LMFDB - Embedded newform 1000.2.t.b.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	1000.101
Dual form			1000.2.t.b.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41390 - 0.0299570i) q^{2} +(0.770982 - 1.06117i) q^{3} +(1.99821 + 0.0847122i) q^{4} +(-1.12188 + 1.47728i) q^{6} -2.31589 q^{7} +(-2.82272 - 0.179635i) q^{8} +(0.395392 + 1.21689i) q^{9} +O(q^{10})$	\(q+(-1.41390 - 0.0299570i) q^{2} +(0.770982 - 1.06117i) q^{3} +(1.99821 + 0.0847122i) q^{4} +(-1.12188 + 1.47728i) q^{6} -2.31589 q^{7} +(-2.82272 - 0.179635i) q^{8} +(0.395392 + 1.21689i) q^{9} +(-0.219837 - 0.0714294i) q^{11} +(1.63047 - 2.05511i) q^{12} +(2.02822 - 0.659008i) q^{13} +(3.27443 + 0.0693772i) q^{14} +(3.98565 + 0.338545i) q^{16} +(-1.84329 + 1.33923i) q^{17} +(-0.522589 - 1.73240i) q^{18} +(0.307368 + 0.423055i) q^{19} +(-1.78551 + 2.45754i) q^{21} +(0.308687 + 0.107579i) q^{22} +(2.14309 - 6.59576i) q^{23} +(-2.36689 + 2.85688i) q^{24} +(-2.88743 + 0.871009i) q^{26} +(5.33859 + 1.73461i) q^{27} +(-4.62763 - 0.196184i) q^{28} +(5.13469 - 7.06729i) q^{29} +(6.95750 - 5.05492i) q^{31} +(-5.62515 - 0.598065i) q^{32} +(-0.245289 + 0.178213i) q^{33} +(2.64634 - 1.83831i) q^{34} +(0.686988 + 2.46509i) q^{36} +(7.58959 - 2.46601i) q^{37} +(-0.421912 - 0.607364i) q^{38} +(0.864403 - 2.66036i) q^{39} +(1.84490 + 5.67801i) q^{41} +(2.59815 - 3.42122i) q^{42} -9.74670i q^{43} +(-0.433228 - 0.161353i) q^{44} +(-3.22770 + 9.26151i) q^{46} +(-0.904676 - 0.657286i) q^{47} +(3.43211 - 3.96842i) q^{48} -1.63664 q^{49} +2.98855i q^{51} +(4.10862 - 1.14502i) q^{52} +(-2.55504 + 3.51671i) q^{53} +(-7.49624 - 2.61249i) q^{54} +(6.53711 + 0.416014i) q^{56} +0.685906 q^{57} +(-7.47163 + 9.83860i) q^{58} +(-4.66275 + 1.51502i) q^{59} +(-2.16726 - 0.704186i) q^{61} +(-9.98861 + 6.93871i) q^{62} +(-0.915685 - 2.81819i) q^{63} +(7.93546 + 1.01411i) q^{64} +(0.352152 - 0.244626i) q^{66} +(1.85821 + 2.55761i) q^{67} +(-3.79672 + 2.51990i) q^{68} +(-5.34690 - 7.35938i) q^{69} +(-5.30236 - 3.85239i) q^{71} +(-0.897484 - 3.50596i) q^{72} +(-1.70573 + 5.24971i) q^{73} +(-10.8048 + 3.25932i) q^{74} +(0.578346 + 0.871389i) q^{76} +(0.509119 + 0.165423i) q^{77} +(-1.30187 + 3.73557i) q^{78} +(10.1775 + 7.39438i) q^{79} +(2.85122 - 2.07153i) q^{81} +(-2.43840 - 8.08339i) q^{82} +(-3.23222 - 4.44876i) q^{83} +(-3.77600 + 4.75942i) q^{84} +(-0.291982 + 13.7808i) q^{86} +(-3.54081 - 10.8975i) q^{87} +(0.607706 + 0.241115i) q^{88} +(4.88895 - 15.0466i) q^{89} +(-4.69713 + 1.52619i) q^{91} +(4.84108 - 12.9981i) q^{92} -11.2803i q^{93} +(1.25943 + 0.956435i) q^{94} +(-4.97154 + 5.50812i) q^{96} +(10.3255 + 7.50193i) q^{97} +(2.31405 + 0.0490290i) q^{98} -0.295760i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.41390	−	0.0299570i	−0.999776	−	0.0211828i
$2$	−1.41390	−	0.0299570i	−0.999776	−	0.0211828i
$3$	0.770982	−	1.06117i	0.445127	−	0.612664i	−0.526215	−	0.850351i	$-0.676389\pi$
$3$	0.770982	−	1.06117i	0.445127	−	0.612664i	0.971342	+	0.237687i	$0.0763893\pi$
$4$	1.99821	+	0.0847122i	0.999103	+	0.0423561i
$5$		0			0
$5$		0			0
$6$	−1.12188	+	1.47728i	−0.458005	+	0.603098i
$7$	−2.31589			−0.875325			−0.437662	−	0.899139i	$-0.644194\pi$
$7$	−2.31589			−0.875325			−0.437662	+	0.899139i	$0.644194\pi$
$8$	−2.82272	−	0.179635i	−0.997981	−	0.0635104i
$9$	0.395392	+	1.21689i	0.131797	+	0.405630i
$10$		0			0
$11$	−0.219837	−	0.0714294i	−0.0662834	−	0.0215368i	0.275688	−	0.961247i	$-0.411094\pi$
$11$	−0.219837	−	0.0714294i	−0.0662834	−	0.0215368i	−0.341971	+	0.939711i	$0.611094\pi$
$12$	1.63047	−	2.05511i	0.470677	−	0.593261i
$13$	2.02822	−	0.659008i	0.562526	−	0.182776i	−0.0139312	−	0.999903i	$-0.504435\pi$
$13$	2.02822	−	0.659008i	0.562526	−	0.182776i	0.576458	+	0.817127i	$0.304435\pi$
$14$	3.27443	+	0.0693772i	0.875128	+	0.0185418i
$15$		0			0
$16$	3.98565	+	0.338545i	0.996412	+	0.0846362i
$17$	−1.84329	+	1.33923i	−0.447063	+	0.324810i	−0.788435	−	0.615118i	$-0.789108\pi$
$17$	−1.84329	+	1.33923i	−0.447063	+	0.324810i	0.341372	+	0.939928i	$0.389108\pi$
$18$	−0.522589	−	1.73240i	−0.123175	−	0.408331i
$19$	0.307368	+	0.423055i	0.0705150	+	0.0970555i	0.842818	−	0.538199i	$-0.180895\pi$
$19$	0.307368	+	0.423055i	0.0705150	+	0.0970555i	−0.772303	+	0.635255i	$0.780895\pi$
$20$		0			0
$21$	−1.78551	+	2.45754i	−0.389630	+	0.536280i
$22$	0.308687	+	0.107579i	0.0658123	+	0.0229360i
$23$	2.14309	−	6.59576i	0.446865	−	1.37531i	−0.433560	−	0.901125i	$-0.642743\pi$
$23$	2.14309	−	6.59576i	0.446865	−	1.37531i	0.880425	−	0.474185i	$-0.157257\pi$
$24$	−2.36689	+	2.85688i	−0.483139	+	0.583157i
$25$		0			0
$26$	−2.88743	+	0.871009i	−0.566272	+	0.170819i
$27$	5.33859	+	1.73461i	1.02741	+	0.333826i
$28$	−4.62763	−	0.196184i	−0.874539	−	0.0370754i
$29$	5.13469	−	7.06729i	0.953487	−	1.31236i	0.00352661	−	0.999994i	$-0.498877\pi$
$29$	5.13469	−	7.06729i	0.953487	−	1.31236i	0.949961	−	0.312369i	$-0.101123\pi$
$30$		0			0
$31$	6.95750	−	5.05492i	1.24960	−	0.907890i	0.251405	−	0.967882i	$-0.419107\pi$
$31$	6.95750	−	5.05492i	1.24960	−	0.907890i	0.998199	+	0.0599915i	$0.0191074\pi$
$32$	−5.62515	−	0.598065i	−0.994396	−	0.105724i
$33$	−0.245289	+	0.178213i	−0.0426993	+	0.0310228i
$34$	2.64634	−	1.83831i	0.453843	−	0.315267i
$35$		0			0
$36$	0.686988	+	2.46509i	0.114498	+	0.410849i
$37$	7.58959	−	2.46601i	1.24772	−	0.405409i	0.390617	−	0.920553i	$-0.372262\pi$
$37$	7.58959	−	2.46601i	1.24772	−	0.405409i	0.857104	+	0.515144i	$0.172262\pi$
$38$	−0.421912	−	0.607364i	−0.0684432	−	0.0985275i
$39$	0.864403	−	2.66036i	0.138415	−	0.425998i
$40$		0			0
$41$	1.84490	+	5.67801i	0.288125	+	0.886756i	0.985445	+	0.169996i	$0.0543756\pi$
$41$	1.84490	+	5.67801i	0.288125	+	0.886756i	−0.697320	+	0.716760i	$0.745624\pi$
$42$	2.59815	−	3.42122i	0.400903	−	0.527906i
$43$		−	9.74670i		−	1.48636i	−0.669093	−	0.743179i	$-0.733317\pi$
$43$		−	9.74670i		−	1.48636i	0.669093	−	0.743179i	$-0.266683\pi$
$44$	−0.433228	−	0.161353i	−0.0653117	−	0.0243249i
$45$		0			0
$46$	−3.22770	+	9.26151i	−0.475898	+	1.36554i
$47$	−0.904676	−	0.657286i	−0.131961	−	0.0958750i	0.519847	−	0.854259i	$-0.325989\pi$
$47$	−0.904676	−	0.657286i	−0.131961	−	0.0958750i	−0.651807	+	0.758384i	$0.725989\pi$
$48$	3.43211	−	3.96842i	0.495383	−	0.572792i
$49$	−1.63664			−0.233806
$50$		0			0
$51$			2.98855i			0.418481i
$52$	4.10862	−	1.14502i	0.569763	−	0.158785i
$53$	−2.55504	+	3.51671i	−0.350962	+	0.483057i	−0.947603	−	0.319451i	$-0.896502\pi$
$53$	−2.55504	+	3.51671i	−0.350962	+	0.483057i	0.596641	+	0.802508i	$0.296502\pi$
$54$	−7.49624	−	2.61249i	−1.02011	−	0.355515i
$55$		0			0
$56$	6.53711	+	0.416014i	0.873558	+	0.0555922i
$57$	0.685906			0.0908505
$58$	−7.47163	+	9.83860i	−0.981073	+	1.29187i
$59$	−4.66275	+	1.51502i	−0.607038	+	0.197239i	−0.596377	−	0.802705i	$-0.703394\pi$
$59$	−4.66275	+	1.51502i	−0.607038	+	0.197239i	−0.0106611	+	0.999943i	$0.503394\pi$
$60$		0			0
$61$	−2.16726	−	0.704186i	−0.277490	−	0.0901618i	0.166966	−	0.985963i	$-0.446603\pi$
$61$	−2.16726	−	0.704186i	−0.277490	−	0.0901618i	−0.444456	+	0.895801i	$0.646603\pi$
$62$	−9.98861	+	6.93871i	−1.26856	+	0.881217i
$63$	−0.915685	−	2.81819i	−0.115365	−	0.355058i
$64$	7.93546	+	1.01411i	0.991933	+	0.126764i
$65$		0			0
$66$	0.352152	−	0.244626i	0.0433469	−	0.0301114i
$67$	1.85821	+	2.55761i	0.227017	+	0.312462i	0.907297	−	0.420490i	$-0.138142\pi$
$67$	1.85821	+	2.55761i	0.227017	+	0.312462i	−0.680280	+	0.732952i	$0.738142\pi$
$68$	−3.79672	+	2.51990i	−0.460419	+	0.305583i
$69$	−5.34690	−	7.35938i	−0.643692	−	0.885966i
$70$		0			0
$71$	−5.30236	−	3.85239i	−0.629274	−	0.457194i	0.226875	−	0.973924i	$-0.427149\pi$
$71$	−5.30236	−	3.85239i	−0.629274	−	0.457194i	−0.856149	+	0.516730i	$0.827149\pi$
$72$	−0.897484	−	3.50596i	−0.105769	−	0.413182i
$73$	−1.70573	+	5.24971i	−0.199641	+	0.614432i	0.800250	+	0.599667i	$0.204700\pi$
$73$	−1.70573	+	5.24971i	−0.199641	+	0.614432i	−0.999891	+	0.0147656i	$0.995300\pi$
$74$	−10.8048	+	3.25932i	−1.25603	+	0.378888i
$75$		0			0
$76$	0.578346	+	0.871389i	0.0663408	+	0.0999552i
$77$	0.509119	+	0.165423i	0.0580195	+	0.0188517i
$78$	−1.30187	+	3.73557i	−0.147408	+	0.422971i
$79$	10.1775	+	7.39438i	1.14506	+	0.831933i	0.987816	−	0.155628i	$-0.0497400\pi$
