LMFDB - Embedded newform 570.2.x.b.217.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, degree $4$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.9
Character	$\chi$	$=$	570.217
Dual form			570.2.x.b.373.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.87574 + 1.21721i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.219288 - 0.219288i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.87574 + 1.21721i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.219288 - 0.219288i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.690261 + 2.12686i) q^{10} +6.33127 q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.962817 - 3.59328i) q^{13} +(0.155060 - 0.268571i) q^{14} +(2.12686 + 0.690261i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.30361 + 0.885199i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-3.97083 + 1.79792i) q^{19} +(-2.23304 - 0.116269i) q^{20} +(-0.268571 - 0.155060i) q^{21} +(1.63865 + 6.11554i) q^{22} +(-2.24611 - 0.601843i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(2.03678 + 4.56635i) q^{25} +3.72004 q^{26} +(0.707107 - 0.707107i) q^{27} +(0.299553 + 0.0802649i) q^{28} +(3.42716 + 5.93602i) q^{29} +(-0.116269 + 2.23304i) q^{30} +2.71491i q^{31} +(0.965926 + 0.258819i) q^{32} +(6.11554 - 1.63865i) q^{33} +(-1.71007 - 2.96193i) q^{34} +(-0.144406 - 0.678246i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.817873 + 0.817873i) q^{37} +(-2.76439 - 3.37019i) q^{38} -3.72004i q^{39} +(-0.465647 - 2.18705i) q^{40} +(-8.81271 - 5.08802i) q^{41} +(0.0802649 - 0.299553i) q^{42} +(2.26304 + 8.44577i) q^{43} +(-5.48304 + 3.16563i) q^{44} +(2.23304 + 0.116269i) q^{45} -2.32534i q^{46} +(2.73086 - 10.1917i) q^{47} +(0.258819 - 0.965926i) q^{48} -6.90383i q^{49} +(-3.88359 + 3.14924i) q^{50} +(-2.96193 + 1.71007i) q^{51} +(0.962817 + 3.59328i) q^{52} +(1.06251 - 3.96536i) q^{53} +(0.866025 + 0.500000i) q^{54} +(11.8758 + 7.70650i) q^{55} +0.310120i q^{56} +(-3.37019 + 2.76439i) q^{57} +(-4.84674 + 4.84674i) q^{58} +(-0.367410 + 0.636373i) q^{59} +(-2.18705 + 0.465647i) q^{60} +(2.17131 + 3.76082i) q^{61} +(-2.62240 + 0.702670i) q^{62} +(-0.299553 - 0.0802649i) q^{63} +1.00000i q^{64} +(6.17978 - 5.56810i) q^{65} +(3.16563 + 5.48304i) q^{66} +(-4.98299 - 1.33519i) q^{67} +(2.41841 - 2.41841i) q^{68} -2.32534 q^{69} +(0.617760 - 0.315029i) q^{70} +(-1.14914 - 0.663459i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(-1.24702 - 4.65396i) q^{73} +(-1.00169 - 0.578323i) q^{74} +(3.14924 + 3.88359i) q^{75} +(2.53987 - 3.54246i) q^{76} +(-1.38837 - 1.38837i) q^{77} +(3.59328 - 0.962817i) q^{78} +(-7.21799 + 12.5019i) q^{79} +(1.99201 - 1.01583i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.63375 - 9.82930i) q^{82} +(-0.190572 + 0.190572i) q^{83} +0.310120 q^{84} +(-7.27418 - 2.36079i) q^{85} +(-7.57227 + 4.37185i) q^{86} +(4.84674 + 4.84674i) q^{87} +(-4.47688 - 4.47688i) q^{88} +(-5.18194 - 8.97538i) q^{89} +(0.465647 + 2.18705i) q^{90} +(-0.999097 + 0.576829i) q^{91} +(2.24611 - 0.601843i) q^{92} +(0.702670 + 2.62240i) q^{93} +10.5512 q^{94} +(-9.63669 - 1.46091i) q^{95} +1.00000 q^{96} +(-4.26158 - 15.9044i) q^{97} +(6.66858 - 1.78684i) q^{98} +(5.48304 - 3.16563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q + 20 * q^6 - 8 * q^7	$ 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.87574	+	1.21721i	0.838855	+	0.544354i
$5$	1.87574	+	1.21721i	0.838855	+	0.544354i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.219288	−	0.219288i	−0.0828830	−	0.0828830i	0.664450	−	0.747333i	$-0.268666\pi$
$7$	−0.219288	−	0.219288i	−0.0828830	−	0.0828830i	−0.747333	+	0.664450i	$0.768666\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−0.690261	+	2.12686i	−0.218280	+	0.672573i
$11$	6.33127			1.90895			0.954475	−	0.298292i	$-0.0964169\pi$
$11$	6.33127			1.90895			0.954475	+	0.298292i	$0.0964169\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	0.962817	−	3.59328i	0.267037	−	0.996597i	−0.693954	−	0.720019i	$-0.744133\pi$
$13$	0.962817	−	3.59328i	0.267037	−	0.996597i	0.960991	−	0.276578i	$-0.0892004\pi$
$14$	0.155060	−	0.268571i	0.0414415	−	0.0717787i
$15$	2.12686	+	0.690261i	0.549153	+	0.178225i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.30361	+	0.885199i	−0.801243	+	0.214692i	−0.636129	−	0.771582i	$-0.719466\pi$
$17$	−3.30361	+	0.885199i	−0.801243	+	0.214692i	−0.165113	+	0.986275i	$0.552799\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−3.97083	+	1.79792i	−0.910970	+	0.412472i
$19$	−3.97083	+	1.79792i	−0.910970	+	0.412472i
$20$	−2.23304	−	0.116269i	−0.499324	−	0.0259985i
$21$	−0.268571	−	0.155060i	−0.0586071	−	0.0338368i
$22$	1.63865	+	6.11554i	0.349362	+	1.30384i
$23$	−2.24611	−	0.601843i	−0.468346	−	0.125493i	0.0169251	−	0.999857i	$-0.494612\pi$
$23$	−2.24611	−	0.601843i	−0.468346	−	0.125493i	−0.485271	+	0.874364i	$0.661279\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	2.03678	+	4.56635i	0.407357	+	0.913269i
$26$	3.72004			0.729560
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	0.299553	+	0.0802649i	0.0566101	+	0.0151686i
$29$	3.42716	+	5.93602i	0.636408	+	1.10229i	0.986215	+	0.165469i	$0.0529137\pi$
$29$	3.42716	+	5.93602i	0.636408	+	1.10229i	−0.349807	+	0.936822i	$0.613753\pi$
$30$	−0.116269	+	2.23304i	−0.0212277	+	0.407696i
$31$			2.71491i			0.487612i	0.969824	+	0.243806i	$0.0783960\pi$
$31$			2.71491i			0.487612i	−0.969824	+	0.243806i	$0.921604\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	6.11554	−	1.63865i	1.06458	−	0.285253i
$34$	−1.71007	−	2.96193i	−0.293275	−	0.507967i
$35$	−0.144406	−	0.678246i	−0.0244091	−	0.114645i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.817873	+	0.817873i	−0.134457	+	0.134457i	−0.771132	−	0.636675i	$-0.780309\pi$
$37$	−0.817873	+	0.817873i	−0.134457	+	0.134457i	0.636675	+	0.771132i	$0.280309\pi$
$38$	−2.76439	−	3.37019i	−0.448443	−	0.546717i
$39$		−	3.72004i		−	0.595683i
$40$	−0.465647	−	2.18705i	−0.0736253	−	0.345802i
$41$	−8.81271	−	5.08802i	−1.37631	−	0.794616i	−0.384601	−	0.923083i	$-0.625661\pi$
$41$	−8.81271	−	5.08802i	−1.37631	−	0.794616i	−0.991714	+	0.128468i	$0.958994\pi$
$42$	0.0802649	−	0.299553i	0.0123851	−	0.0462220i
$43$	2.26304	+	8.44577i	0.345110	+	1.28797i	0.892484	+	0.451079i	$0.148961\pi$
$43$	2.26304	+	8.44577i	0.345110	+	1.28797i	−0.547374	+	0.836888i	$0.684372\pi$
$44$	−5.48304	+	3.16563i	−0.826599	+	0.477237i
$45$	2.23304	+	0.116269i	0.332882	+	0.0173323i
$46$		−	2.32534i		−	0.342853i
$47$	2.73086	−	10.1917i	0.398337	−	1.48661i	−0.417685	−	0.908592i	$-0.637158\pi$
$47$	2.73086	−	10.1917i	0.398337	−	1.48661i	0.816022	−	0.578021i	$-0.196175\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$		−	6.90383i		−	0.986261i
$50$	−3.88359	+	3.14924i	−0.549223	+	0.445370i
$51$	−2.96193	+	1.71007i	−0.414754	+	0.239458i
$52$	0.962817	+	3.59328i	0.133519	+	0.498299i
$53$	1.06251	−	3.96536i	0.145948	−	0.544684i	−0.853764	−	0.520660i	$-0.825686\pi$
$53$	1.06251	−	3.96536i	0.145948	−	0.544684i	0.999711	−	0.0240232i	$-0.00764756\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	11.8758	+	7.70650i	1.60133	+	1.03914i
$56$			0.310120i			0.0414415i
$57$	−3.37019	+	2.76439i	−0.446392	+	0.366152i
$58$	−4.84674	+	4.84674i	−0.636408	+	0.636408i
$59$	−0.367410	+	0.636373i	−0.0478327	+	0.0828487i	−0.888950	−	0.458003i	$-0.848565\pi$
$59$	−0.367410	+	0.636373i	−0.0478327	+	0.0828487i	0.841118	+	0.540852i	$0.181898\pi$
$60$	−2.18705	+	0.465647i	−0.282346	+	0.0601148i
$61$	2.17131	+	3.76082i	0.278008	+	0.481523i	0.970890	−	0.239528i	$-0.0769926\pi$
$61$	2.17131	+	3.76082i	0.278008	+	0.481523i	−0.692882	+	0.721051i	$0.743659\pi$
$62$	−2.62240	+	0.702670i	−0.333045	+	0.0892392i
$63$	−0.299553	−	0.0802649i	−0.0377401	−	0.0101124i
$64$			1.00000i			0.125000i
$65$	6.17978	−	5.56810i	0.766508	−	0.690638i
$66$	3.16563	+	5.48304i	0.389663	+	0.674916i
$67$	−4.98299	−	1.33519i	−0.608769	−	0.163119i	−0.0587518	−	0.998273i	$-0.518712\pi$
$67$	−4.98299	−	1.33519i	−0.608769	−	0.163119i	−0.550017	+	0.835154i	$0.685379\pi$
$68$	2.41841	−	2.41841i	0.293275	−	0.293275i
$69$	−2.32534			−0.279938
$70$	0.617760	−	0.315029i	0.0738365	−	0.0376531i
$71$	−1.14914	−	0.663459i	−0.136378	−	0.0787381i	0.430258	−	0.902706i	$-0.358422\pi$
$71$	−1.14914	−	0.663459i	−0.136378	−	0.0787381i	−0.566637	+	0.823968i	$0.691756\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	−1.24702	−	4.65396i	−0.145953	−	0.544705i	−0.999711	−	0.0240345i	$-0.992349\pi$
$73$	−1.24702	−	4.65396i	−0.145953	−	0.544705i	0.853758	−	0.520670i	$-0.174318\pi$
$74$	−1.00169	−	0.578323i	−0.116444	−	0.0672287i
$75$	3.14924	+	3.88359i	0.363643	+	0.448439i
$76$	2.53987	−	3.54246i	0.291344	−	0.406348i
$77$	−1.38837	−	1.38837i	−0.158219	−	0.158219i
$78$	3.59328	−	0.962817i	0.406859	−	0.109018i
$79$	−7.21799	+	12.5019i	−0.812088	+	1.40658i	0.0993127	+	0.995056i	$0.468336\pi$
$79$	−7.21799	+	12.5019i	−0.812088	+	1.40658i	−0.911400	+	0.411521i	$0.864998\pi$
$80$	1.99201	−	1.01583i	0.222713	−	0.113573i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	2.63375	−	9.82930i	0.290849	−	1.08546i
