LMFDB - Embedded newform 630.2.r.b.59.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(59,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3, 1]))

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

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

chi := DirichletCharacter("630.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.r (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.21
Character	$\chi$	$=$	630.59
Dual form			630.2.r.b.299.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.51613 + 0.837458i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23138 + 0.144779i) q^{5} +(1.48333 - 0.894282i) q^{6} +(-2.37108 + 1.17388i) q^{7} -1.00000 q^{8} +(1.59733 + 2.53940i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.51613 + 0.837458i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23138 + 0.144779i) q^{5} +(1.48333 - 0.894282i) q^{6} +(-2.37108 + 1.17388i) q^{7} -1.00000 q^{8} +(1.59733 + 2.53940i) q^{9} +(1.24107 - 1.86004i) q^{10} -0.745990i q^{11} +(-0.0328072 - 1.73174i) q^{12} +(1.67087 - 2.89402i) q^{13} +(-0.168925 + 2.64035i) q^{14} +(3.26182 + 2.08819i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.20138 + 2.42567i) q^{17} +(2.99785 - 0.113627i) q^{18} +(6.50055 - 3.75309i) q^{19} +(-0.990306 - 2.00482i) q^{20} +(-4.57795 - 0.205912i) q^{21} +(-0.646046 - 0.372995i) q^{22} -1.86701 q^{23} +(-1.51613 - 0.837458i) q^{24} +(4.95808 + 0.646111i) q^{25} +(-1.67087 - 2.89402i) q^{26} +(0.295123 + 5.18776i) q^{27} +(2.20215 + 1.46647i) q^{28} +(-0.644047 + 0.371841i) q^{29} +(3.43933 - 1.78073i) q^{30} +(-4.33139 + 2.50073i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.624735 - 1.13102i) q^{33} +(4.20138 - 2.42567i) q^{34} +(-5.46071 + 2.27609i) q^{35} +(1.40052 - 2.65303i) q^{36} +(-5.78366 + 3.33920i) q^{37} -7.50618i q^{38} +(4.95688 - 2.98845i) q^{39} +(-2.23138 - 0.144779i) q^{40} +(-0.849794 + 1.47189i) q^{41} +(-2.46730 + 3.86166i) q^{42} +(-7.64047 + 4.41123i) q^{43} +(-0.646046 + 0.372995i) q^{44} +(3.19659 + 5.89761i) q^{45} +(-0.933507 + 1.61688i) q^{46} +(-10.0544 - 5.80494i) q^{47} +(-1.48333 + 0.894282i) q^{48} +(4.24400 - 5.56673i) q^{49} +(3.03859 - 3.97077i) q^{50} +(4.33846 + 7.19612i) q^{51} -3.34173 q^{52} +(2.94339 - 5.09811i) q^{53} +(4.64030 + 2.33830i) q^{54} +(0.108003 - 1.66458i) q^{55} +(2.37108 - 1.17388i) q^{56} +(12.9988 - 0.246257i) q^{57} +0.743681i q^{58} +(-2.33158 - 4.03841i) q^{59} +(0.177514 - 3.86891i) q^{60} +(-1.48312 - 0.856279i) q^{61} +5.00146i q^{62} +(-6.76834 - 4.14603i) q^{63} +1.00000 q^{64} +(4.14732 - 6.21575i) q^{65} +(-0.667125 - 1.10655i) q^{66} +(-3.92576 + 2.26654i) q^{67} -4.85133i q^{68} +(-2.83065 - 1.56355i) q^{69} +(-0.759202 + 5.86716i) q^{70} -4.17217i q^{71} +(-1.59733 - 2.53940i) q^{72} +(-5.10736 + 8.84620i) q^{73} +6.67839i q^{74} +(6.97602 + 5.13177i) q^{75} +(-6.50055 - 3.75309i) q^{76} +(0.875705 + 1.76880i) q^{77} +(-0.109633 - 5.78701i) q^{78} +(3.10806 - 5.38333i) q^{79} +(-1.24107 + 1.86004i) q^{80} +(-3.89709 + 8.11250i) q^{81} +(0.849794 + 1.47189i) q^{82} +(-2.26849 + 1.30971i) q^{83} +(2.11065 + 4.06757i) q^{84} +(9.02367 + 6.02085i) q^{85} +8.82245i q^{86} +(-1.28786 + 0.0243981i) q^{87} +0.745990i q^{88} +(-7.58595 - 13.1393i) q^{89} +(6.70578 + 0.180480i) q^{90} +(-0.564503 + 8.82335i) q^{91} +(0.933507 + 1.61688i) q^{92} +(-8.66124 + 0.164084i) q^{93} +(-10.0544 + 5.80494i) q^{94} +(15.0485 - 7.43342i) q^{95} +(0.0328072 + 1.73174i) q^{96} +(2.32004 + 4.01843i) q^{97} +(-2.69893 - 6.45877i) q^{98} +(1.89437 - 1.19159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.51613	+	0.837458i	0.875341	+	0.483507i
$3$	1.51613	+	0.837458i	0.875341	+	0.483507i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.23138	+	0.144779i	0.997902	+	0.0647470i
$5$	2.23138	+	0.144779i	0.997902	+	0.0647470i
$6$	1.48333	−	0.894282i	0.605566	−	0.365089i
$7$	−2.37108	+	1.17388i	−0.896182	+	0.443686i
$7$	−2.37108	+	1.17388i	−0.896182	+	0.443686i
$8$	−1.00000			−0.353553
$9$	1.59733	+	2.53940i	0.532442	+	0.846466i
$10$	1.24107	−	1.86004i	0.392461	−	0.588196i
$11$		−	0.745990i		−	0.224924i	−0.993656	−	0.112462i	$-0.964126\pi$
$11$		−	0.745990i		−	0.224924i	0.993656	−	0.112462i	$-0.0358737\pi$
$12$	−0.0328072	−	1.73174i	−0.00947061	−	0.499910i
$13$	1.67087	−	2.89402i	0.463415	−	0.802658i	−0.535714	−	0.844400i	$-0.679957\pi$
$13$	1.67087	−	2.89402i	0.463415	−	0.802658i	0.999128	+	0.0417418i	$0.0132907\pi$
$14$	−0.168925	+	2.64035i	−0.0451472	+	0.705664i
$15$	3.26182	+	2.08819i	0.842198	+	0.539168i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.20138	+	2.42567i	1.01898	+	0.588311i	0.913810	−	0.406143i	$-0.133127\pi$
$17$	4.20138	+	2.42567i	1.01898	+	0.588311i	0.105175	+	0.994454i	$0.466460\pi$
$18$	2.99785	−	0.113627i	0.706599	−	0.0267821i
$19$	6.50055	−	3.75309i	1.49133	−	0.861018i	0.491377	−	0.870947i	$-0.336494\pi$
$19$	6.50055	−	3.75309i	1.49133	−	0.861018i	0.999951	+	0.00992860i	$0.00316042\pi$
$20$	−0.990306	−	2.00482i	−0.221439	−	0.448291i
$21$	−4.57795	−	0.205912i	−0.998990	−	0.0449337i
$22$	−0.646046	−	0.372995i	−0.137738	−	0.0795228i
$23$	−1.86701			−0.389299			−0.194650	−	0.980873i	$-0.562357\pi$
$23$	−1.86701			−0.389299			−0.194650	+	0.980873i	$0.562357\pi$
$24$	−1.51613	−	0.837458i	−0.309480	−	0.170945i
$25$	4.95808	+	0.646111i	0.991616	+	0.129222i
$26$	−1.67087	−	2.89402i	−0.327684	−	0.567565i
$27$	0.295123	+	5.18776i	0.0567965	+	0.998386i
$28$	2.20215	+	1.46647i	0.416167	+	0.277137i
$29$	−0.644047	+	0.371841i	−0.119597	+	0.0690491i	−0.558605	−	0.829434i	$-0.688663\pi$
$29$	−0.644047	+	0.371841i	−0.119597	+	0.0690491i	0.439008	+	0.898483i	$0.355330\pi$
$30$	3.43933	−	1.78073i	0.627934	−	0.325114i
$31$	−4.33139	+	2.50073i	−0.777941	+	0.449145i	−0.835700	−	0.549186i	$-0.814938\pi$
$31$	−4.33139	+	2.50073i	−0.777941	+	0.449145i	0.0577588	+	0.998331i	$0.481605\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.624735	−	1.13102i	0.108752	−	0.196885i
$34$	4.20138	−	2.42567i	0.720531	−	0.415999i
$35$	−5.46071	+	2.27609i	−0.923029	+	0.384730i
$36$	1.40052	−	2.65303i	0.233420	−	0.442171i
$37$	−5.78366	+	3.33920i	−0.950827	+	0.548960i	−0.893338	−	0.449386i	$-0.851643\pi$
$37$	−5.78366	+	3.33920i	−0.950827	+	0.548960i	−0.0574896	+	0.998346i	$0.518310\pi$
$38$		−	7.50618i		−	1.21766i
$39$	4.95688	−	2.98845i	0.793736	−	0.478535i
$40$	−2.23138	−	0.144779i	−0.352812	−	0.0228915i
$41$	−0.849794	+	1.47189i	−0.132716	+	0.229870i	−0.924722	−	0.380642i	$-0.875703\pi$
$41$	−0.849794	+	1.47189i	−0.132716	+	0.229870i	0.792007	+	0.610512i	$0.209036\pi$
$42$	−2.46730	+	3.86166i	−0.380712	+	0.595867i
$43$	−7.64047	+	4.41123i	−1.16516	+	0.672706i	−0.952535	−	0.304428i	$-0.901535\pi$
$43$	−7.64047	+	4.41123i	−1.16516	+	0.672706i	−0.212625	+	0.977134i	$0.568201\pi$
$44$	−0.646046	+	0.372995i	−0.0973951	+	0.0562311i
$45$	3.19659	+	5.89761i	0.476519	+	0.879164i
$46$	−0.933507	+	1.61688i	−0.137638	+	0.238396i
$47$	−10.0544	−	5.80494i	−1.46659	−	0.846737i	−0.467290	−	0.884104i	$-0.654770\pi$
$47$	−10.0544	−	5.80494i	−1.46659	−	0.846737i	−0.999302	+	0.0373667i	$0.988103\pi$
$48$	−1.48333	+	0.894282i	−0.214100	+	0.129078i
$49$	4.24400	−	5.56673i	0.606285	−	0.795247i
$50$	3.03859	−	3.97077i	0.429721	−	0.561551i
$51$	4.33846	+	7.19612i	0.607506	+	1.00766i
$52$	−3.34173			−0.463415
$53$	2.94339	−	5.09811i	0.404306	−	0.700279i	−0.589934	−	0.807451i	$-0.700846\pi$
$53$	2.94339	−	5.09811i	0.404306	−	0.700279i	0.994240	+	0.107172i	$0.0341797\pi$
$54$	4.64030	+	2.33830i	0.631465	+	0.318202i
$55$	0.108003	−	1.66458i	0.0145632	−	0.224452i
$56$	2.37108	−	1.17388i	0.316848	−	0.156867i
$57$	12.9988	−	0.246257i	1.72173	−	0.0326175i
$58$			0.743681i			0.0976501i
$59$	−2.33158	−	4.03841i	−0.303546	−	0.525757i	0.673391	−	0.739287i	$-0.264837\pi$
$59$	−2.33158	−	4.03841i	−0.303546	−	0.525757i	−0.976936	+	0.213530i	$0.931504\pi$
$60$	0.177514	−	3.86891i	0.0229169	−	0.499475i
$61$	−1.48312	−	0.856279i	−0.189894	−	0.109635i	0.402039	−	0.915623i	$-0.368302\pi$
$61$	−1.48312	−	0.856279i	−0.189894	−	0.109635i	−0.591933	+	0.805987i	$0.701635\pi$
$62$			5.00146i			0.635187i
$63$	−6.76834	−	4.14603i	−0.852731	−	0.522351i
$64$	1.00000			0.125000
$65$	4.14732	−	6.21575i	0.514412	−	0.770969i
$66$	−0.667125	−	1.10655i	−0.0821174	−	0.136207i
$67$	−3.92576	+	2.26654i	−0.479608	+	0.276902i	−0.720253	−	0.693711i	$-0.755974\pi$
$67$	−3.92576	+	2.26654i	−0.479608	+	0.276902i	0.240645	+	0.970613i	$0.422641\pi$
$68$		−	4.85133i		−	0.588311i
$69$	−2.83065	−	1.56355i	−0.340770	−	0.188229i
$70$	−0.759202	+	5.86716i	−0.0907420	+	0.701260i
$71$		−	4.17217i		−	0.495145i	−0.968869	−	0.247573i	$-0.920367\pi$
$71$		−	4.17217i		−	0.495145i	0.968869	−	0.247573i	$-0.0796329\pi$
$72$	−1.59733	−	2.53940i	−0.188247	−	0.299271i
$73$	−5.10736	+	8.84620i	−0.597771	+	1.03537i	0.395378	+	0.918518i	$0.370613\pi$
$73$	−5.10736	+	8.84620i	−0.597771	+	1.03537i	−0.993149	+	0.116851i	$0.962720\pi$
$74$			6.67839i			0.776347i
$75$	6.97602	+	5.13177i	0.805522	+	0.592566i
