LMFDB - Embedded newform 1710.2.t.c.1189.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(919,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1710.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 $ x^20 - 49x^16 - 8x^15 + 72x^13 + 2145x^12 - 648x^11 + 32x^10 - 7056x^9 - 11968x^8 + 10368x^7 + 9344x^6 + 18176x^5 + 56320x^4 + 28160x^3 + 8192x^2 + 4096*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1189.3
Root			$0.686074 - 2.56046i$ of defining polynomial
Character	$\chi$	$=$	1710.1189
Dual form			1710.2.t.c.919.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.118742 + 2.23291i) q^{5} +2.79875i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.118742 + 2.23291i) q^{5} +2.79875i q^{7} -1.00000i q^{8} +(1.01362 - 1.99313i) q^{10} -4.02666 q^{11} +(0.0960560 - 0.0554580i) q^{13} +(1.39938 - 2.42379i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.68457 - 2.12729i) q^{17} +(0.163933 - 4.35582i) q^{19} +(-1.87439 + 1.21929i) q^{20} +(3.48719 + 2.01333i) q^{22} +(-7.65779 + 4.42123i) q^{23} +(-4.97180 + 0.530281i) q^{25} -0.110916 q^{26} +(-2.42379 + 1.39938i) q^{28} +(-0.907996 - 1.57270i) q^{29} +7.88104 q^{31} +(0.866025 - 0.500000i) q^{32} +(2.12729 + 3.68457i) q^{34} +(-6.24938 + 0.332330i) q^{35} +1.68176i q^{37} +(-2.31988 + 3.69028i) q^{38} +(2.23291 - 0.118742i) q^{40} +(3.88203 - 6.72386i) q^{41} +(-6.46509 - 3.73262i) q^{43} +(-2.01333 - 3.48719i) q^{44} +8.84246 q^{46} +(4.17060 - 2.40790i) q^{47} -0.833029 q^{49} +(4.57085 + 2.02666i) q^{50} +(0.0960560 + 0.0554580i) q^{52} +(6.45034 - 3.72410i) q^{53} +(-0.478134 - 8.99119i) q^{55} +2.79875 q^{56} +1.81599i q^{58} +(0.188606 - 0.326675i) q^{59} +(-6.18078 - 10.7054i) q^{61} +(-6.82518 - 3.94052i) q^{62} -1.00000 q^{64} +(0.135239 + 0.207900i) q^{65} +(-3.82862 + 2.21046i) q^{67} -4.25457i q^{68} +(5.57828 + 2.83688i) q^{70} +(5.90675 - 10.2308i) q^{71} +(8.33460 + 4.81199i) q^{73} +(0.840881 - 1.45645i) q^{74} +(3.85421 - 2.03594i) q^{76} -11.2696i q^{77} +(-2.11845 + 3.66927i) q^{79} +(-1.99313 - 1.01362i) q^{80} +(-6.72386 + 3.88203i) q^{82} +8.25792i q^{83} +(4.31253 - 8.47992i) q^{85} +(3.73262 + 6.46509i) q^{86} +4.02666i q^{88} +(-5.01501 - 8.68625i) q^{89} +(0.155213 + 0.268837i) q^{91} +(-7.65779 - 4.42123i) q^{92} -4.81579 q^{94} +(9.74562 - 0.151171i) q^{95} +(-4.52207 - 2.61082i) q^{97} +(0.721424 + 0.416515i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4}+O(q^{10}) $ 20 * q + 10 * q^4	$ 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) $ 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.118742	+	2.23291i	0.0531030	+	0.998589i
$5$	0.118742	+	2.23291i	0.0531030	+	0.998589i
$6$		0			0
$7$			2.79875i			1.05783i	0.848675	+	0.528915i	$0.177401\pi$
$7$			2.79875i			1.05783i	−0.848675	+	0.528915i	$0.822599\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.01362	−	1.99313i	0.320536	−	0.630283i
$11$	−4.02666			−1.21408			−0.607042	−	0.794669i	$-0.707644\pi$
$11$	−4.02666			−1.21408			−0.607042	+	0.794669i	$0.707644\pi$
$12$		0			0
$13$	0.0960560	−	0.0554580i	0.0266411	−	0.0153813i	−0.486620	−	0.873614i	$-0.661770\pi$
$13$	0.0960560	−	0.0554580i	0.0266411	−	0.0153813i	0.513261	+	0.858232i	$0.328437\pi$
$14$	1.39938	−	2.42379i	0.373999	−	0.647786i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.68457	−	2.12729i	−0.893639	−	0.515943i	−0.0185079	−	0.999829i	$-0.505892\pi$
$17$	−3.68457	−	2.12729i	−0.893639	−	0.515943i	−0.875131	+	0.483886i	$0.839225\pi$
$18$		0			0
$19$	0.163933	−	4.35582i	0.0376087	−	0.999293i
$19$	0.163933	−	4.35582i	0.0376087	−	0.999293i
$20$	−1.87439	+	1.21929i	−0.419126	+	0.272642i
$21$		0			0
$22$	3.48719	+	2.01333i	0.743472	+	0.429244i
$23$	−7.65779	+	4.42123i	−1.59676	+	0.921890i	−0.604654	+	0.796489i	$0.706688\pi$
$23$	−7.65779	+	4.42123i	−1.59676	+	0.921890i	−0.992106	+	0.125401i	$0.959978\pi$
$24$		0			0
$25$	−4.97180	+	0.530281i	−0.994360	+	0.106056i
$26$	−0.110916			−0.0217524
$27$		0			0
$28$	−2.42379	+	1.39938i	−0.458054	+	0.264457i
$29$	−0.907996	−	1.57270i	−0.168611	−	0.292042i	0.769321	−	0.638862i	$-0.220595\pi$
$29$	−0.907996	−	1.57270i	−0.168611	−	0.292042i	−0.937932	+	0.346820i	$0.887261\pi$
$30$		0			0
$31$	7.88104			1.41548			0.707739	−	0.706474i	$-0.249715\pi$
$31$	7.88104			1.41548			0.707739	+	0.706474i	$0.249715\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	2.12729	+	3.68457i	0.364827	+	0.631898i
$35$	−6.24938	+	0.332330i	−1.05634	+	0.0561740i
$36$		0			0
$37$			1.68176i			0.276480i	0.990399	+	0.138240i	$0.0441445\pi$
$37$			1.68176i			0.276480i	−0.990399	+	0.138240i	$0.955855\pi$
$38$	−2.31988	+	3.69028i	−0.376334	+	0.598643i
$39$		0			0
$40$	2.23291	−	0.118742i	0.353055	−	0.0187747i
$41$	3.88203	−	6.72386i	0.606270	−	1.05009i	−0.385579	−	0.922675i	$-0.625998\pi$
$41$	3.88203	−	6.72386i	0.606270	−	1.05009i	0.991849	−	0.127416i	$-0.0406684\pi$
$42$		0			0
$43$	−6.46509	−	3.73262i	−0.985917	−	0.569219i	−0.0818657	−	0.996643i	$-0.526088\pi$
$43$	−6.46509	−	3.73262i	−0.985917	−	0.569219i	−0.904051	+	0.427424i	$0.859421\pi$
$44$	−2.01333	−	3.48719i	−0.303521	−	0.525714i
$45$		0			0
$46$	8.84246			1.30375
$47$	4.17060	−	2.40790i	0.608344	−	0.351228i	−0.163973	−	0.986465i	$-0.552431\pi$
$47$	4.17060	−	2.40790i	0.608344	−	0.351228i	0.772317	+	0.635237i	$0.219098\pi$
$48$		0			0
$49$	−0.833029			−0.119004
$50$	4.57085	+	2.02666i	0.646415	+	0.286614i
$51$		0			0
$52$	0.0960560	+	0.0554580i	0.0133206	+	0.00769064i
$53$	6.45034	−	3.72410i	0.886022	−	0.511545i	0.0133827	−	0.999910i	$-0.495740\pi$
$53$	6.45034	−	3.72410i	0.886022	−	0.511545i	0.872639	+	0.488365i	$0.162407\pi$
$54$		0			0
$55$	−0.478134	−	8.99119i	−0.0644716	−	1.21237i
$56$	2.79875			0.373999
$57$		0			0
$58$			1.81599i			0.238451i
$59$	0.188606	−	0.326675i	0.0245544	−	0.0425294i	−0.853487	−	0.521114i	$-0.825517\pi$
$59$	0.188606	−	0.326675i	0.0245544	−	0.0425294i	0.878041	+	0.478585i	$0.158850\pi$
$60$		0			0
$61$	−6.18078	−	10.7054i	−0.791368	−	1.37069i	−0.925120	−	0.379674i	$-0.876036\pi$
$61$	−6.18078	−	10.7054i	−0.791368	−	1.37069i	0.133752	−	0.991015i	$-0.457297\pi$
$62$	−6.82518	−	3.94052i	−0.866799	−	0.500447i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.135239	+	0.207900i	0.0167743	+	0.0257868i
$66$		0			0
$67$	−3.82862	+	2.21046i	−0.467741	+	0.270050i	−0.715293	−	0.698824i	$-0.753707\pi$
$67$	−3.82862	+	2.21046i	−0.467741	+	0.270050i	0.247553	+	0.968874i	$0.420374\pi$
$68$		−	4.25457i		−	0.515943i
$69$		0			0
$70$	5.57828	+	2.83688i	0.666732	+	0.339072i
$71$	5.90675	−	10.2308i	0.701002	−	1.21417i	−0.267113	−	0.963665i	$-0.586070\pi$
$71$	5.90675	−	10.2308i	0.701002	−	1.21417i	0.968115	−	0.250506i	$-0.0805969\pi$
$72$		0			0
$73$	8.33460	+	4.81199i	0.975492	+	0.563200i	0.900906	−	0.434014i	$-0.142903\pi$
$73$	8.33460	+	4.81199i	0.975492	+	0.563200i	0.0745857	+	0.997215i	$0.476237\pi$
$74$	0.840881	−	1.45645i	0.0977504	−	0.169309i
$75$		0			0
$76$	3.85421	−	2.03594i	0.442109	−	0.233538i
$77$		−	11.2696i		−	1.28430i
$78$		0			0
$79$	−2.11845	+	3.66927i	−0.238344	+	0.412825i	−0.960239	−	0.279178i	$-0.909938\pi$
$79$	−2.11845	+	3.66927i	−0.238344	+	0.412825i	0.721895	+	0.692003i	$0.243271\pi$