$83$	−0.190572	+	0.190572i	−0.0209180	+	0.0209180i	−0.717488	−	0.696570i	$-0.754708\pi$
$83$	−0.190572	+	0.190572i	−0.0209180	+	0.0209180i	0.696570	+	0.717488i	$0.254708\pi$
$84$	0.310120			0.0338368
$85$	−7.27418	−	2.36079i	−0.788995	−	0.256064i
$86$	−7.57227	+	4.37185i	−0.816539	+	0.471429i
$87$	4.84674	+	4.84674i	0.519625	+	0.519625i
$88$	−4.47688	−	4.47688i	−0.477237	−	0.477237i
$89$	−5.18194	−	8.97538i	−0.549284	−	0.951388i	−0.998324	−	0.0578761i	$-0.981567\pi$
$89$	−5.18194	−	8.97538i	−0.549284	−	0.951388i	0.449040	−	0.893512i	$-0.351766\pi$
$90$	0.465647	+	2.18705i	0.0490835	+	0.230535i
$91$	−0.999097	+	0.576829i	−0.104734	+	0.0604681i
$92$	2.24611	−	0.601843i	0.234173	−	0.0627464i
$93$	0.702670	+	2.62240i	0.0728635	+	0.271930i
$94$	10.5512			1.08828
$95$	−9.63669	−	1.46091i	−0.988703	−	0.149886i
$96$	1.00000			0.102062
$97$	−4.26158	−	15.9044i	−0.432698	−	1.61485i	−0.746515	−	0.665368i	$-0.768274\pi$
$97$	−4.26158	−	15.9044i	−0.432698	−	1.61485i	0.313817	−	0.949484i	$-0.398392\pi$
$98$	6.66858	−	1.78684i	0.673629	−	0.180498i
$99$	5.48304	−	3.16563i	0.551066	−	0.318158i
$100$	−4.04708	−	2.93618i	−0.404708	−	0.293618i
$101$	−6.97371	−	12.0788i	−0.693910	−	1.20189i	−0.970547	−	0.240913i	$-0.922553\pi$
$101$	−6.97371	−	12.0788i	−0.693910	−	1.20189i	0.276636	−	0.960975i	$-0.410780\pi$
$102$	−2.41841	−	2.41841i	−0.239458	−	0.239458i
$103$	5.59928	+	5.59928i	0.551714	+	0.551714i	0.926935	−	0.375222i	$-0.122433\pi$
$103$	5.59928	+	5.59928i	0.551714	+	0.551714i	−0.375222	+	0.926935i	$0.622433\pi$
$104$	−3.22165	+	1.86002i	−0.315909	+	0.182390i
$105$	−0.315029	−	0.617760i	−0.0307437	−	0.0602872i
$106$	4.10524			0.398736
$107$	−3.36656	+	3.36656i	−0.325458	+	0.325458i	−0.850856	−	0.525399i	$-0.823916\pi$
$107$	−3.36656	+	3.36656i	−0.325458	+	0.325458i	0.525399	+	0.850856i	$0.323916\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	−5.03859	+	8.72710i	−0.482610	+	0.835904i	−0.999801	−	0.0199656i	$-0.993644\pi$
$109$	−5.03859	+	8.72710i	−0.482610	+	0.835904i	0.517191	+	0.855870i	$0.326978\pi$
$110$	−4.37023	+	13.4657i	−0.416685	+	1.28391i
$111$	−0.578323	+	1.00169i	−0.0548920	+	0.0950758i
$112$	−0.299553	+	0.0802649i	−0.0283051	+	0.00758432i
$113$	−13.8254	−	13.8254i	−1.30059	−	1.30059i	−0.927997	−	0.372589i	$-0.878470\pi$
$113$	−13.8254	−	13.8254i	−1.30059	−	1.30059i	−0.372589	−	0.927997i	$-0.621530\pi$
$114$	−3.54246	−	2.53987i	−0.331782	−	0.237881i
$115$	−3.48054	−	3.86289i	−0.324562	−	0.360216i
$116$	−5.93602	−	3.42716i	−0.551145	−	0.318204i
$117$	−0.962817	−	3.59328i	−0.0890125	−	0.332199i
$118$	−0.709781	−	0.190185i	−0.0653407	−	0.0175080i
$119$	0.918554	+	0.530327i	0.0842037	+	0.0486150i
$120$	−1.01583	−	1.99201i	−0.0927322	−	0.181844i
$121$	29.0850			2.64409
$122$	−3.07070	+	3.07070i	−0.278008	+	0.278008i
$123$	−9.82930	−	2.63375i	−0.886278	−	0.237478i
$124$	−1.35745	−	2.35118i	−0.121903	−	0.211142i
$125$	−1.73774	+	11.0445i	−0.155429	+	0.987847i
$126$		−	0.310120i		−	0.0276277i
$127$	−14.1220	−	3.78398i	−1.25312	−	0.335774i	−0.429582	−	0.903028i	$-0.641339\pi$
$127$	−14.1220	−	3.78398i	−1.25312	−	0.335774i	−0.823543	+	0.567254i	$0.808006\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	4.37185	+	7.57227i	0.384920	+	0.666701i
$130$	6.97782	+	4.52808i	0.611995	+	0.397139i
$131$	−1.82083	+	3.15377i	−0.159087	+	0.275546i	−0.934540	−	0.355859i	$-0.884188\pi$
$131$	−1.82083	+	3.15377i	−0.159087	+	0.275546i	0.775453	+	0.631405i	$0.217522\pi$
$132$	−4.47688	+	4.47688i	−0.389663	+	0.389663i
$133$	1.26502	+	0.476491i	0.109691	+	0.0413170i
$134$		−	5.15877i		−	0.445650i
$135$	2.18705	−	0.465647i	0.188231	−	0.0400765i
$136$	2.96193	+	1.71007i	0.253984	+	0.146638i
$137$	2.66833	−	9.95833i	0.227971	−	0.850798i	−0.753222	−	0.657766i	$-0.771501\pi$
$137$	2.66833	−	9.95833i	0.227971	−	0.850798i	0.981193	−	0.193031i	$-0.0618319\pi$
$138$	−0.601843	−	2.24611i	−0.0512322	−	0.191201i
$139$	17.8754	−	10.3204i	1.51617	−	0.875362i	0.516352	−	0.856376i	$-0.327290\pi$
$139$	17.8754	−	10.3204i	1.51617	−	0.875362i	0.999820	−	0.0189860i	$-0.00604381\pi$
$140$	0.464183	+	0.515175i	0.0392306	+	0.0435402i
$141$		−	10.5512i		−	0.888574i
$142$	0.343432	−	1.28170i	0.0288201	−	0.107558i
$143$	6.09586	−	22.7500i	0.509761	−	1.90245i
$144$		−	1.00000i		−	0.0833333i
$145$	−0.796943	+	15.3060i	−0.0661825	+	1.27109i
$146$	4.17262	−	2.40907i	0.345329	−	0.199376i
$147$	−1.78684	−	6.66858i	−0.147376	−	0.550016i
$148$	0.299362	−	1.11723i	0.0246074	−	0.0918361i
$149$	16.7440	+	9.66714i	1.37172	+	0.791963i	0.991145	−	0.132787i	$-0.0423926\pi$
$149$	16.7440	+	9.66714i	1.37172	+	0.791963i	0.380576	+	0.924750i	$0.375726\pi$
$150$	−2.93618	+	4.04708i	−0.239738	+	0.330443i
$151$			0.256188i			0.0208483i	0.999946	+	0.0104241i	$0.00331817\pi$
$151$			0.256188i			0.0208483i	−0.999946	+	0.0104241i	$0.996682\pi$
$152$	4.07912	+	1.53647i	0.330861	+	0.124625i
$153$	−2.41841	+	2.41841i	−0.195517	+	0.195517i
$154$	0.981725	−	1.70040i	0.0791097	−	0.137022i
$155$	−3.30462	+	5.09246i	−0.265434	+	0.409036i
$156$	1.86002	+	3.22165i	0.148921	+	0.257938i
$157$	−9.31270	+	2.49533i	−0.743234	+	0.199149i	−0.610515	−	0.792005i	$-0.709037\pi$
$157$	−9.31270	+	2.49533i	−0.743234	+	0.199149i	−0.132719	+	0.991154i	$0.542371\pi$
$158$	−13.9441	−	3.73631i	−1.10933	−	0.297245i
$159$		−	4.10524i		−	0.325567i
$160$	1.49679	+	1.66121i	0.118331	+	0.131331i
$161$	0.360567	+	0.624520i	0.0284167	+	0.0492191i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−0.0203626	+	0.0203626i	−0.00159492	+	0.00159492i	−0.707904	−	0.706309i	$-0.750359\pi$
$163$	−0.0203626	+	0.0203626i	−0.00159492	+	0.00159492i	0.706309	+	0.707904i	$0.250359\pi$
$164$	10.1760			0.794616
$165$	13.4657	+	4.37023i	1.04831	+	0.340222i
$166$	−0.233403	−	0.134755i	−0.0181156	−	0.0104590i
$167$	−1.74463	−	0.467473i	−0.135004	−	0.0361741i	0.190684	−	0.981651i	$-0.438929\pi$
$167$	−1.74463	−	0.467473i	−0.135004	−	0.0361741i	−0.325688	+	0.945477i	$0.605596\pi$
$168$	0.0802649	+	0.299553i	0.00619257	+	0.0231110i
$169$	−0.726336	−	0.419351i	−0.0558720	−	0.0322577i
$170$	0.397656	−	7.63733i	0.0304988	−	0.585757i
$171$	−2.53987	+	3.54246i	−0.194229	+	0.270899i
$172$	−6.18273	−	6.18273i	−0.471429	−	0.471429i
$173$	22.2763	−	5.96891i	1.69363	−	0.453808i	0.722311	−	0.691568i	$-0.243080\pi$
$173$	22.2763	−	5.96891i	1.69363	−	0.453808i	0.971324	+	0.237760i	$0.0764133\pi$
$174$	−3.42716	+	5.93602i	−0.259812	+	0.450008i
$175$	0.554702	−	1.44799i	0.0419315	−	0.109457i
$176$	3.16563	−	5.48304i	0.238619	−	0.413300i
$177$	−0.190185	+	0.709781i	−0.0142952	+	0.0533504i
$178$	7.32836	−	7.32836i	0.549284	−	0.549284i
$179$	14.9146			1.11477			0.557383	−	0.830255i	$-0.311805\pi$
$179$	14.9146			1.11477			0.557383	+	0.830255i	$0.311805\pi$
$180$	−1.99201	+	1.01583i	−0.148475	+	0.0757155i
$181$	3.95519	−	2.28353i	0.293987	−	0.169733i	−0.345752	−	0.938326i	$-0.612376\pi$
$181$	3.95519	−	2.28353i	0.293987	−	0.169733i	0.639738	+	0.768593i	$0.279043\pi$
$182$	−0.815759	−	0.815759i	−0.0604681	−	0.0604681i
$183$	3.07070	+	3.07070i	0.226992	+	0.226992i
$184$	1.16267	+	2.01380i	0.0857132	+	0.148460i
$185$	−2.52964	+	0.538589i	−0.185983	+	0.0395979i
$186$	−2.35118	+	1.35745i	−0.172397	+	0.0995334i
$187$	−20.9160	+	5.60443i	−1.52953	+	0.409837i
$188$	2.73086	+	10.1917i	0.199168	+	0.743307i
$189$	−0.310120			−0.0225579
$190$	−1.08303	−	9.68644i	−0.0785712	−	0.702728i
$191$	−17.4658			−1.26378			−0.631889	−	0.775059i	$-0.717720\pi$
$191$	−17.4658			−1.26378			−0.631889	+	0.775059i	$0.717720\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	1.71156	−	0.458612i	0.123201	−	0.0330116i	−0.196692	−	0.980465i	$-0.563020\pi$
$193$	1.71156	−	0.458612i	0.123201	−	0.0330116i	0.319893	+	0.947454i	$0.396353\pi$
$194$	14.2595	−	8.23275i	1.02378	−	0.591077i
$195$	4.52808	−	6.97782i	0.324263	−	0.499692i
$196$	3.45191	+	5.97889i	0.246565	+	0.427063i
$197$	−4.89640	−	4.89640i	−0.348854	−	0.348854i	0.510829	−	0.859683i	$-0.329339\pi$
$197$	−4.89640	−	4.89640i	−0.348854	−	0.348854i	−0.859683	+	0.510829i	$0.829339\pi$
$198$	4.47688	+	4.47688i	0.318158	+	0.318158i
$199$	−6.60568	+	3.81379i	−0.468264	+	0.270352i	−0.715513	−	0.698600i	$-0.753807\pi$
$199$	−6.60568	+	3.81379i	−0.468264	+	0.270352i	0.247249	+	0.968952i	$0.420474\pi$
$200$	1.78867	−	4.66912i	0.126478	−	0.330156i
$201$	−5.15877			−0.363871
$202$	9.86232	−	9.86232i	0.693910	−	0.693910i
$203$	0.550161	−	2.05323i	0.0386137	−	0.144108i
$204$	1.71007	−	2.96193i	0.119729	−	0.207377i
$205$	−10.3371	−	20.2707i	−0.721976	−	1.41577i
$206$	−3.95929	+	6.85769i	−0.275857	+	0.477798i
$207$	−2.24611	+	0.601843i	−0.156115	+	0.0418310i
$208$	−2.63047	−	2.63047i	−0.182390	−	0.182390i
$209$	−25.1404	+	11.3831i	−1.73900	+	0.787388i
$210$	0.515175	−	0.464183i	0.0355505	−	0.0320316i
$211$	−0.170890	−	0.0986634i	−0.0117646	−	0.00679227i	0.494106	−	0.869402i	$-0.335495\pi$
$211$	−0.170890	−	0.0986634i	−0.0117646	−	0.00679227i	−0.505871	+	0.862609i	$0.668829\pi$
$212$	1.06251	+	3.96536i	0.0729738	+	0.272342i
$213$	−1.28170	−	0.343432i	−0.0878209	−	0.0235315i
