45} +(-6.46985 + 8.34032i) q^{46} -5.57677i q^{47} +(-1.53136 + 5.26841i) q^{48} +1.00000 q^{49} +(-4.64820 - 5.32862i) q^{50} +(-5.61526 - 5.61526i) q^{51} +(7.31010 + 4.32382i) q^{52} +(-1.29990 - 1.29990i) q^{53} +(-7.92626 + 1.00106i) q^{54} +(-11.5262 - 1.11996i) q^{55} +(2.59569 + 1.12356i) q^{56} +9.31322 q^{57} +(9.21900 - 1.16433i) q^{58} +(5.95731 - 5.95731i) q^{59} +(-0.943335 - 6.06107i) q^{60} +(-3.19445 - 3.19445i) q^{61} +(3.02448 - 3.89887i) q^{62} +1.11867i q^{63} +(5.47524 + 5.83282i) q^{64} +(-9.45108 - 0.918332i) q^{65} +(-7.93758 - 6.15743i) q^{66} +(-0.212495 + 0.212495i) q^{67} +(-11.2157 + 2.87893i) q^{68} +(7.23908 - 7.23908i) q^{69} +(-3.16097 + 0.0909610i) q^{70} +11.9602i q^{71} +(-1.25689 + 2.90374i) q^{72} +0.883279 q^{73} +(-6.54951 + 0.827179i) q^{74} +(3.82509 + 5.69226i) q^{75} +(6.91352 - 11.6884i) q^{76} +(-3.66206 + 3.66206i) q^{77} +(-6.50856 - 5.04890i) q^{78} -3.24034 q^{79} +(-8.30710 - 3.31542i) q^{80} +4.39254 q^{81} +(1.06748 + 0.828080i) q^{82} +(7.95239 - 7.95239i) q^{83} +(-2.36112 - 1.39657i) q^{84} +(9.99665 - 8.22601i) q^{85} +(-7.87389 + 0.994444i) q^{86} -9.01233 q^{87} +(-13.6201 + 5.39104i) q^{88} -10.6216i q^{89} +(-0.101756 - 3.53610i) q^{90} +(-3.00277 + 3.00277i) q^{91} +(-3.71146 - 14.4591i) q^{92} +(-3.38407 + 3.38407i) q^{93} +(6.23160 + 4.83405i) q^{94} +(-1.46835 + 15.1117i) q^{95} +(-4.55962 - 6.27792i) q^{96} +11.7429i q^{97} +(-0.866818 + 1.11742i) q^{98} +(-4.09665 - 4.09665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.866818	+	1.11742i	−0.612933	+	0.790135i
$2$	−0.866818	+	1.11742i	−0.612933	+	0.790135i
$3$	0.969878	−	0.969878i	0.559959	−	0.559959i	−0.369337	−	0.929296i	$-0.620415\pi$
$3$	0.969878	−	0.969878i	0.559959	−	0.559959i	0.929296	+	0.369337i	$0.120415\pi$
$4$	−0.497254	−	1.93720i	−0.248627	−	0.968599i
$5$	1.42081	+	1.72664i	0.635407	+	0.772178i
$5$	1.42081	+	1.72664i	0.635407	+	0.772178i
$6$	0.243053	+	1.92447i	0.0992261	+	0.785661i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.59569	+	1.12356i	0.917716	+	0.397237i
$9$			1.11867i			0.372892i
$10$	−3.16097	+	0.0909610i	−0.999586	+	0.0287644i
$11$	−3.66206	+	3.66206i	−1.10415	+	1.10415i	−0.110247	+	0.993904i	$0.535164\pi$
$11$	−3.66206	+	3.66206i	−1.10415	+	1.10415i	−0.993904	+	0.110247i	$0.964836\pi$
$12$	−2.36112	−	1.39657i	−0.681597	−	0.403155i
$13$	−3.00277	+	3.00277i	−0.832818	+	0.832818i	−0.987901	−	0.155083i	$-0.950435\pi$
$13$	−3.00277	+	3.00277i	−0.832818	+	0.832818i	0.155083	+	0.987901i	$0.450435\pi$
$14$	−0.866818	+	1.11742i	−0.231667	+	0.298643i
$15$	3.05265	+	0.296616i	0.788190	+	0.0765860i
$16$	−3.50548	+	1.92656i	−0.876369	+	0.481640i
$17$		−	5.78965i		−	1.40420i	−0.712080	−	0.702099i	$-0.752247\pi$
$17$		−	5.78965i		−	1.40420i	0.712080	−	0.702099i	$-0.247753\pi$
$18$	−1.25003	−	0.969687i	−0.294635	−	0.228557i
$19$	4.80124	+	4.80124i	1.10148	+	1.10148i	0.994232	+	0.107247i	$0.0342035\pi$
$19$	4.80124	+	4.80124i	1.10148	+	1.10148i	0.107247	+	0.994232i	$0.465796\pi$
$20$	2.63834	−	3.61098i	0.589951	−	0.807439i
$21$	0.969878	−	0.969878i	0.211645	−	0.211645i
$22$	−0.917719	−	7.26639i	−0.195658	−	1.54920i
$23$	7.46391			1.55633			0.778167	−	0.628058i	$-0.216150\pi$
$23$	7.46391			1.55633			0.778167	+	0.628058i	$0.216150\pi$
$24$	3.60722	−	1.42779i	0.736320	−	0.291447i
$25$	−0.962581	+	4.90647i	−0.192516	+	0.981294i
$26$	−0.752500	−	5.95820i	−0.147577	−	1.16850i
$27$	3.99461	+	3.99461i	0.768763	+	0.768763i
$28$	−0.497254	−	1.93720i	−0.0939721	−	0.366096i
$29$	−4.64612	−	4.64612i	−0.862762	−	0.862762i	0.128896	−	0.991658i	$-0.458857\pi$
$29$	−4.64612	−	4.64612i	−0.862762	−	0.862762i	−0.991658	+	0.128896i	$0.958857\pi$
$30$	−2.97753	+	3.15397i	−0.543621	+	0.575834i
$31$	−3.48917			−0.626674			−0.313337	−	0.949642i	$-0.601447\pi$
$31$	−3.48917			−0.626674			−0.313337	+	0.949642i	$0.601447\pi$
$32$	0.885835	−	5.58707i	0.156595	−	0.987663i
$33$			7.10349i			1.23656i
$34$	6.46947	+	5.01857i	1.10951	+	0.860678i
$35$	1.42081	+	1.72664i	0.240161	+	0.291856i
$36$	2.16709	−	0.556265i	0.361182	−	0.0927109i
$37$	3.30077	+	3.30077i	0.542643	+	0.542643i	0.924303	−	0.381660i	$-0.124647\pi$
$37$	3.30077	+	3.30077i	0.542643	+	0.542643i	−0.381660	+	0.924303i	$0.624647\pi$
$38$	−9.52679	+	1.20320i	−1.54545	+	0.195185i
$39$			5.82464i			0.932688i
$40$	1.74801	+	6.07819i	0.276385	+	0.961047i
$41$		−	0.955310i		−	0.149194i	−0.997214	−	0.0745972i	$-0.976233\pi$
$41$		−	0.955310i		−	0.149194i	0.997214	−	0.0745972i	$-0.0237671\pi$
$42$	0.243053	+	1.92447i	0.0375039	+	0.296952i
$43$	3.96822	+	3.96822i	0.605148	+	0.605148i	0.941674	−	0.336526i	$-0.109252\pi$
$43$	3.96822	+	3.96822i	0.605148	+	0.605148i	−0.336526	+	0.941674i	$0.609252\pi$
$44$	8.91510	+	5.27316i	1.34400	+	0.794959i
$45$	−1.93155	+	1.58943i	−0.287938	+	0.236938i
$46$	−6.46985	+	8.34032i	−0.953927	+	1.22971i
$47$		−	5.57677i		−	0.813456i	−0.913549	−	0.406728i	$-0.866670\pi$
$47$		−	5.57677i		−	0.813456i	0.913549	−	0.406728i	$-0.133330\pi$
$48$	−1.53136	+	5.26841i	−0.221032	+	0.760430i
$49$	1.00000			0.142857
$50$	−4.64820	−	5.32862i	−0.657355	−	0.753581i
$51$	−5.61526	−	5.61526i	−0.786293	−	0.786293i
$52$	7.31010	+	4.32382i	1.01373	+	0.599606i
$53$	−1.29990	−	1.29990i	−0.178554	−	0.178554i	0.612171	−	0.790725i	$-0.290296\pi$
$53$	−1.29990	−	1.29990i	−0.178554	−	0.178554i	−0.790725	+	0.612171i	$0.790296\pi$
$54$	−7.92626	+	1.00106i	−1.07863	+	0.136227i
$55$	−11.5262	−	1.11996i	−1.55419	−	0.151016i
$56$	2.59569	+	1.12356i	0.346864	+	0.150142i
$57$	9.31322			1.23357
$58$	9.21900	−	1.16433i	1.21051	−	0.152884i
$59$	5.95731	−	5.95731i	0.775576	−	0.775576i	−0.203499	−	0.979075i	$-0.565231\pi$
$59$	5.95731	−	5.95731i	0.775576	−	0.775576i	0.979075	+	0.203499i	$0.0652315\pi$
$60$	−0.943335	−	6.06107i	−0.121784	−	0.782481i
$61$	−3.19445	−	3.19445i	−0.409007	−	0.409007i	0.472385	−	0.881392i	$-0.343393\pi$
$61$	−3.19445	−	3.19445i	−0.409007	−	0.409007i	−0.881392	+	0.472385i	$0.843393\pi$
$62$	3.02448	−	3.89887i	0.384109	−	0.495157i
$63$			1.11867i			0.140940i
$64$	5.47524	+	5.83282i	0.684405	+	0.729102i
$65$	−9.45108	−	0.918332i	−1.17226	−	0.113905i
$66$	−7.93758	−	6.15743i	−0.977049	−	0.757928i
$67$	−0.212495	+	0.212495i	−0.0259605	+	0.0259605i	−0.719968	−	0.694007i	$-0.755843\pi$
$67$	−0.212495	+	0.212495i	−0.0259605	+	0.0259605i	0.694007	+	0.719968i	$0.255843\pi$
$68$	−11.2157	+	2.87893i	−1.36010	+	0.349121i
$69$	7.23908	−	7.23908i	0.871483	−	0.871483i
$70$	−3.16097	+	0.0909610i	−0.377808	+	0.0108719i
$71$			11.9602i			1.41942i	0.704494	+	0.709710i	$0.251174\pi$
$71$			11.9602i			1.41942i	−0.704494	+	0.709710i	$0.748826\pi$
$72$	−1.25689	+	2.90374i	−0.148126	+	0.342208i
$73$	0.883279			0.103380			0.0516900	−	0.998663i	$-0.483539\pi$
$73$	0.883279			0.103380			0.0516900	+	0.998663i	$0.483539\pi$
$74$	−6.54951	+	0.827179i	−0.761365	+	0.0961576i
$75$	3.82509	+	5.69226i	0.441683	+	0.657286i
$76$	6.91352	−	11.6884i	0.793035	−	1.34075i
$77$	−3.66206	+	3.66206i	−0.417330	+	0.417330i
$78$	−6.50856	−	5.04890i	−0.736950	−	0.571675i
$79$	−3.24034			−0.364566			−0.182283	−	0.983246i	$-0.558349\pi$
$79$	−3.24034			−0.364566			−0.182283	+	0.983246i	$0.558349\pi$
$80$	−8.30710	−	3.31542i	−0.928762	−	0.370675i
$81$	4.39254			0.488060
$82$	1.06748	+	0.828080i	0.117884	+	0.0914461i
$83$	7.95239	−	7.95239i	0.872888	−	0.872888i	−0.119898	−	0.992786i	$-0.538257\pi$
$83$	7.95239	−	7.95239i	0.872888	−	0.872888i	0.992786	+	0.119898i	$0.0382569\pi$
$84$	−2.36112	−	1.39657i	−0.257619	−	0.152378i
$85$	9.99665	−	8.22601i	1.08429	−	0.892236i
$86$	−7.87389	+	0.994444i	−0.849064	+	0.107234i
$87$	−9.01233			−0.966223
$88$	−13.6201	+	5.39104i	−1.45191	+	0.574687i
$89$		−	10.6216i		−	1.12589i	−0.826496	−	0.562943i	$-0.809669\pi$
$89$		−	10.6216i		−	1.12589i	0.826496	−	0.562943i	$-0.190331\pi$
$90$	−0.101756	−	3.53610i	−0.0107260	−	0.372737i
$91$	−3.00277	+	3.00277i	−0.314776	+	0.314776i
$92$	−3.71146	−	14.4591i	−0.386946	−	1.50746i
$93$	−3.38407	+	3.38407i	−0.350912	+	0.350912i
$94$	6.23160	+	4.83405i	0.642740	+	0.498594i
$95$	−1.46835	+	15.1117i	−0.150650	+	1.55043i
$96$	−4.55962	−	6.27792i	−0.465364	−	0.640738i
$97$			11.7429i			1.19231i	0.802868	+	0.596157i	$0.203306\pi$
$97$			11.7429i			1.19231i	−0.802868	+	0.596157i	$0.796694\pi$
$98$	−0.866818	+	1.11742i	−0.0875618	+	0.112876i
$99$	−4.09665	−	4.09665i	−0.411729	−	0.411729i
$100$	9.98345	−	0.575050i	0.998345	−	0.0575050i
