LMFDB - Embedded newform 722.2.e.s.423.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			423.4
Character	$\chi$	$=$	722.423
Dual form			722.2.e.s.99.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(0.437619 - 2.48186i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.88420 - 1.58103i) q^{5} +(-0.437619 - 2.48186i) q^{6} +(1.39680 + 2.41933i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-3.14904 - 1.14616i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(0.437619 - 2.48186i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.88420 - 1.58103i) q^{5} +(-0.437619 - 2.48186i) q^{6} +(1.39680 + 2.41933i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-3.14904 - 1.14616i) q^{9} +(-2.31131 - 0.841250i) q^{10} +(0.839266 - 1.45365i) q^{11} +(-1.26007 - 2.18251i) q^{12} +(-1.10172 - 6.24819i) q^{13} +(2.14003 + 1.79569i) q^{14} +(-4.74846 + 3.98443i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-4.66950 + 1.69956i) q^{17} -3.35114 q^{18} -2.45965 q^{20} +(6.61571 - 2.40792i) q^{21} +(0.291474 - 1.65303i) q^{22} +(-1.91427 + 1.60626i) q^{23} +(-1.93054 - 1.61992i) q^{24} +(0.182309 + 1.03393i) q^{25} +(-3.17229 - 5.49456i) q^{26} +(-0.442463 + 0.766369i) q^{27} +(2.62513 + 0.955469i) q^{28} +(5.57406 + 2.02879i) q^{29} +(-3.09934 + 5.36821i) q^{30} +(3.64204 + 6.30820i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-3.24048 - 2.71909i) q^{33} +(-3.80661 + 3.19412i) q^{34} +(1.19319 - 6.76690i) q^{35} +(-3.14904 + 1.14616i) q^{36} -0.550972 q^{37} -15.9893 q^{39} +(-2.31131 + 0.841250i) q^{40} +(0.452772 - 2.56780i) q^{41} +(5.39318 - 4.52541i) q^{42} +(2.19953 + 1.84563i) q^{43} +(-0.291474 - 1.65303i) q^{44} +(4.12132 + 7.13833i) q^{45} +(-1.24945 + 2.16411i) q^{46} +(-0.700629 - 0.255008i) q^{47} +(-2.36816 - 0.861941i) q^{48} +(-0.402113 + 0.696480i) q^{49} +(0.524938 + 0.909219i) q^{50} +(2.17461 + 12.3328i) q^{51} +(-4.86023 - 4.07822i) q^{52} +(1.12629 - 0.945072i) q^{53} +(-0.153666 + 0.871483i) q^{54} +(-3.87961 + 1.41206i) q^{55} +2.79360 q^{56} +5.93179 q^{58} +(-4.66333 + 1.69731i) q^{59} +(-1.07639 + 6.10451i) q^{60} +(7.15245 - 6.00162i) q^{61} +(5.57993 + 4.68212i) q^{62} +(-1.62565 - 9.21954i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-7.80272 + 13.5147i) q^{65} +(-3.97504 - 1.44680i) q^{66} +(10.8633 + 3.95390i) q^{67} +(-2.48459 + 4.30343i) q^{68} +(3.14880 + 5.45389i) q^{69} +(-1.19319 - 6.76690i) q^{70} +(5.36000 + 4.49757i) q^{71} +(-2.56712 + 2.15407i) q^{72} +(-1.07422 + 6.09221i) q^{73} +(-0.517744 + 0.188444i) q^{74} +2.64584 q^{75} +4.68915 q^{77} +(-15.0250 + 5.46865i) q^{78} +(1.02654 - 5.82177i) q^{79} +(-1.88420 + 1.58103i) q^{80} +(-5.99298 - 5.02871i) q^{81} +(-0.452772 - 2.56780i) q^{82} +(-7.58866 - 13.1439i) q^{83} +(3.52015 - 6.09707i) q^{84} +(11.4853 + 4.18032i) q^{85} +(2.69813 + 0.982038i) q^{86} +(7.47449 - 12.9462i) q^{87} +(-0.839266 - 1.45365i) q^{88} +(-1.19904 - 6.80011i) q^{89} +(6.31422 + 5.29826i) q^{90} +(13.5776 - 11.3929i) q^{91} +(-0.433930 + 2.46094i) q^{92} +(17.2499 - 6.27845i) q^{93} -0.745593 q^{94} -2.52015 q^{96} +(13.5197 - 4.92077i) q^{97} +(-0.139652 + 0.792008i) q^{98} +(-4.30900 + 3.61568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{7} + 12 q^{8}+O(q^{10}) $ 24 * q + 6 * q^7 + 12 * q^8	$ 24 q + 6 q^{7} + 12 q^{8} - 6 q^{11} + 6 q^{12} - 24 q^{18} - 12 q^{20} - 54 q^{26} - 12 q^{27} - 12 q^{30} + 78 q^{31} - 24 q^{37} - 36 q^{39} + 66 q^{45} - 30 q^{46} + 36 q^{49} + 18 q^{50} + 12 q^{56} - 12 q^{58} - 12 q^{64} - 12 q^{65} - 18 q^{68} - 60 q^{69} - 48 q^{75} + 24 q^{77} + 36 q^{83} + 12 q^{84} + 78 q^{87} + 6 q^{88} + 72 q^{94} + 12 q^{96}+O(q^{100}) $ 24 * q + 6 * q^7 + 12 * q^8 - 6 * q^11 + 6 * q^12 - 24 * q^18 - 12 * q^20 - 54 * q^26 - 12 * q^27 - 12 * q^30 + 78 * q^31 - 24 * q^37 - 36 * q^39 + 66 * q^45 - 30 * q^46 + 36 * q^49 + 18 * q^50 + 12 * q^56 - 12 * q^58 - 12 * q^64 - 12 * q^65 - 18 * q^68 - 60 * q^69 - 48 * q^75 + 24 * q^77 + 36 * q^83 + 12 * q^84 + 78 * q^87 + 6 * q^88 + 72 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	0.437619	−	2.48186i	0.252659	−	1.43290i	−0.549351	−	0.835592i	$-0.685125\pi$
$3$	0.437619	−	2.48186i	0.252659	−	1.43290i	0.802010	−	0.597311i	$-0.203764\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−1.88420	−	1.58103i	−0.842640	−	0.707059i	0.115516	−	0.993306i	$-0.463148\pi$
$5$	−1.88420	−	1.58103i	−0.842640	−	0.707059i	−0.958156	+	0.286247i	$0.907592\pi$
$6$	−0.437619	−	2.48186i	−0.178657	−	1.01322i
$7$	1.39680	+	2.41933i	0.527942	+	0.914422i	0.999469	+	0.0325705i	$0.0103694\pi$
$7$	1.39680	+	2.41933i	0.527942	+	0.914422i	−0.471528	+	0.881851i	$0.656297\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−3.14904	−	1.14616i	−1.04968	−	0.382053i
$10$	−2.31131	−	0.841250i	−0.730902	−	0.266027i
$11$	0.839266	−	1.45365i	0.253048	−	0.438292i	−0.711315	−	0.702873i	$-0.751900\pi$
$11$	0.839266	−	1.45365i	0.253048	−	0.438292i	0.964364	+	0.264581i	$0.0852336\pi$
$12$	−1.26007	−	2.18251i	−0.363752	−	0.630037i
$13$	−1.10172	−	6.24819i	−0.305563	−	1.73294i	−0.620841	−	0.783936i	$-0.713209\pi$
$13$	−1.10172	−	6.24819i	−0.305563	−	1.73294i	0.315278	−	0.948999i	$-0.397902\pi$
$14$	2.14003	+	1.79569i	0.571946	+	0.479920i
$15$	−4.74846	+	3.98443i	−1.22605	+	1.02878i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−4.66950	+	1.69956i	−1.13252	+	0.412203i	−0.839206	−	0.543813i	$-0.816980\pi$
$17$	−4.66950	+	1.69956i	−1.13252	+	0.412203i	−0.293313	+	0.956016i	$0.594758\pi$
$18$	−3.35114			−0.789872
$19$		0			0
$19$		0			0
$20$	−2.45965			−0.549994
$21$	6.61571	−	2.40792i	1.44367	−	0.525452i
$22$	0.291474	−	1.65303i	0.0621425	−	0.352427i
$23$	−1.91427	+	1.60626i	−0.399153	+	0.334929i	−0.820166	−	0.572125i	$-0.806119\pi$
$23$	−1.91427	+	1.60626i	−0.399153	+	0.334929i	0.421013	+	0.907055i	$0.361675\pi$
$24$	−1.93054	−	1.61992i	−0.394071	−	0.330665i
$25$	0.182309	+	1.03393i	0.0364618	+	0.206785i
$26$	−3.17229	−	5.49456i	−0.622137	−	1.07757i
$27$	−0.442463	+	0.766369i	−0.0851521	+	0.147488i
$28$	2.62513	+	0.955469i	0.496103	+	0.180567i
$29$	5.57406	+	2.02879i	1.03508	+	0.376737i	0.803012	−	0.595964i	$-0.203230\pi$
$29$	5.57406	+	2.02879i	1.03508	+	0.376737i	0.232065	+	0.972700i	$0.425452\pi$
$30$	−3.09934	+	5.36821i	−0.565859	+	0.980097i
$31$	3.64204	+	6.30820i	0.654130	+	1.13299i	0.982111	+	0.188302i	$0.0602983\pi$
$31$	3.64204	+	6.30820i	0.654130	+	1.13299i	−0.327982	+	0.944684i	$0.606368\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−3.24048	−	2.71909i	−0.564095	−	0.473332i
$34$	−3.80661	+	3.19412i	−0.652828	+	0.547788i
$35$	1.19319	−	6.76690i	0.201685	−	1.14381i
$36$	−3.14904	+	1.14616i	−0.524840	+	0.191026i
$37$	−0.550972			−0.0905792			−0.0452896	−	0.998974i	$-0.514421\pi$
$37$	−0.550972			−0.0905792			−0.0452896	+	0.998974i	$0.514421\pi$
$38$		0			0
$39$	−15.9893			−2.56033
$40$	−2.31131	+	0.841250i	−0.365451	+	0.133013i
$41$	0.452772	−	2.56780i	0.0707112	−	0.401023i	−0.928824	−	0.370522i	$-0.879179\pi$
$41$	0.452772	−	2.56780i	0.0707112	−	0.401023i	0.999535	−	0.0305007i	$-0.00971018\pi$
$42$	5.39318	−	4.52541i	0.832185	−	0.698287i
$43$	2.19953	+	1.84563i	0.335426	+	0.281456i	0.794906	−	0.606732i	$-0.207520\pi$
$43$	2.19953	+	1.84563i	0.335426	+	0.281456i	−0.459481	+	0.888188i	$0.651964\pi$
$44$	−0.291474	−	1.65303i	−0.0439413	−	0.249204i
$45$	4.12132	+	7.13833i	0.614370	+	1.06412i
$46$	−1.24945	+	2.16411i	−0.184222	+	0.319081i
$47$	−0.700629	−	0.255008i	−0.102197	−	0.0371967i	0.290416	−	0.956901i	$-0.406206\pi$
$47$	−0.700629	−	0.255008i	−0.102197	−	0.0371967i	−0.392613	+	0.919704i	$0.628429\pi$
$48$	−2.36816	−	0.861941i	−0.341815	−	0.124410i
$49$	−0.402113	+	0.696480i	−0.0574447	+	0.0994972i
$50$	0.524938	+	0.909219i	0.0742374	+	0.128583i
$51$	2.17461	+	12.3328i	0.304506	+	1.72694i
$52$	−4.86023	−	4.07822i	−0.673992	−	0.565547i
$53$	1.12629	−	0.945072i	0.154708	−	0.129816i	−0.562148	−	0.827037i	$-0.690025\pi$
$53$	1.12629	−	0.945072i	0.154708	−	0.129816i	0.716856	+	0.697221i	$0.245580\pi$
$54$	−0.153666	+	0.871483i	−0.0209113	+	0.118594i
$55$	−3.87961	+	1.41206i	−0.523127	+	0.190403i
$56$	2.79360			0.373311
$57$		0			0
$58$	5.93179			0.778882
$59$	−4.66333	+	1.69731i	−0.607114	+	0.220971i	−0.627240	−	0.778826i	$-0.715815\pi$
$59$	−4.66333	+	1.69731i	−0.607114	+	0.220971i	0.0201262	+	0.999797i	$0.493593\pi$
$60$	−1.07639	+	6.10451i	−0.138961	+	0.788088i
$61$	7.15245	−	6.00162i	0.915777	−	0.768428i	−0.0574320	−	0.998349i	$-0.518291\pi$
$61$	7.15245	−	6.00162i	0.915777	−	0.768428i	0.973209	+	0.229921i	$0.0738468\pi$
$62$	5.57993	+	4.68212i	0.708652	+	0.594629i
$63$	−1.62565	−	9.21954i	−0.204813	−	1.16155i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−7.80272	+	13.5147i	−0.967808	+	1.67629i
$66$	−3.97504	−	1.44680i	−0.489293	−	0.178088i
$67$	10.8633	+	3.95390i	1.32716	+	0.483046i	0.905745	−	0.423822i	$-0.139312\pi$
$67$	10.8633	+	3.95390i	1.32716	+	0.483046i	0.421413	+	0.906869i	$0.361534\pi$
$68$	−2.48459	+	4.30343i	−0.301300	+	0.521868i
$69$	3.14880	+	5.45389i	0.379071	+	0.656571i
$70$	−1.19319	−	6.76690i	−0.142613	−	0.808799i
$71$	5.36000	+	4.49757i	0.636115	+	0.533764i	0.902822	−	0.430014i	$-0.141491\pi$
