LMFDB - Embedded newform 1000.2.t.b.901.55

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			901.55
Character	$\chi$	$=$	1000.901
Dual form			1000.2.t.b.101.55

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40768 - 0.135750i) q^{2} +(1.84742 + 2.54275i) q^{3} +(1.96314 - 0.382186i) q^{4} +(2.94576 + 3.32861i) q^{6} +1.17589 q^{7} +(2.71160 - 0.804493i) q^{8} +(-2.12559 + 6.54190i) q^{9} +O(q^{10})$	\(q+(1.40768 - 0.135750i) q^{2} +(1.84742 + 2.54275i) q^{3} +(1.96314 - 0.382186i) q^{4} +(2.94576 + 3.32861i) q^{6} +1.17589 q^{7} +(2.71160 - 0.804493i) q^{8} +(-2.12559 + 6.54190i) q^{9} +(-3.77756 + 1.22741i) q^{11} +(4.59855 + 4.28574i) q^{12} +(0.864656 + 0.280944i) q^{13} +(1.65528 - 0.159626i) q^{14} +(3.70787 - 1.50057i) 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} +(-5.15099 + 2.24060i) 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} +(2.30843 - 0.449407i) 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} +(-6.79015 - 3.99838i) q^{34} +(-1.67262 + 13.6551i) q^{36} +(6.65712 + 2.16303i) q^{37} +(3.23357 - 5.49133i) q^{38} +(0.883011 + 2.71763i) q^{39} +(1.97065 - 6.06503i) q^{41} +(3.46388 + 3.91406i) q^{42} -2.96089i q^{43} +(-6.94681 + 3.85330i) q^{44} +(-1.23056 - 2.82899i) q^{46} +(-4.30172 + 3.12538i) q^{47} +(10.6656 + 6.65601i) q^{48} -5.61729 q^{49} -17.5127i q^{51} +(1.80482 + 0.221074i) q^{52} +(-7.68016 - 10.5708i) q^{53} +(-15.8089 + 6.87664i) q^{54} +(3.18854 - 0.945992i) q^{56} +14.1629 q^{57} +(5.83343 + 6.59157i) q^{58} +(-1.22277 - 0.397301i) q^{59} +(14.7321 - 4.78675i) q^{61} +(-1.75905 - 1.03582i) q^{62} +(-2.49945 + 7.69253i) q^{63} +(6.70558 - 4.36293i) q^{64} +(-15.2133 - 8.95838i) 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} +(-0.500848 + 19.4491i) 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} +(1.61192 + 3.70569i) 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} +(5.40738 + 5.03954i) q^{84} +(-0.401941 - 4.16800i) q^{86} +(-6.04509 + 18.6049i) q^{87} +(-9.25582 + 6.36726i) q^{88} +(-0.806910 - 2.48341i) q^{89} +(1.01674 + 0.330358i) q^{91} +(-2.11628 - 3.81527i) q^{92} -4.53682i q^{93} +(-5.63118 + 4.98350i) q^{94} +(15.9173 + 7.92171i) q^{96} +(-0.235869 + 0.171369i) q^{97} +(-7.90737 + 0.762547i) 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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$

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 $

$2$	1.40768	−	0.135750i	0.995382	−	0.0959897i
$2$	1.40768	−	0.135750i	0.995382	−	0.0959897i
$3$	1.84742	+	2.54275i	1.06661	+	1.46806i	0.873463	+	0.486890i	$0.161869\pi$
$3$	1.84742	+	2.54275i	1.06661	+	1.46806i	0.193145	+	0.981170i	$0.438131\pi$
$4$	1.96314	−	0.382186i	0.981572	−	0.191093i
$5$		0			0
$5$		0			0
$6$	2.94576	+	3.32861i	1.20260	+	1.35890i
$7$	1.17589			0.444443			0.222222	−	0.974996i	$-0.428669\pi$
$7$	1.17589			0.444443			0.222222	+	0.974996i	$0.428669\pi$
$8$	2.71160	−	0.804493i	0.958696	−	0.284431i
$9$	−2.12559	+	6.54190i	−0.708531	+	2.18063i
$10$		0			0
$11$	−3.77756	+	1.22741i	−1.13898	+	0.370077i	−0.816981	−	0.576664i	$-0.804354\pi$
$11$	−3.77756	+	1.22741i	−1.13898	+	0.370077i	−0.321997	+	0.946741i	$0.604354\pi$
$12$	4.59855	+	4.28574i	1.32749	+	1.23719i
$13$	0.864656	+	0.280944i	0.239812	+	0.0779198i	0.426457	−	0.904508i	$-0.359761\pi$
$13$	0.864656	+	0.280944i	0.239812	+	0.0779198i	−0.186645	+	0.982427i	$0.559761\pi$
$14$	1.65528	−	0.159626i	0.442391	−	0.0426620i
$15$		0			0
$16$	3.70787	−	1.50057i	0.926967	−	0.375143i
$17$	−4.50780	−	3.27511i	−1.09330	−	0.794331i	−0.113348	−	0.993555i	$-0.536158\pi$
$17$	−4.50780	−	3.27511i	−1.09330	−	0.794331i	−0.979954	+	0.199225i	$0.936158\pi$
$18$	−2.10410	+	9.49747i	−0.495940	+	2.23858i
$19$	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
$22$	−5.15099	+	2.24060i	−1.09820	+	0.477698i
$23$	−0.674105	−	2.07468i	−0.140561	−	0.432601i	0.855853	−	0.517220i	$-0.173033\pi$
$23$	−0.674105	−	2.07468i	−0.140561	−	0.432601i	−0.996413	+	0.0846183i	$0.973033\pi$
$24$	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
$28$	2.30843	−	0.449407i	0.436253	−	0.0849299i
$29$	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	$0.741378\pi$
$32$	5.01580	−	2.61567i	0.886677	−	0.462390i
$33$	−10.0997	−	7.33789i	−1.75814	−	1.27736i
$34$	−6.79015	−	3.99838i	−1.16450	−	0.685717i
$35$		0			0
$36$	−1.67262	+	13.6551i	−0.278770	+	2.27584i
$37$	6.65712	+	2.16303i	1.09442	+	0.355600i	0.799954	−	0.600061i	$-0.204857\pi$
$37$	6.65712	+	2.16303i	1.09442	+	0.355600i	0.294470	+	0.955661i	$0.404857\pi$
$38$	3.23357	−	5.49133i	0.524554	−	0.890811i
$39$	0.883011	+	2.71763i	0.141395	+	0.435169i
$40$		0			0
$41$	1.97065	−	6.06503i	0.307763	−	0.947198i	−0.670868	−	0.741577i	$-0.734078\pi$
$41$	1.97065	−	6.06503i	0.307763	−	0.947198i	0.978632	−	0.205622i	$-0.0659216\pi$
$42$	3.46388	+	3.91406i	0.534488	+	0.603953i
$43$		−	2.96089i		−	0.451532i	−0.974182	−	0.225766i	$-0.927512\pi$
$43$		−	2.96089i		−	0.451532i	0.974182	−	0.225766i	$-0.0724884\pi$
$44$	−6.94681	+	3.85330i	−1.04727	+	0.580908i
$45$		0			0
$46$	−1.23056	−	2.82899i	−0.181437	−	0.417111i
$47$	−4.30172	+	3.12538i	−0.627470	+	0.455884i	−0.855523	−	0.517765i	$-0.826764\pi$
$47$	−4.30172	+	3.12538i	−0.627470	+	0.455884i	0.228053	+	0.973649i	$0.426764\pi$
$48$	10.6656	+	6.65601i	1.53944	+	0.960713i
$49$	−5.61729			−0.802470
$50$		0			0
$51$		−	17.5127i		−	2.45227i
$52$	1.80482	+	0.221074i	0.250283	+	0.0306574i
$53$	−7.68016	−	10.5708i	−1.05495	−	1.45202i	−0.884436	−	0.466661i	$-0.845457\pi$
$53$	−7.68016	−	10.5708i	−1.05495	−	1.45202i	−0.170515	−	0.985355i	$-0.554543\pi$
$54$	−15.8089	+	6.87664i	−2.15132	+	0.935792i
$55$		0			0
$56$	3.18854	−	0.945992i	0.426086	−	0.126414i
$57$	14.1629			1.87592
$58$	5.83343	+	6.59157i	0.765967	+	0.865515i
$59$	−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	$-0.141133\pi$
$61$	14.7321	−	4.78675i	1.88625	−	0.612881i	0.982948	−	0.183885i	$-0.0588674\pi$
$62$	−1.75905	−	1.03582i	−0.223399	−	0.131549i
$63$	−2.49945	+	7.69253i	−0.314902	+	0.969167i
$64$	6.70558	−	4.36293i	0.838198	−	0.545367i
$65$		0			0
$66$	−15.2133	−	8.95838i	−1.87263	−	1.10270i
$67$	1.78477	−	2.45652i	0.218044	−	0.300112i	−0.685957	−	0.727642i	$-0.740616\pi$
$67$	1.78477	−	2.45652i	0.218044	−	0.300112i	0.904001	+	0.427530i	$0.140616\pi$
$68$	−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	−0.677690	−	0.735348i	$-0.737019\pi$
$71$	−1.58201	+	1.14940i	−0.187750	+	0.136409i	0.489940	+	0.871756i	$0.337019\pi$
$72$	−0.500848	+	19.4491i	−0.0590255	+	2.29209i
$73$	1.30493	+	4.01616i	0.152731	+	0.470056i	0.997924	−	0.0644044i	$-0.0205148\pi$
