LMFDB - Embedded newform 570.2.bc.b.139.6

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			139.6
Character	$\chi$	$=$	570.139
Dual form			570.2.bc.b.529.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.61459 + 1.54696i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-1.77015 - 1.02199i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.61459 + 1.54696i) 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} +(-2.22288 - 0.242482i) 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} +(-0.901446 - 2.04631i) 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} +(0.213817 - 4.99543i) 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} +(0.988128 - 2.00589i) 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} +(4.43905 - 1.08825i) q^{35} +(0.766044 - 0.642788i) q^{36} +10.1134i q^{37} +(-4.12869 + 1.39783i) q^{38} -2.96622 q^{39} +(0.624797 - 2.14700i) 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} +(2.23122 - 0.147202i) 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} +(3.96416 - 3.04720i) 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} +(-0.750209 - 0.218317i) q^{55} +2.04399 q^{56} +(-3.27490 - 2.87663i) q^{57} -2.14142i q^{58} +(-6.98806 + 5.86368i) q^{59} +(2.17176 - 0.532412i) 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} +(-5.94991 - 2.93100i) 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} +(3.68701 + 2.70100i) 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} +(2.04631 - 0.901446i) 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} +(12.0816 + 1.31792i) 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} +(1.54696 + 1.61459i) q^{90} +(1.05282 - 5.97081i) q^{91} +(2.62619 - 7.21539i) q^{92} +(1.99227 + 2.37429i) q^{93} -12.3315 q^{94} +(-3.72662 - 9.00624i) 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
$5$	−1.61459	+	1.54696i	−0.722068	+	0.691822i
$5$	−1.61459	+	1.54696i	−0.722068	+	0.691822i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	−1.77015	−	1.02199i	−0.669053	−	0.386278i	0.126665	−	0.991946i	$-0.459573\pi$
$7$	−1.77015	−	1.02199i	−0.669053	−	0.386278i	−0.795718	+	0.605668i	$0.792906\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	−2.22288	−	0.242482i	−0.702937	−	0.0766794i
$11$	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	$0.0238282\pi$
$13$	1.01451	+	2.78733i	0.281373	+	0.773067i	−0.715826	+	0.698279i	$0.753950\pi$
$14$	−0.354935	−	2.01294i	−0.0948604	−	0.537980i
$15$	−0.901446	−	2.04631i	−0.232752	−	0.528356i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−3.49363	−	4.16355i	−0.847330	−	1.00981i	−0.999769	−	0.0214954i	$-0.993157\pi$
$17$	−3.49363	−	4.16355i	−0.847330	−	1.00981i	0.152439	−	0.988313i	$-0.451287\pi$
$18$		−	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	−0.684307	−	0.729194i	$-0.739895\pi$
$23$	−7.56180	−	1.33335i	−1.57674	−	0.278023i	−0.892438	+	0.451171i	$0.851006\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	0.213817	−	4.99543i	0.0427635	−	0.999085i
$26$	−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	$0.785935\pi$
$30$	0.988128	−	2.00589i	0.180407	−	0.366224i
$31$	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
$35$	4.43905	−	1.08825i	0.750337	−	0.183947i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$			10.1134i			1.66264i	0.555795	+	0.831319i	$0.312414\pi$
$37$			10.1134i			1.66264i	−0.555795	+	0.831319i	$0.687586\pi$
$38$	−4.12869	+	1.39783i	−0.669762	+	0.226758i
$39$	−2.96622			−0.474975
$40$	0.624797	−	2.14700i	0.0987891	−	0.339471i
$41$	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	0.585137	−	0.810935i	$-0.301041\pi$
$43$	9.26134	−	1.63302i	1.41234	−	0.249034i	0.827205	+	0.561901i	$0.189930\pi$
$44$	−0.328348	+	0.119509i	−0.0495004	+	0.0180167i
$45$	2.23122	−	0.147202i	0.332610	−	0.0219435i
$46$	−3.83923	−	6.64974i	−0.566063	−	0.980450i
$47$	−7.92656	+	9.44650i	−1.15621	+	1.37791i	−0.243198	+	0.969977i	$0.578196\pi$
$47$	−7.92656	+	9.44650i	−1.15621	+	1.37791i	−0.913010	+	0.407938i	$0.866248\pi$
$48$	0.642788	−	0.766044i	0.0927784	−	0.110569i
$49$	−1.41105	−	2.44401i	−0.201579	−	0.349145i
$50$	3.96416	−	3.04720i	0.560617	−	0.430940i
$51$	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	0.709062	−	0.705146i	$-0.249119\pi$
$53$	8.25701	+	1.45593i	1.13419	+	0.199988i	0.425126	+	0.905134i	$0.360230\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	−0.750209	−	0.218317i	−0.101158	−	0.0294379i
$56$	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	$0.480154\pi$
$60$	2.17176	−	0.532412i	0.280373	−	0.0687341i
$61$	−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
$65$	−5.94991	−	2.93100i	−0.737996	−	0.363546i
$66$	−0.267672	−	0.224604i	−0.0329482	−	0.0276468i
$67$	−2.03182	+	2.42142i	−0.248226	+	0.295824i	−0.875742	−	0.482780i	$-0.839627\pi$
$67$	−2.03182	+	2.42142i	−0.248226	+	0.295824i	0.627516	+	0.778604i	$0.284072\pi$
$68$	4.70696	−	2.71756i	0.570802	−	0.329553i
$69$	3.83923	−	6.64974i	0.462189	−	0.800534i
$70$	3.68701	+	2.70100i	0.440682	+	0.322831i
$71$	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	$0.319892\pi$
