LMFDB - Embedded newform 1000.2.o.a.349.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(149,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("1000.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (of order $10$, degree $4$, not 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.13
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.135750 - 1.40768i) q^{2} +(-2.54275 + 1.84742i) q^{3} +(-1.96314 + 0.382186i) q^{4} +(2.94576 + 3.32861i) q^{6} -1.17589i q^{7} +(0.804493 + 2.71160i) q^{8} +(2.12559 - 6.54190i) q^{9} +O(q^{10})$	\(q+(-0.135750 - 1.40768i) q^{2} +(-2.54275 + 1.84742i) q^{3} +(-1.96314 + 0.382186i) q^{4} +(2.94576 + 3.32861i) q^{6} -1.17589i q^{7} +(0.804493 + 2.71160i) q^{8} +(2.12559 - 6.54190i) q^{9} +(-3.77756 + 1.22741i) q^{11} +(4.28574 - 4.59855i) q^{12} +(-0.280944 + 0.864656i) q^{13} +(-1.65528 + 0.159626i) q^{14} +(3.70787 - 1.50057i) q^{16} +(-3.27511 + 4.50780i) q^{17} +(-9.49747 - 2.10410i) q^{18} +(-2.64864 + 3.64555i) q^{19} +(2.17235 + 2.98999i) q^{21} +(2.24060 + 5.15099i) q^{22} +(2.07468 - 0.674105i) q^{23} +(-7.05510 - 5.40870i) q^{24} +(1.25530 + 0.278103i) q^{26} +(3.76703 + 11.5937i) q^{27} +(0.449407 + 2.30843i) q^{28} +(-3.65841 - 5.03536i) q^{29} +(-1.16778 - 0.848445i) q^{31} +(-2.61567 - 5.01580i) q^{32} +(7.33789 - 10.0997i) q^{33} +(6.79015 + 3.99838i) q^{34} +(-1.67262 + 13.6551i) q^{36} +(2.16303 - 6.65712i) q^{37} +(5.49133 + 3.23357i) q^{38} +(-0.883011 - 2.71763i) q^{39} +(1.97065 - 6.06503i) q^{41} +(3.91406 - 3.46388i) q^{42} +2.96089 q^{43} +(6.94681 - 3.85330i) q^{44} +(-1.23056 - 2.82899i) q^{46} +(3.12538 + 4.30172i) q^{47} +(-6.65601 + 10.6656i) q^{48} +5.61729 q^{49} -17.5127i q^{51} +(0.221074 - 1.80482i) q^{52} +(10.5708 - 7.68016i) q^{53} +(15.8089 - 6.87664i) q^{54} +(3.18854 - 0.945992i) q^{56} -14.1629i q^{57} +(-6.59157 + 5.83343i) q^{58} +(1.22277 + 0.397301i) q^{59} +(14.7321 - 4.78675i) q^{61} +(-1.03582 + 1.75905i) q^{62} +(-7.69253 - 2.49945i) q^{63} +(-6.70558 + 4.36293i) q^{64} +(-15.2133 - 8.95838i) q^{66} +(-2.45652 - 1.78477i) q^{67} +(4.70669 - 10.1012i) q^{68} +(-4.03005 + 5.54689i) q^{69} +(-1.58201 + 1.14940i) q^{71} +(19.4491 + 0.500848i) q^{72} +(-4.01616 + 1.30493i) q^{73} +(-9.66475 - 2.14116i) q^{74} +(3.80639 - 8.16901i) q^{76} +(1.44329 + 4.44199i) q^{77} +(-3.70569 + 1.61192i) q^{78} +(2.23200 - 1.62164i) q^{79} +(-14.3025 - 10.3914i) q^{81} +(-8.80515 - 1.95072i) q^{82} +(-7.65878 - 5.56443i) q^{83} +(-5.40738 - 5.03954i) q^{84} +(-0.401941 - 4.16800i) q^{86} +(18.6049 + 6.04509i) q^{87} +(-6.36726 - 9.25582i) q^{88} +(0.806910 + 2.48341i) q^{89} +(1.01674 + 0.330358i) q^{91} +(-3.81527 + 2.11628i) q^{92} +4.53682 q^{93} +(5.63118 - 4.98350i) q^{94} +(15.9173 + 7.92171i) q^{96} +(0.171369 + 0.235869i) q^{97} +(-0.762547 - 7.90737i) q^{98} +27.3214i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

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 $

$2$	−0.135750	−	1.40768i	−0.0959897	−	0.995382i
$2$	−0.135750	−	1.40768i	−0.0959897	−	0.995382i
$3$	−2.54275	+	1.84742i	−1.46806	+	1.06661i	−0.486890	+	0.873463i	$0.661869\pi$
$3$	−2.54275	+	1.84742i	−1.46806	+	1.06661i	−0.981170	+	0.193145i	$0.938131\pi$
$4$	−1.96314	+	0.382186i	−0.981572	+	0.191093i
$5$		0			0
$5$		0			0
$6$	2.94576	+	3.32861i	1.20260	+	1.35890i
$7$		−	1.17589i		−	0.444443i	−0.974996	−	0.222222i	$-0.928669\pi$
$7$		−	1.17589i		−	0.444443i	0.974996	−	0.222222i	$-0.0713308\pi$
$8$	0.804493	+	2.71160i	0.284431	+	0.958696i
$9$	2.12559	−	6.54190i	0.708531	−	2.18063i
$10$		0			0
$11$	−3.77756	+	1.22741i	−1.13898	+	0.370077i	−0.816981	−	0.576664i	$-0.804354\pi$
$11$	−3.77756	+	1.22741i	−1.13898	+	0.370077i	−0.321997	+	0.946741i	$0.604354\pi$
$12$	4.28574	−	4.59855i	1.23719	−	1.32749i
$13$	−0.280944	+	0.864656i	−0.0779198	+	0.239812i	−0.982427	−	0.186645i	$-0.940239\pi$
$13$	−0.280944	+	0.864656i	−0.0779198	+	0.239812i	0.904508	+	0.426457i	$0.140239\pi$
$14$	−1.65528	+	0.159626i	−0.442391	+	0.0426620i
$15$		0			0
$16$	3.70787	−	1.50057i	0.926967	−	0.375143i
$17$	−3.27511	+	4.50780i	−0.794331	+	1.09330i	0.199225	+	0.979954i	$0.436158\pi$
$17$	−3.27511	+	4.50780i	−0.794331	+	1.09330i	−0.993555	+	0.113348i	$0.963842\pi$
$18$	−9.49747	−	2.10410i	−2.23858	−	0.495940i
$19$	−2.64864	+	3.64555i	−0.607641	+	0.836346i	−0.996381	−	0.0850017i	$-0.972910\pi$
$19$	−2.64864	+	3.64555i	−0.607641	+	0.836346i	0.388740	+	0.921348i	$0.372910\pi$
$20$		0			0
$21$	2.17235	+	2.98999i	0.474047	+	0.652469i
$22$	2.24060	+	5.15099i	0.477698	+	1.09820i
$23$	2.07468	−	0.674105i	0.432601	−	0.140561i	−0.0846183	−	0.996413i	$-0.526967\pi$
$23$	2.07468	−	0.674105i	0.432601	−	0.140561i	0.517220	+	0.855853i	$0.326967\pi$
$24$	−7.05510	−	5.40870i	−1.44012	−	1.10405i
$25$		0			0
$26$	1.25530	+	0.278103i	0.246184	+	0.0545404i
$27$	3.76703	+	11.5937i	0.724966	+	2.23122i
$28$	0.449407	+	2.30843i	0.0849299	+	0.436253i
$29$	−3.65841	−	5.03536i	−0.679349	−	0.935044i	0.320577	−	0.947223i	$-0.396123\pi$
$29$	−3.65841	−	5.03536i	−0.679349	−	0.935044i	−0.999926	+	0.0121788i	$0.996123\pi$
$30$		0			0
$31$	−1.16778	−	0.848445i	−0.209740	−	0.152385i	0.477956	−	0.878384i	$-0.341378\pi$
$31$	−1.16778	−	0.848445i	−0.209740	−	0.152385i	−0.687696	+	0.725999i	$0.741378\pi$
$32$	−2.61567	−	5.01580i	−0.462390	−	0.886677i
$33$	7.33789	−	10.0997i	1.27736	−	1.75814i
$34$	6.79015	+	3.99838i	1.16450	+	0.685717i
$35$		0			0
$36$	−1.67262	+	13.6551i	−0.278770	+	2.27584i
$37$	2.16303	−	6.65712i	0.355600	−	1.09442i	−0.600061	−	0.799954i	$-0.704857\pi$
$37$	2.16303	−	6.65712i	0.355600	−	1.09442i	0.955661	−	0.294470i	$-0.0951431\pi$
$38$	5.49133	+	3.23357i	0.890811	+	0.524554i
$39$	−0.883011	−	2.71763i	−0.141395	−	0.435169i
$40$		0			0
$41$	1.97065	−	6.06503i	0.307763	−	0.947198i	−0.670868	−	0.741577i	$-0.734078\pi$
$41$	1.97065	−	6.06503i	0.307763	−	0.947198i	0.978632	−	0.205622i	$-0.0659216\pi$
$42$	3.91406	−	3.46388i	0.603953	−	0.534488i
$43$	2.96089			0.451532			0.225766	−	0.974182i	$-0.427512\pi$
$43$	2.96089			0.451532			0.225766	+	0.974182i	$0.427512\pi$
$44$	6.94681	−	3.85330i	1.04727	−	0.580908i
$45$		0			0
$46$	−1.23056	−	2.82899i	−0.181437	−	0.417111i
$47$	3.12538	+	4.30172i	0.455884	+	0.627470i	0.973649	−	0.228053i	$-0.0732359\pi$
$47$	3.12538	+	4.30172i	0.455884	+	0.627470i	−0.517765	+	0.855523i	$0.673236\pi$
$48$	−6.65601	+	10.6656i	−0.960713	+	1.53944i
$49$	5.61729			0.802470
$50$		0			0
$51$		−	17.5127i		−	2.45227i
$52$	0.221074	−	1.80482i	0.0306574	−	0.250283i
$53$	10.5708	−	7.68016i	1.45202	−	1.05495i	0.466661	−	0.884436i	$-0.345457\pi$
$53$	10.5708	−	7.68016i	1.45202	−	1.05495i	0.985355	−	0.170515i	$-0.0545433\pi$
$54$	15.8089	−	6.87664i	2.15132	−	0.935792i
$55$		0			0
$56$	3.18854	−	0.945992i	0.426086	−	0.126414i
$57$		−	14.1629i		−	1.87592i
$58$	−6.59157	+	5.83343i	−0.865515	+	0.765967i
$59$	1.22277	+	0.397301i	0.159191	+	0.0517242i	0.387528	−	0.921858i	$-0.373329\pi$
$59$	1.22277	+	0.397301i	0.159191	+	0.0517242i	−0.228338	+	0.973582i	$0.573329\pi$
$60$		0			0
$61$	14.7321	−	4.78675i	1.88625	−	0.612881i	0.903306	−	0.428996i	$-0.141133\pi$
$61$	14.7321	−	4.78675i	1.88625	−	0.612881i	0.982948	−	0.183885i	$-0.0588674\pi$
$62$	−1.03582	+	1.75905i	−0.131549	+	0.223399i
$63$	−7.69253	−	2.49945i	−0.969167	−	0.314902i
$64$	−6.70558	+	4.36293i	−0.838198	+	0.545367i
$65$		0			0
$66$	−15.2133	−	8.95838i	−1.87263	−	1.10270i
$67$	−2.45652	−	1.78477i	−0.300112	−	0.218044i	0.427530	−	0.904001i	$-0.359384\pi$
$67$	−2.45652	−	1.78477i	−0.300112	−	0.218044i	−0.727642	+	0.685957i	$0.759384\pi$
$68$	4.70669	−	10.1012i	0.570770	−	1.22495i
$69$	−4.03005	+	5.54689i	−0.485161	+	0.667767i
$70$		0			0
$71$	−1.58201	+	1.14940i	−0.187750	+	0.136409i	−0.677690	−	0.735348i	$-0.737019\pi$
$71$	−1.58201	+	1.14940i	−0.187750	+	0.136409i	0.489940	+	0.871756i	$0.337019\pi$
$72$	19.4491	+	0.500848i	2.29209	+	0.0590255i
$73$	−4.01616	+	1.30493i	−0.470056	+	0.152731i	−0.534461	−	0.845193i	$-0.679485\pi$
$73$	−4.01616	+	1.30493i	−0.470056	+	0.152731i	0.0644044	+	0.997924i	$0.479485\pi$
$74$	−9.66475	−	2.14116i	−1.12350	−	0.248905i
$75$		0			0
$76$	3.80639	−	8.16901i	0.436623	−	0.937049i
$77$	1.44329	+	4.44199i	0.164478	+	0.506211i
$78$	−3.70569	+	1.61192i	−0.419587	+	0.182514i