$73$	1.30493	+	4.01616i	0.152731	+	0.470056i	−0.845193	+	0.534461i	$0.820515\pi$
$74$	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
$78$	1.61192	+	3.70569i	0.182514	+	0.419587i
$79$	−2.23200	+	1.62164i	−0.251119	+	0.182449i	−0.706223	−	0.707990i	$-0.749602\pi$
$79$	−2.23200	+	1.62164i	−0.251119	+	0.182449i	0.455103	+	0.890439i	$0.349602\pi$
$80$		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	−0.996641	−	0.0818950i	$-0.973903\pi$
$83$	−5.56443	+	7.65878i	−0.610775	+	0.840660i	0.385866	+	0.922555i	$0.373903\pi$
$84$	5.40738	+	5.03954i	0.589993	+	0.549859i
$85$		0			0
$86$	−0.401941	−	4.16800i	−0.0433424	−	0.449447i
$87$	−6.04509	+	18.6049i	−0.648101	+	1.99465i
$88$	−9.25582	+	6.36726i	−0.986673	+	0.678752i
$89$	−0.806910	−	2.48341i	−0.0855323	−	0.263241i	0.899139	−	0.437664i	$-0.144194\pi$
$89$	−0.806910	−	2.48341i	−0.0855323	−	0.263241i	−0.984671	+	0.174423i	$0.944194\pi$
$90$		0			0
$91$	1.01674	+	0.330358i	0.106583	+	0.0346309i
$92$	−2.11628	−	3.81527i	−0.220637	−	0.397769i
$93$		−	4.53682i		−	0.470447i
$94$	−5.63118	+	4.98350i	−0.580812	+	0.514009i
$95$		0			0
$96$	15.9173	+	7.92171i	1.62455	+	0.808506i
$97$	−0.235869	+	0.171369i	−0.0239489	+	0.0173999i	−0.599695	−	0.800228i	$-0.704712\pi$
$97$	−0.235869	+	0.171369i	−0.0239489	+	0.0173999i	0.575746	+	0.817628i	$0.304712\pi$
$98$	−7.90737	+	0.762547i	−0.798765	+	0.0770289i
$99$		−	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	$0.872427\pi$
$102$	−2.37735	−	24.6524i	−0.235393	−	2.44095i
$103$	−10.6532	+	7.73997i	−1.04969	+	0.762642i	−0.972153	−	0.234347i	$-0.924705\pi$
$103$	−10.6532	+	7.73997i	−1.04969	+	0.762642i	−0.0775342	+	0.996990i	$0.524705\pi$
$104$	2.57062	+	0.0661980i	0.252070	+	0.00649125i
$105$		0			0
$106$	−12.2462	−	13.8378i	−1.18946	−	1.34405i
$107$			7.00700i			0.677392i	0.940896	+	0.338696i	$0.109986\pi$
$107$			7.00700i			0.677392i	−0.940896	+	0.338696i	$0.890014\pi$
$108$	−21.3205	+	11.8262i	−2.05156	+	1.13798i
$109$	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
$112$	4.36003	−	1.76450i	0.411984	−	0.166730i
$113$	−1.41241	+	4.34695i	−0.132868	+	0.408926i	−0.995252	−	0.0973282i	$-0.968970\pi$
$113$	−1.41241	+	4.34695i	−0.132868	+	0.408926i	0.862384	+	0.506255i	$0.168970\pi$
$114$	19.9369	−	1.92261i	1.86726	−	0.180069i
$115$		0			0
$116$	9.10642	+	8.48695i	0.845510	+	0.787994i
$117$	−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
$122$	20.0883	−	8.73812i	1.81871	−	0.791112i
$123$	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	0.996898	+	0.0786992i	$0.0250767\pi$
$127$	2.66690	+	8.20787i	0.236649	+	0.728330i	−0.760250	+	0.649631i	$0.774923\pi$
$128$	8.84707	−	7.05191i	0.781978	−	0.623307i
$129$	7.52882	−	5.47001i	0.662876	−	0.481607i
$130$		0			0
$131$	5.11250	−	7.03676i	0.446681	−	0.614804i	−0.524999	−	0.851103i	$-0.675934\pi$
$131$	5.11250	−	7.03676i	0.446681	−	0.614804i	0.971680	+	0.236299i	$0.0759343\pi$
$132$	−22.6317	−	10.5454i	−1.96983	−	0.917855i
$133$	3.11451	−	4.28675i	0.270062	−	0.371708i
$134$	2.17891	−	3.70028i	0.188229	−	0.319656i
$135$		0			0
$136$	−14.8582	−	5.25430i	−1.27408	−	0.450553i
$137$	1.12598	−	3.46540i	0.0961988	−	0.296069i	−0.891365	−	0.453285i	$-0.850252\pi$
$137$	1.12598	−	3.46540i	0.0961988	−	0.296069i	0.987564	+	0.157216i	$0.0502519\pi$
$138$	4.92005	−	8.35535i	0.418822	−	0.711254i
$139$	−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
$142$	−2.07094	+	1.83275i	−0.173789	+	0.153801i
$143$	−3.61112			−0.301977
$144$	1.93517	+	27.4461i	0.161264	+	2.28717i
$145$		0			0
$146$	2.38212	+	5.47634i	0.197146	+	0.453225i
$147$	−10.3775	−	14.2834i	−0.855921	−	1.17807i
$148$	13.8956	+	1.70208i	1.14221	+	0.139910i
$149$		−	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	$0.357796\pi$
$152$	4.24926	−	12.0161i	0.344660	−	0.974634i
$153$	31.0072	−	22.5280i	2.50678	−	1.82128i
$154$	−6.05698	+	2.63469i	−0.488086	+	0.212310i
$155$		0			0
$156$	2.77212	+	4.99762i	0.221947	+	0.400130i
$157$		−	3.90358i		−	0.311539i	−0.987793	−	0.155770i	$-0.950214\pi$
$157$		−	3.90358i		−	0.311539i	0.987793	−	0.155770i	$-0.0497857\pi$
$158$	−2.92181	+	2.58575i	−0.232446	+	0.205711i
$159$	12.6906	−	39.0575i	1.00643	−	3.09746i
$160$		0			0
$161$	−0.792671	−	2.43959i	−0.0624712	−	0.192267i
$162$	−21.5441	−	12.6862i	−1.69266	−	0.996724i
$163$	−18.6687	−	6.06584i	−1.46225	−	0.475114i	−0.533493	−	0.845805i	$-0.679121\pi$
$163$	−18.6687	−	6.06584i	−1.46225	−	0.475114i	−0.928756	+	0.370691i	$0.879121\pi$
$164$	1.55070	−	12.6597i	0.121089	−	0.988555i
$165$		0			0
$166$	−6.79327	+	11.5365i	−0.527260	+	0.895406i
$167$	−13.6261	−	9.89993i	−1.05442	−	0.766080i	−0.0813708	−	0.996684i	$-0.525930\pi$
$167$	−13.6261	−	9.89993i	−1.05442	−	0.766080i	−0.973048	+	0.230604i	$0.925930\pi$
$168$	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
$172$	−1.13161	−	5.81266i	−0.0862845	−	0.443211i
$173$	9.68309	−	3.14623i	0.736192	−	0.239203i	0.0831625	−	0.996536i	$-0.473498\pi$
$173$	9.68309	−	3.14623i	0.736192	−	0.239203i	0.653029	+	0.757333i	$0.273498\pi$
$174$	−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
$178$	−1.47300	−	3.38632i	−0.110406	−	0.253815i
$179$	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	$-0.551751\pi$
$181$	11.1217	−	15.3077i	0.826668	−	1.13781i	0.988534	−	0.150998i	$-0.0482489\pi$
$182$	1.47609	+	0.327017i	0.109415	+	0.0242401i
$183$	39.3879	+	28.6170i	2.91164	+	2.11543i
$184$	−3.49697	−	5.08340i	−0.257800	−	0.374753i
$185$		0			0
$186$	−0.615874	−	6.38641i	−0.0451581	−	0.468274i
$187$	21.0484	+	6.83904i	1.53921	+	0.500120i
$188$	−7.25041	+	7.77963i	−0.528791	+	0.567387i
$189$	−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	$0.125835\pi$
$192$	23.4819	+	8.99048i	1.69466	+	0.648832i
$193$	−22.6952			−1.63363			−0.816817	−	0.576896i	$-0.804264\pi$
$193$	−22.6952			−1.63363			−0.816817	+	0.576896i	$0.804264\pi$
$194$	−0.308765	+	0.273252i	−0.0221681	+	0.0196184i
$195$		0			0
$196$	−11.0276	+	2.14685i	−0.787682	+	0.153346i
$197$	−7.63095	−	10.5031i	−0.543682	−	0.748315i	0.445456	−	0.895304i	$-0.353042\pi$
$197$	−7.63095	−	10.5031i	−0.543682	−	0.748315i	−0.989138	+	0.146989i	$0.953042\pi$
$198$	−3.70888	−	38.4599i	−0.263579	−	2.73322i
$199$	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
$202$	1.06451	+	11.0386i	0.0748988	+	0.776676i
$203$	4.30187	+	5.92102i	0.301932	+	0.415574i
$204$	−6.69312	−	34.3800i	−0.468612	−	2.40708i
$205$		0			0
$206$	−13.9456	+	12.3416i	−0.971634	+	0.859880i
$207$	15.0052			1.04294
$208$	3.62761	−	0.255776i	0.251529	−	0.0177349i
$209$	−5.53086	+	17.0222i	−0.382578	+	1.17745i
