LMFDB - Embedded newform 570.2.bf.a.89.11

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			89.11
Character	$\chi$	$=$	570.89
Dual form			570.2.bf.a.269.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(-0.110426 - 1.72853i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.04972 - 0.893663i) q^{5} +(-1.25315 + 1.19567i) q^{6} +(-2.23292 - 1.28917i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.97561 + 0.381749i) q^{9} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.110426 - 1.72853i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.04972 - 0.893663i) q^{5} +(-1.25315 + 1.19567i) q^{6} +(-2.23292 - 1.28917i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.97561 + 0.381749i) q^{9} +(-2.00212 - 0.995744i) q^{10} +(-2.63216 + 1.51968i) q^{11} +(1.72144 + 0.191407i) q^{12} +(-3.00072 + 1.09217i) q^{13} +(0.447726 + 2.53918i) q^{14} +(-1.77106 - 3.44432i) 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} +(-1.98180 + 4.00201i) q^{21} +(2.85606 + 1.03952i) q^{22} +(0.878472 - 4.98206i) q^{23} +(-0.959895 - 1.44174i) q^{24} +(3.40273 - 3.66352i) q^{25} +(2.76548 + 1.59665i) q^{26} +(0.988448 + 5.10127i) q^{27} +(1.65733 - 1.97513i) q^{28} +(0.575080 + 0.482549i) q^{29} +(-1.50008 + 3.57068i) q^{30} +(-7.47727 - 4.31700i) q^{31} +(0.342020 + 0.939693i) q^{32} +(2.91746 + 4.38194i) q^{33} +(2.54668 + 0.449048i) q^{34} +(-5.72895 - 0.646977i) q^{35} +(0.140760 - 2.99670i) q^{36} -6.30256 q^{37} +(-2.79492 + 3.34491i) q^{38} +(2.21921 + 5.06623i) q^{39} +(1.32828 - 1.79880i) q^{40} +(0.243797 + 0.0887348i) q^{41} +(4.33960 - 1.05430i) q^{42} +(5.12343 - 0.903399i) q^{43} +(-1.03952 - 2.85606i) q^{44} +(-5.75803 + 3.44167i) q^{45} +(-4.38115 + 2.52946i) q^{46} +(6.62526 + 5.55925i) q^{47} +(-0.487425 + 1.66205i) q^{48} +(-0.176060 - 0.304944i) q^{49} +(-4.99366 - 0.251777i) q^{50} +(3.09195 + 3.24060i) q^{51} +(-0.554511 - 3.14479i) q^{52} +(4.33290 + 0.764007i) q^{53} +(3.27244 - 4.03623i) q^{54} +(-4.03711 + 5.46718i) q^{55} -2.57835 q^{56} +(-7.33272 + 1.79757i) q^{57} -0.750713i q^{58} +(3.10411 - 2.60465i) q^{59} +(3.69953 - 1.14606i) q^{60} +(-1.76508 + 10.0103i) q^{61} +(1.49928 + 8.50284i) q^{62} +(7.13643 + 2.98367i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-5.17462 + 4.92029i) q^{65} +(1.48145 - 5.05156i) q^{66} +(-9.42846 - 7.91141i) q^{67} +(-1.29298 - 2.23951i) q^{68} +(-8.70863 - 0.968313i) q^{69} +(3.18688 + 4.80450i) q^{70} +(0.792828 + 4.49635i) q^{71} +(-2.38608 + 1.81841i) 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} +(2.45447 - 4.95652i) q^{78} +(5.67129 - 15.5817i) q^{79} +(-2.23176 + 0.138722i) q^{80} +(8.70854 - 2.27187i) q^{81} +(-0.0887348 - 0.243797i) q^{82} +(0.188516 - 0.326520i) q^{83} +(-3.59708 - 2.64663i) q^{84} +(-2.57496 + 5.17742i) q^{85} +(-3.98532 - 3.34408i) q^{86} +(0.770596 - 1.04733i) q^{87} +(-1.51968 + 2.63216i) q^{88} +(12.2942 - 4.47471i) q^{89} +(6.33766 + 2.19864i) q^{90} +(8.10836 + 1.42972i) q^{91} +(4.75383 + 1.73025i) q^{92} +(-6.63637 + 13.4014i) q^{93} -8.64866i q^{94} +(-5.40449 - 8.11119i) q^{95} +(1.58652 - 0.694958i) q^{96} +(1.74154 - 1.46132i) q^{97} +(-0.120432 + 0.330884i) q^{98} +(7.25214 - 5.52679i) 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
$3$	−0.110426	−	1.72853i	−0.0637545	−	0.997966i
$3$	−0.110426	−	1.72853i	−0.0637545	−	0.997966i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	2.04972	−	0.893663i	0.916664	−	0.399658i
$5$	2.04972	−	0.893663i	0.916664	−	0.399658i
$6$	−1.25315	+	1.19567i	−0.511596	+	0.488129i
$7$	−2.23292	−	1.28917i	−0.843963	−	0.487262i	0.0146466	−	0.999893i	$-0.495338\pi$
$7$	−2.23292	−	1.28917i	−0.843963	−	0.487262i	−0.858609	+	0.512631i	$0.828671\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−2.97561	+	0.381749i	−0.991871	+	0.127250i
$10$	−2.00212	−	0.995744i	−0.633127	−	0.314882i
$11$	−2.63216	+	1.51968i	−0.793625	+	0.458199i	−0.841237	−	0.540666i	$-0.818172\pi$
$11$	−2.63216	+	1.51968i	−0.793625	+	0.458199i	0.0476123	+	0.998866i	$0.484839\pi$
$12$	1.72144	+	0.191407i	0.496938	+	0.0552545i
$13$	−3.00072	+	1.09217i	−0.832251	+	0.302915i	−0.722782	−	0.691076i	$-0.757137\pi$
$13$	−3.00072	+	1.09217i	−0.832251	+	0.302915i	−0.109468	+	0.993990i	$0.534915\pi$
$14$	0.447726	+	2.53918i	0.119660	+	0.678624i
$15$	−1.77106	−	3.44432i	−0.457287	−	0.889319i
$16$	−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
$21$	−1.98180	+	4.00201i	−0.432464	+	0.873311i
$22$	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	$-0.121288\pi$
$24$	−0.959895	−	1.44174i	−0.195938	−	0.294293i
$25$	3.40273	−	3.66352i	0.680547	−	0.732705i
$26$	2.76548	+	1.59665i	0.542356	+	0.313129i
$27$	0.988448	+	5.10127i	0.190227	+	0.981740i
$28$	1.65733	−	1.97513i	0.313206	−	0.373264i
$29$	0.575080	+	0.482549i	0.106790	+	0.0896071i	0.694619	−	0.719378i	$-0.255573\pi$
$29$	0.575080	+	0.482549i	0.106790	+	0.0896071i	−0.587829	+	0.808985i	$0.700017\pi$
$30$	−1.50008	+	3.57068i	−0.273877	+	0.651914i
$31$	−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
$33$	2.91746	+	4.38194i	0.507864	+	0.762798i
$34$	2.54668	+	0.449048i	0.436752	+	0.0770111i
$35$	−5.72895	−	0.646977i	−0.968369	−	0.109359i
$36$	0.140760	−	2.99670i	0.0234601	−	0.499449i
$37$	−6.30256			−1.03613			−0.518067	−	0.855340i	$-0.673348\pi$
$37$	−6.30256			−1.03613			−0.518067	+	0.855340i	$0.673348\pi$
$38$	−2.79492	+	3.34491i	−0.453396	+	0.542616i
$39$	2.21921	+	5.06623i	0.355358	+	0.811246i
$40$	1.32828	−	1.79880i	0.210020	−	0.284415i
$41$	0.243797	+	0.0887348i	0.0380747	+	0.0138580i	0.360987	−	0.932571i	$-0.382440\pi$
$41$	0.243797	+	0.0887348i	0.0380747	+	0.0138580i	−0.322913	+	0.946429i	$0.604662\pi$
$42$	4.33960	−	1.05430i	0.669614	−	0.162682i
$43$	5.12343	−	0.903399i	0.781316	−	0.137767i	0.231257	−	0.972893i	$-0.425716\pi$
$43$	5.12343	−	0.903399i	0.781316	−	0.137767i	0.550059	+	0.835126i	$0.314605\pi$
$44$	−1.03952	−	2.85606i	−0.156713	−	0.430567i
$45$	−5.75803	+	3.44167i	−0.858356	+	0.513055i
$46$	−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	$0.504962\pi$
$48$	−0.487425	+	1.66205i	−0.0703537	+	0.239897i
$49$	−0.176060	−	0.304944i	−0.0251514	−	0.0435635i
$50$	−4.99366	−	0.251777i	−0.706210	−	0.0356066i
$51$	3.09195	+	3.24060i	0.432960	+	0.453774i
$52$	−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	$0.457843\pi$
$54$	3.27244	−	4.03623i	0.445322	−	0.549261i
$55$	−4.03711	+	5.46718i	−0.544364	+	0.737194i
$56$	−2.57835			−0.344546
$57$	−7.33272	+	1.79757i	−0.971242	+	0.238094i
$58$		−	0.750713i		−	0.0985735i
$59$	3.10411	−	2.60465i	0.404120	−	0.339097i	−0.417963	−	0.908464i	$-0.637256\pi$
$59$	3.10411	−	2.60465i	0.404120	−	0.339097i	0.822084	+	0.569367i	$0.192812\pi$
$60$	3.69953	−	1.14606i	0.477608	−	0.147955i
$61$	−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
$63$	7.13643	+	2.98367i	0.899106	+	0.375907i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−5.17462	+	4.92029i	−0.641832	+	0.610287i
$66$	1.48145	−	5.05156i	0.182354	−	0.621804i
$67$	−9.42846	−	7.91141i	−1.15187	−	0.966533i	−0.152108	−	0.988364i	$-0.548606\pi$
$67$	−9.42846	−	7.91141i	−1.15187	−	0.966533i	−0.999762	+	0.0218308i	$0.993050\pi$
$68$	−1.29298	−	2.23951i	−0.156797	−	0.271581i
$69$	−8.70863	−	0.968313i	−1.04840	−	0.116571i
$70$	3.18688	+	4.80450i	0.380905	+	0.574247i
$71$	0.792828	+	4.49635i	0.0940914	+	0.533619i	0.995022	+	0.0996557i	$0.0317741\pi$
$71$	0.792828	+	4.49635i	0.0940914	+	0.533619i	−0.900931	+	0.433963i	$0.857115\pi$
$72$	−2.38608	+	1.81841i	−0.281202	+	0.214302i