$101$	−1.87648	+	1.87648i	−0.186716	+	0.186716i	−0.794275	−	0.607559i	$-0.792149\pi$
$101$	−1.87648	+	1.87648i	−0.186716	+	0.186716i	0.607559	+	0.794275i	$0.292149\pi$
$102$	11.1420	−	1.40719i	1.10322	−	0.139333i
$103$	−4.51219			−0.444600			−0.222300	−	0.974978i	$-0.571356\pi$
$103$	−4.51219			−0.444600			−0.222300	+	0.974978i	$0.571356\pi$
$104$	−11.1680	+	4.42048i	−1.09512	+	0.433464i
$105$	3.05265	+	0.296616i	0.297908	+	0.0289468i
$106$	2.57930	−	0.325757i	0.250524	−	0.0316403i
$107$	3.30554	+	3.30554i	0.319559	+	0.319559i	0.848598	−	0.529039i	$-0.177447\pi$
$107$	3.30554	+	3.30554i	0.319559	+	0.319559i	−0.529039	+	0.848598i	$0.677447\pi$
$108$	5.75202	−	9.72469i	0.553488	−	0.935759i
$109$	−7.07807	−	7.07807i	−0.677956	−	0.677956i	0.281582	−	0.959537i	$-0.409141\pi$
$109$	−7.07807	−	7.07807i	−0.677956	−	0.677956i	−0.959537	+	0.281582i	$0.909141\pi$
$110$	11.2425	−	11.9088i	1.07193	−	1.13545i
$111$	6.40268			0.607716
$112$	−3.50548	+	1.92656i	−0.331236	+	0.182043i
$113$		−	15.0538i		−	1.41614i	−0.706140	−	0.708072i	$-0.749565\pi$
$113$		−	15.0538i		−	1.41614i	0.706140	−	0.708072i	$-0.250435\pi$
$114$	−8.07287	+	10.4068i	−0.756093	+	0.974684i
$115$	10.6048	+	12.8875i	0.988905	+	1.20177i
$116$	−6.69015	+	11.3108i	−0.621165	+	1.05018i
$117$	−3.35912	−	3.35912i	−0.310551	−	0.310551i
$118$	1.49291	+	11.8207i	0.137434	+	1.08819i
$119$		−	5.78965i		−	0.530737i
$120$	7.59046	+	4.19975i	0.692911	+	0.383383i
$121$		−	15.8213i		−	1.43830i
$122$	6.33854	−	0.800535i	0.573865	−	0.0724770i
$123$	−0.926534	−	0.926534i	−0.0835427	−	0.0835427i
$124$	1.73501	+	6.75922i	0.155808	+	0.606996i
$125$	−9.83936	+	5.30914i	−0.880059	+	0.474864i
$126$	−1.25003	−	0.969687i	−0.111361	−	0.0863866i
$127$		−	12.1885i		−	1.08156i	−0.841165	−	0.540779i	$-0.818130\pi$
$127$		−	12.1885i		−	1.08156i	0.841165	−	0.540779i	$-0.181870\pi$
$128$	−11.2637	+	1.06215i	−0.995583	+	0.0938818i
$129$	7.69738			0.677716
$130$	9.21852	−	9.76479i	0.808518	−	0.856429i
$131$	9.76640	+	9.76640i	0.853295	+	0.853295i	0.990537	−	0.137243i	$-0.0438241\pi$
$131$	9.76640	+	9.76640i	0.853295	+	0.853295i	−0.137243	+	0.990537i	$0.543824\pi$
$132$	13.7609	−	3.53224i	1.19773	−	0.307442i
$133$	4.80124	+	4.80124i	0.416320	+	0.416320i
$134$	−0.0532518	−	0.421641i	−0.00460025	−	0.0364243i
$135$	−1.22167	+	12.5729i	−0.105144	+	1.08210i
$136$	6.50501	−	15.0282i	0.557800	−	1.28865i
$137$	8.97032			0.766386			0.383193	−	0.923668i	$-0.374824\pi$
$137$	8.97032			0.766386			0.383193	+	0.923668i	$0.374824\pi$
$138$	1.81413	+	14.3641i	0.154429	+	1.22275i
$139$	6.42586	−	6.42586i	0.545035	−	0.545035i	−0.379966	−	0.925000i	$-0.624064\pi$
$139$	6.42586	−	6.42586i	0.545035	−	0.545035i	0.925000	+	0.379966i	$0.124064\pi$
$140$	2.63834	−	3.61098i	0.222981	−	0.305183i
$141$	−5.40879	−	5.40879i	−0.455502	−	0.455502i
$142$	−13.3646	−	10.3673i	−1.12153	−	0.870008i
$143$		−	21.9926i		−	1.83911i
$144$	−2.15519	−	3.92149i	−0.179599	−	0.326791i
$145$	1.42092	−	14.6234i	0.118001	−	1.21441i
$146$	−0.765642	+	0.986993i	−0.0633650	+	0.0816841i
$147$	0.969878	−	0.969878i	0.0799942	−	0.0799942i
$148$	4.75292	−	8.03556i	0.390688	−	0.660519i
$149$	11.6452	−	11.6452i	0.954012	−	0.954012i	−0.0449763	−	0.998988i	$-0.514321\pi$
$149$	11.6452	−	11.6452i	0.954012	−	0.954012i	0.998988	+	0.0449763i	$0.0143212\pi$
$150$	−9.67630	−	0.659923i	−0.790067	−	0.0538825i
$151$		−	11.9554i		−	0.972913i	−0.873705	−	0.486457i	$-0.838289\pi$
$151$		−	11.9554i		−	0.972913i	0.873705	−	0.486457i	$-0.161711\pi$
$152$	7.06807	+	17.8570i	0.573296	+	1.44839i
$153$	6.47674			0.523613
$154$	−0.917719	−	7.26639i	−0.0739519	−	0.585542i
$155$	−4.95746	−	6.02455i	−0.398193	−	0.483904i
$156$	11.2835	−	2.89632i	0.903401	−	0.231891i
$157$	13.6591	−	13.6591i	1.09011	−	1.09011i	0.0945985	−	0.995516i	$-0.469843\pi$
$157$	13.6591	−	13.6591i	1.09011	−	1.09011i	0.995516	−	0.0945985i	$-0.0301567\pi$
$158$	2.80878	−	3.62082i	0.223455	−	0.288057i
$159$	−2.52148			−0.199966
$160$	10.9055	−	6.40866i	0.862153	−	0.506649i
$161$	7.46391			0.588239
$162$	−3.80753	+	4.90831i	−0.299148	+	0.385634i
$163$	−6.08132	+	6.08132i	−0.476326	+	0.476326i	−0.903955	−	0.427628i	$-0.859349\pi$
$163$	−6.08132	+	6.08132i	−0.476326	+	0.476326i	0.427628	+	0.903955i	$0.359349\pi$
$164$	−1.85062	+	0.475031i	−0.144510	+	0.0370937i
$165$	−12.2652	+	10.0927i	−0.954843	+	0.785718i
$166$	1.99288	+	15.7794i	0.154678	+	1.22472i
$167$	1.29964			0.100569			0.0502845	−	0.998735i	$-0.483987\pi$
$167$	1.29964			0.100569			0.0502845	+	0.998735i	$0.483987\pi$
$168$	3.60722	−	1.42779i	0.278303	−	0.110156i
$169$		−	5.03323i		−	0.387172i
$170$	0.526633	+	18.3009i	0.0403909	+	1.40362i
$171$	−5.37102	+	5.37102i	−0.410732	+	0.410732i
$172$	5.71402	−	9.66045i	0.435690	−	0.736602i
$173$	−8.93400	+	8.93400i	−0.679239	+	0.679239i	−0.959828	−	0.280589i	$-0.909470\pi$
$173$	−8.93400	+	8.93400i	−0.679239	+	0.679239i	0.280589	+	0.959828i	$0.409470\pi$
$174$	7.81205	−	10.0706i	0.592230	−	0.763447i
$175$	−0.962581	+	4.90647i	−0.0727643	+	0.370894i
$176$	5.78209	−	19.8924i	0.435841	−	1.49945i
$177$		−	11.5557i		−	0.868581i
$178$	11.8688	+	9.20698i	0.889602	+	0.690093i
$179$	−5.28077	−	5.28077i	−0.394703	−	0.394703i	0.481657	−	0.876360i	$-0.340035\pi$
$179$	−5.28077	−	5.28077i	−0.394703	−	0.394703i	−0.876360	+	0.481657i	$0.840035\pi$
$180$	4.03951	+	2.95145i	0.301087	+	0.219988i
$181$	−14.5619	+	14.5619i	−1.08238	+	1.08238i	−0.0860908	+	0.996287i	$0.527438\pi$
$181$	−14.5619	+	14.5619i	−1.08238	+	1.08238i	−0.996287	+	0.0860908i	$0.972562\pi$
$182$	−0.752500	−	5.95820i	−0.0557790	−	0.441652i
$183$	−6.19645			−0.458055
$184$	19.3740	+	8.38613i	1.42827	+	0.618234i
$185$	−1.00947	+	10.3890i	−0.0742176	+	0.763816i
$186$	−0.848055	−	6.71480i	−0.0621824	−	0.492353i
$187$	21.2020	+	21.2020i	1.55045	+	1.55045i
$188$	−10.8033	+	2.77307i	−0.787913	+	0.202247i
$189$	3.99461	+	3.99461i	0.290565	+	0.290565i
$190$	−15.6133	−	14.7398i	−1.13271	−	1.06934i
$191$	−18.9886			−1.37397			−0.686984	−	0.726673i	$-0.741066\pi$
$191$	−18.9886			−1.37397			−0.686984	+	0.726673i	$0.741066\pi$
$192$	10.9674	+	0.346807i	0.791506	+	0.0250286i
$193$		−	23.1691i		−	1.66775i	−0.551954	−	0.833875i	$-0.686117\pi$
$193$		−	23.1691i		−	1.66775i	0.551954	−	0.833875i	$-0.313883\pi$
$194$	−13.1218	−	10.1790i	−0.942089	−	0.730808i
$195$	−10.0571	+	8.27572i	−0.720201	+	0.592636i
$196$	−0.497254	−	1.93720i	−0.0355181	−	0.138371i
$197$	−6.18476	−	6.18476i	−0.440646	−	0.440646i	0.451583	−	0.892229i	$-0.350859\pi$
$197$	−6.18476	−	6.18476i	−0.440646	−	0.440646i	−0.892229	+	0.451583i	$0.850859\pi$
$198$	8.12873	−	1.02663i	0.577683	−	0.0729593i
$199$			2.20564i			0.156354i	0.996939	+	0.0781770i	$0.0249099\pi$
$199$			2.20564i			0.156354i	−0.996939	+	0.0781770i	$0.975090\pi$
$200$	−8.01126	+	11.6542i	−0.566482	+	0.824074i
$201$			0.412189i			0.0290736i
$202$	−0.470249	−	3.72338i	−0.0330866	−	0.261976i
$203$	−4.64612	−	4.64612i	−0.326094	−	0.326094i
$204$	−8.08566	+	13.6701i	−0.566109	+	0.957096i
$205$	1.64948	−	1.35732i	0.115205	−	0.0947991i
$206$	3.91125	−	5.04201i	0.272510	−	0.351294i
$207$			8.34969i			0.580343i
$208$	4.74113	−	16.3111i	0.328738	−	1.13097i
$209$	−35.1648			−2.43240
$210$	−2.97753	+	3.15397i	−0.205469	+	0.217645i
$211$	4.58731	+	4.58731i	0.315804	+	0.315804i	0.847153	−	0.531349i	$-0.178315\pi$
$211$	4.58731	+	4.58731i	0.315804	+	0.315804i	−0.531349	+	0.847153i	$0.678315\pi$
$212$	−1.87178	+	3.16454i	−0.128554	+	0.217341i
$213$	11.6000	+	11.6000i	0.794817	+	0.794817i
$214$	−6.55898	+	0.828375i	−0.448362	+	0.0566265i
$215$	−1.21360	+	12.4898i	−0.0827665	+	0.851797i
$216$	5.88061	+	14.8570i	0.400125	+	1.01089i
$217$	−3.48917			−0.236861
$218$	14.0446	−	1.77378i	0.951218	−	0.120135i
$219$	0.856672	−	0.856672i	0.0578886	−	0.0578886i
$220$	3.56184	+	22.8854i	0.240139	+	1.54293i
$221$	17.3850	+	17.3850i	1.16944	+	1.16944i
$222$	−5.54996	+	7.15448i	−0.372489	+	0.480177i
$223$		−	2.26167i		−	0.151453i	−0.997129	−	0.0757263i	$-0.975872\pi$
$223$		−	2.26167i		−	0.151453i	0.997129	−	0.0757263i	$-0.0241275\pi$
$224$	0.885835	−	5.58707i	0.0591873	−	0.373301i
$225$	−5.48874	−	1.07682i	−0.365916	−	0.0717877i
$226$	16.8214	+	13.0489i	1.11895	+	0.868002i
$227$	12.1558	−	12.1558i	0.806808	−	0.806808i	−0.177341	−	0.984149i	$-0.556750\pi$
$227$	12.1558	−	12.1558i	0.806808	−	0.806808i	0.984149	+	0.177341i	$0.0567496\pi$
$228$	−4.63104	−	18.0416i	−0.306698	−	1.19483i
$229$	−10.2263	+	10.2263i	−0.675775	+	0.675775i	−0.959041	−	0.283266i	$-0.908582\pi$
