LMFDB - Embedded newform 1000.2.o.a.349.19

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			349.19
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.717591 + 1.21863i) q^{2} +(2.54275 - 1.84742i) q^{3} +(-0.970125 + 1.74896i) q^{4} +(4.07598 + 1.77299i) q^{6} -1.17589i q^{7} +(-2.82749 + 0.0728129i) q^{8} +(2.12559 - 6.54190i) q^{9} +O(q^{10})$	\(q+(0.717591 + 1.21863i) q^{2} +(2.54275 - 1.84742i) q^{3} +(-0.970125 + 1.74896i) q^{4} +(4.07598 + 1.77299i) q^{6} -1.17589i q^{7} +(-2.82749 + 0.0728129i) q^{8} +(2.12559 - 6.54190i) q^{9} +(3.77756 - 1.22741i) q^{11} +(0.764270 + 6.23940i) q^{12} +(0.280944 - 0.864656i) q^{13} +(1.43297 - 0.843806i) q^{14} +(-2.11771 - 3.39342i) 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} +(4.20650 + 3.72268i) 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} +(2.05658 + 1.14076i) 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} +(-7.84354 - 0.756392i) q^{34} +(9.37942 + 10.0640i) q^{36} +(-2.16303 + 6.65712i) q^{37} +(6.34322 + 0.611709i) q^{38} +(-0.883011 - 2.71763i) q^{39} +(1.97065 - 6.06503i) q^{41} +(2.08483 - 4.79289i) q^{42} -2.96089 q^{43} +(-1.51803 + 7.79754i) q^{44} +(2.31026 + 2.04454i) q^{46} +(3.12538 + 4.30172i) q^{47} +(-11.6539 - 4.71632i) q^{48} +5.61729 q^{49} +17.5127i q^{51} +(1.23970 + 1.33018i) q^{52} +(-10.5708 + 7.68016i) q^{53} +(11.4253 - 12.9102i) q^{54} +(0.0856196 + 3.32481i) q^{56} -14.1629i q^{57} +(-3.51101 + 8.07158i) q^{58} +(-1.22277 - 0.397301i) q^{59} +(-14.7321 + 4.78675i) q^{61} +(0.195950 - 2.03194i) q^{62} +(-7.69253 - 2.49945i) q^{63} +(7.98940 - 0.411755i) q^{64} +(17.5735 + 1.69470i) 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} +(-5.53375 + 18.6519i) 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} +(2.67815 - 3.02621i) 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} +(7.33683 - 0.898695i) q^{84} +(-2.12471 - 3.60824i) q^{86} +(18.6049 + 6.04509i) q^{87} +(-10.5917 + 3.74553i) q^{88} +(0.806910 + 2.48341i) q^{89} +(-1.01674 - 0.330358i) q^{91} +(-0.833719 + 4.28250i) q^{92} -4.53682 q^{93} +(-2.99946 + 6.89556i) q^{94} +(-2.61528 - 17.5862i) q^{96} +(0.171369 + 0.235869i) q^{97} +(4.03092 + 6.84541i) 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 $

$2$	0.717591	+	1.21863i	0.507414	+	0.861703i
$2$	0.717591	+	1.21863i	0.507414	+	0.861703i
$3$	2.54275	−	1.84742i	1.46806	−	1.06661i	0.486890	−	0.873463i	$-0.338131\pi$
$3$	2.54275	−	1.84742i	1.46806	−	1.06661i	0.981170	−	0.193145i	$-0.0618687\pi$
$4$	−0.970125	+	1.74896i	−0.485063	+	0.874479i
$5$		0			0
$5$		0			0
$6$	4.07598	+	1.77299i	1.66401	+	0.723819i
$7$		−	1.17589i		−	0.444443i	−0.974996	−	0.222222i	$-0.928669\pi$
$7$		−	1.17589i		−	0.444443i	0.974996	−	0.222222i	$-0.0713308\pi$
$8$	−2.82749	+	0.0728129i	−0.999669	+	0.0257432i
$9$	2.12559	−	6.54190i	0.708531	−	2.18063i
$10$		0			0
$11$	3.77756	−	1.22741i	1.13898	−	0.370077i	0.321997	−	0.946741i	$-0.395646\pi$
$11$	3.77756	−	1.22741i	1.13898	−	0.370077i	0.816981	+	0.576664i	$0.195646\pi$
$12$	0.764270	+	6.23940i	0.220626	+	1.80116i
$13$	0.280944	−	0.864656i	0.0779198	−	0.239812i	−0.904508	−	0.426457i	$-0.859761\pi$
$13$	0.280944	−	0.864656i	0.0779198	−	0.239812i	0.982427	+	0.186645i	$0.0597614\pi$
$14$	1.43297	−	0.843806i	0.382978	−	0.225517i
$15$		0			0
$16$	−2.11771	−	3.39342i	−0.529429	−	0.848355i
$17$	−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	−0.388740	−	0.921348i	$-0.627090\pi$
$19$	2.64864	−	3.64555i	0.607641	−	0.836346i	0.996381	+	0.0850017i	$0.0270896\pi$
$20$		0			0
$21$	−2.17235	−	2.98999i	−0.474047	−	0.652469i
$22$	4.20650	+	3.72268i	0.896829	+	0.793679i
$23$	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
$28$	2.05658	+	1.14076i	0.388656	+	0.215583i
$29$	3.65841	+	5.03536i	0.679349	+	0.935044i	0.999926	−	0.0121788i	$-0.00387674\pi$
$29$	3.65841	+	5.03536i	0.679349	+	0.935044i	−0.320577	+	0.947223i	$0.603877\pi$
$30$		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
$34$	−7.84354	−	0.756392i	−1.34516	−	0.129720i
$35$		0			0
$36$	9.37942	+	10.0640i	1.56324	+	1.67734i
$37$	−2.16303	+	6.65712i	−0.355600	+	1.09442i	0.600061	+	0.799954i	$0.295143\pi$
$37$	−2.16303	+	6.65712i	−0.355600	+	1.09442i	−0.955661	+	0.294470i	$0.904857\pi$
$38$	6.34322	+	0.611709i	1.02901	+	0.0992323i
$39$	−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	$-0.0659216\pi$
$42$	2.08483	−	4.79289i	0.321697	−	0.739559i
$43$	−2.96089			−0.451532			−0.225766	−	0.974182i	$-0.572488\pi$
$43$	−2.96089			−0.451532			−0.225766	+	0.974182i	$0.572488\pi$
$44$	−1.51803	+	7.79754i	−0.228852	+	1.17552i
$45$		0			0
$46$	2.31026	+	2.04454i	0.340629	+	0.301451i
$47$	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	$0.673236\pi$
$48$	−11.6539	−	4.71632i	−1.68209	−	0.680743i
$49$	5.61729			0.802470
$50$		0			0
$51$			17.5127i			2.45227i
$52$	1.23970	+	1.33018i	0.171915	+	0.184463i
$53$	−10.5708	+	7.68016i	−1.45202	+	1.05495i	−0.466661	+	0.884436i	$0.654543\pi$
$53$	−10.5708	+	7.68016i	−1.45202	+	1.05495i	−0.985355	+	0.170515i	$0.945457\pi$
$54$	11.4253	−	12.9102i	1.55479	−	1.75685i
$55$		0			0
$56$	0.0856196	+	3.32481i	0.0114414	+	0.444296i
$57$		−	14.1629i		−	1.87592i
$58$	−3.51101	+	8.07158i	−0.461019	+	1.05985i
$59$	−1.22277	−	0.397301i	−0.159191	−	0.0517242i	0.228338	−	0.973582i	$-0.426671\pi$
$59$	−1.22277	−	0.397301i	−0.159191	−	0.0517242i	−0.387528	+	0.921858i	$0.626671\pi$
$60$		0			0
$61$	−14.7321	+	4.78675i	−1.88625	+	0.612881i	−0.903306	+	0.428996i	$0.858867\pi$
$61$	−14.7321	+	4.78675i	−1.88625	+	0.612881i	−0.982948	+	0.183885i	$0.941133\pi$
$62$	0.195950	−	2.03194i	0.0248857	−	0.258056i
$63$	−7.69253	−	2.49945i	−0.969167	−	0.314902i
$64$	7.98940	−	0.411755i	0.998675	−	0.0514694i
$65$		0			0
$66$	17.5735	+	1.69470i	2.16314	+	0.208603i
$67$	2.45652	+	1.78477i	0.300112	+	0.218044i	0.727642	−	0.685957i	$-0.240616\pi$
$67$	2.45652	+	1.78477i	0.300112	+	0.218044i	−0.427530	+	0.904001i	$0.640616\pi$
