LMFDB - Embedded newform 462.2.n.f.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.1
Character	$\chi$	$=$	462.65
Dual form			462.2.n.f.263.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.72951 - 0.0938734i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.23623 - 1.86844i) q^{5} +(-0.946049 + 1.45086i) q^{6} +(0.830341 - 2.51208i) q^{7} -1.00000 q^{8} +(2.98238 + 0.324709i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.72951 - 0.0938734i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.23623 - 1.86844i) q^{5} +(-0.946049 + 1.45086i) q^{6} +(0.830341 - 2.51208i) q^{7} -1.00000 q^{8} +(2.98238 + 0.324709i) q^{9} +(-3.23623 + 1.86844i) q^{10} +(-1.70984 + 2.84191i) q^{11} +(0.783456 + 1.54473i) q^{12} +4.64070i q^{13} +(-1.76035 - 1.97514i) q^{14} +(5.42167 + 3.53527i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.460807 - 0.798142i) q^{17} +(1.77239 - 2.42046i) q^{18} +(-4.14430 - 2.39271i) q^{19} +3.73687i q^{20} +(-1.67190 + 4.26670i) q^{21} +(1.60625 + 2.90172i) q^{22} +(4.94452 + 2.85472i) q^{23} +(1.72951 + 0.0938734i) q^{24} +(4.48211 + 7.76324i) q^{25} +(4.01896 + 2.32035i) q^{26} +(-5.12755 - 0.841552i) q^{27} +(-2.59069 + 0.536942i) q^{28} -7.73875 q^{29} +(5.77247 - 2.92767i) q^{30} +(1.26564 + 2.19216i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.22395 - 4.75459i) q^{33} -0.921615 q^{34} +(-7.38083 + 6.57821i) q^{35} +(-1.20998 - 2.74517i) q^{36} +(-1.29412 + 2.24149i) q^{37} +(-4.14430 + 2.39271i) q^{38} +(0.435638 - 8.02611i) q^{39} +(3.23623 + 1.86844i) q^{40} -4.10460 q^{41} +(2.85913 + 3.58126i) q^{42} -2.19681i q^{43} +(3.31609 + 0.0598058i) q^{44} +(-9.04495 - 6.62321i) q^{45} +(4.94452 - 2.85472i) q^{46} +(-4.96151 - 2.86453i) q^{47} +(0.946049 - 1.45086i) q^{48} +(-5.62107 - 4.17176i) q^{49} +8.96422 q^{50} +(0.722045 + 1.42365i) q^{51} +(4.01896 - 2.32035i) q^{52} +(-3.30063 + 1.90562i) q^{53} +(-3.29258 + 4.01981i) q^{54} +(10.8433 - 6.00235i) q^{55} +(-0.830341 + 2.51208i) q^{56} +(6.94298 + 4.52725i) q^{57} +(-3.86938 + 6.70196i) q^{58} +(7.65662 - 4.42055i) q^{59} +(0.350793 - 6.46294i) q^{60} +(6.52747 + 3.76863i) q^{61} +2.53129 q^{62} +(3.29208 - 7.22234i) q^{63} +1.00000 q^{64} +(8.67085 - 15.0184i) q^{65} +(-2.50562 - 5.16932i) q^{66} +(0.390387 + 0.676170i) q^{67} +(-0.460807 + 0.798142i) q^{68} +(-8.28358 - 5.40141i) q^{69} +(2.00648 + 9.68109i) q^{70} -11.4978i q^{71} +(-2.98238 - 0.324709i) q^{72} +(-9.35455 + 5.40085i) q^{73} +(1.29412 + 2.24149i) q^{74} +(-7.02307 - 13.8473i) q^{75} +4.78543i q^{76} +(5.71935 + 6.65500i) q^{77} +(-6.73300 - 4.39033i) q^{78} +(-14.9095 - 8.60802i) q^{79} +(3.23623 - 1.86844i) q^{80} +(8.78913 + 1.93681i) q^{81} +(-2.05230 + 3.55469i) q^{82} -12.6784 q^{83} +(4.53102 - 0.685447i) q^{84} +3.44396i q^{85} +(-1.90249 - 1.09840i) q^{86} +(13.3842 + 0.726463i) q^{87} +(1.70984 - 2.84191i) q^{88} +(7.44976 + 4.30112i) q^{89} +(-10.2583 + 4.52155i) q^{90} +(11.6578 + 3.85336i) q^{91} -5.70943i q^{92} +(-1.98315 - 3.91016i) q^{93} +(-4.96151 + 2.86453i) q^{94} +(8.94127 + 15.4867i) q^{95} +(-0.783456 - 1.54473i) q^{96} -12.1684 q^{97} +(-6.42339 + 2.78211i) q^{98} +(-6.02217 + 7.92045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9 + 4 * q^11 + 4 * q^15 - 12 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 - 40 * q^29 + 2 * q^30 - 28 * q^31 + 12 * q^32 + 24 * q^33 - 8 * q^34 + 32 * q^35 + 16 * q^36 - 16 * q^37 + 8 * q^41 + 6 * q^42 + 4 * q^44 - 28 * q^45 - 8 * q^49 + 40 * q^50 + 34 * q^51 - 6 * q^54 + 8 * q^55 - 40 * q^57 - 20 * q^58 - 2 * q^60 - 56 * q^62 + 14 * q^63 + 24 * q^64 + 44 * q^65 - 24 * q^66 - 4 * q^68 - 20 * q^69 + 64 * q^70 + 8 * q^72 + 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 - 144 * q^83 + 6 * q^84 - 8 * q^87 - 4 * q^88 - 56 * q^90 - 32 * q^91 - 22 * q^93 + 44 * q^95 + 64 * q^97 + 8 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.72951	−	0.0938734i	−0.998530	−	0.0541978i
$3$	−1.72951	−	0.0938734i	−0.998530	−	0.0541978i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−3.23623	−	1.86844i	−1.44728	−	0.835590i	−0.448966	−	0.893549i	$-0.648207\pi$
$5$	−3.23623	−	1.86844i	−1.44728	−	0.835590i	−0.998319	+	0.0579588i	$0.981541\pi$
$6$	−0.946049	+	1.45086i	−0.386223	+	0.592311i
$7$	0.830341	−	2.51208i	0.313839	−	0.949476i
$7$	0.830341	−	2.51208i	0.313839	−	0.949476i
$8$	−1.00000			−0.353553
$9$	2.98238	+	0.324709i	0.994125	+	0.108236i
$10$	−3.23623	+	1.86844i	−1.02338	+	0.590852i
$11$	−1.70984	+	2.84191i	−0.515535	+	0.856869i
$11$	−1.70984	+	2.84191i	−0.515535	+	0.856869i
$12$	0.783456	+	1.54473i	0.226164	+	0.445926i
$13$			4.64070i			1.28710i	0.765405	+	0.643549i	$0.222539\pi$
$13$			4.64070i			1.28710i	−0.765405	+	0.643549i	$0.777461\pi$
$14$	−1.76035	−	1.97514i	−0.470474	−	0.527877i
$15$	5.42167	+	3.53527i	1.39987	+	0.912802i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.460807	−	0.798142i	−0.111762	−	0.193578i	0.804719	−	0.593656i	$-0.202316\pi$
$17$	−0.460807	−	0.798142i	−0.111762	−	0.193578i	−0.916481	+	0.400079i	$0.868983\pi$
$18$	1.77239	−	2.42046i	0.417757	−	0.570508i
$19$	−4.14430	−	2.39271i	−0.950768	−	0.548926i	−0.0574485	−	0.998348i	$-0.518296\pi$
$19$	−4.14430	−	2.39271i	−0.950768	−	0.548926i	−0.893319	+	0.449422i	$0.851630\pi$
$20$			3.73687i			0.835590i
$21$	−1.67190	+	4.26670i	−0.364838	+	0.931071i
$22$	1.60625	+	2.90172i	0.342454	+	0.618648i
$23$	4.94452	+	2.85472i	1.03100	+	0.595250i	0.917272	−	0.398262i	$-0.130386\pi$
$23$	4.94452	+	2.85472i	1.03100	+	0.595250i	0.113731	+	0.993512i	$0.463720\pi$
$24$	1.72951	+	0.0938734i	0.353034	+	0.0191618i
$25$	4.48211	+	7.76324i	0.896422	+	1.55265i
$26$	4.01896	+	2.32035i	0.788183	+	0.455058i
$27$	−5.12755	−	0.841552i	−0.986798	−	0.161957i
$28$	−2.59069	+	0.536942i	−0.489595	+	0.101473i
$29$	−7.73875			−1.43705			−0.718525	−	0.695501i	$-0.755182\pi$
$29$	−7.73875			−1.43705			−0.718525	+	0.695501i	$0.755182\pi$
$30$	5.77247	−	2.92767i	1.05390	−	0.534518i
$31$	1.26564	+	2.19216i	0.227316	+	0.393723i	0.957012	−	0.290049i	$-0.0936715\pi$
$31$	1.26564	+	2.19216i	0.227316	+	0.393723i	−0.729696	+	0.683772i	$0.760338\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.22395	−	4.75459i	0.561218	−	0.827668i
$34$	−0.921615			−0.158056
$35$	−7.38083	+	6.57821i	−1.24759	+	1.11192i
$36$	−1.20998	−	2.74517i	−0.201664	−	0.457528i
$37$	−1.29412	+	2.24149i	−0.212752	+	0.368498i	−0.952575	−	0.304304i	$-0.901576\pi$
$37$	−1.29412	+	2.24149i	−0.212752	+	0.368498i	0.739823	+	0.672802i	$0.234909\pi$
$38$	−4.14430	+	2.39271i	−0.672294	+	0.388149i
$39$	0.435638	−	8.02611i	0.0697579	−	1.28521i
$40$	3.23623	+	1.86844i	0.511692	+	0.295426i
$41$	−4.10460			−0.641030			−0.320515	−	0.947243i	$-0.603856\pi$
$41$	−4.10460			−0.641030			−0.320515	+	0.947243i	$0.603856\pi$
$42$	2.85913	+	3.58126i	0.441173	+	0.552600i
$43$		−	2.19681i		−	0.335010i	−0.985871	−	0.167505i	$-0.946429\pi$
$43$		−	2.19681i		−	0.335010i	0.985871	−	0.167505i	$-0.0535711\pi$
$44$	3.31609	+	0.0598058i	0.499919	+	0.00901607i
$45$	−9.04495	−	6.62321i	−1.34834	−	0.987330i
$46$	4.94452	−	2.85472i	0.729029	−	0.420905i
$47$	−4.96151	−	2.86453i	−0.723711	−	0.417835i	0.0924058	−	0.995721i	$-0.470544\pi$
$47$	−4.96151	−	2.86453i	−0.723711	−	0.417835i	−0.816117	+	0.577887i	$0.803878\pi$
$48$	0.946049	−	1.45086i	0.136550	−	0.209413i
$49$	−5.62107	−	4.17176i	−0.803010	−	0.595966i
$50$	8.96422			1.26773
$51$	0.722045	+	1.42365i	0.101106	+	0.199351i
$52$	4.01896	−	2.32035i	0.557330	−	0.321774i
$53$	−3.30063	+	1.90562i	−0.453377	+	0.261757i	−0.709255	−	0.704952i	$-0.750969\pi$
$53$	−3.30063	+	1.90562i	−0.453377	+	0.261757i	0.255878	+	0.966709i	$0.417635\pi$
$54$	−3.29258	+	4.01981i	−0.448064	+	0.547027i
$55$	10.8433	−	6.00235i	1.46212	−	0.809357i
$56$	−0.830341	+	2.51208i	−0.110959	+	0.335690i
$57$	6.94298	+	4.52725i	0.919620	+	0.599649i
$58$	−3.86938	+	6.70196i	−0.508074	+	0.880010i
$59$	7.65662	−	4.42055i	0.996807	−	0.575507i	0.0895048	−	0.995986i	$-0.471472\pi$
$59$	7.65662	−	4.42055i	0.996807	−	0.575507i	0.907302	+	0.420480i	$0.138138\pi$
$60$	0.350793	−	6.46294i	0.0452872	−	0.834362i
$61$	6.52747	+	3.76863i	0.835756	+	0.482524i	0.855819	−	0.517275i	$-0.173053\pi$
$61$	6.52747	+	3.76863i	0.835756	+	0.482524i	−0.0200632	+	0.999799i	$0.506387\pi$
$62$	2.53129			0.321474
$63$	3.29208	−	7.22234i	0.414764	−	0.909929i
$64$	1.00000			0.125000
$65$	8.67085	−	15.0184i	1.07549	−	1.86280i
$66$	−2.50562	−	5.16932i	−0.308421	−	0.636299i
$67$	0.390387	+	0.676170i	0.0476934	+	0.0826073i	0.888887	−	0.458127i	$-0.151480\pi$
$67$	0.390387	+	0.676170i	0.0476934	+	0.0826073i	−0.841193	+	0.540735i	$0.818146\pi$
$68$	−0.460807	+	0.798142i	−0.0558811	+	0.0967889i
$69$	−8.28358	−	5.40141i	−0.997226	−	0.650253i
$70$	2.00648	+	9.68109i	0.239821	+	1.15711i
$71$		−	11.4978i		−	1.36454i	−0.731100	−	0.682271i	$-0.760993\pi$
$71$		−	11.4978i		−	1.36454i	0.731100	−	0.682271i	$-0.239007\pi$
$72$	−2.98238	−	0.324709i	−0.351476	−	0.0382673i