$79$	10.1775	+	7.39438i	1.14506	+	0.831933i	0.157241	+	0.987560i	$0.449740\pi$
$80$		0			0
$81$	2.85122	−	2.07153i	0.316802	−	0.230170i
$82$	−2.43840	−	8.08339i	−0.269276	−	0.892661i
$83$	−3.23222	−	4.44876i	−0.354782	−	0.488315i	0.593904	−	0.804536i	$-0.297586\pi$
$83$	−3.23222	−	4.44876i	−0.354782	−	0.488315i	−0.948686	+	0.316221i	$0.897586\pi$
$84$	−3.77600	+	4.75942i	−0.411995	+	0.519296i
$85$		0			0
$86$	−0.291982	+	13.7808i	−0.0314852	+	1.48602i
$87$	−3.54081	−	10.8975i	−0.379615	−	1.16834i
$88$	0.607706	+	0.241115i	0.0647817	+	0.0257030i
$89$	4.88895	−	15.0466i	0.518227	−	1.59494i	−0.259105	−	0.965849i	$-0.583427\pi$
$89$	4.88895	−	15.0466i	0.518227	−	1.59494i	0.777332	−	0.629091i	$-0.216573\pi$
$90$		0			0
$91$	−4.69713	+	1.52619i	−0.492393	+	0.159988i
$92$	4.84108	−	12.9981i	0.504717	−	1.35515i
$93$		−	11.2803i		−	1.16971i
$94$	1.25943	+	0.956435i	0.129900	+	0.0986487i
$95$		0			0
$96$	−4.97154	+	5.50812i	−0.507405	+	0.562170i
$97$	10.3255	+	7.50193i	1.04840	+	0.761706i	0.971907	−	0.235364i	$-0.0756283\pi$
$97$	10.3255	+	7.50193i	1.04840	+	0.761706i	0.0764911	+	0.997070i	$0.475628\pi$
$98$	2.31405	+	0.0490290i	0.233754	+	0.00495267i
$99$		−	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	$-0.195618\pi$
$102$	0.0895281	−	4.22550i	0.00886461	−	0.418387i
$103$	5.42478	+	3.94133i	0.534519	+	0.388351i	0.822045	−	0.569422i	$-0.192833\pi$
$103$	5.42478	+	3.94133i	0.534519	+	0.388351i	−0.287526	+	0.957773i	$0.592833\pi$
$104$	−5.84346	+	1.49585i	−0.572999	+	0.146681i
$105$		0			0
$106$	3.71791	−	4.89572i	0.361116	−	0.475515i
$107$		−	7.65011i		−	0.739564i	−0.929119	−	0.369782i	$-0.879432\pi$
$107$		−	7.65011i		−	0.739564i	0.929119	−	0.369782i	$-0.120568\pi$
$108$	10.5206	+	3.91835i	1.01235	+	0.377044i
$109$	6.41848	−	2.08549i	0.614779	−	0.199754i	0.0149580	−	0.999888i	$-0.495239\pi$
$109$	6.41848	−	2.08549i	0.614779	−	0.199754i	0.599821	+	0.800134i	$0.295239\pi$
$110$		0			0
$111$	3.23459	−	9.95506i	0.307014	−	0.944892i
$112$	−9.23033	−	0.784033i	−0.872184	−	0.0740842i
$113$	4.69549	+	14.4512i	0.441714	+	1.35946i	0.886047	+	0.463595i	$0.153441\pi$
$113$	4.69549	+	14.4512i	0.441714	+	1.35946i	−0.444333	+	0.895862i	$0.646559\pi$
$114$	−0.969801	−	0.0205477i	−0.0908301	−	0.00192447i
$115$		0			0
$116$	10.8588	−	13.6869i	1.00822	−	1.27080i
$117$	1.60388	+	2.20755i	0.148279	+	0.204088i
$118$	6.63803	−	2.00240i	0.611080	−	0.184336i
$119$	4.26886	−	3.10151i	0.391325	−	0.284315i
$120$		0			0
$121$	−8.85596	−	6.43423i	−0.805087	−	0.584930i
$122$	3.04319	+	1.06057i	0.275517	+	0.0960196i
$123$	7.44769	+	2.41990i	0.671536	+	0.218195i
$124$	14.3307	−	9.51138i	1.28694	−	0.854147i
$125$		0			0
$126$	1.21026	+	4.01206i	0.107818	+	0.357422i
$127$	1.41018	−	4.34009i	0.125133	−	0.385121i	−0.868792	−	0.495177i	$-0.835103\pi$
$127$	1.41018	−	4.34009i	0.125133	−	0.385121i	0.993925	+	0.110056i	$0.0351032\pi$
$128$	−11.1895	−	1.67158i	−0.989025	−	0.147748i
$129$	−10.3429	−	7.51453i	−0.910638	−	0.661618i
$130$		0			0
$131$	−9.12255	−	12.5561i	−0.797041	−	1.09703i	−0.993195	−	0.116460i	$-0.962845\pi$
$131$	−9.12255	−	12.5561i	−0.797041	−	1.09703i	0.196154	−	0.980573i	$-0.437155\pi$
$132$	−0.505234	+	0.335327i	−0.0439750	+	0.0291864i
$133$	−0.711830	−	0.979750i	−0.0617235	−	0.0849551i
$134$	−2.55070	−	3.67186i	−0.220347	−	0.317201i
$135$		0			0
$136$	5.44365	−	3.44914i	0.466789	−	0.295761i
$137$	4.54244	+	13.9802i	0.388087	+	1.19441i	0.934216	+	0.356708i	$0.116101\pi$
$137$	4.54244	+	13.9802i	0.388087	+	1.19441i	−0.546129	+	0.837701i	$0.683899\pi$
$138$	7.33950	+	10.5656i	0.624780	+	0.899402i
$139$	−5.61357	−	1.82396i	−0.476137	−	0.154706i	0.0611104	−	0.998131i	$-0.480536\pi$
$139$	−5.61357	−	1.82396i	−0.476137	−	0.154706i	−0.537247	+	0.843425i	$0.680536\pi$
$140$		0			0
$141$	−1.39498	+	0.453256i	−0.117478	+	0.0381710i
$142$	7.38158	+	5.60572i	0.619448	+	0.470421i
$143$	−0.492950			−0.0412225
$144$	1.16392	+	4.98396i	0.0969934	+	0.415330i
$145$		0			0
$146$	2.56900	−	7.37145i	0.212612	−	0.610066i
$147$	−1.26182	+	1.73675i	−0.104073	+	0.143245i
$148$	15.3745	−	4.28466i	1.26377	−	0.352197i
$149$			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	$0.386273\pi$
$152$	−0.791616	−	1.24938i	−0.0642086	−	0.101338i
$153$	−2.35851	−	1.71356i	−0.190675	−	0.138533i
$154$	−0.714886	−	0.249142i	−0.0576071	−	0.0200765i
$155$		0			0
$156$	1.95262	−	5.24271i	0.156335	−	0.419753i
$157$			4.64663i			0.370842i	0.982659	+	0.185421i	$0.0593648\pi$
$157$			4.64663i			0.370842i	−0.982659	+	0.185421i	$0.940635\pi$
$158$	−14.1684	−	10.7598i	−1.12718	−	0.856002i
$159$	1.76192	+	5.42264i	0.139730	+	0.430043i
$160$		0			0
$161$	−4.96317	+	15.2751i	−0.391152	+	1.20384i
$162$	−4.09338	+	2.84352i	−0.321606	+	0.223408i
$163$	12.4920	−	4.05889i	0.978448	−	0.317917i	0.224226	−	0.974537i	$-0.428015\pi$
$163$	12.4920	−	4.05889i	0.978448	−	0.317917i	0.754221	+	0.656620i	$0.228015\pi$
$164$	3.20549	+	11.5021i	0.250306	+	0.898164i
$165$		0			0
$166$	4.43675	+	6.38692i	0.344358	+	0.495721i
$167$	−16.8935	+	12.2739i	−1.30726	+	0.949780i	−0.999998	−	0.00184537i	$-0.999413\pi$
$167$	−16.8935	+	12.2739i	−1.30726	+	0.949780i	−0.307261	+	0.951625i	$0.599413\pi$
$168$	5.48145	−	6.61621i	0.422903	−	0.510452i
$169$	−6.83785	+	4.96799i	−0.525988	+	0.382153i
$170$		0			0
$171$	−0.393281	+	0.541305i	−0.0300750	+	0.0413947i
$172$	0.825665	−	19.4759i	0.0629563	−	1.48502i
$173$	−7.49277	−	2.43455i	−0.569664	−	0.185095i	0.0100007	−	0.999950i	$-0.496817\pi$
$173$	−7.49277	−	2.43455i	−0.569664	−	0.185095i	−0.579665	+	0.814855i	$0.696817\pi$
$174$	4.67989	+	15.5140i	0.354781	+	1.17611i
$175$		0			0
$176$	−0.852011	−	0.359117i	−0.0642227	−	0.0270695i
$177$	−1.98721	+	6.11600i	−0.149368	+	0.459706i
$178$	−7.36322	+	21.1279i	−0.551896	+	1.58360i
$179$	9.43646	−	12.9882i	0.705314	−	0.970782i	−0.294571	−	0.955630i	$-0.595177\pi$
$179$	9.43646	−	12.9882i	0.705314	−	0.970782i	0.999885	−	0.0151522i	$-0.00482327\pi$
$180$		0			0
$181$	−10.0809	−	13.8751i	−0.749305	−	1.03133i	−0.998029	−	0.0627560i	$-0.980011\pi$
$181$	−10.0809	−	13.8751i	−0.749305	−	1.03133i	0.248723	−	0.968575i	$-0.419989\pi$
$182$	6.68698	−	2.01716i	0.495672	−	0.149522i
$183$	−2.41818	+	1.75691i	−0.178757	+	0.129874i
$184$	−7.23416	+	18.2330i	−0.533310	+	1.34415i
$185$		0			0
$186$	−0.337924	+	15.9492i	−0.0247778	+	1.16945i
$187$	0.500883	−	0.162747i	0.0366282	−	0.0119012i
$188$	−1.75205	−	1.39003i	−0.127781	−	0.101378i
$189$	−12.3636	−	4.01717i	−0.899319	−	0.292206i
$190$		0			0
$191$	−0.923572	−	2.84246i	−0.0668273	−	0.205673i	0.912067	−	0.410042i	$-0.134486\pi$
$191$	−0.923572	−	2.84246i	−0.0668273	−	0.205673i	−0.978894	+	0.204369i	$0.934486\pi$
$192$	7.19424	−	7.63898i	0.519200	−	0.551296i
$193$	14.9349			1.07504			0.537518	−	0.843252i	$-0.319362\pi$
$193$	14.9349			1.07504			0.537518	+	0.843252i	$0.319362\pi$
$194$	−14.3745	−	10.9163i	−1.03203	−	0.783743i
$195$		0			0
$196$	−3.27035	−	0.138644i	−0.233597	−	0.00990313i
$197$	−16.1837	+	22.2749i	−1.15304	+	1.58702i	−0.418887	+	0.908039i	$0.637580\pi$
$197$	−16.1837	+	22.2749i	−1.15304	+	1.58702i	−0.734153	+	0.678984i	$0.762420\pi$
$198$	−0.00886009	+	0.418174i	−0.000629659	+	0.0297184i
$199$	11.3822			0.806862			0.403431	−	0.915010i	$-0.367818\pi$
$199$	11.3822			0.806862			0.403431	+	0.915010i	$0.367818\pi$
$200$		0			0
$201$	4.14670			0.292485
$202$	−0.347183	+	16.3862i	−0.0244277	+	1.15293i
$203$	−11.8914	+	16.3671i	−0.834611	+	1.14874i
$204$	−0.253167	+	5.97174i	−0.0177252	+	0.418106i
$205$		0			0
$206$	−7.55200	−	5.73514i	−0.526173	−	0.399586i
$207$	8.87368			0.616763
$208$	8.30686	−	1.93993i	0.575977	−	0.134510i
$209$	−0.0373522	−	0.114958i	−0.00258371	−	0.00795183i
$210$		0			0
$211$	15.0746	+	4.89802i	1.03778	+	0.337194i	0.777860	−	0.628438i	$-0.216305\pi$
$211$	15.0746	+	4.89802i	1.03778	+	0.337194i	0.259916	+	0.965631i	$0.416305\pi$
$212$	−5.40340	+	6.81067i	−0.371107	+	0.467759i
$213$	−8.17604	+	2.65656i	−0.560213	+	0.182024i
$214$	−0.229174	+	10.8165i	−0.0156660	+	0.739398i
$215$		0			0
$216$	−14.7577	−	5.85531i	−1.00414	−	0.398404i
$217$	−16.1128	+	11.7066i	−1.09381	+	0.794699i
$218$	−9.13754	+	2.75639i	−0.618872	+	0.186686i