$79$	2.23200	−	1.62164i	0.251119	−	0.182449i	−0.455103	−	0.890439i	$-0.650398\pi$
$79$	2.23200	−	1.62164i	0.251119	−	0.182449i	0.706223	+	0.707990i	$0.250398\pi$
$80$		0			0
$81$	−14.3025	−	10.3914i	−1.58917	−	1.15460i
$82$	−8.80515	−	1.95072i	−0.972366	−	0.215421i
$83$	−7.65878	−	5.56443i	−0.840660	−	0.610775i	0.0818950	−	0.996641i	$-0.473903\pi$
$83$	−7.65878	−	5.56443i	−0.840660	−	0.610775i	−0.922555	+	0.385866i	$0.873903\pi$
$84$	−5.40738	−	5.03954i	−0.589993	−	0.549859i
$85$		0			0
$86$	−0.401941	−	4.16800i	−0.0433424	−	0.449447i
$87$	18.6049	+	6.04509i	1.99465	+	0.648101i
$88$	−6.36726	−	9.25582i	−0.678752	−	0.986673i
$89$	0.806910	+	2.48341i	0.0855323	+	0.263241i	0.984671	−	0.174423i	$-0.0558059\pi$
$89$	0.806910	+	2.48341i	0.0855323	+	0.263241i	−0.899139	+	0.437664i	$0.855806\pi$
$90$		0			0
$91$	1.01674	+	0.330358i	0.106583	+	0.0346309i
$92$	−3.81527	+	2.11628i	−0.397769	+	0.220637i
$93$	4.53682			0.470447
$94$	5.63118	−	4.98350i	0.580812	−	0.514009i
$95$		0			0
$96$	15.9173	+	7.92171i	1.62455	+	0.808506i
$97$	0.171369	+	0.235869i	0.0173999	+	0.0239489i	0.817628	−	0.575746i	$-0.195288\pi$
$97$	0.171369	+	0.235869i	0.0173999	+	0.0239489i	−0.800228	+	0.599695i	$0.795288\pi$
$98$	−0.762547	−	7.90737i	−0.0770289	−	0.798765i
$99$			27.3214i			2.74590i
$100$		0			0
$101$			7.84171i			0.780280i	0.920756	+	0.390140i	$0.127573\pi$
$101$			7.84171i			0.780280i	−0.920756	+	0.390140i	$0.872427\pi$
$102$	−24.6524	+	2.37735i	−2.44095	+	0.235393i
$103$	−7.73997	−	10.6532i	−0.762642	−	1.04969i	−0.996990	−	0.0775342i	$-0.975295\pi$
$103$	−7.73997	−	10.6532i	−0.762642	−	1.04969i	0.234347	−	0.972153i	$-0.424705\pi$
$104$	−2.57062	−	0.0661980i	−0.252070	−	0.00649125i
$105$		0			0
$106$	−12.2462	−	13.8378i	−1.18946	−	1.34405i
$107$	7.00700			0.677392			0.338696	−	0.940896i	$-0.390014\pi$
$107$	7.00700			0.677392			0.338696	+	0.940896i	$0.390014\pi$
$108$	−11.8262	−	21.3205i	−1.13798	−	2.05156i
$109$	−2.56991	−	0.835013i	−0.246152	−	0.0799797i	0.183342	−	0.983049i	$-0.441308\pi$
$109$	−2.56991	−	0.835013i	−0.246152	−	0.0799797i	−0.429495	+	0.903069i	$0.641308\pi$
$110$		0			0
$111$	6.79844	+	20.9235i	0.645280	+	1.98597i
$112$	−1.76450	−	4.36003i	−0.166730	−	0.411984i
$113$	−4.34695	−	1.41241i	−0.408926	−	0.132868i	0.0973282	−	0.995252i	$-0.468970\pi$
$113$	−4.34695	−	1.41241i	−0.408926	−	0.132868i	−0.506255	+	0.862384i	$0.668970\pi$
$114$	−19.9369	+	1.92261i	−1.86726	+	0.180069i
$115$		0			0
$116$	9.10642	+	8.48695i	0.845510	+	0.787994i
$117$	5.05932	+	3.67581i	0.467734	+	0.339829i
$118$	0.393283	−	1.77520i	0.0362047	−	0.163420i
$119$	5.30066	+	3.85116i	0.485911	+	0.353035i
$120$		0			0
$121$	3.86428	−	2.80757i	0.351299	−	0.255233i
$122$	−8.73812	−	20.0883i	−0.791112	−	1.81871i
$123$	6.19378	+	19.0625i	0.558474	+	1.71881i
$124$	2.61679	+	1.21931i	0.234995	+	0.109497i
$125$		0			0
$126$	−2.47418	+	11.1679i	−0.220417	+	0.994919i
$127$	8.20787	−	2.66690i	0.728330	−	0.236649i	0.0786992	−	0.996898i	$-0.474923\pi$
$127$	8.20787	−	2.66690i	0.728330	−	0.236649i	0.649631	+	0.760250i	$0.274923\pi$
$128$	7.05191	+	8.84707i	0.623307	+	0.781978i
$129$	−7.52882	+	5.47001i	−0.662876	+	0.481607i
$130$		0			0
$131$	5.11250	−	7.03676i	0.446681	−	0.614804i	−0.524999	−	0.851103i	$-0.675934\pi$
$131$	5.11250	−	7.03676i	0.446681	−	0.614804i	0.971680	+	0.236299i	$0.0759343\pi$
$132$	−10.5454	+	22.6317i	−0.917855	+	1.96983i
$133$	4.28675	+	3.11451i	0.371708	+	0.270062i
$134$	−2.17891	+	3.70028i	−0.188229	+	0.319656i
$135$		0			0
$136$	−14.8582	−	5.25430i	−1.27408	−	0.450553i
$137$	−3.46540	−	1.12598i	−0.296069	−	0.0961988i	0.157216	−	0.987564i	$-0.449748\pi$
$137$	−3.46540	−	1.12598i	−0.296069	−	0.0961988i	−0.453285	+	0.891365i	$0.649748\pi$
$138$	8.35535	+	4.92005i	0.711254	+	0.418822i
$139$	13.2832	−	4.31597i	1.12666	−	0.366075i	0.314357	−	0.949305i	$-0.398211\pi$
$139$	13.2832	−	4.31597i	1.12666	−	0.366075i	0.812307	+	0.583230i	$0.198211\pi$
$140$		0			0
$141$	−15.8941	−	5.16432i	−1.33853	−	0.434914i
$142$	1.83275	+	2.07094i	0.153801	+	0.173789i
$143$		−	3.61112i		−	0.301977i
$144$	−1.93517	−	27.4461i	−0.161264	−	2.28717i
$145$		0			0
$146$	2.38212	+	5.47634i	0.197146	+	0.453225i
$147$	−14.2834	+	10.3775i	−1.17807	+	0.855921i
$148$	−1.70208	+	13.8956i	−0.139910	+	1.14221i
$149$			2.61363i			0.214117i	0.994253	+	0.107059i	$0.0341433\pi$
$149$			2.61363i			0.214117i	−0.994253	+	0.107059i	$0.965857\pi$
$150$		0			0
$151$	10.6178			0.864067			0.432034	−	0.901857i	$-0.357796\pi$
$151$	10.6178			0.864067			0.432034	+	0.901857i	$0.357796\pi$
$152$	−12.0161	−	4.24926i	−0.974634	−	0.344660i
$153$	22.5280	+	31.0072i	1.82128	+	2.50678i
$154$	6.05698	−	2.63469i	0.488086	−	0.212310i
$155$		0			0
$156$	2.77212	+	4.99762i	0.221947	+	0.400130i
$157$	−3.90358			−0.311539			−0.155770	−	0.987793i	$-0.549786\pi$
$157$	−3.90358			−0.311539			−0.155770	+	0.987793i	$0.549786\pi$
$158$	−2.58575	−	2.92181i	−0.205711	−	0.232446i
$159$	−12.6906	+	39.0575i	−1.00643	+	3.09746i
$160$		0			0
$161$	−0.792671	−	2.43959i	−0.0624712	−	0.192267i
$162$	−12.6862	+	21.5441i	−0.996724	+	1.69266i
$163$	6.06584	−	18.6687i	0.475114	−	1.46225i	−0.370691	−	0.928756i	$-0.620879\pi$
$163$	6.06584	−	18.6687i	0.475114	−	1.46225i	0.845805	−	0.533493i	$-0.179121\pi$
$164$	−1.55070	+	12.6597i	−0.121089	+	0.988555i
$165$		0			0
$166$	−6.79327	+	11.5365i	−0.527260	+	0.895406i
$167$	−9.89993	+	13.6261i	−0.766080	+	1.05442i	0.230604	+	0.973048i	$0.425930\pi$
$167$	−9.89993	+	13.6261i	−0.766080	+	1.05442i	−0.996684	+	0.0813708i	$0.974070\pi$
$168$	−6.36002	+	8.29599i	−0.490686	+	0.640050i
$169$	9.84852	+	7.15537i	0.757579	+	0.550413i
$170$		0			0
$171$	18.2189	+	25.0761i	1.39323	+	1.91762i
$172$	−5.81266	+	1.13161i	−0.443211	+	0.0862845i
$173$	3.14623	+	9.68309i	0.239203	+	0.736192i	0.996536	+	0.0831625i	$0.0265020\pi$
$173$	3.14623	+	9.68309i	0.239203	+	0.736192i	−0.757333	+	0.653029i	$0.773498\pi$
$174$	5.98396	−	27.0104i	0.453643	−	2.04765i
$175$		0			0
$176$	−12.1649	+	10.2196i	−0.916964	+	0.770328i
$177$	−3.84317	+	1.24872i	−0.288871	+	0.0938598i
$178$	3.38632	−	1.47300i	0.253815	−	0.110406i
$179$	−8.87687	−	12.2180i	−0.663488	−	0.913214i	0.336102	−	0.941826i	$-0.390891\pi$
$179$	−8.87687	−	12.2180i	−0.663488	−	0.913214i	−0.999591	+	0.0286120i	$0.990891\pi$
$180$		0			0
$181$	11.1217	−	15.3077i	0.826668	−	1.13781i	−0.161866	−	0.986813i	$-0.551751\pi$
$181$	11.1217	−	15.3077i	0.826668	−	1.13781i	0.988534	−	0.150998i	$-0.0482489\pi$
$182$	0.327017	−	1.47609i	0.0242401	−	0.109415i
$183$	−28.6170	+	39.3879i	−2.11543	+	2.91164i
$184$	3.49697	+	5.08340i	0.257800	+	0.374753i
$185$		0			0
$186$	−0.615874	−	6.38641i	−0.0451581	−	0.468274i
$187$	6.83904	−	21.0484i	0.500120	−	1.53921i
$188$	−7.77963	−	7.25041i	−0.567387	−	0.528791i
$189$	13.6329	−	4.42960i	0.991649	−	0.322206i
$190$		0			0
$191$	−0.692493	+	2.13127i	−0.0501070	+	0.154214i	−0.972979	−	0.230893i	$-0.925835\pi$
$191$	−0.692493	+	2.13127i	−0.0501070	+	0.154214i	0.922872	+	0.385106i	$0.125835\pi$
$192$	8.99048	−	23.4819i	0.648832	−	1.69466i
$193$		−	22.6952i		−	1.63363i	−0.576896	−	0.816817i	$-0.695736\pi$
$193$		−	22.6952i		−	1.63363i	0.576896	−	0.816817i	$-0.304264\pi$
$194$	0.308765	−	0.273252i	0.0221681	−	0.0196184i
$195$		0			0
$196$	−11.0276	+	2.14685i	−0.787682	+	0.153346i
$197$	−10.5031	+	7.63095i	−0.748315	+	0.543682i	−0.895304	−	0.445456i	$-0.853042\pi$
$197$	−10.5031	+	7.63095i	−0.748315	+	0.543682i	0.146989	+	0.989138i	$0.453042\pi$
$198$	38.4599	−	3.70888i	2.73322	−	0.263579i
$199$	−18.2166			−1.29134			−0.645672	−	0.763615i	$-0.723423\pi$
$199$	−18.2166			−1.29134			−0.645672	+	0.763615i	$0.723423\pi$
$200$		0			0
$201$	9.54353			0.673149
$202$	11.0386	−	1.06451i	0.776676	−	0.0748988i
$203$	−5.92102	+	4.30187i	−0.415574	+	0.301932i
$204$	6.69312	+	34.3800i	0.468612	+	2.40708i
$205$		0			0
$206$	−13.9456	+	12.3416i	−0.971634	+	0.859880i
$207$		−	15.0052i		−	1.04294i
$208$	0.255776	+	3.62761i	0.0177349	+	0.251529i
$209$	5.53086	−	17.0222i	0.382578	−	1.17745i
$210$		0			0
$211$	1.67102	−	0.542946i	0.115037	−	0.0373779i	−0.250933	−	0.968005i	$-0.580737\pi$
$211$	1.67102	−	0.542946i	0.115037	−	0.0373779i	0.365970	+	0.930627i	$0.380737\pi$
$212$	−17.8168	+	19.1173i	−1.22366	+	1.31298i
$213$	1.89925	−	5.84528i	0.130134	−	0.400512i