$73$	−3.36404	+	9.24263i	−0.393731	+	1.08177i	0.571553	+	0.820565i	$0.306341\pi$
$73$	−3.36404	+	9.24263i	−0.393731	+	1.08177i	−0.965284	+	0.261202i	$0.915881\pi$
$74$	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
$78$	2.45447	−	4.95652i	0.277914	−	0.561216i
$79$	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	$-0.271527\pi$
$80$	−2.23176	+	0.138722i	−0.249518	+	0.0155096i
$81$	8.70854	−	2.27187i	0.967615	−	0.252430i
$82$	−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	$0.160080\pi$
$84$	−3.59708	−	2.64663i	−0.392473	−	0.288772i
$85$	−2.57496	+	5.17742i	−0.279293	+	0.561570i
$86$	−3.98532	−	3.34408i	−0.429748	−	0.360602i
$87$	0.770596	−	1.04733i	0.0826165	−	0.112285i
$88$	−1.51968	+	2.63216i	−0.161998	+	0.280589i
$89$	12.2942	−	4.47471i	1.30318	−	0.474318i	0.405148	−	0.914251i	$-0.367220\pi$
$89$	12.2942	−	4.47471i	1.30318	−	0.474318i	0.898031	+	0.439933i	$0.144998\pi$
$90$	6.33766	+	2.19864i	0.668048	+	0.231757i
$91$	8.10836	+	1.42972i	0.849987	+	0.149876i
$92$	4.75383	+	1.73025i	0.495621	+	0.180391i
$93$	−6.63637	+	13.4014i	−0.688160	+	1.38966i
$94$		−	8.64866i		−	0.892042i
$95$	−5.40449	−	8.11119i	−0.554489	−	0.832191i
$96$	1.58652	−	0.694958i	0.161923	−	0.0709288i
$97$	1.74154	−	1.46132i	0.176826	−	0.148375i	−0.550079	−	0.835113i	$-0.685402\pi$
$97$	1.74154	−	1.46132i	0.176826	−	0.148375i	0.726905	+	0.686738i	$0.240958\pi$
$98$	−0.120432	+	0.330884i	−0.0121655	+	0.0334243i
$99$	7.25214	−	5.52679i	0.728867	−	0.555463i
$100$	3.01699	+	3.98720i	0.301699	+	0.398720i
$101$	−6.04590	−	16.6110i	−0.601590	−	1.65285i	−0.748054	−	0.663638i	$-0.769012\pi$
$101$	−6.04590	−	16.6110i	−0.601590	−	1.65285i	0.146465	−	0.989216i	$-0.453211\pi$
$102$	0.494972	−	4.45159i	0.0490095	−	0.440773i
$103$	−9.43548	−	16.3427i	−0.929706	−	1.61030i	−0.783812	−	0.620998i	$-0.786728\pi$
$103$	−9.43548	−	16.3427i	−0.929706	−	1.61030i	−0.145894	−	0.989300i	$-0.546606\pi$
$104$	−2.05262	+	2.44621i	−0.201276	+	0.239871i
$105$	−0.485692	+	9.97408i	−0.0473987	+	0.973371i
$106$	−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	$0.742456\pi$
$108$	−5.19541	+	0.0876053i	−0.499929	+	0.00842982i
$109$	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	$0.295059\pi$
$110$	6.78311	−	0.421624i	0.646744	−	0.0402003i
$111$	0.695967	+	10.8942i	0.0660583	+	1.03403i
$112$	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	$-0.251389\pi$
$114$	6.09040	+	4.46173i	0.570418	+	0.417879i
$115$	−2.65166	−	10.9969i	−0.247268	−	1.02547i
$116$	−0.575080	+	0.482549i	−0.0533948	+	0.0448036i
$117$	8.51205	−	4.39541i	0.786939	−	0.406356i
$118$	−3.99056	−	0.703644i	−0.367361	−	0.0647756i
$119$	6.56622	−	1.15780i	0.601925	−	0.106136i
$120$	−3.25595	−	2.09734i	−0.297226	−	0.191460i
$121$	−0.881171	+	1.52623i	−0.0801065	+	0.138748i
$122$	8.80290	−	5.08235i	0.796977	−	0.460135i
$123$	0.126459	−	0.431208i	0.0114024	−	0.0388807i
$124$	5.54983	−	6.61403i	0.498390	−	0.593958i
$125$	3.70071	−	10.5501i	0.331001	−	0.943630i
$126$	−2.30159	−	7.38469i	−0.205042	−	0.657880i
$127$	−8.21768	+	2.99099i	−0.729201	+	0.265407i	−0.679827	−	0.733373i	$-0.737945\pi$
$127$	−8.21768	+	2.99099i	−0.729201	+	0.265407i	−0.0493745	+	0.998780i	$0.515723\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	−2.12731	−	8.75623i	−0.187299	−	0.770943i
$130$	7.09534	+	0.801285i	0.622303	+	0.0702774i
$131$	−4.71317	−	5.61694i	−0.411792	−	0.490754i	0.519786	−	0.854296i	$-0.326012\pi$
$131$	−4.71317	−	5.61694i	−0.411792	−	0.490754i	−0.931578	+	0.363542i	$0.881567\pi$
$132$	−4.82198	+	2.11222i	−0.419700	+	0.183845i
$133$	−3.82199	+	10.5689i	−0.331408	+	0.916442i
$134$			12.3080i			1.06325i
$135$	6.58486	+	9.57286i	0.566735	+	0.823900i
$136$	−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	$0.857551\pi$
$138$	4.85603	+	7.29362i	0.413373	+	0.620874i
$139$	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	$0.336682\pi$
$140$	1.63197	−	5.52956i	0.137927	−	0.467333i
$141$	8.87772	−	12.0658i	0.747639	−	1.01613i
$142$	2.93479	−	3.49754i	0.246282	−	0.293507i
$143$	6.23862	−	7.43490i	0.521700	−	0.621737i
$144$	2.92673	+	0.658993i	0.243894	+	0.0549161i
$145$	1.60999	+	0.475165i	0.133702	+	0.0394603i
$146$	9.24263	−	3.36404i	0.764925	−	0.278410i
$147$	−0.507663	+	0.337998i	−0.0418713	+	0.0278776i
$148$	1.09443	−	6.20681i	0.0899615	−	0.510197i
$149$	2.96349	−	8.14212i	0.242779	−	0.667029i	−0.757127	−	0.653268i	$-0.773397\pi$
$149$	2.96349	−	8.14212i	0.242779	−	0.667029i	0.999905	−	0.0137607i	$-0.00438029\pi$
$150$	0.116227	+	8.65947i	0.00948992	+	0.707043i
$151$			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
$155$	−19.1843	−	2.16650i	−1.54092	−	0.174018i
$156$	−5.37462	+	1.30575i	−0.430314	+	0.104544i
$157$	12.0780	−	2.12967i	0.963927	−	0.169966i	0.330532	−	0.943795i	$-0.392772\pi$
$157$	12.0780	−	2.12967i	0.963927	−	0.169966i	0.633395	+	0.773828i	$0.281661\pi$
$158$	−15.5817	+	5.67129i	−1.23962	+	0.451184i
$159$	0.842142	−	7.57390i	0.0667862	−	0.600649i
$160$	1.54082	+	1.62046i	0.121812	+	0.128109i
$161$	−8.38430	+	9.99201i	−0.660775	+	0.787481i
$162$	−7.33809	−	5.21079i	−0.576535	−	0.409399i
$163$	12.7934	−	7.38628i	1.00206	−	0.578538i	0.0932006	−	0.995647i	$-0.470290\pi$
$163$	12.7934	−	7.38628i	1.00206	−	0.578538i	0.908856	+	0.417110i	$0.136957\pi$
$164$	−0.129722	+	0.224684i	−0.0101296	+	0.0175449i
$165$	9.89596	+	6.37454i	0.770400	+	0.496257i
$166$	−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	$0.364779\pi$
$168$	0.284717	+	4.45675i	0.0219664	+	0.343845i
$169$	−2.14708	+	1.80162i	−0.165160	+	0.138586i
$170$	5.62128	−	1.35545i	0.431133	−	0.103958i
$171$	3.91687	+	12.4763i	0.299531	+	0.954087i
$172$			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	$0.672673\pi$
$174$	−1.29763	+	0.0828983i	−0.0983729	+	0.00628450i
$175$	−12.3209	+	3.79362i	−0.931375	+	0.286771i
$176$	2.99318	−	0.527778i	0.225619	−	0.0397828i
$177$	−4.84499	−	5.07791i	−0.364172	−	0.381679i
$178$	−11.3304	−	6.54159i	−0.849246	−	0.490313i
$179$	−9.23826	−	16.0011i	−0.690500	−	1.19598i	−0.971674	−	0.236325i	$-0.924057\pi$
$179$	−9.23826	−	16.0011i	−0.690500	−	1.19598i	0.281174	−	0.959657i	$-0.409276\pi$
$180$	−2.38952	−	6.26819i	−0.178104	−	0.467203i
$181$	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
$183$	17.4980	+	1.94560i	1.29349	+	0.143823i
$184$	−1.73025	−	4.75383i	−0.127556	−	0.350457i
$185$	−12.9185	+	5.63237i	−0.949788	+	0.414100i
$186$	14.5318	−	3.53048i	1.06552	−	0.258867i
$187$	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
$190$	−2.73959	+	9.35386i	−0.198751	+	0.678600i
$191$			1.78914i			0.129458i	0.997903	+	0.0647288i	$0.0206182\pi$
$191$			1.78914i			0.129458i	−0.997903	+	0.0647288i	$0.979382\pi$
$192$	−1.55216	−	0.768632i	−0.112018	−	0.0554712i
$193$	3.02656	+	1.10158i	0.217856	+	0.0792933i	0.448643	−	0.893711i	$-0.351908\pi$
$193$	3.02656	+	1.10158i	0.217856	+	0.0792933i	−0.230786	+	0.973004i	$0.574130\pi$
$194$	−2.23888	−	0.394774i	−0.160742	−	0.0283431i
$195$	9.07627	+	8.40114i	0.649965	+	0.601618i
$196$	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	$0.130168\pi$
$198$	−8.89535	−	2.00291i	−0.632165	−	0.142341i
$199$	−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	$0.759652\pi$
$200$	1.11509	−	4.87407i	0.0788488	−	0.344649i
$201$	−12.6339	+	17.1710i	−0.891130	+	1.21115i
$202$	−8.83851	+	15.3088i	−0.621876	+	1.07712i
$203$	−0.662014	−	1.81887i	−0.0464643	−	0.127660i
$204$	−3.72828	+	2.48225i	−0.261032	+	0.173793i
$205$	0.579015	−	0.0359904i	0.0404402	−	0.00251368i
$206$	−6.45425	+	17.7329i	−0.449689	+	1.23551i
