LMFDB - Embedded newform 507.2.e.d.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(22,507)]

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, 4]))

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

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

chi := DirichletCharacter("507.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.e (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	507.22
Dual form			507.2.e.d.484.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.207107	−	0.358719i	0.146447	−	0.253653i	−0.783465	−	0.621436i	$-0.786550\pi$
$2$	0.207107	−	0.358719i	0.146447	−	0.253653i	0.929912	+	0.367783i	$0.119883\pi$
$3$	−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
$5$	2.82843			1.26491			0.632456	−	0.774597i	$-0.282047\pi$
$5$	2.82843			1.26491			0.632456	+	0.774597i	$0.282047\pi$
$6$	0.207107	+	0.358719i	0.0845510	+	0.146447i
$7$	1.41421	+	2.44949i	0.534522	+	0.925820i	0.999186	+	0.0403329i	$0.0128419\pi$
$7$	1.41421	+	2.44949i	0.534522	+	0.925820i	−0.464664	+	0.885487i	$0.653825\pi$
$8$	1.58579			0.560660
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.585786	−	1.01461i	0.185242	−	0.320848i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	−1.82843			−0.527821
$13$		0			0
$13$		0			0
$14$	1.17157			0.313116
$15$	−1.41421	+	2.44949i	−0.365148	+	0.632456i
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−3.82843	−	6.63103i	−0.928530	−	1.60826i	−0.785783	−	0.618502i	$-0.787740\pi$
$17$	−3.82843	−	6.63103i	−0.928530	−	1.60826i	−0.142747	−	0.989759i	$-0.545593\pi$
$18$	−0.414214			−0.0976311
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	0.656957	−	0.753928i	$-0.271843\pi$
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	−0.981399	+	0.191977i	$0.938510\pi$
$20$	2.58579	+	4.47871i	0.578199	+	1.00147i
$21$	−2.82843			−0.617213
$22$	0.414214	+	0.717439i	0.0883106	+	0.152958i
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$	−0.792893	+	1.37333i	−0.161849	+	0.280330i
$25$	3.00000			0.600000
$26$		0			0
$27$	1.00000			0.192450
$28$	−2.58579	+	4.47871i	−0.488668	+	0.846397i
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$	0.585786	+	1.01461i	0.106949	+	0.185242i
$31$	1.17157			0.210421			0.105210	−	0.994450i	$-0.466448\pi$
$31$	1.17157			0.210421			0.105210	+	0.994450i	$0.466448\pi$
$32$	2.20711	+	3.82282i	0.390165	+	0.675786i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	−3.17157			−0.543920
$35$	4.00000	+	6.92820i	0.676123	+	1.17108i
$36$	0.914214	−	1.58346i	0.152369	−	0.263911i
$37$	−3.82843	+	6.63103i	−0.629390	+	1.09013i	0.358285	+	0.933612i	$0.383362\pi$
$37$	−3.82843	+	6.63103i	−0.629390	+	1.09013i	−0.987674	+	0.156522i	$0.949972\pi$
$38$	−1.17157			−0.190054
$39$		0			0
$40$	4.48528			0.709185
