LMFDB - Embedded newform 722.2.e.s.99.3

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			99.3
Character	$\chi$	$=$	722.99
Dual form			722.2.e.s.423.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.0768330 - 0.435741i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.682922 + 0.573040i) q^{5} +(0.0768330 - 0.435741i) q^{6} +(-1.26007 + 2.18251i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.63511 - 0.959102i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.0768330 - 0.435741i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.682922 + 0.573040i) q^{5} +(0.0768330 - 0.435741i) q^{6} +(-1.26007 + 2.18251i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.63511 - 0.959102i) q^{9} +(-0.837728 + 0.304908i) q^{10} +(-0.975994 - 1.69047i) q^{11} +(0.221232 - 0.383185i) q^{12} +(-1.12171 + 6.36151i) q^{13} +(-1.93054 + 1.61992i) q^{14} +(0.302168 + 0.253549i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.21587 + 1.17048i) q^{17} +2.80423 q^{18} -0.891491 q^{20} +(1.04783 + 0.381377i) q^{21} +(-0.338959 - 1.92233i) q^{22} +(6.27010 + 5.26124i) q^{23} +(0.338947 - 0.284410i) q^{24} +(-0.730233 + 4.14136i) q^{25} +(-3.22982 + 5.59422i) q^{26} +(-1.28408 - 2.22409i) q^{27} +(-2.36816 + 0.861941i) q^{28} +(-4.30440 + 1.56667i) q^{29} +(0.197226 + 0.341606i) q^{30} +(4.39680 - 7.61548i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.661620 + 0.555165i) q^{33} +(2.62160 + 2.19979i) q^{34} +(-0.390134 - 2.21256i) q^{35} +(2.63511 + 0.959102i) q^{36} -5.97980 q^{37} +2.85816 q^{39} +(-0.837728 - 0.304908i) q^{40} +(-0.605914 - 3.43631i) q^{41} +(0.854195 + 0.716755i) q^{42} +(-4.78524 + 4.01529i) q^{43} +(0.338959 - 1.92233i) q^{44} +(-1.24997 + 2.16501i) q^{45} +(4.09252 + 7.08845i) q^{46} +(9.91359 - 3.60825i) q^{47} +(0.415780 - 0.151331i) q^{48} +(0.324429 + 0.561928i) q^{49} +(-2.10262 + 3.64185i) q^{50} +(0.262942 - 1.49122i) q^{51} +(-4.94838 + 4.15218i) q^{52} +(2.88246 + 2.41867i) q^{53} +(-0.445956 - 2.52914i) q^{54} +(1.63524 + 0.595177i) q^{55} -2.52015 q^{56} -4.58064 q^{58} +(-2.67025 - 0.971890i) q^{59} +(0.0684959 + 0.388460i) q^{60} +(-1.88060 - 1.57801i) q^{61} +(6.73629 - 5.65242i) q^{62} +(-1.22718 + 6.95970i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.87936 - 4.98720i) q^{65} +(-0.811597 + 0.295397i) q^{66} +(2.51143 - 0.914086i) q^{67} +(1.71113 + 2.96376i) q^{68} +(1.81079 - 3.13638i) q^{69} +(0.390134 - 2.21256i) q^{70} +(0.0432358 - 0.0362792i) q^{71} +(2.14816 + 1.80252i) q^{72} +(-1.21018 - 6.86330i) q^{73} +(-5.61917 - 2.04521i) q^{74} +1.86067 q^{75} +4.91930 q^{77} +(2.68579 + 0.977548i) q^{78} +(-1.58569 - 8.99289i) q^{79} +(-0.682922 - 0.573040i) q^{80} +(5.57402 - 4.67716i) q^{81} +(0.605914 - 3.43631i) q^{82} +(7.06195 - 12.2317i) q^{83} +(0.557537 + 0.965682i) q^{84} +(-2.86692 + 1.04347i) q^{85} +(-5.86997 + 2.13649i) q^{86} +(1.01338 + 1.75523i) q^{87} +(0.975994 - 1.69047i) q^{88} +(0.324330 - 1.83937i) q^{89} +(-1.91507 + 1.60693i) q^{90} +(-12.4706 - 10.4641i) q^{91} +(1.42132 + 8.06069i) q^{92} +(-3.65620 - 1.33075i) q^{93} +10.5498 q^{94} +0.442463 q^{96} +(-7.35245 - 2.67607i) q^{97} +(0.112673 + 0.639001i) q^{98} +(-4.19319 - 3.51850i) 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 $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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
$3$	−0.0768330	−	0.435741i	−0.0443595	−	0.251575i	0.954562	−	0.298014i	$-0.0963241\pi$
$3$	−0.0768330	−	0.435741i	−0.0443595	−	0.251575i	−0.998921	+	0.0464381i	$0.985213\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.682922	+	0.573040i	−0.305412	+	0.256271i	−0.782593	−	0.622534i	$-0.786103\pi$
$5$	−0.682922	+	0.573040i	−0.305412	+	0.256271i	0.477181	+	0.878805i	$0.341659\pi$
$6$	0.0768330	−	0.435741i	0.0313669	−	0.177891i
$7$	−1.26007	+	2.18251i	−0.476263	+	0.824912i	−0.999630	−	0.0271956i	$-0.991342\pi$
$7$	−1.26007	+	2.18251i	−0.476263	+	0.824912i	0.523367	+	0.852107i	$0.324676\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.63511	−	0.959102i	0.878370	−	0.319701i
$10$	−0.837728	+	0.304908i	−0.264913	+	0.0964204i
$11$	−0.975994	−	1.69047i	−0.294273	−	0.509696i	0.680542	−	0.732709i	$-0.261744\pi$
$11$	−0.975994	−	1.69047i	−0.294273	−	0.509696i	−0.974816	+	0.223012i	$0.928411\pi$
$12$	0.221232	−	0.383185i	0.0638641	−	0.110616i
$13$	−1.12171	+	6.36151i	−0.311105	+	1.76437i	0.282168	+	0.959365i	$0.408946\pi$
$13$	−1.12171	+	6.36151i	−0.311105	+	1.76437i	−0.593273	+	0.805001i	$0.702165\pi$
$14$	−1.93054	+	1.61992i	−0.515960	+	0.432942i
$15$	0.302168	+	0.253549i	0.0780195	+	0.0654661i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	3.21587	+	1.17048i	0.779964	+	0.283884i	0.701158	−	0.713006i	$-0.252667\pi$
$17$	3.21587	+	1.17048i	0.779964	+	0.283884i	0.0788061	+	0.996890i	$0.474889\pi$
$18$	2.80423			0.660962
$19$		0			0
$19$		0			0
$20$	−0.891491			−0.199344
$21$	1.04783	+	0.381377i	0.228654	+	0.0832234i
$22$	−0.338959	−	1.92233i	−0.0722664	−	0.409843i
$23$	6.27010	+	5.26124i	1.30741	+	1.09704i	0.988814	+	0.149153i	$0.0476548\pi$
$23$	6.27010	+	5.26124i	1.30741	+	1.09704i	0.318593	+	0.947892i	$0.396790\pi$
$24$	0.338947	−	0.284410i	0.0691872	−	0.0580550i
$25$	−0.730233	+	4.14136i	−0.146047	+	0.828271i
$26$	−3.22982	+	5.59422i	−0.633421	+	1.09712i
$27$	−1.28408	−	2.22409i	−0.247121	−	0.428026i
$28$	−2.36816	+	0.861941i	−0.447541	+	0.162892i
$29$	−4.30440	+	1.56667i	−0.799307	+	0.290924i	−0.709199	−	0.705008i	$-0.750943\pi$
$29$	−4.30440	+	1.56667i	−0.799307	+	0.290924i	−0.0901075	+	0.995932i	$0.528721\pi$
$30$	0.197226	+	0.341606i	0.0360084	+	0.0623684i
$31$	4.39680	−	7.61548i	0.789689	−	1.36778i	−0.136468	−	0.990644i	$-0.543575\pi$
$31$	4.39680	−	7.61548i	0.789689	−	1.36778i	0.926157	−	0.377137i	$-0.123091\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−0.661620	+	0.555165i	−0.115173	+	0.0966419i
$34$	2.62160	+	2.19979i	0.449601	+	0.377260i
$35$	−0.390134	−	2.21256i	−0.0659446	−	0.373990i
$36$	2.63511	+	0.959102i	0.439185	+	0.159850i
$37$	−5.97980			−0.983073			−0.491536	−	0.870857i	$-0.663564\pi$
$37$	−5.97980			−0.983073			−0.491536	+	0.870857i	$0.663564\pi$
$38$		0			0
$39$	2.85816			0.457672
$40$	−0.837728	−	0.304908i	−0.132456	−	0.0482102i
$41$	−0.605914	−	3.43631i	−0.0946279	−	0.536662i	−0.994861	−	0.101253i	$-0.967715\pi$
$41$	−0.605914	−	3.43631i	−0.0946279	−	0.536662i	0.900233	−	0.435409i	$-0.143396\pi$
$42$	0.854195	+	0.716755i	0.131805	+	0.110598i
$43$	−4.78524	+	4.01529i	−0.729743	+	0.612327i	−0.930061	−	0.367404i	$-0.880247\pi$
$43$	−4.78524	+	4.01529i	−0.729743	+	0.612327i	0.200319	+	0.979731i	$0.435802\pi$
$44$	0.338959	−	1.92233i	0.0511000	−	0.289803i
$45$	−1.24997	+	2.16501i	−0.186335	+	0.322741i
$46$	4.09252	+	7.08845i	0.603409	+	1.04514i
$47$	9.91359	−	3.60825i	1.44605	−	0.526317i	0.504562	−	0.863376i	$-0.331654\pi$
$47$	9.91359	−	3.60825i	1.44605	−	0.526317i	0.941484	+	0.337058i	$0.109432\pi$
$48$	0.415780	−	0.151331i	0.0600126	−	0.0218428i
$49$	0.324429	+	0.561928i	0.0463471	+	0.0802755i
$50$	−2.10262	+	3.64185i	−0.297356	+	0.515035i
$51$	0.262942	−	1.49122i	0.0368193	−	0.208813i
$52$	−4.94838	+	4.15218i	−0.686217	+	0.575804i
$53$	2.88246	+	2.41867i	0.395936	+	0.332230i	0.818920	−	0.573907i	$-0.194573\pi$
$53$	2.88246	+	2.41867i	0.395936	+	0.332230i	−0.422984	+	0.906137i	$0.639017\pi$
$54$	−0.445956	−	2.52914i	−0.0606869	−	0.344173i
$55$	1.63524	+	0.595177i	0.220495	+	0.0802537i
$56$	−2.52015			−0.336769
$57$		0			0
$58$	−4.58064			−0.601468
$59$	−2.67025	−	0.971890i	−0.347636	−	0.126529i	0.162300	−	0.986741i	$-0.448109\pi$
$59$	−2.67025	−	0.971890i	−0.347636	−	0.126529i	−0.509936	+	0.860212i	$0.670331\pi$
$60$	0.0684959	+	0.388460i	0.00884279	+	0.0501499i
$61$	−1.88060	−	1.57801i	−0.240786	−	0.202044i	0.514406	−	0.857547i	$-0.328012\pi$
$61$	−1.88060	−	1.57801i	−0.240786	−	0.202044i	−0.755193	+	0.655503i	$0.772457\pi$
$62$	6.73629	−	5.65242i	0.855510	−	0.717858i
$63$	−1.22718	+	6.95970i	−0.154610	+	0.876839i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.87936	−	4.98720i	−0.357141	−	0.618586i
$66$	−0.811597	+	0.295397i	−0.0999007	+	0.0363609i
$67$	2.51143	−	0.914086i	0.306820	−	0.111673i	−0.184021	−	0.982922i	$-0.558912\pi$
$67$	2.51143	−	0.914086i	0.306820	−	0.111673i	0.490842	+	0.871249i	$0.336689\pi$
$68$	1.71113	+	2.96376i	0.207505	+	0.359409i
$69$	1.81079	−	3.13638i	0.217994	−	0.377576i
$70$	0.390134	−	2.21256i	0.0466299	−	0.264451i
$71$	0.0432358	−	0.0362792i	0.00513115	−	0.00430555i	−0.640218	−	0.768193i	$-0.721156\pi$
$71$	0.0432358	−	0.0362792i	0.00513115	−	0.00430555i	0.645350	+	0.763887i	$0.276712\pi$
$72$	2.14816	+	1.80252i	0.253163	+	0.212429i
$73$	−1.21018	−	6.86330i	−0.141641	−	0.803288i	−0.970003	−	0.243094i	$-0.921838\pi$
$73$	−1.21018	−	6.86330i	−0.141641	−	0.803288i	0.828361	−	0.560194i	$-0.189273\pi$
$74$	−5.61917	−	2.04521i	−0.653215	−	0.237751i
$75$	1.86067			0.214851
$76$		0			0
$77$	4.91930			0.560606
$78$	2.68579	+	0.977548i	0.304106	+	0.110686i
$79$	−1.58569	−	8.99289i	−0.178404	−	1.01178i	−0.934141	−	0.356904i	$-0.883832\pi$