$73$	−3.56438	+	9.79306i	−0.417180	+	1.14619i	−0.953293	+	0.302046i	$0.902330\pi$
$74$	−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	$0.704217\pi$
$80$	2.04631	−	0.901446i	0.228785	−	0.100785i
$81$	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	0.133801	−	0.991008i	$-0.457282\pi$
$83$	−5.99044	−	3.45858i	−0.657537	−	0.379629i	−0.791338	+	0.611379i	$0.790615\pi$
$84$	1.02199	+	1.77015i	0.111509	+	0.193139i
$85$	12.0816	+	1.31792i	1.31044	+	0.142948i
$86$	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	$0.457204\pi$
$90$	1.54696	+	1.61459i	0.163064	+	0.170193i
$91$	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
$95$	−3.72662	−	9.00624i	−0.382343	−	0.924021i
$96$	1.00000			0.102062
$97$	9.58014	+	11.4172i	0.972715	+	1.15924i	0.987223	+	0.159342i	$0.0509373\pi$
$97$	9.58014	+	11.4172i	0.972715	+	1.15924i	−0.0145080	+	0.999895i	$0.504618\pi$
$98$	0.965217	−	2.65191i	0.0975016	−	0.267884i
$99$	0.0606763	−	0.344113i	0.00609820	−	0.0345846i
$100$	4.88241	+	1.07802i	0.488241	+	0.107802i
$101$	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	0.113893	−	0.993493i	$-0.463668\pi$
$103$	10.4658	−	6.04245i	1.03123	−	0.595381i	0.917337	+	0.398113i	$0.130335\pi$
$104$	−2.27226	−	1.90665i	−0.222813	−	0.186962i
$105$	−0.495630	+	4.54355i	−0.0483685	+	0.443405i
$106$	4.19219	+	7.26109i	0.407182	+	0.705260i
$107$	−10.3194	−	5.95793i	−0.997617	−	0.575974i	−0.0900747	−	0.995935i	$-0.528711\pi$
$107$	−10.3194	−	5.95793i	−0.997617	−	0.575974i	−0.907542	+	0.419961i	$0.862044\pi$
$108$	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	$0.749738\pi$
$110$	−0.314984	−	0.715025i	−0.0300326	−	0.0681749i
$111$	−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	$0.0851810\pi$
$113$			5.62168i			0.528843i	−0.964407	+	0.264421i	$0.914819\pi$
$114$	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
$120$	1.80383	+	1.32144i	0.164667	+	0.120630i
$121$	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
$125$	7.38251	+	8.39634i	0.660311	+	0.750992i
$126$	−1.02199	+	1.77015i	−0.0910465	+	0.157697i
$127$	−3.78297	−	10.3936i	−0.335684	−	0.922285i	−0.986603	−	0.163138i	$-0.947839\pi$
$127$	−3.78297	−	10.3936i	−0.335684	−	0.922285i	0.650919	−	0.759147i	$-0.274384\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$	−1.63302	+	9.26134i	−0.143780	+	0.815416i
$130$	−1.57925	−	6.44191i	−0.138509	−	0.564993i
$131$	−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
$135$	−0.624797	+	2.14700i	−0.0537740	+	0.184785i
$136$	5.10735	+	1.85892i	0.437951	+	0.159401i
$137$	11.0576	+	1.94975i	0.944712	+	0.166578i	0.624726	−	0.780844i	$-0.285211\pi$
$137$	11.0576	+	1.94975i	0.944712	+	0.166578i	0.319986	+	0.947422i	$0.396322\pi$
$138$	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	$0.683319\pi$
$140$	0.300879	+	4.56059i	0.0254289	+	0.385440i
$141$	−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
$145$	4.77798	−	0.315221i	0.396790	−	0.0261777i
$146$	−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	$0.726681\pi$
$150$	1.50761	+	4.76729i	0.123096	+	0.389248i
$151$	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
$155$	1.65017	+	6.73119i	0.132545	+	0.540662i
$156$	0.515078	−	2.92115i	0.0412393	−	0.233880i
$157$	6.03952	−	1.06493i	0.482007	−	0.0849908i	0.0726351	−	0.997359i	$-0.476859\pi$
$157$	6.03952	−	1.06493i	0.482007	−	0.0849908i	0.409371	+	0.912368i	$0.365748\pi$
$158$	−1.75311	−	4.81664i	−0.139470	−	0.383191i
$159$	−4.19219	+	7.26109i	−0.332463	+	0.575842i
$160$	2.00589	+	0.988128i	0.158580	+	0.0781184i
$161$	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	0.142676	−	0.989769i	$-0.454429\pi$
$163$	13.6759	−	7.89579i	1.07118	−	0.618446i	0.928504	+	0.371324i	$0.121096\pi$
$164$	−1.86508	+	3.23042i	−0.145639	+	0.252253i
$165$	0.461738	−	0.630297i	0.0359462	−	0.0490685i
$166$	−1.20115	−	6.81208i	−0.0932276	−	0.528720i
$167$	7.40447	+	1.30561i	0.572975	+	0.101031i	0.452626	−	0.891701i	$-0.350487\pi$
$167$	7.40447	+	1.30561i	0.572975	+	0.101031i	0.120349	+	0.992732i	$0.461599\pi$
$168$	−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	0.981300	−	0.192485i	$-0.0616547\pi$
$173$	8.17243	+	9.73952i	0.621338	+	0.740482i	−0.359962	+	0.932967i	$0.617210\pi$
$174$	2.01228	+	0.732410i	0.152551	+	0.0555239i
$175$	−5.48379	+	8.62412i	−0.414535	+	0.651922i
$176$	−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	$-0.396427\pi$
$180$	−0.242482	+	2.22288i	−0.0180735	+	0.165684i
$181$	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
$185$	−15.6451	−	16.3291i	−1.15025	−	1.20054i
$186$	−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
$190$	4.50376	−	8.64385i	0.326737	−	0.627091i
$191$	−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	$-0.693454\pi$
$193$	5.47489	−	15.0421i	0.394091	−	1.08276i	0.965116	−	0.261824i	$-0.0843240\pi$
$194$	−2.58806	+	14.6776i	−0.185812	+	1.05379i
$195$	4.78923	−	4.58863i	0.342964	−	0.328598i
$196$	2.65191	−	0.965217i	0.189422	−	0.0689441i
$197$	−5.33042	−	3.07752i	−0.379777	−	0.219264i	0.297944	−	0.954583i	$-0.403699\pi$
$197$	−5.33042	−	3.07752i	−0.379777	−	0.219264i	−0.677721	+	0.735319i	$0.737032\pi$
