LMFDB - Embedded newform 1000.2.t.b.901.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			901.11
Character	$\chi$	$=$	1000.901
Dual form			1000.2.t.b.101.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16147 + 0.806832i) q^{2} +(0.770982 + 1.06117i) q^{3} +(0.698045 - 1.87423i) q^{4} +(-1.75166 - 0.610464i) q^{6} +2.31589 q^{7} +(0.701425 + 2.74007i) q^{8} +(0.395392 - 1.21689i) q^{9} +O(q^{10})$	\(q+(-1.16147 + 0.806832i) q^{2} +(0.770982 + 1.06117i) q^{3} +(0.698045 - 1.87423i) q^{4} +(-1.75166 - 0.610464i) q^{6} +2.31589 q^{7} +(0.701425 + 2.74007i) q^{8} +(0.395392 - 1.21689i) q^{9} +(0.219837 - 0.0714294i) q^{11} +(2.52705 - 0.704254i) q^{12} +(2.02822 + 0.659008i) q^{13} +(-2.68985 + 1.86853i) q^{14} +(-3.02547 - 2.61659i) 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} +(-0.197704 + 0.260335i) 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} +(1.61660 - 4.34051i) 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} +(-3.22146 - 0.0682549i) q^{34} +(-2.00473 - 1.59050i) q^{36} +(7.58959 + 2.46601i) q^{37} +(0.0156653 - 0.739362i) q^{38} +(0.864403 + 2.66036i) q^{39} +(1.84490 - 5.67801i) q^{41} +(-4.05665 - 1.41377i) q^{42} +9.74670i q^{43} +(0.0195813 - 0.461886i) q^{44} +(7.81081 + 5.93169i) q^{46} +(0.904676 - 0.657286i) q^{47} +(0.444060 - 5.22787i) q^{48} -1.63664 q^{49} +2.98855i q^{51} +(2.65092 - 3.34133i) q^{52} +(-2.55504 - 3.51671i) q^{53} +(-4.80109 + 6.32205i) q^{54} +(1.62442 + 6.34571i) q^{56} -0.685906 q^{57} +(11.6659 + 4.06565i) q^{58} +(4.66275 + 1.51502i) q^{59} +(2.16726 - 0.704186i) q^{61} +(-12.1594 - 0.257629i) q^{62} +(0.915685 - 2.81819i) q^{63} +(-7.01601 + 3.84391i) q^{64} +(-0.428684 - 0.00908277i) 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} +(3.61171 + 0.229845i) 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} +(-3.15044 - 2.39251i) 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} +(5.85237 - 1.63098i) q^{84} +(-7.86395 - 11.3205i) q^{86} +(3.54081 - 10.8975i) q^{87} +(0.349921 + 0.552267i) q^{88} +(4.88895 + 15.0466i) q^{89} +(4.69713 + 1.52619i) q^{91} +(-13.8579 - 0.587495i) q^{92} +11.2803i q^{93} +(-0.520439 + 1.49334i) q^{94} +(3.70224 + 6.43031i) q^{96} +(-10.3255 + 7.50193i) q^{97} +(1.90092 - 1.32050i) 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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.16147	+	0.806832i	−0.821286	+	0.570516i
$2$	−1.16147	+	0.806832i	−0.821286	+	0.570516i
$3$	0.770982	+	1.06117i	0.445127	+	0.612664i	0.971342	−	0.237687i	$-0.0763893\pi$
$3$	0.770982	+	1.06117i	0.445127	+	0.612664i	−0.526215	+	0.850351i	$0.676389\pi$
$4$	0.698045	−	1.87423i	0.349023	−	0.937114i
$5$		0			0
$5$		0			0
$6$	−1.75166	−	0.610464i	−0.715111	−	0.249221i
$7$	2.31589			0.875325			0.437662	−	0.899139i	$-0.355806\pi$
$7$	2.31589			0.875325			0.437662	+	0.899139i	$0.355806\pi$
$8$	0.701425	+	2.74007i	0.247991	+	0.968762i
$9$	0.395392	−	1.21689i	0.131797	−	0.405630i
$10$		0			0
$11$	0.219837	−	0.0714294i	0.0662834	−	0.0215368i	−0.275688	−	0.961247i	$-0.588906\pi$
$11$	0.219837	−	0.0714294i	0.0662834	−	0.0215368i	0.341971	+	0.939711i	$0.388906\pi$
$12$	2.52705	−	0.704254i	0.729496	−	0.203301i
$13$	2.02822	+	0.659008i	0.562526	+	0.182776i	0.576458	−	0.817127i	$-0.304435\pi$
$13$	2.02822	+	0.659008i	0.562526	+	0.182776i	−0.0139312	+	0.999903i	$0.504435\pi$
$14$	−2.68985	+	1.86853i	−0.718892	+	0.499387i
$15$		0			0
$16$	−3.02547	−	2.61659i	−0.756366	−	0.654148i
$17$	1.84329	+	1.33923i	0.447063	+	0.324810i	0.788435	−	0.615118i	$-0.210892\pi$
$17$	1.84329	+	1.33923i	0.447063	+	0.324810i	−0.341372	+	0.939928i	$0.610892\pi$
$18$	0.522589	+	1.73240i	0.123175	+	0.408331i
$19$	−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
$22$	−0.197704	+	0.260335i	−0.0421505	+	0.0555036i
$23$	−2.14309	−	6.59576i	−0.446865	−	1.37531i	−0.880425	−	0.474185i	$-0.842743\pi$
$23$	−2.14309	−	6.59576i	−0.446865	−	1.37531i	0.433560	−	0.901125i	$-0.357257\pi$
$24$	−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
$28$	1.61660	−	4.34051i	0.305508	−	0.820279i
$29$	−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	$0.419107\pi$
$32$	5.62515	+	0.598065i	0.994396	+	0.105724i
$33$	0.245289	+	0.178213i	0.0426993	+	0.0310228i
$34$	−3.22146	−	0.0682549i	−0.552476	−	0.0117056i
$35$		0			0
$36$	−2.00473	−	1.59050i	−0.334122	−	0.265083i
$37$	7.58959	+	2.46601i	1.24772	+	0.405409i	0.857104	−	0.515144i	$-0.172262\pi$
$37$	7.58959	+	2.46601i	1.24772	+	0.405409i	0.390617	+	0.920553i	$0.372262\pi$
$38$	0.0156653	−	0.739362i	0.00254124	−	0.119940i
$39$	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	$-0.0543756\pi$
$42$	−4.05665	−	1.41377i	−0.625955	−	0.218149i
$43$			9.74670i			1.48636i	0.669093	+	0.743179i	$0.266683\pi$
$43$			9.74670i			1.48636i	−0.669093	+	0.743179i	$0.733317\pi$
$44$	0.0195813	−	0.461886i	0.00295198	−	0.0696319i
$45$		0			0
$46$	7.81081	+	5.93169i	1.15164	+	0.874580i
$47$	0.904676	−	0.657286i	0.131961	−	0.0958750i	−0.519847	−	0.854259i	$-0.674011\pi$
$47$	0.904676	−	0.657286i	0.131961	−	0.0958750i	0.651807	+	0.758384i	$0.274011\pi$
$48$	0.444060	−	5.22787i	0.0640945	−	0.754577i
$49$	−1.63664			−0.233806
$50$		0			0
$51$			2.98855i			0.418481i
$52$	2.65092	−	3.34133i	0.367616	−	0.463359i
$53$	−2.55504	−	3.51671i	−0.350962	−	0.483057i	0.596641	−	0.802508i	$-0.296502\pi$
$53$	−2.55504	−	3.51671i	−0.350962	−	0.483057i	−0.947603	+	0.319451i	$0.896502\pi$
$54$	−4.80109	+	6.32205i	−0.653346	+	0.860322i
$55$		0			0
$56$	1.62442	+	6.34571i	0.217073	+	0.847982i
$57$	−0.685906			−0.0908505
$58$	11.6659	+	4.06565i	1.53181	+	0.533846i
$59$	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	−0.166966	−	0.985963i	$-0.553397\pi$
$61$	2.16726	−	0.704186i	0.277490	−	0.0901618i	0.444456	+	0.895801i	$0.353397\pi$
$62$	−12.1594	−	0.257629i	−1.54425	−	0.0327189i
$63$	0.915685	−	2.81819i	0.115365	−	0.355058i
$64$	−7.01601	+	3.84391i	−0.877001	+	0.480489i
$65$		0			0
$66$	−0.428684	−	0.00908277i	−0.0527674	−	0.00111801i
$67$	1.85821	−	2.55761i	0.227017	−	0.312462i	−0.680280	−	0.732952i	$-0.738142\pi$
$67$	1.85821	−	2.55761i	0.227017	−	0.312462i	0.907297	+	0.420490i	$0.138142\pi$
$68$	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	−0.856149	−	0.516730i	$-0.827149\pi$
$71$	−5.30236	+	3.85239i	−0.629274	+	0.457194i	0.226875	+	0.973924i	$0.427149\pi$
$72$	3.61171	+	0.229845i	0.425644	+	0.0270875i
$73$	1.70573	+	5.24971i	0.199641	+	0.614432i	0.999891	+	0.0147656i	$0.00470020\pi$
$73$	1.70573	+	5.24971i	0.199641	+	0.614432i	−0.800250	+	0.599667i	$0.795300\pi$
$74$	−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