$219$	4.25572	+	5.85750i	0.287575	+	0.395813i
$220$		0			0
$221$	−2.85603	+	3.93099i	−0.192117	+	0.264427i
$222$	−4.87160	+	13.9785i	−0.326961	+	0.938177i
$223$	7.19420	−	22.1415i	0.481759	−	1.48270i	−0.354861	−	0.934919i	$-0.615472\pi$
$223$	7.19420	−	22.1415i	0.481759	−	1.48270i	0.836620	−	0.547783i	$-0.184528\pi$
$224$	13.0272	+	1.38505i	0.870419	+	0.0925428i
$225$		0			0
$226$	−6.20602	−	20.5732i	−0.412818	−	1.36851i
$227$	4.25947	+	1.38398i	0.282711	+	0.0918583i	0.446940	−	0.894564i	$-0.352514\pi$
$227$	4.25947	+	1.38398i	0.282711	+	0.0918583i	−0.164229	+	0.986422i	$0.552514\pi$
$228$	1.37058	+	0.0581047i	0.0907690	+	0.00384807i
$229$	−2.99987	+	4.12897i	−0.198237	+	0.272850i	−0.896550	−	0.442943i	$-0.853934\pi$
$229$	−2.99987	+	4.12897i	−0.198237	+	0.272850i	0.698313	+	0.715793i	$0.253934\pi$
$230$		0			0
$231$	0.568062	−	0.412721i	0.0373757	−	0.0271551i
$232$	−15.7633	+	19.0266i	−1.03491	+	1.24916i
$233$	−2.83047	+	2.05646i	−0.185430	+	0.134723i	−0.676628	−	0.736325i	$-0.736559\pi$
$233$	−2.83047	+	2.05646i	−0.185430	+	0.134723i	0.491197	+	0.871048i	$0.336559\pi$
$234$	−2.20159	−	3.16930i	−0.143922	−	0.207184i
$235$		0			0
$236$	−9.44546	+	2.63233i	−0.614847	+	0.171350i
$237$	15.6933	−	5.09907i	1.01939	−	0.331220i
$238$	−6.12863	+	4.25732i	−0.397260	+	0.275961i
$239$	−6.27635	+	19.3166i	−0.405983	+	1.24949i	0.514088	+	0.857738i	$0.328131\pi$
$239$	−6.27635	+	19.3166i	−0.405983	+	1.24949i	−0.920071	+	0.391751i	$0.871869\pi$
$240$		0			0
$241$	5.98561	+	18.4218i	0.385567	+	1.18665i	0.936068	+	0.351819i	$0.114437\pi$
$241$	5.98561	+	18.4218i	0.385567	+	1.18665i	−0.550501	+	0.834835i	$0.685563\pi$
$242$	12.3287	+	9.36263i	0.792516	+	0.601853i
$243$			12.2172i			0.783736i
$244$	−4.27098	−	1.59070i	−0.273422	−	0.101834i
$245$		0			0
$246$	−10.4578	−	3.64460i	−0.666763	−	0.232371i
$247$	0.902205	+	0.655490i	0.0574059	+	0.0417079i
$248$	−20.5471	+	13.0188i	−1.30474	+	0.826695i
$249$	−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	$0.953932\pi$
$252$	−1.59099	−	5.70889i	−0.100223	−	0.359626i
$253$	−0.942261	+	1.29691i	−0.0592395	+	0.0815361i
$254$	−2.12387	+	6.09419i	−0.133263	+	0.382384i
$255$		0			0
$256$	15.7708	+	2.69864i	0.985673	+	0.168665i
$257$	27.4389			1.71159			0.855797	−	0.517312i	$-0.173067\pi$
$257$	27.4389			1.71159			0.855797	+	0.517312i	$0.173067\pi$
$258$	14.3986	+	10.9346i	0.896419	+	0.680759i
$259$	−17.5767	+	5.71101i	−1.09216	+	0.354865i
$260$		0			0
$261$	10.6303	+	3.45400i	0.658001	+	0.213798i
$262$	12.5222	+	18.0263i	0.773624	+	1.11367i
$263$	−3.97845	−	12.2444i	−0.245322	−	0.755022i	−0.995583	−	0.0938814i	$-0.970073\pi$
$263$	−3.97845	−	12.2444i	−0.245322	−	0.755022i	0.750262	−	0.661141i	$-0.229927\pi$
$264$	0.724394	−	0.458982i	0.0445834	−	0.0282484i
$265$		0			0
$266$	0.977104	+	1.40659i	0.0599101	+	0.0862435i
$267$	−12.1977	−	16.7887i	−0.746486	−	1.02745i
$268$	3.49643	+	5.26805i	0.213578	+	0.321797i
$269$	−0.897279	−	1.23500i	−0.0547081	−	0.0752992i	0.780786	−	0.624798i	$-0.214819\pi$
$269$	−0.897279	−	1.23500i	−0.0547081	−	0.0752992i	−0.835495	+	0.549499i	$0.814819\pi$
$270$		0			0
$271$	−19.8030	−	14.3877i	−1.20294	−	0.873990i	−0.208373	−	0.978049i	$-0.566817\pi$
$271$	−19.8030	−	14.3877i	−1.20294	−	0.873990i	−0.994571	+	0.104059i	$0.966817\pi$
$272$	−7.80008	+	4.71365i	−0.472950	+	0.285807i
$273$	−2.00186	+	6.16110i	−0.121158	+	0.372887i
$274$	−6.00374	−	19.9026i	−0.362699	−	1.20236i
$275$		0			0
$276$	−10.0608	−	15.1585i	−0.605588	−	0.912435i
$277$	−26.0565	−	8.46626i	−1.56558	−	0.508689i	−0.607290	−	0.794480i	$-0.707744\pi$
$277$	−26.0565	−	8.46626i	−1.56558	−	0.508689i	−0.958292	+	0.285791i	$0.907744\pi$
$278$	7.88237	+	2.74706i	0.472753	+	0.164757i
$279$	8.90222	+	6.46784i	0.532962	+	0.387220i
$280$		0			0
$281$	−23.5098	+	17.0809i	−1.40248	+	1.01896i	−0.408116	+	0.912930i	$0.633814\pi$
$281$	−23.5098	+	17.0809i	−1.40248	+	1.01896i	−0.994363	+	0.106031i	$0.966186\pi$
$282$	1.98593	−	0.599067i	0.118261	−	0.0356739i
$283$	5.82810	+	8.02169i	0.346444	+	0.476840i	0.946310	−	0.323261i	$-0.104779\pi$
$283$	5.82810	+	8.02169i	0.346444	+	0.476840i	−0.599865	+	0.800101i	$0.704779\pi$
$284$	−10.2689	−	8.14704i	−0.609344	−	0.483438i
$285$		0			0
$286$	0.696980	+	0.0147673i	0.0412133	+	0.000873209i
$287$	−4.27258	−	13.1497i	−0.252203	−	0.776200i
$288$	−1.49636	−	7.08166i	−0.0881738	−	0.417291i
$289$	−3.64911	+	11.2308i	−0.214653	+	0.660635i
$290$		0			0
$291$	15.9216	−	5.17324i	0.933340	−	0.303261i
$292$	−3.85312	+	10.3455i	−0.225487	+	0.605425i
$293$			6.22226i			0.363508i	0.983344	+	0.181754i	$0.0581775\pi$
$293$			6.22226i			0.363508i	−0.983344	+	0.181754i	$0.941823\pi$
$294$	1.83612	−	2.41778i	0.107084	−	0.141008i
$295$		0			0
$296$	−21.8662	+	5.59749i	−1.27095	+	0.325347i
$297$	−1.04972	−	0.762664i	−0.0609107	−	0.0442542i
$298$	0.273823	−	12.9237i	0.0158621	−	0.748652i
$299$		−	14.7899i		−	0.855324i
$300$		0			0
$301$			22.5723i			1.30105i
$302$	−12.1526	−	0.257484i	−0.699304	−	0.0148165i
$303$	−12.2982	−	8.93519i	−0.706515	−	0.513313i
$304$	1.08184	+	1.79021i	0.0620475	+	0.102675i
$305$		0			0
$306$	3.28336	+	2.49345i	0.187697	+	0.142541i
$307$			29.6136i			1.69014i	0.534656	+	0.845070i	$0.320441\pi$
$307$			29.6136i			1.69014i	−0.534656	+	0.845070i	$0.679559\pi$
$308$	1.00331	+	0.373677i	0.0571689	+	0.0212922i
$309$	8.36481	−	2.71789i	0.475857	−	0.154615i
$310$		0			0
$311$	−1.32670	+	4.08315i	−0.0752301	+	0.231534i	−0.981599	−	0.190952i	$-0.938843\pi$
$311$	−1.32670	+	4.08315i	−0.0752301	+	0.231534i	0.906369	+	0.422486i	$0.138843\pi$
$312$	−2.91786	+	7.35416i	−0.165191	+	0.416347i
$313$	4.24400	+	13.0617i	0.239885	+	0.738290i	0.996436	+	0.0843552i	$0.0268830\pi$
$313$	4.24400	+	13.0617i	0.239885	+	0.738290i	−0.756551	+	0.653935i	$0.773117\pi$
$314$	0.139199	−	6.56986i	0.00785547	−	0.370759i
$315$		0			0
$316$	19.7103	+	15.6376i	1.10879	+	0.879686i
$317$	−7.50769	−	10.3334i	−0.421674	−	0.580384i	0.544343	−	0.838863i	$-0.316779\pi$
$317$	−7.50769	−	10.3334i	−0.421674	−	0.580384i	−0.966017	+	0.258478i	$0.916779\pi$
$318$	−2.32873	−	7.71983i	−0.130589	−	0.432907i
$319$	−1.63361	+	1.18688i	−0.0914644	+	0.0664528i
$320$		0			0
$321$	−8.11803	−	5.89809i	−0.453104	−	0.329200i
$322$	7.47500	−	21.4487i	0.416565	−	1.19529i
$323$	−1.13313	−	0.368178i	−0.0630493	−	0.0204859i
$324$	5.87280	−	3.89781i	0.326267	−	0.216545i
$325$		0			0
$326$	−17.7840	+	5.36463i	−0.984963	+	0.297119i
$327$	2.73548	−	8.41894i	0.151272	−	0.465569i
$328$	−4.18766	−	16.3588i	−0.231225	−	0.903265i
$329$	2.09513	+	1.52220i	0.115508	+	0.0839217i
$330$		0			0
$331$	2.79298	+	3.84421i	0.153516	+	0.211297i	0.878847	−	0.477103i	$-0.158313\pi$
$331$	2.79298	+	3.84421i	0.153516	+	0.211297i	−0.725331	+	0.688400i	$0.758313\pi$
$332$	−6.08177	−	9.16335i	−0.333780	−	0.502904i
$333$	6.00172	+	8.26066i	0.328892	+	0.452682i
$334$	24.2534	−	16.8479i	1.32709	−	0.921875i
$335$		0			0
$336$	−7.94841	+	9.19043i	−0.433621	+	0.501379i
$337$	−9.15228	−	28.1678i	−0.498556	−	1.53440i	−0.811340	−	0.584574i	$-0.801261\pi$
$337$	−9.15228	−	28.1678i	−0.498556	−	1.53440i	0.312784	−	0.949824i	$-0.398739\pi$
$338$	9.81683	−	6.81937i	0.533965	−	0.370925i
$339$	18.9553	+	6.15894i	1.02951	+	0.334508i
$340$		0			0
$341$	−1.89059	+	0.614289i	−0.102381	+	0.0332656i
$342$	0.572275	−	0.753568i	0.0309451	−	0.0407483i
$343$	20.0015			1.07998
$344$	−1.75084	+	27.5122i	−0.0943992	+	1.48336i
$345$		0			0
$346$	10.5211	+	3.66666i	0.565616	+	0.197121i
$347$	11.3406	−	15.6090i	0.608797	−	0.837937i	−0.387681	−	0.921794i	$-0.626724\pi$
$347$	11.3406	−	15.6090i	0.608797	−	0.837937i	0.996478	+	0.0838564i	$0.0267237\pi$
$348$	−6.15212	−	22.0754i	−0.329788	−	1.18337i
$349$			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
$352$	1.19390	+	0.533278i	0.0636349	+	0.0284238i
$353$	−10.7507	−	7.81083i	−0.572202	−	0.415729i	0.263703	−	0.964604i	$-0.415056\pi$
$353$	−10.7507	−	7.81083i	−0.572202	−	0.415729i	−0.835904	+	0.548875i	$0.815056\pi$
$354$	2.99292	−	8.58785i	0.159072	−	0.456439i
$355$		0			0
$356$	11.0438	−	29.6521i	0.585318	−	1.57156i
$357$		−	6.92117i		−	0.366307i
$358$	−13.7313	+	18.0812i	−0.725720	+	0.955623i