$80$	−1.99313	−	1.01362i	−0.222839	−	0.113326i
$81$		0			0
$82$	−6.72386	+	3.88203i	−0.742527	+	0.428698i
$83$			8.25792i			0.906425i	0.891403	+	0.453212i	$0.149722\pi$
$83$			8.25792i			0.906425i	−0.891403	+	0.453212i	$0.850278\pi$
$84$		0			0
$85$	4.31253	−	8.47992i	0.467760	−	0.919776i
$86$	3.73262	+	6.46509i	0.402499	+	0.697149i
$87$		0			0
$88$			4.02666i			0.429244i
$89$	−5.01501	−	8.68625i	−0.531590	−	0.920740i	−0.999320	−	0.0368691i	$-0.988262\pi$
$89$	−5.01501	−	8.68625i	−0.531590	−	0.920740i	0.467730	−	0.883871i	$-0.345072\pi$
$90$		0			0
$91$	0.155213	+	0.268837i	0.0162708	+	0.0281818i
$92$	−7.65779	−	4.42123i	−0.798380	−	0.460945i
$93$		0			0
$94$	−4.81579			−0.496711
$95$	9.74562	−	0.151171i	0.999880	−	0.0155098i
$96$		0			0
$97$	−4.52207	−	2.61082i	−0.459146	−	0.265088i	0.252539	−	0.967587i	$-0.418734\pi$
$97$	−4.52207	−	2.61082i	−0.459146	−	0.265088i	−0.711685	+	0.702499i	$0.752068\pi$
$98$	0.721424	+	0.416515i	0.0728749	+	0.0420743i
$99$		0			0
$100$	−2.94514	−	4.04057i	−0.294514	−	0.404057i
$101$	5.86577	+	10.1598i	0.583666	+	1.01094i	0.995040	+	0.0994725i	$0.0317155\pi$
$101$	5.86577	+	10.1598i	0.583666	+	1.01094i	−0.411374	+	0.911466i	$0.634951\pi$
$102$		0			0
$103$		−	17.9496i		−	1.76863i	−0.466890	−	0.884315i	$-0.654626\pi$
$103$		−	17.9496i		−	1.76863i	0.466890	−	0.884315i	$-0.345374\pi$
$104$	−0.0554580	−	0.0960560i	−0.00543810	−	0.00941907i
$105$		0			0
$106$	−7.44821			−0.723434
$107$			15.1358i			1.46324i	0.681714	+	0.731619i	$0.261235\pi$
$107$			15.1358i			1.46324i	−0.681714	+	0.731619i	$0.738765\pi$
$108$		0			0
$109$	−4.29258	+	7.43496i	−0.411154	+	0.712140i	−0.995016	−	0.0997127i	$-0.968208\pi$
$109$	−4.29258	+	7.43496i	−0.411154	+	0.712140i	0.583862	+	0.811853i	$0.301541\pi$
$110$	−4.08152	+	8.02567i	−0.389158	+	0.765217i
$111$		0			0
$112$	−2.42379	−	1.39938i	−0.229027	−	0.132229i
$113$		−	1.24691i		−	0.117299i	−0.998279	−	0.0586497i	$-0.981321\pi$
$113$		−	1.24691i		−	0.117299i	0.998279	−	0.0586497i	$-0.0186795\pi$
$114$		0			0
$115$	−10.7815	−	16.5742i	−1.00538	−	1.54555i
$116$	0.907996	−	1.57270i	0.0843053	−	0.146021i
$117$		0			0
$118$	−0.326675	+	0.188606i	−0.0300728	+	0.0173626i
$119$	5.95375	−	10.3122i	0.545780	−	0.945318i
$120$		0			0
$121$	5.21402			0.474002
$122$			12.3616i			1.11916i
$123$		0			0
$124$	3.94052	+	6.82518i	0.353869	+	0.612920i
$125$	−1.77443	−	11.0386i	−0.158710	−	0.987325i
$126$		0			0
$127$	−11.9143	+	6.87872i	−1.05722	+	0.610388i	−0.924663	−	0.380787i	$-0.875653\pi$
$127$	−11.9143	+	6.87872i	−1.05722	+	0.610388i	−0.132560	+	0.991175i	$0.542320\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−0.0131704	−	0.247666i	−0.00115512	−	0.0217217i
$131$	−6.42860	+	11.1347i	−0.561669	+	0.972840i	0.435682	+	0.900101i	$0.356507\pi$
$131$	−6.42860	+	11.1347i	−0.561669	+	0.972840i	−0.997351	+	0.0727388i	$0.976826\pi$
$132$		0			0
$133$	12.1909	+	0.458807i	1.05708	+	0.0397836i
$134$	4.42091			0.381909
$135$		0			0
$136$	−2.12729	+	3.68457i	−0.182413	+	0.315949i
$137$	−7.06060	+	4.07644i	−0.603228	+	0.348274i	−0.770310	−	0.637669i	$-0.779899\pi$
$137$	−7.06060	+	4.07644i	−0.603228	+	0.348274i	0.167082	+	0.985943i	$0.446565\pi$
$138$		0			0
$139$	1.14277	+	1.97934i	0.0969289	+	0.167886i	0.910412	−	0.413703i	$-0.135765\pi$
$139$	1.14277	+	1.97934i	0.0969289	+	0.167886i	−0.813483	+	0.581589i	$0.802431\pi$
$140$	−3.41249	−	5.24595i	−0.288408	−	0.443364i
$141$		0			0
$142$	−10.2308	+	5.90675i	−0.858549	+	0.495683i
$143$	−0.386785	+	0.223311i	−0.0323446	+	0.0186742i
$144$		0			0
$145$	3.40388	−	2.21422i	0.282676	−	0.183881i
$146$	−4.81199	−	8.33460i	−0.398243	−	0.689777i
$147$		0			0
$148$	−1.45645	+	0.840881i	−0.119719	+	0.0691200i
$149$	9.36462	−	16.2200i	0.767180	−	1.32879i	−0.171907	−	0.985113i	$-0.554993\pi$
$149$	9.36462	−	16.2200i	0.767180	−	1.32879i	0.939086	−	0.343681i	$-0.111674\pi$
$150$		0			0
$151$	−16.1394			−1.31341			−0.656703	−	0.754150i	$-0.728049\pi$
$151$	−16.1394			−1.31341			−0.656703	+	0.754150i	$0.728049\pi$
$152$	−4.35582	−	0.163933i	−0.353303	−	0.0132967i
$153$		0			0
$154$	−5.63482	+	9.75980i	−0.454067	+	0.786467i
$155$	0.935810	+	17.5977i	0.0751661	+	1.41348i
$156$		0			0
$157$	−6.73626	−	3.88918i	−0.537612	−	0.310390i	0.206499	−	0.978447i	$-0.433793\pi$
$157$	−6.73626	−	3.88918i	−0.537612	−	0.310390i	−0.744110	+	0.668057i	$0.767126\pi$
$158$	3.66927	−	2.11845i	0.291911	−	0.168535i
$159$		0			0
$160$	1.21929	+	1.87439i	0.0963933	+	0.148183i
$161$	−12.3739	−	21.4323i	−0.975202	−	1.68910i
$162$		0			0
$163$		−	1.99824i		−	0.156514i	−0.996933	−	0.0782570i	$-0.975065\pi$
$163$		−	1.99824i		−	0.156514i	0.996933	−	0.0782570i	$-0.0249355\pi$
$164$	7.76405			0.606270
$165$		0			0
$166$	4.12896	−	7.15157i	0.320470	−	0.555069i
$167$	−15.5791	+	8.99462i	−1.20555	+	0.696024i	−0.961784	−	0.273810i	$-0.911716\pi$
$167$	−15.5791	+	8.99462i	−1.20555	+	0.696024i	−0.243766	+	0.969834i	$0.578383\pi$
$168$		0			0
$169$	−6.49385	+	11.2477i	−0.499527	+	0.865206i
$170$	−7.97472	+	5.18756i	−0.611633	+	0.397868i
$171$		0			0
$172$		−	7.46524i		−	0.569219i
$173$	−13.2653	−	7.65871i	−1.00854	−	0.582281i	−0.0977767	−	0.995208i	$-0.531173\pi$
$173$	−13.2653	−	7.65871i	−1.00854	−	0.582281i	−0.910764	+	0.412927i	$0.864506\pi$
$174$		0			0
$175$	−1.48413	−	13.9149i	−0.112189	−	1.05186i
$176$	2.01333	−	3.48719i	0.151761	−	0.262857i
$177$		0			0
$178$			10.0300i			0.751781i
$179$	−10.8958			−0.814389			−0.407195	−	0.913341i	$-0.633493\pi$
$179$	−10.8958			−0.814389			−0.407195	+	0.913341i	$0.633493\pi$
$180$		0			0
$181$	−9.12604	−	15.8068i	−0.678333	−	1.17491i	−0.975483	−	0.220076i	$-0.929369\pi$
$181$	−9.12604	−	15.8068i	−0.678333	−	1.17491i	0.297150	−	0.954831i	$-0.403964\pi$
$182$		−	0.310427i		−	0.0230103i
$183$		0			0
$184$	4.42123	+	7.65779i	0.325937	+	0.564540i
$185$	−3.75523	+	0.199696i	−0.276090	+	0.0146819i
$186$		0			0
$187$	14.8365	+	8.56587i	1.08495	+	0.626398i
$188$	4.17060	+	2.40790i	0.304172	+	0.175614i
$189$		0			0
$190$	−8.51554	−	4.74189i	−0.617782	−	0.344013i
$191$	17.2519			1.24830			0.624151	−	0.781304i	$-0.285445\pi$
$191$	17.2519			1.24830			0.624151	+	0.781304i	$0.285445\pi$
$192$		0			0
$193$	−5.47129	−	3.15885i	−0.393832	−	0.227379i	0.289987	−	0.957031i	$-0.406349\pi$
$193$	−5.47129	−	3.15885i	−0.393832	−	0.227379i	−0.683819	+	0.729651i	$0.739682\pi$
$194$	2.61082	+	4.52207i	0.187446	+	0.324665i
$195$		0			0
$196$	−0.416515	−	0.721424i	−0.0297510	−	0.0515303i
$197$			8.79248i			0.626438i	0.949681	+	0.313219i	$0.101407\pi$
$197$			8.79248i			0.626438i	−0.949681	+	0.313219i	$0.898593\pi$
$198$		0			0
$199$	2.38605	+	4.13275i	0.169142	+	0.292963i	0.938119	−	0.346314i	$-0.112567\pi$
$199$	2.38605	+	4.13275i	0.169142	+	0.292963i	−0.768976	+	0.639277i	$0.779234\pi$
$200$	0.530281	+	4.97180i	0.0374965	+	0.351559i
$201$		0			0
$202$		−	11.7315i		−	0.825428i
$203$	4.40159	−	2.54126i	0.308931	−	0.178361i
$204$		0			0
$205$	15.4748	+	7.86982i	1.08080	+	0.549652i
$206$	−8.97482	+	15.5448i	−0.625305	+	1.08306i
$207$		0			0
$208$			0.110916i			0.00769064i
$209$	−0.660101	+	17.5394i	−0.0456601	+	1.21323i
$210$		0			0
$211$	−10.6837	+	18.5047i	−0.735497	+	1.27392i	0.219007	+	0.975723i	$0.429718\pi$