$79$	−1.58569	−	8.99289i	−0.178404	−	1.01178i	0.755737	−	0.654875i	$-0.227279\pi$
$80$	−0.682922	−	0.573040i	−0.0763530	−	0.0640678i
$81$	5.57402	−	4.67716i	0.619335	−	0.519684i
$82$	0.605914	−	3.43631i	0.0669121	−	0.379477i
$83$	7.06195	−	12.2317i	0.775150	−	1.34260i	−0.159561	−	0.987188i	$-0.551008\pi$
$83$	7.06195	−	12.2317i	0.775150	−	1.34260i	0.934710	−	0.355411i	$-0.115659\pi$
$84$	0.557537	+	0.965682i	0.0608322	+	0.105364i
$85$	−2.86692	+	1.04347i	−0.310961	+	0.113181i
$86$	−5.86997	+	2.13649i	−0.632975	+	0.230384i
$87$	1.01338	+	1.75523i	0.108646	+	0.188181i
$88$	0.975994	−	1.69047i	0.104041	−	0.180205i
$89$	0.324330	−	1.83937i	0.0343789	−	0.194972i	−0.962781	−	0.270281i	$-0.912883\pi$
$89$	0.324330	−	1.83937i	0.0343789	−	0.194972i	0.997160	+	0.0753091i	$0.0239943\pi$
$90$	−1.91507	+	1.60693i	−0.201866	+	0.169386i
$91$	−12.4706	−	10.4641i	−1.30728	−	1.09694i
$92$	1.42132	+	8.06069i	0.148183	+	0.840385i
$93$	−3.65620	−	1.33075i	−0.379130	−	0.137992i
$94$	10.5498			1.08813
$95$		0			0
$96$	0.442463			0.0451587
$97$	−7.35245	−	2.67607i	−0.746528	−	0.271714i	−0.0593843	−	0.998235i	$-0.518914\pi$
$97$	−7.35245	−	2.67607i	−0.746528	−	0.271714i	−0.687144	+	0.726521i	$0.741136\pi$
$98$	0.112673	+	0.639001i	0.0113817	+	0.0645489i
$99$	−4.19319	−	3.51850i	−0.421431	−	0.353623i
$100$	−3.22140	+	2.70308i	−0.322140	+	0.270308i
$101$	−0.935073	+	5.30306i	−0.0930432	+	0.527674i	0.902286	+	0.431138i	$0.141888\pi$
$101$	−0.935073	+	5.30306i	−0.0930432	+	0.527674i	−0.995329	+	0.0965368i	$0.969223\pi$
$102$	0.757113	−	1.31136i	0.0749653	−	0.129844i
$103$	2.34734	+	4.06571i	0.231290	+	0.400606i	0.958188	−	0.286139i	$-0.0923720\pi$
$103$	2.34734	+	4.06571i	0.231290	+	0.400606i	−0.726898	+	0.686746i	$0.759039\pi$
$104$	−6.07009	+	2.20933i	−0.595221	+	0.216643i
$105$	−0.934128	+	0.339995i	−0.0911615	+	0.0331801i
$106$	1.88139	+	3.25866i	0.182737	+	0.316509i
$107$	−8.01864	+	13.8887i	−0.775191	+	1.34267i	0.159496	+	0.987199i	$0.449013\pi$
$107$	−8.01864	+	13.8887i	−0.775191	+	1.34267i	−0.934687	+	0.355472i	$0.884320\pi$
$108$	0.445956	−	2.52914i	0.0429121	−	0.243367i
$109$	10.8018	−	9.06381i	1.03463	−	0.868156i	0.0432336	−	0.999065i	$-0.486234\pi$
$109$	10.8018	−	9.06381i	1.03463	−	0.868156i	0.991394	+	0.130909i	$0.0417896\pi$
$110$	1.33306	+	1.11857i	0.127102	+	0.106651i
$111$	0.459446	+	2.60565i	0.0436086	+	0.247317i
$112$	−2.36816	−	0.861941i	−0.223770	−	0.0814458i
$113$	−12.7224			−1.19682			−0.598410	−	0.801190i	$-0.704201\pi$
$113$	−12.7224			−1.19682			−0.598410	+	0.801190i	$0.704201\pi$
$114$		0			0
$115$	−7.29689			−0.680439
$116$	−4.30440	−	1.56667i	−0.399653	−	0.145462i
$117$	3.14552	+	17.8391i	0.290803	+	1.64923i
$118$	−2.17680	−	1.82656i	−0.200391	−	0.168148i
$119$	−6.60683	+	5.54379i	−0.605647	+	0.508198i
$120$	−0.0684959	+	0.388460i	−0.00625280	+	0.0354614i
$121$	3.59487	−	6.22650i	0.326806	−	0.566045i
$122$	−1.22747	−	2.12605i	−0.111130	−	0.192483i
$123$	−1.45079	+	0.528044i	−0.130813	+	0.0476121i
$124$	8.26329	−	3.00759i	0.742065	−	0.270090i
$125$	−4.10320	−	7.10695i	−0.367001	−	0.635665i
$126$	−3.53353	+	6.12026i	−0.314792	+	0.545236i
$127$	1.24582	−	7.06542i	0.110549	−	0.626955i	−0.878309	−	0.478093i	$-0.841328\pi$
$127$	1.24582	−	7.06542i	0.110549	−	0.626955i	0.988858	−	0.148861i	$-0.0475608\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	2.11729	+	1.77662i	0.186417	+	0.156423i
$130$	−0.999992	−	5.67123i	−0.0877051	−	0.497400i
$131$	3.31021	+	1.20482i	0.289215	+	0.105266i	0.482553	−	0.875867i	$-0.339709\pi$
$131$	3.31021	+	1.20482i	0.289215	+	0.105266i	−0.193339	+	0.981132i	$0.561932\pi$
$132$	−0.863684			−0.0751740
$133$		0			0
$134$	2.67261			0.230878
$135$	2.15142	+	0.783052i	0.185165	+	0.0673944i
$136$	0.594269	+	3.37027i	0.0509582	+	0.288998i
$137$	−8.42921	−	7.07294i	−0.720156	−	0.604282i	0.207273	−	0.978283i	$-0.433541\pi$
$137$	−8.42921	−	7.07294i	−0.720156	−	0.604282i	−0.927428	+	0.374001i	$0.877986\pi$
$138$	2.77429	−	2.32791i	0.236163	−	0.198165i
$139$	3.77834	−	21.4280i	0.320475	−	1.81750i	−0.219258	−	0.975667i	$-0.570364\pi$
$139$	3.77834	−	21.4280i	0.320475	−	1.81750i	0.539733	−	0.841836i	$-0.318525\pi$
$140$	1.12334	−	1.94569i	0.0949400	−	0.164441i
$141$	−2.33395	−	4.04253i	−0.196554	−	0.340442i
$142$	0.0530366	−	0.0193038i	0.00445073	−	0.00161993i
$143$	11.8487	−	4.31259i	0.990841	−	0.360637i
$144$	1.40211	+	2.42853i	0.116843	+	0.202378i
$145$	2.04180	−	3.53651i	0.169562	−	0.293691i
$146$	1.21018	−	6.86330i	0.100156	−	0.568011i
$147$	0.219929	−	0.184542i	0.0181394	−	0.0152208i
$148$	−4.58079	−	3.84374i	−0.376539	−	0.315953i
$149$	2.49872	+	14.1710i	0.204703	+	1.16093i	0.897906	+	0.440187i	$0.145088\pi$
$149$	2.49872	+	14.1710i	0.204703	+	1.16093i	−0.693203	+	0.720743i	$0.743801\pi$
$150$	1.74845	+	0.636385i	0.142761	+	0.0519607i
$151$	12.4068			1.00965			0.504824	−	0.863222i	$-0.331557\pi$
$151$	12.4068			1.00965			0.504824	+	0.863222i	$0.331557\pi$
$152$		0			0
$153$	9.59679			0.775855
$154$	4.62263	+	1.68250i	0.372502	+	0.135580i
$155$	1.36130	+	7.72032i	0.109342	+	0.620111i
$156$	2.18948	+	1.83719i	0.175298	+	0.147093i
$157$	−0.345655	+	0.290039i	−0.0275863	+	0.0231476i	−0.656477	−	0.754346i	$-0.727954\pi$
$157$	−0.345655	+	0.290039i	−0.0275863	+	0.0231476i	0.628890	+	0.777494i	$0.283509\pi$
$158$	1.58569	−	8.99289i	0.126151	−	0.715436i
$159$	0.832446	−	1.44184i	0.0660173	−	0.114345i
$160$	−0.445746	−	0.772054i	−0.0352393	−	0.0610362i
$161$	−19.3835	+	7.05502i	−1.52763	+	0.556014i
$162$	6.83754	−	2.48866i	0.537208	−	0.195528i
$163$	0.0346271	+	0.0599759i	0.00271220	+	0.00469768i	0.867378	−	0.497649i	$-0.165803\pi$
$163$	0.0346271	+	0.0599759i	0.00271220	+	0.00469768i	−0.864666	+	0.502347i	$0.832470\pi$
$164$	1.74466	−	3.02184i	0.136235	−	0.235966i
$165$	0.133703	−	0.758269i	0.0104088	−	0.0590312i
$166$	10.8195	−	9.07867i	0.839759	−	0.704641i
$167$	1.66516	+	1.39723i	0.128854	+	0.108121i	0.704937	−	0.709270i	$-0.250975\pi$
$167$	1.66516	+	1.39723i	0.128854	+	0.108121i	−0.576083	+	0.817391i	$0.695420\pi$
$168$	0.193630	+	1.09813i	0.0149389	+	0.0847228i
$169$	−26.9946	−	9.82524i	−2.07651	−	0.755787i
$170$	−3.05092			−0.233995
$171$		0			0
$172$	−6.24669			−0.476306
$173$	15.8332	+	5.76280i	1.20377	+	0.438137i	0.864539	−	0.502565i	$-0.167610\pi$
$173$	15.8332	+	5.76280i	1.20377	+	0.438137i	0.339233	+	0.940702i	$0.389833\pi$
$174$	0.351945	+	1.99598i	0.0266808	+	0.151315i
$175$	−8.11841	−	6.81215i	−0.613694	−	0.514950i
$176$	1.49531	−	1.25471i	0.112713	−	0.0945776i
$177$	−0.218330	+	1.23821i	−0.0164107	+	0.0930695i
$178$	0.933870	−	1.61751i	0.0699965	−	0.121238i
$179$	−9.48276	−	16.4246i	−0.708775	−	1.22763i	−0.965312	−	0.261099i	$-0.915915\pi$
$179$	−9.48276	−	16.4246i	−0.708775	−	1.22763i	0.256537	−	0.966534i	$-0.417418\pi$
$180$	−2.34918	+	0.855031i	−0.175097	+	0.0637303i
$181$	1.86705	−	0.679550i	0.138777	−	0.0505105i	−0.271698	−	0.962383i	$-0.587585\pi$
$181$	1.86705	−	0.679550i	0.138777	−	0.0505105i	0.410475	+	0.911872i	$0.365363\pi$
$182$	−8.13963	−	14.0983i	−0.603350	−	1.04503i
$183$	−0.543113	+	0.940699i	−0.0401481	+	0.0695385i
$184$	−1.42132	+	8.06069i	−0.104781	+	0.594242i
$185$	4.08374	−	3.42666i	0.300242	−	0.251933i
$186$	−2.98056	−	2.50099i	−0.218545	−	0.183381i
$187$	−1.16001	−	6.57873i	−0.0848281	−	0.481084i
$188$	9.91359	+	3.60825i	0.723023	+	0.263159i
$189$	6.47214			0.470779
$190$		0			0
$191$	−20.9259			−1.51415			−0.757074	−	0.653329i	$-0.773372\pi$
$191$	−20.9259			−1.51415			−0.757074	+	0.653329i	$0.773372\pi$
$192$	0.415780	+	0.151331i	0.0300063	+	0.0109214i
$193$	1.35251	+	7.67046i	0.0973558	+	0.552132i	0.994000	+	0.109380i	$0.0348866\pi$
$193$	1.35251	+	7.67046i	0.0973558	+	0.552132i	−0.896644	+	0.442752i	$0.854002\pi$
$194$	−5.99377	−	5.02937i	−0.430328	−	0.361088i
$195$	−1.95190	+	1.63784i	−0.139778	+	0.117288i
$196$	−0.112673	+	0.639001i	−0.00804808	+	0.0456430i
$197$	−0.912571	+	1.58062i	−0.0650180	+	0.112614i	−0.896702	−	0.442635i	$-0.854044\pi$
$197$	−0.912571	+	1.58062i	−0.0650180	+	0.112614i	0.831684	+	0.555249i	$0.187377\pi$
$198$	−2.73691	−	4.74047i	−0.194504	−	0.336890i
$199$	−2.21697	+	0.806913i	−0.157157	+	0.0572005i	−0.419401	−	0.907801i	$-0.637760\pi$
$199$	−2.21697	+	0.806913i	−0.157157	+	0.0572005i	0.262244	+	0.965002i	$0.415538\pi$
$200$	−3.95164	+	1.43828i	−0.279423	+	0.101702i
$201$	−0.591266	−	1.02410i	−0.0417047	−	0.0722346i
$202$	−2.69244	+	4.66343i	−0.189439	+	0.328118i
$203$	2.00458	−	11.3685i	0.140694	−	0.797914i
$204$	1.15996	−	0.973325i	0.0812137	−	0.0681464i
$205$	2.38294	+	1.99952i	0.166431	+	0.139653i
$206$	0.815222	+	4.62336i	0.0567992	+	0.322124i
$207$	21.5685	+	7.85029i	1.49911	+	0.545633i
$208$	−6.45965			−0.447896
$209$		0			0
$210$	−0.994078			−0.0685979
$211$	0.339276	+	0.123486i	0.0233567	+	0.00850116i	0.353672	−	0.935369i	$-0.384933\pi$
$211$	0.339276	+	0.123486i	0.0233567	+	0.00850116i	−0.330315	+	0.943871i	$0.607155\pi$
$212$	0.653400	+	3.70561i	0.0448757	+	0.254503i
$213$	−0.0191303	−	0.0160522i	−0.00131079	−	0.00109988i
