LMFDB - Embedded newform 570.2.bc.b.139.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, 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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			139.5
Character	$\chi$	$=$	570.139
Dual form			570.2.bc.b.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.04631 + 0.901446i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(1.77015 + 1.02199i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.04631 + 0.901446i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(1.77015 + 1.02199i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-0.624797 - 2.14700i) q^{10} +(0.174711 + 0.302608i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-1.01451 - 2.78733i) q^{13} +(-0.354935 - 2.01294i) q^{14} +(1.54696 - 1.61459i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.49363 + 4.16355i) q^{17} +1.00000i q^{18} +(-1.58307 + 4.06127i) q^{19} +(-1.24309 + 1.85869i) q^{20} +(1.56579 - 1.31385i) q^{21} +(0.119509 - 0.328348i) q^{22} +(7.56180 + 1.33335i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(3.37479 + 3.68928i) q^{25} +(-1.48311 + 2.56882i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-1.31385 + 1.56579i) q^{28} +(-1.64043 - 1.37648i) q^{29} +(-2.23122 - 0.147202i) q^{30} +(1.54971 - 2.68418i) q^{31} +(0.342020 + 0.939693i) q^{32} +(0.344113 - 0.0606763i) q^{33} +(0.943799 - 5.35255i) q^{34} +(2.70100 + 3.68701i) q^{35} +(0.766044 - 0.642788i) q^{36} -10.1134i q^{37} +(4.12869 - 1.39783i) q^{38} -2.96622 q^{39} +(2.22288 - 0.242482i) q^{40} +(3.50521 + 1.27579i) q^{41} +(-2.01294 - 0.354935i) q^{42} +(-9.26134 + 1.63302i) q^{43} +(-0.328348 + 0.119509i) q^{44} +(-0.988128 - 2.00589i) q^{45} +(-3.83923 - 6.64974i) q^{46} +(7.92656 - 9.44650i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(-1.41105 - 2.44401i) q^{49} +(0.656878 - 4.95666i) q^{50} +(5.10735 - 1.85892i) q^{51} +(2.92115 - 0.515078i) q^{52} +(-8.25701 - 1.45593i) q^{53} +(0.939693 + 0.342020i) q^{54} +(0.0847282 + 0.776722i) q^{55} +2.04399 q^{56} +(3.27490 + 2.87663i) q^{57} +2.14142i q^{58} +(-6.98806 + 5.86368i) q^{59} +(1.32144 + 1.80383i) q^{60} +(-0.249918 + 1.41735i) q^{61} +(-3.05233 + 0.538208i) q^{62} +(-0.699086 - 1.92072i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.436632 - 6.61828i) q^{65} +(-0.267672 - 0.224604i) q^{66} +(2.03182 - 2.42142i) q^{67} +(-4.70696 + 2.71756i) q^{68} +(3.83923 - 6.64974i) q^{69} +(1.08825 - 4.43905i) q^{70} +(2.42551 + 13.7558i) q^{71} +(-0.984808 - 0.173648i) q^{72} +(3.56438 - 9.79306i) q^{73} +(-7.74734 + 6.50079i) q^{74} +(4.62104 - 1.90946i) q^{75} +(-3.72467 - 2.26425i) q^{76} +0.714213i q^{77} +(1.90665 + 2.27226i) q^{78} +(-4.81664 - 1.75311i) q^{79} +(-1.61459 - 1.54696i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-1.27579 - 3.50521i) q^{82} +(5.99044 + 3.45858i) q^{83} +(1.02199 + 1.77015i) q^{84} +(3.39585 + 11.6692i) q^{85} +(7.20405 + 6.04491i) q^{86} +(-1.85453 + 1.07071i) q^{87} +(0.302608 + 0.174711i) q^{88} +(-3.77608 + 1.37438i) q^{89} +(-0.901446 + 2.04631i) q^{90} +(1.05282 - 5.97081i) q^{91} +(-2.62619 + 7.21539i) q^{92} +(-1.99227 - 2.37429i) q^{93} -12.3315 q^{94} +(-6.90047 + 6.88357i) q^{95} +1.00000 q^{96} +(-9.58014 - 11.4172i) q^{97} +(-0.965217 + 2.65191i) q^{98} +(0.0606763 - 0.344113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5}+O(q^{10}) $ 60 * q + 6 * q^5	$ 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	2.04631	+	0.901446i	0.915139	+	0.403139i
$5$	2.04631	+	0.901446i	0.915139	+	0.403139i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	1.77015	+	1.02199i	0.669053	+	0.386278i	0.795718	−	0.605668i	$-0.207094\pi$
$7$	1.77015	+	1.02199i	0.669053	+	0.386278i	−0.126665	+	0.991946i	$0.540427\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	−0.624797	−	2.14700i	−0.197578	−	0.678942i
$11$	0.174711	+	0.302608i	0.0526772	+	0.0912396i	0.891162	−	0.453686i	$-0.149891\pi$
$11$	0.174711	+	0.302608i	0.0526772	+	0.0912396i	−0.838484	+	0.544926i	$0.816558\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−1.01451	−	2.78733i	−0.281373	−	0.773067i	−0.997199	−	0.0747885i	$-0.976172\pi$
$13$	−1.01451	−	2.78733i	−0.281373	−	0.773067i	0.715826	−	0.698279i	$-0.246050\pi$
$14$	−0.354935	−	2.01294i	−0.0948604	−	0.537980i
$15$	1.54696	−	1.61459i	0.399424	−	0.416886i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.49363	+	4.16355i	0.847330	+	1.00981i	0.999769	+	0.0214954i	$0.00684273\pi$
$17$	3.49363	+	4.16355i	0.847330	+	1.00981i	−0.152439	+	0.988313i	$0.548713\pi$
$18$			1.00000i			0.235702i
$19$	−1.58307	+	4.06127i	−0.363181	+	0.931719i
$19$	−1.58307	+	4.06127i	−0.363181	+	0.931719i
$20$	−1.24309	+	1.85869i	−0.277963	+	0.415616i
$21$	1.56579	−	1.31385i	0.341683	−	0.286706i
$22$	0.119509	−	0.328348i	0.0254794	−	0.0700041i
$23$	7.56180	+	1.33335i	1.57674	+	0.278023i	0.892438	−	0.451171i	$-0.148994\pi$
$23$	7.56180	+	1.33335i	1.57674	+	0.278023i	0.684307	+	0.729194i	$0.260105\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	3.37479	+	3.68928i	0.674958	+	0.737856i
$26$	−1.48311	+	2.56882i	−0.290862	+	0.503787i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−1.31385	+	1.56579i	−0.248295	+	0.295906i
$29$	−1.64043	−	1.37648i	−0.304619	−	0.255606i	0.477645	−	0.878553i	$-0.341491\pi$
$29$	−1.64043	−	1.37648i	−0.304619	−	0.255606i	−0.782264	+	0.622947i	$0.785935\pi$
$30$	−2.23122	−	0.147202i	−0.407363	−	0.0268752i
$31$	1.54971	−	2.68418i	0.278336	−	0.482092i	−0.692635	−	0.721288i	$-0.743550\pi$
$31$	1.54971	−	2.68418i	0.278336	−	0.482092i	0.970971	+	0.239196i	$0.0768838\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	0.344113	−	0.0606763i	0.0599023	−	0.0105624i
$34$	0.943799	−	5.35255i	0.161860	−	0.917955i
$35$	2.70100	+	3.68701i	0.456553	+	0.623219i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$		−	10.1134i		−	1.66264i	−0.555795	−	0.831319i	$-0.687586\pi$
$37$		−	10.1134i		−	1.66264i	0.555795	−	0.831319i	$-0.312414\pi$
$38$	4.12869	−	1.39783i	0.669762	−	0.226758i
$39$	−2.96622			−0.474975
$40$	2.22288	−	0.242482i	0.351468	−	0.0383397i
$41$	3.50521	+	1.27579i	0.547422	+	0.199245i	0.600901	−	0.799324i	$-0.294809\pi$
$41$	3.50521	+	1.27579i	0.547422	+	0.199245i	−0.0534788	+	0.998569i	$0.517031\pi$
$42$	−2.01294	−	0.354935i	−0.310603	−	0.0547677i
$43$	−9.26134	+	1.63302i	−1.41234	+	0.249034i	−0.827205	−	0.561901i	$-0.810070\pi$
$43$	−9.26134	+	1.63302i	−1.41234	+	0.249034i	−0.585137	+	0.810935i	$0.698959\pi$
$44$	−0.328348	+	0.119509i	−0.0495004	+	0.0180167i
$45$	−0.988128	−	2.00589i	−0.147301	−	0.299021i
$46$	−3.83923	−	6.64974i	−0.566063	−	0.980450i
$47$	7.92656	−	9.44650i	1.15621	−	1.37791i	0.243198	−	0.969977i	$-0.421804\pi$
$47$	7.92656	−	9.44650i	1.15621	−	1.37791i	0.913010	−	0.407938i	$-0.133752\pi$
$48$	−0.642788	+	0.766044i	−0.0927784	+	0.110569i
$49$	−1.41105	−	2.44401i	−0.201579	−	0.349145i
$50$	0.656878	−	4.95666i	0.0928965	−	0.700978i
$51$	5.10735	−	1.85892i	0.715171	−	0.260301i
$52$	2.92115	−	0.515078i	0.405091	−	0.0714285i
$53$	−8.25701	−	1.45593i	−1.13419	−	0.199988i	−0.425126	−	0.905134i	$-0.639770\pi$
$53$	−8.25701	−	1.45593i	−1.13419	−	0.199988i	−0.709062	+	0.705146i	$0.750881\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	0.0847282	+	0.776722i	0.0114247	+	0.104733i
$56$	2.04399			0.273140
$57$	3.27490	+	2.87663i	0.433771	+	0.381019i
$58$			2.14142i			0.281183i
$59$	−6.98806	+	5.86368i	−0.909768	+	0.763386i	−0.972075	−	0.234671i	$-0.924599\pi$
$59$	−6.98806	+	5.86368i	−0.909768	+	0.763386i	0.0623070	+	0.998057i	$0.480154\pi$
$60$	1.32144	+	1.80383i	0.170597	+	0.232874i
$61$	−0.249918	+	1.41735i	−0.0319987	+	0.181473i	−0.996618	−	0.0821728i	$-0.973814\pi$
$61$	−0.249918	+	1.41735i	−0.0319987	+	0.181473i	0.964619	+	0.263646i	$0.0849252\pi$
$62$	−3.05233	+	0.538208i	−0.387646	+	0.0683525i
$63$	−0.699086	−	1.92072i	−0.0880765	−	0.241988i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	0.436632	−	6.61828i	0.0541576	−	0.820896i
$66$	−0.267672	−	0.224604i	−0.0329482	−	0.0276468i
$67$	2.03182	−	2.42142i	0.248226	−	0.295824i	−0.627516	−	0.778604i	$-0.715928\pi$
$67$	2.03182	−	2.42142i	0.248226	−	0.295824i	0.875742	+	0.482780i	$0.160373\pi$
$68$	−4.70696	+	2.71756i	−0.570802	+	0.329553i
$69$	3.83923	−	6.64974i	0.462189	−	0.800534i
$70$	1.08825	−	4.43905i	0.130070	−	0.530568i
$71$	2.42551	+	13.7558i	0.287855	+	1.63251i	0.694904	+	0.719102i	$0.255447\pi$
$71$	2.42551	+	13.7558i	0.287855	+	1.63251i	−0.407049	+	0.913406i	$0.633442\pi$
$72$	−0.984808	−	0.173648i	−0.116061	−	0.0204646i
$73$	3.56438	−	9.79306i	0.417180	−	1.14619i	−0.536114	−	0.844146i	$-0.680108\pi$
$73$	3.56438	−	9.79306i	0.417180	−	1.14619i	0.953293	−	0.302046i	$-0.0976695\pi$
$74$	−7.74734	+	6.50079i	−0.900610	+	0.755702i
$75$	4.62104	−	1.90946i	0.533591	−	0.220485i
$76$	−3.72467	−	2.26425i	−0.427249	−	0.259727i
$77$			0.714213i			0.0813922i
$78$	1.90665	+	2.27226i	0.215885	+	0.257282i
$79$	−4.81664	−	1.75311i	−0.541914	−	0.197241i	0.0565361	−	0.998401i	$-0.481994\pi$
$79$	−4.81664	−	1.75311i	−0.541914	−	0.197241i	−0.598450	+	0.801160i	$0.704217\pi$
