LMFDB - Embedded newform 1000.2.o.a.349.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1000.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.9
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.806832 - 1.16147i) q^{2} +(1.06117 - 0.770982i) q^{3} +(-0.698045 + 1.87423i) q^{4} +(-1.75166 - 0.610464i) q^{6} +2.31589i q^{7} +(2.74007 - 0.701425i) q^{8} +(-0.395392 + 1.21689i) q^{9} +O(q^{10})$	\(q+(-0.806832 - 1.16147i) q^{2} +(1.06117 - 0.770982i) q^{3} +(-0.698045 + 1.87423i) q^{4} +(-1.75166 - 0.610464i) q^{6} +2.31589i q^{7} +(2.74007 - 0.701425i) q^{8} +(-0.395392 + 1.21689i) q^{9} +(0.219837 - 0.0714294i) q^{11} +(0.704254 + 2.52705i) q^{12} +(0.659008 - 2.02822i) q^{13} +(2.68985 - 1.86853i) q^{14} +(-3.02547 - 2.61659i) q^{16} +(-1.33923 + 1.84329i) q^{17} +(1.73240 - 0.522589i) q^{18} +(0.307368 - 0.423055i) q^{19} +(1.78551 + 2.45754i) q^{21} +(-0.260335 - 0.197704i) q^{22} +(-6.59576 + 2.14309i) q^{23} +(2.36689 - 2.85688i) q^{24} +(-2.88743 + 0.871009i) q^{26} +(1.73461 + 5.33859i) q^{27} +(-4.34051 - 1.61660i) q^{28} +(5.13469 + 7.06729i) q^{29} +(6.95750 + 5.05492i) q^{31} +(-0.598065 + 5.62515i) q^{32} +(0.178213 - 0.245289i) q^{33} +(3.22146 + 0.0682549i) q^{34} +(-2.00473 - 1.59050i) q^{36} +(-2.46601 + 7.58959i) q^{37} +(-0.739362 - 0.0156653i) q^{38} +(-0.864403 - 2.66036i) q^{39} +(1.84490 - 5.67801i) q^{41} +(1.41377 - 4.05665i) q^{42} +9.74670 q^{43} +(-0.0195813 + 0.461886i) q^{44} +(7.81081 + 5.93169i) q^{46} +(0.657286 + 0.904676i) q^{47} +(-5.22787 - 0.444060i) q^{48} +1.63664 q^{49} +2.98855i q^{51} +(3.34133 + 2.65092i) q^{52} +(-3.51671 + 2.55504i) q^{53} +(4.80109 - 6.32205i) q^{54} +(1.62442 + 6.34571i) q^{56} -0.685906i q^{57} +(4.06565 - 11.6659i) q^{58} +(-4.66275 - 1.51502i) q^{59} +(2.16726 - 0.704186i) q^{61} +(0.257629 - 12.1594i) q^{62} +(-2.81819 - 0.915685i) q^{63} +(7.01601 - 3.84391i) q^{64} +(-0.428684 - 0.00908277i) q^{66} +(2.55761 + 1.85821i) q^{67} +(-2.51990 - 3.79672i) q^{68} +(-5.34690 + 7.35938i) q^{69} +(-5.30236 + 3.85239i) q^{71} +(-0.229845 + 3.61171i) q^{72} +(5.24971 - 1.70573i) q^{73} +(10.8048 - 3.25932i) q^{74} +(0.578346 + 0.871389i) q^{76} +(0.165423 + 0.509119i) q^{77} +(-2.39251 + 3.15044i) q^{78} +(-10.1775 + 7.39438i) q^{79} +(2.85122 + 2.07153i) q^{81} +(-8.08339 + 2.43840i) q^{82} +(4.44876 + 3.23222i) q^{83} +(-5.85237 + 1.63098i) q^{84} +(-7.86395 - 11.3205i) q^{86} +(10.8975 + 3.54081i) q^{87} +(0.552267 - 0.349921i) q^{88} +(-4.88895 - 15.0466i) q^{89} +(4.69713 + 1.52619i) q^{91} +(0.587495 - 13.8579i) q^{92} +11.2803 q^{93} +(0.520439 - 1.49334i) q^{94} +(3.70224 + 6.43031i) q^{96} +(-7.50193 - 10.3255i) q^{97} +(-1.32050 - 1.90092i) q^{98} +0.295760i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.806832	−	1.16147i	−0.570516	−	0.821286i
$2$	−0.806832	−	1.16147i	−0.570516	−	0.821286i
$3$	1.06117	−	0.770982i	0.612664	−	0.445127i	−0.237687	−	0.971342i	$-0.576389\pi$
$3$	1.06117	−	0.770982i	0.612664	−	0.445127i	0.850351	+	0.526215i	$0.176389\pi$
$4$	−0.698045	+	1.87423i	−0.349023	+	0.937114i
$5$		0			0
$5$		0			0
$6$	−1.75166	−	0.610464i	−0.715111	−	0.249221i
$7$			2.31589i			0.875325i	0.899139	+	0.437662i	$0.144194\pi$
$7$			2.31589i			0.875325i	−0.899139	+	0.437662i	$0.855806\pi$
$8$	2.74007	−	0.701425i	0.968762	−	0.247991i
$9$	−0.395392	+	1.21689i	−0.131797	+	0.405630i
$10$		0			0
$11$	0.219837	−	0.0714294i	0.0662834	−	0.0215368i	−0.275688	−	0.961247i	$-0.588906\pi$
$11$	0.219837	−	0.0714294i	0.0662834	−	0.0215368i	0.341971	+	0.939711i	$0.388906\pi$
$12$	0.704254	+	2.52705i	0.203301	+	0.729496i
$13$	0.659008	−	2.02822i	0.182776	−	0.562526i	−0.817127	−	0.576458i	$-0.804435\pi$
$13$	0.659008	−	2.02822i	0.182776	−	0.562526i	0.999903	+	0.0139312i	$0.00443460\pi$
$14$	2.68985	−	1.86853i	0.718892	−	0.499387i
$15$		0			0
$16$	−3.02547	−	2.61659i	−0.756366	−	0.654148i
$17$	−1.33923	+	1.84329i	−0.324810	+	0.447063i	−0.939928	−	0.341372i	$-0.889108\pi$
$17$	−1.33923	+	1.84329i	−0.324810	+	0.447063i	0.615118	+	0.788435i	$0.289108\pi$
$18$	1.73240	−	0.522589i	0.408331	−	0.123175i
$19$	0.307368	−	0.423055i	0.0705150	−	0.0970555i	−0.772303	−	0.635255i	$-0.780895\pi$
$19$	0.307368	−	0.423055i	0.0705150	−	0.0970555i	0.842818	+	0.538199i	$0.180895\pi$
$20$		0			0
$21$	1.78551	+	2.45754i	0.389630	+	0.536280i
$22$	−0.260335	−	0.197704i	−0.0555036	−	0.0421505i
$23$	−6.59576	+	2.14309i	−1.37531	+	0.446865i	−0.901125	−	0.433560i	$-0.857257\pi$
$23$	−6.59576	+	2.14309i	−1.37531	+	0.446865i	−0.474185	+	0.880425i	$0.657257\pi$
$24$	2.36689	−	2.85688i	0.483139	−	0.583157i
$25$		0			0
$26$	−2.88743	+	0.871009i	−0.566272	+	0.170819i
$27$	1.73461	+	5.33859i	0.333826	+	1.02741i
$28$	−4.34051	−	1.61660i	−0.820279	−	0.305508i
$29$	5.13469	+	7.06729i	0.953487	+	1.31236i	0.949961	+	0.312369i	$0.101123\pi$
$29$	5.13469	+	7.06729i	0.953487	+	1.31236i	0.00352661	+	0.999994i	$0.498877\pi$
$30$		0			0
$31$	6.95750	+	5.05492i	1.24960	+	0.907890i	0.998199	−	0.0599915i	$-0.0191074\pi$
$31$	6.95750	+	5.05492i	1.24960	+	0.907890i	0.251405	+	0.967882i	$0.419107\pi$
$32$	−0.598065	+	5.62515i	−0.105724	+	0.994396i
$33$	0.178213	−	0.245289i	0.0310228	−	0.0426993i
$34$	3.22146	+	0.0682549i	0.552476	+	0.0117056i
$35$		0			0
$36$	−2.00473	−	1.59050i	−0.334122	−	0.265083i
$37$	−2.46601	+	7.58959i	−0.405409	+	1.24772i	0.515144	+	0.857104i	$0.327738\pi$
$37$	−2.46601	+	7.58959i	−0.405409	+	1.24772i	−0.920553	+	0.390617i	$0.872262\pi$
$38$	−0.739362	−	0.0156653i	−0.119940	−	0.00254124i
$39$	−0.864403	−	2.66036i	−0.138415	−	0.425998i
$40$		0			0
$41$	1.84490	−	5.67801i	0.288125	−	0.886756i	−0.697320	−	0.716760i	$-0.745624\pi$
$41$	1.84490	−	5.67801i	0.288125	−	0.886756i	0.985445	−	0.169996i	$-0.0543756\pi$
$42$	1.41377	−	4.05665i	0.218149	−	0.625955i
$43$	9.74670			1.48636			0.743179	−	0.669093i	$-0.233317\pi$
$43$	9.74670			1.48636			0.743179	+	0.669093i	$0.233317\pi$
$44$	−0.0195813	+	0.461886i	−0.00295198	+	0.0696319i
$45$		0			0
$46$	7.81081	+	5.93169i	1.15164	+	0.874580i
$47$	0.657286	+	0.904676i	0.0958750	+	0.131961i	0.854259	−	0.519847i	$-0.174011\pi$
$47$	0.657286	+	0.904676i	0.0958750	+	0.131961i	−0.758384	+	0.651807i	$0.774011\pi$
$48$	−5.22787	−	0.444060i	−0.754577	−	0.0640945i
$49$	1.63664			0.233806
$50$		0			0
$51$			2.98855i			0.418481i
$52$	3.34133	+	2.65092i	0.463359	+	0.367616i
$53$	−3.51671	+	2.55504i	−0.483057	+	0.350962i	−0.802508	−	0.596641i	$-0.796502\pi$
$53$	−3.51671	+	2.55504i	−0.483057	+	0.350962i	0.319451	+	0.947603i	$0.396502\pi$
$54$	4.80109	−	6.32205i	0.653346	−	0.860322i
$55$		0			0
$56$	1.62442	+	6.34571i	0.217073	+	0.847982i
$57$		−	0.685906i		−	0.0908505i
$58$	4.06565	−	11.6659i	0.533846	−	1.53181i
$59$	−4.66275	−	1.51502i	−0.607038	−	0.197239i	−0.0106611	−	0.999943i	$-0.503394\pi$
$59$	−4.66275	−	1.51502i	−0.607038	−	0.197239i	−0.596377	+	0.802705i	$0.703394\pi$
$60$		0			0
$61$	2.16726	−	0.704186i	0.277490	−	0.0901618i	−0.166966	−	0.985963i	$-0.553397\pi$
$61$	2.16726	−	0.704186i	0.277490	−	0.0901618i	0.444456	+	0.895801i	$0.353397\pi$
$62$	0.257629	−	12.1594i	0.0327189	−	1.54425i
$63$	−2.81819	−	0.915685i	−0.355058	−	0.115365i
$64$	7.01601	−	3.84391i	0.877001	−	0.480489i
$65$		0			0
$66$	−0.428684	−	0.00908277i	−0.0527674	−	0.00111801i
$67$	2.55761	+	1.85821i	0.312462	+	0.227017i	0.732952	−	0.680280i	$-0.238142\pi$
$67$	2.55761	+	1.85821i	0.312462	+	0.227017i	−0.420490	+	0.907297i	$0.638142\pi$
$68$	−2.51990	−	3.79672i	−0.305583	−	0.460419i
$69$	−5.34690	+	7.35938i	−0.643692	+	0.885966i
$70$		0			0
$71$	−5.30236	+	3.85239i	−0.629274	+	0.457194i	−0.856149	−	0.516730i	$-0.827149\pi$
$71$	−5.30236	+	3.85239i	−0.629274	+	0.457194i	0.226875	+	0.973924i	$0.427149\pi$
$72$	−0.229845	+	3.61171i	−0.0270875	+	0.425644i
$73$	5.24971	−	1.70573i	0.614432	−	0.199641i	0.0147656	−	0.999891i	$-0.495300\pi$
$73$	5.24971	−	1.70573i	0.614432	−	0.199641i	0.599667	+	0.800250i	$0.295300\pi$
$74$	10.8048	−	3.25932i	1.25603	−	0.378888i
$75$		0			0
$76$	0.578346	+	0.871389i	0.0663408	+	0.0999552i
$77$	0.165423	+	0.509119i	0.0188517	+	0.0580195i
$78$	−2.39251	+	3.15044i	−0.270898	+	0.356717i
$79$	−10.1775	+	7.39438i	−1.14506	+	0.831933i	−0.987816	−	0.155628i	$-0.950260\pi$
$79$	−10.1775	+	7.39438i	−1.14506	+	0.831933i	−0.157241	+	0.987560i	$0.550260\pi$