$207$	−0.712095	+	15.1600i	−0.0494940	+	1.05370i
$208$	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
$213$	7.68452	−	1.86694i	0.526535	−	0.127921i
$214$	0.847299	+	4.80527i	0.0579202	+	0.328482i
$215$	9.69429	−	6.43034i	0.661145	−	0.438546i
$216$	3.40666	+	3.92361i	0.231794	+	0.266968i
$217$	11.1307	+	19.2790i	0.755604	+	1.30874i
$218$	−7.23429	−	6.07029i	−0.489968	−	0.411132i
$219$	16.3476	+	4.79421i	1.10467	+	0.323963i
$220$	−4.68308	−	4.92515i	−0.315733	−	0.332053i
$221$	4.12888	−	7.15143i	0.277739	−	0.481058i
$222$	7.89804	−	7.53577i	0.530082	−	0.505768i
$223$	−2.61492	−	14.8299i	−0.175108	−	0.993086i	−0.938019	−	0.346583i	$-0.887342\pi$
$223$	−2.61492	−	14.8299i	−0.175108	−	0.993086i	0.762911	−	0.646503i	$-0.223769\pi$
$224$	0.447726	−	2.53918i	0.0299149	−	0.169656i
$225$	−8.72667	+	12.2002i	−0.581778	+	0.813348i
$226$	−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	$0.869061\pi$
$228$	−0.496949	−	7.53346i	−0.0329112	−	0.498916i
$229$	−14.2770			−0.943452			−0.471726	−	0.881745i	$-0.656369\pi$
$229$	−14.2770			−0.943452			−0.471726	+	0.881745i	$0.656369\pi$
$230$	−6.71966	+	9.09996i	−0.443081	+	0.600034i
$231$	−0.865355	−	13.5456i	−0.0569362	−	0.891236i
$232$	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	$0.895855\pi$
$234$	−8.83852	−	3.69530i	−0.577792	−	0.241569i
$235$	18.5481	+	5.47418i	1.20994	+	0.357096i
$236$	2.02606	+	3.50924i	0.131885	+	0.228432i
$237$	−27.5597	−	8.08235i	−1.79020	−	0.525005i
$238$	−5.10761	−	4.28580i	−0.331077	−	0.277807i
$239$	−19.1425	+	11.0519i	−1.23823	+	0.714891i	−0.968732	−	0.248111i	$-0.920190\pi$
$239$	−19.1425	+	11.0519i	−1.23823	+	0.714891i	−0.269495	+	0.963002i	$0.586857\pi$
$240$	0.486229	+	3.84234i	0.0313859	+	0.248022i
$241$	−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
$243$	−4.88864	−	14.8021i	−0.313607	−	0.949553i
$244$	−9.55170	−	3.47654i	−0.611485	−	0.222562i
$245$	−0.633391	−	0.467713i	−0.0404659	−	0.0298811i
$246$	−0.411611	+	0.180302i	−0.0262433	+	0.0114956i
$247$	6.98461	+	12.0400i	0.444420	+	0.766087i
$248$	−8.63401			−0.548260
$249$	−0.585215	−	0.289799i	−0.0370865	−	0.0183653i
$250$	−10.4606	+	3.94657i	−0.661588	+	0.249603i
$251$	22.8087	+	4.02179i	1.43967	+	0.253853i	0.838340	−	0.545147i	$-0.183526\pi$
$251$	22.8087	+	4.02179i	1.43967	+	0.253853i	0.601331	+	0.799000i	$0.294637\pi$
$252$	−4.17757	+	6.50990i	−0.263162	+	0.410085i
$253$	5.25884	+	14.4485i	0.330621	+	0.908372i
$254$	7.57345	+	4.37254i	0.475201	+	0.274357i
$255$	9.23365	+	3.87916i	0.578233	+	0.242923i
$256$	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	$0.149631\pi$
$258$	−5.34026	+	7.25801i	−0.332470	+	0.451864i
$259$	14.0731	+	8.12510i	0.874459	+	0.504869i
$260$	−3.94698	−	5.95040i	−0.244781	−	0.369028i
$261$	−1.89543	−	1.21634i	−0.117324	−	0.0752897i
$262$	−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	$0.777086\pi$
$264$	4.71756	+	2.33614i	0.290346	+	0.143780i
$265$	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	−0.0265908	−	0.999646i	$-0.508465\pi$
$269$	−11.3090	−	4.11613i	−0.689521	−	0.250965i	−0.662930	+	0.748681i	$0.730687\pi$
$270$	3.10056	−	11.1976i	0.188694	−	0.681465i
$271$	−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
$273$	1.57594	−	14.1734i	0.0953803	−	0.857813i
$274$	11.8132	−	6.82034i	0.713660	−	0.412032i
$275$	−3.38915	+	14.8140i	−0.204374	+	0.893319i
$276$	2.46584	−	8.40818i	0.148426	−	0.506113i
$277$	11.1338	−	6.42812i	0.668967	−	0.386229i	−0.126718	−	0.991939i	$-0.540444\pi$
$277$	11.1338	−	6.42812i	0.668967	−	0.386229i	0.795685	+	0.605710i	$0.207111\pi$
$278$	−3.33422	−	1.92501i	−0.199973	−	0.115455i
$279$	23.8975	+	9.99129i	1.43070	+	0.598163i
$280$	−5.28490	+	2.30417i	−0.315833	+	0.137701i
$281$	−2.78132	+	15.7736i	−0.165919	+	0.940976i	0.782192	+	0.623037i	$0.214102\pi$
$281$	−2.78132	+	15.7736i	−0.165919	+	0.940976i	−0.948111	+	0.317938i	$0.897010\pi$
$282$	−14.9495	+	0.955038i	−0.890227	+	0.0568717i
$283$	12.1556	+	14.4865i	0.722575	+	0.861131i	0.994878	−	0.101080i	$-0.0322299\pi$
$283$	12.1556	+	14.4865i	0.722575	+	0.861131i	−0.272304	+	0.962211i	$0.587785\pi$
$284$	−4.56572			−0.270925
$285$	−13.4236	+	10.2375i	−0.795147	+	0.606417i
$286$	−9.70557			−0.573902
$287$	−0.429983	−	0.512434i	−0.0253811	−	0.0302480i
$288$	−1.37645	−	2.66559i	−0.0811079	−	0.157072i
$289$	−1.79080	+	10.1561i	−0.105341	+	0.597419i
$290$	−0.670885	−	1.53875i	−0.0393957	−	0.0903588i
$291$	−2.71825	−	2.84892i	−0.159346	−	0.167007i
$292$	−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	$0.378871\pi$
$294$	0.585241	+	0.171632i	0.0341319	+	0.0100098i
$295$	4.03488	−	8.11284i	0.234920	−	0.472348i
$296$	−5.45818	+	3.15128i	−0.317250	+	0.183165i
$297$	−10.3540	−	11.9252i	−0.600802	−	0.691971i
$298$	−8.14212	+	2.96349i	−0.471661	+	0.171670i
$299$	2.80523	+	15.9092i	0.162230	+	0.920054i
$300$	6.55883	−	5.65524i	0.378674	−	0.326505i
$301$	−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
$306$	−7.74935	−	0.364001i	−0.443001	−	0.0208086i
$307$	−4.07841	−	1.48442i	−0.232767	−	0.0847202i	0.223003	−	0.974818i	$-0.428414\pi$
$307$	−4.07841	−	1.48442i	−0.232767	−	0.0847202i	−0.455770	+	0.890097i	$0.650636\pi$
$308$	−1.36080	+	7.71745i	−0.0775385	+	0.439743i
$309$	−27.2069	+	18.1142i	−1.54775	+	1.03048i
$310$	10.6718	+	16.0886i	0.606116	+	0.913772i
$311$	−21.6789	−	12.5163i	−1.22930	−	0.709736i	−0.262415	−	0.964955i	$-0.584519\pi$
$311$	−21.6789	−	12.5163i	−1.22930	−	0.709736i	−0.966883	+	0.255219i	$0.917852\pi$
$312$	4.45501	+	3.27788i	0.252215	+	0.185573i
$313$	0.449648	−	0.535870i	0.0254156	−	0.0302892i	−0.753187	−	0.657807i	$-0.771484\pi$
$313$	0.449648	−	0.535870i	0.0254156	−	0.0302892i	0.778603	+	0.627517i	$0.215929\pi$
$314$	−9.39500	−	7.88334i	−0.530190	−	0.444882i
$315$	17.2941	−	0.261867i	0.974412	−	0.0147545i
$316$	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	$-0.254537\pi$
$318$	−6.34326	+	4.22329i	−0.355712	+	0.236830i
$319$	−2.24702	−	0.396210i	−0.125809	−	0.0221835i
$320$	0.250927	−	2.22194i	0.0140272	−	0.124210i
$321$	−3.75046	+	7.57362i	−0.209330	+	0.422718i
$322$	13.0436			0.726894
$323$	8.64982	+	7.22756i	0.481289	+	0.402152i
$324$	0.725137	+	8.97074i	0.0402854	+	0.498374i
$325$	−6.20945	+	14.7096i	−0.344438	+	0.815942i
$326$	−13.8817	−	5.05251i	−0.768834	−	0.279833i
$327$	−3.86156	−	15.8946i	−0.213545	−	0.878973i
$328$	0.255502	−	0.0450518i	0.0141077	−	0.00248757i
$329$	−7.62680	−	20.9545i	−0.420479	−	1.15526i
$330$	−1.47782	−	11.6782i	−0.0813514	−	0.642865i
$331$	−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
$333$	18.7540	−	2.40600i	1.02771	−	0.131848i
$334$	−7.28977	−	12.6263i	−0.398879	−	0.690878i
$335$	−26.3959	−	7.79035i	−1.44216	−	0.425632i
$336$	3.23105	−	3.08285i	0.176268	−	0.168183i
$337$	−2.61113	−	14.8085i	−0.142238	−	0.806669i	−0.969544	−	0.244918i	$-0.921239\pi$
$337$	−2.61113	−	14.8085i	−0.142238	−	0.806669i	0.827306	−	0.561751i	$-0.189872\pi$
$338$	2.76024	+	0.486704i	0.150137	+	0.0264732i
$339$	−26.0986	+	1.66729i	−1.41748	+	0.0905550i
$340$	−4.65162	−	3.43489i	−0.252270	−	0.186283i
$341$	26.2418			1.42107
$342$	7.03968	−	11.0201i	0.380663	−	0.595899i
$343$			18.9563i			1.02355i
$344$	3.98532	−	3.34408i	0.214874	−	0.180301i
$345$	−18.7156	+	5.79781i	−1.00762	+	0.312144i
$346$	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	$0.700090\pi$
$348$	0.897603	+	0.940755i	0.0481166	+	0.0504298i
$349$	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	$0.122606\pi$
$350$	10.8258	+	6.99989i	0.578665	+	0.374160i
$351$	−8.53754	−	14.2279i	−0.455700	−	0.759432i
