LMFDB - Embedded newform 722.2.e.s.415.2

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			415.2
Character	$\chi$	$=$	722.415
Dual form			722.2.e.s.595.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.415780 - 0.151331i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.154806 + 0.877948i) q^{5} +(-0.415780 - 0.151331i) q^{6} +(-1.26007 - 2.18251i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.14816 + 1.80252i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.415780 - 0.151331i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.154806 + 0.877948i) q^{5} +(-0.415780 - 0.151331i) q^{6} +(-1.26007 - 2.18251i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.14816 + 1.80252i) q^{9} +(0.682922 - 0.573040i) q^{10} +(-0.975994 + 1.69047i) q^{11} +(0.221232 + 0.383185i) q^{12} +(6.07009 + 2.20933i) q^{13} +(-0.437619 + 2.48186i) q^{14} +(0.0684959 + 0.388460i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.62160 - 2.19979i) q^{17} +2.80423 q^{18} -0.891491 q^{20} +(-0.854195 - 0.716755i) q^{21} +(1.83427 - 0.667620i) q^{22} +(1.42132 + 8.06069i) q^{23} +(0.0768330 - 0.435741i) q^{24} +(3.95164 + 1.43828i) q^{25} +(-3.22982 - 5.59422i) q^{26} +(-1.28408 + 2.22409i) q^{27} +(1.93054 - 1.61992i) q^{28} +(3.50898 - 2.94438i) q^{29} +(0.197226 - 0.341606i) q^{30} +(4.39680 + 7.61548i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.149977 + 0.850563i) q^{33} +(0.594269 + 3.37027i) q^{34} +(2.11120 - 0.768413i) q^{35} +(-2.14816 - 1.80252i) q^{36} -5.97980 q^{37} +2.85816 q^{39} +(0.682922 + 0.573040i) q^{40} +(3.27889 - 1.19342i) q^{41} +(0.193630 + 1.09813i) q^{42} +(-1.08473 + 6.15179i) q^{43} +(-1.83427 - 0.667620i) q^{44} +(-1.24997 - 2.16501i) q^{45} +(4.09252 - 7.08845i) q^{46} +(-8.08163 + 6.78129i) q^{47} +(-0.338947 + 0.284410i) q^{48} +(0.324429 - 0.561928i) q^{49} +(-2.10262 - 3.64185i) q^{50} +(-1.42291 - 0.517895i) q^{51} +(-1.12171 + 6.36151i) q^{52} +(0.653400 + 3.70561i) q^{53} +(2.41328 - 0.878362i) q^{54} +(-1.33306 - 1.11857i) q^{55} -2.52015 q^{56} -4.58064 q^{58} +(2.17680 + 1.82656i) q^{59} +(-0.370664 + 0.134911i) q^{60} +(-0.426298 - 2.41765i) q^{61} +(1.52699 - 8.66001i) q^{62} +(6.64087 + 2.41708i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.87936 + 4.98720i) q^{65} +(0.661620 - 0.555165i) q^{66} +(-2.04734 + 1.71792i) q^{67} +(1.71113 - 2.96376i) q^{68} +(1.81079 + 3.13638i) q^{69} +(-2.11120 - 0.768413i) q^{70} +(0.00980077 - 0.0555829i) q^{71} +(0.486949 + 2.76162i) q^{72} +(6.54888 - 2.38360i) q^{73} +(4.58079 + 3.84374i) q^{74} +1.86067 q^{75} +4.91930 q^{77} +(-2.18948 - 1.83719i) q^{78} +(8.58091 - 3.12320i) q^{79} +(-0.154806 - 0.877948i) q^{80} +(1.26353 - 7.16582i) q^{81} +(-3.27889 - 1.19342i) q^{82} +(7.06195 + 12.2317i) q^{83} +(0.557537 - 0.965682i) q^{84} +(2.33714 - 1.96109i) q^{85} +(4.78524 - 4.01529i) q^{86} +(1.01338 - 1.75523i) q^{87} +(0.975994 + 1.69047i) q^{88} +(-1.75510 - 0.638805i) q^{89} +(-0.434111 + 2.46196i) q^{90} +(-2.82686 - 16.0319i) q^{91} +(-7.69142 + 2.79945i) q^{92} +(2.98056 + 2.50099i) q^{93} +10.5498 q^{94} +0.442463 q^{96} +(5.99377 + 5.02937i) q^{97} +(-0.609728 + 0.221923i) q^{98} +(-0.950519 - 5.39066i) 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 $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	0.415780	−	0.151331i	0.240051	−	0.0873712i	−0.219193	−	0.975681i	$-0.570343\pi$
$3$	0.415780	−	0.151331i	0.240051	−	0.0873712i	0.459244	+	0.888310i	$0.348120\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.154806	+	0.877948i	−0.0692313	+	0.392630i	0.930427	+	0.366478i	$0.119437\pi$
$5$	−0.154806	+	0.877948i	−0.0692313	+	0.392630i	−0.999658	+	0.0261521i	$0.991675\pi$
$6$	−0.415780	−	0.151331i	−0.169741	−	0.0617808i
$7$	−1.26007	−	2.18251i	−0.476263	−	0.824912i	0.523367	−	0.852107i	$-0.324676\pi$
$7$	−1.26007	−	2.18251i	−0.476263	−	0.824912i	−0.999630	+	0.0271956i	$0.991342\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.14816	+	1.80252i	−0.716054	+	0.600841i
$10$	0.682922	−	0.573040i	0.215959	−	0.181211i
$11$	−0.975994	+	1.69047i	−0.294273	+	0.509696i	−0.974816	−	0.223012i	$-0.928411\pi$
$11$	−0.975994	+	1.69047i	−0.294273	+	0.509696i	0.680542	+	0.732709i	$0.261744\pi$
$12$	0.221232	+	0.383185i	0.0638641	+	0.110616i
$13$	6.07009	+	2.20933i	1.68354	+	0.612758i	0.993788	−	0.111289i	$-0.0354979\pi$
$13$	6.07009	+	2.20933i	1.68354	+	0.612758i	0.689751	+	0.724047i	$0.257720\pi$
$14$	−0.437619	+	2.48186i	−0.116959	+	0.663305i
$15$	0.0684959	+	0.388460i	0.0176856	+	0.100300i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−2.62160	−	2.19979i	−0.635832	−	0.533527i	0.266903	−	0.963723i	$-0.414000\pi$
$17$	−2.62160	−	2.19979i	−0.635832	−	0.533527i	−0.902735	+	0.430197i	$0.858444\pi$
$18$	2.80423			0.660962
$19$		0			0
$19$		0			0
$20$	−0.891491			−0.199344
$21$	−0.854195	−	0.716755i	−0.186401	−	0.156409i
$22$	1.83427	−	0.667620i	0.391068	−	0.142337i
$23$	1.42132	+	8.06069i	0.296365	+	1.68077i	0.661602	+	0.749855i	$0.269877\pi$
$23$	1.42132	+	8.06069i	0.296365	+	1.68077i	−0.365237	+	0.930915i	$0.619012\pi$
$24$	0.0768330	−	0.435741i	0.0156835	−	0.0889454i
$25$	3.95164	+	1.43828i	0.790327	+	0.287656i
$26$	−3.22982	−	5.59422i	−0.633421	−	1.09712i
$27$	−1.28408	+	2.22409i	−0.247121	+	0.428026i
$28$	1.93054	−	1.61992i	0.364839	−	0.306136i
$29$	3.50898	−	2.94438i	0.651601	−	0.546758i	−0.255955	−	0.966689i	$-0.582390\pi$
$29$	3.50898	−	2.94438i	0.651601	−	0.546758i	0.907556	+	0.419931i	$0.137946\pi$
$30$	0.197226	−	0.341606i	0.0360084	−	0.0623684i
$31$	4.39680	+	7.61548i	0.789689	+	1.36778i	0.926157	+	0.377137i	$0.123091\pi$
$31$	4.39680	+	7.61548i	0.789689	+	1.36778i	−0.136468	+	0.990644i	$0.543575\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−0.149977	+	0.850563i	−0.0261077	+	0.148064i
$34$	0.594269	+	3.37027i	0.101916	+	0.577996i
$35$	2.11120	−	0.768413i	0.356858	−	0.129886i
$36$	−2.14816	−	1.80252i	−0.358027	−	0.300420i
$37$	−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
$40$	0.682922	+	0.573040i	0.107979	+	0.0906055i
$41$	3.27889	−	1.19342i	0.512077	−	0.186381i	−0.0730412	−	0.997329i	$-0.523270\pi$
$41$	3.27889	−	1.19342i	0.512077	−	0.186381i	0.585118	+	0.810948i	$0.301048\pi$
$42$	0.193630	+	1.09813i	0.0298778	+	0.169446i
$43$	−1.08473	+	6.15179i	−0.165419	+	0.938139i	0.783212	+	0.621755i	$0.213580\pi$
$43$	−1.08473	+	6.15179i	−0.165419	+	0.938139i	−0.948631	+	0.316384i	$0.897531\pi$
$44$	−1.83427	−	0.667620i	−0.276527	−	0.100647i
$45$	−1.24997	−	2.16501i	−0.186335	−	0.322741i
$46$	4.09252	−	7.08845i	0.603409	−	1.04514i
$47$	−8.08163	+	6.78129i	−1.17883	+	0.989153i	−0.178841	+	0.983878i	$0.557235\pi$
$47$	−8.08163	+	6.78129i	−1.17883	+	0.989153i	−0.999986	+	0.00527527i	$0.998321\pi$
$48$	−0.338947	+	0.284410i	−0.0489227	+	0.0410511i
$49$	0.324429	−	0.561928i	0.0463471	−	0.0802755i
$50$	−2.10262	−	3.64185i	−0.297356	−	0.515035i
$51$	−1.42291	−	0.517895i	−0.199247	−	0.0725199i
$52$	−1.12171	+	6.36151i	−0.155553	+	0.882183i
$53$	0.653400	+	3.70561i	0.0897514	+	0.509005i	0.996230	+	0.0867532i	$0.0276492\pi$
$53$	0.653400	+	3.70561i	0.0897514	+	0.509005i	−0.906478	+	0.422252i	$0.861240\pi$
$54$	2.41328	−	0.878362i	0.328406	−	0.119530i
$55$	−1.33306	−	1.11857i	−0.179749	−	0.150828i
$56$	−2.52015			−0.336769
$57$		0			0
$58$	−4.58064			−0.601468
$59$	2.17680	+	1.82656i	0.283396	+	0.237797i	0.773393	−	0.633927i	$-0.218558\pi$
$59$	2.17680	+	1.82656i	0.283396	+	0.237797i	−0.489998	+	0.871724i	$0.663002\pi$
$60$	−0.370664	+	0.134911i	−0.0478525	+	0.0174169i
$61$	−0.426298	−	2.41765i	−0.0545818	−	0.309549i	0.945278	−	0.326265i	$-0.105790\pi$
$61$	−0.426298	−	2.41765i	−0.0545818	−	0.309549i	−0.999860	+	0.0167158i	$0.994679\pi$
$62$	1.52699	−	8.66001i	0.193928	−	1.09982i
$63$	6.64087	+	2.41708i	0.836670	+	0.304523i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.87936	+	4.98720i	−0.357141	+	0.618586i
$66$	0.661620	−	0.555165i	0.0814398	−	0.0683361i
$67$	−2.04734	+	1.71792i	−0.250122	+	0.209877i	−0.759225	−	0.650828i	$-0.774422\pi$
$67$	−2.04734	+	1.71792i	−0.250122	+	0.209877i	0.509103	+	0.860706i	$0.329977\pi$
$68$	1.71113	−	2.96376i	0.207505	−	0.359409i
$69$	1.81079	+	3.13638i	0.217994	+	0.377576i
$70$	−2.11120	−	0.768413i	−0.252336	−	0.0918429i
$71$	0.00980077	−	0.0555829i	0.00116314	−	0.00659648i	−0.984221	−	0.176945i	$-0.943378\pi$
$71$	0.00980077	−	0.0555829i	0.00116314	−	0.00659648i	0.985384	+	0.170349i	$0.0544895\pi$
$72$	0.486949	+	2.76162i	0.0573875	+	0.325460i
$73$	6.54888	−	2.38360i	0.766489	−	0.278979i	0.0709617	−	0.997479i	$-0.477393\pi$
$73$	6.54888	−	2.38360i	0.766489	−	0.278979i	0.695527	+	0.718500i	$0.255171\pi$
$74$	4.58079	+	3.84374i	0.532506	+	0.446826i
$75$	1.86067			0.214851
$76$		0			0
$77$	4.91930			0.560606
$78$	−2.18948	−	1.83719i	−0.247909	−	0.208021i