$80$		0			0
$81$	2.85122	+	2.07153i	0.316802	+	0.230170i
$82$	−8.08339	+	2.43840i	−0.892661	+	0.269276i
$83$	4.44876	+	3.23222i	0.488315	+	0.354782i	0.804536	−	0.593904i	$-0.202414\pi$
$83$	4.44876	+	3.23222i	0.488315	+	0.354782i	−0.316221	+	0.948686i	$0.602414\pi$
$84$	−5.85237	+	1.63098i	−0.638546	+	0.177954i
$85$		0			0
$86$	−7.86395	−	11.3205i	−0.847991	−	1.22073i
$87$	10.8975	+	3.54081i	1.16834	+	0.379615i
$88$	0.552267	−	0.349921i	0.0588719	−	0.0373017i
$89$	−4.88895	−	15.0466i	−0.518227	−	1.59494i	−0.777332	−	0.629091i	$-0.783427\pi$
$89$	−4.88895	−	15.0466i	−0.518227	−	1.59494i	0.259105	−	0.965849i	$-0.416573\pi$
$90$		0			0
$91$	4.69713	+	1.52619i	0.492393	+	0.159988i
$92$	0.587495	−	13.8579i	0.0612506	−	1.44479i
$93$	11.2803			1.16971
$94$	0.520439	−	1.49334i	0.0536792	−	0.154026i
$95$		0			0
$96$	3.70224	+	6.43031i	0.377859	+	0.656291i
$97$	−7.50193	−	10.3255i	−0.761706	−	1.04840i	−0.997070	−	0.0764911i	$-0.975628\pi$
$97$	−7.50193	−	10.3255i	−0.761706	−	1.04840i	0.235364	−	0.971907i	$-0.424372\pi$
$98$	−1.32050	−	1.90092i	−0.133390	−	0.192022i
$99$			0.295760i			0.0297250i
$100$		0			0
$101$		−	11.5894i		−	1.15318i	−0.817032	−	0.576592i	$-0.804382\pi$
$101$		−	11.5894i		−	1.15318i	0.817032	−	0.576592i	$-0.195618\pi$
$102$	3.47113	−	2.41126i	0.343693	−	0.238750i
$103$	3.94133	+	5.42478i	0.388351	+	0.534519i	0.957773	−	0.287526i	$-0.0928329\pi$
$103$	3.94133	+	5.42478i	0.388351	+	0.534519i	−0.569422	+	0.822045i	$0.692833\pi$
$104$	0.383088	−	6.01971i	0.0375648	−	0.590281i
$105$		0			0
$106$	5.80501	+	2.02308i	0.563832	+	0.196499i
$107$	−7.65011			−0.739564			−0.369782	−	0.929119i	$-0.620568\pi$
$107$	−7.65011			−0.739564			−0.369782	+	0.929119i	$0.620568\pi$
$108$	−11.2166	−	0.475517i	−1.07931	−	0.0457566i
$109$	6.41848	+	2.08549i	0.614779	+	0.199754i	0.599821	−	0.800134i	$-0.295239\pi$
$109$	6.41848	+	2.08549i	0.614779	+	0.199754i	0.0149580	+	0.999888i	$0.495239\pi$
$110$		0			0
$111$	3.23459	+	9.95506i	0.307014	+	0.944892i
$112$	6.05975	−	7.00665i	0.572592	−	0.662066i
$113$	14.4512	+	4.69549i	1.35946	+	0.441714i	0.895862	−	0.444333i	$-0.146559\pi$
$113$	14.4512	+	4.69549i	1.35946	+	0.441714i	0.463595	+	0.886047i	$0.346559\pi$
$114$	−0.796663	+	0.553411i	−0.0746143	+	0.0518317i
$115$		0			0
$116$	−16.8300	+	4.69029i	−1.56262	+	0.435482i
$117$	2.20755	+	1.60388i	0.204088	+	0.148279i
$118$	2.00240	+	6.63803i	0.184336	+	0.611080i
$119$	−4.26886	−	3.10151i	−0.391325	−	0.284315i
$120$		0			0
$121$	−8.85596	+	6.43423i	−0.805087	+	0.584930i
$122$	−2.56651	−	1.94906i	−0.232361	−	0.176460i
$123$	−2.41990	−	7.44769i	−0.218195	−	0.671536i
$124$	−14.3307	+	9.51138i	−1.28694	+	0.854147i
$125$		0			0
$126$	1.21026	+	4.01206i	0.107818	+	0.357422i
$127$	4.34009	−	1.41018i	0.385121	−	0.125133i	−0.110056	−	0.993925i	$-0.535103\pi$
$127$	4.34009	−	1.41018i	0.385121	−	0.125133i	0.495177	+	0.868792i	$0.335103\pi$
$128$	−10.1253	−	5.04752i	−0.894962	−	0.446142i
$129$	10.3429	−	7.51453i	0.910638	−	0.661618i
$130$		0			0
$131$	9.12255	−	12.5561i	0.797041	−	1.09703i	−0.196154	−	0.980573i	$-0.562845\pi$
$131$	9.12255	−	12.5561i	0.797041	−	1.09703i	0.993195	−	0.116460i	$-0.0371547\pi$
$132$	0.335327	+	0.505234i	0.0291864	+	0.0439750i
$133$	0.979750	+	0.711830i	0.0849551	+	0.0617235i
$134$	0.0947055	−	4.46986i	0.00818131	−	0.386138i
$135$		0			0
$136$	−2.37665	+	5.99011i	−0.203796	+	0.513648i
$137$	−13.9802	−	4.54244i	−1.19441	−	0.388087i	−0.356708	−	0.934216i	$-0.616101\pi$
$137$	−13.9802	−	4.54244i	−1.19441	−	0.388087i	−0.837701	+	0.546129i	$0.816101\pi$
$138$	12.8618	+	0.272510i	1.09487	+	0.0231976i
$139$	−5.61357	+	1.82396i	−0.476137	+	0.154706i	−0.537247	−	0.843425i	$-0.680536\pi$
$139$	−5.61357	+	1.82396i	−0.476137	+	0.154706i	0.0611104	+	0.998131i	$0.480536\pi$
$140$		0			0
$141$	1.39498	+	0.453256i	0.117478	+	0.0381710i
$142$	8.75256	+	3.05032i	0.734498	+	0.255977i
$143$		−	0.492950i		−	0.0412225i
$144$	4.38035	−	2.64708i	0.365029	−	0.220590i
$145$		0			0
$146$	−6.21680	−	4.72117i	−0.514506	−	0.390726i
$147$	1.73675	−	1.26182i	0.143245	−	0.104073i
$148$	−12.5032	−	9.91974i	−1.02776	−	0.815398i
$149$		−	9.14052i		−	0.748820i	−0.927263	−	0.374410i	$-0.877845\pi$
$149$		−	9.14052i		−	0.748820i	0.927263	−	0.374410i	$-0.122155\pi$
$150$		0			0
$151$	8.59512			0.699461			0.349730	−	0.936850i	$-0.386273\pi$
$151$	8.59512			0.699461			0.349730	+	0.936850i	$0.386273\pi$
$152$	0.545468	−	1.37480i	0.0442433	−	0.111511i
$153$	−1.71356	−	2.35851i	−0.138533	−	0.190675i
$154$	0.457860	−	0.602907i	0.0368954	−	0.0485837i
$155$		0			0
$156$	5.58951	+	0.236963i	0.447519	+	0.0189722i
$157$	4.64663			0.370842			0.185421	−	0.982659i	$-0.440635\pi$
$157$	4.64663			0.370842			0.185421	+	0.982659i	$0.440635\pi$
$158$	16.7999	+	5.85487i	1.33653	+	0.465789i
$159$	−1.76192	+	5.42264i	−0.139730	+	0.430043i
$160$		0			0
$161$	−4.96317	−	15.2751i	−0.391152	−	1.20384i
$162$	0.105577	−	4.98299i	0.00829495	−	0.391501i
$163$	4.05889	−	12.4920i	0.317917	−	0.978448i	−0.656620	−	0.754221i	$-0.728015\pi$
$163$	4.05889	−	12.4920i	0.317917	−	0.978448i	0.974537	−	0.224226i	$-0.0719855\pi$
$164$	9.35407	+	7.42127i	0.730430	+	0.579504i
$165$		0			0
$166$	0.164733	−	7.77498i	0.0127857	−	0.603455i
$167$	−12.2739	+	16.8935i	−0.949780	+	1.30726i	0.00184537	+	0.999998i	$0.499413\pi$
$167$	−12.2739	+	16.8935i	−0.949780	+	1.30726i	−0.951625	+	0.307261i	$0.900587\pi$
$168$	6.61621	+	5.48145i	0.510452	+	0.422903i
$169$	6.83785	+	4.96799i	0.525988	+	0.382153i
$170$		0			0
$171$	0.393281	+	0.541305i	0.0300750	+	0.0413947i
$172$	−6.80364	+	18.2675i	−0.518773	+	1.39289i
$173$	2.43455	+	7.49277i	0.185095	+	0.569664i	0.999950	−	0.0100007i	$-0.00318338\pi$
$173$	2.43455	+	7.49277i	0.185095	+	0.569664i	−0.814855	+	0.579665i	$0.803183\pi$
$174$	−4.67989	−	15.5140i	−0.354781	−	1.17611i
$175$		0			0
$176$	−0.852011	−	0.359117i	−0.0642227	−	0.0270695i
$177$	−6.11600	+	1.98721i	−0.459706	+	0.149368i
$178$	−13.5317	+	17.8185i	−1.01425	+	1.33555i
$179$	9.43646	+	12.9882i	0.705314	+	0.970782i	0.999885	+	0.0151522i	$0.00482327\pi$
$179$	9.43646	+	12.9882i	0.705314	+	0.970782i	−0.294571	+	0.955630i	$0.595177\pi$
$180$		0			0
$181$	10.0809	−	13.8751i	0.749305	−	1.03133i	−0.248723	−	0.968575i	$-0.580011\pi$
$181$	10.0809	−	13.8751i	0.749305	−	1.03133i	0.998029	−	0.0627560i	$-0.0199890\pi$
$182$	−2.01716	−	6.68698i	−0.149522	−	0.495672i
$183$	1.75691	−	2.41818i	0.129874	−	0.178757i
$184$	−16.5696	+	10.4987i	−1.22153	+	0.773971i
$185$		0			0
$186$	−9.10131	−	13.1018i	−0.667341	−	0.960670i
$187$	−0.162747	+	0.500883i	−0.0119012	+	0.0366282i
$188$	−2.15438	+	0.600398i	−0.157125	+	0.0437886i
$189$	−12.3636	+	4.01717i	−0.899319	+	0.292206i
$190$		0			0
$191$	−0.923572	+	2.84246i	−0.0668273	+	0.205673i	−0.978894	−	0.204369i	$-0.934486\pi$
$191$	−0.923572	+	2.84246i	−0.0668273	+	0.205673i	0.912067	+	0.410042i	$0.134486\pi$
$192$	4.48156	−	9.48824i	0.323429	−	0.684755i
$193$			14.9349i			1.07504i	0.843252	+	0.537518i	$0.180638\pi$
$193$			14.9349i			1.07504i	−0.843252	+	0.537518i	$0.819362\pi$
$194$	−5.94004	+	17.0443i	−0.426470	+	1.22371i
$195$		0			0
$196$	−1.14245	+	3.06745i	−0.0816037	+	0.219103i
$197$	22.2749	−	16.1837i	1.58702	−	1.15304i	0.678984	−	0.734153i	$-0.262420\pi$
$197$	22.2749	−	16.1837i	1.58702	−	1.15304i	0.908039	−	0.418887i	$-0.137580\pi$
$198$	0.343518	−	0.238629i	0.0244128	−	0.0169586i
$199$	−11.3822			−0.806862			−0.403431	−	0.915010i	$-0.632182\pi$
$199$	−11.3822			−0.806862			−0.403431	+	0.915010i	$0.632182\pi$
$200$		0			0
$201$	4.14670			0.292485
$202$	−13.4607	+	9.35066i	−0.947095	+	0.657910i
$203$	−16.3671	+	11.8914i	−1.14874	+	0.834611i
$204$	−5.60123	−	2.08615i	−0.392165	−	0.146059i
$205$		0			0
$206$	3.12075	−	8.95464i	0.217433	−	0.623899i
$207$		−	8.87368i		−	0.616763i
$208$	−7.30083	+	4.41195i	−0.506221	+	0.305913i
$209$	0.0373522	−	0.114958i	0.00258371	−	0.00795183i
$210$		0			0
$211$	−15.0746	+	4.89802i	−1.03778	+	0.337194i	−0.777860	−	0.628438i	$-0.783695\pi$
$211$	−15.0746	+	4.89802i	−1.03778	+	0.337194i	−0.259916	+	0.965631i	$0.583695\pi$
$212$	−2.33391	−	8.37466i	−0.160293	−	0.575174i
$213$	−2.65656	+	8.17604i	−0.182024	+	0.560213i
$214$	6.17235	+	8.88540i	0.421933	+	0.607394i
$215$		0			0
$216$	8.49758	+	13.4114i	0.578187	+	0.912532i
