LMFDB - Embedded newform 722.2.e.r.245.1

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			245.1
Character	$\chi$	$=$	722.245
Dual form			722.2.e.r.389.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-1.93054 - 1.61992i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.31131 - 0.841250i) q^{5} +(-1.93054 + 1.61992i) q^{6} +(1.39680 + 2.41933i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.581920 + 3.30023i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-1.93054 - 1.61992i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.31131 - 0.841250i) q^{5} +(-1.93054 + 1.61992i) q^{6} +(1.39680 + 2.41933i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.581920 + 3.30023i) q^{9} +(-0.427114 - 2.42228i) q^{10} +(0.839266 - 1.45365i) q^{11} +(1.26007 + 2.18251i) q^{12} +(4.86023 - 4.07822i) q^{13} +(2.62513 - 0.955469i) q^{14} +(-5.82485 - 2.12007i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.862888 - 4.89368i) q^{17} +3.35114 q^{18} -2.45965 q^{20} +(1.22253 - 6.93334i) q^{21} +(-1.28583 - 1.07894i) q^{22} +(2.34820 + 0.854675i) q^{23} +(2.36816 - 0.861941i) q^{24} +(0.804252 - 0.674847i) q^{25} +(-3.17229 - 5.49456i) q^{26} +(0.442463 - 0.766369i) q^{27} +(-0.485104 - 2.75116i) q^{28} +(1.03004 + 5.84167i) q^{29} +(-3.09934 + 5.36821i) q^{30} +(-3.64204 - 6.30820i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-3.97504 + 1.44680i) q^{33} +(-4.66950 - 1.69956i) q^{34} +(5.26371 + 4.41678i) q^{35} +(0.581920 - 3.30023i) q^{36} +0.550972 q^{37} -15.9893 q^{39} +(-0.427114 + 2.42228i) q^{40} +(-1.99739 - 1.67601i) q^{41} +(-6.61571 - 2.40792i) q^{42} +(-2.69813 + 0.982038i) q^{43} +(-1.28583 + 1.07894i) q^{44} +(4.12132 + 7.13833i) q^{45} +(1.24945 - 2.16411i) q^{46} +(0.129471 + 0.734266i) q^{47} +(-0.437619 - 2.48186i) q^{48} +(-0.402113 + 0.696480i) q^{49} +(-0.524938 - 0.909219i) q^{50} +(-9.59321 + 8.04966i) q^{51} +(-5.96195 + 2.16997i) q^{52} +(1.38160 + 0.502862i) q^{53} +(-0.677893 - 0.568820i) q^{54} +(0.716924 - 4.06588i) q^{55} -2.79360 q^{56} +5.93179 q^{58} +(-0.861748 + 4.88722i) q^{59} +(4.74846 + 3.98443i) q^{60} +(-8.77378 - 3.19339i) q^{61} +(-6.84480 + 2.49130i) q^{62} +(-7.17153 + 6.01762i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(7.80272 - 13.5147i) q^{65} +(0.734557 + 4.16588i) q^{66} +(2.00745 + 11.3848i) q^{67} +(-2.48459 + 4.30343i) q^{68} +(-3.14880 - 5.45389i) q^{69} +(5.26371 - 4.41678i) q^{70} +(6.57501 - 2.39311i) q^{71} +(-3.14904 - 1.14616i) q^{72} +(-4.73890 - 3.97641i) q^{73} +(0.0956753 - 0.542602i) q^{74} -2.64584 q^{75} +4.68915 q^{77} +(-2.77651 + 15.7464i) q^{78} +(-4.52853 - 3.79989i) q^{79} +(2.31131 + 0.841250i) q^{80} +(7.35148 - 2.67572i) q^{81} +(-1.99739 + 1.67601i) q^{82} +(-7.58866 - 13.1439i) q^{83} +(-3.52015 + 6.09707i) q^{84} +(-2.12240 - 12.0367i) q^{85} +(0.498594 + 2.82767i) q^{86} +(7.47449 - 12.9462i) q^{87} +(0.839266 + 1.45365i) q^{88} +(5.28955 - 4.43846i) q^{89} +(7.74554 - 2.81915i) q^{90} +(16.6553 + 6.06205i) q^{91} +(-1.91427 - 1.60626i) q^{92} +(-3.18765 + 18.0781i) q^{93} +0.745593 q^{94} -2.52015 q^{96} +(2.49834 - 14.1688i) q^{97} +(0.616073 + 0.516947i) q^{98} +(5.28577 + 1.92386i) 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 $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−1.93054	−	1.61992i	−1.11460	−	0.935261i	−0.116281	−	0.993216i	$-0.537097\pi$
$3$	−1.93054	−	1.61992i	−1.11460	−	0.935261i	−0.998319	+	0.0579555i	$0.981542\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	2.31131	−	0.841250i	1.03365	−	0.376218i	0.231181	−	0.972911i	$-0.425741\pi$
$5$	2.31131	−	0.841250i	1.03365	−	0.376218i	0.802470	+	0.596692i	$0.203519\pi$
$6$	−1.93054	+	1.61992i	−0.788142	+	0.661329i
$7$	1.39680	+	2.41933i	0.527942	+	0.914422i	0.999469	+	0.0325705i	$0.0103694\pi$
$7$	1.39680	+	2.41933i	0.527942	+	0.914422i	−0.471528	+	0.881851i	$0.656297\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.581920	+	3.30023i	0.193973	+	1.10008i
$10$	−0.427114	−	2.42228i	−0.135065	−	0.765993i
$11$	0.839266	−	1.45365i	0.253048	−	0.438292i	−0.711315	−	0.702873i	$-0.751900\pi$
$11$	0.839266	−	1.45365i	0.253048	−	0.438292i	0.964364	+	0.264581i	$0.0852336\pi$
$12$	1.26007	+	2.18251i	0.363752	+	0.630037i
$13$	4.86023	−	4.07822i	1.34798	−	1.13109i	0.368488	−	0.929632i	$-0.379876\pi$
$13$	4.86023	−	4.07822i	1.34798	−	1.13109i	0.979497	−	0.201461i	$-0.0645689\pi$
$14$	2.62513	−	0.955469i	0.701595	−	0.255360i
$15$	−5.82485	−	2.12007i	−1.50397	−	0.547400i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.862888	−	4.89368i	0.209281	−	1.18689i	−0.681278	−	0.732025i	$-0.738576\pi$
$17$	0.862888	−	4.89368i	0.209281	−	1.18689i	0.890559	−	0.454867i	$-0.150313\pi$
$18$	3.35114			0.789872
$19$		0			0
$19$		0			0
$20$	−2.45965			−0.549994
$21$	1.22253	−	6.93334i	0.266779	−	1.51298i
$22$	−1.28583	−	1.07894i	−0.274140	−	0.230031i
$23$	2.34820	+	0.854675i	0.489634	+	0.178212i	0.575026	−	0.818135i	$-0.304992\pi$
$23$	2.34820	+	0.854675i	0.489634	+	0.178212i	−0.0853919	+	0.996347i	$0.527214\pi$
$24$	2.36816	−	0.861941i	0.483399	−	0.175943i
$25$	0.804252	−	0.674847i	0.160850	−	0.134969i
$26$	−3.17229	−	5.49456i	−0.622137	−	1.07757i
$27$	0.442463	−	0.766369i	0.0851521	−	0.147488i
$28$	−0.485104	−	2.75116i	−0.0916761	−	0.519921i
$29$	1.03004	+	5.84167i	0.191274	+	1.08477i	0.917625	+	0.397447i	$0.130104\pi$
$29$	1.03004	+	5.84167i	0.191274	+	1.08477i	−0.726351	+	0.687324i	$0.758785\pi$
$30$	−3.09934	+	5.36821i	−0.565859	+	0.980097i
$31$	−3.64204	−	6.30820i	−0.654130	−	1.13299i	−0.982111	−	0.188302i	$-0.939702\pi$
$31$	−3.64204	−	6.30820i	−0.654130	−	1.13299i	0.327982	−	0.944684i	$-0.393632\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−3.97504	+	1.44680i	−0.691965	+	0.251855i
$34$	−4.66950	−	1.69956i	−0.800812	−	0.291472i
$35$	5.26371	+	4.41678i	0.889730	+	0.746572i
$36$	0.581920	−	3.30023i	0.0969866	−	0.550038i
$37$	0.550972			0.0905792			0.0452896	−	0.998974i	$-0.485579\pi$
$37$	0.550972			0.0905792			0.0452896	+	0.998974i	$0.485579\pi$
$38$		0			0
$39$	−15.9893			−2.56033
$40$	−0.427114	+	2.42228i	−0.0675326	+	0.382996i
$41$	−1.99739	−	1.67601i	−0.311941	−	0.261749i	0.473353	−	0.880873i	$-0.343044\pi$
$41$	−1.99739	−	1.67601i	−0.311941	−	0.261749i	−0.785294	+	0.619124i	$0.787488\pi$
$42$	−6.61571	−	2.40792i	−1.02083	−	0.371550i
$43$	−2.69813	+	0.982038i	−0.411461	+	0.149759i	−0.539453	−	0.842016i	$-0.681369\pi$
$43$	−2.69813	+	0.982038i	−0.411461	+	0.149759i	0.127992	+	0.991775i	$0.459147\pi$
$44$	−1.28583	+	1.07894i	−0.193846	+	0.162656i
$45$	4.12132	+	7.13833i	0.614370	+	1.06412i
$46$	1.24945	−	2.16411i	0.184222	−	0.319081i
$47$	0.129471	+	0.734266i	0.0188853	+	0.107104i	0.992793	−	0.119839i	$-0.0382380\pi$
$47$	0.129471	+	0.734266i	0.0188853	+	0.107104i	−0.973908	+	0.226943i	$0.927127\pi$
$48$	−0.437619	−	2.48186i	−0.0631649	−	0.358226i
$49$	−0.402113	+	0.696480i	−0.0574447	+	0.0994972i
$50$	−0.524938	−	0.909219i	−0.0742374	−	0.128583i
$51$	−9.59321	+	8.04966i	−1.34332	+	1.12718i
$52$	−5.96195	+	2.16997i	−0.826774	+	0.300921i
$53$	1.38160	+	0.502862i	0.189778	+	0.0690735i	0.435161	−	0.900353i	$-0.356692\pi$
$53$	1.38160	+	0.502862i	0.189778	+	0.0690735i	−0.245383	+	0.969426i	$0.578914\pi$
$54$	−0.677893	−	0.568820i	−0.0922496	−	0.0774066i
$55$	0.716924	−	4.06588i	0.0966700	−	0.548243i
$56$	−2.79360			−0.373311
$57$		0			0
$58$	5.93179			0.778882
$59$	−0.861748	+	4.88722i	−0.112190	+	0.636261i	0.875913	+	0.482469i	$0.160260\pi$
$59$	−0.861748	+	4.88722i	−0.112190	+	0.636261i	−0.988103	+	0.153793i	$0.950851\pi$
$60$	4.74846	+	3.98443i	0.613024	+	0.514388i
$61$	−8.77378	−	3.19339i	−1.12337	−	0.408872i	−0.287487	−	0.957784i	$-0.592820\pi$
$61$	−8.77378	−	3.19339i	−1.12337	−	0.408872i	−0.835880	+	0.548912i	$0.815042\pi$
$62$	−6.84480	+	2.49130i	−0.869290	+	0.316396i
$63$	−7.17153	+	6.01762i	−0.903527	+	0.758149i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	7.80272	−	13.5147i	0.967808	−	1.67629i
$66$	0.734557	+	4.16588i	0.0904177	+	0.512784i
$67$	2.00745	+	11.3848i	0.245249	+	1.39088i	0.819914	+	0.572487i	$0.194021\pi$
$67$	2.00745	+	11.3848i	0.245249	+	1.39088i	−0.574665	+	0.818389i	$0.694868\pi$
$68$	−2.48459	+	4.30343i	−0.301300	+	0.521868i
$69$	−3.14880	−	5.45389i	−0.379071	−	0.656571i
$70$	5.26371	−	4.41678i	0.629134	−	0.527906i
$71$	6.57501	−	2.39311i	0.780310	−	0.284010i	0.0790083	−	0.996874i	$-0.474825\pi$
$71$	6.57501	−	2.39311i	0.780310	−	0.284010i	0.701302	+	0.712864i	$0.252602\pi$
$72$	−3.14904	−	1.14616i	−0.371118	−	0.135076i
$73$	−4.73890	−	3.97641i	−0.554646	−	0.465403i	0.321865	−	0.946786i	$-0.395690\pi$
$73$	−4.73890	−	3.97641i	−0.554646	−	0.465403i	−0.876511	+	0.481382i	$0.840135\pi$
$74$	0.0956753	−	0.542602i	0.0111220	−	0.0630761i
$75$	−2.64584			−0.305515
$76$		0			0
$77$	4.68915			0.534379
$78$	−2.77651	+	15.7464i	−0.314377	+	1.78292i
