LMFDB - Embedded newform 507.2.j.f.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	507.361
Dual form			507.2.j.f.316.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.358719 + 0.207107i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.914214 + 1.58346i) q^{4} +2.82843i q^{5} +(0.358719 + 0.207107i) q^{6} +(-2.44949 - 1.41421i) q^{7} -1.58579i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.358719 + 0.207107i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.914214 + 1.58346i) q^{4} +2.82843i q^{5} +(0.358719 + 0.207107i) q^{6} +(-2.44949 - 1.41421i) q^{7} -1.58579i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.585786 - 1.01461i) q^{10} +(-1.73205 + 1.00000i) q^{11} +1.82843 q^{12} +1.17157 q^{14} +(2.44949 - 1.41421i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(3.82843 - 6.63103i) q^{17} -0.414214i q^{18} +(-2.44949 - 1.41421i) q^{19} +(-4.47871 - 2.58579i) q^{20} +2.82843i q^{21} +(0.414214 - 0.717439i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.37333 + 0.792893i) q^{24} -3.00000 q^{25} +1.00000 q^{27} +(4.47871 - 2.58579i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(-0.585786 + 1.01461i) q^{30} +1.17157i q^{31} +(3.82282 + 2.20711i) q^{32} +(1.73205 + 1.00000i) q^{33} +3.17157i q^{34} +(4.00000 - 6.92820i) q^{35} +(-0.914214 - 1.58346i) q^{36} +(-6.63103 + 3.82843i) q^{37} +1.17157 q^{38} +4.48528 q^{40} +(-4.47871 + 2.58579i) q^{41} +(-0.585786 - 1.01461i) q^{42} +(-0.828427 + 1.43488i) q^{43} -3.65685i q^{44} +(-2.44949 - 1.41421i) q^{45} +(1.43488 + 0.828427i) q^{46} -11.6569i q^{47} +(-1.50000 + 2.59808i) q^{48} +(0.500000 + 0.866025i) q^{49} +(1.07616 - 0.621320i) q^{50} -7.65685 q^{51} -2.00000 q^{53} +(-0.358719 + 0.207107i) q^{54} +(-2.82843 - 4.89898i) q^{55} +(-2.24264 + 3.88437i) q^{56} +2.82843i q^{57} +(0.717439 + 0.414214i) q^{58} +(-6.63103 - 3.82843i) q^{59} +5.17157i q^{60} +(-6.65685 + 11.5300i) q^{61} +(-0.242641 - 0.420266i) q^{62} +(2.44949 - 1.41421i) q^{63} +4.17157 q^{64} -0.828427 q^{66} +(-5.91359 + 3.41421i) q^{67} +(7.00000 + 12.1244i) q^{68} +(-2.00000 + 3.46410i) q^{69} +3.31371i q^{70} +(1.73205 + 1.00000i) q^{71} +(1.37333 + 0.792893i) q^{72} +0.343146i q^{73} +(1.58579 - 2.74666i) q^{74} +(1.50000 + 2.59808i) q^{75} +(4.47871 - 2.58579i) q^{76} +5.65685 q^{77} -11.3137 q^{79} +(7.34847 - 4.24264i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.07107 - 1.85514i) q^{82} -3.65685i q^{83} +(-4.47871 - 2.58579i) q^{84} +(18.7554 + 10.8284i) q^{85} -0.686292i q^{86} +(-1.00000 + 1.73205i) q^{87} +(1.58579 + 2.74666i) q^{88} +(12.8418 - 7.41421i) q^{89} +1.17157 q^{90} +7.31371 q^{92} +(1.01461 - 0.585786i) q^{93} +(2.41421 + 4.18154i) q^{94} +(4.00000 - 6.92820i) q^{95} -4.41421i q^{96} +(3.16693 + 1.82843i) q^{97} +(-0.358719 - 0.207107i) q^{98} -2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 16 q^{10} - 8 q^{12} + 32 q^{14} - 12 q^{16} + 8 q^{17} - 8 q^{22} - 16 q^{23} - 24 q^{25} + 8 q^{27} - 8 q^{29} - 16 q^{30} + 32 q^{35} + 4 q^{36} + 32 q^{38} - 32 q^{40} - 16 q^{42} + 16 q^{43} - 12 q^{48} + 4 q^{49} - 16 q^{51} - 16 q^{53} + 16 q^{56} - 8 q^{61} + 32 q^{62} + 56 q^{64} + 16 q^{66} + 56 q^{68} - 16 q^{69} + 24 q^{74} + 12 q^{75} - 4 q^{81} - 48 q^{82} - 8 q^{87} + 24 q^{88} + 32 q^{90} - 32 q^{92} + 8 q^{94} + 32 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 16 * q^10 - 8 * q^12 + 32 * q^14 - 12 * q^16 + 8 * q^17 - 8 * q^22 - 16 * q^23 - 24 * q^25 + 8 * q^27 - 8 * q^29 - 16 * q^30 + 32 * q^35 + 4 * q^36 + 32 * q^38 - 32 * q^40 - 16 * q^42 + 16 * q^43 - 12 * q^48 + 4 * q^49 - 16 * q^51 - 16 * q^53 + 16 * q^56 - 8 * q^61 + 32 * q^62 + 56 * q^64 + 16 * q^66 + 56 * q^68 - 16 * q^69 + 24 * q^74 + 12 * q^75 - 4 * q^81 - 48 * q^82 - 8 * q^87 + 24 * q^88 + 32 * q^90 - 32 * q^92 + 8 * q^94 + 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.358719	+	0.207107i	−0.253653	+	0.146447i	−0.621436	−	0.783465i	$-0.713450\pi$
$2$	−0.358719	+	0.207107i	−0.253653	+	0.146447i	0.367783	+	0.929912i	$0.380117\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.914214	+	1.58346i	−0.457107	+	0.791732i
$5$			2.82843i			1.26491i	0.774597	+	0.632456i	$0.217953\pi$
$5$			2.82843i			1.26491i	−0.774597	+	0.632456i	$0.782047\pi$
$6$	0.358719	+	0.207107i	0.146447	+	0.0845510i
$7$	−2.44949	−	1.41421i	−0.925820	−	0.534522i	−0.0403329	−	0.999186i	$-0.512842\pi$
$7$	−2.44949	−	1.41421i	−0.925820	−	0.534522i	−0.885487	+	0.464664i	$0.846175\pi$
$8$		−	1.58579i		−	0.560660i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.585786	−	1.01461i	−0.185242	−	0.320848i
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	−0.737848	−	0.674967i	$-0.764158\pi$
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	0.215615	+	0.976478i	$0.430824\pi$
$12$	1.82843			0.527821
$13$		0			0
$13$		0			0
$14$	1.17157			0.313116
$15$	2.44949	−	1.41421i	0.632456	−	0.365148i
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	3.82843	−	6.63103i	0.928530	−	1.60826i	0.142747	−	0.989759i	$-0.454407\pi$
$17$	3.82843	−	6.63103i	0.928530	−	1.60826i	0.785783	−	0.618502i	$-0.212260\pi$
$18$		−	0.414214i		−	0.0976311i
$19$	−2.44949	−	1.41421i	−0.561951	−	0.324443i	0.191977	−	0.981399i	$-0.438510\pi$
$19$	−2.44949	−	1.41421i	−0.561951	−	0.324443i	−0.753928	+	0.656957i	$0.771843\pi$
$20$	−4.47871	−	2.58579i	−1.00147	−	0.578199i
$21$			2.82843i			0.617213i
$22$	0.414214	−	0.717439i	0.0883106	−	0.152958i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	−1.37333	+	0.792893i	−0.280330	+	0.161849i
$25$	−3.00000			−0.600000
$26$		0			0
$27$	1.00000			0.192450
$28$	4.47871	−	2.58579i	0.846397	−	0.488668i
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	0.758115	−	0.652121i	$-0.226120\pi$
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	−0.943811	+	0.330487i	$0.892787\pi$
$30$	−0.585786	+	1.01461i	−0.106949	+	0.185242i
$31$			1.17157i			0.210421i	0.994450	+	0.105210i	$0.0335516\pi$
$31$			1.17157i			0.210421i	−0.994450	+	0.105210i	$0.966448\pi$
$32$	3.82282	+	2.20711i	0.675786	+	0.390165i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$			3.17157i			0.543920i
$35$	4.00000	−	6.92820i	0.676123	−	1.17108i
$36$	−0.914214	−	1.58346i	−0.152369	−	0.263911i
$37$	−6.63103	+	3.82843i	−1.09013	+	0.629390i	−0.933612	−	0.358285i	$-0.883362\pi$
$37$	−6.63103	+	3.82843i	−1.09013	+	0.629390i	−0.156522	+	0.987674i	$0.550028\pi$
$38$	1.17157			0.190054
$39$		0			0
$40$	4.48528			0.709185
$41$	−4.47871	+	2.58579i	−0.699458	+	0.403832i	−0.807145	−	0.590353i	$-0.798989\pi$
$41$	−4.47871	+	2.58579i	−0.699458	+	0.403832i	0.107688	+	0.994185i	$0.465655\pi$
$42$	−0.585786	−	1.01461i	−0.0903888	−	0.156558i
$43$	−0.828427	+	1.43488i	−0.126334	+	0.218817i	−0.922254	−	0.386585i	$-0.873654\pi$
$43$	−0.828427	+	1.43488i	−0.126334	+	0.218817i	0.795920	+	0.605402i	$0.206988\pi$
$44$		−	3.65685i		−	0.551292i
$45$	−2.44949	−	1.41421i	−0.365148	−	0.210819i
$46$	1.43488	+	0.828427i	0.211561	+	0.122145i
$47$		−	11.6569i		−	1.70033i	−0.526519	−	0.850163i	$-0.676503\pi$
$47$		−	11.6569i		−	1.70033i	0.526519	−	0.850163i	$-0.323497\pi$
$48$	−1.50000	+	2.59808i	−0.216506	+	0.375000i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	1.07616	−	0.621320i	0.152192	−	0.0878680i
$51$	−7.65685			−1.07217
$52$		0			0
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	−0.358719	+	0.207107i	−0.0488155	+	0.0281837i
$55$	−2.82843	−	4.89898i	−0.381385	−	0.660578i
$56$	−2.24264	+	3.88437i	−0.299685	+	0.519070i
$57$			2.82843i			0.374634i
$58$	0.717439	+	0.414214i	0.0942043	+	0.0543889i
$59$	−6.63103	−	3.82843i	−0.863287	−	0.498419i	0.00182490	−	0.999998i	$-0.499419\pi$
$59$	−6.63103	−	3.82843i	−0.863287	−	0.498419i	−0.865112	+	0.501580i	$0.832752\pi$
$60$			5.17157i			0.667647i
$61$	−6.65685	+	11.5300i	−0.852323	+	1.47627i	0.0267837	+	0.999641i	$0.491473\pi$
$61$	−6.65685	+	11.5300i	−0.852323	+	1.47627i	−0.879107	+	0.476625i	$0.841860\pi$
$62$	−0.242641	−	0.420266i	−0.0308154	−	0.0533738i
$63$	2.44949	−	1.41421i	0.308607	−	0.178174i
$64$	4.17157			0.521447
$65$		0			0
$66$	−0.828427			−0.101972
$67$	−5.91359	+	3.41421i	−0.722460	+	0.417113i	−0.815657	−	0.578535i	$-0.803625\pi$
$67$	−5.91359	+	3.41421i	−0.722460	+	0.417113i	0.0931973	+	0.995648i	$0.470291\pi$
$68$	7.00000	+	12.1244i	0.848875	+	1.47029i
$69$	−2.00000	+	3.46410i	−0.240772	+	0.417029i
$70$			3.31371i			0.396064i