$229$	−10.2263	+	10.2263i	−0.675775	+	0.675775i	0.283266	+	0.959041i	$0.408582\pi$
$230$	−23.5932	+	0.678925i	−1.55569	+	0.0447670i
$231$			7.10349i			0.467376i
$232$	−6.83972	−	17.2801i	−0.449049	−	1.13449i
$233$	−26.5938			−1.74222			−0.871108	−	0.491091i	$-0.836598\pi$
$233$	−26.5938			−1.74222			−0.871108	+	0.491091i	$0.836598\pi$
$234$	6.66529	−	0.841802i	0.435724	−	0.0550303i
$235$	9.62909	−	7.92355i	0.628132	−	0.516875i
$236$	−14.5028	−	8.57820i	−0.944051	−	0.558393i
$237$	−3.14273	+	3.14273i	−0.204142	+	0.204142i
$238$	6.46947	+	5.01857i	0.419354	+	0.325306i
$239$	−11.4280			−0.739214			−0.369607	−	0.929188i	$-0.620508\pi$
$239$	−11.4280			−0.739214			−0.369607	+	0.929188i	$0.620508\pi$
$240$	−11.2724	+	4.84132i	−0.727632	+	0.312506i
$241$	18.4227			1.18671			0.593356	−	0.804940i	$-0.297803\pi$
$241$	18.4227			1.18671			0.593356	+	0.804940i	$0.297803\pi$
$242$	17.6790	+	13.7142i	1.13645	+	0.881582i
$243$	−7.72360	+	7.72360i	−0.495469	+	0.495469i
$244$	−4.59983	+	7.77673i	−0.294474	+	0.497854i
$245$	1.42081	+	1.72664i	0.0907724	+	0.110311i
$246$	1.83846	−	0.232191i	0.117216	−	0.0148040i
$247$	−28.8340			−1.83466
$248$	−9.05682	−	3.92029i	−0.575109	−	0.248938i
$249$		−	15.4257i		−	0.977563i
$250$	2.59639	−	15.5968i	0.164210	−	0.986425i
$251$	2.04394	−	2.04394i	0.129013	−	0.129013i	−0.639652	−	0.768665i	$-0.720922\pi$
$251$	2.04394	−	2.04394i	0.129013	−	0.129013i	0.768665	+	0.639652i	$0.220922\pi$
$252$	2.16709	−	0.556265i	0.136514	−	0.0350414i
$253$	−27.3333	+	27.3333i	−1.71843	+	1.71843i
$254$	13.6197	+	10.5652i	0.854577	+	0.662922i
$255$	1.71730	−	17.6738i	0.107542	−	1.10677i
$256$	8.57674	−	13.5070i	0.536046	−	0.844189i
$257$		−	16.4714i		−	1.02746i	−0.857952	−	0.513730i	$-0.828263\pi$
$257$		−	16.4714i		−	1.02746i	0.857952	−	0.513730i	$-0.171737\pi$
$258$	−6.67222	+	8.60120i	−0.415395	+	0.535488i
$259$	3.30077	+	3.30077i	0.205100	+	0.205100i
$260$	2.92059	+	18.7653i	0.181127	+	1.16377i
$261$	5.19749	−	5.19749i	0.321717	−	0.321717i
$262$	−19.3789	+	2.44748i	−1.19723	+	0.151206i
$263$	−7.23918			−0.446387			−0.223193	−	0.974774i	$-0.571648\pi$
$263$	−7.23918			−0.446387			−0.223193	+	0.974774i	$0.571648\pi$
$264$	−7.98118	+	18.4385i	−0.491208	+	1.13481i
$265$	0.397545	−	4.09136i	0.0244210	−	0.251331i
$266$	−9.52679	+	1.20320i	−0.584125	+	0.0737729i
$267$	−10.3016	−	10.3016i	−0.630450	−	0.630450i
$268$	0.517310	+	0.305982i	0.0315997	+	0.0186908i
$269$	6.12387	+	6.12387i	0.373379	+	0.373379i	0.868706	−	0.495327i	$-0.164952\pi$
$269$	6.12387	+	6.12387i	0.373379	+	0.373379i	−0.495327	+	0.868706i	$0.664952\pi$
$270$	−12.9902	−	12.2635i	−0.790558	−	0.746332i
$271$	26.2755			1.59612			0.798060	−	0.602577i	$-0.205859\pi$
$271$	26.2755			1.59612			0.798060	+	0.602577i	$0.205859\pi$
$272$	11.1541	+	20.2955i	0.676317	+	1.23060i
$273$			5.82464i			0.352523i
$274$	−7.77564	+	10.0236i	−0.469743	+	0.605549i
$275$	−14.4427	−	21.4928i	−0.870930	−	1.29606i
$276$	−17.6232	−	10.4239i	−1.06079	−	0.627444i
$277$	−10.6537	−	10.6537i	−0.640116	−	0.640116i	0.310468	−	0.950584i	$-0.399514\pi$
$277$	−10.6537	−	10.6537i	−0.640116	−	0.640116i	−0.950584	+	0.310468i	$0.899514\pi$
$278$	1.61033	+	12.7504i	0.0965814	+	0.764720i
$279$		−	3.90325i		−	0.233681i
$280$	1.74801	+	6.07819i	0.104464	+	0.363242i
$281$			2.01104i			0.119969i	0.998199	+	0.0599844i	$0.0191051\pi$
$281$			2.01104i			0.119969i	−0.998199	+	0.0599844i	$0.980895\pi$
$282$	10.7323	−	1.35545i	0.639100	−	0.0807160i
$283$	7.49224	+	7.49224i	0.445368	+	0.445368i	0.893811	−	0.448444i	$-0.148021\pi$
$283$	7.49224	+	7.49224i	0.445368	+	0.445368i	−0.448444	+	0.893811i	$0.648021\pi$
$284$	23.1694	−	5.94727i	1.37485	−	0.352906i
$285$	13.2324	+	16.0806i	0.783817	+	0.952533i
$286$	24.5750	+	19.0636i	1.45315	+	1.12725i
$287$		−	0.955310i		−	0.0563902i
$288$	6.25011	+	0.990961i	0.368291	+	0.0583929i
$289$	−16.5201			−0.971769
$290$	15.1089	+	14.2636i	0.887222	+	0.837589i
$291$	11.3892	+	11.3892i	0.667647	+	0.667647i
$292$	−0.439214	−	1.71109i	−0.0257030	−	0.100134i
$293$	1.46230	+	1.46230i	0.0854284	+	0.0854284i	0.748530	−	0.663101i	$-0.230760\pi$
$293$	1.46230	+	1.46230i	0.0854284	+	0.0854284i	−0.663101	+	0.748530i	$0.730760\pi$
$294$	0.243053	+	1.92447i	0.0141752	+	0.112237i
$295$	18.7504	+	1.82191i	1.09169	+	0.106076i
$296$	4.85918	+	12.2764i	0.282434	+	0.713550i
$297$	−29.2570			−1.69766
$298$	2.91831	+	23.1068i	0.169053	+	1.33854i
$299$	−22.4124	+	22.4124i	−1.29614	+	1.29614i
$300$	9.12500	−	10.2405i	0.526832	−	0.591233i
$301$	3.96822	+	3.96822i	0.228724	+	0.228724i
$302$	13.3592	+	10.3631i	0.768733	+	0.596330i
$303$			3.63991i			0.209107i
$304$	−26.0805	−	7.58076i	−1.49582	−	0.434786i
$305$	0.976953	−	10.0544i	0.0559402	−	0.575712i
$306$	−5.61415	+	7.23723i	−0.320940	+	0.413725i
$307$	2.91710	−	2.91710i	0.166488	−	0.166488i	−0.618946	−	0.785434i	$-0.712440\pi$
$307$	2.91710	−	2.91710i	0.166488	−	0.166488i	0.785434	+	0.618946i	$0.212440\pi$
$308$	8.91510	+	5.27316i	0.507985	+	0.300466i
$309$	−4.37628	+	4.37628i	−0.248958	+	0.248958i
$310$	11.0292	−	0.317379i	0.626415	−	0.0180259i
$311$			8.89345i			0.504301i	0.967688	+	0.252151i	$0.0811378\pi$
$311$			8.89345i			0.504301i	−0.967688	+	0.252151i	$0.918862\pi$
$312$	−6.54431	+	15.1190i	−0.370499	+	0.855943i
$313$	11.6809			0.660242			0.330121	−	0.943939i	$-0.392910\pi$
$313$	11.6809			0.660242			0.330121	+	0.943939i	$0.392910\pi$
$314$	3.42299	+	27.1029i	0.193171	+	1.52950i
$315$	−1.93155	+	1.58943i	−0.108831	+	0.0895541i
$316$	1.61127	+	6.27718i	0.0906410	+	0.353119i
$317$	12.3721	−	12.3721i	0.694886	−	0.694886i	−0.268417	−	0.963303i	$-0.586500\pi$
$317$	12.3721	−	12.3721i	0.694886	−	0.694886i	0.963303	+	0.268417i	$0.0865004\pi$
$318$	2.18566	−	2.81755i	0.122566	−	0.158000i
$319$	34.0287			1.90524
$320$	−2.29189	+	17.7411i	−0.128121	+	0.991759i
$321$	6.41194			0.357879
$322$	−6.46985	+	8.34032i	−0.360551	+	0.464788i
$323$	27.7975	−	27.7975i	1.54669	−	1.54669i
$324$	−2.18421	−	8.50923i	−0.121345	−	0.472735i
$325$	−11.8426	−	17.6234i	−0.656908	−	0.977570i
$326$	−1.52399	−	12.0668i	−0.0844061	−	0.668318i
$327$	−13.7297			−0.759255
$328$	1.07335	−	2.47969i	0.0592656	−	0.136918i
$329$		−	5.57677i		−	0.307457i
$330$	−0.646141	−	22.4539i	−0.0355689	−	1.23605i
$331$	−15.9444	+	15.9444i	−0.876384	+	0.876384i	−0.993158	−	0.116775i	$-0.962744\pi$
$331$	−15.9444	+	15.9444i	−0.876384	+	0.876384i	0.116775	+	0.993158i	$0.462744\pi$
$332$	−19.3597	−	11.4510i	−1.06250	−	0.628455i
$333$	−3.69248	+	3.69248i	−0.202347	+	0.202347i
$334$	−1.12655	+	1.45224i	−0.0616421	+	0.0794631i
$335$	−0.668820	−	0.0649872i	−0.0365415	−	0.00355063i
$336$	−1.53136	+	5.26841i	−0.0835424	+	0.287415i
$337$			10.1654i			0.553745i	0.960907	+	0.276872i	$0.0892979\pi$
$337$			10.1654i			0.553745i	−0.960907	+	0.276872i	$0.910702\pi$
$338$	5.62423	+	4.36289i	0.305918	+	0.237310i
$339$	−14.6004	−	14.6004i	−0.792983	−	0.792983i
$340$	−20.9063	−	15.2751i	−1.13380	−	0.828408i
$341$	12.7776	−	12.7776i	0.691943	−	0.691943i
$342$	−1.34599	−	10.6574i	−0.0727827	−	0.576285i
$343$	1.00000			0.0539949
$344$	5.84176	+	14.7588i	0.314967	+	0.795741i
$345$	22.7847	+	2.21392i	1.22669	+	0.119193i
$346$	−2.23888	−	17.7272i	−0.120363	−	0.953019i
$347$	18.5590	+	18.5590i	0.996301	+	0.996301i	0.999993	−	0.00369201i	$-0.00117521\pi$
$347$	18.5590	+	18.5590i	0.996301	+	0.996301i	−0.00369201	+	0.999993i	$0.501175\pi$
$348$	4.48142	+	17.4587i	0.240229	+	0.935883i
$349$	14.7036	+	14.7036i	0.787065	+	0.787065i	0.981012	−	0.193947i	$-0.0621290\pi$
$349$	14.7036	+	14.7036i	0.787065	+	0.787065i	−0.193947	+	0.981012i	$0.562129\pi$
$350$	−4.64820	−	5.32862i	−0.248457	−	0.284827i
$351$	−23.9898			−1.28048
$352$	17.2162	+	23.7041i	0.917625	+	1.26343i
$353$			24.9626i			1.32863i	0.747454	+	0.664313i	$0.231276\pi$
$353$			24.9626i			1.32863i	−0.747454	+	0.664313i	$0.768724\pi$
$354$	12.9126	+	10.0167i	0.686297	+	0.532382i
$355$	−20.6510	+	16.9933i	−1.09604	+	0.901909i
$356$	−20.5761	+	5.28163i	−1.09053	+	0.279926i
$357$	−5.61526	−	5.61526i	−0.297191	−	0.297191i
$358$	10.4783	−	1.32337i	0.553795	−	0.0699423i
$359$		−	36.8130i		−	1.94292i	−0.237213	−	0.971458i	$-0.576234\pi$
$359$		−	36.8130i		−	1.94292i	0.237213	−	0.971458i	$-0.423766\pi$
$360$	−6.79952	+	1.95546i	−0.358366	+	0.103062i
$361$			27.1038i			1.42651i
$362$	−3.64924	−	28.8943i	−0.191800	−	1.51865i
$363$	−15.3447	−	15.3447i	−0.805390	−	0.805390i
$364$	7.31010	+	4.32382i	0.383153	+	0.226630i
