LMFDB - Embedded newform 1000.2.o.a.349.14

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			349.14
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0299570 + 1.41390i) q^{2} +(-1.06117 + 0.770982i) q^{3} +(-1.99821 + 0.0847122i) q^{4} +(-1.12188 - 1.47728i) q^{6} +2.31589i q^{7} +(-0.179635 - 2.82272i) q^{8} +(-0.395392 + 1.21689i) q^{9} +O(q^{10})$	\(q+(0.0299570 + 1.41390i) q^{2} +(-1.06117 + 0.770982i) q^{3} +(-1.99821 + 0.0847122i) q^{4} +(-1.12188 - 1.47728i) q^{6} +2.31589i q^{7} +(-0.179635 - 2.82272i) q^{8} +(-0.395392 + 1.21689i) q^{9} +(-0.219837 + 0.0714294i) q^{11} +(2.05511 - 1.63047i) q^{12} +(-0.659008 + 2.02822i) q^{13} +(-3.27443 + 0.0693772i) q^{14} +(3.98565 - 0.338545i) 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} +(-0.107579 - 0.308687i) 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} +(-0.196184 - 4.62763i) 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} +(-2.64634 - 1.83831i) q^{34} +(0.686988 - 2.46509i) q^{36} +(2.46601 - 7.58959i) q^{37} +(-0.607364 - 0.421912i) q^{38} +(-0.864403 - 2.66036i) q^{39} +(1.84490 - 5.67801i) q^{41} +(3.42122 - 2.59815i) q^{42} -9.74670 q^{43} +(0.433228 - 0.161353i) q^{44} +(-3.22770 - 9.26151i) q^{46} +(0.657286 + 0.904676i) q^{47} +(-3.96842 + 3.43211i) q^{48} +1.63664 q^{49} -2.98855i q^{51} +(1.14502 - 4.10862i) q^{52} +(3.51671 - 2.55504i) q^{53} +(7.49624 - 2.61249i) q^{54} +(6.53711 - 0.416014i) q^{56} -0.685906i q^{57} +(9.83860 - 7.47163i) q^{58} +(4.66275 + 1.51502i) q^{59} +(-2.16726 + 0.704186i) q^{61} +(-6.93871 + 9.98861i) q^{62} +(-2.81819 - 0.915685i) q^{63} +(-7.93546 + 1.01411i) q^{64} +(0.352152 + 0.244626i) 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} +(3.50596 + 0.897484i) 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} +(3.73557 - 1.30187i) 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} +(3.77600 + 4.75942i) q^{84} +(-0.291982 - 13.7808i) q^{86} +(10.8975 + 3.54081i) q^{87} +(0.241115 + 0.607706i) q^{88} +(-4.88895 - 15.0466i) q^{89} +(-4.69713 - 1.52619i) q^{91} +(12.9981 - 4.84108i) q^{92} -11.2803 q^{93} +(-1.25943 + 0.956435i) q^{94} +(-4.97154 - 5.50812i) q^{96} +(-7.50193 - 10.3255i) q^{97} +(0.0490290 + 2.31405i) 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 $

$2$	0.0299570	+	1.41390i	0.0211828	+	0.999776i
$2$	0.0299570	+	1.41390i	0.0211828	+	0.999776i
$3$	−1.06117	+	0.770982i	−0.612664	+	0.445127i	−0.850351	−	0.526215i	$-0.823611\pi$
$3$	−1.06117	+	0.770982i	−0.612664	+	0.445127i	0.237687	+	0.971342i	$0.423611\pi$
$4$	−1.99821	+	0.0847122i	−0.999103	+	0.0423561i
$5$		0			0
$5$		0			0
$6$	−1.12188	−	1.47728i	−0.458005	−	0.603098i
$7$			2.31589i			0.875325i	0.899139	+	0.437662i	$0.144194\pi$
$7$			2.31589i			0.875325i	−0.899139	+	0.437662i	$0.855806\pi$
$8$	−0.179635	−	2.82272i	−0.0635104	−	0.997981i
$9$	−0.395392	+	1.21689i	−0.131797	+	0.405630i
$10$		0			0
$11$	−0.219837	+	0.0714294i	−0.0662834	+	0.0215368i	−0.341971	−	0.939711i	$-0.611094\pi$
$11$	−0.219837	+	0.0714294i	−0.0662834	+	0.0215368i	0.275688	+	0.961247i	$0.411094\pi$
$12$	2.05511	−	1.63047i	0.593261	−	0.470677i
$13$	−0.659008	+	2.02822i	−0.182776	+	0.562526i	−0.999903	−	0.0139312i	$-0.995565\pi$
$13$	−0.659008	+	2.02822i	−0.182776	+	0.562526i	0.817127	+	0.576458i	$0.195565\pi$
$14$	−3.27443	+	0.0693772i	−0.875128	+	0.0185418i
$15$		0			0
$16$	3.98565	−	0.338545i	0.996412	−	0.0846362i
$17$	−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	−0.842818	−	0.538199i	$-0.819105\pi$
$19$	−0.307368	+	0.423055i	−0.0705150	+	0.0970555i	0.772303	+	0.635255i	$0.219105\pi$
$20$		0			0
$21$	−1.78551	−	2.45754i	−0.389630	−	0.536280i
$22$	−0.107579	−	0.308687i	−0.0229360	−	0.0658123i
$23$	−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
$28$	−0.196184	−	4.62763i	−0.0370754	−	0.874539i
$29$	−5.13469	−	7.06729i	−0.953487	−	1.31236i	−0.949961	−	0.312369i	$-0.898877\pi$
$29$	−5.13469	−	7.06729i	−0.953487	−	1.31236i	−0.00352661	−	0.999994i	$-0.501123\pi$
$30$		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
$34$	−2.64634	−	1.83831i	−0.453843	−	0.315267i
$35$		0			0
$36$	0.686988	−	2.46509i	0.114498	−	0.410849i
$37$	2.46601	−	7.58959i	0.405409	−	1.24772i	−0.515144	−	0.857104i	$-0.672262\pi$
$37$	2.46601	−	7.58959i	0.405409	−	1.24772i	0.920553	−	0.390617i	$-0.127738\pi$
$38$	−0.607364	−	0.421912i	−0.0985275	−	0.0684432i
$39$	−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	$-0.0543756\pi$
$42$	3.42122	−	2.59815i	0.527906	−	0.400903i
$43$	−9.74670			−1.48636			−0.743179	−	0.669093i	$-0.766683\pi$
$43$	−9.74670			−1.48636			−0.743179	+	0.669093i	$0.766683\pi$
$44$	0.433228	−	0.161353i	0.0653117	−	0.0243249i
$45$		0			0
$46$	−3.22770	−	9.26151i	−0.475898	−	1.36554i
$47$	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	$0.774011\pi$
$48$	−3.96842	+	3.43211i	−0.572792	+	0.495383i
$49$	1.63664			0.233806
$50$		0			0
$51$		−	2.98855i		−	0.418481i
$52$	1.14502	−	4.10862i	0.158785	−	0.569763i
$53$	3.51671	−	2.55504i	0.483057	−	0.350962i	−0.319451	−	0.947603i	$-0.603498\pi$
$53$	3.51671	−	2.55504i	0.483057	−	0.350962i	0.802508	+	0.596641i	$0.203498\pi$
$54$	7.49624	−	2.61249i	1.02011	−	0.355515i
$55$		0			0
$56$	6.53711	−	0.416014i	0.873558	−	0.0555922i
$57$		−	0.685906i		−	0.0908505i
$58$	9.83860	−	7.47163i	1.29187	−	0.981073i
$59$	4.66275	+	1.51502i	0.607038	+	0.197239i	0.596377	−	0.802705i	$-0.296606\pi$
$59$	4.66275	+	1.51502i	0.607038	+	0.197239i	0.0106611	+	0.999943i	$0.496606\pi$
$60$		0			0
$61$	−2.16726	+	0.704186i	−0.277490	+	0.0901618i	−0.444456	−	0.895801i	$-0.646603\pi$
$61$	−2.16726	+	0.704186i	−0.277490	+	0.0901618i	0.166966	+	0.985963i	$0.446603\pi$
$62$	−6.93871	+	9.98861i	−0.881217	+	1.26856i
$63$	−2.81819	−	0.915685i	−0.355058	−	0.115365i
$64$	−7.93546	+	1.01411i	−0.991933	+	0.126764i
$65$		0			0
$66$	0.352152	+	0.244626i	0.0433469	+	0.0301114i
$67$	−2.55761	−	1.85821i	−0.312462	−	0.227017i	0.420490	−	0.907297i	$-0.361858\pi$