$79$	8.58091	−	3.12320i	0.965428	−	0.351387i	0.189270	−	0.981925i	$-0.439388\pi$
$79$	8.58091	−	3.12320i	0.965428	−	0.351387i	0.776158	+	0.630538i	$0.217166\pi$
$80$	−0.154806	−	0.877948i	−0.0173078	−	0.0981575i
$81$	1.26353	−	7.16582i	0.140392	−	0.796202i
$82$	−3.27889	−	1.19342i	−0.362093	−	0.131791i
$83$	7.06195	+	12.2317i	0.775150	+	1.34260i	0.934710	+	0.355411i	$0.115659\pi$
$83$	7.06195	+	12.2317i	0.775150	+	1.34260i	−0.159561	+	0.987188i	$0.551008\pi$
$84$	0.557537	−	0.965682i	0.0608322	−	0.105364i
$85$	2.33714	−	1.96109i	0.253498	−	0.212710i
$86$	4.78524	−	4.01529i	0.516006	−	0.432980i
$87$	1.01338	−	1.75523i	0.108646	−	0.188181i
$88$	0.975994	+	1.69047i	0.104041	+	0.180205i
$89$	−1.75510	−	0.638805i	−0.186040	−	0.0677132i	0.247320	−	0.968934i	$-0.420450\pi$
$89$	−1.75510	−	0.638805i	−0.186040	−	0.0677132i	−0.433361	+	0.901221i	$0.642672\pi$
$90$	−0.434111	+	2.46196i	−0.0457593	+	0.259514i
$91$	−2.82686	−	16.0319i	−0.296336	−	1.68060i
$92$	−7.69142	+	2.79945i	−0.801886	+	0.291863i
$93$	2.98056	+	2.50099i	0.309070	+	0.259341i
$94$	10.5498			1.08813
$95$		0			0
$96$	0.442463			0.0451587
$97$	5.99377	+	5.02937i	0.608576	+	0.510656i	0.894189	−	0.447689i	$-0.147753\pi$
$97$	5.99377	+	5.02937i	0.608576	+	0.510656i	−0.285614	+	0.958345i	$0.592197\pi$
$98$	−0.609728	+	0.221923i	−0.0615918	+	0.0224176i
$99$	−0.950519	−	5.39066i	−0.0955307	−	0.541782i
$100$	−0.730233	+	4.14136i	−0.0730233	+	0.414136i
$101$	5.06012	+	1.84173i	0.503501	+	0.183259i	0.581268	−	0.813712i	$-0.302557\pi$
$101$	5.06012	+	1.84173i	0.503501	+	0.183259i	−0.0777670	+	0.996972i	$0.524779\pi$
$102$	0.757113	+	1.31136i	0.0749653	+	0.129844i
$103$	2.34734	−	4.06571i	0.231290	−	0.400606i	−0.726898	−	0.686746i	$-0.759039\pi$
$103$	2.34734	−	4.06571i	0.231290	−	0.400606i	0.958188	+	0.286139i	$0.0923720\pi$
$104$	4.94838	−	4.15218i	0.485228	−	0.407155i
$105$	0.761508	−	0.638981i	0.0743156	−	0.0623582i
$106$	1.88139	−	3.25866i	0.182737	−	0.316509i
$107$	−8.01864	−	13.8887i	−0.775191	−	1.34267i	−0.934687	−	0.355472i	$-0.884320\pi$
$107$	−8.01864	−	13.8887i	−0.775191	−	1.34267i	0.159496	−	0.987199i	$-0.449013\pi$
$108$	−2.41328	−	0.878362i	−0.232218	−	0.0845204i
$109$	2.44858	−	13.8866i	0.234531	−	1.33009i	−0.609068	−	0.793118i	$-0.708456\pi$
$109$	2.44858	−	13.8866i	0.234531	−	1.33009i	0.843599	−	0.536974i	$-0.180433\pi$
$110$	0.302179	+	1.71374i	0.0288117	+	0.163399i
$111$	−2.48628	+	0.904931i	−0.235987	+	0.0858923i
$112$	1.93054	+	1.61992i	0.182419	+	0.153068i
$113$	−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
$116$	3.50898	+	2.94438i	0.325800	+	0.273379i
$117$	−17.0219	+	6.19546i	−1.57367	+	0.572771i
$118$	−0.493441	−	2.79845i	−0.0454250	−	0.257618i
$119$	−1.49765	+	8.49357i	−0.137289	+	0.778604i
$120$	0.370664	+	0.134911i	0.0338368	+	0.0123156i
$121$	3.59487	+	6.22650i	0.326806	+	0.566045i
$122$	−1.22747	+	2.12605i	−0.111130	+	0.192483i
$123$	1.18269	−	0.992398i	0.106640	−	0.0894815i
$124$	−6.73629	+	5.65242i	−0.604937	+	0.507602i
$125$	−4.10320	+	7.10695i	−0.367001	+	0.635665i
$126$	−3.53353	−	6.12026i	−0.314792	−	0.545236i
$127$	−6.74175	−	2.45380i	−0.598233	−	0.217739i	0.0251135	−	0.999685i	$-0.492005\pi$
$127$	−6.74175	−	2.45380i	−0.598233	−	0.217739i	−0.623347	+	0.781945i	$0.714228\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	0.479952	+	2.72194i	0.0422574	+	0.239654i
$130$	5.41143	−	1.96960i	0.474614	−	0.172745i
$131$	−2.69851	−	2.26432i	−0.235770	−	0.197834i	0.517246	−	0.855837i	$-0.326957\pi$
$131$	−2.69851	−	2.26432i	−0.235770	−	0.197834i	−0.753016	+	0.658002i	$0.771402\pi$
$132$	−0.863684			−0.0751740
$133$		0			0
$134$	2.67261			0.230878
$135$	−1.75385	−	1.47166i	−0.150948	−	0.126660i
$136$	−3.21587	+	1.17048i	−0.275759	+	0.100368i
$137$	−1.91075	−	10.8364i	−0.163246	−	0.925814i	−0.950854	−	0.309638i	$-0.899792\pi$
$137$	−1.91075	−	10.8364i	−0.163246	−	0.925814i	0.787608	−	0.616176i	$-0.211319\pi$
$138$	0.628881	−	3.56656i	0.0535339	−	0.303606i
$139$	−20.4464	−	7.44188i	−1.73424	−	0.631212i	−0.735323	−	0.677716i	$-0.762970\pi$
$139$	−20.4464	−	7.44188i	−1.73424	−	0.631212i	−0.998918	+	0.0465042i	$0.985192\pi$
$140$	1.12334	+	1.94569i	0.0949400	+	0.164441i
$141$	−2.33395	+	4.04253i	−0.196554	+	0.340442i
$142$	−0.0432358	+	0.0362792i	−0.00362827	+	0.00304448i
$143$	−9.65918	+	8.10501i	−0.807741	+	0.677775i
$144$	1.40211	−	2.42853i	0.116843	−	0.202378i
$145$	2.04180	+	3.53651i	0.169562	+	0.293691i
$146$	−6.54888	−	2.38360i	−0.541989	−	0.197268i
$147$	0.0498538	−	0.282735i	0.00411187	−	0.0233196i
$148$	−1.03838	−	5.88895i	−0.0853544	−	0.484069i
$149$	−13.5218	+	4.92152i	−1.10775	+	0.403187i	−0.830166	−	0.557516i	$-0.811755\pi$
$149$	−13.5218	+	4.92152i	−1.10775	+	0.403187i	−0.277580	+	0.960702i	$0.589532\pi$
$150$	−1.42535	−	1.19601i	−0.116380	−	0.0976541i
$151$	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
$154$	−3.76840	−	3.16206i	−0.303666	−	0.254806i
$155$	−7.36665	+	2.68124i	−0.591703	+	0.215362i
$156$	0.496314	+	2.81474i	0.0397369	+	0.225359i
$157$	−0.0783536	+	0.444365i	−0.00625330	+	0.0354642i	−0.987775	−	0.155888i	$-0.950176\pi$
$157$	−0.0783536	+	0.444365i	−0.00625330	+	0.0354642i	0.981521	+	0.191352i	$0.0612872\pi$
$158$	−8.58091	−	3.12320i	−0.682661	−	0.248468i
$159$	0.832446	+	1.44184i	0.0660173	+	0.114345i
$160$	−0.445746	+	0.772054i	−0.0352393	+	0.0610362i
$161$	15.8016	−	13.2591i	1.24534	−	1.04496i
$162$	−5.57402	+	4.67716i	−0.437936	+	0.367472i
$163$	0.0346271	−	0.0599759i	0.00271220	−	0.00469768i	−0.864666	−	0.502347i	$-0.832470\pi$
$163$	0.0346271	−	0.0599759i	0.00271220	−	0.00469768i	0.867378	+	0.497649i	$0.165803\pi$
$164$	1.74466	+	3.02184i	0.136235	+	0.235966i
$165$	−0.723532	−	0.263344i	−0.0563269	−	0.0205013i
$166$	2.45259	−	13.9093i	0.190358	−	1.07957i
$167$	0.377460	+	2.14068i	0.0292087	+	0.165651i	0.995923	−	0.0902075i	$-0.0287530\pi$
$167$	0.377460	+	2.14068i	0.0292087	+	0.165651i	−0.966714	+	0.255858i	$0.917642\pi$
$168$	−1.04783	+	0.381377i	−0.0808415	+	0.0294239i
$169$	22.0062	+	18.4654i	1.69279	+	1.42042i
$170$	−3.05092			−0.233995
$171$		0			0
$172$	−6.24669			−0.476306
$173$	−12.9073	−	10.8305i	−0.981324	−	0.823429i	0.00296446	−	0.999996i	$-0.499056\pi$
$173$	−12.9073	−	10.8305i	−0.981324	−	0.823429i	−0.984289	+	0.176567i	$0.943501\pi$
$174$	−1.90454	+	0.693195i	−0.144383	+	0.0525510i
$175$	−1.84029	−	10.4368i	−0.139113	−	0.788950i
$176$	0.338959	−	1.92233i	0.0255500	−	0.144901i
$177$	1.18149	+	0.430026i	0.0888059	+	0.0323227i
$178$	0.933870	+	1.61751i	0.0699965	+	0.121238i
$179$	−9.48276	+	16.4246i	−0.708775	+	1.22763i	0.256537	+	0.966534i	$0.417418\pi$
$179$	−9.48276	+	16.4246i	−0.708775	+	1.22763i	−0.965312	+	0.261099i	$0.915915\pi$
$180$	1.91507	−	1.60693i	0.142741	−	0.119774i
$181$	−1.52203	+	1.27714i	−0.113132	+	0.0949288i	−0.697599	−	0.716489i	$-0.745748\pi$
$181$	−1.52203	+	1.27714i	−0.113132	+	0.0949288i	0.584467	+	0.811418i	$0.301304\pi$
$182$	−8.13963	+	14.0983i	−0.603350	+	1.04503i
$183$	−0.543113	−	0.940699i	−0.0401481	−	0.0695385i
$184$	7.69142	+	2.79945i	0.567019	+	0.206378i
$185$	0.925708	−	5.24995i	0.0680594	−	0.385984i
$186$	−0.675639	−	3.83174i	−0.0495402	−	0.280957i
$187$	6.27735	−	2.28477i	0.459045	−	0.167079i
$188$	−8.08163	−	6.78129i	−0.589413	−	0.494577i
$189$	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	$0.773372\pi$
$192$	−0.338947	−	0.284410i	−0.0244614	−	0.0205255i
$193$	−7.31907	+	2.66392i	−0.526838	+	0.191753i	−0.591726	−	0.806139i	$-0.701553\pi$
$193$	−7.31907	+	2.66392i	−0.526838	+	0.191753i	0.0648878	+	0.997893i	$0.479331\pi$
$194$	−1.35868	−	7.70545i	−0.0975474	−	0.553219i
$195$	−0.442460	+	2.50931i	−0.0316852	+	0.179696i
$196$	0.609728	+	0.221923i	0.0435520	+	0.0158516i
$197$	−0.912571	−	1.58062i	−0.0650180	−	0.112614i	0.831684	−	0.555249i	$-0.187377\pi$
$197$	−0.912571	−	1.58062i	−0.0650180	−	0.112614i	−0.896702	+	0.442635i	$0.854044\pi$
$198$	−2.73691	+	4.74047i	−0.194504	+	0.336890i
$199$	1.80729	−	1.51650i	0.128116	−	0.107502i	−0.576478	−	0.817112i	$-0.695574\pi$
$199$	1.80729	−	1.51650i	0.128116	−	0.107502i	0.704594	+	0.709611i	$0.251129\pi$
$200$	3.22140	−	2.70308i	0.227788	−	0.191136i
$201$	−0.591266	+	1.02410i	−0.0417047	+	0.0722346i
$202$	−2.69244	−	4.66343i	−0.189439	−	0.328118i
$203$	−10.8477	−	3.94825i	−0.761360	−	0.277113i
$204$	0.262942	−	1.49122i	0.0184097	−	0.104406i
$205$	0.540168	+	3.06344i	0.0377269	+	0.213960i
$206$	−4.41155	+	1.60567i	−0.307368	+	0.111873i
$207$	−17.5828	−	14.7537i	−1.22209	−	1.02545i
$208$	−6.45965			−0.447896
$209$		0			0
$210$	−0.994078			−0.0685979
$211$	−0.276581	−	0.232079i	−0.0190406	−	0.0159770i	0.633218	−	0.773974i	$-0.281734\pi$
$211$	−0.276581	−	0.232079i	−0.0190406	−	0.0159770i	−0.652258	+	0.757997i	$0.726178\pi$
$212$	−3.53586	+	1.28695i	−0.242844	+	0.0883878i
$213$	−0.00433648	−	0.0245934i	−0.000297131	−	0.00168511i