$210$		0			0
$211$	1.67102	−	0.542946i	0.115037	−	0.0373779i	−0.250933	−	0.968005i	$-0.580737\pi$
$211$	1.67102	−	0.542946i	0.115037	−	0.0373779i	0.365970	+	0.930627i	$0.380737\pi$
$212$	−19.1173	−	17.8168i	−1.31298	−	1.22366i
$213$	−5.84528	−	1.89925i	−0.400512	−	0.130134i
$214$	0.951200	+	9.86364i	0.0650227	+	0.674264i
$215$		0			0
$216$	−28.4071	+	19.5418i	−1.93286	+	1.32965i
$217$	−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
$222$	12.4104	+	28.5307i	0.832932	+	1.91486i
$223$	−0.481630	−	1.48230i	−0.0322523	−	0.0992625i	0.933634	−	0.358227i	$-0.116619\pi$
$223$	−0.481630	−	1.48230i	−0.0322523	−	0.0992625i	−0.965887	+	0.258965i	$0.916619\pi$
$224$	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	−0.00311955	−	0.999995i	$-0.500993\pi$
$227$	8.77081	−	2.84981i	0.582139	−	0.189148i	0.585259	+	0.810847i	$0.300993\pi$
$228$	27.8038	−	5.41286i	1.84135	−	0.358475i
$229$	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
$232$	13.9711	+	10.7107i	0.917245	+	0.703195i
$233$	−10.0570	−	7.30682i	−0.658854	−	0.478685i	0.207422	−	0.978252i	$-0.433493\pi$
$233$	−10.0570	−	7.30682i	−0.658854	−	0.478685i	−0.866276	+	0.499566i	$0.833493\pi$
$234$	−4.48757	+	7.62091i	−0.293362	+	0.498194i
$235$		0			0
$236$	−2.55231	−	0.312635i	−0.166141	−	0.0203508i
$237$	−8.24687	−	2.67957i	−0.535692	−	0.174057i
$238$	−7.98445	−	4.70164i	−0.517555	−	0.304762i
$239$	8.53966	+	26.2824i	0.552384	+	1.70006i	0.702752	+	0.711435i	$0.251954\pi$
$239$	8.53966	+	26.2824i	0.552384	+	1.70006i	−0.150368	+	0.988630i	$0.548046\pi$
$240$		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	$0.144056\pi$
$242$	5.05856	−	4.47674i	0.325177	−	0.287776i
$243$		−	18.9940i		−	1.21846i
$244$	27.0918	−	15.0275i	1.73438	−	0.962037i
$245$		0			0
$246$	25.9931	−	11.3066i	1.65726	−	0.720883i
$247$	3.31436	−	2.40802i	0.210888	−	0.153219i
$248$	−3.84914	−	1.36117i	−0.244420	−	0.0864345i
$249$	−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	$0.861012\pi$
$252$	−1.96681	+	16.0568i	−0.123898	+	1.01148i
$253$	5.09295	+	7.00985i	0.320191	+	0.440705i
$254$	4.86836	+	11.1920i	0.305468	+	0.702251i
$255$		0			0
$256$	11.4966	−	11.1278i	0.718536	−	0.695490i
$257$	−7.81899			−0.487735			−0.243868	−	0.969809i	$-0.578416\pi$
$257$	−7.81899			−0.487735			−0.243868	+	0.969809i	$0.578416\pi$
$258$	9.85564	−	8.72208i	0.613585	−	0.543013i
$259$	7.82802	+	2.54348i	0.486409	+	0.158044i
$260$		0			0
$261$	−40.7171	+	13.2298i	−2.52033	+	0.818904i
$262$	6.24154	−	10.5995i	0.385604	−	0.654842i
$263$	8.47975	−	26.0980i	0.522884	−	1.60927i	−0.245579	−	0.969377i	$-0.578978\pi$
$263$	8.47975	−	26.0980i	0.522884	−	1.60927i	0.768463	−	0.639894i	$-0.221022\pi$
$264$	−33.2898	−	11.7723i	−2.04884	−	0.724533i
$265$		0			0
$266$	3.80231	−	6.45718i	0.233135	−	0.395915i
$267$	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	−0.232186	−	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	$0.289669\pi$
$272$	−21.6289	−	5.37939i	−1.31144	−	0.326174i
$273$	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	−0.768635	−	0.639687i	$-0.779064\pi$
$277$	−16.8842	+	5.48602i	−1.01448	+	0.329623i	−0.245840	+	0.969310i	$0.579064\pi$
$278$	−18.1126	+	7.87870i	−1.08632	+	0.472533i
$279$	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	$0.804913\pi$
$282$	−23.0750	−	5.11210i	−1.37410	−	0.304421i
$283$	13.6517	−	18.7899i	0.811509	−	1.11695i	−0.179580	−	0.983743i	$-0.557474\pi$
$283$	13.6517	−	18.7899i	0.811509	−	1.11695i	0.991089	−	0.133203i	$-0.0425261\pi$
$284$	−2.66643	+	2.86106i	−0.158224	+	0.169773i
$285$		0			0
$286$	−5.08332	+	0.490210i	−0.300583	+	0.0289867i
$287$	2.31726	−	7.13178i	0.136783	−	0.420976i
$288$	6.44992	+	38.3727i	0.380065	+	2.26113i
$289$	4.34064	+	13.3591i	0.255332	+	0.785830i
$290$		0			0
$291$	−0.871498	−	0.283167i	−0.0510881	−	0.0165995i
$292$	4.09669	+	7.38558i	0.239740	+	0.432208i
$293$			23.5633i			1.37658i	0.725434	+	0.688291i	$0.241639\pi$
$293$			23.5633i			1.37658i	−0.725434	+	0.688291i	$0.758361\pi$
$294$	−16.5472	−	18.6977i	−0.965052	−	1.09047i
$295$		0			0
$296$	19.7916	+	0.509669i	1.15036	+	0.0296239i
$297$	39.1724	−	28.4604i	2.27301	−	1.65144i
$298$	−0.354801	−	3.67917i	−0.0205531	−	0.213129i
$299$		−	1.98327i		−	0.114696i
$300$		0			0
$301$		−	3.48167i		−	0.200680i
$302$	14.9466	−	1.44137i	0.860077	−	0.0829416i
$303$	−19.9396	+	14.4869i	−1.14550	+	0.832252i
$304$	4.35042	−	17.4917i	0.249514	−	1.00322i
$305$		0			0
$306$	40.5901	−	35.9216i	2.32038	−	2.05350i
$307$			29.1918i			1.66607i	0.553223	+	0.833033i	$0.313398\pi$
$307$			29.1918i			1.66607i	−0.553223	+	0.833033i	$0.686602\pi$
$308$	−8.16865	+	4.53105i	−0.465452	+	0.258180i
$309$	−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	$0.891129\pi$
$312$	4.58069	+	6.65875i	0.259330	+	0.376978i
$313$	2.96079	−	9.11237i	0.167354	−	0.515062i	−0.831848	−	0.555003i	$-0.812717\pi$
$313$	2.96079	−	9.11237i	0.167354	−	0.515062i	0.999202	+	0.0399413i	$0.0127171\pi$
$314$	−0.529910	−	5.49500i	−0.0299046	−	0.310101i
$315$		0			0
$316$	−3.76196	+	4.03655i	−0.211627	+	0.227074i
$317$	−10.8218	+	14.8949i	−0.607811	+	0.836580i	−0.996395	−	0.0848334i	$-0.972964\pi$
$317$	−10.8218	+	14.8949i	−0.607811	+	0.836580i	0.388584	+	0.921413i	$0.372964\pi$
$318$	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
$322$	−1.44700	−	3.32657i	−0.0806384	−	0.185382i
$323$	−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
$328$	0.464338	−	18.0313i	0.0256388	−	0.995613i
$329$	−5.05833	+	3.67509i	−0.278875	+	0.202614i
$330$		0			0
$331$	−4.25106	+	5.85108i	−0.233659	+	0.321604i	−0.909705	−	0.415255i	$-0.863692\pi$
$331$	−4.25106	+	5.85108i	−0.233659	+	0.321604i	0.676046	+	0.736860i	$0.263692\pi$
$332$	−7.99669	+	17.1619i	−0.438876	+	0.941883i
$333$	−28.3007	+	38.9525i	−1.55087	+	2.13458i
$334$	−20.5251	−	12.0862i	−1.12309	−	0.661329i
$335$		0			0
$336$	12.5415	+	7.82671i	0.684195	+	0.426982i
$337$	−2.81684	+	8.66935i	−0.153443	+	0.472250i	−0.998000	−	0.0632165i	$-0.979864\pi$
$337$	−2.81684	+	8.66935i	−0.153443	+	0.472250i	0.844557	+	0.535466i	$0.179864\pi$
$338$	−14.8349	−	8.73556i	−0.806914	−	0.475152i
$339$	−13.6625	+	4.43923i	−0.742047	+	0.241106i
$340$		0			0
$341$	5.45277	+	1.77171i	0.295284	+	0.0959436i
$342$	29.0505	+	32.8260i	1.57087	+	1.77503i
$343$	−14.8365			−0.801096
$344$	−2.38202	−	8.02876i	−0.128430	−	0.432882i
$345$		0			0
$346$	13.2036	−	5.74337i	0.709831	−	0.308765i
$347$	−6.01350	−	8.27687i	−0.322821	−	0.444326i	0.616505	−	0.787351i	$-0.288548\pi$
$347$	−6.01350	−	8.27687i	−0.322821	−	0.444326i	−0.939326	+	0.343026i	$0.888548\pi$