$67$	−2.55761	−	1.85821i	−0.312462	−	0.227017i	−0.732952	+	0.680280i	$0.761858\pi$
$68$	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	$0.427149\pi$
$72$	3.50596	+	0.897484i	0.413182	+	0.105769i
$73$	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
$78$	3.73557	−	1.30187i	0.422971	−	0.147408i
$79$	−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	0.316221	−	0.948686i	$-0.397586\pi$
$83$	−4.44876	−	3.23222i	−0.488315	−	0.354782i	−0.804536	+	0.593904i	$0.797586\pi$
$84$	3.77600	+	4.75942i	0.411995	+	0.519296i
$85$		0			0
$86$	−0.291982	−	13.7808i	−0.0314852	−	1.48602i
$87$	10.8975	+	3.54081i	1.16834	+	0.379615i
$88$	0.241115	+	0.607706i	0.0257030	+	0.0647817i
$89$	−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
$92$	12.9981	−	4.84108i	1.35515	−	0.504717i
$93$	−11.2803			−1.16971
$94$	−1.25943	+	0.956435i	−0.129900	+	0.0986487i
$95$		0			0
$96$	−4.97154	−	5.50812i	−0.507405	−	0.562170i
$97$	−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	$-0.424372\pi$
$98$	0.0490290	+	2.31405i	0.00495267	+	0.233754i
$99$		−	0.295760i		−	0.0297250i
$100$		0			0
$101$			11.5894i			1.15318i	0.817032	+	0.576592i	$0.195618\pi$
$101$			11.5894i			1.15318i	−0.817032	+	0.576592i	$0.804382\pi$
$102$	4.22550	−	0.0895281i	0.418387	−	0.00886461i
$103$	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	$0.692833\pi$
$104$	5.84346	+	1.49585i	0.572999	+	0.146681i
$105$		0			0
$106$	3.71791	+	4.89572i	0.361116	+	0.475515i
$107$	7.65011			0.739564			0.369782	−	0.929119i	$-0.379432\pi$
$107$	7.65011			0.739564			0.369782	+	0.929119i	$0.379432\pi$
$108$	3.91835	+	10.5206i	0.377044	+	1.01235i
$109$	−6.41848	−	2.08549i	−0.614779	−	0.199754i	−0.0149580	−	0.999888i	$-0.504761\pi$
$109$	−6.41848	−	2.08549i	−0.614779	−	0.199754i	−0.599821	+	0.800134i	$0.704761\pi$
$110$		0			0
$111$	3.23459	+	9.95506i	0.307014	+	0.944892i
$112$	0.784033	+	9.23033i	0.0740842	+	0.872184i
$113$	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	$0.346559\pi$
$114$	0.969801	−	0.0205477i	0.0908301	−	0.00192447i
$115$		0			0
$116$	10.8588	+	13.6869i	1.00822	+	1.27080i
$117$	−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
$122$	−1.06057	−	3.04319i	−0.0960196	−	0.275517i
$123$	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	$0.335103\pi$
$128$	−1.67158	−	11.1895i	−0.147748	−	0.989025i
$129$	10.3429	−	7.51453i	0.910638	−	0.661618i
$130$		0			0
$131$	−9.12255	+	12.5561i	−0.797041	+	1.09703i	0.196154	+	0.980573i	$0.437155\pi$
$131$	−9.12255	+	12.5561i	−0.797041	+	1.09703i	−0.993195	+	0.116460i	$0.962845\pi$
$132$	−0.335327	+	0.505234i	−0.0291864	+	0.0439750i
$133$	−0.979750	−	0.711830i	−0.0849551	−	0.0617235i
$134$	2.55070	−	3.67186i	0.220347	−	0.317201i
$135$		0			0
$136$	5.44365	+	3.44914i	0.466789	+	0.295761i
$137$	−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	$0.816101\pi$
$138$	10.5656	+	7.33950i	0.899402	+	0.624780i
$139$	5.61357	−	1.82396i	0.476137	−	0.154706i	−0.0611104	−	0.998131i	$-0.519464\pi$
$139$	5.61357	−	1.82396i	0.476137	−	0.154706i	0.537247	+	0.843425i	$0.319464\pi$
$140$		0			0
$141$	−1.39498	−	0.453256i	−0.117478	−	0.0381710i
$142$	−5.60572	−	7.38158i	−0.470421	−	0.619448i
$143$		−	0.492950i		−	0.0412225i
$144$	−1.16392	+	4.98396i	−0.0969934	+	0.415330i
$145$		0			0
$146$	2.56900	+	7.37145i	0.212612	+	0.610066i
$147$	−1.73675	+	1.26182i	−0.143245	+	0.104073i
$148$	−4.28466	+	15.3745i	−0.352197	+	1.26377i
$149$			9.14052i			0.748820i	0.927263	+	0.374410i	$0.122155\pi$
$149$			9.14052i			0.748820i	−0.927263	+	0.374410i	$0.877845\pi$
$150$		0			0
$151$	8.59512			0.699461			0.349730	−	0.936850i	$-0.386273\pi$
$151$	8.59512			0.699461			0.349730	+	0.936850i	$0.386273\pi$
$152$	1.24938	+	0.791616i	0.101338	+	0.0642086i
$153$	−1.71356	−	2.35851i	−0.138533	−	0.190675i
$154$	0.714886	−	0.249142i	0.0576071	−	0.0200765i
$155$		0			0
$156$	1.95262	+	5.24271i	0.156335	+	0.419753i
$157$	−4.64663			−0.370842			−0.185421	−	0.982659i	$-0.559365\pi$
$157$	−4.64663			−0.370842			−0.185421	+	0.982659i	$0.559365\pi$
$158$	−10.7598	−	14.1684i	−0.856002	−	1.12718i
$159$	−1.76192	+	5.42264i	−0.139730	+	0.430043i
$160$		0			0
$161$	−4.96317	−	15.2751i	−0.391152	−	1.20384i
$162$	−2.84352	+	4.09338i	−0.223408	+	0.321606i
$163$	−4.05889	+	12.4920i	−0.317917	+	0.978448i	0.656620	+	0.754221i	$0.271985\pi$
$163$	−4.05889	+	12.4920i	−0.317917	+	0.978448i	−0.974537	+	0.224226i	$0.928015\pi$
$164$	−3.20549	+	11.5021i	−0.250306	+	0.898164i
$165$		0			0
$166$	4.43675	−	6.38692i	0.344358	−	0.495721i
$167$	−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
$172$	19.4759	−	0.825665i	1.48502	−	0.0629563i
$173$	−2.43455	−	7.49277i	−0.185095	−	0.569664i	0.814855	−	0.579665i	$-0.196817\pi$
$173$	−2.43455	−	7.49277i	−0.185095	−	0.569664i	−0.999950	+	0.0100007i	$0.996817\pi$
$174$	−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
$178$	21.1279	−	7.36322i	1.58360	−	0.551896i
$179$	−9.43646	−	12.9882i	−0.705314	−	0.970782i	−0.999885	−	0.0151522i	$-0.995177\pi$
$179$	−9.43646	−	12.9882i	−0.705314	−	0.970782i	0.294571	−	0.955630i	$-0.404823\pi$
$180$		0			0
$181$	−10.0809	+	13.8751i	−0.749305	+	1.03133i	0.248723	+	0.968575i	$0.419989\pi$
$181$	−10.0809	+	13.8751i	−0.749305	+	1.03133i	−0.998029	+	0.0627560i	$0.980011\pi$
$182$	2.01716	−	6.68698i	0.149522	−	0.495672i
$183$	1.75691	−	2.41818i	0.129874	−	0.178757i
$184$	7.23416	+	18.2330i	0.533310	+	1.34415i
$185$		0			0
$186$	−0.337924	−	15.9492i	−0.0247778	−	1.16945i
$187$	0.162747	−	0.500883i	0.0119012	−	0.0366282i
$188$	−1.39003	−	1.75205i	−0.101378	−	0.127781i
$189$	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	$0.134486\pi$
$192$	7.63898	−	7.19424i	0.551296	−	0.519200i
$193$			14.9349i			1.07504i	0.843252	+	0.537518i	$0.180638\pi$
$193$			14.9349i			1.07504i	−0.843252	+	0.537518i	$0.819362\pi$
$194$	14.3745	−	10.9163i	1.03203	−	0.783743i
$195$		0			0
$196$	−3.27035	+	0.138644i	−0.233597	+	0.00990313i
$197$	−22.2749	+	16.1837i	−1.58702	+	1.15304i	−0.678984	+	0.734153i	$0.737580\pi$