$76$	−6.50055	−	3.75309i	−0.745664	−	0.430509i
$77$	0.875705	+	1.76880i	0.0997958	+	0.201573i
$78$	−0.109633	−	5.78701i	−0.0124135	−	0.655250i
$79$	3.10806	−	5.38333i	0.349685	−	0.605672i	−0.636509	−	0.771269i	$-0.719622\pi$
$79$	3.10806	−	5.38333i	0.349685	−	0.605672i	0.986193	+	0.165598i	$0.0529554\pi$
$80$	−1.24107	+	1.86004i	−0.138756	+	0.207959i
$81$	−3.89709	+	8.11250i	−0.433010	+	0.901389i
$82$	0.849794	+	1.47189i	0.0938441	+	0.162543i
$83$	−2.26849	+	1.30971i	−0.248999	+	0.143760i	−0.619306	−	0.785150i	$-0.712586\pi$
$83$	−2.26849	+	1.30971i	−0.248999	+	0.143760i	0.370307	+	0.928910i	$0.379253\pi$
$84$	2.11065	+	4.06757i	0.230291	+	0.443809i
$85$	9.02367	+	6.02085i	0.978755	+	0.653052i
$86$			8.82245i			0.951349i
$87$	−1.28786	+	0.0243981i	−0.138073	+	0.00261575i
$88$			0.745990i			0.0795228i
$89$	−7.58595	−	13.1393i	−0.804109	−	1.39276i	−0.916891	−	0.399138i	$-0.869309\pi$
$89$	−7.58595	−	13.1393i	−0.804109	−	1.39276i	0.112782	−	0.993620i	$-0.464024\pi$
$90$	6.70578	+	0.180480i	0.706851	+	0.0190242i
$91$	−0.564503	+	8.82335i	−0.0591760	+	0.924938i
$92$	0.933507	+	1.61688i	0.0973249	+	0.168572i
$93$	−8.66124	+	0.164084i	−0.898128	+	0.0170147i
$94$	−10.0544	+	5.80494i	−1.03704	+	0.598734i
$95$	15.0485	−	7.43342i	1.54395	−	0.762653i
$96$	0.0328072	+	1.73174i	0.00334837	+	0.176745i
$97$	2.32004	+	4.01843i	0.235565	+	0.408010i	0.959437	−	0.281924i	$-0.0909728\pi$
$97$	2.32004	+	4.01843i	0.235565	+	0.408010i	−0.723872	+	0.689934i	$0.757639\pi$
$98$	−2.69893	−	6.45877i	−0.272633	−	0.652435i
$99$	1.89437	−	1.19159i	0.190391	−	0.119759i
$100$	−1.91949	−	4.61688i	−0.191949	−	0.461688i
$101$	−10.9742			−1.09197			−0.545986	−	0.837794i	$-0.683845\pi$
$101$	−10.9742			−1.09197			−0.545986	+	0.837794i	$0.683845\pi$
$102$	8.40125	−	0.159158i	0.831848	−	0.0157590i
$103$	6.67426			0.657635			0.328817	−	0.944394i	$-0.393350\pi$
$103$	6.67426			0.657635			0.328817	+	0.944394i	$0.393350\pi$
$104$	−1.67087	+	2.89402i	−0.163842	+	0.283782i
$105$	−10.1853	−	1.12226i	−0.993984	−	0.109521i
$106$	−2.94339	−	5.09811i	−0.285888	−	0.495172i
$107$	−6.82770	−	11.8259i	−0.660058	−	1.14325i	−0.980600	−	0.196020i	$-0.937198\pi$
$107$	−6.82770	−	11.8259i	−0.660058	−	1.14325i	0.320541	−	0.947234i	$-0.396135\pi$
$108$	4.34517	−	2.84947i	0.418115	−	0.274190i
$109$	−5.13894	+	8.90090i	−0.492221	+	0.852551i	−0.999960	−	0.00895944i	$-0.997148\pi$
$109$	−5.13894	+	8.90090i	−0.492221	+	0.852551i	0.507739	+	0.861511i	$0.330481\pi$
$110$	−1.38757	−	0.925826i	−0.132300	−	0.0882740i
$111$	−11.5652	+	0.219099i	−1.09772	+	0.0207960i
$112$	0.168925	−	2.64035i	0.0159619	−	0.249490i
$113$	10.0641	−	17.4316i	0.946754	−	1.63983i	0.194553	−	0.980892i	$-0.437674\pi$
$113$	10.0641	−	17.4316i	0.946754	−	1.63983i	0.752201	−	0.658934i	$-0.228992\pi$
$114$	6.28612	−	11.3804i	0.588749	−	1.06587i
$115$	−4.16601	−	0.270304i	−0.388483	−	0.0252060i
$116$	0.644047	+	0.371841i	0.0597983	+	0.0345245i
$117$	10.0180	−	0.379711i	0.926165	−	0.0351043i
$118$	−4.66316			−0.429278
$119$	−12.8092	−	0.819513i	−1.17422	−	0.0751246i
$120$	−3.26182	−	2.08819i	−0.297762	−	0.190625i
$121$	10.4435			0.949409
$122$	−1.48312	+	0.856279i	−0.134275	+	0.0775238i
$123$	−2.52105	+	1.51991i	−0.227315	+	0.137046i
$124$	4.33139	+	2.50073i	0.388971	+	0.224572i
$125$	10.9698	+	2.15954i	0.981168	+	0.193155i
$126$	−6.97474	+	3.78854i	−0.621359	+	0.337510i
$127$		−	2.11883i		−	0.188015i	−0.995571	−	0.0940077i	$-0.970032\pi$
$127$		−	2.11883i		−	0.188015i	0.995571	−	0.0940077i	$-0.0299678\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−15.2782	+	0.289440i	−1.34517	+	0.0254837i
$130$	−3.30934	−	6.69956i	−0.290248	−	0.587590i
$131$	−15.7575			−1.37674			−0.688370	−	0.725360i	$-0.741673\pi$
$131$	−15.7575			−1.37674			−0.688370	+	0.725360i	$0.741673\pi$
$132$	−1.29186	+	0.0244738i	−0.112442	+	0.00213017i
$133$	−11.0076	+	16.5297i	−0.954480	+	1.43331i
$134$			4.53308i			0.391599i
$135$	−0.0925465	+	11.6186i	−0.00796514	+	0.999968i
$136$	−4.20138	−	2.42567i	−0.360265	−	0.207999i
$137$	−11.0072			−0.940405			−0.470202	−	0.882559i	$-0.655819\pi$
$137$	−11.0072			−0.940405			−0.470202	+	0.882559i	$0.655819\pi$
$138$	−2.76939	+	1.66964i	−0.235746	+	0.142129i
$139$	14.5065	+	8.37531i	1.23042	+	0.710385i	0.967118	−	0.254328i	$-0.0818543\pi$
$139$	14.5065	+	8.37531i	1.23042	+	0.710385i	0.263304	+	0.964713i	$0.415188\pi$
$140$	4.70151	+	3.59107i	0.397350	+	0.303501i
$141$	−10.3825	−	17.2212i	−0.874364	−	1.45029i
$142$	−3.61321	−	2.08609i	−0.303213	−	0.175060i
$143$	−2.15891	−	1.24645i	−0.180537	−	0.104233i
$144$	−2.99785	+	0.113627i	−0.249821	+	0.00946891i
$145$	−1.49095	+	0.736472i	−0.123816	+	0.0611607i
$146$	5.10736	+	8.84620i	0.422688	+	0.732117i
$147$	11.0964	−	4.88574i	0.915214	−	0.402969i
$148$	5.78366	+	3.33920i	0.475414	+	0.274480i
$149$			21.5525i			1.76565i	0.469705	+	0.882823i	$0.344360\pi$
$149$			21.5525i			1.76565i	−0.469705	+	0.882823i	$0.655640\pi$
$150$	7.93226	−	3.47553i	0.647666	−	0.283775i
$151$	−15.3783			−1.25146			−0.625732	−	0.780038i	$-0.715200\pi$
$151$	−15.3783			−1.25146			−0.625732	+	0.780038i	$0.715200\pi$
$152$	−6.50055	+	3.75309i	−0.527264	+	0.304416i
$153$	0.551242	+	14.5436i	0.0445653	+	1.17578i
$154$	1.96968	+	0.126017i	0.158721	+	0.0101547i
$155$	−10.0270	+	4.95298i	−0.805390	+	0.397833i
$156$	−5.06651	−	2.79856i	−0.405646	−	0.224064i
$157$	−3.52158	−	6.09956i	−0.281053	−	0.486798i	0.690591	−	0.723245i	$-0.257350\pi$
$157$	−3.52158	−	6.09956i	−0.281053	−	0.486798i	−0.971644	+	0.236447i	$0.924017\pi$
$158$	−3.10806	−	5.38333i	−0.247264	−	0.428274i
$159$	8.73203	−	5.26445i	0.692495	−	0.417498i
$160$	0.990306	+	2.00482i	0.0782906	+	0.158495i
$161$	4.42683	−	2.19166i	0.348883	−	0.172727i
$162$	5.07709	+	7.43123i	0.398894	+	0.583853i
$163$	6.38815	−	3.68820i	0.500359	−	0.288882i	−0.228503	−	0.973543i	$-0.573383\pi$
$163$	6.38815	−	3.68820i	0.500359	−	0.288882i	0.728862	+	0.684661i	$0.240050\pi$
$164$	1.69959			0.132716
$165$	1.55777	−	2.43329i	0.121272	−	0.189431i
$166$			2.61943i			0.203307i
$167$	14.6090	+	8.43452i	1.13048	+	0.652683i	0.944055	−	0.329787i	$-0.106977\pi$
$167$	14.6090	+	8.43452i	1.13048	+	0.652683i	0.186424	+	0.982469i	$0.440310\pi$
$168$	4.57795	+	0.205912i	0.353196	+	0.0158865i
$169$	0.916415	+	1.58728i	0.0704935	+	0.122098i
$170$	9.72604	−	4.80431i	0.745953	−	0.368473i
$171$	19.9141	+	10.5126i	1.52287	+	0.803916i
$172$	7.64047	+	4.41123i	0.582580	+	0.336353i
$173$	8.87235	+	5.12245i	0.674552	+	0.389453i	0.797799	−	0.602923i	$-0.205997\pi$
$173$	8.87235	+	5.12245i	0.674552	+	0.389453i	−0.123247	+	0.992376i	$0.539331\pi$
$174$	−0.622802	+	1.12752i	−0.0472145	+	0.0854771i
$175$	−12.5144	+	4.28823i	−0.946002	+	0.324159i
$176$	0.646046	+	0.372995i	0.0486976	+	0.0281156i
$177$	−0.152985	−	8.07538i	−0.0114991	−	0.606983i
$178$	−15.1719			−1.13718
$179$	16.4577	+	9.50188i	1.23011	+	0.710204i	0.967053	−	0.254577i	$-0.0819362\pi$
$179$	16.4577	+	9.50188i	1.23011	+	0.710204i	0.263056	+	0.964780i	$0.415269\pi$
$180$	3.50919	−	5.71713i	0.261559	−	0.426130i
$181$			5.53416i			0.411351i	0.978620	+	0.205676i	$0.0659391\pi$
$181$			5.53416i			0.411351i	−0.978620	+	0.205676i	$0.934061\pi$
$182$	7.35899	+	4.90055i	0.545485	+	0.363253i
$183$	−1.53151	−	2.54028i	−0.113212	−	0.187783i
$184$	1.86701			0.137638
$185$	−13.3890	+	6.61365i	−0.984376	+	0.486245i
$186$	−4.18852	+	7.58289i	−0.307117	+	0.556005i
$187$	1.80952	−	3.13419i	0.132325	−	0.229194i
$188$			11.6099i			0.846737i
$189$	−6.78959	−	11.9541i	−0.493870	−	0.869536i
$190$	1.08673	−	16.7491i	0.0788400	−	1.21511i
$191$	−17.3414	−	10.0121i	−1.25478	−	0.724447i	−0.282725	−	0.959201i	$-0.591238\pi$
$191$	−17.3414	−	10.0121i	−1.25478	−	0.724447i	−0.972055	+	0.234754i	$0.924572\pi$
$192$	1.51613	+	0.837458i	0.109418	+	0.0604383i
$193$	16.4666	−	9.50697i	1.18529	−	0.684327i	0.228056	−	0.973648i	$-0.426763\pi$
$193$	16.4666	−	9.50697i	1.18529	−	0.684327i	0.957232	+	0.289321i	$0.0934296\pi$
$194$	4.64008			0.333139
$195$	11.4933	−	5.95071i	0.823054	−	0.426139i
$196$	−6.94293	−	0.892045i	−0.495923	−	0.0637175i
$197$	6.94184			0.494586			0.247293	−	0.968941i	$-0.420459\pi$
$197$	6.94184			0.494586			0.247293	+	0.968941i	$0.420459\pi$
$198$	−0.0847645	−	2.23636i	−0.00602395	−	0.158931i
$199$	−3.90645	−	2.25539i	−0.276921	−	0.159880i	0.355108	−	0.934825i	$-0.384444\pi$
$199$	−3.90645	−	2.25539i	−0.276921	−	0.159880i	−0.632029	+	0.774945i	$0.717777\pi$
$200$	−4.95808	−	0.646111i	−0.350589	−	0.0456869i
$201$	−7.85012	+	0.148718i	−0.553705	+	0.0104897i
$202$	−5.48710	+	9.50393i	−0.386071	+	0.668694i
$203$	1.09059	−	1.63770i	0.0765442	−	0.114944i
$204$	4.06279	−	7.35528i	0.284452	−	0.514972i
$205$	−2.10931	+	3.16130i	−0.147320	+	0.220795i
$206$	3.33713	−	5.78008i	0.232509	−	0.402717i
$207$	−2.98223	−	4.74109i	−0.207280	−	0.329529i
$208$	1.67087	+	2.89402i	0.115854	+	0.200664i
$209$	−2.79977	−	4.84934i	−0.193664	−	0.335436i
$210$	−6.06456	+	8.25961i	−0.418494	+	0.569967i
$211$	3.92397	−	6.79652i	0.270137	−	0.467892i	−0.698759	−	0.715357i	$-0.746264\pi$