$214$	−12.2853	+	10.3086i	−0.839804	+	0.704679i
$215$	0.967024	−	5.48427i	0.0659505	−	0.374024i
$216$	1.28408	−	2.22409i	0.0873705	−	0.151330i
$217$	11.0806	+	19.1921i	0.752199	+	1.30285i
$218$	13.2504	−	4.82275i	0.897431	−	0.326638i
$219$	−2.89764	+	1.05466i	−0.195804	+	0.0712670i
$220$	0.870091	+	1.50704i	0.0586615	+	0.101605i
$221$	−11.0533	+	19.1449i	−0.743525	+	1.28782i
$222$	−0.459446	+	2.60565i	−0.0308360	+	0.174879i
$223$	13.8260	−	11.6014i	0.925860	−	0.776889i	−0.0492095	−	0.998788i	$-0.515670\pi$
$223$	13.8260	−	11.6014i	0.925860	−	0.776889i	0.975069	+	0.221900i	$0.0712258\pi$
$224$	−1.93054	−	1.61992i	−0.128990	−	0.108235i
$225$	2.04774	+	11.6133i	0.136516	+	0.774220i
$226$	−11.9551	−	4.35131i	−0.795243	−	0.289445i
$227$	12.2845			0.815349			0.407675	−	0.913127i	$-0.366340\pi$
$227$	12.2845			0.815349			0.407675	+	0.913127i	$0.366340\pi$
$228$		0			0
$229$	6.79174			0.448811			0.224405	−	0.974496i	$-0.427956\pi$
$229$	6.79174			0.448811			0.224405	+	0.974496i	$0.427956\pi$
$230$	−6.85684	−	2.49568i	−0.452126	−	0.164561i
$231$	−0.377964	−	2.14354i	−0.0248682	−	0.141035i
$232$	−3.50898	−	2.94438i	−0.230376	−	0.193308i
$233$	16.4158	−	13.7745i	1.07544	−	0.902399i	0.0799033	−	0.996803i	$-0.474539\pi$
$233$	16.4158	−	13.7745i	1.07544	−	0.902399i	0.995534	+	0.0944036i	$0.0300944\pi$
$234$	−3.14552	+	17.8391i	−0.205629	+	1.16618i
$235$	−4.70254	+	8.14503i	−0.306760	+	0.531323i
$236$	−1.42081	−	2.46091i	−0.0924867	−	0.160192i
$237$	−3.79674	+	1.38190i	−0.246625	+	0.0897641i
$238$	−8.10447	+	2.94979i	−0.525335	+	0.191206i
$239$	5.91881	+	10.2517i	0.382856	+	0.663126i	0.991469	−	0.130341i	$-0.0416071\pi$
$239$	5.91881	+	10.2517i	0.382856	+	0.663126i	−0.608613	+	0.793467i	$0.708274\pi$
$240$	−0.197226	+	0.341606i	−0.0127309	+	0.0220506i
$241$	−3.77621	+	21.4159i	−0.243247	+	1.37952i	0.581282	+	0.813702i	$0.302551\pi$
$241$	−3.77621	+	21.4159i	−0.243247	+	1.37952i	−0.824529	+	0.565819i	$0.808560\pi$
$242$	5.50766	−	4.62148i	0.354046	−	0.297080i
$243$	−8.36827	−	7.02181i	−0.536825	−	0.450449i
$244$	−0.426298	−	2.41765i	−0.0272909	−	0.154774i
$245$	−0.543567	−	0.197842i	−0.0347272	−	0.0126397i
$246$	−1.54390			−0.0984353
$247$		0			0
$248$	8.79360			0.558394
$249$	−5.87243	−	2.13739i	−0.372150	−	0.135452i
$250$	−1.42503	−	8.08172i	−0.0901265	−	0.511133i
$251$	18.1101	+	15.1962i	1.14310	+	0.959173i	0.999536	−	0.0304681i	$-0.00969981\pi$
$251$	18.1101	+	15.1962i	1.14310	+	0.959173i	0.143562	+	0.989641i	$0.454144\pi$
$252$	−5.41368	+	4.54262i	−0.341030	+	0.286158i
$253$	2.77440	−	15.7344i	0.174425	−	0.989212i
$254$	3.58721	−	6.21323i	0.225082	−	0.389853i
$255$	0.674959	+	1.16906i	0.0422676	+	0.0732096i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	0.867777	−	0.315845i	0.0541304	−	0.0197019i	−0.314813	−	0.949154i	$-0.601942\pi$
$257$	0.867777	−	0.315845i	0.0541304	−	0.0197019i	0.368943	+	0.929452i	$0.379720\pi$
$258$	1.38197	+	2.39364i	0.0860374	+	0.149021i
$259$	7.53498	−	13.0510i	0.468201	−	0.810948i
$260$	0.999992	−	5.67123i	0.0620168	−	0.351715i
$261$	−9.83997	+	8.25671i	−0.609079	+	0.511078i
$262$	2.69851	+	2.26432i	0.166714	+	0.139890i
$263$	0.750103	+	4.25405i	0.0462534	+	0.262316i	0.999161	−	0.0409434i	$-0.0130363\pi$
$263$	0.750103	+	4.25405i	0.0462534	+	0.262316i	−0.952908	+	0.303259i	$0.901925\pi$
$264$	−0.811597	−	0.295397i	−0.0499504	−	0.0181804i
$265$	−3.35449			−0.206064
$266$		0			0
$267$	−0.826407			−0.0505753
$268$	2.51143	+	0.914086i	0.153410	+	0.0558367i
$269$	−1.87459	−	10.6314i	−0.114296	−	0.648205i	−0.987096	−	0.160127i	$-0.948809\pi$
$269$	−1.87459	−	10.6314i	−0.114296	−	0.648205i	0.872800	−	0.488077i	$-0.162302\pi$
$270$	1.75385	+	1.47166i	0.106736	+	0.0895622i
$271$	0.618384	−	0.518886i	0.0375642	−	0.0315201i	−0.623812	−	0.781574i	$-0.714417\pi$
$271$	0.618384	−	0.518886i	0.0375642	−	0.0315201i	0.661376	+	0.750054i	$0.269973\pi$
$272$	−0.594269	+	3.37027i	−0.0360329	+	0.204353i
$273$	−3.60149	+	6.23796i	−0.217972	+	0.377539i
$274$	−5.50177	−	9.52935i	−0.332374	−	0.575689i
$275$	7.71355	−	2.80750i	0.465145	−	0.169299i
$276$	3.40317	−	1.23865i	0.204847	−	0.0745582i
$277$	4.57434	+	7.92300i	0.274846	+	0.476047i	0.970096	−	0.242721i	$-0.0780399\pi$
$277$	4.57434	+	7.92300i	0.274846	+	0.476047i	−0.695250	+	0.718768i	$0.744707\pi$
$278$	10.8793	−	18.8435i	0.652497	−	1.13016i
$279$	4.28203	−	24.2846i	0.256359	−	1.45388i
$280$	1.72106	−	1.44414i	0.102853	−	0.0863041i
$281$	16.2522	+	13.6372i	0.969525	+	0.813528i	0.982476	−	0.186388i	$-0.0596780\pi$
$281$	16.2522	+	13.6372i	0.969525	+	0.813528i	−0.0129508	+	0.999916i	$0.504122\pi$
$282$	−0.810574	−	4.59699i	−0.0482690	−	0.273747i
$283$	−4.87687	−	1.77503i	−0.289900	−	0.105515i	0.192977	−	0.981203i	$-0.438186\pi$
$283$	−4.87687	−	1.77503i	−0.289900	−	0.105515i	−0.482876	+	0.875688i	$0.660408\pi$
$284$	0.0564404			0.00334912
$285$		0			0
$286$	12.6092			0.745596
$287$	8.26329	+	3.00759i	0.487766	+	0.177532i
$288$	0.486949	+	2.76162i	0.0286937	+	0.162730i
$289$	−4.05095	−	3.39915i	−0.238291	−	0.199950i
$290$	3.12822	−	2.62489i	0.183696	−	0.154139i
$291$	−0.601166	+	3.40938i	−0.0352409	+	0.199861i
$292$	3.48459	−	6.03548i	0.203920	−	0.353200i
$293$	8.78298	+	15.2126i	0.513107	+	0.888728i	0.999884	+	0.0152018i	$0.00483906\pi$
$293$	8.78298	+	15.2126i	0.513107	+	0.888728i	−0.486777	+	0.873526i	$0.661828\pi$
$294$	0.269782	−	0.0981928i	0.0157340	−	0.00572672i
$295$	2.38050	−	0.866431i	0.138598	−	0.0504456i
$296$	−2.98990	−	5.17866i	−0.173784	−	0.301003i
$297$	−2.50651	+	4.34140i	−0.145442	+	0.251914i
$298$	−2.49872	+	14.1710i	−0.144747	+	0.820902i
$299$	−40.5027	+	33.9858i	−2.34233	+	1.96545i
$300$	1.42535	+	1.19601i	0.0822928	+	0.0690519i
$301$	−2.73367	−	15.5034i	−0.157566	−	0.893602i
$302$	11.6585	+	4.24336i	0.670873	+	0.244178i
$303$	2.38261			0.136877
$304$		0			0
$305$	2.18857			0.125317
$306$	9.01803	+	3.28230i	0.515527	+	0.187636i
$307$	−3.74531	−	21.2407i	−0.213756	−	1.21227i	−0.883052	−	0.469275i	$-0.844515\pi$
$307$	−3.74531	−	21.2407i	−0.213756	−	1.21227i	0.669296	−	0.742996i	$-0.266596\pi$
$308$	3.76840	+	3.16206i	0.214725	+	0.180175i
$309$	1.59125	−	1.33521i	0.0905228	−	0.0759576i
$310$	−1.36130	+	7.72032i	−0.0773167	+	0.438485i
$311$	1.28684	−	2.22887i	0.0729701	−	0.126388i	−0.827232	−	0.561861i	$-0.810086\pi$
$311$	1.28684	−	2.22887i	0.0729701	−	0.126388i	0.900202	+	0.435473i	$0.143419\pi$
$312$	1.42908	+	2.47524i	0.0809057	+	0.140133i
$313$	4.87126	−	1.77299i	0.275340	−	0.100216i	−0.200660	−	0.979661i	$-0.564309\pi$
$313$	4.87126	−	1.77299i	0.275340	−	0.100216i	0.476000	+	0.879445i	$0.342086\pi$
$314$	−0.424008	+	0.154326i	−0.0239282	+	0.00870914i
$315$	−3.15011	−	5.45616i	−0.177489	−	0.307420i
$316$	4.56581	−	7.90821i	0.256847	−	0.444872i
$317$	−3.51745	+	19.9484i	−0.197559	+	1.12042i	0.711167	+	0.703023i	$0.248167\pi$
$317$	−3.51745	+	19.9484i	−0.197559	+	1.12042i	−0.908727	+	0.417392i	$0.862944\pi$
$318$	1.27538	−	1.07017i	0.0715199	−	0.0600123i
$319$	6.84948	+	5.74740i	0.383498	+	0.321793i
$320$	−0.154806	−	0.877948i	−0.00865391	−	0.0490788i
$321$	6.66797	+	2.42694i	0.372170	+	0.135459i
$322$	−20.6275			−1.14953
$323$		0			0
$324$	7.27636			0.404242
$325$	−25.5262	−	9.29077i	−1.41594	−	0.515359i
$326$	0.0120259	+	0.0682021i	0.000666051	+	0.00377736i
$327$	−4.77942	−	4.01041i	−0.264302	−	0.221776i
$328$	2.67298	−	2.24289i	0.147590	−	0.123843i
$329$	−4.61680	+	26.1832i	−0.254532	+	1.44353i
$330$	0.384983	−	0.666811i	0.0211926	−	0.0367067i
$331$	10.6640	+	18.4706i	0.586146	+	1.01523i	0.994731	+	0.102515i	$0.0326889\pi$
$331$	10.6640	+	18.4706i	0.586146	+	1.01523i	−0.408585	+	0.912720i	$0.633978\pi$
$332$	13.2721	−	4.83066i	0.728402	−	0.265117i
$333$	−15.7574	+	5.73523i	−0.863502	+	0.314289i
$334$	1.08685	+	1.88248i	0.0594699	+	0.103005i
$335$	−1.19130	+	2.06340i	−0.0650879	+	0.112736i
$336$	−0.193630	+	1.09813i	−0.0105634	+	0.0599080i
$337$	−17.4103	+	14.6089i	−0.948397	+	0.795799i	−0.979027	−	0.203731i	$-0.934693\pi$
$337$	−17.4103	+	14.6089i	−0.948397	+	0.795799i	0.0306300	+	0.999531i	$0.490249\pi$
$338$	−22.0062	−	18.4654i	−1.19698	−	1.00439i
$339$	0.977498	+	5.54367i	0.0530904	+	0.301091i
$340$	−2.86692	−	1.04347i	−0.155481	−	0.0565904i
$341$	−17.1650			−0.929538
$342$		0			0
$343$	−19.2762			−1.04082
$344$	−5.86997	−	2.13649i	−0.316487	−	0.115192i
$345$	0.560642	+	3.17956i	0.0301840	+	0.171182i
$346$	12.9073	+	10.8305i	0.693901	+	0.582252i
$347$	−3.77549	+	3.16801i	−0.202679	+	0.170068i	−0.738478	−	0.674278i	$-0.764455\pi$
$347$	−3.77549	+	3.16801i	−0.202679	+	0.170068i	0.535799	+	0.844346i	$0.320011\pi$
$348$	−0.351945	+	1.99598i	−0.0188662	+	0.106996i
$349$	−13.0808	+	22.6565i	−0.700197	+	1.21278i	0.268201	+	0.963363i	$0.413571\pi$
$349$	−13.0808	+	22.6565i	−0.700197	+	1.21278i	−0.968397	+	0.249413i	$0.919762\pi$
$350$	−5.29892	−	9.17799i	−0.283239	−	0.490584i
$351$	15.5889	−	5.67391i	0.832076	−	0.302851i
$352$	1.83427	−	0.667620i	0.0977669	−	0.0355842i
$353$	−1.35407	−	2.34531i	−0.0720697	−	0.124828i	0.827739	−	0.561114i	$-0.189627\pi$