$41$	2.58579	−	4.47871i	0.403832	−	0.699458i	−0.590353	−	0.807145i	$-0.701011\pi$
$41$	2.58579	−	4.47871i	0.403832	−	0.699458i	0.994185	+	0.107688i	$0.0343447\pi$
$42$	−0.585786	+	1.01461i	−0.0903888	+	0.156558i
$43$	0.828427	+	1.43488i	0.126334	+	0.218817i	0.922254	−	0.386585i	$-0.126346\pi$
$43$	0.828427	+	1.43488i	0.126334	+	0.218817i	−0.795920	+	0.605402i	$0.793012\pi$
$44$	−3.65685			−0.551292
$45$	−1.41421	−	2.44949i	−0.210819	−	0.365148i
$46$	−0.828427	−	1.43488i	−0.122145	−	0.211561i
$47$	11.6569			1.70033			0.850163	−	0.526519i	$-0.176503\pi$
$47$	11.6569			1.70033			0.850163	+	0.526519i	$0.176503\pi$
$48$	−1.50000	−	2.59808i	−0.216506	−	0.375000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.621320	−	1.07616i	0.0878680	−	0.152192i
$51$	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	$0.543862\pi$
$54$	0.207107	−	0.358719i	0.0281837	−	0.0488155i
$55$	−2.82843	+	4.89898i	−0.381385	+	0.660578i
$56$	2.24264	+	3.88437i	0.299685	+	0.519070i
$57$	2.82843			0.374634
$58$	0.414214	+	0.717439i	0.0543889	+	0.0942043i
$59$	3.82843	+	6.63103i	0.498419	+	0.863287i	0.999998	−	0.00182490i	$-0.000580884\pi$
$59$	3.82843	+	6.63103i	0.498419	+	0.863287i	−0.501580	+	0.865112i	$0.667248\pi$
$60$	−5.17157			−0.667647
$61$	−6.65685	−	11.5300i	−0.852323	−	1.47627i	−0.879107	−	0.476625i	$-0.841860\pi$
$61$	−6.65685	−	11.5300i	−0.852323	−	1.47627i	0.0267837	−	0.999641i	$-0.491473\pi$
$62$	0.242641	−	0.420266i	0.0308154	−	0.0533738i
$63$	1.41421	−	2.44949i	0.178174	−	0.308607i
$64$	−4.17157			−0.521447
$65$		0			0
$66$	−0.828427			−0.101972
$67$	3.41421	−	5.91359i	0.417113	−	0.722460i	−0.578535	−	0.815657i	$-0.696375\pi$
$67$	3.41421	−	5.91359i	0.417113	−	0.722460i	0.995648	+	0.0931973i	$0.0297087\pi$
$68$	7.00000	−	12.1244i	0.848875	−	1.47029i
$69$	2.00000	+	3.46410i	0.240772	+	0.417029i
$70$	3.31371			0.396064
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	0.919244	−	0.393688i	$-0.128801\pi$
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	−0.800566	+	0.599245i	$0.795468\pi$
$72$	−0.792893	−	1.37333i	−0.0934434	−	0.161849i
$73$	−0.343146			−0.0401622			−0.0200811	−	0.999798i	$-0.506392\pi$
$73$	−0.343146			−0.0401622			−0.0200811	+	0.999798i	$0.506392\pi$
$74$	1.58579	+	2.74666i	0.184344	+	0.319293i
$75$	−1.50000	+	2.59808i	−0.173205	+	0.300000i
$76$	2.58579	−	4.47871i	0.296610	−	0.513744i
$77$	−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	$0.719596\pi$
$80$	−4.24264	+	7.34847i	−0.474342	+	0.821584i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.07107	−	1.85514i	−0.118280	−	0.204866i
$83$	−3.65685			−0.401392			−0.200696	−	0.979654i	$-0.564320\pi$
$83$	−3.65685			−0.401392			−0.200696	+	0.979654i	$0.564320\pi$
$84$	−2.58579	−	4.47871i	−0.282132	−	0.488668i
$85$	−10.8284	−	18.7554i	−1.17451	−	2.03431i
$86$	0.686292			0.0740047
