LMFDB - Embedded newform 570.2.bf.a.89.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.15
Character	$\chi$	$=$	570.89
Dual form			570.2.bf.a.269.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(1.19567 - 1.25315i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.23176 - 0.138722i) q^{5} +(-1.72853 - 0.110426i) q^{6} +(2.23292 + 1.28917i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.140760 - 2.99670i) q^{9} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(1.19567 - 1.25315i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.23176 - 0.138722i) q^{5} +(-1.72853 - 0.110426i) q^{6} +(2.23292 + 1.28917i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.140760 - 2.99670i) q^{9} +(1.32828 + 1.79880i) q^{10} +(2.63216 - 1.51968i) q^{11} +(1.02648 + 1.39511i) q^{12} +(3.00072 - 1.09217i) q^{13} +(-0.447726 - 2.53918i) q^{14} +(-2.84228 + 2.63086i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.98096 + 1.66223i) q^{17} +(-2.20512 + 2.03407i) q^{18} +(-0.765809 - 4.29110i) q^{19} +(0.524156 - 2.17377i) q^{20} +(4.28535 - 1.25675i) q^{21} +(-2.85606 - 1.03952i) q^{22} +(0.878472 - 4.98206i) q^{23} +(0.408904 - 1.68309i) q^{24} +(4.96151 + 0.619188i) q^{25} +(-2.76548 - 1.59665i) q^{26} +(-3.92361 - 3.40666i) q^{27} +(-1.65733 + 1.97513i) q^{28} +(-0.575080 - 0.482549i) q^{29} +(3.84234 + 0.486229i) q^{30} +(-7.47727 - 4.31700i) q^{31} +(0.342020 + 0.939693i) q^{32} +(1.24280 - 5.11551i) q^{33} +(2.54668 + 0.449048i) q^{34} +(-4.80450 - 3.18688i) q^{35} +(2.97561 + 0.381749i) q^{36} +6.30256 q^{37} +(-2.79492 + 3.34491i) q^{38} +(2.21921 - 5.06623i) q^{39} +(-2.00212 + 0.995744i) q^{40} +(-0.243797 - 0.0887348i) q^{41} +(-3.71730 - 2.47494i) q^{42} +(-5.12343 + 0.903399i) q^{43} +(1.03952 + 2.85606i) q^{44} +(-0.101564 + 6.70744i) q^{45} +(-4.38115 + 2.52946i) q^{46} +(6.62526 + 5.55925i) q^{47} +(-1.55216 + 0.768632i) q^{48} +(-0.176060 - 0.304944i) q^{49} +(-2.71487 - 4.19875i) q^{50} +(-0.285558 + 4.46991i) q^{51} +(0.554511 + 3.14479i) q^{52} +(4.33290 + 0.764007i) q^{53} +(-0.0876053 + 5.19541i) q^{54} +(-6.08515 + 3.02642i) q^{55} +2.57835 q^{56} +(-6.29304 - 4.17105i) q^{57} +0.750713i q^{58} +(-3.10411 + 2.60465i) q^{59} +(-2.09734 - 3.25595i) q^{60} +(-1.76508 + 10.0103i) q^{61} +(1.49928 + 8.50284i) q^{62} +(3.54896 - 6.87283i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.84840 + 2.02120i) q^{65} +(-4.71756 + 2.33614i) q^{66} +(9.42846 + 7.91141i) q^{67} +(-1.29298 - 2.23951i) q^{68} +(-5.19290 - 7.05774i) q^{69} +(0.646977 + 5.72895i) q^{70} +(-0.792828 - 4.49635i) q^{71} +(-1.62025 - 2.52483i) q^{72} +(3.36404 - 9.24263i) q^{73} +(-4.05121 - 4.82804i) q^{74} +(6.70825 - 5.47717i) q^{75} +(4.35889 - 0.00903289i) q^{76} +7.83651 q^{77} +(-5.30744 + 1.55649i) q^{78} +(5.67129 - 15.5817i) q^{79} +(2.04972 + 0.893663i) q^{80} +(-8.96037 + 0.843632i) q^{81} +(0.0887348 + 0.243797i) q^{82} +(0.188516 - 0.326520i) q^{83} +(0.493514 + 4.43848i) q^{84} +(4.65162 - 3.43489i) q^{85} +(3.98532 + 3.34408i) q^{86} +(-1.29231 + 0.143692i) q^{87} +(1.51968 - 2.63216i) q^{88} +(-12.2942 + 4.47471i) q^{89} +(5.20348 - 4.23365i) q^{90} +(8.10836 + 1.42972i) q^{91} +(4.75383 + 1.73025i) q^{92} +(-14.3502 + 4.20843i) q^{93} -8.64866i q^{94} +(1.11383 + 9.68294i) q^{95} +(1.58652 + 0.694958i) q^{96} +(-1.74154 + 1.46132i) q^{97} +(-0.120432 + 0.330884i) q^{98} +(-4.92451 - 7.67386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	1.19567	−	1.25315i	0.690319	−	0.723505i
$3$	1.19567	−	1.25315i	0.690319	−	0.723505i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	−2.23176	−	0.138722i	−0.998074	−	0.0620383i
$5$	−2.23176	−	0.138722i	−0.998074	−	0.0620383i
$6$	−1.72853	−	0.110426i	−0.705668	−	0.0450813i
$7$	2.23292	+	1.28917i	0.843963	+	0.487262i	0.858609	−	0.512631i	$-0.171329\pi$
$7$	2.23292	+	1.28917i	0.843963	+	0.487262i	−0.0146466	+	0.999893i	$0.504662\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.140760	−	2.99670i	−0.0469201	−	0.998899i
$10$	1.32828	+	1.79880i	0.420039	+	0.568829i
$11$	2.63216	−	1.51968i	0.793625	−	0.458199i	−0.0476123	−	0.998866i	$-0.515161\pi$
$11$	2.63216	−	1.51968i	0.793625	−	0.458199i	0.841237	+	0.540666i	$0.181828\pi$
$12$	1.02648	+	1.39511i	0.296321	+	0.402733i
$13$	3.00072	−	1.09217i	0.832251	−	0.302915i	0.109468	−	0.993990i	$-0.465085\pi$
$13$	3.00072	−	1.09217i	0.832251	−	0.302915i	0.722782	+	0.691076i	$0.242863\pi$
$14$	−0.447726	−	2.53918i	−0.119660	−	0.678624i
$15$	−2.84228	+	2.63086i	−0.733874	+	0.679286i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.98096	+	1.66223i	−0.480454	+	0.403149i	−0.850591	−	0.525828i	$-0.823755\pi$
$17$	−1.98096	+	1.66223i	−0.480454	+	0.403149i	0.370136	+	0.928977i	$0.379311\pi$
$18$	−2.20512	+	2.03407i	−0.519753	+	0.479434i
$19$	−0.765809	−	4.29110i	−0.175689	−	0.984446i
$19$	−0.765809	−	4.29110i	−0.175689	−	0.984446i
$20$	0.524156	−	2.17377i	0.117205	−	0.486069i
$21$	4.28535	−	1.25675i	0.935140	−	0.274245i
$22$	−2.85606	−	1.03952i	−0.608913	−	0.221626i
$23$	0.878472	−	4.98206i	0.183174	−	1.03883i	−0.745105	−	0.666947i	$-0.767601\pi$
$23$	0.878472	−	4.98206i	0.183174	−	1.03883i	0.928279	−	0.371884i	$-0.121288\pi$
$24$	0.408904	−	1.68309i	0.0834672	−	0.343560i
$25$	4.96151	+	0.619188i	0.992303	+	0.123838i
$26$	−2.76548	−	1.59665i	−0.542356	−	0.313129i
$27$	−3.92361	−	3.40666i	−0.755098	−	0.655611i
$28$	−1.65733	+	1.97513i	−0.313206	+	0.373264i
$29$	−0.575080	−	0.482549i	−0.106790	−	0.0896071i	0.587829	−	0.808985i	$-0.299983\pi$
$29$	−0.575080	−	0.482549i	−0.106790	−	0.0896071i	−0.694619	+	0.719378i	$0.744427\pi$
$30$	3.84234	+	0.486229i	0.701512	+	0.0887729i
$31$	−7.47727	−	4.31700i	−1.34296	−	0.775357i	−0.355717	−	0.934594i	$-0.615763\pi$
$31$	−7.47727	−	4.31700i	−1.34296	−	0.775357i	−0.987240	+	0.159237i	$0.949097\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	1.24280	−	5.11551i	0.216344	−	0.890496i
$34$	2.54668	+	0.449048i	0.436752	+	0.0770111i
$35$	−4.80450	−	3.18688i	−0.812108	−	0.538681i
$36$	2.97561	+	0.381749i	0.495935	+	0.0636248i
$37$	6.30256			1.03613			0.518067	−	0.855340i	$-0.326652\pi$
$37$	6.30256			1.03613			0.518067	+	0.855340i	$0.326652\pi$
$38$	−2.79492	+	3.34491i	−0.453396	+	0.542616i
$39$	2.21921	−	5.06623i	0.355358	−	0.811246i
$40$	−2.00212	+	0.995744i	−0.316563	+	0.157441i
$41$	−0.243797	−	0.0887348i	−0.0380747	−	0.0138580i	0.322913	−	0.946429i	$-0.395338\pi$
$41$	−0.243797	−	0.0887348i	−0.0380747	−	0.0138580i	−0.360987	+	0.932571i	$0.617560\pi$
$42$	−3.71730	−	2.47494i	−0.573591	−	0.381892i
$43$	−5.12343	+	0.903399i	−0.781316	+	0.137767i	−0.550059	−	0.835126i	$-0.685395\pi$
$43$	−5.12343	+	0.903399i	−0.781316	+	0.137767i	−0.231257	+	0.972893i	$0.574284\pi$
$44$	1.03952	+	2.85606i	0.156713	+	0.430567i
$45$	−0.101564	+	6.70744i	−0.0151402	+	0.999885i
$46$	−4.38115	+	2.52946i	−0.645965	+	0.372948i
$47$	6.62526	+	5.55925i	0.966394	+	0.810901i	0.981981	−	0.188978i	$-0.0605175\pi$
$47$	6.62526	+	5.55925i	0.966394	+	0.810901i	−0.0155877	+	0.999879i	$0.504962\pi$
$48$	−1.55216	+	0.768632i	−0.224035	+	0.110942i
$49$	−0.176060	−	0.304944i	−0.0251514	−	0.0435635i
$50$	−2.71487	−	4.19875i	−0.383941	−	0.593792i
$51$	−0.285558	+	4.46991i	−0.0399861	+	0.625912i
$52$	0.554511	+	3.14479i	0.0768969	+	0.436104i
$53$	4.33290	+	0.764007i	0.595169	+	0.104944i	0.463115	−	0.886298i	$-0.346732\pi$
$53$	4.33290	+	0.764007i	0.595169	+	0.104944i	0.132054	+	0.991243i	$0.457843\pi$
$54$	−0.0876053	+	5.19541i	−0.0119216	+	0.707006i
$55$	−6.08515	+	3.02642i	−0.820522	+	0.408082i
$56$	2.57835			0.344546
$57$	−6.29304	−	4.17105i	−0.833533	−	0.552470i
$58$			0.750713i			0.0985735i
$59$	−3.10411	+	2.60465i	−0.404120	+	0.339097i	−0.822084	−	0.569367i	$-0.807188\pi$
$59$	−3.10411	+	2.60465i	−0.404120	+	0.339097i	0.417963	+	0.908464i	$0.362744\pi$
$60$	−2.09734	−	3.25595i	−0.270765	−	0.420341i
$61$	−1.76508	+	10.0103i	−0.225996	+	1.28169i	0.634777	+	0.772696i	$0.281092\pi$
$61$	−1.76508	+	10.0103i	−0.225996	+	1.28169i	−0.860772	+	0.508990i	$0.830019\pi$
$62$	1.49928	+	8.50284i	0.190409	+	1.07986i
$63$	3.54896	−	6.87283i	0.447127	−	0.865896i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−6.84840	+	2.02120i	−0.849440	+	0.250700i
$66$	−4.71756	+	2.33614i	−0.580692	+	0.287559i
$67$	9.42846	+	7.91141i	1.15187	+	0.966533i	0.999762	−	0.0218308i	$-0.00694950\pi$
$67$	9.42846	+	7.91141i	1.15187	+	0.966533i	0.152108	+	0.988364i	$0.451394\pi$
$68$	−1.29298	−	2.23951i	−0.156797	−	0.271581i
$69$	−5.19290	−	7.05774i	−0.625152	−	0.849652i
$70$	0.646977	+	5.72895i	0.0773285	+	0.684740i
$71$	−0.792828	−	4.49635i	−0.0940914	−	0.533619i	−0.995022	−	0.0996557i	$-0.968226\pi$
$71$	−0.792828	−	4.49635i	−0.0940914	−	0.533619i	0.900931	−	0.433963i	$-0.142885\pi$
$72$	−1.62025	−	2.52483i	−0.190948	−	0.297555i
$73$	3.36404	−	9.24263i	0.393731	−	1.08177i	−0.571553	−	0.820565i	$-0.693659\pi$
$73$	3.36404	−	9.24263i	0.393731	−	1.08177i	0.965284	−	0.261202i	$-0.0841190\pi$
$74$	−4.05121	−	4.82804i	−0.470944	−	0.561249i
$75$	6.70825	−	5.47717i	0.774602	−	0.632449i
$76$	4.35889	−	0.00903289i	0.499999	−	0.00103614i
$77$	7.83651			0.893053
$78$	−5.30744	+	1.55649i	−0.600949	+	0.176238i
$79$	5.67129	−	15.5817i	0.638070	−	1.75308i	−0.0196355	−	0.999807i	$-0.506251\pi$
$79$	5.67129	−	15.5817i	0.638070	−	1.75308i	0.657705	−	0.753275i	$-0.271527\pi$