$197$	−22.2749	+	16.1837i	−1.58702	+	1.15304i	−0.908039	+	0.418887i	$0.862420\pi$
$198$	0.418174	−	0.00886009i	0.0297184	−	0.000629659i
$199$	−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
$202$	−16.3862	+	0.347183i	−1.15293	+	0.0244277i
$203$	16.3671	−	11.8914i	1.14874	−	0.834611i
$204$	0.253167	+	5.97174i	0.0177252	+	0.418106i
$205$		0			0
$206$	−7.55200	+	5.73514i	−0.526173	+	0.399586i
$207$		−	8.87368i		−	0.616763i
$208$	−1.93993	+	8.30686i	−0.134510	+	0.575977i
$209$	0.0373522	−	0.114958i	0.00258371	−	0.00795183i
$210$		0			0
$211$	15.0746	−	4.89802i	1.03778	−	0.337194i	0.259916	−	0.965631i	$-0.416305\pi$
$211$	15.0746	−	4.89802i	1.03778	−	0.337194i	0.777860	+	0.628438i	$0.216305\pi$
$212$	−6.81067	+	5.40340i	−0.467759	+	0.371107i
$213$	2.65656	−	8.17604i	0.182024	−	0.560213i
$214$	0.229174	+	10.8165i	0.0156660	+	0.739398i
$215$		0			0
$216$	−14.7577	+	5.85531i	−1.00414	+	0.398404i
$217$	−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
$222$	−13.9785	+	4.87160i	−0.938177	+	0.326961i
$223$	−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	0.894564	−	0.446940i	$-0.147486\pi$
$227$	−1.38398	−	4.25947i	−0.0918583	−	0.282711i	−0.986422	+	0.164229i	$0.947486\pi$
$228$	0.0581047	+	1.37058i	0.00384807	+	0.0907690i
$229$	2.99987	+	4.12897i	0.198237	+	0.272850i	0.896550	−	0.442943i	$-0.146066\pi$
$229$	2.99987	+	4.12897i	0.198237	+	0.272850i	−0.698313	+	0.715793i	$0.746066\pi$
$230$		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	$0.163441\pi$
$234$	2.20159	−	3.16930i	0.143922	−	0.207184i
$235$		0			0
$236$	−9.44546	−	2.63233i	−0.614847	−	0.171350i
$237$	5.09907	−	15.6933i	0.331220	−	1.01939i
$238$	4.25732	−	6.12863i	0.275961	−	0.397260i
$239$	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	$-0.114437\pi$
$242$	−9.36263	−	12.3287i	−0.601853	−	0.792516i
$243$	12.2172			0.783736
$244$	4.27098	−	1.59070i	0.273422	−	0.101834i
$245$		0			0
$246$	−10.4578	+	3.64460i	−0.666763	+	0.232371i
$247$	−0.655490	−	0.902205i	−0.0417079	−	0.0574059i
$248$	13.0188	−	20.5471i	0.826695	−	1.30474i
$249$	7.21286			0.457096
$250$		0			0
$251$		−	4.56980i		−	0.288443i	−0.989545	−	0.144222i	$-0.953932\pi$
$251$		−	4.56980i		−	0.288443i	0.989545	−	0.144222i	$-0.0460679\pi$
$252$	5.70889	+	1.59099i	0.359626	+	0.100223i
$253$	1.29691	−	0.942261i	0.0815361	−	0.0592395i
$254$	2.12387	+	6.09419i	0.133263	+	0.382384i
$255$		0			0
$256$	15.7708	−	2.69864i	0.985673	−	0.168665i
$257$		−	27.4389i		−	1.71159i	−0.517312	−	0.855797i	$-0.673067\pi$
$257$		−	27.4389i		−	1.71159i	0.517312	−	0.855797i	$-0.326933\pi$
$258$	10.9346	+	14.3986i	0.680759	+	0.896419i
$259$	17.5767	+	5.71101i	1.09216	+	0.354865i
$260$		0			0
$261$	10.6303	−	3.45400i	0.658001	−	0.213798i
$262$	−18.0263	−	12.5222i	−1.11367	−	0.773624i
$263$	−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	$0.729927\pi$
$264$	−0.724394	−	0.458982i	−0.0445834	−	0.0282484i
$265$		0			0
$266$	0.977104	−	1.40659i	0.0599101	−	0.0862435i
$267$	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	−0.780786	−	0.624798i	$-0.785181\pi$
$269$	0.897279	−	1.23500i	0.0547081	−	0.0752992i	0.835495	+	0.549499i	$0.185181\pi$
$270$		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	$0.566817\pi$
$272$	−4.71365	+	7.80008i	−0.285807	+	0.472950i
$273$	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	$0.207744\pi$
$277$	8.46626	+	26.0565i	0.508689	+	1.56558i	−0.285791	+	0.958292i	$0.592256\pi$
$278$	2.74706	+	7.88237i	0.164757	+	0.472753i
$279$	−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	0.800101	−	0.599865i	$-0.204779\pi$
$283$	8.02169	+	5.82810i	0.476840	+	0.346444i	−0.323261	+	0.946310i	$0.604779\pi$
$284$	10.2689	−	8.14704i	0.609344	−	0.483438i
$285$		0			0
$286$	0.696980	−	0.0147673i	0.0412133	−	0.000873209i
$287$	13.1497	+	4.27258i	0.776200	+	0.252203i
$288$	−7.08166	−	1.49636i	−0.417291	−	0.0881738i
$289$	3.64911	+	11.2308i	0.214653	+	0.660635i
$290$		0			0
$291$	15.9216	+	5.17324i	0.933340	+	0.303261i
$292$	−10.3455	+	3.85312i	−0.605425	+	0.225487i
$293$	6.22226			0.363508			0.181754	−	0.983344i	$-0.441823\pi$
$293$	6.22226			0.363508			0.181754	+	0.983344i	$0.441823\pi$
$294$	−1.83612	−	2.41778i	−0.107084	−	0.141008i
$295$		0			0
$296$	−21.8662	−	5.59749i	−1.27095	−	0.325347i
$297$	0.762664	+	1.04972i	0.0442542	+	0.0609107i
$298$	−12.9237	+	0.273823i	−0.748652	+	0.0158621i
$299$		−	14.7899i		−	0.855324i
$300$		0			0
$301$		−	22.5723i		−	1.30105i
$302$	0.257484	+	12.1526i	0.0148165	+	0.699304i
$303$	−8.93519	−	12.2982i	−0.513313	−	0.706515i
$304$	−1.08184	+	1.79021i	−0.0620475	+	0.102675i
$305$		0			0
$306$	3.28336	−	2.49345i	0.187697	−	0.142541i
$307$	−29.6136			−1.69014			−0.845070	−	0.534656i	$-0.820441\pi$
$307$	−29.6136			−1.69014			−0.845070	+	0.534656i	$0.820441\pi$
$308$	0.373677	+	1.00331i	0.0212922	+	0.0571689i
$309$	−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	$0.938843\pi$
$312$	−7.35416	+	2.91786i	−0.416347	+	0.165191i
$313$	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	$0.473117\pi$
$314$	−0.139199	−	6.56986i	−0.00785547	−	0.370759i
$315$		0			0
$316$	19.7103	−	15.6376i	1.10879	−	0.879686i
$317$	10.3334	+	7.50769i	0.580384	+	0.421674i	0.838863	−	0.544343i	$-0.183221\pi$
$317$	10.3334	+	7.50769i	0.580384	+	0.421674i	−0.258478	+	0.966017i	$0.583221\pi$
$318$	−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
$322$	21.4487	−	7.47500i	1.19529	−	0.416565i
$323$	−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
$328$	−16.3588	−	4.18766i	−0.903265	−	0.231225i
$329$	−2.09513	+	1.52220i	−0.115508	+	0.0839217i
$330$		0			0
$331$	2.79298	−	3.84421i	0.153516	−	0.211297i	−0.725331	−	0.688400i	$-0.758313\pi$
$331$	2.79298	−	3.84421i	0.153516	−	0.211297i	0.878847	+	0.477103i	$0.158313\pi$
$332$	9.16335	+	6.08177i	0.502904	+	0.333780i
$333$	8.26066	+	6.00172i	0.452682	+	0.328892i
$334$	−24.2534	−	16.8479i	−1.32709	−	0.921875i
$335$		0			0
$336$	−7.94841	−	9.19043i	−0.433621	−	0.501379i