$214$	−2.78484	+	15.7936i	−0.190368	+	1.07963i
$215$	−5.23303	−	1.90467i	−0.356889	−	0.129897i
$216$	1.28408	+	2.22409i	0.0873705	+	0.151330i
$217$	11.0806	−	19.1921i	0.752199	−	1.30285i
$218$	−10.8018	+	9.06381i	−0.731592	+	0.613879i
$219$	2.36218	−	1.98210i	0.159621	−	0.133938i
$220$	0.870091	−	1.50704i	0.0586615	−	0.101605i
$221$	−11.0533	−	19.1449i	−0.743525	−	1.28782i
$222$	2.48628	+	0.904931i	0.166868	+	0.0607350i
$223$	3.13411	−	17.7744i	0.209875	−	1.19026i	−0.679706	−	0.733485i	$-0.737892\pi$
$223$	3.13411	−	17.7744i	0.209875	−	1.19026i	0.889581	−	0.456778i	$-0.150996\pi$
$224$	−0.437619	−	2.48186i	−0.0292396	−	0.165826i
$225$	−11.0813	+	4.03326i	−0.738752	+	0.268884i
$226$	9.74590	+	8.17778i	0.648288	+	0.543978i
$227$	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	$0.427956\pi$
$230$	5.58974	+	4.69035i	0.368577	+	0.309273i
$231$	2.04534	−	0.744445i	0.134574	−	0.0489809i
$232$	−0.795421	−	4.51105i	−0.0522219	−	0.296165i
$233$	3.72117	−	21.1038i	0.243782	−	1.38256i	−0.579523	−	0.814956i	$-0.696761\pi$
$233$	3.72117	−	21.1038i	0.243782	−	1.38256i	0.823305	−	0.567600i	$-0.192128\pi$
$234$	17.0219	+	6.19546i	1.11276	+	0.405010i
$235$	−4.70254	−	8.14503i	−0.306760	−	0.531323i
$236$	−1.42081	+	2.46091i	−0.0924867	+	0.160192i
$237$	3.09513	−	2.59712i	0.201050	−	0.168701i
$238$	6.60683	−	5.54379i	0.428257	−	0.359350i
$239$	5.91881	−	10.2517i	0.382856	−	0.663126i	−0.608613	−	0.793467i	$-0.708274\pi$
$239$	5.91881	−	10.2517i	0.382856	−	0.663126i	0.991469	+	0.130341i	$0.0416071\pi$
$240$	−0.197226	−	0.341606i	−0.0127309	−	0.0220506i
$241$	20.4348	+	7.43767i	1.31632	+	0.479103i	0.902279	−	0.431154i	$-0.141893\pi$
$241$	20.4348	+	7.43767i	1.31632	+	0.479103i	0.414045	+	0.910256i	$0.364115\pi$
$242$	1.24849	−	7.08051i	0.0802557	−	0.455152i
$243$	−1.89693	−	10.7580i	−0.121688	−	0.690129i
$244$	2.30690	−	0.839642i	0.147684	−	0.0537526i
$245$	0.443120	+	0.371822i	0.0283099	+	0.0237548i
$246$	−1.54390			−0.0984353
$247$		0			0
$248$	8.79360			0.558394
$249$	4.78725	+	4.01698i	0.303380	+	0.254566i
$250$	7.71149	−	2.80675i	0.487717	−	0.177515i
$251$	4.10522	+	23.2819i	0.259119	+	1.46954i	0.785273	+	0.619149i	$0.212522\pi$
$251$	4.10522	+	23.2819i	0.259119	+	1.46954i	−0.526154	+	0.850389i	$0.676366\pi$
$252$	−1.22718	+	6.95970i	−0.0773052	+	0.438420i
$253$	−15.0136	−	5.46449i	−0.943895	−	0.343550i
$254$	3.58721	+	6.21323i	0.225082	+	0.389853i
$255$	0.674959	−	1.16906i	0.0422676	−	0.0732096i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−0.707418	+	0.593594i	−0.0441275	+	0.0370274i	−0.664585	−	0.747213i	$-0.731392\pi$
$257$	−0.707418	+	0.593594i	−0.0441275	+	0.0370274i	0.620457	+	0.784240i	$0.286947\pi$
$258$	1.38197	−	2.39364i	0.0860374	−	0.149021i
$259$	7.53498	+	13.0510i	0.468201	+	0.810948i
$260$	−5.41143	−	1.96960i	−0.335603	−	0.122149i
$261$	−2.23054	+	12.6500i	−0.138067	+	0.783016i
$262$	0.611703	+	3.46914i	0.0377911	+	0.214324i
$263$	−4.05917	+	1.47742i	−0.250299	+	0.0911013i	−0.464123	−	0.885771i	$-0.653630\pi$
$263$	−4.05917	+	1.47742i	−0.250299	+	0.0911013i	0.213824	+	0.976872i	$0.431408\pi$
$264$	0.661620	+	0.555165i	0.0407199	+	0.0341681i
$265$	−3.35449			−0.206064
$266$		0			0
$267$	−0.826407			−0.0505753
$268$	−2.04734	−	1.71792i	−0.125061	−	0.104939i
$269$	10.1443	−	3.69223i	0.618510	−	0.225119i	−0.0137127	−	0.999906i	$-0.504365\pi$
$269$	10.1443	−	3.69223i	0.618510	−	0.225119i	0.632223	+	0.774787i	$0.282143\pi$
$270$	0.397566	+	2.25471i	0.0241951	+	0.137217i
$271$	0.140176	−	0.794980i	0.00851511	−	0.0482916i	−0.980254	−	0.197742i	$-0.936639\pi$
$271$	0.140176	−	0.794980i	0.00851511	−	0.0482916i	0.988769	+	0.149450i	$0.0477504\pi$
$272$	3.21587	+	1.17048i	0.194991	+	0.0709709i
$273$	−3.60149	−	6.23796i	−0.217972	−	0.377539i
$274$	−5.50177	+	9.52935i	−0.332374	+	0.575689i
$275$	−6.28814	+	5.27638i	−0.379189	+	0.318178i
$276$	−2.77429	+	2.32791i	−0.166993	+	0.140124i
$277$	4.57434	−	7.92300i	0.274846	−	0.476047i	−0.695250	−	0.718768i	$-0.744707\pi$
$277$	4.57434	−	7.92300i	0.274846	−	0.476047i	0.970096	+	0.242721i	$0.0780399\pi$
$278$	10.8793	+	18.8435i	0.652497	+	1.13016i
$279$	−23.1721	−	8.43396i	−1.38728	−	0.504928i
$280$	0.390134	−	2.21256i	0.0233149	−	0.132226i
$281$	3.68408	+	20.8934i	0.219774	+	1.24640i	0.872428	+	0.488742i	$0.162544\pi$
$281$	3.68408	+	20.8934i	0.219774	+	1.24640i	−0.652655	+	0.757656i	$0.726345\pi$
$282$	4.38640	−	1.59652i	0.261206	−	0.0950713i
$283$	3.97566	+	3.33597i	0.236328	+	0.198303i	0.753259	−	0.657725i	$-0.228481\pi$
$283$	3.97566	+	3.33597i	0.236328	+	0.198303i	−0.516930	+	0.856028i	$0.672925\pi$
$284$	0.0564404			0.00334912
$285$		0			0
$286$	12.6092			0.745596
$287$	−6.73629	−	5.65242i	−0.397631	−	0.333652i
$288$	−2.63511	+	0.959102i	−0.155275	+	0.0565156i
$289$	−0.918275	−	5.20780i	−0.0540162	−	0.306341i
$290$	0.709111	−	4.02157i	0.0416404	−	0.236155i
$291$	3.25319	+	1.18406i	0.190705	+	0.0694111i
$292$	3.48459	+	6.03548i	0.203920	+	0.353200i
$293$	8.78298	−	15.2126i	0.513107	−	0.888728i	−0.486777	−	0.873526i	$-0.661828\pi$
$293$	8.78298	−	15.2126i	0.513107	−	0.888728i	0.999884	−	0.0152018i	$-0.00483906\pi$
$294$	−0.219929	+	0.184542i	−0.0128265	+	0.0107627i
$295$	−1.94060	+	1.62836i	−0.112986	+	0.0948067i
$296$	−2.98990	+	5.17866i	−0.173784	+	0.301003i
$297$	−2.50651	−	4.34140i	−0.145442	−	0.251914i
$298$	13.5218	+	4.92152i	0.783295	+	0.285096i
$299$	−9.18121	+	52.0692i	−0.530963	+	3.01124i
$300$	0.323101	+	1.83240i	0.0186543	+	0.105794i
$301$	14.7932	−	5.38428i	0.852665	−	0.310345i
$302$	−9.50413	−	7.97491i	−0.546901	−	0.458904i
$303$	2.38261			0.136877
$304$		0			0
$305$	2.18857			0.125317
$306$	−7.35157	−	6.16870i	−0.420261	−	0.352641i
$307$	20.2676	−	7.37681i	1.15673	−	0.421017i	0.308805	−	0.951125i	$-0.400071\pi$
$307$	20.2676	−	7.37681i	1.15673	−	0.421017i	0.847930	+	0.530108i	$0.177849\pi$
$308$	0.854227	+	4.84456i	0.0486741	+	0.276045i
$309$	0.360706	−	2.04567i	0.0205199	−	0.116374i
$310$	7.36665	+	2.68124i	0.418398	+	0.152284i
$311$	1.28684	+	2.22887i	0.0729701	+	0.126388i	0.900202	−	0.435473i	$-0.143419\pi$
$311$	1.28684	+	2.22887i	0.0729701	+	0.126388i	−0.827232	+	0.561861i	$0.810086\pi$
$312$	1.42908	−	2.47524i	0.0809057	−	0.140133i
$313$	−3.97109	+	3.33214i	−0.224459	+	0.188344i	−0.748081	−	0.663607i	$-0.769025\pi$
$313$	−3.97109	+	3.33214i	−0.224459	+	0.188344i	0.523622	+	0.851951i	$0.324580\pi$
$314$	0.345655	−	0.290039i	0.0195064	−	0.0163678i
$315$	−3.15011	+	5.45616i	−0.177489	+	0.307420i
$316$	4.56581	+	7.90821i	0.256847	+	0.444872i
$317$	19.0346	+	6.92801i	1.06909	+	0.389116i	0.815835	−	0.578284i	$-0.196278\pi$
$317$	19.0346	+	6.92801i	1.06909	+	0.389116i	0.253252	+	0.967400i	$0.418500\pi$
$318$	0.289106	−	1.63960i	0.0162122	−	0.0919441i
$319$	1.55265	+	8.80553i	0.0869318	+	0.493015i
$320$	0.837728	−	0.304908i	0.0468304	−	0.0170449i
$321$	−5.43578	−	4.56116i	−0.303396	−	0.254579i
$322$	−20.6275			−1.14953
$323$		0			0
$324$	7.27636			0.404242
$325$	20.8091	+	17.4609i	1.15428	+	0.968559i
$326$	−0.0650777	+	0.0236863i	−0.00360432	+	0.00131186i
$327$	−1.08341	−	6.14430i	−0.0599125	−	0.339781i
$328$	0.605914	−	3.43631i	0.0334560	−	0.189739i
$329$	24.9837	+	9.09332i	1.37740	+	0.501331i
$330$	0.384983	+	0.666811i	0.0211926	+	0.0367067i
$331$	10.6640	−	18.4706i	0.586146	−	1.01523i	−0.408585	−	0.912720i	$-0.633978\pi$
$331$	10.6640	−	18.4706i	0.586146	−	1.01523i	0.994731	−	0.102515i	$-0.0326889\pi$
$332$	−10.8195	+	9.07867i	−0.593799	+	0.498257i
$333$	12.8456	−	10.7787i	0.703933	−	0.590670i
$334$	1.08685	−	1.88248i	0.0594699	−	0.103005i
$335$	−1.19130	−	2.06340i	−0.0650879	−	0.112736i
$336$	1.04783	+	0.381377i	0.0571636	+	0.0208058i
$337$	−3.94658	+	22.3822i	−0.214984	+	1.21924i	0.665950	+	0.745996i	$0.268026\pi$
$337$	−3.94658	+	22.3822i	−0.214984	+	1.21924i	−0.880934	+	0.473239i	$0.843085\pi$
$338$	−4.98840	−	28.2906i	−0.271333	−	1.53881i
$339$	−5.28970	+	1.92529i	−0.287297	+	0.104568i
$340$	2.33714	+	1.96109i	0.126749	+	0.106355i
$341$	−17.1650			−0.929538
$342$		0			0
$343$	−19.2762			−1.04082
$344$	4.78524	+	4.01529i	0.258003	+	0.216490i
$345$	−3.03390	+	1.10425i	−0.163340	+	0.0594508i
$346$	2.92585	+	16.5933i	0.157295	+	0.892062i
$347$	−0.855834	+	4.85368i	−0.0459436	+	0.260559i	−0.999124	−	0.0418425i	$-0.986677\pi$
$347$	−0.855834	+	4.85368i	−0.0459436	+	0.260559i	0.953181	+	0.302402i	$0.0977883\pi$
$348$	1.90454	+	0.693195i	0.102094	+	0.0371592i
$349$	−13.0808	−	22.6565i	−0.700197	−	1.21278i	−0.968397	−	0.249413i	$-0.919762\pi$
$349$	−13.0808	−	22.6565i	−0.700197	−	1.21278i	0.268201	−	0.963363i	$-0.413571\pi$
$350$	−5.29892	+	9.17799i	−0.283239	+	0.490584i
$351$	−12.7082	+	10.6635i	−0.678315	+	0.569173i
$352$	−1.49531	+	1.25471i	−0.0797003	+	0.0668765i
$353$	−1.35407	+	2.34531i	−0.0720697	+	0.124828i	−0.899808	−	0.436286i	$-0.856294\pi$