$217$	−11.7066	+	16.1128i	−0.794699	+	1.09381i
$218$	−2.75639	−	9.13754i	−0.186686	−	0.618872i
$219$	4.25572	−	5.85750i	0.287575	−	0.395813i
$220$		0			0
$221$	2.85603	+	3.93099i	0.192117	+	0.264427i
$222$	8.95277	−	11.7890i	0.600871	−	0.791223i
$223$	−22.1415	+	7.19420i	−1.48270	+	0.481759i	−0.934919	−	0.354861i	$-0.884528\pi$
$223$	−22.1415	+	7.19420i	−1.48270	+	0.481759i	−0.547783	+	0.836620i	$0.684528\pi$
$224$	−13.0272	−	1.38505i	−0.870419	−	0.0925428i
$225$		0			0
$226$	−6.20602	−	20.5732i	−0.412818	−	1.36851i
$227$	1.38398	+	4.25947i	0.0918583	+	0.282711i	0.986422	−	0.164229i	$-0.0525137\pi$
$227$	1.38398	+	4.25947i	0.0918583	+	0.282711i	−0.894564	+	0.446940i	$0.852514\pi$
$228$	1.28555	+	0.478794i	0.0851373	+	0.0317089i
$229$	−2.99987	−	4.12897i	−0.198237	−	0.272850i	0.698313	−	0.715793i	$-0.253934\pi$
$229$	−2.99987	−	4.12897i	−0.198237	−	0.272850i	−0.896550	+	0.442943i	$0.853934\pi$
$230$		0			0
$231$	0.568062	+	0.412721i	0.0373757	+	0.0271551i
$232$	19.0266	+	15.7633i	1.24916	+	1.03491i
$233$	2.05646	−	2.83047i	0.134723	−	0.185430i	−0.736325	−	0.676628i	$-0.763441\pi$
$233$	2.05646	−	2.83047i	0.134723	−	0.185430i	0.871048	+	0.491197i	$0.163441\pi$
$234$	0.0817433	−	3.85808i	0.00534372	−	0.252210i
$235$		0			0
$236$	6.09430	−	7.68150i	0.396705	−	0.500023i
$237$	−5.09907	+	15.6933i	−0.331220	+	1.01939i
$238$	−0.158071	+	7.46056i	−0.0102462	+	0.483596i
$239$	6.27635	+	19.3166i	0.405983	+	1.24949i	0.920071	+	0.391751i	$0.128131\pi$
$239$	6.27635	+	19.3166i	0.405983	+	1.24949i	−0.514088	+	0.857738i	$0.671869\pi$
$240$		0			0
$241$	5.98561	−	18.4218i	0.385567	−	1.18665i	−0.550501	−	0.834835i	$-0.685563\pi$
$241$	5.98561	−	18.4218i	0.385567	−	1.18665i	0.936068	−	0.351819i	$-0.114437\pi$
$242$	14.6185	+	5.09463i	0.939711	+	0.327495i
$243$	−12.2172			−0.783736
$244$	−0.193042	+	4.55350i	−0.0123582	+	0.291508i
$245$		0			0
$246$	−6.69785	+	8.81969i	−0.427039	+	0.562323i
$247$	−0.655490	−	0.902205i	−0.0417079	−	0.0574059i
$248$	22.6097	+	8.97069i	1.43572	+	0.569639i
$249$	7.21286			0.457096
$250$		0			0
$251$			4.56980i			0.288443i	0.989545	+	0.144222i	$0.0460679\pi$
$251$			4.56980i			0.288443i	−0.989545	+	0.144222i	$0.953932\pi$
$252$	3.68343	−	4.64274i	0.232034	−	0.292465i
$253$	−1.29691	+	0.942261i	−0.0815361	+	0.0592395i
$254$	−5.13961	−	3.90312i	−0.322488	−	0.244904i
$255$		0			0
$256$	2.30688	+	15.8328i	0.144180	+	0.989551i
$257$		−	27.4389i		−	1.71159i	−0.517312	−	0.855797i	$-0.673067\pi$
$257$		−	27.4389i		−	1.71159i	0.517312	−	0.855797i	$-0.326933\pi$
$258$	−17.0729	−	5.95001i	−1.06291	−	0.370431i
$259$	−17.5767	−	5.71101i	−1.09216	−	0.354865i
$260$		0			0
$261$	−10.6303	+	3.45400i	−0.658001	+	0.213798i
$262$	−21.9440	−	0.464939i	−1.35570	−	0.0287240i
$263$	−12.2444	−	3.97845i	−0.755022	−	0.245322i	−0.0938814	−	0.995583i	$-0.529927\pi$
$263$	−12.2444	−	3.97845i	−0.755022	−	0.245322i	−0.661141	+	0.750262i	$0.729927\pi$
$264$	0.316264	−	0.797112i	0.0194647	−	0.0490589i
$265$		0			0
$266$	0.0362791	−	1.71228i	0.00222441	−	0.104987i
$267$	−16.7887	−	12.1977i	−1.02745	−	0.746486i
$268$	−5.26805	+	3.49643i	−0.321797	+	0.213578i
$269$	−0.897279	+	1.23500i	−0.0547081	+	0.0752992i	−0.835495	−	0.549499i	$-0.814819\pi$
$269$	−0.897279	+	1.23500i	−0.0547081	+	0.0752992i	0.780786	+	0.624798i	$0.214819\pi$
$270$		0			0
$271$	−19.8030	+	14.3877i	−1.20294	+	0.873990i	−0.994571	−	0.104059i	$-0.966817\pi$
$271$	−19.8030	+	14.3877i	−1.20294	+	0.873990i	−0.208373	+	0.978049i	$0.566817\pi$
$272$	8.87492	−	2.07259i	0.538121	−	0.125669i
$273$	6.16110	−	2.00186i	0.372887	−	0.121158i
$274$	6.00374	+	19.9026i	0.362699	+	1.20236i
$275$		0			0
$276$	−10.0608	−	15.1585i	−0.605588	−	0.912435i
$277$	−8.46626	−	26.0565i	−0.508689	−	1.56558i	−0.794480	−	0.607290i	$-0.792256\pi$
$277$	−8.46626	−	26.0565i	−0.508689	−	1.56558i	0.285791	−	0.958292i	$-0.407744\pi$
$278$	6.64769	+	5.04839i	0.398702	+	0.302782i
$279$	−8.90222	+	6.46784i	−0.532962	+	0.387220i
$280$		0			0
$281$	−23.5098	−	17.0809i	−1.40248	−	1.01896i	−0.994363	−	0.106031i	$-0.966186\pi$
$281$	−23.5098	−	17.0809i	−1.40248	−	1.01896i	−0.408116	−	0.912930i	$-0.633814\pi$
$282$	−0.599067	−	1.98593i	−0.0356739	−	0.118261i
$283$	−8.02169	−	5.82810i	−0.476840	−	0.346444i	0.323261	−	0.946310i	$-0.395221\pi$
$283$	−8.02169	−	5.82810i	−0.476840	−	0.346444i	−0.800101	+	0.599865i	$0.795221\pi$
$284$	−3.51897	−	12.6270i	−0.208812	−	0.749273i
$285$		0			0
$286$	−0.572549	+	0.397727i	−0.0338555	+	0.0235181i
$287$	13.1497	+	4.27258i	0.776200	+	0.252203i
$288$	−6.60872	−	2.95192i	−0.389423	−	0.173943i
$289$	3.64911	+	11.2308i	0.214653	+	0.660635i
$290$		0			0
$291$	−15.9216	−	5.17324i	−0.933340	−	0.303261i
$292$	−0.467601	+	11.0298i	−0.0273643	+	0.645473i
$293$	−6.22226			−0.363508			−0.181754	−	0.983344i	$-0.558177\pi$
$293$	−6.22226			−0.363508			−0.181754	+	0.983344i	$0.558177\pi$
$294$	−2.86684	−	0.999113i	−0.167198	−	0.0582694i
$295$		0			0
$296$	−1.43351	+	22.5258i	−0.0833213	+	1.30928i
$297$	0.762664	+	1.04972i	0.0442542	+	0.0609107i
$298$	−10.6165	+	7.37486i	−0.614996	+	0.427214i
$299$			14.7899i			0.855324i
$300$		0			0
$301$			22.5723i			1.30105i
$302$	−6.93481	−	9.98301i	−0.399054	−	0.574457i
$303$	−8.93519	−	12.2982i	−0.513313	−	0.706515i
$304$	−2.03689	+	0.475683i	−0.116824	+	0.0272823i
$305$		0			0
$306$	−1.35680	+	3.89318i	−0.0775630	+	0.222558i
$307$	29.6136			1.69014			0.845070	−	0.534656i	$-0.179559\pi$
$307$	29.6136			1.69014			0.845070	+	0.534656i	$0.179559\pi$
$308$	−1.06968	−	0.0453481i	−0.0609505	−	0.00258395i
$309$	8.36481	+	2.71789i	0.475857	+	0.154615i
$310$		0			0
$311$	−1.32670	−	4.08315i	−0.0752301	−	0.231534i	0.906369	−	0.422486i	$-0.138843\pi$
$311$	−1.32670	−	4.08315i	−0.0752301	−	0.231534i	−0.981599	+	0.190952i	$0.938843\pi$
$312$	−4.23457	−	6.68326i	−0.239735	−	0.378365i
$313$	13.0617	+	4.24400i	0.738290	+	0.239885i	0.653935	−	0.756551i	$-0.273117\pi$
$313$	13.0617	+	4.24400i	0.738290	+	0.239885i	0.0843552	+	0.996436i	$0.473117\pi$
$314$	−3.74905	−	5.39695i	−0.211571	−	0.304567i
$315$		0			0
$316$	−6.75441	−	24.2366i	−0.379965	−	1.36341i
$317$	−10.3334	−	7.50769i	−0.580384	−	0.421674i	0.258478	−	0.966017i	$-0.416779\pi$
$317$	−10.3334	−	7.50769i	−0.580384	−	0.421674i	−0.838863	+	0.544343i	$0.816779\pi$
$318$	7.71983	−	2.32873i	0.432907	−	0.130589i
$319$	1.63361	+	1.18688i	0.0914644	+	0.0664528i
$320$		0			0
$321$	−8.11803	+	5.89809i	−0.453104	+	0.329200i
$322$	−13.7371	+	18.0890i	−0.765541	+	1.00806i
$323$	0.368178	+	1.13313i	0.0204859	+	0.0630493i
$324$	−5.87280	+	3.89781i	−0.326267	+	0.216545i
$325$		0			0
$326$	−17.7840	+	5.36463i	−0.984963	+	0.297119i
$327$	8.41894	−	2.73548i	0.465569	−	0.151272i
$328$	1.07246	−	16.8522i	0.0592165	−	0.930508i
$329$	−2.09513	+	1.52220i	−0.115508	+	0.0839217i
$330$		0			0
$331$	−2.79298	+	3.84421i	−0.153516	+	0.211297i	−0.878847	−	0.477103i	$-0.841687\pi$
$331$	−2.79298	+	3.84421i	−0.153516	+	0.211297i	0.725331	+	0.688400i	$0.241687\pi$
$332$	−9.16335	+	6.08177i	−0.502904	+	0.333780i
$333$	−8.26066	−	6.00172i	−0.452682	−	0.328892i
$334$	29.5243	+	0.625548i	1.61550	+	0.0342285i
$335$		0			0
$336$	1.02839	−	12.1072i	0.0561035	−	0.660500i
$337$	28.1678	+	9.15228i	1.53440	+	0.498556i	0.949824	−	0.312784i	$-0.101261\pi$
$337$	28.1678	+	9.15228i	1.53440	+	0.498556i	0.584574	+	0.811340i	$0.301261\pi$
$338$	0.253198	−	11.9503i	0.0137722	−	0.650011i
$339$	18.9553	−	6.15894i	1.02951	−	0.334508i
$340$		0			0
$341$	1.89059	+	0.614289i	0.102381	+	0.0332656i
$342$	0.311400	−	0.893529i	0.0168386	−	0.0483165i
$343$			20.0015i			1.07998i
$344$	26.7067	−	6.83658i	1.43993	−	0.368604i
$345$		0			0
$346$	6.73839	−	8.87306i	0.362258	−	0.477019i
$347$	−15.6090	+	11.3406i	−0.837937	+	0.608797i	−0.921794	−	0.387681i	$-0.873276\pi$
$347$	−15.6090	+	11.3406i	−0.837937	+	0.608797i	0.0838564	+	0.996478i	$0.473276\pi$
$348$	−14.2432	+	17.9528i	−0.763518	+	0.962369i
$349$		−	33.1221i		−	1.77299i	−0.462742	−	0.886493i	$-0.653134\pi$
$349$		−	33.1221i		−	1.77299i	0.462742	−	0.886493i	$-0.346866\pi$
$350$		0			0
$351$	11.9709			0.638961
$352$	0.270324	+	1.27934i	0.0144083	+	0.0681888i
$353$	−7.81083	−	10.7507i	−0.415729	−	0.572202i	0.548875	−	0.835904i	$-0.315056\pi$
$353$	−7.81083	−	10.7507i	−0.415729	−	0.572202i	−0.964604	+	0.263703i	$0.915056\pi$