$80$	2.04972	+	0.893663i	0.229166	+	0.0999146i
$81$	−8.96037	+	0.843632i	−0.995597	+	0.0937369i
$82$	0.0887348	+	0.243797i	0.00979912	+	0.0269228i
$83$	0.188516	−	0.326520i	0.0206923	−	0.0358402i	−0.855494	−	0.517813i	$-0.826746\pi$
$83$	0.188516	−	0.326520i	0.0206923	−	0.0358402i	0.876186	+	0.481973i	$0.160080\pi$
$84$	0.493514	+	4.43848i	0.0538468	+	0.484278i
$85$	4.65162	−	3.43489i	0.504539	−	0.372566i
$86$	3.98532	+	3.34408i	0.429748	+	0.360602i
$87$	−1.29231	+	0.143692i	−0.138550	+	0.0154054i
$88$	1.51968	−	2.63216i	0.161998	−	0.280589i
$89$	−12.2942	+	4.47471i	−1.30318	+	0.474318i	−0.898031	−	0.439933i	$-0.855002\pi$
$89$	−12.2942	+	4.47471i	−1.30318	+	0.474318i	−0.405148	+	0.914251i	$0.632780\pi$
$90$	5.20348	−	4.23365i	0.548495	−	0.446266i
$91$	8.10836	+	1.42972i	0.849987	+	0.149876i
$92$	4.75383	+	1.73025i	0.495621	+	0.180391i
$93$	−14.3502	+	4.20843i	−1.48804	+	0.436393i
$94$		−	8.64866i		−	0.892042i
$95$	1.11383	+	9.68294i	0.114277	+	0.993449i
$96$	1.58652	+	0.694958i	0.161923	+	0.0709288i
$97$	−1.74154	+	1.46132i	−0.176826	+	0.148375i	−0.726905	−	0.686738i	$-0.759042\pi$
$97$	−1.74154	+	1.46132i	−0.176826	+	0.148375i	0.550079	+	0.835113i	$0.314598\pi$
$98$	−0.120432	+	0.330884i	−0.0121655	+	0.0334243i
$99$	−4.92451	−	7.67386i	−0.494932	−	0.771252i
$100$	−1.47134	+	4.77862i	−0.147134	+	0.477862i
$101$	6.04590	+	16.6110i	0.601590	+	1.65285i	0.748054	+	0.663638i	$0.230988\pi$
$101$	6.04590	+	16.6110i	0.601590	+	1.65285i	−0.146465	+	0.989216i	$0.546789\pi$
$102$	3.60770	−	2.65445i	0.357216	−	0.262830i
$103$	9.43548	+	16.3427i	0.929706	+	1.61030i	0.783812	+	0.620998i	$0.213272\pi$
$103$	9.43548	+	16.3427i	0.929706	+	1.61030i	0.145894	+	0.989300i	$0.453394\pi$
$104$	2.05262	−	2.44621i	0.201276	−	0.239871i
$105$	−9.73821	+	2.21029i	−0.950352	+	0.215703i
$106$	−2.19987	−	3.81029i	−0.213670	−	0.370088i
$107$	−4.22569	−	2.43970i	−0.408513	−	0.235855i	0.281638	−	0.959521i	$-0.409122\pi$
$107$	−4.22569	−	2.43970i	−0.408513	−	0.235855i	−0.690150	+	0.723666i	$0.742456\pi$
$108$	4.03623	−	3.27244i	0.388386	−	0.314891i
$109$	9.30022	−	1.63988i	0.890800	−	0.157072i	0.290526	−	0.956867i	$-0.406170\pi$
$109$	9.30022	−	1.63988i	0.890800	−	0.157072i	0.600273	+	0.799795i	$0.295059\pi$
$110$	6.22983	+	2.71616i	0.593991	+	0.258975i
$111$	7.53577	−	7.89804i	0.715263	−	0.749649i
$112$	−1.65733	−	1.97513i	−0.156603	−	0.186632i
$113$		−	15.0987i		−	1.42037i	−0.704015	−	0.710185i	$-0.748611\pi$
$113$		−	15.0987i		−	1.42037i	0.704015	−	0.710185i	$-0.251389\pi$
$114$	0.849872	+	7.50185i	0.0795978	+	0.702612i
$115$	−2.65166	+	10.9969i	−0.247268	+	1.02547i
$116$	0.575080	−	0.482549i	0.0533948	−	0.0448036i
$117$	−3.69530	−	8.83852i	−0.341630	−	0.817121i
$118$	3.99056	+	0.703644i	0.367361	+	0.0647756i
$119$	−6.56622	+	1.15780i	−0.601925	+	0.106136i
$120$	−1.14606	+	3.69953i	−0.104620	+	0.337720i
$121$	−0.881171	+	1.52623i	−0.0801065	+	0.138748i
$122$	8.80290	−	5.08235i	0.796977	−	0.460135i
$123$	−0.402698	+	0.199416i	−0.0363100	+	0.0179808i
$124$	5.54983	−	6.61403i	0.498390	−	0.593958i
$125$	−10.9870	−	2.07015i	−0.982708	−	0.185160i
$126$	−7.54612	+	1.69911i	−0.672262	+	0.151369i
$127$	8.21768	−	2.99099i	0.729201	−	0.265407i	0.0493745	−	0.998780i	$-0.484277\pi$
$127$	8.21768	−	2.99099i	0.729201	−	0.265407i	0.679827	+	0.733373i	$0.262055\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	−4.99383	+	7.50059i	−0.439682	+	0.660390i
$130$	5.95040	+	3.94698i	0.521885	+	0.346173i
$131$	4.71317	+	5.61694i	0.411792	+	0.490754i	0.931578	−	0.363542i	$-0.118433\pi$
$131$	4.71317	+	5.61694i	0.411792	+	0.490754i	−0.519786	+	0.854296i	$0.673988\pi$
$132$	4.82198	+	2.11222i	0.419700	+	0.183845i
$133$	3.82199	−	10.5689i	0.331408	−	0.916442i
$134$		−	12.3080i		−	1.06325i
$135$	8.28397	+	8.14713i	0.712971	+	0.701194i
$136$	−0.884452	+	2.43001i	−0.0758411	+	0.208372i
$137$	−2.36868	+	13.4335i	−0.202370	+	1.14770i	0.699155	+	0.714970i	$0.253560\pi$
$137$	−2.36868	+	13.4335i	−0.202370	+	1.14770i	−0.901525	+	0.432727i	$0.857551\pi$
$138$	−2.06861	+	8.51462i	−0.176092	+	0.724813i
$139$	3.61784	−	1.31679i	0.306861	−	0.111688i	−0.184000	−	0.982926i	$-0.558905\pi$
$139$	3.61784	−	1.31679i	0.306861	−	0.111688i	0.490861	+	0.871238i	$0.336682\pi$
$140$	3.97276	−	4.17811i	0.335759	−	0.353115i
$141$	14.8882	−	1.65542i	1.25381	−	0.139411i
$142$	−2.93479	+	3.49754i	−0.246282	+	0.293507i
$143$	6.23862	−	7.43490i	0.521700	−	0.621737i
$144$	−0.892659	+	2.86412i	−0.0743882	+	0.238676i
$145$	1.21650	+	1.15671i	0.101025	+	0.0960596i
$146$	−9.24263	+	3.36404i	−0.764925	+	0.278410i
$147$	−0.592649	−	0.143983i	−0.0488809	−	0.0118755i
$148$	−1.09443	+	6.20681i	−0.0899615	+	0.510197i
$149$	−2.96349	+	8.14212i	−0.242779	+	0.667029i	0.757127	+	0.653268i	$0.226603\pi$
$149$	−2.96349	+	8.14212i	−0.242779	+	0.667029i	−0.999905	+	0.0137607i	$0.995620\pi$
$150$	−8.50773	−	1.61816i	−0.694654	−	0.132122i
$151$			20.8663i			1.69808i	0.528329	+	0.849039i	$0.322819\pi$
$151$			20.8663i			1.69808i	−0.528329	+	0.849039i	$0.677181\pi$
$152$	−2.80876	−	3.33330i	−0.227821	−	0.270366i
$153$	5.26003	+	5.70237i	0.425248	+	0.461009i
$154$	−5.03721	−	6.00311i	−0.405910	−	0.483745i
$155$	16.0886	+	10.6718i	1.29227	+	0.857178i
$156$	4.60390	+	3.06524i	0.368607	+	0.245415i
$157$	−12.0780	+	2.12967i	−0.963927	+	0.169966i	−0.633395	−	0.773828i	$-0.718339\pi$
$157$	−12.0780	+	2.12967i	−0.963927	+	0.169966i	−0.330532	+	0.943795i	$0.607228\pi$
$158$	−15.5817	+	5.67129i	−1.23962	+	0.451184i
$159$	6.13812	−	4.51626i	0.486784	−	0.358163i
$160$	−0.632951	−	2.14461i	−0.0500392	−	0.169547i
$161$	8.38430	−	9.99201i	0.660775	−	0.787481i
$162$	6.40588	+	6.32177i	0.503293	+	0.496685i
$163$	−12.7934	+	7.38628i	−1.00206	+	0.578538i	−0.908856	−	0.417110i	$-0.863043\pi$
$163$	−12.7934	+	7.38628i	−1.00206	+	0.578538i	−0.0932006	+	0.995647i	$0.529710\pi$
$164$	0.129722	−	0.224684i	0.0101296	−	0.0175449i
$165$	−3.48327	+	11.2442i	−0.271172	+	0.875359i
$166$	−0.371304	+	0.0654710i	−0.0288188	+	0.00508153i
$167$	14.3580	+	2.53171i	1.11106	+	0.195910i	0.698912	−	0.715208i	$-0.253668\pi$
$167$	14.3580	+	2.53171i	1.11106	+	0.195910i	0.412147	+	0.911117i	$0.364779\pi$
$168$	3.08285	−	3.23105i	0.237847	−	0.249281i
$169$	−2.14708	+	1.80162i	−0.165160	+	0.138586i
$170$	−5.62128	−	1.35545i	−0.431133	−	0.103958i
$171$	−12.7513	+	2.89891i	−0.975118	+	0.221685i
$172$		−	5.20247i		−	0.396685i
$173$	5.48244	+	6.53372i	0.416822	+	0.496749i	0.933072	−	0.359688i	$-0.117117\pi$
$173$	5.48244	+	6.53372i	0.416822	+	0.496749i	−0.516250	+	0.856438i	$0.672673\pi$
$174$	0.940755	+	0.897603i	0.0713184	+	0.0680471i
$175$	10.2804	+	7.77885i	0.777125	+	0.588026i
$176$	−2.99318	+	0.527778i	−0.225619	+	0.0397828i
$177$	−0.447460	+	7.00420i	−0.0336331	+	0.526468i
$178$	11.3304	+	6.54159i	0.849246	+	0.490313i
$179$	9.23826	+	16.0011i	0.690500	+	1.19598i	0.971674	+	0.236325i	$0.0759429\pi$
$179$	9.23826	+	16.0011i	0.690500	+	1.19598i	−0.281174	+	0.959657i	$0.590724\pi$
$180$	−6.58790	−	1.26475i	−0.491033	−	0.0942692i
$181$	1.41286	−	1.68378i	0.105017	−	0.125154i	−0.710976	−	0.703217i	$-0.751746\pi$
$181$	1.41286	−	1.68378i	0.105017	−	0.125154i	0.815993	+	0.578062i	$0.196191\pi$
$182$	−4.11672	−	7.13037i	−0.305152	−	0.528539i
$183$	10.4339	+	14.1809i	0.771297	+	1.04828i
$184$	−1.73025	−	4.75383i	−0.127556	−	0.350457i
$185$	−14.0658	−	0.874303i	−1.03414	−	0.0642800i
$186$	12.4480	+	8.28774i	0.912728	+	0.607687i
$187$	−2.68816	+	7.38566i	−0.196578	+	0.540093i
$188$	−6.62526	+	5.55925i	−0.483197	+	0.405450i
$189$	−4.36931	−	12.6650i	−0.317820	−	0.921242i
$190$	6.70161	−	7.07732i	0.486186	−	0.513443i
$191$		−	1.78914i		−	0.129458i	−0.997903	−	0.0647288i	$-0.979382\pi$
$191$		−	1.78914i		−	0.129458i	0.997903	−	0.0647288i	$-0.0206182\pi$
$192$	−0.487425	−	1.66205i	−0.0351768	−	0.119948i
$193$	−3.02656	−	1.10158i	−0.217856	−	0.0792933i	0.230786	−	0.973004i	$-0.425870\pi$
$193$	−3.02656	−	1.10158i	−0.217856	−	0.0792933i	−0.448643	+	0.893711i	$0.648092\pi$
$194$	2.23888	+	0.394774i	0.160742	+	0.0283431i
$195$	−5.65554	+	10.9988i	−0.405002	+	0.787637i
$196$	0.330884	−	0.120432i	0.0236346	−	0.00860228i
$197$	1.60586	−	2.78142i	0.114413	−	0.198168i	−0.803132	−	0.595801i	$-0.796835\pi$
$197$	1.60586	−	2.78142i	0.114413	−	0.198168i	0.917545	+	0.397633i	$0.130168\pi$
$198$	−2.71310	+	8.70506i	−0.192812	+	0.618641i
$199$	−2.53556	−	2.12759i	−0.179741	−	0.150821i	0.548478	−	0.836165i	$-0.315207\pi$
$199$	−2.53556	−	2.12759i	−0.179741	−	0.150821i	−0.728219	+	0.685344i	$0.759652\pi$
$200$	4.60639	−	1.94452i	0.325721	−	0.137499i
$201$	21.1875	−	2.35583i	1.49445	−	0.166168i
$202$	8.83851	−	15.3088i	0.621876	−	1.07712i
$203$	−0.662014	−	1.81887i	−0.0464643	−	0.127660i
$204$	−4.35241	−	1.05741i	−0.304730	−	0.0740336i
$205$	0.531787	+	0.231855i	0.0371416	+	0.0161934i
$206$	6.45425	−	17.7329i	0.449689	−	1.23551i
$207$	−15.0534	−	1.93124i	−1.04628	−	0.134230i
$208$	−3.19330			−0.221416
$209$	−8.53681	−	10.1311i	−0.590503	−	0.700780i
$210$	7.95279	+	6.03915i	0.548794	+	0.416741i
$211$	−1.65133	−	1.96798i	−0.113683	−	0.135482i	0.706202	−	0.708010i	$-0.250407\pi$
$211$	−1.65133	−	1.96798i	−0.113683	−	0.135482i	−0.819885	+	0.572529i	$0.805963\pi$
$212$	−1.50480	+	4.13440i	−0.103350	+	0.283952i