$211$	3.92397	−	6.79652i	0.270137	−	0.467892i	0.968897	+	0.247465i	$0.0795976\pi$
$212$	−5.88679			−0.404306
$213$	3.49402	−	6.32557i	0.239406	−	0.433421i
$214$	−13.6554			−0.933464
$215$	−17.6874	+	8.73693i	−1.20627	+	0.595854i
$216$	−0.295123	−	5.18776i	−0.0200806	−	0.352983i
$217$	7.33450	−	11.0140i	0.497898	−	0.747677i
$218$	5.13894	+	8.90090i	0.348053	+	0.602845i
$219$	−15.1518	+	9.13484i	−1.02386	+	0.617275i
$220$	−1.49557	+	0.738758i	−0.100832	+	0.0498071i
$221$	14.0399	−	8.10593i	0.944425	−	0.545264i
$222$	−5.59287	+	10.1253i	−0.375369	+	0.679568i
$223$	10.7610	+	18.6387i	0.720612	+	1.24814i	0.960755	+	0.277399i	$0.0894725\pi$
$223$	10.7610	+	18.6387i	0.720612	+	1.24814i	−0.240143	+	0.970738i	$0.577194\pi$
$224$	−2.20215	−	1.46647i	−0.147137	−	0.0979827i
$225$	6.27894	+	13.6226i	0.418596	+	0.908173i
$226$	−10.0641	−	17.4316i	−0.669456	−	1.15953i
$227$			8.02790i			0.532831i	0.963858	+	0.266415i	$0.0858393\pi$
$227$			8.02790i			0.532831i	−0.963858	+	0.266415i	$0.914161\pi$
$228$	−6.71264	−	11.1341i	−0.444556	−	0.737376i
$229$			19.2674i			1.27322i	0.771185	+	0.636612i	$0.219665\pi$
$229$			19.2674i			1.27322i	−0.771185	+	0.636612i	$0.780335\pi$
$230$	−2.31710	+	3.47272i	−0.152785	+	0.228984i
$231$	−0.153608	+	3.41510i	−0.0101067	+	0.224697i
$232$	0.644047	−	0.371841i	0.0422837	−	0.0244125i
$233$	−0.572350	−	0.991339i	−0.0374959	−	0.0649448i	0.846668	−	0.532121i	$-0.178605\pi$
$233$	−0.572350	−	0.991339i	−0.0374959	−	0.0649448i	−0.884164	+	0.467176i	$0.845271\pi$
$234$	4.68016	−	8.86570i	0.305952	−	0.579569i
$235$	−21.5948	−	14.4087i	−1.40869	−	0.939918i
$236$	−2.33158	+	4.03841i	−0.151773	+	0.262878i
$237$	9.22055	−	5.55897i	0.598939	−	0.361094i
$238$	−7.11434	+	10.6834i	−0.461154	+	0.692500i
$239$	10.1997	+	5.88880i	0.659764	+	0.380915i	0.792187	−	0.610279i	$-0.208942\pi$
$239$	10.1997	+	5.88880i	0.659764	+	0.380915i	−0.132423	+	0.991193i	$0.542276\pi$
$240$	−3.43933	+	1.78073i	−0.222008	+	0.114945i
$241$			22.9924i			1.48107i	0.672017	+	0.740536i	$0.265428\pi$
$241$			22.9924i			1.48107i	−0.672017	+	0.740536i	$0.734572\pi$
$242$	5.22175	−	9.04434i	0.335667	−	0.581392i
$243$	−12.7024	+	9.03599i	−0.814859	+	0.579659i
$244$			1.71256i			0.109635i
$245$	10.2759	−	11.8070i	0.656503	−	0.754323i
$246$	0.0557586	+	2.94324i	0.00355504	+	0.187654i
$247$		−	25.0837i		−	1.59603i
$248$	4.33139	−	2.50073i	0.275044	−	0.158797i
$249$	−4.53617	+	0.0859359i	−0.287468	+	0.00544597i
$250$	7.35511	−	8.42035i	0.465178	−	0.532550i
$251$	−1.44964			−0.0915002			−0.0457501	−	0.998953i	$-0.514568\pi$
$251$	−1.44964			−0.0915002			−0.0457501	+	0.998953i	$0.514568\pi$
$252$	−0.206397	+	7.93457i	−0.0130018	+	0.499831i
$253$			1.39277i			0.0875630i
$254$	−1.83496	−	1.05941i	−0.115135	−	0.0664735i
$255$	8.63889	+	16.6854i	0.540989	+	1.04488i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		−	7.01785i		−	0.437762i	−0.975752	−	0.218881i	$-0.929759\pi$
$257$		−	7.01785i		−	0.437762i	0.975752	−	0.218881i	$-0.0702406\pi$
$258$	−7.38843	+	13.3760i	−0.459984	+	0.832755i
$259$	9.79366	−	14.7068i	0.608549	−	0.913838i
$260$	−7.45666	−	0.483811i	−0.462442	−	0.0300047i
$261$	−1.97301	−	1.04154i	−0.122126	−	0.0644697i
$262$	−7.87875	+	13.6464i	−0.486751	+	0.843077i
$263$	2.64989			0.163399			0.0816996	−	0.996657i	$-0.473965\pi$
$263$	2.64989			0.163399			0.0816996	+	0.996657i	$0.473965\pi$
$264$	−0.624735	+	1.13102i	−0.0384498	+	0.0696095i
$265$	7.30592	−	10.9497i	0.448799	−	0.672632i
$266$	8.81138	+	17.7977i	0.540260	+	1.09125i
$267$	−0.497747	−	26.2738i	−0.0304616	−	1.60793i
$268$	3.92576	+	2.26654i	0.239804	+	0.138451i
$269$	11.9338	−	20.6700i	0.727618	−	1.26027i	−0.230269	−	0.973127i	$-0.573961\pi$
$269$	11.9338	−	20.6700i	0.727618	−	1.26027i	0.957887	−	0.287145i	$-0.0927060\pi$
$270$	10.0157	+	5.88944i	0.609537	+	0.358420i
$271$	−16.9678	+	9.79635i	−1.03072	+	0.595086i	−0.917190	−	0.398449i	$-0.869549\pi$
$271$	−16.9678	+	9.79635i	−1.03072	+	0.595086i	−0.113528	+	0.993535i	$0.536215\pi$
$272$	−4.20138	+	2.42567i	−0.254746	+	0.147078i
$273$	−8.24505	+	12.9046i	−0.499013	+	0.781024i
$274$	−5.50358	+	9.53248i	−0.332483	+	0.575878i
$275$	0.481992	−	3.69868i	0.0290652	−	0.223039i
$276$	0.0612514	+	3.23318i	0.00368690	+	0.194615i
$277$		−	19.9426i		−	1.19823i	−0.800662	−	0.599116i	$-0.795519\pi$
$277$		−	19.9426i		−	1.19823i	0.800662	−	0.599116i	$-0.204481\pi$
$278$	14.5065	−	8.37531i	0.870040	−	0.502318i
$279$	−13.2690	−	7.00465i	−0.794395	−	0.419357i
$280$	5.46071	−	2.27609i	0.326340	−	0.136023i
$281$	−2.03902	+	1.17723i	−0.121638	+	0.0702277i	−0.559584	−	0.828773i	$-0.689039\pi$
$281$	−2.03902	+	1.17723i	−0.121638	+	0.0702277i	0.437947	+	0.899001i	$0.355706\pi$
$282$	−20.1053	+	0.380887i	−1.19725	+	0.0226815i
$283$	−4.41483	−	7.64671i	−0.262434	−	0.454550i	0.704454	−	0.709750i	$-0.251192\pi$
$283$	−4.41483	−	7.64671i	−0.262434	−	0.454550i	−0.966888	+	0.255200i	$0.917859\pi$
$284$	−3.61321	+	2.08609i	−0.214404	+	0.123786i
$285$	29.0408	+	1.33245i	1.72023	+	0.0789276i
$286$	−2.15891	+	1.24645i	−0.127659	+	0.0737041i
$287$	0.287103	−	4.48751i	0.0169472	−	0.264889i
$288$	−1.40052	+	2.65303i	−0.0825264	+	0.156331i
$289$	3.26772	+	5.65986i	0.192219	+	0.332933i
$290$	−0.107669	+	1.65943i	−0.00632255	+	0.0974452i
$291$	0.152228	+	8.03542i	0.00892376	+	0.471045i
$292$	10.2147			0.597771
$293$	−8.74058	−	5.04638i	−0.510630	−	0.294812i	0.222463	−	0.974941i	$-0.428590\pi$
$293$	−8.74058	−	5.04638i	−0.510630	−	0.294812i	−0.733093	+	0.680129i	$0.761924\pi$
$294$	1.31701	−	12.0526i	0.0768097	−	0.702923i
$295$	−4.61795	−	9.34878i	−0.268868	−	0.544307i
$296$	5.78366	−	3.33920i	0.336168	−	0.194087i
$297$	3.87002	−	0.220159i	0.224561	−	0.0127749i
$298$	18.6650	+	10.7762i	1.08123	+	0.624250i
$299$	−3.11953	+	5.40319i	−0.180407	+	0.312474i
$300$	0.956236	−	8.60730i	0.0552083	−	0.496943i
$301$	12.9379	−	19.4284i	0.745726	−	1.11983i
$302$	−7.68913	+	13.3180i	−0.442460	+	0.766363i
$303$	−16.6384	−	9.19043i	−0.955848	−	0.527976i
$304$			7.50618i			0.430509i
$305$	−3.18542	−	2.12540i	−0.182397	−	0.121700i
$306$	12.8707	+	6.79439i	0.735770	+	0.388409i
$307$	−10.7285			−0.612306			−0.306153	−	0.951982i	$-0.599042\pi$
$307$	−10.7285			−0.612306			−0.306153	+	0.951982i	$0.599042\pi$
$308$	1.09397	−	1.64278i	0.0623348	−	0.0936062i
$309$	10.1191	+	5.58942i	0.575654	+	0.317971i
$310$	−0.724105	+	11.1601i	−0.0411264	+	0.633854i
$311$	−2.49511	−	4.32165i	−0.141485	−	0.245059i	0.786571	−	0.617500i	$-0.211854\pi$
$311$	−2.49511	−	4.32165i	−0.141485	−	0.245059i	−0.928056	+	0.372441i	$0.878521\pi$
$312$	−4.95688	+	2.98845i	−0.280628	+	0.169188i
$313$	10.0534	−	17.4130i	0.568253	−	0.984243i	−0.428486	−	0.903548i	$-0.640953\pi$
$313$	10.0534	−	17.4130i	0.568253	−	0.984243i	0.996739	−	0.0806942i	$-0.0257137\pi$
$314$	−7.04317			−0.397469
$315$	−14.5025	−	10.2313i	−0.817121	−	0.576466i
$316$	−6.21613			−0.349685
$317$	13.0051	−	22.5255i	0.730440	−	1.26516i	−0.226256	−	0.974068i	$-0.572649\pi$
$317$	13.0051	−	22.5255i	0.730440	−	1.26516i	0.956695	−	0.291091i	$-0.0940181\pi$
$318$	−0.193129	−	10.1944i	−0.0108301	−	0.571673i
$319$	0.277389	+	0.480452i	0.0155308	+	0.0269002i
$320$	2.23138	+	0.144779i	0.124738	+	0.00809337i
$321$	−0.447995	−	23.6476i	−0.0250046	−	1.31988i
$322$	0.315386	−	4.92958i	0.0175758	−	0.274715i
$323$	36.4150			2.02619
$324$	8.97418	−	0.681272i	0.498565	−	0.0378485i
$325$	10.1541	−	13.2692i	0.563251	−	0.736045i
$326$		−	7.37640i		−	0.408541i
$327$	−15.2454	+	9.19132i	−0.843075	+	0.508281i
$328$	0.849794	−	1.47189i	0.0469220	−	0.0812713i
$329$	30.6542	+	1.96120i	1.69002	+	0.108125i
$330$	−1.32840	−	2.56571i	−0.0731262	−	0.141238i
$331$	−6.69898	+	11.6030i	−0.368209	+	0.637757i	−0.989286	−	0.145993i	$-0.953362\pi$
$331$	−6.69898	+	11.6030i	−0.368209	+	0.637757i	0.621076	+	0.783750i	$0.286696\pi$
$332$	2.26849	+	1.30971i	0.124500	+	0.0718798i
$333$	−17.7179	−	9.35322i	−0.970937	−	0.512553i
$334$	14.6090	−	8.43452i	0.799370	−	0.461516i
$335$	−9.08800	+	4.48914i	−0.496531	+	0.245268i
$336$	2.46730	−	3.86166i	0.134602	−	0.210671i
$337$	7.18391	+	4.14763i	0.391333	+	0.225936i	0.682737	−	0.730664i	$-0.260789\pi$
$337$	7.18391	+	4.14763i	0.391333	+	0.225936i	−0.291405	+	0.956600i	$0.594123\pi$
$338$	1.83283			0.0996929
$339$	29.8568	−	18.0003i	1.62160	−	0.977644i
$340$	0.702369	−	10.8252i	0.0380913	−	0.587076i
$341$	1.86552	+	3.23118i	0.101024	+	0.174978i
$342$	19.0612	−	11.9898i	1.03071	−	0.648336i
$343$	−3.52815	+	18.1811i	−0.190502	+	0.981687i
$344$	7.64047	−	4.41123i	0.411946	−	0.237837i
$345$	−6.08987	−	3.89868i	−0.327867	−	0.209898i
$346$	8.87235	−	5.12245i	0.476980	−	0.275385i
$347$	8.22042	+	14.2382i	0.441295	+	0.764346i	0.997786	−	0.0665078i	$-0.0211857\pi$
$347$	8.22042	+	14.2382i	0.441295	+	0.764346i	−0.556490	+	0.830854i	$0.687852\pi$
$348$	0.665061	+	1.10312i	0.0356510	+	0.0591336i
$349$	26.2420	−	15.1508i	1.40470	−	0.811004i	0.409830	−	0.912162i	$-0.365588\pi$
$349$	26.2420	−	15.1508i	1.40470	−	0.811004i	0.994870	+	0.101158i	$0.0322547\pi$