$71$	1.73205	+	1.00000i	0.205557	+	0.118678i	0.599245	−	0.800566i	$-0.295468\pi$
$71$	1.73205	+	1.00000i	0.205557	+	0.118678i	−0.393688	+	0.919244i	$0.628801\pi$
$72$	1.37333	+	0.792893i	0.161849	+	0.0934434i
$73$			0.343146i			0.0401622i	0.999798	+	0.0200811i	$0.00639244\pi$
$73$			0.343146i			0.0401622i	−0.999798	+	0.0200811i	$0.993608\pi$
$74$	1.58579	−	2.74666i	0.184344	−	0.319293i
$75$	1.50000	+	2.59808i	0.173205	+	0.300000i
$76$	4.47871	−	2.58579i	0.513744	−	0.296610i
$77$	5.65685			0.644658
$78$		0			0
$79$	−11.3137			−1.27289			−0.636446	−	0.771321i	$-0.719596\pi$
$79$	−11.3137			−1.27289			−0.636446	+	0.771321i	$0.719596\pi$
$80$	7.34847	−	4.24264i	0.821584	−	0.474342i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.07107	−	1.85514i	0.118280	−	0.204866i
$83$		−	3.65685i		−	0.401392i	−0.979654	−	0.200696i	$-0.935680\pi$
$83$		−	3.65685i		−	0.401392i	0.979654	−	0.200696i	$-0.0643203\pi$
$84$	−4.47871	−	2.58579i	−0.488668	−	0.282132i
$85$	18.7554	+	10.8284i	2.03431	+	1.17451i
$86$		−	0.686292i		−	0.0740047i
$87$	−1.00000	+	1.73205i	−0.107211	+	0.185695i
$88$	1.58579	+	2.74666i	0.169045	+	0.292795i
$89$	12.8418	−	7.41421i	1.36123	−	0.785905i	0.371440	−	0.928457i	$-0.378864\pi$
$89$	12.8418	−	7.41421i	1.36123	−	0.785905i	0.989787	+	0.142552i	$0.0455308\pi$
$90$	1.17157			0.123495
$91$		0			0
$92$	7.31371			0.762507
$93$	1.01461	−	0.585786i	0.105210	−	0.0607432i
$94$	2.41421	+	4.18154i	0.249007	+	0.431293i
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$		−	4.41421i		−	0.450524i
$97$	3.16693	+	1.82843i	0.321553	+	0.185649i	0.652085	−	0.758146i	$-0.273895\pi$
$97$	3.16693	+	1.82843i	0.321553	+	0.185649i	−0.330532	+	0.943795i	$0.607228\pi$
$98$	−0.358719	−	0.207107i	−0.0362361	−	0.0209209i
$99$		−	2.00000i		−	0.201008i
$100$	2.74264	−	4.75039i	0.274264	−	0.475039i
$101$	3.82843	+	6.63103i	0.380943	+	0.659812i	0.991197	−	0.132393i	$-0.0422662\pi$
$101$	3.82843	+	6.63103i	0.380943	+	0.659812i	−0.610255	+	0.792205i	$0.708933\pi$
$102$	2.74666	−	1.58579i	0.271960	−	0.157016i
$103$	−2.34315			−0.230877			−0.115439	−	0.993315i	$-0.536827\pi$
$103$	−2.34315			−0.230877			−0.115439	+	0.993315i	$0.536827\pi$
$104$		0			0
$105$	−8.00000			−0.780720
$106$	0.717439	−	0.414214i	0.0696838	−	0.0402320i
$107$	5.65685	+	9.79796i	0.546869	+	0.947204i	0.998487	+	0.0549930i	$0.0175137\pi$
$107$	5.65685	+	9.79796i	0.546869	+	0.947204i	−0.451618	+	0.892211i	$0.649153\pi$
$108$	−0.914214	+	1.58346i	−0.0879702	+	0.152369i
$109$		−	5.31371i		−	0.508961i	−0.967078	−	0.254480i	$-0.918096\pi$
$109$		−	5.31371i		−	0.508961i	0.967078	−	0.254480i	$-0.0819045\pi$
$110$	2.02922	+	1.17157i	0.193479	+	0.111705i
$111$	6.63103	+	3.82843i	0.629390	+	0.363378i
$112$			8.48528i			0.801784i
$113$	2.65685	−	4.60181i	0.249936	−	0.432902i	−0.713572	−	0.700582i	$-0.752924\pi$
$113$	2.65685	−	4.60181i	0.249936	−	0.432902i	0.963508	+	0.267680i	$0.0862571\pi$
$114$	−0.585786	−	1.01461i	−0.0548639	−	0.0950271i
$115$	9.79796	−	5.65685i	0.913664	−	0.527504i
$116$	3.65685			0.339530
$117$		0			0
$118$	3.17157			0.291967
$119$	−18.7554	+	10.8284i	−1.71930	+	0.992640i
$120$	−2.24264	−	3.88437i	−0.204724	−	0.354593i
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$		−	5.51472i		−	0.499279i
$123$	4.47871	+	2.58579i	0.403832	+	0.233153i
$124$	−1.85514	−	1.07107i	−0.166597	−	0.0961847i
$125$			5.65685i			0.505964i
$126$	−0.585786	+	1.01461i	−0.0521860	+	0.0903888i
$127$	2.82843	+	4.89898i	0.250982	+	0.434714i	0.963797	−	0.266639i	$-0.0859131\pi$
$127$	2.82843	+	4.89898i	0.250982	+	0.434714i	−0.712814	+	0.701353i	$0.752580\pi$
$128$	−9.14207	+	5.27817i	−0.808052	+	0.466529i
$129$	1.65685			0.145878
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	−3.16693	+	1.82843i	−0.275646	+	0.159144i
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$	1.41421	−	2.44949i	0.122169	−	0.211604i
$135$			2.82843i			0.243432i
$136$	−10.5154	−	6.07107i	−0.901688	−	0.520590i
$137$	9.37769	+	5.41421i	0.801190	+	0.462567i	0.843887	−	0.536521i	$-0.180262\pi$
$137$	9.37769	+	5.41421i	0.801190	+	0.462567i	−0.0426968	+	0.999088i	$0.513595\pi$
$138$		−	1.65685i		−	0.141041i
$139$	3.65685	−	6.33386i	0.310170	−	0.537231i	−0.668229	−	0.743956i	$-0.732947\pi$
$139$	3.65685	−	6.33386i	0.310170	−	0.537231i	0.978399	+	0.206725i	$0.0662806\pi$
$140$	7.31371	+	12.6677i	0.618121	+	1.07062i
$141$	−10.0951	+	5.82843i	−0.850163	+	0.490842i
$142$	−0.828427			−0.0695201
$143$		0			0
$144$	3.00000			0.250000
$145$	4.89898	−	2.82843i	0.406838	−	0.234888i
$146$	−0.0710678	−	0.123093i	−0.00588161	−	0.0101873i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$		−	14.0000i		−	1.15079i
$149$	−7.94282	−	4.58579i	−0.650701	−	0.375682i	0.138024	−	0.990429i	$-0.455925\pi$
$149$	−7.94282	−	4.58579i	−0.650701	−	0.375682i	−0.788725	+	0.614747i	$0.789258\pi$
$150$	−1.07616	−	0.621320i	−0.0878680	−	0.0507306i
$151$		−	3.51472i		−	0.286024i	−0.989721	−	0.143012i	$-0.954321\pi$
$151$		−	3.51472i		−	0.286024i	0.989721	−	0.143012i	$-0.0456787\pi$
$152$	−2.24264	+	3.88437i	−0.181902	+	0.315064i
$153$	3.82843	+	6.63103i	0.309510	+	0.536087i
$154$	−2.02922	+	1.17157i	−0.163520	+	0.0944080i
$155$	−3.31371			−0.266163
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	4.05845	−	2.34315i	0.322873	−	0.186411i
$159$	1.00000	+	1.73205i	0.0793052	+	0.137361i
$160$	−6.24264	+	10.8126i	−0.493524	+	0.854809i
$161$			11.3137i			0.891645i
$162$	0.358719	+	0.207107i	0.0281837	+	0.0162718i
$163$	−16.3059	−	9.41421i	−1.27718	−	0.737378i	−0.300848	−	0.953672i	$-0.597270\pi$
$163$	−16.3059	−	9.41421i	−1.27718	−	0.737378i	−0.976328	+	0.216294i	$0.930603\pi$
$164$		−	9.45584i		−	0.738377i
$165$	−2.82843	+	4.89898i	−0.220193	+	0.381385i
$166$	0.757359	+	1.31178i	0.0587825	+	0.101814i
$167$	−3.16693	+	1.82843i	−0.245064	+	0.141488i	−0.617502	−	0.786569i	$-0.711855\pi$
$167$	−3.16693	+	1.82843i	−0.245064	+	0.141488i	0.372438	+	0.928057i	$0.378522\pi$
$168$	4.48528			0.346047
$169$		0			0
$170$	−8.97056			−0.688011
$171$	2.44949	−	1.41421i	0.187317	−	0.108148i
$172$	−1.51472	−	2.62357i	−0.115496	−	0.200045i
$173$	−5.82843	+	10.0951i	−0.443127	+	0.767519i	−0.997920	−	0.0644701i	$-0.979464\pi$
$173$	−5.82843	+	10.0951i	−0.443127	+	0.767519i	0.554793	+	0.831989i	$0.312798\pi$
$174$		−	0.828427i		−	0.0628029i
$175$	7.34847	+	4.24264i	0.555492	+	0.320713i
$176$	5.19615	+	3.00000i	0.391675	+	0.226134i
$177$			7.65685i			0.575524i
$178$	−3.07107	+	5.31925i	−0.230186	+	0.398694i
$179$	−11.6569	−	20.1903i	−0.871274	−	1.50909i	−0.860679	−	0.509147i	$-0.829961\pi$
$179$	−11.6569	−	20.1903i	−0.871274	−	1.50909i	−0.0105948	−	0.999944i	$-0.503372\pi$
$180$	4.47871	−	2.58579i	0.333824	−	0.192733i
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$	13.3137			0.984178
$184$	−5.49333	+	3.17157i	−0.404973	+	0.233811i
$185$	−10.8284	−	18.7554i	−0.796122	−	1.37892i
$186$	−0.242641	+	0.420266i	−0.0177913	+	0.0308154i
$187$			15.3137i			1.11985i
$188$	18.4582	+	10.6569i	1.34620	+	0.777231i
$189$	−2.44949	−	1.41421i	−0.178174	−	0.102869i
$190$			3.31371i			0.240402i
$191$	−1.65685	+	2.86976i	−0.119886	+	0.207648i	−0.919722	−	0.392570i	$-0.871586\pi$
$191$	−1.65685	+	2.86976i	−0.119886	+	0.207648i	0.799836	+	0.600218i	$0.204919\pi$
$192$	−2.08579	−	3.61269i	−0.150529	−	0.260723i
$193$	4.60181	−	2.65685i	0.331245	−	0.191245i	−0.325149	−	0.945663i	$-0.605414\pi$
$193$	4.60181	−	2.65685i	0.331245	−	0.191245i	0.656394	+	0.754418i	$0.272081\pi$
$194$	−1.51472			−0.108750
$195$		0			0
$196$	−1.82843			−0.130602
$197$	−0.420266	+	0.242641i	−0.0299427	+	0.0172874i	−0.514897	−	0.857252i	$-0.672170\pi$
$197$	−0.420266	+	0.242641i	−0.0299427	+	0.0172874i	0.484954	+	0.874540i	$0.338836\pi$
$198$	0.414214	+	0.717439i	0.0294369	+	0.0509862i
$199$	10.8284	−	18.7554i	0.767607	−	1.32953i	−0.171250	−	0.985228i	$-0.554781\pi$
$199$	10.8284	−	18.7554i	0.767607	−	1.32953i	0.938857	−	0.344307i	$-0.111886\pi$
$200$			4.75736i			0.336396i
$201$	5.91359	+	3.41421i	0.417113	+	0.240820i
$202$	−2.74666	−	1.58579i	−0.193255	−	0.111576i
$203$			5.65685i			0.397033i
$204$	7.00000	−	12.1244i	0.490098	−	0.848875i
$205$	−7.31371	−	12.6677i	−0.510812	−	0.884752i
$206$	0.840532	−	0.485281i	0.0585626	−	0.0338112i
$207$	4.00000			0.278019
$208$		0			0
$209$	5.65685			0.391293
$210$	2.86976	−	1.65685i	0.198032	−	0.114334i
$211$	6.00000	+	10.3923i	0.413057	+	0.715436i	0.995222	−	0.0976347i	$-0.0311277\pi$