$80$	−1.61459	−	1.54696i	−0.180517	−	0.172956i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−1.27579	−	3.50521i	−0.140888	−	0.387086i
$83$	5.99044	+	3.45858i	0.657537	+	0.379629i	0.791338	−	0.611379i	$-0.209385\pi$
$83$	5.99044	+	3.45858i	0.657537	+	0.379629i	−0.133801	+	0.991008i	$0.542718\pi$
$84$	1.02199	+	1.77015i	0.111509	+	0.193139i
$85$	3.39585	+	11.6692i	0.368332	+	1.26571i
$86$	7.20405	+	6.04491i	0.776832	+	0.651840i
$87$	−1.85453	+	1.07071i	−0.198826	+	0.114792i
$88$	0.302608	+	0.174711i	0.0322581	+	0.0186242i
$89$	−3.77608	+	1.37438i	−0.400263	+	0.145684i	−0.534305	−	0.845292i	$-0.679427\pi$
$89$	−3.77608	+	1.37438i	−0.400263	+	0.145684i	0.134042	+	0.990976i	$0.457204\pi$
$90$	−0.901446	+	2.04631i	−0.0950207	+	0.215700i
$91$	1.05282	−	5.97081i	0.110365	−	0.625911i
$92$	−2.62619	+	7.21539i	−0.273799	+	0.752256i
$93$	−1.99227	−	2.37429i	−0.206589	−	0.246203i
$94$	−12.3315			−1.27190
$95$	−6.90047	+	6.88357i	−0.707973	+	0.706240i
$96$	1.00000			0.102062
$97$	−9.58014	−	11.4172i	−0.972715	−	1.15924i	−0.987223	−	0.159342i	$-0.949063\pi$
$97$	−9.58014	−	11.4172i	−0.972715	−	1.15924i	0.0145080	−	0.999895i	$-0.495382\pi$
$98$	−0.965217	+	2.65191i	−0.0975016	+	0.267884i
$99$	0.0606763	−	0.344113i	0.00609820	−	0.0345846i
$100$	−4.21926	+	2.68288i	−0.421926	+	0.268288i
$101$	3.04133	−	1.10695i	0.302624	−	0.110146i	−0.186245	−	0.982503i	$-0.559632\pi$
$101$	3.04133	−	1.10695i	0.302624	−	0.110146i	0.488869	+	0.872357i	$0.337410\pi$
$102$	−4.70696	−	2.71756i	−0.466058	−	0.269079i
$103$	−10.4658	+	6.04245i	−1.03123	+	0.595381i	−0.917337	−	0.398113i	$-0.869665\pi$
$103$	−10.4658	+	6.04245i	−1.03123	+	0.595381i	−0.113893	+	0.993493i	$0.536332\pi$
$104$	−2.27226	−	1.90665i	−0.222813	−	0.186962i
$105$	4.38846	−	1.27708i	0.428269	−	0.124630i
$106$	4.19219	+	7.26109i	0.407182	+	0.705260i
$107$	10.3194	+	5.95793i	0.997617	+	0.575974i	0.907542	−	0.419961i	$-0.137956\pi$
$107$	10.3194	+	5.95793i	0.997617	+	0.575974i	0.0900747	+	0.995935i	$0.471289\pi$
$108$	−0.342020	−	0.939693i	−0.0329109	−	0.0904220i
$109$	2.08216	+	11.8085i	0.199435	+	1.13105i	0.905960	+	0.423364i	$0.139151\pi$
$109$	2.08216	+	11.8085i	0.199435	+	1.13105i	−0.706524	+	0.707689i	$0.749738\pi$
$110$	0.540541	−	0.564173i	0.0515386	−	0.0537918i
$111$	−9.50352	−	3.45900i	−0.902034	−	0.328314i
$112$	−1.31385	−	1.56579i	−0.124147	−	0.147953i
$113$		−	5.62168i		−	0.528843i	−0.964407	−	0.264421i	$-0.914819\pi$
$113$		−	5.62168i		−	0.528843i	0.964407	−	0.264421i	$-0.0851810\pi$
$114$	0.0985628	−	4.35778i	0.00923125	−	0.408144i
$115$	14.2719	+	9.54500i	1.33086	+	0.890076i
$116$	1.64043	−	1.37648i	0.152310	−	0.127803i
$117$	−1.01451	+	2.78733i	−0.0937911	+	0.257689i
$118$	8.98368	+	1.58406i	0.827014	+	0.145825i
$119$	1.92912	+	10.9406i	0.176842	+	1.00292i
$120$	0.532412	−	2.17176i	0.0486024	−	0.198254i
$121$	5.43895	−	9.42054i	0.494450	−	0.856413i
$122$	1.24640	−	0.719609i	0.112844	−	0.0651503i
$123$	2.39770	−	2.85747i	0.216194	−	0.257650i
$124$	2.37429	+	1.99227i	0.213218	+	0.178911i
$125$	3.58019	+	10.5916i	0.320222	+	0.947342i
$126$	−1.02199	+	1.77015i	−0.0910465	+	0.157697i
$127$	3.78297	+	10.3936i	0.335684	+	0.922285i	0.986603	+	0.163138i	$0.0521615\pi$
$127$	3.78297	+	10.3936i	0.335684	+	0.922285i	−0.650919	+	0.759147i	$0.725616\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	−1.63302	+	9.26134i	−0.143780	+	0.815416i
$130$	−5.35056	+	3.91967i	−0.469275	+	0.343778i
$131$	−2.10958	+	1.77015i	−0.184315	+	0.154659i	−0.730277	−	0.683152i	$-0.760609\pi$
$131$	−2.10958	+	1.77015i	−0.184315	+	0.154659i	0.545962	+	0.837810i	$0.316164\pi$
$132$			0.349421i			0.0304132i
$133$	−6.95286	+	5.57115i	−0.602889	+	0.483080i
$134$	−3.16094			−0.273064
$135$	−2.22288	+	0.242482i	−0.191315	+	0.0208695i
$136$	5.10735	+	1.85892i	0.437951	+	0.159401i
$137$	−11.0576	−	1.94975i	−0.944712	−	0.166578i	−0.319986	−	0.947422i	$-0.603678\pi$
$137$	−11.0576	−	1.94975i	−0.944712	−	0.166578i	−0.624726	+	0.780844i	$0.714789\pi$
$138$	−7.56180	+	1.33335i	−0.643703	+	0.113502i
$139$	−17.6953	+	6.44055i	−1.50089	+	0.546280i	−0.956291	−	0.292416i	$-0.905541\pi$
$139$	−17.6953	+	6.44055i	−1.50089	+	0.546280i	−0.544601	+	0.838696i	$0.683319\pi$
$140$	−4.10002	+	2.01972i	−0.346515	+	0.170698i
$141$	−6.16577	−	10.6794i	−0.519251	−	0.899370i
$142$	8.97843	−	10.7001i	0.753454	−	0.897931i
$143$	0.666223	−	0.793974i	0.0557124	−	0.0663954i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−2.11600	−	4.29546i	−0.175724	−	0.356719i
$146$	−9.79306	+	3.56438i	−0.810480	+	0.294990i
$147$	−2.77923	+	0.490053i	−0.229227	+	0.0404189i
$148$	9.95979	+	1.75618i	0.818690	+	0.144357i
$149$	−8.14741	−	2.96541i	−0.667462	−	0.242936i	−0.0140072	−	0.999902i	$-0.504459\pi$
$149$	−8.14741	−	2.96541i	−0.667462	−	0.242936i	−0.653455	+	0.756966i	$0.726681\pi$
$150$	−4.43307	−	2.31254i	−0.361959	−	0.188818i
$151$	0.542302			0.0441319			0.0220659	−	0.999757i	$-0.492976\pi$
$151$	0.542302			0.0441319			0.0220659	+	0.999757i	$0.492976\pi$
$152$	0.659656	+	4.30870i	0.0535052	+	0.349481i
$153$		−	5.43512i		−	0.439404i
$154$	0.547119	−	0.459087i	0.0440881	−	0.0369943i
$155$	5.59083	−	4.09568i	0.449066	−	0.328973i
$156$	0.515078	−	2.92115i	0.0412393	−	0.233880i
$157$	−6.03952	+	1.06493i	−0.482007	+	0.0849908i	−0.409371	−	0.912368i	$-0.634252\pi$
$157$	−6.03952	+	1.06493i	−0.482007	+	0.0849908i	−0.0726351	+	0.997359i	$0.523141\pi$
$158$	1.75311	+	4.81664i	0.139470	+	0.383191i
$159$	−4.19219	+	7.26109i	−0.332463	+	0.575842i
$160$	−0.147202	+	2.23122i	−0.0116373	+	0.176393i
$161$	12.0228	+	10.0883i	0.947531	+	0.795073i
$162$	0.642788	−	0.766044i	0.0505022	−	0.0601861i
$163$	−13.6759	+	7.89579i	−1.07118	+	0.618446i	−0.928504	−	0.371324i	$-0.878904\pi$
$163$	−13.6759	+	7.89579i	−1.07118	+	0.618446i	−0.142676	+	0.989769i	$0.545571\pi$
$164$	−1.86508	+	3.23042i	−0.145639	+	0.252253i
$165$	0.758858	+	0.186036i	0.0590771	+	0.0144829i
$166$	−1.20115	−	6.81208i	−0.0932276	−	0.528720i
$167$	−7.40447	−	1.30561i	−0.572975	−	0.101031i	−0.120349	−	0.992732i	$-0.538401\pi$
$167$	−7.40447	−	1.30561i	−0.572975	−	0.101031i	−0.452626	+	0.891701i	$0.649513\pi$
$168$	0.699086	−	1.92072i	0.0539356	−	0.148187i
$169$	3.21857	−	2.70070i	0.247583	−	0.207746i
$170$	6.75634	−	10.1022i	0.518188	−	0.774804i
$171$	3.82323	−	2.09353i	0.292370	−	0.160097i
$172$		−	9.40421i		−	0.717065i
$173$	−8.17243	−	9.73952i	−0.621338	−	0.740482i	0.359962	−	0.932967i	$-0.382790\pi$
$173$	−8.17243	−	9.73952i	−0.621338	−	0.740482i	−0.981300	+	0.192485i	$0.938345\pi$
$174$	2.01228	+	0.732410i	0.152551	+	0.0555239i
$175$	2.20345	+	9.97959i	0.166565	+	0.754386i
$176$	−0.0606763	−	0.344113i	−0.00457365	−	0.0259385i
$177$	3.12000	+	8.57212i	0.234513	+	0.644320i
$178$	3.48005	+	2.00921i	0.260841	+	0.150597i
$179$	−8.84020	−	15.3117i	−0.660747	−	1.14445i	−0.980420	−	0.196920i	$-0.936906\pi$
$179$	−8.84020	−	15.3117i	−0.660747	−	1.14445i	0.319672	−	0.947528i	$-0.396427\pi$
$180$	2.14700	−	0.624797i	0.160028	−	0.0465696i
$181$	2.70258	+	2.26773i	0.200881	+	0.168559i	0.737679	−	0.675152i	$-0.235922\pi$
$181$	2.70258	+	2.26773i	0.200881	+	0.168559i	−0.536798	+	0.843711i	$0.680366\pi$
$182$	−5.25064	+	3.03146i	−0.389204	+	0.224707i
$183$	1.24640	+	0.719609i	0.0921365	+	0.0531950i
$184$	7.21539	−	2.62619i	0.531925	−	0.193605i
$185$	9.11671	−	20.6953i	0.670274	−	1.52155i
$186$	−0.538208	+	3.05233i	−0.0394634	+	0.223808i
$187$	−0.649547	+	1.78461i	−0.0474995	+	0.130504i
$188$	7.92656	+	9.44650i	0.578104	+	0.688957i
$189$	−2.04399			−0.148678
$190$	9.70866	+	0.861388i	0.704340	+	0.0624917i
$191$	−10.9064			−0.789161			−0.394581	−	0.918861i	$-0.629110\pi$
$191$	−10.9064			−0.789161			−0.394581	+	0.918861i	$0.629110\pi$
$192$	−0.642788	−	0.766044i	−0.0463892	−	0.0552845i
$193$	−5.47489	+	15.0421i	−0.394091	+	1.08276i	0.571024	+	0.820933i	$0.306546\pi$
$193$	−5.47489	+	15.0421i	−0.394091	+	1.08276i	−0.965116	+	0.261824i	$0.915676\pi$
$194$	−2.58806	+	14.6776i	−0.185812	+	1.05379i
$195$	−6.06981	−	2.67388i	−0.434668	−	0.191481i
$196$	2.65191	−	0.965217i	0.189422	−	0.0689441i
$197$	5.33042	+	3.07752i	0.379777	+	0.219264i	0.677721	−	0.735319i	$-0.262968\pi$
$197$	5.33042	+	3.07752i	0.379777	+	0.219264i	−0.297944	+	0.954583i	$0.596301\pi$
$198$	−0.302608	+	0.174711i	−0.0215054	+	0.0124161i
$199$	6.01269	+	5.04524i	0.426228	+	0.357648i	0.830526	−	0.556979i	$-0.188040\pi$
$199$	6.01269	+	5.04524i	0.426228	+	0.357648i	−0.404298	+	0.914627i	$0.632484\pi$
$200$	4.76729	+	1.50761i	0.337099	+	0.106604i
$201$	−1.58047	−	2.73746i	−0.111478	−	0.193085i
$202$	−2.80291	−	1.61826i	−0.197212	−	0.113860i
$203$	−1.49704	−	4.11308i	−0.105072	−	0.288682i
$204$	0.943799	+	5.35255i	0.0660792	+	0.374754i
$205$	6.02270	+	5.77042i	0.420643	+	0.403024i
$206$	11.3561	+	4.13328i	0.791217	+	0.287979i
$207$	−4.93562	−	5.88204i	−0.343049	−	0.408830i
$208$			2.96622i			0.205670i
$209$	−1.50555	+	0.230498i	−0.104141	+	0.0159439i
$210$	−3.79914	−	2.54086i	−0.262166	−	0.175336i
$211$	−8.48256	+	7.11771i	−0.583964	+	0.490004i	−0.886246	−	0.463215i	$-0.846696\pi$
$211$	−8.48256	+	7.11771i	−0.583964	+	0.490004i	0.302282	+	0.953218i	$0.402251\pi$
$212$	2.86763	−	7.87875i	0.196950	−	0.541115i
$213$	13.7558	+	2.42551i	0.942529	+	0.166193i
