LMFDB - Embedded newform 1000.2.t.b.101.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(101,1000)]

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, 6]))

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

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.t (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:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.47
Character	$\chi$	$=$	1000.101
Dual form			1000.2.t.b.901.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21863 + 0.717591i) q^{2} +(1.84742 - 2.54275i) q^{3} +(0.970125 + 1.74896i) q^{4} +(4.07598 - 1.77299i) q^{6} -1.17589 q^{7} +(-0.0728129 + 2.82749i) q^{8} +(-2.12559 - 6.54190i) q^{9} +O(q^{10})$	\(q+(1.21863 + 0.717591i) q^{2} +(1.84742 - 2.54275i) q^{3} +(0.970125 + 1.74896i) q^{4} +(4.07598 - 1.77299i) q^{6} -1.17589 q^{7} +(-0.0728129 + 2.82749i) q^{8} +(-2.12559 - 6.54190i) q^{9} +(3.77756 + 1.22741i) q^{11} +(6.23940 + 0.764270i) q^{12} +(0.864656 - 0.280944i) q^{13} +(-1.43297 - 0.843806i) q^{14} +(-2.11771 + 3.39342i) q^{16} +(4.50780 - 3.27511i) q^{17} +(2.10410 - 9.49747i) q^{18} +(-2.64864 - 3.64555i) q^{19} +(-2.17235 + 2.98999i) q^{21} +(3.72268 + 4.20650i) q^{22} +(0.674105 - 2.07468i) q^{23} +(7.05510 + 5.40870i) q^{24} +(1.25530 + 0.278103i) q^{26} +(-11.5937 - 3.76703i) q^{27} +(-1.14076 - 2.05658i) q^{28} +(-3.65841 + 5.03536i) q^{29} +(-1.16778 + 0.848445i) q^{31} +(-5.01580 + 2.61567i) q^{32} +(10.0997 - 7.33789i) q^{33} +(7.84354 - 0.756392i) q^{34} +(9.37942 - 10.0640i) q^{36} +(6.65712 - 2.16303i) q^{37} +(-0.611709 - 6.34322i) q^{38} +(0.883011 - 2.71763i) q^{39} +(1.97065 + 6.06503i) q^{41} +(-4.79289 + 2.08483i) q^{42} +2.96089i q^{43} +(1.51803 + 7.79754i) q^{44} +(2.31026 - 2.04454i) q^{46} +(4.30172 + 3.12538i) q^{47} +(4.71632 + 11.6539i) q^{48} -5.61729 q^{49} -17.5127i q^{51} +(1.33018 + 1.23970i) q^{52} +(-7.68016 + 10.5708i) q^{53} +(-11.4253 - 12.9102i) q^{54} +(0.0856196 - 3.32481i) q^{56} -14.1629 q^{57} +(-8.07158 + 3.51101i) q^{58} +(1.22277 - 0.397301i) q^{59} +(-14.7321 - 4.78675i) q^{61} +(-2.03194 + 0.195950i) q^{62} +(2.49945 + 7.69253i) q^{63} +(-7.98940 - 0.411755i) q^{64} +(17.5735 - 1.69470i) q^{66} +(1.78477 + 2.45652i) q^{67} +(10.1012 + 4.70669i) q^{68} +(-4.03005 - 5.54689i) q^{69} +(-1.58201 - 1.14940i) q^{71} +(18.6519 - 5.53375i) q^{72} +(-1.30493 + 4.01616i) q^{73} +(9.66475 + 2.14116i) q^{74} +(3.80639 - 8.16901i) q^{76} +(-4.44199 - 1.44329i) q^{77} +(3.02621 - 2.67815i) q^{78} +(-2.23200 - 1.62164i) q^{79} +(-14.3025 + 10.3914i) q^{81} +(-1.95072 + 8.80515i) q^{82} +(-5.56443 - 7.65878i) q^{83} +(-7.33683 - 0.898695i) q^{84} +(-2.12471 + 3.60824i) q^{86} +(6.04509 + 18.6049i) q^{87} +(-3.74553 + 10.5917i) q^{88} +(-0.806910 + 2.48341i) q^{89} +(-1.01674 + 0.330358i) q^{91} +(4.28250 - 0.833719i) q^{92} +4.53682i q^{93} +(2.99946 + 6.89556i) q^{94} +(-2.61528 + 17.5862i) q^{96} +(0.235869 + 0.171369i) q^{97} +(-6.84541 - 4.03092i) q^{98} -27.3214i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

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 $

$2$	1.21863	+	0.717591i	0.861703	+	0.507414i
$2$	1.21863	+	0.717591i	0.861703	+	0.507414i
$3$	1.84742	−	2.54275i	1.06661	−	1.46806i	0.193145	−	0.981170i	$-0.438131\pi$
$3$	1.84742	−	2.54275i	1.06661	−	1.46806i	0.873463	−	0.486890i	$-0.161869\pi$
$4$	0.970125	+	1.74896i	0.485063	+	0.874479i
$5$		0			0
$5$		0			0
$6$	4.07598	−	1.77299i	1.66401	−	0.723819i
$7$	−1.17589			−0.444443			−0.222222	−	0.974996i	$-0.571331\pi$
$7$	−1.17589			−0.444443			−0.222222	+	0.974996i	$0.571331\pi$
$8$	−0.0728129	+	2.82749i	−0.0257432	+	0.999669i
$9$	−2.12559	−	6.54190i	−0.708531	−	2.18063i
$10$		0			0
$11$	3.77756	+	1.22741i	1.13898	+	0.370077i	0.816981	−	0.576664i	$-0.195646\pi$
$11$	3.77756	+	1.22741i	1.13898	+	0.370077i	0.321997	+	0.946741i	$0.395646\pi$
$12$	6.23940	+	0.764270i	1.80116	+	0.220626i
$13$	0.864656	−	0.280944i	0.239812	−	0.0779198i	−0.186645	−	0.982427i	$-0.559761\pi$
$13$	0.864656	−	0.280944i	0.239812	−	0.0779198i	0.426457	+	0.904508i	$0.359761\pi$
$14$	−1.43297	−	0.843806i	−0.382978	−	0.225517i
$15$		0			0
$16$	−2.11771	+	3.39342i	−0.529429	+	0.848355i
$17$	4.50780	−	3.27511i	1.09330	−	0.794331i	0.113348	−	0.993555i	$-0.463842\pi$
$17$	4.50780	−	3.27511i	1.09330	−	0.794331i	0.979954	+	0.199225i	$0.0638424\pi$
$18$	2.10410	−	9.49747i	0.495940	−	2.23858i
$19$	−2.64864	−	3.64555i	−0.607641	−	0.836346i	0.388740	−	0.921348i	$-0.372910\pi$
$19$	−2.64864	−	3.64555i	−0.607641	−	0.836346i	−0.996381	+	0.0850017i	$0.972910\pi$
$20$		0			0
$21$	−2.17235	+	2.98999i	−0.474047	+	0.652469i
$22$	3.72268	+	4.20650i	0.793679	+	0.896829i
$23$	0.674105	−	2.07468i	0.140561	−	0.432601i	−0.855853	−	0.517220i	$-0.826967\pi$
$23$	0.674105	−	2.07468i	0.140561	−	0.432601i	0.996413	+	0.0846183i	$0.0269671\pi$
$24$	7.05510	+	5.40870i	1.44012	+	1.10405i
$25$		0			0
$26$	1.25530	+	0.278103i	0.246184	+	0.0545404i
$27$	−11.5937	−	3.76703i	−2.23122	−	0.724966i
$28$	−1.14076	−	2.05658i	−0.215583	−	0.388656i
$29$	−3.65841	+	5.03536i	−0.679349	+	0.935044i	−0.999926	−	0.0121788i	$-0.996123\pi$
$29$	−3.65841	+	5.03536i	−0.679349	+	0.935044i	0.320577	+	0.947223i	$0.396123\pi$
$30$		0			0
$31$	−1.16778	+	0.848445i	−0.209740	+	0.152385i	−0.687696	−	0.725999i	$-0.741378\pi$
$31$	−1.16778	+	0.848445i	−0.209740	+	0.152385i	0.477956	+	0.878384i	$0.341378\pi$
$32$	−5.01580	+	2.61567i	−0.886677	+	0.462390i
$33$	10.0997	−	7.33789i	1.75814	−	1.27736i
$34$	7.84354	−	0.756392i	1.34516	−	0.129720i
$35$		0			0
$36$	9.37942	−	10.0640i	1.56324	−	1.67734i
$37$	6.65712	−	2.16303i	1.09442	−	0.355600i	0.294470	−	0.955661i	$-0.404857\pi$
$37$	6.65712	−	2.16303i	1.09442	−	0.355600i	0.799954	+	0.600061i	$0.204857\pi$
$38$	−0.611709	−	6.34322i	−0.0992323	−	1.02901i
$39$	0.883011	−	2.71763i	0.141395	−	0.435169i
$40$		0			0
$41$	1.97065	+	6.06503i	0.307763	+	0.947198i	0.978632	+	0.205622i	$0.0659216\pi$
$41$	1.97065	+	6.06503i	0.307763	+	0.947198i	−0.670868	+	0.741577i	$0.734078\pi$
$42$	−4.79289	+	2.08483i	−0.739559	+	0.321697i
$43$			2.96089i			0.451532i	0.974182	+	0.225766i	$0.0724884\pi$
$43$			2.96089i			0.451532i	−0.974182	+	0.225766i	$0.927512\pi$
$44$	1.51803	+	7.79754i	0.228852	+	1.17552i
$45$		0			0
$46$	2.31026	−	2.04454i	0.340629	−	0.301451i
$47$	4.30172	+	3.12538i	0.627470	+	0.455884i	0.855523	−	0.517765i	$-0.173236\pi$
$47$	4.30172	+	3.12538i	0.627470	+	0.455884i	−0.228053	+	0.973649i	$0.573236\pi$
$48$	4.71632	+	11.6539i	0.680743	+	1.68209i
$49$	−5.61729			−0.802470
$50$		0			0
$51$		−	17.5127i		−	2.45227i
$52$	1.33018	+	1.23970i	0.184463	+	0.171915i
$53$	−7.68016	+	10.5708i	−1.05495	+	1.45202i	−0.170515	+	0.985355i	$0.554543\pi$
$53$	−7.68016	+	10.5708i	−1.05495	+	1.45202i	−0.884436	+	0.466661i	$0.845457\pi$
$54$	−11.4253	−	12.9102i	−1.55479	−	1.75685i
$55$		0			0
$56$	0.0856196	−	3.32481i	0.0114414	−	0.444296i
$57$	−14.1629			−1.87592
$58$	−8.07158	+	3.51101i	−1.05985	+	0.461019i
$59$	1.22277	−	0.397301i	0.159191	−	0.0517242i	−0.228338	−	0.973582i	$-0.573329\pi$
$59$	1.22277	−	0.397301i	0.159191	−	0.0517242i	0.387528	+	0.921858i	$0.373329\pi$
$60$		0			0
$61$	−14.7321	−	4.78675i	−1.88625	−	0.612881i	−0.982948	−	0.183885i	$-0.941133\pi$
$61$	−14.7321	−	4.78675i	−1.88625	−	0.612881i	−0.903306	−	0.428996i	$-0.858867\pi$
$62$	−2.03194	+	0.195950i	−0.258056	+	0.0248857i
$63$	2.49945	+	7.69253i	0.314902	+	0.969167i
$64$	−7.98940	−	0.411755i	−0.998675	−	0.0514694i
$65$		0			0
$66$	17.5735	−	1.69470i	2.16314	−	0.208603i
$67$	1.78477	+	2.45652i	0.218044	+	0.300112i	0.904001	−	0.427530i	$-0.140616\pi$
$67$	1.78477	+	2.45652i	0.218044	+	0.300112i	−0.685957	+	0.727642i	$0.740616\pi$
$68$	10.1012	+	4.70669i	1.22495	+	0.570770i
$69$	−4.03005	−	5.54689i	−0.485161	−	0.667767i
$70$		0			0
$71$	−1.58201	−	1.14940i	−0.187750	−	0.136409i	0.489940	−	0.871756i	$-0.337019\pi$
$71$	−1.58201	−	1.14940i	−0.187750	−	0.136409i	−0.677690	+	0.735348i	$0.737019\pi$
$72$	18.6519	−	5.53375i	2.19815	−	0.652159i
$73$	−1.30493	+	4.01616i	−0.152731	+	0.470056i	−0.997924	−	0.0644044i	$-0.979485\pi$
$73$	−1.30493	+	4.01616i	−0.152731	+	0.470056i	0.845193	+	0.534461i	$0.179485\pi$