$353$	−1.35407	+	2.34531i	−0.0720697	+	0.124828i	0.827739	+	0.561114i	$0.189627\pi$
$354$	−0.628656	−	1.08886i	−0.0334127	−	0.0578724i
$355$	0.0472817	+	0.0172091i	0.00250945	+	0.000913366i
$356$	0.324330	−	1.83937i	0.0171894	−	0.0974862i
$357$	0.662654	+	3.75810i	0.0350713	+	0.198899i
$358$	17.8218	−	6.48659i	0.941909	−	0.342827i
$359$	−7.13189	−	5.98437i	−0.376407	−	0.315843i	0.434883	−	0.900487i	$-0.356790\pi$
$359$	−7.13189	−	5.98437i	−0.376407	−	0.315843i	−0.811290	+	0.584644i	$0.801234\pi$
$360$	−2.49994			−0.131759
$361$		0			0
$362$	1.98687			0.104428
$363$	2.43694	+	2.04483i	0.127906	+	0.107326i
$364$	15.2975	−	5.56784i	0.801807	−	0.291834i
$365$	1.07887	+	6.11857i	0.0564706	+	0.320261i
$366$	−0.188621	+	1.06972i	−0.00985938	+	0.0559153i
$367$	−7.28677	−	2.65217i	−0.380366	−	0.138442i	0.144759	−	0.989467i	$-0.453759\pi$
$367$	−7.28677	−	2.65217i	−0.380366	−	0.138442i	−0.525125	+	0.851025i	$0.675982\pi$
$368$	−4.09252	−	7.08845i	−0.213337	−	0.369511i
$369$	−4.89242	+	8.47393i	−0.254689	+	0.441135i
$370$	−4.08374	+	3.42666i	−0.212303	+	0.178144i
$371$	7.26421	−	6.09540i	0.377139	−	0.316457i
$372$	−1.94542	+	3.36957i	−0.100866	+	0.174704i
$373$	12.5062	+	21.6614i	0.647546	+	1.12158i	0.983707	+	0.179778i	$0.0575379\pi$
$373$	12.5062	+	21.6614i	0.647546	+	1.12158i	−0.336161	+	0.941804i	$0.609129\pi$
$374$	−6.27735	−	2.28477i	−0.324594	−	0.118143i
$375$	−0.630522	+	3.57587i	−0.0325600	+	0.184657i
$376$	1.83196	+	10.3895i	0.0944760	+	0.535800i
$377$	27.8049	−	10.1202i	1.43203	−	0.521215i
$378$	−4.95794	−	4.16021i	−0.255009	−	0.213978i
$379$	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
$382$	16.0302	+	13.4509i	0.820176	+	0.688209i
$383$	4.54171	−	1.65305i	0.232071	−	0.0844668i	−0.223367	−	0.974734i	$-0.571705\pi$
$383$	4.54171	−	1.65305i	0.232071	−	0.0844668i	0.455438	+	0.890268i	$0.349483\pi$
$384$	0.0768330	+	0.435741i	0.00392087	+	0.0222363i
$385$	−0.761536	+	4.31889i	−0.0388115	+	0.220111i
$386$	7.31907	+	2.66392i	0.372531	+	0.135590i
$387$	−8.75856	−	15.1703i	−0.445223	−	0.771149i
$388$	−3.91216	+	6.77606i	−0.198610	+	0.344002i
$389$	16.6455	−	13.9672i	0.843959	−	0.708166i	−0.114492	−	0.993424i	$-0.536524\pi$
$389$	16.6455	−	13.9672i	0.843959	−	0.708166i	0.958451	+	0.285259i	$0.0920795\pi$
$390$	1.95190	−	1.63784i	0.0988383	−	0.0829352i
$391$	14.0057	−	24.2585i	0.708297	−	1.22681i
$392$	−0.324429	−	0.561928i	−0.0163862	−	0.0283817i
$393$	−1.46465	−	0.533088i	−0.0738817	−	0.0268907i
$394$	−0.316933	+	1.79741i	−0.0159668	+	0.0905524i
$395$	1.41363	+	8.01708i	0.0711273	+	0.403383i
$396$	5.14371	−	1.87216i	0.258481	−	0.0940794i
$397$	8.97345	+	7.52962i	0.450365	+	0.377901i	0.839571	−	0.543250i	$-0.182806\pi$
$397$	8.97345	+	7.52962i	0.450365	+	0.377901i	−0.389206	+	0.921151i	$0.627251\pi$
$398$	−2.35926			−0.118259
$399$		0			0
$400$	−4.20524			−0.210262
$401$	−9.04878	−	7.59283i	−0.451874	−	0.379168i	0.388256	−	0.921551i	$-0.373077\pi$
$401$	−9.04878	−	7.59283i	−0.451874	−	0.379168i	−0.840131	+	0.542384i	$0.817522\pi$
$402$	1.11122	−	0.404450i	0.0554225	−	0.0201721i
$403$	9.86384	+	55.9406i	0.491353	+	2.78660i
$404$	−0.935073	+	5.30306i	−0.0465216	+	0.263837i
$405$	6.09561	+	2.21862i	0.302893	+	0.110244i
$406$	5.77195	+	9.99731i	0.286457	+	0.496158i
$407$	5.83625	−	10.1087i	0.289292	−	0.501069i
$408$	−1.15996	+	0.973325i	−0.0574268	+	0.0481868i
$409$	19.3551	−	16.2408i	0.957047	−	0.803058i	−0.0234228	−	0.999726i	$-0.507456\pi$
$409$	19.3551	−	16.2408i	0.957047	−	0.803058i	0.980470	+	0.196668i	$0.0630120\pi$
$410$	1.55535	−	2.69395i	0.0768133	−	0.133045i
$411$	−2.43433	−	4.21639i	−0.120077	−	0.207979i
$412$	4.41155	+	1.60567i	0.217342	+	0.0791059i
$413$	1.24354	−	7.05249i	0.0611908	−	0.347030i
$414$	3.98569	+	22.6040i	0.195886	+	1.11093i
$415$	−11.8320	+	4.30649i	−0.580809	+	0.211397i
$416$	4.94838	+	4.15218i	0.242614	+	0.203578i
$417$	−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	$0.219142\pi$
$420$	0.761508	+	0.638981i	0.0371578	+	0.0311791i
$421$	2.05766	−	0.748928i	0.100284	−	0.0365005i	−0.291391	−	0.956604i	$-0.594118\pi$
$421$	2.05766	−	0.748928i	0.100284	−	0.0365005i	0.391675	+	0.920104i	$0.371896\pi$
$422$	0.0626957	+	0.355565i	0.00305198	+	0.0173086i
$423$	5.13722	−	29.1346i	0.249780	−	1.41657i
$424$	3.53586	+	1.28695i	0.171716	+	0.0624996i
$425$	−7.19572	−	12.4633i	−0.349044	−	0.604561i
$426$	−0.0124864	+	0.0216271i	−0.000604968	+	0.00104784i
$427$	−4.73939	+	3.97682i	−0.229355	+	0.192452i
$428$	12.2853	−	10.3086i	0.593831	−	0.498283i
$429$	−2.78955	+	4.83164i	−0.134681	+	0.233274i
$430$	2.78444	+	4.82278i	0.134277	+	0.232575i
$431$	1.69494	+	0.616907i	0.0816423	+	0.0297154i	0.382518	−	0.923948i	$-0.375057\pi$
$431$	1.69494	+	0.616907i	0.0816423	+	0.0297154i	−0.300876	+	0.953663i	$0.597279\pi$
$432$	0.445956	−	2.52914i	0.0214561	−	0.121683i
$433$	−1.14127	−	6.47248i	−0.0548461	−	0.311048i	0.945027	−	0.326993i	$-0.106035\pi$
$433$	−1.14127	−	6.47248i	−0.0548461	−	0.311048i	−0.999873	+	0.0159454i	$0.994924\pi$
$434$	−20.8247	+	7.57957i	−0.999617	+	0.363831i
$435$	1.38412	+	1.16142i	0.0663637	+	0.0556858i
$436$	14.1008			0.675305
$437$		0			0
$438$	−3.08361			−0.147340
$439$	−6.99444	−	5.86903i	−0.333827	−	0.280114i	0.460430	−	0.887696i	$-0.347695\pi$
$439$	−6.99444	−	5.86903i	−0.333827	−	0.280114i	−0.794257	+	0.607582i	$0.792140\pi$
$440$	−1.63524	+	0.595177i	−0.0779568	+	0.0283740i
$441$	0.315961	+	1.79190i	0.0150458	+	0.0853288i
$442$	−3.83877	+	21.7708i	−0.182592	+	1.03553i
$443$	25.8120	+	9.39482i	1.22637	+	0.446361i	0.872352	−	0.488878i	$-0.162594\pi$
$443$	25.8120	+	9.39482i	1.22637	+	0.446361i	0.354015	+	0.935240i	$0.384816\pi$
$444$	−1.32292	−	2.29137i	−0.0627830	−	0.108743i
$445$	0.832538	−	1.44200i	0.0394661	−	0.0683572i
$446$	−13.8260	+	11.6014i	−0.654682	+	0.549343i
$447$	−4.87730	+	4.09254i	−0.230688	+	0.193570i
$448$	−1.26007	+	2.18251i	−0.0595329	+	0.103114i
$449$	3.78646	+	6.55835i	0.178694	+	0.309508i	0.941434	−	0.337199i	$-0.109479\pi$
$449$	3.78646	+	6.55835i	0.178694	+	0.309508i	−0.762739	+	0.646706i	$0.776146\pi$
$450$	11.0813	+	4.03326i	0.522377	+	0.190130i
$451$	−1.18274	+	6.70764i	−0.0556930	+	0.315851i
$452$	−2.20922	−	12.5291i	−0.103913	−	0.589319i
$453$	5.15848	−	1.87753i	0.242366	−	0.0882142i
$454$	−9.41045	−	7.89631i	−0.441655	−	0.370592i
$455$	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	$0.670029\pi$
$458$	−5.20277	−	4.36565i	−0.243110	−	0.203993i
$459$	8.25887	−	3.00598i	0.385491	−	0.140307i
$460$	−1.26709	−	7.18604i	−0.0590785	−	0.335051i
$461$	2.07412	−	11.7629i	0.0966014	−	0.547854i	−0.897643	−	0.440722i	$-0.854722\pi$
$461$	2.07412	−	11.7629i	0.0966014	−	0.547854i	0.994245	−	0.107131i	$-0.0341666\pi$
$462$	−2.04534	−	0.744445i	−0.0951580	−	0.0346347i
$463$	4.37685	+	7.58093i	0.203410	+	0.352316i	0.949625	−	0.313389i	$-0.101464\pi$
$463$	4.37685	+	7.58093i	0.203410	+	0.352316i	−0.746215	+	0.665705i	$0.768131\pi$
$464$	−2.29032	+	3.96695i	−0.106326	+	0.184161i
$465$	−2.65715	+	2.22961i	−0.123222	+	0.103396i
$466$	−16.4158	+	13.7745i	−0.760449	+	0.638092i
$467$	−14.6784	+	25.4238i	−0.679236	+	1.17647i	0.295975	+	0.955196i	$0.404355\pi$
$467$	−14.6784	+	25.4238i	−0.679236	+	1.17647i	−0.975211	+	0.221276i	$0.928978\pi$
$468$	−9.05716	−	15.6875i	−0.418667	−	0.725153i
$469$	6.32918	+	2.30363i	0.292254	+	0.106372i
$470$	−1.63317	+	9.26219i	−0.0753327	+	0.427233i
$471$	0.0346686	+	0.196615i	0.00159744	+	0.00905956i
$472$	2.67025	−	0.971890i	0.122908	−	0.0447349i
$473$	−9.34074	−	7.83781i	−0.429488	−	0.360383i
$474$	−4.04041			−0.185582
$475$		0			0
$476$	−8.62460			−0.395308
$477$	−8.08306	−	6.78249i	−0.370098	−	0.310549i
$478$	−11.1237	+	4.04871i	−0.508788	+	0.185184i
$479$	−4.31871	−	24.4926i	−0.197327	−	1.11910i	−0.909066	−	0.416652i	$-0.863203\pi$
$479$	−4.31871	−	24.4926i	−0.197327	−	1.11910i	0.711739	−	0.702444i	$-0.247908\pi$
$480$	−0.0684959	+	0.388460i	−0.00312640	+	0.0177307i
$481$	−36.2979	−	13.2113i	−1.65504	−	0.602386i
$482$	−10.8732	−	18.8329i	−0.495259	−	0.857813i
$483$	4.56346	−	7.90414i	0.207645	−	0.359651i
$484$	−5.50766	+	4.62148i	−0.250348	+	0.210067i
$485$	−5.34340	+	4.48364i	−0.242631	+	0.203592i
$486$	−5.46200	+	9.46046i	−0.247761	+	0.429135i
$487$	4.26883	+	7.39383i	0.193439	+	0.335046i	0.946388	−	0.323033i	$-0.104702\pi$
$487$	4.26883	+	7.39383i	0.193439	+	0.335046i	−0.752949	+	0.658079i	$0.771369\pi$
$488$	−2.30690	−	0.839642i	−0.104428	−	0.0380088i
$489$	0.00532101	−	0.0301769i	0.000240624	−	0.00136465i
$490$	−0.100447	−	0.569664i	−0.00453774	−	0.0257348i
$491$	10.8438	−	3.94681i	0.489373	−	0.178117i	−0.0855352	−	0.996335i	$-0.527260\pi$
$491$	10.8438	−	3.94681i	0.489373	−	0.178117i	0.574908	+	0.818218i	$0.305038\pi$
$492$	1.18269	+	0.992398i	0.0533200	+	0.0447408i
$493$	−15.6762			−0.706019
$494$		0			0