$198$	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	$0.632484\pi$
$200$	2.31254	+	4.43307i	0.163521	+	0.313466i
$201$	−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
$205$	−7.63309	+	3.36254i	−0.533118	+	0.234850i
$206$	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
$215$	−12.4271	+	16.9636i	−0.847519	+	1.15691i
$216$	−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
$220$	0.345273	−	0.700901i	0.0232783	−	0.0472547i
$221$	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	−0.261588	−	0.965180i	$-0.584246\pi$
$223$	−2.64750	+	0.466825i	−0.177289	+	0.0312609i	0.0842985	+	0.996441i	$0.473135\pi$
$224$	−0.354935	+	2.01294i	−0.0237151	+	0.134495i
$225$	−3.37479	+	3.68928i	−0.224986	+	0.245952i
$226$	−4.30645	+	3.61354i	−0.286461	+	0.240369i
$227$		−	6.53924i		−	0.434025i	−0.976169	−	0.217012i	$-0.930369\pi$
$227$		−	6.53924i		−	0.434025i	0.976169	−	0.217012i	$-0.0696312\pi$
$228$	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	$0.652915\pi$
$230$	16.4857	+	4.79748i	1.08703	+	0.316336i
$231$	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	0.343806	−	0.939041i	$-0.388284\pi$
$233$	15.0819	−	2.65935i	0.988048	−	0.174220i	0.644243	+	0.764821i	$0.277173\pi$
$234$	2.78733	−	1.01451i	0.182214	−	0.0663204i
$235$	−1.81522	−	27.5143i	−0.118412	−	1.79484i
$236$	−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	$-0.354602\pi$
$240$	0.147202	+	2.23122i	0.00950182	+	0.144024i
$241$	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
$245$	6.05907	+	1.76324i	0.387100	+	0.112649i
$246$	−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
$250$	−1.68659	+	11.0524i	−0.106669	+	0.699015i
$251$	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
$255$	−5.37060	+	10.9023i	−0.336320	+	0.682727i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	12.9448	−	15.4271i	0.807477	−	0.962314i	−0.192342	−	0.981328i	$-0.561608\pi$
$257$	12.9448	−	15.4271i	0.807477	−	0.962314i	0.999819	+	0.0190140i	$0.00605272\pi$
$258$	−8.14429	+	4.70211i	−0.507041	+	0.292740i
$259$	10.3359	−	17.9023i	0.642240	−	1.11239i
$260$	3.91967	−	5.35056i	0.243087	−	0.331827i
$261$	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	$0.248184\pi$
$263$	−4.63077	+	12.7229i	−0.285545	+	0.784530i	−0.996676	+	0.0814696i	$0.974039\pi$
$264$	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	$0.215564\pi$
$270$	−2.04631	+	0.901446i	−0.124535	+	0.0548602i
$271$	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
$275$	1.54901	−	0.808051i	0.0934088	−	0.0487273i
$276$	5.88204	+	4.93562i	0.354057	+	0.297089i
$277$	18.0769	−	10.4367i	1.08613	−	0.627079i	0.153589	−	0.988135i	$-0.450917\pi$
$277$	18.0769	−	10.4367i	1.08613	−	0.627079i	0.932544	+	0.361056i	$0.117584\pi$
$278$	−16.3080	−	9.41545i	−0.978091	−	0.564701i
$279$	−2.91250	+	1.06006i	−0.174367	+	0.0634643i
$280$	−3.30021	+	3.16197i	−0.197225	+	0.188964i
$281$	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	0.395732	−	0.918366i	$-0.370491\pi$
$283$	−9.71337	−	11.5759i	−0.577400	−	0.688119i	−0.973132	+	0.230247i	$0.926046\pi$
$284$	−13.9680			−0.828846
$285$	9.73767	−	0.421558i	0.576810	−	0.0249709i
$286$	−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
$290$	3.31270	+	3.45753i	0.194528	+	0.203033i
$291$	−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	$0.670911\pi$
$293$	−25.8712	+	14.9368i	−1.51141	+	0.872615i	−0.999911	+	0.0133333i	$0.995756\pi$
$294$	2.16186	+	1.81401i	0.126082	+	0.105795i
$295$	2.21198	−	20.2777i	0.128786	−	1.18061i
$296$	−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
$300$	−2.68288	+	4.21926i	−0.154896	+	0.243599i
$301$	−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	−0.999922	−	0.0125051i	$-0.996019\pi$
$307$	−3.95807	+	10.8747i	−0.225899	+	0.620653i	0.774023	+	0.633158i	$0.218242\pi$
$308$	0.703363	+	0.124022i	0.0400778	+	0.00706680i
$309$	2.09852	+	11.9013i	0.119381	+	0.677042i
$310$	−4.09568	+	5.59083i	−0.232619	+	0.317538i
$311$	−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	$0.476947\pi$
$313$	−16.3195	+	19.4488i	−0.922432	+	1.09931i	−0.994791	+	0.101933i	$0.967497\pi$
$314$	4.69792	+	3.94202i	0.265119	+	0.222461i
$315$	−4.10002	−	2.01972i	−0.231010	−	0.113799i
$316$	2.56288	−	4.43904i	0.144173	−	0.249715i
$317$	−2.79526	−	7.67991i	−0.156997	−	0.431347i	0.836109	−	0.548563i	$-0.184825\pi$
$317$	−2.79526	−	7.67991i	−0.156997	−	0.431347i	−0.993106	+	0.117217i	$0.962603\pi$
$318$	−8.25701	+	1.45593i	−0.463030	+	0.0816447i
$319$	0.129934	−	0.736891i	0.00727489	−	0.0412580i
$320$	0.532412	+	2.17176i	0.0297627	+	0.121405i
$321$	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
$325$	14.1408	−	4.47191i	0.784393	−	0.248057i
$326$	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
$330$	0.779635	−	0.0514354i	0.0429175	−	0.00283142i
$331$	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
$335$	−0.465296	−	7.05275i	−0.0254218	−	0.385333i
$336$	−1.92072	+	0.699086i	−0.104784	+	0.0381383i
$337$	−24.5151	+	4.32268i	−1.33542	+	0.235471i	−0.795352	−	0.606148i	$-0.792714\pi$
$337$	−24.5151	+	4.32268i	−1.33542	+	0.235471i	−0.540072	+	0.841619i	$0.681603\pi$