$213$	−6.58256	−	4.38261i	−0.451029	−	0.300292i
$214$	0.847299	+	4.80527i	0.0579202	+	0.328482i
$215$	11.5596	−	1.30544i	0.788358	−	0.0890302i
$216$	−5.10127	−	0.988448i	−0.347098	−	0.0672554i
$217$	−11.1307	−	19.2790i	−0.755604	−	1.30874i
$218$	−7.23429	−	6.07029i	−0.489968	−	0.411132i
$219$	−7.56011	−	15.2667i	−0.510865	−	1.03163i
$220$	−1.92376	−	6.51824i	−0.129700	−	0.439460i
$221$	−4.12888	+	7.15143i	−0.277739	+	0.481058i
$222$	−10.8942	−	0.695967i	−0.731168	−	0.0467103i
$223$	2.61492	+	14.8299i	0.175108	+	0.993086i	0.938019	+	0.346583i	$0.112658\pi$
$223$	2.61492	+	14.8299i	0.175108	+	0.993086i	−0.762911	+	0.646503i	$0.776231\pi$
$224$	−0.447726	+	2.53918i	−0.0299149	+	0.169656i
$225$	1.15713	−	14.9553i	0.0771422	−	0.997020i
$226$	−11.5663	+	9.70528i	−0.769379	+	0.645586i
$227$			12.0488i			0.799709i	0.916579	+	0.399854i	$0.130939\pi$
$227$			12.0488i			0.799709i	−0.916579	+	0.399854i	$0.869061\pi$
$228$	5.20046	−	5.47313i	0.344409	−	0.362467i
$229$	−14.2770			−0.943452			−0.471726	−	0.881745i	$-0.656369\pi$
$229$	−14.2770			−0.943452			−0.471726	+	0.881745i	$0.656369\pi$
$230$	10.1286	−	5.03738i	0.667858	−	0.332155i
$231$	9.36985	−	9.82030i	0.616491	−	0.646129i
$232$	−0.739308	−	0.130360i	−0.0485380	−	0.00855855i
$233$	0.806091	+	4.57157i	0.0528088	+	0.299493i	0.999761	−	0.0218823i	$-0.00696591\pi$
$233$	0.806091	+	4.57157i	0.0528088	+	0.299493i	−0.946952	+	0.321376i	$0.895855\pi$
$234$	−4.39541	+	8.51205i	−0.287337	+	0.556450i
$235$	−14.0148	−	13.3260i	−0.914225	−	0.869292i
$236$	−2.02606	−	3.50924i	−0.131885	−	0.228432i
$237$	−12.7453	−	25.7375i	−0.827893	−	1.67183i
$238$	5.10761	+	4.28580i	0.331077	+	0.277807i
$239$	19.1425	−	11.0519i	1.23823	−	0.714891i	0.269495	−	0.963002i	$-0.413143\pi$
$239$	19.1425	−	11.0519i	1.23823	−	0.714891i	0.968732	+	0.248111i	$0.0798099\pi$
$240$	3.57068	−	1.50008i	0.230486	−	0.0968300i
$241$	−6.09657	−	16.7502i	−0.392715	−	1.07897i	−0.965757	−	0.259449i	$-0.916459\pi$
$241$	−6.09657	−	16.7502i	−0.392715	−	1.07897i	0.573042	−	0.819526i	$-0.305763\pi$
$242$	1.73557	−	0.306027i	0.111567	−	0.0196722i
$243$	−9.65643	+	12.2374i	−0.619460	+	0.785028i
$244$	−9.55170	−	3.47654i	−0.611485	−	0.222562i
$245$	0.350621	+	0.704986i	0.0224003	+	0.0450399i
$246$	0.411611	+	0.180302i	0.0262433	+	0.0114956i
$247$	−6.98461	−	12.0400i	−0.444420	−	0.766087i
$248$	−8.63401			−0.548260
$249$	−0.183775	−	0.626647i	−0.0116463	−	0.0397122i
$250$	5.47649	+	9.74721i	0.346364	+	0.616468i
$251$	−22.8087	−	4.02179i	−1.43967	−	0.253853i	−0.601331	−	0.799000i	$-0.705363\pi$
$251$	−22.8087	−	4.02179i	−1.43967	−	0.253853i	−0.838340	+	0.545147i	$0.816474\pi$
$252$	6.15215	+	4.68850i	0.387549	+	0.295347i
$253$	−5.25884	−	14.4485i	−0.330621	−	0.908372i
$254$	−7.57345	−	4.37254i	−0.475201	−	0.274357i
$255$	1.25737	−	9.93615i	0.0787396	−	0.622226i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	4.65937	−	5.55282i	0.290644	−	0.346375i	−0.600889	−	0.799333i	$-0.705187\pi$
$257$	4.65937	−	5.55282i	0.290644	−	0.346375i	0.891532	+	0.452957i	$0.149631\pi$
$258$	8.95575	−	0.995790i	0.557561	−	0.0619952i
$259$	14.0731	+	8.12510i	0.874459	+	0.504869i
$260$	−0.801285	−	7.09534i	−0.0496936	−	0.440034i
$261$	−1.36510	+	1.79126i	−0.0844979	+	0.110876i
$262$	1.27326	−	7.22099i	0.0786620	−	0.446115i
$263$	−15.1819	−	5.52575i	−0.936154	−	0.340732i	−0.171508	−	0.985183i	$-0.554864\pi$
$263$	−15.1819	−	5.52575i	−0.936154	−	0.340732i	−0.764646	+	0.644450i	$0.777086\pi$
$264$	−1.48145	−	5.05156i	−0.0911772	−	0.310902i
$265$	−9.56401	−	2.30615i	−0.587512	−	0.141666i
$266$	−10.5530	+	3.86576i	−0.647045	+	0.237025i
$267$	−9.09225	+	20.7567i	−0.556437	+	1.27029i
$268$	−9.42846	+	7.91141i	−0.575935	+	0.483267i
$269$	11.3090	+	4.11613i	0.689521	+	0.250965i	0.662930	−	0.748681i	$-0.269313\pi$
$269$	11.3090	+	4.11613i	0.689521	+	0.250965i	0.0265908	+	0.999646i	$0.491535\pi$
$270$	0.916231	−	11.5828i	0.0557601	−	0.704905i
$271$	−2.06038	−	11.6850i	−0.125159	−	0.709814i	−0.981213	−	0.192927i	$-0.938202\pi$
$271$	−2.06038	−	11.6850i	−0.125159	−	0.709814i	0.856054	−	0.516887i	$-0.172909\pi$
$272$	2.43001	−	0.884452i	0.147341	−	0.0536278i
$273$	11.4866	−	8.45151i	0.695198	−	0.511508i
$274$	11.8132	−	6.82034i	0.713660	−	0.412032i
$275$	14.0004	−	5.91009i	0.844258	−	0.356392i
$276$	7.85225	−	3.88844i	0.472650	−	0.234057i
$277$	−11.1338	+	6.42812i	−0.668967	+	0.386229i	−0.795685	−	0.605710i	$-0.792889\pi$
$277$	−11.1338	+	6.42812i	−0.668967	+	0.386229i	0.126718	+	0.991939i	$0.459556\pi$
$278$	−3.33422	−	1.92501i	−0.199973	−	0.115455i
$279$	−11.8842	+	23.0148i	−0.711491	+	1.37786i
$280$	−5.75426	−	0.357673i	−0.343883	−	0.0213751i
$281$	2.78132	−	15.7736i	0.165919	−	0.940976i	−0.782192	−	0.623037i	$-0.785898\pi$
$281$	2.78132	−	15.7736i	0.165919	−	0.940976i	0.948111	−	0.317938i	$-0.102990\pi$
$282$	−10.8381	−	10.3409i	−0.645397	−	0.615793i
$283$	−12.1556	−	14.4865i	−0.722575	−	0.861131i	0.272304	−	0.962211i	$-0.412215\pi$
$283$	−12.1556	−	14.4865i	−0.722575	−	0.861131i	−0.994878	+	0.101080i	$0.967770\pi$
$284$	4.56572			0.270925
$285$	13.4659	+	10.1818i	0.797653	+	0.603116i
$286$	−9.70557			−0.573902
$287$	−0.429983	−	0.512434i	−0.0253811	−	0.0302480i
$288$	2.76783	−	1.15720i	0.163096	−	0.0681888i
$289$	−1.79080	+	10.1561i	−0.105341	+	0.597419i
$290$	0.104140	−	1.67541i	0.00611533	−	0.0983836i
$291$	−0.251044	+	3.92966i	−0.0147165	+	0.230361i
$292$	8.51805	+	4.91790i	0.498481	+	0.287798i
$293$	−4.22699	+	2.44046i	−0.246944	+	0.142573i	−0.618364	−	0.785892i	$-0.712204\pi$
$293$	−4.22699	+	2.44046i	−0.246944	+	0.142573i	0.371420	+	0.928465i	$0.378871\pi$
$294$	0.270650	+	0.546546i	0.0157846	+	0.0318752i
$295$	7.28894	−	5.38236i	0.424379	−	0.313373i
$296$	5.45818	−	3.15128i	0.317250	−	0.183165i
$297$	−15.5046	−	3.00424i	−0.899666	−	0.174324i
$298$	8.14212	−	2.96349i	0.471661	−	0.171670i
$299$	−2.80523	−	15.9092i	−0.162230	−	0.920054i
$300$	4.22908	+	7.55744i	0.244166	+	0.436329i
$301$	−12.6048	−	4.58778i	−0.726530	−	0.264435i
$302$	15.9845	−	13.4126i	0.919807	−	0.771810i
$303$	28.0449	+	12.2848i	1.61114	+	0.705743i
$304$	−0.748018	+	4.29424i	−0.0429018	+	0.246291i
$305$	5.32789	−	22.0957i	0.305074	−	1.26520i
$306$	0.987189	−	7.69483i	0.0564338	−	0.439884i
$307$	4.07841	+	1.48442i	0.232767	+	0.0847202i	0.455770	−	0.890097i	$-0.349364\pi$
$307$	4.07841	+	1.48442i	0.232767	+	0.0847202i	−0.223003	+	0.974818i	$0.571586\pi$
$308$	−1.36080	+	7.71745i	−0.0775385	+	0.439743i
$309$	31.7616	+	7.71642i	1.80685	+	0.438972i
$310$	−2.16650	−	19.1843i	−0.123049	−	1.08959i
$311$	21.6789	+	12.5163i	1.22930	+	0.709736i	0.966883	−	0.255219i	$-0.0821477\pi$
$311$	21.6789	+	12.5163i	1.22930	+	0.709736i	0.262415	+	0.964955i	$0.415481\pi$
$312$	−0.611221	−	5.49709i	−0.0346036	−	0.311211i
$313$	−0.449648	+	0.535870i	−0.0254156	+	0.0302892i	−0.778603	−	0.627517i	$-0.784071\pi$
$313$	−0.449648	+	0.535870i	−0.0254156	+	0.0302892i	0.753187	+	0.657807i	$0.228516\pi$
$314$	9.39500	+	7.88334i	0.530190	+	0.444882i
$315$	−8.87384	+	14.8462i	−0.499984	+	0.836489i
$316$	14.3602	+	8.29087i	0.807825	+	0.466398i
$317$	−5.30386	−	14.5722i	−0.297894	−	0.818458i	−0.994851	−	0.101345i	$-0.967685\pi$
$317$	−5.30386	−	14.5722i	−0.297894	−	0.818458i	0.696957	−	0.717113i	$-0.254537\pi$
$318$	−7.40516	−	1.79907i	−0.415261	−	0.100887i
$319$	−2.24702	−	0.396210i	−0.125809	−	0.0221835i
$320$	−1.23602	+	1.86340i	−0.0690955	+	0.104167i
$321$	−8.10982	+	2.37834i	−0.452646	+	0.132746i
$322$	−13.0436			−0.726894
$323$	8.64982	+	7.22756i	0.481289	+	0.402152i
$324$	0.725137	−	8.97074i	0.0402854	−	0.498374i
$325$	15.5644	−	3.56082i	0.863357	−	0.197519i
$326$	13.8817	+	5.05251i	0.768834	+	0.279833i
$327$	9.06496	−	13.6153i	0.501293	−	0.752928i
$328$	−0.255502	+	0.0450518i	−0.0141077	+	0.00248757i
$329$	7.62680	+	20.9545i	0.420479	+	1.15526i
$330$	10.8525	−	4.55928i	0.597413	−	0.250980i
$331$	−19.7918	+	11.4268i	−1.08786	+	0.628075i	−0.933005	−	0.359862i	$-0.882824\pi$
$331$	−19.7918	+	11.4268i	−1.08786	+	0.628075i	−0.154853	+	0.987938i	$0.549490\pi$
$332$	0.288823	+	0.242352i	0.0158512	+	0.0133008i
$333$	−0.887151	−	18.8869i	−0.0486156	−	1.03499i
$334$	−7.28977	−	12.6263i	−0.398879	−	0.690878i
$335$	−19.9446	−	18.9643i	−1.08969	−	1.03613i
$336$	−4.45675	−	0.284717i	−0.243135	−	0.0155326i
$337$	2.61113	+	14.8085i	0.142238	+	0.806669i	0.969544	+	0.244918i	$0.0787611\pi$
$337$	2.61113	+	14.8085i	0.142238	+	0.806669i	−0.827306	+	0.561751i	$0.810128\pi$
$338$	2.76024	+	0.486704i	0.150137	+	0.0264732i
$339$	−18.9210	−	18.0531i	−1.02765	−	0.980508i
$340$	2.57496	+	5.17742i	0.139647	+	0.280785i
$341$	−26.2418			−1.42107
$342$	10.4171	+	7.90470i	0.563292	+	0.427437i
$343$		−	18.9563i		−	1.02355i
$344$	−3.98532	+	3.34408i	−0.214874	+	0.180301i
$345$	10.6102	+	16.4716i	0.571236	+	0.886799i
$346$	1.48107	−	8.39959i	0.0796230	−	0.451565i
$347$	4.49271	+	25.4794i	0.241181	+	1.36781i	0.829196	+	0.558957i	$0.188798\pi$
$347$	4.49271	+	25.4794i	0.241181	+	1.36781i	−0.588015	+	0.808850i	$0.700090\pi$
$348$	0.0828983	−	1.29763i	0.00444382	−	0.0695602i
$349$	2.57767	−	4.46466i	0.137980	−	0.238988i	−0.788752	−	0.614711i	$-0.789272\pi$
$349$	2.57767	−	4.46466i	0.137980	−	0.238988i	0.926732	+	0.375724i	$0.122606\pi$
$350$	−0.649168	−	12.8754i	−0.0346995	−	0.688218i
$351$	−15.4943	−	5.93717i	−0.827026	−	0.316903i