$79$	−4.52853	−	3.79989i	−0.509500	−	0.427521i	0.351453	−	0.936205i	$-0.385688\pi$
$79$	−4.52853	−	3.79989i	−0.509500	−	0.427521i	−0.860953	+	0.508684i	$0.830132\pi$
$80$	2.31131	+	0.841250i	0.258413	+	0.0940546i
$81$	7.35148	−	2.67572i	0.816831	−	0.297302i
$82$	−1.99739	+	1.67601i	−0.220575	+	0.185085i
$83$	−7.58866	−	13.1439i	−0.832964	−	1.44274i	−0.895678	−	0.444704i	$-0.853309\pi$
$83$	−7.58866	−	13.1439i	−0.832964	−	1.44274i	0.0627138	−	0.998032i	$-0.480024\pi$
$84$	−3.52015	+	6.09707i	−0.384080	+	0.665245i
$85$	−2.12240	−	12.0367i	−0.230207	−	1.30557i
$86$	0.498594	+	2.82767i	0.0537648	+	0.304915i
$87$	7.47449	−	12.9462i	0.801349	−	1.38798i
$88$	0.839266	+	1.45365i	0.0894660	+	0.154960i
$89$	5.28955	−	4.43846i	0.560691	−	0.470476i	−0.317851	−	0.948141i	$-0.602961\pi$
$89$	5.28955	−	4.43846i	0.560691	−	0.470476i	0.878542	+	0.477665i	$0.158517\pi$
$90$	7.74554	−	2.81915i	0.816452	−	0.297164i
$91$	16.6553	+	6.06205i	1.74595	+	0.635475i
$92$	−1.91427	−	1.60626i	−0.199577	−	0.167465i
$93$	−3.18765	+	18.0781i	−0.330544	+	1.87461i
$94$	0.745593			0.0769021
$95$		0			0
$96$	−2.52015			−0.257211
$97$	2.49834	−	14.1688i	0.253668	−	1.43862i	−0.545800	−	0.837915i	$-0.683774\pi$
$97$	2.49834	−	14.1688i	0.253668	−	1.43862i	0.799468	−	0.600708i	$-0.205115\pi$
$98$	0.616073	+	0.516947i	0.0622328	+	0.0522195i
$99$	5.28577	+	1.92386i	0.531240	+	0.193355i
$100$	−0.986561	+	0.359079i	−0.0986561	+	0.0359079i
$101$	8.64322	−	7.25253i	0.860033	−	0.721653i	−0.101942	−	0.994790i	$-0.532506\pi$
$101$	8.64322	−	7.25253i	0.860033	−	0.721653i	0.961975	+	0.273137i	$0.0880613\pi$
$102$	6.26153	+	10.8453i	0.619983	+	1.07384i
$103$	−7.41399	+	12.8414i	−0.730522	+	1.26530i	0.226138	+	0.974095i	$0.427390\pi$
$103$	−7.41399	+	12.8414i	−0.730522	+	1.26530i	−0.956660	+	0.291206i	$0.905943\pi$
$104$	1.10172	+	6.24819i	0.108033	+	0.612685i
$105$	−3.00701	−	17.0536i	−0.293454	−	1.66426i
$106$	0.735136	−	1.27329i	0.0714027	−	0.123673i
$107$	1.41424	+	2.44954i	0.136720	+	0.236806i	0.926253	−	0.376902i	$-0.123011\pi$
$107$	1.41424	+	2.44954i	0.136720	+	0.236806i	−0.789533	+	0.613708i	$0.789677\pi$
$108$	−0.677893	+	0.568820i	−0.0652303	+	0.0547347i
$109$	−1.62134	+	0.590118i	−0.155296	+	0.0565231i	−0.418498	−	0.908218i	$-0.637443\pi$
$109$	−1.62134	+	0.590118i	−0.155296	+	0.0565231i	0.263203	+	0.964741i	$0.415221\pi$
$110$	−3.87961	−	1.41206i	−0.369907	−	0.134635i
$111$	−1.06368	−	0.892530i	−0.100960	−	0.0847152i
$112$	−0.485104	+	2.75116i	−0.0458381	+	0.259961i
$113$	−0.427785			−0.0402426			−0.0201213	−	0.999798i	$-0.506405\pi$
$113$	−0.427785			−0.0402426			−0.0201213	+	0.999798i	$0.506405\pi$
$114$		0			0
$115$	6.14643			0.573157
$116$	1.03004	−	5.84167i	0.0956372	−	0.542385i
$117$	16.2873	+	13.6667i	1.50576	+	1.26348i
$118$	4.66333	+	1.69731i	0.429294	+	0.156250i
$119$	13.0447	−	4.74789i	1.19581	−	0.435239i
$120$	4.74846	−	3.98443i	0.433473	−	0.363727i
$121$	4.09127	+	7.08628i	0.371933	+	0.644207i
$122$	−4.66843	+	8.08596i	−0.422660	+	0.732068i
$123$	1.14105	+	6.47123i	0.102885	+	0.583491i
$124$	1.26487	+	7.17342i	0.113588	+	0.644192i
$125$	−4.85796	+	8.41423i	−0.434509	+	0.752592i
$126$	4.68088	+	8.10752i	0.417006	+	0.722276i
$127$	−0.870469	+	0.730410i	−0.0772416	+	0.0648134i	−0.680591	−	0.732664i	$-0.738277\pi$
$127$	−0.870469	+	0.730410i	−0.0772416	+	0.0648134i	0.603349	+	0.797477i	$0.293832\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	6.79968	+	2.47488i	0.598678	+	0.217901i
$130$	−11.9545	−	10.0310i	−1.04848	−	0.879775i
$131$	−3.09814	+	17.5705i	−0.270686	+	1.53514i	0.481653	+	0.876362i	$0.340036\pi$
$131$	−3.09814	+	17.5705i	−0.270686	+	1.53514i	−0.752340	+	0.658776i	$0.771075\pi$
$132$	4.23015			0.368187
$133$		0			0
$134$	11.5604			0.998670
$135$	0.377964	−	2.14354i	0.0325300	−	0.184487i
$136$	3.80661	+	3.19412i	0.326414	+	0.273894i
$137$	14.9558	+	5.44347i	1.27776	+	0.465067i	0.889691	−	0.456563i	$-0.150920\pi$
$137$	14.9558	+	5.44347i	1.27776	+	0.465067i	0.388070	+	0.921630i	$0.373142\pi$
$138$	−5.91781	+	2.15391i	−0.503758	+	0.183353i
$139$	7.75250	−	6.50512i	0.657558	−	0.551757i	−0.251795	−	0.967780i	$-0.581021\pi$
$139$	7.75250	−	6.50512i	0.657558	−	0.551757i	0.909354	+	0.416023i	$0.136577\pi$
$140$	−3.43564	−	5.95071i	−0.290365	−	0.502927i
$141$	0.939503	−	1.62727i	0.0791204	−	0.137041i
$142$	−1.21501	−	6.89068i	−0.101962	−	0.578253i
$143$	−1.84928	−	10.4878i	−0.154644	−	0.877032i
$144$	−1.67557	+	2.90217i	−0.139631	+	0.241848i
$145$	7.29506	+	12.6354i	0.605821	+	1.04931i
$146$	−4.73890	+	3.97641i	−0.392194	+	0.329090i
$147$	1.90454	−	0.693195i	0.157084	−	0.0571738i
$148$	−0.517744	−	0.188444i	−0.0425583	−	0.0154900i
$149$	7.19968	+	6.04125i	0.589820	+	0.494918i	0.888155	−	0.459543i	$-0.151987\pi$
$149$	7.19968	+	6.04125i	0.589820	+	0.494918i	−0.298335	+	0.954461i	$0.596431\pi$
$150$	−0.459446	+	2.60565i	−0.0375136	+	0.212750i
$151$	−10.2632			−0.835210			−0.417605	−	0.908629i	$-0.637130\pi$
$151$	−10.2632			−0.835210			−0.417605	+	0.908629i	$0.637130\pi$
$152$		0			0
$153$	16.6524			1.34627
$154$	0.814263	−	4.61791i	0.0656152	−	0.372122i
$155$	−13.7247	−	11.5164i	−1.10239	−	0.925017i
$156$	15.0250	+	5.46865i	1.20296	+	0.437842i
$157$	−2.79453	+	1.01713i	−0.223028	+	0.0811754i	−0.451117	−	0.892465i	$-0.648974\pi$
$157$	−2.79453	+	1.01713i	−0.223028	+	0.0811754i	0.228090	+	0.973640i	$0.426752\pi$
$158$	−4.52853	+	3.79989i	−0.360271	+	0.302303i
$159$	−1.85265	−	3.20888i	−0.146925	−	0.254481i
$160$	1.22982	−	2.13012i	0.0972262	−	0.168401i
$161$	1.21223	+	6.87489i	0.0955370	+	0.541817i
$162$	−1.35850	−	7.70442i	−0.106734	−	0.605317i
$163$	−2.79595	+	4.84273i	−0.218996	+	0.379312i	−0.954501	−	0.298207i	$-0.903612\pi$
$163$	−2.79595	+	4.84273i	−0.218996	+	0.379312i	0.735505	+	0.677519i	$0.236945\pi$
$164$	1.30371	+	2.25809i	0.101802	+	0.176327i
$165$	−7.97044	+	6.68800i	−0.620498	+	0.520660i
$166$	−14.2620	+	5.19095i	−1.10695	+	0.402896i
$167$	6.65641	+	2.42274i	0.515089	+	0.187477i	0.586468	−	0.809972i	$-0.300518\pi$
$167$	6.65641	+	2.42274i	0.515089	+	0.187477i	−0.0713795	+	0.997449i	$0.522740\pi$
$168$	5.39318	+	4.52541i	0.416093	+	0.349143i
$169$	4.73255	−	26.8396i	0.364042	−	2.06459i
$170$	−12.2224			−0.937418
$171$		0			0
$172$	2.87129			0.218934
$173$	−3.99752	+	22.6711i	−0.303926	+	1.72365i	0.324592	+	0.945854i	$0.394773\pi$
$173$	−3.99752	+	22.6711i	−0.303926	+	1.72365i	−0.628518	+	0.777795i	$0.716338\pi$
$174$	−11.4516	−	9.60901i	−0.868142	−	0.728457i
$175$	2.75606	+	1.00312i	0.208339	+	0.0758290i
$176$	1.57730	−	0.574092i	0.118894	−	0.0432738i
$177$	9.58054	−	8.03903i	0.720118	−	0.604250i
$178$	−3.45251	−	5.97992i	−0.258776	−	0.448214i
$179$	−4.10736	+	7.11415i	−0.306998	+	0.531736i	−0.977704	−	0.209987i	$-0.932658\pi$
$179$	−4.10736	+	7.11415i	−0.306998	+	0.531736i	0.670706	+	0.741723i	$0.265991\pi$
$180$	−1.43132	−	8.11741i	−0.106684	−	0.605036i
$181$	−2.25741	−	12.8024i	−0.167792	−	0.951594i	−0.946139	−	0.323760i	$-0.895053\pi$
$181$	−2.25741	−	12.8024i	−0.167792	−	0.951594i	0.778347	−	0.627834i	$-0.216058\pi$
$182$	8.86212	−	15.3496i	0.656904	−	1.13779i
$183$	11.7651	+	20.3778i	0.869703	+	1.50637i
$184$	−1.91427	+	1.60626i	−0.141122	+	0.118415i
$185$	1.27347	−	0.463505i	0.0936274	−	0.0340776i
$186$	17.2499	+	6.27845i	1.26482	+	0.460358i
$187$	−6.38951	−	5.36144i	−0.467247	−	0.392067i
$188$	0.129471	−	0.734266i	0.00944264	−	0.0535519i
$189$	2.47214			0.179821
$190$		0			0
$191$	6.57479			0.475735			0.237868	−	0.971298i	$-0.423552\pi$
$191$	6.57479			0.475735			0.237868	+	0.971298i	$0.423552\pi$
$192$	−0.437619	+	2.48186i	−0.0315824	+	0.179113i
$193$	20.5933	+	17.2798i	1.48234	+	1.24383i	0.903645	+	0.428282i	$0.140881\pi$
$193$	20.5933	+	17.2798i	1.48234	+	1.24383i	0.578692	+	0.815546i	$0.303563\pi$
$194$	−13.5197	−	4.92077i	−0.970659	−	0.353291i
$195$	−36.9562	+	13.4510i	−2.64649	+	0.963244i
$196$	0.616073	−	0.516947i	0.0440052	−	0.0369248i
$197$	4.92470	+	8.52983i	0.350870	+	0.607725i	0.986402	−	0.164349i	$-0.0525524\pi$
$197$	4.92470	+	8.52983i	0.350870	+	0.607725i	−0.635532	+	0.772075i	$0.719219\pi$
$198$	2.81250	−	4.87139i	0.199876	−	0.346195i
$199$	−3.55390	−	20.1552i	−0.251929	−	1.42876i	−0.803833	−	0.594855i	$-0.797210\pi$
$199$	−3.55390	−	20.1552i	−0.251929	−	1.42876i	0.551904	−	0.833908i	$-0.313902\pi$
$200$	0.182309	+	1.03393i	0.0128912	+	0.0731096i
$201$	14.5670	−	25.2308i	1.02748	−	1.77964i
$202$	−5.64146	−	9.77130i	−0.396932	−	0.687506i
$203$	−12.6942	+	10.6517i	−0.890956	+	0.747601i
$204$	11.7678	−	4.28314i	0.823912	−	0.299879i
$205$	−6.02655	−	2.19348i	−0.420913	−	0.153200i
$206$	11.3589	+	9.53124i	0.791411	+	0.664073i
$207$	−1.45416	+	8.24696i	−0.101071	+	0.573203i
$208$	6.34458			0.439917
$209$		0			0
$210$	−17.3167			−1.19496
$211$	1.40938	−	7.99299i	0.0970257	−	0.550260i	−0.897082	−	0.441864i	$-0.854317\pi$
$211$	1.40938	−	7.99299i	0.0970257	−	0.550260i	0.994108	−	0.108396i	$-0.0345715\pi$