$71$	5.36000	+	4.49757i	0.636115	+	0.533764i	−0.266707	+	0.963778i	$0.585936\pi$
$72$	−2.56712	+	2.15407i	−0.302538	+	0.253860i
$73$	−1.07422	+	6.09221i	−0.125728	+	0.713039i	0.855145	+	0.518389i	$0.173468\pi$
$73$	−1.07422	+	6.09221i	−0.125728	+	0.713039i	−0.980873	+	0.194650i	$0.937643\pi$
$74$	−0.517744	+	0.188444i	−0.0601866	+	0.0219061i
$75$	2.64584			0.305515
$76$		0			0
$77$	4.68915			0.534379
$78$	−15.0250	+	5.46865i	−1.70125	+	0.619203i
$79$	1.02654	−	5.82177i	0.115494	−	0.655001i	−0.871010	−	0.491265i	$-0.836535\pi$
$79$	1.02654	−	5.82177i	0.115494	−	0.655001i	0.986504	−	0.163735i	$-0.0523543\pi$
$80$	−1.88420	+	1.58103i	−0.210660	+	0.176765i
$81$	−5.99298	−	5.02871i	−0.665886	−	0.558745i
$82$	−0.452772	−	2.56780i	−0.0500003	−	0.283566i
$83$	−7.58866	−	13.1439i	−0.832964	−	1.44274i	−0.895678	−	0.444704i	$-0.853309\pi$
$83$	−7.58866	−	13.1439i	−0.832964	−	1.44274i	0.0627138	−	0.998032i	$-0.480024\pi$
$84$	3.52015	−	6.09707i	0.384080	−	0.665245i
$85$	11.4853	+	4.18032i	1.24576	+	0.453419i
$86$	2.69813	+	0.982038i	0.290947	+	0.105896i
$87$	7.47449	−	12.9462i	0.801349	−	1.38798i
$88$	−0.839266	−	1.45365i	−0.0894660	−	0.154960i
$89$	−1.19904	−	6.80011i	−0.127098	−	0.720811i	−0.980039	−	0.198803i	$-0.936294\pi$
$89$	−1.19904	−	6.80011i	−0.127098	−	0.720811i	0.852941	−	0.522007i	$-0.174817\pi$
$90$	6.31422	+	5.29826i	0.665578	+	0.558486i
$91$	13.5776	−	11.3929i	1.42331	−	1.19430i
$92$	−0.433930	+	2.46094i	−0.0452403	+	0.256571i
$93$	17.2499	−	6.27845i	1.78873	−	0.651045i
$94$	−0.745593			−0.0769021
$95$		0			0
$96$	−2.52015			−0.257211
$97$	13.5197	−	4.92077i	1.37272	−	0.499629i	0.452756	−	0.891634i	$-0.350441\pi$
$97$	13.5197	−	4.92077i	1.37272	−	0.499629i	0.919963	+	0.392006i	$0.128219\pi$
$98$	−0.139652	+	0.792008i	−0.0141070	+	0.0800049i
$99$	−4.30900	+	3.61568i	−0.433070	+	0.363389i
$100$	0.804252	+	0.674847i	0.0804252	+	0.0674847i
$101$	1.95926	+	11.1115i	0.194954	+	1.10564i	0.912485	+	0.409111i	$0.134161\pi$
$101$	1.95926	+	11.1115i	0.194954	+	1.10564i	−0.717531	+	0.696526i	$0.754728\pi$
$102$	6.26153	+	10.8453i	0.619983	+	1.07384i
$103$	7.41399	−	12.8414i	0.730522	−	1.26530i	−0.226138	−	0.974095i	$-0.572610\pi$
$103$	7.41399	−	12.8414i	0.730522	−	1.26530i	0.956660	−	0.291206i	$-0.0940565\pi$
$104$	−5.96195	−	2.16997i	−0.584617	−	0.212783i
$105$	−16.2723	−	5.92265i	−1.58802	−	0.577991i
$106$	0.735136	−	1.27329i	0.0714027	−	0.123673i
$107$	−1.41424	−	2.44954i	−0.136720	−	0.236806i	0.789533	−	0.613708i	$-0.210323\pi$
$107$	−1.41424	−	2.44954i	−0.136720	−	0.236806i	−0.926253	+	0.376902i	$0.876989\pi$
$108$	0.153666	+	0.871483i	0.0147865	+	0.0838585i
$109$	−1.32173	−	1.10906i	−0.126598	−	0.106229i	0.577290	−	0.816539i	$-0.304110\pi$
$109$	−1.32173	−	1.10906i	−0.126598	−	0.106229i	−0.703889	+	0.710310i	$0.748555\pi$
$110$	−3.16269	+	2.65381i	−0.301551	+	0.253031i
$111$	−0.241116	+	1.36744i	−0.0228857	+	0.129791i
$112$	2.62513	−	0.955469i	0.248051	−	0.0902833i
$113$	0.427785			0.0402426			0.0201213	−	0.999798i	$-0.493595\pi$
$113$	0.427785			0.0402426			0.0201213	+	0.999798i	$0.493595\pi$
$114$		0			0
$115$	6.14643			0.573157
$116$	5.57406	−	2.02879i	0.517538	−	0.188368i
$117$	−3.69203	+	20.9386i	−0.341329	+	1.93577i
$118$	−3.80158	+	3.18990i	−0.349964	+	0.293655i
$119$	−10.6342	−	8.92312i	−0.974832	−	0.817981i
$120$	1.07639	+	6.10451i	0.0982604	+	0.557263i
$121$	4.09127	+	7.08628i	0.371933	+	0.644207i
$122$	4.66843	−	8.08596i	0.422660	−	0.732068i
$123$	−6.17478	−	2.24744i	−0.556761	−	0.202644i
$124$	6.84480	+	2.49130i	0.614681	+	0.223726i
$125$	−4.85796	+	8.41423i	−0.434509	+	0.752592i
$126$	−4.68088	−	8.10752i	−0.417006	−	0.722276i
$127$	0.197319	+	1.11905i	0.0175093	+	0.0992999i	0.992310	−	0.123777i	$-0.0395009\pi$
$127$	0.197319	+	1.11905i	0.0175093	+	0.0992999i	−0.974801	+	0.223077i	$0.928390\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	5.54315	−	4.65125i	0.488047	−	0.409520i
$130$	−2.70986	+	15.3684i	−0.237670	+	1.34789i
$131$	16.7655	−	6.10215i	1.46481	−	0.533148i	0.518125	−	0.855305i	$-0.326630\pi$
$131$	16.7655	−	6.10215i	1.46481	−	0.533148i	0.946686	+	0.322157i	$0.104408\pi$
$132$	−4.23015			−0.368187
$133$		0			0
$134$	11.5604			0.998670
$135$	2.04534	−	0.744445i	0.176035	−	0.0640716i
$136$	−0.862888	+	4.89368i	−0.0739921	+	0.419630i
$137$	−12.1921	+	10.2304i	−1.04164	+	0.874040i	−0.992190	−	0.124737i	$-0.960191\pi$
$137$	−12.1921	+	10.2304i	−1.04164	+	0.874040i	−0.0494504	+	0.998777i	$0.515747\pi$
$138$	4.82425	+	4.04802i	0.410667	+	0.344591i
$139$	1.75735	+	9.96642i	0.149056	+	0.845341i	0.964020	+	0.265829i	$0.0856457\pi$
$139$	1.75735	+	9.96642i	0.149056	+	0.845341i	−0.814964	+	0.579512i	$0.803243\pi$
$140$	−3.43564	−	5.95071i	−0.290365	−	0.502927i
$141$	−0.939503	+	1.62727i	−0.0791204	+	0.137041i
$142$	6.57501	+	2.39311i	0.551763	+	0.200825i
$143$	−10.0073	−	3.64237i	−0.836854	−	0.304590i
$144$	−1.67557	+	2.90217i	−0.139631	+	0.241848i
$145$	−7.29506	−	12.6354i	−0.605821	−	1.04931i
$146$	1.07422	+	6.09221i	0.0889032	+	0.504195i
$147$	1.55259	+	1.30278i	0.128056	+	0.107452i
$148$	−0.422069	+	0.354158i	−0.0346939	+	0.0291116i
$149$	1.63203	−	9.25573i	0.133701	−	0.758259i	−0.842054	−	0.539394i	$-0.818653\pi$
$149$	1.63203	−	9.25573i	0.133701	−	0.758259i	0.975755	−	0.218865i	$-0.0702354\pi$
$150$	2.48628	−	0.904931i	0.203004	−	0.0738873i
$151$	10.2632			0.835210			0.417605	−	0.908629i	$-0.362870\pi$
$151$	10.2632			0.835210			0.417605	+	0.908629i	$0.362870\pi$
$152$		0			0
$153$	16.6524			1.34627
$154$	4.40636	−	1.60378i	0.355075	−	0.129237i
$155$	3.11113	−	17.6441i	0.249892	−	1.41721i
$156$	−12.2485	+	10.2777i	−0.980664	+	0.822875i
$157$	2.27812	+	1.91157i	0.181814	+	0.152560i	0.729152	−	0.684351i	$-0.239915\pi$
$157$	2.27812	+	1.91157i	0.181814	+	0.152560i	−0.547339	+	0.836911i	$0.684359\pi$
$158$	−1.02654	−	5.82177i	−0.0816668	−	0.463155i
$159$	−1.85265	−	3.20888i	−0.146925	−	0.254481i
$160$	−1.22982	+	2.13012i	−0.0972262	+	0.168401i
$161$	−6.55995	−	2.38763i	−0.516996	−	0.188171i
$162$	−7.35148	−	2.67572i	−0.577586	−	0.210224i
$163$	−2.79595	+	4.84273i	−0.218996	+	0.379312i	−0.954501	−	0.298207i	$-0.903612\pi$
$163$	−2.79595	+	4.84273i	−0.218996	+	0.379312i	0.735505	+	0.677519i	$0.236945\pi$
$164$	−1.30371	−	2.25809i	−0.101802	−	0.176327i
$165$	1.80675	+	10.2466i	0.140656	+	0.797697i
$166$	−11.6265	−	9.75579i	−0.902392	−	0.757197i
$167$	5.42636	−	4.55325i	0.419904	−	0.352341i	−0.408223	−	0.912882i	$-0.633851\pi$
$167$	5.42636	−	4.55325i	0.419904	−	0.352341i	0.828127	+	0.560541i	$0.189407\pi$
$168$	1.22253	−	6.93334i	0.0943206	−	0.534918i
$169$	−25.6101	+	9.32130i	−1.97000	+	0.717023i
$170$	12.2224			0.937418
$171$		0			0
$172$	2.87129			0.218934
$173$	−21.6325	+	7.87358i	−1.64469	+	0.598617i	−0.987849	−	0.155415i	$-0.950329\pi$
$173$	−21.6325	+	7.87358i	−1.64469	+	0.598617i	−0.656838	+	0.754032i	$0.728106\pi$
$174$	2.59586	−	14.7219i	0.196792	−	1.11606i
$175$	−2.24676	+	1.88526i	−0.169839	+	0.142512i
$176$	−1.28583	−	1.07894i	−0.0969231	−	0.0813281i
$177$	2.17173	+	12.3165i	0.163237	+	0.925765i
$178$	−3.45251	−	5.97992i	−0.258776	−	0.448214i
$179$	4.10736	−	7.11415i	0.306998	−	0.531736i	−0.670706	−	0.741723i	$-0.734009\pi$
$179$	4.10736	−	7.11415i	0.306998	−	0.531736i	0.977704	+	0.209987i	$0.0673421\pi$
$180$	7.74554	+	2.81915i	0.577319	+	0.210127i
$181$	−12.2159	−	4.44622i	−0.908001	−	0.330485i	−0.154546	−	0.987986i	$-0.549392\pi$
$181$	−12.2159	−	4.44622i	−0.908001	−	0.330485i	−0.753454	+	0.657500i	$0.771614\pi$
$182$	8.86212	−	15.3496i	0.656904	−	1.13779i
$183$	−11.7651	−	20.3778i	−0.869703	−	1.50637i
$184$	0.433930	+	2.46094i	0.0319898	+	0.181423i
$185$	1.03814	+	0.871105i	0.0763257	+	0.0640449i
$186$	14.0622	−	11.7996i	1.03109	−	0.865190i
$187$	−1.44838	+	8.21420i	−0.105916	+	0.600682i
$188$	−0.700629	+	0.255008i	−0.0510986	+	0.0185984i
$189$	−2.47214			−0.179821
$190$		0			0
$191$	6.57479			0.475735			0.237868	−	0.971298i	$-0.423552\pi$
$191$	6.57479			0.475735			0.237868	+	0.971298i	$0.423552\pi$
$192$	−2.36816	+	0.861941i	−0.170907	+	0.0622052i
$193$	−4.66812	+	26.4742i	−0.336019	+	1.90566i	0.0809193	+	0.996721i	$0.474214\pi$
$193$	−4.66812	+	26.4742i	−0.336019	+	1.90566i	−0.416938	+	0.908935i	$0.636897\pi$
$194$	11.0214	−	9.24803i	0.791288	−	0.663970i
$195$	30.1270	+	25.2795i	2.15744	+	1.81031i
$196$	0.139652	+	0.792008i	0.00997517	+	0.0565720i
$197$	4.92470	+	8.52983i	0.350870	+	0.607725i	0.986402	−	0.164349i	$-0.0525524\pi$
$197$	4.92470	+	8.52983i	0.350870	+	0.607725i	−0.635532	+	0.772075i	$0.719219\pi$
$198$	−2.81250	+	4.87139i	−0.199876	+	0.346195i
$199$	19.2318	+	6.99982i	1.36331	+	0.496204i	0.917076	−	0.398713i	$-0.130543\pi$
$199$	19.2318	+	6.99982i	1.36331	+	0.496204i	0.446233	+	0.894917i	$0.352765\pi$
$200$	0.986561	+	0.359079i	0.0697604	+	0.0253907i
$201$	14.5670	−	25.2308i	1.02748	−	1.77964i
$202$	5.64146	+	9.77130i	0.396932	+	0.687506i
$203$	2.87753	+	16.3193i	0.201963	+	1.14539i
$204$	9.59321	+	8.04966i	0.671659	+	0.563589i
$205$	−4.91289	+	4.12240i	−0.343131	+	0.287921i
$206$	2.57485	−	14.6027i	0.179398	−	1.01742i
$207$	7.86915	−	2.86414i	0.546944	−	0.199071i