$353$	−1.35407	−	2.34531i	−0.0720697	−	0.124828i	−0.899808	+	0.436286i	$0.856294\pi$
$354$	−0.628656	+	1.08886i	−0.0334127	+	0.0578724i
$355$	−0.00873730	+	0.0495517i	−0.000463728	+	0.00262993i
$356$	1.43077	−	1.20056i	0.0758308	−	0.0636296i
$357$	2.92328	+	2.45292i	0.154716	+	0.129822i
$358$	−3.29333	−	18.6774i	−0.174058	−	0.987131i
$359$	8.74856	+	3.18422i	0.461731	+	0.168056i	0.562403	−	0.826863i	$-0.309877\pi$
$359$	8.74856	+	3.18422i	0.461731	+	0.168056i	−0.100672	+	0.994920i	$0.532099\pi$
$360$	−2.49994			−0.131759
$361$		0			0
$362$	1.98687			0.104428
$363$	−2.98935	−	1.08803i	−0.156900	−	0.0571069i
$364$	−2.82686	−	16.0319i	−0.148168	−	0.840302i
$365$	4.75940	+	3.99361i	0.249119	+	0.209035i
$366$	−0.832097	+	0.698212i	−0.0434944	+	0.0364961i
$367$	1.34654	−	7.63661i	0.0702889	−	0.398628i	−0.929283	−	0.369369i	$-0.879574\pi$
$367$	1.34654	−	7.63661i	0.0702889	−	0.398628i	0.999572	−	0.0292594i	$-0.00931488\pi$
$368$	−4.09252	+	7.08845i	−0.213337	+	0.369511i
$369$	−4.89242	−	8.47393i	−0.254689	−	0.441135i
$370$	5.00944	−	1.82329i	0.260429	−	0.0947882i
$371$	−8.91088	+	3.24329i	−0.462630	+	0.168383i
$372$	−1.94542	−	3.36957i	−0.100866	−	0.174704i
$373$	12.5062	−	21.6614i	0.647546	−	1.12158i	−0.336161	−	0.941804i	$-0.609129\pi$
$373$	12.5062	−	21.6614i	0.647546	−	1.12158i	0.983707	−	0.179778i	$-0.0575379\pi$
$374$	1.16001	−	6.57873i	0.0599825	−	0.340178i
$375$	−2.78153	+	2.33398i	−0.143638	+	0.120526i
$376$	8.08163	+	6.78129i	0.416778	+	0.349718i
$377$	−5.13814	−	29.1398i	−0.264628	−	1.50078i
$378$	6.08182	+	2.21360i	0.312815	+	0.113855i
$379$	19.1802			0.985222			0.492611	−	0.870250i	$-0.336043\pi$
$379$	19.1802			0.985222			0.492611	+	0.870250i	$0.336043\pi$
$380$		0			0
$381$	−3.17442			−0.162630
$382$	−19.6639	−	7.15709i	−1.00609	−	0.366189i
$383$	−0.839274	−	4.75976i	−0.0428849	−	0.243212i	0.955828	−	0.293925i	$-0.0949617\pi$
$383$	−0.839274	−	4.75976i	−0.0428849	−	0.243212i	−0.998713	+	0.0507130i	$0.983851\pi$
$384$	0.338947	+	0.284410i	0.0172968	+	0.0145137i
$385$	−3.35950	+	2.81895i	−0.171216	+	0.143667i
$386$	−1.35251	+	7.67046i	−0.0688409	+	0.390416i
$387$	−8.75856	+	15.1703i	−0.445223	+	0.771149i
$388$	−3.91216	−	6.77606i	−0.198610	−	0.344002i
$389$	−20.4187	+	7.43180i	−1.03527	+	0.376807i	−0.803085	−	0.595865i	$-0.796809\pi$
$389$	−20.4187	+	7.43180i	−1.03527	+	0.376807i	−0.232184	+	0.972672i	$0.574587\pi$
$390$	−2.39436	+	0.871476i	−0.121243	+	0.0441289i
$391$	14.0057	+	24.2585i	0.708297	+	1.22681i
$392$	−0.324429	+	0.561928i	−0.0163862	+	0.0283817i
$393$	0.270656	−	1.53497i	0.0136528	−	0.0774288i
$394$	−1.39814	+	1.17318i	−0.0704373	+	0.0591039i
$395$	6.23618	+	5.23278i	0.313776	+	0.263290i
$396$	−0.950519	−	5.39066i	−0.0477654	−	0.270891i
$397$	−11.0076	−	4.00643i	−0.552454	−	0.201077i	0.0506824	−	0.998715i	$-0.483860\pi$
$397$	−11.0076	−	4.00643i	−0.552454	−	0.201077i	−0.603137	+	0.797638i	$0.706083\pi$
$398$	−2.35926			−0.118259
$399$		0			0
$400$	−4.20524			−0.210262
$401$	11.1000	+	4.04006i	0.554306	+	0.201751i	0.603959	−	0.797016i	$-0.293589\pi$
$401$	11.1000	+	4.04006i	0.554306	+	0.201751i	−0.0496526	+	0.998767i	$0.515811\pi$
$402$	−0.205345	−	1.16457i	−0.0102417	−	0.0580833i
$403$	43.5141	+	36.5127i	2.16759	+	1.81882i
$404$	−4.12505	+	3.46133i	−0.205229	+	0.172208i
$405$	−1.12642	+	6.38827i	−0.0559724	+	0.317435i
$406$	5.77195	−	9.99731i	0.286457	−	0.496158i
$407$	5.83625	+	10.1087i	0.289292	+	0.501069i
$408$	1.42291	−	0.517895i	0.0704444	−	0.0256396i
$409$	−23.7425	+	8.64157i	−1.17399	+	0.427298i	−0.854076	−	0.520148i	$-0.825877\pi$
$409$	−23.7425	+	8.64157i	−1.17399	+	0.427298i	−0.319916	+	0.947446i	$0.603655\pi$
$410$	1.55535	+	2.69395i	0.0768133	+	0.133045i
$411$	−2.43433	+	4.21639i	−0.120077	+	0.207979i
$412$	−0.815222	+	4.62336i	−0.0401631	+	0.227776i
$413$	5.48587	−	4.60319i	0.269942	−	0.226508i
$414$	17.5828	+	14.7537i	0.864147	+	0.725105i
$415$	2.18646	+	12.4000i	0.107329	+	0.608694i
$416$	−6.07009	−	2.20933i	−0.297610	−	0.108321i
$417$	−9.62739			−0.471455
$418$		0			0
$419$	31.6143			1.54446			0.772229	−	0.635344i	$-0.219142\pi$
$419$	31.6143			1.54446			0.772229	+	0.635344i	$0.219142\pi$
$420$	−0.934128	−	0.339995i	−0.0455808	−	0.0165900i
$421$	−0.380241	−	2.15645i	−0.0185318	−	0.105099i	0.974139	−	0.225950i	$-0.0725487\pi$
$421$	−0.380241	−	2.15645i	−0.0185318	−	0.105099i	−0.992671	+	0.120851i	$0.961438\pi$
$422$	0.276581	+	0.232079i	0.0134637	+	0.0112974i
$423$	22.6627	−	19.0163i	1.10190	−	0.924603i
$424$	−0.653400	+	3.70561i	−0.0317319	+	0.179961i
$425$	−7.19572	+	12.4633i	−0.349044	+	0.604561i
$426$	−0.0124864	−	0.0216271i	−0.000604968	−	0.00104784i
$427$	5.81372	−	2.11602i	0.281346	−	0.102401i
$428$	−15.0701	+	5.48507i	−0.728441	+	0.265131i
$429$	−2.78955	−	4.83164i	−0.134681	−	0.233274i
$430$	2.78444	−	4.82278i	0.134277	−	0.232575i
$431$	−0.313212	+	1.77631i	−0.0150869	+	0.0855620i	−0.991422	−	0.130703i	$-0.958276\pi$
$431$	−0.313212	+	1.77631i	−0.0150869	+	0.0855620i	0.976335	+	0.216265i	$0.0693876\pi$
$432$	1.96732	−	1.65078i	0.0946529	−	0.0794232i
$433$	−5.03470	−	4.22461i	−0.241952	−	0.203022i	0.513746	−	0.857943i	$-0.328258\pi$
$433$	−5.03470	−	4.22461i	−0.241952	−	0.203022i	−0.755698	+	0.654921i	$0.772702\pi$
$434$	3.84825	+	21.8245i	0.184722	+	1.04761i
$435$	−1.69788	−	0.617978i	−0.0814071	−	0.0296298i
$436$	14.1008			0.675305
$437$		0			0
$438$	−3.08361			−0.147340
$439$	8.57995	+	3.12285i	0.409499	+	0.149045i	0.538552	−	0.842592i	$-0.318972\pi$
$439$	8.57995	+	3.12285i	0.409499	+	0.149045i	−0.129053	+	0.991638i	$0.541194\pi$
$440$	0.302179	+	1.71374i	0.0144058	+	0.0816995i
$441$	1.39385	+	1.16958i	0.0663740	+	0.0556944i
$442$	−16.9346	+	14.2098i	−0.805499	+	0.675894i
$443$	−4.76987	+	27.0513i	−0.226624	+	1.28525i	0.632933	+	0.774206i	$0.281851\pi$
$443$	−4.76987	+	27.0513i	−0.226624	+	1.28525i	−0.859557	+	0.511040i	$0.829260\pi$
$444$	−1.32292	+	2.29137i	−0.0627830	+	0.108743i
$445$	0.832538	+	1.44200i	0.0394661	+	0.0683572i
$446$	16.9601	−	6.17299i	0.803086	−	0.292299i
$447$	5.98289	−	2.17759i	0.282981	−	0.102997i
$448$	−1.26007	−	2.18251i	−0.0595329	−	0.103114i
$449$	3.78646	−	6.55835i	0.178694	−	0.309508i	−0.762739	−	0.646706i	$-0.776146\pi$
$449$	3.78646	−	6.55835i	0.178694	−	0.309508i	0.941434	+	0.337199i	$0.109479\pi$
$450$	−2.04774	+	11.6133i	−0.0965313	+	0.547456i
$451$	−5.21762	+	4.37810i	−0.245688	+	0.206157i
$452$	−9.74590	−	8.17778i	−0.458409	−	0.384651i
$453$	−0.953248	−	5.40614i	−0.0447875	−	0.254003i
$454$	11.5436	+	4.20154i	0.541769	+	0.197188i
$455$	14.5128			0.680372
$456$		0			0
$457$	−21.7675			−1.01824			−0.509120	−	0.860696i	$-0.670029\pi$
$457$	−21.7675			−1.01824			−0.509120	+	0.860696i	$0.670029\pi$
$458$	6.38215	+	2.32291i	0.298218	+	0.108543i
$459$	−1.52618	−	8.65538i	−0.0712359	−	0.403999i
$460$	−5.58974	−	4.69035i	−0.260623	−	0.218689i
$461$	9.14993	−	7.67770i	0.426155	−	0.357586i	−0.404344	−	0.914607i	$-0.632500\pi$
$461$	9.14993	−	7.67770i	0.426155	−	0.357586i	0.830499	+	0.557021i	$0.188056\pi$
$462$	0.377964	−	2.14354i	0.0175845	−	0.0997266i
$463$	4.37685	−	7.58093i	0.203410	−	0.352316i	−0.746215	−	0.665705i	$-0.768131\pi$
$463$	4.37685	−	7.58093i	0.203410	−	0.352316i	0.949625	+	0.313389i	$0.101464\pi$
$464$	−2.29032	−	3.96695i	−0.106326	−	0.184161i
$465$	3.25947	−	1.18635i	0.151154	−	0.0550157i
$466$	20.1370	−	7.32927i	0.932829	−	0.339522i
$467$	−14.6784	−	25.4238i	−0.679236	−	1.17647i	−0.975211	−	0.221276i	$-0.928978\pi$
$467$	−14.6784	−	25.4238i	−0.679236	−	1.17647i	0.295975	−	0.955196i	$-0.404355\pi$
$468$	−9.05716	+	15.6875i	−0.418667	+	0.725153i
$469$	−1.16958	+	6.63304i	−0.0540064	+	0.306285i
$470$	−7.20470	+	6.04547i	−0.332328	+	0.278857i
$471$	0.152940	+	0.128332i	0.00704708	+	0.00591321i
$472$	−0.493441	−	2.79845i	−0.0227125	−	0.128809i
$473$	11.4581	+	4.17041i	0.526845	+	0.191756i
$474$	−4.04041			−0.185582
$475$		0			0
$476$	−8.62460			−0.395308
$477$	9.91534	+	3.60889i	0.453992	+	0.165240i
$478$	2.05558	+	11.6578i	0.0940202	+	0.533215i
$479$	−19.0519	−	15.9864i	−0.870503	−	0.730438i	0.0937013	−	0.995600i	$-0.470130\pi$
$479$	−19.0519	−	15.9864i	−0.870503	−	0.730438i	−0.964204	+	0.265162i	$0.914575\pi$
$480$	−0.302168	+	0.253549i	−0.0137920	+	0.0115729i
$481$	6.70758	−	38.0406i	0.305839	−	1.73450i
$482$	−10.8732	+	18.8329i	−0.495259	+	0.857813i
$483$	4.56346	+	7.90414i	0.207645	+	0.359651i
$484$	6.75614	−	2.45904i	0.307097	−	0.111774i
$485$	6.55465	−	2.38570i	0.297631	−	0.108329i
$486$	−5.46200	−	9.46046i	−0.247761	−	0.429135i
$487$	4.26883	−	7.39383i	0.193439	−	0.335046i	−0.752949	−	0.658079i	$-0.771369\pi$
$487$	4.26883	−	7.39383i	0.193439	−	0.335046i	0.946388	+	0.323033i	$0.104702\pi$
$488$	0.426298	−	2.41765i	0.0192976	−	0.109442i
$489$	0.0234735	−	0.0196966i	0.00106151	−	0.000890711i
$490$	−0.443120	−	0.371822i	−0.0200181	−	0.0167972i
$491$	−2.00385	−	11.3644i	−0.0904325	−	0.512868i	−0.996052	−	0.0887760i	$-0.971704\pi$
$491$	−2.00385	−	11.3644i	−0.0904325	−	0.512868i	0.905619	−	0.424092i	$-0.139407\pi$
$492$	−1.45079	−	0.528044i	−0.0654066	−	0.0238061i
$493$	−15.6762			−0.706019