$214$	−2.06917	−	11.7348i	−0.141445	−	0.802176i
$215$	−20.4237	−	5.00692i	−1.39288	−	0.341469i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	5.48643	−	3.16759i	0.372443	−	0.215030i
$218$	7.70748	−	9.18541i	0.522016	−	0.622115i
$219$	−7.98338	−	6.69885i	−0.539467	−	0.452666i
$220$	−0.779635	−	0.0514354i	−0.0525629	−	0.00346777i
$221$	8.06088	−	13.9619i	0.542234	−	0.939176i
$222$	3.45900	+	9.50352i	0.232153	+	0.637835i
$223$	2.64750	−	0.466825i	0.177289	−	0.0312609i	−0.0842985	−	0.996441i	$-0.526865\pi$
$223$	2.64750	−	0.466825i	0.177289	−	0.0312609i	0.261588	+	0.965180i	$0.415754\pi$
$224$	−0.354935	+	2.01294i	−0.0237151	+	0.134495i
$225$	−0.213817	−	4.99543i	−0.0142545	−	0.333028i
$226$	−4.30645	+	3.61354i	−0.286461	+	0.240369i
$227$			6.53924i			0.434025i	0.976169	+	0.217012i	$0.0696312\pi$
$227$			6.53924i			0.434025i	−0.976169	+	0.217012i	$0.930369\pi$
$228$	−3.40161	+	2.72563i	−0.225277	+	0.180509i
$229$	−13.9866			−0.924264			−0.462132	−	0.886811i	$-0.652915\pi$
$229$	−13.9866			−0.924264			−0.462132	+	0.886811i	$0.652915\pi$
$230$	−1.86188	−	17.0683i	−0.122769	−	1.12545i
$231$	0.671141	+	0.244275i	0.0441578	+	0.0160721i
$232$	−2.10889	−	0.371854i	−0.138455	−	0.0244134i
$233$	−15.0819	+	2.65935i	−0.988048	+	0.174220i	−0.644243	−	0.764821i	$-0.722827\pi$
$233$	−15.0819	+	2.65935i	−0.988048	+	0.174220i	−0.343806	+	0.939041i	$0.611716\pi$
$234$	2.78733	−	1.01451i	0.182214	−	0.0663204i
$235$	24.7357	−	12.1851i	1.61358	−	0.794871i
$236$	−4.56113	−	7.90011i	−0.296904	−	0.514253i
$237$	−3.29478	+	3.92656i	−0.214019	+	0.255057i
$238$	7.14094	−	8.51025i	0.462879	−	0.551637i
$239$	−8.60647	−	14.9068i	−0.556706	−	0.964244i	−0.997769	−	0.0667672i	$-0.978732\pi$
$239$	−8.60647	−	14.9068i	−0.556706	−	0.964244i	0.441062	−	0.897477i	$-0.354602\pi$
$240$	−2.00589	+	0.988128i	−0.129480	+	0.0637834i
$241$	11.1496	−	4.05813i	0.718210	−	0.261407i	0.0430445	−	0.999073i	$-0.486294\pi$
$241$	11.1496	−	4.05813i	0.718210	−	0.261407i	0.675166	+	0.737666i	$0.264072\pi$
$242$	−10.7126	+	1.88893i	−0.688635	+	0.121425i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	−1.35242	−	0.492242i	−0.0865800	−	0.0315125i
$245$	−0.684308	−	6.27321i	−0.0437189	−	0.400780i
$246$	−3.73017			−0.237827
$247$	12.9261	+	0.292359i	0.822471	+	0.0186023i
$248$		−	3.09942i		−	0.196813i
$249$	5.29886	−	4.44627i	0.335802	−	0.281771i
$250$	5.81234	−	9.55074i	0.367605	−	0.604042i
$251$	0.703622	−	3.99044i	0.0444122	−	0.251874i	−0.954516	−	0.298160i	$-0.903627\pi$
$251$	0.703622	−	3.99044i	0.0444122	−	0.251874i	0.998928	+	0.0462853i	$0.0147383\pi$
$252$	2.01294	−	0.354935i	0.126803	−	0.0223588i
$253$	0.917645	+	2.52121i	0.0576918	+	0.158507i
$254$	5.53033	−	9.57881i	0.347004	−	0.601028i
$255$	12.1269	+	0.800059i	0.759419	+	0.0501016i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−12.9448	+	15.4271i	−0.807477	+	0.962314i	−0.999819	−	0.0190140i	$-0.993947\pi$
$257$	−12.9448	+	15.4271i	−0.807477	+	0.962314i	0.192342	+	0.981328i	$0.438392\pi$
$258$	8.14429	−	4.70211i	0.507041	−	0.292740i
$259$	10.3359	−	17.9023i	0.642240	−	1.11239i
$260$	6.44191	+	1.57925i	0.399510	+	0.0979410i
$261$	0.371854	+	2.10889i	0.0230172	+	0.130537i
$262$	2.71202	+	0.478203i	0.167549	+	0.0295435i
$263$	4.63077	−	12.7229i	0.285545	−	0.784530i	−0.711130	−	0.703060i	$-0.751816\pi$
$263$	4.63077	−	12.7229i	0.285545	−	0.784530i	0.996676	−	0.0814696i	$-0.0259613\pi$
$264$	0.267672	−	0.224604i	0.0164741	−	0.0138234i
$265$	−15.5840	−	10.4225i	−0.957316	−	0.640252i
$266$	8.73696	+	1.74513i	0.535698	+	0.107001i
$267$			4.01842i			0.245923i
$268$	2.03182	+	2.42142i	0.124113	+	0.147912i
$269$	29.1795	+	10.6205i	1.77910	+	0.647541i	0.999781	+	0.0209171i	$0.00665861\pi$
$269$	29.1795	+	10.6205i	1.77910	+	0.647541i	0.779322	+	0.626624i	$0.215564\pi$
$270$	1.61459	+	1.54696i	0.0982610	+	0.0941451i
$271$	2.02484	+	11.4834i	0.123000	+	0.697569i	0.982476	+	0.186392i	$0.0596793\pi$
$271$	2.02484	+	11.4834i	0.123000	+	0.697569i	−0.859475	+	0.511177i	$0.829210\pi$
$272$	−1.85892	−	5.10735i	−0.112714	−	0.309678i
$273$	−5.25064	−	3.03146i	−0.317783	−	0.183472i
$274$	5.61408	+	9.72386i	0.339159	+	0.587440i
$275$	−0.526792	+	1.66579i	−0.0317668	+	0.100451i
$276$	5.88204	+	4.93562i	0.354057	+	0.297089i
$277$	−18.0769	+	10.4367i	−1.08613	+	0.627079i	−0.932544	−	0.361056i	$-0.882416\pi$
$277$	−18.0769	+	10.4367i	−1.08613	+	0.627079i	−0.153589	+	0.988135i	$0.549083\pi$
$278$	16.3080	+	9.41545i	0.978091	+	0.564701i
$279$	−2.91250	+	1.06006i	−0.174367	+	0.0634643i
$280$	4.18264	+	1.84255i	0.249961	+	0.110113i
$281$	4.42259	−	25.0818i	0.263830	−	1.49625i	−0.508517	−	0.861052i	$-0.669806\pi$
$281$	4.42259	−	25.0818i	0.263830	−	1.49625i	0.772347	−	0.635201i	$-0.219083\pi$
$282$	−4.21763	+	11.5879i	−0.251156	+	0.690047i
$283$	9.71337	+	11.5759i	0.577400	+	0.688119i	0.973132	−	0.230247i	$-0.0739535\pi$
$283$	9.71337	+	11.5759i	0.577400	+	0.688119i	−0.395732	+	0.918366i	$0.629509\pi$
$284$	−13.9680			−0.828846
$285$	4.10834	+	8.83864i	0.243357	+	0.523556i
$286$	−1.03646			−0.0612871
$287$	4.90088	+	5.84065i	0.289290	+	0.344762i
$288$	0.342020	−	0.939693i	0.0201537	−	0.0553719i
$289$	−2.17765	+	12.3500i	−0.128097	+	0.726473i
$290$	−1.93038	+	4.38202i	−0.113356	+	0.257321i
$291$	−14.0052	+	5.09748i	−0.821001	+	0.298820i
$292$	9.02534	+	5.21078i	0.528168	+	0.304938i
$293$	25.8712	−	14.9368i	1.51141	−	0.872615i	0.511503	−	0.859282i	$-0.329089\pi$
$293$	25.8712	−	14.9368i	1.51141	−	0.872615i	0.999911	−	0.0133333i	$-0.00424424\pi$
$294$	2.16186	+	1.81401i	0.126082	+	0.105795i
$295$	−19.5855	+	5.69956i	−1.14031	+	0.331841i
$296$	−5.05672	−	8.75849i	−0.293916	−	0.509077i
$297$	−0.302608	−	0.174711i	−0.0175591	−	0.0101377i
$298$	2.96541	+	8.14741i	0.171782	+	0.471967i
$299$	−3.95501	−	22.4300i	−0.228724	−	1.29716i
$300$	1.07802	+	4.88241i	0.0622393	+	0.281886i
$301$	−18.0629	−	6.57435i	−1.04113	−	0.378939i
$302$	−0.348585	−	0.415427i	−0.0200588	−	0.0239052i
$303$		−	3.23652i		−	0.185933i
$304$	2.87663	−	3.27490i	0.164986	−	0.187828i
$305$	−1.78908	+	2.67506i	−0.102442	+	0.153174i
$306$	−4.16355	+	3.49363i	−0.238014	+	0.199718i
$307$	3.95807	−	10.8747i	0.225899	−	0.620653i	−0.774023	−	0.633158i	$-0.781758\pi$
$307$	3.95807	−	10.8747i	0.225899	−	0.620653i	0.999922	+	0.0125051i	$0.00398061\pi$
$308$	−0.703363	−	0.124022i	−0.0400778	−	0.00706680i
$309$	2.09852	+	11.9013i	0.119381	+	0.677042i
$310$	−6.73119	−	1.65017i	−0.382306	−	0.0937233i
$311$	−4.08519	+	7.07575i	−0.231650	+	0.401229i	−0.958294	−	0.285785i	$-0.907746\pi$
$311$	−4.08519	+	7.07575i	−0.231650	+	0.401229i	0.726644	+	0.687014i	$0.241079\pi$
$312$	−2.56882	+	1.48311i	−0.145431	+	0.0839645i
$313$	16.3195	−	19.4488i	0.922432	−	1.09931i	−0.0723595	−	0.997379i	$-0.523053\pi$
$313$	16.3195	−	19.4488i	0.922432	−	1.09931i	0.994791	−	0.101933i	$-0.0325027\pi$
$314$	4.69792	+	3.94202i	0.265119	+	0.222461i
$315$	0.300879	−	4.56059i	0.0169526	−	0.256960i
$316$	2.56288	−	4.43904i	0.144173	−	0.249715i
$317$	2.79526	+	7.67991i	0.156997	+	0.431347i	0.993106	−	0.117217i	$-0.0373972\pi$
$317$	2.79526	+	7.67991i	0.156997	+	0.431347i	−0.836109	+	0.548563i	$0.815175\pi$
$318$	8.25701	−	1.45593i	0.463030	−	0.0816447i
$319$	0.129934	−	0.736891i	0.00727489	−	0.0412580i
$320$	1.80383	−	1.32144i	0.100837	−	0.0738705i
$321$	9.12807	−	7.65936i	0.509479	−	0.427504i
$322$		−	15.6947i		−	0.874631i
$323$	−22.4399	+	7.59739i	−1.24859	+	0.422730i
$324$	−1.00000			−0.0555556
$325$	6.85950	−	13.1495i	0.380497	−	0.729401i
$326$	14.8392	+	5.40104i	0.821869	+	0.299136i
$327$	11.8085	+	2.08216i	0.653014	+	0.115144i
$328$	3.67350	−	0.647737i	0.202835	−	0.0357653i
$329$	23.6855	−	8.62080i	1.30582	−	0.475280i
$330$	−0.345273	−	0.700901i	−0.0190066	−	0.0385833i
$331$	3.85978	+	6.68533i	0.212153	+	0.367459i	0.952388	−	0.304889i	$-0.0986193\pi$
$331$	3.85978	+	6.68533i	0.212153	+	0.367459i	−0.740235	+	0.672348i	$0.765286\pi$
$332$	−4.44627	+	5.29886i	−0.244021	+	0.290813i
$333$	−6.50079	+	7.74734i	−0.356241	+	0.424552i
$334$	3.75935	+	6.51138i	0.205702	+	0.356287i
$335$	6.34051	−	3.12342i	0.346419	−	0.170651i
$336$	−1.92072	+	0.699086i	−0.104784	+	0.0381383i
$337$	24.5151	−	4.32268i	1.33542	−	0.235471i	0.540072	−	0.841619i	$-0.318397\pi$
$337$	24.5151	−	4.32268i	1.33542	−	0.235471i	0.795352	+	0.606148i	$0.207286\pi$
$338$	−4.13772	−	0.729591i	−0.225062	−	0.0396845i
$339$	−5.28265	−	1.92273i	−0.286914	−	0.104428i
$340$	−12.0816	+	1.31792i	−0.655219	+	0.0714741i
$341$	1.08300			0.0586479
$342$	−4.06127	−	1.58307i	−0.219608	−	0.0856026i
$343$		−	20.0763i		−	1.08402i
$344$	−7.20405	+	6.04491i	−0.388416	+	0.325920i
$345$	13.8506	−	10.1466i	0.745693	−	0.546274i
$346$	−2.20777	+	12.5209i	−0.118690	+	0.673127i
$347$	14.4651	−	2.55058i	0.776526	−	0.136923i	0.228680	−	0.973502i	$-0.426559\pi$
$347$	14.4651	−	2.55058i	0.776526	−	0.136923i	0.547846	+	0.836579i	$0.315448\pi$
$348$	−0.732410	−	2.01228i	−0.0392613	−	0.107870i
$349$	4.20160	−	7.27739i	0.224907	−	0.389550i	−0.731385	−	0.681965i	$-0.761126\pi$
$349$	4.20160	−	7.27739i	0.224907	−	0.389550i	0.956291	+	0.292415i	$0.0944590\pi$
$350$	6.22846	−	8.10270i	0.332925	−	0.433107i