$214$	−0.951200	−	9.86364i	−0.0650227	−	0.674264i
$215$		0			0
$216$	−28.4071	+	19.5418i	−1.93286	+	1.32965i
$217$	−0.997675	+	1.37318i	−0.0677266	+	0.0932177i
$218$	−0.826569	+	3.73097i	−0.0559823	+	0.252693i
$219$	7.80136	−	10.7377i	0.527167	−	0.725583i
$220$		0			0
$221$	−2.97757	−	4.09828i	−0.200293	−	0.275680i
$222$	28.5307	−	12.4104i	1.91486	−	0.832932i
$223$	1.48230	−	0.481630i	0.0992625	−	0.0322523i	−0.258965	−	0.965887i	$-0.583381\pi$
$223$	1.48230	−	0.481630i	0.0992625	−	0.0322523i	0.358227	+	0.933634i	$0.383381\pi$
$224$	−5.89801	+	3.07573i	−0.394077	+	0.205506i
$225$		0			0
$226$	−1.39813	+	6.31086i	−0.0930020	+	0.419792i
$227$	−2.84981	−	8.77081i	−0.189148	−	0.582139i	0.810847	−	0.585259i	$-0.199007\pi$
$227$	−2.84981	−	8.77081i	−0.189148	−	0.582139i	−0.999995	+	0.00311955i	$0.999007\pi$
$228$	5.41286	+	27.8038i	0.358475	+	1.84135i
$229$	−6.64077	−	9.14023i	−0.438834	−	0.604003i	0.531118	−	0.847298i	$-0.321772\pi$
$229$	−6.64077	−	9.14023i	−0.438834	−	0.604003i	−0.969953	+	0.243294i	$0.921772\pi$
$230$		0			0
$231$	−11.8761	−	8.62852i	−0.781393	−	0.567715i
$232$	10.7107	−	13.9711i	0.703195	−	0.917245i
$233$	7.30682	−	10.0570i	0.478685	−	0.658854i	−0.499566	−	0.866276i	$-0.666507\pi$
$233$	7.30682	−	10.0570i	0.478685	−	0.658854i	0.978252	+	0.207422i	$0.0665072\pi$
$234$	4.48757	−	7.62091i	0.293362	−	0.498194i
$235$		0			0
$236$	−2.55231	−	0.312635i	−0.166141	−	0.0203508i
$237$	−2.67957	+	8.24687i	−0.174057	+	0.535692i
$238$	4.70164	−	7.98445i	0.304762	−	0.517555i
$239$	−8.53966	−	26.2824i	−0.552384	−	1.70006i	−0.702752	−	0.711435i	$-0.748046\pi$
$239$	−8.53966	−	26.2824i	−0.552384	−	1.70006i	0.150368	−	0.988630i	$-0.451954\pi$
$240$		0			0
$241$	−1.32369	+	4.07389i	−0.0852663	+	0.262423i	−0.984595	−	0.174851i	$-0.944056\pi$
$241$	−1.32369	+	4.07389i	−0.0852663	+	0.262423i	0.899329	+	0.437273i	$0.144056\pi$
$242$	−4.47674	−	5.05856i	−0.287776	−	0.325177i
$243$	18.9940			1.21846
$244$	−27.0918	+	15.0275i	−1.73438	+	0.962037i
$245$		0			0
$246$	25.9931	−	11.3066i	1.65726	−	0.720883i
$247$	−2.40802	−	3.31436i	−0.153219	−	0.210888i
$248$	1.36117	−	3.84914i	0.0864345	−	0.244420i
$249$	29.7542			1.88560
$250$		0			0
$251$			13.4000i			0.845800i	0.906176	+	0.422900i	$0.138988\pi$
$251$			13.4000i			0.845800i	−0.906176	+	0.422900i	$0.861012\pi$
$252$	16.0568	+	1.96681i	1.01148	+	0.123898i
$253$	−7.00985	+	5.09295i	−0.440705	+	0.320191i
$254$	−4.86836	−	11.1920i	−0.305468	−	0.702251i
$255$		0			0
$256$	11.4966	−	11.1278i	0.718536	−	0.695490i
$257$			7.81899i			0.487735i	0.969809	+	0.243868i	$0.0784162\pi$
$257$			7.81899i			0.487735i	−0.969809	+	0.243868i	$0.921584\pi$
$258$	8.72208	+	9.85564i	0.543013	+	0.613585i
$259$	−7.82802	−	2.54348i	−0.486409	−	0.158044i
$260$		0			0
$261$	−40.7171	+	13.2298i	−2.52033	+	0.818904i
$262$	−10.5995	−	6.24154i	−0.654842	−	0.385604i
$263$	26.0980	+	8.47975i	1.60927	+	0.522884i	0.969377	−	0.245579i	$-0.0789781\pi$
$263$	26.0980	+	8.47975i	1.60927	+	0.522884i	0.639894	+	0.768463i	$0.278978\pi$
$264$	33.2898	+	11.7723i	2.04884	+	0.724533i
$265$		0			0
$266$	3.80231	−	6.45718i	0.233135	−	0.395915i
$267$	−6.63968	−	4.82401i	−0.406342	−	0.295225i
$268$	5.50461	+	2.56490i	0.336248	+	0.156676i
$269$	−12.5408	+	17.2610i	−0.764629	+	1.05242i	0.232186	+	0.972671i	$0.425412\pi$
$269$	−12.5408	+	17.2610i	−0.764629	+	1.05242i	−0.996815	+	0.0797498i	$0.974588\pi$
$270$		0			0
$271$	0.864363	−	0.627996i	0.0525063	−	0.0381481i	−0.561223	−	0.827665i	$-0.689669\pi$
$271$	0.864363	−	0.627996i	0.0525063	−	0.0381481i	0.613729	+	0.789517i	$0.289669\pi$
$272$	−5.37939	+	21.6289i	−0.326174	+	1.31144i
$273$	−3.19562	+	1.03832i	−0.193408	+	0.0628420i
$274$	−1.11459	+	5.03104i	−0.0673350	+	0.303936i
$275$		0			0
$276$	5.79163	−	12.4296i	0.348615	−	0.748173i
$277$	5.48602	+	16.8842i	0.329623	+	1.01448i	0.969310	+	0.245840i	$0.0790639\pi$
$277$	5.48602	+	16.8842i	0.329623	+	1.01448i	−0.639687	+	0.768635i	$0.720936\pi$
$278$	−7.87870	−	18.1126i	−0.472533	−	1.08632i
$279$	−8.03268	+	5.83608i	−0.480904	+	0.349397i
$280$		0			0
$281$	−8.77867	−	6.37807i	−0.523691	−	0.380484i	0.294301	−	0.955713i	$-0.404913\pi$
$281$	−8.77867	−	6.37807i	−0.523691	−	0.380484i	−0.817993	+	0.575229i	$0.804913\pi$
$282$	−5.11210	+	23.0750i	−0.304421	+	1.37410i
$283$	18.7899	+	13.6517i	1.11695	+	0.811509i	0.983743	−	0.179580i	$-0.0574739\pi$
$283$	18.7899	+	13.6517i	1.11695	+	0.811509i	0.133203	+	0.991089i	$0.457474\pi$
$284$	2.66643	−	2.86106i	0.158224	−	0.169773i
$285$		0			0
$286$	−5.08332	+	0.490210i	−0.300583	+	0.0289867i
$287$	−7.13178	−	2.31726i	−0.420976	−	0.136783i
$288$	−38.3727	+	6.44992i	−2.26113	+	0.380065i
$289$	−4.34064	−	13.3591i	−0.255332	−	0.785830i
$290$		0			0
$291$	−0.871498	−	0.283167i	−0.0510881	−	0.0165995i
$292$	7.38558	−	4.09669i	0.432208	−	0.239740i
$293$	−23.5633			−1.37658			−0.688291	−	0.725434i	$-0.741639\pi$
$293$	−23.5633			−1.37658			−0.688291	+	0.725434i	$0.741639\pi$
$294$	16.5472	+	18.6977i	0.965052	+	1.09047i
$295$		0			0
$296$	19.7916	+	0.509669i	1.15036	+	0.0296239i
$297$	−28.4604	−	39.1724i	−1.65144	−	2.27301i
$298$	3.67917	−	0.354801i	0.213129	−	0.0205531i
$299$			1.98327i			0.114696i
$300$		0			0
$301$		−	3.48167i		−	0.200680i
$302$	−1.44137	−	14.9466i	−0.0829416	−	0.860077i
$303$	−14.4869	−	19.9396i	−0.832252	−	1.14550i
$304$	−4.35042	+	17.4917i	−0.249514	+	1.00322i
$305$		0			0
$306$	40.5901	−	35.9216i	2.32038	−	2.05350i
$307$	29.1918			1.66607			0.833033	−	0.553223i	$-0.186602\pi$
$307$	29.1918			1.66607			0.833033	+	0.553223i	$0.186602\pi$
$308$	−4.53105	−	8.16865i	−0.258180	−	0.465452i
$309$	39.3617	+	12.7894i	2.23921	+	0.727563i
$310$		0			0
$311$	0.303724	+	0.934766i	0.0172226	+	0.0530057i	0.959298	−	0.282394i	$-0.0911286\pi$
$311$	0.303724	+	0.934766i	0.0172226	+	0.0530057i	−0.942076	+	0.335400i	$0.891129\pi$
$312$	6.65875	−	4.58069i	0.376978	−	0.259330i
$313$	9.11237	+	2.96079i	0.515062	+	0.167354i	0.555003	−	0.831848i	$-0.312717\pi$
$313$	9.11237	+	2.96079i	0.515062	+	0.167354i	−0.0399413	+	0.999202i	$0.512717\pi$
$314$	0.529910	+	5.49500i	0.0299046	+	0.310101i
$315$		0			0
$316$	−3.76196	+	4.03655i	−0.211627	+	0.227074i
$317$	14.8949	+	10.8218i	0.836580	+	0.607811i	0.921413	−	0.388584i	$-0.127036\pi$
$317$	14.8949	+	10.8218i	0.836580	+	0.607811i	−0.0848334	+	0.996395i	$0.527036\pi$
$318$	56.7034	+	12.5622i	3.17977	+	0.704455i
$319$	20.0003	+	14.5311i	1.11980	+	0.813584i
$320$		0			0
$321$	−17.8171	+	12.9449i	−0.994453	+	0.722512i
$322$	−3.32657	+	1.44700i	−0.185382	+	0.0806384i
$323$	−7.75880	−	23.8791i	−0.431711	−	1.32867i
$324$	32.0494	+	14.9336i	1.78052	+	0.829643i
$325$		0			0
$326$	−27.1031	−	6.00450i	−1.50110	−	0.332559i
$327$	8.07726	−	2.62446i	0.446673	−	0.145133i
$328$	18.0313	+	0.464338i	0.995613	+	0.0256388i
$329$	5.05833	−	3.67509i	0.278875	−	0.202614i
$330$		0			0
$331$	−4.25106	+	5.85108i	−0.233659	+	0.321604i	−0.909705	−	0.415255i	$-0.863692\pi$
$331$	−4.25106	+	5.85108i	−0.233659	+	0.321604i	0.676046	+	0.736860i	$0.263692\pi$
$332$	17.1619	+	7.99669i	0.941883	+	0.438876i
$333$	−38.9525	−	28.3007i	−2.13458	−	1.55087i
$334$	20.5251	+	12.0862i	1.12309	+	0.661329i
$335$		0			0
$336$	12.5415	+	7.82671i	0.684195	+	0.426982i
$337$	8.66935	+	2.81684i	0.472250	+	0.153443i	0.535466	−	0.844557i	$-0.320136\pi$
$337$	8.66935	+	2.81684i	0.472250	+	0.153443i	−0.0632165	+	0.998000i	$0.520136\pi$
$338$	8.73556	−	14.8349i	0.475152	−	0.806914i
$339$	13.6625	−	4.43923i	0.742047	−	0.241106i
$340$		0			0
$341$	5.45277	+	1.77171i	0.295284	+	0.0959436i
$342$	32.8260	−	29.0505i	1.77503	−	1.57087i
$343$		−	14.8365i		−	0.801096i
$344$	2.38202	+	8.02876i	0.128430	+	0.432882i
$345$		0			0
$346$	13.2036	−	5.74337i	0.709831	−	0.308765i
$347$	−8.27687	+	6.01350i	−0.444326	+	0.322821i	−0.787351	−	0.616505i	$-0.788548\pi$
$347$	−8.27687	+	6.01350i	−0.444326	+	0.322821i	0.343026	+	0.939326i	$0.388548\pi$
$348$	−38.8344	−	4.75686i	−2.08174	−	0.254994i
$349$		−	4.76436i		−	0.255030i	−0.991837	−	0.127515i	$-0.959300\pi$
$349$		−	4.76436i		−	0.255030i	0.991837	−	0.127515i	$-0.0407001\pi$
$350$		0			0
$351$	−11.0829			−0.591562
$352$	16.0373	+	15.7370i	0.854790	+	0.838786i
$353$	10.7305	+	14.7692i	0.571126	+	0.786087i	0.992687	−	0.120713i	$-0.0385179\pi$