$73$	−9.35455	+	5.40085i	−1.09487	+	0.632122i	−0.934868	−	0.354995i	$-0.884482\pi$
$73$	−9.35455	+	5.40085i	−1.09487	+	0.632122i	−0.159999	+	0.987117i	$0.551149\pi$
$74$	1.29412	+	2.24149i	0.150439	+	0.260567i
$75$	−7.02307	−	13.8473i	−0.810954	−	1.59895i
$76$			4.78543i			0.548926i
$77$	5.71935	+	6.65500i	0.651781	+	0.758407i
$78$	−6.73300	−	4.39033i	−0.762362	−	0.497107i
$79$	−14.9095	−	8.60802i	−1.67745	−	0.968478i	−0.963276	−	0.268514i	$-0.913467\pi$
$79$	−14.9095	−	8.60802i	−1.67745	−	0.968478i	−0.714178	−	0.699964i	$-0.753199\pi$
$80$	3.23623	−	1.86844i	0.361821	−	0.208898i
$81$	8.78913	+	1.93681i	0.976570	+	0.215201i
$82$	−2.05230	+	3.55469i	−0.226638	+	0.392549i
$83$	−12.6784			−1.39163			−0.695816	−	0.718220i	$-0.744957\pi$
$83$	−12.6784			−1.39163			−0.695816	+	0.718220i	$0.744957\pi$
$84$	4.53102	−	0.685447i	0.494375	−	0.0747884i
$85$			3.44396i			0.373550i
$86$	−1.90249	−	1.09840i	−0.205151	−	0.118444i
$87$	13.3842	+	0.726463i	1.43494	+	0.0778850i
$88$	1.70984	−	2.84191i	0.182269	−	0.302949i
$89$	7.44976	+	4.30112i	0.789673	+	0.455918i	0.839848	−	0.542822i	$-0.182644\pi$
$89$	7.44976	+	4.30112i	0.789673	+	0.455918i	−0.0501742	+	0.998740i	$0.515978\pi$
$90$	−10.2583	+	4.52155i	−1.08132	+	0.476613i
$91$	11.6578	+	3.85336i	1.22207	+	0.403942i
$92$		−	5.70943i		−	0.595250i
$93$	−1.98315	−	3.91016i	−0.205643	−	0.405465i
$94$	−4.96151	+	2.86453i	−0.511741	+	0.295454i
$95$	8.94127	+	15.4867i	0.917354	+	1.58890i
$96$	−0.783456	−	1.54473i	−0.0799611	−	0.157659i
$97$	−12.1684			−1.23551			−0.617756	−	0.786370i	$-0.711958\pi$
$97$	−12.1684			−1.23551			−0.617756	+	0.786370i	$0.711958\pi$
$98$	−6.42339	+	2.78211i	−0.648860	+	0.281035i
$99$	−6.02217	+	7.92045i	−0.605251	+	0.796035i
$100$	4.48211	−	7.76324i	0.448211	−	0.776324i
$101$	0.661912	+	1.14646i	0.0658627	+	0.114077i	0.897076	−	0.441876i	$-0.145687\pi$
$101$	0.661912	+	1.14646i	0.0658627	+	0.114077i	−0.831214	+	0.555953i	$0.812353\pi$
$102$	1.59394	+	0.0865151i	0.157823	+	0.00856628i
$103$	−4.94954	+	8.57285i	−0.487693	+	0.844708i	−0.999900	−	0.0141536i	$-0.995495\pi$
$103$	−4.94954	+	8.57285i	−0.487693	+	0.844708i	0.512207	+	0.858862i	$0.328828\pi$
$104$		−	4.64070i		−	0.455058i
$105$	13.3827	−	10.6842i	1.30602	−	1.04267i
$106$			3.81124i			0.370181i
$107$	5.61684	−	9.72865i	0.543000	−	0.940504i	−0.455730	−	0.890118i	$-0.650622\pi$
$107$	5.61684	−	9.72865i	0.543000	−	0.940504i	0.998730	−	0.0503857i	$-0.0160451\pi$
$108$	1.83497	+	4.86137i	0.176570	+	0.467785i
$109$	−3.95986	+	2.28623i	−0.379286	+	0.218981i	−0.677508	−	0.735516i	$-0.736940\pi$
$109$	−3.95986	+	2.28623i	−0.379286	+	0.218981i	0.298221	+	0.954497i	$0.403607\pi$
$110$	0.223487	−	12.3918i	0.0213086	−	1.18151i
$111$	2.44861	−	3.75518i	0.232412	−	0.356426i
$112$	1.76035	+	1.97514i	0.166338	+	0.186633i
$113$			7.52223i			0.707632i	0.935315	+	0.353816i	$0.115116\pi$
$113$			7.52223i			0.707632i	−0.935315	+	0.353816i	$0.884884\pi$
$114$	7.39220	−	3.74917i	0.692343	−	0.351142i
$115$	−10.6677	−	18.4770i	−0.994770	−	1.72299i
$116$	3.86938	+	6.70196i	0.359263	+	0.622261i
$117$	−1.50688	+	13.8403i	−0.139311	+	1.27954i
$118$		−	8.84110i		−	0.813889i
$119$	−2.38762	+	0.494854i	−0.218873	+	0.0453632i
$120$	−5.42167	−	3.53527i	−0.494929	−	0.322724i
$121$	−5.15292	−	9.71841i	−0.468447	−	0.883491i
$122$	6.52747	−	3.76863i	0.590969	−	0.341196i
$123$	7.09892	+	0.385313i	0.640088	+	0.0347425i
$124$	1.26564	−	2.19216i	0.113658	−	0.196862i
$125$		−	14.8138i		−	1.32499i
$126$	−4.60869	−	6.46220i	−0.410575	−	0.575698i
$127$			5.14870i			0.456873i	0.973559	+	0.228437i	$0.0733614\pi$
$127$			5.14870i			0.456873i	−0.973559	+	0.228437i	$0.926639\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.206222	+	3.79939i	−0.0181568	+	0.334518i
$130$	−8.67085	−	15.0184i	−0.760484	−	1.31720i
$131$	7.91279	−	13.7053i	0.691343	−	1.19744i	−0.280054	−	0.959984i	$-0.590353\pi$
$131$	7.91279	−	13.7053i	0.691343	−	1.19744i	0.971398	−	0.237458i	$-0.0763141\pi$
$132$	−5.72957	−	0.414727i	−0.498695	−	0.0360973i
$133$	−9.45186	+	8.42404i	−0.819581	+	0.730457i
$134$	0.780774			0.0674486
$135$	15.0215	+	12.3040i	1.29285	+	1.05896i
$136$	0.460807	+	0.798142i	0.0395139	+	0.0684401i
$137$	−11.1932	+	6.46241i	−0.956302	+	0.552121i	−0.895033	−	0.446000i	$-0.852848\pi$
$137$	−11.1932	+	6.46241i	−0.956302	+	0.552121i	−0.0612689	+	0.998121i	$0.519515\pi$
$138$	−8.81955	+	4.47309i	−0.750770	+	0.380775i
$139$		−	8.08854i		−	0.686061i	−0.939324	−	0.343031i	$-0.888547\pi$
$139$		−	8.08854i		−	0.686061i	0.939324	−	0.343031i	$-0.111453\pi$
$140$	9.38731	+	3.10288i	0.793373	+	0.262241i
$141$	8.31206	+	5.41998i	0.700002	+	0.456444i
$142$	−9.95741	−	5.74892i	−0.835608	−	0.482438i
$143$	−13.1885	−	7.93483i	−1.10287	−	0.663544i
$144$	−1.77239	+	2.42046i	−0.147700	+	0.201705i
$145$	25.0444	+	14.4594i	2.07982	+	1.20079i
$146$			10.8017i			0.893955i
$147$	9.33005	+	7.74275i	0.769529	+	0.638612i
$148$	2.58824			0.212752
$149$	−6.60066	+	11.4327i	−0.540747	+	0.936602i	0.458114	+	0.888893i	$0.348525\pi$
$149$	−6.60066	+	11.4327i	−0.540747	+	0.936602i	−0.998861	+	0.0477082i	$0.984808\pi$
$150$	−15.5037	−	0.841502i	−1.26587	−	0.0687084i
$151$	−10.3132	+	5.95435i	−0.839279	+	0.484558i	−0.857019	−	0.515285i	$-0.827686\pi$
$151$	−10.3132	+	5.95435i	−0.839279	+	0.484558i	0.0177403	+	0.999843i	$0.494353\pi$
$152$	4.14430	+	2.39271i	0.336147	+	0.194075i
$153$	−1.11514	−	2.52999i	−0.0901535	−	0.204537i
$154$	8.62307	−	1.62561i	0.694867	−	0.130995i
$155$		−	9.45910i		−	0.759773i
$156$	−7.16863	+	3.63578i	−0.573950	+	0.291095i
$157$	6.04984	+	10.4786i	0.482830	+	0.836286i	0.999806	−	0.0197142i	$-0.00627562\pi$
$157$	6.04984	+	10.4786i	0.482830	+	0.836286i	−0.516976	+	0.856000i	$0.672942\pi$
$158$	−14.9095	+	8.60802i	−1.18614	+	0.684818i
$159$	5.88735	−	2.98594i	0.466897	−	0.236801i
$160$		−	3.73687i		−	0.295426i
$161$	11.2769	−	10.0506i	0.888745	−	0.792100i
$162$	6.07189	−	6.64320i	0.477053	−	0.521939i
$163$	0.770417	−	1.33440i	0.0603437	−	0.104518i	−0.834275	−	0.551348i	$-0.814114\pi$
$163$	0.770417	−	1.33440i	0.0603437	−	0.104518i	0.894619	+	0.446830i	$0.147447\pi$
$164$	2.05230	+	3.55469i	0.160258	+	0.277574i
$165$	−19.3171	+	9.36319i	−1.50383	+	0.728924i
$166$	−6.33919	+	10.9798i	−0.492016	+	0.852197i
$167$	−10.2207			−0.790902			−0.395451	−	0.918487i	$-0.629412\pi$
$167$	−10.2207			−0.790902			−0.395451	+	0.918487i	$0.629412\pi$
$168$	1.67190	−	4.26670i	0.128990	−	0.329183i
$169$	−8.53607			−0.656621
$170$	2.98256	+	1.72198i	0.228752	+	0.132070i
$171$	−11.5829	−	8.48166i	−0.885768	−	0.648609i
$172$	−1.90249	+	1.09840i	−0.145064	+	0.0837525i
$173$	−3.49761	+	6.05803i	−0.265918	+	0.460584i	−0.967804	−	0.251706i	$-0.919008\pi$
$173$	−3.49761	+	6.05803i	−0.265918	+	0.460584i	0.701886	+	0.712290i	$0.252342\pi$
$174$	7.32124	−	11.2278i	0.555022	−	0.851180i
$175$	23.2235	−	4.81327i	1.75554	−	0.363849i
$176$	−1.60625	−	2.90172i	−0.121076	−	0.218725i
$177$	−13.6571	+	6.92661i	−1.02653	+	0.520636i
$178$	7.44976	−	4.30112i	0.558383	−	0.322383i
$179$	20.0703	−	11.5876i	1.50012	−	0.866097i	0.500125	−	0.865953i	$-0.333287\pi$
$179$	20.0703	−	11.5876i	1.50012	−	0.866097i	1.00000		0.000143992i	$-4.58340e-5\pi$
$180$	−1.21340	+	11.1448i	−0.0904413	+	0.830681i
$181$	−6.34142			−0.471354			−0.235677	−	0.971831i	$-0.575731\pi$
$181$	−6.34142			−0.471354			−0.235677	+	0.971831i	$0.575731\pi$
$182$	9.16601	−	8.16926i	0.679430	−	0.605546i
$183$	−10.9355	−	7.13063i	−0.808376	−	0.527111i
$184$	−4.94452	−	2.85472i	−0.364515	−	0.210453i
$185$	8.37615	−	4.83597i	0.615827	−	0.355548i
$186$	−4.37787	−	0.237621i	−0.321001	−	0.0174232i
$187$	3.05615	+	0.0551180i	0.223488	+	0.00403062i
$188$			5.72906i			0.417835i
$189$	−6.37166	+	12.1820i	−0.463470	+	0.886113i
$190$	17.8825			1.29734
$191$	−6.08888	−	3.51541i	−0.440576	−	0.254366i	0.263266	−	0.964723i	$-0.415200\pi$
$191$	−6.08888	−	3.51541i	−0.440576	−	0.254366i	−0.703842	+	0.710357i	$0.748534\pi$
$192$	−1.72951	−	0.0938734i	−0.124816	−	0.00677473i
$193$	−7.54828	+	4.35800i	−0.543337	+	0.313696i	−0.746430	−	0.665464i	$-0.768234\pi$
$193$	−7.54828	+	4.35800i	−0.543337	+	0.313696i	0.203093	+	0.979159i	$0.434901\pi$
$194$	−6.08419	+	10.5381i	−0.436819	+	0.756593i
$195$	−16.4061	+	25.1604i	−1.17487	+	1.80177i
$196$	−0.802319	+	6.95387i	−0.0573085	+	0.496705i
$197$	−0.556764			−0.0396678			−0.0198339	−	0.999803i	$-0.506314\pi$
$197$	−0.556764			−0.0396678			−0.0198339	+	0.999803i	$0.506314\pi$
$198$	3.84822	+	9.17557i	0.273481	+	0.652080i
$199$	3.23869	+	5.60958i	0.229585	+	0.397653i	0.957685	−	0.287818i	$-0.0929298\pi$
$199$	3.23869	+	5.60958i	0.229585	+	0.397653i	−0.728100	+	0.685471i	$0.759597\pi$
$200$	−4.48211	−	7.76324i	−0.316933	−	0.548944i
$201$	−0.611702	−	1.20609i	−0.0431461	−	0.0850708i
$202$	1.32382			0.0931439
$203$	−6.42580	+	19.4403i	−0.451003	+	1.36444i
$204$	0.871893	−	1.33713i	0.0610447	−	0.0936180i
$205$	13.2834	+	7.66918i	0.927754	+	0.535639i
$206$	4.94954	+	8.57285i	0.344851	+	0.597299i
$207$	13.8194	+	10.1194i	0.960518	+	0.703345i