$208$	−6.34458			−0.439917
$209$		0			0
$210$	−17.3167			−1.19496
$211$	7.62682	−	2.77594i	0.525052	−	0.191103i	−0.0658756	−	0.997828i	$-0.520984\pi$
$211$	7.62682	−	2.77594i	0.525052	−	0.191103i	0.590928	+	0.806724i	$0.298762\pi$
$212$	0.255310	−	1.44793i	0.0175348	−	0.0994445i
$213$	13.5080	−	11.3345i	0.925552	−	0.776630i
$214$	−2.16675	−	1.81812i	−0.148116	−	0.124284i
$215$	−1.22637	−	6.95507i	−0.0836375	−	0.474332i
$216$	0.442463	+	0.766369i	0.0301058	+	0.0521448i
$217$	−10.1744	+	17.6226i	−0.690684	+	1.19630i
$218$	−1.62134	−	0.590118i	−0.109811	−	0.0399678i
$219$	14.6499	+	5.33213i	0.989949	+	0.360312i
$220$	−2.06430	+	3.57547i	−0.139175	+	0.241058i
$221$	15.7637	+	27.3035i	1.06038	+	1.83663i
$222$	0.241116	+	1.36744i	0.0161826	+	0.0917763i
$223$	−8.23806	−	6.91255i	−0.551661	−	0.462899i	0.323842	−	0.946111i	$-0.395025\pi$
$223$	−8.23806	−	6.91255i	−0.551661	−	0.462899i	−0.875503	+	0.483212i	$0.839470\pi$
$224$	2.14003	−	1.79569i	0.142986	−	0.119980i
$225$	0.610943	−	3.46483i	0.0407296	−	0.230989i
$226$	0.401986	−	0.146311i	0.0267397	−	0.00973246i
$227$	−27.0936			−1.79827			−0.899133	−	0.437676i	$-0.855802\pi$
$227$	−27.0936			−1.79827			−0.899133	+	0.437676i	$0.855802\pi$
$228$		0			0
$229$	9.46557			0.625503			0.312751	−	0.949835i	$-0.398749\pi$
$229$	9.46557			0.625503			0.312751	+	0.949835i	$0.398749\pi$
$230$	5.77575	−	2.10220i	0.380842	−	0.138615i
$231$	2.05206	−	11.6378i	0.135016	−	0.765713i
$232$	4.54401	−	3.81288i	0.298329	−	0.250328i
$233$	17.5134	+	14.6955i	1.14734	+	0.962733i	0.999654	−	0.0263016i	$-0.00837302\pi$
$233$	17.5134	+	14.6955i	1.14734	+	0.962733i	0.147686	+	0.989034i	$0.452817\pi$
$234$	3.69203	+	20.9386i	0.241356	+	1.36880i
$235$	0.916949	+	1.58820i	0.0598152	+	0.103603i
$236$	−2.48131	+	4.29775i	−0.161519	+	0.279759i
$237$	−13.9996	−	5.09544i	−0.909371	−	0.330984i
$238$	−13.0447	−	4.74789i	−0.845564	−	0.307760i
$239$	−4.33306	+	7.50508i	−0.280282	+	0.485463i	−0.971454	−	0.237227i	$-0.923761\pi$
$239$	−4.33306	+	7.50508i	−0.280282	+	0.485463i	0.691172	+	0.722690i	$0.257095\pi$
$240$	3.09934	+	5.36821i	0.200061	+	0.346517i
$241$	−0.982546	−	5.57230i	−0.0632914	−	0.358943i	−0.999962	−	0.00873132i	$-0.997221\pi$
$241$	−0.982546	−	5.57230i	−0.0632914	−	0.358943i	0.936671	−	0.350212i	$-0.113890\pi$
$242$	6.26818	+	5.25963i	0.402934	+	0.338102i
$243$	−17.1369	+	14.3795i	−1.09933	+	0.922448i
$244$	1.62133	−	9.19501i	0.103795	−	0.588650i
$245$	1.85882	−	0.676555i	0.118756	−	0.0432235i
$246$	−6.57106			−0.418956
$247$		0			0
$248$	7.28408			0.462539
$249$	−35.9424	+	13.0820i	−2.27776	+	0.829035i
$250$	−1.68715	+	9.56831i	−0.106705	+	0.605153i
$251$	−10.3839	+	8.71313i	−0.655427	+	0.549968i	−0.908712	−	0.417423i	$-0.862933\pi$
$251$	−10.3839	+	8.71313i	−0.655427	+	0.549968i	0.253286	+	0.967392i	$0.418489\pi$
$252$	−7.17153	−	6.01762i	−0.451764	−	0.379075i
$253$	0.728365	+	4.13077i	0.0457919	+	0.259699i
$254$	0.568158	+	0.984079i	0.0356494	+	0.0617466i
$255$	15.4012	−	26.6756i	0.964458	−	1.67049i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	9.43381	+	3.43363i	0.588465	+	0.214184i	0.619054	−	0.785348i	$-0.287516\pi$
$257$	9.43381	+	3.43363i	0.588465	+	0.214184i	−0.0305891	+	0.999532i	$0.509738\pi$
$258$	3.61803	−	6.26662i	0.225249	−	0.390143i
$259$	−0.769599	−	1.33298i	−0.0478206	−	0.0828276i
$260$	2.70986	+	15.3684i	0.168058	+	0.953105i
$261$	−15.2276	−	12.7775i	−0.942566	−	0.790907i
$262$	13.6674	−	11.4683i	0.844374	−	0.708514i
$263$	−3.26913	+	18.5402i	−0.201583	+	1.14324i	0.701143	+	0.713021i	$0.252673\pi$
$263$	−3.26913	+	18.5402i	−0.201583	+	1.14324i	−0.902726	+	0.430215i	$0.858438\pi$
$264$	−3.97504	+	1.44680i	−0.244647	+	0.0890441i
$265$	−3.61635			−0.222151
$266$		0			0
$267$	−17.4017			−1.06496
$268$	10.8633	−	3.95390i	0.663579	−	0.241523i
$269$	2.84482	−	16.1338i	0.173452	−	0.983694i	−0.766464	−	0.642288i	$-0.777985\pi$
$269$	2.84482	−	16.1338i	0.173452	−	0.983694i	0.939916	−	0.341407i	$-0.110903\pi$
$270$	1.66738	−	1.39910i	0.101474	−	0.0851464i
$271$	−2.11952	−	1.77849i	−0.128752	−	0.108035i	0.576138	−	0.817352i	$-0.304559\pi$
$271$	−2.11952	−	1.77849i	−0.128752	−	0.108035i	−0.704890	+	0.709317i	$0.749004\pi$
$272$	0.862888	+	4.89368i	0.0523203	+	0.296723i
$273$	−22.3338	−	38.6833i	−1.35171	−	2.34122i
$274$	−7.95782	+	13.7833i	−0.480749	+	0.832682i
$275$	1.65597	+	0.602725i	0.0998589	+	0.0363457i
$276$	5.91781	+	2.15391i	0.356210	+	0.129650i
$277$	−12.2661	+	21.2454i	−0.736996	+	1.27651i	0.216846	+	0.976206i	$0.430423\pi$
$277$	−12.2661	+	21.2454i	−0.736996	+	1.27651i	−0.953842	+	0.300309i	$0.902910\pi$
$278$	5.06008	+	8.76432i	0.303484	+	0.525649i
$279$	−4.23875	−	24.0391i	−0.253767	−	1.43919i
$280$	−5.26371	−	4.41678i	−0.314567	−	0.263953i
$281$	−7.79095	+	6.53738i	−0.464769	+	0.389988i	−0.844882	−	0.534952i	$-0.820330\pi$
$281$	−7.79095	+	6.53738i	−0.464769	+	0.389988i	0.380113	+	0.924940i	$0.375885\pi$
$282$	−0.326286	+	1.85046i	−0.0194300	+	0.110193i
$283$	−25.9992	+	9.46294i	−1.54549	+	0.562514i	−0.967355	−	0.253425i	$-0.918443\pi$
$283$	−25.9992	+	9.46294i	−1.54549	+	0.562514i	−0.578138	+	0.815939i	$0.696221\pi$
$284$	6.99698			0.415195
$285$		0			0
$286$	−10.6496			−0.629722
$287$	6.84480	−	2.49130i	0.404035	−	0.147057i
$288$	−0.581920	+	3.30023i	−0.0342899	+	0.194468i
$289$	5.89295	−	4.94477i	0.346644	−	0.290869i
$290$	−11.1767	−	9.37834i	−0.656317	−	0.550715i
$291$	−6.29619	−	35.7075i	−0.369089	−	2.09321i
$292$	3.09310	+	5.35740i	0.181010	+	0.313518i
$293$	11.9193	−	20.6448i	0.696333	−	1.20608i	−0.273396	−	0.961901i	$-0.588147\pi$
$293$	11.9193	−	20.6448i	0.696333	−	1.20608i	0.969729	−	0.244182i	$-0.0785196\pi$
$294$	1.90454	+	0.693195i	0.111075	+	0.0404280i
$295$	11.4702	+	4.17479i	0.667818	+	0.243066i
$296$	−0.275486	+	0.477156i	−0.0160123	+	0.0277341i
$297$	0.742689	+	1.28637i	0.0430952	+	0.0746430i
$298$	−1.63203	−	9.25573i	−0.0945412	−	0.536170i
$299$	12.1452	+	10.1911i	0.702377	+	0.589365i
$300$	2.02683	−	1.70071i	0.117019	−	0.0981908i
$301$	−1.39287	+	7.89938i	−0.0802839	+	0.455313i
$302$	9.64428	−	3.51023i	0.554966	−	0.201991i
$303$	28.4346			1.63353
$304$		0			0
$305$	−22.9654			−1.31500
$306$	15.6481	−	5.69546i	0.894545	−	0.325588i
$307$	−4.51285	+	25.5936i	−0.257562	+	1.46070i	0.531849	+	0.846839i	$0.321497\pi$
$307$	−4.51285	+	25.5936i	−0.257562	+	1.46070i	−0.789411	+	0.613866i	$0.789614\pi$
$308$	3.59210	−	3.01413i	0.204679	−	0.171746i
$309$	−28.6261	−	24.0201i	−1.62848	−	1.36646i
$310$	−3.11113	−	17.6441i	−0.176700	−	1.00212i
$311$	11.5522	+	20.0089i	0.655063	+	1.13460i	0.981878	+	0.189515i	$0.0606914\pi$
$311$	11.5522	+	20.0089i	0.655063	+	1.13460i	−0.326814	+	0.945089i	$0.605975\pi$
$312$	−7.99463	+	13.8471i	−0.452607	+	0.783938i
$313$	−11.5250	−	4.19477i	−0.651434	−	0.237103i	−0.00490043	−	0.999988i	$-0.501560\pi$
$313$	−11.5250	−	4.19477i	−0.651434	−	0.237103i	−0.646534	+	0.762885i	$0.723782\pi$
$314$	2.79453	+	1.01713i	0.157704	+	0.0573997i
$315$	−11.5133	+	19.9417i	−0.648703	+	1.12359i
$316$	−2.95579	−	5.11958i	−0.166276	−	0.287999i
$317$	0.0472853	+	0.268168i	0.00265580	+	0.0150618i	0.986107	−	0.166112i	$-0.0531214\pi$
$317$	0.0472853	+	0.268168i	0.00265580	+	0.0150618i	−0.983451	+	0.181174i	$0.942010\pi$
$318$	−2.83842	−	2.38172i	−0.159171	−	0.133560i
$319$	7.62727	−	6.40004i	0.427045	−	0.358333i
$320$	−0.427114	+	2.42228i	−0.0238764	+	0.135410i
$321$	−6.69832	+	2.43799i	−0.373864	+	0.136075i
$322$	−6.98095			−0.389033
$323$		0			0
$324$	−7.82328			−0.434626
$325$	6.25931	−	2.27820i	0.347204	−	0.126372i
$326$	−0.971025	+	5.50695i	−0.0537801	+	0.305002i
$327$	−3.33094	+	2.79499i	−0.184202	+	0.154563i
$328$	−1.99739	−	1.67601i	−0.110288	−	0.0925423i
$329$	−0.361691	−	2.05125i	−0.0199406	−	0.113089i
$330$	5.20234	+	9.01071i	0.286379	+	0.496024i
$331$	−9.99650	+	17.3144i	−0.549457	+	0.951688i	0.448855	+	0.893605i	$0.351832\pi$
$331$	−9.99650	+	17.3144i	−0.549457	+	0.951688i	−0.998312	+	0.0580830i	$0.981501\pi$
$332$	−14.2620	−	5.19095i	−0.782730	−	0.284890i
$333$	1.73503	+	0.631501i	0.0950793	+	0.0346060i
$334$	3.54180	−	6.13458i	0.193799	−	0.335669i
$335$	−14.2173	−	24.6251i	−0.776775	−	1.34541i
$336$	−1.22253	−	6.93334i	−0.0666947	−	0.378244i
$337$	13.2391	+	11.1089i	0.721180	+	0.605142i	0.927711	−	0.373298i	$-0.121773\pi$
$337$	13.2391	+	11.1089i	0.721180	+	0.605142i	−0.206532	+	0.978440i	$0.566218\pi$
$338$	−20.8775	+	17.5183i	−1.13559	+	0.952870i
$339$	0.187207	−	1.06170i	0.0101677	−	0.0576637i
$340$	11.4853	−	4.18032i	0.622879	−	0.226710i
$341$	12.2266			0.662105
$342$		0			0
$343$	17.3085			0.934573
$344$	2.69813	−	0.982038i	0.145473	−	0.0529480i
$345$	2.68979	−	15.2546i	0.144814	−	0.821279i
$346$	−17.6350	+	14.7975i	−0.948061	+	0.795518i
$347$	−14.2067	−	11.9209i	−0.762658	−	0.639946i	0.176160	−	0.984362i	$-0.443633\pi$
$347$	−14.2067	−	11.9209i	−0.762658	−	0.639946i	−0.938817	+	0.344416i	$0.888077\pi$
$348$	−2.59586	−	14.7219i	−0.139153	−	0.789175i
$349$	10.0605	+	17.4253i	0.538527	+	0.932755i	0.998984	+	0.0450735i	$0.0143522\pi$
$349$	10.0605	+	17.4253i	0.538527	+	0.932755i	−0.460457	+	0.887682i	$0.652314\pi$
$350$	−1.46647	+	2.54000i	−0.0783861	+	0.135769i