$365$	1.25497	+	1.52511i	0.0656883	+	0.0798277i
$366$	5.37119	−	6.92403i	0.280757	−	0.361925i
$367$			3.98949i			0.208250i	0.994564	+	0.104125i	$0.0332042\pi$
$367$			3.98949i			0.208250i	−0.994564	+	0.104125i	$0.966796\pi$
$368$	−26.1646	+	14.3797i	−1.36392	+	0.749592i
$369$	1.06868			0.0556333
$370$	−10.7339	−	10.1334i	−0.558027	−	0.526809i
$371$	−1.29990	−	1.29990i	−0.0674873	−	0.0674873i
$372$	8.23836	+	4.87288i	0.427139	+	0.252647i
$373$	−0.656347	−	0.656347i	−0.0339844	−	0.0339844i	0.689910	−	0.723895i	$-0.257650\pi$
$373$	−0.656347	−	0.656347i	−0.0339844	−	0.0339844i	−0.723895	+	0.689910i	$0.757650\pi$
$374$	−42.0699	+	5.31327i	−2.17538	+	0.274743i
$375$	−4.39376	+	14.6922i	−0.226893	+	0.758702i
$376$	6.26582	−	14.4756i	0.323135	−	0.746521i
$377$	27.9024			1.43705
$378$	−7.92626	+	1.00106i	−0.407683	+	0.0514888i
$379$	16.9431	−	16.9431i	0.870310	−	0.870310i	−0.122196	−	0.992506i	$-0.538994\pi$
$379$	16.9431	−	16.9431i	0.870310	−	0.870310i	0.992506	+	0.122196i	$0.0389936\pi$
$380$	30.0045	−	4.66984i	1.53920	−	0.239558i
$381$	−11.8214	−	11.8214i	−0.605628	−	0.605628i
$382$	16.4597	−	21.2182i	0.842149	−	1.08562i
$383$		−	3.49169i		−	0.178417i	−0.996013	−	0.0892084i	$-0.971566\pi$
$383$		−	3.49169i		−	0.178417i	0.996013	−	0.0892084i	$-0.0284337\pi$
$384$	−9.89429	+	11.9546i	−0.504916	+	0.610056i
$385$	−11.5262	−	1.11996i	−0.587427	−	0.0570785i
$386$	25.8896	+	20.0834i	1.31775	+	1.02222i
$387$	−4.43915	+	4.43915i	−0.225655	+	0.225655i
$388$	22.7484	−	5.83922i	1.15487	−	0.296441i
$389$	2.66763	−	2.66763i	0.135254	−	0.135254i	−0.636238	−	0.771492i	$-0.719511\pi$
$389$	2.66763	−	2.66763i	0.135254	−	0.135254i	0.771492	+	0.636238i	$0.219511\pi$
$390$	−0.529815	−	18.4115i	−0.0268282	−	0.932302i
$391$		−	43.2135i		−	2.18540i
$392$	2.59569	+	1.12356i	0.131102	+	0.0567482i
$393$	18.9444			0.955620
$394$	12.2720	−	1.54991i	0.618256	−	0.0780835i
$395$	−4.60391	−	5.59490i	−0.231648	−	0.281510i
$396$	−5.89895	+	9.97310i	−0.296433	+	0.501167i
$397$	−10.0421	+	10.0421i	−0.503996	+	0.503996i	−0.912677	−	0.408681i	$-0.865989\pi$
$397$	−10.0421	+	10.0421i	−0.503996	+	0.503996i	0.408681	+	0.912677i	$0.365989\pi$
$398$	−2.46463	−	1.91189i	−0.123541	−	0.0958345i
$399$	9.31322			0.466244
$400$	−6.07830	−	19.0540i	−0.303915	−	0.952699i
$401$	15.2481			0.761455			0.380727	−	0.924687i	$-0.375674\pi$
$401$	15.2481			0.761455			0.380727	+	0.924687i	$0.375674\pi$
$402$	−0.460588	−	0.357293i	−0.0229721	−	0.0178202i
$403$	10.4772	−	10.4772i	0.521906	−	0.521906i
$404$	4.56819	+	2.70202i	0.227276	+	0.134431i
$405$	6.24098	+	7.58435i	0.310117	+	0.376869i
$406$	9.21900	−	1.16433i	0.457531	−	0.0577845i
$407$	−24.1752			−1.19832
$408$	−8.26642	−	20.8845i	−0.409249	−	1.03394i
$409$			6.20422i			0.306779i	0.988166	+	0.153389i	$0.0490189\pi$
$409$			6.20422i			0.306779i	−0.988166	+	0.153389i	$0.950981\pi$
$410$	0.0868959	+	3.01970i	0.00429148	+	0.149133i
$411$	8.70012	−	8.70012i	0.429145	−	0.429145i
$412$	2.24371	+	8.74101i	0.110539	+	0.430639i
$413$	5.95731	−	5.95731i	0.293140	−	0.293140i
$414$	−9.33011	−	7.23766i	−0.458550	−	0.355711i
$415$	25.0298	+	2.43207i	1.22866	+	0.119385i
$416$	14.1167	+	19.4366i	0.692128	+	0.952959i
$417$		−	12.4646i		−	0.610394i
$418$	30.4815	−	39.2938i	1.49090	−	1.92192i
$419$	−18.6539	−	18.6539i	−0.911304	−	0.911304i	0.0850709	−	0.996375i	$-0.472888\pi$
$419$	−18.6539	−	18.6539i	−0.911304	−	0.911304i	−0.996375	+	0.0850709i	$0.972888\pi$
$420$	−0.943335	−	6.06107i	−0.0460300	−	0.295750i
$421$	−26.4384	+	26.4384i	−1.28853	+	1.28853i	−0.352845	+	0.935682i	$0.614786\pi$
$421$	−26.4384	+	26.4384i	−1.28853	+	1.28853i	−0.935682	+	0.352845i	$0.885214\pi$
$422$	−9.10232	+	1.14959i	−0.443094	+	0.0559611i
$423$	6.23859			0.303331
$424$	−1.91362	−	4.83464i	−0.0929338	−	0.234791i
$425$	28.4068	+	5.57301i	1.37793	+	0.270331i
$426$	−23.0171	+	2.90697i	−1.11518	+	0.140843i
$427$	−3.19445	−	3.19445i	−0.154590	−	0.154590i
$428$	4.75979	−	8.04718i	0.230073	−	0.388975i
$429$	−21.3301	−	21.3301i	−1.02983	−	1.02983i
$430$	−12.9044	−	12.1825i	−0.622304	−	0.587491i
$431$	−20.5816			−0.991382			−0.495691	−	0.868499i	$-0.665085\pi$
$431$	−20.5816			−0.991382			−0.495691	+	0.868499i	$0.665085\pi$
$432$	−21.6989	−	6.30716i	−1.04399	−	0.303454i
$433$			10.0036i			0.480744i	0.970681	+	0.240372i	$0.0772694\pi$
$433$			10.0036i			0.480744i	−0.970681	+	0.240372i	$0.922731\pi$
$434$	3.02448	−	3.89887i	0.145180	−	0.187152i
$435$	−12.8048	−	15.5611i	−0.613945	−	0.746096i
$436$	−10.1920	+	17.2312i	−0.488109	+	0.825225i
$437$	35.8360	+	35.8360i	1.71427	+	1.71427i
$438$	0.214684	+	1.69984i	0.0102580	+	0.0812216i
$439$			0.836803i			0.0399384i	0.999801	+	0.0199692i	$0.00635682\pi$
$439$			0.836803i			0.0399384i	−0.999801	+	0.0199692i	$0.993643\pi$
$440$	−28.6600	−	15.8574i	−1.36631	−	0.755970i
$441$			1.11867i			0.0532702i
$442$	−34.4959	+	4.35671i	−1.64080	+	0.207228i
$443$	21.3968	+	21.3968i	1.01659	+	1.01659i	0.999860	+	0.0167310i	$0.00532588\pi$
$443$	21.3968	+	21.3968i	1.01659	+	1.01659i	0.0167310	+	0.999860i	$0.494674\pi$
$444$	−3.18376	−	12.4033i	−0.151094	−	0.588633i
$445$	18.3397	−	15.0913i	0.869384	−	0.715396i
$446$	2.52723	+	1.96045i	0.119668	+	0.0928302i
$447$		−	22.5888i		−	1.06842i
$448$	5.47524	+	5.83282i	0.258681	+	0.275575i
$449$	23.0850			1.08945			0.544725	−	0.838615i	$-0.316634\pi$
$449$	23.0850			1.08945			0.544725	+	0.838615i	$0.316634\pi$
$450$	5.96099	−	5.19983i	0.281004	−	0.245122i
$451$	3.49840	+	3.49840i	0.164733	+	0.164733i
$452$	−29.1623	+	7.48557i	−1.37168	+	0.352092i
$453$	−11.5952	−	11.5952i	−0.544792	−	0.544792i
$454$	3.04627	+	24.1200i	0.142968	+	1.13201i
$455$	−9.45108	−	0.918332i	−0.443073	−	0.0430521i
$456$	24.1743	+	10.4639i	1.13206	+	0.490019i
$457$	−23.0849			−1.07986			−0.539932	−	0.841709i	$-0.681550\pi$
$457$	−23.0849			−1.07986			−0.539932	+	0.841709i	$0.681550\pi$
$458$	−2.56274	−	20.2915i	−0.119749	−	0.948158i
$459$	23.1274	−	23.1274i	1.07949	−	1.07949i
$460$	19.6924	−	26.9520i	0.918161	−	1.25664i
$461$	−4.70614	−	4.70614i	−0.219187	−	0.219187i	0.588969	−	0.808156i	$-0.299534\pi$
$461$	−4.70614	−	4.70614i	−0.219187	−	0.219187i	−0.808156	+	0.588969i	$0.799534\pi$
$462$	−7.93758	−	6.15743i	−0.369290	−	0.286470i
$463$		−	39.0018i		−	1.81257i	−0.422668	−	0.906285i	$-0.638906\pi$
$463$		−	39.0018i		−	1.81257i	0.422668	−	0.906285i	$-0.361094\pi$
$464$	25.2379	+	7.33584i	1.17164	+	0.340558i
$465$	−10.6512	−	1.03495i	−0.493938	−	0.0479944i
$466$	23.0520	−	29.7164i	1.06786	−	1.37659i
$467$	7.44413	−	7.44413i	0.344473	−	0.344473i	−0.513573	−	0.858046i	$-0.671678\pi$
$467$	7.44413	−	7.44413i	0.344473	−	0.344473i	0.858046	+	0.513573i	$0.171678\pi$
$468$	−4.83695	+	8.17762i	−0.223588	+	0.378011i
$469$	−0.212495	+	0.212495i	−0.00981213	+	0.00981213i
$470$	0.507269	+	17.6280i	0.0233986	+	0.813119i
$471$		−	26.4953i		−	1.22084i
$472$	22.1567	−	8.76997i	1.01985	−	0.403671i
$473$	−29.0637			−1.33635
$474$	−0.787575	−	6.23593i	−0.0361745	−	0.286426i
$475$	−28.1787	+	18.9355i	−1.29293	+	0.868822i
$476$	−11.2157	+	2.87893i	−0.514071	+	0.131955i
$477$	1.45416	−	1.45416i	0.0665815	−	0.0665815i
$478$	9.90597	−	12.7698i	0.453088	−	0.584079i
$479$	20.2705			0.926184			0.463092	−	0.886310i	$-0.346740\pi$
$479$	20.2705			0.926184			0.463092	+	0.886310i	$0.346740\pi$
$480$	4.36135	−	16.7926i	0.199068	−	0.766473i
$481$	−19.8229			−0.903845
$482$	−15.9691	+	20.5859i	−0.727374	+	0.937662i
$483$	7.23908	−	7.23908i	0.329390	−	0.329390i
$484$	−30.6490	+	7.86721i	−1.39314	+	0.357600i
$485$	−20.2758	+	16.6845i	−0.920678	+	0.757604i
$486$	−1.93555	−	15.3255i	−0.0877983	−	0.695177i
$487$	29.8287			1.35167			0.675834	−	0.737053i	$-0.263783\pi$
$487$	29.8287			1.35167			0.675834	+	0.737053i	$0.263783\pi$
$488$	−4.70266	−	11.8809i	−0.212879	−	0.537825i
$489$			11.7963i			0.533446i
$490$	−3.16097	+	0.0909610i	−0.142798	+	0.00410920i
$491$	−0.733654	+	0.733654i	−0.0331093	+	0.0331093i	−0.723468	−	0.690358i	$-0.757453\pi$
$491$	−0.733654	+	0.733654i	−0.0331093	+	0.0331093i	0.690358	+	0.723468i	$0.257453\pi$
$492$	−1.33416	+	2.25560i	−0.0601485	+	0.101690i
$493$	−26.8994	+	26.8994i	−1.21149	+	1.21149i
$494$	24.9938	−	32.2197i	1.12453	−	1.44963i
$495$	1.25287	−	12.8940i	0.0563124	−	0.579543i
$496$	12.2312	−	6.72210i	0.549198	−	0.301831i
$497$			11.9602i			0.536490i
$498$	17.2370	+	13.3713i	0.772407	+	0.599180i
$499$	4.12107	+	4.12107i	0.184484	+	0.184484i	0.793307	−	0.608822i	$-0.208358\pi$