$351$	2.27226	+	1.90665i	0.121284	+	0.101769i
$352$	−0.224604	+	0.267672i	−0.0119714	+	0.0142670i
$353$	7.39939	−	4.27204i	0.393830	−	0.227378i	−0.289988	−	0.957030i	$-0.593651\pi$
$353$	7.39939	−	4.27204i	0.393830	−	0.227378i	0.683818	+	0.729652i	$0.260318\pi$
$354$	4.56113	−	7.90011i	0.242421	−	0.419886i
$355$	−7.43671	+	30.3351i	−0.394700	+	1.61002i
$356$	−0.697791	−	3.95737i	−0.0369828	−	0.209740i
$357$	10.9406	+	1.92912i	0.579036	+	0.102100i
$358$	−6.04705	+	16.6141i	−0.319597	+	0.878084i
$359$	−0.837001	+	0.702327i	−0.0441752	+	0.0370674i	−0.664608	−	0.747192i	$-0.731401\pi$
$359$	−0.837001	+	0.702327i	−0.0441752	+	0.0370674i	0.620433	+	0.784260i	$0.286957\pi$
$360$	−1.85869	−	1.24309i	−0.0979616	−	0.0655165i
$361$	−13.9878	−	12.8585i	−0.736199	−	0.676765i
$362$		−	3.52797i		−	0.185426i
$363$	−6.99218	−	8.33296i	−0.366994	−	0.437367i
$364$	5.69728	+	2.07364i	0.298619	+	0.108688i
$365$	16.1218	−	16.8266i	0.843851	−	0.880743i
$366$	−0.249918	−	1.41735i	−0.0130634	−	0.0740862i
$367$	−9.05440	−	24.8768i	−0.472636	−	1.29856i	−0.915627	−	0.402030i	$-0.868305\pi$
$367$	−9.05440	−	24.8768i	−0.472636	−	1.29856i	0.442991	−	0.896526i	$-0.353917\pi$
$368$	−6.64974	−	3.83923i	−0.346642	−	0.200134i
$369$	−1.86508	−	3.23042i	−0.0970923	−	0.168169i
$370$	−21.7136	+	6.31885i	−1.12884	+	0.328501i
$371$	−13.1282	−	11.0158i	−0.681580	−	0.571914i
$372$	2.68418	−	1.54971i	0.139168	−	0.0803487i
$373$	−4.74533	−	2.73972i	−0.245704	−	0.141857i	0.372092	−	0.928196i	$-0.378641\pi$
$373$	−4.74533	−	2.73972i	−0.245704	−	0.141857i	−0.617796	+	0.786339i	$0.711974\pi$
$374$	1.78461	−	0.649547i	0.0922802	−	0.0335873i
$375$	11.1774	+	0.258262i	0.577196	+	0.0133366i
$376$	2.14135	−	12.1442i	0.110432	−	0.626289i
$377$	−2.17249	+	5.96886i	−0.111889	+	0.307412i
$378$	1.31385	+	1.56579i	0.0675772	+	0.0805354i
$379$	−13.8050			−0.709113			−0.354557	−	0.935035i	$-0.615368\pi$
$379$	−13.8050			−0.709113			−0.354557	+	0.935035i	$0.615368\pi$
$380$	−5.58074	−	7.99095i	−0.286286	−	0.409927i
$381$	11.0607			0.566655
$382$	7.01052	+	8.35481i	0.358689	+	0.427469i
$383$	−8.11073	+	22.2840i	−0.414439	+	1.13866i	0.540366	+	0.841430i	$0.318286\pi$
$383$	−8.11073	+	22.2840i	−0.414439	+	1.13866i	−0.954805	+	0.297232i	$0.903937\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	−0.643824	+	1.46150i	−0.0328123	+	0.0744851i
$386$	15.0421	−	5.47489i	0.765625	−	0.278665i
$387$	8.14429	+	4.70211i	0.413997	+	0.239022i
$388$	12.9073	−	7.45202i	0.655268	−	0.378319i
$389$	−14.1976	−	11.9132i	−0.719846	−	0.604023i	0.207497	−	0.978236i	$-0.433468\pi$
$389$	−14.1976	−	11.9132i	−0.719846	−	0.604023i	−0.927343	+	0.374213i	$0.877913\pi$
$390$	1.85328	+	6.36848i	0.0938447	+	0.322481i
$391$	20.8667	+	36.1421i	1.05527	+	1.82779i
$392$	−2.44401	−	1.41105i	−0.123441	−	0.0712689i
$393$	0.941876	+	2.58778i	0.0475114	+	0.130536i
$394$	−1.06881	−	6.06153i	−0.0538459	−	0.305375i
$395$	−8.27601	−	7.92936i	−0.416411	−	0.398969i
$396$	0.328348	+	0.119509i	0.0165001	+	0.00600556i
$397$	−12.0630	−	14.3762i	−0.605426	−	0.721519i	0.373066	−	0.927805i	$-0.378307\pi$
$397$	−12.0630	−	14.3762i	−0.605426	−	0.721519i	−0.978492	+	0.206286i	$0.933862\pi$
$398$		−	7.84900i		−	0.393435i
$399$	2.85715	+	8.43900i	0.143037	+	0.422478i
$400$	−1.90946	−	4.62104i	−0.0954729	−	0.231052i
$401$	−20.3934	+	17.1121i	−1.01840	+	0.854538i	−0.989425	−	0.145043i	$-0.953668\pi$
$401$	−20.3934	+	17.1121i	−1.01840	+	0.854538i	−0.0289729	+	0.999580i	$0.509224\pi$
$402$	−1.08111	+	2.97031i	−0.0539207	+	0.148146i
$403$	−9.05388	−	1.59644i	−0.451006	−	0.0795245i
$404$	0.562016	+	3.18735i	0.0279613	+	0.158577i
$405$	−0.532412	+	2.17176i	−0.0264558	+	0.107916i
$406$	−2.18852	+	3.79063i	−0.108615	+	0.188126i
$407$	3.06040	−	1.76692i	0.151699	−	0.0875832i
$408$	3.49363	−	4.16355i	0.172960	−	0.206126i
$409$	−3.13787	−	2.63299i	−0.155158	−	0.130193i	0.561904	−	0.827202i	$-0.310069\pi$
$409$	−3.13787	−	2.63299i	−0.155158	−	0.130193i	−0.717062	+	0.697010i	$0.754513\pi$
$410$	0.549087	−	8.32281i	0.0271175	−	0.411034i
$411$	−5.61408	+	9.72386i	−0.276922	+	0.479643i
$412$	−4.13328	−	11.3561i	−0.203632	−	0.559475i
$413$	−18.3625	+	3.23781i	−0.903562	+	0.159322i
$414$	−1.33335	+	7.56180i	−0.0655306	+	0.371642i
$415$	9.14060	+	12.4774i	0.448694	+	0.612492i
$416$	2.27226	−	1.90665i	0.111406	−	0.0934811i
$417$			18.8309i			0.922153i
$418$	1.14432	+	1.00516i	0.0559705	+	0.0491638i
$419$	15.6065			0.762429			0.381214	−	0.924487i	$-0.375506\pi$
$419$	15.6065			0.762429			0.381214	+	0.924487i	$0.375506\pi$
$420$	0.495630	+	4.54355i	0.0241843	+	0.221702i
$421$	−14.5509	−	5.29611i	−0.709170	−	0.258117i	−0.0378487	−	0.999283i	$-0.512050\pi$
$421$	−14.5509	−	5.29611i	−0.709170	−	0.258117i	−0.671321	+	0.741167i	$0.734273\pi$
$422$	10.9050	+	1.92284i	0.530846	+	0.0936024i
$423$	−12.1442	+	2.14135i	−0.590471	+	0.104116i
$424$	−7.87875	+	2.86763i	−0.382626	+	0.139264i
$425$	−3.57021	+	26.9401i	−0.173181	+	1.30679i
$426$	−6.98398	−	12.0966i	−0.338375	−	0.586083i
$427$	−1.89092	+	2.25351i	−0.0915080	+	0.109055i
$428$	−7.65936	+	9.12807i	−0.370229	+	0.441222i
$429$	−0.518230	−	0.897600i	−0.0250204	−	0.0433365i
$430$	9.29257	+	18.8638i	0.448128	+	0.909695i
$431$	3.47174	−	1.26361i	0.167228	−	0.0608659i	−0.257050	−	0.966398i	$-0.582750\pi$
$431$	3.47174	−	1.26361i	0.167228	−	0.0608659i	0.424277	+	0.905532i	$0.360528\pi$
$432$	0.984808	−	0.173648i	0.0473816	−	0.00835465i
$433$	−1.48447	−	0.261752i	−0.0713390	−	0.0125790i	0.137865	−	0.990451i	$-0.455976\pi$
$433$	−1.48447	−	0.261752i	−0.0713390	−	0.0125790i	−0.209204	+	0.977872i	$0.567087\pi$
$434$	−5.95312	−	2.16676i	−0.285759	−	0.104008i
$435$	−4.76013	+	0.519256i	−0.228231	+	0.0248964i
$436$	−11.9907			−0.574251
$437$	−17.3859	+	28.5997i	−0.831682	+	1.36811i
$438$			10.4216i			0.497961i
$439$	−11.4275	+	9.58884i	−0.545406	+	0.457650i	−0.873382	−	0.487036i	$-0.838078\pi$
$439$	−11.4275	+	9.58884i	−0.545406	+	0.457650i	0.327976	+	0.944686i	$0.393634\pi$
$440$	0.461738	+	0.630297i	0.0220125	+	0.0300482i
$441$	−0.490053	+	2.77923i	−0.0233359	+	0.132344i
$442$	−15.8768	+	2.79951i	−0.755184	+	0.133159i
$443$	−9.92483	−	27.2683i	−0.471543	−	1.29555i	−0.916512	−	0.400008i	$-0.869007\pi$
$443$	−9.92483	−	27.2683i	−0.471543	−	1.29555i	0.444969	−	0.895546i	$-0.353215\pi$
$444$	5.05672	−	8.75849i	0.239981	−	0.415660i
$445$	−8.96596	−	0.591518i	−0.425027	−	0.0280406i
$446$	−2.05939	−	1.72803i	−0.0975148	−	0.0818246i
$447$	−5.57316	+	6.64183i	−0.263601	+	0.314148i
$448$	1.77015	−	1.02199i	0.0836316	−	0.0482847i
$449$	11.5014	−	19.9210i	0.542784	−	0.940130i	−0.455959	−	0.890001i	$-0.650703\pi$
$449$	11.5014	−	19.9210i	0.542784	−	0.940130i	0.998743	−	0.0501288i	$-0.0159632\pi$
$450$	−3.68928	+	3.37479i	−0.173914	+	0.159089i
$451$	0.226333	+	1.28360i	0.0106576	+	0.0604422i
$452$	5.53627	+	0.976194i	0.260404	+	0.0459163i
$453$	0.185478	−	0.509597i	0.00871452	−	0.0239430i
$454$	5.00935	−	4.20334i	0.235100	−	0.197273i
$455$	7.53675	−	11.2691i	0.353328	−	0.528303i
$456$	4.27446	+	0.853787i	0.200170	+	0.0399822i
$457$		−	33.4908i		−	1.56663i	−0.621624	−	0.783316i	$-0.713527\pi$
$457$		−	33.4908i		−	1.56663i	0.621624	−	0.783316i	$-0.286473\pi$
$458$	8.99045	+	10.7144i	0.420096	+	0.500651i
$459$	−5.10735	−	1.85892i	−0.238390	−	0.0867670i
$460$	−11.8783	+	12.3976i	−0.553828	+	0.578040i
$461$	6.55269	+	37.1622i	0.305189	+	1.73081i	0.622612	+	0.782531i	$0.286071\pi$
$461$	6.55269	+	37.1622i	0.305189	+	1.73081i	−0.317423	+	0.948284i	$0.602817\pi$
$462$	−0.244275	−	0.671141i	−0.0113647	−	0.0312243i
$463$	25.6844	+	14.8289i	1.19365	+	0.689156i	0.959133	−	0.282955i	$-0.0913146\pi$
$463$	25.6844	+	14.8289i	1.19365	+	0.689156i	0.234521	+	0.972111i	$0.424648\pi$
$464$	1.07071	+	1.85453i	0.0497065	+	0.0860943i
$465$	−1.93651	−	6.65447i	−0.0898034	−	0.308593i
$466$	11.7316	+	9.84401i	0.543458	+	0.456015i
$467$	−22.3943	+	12.9294i	−1.03629	+	0.598300i	−0.918779	−	0.394772i	$-0.870824\pi$
$467$	−22.3943	+	12.9294i	−1.03629	+	0.598300i	−0.117507	+	0.993072i	$0.537490\pi$
$468$	−2.56882	−	1.48311i	−0.118744	−	0.0685567i
$469$	6.07129	−	2.20977i	0.280346	−	0.102038i
$470$	−25.2342	−	11.1162i	−1.16397	−	0.512753i
$471$	−1.06493	+	6.03952i	−0.0490694	+	0.278287i
$472$	−3.12000	+	8.57212i	−0.143610	+	0.394564i
$473$	−2.11222	−	2.51725i	−0.0971200	−	0.115743i
$474$	5.12576			0.235434
$475$	−20.3257	+	7.86555i	−0.932606	+	0.360896i
$476$	−11.1093			−0.509196
$477$	5.38938	+	6.42281i	0.246763	+	0.294080i
$478$	−5.88717	+	16.1749i	−0.269273	+	0.739822i
$479$	−1.71858	+	9.74656i	−0.0785240	+	0.445332i	0.920043	+	0.391817i	$0.128153\pi$
$479$	−1.71858	+	9.74656i	−0.0785240	+	0.445332i	−0.998567	+	0.0535144i	$0.982958\pi$
$480$	2.04631	+	0.901446i	0.0934010	+	0.0411452i
$481$	−28.1895	+	10.2601i	−1.28533	+	0.467822i
$482$	−10.2755	−	5.93259i	−0.468038	−	0.270222i
$483$	13.5920	−	7.84734i	0.618457	−	0.357066i
$484$	8.33296	+	6.99218i	0.378771	+	0.317826i
$485$	−9.31200	−	31.9991i	−0.422836	−	1.45300i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	12.7030	+	7.33409i	0.575628	+	0.332339i	0.759394	−	0.650631i	$-0.225495\pi$
$487$	12.7030	+	7.33409i	0.575628	+	0.332339i	−0.183766	+	0.982970i	$0.558829\pi$