$212$	−1.12629	−	0.945072i	−0.0773541	−	0.0649078i
$213$	−16.5700	−	6.03099i	−1.13536	−	0.413236i
$214$	2.65791	−	0.967399i	0.181691	−	0.0661301i
$215$	−5.41008	+	4.53960i	−0.368965	+	0.309598i
$216$	0.442463	+	0.766369i	0.0301058	+	0.0521448i
$217$	10.1744	−	17.6226i	0.690684	−	1.19630i
$218$	0.299611	+	1.69918i	0.0202922	+	0.115083i
$219$	2.70719	+	15.3533i	0.182935	+	1.03748i
$220$	−2.06430	+	3.57547i	−0.139175	+	0.241058i
$221$	−15.7637	−	27.3035i	−1.06038	−	1.83663i
$222$	−1.06368	+	0.892530i	−0.0713893	+	0.0599027i
$223$	−10.1055	+	3.67809i	−0.676713	+	0.246303i	−0.657435	−	0.753511i	$-0.728359\pi$
$223$	−10.1055	+	3.67809i	−0.676713	+	0.246303i	−0.0192773	+	0.999814i	$0.506137\pi$
$224$	2.62513	+	0.955469i	0.175399	+	0.0638400i
$225$	2.69516	+	2.26151i	0.179677	+	0.150767i
$226$	−0.0742841	+	0.421286i	−0.00494130	+	0.0280235i
$227$	27.0936			1.79827			0.899133	−	0.437676i	$-0.144198\pi$
$227$	27.0936			1.79827			0.899133	+	0.437676i	$0.144198\pi$
$228$		0			0
$229$	9.46557			0.625503			0.312751	−	0.949835i	$-0.398749\pi$
$229$	9.46557			0.625503			0.312751	+	0.949835i	$0.398749\pi$
$230$	1.06732	−	6.05305i	0.0703767	−	0.399126i
$231$	−9.05262	−	7.59605i	−0.595619	−	0.499783i
$232$	−5.57406	−	2.02879i	−0.365955	−	0.133197i
$233$	−21.4833	+	7.81930i	−1.40742	+	0.512259i	−0.930372	−	0.366617i	$-0.880516\pi$
$233$	−21.4833	+	7.81930i	−1.40742	+	0.512259i	−0.477049	+	0.878877i	$0.658294\pi$
$234$	16.2873	−	13.6667i	1.06473	−	0.893418i
$235$	0.916949	+	1.58820i	0.0598152	+	0.103603i
$236$	2.48131	−	4.29775i	0.161519	−	0.279759i
$237$	2.58702	+	14.6717i	0.168045	+	0.953031i
$238$	−2.41057	−	13.6710i	−0.156254	−	0.886160i
$239$	−4.33306	+	7.50508i	−0.280282	+	0.485463i	−0.971454	−	0.237227i	$-0.923761\pi$
$239$	−4.33306	+	7.50508i	−0.280282	+	0.485463i	0.691172	+	0.722690i	$0.257095\pi$
$240$	−3.09934	−	5.36821i	−0.200061	−	0.346517i
$241$	4.33448	−	3.63706i	0.279208	−	0.234284i	−0.492419	−	0.870358i	$-0.663887\pi$
$241$	4.33448	−	3.63706i	0.279208	−	0.234284i	0.771628	+	0.636075i	$0.219443\pi$
$242$	7.68907	−	2.79859i	0.494272	−	0.179900i
$243$	−21.0215	−	7.65119i	−1.34853	−	0.490824i
$244$	7.15245	+	6.00162i	0.457889	+	0.384214i
$245$	−0.343496	+	1.94806i	−0.0219452	+	0.124457i
$246$	6.57106			0.418956
$247$		0			0
$248$	7.28408			0.462539
$249$	−6.64188	+	37.6680i	−0.420912	+	2.38711i
$250$	7.44283	+	6.24527i	0.470726	+	0.394986i
$251$	12.7378	+	4.63616i	0.804000	+	0.292632i	0.711143	−	0.703048i	$-0.248178\pi$
$251$	12.7378	+	4.63616i	0.804000	+	0.292632i	0.0928568	+	0.995679i	$0.470400\pi$
$252$	8.79718	−	3.20191i	0.554170	−	0.201701i
$253$	3.21316	−	2.69617i	0.202010	−	0.169506i
$254$	0.568158	+	0.984079i	0.0356494	+	0.0617466i
$255$	−15.4012	+	26.6756i	−0.964458	+	1.67049i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	1.74330	+	9.88674i	0.108744	+	0.616718i	0.989659	+	0.143443i	$0.0458172\pi$
$257$	1.74330	+	9.88674i	0.108744	+	0.616718i	−0.880915	+	0.473275i	$0.843072\pi$
$258$	3.61803	−	6.26662i	0.225249	−	0.390143i
$259$	0.769599	+	1.33298i	0.0478206	+	0.0828276i
$260$	−11.9545	+	10.0310i	−0.741384	+	0.622095i
$261$	−18.6794	+	6.79876i	−1.15623	+	0.420833i
$262$	16.7655	+	6.10215i	1.03578	+	0.376992i
$263$	−14.4217	−	12.1012i	−0.889280	−	0.746194i	0.0787859	−	0.996892i	$-0.474896\pi$
$263$	−14.4217	−	12.1012i	−0.889280	−	0.746194i	−0.968066	+	0.250697i	$0.919340\pi$
$264$	0.734557	−	4.16588i	0.0452089	−	0.256392i
$265$	3.61635			0.222151
$266$		0			0
$267$	−17.4017			−1.06496
$268$	2.00745	−	11.3848i	0.122624	−	0.695438i
$269$	−12.5499	−	10.5306i	−0.765178	−	0.642061i	0.174291	−	0.984694i	$-0.444237\pi$
$269$	−12.5499	−	10.5306i	−0.765178	−	0.642061i	−0.939469	+	0.342633i	$0.888681\pi$
$270$	−2.04534	−	0.744445i	−0.124476	−	0.0453055i
$271$	2.59998	−	0.946314i	0.157937	−	0.0574845i	−0.261842	−	0.965111i	$-0.584330\pi$
$271$	2.59998	−	0.946314i	0.157937	−	0.0574845i	0.419779	+	0.907626i	$0.362108\pi$
$272$	3.80661	−	3.19412i	0.230810	−	0.193672i
$273$	−22.3338	−	38.6833i	−1.35171	−	2.34122i
$274$	7.95782	−	13.7833i	0.480749	−	0.832682i
$275$	−0.306011	−	1.73548i	−0.0184532	−	0.104653i
$276$	1.09357	+	6.20193i	0.0658250	+	0.373312i
$277$	−12.2661	+	21.2454i	−0.736996	+	1.27651i	0.216846	+	0.976206i	$0.430423\pi$
$277$	−12.2661	+	21.2454i	−0.736996	+	1.27651i	−0.953842	+	0.300309i	$0.902910\pi$
$278$	−5.06008	−	8.76432i	−0.303484	−	0.525649i
$279$	18.6991	−	15.6904i	1.11949	−	0.939361i
$280$	−6.45690	+	2.35012i	−0.385874	+	0.140446i
$281$	−9.55701	−	3.47847i	−0.570124	−	0.207508i	0.0408414	−	0.999166i	$-0.486996\pi$
$281$	−9.55701	−	3.47847i	−0.570124	−	0.207508i	−0.610965	+	0.791658i	$0.709218\pi$
$282$	−1.43940	−	1.20780i	−0.0857151	−	0.0719235i
$283$	4.80446	−	27.2475i	0.285596	−	1.61969i	−0.417554	−	0.908652i	$-0.637113\pi$
$283$	4.80446	−	27.2475i	0.285596	−	1.61969i	0.703150	−	0.711042i	$-0.251776\pi$
$284$	−6.99698			−0.415195
$285$		0			0
$286$	−10.6496			−0.629722
$287$	1.26487	−	7.17342i	0.0746627	−	0.423433i
$288$	2.56712	+	2.15407i	0.151269	+	0.126930i
$289$	−7.22877	−	2.63106i	−0.425222	−	0.154768i
$290$	13.7102	−	4.99011i	0.805092	−	0.293030i
$291$	−27.7755	+	23.3064i	−1.62823	+	1.36624i
$292$	3.09310	+	5.35740i	0.181010	+	0.313518i
$293$	−11.9193	+	20.6448i	−0.696333	+	1.20608i	0.273396	+	0.961901i	$0.411853\pi$
$293$	−11.9193	+	20.6448i	−0.696333	+	1.20608i	−0.969729	+	0.244182i	$0.921480\pi$
$294$	−0.351945	−	1.99598i	−0.0205258	−	0.116408i
$295$	2.11960	+	12.0208i	0.123408	+	0.699880i
$296$	−0.275486	+	0.477156i	−0.0160123	+	0.0277341i
$297$	−0.742689	−	1.28637i	−0.0430952	−	0.0746430i
$298$	7.19968	−	6.04125i	0.417066	−	0.349960i
$299$	14.8983	−	5.42255i	0.861593	−	0.313594i
$300$	2.48628	+	0.904931i	0.143545	+	0.0522462i
$301$	−6.14463	−	5.15596i	−0.354171	−	0.297184i
$302$	−1.78219	+	10.1073i	−0.102554	+	0.581610i
$303$	−28.4346			−1.63353
$304$		0			0
$305$	−22.9654			−1.31500
$306$	2.89166	−	16.3994i	0.165305	−	0.937492i
$307$	19.9083	+	16.7050i	1.13623	+	0.953407i	0.999309	−	0.0371750i	$-0.0118359\pi$
$307$	19.9083	+	16.7050i	1.13623	+	0.953407i	0.136918	+	0.990582i	$0.456280\pi$
$308$	−4.40636	−	1.60378i	−0.251076	−	0.0913841i
$309$	35.1151	−	12.7808i	1.99763	−	0.727077i
$310$	−13.7247	+	11.5164i	−0.779509	+	0.654086i
$311$	11.5522	+	20.0089i	0.655063	+	1.13460i	0.981878	+	0.189515i	$0.0606914\pi$
$311$	11.5522	+	20.0089i	0.655063	+	1.13460i	−0.326814	+	0.945089i	$0.605975\pi$
$312$	7.99463	−	13.8471i	0.452607	−	0.783938i
$313$	2.12974	+	12.0784i	0.120380	+	0.682710i	0.983945	+	0.178472i	$0.0571154\pi$
$313$	2.12974	+	12.0784i	0.120380	+	0.682710i	−0.863565	+	0.504238i	$0.831773\pi$
$314$	0.516408	+	2.92869i	0.0291426	+	0.165276i
$315$	−11.5133	+	19.9417i	−0.648703	+	1.12359i
$316$	2.95579	+	5.11958i	0.166276	+	0.287999i
$317$	−0.208598	+	0.175034i	−0.0117160	+	0.00983090i	−0.648627	−	0.761107i	$-0.724656\pi$
$317$	−0.208598	+	0.175034i	−0.0117160	+	0.00983090i	0.636911	+	0.770937i	$0.280212\pi$
$318$	−3.48184	+	1.26729i	−0.195252	+	0.0710659i
$319$	9.35623	+	3.40539i	0.523848	+	0.190665i
$320$	−1.88420	−	1.58103i	−0.105330	−	0.0883824i
$321$	1.23780	−	7.01991i	0.0690872	−	0.391813i
$322$	6.98095			0.389033
$323$		0			0
$324$	−7.82328			−0.434626
$325$	1.15667	−	6.55982i	0.0641607	−	0.363873i
$326$	4.28365	+	3.59441i	0.237249	+	0.199076i
$327$	4.08601	+	1.48718i	0.225957	+	0.0822415i
$328$	2.45017	−	0.891788i	0.135288	−	0.0492407i
$329$	−1.59559	+	1.33886i	−0.0879677	+	0.0738136i
$330$	5.20234	+	9.01071i	0.286379	+	0.496024i
$331$	9.99650	−	17.3144i	0.549457	−	0.951688i	−0.448855	−	0.893605i	$-0.648168\pi$
$331$	9.99650	−	17.3144i	0.549457	−	0.951688i	0.998312	−	0.0580830i	$-0.0184988\pi$
$332$	2.63551	+	14.9467i	0.144643	+	0.820309i
$333$	0.320621	+	1.81833i	0.0175699	+	0.0996441i
$334$	3.54180	−	6.13458i	0.193799	−	0.335669i
$335$	14.2173	+	24.6251i	0.776775	+	1.34541i
$336$	5.39318	−	4.52541i	0.294222	−	0.246882i
$337$	16.2402	−	5.91093i	0.884658	−	0.321989i	0.140570	−	0.990071i	$-0.455107\pi$
$337$	16.2402	−	5.91093i	0.884658	−	0.321989i	0.744088	+	0.668082i	$0.232884\pi$
$338$	−25.6101	−	9.32130i	−1.39300	−	0.507012i
$339$	0.825858	+	0.692977i	0.0448544	+	0.0376373i
$340$	−2.12240	+	12.0367i	−0.115103	+	0.652784i
$341$	−12.2266			−0.662105
$342$		0			0
$343$	17.3085			0.934573
$344$	0.498594	−	2.82767i	0.0268824	−	0.152458i
$345$	−11.8660	−	9.95672i	−0.638841	−	0.536052i
$346$	21.6325	+	7.87358i	1.16297	+	0.423286i
$347$	17.4271	−	6.34296i	0.935538	−	0.340508i	0.171136	−	0.985247i	$-0.445256\pi$
$347$	17.4271	−	6.34296i	0.935538	−	0.340508i	0.764402	+	0.644739i	$0.223034\pi$
$348$	−11.4516	+	9.60901i	−0.613869	+	0.515097i
$349$	10.0605	+	17.4253i	0.538527	+	0.932755i	0.998984	+	0.0450735i	$0.0143522\pi$
$349$	10.0605	+	17.4253i	0.538527	+	0.932755i	−0.460457	+	0.887682i	$0.652314\pi$