$74$	9.66475	+	2.14116i	1.12350	+	0.248905i
$75$		0			0
$76$	3.80639	−	8.16901i	0.436623	−	0.937049i
$77$	−4.44199	−	1.44329i	−0.506211	−	0.164478i
$78$	3.02621	−	2.67815i	0.342651	−	0.303240i
$79$	−2.23200	−	1.62164i	−0.251119	−	0.182449i	0.455103	−	0.890439i	$-0.349602\pi$
$79$	−2.23200	−	1.62164i	−0.251119	−	0.182449i	−0.706223	+	0.707990i	$0.749602\pi$
$80$		0			0
$81$	−14.3025	+	10.3914i	−1.58917	+	1.15460i
$82$	−1.95072	+	8.80515i	−0.215421	+	0.972366i
$83$	−5.56443	−	7.65878i	−0.610775	−	0.840660i	0.385866	−	0.922555i	$-0.373903\pi$
$83$	−5.56443	−	7.65878i	−0.610775	−	0.840660i	−0.996641	+	0.0818950i	$0.973903\pi$
$84$	−7.33683	−	0.898695i	−0.800513	−	0.0980557i
$85$		0			0
$86$	−2.12471	+	3.60824i	−0.229113	+	0.389086i
$87$	6.04509	+	18.6049i	0.648101	+	1.99465i
$88$	−3.74553	+	10.5917i	−0.399275	+	1.12907i
$89$	−0.806910	+	2.48341i	−0.0855323	+	0.263241i	−0.984671	−	0.174423i	$-0.944194\pi$
$89$	−0.806910	+	2.48341i	−0.0855323	+	0.263241i	0.899139	+	0.437664i	$0.144194\pi$
$90$		0			0
$91$	−1.01674	+	0.330358i	−0.106583	+	0.0346309i
$92$	4.28250	−	0.833719i	0.446482	−	0.0869213i
$93$			4.53682i			0.470447i
$94$	2.99946	+	6.89556i	0.309371	+	0.711223i
$95$		0			0
$96$	−2.61528	+	17.5862i	−0.266920	+	1.79488i
$97$	0.235869	+	0.171369i	0.0239489	+	0.0173999i	0.599695	−	0.800228i	$-0.295288\pi$
$97$	0.235869	+	0.171369i	0.0239489	+	0.0173999i	−0.575746	+	0.817628i	$0.695288\pi$
$98$	−6.84541	−	4.03092i	−0.691491	−	0.407184i
$99$		−	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	$0.872427\pi$
$102$	12.5670	−	21.3416i	1.24432	−	2.11313i
$103$	10.6532	+	7.73997i	1.04969	+	0.762642i	0.972153	−	0.234347i	$-0.0752953\pi$
$103$	10.6532	+	7.73997i	1.04969	+	0.762642i	0.0775342	+	0.996990i	$0.475295\pi$
$104$	0.731407	+	2.46526i	0.0717204	+	0.241739i
$105$		0			0
$106$	−16.9448	+	7.37074i	−1.64583	+	0.715909i
$107$		−	7.00700i		−	0.677392i	−0.940896	−	0.338696i	$-0.890014\pi$
$107$		−	7.00700i		−	0.677392i	0.940896	−	0.338696i	$-0.109986\pi$
$108$	−4.65899	−	23.9315i	−0.448312	−	2.30281i
$109$	−2.56991	+	0.835013i	−0.246152	+	0.0799797i	−0.429495	−	0.903069i	$-0.641308\pi$
$109$	−2.56991	+	0.835013i	−0.246152	+	0.0799797i	0.183342	+	0.983049i	$0.441308\pi$
$110$		0			0
$111$	6.79844	−	20.9235i	0.645280	−	1.98597i
$112$	2.49019	−	3.99027i	0.235301	−	0.377045i
$113$	1.41241	+	4.34695i	0.132868	+	0.408926i	0.995252	−	0.0973282i	$-0.0310296\pi$
$113$	1.41241	+	4.34695i	0.132868	+	0.408926i	−0.862384	+	0.506255i	$0.831030\pi$
$114$	−17.2593	−	10.1632i	−1.61649	−	0.951868i
$115$		0			0
$116$	−12.3558	−	1.51347i	−1.14720	−	0.140522i
$117$	−3.67581	−	5.05932i	−0.339829	−	0.467734i
$118$	1.77520	+	0.393283i	0.163420	+	0.0362047i
$119$	−5.30066	+	3.85116i	−0.485911	+	0.353035i
$120$		0			0
$121$	3.86428	+	2.80757i	0.351299	+	0.255233i
$122$	−14.5181	−	16.4049i	−1.31441	−	1.48523i
$123$	19.0625	+	6.19378i	1.71881	+	0.558474i
$124$	−2.61679	−	1.21931i	−0.234995	−	0.109497i
$125$		0			0
$126$	−2.47418	+	11.1679i	−0.220417	+	0.994919i
$127$	−2.66690	+	8.20787i	−0.236649	+	0.728330i	0.760250	+	0.649631i	$0.225077\pi$
$127$	−2.66690	+	8.20787i	−0.236649	+	0.728330i	−0.996898	+	0.0786992i	$0.974923\pi$
$128$	−9.44066	−	6.23490i	−0.834444	−	0.551093i
$129$	7.52882	+	5.47001i	0.662876	+	0.481607i
$130$		0			0
$131$	−5.11250	−	7.03676i	−0.446681	−	0.614804i	0.524999	−	0.851103i	$-0.324066\pi$
$131$	−5.11250	−	7.03676i	−0.446681	−	0.614804i	−0.971680	+	0.236299i	$0.924066\pi$
$132$	22.6317	+	10.5454i	1.96983	+	0.917855i
$133$	3.11451	+	4.28675i	0.270062	+	0.371708i
$134$	0.412194	+	4.27432i	0.0356082	+	0.369245i
$135$		0			0
$136$	8.93211	+	12.9842i	0.765922	+	1.11339i
$137$	−1.12598	−	3.46540i	−0.0961988	−	0.296069i	0.891365	−	0.453285i	$-0.149748\pi$
$137$	−1.12598	−	3.46540i	−0.0961988	−	0.296069i	−0.987564	+	0.157216i	$0.949748\pi$
$138$	−0.930747	−	9.65155i	−0.0792305	−	0.821594i
$139$	13.2832	+	4.31597i	1.12666	+	0.366075i	0.812307	−	0.583230i	$-0.198211\pi$
$139$	13.2832	+	4.31597i	1.12666	+	0.366075i	0.314357	+	0.949305i	$0.398211\pi$
$140$		0			0
$141$	15.8941	−	5.16432i	1.33853	−	0.434914i
$142$	−1.10309	−	2.53593i	−0.0925693	−	0.212811i
$143$	3.61112			0.301977
$144$	26.7008	+	6.64085i	2.22507	+	0.553404i
$145$		0			0
$146$	−4.47219	+	3.95781i	−0.370121	+	0.327551i
$147$	−10.3775	+	14.2834i	−0.855921	+	1.17807i
$148$	10.2413	+	9.54463i	0.841829	+	0.784563i
$149$		−	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	$0.357796\pi$
$152$	10.5006	−	7.22357i	0.851711	−	0.585909i
$153$	−31.0072	−	22.5280i	−2.50678	−	1.82128i
$154$	−4.37745	−	4.94637i	−0.352745	−	0.398590i
$155$		0			0
$156$	5.60965	−	1.09209i	0.449132	−	0.0874372i
$157$			3.90358i			0.311539i	0.987793	+	0.155770i	$0.0497857\pi$
$157$			3.90358i			0.311539i	−0.987793	+	0.155770i	$0.950214\pi$
$158$	−1.55631	−	3.57784i	−0.123813	−	0.284638i
$159$	12.6906	+	39.0575i	1.00643	+	3.09746i
$160$		0			0
$161$	−0.792671	+	2.43959i	−0.0624712	+	0.192267i
$162$	−24.8863	+	2.39991i	−1.95525	+	0.188555i
$163$	−18.6687	+	6.06584i	−1.46225	+	0.475114i	−0.928756	−	0.370691i	$-0.879121\pi$
$163$	−18.6687	+	6.06584i	−1.46225	+	0.475114i	−0.533493	+	0.845805i	$0.679121\pi$
$164$	−8.69571	+	9.33042i	−0.679021	+	0.728583i
$165$		0			0
$166$	−1.28511	−	13.3262i	−0.0997441	−	1.03431i
$167$	13.6261	−	9.89993i	1.05442	−	0.766080i	0.0813708	−	0.996684i	$-0.474070\pi$
$167$	13.6261	−	9.89993i	1.05442	−	0.766080i	0.973048	+	0.230604i	$0.0740702\pi$
$168$	−8.29599	−	6.36002i	−0.640050	−	0.490686i
$169$	−9.84852	+	7.15537i	−0.757579	+	0.550413i
$170$		0			0
$171$	−18.2189	+	25.0761i	−1.39323	+	1.91762i
$172$	−5.17848	+	2.87244i	−0.394855	+	0.219021i
$173$	9.68309	+	3.14623i	0.736192	+	0.239203i	0.653029	−	0.757333i	$-0.273498\pi$
$173$	9.68309	+	3.14623i	0.736192	+	0.239203i	0.0831625	+	0.996536i	$0.473498\pi$
$174$	−5.98396	+	27.0104i	−0.453643	+	2.04765i
$175$		0			0
$176$	−12.1649	+	10.2196i	−0.916964	+	0.770328i
$177$	1.24872	−	3.84317i	0.0938598	−	0.288871i
$178$	−2.76540	+	2.44733i	−0.207276	+	0.183435i
$179$	−8.87687	+	12.2180i	−0.663488	+	0.913214i	−0.999591	−	0.0286120i	$-0.990891\pi$
$179$	−8.87687	+	12.2180i	−0.663488	+	0.913214i	0.336102	+	0.941826i	$0.390891\pi$
$180$		0			0
$181$	−11.1217	−	15.3077i	−0.826668	−	1.13781i	−0.988534	−	0.150998i	$-0.951751\pi$
$181$	−11.1217	−	15.3077i	−0.826668	−	1.13781i	0.161866	−	0.986813i	$-0.448249\pi$
$182$	−1.47609	−	0.327017i	−0.109415	−	0.0242401i
$183$	−39.3879	+	28.6170i	−2.91164	+	2.11543i
$184$	5.81706	+	2.05709i	0.428839	+	0.151651i
$185$		0			0
$186$	−3.25559	+	5.52872i	−0.238711	+	0.405385i
$187$	21.0484	−	6.83904i	1.53921	−	0.500120i
$188$	−1.29296	+	10.5555i	−0.0942986	+	0.769841i
$189$	13.6329	+	4.42960i	0.991649	+	0.322206i
$190$		0			0
$191$	−0.692493	−	2.13127i	−0.0501070	−	0.154214i	0.922872	−	0.385106i	$-0.125835\pi$
$191$	−0.692493	−	2.13127i	−0.0501070	−	0.154214i	−0.972979	+	0.230893i	$0.925835\pi$
$192$	−15.8068	+	19.5544i	−1.14075	+	1.41122i
$193$	22.6952			1.63363			0.816817	−	0.576896i	$-0.195736\pi$
$193$	22.6952			1.63363			0.816817	+	0.576896i	$0.195736\pi$
$194$	0.164465	+	0.378093i	0.0118079	+	0.0271455i
$195$		0			0
$196$	−5.44948	−	9.82441i	−0.389248	−	0.701744i
$197$	−7.63095	+	10.5031i	−0.543682	+	0.748315i	−0.989138	−	0.146989i	$-0.953042\pi$
$197$	−7.63095	+	10.5031i	−0.543682	+	0.748315i	0.445456	+	0.895304i	$0.353042\pi$
$198$	19.6056	−	33.2947i	1.39331	−	2.36615i
$199$	18.2166			1.29134			0.645672	−	0.763615i	$-0.276577\pi$
$199$	18.2166			1.29134			0.645672	+	0.763615i	$0.276577\pi$
$200$		0			0
$201$	9.54353			0.673149
$202$	−5.62715	+	9.55616i	−0.395925	+	0.672369i
$203$	4.30187	−	5.92102i	0.301932	−	0.415574i
$204$	30.6290	−	16.9895i	2.14446	−	1.18951i
$205$		0			0
$206$	7.42814	+	17.0768i	0.517543	+	1.18980i
$207$	−15.0052			−1.04294
$208$	−0.877735	+	3.52910i	−0.0608599	+	0.244699i
$209$	−5.53086	−	17.0222i	−0.382578	−	1.17745i
$210$		0			0
$211$	−1.67102	−	0.542946i	−0.115037	−	0.0373779i	0.250933	−	0.968005i	$-0.419263\pi$
$211$	−1.67102	−	0.542946i	−0.115037	−	0.0373779i	−0.365970	+	0.930627i	$0.619263\pi$