$211$	−10.6837	+	18.5047i	−0.735497	+	1.27392i	−0.954505	+	0.298196i	$0.903615\pi$
$212$	6.45034	+	3.72410i	0.443011	+	0.255772i
$213$		0			0
$214$	7.56792	−	13.1080i	0.517333	−	0.896046i
$215$	7.56694	−	14.8792i	0.516061	−	1.01475i
$216$		0			0
$217$			22.0571i			1.49733i
$218$	7.43496	−	4.29258i	0.503559	−	0.290730i
$219$		0			0
$220$	7.54753	−	4.90967i	0.508854	−	0.331010i
$221$	−0.471900			−0.0317434
$222$		0			0
$223$	0.769596	+	0.444327i	0.0515360	+	0.0297543i	0.525547	−	0.850765i	$-0.323861\pi$
$223$	0.769596	+	0.444327i	0.0515360	+	0.0297543i	−0.474011	+	0.880519i	$0.657194\pi$
$224$	1.39938	+	2.42379i	0.0934998	+	0.161946i
$225$		0			0
$226$	−0.623455	+	1.07986i	−0.0414716	+	0.0718309i
$227$			0.227679i			0.0151116i	0.999971	+	0.00755579i	$0.00240511\pi$
$227$			0.227679i			0.0151116i	−0.999971	+	0.00755579i	$0.997595\pi$
$228$		0			0
$229$	−16.2385			−1.07307			−0.536536	−	0.843878i	$-0.680267\pi$
$229$	−16.2385			−1.07307			−0.536536	+	0.843878i	$0.680267\pi$
$230$	1.04997	+	19.7444i	0.0692330	+	1.30191i
$231$		0			0
$232$	−1.57270	+	0.907996i	−0.103253	+	0.0596129i
$233$	2.89217	+	1.66979i	0.189472	+	0.109392i	0.591735	−	0.806132i	$-0.298443\pi$
$233$	2.89217	+	1.66979i	0.189472	+	0.109392i	−0.402263	+	0.915524i	$0.631776\pi$
$234$		0			0
$235$	5.87185	+	9.02666i	0.383037	+	0.588835i
$236$	0.377211			0.0245544
$237$		0			0
$238$	−10.3122	+	5.95375i	−0.668441	+	0.385924i
$239$	−28.3414			−1.83325			−0.916626	−	0.399745i	$-0.869099\pi$
$239$	−28.3414			−1.83325			−0.916626	+	0.399745i	$0.869099\pi$
$240$		0			0
$241$	−7.12956	−	12.3488i	−0.459255	−	0.795453i	0.539667	−	0.841879i	$-0.318550\pi$
$241$	−7.12956	−	12.3488i	−0.459255	−	0.795453i	−0.998922	+	0.0464255i	$0.985217\pi$
$242$	−4.51547	−	2.60701i	−0.290266	−	0.167585i
$243$		0			0
$244$	6.18078	−	10.7054i	0.395684	−	0.685345i
$245$	−0.0989155	−	1.86008i	−0.00631948	−	0.118836i
$246$		0			0
$247$	−0.225818	−	0.427494i	−0.0143685	−	0.0272008i
$248$		−	7.88104i		−	0.500447i
$249$		0			0
$250$	−3.98261	+	10.4470i	−0.251883	+	0.660723i
$251$	−12.1437	−	21.0334i	−0.766501	−	1.32762i	−0.939449	−	0.342687i	$-0.888663\pi$
$251$	−12.1437	−	21.0334i	−0.766501	−	1.32762i	0.172949	−	0.984931i	$-0.444671\pi$
$252$		0			0
$253$	30.8353	−	17.8028i	1.93860	−	1.11925i
$254$	13.7574			0.863219
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.06264	−	1.19086i	0.128664	−	0.0742840i	−0.434287	−	0.900775i	$-0.643000\pi$
$257$	2.06264	−	1.19086i	0.128664	−	0.0742840i	0.562950	+	0.826491i	$0.309666\pi$
$258$		0			0
$259$	−4.70684			−0.292469
$260$	−0.112427	+	0.221070i	−0.00697242	+	0.0137102i
$261$		0			0
$262$	11.1347	−	6.42860i	0.687901	−	0.397160i
$263$	−6.92724	−	3.99944i	−0.427152	−	0.246616i	0.270981	−	0.962585i	$-0.412652\pi$
$263$	−6.92724	−	3.99944i	−0.427152	−	0.246616i	−0.698133	+	0.715969i	$0.745985\pi$
$264$		0			0
$265$	9.08152	+	13.9608i	0.557874	+	0.857607i
$266$	−10.3282	−	6.49277i	−0.633262	−	0.398097i
$267$		0			0
$268$	−3.82862	−	2.21046i	−0.233870	−	0.135025i
$269$	−5.32072	+	9.21576i	−0.324410	+	0.561895i	−0.981393	−	0.192011i	$-0.938499\pi$
$269$	−5.32072	+	9.21576i	−0.324410	+	0.561895i	0.656983	+	0.753906i	$0.271832\pi$
$270$		0			0
$271$	8.07644	−	13.9888i	0.490609	−	0.849759i	−0.509333	−	0.860570i	$-0.670108\pi$
$271$	8.07644	−	13.9888i	0.490609	−	0.849759i	0.999942	+	0.0108102i	$0.00344107\pi$
$272$	3.68457	−	2.12729i	0.223410	−	0.128986i
$273$		0			0
$274$	8.15288			0.492534
$275$	20.0198	−	2.13526i	1.20724	−	0.128761i
$276$		0			0
$277$			21.6950i			1.30352i	0.758423	+	0.651762i	$0.225970\pi$
$277$			21.6950i			1.30352i	−0.758423	+	0.651762i	$0.774030\pi$
$278$		−	2.28555i		−	0.137078i
$279$		0			0
$280$	0.332330	+	6.24938i	0.0198605	+	0.373472i
$281$	0.595143	+	1.03082i	0.0355032	+	0.0614934i	0.883231	−	0.468938i	$-0.155363\pi$
$281$	0.595143	+	1.03082i	0.0355032	+	0.0614934i	−0.847728	+	0.530431i	$0.822030\pi$
$282$		0			0
$283$	0.262002	+	0.151267i	0.0155744	+	0.00899189i	0.507767	−	0.861494i	$-0.330471\pi$
$283$	0.262002	+	0.151267i	0.0155744	+	0.00899189i	−0.492193	+	0.870486i	$0.663804\pi$
$284$	11.8135			0.701002
$285$		0			0
$286$	0.446621			0.0264093
$287$	18.8184	+	10.8648i	1.11082	+	0.641331i
$288$		0			0
$289$	0.550694	+	0.953829i	0.0323937	+	0.0561076i
$290$	−4.05495	+	0.215634i	−0.238115	+	0.0126625i
$291$		0			0
$292$			9.62397i			0.563200i
$293$		−	25.2078i		−	1.47266i	−0.676625	−	0.736328i	$-0.736558\pi$
$293$		−	25.2078i		−	1.47266i	0.676625	−	0.736328i	$-0.263442\pi$
$294$		0			0
$295$	0.751832	+	0.382350i	0.0437733	+	0.0222613i
$296$	1.68176			0.0977504
$297$		0			0
$298$	−16.2200	+	9.36462i	−0.939599	+	0.542478i
$299$	−0.490385	+	0.849371i	−0.0283597	+	0.0491204i
$300$		0			0
$301$	10.4467	−	18.0942i	0.602137	−	1.04293i
$302$	13.9771	+	8.06970i	0.804293	+	0.464359i
$303$		0			0
$304$	3.69028	+	2.31988i	0.211652	+	0.133054i
$305$	23.1704	−	15.0723i	1.32673	−	0.863039i
$306$		0			0
$307$	−19.7299	−	11.3911i	−1.12605	−	0.650123i	−0.183109	−	0.983093i	$-0.558616\pi$
$307$	−19.7299	−	11.3911i	−1.12605	−	0.650123i	−0.942938	+	0.332969i	$0.891950\pi$
$308$	9.75980	−	5.63482i	0.556116	−	0.321074i
$309$		0			0
$310$	7.98841	−	15.7079i	0.453711	−	0.892151i
$311$	12.0752			0.684724			0.342362	−	0.939568i	$-0.388773\pi$
$311$	12.0752			0.684724			0.342362	+	0.939568i	$0.388773\pi$
$312$		0			0
$313$	9.22306	−	5.32494i	0.521318	−	0.300983i	−0.216156	−	0.976359i	$-0.569352\pi$
$313$	9.22306	−	5.32494i	0.521318	−	0.300983i	0.737474	+	0.675376i	$0.236019\pi$
$314$	3.88918	+	6.73626i	0.219479	+	0.380149i
$315$		0			0
$316$	−4.23690			−0.238344
$317$	14.3154	−	8.26498i	0.804031	−	0.464208i	−0.0408477	−	0.999165i	$-0.513006\pi$
$317$	14.3154	−	8.26498i	0.804031	−	0.464208i	0.844879	+	0.534958i	$0.179673\pi$
$318$		0			0
$319$	3.65620	+	6.33272i	0.204708	+	0.354564i
$320$	−0.118742	−	2.23291i	−0.00663788	−	0.124824i
$321$		0			0
$322$			24.7479i			1.37914i
$323$	−9.87009	+	15.7006i	−0.549186	+	0.873603i
$324$		0			0
$325$	−0.448163	+	0.326663i	−0.0248596	+	0.0181200i
$326$	−0.999118	+	1.73052i	−0.0553360	+	0.0958448i
$327$		0			0
$328$	−6.72386	−	3.88203i	−0.371263	−	0.214349i
$329$	6.73911	+	11.6725i	0.371539	+	0.643525i
$330$		0			0
$331$	33.3848			1.83499			0.917496	−	0.397744i	$-0.130207\pi$
$331$	33.3848			1.83499			0.917496	+	0.397744i	$0.130207\pi$
$332$	−7.15157	+	4.12896i	−0.392493	+	0.226606i
$333$		0			0
$334$	17.9892			0.984327
$335$	−5.39037	−	8.28651i	−0.294508	−	0.452740i
$336$		0			0
$337$	−19.2072	−	11.0893i	−1.04628	−	0.604072i	−0.124677	−	0.992197i	$-0.539789\pi$
$337$	−19.2072	−	11.0893i	−1.04628	−	0.604072i	−0.921607	+	0.388125i	$0.873123\pi$
$338$	11.2477	−	6.49385i	0.611793	−	0.353219i
$339$		0			0
$340$	9.50009	−	0.505196i	0.515215	−	0.0273981i
$341$	−31.7343			−1.71851
$342$		0			0
$343$			17.2598i			0.931944i
$344$	−3.73262	+	6.46509i	−0.201249	+	0.348574i
$345$		0			0
$346$	7.65871	+	13.2653i	0.411735	+	0.713146i
$347$	−15.7368	−	9.08564i	−0.844795	−	0.487743i	0.0140963	−	0.999901i	$-0.495513\pi$
$347$	−15.7368	−	9.08564i	−0.844795	−	0.487743i	−0.858891	+	0.512158i	$0.828846\pi$
$348$		0			0
$349$	−5.54988			−0.297078			−0.148539	−	0.988907i	$-0.547457\pi$