$337$	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	$0.301261\pi$
$338$	−6.81937	+	9.81683i	−0.370925	+	0.533965i
$339$	−18.9553	+	6.15894i	−1.02951	+	0.334508i
$340$		0			0
$341$	−1.89059	−	0.614289i	−0.102381	−	0.0332656i
$342$	0.753568	−	0.572275i	0.0407483	−	0.0309451i
$343$			20.0015i			1.07998i
$344$	1.75084	+	27.5122i	0.0943992	+	1.48336i
$345$		0			0
$346$	10.5211	−	3.66666i	0.565616	−	0.197121i
$347$	15.6090	−	11.3406i	0.837937	−	0.608797i	−0.0838564	−	0.996478i	$-0.526724\pi$
$347$	15.6090	−	11.3406i	0.837937	−	0.608797i	0.921794	+	0.387681i	$0.126724\pi$
$348$	−22.0754	−	6.15212i	−1.18337	−	0.329788i
$349$			33.1221i			1.77299i	0.462742	+	0.886493i	$0.346866\pi$
$349$			33.1221i			1.77299i	−0.462742	+	0.886493i	$0.653134\pi$
$350$		0			0
$351$	11.9709			0.638961
$352$	−0.533278	−	1.19390i	−0.0284238	−	0.0636349i
$353$	−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	$0.915056\pi$
$354$	−2.99292	−	8.58785i	−0.159072	−	0.456439i
$355$		0			0
$356$	11.0438	+	29.6521i	0.585318	+	1.57156i
$357$	6.92117			0.366307
$358$	18.0812	−	13.7313i	0.955623	−	0.725720i
$359$	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
$362$	−19.9200	−	13.8377i	−1.04697	−	0.727291i
$363$	4.43696	−	13.6556i	0.232880	−	0.716732i
$364$	9.51512	+	2.65174i	0.498728	+	0.138989i
$365$		0			0
$366$	3.47169	+	2.41165i	0.181468	+	0.126059i
$367$	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
$372$	22.5404	−	0.955580i	1.16866	−	0.0495445i
$373$	−0.310042	−	0.954212i	−0.0160534	−	0.0494072i	0.942709	−	0.333616i	$-0.108269\pi$
$373$	−0.310042	−	0.954212i	−0.0160534	−	0.0494072i	−0.958762	+	0.284209i	$0.908269\pi$
$374$	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
$378$	6.05024	+	17.3605i	0.311191	+	0.892927i
$379$	21.2264	+	29.2157i	1.09033	+	1.50071i	0.847616	+	0.530610i	$0.178037\pi$
$379$	21.2264	+	29.2157i	1.09033	+	1.50071i	0.242712	+	0.970098i	$0.421963\pi$
$380$		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	$-0.0894183\pi$
$384$	10.4008	+	10.5852i	0.530761	+	0.540174i
$385$		0			0
$386$	−21.1164	+	0.447404i	−1.07480	+	0.0227723i
$387$	3.85377	−	11.8607i	0.195898	−	0.602912i
$388$	15.8651	+	19.9970i	0.805428	+	1.01519i
$389$	−1.26254	+	0.410223i	−0.0640132	+	0.0207991i	−0.340849	−	0.940118i	$-0.610714\pi$
$389$	−1.26254	+	0.410223i	−0.0640132	+	0.0207991i	0.276835	+	0.960917i	$0.410714\pi$
$390$		0			0
$391$	4.88288	−	15.0280i	0.246938	−	0.759997i
$392$	−0.293998	−	4.61978i	−0.0148491	−	0.233334i
$393$		−	20.3574i		−	1.02690i
$394$	−23.5493	−	31.0096i	−1.18640	−	1.56224i
$395$		0			0
$396$	0.0250545	+	0.590990i	0.00125904	+	0.0296983i
$397$	−7.80606	+	5.67144i	−0.391775	+	0.284641i	−0.766182	−	0.642623i	$-0.777846\pi$
$397$	−7.80606	+	5.67144i	−0.391775	+	0.284641i	0.374407	+	0.927264i	$0.377846\pi$
$398$	−0.340976	−	16.0932i	−0.0170916	−	0.806681i
$399$	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	$0.405021\pi$
$402$	0.124223	+	5.86300i	0.00619566	+	0.292420i
$403$	−14.8375	+	10.7801i	−0.739110	+	0.536995i
$404$	−0.981760	−	23.1579i	−0.0488444	−	1.15215i
$405$		0			0
$406$	17.3035	+	22.7851i	0.858758	+	1.13081i
$407$			1.84462i			0.0914343i
$408$	−8.43584	+	0.536847i	−0.417636	+	0.0265779i
$409$	−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
$412$	−8.33513	−	10.5059i	−0.410642	−	0.517590i
$413$	−3.50862	+	10.7984i	−0.172648	+	0.531355i
$414$	12.5465	−	0.265829i	0.616625	−	0.0130648i
$415$		0			0
$416$	−11.8032	−	2.49401i	−0.578697	−	0.122279i
$417$	−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	$0.513338\pi$
$419$	−20.0431	+	27.5869i	−0.979168	+	1.34771i	−0.937277	+	0.348587i	$0.886662\pi$
$420$		0			0
$421$	−3.43224	−	4.72407i	−0.167277	−	0.230237i	0.717146	−	0.696923i	$-0.245448\pi$
$421$	−3.43224	−	4.72407i	−0.167277	−	0.230237i	−0.884423	+	0.466686i	$0.845448\pi$
$422$	7.37688	+	21.1671i	0.359101	+	1.03040i
$423$	−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
$428$	−15.2865	+	0.648057i	−0.738900	+	0.0313250i
$429$	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	$0.236476\pi$
$434$	−23.1326	−	16.0693i	−1.11040	−	0.771351i
$435$		0			0
$436$	13.0021	+	3.62351i	0.622688	+	0.173535i
$437$	1.12068	−	3.44909i	0.0536092	−	0.164992i
$438$	−8.40939	−	5.84168i	−0.401816	−	0.279126i
$439$	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
$442$	5.47245	−	4.15589i	0.260298	−	0.197675i
$443$	3.43488			0.163196			0.0815981	−	0.996665i	$-0.473998\pi$
$443$	3.43488			0.163196			0.0815981	+	0.996665i	$0.473998\pi$
$444$	−7.30670	−	19.6182i	−0.346761	−	0.931040i
$445$		0			0
$446$	−10.8351	−	31.0902i	−0.513059	−	1.47216i
$447$	−7.04717	−	9.69960i	−0.333320	−	0.458775i
$448$	−2.34858	−	18.3777i	−0.110960	−	0.868264i
$449$	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
$452$	−29.2743	−	8.15835i	−1.37695	−	0.383737i
$453$	−9.12084	+	6.62668i	−0.428534	+	0.311348i
$454$	5.98098	−	2.08441i	0.280701	−	0.0978263i
$455$		0			0
$456$	−1.93612	+	0.123212i	−0.0906671	+	0.00576995i
$457$		−	3.02813i		−	0.141650i	−0.997489	−	0.0708250i	$-0.977437\pi$
$457$		−	3.02813i		−	0.141650i	0.997489	−	0.0708250i	$-0.0225632\pi$
$458$	−5.74806	+	4.36520i	−0.268589	+	0.203972i
$459$	12.1636	+	3.95219i	0.567748	+	0.184472i
$460$		0			0
$461$	11.9787	−	3.89211i	0.557903	−	0.181274i	−0.0164747	−	0.999864i	$-0.505244\pi$
$461$	11.9787	−	3.89211i	0.557903	−	0.181274i	0.574377	+	0.818591i	$0.305244\pi$
$462$	−0.566528	+	0.815545i	−0.0263573	+	0.0379426i
$463$	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	$0.567541\pi$
$464$	−22.8576	−	26.4294i	−1.06114	−	1.22695i
$465$		0			0
$466$	4.06360	+	2.82283i	0.188243	+	0.130765i
$467$	18.3661	+	13.3438i	0.849883	+	0.617476i	0.925114	−	0.379690i	$-0.123969\pi$
$467$	18.3661	+	13.3438i	0.849883	+	0.617476i	−0.0752308	+	0.997166i	$0.523969\pi$
$468$	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
$472$	3.43888	−	13.4338i	0.158287	−	0.618339i
$473$	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