$351$	5.27589	+	1.92027i	0.281606	+	0.102496i
$352$	−1.57730	−	0.574092i	−0.0840706	−	0.0305992i
$353$	−12.0278	+	20.8328i	−0.640177	+	1.10882i	0.345215	+	0.938523i	$0.387806\pi$
$353$	−12.0278	+	20.8328i	−0.640177	+	1.10882i	−0.985393	+	0.170296i	$0.945527\pi$
$354$	6.25325	+	10.8310i	0.332357	+	0.575659i
$355$	−2.98851	−	16.9487i	−0.158613	−	0.899542i
$356$	−5.28955	−	4.43846i	−0.280346	−	0.235238i
$357$	−26.7996	+	22.4876i	−1.41839	+	1.19017i
$358$	1.42647	−	8.08991i	0.0753913	−	0.427565i
$359$	10.1989	−	3.71210i	0.538278	−	0.195917i	−0.0585527	−	0.998284i	$-0.518649\pi$
$359$	10.1989	−	3.71210i	0.538278	−	0.195917i	0.596831	+	0.802367i	$0.296426\pi$
$360$	8.24263			0.434425
$361$		0			0
$362$	−12.9999			−0.683259
$363$	19.3776	−	7.05286i	1.01706	−	0.370179i
$364$	3.07778	−	17.4550i	0.161320	−	0.914889i
$365$	11.6560	−	9.78057i	0.610104	−	0.511938i
$366$	−18.0252	−	15.1250i	−0.942194	−	0.790594i
$367$	−5.66303	−	32.1166i	−0.295608	−	1.67647i	−0.664723	−	0.747090i	$-0.731450\pi$
$367$	−5.66303	−	32.1166i	−0.295608	−	1.67647i	0.369115	−	0.929384i	$-0.379661\pi$
$368$	1.24945	+	2.16411i	0.0651322	+	0.112812i
$369$	−4.36890	+	7.56716i	−0.227436	+	0.393931i
$370$	1.27347	+	0.463505i	0.0662045	+	0.0240965i
$371$	3.85965	+	1.40480i	0.200383	+	0.0729335i
$372$	9.17848	−	15.8976i	0.475882	−	0.824251i
$373$	−2.65099	−	4.59165i	−0.137263	−	0.237746i	0.789197	−	0.614141i	$-0.210497\pi$
$373$	−2.65099	−	4.59165i	−0.137263	−	0.237746i	−0.926460	+	0.376394i	$0.877164\pi$
$374$	1.44838	+	8.21420i	0.0748942	+	0.424746i
$375$	18.7570	+	15.7390i	0.968608	+	0.812759i
$376$	−0.571158	+	0.479258i	−0.0294552	+	0.0247159i
$377$	6.53519	−	37.0629i	0.336579	−	1.90884i
$378$	−2.32305	+	0.845520i	−0.119485	+	0.0434889i
$379$	−24.6656			−1.26699			−0.633494	−	0.773748i	$-0.718380\pi$
$379$	−24.6656			−1.26699			−0.633494	+	0.773748i	$0.718380\pi$
$380$		0			0
$381$	2.86368			0.146711
$382$	6.17828	−	2.24871i	0.316108	−	0.115054i
$383$	−0.632802	+	3.58880i	−0.0323347	+	0.183379i	−0.996697	−	0.0812045i	$-0.974123\pi$
$383$	−0.632802	+	3.58880i	−0.0323347	+	0.183379i	0.964363	+	0.264583i	$0.0852344\pi$
$384$	−1.93054	+	1.61992i	−0.0985177	+	0.0826662i
$385$	−8.83531	−	7.41370i	−0.450289	−	0.377837i
$386$	4.66812	+	26.4742i	0.237601	+	1.34750i
$387$	−4.81105	−	8.33298i	−0.244559	−	0.423589i
$388$	7.19369	−	12.4598i	0.365204	−	0.632552i
$389$	−2.62506	−	0.955445i	−0.133096	−	0.0484430i	0.274613	−	0.961555i	$-0.411450\pi$
$389$	−2.62506	−	0.955445i	−0.133096	−	0.0484430i	−0.407709	+	0.913112i	$0.633672\pi$
$390$	36.9562	+	13.4510i	1.87135	+	0.681116i
$391$	6.20875	−	10.7539i	0.313990	−	0.543846i
$392$	0.402113	+	0.696480i	0.0203098	+	0.0351776i
$393$	−7.80778	−	44.2801i	−0.393850	−	2.23364i
$394$	7.54508	+	6.33107i	0.380116	+	0.318955i
$395$	−11.1386	+	9.34640i	−0.560444	+	0.470269i
$396$	−0.976770	+	5.53954i	−0.0490846	+	0.278372i
$397$	37.1274	−	13.5133i	1.86337	−	0.678211i	0.887129	−	0.461522i	$-0.152696\pi$
$397$	37.1274	−	13.5133i	1.86337	−	0.678211i	0.976241	−	0.216689i	$-0.0695257\pi$
$398$	20.4661			1.02587
$399$		0			0
$400$	1.04988			0.0524938
$401$	−17.4985	+	6.36892i	−0.873831	+	0.318049i	−0.739718	−	0.672917i	$-0.765041\pi$
$401$	−17.4985	+	6.36892i	−0.873831	+	0.318049i	−0.134114	+	0.990966i	$0.542819\pi$
$402$	5.05907	−	28.6914i	0.252323	−	1.43100i
$403$	35.4023	−	29.7060i	1.76351	−	1.47976i
$404$	8.64322	+	7.25253i	0.430016	+	0.360827i
$405$	3.34143	+	18.9502i	0.166037	+	0.941642i
$406$	8.28553	+	14.3510i	0.411204	+	0.712226i
$407$	−0.462412	+	0.800921i	−0.0229209	+	0.0397002i
$408$	11.7678	+	4.28314i	0.582594	+	0.212047i
$409$	−16.1094	−	5.86335i	−0.796559	−	0.289924i	−0.0884993	−	0.996076i	$-0.528207\pi$
$409$	−16.1094	−	5.86335i	−0.796559	−	0.289924i	−0.708060	+	0.706152i	$0.750429\pi$
$410$	−3.20666	+	5.55410i	−0.158366	+	0.274297i
$411$	20.0549	+	34.7361i	0.989234	+	1.71340i
$412$	−2.57485	−	14.6027i	−0.126854	−	0.719424i
$413$	−10.6201	−	8.91133i	−0.522582	−	0.438498i
$414$	6.41499	−	5.38282i	0.315280	−	0.264551i
$415$	−6.48244	+	36.7638i	−0.318211	+	1.80466i
$416$	−5.96195	+	2.16997i	−0.292309	+	0.106392i
$417$	25.5043			1.24895
$418$		0			0
$419$	−18.5042			−0.903989			−0.451995	−	0.892021i	$-0.649287\pi$
$419$	−18.5042			−0.903989			−0.451995	+	0.892021i	$0.649287\pi$
$420$	−16.2723	+	5.92265i	−0.794009	+	0.288995i
$421$	2.81303	−	15.9535i	0.137099	−	0.777526i	−0.836276	−	0.548308i	$-0.815272\pi$
$421$	2.81303	−	15.9535i	0.137099	−	0.777526i	0.973375	−	0.229218i	$-0.0736168\pi$
$422$	6.21744	−	5.21705i	0.302660	−	0.253962i
$423$	1.91403	+	1.60606i	0.0930633	+	0.0780894i
$424$	−0.255310	−	1.44793i	−0.0123989	−	0.0703179i
$425$	−2.60851	−	4.51807i	−0.126531	−	0.219159i
$426$	8.81671	−	15.2710i	0.427171	−	0.739882i
$427$	24.5105	+	8.92108i	1.18614	+	0.431721i
$428$	−2.65791	−	0.967399i	−0.128475	−	0.0467610i
$429$	−13.4192	+	23.2428i	−0.647887	+	1.12217i
$430$	−3.53118	−	6.11619i	−0.170289	−	0.294949i
$431$	−2.20527	−	12.5067i	−0.106224	−	0.602428i	−0.990724	−	0.135888i	$-0.956611\pi$
$431$	−2.20527	−	12.5067i	−0.106224	−	0.602428i	0.884500	−	0.466540i	$-0.154500\pi$
$432$	0.677893	+	0.568820i	0.0326152	+	0.0273674i
$433$	−10.9047	+	9.15010i	−0.524045	+	0.439726i	−0.866039	−	0.499976i	$-0.833342\pi$
$433$	−10.9047	+	9.15010i	−0.524045	+	0.439726i	0.341994	+	0.939702i	$0.388898\pi$
$434$	−3.53354	+	20.0397i	−0.169615	+	0.961936i
$435$	−34.5518	+	12.5758i	−1.65663	+	0.602964i
$436$	−1.72539			−0.0826312
$437$		0			0
$438$	15.5901			0.744924
$439$	26.4900	−	9.64156i	1.26430	−	0.460166i	0.379088	−	0.925361i	$-0.376238\pi$
$439$	26.4900	−	9.64156i	1.26430	−	0.460166i	0.885209	+	0.465194i	$0.154016\pi$
$440$	−0.716924	+	4.06588i	−0.0341780	+	0.193833i
$441$	2.06455	−	1.73236i	0.0983118	−	0.0824934i
$442$	24.1513	+	20.2654i	1.14876	+	0.963925i
$443$	−5.72941	−	32.4931i	−0.272213	−	1.54379i	−0.747679	−	0.664060i	$-0.768832\pi$
$443$	−5.72941	−	32.4931i	−0.272213	−	1.54379i	0.475467	−	0.879734i	$-0.342279\pi$
$444$	0.694265	+	1.20250i	0.0329484	+	0.0570683i
$445$	−8.49196	+	14.7085i	−0.402558	+	0.697250i
$446$	−10.1055	−	3.67809i	−0.478508	−	0.174163i
$447$	−22.2572	−	8.10096i	−1.05273	−	0.383162i
$448$	1.39680	−	2.41933i	0.0659927	−	0.114303i
$449$	−8.59876	−	14.8935i	−0.405801	−	0.702867i	0.588614	−	0.808415i	$-0.299674\pi$
$449$	−8.59876	−	14.8935i	−0.405801	−	0.702867i	−0.994414	+	0.105547i	$0.966341\pi$
$450$	−0.610943	−	3.46483i	−0.0288001	−	0.163334i
$451$	−3.35269	−	2.81324i	−0.157872	−	0.132470i
$452$	0.327702	−	0.274975i	0.0154138	−	0.0129337i
$453$	4.49139	−	25.4719i	0.211024	−	1.19677i
$454$	−25.4597	+	9.26656i	−1.19488	+	0.434901i
$455$	−43.5954			−2.04378
$456$		0			0
$457$	−31.1517			−1.45722			−0.728608	−	0.684931i	$-0.759832\pi$
$457$	−31.1517			−1.45722			−0.728608	+	0.684931i	$0.759832\pi$
$458$	8.89473	−	3.23742i	0.415623	−	0.151275i
$459$	0.763593	−	4.33055i	0.0356415	−	0.202133i
$460$	4.70844	−	3.95085i	0.219532	−	0.184209i
$461$	11.9051	+	9.98956i	0.554475	+	0.465260i	0.876453	−	0.481487i	$-0.159903\pi$
$461$	11.9051	+	9.98956i	0.554475	+	0.465260i	−0.321978	+	0.946747i	$0.604348\pi$
$462$	−2.05206	−	11.6378i	−0.0954706	−	0.541441i
$463$	−10.3324	−	17.8962i	−0.480187	−	0.831708i	0.519555	−	0.854437i	$-0.326098\pi$
$463$	−10.3324	−	17.8962i	−0.480187	−	0.831708i	−0.999742	+	0.0227291i	$0.992764\pi$
$464$	2.96589	−	5.13708i	0.137688	−	0.238483i
$465$	−42.4287	−	15.4428i	−1.96758	−	0.716142i
$466$	21.4833	+	7.81930i	0.995197	+	0.362222i
$467$	14.2415	−	24.6670i	0.659017	−	1.14145i	−0.321853	−	0.946790i	$-0.604306\pi$
$467$	14.2415	−	24.6670i	0.659017	−	1.14145i	0.980870	−	0.194662i	$-0.0623609\pi$
$468$	10.6308	+	18.4131i	0.491408	+	0.851144i
$469$	5.60802	+	31.8047i	0.258954	+	1.46860i
$470$	1.40485	+	1.17881i	0.0648008	+	0.0543743i
$471$	5.74120	−	4.81744i	0.264540	−	0.221976i
$472$	−0.861748	+	4.88722i	−0.0396652	+	0.224952i
$473$	4.52889	−	1.64838i	0.208239	−	0.0757927i
$474$	−14.8981			−0.684290
$475$		0			0
$476$	−13.8819			−0.636276
$477$	−4.62995	+	1.68516i	−0.211991	+	0.0771583i
$478$	−1.50486	+	8.53446i	−0.0688305	+	0.390357i
$479$	−8.02251	+	6.73169i	−0.366558	+	0.307579i	−0.807398	−	0.590007i	$-0.799125\pi$
$479$	−8.02251	+	6.73169i	−0.366558	+	0.307579i	0.440840	+	0.897586i	$0.354681\pi$
$480$	4.74846	+	3.98443i	0.216737	+	0.181864i
$481$	0.607019	+	3.44258i	0.0276777	+	0.156968i
$482$	−2.82913	−	4.90020i	−0.128863	−	0.223198i
$483$	−8.79651	+	15.2360i	−0.400255	+	0.693262i
$484$	7.68907	+	2.79859i	0.349503	+	0.127209i
$485$	−33.2538	−	12.1034i	−1.50998	−	0.549586i
$486$	−11.1853	+	19.3735i	−0.507375	+	0.878800i
$487$	1.14947	+	1.99094i	0.0520875	+	0.0902181i	0.890894	−	0.454212i	$-0.150079\pi$
$487$	1.14947	+	1.99094i	0.0520875	+	0.0902181i	−0.838806	+	0.544430i	$0.816746\pi$
$488$	−1.62133	−	9.19501i	−0.0733941	−	0.416239i
$489$	10.7954	+	9.05844i	0.488186	+	0.409637i
$490$	1.51532	−	1.27151i	0.0684553	−	0.0574408i
$491$	2.11177	−	11.9764i	0.0953027	−	0.540488i	−0.899352	−	0.437226i	$-0.855961\pi$
$491$	2.11177	−	11.9764i	0.0953027	−	0.540488i	0.994654	−	0.103262i	$-0.0329280\pi$
$492$	−6.17478	+	2.24744i	−0.278381	+	0.101322i