$350$	1.46647	−	2.54000i	0.0783861	−	0.135769i
$351$	−0.974945	−	5.52919i	−0.0520387	−	0.295126i
$352$	−0.291474	−	1.65303i	−0.0155356	−	0.0881068i
$353$	−12.0278	+	20.8328i	−0.640177	+	1.10882i	0.345215	+	0.938523i	$0.387806\pi$
$353$	−12.0278	+	20.8328i	−0.640177	+	1.10882i	−0.985393	+	0.170296i	$0.945527\pi$
$354$	−6.25325	−	10.8310i	−0.332357	−	0.575659i
$355$	13.1837	−	11.0625i	0.699719	−	0.587134i
$356$	−6.48859	+	2.36166i	−0.343895	+	0.125167i
$357$	−32.8746	−	11.9654i	−1.73991	−	0.633275i
$358$	6.29283	+	5.28032i	0.332587	+	0.279073i
$359$	−1.88468	+	10.6886i	−0.0994698	+	0.564121i	0.893816	+	0.448434i	$0.148018\pi$
$359$	−1.88468	+	10.6886i	−0.0994698	+	0.564121i	−0.993286	+	0.115687i	$0.963093\pi$
$360$	−8.24263			−0.434425
$361$		0			0
$362$	−12.9999			−0.683259
$363$	3.58083	−	20.3079i	0.187945	−	1.06589i
$364$	−13.5776	−	11.3929i	−0.711657	−	0.597151i
$365$	−14.2982	−	5.20413i	−0.748404	−	0.272397i
$366$	22.1112	−	8.04782i	1.15577	−	0.420666i
$367$	−24.9823	+	20.9626i	−1.30407	+	1.09424i	−0.314638	+	0.949212i	$0.601883\pi$
$367$	−24.9823	+	20.9626i	−1.30407	+	1.09424i	−0.989427	+	0.145029i	$0.953673\pi$
$368$	1.24945	+	2.16411i	0.0651322	+	0.112812i
$369$	4.36890	−	7.56716i	0.227436	−	0.393931i
$370$	−0.235328	−	1.33461i	−0.0122341	−	0.0693830i
$371$	0.713235	+	4.04496i	0.0370293	+	0.210004i
$372$	9.17848	−	15.8976i	0.475882	−	0.824251i
$373$	2.65099	+	4.59165i	0.137263	+	0.237746i	0.926460	−	0.376394i	$-0.122836\pi$
$373$	2.65099	+	4.59165i	0.137263	+	0.237746i	−0.789197	+	0.614141i	$0.789503\pi$
$374$	−6.38951	+	5.36144i	−0.330394	+	0.277233i
$375$	23.0089	−	8.37455i	1.18817	−	0.432460i
$376$	−0.700629	−	0.255008i	−0.0361322	−	0.0131510i
$377$	28.8298	+	24.1911i	1.48481	+	1.24590i
$378$	0.429282	−	2.43458i	0.0220799	−	0.125221i
$379$	24.6656			1.26699			0.633494	−	0.773748i	$-0.281620\pi$
$379$	24.6656			1.26699			0.633494	+	0.773748i	$0.281620\pi$
$380$		0			0
$381$	2.86368			0.146711
$382$	1.14170	−	6.47491i	0.0584145	−	0.331285i
$383$	2.79159	+	2.34242i	0.142643	+	0.119692i	0.711317	−	0.702871i	$-0.248099\pi$
$383$	2.79159	+	2.34242i	0.142643	+	0.119692i	−0.568674	+	0.822563i	$0.692543\pi$
$384$	2.36816	+	0.861941i	0.120850	+	0.0439857i
$385$	10.8381	−	3.94475i	0.552361	−	0.201043i
$386$	20.5933	−	17.2798i	1.04817	−	0.879519i
$387$	−4.81105	−	8.33298i	−0.244559	−	0.423589i
$388$	−7.19369	+	12.4598i	−0.365204	+	0.632552i
$389$	0.485092	+	2.75109i	0.0245952	+	0.139486i	0.994633	−	0.103469i	$-0.0329943\pi$
$389$	0.485092	+	2.75109i	0.0245952	+	0.139486i	−0.970038	+	0.242955i	$0.921883\pi$
$390$	6.82923	+	38.7305i	0.345812	+	1.96120i
$391$	6.20875	−	10.7539i	0.313990	−	0.543846i
$392$	−0.402113	−	0.696480i	−0.0203098	−	0.0351776i
$393$	34.4438	−	28.9018i	1.73746	−	1.45790i
$394$	9.25541	−	3.36869i	0.466281	−	0.169712i
$395$	−13.6635	−	4.97312i	−0.687487	−	0.250225i
$396$	−4.30900	−	3.61568i	−0.216535	−	0.181695i
$397$	−6.86086	+	38.9099i	−0.344337	+	1.95283i	−0.0438745	+	0.999037i	$0.513970\pi$
$397$	−6.86086	+	38.9099i	−0.344337	+	1.95283i	−0.300462	+	0.953794i	$0.597141\pi$
$398$	−20.4661			−1.02587
$399$		0			0
$400$	1.04988			0.0524938
$401$	−3.23358	+	18.3386i	−0.161477	+	0.915784i	0.791145	+	0.611629i	$0.209485\pi$
$401$	−3.23358	+	18.3386i	−0.161477	+	0.915784i	−0.952622	+	0.304156i	$0.901626\pi$
$402$	−22.3179	−	18.7270i	−1.11312	−	0.934017i
$403$	−43.4273	−	15.8063i	−2.16327	−	0.787366i
$404$	−10.6025	+	3.85899i	−0.527493	+	0.191992i
$405$	14.7406	−	12.3689i	0.732468	−	0.614613i
$406$	8.28553	+	14.3510i	0.411204	+	0.712226i
$407$	0.462412	−	0.800921i	0.0229209	−	0.0397002i
$408$	−2.17461	−	12.3328i	−0.107659	−	0.610564i
$409$	−2.97690	−	16.8828i	−0.147198	−	0.834802i	−0.965576	−	0.260122i	$-0.916237\pi$
$409$	−2.97690	−	16.8828i	−0.147198	−	0.834802i	0.818378	−	0.574681i	$-0.194874\pi$
$410$	−3.20666	+	5.55410i	−0.158366	+	0.274297i
$411$	−20.0549	−	34.7361i	−0.989234	−	1.71340i
$412$	11.3589	−	9.53124i	0.559612	−	0.469570i
$413$	−13.0275	+	4.74162i	−0.641041	+	0.233320i
$414$	7.86915	+	2.86414i	0.386748	+	0.140765i
$415$	−28.5971	−	23.9958i	−1.40378	−	1.17791i
$416$	1.10172	−	6.24819i	0.0540165	−	0.306343i
$417$	−25.5043			−1.24895
$418$		0			0
$419$	−18.5042			−0.903989			−0.451995	−	0.892021i	$-0.649287\pi$
$419$	−18.5042			−0.903989			−0.451995	+	0.892021i	$0.649287\pi$
$420$	−3.00701	+	17.0536i	−0.146727	+	0.832129i
$421$	−12.4096	−	10.4129i	−0.604808	−	0.507494i	0.288179	−	0.957576i	$-0.406950\pi$
$421$	−12.4096	−	10.4129i	−0.604808	−	0.507494i	−0.892987	+	0.450083i	$0.851395\pi$
$422$	−7.62682	−	2.77594i	−0.371268	−	0.135130i
$423$	−2.34791	+	0.854568i	−0.114159	+	0.0415505i
$424$	−1.12629	+	0.945072i	−0.0546976	+	0.0458968i
$425$	−2.60851	−	4.51807i	−0.126531	−	0.219159i
$426$	−8.81671	+	15.2710i	−0.427171	+	0.739882i
$427$	−4.52935	−	25.6872i	−0.219191	−	1.24309i
$428$	−0.491162	−	2.78552i	−0.0237412	−	0.134643i
$429$	−13.4192	+	23.2428i	−0.647887	+	1.12217i
$430$	3.53118	+	6.11619i	0.170289	+	0.294949i
$431$	9.72851	−	8.16319i	0.468606	−	0.393207i	−0.377680	−	0.925936i	$-0.623278\pi$
$431$	9.72851	−	8.16319i	0.468606	−	0.393207i	0.846286	+	0.532729i	$0.178834\pi$
$432$	0.831559	−	0.302663i	0.0400084	−	0.0145619i
$433$	−13.3766	−	4.86867i	−0.642836	−	0.233973i	−2.74106e−5	−	1.00000i	$-0.500009\pi$
$433$	−13.3766	−	4.86867i	−0.642836	−	0.233973i	−0.642809	+	0.766027i	$0.722231\pi$
$434$	−15.5881	−	13.0800i	−0.748253	−	0.627859i
$435$	6.38491	−	36.2106i	0.306133	−	1.73617i
$436$	1.72539			0.0826312
$437$		0			0
$438$	15.5901			0.744924
$439$	4.89515	−	27.7618i	0.233633	−	1.32500i	−0.611842	−	0.790980i	$-0.709571\pi$
$439$	4.89515	−	27.7618i	0.233633	−	1.32500i	0.845474	−	0.534016i	$-0.179318\pi$
$440$	3.16269	+	2.65381i	0.150775	+	0.126516i
$441$	−2.53254	−	0.921770i	−0.120597	−	0.0438938i
$442$	−29.6260	+	10.7830i	−1.40916	+	0.512894i
$443$	−25.2751	+	21.2084i	−1.20086	+	1.00764i	−0.201253	+	0.979539i	$0.564501\pi$
$443$	−25.2751	+	21.2084i	−1.20086	+	1.00764i	−0.999605	+	0.0281007i	$0.991054\pi$
$444$	0.694265	+	1.20250i	0.0329484	+	0.0570683i
$445$	8.49196	−	14.7085i	0.402558	−	0.697250i
$446$	1.86742	+	10.5906i	0.0884247	+	0.501482i
$447$	−4.11297	−	23.3258i	−0.194537	−	1.10327i
$448$	1.39680	−	2.41933i	0.0659927	−	0.114303i
$449$	8.59876	+	14.8935i	0.405801	+	0.702867i	0.994414	−	0.105547i	$-0.0336594\pi$
$449$	8.59876	+	14.8935i	0.405801	+	0.702867i	−0.588614	+	0.808415i	$0.700326\pi$
$450$	2.69516	−	2.26151i	0.127051	−	0.106609i
$451$	−4.11268	+	1.49689i	−0.193659	+	0.0704860i
$452$	0.401986	+	0.146311i	0.0189078	+	0.00688189i
$453$	19.8136	+	16.6256i	0.930926	+	0.781139i
$454$	4.70476	−	26.6820i	0.220805	−	1.25225i
$455$	43.5954			2.04378
$456$		0			0
$457$	−31.1517			−1.45722			−0.728608	−	0.684931i	$-0.759832\pi$
$457$	−31.1517			−1.45722			−0.728608	+	0.684931i	$0.759832\pi$
$458$	1.64368	−	9.32177i	0.0768041	−	0.435578i
$459$	−3.36857	−	2.82657i	−0.157231	−	0.131933i
$460$	−5.77575	−	2.10220i	−0.269296	−	0.0980157i
$461$	−14.6038	+	5.31533i	−0.680165	+	0.247560i	−0.658918	−	0.752215i	$-0.728986\pi$
$461$	−14.6038	+	5.31533i	−0.680165	+	0.247560i	−0.0212465	+	0.999774i	$0.506763\pi$
$462$	−9.05262	+	7.59605i	−0.421166	+	0.353400i
$463$	−10.3324	−	17.8962i	−0.480187	−	0.831708i	0.519555	−	0.854437i	$-0.326098\pi$
$463$	−10.3324	−	17.8962i	−0.480187	−	0.831708i	−0.999742	+	0.0227291i	$0.992764\pi$
$464$	−2.96589	+	5.13708i	−0.137688	+	0.238483i
$465$	7.84050	+	44.4657i	0.363595	+	2.06205i
$466$	3.96996	+	22.5148i	0.183905	+	1.04298i
$467$	14.2415	−	24.6670i	0.659017	−	1.14145i	−0.321853	−	0.946790i	$-0.604306\pi$
$467$	14.2415	−	24.6670i	0.659017	−	1.14145i	0.980870	−	0.194662i	$-0.0623609\pi$
$468$	−10.6308	−	18.4131i	−0.491408	−	0.851144i
$469$	−24.7396	+	20.7590i	−1.14237	+	0.958562i
$470$	1.72330	−	0.627230i	0.0794899	−	0.0289320i
$471$	7.04262	+	2.56330i	0.324507	+	0.118111i
$472$	−3.80158	−	3.18990i	−0.174982	−	0.146827i
$473$	−0.836906	+	4.74633i	−0.0384810	+	0.218236i
$474$	14.8981			0.684290
$475$		0			0
$476$	−13.8819			−0.636276
$477$	−0.855579	+	4.85223i	−0.0391743	+	0.222168i
$478$	6.63863	+	5.57047i	0.303644	+	0.254787i
$479$	9.84107	+	3.58186i	0.449650	+	0.163659i	0.556912	−	0.830572i	$-0.311986\pi$
$479$	9.84107	+	3.58186i	0.449650	+	0.163659i	−0.107262	+	0.994231i	$0.534208\pi$
$480$	−5.82485	+	2.12007i	−0.265867	+	0.0967676i
$481$	2.67785	−	2.24698i	0.122099	−	0.102454i
$482$	−2.82913	−	4.90020i	−0.128863	−	0.223198i
$483$	8.79651	−	15.2360i	0.400255	−	0.693262i
$484$	−1.42088	−	8.05822i	−0.0645855	−	0.366283i
$485$	−6.14505	−	34.8503i	−0.279032	−	1.58247i
$486$	−11.1853	+	19.3735i	−0.507375	+	0.878800i
$487$	−1.14947	−	1.99094i	−0.0520875	−	0.0902181i	0.838806	−	0.544430i	$-0.183254\pi$
$487$	−1.14947	−	1.99094i	−0.0520875	−	0.0902181i	−0.890894	+	0.454212i	$0.849921\pi$
$488$	7.15245	−	6.00162i	0.323776	−	0.271680i