$350$	−2.54351	+	12.9819i	−0.135956	+	0.693913i
$351$	15.5066	+	7.81396i	0.827683	+	0.417079i
$352$	0.646046	−	0.372995i	0.0344344	−	0.0198807i
$353$			12.4615i			0.663257i	0.943410	+	0.331629i	$0.107598\pi$
$353$			12.4615i			0.663257i	−0.943410	+	0.331629i	$0.892402\pi$
$354$	−7.06997	−	3.90520i	−0.375765	−	0.207559i
$355$	0.604041	−	9.30968i	0.0320592	−	0.494107i
$356$	−7.58595	+	13.1393i	−0.402055	+	0.696379i
$357$	−18.7342	−	11.9697i	−0.991520	−	0.633503i
$358$	16.4577	−	9.50188i	0.869818	−	0.502190i
$359$	−1.01914	+	0.588399i	−0.0537880	+	0.0310545i	−0.526653	−	0.850080i	$-0.676553\pi$
$359$	−1.01914	+	0.588399i	−0.0537880	+	0.0310545i	0.472865	+	0.881135i	$0.343220\pi$
$360$	−3.19659	−	5.89761i	−0.168475	−	0.310831i
$361$	18.6714	−	32.3398i	0.982705	−	1.70210i
$362$	4.79273	+	2.76708i	0.251900	+	0.145435i
$363$	15.8337	+	8.74599i	0.831056	+	0.459046i
$364$	7.92350	−	3.92280i	0.415304	−	0.205611i
$365$	−12.6772	+	18.9998i	−0.663554	+	0.994493i
$366$	−2.96570	+	0.0561841i	−0.155020	+	0.00293679i
$367$	35.4401			1.84996			0.924978	−	0.380020i	$-0.124083\pi$
$367$	35.4401			1.84996			0.924978	+	0.380020i	$0.124083\pi$
$368$	0.933507	−	1.61688i	0.0486624	−	0.0842858i
$369$	−5.09511	+	0.193119i	−0.265241	+	0.0100534i
$370$	−0.966888	+	14.9020i	−0.0502661	+	0.774718i
$371$	−0.994427	+	15.5432i	−0.0516281	+	0.806963i
$372$	4.47272	+	7.41881i	0.231900	+	0.384647i
$373$			25.3686i			1.31353i	0.754093	+	0.656767i	$0.228077\pi$
$373$			25.3686i			1.31353i	−0.754093	+	0.656767i	$0.771923\pi$
$374$	−1.80952	−	3.13419i	−0.0935682	−	0.162065i
$375$	14.8232	+	12.4609i	0.765465	+	0.643478i
$376$	10.0544	+	5.80494i	0.518519	+	0.299367i
$377$			2.48518i			0.127993i
$378$	−13.7474	−	0.0971153i	−0.707089	−	0.00499507i
$379$	24.3494			1.25075			0.625373	−	0.780326i	$-0.284947\pi$
$379$	24.3494			1.25075			0.625373	+	0.780326i	$0.284947\pi$
$380$	−13.9618	−	9.31570i	−0.716225	−	0.477885i
$381$	1.77443	−	3.21243i	0.0909067	−	0.164578i
$382$	−17.3414	+	10.0121i	−0.887263	+	0.512262i
$383$		−	13.1254i		−	0.670674i	−0.942098	−	0.335337i	$-0.891150\pi$
$383$		−	13.1254i		−	0.670674i	0.942098	−	0.335337i	$-0.108850\pi$
$384$	1.48333	−	0.894282i	0.0756957	−	0.0456361i
$385$	1.69794	+	4.07364i	0.0865352	+	0.207612i
$386$		−	19.0139i		−	0.967784i
$387$	−23.4062	−	12.3560i	−1.18980	−	0.628092i
$388$	2.32004	−	4.01843i	0.117782	−	0.204005i
$389$		−	19.3282i		−	0.979980i	−0.871728	−	0.489990i	$-0.837000\pi$
$389$		−	19.3282i		−	0.979980i	0.871728	−	0.489990i	$-0.163000\pi$
$390$	0.593203	−	12.9289i	0.0300380	−	0.654679i
$391$	−7.84404	−	4.52876i	−0.396690	−	0.229029i
$392$	−4.24400	+	5.56673i	−0.214354	+	0.281162i
$393$	−23.8905	−	13.1962i	−1.20512	−	0.665663i
$394$	3.47092	−	6.01181i	0.174862	−	0.302871i
$395$	7.71465	−	11.5622i	0.388166	−	0.581760i
$396$	−1.97913	−	1.04477i	−0.0994550	−	0.0525019i
$397$	−18.0143	−	31.2016i	−0.904111	−	1.56597i	−0.822107	−	0.569334i	$-0.807201\pi$
$397$	−18.0143	−	31.2016i	−0.904111	−	1.56597i	−0.0820040	−	0.996632i	$-0.526132\pi$
$398$	−3.90645	+	2.25539i	−0.195812	+	0.113052i
$399$	−30.5320	+	15.8429i	−1.52851	+	0.793138i
$400$	−3.03859	+	3.97077i	−0.151929	+	0.198538i
$401$		−	3.15068i		−	0.157338i	−0.996901	−	0.0786688i	$-0.974933\pi$
$401$		−	3.15068i		−	0.157338i	0.996901	−	0.0786688i	$-0.0250669\pi$
$402$	−3.79627	+	6.87276i	−0.189341	+	0.342782i
$403$			16.7135i			0.832561i
$404$	5.48710	+	9.50393i	0.272993	+	0.472838i
$405$	−9.87039	+	17.5378i	−0.490464	+	0.871462i
$406$	−0.872995	−	1.76332i	−0.0433260	−	0.0875123i
$407$	2.49101	+	4.31455i	0.123475	+	0.213864i
$408$	−4.33846	−	7.19612i	−0.214786	−	0.356261i
$409$	−13.8104	+	7.97346i	−0.682882	+	0.394262i	−0.800940	−	0.598744i	$-0.795667\pi$
$409$	−13.8104	+	7.97346i	−0.682882	+	0.394262i	0.118058	+	0.993007i	$0.462333\pi$
$410$	1.68311	+	3.40736i	0.0831230	+	0.168278i
$411$	−16.6883	−	9.21804i	−0.823175	−	0.454692i
$412$	−3.33713	−	5.78008i	−0.164409	−	0.284764i
$413$	10.2690	+	6.83838i	0.505303	+	0.336495i
$414$	−5.59702	+	0.212143i	−0.275079	+	0.0104263i
$415$	−5.25147	+	2.59403i	−0.257785	+	0.127336i
$416$	3.34173			0.163842
$417$	14.9798	+	24.8467i	0.733563	+	1.21675i
$418$	−5.59954			−0.273882
$419$	−17.4629	+	30.2467i	−0.853120	+	1.47765i	0.0252584	+	0.999681i	$0.491959\pi$
$419$	−17.4629	+	30.2467i	−0.853120	+	1.47765i	−0.878378	+	0.477966i	$0.841374\pi$
$420$	4.12075	+	9.38187i	0.201072	+	0.457788i
$421$	18.6679	+	32.3338i	0.909818	+	1.57585i	0.814315	+	0.580423i	$0.197113\pi$
$421$	18.6679	+	32.3338i	0.909818	+	1.57585i	0.0955030	+	0.995429i	$0.469554\pi$
$422$	−3.92397	−	6.79652i	−0.191016	−	0.330849i
$423$	−1.31919	−	34.8046i	−0.0641414	−	1.69226i
$424$	−2.94339	+	5.09811i	−0.142944	+	0.247586i
$425$	19.2635	+	14.7412i	0.934418	+	0.715054i
$426$	−3.73110	−	6.18869i	−0.180772	−	0.299843i
$427$	4.52176	+	0.289294i	0.218823	+	0.0139999i
$428$	−6.82770	+	11.8259i	−0.330029	+	0.571627i
$429$	−2.22935	−	3.69778i	−0.107634	−	0.178531i
$430$	−1.27730	+	19.6862i	−0.0615970	+	0.949353i
$431$	7.75117	+	4.47514i	0.373361	+	0.215560i	0.674926	−	0.737886i	$-0.264176\pi$
$431$	7.75117	+	4.47514i	0.373361	+	0.215560i	−0.301565	+	0.953446i	$0.597509\pi$
$432$	−4.64030	−	2.33830i	−0.223256	−	0.112501i
$433$	12.0060			0.576972			0.288486	−	0.957484i	$-0.406848\pi$
$433$	12.0060			0.576972			0.288486	+	0.957484i	$0.406848\pi$
$434$	−5.87113	−	11.8588i	−0.281823	−	0.569243i
$435$	−2.87724	−	0.132014i	−0.137953	−	0.00632957i
$436$	10.2779			0.492221
$437$	−12.1366	+	7.00708i	−0.580573	+	0.335194i
$438$	0.335116	+	17.6892i	0.0160125	+	0.845224i
$439$	−28.3831	−	16.3870i	−1.35465	−	0.782108i	−0.365753	−	0.930712i	$-0.619189\pi$
$439$	−28.3831	−	16.3870i	−1.35465	−	0.782108i	−0.988897	+	0.148604i	$0.952522\pi$
$440$	−0.108003	+	1.66458i	−0.00514886	+	0.0793559i
$441$	20.9152	+	1.88531i	0.995962	+	0.0897767i
$442$		−	16.2119i		−	0.771119i
$443$	−3.05270	+	5.28743i	−0.145038	+	0.251213i	−0.929387	−	0.369106i	$-0.879664\pi$
$443$	−3.05270	+	5.28743i	−0.145038	+	0.251213i	0.784349	+	0.620320i	$0.212997\pi$
$444$	5.97237	+	9.90624i	0.283436	+	0.470129i
$445$	−15.0248	−	30.4169i	−0.712245	−	1.44190i
$446$	21.5221			1.01910
$447$	−18.0493	+	32.6764i	−0.853702	+	1.54554i
$448$	−2.37108	+	1.17388i	−0.112023	+	0.0554608i
$449$		−	4.39667i		−	0.207492i	−0.994604	−	0.103746i	$-0.966917\pi$
$449$		−	4.39667i		−	0.207492i	0.994604	−	0.103746i	$-0.0330828\pi$
$450$	14.9370	+	1.37357i	0.704136	+	0.0647508i
$451$	1.09801	+	0.633938i	0.0517034	+	0.0298510i
$452$	−20.1283			−0.946754
$453$	−23.3155	−	12.8786i	−1.09546	−	0.605092i
$454$	6.95237	+	4.01395i	0.326291	+	0.188384i
$455$	−2.53705	+	19.6065i	−0.118939	+	0.919166i
$456$	−12.9988	+	0.246257i	−0.608723	+	0.0115320i
$457$	28.7983	+	16.6267i	1.34713	+	0.777765i	0.987842	−	0.155462i	$-0.0496866\pi$
$457$	28.7983	+	16.6267i	1.34713	+	0.777765i	0.359287	+	0.933227i	$0.383020\pi$
$458$	16.6860	+	9.63368i	0.779687	+	0.450152i
$459$	−11.3439	+	22.5116i	−0.529486	+	1.05075i
$460$	1.84892	+	3.74302i	0.0862062	+	0.174519i
$461$	−6.22235	−	10.7774i	−0.289804	−	0.501955i	0.683959	−	0.729520i	$-0.260257\pi$
$461$	−6.22235	−	10.7774i	−0.289804	−	0.501955i	−0.973763	+	0.227566i	$0.926923\pi$
$462$	2.88076	+	1.84058i	0.134025	+	0.0856315i
$463$	2.79388	+	1.61305i	0.129843	+	0.0749647i	0.563514	−	0.826106i	$-0.309449\pi$
$463$	2.79388	+	1.61305i	0.129843	+	0.0749647i	−0.433672	+	0.901071i	$0.642782\pi$
$464$		−	0.743681i		−	0.0345245i
$465$	−19.3502	−	0.887829i	−0.897345	−	0.0411721i
$466$	−1.14470			−0.0530272
$467$	−36.0480	+	20.8123i	−1.66810	+	0.963080i	−0.699443	+	0.714688i	$0.746569\pi$
$467$	−36.0480	+	20.8123i	−1.66810	+	0.963080i	−0.968660	+	0.248392i	$0.920098\pi$
$468$	−5.33784	−	8.48599i	−0.246742	−	0.392265i
$469$	6.64763	−	9.98253i	0.306959	−	0.460950i
$470$	−23.2757	+	11.4973i	−1.07363	+	0.530332i
$471$	−0.231066	−	12.1969i	−0.0106470	−	0.562005i
$472$	2.33158	+	4.03841i	0.107320	+	0.185883i
$473$	3.29073	+	5.69971i	0.151308	+	0.262073i
$474$	−0.203934	−	10.7647i	−0.00936698	−	0.494440i
$475$	34.6551	−	14.4081i	1.59009	−	0.661087i
$476$	5.69490	+	11.5029i	0.261025	+	0.527234i
$477$	17.6477	−	0.668898i	0.808032	−	0.0306267i
$478$	10.1997	−	5.88880i	0.466523	−	0.269347i
$479$	−23.0103			−1.05137			−0.525683	−	0.850681i	$-0.676190\pi$
$479$	−23.0103			−1.05137			−0.525683	+	0.850681i	$0.676190\pi$
$480$	−0.177514	+	3.86891i	−0.00810236	+	0.176591i
$481$			22.3174i			1.01759i
$482$	19.9120	+	11.4962i	0.906967	+	0.523638i
$483$	8.54709	+	0.384441i	0.388906	+	0.0174927i
$484$	−5.22175	−	9.04434i	−0.237352	−	0.411106i
$485$	4.59510	+	9.30252i	0.208653	+	0.422406i
$486$	1.47420	+	15.5186i	0.0668712	+	0.703938i
$487$	−9.17108	−	5.29492i	−0.415581	−	0.239936i	0.277604	−	0.960696i	$-0.410460\pi$
$487$	−9.17108	−	5.29492i	−0.415581	−	0.239936i	−0.693185	+	0.720760i	$0.743793\pi$
$488$	1.48312	+	0.856279i	0.0671376	+	0.0387619i
$489$	12.7740	−	0.241999i	0.577661	−	0.0109436i
$490$	−5.08724	−	14.8027i	−0.229818	−	0.668718i