$353$	10.7305	+	14.7692i	0.571126	+	0.786087i	−0.421562	+	0.906800i	$0.638518\pi$
$354$	2.27952	+	5.24046i	0.121155	+	0.278527i
$355$		0			0
$356$	−2.53320	−	4.56691i	−0.134260	−	0.242046i
$357$	−20.5930			−1.08990
$358$	−15.9940	+	14.1544i	−0.845309	+	0.748084i
$359$	5.64467	−	17.3725i	0.297914	−	0.916885i	−0.684313	−	0.729188i	$-0.739898\pi$
$359$	5.64467	−	17.3725i	0.297914	−	0.916885i	0.982227	−	0.187697i	$-0.0601022\pi$
$360$		0			0
$361$	−0.403370	−	1.24145i	−0.0212300	−	0.0653393i
$362$	−23.0581	−	13.5778i	−1.21191	−	0.713633i
$363$	−4.63917	+	14.2779i	−0.243493	+	0.749396i
$364$	−2.12226	−	0.259958i	−0.111237	−	0.0136255i
$365$		0			0
$366$	59.3305	+	34.9368i	3.10125	+	1.82617i
$367$	−8.85005	+	12.1811i	−0.461969	+	0.635846i	−0.974916	−	0.222575i	$-0.928554\pi$
$367$	−8.85005	+	12.1811i	−0.461969	+	0.635846i	0.512947	+	0.858421i	$0.328554\pi$
$368$	6.68111	−	5.61270i	0.348277	−	0.292582i
$369$	−35.4880	−	25.7835i	−1.84743	−	1.34224i
$370$		0			0
$371$	−9.03100	−	12.4301i	−0.468866	−	0.645339i
$372$	−8.90644	+	1.73391i	−0.461777	+	0.0898991i
$373$	−0.219092	−	0.674295i	−0.0113441	−	0.0349137i	0.945224	−	0.326422i	$-0.105843\pi$
$373$	−0.219092	−	0.674295i	−0.0113441	−	0.0349137i	−0.956568	+	0.291508i	$0.905843\pi$
$374$	−30.5579	−	6.76988i	−1.58011	−	0.350062i
$375$		0			0
$376$	−9.15020	+	11.9355i	−0.471886	+	0.615526i
$377$	5.38166	−	1.74861i	0.277170	−	0.0900579i
$378$	−8.08615	−	18.5895i	−0.415907	−	0.956141i
$379$	−10.8210	−	14.8938i	−0.555838	−	0.765045i	0.434952	−	0.900454i	$-0.356765\pi$
$379$	−10.8210	−	14.8938i	−0.555838	−	0.765045i	−0.990790	+	0.135408i	$0.956765\pi$
$380$		0			0
$381$	−15.9437	+	21.9446i	−0.816821	+	1.12426i
$382$	3.09416	+	0.685490i	0.158311	+	0.0350727i
$383$	10.5490	−	14.5194i	0.539027	−	0.741907i	−0.449445	−	0.893308i	$-0.648378\pi$
$383$	10.5490	−	14.5194i	0.539027	−	0.741907i	0.988472	+	0.151401i	$0.0483783\pi$
$384$	−34.2755	−	9.46808i	−1.74912	−	0.483166i
$385$		0			0
$386$	−31.9476	+	3.08087i	−1.62609	+	0.156812i
$387$	6.29365	−	19.3699i	0.319924	−	0.984625i
$388$	−0.426567	−	0.397550i	−0.0216557	−	0.0201825i
$389$	−22.7077	+	7.37819i	−1.15133	+	0.374089i	−0.821643	−	0.570002i	$-0.806942\pi$
$389$	−22.7077	+	7.37819i	−1.15133	+	0.374089i	−0.329685	+	0.944091i	$0.606942\pi$
$390$		0			0
$391$	−3.75608	+	11.5600i	−0.189953	+	0.584616i
$392$	4.51907	+	15.2319i	0.228248	+	0.769325i
$393$			27.3377i			1.37900i
$394$	12.1677	+	13.7491i	0.613002	+	0.692671i
$395$		0			0
$396$	−10.4419	−	53.6359i	−0.524723	−	2.69530i
$397$	1.16804	−	0.848630i	0.0586222	−	0.0425915i	−0.558088	−	0.829782i	$-0.688465\pi$
$397$	1.16804	−	0.848630i	0.0586222	−	0.0425915i	0.616710	+	0.787190i	$0.288465\pi$
$398$	2.47291	+	25.6433i	0.123956	+	1.28538i
$399$	−16.6539			−0.833740
$400$		0			0
$401$	−26.0682			−1.30178			−0.650891	−	0.759171i	$-0.725605\pi$
$401$	−26.0682			−1.30178			−0.650891	+	0.759171i	$0.725605\pi$
$402$	−1.29553	−	13.4343i	−0.0646154	−	0.670041i
$403$	1.06170	−	0.771367i	0.0528868	−	0.0384245i
$404$	−2.99699	−	15.3944i	−0.149106	−	0.765901i
$405$		0			0
$406$	6.85945	+	7.75094i	0.340429	+	0.384672i
$407$			27.8026i			1.37813i
$408$	47.4876	−	14.0889i	2.35099	−	0.697503i
$409$	0.312601	−	0.962088i	0.0154571	−	0.0475722i	−0.943030	−	0.332706i	$-0.892038\pi$
$409$	0.312601	−	0.962088i	0.0154571	−	0.0475722i	0.958488	+	0.285134i	$0.0920382\pi$
$410$		0			0
$411$	10.8918	−	3.53897i	0.537254	−	0.174564i
$412$	19.2662	+	17.9556i	0.949176	+	0.884608i
$413$	0.467180	−	1.43783i	0.0229884	−	0.0707512i
$414$	−21.1226	+	2.03696i	−1.03812	+	0.100111i
$415$		0			0
$416$	5.07180	−	0.852499i	0.248665	−	0.0417972i
$417$	−25.8025	+	35.5140i	−1.26355	+	1.73913i
$418$	−24.7127	−	5.47494i	−1.20874	−	0.267788i
$419$	19.6696	−	27.0728i	0.960920	−	1.32259i	0.0144183	−	0.999896i	$-0.495410\pi$
$419$	19.6696	−	27.0728i	0.960920	−	1.32259i	0.946502	−	0.322697i	$-0.104590\pi$
$420$		0			0
$421$	16.1696	+	22.2556i	0.788060	+	1.08467i	0.994347	+	0.106180i	$0.0338621\pi$
$421$	16.1696	+	22.2556i	0.788060	+	1.08467i	−0.206287	+	0.978492i	$0.566138\pi$
$422$	−0.991136	−	2.27856i	−0.0482478	−	0.110918i
$423$	34.7847	−	11.3022i	1.69129	−	0.549533i
$424$	29.3297	+	22.4853i	1.42438	+	1.09198i
$425$		0			0
$426$	−8.48612	−	1.88004i	−0.411154	−	0.0910883i
$427$	−5.62868	−	17.3233i	−0.272391	−	0.838333i
$428$	−13.7558	+	2.67798i	−0.664909	+	0.129445i
$429$	6.67126	+	9.18220i	0.322092	+	0.443321i
$430$		0			0
$431$	21.6348	+	15.7186i	1.04211	+	0.757138i	0.970696	−	0.240309i	$-0.0772488\pi$
$431$	21.6348	+	15.7186i	1.04211	+	0.757138i	0.0714143	+	0.997447i	$0.477249\pi$
$432$	31.3649	+	37.3354i	1.50904	+	1.79630i
$433$	12.1996	−	16.7912i	0.586273	−	0.806936i	−0.408092	−	0.912941i	$-0.633806\pi$
$433$	12.1996	−	16.7912i	0.586273	−	0.806936i	0.994366	+	0.106005i	$0.0338059\pi$
$434$	2.06844	+	1.21800i	0.0992883	+	0.0584659i
$435$		0			0
$436$	5.36422	+	0.657069i	0.256900	+	0.0314679i
$437$	−3.03762	+	9.34882i	−0.145309	+	0.447215i
$438$	−16.1742	−	9.52421i	−0.772835	−	0.455084i
$439$	0.0935999	+	0.288071i	0.00446728	+	0.0137489i	0.953265	−	0.302134i	$-0.0976992\pi$
$439$	0.0935999	+	0.288071i	0.00446728	+	0.0137489i	−0.948798	+	0.315883i	$0.897699\pi$
$440$		0			0
$441$	11.9401	−	36.7478i	0.568575	−	1.74989i
$442$	−5.36487	+	4.74782i	−0.255181	+	0.225831i
$443$	−33.9046			−1.61086			−0.805428	−	0.592693i	$-0.798065\pi$
$443$	−33.9046			−1.61086			−0.805428	+	0.592693i	$0.798065\pi$
$444$	−21.3430	−	38.4775i	−1.01289	−	1.82606i
$445$		0			0
$446$	−0.879205	−	2.02123i	−0.0416316	−	0.0957082i
$447$	−4.82848	−	6.64583i	−0.228379	−	0.314337i
$448$	5.13031	+	7.88500i	0.242384	+	0.372531i
$449$	−12.6049			−0.594860			−0.297430	−	0.954744i	$-0.596129\pi$
$449$	−12.6049			−0.594860			−0.297430	+	0.954744i	$0.596129\pi$
$450$		0			0
$451$			25.3298i			1.19273i
$452$	9.07348	+	1.11142i	0.426781	+	0.0522768i
$453$	−26.9986	+	19.6156i	−1.26850	+	0.921621i
$454$	−11.9597	+	5.20226i	−0.561295	+	0.244154i
$455$		0			0
$456$	38.4041	−	11.3939i	1.79844	−	0.533571i
$457$		−	2.58934i		−	0.121124i	−0.998164	−	0.0605622i	$-0.980711\pi$
$457$		−	2.58934i		−	0.121124i	0.998164	−	0.0605622i	$-0.0192893\pi$
$458$	−11.9651	+	10.5889i	−0.559091	+	0.494786i
$459$	−64.5997	−	20.9897i	−3.01526	−	0.979716i
$460$		0			0
$461$	−6.49523	+	2.11043i	−0.302513	+	0.0982925i	−0.456340	−	0.889805i	$-0.650840\pi$
$461$	−6.49523	+	2.11043i	−0.302513	+	0.0982925i	0.153827	+	0.988098i	$0.450840\pi$
$462$	−10.5340	+	17.8892i	−0.490088	+	0.832279i
$463$	−20.7530	−	6.74304i	−0.964472	−	0.313376i	−0.215889	−	0.976418i	$-0.569265\pi$
$463$	−20.7530	−	6.74304i	−0.964472	−	0.313376i	−0.748582	+	0.663042i	$0.769265\pi$
$464$	−21.1208	−	13.1808i	−0.980509	−	0.611902i
$465$		0			0
$466$	−15.1489	−	8.92045i	−0.701761	−	0.413232i
$467$	2.43118	+	1.76636i	0.112502	+	0.0817373i	0.642614	−	0.766190i	$-0.277850\pi$
$467$	2.43118	+	1.76636i	0.112502	+	0.0817373i	−0.530112	+	0.847928i	$0.677850\pi$
$468$	−11.3370	−	5.28254i	−0.524054	−	0.244186i
$469$	−2.09868	+	2.88859i	−0.0969081	+	0.133383i
$470$		0			0
$471$	9.92583	−	7.21154i	0.457358	−	0.332290i
$472$	−0.0936149	+	3.63528i	−0.00430898	+	0.167327i
$473$	−11.1850	+	3.63421i	−0.514285	+	0.167101i
$474$	11.9727	+	2.65247i	0.549926	+	0.121832i
$475$		0			0
$476$	−11.8778	−	5.53453i	−0.544419	−	0.253675i
$477$	−27.7736	−	85.4782i	−1.27166	−	3.91378i
$478$	−35.8380	+	15.5890i	−1.63919	+	0.713022i
$479$	15.3717	−	11.1682i	0.702349	−	0.510287i	−0.178347	−	0.983968i	$-0.557075\pi$
$479$	15.3717	−	11.1682i	0.702349	−	0.510287i	0.880697	+	0.473681i	$0.157075\pi$
$480$		0			0
$481$	5.14843	+	3.74055i	0.234748	+	0.170555i
$482$	5.91444	+	1.31030i	0.269395	+	0.0596827i
$483$	6.52251	+	4.73888i	0.296785	+	0.215627i
$484$	−6.51313	+	6.98853i	−0.296051	+	0.317661i
$485$		0			0
$486$	−2.57843	−	26.7375i	−0.116960	−	1.21284i
$487$	1.80539	+	0.586607i	0.0818101	+	0.0265817i	0.349636	−	0.936886i	$-0.386305\pi$
$487$	1.80539	+	0.586607i	0.0818101	+	0.0265817i	−0.267826	+	0.963467i	$0.586305\pi$
$488$	24.8317	+	36.0967i	1.12408	+	1.63402i
$489$	19.0651	+	58.6762i	0.862151	+	2.65343i
$490$		0			0
$491$	−29.3750	−	9.54451i	−1.32567	−	0.430738i	−0.441234	−	0.897392i	$-0.645459\pi$