$488$	0.492242	+	1.35242i	0.0222827	+	0.0612213i
$489$	2.74218	+	15.5517i	0.124006	+	0.703271i
$490$	−4.36569	+	4.55655i	−0.197222	+	0.205844i
$491$	20.5839	+	7.49194i	0.928941	+	0.338107i	0.761790	−	0.647825i	$-0.224321\pi$
$491$	20.5839	+	7.49194i	0.928941	+	0.338107i	0.167151	+	0.985931i	$0.446543\pi$
$492$	2.39770	+	2.85747i	0.108097	+	0.128825i
$493$		−	11.6389i		−	0.524190i
$494$	−8.08480	−	10.0899i	−0.363752	−	0.453967i
$495$	0.434362	−	0.649466i	0.0195231	−	0.0291913i
$496$	−2.37429	+	1.99227i	−0.106609	+	0.0894555i
$497$	−9.76480	+	26.8286i	−0.438011	+	1.20343i
$498$	−6.81208	−	1.20115i	−0.305257	−	0.0538250i
$499$	3.06459	+	17.3802i	0.137190	+	0.778043i	0.973310	+	0.229496i	$0.0737077\pi$
$499$	3.06459	+	17.3802i	0.137190	+	0.778043i	−0.836120	+	0.548547i	$0.815181\pi$
$500$	−11.0524	+	1.68659i	−0.494278	+	0.0754266i
$501$	−3.75935	+	6.51138i	−0.167955	+	0.290907i
$502$	−3.50913	+	2.02600i	−0.156620	+	0.0904248i
$503$	0.224225	−	0.267221i	0.00999769	−	0.0119148i	−0.761022	−	0.648726i	$-0.775302\pi$
$503$	0.224225	−	0.267221i	0.00999769	−	0.0119148i	0.771020	+	0.636811i	$0.219747\pi$
$504$	−1.56579	−	1.31385i	−0.0697457	−	0.0585236i
$505$	7.22138	+	0.476421i	0.321347	+	0.0212005i
$506$	1.34151	−	2.32356i	0.0596373	−	0.103295i
$507$	−1.43701	−	3.94816i	−0.0638201	−	0.175344i
$508$	−10.8926	+	1.92066i	−0.483282	+	0.0852157i
$509$	2.80189	−	15.8903i	0.124191	−	0.704325i	−0.857593	−	0.514328i	$-0.828041\pi$
$509$	2.80189	−	15.8903i	0.124191	−	0.704325i	0.981785	−	0.189996i	$-0.0608477\pi$
$510$	−7.18217	−	9.80405i	−0.318032	−	0.434130i
$511$	16.3179	−	13.6924i	0.721863	−	0.605715i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.659656	−	4.30870i	−0.0291245	−	0.190234i
$514$	20.1386			0.888276
$515$	−26.8633	+	2.93037i	−1.18374	+	0.129127i
$516$	−8.83707	−	3.21643i	−0.389030	−	0.141595i
$517$	4.24344	+	0.748233i	0.186626	+	0.0329072i
$518$	−20.3577	+	3.58961i	−0.894467	+	0.157719i
$519$	−11.9473	+	4.34846i	−0.524428	+	0.190876i
$520$	−2.93100	−	5.94991i	−0.128533	−	0.260921i
$521$	−6.97708	−	12.0847i	−0.305671	−	0.529439i	0.671739	−	0.740788i	$-0.265548\pi$
$521$	−6.97708	−	12.0847i	−0.305671	−	0.529439i	−0.977411	+	0.211349i	$0.932214\pi$
$522$	1.37648	−	1.64043i	0.0602469	−	0.0717995i
$523$	−8.09388	+	9.64592i	−0.353921	+	0.421786i	−0.913403	−	0.407056i	$-0.866555\pi$
$523$	−8.09388	+	9.64592i	−0.353921	+	0.421786i	0.559482	+	0.828842i	$0.311000\pi$
$524$	−1.37693	−	2.38491i	−0.0601515	−	0.104185i
$525$	10.1314	+	1.34265i	0.442169	+	0.0585981i
$526$	−12.7229	+	4.63077i	−0.554746	+	0.201911i
$527$	16.5898	−	2.92523i	0.722663	−	0.127425i
$528$	−0.344113	−	0.0606763i	−0.0149756	−	0.00264060i
$529$	33.7901	+	12.2986i	1.46914	+	0.534721i
$530$	2.03306	+	18.6375i	0.0883104	+	0.809561i
$531$	9.12226			0.395872
$532$	−4.27916	−	7.81465i	−0.185525	−	0.338808i
$533$		−	11.0645i		−	0.479256i
$534$	3.07829	−	2.58299i	0.133210	−	0.111777i
$535$	15.7460	+	21.4942i	0.680761	+	0.929275i
$536$	0.548892	−	3.11292i	0.0237085	−	0.134458i
$537$	−17.4118	+	3.07017i	−0.751374	+	0.132488i
$538$	−10.6205	−	29.1795i	−0.457880	−	1.25802i
$539$	0.493052	−	0.853990i	0.0212372	−	0.0367840i
$540$	0.147202	−	2.23122i	0.00633455	−	0.0960163i
$541$	23.2959	+	19.5476i	1.00157	+	0.840416i	0.987201	−	0.159481i	$-0.0509821\pi$
$541$	23.2959	+	19.5476i	1.00157	+	0.840416i	0.0143676	+	0.999897i	$0.495427\pi$
$542$	7.49528	−	8.93252i	0.321950	−	0.383685i
$543$	3.05531	−	1.76398i	0.131116	−	0.0756998i
$544$	−2.71756	+	4.70696i	−0.116514	+	0.201809i
$545$	−6.38400	+	26.0409i	−0.273460	+	1.11547i
$546$	1.05282	+	5.97081i	0.0450563	+	0.255527i
$547$	28.8432	+	5.08583i	1.23325	+	0.217455i	0.752019	−	0.659141i	$-0.229080\pi$
$547$	28.8432	+	5.08583i	1.23325	+	0.217455i	0.481227	+	0.876596i	$0.340191\pi$
$548$	3.84025	−	10.5510i	0.164048	−	0.450717i
$549$	1.10250	−	0.925111i	0.0470538	−	0.0394828i
$550$	1.61469	−	0.667205i	0.0688505	−	0.0284497i
$551$	8.18716	−	4.48314i	0.348785	−	0.190988i
$552$		−	7.67846i		−	0.326817i
$553$	−6.73449	−	8.02585i	−0.286380	−	0.341294i
$554$	19.6145	+	7.13911i	0.833342	+	0.303312i
$555$	−16.3291	−	15.6451i	−0.693131	−	0.664098i
$556$	−3.26995	−	18.5448i	−0.138677	−	0.786475i
$557$	−8.18614	−	22.4912i	−0.346858	−	0.952985i	−0.983353	−	0.181704i	$-0.941839\pi$
$557$	−8.18614	−	22.4912i	−0.346858	−	0.952985i	0.636495	−	0.771281i	$-0.280384\pi$
$558$	2.68418	+	1.54971i	0.113630	+	0.0656044i
$559$	13.9475	+	24.1577i	0.589915	+	1.02176i
$560$	−1.27708	−	4.38846i	−0.0539664	−	0.185446i
$561$	1.45483	+	1.22075i	0.0614230	+	0.0515400i
$562$	−22.0565	+	12.7343i	−0.930399	+	0.537166i
$563$	−27.2196	−	15.7153i	−1.14717	−	0.662319i	−0.198975	−	0.980005i	$-0.563761\pi$
$563$	−27.2196	−	15.7153i	−1.14717	−	0.662319i	−0.948196	+	0.317685i	$0.897094\pi$
$564$	11.5879	−	4.21763i	0.487937	−	0.177594i
$565$	5.06764	−	11.5037i	0.213197	−	0.483965i
$566$	2.62405	−	14.8818i	0.110297	−	0.625527i
$567$	−0.699086	+	1.92072i	−0.0293588	+	0.0806628i
$568$	8.97843	+	10.7001i	0.376727	+	0.448965i
$569$	19.5446			0.819352			0.409676	−	0.912231i	$-0.365642\pi$
$569$	19.5446			0.819352			0.409676	+	0.912231i	$0.365642\pi$
$570$	4.13000	−	8.82854i	0.172986	−	0.369787i
$571$	−19.6120			−0.820735			−0.410368	−	0.911920i	$-0.634600\pi$
$571$	−19.6120			−0.820735			−0.410368	+	0.911920i	$0.634600\pi$
$572$	0.666223	+	0.793974i	0.0278562	+	0.0331977i
$573$	−3.73022	+	10.2487i	−0.155832	+	0.428145i
$574$	1.32397	−	7.50859i	0.0552613	−	0.313402i
$575$	20.6004	+	32.3974i	0.859096	+	1.35106i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	−16.0615	−	9.27314i	−0.668651	−	0.386046i	0.126914	−	0.991914i	$-0.459493\pi$
$577$	−16.0615	−	9.27314i	−0.668651	−	0.386046i	−0.795565	+	0.605868i	$0.792826\pi$
$578$	10.8604	−	6.27028i	0.451735	−	0.260809i
$579$	12.2625	+	10.2894i	0.509611	+	0.427614i
$580$	4.59765	−	1.33796i	0.190907	−	0.0555556i
$581$	7.06931	+	12.2444i	0.293284	+	0.507984i
$582$	12.9073	+	7.45202i	0.535024	+	0.308896i
$583$	−1.00201	−	2.75300i	−0.0414990	−	0.114018i
$584$	−1.80968	−	10.2632i	−0.0748853	−	0.424696i
$585$	−4.58863	+	4.78923i	−0.189716	+	0.198010i
$586$	−28.0719	−	10.2173i	−1.15964	−	0.422075i
$587$	−19.0043	−	22.6484i	−0.784390	−	0.934799i	0.214733	−	0.976673i	$-0.431112\pi$
$587$	−19.0043	−	22.6484i	−0.784390	−	0.934799i	−0.999123	+	0.0418734i	$0.986667\pi$
$588$		−	2.82211i		−	0.116382i
$589$	8.44786	+	10.5430i	0.348088	+	0.434417i
$590$	16.9555	+	11.3398i	0.698045	+	0.466852i
$591$	4.71503	−	3.95638i	0.193951	−	0.162744i
$592$	−3.45900	+	9.50352i	−0.142164	+	0.390592i
$593$	1.04512	+	0.184283i	0.0429181	+	0.00756762i	0.195066	−	0.980790i	$-0.437508\pi$
$593$	1.04512	+	0.184283i	0.0429181	+	0.00756762i	−0.152148	+	0.988358i	$0.548619\pi$
$594$	0.0606763	+	0.344113i	0.00248958	+	0.0141191i
$595$	−5.91475	+	24.1268i	−0.242481	+	0.989103i
$596$	4.33515	−	7.50869i	0.177575	−	0.307568i
$597$	6.79744	−	3.92450i	0.278201	−	0.160619i
$598$	−14.6401	+	17.4474i	−0.598679	+	0.713478i
$599$	34.0731	+	28.5907i	1.39219	+	1.16819i	0.964444	+	0.264287i	$0.0851365\pi$
$599$	34.0731	+	28.5907i	1.39219	+	1.16819i	0.427745	+	0.903899i	$0.359308\pi$
$600$	3.04720	−	3.96416i	0.124402	−	0.161836i
$601$	11.9471	−	20.6929i	0.487332	−	0.844083i	−0.512562	−	0.858650i	$-0.671304\pi$
$601$	11.9471	−	20.6929i	0.487332	−	0.844083i	0.999894	+	0.0145670i	$0.00463699\pi$
$602$	6.57435	+	18.0629i	0.267951	+	0.736188i
$603$	−3.11292	+	0.548892i	−0.126768	+	0.0223526i
$604$	−0.0941697	+	0.534063i	−0.00383171	+	0.0217307i
$605$	19.6219	−	14.3745i	0.797744	−	0.584405i
$606$	−2.47932	+	2.08039i	−0.100715	+	0.0845103i
$607$		−	48.3685i		−	1.96322i	−0.190907	−	0.981608i	$-0.561143\pi$
$607$		−	48.3685i		−	1.96322i	0.190907	−	0.981608i	$-0.438857\pi$
$608$	−4.35778	−	0.0985628i	−0.176731	−	0.00399725i
$609$	−4.37705			−0.177367
$610$	3.19921	−	0.348984i	0.129532	−	0.0141299i
$611$	−34.3721	−	12.5104i	−1.39055	−	0.506118i
$612$	5.35255	+	0.943799i	0.216364	+	0.0381508i
$613$	−31.1581	+	5.49401i	−1.25846	+	0.221901i	−0.762812	−	0.646621i	$-0.776182\pi$
$613$	−31.1581	+	5.49401i	−1.25846	+	0.221901i	−0.495651	+	0.868522i	$0.665071\pi$
$614$	−10.8747	+	3.95807i	−0.438868	+	0.159735i
$615$	7.48231	−	3.68588i	0.301716	−	0.148629i
$616$	0.357107	+	0.618527i	0.0143882	+	0.0249212i
$617$	−3.30517	+	3.93895i	−0.133061	+	0.158576i	−0.828461	−	0.560047i	$-0.810783\pi$
$617$	−3.30517	+	3.93895i	−0.133061	+	0.158576i	0.695400	+	0.718623i	$0.255227\pi$
$618$	7.76803	−	9.25757i	0.312476	−	0.372394i
$619$	−10.3784	−	17.9759i	−0.417143	−	0.722513i	0.578508	−	0.815677i	$-0.303635\pi$
$619$	−10.3784	−	17.9759i	−0.417143	−	0.722513i	−0.995651	+	0.0931642i	$0.970302\pi$
$620$	3.06262	+	6.21710i	0.122998	+	0.249685i
$621$	−7.21539	+	2.62619i	−0.289544	+	0.105385i
$622$	8.04625	−	1.41877i	0.322625	−	0.0568875i
$623$	−8.08882	−	1.42628i	−0.324072	−	0.0571426i
$624$	2.78733	+	1.01451i	0.111583	+	0.0406128i
$625$	−2.22156	+	24.9011i	−0.0888626	+	0.996044i
$626$	−25.3886			−1.01473
$627$	−0.298331	+	1.49359i	−0.0119142	+	0.0596482i
$628$		−	6.13269i		−	0.244721i
$629$	42.1078	−	35.3326i	1.67895	−	1.40880i