$68$	−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	$0.337019\pi$
$72$	−5.53375	+	18.6519i	−0.652159	+	2.19815i
$73$	−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
$78$	2.67815	−	3.02621i	0.303240	−	0.342651i
$79$	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	0.922555	−	0.385866i	$-0.126097\pi$
$83$	7.65878	+	5.56443i	0.840660	+	0.610775i	−0.0818950	+	0.996641i	$0.526097\pi$
$84$	7.33683	−	0.898695i	0.800513	−	0.0980557i
$85$		0			0
$86$	−2.12471	−	3.60824i	−0.229113	−	0.389086i
$87$	18.6049	+	6.04509i	1.99465	+	0.648101i
$88$	−10.5917	+	3.74553i	−1.12907	+	0.399275i
$89$	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
$92$	−0.833719	+	4.28250i	−0.0869213	+	0.446482i
$93$	−4.53682			−0.470447
$94$	−2.99946	+	6.89556i	−0.309371	+	0.711223i
$95$		0			0
$96$	−2.61528	−	17.5862i	−0.266920	−	1.79488i
$97$	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	$0.795288\pi$
$98$	4.03092	+	6.84541i	0.407184	+	0.691491i
$99$		−	27.3214i		−	2.74590i
$100$		0			0
$101$		−	7.84171i		−	0.780280i	−0.920756	−	0.390140i	$-0.872427\pi$
$101$		−	7.84171i		−	0.780280i	0.920756	−	0.390140i	$-0.127573\pi$
$102$	−21.3416	+	12.5670i	−2.11313	+	1.24432i
$103$	−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	$-0.424705\pi$
$104$	−0.731407	+	2.46526i	−0.0717204	+	0.241739i
$105$		0			0
$106$	−16.9448	−	7.37074i	−1.64583	−	0.715909i
$107$	−7.00700			−0.677392			−0.338696	−	0.940896i	$-0.609986\pi$
$107$	−7.00700			−0.677392			−0.338696	+	0.940896i	$0.609986\pi$
$108$	23.9315	+	4.65899i	2.30281	+	0.448312i
$109$	2.56991	+	0.835013i	0.246152	+	0.0799797i	0.429495	−	0.903069i	$-0.358692\pi$
$109$	2.56991	+	0.835013i	0.246152	+	0.0799797i	−0.183342	+	0.983049i	$0.558692\pi$
$110$		0			0
$111$	6.79844	+	20.9235i	0.645280	+	1.98597i
$112$	−3.99027	+	2.49019i	−0.377045	+	0.235301i
$113$	−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	$0.668970\pi$
$114$	17.2593	−	10.1632i	1.61649	−	0.951868i
$115$		0			0
$116$	−12.3558	+	1.51347i	−1.14720	+	0.140522i
$117$	−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
$122$	−16.4049	−	14.5181i	−1.48523	−	1.31441i
$123$	−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	$0.274923\pi$
$128$	6.23490	+	9.44066i	0.551093	+	0.834444i
$129$	−7.52882	+	5.47001i	−0.662876	+	0.481607i
$130$		0			0
$131$	−5.11250	+	7.03676i	−0.446681	+	0.614804i	−0.971680	−	0.236299i	$-0.924066\pi$
$131$	−5.11250	+	7.03676i	−0.446681	+	0.614804i	0.524999	+	0.851103i	$0.324066\pi$
$132$	10.5454	+	22.6317i	0.917855	+	1.96983i
$133$	−4.28675	−	3.11451i	−0.371708	−	0.270062i
$134$	−0.412194	+	4.27432i	−0.0356082	+	0.369245i
$135$		0			0
$136$	8.93211	−	12.9842i	0.765922	−	1.11339i
$137$	−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	$0.649748\pi$
$138$	9.65155	+	0.930747i	0.821594	+	0.0792305i
$139$	−13.2832	+	4.31597i	−1.12666	+	0.366075i	−0.812307	−	0.583230i	$-0.801789\pi$
$139$	−13.2832	+	4.31597i	−1.12666	+	0.366075i	−0.314357	+	0.949305i	$0.601789\pi$
$140$		0			0
$141$	15.8941	+	5.16432i	1.33853	+	0.434914i
$142$	−2.53593	−	1.10309i	−0.212811	−	0.0925693i
$143$		−	3.61112i		−	0.301977i
$144$	−26.7008	+	6.64085i	−2.22507	+	0.553404i
$145$		0			0
$146$	−4.47219	−	3.95781i	−0.370121	−	0.327551i
$147$	14.2834	−	10.3775i	1.17807	−	0.855921i
$148$	−9.54463	−	10.2413i	−0.784563	−	0.841829i
$149$		−	2.61363i		−	0.214117i	−0.994253	−	0.107059i	$-0.965857\pi$
$149$		−	2.61363i		−	0.214117i	0.994253	−	0.107059i	$-0.0341433\pi$
$150$		0			0
$151$	10.6178			0.864067			0.432034	−	0.901857i	$-0.357796\pi$
$151$	10.6178			0.864067			0.432034	+	0.901857i	$0.357796\pi$
$152$	−7.22357	+	10.5006i	−0.585909	+	0.851711i
$153$	22.5280	+	31.0072i	1.82128	+	2.50678i
$154$	4.37745	−	4.94637i	0.352745	−	0.398590i
$155$		0			0
$156$	5.60965	+	1.09209i	0.449132	+	0.0874372i
$157$	3.90358			0.311539			0.155770	−	0.987793i	$-0.450214\pi$
$157$	3.90358			0.311539			0.155770	+	0.987793i	$0.450214\pi$
$158$	3.57784	+	1.55631i	0.284638	+	0.123813i
$159$	−12.6906	+	39.0575i	−1.00643	+	3.09746i
$160$		0			0
$161$	−0.792671	−	2.43959i	−0.0624712	−	0.192267i
$162$	2.39991	−	24.8863i	0.188555	−	1.95525i
$163$	−6.06584	+	18.6687i	−0.475114	+	1.46225i	0.370691	+	0.928756i	$0.379121\pi$
$163$	−6.06584	+	18.6687i	−0.475114	+	1.46225i	−0.845805	+	0.533493i	$0.820879\pi$
$164$	8.69571	+	9.33042i	0.679021	+	0.728583i
$165$		0			0
$166$	−1.28511	+	13.3262i	−0.0997441	+	1.03431i
$167$	−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
$172$	2.87244	−	5.17848i	0.219021	−	0.394855i
$173$	−3.14623	−	9.68309i	−0.239203	−	0.736192i	−0.996536	−	0.0831625i	$-0.973498\pi$
$173$	−3.14623	−	9.68309i	−0.239203	−	0.736192i	0.757333	−	0.653029i	$-0.226502\pi$
$174$	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
$178$	−2.44733	+	2.76540i	−0.183435	+	0.207276i
$179$	8.87687	+	12.2180i	0.663488	+	0.913214i	0.999591	−	0.0286120i	$-0.00910873\pi$
$179$	8.87687	+	12.2180i	0.663488	+	0.913214i	−0.336102	+	0.941826i	$0.609109\pi$
$180$		0			0
$181$	−11.1217	+	15.3077i	−0.826668	+	1.13781i	0.161866	+	0.986813i	$0.448249\pi$
$181$	−11.1217	+	15.3077i	−0.826668	+	1.13781i	−0.988534	+	0.150998i	$0.951751\pi$
$182$	−0.327017	−	1.47609i	−0.0242401	−	0.109415i
$183$	−28.6170	+	39.3879i	−2.11543	+	2.91164i
$184$	−5.81706	+	2.05709i	−0.428839	+	0.151651i
$185$		0			0
$186$	−3.25559	−	5.52872i	−0.238711	−	0.405385i
$187$	−6.83904	+	21.0484i	−0.500120	+	1.53921i
$188$	−10.5555	+	1.29296i	−0.769841	+	0.0942986i
$189$	−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	$0.125835\pi$
$192$	19.5544	−	15.8068i	1.41122	−	1.14075i
$193$		−	22.6952i		−	1.63363i	−0.576896	−	0.816817i	$-0.695736\pi$
$193$		−	22.6952i		−	1.63363i	0.576896	−	0.816817i	$-0.304264\pi$
$194$	−0.164465	+	0.378093i	−0.0118079	+	0.0271455i
$195$		0			0
$196$	−5.44948	+	9.82441i	−0.389248	+	0.701744i
$197$	10.5031	−	7.63095i	0.748315	−	0.543682i	−0.146989	−	0.989138i	$-0.546958\pi$