$352$	2.32828	+	1.95366i	0.124098	+	0.104130i
$353$	8.56038	+	14.8270i	0.455623	+	0.789162i	0.998724	−	0.0505053i	$-0.0160832\pi$
$353$	8.56038	+	14.8270i	0.455623	+	0.789162i	−0.543101	+	0.839668i	$0.682750\pi$
$354$	5.65315	−	4.15944i	0.300462	−	0.221072i
$355$	1.14566	+	10.1448i	0.0608054	+	0.538428i
$356$	−2.27187	−	12.8844i	−0.120409	−	0.682872i
$357$	−6.40012	+	9.61279i	−0.338730	+	0.508763i
$358$	6.31934	−	17.3623i	0.333988	−	0.917624i
$359$	−15.1331	−	18.0349i	−0.798693	−	0.951845i	0.200922	−	0.979607i	$-0.435606\pi$
$359$	−15.1331	−	18.0349i	−0.798693	−	0.951845i	−0.999615	+	0.0277621i	$0.991162\pi$
$360$	3.26576	+	5.85959i	0.172121	+	0.308828i
$361$	−17.8271	+	6.57232i	−0.938267	+	0.345912i
$362$	−2.19802			−0.115525
$363$	0.859009	+	2.92910i	0.0450863	+	0.153738i
$364$	−2.81600	+	7.73691i	−0.147599	+	0.405524i
$365$	−8.78989	+	20.1607i	−0.460084	+	1.05526i
$366$	4.15639	−	17.1081i	0.217258	−	0.894257i
$367$	10.4420	+	28.6892i	0.545068	+	1.49756i	0.840292	+	0.542134i	$0.182383\pi$
$367$	10.4420	+	28.6892i	0.545068	+	1.49756i	−0.295224	+	0.955428i	$0.595394\pi$
$368$	−2.52946	+	4.38115i	−0.131857	+	0.228383i
$369$	−0.231594	+	0.743075i	−0.0120563	+	0.0386829i
$370$	8.37157	+	11.3370i	0.435217	+	0.589384i
$371$	8.69005	+	7.29182i	0.451165	+	0.378573i
$372$	−1.65261	−	14.8629i	−0.0856839	−	0.770608i
$373$	−5.88912	+	10.2003i	−0.304927	+	0.528149i	−0.977245	−	0.212113i	$-0.931965\pi$
$373$	−5.88912	+	10.2003i	−0.304927	+	0.528149i	0.672318	+	0.740263i	$0.265299\pi$
$374$	7.38566	−	2.68816i	0.381903	−	0.139001i
$375$	−15.7310	+	11.2931i	−0.812346	+	0.583176i
$376$	8.51727	+	1.50182i	0.439245	+	0.0774507i
$377$	−2.25268	−	0.819909i	−0.116019	−	0.0422275i
$378$	−6.89341	+	11.4880i	−0.354559	+	0.590878i
$379$		−	10.6930i		−	0.549262i	−0.961550	−	0.274631i	$-0.911444\pi$
$379$		−	10.6930i		−	0.549262i	0.961550	−	0.274631i	$-0.0885557\pi$
$380$	−9.72925	−	0.584514i	−0.499100	−	0.0299849i
$381$	6.07745	−	13.8742i	0.311357	−	0.710797i
$382$	−1.37056	+	1.15004i	−0.0701240	+	0.0588410i
$383$	7.15469	−	19.6574i	0.365588	−	1.00444i	−0.611432	−	0.791297i	$-0.709406\pi$
$383$	7.15469	−	19.6574i	0.365588	−	1.00444i	0.977020	−	0.213147i	$-0.0683715\pi$
$384$	−0.959895	+	1.44174i	−0.0489845	+	0.0735733i
$385$	−17.4892	−	1.08709i	−0.891333	−	0.0554035i
$386$	1.10158	+	3.02656i	0.0560688	+	0.154048i
$387$	3.42839	+	15.2262i	0.174275	+	0.773992i
$388$	−1.13671	−	1.96883i	−0.0577075	−	0.0999524i
$389$	22.7618	−	27.1264i	1.15407	−	1.37536i	0.239517	−	0.970892i	$-0.423011\pi$
$389$	22.7618	−	27.1264i	1.15407	−	1.37536i	0.914550	−	0.404472i	$-0.132545\pi$
$390$	12.0608	−	2.73747i	0.610725	−	0.138617i
$391$	6.54109	+	11.3295i	0.330797	+	0.572957i
$392$	−0.304944	−	0.176060i	−0.0154020	−	0.00889236i
$393$	12.6742	+	0.809687i	0.639331	+	0.0408433i
$394$	−3.16292	+	0.557708i	−0.159346	+	0.0280969i
$395$	−14.8185	+	33.9880i	−0.745599	+	1.71012i
$396$	8.41241	−	3.51714i	0.422739	−	0.176743i
$397$	−14.5922	−	17.3903i	−0.732363	−	0.872796i	0.263406	−	0.964685i	$-0.415154\pi$
$397$	−14.5922	−	17.3903i	−0.732363	−	0.872796i	−0.995769	+	0.0918887i	$0.970710\pi$
$398$			3.30994i			0.165912i
$399$	−8.67460	−	17.4264i	−0.434273	−	0.872413i
$400$	−4.45052	−	2.27878i	−0.222526	−	0.113939i
$401$	−6.54292	+	5.49016i	−0.326738	+	0.274165i	−0.791369	−	0.611339i	$-0.790631\pi$
$401$	−6.54292	+	5.49016i	−0.326738	+	0.274165i	0.464631	+	0.885504i	$0.346187\pi$
$402$	−15.4237	−	14.7162i	−0.769265	−	0.733979i
$403$	−27.1521	−	4.78765i	−1.35254	−	0.238490i
$404$	−17.4085	+	3.06958i	−0.866104	+	0.152718i
$405$	20.1144	−	0.639785i	0.999495	−	0.0317912i
$406$	−0.967800	+	1.67628i	−0.0480311	+	0.0831923i
$407$	16.5893	−	9.57785i	0.822302	−	0.474756i
$408$	1.98765	+	4.01383i	0.0984035	+	0.198714i
$409$	−10.5424	+	12.5639i	−0.521288	+	0.621247i	−0.960885	−	0.276948i	$-0.910677\pi$
$409$	−10.5424	+	12.5639i	−0.521288	+	0.621247i	0.439597	+	0.898195i	$0.355121\pi$
$410$	−0.164215	−	0.556406i	−0.00810999	−	0.0274789i
$411$	14.0020	+	19.0302i	0.690665	+	0.938693i
$412$	−17.7329	+	6.45425i	−0.873638	+	0.317978i
$413$	−10.2891	+	1.81424i	−0.506291	+	0.0892728i
$414$	8.19671	+	12.7729i	0.402846	+	0.627755i
$415$	−0.466018	+	0.702562i	−0.0228759	+	0.0344874i
$416$	2.05262	+	2.44621i	0.100638	+	0.119935i
$417$	2.67561	−	6.10813i	0.131025	−	0.299116i
$418$	−2.27349	+	13.0517i	−0.111200	+	0.638379i
$419$		−	0.129870i		−	0.00634455i	−0.999995	−	0.00317227i	$-0.998990\pi$
$419$		−	0.129870i		−	0.00634455i	0.999995	−	0.00317227i	$-0.00100977\pi$
$420$	−0.485692	−	9.97408i	−0.0236993	−	0.486685i
$421$	4.63152	−	12.7250i	0.225726	−	0.620178i	−0.774192	−	0.632951i	$-0.781844\pi$
$421$	4.63152	−	12.7250i	0.225726	−	0.620178i	0.999918	+	0.0127727i	$0.00406580\pi$
$422$	−0.446106	+	2.52999i	−0.0217161	+	0.123158i
$423$	15.7268	−	20.6364i	0.764664	−	1.00338i
$424$	4.13440	−	1.50480i	0.200784	−	0.0730795i
$425$	−10.8578	+	7.02056i	−0.526681	+	0.340547i
$426$	0.873911	+	7.85962i	0.0423411	+	0.380800i
$427$	−16.8463	+	20.0766i	−0.815249	+	0.971576i
$428$	3.13642	−	3.73784i	0.151605	−	0.180675i
$429$	−1.85772	−	16.7076i	−0.0896913	−	0.806649i
$430$	−8.43039	−	8.01605i	−0.406550	−	0.386568i
$431$	−19.7834	+	7.20058i	−0.952934	+	0.346840i	−0.771261	−	0.636519i	$-0.780373\pi$
$431$	−19.7834	+	7.20058i	−0.952934	+	0.346840i	−0.181673	+	0.983359i	$0.558151\pi$
$432$	2.52184	+	4.54316i	0.121332	+	0.218583i
$433$	1.81665	−	10.3028i	0.0873028	−	0.495119i	−0.909533	−	0.415631i	$-0.863561\pi$
$433$	1.81665	−	10.3028i	0.0873028	−	0.495119i	0.996836	−	0.0794872i	$-0.0253283\pi$
$434$	−7.61387	+	20.9189i	−0.365478	+	1.00414i
$435$	2.90406	−	0.141414i	0.139239	−	0.00678030i
$436$			9.44369i			0.452271i
$437$	−22.0513	+	0.0456966i	−1.05485	+	0.00218597i
$438$	−6.83546	+	15.6047i	−0.326611	+	0.745619i
$439$	16.0603	+	19.1399i	0.766515	+	0.913497i	0.998241	−	0.0592843i	$-0.0188819\pi$
$439$	16.0603	+	19.1399i	0.766515	+	0.913497i	−0.231726	+	0.972781i	$0.574437\pi$
$440$	−3.75669	+	5.66353i	−0.179093	+	0.269998i
$441$	−0.889043	+	0.570521i	−0.0423354	+	0.0271677i
$442$	8.13231	−	1.43395i	0.386815	−	0.0682059i
$443$	34.9513	−	12.7212i	1.66058	−	0.604404i	0.670130	−	0.742243i	$-0.266238\pi$
$443$	34.9513	−	12.7212i	1.66058	−	0.604404i	0.990455	+	0.137840i	$0.0440159\pi$
$444$	6.46948	+	8.79276i	0.307028	+	0.417286i
$445$	28.0584	−	8.28101i	1.33009	−	0.392558i
$446$	9.67956	−	11.5356i	0.458340	−	0.546229i
$447$	6.65994	+	13.4490i	0.315004	+	0.636114i
$448$	2.23292	−	1.28917i	0.105495	−	0.0609078i
$449$	4.62800	−	8.01594i	0.218409	−	0.378295i	−0.735913	−	0.677076i	$-0.763247\pi$
$449$	4.62800	−	8.01594i	0.218409	−	0.378295i	0.954322	+	0.298781i	$0.0965800\pi$
$450$	−12.2002	+	8.72667i	−0.575124	+	0.411379i
$451$	−0.776559	+	0.136928i	−0.0365667	+	0.00644770i
$452$	14.8694	+	2.62187i	0.699396	+	0.123322i
$453$	26.1486	+	24.9492i	1.22857	+	1.17222i
$454$	9.22994	−	7.74484i	0.433182	−	0.363483i
$455$	−17.8976	−	4.31561i	−0.839052	−	0.202319i
$456$	−7.53546	−	0.465721i	−0.352880	−	0.0218094i
$457$		−	5.08806i		−	0.238009i	−0.992894	−	0.119005i	$-0.962030\pi$
$457$		−	5.08806i		−	0.238009i	0.992894	−	0.119005i	$-0.0379703\pi$
$458$	9.17709	+	10.9368i	0.428817	+	0.511044i
$459$	13.4352	+	0.226544i	0.627099	+	0.0105742i
$460$	−10.3694	−	4.52097i	−0.483475	−	0.210791i
$461$	−23.7668	+	4.19072i	−1.10693	+	0.195181i	−0.697095	−	0.716979i	$-0.745524\pi$
$461$	−23.7668	+	4.19072i	−1.10693	+	0.195181i	−0.409834	+	0.912160i	$0.634413\pi$
$462$	−13.5456	−	0.865355i	−0.630199	−	0.0402599i
$463$	−3.09391	−	1.78627i	−0.143786	−	0.0830150i	0.426381	−	0.904544i	$-0.359788\pi$
$463$	−3.09391	−	1.78627i	−0.143786	−	0.0830150i	−0.570167	+	0.821529i	$0.693122\pi$
$464$	0.375357	+	0.650137i	0.0174255	+	0.0301818i
$465$	32.6099	−	7.40152i	1.51225	−	0.343237i
$466$	2.98388	−	3.55605i	0.138226	−	0.164731i
$467$	14.9856	+	25.9559i	0.693452	+	1.20109i	0.970700	+	0.240296i	$0.0772446\pi$
$467$	14.9856	+	25.9559i	0.693452	+	1.20109i	−0.277247	+	0.960799i	$0.589422\pi$
$468$	9.34592	−	2.10436i	0.432015	−	0.0972742i
$469$	10.8538	+	29.8204i	0.501180	+	1.37698i
$470$	−1.19976	+	19.3017i	−0.0553407	+	0.890323i
$471$	−11.7724	+	17.6819i	−0.542445	+	0.814738i
$472$	−1.38591	+	3.80775i	−0.0637916	+	0.175266i
$473$	−12.1128	+	10.1638i	−0.556947	+	0.467334i
$474$	−11.5236	+	26.3072i	−0.529297	+	1.20833i
$475$	−1.14257	−	21.7645i	−0.0524249	−	0.998625i
$476$		−	6.66752i		−	0.305605i
$477$	1.67960	−	13.0919i	0.0769034	−	0.599438i
$478$	−20.7709	−	7.55997i	−0.950037	−	0.345785i
$479$	−14.8496	−	2.61838i	−0.678495	−	0.119637i	−0.176228	−	0.984349i	$-0.556390\pi$
$479$	−14.8496	−	2.61838i	−0.678495	−	0.119637i	−0.502267	+	0.864712i	$0.667501\pi$
$480$	−3.44432	−	1.77106i	−0.157211	−	0.0808376i
$481$	18.9122	−	6.88349i	0.862324	−	0.313860i
$482$	−8.91259	+	15.4371i	−0.405957	+	0.703139i
$483$	−2.49665	−	22.4539i	−0.113601	−	1.02169i
$484$	−1.35003	−	1.13281i	−0.0613651	−	0.0514914i
$485$	4.08941	−	3.01973i	0.185690	−	0.137119i
$486$	15.5814	−	0.468782i	0.706787	−	0.0212644i
$487$	14.0569	−	24.3472i	0.636978	−	1.10328i	−0.349115	−	0.937080i	$-0.613518\pi$
$487$	14.0569	−	24.3472i	0.636978	−	1.10328i	0.986092	−	0.166198i	$-0.0531491\pi$
$488$	3.47654	+	9.55170i	0.157375	+	0.432385i