$349$	−5.54988			−0.297078			−0.148539	+	0.988907i	$0.547457\pi$
$350$	−5.67213	+	12.7927i	−0.303188	+	0.683797i
$351$		0			0
$352$	−3.48719	+	2.01333i	−0.185868	+	0.107311i
$353$			11.9998i			0.638686i	0.947639	+	0.319343i	$0.103462\pi$
$353$			11.9998i			0.638686i	−0.947639	+	0.319343i	$0.896538\pi$
$354$		0			0
$355$	23.5458	+	11.9744i	1.24968	+	0.635537i
$356$	5.01501	−	8.68625i	0.265795	−	0.460370i
$357$		0			0
$358$	9.43602	+	5.44789i	0.498709	+	0.287930i
$359$	−15.8492	+	27.4515i	−0.836487	+	1.44884i	0.0563277	+	0.998412i	$0.482061\pi$
$359$	−15.8492	+	27.4515i	−0.836487	+	1.44884i	−0.892814	+	0.450425i	$0.851272\pi$
$360$		0			0
$361$	−18.9463	−	1.42812i	−0.997171	−	0.0751642i
$362$			18.2521i			0.959308i
$363$		0			0
$364$	−0.155213	+	0.268837i	−0.00813539	+	0.0140909i
$365$	−9.75508	+	19.1818i	−0.510604	+	1.00402i
$366$		0			0
$367$	−3.14212	+	1.81410i	−0.164017	+	0.0946954i	−0.579762	−	0.814786i	$-0.696854\pi$
$367$	−3.14212	+	1.81410i	−0.164017	+	0.0946954i	0.415745	+	0.909481i	$0.363521\pi$
$368$		−	8.84246i		−	0.460945i
$369$		0			0
$370$	3.35197	+	1.70467i	0.174261	+	0.0886217i
$371$	10.4229	+	18.0529i	0.541128	+	0.937260i
$372$		0			0
$373$			7.74901i			0.401228i	0.979670	+	0.200614i	$0.0642938\pi$
$373$			7.74901i			0.401228i	−0.979670	+	0.200614i	$0.935706\pi$
$374$	−8.56587	−	14.8365i	−0.442930	−	0.767178i
$375$		0			0
$376$	−2.40790	−	4.17060i	−0.124178	−	0.215082i
$377$	−0.174437	−	0.100711i	−0.00898396	−	0.00518689i
$378$		0			0
$379$	6.68218			0.343241			0.171620	−	0.985163i	$-0.445100\pi$
$379$	6.68218			0.343241			0.171620	+	0.985163i	$0.445100\pi$
$380$	5.00373	+	8.36437i	0.256686	+	0.429083i
$381$		0			0
$382$	−14.9406	−	8.62594i	−0.764426	−	0.441341i
$383$	17.5053	+	10.1067i	0.894479	+	0.516428i	0.875405	−	0.483390i	$-0.160595\pi$
$383$	17.5053	+	10.1067i	0.894479	+	0.516428i	0.0190744	+	0.999818i	$0.493928\pi$
$384$		0			0
$385$	25.1641	−	1.33818i	1.28248	−	0.0681999i
$386$	3.15885	+	5.47129i	0.160781	+	0.278481i
$387$		0			0
$388$		−	5.22163i		−	0.265088i
$389$	−0.559544	−	0.969159i	−0.0283700	−	0.0491383i	0.851492	−	0.524368i	$-0.175698\pi$
$389$	−0.559544	−	0.969159i	−0.0283700	−	0.0491383i	−0.879862	+	0.475230i	$0.842365\pi$
$390$		0			0
$391$	37.6209			1.90257
$392$			0.833029i			0.0420743i
$393$		0			0
$394$	4.39624	−	7.61451i	0.221479	−	0.383613i
$395$	−8.44470	−	4.29462i	−0.424899	−	0.216086i
$396$		0			0
$397$	−8.44367	−	4.87495i	−0.423776	−	0.244667i	0.272916	−	0.962038i	$-0.412012\pi$
$397$	−8.44367	−	4.87495i	−0.423776	−	0.244667i	−0.696691	+	0.717371i	$0.745345\pi$
$398$		−	4.77209i		−	0.239203i
$399$		0			0
$400$	2.02666	−	4.57085i	0.101333	−	0.228542i
$401$	4.85007	−	8.40056i	0.242201	−	0.419504i	−0.719140	−	0.694865i	$-0.755464\pi$
$401$	4.85007	−	8.40056i	0.242201	−	0.419504i	0.961341	+	0.275361i	$0.0887974\pi$
$402$		0			0
$403$	0.757022	−	0.437067i	0.0377099	−	0.0217718i
$404$	−5.86577	+	10.1598i	−0.291833	+	0.505469i
$405$		0			0
$406$	−5.08252			−0.252241
$407$		−	6.77189i		−	0.335670i
$408$		0			0
$409$	1.03028	+	1.78451i	0.0509443	+	0.0882381i	0.890373	−	0.455232i	$-0.150444\pi$
$409$	1.03028	+	1.78451i	0.0509443	+	0.0882381i	−0.839429	+	0.543470i	$0.817110\pi$
$410$	−9.46663	−	14.5528i	−0.467523	−	0.718714i
$411$		0			0
$412$	15.5448	−	8.97482i	0.765840	−	0.442158i
$413$	0.914282	+	0.527861i	0.0449889	+	0.0259744i
$414$		0			0
$415$	−18.4392	+	0.980562i	−0.905146	+	0.0481339i
$416$	0.0554580	−	0.0960560i	0.00271905	−	0.00470953i
$417$		0			0
$418$	9.34137	−	14.8595i	0.456901	−	0.726803i
$419$	−17.5492			−0.857336			−0.428668	−	0.903462i	$-0.641017\pi$
$419$	−17.5492			−0.857336			−0.428668	+	0.903462i	$0.641017\pi$
$420$		0			0
$421$	−5.86950	+	10.1663i	−0.286062	+	0.495474i	−0.972866	−	0.231369i	$-0.925680\pi$
$421$	−5.86950	+	10.1663i	−0.286062	+	0.495474i	0.686804	+	0.726842i	$0.259013\pi$
$422$	18.5047	−	10.6837i	0.900797	−	0.520075i
$423$		0			0
$424$	−3.72410	−	6.45034i	−0.180858	−	0.313256i
$425$	19.4470	+	8.62259i	0.943318	+	0.418257i
$426$		0			0
$427$	29.9619	−	17.2985i	1.44996	−	0.837133i
$428$	−13.1080	+	7.56792i	−0.633600	+	0.365809i
$429$		0			0
$430$	−13.9928	+	9.10230i	−0.674791	+	0.438952i
$431$	9.77272	+	16.9268i	0.470735	+	0.815337i	0.999440	−	0.0334686i	$-0.0106554\pi$
$431$	9.77272	+	16.9268i	0.470735	+	0.815337i	−0.528705	+	0.848806i	$0.677322\pi$
$432$		0			0
$433$	30.9164	−	17.8496i	1.48575	−	0.857797i	0.485881	−	0.874025i	$-0.338499\pi$
$433$	30.9164	−	17.8496i	1.48575	−	0.857797i	0.999868	+	0.0162277i	$0.00516568\pi$
$434$	11.0286	−	19.1020i	0.529388	−	0.916926i
$435$		0			0
$436$	−8.58516			−0.411154
$437$	18.0027	+	34.0807i	0.861185	+	1.63030i
$438$		0			0
$439$	−19.4194	+	33.6354i	−0.926838	+	1.60533i	−0.138259	+	0.990396i	$0.544151\pi$
$439$	−19.4194	+	33.6354i	−0.926838	+	1.60533i	−0.788579	+	0.614934i	$0.789183\pi$
$440$	−8.99119	+	0.478134i	−0.428638	+	0.0227941i
$441$		0			0
$442$	0.408677	+	0.235950i	0.0194388	+	0.0112230i
$443$	−25.1014	+	14.4923i	−1.19260	+	0.688549i	−0.958896	−	0.283758i	$-0.908419\pi$
$443$	−25.1014	+	14.4923i	−1.19260	+	0.688549i	−0.233707	+	0.972307i	$0.575086\pi$
$444$		0			0
$445$	18.8001	−	12.2295i	0.891212	−	0.579734i
$446$	−0.444327	−	0.769596i	−0.0210395	−	0.0364414i
$447$		0			0
$448$		−	2.79875i		−	0.132229i
$449$	11.5314			0.544201			0.272100	−	0.962269i	$-0.412282\pi$
$449$	11.5314			0.544201			0.272100	+	0.962269i	$0.412282\pi$
$450$		0			0
$451$	−15.6316	+	27.0747i	−0.736064	+	1.27490i
$452$	1.07986	−	0.623455i	0.0507921	−	0.0293248i
$453$		0			0
$454$	0.113839	−	0.197176i	0.00534275	−	0.00925392i
$455$	−0.581860	+	0.378500i	−0.0272780	+	0.0177444i
$456$		0			0
$457$			22.1107i			1.03430i	0.855896	+	0.517148i	$0.173006\pi$
$457$			22.1107i			1.03430i	−0.855896	+	0.517148i	$0.826994\pi$
$458$	14.0630	+	8.11926i	0.657119	+	0.379388i
$459$		0			0
$460$	8.96292	−	17.6242i	0.417898	−	0.821731i
$461$	9.08841	−	15.7416i	0.423289	−	0.733159i	−0.572970	−	0.819577i	$-0.694209\pi$
$461$	9.08841	−	15.7416i	0.423289	−	0.733159i	0.996259	+	0.0864179i	$0.0275420\pi$
$462$		0			0
$463$		−	34.9548i		−	1.62449i	−0.583318	−	0.812244i	$-0.698246\pi$
$463$		−	34.9548i		−	1.62449i	0.583318	−	0.812244i	$-0.301754\pi$
$464$	1.81599			0.0843053
$465$		0			0
$466$	−1.66979	−	2.89217i	−0.0773517	−	0.133977i
$467$		−	13.0120i		−	0.602125i	−0.953604	−	0.301063i	$-0.902659\pi$
$467$		−	13.0120i		−	0.602125i	0.953604	−	0.301063i	$-0.0973414\pi$
$468$		0			0
$469$	−6.18652	−	10.7154i	−0.285667	−	0.494790i
$470$	−0.571836	−	10.7532i	−0.0263768	−	0.496010i
$471$		0			0
$472$	−0.326675	−	0.188606i	−0.0150364	−	0.00868128i
$473$	26.0327	+	15.0300i	1.19699	+	0.691081i
$474$		0			0
$475$	1.49477	+	21.7432i	0.0685845	+	0.997645i
$476$	11.9075			0.545780
$477$		0			0
$478$	24.5444	+	14.1707i	1.12263	+	0.648153i
$479$	15.1415	+	26.2259i	0.691833	+	1.19829i	0.971237	+	0.238117i	$0.0765300\pi$
$479$	15.1415	+	26.2259i	0.691833	+	1.19829i	−0.279403	+	0.960174i	$0.590137\pi$
$480$		0			0
$481$	0.0932671	+	0.161543i	0.00425261	+	0.00736574i
$482$			14.2591i			0.649485i
$483$		0			0
$484$	2.60701	+	4.51547i	0.118500	+	0.205249i