$197$	10.5031	−	7.63095i	0.748315	−	0.543682i	0.895304	+	0.445456i	$0.146958\pi$
$198$	33.2947	−	19.6056i	2.36615	−	1.39331i
$199$	−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
$202$	9.55616	−	5.62715i	0.672369	−	0.395925i
$203$	5.92102	−	4.30187i	0.415574	−	0.301932i
$204$	−30.6290	−	16.9895i	−2.14446	−	1.18951i
$205$		0			0
$206$	7.42814	−	17.0768i	0.517543	−	1.18980i
$207$		−	15.0052i		−	1.04294i
$208$	−3.52910	+	0.877735i	−0.244699	+	0.0608599i
$209$	5.53086	−	17.0222i	0.382578	−	1.17745i
$210$		0			0
$211$	−1.67102	+	0.542946i	−0.115037	+	0.0373779i	−0.365970	−	0.930627i	$-0.619263\pi$
$211$	−1.67102	+	0.542946i	−0.115037	+	0.0373779i	0.250933	+	0.968005i	$0.419263\pi$
$212$	−3.17725	−	25.9387i	−0.218215	−	1.78148i
$213$	−1.89925	+	5.84528i	−0.130134	+	0.400512i
$214$	−5.02816	−	8.53895i	−0.343718	−	0.583711i
$215$		0			0
$216$	11.4954	+	32.5069i	0.782165	+	2.21181i
$217$	−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
$222$	−20.6195	+	23.2993i	−1.38389	+	1.56375i
$223$	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	0.999995	−	0.00311955i	$-0.000992986\pi$
$227$	2.84981	+	8.77081i	0.189148	+	0.582139i	−0.810847	+	0.585259i	$0.800993\pi$
$228$	24.7703	+	13.7398i	1.64045	+	0.909939i
$229$	6.64077	+	9.14023i	0.438834	+	0.604003i	0.969953	−	0.243294i	$-0.0782280\pi$
$229$	6.64077	+	9.14023i	0.438834	+	0.604003i	−0.531118	+	0.847298i	$0.678228\pi$
$230$		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	$0.0665072\pi$
$234$	0.848934	−	8.80318i	0.0554966	−	0.575482i
$235$		0			0
$236$	1.88110	−	1.75314i	0.122449	−	0.114119i
$237$	2.67957	−	8.24687i	0.174057	−	0.535692i
$238$	−0.889430	+	9.22311i	−0.0576532	+	0.597845i
$239$	−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	$0.144056\pi$
$242$	6.19437	+	2.69445i	0.398189	+	0.173206i
$243$	−18.9940			−1.21846
$244$	5.92016	−	30.4096i	0.378999	−	1.94678i
$245$		0			0
$246$	18.7855	−	21.2270i	1.19772	−	1.35338i
$247$	−2.40802	−	3.31436i	−0.153219	−	0.210888i
$248$	3.36368	+	2.31394i	0.213594	+	0.146935i
$249$	29.7542			1.88560
$250$		0			0
$251$		−	13.4000i		−	0.845800i	−0.906176	−	0.422900i	$-0.861012\pi$
$251$		−	13.4000i		−	0.845800i	0.906176	−	0.422900i	$-0.138988\pi$
$252$	11.8342	−	11.0291i	0.745482	−	0.694770i
$253$	7.00985	−	5.09295i	0.440705	−	0.320191i
$254$	9.13986	+	8.08862i	0.573486	+	0.507525i
$255$		0			0
$256$	−7.03057	+	14.3726i	−0.439411	+	0.898286i
$257$			7.81899i			0.487735i	0.969809	+	0.243868i	$0.0784162\pi$
$257$			7.81899i			0.487735i	−0.969809	+	0.243868i	$0.921584\pi$
$258$	−12.0685	−	5.24963i	−0.751355	−	0.326827i
$259$	7.82802	+	2.54348i	0.486409	+	0.158044i
$260$		0			0
$261$	40.7171	−	13.2298i	2.52033	−	0.818904i
$262$	−12.2439	−	1.18074i	−0.756431	−	0.0729464i
$263$	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	$0.278978\pi$
$264$	−20.0124	+	29.0912i	−1.23168	+	1.79044i
$265$		0			0
$266$	0.719300	−	7.45891i	0.0441031	−	0.457335i
$267$	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	$-0.574588\pi$
$269$	12.5408	−	17.2610i	0.764629	−	1.05242i	0.996815	−	0.0797498i	$-0.0254121\pi$
$270$		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	$0.289669\pi$
$272$	22.2326	+	1.56758i	1.34805	+	0.0950485i
$273$	−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	$-0.920936\pi$
$277$	−5.48602	−	16.8842i	−0.329623	−	1.01448i	0.639687	−	0.768635i	$-0.279064\pi$
$278$	−14.7915	−	13.0902i	−0.887133	−	0.785098i
$279$	−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	−0.133203	−	0.991089i	$-0.542526\pi$
$283$	−18.7899	−	13.6517i	−1.11695	−	0.811509i	−0.983743	+	0.179580i	$0.942526\pi$
$284$	−0.475502	−	3.88193i	−0.0282158	−	0.230350i
$285$		0			0
$286$	4.40063	−	2.59131i	0.260215	−	0.153228i
$287$	−7.13178	−	2.31726i	−0.420976	−	0.136783i
$288$	−27.2530	−	27.7730i	−1.60590	−	1.63654i
$289$	−4.34064	−	13.3591i	−0.255332	−	0.785830i
$290$		0			0
$291$	0.871498	+	0.283167i	0.0510881	+	0.0165995i
$292$	1.61391	−	8.29005i	0.0944470	−	0.485138i
$293$	23.5633			1.37658			0.688291	−	0.725434i	$-0.258361\pi$
$293$	23.5633			1.37658			0.688291	+	0.725434i	$0.258361\pi$
$294$	22.8960	+	9.95939i	1.33532	+	0.580844i
$295$		0			0
$296$	5.63122	−	18.9804i	0.327308	−	1.10322i
$297$	−28.4604	−	39.1724i	−1.65144	−	2.27301i
$298$	3.18506	−	1.87552i	0.184505	−	0.108646i
$299$		−	1.98327i		−	0.114696i
$300$		0			0
$301$			3.48167i			0.200680i
$302$	7.61927	+	12.9392i	0.438440	+	0.744569i
$303$	−14.4869	−	19.9396i	−0.832252	−	1.14550i
$304$	−17.9799	−	1.26773i	−1.03122	−	0.0727094i
$305$		0			0
$306$	−21.6204	+	49.7038i	−1.23596	+	2.84138i
$307$	−29.1918			−1.66607			−0.833033	−	0.553223i	$-0.813398\pi$
$307$	−29.1918			−1.66607			−0.833033	+	0.553223i	$0.813398\pi$
$308$	9.16902	+	1.78503i	0.522453	+	0.101712i
$309$	−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	$0.891129\pi$
$312$	2.69458	+	7.61977i	0.152551	+	0.431385i
$313$	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	$0.512717\pi$
$314$	2.80117	+	4.75702i	0.158079	+	0.268454i
$315$		0			0
$316$	0.670866	+	5.47686i	0.0377392	+	0.308098i
$317$	−14.8949	−	10.8218i	−0.836580	−	0.607811i	0.0848334	−	0.996395i	$-0.472964\pi$
$317$	−14.8949	−	10.8218i	−0.836580	−	0.607811i	−0.921413	+	0.388584i	$0.872964\pi$
$318$	−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
$322$	2.40415	−	2.71660i	0.133978	−	0.151390i
$323$	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
$328$	−5.13037	+	17.2923i	−0.283277	+	0.954807i
$329$	5.05833	−	3.67509i	0.278875	−	0.202614i
$330$		0			0
$331$	4.25106	−	5.85108i	0.233659	−	0.321604i	−0.676046	−	0.736860i	$-0.736308\pi$
$331$	4.25106	−	5.85108i	0.233659	−	0.321604i	0.909705	+	0.415255i	$0.136308\pi$
$332$	−17.1619	+	7.99669i	−0.941883	+	0.438876i
$333$	38.9525	+	28.3007i	2.13458	+	1.55087i
$334$	−23.7093	−	2.28641i	−1.29731	−	0.125107i
$335$		0			0
$336$	−5.54586	+	13.7037i	−0.302551	+	0.747596i