$87$	−1.00000	−	1.73205i	−0.107211	−	0.185695i
$88$	−1.58579	+	2.74666i	−0.169045	+	0.292795i
$89$	7.41421	−	12.8418i	0.785905	−	1.36123i	−0.142552	−	0.989787i	$-0.545531\pi$
$89$	7.41421	−	12.8418i	0.785905	−	1.36123i	0.928457	−	0.371440i	$-0.121136\pi$
$90$	−1.17157			−0.123495
$91$		0			0
$92$	7.31371			0.762507
$93$	−0.585786	+	1.01461i	−0.0607432	+	0.105210i
$94$	2.41421	−	4.18154i	0.249007	−	0.431293i
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$	−4.41421			−0.450524
$97$	1.82843	+	3.16693i	0.185649	+	0.321553i	0.943795	−	0.330532i	$-0.107228\pi$
$97$	1.82843	+	3.16693i	0.185649	+	0.321553i	−0.758146	+	0.652085i	$0.773895\pi$
$98$	0.207107	+	0.358719i	0.0209209	+	0.0362361i
$99$	2.00000			0.201008
$100$	2.74264	+	4.75039i	0.274264	+	0.475039i
$101$	−3.82843	+	6.63103i	−0.380943	+	0.659812i	−0.991197	−	0.132393i	$-0.957734\pi$
$101$	−3.82843	+	6.63103i	−0.380943	+	0.659812i	0.610255	+	0.792205i	$0.291067\pi$
$102$	1.58579	−	2.74666i	0.157016	−	0.271960i
$103$	2.34315			0.230877			0.115439	−	0.993315i	$-0.463173\pi$
$103$	2.34315			0.230877			0.115439	+	0.993315i	$0.463173\pi$
$104$		0			0
$105$	−8.00000			−0.780720
$106$	−0.414214	+	0.717439i	−0.0402320	+	0.0696838i
$107$	5.65685	−	9.79796i	0.546869	−	0.947204i	−0.451618	−	0.892211i	$-0.649153\pi$
$107$	5.65685	−	9.79796i	0.546869	−	0.947204i	0.998487	−	0.0549930i	$-0.0175137\pi$
$108$	0.914214	+	1.58346i	0.0879702	+	0.152369i
$109$	−5.31371			−0.508961			−0.254480	−	0.967078i	$-0.581904\pi$
$109$	−5.31371			−0.508961			−0.254480	+	0.967078i	$0.581904\pi$
$110$	1.17157	+	2.02922i	0.111705	+	0.193479i
$111$	−3.82843	−	6.63103i	−0.363378	−	0.629390i
$112$	−8.48528			−0.801784
$113$	2.65685	+	4.60181i	0.249936	+	0.432902i	0.963508	−	0.267680i	$-0.0862571\pi$
$113$	2.65685	+	4.60181i	0.249936	+	0.432902i	−0.713572	+	0.700582i	$0.752924\pi$
$114$	0.585786	−	1.01461i	0.0548639	−	0.0950271i
$115$	5.65685	−	9.79796i	0.527504	−	0.913664i
$116$	−3.65685			−0.339530
$117$		0			0
$118$	3.17157			0.291967
$119$	10.8284	−	18.7554i	0.992640	−	1.71930i
$120$	−2.24264	+	3.88437i	−0.204724	+	0.354593i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−5.51472			−0.499279
$123$	2.58579	+	4.47871i	0.233153	+	0.403832i
$124$	1.07107	+	1.85514i	0.0961847	+	0.166597i
$125$	−5.65685			−0.505964
$126$	−0.585786	−	1.01461i	−0.0521860	−	0.0903888i
$127$	−2.82843	+	4.89898i	−0.250982	+	0.434714i	−0.963797	−	0.266639i	$-0.914087\pi$
$127$	−2.82843	+	4.89898i	−0.250982	+	0.434714i	0.712814	+	0.701353i	$0.247420\pi$
$128$	−5.27817	+	9.14207i	−0.466529	+	0.808052i
$129$	−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	$0.613642\pi$
$132$	1.82843	−	3.16693i	0.159144	−	0.275646i
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$	−1.41421	−	2.44949i	−0.122169	−	0.211604i