$485$	5.29276	−	10.4074i	0.240332	−	0.472575i
$486$		0			0
$487$			35.5166i			1.60941i	0.593674	+	0.804706i	$0.297677\pi$
$487$			35.5166i			1.60941i	−0.593674	+	0.804706i	$0.702323\pi$
$488$	−10.7054	+	6.18078i	−0.484612	+	0.279791i
$489$		0			0
$490$	−0.844377	+	1.66034i	−0.0381451	+	0.0750063i
$491$	−5.36057	+	9.28479i	−0.241919	+	0.419017i	−0.961261	−	0.275640i	$-0.911110\pi$
$491$	−5.36057	+	9.28479i	−0.241919	+	0.419017i	0.719342	+	0.694656i	$0.244444\pi$
$492$		0			0
$493$			7.72627i			0.347974i
$494$	−0.0181827	+	0.483129i	−0.000818080	+	0.0217370i
$495$		0			0
$496$	−3.94052	+	6.82518i	−0.176935	+	0.306460i
$497$	28.6335	+	16.5315i	1.28439	+	0.741541i
$498$		0			0
$499$	12.0259	−	20.8295i	0.538353	−	0.932455i	−0.460640	−	0.887587i	$-0.652380\pi$
$499$	12.0259	−	20.8295i	0.538353	−	0.932455i	0.998993	−	0.0448675i	$-0.0142866\pi$
$500$	8.67252	−	7.05602i	0.387847	−	0.315555i
$501$		0			0
$502$			24.2873i			1.08400i
$503$	34.4057	−	19.8642i	1.53408	−	0.885699i	0.534909	−	0.844910i	$-0.320346\pi$
$503$	34.4057	−	19.8642i	1.53408	−	0.885699i	0.999168	−	0.0407894i	$-0.0129873\pi$
$504$		0			0
$505$	−21.9895	+	14.3041i	−0.978518	+	0.636526i
$506$	−35.6056			−1.58286
$507$		0			0
$508$	−11.9143	−	6.87872i	−0.528611	−	0.305194i
$509$	2.51441	+	4.35509i	0.111449	+	0.193036i	0.916355	−	0.400367i	$-0.131117\pi$
$509$	2.51441	+	4.35509i	0.111449	+	0.193036i	−0.804905	+	0.593403i	$0.797784\pi$
$510$		0			0
$511$	−13.4676	+	23.3265i	−0.595770	+	1.03190i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−2.38173			−0.105053
$515$	40.0800	−	2.13138i	1.76614	−	0.0939196i
$516$		0			0
$517$	−16.7936	+	9.69579i	−0.738581	+	0.426420i
$518$	4.07624	+	2.35342i	0.179100	+	0.103403i
$519$		0			0
$520$	0.207900	−	0.135239i	0.00911700	−	0.00593061i
$521$	43.2225			1.89361			0.946806	−	0.321806i	$-0.104290\pi$
$521$	43.2225			1.89361			0.946806	+	0.321806i	$0.104290\pi$
$522$		0			0
$523$	0.0430629	−	0.0248624i	0.00188301	−	0.00108716i	−0.499058	−	0.866568i	$-0.666321\pi$
$523$	0.0430629	−	0.0248624i	0.00188301	−	0.00108716i	0.500941	+	0.865481i	$0.332987\pi$
$524$	−12.8572			−0.561669
$525$		0			0
$526$	3.99944	+	6.92724i	0.174384	+	0.302042i
$527$	−29.0382	−	16.7652i	−1.26493	−	0.730305i
$528$		0			0
$529$	27.5945	−	47.7951i	1.19976	−	2.07805i
$530$	−0.884415	−	16.6312i	−0.0384165	−	0.722413i
$531$		0			0
$532$	5.69809	+	10.7870i	0.247044	+	0.467676i
$533$		−	0.861157i		−	0.0373008i
$534$		0			0
$535$	−33.7970	+	1.79726i	−1.46117	+	0.0777023i
$536$	2.21046	+	3.82862i	0.0954772	+	0.165371i
$537$		0			0
$538$	9.21576	−	5.32072i	0.397320	−	0.229393i
$539$	3.35433			0.144481
$540$		0			0
$541$	3.67092	+	6.35822i	0.157825	+	0.273361i	0.934084	−	0.357053i	$-0.116218\pi$
$541$	3.67092	+	6.35822i	0.157825	+	0.273361i	−0.776259	+	0.630414i	$0.782885\pi$
$542$	−13.9888	+	8.07644i	−0.600871	+	0.346913i
$543$		0			0
$544$	−4.25457			−0.182413
$545$	−17.1113	−	8.70211i	−0.732969	−	0.372757i
$546$		0			0
$547$	−20.7675	+	11.9901i	−0.887954	+	0.512660i	−0.873273	−	0.487232i	$-0.838007\pi$
$547$	−20.7675	+	11.9901i	−0.887954	+	0.512660i	−0.0146810	+	0.999892i	$0.504673\pi$
$548$	−7.06060	−	4.07644i	−0.301614	−	0.174137i
$549$		0			0
$550$	−18.4053	−	8.16069i	−0.784803	−	0.347973i
$551$	−6.99922	+	3.69725i	−0.298177	+	0.157508i
$552$		0			0
$553$	−10.2694	−	5.92903i	−0.436698	−	0.252128i
$554$	10.8475	−	18.7884i	0.460865	−	0.798242i
$555$		0			0
$556$	−1.14277	+	1.97934i	−0.0484644	+	0.0839429i
$557$	21.6447	−	12.4966i	0.917115	−	0.529497i	0.0344016	−	0.999408i	$-0.489047\pi$
$557$	21.6447	−	12.4966i	0.917115	−	0.529497i	0.882714	+	0.469911i	$0.155714\pi$
$558$		0			0
$559$	−0.828015			−0.0350213
$560$	2.83688	−	5.57828i	0.119880	−	0.235725i
$561$		0			0
$562$		−	1.19029i		−	0.0502092i
$563$			23.2863i			0.981403i	0.871328	+	0.490701i	$0.163259\pi$
$563$			23.2863i			0.981403i	−0.871328	+	0.490701i	$0.836741\pi$
$564$		0			0
$565$	2.78424	−	0.148060i	0.117134	−	0.00622895i
$566$	−0.151267	−	0.262002i	−0.00635822	−	0.0110128i
$567$		0			0
$568$	−10.2308	−	5.90675i	−0.429274	−	0.247842i
$569$	−16.8454			−0.706196			−0.353098	−	0.935586i	$-0.614872\pi$
$569$	−16.8454			−0.706196			−0.353098	+	0.935586i	$0.614872\pi$
$570$		0			0
$571$	−16.1395			−0.675418			−0.337709	−	0.941250i	$-0.609652\pi$
$571$	−16.1395			−0.675418			−0.337709	+	0.941250i	$0.609652\pi$
$572$	−0.386785	−	0.223311i	−0.0161723	−	0.00933709i
$573$		0			0
$574$	−10.8648	−	18.8184i	−0.453490	−	0.785467i
$575$	35.7285	−	26.0422i	1.48998	−	1.08604i
$576$		0			0
$577$		−	3.05772i		−	0.127295i	−0.997972	−	0.0636473i	$-0.979727\pi$
$577$		−	3.05772i		−	0.127295i	0.997972	−	0.0636473i	$-0.0202733\pi$
$578$		−	1.10139i		−	0.0458117i
$579$		0			0
$580$	3.61951	+	1.84073i	0.150292	+	0.0764322i
$581$	−23.1119			−0.958843
$582$		0			0
$583$	−25.9733	+	14.9957i	−1.07571	+	0.621059i
$584$	4.81199	−	8.33460i	0.199121	−	0.344888i
$585$		0			0
$586$	−12.6039	+	21.8306i	−0.520662	+	0.901813i
$587$	−26.8130	−	15.4805i	−1.10669	−	0.638949i	−0.168722	−	0.985664i	$-0.553964\pi$
$587$	−26.8130	−	15.4805i	−1.10669	−	0.638949i	−0.937971	+	0.346714i	$0.887297\pi$
$588$		0			0
$589$	1.29196	−	34.3284i	0.0532343	−	1.41448i
$590$	−0.459930	−	0.707041i	−0.0189350	−	0.0291084i
$591$		0			0
$592$	−1.45645	−	0.840881i	−0.0598597	−	0.0345600i
$593$	21.9486	−	12.6720i	0.901322	−	0.520379i	0.0236932	−	0.999719i	$-0.492458\pi$
$593$	21.9486	−	12.6720i	0.901322	−	0.520379i	0.877629	+	0.479341i	$0.159124\pi$
$594$		0			0
$595$	23.7332	+	12.0697i	0.972967	+	0.494810i
$596$	18.7292			0.767180
$597$		0			0
$598$	0.849371	−	0.490385i	0.0347334	−	0.0200533i
$599$	11.1523	+	19.3163i	0.455670	+	0.789243i	0.998726	−	0.0504529i	$-0.0160665\pi$
$599$	11.1523	+	19.3163i	0.455670	+	0.789243i	−0.543057	+	0.839696i	$0.682733\pi$
$600$		0			0
$601$	27.6758			1.12892			0.564460	−	0.825460i	$-0.309084\pi$
$601$	27.6758			1.12892			0.564460	+	0.825460i	$0.309084\pi$
$602$	−18.0942	+	10.4467i	−0.737465	+	0.425775i
$603$		0			0
$604$	−8.06970	−	13.9771i	−0.328351	−	0.568721i
$605$	0.619123	+	11.6425i	0.0251709	+	0.473333i
$606$		0			0
$607$		−	16.7201i		−	0.678650i	−0.940669	−	0.339325i	$-0.889801\pi$
$607$		−	16.7201i		−	0.678650i	0.940669	−	0.339325i	$-0.110199\pi$
$608$	−2.03594	−	3.85421i	−0.0825682	−	0.156309i
$609$		0			0
$610$	−27.6023	+	1.46784i	−1.11758	+	0.0594309i
$611$	0.267074	−	0.462586i	0.0108047	−	0.0187142i
$612$		0			0
$613$	−25.3849	−	14.6560i	−1.02529	−	0.591950i	−0.109656	−	0.993970i	$-0.534975\pi$
$613$	−25.3849	−	14.6560i	−1.02529	−	0.591950i	−0.915631	+	0.402020i	$0.868308\pi$
$614$	11.3911	+	19.7299i	0.459707	+	0.796235i
$615$		0			0
$616$	−11.2696			−0.454067
$617$	−32.4820	+	18.7535i	−1.30767	+	0.754986i	−0.981708	−	0.190395i	$-0.939023\pi$
$617$	−32.4820	+	18.7535i	−1.30767	+	0.754986i	−0.325967	+	0.945381i	$0.605690\pi$
$618$		0			0
$619$	−39.0394			−1.56912			−0.784562	−	0.620050i	$-0.787112\pi$
$619$	−39.0394			−1.56912			−0.784562	+	0.620050i	$0.787112\pi$
$620$	−14.7721	+	9.60928i	−0.593263	+	0.385918i
$621$		0			0
$622$	−10.4575	−	6.03762i	−0.419306	−	0.242087i
$623$	24.3107	−	14.0358i	0.973987	−	0.562331i
$624$		0			0