$491$	−29.3750	−	9.54451i	−1.32567	−	0.430738i	−0.884440	+	0.466654i	$0.845459\pi$
$492$	−19.4447	−	35.0552i	−0.876634	−	1.58041i
$493$	34.6801			1.56191
$494$	−4.33868	+	3.83966i	−0.195206	+	0.172754i
$495$		0			0
$496$	−5.60315	−	1.39358i	−0.251589	−	0.0625735i
$497$	1.35156	+	1.86027i	0.0606258	+	0.0834443i
$498$	−4.03913	−	41.8845i	−0.180998	−	1.87689i
$499$		−	10.5948i		−	0.474289i	−0.971474	−	0.237145i	$-0.923788\pi$
$499$		−	10.5948i		−	0.474289i	0.971474	−	0.237145i	$-0.0762115\pi$
$500$		0			0
$501$		−	52.9371i		−	2.36506i
$502$	18.8629	−	1.81905i	0.841894	−	0.0811881i
$503$	−15.5618	−	21.4189i	−0.693865	−	0.955024i	−0.999995	−	0.00303389i	$-0.999034\pi$
$503$	−15.5618	−	21.4189i	−0.693865	−	0.955024i	0.306130	−	0.951990i	$-0.400966\pi$
$504$	0.588940	−	22.8699i	0.0262335	−	1.01871i
$505$		0			0
$506$	8.12085	+	9.17628i	0.361016	+	0.407935i
$507$	−38.2613			−1.69925
$508$	−15.0940	+	8.37243i	−0.669687	+	0.371467i
$509$	−17.5095	−	5.68919i	−0.776096	−	0.252169i	−0.105923	−	0.994374i	$-0.533780\pi$
$509$	−17.5095	−	5.68919i	−0.776096	−	0.252169i	−0.670172	+	0.742205i	$0.733780\pi$
$510$		0			0
$511$	1.53445	+	4.72255i	0.0678800	+	0.208913i
$512$	−17.2251	−	14.6729i	−0.761251	−	0.648458i
$513$	−52.2431	−	16.9748i	−2.30659	−	0.749456i
$514$	11.0067	−	1.06143i	0.485483	−	0.0468176i
$515$		0			0
$516$	12.6896	−	13.6158i	0.558628	−	0.599403i
$517$	−17.0863	−	12.4139i	−0.751453	−	0.545963i
$518$	−2.51776	+	11.3646i	−0.110624	+	0.499334i
$519$	−25.8888	−	18.8093i	−1.13639	−	0.825637i
$520$		0			0
$521$	32.7039	−	23.7608i	1.43278	−	1.04098i	0.443295	−	0.896376i	$-0.353809\pi$
$521$	32.7039	−	23.7608i	1.43278	−	1.04098i	0.989490	−	0.144603i	$-0.0461906\pi$
$522$	24.1507	+	55.5209i	1.05705	+	2.43008i
$523$	−5.37852	−	16.5534i	−0.235186	−	0.723828i	−0.997097	−	0.0761461i	$-0.975738\pi$
$523$	−5.37852	−	16.5534i	−0.235186	−	0.723828i	0.761911	−	0.647682i	$-0.224262\pi$
$524$	−7.34723	+	15.7681i	−0.320965	+	0.688832i
$525$		0			0
$526$	8.39400	−	37.8888i	0.365996	−	1.65203i
$527$	7.64925	−	2.48539i	0.333206	−	0.108265i
$528$	12.0525	−	48.4595i	0.524520	−	2.10893i
$529$	−14.7575	+	10.7220i	−0.641630	+	0.466172i
$530$		0			0
$531$	5.19820	−	7.15471i	0.225583	−	0.310488i
$532$	−9.60582	−	4.47589i	−0.416465	−	0.194054i
$533$	4.69052	+	3.40786i	0.203169	+	0.147611i
$534$	−5.88934	+	10.0014i	−0.254857	+	0.432804i
$535$		0			0
$536$	2.86332	−	8.09693i	0.123677	−	0.349734i
$537$	45.1434	+	14.6680i	1.94808	+	0.632970i
$538$	26.0004	+	15.3104i	1.12096	+	0.660076i
$539$	−21.2197	+	6.89469i	−0.913996	+	0.296975i
$540$		0			0
$541$	7.69917	+	2.50161i	0.331013	+	0.107553i	0.469808	−	0.882768i	$-0.344323\pi$
$541$	7.69917	+	2.50161i	0.331013	+	0.107553i	−0.138795	+	0.990321i	$0.544323\pi$
$542$	−1.00136	−	1.13150i	−0.0430120	−	0.0486020i
$543$			59.4701i			2.55211i
$544$	31.1768	+	4.63637i	1.33670	+	0.198783i
$545$		0			0
$546$	1.89543	+	4.35747i	0.0811170	+	0.186483i
$547$	20.7126	−	15.0486i	0.885607	−	0.643431i	−0.0491221	−	0.998793i	$-0.515642\pi$
$547$	20.7126	−	15.0486i	0.885607	−	0.643431i	0.934729	+	0.355362i	$0.115642\pi$
$548$	7.23342	+	0.886029i	0.308996	+	0.0378493i
$549$		−	106.551i		−	4.54747i
$550$		0			0
$551$	28.0465			1.19482
$552$	−18.2831	−	6.46547i	−0.778181	−	0.275189i
$553$	−1.90686	−	2.62457i	−0.0810881	−	0.111608i
$554$	23.0229	−	10.0146i	0.978151	−	0.425480i
$555$		0			0
$556$	−24.4273	+	13.5495i	−1.03595	+	0.574627i
$557$	−1.74254			−0.0738336			−0.0369168	−	0.999318i	$-0.511754\pi$
$557$	−1.74254			−0.0738336			−0.0369168	+	0.999318i	$0.511754\pi$
$558$	9.30579	+	10.5152i	0.393946	+	0.445145i
$559$	−0.831844	+	2.56015i	−0.0351832	+	0.108283i
$560$		0			0
$561$	21.4952	+	66.1555i	0.907529	+	2.79309i
$562$	−7.78660	+	13.2234i	−0.328458	+	0.557796i
$563$	−7.94233	+	24.4440i	−0.334729	+	1.03019i	0.632126	+	0.774866i	$0.282183\pi$
$563$	−7.94233	+	24.4440i	−0.334729	+	1.03019i	−0.966855	+	0.255325i	$0.917817\pi$
$564$	33.1762	+	4.06379i	1.39697	+	0.171116i
$565$		0			0
$566$	16.6665	−	28.3035i	0.700546	−	1.18968i
$567$	−12.2191	+	16.8181i	−0.513154	+	0.706296i
$568$	−4.38943	−	3.36510i	−0.184176	−	0.141197i
$569$	−11.5604	−	8.39915i	−0.484639	−	0.352111i	0.318480	−	0.947930i	$-0.396828\pi$
$569$	−11.5604	−	8.39915i	−0.484639	−	0.352111i	−0.803119	+	0.595819i	$0.796828\pi$
$570$		0			0
$571$	−11.7151	−	16.1245i	−0.490263	−	0.674789i	0.490174	−	0.871625i	$-0.336933\pi$
$571$	−11.7151	−	16.1245i	−0.490263	−	0.674789i	−0.980436	+	0.196836i	$0.936933\pi$
$572$	1.38012	+	7.08916i	0.0577057	+	0.296413i
$573$	−2.17652	−	6.69863i	−0.0909253	−	0.279839i
$574$	−2.29382	+	10.3539i	−0.0957424	+	0.432162i
$575$		0			0
$576$	14.2885	+	53.1410i	0.595356	+	2.21421i
$577$	−14.6528	+	4.76100i	−0.610006	+	0.198203i	−0.597698	−	0.801721i	$-0.703918\pi$
$577$	−14.6528	+	4.76100i	−0.610006	+	0.198203i	−0.0123079	+	0.999924i	$0.503918\pi$
$578$	−18.2162	+	7.92375i	−0.757692	+	0.329584i
$579$	41.9275	+	57.7083i	1.74245	+	2.39827i
$580$		0			0
$581$	−6.54313	+	9.00585i	−0.271455	+	0.373626i
$582$	−0.280303	+	1.26523i	−0.0116189	+	0.0524456i
$583$	−30.5054	+	41.9870i	−1.26340	+	1.73892i
$584$	−6.76943	−	9.84043i	−0.280121	−	0.407200i
$585$		0			0
$586$	3.19872	+	33.1697i	0.132138	+	1.37023i
$587$	−4.25364	+	13.0914i	−0.175567	+	0.540338i	−0.999659	−	0.0261173i	$-0.991686\pi$
$587$	−4.25364	+	13.0914i	−0.175567	+	0.540338i	0.824092	+	0.566455i	$0.191686\pi$
$588$	24.0742	−	25.8314i	0.992804	−	1.06527i
$589$	6.18610	−	2.00998i	0.254894	−	0.0828200i
$590$		0			0
$591$	12.6092	−	38.8072i	0.518675	−	1.59632i
$592$	−1.96926	−	27.9295i	−0.0809360	−	1.14790i
$593$		−	6.37493i		−	0.261787i	−0.991396	−	0.130894i	$-0.958215\pi$
$593$		−	6.37493i		−	0.261787i	0.991396	−	0.130894i	$-0.0417846\pi$
$594$	−51.2789	+	45.3809i	−2.10400	+	1.86200i
$595$		0			0
$596$	−0.998894	−	5.13094i	−0.0409163	−	0.210172i
$597$	46.3205	−	33.6538i	1.89577	−	1.37736i
$598$	2.79182	−	0.269229i	0.114166	−	0.0110096i
$599$	38.8351			1.58676			0.793380	−	0.608727i	$-0.208319\pi$
$599$	38.8351			1.58676			0.793380	+	0.608727i	$0.208319\pi$
$600$		0			0
$601$	41.0478			1.67438			0.837188	−	0.546916i	$-0.184198\pi$
$601$	41.0478			1.67438			0.837188	+	0.546916i	$0.184198\pi$
$602$	−4.90109	+	0.472637i	−0.199754	+	0.0192632i
$603$	−16.8973	+	12.2766i	−0.688112	+	0.499942i
$604$	−20.8443	+	4.05799i	−0.848144	+	0.165117i
$605$		0			0
$606$	−26.1020	+	23.0998i	−1.06032	+	0.938365i
$607$		−	28.6948i		−	1.16469i	−0.812943	−	0.582343i	$-0.802136\pi$
$607$		−	28.6948i		−	1.16469i	0.812943	−	0.582343i	$-0.197864\pi$
$608$	25.2133	+	3.74952i	1.02254	+	0.152063i
$609$	7.10833	−	21.8772i	0.288044	−	0.886509i
$610$		0			0
$611$	−4.59756	+	1.49384i	−0.185997	+	0.0604342i
$612$	−56.0763	−	52.2617i	−2.26675	−	2.11255i
$613$	−2.30831	+	7.10423i	−0.0932316	+	0.286937i	−0.986789	−	0.162012i	$-0.948202\pi$
$613$	−2.30831	+	7.10423i	−0.0932316	+	0.286937i	0.893557	+	0.448949i	$0.148202\pi$
$614$	−3.96279	−	41.0929i	−0.159925	−	1.65837i
$615$		0			0
$616$	−10.8838	+	7.48717i	−0.438520	+	0.301667i
$617$	23.8187	−	32.7837i	0.958906	−	1.31982i	0.0114498	−	0.999934i	$-0.496355\pi$
$617$	23.8187	−	32.7837i	0.958906	−	1.31982i	0.947456	−	0.319886i	$-0.103645\pi$
$618$	12.6601	−	57.1450i	0.509263	−	2.29871i
$619$	5.89273	−	8.11065i	0.236849	−	0.325994i	−0.674003	−	0.738729i	$-0.735426\pi$
$619$	5.89273	−	8.11065i	0.236849	−	0.325994i	0.910851	+	0.412735i	$0.135426\pi$
$620$		0			0
$621$	15.6308	+	21.5140i	0.627242	+	0.863325i
$622$	1.27462	−	0.554441i	0.0511077	−	0.0222311i
$623$	2.92021	−	0.948834i	0.116996	−	0.0380142i
$624$	−7.35208	−	8.75159i	−0.294319	−	0.350344i
$625$		0			0
$626$	2.93085	−	13.2293i	0.117140	−	0.528748i
$627$	17.3836	+	53.5012i	0.694234	+	2.13663i
$628$	7.66328	−	1.49189i	0.305798	−	0.0595329i
$629$	22.9248	+	31.5533i	0.914073	+	1.25811i
$630$		0			0
$631$	−24.4964	−	17.7976i	−0.975184	−	0.708513i	−0.0185571	−	0.999828i	$-0.505907\pi$
$631$	−24.4964	−	17.7976i	−0.975184	−	0.708513i	−0.956627	+	0.291315i	$0.905907\pi$
$632$	6.19287	+	4.74769i	0.246339	+	0.188853i
$633$	−3.24593	+	4.46765i	−0.129014	+	0.177573i
$634$	13.2116	−	22.4363i	0.524701	−	0.891060i
$635$		0			0
$636$	9.98617	−	81.5257i	0.395977	−	3.23271i
$637$	−1.57814	+	4.85702i	−0.0625283	+	0.192442i