$354$	7.24267	+	5.50023i	0.384944	+	0.292334i
$355$		0			0
$356$	31.6135	+	1.34023i	1.67551	+	0.0710320i
$357$	−6.92117			−0.366307
$358$	7.47180	−	21.4395i	0.394897	−	1.13311i
$359$	5.23366	−	16.1076i	0.276222	−	0.850124i	−0.712671	−	0.701498i	$-0.752515\pi$
$359$	5.23366	−	16.1076i	0.276222	−	0.850124i	0.988893	−	0.148626i	$-0.0474851\pi$
$360$		0			0
$361$	5.78682	+	17.8100i	0.304570	+	0.937369i
$362$	−24.2492	−	0.513781i	−1.27451	−	0.0270037i
$363$	−4.43696	+	13.6556i	−0.232880	+	0.716732i
$364$	−6.13924	+	7.73815i	−0.321784	+	0.405589i
$365$		0			0
$366$	−4.22618	−	0.0895425i	−0.220906	−	0.00468046i
$367$	5.13516	−	7.06794i	0.268053	−	0.368944i	−0.653678	−	0.756773i	$-0.726775\pi$
$367$	5.13516	−	7.06794i	0.268053	−	0.368944i	0.921731	+	0.387829i	$0.126775\pi$
$368$	25.5628	+	10.7746i	1.33255	+	0.561663i
$369$	6.18006	+	4.49008i	0.321721	+	0.233744i
$370$		0			0
$371$	−5.91720	−	8.14432i	−0.307206	−	0.422832i
$372$	−7.87417	+	21.1419i	−0.408257	+	1.09616i
$373$	0.310042	+	0.954212i	0.0160534	+	0.0494072i	0.958762	−	0.284209i	$-0.0917310\pi$
$373$	0.310042	+	0.954212i	0.0160534	+	0.0494072i	−0.942709	+	0.333616i	$0.891731\pi$
$374$	0.713072	−	0.215102i	0.0368721	−	0.0111227i
$375$		0			0
$376$	2.43557	+	2.01784i	0.125605	+	0.104062i
$377$	17.7178	−	5.75686i	0.912513	−	0.296494i
$378$	14.6412	+	11.1188i	0.753061	+	0.571890i
$379$	−21.2264	−	29.2157i	−1.09033	−	1.50071i	−0.847616	−	0.530610i	$-0.821963\pi$
$379$	−21.2264	−	29.2157i	−1.09033	−	1.50071i	−0.242712	−	0.970098i	$-0.578037\pi$
$380$		0			0
$381$	3.51833	−	4.84257i	0.180250	−	0.248092i
$382$	4.04661	−	1.22068i	0.207043	−	0.0624556i
$383$	18.1528	−	24.9852i	0.927565	−	1.27668i	−0.0332373	−	0.999447i	$-0.510582\pi$
$383$	18.1528	−	24.9852i	0.927565	−	1.27668i	0.960802	−	0.277236i	$-0.0894183\pi$
$384$	−14.6362	+	2.45020i	−0.746901	+	0.125036i
$385$		0			0
$386$	17.3465	−	12.0499i	0.882913	−	0.613326i
$387$	−3.85377	+	11.8607i	−0.195898	+	0.602912i
$388$	24.5891	−	6.85265i	1.24832	−	0.347891i
$389$	1.26254	−	0.410223i	0.0640132	−	0.0207991i	−0.276835	−	0.960917i	$-0.589286\pi$
$389$	1.26254	−	0.410223i	0.0640132	−	0.0207991i	0.340849	+	0.940118i	$0.389286\pi$
$390$		0			0
$391$	4.88288	−	15.0280i	0.246938	−	0.759997i
$392$	4.48453	−	1.14798i	0.226503	−	0.0579819i
$393$		−	20.3574i		−	1.02690i
$394$	−36.7690	−	12.8142i	−1.85240	−	0.645573i
$395$		0			0
$396$	−0.554322	−	0.206454i	−0.0278557	−	0.0103747i
$397$	7.80606	−	5.67144i	0.391775	−	0.284641i	−0.374407	−	0.927264i	$-0.622154\pi$
$397$	7.80606	−	5.67144i	0.391775	−	0.284641i	0.766182	+	0.642623i	$0.222154\pi$
$398$	9.18351	+	13.2201i	0.460328	+	0.662665i
$399$	1.58849			0.0795237
$400$		0			0
$401$	11.7737			0.587953			0.293976	−	0.955813i	$-0.405021\pi$
$401$	11.7737			0.587953			0.293976	+	0.955813i	$0.405021\pi$
$402$	−3.34569	−	4.81628i	−0.166868	−	0.240214i
$403$	14.8375	−	10.7801i	0.739110	−	0.536995i
$404$	21.7211	+	8.08990i	1.08067	+	0.402488i
$405$		0			0
$406$	27.0170	+	9.41560i	1.34083	+	0.467289i
$407$			1.84462i			0.0914343i
$408$	2.09625	+	8.18886i	0.103780	+	0.405409i
$409$	−0.0454622	+	0.139918i	−0.00224796	+	0.00691851i	−0.952174	−	0.305556i	$-0.901158\pi$
$409$	−0.0454622	+	0.139918i	−0.00224796	+	0.00691851i	0.949926	+	0.312474i	$0.101158\pi$
$410$		0			0
$411$	−18.3375	+	5.95820i	−0.904520	+	0.293896i
$412$	−12.9185	+	3.60021i	−0.636449	+	0.177370i
$413$	3.50862	−	10.7984i	0.172648	−	0.531355i
$414$	−10.3065	+	7.15956i	−0.506539	+	0.351873i
$415$		0			0
$416$	11.0149	+	4.92002i	0.540050	+	0.241224i
$417$	−4.55069	+	6.26349i	−0.222848	+	0.306724i
$418$	−0.163658	+	0.0493683i	−0.00800478	+	0.00241468i
$419$	20.0431	−	27.5869i	0.979168	−	1.34771i	0.0418913	−	0.999122i	$-0.486662\pi$
$419$	20.0431	−	27.5869i	0.979168	−	1.34771i	0.937277	−	0.348587i	$-0.113338\pi$
$420$		0			0
$421$	3.43224	+	4.72407i	0.167277	+	0.230237i	0.884423	−	0.466686i	$-0.154552\pi$
$421$	3.43224	+	4.72407i	0.167277	+	0.230237i	−0.717146	+	0.696923i	$0.754552\pi$
$422$	17.8516	+	13.5568i	0.869000	+	0.659936i
$423$	−1.36078	+	0.442143i	−0.0661633	+	0.0214977i
$424$	−7.84388	+	9.46771i	−0.380932	+	0.459793i
$425$		0			0
$426$	11.6397	−	3.51117i	0.563943	−	0.170117i
$427$	1.63082	+	5.01915i	0.0789209	+	0.242894i
$428$	5.34012	−	14.3380i	0.258125	−	0.693056i
$429$	−0.380055	−	0.523101i	−0.0183492	−	0.0252556i
$430$		0			0
$431$	−3.30954	−	2.40452i	−0.159415	−	0.115822i	0.505218	−	0.862992i	$-0.331412\pi$
$431$	−3.30954	−	2.40452i	−0.159415	−	0.115822i	−0.664633	+	0.747170i	$0.731412\pi$
$432$	8.72090	−	20.6905i	0.419585	−	0.995471i
$433$	−2.79701	+	3.84976i	−0.134416	+	0.185008i	−0.870919	−	0.491427i	$-0.836476\pi$
$433$	−2.79701	+	3.84976i	−0.134416	+	0.185008i	0.736503	+	0.676434i	$0.236476\pi$
$434$	28.1599	+	0.596640i	1.35172	+	0.0286396i
$435$		0			0
$436$	−8.38908	+	10.5739i	−0.401764	+	0.506399i
$437$	−1.12068	+	3.44909i	−0.0536092	+	0.164992i
$438$	−10.2370	−	0.216897i	−0.489142	−	0.0103637i
$439$	0.541600	+	1.66687i	0.0258492	+	0.0795556i	0.963149	−	0.268969i	$-0.0866829\pi$
$439$	0.541600	+	1.66687i	0.0258492	+	0.0795556i	−0.937300	+	0.348524i	$0.886683\pi$
$440$		0			0
$441$	−0.647116	+	1.99162i	−0.0308150	+	0.0948389i
$442$	2.26140	−	6.48885i	0.107564	−	0.308643i
$443$	−3.43488			−0.163196			−0.0815981	−	0.996665i	$-0.526002\pi$
$443$	−3.43488			−0.163196			−0.0815981	+	0.996665i	$0.526002\pi$
$444$	−20.9159	−	0.886714i	−0.992627	−	0.0420816i
$445$		0			0
$446$	26.2203	+	19.9122i	1.24157	+	0.942872i
$447$	−7.04717	−	9.69960i	−0.333320	−	0.458775i
$448$	8.90208	+	16.2483i	0.420584	+	0.767661i
$449$	5.54236			0.261560			0.130780	−	0.991411i	$-0.458252\pi$
$449$	5.54236			0.261560			0.130780	+	0.991411i	$0.458252\pi$
$450$		0			0
$451$		−	1.38002i		−	0.0649825i
$452$	−18.8880	+	23.8072i	−0.888418	+	1.11980i
$453$	9.12084	−	6.62668i	0.428534	−	0.311348i
$454$	3.83062	−	5.04413i	0.179780	−	0.236733i
$455$		0			0
$456$	−0.481112	−	1.87943i	−0.0225301	−	0.0880126i
$457$		−	3.02813i		−	0.141650i	−0.997489	−	0.0708250i	$-0.977437\pi$
$457$		−	3.02813i		−	0.141650i	0.997489	−	0.0708250i	$-0.0225632\pi$
$458$	−2.37530	+	6.81565i	−0.110990	+	0.318475i
$459$	−12.1636	−	3.95219i	−0.567748	−	0.184472i
$460$		0			0
$461$	−11.9787	+	3.89211i	−0.557903	+	0.181274i	−0.574377	−	0.818591i	$-0.694756\pi$
$461$	−11.9787	+	3.89211i	−0.557903	+	0.181274i	0.0164747	+	0.999864i	$0.494756\pi$
$462$	0.0210347	−	0.992786i	0.000978624	−	0.0461886i
$463$	4.16641	+	1.35375i	0.193629	+	0.0629140i	0.404226	−	0.914659i	$-0.367541\pi$
$463$	4.16641	+	1.35375i	0.193629	+	0.0629140i	−0.210597	+	0.977573i	$0.567541\pi$
$464$	2.95741	−	34.8172i	0.137294	−	1.61635i
$465$		0			0
$466$	−4.94674	−	0.104809i	−0.229153	−	0.00485520i
$467$	−18.3661	−	13.3438i	−0.849883	−	0.617476i	0.0752308	−	0.997166i	$-0.476031\pi$
$467$	−18.3661	−	13.3438i	−0.849883	−	0.617476i	−0.925114	+	0.379690i	$0.876031\pi$
$468$	−4.54701	+	3.01788i	−0.210186	+	0.139501i
$469$	−4.30342	+	5.92315i	−0.198714	+	0.273506i
$470$		0			0
$471$	4.93085	−	3.58247i	0.227201	−	0.165072i
$472$	−13.8389	−	0.880694i	−0.636989	−	0.0405372i
$473$	2.14269	−	0.696201i	0.0985208	−	0.0320113i
$474$	22.3415	−	6.73943i	1.02618	−	0.309552i
$475$		0			0
$476$	8.79278	−	5.83582i	0.403017	−	0.267484i
$477$	−1.71873	−	5.28970i	−0.0786951	−	0.242199i
$478$	17.3718	−	22.8751i	0.794568	−	1.04628i
$479$	5.58405	−	4.05705i	0.255142	−	0.185371i	−0.452861	−	0.891581i	$-0.649597\pi$
$479$	5.58405	−	4.05705i	0.255142	−	0.185371i	0.708002	+	0.706210i	$0.249597\pi$
$480$		0			0
$481$	13.7682	+	10.0032i	0.627777	+	0.456107i
$482$	−26.2258	+	7.91117i	−1.19455	+	0.360344i
$483$	−17.0435	−	12.3829i	−0.775508	−	0.563439i
$484$	−5.87736	−	21.0895i	−0.267153	−	0.958613i
$485$		0			0
$486$	9.85726	+	14.1900i	0.447134	+	0.643672i
$487$	34.1041	+	11.0811i	1.54540	+	0.502132i	0.952861	−	0.303407i	$-0.0981242\pi$
$487$	34.1041	+	11.0811i	1.54540	+	0.502132i	0.592543	+	0.805539i	$0.298124\pi$
$488$	5.44453	−	3.44969i	0.246462	−	0.156160i
$489$	−5.32394	−	16.3854i	−0.240757	−	0.740973i
$490$		0			0
$491$	7.36748	+	2.39384i	0.332490	+	0.108032i	0.470504	−	0.882398i	$-0.344072\pi$
$491$	7.36748	+	2.39384i	0.332490	+	0.108032i	−0.138014	+	0.990430i	$0.544072\pi$
$492$	15.6479	+	0.663378i	0.705461	+	0.0299074i