$78$	−3.15044	−	2.39251i	−0.356717	−	0.270898i
$79$	10.1775	−	7.39438i	1.14506	−	0.831933i	0.157241	−	0.987560i	$-0.449740\pi$
$79$	10.1775	−	7.39438i	1.14506	−	0.831933i	0.987816	+	0.155628i	$0.0497400\pi$
$80$		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	−0.948686	−	0.316221i	$-0.897586\pi$
$83$	−3.23222	+	4.44876i	−0.354782	+	0.488315i	0.593904	+	0.804536i	$0.297586\pi$
$84$	5.85237	−	1.63098i	0.638546	−	0.177954i
$85$		0			0
$86$	−7.86395	−	11.3205i	−0.847991	−	1.22073i
$87$	3.54081	−	10.8975i	0.379615	−	1.16834i
$88$	0.349921	+	0.552267i	0.0373017	+	0.0588719i
$89$	4.88895	+	15.0466i	0.518227	+	1.59494i	0.777332	+	0.629091i	$0.216573\pi$
$89$	4.88895	+	15.0466i	0.518227	+	1.59494i	−0.259105	+	0.965849i	$0.583427\pi$
$90$		0			0
$91$	4.69713	+	1.52619i	0.492393	+	0.159988i
$92$	−13.8579	−	0.587495i	−1.44479	−	0.0612506i
$93$			11.2803i			1.16971i
$94$	−0.520439	+	1.49334i	−0.0536792	+	0.154026i
$95$		0			0
$96$	3.70224	+	6.43031i	0.377859	+	0.656291i
$97$	−10.3255	+	7.50193i	−1.04840	+	0.761706i	−0.971907	−	0.235364i	$-0.924372\pi$
$97$	−10.3255	+	7.50193i	−1.04840	+	0.761706i	−0.0764911	+	0.997070i	$0.524372\pi$
$98$	1.90092	−	1.32050i	0.192022	−	0.133390i
$99$		−	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	$-0.195618\pi$
$102$	−2.41126	−	3.47113i	−0.238750	−	0.343693i
$103$	−5.42478	+	3.94133i	−0.534519	+	0.388351i	−0.822045	−	0.569422i	$-0.807167\pi$
$103$	−5.42478	+	3.94133i	−0.534519	+	0.388351i	0.287526	+	0.957773i	$0.407167\pi$
$104$	−0.383088	+	6.01971i	−0.0375648	+	0.590281i
$105$		0			0
$106$	5.80501	+	2.02308i	0.563832	+	0.196499i
$107$			7.65011i			0.739564i	0.929119	+	0.369782i	$0.120568\pi$
$107$			7.65011i			0.739564i	−0.929119	+	0.369782i	$0.879432\pi$
$108$	0.475517	−	11.2166i	0.0457566	−	1.07931i
$109$	−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
$112$	−7.00665	−	6.05975i	−0.662066	−	0.572592i
$113$	−4.69549	+	14.4512i	−0.441714	+	1.35946i	0.444333	+	0.895862i	$0.353441\pi$
$113$	−4.69549	+	14.4512i	−0.441714	+	1.35946i	−0.886047	+	0.463595i	$0.846559\pi$
$114$	0.796663	−	0.553411i	0.0746143	−	0.0518317i
$115$		0			0
$116$	−16.8300	+	4.69029i	−1.56262	+	0.435482i
$117$	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
$122$	−1.94906	+	2.56651i	−0.176460	+	0.232361i
$123$	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	$-0.164897\pi$
$127$	−1.41018	−	4.34009i	−0.125133	−	0.385121i	−0.993925	+	0.110056i	$0.964897\pi$
$128$	5.04752	−	10.1253i	0.446142	−	0.894962i
$129$	−10.3429	+	7.51453i	−0.910638	+	0.661618i
$130$		0			0
$131$	9.12255	−	12.5561i	0.797041	−	1.09703i	−0.196154	−	0.980573i	$-0.562845\pi$
$131$	9.12255	−	12.5561i	0.797041	−	1.09703i	0.993195	−	0.116460i	$-0.0371547\pi$
$132$	0.505234	−	0.335327i	0.0439750	−	0.0291864i
$133$	−0.711830	+	0.979750i	−0.0617235	+	0.0849551i
$134$	−0.0947055	+	4.46986i	−0.00818131	+	0.386138i
$135$		0			0
$136$	−2.37665	+	5.99011i	−0.203796	+	0.513648i
$137$	−4.54244	+	13.9802i	−0.388087	+	1.19441i	0.546129	+	0.837701i	$0.316101\pi$
$137$	−4.54244	+	13.9802i	−0.388087	+	1.19441i	−0.934216	+	0.356708i	$0.883899\pi$
$138$	−0.272510	+	12.8618i	−0.0231976	+	1.09487i
$139$	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
$142$	3.05032	−	8.75256i	0.255977	−	0.734498i
$143$	0.492950			0.0412225
$144$	−4.38035	+	2.64708i	−0.365029	+	0.220590i
$145$		0			0
$146$	−6.21680	−	4.72117i	−0.514506	−	0.390726i
$147$	−1.26182	−	1.73675i	−0.104073	−	0.143245i
$148$	9.91974	−	12.5032i	0.815398	−	1.02776i
$149$			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	$0.386273\pi$
$152$	−1.37480	−	0.545468i	−0.111511	−	0.0442433i
$153$	2.35851	−	1.71356i	0.190675	−	0.138533i
$154$	−0.457860	+	0.602907i	−0.0368954	+	0.0485837i
$155$		0			0
$156$	5.58951	+	0.236963i	0.447519	+	0.0189722i
$157$		−	4.64663i		−	0.370842i	−0.982659	−	0.185421i	$-0.940635\pi$
$157$		−	4.64663i		−	0.370842i	0.982659	−	0.185421i	$-0.0593648\pi$
$158$	−5.85487	+	16.7999i	−0.465789	+	1.33653i
$159$	1.76192	−	5.42264i	0.139730	−	0.430043i
$160$		0			0
$161$	−4.96317	−	15.2751i	−0.391152	−	1.20384i
$162$	−4.98299	−	0.105577i	−0.391501	−	0.00829495i
$163$	12.4920	+	4.05889i	0.978448	+	0.317917i	0.754221	−	0.656620i	$-0.228015\pi$
$163$	12.4920	+	4.05889i	0.978448	+	0.317917i	0.224226	+	0.974537i	$0.428015\pi$
$164$	−9.35407	−	7.42127i	−0.730430	−	0.579504i
$165$		0			0
$166$	0.164733	−	7.77498i	0.0127857	−	0.603455i
$167$	16.8935	+	12.2739i	1.30726	+	0.949780i	0.999998	−	0.00184537i	$-0.000587400\pi$
$167$	16.8935	+	12.2739i	1.30726	+	0.949780i	0.307261	+	0.951625i	$0.400587\pi$
$168$	−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
$172$	18.2675	+	6.80364i	1.39289	+	0.518773i
$173$	−7.49277	+	2.43455i	−0.569664	+	0.185095i	−0.579665	−	0.814855i	$-0.696817\pi$
$173$	−7.49277	+	2.43455i	−0.569664	+	0.185095i	0.0100007	+	0.999950i	$0.496817\pi$
$174$	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
$178$	−17.8185	−	13.5317i	−1.33555	−	1.01425i
$179$	−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	$-0.580011\pi$
$181$	10.0809	−	13.8751i	0.749305	−	1.03133i	0.998029	−	0.0627560i	$-0.0199890\pi$
$182$	−6.68698	+	2.01716i	−0.495672	+	0.149522i
$183$	2.41818	+	1.75691i	0.178757	+	0.129874i
$184$	16.5696	−	10.4987i	1.22153	−	0.773971i
$185$		0			0
$186$	−9.10131	−	13.1018i	−0.667341	−	0.960670i
$187$	0.500883	+	0.162747i	0.0366282	+	0.0119012i
$188$	−0.600398	−	2.15438i	−0.0437886	−	0.157125i
$189$	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	$0.134486\pi$
$192$	−9.48824	−	4.48156i	−0.684755	−	0.323429i
$193$	−14.9349			−1.07504			−0.537518	−	0.843252i	$-0.680638\pi$
$193$	−14.9349			−1.07504			−0.537518	+	0.843252i	$0.680638\pi$
$194$	5.94004	−	17.0443i	0.426470	−	1.22371i
$195$		0			0
$196$	−1.14245	+	3.06745i	−0.0816037	+	0.219103i
$197$	−16.1837	−	22.2749i	−1.15304	−	1.58702i	−0.734153	−	0.678984i	$-0.762420\pi$
$197$	−16.1837	−	22.2749i	−1.15304	−	1.58702i	−0.418887	−	0.908039i	$-0.637580\pi$
$198$	0.238629	+	0.343518i	0.0169586	+	0.0244128i
$199$	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
$202$	9.35066	+	13.4607i	0.657910	+	0.947095i
$203$	−11.8914	−	16.3671i	−0.834611	−	1.14874i
$204$	5.60123	+	2.08615i	0.392165	+	0.146059i
$205$		0			0
$206$	3.12075	−	8.95464i	0.217433	−	0.623899i
$207$	−8.87368			−0.616763
$208$	−4.41195	−	7.30083i	−0.305913	−	0.506221i
$209$	−0.0373522	+	0.114958i	−0.00258371	+	0.00795183i
$210$		0			0
$211$	−15.0746	+	4.89802i	−1.03778	+	0.337194i	−0.777860	−	0.628438i	$-0.783695\pi$
$211$	−15.0746	+	4.89802i	−1.03778	+	0.337194i	−0.259916	+	0.965631i	$0.583695\pi$