$348$	−4.75686	+	38.8344i	−0.254994	+	2.08174i
$349$			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
$352$	−15.7370	+	16.0373i	−0.838786	+	0.854790i
$353$	14.7692	−	10.7305i	0.786087	−	0.571126i	−0.120713	−	0.992687i	$-0.538518\pi$
$353$	14.7692	−	10.7305i	0.786087	−	0.571126i	0.906800	+	0.421562i	$0.138518\pi$
$354$	−2.27952	−	5.24046i	−0.121155	−	0.278527i
$355$		0			0
$356$	−2.53320	−	4.56691i	−0.134260	−	0.242046i
$357$		−	20.5930i		−	1.08990i
$358$	14.1544	+	15.9940i	0.748084	+	0.845309i
$359$	−5.64467	+	17.3725i	−0.297914	+	0.916885i	0.684313	+	0.729188i	$0.260102\pi$
$359$	−5.64467	+	17.3725i	−0.297914	+	0.916885i	−0.982227	+	0.187697i	$0.939898\pi$
$360$		0			0
$361$	−0.403370	−	1.24145i	−0.0212300	−	0.0653393i
$362$	13.5778	−	23.0581i	0.713633	−	1.21191i
$363$	14.2779	+	4.63917i	0.749396	+	0.243493i
$364$	2.12226	+	0.259958i	0.111237	+	0.0136255i
$365$		0			0
$366$	59.3305	+	34.9368i	3.10125	+	1.82617i
$367$	−12.1811	−	8.85005i	−0.635846	−	0.461969i	0.222575	−	0.974916i	$-0.428554\pi$
$367$	−12.1811	−	8.85005i	−0.635846	−	0.461969i	−0.858421	+	0.512947i	$0.828554\pi$
$368$	−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
$372$	−1.73391	−	8.90644i	−0.0898991	−	0.461777i
$373$	−0.674295	+	0.219092i	−0.0349137	+	0.0113441i	−0.326422	−	0.945224i	$-0.605843\pi$
$373$	−0.674295	+	0.219092i	−0.0349137	+	0.0113441i	0.291508	+	0.956568i	$0.405843\pi$
$374$	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
$378$	−18.5895	+	8.08615i	−0.956141	+	0.415907i
$379$	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
$382$	−0.685490	+	3.09416i	−0.0350727	+	0.158311i
$383$	−14.5194	−	10.5490i	−0.741907	−	0.539027i	0.151401	−	0.988472i	$-0.451622\pi$
$383$	−14.5194	−	10.5490i	−0.741907	−	0.539027i	−0.893308	+	0.449445i	$0.851622\pi$
$384$	34.2755	+	9.46808i	1.74912	+	0.483166i
$385$		0			0
$386$	−31.9476	+	3.08087i	−1.62609	+	0.156812i
$387$	19.3699	+	6.29365i	0.984625	+	0.319924i
$388$	−0.397550	+	0.426567i	−0.0201825	+	0.0216557i
$389$	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
$392$	−15.2319	+	4.51907i	−0.769325	+	0.228248i
$393$	27.3377			1.37900
$394$	−12.1677	−	13.7491i	−0.613002	−	0.692671i
$395$		0			0
$396$	−10.4419	−	53.6359i	−0.524723	−	2.69530i
$397$	0.848630	+	1.16804i	0.0425915	+	0.0586222i	0.829782	−	0.558088i	$-0.188465\pi$
$397$	0.848630	+	1.16804i	0.0425915	+	0.0586222i	−0.787190	+	0.616710i	$0.788465\pi$
$398$	25.6433	−	2.47291i	1.28538	−	0.123956i
$399$	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	$0.725605\pi$
$402$	13.4343	−	1.29553i	0.670041	−	0.0646154i
$403$	−0.771367	−	1.06170i	−0.0384245	−	0.0528868i
$404$	2.99699	+	15.3944i	0.149106	+	0.765901i
$405$		0			0
$406$	6.85945	+	7.75094i	0.340429	+	0.384672i
$407$	−27.8026			−1.37813
$408$	−14.0889	−	47.4876i	−0.697503	−	2.35099i
$409$	−0.312601	+	0.962088i	−0.0154571	+	0.0475722i	−0.958488	−	0.285134i	$-0.907962\pi$
$409$	−0.312601	+	0.962088i	−0.0154571	+	0.0475722i	0.943030	+	0.332706i	$0.107962\pi$
$410$		0			0
$411$	10.8918	−	3.53897i	0.537254	−	0.174564i
$412$	−17.9556	+	19.2662i	−0.884608	+	0.949176i
$413$	−1.43783	−	0.467180i	−0.0707512	−	0.0229884i
$414$	21.1226	−	2.03696i	1.03812	−	0.100111i
$415$		0			0
$416$	5.07180	−	0.852499i	0.248665	−	0.0417972i
$417$	−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	−0.0144183	+	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	$0.0338621\pi$
$421$	16.1696	+	22.2556i	0.788060	+	1.08467i	−0.206287	+	0.978492i	$0.566138\pi$
$422$	2.27856	−	0.991136i	0.110918	−	0.0482478i
$423$	−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
$428$	2.67798	+	13.7558i	0.129445	+	0.664909i
$429$	−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	$0.477249\pi$
$432$	−37.3354	+	31.3649i	−1.79630	+	1.50904i
$433$	−16.7912	−	12.1996i	−0.806936	−	0.586273i	0.106005	−	0.994366i	$-0.466194\pi$
$433$	−16.7912	−	12.1996i	−0.806936	−	0.586273i	−0.912941	+	0.408092i	$0.866194\pi$
$434$	−2.06844	−	1.21800i	−0.0992883	−	0.0584659i
$435$		0			0
$436$	5.36422	+	0.657069i	0.256900	+	0.0314679i
$437$	−9.34882	−	3.03762i	−0.447215	−	0.145309i
$438$	−9.52421	+	16.1742i	−0.455084	+	0.772835i
$439$	−0.0935999	−	0.288071i	−0.00446728	−	0.0137489i	0.948798	−	0.315883i	$-0.102301\pi$
$439$	−0.0935999	−	0.288071i	−0.00446728	−	0.0137489i	−0.953265	+	0.302134i	$0.902301\pi$
$440$		0			0
$441$	11.9401	−	36.7478i	0.568575	−	1.74989i
$442$	−4.74782	−	5.36487i	−0.225831	−	0.255181i
$443$			33.9046i			1.61086i	0.592693	+	0.805428i	$0.298065\pi$
$443$			33.9046i			1.61086i	−0.592693	+	0.805428i	$0.701935\pi$
$444$	21.3430	+	38.4775i	1.01289	+	1.82606i
$445$		0			0
$446$	−0.879205	−	2.02123i	−0.0416316	−	0.0957082i
$447$	6.64583	−	4.82848i	0.314337	−	0.228379i
$448$	7.88500	−	5.13031i	0.372531	−	0.242384i
$449$	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
$452$	−1.11142	+	9.07348i	−0.0522768	+	0.426781i
$453$	19.6156	+	26.9986i	0.921621	+	1.26850i
$454$	11.9597	−	5.20226i	0.561295	−	0.244154i
$455$		0			0
$456$	38.4041	−	11.3939i	1.79844	−	0.533571i
$457$	2.58934			0.121124			0.0605622	−	0.998164i	$-0.480711\pi$
$457$	2.58934			0.121124			0.0605622	+	0.998164i	$0.480711\pi$
$458$	10.5889	+	11.9651i	0.494786	+	0.559091i
$459$	64.5997	+	20.9897i	3.01526	+	0.979716i
$460$		0			0
$461$	−6.49523	+	2.11043i	−0.302513	+	0.0982925i	−0.456340	−	0.889805i	$-0.650840\pi$
$461$	−6.49523	+	2.11043i	−0.302513	+	0.0982925i	0.153827	+	0.988098i	$0.450840\pi$
$462$	−17.8892	−	10.5340i	−0.832279	−	0.490088i
$463$	−6.74304	+	20.7530i	−0.313376	+	0.964472i	0.663042	+	0.748582i	$0.269265\pi$
$463$	−6.74304	+	20.7530i	−0.313376	+	0.964472i	−0.976418	+	0.215889i	$0.930735\pi$
$464$	21.1208	+	13.1808i	0.980509	+	0.611902i
$465$		0			0
$466$	−15.1489	−	8.92045i	−0.701761	−	0.413232i
$467$	−1.76636	+	2.43118i	−0.0817373	+	0.112502i	−0.847928	−	0.530112i	$-0.822150\pi$
$467$	−1.76636	+	2.43118i	−0.0817373	+	0.112502i	0.766190	+	0.642614i	$0.222150\pi$
$468$	−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
$472$	−3.63528	−	0.0936149i	−0.167327	−	0.00430898i
$473$	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
$478$	15.5890	+	35.8380i	0.713022	+	1.63919i
$479$	−15.3717	+	11.1682i	−0.702349	+	0.510287i	−0.880697	−	0.473681i	$-0.842925\pi$
$479$	−15.3717	+	11.1682i	−0.702349	+	0.510287i	0.178347	+	0.983968i	$0.442925\pi$
$480$		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
$484$	6.51313	−	6.98853i	0.296051	−	0.317661i
$485$		0			0
$486$	−2.57843	−	26.7375i	−0.116960	−	1.21284i
$487$	−0.586607	+	1.80539i	−0.0265817	+	0.0818101i	−0.963467	−	0.267826i	$-0.913695\pi$