$214$	−4.12318	−	2.38052i	−0.281855	−	0.162729i
$215$	−6.03544	+	18.5966i	−0.411613	+	1.26828i
$216$	−1.00000			−0.0680414
$217$	0.595346	−	0.595346i	0.0404147	−	0.0404147i
$218$	−9.73381	−	2.60817i	−0.659257	−	0.176647i
$219$	−2.40907	−	4.17262i	−0.162790	−	0.281960i
$220$	−14.1380	−	0.736129i	−0.953183	−	0.0496298i
$221$			12.7231i			0.855847i
$222$	−1.11723	−	0.299362i	−0.0749839	−	0.0200919i
$223$	−12.1500	+	3.25559i	−0.813625	+	0.218010i	−0.641557	−	0.767075i	$-0.721711\pi$
$223$	−12.1500	+	3.25559i	−0.813625	+	0.218010i	−0.172067	+	0.985085i	$0.555045\pi$
$224$	−0.155060	−	0.268571i	−0.0103604	−	0.0179447i
$225$	4.04708	+	2.93618i	0.269805	+	0.195745i
$226$	9.77604	−	16.9326i	0.650293	−	1.12634i
$227$	−3.56929	+	3.56929i	−0.236902	+	0.236902i	−0.815566	−	0.578664i	$-0.803574\pi$
$227$	−3.56929	+	3.56929i	−0.236902	+	0.236902i	0.578664	+	0.815566i	$0.303574\pi$
$228$	1.53647	−	4.07912i	0.101755	−	0.270147i
$229$			22.9254i			1.51495i	0.652862	+	0.757476i	$0.273568\pi$
$229$			22.9254i			1.51495i	−0.652862	+	0.757476i	$0.726432\pi$
$230$	2.83044	−	4.36173i	0.186633	−	0.287604i
$231$	−1.70040	−	0.981725i	−0.111878	−	0.0645928i
$232$	1.77403	−	6.62077i	0.116471	−	0.434675i
$233$	−1.62200	−	6.05339i	−0.106261	−	0.396571i	0.892224	−	0.451592i	$-0.149144\pi$
$233$	−1.62200	−	6.05339i	−0.106261	−	0.396571i	−0.998485	+	0.0550216i	$0.982477\pi$
$234$	3.22165	−	1.86002i	0.210606	−	0.121593i
$235$	17.5279	−	15.7929i	1.14339	−	1.03022i
$236$		−	0.734820i		−	0.0478327i
$237$	−3.73631	+	13.9441i	−0.242699	+	0.905766i
$238$	−0.274518	+	1.02451i	−0.0177943	+	0.0664093i
$239$			22.5950i			1.46155i	0.682618	+	0.730775i	$0.260841\pi$
$239$			22.5950i			1.46155i	−0.682618	+	0.730775i	$0.739159\pi$
$240$	1.66121	−	1.49679i	0.107231	−	0.0966171i
$241$	−0.0802518	+	0.0463334i	−0.00516947	+	0.00298460i	−0.502583	−	0.864529i	$-0.667617\pi$
$241$	−0.0802518	+	0.0463334i	−0.00516947	+	0.00298460i	0.497413	+	0.867514i	$0.334283\pi$
$242$	7.52774	+	28.0939i	0.483902	+	1.80595i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−3.76082	−	2.17131i	−0.240762	−	0.139004i
$245$	8.40343	−	12.9498i	0.536875	−	0.827330i
$246$		−	10.1760i		−	0.648801i
$247$	2.63727	+	15.9994i	0.167806	+	1.01802i
$248$	1.91973	−	1.91973i	0.121903	−	0.121903i
$249$	−0.134755	+	0.233403i	−0.00853975	+	0.0147913i
$250$	−11.1179	+	1.17999i	−0.703158	+	0.0746289i
$251$	4.59120	+	7.95219i	0.289794	+	0.501938i	0.973760	−	0.227576i	$-0.0730799\pi$
$251$	4.59120	+	7.95219i	0.289794	+	0.501938i	−0.683966	+	0.729514i	$0.739747\pi$
$252$	0.299553	−	0.0802649i	0.0188700	−	0.00505621i
$253$	−14.2207	−	3.81043i	−0.894048	−	0.239559i
$254$		−	14.6202i		−	0.917351i
$255$	−7.63733	−	0.397656i	−0.478268	−	0.0249022i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.78847	+	2.08691i	0.485831	+	0.130178i	0.493417	−	0.869793i	$-0.335748\pi$
$257$	7.78847	+	2.08691i	0.485831	+	0.130178i	−0.00758535	+	0.999971i	$0.502415\pi$
$258$	−6.18273	+	6.18273i	−0.384920	+	0.384920i
$259$	0.358699			0.0222885
$260$	−2.56780	+	7.91201i	−0.159248	+	0.490682i
$261$	5.93602	+	3.42716i	0.367430	+	0.212136i
$262$	−3.51757	−	0.942531i	−0.217316	−	0.0582297i
$263$	3.87921	+	14.4774i	0.239202	+	0.892715i	0.976209	+	0.216830i	$0.0695717\pi$
$263$	3.87921	+	14.4774i	0.239202	+	0.892715i	−0.737007	+	0.675885i	$0.763762\pi$
$264$	−5.48304	−	3.16563i	−0.337458	−	0.194831i
$265$	6.81968	−	6.14466i	0.418930	−	0.377464i
$266$	−0.132844	+	1.34524i	−0.00814522	+	0.0824818i
$267$	−7.32836	−	7.32836i	−0.448489	−	0.448489i
$268$	4.98299	−	1.33519i	0.304384	−	0.0815595i
$269$	−0.866982	+	1.50166i	−0.0528608	+	0.0915576i	−0.891245	−	0.453522i	$-0.850167\pi$
$269$	−0.866982	+	1.50166i	−0.0528608	+	0.0915576i	0.838384	+	0.545080i	$0.183501\pi$
$270$	1.01583	+	1.99201i	0.0618214	+	0.121230i
$271$	−0.460704	+	0.797963i	−0.0279858	+	0.0484728i	−0.879679	−	0.475568i	$-0.842243\pi$
$271$	−0.460704	+	0.797963i	−0.0279858	+	0.0484728i	0.851693	+	0.524041i	$0.175576\pi$
$272$	−0.885199	+	3.30361i	−0.0536731	+	0.200311i
$273$	−0.815759	+	0.815759i	−0.0493720	+	0.0493720i
$274$	10.3096			0.622827
$275$	12.8954	+	28.9108i	0.777623	+	1.74338i
$276$	2.01380	−	1.16267i	0.121217	−	0.0699845i
$277$	1.31226	+	1.31226i	0.0788458	+	0.0788458i	0.745430	−	0.666584i	$-0.232244\pi$
$277$	1.31226	+	1.31226i	0.0788458	+	0.0788458i	−0.666584	+	0.745430i	$0.732244\pi$
$278$	14.5952	+	14.5952i	0.875362	+	0.875362i
$279$	1.35745	+	2.35118i	0.0812687	+	0.140761i
$280$	−0.377482	+	0.581703i	−0.0225588	+	0.0347634i
$281$	17.2366	−	9.95154i	1.02825	−	0.593659i	0.111766	−	0.993735i	$-0.464349\pi$
$281$	17.2366	−	9.95154i	1.02825	−	0.593659i	0.916482	+	0.400075i	$0.131016\pi$
$282$	10.1917	−	2.73086i	0.606907	−	0.162620i
$283$	8.11799	+	30.2967i	0.482564	+	1.80095i	0.590786	+	0.806828i	$0.298818\pi$
$283$	8.11799	+	30.2967i	0.482564	+	1.80095i	−0.108222	+	0.994127i	$0.534516\pi$
$284$	1.32692			0.0787381
$285$	−9.68644	+	1.08303i	−0.573775	+	0.0641531i
$286$	23.5526			1.39269
$287$	0.816779	+	3.04826i	0.0482129	+	0.179933i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	−4.59219	+	2.65130i	−0.270129	+	0.155959i
$290$	−14.9907	+	3.19169i	−0.880285	+	0.187423i
$291$	−8.23275	−	14.2595i	−0.482612	−	0.835909i
$292$	3.40693	+	3.40693i	0.199376	+	0.199376i
$293$	8.23657	+	8.23657i	0.481185	+	0.481185i	0.905510	−	0.424325i	$-0.139489\pi$
$293$	8.23657	+	8.23657i	0.481185	+	0.481185i	−0.424325	+	0.905510i	$0.639489\pi$
$294$	5.97889	−	3.45191i	0.348696	−	0.201320i
$295$	−1.46377	+	0.746452i	−0.0852237	+	0.0434601i
$296$	1.15665			0.0672287
$297$	4.47688	−	4.47688i	0.259775	−	0.259775i
$298$	−5.00408	+	18.6755i	−0.289879	+	1.08184i
$299$	−4.32518	+	7.49143i	−0.250132	+	0.433241i
$300$	−4.66912	−	1.78867i	−0.269572	−	0.103269i
$301$	1.35580	−	2.34831i	0.0781468	−	0.135354i
$302$	−0.247459	+	0.0663064i	−0.0142397	+	0.00381550i
$303$	−9.86232	−	9.86232i	−0.566576	−	0.566576i
$304$	−0.428365	+	4.33780i	−0.0245684	+	0.248790i
$305$	−0.504911	+	9.69725i	−0.0289111	+	0.555263i
$306$	−2.96193	−	1.71007i	−0.169322	−	0.0977584i
$307$	1.09258	+	4.07756i	0.0623568	+	0.232719i	0.990070	−	0.140575i	$-0.0448950\pi$
$307$	1.09258	+	4.07756i	0.0623568	+	0.232719i	−0.927713	+	0.373294i	$0.878228\pi$
$308$	1.89655	+	0.508178i	0.108066	+	0.0289562i
$309$	6.85769	+	3.95929i	0.390120	+	0.225236i
$310$	−5.77423	−	1.87400i	−0.327954	−	0.106436i
$311$	−11.0780			−0.628178			−0.314089	−	0.949393i	$-0.601699\pi$
$311$	−11.0780			−0.628178			−0.314089	+	0.949393i	$0.601699\pi$
$312$	−2.63047	+	2.63047i	−0.148921	+	0.148921i
$313$	−21.8136	−	5.84492i	−1.23297	−	0.330375i	−0.417238	−	0.908797i	$-0.637002\pi$
$313$	−21.8136	−	5.84492i	−1.23297	−	0.330375i	−0.815737	+	0.578423i	$0.803668\pi$
$314$	−4.82061	−	8.34953i	−0.272043	−	0.471191i
$315$	−0.464183	−	0.515175i	−0.0261537	−	0.0290268i
$316$		−	14.4360i		−	0.812088i
$317$	−17.7251	−	4.74943i	−0.995543	−	0.266755i	−0.275966	−	0.961168i	$-0.588998\pi$
$317$	−17.7251	−	4.74943i	−0.995543	−	0.266755i	−0.719577	+	0.694413i	$0.755664\pi$
$318$	3.96536	−	1.06251i	0.222366	−	0.0595828i
$319$	21.6983	+	37.5825i	1.21487	+	2.10422i
$320$	−1.21721	+	1.87574i	−0.0680443	+	0.104857i
$321$	−2.38052	+	4.12318i	−0.132868	+	0.230133i
$322$	−0.509919	+	0.509919i	−0.0284167	+	0.0284167i
$323$	11.5265	−	9.45461i	0.641353	−	0.526068i
$324$			1.00000i			0.0555556i
$325$	18.3692	−	2.92218i	1.01894	−	0.162094i
$326$	−0.0249390	−	0.0143985i	−0.00138124	−	0.000797461i
$327$	−2.60817	+	9.73381i	−0.144232	+	0.538281i
$328$	2.63375	+	9.82930i	0.145425	+	0.542732i
$329$	−2.83376	+	1.63607i	−0.156230	+	0.0901996i
$330$	−0.736129	+	14.1380i	−0.0405225	+	0.778271i
$331$		−	1.63560i		−	0.0899008i	−0.998989	−	0.0449504i	$-0.985687\pi$
$331$		−	1.63560i		−	0.0899008i	0.998989	−	0.0449504i	$-0.0143130\pi$
$332$	0.0697543	−	0.260327i	0.00382827	−	0.0142873i
$333$	−0.299362	+	1.11723i	−0.0164049	+	0.0612241i
$334$		−	1.80618i		−	0.0988295i
$335$	−7.72157	−	8.56982i	−0.421874	−	0.468219i
$336$	−0.268571	+	0.155060i	−0.0146518	+	0.00845921i
$337$	0.137782	+	0.514208i	0.00750545	+	0.0280107i	0.969577	−	0.244786i	$-0.0787179\pi$
$337$	0.137782	+	0.514208i	0.00750545	+	0.0280107i	−0.962072	+	0.272797i	$0.912051\pi$
$338$	0.217072	−	0.810123i	0.0118072	−	0.0440649i
$339$	−16.9326	−	9.77604i	−0.919653	−	0.530962i
$340$	7.48002	−	1.59258i	0.405661	−	0.0863698i
$341$			17.1888i			0.930826i
$342$	−4.07912	−	1.53647i	−0.220574	−	0.0830830i
$343$	−3.04894	+	3.04894i	−0.164627	+	0.164627i
$344$	4.37185	−	7.57227i	0.235714	−	0.408269i
$345$	−4.36173	−	2.83044i	−0.234828	−	0.152386i
$346$	11.5311	+	19.9724i	0.619913	+	1.07372i
$347$	−1.87220	+	0.501655i	−0.100505	+	0.0269303i	−0.308721	−	0.951153i	$-0.599901\pi$
$347$	−1.87220	+	0.501655i	−0.100505	+	0.0269303i	0.208216	+	0.978083i	$0.433234\pi$
$348$	−6.62077	−	1.77403i	−0.354910	−	0.0950979i
$349$		−	21.3205i		−	1.14126i	−0.821208	−	0.570629i	$-0.806699\pi$
$349$		−	21.3205i		−	1.14126i	0.821208	−	0.570629i	$-0.193301\pi$
$350$	1.54221	+	0.161035i	0.0824348	+	0.00860766i