$211$	6.00000	+	10.3923i	0.413057	+	0.715436i	−0.582165	+	0.813070i	$0.697794\pi$
$212$	1.82843	−	3.16693i	0.125577	−	0.217506i
$213$		−	2.00000i		−	0.137038i
$214$	−4.05845	−	2.34315i	−0.277430	−	0.160174i
$215$	−4.05845	−	2.34315i	−0.276784	−	0.159801i
$216$		−	1.58579i		−	0.107899i
$217$	1.65685	−	2.86976i	0.112475	−	0.194812i
$218$	1.10051	+	1.90613i	0.0745356	+	0.129099i
$219$	0.297173	−	0.171573i	0.0200811	−	0.0115938i
$220$	10.3431			0.697335
$221$		0			0
$222$	−3.17157			−0.212862
$223$	10.8126	−	6.24264i	0.724063	−	0.418038i	−0.0921831	−	0.995742i	$-0.529385\pi$
$223$	10.8126	−	6.24264i	0.724063	−	0.418038i	0.816246	+	0.577704i	$0.196051\pi$
$224$	−6.24264	−	10.8126i	−0.417104	−	0.722445i
$225$	1.50000	−	2.59808i	0.100000	−	0.173205i
$226$			2.20101i			0.146409i
$227$	−14.9941	−	8.65685i	−0.995194	−	0.574576i	−0.0883713	−	0.996088i	$-0.528166\pi$
$227$	−14.9941	−	8.65685i	−0.995194	−	0.574576i	−0.906823	+	0.421512i	$0.861500\pi$
$228$	−4.47871	−	2.58579i	−0.296610	−	0.171248i
$229$		−	1.31371i		−	0.0868123i	−0.999058	−	0.0434062i	$-0.986179\pi$
$229$		−	1.31371i		−	0.0868123i	0.999058	−	0.0434062i	$-0.0138209\pi$
$230$	−2.34315	+	4.05845i	−0.154502	+	0.267606i
$231$	−2.82843	−	4.89898i	−0.186097	−	0.322329i
$232$	−2.74666	+	1.58579i	−0.180327	+	0.104112i
$233$	−6.97056			−0.456657			−0.228328	−	0.973584i	$-0.573326\pi$
$233$	−6.97056			−0.456657			−0.228328	+	0.973584i	$0.573326\pi$
$234$		0			0
$235$	32.9706			2.15076
$236$	12.1244	−	7.00000i	0.789228	−	0.455661i
$237$	5.65685	+	9.79796i	0.367452	+	0.636446i
$238$	4.48528	−	7.76874i	0.290738	−	0.503572i
$239$		−	2.00000i		−	0.129369i	−0.997906	−	0.0646846i	$-0.979396\pi$
$239$		−	2.00000i		−	0.129369i	0.997906	−	0.0646846i	$-0.0206041\pi$
$240$	−7.34847	−	4.24264i	−0.474342	−	0.273861i
$241$	−0.297173	−	0.171573i	−0.0191426	−	0.0110520i	0.490398	−	0.871499i	$-0.336851\pi$
$241$	−0.297173	−	0.171573i	−0.0191426	−	0.0110520i	−0.509541	+	0.860447i	$0.670185\pi$
$242$		−	2.89949i		−	0.186387i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−12.1716	−	21.0818i	−0.779205	−	1.34962i
$245$	−2.44949	+	1.41421i	−0.156492	+	0.0903508i
$246$	−2.14214			−0.136578
$247$		0			0
$248$	1.85786			0.117975
$249$	−3.16693	+	1.82843i	−0.200696	+	0.115872i
$250$	−1.17157	−	2.02922i	−0.0740968	−	0.128339i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$			5.17157i			0.325778i
$253$	6.92820	+	4.00000i	0.435572	+	0.251478i
$254$	−2.02922	−	1.17157i	−0.127325	−	0.0735110i
$255$		−	21.6569i		−	1.35620i
$256$	−1.98528	+	3.43861i	−0.124080	+	0.214913i
$257$	−2.17157	−	3.76127i	−0.135459	−	0.234622i	0.790314	−	0.612702i	$-0.209918\pi$
$257$	−2.17157	−	3.76127i	−0.135459	−	0.234622i	−0.925773	+	0.378081i	$0.876584\pi$
$258$	−0.594346	+	0.343146i	−0.0370024	+	0.0213633i
$259$	21.6569			1.34569
$260$		0			0
$261$	2.00000			0.123797
$262$	2.86976	−	1.65685i	0.177294	−	0.102361i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$	1.58579	−	2.74666i	0.0975984	−	0.169045i
$265$		−	5.65685i		−	0.347498i
$266$	−2.86976	−	1.65685i	−0.175956	−	0.101588i
$267$	−12.8418	−	7.41421i	−0.785905	−	0.453743i
$268$		−	12.4853i		−	0.762660i
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	−0.585786	−	1.01461i	−0.0356498	−	0.0617473i
$271$	−24.0746	+	13.8995i	−1.46243	+	0.844334i	−0.999123	−	0.0418640i	$-0.986670\pi$
$271$	−24.0746	+	13.8995i	−1.46243	+	0.844334i	−0.463306	+	0.886198i	$0.653337\pi$
$272$	−22.9706			−1.39279
$273$		0			0
$274$	−4.48528			−0.270966
$275$	5.19615	−	3.00000i	0.313340	−	0.180907i
$276$	−3.65685	−	6.33386i	−0.220117	−	0.381253i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$			3.02944i			0.181694i
$279$	−1.01461	−	0.585786i	−0.0607432	−	0.0350701i
$280$	−10.9867	−	6.34315i	−0.656578	−	0.379075i
$281$			21.1716i			1.26299i	0.775380	+	0.631495i	$0.217558\pi$
$281$			21.1716i			1.26299i	−0.775380	+	0.631495i	$0.782442\pi$
$282$	2.41421	−	4.18154i	0.143764	−	0.249007i
$283$	14.4853	+	25.0892i	0.861061	+	1.49140i	0.870906	+	0.491449i	$0.163533\pi$
$283$	14.4853	+	25.0892i	0.861061	+	1.49140i	−0.00984565	+	0.999952i	$0.503134\pi$
$284$	−3.16693	+	1.82843i	−0.187923	+	0.108497i
$285$	−8.00000			−0.473879
$286$		0			0
$287$	14.6274			0.863429
$288$	−3.82282	+	2.20711i	−0.225262	+	0.130055i
$289$	−20.8137	−	36.0504i	−1.22434	−	2.12061i
$290$	−1.17157	+	2.02922i	−0.0687971	+	0.119160i
$291$		−	3.65685i		−	0.214369i
$292$	−0.543359	−	0.313708i	−0.0317977	−	0.0183584i
$293$	−1.85514	−	1.07107i	−0.108379	−	0.0625724i	0.444831	−	0.895615i	$-0.353264\pi$
$293$	−1.85514	−	1.07107i	−0.108379	−	0.0625724i	−0.553210	+	0.833042i	$0.686597\pi$
$294$			0.414214i			0.0241574i
$295$	10.8284	−	18.7554i	0.630455	−	1.09198i
$296$	6.07107	+	10.5154i	0.352874	+	0.611195i
$297$	−1.73205	+	1.00000i	−0.100504	+	0.0580259i
$298$	3.79899			0.220070
$299$		0			0
$300$	−5.48528			−0.316693
$301$	4.05845	−	2.34315i	0.233925	−	0.135057i
$302$	0.727922	+	1.26080i	0.0418872	+	0.0725508i
$303$	3.82843	−	6.63103i	0.219937	−	0.380943i
$304$			8.48528i			0.486664i
$305$	−32.6118	−	18.8284i	−1.86735	−	1.07811i
$306$	−2.74666	−	1.58579i	−0.157016	−	0.0906534i
$307$		−	22.8284i		−	1.30289i	−0.758697	−	0.651444i	$-0.774164\pi$
$307$		−	22.8284i		−	1.30289i	0.758697	−	0.651444i	$-0.225836\pi$
$308$	−5.17157	+	8.95743i	−0.294678	+	0.510397i
$309$	1.17157	+	2.02922i	0.0666485	+	0.115439i
$310$	1.18869	−	0.686292i	0.0675132	−	0.0389787i
$311$	10.6274			0.602626			0.301313	−	0.953525i	$-0.402575\pi$
$311$	10.6274			0.602626			0.301313	+	0.953525i	$0.402575\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	3.58719	−	2.07107i	0.202437	−	0.116877i
$315$	4.00000	+	6.92820i	0.225374	+	0.390360i
$316$	10.3431	−	17.9149i	0.581847	−	1.00779i
$317$		−	8.48528i		−	0.476581i	−0.971194	−	0.238290i	$-0.923413\pi$
$317$		−	8.48528i		−	0.476581i	0.971194	−	0.238290i	$-0.0765870\pi$
$318$	−0.717439	−	0.414214i	−0.0402320	−	0.0232279i
$319$	3.46410	+	2.00000i	0.193952	+	0.111979i
$320$			11.7990i			0.659584i
$321$	5.65685	−	9.79796i	0.315735	−	0.546869i
$322$	−2.34315	−	4.05845i	−0.130578	−	0.226168i
$323$	−18.7554	+	10.8284i	−1.04358	+	0.602510i
$324$	1.82843			0.101579
$325$		0			0
$326$	7.79899			0.431946
$327$	−4.60181	+	2.65685i	−0.254480	+	0.146924i
$328$	4.10051	+	7.10228i	0.226413	+	0.392158i
$329$	−16.4853	+	28.5533i	−0.908863	+	1.57420i
$330$		−	2.34315i		−	0.128986i
$331$	22.6398	+	13.0711i	1.24439	+	0.718451i	0.969986	−	0.243163i	$-0.0781848\pi$
$331$	22.6398	+	13.0711i	1.24439	+	0.718451i	0.274408	+	0.961613i	$0.411518\pi$
$332$	5.79050	+	3.34315i	0.317795	+	0.183479i
$333$		−	7.65685i		−	0.419593i
$334$	0.757359	−	1.31178i	0.0414409	−	0.0717777i
$335$	−9.65685	−	16.7262i	−0.527610	−	0.913848i
$336$	7.34847	−	4.24264i	0.400892	−	0.231455i
$337$	−9.31371			−0.507350			−0.253675	−	0.967290i	$-0.581639\pi$
$337$	−9.31371			−0.507350			−0.253675	+	0.967290i	$0.581639\pi$
$338$		0			0
$339$	−5.31371			−0.288601
$340$	−34.2929	+	19.7990i	−1.85979	+	1.07375i
$341$	−1.17157	−	2.02922i	−0.0634442	−	0.109889i
$342$	−0.585786	+	1.01461i	−0.0316757	+	0.0548639i
$343$			16.9706i			0.916324i
$344$	2.27541	+	1.31371i	0.122682	+	0.0708304i
$345$	−9.79796	−	5.65685i	−0.527504	−	0.304555i
$346$		−	4.82843i		−	0.259578i
$347$	4.34315	−	7.52255i	0.233152	−	0.403832i	−0.725582	−	0.688136i	$-0.758429\pi$
$347$	4.34315	−	7.52255i	0.233152	−	0.403832i	0.958734	+	0.284304i	$0.0917626\pi$
$348$	−1.82843	−	3.16693i	−0.0980140	−	0.169765i
$349$	3.16693	−	1.82843i	0.169522	−	0.0978735i	−0.412839	−	0.910804i	$-0.635463\pi$
$349$	3.16693	−	1.82843i	0.169522	−	0.0978735i	0.582360	+	0.812931i	$0.302129\pi$
$350$	−3.51472			−0.187870
$351$		0			0
$352$	−8.82843			−0.470557
$353$	28.9736	−	16.7279i	1.54211	−	0.890337i	0.543404	−	0.839471i	$-0.317135\pi$
$353$	28.9736	−	16.7279i	1.54211	−	0.890337i	0.998705	−	0.0508663i	$-0.0161982\pi$
$354$	−1.58579	−	2.74666i	−0.0842836	−	0.145983i
$355$	−2.82843	+	4.89898i	−0.150117	+	0.260011i
$356$			27.1127i			1.43697i
$357$	18.7554	+	10.8284i	0.992640	+	0.573101i
$358$	8.36308	+	4.82843i	0.442003	+	0.255190i
$359$			34.9706i			1.84568i	0.385189	+	0.922838i	$0.374136\pi$
$359$			34.9706i			1.84568i	−0.385189	+	0.922838i	$0.625864\pi$
$360$	−2.24264	+	3.88437i	−0.118198	+	0.204724i
$361$	−5.50000	−	9.52628i	−0.289474	−	0.501383i
$362$	5.02207	−	2.89949i	0.263954	−	0.152394i
$363$	7.00000			0.367405
$364$		0			0
$365$	−0.970563			−0.0508016