$625$	24.4376	−	5.27290i	0.977504	−	0.210916i
$626$	−10.6499			−0.425655
$627$		0			0
$628$		−	7.77836i		−	0.310390i
$629$	3.57759	−	6.19657i	0.142648	−	0.247073i
$630$		0			0
$631$	13.0406	+	22.5870i	0.519139	+	0.899174i	0.999753	+	0.0222421i	$0.00708045\pi$
$631$	13.0406	+	22.5870i	0.519139	+	0.899174i	−0.480614	+	0.876932i	$0.659586\pi$
$632$	3.66927	+	2.11845i	0.145956	+	0.0842675i
$633$		0			0
$634$	−16.5300			−0.656489
$635$	−16.7743	−	25.7868i	−0.665668	−	1.02332i
$636$		0			0
$637$	−0.0800175	+	0.0461981i	−0.00317041	+	0.00183044i
$638$		−	7.31239i		−	0.289500i
$639$		0			0
$640$	−1.01362	+	1.99313i	−0.0400670	+	0.0787854i
$641$	−1.56243	+	2.70621i	−0.0617122	+	0.106889i	−0.895231	−	0.445603i	$-0.852989\pi$
$641$	−1.56243	+	2.70621i	−0.0617122	+	0.106889i	0.833519	+	0.552491i	$0.186323\pi$
$642$		0			0
$643$	−17.9701	−	10.3750i	−0.708671	−	0.409151i	0.101898	−	0.994795i	$-0.467509\pi$
$643$	−17.9701	−	10.3750i	−0.708671	−	0.409151i	−0.810569	+	0.585644i	$0.800842\pi$
$644$	12.3739	−	21.4323i	0.487601	−	0.844550i
$645$		0			0
$646$	16.3980	−	8.66205i	0.645172	−	0.340804i
$647$		−	16.4405i		−	0.646344i	−0.946340	−	0.323172i	$-0.895251\pi$
$647$		−	16.4405i		−	0.646344i	0.946340	−	0.323172i	$-0.104749\pi$
$648$		0			0
$649$	−0.759452	+	1.31541i	−0.0298111	+	0.0516343i
$650$	0.551452	−	0.0588166i	0.0216297	−	0.00230698i
$651$		0			0
$652$	1.73052	−	0.999118i	0.0677725	−	0.0391285i
$653$		−	6.77814i		−	0.265249i	−0.991166	−	0.132625i	$-0.957660\pi$
$653$		−	6.77814i		−	0.265249i	0.991166	−	0.132625i	$-0.0423405\pi$
$654$		0			0
$655$	−25.6261	−	13.0323i	−1.00129	−	0.509216i
$656$	3.88203	+	6.72386i	0.151568	+	0.262523i
$657$		0			0
$658$		−	13.4782i		−	0.525436i
$659$	−12.0863	−	20.9341i	−0.470817	−	0.815478i	0.528626	−	0.848855i	$-0.322707\pi$
$659$	−12.0863	−	20.9341i	−0.470817	−	0.815478i	−0.999443	+	0.0333765i	$0.989374\pi$
$660$		0			0
$661$	−13.5085	−	23.3974i	−0.525420	−	0.910055i	−0.999562	−	0.0296059i	$-0.990575\pi$
$661$	−13.5085	−	23.3974i	−0.525420	−	0.910055i	0.474141	−	0.880449i	$-0.342759\pi$
$662$	−28.9121	−	16.6924i	−1.12370	−	0.648768i
$663$		0			0
$664$	8.25792			0.320470
$665$	0.423090	+	27.2756i	0.0164067	+	1.05770i
$666$		0			0
$667$	13.9065	+	8.02892i	0.538461	+	0.310881i
$668$	−15.5791	−	8.99462i	−0.602775	−	0.348012i
$669$		0			0
$670$	0.524948	+	9.87151i	0.0202805	+	0.381370i
$671$	24.8879	+	43.1071i	0.960788	+	1.66413i
$672$		0			0
$673$			21.9407i			0.845751i	0.906188	+	0.422875i	$0.138979\pi$
$673$			21.9407i			0.845751i	−0.906188	+	0.422875i	$0.861021\pi$
$674$	11.0893	+	19.2072i	0.427144	+	0.739834i
$675$		0			0
$676$	−12.9877			−0.499527
$677$			18.8185i			0.723254i	0.932323	+	0.361627i	$0.117779\pi$
$677$			18.8185i			0.723254i	−0.932323	+	0.361627i	$0.882221\pi$
$678$		0			0
$679$	7.30703	−	12.6562i	0.280418	−	0.485699i
$680$	−8.47992	−	4.31253i	−0.325190	−	0.165378i
$681$		0			0
$682$	27.4827	+	15.8672i	1.05237	+	0.607585i
$683$			19.3651i			0.740986i	0.928835	+	0.370493i	$0.120811\pi$
$683$			19.3651i			0.740986i	−0.928835	+	0.370493i	$0.879189\pi$
$684$		0			0
$685$	−9.94073	−	15.2817i	−0.379816	−	0.583882i
$686$	8.62992	−	14.9475i	0.329492	−	0.570697i
$687$		0			0
$688$	6.46509	−	3.73262i	0.246479	−	0.142305i
$689$	0.413062	−	0.715445i	0.0157364	−	0.0272563i
$690$		0			0
$691$	0.642365			0.0244367			0.0122184	−	0.999925i	$-0.496111\pi$
$691$	0.642365			0.0244367			0.0122184	+	0.999925i	$0.496111\pi$
$692$		−	15.3174i		−	0.582281i
$693$		0			0
$694$	9.08564	+	15.7368i	0.344886	+	0.597360i
$695$	−4.28401	+	2.78675i	−0.162502	+	0.105707i
$696$		0			0
$697$	−28.6072	+	16.5164i	−1.08357	+	0.625602i
$698$	4.80634	+	2.77494i	0.181923	+	0.105033i
$699$		0			0
$700$	11.3086	−	8.24272i	0.427423	−	0.311545i
$701$	22.4846	−	38.9445i	0.849233	−	1.47091i	−0.0326612	−	0.999466i	$-0.510398\pi$
$701$	22.4846	−	38.9445i	0.849233	−	1.47091i	0.881894	−	0.471448i	$-0.156268\pi$
$702$		0			0
$703$	7.32544	+	0.275695i	0.276284	+	0.0103981i
$704$	4.02666			0.151761
$705$		0			0
$706$	5.99991	−	10.3922i	0.225810	−	0.391114i
$707$	−28.4348	+	16.4169i	−1.06940	+	0.617419i
$708$		0			0
$709$	4.09461	+	7.09207i	0.153776	+	0.266348i	0.932613	−	0.360879i	$-0.117523\pi$
$709$	4.09461	+	7.09207i	0.153776	+	0.266348i	−0.778836	+	0.627227i	$0.784190\pi$
$710$	−14.4041	−	22.1431i	−0.540575	−	0.831015i
$711$		0			0
$712$	−8.68625	+	5.01501i	−0.325531	+	0.187945i
$713$	−60.3514	+	34.8439i	−2.26018	+	1.30491i
$714$		0			0
$715$	−0.544561	−	0.837142i	−0.0203654	−	0.0313073i
$716$	−5.44789	−	9.43602i	−0.203597	−	0.352641i
$717$		0			0
$718$	27.4515	−	15.8492i	1.02448	−	0.591485i
$719$	−25.2772	+	43.7813i	−0.942679	+	1.63277i	−0.182345	+	0.983235i	$0.558369\pi$
$719$	−25.2772	+	43.7813i	−0.942679	+	1.63277i	−0.760334	+	0.649533i	$0.774965\pi$
$720$		0			0
$721$	50.2367			1.87091
$722$	15.6939	+	10.7099i	0.584066	+	0.398582i
$723$		0			0
$724$	9.12604	−	15.8068i	0.339167	−	0.587454i
$725$	5.34835	+	7.33764i	0.198633	+	0.272513i
$726$		0			0
$727$	2.96717	+	1.71310i	0.110046	+	0.0635353i	0.554013	−	0.832508i	$-0.313096\pi$
$727$	2.96717	+	1.71310i	0.110046	+	0.0635353i	−0.443967	+	0.896043i	$0.646429\pi$
$728$	0.268837	−	0.155213i	0.00996377	−	0.00575259i
$729$		0			0
$730$	18.0391	−	11.7344i	0.667656	−	0.434310i
$731$	15.8807	+	27.5062i	0.587369	+	1.01735i
$732$		0			0
$733$			0.420632i			0.0155364i	0.999970	+	0.00776819i	$0.00247272\pi$
$733$			0.420632i			0.0155364i	−0.999970	+	0.00776819i	$0.997527\pi$
$734$	3.62820			0.133919
$735$		0			0
$736$	−4.42123	+	7.65779i	−0.162969	+	0.282270i
$737$	15.4166	−	8.90076i	0.567877	−	0.327864i
$738$		0			0
$739$	6.70752	−	11.6178i	0.246740	−	0.427366i	−0.715879	−	0.698224i	$-0.753974\pi$
$739$	6.70752	−	11.6178i	0.246740	−	0.427366i	0.962619	+	0.270858i	$0.0873073\pi$
$740$	−2.05056	−	3.15228i	−0.0753799	−	0.115880i
$741$		0			0
$742$		−	20.8457i		−	0.765270i
$743$	−29.4635	−	17.0108i	−1.08091	−	0.624064i	−0.149769	−	0.988721i	$-0.547853\pi$
$743$	−29.4635	−	17.0108i	−1.08091	−	0.624064i	−0.931142	+	0.364657i	$0.881186\pi$
$744$		0			0
$745$	37.3298	+	18.9844i	1.36766	+	0.695534i
$746$	3.87450	−	6.71084i	0.141856	−	0.245701i
$747$		0			0
$748$			17.1317i			0.626398i
$749$	−42.3615			−1.54786
$750$		0			0
$751$	−11.0748	−	19.1820i	−0.404123	−	0.699962i	0.590096	−	0.807333i	$-0.299090\pi$
$751$	−11.0748	−	19.1820i	−0.404123	−	0.699962i	−0.994219	+	0.107371i	$0.965757\pi$
$752$			4.81579i			0.175614i
$753$		0			0
$754$	0.100711	+	0.174437i	0.00366769	+	0.00635262i
$755$	−1.91642	−	36.0379i	−0.0697458	−	1.31155i
$756$		0			0
$757$	−5.58767	−	3.22604i	−0.203087	−	0.117252i	0.395008	−	0.918678i	$-0.370742\pi$
$757$	−5.58767	−	3.22604i	−0.203087	−	0.117252i	−0.598095	+	0.801425i	$0.704075\pi$
$758$	−5.78694	−	3.34109i	−0.210191	−	0.121354i
$759$		0			0
$760$	−0.151171	−	9.74562i	−0.00548354	−	0.353511i
$761$	−25.4438			−0.922338			−0.461169	−	0.887312i	$-0.652570\pi$
$761$	−25.4438			−0.922338			−0.461169	+	0.887312i	$0.652570\pi$
$762$		0			0
$763$	−20.8086	−	12.0139i	−0.753323	−	0.434931i
$764$	8.62594	+	14.9406i	0.312075	+	0.540531i
$765$		0			0
$766$	−10.1067	−	17.5053i	−0.365170	−	0.632492i