$487$	−0.586607	+	1.80539i	−0.0265817	+	0.0818101i	0.936886	+	0.349636i	$0.113695\pi$
$488$	36.0967	−	24.8317i	1.63402	−	1.12408i
$489$	−19.0651	−	58.6762i	−0.862151	−	2.65343i
$490$		0			0
$491$	−29.3750	−	9.54451i	−1.32567	−	0.430738i	−0.441234	−	0.897392i	$-0.645459\pi$
$491$	−29.3750	−	9.54451i	−1.32567	−	0.430738i	−0.884440	+	0.466654i	$0.845459\pi$
$492$	35.0552	−	19.4447i	1.58041	−	0.876634i
$493$		−	34.6801i		−	1.56191i
$494$	4.33868	−	3.83966i	0.195206	−	0.172754i
$495$		0			0
$496$	−5.60315	−	1.39358i	−0.251589	−	0.0625735i
$497$	−1.86027	+	1.35156i	−0.0834443	+	0.0606258i
$498$	−41.8845	+	4.03913i	−1.87689	+	0.180998i
$499$			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
$502$	1.81905	+	18.8629i	0.0811881	+	0.841894i
$503$	−21.4189	+	15.5618i	−0.955024	+	0.693865i	−0.951990	−	0.306130i	$-0.900966\pi$
$503$	−21.4189	+	15.5618i	−0.955024	+	0.693865i	−0.00303389	+	0.999995i	$0.500966\pi$
$504$	−0.588940	+	22.8699i	−0.0262335	+	1.01871i
$505$		0			0
$506$	8.12085	+	9.17628i	0.361016	+	0.407935i
$507$		−	38.2613i		−	1.69925i
$508$	8.37243	+	15.0940i	0.371467	+	0.669687i
$509$	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
$512$	14.6729	−	17.2251i	0.648458	−	0.761251i
$513$	−16.9748	+	52.2431i	−0.749456	+	2.30659i
$514$	−11.0067	+	1.06143i	−0.485483	+	0.0468176i
$515$		0			0
$516$	12.6896	−	13.6158i	0.558628	−	0.599403i
$517$	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	0.443295	−	0.896376i	$-0.353809\pi$
$521$	32.7039	−	23.7608i	1.43278	−	1.04098i	0.989490	−	0.144603i	$-0.0461906\pi$
$522$	−55.5209	+	24.1507i	−2.43008	+	1.05705i
$523$	−16.5534	+	5.37852i	−0.723828	+	0.235186i	−0.647682	−	0.761911i	$-0.724262\pi$
$523$	−16.5534	+	5.37852i	−0.723828	+	0.235186i	−0.0761461	+	0.997097i	$0.524262\pi$
$524$	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
$528$	−48.4595	−	12.0525i	−2.10893	−	0.524520i
$529$	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
$534$	5.88934	−	10.0014i	0.254857	−	0.432804i
$535$		0			0
$536$	2.86332	−	8.09693i	0.123677	−	0.349734i
$537$	−14.6680	+	45.1434i	−0.632970	+	1.94808i
$538$	15.3104	−	26.0004i	0.660076	−	1.12096i
$539$	21.2197	−	6.89469i	0.913996	−	0.296975i
$540$		0			0
$541$	7.69917	+	2.50161i	0.331013	+	0.107553i	0.469808	−	0.882768i	$-0.344323\pi$
$541$	7.69917	+	2.50161i	0.331013	+	0.107553i	−0.138795	+	0.990321i	$0.544323\pi$
$542$	1.13150	−	1.00136i	0.0486020	−	0.0430120i
$543$	59.4701			2.55211
$544$	−31.1768	−	4.63637i	−1.33670	−	0.198783i
$545$		0			0
$546$	1.89543	+	4.35747i	0.0811170	+	0.186483i
$547$	15.0486	+	20.7126i	0.643431	+	0.885607i	0.998793	−	0.0491221i	$-0.0156423\pi$
$547$	15.0486	+	20.7126i	0.643431	+	0.885607i	−0.355362	+	0.934729i	$0.615642\pi$
$548$	0.886029	−	7.23342i	0.0378493	−	0.308996i
$549$			106.551i			4.54747i
$550$		0			0
$551$	28.0465			1.19482
$552$	6.46547	−	18.2831i	0.275189	−	0.778181i
$553$	−2.62457	+	1.90686i	−0.111608	+	0.0810881i
$554$	−23.0229	+	10.0146i	−0.978151	+	0.425480i
$555$		0			0
$556$	−24.4273	+	13.5495i	−1.03595	+	0.574627i
$557$		−	1.74254i		−	0.0738336i	−0.999318	−	0.0369168i	$-0.988246\pi$
$557$		−	1.74254i		−	0.0738336i	0.999318	−	0.0369168i	$-0.0117537\pi$
$558$	10.5152	−	9.30579i	0.445145	−	0.393946i
$559$	0.831844	−	2.56015i	0.0351832	−	0.108283i
$560$		0			0
$561$	21.4952	+	66.1555i	0.907529	+	2.79309i
$562$	−13.2234	−	7.78660i	−0.557796	−	0.328458i
$563$	24.4440	+	7.94233i	1.03019	+	0.334729i	0.774866	−	0.632126i	$-0.217817\pi$
$563$	24.4440	+	7.94233i	1.03019	+	0.334729i	0.255325	+	0.966855i	$0.417817\pi$
$564$	−33.1762	−	4.06379i	−1.39697	−	0.171116i
$565$		0			0
$566$	16.6665	−	28.3035i	0.700546	−	1.18968i
$567$	−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	0.803119	−	0.595819i	$-0.203172\pi$
$569$	11.5604	+	8.39915i	0.484639	+	0.352111i	−0.318480	+	0.947930i	$0.603172\pi$
$570$		0			0
$571$	−11.7151	−	16.1245i	−0.490263	−	0.674789i	0.490174	−	0.871625i	$-0.336933\pi$
$571$	−11.7151	−	16.1245i	−0.490263	−	0.674789i	−0.980436	+	0.196836i	$0.936933\pi$
$572$	−7.08916	+	1.38012i	−0.296413	+	0.0577057i
$573$	−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	−0.999924	−	0.0123079i	$-0.996082\pi$
$577$	−4.76100	−	14.6528i	−0.198203	−	0.610006i	0.801721	−	0.597698i	$-0.203918\pi$
$578$	7.92375	+	18.2162i	0.329584	+	0.757692i
$579$	−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
$584$	6.76943	+	9.84043i	0.280121	+	0.407200i
$585$		0			0
$586$	3.19872	+	33.1697i	0.132138	+	1.37023i
$587$	−13.0914	−	4.25364i	−0.540338	−	0.175567i	0.0261173	−	0.999659i	$-0.491686\pi$
$587$	−13.0914	−	4.25364i	−0.540338	−	0.175567i	−0.566455	+	0.824092i	$0.691686\pi$
$588$	−25.8314	−	24.0742i	−1.06527	−	0.992804i
$589$	−6.18610	+	2.00998i	−0.254894	+	0.0828200i
$590$		0			0
$591$	12.6092	−	38.8072i	0.518675	−	1.59632i
$592$	27.9295	−	1.96926i	1.14790	−	0.0809360i
$593$	−6.37493			−0.261787			−0.130894	−	0.991396i	$-0.541785\pi$
$593$	−6.37493			−0.261787			−0.130894	+	0.991396i	$0.541785\pi$
$594$	51.2789	−	45.3809i	2.10400	−	1.86200i
$595$		0			0
$596$	−0.998894	−	5.13094i	−0.0409163	−	0.210172i
$597$	33.6538	+	46.3205i	1.37736	+	1.89577i
$598$	−0.269229	−	2.79182i	−0.0110096	−	0.114166i
$599$	−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	$0.184198\pi$
$602$	−0.472637	−	4.90109i	−0.0192632	−	0.199754i
$603$	12.2766	+	16.8973i	0.499942	+	0.688112i
$604$	20.8443	−	4.05799i	0.848144	−	0.165117i
$605$		0			0
$606$	−26.1020	+	23.0998i	−1.06032	+	0.938365i
$607$	28.6948			1.16469			0.582343	−	0.812943i	$-0.302136\pi$
$607$	28.6948			1.16469			0.582343	+	0.812943i	$0.302136\pi$
$608$	3.74952	−	25.2133i	0.152063	−	1.02254i
$609$	−7.10833	+	21.8772i	−0.288044	+	0.886509i
$610$		0			0
$611$	−4.59756	+	1.49384i	−0.185997	+	0.0604342i
$612$	52.2617	−	56.0763i	2.11255	−	2.26675i
$613$	7.10423	+	2.30831i	0.286937	+	0.0932316i	0.448949	−	0.893557i	$-0.351798\pi$
$613$	7.10423	+	2.30831i	0.286937	+	0.0932316i	−0.162012	+	0.986789i	$0.551798\pi$
$614$	3.96279	+	41.0929i	0.159925	+	1.65837i
$615$		0			0
$616$	−10.8838	+	7.48717i	−0.438520	+	0.301667i
$617$	32.7837	+	23.8187i	1.31982	+	0.958906i	0.999934	+	0.0114498i	$0.00364467\pi$
$617$	32.7837	+	23.8187i	1.31982	+	0.958906i	0.319886	+	0.947456i	$0.396355\pi$
$618$	−57.1450	−	12.6601i	−2.29871	−	0.509263i
$619$	−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
$622$	0.554441	+	1.27462i	0.0222311	+	0.0511077i
$623$	−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
$628$	−1.49189	−	7.66328i	−0.0595329	−	0.305798i
$629$	−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	$0.905907\pi$