$338$	4.13772	+	0.729591i	0.225062	+	0.0396845i
$339$	−5.28265	−	1.92273i	−0.286914	−	0.104428i
$340$	−3.39585	+	11.6692i	−0.184166	+	0.632853i
$341$	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
$345$	4.08810	+	16.6758i	0.220096	+	0.897792i
$346$	−2.20777	+	12.5209i	−0.118690	+	0.673127i
$347$	−14.4651	+	2.55058i	−0.776526	+	0.136923i	−0.547846	−	0.836579i	$-0.684552\pi$
$347$	−14.4651	+	2.55058i	−0.776526	+	0.136923i	−0.228680	+	0.973502i	$0.573441\pi$
$348$	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	$0.0944590\pi$
$350$	−10.1314	+	1.34265i	−0.541544	+	0.0717677i
$351$	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	−0.683818	−	0.729652i	$-0.739682\pi$
$353$	−7.39939	+	4.27204i	−0.393830	+	0.227378i	0.289988	+	0.957030i	$0.406349\pi$
$354$	4.56113	−	7.90011i	0.242421	−	0.419886i
$355$	−25.1959	−	18.4578i	−1.33726	−	0.979637i
$356$	−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
$365$	−9.39447	−	21.3258i	−0.491729	−	1.11624i
$366$	−0.249918	−	1.41735i	−0.0130634	−	0.0740862i
$367$	9.05440	+	24.8768i	0.472636	+	1.29856i	0.915627	+	0.402030i	$0.131695\pi$
$367$	9.05440	+	24.8768i	0.472636	+	1.29856i	−0.442991	+	0.896526i	$0.646083\pi$
$368$	6.64974	+	3.83923i	0.346642	+	0.200134i
$369$	−1.86508	−	3.23042i	−0.0970923	−	0.168169i
$370$	2.45232	−	22.4810i	0.127490	−	1.16873i
$371$	−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	0.617796	−	0.786339i	$-0.288026\pi$
$373$	4.74533	+	2.73972i	0.245704	+	0.141857i	−0.372092	+	0.928196i	$0.621359\pi$
$374$	1.78461	−	0.649547i	0.0922802	−	0.0335873i
$375$	−10.4149	+	4.06557i	−0.537826	+	0.209945i
$376$	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	$0.615368\pi$
$380$	9.51653	−	2.10608i	0.488188	−	0.108040i
$381$	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	$-0.681714\pi$
$383$	8.11073	−	22.2840i	0.414439	−	1.13866i	0.954805	−	0.297232i	$-0.0960634\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	1.10486	+	1.15316i	0.0563089	+	0.0587706i
$386$	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	$0.877913\pi$
$390$	6.59355	+	0.719253i	0.333877	+	0.0364208i
$391$	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
$395$	10.4889	−	4.62059i	0.527754	−	0.232487i
$396$	0.328348	+	0.119509i	0.0165001	+	0.00600556i
$397$	12.0630	+	14.3762i	0.605426	+	0.721519i	0.978492	−	0.206286i	$-0.0661378\pi$
$397$	12.0630	+	14.3762i	0.605426	+	0.721519i	−0.373066	+	0.927805i	$0.621693\pi$
$398$			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
$405$	−1.80383	−	1.32144i	−0.0896331	−	0.0656627i
$406$	−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	$0.754513\pi$
$410$	−7.48231	−	3.68588i	−0.369525	−	0.182033i
$411$	−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
$415$	15.0224	−	3.68278i	0.737422	−	0.180781i
$416$	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	$0.375506\pi$
$420$	−4.38846	−	1.27708i	−0.214135	−	0.0623151i
$421$	−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
$425$	−21.5457	+	16.5619i	−1.04512	+	0.803372i
$426$	−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
$430$	−20.9828	+	1.38432i	−1.01188	+	0.0667576i
$431$	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	0.209204	−	0.977872i	$-0.432913\pi$
$433$	1.48447	+	0.261752i	0.0713390	+	0.0125790i	−0.137865	+	0.990451i	$0.544024\pi$
$434$	−5.95312	−	2.16676i	−0.285759	−	0.104008i
$435$	−1.33796	+	4.59765i	−0.0641500	+	0.220440i
$436$	−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	$0.393634\pi$
$440$	0.758858	−	0.186036i	0.0361772	−	0.00886892i
$441$	−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	$0.130993\pi$
$443$	9.92483	+	27.2683i	0.471543	+	1.29555i	−0.444969	+	0.895546i	$0.646785\pi$
$444$	5.05672	−	8.75849i	0.239981	−	0.415660i
$445$	3.97071	−	8.06051i	0.188230	−	0.382105i
$446$	−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	$-0.0159632\pi$
$450$	−4.99543	−	0.213817i	−0.235487	−	0.0100794i
$451$	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	$0.286473\pi$
$457$			33.4908i			1.56663i	−0.621624	+	0.783316i	$0.713527\pi$
$458$	−8.99045	−	10.7144i	−0.420096	−	0.500651i
$459$	−5.10735	−	1.85892i	−0.238390	−	0.0867670i
$460$	6.92171	+	15.7125i	0.322726	+	0.732600i
$461$	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	−0.234521	−	0.972111i	$-0.575352\pi$
$463$	−25.6844	−	14.8289i	−1.19365	−	0.689156i	−0.959133	+	0.282955i	$0.908685\pi$
$464$	1.07071	+	1.85453i	0.0497065	+	0.0860943i
$465$	−6.88964	−	0.751552i	−0.319499	−	0.0348524i
$466$	11.7316	+	9.84401i	0.543458	+	0.456015i
$467$	22.3943	−	12.9294i	1.03629	−	0.598300i	0.117507	−	0.993072i	$-0.462510\pi$
$467$	22.3943	−	12.9294i	1.03629	−	0.598300i	0.918779	+	0.394772i	$0.129176\pi$
$468$	2.56882	+	1.48311i	0.118744	+	0.0685567i
$469$	6.07129	−	2.20977i	0.280346	−	0.102038i
$470$	19.9104	−	19.0764i	0.918399	−	0.879930i
$471$	−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
$475$	19.9493	+	8.77647i	0.915335	+	0.402692i
$476$	−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	$0.982958\pi$
$480$	−1.61459	+	1.54696i	−0.0736957	+	0.0706088i
$481$	−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