$495$	4.87986			0.219333
$496$	−6.73629	−	5.65242i	−0.302468	−	0.253801i
$497$	−0.133660	+	0.0486483i	−0.00599547	+	0.00218217i
$498$	−1.08518	−	6.15437i	−0.0486281	−	0.275784i
$499$	−5.14156	+	29.1592i	−0.230168	+	1.30535i	0.622388	+	0.782709i	$0.286163\pi$
$499$	−5.14156	+	29.1592i	−0.230168	+	1.30535i	−0.852555	+	0.522637i	$0.824948\pi$
$500$	−7.71149	−	2.80675i	−0.344868	−	0.125522i
$501$	0.480893	+	0.832931i	0.0214847	+	0.0372126i
$502$	11.8205	−	20.4737i	0.527575	−	0.913787i
$503$	4.49536	−	3.77205i	0.200438	−	0.168187i	−0.537044	−	0.843554i	$-0.680459\pi$
$503$	4.49536	−	3.77205i	0.200438	−	0.168187i	0.737482	+	0.675367i	$0.236015\pi$
$504$	5.41368	−	4.54262i	0.241145	−	0.202344i
$505$	−2.40028	+	4.15741i	−0.106811	+	0.185002i
$506$	7.98855	+	13.8366i	0.355135	+	0.615111i
$507$	11.9441	+	4.34731i	0.530458	+	0.193071i
$508$	1.24582	−	7.06542i	0.0552745	−	0.313477i
$509$	4.43996	+	25.1802i	0.196798	+	1.11609i	0.909835	+	0.414969i	$0.136208\pi$
$509$	4.43996	+	25.1802i	0.196798	+	1.11609i	−0.713038	+	0.701125i	$0.752681\pi$
$510$	−1.26851	+	0.461699i	−0.0561705	+	0.0204444i
$511$	−13.4543	−	11.2895i	−0.595183	−	0.499418i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	0.923469			0.0407325
$515$	3.20610	+	2.69024i	0.141278	+	0.118546i
$516$	−2.59725	+	0.945320i	−0.114337	+	0.0416154i
$517$	−3.57596	−	20.2803i	−0.157271	−	0.891925i
$518$	2.61687	−	14.8410i	0.114979	−	0.652077i
$519$	−7.00559	−	2.54983i	−0.307511	−	0.111925i
$520$	2.87936	+	4.98720i	0.126268	+	0.218703i
$521$	−7.01661	+	12.1531i	−0.307403	+	0.532438i	−0.977794	−	0.209571i	$-0.932793\pi$
$521$	−7.01661	+	12.1531i	−0.307403	+	0.532438i	0.670390	+	0.742009i	$0.266127\pi$
$522$	9.83997	−	8.25671i	0.430684	−	0.361386i
$523$	−23.8074	+	19.9768i	−1.04103	+	0.873525i	−0.992122	−	0.125279i	$-0.960018\pi$
$523$	−23.8074	+	19.9768i	−1.04103	+	0.873525i	−0.0489047	+	0.998803i	$0.515573\pi$
$524$	1.76133	−	3.05071i	0.0769439	−	0.133271i
$525$	−2.34458	−	4.06093i	−0.102326	−	0.177233i
$526$	4.05917	+	1.47742i	0.176988	+	0.0644184i
$527$	5.22577	−	29.6368i	0.227638	−	1.29100i
$528$	−0.149977	−	0.850563i	−0.00652692	−	0.0370160i
$529$	−41.3417	+	15.0471i	−1.79746	+	0.654223i
$530$	2.56969	+	2.15622i	0.111620	+	0.0936603i
$531$	−7.96853			−0.345805
$532$		0			0
$533$	22.5398			0.976307
$534$	0.633065	+	0.531204i	0.0273954	+	0.0229875i
$535$	13.4349	−	4.88989i	0.580840	−	0.211409i
$536$	0.464094	+	2.63201i	0.0200458	+	0.113685i
$537$	−1.45718	+	8.26406i	−0.0628818	+	0.356621i
$538$	−10.1443	−	3.69223i	−0.437353	−	0.159183i
$539$	0.633283	+	1.09688i	0.0272774	+	0.0472459i
$540$	1.14475	−	1.98276i	0.0492620	−	0.0853243i
$541$	2.21852	−	1.86156i	0.0953818	−	0.0800349i	−0.593850	−	0.804576i	$-0.702393\pi$
$541$	2.21852	−	1.86156i	0.0953818	−	0.0800349i	0.689232	+	0.724541i	$0.257948\pi$
$542$	−0.618384	+	0.518886i	−0.0265619	+	0.0222881i
$543$	−0.439559	+	0.761338i	−0.0188633	+	0.0326722i
$544$	−1.71113	−	2.96376i	−0.0733641	−	0.127070i
$545$	11.8126	+	4.29944i	0.505997	+	0.184168i
$546$	−1.25078	+	7.09355i	−0.0535286	+	0.303576i
$547$	−5.27649	−	29.9245i	−0.225607	−	1.27948i	−0.861522	−	0.507720i	$-0.830489\pi$
$547$	−5.27649	−	29.9245i	−0.225607	−	1.27948i	0.635916	−	0.771759i	$-0.280623\pi$
$548$	10.3400	−	3.76343i	0.441701	−	0.160766i
$549$	5.27363	+	4.42510i	0.225073	+	0.188859i
$550$	8.20859			0.350015
$551$		0			0
$552$	3.62158			0.154145
$553$	−17.6290	−	14.7925i	−0.749661	−	0.629040i
$554$	−8.59696	+	3.12904i	−0.365250	+	0.132940i
$555$	−0.409592	−	2.32291i	−0.0173862	−	0.0986021i
$556$	3.77834	−	21.4280i	0.160237	−	0.908752i
$557$	5.76419	+	2.09799i	0.244237	+	0.0888949i	0.461238	−	0.887276i	$-0.347405\pi$
$557$	5.76419	+	2.09799i	0.244237	+	0.0888949i	−0.217001	+	0.976171i	$0.569628\pi$
$558$	12.3296	+	21.3555i	0.521955	+	0.904052i
$559$	−20.1757	+	34.9454i	−0.853342	+	1.47803i
$560$	−1.72106	+	1.44414i	−0.0727282	+	0.0610262i
$561$	2.26424	−	1.89992i	0.0955961	−	0.0802147i
$562$	10.6079	−	18.3734i	0.447466	−	0.775034i
$563$	−14.0958	−	24.4147i	−0.594069	−	1.02896i	−0.993678	−	0.112271i	$-0.964187\pi$
$563$	−14.0958	−	24.4147i	−0.594069	−	1.02896i	0.399609	−	0.916686i	$-0.369146\pi$
$564$	−4.38640	−	1.59652i	−0.184701	−	0.0672256i
$565$	1.96950	−	11.1696i	0.0828574	−	0.469908i
$566$	−0.901208	−	5.11101i	−0.0378806	−	0.214832i
$567$	−17.2316	+	6.27180i	−0.723660	+	0.263391i
$568$	−0.0432358	−	0.0362792i	−0.00181414	−	0.00152224i
$569$	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	$0.498888\pi$
$572$	−9.65918	−	8.10501i	−0.403871	−	0.338888i
$573$	−8.70058	+	3.16675i	−0.363472	+	0.132293i
$574$	1.52699	+	8.66001i	0.0637355	+	0.361462i
$575$	−5.97698	+	33.8972i	−0.249257	+	1.41361i
$576$	2.63511	+	0.959102i	0.109796	+	0.0399626i
$577$	9.98157	+	17.2886i	0.415538	+	0.719733i	0.995485	−	0.0949212i	$-0.0302599\pi$
$577$	9.98157	+	17.2886i	0.415538	+	0.719733i	−0.579947	+	0.814655i	$0.696927\pi$
$578$	−2.64407	+	4.57966i	−0.109979	+	0.190489i
$579$	−2.63999	+	2.21521i	−0.109714	+	0.0920610i
$580$	−3.12822	+	2.62489i	−0.129892	+	0.108993i
$581$	17.7972	−	30.8256i	0.738350	−	1.27886i
$582$	−1.73099	−	2.99816i	−0.0717517	−	0.124278i
$583$	−6.90195	−	2.51211i	−0.285850	−	0.104041i
$584$	1.21018	−	6.86330i	0.0500778	−	0.284005i
$585$	−2.80420	−	15.9034i	−0.115940	−	0.657526i
$586$	−16.5066	+	6.00791i	−0.681882	+	0.248185i
$587$	7.77078	+	6.52046i	0.320734	+	0.269128i	0.788912	−	0.614506i	$-0.210645\pi$
$587$	7.77078	+	6.52046i	0.320734	+	0.269128i	−0.468177	+	0.883634i	$0.655089\pi$
$588$	0.287096			0.0118397
$589$		0			0
$590$	2.53328			0.104293
$591$	−0.618626	−	0.519089i	−0.0254469	−	0.0213525i
$592$	5.61917	−	2.04521i	0.230946	−	0.0840576i
$593$	1.29423	+	7.33992i	0.0531475	+	0.301415i	0.999782	−	0.0208955i	$-0.00665174\pi$
$593$	1.29423	+	7.33992i	0.0531475	+	0.301415i	−0.946634	+	0.322310i	$0.895541\pi$
$594$	−0.870501	+	4.93686i	−0.0357171	+	0.202562i
$595$	−7.22507	−	2.62971i	−0.296199	−	0.107808i
$596$	−7.19479	−	12.4617i	−0.294710	−	0.510452i
$597$	0.521942	−	0.904030i	0.0213617	−	0.0369995i
$598$	40.5027	−	33.9858i	1.65628	−	1.38978i
$599$	4.88079	−	4.09547i	0.199424	−	0.167336i	−0.537607	−	0.843195i	$-0.680672\pi$
$599$	4.88079	−	4.09547i	0.199424	−	0.167336i	0.737031	+	0.675859i	$0.236227\pi$
$600$	0.930333	−	1.61138i	0.0379807	−	0.0657845i
$601$	0.873153	+	1.51235i	0.0356166	+	0.0616898i	0.883284	−	0.468838i	$-0.155327\pi$
$601$	0.873153	+	1.51235i	0.0356166	+	0.0616898i	−0.847668	+	0.530528i	$0.821994\pi$
$602$	−14.7932	−	5.38428i	−0.602925	−	0.219447i
$603$	1.30142	−	7.38074i	0.0529981	−	0.300567i
$604$	2.15441	+	12.2183i	0.0876617	+	0.497154i
$605$	−6.02305	+	2.19221i	−0.244872	+	0.0891260i
$606$	−1.82518	−	1.53151i	−0.0741430	−	0.0622134i
$607$	−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
$610$	−1.67654	−	1.40678i	−0.0678811	−	0.0569590i
$611$	−64.0383	+	23.3080i	−2.59071	+	0.942942i
$612$	1.66647	+	9.45099i	0.0673629	+	0.382034i
$613$	2.21653	−	12.5705i	0.0895246	−	0.507719i	−0.906764	−	0.421639i	$-0.861455\pi$
$613$	2.21653	−	12.5705i	0.0895246	−	0.507719i	0.996288	−	0.0860800i	$-0.0274341\pi$
$614$	−20.2676	−	7.37681i	−0.817935	−	0.297704i
$615$	0.688186	+	1.19197i	0.0277503	+	0.0480650i
$616$	2.45965	−	4.26024i	0.0991021	−	0.171650i
$617$	−1.28943	+	1.08196i	−0.0519105	+	0.0435581i	−0.668374	−	0.743826i	$-0.733009\pi$
$617$	−1.28943	+	1.08196i	−0.0519105	+	0.0435581i	0.616463	+	0.787384i	$0.288565\pi$
$618$	−1.59125	+	1.33521i	−0.0640093	+	0.0537102i
$619$	−15.7642	+	27.3045i	−0.633618	+	1.09746i	0.353188	+	0.935552i	$0.385098\pi$
$619$	−15.7642	+	27.3045i	−0.633618	+	1.09746i	−0.986806	+	0.161906i	$0.948236\pi$
$620$	−3.91971	−	6.78914i	−0.157419	−	0.272658i
$621$	−19.7528	−	7.18943i	−0.792652	−	0.288502i
$622$	0.446915	−	2.53458i	0.0179197	−	0.101628i
$623$	0.817359	+	4.63547i	0.0327468	+	0.185716i
$624$	−2.68579	+	0.977548i	−0.107518	+	0.0391332i
$625$	10.5027	+	8.81280i	0.420107	+	0.352512i
$626$	5.18389			0.207190
$627$		0			0
$628$	−0.451220			−0.0180056
$629$	15.6767	+	13.1543i	0.625069	+	0.524495i
$630$	5.92028	−	2.15480i	0.235869	−	0.0858494i
$631$	−5.51615	−	31.2836i	−0.219594	−	1.24538i	−0.872754	−	0.488161i	$-0.837668\pi$
$631$	−5.51615	−	31.2836i	−0.219594	−	1.24538i	0.653160	−	0.757220i	$-0.273443\pi$
$632$	1.58569	−	8.99289i	0.0630753	−	0.357718i
$633$	−0.150117	−	0.0546383i	−0.00596663	−	0.00217168i
$634$	−10.1281	−	17.5423i	−0.402237	−	0.696696i
$635$	3.19797	−	5.53904i	0.126907	−	0.219810i
$636$	−1.27538	+	1.07017i	−0.0505722	+	0.0424351i
$637$	3.21080	−	2.69418i	0.127217	−	0.106747i
$638$	4.47068	−	7.74345i	0.176996	−	0.306566i
$639$	0.0791358	+	0.137067i	0.00313056	+	0.00542230i
$640$	−0.837728	−	0.304908i	−0.0331141	−	0.0120525i
$641$	7.02298	−	39.8293i	0.277391	−	1.57316i	−0.453873	−	0.891067i	$-0.649958\pi$