$632$	−4.74769	+	6.19287i	−0.188853	+	0.246339i
$633$	4.46765	+	3.24593i	0.177573	+	0.129014i
$634$	−13.2116	+	22.4363i	−0.524701	+	0.891060i
$635$		0			0
$636$	9.98617	−	81.5257i	0.395977	−	3.23271i
$637$	−4.85702	−	1.57814i	−0.192442	−	0.0625283i
$638$	−30.1267	−	17.7401i	−1.19273	−	0.702337i
$639$	−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	$0.816393\pi$
$642$	−23.3235	+	20.6409i	−0.920507	+	0.814633i
$643$			15.6623i			0.617660i	0.951117	+	0.308830i	$0.0999375\pi$
$643$			15.6623i			0.617660i	−0.951117	+	0.308830i	$0.900063\pi$
$644$	−2.48850	−	4.48632i	−0.0980608	−	0.176786i
$645$		0			0
$646$	−32.5610	+	14.1635i	−1.28110	+	0.557256i
$647$	26.8579	−	19.5134i	1.05589	−	0.767152i	0.0825693	−	0.996585i	$-0.473687\pi$
$647$	26.8579	−	19.5134i	1.05589	−	0.767152i	0.973324	+	0.229434i	$0.0736874\pi$
$648$	−47.1426	−	16.6711i	−1.85194	−	0.654901i
$649$	5.10673			0.200457
$650$		0			0
$651$		−	5.33479i		−	0.209087i
$652$	−38.9677	−	4.77319i	−1.52609	−	0.186933i
$653$	−2.28117	−	3.13976i	−0.0892690	−	0.122868i	0.762047	−	0.647522i	$-0.224195\pi$
$653$	−2.28117	−	3.13976i	−0.0892690	−	0.122868i	−0.851316	+	0.524654i	$0.824195\pi$
$654$	4.79090	+	11.0139i	0.187339	+	0.430680i
$655$		0			0
$656$	−1.79411	−	25.4454i	−0.0700482	−	0.993477i
$657$	−29.0471			−1.13323
$658$	−6.62163	+	5.86003i	−0.258138	+	0.228448i
$659$	−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	0.489004	−	0.872282i	$-0.337360\pi$
$661$	35.9253	−	11.6728i	1.39733	−	0.454020i	0.908327	+	0.418261i	$0.137360\pi$
$662$	−5.18986	+	8.81355i	−0.201710	+	0.342548i
$663$	4.92009	−	15.1425i	0.191081	−	0.588085i
$664$	−8.92708	+	25.2441i	−0.346438	+	0.979661i
$665$		0			0
$666$	−34.5506	+	58.6746i	−1.33881	+	2.27359i
$667$	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
$672$	18.7169	+	9.31503i	0.722021	+	0.359335i
$673$	0.512274	+	1.57662i	0.0197467	+	0.0607742i	0.960444	−	0.278472i	$-0.0898280\pi$
$673$	0.512274	+	1.57662i	0.0197467	+	0.0607742i	−0.940698	+	0.339246i	$0.889828\pi$
$674$	−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	−0.313161	−	0.949700i	$-0.601388\pi$
$677$	−0.215778	+	0.0701106i	−0.00829304	+	0.00269457i	0.304868	+	0.952395i	$0.401388\pi$
$678$	−18.6299	+	8.10371i	−0.715477	+	0.311221i
$679$	−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	−0.999737	−	0.0229435i	$-0.992696\pi$
$683$	−17.4833	+	24.0637i	−0.668981	+	0.920773i	0.330756	+	0.943716i	$0.392696\pi$
$684$	45.3500	+	42.2650i	1.73400	+	1.61604i
$685$		0			0
$686$	−20.8851	+	2.01405i	−0.797396	+	0.0768969i
$687$	−10.9731	+	33.7717i	−0.418649	+	1.28847i
$688$	−4.44303	−	10.9786i	−0.169389	−	0.418555i
$689$	−3.67089	−	11.2978i	−0.139850	−	0.430413i
$690$		0			0
$691$	−29.9436	−	9.72925i	−1.13911	−	0.370118i	−0.322077	−	0.946714i	$-0.604381\pi$
$691$	−29.9436	−	9.72925i	−1.13911	−	0.370118i	−0.817030	+	0.576595i	$0.804381\pi$
$692$	17.8069	−	9.87723i	0.676915	−	0.375476i
$693$		−	32.1269i		−	1.22040i
$694$	−9.58868	−	10.8349i	−0.363981	−	0.411286i
$695$		0			0
$696$	−1.42439	+	55.3122i	−0.0539913	+	2.09660i
$697$	−28.7469	+	20.8859i	−1.08887	+	0.791108i
$698$	0.646761	+	6.70671i	0.0244803	+	0.253853i
$699$		−	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	$0.986139\pi$
$702$	−15.6012	+	1.50451i	−0.588831	+	0.0567839i
$703$	25.5178	−	18.5398i	0.962422	−	0.699240i
$704$	−19.9757	+	24.7117i	−0.752862	+	0.931358i
$705$		0			0
$706$	19.3337	−	17.1100i	0.727635	−	0.643945i
$707$			9.22096i			0.346790i
$708$	−3.92023	−	7.06746i	−0.147331	−	0.265611i
$709$	−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
$712$	−4.18591	−	6.08488i	−0.156874	−	0.228040i
$713$	−0.973045	+	2.99472i	−0.0364408	+	0.112153i
$714$	−2.79550	−	28.9884i	−0.104619	−	1.08486i
$715$		0			0
$716$	22.0961	+	20.5930i	0.825770	+	0.769597i
$717$	−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	0.333604	−	0.942713i	$-0.391735\pi$
$719$	−12.3313	−	8.95922i	−0.459880	−	0.334123i	−0.793484	+	0.608591i	$0.791735\pi$
$720$		0			0
$721$	−12.5269	+	9.10133i	−0.466526	+	0.338951i
$722$	−0.736344	−	1.69281i	−0.0274039	−	0.0629997i
$723$	−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	$-0.0868523\pi$
$727$	0.688107	+	2.11778i	0.0255205	+	0.0785440i	−0.937485	+	0.348025i	$0.886852\pi$
$728$	3.02276	+	0.0778413i	0.112031	+	0.00288499i
$729$	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	0.209237	−	0.977865i	$-0.432902\pi$
$733$	29.0933	−	40.0434i	1.07458	−	1.47904i	0.865347	−	0.501173i	$-0.167098\pi$
$734$	−18.3485	−	10.8045i	−0.677254	−	0.398801i
$735$		0			0
$736$	−8.80787	−	8.64296i	−0.324662	−	0.318584i
$737$	−3.72692	+	11.4703i	−0.137283	+	0.422513i
$738$	53.4560	+	31.4776i	1.96774	+	1.15871i
$739$	−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
$742$	−14.4002	−	16.2717i	−0.528647	−	0.597352i
$743$	−15.5632			−0.570959			−0.285479	−	0.958385i	$-0.592153\pi$
$743$	−15.5632			−0.570959			−0.285479	+	0.958385i	$0.592153\pi$
$744$	−3.64984	−	12.3021i	−0.133810	−	0.451016i
$745$		0			0
$746$	−0.919452	+	0.399947i	−0.0336635	+	0.0146431i
$747$	−38.2752	−	52.6813i	−1.40042	−	1.92751i
$748$	43.9348	+	5.38162i	1.60642	+	0.196771i
$749$			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	$0.225863\pi$
$752$	−11.2603	+	18.0435i	−0.410622	+	0.657980i
$753$	−34.0729	+	24.7554i	−1.24169	+	0.902137i
$754$	3.19205	+	7.33830i	0.116248	+	0.267245i
$755$		0			0
$756$	−25.0704	+	13.9063i	−0.911803	+	0.505766i
$757$		−	1.83755i		−	0.0667870i	−0.999442	−	0.0333935i	$-0.989369\pi$
$757$		−	1.83755i		−	0.0667870i	0.999442	−	0.0333935i	$-0.0106315\pi$
$758$	17.2544	+	19.4969i	0.626708	+	0.708158i
$759$	−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	$-0.281194\pi$
$762$	−19.4647	+	33.0555i	−0.705132	+	1.19747i
$763$	3.02192	+	0.981880i	0.109401	+	0.0355464i
$764$	−0.544920	+	4.44866i	−0.0197145	+	0.160947i
$765$		0			0
$766$	−21.8708	−	12.8786i	−0.790223	−	0.465323i
$767$	−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	0.441604	−	0.897210i	$-0.354410\pi$
$769$	−7.63237	−	5.54524i	−0.275230	−	0.199966i	−0.716834	+	0.697244i	$0.754410\pi$
$770$		0			0
$771$	−14.4450	−	19.8818i	−0.520222	−	0.716025i
$772$	−44.5539	+	8.67378i	−1.60353	+	0.312176i
$773$	23.0787	−	7.49873i	0.830084	−	0.269711i	0.137003	−	0.990571i	$-0.456253\pi$
$773$	23.0787	−	7.49873i	0.830084	−	0.269711i	0.693081	+	0.720860i	$0.256253\pi$
$774$	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
$778$	30.9637	−	13.4687i	1.11010	−	0.482877i
$779$	−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
$784$	−20.8282	+	8.42915i	−0.743863	+	0.301041i