$638$	17.7401	−	30.1267i	0.702337	−	1.19273i
$639$	4.15654	+	12.7925i	0.164430	+	0.506064i
$640$		0			0
$641$	−12.1688	+	37.4516i	−0.480637	+	1.47925i	0.357564	+	0.933889i	$0.383607\pi$
$641$	−12.1688	+	37.4516i	−0.480637	+	1.47925i	−0.838201	+	0.545361i	$0.816393\pi$
$642$	20.6409	+	23.3235i	0.814633	+	0.920507i
$643$	−15.6623			−0.617660			−0.308830	−	0.951117i	$-0.599937\pi$
$643$	−15.6623			−0.617660			−0.308830	+	0.951117i	$0.599937\pi$
$644$	2.48850	+	4.48632i	0.0980608	+	0.176786i
$645$		0			0
$646$	−32.5610	+	14.1635i	−1.28110	+	0.557256i
$647$	−19.5134	−	26.8579i	−0.767152	−	1.05589i	−0.996585	−	0.0825693i	$-0.973687\pi$
$647$	−19.5134	−	26.8579i	−0.767152	−	1.05589i	0.229434	−	0.973324i	$-0.426313\pi$
$648$	16.6711	−	47.1426i	0.654901	−	1.85194i
$649$	−5.10673			−0.200457
$650$		0			0
$651$		−	5.33479i		−	0.209087i
$652$	−4.77319	+	38.9677i	−0.186933	+	1.52609i
$653$	3.13976	−	2.28117i	0.122868	−	0.0892690i	−0.524654	−	0.851316i	$-0.675805\pi$
$653$	3.13976	−	2.28117i	0.122868	−	0.0892690i	0.647522	+	0.762047i	$0.275805\pi$
$654$	−4.79090	−	11.0139i	−0.187339	−	0.430680i
$655$		0			0
$656$	−1.79411	−	25.4454i	−0.0700482	−	0.993477i
$657$			29.0471i			1.13323i
$658$	−5.86003	−	6.62163i	−0.228448	−	0.258138i
$659$	38.7539	+	12.5919i	1.50964	+	0.490511i	0.942811	−	0.333327i	$-0.108171\pi$
$659$	38.7539	+	12.5919i	1.50964	+	0.490511i	0.566826	+	0.823838i	$0.308171\pi$
$660$		0			0
$661$	35.9253	−	11.6728i	1.39733	−	0.454020i	0.489004	−	0.872282i	$-0.337360\pi$
$661$	35.9253	−	11.6728i	1.39733	−	0.454020i	0.908327	+	0.418261i	$0.137360\pi$
$662$	8.81355	+	5.18986i	0.342548	+	0.201710i
$663$	15.1425	+	4.92009i	0.588085	+	0.191081i
$664$	8.92708	−	25.2441i	0.346438	−	0.979661i
$665$		0			0
$666$	−34.5506	+	58.6746i	−1.33881	+	2.27359i
$667$	−10.9844	−	7.98063i	−0.425318	−	0.309011i
$668$	14.2273	−	30.5336i	0.550471	−	1.18138i
$669$	−2.87936	+	3.96311i	−0.111323	+	0.153223i
$670$		0			0
$671$	−49.7762	+	36.1645i	−1.92159	+	1.39612i
$672$	9.31503	−	18.7169i	0.359335	−	0.722021i
$673$	−1.57662	+	0.512274i	−0.0607742	+	0.0197467i	−0.339246	−	0.940698i	$-0.610172\pi$
$673$	−1.57662	+	0.512274i	−0.0607742	+	0.0197467i	0.278472	+	0.960444i	$0.410172\pi$
$674$	2.78836	−	12.5861i	0.107404	−	0.484798i
$675$		0			0
$676$	−22.0687	−	10.2831i	−0.848798	−	0.395502i
$677$	0.0701106	+	0.215778i	0.00269457	+	0.00829304i	0.952395	−	0.304868i	$-0.0986122\pi$
$677$	0.0701106	+	0.215778i	0.00269457	+	0.00829304i	−0.949700	+	0.313161i	$0.898612\pi$
$678$	−8.10371	−	18.6299i	−0.311221	−	0.715477i
$679$	0.277355	−	0.201510i	0.0106439	−	0.00773325i
$680$		0			0
$681$	23.4497	+	17.0372i	0.898596	+	0.652868i
$682$	1.75380	−	7.91628i	0.0671563	−	0.303130i
$683$	−24.0637	−	17.4833i	−0.920773	−	0.668981i	0.0229435	−	0.999737i	$-0.492696\pi$
$683$	−24.0637	−	17.4833i	−0.920773	−	0.668981i	−0.943716	+	0.330756i	$0.892696\pi$
$684$	−45.3500	−	42.2650i	−1.73400	−	1.61604i
$685$		0			0
$686$	−20.8851	+	2.01405i	−0.797396	+	0.0768969i
$687$	33.7717	+	10.9731i	1.28847	+	0.418649i
$688$	10.9786	−	4.44303i	0.418555	−	0.169389i
$689$	3.67089	+	11.2978i	0.139850	+	0.430413i
$690$		0			0
$691$	−29.9436	−	9.72925i	−1.13911	−	0.370118i	−0.322077	−	0.946714i	$-0.604381\pi$
$691$	−29.9436	−	9.72925i	−1.13911	−	0.370118i	−0.817030	+	0.576595i	$0.804381\pi$
$692$	−9.87723	−	17.8069i	−0.375476	−	0.676915i
$693$	32.1269			1.22040
$694$	9.58868	+	10.8349i	0.363981	+	0.411286i
$695$		0			0
$696$	−1.42439	+	55.3122i	−0.0539913	+	2.09660i
$697$	20.8859	+	28.7469i	0.791108	+	1.08887i
$698$	−6.70671	+	0.646761i	−0.253853	+	0.0244803i
$699$			39.0712i			1.47781i
$700$		0			0
$701$			2.30506i			0.0870611i	0.999052	+	0.0435305i	$0.0138606\pi$
$701$			2.30506i			0.0870611i	−0.999052	+	0.0435305i	$0.986139\pi$
$702$	1.50451	+	15.6012i	0.0567839	+	0.588831i
$703$	18.5398	+	25.5178i	0.699240	+	0.962422i
$704$	19.9757	−	24.7117i	0.752862	−	0.931358i
$705$		0			0
$706$	19.3337	−	17.1100i	0.727635	−	0.643945i
$707$	9.22096			0.346790
$708$	7.06746	−	3.92023i	0.265611	−	0.147331i
$709$	25.4956	+	8.28402i	0.957508	+	0.311113i	0.745763	−	0.666212i	$-0.232085\pi$
$709$	25.4956	+	8.28402i	0.957508	+	0.311113i	0.211745	+	0.977325i	$0.432085\pi$
$710$		0			0
$711$	−5.86429	−	18.0484i	−0.219928	−	0.676869i
$712$	−6.08488	+	4.18591i	−0.228040	+	0.156874i
$713$	−2.99472	−	0.973045i	−0.112153	−	0.0364408i
$714$	2.79550	+	28.9884i	0.104619	+	1.08486i
$715$		0			0
$716$	22.0961	+	20.5930i	0.825770	+	0.769597i
$717$	70.2688	+	51.0533i	2.62424	+	1.90662i
$718$	−25.2212	−	5.58759i	−0.941248	−	0.208527i
$719$	12.3313	+	8.95922i	0.459880	+	0.334123i	0.793484	−	0.608591i	$-0.208265\pi$
$719$	12.3313	+	8.95922i	0.459880	+	0.334123i	−0.333604	+	0.942713i	$0.608265\pi$
$720$		0			0
$721$	−12.5269	+	9.10133i	−0.466526	+	0.338951i
$722$	−1.69281	+	0.736344i	−0.0629997	+	0.0274039i
$723$	−4.16038	−	12.8043i	−0.154726	−	0.476198i
$724$	−15.9831	+	34.3017i	−0.594007	+	1.27481i
$725$		0			0
$726$	20.7285	+	4.59226i	0.769308	+	0.170435i
$727$	2.11778	−	0.688107i	0.0785440	−	0.0255205i	−0.269481	−	0.963006i	$-0.586852\pi$
$727$	2.11778	−	0.688107i	0.0785440	−	0.0255205i	0.348025	+	0.937485i	$0.386852\pi$
$728$	−0.0778413	+	3.02276i	−0.00288499	+	0.112031i
$729$	−5.38937	+	3.91560i	−0.199606	+	0.145022i
$730$		0			0
$731$	−9.69724	+	13.3471i	−0.358665	+	0.493661i
$732$	41.1258	−	88.2612i	1.52005	−	3.26223i
$733$	40.0434	+	29.0933i	1.47904	+	1.07458i	0.977865	+	0.209237i	$0.0670979\pi$
$733$	40.0434	+	29.0933i	1.47904	+	1.07458i	0.501173	+	0.865347i	$0.332902\pi$
$734$	18.3485	+	10.8045i	0.677254	+	0.398801i
$735$		0			0
$736$	−8.80787	−	8.64296i	−0.324662	−	0.318584i
$737$	11.4703	+	3.72692i	0.422513	+	0.137283i
$738$	−31.4776	+	53.4560i	−1.15871	+	1.96774i
$739$	17.2361	−	5.60033i	0.634039	−	0.206012i	0.0256753	−	0.999670i	$-0.491826\pi$
$739$	17.2361	−	5.60033i	0.634039	−	0.206012i	0.608363	+	0.793659i	$0.291826\pi$
$740$		0			0
$741$	12.2460	+	3.97897i	0.449869	+	0.146171i
$742$	−16.2717	+	14.4002i	−0.597352	+	0.528647i
$743$		−	15.5632i		−	0.570959i	−0.958385	−	0.285479i	$-0.907847\pi$
$743$		−	15.5632i		−	0.570959i	0.958385	−	0.285479i	$-0.0921528\pi$
$744$	3.64984	+	12.3021i	0.133810	+	0.451016i
$745$		0			0
$746$	−0.919452	+	0.399947i	−0.0336635	+	0.0146431i
$747$	−52.6813	+	38.2752i	−1.92751	+	1.40042i
$748$	−5.38162	+	43.9348i	−0.196771	+	1.60642i
$749$		−	8.23944i		−	0.301062i
$750$		0			0
$751$	41.5803			1.51729			0.758643	−	0.651507i	$-0.225863\pi$
$751$	41.5803			1.51729			0.758643	+	0.651507i	$0.225863\pi$
$752$	18.0435	+	11.2603i	0.657980	+	0.410622i
$753$	−24.7554	−	34.0729i	−0.902137	−	1.24169i
$754$	−3.19205	−	7.33830i	−0.116248	−	0.267245i
$755$		0			0
$756$	−25.0704	+	13.9063i	−0.911803	+	0.505766i
$757$	−1.83755			−0.0667870			−0.0333935	−	0.999442i	$-0.510631\pi$
$757$	−1.83755			−0.0667870			−0.0333935	+	0.999442i	$0.510631\pi$
$758$	−19.4969	+	17.2544i	−0.708158	+	0.626708i
$759$	8.41550	−	25.9003i	0.305463	−	0.940120i
$760$		0			0
$761$	−9.18935	−	28.2819i	−0.333114	−	1.02522i	−0.967644	−	0.252320i	$-0.918806\pi$
$761$	−9.18935	−	28.2819i	−0.333114	−	1.02522i	0.634530	−	0.772898i	$-0.281194\pi$
$762$	33.0555	+	19.4647i	1.19747	+	0.705132i
$763$	−0.981880	+	3.02192i	−0.0355464	+	0.109401i
$764$	0.544920	−	4.44866i	0.0197145	−	0.160947i
$765$		0			0
$766$	−21.8708	−	12.8786i	−0.790223	−	0.465323i
$767$	−0.687057	+	0.945653i	−0.0248082	+	0.0341455i
$768$	−8.67516	+	49.5344i	−0.313038	+	1.78742i
$769$	7.63237	+	5.54524i	0.275230	+	0.199966i	0.716834	−	0.697244i	$-0.245590\pi$
$769$	7.63237	+	5.54524i	0.275230	+	0.199966i	−0.441604	+	0.897210i	$0.645590\pi$
$770$		0			0
$771$	−14.4450	−	19.8818i	−0.520222	−	0.716025i
$772$	8.67378	+	44.5539i	0.312176	+	1.60353i
$773$	7.49873	+	23.0787i	0.269711	+	0.830084i	0.990571	+	0.137003i	$0.0437471\pi$
$773$	7.49873	+	23.0787i	0.269711	+	0.830084i	−0.720860	+	0.693081i	$0.756253\pi$
$774$	−28.1210	−	6.23000i	−1.01079	−	0.223933i
$775$		0			0
$776$	−0.501718	+	0.654439i	−0.0180106	+	0.0234930i
$777$	24.6036	−	7.99420i	0.882649	−	0.286790i
$778$	13.4687	+	30.9637i	0.482877	+	1.11010i
$779$	16.8908	+	23.2482i	0.605176	+	0.832953i
$780$		0			0
$781$	4.56537	−	6.28370i	0.163362	−	0.224848i
$782$	16.7827	+	3.71810i	0.600150	+	0.132959i