$351$	−1.86002	−	3.22165i	−0.0992805	−	0.171959i
$352$	6.11554	+	1.63865i	0.325959	+	0.0873405i
$353$	18.3308	−	18.3308i	0.975651	−	0.975651i	−0.0240595	−	0.999711i	$-0.507659\pi$
$353$	18.3308	−	18.3308i	0.975651	−	0.975651i	0.999711	+	0.0240595i	$0.00765912\pi$
$354$	−0.734820			−0.0390552
$355$	−1.34792	−	2.64323i	−0.0715403	−	0.140288i
$356$	8.97538	+	5.18194i	0.475694	+	0.274642i
$357$	1.02451	+	0.274518i	0.0542230	+	0.0145290i
$358$	3.86017	+	14.4064i	0.204016	+	0.761400i
$359$	26.9383	+	15.5528i	1.42175	+	0.820847i	0.996448	−	0.0842061i	$-0.0268354\pi$
$359$	26.9383	+	15.5528i	1.42175	+	0.820847i	0.425300	+	0.905053i	$0.360169\pi$
$360$	−1.49679	−	1.66121i	−0.0788875	−	0.0875537i
$361$	12.5349	−	14.2785i	0.659733	−	0.751500i
$362$	3.22940	+	3.22940i	0.169733	+	0.169733i
$363$	28.0939	−	7.52774i	1.47455	−	0.395104i
$364$	0.576829	−	0.999097i	0.0302340	−	0.0523669i
$365$	3.32577	−	10.2475i	0.174079	−	0.536379i
$366$	−2.17131	+	3.76082i	−0.113496	+	0.196581i
$367$	−7.72029	+	28.8125i	−0.402996	+	1.50400i	0.404726	+	0.914438i	$0.367367\pi$
$367$	−7.72029	+	28.8125i	−0.402996	+	1.50400i	−0.807722	+	0.589563i	$0.799300\pi$
$368$	−1.64426	+	1.64426i	−0.0857132	+	0.0857132i
$369$	−10.1760			−0.529744
$370$	−1.17496	−	2.30405i	−0.0610831	−	0.119782i
$371$	−1.10255	+	0.636558i	−0.0572416	+	0.0330484i
$372$	−1.91973	−	1.91973i	−0.0995334	−	0.0995334i
$373$	−13.3691	−	13.3691i	−0.692226	−	0.692226i	0.270495	−	0.962721i	$-0.412813\pi$
$373$	−13.3691	−	13.3691i	−0.692226	−	0.692226i	−0.962721	+	0.270495i	$0.912813\pi$
$374$	−10.8269	−	18.7528i	−0.559847	−	0.969684i
$375$	1.17999	+	11.1179i	0.0609343	+	0.574126i
$376$	−9.13763	+	5.27562i	−0.471237	+	0.272069i
$377$	24.6295	−	6.59946i	1.26848	−	0.339889i
$378$	−0.0802649	−	0.299553i	−0.00412838	−	0.0154073i
$379$	−32.1397			−1.65091			−0.825453	−	0.564471i	$-0.809080\pi$
$379$	−32.1397			−1.65091			−0.825453	+	0.564471i	$0.809080\pi$
$380$	9.07607	−	3.55316i	0.465593	−	0.182273i
$381$	−14.6202			−0.749014
$382$	−4.52047	−	16.8706i	−0.231288	−	0.863177i
$383$	3.51551	−	0.941979i	0.179634	−	0.0481329i	−0.167880	−	0.985807i	$-0.553692\pi$
$383$	3.51551	−	0.941979i	0.179634	−	0.0481329i	0.347515	+	0.937674i	$0.387026\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	−0.914275	−	4.29416i	−0.0465958	−	0.218851i
$386$	0.885971	+	1.53455i	0.0450947	+	0.0781063i
$387$	6.18273	+	6.18273i	0.314286	+	0.314286i
$388$	11.6429	+	11.6429i	0.591077	+	0.591077i
$389$	−12.1029	+	6.98763i	−0.613642	+	0.354287i	−0.774390	−	0.632709i	$-0.781943\pi$
$389$	−12.1029	+	6.98763i	−0.613642	+	0.354287i	0.160747	+	0.986996i	$0.448610\pi$
$390$	7.91201	+	2.56780i	0.400640	+	0.130026i
$391$	7.95301			0.402201
$392$	−4.88174	+	4.88174i	−0.246565	+	0.246565i
$393$	−0.942531	+	3.51757i	−0.0475444	+	0.177438i
$394$	3.46228	−	5.99684i	0.174427	−	0.302116i
$395$	−28.7566	+	14.6645i	−1.44690	+	0.737851i
$396$	−3.16563	+	5.48304i	−0.159079	+	0.275533i
$397$	4.03846	−	1.08210i	0.202684	−	0.0543091i	−0.156048	−	0.987749i	$-0.549876\pi$
$397$	4.03846	−	1.08210i	0.202684	−	0.0543091i	0.358733	+	0.933440i	$0.383209\pi$
$398$	−5.39351	−	5.39351i	−0.270352	−	0.270352i
$399$	1.34524	+	0.132844i	0.0673461	+	0.00665054i
$400$	4.97296	+	0.519266i	0.248648	+	0.0259633i
$401$	26.2536	+	15.1575i	1.31104	+	0.756931i	0.982269	−	0.187477i	$-0.0600310\pi$
$401$	26.2536	+	15.1575i	1.31104	+	0.756931i	0.328775	+	0.944408i	$0.393364\pi$
$402$	−1.33519	−	4.98299i	−0.0665931	−	0.248529i
$403$	9.75543	+	2.61396i	0.485953	+	0.130211i
$404$	12.0788	+	6.97371i	0.600944	+	0.346955i
$405$	1.99201	−	1.01583i	0.0989836	−	0.0504770i
$406$	2.12566			0.105495
$407$	−5.17817	+	5.17817i	−0.256672	+	0.256672i
$408$	3.30361	+	0.885199i	0.163553	+	0.0438239i
$409$	6.92849	+	12.0005i	0.342592	+	0.593387i	0.984913	−	0.173049i	$-0.0553619\pi$
$409$	6.92849	+	12.0005i	0.342592	+	0.593387i	−0.642321	+	0.766435i	$0.722029\pi$
$410$	16.9046	−	15.2314i	0.834858	−	0.752223i
$411$		−	10.3096i		−	0.508536i
$412$	−7.64876	−	2.04948i	−0.376827	−	0.100971i
$413$	0.220117	−	0.0589802i	0.0108313	−	0.00290223i
$414$	−1.16267	−	2.01380i	−0.0571421	−	0.0989731i
$415$	−0.589431	+	0.125497i	−0.0289340	+	0.00616038i
$416$	1.86002	−	3.22165i	0.0911950	−	0.157954i
$417$	14.5952	−	14.5952i	0.714730	−	0.714730i
$418$	−17.5021	−	21.3376i	−0.856055	−	1.04365i
$419$		−	34.6356i		−	1.69206i	−0.533135	−	0.846030i	$-0.678986\pi$
$419$		−	34.6356i		−	1.69206i	0.533135	−	0.846030i	$-0.321014\pi$
$420$	0.581703	+	0.377482i	0.0283842	+	0.0184192i
$421$	−11.2641	−	6.50334i	−0.548979	−	0.316953i	0.199731	−	0.979851i	$-0.435993\pi$
$421$	−11.2641	−	6.50334i	−0.548979	−	0.316953i	−0.748710	+	0.662898i	$0.769326\pi$
$422$	0.0510720	−	0.190603i	0.00248614	−	0.00927842i
$423$	−2.73086	−	10.1917i	−0.132779	−	0.495538i
$424$	−3.55524	+	2.05262i	−0.172658	+	0.0996840i
$425$	−10.7709	−	13.2825i	−0.522463	−	0.644294i
$426$		−	1.32692i		−	0.0642894i
$427$	0.348560	−	1.30084i	0.0168680	−	0.0629522i
$428$	1.23225	−	4.59881i	0.0595629	−	0.222292i
$429$		−	23.5526i		−	1.13713i
$430$	−19.5251	−	1.01662i	−0.941582	−	0.0490257i
$431$	19.2452	−	11.1112i	0.927007	−	0.535208i	0.0411431	−	0.999153i	$-0.486900\pi$
$431$	19.2452	−	11.1112i	0.927007	−	0.535208i	0.885864	+	0.463946i	$0.153567\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	2.99353	−	11.1720i	0.143860	−	0.536892i	−0.855944	−	0.517069i	$-0.827023\pi$
$433$	2.99353	−	11.1720i	0.143860	−	0.536892i	0.999804	−	0.0198230i	$-0.00631027\pi$
$434$	0.729147	+	0.420973i	0.0350002	+	0.0202074i
$435$	3.19169	+	14.9907i	0.153030	+	0.718750i
$436$		−	10.0772i		−	0.482610i
$437$	10.0010	−	1.64852i	0.478411	−	0.0788593i
$438$	3.40693	−	3.40693i	0.162790	−	0.162790i
$439$	5.66009	−	9.80357i	0.270141	−	0.467899i	−0.698756	−	0.715360i	$-0.746263\pi$
$439$	5.66009	−	9.80357i	0.270141	−	0.467899i	0.968898	+	0.247461i	$0.0795962\pi$
$440$	−2.94814	−	13.8468i	−0.140547	−	0.660119i
$441$	−3.45191	−	5.97889i	−0.164377	−	0.284709i
$442$	−12.2896	+	3.29298i	−0.584554	+	0.156631i
$443$	35.8387	+	9.60294i	1.70275	+	0.456250i	0.973629	−	0.228138i	$-0.0732638\pi$
$443$	35.8387	+	9.60294i	1.70275	+	0.456250i	0.729118	+	0.684388i	$0.239931\pi$
$444$		−	1.15665i		−	0.0548920i
$445$	1.20499	−	23.1430i	0.0571222	−	1.09708i
$446$	−6.28931	−	10.8934i	−0.297807	−	0.515817i
$447$	18.6755	+	5.00408i	0.883320	+	0.236685i
$448$	0.219288	−	0.219288i	0.0103604	−	0.0103604i
$449$	−27.2788			−1.28737			−0.643683	−	0.765292i	$-0.722594\pi$
$449$	−27.2788			−1.28737			−0.643683	+	0.765292i	$0.722594\pi$
$450$	−1.78867	+	4.66912i	−0.0843187	+	0.220104i
$451$	−55.7956	−	32.2136i	−2.62731	−	1.51688i
$452$	18.8859	+	5.06045i	0.888316	+	0.238024i
$453$	0.0663064	+	0.247459i	0.00311535	+	0.0116266i
$454$	−4.37146	−	2.52387i	−0.205163	−	0.118451i
$455$	−2.57617	−	0.134134i	−0.120773	−	0.00628831i
$456$	4.33780	+	0.428365i	0.203136	+	0.0200600i
$457$	−9.33785	−	9.33785i	−0.436806	−	0.436806i	0.454129	−	0.890936i	$-0.349950\pi$
$457$	−9.33785	−	9.33785i	−0.436806	−	0.436806i	−0.890936	+	0.454129i	$0.849950\pi$
$458$	−22.1442	+	5.93353i	−1.03473	+	0.277256i
$459$	−1.71007	+	2.96193i	−0.0798194	+	0.138251i
$460$	4.94568	+	1.60509i	0.230593	+	0.0748378i
$461$	−5.69535	+	9.86464i	−0.265259	+	0.459442i	−0.967631	−	0.252368i	$-0.918791\pi$
$461$	−5.69535	+	9.86464i	−0.265259	+	0.459442i	0.702372	+	0.711810i	$0.252124\pi$
$462$	0.508178	−	1.89655i	0.0236426	−	0.0882354i
$463$	−20.8423	+	20.8423i	−0.968626	+	0.968626i	−0.999523	−	0.0308970i	$-0.990164\pi$
$463$	−20.8423	+	20.8423i	−0.968626	+	0.968626i	0.0308970	+	0.999523i	$0.490164\pi$
$464$	6.85432			0.318204
$465$	−1.87400	+	5.77423i	−0.0869045	+	0.267774i
$466$	5.42732	−	3.13347i	0.251416	−	0.145155i
$467$	−14.6449	−	14.6449i	−0.677687	−	0.677687i	0.281790	−	0.959476i	$-0.409072\pi$
$467$	−14.6449	−	14.6449i	−0.677687	−	0.677687i	−0.959476	+	0.281790i	$0.909072\pi$
$468$	2.63047	+	2.63047i	0.121593	+	0.121593i
$469$	0.799917	+	1.38550i	0.0369368	+	0.0639763i
$470$	19.7913	+	12.8431i	0.912906	+	0.592408i
$471$	−8.34953	+	4.82061i	−0.384726	+	0.222122i
$472$	0.709781	−	0.190185i	0.0326703	−	0.00875399i
$473$	14.3279	+	53.4724i	0.658797	+	2.45866i
$474$	−14.4360			−0.663067
$475$	−16.2977	−	14.4702i	−0.747788	−	0.663938i
$476$	−1.06065			−0.0486150
$477$	−1.06251	−	3.96536i	−0.0486492	−	0.181561i
$478$	−21.8251	+	5.84802i	−0.998257	+	0.267482i
$479$	1.00693	−	0.581352i	0.0460079	−	0.0265627i	−0.476820	−	0.879001i	$-0.658211\pi$
$479$	1.00693	−	0.581352i	0.0460079	−	0.0265627i	0.522828	+	0.852438i	$0.324877\pi$
$480$	1.87574	+	1.21721i	0.0856153	+	0.0555579i
$481$	2.15139	+	3.72631i	0.0980948	+	0.169905i
$482$	−0.0655253	−	0.0655253i	−0.00298460	−	0.00298460i
$483$	0.509919	+	0.509919i	0.0232021	+	0.0232021i
$484$	−25.1883	+	14.5425i	−1.14492	+	0.661022i
$485$	11.3655	−	35.0198i	0.516080	−	1.59017i
$486$	1.00000			0.0453609
$487$	5.04003	−	5.04003i	0.228386	−	0.228386i	−0.583632	−	0.812018i	$-0.698369\pi$
$487$	5.04003	−	5.04003i	0.228386	−	0.228386i	0.812018	+	0.583632i	$0.198369\pi$