$489$	−6.04056	+	24.8636i	−0.273163	+	1.12437i
$490$	0.314676	−	0.721747i	0.0142156	−	0.0326052i
$491$	5.34417	−	14.6830i	0.241179	−	0.662634i	−0.758758	−	0.651373i	$-0.774193\pi$
$491$	5.34417	−	14.6830i	0.241179	−	0.662634i	0.999937	−	0.0112608i	$-0.00358449\pi$
$492$	−0.126459	−	0.431208i	−0.00570121	−	0.0194404i
$493$	1.94132			0.0874325
$494$	−4.73356	+	13.0897i	−0.212973	+	0.588933i
$495$	9.92579	+	17.8094i	0.446131	+	0.800471i
$496$	5.54983	+	6.61403i	0.249195	+	0.296979i
$497$	4.02626	−	11.0621i	0.180603	−	0.496202i
$498$	−0.361911	+	0.543581i	−0.0162176	+	0.0243584i
$499$	4.28754	+	24.3158i	0.191936	+	1.08853i	0.916714	+	0.399543i	$0.130831\pi$
$499$	4.28754	+	24.3158i	0.191936	+	1.08853i	−0.724778	+	0.688982i	$0.758058\pi$
$500$	3.94657	−	10.4606i	0.176496	−	0.467813i
$501$	20.3401	−	14.9657i	0.908727	−	0.668617i
$502$	11.5803	+	20.0576i	0.516853	+	0.895215i
$503$	−13.5745	−	11.3904i	−0.605259	−	0.507872i	0.287872	−	0.957669i	$-0.407052\pi$
$503$	−13.5745	−	11.3904i	−0.605259	−	0.507872i	−0.893131	+	0.449796i	$0.851497\pi$
$504$	−0.362929	−	7.72653i	−0.0161662	−	0.344167i
$505$	−11.1887	−	37.9104i	−0.497891	−	1.68699i
$506$	−7.68791	+	13.3159i	−0.341769	+	0.591962i
$507$	−0.309504	+	4.84475i	−0.0137456	+	0.215163i
$508$	1.51857	+	8.61221i	0.0673755	+	0.382105i
$509$	−6.74016	+	38.2254i	−0.298753	+	1.69431i	0.352794	+	0.935701i	$0.385232\pi$
$509$	−6.74016	+	38.2254i	−0.298753	+	1.69431i	−0.651547	+	0.758609i	$0.725879\pi$
$510$	−8.41976	+	5.42363i	−0.372833	+	0.240163i
$511$	19.4270	−	16.3012i	0.859399	−	0.721121i
$512$		−	1.00000i		−	0.0441942i
$513$	−11.6136	+	19.4454i	−0.512752	+	0.858537i
$514$	−7.24869			−0.319726
$515$	−18.7907	−	37.7820i	−0.828015	−	1.66487i
$516$	−6.51947	−	6.22042i	−0.287003	−	0.273839i
$517$	25.8870	+	4.56457i	1.13851	+	0.200750i
$518$	−2.82182	−	16.0033i	−0.123984	−	0.703146i
$519$	14.7429	+	0.941842i	0.647141	+	0.0413423i
$520$	−4.92029	+	5.17462i	−0.215769	+	0.226922i
$521$	10.3124	+	17.8616i	0.451794	+	0.782530i	0.998498	−	0.0547960i	$-0.0174508\pi$
$521$	10.3124	+	17.8616i	0.451794	+	0.782530i	−0.546703	+	0.837326i	$0.684118\pi$
$522$	2.24966	−	0.105671i	0.0984649	−	0.00462508i
$523$	0.0694571	+	0.0582814i	0.00303715	+	0.00254847i	0.644305	−	0.764769i	$-0.277147\pi$
$523$	0.0694571	+	0.0582814i	0.00303715	+	0.00254847i	−0.641268	+	0.767317i	$0.721591\pi$
$524$	−6.35004	+	3.66620i	−0.277403	+	0.160158i
$525$	22.0400	−	3.58195i	0.961904	−	0.156329i
$526$	5.52575	+	15.1819i	0.240934	+	0.661961i
$527$	21.9880	−	3.87708i	0.957814	−	0.168888i
$528$	−2.91746	+	4.38194i	−0.126966	+	0.190699i
$529$	−2.43628	−	0.886732i	−0.105925	−	0.0385536i
$530$	4.38101	+	8.80882i	0.190299	+	0.382631i
$531$	8.24229	+	8.93543i	0.357685	+	0.387765i
$532$	9.74468	+	5.59920i	0.422485	+	0.242756i
$533$	−0.828480			−0.0358855
$534$	21.7449	−	6.37706i	0.940995	−	0.275962i
$535$	9.09228	+	6.03102i	0.393094	+	0.260744i
$536$	12.1210	+	2.13726i	0.523547	+	0.0923155i
$537$	31.0977	+	7.55513i	1.34196	+	0.326028i
$538$	−4.11613	−	11.3090i	−0.177459	−	0.487565i
$539$	−0.926833	−	0.535107i	−0.0399215	−	0.0230487i
$540$	−9.46186	+	6.74339i	−0.407174	+	0.290189i
$541$	−28.0937	−	23.5734i	−1.20784	−	1.01350i	−0.999371	−	0.0354725i	$-0.988706\pi$
$541$	−28.0937	−	23.5734i	−1.20784	−	1.01350i	−0.208472	−	0.978028i	$-0.566849\pi$
$542$	−7.62685	+	9.08932i	−0.327601	+	0.390420i
$543$	−0.420717	−	3.78376i	−0.0180547	−	0.162377i
$544$	−2.23951	−	1.29298i	−0.0960182	−	0.0554361i
$545$	−20.9834	+	2.36968i	−0.898828	+	0.101506i
$546$	−13.8576	−	3.36669i	−0.593053	−	0.144081i
$547$	5.59380	−	31.7240i	0.239174	−	1.35642i	−0.594469	−	0.804118i	$-0.702638\pi$
$547$	5.59380	−	31.7240i	0.239174	−	1.35642i	0.833643	−	0.552303i	$-0.186251\pi$
$548$	−12.8181	−	4.66539i	−0.547560	−	0.199296i
$549$	30.2462	+	3.88037i	1.29088	+	0.165610i
$550$	−13.5267	−	6.92602i	−0.576780	−	0.295327i
$551$	−1.63027	+	2.83726i	−0.0694516	+	0.120872i
$552$	−8.02605	−	3.51573i	−0.341611	−	0.149640i
$553$	32.7511	−	27.4814i	1.39272	−	1.16863i
$554$	12.0809	+	4.39710i	0.513269	+	0.186815i
$555$	−17.9137	+	16.5812i	−0.760393	+	0.703832i
$556$	0.668550	+	3.79154i	0.0283528	+	0.160797i
$557$	−7.80737	+	2.84165i	−0.330809	+	0.120405i	−0.502085	−	0.864819i	$-0.667433\pi$
$557$	−7.80737	+	2.84165i	−0.330809	+	0.120405i	0.171276	+	0.985223i	$0.445211\pi$
$558$	25.2694	−	5.68975i	1.06974	−	0.240866i
$559$	−14.3873	+	8.30653i	−0.608519	+	0.351329i
$560$	3.42477	+	4.63792i	0.144723	+	0.195988i
$561$	6.04118	+	12.1995i	0.255059	+	0.515061i
$562$	−13.8711	+	8.00848i	−0.585117	+	0.337817i
$563$	13.7591	+	7.94379i	0.579875	+	0.334791i	0.761084	−	0.648654i	$-0.224668\pi$
$563$	13.7591	+	7.94379i	0.579875	+	0.334791i	−0.181209	+	0.983445i	$0.558001\pi$
$564$	−0.955038	+	14.9495i	−0.0402144	+	0.629485i
$565$	−2.09453	+	33.6968i	−0.0881173	+	1.41763i
$566$	−3.28382	+	18.6234i	−0.138029	+	0.782802i
$567$	−21.0953	−	9.66772i	−0.885921	−	0.406006i
$568$	−2.93479	−	3.49754i	−0.123141	−	0.146754i
$569$	−35.5477			−1.49024			−0.745119	−	0.666932i	$-0.767607\pi$
$569$	−35.5477			−1.49024			−0.745119	+	0.666932i	$0.767607\pi$
$570$	−0.856041	−	16.8602i	−0.0358556	−	0.706197i
$571$	−5.29456			−0.221570			−0.110785	−	0.993844i	$-0.535337\pi$
$571$	−5.29456			−0.221570			−0.110785	+	0.993844i	$0.535337\pi$
$572$	6.23862	+	7.43490i	0.260850	+	0.310869i
$573$	−2.24206	−	2.13922i	−0.0936633	−	0.0893670i
$574$	−0.116159	+	0.658772i	−0.00484840	+	0.0274966i
$575$	7.44338	−	24.1746i	0.310410	−	1.00815i
$576$	−2.66559	−	1.37645i	−0.111066	−	0.0573519i
$577$	−34.4185	−	19.8715i	−1.43286	−	0.827262i	−0.435522	−	0.900178i	$-0.643436\pi$
$577$	−34.4185	−	19.8715i	−1.43286	−	0.827262i	−0.997338	+	0.0729164i	$0.976769\pi$
$578$	8.93114	−	5.15640i	0.371486	−	0.214478i
$579$	−4.99920	+	2.47561i	−0.207759	+	0.102883i
$580$	−1.35038	+	0.997158i	−0.0560715	+	0.0414047i
$581$	0.841881	−	0.486060i	0.0349271	−	0.0201652i
$582$	3.17166	−	2.33362i	0.131470	−	0.0967318i
$583$	12.5659	−	4.57361i	0.520427	−	0.189420i
$584$	−1.70797	−	9.68637i	−0.0706762	−	0.400825i
$585$	7.02092	+	20.2381i	0.290279	+	0.836742i
$586$	4.58656	+	1.66937i	0.189469	+	0.0689610i
$587$	22.3590	−	18.7615i	0.922857	−	0.774369i	−0.0516644	−	0.998665i	$-0.516453\pi$
$587$	22.3590	−	18.7615i	0.922857	−	0.774369i	0.974521	+	0.224296i	$0.0720082\pi$
$588$	0.244708	−	0.558643i	0.0100916	−	0.0230380i
$589$	−12.7985	+	35.3917i	−0.527354	+	1.45829i
$590$	−8.80837	−	2.12394i	−0.362635	−	0.0874413i
$591$	−1.56547	−	5.33803i	−0.0643947	−	0.219577i
$592$	−5.92247	−	2.15560i	−0.243412	−	0.0885948i
$593$	4.43465	−	25.1502i	0.182109	−	1.03279i	−0.747504	−	0.664257i	$-0.768748\pi$
$593$	4.43465	−	25.1502i	0.182109	−	1.03279i	0.929613	−	0.368536i	$-0.120141\pi$
$594$	7.66475	+	13.8083i	0.314489	+	0.566560i
$595$	14.8148	−	1.67306i	0.607350	−	0.0685887i
$596$	−7.50382	−	4.33233i	−0.307368	−	0.177459i
$597$	−5.69788	+	0.633547i	−0.233199	+	0.0259293i
$598$	−10.3840	+	12.3752i	−0.424634	+	0.506059i
$599$	25.1675	+	21.1180i	1.02831	+	0.862858i	0.990649	−	0.136432i	$-0.0435636\pi$
$599$	25.1675	+	21.1180i	1.02831	+	0.862858i	0.0376649	+	0.999290i	$0.488008\pi$
$600$	3.07093	−	8.09749i	0.125370	−	0.330579i
$601$	−11.3807	−	6.57065i	−0.464228	−	0.268022i	0.249592	−	0.968351i	$-0.419703\pi$
$601$	−11.3807	−	6.57065i	−0.464228	−	0.268022i	−0.713820	+	0.700329i	$0.753037\pi$
$602$	4.58778	+	12.6048i	0.186984	+	0.513735i
$603$	22.3810	−	29.3678i	0.911423	−	1.19595i
$604$	−20.5493	−	3.62340i	−0.836141	−	0.147434i
$605$	2.17828	−	3.28395i	0.0885599	−	0.133512i
$606$	−8.61622	−	29.3801i	−0.350010	−	1.19349i
$607$	3.08925			0.125389			0.0626943	−	0.998033i	$-0.480031\pi$
$607$	3.08925			0.125389			0.0626943	+	0.998033i	$0.480031\pi$
$608$	3.77039	−	2.18727i	0.152910	−	0.0887054i
$609$	−3.07086	−	1.34516i	−0.124438	−	0.0545086i
$610$	−20.3510	+	10.1214i	−0.823988	+	0.409805i
$611$	25.9522	+	9.44584i	1.04992	+	0.382138i
$612$	−6.52913	+	4.18991i	−0.263924	+	0.169367i
$613$	3.85039	−	0.678928i	0.155516	−	0.0274216i	−0.0953481	−	0.995444i	$-0.530396\pi$
$613$	3.85039	−	0.678928i	0.155516	−	0.0274216i	0.250864	+	0.968022i	$0.419285\pi$
$614$	−1.48442	−	4.07841i	−0.0599062	−	0.164591i
$615$	0.926388	−	0.389186i	0.0373556	−	0.0156935i
$616$	6.78661	−	3.91825i	0.273440	−	0.157871i
$617$	−15.1487	−	12.7112i	−0.609862	−	0.511735i	0.284736	−	0.958606i	$-0.408094\pi$
$617$	−15.1487	−	12.7112i	−0.609862	−	0.511735i	−0.894599	+	0.446871i	$0.852538\pi$
$618$	−14.5048	−	29.2908i	−0.583470	−	1.17825i
$619$	19.5527	+	33.8662i	0.785888	+	1.36120i	0.928467	+	0.371414i	$0.121127\pi$
$619$	19.5527	+	33.8662i	0.785888	+	1.36120i	−0.142579	+	0.989783i	$0.545540\pi$
$620$	−13.3034	+	13.9911i	−0.534278	+	0.561894i
$621$	−20.4189	+	16.5550i	−0.819384	+	0.664329i
$622$	−4.34687	−	24.6523i	−0.174294	−	0.988469i
$623$	−33.2205	−	5.85767i	−1.33095	−	0.234683i
$624$	−3.81813	+	4.00168i	−0.152847	+	0.160195i
$625$	24.2332	+	6.14422i	0.969329	+	0.245769i
$626$	0.699529			0.0279588
$627$	−22.9029	−	1.41549i	−0.914654	−	0.0565293i
$628$		−	12.2643i		−	0.489399i
$629$	−12.4851	+	10.4763i	−0.497815	+	0.417717i
$630$	17.0768	−	2.74520i	0.680358	−	0.109371i
$631$	3.34106	−	18.9481i	0.133005	−	0.754312i	−0.843222	−	0.537565i	$-0.819344\pi$