$212$	−25.9387	−	3.17725i	−1.78148	−	0.218215i
$213$	−5.84528	+	1.89925i	−0.400512	+	0.130134i
$214$	5.02816	−	8.53895i	0.343718	−	0.583711i
$215$		0			0
$216$	11.4954	−	32.5069i	0.782165	−	2.21181i
$217$	1.37318	−	0.997675i	0.0932177	−	0.0677266i
$218$	−3.73097	−	0.826569i	−0.252693	−	0.0559823i
$219$	7.80136	+	10.7377i	0.527167	+	0.725583i
$220$		0			0
$221$	2.97757	−	4.09828i	0.200293	−	0.275680i
$222$	23.2993	−	20.6195i	1.56375	−	1.38389i
$223$	0.481630	−	1.48230i	0.0322523	−	0.0992625i	−0.933634	−	0.358227i	$-0.883381\pi$
$223$	0.481630	−	1.48230i	0.0322523	−	0.0992625i	0.965887	+	0.258965i	$0.0833813\pi$
$224$	5.89801	−	3.07573i	0.394077	−	0.205506i
$225$		0			0
$226$	−1.39813	+	6.31086i	−0.0930020	+	0.419792i
$227$	8.77081	+	2.84981i	0.582139	+	0.189148i	0.585259	−	0.810847i	$-0.300993\pi$
$227$	8.77081	+	2.84981i	0.582139	+	0.189148i	−0.00311955	+	0.999995i	$0.500993\pi$
$228$	−13.7398	−	24.7703i	−0.909939	−	1.64045i
$229$	−6.64077	+	9.14023i	−0.438834	+	0.604003i	−0.969953	−	0.243294i	$-0.921772\pi$
$229$	−6.64077	+	9.14023i	−0.438834	+	0.604003i	0.531118	+	0.847298i	$0.321772\pi$
$230$		0			0
$231$	−11.8761	+	8.62852i	−0.781393	+	0.567715i
$232$	−13.9711	−	10.7107i	−0.917245	−	0.703195i
$233$	10.0570	−	7.30682i	0.658854	−	0.478685i	−0.207422	−	0.978252i	$-0.566507\pi$
$233$	10.0570	−	7.30682i	0.658854	−	0.478685i	0.866276	+	0.499566i	$0.166507\pi$
$234$	−0.848934	−	8.80318i	−0.0554966	−	0.575482i
$235$		0			0
$236$	1.88110	+	1.75314i	0.122449	+	0.114119i
$237$	−8.24687	+	2.67957i	−0.535692	+	0.174057i
$238$	−9.22311	+	0.889430i	−0.597845	+	0.0576532i
$239$	8.53966	−	26.2824i	0.552384	−	1.70006i	−0.150368	−	0.988630i	$-0.548046\pi$
$239$	8.53966	−	26.2824i	0.552384	−	1.70006i	0.702752	−	0.711435i	$-0.251954\pi$
$240$		0			0
$241$	−1.32369	−	4.07389i	−0.0852663	−	0.262423i	0.899329	−	0.437273i	$-0.144056\pi$
$241$	−1.32369	−	4.07389i	−0.0852663	−	0.262423i	−0.984595	+	0.174851i	$0.944056\pi$
$242$	2.69445	+	6.19437i	0.173206	+	0.398189i
$243$			18.9940i			1.21846i
$244$	−5.92016	−	30.4096i	−0.378999	−	1.94678i
$245$		0			0
$246$	18.7855	+	21.2270i	1.19772	+	1.35338i
$247$	−3.31436	−	2.40802i	−0.210888	−	0.153219i
$248$	−2.31394	−	3.36368i	−0.146935	−	0.213594i
$249$	−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	$0.861012\pi$
$252$	−11.0291	+	11.8342i	−0.694770	+	0.745482i
$253$	5.09295	−	7.00985i	0.320191	−	0.440705i
$254$	−9.13986	+	8.08862i	−0.573486	+	0.507525i
$255$		0			0
$256$	−7.03057	−	14.3726i	−0.439411	−	0.898286i
$257$	7.81899			0.487735			0.243868	−	0.969809i	$-0.421584\pi$
$257$	7.81899			0.487735			0.243868	+	0.969809i	$0.421584\pi$
$258$	5.24963	+	12.0685i	0.326827	+	0.751355i
$259$	−7.82802	+	2.54348i	−0.486409	+	0.158044i
$260$		0			0
$261$	40.7171	+	13.2298i	2.52033	+	0.818904i
$262$	−1.18074	−	12.2439i	−0.0729464	−	0.756431i
$263$	−8.47975	−	26.0980i	−0.522884	−	1.60927i	−0.768463	−	0.639894i	$-0.778978\pi$
$263$	−8.47975	−	26.0980i	−0.522884	−	1.60927i	0.245579	−	0.969377i	$-0.421022\pi$
$264$	20.0124	+	29.0912i	1.23168	+	1.79044i
$265$		0			0
$266$	0.719300	+	7.45891i	0.0441031	+	0.457335i
$267$	4.82401	+	6.63968i	0.295225	+	0.406342i
$268$	−2.56490	+	5.50461i	−0.156676	+	0.336248i
$269$	−12.5408	−	17.2610i	−0.764629	−	1.05242i	−0.996815	−	0.0797498i	$-0.974588\pi$
$269$	−12.5408	−	17.2610i	−0.764629	−	1.05242i	0.232186	−	0.972671i	$-0.425412\pi$
$270$		0			0
$271$	0.864363	+	0.627996i	0.0525063	+	0.0381481i	0.613729	−	0.789517i	$-0.289669\pi$
$271$	0.864363	+	0.627996i	0.0525063	+	0.0381481i	−0.561223	+	0.827665i	$0.689669\pi$
$272$	1.56758	+	22.2326i	0.0950485	+	1.34805i
$273$	−1.03832	+	3.19562i	−0.0628420	+	0.193408i
$274$	1.11459	−	5.03104i	0.0673350	−	0.303936i
$275$		0			0
$276$	5.79163	−	12.4296i	0.348615	−	0.748173i
$277$	−16.8842	−	5.48602i	−1.01448	−	0.329623i	−0.245840	−	0.969310i	$-0.579064\pi$
$277$	−16.8842	−	5.48602i	−1.01448	−	0.329623i	−0.768635	+	0.639687i	$0.779064\pi$
$278$	13.0902	+	14.7915i	0.785098	+	0.887133i
$279$	8.03268	+	5.83608i	0.480904	+	0.349397i
$280$		0			0
$281$	−8.77867	+	6.37807i	−0.523691	+	0.380484i	−0.817993	−	0.575229i	$-0.804913\pi$
$281$	−8.77867	+	6.37807i	−0.523691	+	0.380484i	0.294301	+	0.955713i	$0.404913\pi$
$282$	23.0750	+	5.11210i	1.37410	+	0.304421i
$283$	13.6517	+	18.7899i	0.811509	+	1.11695i	0.991089	+	0.133203i	$0.0425261\pi$
$283$	13.6517	+	18.7899i	0.811509	+	1.11695i	−0.179580	+	0.983743i	$0.557474\pi$
$284$	0.475502	−	3.88193i	0.0282158	−	0.230350i
$285$		0			0
$286$	4.40063	+	2.59131i	0.260215	+	0.153228i
$287$	−2.31726	−	7.13178i	−0.136783	−	0.420976i
$288$	27.7730	+	27.2530i	1.63654	+	1.60590i
$289$	4.34064	−	13.3591i	0.255332	−	0.785830i
$290$		0			0
$291$	0.871498	−	0.283167i	0.0510881	−	0.0165995i
$292$	−8.29005	+	1.61391i	−0.485138	+	0.0944470i
$293$		−	23.5633i		−	1.37658i	−0.725434	−	0.688291i	$-0.758361\pi$
$293$		−	23.5633i		−	1.37658i	0.725434	−	0.688291i	$-0.241639\pi$
$294$	−22.8960	+	9.95939i	−1.33532	+	0.580844i
$295$		0			0
$296$	5.63122	+	18.9804i	0.327308	+	1.10322i
$297$	−39.1724	−	28.4604i	−2.27301	−	1.65144i
$298$	1.87552	−	3.18506i	0.108646	−	0.184505i
$299$		−	1.98327i		−	0.114696i
$300$		0			0
$301$		−	3.48167i		−	0.200680i
$302$	12.9392	+	7.61927i	0.744569	+	0.438440i
$303$	19.9396	+	14.4869i	1.14550	+	0.832252i
$304$	17.9799	−	1.26773i	1.03122	−	0.0727094i
$305$		0			0
$306$	−21.6204	−	49.7038i	−1.23596	−	2.84138i
$307$		−	29.1918i		−	1.66607i	−0.553223	−	0.833033i	$-0.686602\pi$
$307$		−	29.1918i		−	1.66607i	0.553223	−	0.833033i	$-0.313398\pi$
$308$	−1.78503	−	9.16902i	−0.101712	−	0.522453i
$309$	39.3617	−	12.7894i	2.23921	−	0.727563i
$310$		0			0
$311$	0.303724	−	0.934766i	0.0172226	−	0.0530057i	−0.942076	−	0.335400i	$-0.891129\pi$
$311$	0.303724	−	0.934766i	0.0172226	−	0.0530057i	0.959298	+	0.282394i	$0.0911286\pi$
$312$	7.61977	+	2.69458i	0.431385	+	0.152551i
$313$	−2.96079	−	9.11237i	−0.167354	−	0.515062i	0.831848	−	0.555003i	$-0.187283\pi$
$313$	−2.96079	−	9.11237i	−0.167354	−	0.515062i	−0.999202	+	0.0399413i	$0.987283\pi$
$314$	−2.80117	+	4.75702i	−0.158079	+	0.268454i
$315$		0			0
$316$	0.670866	−	5.47686i	0.0377392	−	0.308098i
$317$	−10.8218	−	14.8949i	−0.607811	−	0.836580i	0.388584	−	0.921413i	$-0.372964\pi$
$317$	−10.8218	−	14.8949i	−0.607811	−	0.836580i	−0.996395	+	0.0848334i	$0.972964\pi$
$318$	−12.5622	+	56.7034i	−0.704455	+	3.17977i
$319$	−20.0003	+	14.5311i	−1.11980	+	0.813584i
$320$		0			0
$321$	−17.8171	−	12.9449i	−0.994453	−	0.722512i
$322$	−2.71660	+	2.40415i	−0.151390	+	0.133978i
$323$	−23.8791	−	7.75880i	−1.32867	−	0.431711i
$324$	−32.0494	−	14.9336i	−1.78052	−	0.829643i
$325$		0			0
$326$	−27.1031	−	6.00450i	−1.50110	−	0.332559i
$327$	−2.62446	+	8.07726i	−0.145133	+	0.446673i
$328$	−17.2923	+	5.13037i	−0.954807	+	0.283277i
$329$	−5.05833	−	3.67509i	−0.278875	−	0.202614i
$330$		0			0
$331$	4.25106	+	5.85108i	0.233659	+	0.321604i	0.909705	−	0.415255i	$-0.136308\pi$
$331$	4.25106	+	5.85108i	0.233659	+	0.321604i	−0.676046	+	0.736860i	$0.736308\pi$
$332$	7.99669	−	17.1619i	0.438876	−	0.941883i
$333$	−28.3007	−	38.9525i	−1.55087	−	2.13458i
$334$	23.7093	−	2.28641i	1.29731	−	0.125107i
$335$		0			0
$336$	−5.54586	−	13.7037i	−0.302551	−	0.747596i
$337$	2.81684	+	8.66935i	0.153443	+	0.472250i	0.998000	−	0.0632165i	$-0.0201359\pi$
$337$	2.81684	+	8.66935i	0.153443	+	0.472250i	−0.844557	+	0.535466i	$0.820136\pi$
$338$	−17.1363	+	1.65254i	−0.932094	+	0.0898865i
$339$	13.6625	+	4.43923i	0.742047	+	0.241106i
$340$		0			0
$341$	−5.45277	+	1.77171i	−0.295284	+	0.0959436i
$342$	−40.1965	+	17.4848i	−2.17358	+	0.945472i
$343$	14.8365			0.801096
$344$	−8.37189	−	0.215591i	−0.451382	−	0.0116239i
$345$		0			0
$346$	9.54241	+	10.7826i	0.513003	+	0.579676i
$347$	−6.01350	+	8.27687i	−0.322821	+	0.444326i	−0.939326	−	0.343026i	$-0.888548\pi$
$347$	−6.01350	+	8.27687i	−0.322821	+	0.444326i	0.616505	+	0.787351i	$0.288548\pi$
$348$	−26.6746	+	28.6216i	−1.42991	+	1.53428i
$349$			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
$352$	−22.1580	+	3.72445i	−1.18103	+	0.198514i
$353$	−14.7692	−	10.7305i	−0.786087	−	0.571126i	0.120713	−	0.992687i	$-0.461482\pi$