$493$	−29.4761			−1.32754
$494$		0			0
$495$	13.8355			0.621860
$496$	6.84480	−	2.49130i	0.307340	−	0.111863i
$497$	−3.39427	+	19.2498i	−0.152254	+	0.863473i
$498$	−29.3005	+	24.5860i	−1.31299	+	1.10173i
$499$	11.5940	+	9.72849i	0.519017	+	0.435507i	0.864289	−	0.502996i	$-0.167769\pi$
$499$	11.5940	+	9.72849i	0.519017	+	0.435507i	−0.345272	+	0.938503i	$0.612213\pi$
$500$	1.68715	+	9.56831i	0.0754517	+	0.427908i
$501$	−8.92586	−	15.4600i	−0.398778	−	0.690704i
$502$	−6.77762	+	11.7392i	−0.302500	+	0.523945i
$503$	0.539086	+	0.196211i	0.0240366	+	0.00874862i	0.354010	−	0.935241i	$-0.384818\pi$
$503$	0.539086	+	0.196211i	0.0240366	+	0.00874862i	−0.329974	+	0.943990i	$0.607040\pi$
$504$	−8.79718	−	3.20191i	−0.391858	−	0.142624i
$505$	13.8760	−	24.0340i	0.617475	−	1.06950i
$506$	2.09724	+	3.63253i	0.0932339	+	0.161486i
$507$	11.9267	+	67.6398i	0.529684	+	3.00399i
$508$	0.870469	+	0.730410i	0.0386208	+	0.0324067i
$509$	20.0828	−	16.8515i	0.890155	−	0.746929i	−0.0780859	−	0.996947i	$-0.524881\pi$
$509$	20.0828	−	16.8515i	0.890155	−	0.746929i	0.968241	+	0.250018i	$0.0804364\pi$
$510$	5.34877	−	30.3344i	0.236847	−	1.34323i
$511$	−16.2396	+	5.91071i	−0.718396	+	0.261475i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	10.0393			0.442813
$515$	−34.2721	+	12.4740i	−1.51021	+	0.549671i
$516$	1.25653	−	7.12614i	0.0553156	−	0.313711i
$517$	−0.958706	+	0.804450i	−0.0421638	+	0.0353797i
$518$	−1.17909	−	0.989377i	−0.0518064	−	0.0434707i
$519$	10.0743	+	57.1344i	0.442214	+	2.50792i
$520$	7.80272	+	13.5147i	0.342172	+	0.592659i
$521$	−6.48183	+	11.2269i	−0.283974	+	0.491857i	−0.972360	−	0.233487i	$-0.924986\pi$
$521$	−6.48183	+	11.2269i	−0.283974	+	0.491857i	0.688386	+	0.725345i	$0.258320\pi$
$522$	−18.6794	−	6.79876i	−0.817577	−	0.297574i
$523$	16.7070	+	6.08086i	0.730548	+	0.265898i	0.680397	−	0.732844i	$-0.261808\pi$
$523$	16.7070	+	6.08086i	0.730548	+	0.265898i	0.0501509	+	0.998742i	$0.484030\pi$
$524$	8.92075	−	15.4512i	0.389705	−	0.674989i
$525$	3.69572	+	6.40117i	0.161294	+	0.279370i
$526$	3.26913	+	18.5402i	0.142541	+	0.808390i
$527$	−27.7276	−	23.2663i	−1.20783	−	1.01349i
$528$	−3.24048	+	2.71909i	−0.141024	+	0.118333i
$529$	−2.90956	+	16.5009i	−0.126503	+	0.717432i
$530$	−3.39826	+	1.23687i	−0.147611	+	0.0537260i
$531$	16.6304			0.721698
$532$		0			0
$533$	−16.5429			−0.716554
$534$	−16.3522	+	5.95172i	−0.707629	+	0.257556i
$535$	−1.20809	+	6.85139i	−0.0522301	+	0.296212i
$536$	8.85581	−	7.43091i	0.382513	−	0.320966i
$537$	−15.8589	−	13.3072i	−0.684361	−	0.574247i
$538$	−2.84482	−	16.1338i	−0.122649	−	0.695577i
$539$	0.674959	+	1.16906i	0.0290726	+	0.0503551i
$540$	1.08831	−	1.88500i	0.0468332	−	0.0811175i
$541$	5.02189	+	1.82782i	0.215908	+	0.0785840i	0.447710	−	0.894179i	$-0.352240\pi$
$541$	5.02189	+	1.82782i	0.215908	+	0.0785840i	−0.231802	+	0.972763i	$0.574462\pi$
$542$	−2.59998	−	0.946314i	−0.111679	−	0.0406477i
$543$	−16.3808	+	28.3724i	−0.702968	+	1.21758i
$544$	2.48459	+	4.30343i	0.106526	+	0.184508i
$545$	0.736938	+	4.17938i	0.0315669	+	0.179025i
$546$	−34.2174	−	28.7118i	−1.46437	−	1.22875i
$547$	−3.90768	+	3.27894i	−0.167080	+	0.140197i	−0.722494	−	0.691377i	$-0.757004\pi$
$547$	−3.90768	+	3.27894i	−0.167080	+	0.140197i	0.555414	+	0.831574i	$0.312560\pi$
$548$	−2.76372	+	15.6738i	−0.118060	+	0.669553i
$549$	−29.4022	+	10.7015i	−1.25485	+	0.456729i
$550$	1.76225			0.0751426
$551$		0			0
$552$	6.29761			0.268044
$553$	15.5187	−	5.64833i	0.659921	−	0.240192i
$554$	−4.25996	+	24.1594i	−0.180988	+	1.02644i
$555$	2.61627	−	2.19531i	0.111054	−	0.0931858i
$556$	7.75250	+	6.50512i	0.328779	+	0.275879i
$557$	−1.86212	−	10.5606i	−0.0789006	−	0.447467i	−0.998507	−	0.0546262i	$-0.982603\pi$
$557$	−1.86212	−	10.5606i	−0.0789006	−	0.447467i	0.919606	−	0.392841i	$-0.128508\pi$
$558$	−12.2050	−	21.1397i	−0.516678	−	0.894913i
$559$	9.10855	−	15.7765i	0.385251	−	0.667274i
$560$	−6.45690	−	2.35012i	−0.272854	−	0.0993107i
$561$	19.7527	+	7.18938i	0.833958	+	0.303536i
$562$	−5.08518	+	8.80779i	−0.214505	+	0.371534i
$563$	4.88142	+	8.45488i	0.205728	+	0.356331i	0.950364	−	0.311139i	$-0.100711\pi$
$563$	4.88142	+	8.45488i	0.205728	+	0.356331i	−0.744637	+	0.667470i	$0.767377\pi$
$564$	0.326286	+	1.85046i	0.0137391	+	0.0779184i
$565$	−0.806033	−	0.676342i	−0.0339100	−	0.0284539i
$566$	−21.1948	+	17.7845i	−0.890882	+	0.747539i
$567$	3.79511	−	21.5231i	0.159379	−	0.903886i
$568$	6.57501	−	2.39311i	0.275881	−	0.100413i
$569$	8.84194			0.370674			0.185337	−	0.982675i	$-0.440662\pi$
$569$	8.84194			0.370674			0.185337	+	0.982675i	$0.440662\pi$
$570$		0			0
$571$	22.8411			0.955871			0.477935	−	0.878395i	$-0.341385\pi$
$571$	22.8411			0.955871			0.477935	+	0.878395i	$0.341385\pi$
$572$	−10.0073	+	3.64237i	−0.418427	+	0.152295i
$573$	2.87725	−	16.3177i	0.120199	−	0.681682i
$574$	5.57993	−	4.68212i	0.232902	−	0.195428i
$575$	−2.00975	−	1.68638i	−0.0838123	−	0.0703268i
$576$	0.581920	+	3.30023i	0.0242466	+	0.137510i
$577$	7.00879	+	12.1396i	0.291780	+	0.505377i	0.974231	−	0.225554i	$-0.0724192\pi$
$577$	7.00879	+	12.1396i	0.291780	+	0.505377i	−0.682451	+	0.730931i	$0.739086\pi$
$578$	3.84635	−	6.66207i	0.159987	−	0.277106i
$579$	63.6624	+	23.1712i	2.64572	+	0.962964i
$580$	−13.7102	−	4.99011i	−0.569286	−	0.207203i
$581$	21.1997	−	36.7190i	0.879513	−	1.52336i
$582$	−18.1292	−	31.4006i	−0.751478	−	1.30160i
$583$	−0.428546	−	2.43040i	−0.0177485	−	0.100657i
$584$	4.73890	+	3.97641i	0.196097	+	0.164545i
$585$	40.0611	−	33.6152i	1.65632	−	1.38982i
$586$	4.13953	−	23.4764i	0.171002	−	0.969803i
$587$	−19.7670	+	7.19460i	−0.815871	+	0.296953i	−0.716047	−	0.698052i	$-0.754050\pi$
$587$	−19.7670	+	7.19460i	−0.815871	+	0.296953i	−0.0998243	+	0.995005i	$0.531828\pi$
$588$	2.02677			0.0835825
$589$		0			0
$590$	12.2063			0.502525
$591$	23.3250	−	8.48960i	0.959462	−	0.349216i
$592$	−0.0956753	+	0.542602i	−0.00393223	+	0.0223008i
$593$	−26.7497	+	22.4457i	−1.09848	+	0.921733i	−0.997322	−	0.0731375i	$-0.976699\pi$
$593$	−26.7497	+	22.4457i	−1.09848	+	0.921733i	−0.101157	+	0.994871i	$0.532254\pi$
$594$	1.13787	+	0.954782i	0.0466872	+	0.0391752i
$595$	5.92915	+	33.6259i	0.243072	+	1.37853i
$596$	−4.69925	−	8.13935i	−0.192489	−	0.333401i
$597$	25.7888	−	44.6675i	1.05546	−	1.82812i
$598$	14.8983	+	5.42255i	0.609239	+	0.221745i
$599$	20.2134	+	7.35707i	0.825897	+	0.300602i	0.720174	−	0.693794i	$-0.244062\pi$
$599$	20.2134	+	7.35707i	0.825897	+	0.300602i	0.105723	+	0.994396i	$0.466284\pi$
$600$	1.32292	−	2.29137i	0.0540080	−	0.0935446i
$601$	−7.17087	−	12.4203i	−0.292506	−	0.506635i	0.681896	−	0.731449i	$-0.261156\pi$
$601$	−7.17087	−	12.4203i	−0.292506	−	0.506635i	−0.974402	+	0.224814i	$0.927822\pi$
$602$	1.39287	+	7.89938i	0.0567693	+	0.321955i
$603$	−29.6771	−	24.9020i	−1.20854	−	1.01409i
$604$	7.86209	−	6.59708i	0.319904	−	0.268431i
$605$	3.49487	−	19.8204i	0.142087	−	0.805814i
$606$	26.7198	−	9.72522i	1.08542	−	0.395060i
$607$	10.3488			0.420046			0.210023	−	0.977696i	$-0.432646\pi$
$607$	10.3488			0.420046			0.210023	+	0.977696i	$0.432646\pi$
$608$		0			0
$609$	41.7615			1.69226
$610$	−21.5804	+	7.85463i	−0.873766	+	0.318025i
$611$	−0.821438	+	4.65861i	−0.0332318	+	0.188467i
$612$	12.7565	−	10.7040i	0.515650	−	0.432682i
$613$	14.9895	+	12.5777i	0.605420	+	0.508008i	0.893183	−	0.449694i	$-0.148467\pi$
$613$	14.9895	+	12.5777i	0.605420	+	0.508008i	−0.287763	+	0.957702i	$0.592911\pi$
$614$	4.51285	+	25.5936i	0.182124	+	1.03287i
$615$	8.08126	+	13.9971i	0.325868	+	0.564419i
$616$	2.34458	−	4.06093i	0.0944657	−	0.163619i
$617$	5.56789	+	2.02654i	0.224155	+	0.0815856i	0.451656	−	0.892192i	$-0.350833\pi$
$617$	5.56789	+	2.02654i	0.224155	+	0.0815856i	−0.227501	+	0.973778i	$0.573056\pi$
$618$	−35.1151	−	12.7808i	−1.41254	−	0.514121i
$619$	−4.01979	+	6.96248i	−0.161569	+	0.279846i	−0.935432	−	0.353508i	$-0.884989\pi$
$619$	−4.01979	+	6.96248i	−0.161569	+	0.279846i	0.773863	+	0.633354i	$0.218322\pi$
$620$	−8.95814	−	15.5160i	−0.359768	−	0.623136i
$621$	−0.383996	−	2.17775i	−0.0154092	−	0.0873902i
$622$	17.6990	+	14.8512i	0.709663	+	0.595478i
$623$	14.7769	−	12.3993i	0.592024	−	0.496768i
$624$	−2.77651	+	15.7464i	−0.111149	+	0.630359i
$625$	27.3894	−	9.96891i	1.09557	−	0.398756i
$626$	−12.2647			−0.490196
$627$		0			0
$628$	2.97387			0.118671
$629$	2.57276	−	0.936409i	0.102583	−	0.0373371i
$630$	−3.99854	+	22.6768i	−0.159306	+	0.903466i
$631$	−9.88247	+	8.29237i	−0.393415	+	0.330114i	−0.817942	−	0.575301i	$-0.804885\pi$
$631$	−9.88247	+	8.29237i	−0.393415	+	0.330114i	0.424527	+	0.905415i	$0.360440\pi$
$632$	−4.52853	−	3.79989i	−0.180135	−	0.151152i
$633$	−3.55184	−	20.1435i	−0.141173	−	0.800633i
$634$	0.136152	+	0.235823i	0.00540731	+	0.00936573i
$635$	1.39747	−	2.42049i	0.0554569	−	0.0960542i
$636$	−3.48184	−	1.26729i	−0.138064	−	0.0502512i
$637$	4.79476	+	1.74515i	0.189975	+	0.0691453i
$638$	4.97834	−	8.62275i	0.197095	−	0.341378i
$639$	−11.7239	−	20.3065i	−0.463792	−	0.803311i
$640$	0.427114	+	2.42228i	0.0168831	+	0.0957491i
$641$	22.1110	+	18.5534i	0.873333	+	0.732814i	0.964797	−	0.262995i	$-0.0847102\pi$
$641$	22.1110	+	18.5534i	0.873333	+	0.732814i	−0.0914641	+	0.995808i	$0.529155\pi$