$366$	−4.77589	+	2.75736i	−0.249640	+	0.144129i
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	0.988269	+	0.152721i	$0.0488036\pi$
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	−0.361874	+	0.932227i	$0.617863\pi$
$368$	−6.00000	+	10.3923i	−0.312772	+	0.541736i
$369$		−	5.17157i		−	0.269221i
$370$	7.76874	+	4.48528i	0.403877	+	0.233179i
$371$	4.89898	+	2.82843i	0.254342	+	0.146845i
$372$			2.14214i			0.111065i
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	−0.965945	−	0.258748i	$-0.916690\pi$
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	0.707055	+	0.707159i	$0.250023\pi$
$374$	−3.17157	−	5.49333i	−0.163998	−	0.284053i
$375$	4.89898	−	2.82843i	0.252982	−	0.146059i
$376$	−18.4853			−0.953306
$377$		0			0
$378$	1.17157			0.0602592
$379$	−0.420266	+	0.242641i	−0.0215876	+	0.0124636i	−0.510755	−	0.859726i	$-0.670634\pi$
$379$	−0.420266	+	0.242641i	−0.0215876	+	0.0124636i	0.489167	+	0.872190i	$0.337301\pi$
$380$	7.31371	+	12.6677i	0.375185	+	0.649840i
$381$	2.82843	−	4.89898i	0.144905	−	0.250982i
$382$		−	1.37258i		−	0.0702275i
$383$	26.8213	+	15.4853i	1.37050	+	0.791261i	0.990991	−	0.133926i	$-0.0427583\pi$
$383$	26.8213	+	15.4853i	1.37050	+	0.791261i	0.379513	+	0.925187i	$0.376092\pi$
$384$	9.14207	+	5.27817i	0.466529	+	0.269351i
$385$			16.0000i			0.815436i
$386$	−1.10051	+	1.90613i	−0.0560142	+	0.0970195i
$387$	−0.828427	−	1.43488i	−0.0421113	−	0.0729389i
$388$	−5.79050	+	3.34315i	−0.293968	+	0.169723i
$389$	26.9706			1.36746			0.683731	−	0.729734i	$-0.260356\pi$
$389$	26.9706			1.36746			0.683731	+	0.729734i	$0.260356\pi$
$390$		0			0
$391$	−30.6274			−1.54890
$392$	1.37333	−	0.792893i	0.0693637	−	0.0400472i
$393$	4.00000	+	6.92820i	0.201773	+	0.349482i
$394$	0.100505	−	0.174080i	0.00506337	−	0.00877002i
$395$		−	32.0000i		−	1.61009i
$396$	3.16693	+	1.82843i	0.159144	+	0.0918819i
$397$	−26.8213	−	15.4853i	−1.34612	−	0.777184i	−0.358424	−	0.933559i	$-0.616686\pi$
$397$	−26.8213	−	15.4853i	−1.34612	−	0.777184i	−0.987698	+	0.156375i	$0.950019\pi$
$398$			8.97056i			0.449654i
$399$	4.00000	−	6.92820i	0.200250	−	0.346844i
$400$	4.50000	+	7.79423i	0.225000	+	0.389711i
$401$	22.6398	−	13.0711i	1.13058	−	0.652738i	0.186496	−	0.982456i	$-0.440287\pi$
$401$	22.6398	−	13.0711i	1.13058	−	0.652738i	0.944080	+	0.329718i	$0.106954\pi$
$402$	−2.82843			−0.141069
$403$		0			0
$404$	−14.0000			−0.696526
$405$	2.44949	−	1.41421i	0.121716	−	0.0702728i
$406$	−1.17157	−	2.02922i	−0.0581442	−	0.100709i
$407$	7.65685	−	13.2621i	0.379536	−	0.657376i
$408$			12.1421i			0.601125i
$409$	−30.2854	−	17.4853i	−1.49752	−	0.864592i	−0.497521	−	0.867452i	$-0.665756\pi$
$409$	−30.2854	−	17.4853i	−1.49752	−	0.864592i	−0.999996	+	0.00286068i	$0.999089\pi$
$410$	5.24714	+	3.02944i	0.259138	+	0.149613i
$411$		−	10.8284i		−	0.534127i
$412$	2.14214	−	3.71029i	0.105535	−	0.182793i
$413$	10.8284	+	18.7554i	0.532832	+	0.922892i
$414$	−1.43488	+	0.828427i	−0.0705204	+	0.0407150i
$415$	10.3431			0.507725
$416$		0			0
$417$	−7.31371			−0.358154
$418$	−2.02922	+	1.17157i	−0.0992526	+	0.0573035i
$419$	−7.31371	−	12.6677i	−0.357298	−	0.618858i	0.630210	−	0.776424i	$-0.282969\pi$
$419$	−7.31371	−	12.6677i	−0.357298	−	0.618858i	−0.987508	+	0.157566i	$0.949635\pi$
$420$	7.31371	−	12.6677i	0.356872	−	0.618121i
$421$		−	37.3137i		−	1.81856i	−0.416186	−	0.909279i	$-0.636634\pi$
$421$		−	37.3137i		−	1.81856i	0.416186	−	0.909279i	$-0.363366\pi$
$422$	−4.30463	−	2.48528i	−0.209546	−	0.120982i
$423$	10.0951	+	5.82843i	0.490842	+	0.283388i
$424$			3.17157i			0.154025i
$425$	−11.4853	+	19.8931i	−0.557118	+	0.964957i
$426$	0.414214	+	0.717439i	0.0200687	+	0.0347600i
$427$	32.6118	−	18.8284i	1.57820	−	0.911171i
$428$	−20.6863			−0.999910
$429$		0			0
$430$	1.94113			0.0936094
$431$	−7.22538	+	4.17157i	−0.348034	+	0.200938i	−0.663819	−	0.747893i	$-0.731066\pi$
$431$	−7.22538	+	4.17157i	−0.348034	+	0.200938i	0.315785	+	0.948831i	$0.397732\pi$
$432$	−1.50000	−	2.59808i	−0.0721688	−	0.125000i
$433$	−10.6569	+	18.4582i	−0.512136	+	0.887045i	0.487765	+	0.872975i	$0.337812\pi$
$433$	−10.6569	+	18.4582i	−0.512136	+	0.887045i	−0.999901	+	0.0140703i	$0.995521\pi$
$434$			1.37258i			0.0658861i
$435$	−4.89898	−	2.82843i	−0.234888	−	0.135613i
$436$	8.41407	+	4.85786i	0.402961	+	0.232650i
$437$			11.3137i			0.541208i
$438$	−0.0710678	+	0.123093i	−0.00339575	+	0.00588161i
$439$	8.48528	+	14.6969i	0.404980	+	0.701447i	0.994319	−	0.106439i	$-0.0339450\pi$
$439$	8.48528	+	14.6969i	0.404980	+	0.701447i	−0.589339	+	0.807886i	$0.700612\pi$
$440$	−7.76874	+	4.48528i	−0.370360	+	0.213827i
$441$	−1.00000			−0.0476190
$442$		0			0
$443$	−25.9411			−1.23250			−0.616250	−	0.787551i	$-0.711349\pi$
$443$	−25.9411			−1.23250			−0.616250	+	0.787551i	$0.711349\pi$
$444$	−12.1244	+	7.00000i	−0.575396	+	0.332205i
$445$	20.9706	+	36.3221i	0.994100	+	1.72183i
$446$	−2.58579	+	4.47871i	−0.122441	+	0.212073i
$447$			9.17157i			0.433801i
$448$	−10.2182	−	5.89949i	−0.482766	−	0.278725i
$449$	27.5387	+	15.8995i	1.29963	+	0.750344i	0.980341	−	0.197313i	$-0.0632214\pi$
$449$	27.5387	+	15.8995i	1.29963	+	0.750344i	0.319293	+	0.947656i	$0.396555\pi$
$450$			1.24264i			0.0585786i
$451$	5.17157	−	8.95743i	0.243520	−	0.421789i
$452$	4.85786	+	8.41407i	0.228495	+	0.395764i
$453$	−3.04384	+	1.75736i	−0.143012	+	0.0825679i
$454$	7.17157			0.336579
$455$		0			0
$456$	4.48528			0.210043
$457$	6.63103	−	3.82843i	0.310187	−	0.179086i	−0.336823	−	0.941568i	$-0.609353\pi$
$457$	6.63103	−	3.82843i	0.310187	−	0.179086i	0.647010	+	0.762482i	$0.276019\pi$
$458$	0.272078	+	0.471253i	0.0127134	+	0.0220202i
$459$	3.82843	−	6.63103i	0.178696	−	0.309510i
$460$			20.6863i			0.964503i
$461$	4.47871	+	2.58579i	0.208594	+	0.120432i	0.600658	−	0.799506i	$-0.294905\pi$
$461$	4.47871	+	2.58579i	0.208594	+	0.120432i	−0.392064	+	0.919938i	$0.628239\pi$
$462$	2.02922	+	1.17157i	0.0944080	+	0.0545065i
$463$		−	24.4853i		−	1.13793i	−0.822363	−	0.568964i	$-0.807344\pi$
$463$		−	24.4853i		−	1.13793i	0.822363	−	0.568964i	$-0.192656\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	1.65685	+	2.86976i	0.0768348	+	0.133082i
$466$	2.50048	−	1.44365i	0.115832	−	0.0668758i
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	19.3137			0.891824
$470$	−11.8272	+	6.82843i	−0.545547	+	0.314972i
$471$	5.00000	+	8.66025i	0.230388	+	0.399043i
$472$	−6.07107	+	10.5154i	−0.279444	+	0.484010i
$473$		−	3.31371i		−	0.152364i
$474$	−4.05845	−	2.34315i	−0.186411	−	0.107624i
$475$	7.34847	+	4.24264i	0.337171	+	0.194666i
$476$		−	39.5980i		−	1.81497i
$477$	1.00000	−	1.73205i	0.0457869	−	0.0793052i
$478$	0.414214	+	0.717439i	0.0189457	+	0.0328149i
$479$	21.9223	−	12.6569i	1.00166	−	0.578306i	0.0929182	−	0.995674i	$-0.470380\pi$
$479$	21.9223	−	12.6569i	1.00166	−	0.578306i	0.908738	+	0.417367i	$0.137047\pi$
$480$	12.4853			0.569873
$481$		0			0
$482$	0.142136			0.00647410
$483$	9.79796	−	5.65685i	0.445823	−	0.257396i
$484$	−6.39949	−	11.0843i	−0.290886	−	0.503830i
$485$	−5.17157	+	8.95743i	−0.234829	+	0.406736i
$486$		−	0.414214i		−	0.0187891i
$487$	−6.75412	−	3.89949i	−0.306059	−	0.176703i	0.339103	−	0.940749i	$-0.389877\pi$
$487$	−6.75412	−	3.89949i	−0.306059	−	0.176703i	−0.645161	+	0.764046i	$0.723210\pi$
$488$	18.2841	+	10.5563i	0.827684	+	0.477863i
$489$			18.8284i			0.851451i
$490$	0.585786	−	1.01461i	0.0264631	−	0.0458355i
$491$	15.3137	+	26.5241i	0.691098	+	1.19702i	0.971478	+	0.237128i	$0.0762060\pi$
$491$	15.3137	+	26.5241i	0.691098	+	1.19702i	−0.280380	+	0.959889i	$0.590461\pi$
$492$	−8.18900	+	4.72792i	−0.369189	+	0.213151i
$493$	−15.3137			−0.689695
$494$		0			0
$495$	5.65685			0.254257
$496$	3.04384	−	1.75736i	0.136672	−	0.0789078i
$497$	−2.82843	−	4.89898i	−0.126872	−	0.219749i
$498$	0.757359	−	1.31178i	0.0339381	−	0.0587825i
$499$		−	26.1421i		−	1.17028i	−0.810931	−	0.585141i	$-0.801039\pi$
$499$		−	26.1421i		−	1.17028i	0.810931	−	0.585141i	$-0.198961\pi$
$500$	−8.95743	−	5.17157i	−0.400588	−	0.231280i
$501$	3.16693	+	1.82843i	0.141488	+	0.0816881i
$502$		0			0
$503$	3.65685	−	6.33386i	0.163051	−	0.282413i	−0.772910	−	0.634515i	$-0.781200\pi$
$503$	3.65685	−	6.33386i	0.163051	−	0.282413i	0.935961	+	0.352102i	$0.114533\pi$
$504$	−2.24264	−	3.88437i	−0.0998952	−	0.173023i
$505$	−18.7554	+	10.8284i	−0.834604	+	0.481859i
$506$	−3.31371			−0.147312
$507$		0			0
$508$	−10.3431			−0.458903
$509$	−10.2182	+	5.89949i	−0.452915	+	0.261491i	−0.709060	−	0.705148i	$-0.750881\pi$