$491$	2.99490	+	1.72911i	0.135158	+	0.0780336i	0.566054	−	0.824368i	$-0.308469\pi$
$491$	2.99490	+	1.72911i	0.135158	+	0.0780336i	−0.430896	+	0.902401i	$0.641803\pi$
$492$	2.57680	+	1.42333i	0.116171	+	0.0641689i
$493$	−3.60785			−0.162489
$494$	−21.7231	−	12.5418i	−0.977368	−	0.564283i
$495$	4.39956	−	2.38462i	0.197745	−	0.107181i
$496$		−	5.00146i		−	0.224572i
$497$	4.89764	+	9.89253i	0.219689	+	0.443741i
$498$	−2.19366	+	3.97140i	−0.0983003	+	0.177963i
$499$	−14.4692			−0.647730			−0.323865	−	0.946103i	$-0.604982\pi$
$499$	−14.4692			−0.647730			−0.323865	+	0.946103i	$0.604982\pi$
$500$	−3.61468	−	10.5799i	−0.161653	−	0.473147i
$501$	15.0857	+	25.0223i	0.673978	+	1.11791i
$502$	−0.724818	+	1.25542i	−0.0323502	+	0.0560322i
$503$		−	33.2244i		−	1.48140i	−0.671833	−	0.740702i	$-0.734493\pi$
$503$		−	33.2244i		−	1.48140i	0.671833	−	0.740702i	$-0.265507\pi$
$504$	6.76834	+	4.14603i	0.301486	+	0.184679i
$505$	−24.4876	−	1.58883i	−1.08968	−	0.0707019i
$506$	1.20618	+	0.696387i	0.0536211	+	0.0309582i
$507$	0.0601300	+	3.17399i	0.00267047	+	0.140962i
$508$	−1.83496	+	1.05941i	−0.0814131	+	0.0470039i
$509$	−41.8292			−1.85405			−0.927023	−	0.375005i	$-0.877641\pi$
$509$	−41.8292			−1.85405			−0.927023	+	0.375005i	$0.877641\pi$
$510$	18.7694	+	0.861179i	0.831123	+	0.0381336i
$511$	1.72552	−	26.9705i	0.0763327	−	1.19310i
$512$	−1.00000			−0.0441942
$513$	21.3886	+	32.6157i	0.944331	+	1.44002i
$514$	−6.07764	−	3.50893i	−0.268073	−	0.154772i
$515$	14.8928	+	0.966290i	0.656255	+	0.0425798i
$516$	7.88976	+	13.0866i	0.347327	+	0.576105i
$517$	−4.33043	+	7.50052i	−0.190452	+	0.329872i
$518$	−7.83965	−	15.8350i	−0.344454	−	0.695749i
$519$	9.16183	+	15.1965i	0.402160	+	0.667054i
$520$	−4.14732	+	6.21575i	−0.181872	+	0.272579i
$521$	11.1096	−	19.2425i	0.486722	−	0.843027i	−0.513161	−	0.858292i	$-0.671526\pi$
$521$	11.1096	−	19.2425i	0.486722	−	0.843027i	0.999883	+	0.0152648i	$0.00485914\pi$
$522$	−1.88850	+	1.18790i	−0.0826575	+	0.0519931i
$523$	15.3867	+	26.6505i	0.672813	+	1.16535i	0.977103	+	0.212766i	$0.0682473\pi$
$523$	15.3867	+	26.6505i	0.672813	+	1.16535i	−0.304291	+	0.952579i	$0.598419\pi$
$524$	7.87875	+	13.6464i	0.344185	+	0.596146i
$525$	−22.5648	−	3.97879i	−0.984808	−	0.173649i
$526$	1.32494	−	2.29487i	0.0577703	−	0.100061i
$527$	−24.2638			−1.05695
$528$	0.667125	+	1.10655i	0.0290329	+	0.0481563i
$529$	−19.5143			−0.848446
$530$	−5.82972	−	11.8019i	−0.253227	−	0.512643i
$531$	6.53085	−	12.3715i	0.283415	−	0.536876i
$532$	19.8190	+	1.26798i	0.859262	+	0.0549741i
$533$	2.83978	+	4.91865i	0.123005	+	0.213050i
$534$	−23.0026	−	12.7058i	−0.995422	−	0.549835i
$535$	−13.5230	−	27.3766i	−0.584651	−	1.18359i
$536$	3.92576	−	2.26654i	0.169567	−	0.0978996i
$537$	16.9947	+	28.1888i	0.733376	+	1.21644i
$538$	−11.9338	−	20.6700i	−0.514504	−	0.891147i
$539$	−4.15272	−	3.16598i	−0.178871	−	0.136368i
$540$	10.1083	−	5.72914i	0.434990	−	0.246543i
$541$	2.61686	+	4.53253i	0.112508	+	0.194869i	0.916781	−	0.399391i	$-0.130778\pi$
$541$	2.61686	+	4.53253i	0.112508	+	0.194869i	−0.804273	+	0.594260i	$0.797445\pi$
$542$			19.5927i			0.841578i
$543$	−4.63463	+	8.39053i	−0.198891	+	0.360072i
$544$			4.85133i			0.207999i
$545$	−12.7556	+	19.1172i	−0.546388	+	0.818893i
$546$	7.05322	+	13.5927i	0.301850	+	0.581716i
$547$	3.57961	−	2.06669i	0.153053	−	0.0883652i	−0.421518	−	0.906820i	$-0.638502\pi$
$547$	3.57961	−	2.06669i	0.153053	−	0.0883652i	0.574571	+	0.818455i	$0.305169\pi$
$548$	5.50358	+	9.53248i	0.235101	+	0.407207i
$549$	−0.194593	−	5.13398i	−0.00830501	−	0.219113i
$550$	−2.96215	−	2.26676i	−0.126307	−	0.0966548i
$551$	−2.79110	+	4.83433i	−0.118905	+	0.205950i
$552$	2.83065	+	1.56355i	0.120480	+	0.0665490i
$553$	−1.05006	+	16.4128i	−0.0446532	+	0.697942i
$554$	−17.2708	−	9.97128i	−0.733765	−	0.423639i
$555$	−25.8381	−	1.18551i	−1.09677	−	0.0503220i
$556$		−	16.7506i		−	0.710385i
$557$	6.66281	−	11.5403i	0.282312	−	0.488979i	−0.689642	−	0.724151i	$-0.742232\pi$
$557$	6.66281	−	11.5403i	0.282312	−	0.488979i	0.971954	+	0.235172i	$0.0755652\pi$
$558$	−12.7007	+	7.98898i	−0.537664	+	0.338200i
$559$			29.4823i			1.24697i
$560$	0.759202	−	5.86716i	0.0320822	−	0.247933i
$561$	5.36823	−	3.23645i	0.226647	−	0.136643i
$562$			2.35446i			0.0993170i
$563$	−8.13242	+	4.69526i	−0.342741	+	0.197881i	−0.661483	−	0.749960i	$-0.730073\pi$
$563$	−8.13242	+	4.69526i	−0.342741	+	0.197881i	0.318743	+	0.947841i	$0.396739\pi$
$564$	−9.72279	+	17.6021i	−0.409403	+	0.741184i
$565$	24.9806	−	37.4394i	1.05094	−	1.57509i
$566$	−8.82966			−0.371138
$567$	−0.282834	−	23.8101i	−0.0118779	−	0.999929i
$568$			4.17217i			0.175060i
$569$	30.0367	+	17.3417i	1.25921	+	0.727002i	0.972920	−	0.231142i	$-0.0742462\pi$
$569$	30.0367	+	17.3417i	1.25921	+	0.727002i	0.286285	+	0.958144i	$0.407580\pi$
$570$	15.6743	−	24.4838i	0.656525	−	1.02551i
$571$	−5.74730	−	9.95461i	−0.240517	−	0.416588i	0.720345	−	0.693616i	$-0.243984\pi$
$571$	−5.74730	−	9.95461i	−0.240517	−	0.416588i	−0.960862	+	0.277029i	$0.910650\pi$
$572$			2.49290i			0.104233i
$573$	−17.9072	−	29.7023i	−0.748085	−	1.24083i
$574$	−3.74275	−	2.49240i	−0.156219	−	0.104031i
$575$	−9.25680	−	1.20630i	−0.386035	−	0.0503061i
$576$	1.59733	+	2.53940i	0.0665553	+	0.105808i
$577$	8.61149	−	14.9155i	0.358501	−	0.620942i	−0.629209	−	0.777236i	$-0.716621\pi$
$577$	8.61149	−	14.9155i	0.358501	−	0.620942i	0.987711	+	0.156293i	$0.0499546\pi$
$578$	6.53545			0.271839
$579$	32.9272	−	0.623793i	1.36841	−	0.0259240i
$580$	1.38328	+	0.922960i	0.0574374	+	0.0383238i
$581$	3.84131	−	5.76837i	0.159364	−	0.239312i
$582$	7.03499	+	3.88588i	0.291610	+	0.161075i
$583$	−3.80314	−	2.19574i	−0.157510	−	0.0909384i
$584$	5.10736	−	8.84620i	0.211344	−	0.366059i
$585$	22.4089	+	0.603115i	0.926494	+	0.0249357i
$586$	−8.74058	+	5.04638i	−0.361070	+	0.208464i
$587$	−18.3983	+	10.6223i	−0.759380	+	0.438428i	−0.829073	−	0.559140i	$-0.811131\pi$
$587$	−18.3983	+	10.6223i	−0.759380	+	0.438428i	0.0696932	+	0.997568i	$0.477798\pi$
$588$	−9.77936	−	7.16687i	−0.403294	−	0.295557i
$589$	−18.7710	+	32.5122i	−0.773444	+	1.33964i
$590$	−10.4053	−	0.675125i	−0.428378	−	0.0277945i
$591$	10.5248	+	5.81350i	0.432931	+	0.239135i
$592$		−	6.67839i		−	0.274480i
$593$	−5.35047	+	3.08910i	−0.219718	+	0.126854i	−0.605819	−	0.795602i	$-0.707155\pi$
$593$	−5.35047	+	3.08910i	−0.219718	+	0.126854i	0.386102	+	0.922456i	$0.373821\pi$
$594$	1.74435	−	3.46162i	0.0715714	−	0.142032i
$595$	−28.4636	−	3.68315i	−1.16689	−	0.150994i
$596$	18.6650	−	10.7762i	0.764547	−	0.441412i
$597$	−4.03390	−	6.69096i	−0.165097	−	0.273843i
$598$	3.11953	+	5.40319i	0.127567	+	0.220953i
$599$	17.5461	−	10.1302i	0.716914	−	0.413911i	−0.0967017	−	0.995313i	$-0.530829\pi$
$599$	17.5461	−	10.1302i	0.716914	−	0.413911i	0.813616	+	0.581403i	$0.197496\pi$
$600$	−6.97602	−	5.13177i	−0.284795	−	0.209504i
$601$	1.81095	−	1.04555i	0.0738700	−	0.0426489i	−0.462610	−	0.886562i	$-0.653087\pi$
$601$	1.81095	−	1.04555i	0.0738700	−	0.0426489i	0.536480	+	0.843913i	$0.319754\pi$
$602$	−10.3565	−	20.9187i	−0.422100	−	0.852583i
$603$	−12.0264	−	6.34867i	−0.489752	−	0.258538i
$604$	7.68913	+	13.3180i	0.312866	+	0.541900i
$605$	23.3034	+	1.51200i	0.947417	+	0.0614713i
$606$	−16.2783	+	9.81402i	−0.661262	+	0.398667i
$607$	−13.4794			−0.547111			−0.273555	−	0.961856i	$-0.588200\pi$
$607$	−13.4794			−0.547111			−0.273555	+	0.961856i	$0.588200\pi$
$608$	6.50055	+	3.75309i	0.263632	+	0.152208i
$609$	3.02498	−	1.56965i	0.122578	−	0.0636054i
$610$	−3.43336	+	1.69596i	−0.139013	+	0.0686672i
$611$	−33.5993	+	19.3985i	−1.35928	+	0.784781i
$612$	12.3195	−	7.74917i	0.497985	−	0.313242i
$613$	9.41875	+	5.43792i	0.380420	+	0.219636i	0.678001	−	0.735061i	$-0.262847\pi$
$613$	9.41875	+	5.43792i	0.380420	+	0.219636i	−0.297581	+	0.954697i	$0.596180\pi$
$614$	−5.36423	+	9.29112i	−0.216483	+	0.374959i
$615$	−5.84545	+	3.02650i	−0.235711	+	0.122040i
$616$	−0.875705	−	1.76880i	−0.0352832	−	0.0712669i
$617$	0.714583	−	1.23769i	0.0287680	−	0.0498277i	−0.851283	−	0.524707i	$-0.824175\pi$
$617$	0.714583	−	1.23769i	0.0287680	−	0.0498277i	0.880051	+	0.474879i	$0.157508\pi$
$618$	9.90011	−	5.96867i	0.398241	−	0.240095i
$619$		−	22.2859i		−	0.895747i	−0.894097	−	0.447873i	$-0.852182\pi$
$619$		−	22.2859i		−	0.895747i	0.894097	−	0.447873i	$-0.147818\pi$
$620$	9.30292	+	6.20717i	0.373614	+	0.249286i
$621$	−0.550999	−	9.68563i	−0.0221108	−	0.388671i
$622$	−4.99022			−0.200089
$623$	33.4108	+	22.2491i	1.33858	+	0.891393i
$624$	0.109633	+	5.78701i	0.00438882	+	0.231666i
$625$	24.1651	+	6.40694i	0.966603	+	0.256278i
$626$	−10.0534	−	17.4130i	−0.401815	−	0.695965i
$627$	−0.183705	−	9.69694i	−0.00733647	−	0.387259i
$628$	−3.52158	+	6.09956i	−0.140526	+	0.243399i
$629$	−32.3991			−1.29184
$630$	−16.1118	+	7.44386i	−0.641908	+	0.296571i
$631$	13.9478			0.555255			0.277627	−	0.960689i	$-0.410452\pi$
$631$	13.9478			0.555255			0.277627	+	0.960689i	$0.410452\pi$
$632$	−3.10806	+	5.38333i	−0.123632	+	0.214137i
$633$	11.6411	−	7.01827i	0.462691	−	0.278951i
$634$	−13.0051	−	22.5255i	−0.516499	−	0.894602i