$641$	7.02298	−	39.8293i	0.277391	−	1.57316i	0.731263	−	0.682095i	$-0.238931\pi$
$642$	1.23219	+	6.98811i	0.0486307	+	0.275799i
$643$	24.5290	−	8.92784i	0.967331	−	0.352080i	0.190429	−	0.981701i	$-0.439012\pi$
$643$	24.5290	−	8.92784i	0.967331	−	0.352080i	0.776902	+	0.629621i	$0.216790\pi$
$644$	15.8016	+	13.2591i	0.622670	+	0.522482i
$645$	−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	$0.908198\pi$
$648$	−5.57402	−	4.67716i	−0.218968	−	0.183736i
$649$	−5.21229	+	1.89712i	−0.204600	+	0.0744684i
$650$	−4.71705	−	26.7517i	−0.185018	−	1.04929i
$651$	1.70271	−	9.65654i	0.0667344	−	0.378470i
$652$	0.0650777	+	0.0236863i	0.00254864	+	0.000927628i
$653$	21.5915	+	37.3976i	0.844942	+	1.46348i	0.885672	+	0.464312i	$0.153698\pi$
$653$	21.5915	+	37.3976i	0.844942	+	1.46348i	−0.0407298	+	0.999170i	$0.512968\pi$
$654$	−3.11954	+	5.40321i	−0.121984	+	0.211282i
$655$	2.40570	−	2.01862i	0.0939984	−	0.0788740i
$656$	−2.67298	+	2.24289i	−0.104362	+	0.0875703i
$657$	−9.77157	+	16.9249i	−0.381225	+	0.660302i
$658$	−13.2935	−	23.0251i	−0.518236	−	0.897612i
$659$	−13.4159	−	4.88298i	−0.522608	−	0.190214i	0.0672267	−	0.997738i	$-0.478585\pi$
$659$	−13.4159	−	4.88298i	−0.522608	−	0.190214i	−0.589835	+	0.807524i	$0.700807\pi$
$660$	0.133703	−	0.758269i	0.00520439	−	0.0295156i
$661$	−6.20787	−	35.2066i	−0.241458	−	1.36938i	−0.828577	−	0.559875i	$-0.810849\pi$
$661$	−6.20787	−	35.2066i	−0.241458	−	1.36938i	0.587119	−	0.809501i	$-0.300262\pi$
$662$	−20.0418	+	7.29460i	−0.778945	+	0.283513i
$663$	−7.49296	−	6.28734i	−0.291002	−	0.244180i
$664$	14.1239			0.548114
$665$		0			0
$666$	−16.7687			−0.649774
$667$	28.7211	+	24.0999i	1.11209	+	0.933151i
$668$	−2.04262	+	0.743451i	−0.0790312	+	0.0287650i
$669$	−1.38673	−	7.86453i	−0.0536140	−	0.304060i
$670$	−0.413736	+	2.34641i	−0.0159840	+	0.0906498i
$671$	4.50304	+	1.63897i	0.173838	+	0.0632718i
$672$	−0.557537	−	0.965682i	−0.0215074	−	0.0372520i
$673$	5.17870	−	8.96976i	0.199624	−	0.345759i	−0.748783	−	0.662816i	$-0.769361\pi$
$673$	5.17870	−	8.96976i	0.199624	−	0.345759i	0.948407	+	0.317057i	$0.102695\pi$
$674$	17.4103	−	14.6089i	0.670618	−	0.562715i
$675$	−8.27307	+	6.94193i	−0.318431	+	0.267195i
$676$	−14.3635	+	24.8784i	−0.552444	+	0.956861i
$677$	−5.35854	−	9.28126i	−0.205945	−	0.356708i	0.744488	−	0.667636i	$-0.232694\pi$
$677$	−5.35854	−	9.28126i	−0.205945	−	0.356708i	−0.950434	+	0.310928i	$0.899360\pi$
$678$	5.28970	+	1.92529i	0.203150	+	0.0739405i
$679$	3.42407	−	19.4189i	0.131404	−	0.745227i
$680$	−0.529786	−	3.00457i	−0.0203164	−	0.115220i
$681$	5.10764	−	1.85903i	0.195725	−	0.0712381i
$682$	13.1492	+	11.0335i	0.503508	+	0.422493i
$683$	−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
$686$	14.7665	+	12.3905i	0.563786	+	0.473073i
$687$	2.82387	−	1.02780i	0.107737	−	0.0392132i
$688$	−1.08473	−	6.15179i	−0.0413548	−	0.234535i
$689$	−4.22073	+	23.9370i	−0.160797	+	0.911926i
$690$	3.03390	+	1.10425i	0.115499	+	0.0420380i
$691$	12.6407	+	21.8944i	0.480876	+	0.832902i	0.999759	−	0.0219435i	$-0.00698538\pi$
$691$	12.6407	+	21.8944i	0.480876	+	0.832902i	−0.518883	+	0.854845i	$0.673652\pi$
$692$	8.42464	−	14.5919i	0.320257	−	0.554701i
$693$	−10.5675	+	8.86714i	−0.401424	+	0.336835i
$694$	3.77549	−	3.16801i	0.143316	−	0.120256i
$695$	9.69881	−	16.7988i	0.367897	−	0.637216i
$696$	−1.01338	−	1.75523i	−0.0384122	−	0.0665319i
$697$	−11.2212	−	4.08419i	−0.425034	−	0.154700i
$698$	−4.54290	+	25.7641i	−0.171951	+	0.975184i
$699$	−1.64648	−	9.33766i	−0.0622756	−	0.353183i
$700$	9.95870	−	3.62467i	0.376404	−	0.137000i
$701$	−3.96265	−	3.32506i	−0.149667	−	0.125586i	0.564880	−	0.825173i	$-0.308923\pi$
$701$	−3.96265	−	3.32506i	−0.149667	−	0.125586i	−0.714547	+	0.699588i	$0.753367\pi$
$702$	16.5894			0.626127
$703$		0			0
$704$	1.95199			0.0735684
$705$	−3.18782	−	2.67490i	−0.120060	−	0.100742i
$706$	2.54481	−	0.926236i	0.0957753	−	0.0348594i
$707$	−2.35652	−	13.3645i	−0.0886261	−	0.502624i
$708$	−0.218330	+	1.23821i	−0.00820534	+	0.0465348i
$709$	28.1820	+	10.2574i	1.05840	+	0.385226i	0.811826	−	0.583899i	$-0.198473\pi$
$709$	28.1820	+	10.2574i	1.05840	+	0.385226i	0.246572	+	0.969124i	$0.420696\pi$
$710$	−0.0251581	−	0.0435750i	−0.000944165	−	0.00163534i
$711$	−12.8036	+	22.1764i	−0.480171	+	0.831680i
$712$	−1.43077	+	1.20056i	−0.0536205	+	0.0449929i
$713$	−55.1368	+	46.2653i	−2.06489	+	1.73265i
$714$	1.90803	−	3.30481i	0.0714064	−	0.123680i
$715$	−5.62048	−	9.73496i	−0.210194	−	0.364067i
$716$	−17.8218	−	6.48659i	−0.666030	−	0.242415i
$717$	0.909520	−	5.15815i	0.0339667	−	0.192634i
$718$	1.61667	+	9.16858i	0.0603335	+	0.342168i
$719$	21.3341	−	7.76497i	0.795627	−	0.289584i	0.0879538	−	0.996125i	$-0.471967\pi$
$719$	21.3341	−	7.76497i	0.795627	−	0.289584i	0.707673	+	0.706540i	$0.249745\pi$
$720$	1.91507	+	1.60693i	0.0713704	+	0.0598868i
$721$	−11.8313			−0.440620
$722$		0			0
$723$	9.62195			0.357844
$724$	−1.52203	−	1.27714i	−0.0565659	−	0.0474644i
$725$	18.1010	−	6.58824i	0.672256	−	0.244681i
$726$	−0.552409	−	3.13287i	−0.0205018	−	0.116272i
$727$	6.35443	−	36.0378i	0.235673	−	1.33657i	−0.605519	−	0.795831i	$-0.707034\pi$
$727$	6.35443	−	36.0378i	0.235673	−	1.33657i	0.841192	−	0.540737i	$-0.181854\pi$
$728$	−15.2975	−	5.56784i	−0.566963	−	0.206358i
$729$	8.49781	+	14.7186i	0.314734	+	0.545135i
$730$	3.10648	−	5.38058i	0.114976	−	0.199144i
$731$	16.3763	−	13.7414i	0.605701	−	0.508243i
$732$	0.832097	−	0.698212i	0.0307552	−	0.0258067i
$733$	−10.5761	+	18.3184i	−0.390637	+	0.676604i	−0.992534	−	0.121970i	$-0.961079\pi$
$733$	−10.5761	+	18.3184i	−0.390637	+	0.676604i	0.601896	+	0.798574i	$0.294412\pi$
$734$	3.87721	+	6.71552i	0.143110	+	0.247875i
$735$	0.240509	+	0.0875380i	0.00887130	+	0.00322889i
$736$	−1.42132	+	8.06069i	−0.0523904	+	0.297121i
$737$	−0.905906	−	5.13765i	−0.0333695	−	0.189248i
$738$	9.19475	−	3.34662i	0.338463	−	0.123191i
$739$	37.0050	+	31.0509i	1.36125	+	1.14223i	0.975594	+	0.219584i	$0.0704701\pi$
$739$	37.0050	+	31.0509i	1.36125	+	1.14223i	0.385658	+	0.922642i	$0.373974\pi$
$740$	5.33094			0.195969
$741$		0			0
$742$	−9.48276			−0.348123
$743$	−24.4061	−	20.4791i	−0.895371	−	0.751306i	0.0739089	−	0.997265i	$-0.476453\pi$
$743$	−24.4061	−	20.4791i	−0.895371	−	0.751306i	−0.969280	+	0.245959i	$0.920897\pi$
$744$	3.65620	−	1.33075i	0.134043	−	0.0487876i
$745$	−2.22759	−	12.6333i	−0.0816126	−	0.462848i
$746$	4.34335	−	24.6324i	0.159021	−	0.901855i
$747$	−37.2180	−	13.5463i	−1.36174	−	0.495632i
$748$	3.34011	+	5.78523i	0.122126	+	0.211529i
$749$	−20.2081	+	35.0015i	−0.738390	+	1.27893i
$750$	2.78153	−	2.33398i	0.101567	−	0.0852249i
$751$	31.4049	−	26.3519i	1.14598	−	0.961594i	0.146365	−	0.989231i	$-0.453243\pi$
$751$	31.4049	−	26.3519i	1.14598	−	0.961594i	0.999618	+	0.0276369i	$0.00879823\pi$
$752$	5.27491	−	9.13641i	0.192356	−	0.333171i
$753$	5.23015	+	9.05888i	0.190597	+	0.330124i
$754$	−27.8049	−	10.1202i	−1.01259	−	0.368554i
$755$	−1.92064	+	10.8925i	−0.0698992	+	0.396418i
$756$	1.12387	+	6.37381i	0.0408749	+	0.231813i
$757$	12.0483	−	4.38522i	0.437903	−	0.159384i	−0.113655	−	0.993520i	$-0.536256\pi$
$757$	12.0483	−	4.38522i	0.437903	−	0.159384i	0.551558	+	0.834137i	$0.314034\pi$
$758$	−14.6929	−	12.3288i	−0.533670	−	0.447803i
$759$	−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	$0.276465\pi$
$762$	2.43175	+	2.04048i	0.0880928	+	0.0739187i
$763$	−33.3930	+	12.1541i	−1.20891	+	0.440006i
$764$	−3.63375	−	20.6080i	−0.131464	−	0.745572i
$765$	−1.48564	+	8.42548i	−0.0537134	+	0.304624i
$766$	−4.54171	−	1.65305i	−0.164099	−	0.0597270i
$767$	9.17792	+	15.8966i	0.331395	+	0.573994i
$768$	0.221232	−	0.383185i	0.00798301	−	0.0138270i
$769$	−4.26994	+	3.58290i	−0.153978	+	0.129203i	−0.716522	−	0.697564i	$-0.754267\pi$
$769$	−4.26994	+	3.58290i	−0.153978	+	0.129203i	0.562544	+	0.826767i	$0.309823\pi$
$770$	3.35950	−	2.81895i	0.121068	−	0.101588i
$771$	−0.204301	+	0.353859i	−0.00735771	+	0.0127439i
$772$	−3.89440	−	6.74529i	−0.140162	−	0.242768i
$773$	−34.2160	−	12.4536i	−1.23066	−	0.447925i	−0.356839	−	0.934166i	$-0.616146\pi$
$773$	−34.2160	−	12.4536i	−1.23066	−	0.447925i	−0.873825	+	0.486240i	$0.838368\pi$
$774$	−3.04182	+	17.2510i	−0.109336	+	0.620075i
$775$	6.42138	+	36.4174i	0.230663	+	1.30815i
$776$	7.35245	−	2.67607i	0.263938	−	0.0960655i
$777$	5.10792	+	4.28605i	0.183245	+	0.153761i
$778$	−21.7291			−0.779027
$779$		0			0
$780$	−2.54802			−0.0912339
$781$	0.0843959	+	0.0708166i	0.00301992	+	0.00253402i
$782$	−26.3220	+	9.58044i	−0.941274	+	0.342596i
$783$	2.04277	+	11.5851i	0.0730025	+	0.414018i
$784$	−0.112673	+	0.639001i	−0.00402404	+	0.0228215i
$785$	−0.378000	−	0.137581i	−0.0134914	−	0.00491046i
$786$	0.779323	+	1.34983i	0.0277975	+	0.0481467i
$787$	−15.9523	+	27.6302i	−0.568638	+	0.984909i	0.428063	+	0.903749i	$0.359196\pi$