$493$	−19.9036			−0.896411
$494$	−0.519018	+	1.48926i	−0.0233517	+	0.0670051i
$495$		0			0
$496$	−7.82300	−	33.4984i	−0.351263	−	1.50412i
$497$	−8.92171	−	12.2797i	−0.400194	−	0.550819i
$498$	−5.81956	−	8.37755i	−0.260781	−	0.375407i
$499$			36.4452i			1.63151i	0.578396	+	0.815756i	$0.303679\pi$
$499$			36.4452i			1.63151i	−0.578396	+	0.815756i	$0.696321\pi$
$500$		0			0
$501$			27.3897i			1.22368i
$502$	5.30771	−	3.68706i	0.236895	−	0.164562i
$503$	7.52915	+	10.3630i	0.335708	+	0.462063i	0.943182	−	0.332277i	$-0.107817\pi$
$503$	7.52915	+	10.3630i	0.335708	+	0.462063i	−0.607473	+	0.794340i	$0.707817\pi$
$504$	−8.36433	−	0.532296i	−0.372577	−	0.0237104i
$505$		0			0
$506$	2.14080	+	0.746083i	0.0951702	+	0.0331674i
$507$	11.0863			0.492360
$508$	−0.386579	+	9.11869i	−0.0171517	+	0.404576i
$509$	40.6350	+	13.2031i	1.80111	+	0.585217i	0.999913	−	0.0131803i	$-0.00419554\pi$
$509$	40.6350	+	13.2031i	1.80111	+	0.585217i	0.801200	+	0.598397i	$0.204196\pi$
$510$		0			0
$511$	3.95030	+	12.1578i	0.174751	+	0.537828i
$512$	16.5282	−	15.4538i	0.730448	−	0.682968i
$513$	2.79168	+	0.907072i	0.123256	+	0.0400482i
$514$	−31.8696	+	22.1386i	−1.40571	+	0.976492i
$515$		0			0
$516$	6.86416	+	24.6304i	0.302178	+	1.08429i
$517$	0.209116	+	0.151932i	0.00919692	+	0.00668195i
$518$	7.54823	+	25.0227i	0.331650	+	1.09943i
$519$	8.36024	+	6.07407i	0.366974	+	0.266622i
$520$		0			0
$521$	−1.68871	+	1.22692i	−0.0739836	+	0.0537522i	−0.624162	−	0.781295i	$-0.714560\pi$
$521$	−1.68871	+	1.22692i	−0.0739836	+	0.0537522i	0.550179	+	0.835047i	$0.314560\pi$
$522$	12.5886	+	9.56006i	0.550989	+	0.418432i
$523$	10.0536	+	30.9419i	0.439615	+	1.35300i	0.888283	+	0.459297i	$0.151899\pi$
$523$	10.0536	+	30.9419i	0.439615	+	1.35300i	−0.448668	+	0.893699i	$0.648101\pi$
$524$	17.1651	+	25.8625i	0.749860	+	1.12981i
$525$		0			0
$526$	5.25831	+	17.4315i	0.229273	+	0.760049i
$527$	−18.6353	+	6.05499i	−0.811768	+	0.263760i
$528$	−1.18100	+	0.275802i	−0.0513963	+	0.0120028i
$529$	20.3038	−	14.7515i	0.882772	−	0.641372i
$530$		0			0
$531$	3.68722	−	5.07503i	0.160012	−	0.220237i
$532$	−2.01804	+	1.33939i	−0.0874932	+	0.0580697i
$533$	−10.3004	−	7.48371i	−0.446162	−	0.324155i
$534$	−0.621666	+	29.3411i	−0.0269021	+	1.26971i
$535$		0			0
$536$	8.31144	+	3.29767i	0.359000	+	0.142438i
$537$	20.0273	+	6.50726i	0.864242	+	0.280809i
$538$	2.15837	+	0.0457307i	0.0930541	+	0.00197159i
$539$	0.359795	−	0.116904i	0.0154975	−	0.00503543i
$540$		0			0
$541$	5.01695	+	1.63011i	0.215696	+	0.0700838i	0.414872	−	0.909880i	$-0.363826\pi$
$541$	5.01695	+	1.63011i	0.215696	+	0.0700838i	−0.199176	+	0.979964i	$0.563826\pi$
$542$	32.6886	+	11.3922i	1.40410	+	0.489336i
$543$		−	22.4960i		−	0.965395i
$544$	−9.56783	−	8.63576i	−0.410217	−	0.370255i
$545$		0			0
$546$	−7.29608	−	5.54079i	−0.312244	−	0.237124i
$547$	12.2753	−	8.91852i	0.524854	−	0.381329i	−0.293575	−	0.955936i	$-0.594845\pi$
$547$	12.2753	−	8.91852i	0.524854	−	0.381329i	0.818429	+	0.574607i	$0.194845\pi$
$548$	18.2724	−	23.0313i	0.780558	−	0.983847i
$549$			2.91575i			0.124441i
$550$		0			0
$551$	4.56809			0.194607
$552$	−9.48886	+	23.9157i	−0.403873	+	1.01792i
$553$	−17.1246	−	23.5700i	−0.728211	−	1.00230i
$554$	−23.4331	+	30.8565i	−0.995576	+	1.31097i
$555$		0			0
$556$	0.500010	−	11.7943i	0.0212052	−	0.500191i
$557$	−21.0806			−0.893213			−0.446606	−	0.894731i	$-0.647368\pi$
$557$	−21.0806			−0.893213			−0.446606	+	0.894731i	$0.647368\pi$
$558$	14.6948	+	5.12124i	0.622082	+	0.216800i
$559$	6.42315	−	19.7684i	0.271670	−	0.836116i
$560$		0			0
$561$	0.213470	+	0.656995i	0.00901273	+	0.0277383i
$562$	−0.870543	+	41.0875i	−0.0367217	+	1.73317i
$563$	5.40722	−	16.6417i	0.227887	−	0.701365i	−0.770099	−	0.637925i	$-0.779793\pi$
$563$	5.40722	−	16.6417i	0.227887	−	0.701365i	0.997986	−	0.0634396i	$-0.0202070\pi$
$564$	−1.82326	+	2.29811i	−0.0767732	+	0.0967680i
$565$		0			0
$566$	−0.297034	+	14.0193i	−0.0124853	+	0.589274i
$567$	−4.79744	+	6.60311i	−0.201474	+	0.277305i
$568$	−11.8267	+	14.2750i	−0.496237	+	0.598967i
$569$	−26.4646	−	19.2277i	−1.10945	−	0.806065i	−0.126876	−	0.991919i	$-0.540495\pi$
$569$	−26.4646	−	19.2277i	−1.10945	−	0.806065i	−0.982578	+	0.185853i	$0.940495\pi$
$570$		0			0
$571$	17.4500	+	24.0179i	0.730261	+	1.00512i	0.999120	+	0.0419380i	$0.0133532\pi$
$571$	17.4500	+	24.0179i	0.730261	+	1.00512i	−0.268860	+	0.963179i	$0.586647\pi$
$572$	0.923901	+	0.344101i	0.0386302	+	0.0143876i
$573$	1.21142	+	3.72838i	0.0506080	+	0.155755i
$574$	−5.64707	−	18.7202i	−0.235704	−	0.781368i
$575$		0			0
$576$	1.90355	+	10.0576i	0.0793146	+	0.419065i
$577$	7.08229	−	2.30117i	0.294839	−	0.0957992i	−0.157862	−	0.987461i	$-0.550460\pi$
$577$	7.08229	−	2.30117i	0.294839	−	0.0957992i	0.452702	+	0.891662i	$0.350460\pi$
$578$	10.1001	−	13.2997i	0.420107	−	0.553195i
$579$	11.5145	+	15.8484i	0.478527	+	0.658636i
$580$		0			0
$581$	−7.48546	+	10.3029i	−0.310549	+	0.427435i
$582$	6.83746	+	22.6664i	0.283422	+	0.939554i
$583$	−0.590598	+	0.812889i	−0.0244601	+	0.0336664i
$584$	13.1882	−	8.35612i	0.545730	−	0.345779i
$585$		0			0
$586$	5.02031	+	7.22699i	0.207387	+	0.298544i
$587$	4.32742	−	13.3184i	0.178612	−	0.549710i	−0.821168	−	0.570686i	$-0.806677\pi$
$587$	4.32742	−	13.3184i	0.178612	−	0.549710i	0.999780	+	0.0209758i	$0.00667728\pi$
$588$	1.15261	+	4.13588i	0.0475330	+	0.170561i
$589$	4.27702	−	1.38969i	0.176232	−	0.0572611i
$590$		0			0
$591$	11.1601	−	34.3471i	0.459063	−	1.41285i
$592$	27.3197	−	16.5095i	1.12283	−	0.678536i
$593$			10.4531i			0.429258i	0.976696	+	0.214629i	$0.0688542\pi$
$593$			10.4531i			0.429258i	−0.976696	+	0.214629i	$0.931146\pi$
$594$	0.603878	−	1.73276i	0.0247774	−	0.0710960i
$595$		0			0
$596$	17.1314	+	6.38050i	0.701730	+	0.261355i
$597$	−12.0784	+	8.77546i	−0.494335	+	0.359156i
$598$	17.1781	−	11.9330i	0.702466	−	0.487976i
$599$	25.1691			1.02838			0.514191	−	0.857676i	$-0.328092\pi$
$599$	25.1691			1.02838			0.514191	+	0.857676i	$0.328092\pi$
$600$		0			0
$601$	−9.80217			−0.399839			−0.199919	−	0.979812i	$-0.564068\pi$
$601$	−9.80217			−0.399839			−0.199919	+	0.979812i	$0.564068\pi$
$602$	26.2172	−	18.2121i	1.06853	−	0.742268i
$603$	−3.27250	+	2.37761i	−0.133267	+	0.0968238i
$604$	−5.99978	+	16.1092i	−0.244128	+	0.655474i
$605$		0			0
$606$	−7.07489	+	20.3006i	−0.287398	+	0.824655i
$607$		−	2.47771i		−	0.100567i	−0.998735	−	0.0502836i	$-0.983987\pi$
$607$		−	2.47771i		−	0.100567i	0.998735	−	0.0502836i	$-0.0160125\pi$
$608$	2.19592	+	1.98200i	0.0890565	+	0.0803809i
$609$	−8.20014	+	25.2374i	−0.332287	+	1.02267i
$610$		0			0
$611$	2.26804	−	0.736930i	0.0917549	−	0.0298130i
$612$	5.61654	−	1.56525i	0.227035	−	0.0632717i
$613$	0.797806	−	2.45539i	0.0322231	−	0.0991725i	−0.933651	−	0.358183i	$-0.883396\pi$
$613$	0.797806	−	2.45539i	0.0322231	−	0.0991725i	0.965875	+	0.259010i	$0.0833964\pi$
$614$	−23.8932	−	34.3955i	−0.964252	−	1.38809i
$615$		0			0
$616$	0.810379	+	1.27899i	0.0326511	+	0.0515320i
$617$	−10.4128	+	14.3320i	−0.419205	+	0.576986i	−0.965433	−	0.260650i	$-0.916063\pi$
$617$	−10.4128	+	14.3320i	−0.419205	+	0.576986i	0.546228	+	0.837636i	$0.316063\pi$
$618$	−3.59223	−	11.9084i	−0.144501	−	0.479026i
$619$	12.1197	−	16.6813i	0.487130	−	0.670477i	−0.492726	−	0.870185i	$-0.663999\pi$
$619$	12.1197	−	16.6813i	0.487130	−	0.670477i	0.979855	+	0.199708i	$0.0639993\pi$
$620$		0			0
$621$	−22.8822	−	31.4946i	−0.918229	−	1.26383i
$622$	−3.67206	+	4.83534i	−0.147236	+	0.193880i
$623$	34.8464	−	11.3223i	1.39609	−	0.453617i
$624$	−4.34585	+	10.3106i	−0.173973	+	0.412755i
$625$		0			0
$626$	−5.60929	−	18.5950i	−0.224192	−	0.743206i
$627$	−0.0489939	−	0.150788i	−0.00195663	−	0.00602188i
$628$	−3.24356	+	8.70885i	−0.129432	+	0.347521i
$629$	−10.6873	−	14.7097i	−0.426129	−	0.586516i
$630$		0			0
$631$	−26.5548	−	19.2932i	−1.05713	−	0.768050i	−0.0835747	−	0.996502i	$-0.526634\pi$
$631$	−26.5548	−	19.2932i	−1.05713	−	0.768050i	−0.973555	+	0.228452i	$0.926634\pi$
$632$	−22.7005	+	27.3999i	−0.902976	+	1.08991i
$633$	−12.2203	+	16.8198i	−0.485714	+	0.668528i
$634$	−0.382636	+	18.0595i	−0.0151964	+	0.717233i
$635$		0			0
$636$	−8.93337	−	7.08750i	−0.354231	−	0.281038i
$637$	1.07856	−	3.31947i	0.0427342	−	0.131522i
$638$	0.0604906	−	2.85501i	0.00239485	−	0.113031i
$639$	−2.59143	−	7.97559i	−0.102515	−	0.315510i