$635$	0.306761	−	4.72790i	0.0121734	−	0.187621i
$636$	−8.92516	−	4.92994i	−0.353906	−	0.195485i
$637$	−9.01910	−	21.5835i	−0.357350	−	0.855169i
$638$	0.554779			0.0219639
$639$	10.5948	−	6.66432i	0.419124	−	0.263637i
$640$	1.24107	−	1.86004i	0.0490576	−	0.0735245i
$641$		−	8.71120i		−	0.344072i	−0.985091	−	0.172036i	$-0.944965\pi$
$641$		−	8.71120i		−	0.344072i	0.985091	−	0.172036i	$-0.0550345\pi$
$642$	−20.7034	−	11.4358i	−0.817099	−	0.451336i
$643$	21.6235	−	37.4529i	0.852746	−	1.47700i	−0.0259739	−	0.999663i	$-0.508269\pi$
$643$	21.6235	−	37.4529i	0.852746	−	1.47700i	0.878720	−	0.477337i	$-0.158398\pi$
$644$	−4.11145	−	2.73792i	−0.162014	−	0.107889i
$645$	−34.1333	−	1.56611i	−1.34400	−	0.0616654i
$646$	18.2075	−	31.5363i	0.716365	−	1.24078i
$647$	31.0729	+	17.9400i	1.22160	+	0.705293i	0.965260	−	0.261293i	$-0.0841487\pi$
$647$	31.0729	+	17.9400i	1.22160	+	0.705293i	0.256344	+	0.966586i	$0.417482\pi$
$648$	3.89709	−	8.11250i	0.153092	−	0.318689i
$649$	−3.01262	+	1.73933i	−0.118256	+	0.0682748i
$650$	−6.41442	−	15.4284i	−0.251594	−	0.605150i
$651$	20.3438	−	10.5563i	0.797337	−	0.413735i
$652$	−6.38815	−	3.68820i	−0.250179	−	0.144441i
$653$	−3.88543			−0.152049			−0.0760243	−	0.997106i	$-0.524223\pi$
$653$	−3.88543			−0.152049			−0.0760243	+	0.997106i	$0.524223\pi$
$654$	0.337188	+	17.7986i	0.0131851	+	0.695980i
$655$	−35.1609	−	2.28135i	−1.37385	−	0.0891397i
$656$	−0.849794	−	1.47189i	−0.0331789	−	0.0574675i
$657$	−30.6222	+	1.16067i	−1.19468	+	0.0452819i
$658$	17.0255	−	25.5667i	0.663725	−	0.996693i
$659$	−12.1007	+	6.98632i	−0.471375	+	0.272149i	−0.716815	−	0.697263i	$-0.754401\pi$
$659$	−12.1007	+	6.98632i	−0.471375	+	0.272149i	0.245440	+	0.969412i	$0.421068\pi$
$660$	−2.88617	−	0.132424i	−0.112344	−	0.00515458i
$661$	−38.7265	+	22.3587i	−1.50628	+	0.869654i	−0.506311	+	0.862351i	$0.668991\pi$
$661$	−38.7265	+	22.3587i	−1.50628	+	0.869654i	−0.999973	+	0.00730324i	$0.997675\pi$
$662$	6.69898	+	11.6030i	0.260363	+	0.450962i
$663$	28.0747	−	0.531865i	1.09033	−	0.0206559i
$664$	2.26849	−	1.30971i	0.0880345	−	0.0508267i
$665$	−26.9552	+	35.2904i	−1.04528	+	1.36850i
$666$	−16.9591	+	10.6676i	−0.657152	+	0.413360i
$667$	1.20244	−	0.694232i	0.0465589	−	0.0268808i
$668$		−	16.8690i		−	0.652683i
$669$	0.706078	+	37.2706i	0.0272985	+	1.44097i
$670$	−0.656293	+	10.1150i	−0.0253548	+	0.390777i
$671$	−0.638775	+	1.10639i	−0.0246596	+	0.0427118i
$672$	−2.11065	−	4.06757i	−0.0814200	−	0.156910i
$673$	−32.2357	+	18.6113i	−1.24259	+	0.717412i	−0.969622	−	0.244610i	$-0.921340\pi$
$673$	−32.2357	+	18.6113i	−1.24259	+	0.717412i	−0.272973	+	0.962022i	$0.588007\pi$
$674$	7.18391	−	4.14763i	0.276714	−	0.159761i
$675$	−1.88863	+	25.9120i	−0.0726933	+	0.997354i
$676$	0.916415	−	1.58728i	0.0352467	−	0.0610492i
$677$	−10.8972	−	6.29151i	−0.418814	−	0.241803i	0.275756	−	0.961228i	$-0.411072\pi$
$677$	−10.8972	−	6.29151i	−0.418814	−	0.241803i	−0.694570	+	0.719425i	$0.744405\pi$
$678$	−0.660351	−	34.8569i	−0.0253606	−	1.33867i
$679$	−10.2182	−	6.80454i	−0.392137	−	0.261134i
$680$	−9.02367	−	6.02085i	−0.346042	−	0.230889i
$681$	−6.72303	+	12.1714i	−0.257627	+	0.466408i
$682$	3.73104			0.142869
$683$	8.98544	−	15.5632i	0.343818	−	0.595511i	−0.641320	−	0.767274i	$-0.721613\pi$
$683$	8.98544	−	15.5632i	0.343818	−	0.595511i	0.985138	+	0.171763i	$0.0549462\pi$
$684$	−0.852905	−	22.5024i	−0.0326116	−	0.860401i
$685$	−24.5611	−	1.59360i	−0.938432	−	0.0608884i
$686$	13.9812	+	12.1460i	0.533805	+	0.463737i
$687$	−16.1356	+	29.2119i	−0.615612	+	1.11450i
$688$		−	8.82245i		−	0.336353i
$689$	−9.83603	−	17.0365i	−0.374723	−	0.649039i
$690$	−6.42129	+	3.32464i	−0.244454	+	0.126567i
$691$	38.3130	+	22.1200i	1.45750	+	0.841485i	0.998888	−	0.0471537i	$-0.0150151\pi$
$691$	38.3130	+	22.1200i	1.45750	+	0.841485i	0.458608	+	0.888639i	$0.348348\pi$
$692$		−	10.2449i		−	0.389453i
$693$	−3.09290	+	5.04911i	−0.117489	+	0.191800i
$694$	16.4408			0.624086
$695$	31.1568	+	20.7887i	1.18185	+	0.788560i
$696$	1.28786	−	0.0243981i	0.0488163	−	0.000924806i
$697$	−7.14061	+	4.12264i	−0.270470	+	0.156156i
$698$		−	30.3016i		−	1.14693i
$699$	−0.0375544	−	1.98232i	−0.00142044	−	0.0749783i
$700$	9.97093	+	8.69371i	0.376866	+	0.328591i
$701$		−	29.6654i		−	1.12045i	−0.828342	−	0.560223i	$-0.810716\pi$
$701$		−	29.6654i		−	1.12045i	0.828342	−	0.560223i	$-0.189284\pi$
$702$	14.5204	−	9.52215i	0.548037	−	0.359390i
$703$	−25.0646	+	43.4132i	−0.945330	+	1.63736i
$704$		−	0.745990i		−	0.0281156i
$705$	−20.6740	−	39.9302i	−0.778628	−	1.50386i
$706$	10.7919	+	6.23074i	0.406160	+	0.234497i
$707$	26.0206	−	12.8824i	0.978607	−	0.484493i
$708$	−6.91699	+	4.17018i	−0.259956	+	0.156725i
$709$	−18.3682	+	31.8146i	−0.689831	+	1.19482i	0.282062	+	0.959396i	$0.408982\pi$
$709$	−18.3682	+	31.8146i	−0.689831	+	1.19482i	−0.971892	+	0.235425i	$0.924352\pi$
$710$	−7.76040	−	5.17796i	−0.291243	−	0.194325i
$711$	18.6350	−	0.706320i	0.698867	−	0.0264891i
$712$	7.58595	+	13.1393i	0.284296	+	0.492414i
$713$	8.08678	−	4.66890i	0.302852	−	0.174852i
$714$	−19.7332	+	10.2395i	−0.738495	+	0.383202i
$715$	−4.63689	−	3.09386i	−0.173410	−	0.115704i
$716$		−	19.0038i		−	0.710204i
$717$	10.5325	+	17.4700i	0.393343	+	0.652430i
$718$			1.17680i			0.0439177i
$719$	15.0842	+	26.1266i	0.562546	+	0.974358i	0.997273	+	0.0737961i	$0.0235114\pi$
$719$	15.0842	+	26.1266i	0.562546	+	0.974358i	−0.434727	+	0.900562i	$0.643155\pi$
$720$	−6.70578	−	0.180480i	−0.249910	−	0.00672608i
$721$	−15.8252	+	7.83480i	−0.589360	+	0.291783i
$722$	−18.6714	−	32.3398i	−0.694878	−	1.20356i
$723$	−19.2552	+	34.8596i	−0.716108	+	1.29644i
$724$	4.79273	−	2.76708i	0.178120	−	0.102838i
$725$	−3.43349	+	1.42749i	−0.127516	+	0.0530156i
$726$	15.4911	−	9.33943i	0.574930	−	0.346619i
$727$	−2.77440	−	4.80540i	−0.102897	−	0.178222i	0.809980	−	0.586457i	$-0.199478\pi$
$727$	−2.77440	−	4.80540i	−0.102897	−	0.178222i	−0.912877	+	0.408235i	$0.866144\pi$
$728$	0.564503	−	8.82335i	0.0209219	−	0.327015i
$729$	−26.8258	+	3.06206i	−0.993548	+	0.113410i
$730$	10.1157	+	20.4786i	0.374399	+	0.757949i
$731$	−42.8007			−1.58304
$732$	−1.43419	+	2.59647i	−0.0530094	+	0.0959682i
$733$	−20.2714			−0.748740			−0.374370	−	0.927279i	$-0.622141\pi$
$733$	−20.2714			−0.748740			−0.374370	+	0.927279i	$0.622141\pi$
$734$	17.7200	−	30.6920i	0.654059	−	1.13286i
$735$	25.4675	−	9.29541i	0.939384	−	0.342866i
$736$	−0.933507	−	1.61688i	−0.0344095	−	0.0595991i
$737$	1.69082	+	2.92858i	0.0622820	+	0.107876i
$738$	−2.38031	+	4.50905i	−0.0876203	+	0.165980i
$739$	24.5774	−	42.5693i	0.904095	−	1.56594i	0.0819667	−	0.996635i	$-0.473880\pi$
$739$	24.5774	−	42.5693i	0.904095	−	1.56594i	0.822128	−	0.569303i	$-0.192787\pi$
$740$	12.4221	+	8.28835i	0.456644	+	0.304686i
$741$	21.0065	−	38.0302i	0.771693	−	1.39707i
$742$	12.9636	+	8.63280i	0.475908	+	0.316920i
$743$	13.5537	−	23.4757i	0.497237	−	0.861240i	−0.502758	−	0.864427i	$-0.667681\pi$
$743$	13.5537	−	23.4757i	0.497237	−	0.861240i	0.999995	+	0.00318755i	$0.00101463\pi$
$744$	8.66124	−	0.164084i	0.317536	−	0.00601560i
$745$	−3.12033	+	48.0916i	−0.114320	+	1.76194i
$746$	21.9698	+	12.6843i	0.804372	+	0.464405i
$747$	−6.94940	−	3.66856i	−0.254265	−	0.134226i
$748$	−3.61905			−0.132325
$749$	30.0712	+	20.0252i	1.09878	+	0.731706i
$750$	18.2030	−	6.60678i	0.664681	−	0.241246i
$751$	41.2806			1.50635			0.753174	−	0.657821i	$-0.228522\pi$
$751$	41.2806			1.50635			0.753174	+	0.657821i	$0.228522\pi$
$752$	10.0544	−	5.80494i	0.366648	−	0.211684i
$753$	−2.19784	−	1.21401i	−0.0800938	−	0.0442410i
$754$	2.15223	+	1.24259i	0.0783797	+	0.0452525i
$755$	−34.3147	−	2.22644i	−1.24884	−	0.0810285i
$756$	−6.95780	+	11.8570i	−0.253053	+	0.431236i
$757$			37.6630i			1.36888i	0.729067	+	0.684442i	$0.239954\pi$
$757$			37.6630i			1.36888i	−0.729067	+	0.684442i	$0.760046\pi$
$758$	12.1747	−	21.0872i	0.442206	−	0.765923i
$759$	−1.16639	+	2.11163i	−0.0423373	+	0.0766474i
$760$	−15.0485	+	7.43342i	−0.545868	+	0.269638i
$761$	20.1064			0.728855			0.364427	−	0.931232i	$-0.381265\pi$
$761$	20.1064			0.728855			0.364427	+	0.931232i	$0.381265\pi$
$762$	−1.89483	−	3.14291i	−0.0686424	−	0.113856i
$763$	1.73619	−	27.1372i	0.0628544	−	0.982433i
$764$			20.0241i			0.724447i
$765$	−0.875567	+	32.5320i	−0.0316562	+	1.17620i
$766$	−11.3669	−	6.56268i	−0.410702	−	0.237119i
$767$	−15.5830			−0.562670
$768$	−0.0328072	−	1.73174i	−0.00118383	−	0.0624888i
$769$	−24.3791	−	14.0753i	−0.879134	−	0.507568i	−0.00876117	−	0.999962i	$-0.502789\pi$
$769$	−24.3791	−	14.0753i	−0.879134	−	0.507568i	−0.870373	+	0.492393i	$0.836122\pi$
$770$	4.37685	+	0.566357i	0.157731	+	0.0204101i
$771$	5.87716	−	10.6400i	0.211661	−	0.383191i
$772$	−16.4666	−	9.50697i	−0.592644	−	0.342163i
$773$	−37.3009	−	21.5357i	−1.34162	−	0.774585i	−0.354576	−	0.935027i	$-0.615375\pi$
$773$	−37.3009	−	21.5357i	−1.34162	−	0.774585i	−0.987045	+	0.160442i	$0.948708\pi$
$774$	−22.4037	+	14.0923i	−0.805285	+	0.506539i
$775$	−23.0911	+	9.60026i	−0.829458	+	0.344852i
$776$	−2.32004	−	4.01843i	−0.0832846	−	0.144253i