$208$	−4.01896	−	2.32035i	−0.278665	−	0.160887i
$209$	13.8860	−	7.68659i	0.960512	−	0.531692i
$210$	−2.56143	−	16.9319i	−0.176755	−	1.16841i
$211$		−	17.8142i		−	1.22638i	−0.789936	−	0.613189i	$-0.789886\pi$
$211$		−	17.8142i		−	1.22638i	0.789936	−	0.613189i	$-0.210114\pi$
$212$	3.30063	+	1.90562i	0.226688	+	0.130879i
$213$	−1.07934	+	19.8856i	−0.0739552	+	1.36254i
$214$	−5.61684	−	9.72865i	−0.383959	−	0.665037i
$215$	−4.10460	+	7.10937i	−0.279931	+	0.484855i
$216$	5.12755	+	0.841552i	0.348886	+	0.0572603i
$217$	6.55779	−	1.35916i	0.445172	−	0.0922655i
$218$			4.57246i			0.309686i
$219$	16.6857	−	8.46266i	1.12752	−	0.571853i
$220$	−10.6199	−	6.38944i	−0.715991	−	0.430776i
$221$	3.70394	−	2.13847i	0.249154	−	0.143849i
$222$	−2.02778	−	3.99814i	−0.136095	−	0.268338i
$223$	9.10963			0.610026			0.305013	−	0.952348i	$-0.401339\pi$
$223$	9.10963			0.610026			0.305013	+	0.952348i	$0.401339\pi$
$224$	2.59069	−	0.536942i	0.173098	−	0.0358760i
$225$	10.8465	+	24.6083i	0.723103	+	1.64055i
$226$	6.51444	+	3.76112i	0.433334	+	0.250186i
$227$	−12.5369	−	21.7145i	−0.832101	−	1.44124i	−0.896369	−	0.443308i	$-0.853805\pi$
$227$	−12.5369	−	21.7145i	−0.832101	−	1.44124i	0.0642687	−	0.997933i	$-0.479529\pi$
$228$	0.449224	−	8.27642i	0.0297506	−	0.548119i
$229$	11.5525	−	20.0095i	0.763408	−	1.32226i	−0.177676	−	0.984089i	$-0.556858\pi$
$229$	11.5525	−	20.0095i	0.763408	−	1.32226i	0.941084	−	0.338173i	$-0.109809\pi$
$230$	−21.3354			−1.40682
$231$	−9.26693	−	12.0467i	−0.609719	−	0.792618i
$232$	7.73875			0.508074
$233$	11.6393	−	20.1599i	0.762517	−	1.32072i	−0.179033	−	0.983843i	$-0.557297\pi$
$233$	11.6393	−	20.1599i	0.762517	−	1.32072i	0.941549	−	0.336875i	$-0.109370\pi$
$234$	11.2326	+	8.22514i	0.734299	+	0.537695i
$235$	10.7044	+	18.5406i	0.698278	+	1.20945i
$236$	−7.65662	−	4.42055i	−0.498403	−	0.287753i
$237$	24.9780	+	16.2872i	1.62250	+	1.05797i
$238$	−0.765255	+	2.31517i	−0.0496041	+	0.150070i
$239$	2.95273			0.190996			0.0954981	−	0.995430i	$-0.469556\pi$
$239$	2.95273			0.190996			0.0954981	+	0.995430i	$0.469556\pi$
$240$	−5.77247	+	2.92767i	−0.372611	+	0.188981i
$241$	3.18416	−	1.83837i	0.205110	−	0.118420i	−0.393927	−	0.919142i	$-0.628884\pi$
$241$	3.18416	−	1.83837i	0.205110	−	0.118420i	0.599037	+	0.800722i	$0.295550\pi$
$242$	−10.9928	−	0.396643i	−0.706647	−	0.0254971i
$243$	−15.0190	−	4.17479i	−0.963471	−	0.267813i
$244$		−	7.53727i		−	0.482524i
$245$	10.3964	+	24.0034i	0.664200	+	1.53352i
$246$	3.88315	−	5.95519i	0.247581	−	0.379689i
$247$	11.1039	−	19.2324i	0.706522	−	1.22373i
$248$	−1.26564	−	2.19216i	−0.0803685	−	0.139202i
$249$	21.9273	+	1.19016i	1.38959	+	0.0754235i
$250$	−12.8291	−	7.40689i	−0.811385	−	0.468453i
$251$			27.0815i			1.70937i	0.519147	+	0.854685i	$0.326250\pi$
$251$			27.0815i			1.70937i	−0.519147	+	0.854685i	$0.673750\pi$
$252$	−7.90077	+	0.760142i	−0.497702	+	0.0478844i
$253$	−16.5672	+	9.17078i	−1.04157	+	0.576562i
$254$	4.45890	+	2.57435i	0.279777	+	0.161529i
$255$	0.323296	−	5.95634i	0.0202456	−	0.373001i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.5519	+	7.24684i	0.782965	+	0.452045i	0.837480	−	0.546468i	$-0.184028\pi$
$257$	12.5519	+	7.24684i	0.782965	+	0.452045i	−0.0545147	+	0.998513i	$0.517361\pi$
$258$	3.18726	+	2.07829i	0.198430	+	0.129389i
$259$	4.55622	+	5.11213i	0.283110	+	0.317653i
$260$	−17.3417			−1.07549
$261$	−23.0799	−	2.51284i	−1.42861	−	0.155541i
$262$	−7.91279	−	13.7053i	−0.488854	−	0.846719i
$263$	7.25088	+	12.5589i	0.447108	+	0.774414i	0.998196	−	0.0600330i	$-0.0191206\pi$
$263$	7.25088	+	12.5589i	0.447108	+	0.774414i	−0.551088	+	0.834447i	$0.685787\pi$
$264$	−3.22395	+	4.75459i	−0.198420	+	0.292625i
$265$	14.2421			0.874887
$266$	2.56950	+	12.3976i	0.157546	+	0.760144i
$267$	−12.4806	−	8.13815i	−0.763803	−	0.498047i
$268$	0.390387	−	0.676170i	0.0238467	−	0.0413037i
$269$	−6.66567	+	3.84843i	−0.406413	+	0.234643i	−0.689248	−	0.724526i	$-0.742059\pi$
$269$	−6.66567	+	3.84843i	−0.406413	+	0.234643i	0.282834	+	0.959169i	$0.408725\pi$
$270$	18.1663	−	6.85705i	1.10557	−	0.417307i
$271$	2.86928	+	1.65658i	0.174296	+	0.100630i	0.584610	−	0.811314i	$-0.301248\pi$
$271$	2.86928	+	1.65658i	0.174296	+	0.100630i	−0.410314	+	0.911944i	$0.634581\pi$
$272$	0.921615			0.0558811
$273$	−19.8005	−	7.75877i	−1.19838	−	0.469582i
$274$			12.9248i			0.780817i
$275$	−29.7261	−	0.536113i	−1.79255	−	0.0323288i
$276$	−0.535964	+	9.87450i	−0.0322613	+	0.594375i
$277$	−7.75856	+	4.47940i	−0.466166	+	0.269141i	−0.714634	−	0.699499i	$-0.753407\pi$
$277$	−7.75856	+	4.47940i	−0.466166	+	0.269141i	0.248467	+	0.968640i	$0.420073\pi$
$278$	−7.00488	−	4.04427i	−0.420125	−	0.242559i
$279$	3.06281	+	6.94881i	0.183366	+	0.416014i
$280$	7.38083	−	6.57821i	0.441089	−	0.393123i
$281$	−22.9477			−1.36894			−0.684471	−	0.729040i	$-0.739967\pi$
$281$	−22.9477			−1.36894			−0.684471	+	0.729040i	$0.739967\pi$
$282$	8.84987	−	4.48847i	0.527002	−	0.267284i
$283$	22.4674	−	12.9715i	1.33555	−	0.771078i	0.349402	−	0.936973i	$-0.386385\pi$
$283$	22.4674	−	12.9715i	1.33555	−	0.771078i	0.986143	+	0.165895i	$0.0530513\pi$
$284$	−9.95741	+	5.74892i	−0.590864	+	0.341135i
$285$	−14.0102	−	27.6237i	−0.829891	−	1.63629i
$286$	−13.4660	+	7.45412i	−0.796261	+	0.440771i
$287$	−3.40822	+	10.3111i	−0.201181	+	0.608643i
$288$	1.20998	+	2.74517i	0.0712988	+	0.161761i
$289$	8.07531	−	13.9869i	0.475018	−	0.822756i
$290$	25.0444	−	14.4594i	1.47066	−	0.849083i
$291$	21.0453	+	1.14229i	1.23370	+	0.0669621i
$292$	9.35455	+	5.40085i	0.547434	+	0.316061i
$293$	5.56705			0.325230			0.162615	−	0.986690i	$-0.448007\pi$
$293$	5.56705			0.325230			0.162615	+	0.986690i	$0.448007\pi$
$294$	11.3704	−	4.20868i	0.663138	−	0.245455i
$295$	−33.0381			−1.92355
$296$	1.29412	−	2.24149i	0.0752193	−	0.130284i
$297$	11.1589	−	13.1331i	0.647504	−	0.762062i
$298$	6.60066	+	11.4327i	0.382366	+	0.662277i
$299$	−13.2479	+	22.9460i	−0.766145	+	1.32700i
$300$	−8.48059	+	13.0058i	−0.489627	+	0.750891i
$301$	−5.51855	−	1.82410i	−0.318084	−	0.105139i
$302$			11.9087i			0.685268i
$303$	−1.03716	−	2.04495i	−0.0595831	−	0.117479i
$304$	4.14430	−	2.39271i	0.237692	−	0.137232i
$305$	−14.0829	−	24.3923i	−0.806385	−	1.39670i
$306$	−2.74860	−	0.299257i	−0.157127	−	0.0171074i
$307$			30.2069i			1.72400i	0.506909	+	0.862000i	$0.330788\pi$
$307$			30.2069i			1.72400i	−0.506909	+	0.862000i	$0.669212\pi$
$308$	2.90372	−	8.28060i	0.165455	−	0.471831i
$309$	9.36502	−	14.3622i	0.532757	−	0.817035i
$310$	−8.19182	−	4.72955i	−0.465264	−	0.268620i
$311$	0.793092	−	0.457892i	0.0449721	−	0.0259647i	−0.477345	−	0.878716i	$-0.658401\pi$
$311$	0.793092	−	0.457892i	0.0449721	−	0.0259647i	0.522318	+	0.852751i	$0.325068\pi$
$312$	−0.435638	+	8.02611i	−0.0246632	+	0.454389i
$313$	2.87594	−	4.98127i	0.162558	−	0.281558i	−0.773228	−	0.634129i	$-0.781359\pi$
$313$	2.87594	−	4.98127i	0.162558	−	0.281558i	0.935785	+	0.352571i	$0.114692\pi$
$314$	12.0997			0.682825
$315$	−24.1484	+	17.2221i	−1.36061	+	0.970354i
$316$			17.2160i			0.968478i
$317$	9.09364	+	5.25022i	0.510750	+	0.294882i	0.733142	−	0.680076i	$-0.238053\pi$
$317$	9.09364	+	5.25022i	0.510750	+	0.294882i	−0.222392	+	0.974957i	$0.571386\pi$
$318$	0.357774	−	6.59157i	0.0200630	−	0.369637i
$319$	13.2320	−	21.9928i	0.740850	−	1.23136i
$320$	−3.23623	−	1.86844i	−0.180911	−	0.104449i
$321$	−10.6276	+	16.2985i	−0.593175	+	0.909692i
$322$	−3.06564	−	14.7914i	−0.170841	−	0.824292i
$323$			4.41032i			0.245397i
$324$	−2.71724	−	8.58001i	−0.150958	−	0.476667i
$325$	−36.0269	+	20.8001i	−1.99841	+	1.15378i
$326$	−0.770417	−	1.33440i	−0.0426695	−	0.0739057i
$327$	7.06322	−	3.58232i	0.390597	−	0.198103i
$328$	4.10460			0.226638
$329$	−11.3157	+	10.0852i	−0.623853	+	0.556013i
$330$	−1.54978	+	21.4107i	−0.0853127	+	1.17862i
$331$	7.54164	−	13.0625i	0.414526	−	0.717981i	−0.580852	−	0.814009i	$-0.697281\pi$
$331$	7.54164	−	13.0625i	0.414526	−	0.717981i	0.995379	+	0.0960284i	$0.0306140\pi$
$332$	6.33919	+	10.9798i	0.347908	+	0.602594i
$333$	−4.58739	+	6.26474i	−0.251387	+	0.343306i
$334$	−5.11035	+	8.85139i	−0.279626	+	0.484327i
$335$		−	2.91765i		−	0.159408i
$336$	−2.85913	−	3.58126i	−0.155978	−	0.195374i
$337$		−	14.8370i		−	0.808223i	−0.914710	−	0.404111i	$-0.867581\pi$
$337$		−	14.8370i		−	0.808223i	0.914710	−	0.404111i	$-0.132419\pi$
$338$	−4.26804	+	7.39246i	−0.232151	+	0.402097i
$339$	0.706137	−	13.0097i	0.0383521	−	0.706592i
$340$	2.98256	−	1.72198i	0.161752	−	0.0933874i
$341$	−8.39397	−	0.151386i	−0.454559	−	0.00819800i
$342$	−13.1368	+	5.79028i	−0.710357	+	0.313102i
$343$	−15.1472	+	10.6566i	−0.817872	+	0.575401i
$344$			2.19681i			0.118444i
$345$	16.7154	+	32.9575i	0.899925	+	1.77437i
$346$	3.49761	+	6.05803i	0.188033	+	0.325682i
$347$	−0.849785	−	1.47187i	−0.0456188	−	0.0790141i	0.842314	−	0.538987i	$-0.181193\pi$
$347$	−0.849785	−	1.47187i	−0.0456188	−	0.0790141i	−0.887933	+	0.459972i	$0.847859\pi$
$348$	−6.06297	−	11.9543i	−0.325009	−	0.640818i