$642$	−5.46052	+	4.58192i	−0.215510	+	0.180834i
$643$	4.57380	−	25.9393i	0.180373	−	1.02295i	−0.751385	−	0.659864i	$-0.770614\pi$
$643$	4.57380	−	25.9393i	0.180373	−	1.02295i	0.931758	−	0.363081i	$-0.118275\pi$
$644$	−6.55995	+	2.38763i	−0.258498	+	0.0940856i
$645$	−17.7982			−0.700803
$646$		0			0
$647$	−3.04601			−0.119751			−0.0598756	−	0.998206i	$-0.519070\pi$
$647$	−3.04601			−0.119751			−0.0598756	+	0.998206i	$0.519070\pi$
$648$	−7.35148	+	2.67572i	−0.288793	+	0.105112i
$649$	−1.44647	+	8.20335i	−0.0567790	+	0.322010i
$650$	5.10264	−	4.28162i	0.200142	−	0.167939i
$651$	39.2843	+	32.9635i	1.53967	+	1.29194i
$652$	0.971025	+	5.50695i	0.0380283	+	0.215669i
$653$	7.59866	+	13.1613i	0.297359	+	0.515040i	0.975531	−	0.219863i	$-0.0705610\pi$
$653$	7.59866	+	13.1613i	0.297359	+	0.515040i	−0.678172	+	0.734903i	$0.737228\pi$
$654$	−2.17412	+	3.76568i	−0.0850148	+	0.147250i
$655$	−41.2373	−	15.0092i	−1.61128	−	0.586456i
$656$	−2.45017	−	0.891788i	−0.0956629	−	0.0348185i
$657$	10.3654	−	17.9534i	0.404393	−	0.700429i
$658$	−1.04145	−	1.80384i	−0.0405998	−	0.0703209i
$659$	−3.10380	−	17.6025i	−0.120907	−	0.685697i	−0.983655	−	0.180063i	$-0.942370\pi$
$659$	−3.10380	−	17.6025i	−0.120907	−	0.685697i	0.862748	−	0.505634i	$-0.168741\pi$
$660$	7.97044	+	6.68800i	0.310249	+	0.260330i
$661$	−28.9967	+	24.3311i	−1.12784	+	0.946371i	−0.998974	−	0.0452905i	$-0.985579\pi$
$661$	−28.9967	+	24.3311i	−1.12784	+	0.946371i	−0.128868	+	0.991662i	$0.541134\pi$
$662$	−3.47175	+	19.6893i	−0.134933	+	0.765245i
$663$	74.6618	−	27.1747i	2.89963	−	1.05538i
$664$	−15.1773			−0.588994
$665$		0			0
$666$	1.84638			0.0715460
$667$	−13.9290	+	5.06975i	−0.539334	+	0.196302i
$668$	1.23006	−	6.97599i	0.0475923	−	0.269909i
$669$	−20.7611	+	17.4206i	−0.802671	+	0.673521i
$670$	−21.7822	−	18.2774i	−0.841520	−	0.706119i
$671$	−2.72145	−	15.4341i	−0.105060	−	0.595827i
$672$	−3.52015	−	6.09707i	−0.135793	−	0.235200i
$673$	−4.14230	+	7.17468i	−0.159674	+	0.276564i	−0.934751	−	0.355303i	$-0.884378\pi$
$673$	−4.14230	+	7.17468i	−0.159674	+	0.276564i	0.775077	+	0.631867i	$0.217711\pi$
$674$	16.2402	+	5.91093i	0.625548	+	0.227681i
$675$	−0.873034	−	0.317758i	−0.0336031	−	0.0122305i
$676$	−13.6268	+	23.6024i	−0.524109	+	0.907783i
$677$	−9.16167	−	15.8685i	−0.352111	−	0.609875i	0.634508	−	0.772917i	$-0.281203\pi$
$677$	−9.16167	−	15.8685i	−0.352111	−	0.609875i	−0.986619	+	0.163042i	$0.947870\pi$
$678$	−0.187207	−	1.06170i	−0.00718963	−	0.0407744i
$679$	30.7894	+	25.8353i	1.18159	+	0.991469i
$680$	9.36292	−	7.85643i	0.359052	−	0.301280i
$681$	−11.8567	+	67.2425i	−0.454349	+	2.57674i
$682$	11.4892	−	4.18173i	0.439944	−	0.160127i
$683$	49.2217			1.88342			0.941709	−	0.336429i	$-0.109219\pi$
$683$	49.2217			1.88342			0.941709	+	0.336429i	$0.109219\pi$
$684$		0			0
$685$	39.1469			1.49573
$686$	16.2647	−	5.91987i	0.620989	−	0.226022i
$687$	4.14231	−	23.4922i	0.158039	−	0.896284i
$688$	2.19953	−	1.84563i	0.0838565	−	0.0703639i
$689$	−7.14585	−	5.99608i	−0.272235	−	0.228433i
$690$	−2.68979	−	15.2546i	−0.102399	−	0.580732i
$691$	−8.33895	−	14.4435i	−0.317229	−	0.549456i	0.662680	−	0.748903i	$-0.269419\pi$
$691$	−8.33895	−	14.4435i	−0.317229	−	0.549456i	−0.979909	+	0.199446i	$0.936086\pi$
$692$	−11.5104	+	19.9366i	−0.437560	+	0.757876i
$693$	−14.7663	−	5.37451i	−0.560927	−	0.204161i
$694$	−17.4271	−	6.34296i	−0.661525	−	0.240776i
$695$	12.4460	−	21.5572i	0.472105	−	0.817710i
$696$	−7.47449	−	12.9462i	−0.283320	−	0.490724i
$697$	2.24991	+	12.7598i	0.0852212	+	0.483314i
$698$	15.4136	+	12.9335i	0.583413	+	0.489542i
$699$	44.1363	−	37.0348i	1.66939	−	1.40078i
$700$	−0.509299	+	2.88838i	−0.0192497	+	0.109171i
$701$	29.0427	−	10.5707i	1.09693	−	0.399249i	0.270745	−	0.962651i	$-0.412730\pi$
$701$	29.0427	−	10.5707i	1.09693	−	0.399249i	0.826183	+	0.563402i	$0.190508\pi$
$702$	5.61449			0.211905
$703$		0			0
$704$	−1.67853			−0.0632620
$705$	4.34297	−	1.58071i	0.163566	−	0.0595331i
$706$	−4.17723	+	23.6902i	−0.157212	+	0.891593i
$707$	−24.1457	+	20.2607i	−0.908094	+	0.761982i
$708$	9.58054	+	8.03903i	0.360059	+	0.302125i
$709$	6.96426	+	39.4963i	0.261548	+	1.48331i	0.778687	+	0.627413i	$0.215886\pi$
$709$	6.96426	+	39.4963i	0.261548	+	1.48331i	−0.517139	+	0.855902i	$0.673003\pi$
$710$	−8.60506	−	14.9044i	−0.322942	−	0.559352i
$711$	−9.90527	+	17.1564i	−0.371477	+	0.643417i
$712$	−6.48859	−	2.36166i	−0.243170	−	0.0885068i
$713$	−17.1045	−	6.22552i	−0.640568	−	0.233148i
$714$	−17.4922	+	30.2974i	−0.654630	+	1.13385i
$715$	13.0971	+	22.6849i	0.489804	+	0.848365i
$716$	−1.42647	−	8.08991i	−0.0533097	−	0.302334i
$717$	16.7303	+	14.0384i	0.624805	+	0.524274i
$718$	8.31423	−	6.97647i	0.310284	−	0.260360i
$719$	−7.92754	+	44.9593i	−0.295647	+	1.67670i	0.368913	+	0.929464i	$0.379730\pi$
$719$	−7.92754	+	44.9593i	−0.295647	+	1.67670i	−0.664560	+	0.747235i	$0.731381\pi$
$720$	7.74554	−	2.81915i	0.288659	−	0.105063i
$721$	41.4235			1.54269
$722$		0			0
$723$	−14.2596			−0.530322
$724$	−12.2159	+	4.44622i	−0.454000	+	0.165243i
$725$	−1.08142	+	6.13303i	−0.0401629	+	0.227775i
$726$	15.7967	−	13.2550i	0.586272	−	0.491941i
$727$	−11.6294	−	9.75819i	−0.431309	−	0.361911i	0.401136	−	0.916018i	$-0.368615\pi$
$727$	−11.6294	−	9.75819i	−0.431309	−	0.361911i	−0.832445	+	0.554107i	$0.813060\pi$
$728$	−3.07778	−	17.4550i	−0.114070	−	0.646924i
$729$	16.4537	+	28.4986i	0.609395	+	1.05550i
$730$	7.60793	−	13.1773i	0.281582	−	0.487715i
$731$	−13.4075	−	4.87992i	−0.495893	−	0.180490i
$732$	−22.1112	−	8.04782i	−0.817254	−	0.297456i
$733$	13.4993	−	23.3815i	0.498608	−	0.863615i	−0.501390	−	0.865221i	$-0.667178\pi$
$733$	13.4993	−	23.3815i	0.498608	−	0.863615i	0.999999	+	0.00160611i	$0.000511240\pi$
$734$	−16.3060	−	28.2429i	−0.601867	−	1.04246i
$735$	−0.865660	−	4.90940i	−0.0319304	−	0.181086i
$736$	1.91427	+	1.60626i	0.0705610	+	0.0592077i
$737$	14.8648	−	12.4730i	0.547550	−	0.459449i
$738$	−1.51730	+	8.60506i	−0.0558527	+	0.316757i
$739$	4.89375	−	1.78118i	0.180020	−	0.0655217i	−0.250438	−	0.968133i	$-0.580575\pi$
$739$	4.89375	−	1.78118i	0.180020	−	0.0655217i	0.430457	+	0.902611i	$0.358352\pi$
$740$	1.35520			0.0498181
$741$		0			0
$742$	4.10736			0.150786
$743$	20.7746	−	7.56134i	0.762146	−	0.277398i	0.0684386	−	0.997655i	$-0.478198\pi$
$743$	20.7746	−	7.56134i	0.762146	−	0.277398i	0.693707	+	0.720257i	$0.255976\pi$
$744$	3.18765	−	18.0781i	0.116865	−	0.662774i
$745$	−17.7087	+	14.8593i	−0.648796	+	0.544404i
$746$	−4.06155	−	3.40805i	−0.148704	−	0.124777i
$747$	8.83198	+	50.0886i	0.323145	+	1.83265i
$748$	4.17046	+	7.22345i	0.152487	+	0.264115i
$749$	3.95084	−	6.84305i	0.144360	−	0.250040i
$750$	23.0089	+	8.37455i	0.840166	+	0.305795i
$751$	−11.7424	−	4.27387i	−0.428485	−	0.155956i	0.118770	−	0.992922i	$-0.462105\pi$
$751$	−11.7424	−	4.27387i	−0.428485	−	0.155956i	−0.547255	+	0.836966i	$0.684327\pi$
$752$	−0.372797	+	0.645703i	−0.0135945	+	0.0235464i
$753$	17.0806	+	29.5844i	0.622451	+	1.07812i
$754$	−6.53519	−	37.0629i	−0.237998	−	1.34975i
$755$	−19.3380	−	16.2265i	−0.703782	−	0.590543i
$756$	−1.89377	+	1.58906i	−0.0688756	+	0.0577935i
$757$	−5.38289	+	30.5279i	−0.195645	+	1.10956i	0.715853	+	0.698251i	$0.246038\pi$
$757$	−5.38289	+	30.5279i	−0.195645	+	1.10956i	−0.911498	+	0.411305i	$0.865073\pi$
$758$	−23.1781	+	8.43613i	−0.841866	+	0.306414i
$759$	10.5707			0.383693
$760$		0			0
$761$	1.96398			0.0711941			0.0355971	−	0.999366i	$-0.488667\pi$
$761$	1.96398			0.0711941			0.0355971	+	0.999366i	$0.488667\pi$
$762$	2.69098	−	0.979438i	0.0974840	−	0.0354813i
$763$	0.836994	−	4.74683i	0.0303012	−	0.171847i
$764$	5.03658	−	4.22620i	0.182217	−	0.152898i
$765$	−31.3765	−	26.3280i	−1.13442	−	0.951891i
$766$	0.632802	+	3.58880i	0.0228641	+	0.129668i
$767$	15.7428	+	27.2674i	0.568441	+	0.984568i
$768$	−1.26007	+	2.18251i	−0.0454690	+	0.0787546i
$769$	20.9854	+	7.63805i	0.756752	+	0.275435i	0.691444	−	0.722430i	$-0.256975\pi$
$769$	20.9854	+	7.63805i	0.756752	+	0.275435i	0.0653077	+	0.997865i	$0.479197\pi$
$770$	−10.8381	−	3.94475i	−0.390578	−	0.142159i
$771$	12.6502	−	21.9108i	0.455586	−	0.789098i
$772$	13.4413	+	23.2810i	0.483763	+	0.837903i
$773$	−4.75020	−	26.9397i	−0.170853	−	0.968954i	−0.942823	−	0.333295i	$-0.891840\pi$
$773$	−4.75020	−	26.9397i	−0.170853	−	0.968954i	0.771970	−	0.635659i	$-0.219272\pi$
$774$	−7.37095	−	6.18496i	−0.264943	−	0.222314i
$775$	−5.85823	+	4.91564i	−0.210434	+	0.176575i
$776$	2.49834	−	14.1688i	0.0896852	−	0.508630i
$777$	−3.64507	+	1.32670i	−0.130766	+	0.0475950i
$778$	−2.79353			−0.100153
$779$		0			0
$780$	39.3280			1.40817
$781$	11.0364	−	4.01691i	0.394912	−	0.143736i
$782$	2.15627	−	12.2288i	0.0771082	−	0.437302i
$783$	−4.02112	+	3.37412i	−0.143703	+	0.120581i
$784$	0.616073	+	0.516947i	0.0220026	+	0.0184624i
$785$	−1.27018	−	7.20356i	−0.0453348	−	0.257106i
$786$	−22.4816	−	38.9393i	−0.801892	−	1.38892i
$787$	3.89481	−	6.74601i	0.138835	−	0.240469i	−0.788221	−	0.615392i	$-0.788998\pi$
$787$	3.89481	−	6.74601i	0.138835	−	0.240469i	0.927056	+	0.374923i	$0.122331\pi$
$788$	9.25541	+	3.36869i	0.329710	+	0.120005i
$789$	44.5835	+	16.2271i	1.58721	+	0.577699i
$790$	−7.27021	+	12.5924i	−0.258662	+	0.448017i