$631$	3.34106	−	18.9481i	0.133005	−	0.754312i	0.976228	−	0.216747i	$-0.0695446\pi$
$632$	−2.87939	−	16.3298i	−0.114536	−	0.649566i
$633$	−4.44062	−	0.283687i	−0.176499	−	0.0112755i
$634$	−7.75372	+	13.4298i	−0.307940	+	0.533367i
$635$	−18.7548	+	5.53520i	−0.744262	+	0.219658i
$636$	3.38178	+	6.82911i	0.134096	+	0.270792i
$637$	−0.861358	−	0.722766i	−0.0341283	−	0.0286370i
$638$	1.14084	+	1.97599i	0.0451663	+	0.0782304i
$639$	−13.3626	+	3.00877i	−0.528616	+	0.119025i
$640$	2.22194	−	0.250927i	0.0878301	−	0.00991875i
$641$	−4.47239	−	25.3642i	−0.176649	−	1.00182i	−0.936224	−	0.351405i	$-0.885704\pi$
$641$	−4.47239	−	25.3642i	−0.176649	−	1.00182i	0.759575	−	0.650420i	$-0.225407\pi$
$642$	7.03481	+	4.68372i	0.277642	+	0.184852i
$643$	5.91400	−	16.2486i	0.233226	−	0.640782i	−0.766774	−	0.641917i	$-0.778139\pi$
$643$	5.91400	−	16.2486i	0.233226	−	0.640782i	0.999999	+	0.00113539i	$0.000361407\pi$
$644$	8.38430	+	9.99201i	0.330388	+	0.393741i
$645$	12.1855	−	16.0468i	0.479804	−	0.631841i
$646$	−0.0233587	−	11.2719i	−0.000919037	−	0.443488i
$647$	−15.5424			−0.611035			−0.305518	−	0.952186i	$-0.598830\pi$
$647$	−15.5424			−0.611035			−0.305518	+	0.952186i	$0.598830\pi$
$648$	−7.33809	+	5.21079i	−0.288268	+	0.204699i
$649$	−4.21226	+	11.5731i	−0.165346	+	0.454283i
$650$	−12.7323	−	9.63416i	−0.499404	−	0.377883i
$651$	−37.4681	−	9.10281i	−1.46849	−	0.356767i
$652$	−5.05251	−	13.8817i	−0.197872	−	0.543648i
$653$	6.62802	−	11.4801i	0.259375	−	0.449250i	−0.706700	−	0.707513i	$-0.749817\pi$
$653$	6.62802	−	11.4801i	0.259375	−	0.449250i	0.966075	+	0.258263i	$0.0831503\pi$
$654$	−16.2568	+	1.80759i	−0.635690	+	0.0706824i
$655$	−9.73948	−	13.1895i	−0.380553	−	0.515356i
$656$	0.198745	+	0.166767i	0.00775969	+	0.00651115i
$657$	−28.1709	−	8.78001i	−1.09905	−	0.342541i
$658$	11.1496	−	19.3117i	0.434658	−	0.752850i
$659$	31.9611	−	11.6329i	1.24503	−	0.453153i	0.366309	−	0.930493i	$-0.380621\pi$
$659$	31.9611	−	11.6329i	1.24503	−	0.453153i	0.878719	+	0.477340i	$0.158399\pi$
$660$	−10.4685	−	5.38289i	−0.407486	−	0.209529i
$661$	45.3644	+	7.99896i	1.76447	+	0.311124i	0.959398	−	0.282055i	$-0.0910161\pi$
$661$	45.3644	+	7.99896i	1.76447	+	0.311124i	0.805071	+	0.593179i	$0.202127\pi$
$662$	21.4754	+	7.81641i	0.834665	+	0.303793i
$663$	4.02504	+	13.7248i	0.156320	+	0.533029i
$664$		−	0.377032i		−	0.0146317i
$665$	−9.99591	+	23.0571i	−0.387625	+	0.894117i
$666$	−13.8979	+	12.8198i	−0.538534	+	0.496759i
$667$	−2.90928	+	2.44118i	−0.112648	+	0.0945227i
$668$	−4.98650	+	13.7003i	−0.192933	+	0.530080i
$669$	21.7107	+	14.4548i	0.839384	+	0.558855i
$670$	−1.70739	+	27.4685i	−0.0659620	+	1.06120i
$671$	10.5664	+	29.0310i	0.407912	+	1.12073i
$672$	2.64663	+	3.59708i	0.102096	+	0.138760i
$673$	25.4433	+	44.0691i	0.980768	+	1.69874i	0.659414	+	0.751780i	$0.270804\pi$
$673$	25.4433	+	44.0691i	0.980768	+	1.69874i	0.321353	+	0.946959i	$0.395862\pi$
$674$	9.66555	−	11.5190i	0.372303	−	0.443694i
$675$	−17.3577	−	19.3316i	−0.668097	−	0.744074i
$676$	−1.40141	−	2.42731i	−0.0539003	−	0.0933581i
$677$	40.5615	+	23.4182i	1.55891	+	0.900035i	0.997362	+	0.0725886i	$0.0231260\pi$
$677$	40.5615	+	23.4182i	1.55891	+	0.900035i	0.561545	+	0.827447i	$0.310207\pi$
$678$	−1.66729	+	26.0986i	−0.0640321	+	1.00231i
$679$	−5.77260	+	1.01787i	−0.221532	+	0.0390621i
$680$	2.31098	−	5.30051i	0.0886221	−	0.203265i
$681$	15.0990	+	14.4064i	0.578594	+	0.552054i
$682$	16.8679	+	20.1024i	0.645905	+	0.769759i
$683$			33.4053i			1.27822i	0.769116	+	0.639110i	$0.220697\pi$
$683$			33.4053i			1.27822i	−0.769116	+	0.639110i	$0.779303\pi$
$684$	−0.640628	−	13.0610i	−0.0244950	−	0.499400i
$685$	7.14984	−	29.6517i	0.273181	−	1.13293i
$686$	−14.5214	+	12.1849i	−0.554429	+	0.465221i
$687$	−17.0706	+	17.8912i	−0.651282	+	0.682592i
$688$	5.12343	+	0.903399i	0.195329	+	0.0344418i
$689$	13.8363	−	2.43970i	0.527119	−	0.0929453i
$690$	5.79781	−	18.7156i	0.220719	−	0.712492i
$691$	23.1480	−	40.0935i	0.880591	−	1.52523i	0.0299064	−	0.999553i	$-0.490479\pi$
$691$	23.1480	−	40.0935i	0.880591	−	1.52523i	0.850685	−	0.525676i	$-0.176188\pi$
$692$	−7.38647	+	4.26458i	−0.280792	+	0.162115i
$693$	−1.10307	−	23.4836i	−0.0419021	−	0.892069i
$694$	16.6305	−	19.8195i	0.631286	−	0.752337i
$695$	−8.25682	+	2.43688i	−0.313199	+	0.0924361i
$696$	−1.04733	+	0.770596i	−0.0396988	+	0.0292093i
$697$	0.630450	−	0.229465i	0.0238800	−	0.00869160i
$698$	−5.07703	+	0.895217i	−0.192168	+	0.0338845i
$699$	6.69267	+	4.45592i	0.253140	+	0.168538i
$700$	−9.44584	+	8.77343i	−0.357019	+	0.331605i
$701$	−5.16255	−	6.15249i	−0.194987	−	0.232376i	0.659688	−	0.751539i	$-0.270688\pi$
$701$	−5.16255	−	6.15249i	−0.194987	−	0.232376i	−0.854675	+	0.519163i	$0.826244\pi$
$702$	5.41142	+	15.6857i	0.204241	+	0.592018i
$703$	−4.82656	−	27.0449i	−0.182037	−	1.02002i
$704$		−	3.03935i		−	0.114550i
$705$	−33.4565	+	1.62918i	−1.26004	+	0.0613584i
$706$	5.85564	−	16.0882i	0.220380	−	0.605489i
$707$	−7.91446	+	44.8851i	−0.297654	+	1.68808i
$708$	−6.82009	−	1.65693i	−0.256315	−	0.0622712i
$709$	7.71715	−	2.80881i	0.289824	−	0.105487i	−0.193017	−	0.981195i	$-0.561827\pi$
$709$	7.71715	−	2.80881i	0.289824	−	0.105487i	0.482841	+	0.875708i	$0.339605\pi$
$710$	7.03493	−	7.39856i	0.264016	−	0.277663i
$711$	−47.4920	−	14.8018i	−1.78109	−	0.555112i
$712$	−8.40970	+	10.0223i	−0.315167	+	0.375601i
$713$	−28.0761	+	33.4598i	−1.05146	+	1.25308i
$714$	11.4777	−	1.27621i	0.429544	−	0.0477610i
$715$	−14.9545	+	15.7275i	−0.559266	+	0.588174i
$716$	−17.3623	+	6.31934i	−0.648858	+	0.236165i
$717$	9.03836	−	37.2029i	0.337544	−	1.38937i
$718$	−4.08818	+	23.1852i	−0.152569	+	0.865264i
$719$	8.72890	−	23.9825i	0.325533	−	0.894395i	−0.663694	−	0.748004i	$-0.731012\pi$
$719$	8.72890	−	23.9825i	0.325533	−	0.894395i	0.989227	−	0.146390i	$-0.0467656\pi$
$720$	2.38952	−	6.26819i	0.0890520	−	0.233602i
$721$			48.6559i			1.81204i
$722$	16.4937	+	9.43172i	0.613833	+	0.351012i
$723$	−28.2799	−	12.3877i	−1.05174	−	0.460705i
$724$	1.41286	+	1.68378i	0.0525085	+	0.0625772i
$725$	−2.55448	−	2.75026i	−0.0948709	−	0.102142i
$726$	1.69166	−	2.54083i	0.0627835	−	0.0942991i
$727$	36.4034	−	6.41890i	1.35013	−	0.238064i	0.548632	−	0.836064i	$-0.315149\pi$
$727$	36.4034	−	6.41890i	1.35013	−	0.238064i	0.801496	+	0.598000i	$0.204038\pi$
$728$	7.73691	−	2.81600i	0.286749	−	0.104368i
$729$	3.78937	+	26.7328i	0.140347	+	0.990102i
$730$	21.0940	−	6.22558i	0.780724	−	0.230419i
$731$	8.64768	−	10.3059i	0.319846	−	0.381178i
$732$	−15.7773	+	7.81292i	−0.583145	+	0.288774i
$733$	−40.2287	+	23.2261i	−1.48588	+	0.857874i	−0.999871	−	0.0160785i	$-0.994882\pi$
$733$	−40.2287	+	23.2261i	−1.48588	+	0.857874i	−0.486011	+	0.873953i	$0.661548\pi$
$734$	15.2652	−	26.4401i	0.563448	−	0.975921i
$735$	1.30268	+	0.403549i	0.0480500	+	0.0148851i
$736$	4.98206	−	0.878472i	0.183641	−	0.0323809i
$737$	36.8400	+	6.49588i	1.35702	+	0.239279i
$738$	0.718094	−	0.300228i	0.0264334	−	0.0110515i
$739$	−20.3684	+	17.0911i	−0.749264	+	0.628707i	−0.935308	−	0.353834i	$-0.884878\pi$
$739$	−20.3684	+	17.0911i	−0.749264	+	0.628707i	0.186044	+	0.982541i	$0.440433\pi$
$740$	3.30352	−	13.7003i	0.121440	−	0.503633i
$741$	−23.4392	−	5.64309i	−0.861060	−	0.207304i
$742$		−	11.3441i		−	0.416454i
$743$	−12.7757	−	15.2255i	−0.468696	−	0.558570i	0.478971	−	0.877831i	$-0.341010\pi$
$743$	−12.7757	−	15.2255i	−0.468696	−	0.558570i	−0.947667	+	0.319261i	$0.896565\pi$
$744$	−10.3234	+	10.8197i	−0.378474	+	0.396669i
$745$	7.74329	−	17.7602i	0.283692	−	0.650682i
$746$	11.5993	−	2.04527i	0.424681	−	0.0748827i
$747$	−1.00502	−	0.518964i	−0.0367716	−	0.0189879i
$748$	−6.80666	−	3.92983i	−0.248876	−	0.143689i
$749$	−6.29040	−	10.8953i	−0.229846	−	0.398105i
$750$	18.7628	+	4.79156i	0.685119	+	0.174963i
$751$	11.3522	−	13.5290i	0.414246	−	0.493679i	−0.518063	−	0.855343i	$-0.673347\pi$
$751$	11.3522	−	13.5290i	0.414246	−	0.493679i	0.932309	+	0.361663i	$0.117791\pi$
$752$	−4.32433	−	7.48996i	−0.157692	−	0.273131i
$753$	−32.3115	+	23.7739i	−1.17750	+	0.866370i
$754$	0.819909	+	2.25268i	0.0298593	+	0.0820379i
$755$	2.89462	−	46.5687i	0.105346	−	1.69481i
$756$	13.2313	−	2.10367i	0.481218	−	0.0765099i
$757$	−1.57621	+	4.33061i	−0.0572884	+	0.157399i	−0.965035	−	0.262119i	$-0.915579\pi$
$757$	−1.57621	+	4.33061i	−0.0572884	+	0.157399i	0.907747	+	0.419518i	$0.137801\pi$
$758$	−8.19130	+	6.87332i	−0.297522	+	0.249650i
$759$	−24.3940	−	10.6855i	−0.885446	−	0.387861i
$760$	5.80608	+	7.82876i	0.210609	+	0.283979i
$761$		−	53.4428i		−	1.93730i	−0.248430	−	0.968650i	$-0.579915\pi$
$761$		−	53.4428i		−	1.93730i	0.248430	−	0.968650i	$-0.420085\pi$
$762$	−14.5348	+	4.26256i	−0.526539	+	0.154416i
$763$	22.8807	+	8.32789i	0.828337	+	0.301490i
$764$	1.76196	+	0.310681i	0.0637454	+	0.0112400i
$765$	−10.9481	−	13.4560i	−0.395829	−	0.486503i
$766$	−19.6574	+	7.15469i	−0.710249	+	0.258510i
$767$	−6.46983	+	11.2061i	−0.233612	+	0.404628i
$768$	1.72144	−	0.191407i	0.0621172	−	0.00690681i
$769$	2.36333	+	1.98307i	0.0852238	+	0.0715112i	0.684404	−	0.729103i	$-0.260062\pi$
$769$	2.36333	+	1.98307i	0.0852238	+	0.0715112i	−0.599180	+	0.800614i	$0.704507\pi$
$770$	10.4091	+	14.0963i	0.375117	+	0.507995i
$771$	−1.38745	−	12.4782i	−0.0499678	−	0.449392i
$772$	1.61040	−	2.78929i	0.0579595	−	0.100389i
$773$	7.47640	+	20.5413i	0.268908	+	0.738817i	0.998490	+	0.0549251i	$0.0174920\pi$