$135$	2.82843			0.243432
$136$	−6.07107	−	10.5154i	−0.520590	−	0.901688i
$137$	−5.41421	−	9.37769i	−0.462567	−	0.801190i	0.536521	−	0.843887i	$-0.319738\pi$
$137$	−5.41421	−	9.37769i	−0.462567	−	0.801190i	−0.999088	+	0.0426968i	$0.986405\pi$
$138$	1.65685			0.141041
$139$	3.65685	+	6.33386i	0.310170	+	0.537231i	0.978399	−	0.206725i	$-0.0662806\pi$
$139$	3.65685	+	6.33386i	0.310170	+	0.537231i	−0.668229	+	0.743956i	$0.732947\pi$
$140$	−7.31371	+	12.6677i	−0.618121	+	1.07062i
$141$	−5.82843	+	10.0951i	−0.490842	+	0.850163i
$142$	0.828427			0.0695201
$143$		0			0
$144$	3.00000			0.250000
$145$	−2.82843	+	4.89898i	−0.234888	+	0.406838i
$146$	−0.0710678	+	0.123093i	−0.00588161	+	0.0101873i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	−14.0000			−1.15079
$149$	−4.58579	−	7.94282i	−0.375682	−	0.650701i	0.614747	−	0.788725i	$-0.289258\pi$
$149$	−4.58579	−	7.94282i	−0.375682	−	0.650701i	−0.990429	+	0.138024i	$0.955925\pi$
$150$	0.621320	+	1.07616i	0.0507306	+	0.0878680i
$151$	3.51472			0.286024			0.143012	−	0.989721i	$-0.454321\pi$
$151$	3.51472			0.286024			0.143012	+	0.989721i	$0.454321\pi$
$152$	−2.24264	−	3.88437i	−0.181902	−	0.315064i
$153$	−3.82843	+	6.63103i	−0.309510	+	0.536087i
$154$	−1.17157	+	2.02922i	−0.0944080	+	0.163520i
$155$	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	$0.630658\pi$
$158$	−2.34315	+	4.05845i	−0.186411	+	0.322873i
$159$	1.00000	−	1.73205i	0.0793052	−	0.137361i
$160$	6.24264	+	10.8126i	0.493524	+	0.854809i
$161$	11.3137			0.891645
$162$	0.207107	+	0.358719i	0.0162718	+	0.0281837i
$163$	9.41421	+	16.3059i	0.737378	+	1.27718i	0.953672	+	0.300848i	$0.0972697\pi$
$163$	9.41421	+	16.3059i	0.737378	+	1.27718i	−0.216294	+	0.976328i	$0.569397\pi$
$164$	9.45584			0.738377
$165$	−2.82843	−	4.89898i	−0.220193	−	0.381385i
$166$	−0.757359	+	1.31178i	−0.0587825	+	0.101814i
$167$	−1.82843	+	3.16693i	−0.141488	+	0.245064i	−0.928057	−	0.372438i	$-0.878522\pi$
$167$	−1.82843	+	3.16693i	−0.141488	+	0.245064i	0.786569	+	0.617502i	$0.211855\pi$
$168$	−4.48528			−0.346047
$169$		0			0
$170$	−8.97056			−0.688011
$171$	−1.41421	+	2.44949i	−0.108148	+	0.187317i
$172$	−1.51472	+	2.62357i	−0.115496	+	0.200045i
$173$	5.82843	+	10.0951i	0.443127	+	0.767519i	0.997920	−	0.0644701i	$-0.0205357\pi$
$173$	5.82843	+	10.0951i	0.443127	+	0.767519i	−0.554793	+	0.831989i	$0.687202\pi$
$174$	−0.828427			−0.0628029
$175$	4.24264	+	7.34847i	0.320713	+	0.555492i
$176$	−3.00000	−	5.19615i	−0.226134	−	0.391675i
$177$	−7.65685			−0.575524
$178$	−3.07107	−	5.31925i	−0.230186	−	0.398694i
$179$	11.6569	−	20.1903i	0.871274	−	1.50909i	0.0105948	−	0.999944i	$-0.496628\pi$
$179$	11.6569	−	20.1903i	0.871274	−	1.50909i	0.860679	−	0.509147i	$-0.170039\pi$
$180$	2.58579	−	4.47871i	0.192733	−	0.333824i