$791$	0.597531	+	1.03495i	0.0212457	+	0.0367987i
$792$	0.976770	+	5.53954i	0.0347080	+	0.196839i
$793$	−45.3793	−	38.0777i	−1.61146	−	1.35218i
$794$	30.2665	−	25.3966i	1.07412	−	0.901292i
$795$	−1.58258	+	8.97528i	−0.0561285	+	0.318320i
$796$	19.2318	−	6.99982i	0.681655	−	0.248102i
$797$	6.09655			0.215951			0.107975	−	0.994154i	$-0.465563\pi$
$797$	6.09655			0.215951			0.107975	+	0.994154i	$0.465563\pi$
$798$		0			0
$799$	3.70498			0.131073
$800$	0.986561	−	0.359079i	0.0348802	−	0.0126953i
$801$	−4.01816	+	22.7881i	−0.141975	+	0.805179i
$802$	−14.2649	+	11.9696i	−0.503710	+	0.422663i
$803$	7.95439	+	6.67453i	0.280704	+	0.235539i
$804$	−5.05907	−	28.6914i	−0.178420	−	1.01187i
$805$	8.58534	+	14.8703i	0.302594	+	0.524108i
$806$	23.1072	−	40.0228i	0.813916	−	1.40974i
$807$	−38.7969	−	14.1209i	−1.36571	−	0.497079i
$808$	10.6025	+	3.85899i	0.372994	+	0.135759i
$809$	−28.4228	+	49.2297i	−0.999291	+	1.73082i	−0.467047	+	0.884232i	$0.654682\pi$
$809$	−28.4228	+	49.2297i	−0.999291	+	1.73082i	−0.532244	+	0.846591i	$0.678651\pi$
$810$	9.62126	+	16.6645i	0.338057	+	0.585531i
$811$	3.63287	+	20.6030i	0.127567	+	0.723470i	0.979750	+	0.200226i	$0.0641675\pi$
$811$	3.63287	+	20.6030i	0.127567	+	0.723470i	−0.852182	+	0.523245i	$0.824721\pi$
$812$	12.6942	+	10.6517i	0.445478	+	0.373800i
$813$	−5.34150	+	4.48205i	−0.187335	+	0.157192i
$814$	−0.160594	+	0.910774i	−0.00562882	+	0.0319226i
$815$	12.9247	−	4.70419i	0.452731	−	0.164781i
$816$	12.5231			0.438394
$817$		0			0
$818$	−17.1433			−0.599401
$819$	−55.8144	+	20.3148i	−1.95031	+	0.709856i
$820$	−1.11366	+	6.31589i	−0.0388907	+	0.220560i
$821$	12.4545	−	10.4506i	0.434666	−	0.364728i	−0.399043	−	0.916932i	$-0.630658\pi$
$821$	12.4545	−	10.4506i	0.434666	−	0.364728i	0.833709	+	0.552204i	$0.186213\pi$
$822$	30.7259	+	25.7821i	1.07169	+	0.899252i
$823$	−3.04455	−	17.2665i	−0.106126	−	0.601872i	−0.990765	−	0.135594i	$-0.956706\pi$
$823$	−3.04455	−	17.2665i	−0.106126	−	0.601872i	0.884638	−	0.466278i	$-0.154405\pi$
$824$	−7.41399	−	12.8414i	−0.258279	−	0.447352i
$825$	2.22056	−	3.84613i	0.0773101	−	0.133905i
$826$	−13.0275	−	4.74162i	−0.453285	−	0.164982i
$827$	−15.9986	−	5.82302i	−0.556326	−	0.202486i	0.0485288	−	0.998822i	$-0.484547\pi$
$827$	−15.9986	−	5.82302i	−0.556326	−	0.202486i	−0.604855	+	0.796336i	$0.706769\pi$
$828$	4.18709	−	7.25225i	0.145511	−	0.252033i
$829$	−2.88103	−	4.99010i	−0.100062	−	0.173313i	0.811648	−	0.584147i	$-0.198571\pi$
$829$	−2.88103	−	4.99010i	−0.100062	−	0.173313i	−0.911710	+	0.410834i	$0.865238\pi$
$830$	6.48244	+	36.7638i	0.225009	+	1.27609i
$831$	47.3604	+	39.7401i	1.64291	+	1.37857i
$832$	−4.86023	+	4.07822i	−0.168498	+	0.141387i
$833$	0.693957	−	3.93563i	0.0240442	−	0.136361i
$834$	23.9662	−	8.72299i	0.829882	−	0.302052i
$835$	−17.4232			−0.602954
$836$		0			0
$837$	−6.44588			−0.222802
$838$	−17.3883	+	6.32881i	−0.600668	+	0.218625i
$839$	−1.54539	+	8.76433i	−0.0533527	+	0.302578i	−0.999794	−	0.0202977i	$-0.993539\pi$
$839$	−1.54539	+	8.76433i	−0.0533527	+	0.302578i	0.946441	+	0.322876i	$0.104650\pi$
$840$	−13.2653	+	11.1309i	−0.457697	+	0.384054i
$841$	4.73881	+	3.97634i	0.163407	+	0.137115i
$842$	−2.81303	−	15.9535i	−0.0969435	−	0.549794i
$843$	12.8154	+	22.1969i	0.441386	+	0.764503i
$844$	4.05815	−	7.02892i	0.139687	−	0.241945i
$845$	62.9918	+	22.9271i	2.16698	+	0.788717i
$846$	2.34791	+	0.854568i	0.0807226	+	0.0293806i
$847$	−11.4294	+	19.7963i	−0.392718	+	0.680208i
$848$	−0.735136	−	1.27329i	−0.0252447	−	0.0437250i
$849$	12.1080	+	68.6676i	0.415544	+	2.35667i
$850$	−3.99647	−	3.35343i	−0.137078	−	0.115022i
$851$	1.05471	−	0.885007i	0.0361550	−	0.0303376i
$852$	3.06201	−	17.3655i	0.104903	−	0.594933i
$853$	−2.62094	+	0.953946i	−0.0897394	+	0.0326625i	−0.386500	−	0.922290i	$-0.626316\pi$
$853$	−2.62094	+	0.953946i	−0.0897394	+	0.0326625i	0.296760	+	0.954952i	$0.404094\pi$
$854$	26.0835			0.892559
$855$		0			0
$856$	−2.82849			−0.0966757
$857$	15.4058	−	5.60724i	0.526251	−	0.191540i	−0.0652127	−	0.997871i	$-0.520773\pi$
$857$	15.4058	−	5.60724i	0.526251	−	0.191540i	0.591464	+	0.806332i	$0.298550\pi$
$858$	−4.66045	+	26.4307i	−0.159105	+	0.902331i
$859$	7.29661	−	6.12258i	0.248957	−	0.208900i	−0.509766	−	0.860313i	$-0.670268\pi$
$859$	7.29661	−	6.12258i	0.248957	−	0.208900i	0.758723	+	0.651413i	$0.225824\pi$
$860$	−5.41008	−	4.53960i	−0.184482	−	0.154799i
$861$	−3.18765	−	18.0781i	−0.108635	−	0.616099i
$862$	−6.34983	−	10.9982i	−0.216276	−	0.374601i
$863$	−25.3382	+	43.8871i	−0.862523	+	1.49393i	0.00696312	+	0.999976i	$0.497784\pi$
$863$	−25.3382	+	43.8871i	−0.862523	+	1.49393i	−0.869486	+	0.493958i	$0.835550\pi$
$864$	0.831559	+	0.302663i	0.0282902	+	0.0102968i
$865$	53.2083	+	19.3662i	1.80914	+	0.658472i
$866$	−7.11751	+	12.3279i	−0.241863	+	0.418919i
$867$	−9.69337	−	16.7894i	−0.329204	−	0.570198i
$868$	3.53354	+	20.0397i	0.119936	+	0.680191i
$869$	−7.60129	−	6.37824i	−0.257856	−	0.216367i
$870$	−28.1669	+	23.6348i	−0.954946	+	0.801295i
$871$	12.7364	−	72.2318i	0.431557	−	2.44748i
$872$	−1.62134	+	0.590118i	−0.0549054	+	0.0199839i
$873$	−48.2141			−1.63180
$874$		0			0
$875$	−27.1424			−0.917582
$876$	14.6499	−	5.33213i	0.494975	−	0.180156i
$877$	−3.34409	+	18.9653i	−0.112922	+	0.640412i	0.874836	+	0.484419i	$0.160969\pi$
$877$	−3.34409	+	18.9653i	−0.112922	+	0.640412i	−0.987758	+	0.155993i	$0.950142\pi$
$878$	21.5948	−	18.1202i	0.728790	−	0.611527i
$879$	−46.0215	−	38.6166i	−1.55227	−	1.30251i
$880$	0.716924	+	4.06588i	0.0241675	+	0.137061i
$881$	−9.55379	−	16.5476i	−0.321875	−	0.557504i	0.659000	−	0.752143i	$-0.270980\pi$
$881$	−9.55379	−	16.5476i	−0.321875	−	0.557504i	−0.980875	+	0.194639i	$0.937646\pi$
$882$	1.34754	−	2.33400i	0.0453739	−	0.0785900i
$883$	−46.9827	−	17.1003i	−1.58109	−	0.575471i	−0.605653	−	0.795729i	$-0.707088\pi$
$883$	−46.9827	−	17.1003i	−1.58109	−	0.575471i	−0.975442	+	0.220257i	$0.929310\pi$
$884$	29.6260	+	10.7830i	0.996430	+	0.362671i
$885$	15.3808	−	26.6404i	0.517020	−	0.895506i
$886$	−16.4972	−	28.5740i	−0.554234	−	0.959961i
$887$	−6.87985	−	39.0176i	−0.231003	−	1.31008i	−0.850871	−	0.525375i	$-0.823925\pi$
$887$	−6.87985	−	39.0176i	−0.231003	−	1.31008i	0.619868	−	0.784706i	$-0.287186\pi$
$888$	1.06368	+	0.892530i	0.0356946	+	0.0299514i
$889$	−2.43175	+	2.04048i	−0.0815581	+	0.0684354i
$890$	−2.94923	+	16.7259i	−0.0988583	+	0.560653i
$891$	−12.3397	+	4.49128i	−0.413395	+	0.150463i
$892$	−10.7540			−0.360071
$893$		0			0
$894$	−23.6856			−0.792166
$895$	−18.9868	+	6.91062i	−0.634658	+	0.230997i
$896$	0.485104	−	2.75116i	0.0162062	−	0.0919099i
$897$	30.6078	−	25.6830i	1.02196	−	0.857530i
$898$	−13.1741	−	11.0544i	−0.439624	−	0.368889i
$899$	7.50292	+	42.5512i	0.250236	+	1.41916i
$900$	−1.75914	−	3.04692i	−0.0586380	−	0.101564i
$901$	−3.65302	+	6.32721i	−0.121700	+	0.210790i
$902$	−4.11268	−	1.49689i	−0.136937	−	0.0498411i
$903$	18.9956	+	6.91384i	0.632135	+	0.230078i
$904$	0.213892	−	0.370473i	0.00711396	−	0.0123217i
$905$	15.9876	+	27.6913i	0.531445	+	0.920490i
$906$	−4.49139	−	25.4719i	−0.149216	−	0.846248i
$907$	−42.3274	−	35.5169i	−1.40546	−	1.17932i	−0.958614	−	0.284707i	$-0.908104\pi$
$907$	−42.3274	−	35.5169i	−1.40546	−	1.17932i	−0.446844	−	0.894612i	$-0.647452\pi$
$908$	−20.7549	+	17.4154i	−0.688776	+	0.577951i
$909$	6.56576	−	37.2362i	0.217772	−	1.23505i
$910$	−40.9663	+	14.9105i	−1.35802	+	0.494279i
$911$	−27.7087			−0.918031			−0.459015	−	0.888428i	$-0.651798\pi$
$911$	−27.7087			−0.918031			−0.459015	+	0.888428i	$0.651798\pi$
$912$		0			0
$913$	−25.4756			−0.843120
$914$	−29.2730	+	10.6545i	−0.968266	+	0.352420i
$915$	−10.0501	+	56.9969i	−0.332246	+	1.88426i
$916$	7.25105	−	6.08435i	0.239581	−	0.201033i
$917$	38.1813	+	32.0379i	1.26086	+	1.05798i
$918$	−0.763593	−	4.33055i	−0.0252023	−	0.142929i
$919$	−13.6250	−	23.5992i	−0.449447	−	0.778465i	0.548903	−	0.835886i	$-0.315046\pi$
$919$	−13.6250	−	23.5992i	−0.449447	−	0.778465i	−0.998350	+	0.0574208i	$0.981712\pi$
$920$	3.07321	−	5.32296i	0.101321	−	0.175493i
$921$	61.5449	+	22.4005i	2.02797	+	0.738122i
$922$	14.6038	+	5.31533i	0.480949	+	0.175051i
$923$	22.1964	−	38.4454i	0.730605	−	1.26544i
$924$	−5.90868	−	10.2341i	−0.194381	−	0.336678i
$925$	−0.100447	−	0.569664i	−0.00330268	−	0.0187304i
$926$	−15.8301	−	13.2831i	−0.520211	−	0.436509i
$927$	−38.0652	+	31.9405i	−1.25023	+	1.04906i
$928$	1.03004	−	5.84167i	0.0338128	−	0.191762i
$929$	−41.7609	+	15.1997i	−1.37013	+	0.498686i	−0.919171	−	0.393859i	$-0.871140\pi$
$929$	−41.7609	+	15.1997i	−1.37013	+	0.498686i	−0.450958	+	0.892545i	$0.648918\pi$
$930$	−45.1517			−1.48058
$931$		0			0
$932$	22.8621			0.748873
$933$	54.7149	−	19.9146i	1.79128	−	0.651974i
$934$	4.94601	−	28.0502i	0.161839	−	0.917832i
$935$	15.7160	−	13.1873i	0.513967	−	0.431269i
$936$	16.2873	+	13.6667i	0.532367	+	0.446709i
$937$	−3.16208	−	17.9331i	−0.103301	−	0.585847i	−0.991885	−	0.127135i	$-0.959422\pi$
$937$	−3.16208	−	17.9331i	−0.103301	−	0.585847i	0.888585	−	0.458712i	$-0.151689\pi$
$938$	16.1477	+	27.9686i	0.527239	+	0.913206i
$939$	−15.4544	+	26.7678i	−0.504336	+	0.873536i
$940$	1.72330	+	0.627230i	0.0562079	+	0.0204580i
$941$	−37.8396	−	13.7725i	−1.23353	−	0.448970i	−0.358728	−	0.933442i	$-0.616789\pi$