$499$	4.12107	+	4.12107i	0.184484	+	0.184484i	−0.608822	+	0.793307i	$0.708358\pi$
$500$	15.1775	+	16.4208i	0.678759	+	0.734361i
$501$	1.26049	−	1.26049i	0.0563146	−	0.0563146i
$502$	0.512216	+	4.05567i	0.0228613	+	0.181013i
$503$	23.0335			1.02701			0.513507	−	0.858085i	$-0.328346\pi$
$503$	23.0335			1.02701			0.513507	+	0.858085i	$0.328346\pi$
$504$	−1.25689	+	2.90374i	−0.0559865	+	0.129343i
$505$	−5.90612	−	0.573880i	−0.262819	−	0.0255373i
$506$	−6.84977	−	54.2357i	−0.304509	−	2.41107i
$507$	−4.88162	−	4.88162i	−0.216800	−	0.216800i
$508$	−23.6116	+	6.06080i	−1.04760	+	0.268904i
$509$	17.6160	+	17.6160i	0.780817	+	0.780817i	0.979969	−	0.199151i	$-0.0638185\pi$
$509$	17.6160	+	17.6160i	0.780817	+	0.780817i	−0.199151	+	0.979969i	$0.563819\pi$
$510$	18.2604	+	17.2389i	0.808585	+	0.763350i
$511$	0.883279			0.0390740
$512$	7.65854	+	21.2919i	0.338463	+	0.940980i
$513$			38.3581i			1.69355i
$514$	18.4055	+	14.2777i	0.811832	+	0.629764i
$515$	−6.41098	−	7.79094i	−0.282502	−	0.343310i
$516$	−3.82755	−	14.9114i	−0.168499	−	0.656436i
$517$	20.4225	+	20.4225i	0.898179	+	0.898179i
$518$	−6.54951	+	0.827179i	−0.287769	+	0.0363442i
$519$			17.3298i			0.760693i
$520$	−23.5003	−	13.0025i	−1.03056	−	0.570199i
$521$			38.3975i			1.68222i	0.540861	+	0.841112i	$0.318098\pi$
$521$			38.3975i			1.68222i	−0.540861	+	0.841112i	$0.681902\pi$
$522$	1.30250	+	10.3131i	0.0570090	+	0.451391i
$523$	4.38086	+	4.38086i	0.191562	+	0.191562i	0.796371	−	0.604809i	$-0.206751\pi$
$523$	4.38086	+	4.38086i	0.191562	+	0.191562i	−0.604809	+	0.796371i	$0.706751\pi$
$524$	14.0631	−	23.7758i	0.614349	−	1.03865i
$525$	3.82509	+	5.69226i	0.166941	+	0.248431i
$526$	6.27505	−	8.08920i	0.273605	−	0.352706i
$527$			20.2011i			0.879974i
$528$	−13.6853	−	24.9011i	−0.595576	−	1.08368i
$529$	32.7100			1.42217
$530$	4.22717	+	3.99069i	0.183617	+	0.173345i
$531$	6.66429	+	6.66429i	0.289206	+	0.289206i
$532$	6.91352	−	11.6884i	0.299739	−	0.506756i
$533$	2.86857	+	2.86857i	0.124252	+	0.124252i
$534$	20.4409	−	2.58161i	0.884565	−	0.111717i
$535$	−1.01093	+	10.4040i	−0.0437062	+	0.449806i
$536$	−0.790324	+	0.312822i	−0.0341368	+	0.0135119i
$537$	−10.2434			−0.442035
$538$	−12.1512	+	1.53465i	−0.523876	+	0.0661636i
$539$	−3.66206	+	3.66206i	−0.157736	+	0.157736i
$540$	24.9636	−	3.88529i	1.07426	−	0.167196i
$541$	−5.64648	−	5.64648i	−0.242761	−	0.242761i	0.575230	−	0.817991i	$-0.304912\pi$
$541$	−5.64648	−	5.64648i	−0.242761	−	0.242761i	−0.817991	+	0.575230i	$0.804912\pi$
$542$	−22.7760	+	29.3607i	−0.978315	+	1.26115i
$543$			28.2465i			1.21218i
$544$	−32.3472	−	5.12868i	−1.38687	−	0.219890i
$545$	2.16467	−	22.2779i	0.0927244	−	0.954280i
$546$	−6.50856	−	5.04890i	−0.278541	−	0.216073i
$547$	−31.1275	+	31.1275i	−1.33091	+	1.33091i	−0.426362	+	0.904553i	$0.640205\pi$
$547$	−31.1275	+	31.1275i	−1.33091	+	1.33091i	−0.904553	+	0.426362i	$0.859795\pi$
$548$	−4.46053	−	17.3773i	−0.190544	−	0.742321i
$549$	3.57355	−	3.57355i	0.152515	−	0.152515i
$550$	36.5357	+	2.49173i	1.55789	+	0.106248i
$551$		−	44.6142i		−	1.90063i
$552$	26.9239	−	10.6569i	1.14596	−	0.453588i
$553$	−3.24034			−0.137793
$554$	21.1394	−	2.66983i	0.898126	−	0.113430i
$555$	9.09701	+	11.0551i	0.386147	+	0.469264i
$556$	−15.6435	−	9.25289i	−0.663430	−	0.392410i
$557$	20.8207	−	20.8207i	0.882199	−	0.882199i	−0.111559	−	0.993758i	$-0.535584\pi$
$557$	20.8207	−	20.8207i	0.882199	−	0.882199i	0.993758	+	0.111559i	$0.0355843\pi$
$558$	4.36157	+	3.38341i	0.184640	+	0.143231i
$559$	−23.8313			−1.00796
$560$	−8.30710	−	3.31542i	−0.351039	−	0.140102i
$561$	41.1268			1.73637
$562$	−2.24718	−	1.74321i	−0.0947915	−	0.0735328i
$563$	−12.4276	+	12.4276i	−0.523760	+	0.523760i	−0.918705	−	0.394945i	$-0.870764\pi$
$563$	−12.4276	+	12.4276i	−0.523760	+	0.523760i	0.394945	+	0.918705i	$0.370764\pi$
$564$	−7.78836	+	13.1674i	−0.327949	+	0.554449i
$565$	25.9926	−	21.3887i	1.09352	−	0.899828i
$566$	−14.8664	+	1.87757i	−0.624881	+	0.0789202i
$567$	4.39254			0.184469
$568$	−13.4380	+	31.0451i	−0.563846	+	1.30262i
$569$		−	8.36804i		−	0.350807i	−0.984497	−	0.175403i	$-0.943877\pi$
$569$		−	8.36804i		−	0.350807i	0.984497	−	0.175403i	$-0.0561229\pi$
$570$	−29.4388	+	0.847140i	−1.23306	+	0.0354828i
$571$	−6.81735	+	6.81735i	−0.285297	+	0.285297i	−0.835217	−	0.549920i	$-0.814658\pi$
$571$	−6.81735	+	6.81735i	−0.285297	+	0.285297i	0.549920	+	0.835217i	$0.314658\pi$
$572$	−42.6041	+	10.9359i	−1.78137	+	0.457253i
$573$	−18.4166	+	18.4166i	−0.769365	+	0.769365i
$574$	1.06748	+	0.828080i	0.0445558	+	0.0345634i
$575$	−7.18462	+	36.6214i	−0.299619	+	1.52722i
$576$	−6.52502	+	6.12501i	−0.271876	+	0.255209i
$577$			13.4147i			0.558462i	0.960224	+	0.279231i	$0.0900796\pi$
$577$			13.4147i			0.558462i	−0.960224	+	0.279231i	$0.909920\pi$
$578$	14.3199	−	18.4599i	0.595629	−	0.767829i
$579$	−22.4712	−	22.4712i	−0.933872	−	0.933872i
$580$	−29.0351	+	4.51897i	−1.20562	+	0.187640i
$581$	7.95239	−	7.95239i	0.329921	−	0.329921i
$582$	−22.5989	+	2.85416i	−0.936754	+	0.118309i
$583$	9.52059			0.394302
$584$	2.29272	+	0.992414i	0.0948734	+	0.0410664i
$585$	1.02731	−	10.5727i	0.0424742	−	0.437126i
$586$	−2.90155	+	0.366455i	−0.119862	+	0.0151381i
$587$	7.85758	+	7.85758i	0.324317	+	0.324317i	0.850421	−	0.526103i	$-0.176348\pi$
$587$	7.85758	+	7.85758i	0.324317	+	0.324317i	−0.526103	+	0.850421i	$0.676348\pi$
$588$	−2.36112	−	1.39657i	−0.0973710	−	0.0575936i
$589$	−16.7524	−	16.7524i	−0.690269	−	0.690269i
$590$	−18.2890	+	19.3728i	−0.752946	+	0.797564i
$591$	−11.9969			−0.493487
$592$	−17.9299	−	5.21164i	−0.736914	−	0.214197i
$593$		−	6.94897i		−	0.285360i	−0.989769	−	0.142680i	$-0.954428\pi$
$593$		−	6.94897i		−	0.285360i	0.989769	−	0.142680i	$-0.0455719\pi$
$594$	25.3605	−	32.6923i	1.04055	−	1.34138i
$595$	9.99665	−	8.22601i	0.409823	−	0.337234i
$596$	−28.3497	−	16.7684i	−1.16125	−	0.686862i
$597$	2.13921	+	2.13921i	0.0875518	+	0.0875518i
$598$	−5.61659	−	44.4715i	−0.229679	−	1.81858i
$599$		−	0.595777i		−	0.0243428i	−0.999926	−	0.0121714i	$-0.996126\pi$
$599$		−	0.595777i		−	0.0243428i	0.999926	−	0.0121714i	$-0.00387437\pi$
$600$	3.53318	+	19.0731i	0.144241	+	0.778655i
$601$		−	22.7843i		−	0.929391i	−0.885471	−	0.464696i	$-0.846164\pi$
$601$		−	22.7843i		−	0.929391i	0.885471	−	0.464696i	$-0.153836\pi$
$602$	−7.87389	+	0.994444i	−0.320916	+	0.0405305i
$603$	−0.237713	−	0.237713i	−0.00968043	−	0.00968043i
$604$	−23.1599	+	5.94485i	−0.942363	+	0.241892i
$605$	27.3177	−	22.4791i	1.11062	−	0.913906i
$606$	−4.06730	−	3.15513i	−0.165223	−	0.128169i
$607$			12.1405i			0.492768i	0.969172	+	0.246384i	$0.0792425\pi$
$607$			12.1405i			0.492768i	−0.969172	+	0.246384i	$0.920758\pi$
$608$	31.0779	−	22.5717i	1.26038	−	0.915404i
$609$	−9.01233			−0.365198
$610$	10.3881	+	9.80698i	0.420603	+	0.397073i
$611$	16.7458	+	16.7458i	0.677461	+	0.677461i
$612$	−3.22058	−	12.5467i	−0.130184	−	0.507171i
$613$	−11.7440	−	11.7440i	−0.474335	−	0.474335i	0.428979	−	0.903314i	$-0.358873\pi$
$613$	−11.7440	−	11.7440i	−0.474335	−	0.474335i	−0.903314	+	0.428979i	$0.858873\pi$
$614$	0.731032	+	5.78822i	0.0295020	+	0.233594i
$615$	0.283360	−	2.91622i	0.0114262	−	0.117593i
$616$	−13.6201	+	5.39104i	−0.548770	+	0.217211i
$617$	27.2475			1.09694			0.548471	−	0.836170i	$-0.315210\pi$
$617$	27.2475			1.09694			0.548471	+	0.836170i	$0.315210\pi$
$618$	−1.09670	−	8.68357i	−0.0441159	−	0.349304i
$619$	22.8772	−	22.8772i	0.919512	−	0.919512i	−0.0774817	−	0.996994i	$-0.524688\pi$
$619$	22.8772	−	22.8772i	0.919512	−	0.919512i	0.996994	+	0.0774817i	$0.0246879\pi$
$620$	−9.20564	+	12.5993i	−0.369707	+	0.506001i
$621$	29.8154	+	29.8154i	1.19645	+	1.19645i
$622$	−9.93772	−	7.70900i	−0.398466	−	0.309103i
$623$		−	10.6216i		−	0.425545i
$624$	−11.2215	−	20.4181i	−0.449220	−	0.817379i
$625$	−23.1469	−	9.44575i	−0.925875	−	0.377830i
$626$	−10.1252	+	13.0524i	−0.404684	+	0.521680i
$627$	−34.1056	+	34.1056i	−1.36204	+	1.36204i
$628$	−33.2524	−	19.6683i	−1.32692	−	0.784852i
$629$	19.1103	−	19.1103i	0.761977	−	0.761977i
$630$	−0.101756	−	3.53610i	−0.00405405	−	0.140881i
$631$			11.9350i			0.475127i	0.971372	+	0.237563i	$0.0763488\pi$
$631$			11.9350i			0.475127i	−0.971372	+	0.237563i	$0.923651\pi$
$632$	−8.41092	−	3.64070i	−0.334568	−	0.144819i
$633$	8.89826			0.353674
$634$	3.10047	+	24.5492i	0.123135	+	0.974973i
$635$	21.0452	−	17.3176i	0.835155	−	0.687229i
$636$	1.25382	+	4.88461i	0.0497170	+	0.193687i
$637$	−3.00277	+	3.00277i	−0.118974	+	0.118974i