$349$		−	20.1684i		−	1.07959i	−0.841796	−	0.539796i	$-0.818502\pi$
$349$		−	20.1684i		−	1.07959i	0.841796	−	0.539796i	$-0.181498\pi$
$350$	7.44336	−	22.5188i	0.397864	−	1.20368i
$351$	3.90539	−	23.7954i	0.208454	−	1.27011i
$352$	−3.31609	−	0.0598058i	−0.176748	−	0.00318766i
$353$	9.88903	−	5.70943i	0.526340	−	0.303883i	−0.213185	−	0.977012i	$-0.568384\pi$
$353$	9.88903	−	5.70943i	0.526340	−	0.303883i	0.739525	+	0.673129i	$0.235050\pi$
$354$	−0.829944	+	15.2907i	−0.0441110	+	0.812693i
$355$	−21.4830	+	37.2096i	−1.14020	+	1.97488i
$356$		−	8.60225i		−	0.455918i
$357$	4.17586	−	0.631718i	0.221010	−	0.0334341i
$358$		−	23.1752i		−	1.22485i
$359$	−4.22498	+	7.31788i	−0.222986	+	0.386223i	−0.955713	−	0.294299i	$-0.904914\pi$
$359$	−4.22498	+	7.31788i	−0.222986	+	0.386223i	0.732727	+	0.680522i	$0.238247\pi$
$360$	9.04495	+	6.62321i	0.476711	+	0.349074i
$361$	1.95015	+	3.37776i	0.102640	+	0.177777i
$362$	−3.17071	+	5.49183i	−0.166649	+	0.288644i
$363$	7.99970	+	17.2918i	0.419875	+	0.907582i
$364$	−2.49179	−	12.0226i	−0.130605	−	0.630157i
$365$	40.3646			2.11278
$366$	−11.6431	+	5.90512i	−0.608592	+	0.308665i
$367$	−0.156031	−	0.270253i	−0.00814474	−	0.0141071i	0.861924	−	0.507037i	$-0.169259\pi$
$367$	−0.156031	−	0.270253i	−0.00814474	−	0.0141071i	−0.870069	+	0.492930i	$0.835926\pi$
$368$	−4.94452	+	2.85472i	−0.257751	+	0.148812i
$369$	−12.2415	−	1.33280i	−0.637264	−	0.0693828i
$370$		−	9.67194i		−	0.502820i
$371$	2.04642	+	9.87376i	0.106245	+	0.512620i
$372$	−2.39472	+	3.67254i	−0.124161	+	0.190412i
$373$	−29.1559	−	16.8331i	−1.50963	−	0.871587i	−0.999937	−	0.0112328i	$-0.996424\pi$
$373$	−29.1559	−	16.8331i	−1.50963	−	0.871587i	−0.509696	−	0.860354i	$-0.670242\pi$
$374$	1.57581	−	2.61915i	0.0814832	−	0.135433i
$375$	−1.39062	+	25.6205i	−0.0718114	+	1.32304i
$376$	4.96151	+	2.86453i	0.255871	+	0.147727i
$377$		−	35.9132i		−	1.84962i
$378$	7.36412	+	11.6090i	0.378769	+	0.597104i
$379$	8.97243			0.460883			0.230441	−	0.973086i	$-0.425983\pi$
$379$	8.97243			0.460883			0.230441	+	0.973086i	$0.425983\pi$
$380$	8.94127	−	15.4867i	0.458677	−	0.794452i
$381$	0.483326	−	8.90470i	0.0247615	−	0.456202i
$382$	−6.08888	+	3.51541i	−0.311534	+	0.179864i
$383$	−6.48945	−	3.74669i	−0.331596	−	0.191447i	0.324954	−	0.945730i	$-0.394651\pi$
$383$	−6.48945	−	3.74669i	−0.331596	−	0.191447i	−0.656549	+	0.754283i	$0.727985\pi$
$384$	−0.946049	+	1.45086i	−0.0482779	+	0.0740388i
$385$	−6.07469	−	32.2233i	−0.309595	−	1.64225i
$386$			8.71600i			0.443633i
$387$	0.713324	−	6.55171i	0.0362603	−	0.333042i
$388$	6.08419	+	10.5381i	0.308878	+	0.534992i
$389$	9.97406	−	5.75853i	0.505705	−	0.291969i	−0.225361	−	0.974275i	$-0.572356\pi$
$389$	9.97406	−	5.75853i	0.505705	−	0.291969i	0.731066	+	0.682306i	$0.239023\pi$
$390$	13.5865	+	26.7883i	0.687977	+	1.35648i
$391$		−	5.26190i		−	0.266106i
$392$	5.62107	+	4.17176i	0.283907	+	0.210706i
$393$	−14.9718	+	22.9607i	−0.755226	+	1.15821i
$394$	−0.278382	+	0.482171i	−0.0140247	+	0.0242914i
$395$	32.1671	+	55.7150i	1.61850	+	2.80333i
$396$	9.87039	+	1.25513i	0.496006	+	0.0630725i
$397$	10.4828	−	18.1567i	0.526115	−	0.911258i	−0.473422	−	0.880836i	$-0.656981\pi$
$397$	10.4828	−	18.1567i	0.526115	−	0.911258i	0.999537	−	0.0304226i	$-0.00968532\pi$
$398$	6.47738			0.324682
$399$	17.1378	−	13.6821i	0.857965	−	0.684964i
$400$	−8.96422			−0.448211
$401$	−20.3964	−	11.7758i	−1.01855	−	0.588057i	−0.104863	−	0.994487i	$-0.533440\pi$
$401$	−20.3964	−	11.7758i	−1.01855	−	0.588057i	−0.913682	+	0.406429i	$0.866774\pi$
$402$	−1.35035	−	0.0732939i	−0.0673495	−	0.00365557i
$403$	−10.1731	+	5.87347i	−0.506761	+	0.292578i
$404$	0.661912	−	1.14646i	0.0329313	−	0.0570387i
$405$	−24.8248	−	22.6899i	−1.23355	−	1.12747i
$406$	13.6229	+	15.2851i	0.676095	+	0.758586i
$407$	−4.15737	−	7.51035i	−0.206073	−	0.372274i
$408$	−0.722045	−	1.42365i	−0.0357465	−	0.0704811i
$409$	10.2853	−	5.93820i	0.508573	−	0.293625i	−0.223674	−	0.974664i	$-0.571805\pi$
$409$	10.2853	−	5.93820i	0.508573	−	0.293625i	0.732247	+	0.681039i	$0.238472\pi$
$410$	13.2834	−	7.66918i	0.656021	−	0.378754i
$411$	19.9654	−	10.1260i	0.984820	−	0.499480i
$412$	9.89908			0.487693
$413$	−4.74716	−	22.9046i	−0.233593	−	1.12706i
$414$	15.6734	−	6.90831i	0.770303	−	0.339525i
$415$	41.0301	+	23.6887i	2.01409	+	1.16283i
$416$	−4.01896	+	2.32035i	−0.197046	+	0.113764i
$417$	−0.759299	+	13.9892i	−0.0371830	+	0.685053i
$418$	0.286196	−	15.8689i	0.0139983	−	0.776172i
$419$			21.5571i			1.05313i	0.850134	+	0.526567i	$0.176521\pi$
$419$			21.5571i			1.05313i	−0.850134	+	0.526567i	$0.823479\pi$
$420$	−15.9441	−	6.24767i	−0.777994	−	0.304855i
$421$	−12.1688			−0.593070			−0.296535	−	0.955022i	$-0.595831\pi$
$421$	−12.1688			−0.593070			−0.296535	+	0.955022i	$0.595831\pi$
$422$	−15.4275	−	8.90708i	−0.751000	−	0.433590i
$423$	−13.8670	−	10.1542i	−0.674235	−	0.493712i
$424$	3.30063	−	1.90562i	0.160293	−	0.0925452i
$425$	4.13078	−	7.15472i	0.200372	−	0.347055i
$426$	16.6817	+	10.8775i	0.808232	+	0.527017i
$427$	14.8871	−	13.2682i	0.720438	−	0.642095i
$428$	−11.2337			−0.543000
$429$	22.0646	+	14.9614i	1.06529	+	0.722342i
$430$	4.10460	+	7.10937i	0.197941	+	0.342844i
$431$	−6.76221	−	11.7125i	−0.325724	−	0.564171i	0.655934	−	0.754818i	$-0.272275\pi$
$431$	−6.76221	−	11.7125i	−0.325724	−	0.564171i	−0.981659	+	0.190647i	$0.938941\pi$
$432$	3.29258	−	4.01981i	0.158414	−	0.193403i
$433$	34.3316			1.64987			0.824937	−	0.565225i	$-0.191211\pi$
$433$	34.3316			1.64987			0.824937	+	0.565225i	$0.191211\pi$
$434$	2.10183	−	6.35879i	0.100891	−	0.305232i
$435$	−41.9570	−	27.3585i	−2.01168	−	1.31174i
$436$	3.95986	+	2.28623i	0.189643	+	0.109490i
$437$	−13.6610	−	23.6616i	−0.653496	−	1.13189i
$438$	1.01399	−	18.6816i	0.0484505	−	0.892641i
$439$	−2.95877	−	1.70824i	−0.141214	−	0.0815301i	0.427728	−	0.903907i	$-0.359314\pi$
$439$	−2.95877	−	1.70824i	−0.141214	−	0.0815301i	−0.568943	+	0.822377i	$0.692647\pi$
$440$	−10.8433	+	6.00235i	−0.516936	+	0.286151i
$441$	−15.4095	−	14.2670i	−0.733787	−	0.679380i
$442$		−	4.27694i		−	0.203433i
$443$	−21.5391	−	12.4356i	−1.02336	−	0.590835i	−0.108281	−	0.994120i	$-0.534535\pi$
$443$	−21.5391	−	12.4356i	−1.02336	−	0.590835i	−0.915074	+	0.403286i	$0.867868\pi$
$444$	−4.47638	−	0.242967i	−0.212440	−	0.0115307i
$445$	−16.0727	−	27.8388i	−0.761921	−	1.31969i
$446$	4.55482	−	7.88917i	0.215677	−	0.373563i
$447$	12.4891	−	19.1532i	0.590714	−	0.905918i
$448$	0.830341	−	2.51208i	0.0392299	−	0.118685i
$449$		−	12.2457i		−	0.577908i	−0.957343	−	0.288954i	$-0.906693\pi$
$449$		−	12.2457i		−	0.577908i	0.957343	−	0.288954i	$-0.0933075\pi$
$450$	26.7347	+	2.91076i	1.26028	+	0.137215i
$451$	7.01819	−	11.6649i	0.330474	−	0.549279i
$452$	6.51444	−	3.76112i	0.306414	−	0.176908i
$453$	18.3957	−	9.32993i	0.864307	−	0.438358i
$454$	−25.0737			−1.17677
$455$	−30.5275	−	34.2522i	−1.43115	−	1.60577i
$456$	−6.94298	−	4.52725i	−0.325135	−	0.212008i
$457$	26.7154	+	15.4241i	1.24969	+	0.721511i	0.971048	−	0.238883i	$-0.0767814\pi$
$457$	26.7154	+	15.4241i	1.24969	+	0.721511i	0.278645	+	0.960394i	$0.410115\pi$
$458$	−11.5525	−	20.0095i	−0.539811	−	0.934980i
$459$	1.69114	+	4.48031i	0.0789355	+	0.209123i
$460$	−10.6677	+	18.4770i	−0.497385	+	0.861496i
$461$	3.40330			0.158507			0.0792537	−	0.996854i	$-0.474746\pi$
$461$	3.40330			0.158507			0.0792537	+	0.996854i	$0.474746\pi$
$462$	−15.0663	+	2.00202i	−0.700945	+	0.0931424i
$463$	−15.8266			−0.735522			−0.367761	−	0.929920i	$-0.619876\pi$
$463$	−15.8266			−0.735522			−0.367761	+	0.929920i	$0.619876\pi$
$464$	3.86938	−	6.70196i	0.179631	−	0.311130i
$465$	−0.887958	+	16.3596i	−0.0411781	+	0.758656i
$466$	−11.6393	−	20.1599i	−0.539181	−	0.933889i
$467$	−18.9467	−	10.9389i	−0.876750	−	0.506192i	−0.00716472	−	0.999974i	$-0.502281\pi$
$467$	−18.9467	−	10.9389i	−0.876750	−	0.506192i	−0.869586	+	0.493782i	$0.835614\pi$
$468$	12.7395	−	5.61516i	0.588883	−	0.259561i
$469$	2.02275	−	0.419231i	0.0934017	−	0.0193583i
$470$	21.4088			0.987514
$471$	−9.47957	−	18.6908i	−0.436795	−	0.861225i
$472$	−7.65662	+	4.42055i	−0.352424	+	0.203472i
$473$	6.24314	+	3.75618i	0.287060	+	0.172709i
$474$	26.5942	−	13.4880i	1.22151	−	0.619525i
$475$		−	42.8976i		−	1.96828i
$476$	1.62237	+	1.82031i	0.0743611	+	0.0834340i
$477$	−10.4625	+	4.61153i	−0.479045	+	0.211148i
$478$	1.47636	−	2.55714i	0.0675273	−	0.116961i
$479$	12.2718	+	21.2553i	0.560711	+	0.971180i	0.997435	+	0.0715839i	$0.0228054\pi$
$479$	12.2718	+	21.2553i	0.560711	+	0.971180i	−0.436724	+	0.899596i	$0.643861\pi$
$480$	−0.350793	+	6.46294i	−0.0160114	+	0.294992i
$481$	−10.4021	−	6.00563i	−0.474293	−	0.273833i
$482$		−	3.67675i		−	0.167471i
$483$	−20.4470	+	16.3240i	−0.930369	+	0.742767i
$484$	−5.83993	+	9.32176i	−0.265451	+	0.423717i
$485$	39.3796	+	22.7358i	1.78814	+	1.03238i
$486$	−11.1250	+	10.9195i	−0.504640	+	0.495317i
$487$	−18.0891	−	31.3313i	−0.819697	−	1.41976i	−0.905905	−	0.423480i	$-0.860808\pi$
$487$	−18.0891	−	31.3313i	−0.819697	−	1.41976i	0.0862081	−	0.996277i	$-0.472525\pi$