$488$	1.12395	−	4.19465i	0.0508789	−	0.189883i
$489$	−0.0143985	+	0.0249390i	−0.000651124	+	0.00112778i
$490$	14.6835	+	4.76544i	0.663332	+	0.215281i
$491$	6.22692	−	10.7853i	0.281017	−	0.486736i	−0.690618	−	0.723219i	$-0.742662\pi$
$491$	6.22692	−	10.7853i	0.281017	−	0.486736i	0.971636	+	0.236483i	$0.0759949\pi$
$492$	9.82930	−	2.63375i	0.443139	−	0.118739i
$493$	−16.5765	−	16.5765i	−0.746570	−	0.746570i
$494$	−14.7716	+	6.68835i	−0.664607	+	0.300923i
$495$	14.1380	+	0.736129i	0.635456	+	0.0330865i
$496$	2.35118	+	1.35745i	0.105571	+	0.0609515i
$497$	0.106505	+	0.397482i	0.00477740	+	0.0178295i
$498$	−0.260327	−	0.0697543i	−0.0116655	−	0.00312577i
$499$	18.2705	+	10.5485i	0.817900	+	0.472215i	0.849692	−	0.527280i	$-0.176788\pi$
$499$	18.2705	+	10.5485i	0.817900	+	0.472215i	−0.0317917	+	0.999495i	$0.510121\pi$
$500$	−4.01730	−	10.4337i	−0.179659	−	0.466607i
$501$	−1.80618			−0.0806940
$502$	−6.49294	+	6.49294i	−0.289794	+	0.289794i
$503$	23.0795	+	6.18413i	1.02906	+	0.275737i	0.733574	−	0.679610i	$-0.237851\pi$
$503$	23.0795	+	6.18413i	1.02906	+	0.275737i	0.295489	+	0.955346i	$0.404517\pi$
$504$	0.155060	+	0.268571i	0.00690691	+	0.0119631i
$505$	1.62165	−	31.1452i	0.0721625	−	1.38594i
$506$		−	14.7224i		−	0.654489i
$507$	−0.810123	−	0.217072i	−0.0359788	−	0.00964050i
$508$	14.1220	−	3.78398i	0.626562	−	0.167887i
$509$	4.73071	+	8.19383i	0.209685	+	0.363185i	0.951615	−	0.307292i	$-0.0994228\pi$
$509$	4.73071	+	8.19383i	0.209685	+	0.363185i	−0.741930	+	0.670477i	$0.766089\pi$
$510$	−1.59258	−	7.48002i	−0.0705207	−	0.331221i
$511$	−0.747099	+	1.29401i	−0.0330497	+	0.0572438i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.53647	+	4.07912i	−0.0678370	+	0.180098i
$514$			8.06321i			0.355653i
$515$	3.68726	+	17.3183i	0.162480	+	0.763135i
$516$	−7.57227	−	4.37185i	−0.333351	−	0.192460i
$517$	17.2898	−	64.5264i	0.760405	−	2.83787i
$518$	0.0928381	+	0.346476i	0.00407907	+	0.0152233i
$519$	19.9724	−	11.5311i	0.876690	−	0.506157i
$520$	−8.30701	−	0.432524i	−0.364287	−	0.0189674i
$521$			38.6070i			1.69140i	0.533656	+	0.845702i	$0.320818\pi$
$521$			38.6070i			1.69140i	−0.533656	+	0.845702i	$0.679182\pi$
$522$	−1.77403	+	6.62077i	−0.0776471	+	0.289783i
$523$	−9.86642	+	36.8220i	−0.431428	+	1.61011i	0.318043	+	0.948076i	$0.396974\pi$
$523$	−9.86642	+	36.8220i	−0.431428	+	1.61011i	−0.749472	+	0.662037i	$0.769692\pi$
$524$		−	3.64166i		−	0.159087i
$525$	0.161035	−	1.54221i	0.00702813	−	0.0673077i
$526$	−12.9801	+	7.49405i	−0.565959	+	0.326756i
$527$	−2.40323	−	8.96899i	−0.104687	−	0.390695i
$528$	1.63865	−	6.11554i	0.0713132	−	0.266145i
$529$	−15.2358	−	8.79639i	−0.662426	−	0.382452i
$530$	7.70035	+	4.99695i	0.334482	+	0.217054i
$531$			0.734820i			0.0318885i
$532$	−1.33378	+	0.219855i	−0.0578268	+	0.00953192i
$533$	−26.7677	+	26.7677i	−1.15944	+	1.15944i
$534$	5.18194	−	8.97538i	0.224244	−	0.388402i
$535$	−10.4126	+	2.21696i	−0.450176	+	0.0958476i
$536$	2.57938	+	4.46762i	0.111412	+	0.192972i
$537$	14.4064	−	3.86017i	0.621680	−	0.166579i
$538$	−1.67488	−	0.448783i	−0.0722092	−	0.0193484i
$539$		−	43.7100i		−	1.88272i
$540$	−1.66121	+	1.49679i	−0.0714873	+	0.0644114i
$541$	22.8304	+	39.5434i	0.981554	+	1.70010i	0.656347	+	0.754459i	$0.272101\pi$
$541$	22.8304	+	39.5434i	0.981554	+	1.70010i	0.325208	+	0.945643i	$0.394566\pi$
$542$	−0.890012	−	0.238478i	−0.0382293	−	0.0102435i
$543$	3.22940	−	3.22940i	0.138587	−	0.138587i
$544$	−3.42015			−0.146638
$545$	−20.0738	+	10.2367i	−0.859868	+	0.438492i
$546$	−0.999097	−	0.576829i	−0.0427574	−	0.0246860i
$547$	43.2001	+	11.5754i	1.84710	+	0.494930i	0.999370	−	0.0354931i	$-0.0113002\pi$
$547$	43.2001	+	11.5754i	1.84710	+	0.494930i	0.847733	+	0.530423i	$0.177967\pi$
$548$	2.66833	+	9.95833i	0.113985	+	0.425399i
$549$	3.76082	+	2.17131i	0.160508	+	0.0926692i
$550$	−24.5881	+	19.9387i	−1.04844	+	0.850188i
$551$	−24.2812	−	17.4091i	−1.03441	−	0.741653i
$552$	1.64426	+	1.64426i	0.0699845	+	0.0699845i
$553$	4.32434	−	1.15870i	0.183889	−	0.0492730i
$554$	−0.927905	+	1.60718i	−0.0394229	+	0.0682825i
$555$	−2.30405	+	1.17496i	−0.0978014	+	0.0498741i
$556$	−10.3204	+	17.8754i	−0.437681	+	0.758086i
$557$	−4.94082	+	18.4394i	−0.209349	+	0.781302i	0.778730	+	0.627359i	$0.215864\pi$
$557$	−4.94082	+	18.4394i	−0.209349	+	0.781302i	−0.988080	+	0.153943i	$0.950803\pi$
$558$	−1.91973	+	1.91973i	−0.0812687	+	0.0812687i
$559$	32.5269			1.37574
$560$	−0.659581	−	0.214064i	−0.0278724	−	0.00904583i
$561$	−18.7528	+	10.8269i	−0.791744	+	0.457113i
$562$	14.0736	+	14.0736i	0.593659	+	0.593659i
$563$	−22.6314	−	22.6314i	−0.953800	−	0.953800i	0.0451787	−	0.998979i	$-0.485614\pi$
$563$	−22.6314	−	22.6314i	−0.953800	−	0.953800i	−0.998979	+	0.0451787i	$0.985614\pi$
$564$	5.27562	+	9.13763i	0.222143	+	0.384764i
$565$	−9.10437	−	42.7613i	−0.383024	−	1.79898i
$566$	−27.1633	+	15.6828i	−1.14176	+	0.659195i
$567$	−0.299553	+	0.0802649i	−0.0125800	+	0.00337081i
$568$	0.343432	+	1.28170i	0.0144101	+	0.0537791i
$569$	21.8851			0.917470			0.458735	−	0.888573i	$-0.348303\pi$
$569$	21.8851			0.917470			0.458735	+	0.888573i	$0.348303\pi$
$570$	−3.55316	−	9.07607i	−0.148825	−	0.380155i
$571$	−7.33723			−0.307053			−0.153527	−	0.988145i	$-0.549063\pi$
$571$	−7.33723			−0.307053			−0.153527	+	0.988145i	$0.549063\pi$
$572$	6.09586	+	22.7500i	0.254881	+	0.951227i
$573$	−16.8706	+	4.52047i	−0.704781	+	0.188846i
$574$	−2.73300	+	1.57790i	−0.114073	+	0.0658601i
$575$	−1.82661	−	11.4823i	−0.0761751	−	0.478846i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	18.6090	+	18.6090i	0.774705	+	0.774705i	0.978925	−	0.204220i	$-0.0654659\pi$
$577$	18.6090	+	18.6090i	0.774705	+	0.774705i	−0.204220	+	0.978925i	$0.565466\pi$
$578$	−3.74950	−	3.74950i	−0.155959	−	0.155959i
$579$	1.53455	−	0.885971i	0.0637736	−	0.0368197i
$580$	−6.96282	−	13.6539i	−0.289116	−	0.566945i
$581$	0.0835804			0.00346750
$582$	11.6429	−	11.6429i	0.482612	−	0.482612i
$583$	6.72706	−	25.1057i	0.278606	−	1.03977i
$584$	−2.40907	+	4.17262i	−0.0996879	+	0.172664i
$585$	2.56780	−	7.91201i	0.106165	−	0.327121i
$586$	−5.82413	+	10.0877i	−0.240593	+	0.416719i
$587$	36.0445	−	9.65810i	1.48772	−	0.398632i	0.578751	−	0.815504i	$-0.303540\pi$
$587$	36.0445	−	9.65810i	1.48772	−	0.398632i	0.908965	+	0.416872i	$0.136874\pi$
$588$	4.88174	+	4.88174i	0.201320	+	0.201320i
$589$	−4.88120	−	10.7804i	−0.201126	−	0.444200i
$590$	−1.09987	−	1.22069i	−0.0452808	−	0.0502551i
$591$	−5.99684	−	3.46228i	−0.246677	−	0.142419i
$592$	0.299362	+	1.11723i	0.0123037	+	0.0459181i
$593$	−23.3500	−	6.25662i	−0.958871	−	0.256929i	−0.254749	−	0.967007i	$-0.581993\pi$
$593$	−23.3500	−	6.25662i	−0.958871	−	0.256929i	−0.704122	+	0.710079i	$0.748659\pi$
$594$	5.48304	+	3.16563i	0.224972	+	0.129888i
$595$	1.07744	+	2.11283i	0.0441709	+	0.0866176i
$596$	−19.3343			−0.791963
$597$	−5.39351	+	5.39351i	−0.220742	+	0.220742i
$598$	−8.35561	−	2.23888i	−0.341686	−	0.0915546i
$599$	−9.76934	−	16.9210i	−0.399165	−	0.691373i	0.594459	−	0.804126i	$-0.297366\pi$
$599$	−9.76934	−	16.9210i	−0.399165	−	0.691373i	−0.993623	+	0.112753i	$0.964033\pi$
$600$	0.519266	−	4.97296i	0.0211990	−	0.203020i
$601$			22.9520i			0.936231i	0.883667	+	0.468116i	$0.155067\pi$
$601$			22.9520i			0.936231i	−0.883667	+	0.468116i	$0.844933\pi$
$602$	2.61920	+	0.701812i	0.106751	+	0.0286037i
$603$	−4.98299	+	1.33519i	−0.202923	+	0.0543730i
$604$	−0.128094	−	0.221865i	−0.00521207	−	0.00902758i
$605$	54.5558	+	35.4026i	2.21801	+	1.43932i
$606$	6.97371	−	12.0788i	0.283288	−	0.490669i
$607$	11.8605	−	11.8605i	0.481402	−	0.481402i	−0.424177	−	0.905579i	$-0.639437\pi$
$607$	11.8605	−	11.8605i	0.481402	−	0.481402i	0.905579	+	0.424177i	$0.139437\pi$
$608$	−4.30086	+	0.708936i	−0.174423	+	0.0287512i
$609$		−	2.12566i		−	0.0861361i
$610$	−9.49751	+	2.02213i	−0.384543	+	0.0818736i
$611$	−33.9924	−	19.6255i	−1.37518	−	0.793963i
$612$	0.885199	−	3.30361i	0.0357820	−	0.133540i
$613$	7.04726	+	26.3007i	0.284636	+	1.06228i	0.949105	+	0.314961i	$0.101991\pi$
$613$	7.04726	+	26.3007i	0.284636	+	1.06228i	−0.664468	+	0.747316i	$0.731342\pi$
$614$	−3.65584	+	2.11070i	−0.147538	+	0.0851810i
$615$	−15.2314	−	16.9046i	−0.614188	−	0.681659i
$616$			1.96345i			0.0791097i
$617$	6.58811	−	24.5872i	0.265227	−	0.989842i	−0.696884	−	0.717184i	$-0.745431\pi$
$617$	6.58811	−	24.5872i	0.265227	−	0.989842i	0.962111	−	0.272658i	$-0.0879028\pi$
$618$	−2.04948	+	7.64876i	−0.0824421	+	0.307678i
$619$		−	4.00889i		−	0.161131i	−0.996749	−	0.0805654i	$-0.974327\pi$
$619$		−	4.00889i		−	0.161131i	0.996749	−	0.0805654i	$-0.0256726\pi$
$620$	0.315659	−	6.06251i	0.0126772	−	0.243476i
$621$	−2.01380	+	1.16267i	−0.0808112	+	0.0466564i
$622$	−2.86721	−	10.7006i	−0.114965	−	0.429054i
$623$	−0.831855	+	3.10452i	−0.0333276	+	0.124380i
$624$	−3.22165	−	1.86002i	−0.128969	−	0.0744604i
$625$	−16.7030	+	18.6013i	−0.668121	+	0.744053i
$626$		−	22.5831i		−	0.902600i
$627$	−21.3376	+	17.5021i	−0.852140	+	0.698966i
$628$	6.81737	−	6.81737i	0.272043	−	0.272043i
$629$	1.97795	−	3.42591i	0.0788661	−	0.136600i