$767$		−	0.0418388i		−	0.00151071i
$768$		0			0
$769$	22.8321	+	39.5464i	0.823348	+	1.42608i	0.903175	+	0.429272i	$0.141230\pi$
$769$	22.8321	+	39.5464i	0.823348	+	1.42608i	−0.0798275	+	0.996809i	$0.525437\pi$
$770$	−22.4619	−	11.4232i	−0.809470	−	0.411662i
$771$		0			0
$772$		−	6.31770i		−	0.227379i
$773$	23.3288	−	13.4689i	0.839080	−	0.484443i	−0.0178717	−	0.999840i	$-0.505689\pi$
$773$	23.3288	−	13.4689i	0.839080	−	0.484443i	0.856951	+	0.515397i	$0.172356\pi$
$774$		0			0
$775$	−39.1830	+	4.17917i	−1.40749	+	0.150120i
$776$	−2.61082	+	4.52207i	−0.0937228	+	0.162333i
$777$		0			0
$778$			1.11909i			0.0401213i
$779$	−28.6515	−	18.0116i	−1.02655	−	0.645334i
$780$		0			0
$781$	−23.7845	+	41.1959i	−0.851076	+	1.47411i
$782$	−32.5806	−	18.8104i	−1.16508	−	0.672660i
$783$		0			0
$784$	0.416515	−	0.721424i	0.0148755	−	0.0257652i
$785$	7.88432	−	15.5033i	0.281404	−	0.553336i
$786$		0			0
$787$			13.7880i			0.491488i	0.969335	+	0.245744i	$0.0790322\pi$
$787$			13.7880i			0.491488i	−0.969335	+	0.245744i	$0.920968\pi$
$788$	−7.61451	+	4.39624i	−0.271256	+	0.156610i
$789$		0			0
$790$	5.16602	+	7.94160i	0.183799	+	0.282550i
$791$	3.48979			0.124083
$792$		0			0
$793$	−1.18740	−	0.685547i	−0.0421659	−	0.0243445i
$794$	4.87495	+	8.44367i	0.173006	+	0.299655i
$795$		0			0
$796$	−2.38605	+	4.13275i	−0.0845711	+	0.146482i
$797$		−	18.6991i		−	0.662354i	−0.943569	−	0.331177i	$-0.892554\pi$
$797$		−	18.6991i		−	0.662354i	0.943569	−	0.331177i	$-0.107446\pi$
$798$		0			0
$799$	−20.4891			−0.724853
$800$	−4.04057	+	2.94514i	−0.142856	+	0.104126i
$801$		0			0
$802$	−8.40056	+	4.85007i	−0.296634	+	0.171262i
$803$	−33.5607	−	19.3763i	−1.18433	−	0.683773i
$804$		0			0
$805$	46.3871	−	30.1748i	1.63493	−	1.06352i
$806$	−0.874133			−0.0307900
$807$		0			0
$808$	10.1598	−	5.86577i	0.357421	−	0.206357i
$809$	−1.32846			−0.0467063			−0.0233531	−	0.999727i	$-0.507434\pi$
$809$	−1.32846			−0.0467063			−0.0233531	+	0.999727i	$0.507434\pi$
$810$		0			0
$811$	13.6087	+	23.5710i	0.477866	+	0.827688i	0.999678	−	0.0253723i	$-0.00807712\pi$
$811$	13.6087	+	23.5710i	0.477866	+	0.827688i	−0.521812	+	0.853060i	$0.674744\pi$
$812$	4.40159	+	2.54126i	0.154466	+	0.0891807i
$813$		0			0
$814$	−3.38595	+	5.86463i	−0.118677	+	0.205555i
$815$	4.46189	−	0.237274i	0.156293	−	0.00831136i
$816$		0			0
$817$	−17.3184	+	27.5488i	−0.605896	+	0.963812i
$818$		−	2.06057i		−	0.0720461i
$819$		0			0
$820$	0.921918	+	17.3364i	0.0321948	+	0.605415i
$821$	−8.87124	−	15.3654i	−0.309608	−	0.536258i	0.668668	−	0.743561i	$-0.266865\pi$
$821$	−8.87124	−	15.3654i	−0.309608	−	0.536258i	−0.978277	+	0.207303i	$0.933531\pi$
$822$		0			0
$823$	−0.288501	+	0.166566i	−0.0100565	+	0.00580614i	−0.505020	−	0.863108i	$-0.668515\pi$
$823$	−0.288501	+	0.166566i	−0.0100565	+	0.00580614i	0.494963	+	0.868914i	$0.335181\pi$
$824$	−17.9496			−0.625305
$825$		0			0
$826$	−0.527861	−	0.914282i	−0.0183666	−	0.0318120i
$827$	−45.8579	+	26.4760i	−1.59463	+	0.920662i	−0.602137	+	0.798393i	$0.705684\pi$
$827$	−45.8579	+	26.4760i	−1.59463	+	0.920662i	−0.992497	+	0.122270i	$0.960983\pi$
$828$		0			0
$829$	15.5012			0.538380			0.269190	−	0.963087i	$-0.413244\pi$
$829$	15.5012			0.538380			0.269190	+	0.963087i	$0.413244\pi$
$830$	16.4591	+	8.37042i	0.571304	+	0.290541i
$831$		0			0
$832$	−0.0960560	+	0.0554580i	−0.00333014	+	0.00192266i
$833$	3.06935	+	1.77209i	0.106347	+	0.0613993i
$834$		0			0
$835$	−21.9341	−	33.7188i	−0.759060	−	1.16689i
$836$	−15.5196	+	8.19804i	−0.536757	+	0.283535i
$837$		0			0
$838$	15.1981	+	8.77461i	0.525009	+	0.303114i
$839$	−1.03450	+	1.79181i	−0.0357150	+	0.0618603i	−0.883330	−	0.468751i	$-0.844704\pi$
$839$	−1.03450	+	1.79181i	−0.0357150	+	0.0618603i	0.847615	+	0.530611i	$0.178038\pi$
$840$		0			0
$841$	12.8511	−	22.2587i	0.443141	−	0.767543i
$842$	10.1663	−	5.86950i	0.350353	−	0.202276i
$843$		0			0
$844$	−21.3674			−0.735497
$845$	−25.8862	−	13.1646i	−0.890511	−	0.452877i
$846$		0			0
$847$			14.5928i			0.501413i
$848$			7.44821i			0.255772i
$849$		0			0
$850$	−12.5303	−	17.1909i	−0.429786	−	0.589642i
$851$	−7.43545	−	12.8786i	−0.254884	−	0.441472i
$852$		0			0
$853$	8.36952	+	4.83215i	0.286567	+	0.165450i	0.636393	−	0.771365i	$-0.280426\pi$
$853$	8.36952	+	4.83215i	0.286567	+	0.165450i	−0.349826	+	0.936815i	$0.613759\pi$
$854$	−34.5970			−1.18388
$855$		0			0
$856$	15.1358			0.517333
$857$	15.4663	+	8.92948i	0.528319	+	0.305025i	0.740332	−	0.672242i	$-0.234668\pi$
$857$	15.4663	+	8.92948i	0.528319	+	0.305025i	−0.212013	+	0.977267i	$0.568002\pi$
$858$		0			0
$859$	11.9479	+	20.6944i	0.407658	+	0.706084i	0.994627	−	0.103526i	$-0.0330123\pi$
$859$	11.9479	+	20.6944i	0.407658	+	0.706084i	−0.586969	+	0.809609i	$0.699679\pi$
$860$	16.6692	−	0.886437i	0.568416	−	0.0302273i
$861$		0			0
$862$		−	19.5454i		−	0.665720i
$863$		−	25.3969i		−	0.864520i	−0.901749	−	0.432260i	$-0.857716\pi$
$863$		−	25.3969i		−	0.864520i	0.901749	−	0.432260i	$-0.142284\pi$
$864$		0			0
$865$	15.5261	−	30.5296i	0.527903	−	1.03804i
$866$	−35.6992			−1.21311
$867$		0			0
$868$	−19.1020	+	11.0286i	−0.648365	+	0.374334i
$869$	8.53029	−	14.7749i	0.289370	−	0.501204i
$870$		0			0
$871$	−0.245175	+	0.424655i	−0.00830743	+	0.0143889i
$872$	7.43496	+	4.29258i	0.251780	+	0.145365i
$873$		0			0
$874$	1.44957	−	38.5161i	0.0490323	−	1.30283i
$875$	30.8944	−	4.96620i	1.04442	−	0.167888i
$876$		0			0
$877$	10.4421	+	6.02877i	0.352606	+	0.203577i	0.665832	−	0.746101i	$-0.268077\pi$
$877$	10.4421	+	6.02877i	0.352606	+	0.203577i	−0.313226	+	0.949678i	$0.601410\pi$
$878$	33.6354	−	19.4194i	1.13514	−	0.655373i
$879$		0			0
$880$	8.02567	+	4.08152i	0.270545	+	0.137588i
$881$	1.15688			0.0389762			0.0194881	−	0.999810i	$-0.493796\pi$
$881$	1.15688			0.0389762			0.0194881	+	0.999810i	$0.493796\pi$
$882$		0			0
$883$	−1.74123	+	1.00530i	−0.0585970	+	0.0338310i	−0.529012	−	0.848614i	$-0.677437\pi$
$883$	−1.74123	+	1.00530i	−0.0585970	+	0.0338310i	0.470415	+	0.882445i	$0.344104\pi$
$884$	−0.235950	−	0.408677i	−0.00793586	−	0.0137453i
$885$		0			0
$886$	28.9846			0.973756
$887$	27.5504	−	15.9062i	0.925051	−	0.534078i	0.0398079	−	0.999207i	$-0.487325\pi$
$887$	27.5504	−	15.9062i	0.925051	−	0.534078i	0.885243	+	0.465129i	$0.153992\pi$
$888$		0			0
$889$	−19.2519	−	33.3452i	−0.645686	−	1.11836i
$890$	−22.3961	+	1.19098i	−0.750721	+	0.0399218i
$891$		0			0
$892$			0.888653i			0.0297543i
$893$	−9.80465	−	18.5611i	−0.328100	−	0.621123i
$894$		0			0
$895$	−1.29379	−	24.3293i	−0.0432465	−	0.813240i
$896$	−1.39938	+	2.42379i	−0.0467499	+	0.0809732i
$897$		0			0
$898$	−9.98649	−	5.76570i	−0.333254	−	0.192404i
$899$	−7.15596	−	12.3945i	−0.238665	−	0.413379i
$900$		0			0
$901$	−31.6889			−1.05571
$902$	27.0747	−	15.6316i	0.901490	−	0.520476i
$903$		0			0
$904$	−1.24691			−0.0414716
$905$	34.2115	−	22.2546i	1.13723	−	0.739767i
$906$		0			0
$907$	−16.4814	−	9.51555i	−0.547257	−	0.315959i	0.200758	−	0.979641i	$-0.435659\pi$
$907$	−16.4814	−	9.51555i	−0.547257	−	0.315959i	−0.748015	+	0.663682i	$0.768993\pi$
$908$	−0.197176	+	0.113839i	−0.00654351	+	0.00377790i
$909$		0			0
$910$	0.693155	−	0.0368606i	0.0229779	−	0.00122192i
$911$	28.9516			0.959208			0.479604	−	0.877485i	$-0.340780\pi$