$337$	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	$0.520136\pi$
$338$	−1.65254	+	17.1363i	−0.0898865	+	0.932094i
$339$	−13.6625	+	4.43923i	−0.742047	+	0.241106i
$340$		0			0
$341$	−5.45277	−	1.77171i	−0.295284	−	0.0959436i
$342$	17.4848	−	40.1965i	0.945472	−	2.17358i
$343$		−	14.8365i		−	0.801096i
$344$	8.37189	−	0.215591i	0.451382	−	0.0116239i
$345$		0			0
$346$	9.54241	−	10.7826i	0.513003	−	0.579676i
$347$	8.27687	−	6.01350i	0.444326	−	0.322821i	−0.343026	−	0.939326i	$-0.611452\pi$
$347$	8.27687	−	6.01350i	0.444326	−	0.322821i	0.787351	+	0.616505i	$0.211452\pi$
$348$	−28.6216	+	26.6746i	−1.53428	+	1.42991i
$349$			4.76436i			0.255030i	0.991837	+	0.127515i	$0.0407001\pi$
$349$			4.76436i			0.255030i	−0.991837	+	0.127515i	$0.959300\pi$
$350$		0			0
$351$	−11.0829			−0.591562
$352$	3.72445	−	22.1580i	0.198514	−	1.18103i
$353$	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	$0.638518\pi$
$354$	−4.27956	−	3.78734i	−0.227456	−	0.201295i
$355$		0			0
$356$	−5.12619	−	0.997969i	−0.271688	−	0.0528923i
$357$	20.5930			1.08990
$358$	−8.51923	+	19.5851i	−0.450255	+	1.03511i
$359$	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
$362$	−26.6353	−	2.56857i	−1.39992	−	0.135001i
$363$	4.63917	−	14.2779i	0.243493	−	0.749396i
$364$	1.56414	−	1.45774i	0.0819834	−	0.0764065i
$365$		0			0
$366$	−68.5347	−	6.60914i	−3.58237	−	0.345466i
$367$	−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
$372$	4.40129	−	7.93472i	0.228196	−	0.411396i
$373$	0.219092	+	0.674295i	0.0113441	+	0.0349137i	0.956568	−	0.291508i	$-0.0941570\pi$
$373$	0.219092	+	0.674295i	0.0113441	+	0.0349137i	−0.945224	+	0.326422i	$0.894157\pi$
$374$	−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
$378$	−15.1809	−	13.4349i	−0.780822	−	0.691015i
$379$	10.8210	+	14.8938i	0.555838	+	0.765045i	0.990790	−	0.135408i	$-0.0432347\pi$
$379$	10.8210	+	14.8938i	0.555838	+	0.765045i	−0.434952	+	0.900454i	$0.643235\pi$
$380$		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	$0.0483783\pi$
$384$	33.2947	+	12.4868i	1.69906	+	0.637214i
$385$		0			0
$386$	27.6571	−	16.2859i	1.40771	−	0.828929i
$387$	−6.29365	+	19.3699i	−0.319924	+	0.984625i
$388$	−0.578774	+	0.0708946i	−0.0293828	+	0.00359913i
$389$	22.7077	−	7.37819i	1.15133	−	0.374089i	0.329685	−	0.944091i	$-0.393058\pi$
$389$	22.7077	−	7.37819i	1.15133	−	0.374089i	0.821643	+	0.570002i	$0.193058\pi$
$390$		0			0
$391$	−3.75608	+	11.5600i	−0.189953	+	0.584616i
$392$	−15.8828	+	0.409011i	−0.802204	+	0.0206582i
$393$			27.3377i			1.37900i
$394$	16.8362	+	7.32350i	0.848198	+	0.368953i
$395$		0			0
$396$	47.7840	+	26.5052i	2.40124	+	1.33194i
$397$	−1.16804	+	0.848630i	−0.0586222	+	0.0425915i	−0.616710	−	0.787190i	$-0.711535\pi$
$397$	−1.16804	+	0.848630i	−0.0586222	+	0.0425915i	0.558088	+	0.829782i	$0.311535\pi$
$398$	−13.0721	−	22.1994i	−0.655246	−	1.11275i
$399$	−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	$0.725605\pi$
$402$	6.84836	+	11.6300i	0.341565	+	0.580054i
$403$	−1.06170	+	0.771367i	−0.0528868	+	0.0384245i
$404$	13.7148	+	7.60744i	0.682338	+	0.378484i
$405$		0			0
$406$	9.49126	+	4.12855i	0.471043	+	0.204897i
$407$			27.8026i			1.37813i
$408$	−1.27515	−	49.5171i	−0.0631294	−	2.45146i
$409$	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
$412$	26.1407	−	3.20200i	1.28786	−	0.157751i
$413$	−0.467180	+	1.43783i	−0.0229884	+	0.0707512i
$414$	18.2859	−	10.7676i	0.898701	−	0.529200i
$415$		0			0
$416$	−3.60208	−	3.67081i	−0.176607	−	0.179976i
$417$	−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	$0.504590\pi$
$419$	−19.6696	+	27.0728i	−0.960920	+	1.32259i	−0.946502	+	0.322697i	$0.895410\pi$
$420$		0			0
$421$	−16.1696	−	22.2556i	−0.788060	−	1.08467i	−0.994347	−	0.106180i	$-0.966138\pi$
$421$	−16.1696	−	22.2556i	−0.788060	−	1.08467i	0.206287	−	0.978492i	$-0.433862\pi$
$422$	−1.86076	−	1.64674i	−0.0905803	−	0.0801620i
$423$	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
$428$	6.79767	−	12.2550i	0.328578	−	0.592366i
$429$	−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	$0.0338059\pi$
$434$	−2.38933	−	0.230415i	−0.114691	−	0.0110603i
$435$		0			0
$436$	−3.95353	+	3.68459i	−0.189340	+	0.176460i
$437$	3.03762	−	9.34882i	0.145309	−	0.447215i
$438$	−18.6834	−	1.80174i	−0.892729	−	0.0860903i
$439$	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
$442$	−2.85761	+	6.56946i	−0.135923	+	0.312477i
$443$	33.9046			1.61086			0.805428	−	0.592693i	$-0.201935\pi$
$443$	33.9046			1.61086			0.805428	+	0.592693i	$0.201935\pi$
$444$	−43.1896	−	8.40817i	−2.04969	−	0.399034i
$445$		0			0
$446$	1.65062	+	1.46077i	0.0781591	+	0.0691694i
$447$	−4.82848	−	6.64583i	−0.228379	−	0.314337i
$448$	−0.484177	−	9.39462i	−0.0228752	−	0.443854i
$449$	−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
$452$	6.68733	−	6.23242i	0.314545	−	0.293148i
$453$	26.9986	−	19.6156i	1.26850	−	0.921621i
$454$	−8.64339	+	9.76672i	−0.405654	+	0.458375i
$455$		0			0
$456$	1.03124	+	40.0454i	0.0482923	+	1.87530i
$457$		−	2.58934i		−	0.121124i	−0.998164	−	0.0605622i	$-0.980711\pi$
$457$		−	2.58934i		−	0.121124i	0.998164	−	0.0605622i	$-0.0192893\pi$
$458$	−6.37322	+	14.6516i	−0.297801	+	0.684624i
$459$	64.5997	+	20.9897i	3.01526	+	0.979716i
$460$		0			0
$461$	6.49523	−	2.11043i	0.302513	−	0.0982925i	−0.153827	−	0.988098i	$-0.549160\pi$
$461$	6.49523	−	2.11043i	0.302513	−	0.0982925i	0.456340	+	0.889805i	$0.349160\pi$
$462$	1.99277	−	20.6644i	0.0927121	−	0.961394i
$463$	−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	$0.769265\pi$
$464$	9.33964	−	23.0780i	0.433582	−	1.07137i
$465$		0			0
$466$	17.4990	+	1.68752i	0.810628	+	0.0781729i
$467$	−2.43118	−	1.76636i	−0.112502	−	0.0817373i	0.530112	−	0.847928i	$-0.322150\pi$
$467$	−2.43118	−	1.76636i	−0.112502	−	0.0817373i	−0.642614	+	0.766190i	$0.722150\pi$
$468$	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
$472$	3.48629	+	1.03433i	0.160469	+	0.0476089i
$473$	−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