$509$	−10.2182	+	5.89949i	−0.452915	+	0.261491i	0.256146	+	0.966638i	$0.417547\pi$
$510$	4.48528	+	7.76874i	0.198612	+	0.344005i
$511$	0.485281	−	0.840532i	0.0214676	−	0.0371829i
$512$		−	22.7574i		−	1.00574i
$513$	−2.44949	−	1.41421i	−0.108148	−	0.0624391i
$514$	1.55797	+	0.899495i	0.0687192	+	0.0396750i
$515$		−	6.62742i		−	0.292039i
$516$	−1.51472	+	2.62357i	−0.0666818	+	0.115496i
$517$	11.6569	+	20.1903i	0.512668	+	0.887967i
$518$	−7.76874	+	4.48528i	−0.341339	+	0.197072i
$519$	11.6569			0.511679
$520$		0			0
$521$	25.3137			1.10901			0.554507	−	0.832179i	$-0.312907\pi$
$521$	25.3137			1.10901			0.554507	+	0.832179i	$0.312907\pi$
$522$	−0.717439	+	0.414214i	−0.0314014	+	0.0181296i
$523$	7.65685	+	13.2621i	0.334811	+	0.579909i	0.983448	−	0.181188i	$-0.0579942\pi$
$523$	7.65685	+	13.2621i	0.334811	+	0.579909i	−0.648638	+	0.761097i	$0.724661\pi$
$524$	7.31371	−	12.6677i	0.319501	−	0.553392i
$525$		−	8.48528i		−	0.370328i
$526$	4.30463	+	2.48528i	0.187691	+	0.108363i
$527$	7.76874	+	4.48528i	0.338411	+	0.195382i
$528$		−	6.00000i		−	0.261116i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	1.17157	+	2.02922i	0.0508899	+	0.0881438i
$531$	6.63103	−	3.82843i	0.287762	−	0.166140i
$532$	−14.6274			−0.634179
$533$		0			0
$534$	6.14214			0.265796
$535$	−27.7128	+	16.0000i	−1.19813	+	0.691740i
$536$	5.41421	+	9.37769i	0.233858	+	0.405055i
$537$	−11.6569	+	20.1903i	−0.503030	+	0.871274i
$538$		−	7.45584i		−	0.321444i
$539$	−1.73205	−	1.00000i	−0.0746047	−	0.0430730i
$540$	−4.47871	−	2.58579i	−0.192733	−	0.111275i
$541$			10.0000i			0.429934i	0.976621	+	0.214967i	$0.0689643\pi$
$541$			10.0000i			0.429934i	−0.976621	+	0.214967i	$0.931036\pi$
$542$	5.75736	−	9.97204i	0.247300	−	0.428336i
$543$	7.00000	+	12.1244i	0.300399	+	0.520306i
$544$	29.2708	−	16.8995i	1.25497	−	0.724560i
$545$	15.0294			0.643790
$546$		0			0
$547$	23.3137			0.996822			0.498411	−	0.866941i	$-0.333917\pi$
$547$	23.3137			0.996822			0.498411	+	0.866941i	$0.333917\pi$
$548$	−17.1464	+	9.89949i	−0.732459	+	0.422885i
$549$	−6.65685	−	11.5300i	−0.284108	−	0.492089i
$550$	−1.24264	+	2.15232i	−0.0529864	+	0.0917751i
$551$			5.65685i			0.240990i
$552$	5.49333	+	3.17157i	0.233811	+	0.134991i
$553$	27.7128	+	16.0000i	1.17847	+	0.680389i
$554$		−	0.828427i		−	0.0351965i
$555$	−10.8284	+	18.7554i	−0.459641	+	0.796122i
$556$	6.68629	+	11.5810i	0.283562	+	0.491144i
$557$	−6.75412	+	3.89949i	−0.286181	+	0.165227i	−0.636218	−	0.771509i	$-0.719502\pi$
$557$	−6.75412	+	3.89949i	−0.286181	+	0.165227i	0.350037	+	0.936736i	$0.386169\pi$
$558$	0.485281			0.0205436
$559$		0			0
$560$	−24.0000			−1.01419
$561$	13.2621	−	7.65685i	0.559925	−	0.323273i
$562$	−4.38478	−	7.59466i	−0.184961	−	0.320361i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		−	21.3137i		−	0.897469i
$565$	13.0159	+	7.51472i	0.547582	+	0.316147i
$566$	−10.3923	−	6.00000i	−0.436821	−	0.252199i
$567$			2.82843i			0.118783i
$568$	1.58579	−	2.74666i	0.0665381	−	0.115247i
$569$	−21.4853	−	37.2136i	−0.900710	−	1.56008i	−0.826575	−	0.562827i	$-0.809714\pi$
$569$	−21.4853	−	37.2136i	−0.900710	−	1.56008i	−0.0741351	−	0.997248i	$-0.523620\pi$
$570$	2.86976	−	1.65685i	0.120201	−	0.0693980i
$571$	12.9706			0.542801			0.271401	−	0.962466i	$-0.412513\pi$
$571$	12.9706			0.542801			0.271401	+	0.962466i	$0.412513\pi$
$572$		0			0
$573$	3.31371			0.138432
$574$	−5.24714	+	3.02944i	−0.219011	+	0.126446i
$575$	6.00000	+	10.3923i	0.250217	+	0.433389i
$576$	−2.08579	+	3.61269i	−0.0869078	+	0.150529i
$577$			31.9411i			1.32973i	0.746965	+	0.664863i	$0.231510\pi$
$577$			31.9411i			1.32973i	−0.746965	+	0.664863i	$0.768490\pi$
$578$	14.9326	+	8.62132i	0.621113	+	0.358600i
$579$	−4.60181	−	2.65685i	−0.191245	−	0.110415i
$580$			10.3431i			0.429476i
$581$	−5.17157	+	8.95743i	−0.214553	+	0.371617i
$582$	0.757359	+	1.31178i	0.0313936	+	0.0543752i
$583$	3.46410	−	2.00000i	0.143468	−	0.0828315i
$584$	0.544156			0.0225173
$585$		0			0
$586$	0.887302			0.0366541
$587$	9.50079	−	5.48528i	0.392139	−	0.226402i	−0.290947	−	0.956739i	$-0.593970\pi$
$587$	9.50079	−	5.48528i	0.392139	−	0.226402i	0.683087	+	0.730337i	$0.260637\pi$
$588$	0.914214	+	1.58346i	0.0377015	+	0.0653010i
$589$	1.65685	−	2.86976i	0.0682695	−	0.118246i
$590$			8.97056i			0.369312i
$591$	0.420266	+	0.242641i	0.0172874	+	0.00998090i
$592$	19.8931	+	11.4853i	0.817601	+	0.472042i
$593$		−	20.4853i		−	0.841230i	−0.907239	−	0.420615i	$-0.861814\pi$
$593$		−	20.4853i		−	0.841230i	0.907239	−	0.420615i	$-0.138186\pi$
$594$	0.414214	−	0.717439i	0.0169954	−	0.0294369i
$595$	−30.6274	−	53.0482i	−1.25560	−	2.17477i
$596$	14.5229	−	8.38478i	0.594879	−	0.343454i
$597$	−21.6569			−0.886356
$598$		0			0
$599$	−23.3137			−0.952572			−0.476286	−	0.879290i	$-0.658017\pi$
$599$	−23.3137			−0.952572			−0.476286	+	0.879290i	$0.658017\pi$
$600$	4.11999	−	2.37868i	0.168198	−	0.0971092i
$601$	0.313708	+	0.543359i	0.0127964	+	0.0221641i	0.872353	−	0.488877i	$-0.162593\pi$
$601$	0.313708	+	0.543359i	0.0127964	+	0.0221641i	−0.859556	+	0.511041i	$0.829260\pi$
$602$	−0.970563	+	1.68106i	−0.0395572	+	0.0685151i
$603$		−	6.82843i		−	0.278075i
$604$	5.56543	+	3.21320i	0.226454	+	0.130743i
$605$	−17.1464	−	9.89949i	−0.697101	−	0.402472i
$606$			3.17157i			0.128836i
$607$	−20.9706	+	36.3221i	−0.851169	+	1.47427i	0.0289853	+	0.999580i	$0.490772\pi$
$607$	−20.9706	+	36.3221i	−0.851169	+	1.47427i	−0.880154	+	0.474688i	$0.842561\pi$
$608$	−6.24264	−	10.8126i	−0.253173	−	0.438508i
$609$	4.89898	−	2.82843i	0.198517	−	0.114614i
$610$	15.5980			0.631544
$611$		0			0
$612$	−14.0000			−0.565916
$613$	41.2720	−	23.8284i	1.66696	−	0.962421i	0.697700	−	0.716390i	$-0.254207\pi$
$613$	41.2720	−	23.8284i	1.66696	−	0.962421i	0.969262	−	0.246031i	$-0.0791267\pi$
$614$	4.72792	+	8.18900i	0.190803	+	0.330481i
$615$	−7.31371	+	12.6677i	−0.294917	+	0.510812i
$616$		−	8.97056i		−	0.361434i
$617$	−30.1623	−	17.4142i	−1.21429	−	0.701070i	−0.250598	−	0.968091i	$-0.580627\pi$
$617$	−30.1623	−	17.4142i	−1.21429	−	0.701070i	−0.963691	+	0.267021i	$0.913961\pi$
$618$	−0.840532	−	0.485281i	−0.0338112	−	0.0195209i
$619$			23.7990i			0.956562i	0.878207	+	0.478281i	$0.158740\pi$
$619$			23.7990i			0.956562i	−0.878207	+	0.478281i	$0.841260\pi$
$620$	3.02944	−	5.24714i	0.121665	−	0.210730i
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	−3.81226	+	2.20101i	−0.152858	+	0.0882525i
$623$	−41.9411			−1.68034
$624$		0			0
$625$	−31.0000			−1.24000
$626$	−2.15232	+	1.24264i	−0.0860239	+	0.0496659i
$627$	−2.82843	−	4.89898i	−0.112956	−	0.195646i
$628$	9.14214	−	15.8346i	0.364811	−	0.631871i
$629$			58.6274i			2.33763i
$630$	−2.86976	−	1.65685i	−0.114334	−	0.0660107i
$631$	−37.3367	−	21.5563i	−1.48635	−	0.858145i	−0.486471	−	0.873697i	$-0.661716\pi$
$631$	−37.3367	−	21.5563i	−1.48635	−	0.858145i	−0.999879	+	0.0155519i	$0.995049\pi$
$632$			17.9411i			0.713660i
$633$	6.00000	−	10.3923i	0.238479	−	0.413057i
$634$	1.75736	+	3.04384i	0.0697937	+	0.120886i
$635$	−13.8564	+	8.00000i	−0.549875	+	0.317470i
$636$	−3.65685			−0.145004
$637$		0			0
$638$	−1.65685			−0.0655955
$639$	−1.73205	+	1.00000i	−0.0685189	+	0.0395594i
$640$	−14.9289	−	25.8577i	−0.590118	−	1.02211i
$641$	15.1421	−	26.2269i	0.598078	−	1.03590i	−0.395026	−	0.918670i	$-0.629264\pi$
$641$	15.1421	−	26.2269i	0.598078	−	1.03590i	0.993105	−	0.117232i	$-0.0374022\pi$
$642$			4.68629i			0.184953i
$643$	19.7700	+	11.4142i	0.779653	+	0.450133i	0.836307	−	0.548261i	$-0.184710\pi$
$643$	19.7700	+	11.4142i	0.779653	+	0.450133i	−0.0566545	+	0.998394i	$0.518043\pi$
$644$	−17.9149	−	10.3431i	−0.705944	−	0.407577i
$645$			4.68629i			0.184523i
$646$	4.48528	−	7.76874i	0.176471	−	0.305657i
$647$	5.65685	+	9.79796i	0.222394	+	0.385198i	0.955534	−	0.294880i	$-0.0952796\pi$
$647$	5.65685	+	9.79796i	0.222394	+	0.385198i	−0.733140	+	0.680077i	$0.761946\pi$
$648$	−1.37333	+	0.792893i	−0.0539496	+	0.0311478i
$649$	15.3137			0.601116
$650$		0			0
$651$	−3.31371			−0.129874
$652$	29.8141	−	17.2132i	1.16761	−	0.674121i
$653$	12.6569	+	21.9223i	0.495301	+	0.857886i	0.999985	−	0.00541749i	$-0.00172445\pi$
$653$	12.6569	+	21.9223i	0.495301	+	0.857886i	−0.504684	+	0.863304i	$0.668391\pi$
$654$	1.10051	−	1.90613i	0.0430332	−	0.0745356i
$655$		−	22.6274i		−	0.884126i
$656$	13.4361	+	7.75736i	0.524593	+	0.302874i
$657$	−0.297173	−	0.171573i	−0.0115938	−	0.00669370i
$658$		−	13.6569i		−	0.532400i