$494$		0			0
$495$	4.87986			0.219333
$496$	8.26329	+	3.00759i	0.371032	+	0.135045i
$497$	0.0246994	+	0.140077i	0.00110792	+	0.00628332i
$498$	−4.78725	−	4.01698i	−0.214522	−	0.180005i
$499$	−22.6818	+	19.0323i	−1.01538	+	0.852004i	−0.989040	−	0.147649i	$-0.952829\pi$
$499$	−22.6818	+	19.0323i	−1.01538	+	0.852004i	−0.0263392	+	0.999653i	$0.508385\pi$
$500$	1.42503	−	8.08172i	0.0637291	−	0.361426i
$501$	0.480893	−	0.832931i	0.0214847	−	0.0372126i
$502$	11.8205	+	20.4737i	0.527575	+	0.913787i
$503$	−5.51437	+	2.00707i	−0.245874	+	0.0894907i	−0.462017	−	0.886871i	$-0.652874\pi$
$503$	−5.51437	+	2.00707i	−0.245874	+	0.0894907i	0.216144	+	0.976362i	$0.430652\pi$
$504$	−6.64087	+	2.41708i	−0.295808	+	0.107665i
$505$	−2.40028	−	4.15741i	−0.106811	−	0.185002i
$506$	7.98855	−	13.8366i	0.355135	−	0.615111i
$507$	−2.20719	+	12.5176i	−0.0980246	+	0.555925i
$508$	5.49592	−	4.61163i	0.243842	−	0.204608i
$509$	19.5868	+	16.4352i	0.868167	+	0.728479i	0.963711	−	0.266946i	$-0.0860146\pi$
$509$	19.5868	+	16.4352i	0.868167	+	0.728479i	−0.0955439	+	0.995425i	$0.530459\pi$
$510$	0.234411	+	1.32941i	0.0103799	+	0.0588673i
$511$	16.5041	+	6.00702i	0.730100	+	0.265735i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	0.923469			0.0407325
$515$	−3.93286	−	1.43144i	−0.173303	−	0.0630770i
$516$	0.479952	+	2.72194i	0.0211287	+	0.119827i
$517$	−15.7753	−	13.2370i	−0.693795	−	0.582163i
$518$	11.5443	−	9.68679i	0.507226	−	0.425613i
$519$	1.29458	−	7.34193i	0.0568258	−	0.322275i
$520$	2.87936	−	4.98720i	0.126268	−	0.218703i
$521$	−7.01661	−	12.1531i	−0.307403	−	0.532438i	0.670390	−	0.742009i	$-0.266127\pi$
$521$	−7.01661	−	12.1531i	−0.307403	−	0.532438i	−0.977794	+	0.209571i	$0.932793\pi$
$522$	−12.0705	+	4.39330i	−0.528312	+	0.192290i
$523$	29.2041	−	10.6294i	1.27701	−	0.464793i	0.387566	−	0.921842i	$-0.373316\pi$
$523$	29.2041	−	10.6294i	1.27701	−	0.464793i	0.889442	+	0.457049i	$0.151094\pi$
$524$	1.76133	+	3.05071i	0.0769439	+	0.133271i
$525$	−2.34458	+	4.06093i	−0.102326	+	0.177233i
$526$	−0.750103	+	4.25405i	−0.0327061	+	0.185485i
$527$	23.0533	−	19.3441i	1.00422	−	0.842640i
$528$	−0.661620	−	0.555165i	−0.0287933	−	0.0241605i
$529$	7.63963	+	43.3265i	0.332158	+	1.88376i
$530$	−3.15219	−	1.14730i	−0.136922	−	0.0498356i
$531$	−7.96853			−0.345805
$532$		0			0
$533$	22.5398			0.976307
$534$	−0.776569	−	0.282648i	−0.0336054	−	0.0122314i
$535$	−2.48266	−	14.0799i	−0.107335	−	0.608727i
$536$	2.04734	+	1.71792i	0.0884315	+	0.0742029i
$537$	−6.42830	+	5.39398i	−0.277402	+	0.232768i
$538$	1.87459	−	10.6314i	0.0808195	−	0.458350i
$539$	0.633283	−	1.09688i	0.0272774	−	0.0472459i
$540$	1.14475	+	1.98276i	0.0492620	+	0.0853243i
$541$	−2.72142	+	0.990517i	−0.117003	+	0.0425857i	−0.399858	−	0.916577i	$-0.630941\pi$
$541$	−2.72142	+	0.990517i	−0.117003	+	0.0425857i	0.282855	+	0.959163i	$0.408718\pi$
$542$	0.758561	−	0.276094i	0.0325830	−	0.0118592i
$543$	−0.439559	−	0.761338i	−0.0188633	−	0.0326722i
$544$	−1.71113	+	2.96376i	−0.0733641	+	0.127070i
$545$	−2.18289	+	12.3798i	−0.0935045	+	0.530291i
$546$	−5.51780	+	4.62999i	−0.236140	+	0.198145i
$547$	−23.2771	−	19.5318i	−0.995257	−	0.835120i	−0.00893713	−	0.999960i	$-0.502845\pi$
$547$	−23.2771	−	19.5318i	−0.995257	−	0.835120i	−0.986320	+	0.164840i	$0.947289\pi$
$548$	−1.91075	−	10.8364i	−0.0816230	−	0.462907i
$549$	−6.46906	−	2.35455i	−0.276093	−	0.100490i
$550$	8.20859			0.350015
$551$		0			0
$552$	3.62158			0.154145
$553$	21.6252	+	7.87092i	0.919595	+	0.334705i
$554$	1.58865	+	9.00970i	0.0674954	+	0.382785i
$555$	−1.80690	−	1.51617i	−0.0766988	−	0.0643579i
$556$	16.6681	−	13.9862i	0.706883	−	0.593146i
$557$	−1.06518	+	6.04093i	−0.0451331	+	0.255963i	−0.999023	−	0.0441943i	$-0.985928\pi$
$557$	−1.06518	+	6.04093i	−0.0451331	+	0.255963i	0.953890	+	0.300157i	$0.0970390\pi$
$558$	12.3296	−	21.3555i	0.521955	−	0.904052i
$559$	−20.1757	−	34.9454i	−0.853342	−	1.47803i
$560$	2.11120	−	0.768413i	0.0892144	−	0.0324714i
$561$	−2.77750	+	1.01093i	−0.117266	+	0.0426813i
$562$	10.6079	+	18.3734i	0.447466	+	0.775034i
$563$	−14.0958	+	24.4147i	−0.594069	+	1.02896i	0.399609	+	0.916686i	$0.369146\pi$
$563$	−14.0958	+	24.4147i	−0.594069	+	1.02896i	−0.993678	+	0.112271i	$0.964187\pi$
$564$	0.810574	−	4.59699i	0.0341313	−	0.193568i
$565$	8.68839	−	7.29042i	0.365523	−	0.306710i
$566$	−3.97566	−	3.33597i	−0.167109	−	0.140221i
$567$	3.18427	+	18.0589i	0.133727	+	0.758403i
$568$	0.0530366	+	0.0193038i	0.00222537	+	0.000809967i
$569$	42.1145			1.76553			0.882766	−	0.469812i	$-0.155678\pi$
$569$	42.1145			1.76553			0.882766	+	0.469812i	$0.155678\pi$
$570$		0			0
$571$	0.166927			0.00698566			0.00349283	−	0.999994i	$-0.498888\pi$
$571$	0.166927			0.00698566			0.00349283	+	0.999994i	$0.498888\pi$
$572$	11.8487	+	4.31259i	0.495421	+	0.180318i
$573$	1.60780	+	9.11830i	0.0671669	+	0.380922i
$574$	6.73629	+	5.65242i	0.281167	+	0.235927i
$575$	−26.3673	+	22.1248i	−1.09959	+	0.922668i
$576$	−0.486949	+	2.76162i	−0.0202895	+	0.115068i
$577$	9.98157	−	17.2886i	0.415538	−	0.719733i	−0.579947	−	0.814655i	$-0.696927\pi$
$577$	9.98157	−	17.2886i	0.415538	−	0.719733i	0.995485	+	0.0949212i	$0.0302599\pi$
$578$	−2.64407	−	4.57966i	−0.109979	−	0.190489i
$579$	3.23842	−	1.17869i	0.134584	−	0.0489846i
$580$	3.83733	−	1.39668i	0.159337	−	0.0579938i
$581$	17.7972	+	30.8256i	0.738350	+	1.27886i
$582$	−1.73099	+	2.99816i	−0.0717517	+	0.124278i
$583$	1.27543	−	7.23332i	0.0528229	−	0.299573i
$584$	5.33870	−	4.47970i	0.220917	−	0.185371i
$585$	−12.3707	−	10.3802i	−0.511464	−	0.429169i
$586$	3.05030	+	17.2991i	0.126007	+	0.714619i
$587$	−9.53227	−	3.46946i	−0.393439	−	0.143200i	0.137722	−	0.990471i	$-0.456022\pi$
$587$	−9.53227	−	3.46946i	−0.393439	−	0.143200i	−0.531161	+	0.847271i	$0.678244\pi$
$588$	0.287096			0.0118397
$589$		0			0
$590$	2.53328			0.104293
$591$	0.758857	+	0.276201i	0.0312152	+	0.0113614i
$592$	−1.03838	−	5.88895i	−0.0426772	−	0.242034i
$593$	5.70945	+	4.79080i	0.234459	+	0.196734i	0.752446	−	0.658654i	$-0.228874\pi$
$593$	5.70945	+	4.79080i	0.234459	+	0.196734i	−0.517987	+	0.855389i	$0.673318\pi$
$594$	−3.84019	+	3.22230i	−0.157565	+	0.132213i
$595$	1.33514	−	7.57195i	0.0547353	−	0.310420i
$596$	−7.19479	+	12.4617i	−0.294710	+	0.510452i
$597$	0.521942	+	0.904030i	0.0213617	+	0.0369995i
$598$	−49.6839	+	18.0835i	−2.03173	+	0.739487i
$599$	−5.98717	+	2.17915i	−0.244629	+	0.0890377i	−0.461425	−	0.887179i	$-0.652662\pi$
$599$	−5.98717	+	2.17915i	−0.244629	+	0.0890377i	0.216796	+	0.976217i	$0.430439\pi$
$600$	0.930333	+	1.61138i	0.0379807	+	0.0657845i
$601$	0.873153	−	1.51235i	0.0356166	−	0.0616898i	−0.847668	−	0.530528i	$-0.821994\pi$
$601$	0.873153	−	1.51235i	0.0356166	−	0.0616898i	0.883284	+	0.468838i	$0.155327\pi$
$602$	2.73367	−	15.5034i	0.111416	−	0.631872i
$603$	5.74120	−	4.81744i	0.233800	−	0.196181i
$604$	9.50413	+	7.97491i	0.386717	+	0.324494i
$605$	1.11301	+	6.31222i	0.0452504	+	0.256628i
$606$	2.23892	+	0.814900i	0.0909499	+	0.0331031i
$607$	−32.1612			−1.30538			−0.652691	−	0.757624i	$-0.726360\pi$
$607$	−32.1612			−1.30538			−0.652691	+	0.757624i	$0.726360\pi$
$608$		0			0
$609$	−5.10775			−0.206977
$610$	2.05658	+	0.748534i	0.0832685	+	0.0303073i
$611$	11.8338	+	67.1128i	0.478744	+	2.71509i
$612$	7.35157	+	6.16870i	0.297170	+	0.249355i
$613$	9.77815	−	8.20484i	0.394936	−	0.331390i	−0.423597	−	0.905851i	$-0.639233\pi$
$613$	9.77815	−	8.20484i	0.394936	−	0.331390i	0.818532	+	0.574461i	$0.194788\pi$
$614$	3.74531	−	21.2407i	0.151148	−	0.857204i
$615$	0.688186	−	1.19197i	0.0277503	−	0.0480650i
$616$	2.45965	+	4.26024i	0.0991021	+	0.171650i
$617$	1.58172	−	0.575699i	0.0636776	−	0.0231768i	−0.309985	−	0.950741i	$-0.600324\pi$
$617$	1.58172	−	0.575699i	0.0636776	−	0.0231768i	0.373663	+	0.927565i	$0.378102\pi$
$618$	1.95195	−	0.710452i	0.0785190	−	0.0285786i
$619$	−15.7642	−	27.3045i	−0.633618	−	1.09746i	−0.986806	−	0.161906i	$-0.948236\pi$
$619$	−15.7642	−	27.3045i	−0.633618	−	1.09746i	0.353188	−	0.935552i	$-0.385098\pi$
$620$	−3.91971	+	6.78914i	−0.157419	+	0.272658i
$621$	3.65017	−	20.7011i	0.146476	−	0.830708i
$622$	1.97156	−	1.65433i	0.0790522	−	0.0663326i
$623$	3.60576	+	3.02559i	0.144462	+	0.121218i
$624$	0.496314	+	2.81474i	0.0198685	+	0.112680i
$625$	−12.8835	−	4.68919i	−0.515338	−	0.187568i
$626$	5.18389			0.207190
$627$		0			0
$628$	−0.451220			−0.0180056
$629$	−19.2303	−	6.99924i	−0.766761	−	0.279078i
$630$	−1.09402	−	6.20451i	−0.0435869	−	0.247194i
$631$	−24.3343	−	20.4189i	−0.968734	−	0.812865i	0.0136174	−	0.999907i	$-0.495665\pi$
$631$	−24.3343	−	20.4189i	−0.968734	−	0.812865i	−0.982352	+	0.187043i	$0.940110\pi$
$632$	6.99522	−	5.86969i	0.278255	−	0.233484i
$633$	0.0277406	−	0.157325i	0.00110259	−	0.00625309i
$634$	−10.1281	+	17.5423i	−0.402237	+	0.696696i
$635$	3.19797	+	5.53904i	0.126907	+	0.219810i
$636$	1.56449	−	0.569427i	0.0620360	−	0.0225792i
$637$	−3.93863	+	1.43354i	−0.156054	+	0.0567991i
$638$	4.47068	+	7.74345i	0.176996	+	0.306566i
$639$	0.0791358	−	0.137067i	0.00313056	−	0.00542230i
$640$	0.154806	−	0.877948i	0.00611924	−	0.0347039i