$630$	−3.68701	+	2.70100i	−0.146894	+	0.107610i
$631$	6.86085	−	38.9098i	0.273126	−	1.54897i	−0.471726	−	0.881745i	$-0.656369\pi$
$631$	6.86085	−	38.9098i	0.273126	−	1.54897i	0.744852	−	0.667229i	$-0.232520\pi$
$632$	−5.04789	+	0.890079i	−0.200794	+	0.0354054i
$633$	3.78726	+	10.4054i	0.150530	+	0.413578i
$634$	4.08639	−	7.07784i	0.162291	−	0.281097i
$635$	−1.62815	+	24.6787i	−0.0646111	+	0.979346i
$636$	−6.42281	−	5.38938i	−0.254681	−	0.213703i
$637$	−5.38076	+	6.41254i	−0.213194	+	0.254074i
$638$	−0.648011	+	0.374129i	−0.0256550	+	0.0148119i
$639$	6.98398	−	12.0966i	0.276282	−	0.478535i
$640$	−2.17176	−	0.532412i	−0.0858463	−	0.0210454i
$641$	5.16703	+	29.3037i	0.204085	+	1.15743i	0.898873	+	0.438210i	$0.144387\pi$
$641$	5.16703	+	29.3037i	0.204085	+	1.15743i	−0.694787	+	0.719215i	$0.744502\pi$
$642$	−11.7348	−	2.06917i	−0.463137	−	0.0816635i
$643$	−7.67785	+	21.0947i	−0.302785	+	0.831894i	0.691229	+	0.722636i	$0.257070\pi$
$643$	−7.67785	+	21.0947i	−0.302785	+	0.831894i	−0.994013	+	0.109258i	$0.965153\pi$
$644$	−12.0228	+	10.0883i	−0.473766	+	0.397537i
$645$	−11.6903	+	17.4795i	−0.460304	+	0.688255i
$646$	20.2440	+	12.3065i	0.796491	+	0.484192i
$647$		−	19.0108i		−	0.747393i	−0.927551	−	0.373697i	$-0.878090\pi$
$647$		−	19.0108i		−	0.747393i	0.927551	−	0.373697i	$-0.121910\pi$
$648$	0.642788	+	0.766044i	0.0252511	+	0.0300931i
$649$	−2.99528	−	1.09019i	−0.117575	−	0.0427938i
$650$	−14.4823	+	3.19763i	−0.568042	+	0.125421i
$651$	−1.10009	−	6.23893i	−0.0431160	−	0.244523i
$652$	−5.40104	−	14.8392i	−0.211521	−	0.581149i
$653$	7.19600	+	4.15461i	0.281601	+	0.162582i	0.634148	−	0.773212i	$-0.281351\pi$
$653$	7.19600	+	4.15461i	0.281601	+	0.162582i	−0.352547	+	0.935794i	$0.614684\pi$
$654$	−5.99535	−	10.3843i	−0.234437	−	0.406056i
$655$	−5.91255	+	1.72060i	−0.231023	+	0.0672296i
$656$	−2.85747	−	2.39770i	−0.111566	−	0.0936146i
$657$	−9.02534	+	5.21078i	−0.352112	+	0.203292i
$658$	−21.8286	−	12.6028i	−0.850969	−	0.491307i
$659$	31.8126	−	11.5788i	1.23924	−	0.451047i	0.362489	−	0.931988i	$-0.381927\pi$
$659$	31.8126	−	11.5788i	1.23924	−	0.451047i	0.876753	+	0.480941i	$0.159705\pi$
$660$	−0.314984	+	0.715025i	−0.0122607	+	0.0278323i
$661$	−5.23421	+	29.6847i	−0.203587	+	1.15460i	0.696060	+	0.717984i	$0.254935\pi$
$661$	−5.23421	+	29.6847i	−0.203587	+	1.15460i	−0.899647	+	0.436617i	$0.856176\pi$
$662$	2.64024	−	7.25401i	0.102616	−	0.281935i
$663$	−10.3629	−	12.3500i	−0.402460	−	0.479634i
$664$	6.91717			0.268438
$665$	−19.2498	+	5.13270i	−0.746476	+	0.199037i
$666$	10.1134			0.391888
$667$	−10.5692	−	12.5959i	−0.409243	−	0.487717i
$668$	2.57154	−	7.06526i	0.0994960	−	0.273363i
$669$	0.466825	−	2.64750i	0.0180485	−	0.102358i
$670$	−6.46828	−	2.84942i	−0.249891	−	0.110083i
$671$	−0.472565	+	0.172000i	−0.0182432	+	0.00663997i
$672$	1.77015	+	1.02199i	0.0682849	+	0.0394243i
$673$	9.70852	−	5.60522i	0.374236	−	0.216065i	−0.301071	−	0.953602i	$-0.597344\pi$
$673$	9.70852	−	5.60522i	0.374236	−	0.216065i	0.675307	+	0.737536i	$0.264011\pi$
$674$	−19.0694	−	16.0011i	−0.734525	−	0.616340i
$675$	−4.76729	−	1.50761i	−0.183493	−	0.0580281i
$676$	2.10077	+	3.63865i	0.0807990	+	0.139948i
$677$	31.5618	+	18.2222i	1.21302	+	0.700337i	0.963416	−	0.268012i	$-0.0863666\pi$
$677$	31.5618	+	18.2222i	1.21302	+	0.700337i	0.249603	+	0.968348i	$0.419700\pi$
$678$	1.92273	+	5.28265i	0.0738419	+	0.202879i
$679$	−5.28997	−	30.0009i	−0.203010	−	1.15133i
$680$	8.77551	+	8.40793i	0.336525	+	0.322429i
$681$	6.14487	+	2.23655i	0.235472	+	0.0857048i
$682$	−0.696140	−	0.829628i	−0.0266566	−	0.0317681i
$683$			1.45032i			0.0554950i	0.999615	+	0.0277475i	$0.00883344\pi$
$683$			1.45032i			0.0554950i	−0.999615	+	0.0277475i	$0.991167\pi$
$684$	1.39783	+	4.12869i	0.0534474	+	0.157864i
$685$	−20.8697	−	13.9576i	−0.797388	−	0.533292i
$686$	−15.3793	+	12.9048i	−0.587185	+	0.492707i
$687$	−4.78372	+	13.1432i	−0.182510	+	0.501443i
$688$	9.26134	+	1.63302i	0.353085	+	0.0622585i
$689$	4.31862	+	24.4921i	0.164526	+	0.933074i
$690$	−16.6758	−	4.08810i	−0.634835	−	0.155631i
$691$	18.9140	−	32.7599i	0.719521	−	1.24625i	−0.241669	−	0.970359i	$-0.577695\pi$
$691$	18.9140	−	32.7599i	0.719521	−	1.24625i	0.961190	−	0.275888i	$-0.0889719\pi$
$692$	11.0107	−	6.35702i	0.418563	−	0.241658i
$693$	0.459087	−	0.547119i	0.0174393	−	0.0207833i
$694$	−11.2518	−	9.44141i	−0.427114	−	0.358391i
$695$	−42.0158	−	2.77194i	−1.59375	−	0.105146i
$696$	−1.07071	+	1.85453i	−0.0405852	+	0.0702957i
$697$	6.93409	+	19.0512i	0.262647	+	0.721617i
$698$	−8.27554	+	1.45920i	−0.313234	+	0.0552316i
$699$	−2.65935	+	15.0819i	−0.100586	+	0.570450i
$700$	−10.2106	+	0.437040i	−0.385924	+	0.0165186i
$701$	−14.9940	+	12.5815i	−0.566317	+	0.475197i	−0.880422	−	0.474192i	$-0.842740\pi$
$701$	−14.9940	+	12.5815i	−0.566317	+	0.475197i	0.314104	+	0.949389i	$0.398296\pi$
$702$		−	2.96622i		−	0.111953i
$703$	41.0734	+	16.0103i	1.54911	+	0.603839i
$704$	0.349421			0.0131693
$705$	−2.99017	−	27.4115i	−0.112616	−	1.03238i
$706$	−8.02881	−	2.92225i	−0.302168	−	0.109980i
$707$	6.51491	+	1.14875i	0.245018	+	0.0432034i
$708$	−8.98368	+	1.58406i	−0.337627	+	0.0595328i
$709$	−34.9426	+	12.7181i	−1.31230	+	0.477637i	−0.900982	−	0.433857i	$-0.857152\pi$
$709$	−34.9426	+	12.7181i	−1.31230	+	0.477637i	−0.411314	+	0.911494i	$0.634930\pi$
$710$	28.0182	−	13.8021i	1.05151	−	0.517985i
$711$	2.56288	+	4.43904i	0.0961155	+	0.166477i
$712$	−2.58299	+	3.07829i	−0.0968016	+	0.115364i
$713$	15.2975	−	18.2309i	0.572897	−	0.682753i
$714$	−5.55467	−	9.62097i	−0.207878	−	0.360056i
$715$	2.07903	−	1.02415i	0.0777511	−	0.0383012i
$716$	16.6141	−	6.04705i	0.620899	−	0.225989i
$717$	−16.9514	+	2.98900i	−0.633063	+	0.111626i
$718$	1.07603	+	0.189733i	0.0401570	+	0.00708076i
$719$	26.5698	+	9.67060i	0.990885	+	0.360653i	0.786063	−	0.618147i	$-0.212116\pi$
$719$	26.5698	+	9.67060i	0.990885	+	0.360653i	0.204822	+	0.978799i	$0.434338\pi$
$720$	0.242482	+	2.22288i	0.00903675	+	0.0828419i
$721$	−24.7014			−0.919929
$722$	−0.859031	+	18.9806i	−0.0319698	+	0.706384i
$723$		−	11.8652i		−	0.441271i
$724$	−2.70258	+	2.26773i	−0.100441	+	0.0842796i
$725$	−0.457873	−	10.6973i	−0.0170050	−	0.397289i
$726$	−1.88893	+	10.7126i	−0.0701047	+	0.397584i
$727$	14.6821	−	2.58886i	0.544531	−	0.0960155i	0.105385	−	0.994431i	$-0.466392\pi$
$727$	14.6821	−	2.58886i	0.544531	−	0.0960155i	0.439145	+	0.898416i	$0.355281\pi$
$728$	−2.07364	−	5.69728i	−0.0768542	−	0.211155i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−23.2528	−	1.53407i	−0.860624	−	0.0567785i
$731$	−39.1549	−	32.8548i	−1.44820	−	1.21518i
$732$	−0.925111	+	1.10250i	−0.0341931	+	0.0407498i
$733$	33.0148	−	19.0611i	1.21943	−	0.704037i	0.254633	−	0.967038i	$-0.418045\pi$
$733$	33.0148	−	19.0611i	1.21943	−	0.704037i	0.964796	+	0.263001i	$0.0847121\pi$
$734$	−13.2366	+	22.9265i	−0.488574	+	0.846234i
$735$	−6.12893	−	1.50252i	−0.226069	−	0.0554214i
$736$	1.33335	+	7.56180i	0.0491479	+	0.278732i
$737$	1.08772	+	0.191794i	0.0400667	+	0.00706484i
$738$	−1.27579	+	3.50521i	−0.0469625	+	0.129029i
$739$	39.8602	−	33.4467i	1.46628	−	1.23036i	0.546779	−	0.837277i	$-0.315854\pi$
$739$	39.8602	−	33.4467i	1.46628	−	1.23036i	0.919504	−	0.393080i	$-0.128590\pi$
$740$	18.7977	+	12.5719i	0.691019	+	0.462152i
$741$	4.69573	−	12.0466i	0.172502	−	0.442543i
$742$			17.1376i			0.629141i
$743$	28.0412	+	33.4182i	1.02873	+	1.22599i	0.973777	+	0.227506i	$0.0730571\pi$
$743$	28.0412	+	33.4182i	1.02873	+	1.22599i	0.0549550	+	0.998489i	$0.482498\pi$
$744$	−2.91250	−	1.06006i	−0.106777	−	0.0388638i
$745$	−13.9990	−	13.4126i	−0.512883	−	0.491400i
$746$	0.951494	+	5.39619i	0.0348367	+	0.197569i
$747$	−2.36581	−	6.50001i	−0.0865605	−	0.237823i
$748$	−1.64471	−	0.949573i	−0.0601365	−	0.0347198i
$749$	12.1779	+	21.0928i	0.444972	+	0.770715i
$750$	−6.98683	−	8.72836i	−0.255123	−	0.318715i
$751$	8.99893	+	7.55100i	0.328376	+	0.275540i	0.792038	−	0.610472i	$-0.209020\pi$
$751$	8.99893	+	7.55100i	0.328376	+	0.275540i	−0.463662	+	0.886012i	$0.653465\pi$
$752$	−10.6794	+	6.16577i	−0.389439	+	0.224842i
$753$	−3.50913	−	2.02600i	−0.127880	−	0.0738315i
$754$	5.96886	−	2.17249i	0.217373	−	0.0791173i
$755$	1.10972	+	0.488856i	0.0403868	+	0.0177913i
$756$	0.354935	−	2.01294i	0.0129089	−	0.0732098i
$757$	5.49557	−	15.0989i	0.199740	−	0.548781i	−0.798869	−	0.601505i	$-0.794568\pi$
$757$	5.49557	−	15.0989i	0.199740	−	0.548781i	0.998609	+	0.0527240i	$0.0167904\pi$
$758$	8.87366	+	10.5752i	0.322306	+	0.384109i
$759$	2.68301			0.0973873
$760$	−2.53419	+	9.41158i	−0.0919248	+	0.341394i
$761$	−27.0147			−0.979283			−0.489641	−	0.871924i	$-0.662872\pi$
$761$	−27.0147			−0.979283			−0.489641	+	0.871924i	$0.662872\pi$
$762$	−7.10966	−	8.47296i	−0.257556	−	0.306943i
$763$	−8.38253	+	23.0308i	−0.303468	+	0.833771i
$764$	1.89388	−	10.7407i	0.0685182	−	0.388586i
$765$	4.89947	−	11.1220i	0.177141	−	0.402115i
$766$	22.2840	−	8.11073i	0.805155	−	0.293053i
$767$	23.4335	+	13.5293i	0.846133	+	0.488515i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−33.2331	−	27.8859i	−1.19842	−	1.00559i	−0.999674	−	0.0255404i	$-0.991869\pi$
$769$	−33.2331	−	27.8859i	−1.19842	−	1.00559i	−0.198744	−	0.980051i	$-0.563686\pi$