$630$	0.377482	−	0.581703i	0.0150392	−	0.0231756i
$631$	−5.52757	−	9.57403i	−0.220049	−	0.381136i	0.734774	−	0.678312i	$-0.237288\pi$
$631$	−5.52757	−	9.57403i	−0.220049	−	0.381136i	−0.954823	+	0.297176i	$0.903955\pi$
$632$	13.9441	−	3.73631i	0.554666	−	0.148622i
$633$	−0.190603	−	0.0510720i	−0.00757579	−	0.00202993i
$634$		−	18.3504i		−	0.728788i
$635$	−21.8833	−	24.2872i	−0.868411	−	0.963810i
$636$	2.05262	+	3.55524i	0.0813917	+	0.140974i
$637$	−24.8074	−	6.64712i	−0.982905	−	0.263369i
$638$	−30.6860	+	30.6860i	−1.21487	+	1.21487i
$639$	−1.32692			−0.0524921
$640$	−2.12686	−	0.690261i	−0.0840716	−	0.0272850i
$641$	−38.7197	−	22.3548i	−1.52934	−	0.882963i	−0.999390	−	0.0349331i	$-0.988878\pi$
$641$	−38.7197	−	22.3548i	−1.52934	−	0.882963i	−0.529948	−	0.848030i	$-0.677788\pi$
$642$	−4.59881	−	1.23225i	−0.181500	−	0.0486329i
$643$	6.15697	+	22.9781i	0.242807	+	0.906169i	0.974473	+	0.224505i	$0.0720766\pi$
$643$	6.15697	+	22.9781i	0.242807	+	0.906169i	−0.731666	+	0.681664i	$0.761257\pi$
$644$	−0.624520	−	0.360567i	−0.0246095	−	0.0142083i
$645$	−1.01662	+	19.5251i	−0.0400293	+	0.768799i
$646$	12.1157	+	8.68674i	0.476687	+	0.341775i
$647$	20.9244	+	20.9244i	0.822622	+	0.822622i	0.986483	−	0.163862i	$-0.0523951\pi$
$647$	20.9244	+	20.9244i	0.822622	+	0.822622i	−0.163862	+	0.986483i	$0.552395\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−2.32617	+	4.02905i	−0.0913102	+	0.158154i
$650$	7.57692	+	16.9870i	0.297191	+	0.666285i
$651$	0.420973	−	0.729147i	0.0164992	−	0.0285775i
$652$	0.00745323	−	0.0278158i	0.000291891	−	0.00108935i
$653$	30.2481	−	30.2481i	1.18370	−	1.18370i	0.204920	−	0.978779i	$-0.434306\pi$
$653$	30.2481	−	30.2481i	1.18370	−	1.18370i	0.978779	−	0.204920i	$-0.0656935\pi$
$654$	−10.0772			−0.394049
$655$	−7.25421	+	3.69931i	−0.283445	+	0.144544i
$656$	−8.81271	+	5.08802i	−0.344079	+	0.198654i
$657$	−3.40693	−	3.40693i	−0.132917	−	0.132917i
$658$	−2.31375	−	2.31375i	−0.0901996	−	0.0901996i
$659$	−13.4067	−	23.2211i	−0.522252	−	0.904567i	−0.999665	−	0.0258876i	$-0.991759\pi$
$659$	−13.4067	−	23.2211i	−0.522252	−	0.904567i	0.477413	−	0.878679i	$-0.341575\pi$
$660$	−13.8468	+	2.94814i	−0.538985	+	0.114756i
$661$	7.07026	−	4.08202i	0.275001	−	0.158772i	−0.356157	−	0.934426i	$-0.615913\pi$
$661$	7.07026	−	4.08202i	0.275001	−	0.158772i	0.631158	+	0.775654i	$0.282580\pi$
$662$	1.57987	−	0.423325i	0.0614034	−	0.0164530i
$663$	3.29298	+	12.2896i	0.127889	+	0.477287i
$664$	0.269510			0.0104590
$665$	1.79285	+	2.43357i	0.0695237	+	0.0943697i
$666$	−1.15665			−0.0448192
$667$	−4.12522	−	15.3955i	−0.159729	−	0.596118i
$668$	1.74463	−	0.467473i	0.0675018	−	0.0180871i
$669$	−10.8934	+	6.28931i	−0.421163	+	0.243159i
$670$	6.27932	−	9.67649i	0.242591	−	0.373836i
$671$	13.7471	+	23.8108i	0.530703	+	0.919204i
$672$	−0.219288	−	0.219288i	−0.00845921	−	0.00845921i
$673$	−19.6072	−	19.6072i	−0.755803	−	0.755803i	0.219752	−	0.975556i	$-0.429475\pi$
$673$	−19.6072	−	19.6072i	−0.755803	−	0.755803i	−0.975556	+	0.219752i	$0.929475\pi$
$674$	−0.461027	+	0.266174i	−0.0177581	+	0.0102526i
$675$	4.66912	+	1.78867i	0.179714	+	0.0688459i
$676$	0.838701			0.0322577
$677$	17.7081	−	17.7081i	0.680577	−	0.680577i	−0.279553	−	0.960130i	$-0.590186\pi$
$677$	17.7081	−	17.7081i	0.680577	−	0.680577i	0.960130	+	0.279553i	$0.0901863\pi$
$678$	5.06045	−	18.8859i	0.194345	−	0.725307i
$679$	−2.55314	+	4.42216i	−0.0979804	+	0.169707i
$680$	3.47429	+	6.81295i	0.133233	+	0.261265i
$681$	−2.52387	+	4.37146i	−0.0967148	+	0.167515i
$682$	−16.6031	+	4.44879i	−0.635766	+	0.170353i
$683$	−26.8964	−	26.8964i	−1.02916	−	1.02916i	−0.999562	−	0.0295985i	$-0.990577\pi$
$683$	−26.8964	−	26.8964i	−1.02916	−	1.02916i	−0.0295985	−	0.999562i	$-0.509423\pi$
$684$	0.428365	−	4.33780i	0.0163790	−	0.165860i
$685$	17.1265	−	15.4313i	0.654370	−	0.589599i
$686$	−3.73417	−	2.15592i	−0.142571	−	0.0823136i
$687$	5.93353	+	22.1442i	0.226378	+	0.844855i
$688$	8.44577	+	2.26304i	0.321992	+	0.0862775i
$689$	−13.2256	−	7.63583i	−0.503857	−	0.290902i
$690$	1.60509	−	4.94568i	0.0611048	−	0.188279i
$691$	10.0289			0.381516			0.190758	−	0.981637i	$-0.438905\pi$
$691$	10.0289			0.381516			0.190758	+	0.981637i	$0.438905\pi$
$692$	−16.3074	+	16.3074i	−0.619913	+	0.619913i
$693$	−1.89655	−	0.508178i	−0.0720439	−	0.0193041i
$694$	−0.969124	−	1.67857i	−0.0367874	−	0.0637177i
$695$	46.0917	+	2.39987i	1.74836	+	0.0910324i
$696$		−	6.85432i		−	0.259812i
$697$	33.6177	+	9.00782i	1.27336	+	0.341196i
$698$	20.5940	−	5.51814i	0.779494	−	0.208865i
$699$	−3.13347	−	5.42732i	−0.118519	−	0.205280i
$700$	0.243607	+	1.53134i	0.00920747	+	0.0578793i
$701$	−18.8206	+	32.5983i	−0.710845	+	1.23122i	0.253696	+	0.967284i	$0.418354\pi$
$701$	−18.8206	+	32.5983i	−0.710845	+	1.23122i	−0.964540	+	0.263935i	$0.914980\pi$
$702$	2.63047	−	2.63047i	0.0992805	−	0.0992805i
$703$	1.77716	−	4.71810i	0.0670268	−	0.177947i
$704$			6.33127i			0.238619i
$705$	12.8431	−	19.7913i	0.483699	−	0.745385i
$706$	22.4506	+	12.9618i	0.844939	+	0.487826i
$707$	−1.11949	+	4.17799i	−0.0421027	+	0.157129i
$708$	−0.190185	−	0.709781i	−0.00714760	−	0.0266752i
$709$	−0.257513	+	0.148675i	−0.00967110	+	0.00558361i	−0.504828	−	0.863220i	$-0.668444\pi$
$709$	−0.257513	+	0.148675i	−0.00967110	+	0.00558361i	0.495157	+	0.868804i	$0.335111\pi$
$710$	2.20429	−	1.98611i	0.0827257	−	0.0745374i
$711$			14.4360i			0.541392i
$712$	−2.68237	+	10.0107i	−0.100526	+	0.375168i
$713$	1.63395	−	6.09797i	0.0611918	−	0.228371i
$714$			1.06065i			0.0396940i
$715$	39.1259	−	35.2532i	1.46322	−	1.31839i
$716$	−12.9164	+	7.45728i	−0.482708	+	0.278692i
$717$	5.84802	+	21.8251i	0.218398	+	0.815074i
$718$	−8.05073	+	30.0457i	−0.300451	+	1.12130i
$719$	−10.2040	−	5.89129i	−0.380546	−	0.219708i	0.297510	−	0.954719i	$-0.403844\pi$
$719$	−10.2040	−	5.89129i	−0.380546	−	0.219708i	−0.678056	+	0.735011i	$0.737177\pi$
$720$	1.21721	−	1.87574i	0.0453629	−	0.0699046i
$721$		−	2.45571i		−	0.0914553i
$722$	17.0362	+	8.41227i	0.634023	+	0.313072i
$723$	−0.0655253	+	0.0655253i	−0.00243691	+	0.00243691i
$724$	−2.28353	+	3.95519i	−0.0848667	+	0.146993i
$725$	−20.1255	+	27.7400i	−0.747443	+	1.03024i
$726$	14.5425	+	25.1883i	0.539722	+	0.934826i
$727$	3.21708	−	0.862014i	0.119315	−	0.0319703i	−0.198668	−	0.980067i	$-0.563661\pi$
$727$	3.21708	−	0.862014i	0.119315	−	0.0319703i	0.317982	+	0.948097i	$0.396995\pi$
$728$	1.11435	+	0.298589i	0.0413005	+	0.0110664i
$729$		−	1.00000i		−	0.0370370i
$730$	10.7591	+	0.560198i	0.398212	+	0.0207339i
$731$	−14.9524	−	25.8983i	−0.553033	−	0.957882i
$732$	−4.19465	−	1.12395i	−0.155039	−	0.0415425i
$733$	−2.34690	+	2.34690i	−0.0866846	+	0.0866846i	−0.749120	−	0.662435i	$-0.769523\pi$
$733$	−2.34690	+	2.34690i	−0.0866846	+	0.0866846i	0.662435	+	0.749120i	$0.269523\pi$
$734$	−29.8289			−1.10101
$735$	4.76544	−	14.6835i	0.175776	−	0.541608i
$736$	−2.01380	−	1.16267i	−0.0742298	−	0.0428566i
$737$	−31.5486	−	8.45343i	−1.16211	−	0.311386i
$738$	−2.63375	−	9.82930i	−0.0969498	−	0.361822i
$739$	−28.6071	−	16.5163i	−1.05233	−	0.607562i	−0.129028	−	0.991641i	$-0.541186\pi$
$739$	−28.6071	−	16.5163i	−1.05233	−	0.607562i	−0.923300	+	0.384079i	$0.874519\pi$
$740$	1.92144	−	1.73125i	0.0706335	−	0.0636421i
$741$	6.68835	+	14.7716i	0.245703	+	0.542650i
$742$	−0.900228	−	0.900228i	−0.0330484	−	0.0330484i
$743$	−21.2907	+	5.70483i	−0.781081	+	0.209290i	−0.627261	−	0.778809i	$-0.715824\pi$
$743$	−21.2907	+	5.70483i	−0.781081	+	0.209290i	−0.153820	+	0.988099i	$0.549157\pi$
$744$	1.35745	−	2.35118i	0.0497667	−	0.0861984i
$745$	19.6403	+	38.5140i	0.719566	+	1.41104i
$746$	9.45339	−	16.3737i	0.346113	−	0.599486i
$747$	−0.0697543	+	0.260327i	−0.00255218	+	0.00952486i
$748$	15.3116	−	15.3116i	0.559847	−	0.559847i
$749$	1.47649			0.0539498
$750$	−10.4337	+	4.01730i	−0.380983	+	0.146691i
$751$	40.4682	−	23.3643i	1.47671	−	0.852577i	0.477053	−	0.878875i	$-0.341705\pi$
$751$	40.4682	−	23.3643i	1.47671	−	0.852577i	0.999654	+	0.0262976i	$0.00837175\pi$
$752$	−7.46085	−	7.46085i	−0.272069	−	0.272069i
$753$	6.49294	+	6.49294i	0.236616	+	0.236616i
$754$	12.7492	+	22.0822i	0.464298	+	0.804187i
$755$	−0.311836	+	0.480542i	−0.0113489	+	0.0174887i
$756$	0.268571	−	0.155060i	0.00976785	−	0.00563947i
$757$	0.0766719	−	0.0205442i	0.00278669	−	0.000746691i	−0.257425	−	0.966298i	$-0.582874\pi$
$757$	0.0766719	−	0.0205442i	0.00278669	−	0.000746691i	0.260212	+	0.965551i	$0.416208\pi$
$758$	−8.31837	−	31.0446i	−0.302137	−	1.12759i
$759$	−14.7224			−0.534388
$760$	5.78115	+	7.84719i	0.209704	+	0.284647i
$761$	18.4883			0.670201			0.335101	−	0.942182i	$-0.391230\pi$
$761$	18.4883			0.670201			0.335101	+	0.942182i	$0.391230\pi$
$762$	−3.78398	−	14.1220i	−0.137079	−	0.511586i
$763$	3.01865	−	0.808844i	0.109282	−	0.0292821i
$764$	15.1258	−	8.73289i	0.547232	−	0.315945i
$765$	−7.48002	+	1.59258i	−0.270441	+	0.0575799i
$766$	1.81976	+	3.15192i	0.0657508	+	0.113884i
$767$	1.93292	+	1.93292i	0.0697936	+	0.0697936i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	10.6383	−	6.14205i	0.383628	−	0.221488i	−0.295767	−	0.955260i	$-0.595575\pi$