$640$		0			0
$641$	6.10344	−	18.7845i	0.241072	−	0.741942i	−0.755186	−	0.655510i	$-0.772454\pi$
$641$	6.10344	−	18.7845i	0.241072	−	0.741942i	0.996258	−	0.0864316i	$-0.0275464\pi$
$642$	13.4004	+	4.67012i	0.528870	+	0.184315i
$643$	21.0042			0.828324			0.414162	−	0.910203i	$-0.364075\pi$
$643$	21.0042			0.828324			0.414162	+	0.910203i	$0.364075\pi$
$644$	32.0935	+	1.36058i	1.26466	+	0.0536142i
$645$		0			0
$646$	1.01905	−	1.34188i	0.0400939	−	0.0527955i
$647$	−19.4638	−	26.7896i	−0.765202	−	1.05321i	−0.996764	−	0.0803896i	$-0.974384\pi$
$647$	−19.4638	−	26.7896i	−0.765202	−	1.05321i	0.231562	−	0.972820i	$-0.425616\pi$
$648$	9.26557	+	3.67623i	0.363986	+	0.144416i
$649$	−1.13326			−0.0444844
$650$		0			0
$651$			26.1240i			1.02388i
$652$	20.5795	+	16.3273i	0.805957	+	0.639425i
$653$	0.267998	−	0.194712i	0.0104876	−	0.00761966i	−0.582529	−	0.812810i	$-0.697937\pi$
$653$	0.267998	−	0.194712i	0.0104876	−	0.00761966i	0.593017	+	0.805190i	$0.297937\pi$
$654$	−9.96986	−	7.57132i	−0.389852	−	0.296062i
$655$		0			0
$656$	−20.4387	+	12.3513i	−0.797998	+	0.482236i
$657$			7.06276i			0.275545i
$658$	3.45842	+	1.20528i	0.134823	+	0.0469867i
$659$	2.06861	+	0.672132i	0.0805816	+	0.0261826i	0.349030	−	0.937111i	$-0.386511\pi$
$659$	2.06861	+	0.672132i	0.0805816	+	0.0261826i	−0.268449	+	0.963294i	$0.586511\pi$
$660$		0			0
$661$	−14.4168	+	4.68430i	−0.560748	+	0.182198i	−0.575658	−	0.817691i	$-0.695254\pi$
$661$	−14.4168	+	4.68430i	−0.560748	+	0.182198i	0.0149097	+	0.999889i	$0.495254\pi$
$662$	6.71842	+	0.142347i	0.261119	+	0.00553247i
$663$	6.06144	+	1.96948i	0.235407	+	0.0764883i
$664$	14.4571	+	5.73604i	0.561044	+	0.222601i
$665$		0			0
$666$	−0.305883	+	14.4369i	−0.0118527	+	0.559420i
$667$	−49.0130	−	35.6100i	−1.89779	−	1.37883i
$668$	−23.0946	−	34.7965i	−0.893557	−	1.34632i
$669$	−17.9492	+	24.7049i	−0.693955	+	0.955147i
$670$		0			0
$671$	0.426145	−	0.309612i	0.0164511	−	0.0119525i
$672$	−14.8919	+	8.57399i	−0.574468	+	0.330749i
$673$	−3.94041	+	1.28032i	−0.151892	+	0.0493526i	−0.383976	−	0.923343i	$-0.625445\pi$
$673$	−3.94041	+	1.28032i	−0.151892	+	0.0493526i	0.232084	+	0.972696i	$0.425445\pi$
$674$	−12.0965	−	40.1005i	−0.465942	−	1.54462i
$675$		0			0
$676$	−14.0843	+	9.34781i	−0.541703	+	0.359531i
$677$	6.92852	+	21.3238i	0.266285	+	0.819540i	0.991395	+	0.130907i	$0.0417890\pi$
$677$	6.92852	+	21.3238i	0.266285	+	0.819540i	−0.725110	+	0.688633i	$0.758211\pi$
$678$	−22.4472	−	17.0468i	−0.862079	−	0.654680i
$679$	23.9128	−	17.3737i	0.917689	−	0.666740i
$680$		0			0
$681$	4.75261	+	3.45297i	0.182120	+	0.132318i
$682$	−0.811904	−	2.69149i	−0.0310894	−	0.103063i
$683$	26.5359	+	19.2795i	1.01537	+	0.737709i	0.965328	−	0.261038i	$-0.0840649\pi$
$683$	26.5359	+	19.2795i	1.01537	+	0.737709i	0.0500406	+	0.998747i	$0.484065\pi$
$684$	−1.28906	+	0.359243i	−0.0492884	+	0.0137360i
$685$		0			0
$686$	23.2313	−	16.1379i	0.886974	−	0.616147i
$687$	−6.36672	−	2.06867i	−0.242905	−	0.0789247i
$688$	−29.4883	−	25.5032i	−1.12423	−	0.972299i
$689$	2.86464	+	8.81645i	0.109134	+	0.335880i
$690$		0			0
$691$	35.7160	+	11.6048i	1.35870	+	0.441468i	0.895609	−	0.444843i	$-0.146741\pi$
$691$	35.7160	+	11.6048i	1.35870	+	0.441468i	0.463090	+	0.886311i	$0.346741\pi$
$692$	−15.7426	−	0.667393i	−0.598443	−	0.0253705i
$693$	−0.684949			−0.0260190
$694$	25.7657	+	8.97952i	0.978053	+	0.340858i
$695$		0			0
$696$	32.3436	+	2.05831i	1.22598	+	0.0780200i
$697$	7.99547	+	11.0048i	0.302850	+	0.416837i
$698$	−38.4705	+	26.7240i	−1.45613	+	1.01152i
$699$		−	4.58909i		−	0.173575i
$700$		0			0
$701$		−	23.3655i		−	0.882503i	−0.897383	−	0.441252i	$-0.854535\pi$
$701$		−	23.3655i		−	0.882503i	0.897383	−	0.441252i	$-0.145465\pi$
$702$	−9.65853	−	13.9039i	−0.364538	−	0.524770i
$703$	2.45284	+	3.37605i	0.0925108	+	0.127330i
$704$	1.26781	−	1.34618i	0.0477824	−	0.0507362i
$705$		0			0
$706$	−6.18462	+	17.7461i	−0.232761	+	0.667883i
$707$	26.8397			1.00941
$708$	0.544762	−	12.8499i	0.0204734	−	0.482930i
$709$	12.3034	+	3.99762i	0.462064	+	0.150134i	0.530793	−	0.847502i	$-0.321894\pi$
$709$	12.3034	+	3.99762i	0.462064	+	0.150134i	−0.0687289	+	0.997635i	$0.521894\pi$
$710$		0			0
$711$	−4.97406	−	15.3086i	−0.186542	−	0.574116i
$712$	−23.9502	−	37.7996i	−0.897570	−	1.41660i
$713$	−56.7231	−	18.4305i	−2.12430	−	0.690226i
$714$	5.58422	+	8.03876i	0.208984	+	0.300843i
$715$		0			0
$716$	−30.9299	+	8.61975i	−1.15590	+	0.322135i
$717$	21.5530	+	15.6592i	0.804912	+	0.584803i
$718$	−22.9312	+	6.91732i	−0.855785	+	0.258152i
$719$	−1.77973	−	1.29305i	−0.0663726	−	0.0482225i	0.554104	−	0.832447i	$-0.313061\pi$
$719$	−1.77973	−	1.29305i	−0.0663726	−	0.0482225i	−0.620477	+	0.784225i	$0.713061\pi$
$720$		0			0
$721$	−12.5632	+	9.12770i	−0.467878	+	0.339933i
$722$	16.0169	−	21.0909i	0.596086	−	0.784923i
$723$	−7.85116	−	24.1634i	−0.291988	−	0.898646i
$724$	18.9683	+	28.5793i	0.704950	+	1.06214i
$725$		0			0
$726$	19.4405	−	5.86433i	0.721504	−	0.217646i
$727$	−4.25417	+	1.38226i	−0.157778	+	0.0512653i	−0.386841	−	0.922146i	$-0.626434\pi$
$727$	−4.25417	+	1.38226i	−0.157778	+	0.0512653i	0.229063	+	0.973412i	$0.426434\pi$
$728$	13.9410	+	0.887189i	0.516688	+	0.0328814i
$729$	−21.5182	+	15.6339i	−0.796969	+	0.579032i
$730$		0			0
$731$	−13.0530	+	17.9660i	−0.482784	+	0.664496i
$732$	3.30582	+	4.98085i	0.122186	+	0.184097i
$733$	10.5599	+	7.67219i	0.390037	+	0.283379i	0.765471	−	0.643471i	$-0.222506\pi$
$733$	10.5599	+	7.67219i	0.390037	+	0.283379i	−0.375433	+	0.926849i	$0.622506\pi$
$734$	−12.3524	−	0.261718i	−0.455937	−	0.00966019i
$735$		0			0
$736$	−8.11052	−	38.3838i	−0.298958	−	1.41485i
$737$	0.694989	+	0.225815i	0.0256002	+	0.00831802i
$738$	0.228841	−	10.8007i	0.00842375	−	0.397580i
$739$	29.8146	−	9.68735i	1.09675	−	0.356355i	0.295898	−	0.955220i	$-0.404381\pi$
$739$	29.8146	−	9.68735i	1.09675	−	0.356355i	0.800850	+	0.598865i	$0.204381\pi$
$740$		0			0
$741$	−1.39117	−	0.452018i	−0.0511058	−	0.0166053i
$742$	−4.68524	+	13.4438i	−0.172001	+	0.493536i
$743$		−	28.1541i		−	1.03287i	−0.856325	−	0.516437i	$-0.827258\pi$
$743$		−	28.1541i		−	1.03287i	0.856325	−	0.516437i	$-0.172742\pi$
$744$	30.9089	−	7.91229i	1.13317	−	0.290079i
$745$		0			0
$746$	0.858141	−	1.12999i	0.0314188	−	0.0413720i
$747$	−5.69226	+	4.13567i	−0.208269	+	0.151316i
$748$	−0.825165	−	0.654664i	−0.0301710	−	0.0239369i
$749$		−	17.7168i		−	0.647359i
$750$		0			0
$751$	−12.9756			−0.473487			−0.236743	−	0.971572i	$-0.576080\pi$
$751$	−12.9756			−0.473487			−0.236743	+	0.971572i	$0.576080\pi$
$752$	0.378575	−	4.45692i	0.0138052	−	0.162527i
$753$	3.52324	+	4.84932i	0.128394	+	0.176719i
$754$	−20.9817	−	15.9340i	−0.764110	−	0.580280i
$755$		0			0
$756$	1.10125	−	25.9764i	0.0400519	−	0.944751i
$757$	−16.0395			−0.582965			−0.291482	−	0.956576i	$-0.594149\pi$
$757$	−16.0395			−0.582965			−0.291482	+	0.956576i	$0.594149\pi$
$758$	−16.8071	+	48.2261i	−0.610461	+	1.75165i
$759$	−0.649771	+	1.99979i	−0.0235852	+	0.0725878i
$760$		0			0
$761$	3.49479	+	10.7559i	0.126686	+	0.389900i	0.994205	−	0.107505i	$-0.0342863\pi$
$761$	3.49479	+	10.7559i	0.126686	+	0.389900i	−0.867518	+	0.497405i	$0.834286\pi$
$762$	−8.46322	−	0.179315i	−0.306590	−	0.00649589i
$763$	−4.82977	+	14.8645i	−0.174849	+	0.538131i
$764$	−4.68273	−	3.71515i	−0.169415	−	0.134410i
$765$		0			0
$766$	−43.6659	−	0.925174i	−1.57771	−	0.0334279i
$767$	−6.14557	+	8.45866i	−0.221904	+	0.305424i
$768$	14.6548	+	15.0227i	0.528810	+	0.542084i
$769$	3.25219	+	2.36285i	0.117277	+	0.0852066i	0.644878	−	0.764286i	$-0.276908\pi$
$769$	3.25219	+	2.36285i	0.117277	+	0.0852066i	−0.527601	+	0.849492i	$0.676908\pi$
$770$		0			0
$771$	−21.1549	−	29.1173i	−0.761876	−	1.04863i
$772$	−27.9914	−	10.4252i	−1.00743	−	0.375212i
$773$	0.759693	+	2.33810i	0.0273243	+	0.0840955i	0.963789	−	0.266667i	$-0.0859224\pi$
$773$	0.759693	+	2.33810i	0.0273243	+	0.0840955i	−0.936464	+	0.350763i	$0.885922\pi$
$774$	16.8852	−	5.09352i	0.606926	−	0.183083i
$775$		0			0
$776$	−27.7984	−	23.0307i	−0.997906	−	0.826752i
$777$	−23.0548	+	7.49097i	−0.827088	+	0.268737i
$778$	−1.49512	−	1.13542i	−0.0536026	−	0.0407069i
$779$	−1.83505	−	2.52573i	−0.0657475	−	0.0904937i
$780$		0			0
$781$	−0.890481	+	1.22564i	−0.0318639	+	0.0438569i
$782$	−21.3943	+	6.45369i	−0.765057	+	0.230784i