$489$	13.2426	−	4.81990i	0.598849	−	0.217963i
$490$	1.85882	+	0.676555i	0.0839729	+	0.0305636i
$491$	9.31600	+	7.81705i	0.420425	+	0.352779i	0.828325	−	0.560248i	$-0.189294\pi$
$491$	9.31600	+	7.81705i	0.420425	+	0.352779i	−0.407900	+	0.913027i	$0.633739\pi$
$492$	1.14105	−	6.47123i	0.0514426	−	0.291746i
$493$	29.4761			1.32754
$494$		0			0
$495$	13.8355			0.621860
$496$	1.26487	−	7.17342i	0.0567942	−	0.322096i
$497$	14.9737	+	12.5644i	0.671663	+	0.563592i
$498$	35.9424	+	13.0820i	1.61062	+	0.586217i
$499$	−14.2221	+	5.17642i	−0.636668	+	0.231728i	−0.640131	−	0.768266i	$-0.721120\pi$
$499$	−14.2221	+	5.17642i	−0.636668	+	0.231728i	0.00346276	+	0.999994i	$0.498898\pi$
$500$	7.44283	−	6.24527i	0.332853	−	0.279297i
$501$	−8.92586	−	15.4600i	−0.398778	−	0.690704i
$502$	6.77762	−	11.7392i	0.302500	−	0.523945i
$503$	−0.0996190	−	0.564967i	−0.00444179	−	0.0251906i	0.982506	−	0.186229i	$-0.0596267\pi$
$503$	−0.0996190	−	0.564967i	−0.00444179	−	0.0251906i	−0.986948	+	0.161039i	$0.948516\pi$
$504$	−1.62565	−	9.21954i	−0.0724123	−	0.410671i
$505$	13.8760	−	24.0340i	0.617475	−	1.06950i
$506$	−2.09724	−	3.63253i	−0.0932339	−	0.161486i
$507$	−52.6144	+	44.1487i	−2.33669	+	1.96071i
$508$	1.06779	−	0.388643i	0.0473754	−	0.0172432i
$509$	24.6352	+	8.96649i	1.09194	+	0.397433i	0.824338	−	0.566098i	$-0.191548\pi$
$509$	24.6352	+	8.96649i	1.09194	+	0.397433i	0.267599	+	0.963530i	$0.413770\pi$
$510$	23.5959	+	19.7993i	1.04485	+	0.876730i
$511$	3.00095	−	17.0192i	0.132754	−	0.752886i
$512$	1.00000			0.0441942
$513$		0			0
$514$	10.0393			0.442813
$515$	−6.33323	+	35.9175i	−0.279076	+	1.58272i
$516$	−5.54315	−	4.65125i	−0.244024	−	0.204760i
$517$	1.17603	+	0.428039i	0.0517216	+	0.0188251i
$518$	1.44637	−	0.526437i	0.0635500	−	0.0231303i
$519$	44.4427	−	37.2918i	1.95082	−	1.63693i
$520$	7.80272	+	13.5147i	0.342172	+	0.592659i
$521$	6.48183	−	11.2269i	0.283974	−	0.491857i	−0.688386	−	0.725345i	$-0.741680\pi$
$521$	6.48183	−	11.2269i	0.283974	−	0.491857i	0.972360	+	0.233487i	$0.0750138\pi$
$522$	3.45182	+	19.5763i	0.151082	+	0.856829i
$523$	3.08733	+	17.5091i	0.135000	+	0.765622i	0.974860	+	0.222819i	$0.0715258\pi$
$523$	3.08733	+	17.5091i	0.135000	+	0.765622i	−0.839860	+	0.542803i	$0.817363\pi$
$524$	8.92075	−	15.4512i	0.389705	−	0.674989i
$525$	−3.69572	−	6.40117i	−0.161294	−	0.279370i
$526$	−14.4217	+	12.1012i	−0.628816	+	0.527639i
$527$	−34.0130	+	12.3797i	−1.48163	+	0.539269i
$528$	−3.97504	−	1.44680i	−0.172991	−	0.0629637i
$529$	−12.8354	−	10.7702i	−0.558063	−	0.468270i
$530$	0.627973	−	3.56141i	0.0272774	−	0.154698i
$531$	−16.6304			−0.721698
$532$		0			0
$533$	−16.5429			−0.716554
$534$	−3.02177	+	17.1373i	−0.130765	+	0.741603i
$535$	5.32944	+	4.47193i	0.230412	+	0.193338i
$536$	−10.8633	−	3.95390i	−0.469221	−	0.170783i
$537$	19.4538	−	7.08060i	0.839493	−	0.305550i
$538$	−12.5499	+	10.5306i	−0.541063	+	0.454006i
$539$	0.674959	+	1.16906i	0.0290726	+	0.0503551i
$540$	−1.08831	+	1.88500i	−0.0468332	+	0.0811175i
$541$	−0.928007	−	5.26299i	−0.0398981	−	0.226274i	0.958338	−	0.285635i	$-0.0922046\pi$
$541$	−0.928007	−	5.26299i	−0.0398981	−	0.226274i	−0.998237	+	0.0593617i	$0.981093\pi$
$542$	−0.480456	−	2.72480i	−0.0206374	−	0.117040i
$543$	−16.3808	+	28.3724i	−0.702968	+	1.21758i
$544$	−2.48459	−	4.30343i	−0.106526	−	0.184508i
$545$	−3.25098	+	2.72790i	−0.139257	+	0.116850i
$546$	−41.9739	+	15.2772i	−1.79632	+	0.653806i
$547$	−4.79348	−	1.74469i	−0.204955	−	0.0745974i	0.237503	−	0.971387i	$-0.423671\pi$
$547$	−4.79348	−	1.74469i	−0.204955	−	0.0745974i	−0.442458	+	0.896789i	$0.645893\pi$
$548$	−12.1921	−	10.2304i	−0.520820	−	0.437020i
$549$	5.43330	−	30.8138i	0.231888	−	1.31510i
$550$	−1.76225			−0.0751426
$551$		0			0
$552$	6.29761			0.268044
$553$	2.86773	−	16.2637i	0.121948	−	0.691604i
$554$	18.7927	+	15.7689i	0.798425	+	0.669958i
$555$	−3.20933	−	1.16810i	−0.136229	−	0.0495831i
$556$	−9.50985	+	3.46130i	−0.403307	+	0.146792i
$557$	−8.21470	+	6.89295i	−0.348068	+	0.292064i	−0.800014	−	0.599982i	$-0.795174\pi$
$557$	−8.21470	+	6.89295i	−0.348068	+	0.292064i	0.451946	+	0.892045i	$0.350730\pi$
$558$	−12.2050	−	21.1397i	−0.516678	−	0.894913i
$559$	−9.10855	+	15.7765i	−0.385251	+	0.667274i
$560$	1.19319	+	6.76690i	0.0504213	+	0.285954i
$561$	3.65014	+	20.7010i	0.154109	+	0.873996i
$562$	−5.08518	+	8.80779i	−0.214505	+	0.371534i
$563$	−4.88142	−	8.45488i	−0.205728	−	0.356331i	0.744637	−	0.667470i	$-0.232623\pi$
$563$	−4.88142	−	8.45488i	−0.205728	−	0.356331i	−0.950364	+	0.311139i	$0.899289\pi$
$564$	−1.43940	+	1.20780i	−0.0606097	+	0.0508576i
$565$	−0.988745	+	0.359874i	−0.0415968	+	0.0151400i
$566$	−25.9992	−	9.46294i	−1.09283	−	0.397757i
$567$	16.7420	+	14.0482i	0.703098	+	0.589970i
$568$	−1.21501	+	6.89068i	−0.0509808	+	0.289127i
$569$	−8.84194			−0.370674			−0.185337	−	0.982675i	$-0.559338\pi$
$569$	−8.84194			−0.370674			−0.185337	+	0.982675i	$0.559338\pi$
$570$		0			0
$571$	22.8411			0.955871			0.477935	−	0.878395i	$-0.341385\pi$
$571$	22.8411			0.955871			0.477935	+	0.878395i	$0.341385\pi$
$572$	−1.84928	+	10.4878i	−0.0773222	+	0.438516i
$573$	−12.6929	−	10.6506i	−0.530255	−	0.444937i
$574$	−6.84480	−	2.49130i	−0.285696	−	0.103985i
$575$	2.46532	−	0.897303i	0.102811	−	0.0374201i
$576$	2.56712	−	2.15407i	0.106963	−	0.0897530i
$577$	7.00879	+	12.1396i	0.291780	+	0.505377i	0.974231	−	0.225554i	$-0.0724192\pi$
$577$	7.00879	+	12.1396i	0.291780	+	0.505377i	−0.682451	+	0.730931i	$0.739086\pi$
$578$	−3.84635	+	6.66207i	−0.159987	+	0.277106i
$579$	−11.7643	−	66.7189i	−0.488909	−	2.77274i
$580$	−2.53355	−	14.3685i	−0.105200	−	0.596618i
$581$	21.1997	−	36.7190i	0.879513	−	1.52336i
$582$	18.1292	+	31.4006i	0.751478	+	1.30160i
$583$	1.89052	−	1.58633i	0.0782973	−	0.0656992i
$584$	5.81312	−	2.11580i	0.240549	−	0.0875525i
$585$	49.1422	+	17.8863i	2.03178	+	0.739507i
$586$	18.2614	+	15.3232i	0.754373	+	0.632994i
$587$	3.65279	−	20.7160i	0.150767	−	0.855042i	−0.811788	−	0.583953i	$-0.801505\pi$
$587$	3.65279	−	20.7160i	0.150767	−	0.855042i	0.962554	−	0.271089i	$-0.0873836\pi$
$588$	−2.02677			−0.0835825
$589$		0			0
$590$	12.2063			0.502525
$591$	4.31028	−	24.4448i	0.177301	−	1.00553i
$592$	0.422069	+	0.354158i	0.0173469	+	0.0145558i
$593$	32.8134	+	11.9431i	1.34748	+	0.490444i	0.912161	−	0.409831i	$-0.134412\pi$
$593$	32.8134	+	11.9431i	1.34748	+	0.490444i	0.435322	+	0.900275i	$0.356635\pi$
$594$	−1.39580	+	0.508029i	−0.0572703	+	0.0208447i
$595$	26.1563	−	21.9477i	1.07230	−	0.899770i
$596$	−4.69925	−	8.13935i	−0.192489	−	0.333401i
$597$	−25.7888	+	44.6675i	−1.05546	+	1.82812i
$598$	−2.75310	−	15.6136i	−0.112583	−	0.638488i
$599$	3.73528	+	21.1838i	0.152620	+	0.865548i	0.960930	+	0.276792i	$0.0892712\pi$
$599$	3.73528	+	21.1838i	0.152620	+	0.865548i	−0.808310	+	0.588757i	$0.799618\pi$
$600$	1.32292	−	2.29137i	0.0540080	−	0.0935446i
$601$	7.17087	+	12.4203i	0.292506	+	0.506635i	0.974402	−	0.224814i	$-0.0721775\pi$
$601$	7.17087	+	12.4203i	0.292506	+	0.506635i	−0.681896	+	0.731449i	$0.738844\pi$
$602$	−6.14463	+	5.15596i	−0.250436	+	0.210141i
$603$	−36.4043	+	13.2501i	−1.48250	+	0.539585i
$604$	9.64428	+	3.51023i	0.392420	+	0.142829i
$605$	15.4175	+	12.9368i	0.626812	+	0.525958i
$606$	−4.93762	+	28.0026i	−0.200577	+	1.13753i
$607$	−10.3488			−0.420046			−0.210023	−	0.977696i	$-0.567354\pi$
$607$	−10.3488			−0.420046			−0.210023	+	0.977696i	$0.567354\pi$
$608$		0			0
$609$	41.7615			1.69226
$610$	−3.98790	+	22.6165i	−0.161465	+	0.915716i
$611$	3.62375	+	3.04069i	0.146601	+	0.123013i
$612$	−15.6481	−	5.69546i	−0.632539	−	0.230225i
$613$	−18.3873	+	6.69245i	−0.742658	+	0.270305i	−0.685513	−	0.728061i	$-0.740422\pi$
$613$	−18.3873	+	6.69245i	−0.742658	+	0.270305i	−0.0571450	+	0.998366i	$0.518200\pi$
$614$	19.9083	−	16.7050i	0.803434	−	0.674161i
$615$	8.08126	+	13.9971i	0.325868	+	0.564419i
$616$	−2.34458	+	4.06093i	−0.0944657	+	0.163619i
$617$	−1.02890	−	5.83520i	−0.0414221	−	0.234916i	0.957067	−	0.289867i	$-0.0936110\pi$
$617$	−1.02890	−	5.83520i	−0.0414221	−	0.234916i	−0.998489	+	0.0549504i	$0.982500\pi$
$618$	−6.48900	−	36.8010i	−0.261026	−	1.48035i
$619$	−4.01979	+	6.96248i	−0.161569	+	0.279846i	−0.935432	−	0.353508i	$-0.884989\pi$
$619$	−4.01979	+	6.96248i	−0.161569	+	0.279846i	0.773863	+	0.633354i	$0.218322\pi$
$620$	8.95814	+	15.5160i	0.359768	+	0.623136i
$621$	1.69399	−	1.42143i	0.0679775	−	0.0570399i
$622$	21.7110	−	7.90215i	0.870531	−	0.316847i
$623$	18.1266	+	6.59753i	0.726226	+	0.264324i
$624$	−12.2485	−	10.2777i	−0.490332	−	0.411437i
$625$	−5.06135	+	28.7043i	−0.202454	+	1.14817i
$626$	12.2647			0.490196
$627$		0			0
$628$	2.97387			0.118671
$629$	0.475427	−	2.69628i	0.0189565	−	0.107508i
$630$	17.6394	+	14.8012i	0.702772	+	0.589696i
$631$	12.1226	+	4.41228i	0.482595	+	0.175650i	0.571849	−	0.820359i	$-0.306226\pi$
$631$	12.1226	+	4.41228i	0.482595	+	0.175650i	−0.0892545	+	0.996009i	$0.528448\pi$