$359$	−5.23366	−	16.1076i	−0.276222	−	0.850124i	−0.988893	−	0.148626i	$-0.952515\pi$
$359$	−5.23366	−	16.1076i	−0.276222	−	0.850124i	0.712671	−	0.701498i	$-0.247485\pi$
$360$		0			0
$361$	5.78682	−	17.8100i	0.304570	−	0.937369i
$362$	13.8377	+	19.9200i	0.727291	+	1.04697i
$363$	−13.6556	+	4.43696i	−0.716732	+	0.232880i
$364$	−9.51512	+	2.65174i	−0.498728	+	0.138989i
$365$		0			0
$366$	3.47169	−	2.41165i	0.181468	−	0.126059i
$367$	7.06794	−	5.13516i	0.368944	−	0.268053i	−0.387829	−	0.921731i	$-0.626775\pi$
$367$	7.06794	−	5.13516i	0.368944	−	0.268053i	0.756773	+	0.653678i	$0.226775\pi$
$368$	10.7746	−	25.5628i	0.561663	−	1.33255i
$369$	−6.18006	+	4.49008i	−0.321721	+	0.233744i
$370$		0			0
$371$	5.91720	−	8.14432i	0.307206	−	0.422832i
$372$	0.955580	−	22.5404i	0.0495445	−	1.16866i
$373$	−0.954212	−	0.310042i	−0.0494072	−	0.0160534i	0.284209	−	0.958762i	$-0.408269\pi$
$373$	−0.954212	−	0.310042i	−0.0494072	−	0.0160534i	−0.333616	+	0.942709i	$0.608269\pi$
$374$	−0.713072	+	0.215102i	−0.0368721	+	0.0111227i
$375$		0			0
$376$	2.43557	+	2.01784i	0.125605	+	0.104062i
$377$	5.75686	−	17.7178i	0.296494	−	0.912513i
$378$	17.3605	+	6.05024i	0.892927	+	0.311191i
$379$	−21.2264	+	29.2157i	−1.09033	+	1.50071i	−0.242712	+	0.970098i	$0.578037\pi$
$379$	−21.2264	+	29.2157i	−1.09033	+	1.50071i	−0.847616	+	0.530610i	$0.821963\pi$
$380$		0			0
$381$	−3.51833	−	4.84257i	−0.180250	−	0.248092i
$382$	1.22068	+	4.04661i	0.0624556	+	0.207043i
$383$	−24.9852	+	18.1528i	−1.27668	+	0.927565i	−0.999447	−	0.0332373i	$-0.989418\pi$
$383$	−24.9852	+	18.1528i	−1.27668	+	0.927565i	−0.277236	+	0.960802i	$0.589418\pi$
$384$	−10.4008	+	10.5852i	−0.530761	+	0.540174i
$385$		0			0
$386$	−21.1164	−	0.447404i	−1.07480	−	0.0227723i
$387$	11.8607	−	3.85377i	0.602912	−	0.195898i
$388$	19.9970	+	15.8651i	1.01519	+	0.805428i
$389$	1.26254	+	0.410223i	0.0640132	+	0.0207991i	0.340849	−	0.940118i	$-0.389286\pi$
$389$	1.26254	+	0.410223i	0.0640132	+	0.0207991i	−0.276835	+	0.960917i	$0.589286\pi$
$390$		0			0
$391$	4.88288	+	15.0280i	0.246938	+	0.759997i
$392$	4.61978	+	0.293998i	0.233334	+	0.0148491i
$393$	−20.3574			−1.02690
$394$	23.5493	−	31.0096i	1.18640	−	1.56224i
$395$		0			0
$396$	0.0250545	−	0.590990i	0.00125904	−	0.0296983i
$397$	−5.67144	+	7.80606i	−0.284641	+	0.391775i	−0.927264	−	0.374407i	$-0.877846\pi$
$397$	−5.67144	+	7.80606i	−0.284641	+	0.391775i	0.642623	+	0.766182i	$0.277846\pi$
$398$	−16.0932	−	0.340976i	−0.806681	−	0.0170916i
$399$	−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	$0.405021\pi$
$402$	−5.86300	−	0.124223i	−0.292420	−	0.00619566i
$403$	10.7801	−	14.8375i	0.536995	−	0.739110i
$404$	0.981760	−	23.1579i	0.0488444	−	1.15215i
$405$		0			0
$406$	17.3035	−	22.7851i	0.858758	−	1.13081i
$407$	−1.84462			−0.0914343
$408$	0.536847	−	8.43584i	0.0265779	−	0.417636i
$409$	0.0454622	+	0.139918i	0.00224796	+	0.00691851i	0.952174	−	0.305556i	$-0.0988422\pi$
$409$	0.0454622	+	0.139918i	0.00224796	+	0.00691851i	−0.949926	+	0.312474i	$0.898842\pi$
$410$		0			0
$411$	18.3375	+	5.95820i	0.904520	+	0.293896i
$412$	10.5059	+	8.33513i	0.517590	+	0.410642i
$413$	10.7984	−	3.50862i	0.531355	−	0.172648i
$414$	−12.5465	−	0.265829i	−0.616625	−	0.0130648i
$415$		0			0
$416$	−11.8032	+	2.49401i	−0.578697	+	0.122279i
$417$	−6.26349	+	4.55069i	−0.306724	+	0.222848i
$418$	0.0493683	+	0.163658i	0.00241468	+	0.00800478i
$419$	20.0431	+	27.5869i	0.979168	+	1.34771i	0.937277	+	0.348587i	$0.113338\pi$
$419$	20.0431	+	27.5869i	0.979168	+	1.34771i	0.0418913	+	0.999122i	$0.486662\pi$
$420$		0			0
$421$	−3.43224	+	4.72407i	−0.167277	+	0.230237i	−0.884423	−	0.466686i	$-0.845448\pi$
$421$	−3.43224	+	4.72407i	−0.167277	+	0.230237i	0.717146	+	0.696923i	$0.245448\pi$
$422$	−21.1671	−	7.37688i	−1.03040	−	0.359101i
$423$	0.442143	−	1.36078i	0.0214977	−	0.0661633i
$424$	7.84388	−	9.46771i	0.380932	−	0.459793i
$425$		0			0
$426$	11.6397	−	3.51117i	0.563943	−	0.170117i
$427$	5.01915	+	1.63082i	0.242894	+	0.0789209i
$428$	0.648057	−	15.2865i	0.0313250	−	0.738900i
$429$	−0.380055	+	0.523101i	−0.0183492	+	0.0252556i
$430$		0			0
$431$	−3.30954	+	2.40452i	−0.159415	+	0.115822i	−0.664633	−	0.747170i	$-0.731412\pi$
$431$	−3.30954	+	2.40452i	−0.159415	+	0.115822i	0.505218	+	0.862992i	$0.331412\pi$
$432$	20.6905	+	8.72090i	0.995471	+	0.419585i
$433$	3.84976	−	2.79701i	0.185008	−	0.134416i	−0.491427	−	0.870919i	$-0.663524\pi$
$433$	3.84976	−	2.79701i	0.185008	−	0.134416i	0.676434	+	0.736503i	$0.263524\pi$
$434$	23.1326	−	16.0693i	1.11040	−	0.771351i
$435$		0			0
$436$	13.0021	−	3.62351i	0.622688	−	0.173535i
$437$	3.44909	−	1.12068i	0.164992	−	0.0536092i
$438$	−5.84168	−	8.40939i	−0.279126	−	0.401816i
$439$	−0.541600	+	1.66687i	−0.0258492	+	0.0795556i	−0.963149	−	0.268969i	$-0.913317\pi$
$439$	−0.541600	+	1.66687i	−0.0258492	+	0.0795556i	0.937300	+	0.348524i	$0.113317\pi$
$440$		0			0
$441$	−0.647116	−	1.99162i	−0.0308150	−	0.0948389i
$442$	4.15589	−	5.47245i	0.197675	−	0.260298i
$443$			3.43488i			0.163196i	0.996665	+	0.0815981i	$0.0260024\pi$
$443$			3.43488i			0.163196i	−0.996665	+	0.0815981i	$0.973998\pi$
$444$	7.30670	−	19.6182i	0.346761	−	0.931040i
$445$		0			0
$446$	−10.8351	+	31.0902i	−0.513059	+	1.47216i
$447$	9.69960	+	7.04717i	0.458775	+	0.333320i
$448$	−18.3777	−	2.34858i	−0.868264	−	0.110960i
$449$	−5.54236			−0.261560			−0.130780	−	0.991411i	$-0.541748\pi$
$449$	−5.54236			−0.261560			−0.130780	+	0.991411i	$0.541748\pi$
$450$		0			0
$451$		−	1.38002i		−	0.0649825i
$452$	8.15835	+	29.2743i	0.383737	+	1.37695i
$453$	6.62668	−	9.12084i	0.311348	−	0.428534i
$454$	−5.98098	−	2.08441i	−0.280701	−	0.0978263i
$455$		0			0
$456$	−1.93612	−	0.123212i	−0.0906671	−	0.00576995i
$457$	3.02813			0.141650			0.0708250	−	0.997489i	$-0.477437\pi$
$457$	3.02813			0.141650			0.0708250	+	0.997489i	$0.477437\pi$
$458$	4.36520	−	5.74806i	0.203972	−	0.268589i
$459$	−12.1636	+	3.95219i	−0.567748	+	0.184472i
$460$		0			0
$461$	11.9787	+	3.89211i	0.557903	+	0.181274i	0.574377	−	0.818591i	$-0.305244\pi$
$461$	11.9787	+	3.89211i	0.557903	+	0.181274i	−0.0164747	+	0.999864i	$0.505244\pi$
$462$	−0.815545	+	0.566528i	−0.0379426	+	0.0263573i
$463$	1.35375	+	4.16641i	0.0629140	+	0.193629i	0.977573	−	0.210597i	$-0.0675408\pi$
$463$	1.35375	+	4.16641i	0.0629140	+	0.193629i	−0.914659	+	0.404226i	$0.867541\pi$
$464$	22.8576	−	26.4294i	1.06114	−	1.22695i
$465$		0			0
$466$	4.06360	−	2.82283i	0.188243	−	0.130765i
$467$	−13.3438	−	18.3661i	−0.617476	−	0.849883i	0.379690	−	0.925114i	$-0.376031\pi$
$467$	−13.3438	−	18.3661i	−0.617476	−	0.849883i	−0.997166	+	0.0752308i	$0.976031\pi$
$468$	3.01788	+	4.54701i	0.139501	+	0.210186i
$469$	−4.30342	−	5.92315i	−0.198714	−	0.273506i
$470$		0			0
$471$	4.93085	+	3.58247i	0.227201	+	0.165072i
$472$	13.4338	−	3.43888i	0.618339	−	0.158287i
$473$	−0.696201	+	2.14269i	−0.0320113	+	0.0985208i
$474$	−22.3415	+	6.73943i	−1.02618	+	0.309552i
$475$		0			0
$476$	8.79278	−	5.83582i	0.403017	−	0.267484i
$477$	−5.28970	−	1.71873i	−0.242199	−	0.0786951i
$478$	9.45278	−	27.1237i	0.432360	−	1.24061i
$479$	−5.58405	−	4.05705i	−0.255142	−	0.185371i	0.452861	−	0.891581i	$-0.350403\pi$
$479$	−5.58405	−	4.05705i	−0.255142	−	0.185371i	−0.708002	+	0.706210i	$0.750403\pi$
$480$		0			0
$481$	13.7682	−	10.0032i	0.627777	−	0.456107i
$482$	−7.91117	−	26.2258i	−0.360344	−	1.19455i
$483$	12.3829	+	17.0435i	0.563439	+	0.775508i
$484$	−17.1510	−	13.6071i	−0.779589	−	0.618506i
$485$		0			0
$486$	0.365992	−	17.2739i	0.0166017	−	0.783561i
$487$	−11.0811	−	34.1041i	−0.502132	−	1.54540i	−0.805539	−	0.592543i	$-0.798124\pi$
$487$	−11.0811	−	34.1041i	−0.502132	−	1.54540i	0.303407	−	0.952861i	$-0.401876\pi$
$488$	5.99107	+	2.37703i	0.271203	+	0.107603i
$489$	5.32394	−	16.3854i	0.240757	−	0.740973i
$490$		0			0
$491$	−7.36748	+	2.39384i	−0.332490	+	0.108032i	−0.470504	−	0.882398i	$-0.655928\pi$
$491$	−7.36748	+	2.39384i	−0.332490	+	0.108032i	0.138014	+	0.990430i	$0.455928\pi$
$492$	14.6770	+	5.46637i	0.661691	+	0.246443i
$493$			19.9036i			0.896411i
$494$	−1.25599	−	0.953823i	−0.0565096	−	0.0429145i
$495$		0			0
$496$	29.4415	−	17.7917i	1.32196	−	0.798871i
$497$	12.2797	+	8.92171i	0.550819	+	0.400194i