$478$	−27.1237	+	9.45278i	−1.24061	+	0.432360i
$479$	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
$484$	17.1510	−	13.6071i	0.779589	−	0.618506i
$485$		0			0
$486$	0.365992	+	17.2739i	0.0166017	+	0.783561i
$487$	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	$0.298124\pi$
$488$	2.37703	+	5.99107i	0.107603	+	0.271203i
$489$	−5.32394	−	16.3854i	−0.240757	−	0.740973i
$490$		0			0
$491$	−7.36748	−	2.39384i	−0.332490	−	0.108032i	0.138014	−	0.990430i	$-0.455928\pi$
$491$	−7.36748	−	2.39384i	−0.332490	−	0.108032i	−0.470504	+	0.882398i	$0.655928\pi$
$492$	−5.46637	−	14.6770i	−0.246443	−	0.661691i
$493$	19.9036			0.896411
$494$	1.25599	−	0.953823i	0.0565096	−	0.0429145i
$495$		0			0
$496$	29.4415	+	17.7917i	1.32196	+	0.798871i
$497$	−8.92171	−	12.2797i	−0.400194	−	0.550819i
$498$	0.216076	+	10.1982i	0.00968258	+	0.456994i
$499$		−	36.4452i		−	1.63151i	−0.578396	−	0.815756i	$-0.696321\pi$
$499$		−	36.4452i		−	1.63151i	0.578396	−	0.815756i	$-0.303679\pi$
$500$		0			0
$501$		−	27.3897i		−	1.22368i
$502$	6.46123	−	0.136898i	0.288379	−	0.00611004i
$503$	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	$0.707817\pi$
$504$	−2.07847	+	8.11943i	−0.0925826	+	0.361668i
$505$		0			0
$506$	1.37111	+	1.80547i	0.0609533	+	0.0802630i
$507$	−11.0863			−0.492360
$508$	−8.55293	+	3.18549i	−0.379475	+	0.141333i
$509$	−40.6350	−	13.2031i	−1.80111	−	0.585217i	−0.801200	−	0.598397i	$-0.795804\pi$
$509$	−40.6350	−	13.2031i	−1.80111	−	0.585217i	−0.999913	+	0.0131803i	$0.995804\pi$
$510$		0			0
$511$	3.95030	+	12.1578i	0.174751	+	0.537828i
$512$	4.28804	+	22.2174i	0.189506	+	0.981879i
$513$	2.79168	+	0.907072i	0.123256	+	0.0400482i
$514$	38.7958	−	0.821989i	1.71121	−	0.0362564i
$515$		0			0
$516$	−20.0306	+	15.8917i	−0.881798	+	0.699595i
$517$	−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	$0.314560\pi$
$522$	5.20206	+	14.9267i	0.227688	+	0.653325i
$523$	−10.0536	−	30.9419i	−0.439615	−	1.35300i	−0.888283	−	0.459297i	$-0.848101\pi$
$523$	−10.0536	−	30.9419i	−0.439615	−	1.35300i	0.448668	−	0.893699i	$-0.351899\pi$
$524$	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
$528$	0.627252	−	1.03797i	0.0272976	−	0.0451717i
$529$	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
$534$	−16.7433	+	24.1028i	−0.724554	+	1.04303i
$535$		0			0
$536$	−4.78577	+	7.55321i	−0.206714	+	0.326249i
$537$	20.0273	+	6.50726i	0.864242	+	0.280809i
$538$	1.77304	+	1.23166i	0.0764412	+	0.0531008i
$539$	−0.359795	+	0.116904i	−0.0154975	+	0.00503543i
$540$		0			0
$541$	−5.01695	−	1.63011i	−0.215696	−	0.0700838i	0.199176	−	0.979964i	$-0.436174\pi$
$541$	−5.01695	−	1.63011i	−0.215696	−	0.0700838i	−0.414872	+	0.909880i	$0.636174\pi$
$542$	−20.9360	−	27.5683i	−0.899276	−	1.18416i
$543$		−	22.4960i		−	0.965395i
$544$	−11.1697	−	6.43095i	−0.478898	−	0.275725i
$545$		0			0
$546$	3.01499	+	8.65119i	0.129030	+	0.370237i
$547$	−12.2753	+	8.91852i	−0.524854	+	0.381329i	−0.818429	−	0.574607i	$-0.805155\pi$
$547$	−12.2753	+	8.91852i	−0.524854	+	0.381329i	0.293575	+	0.955936i	$0.405155\pi$
$548$	28.3201	+	7.89244i	1.20978	+	0.337148i
$549$		−	2.91575i		−	0.124441i
$550$		0			0
$551$	4.56809			0.194607
$552$	−21.7339	−	13.7708i	−0.925058	−	0.586124i
$553$	−17.1246	−	23.5700i	−0.728211	−	1.00230i
$554$	−36.5875	+	12.7510i	−1.55446	+	0.541738i
$555$		0			0
$556$	−11.0626	+	4.12018i	−0.469157	+	0.174735i
$557$	21.0806			0.893213			0.446606	−	0.894731i	$-0.352632\pi$
$557$	21.0806			0.893213			0.446606	+	0.894731i	$0.352632\pi$
$558$	−9.41154	−	12.3931i	−0.398422	−	0.524640i
$559$	6.42315	−	19.7684i	0.271670	−	0.836116i
$560$		0			0
$561$	0.213470	+	0.656995i	0.00901273	+	0.0277383i
$562$	23.4463	−	33.7522i	0.989024	−	1.42375i
$563$	−5.40722	+	16.6417i	−0.227887	+	0.701365i	0.770099	+	0.637925i	$0.220207\pi$
$563$	−5.40722	+	16.6417i	−0.227887	+	0.701365i	−0.997986	+	0.0634396i	$0.979793\pi$
$564$	2.82585	+	0.787526i	0.118990	+	0.0331608i
$565$		0			0
$566$	−8.00002	+	11.5164i	−0.336266	+	0.484071i
$567$	−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	$-0.986647\pi$
$571$	−17.4500	−	24.0179i	−0.730261	−	1.00512i	0.268860	−	0.963179i	$-0.413353\pi$
$572$	0.0417589	+	0.985015i	0.00174603	+	0.0411855i
$573$	−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	$0.350460\pi$
$578$	−15.7699	+	5.49590i	−0.655940	+	0.228599i
$579$	−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
$584$	−5.75784	−	14.5120i	−0.238261	−	0.600513i
$585$		0			0
$586$	0.186400	+	8.79762i	0.00770012	+	0.363427i
$587$	−4.32742	+	13.3184i	−0.178612	+	0.549710i	−0.999780	−	0.0209758i	$-0.993323\pi$
$587$	−4.32742	+	13.3184i	−0.178612	+	0.549710i	0.821168	+	0.570686i	$0.193323\pi$
$588$	3.36349	−	2.66851i	0.138708	−	0.110047i
$589$	−4.27702	+	1.38969i	−0.176232	+	0.0572611i
$590$		0			0
$591$	11.1601	−	34.3471i	0.459063	−	1.41285i
$592$	7.25922	−	31.0843i	0.298352	−	1.27756i
$593$			10.4531i			0.429258i	0.976696	+	0.214629i	$0.0688542\pi$
$593$			10.4531i			0.429258i	−0.976696	+	0.214629i	$0.931146\pi$
$594$	−1.46134	+	1.10977i	−0.0599596	+	0.0455346i
$595$		0			0
$596$	−0.774313	−	18.2646i	−0.0317171	−	0.748148i
$597$	12.0784	−	8.77546i	0.494335	−	0.359156i
$598$	20.9114	−	0.443062i	0.855132	−	0.0181182i
$599$	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	$0.564068\pi$
$602$	31.9149	−	0.676199i	1.30075	−	0.0275598i
$603$	3.27250	−	2.37761i	0.133267	−	0.0968238i
$604$	−17.1748	+	0.728111i	−0.698833	+	0.0296264i
$605$		0			0
$606$	17.1207	−	13.0018i	0.695483	−	0.528164i
$607$		−	2.47771i		−	0.100567i	−0.998735	−	0.0502836i	$-0.983987\pi$
$607$		−	2.47771i		−	0.100567i	0.998735	−	0.0502836i	$-0.0160125\pi$
$608$	−2.56358	−	1.47597i	−0.103967	−	0.0598587i
$609$	−8.20014	+	25.2374i	−0.332287	+	1.02267i
$610$		0			0
$611$	−2.26804	+	0.736930i	−0.0917549	+	0.0298130i
$612$	3.62384	+	4.56764i	0.146485	+	0.184636i
$613$	−0.797806	+	2.45539i	−0.0322231	+	0.0991725i	−0.965875	−	0.259010i	$-0.916604\pi$