$353$	−14.7692	−	10.7305i	−0.786087	−	0.571126i	−0.906800	+	0.421562i	$0.861482\pi$
$354$	4.27956	−	3.78734i	0.227456	−	0.201295i
$355$		0			0
$356$	−5.12619	+	0.997969i	−0.271688	+	0.0528923i
$357$			20.5930i			1.08990i
$358$	−19.5851	+	8.51923i	−1.03511	+	0.450255i
$359$	−5.64467	−	17.3725i	−0.297914	−	0.916885i	−0.982227	−	0.187697i	$-0.939898\pi$
$359$	−5.64467	−	17.3725i	−0.297914	−	0.916885i	0.684313	−	0.729188i	$-0.260102\pi$
$360$		0			0
$361$	−0.403370	+	1.24145i	−0.0212300	+	0.0653393i
$362$	−2.56857	−	26.6353i	−0.135001	−	1.39992i
$363$	14.2779	−	4.63917i	0.749396	−	0.243493i
$364$	−1.56414	−	1.45774i	−0.0819834	−	0.0764065i
$365$		0			0
$366$	−68.5347	+	6.60914i	−3.58237	+	0.345466i
$367$	12.1811	−	8.85005i	0.635846	−	0.461969i	−0.222575	−	0.974916i	$-0.571446\pi$
$367$	12.1811	−	8.85005i	0.635846	−	0.461969i	0.858421	+	0.512947i	$0.171446\pi$
$368$	5.61270	+	6.68111i	0.292582	+	0.348277i
$369$	35.4880	−	25.7835i	1.84743	−	1.34224i
$370$		0			0
$371$	9.03100	−	12.4301i	0.468866	−	0.645339i
$372$	−7.93472	+	4.40129i	−0.411396	+	0.228196i
$373$	−0.674295	−	0.219092i	−0.0349137	−	0.0113441i	0.291508	−	0.956568i	$-0.405843\pi$
$373$	−0.674295	−	0.219092i	−0.0349137	−	0.0113441i	−0.326422	+	0.945224i	$0.605843\pi$
$374$	30.5579	+	6.76988i	1.58011	+	0.350062i
$375$		0			0
$376$	−9.15020	+	11.9355i	−0.471886	+	0.615526i
$377$	−1.74861	+	5.38166i	−0.0900579	+	0.277170i
$378$	13.4349	+	15.1809i	0.691015	+	0.780822i
$379$	−10.8210	+	14.8938i	−0.555838	+	0.765045i	−0.990790	−	0.135408i	$-0.956765\pi$
$379$	−10.8210	+	14.8938i	−0.555838	+	0.765045i	0.434952	+	0.900454i	$0.356765\pi$
$380$		0			0
$381$	15.9437	+	21.9446i	0.816821	+	1.12426i
$382$	0.685490	−	3.09416i	0.0350727	−	0.158311i
$383$	14.5194	−	10.5490i	0.741907	−	0.539027i	−0.151401	−	0.988472i	$-0.548378\pi$
$383$	14.5194	−	10.5490i	0.741907	−	0.539027i	0.893308	+	0.449445i	$0.148378\pi$
$384$	−33.2947	+	12.4868i	−1.69906	+	0.637214i
$385$		0			0
$386$	27.6571	+	16.2859i	1.40771	+	0.828929i
$387$	19.3699	−	6.29365i	0.984625	−	0.319924i
$388$	−0.0708946	+	0.578774i	−0.00359913	+	0.0293828i
$389$	−22.7077	−	7.37819i	−1.15133	−	0.374089i	−0.329685	−	0.944091i	$-0.606942\pi$
$389$	−22.7077	−	7.37819i	−1.15133	−	0.374089i	−0.821643	+	0.570002i	$0.806942\pi$
$390$		0			0
$391$	−3.75608	−	11.5600i	−0.189953	−	0.584616i
$392$	0.409011	−	15.8828i	0.0206582	−	0.802204i
$393$	−27.3377			−1.37900
$394$	−16.8362	+	7.32350i	−0.848198	+	0.368953i
$395$		0			0
$396$	47.7840	−	26.5052i	2.40124	−	1.33194i
$397$	0.848630	−	1.16804i	0.0425915	−	0.0586222i	−0.787190	−	0.616710i	$-0.788465\pi$
$397$	0.848630	−	1.16804i	0.0425915	−	0.0586222i	0.829782	+	0.558088i	$0.188465\pi$
$398$	22.1994	+	13.0721i	1.11275	+	0.655246i
$399$	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	$0.725605\pi$
$402$	11.6300	+	6.84836i	0.580054	+	0.341565i
$403$	−0.771367	+	1.06170i	−0.0384245	+	0.0528868i
$404$	−13.7148	+	7.60744i	−0.682338	+	0.378484i
$405$		0			0
$406$	9.49126	−	4.12855i	0.471043	−	0.204897i
$407$	27.8026			1.37813
$408$	49.5171	+	1.27515i	2.45146	+	0.0631294i
$409$	−0.312601	−	0.962088i	−0.0154571	−	0.0475722i	0.943030	−	0.332706i	$-0.107962\pi$
$409$	−0.312601	−	0.962088i	−0.0154571	−	0.0475722i	−0.958488	+	0.285134i	$0.907962\pi$
$410$		0			0
$411$	−10.8918	−	3.53897i	−0.537254	−	0.174564i
$412$	−3.20200	+	26.1407i	−0.157751	+	1.28786i
$413$	−1.43783	+	0.467180i	−0.0707512	+	0.0229884i
$414$	−18.2859	−	10.7676i	−0.898701	−	0.529200i
$415$		0			0
$416$	−3.60208	+	3.67081i	−0.176607	+	0.179976i
$417$	35.5140	−	25.8025i	1.73913	−	1.26355i
$418$	5.47494	−	24.7127i	0.267788	−	1.20874i
$419$	19.6696	+	27.0728i	0.960920	+	1.32259i	0.946502	+	0.322697i	$0.104590\pi$
$419$	19.6696	+	27.0728i	0.960920	+	1.32259i	0.0144183	+	0.999896i	$0.495410\pi$
$420$		0			0
$421$	−16.1696	+	22.2556i	−0.788060	+	1.08467i	0.206287	+	0.978492i	$0.433862\pi$
$421$	−16.1696	+	22.2556i	−0.788060	+	1.08467i	−0.994347	+	0.106180i	$0.966138\pi$
$422$	−1.64674	−	1.86076i	−0.0801620	−	0.0905803i
$423$	11.3022	−	34.7847i	0.549533	−	1.69129i
$424$	−29.3297	−	22.4853i	−1.42438	−	1.09198i
$425$		0			0
$426$	−8.48612	−	1.88004i	−0.411154	−	0.0910883i
$427$	17.3233	+	5.62868i	0.838333	+	0.272391i
$428$	12.2550	−	6.79767i	0.592366	−	0.328578i
$429$	6.67126	−	9.18220i	0.322092	−	0.443321i
$430$		0			0
$431$	21.6348	−	15.7186i	1.04211	−	0.757138i	0.0714143	−	0.997447i	$-0.477249\pi$
$431$	21.6348	−	15.7186i	1.04211	−	0.757138i	0.970696	+	0.240309i	$0.0772488\pi$
$432$	37.3354	−	31.3649i	1.79630	−	1.50904i
$433$	16.7912	−	12.1996i	0.806936	−	0.586273i	−0.106005	−	0.994366i	$-0.533806\pi$
$433$	16.7912	−	12.1996i	0.806936	−	0.586273i	0.912941	+	0.408092i	$0.133806\pi$
$434$	2.38933	−	0.230415i	0.114691	−	0.0110603i
$435$		0			0
$436$	−3.95353	−	3.68459i	−0.189340	−	0.176460i
$437$	−9.34882	+	3.03762i	−0.447215	+	0.145309i
$438$	1.80174	+	18.6834i	0.0860903	+	0.892729i
$439$	−0.0935999	+	0.288071i	−0.00446728	+	0.0137489i	−0.953265	−	0.302134i	$-0.902301\pi$
$439$	−0.0935999	+	0.288071i	−0.00446728	+	0.0137489i	0.948798	+	0.315883i	$0.102301\pi$
$440$		0			0
$441$	11.9401	+	36.7478i	0.568575	+	1.74989i
$442$	6.56946	−	2.85761i	0.312477	−	0.135923i
$443$		−	33.9046i		−	1.61086i	−0.592693	−	0.805428i	$-0.701935\pi$
$443$		−	33.9046i		−	1.61086i	0.592693	−	0.805428i	$-0.298065\pi$
$444$	43.1896	−	8.40817i	2.04969	−	0.399034i
$445$		0			0
$446$	1.65062	−	1.46077i	0.0781591	−	0.0691694i
$447$	−6.64583	−	4.82848i	−0.314337	−	0.228379i
$448$	9.39462	+	0.484177i	0.443854	+	0.0228752i
$449$	12.6049			0.594860			0.297430	−	0.954744i	$-0.403871\pi$
$449$	12.6049			0.594860			0.297430	+	0.954744i	$0.403871\pi$
$450$		0			0
$451$			25.3298i			1.19273i
$452$	−6.23242	+	6.68733i	−0.293148	+	0.314545i
$453$	19.6156	−	26.9986i	0.921621	−	1.26850i
$454$	8.64339	+	9.76672i	0.405654	+	0.458375i
$455$		0			0
$456$	1.03124	−	40.0454i	0.0482923	−	1.87530i
$457$	−2.58934			−0.121124			−0.0605622	−	0.998164i	$-0.519289\pi$
$457$	−2.58934			−0.121124			−0.0605622	+	0.998164i	$0.519289\pi$
$458$	−14.6516	+	6.37322i	−0.684624	+	0.297801i
$459$	−64.5997	+	20.9897i	−3.01526	+	0.979716i
$460$		0			0
$461$	6.49523	+	2.11043i	0.302513	+	0.0982925i	0.456340	−	0.889805i	$-0.349160\pi$
$461$	6.49523	+	2.11043i	0.302513	+	0.0982925i	−0.153827	+	0.988098i	$0.549160\pi$
$462$	−20.6644	+	1.99277i	−0.961394	+	0.0927121i
$463$	6.74304	+	20.7530i	0.313376	+	0.964472i	0.976418	+	0.215889i	$0.0692651\pi$
$463$	6.74304	+	20.7530i	0.313376	+	0.964472i	−0.663042	+	0.748582i	$0.730735\pi$
$464$	−9.33964	−	23.0780i	−0.433582	−	1.07137i
$465$		0			0
$466$	17.4990	−	1.68752i	0.810628	−	0.0781729i
$467$	−1.76636	−	2.43118i	−0.0817373	−	0.112502i	0.766190	−	0.642614i	$-0.222150\pi$
$467$	−1.76636	−	2.43118i	−0.0817373	−	0.112502i	−0.847928	+	0.530112i	$0.822150\pi$
$468$	5.28254	−	11.3370i	0.244186	−	0.524054i
$469$	−2.09868	−	2.88859i	−0.0969081	−	0.133383i
$470$		0			0
$471$	9.92583	+	7.21154i	0.457358	+	0.332290i
$472$	1.03433	+	3.48629i	0.0476089	+	0.160469i
$473$	−3.63421	+	11.1850i	−0.167101	+	0.514285i
$474$	−11.9727	−	2.65247i	−0.549926	−	0.121832i
$475$		0			0
$476$	−11.8778	−	5.53453i	−0.544419	−	0.253675i
$477$	85.4782	+	27.7736i	3.91378	+	1.27166i
$478$	29.2667	−	25.9005i	1.33863	−	1.18466i
$479$	−15.3717	−	11.1682i	−0.702349	−	0.510287i	0.178347	−	0.983968i	$-0.442925\pi$
$479$	−15.3717	−	11.1682i	−0.702349	−	0.510287i	−0.880697	+	0.473681i	$0.842925\pi$
$480$		0			0
$481$	5.14843	−	3.74055i	0.234748	−	0.170555i
$482$	1.31030	−	5.91444i	0.0596827	−	0.269395i
$483$	4.73888	+	6.52251i	0.215627	+	0.296785i
$484$	−1.16148	+	9.48216i	−0.0527945	+	0.431007i
$485$		0			0
$486$	−13.6299	+	23.1466i	−0.618265	+	1.04995i
$487$	0.586607	+	1.80539i	0.0265817	+	0.0818101i	0.963467	−	0.267826i	$-0.0863052\pi$
$487$	0.586607	+	1.80539i	0.0265817	+	0.0818101i	−0.936886	+	0.349636i	$0.886305\pi$
$488$	14.6072	−	41.3064i	0.661236	−	1.86985i
$489$	−19.0651	+	58.6762i	−0.862151	+	2.65343i
$490$		0			0
$491$	29.3750	−	9.54451i	1.32567	−	0.430738i	0.441234	−	0.897392i	$-0.354541\pi$
$491$	29.3750	−	9.54451i	1.32567	−	0.430738i	0.884440	+	0.466654i	$0.154541\pi$