$488$	−6.52747	−	3.76863i	−0.295484	−	0.170598i
$489$	−1.45771	+	2.23553i	−0.0659197	+	0.101094i
$490$	25.9857	+	2.99816i	1.17392	+	0.135443i
$491$	39.6660			1.79010			0.895050	−	0.445965i	$-0.147139\pi$
$491$	39.6660			1.79010			0.895050	+	0.445965i	$0.147139\pi$
$492$	−3.21577	−	6.34050i	−0.144978	−	0.285852i
$493$	3.56607	+	6.17662i	0.160608	+	0.278181i
$494$	−11.1039	−	19.2324i	−0.499586	−	0.865309i
$495$	34.2880	−	14.3803i	1.54113	−	0.646348i
$496$	−2.53129			−0.113658
$497$	−28.8834	−	9.54712i	−1.29560	−	0.428247i
$498$	11.9944	−	18.3945i	0.537480	−	0.824278i
$499$	−16.0605	+	27.8176i	−0.718966	+	1.24529i	0.242444	+	0.970165i	$0.422051\pi$
$499$	−16.0605	+	27.8176i	−0.718966	+	1.24529i	−0.961410	+	0.275120i	$0.911282\pi$
$500$	−12.8291	+	7.40689i	−0.573736	+	0.331246i
$501$	17.6768	+	0.959453i	0.789740	+	0.0428652i
$502$	23.4533	+	13.5408i	1.04677	+	0.604353i
$503$	−8.24994			−0.367847			−0.183923	−	0.982941i	$-0.558880\pi$
$503$	−8.24994			−0.367847			−0.183923	+	0.982941i	$0.558880\pi$
$504$	−3.29208	+	7.22234i	−0.146641	+	0.321709i
$505$		−	4.94696i		−	0.220137i
$506$	−0.341458	+	18.9330i	−0.0151796	+	0.841673i
$507$	14.7632	+	0.801310i	0.655656	+	0.0355874i
$508$	4.45890	−	2.57435i	0.197832	−	0.114218i
$509$	−3.24742	−	1.87490i	−0.143939	−	0.0831033i	0.426301	−	0.904581i	$-0.359816\pi$
$509$	−3.24742	−	1.87490i	−0.143939	−	0.0831033i	−0.570240	+	0.821478i	$0.693150\pi$
$510$	−4.99670	−	3.25815i	−0.221257	−	0.144273i
$511$	5.79989	+	27.9839i	0.256572	+	1.23793i
$512$	−1.00000			−0.0441942
$513$	19.2365	+	15.7564i	0.849313	+	0.695662i
$514$	12.5519	−	7.24684i	0.553640	−	0.319644i
$515$	32.0357	−	18.4958i	1.41166	−	0.815022i
$516$	3.39348	−	1.72110i	0.149390	−	0.0757673i
$517$	16.6241	−	9.20231i	0.731128	−	0.404717i
$518$	6.70535	−	1.38974i	0.294616	−	0.0610616i
$519$	6.61782	−	10.1491i	0.290490	−	0.445495i
$520$	−8.67085	+	15.0184i	−0.380242	+	0.658598i
$521$	−20.4859	+	11.8275i	−0.897504	+	0.518174i	−0.876389	−	0.481603i	$-0.840055\pi$
$521$	−20.4859	+	11.8275i	−0.897504	+	0.518174i	−0.0211142	+	0.999777i	$0.506721\pi$
$522$	−13.7161	+	18.7313i	−0.600338	+	0.819848i
$523$	−16.3582	−	9.44443i	−0.715295	−	0.412976i	0.0977232	−	0.995214i	$-0.468844\pi$
$523$	−16.3582	−	9.44443i	−0.715295	−	0.412976i	−0.813019	+	0.582238i	$0.802177\pi$
$524$	−15.8256			−0.691343
$525$	−40.6171	+	6.14450i	−1.77267	+	0.268168i
$526$	14.5018			0.632306
$527$	1.16644	−	2.02033i	0.0508108	−	0.0880068i
$528$	2.50562	+	5.16932i	0.109043	+	0.224966i
$529$	4.79882	+	8.31181i	0.208645	+	0.361383i
$530$	7.12107	−	12.3341i	0.309319	−	0.535757i
$531$	24.2703	−	10.6976i	1.05324	−	0.464235i
$532$	12.0214	+	3.97354i	0.521192	+	0.172275i
$533$		−	19.0482i		−	0.825069i
$534$	−13.2882	+	6.73948i	−0.575035	+	0.291646i
$535$	−36.3547	+	20.9894i	−1.57175	+	0.907451i
$536$	−0.390387	−	0.676170i	−0.0168622	−	0.0292061i
$537$	−35.7995	+	18.1567i	−1.54486	+	0.783521i
$538$			7.69686i			0.331835i
$539$	21.4669	−	8.84154i	0.924644	−	0.380832i
$540$	3.14477	−	19.1610i	0.135329	−	0.824559i
$541$	−30.8245	−	17.7966i	−1.32525	−	0.765134i	−0.340690	−	0.940176i	$-0.610661\pi$
$541$	−30.8245	−	17.7966i	−1.32525	−	0.765134i	−0.984561	+	0.175042i	$0.943994\pi$
$542$	2.86928	−	1.65658i	0.123246	−	0.0711561i
$543$	10.9675	+	0.595291i	0.470662	+	0.0255464i
$544$	0.460807	−	0.798142i	0.0197570	−	0.0342201i
$545$	17.0867			0.731913
$546$	−16.6195	+	13.2683i	−0.711250	+	0.567832i
$547$			31.2280i			1.33521i	0.744514	+	0.667607i	$0.232681\pi$
$547$			31.2280i			1.33521i	−0.744514	+	0.667607i	$0.767319\pi$
$548$	11.1932	+	6.46241i	0.478151	+	0.276061i
$549$	18.2436	+	13.3590i	0.778620	+	0.570149i
$550$	−15.3273	+	25.4755i	−0.653560	+	1.08628i
$551$	32.0717	+	18.5166i	1.36630	+	0.788834i
$552$	8.28358	+	5.40141i	0.352573	+	0.229899i
$553$	−34.0040	+	30.3063i	−1.44600	+	1.28876i
$554$			8.95881i			0.380623i
$555$	−14.9406	+	7.57754i	−0.634191	+	0.321649i
$556$	−7.00488	+	4.04427i	−0.297073	+	0.171515i
$557$	7.73600	+	13.3991i	0.327785	+	0.567740i	0.982072	−	0.188506i	$-0.0603645\pi$
$557$	7.73600	+	13.3991i	0.327785	+	0.567740i	−0.654287	+	0.756246i	$0.727031\pi$
$558$	7.54925	+	0.821932i	0.319585	+	0.0347952i
$559$	10.1947			0.431191
$560$	−2.00648	−	9.68109i	−0.0847895	−	0.409101i
$561$	−5.28046	−	0.382218i	−0.222941	−	0.0161373i
$562$	−11.4738	+	19.8733i	−0.483994	+	0.838303i
$563$	−0.771946	−	1.33705i	−0.0325336	−	0.0563499i	0.849300	−	0.527910i	$-0.177024\pi$
$563$	−0.771946	−	1.33705i	−0.0325336	−	0.0563499i	−0.881834	+	0.471560i	$0.843691\pi$
$564$	0.537807	−	9.90844i	0.0226458	−	0.417221i
$565$	14.0548	−	24.3436i	0.591290	−	1.02414i
$566$		−	25.9431i		−	1.09047i
$567$	12.1634	−	20.4708i	0.510814	−	0.859691i
$568$			11.4978i			0.482438i
$569$	−11.5873	+	20.0697i	−0.485763	+	0.841366i	−0.999866	−	0.0163623i	$-0.994791\pi$
$569$	−11.5873	+	20.0697i	−0.485763	+	0.841366i	0.514103	+	0.857728i	$0.328125\pi$
$570$	−30.9279	−	1.67869i	−1.29543	−	0.0703128i
$571$	−7.03226	+	4.06008i	−0.294291	+	0.169909i	−0.639875	−	0.768479i	$-0.721014\pi$
$571$	−7.03226	+	4.06008i	−0.294291	+	0.169909i	0.345584	+	0.938388i	$0.387681\pi$
$572$	−0.277541	+	15.3889i	−0.0116046	+	0.643444i
$573$	10.2007	+	6.65151i	0.426142	+	0.277871i
$574$	7.22554	+	8.10714i	0.301588	+	0.338385i
$575$			51.1806i			2.13438i
$576$	2.98238	+	0.324709i	0.124266	+	0.0135295i
$577$	22.9056	+	39.6736i	0.953571	+	1.65163i	0.737605	+	0.675232i	$0.235957\pi$
$577$	22.9056	+	39.6736i	0.953571	+	1.65163i	0.215965	+	0.976401i	$0.430710\pi$
$578$	−8.07531	−	13.9869i	−0.335889	−	0.581776i
$579$	13.4639	−	6.82860i	0.559540	−	0.283787i
$580$		−	28.9187i		−	1.20079i
$581$	−10.5274	+	31.8491i	−0.436749	+	1.32132i
$582$	11.5119	−	17.6546i	0.477183	−	0.731807i
$583$	0.227935	−	12.6384i	0.00944009	−	0.523429i
$584$	9.35455	−	5.40085i	0.387094	−	0.223489i
$585$	30.7363	−	41.9749i	1.27079	−	1.73545i
$586$	2.78352	−	4.82120i	0.114986	−	0.199162i
$587$			8.71794i			0.359828i	0.983682	+	0.179914i	$0.0575820\pi$
$587$			8.71794i			0.359828i	−0.983682	+	0.179914i	$0.942418\pi$
$588$	2.04040	−	11.9514i	0.0841446	−	0.492869i
$589$		−	12.1133i		−	0.499119i
$590$	−16.5190	+	28.6118i	−0.680078	+	1.17793i
$591$	0.962925	+	0.0522653i	0.0396095	+	0.00214991i
$592$	−1.29412	−	2.24149i	−0.0531881	−	0.0921245i
$593$	−11.1048	+	19.2340i	−0.456019	+	0.789848i	−0.998746	−	0.0500613i	$-0.984058\pi$
$593$	−11.1048	+	19.2340i	−0.456019	+	0.789848i	0.542727	+	0.839909i	$0.317392\pi$
$594$	−5.79418	−	16.2304i	−0.237738	−	0.665943i
$595$	8.65149	+	2.85966i	0.354676	+	0.117235i
$596$	13.2013			0.540747
$597$	−5.07474	−	10.0058i	−0.207695	−	0.409511i
$598$	13.2479	+	22.9460i	0.541746	+	0.938332i
$599$	6.10885	−	3.52694i	0.249601	−	0.144107i	−0.369981	−	0.929039i	$-0.620636\pi$
$599$	6.10885	−	3.52694i	0.249601	−	0.144107i	0.619581	+	0.784932i	$0.287302\pi$
$600$	7.02307	+	13.8473i	0.286716	+	0.565314i
$601$		−	19.4191i		−	0.792122i	−0.918224	−	0.396061i	$-0.870377\pi$
$601$		−	19.4191i		−	0.792122i	0.918224	−	0.396061i	$-0.129623\pi$
$602$	−4.33899	+	3.86716i	−0.176844	+	0.157614i
$603$	0.944722	+	2.14336i	0.0384721	+	0.0872842i
$604$	10.3132	+	5.95435i	0.419639	+	0.242279i
$605$	−1.48220	+	41.0789i	−0.0602601	+	1.67009i
$606$	−2.28956	−	0.124272i	−0.0930070	−	0.00504820i
$607$	17.1496	+	9.90133i	0.696081	+	0.401882i	0.805886	−	0.592071i	$-0.201689\pi$
$607$	17.1496	+	9.90133i	0.696081	+	0.401882i	−0.109805	+	0.993953i	$0.535023\pi$
$608$		−	4.78543i		−	0.194075i
$609$	12.9384	−	33.0190i	0.524290	−	1.33800i
$610$	−28.1658			−1.14040
$611$	13.2934	−	23.0249i	0.537794	−	0.931487i
$612$	−1.63346	+	2.23073i	−0.0660289	+	0.0901719i
$613$	−41.1230	+	23.7424i	−1.66094	+	0.958945i	−0.688675	+	0.725070i	$0.741807\pi$
$613$	−41.1230	+	23.7424i	−1.66094	+	0.958945i	−0.972267	+	0.233875i	$0.924859\pi$
$614$	26.1600	+	15.1035i	1.05573	+	0.609526i
$615$	−22.2538	−	14.5108i	−0.897359	−	0.585134i
$616$	−5.71935	−	6.65500i	−0.230439	−	0.268137i
$617$			38.1302i			1.53506i	0.641011	+	0.767532i	$0.278515\pi$
$617$			38.1302i			1.53506i	−0.641011	+	0.767532i	$0.721485\pi$
$618$	−7.75549	−	15.2914i	−0.311972	−	0.615111i
$619$	−23.0035	−	39.8432i	−0.924588	−	1.60143i	−0.792222	−	0.610233i	$-0.791076\pi$
$619$	−23.0035	−	39.8432i	−0.924588	−	1.60143i	−0.132366	−	0.991201i	$-0.542257\pi$
$620$	−8.19182	+	4.72955i	−0.328991	+	0.189943i
$621$	−22.9509	−	18.7988i	−0.920987	−	0.754369i
$622$		−	0.915784i		−	0.0367196i
$623$	16.9906	−	15.1430i	0.680714	−	0.606691i
$624$	6.73300	+	4.39033i	0.269536	+	0.175754i
$625$	−5.26807	+	9.12457i	−0.210723	+	0.364983i
$626$	−2.87594	−	4.98127i	−0.114946	−	0.199092i
$627$	−24.7374	+	11.9905i	−0.987916	+	0.478853i
$628$	6.04984	−	10.4786i	0.241415	−	0.418143i
$629$	2.38536			0.0951107
$630$	2.84055	+	29.5242i	0.113170	+	1.17627i
$631$	30.5055			1.21441			0.607203	−	0.794547i	$-0.292292\pi$
$631$	30.5055			1.21441			0.607203	+	0.794547i	$0.292292\pi$
$632$	14.9095	+	8.60802i	0.593069	+	0.342409i