$478$	25.9005	−	29.2667i	1.18466	−	1.33863i
$479$	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
$484$	1.16148	+	9.48216i	0.0527945	+	0.431007i
$485$		0			0
$486$	−13.6299	−	23.1466i	−0.618265	−	1.04995i
$487$	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	$0.586305\pi$
$488$	41.3064	−	14.6072i	1.86985	−	0.661236i
$489$	19.0651	+	58.6762i	0.862151	+	2.65343i
$490$		0			0
$491$	29.3750	+	9.54451i	1.32567	+	0.430738i	0.884440	−	0.466654i	$-0.154541\pi$
$491$	29.3750	+	9.54451i	1.32567	+	0.430738i	0.441234	+	0.897392i	$0.354541\pi$
$492$	39.3482	+	7.66034i	1.77396	+	0.345355i
$493$	−34.6801			−1.56191
$494$	2.31101	−	5.31285i	0.103977	−	0.239036i
$495$		0			0
$496$	−0.406095	+	5.75955i	−0.0182342	+	0.258611i
$497$	1.35156	+	1.86027i	0.0606258	+	0.0834443i
$498$	21.3514	+	36.2594i	0.956778	+	1.62482i
$499$			10.5948i			0.474289i	0.971474	+	0.237145i	$0.0762115\pi$
$499$			10.5948i			0.474289i	−0.971474	+	0.237145i	$0.923788\pi$
$500$		0			0
$501$			52.9371i			2.36506i
$502$	16.3297	−	9.61572i	0.728828	−	0.429171i
$503$	−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	$-0.400966\pi$
$504$	21.9325	+	6.50707i	0.976953	+	0.289848i
$505$		0			0
$506$	11.2366	+	4.88776i	0.499529	+	0.217288i
$507$	38.2613			1.69925
$508$	−3.29836	+	16.9424i	−0.146341	+	0.751699i
$509$	17.5095	+	5.68919i	0.776096	+	0.252169i	0.670172	−	0.742205i	$-0.266220\pi$
$509$	17.5095	+	5.68919i	0.776096	+	0.252169i	0.105923	+	0.994374i	$0.466220\pi$
$510$		0			0
$511$	1.53445	+	4.72255i	0.0678800	+	0.208913i
$512$	−22.5600	+	1.74596i	−0.997019	+	0.0771615i
$513$	−52.2431	−	16.9748i	−2.30659	−	0.749456i
$514$	−9.52847	+	5.61084i	−0.420283	+	0.247484i
$515$		0			0
$516$	−2.26292	−	18.4742i	−0.0996196	−	0.813281i
$517$	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	$-0.0461906\pi$
$522$	45.3405	+	40.1256i	1.98450	+	1.75625i
$523$	5.37852	+	16.5534i	0.235186	+	0.723828i	0.997097	+	0.0761461i	$0.0242615\pi$
$523$	5.37852	+	16.5534i	0.235186	+	0.723828i	−0.761911	+	0.647682i	$0.775738\pi$
$524$	−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
$528$	−49.8122	−	3.51216i	−2.16780	−	0.152847i
$529$	−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
$534$	−1.11411	+	11.5530i	−0.0482124	+	0.499947i
$535$		0			0
$536$	−7.07573	−	4.86754i	−0.305625	−	0.210246i
$537$	45.1434	+	14.6680i	1.94808	+	0.632970i
$538$	30.0340	+	2.89633i	1.29486	+	0.124870i
$539$	21.2197	−	6.89469i	0.913996	−	0.296975i
$540$		0			0
$541$	−7.69917	−	2.50161i	−0.331013	−	0.107553i	0.138795	−	0.990321i	$-0.455677\pi$
$541$	−7.69917	−	2.50161i	−0.331013	−	0.107553i	−0.469808	+	0.882768i	$0.655677\pi$
$542$	1.38556	+	0.602695i	0.0595147	+	0.0258880i
$543$			59.4701i			2.55211i
$544$	14.0436	+	28.2182i	0.602115	+	1.20985i
$545$		0			0
$546$	−3.55848	−	3.14920i	−0.152289	−	0.134773i
$547$	−20.7126	+	15.0486i	−0.885607	+	0.643431i	−0.934729	−	0.355362i	$-0.884358\pi$
$547$	−20.7126	+	15.0486i	−0.885607	+	0.643431i	0.0491221	+	0.998793i	$0.484358\pi$
$548$	5.33117	−	4.96851i	0.227736	−	0.212244i
$549$			106.551i			4.54747i
$550$		0			0
$551$	28.0465			1.19482
$552$	−10.9911	+	15.9772i	−0.467810	+	0.680036i
$553$	−1.90686	−	2.62457i	−0.0810881	−	0.111608i
$554$	16.6389	−	18.8014i	0.706921	−	0.798796i
$555$		0			0
$556$	5.33790	−	27.4188i	0.226377	−	1.16281i
$557$	1.74254			0.0738336			0.0369168	−	0.999318i	$-0.488246\pi$
$557$	1.74254			0.0738336			0.0369168	+	0.999318i	$0.488246\pi$
$558$	−12.8762	−	5.60095i	−0.545094	−	0.237107i
$559$	−0.831844	+	2.56015i	−0.0351832	+	0.108283i
$560$		0			0
$561$	21.4952	+	66.1555i	0.907529	+	2.79309i
$562$	1.47303	−	15.2748i	0.0621359	−	0.644329i
$563$	7.94233	−	24.4440i	0.334729	−	1.03019i	−0.632126	−	0.774866i	$-0.717817\pi$
$563$	7.94233	−	24.4440i	0.334729	−	1.03019i	0.966855	−	0.255325i	$-0.0821826\pi$
$564$	−24.4515	+	22.7882i	−1.02959	+	0.959555i
$565$		0			0
$566$	3.15288	−	32.6943i	0.132525	−	1.37425i
$567$	−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	0.980436	−	0.196836i	$-0.0630666\pi$
$571$	11.7151	+	16.1245i	0.490263	+	0.674789i	−0.490174	+	0.871625i	$0.663067\pi$
$572$	6.31571	+	3.50324i	0.264073	+	0.146478i
$573$	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	$0.503918\pi$
$578$	13.1650	−	14.8760i	0.547593	−	0.618761i
$579$	−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
$584$	11.2606	−	3.98210i	0.465969	−	0.164781i
$585$		0			0
$586$	16.9088	+	28.7150i	0.698497	+	1.18620i
$587$	4.25364	−	13.0914i	0.175567	−	0.540338i	−0.824092	−	0.566455i	$-0.808314\pi$
$587$	4.25364	−	13.0914i	0.175567	−	0.540338i	0.999659	+	0.0261173i	$0.00831433\pi$
$588$	4.29313	+	35.0485i	0.177046	+	1.44538i
$589$	−6.18610	+	2.00998i	−0.254894	+	0.0828200i
$590$		0			0
$591$	12.6092	−	38.8072i	0.518675	−	1.59632i
$592$	27.1711	−	6.75782i	1.11672	−	0.277745i
$593$		−	6.37493i		−	0.261787i	−0.991396	−	0.130894i	$-0.958215\pi$
$593$		−	6.37493i		−	0.261787i	0.991396	−	0.130894i	$-0.0417846\pi$
$594$	27.3138	−	62.7926i	1.12070	−	2.57641i
$595$		0			0
$596$	4.57114	+	2.53555i	0.187241	+	0.103860i
$597$	−46.3205	+	33.6538i	−1.89577	+	1.37736i
$598$	2.41688	−	1.42318i	0.0988335	−	0.0581981i
$599$	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	$0.184198\pi$
$602$	−4.24287	+	2.49842i	−0.172927	+	0.101828i
$603$	16.8973	−	12.2766i	0.688112	−	0.499942i
$604$	−10.3006	+	18.5702i	−0.419127	+	0.755609i
$605$		0			0
$606$	13.9033	−	31.9627i	0.564782	−	1.29840i
$607$		−	28.6948i		−	1.16469i	−0.812943	−	0.582343i	$-0.802136\pi$
$607$		−	28.6948i		−	1.16469i	0.812943	−	0.582343i	$-0.197864\pi$
$608$	−11.3574	−	22.8206i	−0.460601	−	0.925499i
$609$	7.10833	−	21.8772i	0.288044	−	0.886509i
$610$		0			0
$611$	4.59756	−	1.49384i	0.185997	−	0.0604342i
$612$	−76.0853	+	9.31976i	−3.07557	+	0.376729i
$613$	2.30831	−	7.10423i	0.0932316	−	0.286937i	−0.893557	−	0.448949i	$-0.851798\pi$
$613$	2.30831	−	7.10423i	0.0932316	−	0.286937i	0.986789	+	0.162012i	$0.0517983\pi$