$638$	−29.4967	+	38.0243i	−1.16778	+	1.50540i
$639$	−13.3796			−0.529289
$640$	−17.8376	−	17.9393i	−0.705094	−	0.709114i
$641$	−33.3731			−1.31816			−0.659080	−	0.752073i	$-0.729054\pi$
$641$	−33.3731			−1.31816			−0.659080	+	0.752073i	$0.729054\pi$
$642$	−5.55798	+	7.16483i	−0.219356	+	0.282773i
$643$	8.72526	−	8.72526i	0.344091	−	0.344091i	−0.513812	−	0.857903i	$-0.671767\pi$
$643$	8.72526	−	8.72526i	0.344091	−	0.344091i	0.857903	+	0.513812i	$0.171767\pi$
$644$	−3.71146	−	14.4591i	−0.146252	−	0.569768i
$645$	10.9365	+	13.2906i	0.430626	+	0.523317i
$646$	6.96611	+	55.1568i	0.274078	+	2.17012i
$647$	3.89063			0.152956			0.0764782	−	0.997071i	$-0.475632\pi$
$647$	3.89063			0.152956			0.0764782	+	0.997071i	$0.475632\pi$
$648$	11.4017	+	4.93527i	0.447901	+	0.193876i
$649$			43.6320i			1.71271i
$650$	29.9581	+	2.04314i	1.17505	+	0.0801385i
$651$	−3.38407	+	3.38407i	−0.132632	+	0.132632i
$652$	14.8047	+	8.75677i	0.579797	+	0.342942i
$653$	17.8201	−	17.8201i	0.697354	−	0.697354i	−0.266485	−	0.963839i	$-0.585862\pi$
$653$	17.8201	−	17.8201i	0.697354	−	0.697354i	0.963839	+	0.266485i	$0.0858624\pi$
$654$	11.9012	−	15.3419i	0.465372	−	0.599914i
$655$	−2.98684	+	30.7393i	−0.116706	+	1.20108i
$656$	1.84046	+	3.34882i	0.0718579	+	0.130749i
$657$			0.988102i			0.0385495i
$658$	6.23160	+	4.83405i	0.242933	+	0.188451i
$659$	0.801581	+	0.801581i	0.0312252	+	0.0312252i	0.722547	−	0.691322i	$-0.242971\pi$
$659$	0.801581	+	0.801581i	0.0312252	+	0.0312252i	−0.691322	+	0.722547i	$0.742971\pi$
$660$	25.6505	+	18.7414i	0.998446	+	0.729510i
$661$	−23.7051	+	23.7051i	−0.922021	+	0.922021i	−0.997172	−	0.0751509i	$-0.976056\pi$
$661$	−23.7051	+	23.7051i	−0.922021	+	0.922021i	0.0751509	+	0.997172i	$0.476056\pi$
$662$	−3.99570	−	31.6375i	−0.155297	−	1.22963i
$663$	33.7226			1.30968
$664$	29.5769	−	11.7070i	1.14781	−	0.454319i
$665$	−1.46835	+	15.1117i	−0.0569404	+	0.586006i
$666$	−0.925344	−	7.32677i	−0.0358564	−	0.283906i
$667$	−34.6782	−	34.6782i	−1.34275	−	1.34275i
$668$	−0.646250	−	2.51766i	−0.0250042	−	0.0974111i
$669$	−2.19354	−	2.19354i	−0.0848072	−	0.0848072i
$670$	0.652363	−	0.691020i	0.0252030	−	0.0266964i
$671$	23.3965			0.903212
$672$	−4.55962	−	6.27792i	−0.175891	−	0.242176i
$673$			6.15593i			0.237294i	0.992937	+	0.118647i	$0.0378556\pi$
$673$			6.15593i			0.237294i	−0.992937	+	0.118647i	$0.962144\pi$
$674$	−11.3590	−	8.81155i	−0.437533	−	0.339408i
$675$	−23.4446	+	15.7543i	−0.902382	+	0.606383i
$676$	−9.75037	+	2.50279i	−0.375014	+	0.0962613i
$677$	−32.6473	−	32.6473i	−1.25474	−	1.25474i	−0.953572	−	0.301164i	$-0.902625\pi$
$677$	−32.6473	−	32.6473i	−1.25474	−	1.25474i	−0.301164	−	0.953572i	$-0.597375\pi$
$678$	28.9706	−	3.65888i	1.11261	−	0.140519i
$679$			11.7429i			0.450652i
$680$	35.1906	−	10.1204i	1.34950	−	0.388099i
$681$		−	23.5793i		−	0.903559i
$682$	3.20208	+	25.3537i	0.122614	+	0.970843i
$683$	−21.9119	−	21.9119i	−0.838435	−	0.838435i	0.150218	−	0.988653i	$-0.452003\pi$
$683$	−21.9119	−	21.9119i	−0.838435	−	0.838435i	−0.988653	+	0.150218i	$0.952003\pi$
$684$	13.0755	+	7.73398i	0.499954	+	0.295716i
$685$	12.7452	+	15.4885i	0.486967	+	0.591786i
$686$	−0.866818	+	1.11742i	−0.0330953	+	0.0426633i
$687$			19.8366i			0.756813i
$688$	−21.5555	−	6.26550i	−0.821797	−	0.238870i
$689$	7.80657			0.297407
$690$	−22.2240	+	23.5410i	−0.846055	+	0.896190i
$691$	23.1803	+	23.1803i	0.881820	+	0.881820i	0.993720	−	0.111899i	$-0.0356934\pi$
$691$	23.1803	+	23.1803i	0.881820	+	0.881820i	−0.111899	+	0.993720i	$0.535693\pi$
$692$	21.7494	+	12.8645i	0.826788	+	0.489034i
$693$	−4.09665	−	4.09665i	−0.155619	−	0.155619i
$694$	−36.8255	+	4.65093i	−1.39788	+	0.176547i
$695$	20.2251	+	1.96521i	0.767182	+	0.0745447i
$696$	−23.3932	−	10.1259i	−0.886719	−	0.383820i
$697$	−5.53091			−0.209498
$698$	−29.1754	+	3.68475i	−1.10431	+	0.139470i
$699$	−25.7927	+	25.7927i	−0.975570	+	0.975570i
$700$	9.98345	−	0.575050i	0.377339	−	0.0217348i
$701$	−32.9569	−	32.9569i	−1.24476	−	1.24476i	−0.958002	−	0.286763i	$-0.907421\pi$
$701$	−32.9569	−	32.9569i	−1.24476	−	1.24476i	−0.286763	−	0.958002i	$-0.592579\pi$
$702$	20.7948	−	26.8067i	0.784848	−	1.01175i
$703$			31.6955i			1.19542i
$704$	−41.4107	−	1.30947i	−1.56073	−	0.0493525i
$705$	1.65416	−	17.0239i	0.0622993	−	0.641158i
$706$	−27.8937	−	21.6380i	−1.04979	−	0.814359i
$707$	−1.87648	+	1.87648i	−0.0705722	+	0.0705722i
$708$	−22.3857	+	5.74613i	−0.841307	+	0.215953i
$709$	−1.67927	+	1.67927i	−0.0630662	+	0.0630662i	−0.737936	−	0.674870i	$-0.764200\pi$
$709$	−1.67927	+	1.67927i	−0.0630662	+	0.0630662i	0.674870	+	0.737936i	$0.264200\pi$
$710$	−1.08791	−	37.8059i	−0.0408287	−	1.41883i
$711$		−	3.62488i		−	0.135944i
$712$	11.9340	−	27.5704i	0.447244	−	1.03324i
$713$	−26.0429			−0.975314
$714$	11.1420	−	1.40719i	0.416979	−	0.0526629i
$715$	37.9734	−	31.2474i	1.42012	−	1.16859i
$716$	−7.60402	+	12.8558i	−0.284175	+	0.480443i
$717$	−11.0837	+	11.0837i	−0.413930	+	0.413930i
$718$	41.1356	+	31.9102i	1.53517	+	1.19088i
$719$	1.62466			0.0605897			0.0302949	−	0.999541i	$-0.490355\pi$
$719$	1.62466			0.0605897			0.0302949	+	0.999541i	$0.490355\pi$
$720$	3.70888	−	9.29295i	0.138222	−	0.346328i
$721$	−4.51219			−0.168043
$722$	−30.2863	−	23.4940i	−1.12714	−	0.874357i
$723$	17.8678	−	17.8678i	0.664510	−	0.664510i
$724$	35.4503	+	20.9683i	1.31750	+	0.779282i
$725$	27.2683	−	18.3238i	1.01272	−	0.680528i
$726$	30.4476	−	3.84542i	1.13002	−	0.142717i
$727$	−23.1359			−0.858063			−0.429032	−	0.903289i	$-0.641145\pi$
$727$	−23.1359			−0.858063			−0.429032	+	0.903289i	$0.641145\pi$
$728$	−11.1680	+	4.42048i	−0.413915	+	0.163834i
$729$			28.1595i			1.04295i
$730$	−2.79202	+	0.0803439i	−0.103337	+	0.00297366i
$731$	22.9746	−	22.9746i	0.849747	−	0.849747i
$732$	3.08121	+	12.0038i	0.113885	+	0.443671i
$733$	22.8713	−	22.8713i	0.844771	−	0.844771i	−0.144704	−	0.989475i	$-0.546223\pi$
$733$	22.8713	−	22.8713i	0.844771	−	0.844771i	0.989475	+	0.144704i	$0.0462231\pi$
$734$	−4.45794	−	3.45816i	−0.164545	−	0.127643i
$735$	3.05265	+	0.296616i	0.112599	+	0.0109409i
$736$	6.61179	−	41.7014i	0.243714	−	1.53713i
$737$		−	1.55634i		−	0.0573286i
$738$	−0.926352	+	1.19417i	−0.0340995	+	0.0439578i
$739$	−1.53094	−	1.53094i	−0.0563164	−	0.0563164i	0.678388	−	0.734704i	$-0.262679\pi$
$739$	−1.53094	−	1.53094i	−0.0563164	−	0.0563164i	−0.734704	+	0.678388i	$0.762679\pi$
$740$	20.6275	−	3.21044i	0.758284	−	0.118018i
$741$	−27.9655	+	27.9655i	−1.02734	+	1.02734i
$742$	2.57930	−	0.325757i	0.0946892	−	0.0119589i
$743$	14.3915			0.527974			0.263987	−	0.964526i	$-0.414962\pi$
$743$	14.3915			0.527974			0.263987	+	0.964526i	$0.414962\pi$
$744$	−12.5862	+	4.98181i	−0.461433	+	0.182642i
$745$	36.6527	+	3.56143i	1.34285	+	0.130481i
$746$	1.30235	−	0.164482i	0.0476824	−	0.00602211i
$747$	8.89613	+	8.89613i	0.325492	+	0.325492i
$748$	30.5298	−	51.6153i	1.11628	−	1.88724i
$749$	3.30554	+	3.30554i	0.120782	+	0.120782i
$750$	−12.6088	−	17.6451i	−0.460407	−	0.644309i
$751$	1.40961			0.0514375			0.0257188	−	0.999669i	$-0.491813\pi$
$751$	1.40961			0.0514375			0.0257188	+	0.999669i	$0.491813\pi$
$752$	10.7440	+	19.5492i	0.391793	+	0.712888i
$753$		−	3.96475i		−	0.144484i
$754$	−24.1863	+	31.1787i	−0.880814	+	1.13546i
$755$	20.6426	−	16.9863i	0.751262	−	0.618196i
$756$	5.75202	−	9.72469i	0.209199	−	0.353684i
$757$	−13.6358	−	13.6358i	−0.495603	−	0.495603i	0.414463	−	0.910066i	$-0.363969\pi$
$757$	−13.6358	−	13.6358i	−0.495603	−	0.495603i	−0.910066	+	0.414463i	$0.863969\pi$
$758$	4.24598	+	33.6192i	0.154221	+	1.22110i
$759$			53.0198i			1.92450i
$760$	−20.7902	+	37.5755i	−0.754141	+	1.36301i
$761$		−	28.5685i		−	1.03561i	−0.855499	−	0.517804i	$-0.826750\pi$
$761$		−	28.5685i		−	1.03561i	0.855499	−	0.517804i	$-0.173250\pi$
$762$	23.4564	−	2.96246i	0.849737	−	0.107319i
$763$	−7.07807	−	7.07807i	−0.256243	−	0.256243i
$764$	9.44216	+	36.7847i	0.341605	+	1.33082i
$765$	9.20223	+	11.1830i	0.332707	+	0.404322i
$766$	3.90168	+	3.02666i	0.140973	+	0.109358i
$767$			35.7768i			1.29183i
$768$	−4.78176	−	21.4185i	−0.172547	−	0.772875i
$769$	−19.1680			−0.691214			−0.345607	−	0.938379i	$-0.612327\pi$
$769$	−19.1680			−0.691214			−0.345607	+	0.938379i	$0.612327\pi$
$770$	11.2425	−	11.9088i	0.405153	−	0.429162i
$771$	−15.9753	−	15.9753i	−0.575335	−	0.575335i
$772$	−44.8832	+	11.5209i	−1.61538	+	0.414647i
$773$	12.4101	+	12.4101i	0.446359	+	0.446359i	0.894142	−	0.447783i	$-0.147786\pi$