$352$	−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	$0.682750\pi$
$354$	−0.775605	+	6.97549i	−0.0412229	+	0.370743i
$355$	5.64330	+	8.50776i	0.299515	+	0.451545i
$356$	2.27187	+	12.8844i	0.120409	+	0.682872i
$357$	−2.72637	−	11.2220i	−0.144295	−	0.593933i
$358$	−6.31934	+	17.3623i	−0.333988	+	0.917624i
$359$	15.1331	+	18.0349i	0.798693	+	0.951845i	0.999615	−	0.0277621i	$-0.00883808\pi$
$359$	15.1331	+	18.0349i	0.798693	+	0.951845i	−0.200922	+	0.979607i	$0.564394\pi$
$360$	−3.26576	+	5.85959i	−0.172121	+	0.308828i
$361$	−17.8271	+	6.57232i	−0.938267	+	0.345912i
$362$	−2.19802			−0.115525
$363$	2.73544	+	1.35459i	0.143573	+	0.0710976i
$364$	−2.81600	+	7.73691i	−0.147599	+	0.405524i
$365$	1.36444	+	21.9511i	0.0714181	+	1.14898i
$366$	−9.75706	−	14.6548i	−0.510010	−	0.766020i
$367$	−10.4420	−	28.6892i	−0.545068	−	1.49756i	−0.840292	−	0.542134i	$-0.817617\pi$
$367$	−10.4420	−	28.6892i	−0.545068	−	1.49756i	0.295224	−	0.955428i	$-0.404606\pi$
$368$	−2.52946	+	4.38115i	−0.131857	+	0.228383i
$369$	−0.759319	−	0.170971i	−0.0395286	−	0.00890040i
$370$	12.6185	+	6.27574i	0.656005	+	0.326260i
$371$	−8.69005	−	7.29182i	−0.451165	−	0.378573i
$372$	−12.0454	−	8.86267i	−0.624524	−	0.459508i
$373$	5.88912	−	10.2003i	0.304927	−	0.528149i	−0.672318	−	0.740263i	$-0.734701\pi$
$373$	5.88912	−	10.2003i	0.304927	−	0.528149i	0.977245	+	0.212113i	$0.0680345\pi$
$374$	−7.38566	+	2.68816i	−0.381903	+	0.139001i
$375$	−18.6448	−	5.23176i	−0.962813	−	0.270167i
$376$	8.51727	+	1.50182i	0.439245	+	0.0774507i
$377$	−2.25268	−	0.819909i	−0.116019	−	0.0422275i
$378$	−12.5105	+	4.79382i	−0.643470	+	0.246567i
$379$		−	10.6930i		−	0.549262i	−0.961550	−	0.274631i	$-0.911444\pi$
$379$		−	10.6930i		−	0.549262i	0.961550	−	0.274631i	$-0.0885557\pi$
$380$	8.92645	−	3.91389i	0.457917	−	0.200778i
$381$	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	$-0.0683715\pi$
$384$	0.408904	+	1.68309i	0.0208668	+	0.0858899i
$385$	16.0627	−	7.00320i	0.818630	−	0.356916i
$386$	−1.10158	−	3.02656i	−0.0560688	−	0.154048i
$387$	−14.9005	+	4.64403i	−0.757434	+	0.236069i
$388$	1.13671	+	1.96883i	0.0577075	+	0.0999524i
$389$	−22.7618	+	27.1264i	−1.15407	+	1.37536i	−0.239517	+	0.970892i	$0.576989\pi$
$389$	−22.7618	+	27.1264i	−1.15407	+	1.37536i	−0.914550	+	0.404472i	$0.867455\pi$
$390$	0.601533	−	12.3530i	0.0304598	−	0.625517i
$391$	6.54109	+	11.3295i	0.330797	+	0.572957i
$392$	−0.304944	−	0.176060i	−0.0154020	−	0.00889236i
$393$	−9.18857	+	8.76710i	−0.463502	+	0.442242i
$394$	−3.16292	+	0.557708i	−0.159346	+	0.0280969i
$395$	−2.30025	−	37.0065i	−0.115738	−	1.86200i
$396$	4.18350	+	8.10168i	0.210229	+	0.407125i
$397$	14.5922	+	17.3903i	0.732363	+	0.872796i	0.995769	−	0.0918887i	$-0.0292904\pi$
$397$	14.5922	+	17.3903i	0.732363	+	0.872796i	−0.263406	+	0.964685i	$0.584846\pi$
$398$			3.30994i			0.165912i
$399$	18.6907	+	5.43933i	0.935706	+	0.272307i
$400$	−4.45052	+	2.27878i	−0.222526	+	0.113939i
$401$	6.54292	−	5.49016i	0.326738	−	0.274165i	−0.464631	−	0.885504i	$-0.653813\pi$
$401$	6.54292	−	5.49016i	0.326738	−	0.274165i	0.791369	+	0.611339i	$0.209369\pi$
$402$	21.2747	−	1.35912i	1.06108	−	0.0677868i
$403$	27.1521	+	4.78765i	1.35254	+	0.238490i
$404$	17.4085	−	3.06958i	0.866104	−	0.152718i
$405$	15.8198	−	12.4392i	0.786092	−	0.618109i
$406$	−0.967800	+	1.67628i	−0.0480311	+	0.0831923i
$407$	16.5893	−	9.57785i	0.822302	−	0.474756i
$408$	4.29801	+	1.26046i	0.212783	+	0.0624022i
$409$	−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	$0.355121\pi$
$410$	−0.399754	−	0.420417i	−0.0197424	−	0.0207629i
$411$	23.4817	+	2.61092i	1.15826	+	0.128787i
$412$	17.7329	−	6.45425i	0.873638	−	0.317978i
$413$	−10.2891	+	1.81424i	−0.506291	+	0.0892728i
$414$	12.0710	−	9.19919i	0.593257	−	0.452115i
$415$	0.0946075	−	0.837745i	0.00464410	−	0.0411233i
$416$	−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	$0.00100977\pi$
$419$			0.129870i			0.00634455i	−0.999995	+	0.00317227i	$0.998990\pi$
$420$	−9.73821	−	2.21029i	−0.475176	−	0.107851i
$421$	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
$423$	−21.8364	−	14.0130i	−1.06172	−	0.681335i
$424$	4.13440	−	1.50480i	0.200784	−	0.0730795i
$425$	−0.651085	+	12.9134i	−0.0315823	+	0.626393i
$426$	−6.36967	−	4.68664i	−0.308612	−	0.227068i
$427$	16.8463	−	20.0766i	0.815249	−	0.971576i
$428$	3.13642	−	3.73784i	0.151605	−	0.180675i
$429$	−13.5403	−	9.96262i	−0.653733	−	0.481000i
$430$	−11.1573	−	3.29291i	−0.538053	−	0.158798i
$431$	19.7834	−	7.20058i	0.952934	−	0.346840i	0.181673	−	0.983359i	$-0.441849\pi$
$431$	19.7834	−	7.20058i	0.952934	−	0.346840i	0.771261	+	0.636519i	$0.219627\pi$
$432$	0.815900	−	5.13170i	0.0392550	−	0.246899i
$433$	−1.81665	+	10.3028i	−0.0873028	+	0.495119i	0.909533	+	0.415631i	$0.136439\pi$
$433$	−1.81665	+	10.3028i	−0.0873028	+	0.495119i	−0.996836	+	0.0794872i	$0.974672\pi$
$434$	7.61387	−	20.9189i	0.365478	−	1.00414i
$435$	0.643550	−	2.83538i	0.0308559	−	0.135946i
$436$			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	$0.574437\pi$
$440$	−0.762655	+	6.75327i	−0.0363581	+	0.321949i
$441$	0.640297	+	0.840185i	0.0304904	+	0.0400088i
$442$	−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	$0.0440159\pi$
$444$	−10.8495	−	1.20636i	−0.514894	−	0.0572511i
$445$	21.2007	−	20.1588i	1.00501	−	0.955617i
$446$	−9.67956	+	11.5356i	−0.458340	+	0.546229i
$447$	−14.4011	−	4.22337i	−0.681150	−	0.199759i
$448$	−2.23292	+	1.28917i	−0.105495	+	0.0609078i
$449$	−4.62800	+	8.01594i	−0.218409	+	0.378295i	−0.954322	−	0.298781i	$-0.903420\pi$
$449$	−4.62800	+	8.01594i	−0.218409	+	0.378295i	0.735913	+	0.677076i	$0.236753\pi$
$450$	14.9553	−	1.15713i	0.705000	−	0.0545478i
$451$	−0.776559	+	0.136928i	−0.0365667	+	0.00644770i
$452$	14.8694	+	2.62187i	0.699396	+	0.123322i
$453$	36.0680	−	2.30419i	1.69462	−	0.108260i
$454$	9.22994	−	7.74484i	0.433182	−	0.363483i
$455$	17.8976	−	4.31561i	0.839052	−	0.202319i
$456$	−5.45153	+	5.22310i	−0.255291	+	0.244594i
$457$			5.08806i			0.238009i	0.992894	+	0.119005i	$0.0379703\pi$
$457$			5.08806i			0.238009i	−0.992894	+	0.119005i	$0.962030\pi$
$458$	9.17709	+	10.9368i	0.428817	+	0.511044i
$459$	−10.4375	−	8.46241i	−0.487183	−	0.394991i
$460$	11.2903	−	0.701782i	0.526413	−	0.0327208i
$461$	23.7668	−	4.19072i	1.10693	−	0.195181i	0.409834	−	0.912160i	$-0.365587\pi$
$461$	23.7668	−	4.19072i	1.10693	−	0.195181i	0.697095	+	0.716979i	$0.254476\pi$
$462$	−9.82030	+	9.36985i	−0.456882	+	0.435925i
$463$	3.09391	+	1.78627i	0.143786	+	0.0830150i	0.570167	−	0.821529i	$-0.306878\pi$
$463$	3.09391	+	1.78627i	0.143786	+	0.0830150i	−0.426381	+	0.904544i	$0.640212\pi$
$464$	−0.375357	−	0.650137i	−0.0174255	−	0.0301818i
$465$	−1.62642	+	33.3998i	−0.0754233	+	1.54888i
$466$	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	$0.589422\pi$
$468$	2.85053	+	9.14599i	0.131766	+	0.422774i
$469$	10.8538	+	29.8204i	0.501180	+	1.37698i
$470$	−7.72899	−	17.7274i	−0.356512	−	0.817703i
$471$	−5.01492	−	20.6419i	−0.231075	−	0.951130i
$472$	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
$475$	−18.3264	−	11.7959i	−0.840872	−	0.541233i
$476$			6.66752i			0.305605i
$477$	−13.1847	−	0.619309i	−0.603685	−	0.0283562i
$478$	20.7709	+	7.55997i	0.950037	+	0.345785i
$479$	14.8496	+	2.61838i	0.678495	+	0.119637i	0.502267	−	0.864712i	$-0.332499\pi$
$479$	14.8496	+	2.61838i	0.678495	+	0.119637i	0.176228	+	0.984349i	$0.443610\pi$
$480$	2.63086	−	2.84228i	0.120082	−	0.129732i
$481$	18.9122	−	6.88349i	0.862324	−	0.313860i
$482$	−8.91259	+	15.4371i	−0.405957	+	0.703139i
$483$	18.1973	+	13.3891i	0.828006	+	0.609225i