$659$	23.6569	−	40.9749i	0.921540	−	1.59615i	0.124507	−	0.992219i	$-0.460265\pi$
$659$	23.6569	−	40.9749i	0.921540	−	1.59615i	0.797033	−	0.603936i	$-0.206402\pi$
$660$	−5.17157	−	8.95743i	−0.201303	−	0.348667i
$661$	−30.2854	+	17.4853i	−1.17797	+	0.680099i	−0.955543	−	0.294852i	$-0.904730\pi$
$661$	−30.2854	+	17.4853i	−1.17797	+	0.680099i	−0.222422	+	0.974950i	$0.571396\pi$
$662$	−10.8284			−0.420859
$663$		0			0
$664$	−5.79899			−0.225044
$665$	−19.5959	+	11.3137i	−0.759897	+	0.438727i
$666$	1.58579	+	2.74666i	0.0614480	+	0.106431i
$667$	−4.00000	+	6.92820i	−0.154881	+	0.268261i
$668$		−	6.68629i		−	0.258700i
$669$	−10.8126	−	6.24264i	−0.418038	−	0.241354i
$670$	6.92820	+	4.00000i	0.267660	+	0.154533i
$671$		−	26.6274i		−	1.02794i
$672$	−6.24264	+	10.8126i	−0.240815	+	0.417104i
$673$	8.31371	+	14.3998i	0.320470	+	0.555070i	0.980585	−	0.196094i	$-0.0628259\pi$
$673$	8.31371	+	14.3998i	0.320470	+	0.555070i	−0.660115	+	0.751164i	$0.729493\pi$
$674$	3.34101	−	1.92893i	0.128691	−	0.0742997i
$675$	−3.00000			−0.115470
$676$		0			0
$677$	26.6863			1.02564			0.512819	−	0.858497i	$-0.328601\pi$
$677$	26.6863			1.02564			0.512819	+	0.858497i	$0.328601\pi$
$678$	1.90613	−	1.10051i	0.0732045	−	0.0422646i
$679$	−5.17157	−	8.95743i	−0.198467	−	0.343754i
$680$	17.1716	−	29.7420i	0.658500	−	1.14056i
$681$			17.3137i			0.663463i
$682$	0.840532	+	0.485281i	0.0321856	+	0.0185824i
$683$	−41.5182	−	23.9706i	−1.58865	−	0.917208i	−0.993530	−	0.113572i	$-0.963771\pi$
$683$	−41.5182	−	23.9706i	−1.58865	−	0.917208i	−0.595121	−	0.803636i	$-0.702896\pi$
$684$			5.17157i			0.197740i
$685$	−15.3137	+	26.5241i	−0.585107	+	1.01343i
$686$	−3.51472	−	6.08767i	−0.134193	−	0.232428i
$687$	−1.13770	+	0.656854i	−0.0434062	+	0.0250606i
$688$	4.97056			0.189501
$689$		0			0
$690$	4.68629			0.178404
$691$	5.07306	−	2.92893i	0.192988	−	0.111422i	−0.400392	−	0.916344i	$-0.631126\pi$
$691$	5.07306	−	2.92893i	0.192988	−	0.111422i	0.593381	+	0.804922i	$0.297793\pi$
$692$	−10.6569	−	18.4582i	−0.405113	−	0.701676i
$693$	−2.82843	+	4.89898i	−0.107443	+	0.186097i
$694$			3.59798i			0.136577i
$695$	17.9149	+	10.3431i	0.679549	+	0.392338i
$696$	2.74666	+	1.58579i	0.104112	+	0.0601091i
$697$			39.5980i			1.49988i
$698$	−0.757359	+	1.31178i	−0.0286665	+	0.0496518i
$699$	3.48528	+	6.03668i	0.131825	+	0.228328i
$700$	−13.4361	+	7.75736i	−0.507838	+	0.293201i
$701$	−5.02944			−0.189959			−0.0949796	−	0.995479i	$-0.530279\pi$
$701$	−5.02944			−0.189959			−0.0949796	+	0.995479i	$0.530279\pi$
$702$		0			0
$703$	21.6569			0.816804
$704$	−7.22538	+	4.17157i	−0.272317	+	0.157222i
$705$	−16.4853	−	28.5533i	−0.620872	−	1.07538i
$706$	−6.92893	+	12.0013i	−0.260774	+	0.451673i
$707$		−	21.6569i		−	0.814490i
$708$	−12.1244	−	7.00000i	−0.455661	−	0.263076i
$709$	4.00746	+	2.31371i	0.150503	+	0.0868931i	0.573360	−	0.819303i	$-0.305639\pi$
$709$	4.00746	+	2.31371i	0.150503	+	0.0868931i	−0.422857	+	0.906196i	$0.638973\pi$
$710$		−	2.34315i		−	0.0879367i
$711$	5.65685	−	9.79796i	0.212149	−	0.367452i
$712$	−11.7574	−	20.3643i	−0.440626	−	0.763186i
$713$	4.05845	−	2.34315i	0.151990	−	0.0877515i
$714$	−8.97056			−0.335715
$715$		0			0
$716$	42.6274			1.59306
$717$	−1.73205	+	1.00000i	−0.0646846	+	0.0373457i
$718$	−7.24264	−	12.5446i	−0.270293	−	0.468161i
$719$	−14.9706	+	25.9298i	−0.558308	+	0.967017i	0.439330	+	0.898326i	$0.355216\pi$
$719$	−14.9706	+	25.9298i	−0.558308	+	0.967017i	−0.997638	+	0.0686918i	$0.978117\pi$
$720$			8.48528i			0.316228i
$721$	5.73951	+	3.31371i	0.213751	+	0.123409i
$722$	3.94591	+	2.27817i	0.146852	+	0.0847849i
$723$			0.343146i			0.0127617i
$724$	12.7990	−	22.1685i	0.475671	−	0.823886i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$	−2.51104	+	1.44975i	−0.0931933	+	0.0538052i
$727$	10.3431			0.383606			0.191803	−	0.981433i	$-0.438567\pi$
$727$	10.3431			0.383606			0.191803	+	0.981433i	$0.438567\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	0.348160	−	0.201010i	0.0128860	−	0.00743972i
$731$	6.34315	+	10.9867i	0.234610	+	0.406356i
$732$	−12.1716	+	21.0818i	−0.449874	+	0.779205i
$733$			36.6274i			1.35286i	0.736505	+	0.676432i	$0.236475\pi$
$733$			36.6274i			1.35286i	−0.736505	+	0.676432i	$0.763525\pi$
$734$	−8.60927	−	4.97056i	−0.317774	−	0.183467i
$735$	2.44949	+	1.41421i	0.0903508	+	0.0521641i
$736$		−	17.6569i		−	0.650840i
$737$	6.82843	−	11.8272i	0.251528	−	0.435660i
$738$	1.07107	+	1.85514i	0.0394266	+	0.0682888i
$739$	−15.7116	+	9.07107i	−0.577959	+	0.333685i	−0.760322	−	0.649547i	$-0.774959\pi$
$739$	−15.7116	+	9.07107i	−0.577959	+	0.333685i	0.182363	+	0.983231i	$0.441625\pi$
$740$	39.5980			1.45565
$741$		0			0
$742$	−2.34315			−0.0860196
$743$	−1.73205	+	1.00000i	−0.0635428	+	0.0366864i	−0.531435	−	0.847099i	$-0.678347\pi$
$743$	−1.73205	+	1.00000i	−0.0635428	+	0.0366864i	0.467892	+	0.883786i	$0.345014\pi$
$744$	−0.928932	−	1.60896i	−0.0340563	−	0.0589873i
$745$	12.9706	−	22.4657i	0.475205	−	0.823079i
$746$		−	4.14214i		−	0.151654i
$747$	3.16693	+	1.82843i	0.115872	+	0.0668987i
$748$	−24.2487	−	14.0000i	−0.886621	−	0.511891i
$749$		−	32.0000i		−	1.16925i
$750$	−1.17157	+	2.02922i	−0.0427798	+	0.0740968i
$751$	−0.485281	−	0.840532i	−0.0177082	−	0.0306714i	0.857036	−	0.515257i	$-0.172304\pi$
$751$	−0.485281	−	0.840532i	−0.0177082	−	0.0306714i	−0.874744	+	0.484586i	$0.838970\pi$
$752$	−30.2854	+	17.4853i	−1.10439	+	0.637623i
$753$		0			0
$754$		0			0
$755$	9.94113			0.361795
$756$	4.47871	−	2.58579i	0.162889	−	0.0940441i
$757$	−25.9706	−	44.9823i	−0.943916	−	1.63491i	−0.757907	−	0.652363i	$-0.773778\pi$
$757$	−25.9706	−	44.9823i	−0.943916	−	1.63491i	−0.186009	−	0.982548i	$-0.559555\pi$
$758$	0.100505	−	0.174080i	0.00365051	−	0.00632287i
$759$		−	8.00000i		−	0.290382i
$760$	−10.9867	−	6.34315i	−0.398528	−	0.230090i
$761$	−28.1331	−	16.2426i	−1.01982	−	0.588795i	−0.105771	−	0.994391i	$-0.533731\pi$
$761$	−28.1331	−	16.2426i	−1.01982	−	0.588795i	−0.914053	+	0.405595i	$0.867064\pi$
$762$			2.34315i			0.0848832i
$763$	−7.51472	+	13.0159i	−0.272051	+	0.471206i
$764$	−3.02944	−	5.24714i	−0.109601	−	0.189835i
$765$	−18.7554	+	10.8284i	−0.678102	+	0.391503i
$766$	−12.8284			−0.463510
$767$		0			0
$768$	3.97056			0.143275
$769$	−36.3731	+	21.0000i	−1.31165	+	0.757279i	−0.982369	−	0.186954i	$-0.940139\pi$
$769$	−36.3731	+	21.0000i	−1.31165	+	0.757279i	−0.329278	+	0.944233i	$0.606805\pi$
$770$	−3.31371	−	5.73951i	−0.119418	−	0.206838i
$771$	−2.17157	+	3.76127i	−0.0782073	+	0.135459i
$772$			9.71573i			0.349677i
$773$	29.5680	+	17.0711i	1.06349	+	0.614004i	0.926394	−	0.376555i	$-0.122891\pi$
$773$	29.5680	+	17.0711i	1.06349	+	0.614004i	0.137091	+	0.990558i	$0.456225\pi$
$774$	0.594346	+	0.343146i	0.0213633	+	0.0123341i
$775$		−	3.51472i		−	0.126252i
$776$	2.89949	−	5.02207i	0.104086	−	0.180282i
$777$	−10.8284	−	18.7554i	−0.388468	−	0.672846i
$778$	−9.67487	+	5.58579i	−0.346861	+	0.200260i
$779$	14.6274			0.524082
$780$		0			0
$781$	−4.00000			−0.143131
$782$	10.9867	−	6.34315i	0.392882	−	0.226830i
$783$	−1.00000	−	1.73205i	−0.0357371	−	0.0618984i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$		−	28.2843i		−	1.00951i
$786$	−2.86976	−	1.65685i	−0.102361	−	0.0590980i
$787$	35.3075	+	20.3848i	1.25858	+	0.726639i	0.972798	−	0.231657i	$-0.0744147\pi$
$787$	35.3075	+	20.3848i	1.25858	+	0.726639i	0.285778	+	0.958296i	$0.407748\pi$
$788$		−	0.887302i		−	0.0316088i
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$	6.62742	+	11.4790i	0.235793	+	0.408405i
$791$	−13.0159	+	7.51472i	−0.462791	+	0.267193i
$792$	−3.17157			−0.112697
$793$		0			0
$794$	12.8284			0.455264
$795$	−4.89898	+	2.82843i	−0.173749	+	0.100314i
$796$	19.7990	+	34.2929i	0.701757	+	1.21548i
$797$	12.1716	−	21.0818i	0.431139	−	0.746755i	−0.565832	−	0.824520i	$-0.691445\pi$
$797$	12.1716	−	21.0818i	0.431139	−	0.746755i	0.996972	+	0.0777652i	$0.0247784\pi$
$798$			3.31371i			0.117304i
$799$	−77.2970	−	44.6274i	−2.73457	−	1.57880i
$800$	−11.4685	−	6.62132i	−0.405471	−	0.234099i
$801$			14.8284i			0.523937i
$802$	−5.41421	+	9.37769i	−0.191183	+	0.331138i
$803$	−0.343146	−	0.594346i	−0.0121094	−	0.0209740i
$804$	−10.8126	+	6.24264i	−0.381330	+	0.220161i
$805$	−32.0000			−1.12785
$806$		0			0
$807$	18.0000			0.633630
$808$	10.5154	−	6.07107i	0.369930	−	0.213579i
$809$	−9.34315	−	16.1828i	−0.328488	−	0.568957i	0.653724	−	0.756733i	$-0.273206\pi$
$809$	−9.34315	−	16.1828i	−0.328488	−	0.568957i	−0.982212	+	0.187776i	$0.939872\pi$