$785$		0			0
$786$	38.4828	−	3.71109i	1.37264	−	0.132370i
$787$	35.4350	+	11.5135i	1.26312	+	0.410413i	0.862606	−	0.505877i	$-0.168831\pi$
$787$	35.4350	+	11.5135i	1.26312	+	0.410413i	0.400515	+	0.916290i	$0.368831\pi$
$788$	−18.9948	−	17.7026i	−0.676661	−	0.630631i
$789$	82.0264	−	26.6520i	2.92022	−	0.948837i
$790$		0			0
$791$	−1.66083	+	5.11151i	−0.0590524	+	0.181745i
$792$	−21.9799	−	74.0848i	−0.781021	−	2.63249i
$793$	14.0830			0.500103
$794$	1.35316	+	1.52903i	0.0480220	+	0.0542632i
$795$		0			0
$796$	35.7619	−	6.96214i	1.26755	−	0.246767i
$797$	2.93174	+	4.03520i	0.103848	+	0.142934i	0.857778	−	0.514020i	$-0.171844\pi$
$797$	2.93174	+	4.03520i	0.103848	+	0.142934i	−0.753930	+	0.656954i	$0.771844\pi$
$798$	23.4435	−	2.26077i	0.829890	−	0.0800305i
$799$	29.6272			1.04814
$800$		0			0
$801$	17.9614			0.634635
$802$	−36.6957	+	3.53875i	−1.29577	+	0.124958i
$803$	−9.85892	−	13.5696i	−0.347914	−	0.478862i
$804$	18.7353	−	3.64740i	0.660744	−	0.128634i
$805$		0			0
$806$	−1.22996	−	1.38982i	−0.0433237	−	0.0489542i
$807$	67.0587			2.36058
$808$	6.30860	+	21.2636i	0.221936	+	0.748051i
$809$	2.74204	−	8.43914i	0.0964051	−	0.296704i	−0.891212	−	0.453587i	$-0.850144\pi$
$809$	2.74204	−	8.43914i	0.0964051	−	0.296704i	0.987617	+	0.156882i	$0.0501443\pi$
$810$		0			0
$811$	20.7338	−	6.73681i	0.728062	−	0.236562i	0.0785467	−	0.996910i	$-0.474972\pi$
$811$	20.7338	−	6.73681i	0.728062	−	0.236562i	0.649515	+	0.760349i	$0.274972\pi$
$812$	10.7081	+	9.97969i	0.375781	+	0.350219i
$813$	3.19368	+	1.03769i	0.112007	+	0.0363934i
$814$	−39.1373	+	3.77421i	−1.37176	+	0.132286i
$815$		0			0
$816$	−26.2791	−	64.9349i	−0.919953	−	2.27318i
$817$	−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	−0.997881	−	0.0650589i	$-0.979276\pi$
$821$	−21.5298	−	29.6332i	−0.751394	−	1.03420i	0.246488	−	0.969146i	$-0.420724\pi$
$822$	14.8518	−	6.46031i	0.518017	−	0.225329i
$823$	−1.83068	−	5.63427i	−0.0638136	−	0.196398i	0.914066	−	0.405564i	$-0.132925\pi$
$823$	−1.83068	−	5.63427i	−0.0638136	−	0.196398i	−0.977880	+	0.209166i	$0.932925\pi$
$824$	−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	−0.549854	−	0.835261i	$-0.685317\pi$
$827$	−14.4864	+	4.70692i	−0.503742	+	0.163676i	0.0461123	+	0.998936i	$0.485317\pi$
$828$	29.4574	−	5.73479i	1.02372	−	0.199298i
$829$	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
$832$	7.02376	−	1.88854i	0.243505	−	0.0654735i
$833$	25.3216	+	18.3972i	0.877343	+	0.637427i
$834$	−53.4952	−	31.5007i	−1.85239	−	1.09078i
$835$		0			0
$836$	−4.35222	+	35.5309i	−0.150525	+	1.22886i
$837$	16.7351	+	5.43757i	0.578450	+	0.187950i
$838$	−24.0134	+	40.7801i	−0.829528	+	1.40872i
$839$	−14.0891	−	43.3617i	−0.486409	−	1.49701i	−0.829930	−	0.557868i	$-0.811620\pi$
$839$	−14.0891	−	43.3617i	−0.486409	−	1.49701i	0.343521	−	0.939145i	$-0.388380\pi$
$840$		0			0
$841$	−3.00946	+	9.26218i	−0.103775	+	0.319385i
$842$	25.7829	+	29.1338i	0.888539	+	1.00402i
$843$		−	34.1050i		−	1.17464i
$844$	3.07294	−	1.70452i	0.105775	−	0.0586720i
$845$		0			0
$846$	−20.6320	−	47.4315i	−0.709342	−	1.63073i
$847$	4.54396	−	3.30138i	0.156132	−	0.113437i
$848$	−44.3393	−	27.6706i	−1.52262	−	0.950214i
$849$	72.9986			2.50531
$850$		0			0
$851$		−	15.2695i		−	0.523433i
$852$	−12.2010	−	1.49451i	−0.417999	−	0.0512011i
$853$	−28.9855	−	39.8951i	−0.992445	−	1.36598i	−0.929848	−	0.367944i	$-0.880062\pi$
$853$	−28.9855	−	39.8951i	−0.992445	−	1.36598i	−0.0625971	−	0.998039i	$-0.519938\pi$
$854$	23.6216	−	10.2750i	0.808315	−	0.351604i
$855$		0			0
$856$	5.63709	+	19.0002i	0.192672	+	0.649414i
$857$	57.0345			1.94826			0.974130	−	0.225989i	$-0.0725613\pi$
$857$	57.0345			1.94826			0.974130	+	0.225989i	$0.0725613\pi$
$858$	−10.6375	−	12.0200i	−0.363159	−	0.410356i
$859$	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
$862$	32.5887	+	19.1899i	1.10998	+	0.653610i
$863$	5.84794	−	17.9981i	0.199066	−	0.612663i	−0.800839	−	0.598880i	$-0.795613\pi$
$863$	5.84794	−	17.9981i	0.199066	−	0.612663i	0.999905	−	0.0137830i	$-0.00438742\pi$
$864$	−48.2986	+	49.2201i	−1.64315	+	1.67450i
$865$		0			0
$866$	−25.2928	−	14.8937i	−0.859486	−	0.506108i
$867$	−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
$872$	7.64033	+	0.196752i	0.258734	+	0.00666286i
$873$	−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	−0.0766761	−	0.997056i	$-0.524431\pi$
$877$	13.2478	−	4.30447i	0.447347	−	0.145352i	0.524023	+	0.851704i	$0.324431\pi$
$878$	−0.170865	−	0.392807i	−0.00576640	−	0.0132566i
$879$	−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	$0.938670\pi$
$882$	11.8193	−	53.3501i	0.397977	−	1.79639i
$883$	2.40648	−	3.31224i	0.0809845	−	0.111466i	−0.766603	−	0.642122i	$-0.778054\pi$
$883$	2.40648	−	3.31224i	0.0809845	−	0.111466i	0.847587	+	0.530656i	$0.178054\pi$
$884$	−7.41171	−	6.90753i	−0.249283	−	0.232325i
$885$		0			0
$886$	4.60255	+	47.7270i	0.154626	+	1.60342i
$887$	1.75339	−	5.39637i	0.0588730	−	0.181192i	−0.917295	−	0.398208i	$-0.869632\pi$
$887$	1.75339	−	5.39637i	0.0588730	−	0.181192i	0.976168	+	0.217016i	$0.0696322\pi$
$888$	35.2675	+	51.2668i	1.18350	+	1.72040i
$889$	3.13597	+	9.65152i	0.105177	+	0.323701i
$890$		0			0
$891$	66.7832	+	21.6992i	2.23732	+	0.726950i
$892$	−1.51202	−	2.72591i	−0.0506263	−	0.0912701i
$893$			23.9601i			0.801795i
$894$	8.69976	−	7.69914i	0.290963	−	0.257498i
$895$		0			0
$896$	10.4031	−	8.29224i	0.347545	−	0.277024i
$897$	5.04297	−	3.66394i	0.168380	−	0.122335i
$898$	17.7436	−	1.71111i	0.592113	−	0.0571004i
$899$		−	8.98418i		−	0.299639i
$900$		0			0
$901$			72.8046i			2.42547i
$902$	3.43852	+	35.6564i	0.114490	+	1.18723i
$903$	8.85304	−	6.43211i	0.294611	−	0.214047i
$904$	−0.332802	+	12.9235i	−0.0110688	+	0.429828i
$905$		0			0
$906$	31.2776	+	35.3426i	1.03913	+	1.17418i
$907$		−	49.8362i		−	1.65478i	−0.561625	−	0.827392i	$-0.689824\pi$
$907$		−	49.8362i		−	1.65478i	0.561625	−	0.827392i	$-0.310176\pi$
$908$	16.1292	−	8.94666i	0.535266	−	0.296905i
$909$	−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	$0.881548\pi$
$912$	52.5141	−	21.2524i	1.73892	−	0.703738i
$913$	11.6196	−	35.7613i	0.384551	−	1.18353i
$914$	3.64497	−	0.351503i	0.120565	−	0.0116267i
$915$		0			0
$916$	16.5300	+	15.4056i	0.546168	+	0.509015i
$917$	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	0.990085	−	0.140471i	$-0.0448616\pi$
$919$	35.2395	+	25.6030i	1.16244	+	0.844564i	0.172357	+	0.985034i	$0.444862\pi$
$920$		0			0
$921$	−74.2277	+	53.9296i	−2.44589	+	1.77704i
$922$	−8.85674	+	3.85254i	−0.291681	+	0.126877i
$923$	−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