$485$	−33.1299	−	3.61396i	−1.50435	−	0.164101i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−12.7030	−	7.33409i	−0.575628	−	0.332339i	0.183766	−	0.982970i	$-0.441171\pi$
$487$	−12.7030	−	7.33409i	−0.575628	−	0.332339i	−0.759394	+	0.650631i	$0.774505\pi$
$488$	−0.492242	−	1.35242i	−0.0222827	−	0.0612213i
$489$	2.74218	+	15.5517i	0.124006	+	0.703271i
$490$	2.54397	+	5.77491i	0.114925	+	0.260884i
$491$	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	$0.815181\pi$
$500$	−9.55074	+	5.81234i	−0.427122	+	0.259936i
$501$	−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	−0.771020	−	0.636811i	$-0.780253\pi$
$503$	−0.224225	+	0.267221i	−0.00999769	+	0.0119148i	0.761022	+	0.648726i	$0.224698\pi$
$504$	−1.56579	−	1.31385i	−0.0697457	−	0.0585236i
$505$	−3.19810	+	6.49211i	−0.142313	+	0.288895i
$506$	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	$-0.0608477\pi$
$510$	−11.8038	+	2.89373i	−0.522680	+	0.128136i
$511$	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
$515$	−7.55061	+	25.9463i	−0.332720	+	1.14333i
$516$	−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
$520$	6.61828	−	0.436632i	0.290231	−	0.0191476i
$521$	−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	−0.559482	−	0.828842i	$-0.689000\pi$
$523$	8.09388	−	9.64592i	0.353921	−	0.421786i	0.913403	+	0.407056i	$0.133445\pi$
$524$	−1.37693	−	2.38491i	−0.0601515	−	0.104185i
$525$	−6.22846	−	8.10270i	−0.271832	−	0.353631i
$526$	−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
$530$	−18.0013	−	5.23854i	−0.781927	−	0.227548i
$531$	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
$535$	25.8784	−	6.34414i	1.11882	−	0.274281i
$536$	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
$540$	−2.00589	−	0.988128i	−0.0863198	−	0.0425223i
$541$	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
$545$	−21.6292	−	15.8449i	−0.926493	−	0.678723i
$546$	1.05282	+	5.97081i	0.0450563	+	0.255527i
$547$	−28.8432	−	5.08583i	−1.23325	−	0.217455i	−0.481227	−	0.876596i	$-0.659809\pi$
$547$	−28.8432	−	5.08583i	−1.23325	−	0.217455i	−0.752019	+	0.659141i	$0.770920\pi$
$548$	−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
$555$	20.6953	−	9.11671i	0.878465	−	0.386983i
$556$	−3.26995	−	18.5448i	−0.138677	−	0.786475i
$557$	8.18614	+	22.4912i	0.346858	+	0.952985i	0.983353	+	0.181704i	$0.0581613\pi$
$557$	8.18614	+	22.4912i	0.346858	+	0.952985i	−0.636495	+	0.771281i	$0.719616\pi$
$558$	−2.68418	−	1.54971i	−0.113630	−	0.0656044i
$559$	13.9475	+	24.1577i	0.589915	+	1.02176i
$560$	−4.54355	−	0.495630i	−0.192000	−	0.0209442i
$561$	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	0.948196	−	0.317685i	$-0.102906\pi$
$563$	27.2196	+	15.7153i	1.14717	+	0.662319i	0.198975	+	0.980005i	$0.436239\pi$
$564$	11.5879	−	4.21763i	0.487937	−	0.177594i
$565$	−8.69652	−	9.07671i	−0.365865	−	0.381860i
$566$	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	$0.365642\pi$
$570$	6.58219	+	7.18852i	0.275698	+	0.301094i
$571$	−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
$575$	−8.27749	+	37.4893i	−0.345195	+	1.56341i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	16.0615	+	9.27314i	0.668651	+	0.386046i	0.795565	−	0.605868i	$-0.207174\pi$
$577$	16.0615	+	9.27314i	0.668651	+	0.386046i	−0.126914	+	0.991914i	$0.540507\pi$
$578$	−10.8604	+	6.27028i	−0.451735	+	0.260809i
$579$	12.2625	+	10.2894i	0.509611	+	0.427614i
$580$	−0.519256	+	4.76013i	−0.0215609	+	0.197654i
$581$	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
$585$	2.67388	+	6.06981i	0.110552	+	0.250956i
$586$	−28.0719	−	10.2173i	−1.15964	−	0.422075i
$587$	19.0043	+	22.6484i	0.784390	+	0.934799i	0.999123	−	0.0418734i	$-0.0133326\pi$
$587$	19.0043	+	22.6484i	0.784390	+	0.934799i	−0.214733	+	0.976673i	$0.568888\pi$
$588$			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	0.152148	−	0.988358i	$-0.451381\pi$
$593$	−1.04512	−	0.184283i	−0.0429181	−	0.00756762i	−0.195066	+	0.980790i	$0.562492\pi$
$594$	0.0606763	+	0.344113i	0.00248958	+	0.0141191i
$595$	−20.0394	−	14.6803i	−0.821534	−	0.601833i
$596$	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	$0.359308\pi$
$600$	−4.95666	+	0.656878i	−0.202355	+	0.0268169i
$601$	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
$605$	5.79153	+	23.6242i	0.235459	+	0.960460i
$606$	−2.47932	+	2.08039i	−0.100715	+	0.0845103i
$607$			48.3685i			1.96322i	0.190907	+	0.981608i	$0.438857\pi$
$607$			48.3685i			1.96322i	−0.190907	+	0.981608i	$0.561143\pi$
$608$	4.35778	+	0.0985628i	0.176731	+	0.00399725i
$609$	−4.37705			−0.177367
$610$	0.899219	−	3.09001i	0.0364083	−	0.125111i
$611$	−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	0.495651	−	0.868522i	$-0.334929\pi$
$613$	31.1581	−	5.49401i	1.25846	−	0.221901i	0.762812	+	0.646621i	$0.223818\pi$
$614$	−10.8747	+	3.95807i	−0.438868	+	0.159735i
$615$	−0.549087	−	8.32281i	−0.0221413	−	0.335608i
$616$	0.357107	+	0.618527i	0.0143882	+	0.0249212i
$617$	3.30517	−	3.93895i	0.133061	−	0.158576i	−0.695400	−	0.718623i	$-0.744773\pi$
$617$	3.30517	−	3.93895i	0.133061	−	0.158576i	0.828461	+	0.560047i	$0.189217\pi$