$773$	7.47640	+	20.5413i	0.268908	+	0.738817i	−0.729583	+	0.683892i	$0.760286\pi$
$774$	9.46023	−	12.4135i	0.340041	−	0.446195i
$775$	−34.4255	−	26.0487i	−1.23660	−	0.935697i
$776$	−0.777553	+	2.13631i	−0.0279125	+	0.0766891i
$777$	27.0087	−	7.92075i	0.968931	−	0.284155i
$778$	−35.4110			−1.26955
$779$	−0.194068	+	1.11411i	−0.00695321	+	0.0399171i
$780$	−9.84958	−	7.47954i	−0.352672	−	0.267810i
$781$	−8.91985	−	10.6303i	−0.319177	−	0.380381i
$782$	4.47437	−	12.2932i	0.160003	−	0.439605i
$783$	0.612507	+	3.85243i	0.0218892	+	0.137675i
$784$	0.0611449	+	0.346770i	0.00218375	+	0.0123846i
$785$	27.2506	−	3.07744i	0.972615	−	0.109839i
$786$	−7.52659	−	10.2295i	−0.268464	−	0.364874i
$787$	−8.84289	−	15.3163i	−0.315215	−	0.545969i	0.664268	−	0.747494i	$-0.268743\pi$
$787$	−8.84289	−	15.3163i	−0.315215	−	0.545969i	−0.979483	+	0.201526i	$0.935410\pi$
$788$	2.46031	+	2.06445i	0.0876451	+	0.0735430i
$789$	−25.0770	+	12.4182i	−0.892767	+	0.442099i
$790$	35.5614	−	10.4954i	1.26522	−	0.373411i
$791$	19.4649	−	33.7142i	0.692092	−	1.19874i
$792$	−8.10168	−	4.18350i	−0.287881	−	0.148654i
$793$	5.63645	+	31.9659i	0.200156	+	1.13514i
$794$	−3.94207	+	22.3566i	−0.139899	+	0.793406i
$795$	−14.3253	+	9.22773i	−0.508066	+	0.327274i
$796$	2.53556	−	2.12759i	0.0898707	−	0.0754104i
$797$		−	33.2416i		−	1.17748i	−0.808323	−	0.588739i	$-0.799624\pi$
$797$		−	33.2416i		−	1.17748i	0.808323	−	0.588739i	$-0.200376\pi$
$798$	−7.77350	+	17.8466i	−0.275179	+	0.631764i
$799$	−22.3651			−0.791222
$800$	1.11509	+	4.87407i	0.0394244	+	0.172324i
$801$	15.1399	+	36.2120i	0.534941	+	1.27949i
$802$	8.41141	+	1.48316i	0.297017	+	0.0523721i
$803$	−5.19112	−	29.4403i	−0.183191	−	1.03893i
$804$	−1.35912	+	21.2747i	−0.0479325	+	0.750300i
$805$	−20.0979	+	21.1367i	−0.708356	+	0.744971i
$806$	13.7855	+	23.8772i	0.485573	+	0.841038i
$807$	18.6799	−	9.25031i	0.657564	−	0.325626i
$808$	13.5414	+	11.3626i	0.476384	+	0.399734i
$809$	10.5267	−	6.07759i	0.370099	−	0.213677i	−0.303403	−	0.952862i	$-0.598123\pi$
$809$	10.5267	−	6.07759i	0.370099	−	0.213677i	0.673502	+	0.739186i	$0.264789\pi$
$810$	−13.4194	−	14.9973i	−0.471510	−	0.526952i
$811$	−1.13858	−	3.12822i	−0.0399810	−	0.109847i	0.918096	−	0.396359i	$-0.129726\pi$
$811$	−1.13858	−	3.12822i	−0.0399810	−	0.109847i	−0.958077	+	0.286512i	$0.907504\pi$
$812$	1.90619	−	0.336113i	0.0668943	−	0.0117953i
$813$	−17.1066	−	11.3894i	−0.599954	−	0.399444i
$814$	−18.0005	−	6.55164i	−0.630916	−	0.229635i
$815$	29.5765	−	14.7097i	1.03602	−	0.515257i
$816$	1.79714	−	4.10267i	0.0629123	−	0.143622i
$817$	7.80015	+	21.2933i	0.272893	+	0.744959i
$818$	16.4011			0.573449
$819$	3.14311	−	24.4995i	0.109829	−	0.856083i
$820$	−0.320676	+	0.483446i	−0.0111985	+	0.0168827i
$821$	−5.30027	−	0.934581i	−0.184981	−	0.0326171i	0.0803903	−	0.996763i	$-0.474383\pi$
$821$	−5.30027	−	0.934581i	−0.184981	−	0.0326171i	−0.265371	+	0.964146i	$0.585494\pi$
$822$	5.57773	−	22.9585i	0.194546	−	0.800771i
$823$	17.5144	+	48.1204i	0.610514	+	1.67737i	0.729082	+	0.684426i	$0.239947\pi$
$823$	17.5144	+	48.1204i	0.610514	+	1.67737i	−0.118568	+	0.992946i	$0.537830\pi$
$824$	16.3427	+	9.43548i	0.569326	+	0.328701i
$825$	9.33364	−	24.6111i	0.324956	−	0.856849i
$826$	8.00347	+	6.71571i	0.278476	+	0.233669i
$827$	−21.7299	+	25.8966i	−0.755621	+	0.900514i	−0.997563	−	0.0697767i	$-0.977771\pi$
$827$	−21.7299	+	25.8966i	−0.755621	+	0.900514i	0.241942	+	0.970291i	$0.422216\pi$
$828$	4.51589	−	14.4893i	0.156938	−	0.503539i
$829$	−5.36663	−	3.09842i	−0.186391	−	0.107613i	0.403901	−	0.914803i	$-0.367654\pi$
$829$	−5.36663	−	3.09842i	−0.186391	−	0.107613i	−0.590292	+	0.807190i	$0.700987\pi$
$830$	0.837745	−	0.0946075i	0.0290785	−	0.00328387i
$831$	−5.25697	+	21.6382i	−0.182362	+	0.750622i
$832$	0.554511	−	3.14479i	0.0192242	−	0.109026i
$833$	0.855654	+	0.311433i	0.0296466	+	0.0107905i
$834$	−6.39895	+	1.87660i	−0.221577	+	0.0649813i
$835$	−31.6925	−	7.64195i	−1.09677	−	0.264461i
$836$	11.4595	−	6.64787i	0.396337	−	0.229922i
$837$	14.6313	+	42.4107i	0.505732	+	1.46593i
$838$	−0.0994859	+	0.0834786i	−0.00343668	+	0.00288372i
$839$	41.3068	+	15.0344i	1.42607	+	0.519047i	0.935802	−	0.352526i	$-0.114677\pi$
$839$	41.3068	+	15.0344i	1.42607	+	0.519047i	0.490267	+	0.871572i	$0.336899\pi$
$840$	−7.32839	+	6.78328i	−0.252854	+	0.234045i
$841$	−4.93793	−	28.0044i	−0.170274	−	0.965670i
$842$	−12.7250	+	4.63152i	−0.438532	+	0.159613i
$843$	−16.4412	−	22.3454i	−0.566264	−	0.769617i
$844$	2.22484	−	1.28451i	0.0765820	−	0.0442146i
$845$	5.04170	−	3.72293i	0.173440	−	0.128073i
$846$	−25.9174	+	1.21739i	−0.891059	+	0.0418547i
$847$	−3.93516	+	2.27197i	−0.135214	+	0.0780657i
$848$	−3.81029	−	2.19987i	−0.130846	−	0.0755438i
$849$	−32.6877	−	2.08824i	−1.12184	−	0.0716682i
$850$	12.3573	+	3.80483i	0.423853	+	0.130505i
$851$	5.53662	−	31.3997i	0.189793	−	1.07637i
$852$	5.45908	−	5.72152i	0.187025	−	0.196016i
$853$	30.9769	+	36.9168i	1.06063	+	1.26401i	0.963206	+	0.268764i	$0.0866150\pi$
$853$	30.9769	+	36.9168i	1.06063	+	1.26401i	0.0974214	+	0.995243i	$0.468941\pi$
$854$	26.2082			0.896825
$855$	28.8601	−	4.70079i	0.986993	−	0.160764i
$856$	−4.87940			−0.166775
$857$	−33.1233	−	39.4748i	−1.13147	−	1.34843i	−0.929404	−	0.369063i	$-0.879679\pi$
$857$	−33.1233	−	39.4748i	−1.13147	−	1.34843i	−0.202066	−	0.979372i	$-0.564766\pi$
$858$	−11.6046	+	12.1625i	−0.396176	+	0.415221i
$859$	1.80363	−	10.2289i	0.0615389	−	0.349005i	−0.938455	−	0.345403i	$-0.887742\pi$
$859$	1.80363	−	10.2289i	0.0615389	−	0.349005i	0.999994	−	0.00360200i	$-0.00114656\pi$
$860$	−0.721696	+	11.6107i	−0.0246096	+	0.395921i
$861$	−1.15627	−	0.0738678i	−0.0394056	−	0.00251741i
$862$	18.2325	+	10.5265i	0.621001	+	0.358535i
$863$	−30.2707	+	17.4768i	−1.03043	+	0.594916i	−0.917106	−	0.398642i	$-0.869481\pi$
$863$	−30.2707	+	17.4768i	−1.03043	+	0.594916i	−0.113319	+	0.993559i	$0.536148\pi$
$864$	1.85926	−	4.85213i	0.0632532	−	0.165073i
$865$	−11.3291	−	15.3422i	−0.385202	−	0.521651i
$866$	−9.06009	+	5.23084i	−0.307874	+	0.177751i
$867$	10.5859	+	14.3875i	0.359517	+	0.488624i
$868$	20.9189	−	7.61387i	0.710035	−	0.258432i
$869$	−8.75147	−	49.6321i	−0.296873	−	1.68365i
$870$	−1.97502	−	2.13374i	−0.0669595	−	0.0723405i
$871$	36.9328	+	13.4425i	1.25142	+	0.455480i
$872$	7.23429	−	6.07029i	0.244984	−	0.205566i
$873$	4.62428	+	5.01316i	0.156508	+	0.169670i
$874$	14.2093	+	16.8629i	0.480636	+	0.570395i
$875$	−21.8643	−	18.7866i	−0.739148	−	0.635104i
$876$	16.3476	−	4.79421i	0.552335	−	0.161981i
$877$	48.5858	+	17.6838i	1.64063	+	0.597139i	0.987148	−	0.159806i	$-0.0510869\pi$
$877$	48.5858	+	17.6838i	1.64063	+	0.597139i	0.653478	+	0.756945i	$0.273309\pi$
$878$	4.33866	−	24.6058i	0.146423	−	0.830404i
$879$	−1.99582	+	8.21502i	−0.0673175	+	0.277086i
$880$	6.75327	−	0.762655i	0.227653	−	0.0257091i
$881$	−14.5985	−	8.42846i	−0.491837	−	0.283962i	0.233499	−	0.972357i	$-0.424982\pi$
$881$	−14.5985	−	8.42846i	−0.491837	−	0.283962i	−0.725336	+	0.688395i	$0.758316\pi$
$882$	1.00851	+	0.314322i	0.0339583	+	0.0105838i
$883$	−21.3174	+	25.4051i	−0.717387	+	0.854949i	−0.994374	−	0.105925i	$-0.966220\pi$
$883$	−21.3174	+	25.4051i	−0.717387	+	0.854949i	0.276987	+	0.960874i	$0.410664\pi$
$884$	−6.32582	−	5.30799i	−0.212760	−	0.178527i
$885$	1.97026	−	15.5696i	0.0662295	−	0.523367i
$886$	−32.2113	−	18.5972i	−1.08216	−	0.624785i
$887$	12.4909	+	34.3185i	0.419404	+	1.15230i	0.952044	+	0.305960i	$0.0989775\pi$
$887$	12.4909	+	34.3185i	0.419404	+	1.15230i	−0.532641	+	0.846341i	$0.678800\pi$
$888$	2.57714	−	10.6078i	0.0864833	−	0.355974i
$889$	22.2053	+	3.91539i	0.744741	+	0.131318i
$890$	−24.3792	−	16.1710i	−0.817192	−	0.542054i
$891$	−22.3030	+	15.8374i	−0.747180	+	0.530574i
$892$	−15.0587			−0.504203
$893$	18.7816	−	32.6870i	0.628503	−	1.09383i
$894$	6.02158	−	13.7466i	0.201392	−	0.459756i
$895$	−18.3979	−	36.9923i	−0.614974	−	1.23652i
$896$	−2.42286	−	0.881847i	−0.0809419	−	0.0294604i
$897$	−23.2907	−	15.5068i	−0.777655	−	0.517756i
$898$	−9.11539	+	1.60729i	−0.304184	+	0.0536359i
$899$	2.21686	+	6.09077i	0.0739364	+	0.203139i
$900$	14.5272	+	3.73652i	0.484239	+	0.124551i
$901$	−9.85326	+	5.68878i	−0.328260	+	0.189521i
$902$	0.604056	+	0.506863i	0.0201129	+	0.0168767i
$903$	−20.8204	+	10.3103i	−0.692858	+	0.343104i
$904$	−7.54937	−	13.0759i	−0.251088	−	0.434898i
$905$	−3.38674	+	3.56180i	−0.112579	+	0.118398i
$906$	2.30419	−	36.0680i	0.0765515	−	1.19828i
$907$	−1.37938	−	7.82283i	−0.0458015	−	0.259753i	0.953305	−	0.302008i	$-0.0976569\pi$
$907$	−1.37938	−	7.82283i	−0.0458015	−	0.259753i	−0.999107	+	0.0422550i	$0.986546\pi$
$908$	−11.8658	−	2.09226i	−0.393780	−	0.0694340i
$909$	48.9270	−	20.4559i	1.62281	−	0.678479i
$910$	8.19840	+	16.4844i	0.271774	+	0.546452i
$911$	51.3737			1.70209			0.851044	−	0.525095i	$-0.175970\pi$
$911$	51.3737			1.70209			0.851044	+	0.525095i	$0.175970\pi$
$912$	4.48693	+	6.07185i	0.148577	+	0.201059i
$913$		−	1.14593i		−	0.0379249i
$914$	−3.89768	+	3.27054i	−0.128924	+	0.108180i
$915$	−21.3188	−	33.0957i	−0.704778	−	1.09411i
$916$	2.47918	−	14.0601i	0.0819143	−	0.464559i
$917$	3.28290	+	18.6182i	0.108411	+	0.614828i
$918$	−8.46241	−	10.4375i	−0.279301	−	0.344490i
$919$	−10.5103	+	18.2044i	−0.346704	+	0.600509i	−0.985662	−	0.168733i	$-0.946033\pi$