$212$	−8.37466	+	2.33391i	−0.575174	+	0.160293i
$213$	−8.17604	−	2.65656i	−0.560213	−	0.182024i
$214$	−6.17235	−	8.88540i	−0.421933	−	0.607394i
$215$		0			0
$216$	8.49758	+	13.4114i	0.578187	+	0.912532i
$217$	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
$222$	−11.7890	−	8.95277i	−0.791223	−	0.600871i
$223$	−7.19420	−	22.1415i	−0.481759	−	1.48270i	−0.836620	−	0.547783i	$-0.815472\pi$
$223$	−7.19420	−	22.1415i	−0.481759	−	1.48270i	0.354861	−	0.934919i	$-0.384528\pi$
$224$	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	−0.164229	−	0.986422i	$-0.552514\pi$
$227$	4.25947	−	1.38398i	0.282711	−	0.0918583i	0.446940	+	0.894564i	$0.352514\pi$
$228$	−0.478794	+	1.28555i	−0.0317089	+	0.0851373i
$229$	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
$232$	15.7633	−	19.0266i	1.03491	−	1.24916i
$233$	2.83047	+	2.05646i	0.185430	+	0.134723i	0.676628	−	0.736325i	$-0.263441\pi$
$233$	2.83047	+	2.05646i	0.185430	+	0.134723i	−0.491197	+	0.871048i	$0.663441\pi$
$234$	−0.0817433	+	3.85808i	−0.00534372	+	0.252210i
$235$		0			0
$236$	6.09430	−	7.68150i	0.396705	−	0.500023i
$237$	15.6933	+	5.09907i	1.01939	+	0.331220i
$238$	−7.46056	−	0.158071i	−0.483596	−	0.0102462i
$239$	−6.27635	−	19.3166i	−0.405983	−	1.24949i	−0.920071	−	0.391751i	$-0.871869\pi$
$239$	−6.27635	−	19.3166i	−0.405983	−	1.24949i	0.514088	−	0.857738i	$-0.328131\pi$
$240$		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	$-0.114437\pi$
$242$	5.09463	−	14.6185i	0.327495	−	0.939711i
$243$		−	12.2172i		−	0.783736i
$244$	0.193042	−	4.55350i	0.0123582	−	0.291508i
$245$		0			0
$246$	−6.69785	+	8.81969i	−0.427039	+	0.562323i
$247$	−0.902205	+	0.655490i	−0.0574059	+	0.0417079i
$248$	−8.97069	+	22.6097i	−0.569639	+	1.43572i
$249$	−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	$0.953932\pi$
$252$	−4.64274	−	3.68343i	−0.292465	−	0.232034i
$253$	−0.942261	−	1.29691i	−0.0592395	−	0.0815361i
$254$	5.13961	+	3.90312i	0.322488	+	0.244904i
$255$		0			0
$256$	2.30688	+	15.8328i	0.144180	+	0.989551i
$257$	−27.4389			−1.71159			−0.855797	−	0.517312i	$-0.826933\pi$
$257$	−27.4389			−1.71159			−0.855797	+	0.517312i	$0.826933\pi$
$258$	5.95001	−	17.0729i	0.370431	−	1.06291i
$259$	17.5767	+	5.71101i	1.09216	+	0.354865i
$260$		0			0
$261$	−10.6303	+	3.45400i	−0.658001	+	0.213798i
$262$	−0.464939	+	21.9440i	−0.0287240	+	1.35570i
$263$	3.97845	−	12.2444i	0.245322	−	0.755022i	−0.750262	−	0.661141i	$-0.770073\pi$
$263$	3.97845	−	12.2444i	0.245322	−	0.755022i	0.995583	−	0.0938814i	$-0.0299274\pi$
$264$	−0.316264	+	0.797112i	−0.0194647	+	0.0490589i
$265$		0			0
$266$	0.0362791	−	1.71228i	0.00222441	−	0.104987i
$267$	−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	$-0.785181\pi$
$269$	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	$0.566817\pi$
$272$	−2.07259	−	8.87492i	−0.125669	−	0.538121i
$273$	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	−0.958292	−	0.285791i	$-0.907744\pi$
$277$	−26.0565	+	8.46626i	−1.56558	+	0.508689i	−0.607290	+	0.794480i	$0.707744\pi$
$278$	−5.04839	+	6.64769i	−0.302782	+	0.398702i
$279$	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	$-0.633814\pi$
$282$	−1.98593	+	0.599067i	−0.118261	+	0.0356739i
$283$	5.82810	−	8.02169i	0.346444	−	0.476840i	−0.599865	−	0.800101i	$-0.704779\pi$
$283$	5.82810	−	8.02169i	0.346444	−	0.476840i	0.946310	+	0.323261i	$0.104779\pi$
$284$	3.51897	+	12.6270i	0.208812	+	0.749273i
$285$		0			0
$286$	−0.572549	+	0.397727i	−0.0338555	+	0.0235181i
$287$	4.27258	−	13.1497i	0.252203	−	0.776200i
$288$	2.95192	−	6.60872i	0.173943	−	0.389423i
$289$	−3.64911	−	11.2308i	−0.214653	−	0.660635i
$290$		0			0
$291$	−15.9216	−	5.17324i	−0.933340	−	0.303261i
$292$	11.0298	+	0.467601i	0.645473	+	0.0273643i
$293$		−	6.22226i		−	0.363508i	−0.983344	−	0.181754i	$-0.941823\pi$
$293$		−	6.22226i		−	0.363508i	0.983344	−	0.181754i	$-0.0581775\pi$
$294$	2.86684	+	0.999113i	0.167198	+	0.0582694i
$295$		0			0
$296$	−1.43351	+	22.5258i	−0.0833213	+	1.30928i
$297$	1.04972	−	0.762664i	0.0609107	−	0.0442542i
$298$	−7.37486	−	10.6165i	−0.427214	−	0.614996i
$299$		−	14.7899i		−	0.855324i
$300$		0			0
$301$			22.5723i			1.30105i
$302$	−9.98301	+	6.93481i	−0.574457	+	0.399054i
$303$	12.2982	−	8.93519i	0.706515	−	0.513313i
$304$	2.03689	−	0.475683i	0.116824	−	0.0272823i
$305$		0			0
$306$	−1.35680	+	3.89318i	−0.0775630	+	0.222558i
$307$		−	29.6136i		−	1.69014i	−0.534656	−	0.845070i	$-0.679559\pi$
$307$		−	29.6136i		−	1.69014i	0.534656	−	0.845070i	$-0.320441\pi$
$308$	0.0453481	−	1.06968i	0.00258395	−	0.0609505i
$309$	−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	$0.938843\pi$
$312$	−6.68326	+	4.23457i	−0.378365	+	0.239735i
$313$	−4.24400	+	13.0617i	−0.239885	+	0.738290i	0.756551	+	0.653935i	$0.226883\pi$
$313$	−4.24400	+	13.0617i	−0.239885	+	0.738290i	−0.996436	+	0.0843552i	$0.973117\pi$
$314$	3.74905	+	5.39695i	0.211571	+	0.304567i
$315$		0			0
$316$	−6.75441	−	24.2366i	−0.379965	−	1.36341i
$317$	−7.50769	+	10.3334i	−0.421674	+	0.580384i	−0.966017	−	0.258478i	$-0.916779\pi$
$317$	−7.50769	+	10.3334i	−0.421674	+	0.580384i	0.544343	+	0.838863i	$0.316779\pi$
$318$	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
$322$	18.0890	+	13.7371i	1.00806	+	0.765541i
$323$	−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
$328$	16.8522	+	1.07246i	0.930508	+	0.0592165i
$329$	2.09513	−	1.52220i	0.115508	−	0.0839217i
$330$		0			0
$331$	−2.79298	+	3.84421i	−0.153516	+	0.211297i	−0.878847	−	0.477103i	$-0.841687\pi$
$331$	−2.79298	+	3.84421i	−0.153516	+	0.211297i	0.725331	+	0.688400i	$0.241687\pi$
$332$	6.08177	+	9.16335i	0.333780	+	0.502904i
$333$	6.00172	−	8.26066i	0.328892	−	0.452682i
$334$	−29.5243	−	0.625548i	−1.61550	−	0.0342285i
$335$		0			0
$336$	1.02839	−	12.1072i	0.0561035	−	0.660500i
$337$	9.15228	−	28.1678i	0.498556	−	1.53440i	−0.312784	−	0.949824i	$-0.601261\pi$
$337$	9.15228	−	28.1678i	0.498556	−	1.53440i	0.811340	−	0.584574i	$-0.198739\pi$
$338$	11.9503	+	0.253198i	0.650011	+	0.0137722i
$339$	−18.9553	+	6.15894i	−1.02951	+	0.334508i
$340$		0			0
$341$	1.89059	+	0.614289i	0.102381	+	0.0332656i
$342$	−0.893529	−	0.311400i	−0.0483165	−	0.0168386i
$343$	−20.0015			−1.07998
$344$	−26.7067	+	6.83658i	−1.43993	+	0.368604i
$345$		0			0
$346$	6.73839	−	8.87306i	0.362258	−	0.477019i
$347$	11.3406	+	15.6090i	0.608797	+	0.837937i	0.996478	−	0.0838564i	$-0.0267237\pi$
$347$	11.3406	+	15.6090i	0.608797	+	0.837937i	−0.387681	+	0.921794i	$0.626724\pi$
$348$	−17.9528	−	14.2432i	−0.962369	−	0.763518i
$349$			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