$633$	−1.67228	+	30.8097i	−0.0664670	+	1.22458i
$634$	9.09364	−	5.25022i	0.361155	−	0.208513i
$635$	9.62002	−	16.6624i	0.381759	−	0.661226i
$636$	−5.52958	−	3.60562i	−0.219262	−	0.142972i
$637$	19.3599	−	26.0857i	0.767067	−	1.03355i
$638$	−12.4304	−	22.4557i	−0.492123	−	0.889028i
$639$	3.73345	−	34.2909i	0.147693	−	1.35653i
$640$	−3.23623	+	1.86844i	−0.127923	+	0.0738564i
$641$	10.5012	−	6.06289i	0.414774	−	0.239470i	−0.278065	−	0.960562i	$-0.589693\pi$
$641$	10.5012	−	6.06289i	0.414774	−	0.239470i	0.692839	+	0.721092i	$0.256360\pi$
$642$	8.80109	+	17.3530i	0.347351	+	0.684869i
$643$	11.5883			0.456999			0.228499	−	0.973544i	$-0.426618\pi$
$643$	11.5883			0.456999			0.228499	+	0.973544i	$0.426618\pi$
$644$	−14.3425	−	4.74078i	−0.565175	−	0.186813i
$645$	7.76630	−	11.9104i	0.305798	−	0.468971i
$646$	3.81945	+	2.20516i	0.150274	+	0.0867609i
$647$	−17.3213	+	10.0004i	−0.680969	+	0.393158i	−0.800220	−	0.599707i	$-0.795284\pi$
$647$	−17.3213	+	10.0004i	−0.680969	+	0.393158i	0.119251	+	0.992864i	$0.461951\pi$
$648$	−8.78913	−	1.93681i	−0.345270	−	0.0760850i
$649$	−0.528749	+	29.3178i	−0.0207552	+	1.15083i
$650$			41.6002i			1.63170i
$651$	−11.4693	+	1.73506i	−0.449518	+	0.0680025i
$652$	−1.54083			−0.0603437
$653$	−18.1507	−	10.4793i	−0.710291	−	0.410087i	0.100878	−	0.994899i	$-0.467835\pi$
$653$	−18.1507	−	10.4793i	−0.710291	−	0.410087i	−0.811169	+	0.584812i	$0.801168\pi$
$654$	0.429232	−	7.90809i	0.0167843	−	0.309231i
$655$	−51.2151	+	29.5691i	−2.00114	+	1.15536i
$656$	2.05230	−	3.55469i	0.0801288	−	0.138787i
$657$	−29.6525	+	13.0699i	−1.15685	+	0.509904i
$658$	3.07618	+	14.8422i	0.119922	+	0.578611i
$659$	8.15565			0.317699			0.158850	−	0.987303i	$-0.449222\pi$
$659$	8.15565			0.317699			0.158850	+	0.987303i	$0.449222\pi$
$660$	17.7673	+	12.0475i	0.691591	+	0.468948i
$661$	−17.6023	−	30.4881i	−0.684650	−	1.18585i	−0.973547	−	0.228489i	$-0.926622\pi$
$661$	−17.6023	−	30.4881i	−0.684650	−	1.18585i	0.288896	−	0.957360i	$-0.406712\pi$
$662$	−7.54164	−	13.0625i	−0.293114	−	0.507689i
$663$	−6.60672	+	3.35079i	−0.256584	+	0.130134i
$664$	12.6784			0.492016
$665$	46.3282	−	9.60189i	1.79653	−	0.372345i
$666$	3.13173	+	7.10517i	0.121352	+	0.275320i
$667$	−38.2644	−	22.0919i	−1.48160	−	0.855404i
$668$	5.11035	+	8.85139i	0.197726	+	0.342471i
$669$	−15.7552	−	0.855152i	−0.609129	−	0.0330621i
$670$	−2.52676	−	1.45883i	−0.0976173	−	0.0563594i
$671$	−21.8710	+	12.1067i	−0.844321	+	0.467375i
$672$	−4.53102	+	0.685447i	−0.174788	+	0.0264417i
$673$			20.2008i			0.778685i	0.921093	+	0.389342i	$0.127298\pi$
$673$			20.2008i			0.778685i	−0.921093	+	0.389342i	$0.872702\pi$
$674$	−12.8492	−	7.41850i	−0.494933	−	0.285750i
$675$	−16.4491	−	43.5784i	−0.633125	−	1.67733i
$676$	4.26804	+	7.39246i	0.164155	+	0.284325i
$677$	−0.814387	+	1.41056i	−0.0312995	+	0.0542122i	−0.881251	−	0.472649i	$-0.843298\pi$
$677$	−0.814387	+	1.41056i	−0.0312995	+	0.0542122i	0.849951	+	0.526861i	$0.176631\pi$
$678$	−10.9137	−	7.11640i	−0.419138	−	0.273304i
$679$	−10.1039	+	30.5679i	−0.387752	+	1.17309i
$680$		−	3.44396i		−	0.132070i
$681$	19.6442	+	38.7322i	0.752766	+	1.48422i
$682$	−4.32809	+	7.19369i	−0.165731	+	0.275461i
$683$	−26.5384	+	15.3220i	−1.01546	+	0.586278i	−0.912787	−	0.408436i	$-0.866074\pi$
$683$	−26.5384	+	15.3220i	−1.01546	+	0.586278i	−0.102677	+	0.994715i	$0.532741\pi$
$684$	−1.55387	+	14.2719i	−0.0594138	+	0.545701i
$685$	48.2984			1.84539
$686$	1.65526	+	18.4461i	0.0631982	+	0.704277i
$687$	−21.8584	+	33.5220i	−0.833950	+	1.27894i
$688$	1.90249	+	1.09840i	0.0725318	+	0.0418763i
$689$	−8.84341	−	15.3172i	−0.336907	−	0.583540i
$690$	36.8997	+	2.00283i	1.40475	+	0.0762464i
$691$	−0.398760	+	0.690673i	−0.0151696	+	0.0262744i	−0.873511	−	0.486805i	$-0.838162\pi$
$691$	−0.398760	+	0.690673i	−0.0151696	+	0.0262744i	0.858341	+	0.513080i	$0.171495\pi$
$692$	6.99522			0.265918
$693$	14.8963	+	21.7048i	0.565865	+	0.824498i
$694$	−1.69957			−0.0645148
$695$	−15.1129	+	26.1764i	−0.573266	+	0.992926i
$696$	−13.3842	−	0.726463i	−0.507327	−	0.0275365i
$697$	1.89143	+	3.27605i	0.0716430	+	0.124089i
$698$	−17.4664	−	10.0842i	−0.661112	−	0.381693i
$699$	−22.0227	+	33.7740i	−0.832976	+	1.27745i
$700$	−15.7802	−	17.7055i	−0.596435	−	0.669207i
$701$	−31.8559			−1.20318			−0.601591	−	0.798804i	$-0.705466\pi$
$701$	−31.8559			−1.20318			−0.601591	+	0.798804i	$0.705466\pi$
$702$	−18.6547	−	15.2799i	−0.704078	−	0.576702i
$703$	10.7265	−	6.19293i	0.404556	−	0.233571i
$704$	−1.70984	+	2.84191i	−0.0644419	+	0.107109i
$705$	−16.7728	−	33.0708i	−0.631702	−	1.24552i
$706$		−	11.4189i		−	0.429755i
$707$	3.42962	−	0.710817i	0.128984	−	0.0267330i
$708$	12.8272	+	8.36412i	0.482075	+	0.314343i
$709$	−15.7500	+	27.2797i	−0.591502	+	1.02451i	0.402528	+	0.915408i	$0.368132\pi$
$709$	−15.7500	+	27.2797i	−0.591502	+	1.02451i	−0.994030	+	0.109104i	$0.965202\pi$
$710$	21.4830	+	37.2096i	0.806241	+	1.39645i
$711$	−41.6707	−	30.5136i	−1.56277	−	1.14435i
$712$	−7.44976	−	4.30112i	−0.279192	−	0.161191i
$713$			14.4522i			0.541240i
$714$	1.54084	−	3.93226i	0.0576647	−	0.147161i
$715$	27.8551	+	50.3207i	1.04172	+	1.88189i
$716$	−20.0703	−	11.5876i	−0.750062	−	0.433049i
$717$	−5.10676	−	0.277183i	−0.190715	−	0.0103516i
$718$	4.22498	+	7.31788i	0.157675	+	0.273101i
$719$	6.04825	+	3.49196i	0.225562	+	0.130228i	0.608523	−	0.793536i	$-0.291762\pi$
$719$	6.04825	+	3.49196i	0.225562	+	0.130228i	−0.382961	+	0.923764i	$0.625096\pi$
$720$	10.2583	−	4.52155i	0.382306	−	0.168508i
$721$	17.4259	+	19.5520i	0.648973	+	0.728155i
$722$	3.90031			0.145154
$723$	−5.67959	+	2.88057i	−0.211226	+	0.107130i
$724$	3.17071	+	5.49183i	0.117839	+	0.204102i
$725$	−34.6859	−	60.0778i	−1.28820	−	2.23123i
$726$	18.9749	+	1.71793i	0.704226	+	0.0637584i
$727$	−33.1623			−1.22992			−0.614960	−	0.788558i	$-0.710828\pi$
$727$	−33.1623			−1.22992			−0.614960	+	0.788558i	$0.710828\pi$
$728$	−11.6578	−	3.85336i	−0.432067	−	0.142815i
$729$	25.5836	+	8.63020i	0.947540	+	0.319637i
$730$	20.1823	−	34.9568i	0.746980	−	1.29381i
$731$	−1.75336	+	1.01231i	−0.0648505	+	0.0374415i
$732$	−0.707549	+	13.0357i	−0.0261518	+	0.481815i
$733$	21.5001	+	12.4131i	0.794123	+	0.458487i	0.841412	−	0.540394i	$-0.181725\pi$
$733$	21.5001	+	12.4131i	0.794123	+	0.458487i	−0.0472893	+	0.998881i	$0.515058\pi$
$734$	−0.312061			−0.0115184
$735$	−15.7273	−	42.4899i	−0.580110	−	1.56726i
$736$			5.70943i			0.210453i
$737$	−2.58911	−	0.0466948i	−0.0953712	−	0.00172003i
$738$	−7.27496	+	9.93501i	−0.267795	+	0.365713i
$739$	1.10754	−	0.639441i	0.0407417	−	0.0235222i	−0.479491	−	0.877547i	$-0.659179\pi$
$739$	1.10754	−	0.639441i	0.0407417	−	0.0235222i	0.520233	+	0.854025i	$0.325845\pi$
$740$	−8.37615	−	4.83597i	−0.307913	−	0.177774i
$741$	−21.0096	+	32.2203i	−0.771807	+	1.18364i
$742$	9.57414	+	3.16463i	0.351478	+	0.116177i
$743$	0.935605			0.0343240			0.0171620	−	0.999853i	$-0.494537\pi$
$743$	0.935605			0.0343240			0.0171620	+	0.999853i	$0.494537\pi$
$744$	1.98315	+	3.91016i	0.0727059	+	0.143353i
$745$	42.7225	−	24.6658i	1.56523	−	0.903686i
$746$	−29.1559	+	16.8331i	−1.06747	+	0.616305i
$747$	−37.8117	−	4.11678i	−1.38346	−	0.150625i
$748$	−1.48034	−	2.67427i	−0.0541267	−	0.0977808i
$749$	−19.7752	−	22.1880i	−0.722571	−	0.810733i
$750$	21.4927	+	14.0146i	0.784803	+	0.511740i
$751$	−3.90274	+	6.75974i	−0.142413	+	0.246666i	−0.928405	−	0.371570i	$-0.878819\pi$
$751$	−3.90274	+	6.75974i	−0.142413	+	0.246666i	0.785992	+	0.618237i	$0.212153\pi$
$752$	4.96151	−	2.86453i	0.180928	−	0.104459i
$753$	2.54223	−	46.8376i	0.0926441	−	1.70686i
$754$	−31.1017	−	17.9566i	−1.13266	−	0.653941i
$755$	44.5013			1.61957
$756$	13.7358	−	0.572996i	0.499566	−	0.0208397i
$757$	48.4080			1.75942			0.879710	−	0.475510i	$-0.157737\pi$
$757$	48.4080			1.75942			0.879710	+	0.475510i	$0.157737\pi$
$758$	4.48621	−	7.77035i	0.162947	−	0.282232i
$759$	29.5139	−	14.3057i	1.07129	−	0.519264i
$760$	−8.94127	−	15.4867i	−0.324334	−	0.561763i
$761$	25.7356	−	44.5754i	0.932915	−	1.61586i	0.154604	−	0.987977i	$-0.450590\pi$
$761$	25.7356	−	44.5754i	0.932915	−	1.61586i	0.778311	−	0.627879i	$-0.216077\pi$
$762$	−7.47004	−	4.87092i	−0.270611	−	0.176455i
$763$	2.45515	+	11.8458i	0.0888822	+	0.428848i
$764$			7.03083i			0.254366i
$765$	−1.11828	+	10.2712i	−0.0404317	+	0.371355i
$766$	−6.48945	+	3.74669i	−0.234473	+	0.135373i
$767$	20.5144	+	35.5320i	0.740733	+	1.28299i
$768$	0.783456	+	1.54473i	0.0282705	+	0.0557407i
$769$			2.65444i			0.0957217i	0.998854	+	0.0478609i	$0.0152404\pi$
$769$			2.65444i			0.0957217i	−0.998854	+	0.0478609i	$0.984760\pi$
$770$	−30.9436	−	10.8508i	−1.11513	−	0.391037i
$771$	−21.0283	−	13.7117i	−0.757315	−	0.493816i
$772$	7.54828	+	4.35800i	0.271668	+	0.156848i
$773$	−19.4199	+	11.2121i	−0.698487	+	0.403272i	−0.806784	−	0.590847i	$-0.798794\pi$
$773$	−19.4199	+	11.2121i	−0.698487	+	0.403272i	0.108297	+	0.994119i	$0.465460\pi$
$774$	−5.31728	−	3.89361i	−0.191126	−	0.139953i
$775$	−11.3455	+	19.6510i	−0.407543	+	0.705885i
$776$	12.1684			0.436819