$484$	−1.35003	−	1.13281i	−0.0613651	−	0.0514914i
$485$	2.26374	−	4.55165i	0.102791	−	0.206680i
$486$	−8.19668	+	13.2595i	−0.371809	+	0.601463i
$487$	−14.0569	+	24.3472i	−0.636978	+	1.10328i	0.349115	+	0.937080i	$0.386482\pi$
$487$	−14.0569	+	24.3472i	−0.636978	+	1.10328i	−0.986092	+	0.166198i	$0.946851\pi$
$488$	3.47654	+	9.55170i	0.157375	+	0.432385i
$489$	−14.1801	−	21.2981i	−0.641246	−	0.963134i
$490$	0.0488466	+	0.785846i	0.00220667	+	0.0355009i
$491$	−5.34417	+	14.6830i	−0.241179	+	0.662634i	0.758758	+	0.651373i	$0.225807\pi$
$491$	−5.34417	+	14.6830i	−0.241179	+	0.662634i	−0.999937	+	0.0112608i	$0.996416\pi$
$492$	0.402698	+	0.199416i	0.0181550	+	0.00899038i
$493$	−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
$498$	0.154170	+	0.634580i	0.00690852	+	0.0284362i
$499$	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	$0.758058\pi$
$500$	9.74721	+	5.47649i	0.435908	+	0.244916i
$501$	2.79063	−	25.0978i	0.124676	−	1.12129i
$502$	−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	$0.851497\pi$
$504$	7.67217	−	0.984282i	0.341745	−	0.0438434i
$505$	−27.2370	−	28.6449i	−1.21203	−	1.27468i
$506$	7.68791	−	13.3159i	0.341769	−	0.591962i
$507$	3.35124	+	3.51235i	0.148834	+	0.155989i
$508$	−1.51857	−	8.61221i	−0.0673755	−	0.382105i
$509$	6.74016	−	38.2254i	0.298753	−	1.69431i	−0.352794	−	0.935701i	$-0.614768\pi$
$509$	6.74016	−	38.2254i	0.298753	−	1.69431i	0.651547	−	0.758609i	$-0.274121\pi$
$510$	−2.96366	−	9.56686i	−0.131233	−	0.423628i
$511$	19.4270	−	16.3012i	0.859399	−	0.721121i
$512$		−	1.00000i		−	0.0441942i
$513$	21.1331	−	8.14813i	0.933049	−	0.359749i
$514$	−7.24869			−0.319726
$515$	−33.9450	−	25.0660i	−1.49580	−	1.10454i
$516$	8.99261	−	0.574488i	0.395878	−	0.0252904i
$517$	−25.8870	−	4.56457i	−1.13851	−	0.200750i
$518$	−2.82182	−	16.0033i	−0.123984	−	0.703146i
$519$	10.6883	−	10.1980i	0.469165	−	0.447644i
$520$	−2.02120	+	6.84840i	−0.0886357	+	0.300322i
$521$	−10.3124	−	17.8616i	−0.451794	−	0.782530i	0.546703	−	0.837326i	$-0.315882\pi$
$521$	−10.3124	−	17.8616i	−0.451794	−	0.782530i	−0.998498	+	0.0547960i	$0.982549\pi$
$522$	0.286584	+	2.23383i	0.0125434	+	0.0977721i
$523$	−0.0694571	−	0.0582814i	−0.00303715	−	0.00254847i	0.641268	−	0.767317i	$-0.278409\pi$
$523$	−0.0694571	−	0.0582814i	−0.00303715	−	0.00254847i	−0.644305	+	0.764769i	$0.722853\pi$
$524$	6.35004	−	3.66620i	0.277403	−	0.160158i
$525$	7.91793	+	20.8782i	0.345567	+	0.911197i
$526$	5.52575	+	15.1819i	0.240934	+	0.661961i
$527$	21.9880	−	3.87708i	0.957814	−	0.168888i
$528$	−1.24280	−	5.11551i	−0.0540861	−	0.222624i
$529$	−2.43628	−	0.886732i	−0.105925	−	0.0385536i
$530$	−7.91424	−	5.84409i	−0.343772	−	0.253851i
$531$	−8.24229	+	8.93543i	−0.357685	+	0.387765i
$532$	−9.74468	−	5.59920i	−0.422485	−	0.242756i
$533$	−0.828480			−0.0358855
$534$	−10.0561	+	20.3072i	−0.435172	+	0.878778i
$535$	−10.8418	−	1.22437i	−0.468730	−	0.0529343i
$536$	−12.1210	−	2.13726i	−0.523547	−	0.0923155i
$537$	−26.6383	+	17.7355i	−1.14953	+	0.765345i
$538$	4.11613	+	11.3090i	0.177459	+	0.487565i
$539$	0.926833	+	0.535107i	0.0399215	+	0.0230487i
$540$	−10.5709	+	4.82252i	−0.454898	+	0.207528i
$541$	−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
$543$	−3.06648	−	2.25623i	−0.131595	−	0.0968242i
$544$	−2.23951	−	1.29298i	−0.0960182	−	0.0554361i
$545$	17.5974	−	11.6726i	0.753789	−	0.499998i
$546$	−11.8705	+	7.90325i	−0.508008	+	0.338228i
$547$	−5.59380	+	31.7240i	−0.239174	+	1.35642i	0.594469	+	0.804118i	$0.297362\pi$
$547$	−5.59380	+	31.7240i	−0.239174	+	1.35642i	−0.833643	+	0.552303i	$0.813749\pi$
$548$	−12.8181	−	4.66539i	−0.547560	−	0.199296i
$549$	1.43079	−	30.4605i	0.0610645	−	1.30002i
$550$	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
$555$	11.1622	+	21.7080i	0.473811	+	0.921455i
$556$	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	$0.445211\pi$
$558$	−7.70722	−	24.7288i	−0.326273	−	1.04685i
$559$	−14.3873	+	8.30653i	−0.608519	+	0.351329i
$560$	5.16217	+	2.56737i	0.218141	+	0.108491i
$561$	−13.0632	−	3.83099i	−0.551527	−	0.161744i
$562$	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	$0.558001\pi$
$564$	10.3409	+	10.8381i	0.435431	+	0.456365i
$565$	−13.4932	−	30.9482i	−0.567663	−	1.30200i
$566$	3.28382	−	18.6234i	0.138029	−	0.782802i
$567$	−22.3743	−	6.15392i	−0.939631	−	0.258440i
$568$	2.93479	+	3.49754i	0.123141	+	0.146754i
$569$	35.5477			1.49024			0.745119	−	0.666932i	$-0.232393\pi$
$569$	35.5477			1.49024			0.745119	+	0.666932i	$0.232393\pi$
$570$	16.4709	+	3.70255i	0.689891	+	0.155083i
$571$	−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
$573$	3.09258	−	0.197568i	0.129194	−	0.00825351i
$574$	−0.116159	+	0.658772i	−0.00484840	+	0.0274966i
$575$	−15.2627	−	20.1709i	−0.636498	−	0.841186i
$576$	−1.15720	+	2.76783i	−0.0482167	+	0.115326i
$577$	34.4185	+	19.8715i	1.43286	+	0.827262i	0.997338	−	0.0729164i	$-0.0232306\pi$
$577$	34.4185	+	19.8715i	1.43286	+	0.827262i	0.435522	+	0.900178i	$0.356564\pi$
$578$	8.93114	−	5.15640i	0.371486	−	0.214478i
$579$	1.56990	−	5.35313i	0.0652426	−	0.222469i
$580$	−0.747518	+	1.50302i	−0.0310390	+	0.0624095i
$581$	−0.841881	+	0.486060i	−0.0349271	+	0.0201652i
$582$	−0.435148	+	3.91355i	−0.0180374	+	0.162222i
$583$	−12.5659	+	4.57361i	−0.520427	+	0.189420i
$584$	1.70797	+	9.68637i	0.0706762	+	0.400825i
$585$	13.5193	−	16.6163i	0.558956	−	0.686999i
$586$	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
$591$	−4.98510	−	2.46862i	−0.205059	−	0.101546i
$592$	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	$-0.120141\pi$
$594$	−2.47981	+	15.5970i	−0.101748	+	0.639954i
$595$	12.4243	−	8.24116i	0.509345	−	0.337855i
$596$	7.50382	+	4.33233i	0.307368	+	0.177459i
$597$	−3.39761	+	4.61773i	−0.139055	+	0.188991i
$598$	10.3840	−	12.3752i	0.424634	−	0.506059i
$599$	−25.1675	−	21.1180i	−1.02831	−	0.862858i	−0.0376649	−	0.999290i	$-0.511992\pi$
$599$	−25.1675	−	21.1180i	−1.02831	−	0.862858i	−0.990649	+	0.136432i	$0.956436\pi$
$600$	−8.54810	−	1.38924i	−0.348975	−	0.0567155i
$601$	−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
$603$	31.0756	+	19.9420i	1.26550	+	0.812101i
$604$	−20.5493	−	3.62340i	−0.836141	−	0.147434i
$605$	−0.442219	+	3.91583i	−0.0179788	+	0.159201i
$606$	27.4376	+	13.5871i	1.11458	+	0.551939i
$607$	−3.08925			−0.125389			−0.0626943	−	0.998033i	$-0.519969\pi$
$607$	−3.08925			−0.125389			−0.0626943	+	0.998033i	$0.519969\pi$
$608$	3.77039	−	2.18727i	0.152910	−	0.0887054i
$609$	−3.07086	+	1.34516i	−0.124438	+	0.0545086i
$610$	13.5016	−	18.2842i	0.546663	−	0.740307i
$611$	−25.9522	−	9.44584i	−1.04992	−	0.382138i
$612$	4.70234	+	6.17032i	0.190081	+	0.249420i
$613$	−3.85039	+	0.678928i	−0.155516	+	0.0274216i	−0.250864	−	0.968022i	$-0.580715\pi$
$613$	−3.85039	+	0.678928i	−0.155516	+	0.0274216i	0.0953481	+	0.995444i	$0.469604\pi$
$614$	1.48442	+	4.07841i	0.0599062	+	0.164591i
$615$	−0.126149	−	0.996869i	−0.00508681	−	0.0401976i
$616$	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	$0.852538\pi$
$618$	31.3645	+	9.19817i	1.26167	+	0.370005i
$619$	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	$0.545540\pi$
$620$	5.46490	−	18.5166i	0.219476	−	0.743645i
$621$	26.2832	−	0.443188i	1.05471	−	0.0177845i
$622$	4.34687	+	24.6523i	0.174294	+	0.988469i
$623$	−33.2205	−	5.85767i	−1.33095	−	0.234683i
$624$	−0.352624	−	5.51971i	−0.0141163	−	0.220965i
$625$	−1.84282	−	24.9320i	−0.0737128	−	0.997280i
$626$	−0.699529			−0.0279588
$627$	16.5691	−	15.8748i	0.661707	−	0.633980i
$628$			12.2643i			0.489399i
$629$	12.4851	−	10.4763i	0.497815	−	0.417717i