$614$	−20.9478	−	35.5741i	−0.845385	−	1.43565i
$615$		0			0
$616$	4.40432	+	12.4546i	0.177455	+	0.501809i
$617$	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	−0.910851	−	0.412735i	$-0.864574\pi$
$619$	−5.89273	+	8.11065i	−0.236849	+	0.325994i	0.674003	+	0.738729i	$0.264574\pi$
$620$		0			0
$621$	−15.6308	−	21.5140i	−0.627242	−	0.863325i
$622$	−0.921185	+	1.04091i	−0.0369362	+	0.0417366i
$623$	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
$628$	−3.78696	+	6.82719i	−0.151116	+	0.272435i
$629$	−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
$634$	2.49930	−	25.9170i	0.0992600	−	1.02929i
$635$		0			0
$636$	−55.9986	−	60.0860i	−2.22049	−	2.38256i
$637$	1.57814	−	4.85702i	0.0625283	−	0.192442i
$638$	−3.35597	+	34.8004i	−0.132864	+	1.37776i
$639$	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	$0.816393\pi$
$642$	−28.5604	−	12.4233i	−1.12719	−	0.490310i
$643$	15.6623			0.617660			0.308830	−	0.951117i	$-0.400063\pi$
$643$	15.6623			0.617660			0.308830	+	0.951117i	$0.400063\pi$
$644$	5.03573	+	0.980359i	0.198436	+	0.0386316i
$645$		0			0
$646$	−23.5322	+	26.5906i	−0.925862	+	1.04619i
$647$	−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	$-0.426313\pi$
$648$	41.1969	+	28.3402i	1.61837	+	1.11331i
$649$	−5.10673			−0.200457
$650$		0			0
$651$			5.33479i			0.209087i
$652$	−26.7662	−	28.7199i	−1.04825	−	1.12476i
$653$	−3.13976	+	2.28117i	−0.122868	+	0.0892690i	−0.647522	−	0.762047i	$-0.724195\pi$
$653$	−3.13976	+	2.28117i	−0.122868	+	0.0892690i	0.524654	+	0.851316i	$0.324195\pi$
$654$	8.99442	+	7.95991i	0.351710	+	0.311257i
$655$		0			0
$656$	−24.7544	+	6.15677i	−0.966499	+	0.240381i
$657$			29.0471i			1.13323i
$658$	8.10839	+	3.52702i	0.316098	+	0.137498i
$659$	−38.7539	−	12.5919i	−1.50964	−	0.490511i	−0.566826	−	0.823838i	$-0.691829\pi$
$659$	−38.7539	−	12.5919i	−1.50964	−	0.490511i	−0.942811	+	0.333327i	$0.891829\pi$
$660$		0			0
$661$	−35.9253	+	11.6728i	−1.39733	+	0.454020i	−0.908327	−	0.418261i	$-0.862640\pi$
$661$	−35.9253	+	11.6728i	−1.39733	+	0.454020i	−0.489004	+	0.872282i	$0.662640\pi$
$662$	10.1808	+	0.981789i	0.395689	+	0.0381583i
$663$	15.1425	+	4.92009i	0.588085	+	0.191081i
$664$	−22.0603	−	15.1757i	−0.856105	−	0.588931i
$665$		0			0
$666$	−6.53608	+	67.7771i	−0.253268	+	2.62631i
$667$	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
$672$	−20.6794	+	3.07527i	−0.797724	+	0.118631i
$673$	−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	0.949700	−	0.313161i	$-0.101388\pi$
$677$	−0.0701106	−	0.215778i	−0.00269457	−	0.00829304i	−0.952395	+	0.304868i	$0.901388\pi$
$678$	−15.2139	−	13.4640i	−0.584286	−	0.517083i
$679$	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	0.943716	−	0.330756i	$-0.107304\pi$
$683$	24.0637	+	17.4833i	0.920773	+	0.668981i	−0.0229435	+	0.999737i	$0.507304\pi$
$684$	61.5317	−	7.53707i	2.35272	−	0.288187i
$685$		0			0
$686$	18.0802	−	10.6465i	0.690306	−	0.406487i
$687$	33.7717	+	10.9731i	1.28847	+	0.418649i
$688$	6.27032	+	10.0475i	0.239054	+	0.383059i
$689$	3.67089	+	11.2978i	0.139850	+	0.430413i
$690$		0			0
$691$	29.9436	+	9.72925i	1.13911	+	0.370118i	0.817030	−	0.576595i	$-0.195619\pi$
$691$	29.9436	+	9.72925i	1.13911	+	0.370118i	0.322077	+	0.946714i	$0.395619\pi$
$692$	19.9876	+	3.89119i	0.759813	+	0.147921i
$693$	−32.1269			−1.22040
$694$	13.2676	+	5.77122i	0.503633	+	0.219072i
$695$		0			0
$696$	−53.0452	−	15.7377i	−2.01067	−	0.596538i
$697$	20.8859	+	28.7469i	0.791108	+	1.08887i
$698$	−5.80600	+	3.41886i	−0.219760	+	0.129406i
$699$		−	39.0712i		−	1.47781i
$700$		0			0
$701$		−	2.30506i		−	0.0870611i	−0.999052	−	0.0435305i	$-0.986139\pi$
$701$		−	2.30506i		−	0.0870611i	0.999052	−	0.0435305i	$-0.0138606\pi$
$702$	−7.95301	−	13.5060i	−0.300167	−	0.509751i
$703$	18.5398	+	25.5178i	0.699240	+	0.962422i
$704$	29.6751	−	11.3617i	1.11842	−	0.428209i
$705$		0			0
$706$	−10.2982	+	23.6748i	−0.387576	+	0.891012i
$707$	−9.22096			−0.346790
$708$	1.54440	−	7.93297i	0.0580419	−	0.298139i
$709$	−25.4956	−	8.28402i	−0.957508	−	0.311113i	−0.211745	−	0.977325i	$-0.567915\pi$
$709$	−25.4956	−	8.28402i	−0.957508	−	0.311113i	−0.745763	+	0.666212i	$0.767915\pi$
$710$		0			0
$711$	−5.86429	−	18.0484i	−0.219928	−	0.676869i
$712$	−2.46235	−	6.96307i	−0.0922806	−	0.260952i
$713$	−2.99472	−	0.973045i	−0.112153	−	0.0364408i
$714$	14.7773	+	25.0953i	0.553028	+	0.939166i
$715$		0			0
$716$	−29.9804	+	3.67233i	−1.12042	+	0.137241i
$717$	−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
$722$	1.22341	−	1.38241i	0.0455306	−	0.0514480i
$723$	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	$0.386852\pi$
$728$	2.89887	+	0.860052i	0.107439	+	0.0318756i
$729$	−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	$-0.932902\pi$
$733$	−40.0434	−	29.0933i	−1.47904	−	1.07458i	−0.501173	−	0.865347i	$-0.667098\pi$
$734$	−21.1949	−	2.04393i	−0.782319	−	0.0754430i
$735$		0			0
$736$	2.04551	−	12.1694i	0.0753986	−	0.448571i
$737$	11.4703	+	3.72692i	0.422513	+	0.137283i
$738$	5.95475	−	61.7488i	0.219197	−	2.27301i
$739$	−17.2361	+	5.60033i	−0.634039	+	0.206012i	−0.608363	−	0.793659i	$-0.708174\pi$
$739$	−17.2361	+	5.60033i	−0.634039	+	0.206012i	−0.0256753	+	0.999670i	$0.508174\pi$
$740$		0			0
$741$	−12.2460	−	3.97897i	−0.449869	−	0.146171i
$742$	−8.66715	+	19.9252i	−0.318181	+	0.731477i
$743$		−	15.5632i		−	0.570959i	−0.958385	−	0.285479i	$-0.907847\pi$
$743$		−	15.5632i		−	0.570959i	0.958385	−	0.285479i	$-0.0921528\pi$
$744$	12.8278	−	0.330339i	0.470291	−	0.0121108i
$745$		0			0
$746$	−0.664499	+	0.750860i	−0.0243290	+	0.0274910i
$747$	52.6813	−	38.2752i	1.92751	−	1.40042i
$748$	−30.1781	−	32.3808i	−1.10342	−	1.18396i
$749$			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	$0.225863\pi$
$752$	7.97886	−	19.7155i	0.290959	−	0.718951i
$753$	−24.7554	−	34.0729i	−0.902137	−	1.24169i
$754$	5.99274	+	5.30348i	0.218243	+	0.193141i
$755$		0			0