$911$	28.9516			0.959208			0.479604	+	0.877485i	$0.340780\pi$
$912$		0			0
$913$		−	33.2519i		−	1.10048i
$914$	11.0554	−	19.1485i	0.365679	−	0.633375i
$915$		0			0
$916$	−8.11926	−	14.0630i	−0.268268	−	0.464654i
$917$	−31.1632	−	17.9921i	−1.02910	−	0.594150i
$918$		0			0
$919$	21.7479			0.717398			0.358699	−	0.933453i	$-0.383220\pi$
$919$	21.7479			0.717398			0.358699	+	0.933453i	$0.383220\pi$
$920$	−16.5742	+	10.7815i	−0.546435	+	0.355456i
$921$		0			0
$922$	−15.7416	+	9.08841i	−0.518422	+	0.299311i
$923$		−	1.31030i		−	0.0431292i
$924$		0			0
$925$	−0.891806	−	8.36139i	−0.0293224	−	0.274921i
$926$	−17.4774	+	30.2718i	−0.574343	+	0.994791i
$927$		0			0
$928$	−1.57270	−	0.907996i	−0.0516263	−	0.0298064i
$929$	−20.2037	+	34.9938i	−0.662862	+	1.14811i	0.316998	+	0.948426i	$0.397325\pi$
$929$	−20.2037	+	34.9938i	−0.662862	+	1.14811i	−0.979860	+	0.199685i	$0.936008\pi$
$930$		0			0
$931$	−0.136561	+	3.62852i	−0.00447559	+	0.118920i
$932$			3.33959i			0.109392i
$933$		0			0
$934$	−6.50602	+	11.2688i	−0.212883	+	0.368725i
$935$	−17.3651	+	34.1458i	−0.567900	+	1.11669i
$936$		0			0
$937$	17.2215	−	9.94286i	0.562603	−	0.324819i	−0.191587	−	0.981476i	$-0.561363\pi$
$937$	17.2215	−	9.94286i	0.562603	−	0.324819i	0.754190	+	0.656657i	$0.228030\pi$
$938$			12.3730i			0.403994i
$939$		0			0
$940$	−4.88140	+	9.59850i	−0.159214	+	0.313069i
$941$	−11.7807	−	20.4048i	−0.384040	−	0.665176i	0.607596	−	0.794246i	$-0.292134\pi$
$941$	−11.7807	−	20.4048i	−0.384040	−	0.665176i	−0.991635	+	0.129070i	$0.958801\pi$
$942$		0			0
$943$			68.6533i			2.23566i
$944$	0.188606	+	0.326675i	0.00613859	+	0.0106324i
$945$		0			0
$946$	−15.0300	−	26.0327i	−0.488668	−	0.846398i
$947$	−37.0234	−	21.3755i	−1.20310	−	0.694610i	−0.241857	−	0.970312i	$-0.577757\pi$
$947$	−37.0234	−	21.3755i	−1.20310	−	0.694610i	−0.961243	+	0.275702i	$0.911090\pi$
$948$		0			0
$949$	1.06745			0.0346510
$950$	9.57708	−	19.5775i	0.310722	−	0.635179i
$951$		0			0
$952$	−10.3122	−	5.95375i	−0.334220	−	0.192962i
$953$	−20.0662	−	11.5852i	−0.650007	−	0.375282i	0.138452	−	0.990369i	$-0.455787\pi$
$953$	−20.0662	−	11.5852i	−0.650007	−	0.375282i	−0.788459	+	0.615087i	$0.789121\pi$
$954$		0			0
$955$	2.04852	+	38.5219i	0.0662886	+	1.24654i
$956$	−14.1707	−	24.5444i	−0.458313	−	0.793822i
$957$		0			0
$958$		−	30.2830i		−	0.978400i
$959$	−11.4090	−	19.7609i	−0.368414	−	0.638113i
$960$		0			0
$961$	31.1108			1.00358
$962$		−	0.186534i		−	0.00601411i
$963$		0			0
$964$	7.12956	−	12.3488i	0.229628	−	0.397727i
$965$	6.40377	−	12.5920i	0.206145	−	0.405351i
$966$		0			0
$967$	−29.3348	−	16.9365i	−0.943344	−	0.544640i	−0.0523370	−	0.998629i	$-0.516667\pi$
$967$	−29.3348	−	16.9365i	−0.943344	−	0.544640i	−0.891007	+	0.453990i	$0.850000\pi$
$968$		−	5.21402i		−	0.167585i
$969$		0			0
$970$	−9.78736	+	6.36668i	−0.314253	+	0.204422i
$971$	3.13260	−	5.42583i	0.100530	−	0.174123i	−0.811373	−	0.584529i	$-0.801279\pi$
$971$	3.13260	−	5.42583i	0.100530	−	0.174123i	0.911903	+	0.410405i	$0.134613\pi$
$972$		0			0
$973$	−5.53970	+	3.19835i	−0.177595	+	0.102534i
$974$	17.7583	−	30.7583i	0.569013	−	0.985560i
$975$		0			0
$976$	12.3616			0.395684
$977$			10.4850i			0.335446i	0.985834	+	0.167723i	$0.0536414\pi$
$977$			10.4850i			0.335446i	−0.985834	+	0.167723i	$0.946359\pi$
$978$		0			0
$979$	20.1937	+	34.9766i	0.645395	+	1.11786i
$980$	1.56142	−	1.01570i	0.0498777	−	0.0324455i
$981$		0			0
$982$	9.28479	−	5.36057i	0.296289	−	0.171063i
$983$	−46.9978	−	27.1342i	−1.49900	−	0.865446i	−0.498997	−	0.866603i	$-0.666298\pi$
$983$	−46.9978	−	27.1342i	−1.49900	−	0.865446i	−0.999999	+	0.00115735i	$0.999632\pi$
$984$		0			0
$985$	−19.6328	+	1.04404i	−0.625554	+	0.0332657i
$986$	3.86314	−	6.69115i	0.123027	−	0.213090i
$987$		0			0
$988$	0.257311	−	0.409311i	0.00818617	−	0.0130219i
$989$	66.0111			2.09903
$990$		0			0
$991$	−11.8865	+	20.5881i	−0.377588	+	0.654001i	−0.990711	−	0.135986i	$-0.956580\pi$
$991$	−11.8865	+	20.5881i	−0.377588	+	0.654001i	0.613123	+	0.789987i	$0.289913\pi$
$992$	6.82518	−	3.94052i	0.216700	−	0.125112i
$993$		0			0
$994$	−16.5315	−	28.6335i	−0.524349	−	0.908198i
$995$	−8.94475	+	5.81856i	−0.283568	+	0.184461i
$996$		0			0
$997$	−2.37529	+	1.37138i	−0.0752263	+	0.0434319i	−0.537141	−	0.843492i	$-0.680496\pi$
$997$	−2.37529	+	1.37138i	−0.0752263	+	0.0434319i	0.461915	+	0.886924i	$0.347162\pi$
$998$	−20.8295	+	12.0259i	−0.659345	+	0.380673i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.t.c.1189.3		20
3.2	odd	2		570.2.q.c.49.8	yes	20
5.4	even	2	inner	1710.2.t.c.1189.7		20
15.14	odd	2		570.2.q.c.49.4	✓	20
19.7	even	3	inner	1710.2.t.c.919.7		20
57.26	odd	6		570.2.q.c.349.4	yes	20
95.64	even	6	inner	1710.2.t.c.919.3		20
285.254	odd	6		570.2.q.c.349.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.c.49.4	✓	20	15.14	odd	2
570.2.q.c.49.8	yes	20	3.2	odd	2
570.2.q.c.349.4	yes	20	57.26	odd	6
570.2.q.c.349.8	yes	20	285.254	odd	6
1710.2.t.c.919.3		20	95.64	even	6	inner
1710.2.t.c.919.7		20	19.7	even	3	inner
1710.2.t.c.1189.3		20	1.1	even	1	trivial
1710.2.t.c.1189.7		20	5.4	even	2	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.118742 + 2.23291i) q^{5} +2.79875i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.118742 + 2.23291i) q^{5} +2.79875i q^{7} -1.00000i q^{8} +(1.01362 - 1.99313i) q^{10} -4.02666 q^{11} +(0.0960560 - 0.0554580i) q^{13} +(1.39938 - 2.42379i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.68457 - 2.12729i) q^{17} +(0.163933 - 4.35582i) q^{19} +(-1.87439 + 1.21929i) q^{20} +(3.48719 + 2.01333i) q^{22} +(-7.65779 + 4.42123i) q^{23} +(-4.97180 + 0.530281i) q^{25} -0.110916 q^{26} +(-2.42379 + 1.39938i) q^{28} +(-0.907996 - 1.57270i) q^{29} +7.88104 q^{31} +(0.866025 - 0.500000i) q^{32} +(2.12729 + 3.68457i) q^{34} +(-6.24938 + 0.332330i) q^{35} +1.68176i q^{37} +(-2.31988 + 3.69028i) q^{38} +(2.23291 - 0.118742i) q^{40} +(3.88203 - 6.72386i) q^{41} +(-6.46509 - 3.73262i) q^{43} +(-2.01333 - 3.48719i) q^{44} +8.84246 q^{46} +(4.17060 - 2.40790i) q^{47} -0.833029 q^{49} +(4.57085 + 2.02666i) q^{50} +(0.0960560 + 0.0554580i) q^{52} +(6.45034 - 3.72410i) q^{53} +(-0.478134 - 8.99119i) q^{55} +2.79875 q^{56} +1.81599i q^{58} +(0.188606 - 0.326675i) q^{59} +(-6.18078 - 10.7054i) q^{61} +(-6.82518 - 3.94052i) q^{62} -1.00000 q^{64} +(0.135239 + 0.207900i) q^{65} +(-3.82862 + 2.21046i) q^{67} -4.25457i q^{68} +(5.57828 + 2.83688i) q^{70} +(5.90675 - 10.2308i) q^{71} +(8.33460 + 4.81199i) q^{73} +(0.840881 - 1.45645i) q^{74} +(3.85421 - 2.03594i) q^{76} -11.2696i q^{77} +(-2.11845 + 3.66927i) q^{79} +(-1.99313 - 1.01362i) q^{80} +(-6.72386 + 3.88203i) q^{82} +8.25792i q^{83} +(4.31253 - 8.47992i) q^{85} +(3.73262 + 6.46509i) q^{86} +4.02666i q^{88} +(-5.01501 - 8.68625i) q^{89} +(0.155213 + 0.268837i) q^{91} +(-7.65779 - 4.42123i) q^{92} -4.81579 q^{94} +(9.74562 - 0.151171i) q^{95} +(-4.52207 - 2.61082i) q^{97} +(0.721424 + 0.416515i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4}+O(q^{10}) \) 20 * q + 10 * q^4	\( 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) \) 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

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