$783$	−28.8227	+	39.6710i	−1.03004	+	1.41773i
$784$	−4.95161	−	4.28243i	−0.176843	−	0.152944i
$785$		0			0
$786$	−23.6446	+	16.4250i	−0.843377	+	0.585861i
$787$	9.27720	−	28.5523i	0.330697	−	1.01778i	−0.638107	−	0.769948i	$-0.720282\pi$
$787$	9.27720	−	28.5523i	0.330697	−	1.01778i	0.968803	−	0.247831i	$-0.0797179\pi$
$788$	14.7830	+	53.0452i	0.526623	+	1.88966i
$789$	−16.0606	+	5.21842i	−0.571774	+	0.185781i
$790$		0			0
$791$	−10.8742	+	33.4675i	−0.386644	+	1.18997i
$792$	0.207454	+	0.810405i	0.00737154	+	0.0287965i
$793$		−	4.85974i		−	0.172575i
$794$	−12.8854	−	4.49065i	−0.457286	−	0.159367i
$795$		0			0
$796$	7.94528	−	21.3328i	0.281613	−	0.756122i
$797$	17.9888	−	13.0696i	0.637196	−	0.462950i	−0.221690	−	0.975117i	$-0.571157\pi$
$797$	17.9888	−	13.0696i	0.637196	−	0.462950i	0.858886	+	0.512167i	$0.171157\pi$
$798$	−1.28164	−	1.84498i	−0.0453696	−	0.0653118i
$799$	−2.54783			−0.0901359
$800$		0			0
$801$	20.2432			0.715257
$802$	−9.49943	−	13.6749i	−0.335437	−	0.482878i
$803$	1.03224	−	0.749967i	0.0364270	−	0.0264658i
$804$	−2.89458	+	7.77186i	−0.102084	+	0.274092i
$805$		0			0
$806$	−24.4922	−	8.53569i	−0.862700	−	0.300657i
$807$			2.00232i			0.0704852i
$808$	−8.12907	−	31.7557i	−0.285980	−	1.11716i
$809$	−10.2871	+	31.6605i	−0.361676	+	1.11313i	0.590360	+	0.807140i	$0.298986\pi$
$809$	−10.2871	+	31.6605i	−0.361676	+	1.11313i	−0.952036	+	0.305985i	$0.901014\pi$
$810$		0			0
$811$	41.7447	−	13.5637i	1.46585	−	0.476285i	0.536002	−	0.844217i	$-0.319934\pi$
$811$	41.7447	−	13.5637i	1.46585	−	0.476285i	0.929853	+	0.367932i	$0.119934\pi$
$812$	−10.8622	−	38.9764i	−0.381188	−	1.36780i
$813$	−9.92157	+	30.5355i	−0.347965	+	1.07093i
$814$	2.14248	−	1.48830i	0.0750938	−	0.0521648i
$815$		0			0
$816$	7.81983	−	9.04176i	0.273749	−	0.316525i
$817$	2.99582	−	4.12339i	0.104810	−	0.144259i
$818$	0.199192	−	0.0600873i	0.00696458	−	0.00210090i
$819$	−3.71442	+	5.11245i	−0.129792	+	0.178644i
$820$		0			0
$821$	−17.1793	−	23.6453i	−0.599561	−	0.825225i	0.396107	−	0.918205i	$-0.370361\pi$
$821$	−17.1793	−	23.6453i	−0.599561	−	0.825225i	−0.995668	+	0.0929790i	$0.970361\pi$
$822$	21.7155	+	16.4912i	0.757416	+	0.575197i
$823$	12.8489	−	4.17485i	0.447883	−	0.145526i	−0.0763866	−	0.997078i	$-0.524338\pi$
$823$	12.8489	−	4.17485i	0.447883	−	0.145526i	0.524270	+	0.851552i	$0.324338\pi$
$824$	14.6046	+	12.0997i	0.508776	+	0.421514i
$825$		0			0
$826$	−15.3729	+	4.63733i	−0.534893	+	0.161353i
$827$	8.92624	+	27.4721i	0.310396	+	0.955300i	0.977608	+	0.210433i	$0.0674872\pi$
$827$	8.92624	+	27.4721i	0.310396	+	0.955300i	−0.667213	+	0.744867i	$0.732513\pi$
$828$	16.6313	+	6.19423i	0.577977	+	0.215264i
$829$	−21.9589	−	30.2238i	−0.762663	−	1.04972i	−0.996988	−	0.0775572i	$-0.975288\pi$
$829$	−21.9589	−	30.2238i	−0.762663	−	1.04972i	0.234325	−	0.972158i	$-0.424712\pi$
$830$		0			0
$831$	−29.0732	−	21.1229i	−1.00854	−	0.732745i
$832$	−3.17269	−	16.7632i	−0.109993	−	0.581158i
$833$	−2.19184	+	3.01681i	−0.0759427	+	0.104526i
$834$	10.9465	+	0.231930i	0.379047	+	0.00803108i
$835$		0			0
$836$	0.189385	+	0.150253i	0.00655000	+	0.00519660i
$837$	−14.9176	+	45.9115i	−0.515627	+	1.58694i
$838$	−48.2129	−	1.02151i	−1.66549	−	0.0352876i
$839$	2.47513	+	7.61767i	0.0854510	+	0.262991i	0.984648	−	0.174553i	$-0.0558482\pi$
$839$	2.47513	+	7.61767i	0.0854510	+	0.262991i	−0.899197	+	0.437545i	$0.855848\pi$
$840$		0			0
$841$	−14.6201	+	44.9960i	−0.504141	+	1.55159i
$842$	2.71765	−	7.79799i	0.0936564	−	0.268736i
$843$	−38.1169			−1.31282
$844$	1.34272	−	31.6722i	0.0462182	−	1.09020i
$845$		0			0
$846$	1.61146	+	1.22377i	0.0554030	+	0.0420742i
$847$	−14.9010	−	20.5094i	−0.512004	−	0.704713i
$848$	17.3252	+	1.47162i	0.594949	+	0.0505356i
$849$	−13.0057			−0.446354
$850$		0			0
$851$		−	55.3440i		−	1.89717i
$852$	−13.4694	−	10.6862i	−0.461453	−	0.366105i
$853$	13.5745	−	9.86242i	0.464780	−	0.337683i	−0.330623	−	0.943763i	$-0.607259\pi$
$853$	13.5745	−	9.86242i	0.464780	−	0.337683i	0.795404	+	0.606080i	$0.207259\pi$
$854$	4.51381	−	5.94376i	0.154459	−	0.203391i
$855$		0			0
$856$	−20.9619	+	5.36598i	−0.716462	+	0.183405i
$857$			12.0516i			0.411675i	0.978586	+	0.205837i	$0.0659918\pi$
$857$			12.0516i			0.411675i	−0.978586	+	0.205837i	$0.934008\pi$
$858$	−0.300928	+	0.863479i	−0.0102735	+	0.0294787i
$859$	−53.1530	−	17.2704i	−1.81356	−	0.589260i	−0.999969	−	0.00781665i	$-0.997512\pi$
$859$	−53.1530	−	17.2704i	−1.81356	−	0.589260i	−0.813587	−	0.581443i	$-0.802488\pi$
$860$		0			0
$861$	17.2481	−	5.60423i	0.587812	−	0.190992i
$862$	−0.122548	+	5.78398i	−0.00417402	+	0.197003i
$863$	27.1681	+	8.82744i	0.924812	+	0.300490i	0.732439	−	0.680832i	$-0.238382\pi$
$863$	27.1681	+	8.82744i	0.924812	+	0.300490i	0.192373	+	0.981322i	$0.438382\pi$
$864$	−31.0678	+	6.56463i	−1.05695	+	0.223333i
$865$		0			0
$866$	6.72811	+	0.142552i	0.228631	+	0.00484412i
$867$	12.5310	+	9.10434i	0.425577	+	0.309200i
$868$	−22.0273	−	33.1884i	−0.747656	−	1.12649i
$869$	−1.70921	+	2.35253i	−0.0579811	+	0.0798041i
$870$		0			0
$871$	5.45435	−	3.96281i	0.184813	−	0.134275i
$872$	19.0499	+	1.21232i	0.645112	+	0.0410542i
$873$	15.5312	−	5.04641i	0.525653	−	0.170795i
$874$	4.91022	−	1.48120i	0.166091	−	0.0501022i
$875$		0			0
$876$	8.00761	+	12.0650i	0.270552	+	0.407639i
$877$	1.52668	+	4.69863i	0.0515522	+	0.158661i	0.973518	−	0.228609i	$-0.0734178\pi$
$877$	1.52668	+	4.69863i	0.0515522	+	0.158661i	−0.921966	+	0.387271i	$0.873418\pi$
$878$	1.49905	−	1.97394i	0.0505906	−	0.0666173i
$879$	−6.60284	+	4.79725i	−0.222708	+	0.161807i
$880$		0			0
$881$	−0.550583	−	0.400022i	−0.0185496	−	0.0134771i	0.578472	−	0.815702i	$-0.303649\pi$
$881$	−0.550583	−	0.400022i	−0.0185496	−	0.0134771i	−0.597021	+	0.802225i	$0.703649\pi$
$882$	2.83533	−	0.855292i	0.0954704	−	0.0287992i
$883$	−1.43973	−	1.04603i	−0.0484509	−	0.0352017i	0.563296	−	0.826255i	$-0.309533\pi$
$883$	−1.43973	−	1.04603i	−0.0484509	−	0.0352017i	−0.611747	+	0.791053i	$0.709533\pi$
$884$	−9.36120	+	2.60884i	−0.314851	+	0.0877449i
$885$		0			0
$886$	2.77137	+	3.98953i	0.0931060	+	0.134031i
$887$	−42.8681	−	13.9287i	−1.43937	−	0.467680i	−0.517669	−	0.855581i	$-0.673200\pi$
$887$	−42.8681	−	13.9287i	−1.43937	−	0.467680i	−0.921701	+	0.387901i	$0.873200\pi$
$888$	15.8458	+	25.0088i	0.531749	+	0.839239i
$889$	3.26583	+	10.0512i	0.109532	+	0.337106i
$890$		0			0
$891$	0.774771	+	0.251738i	0.0259558	+	0.00843355i
$892$	1.97218	−	46.5200i	0.0660334	−	1.55761i
$893$	0.584756			0.0195681
$894$	−5.57996	+	16.0111i	−0.186622	+	0.535490i
$895$		0			0
$896$	11.6895	−	23.4492i	0.390519	−	0.783383i
$897$	11.4028	+	15.6946i	0.380728	+	0.524027i
$898$	−4.47175	−	6.43731i	−0.149224	−	0.214816i
$899$			75.1261i			2.50560i
$900$		0			0
$901$		−	9.90409i		−	0.329953i
$902$	−1.60285	+	1.11344i	−0.0533692	+	0.0370735i
$903$	17.4028	+	23.9530i	0.579130	+	0.797104i
$904$	42.8910	+	2.72953i	1.42653	+	0.0907829i
$905$		0			0
$906$	−15.0557	−	5.24701i	−0.500192	−	0.174320i
$907$	22.9525			0.762127			0.381063	−	0.924549i	$-0.375558\pi$
$907$	22.9525			0.762127			0.381063	+	0.924549i	$0.375558\pi$
$908$	−8.94930	−	0.379398i	−0.296993	−	0.0125908i
$909$	14.1030	+	4.58234i	0.467766	+	0.151987i
$910$		0			0
$911$	1.55833	+	4.79606i	0.0516299	+	0.158900i	0.973547	−	0.228487i	$-0.0733777\pi$
$911$	1.55833	+	4.79606i	0.0516299	+	0.158900i	−0.921917	+	0.387387i	$0.873378\pi$
$912$	−1.79474	+	2.07519i	−0.0594297	+	0.0687163i
$913$	1.20888	+	0.392788i	0.0400080	+	0.0129994i
$914$	−3.51710	+	2.44319i	−0.116335	+	0.0808136i
$915$		0			0
$916$	9.83267	−	2.74024i	0.324881	−	0.0905399i
$917$	29.0786	+	21.1268i	0.960260	+	0.697670i
$918$	5.22360	+	17.3165i	0.172405	+	0.571528i
$919$	−0.772993	−	0.561613i	−0.0254987	−	0.0185259i	0.574963	−	0.818179i	$-0.305016\pi$
$919$	−0.772993	−	0.561613i	−0.0254987	−	0.0185259i	−0.600462	+	0.799654i	$0.705016\pi$
$920$		0			0
$921$	31.4250	−	22.8316i	1.03549	−	0.752326i
$922$	14.1854	+	10.7726i	0.467170	+	0.354778i
$923$	4.31919	+	13.2931i	0.142168	+	0.437547i
$924$	−1.17007	+	0.776580i	−0.0384924	+	0.0255476i
$925$		0			0
$926$	−1.78925	−	5.93142i	−0.0587983	−	0.194919i
$927$	−8.15973	+	2.65126i	−0.268001	+	0.0870787i
$928$	−42.8254	+	24.6567i	−1.40581	+	0.809395i
$929$	−46.5656	+	33.8319i	−1.52777	+	1.10999i	−0.570304	+	0.821433i	$0.693175\pi$