$492$	7.66034	+	39.3482i	0.345355	+	1.77396i
$493$			34.6801i			1.56191i
$494$	−2.31101	−	5.31285i	−0.103977	−	0.239036i
$495$		0			0
$496$	−0.406095	−	5.75955i	−0.0182342	−	0.258611i
$497$	1.86027	+	1.35156i	0.0834443	+	0.0606258i
$498$	−36.2594	−	21.3514i	−1.62482	−	0.956778i
$499$			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
$502$	−9.61572	+	16.3297i	−0.429171	+	0.728828i
$503$	21.4189	+	15.5618i	0.955024	+	0.693865i	0.951990	−	0.306130i	$-0.0990343\pi$
$503$	21.4189	+	15.5618i	0.955024	+	0.693865i	0.00303389	+	0.999995i	$0.499034\pi$
$504$	−21.9325	+	6.50707i	−0.976953	+	0.289848i
$505$		0			0
$506$	11.2366	−	4.88776i	0.499529	−	0.217288i
$507$			38.2613i			1.69925i
$508$	−16.9424	+	3.29836i	−0.751699	+	0.146341i
$509$	−17.5095	+	5.68919i	−0.776096	+	0.252169i	−0.670172	−	0.742205i	$-0.733780\pi$
$509$	−17.5095	+	5.68919i	−0.776096	+	0.252169i	−0.105923	+	0.994374i	$0.533780\pi$
$510$		0			0
$511$	1.53445	−	4.72255i	0.0678800	−	0.208913i
$512$	1.74596	−	22.5600i	0.0771615	−	0.997019i
$513$	16.9748	+	52.2431i	0.749456	+	2.30659i
$514$	9.52847	+	5.61084i	0.420283	+	0.247484i
$515$		0			0
$516$	−2.26292	+	18.4742i	−0.0996196	+	0.813281i
$517$	12.4139	+	17.0863i	0.545963	+	0.751453i
$518$	−11.3646	−	2.51776i	−0.499334	−	0.110624i
$519$	25.8888	−	18.8093i	1.13639	−	0.825637i
$520$		0			0
$521$	32.7039	+	23.7608i	1.43278	+	1.04098i	0.989490	+	0.144603i	$0.0461906\pi$
$521$	32.7039	+	23.7608i	1.43278	+	1.04098i	0.443295	+	0.896376i	$0.353809\pi$
$522$	40.1256	+	45.3405i	1.75625	+	1.98450i
$523$	−16.5534	−	5.37852i	−0.723828	−	0.235186i	−0.0761461	−	0.997097i	$-0.524262\pi$
$523$	−16.5534	−	5.37852i	−0.723828	−	0.235186i	−0.647682	+	0.761911i	$0.724262\pi$
$524$	7.34723	−	15.7681i	0.320965	−	0.688832i
$525$		0			0
$526$	8.39400	−	37.8888i	0.365996	−	1.65203i
$527$	−2.48539	+	7.64925i	−0.108265	+	0.333206i
$528$	3.51216	+	49.8122i	0.152847	+	2.16780i
$529$	14.7575	+	10.7220i	0.641630	+	0.466172i
$530$		0			0
$531$	−5.19820	−	7.15471i	−0.225583	−	0.310488i
$532$	−4.47589	+	9.60582i	−0.194054	+	0.416465i
$533$	3.40786	+	4.69052i	0.147611	+	0.203169i
$534$	1.11411	+	11.5530i	0.0482124	+	0.499947i
$535$		0			0
$536$	−7.07573	+	4.86754i	−0.305625	+	0.210246i
$537$	14.6680	+	45.1434i	0.632970	+	1.94808i
$538$	−2.89633	−	30.0340i	−0.124870	−	1.29486i
$539$	−21.2197	−	6.89469i	−0.913996	−	0.296975i
$540$		0			0
$541$	−7.69917	+	2.50161i	−0.331013	+	0.107553i	−0.469808	−	0.882768i	$-0.655677\pi$
$541$	−7.69917	+	2.50161i	−0.331013	+	0.107553i	0.138795	+	0.990321i	$0.455677\pi$
$542$	0.602695	+	1.38556i	0.0258880	+	0.0595147i
$543$	−59.4701			−2.55211
$544$	−14.0436	+	28.2182i	−0.602115	+	1.20985i
$545$		0			0
$546$	−3.55848	+	3.14920i	−0.152289	+	0.134773i
$547$	15.0486	−	20.7126i	0.643431	−	0.885607i	−0.355362	−	0.934729i	$-0.615642\pi$
$547$	15.0486	−	20.7126i	0.643431	−	0.885607i	0.998793	+	0.0491221i	$0.0156423\pi$
$548$	4.96851	−	5.33117i	0.212244	−	0.227736i
$549$			106.551i			4.54747i
$550$		0			0
$551$	28.0465			1.19482
$552$	15.9772	−	10.9911i	0.680036	−	0.467810i
$553$	2.62457	+	1.90686i	0.111608	+	0.0810881i
$554$	−16.6389	−	18.8014i	−0.706921	−	0.798796i
$555$		0			0
$556$	5.33790	+	27.4188i	0.226377	+	1.16281i
$557$			1.74254i			0.0738336i	0.999318	+	0.0369168i	$0.0117537\pi$
$557$			1.74254i			0.0738336i	−0.999318	+	0.0369168i	$0.988246\pi$
$558$	5.60095	+	12.8762i	0.237107	+	0.545094i
$559$	0.831844	+	2.56015i	0.0351832	+	0.108283i
$560$		0			0
$561$	21.4952	−	66.1555i	0.907529	−	2.79309i
$562$	−15.2748	+	1.47303i	−0.644329	+	0.0621359i
$563$	24.4440	−	7.94233i	1.03019	−	0.334729i	0.255325	−	0.966855i	$-0.417817\pi$
$563$	24.4440	−	7.94233i	1.03019	−	0.334729i	0.774866	+	0.632126i	$0.217817\pi$
$564$	24.4515	+	22.7882i	1.02959	+	0.959555i
$565$		0			0
$566$	3.15288	+	32.6943i	0.132525	+	1.37425i
$567$	16.8181	−	12.2191i	0.706296	−	0.513154i
$568$	3.36510	−	4.38943i	0.141197	−	0.184176i
$569$	11.5604	−	8.39915i	0.484639	−	0.352111i	−0.318480	−	0.947930i	$-0.603172\pi$
$569$	11.5604	−	8.39915i	0.484639	−	0.352111i	0.803119	+	0.595819i	$0.203172\pi$
$570$		0			0
$571$	11.7151	−	16.1245i	0.490263	−	0.674789i	−0.490174	−	0.871625i	$-0.663067\pi$
$571$	11.7151	−	16.1245i	0.490263	−	0.674789i	0.980436	+	0.196836i	$0.0630666\pi$
$572$	3.50324	+	6.31571i	0.146478	+	0.264073i
$573$	−6.69863	−	2.17652i	−0.279839	−	0.0909253i
$574$	2.29382	−	10.3539i	0.0957424	−	0.432162i
$575$		0			0
$576$	14.2885	+	53.1410i	0.595356	+	2.21421i
$577$	4.76100	−	14.6528i	0.198203	−	0.610006i	−0.801721	−	0.597698i	$-0.796082\pi$
$577$	4.76100	−	14.6528i	0.198203	−	0.610006i	0.999924	−	0.0123079i	$-0.00391783\pi$
$578$	14.8760	−	13.1650i	0.618761	−	0.547593i
$579$	41.9275	−	57.7083i	1.74245	−	2.39827i
$580$		0			0
$581$	6.54313	+	9.00585i	0.271455	+	0.373626i
$582$	1.26523	+	0.280303i	0.0524456	+	0.0116189i
$583$	−41.9870	+	30.5054i	−1.73892	+	1.26340i
$584$	−11.2606	−	3.98210i	−0.465969	−	0.164781i
$585$		0			0
$586$	16.9088	−	28.7150i	0.698497	−	1.18620i
$587$	−13.0914	+	4.25364i	−0.540338	+	0.175567i	−0.566455	−	0.824092i	$-0.691686\pi$
$587$	−13.0914	+	4.25364i	−0.540338	+	0.175567i	0.0261173	+	0.999659i	$0.491686\pi$
$588$	−35.0485	−	4.29313i	−1.44538	−	0.177046i
$589$	6.18610	+	2.00998i	0.254894	+	0.0828200i
$590$		0			0
$591$	12.6092	+	38.8072i	0.518675	+	1.59632i
$592$	−6.75782	+	27.1711i	−0.277745	+	1.11672i
$593$	6.37493			0.261787			0.130894	−	0.991396i	$-0.458215\pi$
$593$	6.37493			0.261787			0.130894	+	0.991396i	$0.458215\pi$
$594$	−27.3138	−	62.7926i	−1.12070	−	2.57641i
$595$		0			0
$596$	4.57114	−	2.53555i	0.187241	−	0.103860i
$597$	33.6538	−	46.3205i	1.37736	−	1.89577i
$598$	1.42318	−	2.41688i	0.0581981	−	0.0988335i
$599$	−38.8351			−1.58676			−0.793380	−	0.608727i	$-0.791681\pi$
$599$	−38.8351			−1.58676			−0.793380	+	0.608727i	$0.791681\pi$
$600$		0			0
$601$	41.0478			1.67438			0.837188	−	0.546916i	$-0.184198\pi$
$601$	41.0478			1.67438			0.837188	+	0.546916i	$0.184198\pi$
$602$	2.49842	−	4.24287i	0.101828	−	0.172927i
$603$	12.2766	−	16.8973i	0.499942	−	0.688112i
$604$	10.3006	+	18.5702i	0.419127	+	0.755609i
$605$		0			0
$606$	13.9033	+	31.9627i	0.564782	+	1.29840i
$607$	−28.6948			−1.16469			−0.582343	−	0.812943i	$-0.697864\pi$
$607$	−28.6948			−1.16469			−0.582343	+	0.812943i	$0.697864\pi$
$608$	22.8206	+	11.3574i	0.925499	+	0.460601i
$609$	−7.10833	−	21.8772i	−0.288044	−	0.886509i
$610$		0			0
$611$	4.59756	+	1.49384i	0.185997	+	0.0604342i
$612$	9.31976	−	76.0853i	0.376729	−	3.07557i
$613$	7.10423	−	2.30831i	0.286937	−	0.0932316i	−0.162012	−	0.986789i	$-0.551798\pi$
$613$	7.10423	−	2.30831i	0.286937	−	0.0932316i	0.448949	+	0.893557i	$0.351798\pi$
$614$	20.9478	−	35.5741i	0.845385	−	1.43565i
$615$		0			0
$616$	4.40432	−	12.4546i	0.177455	−	0.501809i
$617$	−32.7837	+	23.8187i	−1.31982	+	0.958906i	−0.319886	+	0.947456i	$0.603645\pi$
$617$	−32.7837	+	23.8187i	−1.31982	+	0.958906i	−0.999934	+	0.0114498i	$0.996355\pi$
$618$	57.1450	+	12.6601i	2.29871	+	0.509263i
$619$	5.89273	+	8.11065i	0.236849	+	0.325994i	0.910851	−	0.412735i	$-0.135426\pi$
$619$	5.89273	+	8.11065i	0.236849	+	0.325994i	−0.674003	+	0.738729i	$0.735426\pi$
$620$		0			0
$621$	−15.6308	+	21.5140i	−0.627242	+	0.863325i
$622$	1.04091	−	0.921185i	0.0417366	−	0.0369362i
$623$	0.948834	−	2.92021i	0.0380142	−	0.116996i
$624$	7.35208	+	8.75159i	0.294319	+	0.350344i
$625$		0			0
$626$	2.93085	−	13.2293i	0.117140	−	0.528748i
$627$	−53.5012	−	17.3836i	−2.13663	−	0.694234i
$628$	−6.82719	+	3.78696i	−0.272435	+	0.151116i
$629$	22.9248	−	31.5533i	0.914073	−	1.25811i
$630$		0			0
$631$	−24.4964	+	17.7976i	−0.975184	+	0.708513i	−0.956627	−	0.291315i	$-0.905907\pi$
$631$	−24.4964	+	17.7976i	−0.975184	+	0.708513i	−0.0185571	+	0.999828i	$0.505907\pi$
$632$	4.74769	−	6.19287i	0.188853	−	0.246339i
$633$	−4.46765	+	3.24593i	−0.177573	+	0.129014i
$634$	−2.49930	−	25.9170i	−0.0992600	−	1.02929i
$635$		0			0
$636$	−55.9986	+	60.0860i	−2.22049	+	2.38256i
$637$	−4.85702	+	1.57814i	−0.192442	+	0.0625283i
$638$	−34.8004	+	3.35597i	−1.37776	+	0.132864i
$639$	−4.15654	+	12.7925i	−0.164430	+	0.506064i
$640$		0			0