$618$	−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	$0.970302\pi$
$620$	−6.91548	+	0.456239i	−0.277732	+	0.0183230i
$621$	−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
$625$	−24.9086	−	2.13622i	−0.996343	−	0.0854487i
$626$	−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
$630$	−1.08825	−	4.43905i	−0.0433567	−	0.176856i
$631$	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
$635$	22.1865	+	10.9294i	0.880444	+	0.433718i
$636$	−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
$640$	−1.32144	+	1.80383i	−0.0522343	+	0.0713027i
$641$	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	$-0.742930\pi$
$643$	7.67785	−	21.0947i	0.302785	−	0.831894i	0.994013	−	0.109258i	$-0.0348475\pi$
$644$	−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	$0.121910\pi$
$647$			19.0108i			0.747393i	−0.927551	+	0.373697i	$0.878090\pi$
$648$	−0.642788	−	0.766044i	−0.0252511	−	0.0300931i
$649$	−2.99528	−	1.09019i	−0.117575	−	0.0427938i
$650$	12.5152	+	7.95802i	0.490888	+	0.312139i
$651$	−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	0.352547	−	0.935794i	$-0.385316\pi$
$653$	−7.19600	−	4.15461i	−0.281601	−	0.162582i	−0.634148	+	0.773212i	$0.718649\pi$
$654$	−5.99535	−	10.3843i	−0.234437	−	0.406056i
$655$	0.667761	−	6.12151i	0.0260916	−	0.239187i
$656$	−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	$0.159705\pi$
$660$	0.540541	+	0.564173i	0.0210405	+	0.0219604i
$661$	−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
$665$	−2.60767	+	19.7510i	−0.101121	+	0.765909i
$666$	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
$670$	5.10363	−	4.88986i	0.197171	−	0.188912i
$671$	−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	−0.675307	−	0.737536i	$-0.735989\pi$
$673$	−9.70852	+	5.60522i	−0.374236	+	0.216065i	0.301071	+	0.953602i	$0.402656\pi$
$674$	−19.0694	−	16.0011i	−0.734525	−	0.616340i
$675$	−2.31254	−	4.43307i	−0.0890098	−	0.170629i
$676$	2.10077	+	3.63865i	0.0807990	+	0.139948i
$677$	−31.5618	−	18.2222i	−1.21302	−	0.700337i	−0.249603	−	0.968348i	$-0.580300\pi$
$677$	−31.5618	−	18.2222i	−1.21302	−	0.700337i	−0.963416	+	0.268012i	$0.913633\pi$
$678$	−1.92273	−	5.28265i	−0.0738419	−	0.202879i
$679$	−5.28997	−	30.0009i	−0.203010	−	1.15133i
$680$	−11.1220	+	4.89947i	−0.426508	+	0.187886i
$681$	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	$-0.991167\pi$
$683$		−	1.45032i		−	0.0554950i	0.999615	−	0.0277475i	$-0.00883344\pi$
$684$	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
$690$	−10.1466	+	13.8506i	−0.386274	+	0.527285i
$691$	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
$695$	18.6073	−	37.7727i	0.705817	−	1.43280i
$696$	−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
$700$	−7.54085	−	6.89804i	−0.285017	−	0.260721i
$701$	−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
$705$	26.4759	+	7.70471i	0.997139	+	0.290176i
$706$	−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	$0.634930\pi$
$710$	−2.05611	−	31.1656i	−0.0771643	−	1.16962i
$711$	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
$715$	−0.152569	−	2.31257i	−0.00570574	−	0.0864851i
$716$	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	$0.434338\pi$
$720$	−2.14700	−	0.624797i	−0.0800141	−	0.0232848i
$721$	−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
$725$	−7.22686	+	7.90031i	−0.268399	+	0.293410i
$726$	−1.88893	+	10.7126i	−0.0701047	+	0.397584i
$727$	−14.6821	+	2.58886i	−0.544531	+	0.0960155i	−0.439145	−	0.898416i	$-0.644719\pi$
$727$	−14.6821	+	2.58886i	−0.544531	+	0.0960155i	−0.105385	+	0.994431i	$0.533608\pi$
$728$	2.07364	+	5.69728i	0.0768542	+	0.211155i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	10.2978	−	20.9045i	0.381140	−	0.773711i
$731$	−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	−0.964796	−	0.263001i	$-0.915288\pi$
$733$	−33.0148	+	19.0611i	−1.21943	+	0.704037i	−0.254633	+	0.967038i	$0.581955\pi$
$734$	−13.2366	+	22.9265i	−0.488574	+	0.846234i
$735$	−3.72923	+	5.09060i	−0.137555	+	0.187770i
$736$	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	$-0.926943\pi$
$743$	−28.0412	−	33.4182i	−1.02873	−	1.22599i	−0.0549550	−	0.998489i	$-0.517502\pi$
$744$	−2.91250	−	1.06006i	−0.106777	−	0.0388638i
$745$	17.7421	−	7.81580i	0.650021	−	0.286349i
$746$	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
$750$	−9.80901	−	5.36502i	−0.358174	−	0.195903i
$751$	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
$755$	−0.875596	+	0.838920i	−0.0318662	+	0.0305314i
$756$	0.354935	−	2.01294i	0.0129089	−	0.0732098i
$757$	−5.49557	+	15.0989i	−0.199740	+	0.548781i	−0.998609	−	0.0527240i	$-0.983210\pi$
$757$	−5.49557	+	15.0989i	−0.199740	+	0.548781i	0.798869	+	0.601505i	$0.205432\pi$
$758$	−8.87366	−	10.5752i	−0.322306	−	0.384109i
$759$	2.68301			0.0973873
$760$	7.73046	+	5.93632i	0.280413	+	0.215333i
$761$	−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
$765$	−8.40793	−	8.77551i	−0.303989	−	0.317279i
$766$	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	$-0.563686\pi$
$770$	−0.173184	+	1.58761i	−0.00624110	+	0.0572135i
$771$	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	$-0.885140\pi$