$613$	−0.797806	+	2.45539i	−0.0322231	+	0.0991725i	0.933651	+	0.358183i	$0.116604\pi$
$614$	−0.887136	−	41.8706i	−0.0358019	−	1.68976i
$615$		0			0
$616$	−1.40738	+	0.558397i	−0.0567051	+	0.0224984i
$617$	−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	−0.979855	−	0.199708i	$-0.936001\pi$
$619$	−12.1197	+	16.6813i	−0.487130	+	0.670477i	0.492726	+	0.870185i	$0.336001\pi$
$620$		0			0
$621$	22.8822	+	31.4946i	0.918229	+	1.26383i
$622$	5.73341	−	1.99813i	0.229889	−	0.0801178i
$623$	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
$628$	9.28493	−	0.393627i	0.370509	−	0.0157074i
$629$	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
$634$	−10.3055	+	14.8353i	−0.409285	+	0.589186i
$635$		0			0
$636$	3.06132	−	10.9848i	0.121389	−	0.435576i
$637$	−1.07856	+	3.31947i	−0.0427342	+	0.131522i
$638$	−1.62919	+	2.34531i	−0.0645004	+	0.0928515i
$639$	−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	$-0.0275464\pi$
$642$	−8.58249	−	11.3014i	−0.338724	−	0.446029i
$643$	−21.0042			−0.828324			−0.414162	−	0.910203i	$-0.635925\pi$
$643$	−21.0042			−0.828324			−0.414162	+	0.910203i	$0.635925\pi$
$644$	11.2114	+	30.1023i	0.441791	+	1.18620i
$645$		0			0
$646$	1.59110	−	0.554510i	0.0626012	−	0.0218169i
$647$	−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	$-0.425616\pi$
$648$	5.33517	−	8.42030i	0.209585	−	0.330781i
$649$	−1.13326			−0.0444844
$650$		0			0
$651$		−	26.1240i		−	1.02388i
$652$	7.05227	−	25.3054i	0.276188	−	0.991035i
$653$	−0.267998	+	0.194712i	−0.0104876	+	0.00761966i	−0.593017	−	0.805190i	$-0.702063\pi$
$653$	−0.267998	+	0.194712i	−0.0104876	+	0.00761966i	0.582529	+	0.812810i	$0.302063\pi$
$654$	4.11989	+	11.8216i	0.161101	+	0.462260i
$655$		0			0
$656$	5.43085	−	23.2551i	0.212039	−	0.907960i
$657$			7.06276i			0.275545i
$658$	−2.21500	−	2.91670i	−0.0863497	−	0.113705i
$659$	−2.06861	−	0.672132i	−0.0805816	−	0.0261826i	0.268449	−	0.963294i	$-0.413489\pi$
$659$	−2.06861	−	0.672132i	−0.0805816	−	0.0261826i	−0.349030	+	0.937111i	$0.613489\pi$
$660$		0			0
$661$	14.4168	−	4.68430i	0.560748	−	0.182198i	−0.0149097	−	0.999889i	$-0.504746\pi$
$661$	14.4168	−	4.68430i	0.560748	−	0.182198i	0.575658	+	0.817691i	$0.304746\pi$
$662$	5.51899	+	3.83383i	0.214501	+	0.149006i
$663$	6.06144	+	1.96948i	0.235407	+	0.0764883i
$664$	−8.32448	+	13.1382i	−0.323052	+	0.509862i
$665$		0			0
$666$	−8.23835	+	11.8595i	−0.319230	+	0.459547i
$667$	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
$672$	12.7562	−	11.5135i	0.492081	−	0.444144i
$673$	−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	$-0.958211\pi$
$677$	−6.92852	−	21.3238i	−0.266285	−	0.819540i	0.725110	−	0.688633i	$-0.241789\pi$
$678$	−9.27595	−	26.6163i	−0.356241	−	1.02219i
$679$	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	−0.0500406	−	0.998747i	$-0.515935\pi$
$683$	−26.5359	−	19.2795i	−1.01537	−	0.737709i	−0.965328	+	0.261038i	$0.915935\pi$
$684$	0.831712	+	1.04832i	0.0318013	+	0.0400836i
$685$		0			0
$686$	−28.2801	+	0.599186i	−1.07974	+	0.0228770i
$687$	−6.36672	−	2.06867i	−0.242905	−	0.0789247i
$688$	−38.8469	+	3.29969i	−1.48103	+	0.125800i
$689$	2.86464	+	8.81645i	0.109134	+	0.335880i
$690$		0			0
$691$	−35.7160	−	11.6048i	−1.35870	−	0.441468i	−0.463090	−	0.886311i	$-0.653259\pi$
$691$	−35.7160	−	11.6048i	−1.35870	−	0.441468i	−0.895609	+	0.444843i	$0.853259\pi$
$692$	5.49945	+	14.7658i	0.209058	+	0.561313i
$693$	0.684949			0.0260190
$694$	16.5021	+	21.7298i	0.626410	+	0.824853i
$695$		0			0
$696$	8.03715	−	31.3966i	0.304647	−	1.19009i
$697$	7.99547	+	11.0048i	0.302850	+	0.416837i
$698$	−46.8312	+	0.992240i	−1.77259	+	0.0375568i
$699$			4.58909i			0.173575i
$700$		0			0
$701$			23.3655i			0.882503i	0.897383	+	0.441252i	$0.145465\pi$
$701$			23.3655i			0.882503i	−0.897383	+	0.441252i	$0.854535\pi$
$702$	0.358614	+	16.9257i	0.0135350	+	0.638818i
$703$	2.45284	+	3.37605i	0.0925108	+	0.127330i
$704$	1.67207	−	0.789765i	0.0630185	−	0.0297654i
$705$		0			0
$706$	14.9664	−	11.3658i	0.563267	−	0.427756i
$707$	−26.8397			−1.00941
$708$	12.0527	−	4.48895i	0.452967	−	0.168705i
$709$	−12.3034	−	3.99762i	−0.462064	−	0.150134i	0.0687289	−	0.997635i	$-0.478106\pi$
$709$	−12.3034	−	3.99762i	−0.462064	−	0.150134i	−0.530793	+	0.847502i	$0.678106\pi$
$710$		0			0
$711$	−4.97406	−	15.3086i	−0.186542	−	0.574116i
$712$	−41.5942	+	16.5030i	−1.55881	+	0.618476i
$713$	−56.7231	−	18.4305i	−2.12430	−	0.690226i
$714$	0.207337	+	9.78581i	0.00775941	+	0.366225i
$715$		0			0
$716$	19.9562	+	25.1537i	0.745800	+	0.940036i
$717$	−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
$722$	−25.0081	+	8.71550i	−0.930707	+	0.324357i
$723$	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	$0.426434\pi$
$728$	−3.46424	+	13.5328i	−0.128393	+	0.501560i
$729$	−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	0.375433	−	0.926849i	$-0.377494\pi$
$733$	−10.5599	−	7.67219i	−0.390037	−	0.283379i	−0.765471	+	0.643471i	$0.777494\pi$
$734$	10.1472	+	7.04885i	0.374539	+	0.260178i
$735$		0			0
$736$	−15.9999	−	35.8204i	−0.589764	−	1.32036i
$737$	0.694989	+	0.225815i	0.0256002	+	0.00831802i
$738$	−6.16337	+	8.87248i	−0.226877	+	0.326600i
$739$	−29.8146	+	9.68735i	−1.09675	+	0.356355i	−0.800850	−	0.598865i	$-0.795619\pi$
$739$	−29.8146	+	9.68735i	−1.09675	+	0.356355i	−0.295898	+	0.955220i	$0.595619\pi$
$740$		0			0
$741$	1.39117	+	0.452018i	0.0511058	+	0.0166053i
$742$	−11.3380	+	8.61028i	−0.416230	+	0.316093i
$743$		−	28.1541i		−	1.03287i	−0.856325	−	0.516437i	$-0.827258\pi$
$743$		−	28.1541i		−	1.03287i	0.856325	−	0.516437i	$-0.172742\pi$
$744$	2.02633	+	31.8411i	0.0742890	+	1.16735i
$745$		0			0
$746$	1.33987	−	0.466953i	0.0490561	−	0.0170964i
$747$	5.69226	−	4.13567i	0.208269	−	0.151316i
$748$	−0.282771	+	1.01465i	−0.0103391	+	0.0370994i
$749$			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	$0.576080\pi$
$752$	2.92598	+	3.38320i	0.106700	+	0.123373i
$753$	3.52324	+	4.84932i	0.128394	+	0.176719i
$754$	8.67038	+	24.8787i	0.315757	+	0.906028i
$755$		0			0