$641$	−12.1688	−	37.4516i	−0.480637	−	1.47925i	−0.838201	−	0.545361i	$-0.816393\pi$
$641$	−12.1688	−	37.4516i	−0.480637	−	1.47925i	0.357564	−	0.933889i	$-0.383607\pi$
$642$	−12.4233	−	28.5604i	−0.490310	−	1.12719i
$643$		−	15.6623i		−	0.617660i	−0.951117	−	0.308830i	$-0.900063\pi$
$643$		−	15.6623i		−	0.617660i	0.951117	−	0.308830i	$-0.0999375\pi$
$644$	−5.03573	+	0.980359i	−0.198436	+	0.0386316i
$645$		0			0
$646$	−23.5322	−	26.5906i	−0.925862	−	1.04619i
$647$	−26.8579	−	19.5134i	−1.05589	−	0.767152i	−0.0825693	−	0.996585i	$-0.526313\pi$
$647$	−26.8579	−	19.5134i	−1.05589	−	0.767152i	−0.973324	+	0.229434i	$0.926313\pi$
$648$	−28.3402	−	41.1969i	−1.11331	−	1.61837i
$649$	5.10673			0.200457
$650$		0			0
$651$		−	5.33479i		−	0.209087i
$652$	−28.7199	−	26.7662i	−1.12476	−	1.04825i
$653$	−2.28117	+	3.13976i	−0.0892690	+	0.122868i	−0.851316	−	0.524654i	$-0.824195\pi$
$653$	−2.28117	+	3.13976i	−0.0892690	+	0.122868i	0.762047	+	0.647522i	$0.224195\pi$
$654$	−8.99442	+	7.95991i	−0.351710	+	0.311257i
$655$		0			0
$656$	−24.7544	−	6.15677i	−0.966499	−	0.240381i
$657$	29.0471			1.13323
$658$	−3.52702	−	8.10839i	−0.137498	−	0.316098i
$659$	38.7539	−	12.5919i	1.50964	−	0.490511i	0.566826	−	0.823838i	$-0.308171\pi$
$659$	38.7539	−	12.5919i	1.50964	−	0.490511i	0.942811	+	0.333327i	$0.108171\pi$
$660$		0			0
$661$	−35.9253	−	11.6728i	−1.39733	−	0.454020i	−0.489004	−	0.872282i	$-0.662640\pi$
$661$	−35.9253	−	11.6728i	−1.39733	−	0.454020i	−0.908327	+	0.418261i	$0.862640\pi$
$662$	0.981789	+	10.1808i	0.0381583	+	0.395689i
$663$	−4.92009	−	15.1425i	−0.191081	−	0.588085i
$664$	22.0603	−	15.1757i	0.856105	−	0.588931i
$665$		0			0
$666$	−6.53608	−	67.7771i	−0.253268	−	2.62631i
$667$	7.98063	+	10.9844i	0.309011	+	0.425318i
$668$	30.5336	+	14.2273i	1.18138	+	0.550471i
$669$	−2.87936	−	3.96311i	−0.111323	−	0.153223i
$670$		0			0
$671$	−49.7762	−	36.1645i	−1.92159	−	1.39612i
$672$	3.07527	−	20.6794i	0.118631	−	0.797724i
$673$	−0.512274	+	1.57662i	−0.0197467	+	0.0607742i	−0.960444	−	0.278472i	$-0.910172\pi$
$673$	−0.512274	+	1.57662i	−0.0197467	+	0.0607742i	0.940698	+	0.339246i	$0.110172\pi$
$674$	−2.78836	+	12.5861i	−0.107404	+	0.484798i
$675$		0			0
$676$	−22.0687	−	10.2831i	−0.848798	−	0.395502i
$677$	−0.215778	−	0.0701106i	−0.00829304	−	0.00269457i	0.304868	−	0.952395i	$-0.401388\pi$
$677$	−0.215778	−	0.0701106i	−0.00829304	−	0.00269457i	−0.313161	+	0.949700i	$0.601388\pi$
$678$	13.4640	+	15.2139i	0.517083	+	0.584286i
$679$	−0.277355	−	0.201510i	−0.0106439	−	0.00773325i
$680$		0			0
$681$	23.4497	−	17.0372i	0.898596	−	0.652868i
$682$	−7.91628	−	1.75380i	−0.303130	−	0.0671563i
$683$	−17.4833	−	24.0637i	−0.668981	−	0.920773i	0.330756	−	0.943716i	$-0.392696\pi$
$683$	−17.4833	−	24.0637i	−0.668981	−	0.920773i	−0.999737	+	0.0229435i	$0.992696\pi$
$684$	−61.5317	−	7.53707i	−2.35272	−	0.288187i
$685$		0			0
$686$	18.0802	+	10.6465i	0.690306	+	0.406487i
$687$	10.9731	+	33.7717i	0.418649	+	1.28847i
$688$	−10.0475	−	6.27032i	−0.383059	−	0.239054i
$689$	−3.67089	+	11.2978i	−0.139850	+	0.430413i
$690$		0			0
$691$	29.9436	−	9.72925i	1.13911	−	0.370118i	0.322077	−	0.946714i	$-0.395619\pi$
$691$	29.9436	−	9.72925i	1.13911	−	0.370118i	0.817030	+	0.576595i	$0.195619\pi$
$692$	3.89119	+	19.9876i	0.147921	+	0.759813i
$693$			32.1269i			1.22040i
$694$	−13.2676	+	5.77122i	−0.503633	+	0.219072i
$695$		0			0
$696$	−53.0452	+	15.7377i	−2.01067	+	0.596538i
$697$	28.7469	+	20.8859i	1.08887	+	0.791108i
$698$	−3.41886	+	5.80600i	−0.129406	+	0.219760i
$699$		−	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	$0.986139\pi$
$702$	−13.5060	−	7.95301i	−0.509751	−	0.300167i
$703$	−25.5178	−	18.5398i	−0.962422	−	0.699240i
$704$	−29.6751	−	11.3617i	−1.11842	−	0.428209i
$705$		0			0
$706$	−10.2982	−	23.6748i	−0.387576	−	0.891012i
$707$		−	9.22096i		−	0.346790i
$708$	7.93297	−	1.54440i	0.298139	−	0.0580419i
$709$	25.4956	−	8.28402i	0.957508	−	0.311113i	0.211745	−	0.977325i	$-0.432085\pi$
$709$	25.4956	−	8.28402i	0.957508	−	0.311113i	0.745763	+	0.666212i	$0.232085\pi$
$710$		0			0
$711$	−5.86429	+	18.0484i	−0.219928	+	0.676869i
$712$	−6.96307	−	2.46235i	−0.260952	−	0.0922806i
$713$	0.973045	+	2.99472i	0.0364408	+	0.112153i
$714$	−14.7773	+	25.0953i	−0.553028	+	0.939166i
$715$		0			0
$716$	−29.9804	−	3.67233i	−1.12042	−	0.137241i
$717$	−51.0533	−	70.2688i	−1.90662	−	2.62424i
$718$	5.58759	−	25.2212i	0.208527	−	0.941248i
$719$	−12.3313	+	8.95922i	−0.459880	+	0.334123i	−0.793484	−	0.608591i	$-0.791735\pi$
$719$	−12.3313	+	8.95922i	−0.459880	+	0.334123i	0.333604	+	0.942713i	$0.391735\pi$
$720$		0			0
$721$	−12.5269	−	9.10133i	−0.466526	−	0.338951i
$722$	−1.38241	+	1.22341i	−0.0514480	+	0.0455306i
$723$	−12.8043	−	4.16038i	−0.476198	−	0.154726i
$724$	15.9831	−	34.3017i	0.594007	−	1.27481i
$725$		0			0
$726$	20.7285	+	4.59226i	0.769308	+	0.170435i
$727$	−0.688107	+	2.11778i	−0.0255205	+	0.0785440i	−0.963006	−	0.269481i	$-0.913148\pi$
$727$	−0.688107	+	2.11778i	−0.0255205	+	0.0785440i	0.937485	+	0.348025i	$0.113148\pi$
$728$	−0.860052	−	2.89887i	−0.0318756	−	0.107439i
$729$	5.38937	+	3.91560i	0.199606	+	0.145022i
$730$		0			0
$731$	9.69724	+	13.3471i	0.358665	+	0.493661i
$732$	−88.2612	−	41.1258i	−3.26223	−	1.52005i
$733$	29.0933	+	40.0434i	1.07458	+	1.47904i	0.865347	+	0.501173i	$0.167098\pi$
$733$	29.0933	+	40.0434i	1.07458	+	1.47904i	0.209237	+	0.977865i	$0.432902\pi$
$734$	21.1949	−	2.04393i	0.782319	−	0.0754430i
$735$		0			0
$736$	2.04551	+	12.1694i	0.0753986	+	0.448571i
$737$	3.72692	+	11.4703i	0.137283	+	0.422513i
$738$	61.7488	−	5.95475i	2.27301	−	0.219197i
$739$	17.2361	+	5.60033i	0.634039	+	0.206012i	0.608363	−	0.793659i	$-0.291826\pi$
$739$	17.2361	+	5.60033i	0.634039	+	0.206012i	0.0256753	+	0.999670i	$0.491826\pi$
$740$		0			0
$741$	−12.2460	+	3.97897i	−0.449869	+	0.146171i
$742$	19.9252	−	8.66715i	0.731477	−	0.318181i
$743$	15.5632			0.570959			0.285479	−	0.958385i	$-0.407847\pi$
$743$	15.5632			0.570959			0.285479	+	0.958385i	$0.407847\pi$
$744$	−12.8278	−	0.330339i	−0.470291	−	0.0121108i
$745$		0			0
$746$	−0.664499	−	0.750860i	−0.0243290	−	0.0274910i
$747$	−38.2752	+	52.6813i	−1.40042	+	1.92751i
$748$	32.3808	+	30.1781i	1.18396	+	1.10342i
$749$			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	$0.225863\pi$
$752$	−19.7155	+	7.97886i	−0.718951	+	0.290959i
$753$	34.0729	+	24.7554i	1.24169	+	0.902137i
$754$	−5.99274	+	5.30348i	−0.218243	+	0.193141i
$755$		0			0
$756$	5.47844	+	28.1407i	0.199249	+	1.02347i
$757$			1.83755i			0.0667870i	0.999442	+	0.0333935i	$0.0106315\pi$
$757$			1.83755i			0.0667870i	−0.999442	+	0.0333935i	$0.989369\pi$
$758$	−23.8745	+	10.3850i	−0.867161	+	0.377202i
$759$	−8.41550	−	25.9003i	−0.305463	−	0.940120i
$760$		0			0
$761$	−9.18935	+	28.2819i	−0.333114	+	1.02522i	0.634530	+	0.772898i	$0.281194\pi$
$761$	−9.18935	+	28.2819i	−0.333114	+	1.02522i	−0.967644	+	0.252320i	$0.918806\pi$
$762$	3.68223	+	38.1835i	0.133393	+	1.38324i
$763$	3.02192	−	0.981880i	0.109401	−	0.0355464i
$764$	3.05570	−	3.27874i	0.110552	−	0.118621i
$765$		0			0
$766$	25.2637	−	2.43630i	0.912813	−	0.0880272i
$767$	0.945653	−	0.687057i	0.0341455	−	0.0248082i
$768$	−49.5344	−	8.67516i	−1.78742	−	0.313038i
$769$	−7.63237	+	5.54524i	−0.275230	+	0.199966i	−0.716834	−	0.697244i	$-0.754410\pi$
$769$	−7.63237	+	5.54524i	−0.275230	+	0.199966i	0.441604	+	0.897210i	$0.354410\pi$
$770$		0			0
$771$	14.4450	−	19.8818i	0.520222	−	0.716025i
$772$	22.0172	+	39.6929i	0.792415	+	1.42858i
$773$	23.0787	+	7.49873i	0.830084	+	0.269711i	0.693081	−	0.720860i	$-0.256253\pi$
$773$	23.0787	+	7.49873i	0.830084	+	0.269711i	0.137003	+	0.990571i	$0.456253\pi$
$774$	28.1210	+	6.23000i	1.01079	+	0.223933i
$775$		0			0
$776$	−0.501718	+	0.654439i	−0.0180106	+	0.0234930i
$777$	−7.99420	+	24.6036i	−0.286790	+	0.882649i
$778$	−22.3778	−	25.2862i	−0.802284	−	0.906553i
$779$	16.8908	−	23.2482i	0.605176	−	0.832953i
$780$		0			0
$781$	−4.56537	−	6.28370i	−0.163362	−	0.224848i
$782$	3.71810	−	16.7827i	0.132959	−	0.600150i
$783$	61.3830	−	44.5974i	2.19365	−	1.59378i
$784$	11.8958	−	19.0618i	0.424851	−	0.680779i
$785$		0			0
$786$	−33.3146	−	19.6173i	−1.18829	−	0.699725i