$773$	−12.3954	−	34.0562i	−0.445833	−	1.22492i	0.489766	−	0.871854i	$-0.337082\pi$
$774$	−1.63302	−	9.26134i	−0.0586979	−	0.332892i
$775$	−13.0772	−	8.31538i	−0.469748	−	0.298697i
$776$	−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
$785$	−8.10396	+	11.0623i	−0.289243	+	0.394832i
$786$	1.37693	−	2.38491i	0.0491135	−	0.0850671i
$787$	−10.7802	+	6.22393i	−0.384271	+	0.221859i	−0.679675	−	0.733513i	$-0.737879\pi$
$787$	−10.7802	+	6.22393i	−0.384271	+	0.221859i	0.295404	+	0.955372i	$0.404546\pi$
$788$	3.95638	−	4.71503i	0.140940	−	0.167966i
$789$	−10.3718	−	8.70300i	−0.369247	−	0.309835i
$790$	10.2817	+	5.06491i	0.365807	+	0.180201i
$791$	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
$795$	−4.46395	−	18.2089i	−0.158320	−	0.645802i
$796$	−6.01269	+	5.04524i	−0.213114	+	0.178824i
$797$			31.2905i			1.10837i	0.832394	+	0.554184i	$0.186970\pi$
$797$			31.2905i			1.10837i	−0.832394	+	0.554184i	$0.813030\pi$
$798$	−4.62810	+	7.61319i	−0.163833	+	0.269504i
$799$	67.0234			2.37112
$800$	−4.76729	+	1.50761i	−0.168549	+	0.0533022i
$801$	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
$805$	−35.0183	+	2.31028i	−1.23423	+	0.0814268i
$806$	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	$0.677229\pi$
$810$	−0.147202	−	2.23122i	−0.00517214	−	0.0783970i
$811$	−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
$815$	−9.86653	+	33.9046i	−0.345610	+	1.18763i
$816$	−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
$820$	−1.98599	−	8.10102i	−0.0693536	−	0.282900i
$821$	−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	$-0.992670\pi$
$823$	−7.13452	−	19.6019i	−0.248694	−	0.683280i	0.751041	−	0.660255i	$-0.229552\pi$
$824$	−6.04245	+	10.4658i	−0.210499	+	0.364595i
$825$	0.229527	+	1.73196i	0.00799110	+	0.0602992i
$826$	14.2835	+	11.9853i	0.496987	+	0.417022i
$827$	9.63949	−	11.4879i	0.335198	−	0.399474i	−0.571948	−	0.820290i	$-0.693812\pi$
$827$	9.63949	−	11.4879i	0.335198	−	0.399474i	0.907146	+	0.420817i	$0.138256\pi$
$828$	−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	$0.0689768\pi$
$830$	12.4774	+	9.14060i	0.433097	+	0.317275i
$831$	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	$0.629886\pi$
$840$	−1.84255	−	4.18264i	−0.0635739	−	0.144315i
$841$	−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
$845$	−1.01880	+	9.33955i	−0.0350477	+	0.321290i
$846$	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
$850$	−26.5365	−	5.85915i	−0.910194	−	0.200967i
$851$	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	0.608406	−	0.793626i	$-0.291809\pi$
$853$	−8.14303	−	9.70448i	−0.278812	−	0.332275i	−0.887218	+	0.461351i	$0.847365\pi$
$854$	2.94175			0.100665
$855$	−2.93435	+	9.29460i	−0.100353	+	0.317869i
$856$	11.9159			0.407275
$857$	−20.8253	−	24.8187i	−0.711379	−	0.847789i	0.282384	−	0.959302i	$-0.408875\pi$
$857$	−20.8253	−	24.8187i	−0.711379	−	0.847789i	−0.993763	+	0.111513i	$0.964430\pi$
$858$	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	$-0.146840\pi$
$860$	−14.5480	−	15.1840i	−0.496081	−	0.517769i
$861$	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	−0.627327	−	0.778756i	$-0.715851\pi$
$863$	−7.83091	+	4.52118i	−0.266567	+	0.153903i	0.360759	+	0.932659i	$0.382518\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	−28.2618	−	3.08292i	−0.960930	−	0.104822i
$866$	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
$870$	−4.38202	+	1.93038i	−0.148564	+	0.0654459i
$871$	−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	$-0.628534\pi$
$877$	14.7824	−	40.6142i	0.499165	−	1.37144i	0.892083	−	0.451871i	$-0.149243\pi$
$878$	−14.6910	−	2.59041i	−0.495796	−	0.0874222i
$879$	−5.18748	−	29.4197i	−0.174969	−	0.992301i
$880$	0.630297	+	0.461738i	0.0212473	+	0.0155652i
$881$	−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	−0.918377	−	0.395707i	$-0.870500\pi$
$883$	−10.9711	+	13.0748i	−0.369207	+	0.440004i	0.549170	+	0.835711i	$0.314944\pi$
$884$	12.3500	+	10.3629i	0.415375	+	0.348541i
$885$	18.2983	+	9.01397i	0.615090	+	0.303001i
$886$	−14.5091	+	25.1306i	−0.487444	+	0.844278i
$887$	14.7764	+	40.5978i	0.496143	+	1.36314i	0.894974	+	0.446118i	$0.147194\pi$
$887$	14.7764	+	40.5978i	0.496143	+	1.36314i	−0.398831	+	0.917024i	$0.630584\pi$
$888$	9.95979	−	1.75618i	0.334229	−	0.0589335i
$889$	−3.92582	+	22.2644i	−0.131668	+	0.746725i
$890$	8.72704	−	2.13945i	0.292531	−	0.0717147i
$891$	−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
$895$	37.9599	+	11.0467i	1.26886	+	0.369249i
$896$	−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
$900$	−3.04720	−	3.96416i	−0.101573	−	0.132139i
$901$	−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
$905$	−7.87166	+	0.519322i	−0.261663	+	0.0172629i
$906$	−0.509597	+	0.185478i	−0.0169302	+	0.00616210i
$907$	−47.3246	+	8.34461i	−1.57139	+	0.277078i	−0.890387	−	0.455204i	$-0.849566\pi$
$907$	−47.3246	+	8.34461i	−1.57139	+	0.277078i	−0.681001	+	0.732282i	$0.738455\pi$
$908$	6.43989	+	1.13553i	0.213715	+	0.0376838i
$909$	−3.04133	−	1.10695i	−0.100875	−	0.0367154i
$910$	−3.78809	+	13.0171i	−0.125574	+	0.431513i
$911$	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