$773$	12.4101	+	12.4101i	0.446359	+	0.446359i	−0.447783	+	0.894142i	$0.647786\pi$
$774$	−1.11246	−	8.80833i	−0.0399865	−	0.316609i
$775$	3.35861	−	17.1195i	0.120645	−	0.614951i
$776$	−13.1938	+	30.4810i	−0.473631	+	1.09421i
$777$	6.40268			0.229695
$778$	0.668512	+	5.29320i	0.0239673	+	0.189771i
$779$	4.58667	−	4.58667i	0.164334	−	0.164334i
$780$	21.0326	+	15.3674i	0.753089	+	0.550241i
$781$	−43.7991	−	43.7991i	−1.56725	−	1.56725i
$782$	48.2876	+	37.4582i	1.72676	+	1.33950i
$783$		−	37.1189i		−	1.32652i
$784$	−3.50548	+	1.92656i	−0.125196	+	0.0688057i
$785$	42.9914	+	4.17734i	1.53443	+	0.149096i
$786$	−16.4214	+	21.1689i	−0.585731	+	0.755069i
$787$	29.0233	−	29.0233i	1.03457	−	1.03457i	0.0351867	−	0.999381i	$-0.488797\pi$
$787$	29.0233	−	29.0233i	1.03457	−	1.03457i	0.999381	−	0.0351867i	$-0.0112026\pi$
$788$	−8.90571	+	15.0565i	−0.317253	+	0.536366i
$789$	−7.02112	+	7.02112i	−0.249958	+	0.249958i
$790$	10.2426	−	0.294744i	0.364416	−	0.0104865i
$791$		−	15.0538i		−	0.535252i
$792$	−6.03082	−	15.2365i	−0.214296	−	0.541404i
$793$	19.1844			0.681257
$794$	−2.51656	−	19.9258i	−0.0893093	−	0.707141i
$795$	−3.58255	−	4.35369i	−0.127060	−	0.154410i
$796$	4.27277	−	1.09677i	0.151444	−	0.0388738i
$797$	4.74896	−	4.74896i	0.168217	−	0.168217i	−0.617978	−	0.786195i	$-0.712048\pi$
$797$	4.74896	−	4.74896i	0.168217	−	0.168217i	0.786195	+	0.617978i	$0.212048\pi$
$798$	−8.07287	+	10.4068i	−0.285776	+	0.368396i
$799$	−32.2876			−1.14225
$800$	26.5601	+	9.72433i	0.939040	+	0.343807i
$801$	11.8821			0.419833
$802$	−13.2173	+	17.0385i	−0.466720	+	0.601652i
$803$	−3.23462	+	3.23462i	−0.114147	+	0.114147i
$804$	0.798492	−	0.204963i	0.0281607	−	0.00722848i
$805$	10.6048	+	12.8875i	0.373771	+	0.454225i
$806$	2.62560	+	20.7892i	0.0924829	+	0.732269i
$807$	11.8788			0.418154
$808$	−6.97908	+	2.76243i	−0.245523	+	0.0971819i
$809$			39.8339i			1.40049i	0.713905	+	0.700243i	$0.246925\pi$
$809$			39.8339i			1.40049i	−0.713905	+	0.700243i	$0.753075\pi$
$810$	−13.8847	+	0.399550i	−0.487858	+	0.0140388i
$811$	12.4990	−	12.4990i	0.438901	−	0.438901i	−0.452741	−	0.891642i	$-0.649554\pi$
$811$	12.4990	−	12.4990i	0.438901	−	0.438901i	0.891642	+	0.452741i	$0.149554\pi$
$812$	−6.69015	+	11.3108i	−0.234778	+	0.396930i
$813$	25.4840	−	25.4840i	0.893763	−	0.893763i
$814$	20.9555	−	27.0138i	0.734489	−	0.946835i
$815$	−19.1407	−	1.85984i	−0.670469	−	0.0651474i
$816$	30.5023	+	8.86603i	1.06779	+	0.310373i
$817$			38.1047i			1.33312i
$818$	−6.93272	−	5.37793i	−0.242397	−	0.188035i
$819$	−3.35912	−	3.35912i	−0.117377	−	0.117377i
$820$	−3.44960	−	2.52043i	−0.120465	−	0.0880174i
$821$	−22.4655	+	22.4655i	−0.784051	+	0.784051i	−0.980512	−	0.196461i	$-0.937055\pi$
$821$	−22.4655	+	22.4655i	−0.784051	+	0.784051i	0.196461	+	0.980512i	$0.437055\pi$
$822$	2.18027	+	17.2631i	0.0760455	+	0.602120i
$823$	17.4258			0.607426			0.303713	−	0.952764i	$-0.401774\pi$
$823$	17.4258			0.607426			0.303713	+	0.952764i	$0.401774\pi$
$824$	−11.7123	−	5.06971i	−0.408016	−	0.176612i
$825$	−34.8531	−	6.83769i	−1.21343	−	0.238058i
$826$	1.49291	+	11.8207i	0.0519451	+	0.411295i
$827$	12.7810	+	12.7810i	0.444438	+	0.444438i	0.893500	−	0.449063i	$-0.148242\pi$
$827$	12.7810	+	12.7810i	0.444438	+	0.444438i	−0.449063	+	0.893500i	$0.648242\pi$
$828$	16.1750	−	4.15191i	0.562120	−	0.144289i
$829$	16.4231	+	16.4231i	0.570398	+	0.570398i	0.932240	−	0.361842i	$-0.117852\pi$
$829$	16.4231	+	16.4231i	0.570398	+	0.570398i	−0.361842	+	0.932240i	$0.617852\pi$
$830$	−24.4139	+	25.8606i	−0.847418	+	0.897635i
$831$	−20.6655			−0.716878
$832$	−33.9555	−	1.07372i	−1.17719	−	0.0372246i
$833$		−	5.78965i		−	0.200600i
$834$	13.9282	+	10.8045i	0.482294	+	0.374131i
$835$	1.84654	+	2.24401i	0.0639023	+	0.0776572i
$836$	17.4858	+	68.1212i	0.604760	+	2.35602i
$837$	−13.9379	−	13.9379i	−0.481764	−	0.481764i
$838$	37.0138	−	4.67471i	1.27862	−	0.161485i
$839$			15.8516i			0.547257i	0.961835	+	0.273628i	$0.0882239\pi$
$839$			15.8516i			0.547257i	−0.961835	+	0.273628i	$0.911776\pi$
$840$	7.59046	+	4.19975i	0.261896	+	0.144905i
$841$			14.1728i			0.488718i
$842$	−6.62550	−	52.4600i	−0.228330	−	1.80789i
$843$	1.95047	+	1.95047i	0.0671776	+	0.0671776i
$844$	6.60548	−	11.1676i	0.227370	−	0.384404i
$845$	8.69059	−	7.15128i	0.298965	−	0.246012i
$846$	−5.40772	+	6.97113i	−0.185921	+	0.239672i
$847$		−	15.8213i		−	0.543627i
$848$	7.06108	+	2.05243i	0.242479	+	0.0704807i
$849$	14.5331			0.498775
$850$	−30.8509	+	26.9115i	−1.05818	+	0.923056i
$851$	24.6366	+	24.6366i	0.844533	+	0.844533i
$852$	16.7033	−	28.2396i	0.572246	−	0.967472i
$853$	−11.1537	−	11.1537i	−0.381896	−	0.381896i	0.489889	−	0.871785i	$-0.337037\pi$
$853$	−11.1537	−	11.1537i	−0.381896	−	0.381896i	−0.871785	+	0.489889i	$0.837037\pi$
$854$	6.33854	−	0.800535i	0.216901	−	0.0273937i
$855$	−16.9050	−	1.64261i	−0.578140	−	0.0561761i
$856$	4.86620	+	12.2941i	0.166323	+	0.420205i
$857$	−37.0039			−1.26403			−0.632014	−	0.774957i	$-0.717772\pi$
$857$	−37.0039			−1.26403			−0.632014	+	0.774957i	$0.717772\pi$
$858$	42.3241	−	5.34538i	1.44492	−	0.182488i
$859$	−16.5090	+	16.5090i	−0.563281	+	0.563281i	−0.930238	−	0.366957i	$-0.880400\pi$
$859$	−16.5090	+	16.5090i	−0.563281	+	0.563281i	0.366957	+	0.930238i	$0.380400\pi$
$860$	24.7987	−	3.85962i	0.845628	−	0.131612i
$861$	−0.926534	−	0.926534i	−0.0315762	−	0.0315762i
$862$	17.8405	−	22.9983i	0.607650	−	0.783326i
$863$			9.05165i			0.308122i	0.988061	+	0.154061i	$0.0492352\pi$
$863$			9.05165i			0.308122i	−0.988061	+	0.154061i	$0.950765\pi$
$864$	25.8567	−	18.7796i	0.879663	−	0.638894i
$865$	−28.1194	−	2.73227i	−0.956087	−	0.0929000i
$866$	−11.1783	−	8.67133i	−0.379853	−	0.294664i
$867$	−16.0225	+	16.0225i	−0.544151	+	0.544151i
$868$	1.73501	+	6.75922i	0.0588899	+	0.229423i
$869$	11.8663	−	11.8663i	0.402537	−	0.402537i
$870$	28.4877	−	0.819771i	0.965824	−	0.0277928i
$871$		−	1.27615i		−	0.0432407i
$872$	−10.4199	−	26.3251i	−0.352861	−	0.891480i
$873$	−13.1365			−0.444604
$874$	−71.1071	+	8.98057i	−2.40524	+	0.303772i
$875$	−9.83936	+	5.30914i	−0.332631	+	0.179482i
$876$	−2.08553	−	1.23356i	−0.0704635	−	0.0416782i
$877$	11.1276	−	11.1276i	0.375751	−	0.375751i	−0.493816	−	0.869567i	$-0.664398\pi$
$877$	11.1276	−	11.1276i	0.375751	−	0.375751i	0.869567	+	0.493816i	$0.164398\pi$
$878$	−0.935061	−	0.725356i	−0.0315568	−	0.0244796i
$879$	2.83650			0.0956728
$880$	42.5623	−	18.2798i	1.43478	−	0.616213i
$881$	26.6218			0.896913			0.448456	−	0.893805i	$-0.351974\pi$
$881$	26.6218			0.896913			0.448456	+	0.893805i	$0.351974\pi$
$882$	−1.25003	−	0.969687i	−0.0420907	−	0.0326511i
$883$	−8.53819	+	8.53819i	−0.287333	+	0.287333i	−0.836025	−	0.548692i	$-0.815126\pi$
$883$	−8.53819	+	8.53819i	−0.287333	+	0.287333i	0.548692	+	0.836025i	$0.315126\pi$
$884$	25.0334	−	42.3229i	0.841965	−	1.42347i
$885$	19.9526	−	16.4185i	0.670699	−	0.551903i
$886$	−42.4563	+	5.36207i	−1.42635	+	0.180142i
$887$	−21.6724			−0.727689			−0.363844	−	0.931460i	$-0.618536\pi$
$887$	−21.6724			−0.727689			−0.363844	+	0.931460i	$0.618536\pi$
$888$	16.6194	+	7.19378i	0.557710	+	0.241407i
$889$		−	12.1885i		−	0.408790i
$890$	0.966150	+	33.5745i	0.0323854	+	1.12542i
$891$	−16.0857	+	16.0857i	−0.538893	+	0.538893i
$892$	−4.38130	+	1.12462i	−0.146697	+	0.0376552i
$893$	26.7754	−	26.7754i	0.896005	−	0.896005i
$894$	25.2412	+	19.5804i	0.844192	+	0.654867i
$895$	1.61501	−	16.6210i	0.0539838	−	0.555578i
$896$	−11.2637	+	1.06215i	−0.376295	+	0.0354840i
$897$			43.4746i			1.45157i
$898$	−20.0105	+	25.7957i	−0.667759	+	0.860813i
$899$	16.2111	+	16.2111i	0.540671	+	0.540671i
$900$	0.643294	+	11.1682i	0.0214431	+	0.372274i
$901$	−7.52595	+	7.52595i	−0.250726	+	0.250726i
$902$	−6.94165	+	0.876706i	−0.231132	+	0.0291911i
$903$	7.69738			0.256153
$904$	16.9138	−	39.0751i	0.562546	−	1.29962i
$905$	−45.8329	−	4.45345i	−1.52354	−	0.148038i
$906$	23.0077	−	2.90579i	0.764380	−	0.0965384i
$907$	1.78177	+	1.78177i	0.0591627	+	0.0591627i	0.736069	−	0.676906i	$-0.236680\pi$
$907$	1.78177	+	1.78177i	0.0591627	+	0.0591627i	−0.676906	+	0.736069i	$0.736680\pi$
$908$	−29.5927	−	17.5037i	−0.982068	−	0.580880i
$909$	−2.09917	−	2.09917i	−0.0696250	−	0.0696250i
$910$	9.21852	−	9.76479i	0.305591	−	0.323700i
$911$	13.4053			0.444136			0.222068	−	0.975031i	$-0.428719\pi$
$911$	13.4053			0.444136			0.222068	+	0.975031i	$0.428719\pi$
$912$	−32.6473	+	17.9425i	−1.08106	+	0.594135i
$913$			58.2442i			1.92760i
$914$	20.0104	−	25.7955i	0.661884	−	0.853239i
$915$	−8.80399	−	10.6990i	−0.291051	−	0.353699i