$632$	5.55507	−	2.02188i	0.220969	−	0.0804261i
$633$	−15.6689	+	13.1477i	−0.622782	+	0.522576i
$634$	0.136152	+	0.235823i	0.00540731	+	0.00936573i
$635$	−1.39747	+	2.42049i	−0.0554569	+	0.0960542i
$636$	0.643418	+	3.64901i	0.0255132	+	0.144693i
$637$	0.886035	+	5.02496i	0.0351060	+	0.199096i
$638$	4.97834	−	8.62275i	0.197095	−	0.341378i
$639$	11.7239	+	20.3065i	0.463792	+	0.803311i
$640$	−1.88420	+	1.58103i	−0.0744796	+	0.0624958i
$641$	27.1232	−	9.87203i	1.07130	−	0.389922i	0.254638	−	0.967036i	$-0.418044\pi$
$641$	27.1232	−	9.87203i	1.07130	−	0.389922i	0.816663	+	0.577114i	$0.195821\pi$
$642$	−6.69832	−	2.43799i	−0.264362	−	0.0962197i
$643$	20.1772	+	16.9307i	0.795710	+	0.667680i	0.947152	−	0.320786i	$-0.103947\pi$
$643$	20.1772	+	16.9307i	0.795710	+	0.667680i	−0.151441	+	0.988466i	$0.548391\pi$
$644$	1.21223	−	6.87489i	0.0477685	−	0.270909i
$645$	17.7982			0.700803
$646$		0			0
$647$	−3.04601			−0.119751			−0.0598756	−	0.998206i	$-0.519070\pi$
$647$	−3.04601			−0.119751			−0.0598756	+	0.998206i	$0.519070\pi$
$648$	−1.35850	+	7.70442i	−0.0533668	+	0.302658i
$649$	6.38107	+	5.35436i	0.250479	+	0.210177i
$650$	−6.25931	−	2.27820i	−0.245510	−	0.0893584i
$651$	−48.1894	+	17.5395i	−1.88869	+	0.687427i
$652$	4.28365	−	3.59441i	0.167761	−	0.140768i
$653$	7.59866	+	13.1613i	0.297359	+	0.515040i	0.975531	−	0.219863i	$-0.0705610\pi$
$653$	7.59866	+	13.1613i	0.297359	+	0.515040i	−0.678172	+	0.734903i	$0.737228\pi$
$654$	2.17412	−	3.76568i	0.0850148	−	0.147250i
$655$	7.62035	+	43.2171i	0.297752	+	1.68863i
$656$	−0.452772	−	2.56780i	−0.0176778	−	0.100256i
$657$	10.3654	−	17.9534i	0.404393	−	0.700429i
$658$	1.04145	+	1.80384i	0.0405998	+	0.0703209i
$659$	13.6923	−	11.4892i	0.533378	−	0.447557i	−0.335888	−	0.941902i	$-0.609036\pi$
$659$	13.6923	−	11.4892i	0.533378	−	0.447557i	0.869266	+	0.494345i	$0.164592\pi$
$660$	9.77720	−	3.55861i	0.380577	−	0.138519i
$661$	−35.5697	−	12.9463i	−1.38350	−	0.503554i	−0.460264	−	0.887782i	$-0.652245\pi$
$661$	−35.5697	−	12.9463i	−1.38350	−	0.503554i	−0.923238	+	0.384228i	$0.874468\pi$
$662$	−15.3155	−	12.8512i	−0.595255	−	0.499478i
$663$	−13.7969	+	78.2464i	−0.535829	+	3.03884i
$664$	15.1773			0.588994
$665$		0			0
$666$	1.84638			0.0715460
$667$	−2.57398	+	14.5978i	−0.0996649	+	0.565228i
$668$	−5.42636	−	4.55325i	−0.209952	−	0.176171i
$669$	25.4673	+	9.26933i	0.984622	+	0.358373i
$670$	26.7198	−	9.72522i	1.03228	−	0.375718i
$671$	−12.0056	+	10.0739i	−0.463471	+	0.388899i
$672$	−3.52015	−	6.09707i	−0.135793	−	0.235200i
$673$	4.14230	−	7.17468i	0.159674	−	0.276564i	−0.775077	−	0.631867i	$-0.782289\pi$
$673$	4.14230	−	7.17468i	0.159674	−	0.276564i	0.934751	+	0.355303i	$0.115622\pi$
$674$	−3.00106	−	17.0199i	−0.115597	−	0.655580i
$675$	−0.161330	−	0.914949i	−0.00620960	−	0.0352164i
$676$	−13.6268	+	23.6024i	−0.524109	+	0.907783i
$677$	9.16167	+	15.8685i	0.352111	+	0.609875i	0.986619	−	0.163042i	$-0.0521305\pi$
$677$	9.16167	+	15.8685i	0.352111	+	0.609875i	−0.634508	+	0.772917i	$0.718797\pi$
$678$	0.825858	−	0.692977i	0.0317169	−	0.0266136i
$679$	37.7687	−	13.7467i	1.44943	−	0.527550i
$680$	11.4853	+	4.18032i	0.440442	+	0.160308i
$681$	−52.3054	−	43.8895i	−2.00435	−	1.68185i
$682$	−2.12312	+	12.0408i	−0.0812984	+	0.461066i
$683$	−49.2217			−1.88342			−0.941709	−	0.336429i	$-0.890781\pi$
$683$	−49.2217			−1.88342			−0.941709	+	0.336429i	$0.890781\pi$
$684$		0			0
$685$	39.1469			1.49573
$686$	3.00560	−	17.0456i	0.114754	−	0.650804i
$687$	−18.2737	−	15.3335i	−0.697185	−	0.585008i
$688$	−2.69813	−	0.982038i	−0.102865	−	0.0374399i
$689$	8.76569	−	3.19045i	0.333946	−	0.121546i
$690$	−11.8660	+	9.95672i	−0.451729	+	0.379046i
$691$	−8.33895	−	14.4435i	−0.317229	−	0.549456i	0.662680	−	0.748903i	$-0.269419\pi$
$691$	−8.33895	−	14.4435i	−0.317229	−	0.549456i	−0.979909	+	0.199446i	$0.936086\pi$
$692$	11.5104	−	19.9366i	0.437560	−	0.757876i
$693$	2.72871	+	15.4753i	0.103655	+	0.587857i
$694$	−3.22041	−	18.2638i	−0.122245	−	0.693286i
$695$	12.4460	−	21.5572i	0.472105	−	0.817710i
$696$	7.47449	+	12.9462i	0.283320	+	0.490724i
$697$	−9.92540	+	8.32840i	−0.375951	+	0.315461i
$698$	18.9076	−	6.88179i	0.715662	−	0.260480i
$699$	54.1412	+	19.7058i	2.04781	+	0.745341i
$700$	−2.24676	−	1.88526i	−0.0849196	−	0.0712560i
$701$	−5.36687	+	30.4370i	−0.202704	+	1.14959i	0.698308	+	0.715797i	$0.253937\pi$
$701$	−5.36687	+	30.4370i	−0.202704	+	1.14959i	−0.901012	+	0.433794i	$0.857175\pi$
$702$	−5.61449			−0.211905
$703$		0			0
$704$	−1.67853			−0.0632620
$705$	0.802549	−	4.55148i	0.0302257	−	0.171419i
$706$	18.4277	+	15.4627i	0.693537	+	0.581946i
$707$	29.6191	+	10.7805i	1.11394	+	0.405442i
$708$	−11.7523	+	4.27748i	−0.441677	+	0.160757i
$709$	30.7227	−	25.7794i	1.15381	−	0.968165i	0.154012	−	0.988069i	$-0.450781\pi$
$709$	30.7227	−	25.7794i	1.15381	−	0.968165i	0.999802	+	0.0199044i	$0.00633620\pi$
$710$	−8.60506	−	14.9044i	−0.322942	−	0.559352i
$711$	9.90527	−	17.1564i	0.371477	−	0.643417i
$712$	1.19904	+	6.80011i	0.0449361	+	0.254845i
$713$	−3.16078	−	17.9257i	−0.118372	−	0.671322i
$714$	−17.4922	+	30.2974i	−0.654630	+	1.13385i
$715$	−13.0971	−	22.6849i	−0.489804	−	0.848365i
$716$	6.29283	−	5.28032i	0.235174	−	0.197335i
$717$	20.5228	−	7.46968i	0.766437	−	0.278960i
$718$	10.1989	+	3.71210i	0.380620	+	0.138534i
$719$	−34.9721	−	29.3451i	−1.30424	−	1.09439i	−0.989396	−	0.145244i	$-0.953603\pi$
$719$	−34.9721	−	29.3451i	−1.30424	−	1.09439i	−0.314845	−	0.949143i	$-0.601952\pi$
$720$	−1.43132	+	8.11741i	−0.0533421	+	0.302518i
$721$	−41.4235			−1.54269
$722$		0			0
$723$	−14.2596			−0.530322
$724$	−2.25741	+	12.8024i	−0.0838959	+	0.475797i
$725$	4.77065	+	4.00305i	0.177177	+	0.148670i
$726$	−19.3776	−	7.05286i	−0.719169	−	0.261756i
$727$	14.2655	−	5.19223i	0.529079	−	0.192569i	−0.0636481	−	0.997972i	$-0.520274\pi$
$727$	14.2655	−	5.19223i	0.529079	−	0.192569i	0.592727	+	0.805403i	$0.298051\pi$
$728$	−13.5776	+	11.3929i	−0.503218	+	0.422250i
$729$	16.4537	+	28.4986i	0.609395	+	1.05550i
$730$	−7.60793	+	13.1773i	−0.281582	+	0.487715i
$731$	2.47760	+	14.0512i	0.0916374	+	0.519701i
$732$	−4.08599	−	23.1728i	−0.151022	−	0.856491i
$733$	13.4993	−	23.3815i	0.498608	−	0.863615i	−0.501390	−	0.865221i	$-0.667178\pi$
$733$	13.4993	−	23.3815i	0.498608	−	0.863615i	0.999999	+	0.00160611i	$0.000511240\pi$
$734$	16.3060	+	28.2429i	0.601867	+	1.04246i
$735$	3.81884	−	3.20439i	0.140860	−	0.118196i
$736$	2.34820	−	0.854675i	0.0865559	−	0.0315038i
$737$	18.2343	+	6.63675i	0.671670	+	0.244468i
$738$	−6.69355	−	5.61655i	−0.246393	−	0.206748i
$739$	−0.904328	+	5.12870i	−0.0332663	+	0.188662i	−0.996913	−	0.0785186i	$-0.974981\pi$
$739$	−0.904328	+	5.12870i	−0.0332663	+	0.188662i	0.963646	+	0.267181i	$0.0860921\pi$
$740$	−1.35520			−0.0498181
$741$		0			0
$742$	4.10736			0.150786
$743$	3.83899	−	21.7720i	0.140839	−	0.798737i	−0.829776	−	0.558097i	$-0.811532\pi$
$743$	3.83899	−	21.7720i	0.140839	−	0.798737i	0.970614	−	0.240640i	$-0.0773573\pi$
$744$	−14.0622	−	11.7996i	−0.515547	−	0.432595i
$745$	21.7229	+	7.90649i	0.795866	+	0.289671i
$746$	4.98223	−	1.81338i	0.182412	−	0.0663927i
$747$	38.9621	−	32.6930i	1.42555	−	1.19618i
$748$	4.17046	+	7.22345i	0.152487	+	0.264115i
$749$	−3.95084	+	6.84305i	−0.144360	+	0.250040i
$750$	−4.25187	−	24.1136i	−0.155256	−	0.880503i
$751$	−2.16990	−	12.3061i	−0.0791809	−	0.449057i	−0.998461	−	0.0554537i	$-0.982339\pi$
$751$	−2.16990	−	12.3061i	−0.0791809	−	0.449057i	0.919280	−	0.393603i	$-0.128772\pi$
$752$	−0.372797	+	0.645703i	−0.0135945	+	0.0235464i
$753$	−17.0806	−	29.5844i	−0.622451	−	1.07812i
$754$	28.8298	−	24.1911i	1.04992	−	0.880988i
$755$	−23.7216	+	8.63394i	−0.863316	+	0.314221i
$756$	−2.32305	−	0.845520i	−0.0844884	−	0.0307513i
$757$	−23.7465	−	19.9257i	−0.863081	−	0.724211i	0.0995485	−	0.995033i	$-0.468260\pi$
$757$	−23.7465	−	19.9257i	−0.863081	−	0.724211i	−0.962630	+	0.270822i	$0.912705\pi$
$758$	4.28314	−	24.2909i	0.155571	−	0.882284i
$759$	−10.5707			−0.383693
$760$		0			0
$761$	1.96398			0.0711941			0.0355971	−	0.999366i	$-0.488667\pi$
$761$	1.96398			0.0711941			0.0355971	+	0.999366i	$0.488667\pi$
$762$	0.497273	−	2.82018i	0.0180143	−	0.102164i
$763$	−3.69238	−	3.09827i	−0.133673	−	0.112165i
$764$	−6.17828	−	2.24871i	−0.223522	−	0.0813555i
$765$	38.4889	−	14.0088i	1.39157	−	0.506490i
$766$	2.79159	−	2.34242i	0.100864	−	0.0846351i
$767$	15.7428	+	27.2674i	0.568441	+	0.984568i
$768$	1.26007	−	2.18251i	0.0454690	−	0.0787546i
$769$	−3.87794	−	21.9929i	−0.139842	−	0.793084i	−0.971365	−	0.237593i	$-0.923642\pi$
$769$	−3.87794	−	21.9929i	−0.139842	−	0.793084i	0.831523	−	0.555491i	$-0.187470\pi$
$770$	−2.00280	−	11.3585i	−0.0721759	−	0.409330i
$771$	12.6502	−	21.9108i	0.455586	−	0.789098i
$772$	−13.4413	−	23.2810i	−0.483763	−	0.837903i
$773$	20.9554	−	17.5836i	0.753712	−	0.632440i	−0.182770	−	0.983156i	$-0.558506\pi$