$783$	44.5974	−	61.3830i	1.59378	−	2.19365i
$784$	20.8282	−	8.42915i	0.743863	−	0.301041i
$785$		0			0
$786$	38.4828	−	3.71109i	1.37264	−	0.132370i
$787$	11.5135	−	35.4350i	0.410413	−	1.26312i	−0.505877	−	0.862606i	$-0.668831\pi$
$787$	11.5135	−	35.4350i	0.410413	−	1.26312i	0.916290	−	0.400515i	$-0.131169\pi$
$788$	17.7026	−	18.9948i	0.630631	−	0.676661i
$789$	−82.0264	+	26.6520i	−2.92022	+	0.948837i
$790$		0			0
$791$	−1.66083	+	5.11151i	−0.0590524	+	0.181745i
$792$	−74.0848	+	21.9799i	−2.63249	+	0.781021i
$793$			14.0830i			0.500103i
$794$	−1.35316	−	1.52903i	−0.0480220	−	0.0542632i
$795$		0			0
$796$	35.7619	−	6.96214i	1.26755	−	0.246767i
$797$	4.03520	−	2.93174i	0.142934	−	0.103848i	−0.514020	−	0.857778i	$-0.671844\pi$
$797$	4.03520	−	2.93174i	0.142934	−	0.103848i	0.656954	+	0.753930i	$0.271844\pi$
$798$	2.26077	+	23.4435i	0.0800305	+	0.829890i
$799$	−29.6272			−1.04814
$800$		0			0
$801$	17.9614			0.634635
$802$	3.53875	+	36.6957i	0.124958	+	1.29577i
$803$	13.5696	−	9.85892i	0.478862	−	0.347914i
$804$	−18.7353	+	3.64740i	−0.660744	+	0.128634i
$805$		0			0
$806$	−1.22996	−	1.38982i	−0.0433237	−	0.0489542i
$807$		−	67.0587i		−	2.36058i
$808$	−21.2636	+	6.30860i	−0.748051	+	0.221936i
$809$	−2.74204	+	8.43914i	−0.0964051	+	0.296704i	−0.987617	−	0.156882i	$-0.949856\pi$
$809$	−2.74204	+	8.43914i	−0.0964051	+	0.296704i	0.891212	+	0.453587i	$0.149856\pi$
$810$		0			0
$811$	20.7338	−	6.73681i	0.728062	−	0.236562i	0.0785467	−	0.996910i	$-0.474972\pi$
$811$	20.7338	−	6.73681i	0.728062	−	0.236562i	0.649515	+	0.760349i	$0.274972\pi$
$812$	9.97969	−	10.7081i	0.350219	−	0.375781i
$813$	−1.03769	+	3.19368i	−0.0363934	+	0.112007i
$814$	39.1373	−	3.77421i	1.37176	−	0.132286i
$815$		0			0
$816$	−26.2791	−	64.9349i	−0.919953	−	2.27318i
$817$	−7.84235	+	10.7941i	−0.274369	+	0.377637i
$818$	−1.39675	−	0.309440i	−0.0488362	−	0.0108193i
$819$	4.32233	−	5.94918i	0.151035	−	0.207881i
$820$		0			0
$821$	−21.5298	−	29.6332i	−0.751394	−	1.03420i	−0.997881	−	0.0650589i	$-0.979276\pi$
$821$	−21.5298	−	29.6332i	−0.751394	−	1.03420i	0.246488	−	0.969146i	$-0.420724\pi$
$822$	−6.46031	−	14.8518i	−0.225329	−	0.518017i
$823$	5.63427	−	1.83068i	0.196398	−	0.0638136i	−0.209166	−	0.977880i	$-0.567075\pi$
$823$	5.63427	−	1.83068i	0.196398	−	0.0638136i	0.405564	+	0.914066i	$0.367075\pi$
$824$	22.6604	−	29.5581i	0.789412	−	1.02971i
$825$		0			0
$826$	−2.08743	−	0.462456i	−0.0726311	−	0.0160909i
$827$	4.70692	+	14.4864i	0.163676	+	0.503742i	0.998936	−	0.0461123i	$-0.0146832\pi$
$827$	4.70692	+	14.4864i	0.163676	+	0.503742i	−0.835261	+	0.549854i	$0.814683\pi$
$828$	5.73479	+	29.4574i	0.199298	+	1.02372i
$829$	−25.2244	−	34.7183i	−0.876078	−	1.20582i	−0.977492	−	0.210974i	$-0.932337\pi$
$829$	−25.2244	−	34.7183i	−0.876078	−	1.20582i	0.101414	−	0.994844i	$-0.467663\pi$
$830$		0			0
$831$	−45.1419	−	32.7975i	−1.56595	−	1.13773i
$832$	−1.88854	−	7.02376i	−0.0654735	−	0.243505i
$833$	−18.3972	+	25.3216i	−0.637427	+	0.877343i
$834$	53.4952	+	31.5007i	1.85239	+	1.09078i
$835$		0			0
$836$	−4.35222	+	35.5309i	−0.150525	+	1.22886i
$837$	5.43757	−	16.7351i	0.187950	−	0.578450i
$838$	−40.7801	−	24.0134i	−1.40872	−	0.829528i
$839$	14.0891	+	43.3617i	0.486409	+	1.49701i	0.829930	+	0.557868i	$0.188380\pi$
$839$	14.0891	+	43.3617i	0.486409	+	1.49701i	−0.343521	+	0.939145i	$0.611620\pi$
$840$		0			0
$841$	−3.00946	+	9.26218i	−0.103775	+	0.319385i
$842$	29.1338	−	25.7829i	1.00402	−	0.888539i
$843$	34.1050			1.17464
$844$	−3.07294	+	1.70452i	−0.105775	+	0.0586720i
$845$		0			0
$846$	−20.6320	−	47.4315i	−0.709342	−	1.63073i
$847$	−3.30138	−	4.54396i	−0.113437	−	0.156132i
$848$	27.6706	−	44.3393i	0.950214	−	1.52262i
$849$	−72.9986			−2.50531
$850$		0			0
$851$		−	15.2695i		−	0.523433i
$852$	−1.49451	+	12.2010i	−0.0512011	+	0.417999i
$853$	39.8951	−	28.9855i	1.36598	−	0.992445i	0.367944	−	0.929848i	$-0.380062\pi$
$853$	39.8951	−	28.9855i	1.36598	−	0.992445i	0.998039	−	0.0625971i	$-0.0199383\pi$
$854$	−23.6216	+	10.2750i	−0.808315	+	0.351604i
$855$		0			0
$856$	5.63709	+	19.0002i	0.192672	+	0.649414i
$857$		−	57.0345i		−	1.94826i	−0.225989	−	0.974130i	$-0.572561\pi$
$857$		−	57.0345i		−	1.94826i	0.225989	−	0.974130i	$-0.427439\pi$
$858$	12.0200	−	10.6375i	0.410356	−	0.363159i
$859$	−20.6564	−	6.71166i	−0.704786	−	0.228999i	−0.0653714	−	0.997861i	$-0.520823\pi$
$859$	−20.6564	−	6.71166i	−0.704786	−	0.228999i	−0.639415	+	0.768862i	$0.720823\pi$
$860$		0			0
$861$	22.4153	−	7.28318i	0.763912	−	0.248210i
$862$	19.1899	−	32.5887i	0.653610	−	1.10998i
$863$	17.9981	+	5.84794i	0.612663	+	0.199066i	0.598880	−	0.800839i	$-0.295613\pi$
$863$	17.9981	+	5.84794i	0.612663	+	0.199066i	0.0137830	+	0.999905i	$0.495613\pi$
$864$	48.2986	−	49.2201i	1.64315	−	1.67450i
$865$		0			0
$866$	−25.2928	−	14.8937i	−0.859486	−	0.506108i
$867$	35.7171	+	25.9500i	1.21302	+	0.881307i
$868$	1.43377	−	3.07705i	0.0486653	−	0.104442i
$869$	−6.44110	+	8.86542i	−0.218499	+	0.300739i
$870$		0			0
$871$	2.23335	−	1.62262i	0.0756742	−	0.0549805i
$872$	0.196752	−	7.64033i	0.00666286	−	0.258734i
$873$	1.90729	−	0.619716i	0.0645520	−	0.0209742i
$874$	13.5725	+	3.00690i	0.459098	+	0.101710i
$875$		0			0
$876$	−11.2114	+	24.0611i	−0.378799	+	0.812950i
$877$	−4.30447	−	13.2478i	−0.145352	−	0.447347i	0.851704	−	0.524023i	$-0.175569\pi$
$877$	−4.30447	−	13.2478i	−0.145352	−	0.447347i	−0.997056	+	0.0766761i	$0.975569\pi$
$878$	0.392807	−	0.170865i	0.0132566	−	0.00576640i
$879$	59.9157	−	43.5313i	2.02091	−	1.46827i
$880$		0			0
$881$	−32.7294	−	23.7793i	−1.10268	−	0.801145i	−0.121186	−	0.992630i	$-0.538670\pi$
$881$	−32.7294	−	23.7793i	−1.10268	−	0.801145i	−0.981496	+	0.191485i	$0.938670\pi$
$882$	−53.3501	−	11.8193i	−1.79639	−	0.397977i
$883$	3.31224	+	2.40648i	0.111466	+	0.0809845i	0.642122	−	0.766603i	$-0.278054\pi$
$883$	3.31224	+	2.40648i	0.111466	+	0.0809845i	−0.530656	+	0.847587i	$0.678054\pi$
$884$	7.41171	+	6.90753i	0.249283	+	0.232325i
$885$		0			0
$886$	4.60255	+	47.7270i	0.154626	+	1.60342i
$887$	−5.39637	−	1.75339i	−0.181192	−	0.0588730i	0.217016	−	0.976168i	$-0.430368\pi$
$887$	−5.39637	−	1.75339i	−0.181192	−	0.0588730i	−0.398208	+	0.917295i	$0.630368\pi$
$888$	−51.2668	+	35.2675i	−1.72040	+	1.18350i
$889$	−3.13597	−	9.65152i	−0.105177	−	0.323701i
$890$		0			0
$891$	66.7832	+	21.6992i	2.23732	+	0.726950i
$892$	−2.72591	+	1.51202i	−0.0912701	+	0.0506263i
$893$	−23.9601			−0.801795
$894$	−8.69976	+	7.69914i	−0.290963	+	0.257498i
$895$		0			0
$896$	10.4031	−	8.29224i	0.347545	−	0.277024i
$897$	−3.66394	−	5.04297i	−0.122335	−	0.168380i
$898$	1.71111	+	17.7436i	0.0571004	+	0.592113i
$899$			8.98418i			0.299639i
$900$		0			0
$901$			72.8046i			2.42547i
$902$	35.6564	−	3.43852i	1.18723	−	0.114490i
$903$	6.43211	+	8.85304i	0.214047	+	0.294611i
$904$	0.332802	−	12.9235i	0.0110688	−	0.429828i
$905$		0			0
$906$	31.2776	+	35.3426i	1.03913	+	1.17418i
$907$	−49.8362			−1.65478			−0.827392	−	0.561625i	$-0.810176\pi$
$907$	−49.8362			−1.65478			−0.827392	+	0.561625i	$0.810176\pi$
$908$	8.94666	+	16.1292i	0.296905	+	0.535266i
$909$	51.2997	+	16.6683i	1.70150	+	0.552852i
$910$		0			0
$911$	1.08071	+	3.32610i	0.0358057	+	0.110199i	0.967362	−	0.253399i	$-0.0815485\pi$
$911$	1.08071	+	3.32610i	0.0358057	+	0.110199i	−0.931556	+	0.363597i	$0.881548\pi$
$912$	−21.2524	−	52.5141i	−0.703738	−	1.73892i
$913$	35.7613	+	11.6196i	1.18353	+	0.384551i
$914$	−3.64497	+	0.351503i	−0.120565	+	0.0116267i
$915$		0			0
$916$	16.5300	+	15.4056i	0.546168	+	0.509015i
$917$	−8.27442	−	6.01172i	−0.273246	−	0.198525i
$918$	−20.7775	+	93.7853i	−0.685759	+	3.09538i
$919$	−35.2395	−	25.6030i	−1.16244	−	0.844564i	−0.172357	−	0.985034i	$-0.555138\pi$
$919$	−35.2395	−	25.6030i	−1.16244	−	0.844564i	−0.990085	+	0.140471i	$0.955138\pi$
$920$		0			0
$921$	−74.2277	+	53.9296i	−2.44589	+	1.77704i
$922$	3.85254	+	8.85674i	0.126877	+	0.291681i
$923$	−0.549378	−	1.69081i	−0.0180830	−	0.0556538i
$924$	26.6123	+	12.4001i	0.875479	+	0.407935i
$925$		0			0
$926$	−6.67486	+	30.1290i	−0.219349	+	0.990099i
$927$	−86.1439	+	27.9899i	−2.82934	+	0.919307i
$928$	−15.6872	+	31.5207i	−0.514957	+	1.03472i
$929$	−20.6493	+	15.0026i	−0.677483	+	0.492220i	−0.872522	−	0.488576i	$-0.837517\pi$