$787$	−15.9523	+	27.6302i	−0.568638	+	0.984909i	−0.996701	+	0.0811606i	$0.974137\pi$
$788$	1.39814	−	1.17318i	0.0498067	−	0.0417928i
$789$	−1.46414	+	1.22856i	−0.0521247	+	0.0437378i
$790$	4.07038	−	7.05010i	0.144818	−	0.250831i
$791$	16.0311	+	27.7667i	0.570001	+	0.987271i
$792$	−5.14371	−	1.87216i	−0.182774	−	0.0665242i
$793$	2.75373	−	15.6172i	0.0977879	−	0.554583i
$794$	−2.03412	−	11.5361i	−0.0721881	−	0.409399i
$795$	−1.39473	+	0.507639i	−0.0494659	+	0.0180041i
$796$	1.80729	+	1.51650i	0.0640578	+	0.0537509i
$797$	−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
$800$	3.22140	+	2.70308i	0.113894	+	0.0955682i
$801$	4.92170	−	1.79135i	0.173900	−	0.0632944i
$802$	2.05119	+	11.6329i	0.0724301	+	0.410771i
$803$	−2.36227	+	13.3971i	−0.0833626	+	0.472773i
$804$	−1.11122	−	0.404450i	−0.0391896	−	0.0142638i
$805$	9.19462	+	15.9256i	0.324068	+	0.561302i
$806$	28.4018	−	49.1934i	1.00041	−	1.73276i
$807$	3.65905	−	3.07031i	0.128805	−	0.108080i
$808$	4.12505	−	3.46133i	0.145119	−	0.121769i
$809$	15.0360	−	26.0430i	0.528636	−	0.915625i	−0.470806	−	0.882237i	$-0.656037\pi$
$809$	15.0360	−	26.0430i	0.528636	−	0.915625i	0.999442	−	0.0333880i	$-0.0106297\pi$
$810$	−3.24341	−	5.61775i	−0.113962	−	0.197387i
$811$	−0.773923	−	0.281685i	−0.0271761	−	0.00989130i	0.328396	−	0.944540i	$-0.393492\pi$
$811$	−0.773923	−	0.281685i	−0.0271761	−	0.00989130i	−0.355572	+	0.934649i	$0.615714\pi$
$812$	2.00458	−	11.3685i	0.0703469	−	0.398957i
$813$	−0.0620229	−	0.351749i	−0.00217524	−	0.0123364i
$814$	−10.9686	+	3.99223i	−0.384448	+	0.139928i
$815$	0.0472952	+	0.0396854i	0.00165668	+	0.00139012i
$816$	1.51423			0.0530085
$817$		0			0
$818$	−25.2663			−0.883414
$819$	34.9705	+	29.3437i	1.22197	+	1.02535i
$820$	−2.92310	+	1.06392i	−0.102079	+	0.0371538i
$821$	1.33904	+	7.59409i	0.0467329	+	0.265036i	0.999218	−	0.0395511i	$-0.0125928\pi$
$821$	1.33904	+	7.59409i	0.0467329	+	0.265036i	−0.952485	+	0.304587i	$0.901482\pi$
$822$	−0.845435	+	4.79470i	−0.0294879	+	0.167234i
$823$	23.3157	+	8.48621i	0.812734	+	0.295811i	0.714753	−	0.699377i	$-0.246539\pi$
$823$	23.3157	+	8.48621i	0.812734	+	0.295811i	0.0979811	+	0.995188i	$0.468762\pi$
$824$	−2.34734	−	4.06571i	−0.0817734	−	0.141636i
$825$	−1.81600	+	3.14540i	−0.0632250	+	0.109509i
$826$	−5.48587	+	4.60319i	−0.190878	+	0.160165i
$827$	8.14188	−	6.83185i	0.283121	−	0.237567i	−0.490157	−	0.871634i	$-0.663060\pi$
$827$	8.14188	−	6.83185i	0.283121	−	0.237567i	0.773278	+	0.634068i	$0.218616\pi$
$828$	11.4764	−	19.8776i	0.398831	−	0.690795i
$829$	−10.7355	−	18.5944i	−0.372859	−	0.645811i	0.617145	−	0.786849i	$-0.288289\pi$
$829$	−10.7355	−	18.5944i	−0.372859	−	0.645811i	−0.990004	+	0.141039i	$0.954956\pi$
$830$	11.8320	+	4.30649i	0.410694	+	0.149480i
$831$	0.702921	−	3.98646i	0.0243841	−	0.138289i
$832$	−1.12171	−	6.36151i	−0.0388882	−	0.220546i
$833$	−2.08665	+	0.759478i	−0.0722981	+	0.0263143i
$834$	7.37501	+	6.18837i	0.255376	+	0.214286i
$835$	−1.93784			−0.0670617
$836$		0			0
$837$	−22.5834			−0.780595
$838$	−24.2179	−	20.3213i	−0.836594	−	0.701986i
$839$	45.8794	−	16.6987i	1.58393	−	0.576505i	0.607879	−	0.794030i	$-0.292020\pi$
$839$	45.8794	−	16.6987i	1.58393	−	0.576505i	0.976055	+	0.217525i	$0.0697983\pi$
$840$	−0.172620	−	0.978976i	−0.00595595	−	0.0337779i
$841$	−1.39226	+	7.89589i	−0.0480089	+	0.272272i
$842$	−2.05766	−	0.748928i	−0.0709118	−	0.0258098i
$843$	4.69360	+	8.12955i	0.161656	+	0.279997i
$844$	0.180525	−	0.312679i	0.00621393	−	0.0107628i
$845$	−19.6184	+	16.4618i	−0.674892	+	0.566301i
$846$	−22.6627	+	19.0163i	−0.779160	+	0.653793i
$847$	9.05960	−	15.6917i	0.311292	−	0.539173i
$848$	−1.88139	−	3.25866i	−0.0646072	−	0.111903i
$849$	2.15783	+	0.785388i	0.0740567	+	0.0269544i
$850$	−2.49905	+	14.1728i	−0.0857166	+	0.486123i
$851$	−8.49919	−	48.2013i	−0.291348	−	1.65232i
$852$	0.0234668	−	0.00854121i	0.000803958	−	0.000292617i
$853$	−16.0954	−	13.5056i	−0.551096	−	0.462424i	0.324216	−	0.945983i	$-0.394899\pi$
$853$	−16.0954	−	13.5056i	−0.551096	−	0.462424i	−0.875312	+	0.483559i	$0.839344\pi$
$854$	6.18683			0.211709
$855$		0			0
$856$	−16.0373			−0.548143
$857$	24.6967	+	20.7230i	0.843621	+	0.707882i	0.958375	−	0.285511i	$-0.0921635\pi$
$857$	24.6967	+	20.7230i	0.843621	+	0.707882i	−0.114754	+	0.993394i	$0.536608\pi$
$858$	5.24263	−	1.90816i	0.178981	−	0.0651436i
$859$	−7.15907	−	40.6011i	−0.244264	−	1.38529i	−0.822195	−	0.569205i	$-0.807251\pi$
$859$	−7.15907	−	40.6011i	−0.244264	−	1.38529i	0.577931	−	0.816085i	$-0.303860\pi$
$860$	0.967024	−	5.48427i	0.0329753	−	0.187012i
$861$	−3.65620	−	1.33075i	−0.124603	−	0.0453518i
$862$	−0.901858	−	1.56206i	−0.0307174	−	0.0532041i
$863$	21.0325	−	36.4293i	0.715953	−	1.24007i	−0.246637	−	0.969108i	$-0.579326\pi$
$863$	21.0325	−	36.4293i	0.715953	−	1.24007i	0.962591	−	0.270960i	$-0.0873410\pi$
$864$	−1.96732	+	1.65078i	−0.0669297	+	0.0561607i
$865$	11.5068	−	9.65531i	0.391241	−	0.328290i
$866$	−3.28616	+	5.69180i	−0.111668	+	0.193415i
$867$	−1.16990	−	2.02633i	−0.0397320	−	0.0688179i
$868$	20.8247	+	7.57957i	0.706836	+	0.257267i
$869$	−3.09525	+	17.5540i	−0.104999	+	0.595479i
$870$	−0.313756	−	1.77940i	−0.0106373	−	0.0603272i
$871$	−16.2230	+	5.90468i	−0.549694	+	0.200072i
$872$	−10.8018	−	9.06381i	−0.365796	−	0.306939i
$873$	−21.9412			−0.742596
$874$		0			0
$875$	20.6813			0.699156
$876$	2.36218	+	1.98210i	0.0798106	+	0.0669691i
$877$	2.21346	−	0.805633i	0.0747432	−	0.0272043i	−0.304378	−	0.952551i	$-0.598449\pi$
$877$	2.21346	−	0.805633i	0.0747432	−	0.0272043i	0.379121	+	0.925347i	$0.376226\pi$
$878$	1.58551	+	8.99188i	0.0535084	+	0.303461i
$879$	1.34965	−	7.65422i	0.0455224	−	0.258170i
$880$	1.63524	+	0.595177i	0.0551238	+	0.0200634i
$881$	−11.5677	−	20.0358i	−0.389725	−	0.675024i	0.602687	−	0.797977i	$-0.294097\pi$
$881$	−11.5677	−	20.0358i	−0.389725	−	0.675024i	−0.992412	+	0.122954i	$0.960763\pi$
$882$	0.909774	−	1.57577i	0.0306337	−	0.0530591i
$883$	5.37143	−	4.50717i	0.180763	−	0.151678i	−0.547916	−	0.836533i	$-0.684579\pi$
$883$	5.37143	−	4.50717i	0.180763	−	0.151678i	0.728680	+	0.684855i	$0.240134\pi$
$884$	16.9346	−	14.2098i	0.569574	−	0.477929i
$885$	−0.560441	+	0.970712i	−0.0188390	+	0.0326301i
$886$	−13.7343	−	23.7885i	−0.461413	−	0.799191i
$887$	45.9785	+	16.7348i	1.54381	+	0.561900i	0.966955	−	0.254949i	$-0.0820586\pi$
$887$	45.9785	+	16.7348i	1.54381	+	0.561900i	0.576852	+	0.816848i	$0.304281\pi$
$888$	−0.459446	+	2.60565i	−0.0154180	+	0.0874397i
$889$	3.13966	+	17.8059i	0.105301	+	0.597191i
$890$	−1.56466	+	0.569489i	−0.0524475	+	0.0190893i
$891$	10.8804	+	9.12976i	0.364508	+	0.305858i
$892$	18.0486			0.604312
$893$		0			0
$894$	6.36686			0.212940
$895$	−12.9520	−	10.8680i	−0.432937	−	0.363277i
$896$	2.36816	−	0.861941i	0.0791148	−	0.0287954i
$897$	4.06235	+	23.0387i	0.135638	+	0.769241i
$898$	1.31503	−	7.45788i	0.0438830	−	0.248873i
$899$	37.8512	+	13.7767i	1.26241	+	0.459479i
$900$	−5.89623	−	10.2126i	−0.196541	−	0.340419i
$901$	6.43860	−	11.1520i	0.214501	−	0.371527i
$902$	5.21762	−	4.37810i	0.173728	−	0.145775i
$903$	5.33589	−	4.47735i	0.177567	−	0.148997i
$904$	−6.36119	+	11.0179i	−0.211570	+	0.366450i
$905$	−0.885639	−	1.53397i	−0.0294396	−	0.0509910i
$906$	−5.15848	−	1.87753i	−0.171379	−	0.0623768i
$907$	0.207169	−	1.17492i	0.00687895	−	0.0390124i	−0.981175	−	0.193120i	$-0.938139\pi$
$907$	0.207169	−	1.17492i	0.00687895	−	0.0390124i	0.988054	+	0.154108i	$0.0492503\pi$
$908$	2.13318	+	12.0978i	0.0707920	+	0.401481i
$909$	−14.1897	+	5.16464i	−0.470644	+	0.171300i
$910$	−11.1175	−	9.32867i	−0.368541	−	0.309242i
$911$	−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
$914$	16.6749	+	13.9919i	0.551555	+	0.462810i
$915$	0.909962	−	0.331199i	0.0300824	−	0.0109491i
$916$	1.17937	+	6.68856i	0.0389676	+	0.220996i
$917$	−1.54158	+	8.74274i	−0.0509075	+	0.288711i
$918$	−8.25887	−	3.00598i	−0.272583	−	0.0992122i
$919$	−13.4738	−	23.3373i	−0.444460	−	0.769828i	0.553554	−	0.832813i	$-0.313271\pi$
$919$	−13.4738	−	23.3373i	−0.444460	−	0.769828i	−0.998014	+	0.0629854i	$0.979938\pi$
$920$	−3.64845	+	6.31929i	−0.120286	+	0.208341i
$921$	7.31052	−	6.13426i	0.240890	−	0.202131i
$922$	−9.14993	+	7.67770i	−0.301337	+	0.252852i
$923$	0.182293	−	0.315740i	0.00600023	−	0.0103927i
$924$	1.08831	+	1.88500i	0.0358026	+	0.0620119i
$925$	−23.6300	−	8.60061i	−0.776949	−	0.282786i
$926$	1.52007	−	8.62072i	0.0499524	−	0.283294i
$927$	2.28607	+	12.9649i	0.0750843	+	0.425824i
$928$	4.30440	−	1.56667i	0.141299	−	0.0514286i
$929$	−13.6777	−	11.4770i	−0.448752	−	0.376547i	0.390221	−	0.920721i	$-0.372399\pi$
$929$	−13.6777	−	11.4770i	−0.448752	−	0.376547i	−0.838972	+	0.544174i	$0.816843\pi$
$930$	3.46866			0.113742
$931$		0			0
$932$	21.4294			0.701942
$933$	0.872341	+	0.731981i	0.0285592	+	0.0239640i
$934$	27.5864	−	10.0406i	0.902655	−	0.328539i
$935$	1.03414	+	5.86488i	0.0338199	+	0.191802i