$769$	10.6383	−	6.14205i	0.383628	−	0.221488i	0.679396	+	0.733772i	$0.262242\pi$
$770$	3.91121	−	1.99453i	0.140950	−	0.0718779i
$771$	8.06321			0.290390
$772$	−1.25295	+	1.25295i	−0.0450947	+	0.0450947i
$773$	−0.795386	+	2.96842i	−0.0286081	+	0.106767i	−0.978754	−	0.205040i	$-0.934268\pi$
$773$	−0.795386	+	2.96842i	−0.0286081	+	0.106767i	0.950146	+	0.311807i	$0.100934\pi$
$774$	−4.37185	+	7.57227i	−0.157143	+	0.272180i
$775$	−12.3972	+	5.52968i	−0.445321	+	0.198632i
$776$	−8.23275	+	14.2595i	−0.295538	+	0.511888i
$777$	0.346476	−	0.0928381i	0.0124298	−	0.00333055i
$778$	−9.88199	−	9.88199i	−0.354287	−	0.354287i
$779$	44.1416	+	4.35906i	1.58154	+	0.156180i
$780$	−0.432524	+	8.30701i	−0.0154869	+	0.297439i
$781$	−7.27554	−	4.20054i	−0.260339	−	0.150307i
$782$	2.05839	+	7.68201i	0.0736079	+	0.274708i
$783$	6.62077	+	1.77403i	0.236607	+	0.0633986i
$784$	−5.97889	−	3.45191i	−0.213532	−	0.123283i
$785$	−20.5055	−	6.65495i	−0.731873	−	0.237525i
$786$	−3.64166			−0.129894
$787$	16.0590	−	16.0590i	0.572443	−	0.572443i	−0.360367	−	0.932810i	$-0.617349\pi$
$787$	16.0590	−	16.0590i	0.572443	−	0.572443i	0.932810	+	0.360367i	$0.117349\pi$
$788$	6.68860	+	1.79221i	0.238272	+	0.0638447i
$789$	7.49405	+	12.9801i	0.266795	+	0.462103i
$790$	−21.6076	−	23.9813i	−0.768763	−	0.853215i
$791$			6.06348i			0.215593i
$792$	−6.11554	−	1.63865i	−0.217306	−	0.0582270i
$793$	15.6043	−	4.18115i	0.554123	−	0.148477i
$794$	2.09046	+	3.62078i	0.0741876	+	0.128497i
$795$	4.99695	−	7.70035i	0.177224	−	0.273103i
$796$	3.81379	−	6.60568i	0.135176	−	0.234132i
$797$	−21.2908	+	21.2908i	−0.754160	+	0.754160i	−0.975253	−	0.221093i	$-0.929038\pi$
$797$	−21.2908	+	21.2908i	−0.754160	+	0.754160i	0.221093	+	0.975253i	$0.429038\pi$
$798$	0.219855	+	1.33378i	0.00778278	+	0.0472154i
$799$			36.0867i			1.27666i
$800$	0.785525	+	4.93791i	0.0277725	+	0.174581i
$801$	−8.97538	−	5.18194i	−0.317129	−	0.183095i
$802$	−7.84612	+	29.2821i	−0.277056	+	1.03399i
$803$	−7.89525	−	29.4655i	−0.278617	−	1.03981i
$804$	4.46762	−	2.57938i	0.157561	−	0.0909678i
$805$	−0.0838453	+	1.61032i	−0.00295516	+	0.0567564i
$806$			10.0996i			0.355742i
$807$	−0.448783	+	1.67488i	−0.0157979	+	0.0589586i
$808$	−3.60986	+	13.4722i	−0.126994	+	0.473950i
$809$		−	10.3294i		−	0.363162i	−0.983376	−	0.181581i	$-0.941878\pi$
$809$		−	10.3294i		−	0.363162i	0.983376	−	0.181581i	$-0.0581215\pi$
$810$	1.49679	+	1.66121i	0.0525917	+	0.0583691i
$811$	6.89851	−	3.98286i	0.242240	−	0.139857i	−0.373966	−	0.927442i	$-0.622002\pi$
$811$	6.89851	−	3.98286i	0.242240	−	0.139857i	0.616206	+	0.787585i	$0.288669\pi$
$812$	0.550161	+	2.05323i	0.0193069	+	0.0720542i
$813$	−0.238478	+	0.890012i	−0.00836379	+	0.0312141i
$814$	−6.34194	−	3.66152i	−0.222285	−	0.128336i
$815$	−0.0629806	+	0.0134093i	−0.00220611	+	0.000469706i
$816$			3.42015i			0.119729i
$817$	−24.1710	−	29.4679i	−0.845636	−	1.03095i
$818$	−9.79837	+	9.79837i	−0.342592	+	0.342592i
$819$	−0.576829	+	0.999097i	−0.0201560	+	0.0349113i
$820$	19.0876	+	12.3864i	0.666568	+	0.432552i
$821$	12.0173	+	20.8146i	0.419407	+	0.726434i	0.995880	−	0.0906824i	$-0.0289048\pi$
$821$	12.0173	+	20.8146i	0.419407	+	0.726434i	−0.576473	+	0.817116i	$0.695571\pi$
$822$	9.95833	−	2.66833i	0.347337	−	0.0930686i
$823$	26.9991	+	7.23439i	0.941129	+	0.252175i	0.696594	−	0.717466i	$-0.254698\pi$
$823$	26.9991	+	7.23439i	0.941129	+	0.252175i	0.244535	+	0.969640i	$0.421365\pi$
$824$		−	7.91858i		−	0.275857i
$825$	19.9387	+	24.5881i	0.694176	+	0.856047i
$826$	0.113941	+	0.197352i	0.00396451	+	0.00686674i
$827$	−45.8870	−	12.2954i	−1.59565	−	0.427552i	−0.651923	−	0.758285i	$-0.726037\pi$
$827$	−45.8870	−	12.2954i	−1.59565	−	0.427552i	−0.943724	+	0.330733i	$0.892704\pi$
$828$	1.64426	−	1.64426i	0.0571421	−	0.0571421i
$829$	10.6170			0.368745			0.184373	−	0.982856i	$-0.440975\pi$
$829$	10.6170			0.368745			0.184373	+	0.982856i	$0.440975\pi$
$830$	−0.273776	−	0.536866i	−0.00950292	−	0.0186349i
$831$	1.60718	+	0.927905i	0.0557524	+	0.0321887i
$832$	3.59328	+	0.962817i	0.124575	+	0.0333797i
$833$	6.11126	+	22.8075i	0.211743	+	0.790234i
$834$	17.8754	+	10.3204i	0.618975	+	0.357365i
$835$	−2.70346	−	3.00045i	−0.0935570	−	0.103835i
$836$	16.0806	−	22.4283i	0.556160	−	0.775698i
$837$	1.91973	+	1.91973i	0.0663556	+	0.0663556i
$838$	33.4554	−	8.96436i	1.15570	−	0.309669i
$839$	6.26045	−	10.8434i	0.216135	−	0.374357i	−0.737488	−	0.675360i	$-0.763988\pi$
$839$	6.26045	−	10.8434i	0.216135	−	0.374357i	0.953623	+	0.301003i	$0.0973216\pi$
$840$	−0.214064	+	0.659581i	−0.00738589	+	0.0227577i
$841$	−8.99086	+	15.5726i	−0.310030	+	0.536987i
$842$	3.36637	−	12.5635i	0.116013	−	0.432966i
$843$	14.0736	−	14.0736i	0.484721	−	0.484721i
$844$	0.197327			0.00679227
$845$	−0.851978	−	1.67070i	−0.0293089	−	0.0574738i
$846$	9.13763	−	5.27562i	0.314158	−	0.181379i
$847$	−6.37797	−	6.37797i	−0.219150	−	0.219150i
$848$	−2.90284	−	2.90284i	−0.0996840	−	0.0996840i
$849$	15.6828	+	27.1633i	0.538231	+	0.932243i
$850$	10.0422	−	13.8416i	0.344443	−	0.474763i
$851$	2.32926	−	1.34480i	0.0798460	−	0.0460991i
$852$	1.28170	−	0.343432i	0.0439105	−	0.0117658i
$853$	−7.23330	−	26.9951i	−0.247664	−	0.924293i	−0.972026	−	0.234874i	$-0.924532\pi$
$853$	−7.23330	−	26.9951i	−0.247664	−	0.924293i	0.724362	−	0.689419i	$-0.242134\pi$
$854$	1.34673			0.0460842
$855$	−9.07607	+	3.55316i	−0.310395	+	0.121516i
$856$	4.76103			0.162729
$857$	9.59390	+	35.8049i	0.327721	+	1.22307i	0.911548	+	0.411195i	$0.134888\pi$
$857$	9.59390	+	35.8049i	0.327721	+	1.22307i	−0.583826	+	0.811879i	$0.698445\pi$
$858$	22.7500	−	6.09586i	0.776674	−	0.208109i
$859$	29.0736	−	16.7857i	0.991979	−	0.572719i	0.0861135	−	0.996285i	$-0.472555\pi$
$859$	29.0736	−	16.7857i	0.991979	−	0.572719i	0.905865	+	0.423566i	$0.139222\pi$
$860$	−4.07148	−	19.1229i	−0.138836	−	0.652085i
$861$	1.57790	+	2.73300i	0.0537745	+	0.0931402i
$862$	15.7136	+	15.7136i	0.535208	+	0.535208i
$863$	−0.511254	−	0.511254i	−0.0174033	−	0.0174033i	0.698352	−	0.715755i	$-0.253917\pi$
$863$	−0.511254	−	0.511254i	−0.0174033	−	0.0174033i	−0.715755	+	0.698352i	$0.753917\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	49.0499	+	15.9189i	1.66775	+	0.541258i
$866$	11.5661			0.393032
$867$	−3.74950	+	3.74950i	−0.127340	+	0.127340i
$868$	−0.217912	+	0.813258i	−0.00739641	+	0.0276038i
$869$	−45.6991	+	79.1531i	−1.55023	+	2.68508i
$870$	−13.6539	+	6.96282i	−0.462909	+	0.236062i
$871$	−9.59541	+	16.6197i	−0.325128	+	0.563138i
$872$	9.73381	−	2.60817i	0.329628	−	0.0883237i
$873$	−11.6429	−	11.6429i	−0.394051	−	0.394051i
$874$	4.18079	+	9.23353i	0.141417	+	0.312329i
$875$	2.80298	−	2.04085i	0.0947581	−	0.0689933i
$876$	4.17262	+	2.40907i	0.140980	+	0.0813948i
$877$	11.8206	+	44.1152i	0.399154	+	1.48966i	0.814588	+	0.580040i	$0.196963\pi$
$877$	11.8206	+	44.1152i	0.399154	+	1.48966i	−0.415434	+	0.909623i	$0.636370\pi$
$878$	10.9345	+	2.92988i	0.369020	+	0.0988786i
$879$	10.0877	+	5.82413i	0.340249	+	0.196443i
$880$	12.6119	−	6.43149i	0.425148	−	0.216806i
$881$	−5.08922			−0.171460			−0.0857301	−	0.996318i	$-0.527322\pi$
$881$	−5.08922			−0.171460			−0.0857301	+	0.996318i	$0.527322\pi$
$882$	4.88174	−	4.88174i	0.164377	−	0.164377i
$883$	6.01323	+	1.61124i	0.202361	+	0.0542225i	0.358576	−	0.933501i	$-0.383262\pi$
$883$	6.01323	+	1.61124i	0.202361	+	0.0542225i	−0.156215	+	0.987723i	$0.549929\pi$
$884$	−6.36154	−	11.0185i	−0.213962	−	0.370593i
$885$	−1.22069	+	1.09987i	−0.0410331	+	0.0369716i
$886$			37.1029i			1.24650i
$887$	46.8634	+	12.5570i	1.57352	+	0.421623i	0.936912	−	0.349564i	$-0.113670\pi$
$887$	46.8634	+	12.5570i	1.57352	+	0.421623i	0.636608	+	0.771188i	$0.280337\pi$
$888$	1.11723	−	0.299362i	0.0374920	−	0.0100459i
$889$	2.26700	+	3.92656i	0.0760328	+	0.131693i
$890$	22.6663	−	4.82591i	0.759775	−	0.161765i
$891$	3.16563	−	5.48304i	0.106053	−	0.183689i
$892$	8.89442	−	8.89442i	0.297807	−	0.297807i
$893$	7.48015	+	45.3794i	0.250314	+	1.51856i
$894$			19.3343i			0.646635i
$895$	27.9758	+	18.1542i	0.935128	+	0.606828i
$896$	0.268571	+	0.155060i	0.00897234	+	0.00518018i
$897$	−2.23888	+	8.35561i	−0.0747540	+	0.278986i
$898$	−7.06027	−	26.3493i	−0.235604	−	0.879287i
$899$	−16.1157	+	9.30443i	−0.537490	+	0.310320i
$900$	−4.97296	−	0.519266i	−0.165765	−	0.0173089i
$901$			14.0405i			0.467757i
$902$	16.6750	−	62.2320i	0.555217	−	2.07210i
$903$	0.701812	−	2.61920i	0.0233548	−	0.0871615i
$904$			19.5521i			0.650293i
$905$	10.1984	+	0.531006i	0.339008	+	0.0176512i
$906$	−0.221865	+	0.128094i	−0.00737099	+	0.00425564i
$907$	3.82540	+	14.2766i	0.127020	+	0.474046i	0.999904	−	0.0138828i	$-0.00441918\pi$
$907$	3.82540	+	14.2766i	0.127020	+	0.474046i	−0.872883	+	0.487929i	$0.837753\pi$
$908$	1.30645	−	4.87573i	0.0433560	−	0.161807i
$909$	−12.0788	−	6.97371i	−0.400629	−	0.231303i
$910$	−0.537197	−	2.52310i	−0.0178079	−	0.0836400i
$911$			40.7085i			1.34873i	0.738397	+	0.674366i	$0.235583\pi$
$911$			40.7085i			1.34873i	−0.738397	+	0.674366i	$0.764417\pi$
$912$	0.708936	+	4.30086i	0.0234752	+	0.142416i
$913$	−1.20656	+	1.20656i	−0.0399315	+	0.0399315i