$777$	27.1649	−	14.0957i	0.974534	−	0.505682i
$778$	−16.7387	−	9.66411i	−0.600113	−	0.346475i
$779$			12.7574i			0.457082i
$780$	−10.9001	−	6.97816i	−0.390287	−	0.249858i
$781$	−3.11240			−0.111370
$782$	−7.84404	+	4.52876i	−0.280502	+	0.161948i
$783$	−2.11909	−	3.23142i	−0.0757303	−	0.115482i
$784$	2.69893	+	6.45877i	0.0963904	+	0.230671i
$785$	−6.97489	−	14.1203i	−0.248945	−	0.503974i
$786$	−23.3735	+	14.0916i	−0.833706	+	0.502632i
$787$	17.6587	+	30.5858i	0.629466	+	1.09027i	0.987659	+	0.156620i	$0.0500596\pi$
$787$	17.6587	+	30.5858i	0.629466	+	1.09027i	−0.358193	+	0.933648i	$0.616607\pi$
$788$	−3.47092	−	6.01181i	−0.123646	−	0.214162i
$789$	4.01759	+	2.21917i	0.143030	+	0.0790046i
$790$	−6.15587	−	12.4622i	−0.219016	−	0.443385i
$791$	−3.40017	+	53.1457i	−0.120896	+	1.88964i
$792$	−1.89437	+	1.19159i	−0.0673134	+	0.0423413i
$793$	−4.95618	+	2.86145i	−0.175999	+	0.101613i
$794$	−36.0286			−1.27861
$795$	20.2466	−	10.4828i	0.718074	−	0.371785i
$796$			4.51077i			0.159880i
$797$	−14.2561	−	8.23077i	−0.504978	−	0.291549i	0.225789	−	0.974176i	$-0.427504\pi$
$797$	−14.2561	−	8.23077i	−0.504978	−	0.291549i	−0.730767	+	0.682627i	$0.760837\pi$
$798$	−1.54562	+	34.3629i	−0.0547142	+	1.21643i
$799$	−28.1617	−	48.7775i	−0.996289	−	1.72562i
$800$	1.91949	+	4.61688i	0.0678642	+	0.163231i
$801$	21.2486	−	40.2514i	0.750781	−	1.42221i
$802$	−2.72857	−	1.57534i	−0.0963492	−	0.0556272i
$803$	6.59918	+	3.81004i	0.232880	+	0.134453i
$804$	4.05385	+	6.72404i	0.142968	+	0.237139i
$805$	10.1952	−	4.24950i	0.359335	−	0.149775i
$806$	14.4744	+	8.35677i	0.509838	+	0.294355i
$807$	35.4035	−	21.3444i	1.24626	−	0.751359i
$808$	10.9742			0.386071
$809$	21.2722	+	12.2815i	0.747890	+	0.431795i	0.824931	−	0.565233i	$-0.191214\pi$
$809$	21.2722	+	12.2815i	0.747890	+	0.431795i	−0.0770407	+	0.997028i	$0.524547\pi$
$810$	10.2530	+	17.3169i	0.360254	+	0.608455i
$811$			7.28238i			0.255719i	0.991792	+	0.127860i	$0.0408107\pi$
$811$			7.28238i			0.255719i	−0.991792	+	0.127860i	$0.959189\pi$
$812$	−1.96358	−	0.125627i	−0.0689082	−	0.00440863i
$813$	−33.9295	+	0.642781i	−1.18996	+	0.0225433i
$814$	4.98201			0.174619
$815$	14.7883	−	7.30490i	0.518013	−	0.255879i
$816$	−8.40125	+	0.159158i	−0.294103	+	0.00557166i
$817$	−33.1115	+	57.3508i	−1.15842	+	2.00645i
$818$			15.9469i			0.557571i
$819$	−23.3077	+	12.6603i	−0.814437	+	0.442386i
$820$	3.79242	+	0.246064i	0.132437	+	0.00859293i
$821$	5.79033	+	3.34305i	0.202084	+	0.116673i	0.597627	−	0.801774i	$-0.296110\pi$
$821$	5.79033	+	3.34305i	0.202084	+	0.116673i	−0.395543	+	0.918447i	$0.629444\pi$
$822$	−16.3272	+	9.84350i	−0.569477	+	0.343332i
$823$	9.87790	−	5.70301i	0.344322	−	0.198794i	−0.317860	−	0.948138i	$-0.602964\pi$
$823$	9.87790	−	5.70301i	0.344322	−	0.198794i	0.662182	+	0.749343i	$0.269631\pi$
$824$	−6.67426			−0.232509
$825$	3.82825	−	5.20404i	0.133283	−	0.181182i
$826$	11.0567	−	5.47400i	0.384712	−	0.190465i
$827$	−9.16990			−0.318868			−0.159434	−	0.987209i	$-0.550967\pi$
$827$	−9.16990			−0.318868			−0.159434	+	0.987209i	$0.550967\pi$
$828$	−2.61479	+	4.95324i	−0.0908703	+	0.172137i
$829$	13.6953	+	7.90700i	0.475659	+	0.274622i	0.718605	−	0.695418i	$-0.244781\pi$
$829$	13.6953	+	7.90700i	0.475659	+	0.274622i	−0.242947	+	0.970040i	$0.578114\pi$
$830$	−0.379237	+	5.84493i	−0.0131635	+	0.202880i
$831$	16.7011	−	30.2356i	0.579354	−	1.04886i
$832$	1.67087	−	2.89402i	0.0579268	−	0.100332i
$833$	31.3337	−	13.0934i	1.08565	−	0.453660i
$834$	29.0077	−	0.549540i	1.00446	−	0.0190290i
$835$	31.3771	+	20.9357i	1.08585	+	0.724508i
$836$	−2.79977	+	4.84934i	−0.0968320	+	0.167718i
$837$	−14.2515	−	21.7322i	−0.492604	−	0.751176i
$838$	17.4629	+	30.2467i	0.603247	+	1.04485i
$839$	14.0897	+	24.4040i	0.486429	+	0.842520i	0.999878	−	0.0156002i	$-0.00496589\pi$
$839$	14.0897	+	24.4040i	0.486429	+	0.842520i	−0.513449	+	0.858120i	$0.671633\pi$
$840$	10.1853	+	1.12226i	0.351427	+	0.0387215i
$841$	−14.2235	+	24.6358i	−0.490464	+	0.849509i
$842$	37.3358			1.28668
$843$	−4.07732	+	0.0772432i	−0.140430	+	0.00266040i
$844$	−7.84794			−0.270137
$845$	1.81506	+	3.67449i	0.0624401	+	0.126406i
$846$	−30.8013	−	16.2599i	−1.05897	−	0.559026i
$847$	−24.7623	+	12.2594i	−0.850844	+	0.421240i
$848$	2.94339	+	5.09811i	0.101077	+	0.175070i
$849$	−0.289676	−	15.2907i	−0.00994166	−	0.524775i
$850$	22.3980	−	9.31209i	0.768246	−	0.319402i
$851$	10.7982	−	6.23433i	0.370157	−	0.213710i
$852$	−7.22511	+	0.136877i	−0.247528	+	0.00468933i
$853$	4.37925	+	7.58508i	0.149943	+	0.259708i	0.931206	−	0.364493i	$-0.118758\pi$
$853$	4.37925	+	7.58508i	0.149943	+	0.259708i	−0.781263	+	0.624201i	$0.785424\pi$
$854$	2.51141	−	3.77131i	0.0859388	−	0.129051i
$855$	42.9138	+	26.3406i	1.46762	+	0.900830i
$856$	6.82770	+	11.8259i	0.233366	+	0.404202i
$857$		−	31.9068i		−	1.08992i	−0.838464	−	0.544958i	$-0.816546\pi$
$857$		−	31.9068i		−	1.08992i	0.838464	−	0.544958i	$-0.183454\pi$
$858$	−4.31705	+	0.0817849i	−0.147382	+	0.00279209i
$859$		−	45.7568i		−	1.56120i	−0.625030	−	0.780601i	$-0.714913\pi$
$859$		−	45.7568i		−	1.56120i	0.625030	−	0.780601i	$-0.285087\pi$
$860$	16.4101	+	10.9493i	0.559580	+	0.373367i
$861$	4.19339	−	6.56324i	0.142910	−	0.223674i
$862$	7.75117	−	4.47514i	0.264006	−	0.152424i
$863$	21.5708	+	37.3618i	0.734280	+	1.27181i	0.955039	+	0.296481i	$0.0958132\pi$
$863$	21.5708	+	37.3618i	0.734280	+	1.27181i	−0.220759	+	0.975328i	$0.570853\pi$
$864$	−4.34517	+	2.84947i	−0.147826	+	0.0969408i
$865$	19.0559	+	12.7146i	0.647921	+	0.432311i
$866$	6.00301	−	10.3975i	0.203991	−	0.353322i
$867$	0.214409	+	11.3177i	0.00728173	+	0.384369i
$868$	−13.2056	−	0.844874i	−0.448228	−	0.0286769i
$869$	−4.01591	−	2.31859i	−0.136230	−	0.0786526i
$870$	−1.55295	+	2.42575i	−0.0526498	+	0.0822408i
$871$			15.1483i			0.513282i
$872$	5.13894	−	8.90090i	0.174026	−	0.301422i
$873$	−6.49853	+	12.3103i	−0.219942	+	0.416639i
$874$			14.0142i			0.474036i
$875$	−28.5453	+	7.75682i	−0.965006	+	0.262228i
$876$	15.4869	+	8.55440i	0.523253	+	0.289026i
$877$		−	18.3979i		−	0.621255i	−0.950532	−	0.310627i	$-0.899461\pi$
$877$		−	18.3979i		−	0.621255i	0.950532	−	0.310627i	$-0.100539\pi$
$878$	−28.3831	+	16.3870i	−0.957882	+	0.553034i
$879$	−9.02576	−	14.9709i	−0.304431	−	0.504954i
$880$	1.38757	+	0.925826i	0.0467750	+	0.0312096i
$881$	8.81308			0.296920			0.148460	−	0.988918i	$-0.452568\pi$
$881$	8.81308			0.296920			0.148460	+	0.988918i	$0.452568\pi$
$882$	12.0903	−	17.1704i	0.407102	−	0.578159i
$883$			2.02023i			0.0679863i	0.999422	+	0.0339931i	$0.0108224\pi$
$883$			2.02023i			0.0679863i	−0.999422	+	0.0339931i	$0.989178\pi$
$884$	−14.0399	−	8.10593i	−0.472212	−	0.272632i
$885$	0.827775	−	18.0414i	0.0278253	−	0.606453i
$886$	3.05270	+	5.28743i	0.102557	+	0.177635i
$887$			33.2724i			1.11718i	0.829445	+	0.558589i	$0.188657\pi$
$887$			33.2724i			1.11718i	−0.829445	+	0.558589i	$0.811343\pi$
$888$	11.5652	−	0.219099i	0.388104	−	0.00735248i
$889$	2.48725	+	5.02390i	0.0834198	+	0.168496i
$890$	−33.8542	−	2.19657i	−1.13480	−	0.0736291i
$891$	6.05185	+	2.90719i	0.202744	+	0.0973945i
$892$	10.7610	−	18.6387i	0.360306	−	0.624068i
$893$	−87.1459			−2.91623
$894$	19.2740	+	31.9694i	0.644618	+	1.06922i
$895$	35.3477	+	23.5850i	1.18154	+	0.788359i
$896$	−0.168925	+	2.64035i	−0.00564340	+	0.0882080i
$897$	−9.25457	+	5.57948i	−0.309001	+	0.186293i
$898$	−3.80762	−	2.19833i	−0.127062	−	0.0733593i
$899$	1.85975	−	3.22118i	0.0620261	−	0.107432i
$900$	8.65804	−	12.2490i	0.288601	−	0.408301i
$901$	24.7326	−	14.2794i	0.823963	−	0.475715i
$902$	1.09801	−	0.633938i	0.0365598	−	0.0211078i
$903$	35.8860	−	18.6211i	1.19421	−	0.619671i
$904$	−10.0641	+	17.4316i	−0.334728	+	0.579766i
$905$	−0.801228	+	12.3488i	−0.0266337	+	0.410488i
$906$	−22.8110	+	13.7525i	−0.757844	+	0.456896i
$907$			11.1534i			0.370344i	0.982706	+	0.185172i	$0.0592842\pi$
$907$			11.1534i			0.370344i	−0.982706	+	0.185172i	$0.940716\pi$
$908$	6.95237	−	4.01395i	0.230722	−	0.133208i
$909$	−17.5294	−	27.8678i	−0.581413	−	0.924318i
$910$	15.7112	+	12.0004i	0.520821	+	0.397809i
$911$	33.9893	−	19.6237i	1.12612	−	0.650163i	0.183160	−	0.983083i	$-0.441367\pi$
$911$	33.9893	−	19.6237i	1.12612	−	0.650163i	0.942955	+	0.332920i	$0.108034\pi$
$912$	−6.28612	+	11.3804i	−0.208154	+	0.376842i
$913$	0.977033	+	1.69227i	0.0323351	+	0.0560060i
$914$	28.7983	−	16.6267i	0.952564	−	0.549963i
$915$	−3.04959	−	5.89006i	−0.100816	−	0.194719i
$916$	16.6860	−	9.63368i	0.551322	−	0.318306i
$917$	37.3622	−	18.4975i	1.23381	−	0.610840i
$918$	13.8237	+	21.0799i	0.456251	+	0.695740i
$919$	−13.5598	−	23.4863i	−0.447298	−	0.774743i	0.550911	−	0.834564i	$-0.314280\pi$
$919$	−13.5598	−	23.4863i	−0.447298	−	0.774743i	−0.998209	+	0.0598209i	$0.980947\pi$
$920$	4.16601	+	0.270304i	0.137349	+	0.00891165i
$921$	−16.2658	−	8.98464i	−0.535976	−	0.296054i
$922$	−12.4447			−0.409844
$923$	−12.0744	−	6.97114i	−0.397432	−	0.229458i
$924$	3.03437	−	1.57452i	0.0998234	−	0.0517980i
$925$	−30.8333	+	12.8191i	−1.01379	+	0.421490i
$926$	2.79388	−	1.61305i	0.0918126	−	0.0530080i