$936$	−3.14552	+	17.8391i	−0.102814	+	0.583090i
$937$	22.3953	+	8.15122i	0.731622	+	0.266289i	0.680851	−	0.732422i	$-0.261610\pi$
$937$	22.3953	+	8.15122i	0.731622	+	0.266289i	0.0507708	+	0.998710i	$0.483832\pi$
$938$	−3.36768	−	5.83300i	−0.109959	−	0.190454i
$939$	−1.14684	+	1.98639i	−0.0374257	+	0.0648232i
$940$	7.20470	−	6.04547i	0.234992	−	0.197181i
$941$	−15.6005	+	13.0904i	−0.508563	+	0.426735i	−0.860623	−	0.509242i	$-0.829926\pi$
$941$	−15.6005	+	13.0904i	−0.508563	+	0.426735i	0.352060	+	0.935977i	$0.385481\pi$
$942$	0.0998242	−	0.172901i	0.00325245	−	0.00563341i
$943$	14.2801	+	24.7339i	0.465025	+	0.805446i
$944$	−2.67025	−	0.971890i	−0.0869091	−	0.0316323i
$945$	−1.00192	+	5.68220i	−0.0325926	+	0.184842i
$946$	2.11737	+	12.0082i	0.0688418	+	0.390421i
$947$	3.20989	−	1.16831i	0.104308	−	0.0379648i	−0.289339	−	0.957227i	$-0.593436\pi$
$947$	3.20989	−	1.16831i	0.104308	−	0.0379648i	0.393647	+	0.919262i	$0.371213\pi$
$948$	3.09513	+	2.59712i	0.100525	+	0.0843506i
$949$	45.0184			1.46136
$950$		0			0
$951$	8.96261			0.290633
$952$	6.60683	+	5.54379i	0.214128	+	0.179675i
$953$	−16.6695	+	6.06721i	−0.539979	+	0.196536i	−0.597589	−	0.801803i	$-0.703874\pi$
$953$	−16.6695	+	6.06721i	−0.539979	+	0.196536i	0.0576095	+	0.998339i	$0.481652\pi$
$954$	1.83228	+	10.3914i	0.0593223	+	0.336433i
$955$	3.23946	−	18.3719i	0.104826	−	0.594500i
$956$	11.1237	+	4.04871i	0.359767	+	0.130945i
$957$	1.97811	+	3.42619i	0.0639434	+	0.110753i
$958$	−12.4352	+	21.5385i	−0.401764	+	0.695876i
$959$	−21.2428	+	17.8249i	−0.685967	+	0.575595i
$960$	0.302168	−	0.253549i	0.00975243	−	0.00818326i
$961$	−23.1637	+	40.1208i	−0.747217	+	1.29422i
$962$	19.3137	+	33.4523i	0.622699	+	1.07855i
$963$	42.2600	+	15.3814i	1.36181	+	0.495658i
$964$	−3.77621	+	21.4159i	−0.121623	+	0.689761i
$965$	−1.20575	−	6.83815i	−0.0388145	−	0.220128i
$966$	−8.57650	+	3.12159i	−0.275944	+	0.100435i
$967$	−32.7523	−	27.4825i	−1.05324	−	0.883777i	−0.0598130	−	0.998210i	$-0.519050\pi$
$967$	−32.7523	−	27.4825i	−1.05324	−	0.883777i	−0.993431	+	0.114433i	$0.963495\pi$
$968$	7.18974			0.231087
$969$		0			0
$970$	6.97531			0.223964
$971$	−40.6377	−	34.0990i	−1.30412	−	1.09429i	−0.989417	−	0.145102i	$-0.953649\pi$
$971$	−40.6377	−	34.0990i	−1.30412	−	1.09429i	−0.314708	−	0.949189i	$-0.601906\pi$
$972$	10.2652	−	3.73623i	0.329256	−	0.119840i
$973$	9.52198	+	54.0018i	0.305261	+	1.73122i
$974$	1.48255	−	8.40795i	0.0475039	−	0.269408i
$975$	11.2944	+	4.11083i	0.361710	+	0.131652i
$976$	1.22747	+	2.12605i	0.0392905	+	0.0680532i
$977$	−6.16319	+	10.6750i	−0.197178	+	0.341522i	−0.947612	−	0.319423i	$-0.896511\pi$
$977$	−6.16319	+	10.6750i	−0.197178	+	0.341522i	0.750434	+	0.660945i	$0.229844\pi$
$978$	−0.0234735	+	0.0196966i	−0.000750599	+	0.000629828i
$979$	2.79285	−	2.34348i	0.0892599	−	0.0748980i
$980$	−0.289226	+	0.500954i	−0.00923899	+	0.0160024i
$981$	19.7709	+	34.2442i	0.631236	+	1.09333i
$982$	−10.8438	−	3.94681i	−0.346039	−	0.125948i
$983$	5.60109	−	31.7654i	0.178647	−	1.01316i	−0.755202	−	0.655492i	$-0.772461\pi$
$983$	5.60109	−	31.7654i	0.178647	−	1.01316i	0.933849	−	0.357666i	$-0.116427\pi$
$984$	−0.268095	−	1.52044i	−0.00854656	−	0.0484699i
$985$	1.52897	−	0.556500i	0.0487171	−	0.0177316i
$986$	12.0086	+	10.0764i	0.382433	+	0.320899i
$987$	11.7638			0.374446
$988$		0			0
$989$	−51.1294			−1.62582
$990$	−3.73819	−	3.13671i	−0.118808	−	0.0996913i
$991$	26.1578	−	9.52067i	0.830931	−	0.302434i	0.108690	−	0.994076i	$-0.465334\pi$
$991$	26.1578	−	9.52067i	0.830931	−	0.302434i	0.722241	+	0.691642i	$0.243112\pi$
$992$	1.52699	+	8.66001i	0.0484821	+	0.274956i
$993$	1.63869	−	9.29349i	0.0520023	−	0.294920i
$994$	0.133660	+	0.0486483i	0.00423944	+	0.00154303i
$995$	1.05163	+	1.82147i	0.0333388	+	0.0577446i
$996$	−3.12465	+	5.41206i	−0.0990085	+	0.171488i
$997$	−33.1937	+	27.8528i	−1.05126	+	0.882108i	−0.993225	−	0.116206i	$-0.962927\pi$
$997$	−33.1937	+	27.8528i	−1.05126	+	0.882108i	−0.0580308	+	0.998315i	$0.518482\pi$
$998$	22.6818	−	19.0323i	0.717981	−	0.602458i
$999$	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.415.2		24
19.2	odd	18		722.2.c.m.653.3		8
19.3	odd	18		722.2.c.m.429.3		8
19.4	even	9	inner	722.2.e.s.389.3		24
19.5	even	9		722.2.a.m.1.3	✓	4
19.6	even	9	inner	722.2.e.s.595.2		24
19.7	even	3	inner	722.2.e.s.423.3		24
19.8	odd	6		722.2.e.r.245.2		24
19.9	even	9	inner	722.2.e.s.99.3		24
19.10	odd	18		722.2.e.r.99.2		24
19.11	even	3	inner	722.2.e.s.245.3		24
19.12	odd	6		722.2.e.r.423.2		24
19.13	odd	18		722.2.e.r.595.3		24
19.14	odd	18		722.2.a.n.1.2	yes	4
19.15	odd	18		722.2.e.r.389.2		24
19.16	even	9		722.2.c.n.429.2		8
19.17	even	9		722.2.c.n.653.2		8
19.18	odd	2		722.2.e.r.415.3		24
57.5	odd	18		6498.2.a.ca.1.2		4
57.14	even	18		6498.2.a.bx.1.2		4
76.43	odd	18		5776.2.a.bv.1.2		4
76.71	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	19.5	even	9
722.2.a.n.1.2	yes	4	19.14	odd	18
722.2.c.m.429.3		8	19.3	odd	18
722.2.c.m.653.3		8	19.2	odd	18
722.2.c.n.429.2		8	19.16	even	9
722.2.c.n.653.2		8	19.17	even	9
722.2.e.r.99.2		24	19.10	odd	18
722.2.e.r.245.2		24	19.8	odd	6
722.2.e.r.389.2		24	19.15	odd	18
722.2.e.r.415.3		24	19.18	odd	2
722.2.e.r.423.2		24	19.12	odd	6
722.2.e.r.595.3		24	19.13	odd	18
722.2.e.s.99.3		24	19.9	even	9	inner
722.2.e.s.245.3		24	19.11	even	3	inner
722.2.e.s.389.3		24	19.4	even	9	inner
722.2.e.s.415.2		24	1.1	even	1	trivial
722.2.e.s.423.3		24	19.7	even	3	inner
722.2.e.s.595.2		24	19.6	even	9	inner
5776.2.a.bt.1.3		4	76.71	even	18
5776.2.a.bv.1.2		4	76.43	odd	18
6498.2.a.bx.1.2		4	57.14	even	18
6498.2.a.ca.1.2		4	57.5	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)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.415780 - 0.151331i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.154806 + 0.877948i) q^{5} +(-0.415780 - 0.151331i) q^{6} +(-1.26007 - 2.18251i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.14816 + 1.80252i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.415780 - 0.151331i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.154806 + 0.877948i) q^{5} +(-0.415780 - 0.151331i) q^{6} +(-1.26007 - 2.18251i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.14816 + 1.80252i) q^{9} +(0.682922 - 0.573040i) q^{10} +(-0.975994 + 1.69047i) q^{11} +(0.221232 + 0.383185i) q^{12} +(6.07009 + 2.20933i) q^{13} +(-0.437619 + 2.48186i) q^{14} +(0.0684959 + 0.388460i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.62160 - 2.19979i) q^{17} +2.80423 q^{18} -0.891491 q^{20} +(-0.854195 - 0.716755i) q^{21} +(1.83427 - 0.667620i) q^{22} +(1.42132 + 8.06069i) q^{23} +(0.0768330 - 0.435741i) q^{24} +(3.95164 + 1.43828i) q^{25} +(-3.22982 - 5.59422i) q^{26} +(-1.28408 + 2.22409i) q^{27} +(1.93054 - 1.61992i) q^{28} +(3.50898 - 2.94438i) q^{29} +(0.197226 - 0.341606i) q^{30} +(4.39680 + 7.61548i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.149977 + 0.850563i) q^{33} +(0.594269 + 3.37027i) q^{34} +(2.11120 - 0.768413i) q^{35} +(-2.14816 - 1.80252i) q^{36} -5.97980 q^{37} +2.85816 q^{39} +(0.682922 + 0.573040i) q^{40} +(3.27889 - 1.19342i) q^{41} +(0.193630 + 1.09813i) q^{42} +(-1.08473 + 6.15179i) q^{43} +(-1.83427 - 0.667620i) q^{44} +(-1.24997 - 2.16501i) q^{45} +(4.09252 - 7.08845i) q^{46} +(-8.08163 + 6.78129i) q^{47} +(-0.338947 + 0.284410i) q^{48} +(0.324429 - 0.561928i) q^{49} +(-2.10262 - 3.64185i) q^{50} +(-1.42291 - 0.517895i) q^{51} +(-1.12171 + 6.36151i) q^{52} +(0.653400 + 3.70561i) q^{53} +(2.41328 - 0.878362i) q^{54} +(-1.33306 - 1.11857i) q^{55} -2.52015 q^{56} -4.58064 q^{58} +(2.17680 + 1.82656i) q^{59} +(-0.370664 + 0.134911i) q^{60} +(-0.426298 - 2.41765i) q^{61} +(1.52699 - 8.66001i) q^{62} +(6.64087 + 2.41708i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.87936 + 4.98720i) q^{65} +(0.661620 - 0.555165i) q^{66} +(-2.04734 + 1.71792i) q^{67} +(1.71113 - 2.96376i) q^{68} +(1.81079 + 3.13638i) q^{69} +(-2.11120 - 0.768413i) q^{70} +(0.00980077 - 0.0555829i) q^{71} +(0.486949 + 2.76162i) q^{72} +(6.54888 - 2.38360i) q^{73} +(4.58079 + 3.84374i) q^{74} +1.86067 q^{75} +4.91930 q^{77} +(-2.18948 - 1.83719i) q^{78} +(8.58091 - 3.12320i) q^{79} +(-0.154806 - 0.877948i) q^{80} +(1.26353 - 7.16582i) q^{81} +(-3.27889 - 1.19342i) q^{82} +(7.06195 + 12.2317i) q^{83} +(0.557537 - 0.965682i) q^{84} +(2.33714 - 1.96109i) q^{85} +(4.78524 - 4.01529i) q^{86} +(1.01338 - 1.75523i) q^{87} +(0.975994 + 1.69047i) q^{88} +(-1.75510 - 0.638805i) q^{89} +(-0.434111 + 2.46196i) q^{90} +(-2.82686 - 16.0319i) q^{91} +(-7.69142 + 2.79945i) q^{92} +(2.98056 + 2.50099i) q^{93} +10.5498 q^{94} +0.442463 q^{96} +(5.99377 + 5.02937i) q^{97} +(-0.609728 + 0.221923i) q^{98} +(-0.950519 - 5.39066i) 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

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