$787$	35.4350	−	11.5135i	1.26312	−	0.410413i	0.400515	−	0.916290i	$-0.368831\pi$
$787$	35.4350	−	11.5135i	1.26312	−	0.410413i	0.862606	+	0.505877i	$0.168831\pi$
$788$	−25.7725	−	3.15689i	−0.918106	−	0.112460i
$789$	−82.0264	−	26.6520i	−2.92022	−	0.948837i
$790$		0			0
$791$	−1.66083	−	5.11151i	−0.0590524	−	0.181745i
$792$	77.2510	+	1.98935i	2.74499	+	0.0706885i
$793$	−14.0830			−0.500103
$794$	1.87234	−	0.814440i	0.0664469	−	0.0289034i
$795$		0			0
$796$	17.6724	+	31.8602i	0.626383	+	1.12925i
$797$	2.93174	−	4.03520i	0.103848	−	0.142934i	−0.753930	−	0.656954i	$-0.771844\pi$
$797$	2.93174	−	4.03520i	0.103848	−	0.142934i	0.857778	+	0.514020i	$0.171844\pi$
$798$	20.2950	+	11.9507i	0.718436	+	0.423051i
$799$	29.6272			1.04814
$800$		0			0
$801$	17.9614			0.634635
$802$	−31.7675	−	18.7063i	−1.12175	−	0.660542i
$803$	−9.85892	+	13.5696i	−0.347914	+	0.478862i
$804$	9.25842	+	16.6912i	0.326519	+	0.588655i
$805$		0			0
$806$	−1.70187	+	0.740289i	−0.0599460	+	0.0260756i
$807$	−67.0587			−2.36058
$808$	−22.1724	−	0.570978i	−0.780021	−	0.0200869i
$809$	2.74204	+	8.43914i	0.0964051	+	0.296704i	0.987617	−	0.156882i	$-0.0501443\pi$
$809$	2.74204	+	8.43914i	0.0964051	+	0.296704i	−0.891212	+	0.453587i	$0.850144\pi$
$810$		0			0
$811$	−20.7338	−	6.73681i	−0.728062	−	0.236562i	−0.0785467	−	0.996910i	$-0.525028\pi$
$811$	−20.7338	−	6.73681i	−0.728062	−	0.236562i	−0.649515	+	0.760349i	$0.725028\pi$
$812$	14.5290	+	1.77967i	0.509867	+	0.0624541i
$813$	3.19368	−	1.03769i	0.112007	−	0.0363934i
$814$	33.8812	+	19.9509i	1.18753	+	0.699280i
$815$		0			0
$816$	59.4280	+	37.0870i	2.08040	+	1.29830i
$817$	10.7941	−	7.84235i	0.377637	−	0.274369i
$818$	0.309440	−	1.39675i	0.0108193	−	0.0488362i
$819$	4.32233	+	5.94918i	0.151035	+	0.207881i
$820$		0			0
$821$	21.5298	−	29.6332i	0.751394	−	1.03420i	−0.246488	−	0.969146i	$-0.579276\pi$
$821$	21.5298	−	29.6332i	0.751394	−	1.03420i	0.997881	−	0.0650589i	$-0.0207235\pi$
$822$	−10.7336	−	12.1286i	−0.374377	−	0.423033i
$823$	1.83068	−	5.63427i	0.0638136	−	0.196398i	−0.914066	−	0.405564i	$-0.867075\pi$
$823$	1.83068	−	5.63427i	0.0638136	−	0.196398i	0.977880	+	0.209166i	$0.0670750\pi$
$824$	−22.6604	+	29.5581i	−0.789412	+	1.02971i
$825$		0			0
$826$	−2.08743	−	0.462456i	−0.0726311	−	0.0160909i
$827$	−14.4864	−	4.70692i	−0.503742	−	0.163676i	0.0461123	−	0.998936i	$-0.485317\pi$
$827$	−14.4864	−	4.70692i	−0.503742	−	0.163676i	−0.549854	+	0.835261i	$0.685317\pi$
$828$	−14.5570	−	26.2435i	−0.505889	−	0.912026i
$829$	−25.2244	+	34.7183i	−0.876078	+	1.20582i	0.101414	+	0.994844i	$0.467663\pi$
$829$	−25.2244	+	34.7183i	−0.876078	+	1.20582i	−0.977492	+	0.210974i	$0.932337\pi$
$830$		0			0
$831$	−45.1419	+	32.7975i	−1.56595	+	1.13773i
$832$	−7.02376	+	1.88854i	−0.243505	+	0.0654735i
$833$	−25.3216	+	18.3972i	−0.877343	+	0.637427i
$834$	61.7941	−	5.95912i	2.13976	−	0.206347i
$835$		0			0
$836$	24.4056	−	26.1870i	0.844085	−	0.905695i
$837$	16.7351	−	5.43757i	0.578450	−	0.187950i
$838$	4.54271	+	47.1065i	0.156925	+	1.62727i
$839$	−14.0891	+	43.3617i	−0.486409	+	1.49701i	0.343521	+	0.939145i	$0.388380\pi$
$839$	−14.0891	+	43.3617i	−0.486409	+	1.49701i	−0.829930	+	0.557868i	$0.811620\pi$
$840$		0			0
$841$	−3.00946	−	9.26218i	−0.103775	−	0.319385i
$842$	−35.6753	+	15.5182i	−1.22945	+	0.534792i
$843$			34.1050i			1.17464i
$844$	−0.671504	−	3.44926i	−0.0231141	−	0.118729i
$845$		0			0
$846$	38.7344	−	34.2793i	1.33172	−	1.17855i
$847$	−4.54396	−	3.30138i	−0.156132	−	0.113437i
$848$	−19.6069	−	48.4480i	−0.673303	−	1.66371i
$849$	72.9986			2.50531
$850$		0			0
$851$		−	15.2695i		−	0.523433i
$852$	−8.99235	−	8.38064i	−0.308073	−	0.287116i
$853$	−28.9855	+	39.8951i	−0.992445	+	1.36598i	−0.0625971	+	0.998039i	$0.519938\pi$
$853$	−28.9855	+	39.8951i	−0.992445	+	1.36598i	−0.929848	+	0.367944i	$0.880062\pi$
$854$	17.0716	+	19.2903i	0.584179	+	0.660101i
$855$		0			0
$856$	19.8122	+	0.510200i	0.677168	+	0.0174383i
$857$	−57.0345			−1.94826			−0.974130	−	0.225989i	$-0.927439\pi$
$857$	−57.0345			−1.94826			−0.974130	+	0.225989i	$0.927439\pi$
$858$	14.7189	−	6.40248i	0.502494	−	0.218577i
$859$	−20.6564	+	6.71166i	−0.704786	+	0.228999i	−0.639415	−	0.768862i	$-0.720823\pi$
$859$	−20.6564	+	6.71166i	−0.704786	+	0.228999i	−0.0653714	+	0.997861i	$0.520823\pi$
$860$		0			0
$861$	−22.4153	−	7.28318i	−0.763912	−	0.248210i
$862$	37.6443	−	3.63023i	1.28217	−	0.123646i
$863$	−5.84794	−	17.9981i	−0.199066	−	0.612663i	−0.999905	−	0.0137830i	$-0.995613\pi$
$863$	−5.84794	−	17.9981i	−0.199066	−	0.612663i	0.800839	−	0.598880i	$-0.204387\pi$
$864$	68.0052	−	11.4307i	2.31358	−	0.388881i
$865$		0			0
$866$	29.2166	−	2.81751i	0.992822	−	0.0957428i
$867$	−25.9500	−	35.7171i	−0.881307	−	1.21302i
$868$	3.07705	+	1.43377i	0.104442	+	0.0486653i
$869$	−6.44110	−	8.86542i	−0.218499	−	0.300739i
$870$		0			0
$871$	2.23335	+	1.62262i	0.0756742	+	0.0549805i
$872$	−2.17387	−	7.32718i	−0.0736165	−	0.248130i
$873$	0.619716	−	1.90729i	0.0209742	−	0.0645520i
$874$	−13.5725	−	3.00690i	−0.459098	−	0.101710i
$875$		0			0
$876$	−11.2114	+	24.0611i	−0.378799	+	0.812950i
$877$	13.2478	+	4.30447i	0.447347	+	0.145352i	0.524023	−	0.851704i	$-0.324431\pi$
$877$	13.2478	+	4.30447i	0.447347	+	0.145352i	−0.0766761	+	0.997056i	$0.524431\pi$
$878$	−0.320781	+	0.283886i	−0.0108258	+	0.00958068i
$879$	−59.9157	−	43.5313i	−2.02091	−	1.46827i
$880$		0			0
$881$	−32.7294	+	23.7793i	−1.10268	+	0.801145i	−0.981496	−	0.191485i	$-0.938670\pi$
$881$	−32.7294	+	23.7793i	−1.10268	+	0.801145i	−0.121186	+	0.992630i	$0.538670\pi$
$882$	−11.8193	+	53.3501i	−0.397977	+	1.79639i
$883$	2.40648	+	3.31224i	0.0809845	+	0.111466i	0.847587	−	0.530656i	$-0.178054\pi$
$883$	2.40648	+	3.31224i	0.0809845	+	0.111466i	−0.766603	+	0.642122i	$0.778054\pi$
$884$	10.0563	+	1.23181i	0.338231	+	0.0414303i
$885$		0			0
$886$	24.3297	−	41.3172i	0.817371	−	1.38808i
$887$	−1.75339	−	5.39637i	−0.0588730	−	0.181192i	0.917295	−	0.398208i	$-0.130368\pi$
$887$	−1.75339	−	5.39637i	−0.0588730	−	0.181192i	−0.976168	+	0.217016i	$0.930368\pi$
$888$	58.6658	+	20.7460i	1.96870	+	0.696191i
$889$	3.13597	−	9.65152i	0.105177	−	0.323701i
$890$		0			0
$891$	−66.7832	+	21.6992i	−2.23732	+	0.726950i
$892$	3.05973	−	0.595670i	0.102447	−	0.0199445i
$893$		−	23.9601i		−	0.801795i
$894$	−4.63394	−	10.6531i	−0.154982	−	0.356294i
$895$		0			0
$896$	11.1011	+	7.33153i	0.370863	+	0.244929i
$897$	−5.04297	−	3.66394i	−0.168380	−	0.122335i
$898$	15.3607	+	9.04513i	0.512592	+	0.301840i
$899$		−	8.98418i		−	0.299639i
$900$		0			0
$901$			72.8046i			2.42547i
$902$	−18.1765	+	30.8677i	−0.605210	+	1.02778i
$903$	−8.85304	−	6.43211i	−0.294611	−	0.214047i
$904$	−12.3938	+	3.67706i	−0.412211	+	0.122297i
$905$		0			0
$906$	43.2781	−	18.8253i	1.43782	−	0.625429i
$907$			49.8362i			1.65478i	0.561625	+	0.827392i	$0.310176\pi$
$907$			49.8362i			1.65478i	−0.561625	+	0.827392i	$0.689824\pi$
$908$	3.52458	+	18.1045i	0.116967	+	0.600817i
$909$	51.2997	−	16.6683i	1.70150	−	0.552852i
$910$		0			0
$911$	1.08071	−	3.32610i	0.0358057	−	0.110199i	−0.931556	−	0.363597i	$-0.881548\pi$
$911$	1.08071	−	3.32610i	0.0358057	−	0.110199i	0.967362	+	0.253399i	$0.0815485\pi$
$912$	29.9930	−	48.0606i	0.993166	−	1.59145i
$913$	−11.6196	−	35.7613i	−0.384551	−	1.18353i
$914$	−3.15545	−	1.85809i	−0.104373	−	0.0614602i
$915$		0			0
$916$	−22.4283	−	2.74726i	−0.741051	−	0.0907720i
$917$	6.01172	+	8.27442i	0.198525	+	0.273246i
$918$	−93.7853	−	20.7775i	−3.09538	−	0.685759i
$919$	35.2395	−	25.6030i	1.16244	−	0.844564i	0.172357	−	0.985034i	$-0.444862\pi$
$919$	35.2395	−	25.6030i	1.16244	−	0.844564i	0.990085	+	0.140471i	$0.0448616\pi$
$920$		0			0
$921$	−74.2277	−	53.9296i	−2.44589	−	1.77704i
$922$	6.40087	+	7.23276i	0.210801	+	0.238198i
$923$	−1.69081	−	0.549378i	−0.0556538	−	0.0180830i
$924$	−26.6123	−	12.4001i	−0.875479	−	0.407935i
$925$		0			0
$926$	−6.67486	+	30.1290i	−0.219349	+	0.990099i
$927$	27.9899	−	86.1439i	0.919307	−	2.82934i
$928$	5.17898	−	34.8256i	0.170008	−	1.14321i
$929$	20.6493	+	15.0026i	0.677483	+	0.492220i	0.872522	−	0.488576i	$-0.162483\pi$
$929$	20.6493	+	15.0026i	0.677483	+	0.492220i	−0.195039	+	0.980795i	$0.562483\pi$
$930$		0			0