$916$	24.8955	+	14.7254i	0.822571	+	0.486539i
$917$	9.76640	+	9.76640i	0.322515	+	0.322515i
$918$	5.79577	+	45.8903i	0.191289	+	1.51460i
$919$		−	21.8900i		−	0.722084i	−0.932550	−	0.361042i	$-0.882421\pi$
$919$		−	21.8900i		−	0.722084i	0.932550	−	0.361042i	$-0.117579\pi$
$920$	13.0470	+	45.3671i	0.430147	+	1.49571i
$921$		−	5.65846i		−	0.186453i
$922$	9.33811	−	1.17937i	0.307534	−	0.0388404i
$923$	−35.9138	−	35.9138i	−1.18212	−	1.18212i
$924$	13.7609	−	3.53224i	0.452700	−	0.116202i
$925$	−19.3724	+	13.0179i	−0.636960	+	0.428024i
$926$	43.5814	+	33.8075i	1.43217	+	1.11098i
$927$		−	5.04768i		−	0.165787i
$928$	−30.0739	+	21.8425i	−0.987223	+	0.717014i
$929$	−46.2374			−1.51700			−0.758500	−	0.651673i	$-0.774067\pi$
$929$	−46.2374			−1.51700			−0.758500	+	0.651673i	$0.774067\pi$
$930$	10.3891	−	11.0048i	0.340673	−	0.360860i
$931$	4.80124	+	4.80124i	0.157354	+	0.157354i
$932$	13.2239	+	51.5174i	0.433162	+	1.68751i
$933$	8.62556	+	8.62556i	0.282388	+	0.282388i
$934$	1.86551	+	14.7709i	0.0610415	+	0.483319i
$935$	−6.48419	+	66.7324i	−0.212056	+	2.18238i
$936$	−4.94508	−	12.4934i	−0.161635	−	0.408360i
$937$	16.9988			0.555326			0.277663	−	0.960679i	$-0.410440\pi$
$937$	16.9988			0.555326			0.277663	+	0.960679i	$0.410440\pi$
$938$	−0.0532518	−	0.421641i	−0.00173873	−	0.0137671i
$939$	11.3290	−	11.3290i	0.369708	−	0.369708i
$940$	−20.1376	−	14.7134i	−0.656816	−	0.479899i
$941$	−15.0793	−	15.0793i	−0.491570	−	0.491570i	0.417230	−	0.908801i	$-0.363001\pi$
$941$	−15.0793	−	15.0793i	−0.491570	−	0.491570i	−0.908801	+	0.417230i	$0.863001\pi$
$942$	29.6064	+	22.9666i	0.964627	+	0.748292i
$943$		−	7.13035i		−	0.232196i
$944$	−9.40611	+	32.3603i	−0.306143	+	1.05324i
$945$	−1.22167	+	12.5729i	−0.0397408	+	0.408995i
$946$	25.1929	−	32.4764i	0.819093	−	1.05590i
$947$	−6.64827	+	6.64827i	−0.216040	+	0.216040i	−0.806827	−	0.590787i	$-0.798817\pi$
$947$	−6.64827	+	6.64827i	−0.216040	+	0.216040i	0.590787	+	0.806827i	$0.298817\pi$
$948$	7.65083	+	4.52536i	0.248487	+	0.146977i
$949$	−2.65228	+	2.65228i	−0.0860967	+	0.0860967i
$950$	3.26685	−	47.9011i	0.105991	−	1.55412i
$951$		−	23.9988i		−	0.778216i
$952$	6.50501	−	15.0282i	0.210828	−	0.487065i
$953$	−32.2821			−1.04572			−0.522859	−	0.852419i	$-0.675135\pi$
$953$	−32.2821			−1.04572			−0.522859	+	0.852419i	$0.675135\pi$
$954$	0.364416	+	2.88540i	0.0117984	+	0.0934183i
$955$	−26.9793	−	32.7865i	−0.873028	−	1.06095i
$956$	5.68260	+	22.1382i	0.183788	+	0.716002i
$957$	33.0037	−	33.0037i	1.06686	−	1.06686i
$958$	−17.5708	+	22.6507i	−0.567688	+	0.731810i
$959$	8.97032			0.289667
$960$	14.9839	+	19.4296i	0.483602	+	0.627087i
$961$	−18.8257			−0.607280
$962$	17.1828	−	22.1505i	0.553996	−	0.714160i
$963$	−3.69782	+	3.69782i	−0.119161	+	0.119161i
$964$	−9.16077	−	35.6885i	−0.295048	−	1.14945i
$965$	40.0048	−	32.9190i	1.28780	−	1.05970i
$966$	1.81413	+	14.3641i	0.0583686	+	0.462156i
$967$	20.2791			0.652132			0.326066	−	0.945347i	$-0.394277\pi$
$967$	20.2791			0.652132			0.326066	+	0.945347i	$0.394277\pi$
$968$	17.7761	−	41.0673i	0.571347	−	1.31995i
$969$		−	53.9203i		−	1.73217i
$970$	−1.06815	−	37.1190i	−0.0342962	−	1.19182i
$971$	−35.7551	+	35.7551i	−1.14744	+	1.14744i	−0.160381	+	0.987055i	$0.551272\pi$
$971$	−35.7551	+	35.7551i	−1.14744	+	1.14744i	−0.987055	+	0.160381i	$0.948728\pi$
$972$	18.8027	+	11.1216i	0.603098	+	0.356724i
$973$	6.42586	−	6.42586i	0.206004	−	0.206004i
$974$	−25.8561	+	33.3312i	−0.828482	+	1.06800i
$975$	−28.5784	−	5.60668i	−0.915241	−	0.179558i
$976$	17.3524	+	5.04377i	0.555435	+	0.161447i
$977$		−	23.8102i		−	0.761756i	−0.924625	−	0.380878i	$-0.875622\pi$
$977$		−	23.8102i		−	0.761756i	0.924625	−	0.380878i	$-0.124378\pi$
$978$	−13.1814	−	10.2252i	−0.421495	−	0.326967i
$979$	38.8969	+	38.8969i	1.24315	+	1.24315i
$980$	2.63834	−	3.61098i	0.0842788	−	0.115348i
$981$	7.91805	−	7.91805i	0.252804	−	0.252804i
$982$	−0.183855	−	1.45574i	−0.00586705	−	0.0464546i
$983$	−16.9307			−0.540007			−0.270003	−	0.962859i	$-0.587025\pi$
$983$	−16.9307			−0.540007			−0.270003	+	0.962859i	$0.587025\pi$
$984$	−1.36398	−	3.44601i	−0.0434822	−	0.109855i
$985$	1.89148	−	19.4662i	0.0602674	−	0.620246i
$986$	−6.74105	−	53.3748i	−0.214679	−	1.69980i
$987$	−5.40879	−	5.40879i	−0.172164	−	0.172164i
$988$	14.3378	+	55.8572i	0.456147	+	1.77705i
$989$	29.6185	+	29.6185i	0.941812	+	0.941812i
$990$	13.3220	+	12.5767i	0.423402	+	0.399715i
$991$	−3.49407			−0.110993			−0.0554964	−	0.998459i	$-0.517674\pi$
$991$	−3.49407			−0.110993			−0.0554964	+	0.998459i	$0.517674\pi$
$992$	−3.09083	+	19.4942i	−0.0981340	+	0.618943i
$993$			30.9282i			0.981478i
$994$	−13.3646	−	10.3673i	−0.423900	−	0.328832i
$995$	−3.80836	+	3.13381i	−0.120733	+	0.0993484i
$996$	−29.8826	+	7.67048i	−0.946867	+	0.243048i
$997$	−17.6966	−	17.6966i	−0.560456	−	0.560456i	0.368981	−	0.929437i	$-0.379707\pi$
$997$	−17.6966	−	17.6966i	−0.560456	−	0.560456i	−0.929437	+	0.368981i	$0.879707\pi$
$998$	−8.17718	+	1.03275i	−0.258844	+	0.0326911i
$999$			26.3706i			0.834328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.d.29.10	yes	70
5.4	even	2		560.2.bb.c.29.26	✓	70
16.5	even	4		560.2.bb.c.309.26	yes	70
80.69	even	4	inner	560.2.bb.d.309.10	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.26	✓	70	5.4	even	2
560.2.bb.c.309.26	yes	70	16.5	even	4
560.2.bb.d.29.10	yes	70	1.1	even	1	trivial
560.2.bb.d.309.10	yes	70	80.69	even	4	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866818 + 1.11742i) q^{2} +(0.969878 - 0.969878i) q^{3} +(-0.497254 - 1.93720i) q^{4} +(1.42081 + 1.72664i) q^{5} +(0.243053 + 1.92447i) q^{6} +1.00000 q^{7} +(2.59569 + 1.12356i) q^{8} +1.11867i q^{9} +O(q^{10})\)	\(q+(-0.866818 + 1.11742i) q^{2} +(0.969878 - 0.969878i) q^{3} +(-0.497254 - 1.93720i) q^{4} +(1.42081 + 1.72664i) q^{5} +(0.243053 + 1.92447i) q^{6} +1.00000 q^{7} +(2.59569 + 1.12356i) q^{8} +1.11867i q^{9} +(-3.16097 + 0.0909610i) q^{10} +(-3.66206 + 3.66206i) q^{11} +(-2.36112 - 1.39657i) q^{12} +(-3.00277 + 3.00277i) q^{13} +(-0.866818 + 1.11742i) q^{14} +(3.05265 + 0.296616i) q^{15} +(-3.50548 + 1.92656i) q^{16} -5.78965i q^{17} +(-1.25003 - 0.969687i) q^{18} +(4.80124 + 4.80124i) q^{19} +(2.63834 - 3.61098i) q^{20} +(0.969878 - 0.969878i) q^{21} +(-0.917719 - 7.26639i) q^{22} +7.46391 q^{23} +(3.60722 - 1.42779i) q^{24} +(-0.962581 + 4.90647i) q^{25} +(-0.752500 - 5.95820i) q^{26} +(3.99461 + 3.99461i) q^{27} +(-0.497254 - 1.93720i) q^{28} +(-4.64612 - 4.64612i) q^{29} +(-2.97753 + 3.15397i) q^{30} -3.48917 q^{31} +(0.885835 - 5.58707i) q^{32} +7.10349i q^{33} +(6.46947 + 5.01857i) q^{34} +(1.42081 + 1.72664i) q^{35} +(2.16709 - 0.556265i) q^{36} +(3.30077 + 3.30077i) q^{37} +(-9.52679 + 1.20320i) q^{38} +5.82464i q^{39} +(1.74801 + 6.07819i) q^{40} -0.955310i q^{41} +(0.243053 + 1.92447i) q^{42} +(3.96822 + 3.96822i) q^{43} +(8.91510 + 5.27316i) q^{44} +(-1.93155 + 1.58943i) q^{45} +(-6.46985 + 8.34032i) q^{46} -5.57677i q^{47} +(-1.53136 + 5.26841i) q^{48} +1.00000 q^{49} +(-4.64820 - 5.32862i) q^{50} +(-5.61526 - 5.61526i) q^{51} +(7.31010 + 4.32382i) q^{52} +(-1.29990 - 1.29990i) q^{53} +(-7.92626 + 1.00106i) q^{54} +(-11.5262 - 1.11996i) q^{55} +(2.59569 + 1.12356i) q^{56} +9.31322 q^{57} +(9.21900 - 1.16433i) q^{58} +(5.95731 - 5.95731i) q^{59} +(-0.943335 - 6.06107i) q^{60} +(-3.19445 - 3.19445i) q^{61} +(3.02448 - 3.89887i) q^{62} +1.11867i q^{63} +(5.47524 + 5.83282i) q^{64} +(-9.45108 - 0.918332i) q^{65} +(-7.93758 - 6.15743i) q^{66} +(-0.212495 + 0.212495i) q^{67} +(-11.2157 + 2.87893i) q^{68} +(7.23908 - 7.23908i) q^{69} +(-3.16097 + 0.0909610i) q^{70} +11.9602i q^{71} +(-1.25689 + 2.90374i) q^{72} +0.883279 q^{73} +(-6.54951 + 0.827179i) q^{74} +(3.82509 + 5.69226i) q^{75} +(6.91352 - 11.6884i) q^{76} +(-3.66206 + 3.66206i) q^{77} +(-6.50856 - 5.04890i) q^{78} -3.24034 q^{79} +(-8.30710 - 3.31542i) q^{80} +4.39254 q^{81} +(1.06748 + 0.828080i) q^{82} +(7.95239 - 7.95239i) q^{83} +(-2.36112 - 1.39657i) q^{84} +(9.99665 - 8.22601i) q^{85} +(-7.87389 + 0.994444i) q^{86} -9.01233 q^{87} +(-13.6201 + 5.39104i) q^{88} -10.6216i q^{89} +(-0.101756 - 3.53610i) q^{90} +(-3.00277 + 3.00277i) q^{91} +(-3.71146 - 14.4591i) q^{92} +(-3.38407 + 3.38407i) q^{93} +(6.23160 + 4.83405i) q^{94} +(-1.46835 + 15.1117i) q^{95} +(-4.55962 - 6.27792i) q^{96} +11.7429i q^{97} +(-0.866818 + 1.11742i) q^{98} +(-4.09665 - 4.09665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more