$810$	−0.585786	+	1.01461i	−0.0205824	+	0.0356498i
$811$			30.1421i			1.05843i	0.848487	+	0.529217i	$0.177514\pi$
$811$			30.1421i			1.05843i	−0.848487	+	0.529217i	$0.822486\pi$
$812$	−8.95743	−	5.17157i	−0.314344	−	0.181487i
$813$	24.0746	+	13.8995i	0.844334	+	0.487477i
$814$			6.34315i			0.222327i
$815$	26.6274	−	46.1200i	0.932718	−	1.61551i
$816$	11.4853	+	19.8931i	0.402065	+	0.696397i
$817$	4.05845	−	2.34315i	0.141987	−	0.0819763i
$818$	14.4853			0.506466
$819$		0			0
$820$	26.7452			0.933982
$821$	20.6105	−	11.8995i	0.719312	−	0.415295i	−0.0951871	−	0.995459i	$-0.530345\pi$
$821$	20.6105	−	11.8995i	0.719312	−	0.415295i	0.814500	+	0.580164i	$0.197012\pi$
$822$	2.24264	+	3.88437i	0.0782211	+	0.135483i
$823$	7.51472	−	13.0159i	0.261947	−	0.453705i	−0.704813	−	0.709394i	$-0.748969\pi$
$823$	7.51472	−	13.0159i	0.261947	−	0.453705i	0.966759	+	0.255689i	$0.0823022\pi$
$824$			3.71573i			0.129444i
$825$	−5.19615	−	3.00000i	−0.180907	−	0.104447i
$826$	−7.76874	−	4.48528i	−0.270309	−	0.156063i
$827$		−	26.0000i		−	0.904109i	−0.891990	−	0.452054i	$-0.850691\pi$
$827$		−	26.0000i		−	0.904109i	0.891990	−	0.452054i	$-0.149309\pi$
$828$	−3.65685	+	6.33386i	−0.127084	+	0.220117i
$829$	−8.65685	−	14.9941i	−0.300665	−	0.520767i	0.675622	−	0.737248i	$-0.263875\pi$
$829$	−8.65685	−	14.9941i	−0.300665	−	0.520767i	−0.976287	+	0.216481i	$0.930542\pi$
$830$	−3.71029	+	2.14214i	−0.128786	+	0.0743546i
$831$	2.00000			0.0693792
$832$		0			0
$833$	7.65685			0.265294
$834$	2.62357	−	1.51472i	0.0908468	−	0.0524504i
$835$	−5.17157	−	8.95743i	−0.178970	−	0.309985i
$836$	−5.17157	+	8.95743i	−0.178863	+	0.309799i
$837$			1.17157i			0.0404955i
$838$	5.24714	+	3.02944i	0.181259	+	0.104650i
$839$	−37.4598	−	21.6274i	−1.29326	−	0.746661i	−0.314026	−	0.949415i	$-0.601678\pi$
$839$	−37.4598	−	21.6274i	−1.29326	−	0.746661i	−0.979230	+	0.202753i	$0.935011\pi$
$840$			12.6863i			0.437719i
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	7.72792	+	13.3852i	0.266322	+	0.461283i
$843$	18.3351	−	10.5858i	0.631495	−	0.364594i
$844$	−21.9411			−0.755245
$845$		0			0
$846$	−4.82843			−0.166005
$847$	17.1464	−	9.89949i	0.589158	−	0.340151i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$	14.4853	−	25.0892i	0.497134	−	0.861061i
$850$		−	9.51472i		−	0.326352i
$851$	26.5241	+	15.3137i	0.909235	+	0.524947i
$852$	3.16693	+	1.82843i	0.108497	+	0.0626409i
$853$			3.65685i			0.125208i	0.998038	+	0.0626042i	$0.0199406\pi$
$853$			3.65685i			0.125208i	−0.998038	+	0.0626042i	$0.980059\pi$
$854$	−7.79899	+	13.5082i	−0.266876	+	0.462243i
$855$	4.00000	+	6.92820i	0.136797	+	0.236940i
$856$	15.5375	−	8.97056i	0.531060	−	0.306608i
$857$	49.5980			1.69423			0.847117	−	0.531406i	$-0.178336\pi$
$857$	49.5980			1.69423			0.847117	+	0.531406i	$0.178336\pi$
$858$		0			0
$859$	−0.686292			−0.0234160			−0.0117080	−	0.999931i	$-0.503727\pi$
$859$	−0.686292			−0.0234160			−0.0117080	+	0.999931i	$0.503727\pi$
$860$	7.42058	−	4.28427i	0.253040	−	0.146092i
$861$	−7.31371	−	12.6677i	−0.249251	−	0.431715i
$862$	1.72792	−	2.99285i	0.0588533	−	0.101937i
$863$			28.3431i			0.964812i	0.875948	+	0.482406i	$0.160237\pi$
$863$			28.3431i			0.964812i	−0.875948	+	0.482406i	$0.839763\pi$
$864$	3.82282	+	2.20711i	0.130055	+	0.0750873i
$865$	−28.5533	−	16.4853i	−0.970843	−	0.560516i
$866$		−	8.82843i		−	0.300002i
$867$	−20.8137	+	36.0504i	−0.706871	+	1.22434i
$868$	3.02944	+	5.24714i	0.102826	+	0.178100i
$869$	19.5959	−	11.3137i	0.664746	−	0.383791i
$870$	2.34315			0.0794401
$871$		0			0
$872$	−8.42641			−0.285354
$873$	−3.16693	+	1.82843i	−0.107184	+	0.0618829i
$874$	−2.34315	−	4.05845i	−0.0792581	−	0.137279i
$875$	8.00000	−	13.8564i	0.270449	−	0.468432i
$876$			0.627417i			0.0211985i
$877$	36.6193	+	21.1421i	1.23654	+	0.713919i	0.968386	−	0.249456i	$-0.0802517\pi$
$877$	36.6193	+	21.1421i	1.23654	+	0.713919i	0.268158	+	0.963375i	$0.413585\pi$
$878$	−6.08767	−	3.51472i	−0.205449	−	0.118616i
$879$			2.14214i			0.0722524i
$880$	−8.48528	+	14.6969i	−0.286039	+	0.495434i
$881$	−12.7990	−	22.1685i	−0.431209	−	0.746876i	0.565769	−	0.824564i	$-0.308579\pi$
$881$	−12.7990	−	22.1685i	−0.431209	−	0.746876i	−0.996978	+	0.0776882i	$0.975246\pi$
$882$	0.358719	−	0.207107i	0.0120787	−	0.00697365i
$883$	−27.5980			−0.928746			−0.464373	−	0.885640i	$-0.653720\pi$
$883$	−27.5980			−0.928746			−0.464373	+	0.885640i	$0.653720\pi$
$884$		0			0
$885$	−21.6569			−0.727987
$886$	9.30559	−	5.37258i	0.312627	−	0.180495i
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$	6.07107	−	10.5154i	0.203732	−	0.352874i
$889$		−	16.0000i		−	0.536623i
$890$	−15.0451	−	8.68629i	−0.504313	−	0.291165i
$891$	1.73205	+	1.00000i	0.0580259	+	0.0335013i
$892$			22.8284i			0.764352i
$893$	−16.4853	+	28.5533i	−0.551659	+	0.955501i
$894$	−1.89949	−	3.29002i	−0.0635286	−	0.110035i
$895$	57.1067	−	32.9706i	1.90887	−	1.10208i
$896$	29.8579			0.997481
$897$		0			0
$898$	−13.1716			−0.439541
$899$	2.02922	−	1.17157i	0.0676784	−	0.0390741i
$900$	2.74264	+	4.75039i	0.0914214	+	0.158346i
$901$	−7.65685	+	13.2621i	−0.255087	+	0.441823i
$902$			4.28427i			0.142651i
$903$	−4.05845	−	2.34315i	−0.135057	−	0.0779750i
$904$	−7.29748	−	4.21320i	−0.242711	−	0.140129i
$905$		−	39.5980i		−	1.31628i
$906$	0.727922	−	1.26080i	0.0241836	−	0.0418872i
$907$	−6.48528	−	11.2328i	−0.215340	−	0.372980i	0.738038	−	0.674760i	$-0.235753\pi$
$907$	−6.48528	−	11.2328i	−0.215340	−	0.372980i	−0.953378	+	0.301779i	$0.902419\pi$
$908$	27.4156	−	15.8284i	0.909820	−	0.525285i
$909$	−7.65685			−0.253962
$910$		0			0
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$	7.34847	−	4.24264i	0.243332	−	0.140488i
$913$	3.65685	+	6.33386i	0.121024	+	0.209620i
$914$	−1.58579	+	2.74666i	−0.0524532	+	0.0908515i
$915$			37.6569i			1.24490i
$916$	2.08021	+	1.20101i	0.0687321	+	0.0396825i
$917$	19.5959	+	11.3137i	0.647114	+	0.373612i
$918$			3.17157i			0.104678i
$919$	−1.65685	+	2.86976i	−0.0546546	+	0.0946645i	−0.892058	−	0.451920i	$-0.850739\pi$
$919$	−1.65685	+	2.86976i	−0.0546546	+	0.0946645i	0.837404	+	0.546585i	$0.184072\pi$
$920$	−8.97056	−	15.5375i	−0.295751	−	0.512255i
$921$	−19.7700	+	11.4142i	−0.651444	+	0.376111i
$922$	−2.14214			−0.0705475
$923$		0			0
$924$	10.3431			0.340265
$925$	19.8931	−	11.4853i	0.654081	−	0.377634i
$926$	5.07107	+	8.78335i	0.166646	+	0.288639i
$927$	1.17157	−	2.02922i	0.0384795	−	0.0666485i
$928$		−	8.82843i		−	0.289807i
$929$	10.2182	+	5.89949i	0.335249	+	0.193556i	0.658169	−	0.752870i	$-0.271331\pi$
$929$	10.2182	+	5.89949i	0.335249	+	0.193556i	−0.322920	+	0.946426i	$0.604664\pi$
$930$	−1.18869	−	0.686292i	−0.0389787	−	0.0225044i
$931$		−	2.82843i		−	0.0926980i
$932$	6.37258	−	11.0376i	0.208741	−	0.361550i
$933$	−5.31371	−	9.20361i	−0.173963	−	0.301313i
$934$	−2.86976	+	1.65685i	−0.0939013	+	0.0542139i
$935$	−43.3137			−1.41651
$936$		0			0
$937$	−21.3137			−0.696289			−0.348144	−	0.937441i	$-0.613188\pi$
$937$	−21.3137			−0.696289			−0.348144	+	0.937441i	$0.613188\pi$
$938$	−6.92820	+	4.00000i	−0.226214	+	0.130605i
$939$	−3.00000	−	5.19615i	−0.0979013	−	0.169570i
$940$	−30.1421	+	52.2077i	−0.983128	+	1.70283i
$941$		−	34.1421i		−	1.11300i	−0.830847	−	0.556501i	$-0.812144\pi$
$941$		−	34.1421i		−	1.11300i	0.830847	−	0.556501i	$-0.187856\pi$
$942$	−3.58719	−	2.07107i	−0.116877	−	0.0674790i
$943$	17.9149	+	10.3431i	0.583388	+	0.336819i
$944$			22.9706i			0.747628i
$945$	4.00000	−	6.92820i	0.130120	−	0.225374i
$946$	0.686292	+	1.18869i	0.0223133	+	0.0386477i
$947$	−18.2120	+	10.5147i	−0.591811	+	0.341682i	−0.765813	−	0.643063i	$-0.777663\pi$
$947$	−18.2120	+	10.5147i	−0.591811	+	0.341682i	0.174002	+	0.984745i	$0.444330\pi$
$948$	−20.6863			−0.671860
$949$		0			0
$950$	−3.51472			−0.114033
$951$	−7.34847	+	4.24264i	−0.238290	+	0.137577i
$952$	17.1716	+	29.7420i	0.556534	+	0.963945i
$953$	20.1716	−	34.9382i	0.653421	−	1.13176i	−0.328866	−	0.944377i	$-0.606666\pi$
$953$	20.1716	−	34.9382i	0.653421	−	1.13176i	0.982287	−	0.187382i	$-0.0600003\pi$
$954$			0.828427i			0.0268213i
$955$	−8.11689	−	4.68629i	−0.262657	−	0.151645i
$956$	3.16693	+	1.82843i	0.102426	+	0.0591356i
$957$		−	4.00000i		−	0.129302i
$958$	−5.24264	+	9.08052i	−0.169382	+	0.293378i
$959$	−15.3137	−	26.5241i	−0.494505	−	0.856509i
$960$	10.2182	−	5.89949i	0.329792	−	0.190405i
$961$	29.6274			0.955723
$962$		0			0
$963$	−11.3137			−0.364579
$964$	0.543359	−	0.313708i	0.0175004	−	0.0101039i