$498$	10.1982	+	0.216076i	0.456994	+	0.00968258i
$499$		−	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
$502$	0.136898	−	6.46123i	0.00611004	−	0.288379i
$503$	10.3630	+	7.52915i	0.462063	+	0.335708i	0.794340	−	0.607473i	$-0.207817\pi$
$503$	10.3630	+	7.52915i	0.462063	+	0.335708i	−0.332277	+	0.943182i	$0.607817\pi$
$504$	2.07847	+	8.11943i	0.0925826	+	0.361668i
$505$		0			0
$506$	1.37111	−	1.80547i	0.0609533	−	0.0802630i
$507$			11.0863i			0.492360i
$508$	3.18549	−	8.55293i	0.141333	−	0.379475i
$509$	40.6350	−	13.2031i	1.80111	−	0.585217i	0.801200	−	0.598397i	$-0.204196\pi$
$509$	40.6350	−	13.2031i	1.80111	−	0.585217i	0.999913	+	0.0131803i	$0.00419554\pi$
$510$		0			0
$511$	3.95030	−	12.1578i	0.174751	−	0.537828i
$512$	−22.2174	−	4.28804i	−0.981879	−	0.189506i
$513$	0.907072	+	2.79168i	0.0400482	+	0.123256i
$514$	−38.7958	−	0.821989i	−1.71121	−	0.0362564i
$515$		0			0
$516$	−20.0306	−	15.8917i	−0.881798	−	0.699595i
$517$	0.151932	+	0.209116i	0.00668195	+	0.00919692i
$518$	25.0227	−	7.54823i	1.09943	−	0.331650i
$519$	−8.36024	+	6.07407i	−0.366974	+	0.266622i
$520$		0			0
$521$	−1.68871	−	1.22692i	−0.0739836	−	0.0537522i	0.550179	−	0.835047i	$-0.314560\pi$
$521$	−1.68871	−	1.22692i	−0.0739836	−	0.0537522i	−0.624162	+	0.781295i	$0.714560\pi$
$522$	−14.9267	−	5.20206i	−0.653325	−	0.227688i
$523$	−30.9419	−	10.0536i	−1.35300	−	0.439615i	−0.459297	−	0.888283i	$-0.651899\pi$
$523$	−30.9419	−	10.0536i	−1.35300	−	0.439615i	−0.893699	+	0.448668i	$0.851899\pi$
$524$	−17.1651	−	25.8625i	−0.749860	−	1.12981i
$525$		0			0
$526$	5.25831	+	17.4315i	0.229273	+	0.760049i
$527$	−6.05499	+	18.6353i	−0.263760	+	0.811768i
$528$	−1.03797	+	0.627252i	−0.0451717	+	0.0272976i
$529$	−20.3038	−	14.7515i	−0.882772	−	0.641372i
$530$		0			0
$531$	−3.68722	−	5.07503i	−0.160012	−	0.220237i
$532$	−1.33939	−	2.01804i	−0.0580697	−	0.0874932i
$533$	7.48371	+	10.3004i	0.324155	+	0.446162i
$534$	16.7433	+	24.1028i	0.724554	+	1.04303i
$535$		0			0
$536$	−4.78577	−	7.55321i	−0.206714	−	0.326249i
$537$	−6.50726	−	20.0273i	−0.280809	−	0.864242i
$538$	1.23166	+	1.77304i	0.0531008	+	0.0764412i
$539$	0.359795	+	0.116904i	0.0154975	+	0.00503543i
$540$		0			0
$541$	−5.01695	+	1.63011i	−0.215696	+	0.0700838i	−0.414872	−	0.909880i	$-0.636174\pi$
$541$	−5.01695	+	1.63011i	−0.215696	+	0.0700838i	0.199176	+	0.979964i	$0.436174\pi$
$542$	27.5683	+	20.9360i	1.18416	+	0.899276i
$543$	−22.4960			−0.965395
$544$	11.1697	−	6.43095i	0.478898	−	0.275725i
$545$		0			0
$546$	3.01499	−	8.65119i	0.129030	−	0.370237i
$547$	−8.91852	+	12.2753i	−0.381329	+	0.524854i	−0.955936	−	0.293575i	$-0.905155\pi$
$547$	−8.91852	+	12.2753i	−0.381329	+	0.524854i	0.574607	+	0.818429i	$0.305155\pi$
$548$	7.89244	+	28.3201i	0.337148	+	1.20978i
$549$		−	2.91575i		−	0.124441i
$550$		0			0
$551$	4.56809			0.194607
$552$	13.7708	+	21.7339i	0.586124	+	0.925058i
$553$	−23.5700	−	17.1246i	−1.00230	−	0.728211i
$554$	36.5875	+	12.7510i	1.55446	+	0.541738i
$555$		0			0
$556$	−11.0626	−	4.12018i	−0.469157	−	0.174735i
$557$		−	21.0806i		−	0.893213i	−0.894731	−	0.446606i	$-0.852632\pi$
$557$		−	21.0806i		−	0.893213i	0.894731	−	0.446606i	$-0.147368\pi$
$558$	−12.3931	−	9.41154i	−0.524640	−	0.398422i
$559$	−6.42315	−	19.7684i	−0.271670	−	0.836116i
$560$		0			0
$561$	0.213470	−	0.656995i	0.00901273	−	0.0277383i
$562$	33.7522	−	23.4463i	1.42375	−	0.989024i
$563$	16.6417	−	5.40722i	0.701365	−	0.227887i	0.0634396	−	0.997986i	$-0.479793\pi$
$563$	16.6417	−	5.40722i	0.701365	−	0.227887i	0.637925	+	0.770099i	$0.279793\pi$
$564$	−2.82585	+	0.787526i	−0.118990	+	0.0331608i
$565$		0			0
$566$	−8.00002	−	11.5164i	−0.336266	−	0.484071i
$567$	−6.60311	+	4.79744i	−0.277305	+	0.201474i
$568$	14.2750	+	11.8267i	0.598967	+	0.496237i
$569$	26.4646	−	19.2277i	1.10945	−	0.806065i	0.126876	−	0.991919i	$-0.459505\pi$
$569$	26.4646	−	19.2277i	1.10945	−	0.806065i	0.982578	+	0.185853i	$0.0595049\pi$
$570$		0			0
$571$	−17.4500	+	24.0179i	−0.730261	+	1.00512i	0.268860	+	0.963179i	$0.413353\pi$
$571$	−17.4500	+	24.0179i	−0.730261	+	1.00512i	−0.999120	+	0.0419380i	$0.986647\pi$
$572$	−0.985015	−	0.0417589i	−0.0411855	−	0.00174603i
$573$	−3.72838	−	1.21142i	−0.155755	−	0.0506080i
$574$	5.64707	+	18.7202i	0.235704	+	0.781368i
$575$		0			0
$576$	1.90355	+	10.0576i	0.0793146	+	0.419065i
$577$	2.30117	−	7.08229i	0.0957992	−	0.294839i	−0.891662	−	0.452702i	$-0.850460\pi$
$577$	2.30117	−	7.08229i	0.0957992	−	0.294839i	0.987461	+	0.157862i	$0.0504602\pi$
$578$	5.49590	−	15.7699i	0.228599	−	0.655940i
$579$	11.5145	−	15.8484i	0.478527	−	0.658636i
$580$		0			0
$581$	7.48546	+	10.3029i	0.310549	+	0.427435i
$582$	−22.6664	+	6.83746i	−0.939554	+	0.283422i
$583$	0.812889	−	0.590598i	0.0336664	−	0.0244601i
$584$	5.75784	−	14.5120i	0.238261	−	0.600513i
$585$		0			0
$586$	0.186400	−	8.79762i	0.00770012	−	0.363427i
$587$	−13.3184	+	4.32742i	−0.549710	+	0.178612i	−0.570686	−	0.821168i	$-0.693323\pi$
$587$	−13.3184	+	4.32742i	−0.549710	+	0.178612i	0.0209758	+	0.999780i	$0.493323\pi$
$588$	−2.66851	+	3.36349i	−0.110047	+	0.138708i
$589$	4.27702	+	1.38969i	0.176232	+	0.0572611i
$590$		0			0
$591$	11.1601	+	34.3471i	0.459063	+	1.41285i
$592$	31.0843	−	7.25922i	1.27756	−	0.298352i
$593$	10.4531			0.429258			0.214629	−	0.976696i	$-0.431146\pi$
$593$	10.4531			0.429258			0.214629	+	0.976696i	$0.431146\pi$
$594$	1.46134	+	1.10977i	0.0599596	+	0.0455346i
$595$		0			0
$596$	−0.774313	+	18.2646i	−0.0317171	+	0.748148i
$597$	8.77546	−	12.0784i	0.359156	−	0.494335i
$598$	−0.443062	+	20.9114i	−0.0181182	+	0.855132i
$599$	−25.1691			−1.02838			−0.514191	−	0.857676i	$-0.671908\pi$
$599$	−25.1691			−1.02838			−0.514191	+	0.857676i	$0.671908\pi$
$600$		0			0
$601$	−9.80217			−0.399839			−0.199919	−	0.979812i	$-0.564068\pi$
$601$	−9.80217			−0.399839			−0.199919	+	0.979812i	$0.564068\pi$
$602$	0.676199	−	31.9149i	0.0275598	−	1.30075i
$603$	−2.37761	+	3.27250i	−0.0968238	+	0.133267i
$604$	17.1748	+	0.728111i	0.698833	+	0.0296264i
$605$		0			0
$606$	17.1207	+	13.0018i	0.695483	+	0.528164i
$607$	2.47771			0.100567			0.0502836	−	0.998735i	$-0.483987\pi$
$607$	2.47771			0.100567			0.0502836	+	0.998735i	$0.483987\pi$
$608$	−1.47597	−	2.56358i	−0.0598587	−	0.103967i
$609$	8.20014	+	25.2374i	0.332287	+	1.02267i
$610$		0			0
$611$	−2.26804	−	0.736930i	−0.0917549	−	0.0298130i
$612$	−4.56764	−	3.62384i	−0.184636	−	0.146485i
$613$	2.45539	−	0.797806i	0.0991725	−	0.0322231i	−0.259010	−	0.965875i	$-0.583396\pi$
$613$	2.45539	−	0.797806i	0.0991725	−	0.0322231i	0.358183	+	0.933651i	$0.383396\pi$
$614$	0.887136	−	41.8706i	0.0358019	−	1.68976i
$615$		0			0
$616$	−1.40738	−	0.558397i	−0.0567051	−	0.0224984i
$617$	−14.3320	+	10.4128i	−0.576986	+	0.419205i	−0.837636	−	0.546228i	$-0.816063\pi$
$617$	−14.3320	+	10.4128i	−0.576986	+	0.419205i	0.260650	+	0.965433i	$0.416063\pi$
$618$	−11.9084	+	3.59223i	−0.479026	+	0.144501i
$619$	12.1197	+	16.6813i	0.487130	+	0.670477i	0.979855	−	0.199708i	$-0.0639993\pi$
$619$	12.1197	+	16.6813i	0.487130	+	0.670477i	−0.492726	+	0.870185i	$0.663999\pi$
$620$		0			0
$621$	22.8822	−	31.4946i	0.918229	−	1.26383i
$622$	1.99813	−	5.73341i	0.0801178	−	0.229889i
$623$	−11.3223	+	34.8464i	−0.453617	+	1.39609i
$624$	4.34585	−	10.3106i	0.173973	−	0.412755i
$625$		0			0
$626$	−5.60929	−	18.5950i	−0.224192	−	0.743206i
$627$	−0.150788	−	0.0489939i	−0.00602188	−	0.00195663i
$628$	−0.393627	+	9.28493i	−0.0157074	+	0.370509i
$629$	−10.6873	+	14.7097i	−0.426129	+	0.586516i
$630$		0			0
$631$	−26.5548	+	19.2932i	−1.05713	+	0.768050i	−0.973555	−	0.228452i	$-0.926634\pi$
$631$	−26.5548	+	19.2932i	−1.05713	+	0.768050i	−0.0835747	+	0.996502i	$0.526634\pi$
$632$	−27.3999	−	22.7005i	−1.08991	−	0.902976i
$633$	16.8198	−	12.2203i	0.668528	−	0.485714i
$634$	10.3055	+	14.8353i	0.409285	+	0.589186i
$635$		0			0
$636$	3.06132	+	10.9848i	0.121389	+	0.435576i
$637$	−3.31947	+	1.07856i	−0.131522	+	0.0427342i
$638$	2.34531	−	1.62919i	0.0928515	−	0.0645004i
$639$	2.59143	−	7.97559i	0.102515	−	0.315510i
$640$		0			0
$641$	6.10344	+	18.7845i	0.241072	+	0.741942i	0.996258	+	0.0864316i	$0.0275464\pi$
$641$	6.10344	+	18.7845i	0.241072	+	0.741942i	−0.755186	+	0.655510i	$0.772454\pi$