$770$	1.53342	−	0.446238i	0.0552606	−	0.0160813i
$771$	10.0693	+	17.4405i	0.362637	+	0.628106i
$772$	−13.8629	−	8.00376i	−0.498937	−	0.288062i
$773$	12.3954	+	34.0562i	0.445833	+	1.22492i	0.935599	+	0.353063i	$0.114860\pi$
$773$	12.3954	+	34.0562i	0.445833	+	1.22492i	−0.489766	+	0.871854i	$0.662918\pi$
$774$	−1.63302	−	9.26134i	−0.0586979	−	0.332892i
$775$	15.1326	−	3.34122i	0.543580	−	0.120020i
$776$	−14.0052	−	5.09748i	−0.502758	−	0.182989i
$777$	−13.2876	−	15.8355i	−0.476688	−	0.568095i
$778$			18.5336i			0.664463i
$779$	−10.7303	+	12.2159i	−0.384454	+	0.437681i
$780$	3.68727	−	5.51328i	0.132026	−	0.197407i
$781$	−3.73883	+	3.13725i	−0.133786	+	0.112260i
$782$	14.2736	−	39.2165i	0.510425	−	1.40238i
$783$	2.10889	+	0.371854i	0.0753656	+	0.0132890i
$784$	0.490053	+	2.77923i	0.0175019	+	0.0992583i
$785$	−13.3187	−	3.26512i	−0.475366	−	0.116537i
$786$	1.37693	−	2.38491i	0.0491135	−	0.0850671i
$787$	10.7802	−	6.22393i	0.384271	−	0.221859i	−0.295404	−	0.955372i	$-0.595454\pi$
$787$	10.7802	−	6.22393i	0.384271	−	0.221859i	0.679675	+	0.733513i	$0.262121\pi$
$788$	−3.95638	+	4.71503i	−0.140940	+	0.167966i
$789$	−10.3718	−	8.70300i	−0.369247	−	0.309835i
$790$	−0.754520	+	11.4367i	−0.0268446	+	0.406899i
$791$	5.74532	−	9.95119i	0.204280	−	0.353824i
$792$	−0.119509	−	0.328348i	−0.00424657	−	0.0116674i
$793$	4.20418	−	0.741310i	0.149295	−	0.0263247i
$794$	−3.25881	+	18.4816i	−0.115651	+	0.655888i
$795$	−15.1240	+	11.0794i	−0.536394	+	0.392947i
$796$	−6.01269	+	5.04524i	−0.213114	+	0.178824i
$797$		−	31.2905i		−	1.10837i	−0.832394	−	0.554184i	$-0.813030\pi$
$797$		−	31.2905i		−	1.10837i	0.832394	−	0.554184i	$-0.186970\pi$
$798$	4.62810	−	7.61319i	0.163833	−	0.269504i
$799$	67.0234			2.37112
$800$	−2.31254	+	4.43307i	−0.0817607	+	0.156733i
$801$	3.77608	+	1.37438i	0.133421	+	0.0485613i
$802$	26.2173	+	4.62281i	0.925764	+	0.163237i
$803$	3.58619	−	0.632342i	0.126554	−	0.0223149i
$804$	2.97031	−	1.08111i	0.104755	−	0.0381277i
$805$	15.5084	+	31.4818i	0.546598	+	1.10959i
$806$	4.59678	+	7.96185i	0.161915	+	0.280444i
$807$	19.9599	−	23.7873i	0.702623	−	0.837353i
$808$	2.08039	−	2.47932i	0.0731880	−	0.0872221i
$809$	13.3965	+	23.2033i	0.470994	+	0.815786i	0.999450	−	0.0331752i	$-0.0105619\pi$
$809$	13.3965	+	23.2033i	0.470994	+	0.815786i	−0.528455	+	0.848961i	$0.677229\pi$
$810$	2.00589	−	0.988128i	0.0704799	−	0.0347193i
$811$	−16.3882	+	5.96482i	−0.575468	+	0.209453i	−0.613326	−	0.789830i	$-0.710169\pi$
$811$	−16.3882	+	5.96482i	−0.575468	+	0.209453i	0.0378580	+	0.999283i	$0.487947\pi$
$812$	4.31055	−	0.760066i	0.151271	−	0.0266731i
$813$	11.4834	+	2.02484i	0.402742	+	0.0710142i
$814$	−3.32073	−	1.20865i	−0.116392	−	0.0423631i
$815$	−35.1028	+	3.82917i	−1.22960	+	0.134130i
$816$	−5.43512			−0.190267
$817$	8.02919	−	40.1980i	0.280906	−	1.40635i
$818$			4.09620i			0.143220i
$819$	−4.64447	+	3.89717i	−0.162291	+	0.136178i
$820$	−6.72859	+	4.92918i	−0.234973	+	0.172134i
$821$	−1.79355	+	10.1717i	−0.0625952	+	0.354995i	0.937382	+	0.348302i	$0.113242\pi$
$821$	−1.79355	+	10.1717i	−0.0625952	+	0.354995i	−0.999978	+	0.00669305i	$0.997870\pi$
$822$	11.0576	−	1.94975i	0.385677	−	0.0680053i
$823$	7.13452	+	19.6019i	0.248694	+	0.683280i	0.999735	+	0.0230248i	$0.00732966\pi$
$823$	7.13452	+	19.6019i	0.248694	+	0.683280i	−0.751041	+	0.660255i	$0.770448\pi$
$824$	−6.04245	+	10.4658i	−0.210499	+	0.364595i
$825$	1.38516	+	1.06476i	0.0482251	+	0.0370701i
$826$	14.2835	+	11.9853i	0.496987	+	0.417022i
$827$	−9.63949	+	11.4879i	−0.335198	+	0.399474i	−0.907146	−	0.420817i	$-0.861744\pi$
$827$	−9.63949	+	11.4879i	−0.335198	+	0.399474i	0.571948	+	0.820290i	$0.306188\pi$
$828$	6.64974	−	3.83923i	0.231094	−	0.133422i
$829$	8.69837	−	15.0660i	0.302107	−	0.523264i	−0.674506	−	0.738269i	$-0.735643\pi$
$829$	8.69837	−	15.0660i	0.302107	−	0.523264i	0.976613	+	0.215005i	$0.0689768\pi$
$830$	3.68278	−	15.0224i	0.127831	−	0.521436i
$831$	3.62462	+	20.5562i	0.125737	+	0.713088i
$832$	−2.92115	−	0.515078i	−0.101273	−	0.0178571i
$833$	5.24607	−	14.4135i	0.181766	−	0.499397i
$834$	14.4253	−	12.1043i	0.499507	−	0.419136i
$835$	−13.9749	−	9.34641i	−0.483622	−	0.323446i
$836$	0.0344399	−	1.52270i	0.00119113	−	0.0526637i
$837$			3.09942i			0.107132i
$838$	−10.0317	−	11.9553i	−0.346539	−	0.412989i
$839$	−3.20894	−	1.16796i	−0.110785	−	0.0403224i	0.286033	−	0.958220i	$-0.407663\pi$
$839$	−3.20894	−	1.16796i	−0.110785	−	0.0403224i	−0.396818	+	0.917897i	$0.629886\pi$
$840$	3.16197	−	3.30021i	0.109098	−	0.113868i
$841$	−4.23950	−	24.0434i	−0.146190	−	0.829083i
$842$	5.29611	+	14.5509i	0.182516	+	0.501459i
$843$	−22.0565	−	12.7343i	−0.759668	−	0.438594i
$844$	−5.53660	−	9.58967i	−0.190578	−	0.330090i
$845$	9.02075	−	2.62512i	0.310323	−	0.0903067i
$846$	9.44650	+	7.92656i	0.324778	+	0.272521i
$847$	19.2555	−	11.1172i	0.661627	−	0.381990i
$848$	7.26109	+	4.19219i	0.249347	+	0.143961i
$849$	14.2000	−	5.16838i	0.487343	−	0.177378i
$850$	22.9322	−	14.5818i	0.786567	−	0.500152i
$851$	13.4848	−	76.4758i	0.462251	−	2.62156i
$852$	−4.77733	+	13.1256i	−0.163668	+	0.449675i
$853$	8.14303	+	9.70448i	0.278812	+	0.332275i	0.887218	−	0.461351i	$-0.152635\pi$
$853$	8.14303	+	9.70448i	0.278812	+	0.332275i	−0.608406	+	0.793626i	$0.708191\pi$
$854$	2.94175			0.100665
$855$	9.71074	−	0.837589i	0.332100	−	0.0286449i
$856$	11.9159			0.407275
$857$	20.8253	+	24.8187i	0.711379	+	0.847789i	0.993763	−	0.111513i	$-0.0355695\pi$
$857$	20.8253	+	24.8187i	0.711379	+	0.847789i	−0.282384	+	0.959302i	$0.591125\pi$
$858$	−0.354490	+	0.973953i	−0.0121021	+	0.0332502i
$859$	6.04475	−	34.2815i	0.206244	−	1.16967i	−0.689225	−	0.724547i	$-0.742049\pi$
$859$	6.04475	−	34.2815i	0.206244	−	1.16967i	0.895470	−	0.445123i	$-0.146840\pi$
$860$	8.47739	−	19.2440i	0.289077	−	0.656214i
$861$	7.16461	−	2.60771i	0.244169	−	0.0888704i
$862$	−3.19957	−	1.84727i	−0.108978	−	0.0629183i
$863$	7.83091	−	4.52118i	0.266567	−	0.153903i	−0.360759	−	0.932659i	$-0.617482\pi$
$863$	7.83091	−	4.52118i	0.266567	−	0.153903i	0.627327	+	0.778756i	$0.284149\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	−7.94370	−	27.2971i	−0.270094	−	0.928129i
$866$	0.753684	+	1.30542i	0.0256112	+	0.0443600i
$867$	10.8604	+	6.27028i	0.368840	+	0.212950i
$868$	2.16676	+	5.95312i	0.0735446	+	0.202062i
$869$	−0.311012	−	1.76384i	−0.0105504	−	0.0598341i
$870$	3.45753	+	3.31270i	0.117221	+	0.112311i
$871$	−8.81060	−	3.20680i	−0.298536	−	0.108658i
$872$	7.70748	+	9.18541i	0.261008	+	0.311057i
$873$			14.9040i			0.504425i
$874$	33.0841	−	5.06514i	1.11909	−	0.171331i
$875$	−4.48710	+	22.4076i	−0.151692	+	0.757517i
$876$	7.98338	−	6.69885i	0.269733	−	0.226333i
$877$	−14.7824	+	40.6142i	−0.499165	+	1.37144i	0.392918	+	0.919574i	$0.371466\pi$
$877$	−14.7824	+	40.6142i	−0.499165	+	1.37144i	−0.892083	+	0.451871i	$0.850757\pi$
$878$	14.6910	+	2.59041i	0.495796	+	0.0874222i
$879$	−5.18748	−	29.4197i	−0.174969	−	0.992301i
$880$	0.186036	−	0.758858i	0.00627127	−	0.0255811i
$881$	−24.3925	+	42.2491i	−0.821805	+	1.42341i	0.0825312	+	0.996588i	$0.473700\pi$
$881$	−24.3925	+	42.2491i	−0.821805	+	1.42341i	−0.904337	+	0.426820i	$0.859634\pi$
$882$	2.44401	−	1.41105i	0.0822943	−	0.0475126i
$883$	10.9711	−	13.0748i	0.369207	−	0.440004i	−0.549170	−	0.835711i	$-0.685056\pi$
$883$	10.9711	−	13.0748i	0.369207	−	0.440004i	0.918377	+	0.395707i	$0.129500\pi$
$884$	12.3500	+	10.3629i	0.415375	+	0.348541i
$885$	−1.34281	+	20.3538i	−0.0451381	+	0.684184i
$886$	−14.5091	+	25.1306i	−0.487444	+	0.844278i
$887$	−14.7764	−	40.5978i	−0.496143	−	1.36314i	−0.894974	−	0.446118i	$-0.852806\pi$
$887$	−14.7764	−	40.5978i	−0.496143	−	1.36314i	0.398831	−	0.917024i	$-0.369416\pi$
$888$	−9.95979	+	1.75618i	−0.334229	+	0.0589335i
$889$	−3.92582	+	22.2644i	−0.131668	+	0.746725i
$890$	5.31008	+	7.24855i	0.177994	+	0.242972i
$891$	−0.267672	+	0.224604i	−0.00896735	+	0.00752450i
$892$			2.68834i			0.0900122i
$893$	25.8165	+	47.1463i	0.863916	+	1.57769i
$894$	8.67029			0.289978
$895$	−4.28717	−	39.3014i	−0.143304	−	1.31370i
$896$	−1.92072	−	0.699086i	−0.0641668	−	0.0233548i
$897$	−22.4300	−	3.95501i	−0.748914	−	0.132054i
$898$	−22.6533	+	3.99439i	−0.755951	+	0.133295i
$899$	−6.23690	+	2.27005i	−0.208012	+	0.0757102i
$900$	4.95666	+	0.656878i	0.165222	+	0.0218959i
$901$	−22.7851	−	39.4649i	−0.759081	−	1.31477i
$902$	0.837809	−	0.998461i	0.0278960	−	0.0332451i
$903$	−12.3557	+	14.7250i	−0.411173	+	0.490017i
$904$	−2.81084	−	4.86851i	−0.0934871	−	0.161924i
$905$	3.48608	+	7.07672i	0.115881	+	0.235238i
$906$	−0.509597	+	0.185478i	−0.0169302	+	0.00616210i
$907$	47.3246	−	8.34461i	1.57139	−	0.277078i	0.681001	−	0.732282i	$-0.261545\pi$
$907$	47.3246	−	8.34461i	1.57139	−	0.277078i	0.890387	+	0.455204i	$0.150434\pi$
$908$	−6.43989	−	1.13553i	−0.213715	−	0.0376838i
$909$	−3.04133	−	1.10695i	−0.100875	−	0.0367154i
$910$	−13.4772	+	1.47015i	−0.446763	+	0.0487349i
$911$	11.0430			0.365871			0.182936	−	0.983125i	$-0.441440\pi$
$911$	11.0430			0.365871			0.182936	+	0.983125i	$0.441440\pi$
$912$	−2.09353	−	3.82323i	−0.0693238	−	0.126600i
$913$			2.41700i			0.0799912i
$914$	−25.6554	+	21.5274i	−0.848606	+	0.712065i