$756$	−24.3647	+	9.07449i	−0.886135	+	0.330036i
$757$	16.0395			0.582965			0.291482	−	0.956576i	$-0.405851\pi$
$757$	16.0395			0.582965			0.291482	+	0.956576i	$0.405851\pi$
$758$	−40.6720	+	30.8872i	−1.47728	+	1.12187i
$759$	−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	$0.834286\pi$
$762$	−6.95228	−	4.82948i	−0.251855	−	0.174954i
$763$	4.82977	−	14.8645i	0.174849	−	0.538131i
$764$	1.60470	−	5.75806i	0.0580558	−	0.208319i
$765$		0			0
$766$	35.8703	+	24.9177i	1.29605	+	0.900313i
$767$	−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
$772$	−1.26517	−	29.8430i	−0.0455343	−	1.07407i
$773$	−0.759693	−	2.33810i	−0.0273243	−	0.0840955i	0.936464	−	0.350763i	$-0.114078\pi$
$773$	−0.759693	−	2.33810i	−0.0273243	−	0.0840955i	−0.963789	+	0.266667i	$0.914078\pi$
$774$	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
$778$	−0.617835	−	1.77281i	−0.0221505	−	0.0635582i
$779$	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
$784$	6.52309	−	0.554077i	0.232967	−	0.0197885i
$785$		0			0
$786$	28.7833	−	0.609848i	1.02667	−	0.0217526i
$787$	−9.27720	+	28.5523i	−0.330697	+	1.01778i	0.638107	+	0.769948i	$0.279718\pi$
$787$	−9.27720	+	28.5523i	−0.330697	+	1.01778i	−0.968803	+	0.247831i	$0.920282\pi$
$788$	43.1389	−	34.2253i	1.53676	−	1.21922i
$789$	16.0606	−	5.21842i	0.571774	−	0.185781i
$790$		0			0
$791$	−10.8742	+	33.4675i	−0.386644	+	1.18997i
$792$	−0.834847	+	0.0531287i	−0.0296650	+	0.00188785i
$793$		−	4.85974i		−	0.172575i
$794$	−8.25267	−	10.8671i	−0.292876	−	0.385658i
$795$		0			0
$796$	22.7439	−	0.964210i	0.806138	−	0.0341755i
$797$	−17.9888	+	13.0696i	−0.637196	+	0.462950i	−0.858886	−	0.512167i	$-0.828843\pi$
$797$	−17.9888	+	13.0696i	−0.637196	+	0.462950i	0.221690	+	0.975117i	$0.428843\pi$
$798$	0.0475863	+	2.24595i	0.00168454	+	0.0795059i
$799$	−2.54783			−0.0901359
$800$		0			0
$801$	20.2432			0.715257
$802$	0.352706	+	16.6469i	0.0124545	+	0.587821i
$803$	−1.03224	+	0.749967i	−0.0364270	+	0.0264658i
$804$	−8.28595	+	0.351276i	−0.292223	+	0.0123885i
$805$		0			0
$806$	−15.6864	−	20.6558i	−0.552531	−	0.727569i
$807$			2.00232i			0.0704852i
$808$	32.7135	−	2.08185i	1.15086	−	0.0732392i
$809$	−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	−0.929853	−	0.367932i	$-0.880066\pi$
$811$	−41.7447	+	13.5637i	−1.46585	+	0.476285i	−0.536002	+	0.844217i	$0.680066\pi$
$812$	−31.6974	+	25.1479i	−1.11236	+	0.882519i
$813$	9.92157	−	30.5355i	0.347965	−	1.07093i
$814$	−2.60810	+	0.0552592i	−0.0914138	+	0.00193684i
$815$		0			0
$816$	−1.01176	−	11.9113i	−0.0354187	−	0.416980i
$817$	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	0.995668	−	0.0929790i	$-0.0296390\pi$
$821$	17.1793	+	23.6453i	0.599561	+	0.825225i	−0.396107	+	0.918205i	$0.629639\pi$
$822$	8.97361	+	25.7488i	0.312991	+	0.898092i
$823$	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	$-0.932513\pi$
$827$	−8.92624	−	27.4721i	−0.310396	−	0.955300i	0.667213	−	0.744867i	$-0.267487\pi$
$828$	0.751709	+	17.7314i	0.0261237	+	0.616210i
$829$	21.9589	+	30.2238i	0.762663	+	1.04972i	0.996988	+	0.0775572i	$0.0247120\pi$
$829$	21.9589	+	30.2238i	0.762663	+	1.04972i	−0.234325	+	0.972158i	$0.575288\pi$
$830$		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
$834$	−8.99224	−	6.24657i	−0.311376	−	0.216301i
$835$		0			0
$836$	−0.0648990	+	0.232874i	−0.00224458	+	0.00805413i
$837$	14.9176	−	45.9115i	0.515627	−	1.58694i
$838$	−39.6055	−	27.5124i	−1.36815	−	0.950400i
$839$	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
$842$	6.57653	−	4.99435i	0.226642	−	0.172117i
$843$	38.1169			1.31282
$844$	−29.7071	+	11.0643i	−1.02256	+	0.380847i
$845$		0			0
$846$	−0.665910	−	1.91075i	−0.0228944	−	0.0656930i
$847$	−14.9010	−	20.5094i	−0.512004	−	0.704713i
$848$	13.1514	−	11.3741i	0.451620	−	0.390587i
$849$	−13.0057			−0.446354
$850$		0			0
$851$			55.3440i			1.89717i
$852$	−4.61574	+	16.5625i	−0.158132	+	0.567420i
$853$	−13.5745	+	9.86242i	−0.464780	+	0.337683i	−0.795404	−	0.606080i	$-0.792741\pi$
$853$	−13.5745	+	9.86242i	−0.464780	+	0.337683i	0.330623	+	0.943763i	$0.392741\pi$
$854$	7.04770	−	2.45617i	0.241167	−	0.0840483i
$855$		0			0
$856$	−1.37422	−	21.5941i	−0.0469700	−	0.738071i
$857$			12.0516i			0.411675i	0.978586	+	0.205837i	$0.0659918\pi$
$857$			12.0516i			0.411675i	−0.978586	+	0.205837i	$0.934008\pi$
$858$	−0.728226	+	0.553029i	−0.0248612	+	0.0188801i
$859$	53.1530	+	17.2704i	1.81356	+	0.589260i	0.999969	+	0.00781665i	$0.00248814\pi$
$859$	53.1530	+	17.2704i	1.81356	+	0.589260i	0.813587	+	0.581443i	$0.197512\pi$
$860$		0			0
$861$	−17.2481	+	5.60423i	−0.587812	+	0.190992i
$862$	3.30060	−	4.75137i	0.112419	−	0.161832i
$863$	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	$0.438382\pi$
$864$	28.9929	−	12.9503i	0.986360	−	0.440577i
$865$		0			0
$866$	−5.52695	−	3.83936i	−0.187813	−	0.130467i
$867$	−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
$872$	−4.73377	+	18.4922i	−0.160306	+	0.626224i
$873$	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	0.921966	−	0.387271i	$-0.126582\pi$
$877$	−1.52668	−	4.69863i	−0.0515522	−	0.158661i	−0.973518	+	0.228609i	$0.926582\pi$
$878$	−2.34056	+	0.815701i	−0.0789902	+	0.0275286i
$879$	−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	0.611747	−	0.791053i	$-0.290467\pi$
$883$	1.43973	+	1.04603i	0.0484509	+	0.0352017i	−0.563296	+	0.826255i	$0.690467\pi$
$884$	6.03993	+	7.61297i	0.203145	+	0.256052i
$885$		0			0
$886$	0.102899	+	4.85657i	0.00345695	+	0.163159i
$887$	−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	$0.873200\pi$
$888$	27.5193	−	10.9186i	0.923486	−	0.366405i
$889$	3.26583	+	10.0512i	0.109532	+	0.337106i
$890$		0			0
$891$	−0.774771	−	0.251738i	−0.0259558	−	0.00843355i
$892$	43.6338	−	16.2511i	1.46097	−	0.544128i
$893$	−0.584756			−0.0195681
$894$	13.5031	−	10.2545i	0.451612	−	0.342963i
$895$		0			0
$896$	25.9138	−	3.87119i	0.865718	−	0.129327i
$897$	11.4028	+	15.6946i	0.380728	+	0.524027i
$898$	0.166033	+	7.83632i	0.00554058	+	0.261501i