$630$	−11.3170	−	13.0797i	−0.450882	−	0.521109i
$631$	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
$633$	−3.21936	+	3.07169i	−0.127958	+	0.122089i
$634$	−7.75372	+	13.4298i	−0.307940	+	0.533367i
$635$	−14.1710	+	13.4745i	−0.562360	+	0.534721i
$636$	7.31260	+	2.14454i	0.289963	+	0.0850366i
$637$	0.861358	+	0.722766i	0.0341283	+	0.0286370i
$638$	1.14084	+	1.97599i	0.0451663	+	0.0782304i
$639$	−4.07563	−	13.0767i	−0.161229	−	0.517308i
$640$	−1.86340	+	1.23602i	−0.0736574	+	0.0488579i
$641$	4.47239	+	25.3642i	0.176649	+	1.00182i	0.936224	+	0.351405i	$0.114296\pi$
$641$	4.47239	+	25.3642i	0.176649	+	1.00182i	−0.759575	+	0.650420i	$0.774593\pi$
$642$	8.21248	−	1.99521i	0.324121	−	0.0787445i
$643$	−5.91400	+	16.2486i	−0.233226	+	0.640782i	−0.999999	−	0.00113539i	$-0.999639\pi$
$643$	−5.91400	+	16.2486i	−0.233226	+	0.640782i	0.766774	+	0.641917i	$0.221861\pi$
$644$	−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	$0.598830\pi$
$648$	6.40588	−	6.32177i	0.251647	−	0.248342i
$649$	−4.21226	+	11.5731i	−0.165346	+	0.454283i
$650$	15.2596	−	4.69843i	0.598529	−	0.184288i
$651$	32.0952	−	21.3687i	1.25791	−	0.837505i
$652$	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	$0.0831503\pi$
$654$	−9.69380	+	13.1750i	−0.379058	+	0.515182i
$655$	−14.6803	−	7.30118i	−0.573608	−	0.285281i
$656$	−0.198745	−	0.166767i	−0.00775969	−	0.00651115i
$657$	6.48172	−	28.7867i	0.252876	−	1.12308i
$658$	−11.1496	+	19.3117i	−0.434658	+	0.752850i
$659$	−31.9611	+	11.6329i	−1.24503	+	0.453153i	−0.878719	−	0.477340i	$-0.841601\pi$
$659$	−31.9611	+	11.6329i	−1.24503	+	0.453153i	−0.366309	+	0.930493i	$0.619379\pi$
$660$	−7.99611	+	8.63869i	−0.311248	+	0.336261i
$661$	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
$663$	−12.8174	−	6.34718i	−0.497786	−	0.246504i
$664$		−	0.377032i		−	0.0146317i
$665$	1.61104	+	25.0789i	0.0624733	+	0.972520i
$666$	−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
$669$	−25.3452	+	6.15757i	−0.979902	+	0.238065i
$670$	10.9992	+	25.2279i	0.424936	+	0.974641i
$671$	−10.5664	−	29.0310i	−0.407912	−	1.12073i
$672$	−4.43848	−	0.493514i	−0.171218	−	0.0190377i
$673$	−25.4433	−	44.0691i	−0.980768	−	1.69874i	−0.659414	−	0.751780i	$-0.729196\pi$
$673$	−25.4433	−	44.0691i	−0.980768	−	1.69874i	−0.321353	−	0.946959i	$-0.604138\pi$
$674$	−9.66555	+	11.5190i	−0.372303	+	0.443694i
$675$	22.0521	+	13.7371i	0.848784	+	0.528740i
$676$	−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	$0.310207\pi$
$678$	18.0531	+	18.9210i	0.693324	+	0.726655i
$679$	−5.77260	+	1.01787i	−0.221532	+	0.0390621i
$680$	0.358730	+	5.77125i	0.0137567	+	0.221317i
$681$	20.8267	−	1.33050i	0.798082	−	0.0509850i
$682$	−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	$0.779303\pi$
$684$	−12.9669	+	1.69088i	−0.495802	+	0.0646524i
$685$	7.14984	+	29.6517i	0.273181	+	1.13293i
$686$	14.5214	−	12.1849i	0.554429	−	0.465221i
$687$	1.57655	+	24.6782i	0.0601493	+	0.941532i
$688$	−5.12343	−	0.903399i	−0.195329	−	0.0344418i
$689$	−13.8363	+	2.43970i	−0.527119	+	0.0929453i
$690$	16.4716	+	10.6102i	0.627061	+	0.403925i
$691$	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
$693$	−23.3184	+	2.99158i	−0.885793	+	0.113641i
$694$	16.6305	−	19.8195i	0.631286	−	0.752337i
$695$	6.23881	−	5.93218i	0.236652	−	0.225020i
$696$	0.143692	−	1.29231i	0.00544663	−	0.0489849i
$697$	−0.630450	+	0.229465i	−0.0238800	+	0.00869160i
$698$	−5.07703	+	0.895217i	−0.192168	+	0.0338845i
$699$	7.81306	−	1.89817i	0.295517	−	0.0717954i
$700$	−1.59648	−	12.7925i	−0.0603414	−	0.483511i
$701$	5.16255	+	6.15249i	0.194987	+	0.232376i	0.854675	−	0.519163i	$-0.173756\pi$
$701$	5.16255	+	6.15249i	0.194987	+	0.232376i	−0.659688	+	0.751539i	$0.729312\pi$
$702$	−5.41142	+	15.6857i	−0.204241	+	0.592018i
$703$	4.82656	+	27.0449i	0.182037	+	1.02002i
$704$			3.03935i			0.114550i
$705$	7.41408	−	32.6653i	0.279231	−	1.23025i
$706$	5.85564	−	16.0882i	0.220380	−	0.605489i
$707$	−7.91446	+	44.8851i	−0.297654	+	1.68808i
$708$	5.84209	−	3.88961i	0.219559	−	0.146181i
$709$	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	$0.339605\pi$
$710$	2.88988	−	9.79170i	0.108455	−	0.367476i
$711$	−10.9272	+	48.5302i	−0.409804	+	1.82003i
$712$	8.40970	−	10.0223i	0.315167	−	0.375601i
$713$	−28.0761	+	33.4598i	−1.05146	+	1.25308i
$714$	−6.84410	+	9.30191i	−0.256134	+	0.348115i
$715$	6.14315	−	20.8147i	0.229741	−	0.778426i
$716$	17.3623	−	6.31934i	0.648858	−	0.236165i
$717$	21.2174	+	31.8679i	0.792379	+	1.19013i
$718$	4.08818	−	23.1852i	0.152569	−	0.865264i
$719$	−8.72890	+	23.9825i	−0.325533	+	0.894395i	0.663694	+	0.748004i	$0.268988\pi$
$719$	−8.72890	+	23.9825i	−0.325533	+	0.894395i	−0.989227	+	0.146390i	$0.953234\pi$
$720$	6.58790	−	1.26475i	0.245516	−	0.0471346i
$721$			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
$725$	3.72467	−	0.464833i	0.138331	−	0.0172634i
$726$	−0.720629	−	2.96618i	−0.0267450	−	0.110085i
$727$	−36.4034	+	6.41890i	−1.35013	+	0.238064i	−0.801496	−	0.598000i	$-0.795962\pi$
$727$	−36.4034	+	6.41890i	−1.35013	+	0.238064i	−0.548632	+	0.836064i	$0.684851\pi$
$728$	7.73691	−	2.81600i	0.286749	−	0.104368i
$729$	−25.0459	+	10.0847i	−0.927627	+	0.373507i
$730$	15.9385	−	15.1551i	0.589911	−	0.560917i
$731$	−8.64768	+	10.3059i	−0.319846	+	0.381178i
$732$	−4.95453	+	16.8943i	−0.183125	+	0.624430i
$733$	40.2287	−	23.2261i	1.48588	−	0.857874i	0.486011	−	0.873953i	$-0.338452\pi$
$733$	40.2287	−	23.2261i	1.48588	−	0.857874i	0.999871	+	0.0160785i	$0.00511818\pi$
$734$	−15.2652	+	26.4401i	−0.563448	+	0.975921i
$735$	−0.738512	+	1.14648i	−0.0272404	+	0.0422886i
$736$	4.98206	−	0.878472i	0.183641	−	0.0323809i
$737$	36.8400	+	6.49588i	1.35702	+	0.239279i
$738$	0.357109	+	0.691570i	0.0131454	+	0.0254571i
$739$	−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
$741$	20.0402	−	13.4026i	0.736195	−	0.492357i
$742$			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	$0.896565\pi$
$744$	0.953419	+	14.9241i	0.0349540	+	0.547145i
$745$	−1.20198	−	19.3375i	−0.0440371	−	0.708470i
$746$	−11.5993	+	2.04527i	−0.424681	+	0.0748827i
$747$	−0.436302	+	1.04356i	−0.0159635	+	0.0381819i
$748$	6.80666	+	3.92983i	0.248876	+	0.143689i
$749$	6.29040	+	10.8953i	0.229846	+	0.398105i
$750$	7.97689	+	17.6457i	0.291275	+	0.644328i
$751$	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
$753$	4.43309	−	39.8695i	0.161551	−	1.45293i
$754$	0.819909	+	2.25268i	0.0298593	+	0.0820379i
$755$	18.6475	+	42.7702i	0.678651	+	1.55657i
$756$	11.7139	+	6.50218i	0.426029	+	0.236482i
$757$	1.57621	−	4.33061i	0.0572884	−	0.157399i	−0.907747	−	0.419518i	$-0.862199\pi$
$757$	1.57621	−	4.33061i	0.0572884	−	0.157399i	0.965035	+	0.262119i	$0.0844214\pi$
$758$	−8.19130	+	6.87332i	−0.297522	+	0.249650i
$759$	24.3940	−	10.6855i	0.885446	−	0.387861i
$760$	−8.73603	−	4.32225i	−0.316889	−	0.156785i
$761$			53.4428i			1.93730i	0.248430	+	0.968650i	$0.420085\pi$
$761$			53.4428i			1.93730i	−0.248430	+	0.968650i	$0.579915\pi$
$762$	6.72174	−	13.5738i	0.243503	−	0.491726i
$763$	−22.8807	−	8.32789i	−0.828337	−	0.301490i
$764$	−1.76196	−	0.310681i	−0.0637454	−	0.0112400i
$765$	5.68560	−	16.3890i	0.205563	−	0.592544i
$766$	−19.6574	+	7.15469i	−0.710249	+	0.258510i
$767$	−6.46983	+	11.2061i	−0.233612	+	0.404628i
$768$	1.02648	−	1.39511i	0.0370401	−	0.0503417i
$769$	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	$0.704507\pi$
$770$	−15.6896	−	7.80315i	−0.565416	−	0.281206i
$771$	−10.1127	−	7.44067i	−0.364201	−	0.267969i
$772$	−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	$0.760286\pi$