$915$	1.90183	+	2.59611i	0.0628727	+	0.0858246i
$916$	2.42876	−	13.7742i	0.0802484	−	0.455111i
$917$	−5.54335	+	0.977442i	−0.183058	+	0.0322780i
$918$	1.85892	+	5.10735i	0.0613536	+	0.168568i
$919$	−14.6425	+	25.3616i	−0.483012	+	0.836601i	−0.999810	−	0.0195066i	$-0.993790\pi$
$919$	−14.6425	+	25.3616i	−0.483012	+	0.836601i	0.516798	+	0.856107i	$0.327124\pi$
$920$	17.1323	+	1.13028i	0.564835	+	0.0372643i
$921$	−8.86515	−	7.43874i	−0.292117	−	0.245115i
$922$	24.2559	−	28.9070i	0.798825	−	0.952003i
$923$	35.8812	−	20.7160i	1.18104	−	0.681876i
$924$	−0.357107	+	0.618527i	−0.0117479	+	0.0203480i
$925$	37.3113	−	34.1307i	1.22679	−	1.12221i
$926$	−5.15002	−	29.2072i	−0.169240	−	0.959808i
$927$	11.9013	+	2.09852i	0.390890	+	0.0689245i
$928$	0.732410	−	2.01228i	0.0240425	−	0.0660563i
$929$	−21.6786	+	18.1905i	−0.711251	+	0.596811i	−0.924950	−	0.380089i	$-0.875893\pi$
$929$	−21.6786	+	18.1905i	−0.711251	+	0.596811i	0.213699	+	0.976900i	$0.431449\pi$
$930$	−3.85285	+	5.76086i	−0.126340	+	0.188906i
$931$	12.1596	−	1.86162i	0.398515	−	0.0610121i
$932$		−	15.3146i		−	0.501645i
$933$	5.25181	+	6.25887i	0.171937	+	0.204906i
$934$	24.2993	+	8.84422i	0.795097	+	0.289392i
$935$	−2.93791	+	3.06635i	−0.0960799	+	0.100280i
$936$	0.515078	+	2.92115i	0.0168359	+	0.0954809i
$937$	9.48853	+	26.0695i	0.309977	+	0.851654i	0.992660	+	0.120940i	$0.0385908\pi$
$937$	9.48853	+	26.0695i	0.309977	+	0.851654i	−0.682683	+	0.730715i	$0.739187\pi$
$938$	−5.59533	−	3.23047i	−0.182694	−	0.105479i
$939$	−12.6943	−	21.9872i	−0.414263	−	0.717525i
$940$	7.70471	+	26.4759i	0.251300	+	0.863548i
$941$	14.8163	+	12.4324i	0.482999	+	0.405284i	0.851509	−	0.524339i	$-0.175688\pi$
$941$	14.8163	+	12.4324i	0.482999	+	0.405284i	−0.368510	+	0.929624i	$0.620132\pi$
$942$	5.31107	−	3.06635i	0.173044	−	0.0999070i
$943$	24.8046	+	14.3210i	0.807750	+	0.466355i
$944$	8.57212	−	3.12000i	0.278999	−	0.101547i
$945$	−4.18264	−	1.84255i	−0.136061	−	0.0599380i
$946$	−0.570613	+	3.23611i	−0.0185522	+	0.105215i
$947$	5.96764	−	16.3960i	0.193922	−	0.532797i	−0.804179	−	0.594387i	$-0.797395\pi$
$947$	5.96764	−	16.3960i	0.193922	−	0.532797i	0.998102	+	0.0615897i	$0.0196170\pi$
$948$	−3.29478	−	3.92656i	−0.107009	−	0.127529i
$949$	−30.9126			−1.00347
$950$	19.0905	+	10.5145i	0.619376	+	0.341135i
$951$	8.17279			0.265021
$952$	7.14094	+	8.51025i	0.231439	+	0.275819i
$953$	−14.7594	+	40.5511i	−0.478104	+	1.31358i	0.432996	+	0.901396i	$0.357456\pi$
$953$	−14.7594	+	40.5511i	−0.478104	+	1.31358i	−0.911100	+	0.412184i	$0.864766\pi$
$954$	1.45593	−	8.25701i	0.0471376	−	0.267331i
$955$	−22.3180	−	9.83155i	−0.722192	−	0.318141i
$956$	16.1749	−	5.88717i	0.523133	−	0.190405i
$957$	−0.648011	−	0.374129i	−0.0209472	−	0.0120939i
$958$	8.57098	−	4.94846i	0.276916	−	0.159877i
$959$	−17.5809	−	14.7521i	−0.567717	−	0.476371i
$960$	−0.624797	−	2.14700i	−0.0201652	−	0.0692943i
$961$	10.6968	+	18.5274i	0.345058	+	0.597658i
$962$	25.9796	+	14.9993i	0.837616	+	0.483598i
$963$	−4.07546	−	11.1972i	−0.131330	−	0.360826i
$964$	2.06037	+	11.6849i	0.0663599	+	0.376346i
$965$	−24.7630	+	25.8456i	−0.797150	+	0.832000i
$966$	−14.7482	−	5.36790i	−0.474515	−	0.172709i
$967$	6.80451	+	8.10930i	0.218818	+	0.260778i	0.864275	−	0.503019i	$-0.167777\pi$
$967$	6.80451	+	8.10930i	0.218818	+	0.260778i	−0.645457	+	0.763797i	$0.723333\pi$
$968$		−	10.8779i		−	0.349629i
$969$	−0.535701	+	23.6851i	−0.0172092	+	0.760875i
$970$	−18.5271	+	27.7020i	−0.594868	+	0.889458i
$971$	−37.2238	+	31.2344i	−1.19457	+	1.00236i	−0.194799	+	0.980843i	$0.562405\pi$
$971$	−37.2238	+	31.2344i	−1.19457	+	1.00236i	−0.999768	+	0.0215177i	$0.993150\pi$
$972$	−0.342020	+	0.939693i	−0.0109703	+	0.0301407i
$973$	−37.9054	−	6.68375i	−1.21519	−	0.214271i
$974$	−2.54710	−	14.4453i	−0.0816144	−	0.462858i
$975$	−10.0104	−	10.9432i	−0.320588	−	0.350463i
$976$	0.719609	−	1.24640i	0.0230341	−	0.0398963i
$977$	−4.70569	+	2.71683i	−0.150548	+	0.0869191i	−0.573382	−	0.819288i	$-0.694369\pi$
$977$	−4.70569	+	2.71683i	−0.150548	+	0.0869191i	0.422833	+	0.906207i	$0.361036\pi$
$978$	10.1506	−	12.0971i	0.324581	−	0.386821i
$979$	−1.07562	−	0.902551i	−0.0343769	−	0.0288457i
$980$	6.29673	+	0.415419i	0.201142	+	0.0132701i
$981$	5.99535	−	10.3843i	0.191417	−	0.331544i
$982$	−7.49194	−	20.5839i	−0.239078	−	0.656860i
$983$	13.5037	−	2.38107i	0.430702	−	0.0759445i	0.0459057	−	0.998946i	$-0.485383\pi$
$983$	13.5037	−	2.38107i	0.430702	−	0.0759445i	0.384797	+	0.923001i	$0.374272\pi$
$984$	0.647737	−	3.67350i	0.0206491	−	0.117107i
$985$	8.13349	+	11.1027i	0.259155	+	0.353760i
$986$	−8.91592	+	7.48134i	−0.283941	+	0.238254i
$987$		−	25.2055i		−	0.802301i
$988$	−2.53252	+	12.6790i	−0.0805701	+	0.403373i
$989$	−72.2098			−2.29614
$990$	−0.776722	+	0.0847282i	−0.0246858	+	0.00269284i
$991$	2.19570	+	0.799170i	0.0697488	+	0.0253865i	0.376659	−	0.926352i	$-0.377073\pi$
$991$	2.19570	+	0.799170i	0.0697488	+	0.0253865i	−0.306910	+	0.951739i	$0.599295\pi$
$992$	3.05233	+	0.538208i	0.0969116	+	0.0170881i
$993$	7.60228	−	1.34049i	0.241251	−	0.0425391i
$994$	26.8286	−	9.76480i	0.850951	−	0.309721i
$995$	7.75582	+	15.7443i	0.245876	+	0.499126i
$996$	3.45858	+	5.99044i	0.109589	+	0.189814i
$997$	−28.8756	+	34.4126i	−0.914500	+	1.08986i	0.0811511	+	0.996702i	$0.474140\pi$
$997$	−28.8756	+	34.4126i	−0.914500	+	1.08986i	−0.995651	+	0.0931572i	$0.970304\pi$
$998$	11.3441	−	13.5194i	0.359091	−	0.427948i
$999$	5.05672	+	8.75849i	0.159988	+	0.277106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.b.139.5	✓	60
5.4	even	2	inner	570.2.bc.b.139.6	yes	60
19.16	even	9	inner	570.2.bc.b.529.6	yes	60
95.54	even	18	inner	570.2.bc.b.529.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.b.139.5	✓	60	1.1	even	1	trivial
570.2.bc.b.139.6	yes	60	5.4	even	2	inner
570.2.bc.b.529.5	yes	60	95.54	even	18	inner
570.2.bc.b.529.6	yes	60	19.16	even	9	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.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.04631 + 0.901446i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(1.77015 + 1.02199i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.04631 + 0.901446i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(1.77015 + 1.02199i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-0.624797 - 2.14700i) q^{10} +(0.174711 + 0.302608i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-1.01451 - 2.78733i) q^{13} +(-0.354935 - 2.01294i) q^{14} +(1.54696 - 1.61459i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.49363 + 4.16355i) q^{17} +1.00000i q^{18} +(-1.58307 + 4.06127i) q^{19} +(-1.24309 + 1.85869i) q^{20} +(1.56579 - 1.31385i) q^{21} +(0.119509 - 0.328348i) q^{22} +(7.56180 + 1.33335i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(3.37479 + 3.68928i) q^{25} +(-1.48311 + 2.56882i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-1.31385 + 1.56579i) q^{28} +(-1.64043 - 1.37648i) q^{29} +(-2.23122 - 0.147202i) q^{30} +(1.54971 - 2.68418i) q^{31} +(0.342020 + 0.939693i) q^{32} +(0.344113 - 0.0606763i) q^{33} +(0.943799 - 5.35255i) q^{34} +(2.70100 + 3.68701i) q^{35} +(0.766044 - 0.642788i) q^{36} -10.1134i q^{37} +(4.12869 - 1.39783i) q^{38} -2.96622 q^{39} +(2.22288 - 0.242482i) q^{40} +(3.50521 + 1.27579i) q^{41} +(-2.01294 - 0.354935i) q^{42} +(-9.26134 + 1.63302i) q^{43} +(-0.328348 + 0.119509i) q^{44} +(-0.988128 - 2.00589i) q^{45} +(-3.83923 - 6.64974i) q^{46} +(7.92656 - 9.44650i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(-1.41105 - 2.44401i) q^{49} +(0.656878 - 4.95666i) q^{50} +(5.10735 - 1.85892i) q^{51} +(2.92115 - 0.515078i) q^{52} +(-8.25701 - 1.45593i) q^{53} +(0.939693 + 0.342020i) q^{54} +(0.0847282 + 0.776722i) q^{55} +2.04399 q^{56} +(3.27490 + 2.87663i) q^{57} +2.14142i q^{58} +(-6.98806 + 5.86368i) q^{59} +(1.32144 + 1.80383i) q^{60} +(-0.249918 + 1.41735i) q^{61} +(-3.05233 + 0.538208i) q^{62} +(-0.699086 - 1.92072i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.436632 - 6.61828i) q^{65} +(-0.267672 - 0.224604i) q^{66} +(2.03182 - 2.42142i) q^{67} +(-4.70696 + 2.71756i) q^{68} +(3.83923 - 6.64974i) q^{69} +(1.08825 - 4.43905i) q^{70} +(2.42551 + 13.7558i) q^{71} +(-0.984808 - 0.173648i) q^{72} +(3.56438 - 9.79306i) q^{73} +(-7.74734 + 6.50079i) q^{74} +(4.62104 - 1.90946i) q^{75} +(-3.72467 - 2.26425i) q^{76} +0.714213i q^{77} +(1.90665 + 2.27226i) q^{78} +(-4.81664 - 1.75311i) q^{79} +(-1.61459 - 1.54696i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-1.27579 - 3.50521i) q^{82} +(5.99044 + 3.45858i) q^{83} +(1.02199 + 1.77015i) q^{84} +(3.39585 + 11.6692i) q^{85} +(7.20405 + 6.04491i) q^{86} +(-1.85453 + 1.07071i) q^{87} +(0.302608 + 0.174711i) q^{88} +(-3.77608 + 1.37438i) q^{89} +(-0.901446 + 2.04631i) q^{90} +(1.05282 - 5.97081i) q^{91} +(-2.62619 + 7.21539i) q^{92} +(-1.99227 - 2.37429i) q^{93} -12.3315 q^{94} +(-6.90047 + 6.88357i) q^{95} +1.00000 q^{96} +(-9.58014 - 11.4172i) q^{97} +(-0.965217 + 2.65191i) q^{98} +(0.0606763 - 0.344113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5}+O(q^{10}) \) 60 * q + 6 * q^5	\( 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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