$927$	10.6610	+	16.9486i	0.350153	+	0.556665i
$928$	−0.644047	−	0.371841i	−0.0211419	−	0.0122063i
$929$	22.0537	−	38.1982i	0.723559	−	1.25324i	−0.236005	−	0.971752i	$-0.575838\pi$
$929$	22.0537	−	38.1982i	0.723559	−	1.25324i	0.959564	−	0.281490i	$-0.0908285\pi$
$930$	−10.4440	+	16.3139i	−0.342472	+	0.534953i
$931$	6.69585	−	52.1149i	0.219448	−	1.70800i
$932$	−0.572350	+	0.991339i	−0.0187479	+	0.0324724i
$933$	−0.163715	−	8.64176i	−0.00535978	−	0.282918i
$934$			41.6247i			1.36200i
$935$	4.49149	−	6.73157i	0.146887	−	0.220146i
$936$	−10.0180	+	0.379711i	−0.327449	+	0.0124112i
$937$	31.2098			1.01958			0.509789	−	0.860299i	$-0.329723\pi$
$937$	31.2098			1.01958			0.509789	+	0.860299i	$0.329723\pi$
$938$	−5.32131	−	10.7483i	−0.173747	−	0.350944i
$939$	29.8250	−	17.9812i	0.973303	−	0.586793i
$940$	−1.68086	+	25.9060i	−0.0548237	+	0.844961i
$941$	3.25513	+	5.63804i	0.106114	+	0.183795i	0.914193	−	0.405280i	$-0.132826\pi$
$941$	3.25513	+	5.63804i	0.106114	+	0.183795i	−0.808079	+	0.589074i	$0.799492\pi$
$942$	−10.6784	−	5.89836i	−0.347921	−	0.192179i
$943$	1.58658	−	2.74803i	0.0516661	−	0.0894883i
$944$	4.66316			0.151773
$945$	−13.4194	−	27.6572i	−0.436534	−	0.899688i
$946$	6.58146			0.213982
$947$	16.7485	−	29.0092i	0.544252	−	0.942672i	−0.454402	−	0.890797i	$-0.650147\pi$
$947$	16.7485	−	29.0092i	0.544252	−	0.942672i	0.998654	−	0.0518752i	$-0.0165198\pi$
$948$	−9.42449	−	5.20575i	−0.306093	−	0.169075i
$949$	17.0674	+	29.5616i	0.554032	+	0.959611i
$950$	4.84983	−	37.2163i	0.157349	−	1.20745i
$951$	38.5817	−	23.2605i	1.25110	−	0.754272i
$952$	12.8092	+	0.819513i	0.415150	+	0.0265606i
$953$	−9.08698			−0.294356			−0.147178	−	0.989110i	$-0.547019\pi$
$953$	−9.08698			−0.294356			−0.147178	+	0.989110i	$0.547019\pi$
$954$	8.24456	−	15.6178i	0.266928	−	0.505645i
$955$	−37.2457	−	24.8513i	−1.20524	−	0.804171i
$956$		−	11.7776i		−	0.380915i
$957$	0.0182007	+	0.960733i	0.000588345	+	0.0310561i
$958$	−11.5051	+	19.9275i	−0.371714	+	0.643827i
$959$	26.0988	−	12.9211i	0.842774	−	0.417245i
$960$	3.26182	+	2.08819i	0.105275	+	0.0673960i
$961$	−2.99268	+	5.18347i	−0.0965380	+	0.167209i
$962$	19.3274	+	11.1587i	0.623141	+	0.359771i
$963$	19.1247	−	36.2281i	0.616283	−	1.16743i
$964$	19.9120	−	11.4962i	0.641323	−	0.370268i
$965$	38.1195	−	18.8296i	1.22711	−	0.606147i
$966$	4.60648	−	7.20978i	0.148211	−	0.231971i
$967$	−0.584986	−	0.337742i	−0.0188119	−	0.0108610i	0.490565	−	0.871405i	$-0.336791\pi$
$967$	−0.584986	−	0.337742i	−0.0188119	−	0.0108610i	−0.509376	+	0.860544i	$0.670124\pi$
$968$	−10.4435			−0.335667
$969$	55.2101	+	30.4961i	1.77360	+	0.979674i
$970$	10.3538	+	0.671785i	0.332440	+	0.0215697i
$971$	3.90049	+	6.75585i	0.125173	+	0.216805i	0.921800	−	0.387665i	$-0.126718\pi$
$971$	3.90049	+	6.75585i	0.125173	+	0.216805i	−0.796628	+	0.604470i	$0.793385\pi$
$972$	14.1766	+	6.48260i	0.454715	+	0.207929i
$973$	−44.2276	−	2.82960i	−1.41787	−	0.0907129i
$974$	−9.17108	+	5.29492i	−0.293860	+	0.169660i
$975$	26.5075	−	11.6143i	0.848919	−	0.371954i
$976$	1.48312	−	0.856279i	0.0474734	−	0.0274088i
$977$	22.7250	+	39.3609i	0.727037	+	1.25927i	0.958130	+	0.286334i	$0.0924366\pi$
$977$	22.7250	+	39.3609i	0.727037	+	1.25927i	−0.231093	+	0.972932i	$0.574230\pi$
$978$	6.17743	−	11.1836i	0.197532	−	0.357613i
$979$	−9.80175	+	5.65904i	−0.313265	+	0.180864i
$980$	−15.3631	−	2.99567i	−0.490757	−	0.0956933i
$981$	−30.8115	+	1.16784i	−0.983735	+	0.0372864i
$982$	2.99490	−	1.72911i	0.0955713	−	0.0551781i
$983$		−	59.2020i		−	1.88825i	−0.329587	−	0.944125i	$-0.606909\pi$
$983$		−	59.2020i		−	1.88825i	0.329587	−	0.944125i	$-0.393091\pi$
$984$	2.52105	−	1.51991i	0.0803680	−	0.0484530i
$985$	15.4899	+	1.00503i	0.493548	+	0.0320229i
$986$	−1.80392	+	3.12449i	−0.0574486	+	0.0995039i
$987$	44.8334	+	28.6450i	1.42706	+	0.911781i
$988$	−21.7231	+	12.5418i	−0.691103	+	0.399009i
$989$	14.2649	−	8.23582i	0.453596	−	0.261884i
$990$	0.134636	−	5.00244i	0.00427901	−	0.158988i
$991$	−3.52175	+	6.09985i	−0.111872	+	0.193768i	−0.916525	−	0.399977i	$-0.869018\pi$
$991$	−3.52175	+	6.09985i	−0.111872	+	0.193768i	0.804653	+	0.593745i	$0.202351\pi$
$992$	−4.33139	−	2.50073i	−0.137522	−	0.0793983i
$993$	−19.8736	+	11.9816i	−0.630668	+	0.380223i
$994$	11.0160	+	0.704785i	0.349406	+	0.0223544i
$995$	−8.39022	−	5.59819i	−0.265988	−	0.177474i
$996$	2.34251	+	3.88547i	0.0742251	+	0.123116i
$997$	−43.8171			−1.38770			−0.693851	−	0.720119i	$-0.744087\pi$
$997$	−43.8171			−1.38770			−0.693851	+	0.720119i	$0.744087\pi$
$998$	−7.23460	+	12.5307i	−0.229007	+	0.396652i
$999$	−19.0299	−	29.0188i	−0.602078	−	0.918114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.b.59.21	yes	48
3.2	odd	2		1890.2.r.a.1529.1		48
5.4	even	2		630.2.r.a.59.4	✓	48
7.5	odd	6		630.2.bi.a.509.20	yes	48
9.2	odd	6		630.2.bi.b.479.5	yes	48
9.7	even	3		1890.2.bi.a.899.7		48
15.14	odd	2		1890.2.r.b.1529.1		48
21.5	even	6		1890.2.bi.b.719.9		48
35.19	odd	6		630.2.bi.b.509.5	yes	48
45.29	odd	6		630.2.bi.a.479.20	yes	48
45.34	even	6		1890.2.bi.b.899.9		48
63.47	even	6		630.2.r.a.299.4	yes	48
63.61	odd	6		1890.2.r.b.89.1		48
105.89	even	6		1890.2.bi.a.719.7		48
315.124	odd	6		1890.2.r.a.89.1		48
315.299	even	6	inner	630.2.r.b.299.21	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.4	✓	48	5.4	even	2
630.2.r.a.299.4	yes	48	63.47	even	6
630.2.r.b.59.21	yes	48	1.1	even	1	trivial
630.2.r.b.299.21	yes	48	315.299	even	6	inner
630.2.bi.a.479.20	yes	48	45.29	odd	6
630.2.bi.a.509.20	yes	48	7.5	odd	6
630.2.bi.b.479.5	yes	48	9.2	odd	6
630.2.bi.b.509.5	yes	48	35.19	odd	6
1890.2.r.a.89.1		48	315.124	odd	6
1890.2.r.a.1529.1		48	3.2	odd	2
1890.2.r.b.89.1		48	63.61	odd	6
1890.2.r.b.1529.1		48	15.14	odd	2
1890.2.bi.a.719.7		48	105.89	even	6
1890.2.bi.a.899.7		48	9.7	even	3
1890.2.bi.b.719.9		48	21.5	even	6
1890.2.bi.b.899.9		48	45.34	even	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.51613 + 0.837458i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23138 + 0.144779i) q^{5} +(1.48333 - 0.894282i) q^{6} +(-2.37108 + 1.17388i) q^{7} -1.00000 q^{8} +(1.59733 + 2.53940i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.51613 + 0.837458i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23138 + 0.144779i) q^{5} +(1.48333 - 0.894282i) q^{6} +(-2.37108 + 1.17388i) q^{7} -1.00000 q^{8} +(1.59733 + 2.53940i) q^{9} +(1.24107 - 1.86004i) q^{10} -0.745990i q^{11} +(-0.0328072 - 1.73174i) q^{12} +(1.67087 - 2.89402i) q^{13} +(-0.168925 + 2.64035i) q^{14} +(3.26182 + 2.08819i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.20138 + 2.42567i) q^{17} +(2.99785 - 0.113627i) q^{18} +(6.50055 - 3.75309i) q^{19} +(-0.990306 - 2.00482i) q^{20} +(-4.57795 - 0.205912i) q^{21} +(-0.646046 - 0.372995i) q^{22} -1.86701 q^{23} +(-1.51613 - 0.837458i) q^{24} +(4.95808 + 0.646111i) q^{25} +(-1.67087 - 2.89402i) q^{26} +(0.295123 + 5.18776i) q^{27} +(2.20215 + 1.46647i) q^{28} +(-0.644047 + 0.371841i) q^{29} +(3.43933 - 1.78073i) q^{30} +(-4.33139 + 2.50073i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.624735 - 1.13102i) q^{33} +(4.20138 - 2.42567i) q^{34} +(-5.46071 + 2.27609i) q^{35} +(1.40052 - 2.65303i) q^{36} +(-5.78366 + 3.33920i) q^{37} -7.50618i q^{38} +(4.95688 - 2.98845i) q^{39} +(-2.23138 - 0.144779i) q^{40} +(-0.849794 + 1.47189i) q^{41} +(-2.46730 + 3.86166i) q^{42} +(-7.64047 + 4.41123i) q^{43} +(-0.646046 + 0.372995i) q^{44} +(3.19659 + 5.89761i) q^{45} +(-0.933507 + 1.61688i) q^{46} +(-10.0544 - 5.80494i) q^{47} +(-1.48333 + 0.894282i) q^{48} +(4.24400 - 5.56673i) q^{49} +(3.03859 - 3.97077i) q^{50} +(4.33846 + 7.19612i) q^{51} -3.34173 q^{52} +(2.94339 - 5.09811i) q^{53} +(4.64030 + 2.33830i) q^{54} +(0.108003 - 1.66458i) q^{55} +(2.37108 - 1.17388i) q^{56} +(12.9988 - 0.246257i) q^{57} +0.743681i q^{58} +(-2.33158 - 4.03841i) q^{59} +(0.177514 - 3.86891i) q^{60} +(-1.48312 - 0.856279i) q^{61} +5.00146i q^{62} +(-6.76834 - 4.14603i) q^{63} +1.00000 q^{64} +(4.14732 - 6.21575i) q^{65} +(-0.667125 - 1.10655i) q^{66} +(-3.92576 + 2.26654i) q^{67} -4.85133i q^{68} +(-2.83065 - 1.56355i) q^{69} +(-0.759202 + 5.86716i) q^{70} -4.17217i q^{71} +(-1.59733 - 2.53940i) q^{72} +(-5.10736 + 8.84620i) q^{73} +6.67839i q^{74} +(6.97602 + 5.13177i) q^{75} +(-6.50055 - 3.75309i) q^{76} +(0.875705 + 1.76880i) q^{77} +(-0.109633 - 5.78701i) q^{78} +(3.10806 - 5.38333i) q^{79} +(-1.24107 + 1.86004i) q^{80} +(-3.89709 + 8.11250i) q^{81} +(0.849794 + 1.47189i) q^{82} +(-2.26849 + 1.30971i) q^{83} +(2.11065 + 4.06757i) q^{84} +(9.02367 + 6.02085i) q^{85} +8.82245i q^{86} +(-1.28786 + 0.0243981i) q^{87} +0.745990i q^{88} +(-7.58595 - 13.1393i) q^{89} +(6.70578 + 0.180480i) q^{90} +(-0.564503 + 8.82335i) q^{91} +(0.933507 + 1.61688i) q^{92} +(-8.66124 + 0.164084i) q^{93} +(-10.0544 + 5.80494i) q^{94} +(15.0485 - 7.43342i) q^{95} +(0.0328072 + 1.73174i) q^{96} +(2.32004 + 4.01843i) q^{97} +(-2.69893 - 6.45877i) q^{98} +(1.89437 - 1.19159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

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