$774$	13.1354	+	8.42930i	0.472141	+	0.302985i
$775$	−41.2586	+	12.7035i	−1.48205	+	0.456325i
$776$	0.777553	−	2.13631i	0.0279125	−	0.0766891i
$777$	12.4904	−	25.2229i	0.448091	−	0.904868i
$778$	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
$783$	−1.89318	+	3.41061i	−0.0676566	+	0.121885i
$784$	0.0611449	+	0.346770i	0.00218375	+	0.0123846i
$785$	22.8533	−	15.1589i	0.815669	−	0.541044i
$786$	12.6223	+	1.40347i	0.450222	+	0.0500602i
$787$	8.84289	+	15.3163i	0.315215	+	0.545969i	0.979483	−	0.201526i	$-0.0645900\pi$
$787$	8.84289	+	15.3163i	0.315215	+	0.545969i	−0.664268	+	0.747494i	$0.731257\pi$
$788$	2.46031	+	2.06445i	0.0876451	+	0.0735430i
$789$	−7.87493	+	26.8525i	−0.280355	+	0.955973i
$790$	−26.8700	+	25.5494i	−0.955993	+	0.909007i
$791$	−19.4649	+	33.7142i	−0.692092	+	1.19874i
$792$	3.51714	−	8.41241i	0.124976	−	0.298922i
$793$	−5.63645	−	31.9659i	−0.200156	−	1.13514i
$794$	3.94207	−	22.3566i	0.139899	−	0.793406i
$795$	−5.04235	−	16.2770i	−0.178834	−	0.577285i
$796$	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	$-0.200376\pi$
$798$	−7.84740	−	17.8143i	−0.277795	−	0.630618i
$799$	−22.3651			−0.791222
$800$	4.60639	+	1.94452i	0.162860	+	0.0687493i
$801$	−34.8744	+	18.0083i	−1.23223	+	0.636291i
$802$	−8.41141	−	1.48316i	−0.297017	−	0.0523721i
$803$	−5.19112	−	29.4403i	−0.183191	−	1.03893i
$804$	−14.7162	−	15.4237i	−0.519002	−	0.543953i
$805$	−8.25599	+	27.9736i	−0.290986	+	0.985940i
$806$	−13.7855	−	23.8772i	−0.485573	−	0.841038i
$807$	−5.86604	+	20.0024i	−0.206494	+	0.704118i
$808$	−13.5414	−	11.3626i	−0.476384	−	0.399734i
$809$	−10.5267	+	6.07759i	−0.370099	+	0.213677i	−0.673502	−	0.739186i	$-0.735211\pi$
$809$	−10.5267	+	6.07759i	−0.370099	+	0.213677i	0.303403	+	0.952862i	$0.401877\pi$
$810$	−19.6978	−	4.12290i	−0.692109	−	0.144864i
$811$	−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
$813$	−19.9703	+	4.85176i	−0.700390	+	0.170158i
$814$	−18.0005	−	6.55164i	−0.630916	−	0.229635i
$815$	19.6221	−	26.5728i	0.687332	−	0.930805i
$816$	−1.79714	−	4.10267i	−0.0629123	−	0.143622i
$817$	−7.80015	−	21.2933i	−0.272893	−	0.744959i
$818$	16.4011			0.573449
$819$	−24.6731	−	1.15894i	−0.862149	−	0.0404967i
$820$	−0.0651012	+	0.576468i	−0.00227343	+	0.0201311i
$821$	5.30027	+	0.934581i	0.184981	+	0.0326171i	0.265371	−	0.964146i	$-0.414506\pi$
$821$	5.30027	+	0.934581i	0.184981	+	0.0326171i	−0.0803903	+	0.996763i	$0.525617\pi$
$822$	−13.0936	−	19.6663i	−0.456693	−	0.685940i
$823$	−17.5144	−	48.1204i	−0.610514	−	1.67737i	−0.729082	−	0.684426i	$-0.760053\pi$
$823$	−17.5144	−	48.1204i	−0.610514	−	1.67737i	0.118568	−	0.992946i	$-0.462170\pi$
$824$	−16.3427	−	9.43548i	−0.569326	−	0.328701i
$825$	25.9807	+	4.22239i	0.904531	+	0.147005i
$826$	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	$0.422216\pi$
$828$	−14.8061	−	3.33379i	−0.514546	−	0.115857i
$829$	−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	$0.700987\pi$
$830$	−0.702562	+	0.466018i	−0.0243863	+	0.0161757i
$831$	−12.3407	−	18.5353i	−0.428093	−	0.642983i
$832$	−0.554511	+	3.14479i	−0.0192242	+	0.109026i
$833$	0.855654	+	0.311433i	0.0296466	+	0.0107905i
$834$	−2.95925	+	5.97586i	−0.102471	+	0.206927i
$835$	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	−0.490267	−	0.871572i	$-0.663101\pi$
$839$	−41.3068	−	15.0344i	−1.42607	−	0.519047i	−0.935802	+	0.352526i	$0.885323\pi$
$840$	4.56642	+	8.88065i	0.157556	+	0.306412i
$841$	−4.93793	−	28.0044i	−0.170274	−	0.965670i
$842$	−12.7250	+	4.63152i	−0.438532	+	0.159613i
$843$	27.5723	+	3.06576i	0.949639	+	0.105590i
$844$	2.22484	−	1.28451i	0.0765820	−	0.0442146i
$845$	−2.79089	+	5.61158i	−0.0960095	+	0.193044i
$846$	3.30162	+	25.7351i	0.113512	+	0.884790i
$847$	3.93516	−	2.27197i	0.135214	−	0.0780657i
$848$	−3.81029	−	2.19987i	−0.130846	−	0.0755438i
$849$	23.6980	−	22.6109i	0.813312	−	0.776006i
$850$	10.3108	−	7.80182i	0.353656	−	0.267600i
$851$	−5.53662	+	31.3997i	−0.189793	+	1.07637i
$852$	0.504174	+	7.89197i	0.0172727	+	0.270374i
$853$	−30.9769	−	36.9168i	−1.06063	−	1.26401i	−0.963206	−	0.268764i	$-0.913385\pi$
$853$	−30.9769	−	36.9168i	−1.06063	−	1.26401i	−0.0974214	−	0.995243i	$-0.531059\pi$
$854$	−26.2082			−0.896825
$855$	19.1781	+	22.0726i	0.655878	+	0.754867i
$856$	−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	$-0.564766\pi$
$858$	1.07175	+	16.7763i	0.0365889	+	0.572735i
$859$	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	$-0.00114656\pi$
$860$	4.64926	+	10.6636i	0.158538	+	0.363627i
$861$	−0.838274	+	0.799823i	−0.0285683	+	0.0272579i
$862$	−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	$0.536148\pi$
$864$	−4.45556	+	2.67358i	−0.151581	+	0.0909569i
$865$	17.0764	+	8.49286i	0.580616	+	0.288766i
$866$	9.06009	−	5.23084i	0.307874	−	0.177751i
$867$	17.7529	+	1.97394i	0.602919	+	0.0670386i
$868$	−20.9189	+	7.61387i	−0.710035	+	0.258432i
$869$	8.75147	+	49.6321i	0.296873	+	1.68365i
$870$	−2.58570	+	1.32956i	−0.0876633	+	0.0450763i
$871$	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
$876$	−7.56011	+	15.2667i	−0.255432	+	0.515816i
$877$	−48.5858	−	17.6838i	−1.64063	−	0.597139i	−0.653478	−	0.756945i	$-0.726691\pi$
$877$	−48.5858	−	17.6838i	−1.64063	−	0.597139i	−0.987148	+	0.159806i	$0.948913\pi$
$878$	4.33866	−	24.6058i	0.146423	−	0.830404i
$879$	4.68516	+	7.03698i	0.158027	+	0.237352i
$880$	5.66353	−	3.75669i	0.190918	−	0.126638i
$881$	14.5985	+	8.42846i	0.491837	+	0.283962i	0.725336	−	0.688395i	$-0.241684\pi$
$881$	14.5985	+	8.42846i	0.491837	+	0.283962i	−0.233499	+	0.972357i	$0.575018\pi$
$882$	0.232044	−	1.03056i	0.00781333	−	0.0347007i
$883$	21.3174	−	25.4051i	0.717387	−	0.854949i	−0.276987	−	0.960874i	$-0.589336\pi$
$883$	21.3174	−	25.4051i	0.717387	−	0.854949i	0.994374	+	0.105925i	$0.0337804\pi$
$884$	6.32582	+	5.30799i	0.212760	+	0.178527i
$885$	−14.4688	−	6.07852i	−0.486364	−	0.204327i
$886$	−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	$0.678800\pi$
$888$	6.04980	+	9.08663i	0.203018	+	0.304927i
$889$	22.2053	+	3.91539i	0.744741	+	0.131318i
$890$	−29.0701	−	3.28292i	−0.974431	−	0.110044i
$891$	−19.4697	+	19.2141i	−0.652260	+	0.643696i
$892$	15.0587			0.504203
$893$	18.7816	−	32.6870i	0.628503	−	1.09383i
$894$	6.02158	+	13.7466i	0.201392	+	0.459756i
$895$	−33.2355	−	24.5420i	−1.11094	−	0.820349i
$896$	2.42286	+	0.881847i	0.0809419	+	0.0294604i
$897$	27.1898	−	6.60570i	0.907840	−	0.220558i
$898$	9.11539	−	1.60729i	0.304184	−	0.0536359i
$899$	−2.21686	−	6.09077i	−0.0739364	−	0.203139i
$900$	−10.4995	−	10.7126i	−0.349983	−	0.357088i
$901$	−9.85326	+	5.68878i	−0.328260	+	0.189521i
$902$	0.604056	+	0.506863i	0.0201129	+	0.0168767i
$903$	−6.53821	+	22.2944i	−0.217578	+	0.741911i
$904$	−7.54937	−	13.0759i	−0.251088	−	0.434898i
$905$	1.39124	−	4.71391i	0.0462464	−	0.156696i
$906$	−24.9492	−	26.1486i	−0.828882	−	0.868730i
$907$	1.37938	+	7.82283i	0.0458015	+	0.259753i	0.999107	−	0.0422550i	$-0.0134542\pi$
$907$	1.37938	+	7.82283i	0.0458015	+	0.259753i	−0.953305	+	0.302008i	$0.902343\pi$
$908$	−11.8658	−	2.09226i	−0.393780	−	0.0694340i
$909$	24.3315	+	47.1198i	0.807024	+	1.56287i
$910$	−14.8103	−	10.9363i	−0.490957	−	0.362536i
$911$	−51.3737			−1.70209			−0.851044	−	0.525095i	$-0.824030\pi$
$911$	−51.3737			−1.70209			−0.851044	+	0.525095i	$0.824030\pi$
$912$	7.50531	+	0.818773i	0.248525	+	0.0271123i
$913$			1.14593i			0.0379249i
$914$	3.89768	−	3.27054i	0.128924	−	0.108180i
$915$	37.6047	−	11.6493i	1.24317	−	0.385115i
$916$	2.47918	−	14.0601i	0.0819143	−	0.464559i
$917$	3.28290	+	18.6182i	0.108411	+	0.614828i