$642$	11.3014	+	8.58249i	0.446029	+	0.338724i
$643$		−	21.0042i		−	0.828324i	−0.910203	−	0.414162i	$-0.864075\pi$
$643$		−	21.0042i		−	0.828324i	0.910203	−	0.414162i	$-0.135925\pi$
$644$	−11.2114	+	30.1023i	−0.441791	+	1.18620i
$645$		0			0
$646$	1.59110	+	0.554510i	0.0626012	+	0.0218169i
$647$	26.7896	+	19.4638i	1.05321	+	0.765202i	0.972820	−	0.231562i	$-0.0743836\pi$
$647$	26.7896	+	19.4638i	1.05321	+	0.765202i	0.0803896	+	0.996764i	$0.474384\pi$
$648$	−8.42030	+	5.33517i	−0.330781	+	0.209585i
$649$	1.13326			0.0444844
$650$		0			0
$651$			26.1240i			1.02388i
$652$	25.3054	−	7.05227i	0.991035	−	0.276188i
$653$	0.194712	−	0.267998i	0.00761966	−	0.0104876i	−0.805190	−	0.593017i	$-0.797937\pi$
$653$	0.194712	−	0.267998i	0.00761966	−	0.0104876i	0.812810	+	0.582529i	$0.197937\pi$
$654$	−4.11989	+	11.8216i	−0.161101	+	0.462260i
$655$		0			0
$656$	5.43085	+	23.2551i	0.212039	+	0.907960i
$657$	−7.06276			−0.275545
$658$	−2.91670	−	2.21500i	−0.113705	−	0.0863497i
$659$	2.06861	−	0.672132i	0.0805816	−	0.0261826i	−0.268449	−	0.963294i	$-0.586511\pi$
$659$	2.06861	−	0.672132i	0.0805816	−	0.0261826i	0.349030	+	0.937111i	$0.386511\pi$
$660$		0			0
$661$	14.4168	+	4.68430i	0.560748	+	0.182198i	0.575658	−	0.817691i	$-0.304746\pi$
$661$	14.4168	+	4.68430i	0.560748	+	0.182198i	−0.0149097	+	0.999889i	$0.504746\pi$
$662$	−3.83383	−	5.51899i	−0.149006	−	0.214501i
$663$	1.96948	+	6.06144i	0.0764883	+	0.235407i
$664$	8.32448	+	13.1382i	0.323052	+	0.509862i
$665$		0			0
$666$	−8.23835	−	11.8595i	−0.319230	−	0.459547i
$667$	−35.6100	−	49.0130i	−1.37883	−	1.89779i
$668$	−34.7965	+	23.0946i	−1.34632	+	0.893557i
$669$	−17.9492	−	24.7049i	−0.693955	−	0.955147i
$670$		0			0
$671$	0.426145	+	0.309612i	0.0164511	+	0.0119525i
$672$	11.5135	−	12.7562i	0.444144	−	0.492081i
$673$	1.28032	−	3.94041i	0.0493526	−	0.151892i	−0.923343	−	0.383976i	$-0.874555\pi$
$673$	1.28032	−	3.94041i	0.0493526	−	0.151892i	0.972696	+	0.232084i	$0.0745545\pi$
$674$	12.0965	+	40.1005i	0.465942	+	1.54462i
$675$		0			0
$676$	−14.0843	+	9.34781i	−0.541703	+	0.359531i
$677$	21.3238	+	6.92852i	0.819540	+	0.266285i	0.688633	−	0.725110i	$-0.258211\pi$
$677$	21.3238	+	6.92852i	0.819540	+	0.266285i	0.130907	+	0.991395i	$0.458211\pi$
$678$	−26.6163	−	9.27595i	−1.02219	−	0.356241i
$679$	−23.9128	−	17.3737i	−0.917689	−	0.666740i
$680$		0			0
$681$	4.75261	−	3.45297i	0.182120	−	0.132318i
$682$	2.69149	−	0.811904i	0.103063	−	0.0310894i
$683$	−19.2795	−	26.5359i	−0.737709	−	1.01537i	−0.998747	−	0.0500406i	$-0.984065\pi$
$683$	−19.2795	−	26.5359i	−0.737709	−	1.01537i	0.261038	−	0.965328i	$-0.415935\pi$
$684$	−0.831712	+	1.04832i	−0.0318013	+	0.0400836i
$685$		0			0
$686$	−28.2801	−	0.599186i	−1.07974	−	0.0228770i
$687$	2.06867	+	6.36672i	0.0789247	+	0.242905i
$688$	3.29969	−	38.8469i	0.125800	−	1.48103i
$689$	−2.86464	+	8.81645i	−0.109134	+	0.335880i
$690$		0			0
$691$	−35.7160	+	11.6048i	−1.35870	+	0.441468i	−0.895609	−	0.444843i	$-0.853259\pi$
$691$	−35.7160	+	11.6048i	−1.35870	+	0.441468i	−0.463090	+	0.886311i	$0.653259\pi$
$692$	−14.7658	−	5.49945i	−0.561313	−	0.209058i
$693$			0.684949i			0.0260190i
$694$	−16.5021	+	21.7298i	−0.626410	+	0.824853i
$695$		0			0
$696$	8.03715	+	31.3966i	0.304647	+	1.19009i
$697$	−11.0048	−	7.99547i	−0.416837	−	0.302850i
$698$	0.992240	−	46.8312i	0.0375568	−	1.77259i
$699$			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	$-0.145465\pi$
$702$	−16.9257	−	0.358614i	−0.638818	−	0.0135350i
$703$	3.37605	+	2.45284i	0.127330	+	0.0925108i
$704$	−1.67207	−	0.789765i	−0.0630185	−	0.0297654i
$705$		0			0
$706$	14.9664	+	11.3658i	0.563267	+	0.427756i
$707$			26.8397i			1.00941i
$708$	−4.48895	+	12.0527i	−0.168705	+	0.452967i
$709$	12.3034	−	3.99762i	0.462064	−	0.150134i	−0.0687289	−	0.997635i	$-0.521894\pi$
$709$	12.3034	−	3.99762i	0.462064	−	0.150134i	0.530793	+	0.847502i	$0.321894\pi$
$710$		0			0
$711$	−4.97406	+	15.3086i	−0.186542	+	0.574116i
$712$	−16.5030	+	41.5942i	−0.618476	+	1.55881i
$713$	−18.4305	−	56.7231i	−0.690226	−	2.12430i
$714$	−0.207337	+	9.78581i	−0.00775941	+	0.366225i
$715$		0			0
$716$	19.9562	−	25.1537i	0.745800	−	0.940036i
$717$	15.6592	+	21.5530i	0.584803	+	0.804912i
$718$	6.91732	+	22.9312i	0.258152	+	0.855785i
$719$	1.77973	−	1.29305i	0.0663726	−	0.0482225i	−0.554104	−	0.832447i	$-0.686939\pi$
$719$	1.77973	−	1.29305i	0.0663726	−	0.0482225i	0.620477	+	0.784225i	$0.286939\pi$
$720$		0			0
$721$	−12.5632	−	9.12770i	−0.467878	−	0.339933i
$722$	−8.71550	+	25.0081i	−0.324357	+	0.930707i
$723$	24.1634	+	7.85116i	0.898646	+	0.291988i
$724$	−18.9683	−	28.5793i	−0.704950	−	1.06214i
$725$		0			0
$726$	19.4405	−	5.86433i	0.721504	−	0.217646i
$727$	−1.38226	+	4.25417i	−0.0512653	+	0.157778i	−0.973412	−	0.229063i	$-0.926434\pi$
$727$	−1.38226	+	4.25417i	−0.0512653	+	0.157778i	0.922146	+	0.386841i	$0.126434\pi$
$728$	13.5328	−	3.46424i	0.501560	−	0.128393i
$729$	21.5182	+	15.6339i	0.796969	+	0.579032i
$730$		0			0
$731$	13.0530	+	17.9660i	0.482784	+	0.664496i
$732$	−4.98085	+	3.30582i	−0.184097	+	0.122186i
$733$	−7.67219	−	10.5599i	−0.283379	−	0.390037i	0.643471	−	0.765471i	$-0.277494\pi$
$733$	−7.67219	−	10.5599i	−0.283379	−	0.390037i	−0.926849	+	0.375433i	$0.877494\pi$
$734$	−10.1472	+	7.04885i	−0.374539	+	0.260178i
$735$		0			0
$736$	−15.9999	+	35.8204i	−0.589764	+	1.32036i
$737$	−0.225815	−	0.694989i	−0.00831802	−	0.0256002i
$738$	8.87248	−	6.16337i	0.326600	−	0.226877i
$739$	29.8146	+	9.68735i	1.09675	+	0.356355i	0.800850	−	0.598865i	$-0.204381\pi$
$739$	29.8146	+	9.68735i	1.09675	+	0.356355i	0.295898	+	0.955220i	$0.404381\pi$
$740$		0			0
$741$	1.39117	−	0.452018i	0.0511058	−	0.0166053i
$742$	−8.61028	+	11.3380i	−0.316093	+	0.416230i
$743$	−28.1541			−1.03287			−0.516437	−	0.856325i	$-0.672742\pi$
$743$	−28.1541			−1.03287			−0.516437	+	0.856325i	$0.672742\pi$
$744$	−2.02633	+	31.8411i	−0.0742890	+	1.16735i
$745$		0			0
$746$	1.33987	+	0.466953i	0.0490561	+	0.0170964i
$747$	4.13567	−	5.69226i	0.151316	−	0.208269i
$748$	1.01465	−	0.282771i	0.0370994	−	0.0103391i
$749$			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	$0.576080\pi$
$752$	−3.38320	−	2.92598i	−0.123373	−	0.106700i
$753$	4.84932	+	3.52324i	0.176719	+	0.128394i
$754$	−8.67038	+	24.8787i	−0.315757	+	0.906028i
$755$		0			0
$756$	−24.3647	−	9.07449i	−0.886135	−	0.330036i
$757$		−	16.0395i		−	0.582965i	−0.956576	−	0.291482i	$-0.905851\pi$
$757$		−	16.0395i		−	0.582965i	0.956576	−	0.291482i	$-0.0941485\pi$
$758$	30.8872	−	40.6720i	1.12187	−	1.47728i
$759$	0.649771	+	1.99979i	0.0235852	+	0.0725878i
$760$		0			0
$761$	3.49479	−	10.7559i	0.126686	−	0.389900i	−0.867518	−	0.497405i	$-0.834286\pi$
$761$	3.49479	−	10.7559i	0.126686	−	0.389900i	0.994205	+	0.107505i	$0.0342863\pi$
$762$	4.82948	+	6.95228i	0.174954	+	0.251855i
$763$	−14.8645	+	4.82977i	−0.538131	+	0.174849i
$764$	−1.60470	−	5.75806i	−0.0580558	−	0.208319i
$765$		0			0
$766$	35.8703	−	24.9177i	1.29605	−	0.900313i
$767$	−8.45866	+	6.14557i	−0.305424	+	0.221904i
$768$	15.0227	−	14.6548i	0.542084	−	0.528810i
$769$	−3.25219	+	2.36285i	−0.117277	+	0.0852066i	−0.644878	−	0.764286i	$-0.723092\pi$
$769$	−3.25219	+	2.36285i	−0.117277	+	0.0852066i	0.527601	+	0.849492i	$0.323092\pi$
$770$		0			0
$771$	21.1549	−	29.1173i	0.761876	−	1.04863i
$772$	29.8430	+	1.26517i	1.07407	+	0.0455343i
$773$	−2.33810	−	0.759693i	−0.0840955	−	0.0273243i	0.266667	−	0.963789i	$-0.414078\pi$
$773$	−2.33810	−	0.759693i	−0.0840955	−	0.0273243i	−0.350763	+	0.936464i	$0.614078\pi$
$774$	−16.8852	+	5.09352i	−0.606926	+	0.183083i
$775$		0			0
$776$	−27.7984	−	23.0307i	−0.997906	−	0.826752i
$777$	−7.49097	+	23.0548i	−0.268737	+	0.827088i
$778$	−1.77281	−	0.617835i	−0.0635582	−	0.0221505i
$779$	−1.83505	+	2.52573i	−0.0657475	+	0.0904937i
$780$		0			0
$781$	0.890481	+	1.22564i	0.0318639	+	0.0438569i
$782$	−6.45369	−	21.3943i	−0.230784	−	0.765057i
$783$	39.6710	−	28.8227i	1.41773	−	1.03004i
$784$	−6.52309	−	0.554077i	−0.232967	−	0.0197885i
$785$		0			0
$786$	28.7833	+	0.609848i	1.02667	+	0.0217526i
$787$	−28.5523	+	9.27720i	−1.01778	+	0.330697i	−0.769948	−	0.638107i	$-0.779718\pi$
$787$	−28.5523	+	9.27720i	−1.01778	+	0.330697i	−0.247831	+	0.968803i	$0.579718\pi$