$941$	−37.8396	−	13.7725i	−1.23353	−	0.448970i	−0.874807	+	0.484472i	$0.839012\pi$
$942$	3.74730	−	6.49052i	0.122094	−	0.211472i
$943$	3.25784	+	5.64274i	0.106090	+	0.183753i
$944$	0.861748	+	4.88722i	0.0280475	+	0.159065i
$945$	4.65800	+	3.90853i	0.151525	+	0.127144i
$946$	3.69199	−	3.09795i	0.120037	−	0.100723i
$947$	1.10538	−	6.26890i	0.0359199	−	0.203712i	−0.961566	−	0.274573i	$-0.911464\pi$
$947$	1.10538	−	6.26890i	0.0359199	−	0.203712i	0.997486	+	0.0708610i	$0.0225747\pi$
$948$	−13.9996	+	5.09544i	−0.454686	+	0.165492i
$949$	39.2488			1.27407
$950$		0			0
$951$	0.686248			0.0222531
$952$	−13.0447	+	4.74789i	−0.422782	+	0.153880i
$953$	5.67732	−	32.1977i	0.183906	−	1.04299i	−0.743446	−	0.668796i	$-0.766810\pi$
$953$	5.67732	−	32.1977i	0.183906	−	1.04299i	0.927352	−	0.374189i	$-0.122079\pi$
$954$	−3.77437	+	3.16707i	−0.122200	+	0.102538i
$955$	−12.3882	−	10.3950i	−0.400874	−	0.336373i
$956$	1.50486	+	8.53446i	0.0486705	+	0.276024i
$957$	−12.5462	−	21.7306i	−0.405560	−	0.702450i
$958$	−5.23632	+	9.06958i	−0.169178	+	0.293025i
$959$	−41.7806	−	15.2069i	−1.34917	−	0.491056i
$960$	5.82485	+	2.12007i	0.187996	+	0.0684251i
$961$	−11.0289	+	19.1026i	−0.355771	+	0.616214i
$962$	1.74784	+	3.02735i	0.0563527	+	0.0976057i
$963$	1.64595	+	9.33466i	0.0530400	+	0.300805i
$964$	−4.33448	−	3.63706i	−0.139604	−	0.117142i
$965$	50.6523	−	42.5023i	1.63055	−	1.36820i
$966$	−3.05500	+	17.3257i	−0.0982929	+	0.557447i
$967$	−8.04317	+	2.92747i	−0.258651	+	0.0941412i	−0.468091	−	0.883680i	$-0.655058\pi$
$967$	−8.04317	+	2.92747i	−0.258651	+	0.0941412i	0.209440	+	0.977821i	$0.432836\pi$
$968$	8.18253			0.262997
$969$		0			0
$970$	−35.3879			−1.13624
$971$	−39.3533	+	14.3234i	−1.26291	+	0.459660i	−0.884743	−	0.466079i	$-0.845666\pi$
$971$	−39.3533	+	14.3234i	−1.26291	+	0.459660i	−0.378163	+	0.925739i	$0.623444\pi$
$972$	−3.88461	+	22.0307i	−0.124599	+	0.706636i
$973$	−21.6574	+	18.1727i	−0.694305	+	0.582591i
$974$	1.76109	+	1.47773i	0.0564290	+	0.0473495i
$975$	−2.91499	−	16.5317i	−0.0933543	−	0.529439i
$976$	−4.66843	−	8.08596i	−0.149433	−	0.258825i
$977$	−3.09010	+	5.35222i	−0.0988612	+	0.171233i	−0.911214	−	0.411934i	$-0.864853\pi$
$977$	−3.09010	+	5.35222i	−0.0988612	+	0.171233i	0.812352	+	0.583167i	$0.198187\pi$
$978$	13.2426	+	4.81990i	0.423450	+	0.154123i
$979$	−10.8913	−	3.96411i	−0.348088	−	0.126694i
$980$	0.989057	−	1.71310i	0.0315943	−	0.0547229i
$981$	2.89101	+	5.00738i	0.0923029	+	0.159873i
$982$	−2.11177	−	11.9764i	−0.0673892	−	0.382183i
$983$	−25.7193	−	21.5811i	−0.820318	−	0.688329i	0.132728	−	0.991152i	$-0.457626\pi$
$983$	−25.7193	−	21.5811i	−0.820318	−	0.688329i	−0.953047	+	0.302824i	$0.902071\pi$
$984$	−5.03373	+	4.22380i	−0.160469	+	0.134650i
$985$	4.20681	−	23.8580i	0.134040	−	0.760180i
$986$	−27.6985	+	10.0814i	−0.882099	+	0.321058i
$987$	−5.24920			−0.167084
$988$		0			0
$989$	−7.17507			−0.228154
$990$	13.0011	−	4.73203i	0.413203	−	0.150394i
$991$	8.01814	−	45.4731i	0.254705	−	1.44450i	−0.542125	−	0.840298i	$-0.682380\pi$
$991$	8.01814	−	45.4731i	0.254705	−	1.44450i	0.796830	−	0.604204i	$-0.206509\pi$
$992$	5.57993	−	4.68212i	0.177163	−	0.148657i
$993$	38.5974	+	32.3870i	1.22485	+	1.02777i
$994$	3.39427	+	19.2498i	0.107660	+	0.610568i
$995$	−25.1697	−	43.5952i	−0.797934	−	1.38206i
$996$	−19.1245	+	33.1247i	−0.605984	+	1.04960i
$997$	0.769731	+	0.280159i	0.0243776	+	0.00887273i	0.354180	−	0.935177i	$-0.384760\pi$
$997$	0.769731	+	0.280159i	0.0243776	+	0.00887273i	−0.329803	+	0.944050i	$0.606982\pi$
$998$	14.2221	+	5.17642i	0.450193	+	0.163857i
$999$	0.243785	−	0.422248i	0.00771302	−	0.0133593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.s.423.4		24
19.2	odd	18		722.2.a.n.1.1	yes	4
19.3	odd	18		722.2.c.m.653.4		8
19.4	even	9	inner	722.2.e.s.99.4		24
19.5	even	9		722.2.c.n.429.1		8
19.6	even	9	inner	722.2.e.s.389.4		24
19.7	even	3	inner	722.2.e.s.245.4		24
19.8	odd	6		722.2.e.r.415.4		24
19.9	even	9	inner	722.2.e.s.595.1		24
19.10	odd	18		722.2.e.r.595.4		24
19.11	even	3	inner	722.2.e.s.415.1		24
19.12	odd	6		722.2.e.r.245.1		24
19.13	odd	18		722.2.e.r.389.1		24
19.14	odd	18		722.2.c.m.429.4		8
19.15	odd	18		722.2.e.r.99.1		24
19.16	even	9		722.2.c.n.653.1		8
19.17	even	9		722.2.a.m.1.4	✓	4
19.18	odd	2		722.2.e.r.423.1		24
57.2	even	18		6498.2.a.bx.1.4		4
57.17	odd	18		6498.2.a.ca.1.4		4
76.55	odd	18		5776.2.a.bv.1.1		4
76.59	even	18		5776.2.a.bt.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.4	✓	4	19.17	even	9
722.2.a.n.1.1	yes	4	19.2	odd	18
722.2.c.m.429.4		8	19.14	odd	18
722.2.c.m.653.4		8	19.3	odd	18
722.2.c.n.429.1		8	19.5	even	9
722.2.c.n.653.1		8	19.16	even	9
722.2.e.r.99.1		24	19.15	odd	18
722.2.e.r.245.1		24	19.12	odd	6
722.2.e.r.389.1		24	19.13	odd	18
722.2.e.r.415.4		24	19.8	odd	6
722.2.e.r.423.1		24	19.18	odd	2
722.2.e.r.595.4		24	19.10	odd	18
722.2.e.s.99.4		24	19.4	even	9	inner
722.2.e.s.245.4		24	19.7	even	3	inner
722.2.e.s.389.4		24	19.6	even	9	inner
722.2.e.s.415.1		24	19.11	even	3	inner
722.2.e.s.423.4		24	1.1	even	1	trivial
722.2.e.s.595.1		24	19.9	even	9	inner
5776.2.a.bt.1.4		4	76.59	even	18
5776.2.a.bv.1.1		4	76.55	odd	18
6498.2.a.bx.1.4		4	57.2	even	18
6498.2.a.ca.1.4		4	57.17	odd	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.437619 - 2.48186i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.88420 - 1.58103i) q^{5} +(-0.437619 - 2.48186i) q^{6} +(1.39680 + 2.41933i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-3.14904 - 1.14616i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.437619 - 2.48186i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.88420 - 1.58103i) q^{5} +(-0.437619 - 2.48186i) q^{6} +(1.39680 + 2.41933i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-3.14904 - 1.14616i) q^{9} +(-2.31131 - 0.841250i) q^{10} +(0.839266 - 1.45365i) q^{11} +(-1.26007 - 2.18251i) q^{12} +(-1.10172 - 6.24819i) q^{13} +(2.14003 + 1.79569i) q^{14} +(-4.74846 + 3.98443i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-4.66950 + 1.69956i) q^{17} -3.35114 q^{18} -2.45965 q^{20} +(6.61571 - 2.40792i) q^{21} +(0.291474 - 1.65303i) q^{22} +(-1.91427 + 1.60626i) q^{23} +(-1.93054 - 1.61992i) q^{24} +(0.182309 + 1.03393i) q^{25} +(-3.17229 - 5.49456i) q^{26} +(-0.442463 + 0.766369i) q^{27} +(2.62513 + 0.955469i) q^{28} +(5.57406 + 2.02879i) q^{29} +(-3.09934 + 5.36821i) q^{30} +(3.64204 + 6.30820i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-3.24048 - 2.71909i) q^{33} +(-3.80661 + 3.19412i) q^{34} +(1.19319 - 6.76690i) q^{35} +(-3.14904 + 1.14616i) q^{36} -0.550972 q^{37} -15.9893 q^{39} +(-2.31131 + 0.841250i) q^{40} +(0.452772 - 2.56780i) q^{41} +(5.39318 - 4.52541i) q^{42} +(2.19953 + 1.84563i) q^{43} +(-0.291474 - 1.65303i) q^{44} +(4.12132 + 7.13833i) q^{45} +(-1.24945 + 2.16411i) q^{46} +(-0.700629 - 0.255008i) q^{47} +(-2.36816 - 0.861941i) q^{48} +(-0.402113 + 0.696480i) q^{49} +(0.524938 + 0.909219i) q^{50} +(2.17461 + 12.3328i) q^{51} +(-4.86023 - 4.07822i) q^{52} +(1.12629 - 0.945072i) q^{53} +(-0.153666 + 0.871483i) q^{54} +(-3.87961 + 1.41206i) q^{55} +2.79360 q^{56} +5.93179 q^{58} +(-4.66333 + 1.69731i) q^{59} +(-1.07639 + 6.10451i) q^{60} +(7.15245 - 6.00162i) q^{61} +(5.57993 + 4.68212i) q^{62} +(-1.62565 - 9.21954i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-7.80272 + 13.5147i) q^{65} +(-3.97504 - 1.44680i) q^{66} +(10.8633 + 3.95390i) q^{67} +(-2.48459 + 4.30343i) q^{68} +(3.14880 + 5.45389i) q^{69} +(-1.19319 - 6.76690i) q^{70} +(5.36000 + 4.49757i) q^{71} +(-2.56712 + 2.15407i) q^{72} +(-1.07422 + 6.09221i) q^{73} +(-0.517744 + 0.188444i) q^{74} +2.64584 q^{75} +4.68915 q^{77} +(-15.0250 + 5.46865i) q^{78} +(1.02654 - 5.82177i) q^{79} +(-1.88420 + 1.58103i) q^{80} +(-5.99298 - 5.02871i) q^{81} +(-0.452772 - 2.56780i) q^{82} +(-7.58866 - 13.1439i) q^{83} +(3.52015 - 6.09707i) q^{84} +(11.4853 + 4.18032i) q^{85} +(2.69813 + 0.982038i) q^{86} +(7.47449 - 12.9462i) q^{87} +(-0.839266 - 1.45365i) q^{88} +(-1.19904 - 6.80011i) q^{89} +(6.31422 + 5.29826i) q^{90} +(13.5776 - 11.3929i) q^{91} +(-0.433930 + 2.46094i) q^{92} +(17.2499 - 6.27845i) q^{93} -0.745593 q^{94} -2.52015 q^{96} +(13.5197 - 4.92077i) q^{97} +(-0.139652 + 0.792008i) q^{98} +(-4.30900 + 3.61568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{7} + 12 q^{8}+O(q^{10}) \) 24 * q + 6 * q^7 + 12 * q^8	\( 24 q + 6 q^{7} + 12 q^{8} - 6 q^{11} + 6 q^{12} - 24 q^{18} - 12 q^{20} - 54 q^{26} - 12 q^{27} - 12 q^{30} + 78 q^{31} - 24 q^{37} - 36 q^{39} + 66 q^{45} - 30 q^{46} + 36 q^{49} + 18 q^{50} + 12 q^{56} - 12 q^{58} - 12 q^{64} - 12 q^{65} - 18 q^{68} - 60 q^{69} - 48 q^{75} + 24 q^{77} + 36 q^{83} + 12 q^{84} + 78 q^{87} + 6 q^{88} + 72 q^{94} + 12 q^{96}+O(q^{100}) \) 24 * q + 6 * q^7 + 12 * q^8 - 6 * q^11 + 6 * q^12 - 24 * q^18 - 12 * q^20 - 54 * q^26 - 12 * q^27 - 12 * q^30 + 78 * q^31 - 24 * q^37 - 36 * q^39 + 66 * q^45 - 30 * q^46 + 36 * q^49 + 18 * q^50 + 12 * q^56 - 12 * q^58 - 12 * q^64 - 12 * q^65 - 18 * q^68 - 60 * q^69 - 48 * q^75 + 24 * q^77 + 36 * q^83 + 12 * q^84 + 78 * q^87 + 6 * q^88 + 72 * q^94 + 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more