$773$	20.9554	−	17.5836i	0.753712	−	0.632440i	0.936482	+	0.350716i	$0.114062\pi$
$774$	−9.04181	+	3.29095i	−0.325001	+	0.118291i
$775$	−7.18619	−	2.61556i	−0.258135	−	0.0939536i
$776$	11.0214	+	9.24803i	0.395644	+	0.331985i
$777$	0.673582	−	3.82007i	0.0241646	−	0.137044i
$778$	2.79353			0.100153
$779$		0			0
$780$	39.3280			1.40817
$781$	2.03944	−	11.5662i	0.0729768	−	0.413872i
$782$	−9.51235	−	7.98181i	−0.340161	−	0.285429i
$783$	4.93263	+	1.79533i	0.176278	+	0.0641599i
$784$	−0.755725	+	0.275062i	−0.0269902	+	0.00982363i
$785$	−5.60338	+	4.70179i	−0.199993	+	0.167814i
$786$	−22.4816	−	38.9393i	−0.801892	−	1.38892i
$787$	−3.89481	+	6.74601i	−0.138835	+	0.240469i	−0.927056	−	0.374923i	$-0.877669\pi$
$787$	−3.89481	+	6.74601i	−0.138835	+	0.240469i	0.788221	+	0.615392i	$0.211002\pi$
$788$	−1.71033	−	9.69977i	−0.0609280	−	0.345540i
$789$	8.23869	+	46.7240i	0.293305	+	1.66342i
$790$	−7.27021	+	12.5924i	−0.258662	+	0.448017i
$791$	−0.597531	−	1.03495i	−0.0212457	−	0.0367987i
$792$	−4.30900	+	3.61568i	−0.153114	+	0.128478i
$793$	−55.6659	+	20.2607i	−1.97675	+	0.719480i
$794$	37.1274	+	13.5133i	1.31760	+	0.479568i
$795$	−6.98153	−	5.85820i	−0.247609	−	0.207769i
$796$	−3.55390	+	20.1552i	−0.125965	+	0.714381i
$797$	−6.09655			−0.215951			−0.107975	−	0.994154i	$-0.534437\pi$
$797$	−6.09655			−0.215951			−0.107975	+	0.994154i	$0.534437\pi$
$798$		0			0
$799$	3.70498			0.131073
$800$	0.182309	−	1.03393i	0.00644560	−	0.0365548i
$801$	17.7260	+	14.8739i	0.626318	+	0.525544i
$802$	17.4985	+	6.36892i	0.617892	+	0.224894i
$803$	−9.75750	+	3.55144i	−0.344335	+	0.125328i
$804$	−22.3179	+	18.7270i	−0.787093	+	0.660450i
$805$	8.58534	+	14.8703i	0.302594	+	0.524108i
$806$	−23.1072	+	40.0228i	−0.813916	+	1.40974i
$807$	7.16937	+	40.6595i	0.252374	+	1.43128i
$808$	1.95926	+	11.1115i	0.0689265	+	0.390902i
$809$	−28.4228	+	49.2297i	−0.999291	+	1.73082i	−0.467047	+	0.884232i	$0.654682\pi$
$809$	−28.4228	+	49.2297i	−0.999291	+	1.73082i	−0.532244	+	0.846591i	$0.678651\pi$
$810$	−9.62126	−	16.6645i	−0.338057	−	0.585531i
$811$	−16.0263	+	13.4477i	−0.562760	+	0.472212i	−0.879234	−	0.476389i	$-0.841945\pi$
$811$	−16.0263	+	13.4477i	−0.562760	+	0.472212i	0.316474	+	0.948601i	$0.397501\pi$
$812$	15.5717	−	5.66764i	0.546460	−	0.198895i
$813$	−6.55232	−	2.38485i	−0.229800	−	0.0836403i
$814$	−0.708456	−	0.594465i	−0.0248314	−	0.0208360i
$815$	−2.38838	+	13.5452i	−0.0836613	+	0.474467i
$816$	−12.5231			−0.438394
$817$		0			0
$818$	−17.1433			−0.599401
$819$	−10.3141	+	58.4941i	−0.360403	+	2.04395i
$820$	4.91289	+	4.12240i	0.171566	+	0.143961i
$821$	−15.2777	−	5.56064i	−0.533197	−	0.194068i	0.0613683	−	0.998115i	$-0.480454\pi$
$821$	−15.2777	−	5.56064i	−0.533197	−	0.194068i	−0.594565	+	0.804047i	$0.702676\pi$
$822$	−37.6908	+	13.7183i	−1.31462	+	0.478482i
$823$	−13.4309	+	11.2699i	−0.468173	+	0.392844i	−0.846128	−	0.532980i	$-0.821072\pi$
$823$	−13.4309	+	11.2699i	−0.468173	+	0.392844i	0.377955	+	0.925824i	$0.376628\pi$
$824$	−7.41399	−	12.8414i	−0.258279	−	0.447352i
$825$	−2.22056	+	3.84613i	−0.0773101	+	0.133905i
$826$	2.40738	+	13.6530i	0.0837636	+	0.475047i
$827$	−2.95642	−	16.7667i	−0.102805	−	0.583036i	−0.992074	−	0.125652i	$-0.959898\pi$
$827$	−2.95642	−	16.7667i	−0.102805	−	0.583036i	0.889269	−	0.457384i	$-0.151213\pi$
$828$	4.18709	−	7.25225i	0.145511	−	0.252033i
$829$	2.88103	+	4.99010i	0.100062	+	0.173313i	0.911710	−	0.410834i	$-0.134762\pi$
$829$	2.88103	+	4.99010i	0.100062	+	0.173313i	−0.811648	+	0.584147i	$0.801429\pi$
$830$	−28.5971	+	23.9958i	−0.992621	+	0.832908i
$831$	58.0961	−	21.1452i	2.01533	−	0.733520i
$832$	−5.96195	−	2.16997i	−0.206693	−	0.0752303i
$833$	3.06137	+	2.56880i	0.106070	+	0.0890036i
$834$	−4.42878	+	25.1168i	−0.153356	+	0.869725i
$835$	17.4232			0.602954
$836$		0			0
$837$	−6.44588			−0.222802
$838$	−3.21322	+	18.2231i	−0.110999	+	0.629506i
$839$	6.81744	+	5.72051i	0.235364	+	0.197494i	0.752839	−	0.658204i	$-0.228684\pi$
$839$	6.81744	+	5.72051i	0.235364	+	0.197494i	−0.517475	+	0.855698i	$0.673128\pi$
$840$	16.2723	+	5.92265i	0.561449	+	0.204351i
$841$	−5.81301	+	2.11576i	−0.200449	+	0.0729574i
$842$	−12.4096	+	10.4129i	−0.427664	+	0.358852i
$843$	12.8154	+	22.1969i	0.441386	+	0.764503i
$844$	−4.05815	+	7.02892i	−0.139687	+	0.241945i
$845$	−11.6404	−	66.0160i	−0.400442	−	2.27102i
$846$	0.433875	+	2.46063i	0.0149169	+	0.0845982i
$847$	−11.4294	+	19.7963i	−0.392718	+	0.680208i
$848$	0.735136	+	1.27329i	0.0252447	+	0.0437250i
$849$	−53.4139	+	44.8196i	−1.83316	+	1.53820i
$850$	−4.90239	+	1.78432i	−0.168151	+	0.0612018i
$851$	1.29379	+	0.470902i	0.0443507	+	0.0161423i
$852$	13.5080	+	11.3345i	0.462776	+	0.388315i
$853$	0.484331	−	2.74678i	0.0165832	−	0.0940478i	−0.975393	−	0.220474i	$-0.929240\pi$
$853$	0.484331	−	2.74678i	0.0165832	−	0.0940478i	0.991976	+	0.126426i	$0.0403507\pi$
$854$	−26.0835			−0.892559
$855$		0			0
$856$	−2.82849			−0.0966757
$857$	2.84687	−	16.1454i	0.0972472	−	0.551516i	−0.896788	−	0.442460i	$-0.854106\pi$
$857$	2.84687	−	16.1454i	0.0972472	−	0.551516i	0.994036	−	0.109057i	$-0.0347830\pi$
$858$	20.5595	+	17.2514i	0.701889	+	0.588955i
$859$	−8.95062	−	3.25776i	−0.305391	−	0.111153i	0.184779	−	0.982780i	$-0.440843\pi$
$859$	−8.95062	−	3.25776i	−0.305391	−	0.111153i	−0.490170	+	0.871627i	$0.663065\pi$
$860$	6.63645	−	2.41547i	0.226301	−	0.0823668i
$861$	−14.0622	+	11.7996i	−0.479240	+	0.402130i
$862$	−6.34983	−	10.9982i	−0.216276	−	0.374601i
$863$	25.3382	−	43.8871i	0.862523	−	1.49393i	−0.00696312	−	0.999976i	$-0.502216\pi$
$863$	25.3382	−	43.8871i	0.862523	−	1.49393i	0.869486	−	0.493958i	$-0.164450\pi$
$864$	−0.153666	−	0.871483i	−0.00522782	−	0.0296485i
$865$	9.83250	+	55.7629i	0.334315	+	1.89599i
$866$	−7.11751	+	12.3279i	−0.241863	+	0.418919i
$867$	9.69337	+	16.7894i	0.329204	+	0.570198i
$868$	−15.5881	+	13.0800i	−0.529095	+	0.443963i
$869$	−9.32436	+	3.39379i	−0.316307	+	0.115126i
$870$	−34.5518	−	12.5758i	−1.17141	−	0.426360i
$871$	56.1864	+	47.1460i	1.90380	+	1.59748i
$872$	0.299611	−	1.69918i	0.0101461	−	0.0575414i
$873$	48.2141			1.63180
$874$		0			0
$875$	−27.1424			−0.917582
$876$	2.70719	−	15.3533i	0.0914676	−	0.518739i
$877$	14.7524	+	12.3787i	0.498152	+	0.417999i	0.856937	−	0.515421i	$-0.172364\pi$
$877$	14.7524	+	12.3787i	0.498152	+	0.417999i	−0.358785	+	0.933420i	$0.616809\pi$
$878$	−26.4900	−	9.64156i	−0.893993	−	0.325387i
$879$	56.4537	−	20.5475i	1.90414	−	0.693049i
$880$	3.16269	−	2.65381i	0.106614	−	0.0894600i
$881$	−9.55379	−	16.5476i	−0.321875	−	0.557504i	0.659000	−	0.752143i	$-0.270980\pi$
$881$	−9.55379	−	16.5476i	−0.321875	−	0.557504i	−0.980875	+	0.194639i	$0.937646\pi$
$882$	−1.34754	+	2.33400i	−0.0453739	+	0.0785900i
$883$	8.68206	+	49.2384i	0.292175	+	1.65700i	0.678469	+	0.734629i	$0.262644\pi$
$883$	8.68206	+	49.2384i	0.292175	+	1.65700i	−0.386295	+	0.922375i	$0.626245\pi$
$884$	5.47466	+	31.0483i	0.184133	+	1.04427i
$885$	15.3808	−	26.6404i	0.517020	−	0.895506i
$886$	16.4972	+	28.5740i	0.554234	+	0.959961i
$887$	30.3503	−	25.4669i	1.01906	−	0.855095i	0.0295531	−	0.999563i	$-0.490592\pi$
$887$	30.3503	−	25.4669i	1.01906	−	0.855095i	0.989509	+	0.144468i	$0.0461471\pi$
$888$	1.30479	−	0.474905i	0.0437859	−	0.0159368i
$889$	−2.98298	−	1.08571i	−0.100046	−	0.0364137i
$890$	−13.0104	−	10.9171i	−0.436111	−	0.365941i
$891$	2.28028	−	12.9321i	0.0763923	−	0.433242i
$892$	10.7540			0.360071
$893$		0			0
$894$	−23.6856			−0.792166
$895$	−3.50862	+	19.8983i	−0.117280	+	0.665128i
$896$	−2.14003	−	1.79569i	−0.0714932	−	0.0599899i
$897$	−37.5460	−	13.6656i	−1.25363	−	0.456282i
$898$	16.1604	−	5.88190i	0.539279	−	0.196282i
$899$	33.0989	−	27.7733i	1.10391	−	0.926292i
$900$	−1.75914	−	3.04692i	−0.0586380	−	0.101564i
$901$	3.65302	−	6.32721i	0.121700	−	0.210790i
$902$	0.759993	+	4.31013i	0.0253050	+	0.143512i
$903$	3.51025	+	19.9076i	0.116814	+	0.662484i
$904$	0.213892	−	0.370473i	0.00711396	−	0.0123217i
$905$	−15.9876	−	27.6913i	−0.531445	−	0.920490i
$906$	19.8136	−	16.6256i	0.658264	−	0.552349i
$907$	−51.9222	+	18.8982i	−1.72405	+	0.627503i	−0.998179	−	0.0603279i	$-0.980785\pi$
$907$	−51.9222	+	18.8982i	−1.72405	+	0.627503i	−0.725871	+	0.687831i	$0.758563\pi$
$908$	−25.4597	−	9.26656i	−0.844908	−	0.307522i
$909$	28.9647	+	24.3042i	0.960697	+	0.806121i
$910$	7.57026	−	42.9331i	0.250952	−	1.42322i
$911$	27.7087			0.918031			0.459015	−	0.888428i	$-0.348202\pi$
$911$	27.7087			0.918031			0.459015	+	0.888428i	$0.348202\pi$
$912$		0			0
$913$	−25.4756			−0.843120
$914$	−5.40944	+	30.6784i	−0.178928	+	1.01475i
$915$	44.3357	+	37.2021i	1.46569	+	1.22986i
$916$	−8.89473	−	3.23742i	−0.293890	−	0.106967i
$917$	−46.8363	+	17.0470i	−1.54667	+	0.562942i
$918$	−3.36857	+	2.82657i	−0.111179	+	0.0932906i
$919$	−13.6250	−	23.5992i	−0.449447	−	0.778465i	0.548903	−	0.835886i	$-0.315046\pi$
$919$	−13.6250	−	23.5992i	−0.449447	−	0.778465i	−0.998350	+	0.0574208i	$0.981712\pi$