$756$	5.47844	−	28.1407i	0.199249	−	1.02347i
$757$	1.83755			0.0667870			0.0333935	−	0.999442i	$-0.489369\pi$
$757$	1.83755			0.0667870			0.0333935	+	0.999442i	$0.489369\pi$
$758$	−10.3850	+	23.8745i	−0.377202	+	0.867161i
$759$	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	$-0.281194\pi$
$762$	38.1835	+	3.68223i	1.38324	+	0.133393i
$763$	0.981880	−	3.02192i	0.0355464	−	0.109401i
$764$	−3.05570	−	3.27874i	−0.110552	−	0.118621i
$765$		0			0
$766$	25.2637	+	2.43630i	0.912813	+	0.0880272i
$767$	−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
$772$	39.6929	+	22.0172i	1.42858	+	0.792415i
$773$	−7.49873	−	23.0787i	−0.269711	−	0.830084i	−0.990571	−	0.137003i	$-0.956253\pi$
$773$	−7.49873	−	23.0787i	−0.269711	−	0.830084i	0.720860	−	0.693081i	$-0.243747\pi$
$774$	−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
$778$	25.2862	+	22.3778i	0.906553	+	0.802284i
$779$	−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
$784$	−11.8958	−	19.0618i	−0.424851	−	0.680779i
$785$		0			0
$786$	−33.3146	+	19.6173i	−1.18829	+	0.699725i
$787$	−11.5135	+	35.4350i	−0.410413	+	1.26312i	0.505877	+	0.862606i	$0.331169\pi$
$787$	−11.5135	+	35.4350i	−0.410413	+	1.26312i	−0.916290	+	0.400515i	$0.868831\pi$
$788$	3.15689	+	25.7725i	0.112460	+	0.918106i
$789$	82.0264	−	26.6520i	2.92022	−	0.948837i
$790$		0			0
$791$	−1.66083	+	5.11151i	−0.0590524	+	0.181745i
$792$	1.98935	+	77.2510i	0.0706885	+	2.74499i
$793$			14.0830i			0.500103i
$794$	−1.87234	−	0.814440i	−0.0664469	−	0.0289034i
$795$		0			0
$796$	17.6724	−	31.8602i	0.626383	−	1.12925i
$797$	−4.03520	+	2.93174i	−0.142934	+	0.103848i	−0.656954	−	0.753930i	$-0.728156\pi$
$797$	−4.03520	+	2.93174i	−0.142934	+	0.103848i	0.514020	+	0.857778i	$0.328156\pi$
$798$	−11.9507	−	20.2950i	−0.423051	−	0.718436i
$799$	−29.6272			−1.04814
$800$		0			0
$801$	17.9614			0.634635
$802$	−18.7063	−	31.7675i	−0.660542	−	1.12175i
$803$	−13.5696	+	9.85892i	−0.478862	+	0.347914i
$804$	−9.25842	+	16.6912i	−0.326519	+	0.588655i
$805$		0			0
$806$	−1.70187	−	0.740289i	−0.0599460	−	0.0260756i
$807$		−	67.0587i		−	2.36058i
$808$	0.570978	+	22.1724i	0.0200869	+	0.780021i
$809$	−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	−0.649515	−	0.760349i	$-0.725028\pi$
$811$	−20.7338	+	6.73681i	−0.728062	+	0.236562i	−0.0785467	+	0.996910i	$0.525028\pi$
$812$	1.77967	+	14.5290i	0.0624541	+	0.509867i
$813$	1.03769	−	3.19368i	0.0363934	−	0.112007i
$814$	−33.8812	+	19.9509i	−1.18753	+	0.699280i
$815$		0			0
$816$	59.4280	−	37.0870i	2.08040	−	1.29830i
$817$	−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	$0.0207235\pi$
$821$	21.5298	+	29.6332i	0.751394	+	1.03420i	−0.246488	+	0.969146i	$0.579276\pi$
$822$	−12.1286	−	10.7336i	−0.423033	−	0.374377i
$823$	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	0.835261	−	0.549854i	$-0.185317\pi$
$827$	−4.70692	−	14.4864i	−0.163676	−	0.503742i	−0.998936	+	0.0461123i	$0.985317\pi$
$828$	26.2435	+	14.5570i	0.912026	+	0.505889i
$829$	25.2244	+	34.7183i	0.876078	+	1.20582i	0.977492	+	0.210974i	$0.0676634\pi$
$829$	25.2244	+	34.7183i	0.876078	+	1.20582i	−0.101414	+	0.994844i	$0.532337\pi$
$830$		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
$834$	−61.7941	−	5.95912i	−2.13976	−	0.206347i
$835$		0			0
$836$	24.4056	+	26.1870i	0.844085	+	0.905695i
$837$	−5.43757	+	16.7351i	−0.187950	+	0.578450i
$838$	−47.1065	−	4.54271i	−1.62727	−	0.156925i
$839$	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
$842$	15.5182	−	35.6753i	0.534792	−	1.22945i
$843$	−34.1050			−1.17464
$844$	0.671504	−	3.44926i	0.0231141	−	0.118729i
$845$		0			0
$846$	38.7344	+	34.2793i	1.33172	+	1.17855i
$847$	−3.30138	−	4.54396i	−0.113437	−	0.156132i
$848$	48.4480	+	19.6069i	1.66371	+	0.673303i
$849$	−72.9986			−2.50531
$850$		0			0
$851$			15.2695i			0.523433i
$852$	−8.38064	−	8.99235i	−0.287116	−	0.308073i
$853$	−39.8951	+	28.9855i	−1.36598	+	0.992445i	−0.367944	+	0.929848i	$0.619938\pi$
$853$	−39.8951	+	28.9855i	−1.36598	+	0.992445i	−0.998039	+	0.0625971i	$0.980062\pi$
$854$	−17.0716	+	19.2903i	−0.584179	+	0.660101i
$855$		0			0
$856$	19.8122	−	0.510200i	0.677168	−	0.0174383i
$857$		−	57.0345i		−	1.94826i	−0.225989	−	0.974130i	$-0.572561\pi$
$857$		−	57.0345i		−	1.94826i	0.225989	−	0.974130i	$-0.427439\pi$
$858$	6.40248	−	14.7189i	0.218577	−	0.502494i
$859$	20.6564	+	6.71166i	0.704786	+	0.228999i	0.639415	−	0.768862i	$-0.279177\pi$
$859$	20.6564	+	6.71166i	0.704786	+	0.228999i	0.0653714	+	0.997861i	$0.479177\pi$
$860$		0			0
$861$	−22.4153	+	7.28318i	−0.763912	+	0.248210i
$862$	−3.63023	+	37.6443i	−0.123646	+	1.28217i
$863$	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	$0.495613\pi$
$864$	−68.0052	−	11.4307i	−2.31358	−	0.388881i
$865$		0			0
$866$	29.2166	+	2.81751i	0.992822	+	0.0957428i
$867$	−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
$872$	−7.32718	−	2.17387i	−0.248130	−	0.0736165i
$873$	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	0.997056	−	0.0766761i	$-0.0244307\pi$
$877$	4.30447	+	13.2478i	0.145352	+	0.447347i	−0.851704	+	0.524023i	$0.824431\pi$
$878$	−0.283886	+	0.320781i	−0.00958068	+	0.0108258i
$879$	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	0.530656	−	0.847587i	$-0.321946\pi$
$883$	−3.31224	−	2.40648i	−0.111466	−	0.0809845i	−0.642122	+	0.766603i	$0.721946\pi$
$884$	−10.0563	+	1.23181i	−0.338231	+	0.0414303i
$885$		0			0
$886$	24.3297	+	41.3172i	0.817371	+	1.38808i
$887$	−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	$0.630368\pi$
$888$	−20.7460	−	58.6658i	−0.696191	−	1.96870i
$889$	−3.13597	−	9.65152i	−0.105177	−	0.323701i
$890$		0			0
$891$	−66.7832	−	21.6992i	−2.23732	−	0.726950i
$892$	−0.595670	+	3.05973i	−0.0199445	+	0.102447i
$893$	23.9601			0.801795
$894$	4.63394	−	10.6531i	0.154982	−	0.356294i
$895$		0			0
$896$	11.1011	−	7.33153i	0.370863	−	0.244929i
$897$	−3.66394	−	5.04297i	−0.122335	−	0.168380i
$898$	−9.04513	−	15.3607i	−0.301840	−	0.512592i