$915$	3.12563	−	0.766257i	0.103330	−	0.0253317i
$916$	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	$0.327124\pi$
$920$	−7.58730	+	15.4022i	−0.250146	+	0.507794i
$921$	−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
$925$	50.5209	+	2.16243i	1.66112	+	0.0711002i
$926$	−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
$935$	1.71198	+	3.88625i	0.0559877	+	0.127094i
$936$	0.515078	+	2.92115i	0.0168359	+	0.0954809i
$937$	−9.48853	−	26.0695i	−0.309977	−	0.851654i	−0.992660	−	0.120940i	$-0.961409\pi$
$937$	−9.48853	−	26.0695i	−0.309977	−	0.851654i	0.682683	−	0.730715i	$-0.260813\pi$
$938$	5.59533	+	3.23047i	0.182694	+	0.105479i
$939$	−12.6943	−	21.9872i	−0.414263	−	0.717525i
$940$	27.4115	+	2.99017i	0.894066	+	0.0975286i
$941$	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
$945$	3.30021	−	3.16197i	0.107356	−	0.102859i
$946$	−0.570613	+	3.23611i	−0.0185522	+	0.105215i
$947$	−5.96764	+	16.3960i	−0.193922	+	0.532797i	−0.998102	−	0.0615897i	$-0.980383\pi$
$947$	−5.96764	+	16.3960i	−0.193922	+	0.532797i	0.804179	+	0.594387i	$0.202605\pi$
$948$	3.29478	+	3.92656i	0.107009	+	0.127529i
$949$	−30.9126			−1.00347
$950$	6.09998	+	20.9234i	0.197909	+	0.678846i
$951$	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	$-0.642544\pi$
$953$	14.7594	−	40.5511i	0.478104	−	1.31358i	0.911100	−	0.412184i	$-0.135234\pi$
$954$	1.45593	−	8.25701i	0.0471376	−	0.267331i
$955$	17.6094	−	16.8718i	0.569828	−	0.545959i
$956$	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
$960$	−2.22288	−	0.242482i	−0.0717432	−	0.00782606i
$961$	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
$965$	14.4299	+	32.7564i	0.464515	+	1.05447i
$966$	−14.7482	−	5.36790i	−0.474515	−	0.172709i
$967$	−6.80451	−	8.10930i	−0.218818	−	0.260778i	0.645457	−	0.763797i	$-0.276667\pi$
$967$	−6.80451	−	8.10930i	−0.218818	−	0.260778i	−0.864275	+	0.503019i	$0.832223\pi$
$968$			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
$975$	−0.634229	+	14.8175i	−0.0203116	+	0.474541i
$976$	0.719609	−	1.24640i	0.0230341	−	0.0398963i
$977$	4.70569	−	2.71683i	0.150548	−	0.0869191i	−0.422833	−	0.906207i	$-0.638964\pi$
$977$	4.70569	−	2.71683i	0.150548	−	0.0869191i	0.573382	+	0.819288i	$0.305631\pi$
$978$	−10.1506	+	12.0971i	−0.324581	+	0.386821i
$979$	−1.07562	−	0.902551i	−0.0343769	−	0.0288457i
$980$	−2.78860	+	5.66084i	−0.0890786	+	0.180829i
$981$	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	−0.384797	−	0.923001i	$-0.625728\pi$
$983$	−13.5037	+	2.38107i	−0.430702	+	0.0759445i	−0.0459057	+	0.998946i	$0.514617\pi$
$984$	0.647737	−	3.67350i	0.0206491	−	0.117107i
$985$	13.3673	−	3.27702i	0.425916	−	0.104414i
$986$	−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
$990$	−0.218317	+	0.750209i	−0.00693858	+	0.0238432i
$991$	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
$995$	−17.5128	+	1.15539i	−0.555194	+	0.0366282i
$996$	3.45858	+	5.99044i	0.109589	+	0.189814i
$997$	28.8756	−	34.4126i	0.914500	−	1.08986i	−0.0811511	−	0.996702i	$-0.525860\pi$
$997$	28.8756	−	34.4126i	0.914500	−	1.08986i	0.995651	−	0.0931572i	$-0.0296959\pi$
$998$	−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.139.6	yes	60
5.4	even	2	inner	570.2.bc.b.139.5	✓	60
19.16	even	9	inner	570.2.bc.b.529.5	yes	60
95.54	even	18	inner	570.2.bc.b.529.6	yes	60

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

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.61459 + 1.54696i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-1.77015 - 1.02199i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.61459 + 1.54696i) 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} +(-2.22288 - 0.242482i) 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} +(-0.901446 - 2.04631i) 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} +(0.213817 - 4.99543i) 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} +(0.988128 - 2.00589i) 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} +(4.43905 - 1.08825i) q^{35} +(0.766044 - 0.642788i) q^{36} +10.1134i q^{37} +(-4.12869 + 1.39783i) q^{38} -2.96622 q^{39} +(0.624797 - 2.14700i) 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} +(2.23122 - 0.147202i) 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} +(3.96416 - 3.04720i) 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} +(-0.750209 - 0.218317i) q^{55} +2.04399 q^{56} +(-3.27490 - 2.87663i) q^{57} -2.14142i q^{58} +(-6.98806 + 5.86368i) q^{59} +(2.17176 - 0.532412i) 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} +(-5.94991 - 2.93100i) 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} +(3.68701 + 2.70100i) 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} +(2.04631 - 0.901446i) 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} +(12.0816 + 1.31792i) 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} +(1.54696 + 1.61459i) q^{90} +(1.05282 - 5.97081i) q^{91} +(2.62619 - 7.21539i) q^{92} +(1.99227 + 2.37429i) q^{93} -12.3315 q^{94} +(-3.72662 - 9.00624i) 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

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