$777$	−7.40012	−	9.26917i	−0.265478	−	0.332530i
$778$		−	11.5171i		−	0.412906i
$779$	17.0107	+	9.82112i	0.609471	+	0.351878i
$780$	29.9926	+	1.62792i	1.07391	+	0.0582890i
$781$	32.6758	+	19.6594i	1.16923	+	0.703469i
$782$	−4.55694	−	2.63095i	−0.162956	−	0.0940826i
$783$	39.6809	+	6.51256i	1.41808	+	0.232740i
$784$	6.42339	−	2.78211i	0.229407	−	0.0993609i
$785$		−	45.2150i		−	1.61379i
$786$	12.3986	+	24.4463i	0.442245	+	0.871970i
$787$	15.3260	−	8.84845i	0.546312	−	0.315413i	−0.201321	−	0.979525i	$-0.564524\pi$
$787$	15.3260	−	8.84845i	0.546312	−	0.315413i	0.747633	+	0.664112i	$0.231190\pi$
$788$	0.278382	+	0.482171i	0.00991694	+	0.0171766i
$789$	−11.3615	−	22.4013i	−0.404479	−	0.797508i
$790$	64.3342			2.28891
$791$	18.8964	+	6.24602i	0.671880	+	0.222083i
$792$	6.02217	−	7.92045i	0.213988	−	0.281441i
$793$	−17.4891	+	30.2920i	−0.621056	+	1.07570i
$794$	−10.4828	−	18.1567i	−0.372020	−	0.644357i
$795$	−24.6318	−	1.33696i	−0.873601	−	0.0474170i
$796$	3.23869	−	5.60958i	0.114792	−	0.198826i
$797$			28.8638i			1.02241i	0.859459	+	0.511205i	$0.170801\pi$
$797$			28.8638i			1.02241i	−0.859459	+	0.511205i	$0.829199\pi$
$798$	−3.28016	−	21.6829i	−0.116116	−	0.767565i
$799$			5.27999i			0.186793i
$800$	−4.48211	+	7.76324i	−0.158467	+	0.274472i
$801$	20.8214	+	15.2466i	0.735687	+	0.538711i
$802$	−20.3964	+	11.7758i	−0.720220	+	0.415819i
$803$	0.646005	−	35.8194i	0.0227970	−	1.26404i
$804$	−0.738651	+	1.13279i	−0.0260502	+	0.0399505i
$805$	−55.2736	+	11.4559i	−1.94814	+	0.403767i
$806$			11.7469i			0.413768i
$807$	11.8896	−	6.03015i	0.418533	−	0.212271i
$808$	−0.661912	−	1.14646i	−0.0232860	−	0.0403325i
$809$	4.95952	+	8.59014i	0.174367	+	0.302013i	0.939942	−	0.341334i	$-0.110879\pi$
$809$	4.95952	+	8.59014i	0.174367	+	0.302013i	−0.765575	+	0.643347i	$0.777545\pi$
$810$	−32.0624	+	10.1540i	−1.12656	+	0.356774i
$811$		−	47.8705i		−	1.68096i	−0.541841	−	0.840481i	$-0.682273\pi$
$811$		−	47.8705i		−	1.68096i	0.541841	−	0.840481i	$-0.317727\pi$
$812$	20.0487	−	4.15526i	0.703573	−	0.145821i
$813$	−4.80692	−	3.13441i	−0.168586	−	0.109928i
$814$	−8.58284	−	0.154792i	−0.300828	−	0.00542546i
$815$	−4.98649	+	2.87895i	−0.174669	+	0.100845i
$816$	−1.59394	−	0.0865151i	−0.0557990	−	0.00302864i
$817$	−5.25633	+	9.10424i	−0.183896	+	0.318517i
$818$		−	11.8764i		−	0.415248i
$819$	33.5167	+	15.2776i	1.17117	+	0.533841i
$820$		−	15.3384i		−	0.535639i
$821$	−14.3341	+	24.8274i	−0.500264	+	0.866482i	0.499736	+	0.866178i	$0.333430\pi$
$821$	−14.3341	+	24.8274i	−0.500264	+	0.866482i	−1.00000		0.000304753i	$0.999903\pi$
$822$	1.21330	−	22.3535i	0.0423186	−	0.779670i
$823$	20.0175	+	34.6713i	0.697766	+	1.20857i	0.969239	+	0.246120i	$0.0791556\pi$
$823$	20.0175	+	34.6713i	0.697766	+	1.20857i	−0.271474	+	0.962446i	$0.587511\pi$
$824$	4.94954	−	8.57285i	0.172425	−	0.298649i
$825$	51.3612	+	3.71770i	1.78817	+	0.129434i
$826$	−22.2095	−	7.34113i	−0.772768	−	0.255431i
$827$	−5.40955			−0.188109			−0.0940543	−	0.995567i	$-0.529983\pi$
$827$	−5.40955			−0.188109			−0.0940543	+	0.995567i	$0.529983\pi$
$828$	1.85391	−	17.0277i	0.0644277	−	0.591753i
$829$	4.25136	+	7.36358i	0.147656	+	0.255748i	0.930361	−	0.366646i	$-0.119494\pi$
$829$	4.25136	+	7.36358i	0.147656	+	0.255748i	−0.782705	+	0.622393i	$0.786160\pi$
$830$	41.0301	−	23.6887i	1.42418	−	0.822248i
$831$	13.8390	−	7.01883i	0.480068	−	0.243481i
$832$			4.64070i			0.160887i
$833$	−0.739429	+	6.40879i	−0.0256197	+	0.222051i
$834$	11.7353	+	7.65216i	0.406361	+	0.264973i
$835$	33.0765	+	19.0967i	1.14466	+	0.660870i
$836$	−13.5998	−	8.18230i	−0.470357	−	0.282991i
$837$	−4.64484	−	12.3055i	−0.160549	−	0.425341i
$838$	18.6690	+	10.7785i	0.644910	+	0.372339i
$839$		−	6.66926i		−	0.230248i	−0.993351	−	0.115124i	$-0.963273\pi$
$839$		−	6.66926i		−	0.230248i	0.993351	−	0.115124i	$-0.0367266\pi$
$840$	−13.3827	+	10.6842i	−0.461747	+	0.368640i
$841$	30.8883			1.06511
$842$	−6.08439	+	10.5385i	−0.209682	+	0.363180i
$843$	39.6881	+	2.15418i	1.36693	+	0.0741937i
$844$	−15.4275	+	8.90708i	−0.531037	+	0.306594i
$845$	27.6247	+	15.9491i	0.950317	+	0.548666i
$846$	−15.7272	+	6.93206i	−0.540714	+	0.238329i
$847$	−28.6921	+	4.87494i	−0.985871	+	0.167505i
$848$		−	3.81124i		−	0.130879i
$849$	−40.0751	+	20.3252i	−1.37537	+	0.697561i
$850$	−4.13078	−	7.15472i	−0.141685	−	0.245405i
$851$	−12.7976	+	7.38871i	−0.438697	+	0.253282i
$852$	17.7611	−	9.00804i	0.608484	−	0.308610i
$853$			14.2558i			0.488109i	0.969761	+	0.244055i	$0.0784776\pi$
$853$			14.2558i			0.488109i	−0.969761	+	0.244055i	$0.921522\pi$
$854$	−4.04708	−	19.5268i	−0.138488	−	0.668192i
$855$	21.6375	+	49.0905i	0.739988	+	1.67886i
$856$	−5.61684	+	9.72865i	−0.191980	+	0.332518i
$857$	−18.2335	−	31.5813i	−0.622844	−	1.07880i	−0.988954	−	0.148225i	$-0.952644\pi$
$857$	−18.2335	−	31.5813i	−0.622844	−	1.07880i	0.366110	−	0.930572i	$-0.380689\pi$
$858$	23.9892	−	11.6278i	0.818979	−	0.396968i
$859$	−10.1170	+	17.5232i	−0.345189	+	0.597884i	−0.985388	−	0.170325i	$-0.945518\pi$
$859$	−10.1170	+	17.5232i	−0.345189	+	0.597884i	0.640199	+	0.768209i	$0.278852\pi$
$860$	8.20919			0.279931
$861$	6.86246	−	17.5131i	0.233872	−	0.596845i
$862$	−13.5244			−0.460644
$863$	−6.55825	−	3.78641i	−0.223245	−	0.128891i	0.384207	−	0.923247i	$-0.374475\pi$
$863$	−6.55825	−	3.78641i	−0.223245	−	0.128891i	−0.607452	+	0.794356i	$0.707808\pi$
$864$	−1.83497	−	4.86137i	−0.0624270	−	0.165387i
$865$	22.6381	−	13.0701i	0.769719	−	0.444397i
$866$	17.1658	−	29.7321i	0.583318	−	1.01034i
$867$	−15.2793	+	23.4323i	−0.518912	+	0.795802i
$868$	−4.45596	−	4.99964i	−0.151245	−	0.169699i
$869$	49.9561	−	27.6533i	1.69464	−	0.938073i
$870$	−44.6717	+	22.6565i	−1.51451	+	0.768129i
$871$	−3.13790	+	1.81167i	−0.106324	+	0.0613860i
$872$	3.95986	−	2.28623i	0.134098	−	0.0774215i
$873$	−36.2907	−	3.95118i	−1.22825	−	0.133727i
$874$	−27.3221			−0.924183
$875$	−37.2134	−	12.3005i	−1.25804	−	0.415833i
$876$	−15.6717	−	10.2189i	−0.529499	−	0.345266i
$877$	33.6074	+	19.4033i	1.13484	+	0.655202i	0.945148	−	0.326641i	$-0.105917\pi$
$877$	33.6074	+	19.4033i	1.13484	+	0.655202i	0.189694	+	0.981843i	$0.439250\pi$
$878$	−2.95877	+	1.70824i	−0.0998536	+	0.0576505i
$879$	−9.62824	−	0.522598i	−0.324752	−	0.0176268i
$880$	−0.223487	+	12.3918i	−0.00753374	+	0.417727i
$881$		−	38.0866i		−	1.28317i	−0.767052	−	0.641584i	$-0.778277\pi$
$881$		−	38.0866i		−	1.28317i	0.767052	−	0.641584i	$-0.221723\pi$
$882$	−20.0603	+	6.21155i	−0.675466	+	0.209154i
$883$	17.6201			0.592964			0.296482	−	0.955038i	$-0.404187\pi$
$883$	17.6201			0.592964			0.296482	+	0.955038i	$0.404187\pi$
$884$	−3.70394	−	2.13847i	−0.124577	−	0.0719245i
$885$	57.1395	+	3.10140i	1.92072	+	0.104252i
$886$	−21.5391	+	12.4356i	−0.723622	+	0.417783i
$887$	−13.6872	+	23.7070i	−0.459572	+	0.796002i	−0.998938	−	0.0460690i	$-0.985331\pi$
$887$	−13.6872	+	23.7070i	−0.459572	+	0.796002i	0.539366	+	0.842071i	$0.318664\pi$
$888$	−2.44861	+	3.75518i	−0.0821699	+	0.126015i
$889$	12.9339	+	4.27518i	0.433790	+	0.143385i
$890$	−32.1455			−1.07752
$891$	−20.5322	+	21.6663i	−0.687855	+	0.725848i
$892$	−4.55482	−	7.88917i	−0.152507	−	0.264149i
$893$	13.7080	+	23.7430i	0.458721	+	0.794528i
$894$	−10.3427	−	20.3925i	−0.345910	−	0.682027i
$895$	−86.6027			−2.89481
$896$	−1.76035	−	1.97514i	−0.0588092	−	0.0659846i
$897$	25.0663	−	38.4416i	0.836939	−	1.28353i
$898$	−10.6050	−	6.12283i	−0.353895	−	0.204321i
$899$	−9.79450	−	16.9646i	−0.326665	−	0.565800i
$900$	15.8881	−	21.6975i	0.529604	−	0.723251i
$901$	3.04191	+	1.75625i	0.101341	+	0.0585092i
$902$	−6.59301	−	11.9104i	−0.219523	−	0.396572i
$903$	9.37313	+	3.67284i	0.311918	+	0.122224i
$904$		−	7.52223i		−	0.250186i
$905$	20.5223	+	11.8485i	0.682184	+	0.393859i
$906$	1.11791	−	20.5961i	0.0371401	−	0.684261i
$907$	−6.46073	−	11.1903i	−0.214525	−	0.371568i	0.738600	−	0.674143i	$-0.235487\pi$
$907$	−6.46073	−	11.1903i	−0.214525	−	0.371568i	−0.953126	+	0.302575i	$0.902154\pi$
$908$	−12.5369	+	21.7145i	−0.416050	+	0.720620i
$909$	1.60180	+	3.63412i	0.0531284	+	0.120536i
$910$	−44.9270	+	9.31149i	−1.48932	+	0.308673i
$911$			2.02350i			0.0670416i	0.999438	+	0.0335208i	$0.0106720\pi$
$911$			2.02350i			0.0670416i	−0.999438	+	0.0335208i	$0.989328\pi$
$912$	−7.39220	+	3.74917i	−0.244780	+	0.124147i
$913$	21.6779	−	36.0308i	0.717435	−	1.19245i
$914$	26.7154	−	15.4241i	0.883667	−	0.510185i
$915$	22.0667	+	43.5086i	0.729502	+	1.43835i
$916$	−23.1049			−0.763408
$917$	−27.8586	−	31.2576i	−0.919972	−	1.03222i
$918$	4.72563	+	0.775587i	0.155969	+	0.0255982i
$919$	23.8097	+	13.7465i	0.785410	+	0.453457i	0.838344	−	0.545141i	$-0.183524\pi$
$919$	23.8097	+	13.7465i	0.785410	+	0.453457i	−0.0529342	+	0.998598i	$0.516857\pi$
$920$	10.6677	+	18.4770i	0.351704	+	0.609170i
$921$	2.83563	−	52.2430i	0.0934371	−	1.72147i
$922$	1.70165	−	2.94734i	0.0560408	−	0.0970655i
$923$	53.3580			1.75630
$924$	−5.79933	+	14.0488i	−0.190784	+	0.462170i
$925$	−23.2016			−0.762864
$926$	−7.91328	+	13.7062i	−0.260046	+	0.450414i
$927$	−17.5451	+	23.9603i	−0.576256	+	0.786960i