$352$	1.27934	−	0.270324i	0.0681888	−	0.0144083i
$353$	10.7507	−	7.81083i	0.572202	−	0.415729i	−0.263703	−	0.964604i	$-0.584944\pi$
$353$	10.7507	−	7.81083i	0.572202	−	0.415729i	0.835904	+	0.548875i	$0.184944\pi$
$354$	−7.24267	−	5.50023i	−0.384944	−	0.292334i
$355$		0			0
$356$	31.6135	+	1.34023i	1.67551	+	0.0710320i
$357$			6.92117i			0.366307i
$358$	21.4395	+	7.47180i	1.13311	+	0.394897i
$359$	−5.23366	+	16.1076i	−0.276222	+	0.850124i	0.712671	+	0.701498i	$0.247485\pi$
$359$	−5.23366	+	16.1076i	−0.276222	+	0.850124i	−0.988893	+	0.148626i	$0.952515\pi$
$360$		0			0
$361$	5.78682	+	17.8100i	0.304570	+	0.937369i
$362$	−0.513781	+	24.2492i	−0.0270037	+	1.27451i
$363$	−13.6556	−	4.43696i	−0.716732	−	0.232880i
$364$	6.13924	−	7.73815i	0.321784	−	0.405589i
$365$		0			0
$366$	−4.22618	−	0.0895425i	−0.220906	−	0.00468046i
$367$	−7.06794	−	5.13516i	−0.368944	−	0.268053i	0.387829	−	0.921731i	$-0.373225\pi$
$367$	−7.06794	−	5.13516i	−0.368944	−	0.268053i	−0.756773	+	0.653678i	$0.773225\pi$
$368$	−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
$372$	21.1419	+	7.87417i	1.09616	+	0.408257i
$373$	−0.954212	+	0.310042i	−0.0494072	+	0.0160534i	−0.333616	−	0.942709i	$-0.608269\pi$
$373$	−0.954212	+	0.310042i	−0.0494072	+	0.0160534i	0.284209	+	0.958762i	$0.408269\pi$
$374$	−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
$378$	−11.1188	+	14.6412i	−0.571890	+	0.753061i
$379$	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
$382$	−1.22068	−	4.04661i	−0.0624556	−	0.207043i
$383$	24.9852	+	18.1528i	1.27668	+	0.927565i	0.999447	−	0.0332373i	$-0.0105817\pi$
$383$	24.9852	+	18.1528i	1.27668	+	0.927565i	0.277236	+	0.960802i	$0.410582\pi$
$384$	14.6362	−	2.45020i	0.746901	−	0.125036i
$385$		0			0
$386$	17.3465	−	12.0499i	0.882913	−	0.613326i
$387$	11.8607	+	3.85377i	0.602912	+	0.195898i
$388$	6.85265	+	24.5891i	0.347891	+	1.24832i
$389$	−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
$392$	−1.14798	−	4.48453i	−0.0579819	−	0.226503i
$393$	20.3574			1.02690
$394$	36.7690	+	12.8142i	1.85240	+	0.645573i
$395$		0			0
$396$	−0.554322	−	0.206454i	−0.0278557	−	0.0103747i
$397$	−5.67144	−	7.80606i	−0.284641	−	0.391775i	0.642623	−	0.766182i	$-0.277846\pi$
$397$	−5.67144	−	7.80606i	−0.284641	−	0.391775i	−0.927264	+	0.374407i	$0.877846\pi$
$398$	−13.2201	+	9.18351i	−0.662665	+	0.460328i
$399$	−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	$0.405021\pi$
$402$	−4.81628	+	3.34569i	−0.240214	+	0.166868i
$403$	10.7801	+	14.8375i	0.536995	+	0.739110i
$404$	−21.7211	−	8.08990i	−1.08067	−	0.402488i
$405$		0			0
$406$	27.0170	+	9.41560i	1.34083	+	0.467289i
$407$	1.84462			0.0914343
$408$	−8.18886	+	2.09625i	−0.405409	+	0.103780i
$409$	0.0454622	−	0.139918i	0.00224796	−	0.00691851i	−0.949926	−	0.312474i	$-0.898842\pi$
$409$	0.0454622	−	0.139918i	0.00224796	−	0.00691851i	0.952174	+	0.305556i	$0.0988422\pi$
$410$		0			0
$411$	−18.3375	+	5.95820i	−0.904520	+	0.293896i
$412$	3.60021	+	12.9185i	0.177370	+	0.636449i
$413$	10.7984	+	3.50862i	0.531355	+	0.172648i
$414$	10.3065	−	7.15956i	0.506539	−	0.351873i
$415$		0			0
$416$	11.0149	+	4.92002i	0.540050	+	0.241224i
$417$	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	−0.0418913	+	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	0.884423	−	0.466686i	$-0.154552\pi$
$421$	3.43224	+	4.72407i	0.167277	+	0.230237i	−0.717146	+	0.696923i	$0.754552\pi$
$422$	13.5568	−	17.8516i	0.659936	−	0.869000i
$423$	−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
$428$	14.3380	+	5.34012i	0.693056	+	0.258125i
$429$	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	$0.731412\pi$
$432$	−20.6905	−	8.72090i	−0.995471	−	0.419585i
$433$	−3.84976	−	2.79701i	−0.185008	−	0.134416i	0.491427	−	0.870919i	$-0.336476\pi$
$433$	−3.84976	−	2.79701i	−0.185008	−	0.134416i	−0.676434	+	0.736503i	$0.736476\pi$
$434$	−28.1599	−	0.596640i	−1.35172	−	0.0286396i
$435$		0			0
$436$	−8.38908	+	10.5739i	−0.401764	+	0.506399i
$437$	3.44909	+	1.12068i	0.164992	+	0.0536092i
$438$	0.216897	−	10.2370i	0.0103637	−	0.489142i
$439$	−0.541600	−	1.66687i	−0.0258492	−	0.0795556i	0.937300	−	0.348524i	$-0.113317\pi$
$439$	−0.541600	−	1.66687i	−0.0258492	−	0.0795556i	−0.963149	+	0.268969i	$0.913317\pi$
$440$		0			0
$441$	−0.647116	+	1.99162i	−0.0308150	+	0.0948389i
$442$	−6.48885	−	2.26140i	−0.308643	−	0.107564i
$443$		−	3.43488i		−	0.163196i	−0.996665	−	0.0815981i	$-0.973998\pi$
$443$		−	3.43488i		−	0.163196i	0.996665	−	0.0815981i	$-0.0260024\pi$
$444$	20.9159	+	0.886714i	0.992627	+	0.0420816i
$445$		0			0
$446$	26.2203	+	19.9122i	1.24157	+	0.942872i
$447$	−9.69960	+	7.04717i	−0.458775	+	0.333320i
$448$	−16.2483	+	8.90208i	−0.767661	+	0.420584i
$449$	−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
$452$	23.8072	+	18.8880i	1.11980	+	0.888418i
$453$	6.62668	+	9.12084i	0.311348	+	0.428534i
$454$	−3.83062	+	5.04413i	−0.179780	+	0.236733i
$455$		0			0
$456$	−0.481112	−	1.87943i	−0.0225301	−	0.0880126i
$457$	−3.02813			−0.141650			−0.0708250	−	0.997489i	$-0.522563\pi$
$457$	−3.02813			−0.141650			−0.0708250	+	0.997489i	$0.522563\pi$
$458$	−6.81565	−	2.37530i	−0.318475	−	0.110990i
$459$	12.1636	+	3.95219i	0.567748	+	0.184472i
$460$		0			0
$461$	−11.9787	+	3.89211i	−0.557903	+	0.181274i	−0.574377	−	0.818591i	$-0.694756\pi$
$461$	−11.9787	+	3.89211i	−0.557903	+	0.181274i	0.0164747	+	0.999864i	$0.494756\pi$
$462$	−0.992786	−	0.0210347i	−0.0461886	−	0.000978624i
$463$	−1.35375	+	4.16641i	−0.0629140	+	0.193629i	−0.977573	−	0.210597i	$-0.932459\pi$
$463$	−1.35375	+	4.16641i	−0.0629140	+	0.193629i	0.914659	+	0.404226i	$0.132459\pi$
$464$	−2.95741	+	34.8172i	−0.137294	+	1.61635i
$465$		0			0
$466$	−4.94674	−	0.104809i	−0.229153	−	0.00485520i
$467$	−13.3438	+	18.3661i	−0.617476	+	0.849883i	−0.997166	−	0.0752308i	$-0.976031\pi$
$467$	−13.3438	+	18.3661i	−0.617476	+	0.849883i	0.379690	+	0.925114i	$0.376031\pi$
$468$	−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
$472$	−0.880694	+	13.8389i	−0.0405372	+	0.636989i
$473$	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
$478$	22.8751	+	17.3718i	1.04628	+	0.794568i
$479$	−5.58405	+	4.05705i	−0.255142	+	0.185371i	−0.708002	−	0.706210i	$-0.750403\pi$
$479$	−5.58405	+	4.05705i	−0.255142	+	0.185371i	0.452861	+	0.891581i	$0.350403\pi$
$480$		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
$484$	5.87736	+	21.0895i	0.267153	+	0.958613i
$485$		0			0
$486$	9.85726	+	14.1900i	0.447134	+	0.643672i
$487$	11.0811	−	34.1041i	0.502132	−	1.54540i	−0.303407	−	0.952861i	$-0.598124\pi$