$788$	−34.2253	+	43.1389i	−1.21922	+	1.53676i
$789$	−16.0606	−	5.21842i	−0.571774	−	0.185781i
$790$		0			0
$791$	−10.8742	−	33.4675i	−0.386644	−	1.18997i
$792$	−0.0531287	+	0.834847i	−0.00188785	+	0.0296650i
$793$	−4.85974			−0.172575
$794$	8.25267	−	10.8671i	0.292876	−	0.385658i
$795$		0			0
$796$	22.7439	+	0.964210i	0.806138	+	0.0341755i
$797$	−13.0696	+	17.9888i	−0.462950	+	0.637196i	−0.975117	−	0.221690i	$-0.928843\pi$
$797$	−13.0696	+	17.9888i	−0.462950	+	0.637196i	0.512167	+	0.858886i	$0.328843\pi$
$798$	2.24595	+	0.0475863i	0.0795059	+	0.00168454i
$799$	2.54783			0.0901359
$800$		0			0
$801$	20.2432			0.715257
$802$	−16.6469	−	0.352706i	−0.587821	−	0.0124545i
$803$	0.749967	−	1.03224i	0.0264658	−	0.0364270i
$804$	8.28595	+	0.351276i	0.292223	+	0.0123885i
$805$		0			0
$806$	−15.6864	+	20.6558i	−0.552531	+	0.727569i
$807$	−2.00232			−0.0704852
$808$	−2.08185	+	32.7135i	−0.0732392	+	1.15086i
$809$	10.2871	+	31.6605i	0.361676	+	1.11313i	0.952036	+	0.305985i	$0.0989859\pi$
$809$	10.2871	+	31.6605i	0.361676	+	1.11313i	−0.590360	+	0.807140i	$0.701014\pi$
$810$		0			0
$811$	−41.7447	−	13.5637i	−1.46585	−	0.476285i	−0.536002	−	0.844217i	$-0.680066\pi$
$811$	−41.7447	−	13.5637i	−1.46585	−	0.476285i	−0.929853	+	0.367932i	$0.880066\pi$
$812$	−25.1479	+	31.6974i	−0.882519	+	1.11236i
$813$	−30.5355	+	9.92157i	−1.07093	+	0.347965i
$814$	2.60810	+	0.0552592i	0.0914138	+	0.00193684i
$815$		0			0
$816$	−1.01176	+	11.9113i	−0.0354187	+	0.416980i
$817$	4.12339	−	2.99582i	0.144259	−	0.104810i
$818$	−0.0600873	−	0.199192i	−0.00210090	−	0.00696458i
$819$	−3.71442	−	5.11245i	−0.129792	−	0.178644i
$820$		0			0
$821$	17.1793	−	23.6453i	0.599561	−	0.825225i	−0.396107	−	0.918205i	$-0.629639\pi$
$821$	17.1793	−	23.6453i	0.599561	−	0.825225i	0.995668	+	0.0929790i	$0.0296390\pi$
$822$	−25.7488	−	8.97361i	−0.898092	−	0.312991i
$823$	−4.17485	+	12.8489i	−0.145526	+	0.447883i	−0.997078	−	0.0763866i	$-0.975662\pi$
$823$	−4.17485	+	12.8489i	−0.145526	+	0.447883i	0.851552	+	0.524270i	$0.175662\pi$
$824$	−14.6046	−	12.0997i	−0.508776	−	0.421514i
$825$		0			0
$826$	−15.3729	+	4.63733i	−0.534893	+	0.161353i
$827$	27.4721	+	8.92624i	0.955300	+	0.310396i	0.744867	−	0.667213i	$-0.232513\pi$
$827$	27.4721	+	8.92624i	0.955300	+	0.310396i	0.210433	+	0.977608i	$0.432513\pi$
$828$	17.7314	+	0.751709i	0.616210	+	0.0261237i
$829$	−21.9589	+	30.2238i	−0.762663	+	1.04972i	0.234325	+	0.972158i	$0.424712\pi$
$829$	−21.9589	+	30.2238i	−0.762663	+	1.04972i	−0.996988	+	0.0775572i	$0.975288\pi$
$830$		0			0
$831$	−29.0732	+	21.1229i	−1.00854	+	0.732745i
$832$	16.7632	−	3.17269i	0.581158	−	0.109993i
$833$	3.01681	−	2.19184i	0.104526	−	0.0759427i
$834$	8.99224	−	6.24657i	0.311376	−	0.216301i
$835$		0			0
$836$	−0.0648990	−	0.232874i	−0.00224458	−	0.00805413i
$837$	45.9115	−	14.9176i	1.58694	−	0.515627i
$838$	−27.5124	−	39.6055i	−0.950400	−	1.36815i
$839$	−2.47513	+	7.61767i	−0.0854510	+	0.262991i	−0.984648	−	0.174553i	$-0.944152\pi$
$839$	−2.47513	+	7.61767i	−0.0854510	+	0.262991i	0.899197	+	0.437545i	$0.144152\pi$
$840$		0			0
$841$	−14.6201	−	44.9960i	−0.504141	−	1.55159i
$842$	4.99435	−	6.57653i	0.172117	−	0.226642i
$843$			38.1169i			1.31282i
$844$	29.7071	+	11.0643i	1.02256	+	0.380847i
$845$		0			0
$846$	−0.665910	+	1.91075i	−0.0228944	+	0.0656930i
$847$	20.5094	+	14.9010i	0.704713	+	0.512004i
$848$	−11.3741	+	13.1514i	−0.390587	+	0.451620i
$849$	13.0057			0.446354
$850$		0			0
$851$		−	55.3440i		−	1.89717i
$852$	−16.5625	+	4.61574i	−0.567420	+	0.158132i
$853$	9.86242	−	13.5745i	0.337683	−	0.464780i	−0.606080	−	0.795404i	$-0.707259\pi$
$853$	9.86242	−	13.5745i	0.337683	−	0.464780i	0.943763	+	0.330623i	$0.107259\pi$
$854$	−7.04770	−	2.45617i	−0.241167	−	0.0840483i
$855$		0			0
$856$	−1.37422	+	21.5941i	−0.0469700	+	0.738071i
$857$	−12.0516			−0.411675			−0.205837	−	0.978586i	$-0.565992\pi$
$857$	−12.0516			−0.411675			−0.205837	+	0.978586i	$0.565992\pi$
$858$	0.553029	−	0.728226i	0.0188801	−	0.0248612i
$859$	−53.1530	+	17.2704i	−1.81356	+	0.589260i	−0.813587	+	0.581443i	$0.802488\pi$
$859$	−53.1530	+	17.2704i	−1.81356	+	0.589260i	−0.999969	+	0.00781665i	$0.997512\pi$
$860$		0			0
$861$	−17.2481	−	5.60423i	−0.587812	−	0.190992i
$862$	4.75137	−	3.30060i	0.161832	−	0.112419i
$863$	8.82744	+	27.1681i	0.300490	+	0.924812i	0.981322	+	0.192373i	$0.0616183\pi$
$863$	8.82744	+	27.1681i	0.300490	+	0.924812i	−0.680832	+	0.732439i	$0.738382\pi$
$864$	−28.9929	−	12.9503i	−0.986360	−	0.440577i
$865$		0			0
$866$	−5.52695	+	3.83936i	−0.187813	+	0.130467i
$867$	9.10434	+	12.5310i	0.309200	+	0.425577i
$868$	−33.1884	+	22.0273i	−1.12649	+	0.747656i
$869$	−1.70921	−	2.35253i	−0.0579811	−	0.0798041i
$870$		0			0
$871$	5.45435	+	3.96281i	0.184813	+	0.134275i
$872$	−18.4922	+	4.73377i	−0.626224	+	0.160306i
$873$	−5.04641	+	15.5312i	−0.170795	+	0.525653i
$874$	−4.91022	+	1.48120i	−0.166091	+	0.0501022i
$875$		0			0
$876$	8.00761	+	12.0650i	0.270552	+	0.407639i
$877$	4.69863	+	1.52668i	0.158661	+	0.0515522i	0.387271	−	0.921966i	$-0.373418\pi$
$877$	4.69863	+	1.52668i	0.158661	+	0.0515522i	−0.228609	+	0.973518i	$0.573418\pi$
$878$	0.815701	−	2.34056i	0.0275286	−	0.0789902i
$879$	6.60284	+	4.79725i	0.222708	+	0.161807i
$880$		0			0
$881$	−0.550583	+	0.400022i	−0.0185496	+	0.0134771i	−0.597021	−	0.802225i	$-0.703649\pi$
$881$	−0.550583	+	0.400022i	−0.0185496	+	0.0134771i	0.578472	+	0.815702i	$0.303649\pi$
$882$	0.855292	+	2.83533i	0.0287992	+	0.0954704i
$883$	1.04603	+	1.43973i	0.0352017	+	0.0484509i	0.826255	−	0.563296i	$-0.190467\pi$
$883$	1.04603	+	1.43973i	0.0352017	+	0.0484509i	−0.791053	+	0.611747i	$0.790467\pi$
$884$	−6.03993	+	7.61297i	−0.203145	+	0.256052i
$885$		0			0
$886$	0.102899	−	4.85657i	0.00345695	−	0.163159i
$887$	13.9287	+	42.8681i	0.467680	+	1.43937i	0.855581	+	0.517669i	$0.173200\pi$
$887$	13.9287	+	42.8681i	0.467680	+	1.43937i	−0.387901	+	0.921701i	$0.626800\pi$
$888$	−10.9186	+	27.5193i	−0.366405	+	0.923486i
$889$	−3.26583	+	10.0512i	−0.109532	+	0.337106i
$890$		0			0
$891$	−0.774771	+	0.251738i	−0.0259558	+	0.00843355i
$892$	16.2511	−	43.6338i	0.544128	−	1.46097i
$893$		−	0.584756i		−	0.0195681i
$894$	−13.5031	−	10.2545i	−0.451612	−	0.342963i
$895$		0			0
$896$	25.9138	+	3.87119i	0.865718	+	0.129327i
$897$	−15.6946	−	11.4028i	−0.524027	−	0.380728i
$898$	7.83632	+	0.166033i	0.261501	+	0.00554058i
$899$		−	75.1261i		−	2.50560i
$900$		0			0
$901$		−	9.90409i		−	0.329953i
$902$	−0.0413412	+	1.95120i	−0.00137651	+	0.0649679i
$903$	23.9530	+	17.4028i	0.797104	+	0.579130i
$904$	−10.6581	−	41.6352i	−0.354483	−	1.38477i
$905$		0			0
$906$	−9.64267	+	12.6974i	−0.320356	+	0.421843i
$907$			22.9525i			0.762127i	0.924549	+	0.381063i	$0.124442\pi$
$907$			22.9525i			0.762127i	−0.924549	+	0.381063i	$0.875558\pi$
$908$	8.39405	+	3.12631i	0.278566	+	0.103750i
$909$	14.1030	−	4.58234i	0.467766	−	0.151987i
$910$		0			0
$911$	1.55833	−	4.79606i	0.0516299	−	0.158900i	−0.921917	−	0.387387i	$-0.873378\pi$
$911$	1.55833	−	4.79606i	0.0516299	−	0.158900i	0.973547	+	0.228487i	$0.0733777\pi$
$912$	2.73378	+	0.232210i	0.0905246	+	0.00768924i
$913$	0.392788	+	1.20888i	0.0129994	+	0.0400080i
$914$	−4.28146	−	0.0907138i	−0.141618	−	0.00300054i
$915$		0			0
$916$	−6.34413	+	7.99640i	−0.209616	+	0.264208i
$917$	21.1268	+	29.0786i	0.697670	+	0.960260i
$918$	17.3165	−	5.22360i	0.571528	−	0.172405i
$919$	0.772993	−	0.561613i	0.0254987	−	0.0185259i	−0.574963	−	0.818179i	$-0.694984\pi$
$919$	0.772993	−	0.561613i	0.0254987	−	0.0185259i	0.600462	+	0.799654i	$0.294984\pi$
$920$		0			0
$921$	31.4250	+	22.8316i	1.03549	+	0.752326i
$922$	−16.8200	−	5.86188i	−0.553937	−	0.193051i
$923$	−13.2931	−	4.31919i	−0.437547	−	0.142168i
$924$	1.17007	−	0.776580i	0.0384924	−	0.0255476i
$925$		0			0
$926$	−1.78925	−	5.93142i	−0.0587983	−	0.194919i
$927$	−2.65126	+	8.15973i	−0.0870787	+	0.268001i
$928$	−33.1101	+	36.6837i	−1.08689	+	1.20420i
$929$	46.5656	+	33.8319i	1.52777	+	1.10999i	0.957463	+	0.288555i	$0.0931748\pi$
$929$	46.5656	+	33.8319i	1.52777	+	1.10999i	0.570304	+	0.821433i	$0.306825\pi$
$930$		0			0
$931$	−0.503052	−	0.692391i	−0.0164868	−	0.0226922i
$932$	−5.83007	+	3.86945i	−0.190970	+	0.126748i