$899$		−	8.98418i		−	0.299639i
$900$		0			0
$901$		−	72.8046i		−	2.42547i
$902$	30.8677	−	18.1765i	1.02778	−	0.605210i
$903$	6.43211	+	8.85304i	0.214047	+	0.294611i
$904$	12.3938	+	3.67706i	0.412211	+	0.122297i
$905$		0			0
$906$	43.2781	+	18.8253i	1.43782	+	0.625429i
$907$	49.8362			1.65478			0.827392	−	0.561625i	$-0.189824\pi$
$907$	49.8362			1.65478			0.827392	+	0.561625i	$0.189824\pi$
$908$	−18.1045	−	3.52458i	−0.600817	−	0.116967i
$909$	−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	$0.881548\pi$
$912$	−48.0606	+	29.9930i	−1.59145	+	0.993166i
$913$	35.7613	+	11.6196i	1.18353	+	0.384551i
$914$	3.15545	−	1.85809i	0.104373	−	0.0614602i
$915$		0			0
$916$	−22.4283	+	2.74726i	−0.741051	+	0.0907720i
$917$	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
$922$	7.23276	+	6.40087i	0.238198	+	0.210801i
$923$	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
$928$	34.8256	−	5.17898i	1.14321	−	0.170008i
$929$	−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
$934$	0.407943	−	4.23024i	0.0133483	−	0.138418i
$935$		0			0
$936$	14.5728	+	10.0249i	0.476327	+	0.327675i
$937$	−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	$0.620593\pi$
$938$	5.02612	+	0.484694i	0.164109	+	0.0158258i
$939$	28.6403	−	9.30581i	0.934642	−	0.303684i
$940$		0			0
$941$	7.54079	+	2.45015i	0.245823	+	0.0798727i	0.429337	−	0.903144i	$-0.358747\pi$
$941$	7.54079	+	2.45015i	0.245823	+	0.0798727i	−0.183514	+	0.983017i	$0.558747\pi$
$942$	15.9109	+	6.92099i	0.518405	+	0.225498i
$943$		−	13.9114i		−	0.453018i
$944$	1.24126	+	4.99073i	0.0403996	+	0.162434i
$945$		0			0
$946$	−12.4550	−	11.0225i	−0.404947	−	0.358371i
$947$	−0.630350	+	0.457976i	−0.0204836	+	0.0148822i	−0.597980	−	0.801511i	$-0.704030\pi$
$947$	−0.630350	+	0.457976i	−0.0204836	+	0.0148822i	0.577496	+	0.816393i	$0.304030\pi$
$948$	11.8239	+	12.6870i	0.384023	+	0.412053i
$949$			3.83921i			0.124626i
$950$		0			0
$951$	−57.8664			−1.87645
$952$	−15.2680	−	10.5031i	−0.494838	−	0.340409i
$953$	−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	$0.855489\pi$
$954$	−84.2364	+	95.1842i	−2.72725	+	3.08170i
$955$		0			0
$956$	54.2513	+	10.5617i	1.75461	+	0.341589i
$957$	77.7008			2.51171
$958$	24.6405	+	10.7182i	0.796097	+	0.346290i
$959$	−1.32402	+	4.07492i	−0.0427549	+	0.131586i
$960$		0			0
$961$	−8.93566	−	27.5011i	−0.288247	−	0.887134i
$962$	−0.863887	+	8.95823i	−0.0278528	+	0.288825i
$963$	−14.8940	+	45.8391i	−0.479953	+	1.47714i
$964$	−5.84093	−	6.26726i	−0.188124	−	0.201855i
$965$		0			0
$966$	1.09445	−	11.3491i	0.0352134	−	0.365152i
$967$	−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	0.490450	−	0.871469i	$-0.336833\pi$
$971$	−15.2665	−	21.0125i	−0.489924	−	0.674323i	−0.980374	+	0.197147i	$0.936833\pi$
$972$	18.4265	−	33.2196i	0.591031	−	1.06552i
$973$	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	$0.562393\pi$
$978$	−57.8237	+	65.3388i	−1.84900	+	2.08930i
$979$	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	$-0.0202515\pi$
$984$	18.9008	+	53.4480i	0.602537	+	1.70386i
$985$		0			0
$986$	−24.8861	−	42.2623i	−0.792536	−	1.34590i
$987$	6.07265	−	18.6897i	0.193295	−	0.594900i
$988$	8.13276	−	0.996190i	0.258738	−	0.0316930i
$989$	−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	$-0.177132\pi$
$992$	−7.31018	+	3.63812i	−0.232098	+	0.115510i
$993$		−	22.7314i		−	0.721358i
$994$	−1.29711	+	2.98197i	−0.0411418	+	0.0945822i
$995$		0			0
$996$	−28.8653	+	52.0389i	−0.914633	+	1.64892i
$997$	−0.969621	+	0.704471i	−0.0307082	+	0.0223108i	−0.603033	−	0.797716i	$-0.706041\pi$
$997$	−0.969621	+	0.704471i	−0.0307082	+	0.0223108i	0.572325	+	0.820027i	$0.306041\pi$
$998$	−12.9112	+	7.60275i	−0.408696	+	0.240661i
$999$	85.3292			2.69970

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.717591 + 1.21863i) q^{2} +(2.54275 - 1.84742i) q^{3} +(-0.970125 + 1.74896i) q^{4} +(4.07598 + 1.77299i) q^{6} -1.17589i q^{7} +(-2.82749 + 0.0728129i) q^{8} +(2.12559 - 6.54190i) q^{9} +O(q^{10})\)	\(q+(0.717591 + 1.21863i) q^{2} +(2.54275 - 1.84742i) q^{3} +(-0.970125 + 1.74896i) q^{4} +(4.07598 + 1.77299i) q^{6} -1.17589i q^{7} +(-2.82749 + 0.0728129i) q^{8} +(2.12559 - 6.54190i) q^{9} +(3.77756 - 1.22741i) q^{11} +(0.764270 + 6.23940i) q^{12} +(0.280944 - 0.864656i) q^{13} +(1.43297 - 0.843806i) q^{14} +(-2.11771 - 3.39342i) 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} +(4.20650 + 3.72268i) 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} +(2.05658 + 1.14076i) 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} +(-7.84354 - 0.756392i) q^{34} +(9.37942 + 10.0640i) q^{36} +(-2.16303 + 6.65712i) q^{37} +(6.34322 + 0.611709i) q^{38} +(-0.883011 - 2.71763i) q^{39} +(1.97065 - 6.06503i) q^{41} +(2.08483 - 4.79289i) q^{42} -2.96089 q^{43} +(-1.51803 + 7.79754i) q^{44} +(2.31026 + 2.04454i) q^{46} +(3.12538 + 4.30172i) q^{47} +(-11.6539 - 4.71632i) q^{48} +5.61729 q^{49} +17.5127i q^{51} +(1.23970 + 1.33018i) q^{52} +(-10.5708 + 7.68016i) q^{53} +(11.4253 - 12.9102i) q^{54} +(0.0856196 + 3.32481i) q^{56} -14.1629i q^{57} +(-3.51101 + 8.07158i) q^{58} +(-1.22277 - 0.397301i) q^{59} +(-14.7321 + 4.78675i) q^{61} +(0.195950 - 2.03194i) q^{62} +(-7.69253 - 2.49945i) q^{63} +(7.98940 - 0.411755i) q^{64} +(17.5735 + 1.69470i) 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} +(-5.53375 + 18.6519i) 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} +(2.67815 - 3.02621i) 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} +(7.33683 - 0.898695i) q^{84} +(-2.12471 - 3.60824i) q^{86} +(18.6049 + 6.04509i) q^{87} +(-10.5917 + 3.74553i) q^{88} +(0.806910 + 2.48341i) q^{89} +(-1.01674 - 0.330358i) q^{91} +(-0.833719 + 4.28250i) q^{92} -4.53682 q^{93} +(-2.99946 + 6.89556i) q^{94} +(-2.61528 - 17.5862i) q^{96} +(0.171369 + 0.235869i) q^{97} +(4.03092 + 6.84541i) 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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