$641$	30.9817	−	25.9967i	1.22370	−	1.02681i	0.225080	−	0.974340i	$-0.427736\pi$
$641$	30.9817	−	25.9967i	1.22370	−	1.02681i	0.998623	−	0.0524681i	$-0.0167088\pi$
$642$	5.43578	+	4.56116i	0.214533	+	0.180015i
$643$	−4.53278	−	25.7067i	−0.178756	−	1.01377i	−0.933719	−	0.358006i	$-0.883457\pi$
$643$	−4.53278	−	25.7067i	−0.178756	−	1.01377i	0.754964	−	0.655767i	$-0.227654\pi$
$644$	−19.3835	−	7.05502i	−0.763817	−	0.278007i
$645$	−2.46402			−0.0970208
$646$		0			0
$647$	−48.7713			−1.91740			−0.958699	−	0.284423i	$-0.908198\pi$
$647$	−48.7713			−1.91740			−0.958699	+	0.284423i	$0.908198\pi$
$648$	6.83754	+	2.48866i	0.268604	+	0.0977639i
$649$	0.963192	+	5.46253i	0.0378086	+	0.214423i
$650$	−20.8091	−	17.4609i	−0.816201	−	0.684874i
$651$	7.51146	−	6.30286i	0.294397	−	0.247029i
$652$	−0.0120259	+	0.0682021i	−0.000470969	+	0.00267100i
$653$	21.5915	−	37.3976i	0.844942	−	1.46348i	−0.0407298	−	0.999170i	$-0.512968\pi$
$653$	21.5915	−	37.3976i	0.844942	−	1.46348i	0.885672	−	0.464312i	$-0.153698\pi$
$654$	−3.11954	−	5.40321i	−0.121984	−	0.211282i
$655$	−2.95103	+	1.07409i	−0.115306	+	0.0419680i
$656$	3.27889	−	1.19342i	0.128019	−	0.0465952i
$657$	−9.77157	−	16.9249i	−0.381225	−	0.660302i
$658$	−13.2935	+	23.0251i	−0.518236	+	0.897612i
$659$	2.47915	−	14.0600i	0.0965741	−	0.547699i	−0.897680	−	0.440649i	$-0.854748\pi$
$659$	2.47915	−	14.0600i	0.0965741	−	0.547699i	0.994254	−	0.107050i	$-0.0341405\pi$
$660$	0.589829	−	0.494925i	0.0229591	−	0.0192649i
$661$	−27.3858	−	22.9794i	−1.06519	−	0.893797i	−0.0705779	−	0.997506i	$-0.522484\pi$
$661$	−27.3858	−	22.9794i	−1.06519	−	0.893797i	−0.994608	+	0.103709i	$0.966929\pi$
$662$	3.70357	+	21.0040i	0.143943	+	0.816342i
$663$	9.19148	+	3.34542i	0.356967	+	0.129925i
$664$	14.1239			0.548114
$665$		0			0
$666$	−16.7687			−0.649774
$667$	−35.2317	−	12.8233i	−1.36418	−	0.496519i
$668$	0.377460	+	2.14068i	0.0146044	+	0.0828255i
$669$	−6.11752	−	5.13321i	−0.236517	−	0.198461i
$670$	−1.82518	+	1.53151i	−0.0705130	+	0.0591674i
$671$	−0.832128	+	4.71923i	−0.0321240	+	0.182184i
$672$	−0.557537	+	0.965682i	−0.0215074	+	0.0372520i
$673$	5.17870	+	8.96976i	0.199624	+	0.345759i	0.948407	−	0.317057i	$-0.102695\pi$
$673$	5.17870	+	8.96976i	0.199624	+	0.345759i	−0.748783	+	0.662816i	$0.769361\pi$
$674$	−21.3568	+	7.77325i	−0.822635	+	0.299414i
$675$	10.1484	−	3.69372i	0.390613	−	0.142172i
$676$	−14.3635	−	24.8784i	−0.552444	−	0.956861i
$677$	−5.35854	+	9.28126i	−0.205945	+	0.356708i	−0.950434	−	0.310928i	$-0.899360\pi$
$677$	−5.35854	+	9.28126i	−0.205945	+	0.356708i	0.744488	+	0.667636i	$0.232694\pi$
$678$	−0.977498	+	5.54367i	−0.0375406	+	0.212903i
$679$	15.1052	−	12.6748i	0.579684	−	0.486413i
$680$	−2.33714	−	1.96109i	−0.0896251	−	0.0752044i
$681$	−0.943853	−	5.35286i	−0.0361685	−	0.205122i
$682$	−16.1298	−	5.87078i	−0.617644	−	0.224804i
$683$	−0.122930			−0.00470377			−0.00235188	−	0.999997i	$-0.500749\pi$
$683$	−0.122930			−0.00470377			−0.00235188	+	0.999997i	$0.500749\pi$
$684$		0			0
$685$	9.80957			0.374804
$686$	−18.1137	−	6.59287i	−0.691586	−	0.251717i
$687$	−0.521830	−	2.95944i	−0.0199090	−	0.112910i
$688$	−4.78524	−	4.01529i	−0.182436	−	0.153082i
$689$	−18.6197	+	15.6237i	−0.709352	+	0.595217i
$690$	−0.560642	+	3.17956i	−0.0213433	+	0.121044i
$691$	12.6407	−	21.8944i	0.480876	−	0.832902i	−0.518883	−	0.854845i	$-0.673652\pi$
$691$	12.6407	−	21.8944i	0.480876	−	0.832902i	0.999759	+	0.0219435i	$0.00698538\pi$
$692$	8.42464	+	14.5919i	0.320257	+	0.554701i
$693$	12.9629	−	4.71811i	0.492420	−	0.179226i
$694$	−4.63133	+	1.68566i	−0.175803	+	0.0639870i
$695$	9.69881	+	16.7988i	0.367897	+	0.637216i
$696$	−1.01338	+	1.75523i	−0.0384122	+	0.0665319i
$697$	2.07360	−	11.7600i	0.0785431	−	0.445440i
$698$	−20.0409	+	16.8163i	−0.758558	+	0.636506i
$699$	−7.26341	−	6.09472i	−0.274727	−	0.230524i
$700$	−1.84029	−	10.4368i	−0.0695566	−	0.394475i
$701$	4.86091	+	1.76923i	0.183594	+	0.0668227i	0.432181	−	0.901787i	$-0.357744\pi$
$701$	4.86091	+	1.76923i	0.183594	+	0.0668227i	−0.248587	+	0.968609i	$0.579966\pi$
$702$	16.5894			0.626127
$703$		0			0
$704$	1.95199			0.0735684
$705$	3.91044	+	1.42328i	0.147276	+	0.0536039i
$706$	−0.470263	−	2.66699i	−0.0176986	−	0.100374i
$707$	−10.3957	−	8.72306i	−0.390972	−	0.328064i
$708$	−0.963156	+	0.808184i	−0.0361976	+	0.0303734i
$709$	−5.20783	+	29.5351i	−0.195584	+	1.10921i	0.716000	+	0.698100i	$0.245971\pi$
$709$	−5.20783	+	29.5351i	−0.195584	+	1.10921i	−0.911584	+	0.411113i	$0.865140\pi$
$710$	−0.0251581	+	0.0435750i	−0.000944165	+	0.00163534i
$711$	−12.8036	−	22.1764i	−0.480171	−	0.831680i
$712$	1.75510	−	0.638805i	0.0657752	−	0.0239402i
$713$	67.6353	−	24.6172i	2.53296	−	0.921923i
$714$	1.90803	+	3.30481i	0.0714064	+	0.123680i
$715$	−5.62048	+	9.73496i	−0.210194	+	0.364067i
$716$	3.29333	−	18.6774i	0.123077	−	0.698007i
$717$	4.01232	−	3.36674i	0.149843	−	0.125733i
$718$	7.13189	+	5.98437i	0.266160	+	0.223335i
$719$	−3.94238	−	22.3583i	−0.147026	−	0.833825i	−0.965718	−	0.259593i	$-0.916412\pi$
$719$	−3.94238	−	22.3583i	−0.147026	−	0.833825i	0.818692	−	0.574233i	$-0.194699\pi$
$720$	−2.34918	−	0.855031i	−0.0875487	−	0.0318651i
$721$	−11.8313			−0.440620
$722$		0			0
$723$	9.62195			0.357844
$724$	1.86705	+	0.679550i	0.0693883	+	0.0252553i
$725$	−3.34494	−	18.9701i	−0.124228	−	0.704531i
$726$	−2.43694	−	2.04483i	−0.0904433	−	0.0758909i
$727$	28.0324	−	23.5220i	1.03967	−	0.872383i	0.0476958	−	0.998862i	$-0.484812\pi$
$727$	28.0324	−	23.5220i	1.03967	−	0.872383i	0.991969	+	0.126479i	$0.0403677\pi$
$728$	2.82686	−	16.0319i	0.104771	−	0.594184i
$729$	8.49781	−	14.7186i	0.314734	−	0.545135i
$730$	3.10648	+	5.38058i	0.114976	+	0.199144i
$731$	−20.0886	+	7.31164i	−0.743002	+	0.270431i
$732$	−1.02072	+	0.371511i	−0.0377268	+	0.0137314i
$733$	−10.5761	−	18.3184i	−0.390637	−	0.676604i	0.601896	−	0.798574i	$-0.294412\pi$
$733$	−10.5761	−	18.3184i	−0.390637	−	0.676604i	−0.992534	+	0.121970i	$0.961079\pi$
$734$	3.87721	−	6.71552i	0.143110	−	0.247875i
$735$	−0.0444442	+	0.252056i	−0.00163935	+	0.00929721i
$736$	−6.27010	+	5.26124i	−0.231119	+	0.193932i
$737$	−3.99638	−	3.35336i	−0.147209	−	0.123523i
$738$	−1.69912	−	9.63619i	−0.0625455	−	0.354713i
$739$	−45.3934	−	16.5218i	−1.66982	−	0.607766i	−0.677962	−	0.735097i	$-0.737137\pi$
$739$	−45.3934	−	16.5218i	−1.66982	−	0.607766i	−0.991860	+	0.127331i	$0.959359\pi$
$740$	5.33094			0.195969
$741$		0			0
$742$	−9.48276			−0.348123
$743$	29.9385	+	10.8967i	1.09834	+	0.399761i	0.826702	−	0.562639i	$-0.190214\pi$
$743$	29.9385	+	10.8967i	1.09834	+	0.399761i	0.271633	+	0.962401i	$0.412436\pi$
$744$	−0.675639	−	3.83174i	−0.0247701	−	0.140478i
$745$	−9.82696	−	8.24579i	−0.360032	−	0.302103i
$746$	19.1606	−	16.0776i	0.701519	−	0.588644i
$747$	6.87762	−	39.0049i	0.251639	−	1.42711i
$748$	3.34011	−	5.78523i	0.122126	−	0.211529i
$749$	−20.2081	−	35.0015i	−0.738390	−	1.27893i
$750$	−3.41205	+	1.24189i	−0.124591	+	0.0453472i
$751$	−38.5239	+	14.0215i	−1.40576	+	0.511653i	−0.929881	−	0.367860i	$-0.880091\pi$
$751$	−38.5239	+	14.0215i	−1.40576	+	0.511653i	−0.475875	+	0.879513i	$0.657868\pi$
$752$	5.27491	+	9.13641i	0.192356	+	0.333171i
$753$	5.23015	−	9.05888i	0.190597	−	0.330124i
$754$	5.13814	−	29.1398i	0.187120	−	1.06121i
$755$	−8.47285	+	7.10956i	−0.308359	+	0.258744i
$756$	4.95794	+	4.16021i	0.180319	+	0.151305i
$757$	−2.22643	−	12.6267i	−0.0809211	−	0.458927i	−0.998162	−	0.0605946i	$-0.980700\pi$
$757$	−2.22643	−	12.6267i	−0.0809211	−	0.458927i	0.917241	−	0.398332i	$-0.130411\pi$
$758$	18.0235	+	6.56002i	0.654644	+	0.238271i
$759$	−7.06929			−0.256599
$760$		0			0
$761$	35.6382			1.29188			0.645942	−	0.763386i	$-0.276465\pi$
$761$	35.6382			1.29188			0.645942	+	0.763386i	$0.276465\pi$
$762$	−2.98298	−	1.08571i	−0.108062	−	0.0393313i
$763$	6.17077	+	34.9962i	0.223397	+	1.26695i
$764$	−16.0302	−	13.4509i	−0.579952	−	0.486638i
$765$	−6.55386	+	5.49934i	−0.236955	+	0.198829i
$766$	0.839274	−	4.75976i	0.0303242	−	0.171977i
$767$	9.17792	−	15.8966i	0.331395	−	0.573994i
$768$	0.221232	+	0.383185i	0.00798301	+	0.0138270i
$769$	5.23786	−	1.90642i	0.188882	−	0.0687474i	−0.245847	−	0.969309i	$-0.579066\pi$
$769$	5.23786	−	1.90642i	0.188882	−	0.0687474i	0.434729	+	0.900561i	$0.356844\pi$
$770$	−4.12103	+	1.49993i	−0.148512	+	0.0540539i
$771$	−0.204301	−	0.353859i	−0.00735771	−	0.0127439i
$772$	−3.89440	+	6.74529i	−0.140162	+	0.242768i
$773$	6.32286	−	35.8587i	0.227418	−	1.28975i	−0.630592	−	0.776115i	$-0.717188\pi$
$773$	6.32286	−	35.8587i	0.227418	−	1.28975i	0.858009	−	0.513634i	$-0.171701\pi$
$774$	−13.4189	+	11.2598i	−0.482332	+	0.404725i
$775$	28.3277	+	23.7698i	1.01756	+	0.853836i
$776$	−1.35868	−	7.70545i	−0.0487737	−	0.276609i
$777$	−6.26579	−	2.28056i	−0.224784	−	0.0818146i
$778$	−21.7291			−0.779027
$779$		0			0
$780$	−2.54802			−0.0912339
$781$	−0.103527	−	0.0376807i	−0.00370448	−	0.00134832i
$782$	4.86412	+	27.5858i	0.173940	+	0.986465i
$783$	9.01161	+	7.56164i	0.322049	+	0.270231i
$784$	−0.497055	+	0.417079i	−0.0177520	+	0.0148957i
$785$	0.0698515	−	0.396148i	0.00249311	−	0.0141391i