$919$	−10.5103	+	18.2044i	−0.346704	+	0.600509i	0.638958	+	0.769242i	$0.279366\pi$
$920$	3.20205	+	10.8494i	0.105568	+	0.357695i
$921$	6.73661	−	3.33598i	0.221979	−	0.109924i
$922$	18.4873	+	15.5127i	0.608846	+	0.510882i
$923$	−7.28986	−	12.6264i	−0.239949	−	0.415603i
$924$	8.04405	+	10.9328i	0.264630	+	0.359662i
$925$	31.2702	+	3.90247i	1.02816	+	0.128312i
$926$	0.620365	+	3.51827i	0.0203865	+	0.115617i
$927$	47.6461	−	30.5757i	1.56490	−	1.00424i
$928$	0.256759	−	0.705440i	0.00842853	−	0.0231572i
$929$	−21.1905	−	25.2538i	−0.695237	−	0.828552i	0.296741	−	0.954958i	$-0.404100\pi$
$929$	−21.1905	−	25.2538i	−0.695237	−	0.828552i	−0.991979	+	0.126406i	$0.959656\pi$
$930$	−26.6312	−	20.2231i	−0.873270	−	0.663140i
$931$	−1.17372	+	0.989019i	−0.0384671	+	0.0324138i
$932$	−4.64209			−0.152057
$933$	41.6056	−	12.2015i	1.36211	−	0.399460i
$934$	10.2508	−	28.1638i	0.335416	−	0.921547i
$935$	7.02388	−	16.1101i	0.229705	−	0.526857i
$936$	−7.61948	−	5.80673i	−0.249050	−	0.189799i
$937$	12.1962	+	33.5088i	0.398433	+	1.09469i	0.963048	+	0.269331i	$0.0868026\pi$
$937$	12.1962	+	33.5088i	0.398433	+	1.09469i	−0.564615	+	0.825355i	$0.690975\pi$
$938$	15.8671	−	27.4827i	0.518080	−	0.897341i
$939$	0.133895	+	1.20420i	0.00436949	+	0.0392975i
$940$	15.5572	−	11.4879i	0.507420	−	0.374693i
$941$	−15.2406	−	12.7884i	−0.496828	−	0.416888i	0.359638	−	0.933092i	$-0.382900\pi$
$941$	−15.2406	−	12.7884i	−0.496828	−	0.416888i	−0.856466	+	0.516204i	$0.827345\pi$
$942$	21.1123	−	2.34747i	0.687875	−	0.0764848i
$943$	−0.656250	+	1.13666i	−0.0213705	+	0.0370147i
$944$	3.80775	−	1.38591i	0.123932	−	0.0451074i
$945$	7.99433	+	28.8713i	0.260056	+	0.939185i
$946$	15.5719	+	2.74575i	0.506287	+	0.0892720i
$947$	6.53179	+	2.37738i	0.212255	+	0.0772544i	0.445959	−	0.895053i	$-0.352863\pi$
$947$	6.53179	+	2.37738i	0.212255	+	0.0772544i	−0.233705	+	0.972308i	$0.575085\pi$
$948$	27.5597	−	8.08235i	0.895098	−	0.262502i
$949$		−	31.4087i		−	1.01957i
$950$	−15.9382	+	14.8652i	−0.517102	+	0.482292i
$951$	−24.6028	−	10.7770i	−0.797801	−	0.349469i
$952$	−5.10761	+	4.28580i	−0.165539	+	0.138903i
$953$	5.10711	−	14.0317i	0.165436	−	0.454531i	−0.829079	−	0.559132i	$-0.811134\pi$
$953$	5.10711	−	14.0317i	0.165436	−	0.454531i	0.994514	+	0.104601i	$0.0333567\pi$
$954$	−11.1086	+	7.12868i	−0.359655	+	0.230799i
$955$	−0.248193	+	3.99293i	−0.00803133	+	0.129208i
$956$	7.55997	+	20.7709i	0.244507	+	0.671777i
$957$	−3.18319	+	2.34211i	−0.102898	+	0.0757097i
$958$	7.53934	+	13.0585i	0.243585	+	0.421901i
$959$	−22.6071	+	26.9421i	−0.730022	+	0.870007i
$960$	0.857252	+	3.77692i	0.0276677	+	0.121900i
$961$	21.7730	+	37.7120i	0.702356	+	1.21652i
$962$	−17.4296	−	10.0630i	−0.561953	−	0.324444i
$963$	−6.71623	+	13.0065i	−0.216428	+	0.419129i
$964$	17.5544	−	3.09531i	0.565388	−	0.0996932i
$965$	6.60174	+	2.87831i	0.212518	+	0.0926560i
$966$	−15.5959	+	16.3456i	−0.501789	+	0.525912i
$967$	−0.868335	−	1.03484i	−0.0279238	−	0.0332783i	0.751902	−	0.659275i	$-0.229137\pi$
$967$	−0.868335	−	1.03484i	−0.0279238	−	0.0332783i	−0.779826	+	0.625997i	$0.784692\pi$
$968$			1.76234i			0.0566438i
$969$	19.3995	−	2.19774i	0.623202	−	0.0706015i
$970$	−4.94187	−	1.19162i	−0.158674	−	0.0382607i
$971$	1.01292	−	0.849937i	0.0325060	−	0.0272758i	−0.626390	−	0.779510i	$-0.715468\pi$
$971$	1.01292	−	0.849937i	0.0325060	−	0.0272758i	0.658896	+	0.752234i	$0.271024\pi$
$972$	−10.3746	−	11.6347i	−0.332767	−	0.373184i
$973$	9.77590	+	1.72376i	0.313401	+	0.0552611i
$974$	−27.6866	+	4.88190i	−0.887137	+	0.156426i
$975$	14.1476	−	23.7620i	0.453085	−	0.760994i
$976$	5.08235	−	8.80290i	0.162682	−	0.281774i
$977$	52.9508	−	30.5712i	1.69405	−	0.978059i	0.742860	−	0.669447i	$-0.233469\pi$
$977$	52.9508	−	30.5712i	1.69405	−	0.978059i	0.951188	−	0.308612i	$-0.0998643\pi$
$978$	22.9294	−	11.3547i	0.733201	−	0.363082i
$979$	−25.5600	+	30.4613i	−0.816902	+	0.973546i
$980$	−0.755160	+	0.222874i	−0.0241227	+	0.00711946i
$981$	−6.22332	−	27.6391i	−0.198695	−	0.882449i
$982$	−14.6830	+	5.34417i	−0.468553	+	0.170539i
$983$	−22.7822	+	4.01712i	−0.726640	+	0.128126i	−0.524719	−	0.851276i	$-0.675829\pi$
$983$	−22.7822	+	4.01712i	−0.726640	+	0.128126i	−0.201921	+	0.979402i	$0.564718\pi$
$984$	−0.249038	+	0.374048i	−0.00793905	+	0.0119242i
$985$	−3.96973	+	5.98471i	−0.126486	+	0.190689i
$986$	−1.24785	−	1.48714i	−0.0397398	−	0.0473600i
$987$	35.3782	+	15.4970i	1.12610	+	0.493276i
$988$	13.0700	−	4.78777i	0.415811	−	0.152319i
$989$			26.3189i			0.836891i
$990$	7.26258	−	19.0512i	0.230820	−	0.605488i
$991$	16.8173	−	46.2051i	0.534218	−	1.46775i	−0.319788	−	0.947489i	$-0.603612\pi$
$991$	16.8173	−	46.2051i	0.534218	−	1.46775i	0.854006	−	0.520263i	$-0.174166\pi$
$992$	1.49928	−	8.50284i	0.0476022	−	0.269965i
$993$	−9.34495	+	38.4648i	−0.296553	+	1.22064i
$994$	−11.0621	+	4.02626i	−0.350868	+	0.127705i
$995$	5.36363	+	5.10001i	0.170038	+	0.161681i
$996$	0.649039	−	0.0721667i	0.0205656	−	0.00228669i
$997$	−28.3530	+	33.7898i	−0.897948	+	1.07013i	0.0992304	+	0.995064i	$0.468362\pi$
$997$	−28.3530	+	33.7898i	−0.897948	+	1.07013i	−0.997178	+	0.0750682i	$0.976083\pi$
$998$	15.8710	−	18.9144i	0.502388	−	0.598723i
$999$	−24.7288	−	21.4707i	−0.782384	−	0.679302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.89.15	yes	240
3.2	odd	2	inner	570.2.bf.a.89.30	yes	240
5.4	even	2	inner	570.2.bf.a.89.26	yes	240
15.14	odd	2	inner	570.2.bf.a.89.11	✓	240
19.3	odd	18	inner	570.2.bf.a.269.11	yes	240
57.41	even	18	inner	570.2.bf.a.269.26	yes	240
95.79	odd	18	inner	570.2.bf.a.269.30	yes	240
285.269	even	18	inner	570.2.bf.a.269.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.89.11	✓	240	15.14	odd	2	inner
570.2.bf.a.89.15	yes	240	1.1	even	1	trivial
570.2.bf.a.89.26	yes	240	5.4	even	2	inner
570.2.bf.a.89.30	yes	240	3.2	odd	2	inner
570.2.bf.a.269.11	yes	240	19.3	odd	18	inner
570.2.bf.a.269.15	yes	240	285.269	even	18	inner
570.2.bf.a.269.26	yes	240	57.41	even	18	inner
570.2.bf.a.269.30	yes	240	95.79	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(1.19567 - 1.25315i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.23176 - 0.138722i) q^{5} +(-1.72853 - 0.110426i) q^{6} +(2.23292 + 1.28917i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.140760 - 2.99670i) q^{9} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(1.19567 - 1.25315i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.23176 - 0.138722i) q^{5} +(-1.72853 - 0.110426i) q^{6} +(2.23292 + 1.28917i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.140760 - 2.99670i) q^{9} +(1.32828 + 1.79880i) q^{10} +(2.63216 - 1.51968i) q^{11} +(1.02648 + 1.39511i) q^{12} +(3.00072 - 1.09217i) q^{13} +(-0.447726 - 2.53918i) q^{14} +(-2.84228 + 2.63086i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.98096 + 1.66223i) q^{17} +(-2.20512 + 2.03407i) q^{18} +(-0.765809 - 4.29110i) q^{19} +(0.524156 - 2.17377i) q^{20} +(4.28535 - 1.25675i) q^{21} +(-2.85606 - 1.03952i) q^{22} +(0.878472 - 4.98206i) q^{23} +(0.408904 - 1.68309i) q^{24} +(4.96151 + 0.619188i) q^{25} +(-2.76548 - 1.59665i) q^{26} +(-3.92361 - 3.40666i) q^{27} +(-1.65733 + 1.97513i) q^{28} +(-0.575080 - 0.482549i) q^{29} +(3.84234 + 0.486229i) q^{30} +(-7.47727 - 4.31700i) q^{31} +(0.342020 + 0.939693i) q^{32} +(1.24280 - 5.11551i) q^{33} +(2.54668 + 0.449048i) q^{34} +(-4.80450 - 3.18688i) q^{35} +(2.97561 + 0.381749i) q^{36} +6.30256 q^{37} +(-2.79492 + 3.34491i) q^{38} +(2.21921 - 5.06623i) q^{39} +(-2.00212 + 0.995744i) q^{40} +(-0.243797 - 0.0887348i) q^{41} +(-3.71730 - 2.47494i) q^{42} +(-5.12343 + 0.903399i) q^{43} +(1.03952 + 2.85606i) q^{44} +(-0.101564 + 6.70744i) q^{45} +(-4.38115 + 2.52946i) q^{46} +(6.62526 + 5.55925i) q^{47} +(-1.55216 + 0.768632i) q^{48} +(-0.176060 - 0.304944i) q^{49} +(-2.71487 - 4.19875i) q^{50} +(-0.285558 + 4.46991i) q^{51} +(0.554511 + 3.14479i) q^{52} +(4.33290 + 0.764007i) q^{53} +(-0.0876053 + 5.19541i) q^{54} +(-6.08515 + 3.02642i) q^{55} +2.57835 q^{56} +(-6.29304 - 4.17105i) q^{57} +0.750713i q^{58} +(-3.10411 + 2.60465i) q^{59} +(-2.09734 - 3.25595i) q^{60} +(-1.76508 + 10.0103i) q^{61} +(1.49928 + 8.50284i) q^{62} +(3.54896 - 6.87283i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.84840 + 2.02120i) q^{65} +(-4.71756 + 2.33614i) q^{66} +(9.42846 + 7.91141i) q^{67} +(-1.29298 - 2.23951i) q^{68} +(-5.19290 - 7.05774i) q^{69} +(0.646977 + 5.72895i) q^{70} +(-0.792828 - 4.49635i) q^{71} +(-1.62025 - 2.52483i) q^{72} +(3.36404 - 9.24263i) q^{73} +(-4.05121 - 4.82804i) q^{74} +(6.70825 - 5.47717i) q^{75} +(4.35889 - 0.00903289i) q^{76} +7.83651 q^{77} +(-5.30744 + 1.55649i) q^{78} +(5.67129 - 15.5817i) q^{79} +(2.04972 + 0.893663i) q^{80} +(-8.96037 + 0.843632i) q^{81} +(0.0887348 + 0.243797i) q^{82} +(0.188516 - 0.326520i) q^{83} +(0.493514 + 4.43848i) q^{84} +(4.65162 - 3.43489i) q^{85} +(3.98532 + 3.34408i) q^{86} +(-1.29231 + 0.143692i) q^{87} +(1.51968 - 2.63216i) q^{88} +(-12.2942 + 4.47471i) q^{89} +(5.20348 - 4.23365i) q^{90} +(8.10836 + 1.42972i) q^{91} +(4.75383 + 1.73025i) q^{92} +(-14.3502 + 4.20843i) q^{93} -8.64866i q^{94} +(1.11383 + 9.68294i) q^{95} +(1.58652 + 0.694958i) q^{96} +(-1.74154 + 1.46132i) q^{97} +(-0.120432 + 0.330884i) q^{98} +(-4.92451 - 7.67386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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