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$	13.3137			0.984178
$184$	3.17157	−	5.49333i	0.233811	−	0.404973i
$185$	−10.8284	+	18.7554i	−0.796122	+	1.37892i
$186$	0.242641	+	0.420266i	0.0177913	+	0.0308154i
$187$	15.3137			1.11985
$188$	10.6569	+	18.4582i	0.777231	+	1.34620i
$189$	1.41421	+	2.44949i	0.102869	+	0.178174i
$190$	−3.31371			−0.240402
$191$	−1.65685	−	2.86976i	−0.119886	−	0.207648i	0.799836	−	0.600218i	$-0.204919\pi$
$191$	−1.65685	−	2.86976i	−0.119886	−	0.207648i	−0.919722	+	0.392570i	$0.871586\pi$
$192$	2.08579	−	3.61269i	0.150529	−	0.260723i
$193$	2.65685	−	4.60181i	0.191245	−	0.331245i	−0.754418	−	0.656394i	$-0.772081\pi$
$193$	2.65685	−	4.60181i	0.191245	−	0.331245i	0.945663	+	0.325149i	$0.105414\pi$
$194$	1.51472			0.108750
$195$		0			0
$196$	−1.82843			−0.130602
$197$	0.242641	−	0.420266i	0.0172874	−	0.0299427i	−0.857252	−	0.514897i	$-0.827830\pi$
$197$	0.242641	−	0.420266i	0.0172874	−	0.0299427i	0.874540	+	0.484954i	$0.161164\pi$
$198$	0.414214	−	0.717439i	0.0294369	−	0.0509862i
$199$	−10.8284	−	18.7554i	−0.767607	−	1.32953i	−0.938857	−	0.344307i	$-0.888114\pi$
$199$	−10.8284	−	18.7554i	−0.767607	−	1.32953i	0.171250	−	0.985228i	$-0.445219\pi$
$200$	4.75736			0.336396
$201$	3.41421	+	5.91359i	0.240820	+	0.417113i
$202$	1.58579	+	2.74666i	0.111576	+	0.193255i
$203$	−5.65685			−0.397033
$204$	7.00000	+	12.1244i	0.490098	+	0.848875i
$205$	7.31371	−	12.6677i	0.510812	−	0.884752i
$206$	0.485281	−	0.840532i	0.0338112	−	0.0585626i
$207$	−4.00000			−0.278019
$208$		0			0
$209$	5.65685			0.391293
$210$	−1.65685	+	2.86976i	−0.114334	+	0.198032i
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$	−1.82843	−	3.16693i	−0.125577	−	0.217506i
$213$	−2.00000			−0.137038
$214$	−2.34315	−	4.05845i	−0.160174	−	0.277430i
$215$	2.34315	+	4.05845i	0.159801	+	0.276784i
$216$	1.58579			0.107899
$217$	1.65685	+	2.86976i	0.112475	+	0.194812i
$218$	−1.10051	+	1.90613i	−0.0745356	+	0.129099i
$219$	0.171573	−	0.297173i	0.0115938	−	0.0200811i
$220$	−10.3431			−0.697335
$221$		0			0
$222$	−3.17157			−0.212862
$223$	−6.24264	+	10.8126i	−0.418038	+	0.724063i	−0.995742	−	0.0921831i	$-0.970615\pi$
$223$	−6.24264	+	10.8126i	−0.418038	+	0.724063i	0.577704	+	0.816246i	$0.303949\pi$
$224$	−6.24264	+	10.8126i	−0.417104	+	0.722445i
$225$	−1.50000	−	2.59808i	−0.100000	−	0.173205i
$226$	2.20101			0.146409
$227$	−8.65685	−	14.9941i	−0.574576	−	0.995194i	−0.996088	−	0.0883713i	$-0.971834\pi$
$227$	−8.65685	−	14.9941i	−0.574576	−	0.995194i	0.421512	−	0.906823i	$-0.361500\pi$
$228$	2.58579	+	4.47871i	0.171248	+	0.296610i
$229$	1.31371			0.0868123			0.0434062	−	0.999058i	$-0.486179\pi$
$229$	1.31371			0.0868123			0.0434062	+	0.999058i	$0.486179\pi$
$230$	−2.34315	−	4.05845i	−0.154502	−	0.267606i
$231$	2.82843	−	4.89898i	0.186097	−	0.322329i