$786$	0.779323	−	1.34983i	0.0277975	−	0.0481467i
$787$	−15.9523	−	27.6302i	−0.568638	−	0.984909i	−0.996701	−	0.0811606i	$-0.974137\pi$
$787$	−15.9523	−	27.6302i	−0.568638	−	0.984909i	0.428063	−	0.903749i	$-0.359196\pi$
$788$	−1.71507	+	0.624235i	−0.0610969	+	0.0222375i
$789$	1.79603	−	0.653702i	0.0639404	−	0.0232724i
$790$	4.07038	+	7.05010i	0.144818	+	0.250831i
$791$	16.0311	−	27.7667i	0.570001	−	0.987271i
$792$	0.950519	−	5.39066i	0.0337752	−	0.191549i
$793$	12.1480	−	10.1934i	0.431389	−	0.361978i
$794$	−8.97345	−	7.52962i	−0.318456	−	0.267216i
$795$	0.257735	+	1.46169i	0.00914092	+	0.0518408i
$796$	−2.21697	−	0.806913i	−0.0785786	−	0.0286003i
$797$	−2.09165			−0.0740900			−0.0370450	−	0.999314i	$-0.511794\pi$
$797$	−2.09165			−0.0740900			−0.0370450	+	0.999314i	$0.511794\pi$
$798$		0			0
$799$	36.1042			1.27728
$800$	−3.95164	−	1.43828i	−0.139711	−	0.0508508i
$801$	−0.909494	−	5.15800i	−0.0321354	−	0.182249i
$802$	9.04878	+	7.59283i	0.319523	+	0.268112i
$803$	−10.4211	+	8.74432i	−0.367752	+	0.308580i
$804$	0.205345	−	1.16457i	0.00724194	−	0.0410711i
$805$	9.19462	−	15.9256i	0.324068	−	0.561302i
$806$	28.4018	+	49.1934i	1.00041	+	1.73276i
$807$	−4.48849	+	1.63368i	−0.158002	+	0.0575081i
$808$	−5.06012	+	1.84173i	−0.178015	+	0.0647920i
$809$	15.0360	+	26.0430i	0.528636	+	0.915625i	0.999442	+	0.0333880i	$0.0106297\pi$
$809$	15.0360	+	26.0430i	0.528636	+	0.915625i	−0.470806	+	0.882237i	$0.656037\pi$
$810$	−3.24341	+	5.61775i	−0.113962	+	0.197387i
$811$	0.143015	−	0.811080i	0.00502195	−	0.0284809i	−0.982194	−	0.187870i	$-0.939841\pi$
$811$	0.143015	−	0.811080i	0.00502195	−	0.0284809i	0.987216	+	0.159390i	$0.0509526\pi$
$812$	8.84314	−	7.42027i	0.310333	−	0.260401i
$813$	−0.273612	−	0.229588i	−0.00959601	−	0.00805201i
$814$	2.02691	+	11.4952i	0.0710431	+	0.402905i
$815$	−0.0580162	−	0.0211162i	−0.00203222	−	0.000739667i
$816$	1.51423			0.0530085
$817$		0			0
$818$	−25.2663			−0.883414
$819$	−42.8977	−	15.6135i	−1.49897	−	0.545579i
$820$	0.540168	+	3.06344i	0.0188635	+	0.106980i
$821$	5.90715	+	4.95669i	0.206161	+	0.172990i	0.740022	−	0.672583i	$-0.234815\pi$
$821$	5.90715	+	4.95669i	0.206161	+	0.172990i	−0.533861	+	0.845572i	$0.679259\pi$
$822$	−3.72962	+	3.12952i	−0.130085	+	0.109155i
$823$	−4.30856	+	24.4351i	−0.150187	+	0.851753i	0.812868	+	0.582448i	$0.197905\pi$
$823$	−4.30856	+	24.4351i	−0.150187	+	0.851753i	−0.963055	+	0.269305i	$0.913206\pi$
$824$	−2.34734	+	4.06571i	−0.0817734	+	0.141636i
$825$	−1.81600	−	3.14540i	−0.0632250	−	0.109509i
$826$	6.72941	−	2.44931i	0.234146	−	0.0852222i
$827$	−9.98750	+	3.63515i	−0.347299	+	0.126407i	−0.509779	−	0.860305i	$-0.670273\pi$
$827$	−9.98750	+	3.63515i	−0.347299	+	0.126407i	0.162480	+	0.986712i	$0.448051\pi$
$828$	11.4764	+	19.8776i	0.398831	+	0.690795i
$829$	−10.7355	+	18.5944i	−0.372859	+	0.645811i	−0.990004	−	0.141039i	$-0.954956\pi$
$829$	−10.7355	+	18.5944i	−0.372859	+	0.645811i	0.617145	+	0.786849i	$0.288289\pi$
$830$	−2.18646	+	12.4000i	−0.0758932	+	0.430412i
$831$	3.10092	−	2.60198i	0.107570	−	0.0902617i
$832$	−4.94838	−	4.15218i	−0.171554	−	0.143951i
$833$	0.385597	+	2.18683i	0.0133601	+	0.0757691i
$834$	−9.04679	−	3.29276i	−0.313265	−	0.114019i
$835$	−1.93784			−0.0670617
$836$		0			0
$837$	−22.5834			−0.780595
$838$	29.7077	+	10.8127i	1.02624	+	0.373519i
$839$	−8.47818	−	48.0821i	−0.292699	−	1.65998i	−0.676409	−	0.736526i	$-0.736465\pi$
$839$	−8.47818	−	48.0821i	−0.292699	−	1.65998i	0.383710	−	0.923454i	$-0.374646\pi$
$840$	−0.761508	−	0.638981i	−0.0262745	−	0.0220469i
$841$	−6.14191	+	5.15368i	−0.211790	+	0.177713i
$842$	0.380241	−	2.15645i	0.0131040	−	0.0743163i
$843$	4.69360	−	8.12955i	0.161656	−	0.279997i
$844$	0.180525	+	0.312679i	0.00621393	+	0.0107628i
$845$	24.0655	−	8.75912i	0.827877	−	0.301323i
$846$	27.7999	−	10.1184i	0.955782	−	0.347876i
$847$	9.05960	+	15.6917i	0.311292	+	0.539173i
$848$	−1.88139	+	3.25866i	−0.0646072	+	0.111903i
$849$	−0.398752	+	2.26143i	−0.0136851	+	0.0776122i
$850$	−11.0245	+	9.25064i	−0.378137	+	0.317294i
$851$	−37.4939	−	31.4612i	−1.28528	−	1.07847i
$852$	−0.00433648	−	0.0245934i	−0.000148565	−	0.000842557i
$853$	19.7439	+	7.18620i	0.676019	+	0.246051i	0.657137	−	0.753771i	$-0.271767\pi$
$853$	19.7439	+	7.18620i	0.676019	+	0.246051i	0.0188817	+	0.999822i	$0.493989\pi$
$854$	6.18683			0.211709
$855$		0			0
$856$	−16.0373			−0.548143
$857$	−30.2949	−	11.0265i	−1.03485	−	0.376656i	−0.231927	−	0.972733i	$-0.574503\pi$
$857$	−30.2949	−	11.0265i	−1.03485	−	0.376656i	−0.802928	+	0.596077i	$0.796725\pi$
$858$	−0.968800	−	5.49434i	−0.0330743	−	0.187574i
$859$	−31.5820	−	26.5005i	−1.07756	−	0.904184i	−0.0818486	−	0.996645i	$-0.526082\pi$
$859$	−31.5820	−	26.5005i	−1.07756	−	0.904184i	−0.995716	+	0.0924604i	$0.970527\pi$
$860$	4.26600	−	3.57960i	0.145469	−	0.122063i
$861$	0.675639	−	3.83174i	0.0230257	−	0.130585i
$862$	−0.901858	+	1.56206i	−0.0307174	+	0.0532041i
$863$	21.0325	+	36.4293i	0.715953	+	1.24007i	0.962591	+	0.270960i	$0.0873410\pi$
$863$	21.0325	+	36.4293i	0.715953	+	1.24007i	−0.246637	+	0.969108i	$0.579326\pi$
$864$	2.41328	−	0.878362i	0.0821014	−	0.0298825i
$865$	−14.1151	+	5.13748i	−0.479929	+	0.174680i
$866$	−3.28616	−	5.69180i	−0.111668	−	0.193415i
$867$	−1.16990	+	2.02633i	−0.0397320	+	0.0688179i
$868$	−3.84825	+	21.8245i	−0.130618	+	0.740772i
$869$	−13.6546	+	11.4576i	−0.463201	+	0.388671i
$870$	−1.38412	−	1.16142i	−0.0469262	−	0.0393758i
$871$	2.99788	+	17.0018i	0.101579	+	0.576085i
$872$	13.2504	+	4.82275i	0.448715	+	0.163319i
$873$	−21.9412			−0.742596
$874$		0			0
$875$	20.6813			0.699156
$876$	−2.89764	−	1.05466i	−0.0979022	−	0.0356335i
$877$	−0.409031	−	2.31973i	−0.0138120	−	0.0783316i	0.977123	−	0.212677i	$-0.0682181\pi$
$877$	−0.409031	−	2.31973i	−0.0138120	−	0.0783316i	−0.990935	+	0.134345i	$0.957107\pi$
$878$	6.99444	+	5.86903i	0.236051	+	0.198070i
$879$	5.95393	−	4.99594i	0.200821	−	0.168509i
$880$	−0.302179	+	1.71374i	−0.0101865	+	0.0577703i
$881$	−11.5677	+	20.0358i	−0.389725	+	0.675024i	−0.992412	−	0.122954i	$-0.960763\pi$
$881$	−11.5677	+	20.0358i	−0.389725	+	0.675024i	0.602687	+	0.797977i	$0.294097\pi$
$882$	0.909774	+	1.57577i	0.0306337	+	0.0530591i
$883$	−6.58904	+	2.39821i	−0.221739	+	0.0807063i	−0.450501	−	0.892776i	$-0.648754\pi$
$883$	−6.58904	+	2.39821i	−0.221739	+	0.0807063i	0.228762	+	0.973482i	$0.426532\pi$
$884$	−20.7734	+	7.56090i	−0.698685	+	0.254301i
$885$	−0.560441	−	0.970712i	−0.0188390	−	0.0326301i
$886$	−13.7343	+	23.7885i	−0.461413	+	0.799191i
$887$	−8.49648	+	48.1860i	−0.285284	+	1.61793i	0.418985	+	0.907993i	$0.362386\pi$
$887$	−8.49648	+	48.1860i	−0.285284	+	1.61793i	−0.704269	+	0.709933i	$0.748725\pi$
$888$	−2.02683	+	1.70071i	−0.0680160	+	0.0570722i
$889$	13.8505	+	11.6220i	0.464532	+	0.389789i
$890$	0.289137	+	1.63978i	0.00969190	+	0.0549655i
$891$	−13.3468	−	4.85784i	−0.447135	−	0.162744i
$892$	18.0486			0.604312
$893$		0			0
$894$	6.36686			0.212940
$895$	15.8879	+	5.78274i	0.531075	+	0.193296i
$896$	−0.437619	−	2.48186i	−0.0146198	−	0.0829131i
$897$	17.9210	+	15.0375i	0.598363	+	0.502086i
$898$	5.80120	−	4.86778i	0.193589	−	0.162440i
$899$	−6.99461	+	39.6684i	−0.233283	+	1.32302i
$900$	−5.89623	+	10.2126i	−0.196541	+	0.340419i
$901$	6.43860	+	11.1520i	0.214501	+	0.371527i
$902$	−6.40036	+	2.32954i	−0.213109	+	0.0775652i
$903$	−6.54544	+	2.38235i	−0.217819	+	0.0792795i
$904$	−6.36119	−	11.0179i	−0.211570	−	0.366450i
$905$	−0.885639	+	1.53397i	−0.0294396	+	0.0509910i
$906$	0.953248	−	5.40614i	0.0316695	−	0.179607i
$907$	0.913922	−	0.766872i	0.0303463	−	0.0254636i	−0.627488	−	0.778626i	$-0.715917\pi$
$907$	0.913922	−	0.766872i	0.0303463	−	0.0254636i	0.657835	+	0.753162i	$0.271473\pi$
$908$	9.41045	+	7.89631i	0.312297	+	0.262048i
$909$	2.62216	+	14.8710i	0.0869714	+	0.493239i
$910$	13.6376	+	4.96368i	0.452082	+	0.164544i
$911$	−37.6344			−1.24688			−0.623442	−	0.781870i	$-0.714266\pi$
$911$	−37.6344			−1.24688			−0.623442	+	0.781870i	$0.714266\pi$
$912$		0			0
$913$	−27.5697			−0.912424
$914$	−20.4547	−	7.44492i	−0.676583	−	0.246256i
$915$	−0.168154	−	0.953649i	−0.00555900	−	0.0315267i
$916$	5.20277	+	4.36565i	0.171905	+	0.144245i
$917$	−6.80064	+	5.70642i	−0.224577	+	0.188442i
$918$	1.52618	−	8.65538i	0.0503714	−	0.285670i
$919$	−13.4738	+	23.3373i	−0.444460	+	0.769828i	−0.998014	−	0.0629854i	$-0.979938\pi$
$919$	−13.4738	+	23.3373i	−0.444460	+	0.769828i	0.553554	+	0.832813i	$0.313271\pi$
$920$	−3.64845	−	6.31929i	−0.120286	−	0.208341i
$921$	−8.96769	+	3.26397i	−0.295495	+	0.107551i
$922$	11.2241	−	4.08522i	0.369644	−	0.134540i
$923$	0.182293	+	0.315740i	0.00600023	+	0.0103927i
$924$	1.08831	−	1.88500i	0.0358026	−	0.0620119i
$925$	4.36664	−	24.7645i	0.143574	−	0.814251i
$926$	6.70573	−	5.62677i	0.220364	−	0.184907i
$927$	10.0849	+	8.46226i	0.331232	+	0.277937i
$928$	−0.795421	−	4.51105i	−0.0261110	−	0.148083i
$929$	16.7782	+	6.10677i	0.550476	+	0.200357i	0.602258	−	0.798302i	$-0.294268\pi$
$929$	16.7782	+	6.10677i	0.550476	+	0.200357i	−0.0517822	+	0.998658i	$0.516490\pi$
$930$	3.46866			0.113742
$931$		0			0