$487$	11.0811	−	34.1041i	0.502132	−	1.54540i	0.805539	−	0.592543i	$-0.201876\pi$
$488$	3.44969	+	5.44453i	0.156160	+	0.246462i
$489$	5.32394	+	16.3854i	0.240757	+	0.740973i
$490$		0			0
$491$	7.36748	+	2.39384i	0.332490	+	0.108032i	0.470504	−	0.882398i	$-0.344072\pi$
$491$	7.36748	+	2.39384i	0.332490	+	0.108032i	−0.138014	+	0.990430i	$0.544072\pi$
$492$	0.663378	−	15.6479i	0.0299074	−	0.705461i
$493$		−	19.9036i		−	0.896411i
$494$	0.519018	−	1.48926i	0.0233517	−	0.0670051i
$495$		0			0
$496$	−7.82300	−	33.4984i	−0.351263	−	1.50412i
$497$	−12.2797	+	8.92171i	−0.550819	+	0.400194i
$498$	8.37755	−	5.81956i	0.375407	−	0.260781i
$499$		−	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
$502$	−3.68706	−	5.30771i	−0.164562	−	0.236895i
$503$	−10.3630	+	7.52915i	−0.462063	+	0.335708i	−0.794340	−	0.607473i	$-0.792183\pi$
$503$	−10.3630	+	7.52915i	−0.462063	+	0.335708i	0.332277	+	0.943182i	$0.392183\pi$
$504$	8.36433	+	0.532296i	0.372577	+	0.0237104i
$505$		0			0
$506$	2.14080	+	0.746083i	0.0951702	+	0.0331674i
$507$		−	11.0863i		−	0.492360i
$508$	−9.11869	−	0.386579i	−0.404576	−	0.0171517i
$509$	−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
$512$	−15.4538	−	16.5282i	−0.682968	−	0.730448i
$513$	−0.907072	+	2.79168i	−0.0400482	+	0.123256i
$514$	31.8696	−	22.1386i	1.40571	−	0.976492i
$515$		0			0
$516$	6.86416	+	24.6304i	0.302178	+	1.08429i
$517$	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	−0.624162	−	0.781295i	$-0.714560\pi$
$521$	−1.68871	+	1.22692i	−0.0739836	+	0.0537522i	0.550179	+	0.835047i	$0.314560\pi$
$522$	9.56006	−	12.5886i	0.418432	−	0.550989i
$523$	−30.9419	+	10.0536i	−1.35300	+	0.439615i	−0.893699	−	0.448668i	$-0.851899\pi$
$523$	−30.9419	+	10.0536i	−1.35300	+	0.439615i	−0.459297	+	0.888283i	$0.651899\pi$
$524$	−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
$528$	−0.275802	−	1.18100i	−0.0120028	−	0.0513963i
$529$	−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
$534$	0.621666	−	29.3411i	0.0269021	−	1.26971i
$535$		0			0
$536$	8.31144	+	3.29767i	0.359000	+	0.142438i
$537$	6.50726	−	20.0273i	0.280809	−	0.864242i
$538$	−0.0457307	+	2.15837i	−0.00197159	+	0.0930541i
$539$	−0.359795	+	0.116904i	−0.0154975	+	0.00503543i
$540$		0			0
$541$	5.01695	+	1.63011i	0.215696	+	0.0700838i	0.414872	−	0.909880i	$-0.363826\pi$
$541$	5.01695	+	1.63011i	0.215696	+	0.0700838i	−0.199176	+	0.979964i	$0.563826\pi$
$542$	11.3922	−	32.6886i	0.489336	−	1.40410i
$543$	22.4960			0.965395
$544$	9.56783	+	8.63576i	0.410217	+	0.370255i
$545$		0			0
$546$	−7.29608	−	5.54079i	−0.312244	−	0.237124i
$547$	−8.91852	−	12.2753i	−0.381329	−	0.524854i	0.574607	−	0.818429i	$-0.305155\pi$
$547$	−8.91852	−	12.2753i	−0.381329	−	0.524854i	−0.955936	+	0.293575i	$0.905155\pi$
$548$	23.0313	+	18.2724i	0.983847	+	0.780558i
$549$		−	2.91575i		−	0.124441i
$550$		0			0
$551$	4.56809			0.194607
$552$	23.9157	+	9.48886i	1.01792	+	0.403873i
$553$	23.5700	−	17.1246i	1.00230	−	0.728211i
$554$	23.4331	−	30.8565i	0.995576	−	1.31097i
$555$		0			0
$556$	0.500010	−	11.7943i	0.0212052	−	0.500191i
$557$			21.0806i			0.893213i	0.894731	+	0.446606i	$0.147368\pi$
$557$			21.0806i			0.893213i	−0.894731	+	0.446606i	$0.852632\pi$
$558$	−5.12124	+	14.6948i	−0.216800	+	0.622082i
$559$	−6.42315	+	19.7684i	−0.271670	+	0.836116i
$560$		0			0
$561$	0.213470	+	0.656995i	0.00901273	+	0.0277383i
$562$	41.0875	+	0.870543i	1.73317	+	0.0367217i
$563$	16.6417	+	5.40722i	0.701365	+	0.227887i	0.637925	−	0.770099i	$-0.279793\pi$
$563$	16.6417	+	5.40722i	0.701365	+	0.227887i	0.0634396	+	0.997986i	$0.479793\pi$
$564$	1.82326	−	2.29811i	0.0767732	−	0.0967680i
$565$		0			0
$566$	−0.297034	+	14.0193i	−0.0124853	+	0.589274i
$567$	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	0.982578	−	0.185853i	$-0.0595049\pi$
$569$	26.4646	+	19.2277i	1.10945	+	0.806065i	0.126876	+	0.991919i	$0.459505\pi$
$570$		0			0
$571$	17.4500	+	24.0179i	0.730261	+	1.00512i	0.999120	+	0.0419380i	$0.0133532\pi$
$571$	17.4500	+	24.0179i	0.730261	+	1.00512i	−0.268860	+	0.963179i	$0.586647\pi$
$572$	0.344101	−	0.923901i	0.0143876	−	0.0386302i
$573$	−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	$-0.149540\pi$
$577$	−2.30117	−	7.08229i	−0.0957992	−	0.294839i	−0.987461	+	0.157862i	$0.949540\pi$
$578$	13.2997	+	10.1001i	0.553195	+	0.420107i
$579$	−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
$584$	−13.1882	+	8.35612i	−0.545730	+	0.345779i
$585$		0			0
$586$	5.02031	+	7.22699i	0.207387	+	0.298544i
$587$	−13.3184	−	4.32742i	−0.549710	−	0.178612i	0.0209758	−	0.999780i	$-0.493323\pi$
$587$	−13.3184	−	4.32742i	−0.549710	−	0.178612i	−0.570686	+	0.821168i	$0.693323\pi$
$588$	−4.13588	+	1.15261i	−0.170561	+	0.0475330i
$589$	−4.27702	+	1.38969i	−0.176232	+	0.0572611i
$590$		0			0
$591$	11.1601	−	34.3471i	0.459063	−	1.41285i
$592$	−16.5095	−	27.3197i	−0.678536	−	1.12283i
$593$	−10.4531			−0.429258			−0.214629	−	0.976696i	$-0.568854\pi$
$593$	−10.4531			−0.429258			−0.214629	+	0.976696i	$0.568854\pi$
$594$	−0.603878	+	1.73276i	−0.0247774	+	0.0710960i
$595$		0			0
$596$	17.1314	+	6.38050i	0.701730	+	0.261355i
$597$	8.77546	+	12.0784i	0.359156	+	0.494335i
$598$	11.9330	+	17.1781i	0.487976	+	0.702466i
$599$	−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	$0.564068\pi$
$602$	−18.2121	−	26.2172i	−0.742268	−	1.06853i
$603$	−2.37761	−	3.27250i	−0.0968238	−	0.133267i
$604$	5.99978	−	16.1092i	0.244128	−	0.655474i
$605$		0			0
$606$	−7.07489	+	20.3006i	−0.287398	+	0.824655i
$607$	−2.47771			−0.100567			−0.0502836	−	0.998735i	$-0.516013\pi$
$607$	−2.47771			−0.100567			−0.0502836	+	0.998735i	$0.516013\pi$
$608$	−1.98200	+	2.19592i	−0.0803809	+	0.0890565i
$609$	8.20014	−	25.2374i	0.332287	−	1.02267i
$610$		0			0
$611$	2.26804	−	0.736930i	0.0917549	−	0.0298130i
$612$	−1.56525	−	5.61654i	−0.0632717	−	0.227035i
$613$	2.45539	+	0.797806i	0.0991725	+	0.0322231i	0.358183	−	0.933651i	$-0.383396\pi$
$613$	2.45539	+	0.797806i	0.0991725	+	0.0322231i	−0.259010	+	0.965875i	$0.583396\pi$
$614$	23.8932	+	34.3955i	0.964252	+	1.38809i
$615$		0			0
$616$	0.810379	+	1.27899i	0.0326511	+	0.0515320i
$617$	14.3320	+	10.4128i	0.576986	+	0.419205i	0.837636	−	0.546228i	$-0.183937\pi$
$617$	14.3320	+	10.4128i	0.576986	+	0.419205i	−0.260650	+	0.965433i	$0.583937\pi$
$618$	11.9084	−	3.59223i	0.479026	−	0.144501i
$619$	−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
$622$	4.83534	+	3.67206i	0.193880	+	0.147236i
$623$	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
$628$	−8.70885	−	3.24356i	−0.347521	−	0.129432i
$629$	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	$0.926634\pi$