$928$	−3.86938	−	6.70196i	−0.127018	−	0.220002i
$929$	16.7462	+	9.66845i	0.549426	+	0.317212i	0.748891	−	0.662694i	$-0.230587\pi$
$929$	16.7462	+	9.66845i	0.549426	+	0.317212i	−0.199464	+	0.979905i	$0.563920\pi$
$930$	13.7238	+	8.94877i	0.450022	+	0.293442i
$931$	13.3136	+	30.7386i	0.436334	+	1.00742i
$932$	−23.2786			−0.762517
$933$	−1.41464	+	0.717476i	−0.0463133	+	0.0234891i
$934$	−18.9467	+	10.9389i	−0.619956	+	0.357932i
$935$	−9.78742	−	5.88860i	−0.320083	−	0.192578i
$936$	1.50688	−	13.8403i	0.0492538	−	0.452384i
$937$			6.07745i			0.198542i	0.995060	+	0.0992708i	$0.0316510\pi$
$937$			6.07745i			0.198542i	−0.995060	+	0.0992708i	$0.968349\pi$
$938$	0.648309	−	1.96136i	0.0211680	−	0.0640408i
$939$	−5.44156	+	8.34516i	−0.177579	+	0.272334i
$940$	10.7044	−	18.5406i	0.349139	−	0.604726i
$941$	−1.16233	−	2.01322i	−0.0378910	−	0.0656292i	0.846458	−	0.532456i	$-0.178731\pi$
$941$	−1.16233	−	2.01322i	−0.0378910	−	0.0656292i	−0.884349	+	0.466826i	$0.845397\pi$
$942$	−20.9265	−	1.13584i	−0.681821	−	0.0370076i
$943$	−20.2952	−	11.7175i	−0.660904	−	0.381573i
$944$			8.84110i			0.287753i
$945$	43.3815	−	27.5188i	1.41120	−	0.895186i
$946$	6.37452	−	3.52862i	0.207253	−	0.114725i
$947$	7.66708	+	4.42659i	0.249147	+	0.143845i	0.619374	−	0.785096i	$-0.287387\pi$
$947$	7.66708	+	4.42659i	0.249147	+	0.143845i	−0.370227	+	0.928941i	$0.620720\pi$
$948$	1.61613	−	29.7752i	0.0524894	−	0.967055i
$949$	−25.0637	−	43.4116i	−0.813603	−	1.40920i
$950$	−37.1504	−	21.4488i	−1.20532	−	0.695891i
$951$	−15.2346	−	9.93393i	−0.494017	−	0.322130i
$952$	2.38762	−	0.494854i	0.0773833	−	0.0160383i
$953$	−15.5373			−0.503303			−0.251651	−	0.967818i	$-0.580974\pi$
$953$	−15.5373			−0.503303			−0.251651	+	0.967818i	$0.580974\pi$
$954$	−1.23755	+	11.3666i	−0.0400670	+	0.368006i
$955$	13.1367	+	22.7534i	0.425092	+	0.736281i
$956$	−1.47636	−	2.55714i	−0.0477490	−	0.0827038i
$957$	−24.9493	+	36.7946i	−0.806498	+	1.18940i
$958$	24.5435			0.792965
$959$	6.93988	+	33.4843i	0.224101	+	1.08126i
$960$	5.42167	+	3.53527i	0.174984	+	0.114100i
$961$	12.2963	−	21.2978i	0.396655	−	0.687026i
$962$	−10.4021	+	6.00563i	−0.335376	+	0.193629i
$963$	19.9105	−	27.1906i	0.641607	−	0.876206i
$964$	−3.18416	−	1.83837i	−0.102555	−	0.0592100i
$965$	32.5706			1.04848
$966$	3.91352	+	25.8696i	0.125915	+	0.832340i
$967$		−	50.7815i		−	1.63302i	−0.577329	−	0.816512i	$-0.695905\pi$
$967$		−	50.7815i		−	1.63302i	0.577329	−	0.816512i	$-0.304095\pi$
$968$	5.15292	+	9.71841i	0.165621	+	0.312361i
$969$	0.414012	−	7.62767i	0.0133000	−	0.245036i
$970$	39.3796	−	22.7358i	1.26440	−	0.730004i
$971$	31.0032	+	17.8997i	0.994941	+	0.574429i	0.906748	−	0.421674i	$-0.138557\pi$
$971$	31.0032	+	17.8997i	0.994941	+	0.574429i	0.0881935	+	0.996103i	$0.471891\pi$
$972$	3.89404	+	15.0943i	0.124901	+	0.484148i
$973$	−20.3190	−	6.71625i	−0.651399	−	0.215313i
$974$	−36.1783			−1.15923
$975$	64.2612	−	32.5919i	2.05801	−	1.04378i
$976$	−6.52747	+	3.76863i	−0.208939	+	0.120631i
$977$	15.2247	−	8.79000i	0.487082	−	0.281217i	−0.236281	−	0.971685i	$-0.575929\pi$
$977$	15.2247	−	8.79000i	0.487082	−	0.281217i	0.723363	+	0.690468i	$0.242595\pi$
$978$	1.20718	+	2.38018i	0.0386012	+	0.0761096i
$979$	−24.9613	+	13.8174i	−0.797766	+	0.441604i
$980$	15.5893	−	21.0052i	0.497983	−	0.670987i
$981$	−12.5522	+	5.53259i	−0.400760	+	0.176642i
$982$	19.8330	−	34.3518i	0.632896	−	1.09621i
$983$	−31.5232	+	18.1999i	−1.00543	+	0.580487i	−0.909851	−	0.414935i	$-0.863804\pi$
$983$	−31.5232	+	18.1999i	−1.00543	+	0.580487i	−0.0955818	+	0.995422i	$0.530471\pi$
$984$	−7.09892	−	0.385313i	−0.226305	−	0.0122833i
$985$	1.80181	+	1.04028i	0.0574105	+	0.0331460i
$986$	7.13215			0.227134
$987$	20.5172	−	16.3801i	0.653071	−	0.521385i
$988$	−22.2077			−0.706522
$989$	6.27127	−	10.8622i	0.199415	−	0.345396i
$990$	4.69025	−	36.8844i	0.149066	−	1.17226i
$991$	4.46111	+	7.72687i	0.141712	+	0.245452i	0.928141	−	0.372228i	$-0.121406\pi$
$991$	4.46111	+	7.72687i	0.141712	+	0.245452i	−0.786429	+	0.617680i	$0.788073\pi$
$992$	−1.26564	+	2.19216i	−0.0401842	+	0.0696011i
$993$	−14.2695	+	21.8837i	−0.452830	+	0.694459i
$994$	−22.7098	+	20.2402i	−0.720310	+	0.641981i
$995$		−	24.2052i		−	0.767355i
$996$	−9.93294	−	19.5847i	−0.314737	−	0.620565i
$997$	−0.0417701	+	0.0241160i	−0.00132287	+	0.000763761i	−0.500661	−	0.865643i	$-0.666910\pi$
$997$	−0.0417701	+	0.0241160i	−0.00132287	+	0.000763761i	0.499338	+	0.866407i	$0.333576\pi$
$998$	16.0605	+	27.8176i	0.508386	+	0.880550i
$999$	8.52201	−	10.4043i	0.269624	−	0.329176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.f.65.1	yes	24
3.2	odd	2		462.2.n.e.65.9	yes	24
7.4	even	3	inner	462.2.n.f.263.9	yes	24
11.10	odd	2		462.2.n.e.65.1	✓	24
21.11	odd	6		462.2.n.e.263.1	yes	24
33.32	even	2	inner	462.2.n.f.65.9	yes	24
77.32	odd	6		462.2.n.e.263.9	yes	24
231.32	even	6	inner	462.2.n.f.263.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.1	✓	24	11.10	odd	2
462.2.n.e.65.9	yes	24	3.2	odd	2
462.2.n.e.263.1	yes	24	21.11	odd	6
462.2.n.e.263.9	yes	24	77.32	odd	6
462.2.n.f.65.1	yes	24	1.1	even	1	trivial
462.2.n.f.65.9	yes	24	33.32	even	2	inner
462.2.n.f.263.1	yes	24	231.32	even	6	inner
462.2.n.f.263.9	yes	24	7.4	even	3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.72951 - 0.0938734i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.23623 - 1.86844i) q^{5} +(-0.946049 + 1.45086i) q^{6} +(0.830341 - 2.51208i) q^{7} -1.00000 q^{8} +(2.98238 + 0.324709i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.72951 - 0.0938734i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.23623 - 1.86844i) q^{5} +(-0.946049 + 1.45086i) q^{6} +(0.830341 - 2.51208i) q^{7} -1.00000 q^{8} +(2.98238 + 0.324709i) q^{9} +(-3.23623 + 1.86844i) q^{10} +(-1.70984 + 2.84191i) q^{11} +(0.783456 + 1.54473i) q^{12} +4.64070i q^{13} +(-1.76035 - 1.97514i) q^{14} +(5.42167 + 3.53527i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.460807 - 0.798142i) q^{17} +(1.77239 - 2.42046i) q^{18} +(-4.14430 - 2.39271i) q^{19} +3.73687i q^{20} +(-1.67190 + 4.26670i) q^{21} +(1.60625 + 2.90172i) q^{22} +(4.94452 + 2.85472i) q^{23} +(1.72951 + 0.0938734i) q^{24} +(4.48211 + 7.76324i) q^{25} +(4.01896 + 2.32035i) q^{26} +(-5.12755 - 0.841552i) q^{27} +(-2.59069 + 0.536942i) q^{28} -7.73875 q^{29} +(5.77247 - 2.92767i) q^{30} +(1.26564 + 2.19216i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.22395 - 4.75459i) q^{33} -0.921615 q^{34} +(-7.38083 + 6.57821i) q^{35} +(-1.20998 - 2.74517i) q^{36} +(-1.29412 + 2.24149i) q^{37} +(-4.14430 + 2.39271i) q^{38} +(0.435638 - 8.02611i) q^{39} +(3.23623 + 1.86844i) q^{40} -4.10460 q^{41} +(2.85913 + 3.58126i) q^{42} -2.19681i q^{43} +(3.31609 + 0.0598058i) q^{44} +(-9.04495 - 6.62321i) q^{45} +(4.94452 - 2.85472i) q^{46} +(-4.96151 - 2.86453i) q^{47} +(0.946049 - 1.45086i) q^{48} +(-5.62107 - 4.17176i) q^{49} +8.96422 q^{50} +(0.722045 + 1.42365i) q^{51} +(4.01896 - 2.32035i) q^{52} +(-3.30063 + 1.90562i) q^{53} +(-3.29258 + 4.01981i) q^{54} +(10.8433 - 6.00235i) q^{55} +(-0.830341 + 2.51208i) q^{56} +(6.94298 + 4.52725i) q^{57} +(-3.86938 + 6.70196i) q^{58} +(7.65662 - 4.42055i) q^{59} +(0.350793 - 6.46294i) q^{60} +(6.52747 + 3.76863i) q^{61} +2.53129 q^{62} +(3.29208 - 7.22234i) q^{63} +1.00000 q^{64} +(8.67085 - 15.0184i) q^{65} +(-2.50562 - 5.16932i) q^{66} +(0.390387 + 0.676170i) q^{67} +(-0.460807 + 0.798142i) q^{68} +(-8.28358 - 5.40141i) q^{69} +(2.00648 + 9.68109i) q^{70} -11.4978i q^{71} +(-2.98238 - 0.324709i) q^{72} +(-9.35455 + 5.40085i) q^{73} +(1.29412 + 2.24149i) q^{74} +(-7.02307 - 13.8473i) q^{75} +4.78543i q^{76} +(5.71935 + 6.65500i) q^{77} +(-6.73300 - 4.39033i) q^{78} +(-14.9095 - 8.60802i) q^{79} +(3.23623 - 1.86844i) q^{80} +(8.78913 + 1.93681i) q^{81} +(-2.05230 + 3.55469i) q^{82} -12.6784 q^{83} +(4.53102 - 0.685447i) q^{84} +3.44396i q^{85} +(-1.90249 - 1.09840i) q^{86} +(13.3842 + 0.726463i) q^{87} +(1.70984 - 2.84191i) q^{88} +(7.44976 + 4.30112i) q^{89} +(-10.2583 + 4.52155i) q^{90} +(11.6578 + 3.85336i) q^{91} -5.70943i q^{92} +(-1.98315 - 3.91016i) q^{93} +(-4.96151 + 2.86453i) q^{94} +(8.94127 + 15.4867i) q^{95} +(-0.783456 - 1.54473i) q^{96} -12.1684 q^{97} +(-6.42339 + 2.78211i) q^{98} +(-6.02217 + 7.92045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9 + 4 * q^11 + 4 * q^15 - 12 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 - 40 * q^29 + 2 * q^30 - 28 * q^31 + 12 * q^32 + 24 * q^33 - 8 * q^34 + 32 * q^35 + 16 * q^36 - 16 * q^37 + 8 * q^41 + 6 * q^42 + 4 * q^44 - 28 * q^45 - 8 * q^49 + 40 * q^50 + 34 * q^51 - 6 * q^54 + 8 * q^55 - 40 * q^57 - 20 * q^58 - 2 * q^60 - 56 * q^62 + 14 * q^63 + 24 * q^64 + 44 * q^65 - 24 * q^66 - 4 * q^68 - 20 * q^69 + 64 * q^70 + 8 * q^72 + 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 - 144 * q^83 + 6 * q^84 - 8 * q^87 - 4 * q^88 - 56 * q^90 - 32 * q^91 - 22 * q^93 + 44 * q^95 + 64 * q^97 + 8 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more