$914$	6.60286	−	11.4365i	0.218403	−	0.378285i
$915$	2.02213	+	9.49751i	0.0668495	+	0.313978i
$916$	−11.4627	−	19.8540i	−0.378738	−	0.655994i
$917$	1.09087	−	0.292297i	0.0360236	−	0.00965250i
$918$	−3.30361	−	0.885199i	−0.109035	−	0.0292159i
$919$			23.2487i			0.766905i	0.923561	+	0.383453i	$0.125265\pi$
$919$			23.2487i			0.766905i	−0.923561	+	0.383453i	$0.874735\pi$
$920$	−0.270364	+	5.19259i	−0.00891365	+	0.171195i
$921$	2.11070	+	3.65584i	0.0695500	+	0.120464i
$922$	−11.0026	−	2.94813i	−0.362351	−	0.0970916i
$923$	−3.49041	+	3.49041i	−0.114888	+	0.114888i
$924$	1.96345			0.0645928
$925$	−5.40052	−	2.06886i	−0.177568	−	0.0680237i
$926$	−25.5265	−	14.7378i	−0.838854	−	0.484313i
$927$	7.64876	+	2.04948i	0.251218	+	0.0673137i
$928$	1.77403	+	6.62077i	0.0582354	+	0.217337i
$929$	−17.4209	−	10.0580i	−0.571563	−	0.329992i	0.186211	−	0.982510i	$-0.440379\pi$
$929$	−17.4209	−	10.0580i	−0.571563	−	0.329992i	−0.757773	+	0.652518i	$0.773713\pi$
$930$	−6.06251	−	0.315659i	−0.198797	−	0.0103509i
$931$	12.4126	+	27.4139i	0.406805	+	0.898454i
$932$	4.43139	+	4.43139i	0.145155	+	0.145155i
$933$	−10.7006	+	2.86721i	−0.350321	+	0.0938682i
$934$	10.3555	−	17.9363i	0.338843	−	0.586894i
$935$	−46.0548	−	14.9468i	−1.50615	−	0.488813i
$936$	−1.86002	+	3.22165i	−0.0607967	+	0.105303i
$937$	−12.0391	+	44.9305i	−0.393300	+	1.46782i	0.431355	+	0.902182i	$0.358036\pi$
$937$	−12.0391	+	44.9305i	−0.393300	+	1.46782i	−0.824656	+	0.565635i	$0.808631\pi$
$938$	−1.13125	+	1.13125i	−0.0369368	+	0.0369368i
$939$	−22.5831			−0.736970
$940$	−7.28310	+	22.4410i	−0.237549	+	0.731945i
$941$	22.8383	−	13.1857i	0.744508	−	0.429842i	−0.0791980	−	0.996859i	$-0.525236\pi$
$941$	22.8383	−	13.1857i	0.744508	−	0.429842i	0.823706	+	0.567017i	$0.191903\pi$
$942$	−6.81737	−	6.81737i	−0.222122	−	0.222122i
$943$	16.7321	+	16.7321i	0.544872	+	0.544872i
$944$	0.367410	+	0.636373i	0.0119582	+	0.0207122i
$945$	−0.581703	−	0.377482i	−0.0189228	−	0.0122795i
$946$	−47.9421	+	27.6794i	−1.55873	+	0.899934i
$947$	12.9561	−	3.47159i	0.421018	−	0.112812i	−0.0420887	−	0.999114i	$-0.513401\pi$
$947$	12.9561	−	3.47159i	0.421018	−	0.112812i	0.463107	+	0.886302i	$0.346735\pi$
$948$	−3.73631	−	13.9441i	−0.121350	−	0.452883i
$949$	−17.9236			−0.581826
$950$	9.75898	−	19.4875i	0.316623	−	0.632258i
$951$	−18.3504			−0.595053
$952$	−0.274518	−	1.02451i	−0.00889717	−	0.0332047i
$953$	−29.2494	+	7.83734i	−0.947480	+	0.253876i	−0.699292	−	0.714836i	$-0.746501\pi$
$953$	−29.2494	+	7.83734i	−0.947480	+	0.253876i	−0.248187	+	0.968712i	$0.579835\pi$
$954$	3.55524	−	2.05262i	0.115105	−	0.0664560i
$955$	−32.7612	−	21.2596i	−1.06013	−	0.687943i
$956$	−11.2975	−	19.5679i	−0.365388	−	0.632870i
$957$	30.6860	+	30.6860i	0.991937	+	0.991937i
$958$	0.822156	+	0.822156i	0.0265627	+	0.0265627i
$959$	−2.76887	+	1.59861i	−0.0894115	+	0.0516217i
$960$	−0.690261	+	2.12686i	−0.0222781	+	0.0686442i
$961$	23.6293			0.762235
$962$	−3.04252	+	3.04252i	−0.0980948	+	0.0980948i
$963$	−1.23225	+	4.59881i	−0.0397086	+	0.148194i
$964$	0.0463334	−	0.0802518i	0.00149230	−	0.00258474i
$965$	3.76867	+	1.22310i	0.121318	+	0.0393730i
$966$	−0.360567	+	0.624520i	−0.0116011	+	0.0200936i
$967$	2.25233	−	0.603511i	0.0724302	−	0.0194076i	−0.222422	−	0.974950i	$-0.571396\pi$
$967$	2.25233	−	0.603511i	0.0724302	−	0.0194076i	0.294852	+	0.955543i	$0.404730\pi$
$968$	−20.5662	−	20.5662i	−0.661022	−	0.661022i
$969$	8.68674	−	12.1157i	0.279058	−	0.389214i
$970$	36.7682	+	1.91442i	1.18055	+	0.0614684i
$971$	1.20002	+	0.692830i	0.0385103	+	0.0222340i	0.519132	−	0.854694i	$-0.326255\pi$
$971$	1.20002	+	0.692830i	0.0385103	+	0.0222340i	−0.480621	+	0.876928i	$0.659589\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	−6.18299	−	1.65673i	−0.198217	−	0.0531122i
$974$	6.17275	+	3.56384i	0.197788	+	0.114193i
$975$	16.9870	−	7.57692i	0.544019	−	0.242656i
$976$	4.34262			0.139004
$977$	3.89608	−	3.89608i	0.124647	−	0.124647i	−0.642032	−	0.766678i	$-0.721908\pi$
$977$	3.89608	−	3.89608i	0.124647	−	0.124647i	0.766678	+	0.642032i	$0.221908\pi$
$978$	−0.0278158	−	0.00745323i	−0.000889453	−	0.000238328i
$979$	−32.8082	−	56.8255i	−1.04856	−	1.81615i
$980$	−0.802699	+	15.4165i	−0.0256413	+	0.492463i
$981$			10.0772i			0.321740i
$982$	12.0295	+	3.22329i	0.383877	+	0.102859i
$983$	0.993259	−	0.266143i	0.0316801	−	0.00848865i	−0.242944	−	0.970040i	$-0.578113\pi$
$983$	0.993259	−	0.266143i	0.0316801	−	0.00848865i	0.274624	+	0.961552i	$0.411447\pi$
$984$	5.08802	+	8.81271i	0.162200	+	0.280939i
$985$	−3.22440	−	15.1443i	−0.102738	−	0.482538i
$986$	11.7214	−	20.3020i	0.373285	−	0.646549i
$987$	−2.31375	+	2.31375i	−0.0736476	+	0.0736476i
$988$	−10.2836	−	12.5372i	−0.327166	−	0.398863i
$989$		−	20.3321i		−	0.646523i
$990$	2.94814	+	13.8468i	0.0936979	+	0.440080i
$991$	22.6210	+	13.0602i	0.718579	+	0.414872i	0.814230	−	0.580543i	$-0.197160\pi$
$991$	22.6210	+	13.0602i	0.718579	+	0.414872i	−0.0956503	+	0.995415i	$0.530493\pi$
$992$	−0.702670	+	2.62240i	−0.0223098	+	0.0832613i
$993$	−0.423325	−	1.57987i	−0.0134338	−	0.0501357i
$994$	−0.356372	+	0.205752i	−0.0113034	+	0.00652604i
$995$	−17.0327	−	0.886849i	−0.539973	−	0.0281150i
$996$		−	0.269510i		−	0.00853975i
$997$	−0.00289465	+	0.0108030i	−9.16743e−5	+	0.000342133i	−0.965972	−	0.258648i	$-0.916723\pi$
$997$	−0.00289465	+	0.0108030i	−9.16743e−5	+	0.000342133i	0.965880	+	0.258990i	$0.0833897\pi$
$998$	−5.46030	+	20.3781i	−0.172843	+	0.645058i
$999$			1.15665i			0.0365947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.b.217.9	yes	40
5.3	odd	4	inner	570.2.x.b.103.6	✓	40
19.12	odd	6	inner	570.2.x.b.487.6	yes	40
95.88	even	12	inner	570.2.x.b.373.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.6	✓	40	5.3	odd	4	inner
570.2.x.b.217.9	yes	40	1.1	even	1	trivial
570.2.x.b.373.9	yes	40	95.88	even	12	inner
570.2.x.b.487.6	yes	40	19.12	odd	6	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.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.87574 + 1.21721i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.219288 - 0.219288i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.87574 + 1.21721i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.219288 - 0.219288i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.690261 + 2.12686i) q^{10} +6.33127 q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.962817 - 3.59328i) q^{13} +(0.155060 - 0.268571i) q^{14} +(2.12686 + 0.690261i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.30361 + 0.885199i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-3.97083 + 1.79792i) q^{19} +(-2.23304 - 0.116269i) q^{20} +(-0.268571 - 0.155060i) q^{21} +(1.63865 + 6.11554i) q^{22} +(-2.24611 - 0.601843i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(2.03678 + 4.56635i) q^{25} +3.72004 q^{26} +(0.707107 - 0.707107i) q^{27} +(0.299553 + 0.0802649i) q^{28} +(3.42716 + 5.93602i) q^{29} +(-0.116269 + 2.23304i) q^{30} +2.71491i q^{31} +(0.965926 + 0.258819i) q^{32} +(6.11554 - 1.63865i) q^{33} +(-1.71007 - 2.96193i) q^{34} +(-0.144406 - 0.678246i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.817873 + 0.817873i) q^{37} +(-2.76439 - 3.37019i) q^{38} -3.72004i q^{39} +(-0.465647 - 2.18705i) q^{40} +(-8.81271 - 5.08802i) q^{41} +(0.0802649 - 0.299553i) q^{42} +(2.26304 + 8.44577i) q^{43} +(-5.48304 + 3.16563i) q^{44} +(2.23304 + 0.116269i) q^{45} -2.32534i q^{46} +(2.73086 - 10.1917i) q^{47} +(0.258819 - 0.965926i) q^{48} -6.90383i q^{49} +(-3.88359 + 3.14924i) q^{50} +(-2.96193 + 1.71007i) q^{51} +(0.962817 + 3.59328i) q^{52} +(1.06251 - 3.96536i) q^{53} +(0.866025 + 0.500000i) q^{54} +(11.8758 + 7.70650i) q^{55} +0.310120i q^{56} +(-3.37019 + 2.76439i) q^{57} +(-4.84674 + 4.84674i) q^{58} +(-0.367410 + 0.636373i) q^{59} +(-2.18705 + 0.465647i) q^{60} +(2.17131 + 3.76082i) q^{61} +(-2.62240 + 0.702670i) q^{62} +(-0.299553 - 0.0802649i) q^{63} +1.00000i q^{64} +(6.17978 - 5.56810i) q^{65} +(3.16563 + 5.48304i) q^{66} +(-4.98299 - 1.33519i) q^{67} +(2.41841 - 2.41841i) q^{68} -2.32534 q^{69} +(0.617760 - 0.315029i) q^{70} +(-1.14914 - 0.663459i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(-1.24702 - 4.65396i) q^{73} +(-1.00169 - 0.578323i) q^{74} +(3.14924 + 3.88359i) q^{75} +(2.53987 - 3.54246i) q^{76} +(-1.38837 - 1.38837i) q^{77} +(3.59328 - 0.962817i) q^{78} +(-7.21799 + 12.5019i) q^{79} +(1.99201 - 1.01583i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.63375 - 9.82930i) q^{82} +(-0.190572 + 0.190572i) q^{83} +0.310120 q^{84} +(-7.27418 - 2.36079i) q^{85} +(-7.57227 + 4.37185i) q^{86} +(4.84674 + 4.84674i) q^{87} +(-4.47688 - 4.47688i) q^{88} +(-5.18194 - 8.97538i) q^{89} +(0.465647 + 2.18705i) q^{90} +(-0.999097 + 0.576829i) q^{91} +(2.24611 - 0.601843i) q^{92} +(0.702670 + 2.62240i) q^{93} +10.5512 q^{94} +(-9.63669 - 1.46091i) q^{95} +1.00000 q^{96} +(-4.26158 - 15.9044i) q^{97} +(6.66858 - 1.78684i) q^{98} +(5.48304 - 3.16563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q + 20 * q^6 - 8 * q^7	\( 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more