$933$	3.31004	+	4.55588i	0.108366	+	0.149153i
$934$	18.3165	+	26.3675i	0.599335	+	0.862772i
$935$		0			0
$936$	−4.13075	−	6.51941i	−0.135018	−	0.213094i
$937$	−10.9461	−	33.6886i	−0.357593	−	1.10056i	−0.954491	−	0.298240i	$-0.903600\pi$
$937$	−10.9461	−	33.6886i	−0.357593	−	1.10056i	0.596898	−	0.802317i	$-0.296400\pi$
$938$	5.90715	+	8.50364i	0.192875	+	0.277654i
$939$	17.1327	+	5.56674i	0.559103	+	0.181664i
$940$		0			0
$941$	−0.202380	+	0.0657573i	−0.00659741	+	0.00214363i	−0.312314	−	0.949979i	$-0.601104\pi$
$941$	−0.202380	+	0.0657573i	−0.00659741	+	0.00214363i	0.305716	+	0.952123i	$0.401104\pi$
$942$	−6.86439	−	5.21295i	−0.223654	−	0.169847i
$943$	41.4046			1.34832
$944$	−19.0970	+	4.45978i	−0.621553	+	0.145153i
$945$		0			0
$946$	1.04854	−	3.00868i	0.0340911	−	0.0978206i
$947$	−3.47868	+	4.78799i	−0.113042	+	0.155589i	−0.861789	−	0.507267i	$-0.830656\pi$
$947$	−3.47868	+	4.78799i	−0.113042	+	0.155589i	0.748747	+	0.662856i	$0.230656\pi$
$948$	31.7904	−	8.85957i	1.03251	−	0.287745i
$949$			11.7717i			0.382124i
$950$		0			0
$951$	−16.7538			−0.543279
$952$	−12.6069	+	7.98784i	−0.408592	+	0.258887i
$953$	41.8326	+	30.3932i	1.35509	+	0.984531i	0.998740	+	0.0501787i	$0.0159791\pi$
$953$	41.8326	+	30.3932i	1.35509	+	0.984531i	0.356351	+	0.934352i	$0.384021\pi$
$954$	7.42759	+	2.58856i	0.240477	+	0.0838079i
$955$		0			0
$956$	−14.1778	+	38.0669i	−0.458543	+	1.23117i
$957$			2.64859i			0.0856169i
$958$	7.77373	+	5.90353i	0.251158	+	0.190734i
$959$	−10.5198	−	32.3766i	−0.339702	−	1.04550i
$960$		0			0
$961$	13.2751	−	40.8565i	0.428228	−	1.31795i
$962$	−19.7665	+	13.7310i	−0.637298	+	0.442706i
$963$	9.30935	−	3.02479i	0.299989	−	0.0974725i
$964$	10.3999	+	37.3176i	0.334959	+	1.20192i
$965$		0			0
$966$	−16.9975	−	24.4687i	−0.546885	−	0.787269i
$967$	15.9937	−	11.6201i	0.514323	−	0.373677i	−0.300138	−	0.953896i	$-0.597033\pi$
$967$	15.9937	−	11.6201i	0.514323	−	0.373677i	0.814461	+	0.580218i	$0.197033\pi$
$968$	23.8421	+	19.7529i	0.766313	+	0.634881i
$969$	−1.26432	+	0.918585i	−0.0406159	+	0.0295092i
$970$		0			0
$971$	−11.7741	+	16.2057i	−0.377850	+	0.520065i	−0.955013	−	0.296563i	$-0.904159\pi$
$971$	−11.7741	+	16.2057i	−0.377850	+	0.520065i	0.577164	+	0.816628i	$0.304159\pi$
$972$	−1.03495	+	24.4126i	−0.0331960	+	0.783033i
$973$	13.0004	+	4.22409i	0.416775	+	0.135418i
$974$	14.6459	+	48.5516i	0.469283	+	1.55569i
$975$		0			0
$976$	−8.39955	−	3.54035i	−0.268863	−	0.113324i
$977$	14.3762	−	44.2455i	0.459937	−	1.41554i	−0.405304	−	0.914182i	$-0.632834\pi$
$977$	14.3762	−	44.2455i	0.459937	−	1.41554i	0.865240	−	0.501357i	$-0.167166\pi$
$978$	−8.01835	+	23.0078i	−0.256399	+	0.735707i
$979$	−2.14954	+	2.95859i	−0.0686997	+	0.0945570i
$980$		0			0
$981$	5.07563	+	6.98600i	0.162052	+	0.223046i
$982$	10.4886	−	3.16393i	0.334704	−	0.100965i
$983$	−25.1326	+	18.2599i	−0.801606	+	0.582401i	−0.911385	−	0.411555i	$-0.864986\pi$
$983$	−25.1326	+	18.2599i	−0.801606	+	0.582401i	0.109779	+	0.993956i	$0.464986\pi$
$984$	−20.5880	−	8.16856i	−0.656322	−	0.260404i
$985$		0			0
$986$	0.596251	−	28.1416i	0.0189885	−	0.896210i
$987$	3.23062	−	1.04969i	0.102832	−	0.0334120i
$988$	1.74726	+	1.38623i	0.0555878	+	0.0441019i
$989$	−64.2869	−	20.8881i	−2.04420	−	0.664202i
$990$		0			0
$991$	4.56887	+	14.0615i	0.145135	+	0.446679i	0.997028	−	0.0770360i	$-0.0245457\pi$
$991$	4.56887	+	14.0615i	0.145135	+	0.446679i	−0.851893	+	0.523715i	$0.824546\pi$
$992$	−42.1602	+	24.2736i	−1.33859	+	0.770689i
$993$	6.23268			0.197788
$994$	−17.0949	−	12.9822i	−0.542218	−	0.411772i
$995$		0			0
$996$	−14.4128	−	0.611017i	−0.456686	−	0.0193608i
$997$	−15.2722	+	21.0204i	−0.483676	+	0.665723i	−0.979206	−	0.202868i	$-0.934974\pi$
$997$	−15.2722	+	21.0204i	−0.483676	+	0.665723i	0.495530	+	0.868591i	$0.334974\pi$
$998$	−1.09179	+	51.5298i	−0.0345600	+	1.63115i
$999$	44.7952			1.41726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.t.b.101.1		224
5.2	odd	4		1000.2.o.a.149.14		112
5.3	odd	4		200.2.o.a.29.15	✓	112
5.4	even	2	inner	1000.2.t.b.101.56		224
8.5	even	2	inner	1000.2.t.b.101.46		224
20.3	even	4		800.2.be.a.529.10		112
25.6	even	5	inner	1000.2.t.b.901.46		224
25.8	odd	20		1000.2.o.a.349.9		112
25.17	odd	20		200.2.o.a.69.20	yes	112
25.19	even	10	inner	1000.2.t.b.901.11		224
40.3	even	4		800.2.be.a.529.19		112
40.13	odd	4		200.2.o.a.29.20	yes	112
40.29	even	2	inner	1000.2.t.b.101.11		224
40.37	odd	4		1000.2.o.a.149.9		112
100.67	even	20		800.2.be.a.369.19		112
200.67	even	20		800.2.be.a.369.10		112
200.69	even	10	inner	1000.2.t.b.901.56		224
200.117	odd	20		200.2.o.a.69.15	yes	112
200.133	odd	20		1000.2.o.a.349.14		112
200.181	even	10	inner	1000.2.t.b.901.1		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.15	✓	112	5.3	odd	4
200.2.o.a.29.20	yes	112	40.13	odd	4
200.2.o.a.69.15	yes	112	200.117	odd	20
200.2.o.a.69.20	yes	112	25.17	odd	20
800.2.be.a.369.10		112	200.67	even	20
800.2.be.a.369.19		112	100.67	even	20
800.2.be.a.529.10		112	20.3	even	4
800.2.be.a.529.19		112	40.3	even	4
1000.2.o.a.149.9		112	40.37	odd	4
1000.2.o.a.149.14		112	5.2	odd	4
1000.2.o.a.349.9		112	25.8	odd	20
1000.2.o.a.349.14		112	200.133	odd	20
1000.2.t.b.101.1		224	1.1	even	1	trivial
1000.2.t.b.101.11		224	40.29	even	2	inner
1000.2.t.b.101.46		224	8.5	even	2	inner
1000.2.t.b.101.56		224	5.4	even	2	inner
1000.2.t.b.901.1		224	200.181	even	10	inner
1000.2.t.b.901.11		224	25.19	even	10	inner
1000.2.t.b.901.46		224	25.6	even	5	inner
1000.2.t.b.901.56		224	200.69	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41390 - 0.0299570i) q^{2} +(0.770982 - 1.06117i) q^{3} +(1.99821 + 0.0847122i) q^{4} +(-1.12188 + 1.47728i) q^{6} -2.31589 q^{7} +(-2.82272 - 0.179635i) q^{8} +(0.395392 + 1.21689i) q^{9} +O(q^{10})\)	\(q+(-1.41390 - 0.0299570i) q^{2} +(0.770982 - 1.06117i) q^{3} +(1.99821 + 0.0847122i) q^{4} +(-1.12188 + 1.47728i) q^{6} -2.31589 q^{7} +(-2.82272 - 0.179635i) q^{8} +(0.395392 + 1.21689i) q^{9} +(-0.219837 - 0.0714294i) q^{11} +(1.63047 - 2.05511i) q^{12} +(2.02822 - 0.659008i) q^{13} +(3.27443 + 0.0693772i) q^{14} +(3.98565 + 0.338545i) q^{16} +(-1.84329 + 1.33923i) q^{17} +(-0.522589 - 1.73240i) q^{18} +(0.307368 + 0.423055i) q^{19} +(-1.78551 + 2.45754i) q^{21} +(0.308687 + 0.107579i) q^{22} +(2.14309 - 6.59576i) q^{23} +(-2.36689 + 2.85688i) q^{24} +(-2.88743 + 0.871009i) q^{26} +(5.33859 + 1.73461i) q^{27} +(-4.62763 - 0.196184i) q^{28} +(5.13469 - 7.06729i) q^{29} +(6.95750 - 5.05492i) q^{31} +(-5.62515 - 0.598065i) q^{32} +(-0.245289 + 0.178213i) q^{33} +(2.64634 - 1.83831i) q^{34} +(0.686988 + 2.46509i) q^{36} +(7.58959 - 2.46601i) q^{37} +(-0.421912 - 0.607364i) q^{38} +(0.864403 - 2.66036i) q^{39} +(1.84490 + 5.67801i) q^{41} +(2.59815 - 3.42122i) q^{42} -9.74670i q^{43} +(-0.433228 - 0.161353i) q^{44} +(-3.22770 + 9.26151i) q^{46} +(-0.904676 - 0.657286i) q^{47} +(3.43211 - 3.96842i) q^{48} -1.63664 q^{49} +2.98855i q^{51} +(4.10862 - 1.14502i) q^{52} +(-2.55504 + 3.51671i) q^{53} +(-7.49624 - 2.61249i) q^{54} +(6.53711 + 0.416014i) q^{56} +0.685906 q^{57} +(-7.47163 + 9.83860i) q^{58} +(-4.66275 + 1.51502i) q^{59} +(-2.16726 - 0.704186i) q^{61} +(-9.98861 + 6.93871i) q^{62} +(-0.915685 - 2.81819i) q^{63} +(7.93546 + 1.01411i) q^{64} +(0.352152 - 0.244626i) q^{66} +(1.85821 + 2.55761i) q^{67} +(-3.79672 + 2.51990i) q^{68} +(-5.34690 - 7.35938i) q^{69} +(-5.30236 - 3.85239i) q^{71} +(-0.897484 - 3.50596i) q^{72} +(-1.70573 + 5.24971i) q^{73} +(-10.8048 + 3.25932i) q^{74} +(0.578346 + 0.871389i) q^{76} +(0.509119 + 0.165423i) q^{77} +(-1.30187 + 3.73557i) q^{78} +(10.1775 + 7.39438i) q^{79} +(2.85122 - 2.07153i) q^{81} +(-2.43840 - 8.08339i) q^{82} +(-3.23222 - 4.44876i) q^{83} +(-3.77600 + 4.75942i) q^{84} +(-0.291982 + 13.7808i) q^{86} +(-3.54081 - 10.8975i) q^{87} +(0.607706 + 0.241115i) q^{88} +(4.88895 - 15.0466i) q^{89} +(-4.69713 + 1.52619i) q^{91} +(4.84108 - 12.9981i) q^{92} -11.2803i q^{93} +(1.25943 + 0.956435i) q^{94} +(-4.97154 + 5.50812i) q^{96} +(10.3255 + 7.50193i) q^{97} +(2.31405 + 0.0490290i) q^{98} -0.295760i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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