$918$	0.226544	+	13.4352i	0.00747707	+	0.443426i
$919$	−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	$0.279366\pi$
$920$	−7.79486	−	8.19777i	−0.256989	−	0.270272i
$921$	−2.11549	+	7.21355i	−0.0697079	+	0.237695i
$922$	−18.4873	−	15.5127i	−0.608846	−	0.510882i
$923$	−7.28986	−	12.6264i	−0.239949	−	0.415603i
$924$	13.4901	+	1.49996i	0.443792	+	0.0493452i
$925$	−21.4459	+	23.0896i	−0.705138	+	0.759181i
$926$	−0.620365	−	3.51827i	−0.0203865	−	0.115617i
$927$	34.3152	+	45.0277i	1.12706	+	1.47890i
$928$	−0.256759	+	0.705440i	−0.00842853	+	0.0231572i
$929$	21.1905	+	25.2538i	0.695237	+	0.828552i	0.991979	−	0.126406i	$-0.0403443\pi$
$929$	21.1905	+	25.2538i	0.695237	+	0.828552i	−0.296741	+	0.954958i	$0.595900\pi$
$930$	26.6312	−	20.2231i	0.873270	−	0.663140i
$931$	−1.17372	+	0.989019i	−0.0384671	+	0.0324138i
$932$	−4.64209			−0.152057
$933$	−19.2409	+	38.8547i	−0.629918	+	1.27205i
$934$	10.2508	−	28.1638i	0.335416	−	0.921547i
$935$	−1.09031	−	17.5409i	−0.0356568	−	0.573648i
$936$	5.17395	−	8.06256i	0.169116	−	0.263533i
$937$	−12.1962	−	33.5088i	−0.398433	−	1.09469i	−0.963048	−	0.269331i	$-0.913197\pi$
$937$	−12.1962	−	33.5088i	−0.398433	−	1.09469i	0.564615	−	0.825355i	$-0.309025\pi$
$938$	15.8671	−	27.4827i	0.518080	−	0.897341i
$939$	−0.975919	−	0.718056i	−0.0318479	−	0.0234329i
$940$	−8.61185	+	17.3157i	−0.280888	+	0.564775i
$941$	15.2406	+	12.7884i	0.496828	+	0.416888i	0.856466	−	0.516204i	$-0.172655\pi$
$941$	15.2406	+	12.7884i	0.496828	+	0.416888i	−0.359638	+	0.933092i	$0.617100\pi$
$942$	−12.5891	+	17.1100i	−0.410175	+	0.557475i
$943$	0.656250	−	1.13666i	0.0213705	−	0.0370147i
$944$	−3.80775	+	1.38591i	−0.123932	+	0.0451074i
$945$	−2.36236	−	29.8644i	−0.0768477	−	0.971489i
$946$	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	$0.575085\pi$
$948$	12.7453	−	25.7375i	0.413947	−	0.835916i
$949$		−	31.4087i		−	1.01957i
$950$	2.74379	+	21.6211i	0.0890203	+	0.701481i
$951$	−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	$0.0333567\pi$
$954$	8.00053	+	10.4981i	0.259027	+	0.339890i
$955$	1.59889	+	3.66724i	0.0517388	+	0.118669i
$956$	−7.55997	−	20.7709i	−0.244507	−	0.671777i
$957$	−0.436730	+	3.92778i	−0.0141175	+	0.126967i
$958$	−7.53934	−	13.0585i	−0.243585	−	0.421901i
$959$	22.6071	−	26.9421i	0.730022	−	0.870007i
$960$	−3.86840	−	0.188373i	−0.124852	−	0.00607972i
$961$	21.7730	+	37.7120i	0.702356	+	1.21652i
$962$	−17.4296	−	10.0630i	−0.561953	−	0.324444i
$963$	13.5054	+	5.64645i	0.435204	+	0.181954i
$964$	17.5544	−	3.09531i	0.565388	−	0.0996932i
$965$	7.18805	−	0.446795i	0.231391	−	0.0143828i
$966$	−1.44036	−	22.5463i	−0.0463428	−	0.725415i
$967$	0.868335	+	1.03484i	0.0279238	+	0.0332783i	0.779826	−	0.625997i	$-0.215308\pi$
$967$	0.868335	+	1.03484i	0.0279238	+	0.0332783i	−0.751902	+	0.659275i	$0.770863\pi$
$968$			1.76234i			0.0566438i
$969$	11.5379	−	15.7496i	0.370650	−	0.505948i
$970$	−4.94187	+	1.19162i	−0.158674	+	0.0382607i
$971$	−1.01292	+	0.849937i	−0.0325060	+	0.0272758i	−0.658896	−	0.752234i	$-0.728976\pi$
$971$	−1.01292	+	0.849937i	−0.0325060	+	0.0272758i	0.626390	+	0.779510i	$0.284532\pi$
$972$	15.4261	−	2.24402i	0.494792	−	0.0719771i
$973$	−9.77590	−	1.72376i	−0.313401	−	0.0552611i
$974$	27.6866	−	4.88190i	0.887137	−	0.156426i
$975$	26.1116	+	9.10889i	0.836241	+	0.291718i
$976$	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	$-0.0998643\pi$
$978$	−7.20050	+	24.5527i	−0.230247	+	0.785110i
$979$	−25.5600	+	30.4613i	−0.816902	+	0.973546i
$980$	0.570595	−	0.542551i	0.0182270	−	0.0173311i
$981$	−27.0478	+	8.42999i	−0.863571	+	0.269149i
$982$	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	$0.564718\pi$
$984$	−0.106087	−	0.436667i	−0.00338194	−	0.0139204i
$985$	0.805905	−	7.13625i	0.0256783	−	0.227380i
$986$	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
$990$	−20.0229	+	3.84403i	−0.636371	+	0.122171i
$991$	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
$993$	21.9371	+	32.9489i	0.696153	+	1.04560i
$994$	−11.0621	+	4.02626i	−0.350868	+	0.127705i
$995$	−7.09855	−	2.09503i	−0.225039	−	0.0664170i
$996$	0.387018	−	0.526001i	0.0122631	−	0.0166670i
$997$	28.3530	−	33.7898i	0.897948	−	1.07013i	−0.0992304	−	0.995064i	$-0.531638\pi$
$997$	28.3530	−	33.7898i	0.897948	−	1.07013i	0.997178	−	0.0750682i	$-0.0239175\pi$
$998$	15.8710	−	18.9144i	0.502388	−	0.598723i
$999$	−6.22976	−	32.1511i	−0.197101	−	1.01722i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.110426 - 1.72853i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.04972 - 0.893663i) q^{5} +(-1.25315 + 1.19567i) q^{6} +(-2.23292 - 1.28917i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.97561 + 0.381749i) q^{9} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.110426 - 1.72853i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.04972 - 0.893663i) q^{5} +(-1.25315 + 1.19567i) q^{6} +(-2.23292 - 1.28917i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.97561 + 0.381749i) q^{9} +(-2.00212 - 0.995744i) q^{10} +(-2.63216 + 1.51968i) q^{11} +(1.72144 + 0.191407i) q^{12} +(-3.00072 + 1.09217i) q^{13} +(0.447726 + 2.53918i) q^{14} +(-1.77106 - 3.44432i) 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} +(-1.98180 + 4.00201i) q^{21} +(2.85606 + 1.03952i) q^{22} +(0.878472 - 4.98206i) q^{23} +(-0.959895 - 1.44174i) q^{24} +(3.40273 - 3.66352i) q^{25} +(2.76548 + 1.59665i) q^{26} +(0.988448 + 5.10127i) q^{27} +(1.65733 - 1.97513i) q^{28} +(0.575080 + 0.482549i) q^{29} +(-1.50008 + 3.57068i) q^{30} +(-7.47727 - 4.31700i) q^{31} +(0.342020 + 0.939693i) q^{32} +(2.91746 + 4.38194i) q^{33} +(2.54668 + 0.449048i) q^{34} +(-5.72895 - 0.646977i) q^{35} +(0.140760 - 2.99670i) q^{36} -6.30256 q^{37} +(-2.79492 + 3.34491i) q^{38} +(2.21921 + 5.06623i) q^{39} +(1.32828 - 1.79880i) q^{40} +(0.243797 + 0.0887348i) q^{41} +(4.33960 - 1.05430i) q^{42} +(5.12343 - 0.903399i) q^{43} +(-1.03952 - 2.85606i) q^{44} +(-5.75803 + 3.44167i) q^{45} +(-4.38115 + 2.52946i) q^{46} +(6.62526 + 5.55925i) q^{47} +(-0.487425 + 1.66205i) q^{48} +(-0.176060 - 0.304944i) q^{49} +(-4.99366 - 0.251777i) q^{50} +(3.09195 + 3.24060i) q^{51} +(-0.554511 - 3.14479i) q^{52} +(4.33290 + 0.764007i) q^{53} +(3.27244 - 4.03623i) q^{54} +(-4.03711 + 5.46718i) q^{55} -2.57835 q^{56} +(-7.33272 + 1.79757i) q^{57} -0.750713i q^{58} +(3.10411 - 2.60465i) q^{59} +(3.69953 - 1.14606i) q^{60} +(-1.76508 + 10.0103i) q^{61} +(1.49928 + 8.50284i) q^{62} +(7.13643 + 2.98367i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-5.17462 + 4.92029i) q^{65} +(1.48145 - 5.05156i) q^{66} +(-9.42846 - 7.91141i) q^{67} +(-1.29298 - 2.23951i) q^{68} +(-8.70863 - 0.968313i) q^{69} +(3.18688 + 4.80450i) q^{70} +(0.792828 + 4.49635i) q^{71} +(-2.38608 + 1.81841i) 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} +(2.45447 - 4.95652i) q^{78} +(5.67129 - 15.5817i) q^{79} +(-2.23176 + 0.138722i) q^{80} +(8.70854 - 2.27187i) q^{81} +(-0.0887348 - 0.243797i) q^{82} +(0.188516 - 0.326520i) q^{83} +(-3.59708 - 2.64663i) q^{84} +(-2.57496 + 5.17742i) q^{85} +(-3.98532 - 3.34408i) q^{86} +(0.770596 - 1.04733i) q^{87} +(-1.51968 + 2.63216i) q^{88} +(12.2942 - 4.47471i) q^{89} +(6.33766 + 2.19864i) q^{90} +(8.10836 + 1.42972i) q^{91} +(4.75383 + 1.73025i) q^{92} +(-6.63637 + 13.4014i) q^{93} -8.64866i q^{94} +(-5.40449 - 8.11119i) q^{95} +(1.58652 - 0.694958i) q^{96} +(1.74154 - 1.46132i) q^{97} +(-0.120432 + 0.330884i) q^{98} +(7.25214 - 5.52679i) 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

Related objects

Downloads

Learn more