$632$	27.3999	+	22.7005i	1.08991	+	0.902976i
$633$	−16.8198	−	12.2203i	−0.668528	−	0.485714i
$634$	0.382636	−	18.0595i	0.0151964	−	0.717233i
$635$		0			0
$636$	−8.93337	−	7.08750i	−0.354231	−	0.281038i
$637$	−3.31947	−	1.07856i	−0.131522	−	0.0427342i
$638$	2.85501	+	0.0604906i	0.113031	+	0.00239485i
$639$	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	$-0.0275464\pi$
$642$	4.67012	−	13.4004i	0.184315	−	0.528870i
$643$			21.0042i			0.828324i	0.910203	+	0.414162i	$0.135925\pi$
$643$			21.0042i			0.828324i	−0.910203	+	0.414162i	$0.864075\pi$
$644$	−32.0935	−	1.36058i	−1.26466	−	0.0536142i
$645$		0			0
$646$	1.01905	−	1.34188i	0.0400939	−	0.0527955i
$647$	−26.7896	+	19.4638i	−1.05321	+	0.765202i	−0.972820	−	0.231562i	$-0.925616\pi$
$647$	−26.7896	+	19.4638i	−1.05321	+	0.765202i	−0.0803896	+	0.996764i	$0.525616\pi$
$648$	−3.67623	+	9.26557i	−0.144416	+	0.363986i
$649$	1.13326			0.0444844
$650$		0			0
$651$			26.1240i			1.02388i
$652$	16.3273	−	20.5795i	0.639425	−	0.805957i
$653$	0.194712	+	0.267998i	0.00761966	+	0.0104876i	0.812810	−	0.582529i	$-0.197937\pi$
$653$	0.194712	+	0.267998i	0.00761966	+	0.0104876i	−0.805190	+	0.593017i	$0.797937\pi$
$654$	9.96986	+	7.57132i	0.389852	+	0.296062i
$655$		0			0
$656$	−20.4387	+	12.3513i	−0.797998	+	0.482236i
$657$	7.06276			0.275545
$658$	−1.20528	+	3.45842i	−0.0469867	+	0.134823i
$659$	−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	−0.575658	−	0.817691i	$-0.695254\pi$
$661$	−14.4168	+	4.68430i	−0.560748	+	0.182198i	0.0149097	+	0.999889i	$0.495254\pi$
$662$	0.142347	−	6.71842i	0.00553247	−	0.261119i
$663$	−1.96948	+	6.06144i	−0.0764883	+	0.235407i
$664$	−14.4571	−	5.73604i	−0.561044	−	0.222601i
$665$		0			0
$666$	−0.305883	+	14.4369i	−0.0118527	+	0.559420i
$667$	−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
$672$	8.57399	+	14.8919i	0.330749	+	0.574468i
$673$	−1.28032	−	3.94041i	−0.0493526	−	0.151892i	0.923343	−	0.383976i	$-0.125445\pi$
$673$	−1.28032	−	3.94041i	−0.0493526	−	0.151892i	−0.972696	+	0.232084i	$0.925445\pi$
$674$	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	0.130907	−	0.991395i	$-0.458211\pi$
$677$	21.3238	−	6.92852i	0.819540	−	0.266285i	0.688633	+	0.725110i	$0.258211\pi$
$678$	17.0468	−	22.4472i	0.654680	−	0.862079i
$679$	−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	0.261038	+	0.965328i	$0.415935\pi$
$683$	−19.2795	+	26.5359i	−0.737709	+	1.01537i	−0.998747	+	0.0500406i	$0.984065\pi$
$684$	1.28906	−	0.359243i	0.0492884	−	0.0137360i
$685$		0			0
$686$	23.2313	−	16.1379i	0.886974	−	0.616147i
$687$	−2.06867	+	6.36672i	−0.0789247	+	0.242905i
$688$	25.5032	−	29.4883i	0.972299	−	1.12423i
$689$	−2.86464	−	8.81645i	−0.109134	−	0.335880i
$690$		0			0
$691$	35.7160	+	11.6048i	1.35870	+	0.441468i	0.895609	−	0.444843i	$-0.146741\pi$
$691$	35.7160	+	11.6048i	1.35870	+	0.441468i	0.463090	+	0.886311i	$0.346741\pi$
$692$	−0.667393	+	15.7426i	−0.0253705	+	0.598443i
$693$		−	0.684949i		−	0.0260190i
$694$	−25.7657	−	8.97952i	−0.978053	−	0.340858i
$695$		0			0
$696$	32.3436	+	2.05831i	1.22598	+	0.0780200i
$697$	11.0048	−	7.99547i	0.416837	−	0.302850i
$698$	−26.7240	−	38.4705i	−1.01152	−	1.45613i
$699$			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	$-0.145465\pi$
$702$	−13.9039	+	9.65853i	−0.524770	+	0.364538i
$703$	−3.37605	+	2.45284i	−0.127330	+	0.0925108i
$704$	−1.26781	+	1.34618i	−0.0477824	+	0.0507362i
$705$		0			0
$706$	−6.18462	+	17.7461i	−0.232761	+	0.667883i
$707$		−	26.8397i		−	1.00941i
$708$	12.8499	+	0.544762i	0.482930	+	0.0204734i
$709$	−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
$712$	−37.7996	+	23.9502i	−1.41660	+	0.897570i
$713$	18.4305	−	56.7231i	0.690226	−	2.12430i
$714$	−5.58422	−	8.03876i	−0.208984	−	0.300843i
$715$		0			0
$716$	−30.9299	+	8.61975i	−1.15590	+	0.322135i
$717$	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	0.620477	−	0.784225i	$-0.286939\pi$
$719$	1.77973	+	1.29305i	0.0663726	+	0.0482225i	−0.554104	+	0.832447i	$0.686939\pi$
$720$		0			0
$721$	−12.5632	+	9.12770i	−0.467878	+	0.339933i
$722$	−21.0909	−	16.0169i	−0.784923	−	0.596086i
$723$	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	$-0.0735662\pi$
$727$	1.38226	+	4.25417i	0.0512653	+	0.157778i	−0.922146	+	0.386841i	$0.873566\pi$
$728$	−0.887189	+	13.9410i	−0.0328814	+	0.516688i
$729$	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	−0.926849	−	0.375433i	$-0.877494\pi$
$733$	−7.67219	+	10.5599i	−0.283379	+	0.390037i	0.643471	+	0.765471i	$0.277494\pi$
$734$	12.3524	+	0.261718i	0.455937	+	0.00966019i
$735$		0			0
$736$	−8.11052	−	38.3838i	−0.298958	−	1.41485i
$737$	0.225815	−	0.694989i	0.00831802	−	0.0256002i
$738$	10.8007	+	0.228841i	0.397580	+	0.00842375i
$739$	−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
$742$	13.4438	+	4.68524i	0.493536	+	0.172001i
$743$	28.1541			1.03287			0.516437	−	0.856325i	$-0.327258\pi$
$743$	28.1541			1.03287			0.516437	+	0.856325i	$0.327258\pi$
$744$	−30.9089	+	7.91229i	−1.13317	+	0.290079i
$745$		0			0
$746$	0.858141	−	1.12999i	0.0314188	−	0.0413720i
$747$	4.13567	+	5.69226i	0.151316	+	0.208269i
$748$	0.654664	−	0.825165i	0.0239369	−	0.0301710i
$749$			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	$0.576080\pi$
$752$	−4.45692	−	0.378575i	−0.162527	−	0.0138052i
$753$	−4.84932	+	3.52324i	−0.176719	+	0.128394i
$754$	20.9817	+	15.9340i	0.764110	+	0.580280i
$755$		0			0
$756$	1.10125	−	25.9764i	0.0400519	−	0.944751i
$757$			16.0395i			0.582965i	0.956576	+	0.291482i	$0.0941485\pi$
$757$			16.0395i			0.582965i	−0.956576	+	0.291482i	$0.905851\pi$
$758$	−48.2261	−	16.8071i	−1.75165	−	0.610461i
$759$	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	$0.834286\pi$
$762$	−0.179315	+	8.46322i	−0.00649589	+	0.306590i
$763$	−14.8645	−	4.82977i	−0.538131	−	0.174849i
$764$	4.68273	+	3.71515i	0.169415	+	0.134410i
$765$		0			0
$766$	−43.6659	−	0.925174i	−1.57771	−	0.0334279i
$767$	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	0.527601	−	0.849492i	$-0.323092\pi$
$769$	−3.25219	−	2.36285i	−0.117277	−	0.0852066i	−0.644878	+	0.764286i	$0.723092\pi$
$770$		0			0
$771$	−21.1549	−	29.1173i	−0.761876	−	1.04863i
$772$	−10.4252	+	27.9914i	−0.375212	+	1.00743i
$773$	−2.33810	+	0.759693i	−0.0840955	+	0.0273243i	−0.350763	−	0.936464i	$-0.614078\pi$
$773$	−2.33810	+	0.759693i	−0.0840955	+	0.0273243i	0.266667	+	0.963789i	$0.414078\pi$
$774$	−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
$778$	1.13542	−	1.49512i	0.0407069	−	0.0536026i
$779$	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
$784$	4.95161	+	4.28243i	0.176843	+	0.152944i
$785$		0			0