$929$	−46.5656	+	33.8319i	−1.52777	+	1.10999i	−0.957463	+	0.288555i	$0.906825\pi$
$930$		0			0
$931$	0.503052	−	0.692391i	0.0164868	−	0.0226922i
$932$	3.86945	+	5.83007i	0.126748	+	0.190970i
$933$	−4.55588	−	3.31004i	−0.149153	−	0.108366i
$934$	−0.680077	+	32.0980i	−0.0222528	+	1.05028i
$935$		0			0
$936$	7.17386	+	2.84632i	0.234485	+	0.0930349i
$937$	33.6886	+	10.9461i	1.10056	+	0.357593i	0.802317	−	0.596898i	$-0.203600\pi$
$937$	33.6886	+	10.9461i	1.10056	+	0.357593i	0.298240	+	0.954491i	$0.403600\pi$
$938$	10.3517	+	0.219328i	0.337996	+	0.00716131i
$939$	17.1327	−	5.56674i	0.559103	−	0.181664i
$940$		0			0
$941$	0.202380	+	0.0657573i	0.00659741	+	0.00214363i	0.312314	−	0.949979i	$-0.398896\pi$
$941$	0.202380	+	0.0657573i	0.00659741	+	0.00214363i	−0.305716	+	0.952123i	$0.598896\pi$
$942$	−8.13931	−	2.83660i	−0.265193	−	0.0924215i
$943$			41.4046i			1.34832i
$944$	10.1428	+	16.7841i	0.330120	+	0.546277i
$945$		0			0
$946$	−2.53741	−	1.92696i	−0.0824982	−	0.0626508i
$947$	4.78799	−	3.47868i	0.155589	−	0.113042i	−0.507267	−	0.861789i	$-0.669344\pi$
$947$	4.78799	−	3.47868i	0.155589	−	0.113042i	0.662856	+	0.748747i	$0.269344\pi$
$948$	−25.8535	−	20.5115i	−0.839682	−	0.666182i
$949$		−	11.7717i		−	0.382124i
$950$		0			0
$951$	−16.7538			−0.543279
$952$	−13.8725	−	5.50407i	−0.449609	−	0.178388i
$953$	30.3932	+	41.8326i	0.984531	+	1.35509i	0.934352	+	0.356351i	$0.115979\pi$
$953$	30.3932	+	41.8326i	0.984531	+	1.35509i	0.0501787	+	0.998740i	$0.484021\pi$
$954$	−4.75712	+	6.26415i	−0.154018	+	0.202809i
$955$		0			0
$956$	−40.5850	−	1.72056i	−1.31261	−	0.0556470i
$957$	2.64859			0.0856169
$958$	−9.21755	−	3.21237i	−0.297805	−	0.103787i
$959$	10.5198	−	32.3766i	0.339702	−	1.04550i
$960$		0			0
$961$	13.2751	+	40.8565i	0.428228	+	1.31795i
$962$	0.509822	−	24.0623i	0.0164373	−	0.775801i
$963$	3.02479	−	9.30935i	0.0974725	−	0.299989i
$964$	30.3485	+	24.0777i	0.977458	+	0.775489i
$965$		0			0
$966$	−0.631103	+	29.7865i	−0.0203054	+	0.958365i
$967$	11.6201	−	15.9937i	0.373677	−	0.514323i	−0.580218	−	0.814461i	$-0.697033\pi$
$967$	11.6201	−	15.9937i	0.373677	−	0.514323i	0.953896	+	0.300138i	$0.0970328\pi$
$968$	−19.7529	+	23.8421i	−0.634881	+	0.766313i
$969$	1.26432	+	0.918585i	0.0406159	+	0.0295092i
$970$		0			0
$971$	11.7741	+	16.2057i	0.377850	+	0.520065i	0.955013	−	0.296563i	$-0.0958405\pi$
$971$	11.7741	+	16.2057i	0.377850	+	0.520065i	−0.577164	+	0.816628i	$0.695841\pi$
$972$	8.52819	−	22.8979i	0.273542	−	0.734451i
$973$	−4.22409	−	13.0004i	−0.135418	−	0.416775i
$974$	−14.6459	−	48.5516i	−0.469283	−	1.55569i
$975$		0			0
$976$	−8.39955	−	3.54035i	−0.268863	−	0.113324i
$977$	44.2455	−	14.3762i	1.41554	−	0.459937i	0.501357	−	0.865240i	$-0.332834\pi$
$977$	44.2455	−	14.3762i	1.41554	−	0.459937i	0.914182	+	0.405304i	$0.132834\pi$
$978$	−14.7357	+	19.4039i	−0.471196	+	0.620467i
$979$	−2.14954	−	2.95859i	−0.0686997	−	0.0945570i
$980$		0			0
$981$	−5.07563	+	6.98600i	−0.162052	+	0.223046i
$982$	−3.16393	−	10.4886i	−0.100965	−	0.334704i
$983$	18.2599	−	25.1326i	0.582401	−	0.801606i	−0.411555	−	0.911385i	$-0.635014\pi$
$983$	18.2599	−	25.1326i	0.582401	−	0.801606i	0.993956	+	0.109779i	$0.0350142\pi$
$984$	−11.8547	−	18.7098i	−0.377914	−	0.596448i
$985$		0			0
$986$	16.0588	+	23.1175i	0.511417	+	0.736210i
$987$	−1.04969	+	3.23062i	−0.0334120	+	0.102832i
$988$	2.14850	−	0.598759i	0.0683529	−	0.0190490i
$989$	−64.2869	+	20.8881i	−2.04420	+	0.664202i
$990$		0			0
$991$	4.56887	−	14.0615i	0.145135	−	0.446679i	−0.851893	−	0.523715i	$-0.824546\pi$
$991$	4.56887	−	14.0615i	0.145135	−	0.446679i	0.997028	+	0.0770360i	$0.0245457\pi$
$992$	−32.5957	+	36.1138i	−1.03492	+	1.14661i
$993$			6.23268i			0.197788i
$994$	−7.06422	+	20.2700i	−0.224063	+	0.642925i
$995$		0			0
$996$	−5.03490	+	13.5185i	−0.159537	+	0.428351i
$997$	21.0204	−	15.2722i	0.665723	−	0.483676i	−0.202868	−	0.979206i	$-0.565026\pi$
$997$	21.0204	−	15.2722i	0.665723	−	0.483676i	0.868591	+	0.495530i	$0.165026\pi$
$998$	42.3302	−	29.4052i	1.33994	−	0.930804i
$999$	−44.7952			−1.41726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.349.9		112
5.2	odd	4		1000.2.t.b.901.46		224
5.3	odd	4		1000.2.t.b.901.11		224
5.4	even	2		200.2.o.a.69.20	yes	112
8.5	even	2	inner	1000.2.o.a.349.14		112
20.19	odd	2		800.2.be.a.369.19		112
25.3	odd	20		1000.2.t.b.101.56		224
25.4	even	10	inner	1000.2.o.a.149.14		112
25.21	even	5		200.2.o.a.29.15	✓	112
25.22	odd	20		1000.2.t.b.101.1		224
40.13	odd	4		1000.2.t.b.901.56		224
40.19	odd	2		800.2.be.a.369.10		112
40.29	even	2		200.2.o.a.69.15	yes	112
40.37	odd	4		1000.2.t.b.901.1		224
100.71	odd	10		800.2.be.a.529.10		112
200.21	even	10		200.2.o.a.29.20	yes	112
200.29	even	10	inner	1000.2.o.a.149.9		112
200.53	odd	20		1000.2.t.b.101.11		224
200.171	odd	10		800.2.be.a.529.19		112
200.197	odd	20		1000.2.t.b.101.46		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.15	✓	112	25.21	even	5
200.2.o.a.29.20	yes	112	200.21	even	10
200.2.o.a.69.15	yes	112	40.29	even	2
200.2.o.a.69.20	yes	112	5.4	even	2
800.2.be.a.369.10		112	40.19	odd	2
800.2.be.a.369.19		112	20.19	odd	2
800.2.be.a.529.10		112	100.71	odd	10
800.2.be.a.529.19		112	200.171	odd	10
1000.2.o.a.149.9		112	200.29	even	10	inner
1000.2.o.a.149.14		112	25.4	even	10	inner
1000.2.o.a.349.9		112	1.1	even	1	trivial
1000.2.o.a.349.14		112	8.5	even	2	inner
1000.2.t.b.101.1		224	25.22	odd	20
1000.2.t.b.101.11		224	200.53	odd	20
1000.2.t.b.101.46		224	200.197	odd	20
1000.2.t.b.101.56		224	25.3	odd	20
1000.2.t.b.901.1		224	40.37	odd	4
1000.2.t.b.901.11		224	5.3	odd	4
1000.2.t.b.901.46		224	5.2	odd	4
1000.2.t.b.901.56		224	40.13	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.806832 - 1.16147i) q^{2} +(1.06117 - 0.770982i) q^{3} +(-0.698045 + 1.87423i) q^{4} +(-1.75166 - 0.610464i) q^{6} +2.31589i q^{7} +(2.74007 - 0.701425i) q^{8} +(-0.395392 + 1.21689i) q^{9} +O(q^{10})\)	\(q+(-0.806832 - 1.16147i) q^{2} +(1.06117 - 0.770982i) q^{3} +(-0.698045 + 1.87423i) q^{4} +(-1.75166 - 0.610464i) q^{6} +2.31589i q^{7} +(2.74007 - 0.701425i) q^{8} +(-0.395392 + 1.21689i) q^{9} +(0.219837 - 0.0714294i) q^{11} +(0.704254 + 2.52705i) q^{12} +(0.659008 - 2.02822i) q^{13} +(2.68985 - 1.86853i) q^{14} +(-3.02547 - 2.61659i) q^{16} +(-1.33923 + 1.84329i) q^{17} +(1.73240 - 0.522589i) q^{18} +(0.307368 - 0.423055i) q^{19} +(1.78551 + 2.45754i) q^{21} +(-0.260335 - 0.197704i) q^{22} +(-6.59576 + 2.14309i) q^{23} +(2.36689 - 2.85688i) q^{24} +(-2.88743 + 0.871009i) q^{26} +(1.73461 + 5.33859i) q^{27} +(-4.34051 - 1.61660i) q^{28} +(5.13469 + 7.06729i) q^{29} +(6.95750 + 5.05492i) q^{31} +(-0.598065 + 5.62515i) q^{32} +(0.178213 - 0.245289i) q^{33} +(3.22146 + 0.0682549i) q^{34} +(-2.00473 - 1.59050i) q^{36} +(-2.46601 + 7.58959i) q^{37} +(-0.739362 - 0.0156653i) q^{38} +(-0.864403 - 2.66036i) q^{39} +(1.84490 - 5.67801i) q^{41} +(1.41377 - 4.05665i) q^{42} +9.74670 q^{43} +(-0.0195813 + 0.461886i) q^{44} +(7.81081 + 5.93169i) q^{46} +(0.657286 + 0.904676i) q^{47} +(-5.22787 - 0.444060i) q^{48} +1.63664 q^{49} +2.98855i q^{51} +(3.34133 + 2.65092i) q^{52} +(-3.51671 + 2.55504i) q^{53} +(4.80109 - 6.32205i) q^{54} +(1.62442 + 6.34571i) q^{56} -0.685906i q^{57} +(4.06565 - 11.6659i) q^{58} +(-4.66275 - 1.51502i) q^{59} +(2.16726 - 0.704186i) q^{61} +(0.257629 - 12.1594i) q^{62} +(-2.81819 - 0.915685i) q^{63} +(7.01601 - 3.84391i) q^{64} +(-0.428684 - 0.00908277i) q^{66} +(2.55761 + 1.85821i) q^{67} +(-2.51990 - 3.79672i) q^{68} +(-5.34690 + 7.35938i) q^{69} +(-5.30236 + 3.85239i) q^{71} +(-0.229845 + 3.61171i) q^{72} +(5.24971 - 1.70573i) q^{73} +(10.8048 - 3.25932i) q^{74} +(0.578346 + 0.871389i) q^{76} +(0.165423 + 0.509119i) q^{77} +(-2.39251 + 3.15044i) q^{78} +(-10.1775 + 7.39438i) q^{79} +(2.85122 + 2.07153i) q^{81} +(-8.08339 + 2.43840i) q^{82} +(4.44876 + 3.23222i) q^{83} +(-5.85237 + 1.63098i) q^{84} +(-7.86395 - 11.3205i) q^{86} +(10.8975 + 3.54081i) q^{87} +(0.552267 - 0.349921i) q^{88} +(-4.88895 - 15.0466i) q^{89} +(4.69713 + 1.52619i) q^{91} +(0.587495 - 13.8579i) q^{92} +11.2803 q^{93} +(0.520439 - 1.49334i) q^{94} +(3.70224 + 6.43031i) q^{96} +(-7.50193 - 10.3255i) q^{97} +(-1.32050 - 1.90092i) q^{98} +0.295760i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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