$899$		−	75.1261i		−	2.50560i
$900$		0			0
$901$			9.90409i			0.329953i
$902$	−1.95120	+	0.0413412i	−0.0649679	+	0.00137651i
$903$	17.4028	+	23.9530i	0.579130	+	0.797104i
$904$	10.6581	−	41.6352i	0.354483	−	1.38477i
$905$		0			0
$906$	−9.64267	−	12.6974i	−0.320356	−	0.421843i
$907$	−22.9525			−0.762127			−0.381063	−	0.924549i	$-0.624442\pi$
$907$	−22.9525			−0.762127			−0.381063	+	0.924549i	$0.624442\pi$
$908$	3.12631	+	8.39405i	0.103750	+	0.278566i
$909$	−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	$0.873378\pi$
$912$	−0.232210	−	2.73378i	−0.00768924	−	0.0905246i
$913$	1.20888	+	0.392788i	0.0400080	+	0.0129994i
$914$	4.28146	−	0.0907138i	0.141618	−	0.00300054i
$915$		0			0
$916$	−6.34413	−	7.99640i	−0.209616	−	0.264208i
$917$	−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
$922$	5.86188	+	16.8200i	0.193051	+	0.553937i
$923$	−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
$928$	36.6837	−	33.1101i	1.20420	−	1.08689i
$929$	−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
$934$	−18.3165	+	26.3675i	−0.599335	+	0.862772i
$935$		0			0
$936$	−4.13075	+	6.51941i	−0.135018	+	0.213094i
$937$	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	$0.403600\pi$
$938$	8.50364	+	5.90715i	0.277654	+	0.192875i
$939$	−17.1327	+	5.56674i	−0.559103	+	0.181664i
$940$		0			0
$941$	−0.202380	−	0.0657573i	−0.00659741	−	0.00214363i	0.305716	−	0.952123i	$-0.401104\pi$
$941$	−0.202380	−	0.0657573i	−0.00659741	−	0.00214363i	−0.312314	+	0.949979i	$0.601104\pi$
$942$	5.21295	+	6.86439i	0.169847	+	0.223654i
$943$			41.4046i			1.34832i
$944$	19.0970	+	4.45978i	0.621553	+	0.145153i
$945$		0			0
$946$	1.04854	+	3.00868i	0.0340911	+	0.0978206i
$947$	−4.78799	+	3.47868i	−0.155589	+	0.113042i	−0.662856	−	0.748747i	$-0.730656\pi$
$947$	−4.78799	+	3.47868i	−0.155589	+	0.113042i	0.507267	+	0.861789i	$0.330656\pi$
$948$	−8.85957	+	31.7904i	−0.287745	+	1.03251i
$949$			11.7717i			0.382124i
$950$		0			0
$951$	−16.7538			−0.543279
$952$	−7.98784	+	12.6069i	−0.258887	+	0.408592i
$953$	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	$0.484021\pi$
$954$	−7.42759	+	2.58856i	−0.240477	+	0.0838079i
$955$		0			0
$956$	−14.1778	−	38.0669i	−0.458543	−	1.23117i
$957$	−2.64859			−0.0856169
$958$	5.90353	+	7.77373i	0.190734	+	0.251158i
$959$	10.5198	−	32.3766i	0.339702	−	1.04550i
$960$		0			0
$961$	13.2751	+	40.8565i	0.428228	+	1.31795i
$962$	−13.7310	+	19.7665i	−0.442706	+	0.637298i
$963$	−3.02479	+	9.30935i	−0.0974725	+	0.299989i
$964$	−10.3999	+	37.3176i	−0.334959	+	1.20192i
$965$		0			0
$966$	−16.9975	+	24.4687i	−0.546885	+	0.787269i
$967$	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	0.577164	−	0.816628i	$-0.304159\pi$
$971$	−11.7741	−	16.2057i	−0.377850	−	0.520065i	−0.955013	+	0.296563i	$0.904159\pi$
$972$	−24.4126	+	1.03495i	−0.783033	+	0.0331960i
$973$	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	$0.132834\pi$
$978$	23.0078	−	8.01835i	0.735707	−	0.256399i
$979$	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	$0.0350142\pi$
$984$	20.5880	−	8.16856i	0.656322	−	0.260404i
$985$		0			0
$986$	0.596251	+	28.1416i	0.0189885	+	0.896210i
$987$	1.04969	−	3.23062i	0.0334120	−	0.102832i
$988$	1.38623	+	1.74726i	0.0441019	+	0.0555878i
$989$	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	$0.0245457\pi$
$992$	−24.2736	+	42.1602i	−0.770689	+	1.33859i
$993$			6.23268i			0.197788i
$994$	17.0949	−	12.9822i	0.542218	−	0.411772i
$995$		0			0
$996$	−14.4128	+	0.611017i	−0.456686	+	0.0193608i
$997$	−21.0204	+	15.2722i	−0.665723	+	0.483676i	−0.868591	−	0.495530i	$-0.834974\pi$
$997$	−21.0204	+	15.2722i	−0.665723	+	0.483676i	0.202868	+	0.979206i	$0.434974\pi$
$998$	51.5298	−	1.09179i	1.63115	−	0.0345600i
$999$	−44.7952			−1.41726

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.0299570 + 1.41390i) q^{2} +(-1.06117 + 0.770982i) q^{3} +(-1.99821 + 0.0847122i) q^{4} +(-1.12188 - 1.47728i) q^{6} +2.31589i q^{7} +(-0.179635 - 2.82272i) q^{8} +(-0.395392 + 1.21689i) q^{9} +O(q^{10})\)	\(q+(0.0299570 + 1.41390i) q^{2} +(-1.06117 + 0.770982i) q^{3} +(-1.99821 + 0.0847122i) q^{4} +(-1.12188 - 1.47728i) q^{6} +2.31589i q^{7} +(-0.179635 - 2.82272i) q^{8} +(-0.395392 + 1.21689i) q^{9} +(-0.219837 + 0.0714294i) q^{11} +(2.05511 - 1.63047i) q^{12} +(-0.659008 + 2.02822i) q^{13} +(-3.27443 + 0.0693772i) q^{14} +(3.98565 - 0.338545i) 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} +(-0.107579 - 0.308687i) 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} +(-0.196184 - 4.62763i) 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} +(-2.64634 - 1.83831i) q^{34} +(0.686988 - 2.46509i) q^{36} +(2.46601 - 7.58959i) q^{37} +(-0.607364 - 0.421912i) q^{38} +(-0.864403 - 2.66036i) q^{39} +(1.84490 - 5.67801i) q^{41} +(3.42122 - 2.59815i) q^{42} -9.74670 q^{43} +(0.433228 - 0.161353i) q^{44} +(-3.22770 - 9.26151i) q^{46} +(0.657286 + 0.904676i) q^{47} +(-3.96842 + 3.43211i) q^{48} +1.63664 q^{49} -2.98855i q^{51} +(1.14502 - 4.10862i) q^{52} +(3.51671 - 2.55504i) q^{53} +(7.49624 - 2.61249i) q^{54} +(6.53711 - 0.416014i) q^{56} -0.685906i q^{57} +(9.83860 - 7.47163i) q^{58} +(4.66275 + 1.51502i) q^{59} +(-2.16726 + 0.704186i) q^{61} +(-6.93871 + 9.98861i) q^{62} +(-2.81819 - 0.915685i) q^{63} +(-7.93546 + 1.01411i) q^{64} +(0.352152 + 0.244626i) 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} +(3.50596 + 0.897484i) 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} +(3.73557 - 1.30187i) 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} +(3.77600 + 4.75942i) q^{84} +(-0.291982 - 13.7808i) q^{86} +(10.8975 + 3.54081i) q^{87} +(0.241115 + 0.607706i) q^{88} +(-4.88895 - 15.0466i) q^{89} +(-4.69713 - 1.52619i) q^{91} +(12.9981 - 4.84108i) q^{92} -11.2803 q^{93} +(-1.25943 + 0.956435i) q^{94} +(-4.97154 - 5.50812i) q^{96} +(-7.50193 - 10.3255i) q^{97} +(0.0490290 + 2.31405i) 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

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