$786$	−23.6446	+	16.4250i	−0.843377	+	0.585861i
$787$	−28.5523	−	9.27720i	−1.01778	−	0.330697i	−0.247831	−	0.968803i	$-0.579718\pi$
$787$	−28.5523	−	9.27720i	−1.01778	−	0.330697i	−0.769948	+	0.638107i	$0.779718\pi$
$788$	−53.0452	+	14.7830i	−1.88966	+	0.526623i
$789$	16.0606	−	5.21842i	0.571774	−	0.185781i
$790$		0			0
$791$	−10.8742	+	33.4675i	−0.386644	+	1.18997i
$792$	0.810405	−	0.207454i	0.0287965	−	0.00737154i
$793$	4.85974			0.172575
$794$	12.8854	+	4.49065i	0.457286	+	0.159367i
$795$		0			0
$796$	7.94528	−	21.3328i	0.281613	−	0.756122i
$797$	−13.0696	−	17.9888i	−0.462950	−	0.637196i	0.512167	−	0.858886i	$-0.328843\pi$
$797$	−13.0696	−	17.9888i	−0.462950	−	0.637196i	−0.975117	+	0.221690i	$0.928843\pi$
$798$	1.84498	−	1.28164i	0.0653118	−	0.0453696i
$799$	2.54783			0.0901359
$800$		0			0
$801$	20.2432			0.715257
$802$	−13.6749	+	9.49943i	−0.482878	+	0.335437i
$803$	0.749967	+	1.03224i	0.0264658	+	0.0364270i
$804$	2.89458	−	7.77186i	0.102084	−	0.274092i
$805$		0			0
$806$	−24.4922	−	8.53569i	−0.862700	−	0.300657i
$807$	2.00232			0.0704852
$808$	31.7557	−	8.12907i	1.11716	−	0.285980i
$809$	10.2871	−	31.6605i	0.361676	−	1.11313i	−0.590360	−	0.807140i	$-0.701014\pi$
$809$	10.2871	−	31.6605i	0.361676	−	1.11313i	0.952036	−	0.305985i	$-0.0989859\pi$
$810$		0			0
$811$	41.7447	−	13.5637i	1.46585	−	0.476285i	0.536002	−	0.844217i	$-0.319934\pi$
$811$	41.7447	−	13.5637i	1.46585	−	0.476285i	0.929853	+	0.367932i	$0.119934\pi$
$812$	−38.9764	+	10.8622i	−1.36780	+	0.381188i
$813$	−30.5355	−	9.92157i	−1.07093	−	0.347965i
$814$	−2.14248	+	1.48830i	−0.0750938	+	0.0521648i
$815$		0			0
$816$	7.81983	−	9.04176i	0.273749	−	0.316525i
$817$	−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	$-0.370361\pi$
$821$	−17.1793	−	23.6453i	−0.599561	−	0.825225i	−0.995668	+	0.0929790i	$0.970361\pi$
$822$	16.4912	−	21.7155i	0.575197	−	0.757416i
$823$	4.17485	+	12.8489i	0.145526	+	0.447883i	0.997078	−	0.0763866i	$-0.0243383\pi$
$823$	4.17485	+	12.8489i	0.145526	+	0.447883i	−0.851552	+	0.524270i	$0.824338\pi$
$824$	−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	0.210433	−	0.977608i	$-0.432513\pi$
$827$	27.4721	−	8.92624i	0.955300	−	0.310396i	0.744867	+	0.667213i	$0.232513\pi$
$828$	−6.19423	+	16.6313i	−0.215264	+	0.577977i
$829$	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
$832$	−16.7632	+	3.17269i	−0.581158	+	0.109993i
$833$	−3.01681	−	2.19184i	−0.104526	−	0.0759427i
$834$	−10.9465	−	0.231930i	−0.379047	−	0.00803108i
$835$		0			0
$836$	0.189385	+	0.150253i	0.00655000	+	0.00519660i
$837$	45.9115	+	14.9176i	1.58694	+	0.515627i
$838$	1.02151	−	48.2129i	0.0352876	−	1.66549i
$839$	−2.47513	−	7.61767i	−0.0854510	−	0.262991i	0.899197	−	0.437545i	$-0.144152\pi$
$839$	−2.47513	−	7.61767i	−0.0854510	−	0.262991i	−0.984648	+	0.174553i	$0.944152\pi$
$840$		0			0
$841$	−14.6201	+	44.9960i	−0.504141	+	1.55159i
$842$	−7.79799	−	2.71765i	−0.268736	−	0.0936564i
$843$		−	38.1169i		−	1.31282i
$844$	−1.34272	+	31.6722i	−0.0462182	+	1.09020i
$845$		0			0
$846$	1.61146	+	1.22377i	0.0554030	+	0.0420742i
$847$	−20.5094	+	14.9010i	−0.704713	+	0.512004i
$848$	−1.47162	+	17.3252i	−0.0505356	+	0.594949i
$849$	13.0057			0.446354
$850$		0			0
$851$		−	55.3440i		−	1.89717i
$852$	−10.6862	+	13.4694i	−0.366105	+	0.461453i
$853$	9.86242	+	13.5745i	0.337683	+	0.464780i	0.943763	−	0.330623i	$-0.107259\pi$
$853$	9.86242	+	13.5745i	0.337683	+	0.464780i	−0.606080	+	0.795404i	$0.707259\pi$
$854$	−4.51381	+	5.94376i	−0.154459	+	0.203391i
$855$		0			0
$856$	−20.9619	+	5.36598i	−0.716462	+	0.183405i
$857$	12.0516			0.411675			0.205837	−	0.978586i	$-0.434008\pi$
$857$	12.0516			0.411675			0.205837	+	0.978586i	$0.434008\pi$
$858$	−0.863479	−	0.300928i	−0.0294787	−	0.0102735i
$859$	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
$862$	5.78398	+	0.122548i	0.197003	+	0.00417402i
$863$	−8.82744	+	27.1681i	−0.300490	+	0.924812i	0.680832	+	0.732439i	$0.261618\pi$
$863$	−8.82744	+	27.1681i	−0.300490	+	0.924812i	−0.981322	+	0.192373i	$0.938382\pi$
$864$	31.0678	−	6.56463i	1.05695	−	0.223333i
$865$		0			0
$866$	6.72811	+	0.142552i	0.228631	+	0.00484412i
$867$	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
$872$	1.21232	−	19.0499i	0.0410542	−	0.645112i
$873$	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	−0.228609	−	0.973518i	$-0.573418\pi$
$877$	4.69863	−	1.52668i	0.158661	−	0.0515522i	0.387271	+	0.921966i	$0.373418\pi$
$878$	1.97394	+	1.49905i	0.0666173	+	0.0505906i
$879$	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	$0.703649\pi$
$882$	−0.855292	−	2.83533i	−0.0287992	−	0.0954704i
$883$	1.04603	−	1.43973i	0.0352017	−	0.0484509i	−0.791053	−	0.611747i	$-0.790467\pi$
$883$	1.04603	−	1.43973i	0.0352017	−	0.0484509i	0.826255	+	0.563296i	$0.190467\pi$
$884$	9.36120	−	2.60884i	0.314851	−	0.0877449i
$885$		0			0
$886$	2.77137	+	3.98953i	0.0931060	+	0.134031i
$887$	−13.9287	+	42.8681i	−0.467680	+	1.43937i	0.387901	+	0.921701i	$0.373200\pi$
$887$	−13.9287	+	42.8681i	−0.467680	+	1.43937i	−0.855581	+	0.517669i	$0.826800\pi$
$888$	−25.0088	+	15.8458i	−0.839239	+	0.531749i
$889$	−3.26583	−	10.0512i	−0.109532	−	0.337106i
$890$		0			0
$891$	0.774771	+	0.251738i	0.0259558	+	0.00843355i
$892$	−46.5200	−	1.97218i	−1.55761	−	0.0660334i
$893$			0.584756i			0.0195681i
$894$	5.57996	−	16.0111i	0.186622	−	0.535490i
$895$		0			0
$896$	11.6895	−	23.4492i	0.390519	−	0.783383i
$897$	15.6946	−	11.4028i	0.524027	−	0.380728i
$898$	6.43731	−	4.47175i	0.214816	−	0.149224i
$899$		−	75.1261i		−	2.50560i
$900$		0			0
$901$		−	9.90409i		−	0.329953i
$902$	1.11344	+	1.60285i	0.0370735	+	0.0533692i
$903$	−23.9530	+	17.4028i	−0.797104	+	0.579130i
$904$	−42.8910	−	2.72953i	−1.42653	−	0.0907829i
$905$		0			0
$906$	−15.0557	−	5.24701i	−0.500192	−	0.174320i
$907$		−	22.9525i		−	0.762127i	−0.924549	−	0.381063i	$-0.875558\pi$
$907$		−	22.9525i		−	0.762127i	0.924549	−	0.381063i	$-0.124442\pi$
$908$	0.379398	−	8.94930i	0.0125908	−	0.296993i
$909$	−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	$0.873378\pi$
$912$	2.07519	+	1.79474i	0.0687163	+	0.0594297i
$913$	−0.392788	+	1.20888i	−0.0129994	+	0.0400080i
$914$	3.51710	−	2.44319i	0.116335	−	0.0808136i
$915$		0			0
$916$	9.83267	−	2.74024i	0.324881	−	0.0905399i
$917$	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	0.600462	−	0.799654i	$-0.294984\pi$
$919$	0.772993	+	0.561613i	0.0254987	+	0.0185259i	−0.574963	+	0.818179i	$0.694984\pi$
$920$		0			0
$921$	31.4250	−	22.8316i	1.03549	−	0.752326i
$922$	10.7726	−	14.1854i	0.354778	−	0.467170i
$923$	−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