$965$	7.51472	+	13.0159i	0.241907	+	0.418996i
$966$	−2.34315	+	4.05845i	−0.0753895	+	0.130578i
$967$		−	18.1421i		−	0.583412i	−0.956508	−	0.291706i	$-0.905777\pi$
$967$		−	18.1421i		−	0.583412i	0.956508	−	0.291706i	$-0.0942228\pi$
$968$	9.61332	+	5.55025i	0.308984	+	0.178392i
$969$	18.7554	+	10.8284i	0.602510	+	0.347859i
$970$		−	4.28427i		−	0.137560i
$971$	7.65685	−	13.2621i	0.245720	−	0.425600i	−0.716614	−	0.697470i	$-0.754309\pi$
$971$	7.65685	−	13.2621i	0.245720	−	0.425600i	0.962334	+	0.271871i	$0.0876422\pi$
$972$	−0.914214	−	1.58346i	−0.0293234	−	0.0507896i
$973$	−17.9149	+	10.3431i	−0.574324	+	0.331586i
$974$	3.23045			0.103510
$975$		0			0
$976$	39.9411			1.27848
$977$	−36.4962	+	21.0711i	−1.16762	+	0.674123i	−0.953117	−	0.302601i	$-0.902145\pi$
$977$	−36.4962	+	21.0711i	−1.16762	+	0.674123i	−0.214498	+	0.976724i	$0.568812\pi$
$978$	−3.89949	−	6.75412i	−0.124692	−	0.215973i
$979$	−14.8284	+	25.6836i	−0.473919	+	0.820851i
$980$		−	5.17157i		−	0.165200i
$981$	4.60181	+	2.65685i	0.146924	+	0.0848268i
$982$	−10.9867	−	6.34315i	−0.350598	−	0.202418i
$983$			25.3137i			0.807382i	0.914895	+	0.403691i	$0.132273\pi$
$983$			25.3137i			0.807382i	−0.914895	+	0.403691i	$0.867727\pi$
$984$	4.10051	−	7.10228i	0.130719	−	0.226413i
$985$	−0.686292	−	1.18869i	−0.0218671	−	0.0378749i
$986$	5.49333	−	3.17157i	0.174943	−	0.101003i
$987$	32.9706			1.04946
$988$		0			0
$989$	6.62742			0.210740
$990$	−2.02922	+	1.17157i	−0.0644930	+	0.0372350i
$991$	−2.34315	−	4.05845i	−0.0744325	−	0.128921i	0.826407	−	0.563073i	$-0.190381\pi$
$991$	−2.34315	−	4.05845i	−0.0744325	−	0.128921i	−0.900839	+	0.434153i	$0.857048\pi$
$992$	−2.58579	+	4.47871i	−0.0820988	+	0.142199i
$993$		−	26.1421i		−	0.829596i
$994$	2.02922	+	1.17157i	0.0643631	+	0.0371600i
$995$	53.0482	+	30.6274i	1.68174	+	0.970954i
$996$		−	6.68629i		−	0.211863i
$997$	19.6274	−	33.9957i	0.621607	−	1.07665i	−0.367580	−	0.929992i	$-0.619814\pi$
$997$	19.6274	−	33.9957i	0.621607	−	1.07665i	0.989187	−	0.146662i	$-0.0468530\pi$
$998$	5.41421	+	9.37769i	0.171384	+	0.296846i
$999$	−6.63103	+	3.82843i	−0.209797	+	0.121126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.f.361.2		8
13.2	odd	12		507.2.a.h.1.1		2
13.3	even	3		507.2.b.e.337.2		4
13.4	even	6	inner	507.2.j.f.316.2		8
13.5	odd	4		507.2.e.d.484.2		4
13.6	odd	12		507.2.e.d.22.2		4
13.7	odd	12		507.2.e.h.22.1		4
13.8	odd	4		507.2.e.h.484.1		4
13.9	even	3	inner	507.2.j.f.316.3		8
13.10	even	6		507.2.b.e.337.3		4
13.11	odd	12		39.2.a.b.1.2	✓	2
13.12	even	2	inner	507.2.j.f.361.3		8
39.2	even	12		1521.2.a.f.1.2		2
39.11	even	12		117.2.a.c.1.1		2
39.23	odd	6		1521.2.b.j.1351.2		4
39.29	odd	6		1521.2.b.j.1351.3		4
52.11	even	12		624.2.a.k.1.1		2
52.15	even	12		8112.2.a.bm.1.2		2
65.24	odd	12		975.2.a.l.1.1		2
65.37	even	12		975.2.c.h.274.3		4
65.63	even	12		975.2.c.h.274.2		4
91.76	even	12		1911.2.a.h.1.2		2
104.11	even	12		2496.2.a.bi.1.2		2
104.37	odd	12		2496.2.a.bf.1.2		2
117.11	even	12		1053.2.e.e.352.2		4
117.50	even	12		1053.2.e.e.703.2		4
117.76	odd	12		1053.2.e.m.703.1		4
117.115	odd	12		1053.2.e.m.352.1		4
143.76	even	12		4719.2.a.p.1.1		2
156.11	odd	12		1872.2.a.w.1.2		2
195.89	even	12		2925.2.a.v.1.2		2
195.128	odd	12		2925.2.c.u.2224.3		4
195.167	odd	12		2925.2.c.u.2224.2		4
273.167	odd	12		5733.2.a.u.1.1		2
312.11	odd	12		7488.2.a.co.1.1		2
312.245	even	12		7488.2.a.cl.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.a.b.1.2	✓	2	13.11	odd	12
117.2.a.c.1.1		2	39.11	even	12
507.2.a.h.1.1		2	13.2	odd	12
507.2.b.e.337.2		4	13.3	even	3
507.2.b.e.337.3		4	13.10	even	6
507.2.e.d.22.2		4	13.6	odd	12
507.2.e.d.484.2		4	13.5	odd	4
507.2.e.h.22.1		4	13.7	odd	12
507.2.e.h.484.1		4	13.8	odd	4
507.2.j.f.316.2		8	13.4	even	6	inner
507.2.j.f.316.3		8	13.9	even	3	inner
507.2.j.f.361.2		8	1.1	even	1	trivial
507.2.j.f.361.3		8	13.12	even	2	inner
624.2.a.k.1.1		2	52.11	even	12
975.2.a.l.1.1		2	65.24	odd	12
975.2.c.h.274.2		4	65.63	even	12
975.2.c.h.274.3		4	65.37	even	12
1053.2.e.e.352.2		4	117.11	even	12
1053.2.e.e.703.2		4	117.50	even	12
1053.2.e.m.352.1		4	117.115	odd	12
1053.2.e.m.703.1		4	117.76	odd	12
1521.2.a.f.1.2		2	39.2	even	12
1521.2.b.j.1351.2		4	39.23	odd	6
1521.2.b.j.1351.3		4	39.29	odd	6
1872.2.a.w.1.2		2	156.11	odd	12
1911.2.a.h.1.2		2	91.76	even	12
2496.2.a.bf.1.2		2	104.37	odd	12
2496.2.a.bi.1.2		2	104.11	even	12
2925.2.a.v.1.2		2	195.89	even	12
2925.2.c.u.2224.2		4	195.167	odd	12
2925.2.c.u.2224.3		4	195.128	odd	12
4719.2.a.p.1.1		2	143.76	even	12
5733.2.a.u.1.1		2	273.167	odd	12
7488.2.a.cl.1.1		2	312.245	even	12
7488.2.a.co.1.1		2	312.11	odd	12
8112.2.a.bm.1.2		2	52.15	even	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.358719 + 0.207107i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.914214 + 1.58346i) q^{4} +2.82843i q^{5} +(0.358719 + 0.207107i) q^{6} +(-2.44949 - 1.41421i) q^{7} -1.58579i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.358719 + 0.207107i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.914214 + 1.58346i) q^{4} +2.82843i q^{5} +(0.358719 + 0.207107i) q^{6} +(-2.44949 - 1.41421i) q^{7} -1.58579i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.585786 - 1.01461i) q^{10} +(-1.73205 + 1.00000i) q^{11} +1.82843 q^{12} +1.17157 q^{14} +(2.44949 - 1.41421i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(3.82843 - 6.63103i) q^{17} -0.414214i q^{18} +(-2.44949 - 1.41421i) q^{19} +(-4.47871 - 2.58579i) q^{20} +2.82843i q^{21} +(0.414214 - 0.717439i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.37333 + 0.792893i) q^{24} -3.00000 q^{25} +1.00000 q^{27} +(4.47871 - 2.58579i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(-0.585786 + 1.01461i) q^{30} +1.17157i q^{31} +(3.82282 + 2.20711i) q^{32} +(1.73205 + 1.00000i) q^{33} +3.17157i q^{34} +(4.00000 - 6.92820i) q^{35} +(-0.914214 - 1.58346i) q^{36} +(-6.63103 + 3.82843i) q^{37} +1.17157 q^{38} +4.48528 q^{40} +(-4.47871 + 2.58579i) q^{41} +(-0.585786 - 1.01461i) q^{42} +(-0.828427 + 1.43488i) q^{43} -3.65685i q^{44} +(-2.44949 - 1.41421i) q^{45} +(1.43488 + 0.828427i) q^{46} -11.6569i q^{47} +(-1.50000 + 2.59808i) q^{48} +(0.500000 + 0.866025i) q^{49} +(1.07616 - 0.621320i) q^{50} -7.65685 q^{51} -2.00000 q^{53} +(-0.358719 + 0.207107i) q^{54} +(-2.82843 - 4.89898i) q^{55} +(-2.24264 + 3.88437i) q^{56} +2.82843i q^{57} +(0.717439 + 0.414214i) q^{58} +(-6.63103 - 3.82843i) q^{59} +5.17157i q^{60} +(-6.65685 + 11.5300i) q^{61} +(-0.242641 - 0.420266i) q^{62} +(2.44949 - 1.41421i) q^{63} +4.17157 q^{64} -0.828427 q^{66} +(-5.91359 + 3.41421i) q^{67} +(7.00000 + 12.1244i) q^{68} +(-2.00000 + 3.46410i) q^{69} +3.31371i q^{70} +(1.73205 + 1.00000i) q^{71} +(1.37333 + 0.792893i) q^{72} +0.343146i q^{73} +(1.58579 - 2.74666i) q^{74} +(1.50000 + 2.59808i) q^{75} +(4.47871 - 2.58579i) q^{76} +5.65685 q^{77} -11.3137 q^{79} +(7.34847 - 4.24264i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.07107 - 1.85514i) q^{82} -3.65685i q^{83} +(-4.47871 - 2.58579i) q^{84} +(18.7554 + 10.8284i) q^{85} -0.686292i q^{86} +(-1.00000 + 1.73205i) q^{87} +(1.58579 + 2.74666i) q^{88} +(12.8418 - 7.41421i) q^{89} +1.17157 q^{90} +7.31371 q^{92} +(1.01461 - 0.585786i) q^{93} +(2.41421 + 4.18154i) q^{94} +(4.00000 - 6.92820i) q^{95} -4.41421i q^{96} +(3.16693 + 1.82843i) q^{97} +(-0.358719 - 0.207107i) q^{98} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 16 q^{10} - 8 q^{12} + 32 q^{14} - 12 q^{16} + 8 q^{17} - 8 q^{22} - 16 q^{23} - 24 q^{25} + 8 q^{27} - 8 q^{29} - 16 q^{30} + 32 q^{35} + 4 q^{36} + 32 q^{38} - 32 q^{40} - 16 q^{42} + 16 q^{43} - 12 q^{48} + 4 q^{49} - 16 q^{51} - 16 q^{53} + 16 q^{56} - 8 q^{61} + 32 q^{62} + 56 q^{64} + 16 q^{66} + 56 q^{68} - 16 q^{69} + 24 q^{74} + 12 q^{75} - 4 q^{81} - 48 q^{82} - 8 q^{87} + 24 q^{88} + 32 q^{90} - 32 q^{92} + 8 q^{94} + 32 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 16 * q^10 - 8 * q^12 + 32 * q^14 - 12 * q^16 + 8 * q^17 - 8 * q^22 - 16 * q^23 - 24 * q^25 + 8 * q^27 - 8 * q^29 - 16 * q^30 + 32 * q^35 + 4 * q^36 + 32 * q^38 - 32 * q^40 - 16 * q^42 + 16 * q^43 - 12 * q^48 + 4 * q^49 - 16 * q^51 - 16 * q^53 + 16 * q^56 - 8 * q^61 + 32 * q^62 + 56 * q^64 + 16 * q^66 + 56 * q^68 - 16 * q^69 + 24 * q^74 + 12 * q^75 - 4 * q^81 - 48 * q^82 - 8 * q^87 + 24 * q^88 + 32 * q^90 - 32 * q^92 + 8 * q^94 + 32 * q^95

Introduction

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