$928$	31.5207	+	15.6872i	1.03472	+	0.514957i
$929$	20.6493	−	15.0026i	0.677483	−	0.492220i	−0.195039	−	0.980795i	$-0.562483\pi$
$929$	20.6493	−	15.0026i	0.677483	−	0.492220i	0.872522	+	0.488576i	$0.162483\pi$
$930$		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
$934$	−2.15644	+	3.66212i	−0.0705608	+	0.119828i
$935$		0			0
$936$	−5.89715	+	16.6760i	−0.192754	+	0.545073i
$937$	1.22309	−	3.76427i	0.0399565	−	0.122973i	−0.929089	−	0.369857i	$-0.879407\pi$
$937$	1.22309	−	3.76427i	0.0399565	−	0.122973i	0.969045	+	0.246884i	$0.0794066\pi$
$938$	2.56215	−	4.35111i	0.0836572	−	0.142069i
$939$	28.6403	−	9.30581i	0.934642	−	0.303684i
$940$		0			0
$941$	−7.54079	−	2.45015i	−0.245823	−	0.0798727i	0.183514	−	0.983017i	$-0.441253\pi$
$941$	−7.54079	−	2.45015i	−0.245823	−	0.0798727i	−0.429337	+	0.903144i	$0.641253\pi$
$942$	12.9935	−	11.4990i	0.423350	−	0.374658i
$943$	−13.9114			−0.453018
$944$	−5.13003	+	0.361709i	−0.166968	+	0.0117726i
$945$		0			0
$946$	6.63418	+	15.2515i	0.215696	+	0.495870i
$947$	0.457976	+	0.630350i	0.0148822	+	0.0204836i	0.816393	−	0.577496i	$-0.195970\pi$
$947$	0.457976	+	0.630350i	0.0148822	+	0.0204836i	−0.801511	+	0.597980i	$0.795970\pi$
$948$	−17.2139	−	2.10854i	−0.559081	−	0.0684824i
$949$			3.83921i			0.124626i
$950$		0			0
$951$	−57.8664			−1.87645
$952$	−17.4715	−	6.17846i	−0.566255	−	0.200245i
$953$	−8.66334	+	6.29429i	−0.280633	+	0.203892i	−0.719194	−	0.694810i	$-0.755489\pi$
$953$	−8.66334	+	6.29429i	−0.280633	+	0.203892i	0.438560	+	0.898702i	$0.355489\pi$
$954$	116.556	−	50.7000i	3.77364	−	1.64147i
$955$		0			0
$956$	26.8093	+	48.3323i	0.867075	+	1.56318i
$957$		−	77.7008i		−	2.51171i
$958$	−20.1224	+	17.8079i	−0.650124	+	0.575349i
$959$	1.32402	−	4.07492i	0.0427549	−	0.131586i
$960$		0			0
$961$	−8.93566	−	27.5011i	−0.288247	−	0.887134i
$962$	7.75514	+	4.56662i	0.250036	+	0.147234i
$963$	−45.8391	−	14.8940i	−1.47714	−	0.479953i
$964$	−1.04161	+	8.50353i	−0.0335479	+	0.273880i
$965$		0			0
$966$	5.78542	−	9.82494i	0.186143	−	0.316112i
$967$	−7.39419	−	5.37219i	−0.237781	−	0.172758i	0.462513	−	0.886612i	$-0.346948\pi$
$967$	−7.39419	−	5.37219i	−0.237781	−	0.172758i	−0.700294	+	0.713854i	$0.746948\pi$
$968$	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	$-0.0631675\pi$
$971$	15.2665	+	21.0125i	0.489924	+	0.674323i	−0.490450	+	0.871469i	$0.663167\pi$
$972$	−7.25922	−	37.2879i	−0.232840	−	1.19601i
$973$	−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	−0.980851	−	0.194760i	$-0.937607\pi$
$977$	−9.43346	−	29.0332i	−0.301803	−	0.928855i	0.679048	−	0.734094i	$-0.262393\pi$
$978$	−34.8028	−	80.0094i	−1.11287	−	2.55842i
$979$	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	$-0.520252\pi$
$983$	−32.3674	−	23.5163i	−1.03236	−	0.750052i	−0.968779	+	0.247924i	$0.920252\pi$
$984$	46.7070	−	32.1307i	1.48897	−	1.02429i
$985$		0			0
$986$	−4.70782	−	48.8186i	−0.149928	−	1.55470i
$987$	−18.6897	−	6.07265i	−0.594900	−	0.193295i
$988$	5.58625	−	5.99400i	0.177722	−	0.190694i
$989$	−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	$-0.177132\pi$
$992$	−8.07663	−	1.20109i	−0.256433	−	0.0381347i
$993$	−22.7314			−0.721358
$994$	−2.43519	+	2.15510i	−0.0772395	+	0.0683557i
$995$		0			0
$996$	−58.4118	+	11.3716i	−1.85085	+	0.360324i
$997$	0.704471	+	0.969621i	0.0223108	+	0.0307082i	0.820027	−	0.572325i	$-0.193959\pi$
$997$	0.704471	+	0.969621i	0.0223108	+	0.0307082i	−0.797716	+	0.603033i	$0.793959\pi$
$998$	1.43825	+	14.9141i	0.0455269	+	0.472099i
$999$	−85.3292			−2.69970

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.10	✓	112	25.3	odd	20
200.2.o.a.29.16	yes	112	200.53	odd	20
200.2.o.a.69.10	yes	112	40.37	odd	4
200.2.o.a.69.16	yes	112	5.2	odd	4
800.2.be.a.369.2		112	20.7	even	4
800.2.be.a.369.27		112	40.27	even	4
800.2.be.a.529.2		112	200.3	even	20
800.2.be.a.529.27		112	100.3	even	20
1000.2.o.a.149.13		112	200.197	odd	20
1000.2.o.a.149.19		112	25.22	odd	20
1000.2.o.a.349.13		112	5.3	odd	4
1000.2.o.a.349.19		112	40.13	odd	4
1000.2.t.b.101.2		224	200.29	even	10	inner
1000.2.t.b.101.10		224	25.21	even	5	inner
1000.2.t.b.101.47		224	25.4	even	10	inner
1000.2.t.b.101.55		224	200.21	even	10	inner
1000.2.t.b.901.2		224	5.4	even	2	inner
1000.2.t.b.901.10		224	8.5	even	2	inner
1000.2.t.b.901.47		224	40.29	even	2	inner
1000.2.t.b.901.55		224	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.40768 - 0.135750i) q^{2} +(1.84742 + 2.54275i) q^{3} +(1.96314 - 0.382186i) q^{4} +(2.94576 + 3.32861i) q^{6} +1.17589 q^{7} +(2.71160 - 0.804493i) q^{8} +(-2.12559 + 6.54190i) q^{9} +O(q^{10})\)	\(q+(1.40768 - 0.135750i) q^{2} +(1.84742 + 2.54275i) q^{3} +(1.96314 - 0.382186i) q^{4} +(2.94576 + 3.32861i) q^{6} +1.17589 q^{7} +(2.71160 - 0.804493i) q^{8} +(-2.12559 + 6.54190i) q^{9} +(-3.77756 + 1.22741i) q^{11} +(4.59855 + 4.28574i) q^{12} +(0.864656 + 0.280944i) q^{13} +(1.65528 - 0.159626i) q^{14} +(3.70787 - 1.50057i) 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} +(-5.15099 + 2.24060i) 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} +(2.30843 - 0.449407i) 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} +(-6.79015 - 3.99838i) q^{34} +(-1.67262 + 13.6551i) q^{36} +(6.65712 + 2.16303i) q^{37} +(3.23357 - 5.49133i) q^{38} +(0.883011 + 2.71763i) q^{39} +(1.97065 - 6.06503i) q^{41} +(3.46388 + 3.91406i) q^{42} -2.96089i q^{43} +(-6.94681 + 3.85330i) q^{44} +(-1.23056 - 2.82899i) q^{46} +(-4.30172 + 3.12538i) q^{47} +(10.6656 + 6.65601i) q^{48} -5.61729 q^{49} -17.5127i q^{51} +(1.80482 + 0.221074i) q^{52} +(-7.68016 - 10.5708i) q^{53} +(-15.8089 + 6.87664i) q^{54} +(3.18854 - 0.945992i) q^{56} +14.1629 q^{57} +(5.83343 + 6.59157i) q^{58} +(-1.22277 - 0.397301i) q^{59} +(14.7321 - 4.78675i) q^{61} +(-1.75905 - 1.03582i) q^{62} +(-2.49945 + 7.69253i) q^{63} +(6.70558 - 4.36293i) q^{64} +(-15.2133 - 8.95838i) 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} +(-0.500848 + 19.4491i) 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} +(1.61192 + 3.70569i) 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} +(5.40738 + 5.03954i) q^{84} +(-0.401941 - 4.16800i) q^{86} +(-6.04509 + 18.6049i) q^{87} +(-9.25582 + 6.36726i) q^{88} +(-0.806910 - 2.48341i) q^{89} +(1.01674 + 0.330358i) q^{91} +(-2.11628 - 3.81527i) q^{92} -4.53682i q^{93} +(-5.63118 + 4.98350i) q^{94} +(15.9173 + 7.92171i) q^{96} +(-0.235869 + 0.171369i) q^{97} +(-7.90737 + 0.762547i) 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

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Groups

Database

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