$929$	−20.6493	+	15.0026i	−0.677483	+	0.492220i	0.195039	+	0.980795i	$0.437517\pi$
$930$		0			0
$931$	−14.8782	+	20.4781i	−0.487614	+	0.671143i
$932$	−10.5007	+	22.5358i	−0.343962	+	0.738186i
$933$	−2.49920	−	1.81577i	−0.0818201	−	0.0594458i
$934$	2.15644	−	3.66212i	0.0705608	−	0.119828i
$935$		0			0
$936$	−5.89715	+	16.6760i	−0.192754	+	0.545073i
$937$	−3.76427	−	1.22309i	−0.122973	−	0.0399565i	0.246884	−	0.969045i	$-0.420593\pi$
$937$	−3.76427	−	1.22309i	−0.122973	−	0.0399565i	−0.369857	+	0.929089i	$0.620593\pi$
$938$	4.35111	+	2.56215i	0.142069	+	0.0836572i
$939$	−28.6403	+	9.30581i	−0.934642	+	0.303684i
$940$		0			0
$941$	−7.54079	−	2.45015i	−0.245823	−	0.0798727i	0.183514	−	0.983017i	$-0.441253\pi$
$941$	−7.54079	−	2.45015i	−0.245823	−	0.0798727i	−0.429337	+	0.903144i	$0.641253\pi$
$942$	−11.4990	−	12.9935i	−0.374658	−	0.423350i
$943$		−	13.9114i		−	0.453018i
$944$	5.13003	−	0.361709i	0.166968	−	0.0117726i
$945$		0			0
$946$	6.63418	+	15.2515i	0.215696	+	0.495870i
$947$	0.630350	−	0.457976i	0.0204836	−	0.0148822i	−0.577496	−	0.816393i	$-0.695970\pi$
$947$	0.630350	−	0.457976i	0.0204836	−	0.0148822i	0.597980	+	0.801511i	$0.295970\pi$
$948$	2.10854	−	17.2139i	0.0684824	−	0.559081i
$949$		−	3.83921i		−	0.124626i
$950$		0			0
$951$	−57.8664			−1.87645
$952$	−6.17846	+	17.4715i	−0.200245	+	0.566255i
$953$	−6.29429	−	8.66334i	−0.203892	−	0.280633i	0.694810	−	0.719194i	$-0.255489\pi$
$953$	−6.29429	−	8.66334i	−0.203892	−	0.280633i	−0.898702	+	0.438560i	$0.855489\pi$
$954$	−116.556	+	50.7000i	−3.77364	+	1.64147i
$955$		0			0
$956$	26.8093	+	48.3323i	0.867075	+	1.56318i
$957$	−77.7008			−2.51171
$958$	−17.8079	−	20.1224i	−0.575349	−	0.650124i
$959$	−1.32402	+	4.07492i	−0.0427549	+	0.131586i
$960$		0			0
$961$	−8.93566	−	27.5011i	−0.288247	−	0.887134i
$962$	4.56662	−	7.75514i	0.147234	−	0.250036i
$963$	14.8940	−	45.8391i	0.479953	−	1.47714i
$964$	1.04161	−	8.50353i	0.0335479	−	0.273880i
$965$		0			0
$966$	5.78542	−	9.82494i	0.186143	−	0.316112i
$967$	−5.37219	+	7.39419i	−0.172758	+	0.237781i	−0.886612	−	0.462513i	$-0.846948\pi$
$967$	−5.37219	+	7.39419i	−0.172758	+	0.237781i	0.713854	+	0.700294i	$0.246948\pi$
$968$	10.7218	+	8.21973i	0.344612	+	0.264192i
$969$	63.8435	+	46.3850i	2.05095	+	1.49010i
$970$		0			0
$971$	15.2665	+	21.0125i	0.489924	+	0.674323i	0.980374	−	0.197147i	$-0.0631675\pi$
$971$	15.2665	+	21.0125i	0.489924	+	0.674323i	−0.490450	+	0.871469i	$0.663167\pi$
$972$	−37.2879	+	7.25922i	−1.19601	+	0.232840i
$973$	−5.07508	−	15.6195i	−0.162700	−	0.500738i
$974$	0.580675	−	2.62105i	0.0186060	−	0.0839839i
$975$		0			0
$976$	47.4419	−	39.8552i	1.51858	−	1.27574i
$977$	−29.0332	+	9.43346i	−0.928855	+	0.301803i	−0.734094	−	0.679048i	$-0.762393\pi$
$977$	−29.0332	+	9.43346i	−0.928855	+	0.301803i	−0.194760	+	0.980851i	$0.562393\pi$
$978$	80.0094	−	34.8028i	2.55842	−	1.11287i
$979$	−6.09631	−	8.39085i	−0.194839	−	0.268173i
$980$		0			0
$981$	−10.9251	+	15.0372i	−0.348813	+	0.480100i
$982$	−9.44799	+	42.6463i	−0.301498	+	1.36090i
$983$	23.5163	−	32.3674i	0.750052	−	1.03236i	−0.247924	−	0.968779i	$-0.579748\pi$
$983$	23.5163	−	32.3674i	0.750052	−	1.03236i	0.997977	−	0.0635791i	$-0.0202515\pi$
$984$	−46.7070	+	32.1307i	−1.48897	+	1.02429i
$985$		0			0
$986$	−4.70782	−	48.8186i	−0.149928	−	1.55470i
$987$	−6.07265	+	18.6897i	−0.193295	+	0.594900i
$988$	5.99400	+	5.58625i	0.190694	+	0.177722i
$989$	6.14291	−	1.99595i	0.195333	−	0.0634676i
$990$		0			0
$991$	14.8786	−	45.7916i	0.472634	−	1.45462i	−0.376488	−	0.926422i	$-0.622868\pi$
$991$	14.8786	−	45.7916i	0.472634	−	1.45462i	0.849122	−	0.528197i	$-0.177132\pi$
$992$	−1.20109	+	8.07663i	−0.0381347	+	0.256433i
$993$		−	22.7314i		−	0.721358i
$994$	2.43519	−	2.15510i	0.0772395	−	0.0683557i
$995$		0			0
$996$	−58.4118	+	11.3716i	−1.85085	+	0.360324i
$997$	0.969621	−	0.704471i	0.0307082	−	0.0223108i	−0.572325	−	0.820027i	$-0.693959\pi$
$997$	0.969621	−	0.704471i	0.0307082	−	0.0223108i	0.603033	+	0.797716i	$0.293959\pi$
$998$	−14.9141	+	1.43825i	−0.472099	+	0.0455269i
$999$	85.3292			2.69970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.349.13		112
5.2	odd	4		1000.2.t.b.901.55		224
5.3	odd	4		1000.2.t.b.901.2		224
5.4	even	2		200.2.o.a.69.16	yes	112
8.5	even	2	inner	1000.2.o.a.349.19		112
20.19	odd	2		800.2.be.a.369.2		112
25.3	odd	20		1000.2.t.b.101.47		224
25.4	even	10	inner	1000.2.o.a.149.19		112
25.21	even	5		200.2.o.a.29.10	✓	112
25.22	odd	20		1000.2.t.b.101.10		224
40.13	odd	4		1000.2.t.b.901.47		224
40.19	odd	2		800.2.be.a.369.27		112
40.29	even	2		200.2.o.a.69.10	yes	112
40.37	odd	4		1000.2.t.b.901.10		224
100.71	odd	10		800.2.be.a.529.27		112
200.21	even	10		200.2.o.a.29.16	yes	112
200.29	even	10	inner	1000.2.o.a.149.13		112
200.53	odd	20		1000.2.t.b.101.2		224
200.171	odd	10		800.2.be.a.529.2		112
200.197	odd	20		1000.2.t.b.101.55		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.10	✓	112	25.21	even	5
200.2.o.a.29.16	yes	112	200.21	even	10
200.2.o.a.69.10	yes	112	40.29	even	2
200.2.o.a.69.16	yes	112	5.4	even	2
800.2.be.a.369.2		112	20.19	odd	2
800.2.be.a.369.27		112	40.19	odd	2
800.2.be.a.529.2		112	200.171	odd	10
800.2.be.a.529.27		112	100.71	odd	10
1000.2.o.a.149.13		112	200.29	even	10	inner
1000.2.o.a.149.19		112	25.4	even	10	inner
1000.2.o.a.349.13		112	1.1	even	1	trivial
1000.2.o.a.349.19		112	8.5	even	2	inner
1000.2.t.b.101.2		224	200.53	odd	20
1000.2.t.b.101.10		224	25.22	odd	20
1000.2.t.b.101.47		224	25.3	odd	20
1000.2.t.b.101.55		224	200.197	odd	20
1000.2.t.b.901.2		224	5.3	odd	4
1000.2.t.b.901.10		224	40.37	odd	4
1000.2.t.b.901.47		224	40.13	odd	4
1000.2.t.b.901.55		224	5.2	odd	4

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.135750 - 1.40768i) q^{2} +(-2.54275 + 1.84742i) q^{3} +(-1.96314 + 0.382186i) q^{4} +(2.94576 + 3.32861i) q^{6} -1.17589i q^{7} +(0.804493 + 2.71160i) q^{8} +(2.12559 - 6.54190i) q^{9} +O(q^{10})\)	\(q+(-0.135750 - 1.40768i) q^{2} +(-2.54275 + 1.84742i) q^{3} +(-1.96314 + 0.382186i) q^{4} +(2.94576 + 3.32861i) q^{6} -1.17589i q^{7} +(0.804493 + 2.71160i) q^{8} +(2.12559 - 6.54190i) q^{9} +(-3.77756 + 1.22741i) q^{11} +(4.28574 - 4.59855i) q^{12} +(-0.280944 + 0.864656i) q^{13} +(-1.65528 + 0.159626i) q^{14} +(3.70787 - 1.50057i) q^{16} +(-3.27511 + 4.50780i) q^{17} +(-9.49747 - 2.10410i) q^{18} +(-2.64864 + 3.64555i) q^{19} +(2.17235 + 2.98999i) q^{21} +(2.24060 + 5.15099i) q^{22} +(2.07468 - 0.674105i) q^{23} +(-7.05510 - 5.40870i) q^{24} +(1.25530 + 0.278103i) q^{26} +(3.76703 + 11.5937i) q^{27} +(0.449407 + 2.30843i) q^{28} +(-3.65841 - 5.03536i) q^{29} +(-1.16778 - 0.848445i) q^{31} +(-2.61567 - 5.01580i) q^{32} +(7.33789 - 10.0997i) q^{33} +(6.79015 + 3.99838i) q^{34} +(-1.67262 + 13.6551i) q^{36} +(2.16303 - 6.65712i) q^{37} +(5.49133 + 3.23357i) q^{38} +(-0.883011 - 2.71763i) q^{39} +(1.97065 - 6.06503i) q^{41} +(3.91406 - 3.46388i) q^{42} +2.96089 q^{43} +(6.94681 - 3.85330i) q^{44} +(-1.23056 - 2.82899i) q^{46} +(3.12538 + 4.30172i) q^{47} +(-6.65601 + 10.6656i) q^{48} +5.61729 q^{49} -17.5127i q^{51} +(0.221074 - 1.80482i) q^{52} +(10.5708 - 7.68016i) q^{53} +(15.8089 - 6.87664i) q^{54} +(3.18854 - 0.945992i) q^{56} -14.1629i q^{57} +(-6.59157 + 5.83343i) q^{58} +(1.22277 + 0.397301i) q^{59} +(14.7321 - 4.78675i) q^{61} +(-1.03582 + 1.75905i) q^{62} +(-7.69253 - 2.49945i) q^{63} +(-6.70558 + 4.36293i) q^{64} +(-15.2133 - 8.95838i) q^{66} +(-2.45652 - 1.78477i) q^{67} +(4.70669 - 10.1012i) q^{68} +(-4.03005 + 5.54689i) q^{69} +(-1.58201 + 1.14940i) q^{71} +(19.4491 + 0.500848i) q^{72} +(-4.01616 + 1.30493i) q^{73} +(-9.66475 - 2.14116i) q^{74} +(3.80639 - 8.16901i) q^{76} +(1.44329 + 4.44199i) q^{77} +(-3.70569 + 1.61192i) q^{78} +(2.23200 - 1.62164i) q^{79} +(-14.3025 - 10.3914i) q^{81} +(-8.80515 - 1.95072i) q^{82} +(-7.65878 - 5.56443i) q^{83} +(-5.40738 - 5.03954i) q^{84} +(-0.401941 - 4.16800i) q^{86} +(18.6049 + 6.04509i) q^{87} +(-6.36726 - 9.25582i) q^{88} +(0.806910 + 2.48341i) q^{89} +(1.01674 + 0.330358i) q^{91} +(-3.81527 + 2.11628i) q^{92} +4.53682 q^{93} +(5.63118 - 4.98350i) q^{94} +(15.9173 + 7.92171i) q^{96} +(0.171369 + 0.235869i) q^{97} +(-0.762547 - 7.90737i) q^{98} +27.3214i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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