$920$	−3.07321	+	5.32296i	−0.101321	+	0.175493i
$921$	−11.3730	−	64.4997i	−0.374754	−	2.12534i
$922$	2.69867	+	15.3049i	0.0888758	+	0.504040i
$923$	22.1964	−	38.4454i	0.730605	−	1.26544i
$924$	5.90868	+	10.2341i	0.194381	+	0.336678i
$925$	0.443120	−	0.371822i	0.0145697	−	0.0122254i
$926$	−19.4185	+	7.06777i	−0.638133	+	0.232261i
$927$	−46.6939	−	16.9952i	−1.53363	−	0.558196i
$928$	4.54401	+	3.81288i	0.149164	+	0.125164i
$929$	7.71709	−	43.7658i	0.253190	−	1.43591i	−0.547488	−	0.836814i	$-0.684416\pi$
$929$	7.71709	−	43.7658i	0.253190	−	1.43591i	0.800677	−	0.599096i	$-0.204473\pi$
$930$	45.1517			1.48058
$931$		0			0
$932$	22.8621			0.748873
$933$	10.1109	−	57.3417i	0.331016	−	1.87728i
$934$	−21.8192	−	18.3085i	−0.713946	−	0.599072i
$935$	−19.2785	−	7.01679i	−0.630474	−	0.229474i
$936$	−19.9793	+	7.27189i	−0.653045	+	0.237689i
$937$	−13.9494	+	11.7050i	−0.455708	+	0.382385i	−0.841549	−	0.540181i	$-0.818356\pi$
$937$	−13.9494	+	11.7050i	−0.455708	+	0.382385i	0.385841	+	0.922565i	$0.373911\pi$
$938$	16.1477	+	27.9686i	0.527239	+	0.913206i
$939$	15.4544	−	26.7678i	0.504336	−	0.873536i
$940$	−0.318453	−	1.80604i	−0.0103868	−	0.0589064i
$941$	−6.99247	−	39.6563i	−0.227948	−	1.29276i	−0.856969	−	0.515369i	$-0.827655\pi$
$941$	−6.99247	−	39.6563i	−0.227948	−	1.29276i	0.629021	−	0.777389i	$-0.283456\pi$
$942$	3.74730	−	6.49052i	0.122094	−	0.211472i
$943$	−3.25784	−	5.64274i	−0.106090	−	0.183753i
$944$	−3.80158	+	3.18990i	−0.123731	+	0.103823i
$945$	5.71388	−	2.07968i	0.185873	−	0.0676521i
$946$	4.52889	+	1.64838i	0.147247	+	0.0535935i
$947$	4.87634	+	4.09173i	0.158460	+	0.132963i	0.718570	−	0.695454i	$-0.244797\pi$
$947$	4.87634	+	4.09173i	0.158460	+	0.132963i	−0.560111	+	0.828418i	$0.689241\pi$
$948$	2.58702	−	14.6717i	0.0840225	−	0.476515i
$949$	−39.2488			−1.27407
$950$		0			0
$951$	0.686248			0.0222531
$952$	−2.41057	+	13.6710i	−0.0781270	+	0.443080i
$953$	−25.0453	−	21.0155i	−0.811298	−	0.680760i	0.139619	−	0.990205i	$-0.455412\pi$
$953$	−25.0453	−	21.0155i	−0.811298	−	0.680760i	−0.950917	+	0.309445i	$0.899857\pi$
$954$	4.62995	+	1.68516i	0.149900	+	0.0545592i
$955$	15.1964	−	5.53104i	0.491744	−	0.178980i
$956$	6.63863	−	5.57047i	0.214709	−	0.180162i
$957$	−12.5462	−	21.7306i	−0.405560	−	0.702450i
$958$	5.23632	−	9.06958i	0.169178	−	0.293025i
$959$	7.72075	+	43.7865i	0.249316	+	1.41394i
$960$	1.07639	+	6.10451i	0.0347403	+	0.197022i
$961$	−11.0289	+	19.1026i	−0.355771	+	0.616214i
$962$	−1.74784	−	3.02735i	−0.0563527	−	0.0976057i
$963$	−7.26107	+	6.09276i	−0.233985	+	0.196337i
$964$	−5.31702	+	1.93524i	−0.171250	+	0.0623298i
$965$	62.1342	+	22.6150i	2.00017	+	0.728003i
$966$	−13.4770	−	11.3086i	−0.433616	−	0.363847i
$967$	1.48632	−	8.42932i	0.0477967	−	0.271069i	−0.951538	−	0.307530i	$-0.900497\pi$
$967$	1.48632	−	8.42932i	0.0477967	−	0.271069i	0.999335	+	0.0364614i	$0.0116086\pi$
$968$	−8.18253			−0.262997
$969$		0			0
$970$	−35.3879			−1.13624
$971$	−7.27219	+	41.2426i	−0.233376	+	1.32354i	0.612632	+	0.790368i	$0.290111\pi$
$971$	−7.27219	+	41.2426i	−0.233376	+	1.32354i	−0.846008	+	0.533171i	$0.821000\pi$
$972$	17.1369	+	14.3795i	0.549665	+	0.461224i
$973$	26.5668	+	9.66951i	0.851691	+	0.309990i
$974$	−2.16030	+	0.786284i	−0.0692204	+	0.0251942i
$975$	−12.8594	+	10.7903i	−0.411830	+	0.345567i
$976$	−4.66843	−	8.08596i	−0.149433	−	0.258825i
$977$	3.09010	−	5.35222i	0.0988612	−	0.171233i	−0.812352	−	0.583167i	$-0.801813\pi$
$977$	3.09010	−	5.35222i	0.0988612	−	0.171233i	0.911214	+	0.411934i	$0.135147\pi$
$978$	−2.44713	−	13.8783i	−0.0782504	−	0.443780i
$979$	−2.01263	−	11.4142i	−0.0643240	−	0.364800i
$980$	0.989057	−	1.71310i	0.0315943	−	0.0547229i
$981$	−2.89101	−	5.00738i	−0.0923029	−	0.159873i
$982$	9.31600	−	7.81705i	0.297286	−	0.249452i
$983$	−31.5494	+	11.4830i	−1.00627	+	0.366252i	−0.791999	−	0.610522i	$-0.790960\pi$
$983$	−31.5494	+	11.4830i	−1.00627	+	0.366252i	−0.214270	+	0.976774i	$0.568737\pi$
$984$	−6.17478	−	2.24744i	−0.196845	−	0.0716456i
$985$	18.5583	+	15.5722i	0.591315	+	0.496172i
$986$	5.11847	−	29.0283i	0.163005	−	0.924449i
$987$	5.24920			0.167084
$988$		0			0
$989$	−7.17507			−0.228154
$990$	2.40251	−	13.6253i	0.0763569	−	0.433041i
$991$	−35.3718	−	29.6805i	−1.12362	−	0.942831i	−0.124841	−	0.992177i	$-0.539842\pi$
$991$	−35.3718	−	29.6805i	−1.12362	−	0.942831i	−0.998782	+	0.0493455i	$0.984286\pi$
$992$	−6.84480	−	2.49130i	−0.217322	−	0.0790989i
$993$	−47.3467	+	17.2328i	−1.50250	+	0.546866i
$994$	14.9737	−	12.5644i	0.474938	−	0.398520i
$995$	−25.1697	−	43.5952i	−0.797934	−	1.38206i
$996$	19.1245	−	33.1247i	0.605984	−	1.04960i
$997$	−0.142240	−	0.806686i	−0.00450480	−	0.0255480i	0.982473	−	0.186408i	$-0.0596845\pi$
$997$	−0.142240	−	0.806686i	−0.00450480	−	0.0255480i	−0.986977	+	0.160860i	$0.948573\pi$
$998$	2.62814	+	14.9049i	0.0831922	+	0.471806i
$999$	0.243785	−	0.422248i	0.00771302	−	0.0133593i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.4	✓	4	19.3	odd	18
722.2.a.n.1.1	yes	4	19.16	even	9
722.2.c.m.429.4		8	19.17	even	9
722.2.c.m.653.4		8	19.5	even	9
722.2.c.n.429.1		8	19.2	odd	18
722.2.c.n.653.1		8	19.14	odd	18
722.2.e.r.99.1		24	19.6	even	9	inner
722.2.e.r.245.1		24	1.1	even	1	trivial
722.2.e.r.389.1		24	19.9	even	9	inner
722.2.e.r.415.4		24	19.7	even	3	inner
722.2.e.r.423.1		24	19.11	even	3	inner
722.2.e.r.595.4		24	19.4	even	9	inner
722.2.e.s.99.4		24	19.13	odd	18
722.2.e.s.245.4		24	19.18	odd	2
722.2.e.s.389.4		24	19.10	odd	18
722.2.e.s.415.1		24	19.12	odd	6
722.2.e.s.423.4		24	19.8	odd	6
722.2.e.s.595.1		24	19.15	odd	18
5776.2.a.bt.1.4		4	76.35	odd	18
5776.2.a.bv.1.1		4	76.3	even	18
6498.2.a.bx.1.4		4	57.35	odd	18
6498.2.a.ca.1.4		4	57.41	even	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)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-1.93054 - 1.61992i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.31131 - 0.841250i) q^{5} +(-1.93054 + 1.61992i) q^{6} +(1.39680 + 2.41933i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.581920 + 3.30023i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-1.93054 - 1.61992i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.31131 - 0.841250i) q^{5} +(-1.93054 + 1.61992i) q^{6} +(1.39680 + 2.41933i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.581920 + 3.30023i) q^{9} +(-0.427114 - 2.42228i) q^{10} +(0.839266 - 1.45365i) q^{11} +(1.26007 + 2.18251i) q^{12} +(4.86023 - 4.07822i) q^{13} +(2.62513 - 0.955469i) q^{14} +(-5.82485 - 2.12007i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.862888 - 4.89368i) q^{17} +3.35114 q^{18} -2.45965 q^{20} +(1.22253 - 6.93334i) q^{21} +(-1.28583 - 1.07894i) q^{22} +(2.34820 + 0.854675i) q^{23} +(2.36816 - 0.861941i) q^{24} +(0.804252 - 0.674847i) q^{25} +(-3.17229 - 5.49456i) q^{26} +(0.442463 - 0.766369i) q^{27} +(-0.485104 - 2.75116i) q^{28} +(1.03004 + 5.84167i) q^{29} +(-3.09934 + 5.36821i) q^{30} +(-3.64204 - 6.30820i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-3.97504 + 1.44680i) q^{33} +(-4.66950 - 1.69956i) q^{34} +(5.26371 + 4.41678i) q^{35} +(0.581920 - 3.30023i) q^{36} +0.550972 q^{37} -15.9893 q^{39} +(-0.427114 + 2.42228i) q^{40} +(-1.99739 - 1.67601i) q^{41} +(-6.61571 - 2.40792i) q^{42} +(-2.69813 + 0.982038i) q^{43} +(-1.28583 + 1.07894i) q^{44} +(4.12132 + 7.13833i) q^{45} +(1.24945 - 2.16411i) q^{46} +(0.129471 + 0.734266i) q^{47} +(-0.437619 - 2.48186i) q^{48} +(-0.402113 + 0.696480i) q^{49} +(-0.524938 - 0.909219i) q^{50} +(-9.59321 + 8.04966i) q^{51} +(-5.96195 + 2.16997i) q^{52} +(1.38160 + 0.502862i) q^{53} +(-0.677893 - 0.568820i) q^{54} +(0.716924 - 4.06588i) q^{55} -2.79360 q^{56} +5.93179 q^{58} +(-0.861748 + 4.88722i) q^{59} +(4.74846 + 3.98443i) q^{60} +(-8.77378 - 3.19339i) q^{61} +(-6.84480 + 2.49130i) q^{62} +(-7.17153 + 6.01762i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(7.80272 - 13.5147i) q^{65} +(0.734557 + 4.16588i) q^{66} +(2.00745 + 11.3848i) q^{67} +(-2.48459 + 4.30343i) q^{68} +(-3.14880 - 5.45389i) q^{69} +(5.26371 - 4.41678i) q^{70} +(6.57501 - 2.39311i) q^{71} +(-3.14904 - 1.14616i) q^{72} +(-4.73890 - 3.97641i) q^{73} +(0.0956753 - 0.542602i) q^{74} -2.64584 q^{75} +4.68915 q^{77} +(-2.77651 + 15.7464i) q^{78} +(-4.52853 - 3.79989i) q^{79} +(2.31131 + 0.841250i) q^{80} +(7.35148 - 2.67572i) q^{81} +(-1.99739 + 1.67601i) q^{82} +(-7.58866 - 13.1439i) q^{83} +(-3.52015 + 6.09707i) q^{84} +(-2.12240 - 12.0367i) q^{85} +(0.498594 + 2.82767i) q^{86} +(7.47449 - 12.9462i) q^{87} +(0.839266 + 1.45365i) q^{88} +(5.28955 - 4.43846i) q^{89} +(7.74554 - 2.81915i) q^{90} +(16.6553 + 6.06205i) q^{91} +(-1.91427 - 1.60626i) q^{92} +(-3.18765 + 18.0781i) q^{93} +0.745593 q^{94} -2.52015 q^{96} +(2.49834 - 14.1688i) q^{97} +(0.616073 + 0.516947i) q^{98} +(5.28577 + 1.92386i) 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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