$928$	−24.6567	−	42.8254i	−0.809395	−	1.40581i
$929$	46.5656	−	33.8319i	1.52777	−	1.10999i	0.570304	−	0.821433i	$-0.306825\pi$
$929$	46.5656	−	33.8319i	1.52777	−	1.10999i	0.957463	−	0.288555i	$-0.0931748\pi$
$930$		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
$934$	0.680077	−	32.0980i	0.0222528	−	1.05028i
$935$		0			0
$936$	7.17386	+	2.84632i	0.234485	+	0.0930349i
$937$	10.9461	−	33.6886i	0.357593	−	1.10056i	−0.596898	−	0.802317i	$-0.703600\pi$
$937$	10.9461	−	33.6886i	0.357593	−	1.10056i	0.954491	−	0.298240i	$-0.0963996\pi$
$938$	−0.219328	+	10.3517i	−0.00716131	+	0.337996i
$939$	−17.1327	+	5.56674i	−0.559103	+	0.181664i
$940$		0			0
$941$	0.202380	+	0.0657573i	0.00659741	+	0.00214363i	0.312314	−	0.949979i	$-0.398896\pi$
$941$	0.202380	+	0.0657573i	0.00659741	+	0.00214363i	−0.305716	+	0.952123i	$0.598896\pi$
$942$	−2.83660	+	8.13931i	−0.0924215	+	0.265193i
$943$	−41.4046			−1.34832
$944$	−10.1428	−	16.7841i	−0.330120	−	0.546277i
$945$		0			0
$946$	−2.53741	−	1.92696i	−0.0824982	−	0.0626508i
$947$	−3.47868	−	4.78799i	−0.113042	−	0.155589i	0.748747	−	0.662856i	$-0.230656\pi$
$947$	−3.47868	−	4.78799i	−0.113042	−	0.155589i	−0.861789	+	0.507267i	$0.830656\pi$
$948$	20.5115	−	25.8535i	0.666182	−	0.839682i
$949$			11.7717i			0.382124i
$950$		0			0
$951$	−16.7538			−0.543279
$952$	−5.50407	+	13.8725i	−0.178388	+	0.449609i
$953$	−41.8326	+	30.3932i	−1.35509	+	0.984531i	−0.356351	+	0.934352i	$0.615979\pi$
$953$	−41.8326	+	30.3932i	−1.35509	+	0.984531i	−0.998740	+	0.0501787i	$0.984021\pi$
$954$	4.75712	−	6.26415i	0.154018	−	0.202809i
$955$		0			0
$956$	−40.5850	−	1.72056i	−1.31261	−	0.0556470i
$957$		−	2.64859i		−	0.0856169i
$958$	3.21237	−	9.21755i	0.103787	−	0.297805i
$959$	−10.5198	+	32.3766i	−0.339702	+	1.04550i
$960$		0			0
$961$	13.2751	+	40.8565i	0.428228	+	1.31795i
$962$	−24.0623	−	0.509822i	−0.775801	−	0.0164373i
$963$	9.30935	+	3.02479i	0.299989	+	0.0974725i
$964$	−30.3485	−	24.0777i	−0.977458	−	0.775489i
$965$		0			0
$966$	−0.631103	+	29.7865i	−0.0203054	+	0.958365i
$967$	−15.9937	−	11.6201i	−0.514323	−	0.373677i	0.300138	−	0.953896i	$-0.402967\pi$
$967$	−15.9937	−	11.6201i	−0.514323	−	0.373677i	−0.814461	+	0.580218i	$0.802967\pi$
$968$	−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	$-0.0958405\pi$
$971$	11.7741	+	16.2057i	0.377850	+	0.520065i	−0.577164	+	0.816628i	$0.695841\pi$
$972$	−22.8979	−	8.52819i	−0.734451	−	0.273542i
$973$	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	−0.865240	−	0.501357i	$-0.832834\pi$
$977$	−14.3762	−	44.2455i	−0.459937	−	1.41554i	0.405304	−	0.914182i	$-0.367166\pi$
$978$	−19.4039	−	14.7357i	−0.620467	−	0.471196i
$979$	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	$-0.135014\pi$
$983$	25.1326	+	18.2599i	0.801606	+	0.582401i	−0.109779	+	0.993956i	$0.535014\pi$
$984$	11.8547	+	18.7098i	0.377914	+	0.596448i
$985$		0			0
$986$	16.0588	+	23.1175i	0.511417	+	0.736210i
$987$	3.23062	+	1.04969i	0.102832	+	0.0334120i
$988$	0.598759	+	2.14850i	0.0190490	+	0.0683529i
$989$	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	$0.0245457\pi$
$992$	36.1138	+	32.5957i	1.14661	+	1.03492i
$993$	−6.23268			−0.197788
$994$	7.06422	−	20.2700i	0.224063	−	0.642925i
$995$		0			0
$996$	−5.03490	+	13.5185i	−0.159537	+	0.428351i
$997$	−15.2722	−	21.0204i	−0.483676	−	0.665723i	0.495530	−	0.868591i	$-0.334974\pi$
$997$	−15.2722	−	21.0204i	−0.483676	−	0.665723i	−0.979206	+	0.202868i	$0.934974\pi$
$998$	29.4052	+	42.3302i	0.930804	+	1.33994i
$999$	44.7952			1.41726

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.15	✓	112	25.22	odd	20
200.2.o.a.29.20	yes	112	200.197	odd	20
200.2.o.a.69.15	yes	112	40.13	odd	4
200.2.o.a.69.20	yes	112	5.3	odd	4
800.2.be.a.369.10		112	40.3	even	4
800.2.be.a.369.19		112	20.3	even	4
800.2.be.a.529.10		112	100.47	even	20
800.2.be.a.529.19		112	200.147	even	20
1000.2.o.a.149.9		112	200.53	odd	20
1000.2.o.a.149.14		112	25.3	odd	20
1000.2.o.a.349.9		112	5.2	odd	4
1000.2.o.a.349.14		112	40.37	odd	4
1000.2.t.b.101.1		224	25.4	even	10	inner
1000.2.t.b.101.11		224	200.21	even	10	inner
1000.2.t.b.101.46		224	200.29	even	10	inner
1000.2.t.b.101.56		224	25.21	even	5	inner
1000.2.t.b.901.1		224	40.29	even	2	inner
1000.2.t.b.901.11		224	1.1	even	1	trivial
1000.2.t.b.901.46		224	5.4	even	2	inner
1000.2.t.b.901.56		224	8.5	even	2	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)

\(f(q)\)	\(=\)	\(q+(-1.16147 + 0.806832i) q^{2} +(0.770982 + 1.06117i) q^{3} +(0.698045 - 1.87423i) q^{4} +(-1.75166 - 0.610464i) q^{6} +2.31589 q^{7} +(0.701425 + 2.74007i) q^{8} +(0.395392 - 1.21689i) q^{9} +O(q^{10})\)	\(q+(-1.16147 + 0.806832i) q^{2} +(0.770982 + 1.06117i) q^{3} +(0.698045 - 1.87423i) q^{4} +(-1.75166 - 0.610464i) q^{6} +2.31589 q^{7} +(0.701425 + 2.74007i) q^{8} +(0.395392 - 1.21689i) q^{9} +(0.219837 - 0.0714294i) q^{11} +(2.52705 - 0.704254i) q^{12} +(2.02822 + 0.659008i) q^{13} +(-2.68985 + 1.86853i) q^{14} +(-3.02547 - 2.61659i) 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} +(-0.197704 + 0.260335i) 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} +(1.61660 - 4.34051i) 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} +(-3.22146 - 0.0682549i) q^{34} +(-2.00473 - 1.59050i) q^{36} +(7.58959 + 2.46601i) q^{37} +(0.0156653 - 0.739362i) q^{38} +(0.864403 + 2.66036i) q^{39} +(1.84490 - 5.67801i) q^{41} +(-4.05665 - 1.41377i) q^{42} +9.74670i q^{43} +(0.0195813 - 0.461886i) q^{44} +(7.81081 + 5.93169i) q^{46} +(0.904676 - 0.657286i) q^{47} +(0.444060 - 5.22787i) q^{48} -1.63664 q^{49} +2.98855i q^{51} +(2.65092 - 3.34133i) q^{52} +(-2.55504 - 3.51671i) q^{53} +(-4.80109 + 6.32205i) q^{54} +(1.62442 + 6.34571i) q^{56} -0.685906 q^{57} +(11.6659 + 4.06565i) q^{58} +(4.66275 + 1.51502i) q^{59} +(2.16726 - 0.704186i) q^{61} +(-12.1594 - 0.257629i) q^{62} +(0.915685 - 2.81819i) q^{63} +(-7.01601 + 3.84391i) q^{64} +(-0.428684 - 0.00908277i) 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} +(3.61171 + 0.229845i) 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} +(-3.15044 - 2.39251i) 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} +(5.85237 - 1.63098i) q^{84} +(-7.86395 - 11.3205i) q^{86} +(3.54081 - 10.8975i) q^{87} +(0.349921 + 0.552267i) q^{88} +(4.88895 + 15.0466i) q^{89} +(4.69713 + 1.52619i) q^{91} +(-13.8579 - 0.587495i) q^{92} +11.2803i q^{93} +(-0.520439 + 1.49334i) q^{94} +(3.70224 + 6.43031i) q^{96} +(-10.3255 + 7.50193i) q^{97} +(1.90092 - 1.32050i) 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

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