$931$	14.8782	+	20.4781i	0.487614	+	0.671143i
$932$	22.5358	+	10.5007i	0.738186	+	0.343962i
$933$	−1.81577	−	2.49920i	−0.0594458	−	0.0818201i
$934$	−0.407943	−	4.23024i	−0.0133483	−	0.138418i
$935$		0			0
$936$	14.5728	−	10.0249i	0.476327	−	0.327675i
$937$	−1.22309	−	3.76427i	−0.0399565	−	0.122973i	0.929089	−	0.369857i	$-0.120593\pi$
$937$	−1.22309	−	3.76427i	−0.0399565	−	0.122973i	−0.969045	+	0.246884i	$0.920593\pi$
$938$	−0.484694	−	5.02612i	−0.0158258	−	0.164109i
$939$	−28.6403	−	9.30581i	−0.934642	−	0.303684i
$940$		0			0
$941$	7.54079	−	2.45015i	0.245823	−	0.0798727i	−0.183514	−	0.983017i	$-0.558747\pi$
$941$	7.54079	−	2.45015i	0.245823	−	0.0798727i	0.429337	+	0.903144i	$0.358747\pi$
$942$	6.92099	+	15.9109i	0.225498	+	0.518405i
$943$	13.9114			0.453018
$944$	−1.24126	+	4.99073i	−0.0403996	+	0.162434i
$945$		0			0
$946$	−12.4550	+	11.0225i	−0.404947	+	0.358371i
$947$	0.457976	−	0.630350i	0.0148822	−	0.0204836i	−0.801511	−	0.597980i	$-0.795970\pi$
$947$	0.457976	−	0.630350i	0.0148822	−	0.0204836i	0.816393	+	0.577496i	$0.195970\pi$
$948$	−12.6870	−	11.8239i	−0.412053	−	0.384023i
$949$			3.83921i			0.124626i
$950$		0			0
$951$	−57.8664			−1.87645
$952$	−10.5031	−	15.2680i	−0.340409	−	0.494838i
$953$	8.66334	+	6.29429i	0.280633	+	0.203892i	0.719194	−	0.694810i	$-0.244511\pi$
$953$	8.66334	+	6.29429i	0.280633	+	0.203892i	−0.438560	+	0.898702i	$0.644511\pi$
$954$	84.2364	+	95.1842i	2.72725	+	3.08170i
$955$		0			0
$956$	54.2513	−	10.5617i	1.75461	−	0.341589i
$957$			77.7008i			2.51171i
$958$	−10.7182	−	24.6405i	−0.346290	−	0.796097i
$959$	1.32402	+	4.07492i	0.0427549	+	0.131586i
$960$		0			0
$961$	−8.93566	+	27.5011i	−0.288247	+	0.887134i
$962$	8.95823	−	0.863887i	0.288825	−	0.0278528i
$963$	−45.8391	+	14.8940i	−1.47714	+	0.479953i
$964$	5.84093	−	6.26726i	0.188124	−	0.201855i
$965$		0			0
$966$	1.09445	+	11.3491i	0.0352134	+	0.365152i
$967$	7.39419	−	5.37219i	0.237781	−	0.172758i	−0.462513	−	0.886612i	$-0.653052\pi$
$967$	7.39419	−	5.37219i	0.237781	−	0.172758i	0.700294	+	0.713854i	$0.253052\pi$
$968$	−8.21973	+	10.7218i	−0.264192	+	0.344612i
$969$	−63.8435	+	46.3850i	−2.05095	+	1.49010i
$970$		0			0
$971$	−15.2665	+	21.0125i	−0.489924	+	0.674323i	−0.980374	−	0.197147i	$-0.936833\pi$
$971$	−15.2665	+	21.0125i	−0.489924	+	0.674323i	0.490450	+	0.871469i	$0.336833\pi$
$972$	−33.2196	+	18.4265i	−1.06552	+	0.591031i
$973$	−15.6195	−	5.07508i	−0.500738	−	0.162700i
$974$	−0.580675	+	2.62105i	−0.0186060	+	0.0839839i
$975$		0			0
$976$	47.4419	−	39.8552i	1.51858	−	1.27574i
$977$	9.43346	−	29.0332i	0.301803	−	0.928855i	−0.679048	−	0.734094i	$-0.737607\pi$
$977$	9.43346	−	29.0332i	0.301803	−	0.928855i	0.980851	−	0.194760i	$-0.0623929\pi$
$978$	−65.3388	+	57.8237i	−2.08930	+	1.84900i
$979$	−6.09631	+	8.39085i	−0.194839	+	0.268173i
$980$		0			0
$981$	10.9251	+	15.0372i	0.348813	+	0.480100i
$982$	42.6463	+	9.44799i	1.36090	+	0.301498i
$983$	32.3674	−	23.5163i	1.03236	−	0.750052i	0.0635791	−	0.997977i	$-0.479748\pi$
$983$	32.3674	−	23.5163i	1.03236	−	0.750052i	0.968779	+	0.247924i	$0.0797485\pi$
$984$	−18.9008	+	53.4480i	−0.602537	+	1.70386i
$985$		0			0
$986$	−24.8861	+	42.2623i	−0.792536	+	1.34590i
$987$	−18.6897	+	6.07265i	−0.594900	+	0.193295i
$988$	0.996190	−	8.13276i	0.0316930	−	0.258738i
$989$	6.14291	+	1.99595i	0.195333	+	0.0634676i
$990$		0			0
$991$	14.8786	+	45.7916i	0.472634	+	1.45462i	0.849122	+	0.528197i	$0.177132\pi$
$991$	14.8786	+	45.7916i	0.472634	+	1.45462i	−0.376488	+	0.926422i	$0.622868\pi$
$992$	3.63812	−	7.31018i	0.115510	−	0.232098i
$993$	22.7314			0.721358
$994$	1.29711	+	2.98197i	0.0411418	+	0.0945822i
$995$		0			0
$996$	−28.8653	−	52.0389i	−0.914633	−	1.64892i
$997$	0.704471	−	0.969621i	0.0223108	−	0.0307082i	−0.797716	−	0.603033i	$-0.793959\pi$
$997$	0.704471	−	0.969621i	0.0223108	−	0.0307082i	0.820027	+	0.572325i	$0.193959\pi$
$998$	−7.60275	+	12.9112i	−0.240661	+	0.408696i
$999$	−85.3292			−2.69970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.t.b.101.47		224
5.2	odd	4		200.2.o.a.29.10	✓	112
5.3	odd	4		1000.2.o.a.149.19		112
5.4	even	2	inner	1000.2.t.b.101.10		224
8.5	even	2	inner	1000.2.t.b.101.2		224
20.7	even	4		800.2.be.a.529.27		112
25.6	even	5	inner	1000.2.t.b.901.2		224
25.8	odd	20		200.2.o.a.69.16	yes	112
25.17	odd	20		1000.2.o.a.349.13		112
25.19	even	10	inner	1000.2.t.b.901.55		224
40.13	odd	4		1000.2.o.a.149.13		112
40.27	even	4		800.2.be.a.529.2		112
40.29	even	2	inner	1000.2.t.b.101.55		224
40.37	odd	4		200.2.o.a.29.16	yes	112
100.83	even	20		800.2.be.a.369.2		112
200.69	even	10	inner	1000.2.t.b.901.10		224
200.83	even	20		800.2.be.a.369.27		112
200.117	odd	20		1000.2.o.a.349.19		112
200.133	odd	20		200.2.o.a.69.10	yes	112
200.181	even	10	inner	1000.2.t.b.901.47		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.10	✓	112	5.2	odd	4
200.2.o.a.29.16	yes	112	40.37	odd	4
200.2.o.a.69.10	yes	112	200.133	odd	20
200.2.o.a.69.16	yes	112	25.8	odd	20
800.2.be.a.369.2		112	100.83	even	20
800.2.be.a.369.27		112	200.83	even	20
800.2.be.a.529.2		112	40.27	even	4
800.2.be.a.529.27		112	20.7	even	4
1000.2.o.a.149.13		112	40.13	odd	4
1000.2.o.a.149.19		112	5.3	odd	4
1000.2.o.a.349.13		112	25.17	odd	20
1000.2.o.a.349.19		112	200.117	odd	20
1000.2.t.b.101.2		224	8.5	even	2	inner
1000.2.t.b.101.10		224	5.4	even	2	inner
1000.2.t.b.101.47		224	1.1	even	1	trivial
1000.2.t.b.101.55		224	40.29	even	2	inner
1000.2.t.b.901.2		224	25.6	even	5	inner
1000.2.t.b.901.10		224	200.69	even	10	inner
1000.2.t.b.901.47		224	200.181	even	10	inner
1000.2.t.b.901.55		224	25.19	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.21863 + 0.717591i) q^{2} +(1.84742 - 2.54275i) q^{3} +(0.970125 + 1.74896i) q^{4} +(4.07598 - 1.77299i) q^{6} -1.17589 q^{7} +(-0.0728129 + 2.82749i) q^{8} +(-2.12559 - 6.54190i) q^{9} +O(q^{10})\)	\(q+(1.21863 + 0.717591i) q^{2} +(1.84742 - 2.54275i) q^{3} +(0.970125 + 1.74896i) q^{4} +(4.07598 - 1.77299i) q^{6} -1.17589 q^{7} +(-0.0728129 + 2.82749i) q^{8} +(-2.12559 - 6.54190i) q^{9} +(3.77756 + 1.22741i) q^{11} +(6.23940 + 0.764270i) q^{12} +(0.864656 - 0.280944i) q^{13} +(-1.43297 - 0.843806i) q^{14} +(-2.11771 + 3.39342i) q^{16} +(4.50780 - 3.27511i) q^{17} +(2.10410 - 9.49747i) q^{18} +(-2.64864 - 3.64555i) q^{19} +(-2.17235 + 2.98999i) q^{21} +(3.72268 + 4.20650i) q^{22} +(0.674105 - 2.07468i) q^{23} +(7.05510 + 5.40870i) q^{24} +(1.25530 + 0.278103i) q^{26} +(-11.5937 - 3.76703i) q^{27} +(-1.14076 - 2.05658i) q^{28} +(-3.65841 + 5.03536i) q^{29} +(-1.16778 + 0.848445i) q^{31} +(-5.01580 + 2.61567i) q^{32} +(10.0997 - 7.33789i) q^{33} +(7.84354 - 0.756392i) q^{34} +(9.37942 - 10.0640i) q^{36} +(6.65712 - 2.16303i) q^{37} +(-0.611709 - 6.34322i) q^{38} +(0.883011 - 2.71763i) q^{39} +(1.97065 + 6.06503i) q^{41} +(-4.79289 + 2.08483i) q^{42} +2.96089i q^{43} +(1.51803 + 7.79754i) q^{44} +(2.31026 - 2.04454i) q^{46} +(4.30172 + 3.12538i) q^{47} +(4.71632 + 11.6539i) q^{48} -5.61729 q^{49} -17.5127i q^{51} +(1.33018 + 1.23970i) q^{52} +(-7.68016 + 10.5708i) q^{53} +(-11.4253 - 12.9102i) q^{54} +(0.0856196 - 3.32481i) q^{56} -14.1629 q^{57} +(-8.07158 + 3.51101i) q^{58} +(1.22277 - 0.397301i) q^{59} +(-14.7321 - 4.78675i) q^{61} +(-2.03194 + 0.195950i) q^{62} +(2.49945 + 7.69253i) q^{63} +(-7.98940 - 0.411755i) q^{64} +(17.5735 - 1.69470i) q^{66} +(1.78477 + 2.45652i) q^{67} +(10.1012 + 4.70669i) q^{68} +(-4.03005 - 5.54689i) q^{69} +(-1.58201 - 1.14940i) q^{71} +(18.6519 - 5.53375i) q^{72} +(-1.30493 + 4.01616i) q^{73} +(9.66475 + 2.14116i) q^{74} +(3.80639 - 8.16901i) q^{76} +(-4.44199 - 1.44329i) q^{77} +(3.02621 - 2.67815i) q^{78} +(-2.23200 - 1.62164i) q^{79} +(-14.3025 + 10.3914i) q^{81} +(-1.95072 + 8.80515i) q^{82} +(-5.56443 - 7.65878i) q^{83} +(-7.33683 - 0.898695i) q^{84} +(-2.12471 + 3.60824i) q^{86} +(6.04509 + 18.6049i) q^{87} +(-3.74553 + 10.5917i) q^{88} +(-0.806910 + 2.48341i) q^{89} +(-1.01674 + 0.330358i) q^{91} +(4.28250 - 0.833719i) q^{92} +4.53682i q^{93} +(2.99946 + 6.89556i) q^{94} +(-2.61528 + 17.5862i) q^{96} +(0.235869 + 0.171369i) q^{97} +(-6.84541 - 4.03092i) q^{98} -27.3214i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more