$932$	21.4294			0.701942
$933$	−1.07009	−	0.389479i	−0.0350330	−	0.0127510i
$934$	−5.09776	−	28.9108i	−0.166804	−	0.945992i
$935$	4.56207	+	3.82803i	0.149195	+	0.125190i
$936$	−13.8764	+	11.6437i	−0.453563	+	0.380585i
$937$	−4.13848	+	23.4705i	−0.135198	+	0.766748i	0.839523	+	0.543324i	$0.182834\pi$
$937$	−4.13848	+	23.4705i	−0.135198	+	0.766748i	−0.974721	+	0.223424i	$0.928277\pi$
$938$	−3.36768	+	5.83300i	−0.109959	+	0.190454i
$939$	−1.14684	−	1.98639i	−0.0374257	−	0.0648232i
$940$	−8.83788	+	3.21672i	−0.288260	+	0.104918i
$941$	19.1369	−	6.96526i	0.623845	−	0.227061i	−0.0107051	−	0.999943i	$-0.503408\pi$
$941$	19.1369	−	6.96526i	0.623845	−	0.227061i	0.634550	+	0.772882i	$0.281185\pi$
$942$	0.0998242	+	0.172901i	0.00325245	+	0.00563341i
$943$	14.2801	−	24.7339i	0.465025	−	0.805446i
$944$	0.493441	−	2.79845i	0.0160601	−	0.0910816i
$945$	−4.41996	+	3.70879i	−0.143781	+	0.120647i
$946$	9.34074	+	7.83781i	0.303694	+	0.254829i
$947$	−0.593164	−	3.36400i	−0.0192753	−	0.109315i	0.973652	−	0.228038i	$-0.0732311\pi$
$947$	−0.593164	−	3.36400i	−0.0192753	−	0.109315i	−0.992927	+	0.118723i	$0.962120\pi$
$948$	−3.79674	−	1.38190i	−0.123312	−	0.0448820i
$949$	45.0184			1.46136
$950$		0			0
$951$	8.96261			0.290633
$952$	−8.10447	−	2.94979i	−0.262667	−	0.0956031i
$953$	3.08040	+	17.4698i	0.0997841	+	0.565904i	0.993176	+	0.116625i	$0.0372077\pi$
$953$	3.08040	+	17.4698i	0.0997841	+	0.565904i	−0.893392	+	0.449278i	$0.851681\pi$
$954$	8.08306	+	6.78249i	0.261699	+	0.219591i
$955$	14.2908	−	11.9914i	0.462439	−	0.388032i
$956$	−2.05558	+	11.6578i	−0.0664823	+	0.377040i
$957$	1.97811	−	3.42619i	0.0639434	−	0.110753i
$958$	−12.4352	−	21.5385i	−0.401764	−	0.695876i
$959$	26.0582	−	9.48441i	0.841463	−	0.306268i
$960$	−0.370664	+	0.134911i	−0.0119631	+	0.00435422i
$961$	−23.1637	−	40.1208i	−0.747217	−	1.29422i
$962$	19.3137	−	33.4523i	0.622699	−	1.07855i
$963$	−7.80933	+	44.2889i	−0.251652	+	1.42719i
$964$	−16.6586	+	13.9783i	−0.536539	+	0.450209i
$965$	−5.31914	−	4.46329i	−0.171229	−	0.143678i
$966$	1.58487	+	8.98826i	0.0509924	+	0.289192i
$967$	40.1767	+	14.6231i	1.29200	+	0.470248i	0.894381	−	0.447305i	$-0.147616\pi$
$967$	40.1767	+	14.6231i	1.29200	+	0.470248i	0.397614	+	0.917553i	$0.369838\pi$
$968$	7.18974			0.231087
$969$		0			0
$970$	6.97531			0.223964
$971$	49.8495	+	18.1437i	1.59975	+	0.582260i	0.979375	−	0.202049i	$-0.0647602\pi$
$971$	49.8495	+	18.1437i	1.59975	+	0.582260i	0.620370	+	0.784309i	$0.286982\pi$
$972$	−1.89693	−	10.7580i	−0.0608441	−	0.345064i
$973$	42.0060	+	35.2472i	1.34665	+	1.12997i
$974$	6.54023	−	5.48790i	0.209562	−	0.175844i
$975$	−2.08712	+	11.8367i	−0.0668414	+	0.379076i
$976$	1.22747	−	2.12605i	0.0392905	−	0.0680532i
$977$	−6.16319	−	10.6750i	−0.197178	−	0.341522i	0.750434	−	0.660945i	$-0.229844\pi$
$977$	−6.16319	−	10.6750i	−0.197178	−	0.341522i	−0.947612	+	0.319423i	$0.896511\pi$
$978$	0.0287945	−	0.0104803i	0.000920746	−	0.000335124i
$979$	−3.42594	+	1.24694i	−0.109494	+	0.0398524i
$980$	−0.289226	−	0.500954i	−0.00923899	−	0.0160024i
$981$	19.7709	−	34.2442i	0.631236	−	1.09333i
$982$	2.00385	−	11.3644i	0.0639454	−	0.362652i
$983$	24.7091	−	20.7334i	0.788097	−	0.661292i	−0.157177	−	0.987571i	$-0.550239\pi$
$983$	24.7091	−	20.7334i	0.788097	−	0.661292i	0.945274	+	0.326279i	$0.105795\pi$
$984$	−1.18269	−	0.992398i	−0.0377029	−	0.0316365i
$985$	−0.282543	−	1.60238i	−0.00900256	−	0.0510560i
$986$	−14.7308	−	5.36156i	−0.469123	−	0.170747i
$987$	11.7638			0.374446
$988$		0			0
$989$	−51.1294			−1.62582
$990$	4.58557	+	1.66901i	0.145739	+	0.0530447i
$991$	−4.83377	−	27.4137i	−0.153550	−	0.870824i	−0.960100	−	0.279658i	$-0.909779\pi$
$991$	−4.83377	−	27.4137i	−0.153550	−	0.870824i	0.806550	−	0.591166i	$-0.201332\pi$
$992$	6.73629	+	5.65242i	0.213877	+	0.179465i
$993$	7.22905	−	6.06589i	0.229407	−	0.192495i
$994$	−0.0246994	+	0.140077i	−0.000783417	+	0.00444298i
$995$	1.05163	−	1.82147i	0.0333388	−	0.0577446i
$996$	−3.12465	−	5.41206i	−0.0990085	−	0.171488i
$997$	40.7181	−	14.8202i	1.28956	−	0.469360i	0.395975	−	0.918261i	$-0.370407\pi$
$997$	40.7181	−	14.8202i	1.28956	−	0.469360i	0.893581	+	0.448901i	$0.148184\pi$
$998$	−27.8234	+	10.1269i	−0.880735	+	0.320561i
$999$	7.67853	+	13.2996i	0.242938	+	0.420781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.s.99.3		24
19.2	odd	18		722.2.e.r.415.3		24
19.3	odd	18		722.2.e.r.245.2		24
19.4	even	9		722.2.c.n.653.2		8
19.5	even	9	inner	722.2.e.s.423.3		24
19.6	even	9		722.2.c.n.429.2		8
19.7	even	3	inner	722.2.e.s.595.2		24
19.8	odd	6		722.2.e.r.389.2		24
19.9	even	9		722.2.a.m.1.3	✓	4
19.10	odd	18		722.2.a.n.1.2	yes	4
19.11	even	3	inner	722.2.e.s.389.3		24
19.12	odd	6		722.2.e.r.595.3		24
19.13	odd	18		722.2.c.m.429.3		8
19.14	odd	18		722.2.e.r.423.2		24
19.15	odd	18		722.2.c.m.653.3		8
19.16	even	9	inner	722.2.e.s.245.3		24
19.17	even	9	inner	722.2.e.s.415.2		24
19.18	odd	2		722.2.e.r.99.2		24
57.29	even	18		6498.2.a.bx.1.2		4
57.47	odd	18		6498.2.a.ca.1.2		4
76.47	odd	18		5776.2.a.bv.1.2		4
76.67	even	18		5776.2.a.bt.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.3	✓	4	19.9	even	9
722.2.a.n.1.2	yes	4	19.10	odd	18
722.2.c.m.429.3		8	19.13	odd	18
722.2.c.m.653.3		8	19.15	odd	18
722.2.c.n.429.2		8	19.6	even	9
722.2.c.n.653.2		8	19.4	even	9
722.2.e.r.99.2		24	19.18	odd	2
722.2.e.r.245.2		24	19.3	odd	18
722.2.e.r.389.2		24	19.8	odd	6
722.2.e.r.415.3		24	19.2	odd	18
722.2.e.r.423.2		24	19.14	odd	18
722.2.e.r.595.3		24	19.12	odd	6
722.2.e.s.99.3		24	1.1	even	1	trivial
722.2.e.s.245.3		24	19.16	even	9	inner
722.2.e.s.389.3		24	19.11	even	3	inner
722.2.e.s.415.2		24	19.17	even	9	inner
722.2.e.s.423.3		24	19.5	even	9	inner
722.2.e.s.595.2		24	19.7	even	3	inner
5776.2.a.bt.1.3		4	76.67	even	18
5776.2.a.bv.1.2		4	76.47	odd	18
6498.2.a.bx.1.2		4	57.29	even	18
6498.2.a.ca.1.2		4	57.47	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)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.0768330 - 0.435741i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.682922 + 0.573040i) q^{5} +(0.0768330 - 0.435741i) q^{6} +(-1.26007 + 2.18251i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.63511 - 0.959102i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.0768330 - 0.435741i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.682922 + 0.573040i) q^{5} +(0.0768330 - 0.435741i) q^{6} +(-1.26007 + 2.18251i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.63511 - 0.959102i) q^{9} +(-0.837728 + 0.304908i) q^{10} +(-0.975994 - 1.69047i) q^{11} +(0.221232 - 0.383185i) q^{12} +(-1.12171 + 6.36151i) q^{13} +(-1.93054 + 1.61992i) q^{14} +(0.302168 + 0.253549i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.21587 + 1.17048i) q^{17} +2.80423 q^{18} -0.891491 q^{20} +(1.04783 + 0.381377i) q^{21} +(-0.338959 - 1.92233i) q^{22} +(6.27010 + 5.26124i) q^{23} +(0.338947 - 0.284410i) q^{24} +(-0.730233 + 4.14136i) q^{25} +(-3.22982 + 5.59422i) q^{26} +(-1.28408 - 2.22409i) q^{27} +(-2.36816 + 0.861941i) q^{28} +(-4.30440 + 1.56667i) q^{29} +(0.197226 + 0.341606i) q^{30} +(4.39680 - 7.61548i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.661620 + 0.555165i) q^{33} +(2.62160 + 2.19979i) q^{34} +(-0.390134 - 2.21256i) q^{35} +(2.63511 + 0.959102i) q^{36} -5.97980 q^{37} +2.85816 q^{39} +(-0.837728 - 0.304908i) q^{40} +(-0.605914 - 3.43631i) q^{41} +(0.854195 + 0.716755i) q^{42} +(-4.78524 + 4.01529i) q^{43} +(0.338959 - 1.92233i) q^{44} +(-1.24997 + 2.16501i) q^{45} +(4.09252 + 7.08845i) q^{46} +(9.91359 - 3.60825i) q^{47} +(0.415780 - 0.151331i) q^{48} +(0.324429 + 0.561928i) q^{49} +(-2.10262 + 3.64185i) q^{50} +(0.262942 - 1.49122i) q^{51} +(-4.94838 + 4.15218i) q^{52} +(2.88246 + 2.41867i) q^{53} +(-0.445956 - 2.52914i) q^{54} +(1.63524 + 0.595177i) q^{55} -2.52015 q^{56} -4.58064 q^{58} +(-2.67025 - 0.971890i) q^{59} +(0.0684959 + 0.388460i) q^{60} +(-1.88060 - 1.57801i) q^{61} +(6.73629 - 5.65242i) q^{62} +(-1.22718 + 6.95970i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.87936 - 4.98720i) q^{65} +(-0.811597 + 0.295397i) q^{66} +(2.51143 - 0.914086i) q^{67} +(1.71113 + 2.96376i) q^{68} +(1.81079 - 3.13638i) q^{69} +(0.390134 - 2.21256i) q^{70} +(0.0432358 - 0.0362792i) q^{71} +(2.14816 + 1.80252i) q^{72} +(-1.21018 - 6.86330i) q^{73} +(-5.61917 - 2.04521i) q^{74} +1.86067 q^{75} +4.91930 q^{77} +(2.68579 + 0.977548i) q^{78} +(-1.58569 - 8.99289i) q^{79} +(-0.682922 - 0.573040i) q^{80} +(5.57402 - 4.67716i) q^{81} +(0.605914 - 3.43631i) q^{82} +(7.06195 - 12.2317i) q^{83} +(0.557537 + 0.965682i) q^{84} +(-2.86692 + 1.04347i) q^{85} +(-5.86997 + 2.13649i) q^{86} +(1.01338 + 1.75523i) q^{87} +(0.975994 - 1.69047i) q^{88} +(0.324330 - 1.83937i) q^{89} +(-1.91507 + 1.60693i) q^{90} +(-12.4706 - 10.4641i) q^{91} +(1.42132 + 8.06069i) q^{92} +(-3.65620 - 1.33075i) q^{93} +10.5498 q^{94} +0.442463 q^{96} +(-7.35245 - 2.67607i) q^{97} +(0.112673 + 0.639001i) q^{98} +(-4.19319 - 3.51850i) 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

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