$232$	−1.58579	+	2.74666i	−0.104112	+	0.180327i
$233$	6.97056			0.456657			0.228328	−	0.973584i	$-0.426674\pi$
$233$	6.97056			0.456657			0.228328	+	0.973584i	$0.426674\pi$
$234$		0			0
$235$	32.9706			2.15076
$236$	−7.00000	+	12.1244i	−0.455661	+	0.789228i
$237$	5.65685	−	9.79796i	0.367452	−	0.636446i
$238$	−4.48528	−	7.76874i	−0.290738	−	0.503572i
$239$	−2.00000			−0.129369			−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000			−0.129369			−0.0646846	+	0.997906i	$0.520604\pi$
$240$	−4.24264	−	7.34847i	−0.273861	−	0.474342i
$241$	0.171573	+	0.297173i	0.0110520	+	0.0191426i	0.871499	−	0.490398i	$-0.163149\pi$
$241$	0.171573	+	0.297173i	0.0110520	+	0.0191426i	−0.860447	+	0.509541i	$0.829815\pi$
$242$	2.89949			0.186387
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	12.1716	−	21.0818i	0.779205	−	1.34962i
$245$	−1.41421	+	2.44949i	−0.0903508	+	0.156492i
$246$	2.14214			0.136578
$247$		0			0
$248$	1.85786			0.117975
$249$	1.82843	−	3.16693i	0.115872	−	0.200696i
$250$	−1.17157	+	2.02922i	−0.0740968	+	0.128339i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$	5.17157			0.325778
$253$	4.00000	+	6.92820i	0.251478	+	0.435572i
$254$	1.17157	+	2.02922i	0.0735110	+	0.127325i
$255$	21.6569			1.35620
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	2.17157	−	3.76127i	0.135459	−	0.234622i	−0.790314	−	0.612702i	$-0.790082\pi$
$257$	2.17157	−	3.76127i	0.135459	−	0.234622i	0.925773	+	0.378081i	$0.123416\pi$
$258$	−0.343146	+	0.594346i	−0.0213633	+	0.0370024i
$259$	−21.6569			−1.34569
$260$		0			0
$261$	2.00000			0.123797
$262$	−1.65685	+	2.86976i	−0.102361	+	0.177294i
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$	−1.58579	−	2.74666i	−0.0975984	−	0.169045i
$265$	−5.65685			−0.347498
$266$	−1.65685	−	2.86976i	−0.101588	−	0.175956i
$267$	7.41421	+	12.8418i	0.453743	+	0.785905i
$268$	12.4853			0.762660
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$	0.585786	−	1.01461i	0.0356498	−	0.0617473i
$271$	−13.8995	+	24.0746i	−0.844334	+	1.46243i	0.0418640	+	0.999123i	$0.486670\pi$
$271$	−13.8995	+	24.0746i	−0.844334	+	1.46243i	−0.886198	+	0.463306i	$0.846663\pi$
$272$	22.9706			1.39279
$273$		0			0
$274$	−4.48528			−0.270966
$275$	−3.00000	+	5.19615i	−0.180907	+	0.313340i
$276$	−3.65685	+	6.33386i	−0.220117	+	0.381253i
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	3.02944			0.181694
$279$	−0.585786	−	1.01461i	−0.0350701	−	0.0607432i
$280$	6.34315	+	10.9867i	0.379075	+	0.656578i
$281$	−21.1716			−1.26299			−0.631495	−	0.775380i	$-0.717558\pi$
$281$	−21.1716			−1.26299			−0.631495	+	0.775380i	$0.717558\pi$
$282$	2.41421	+	4.18154i	0.143764	+	0.249007i
$283$	−14.4853	+	25.0892i	−0.861061	+	1.49140i	0.00984565	+	0.999952i	$0.496866\pi$
$283$	−14.4853	+	25.0892i	−0.861061	+	1.49140i	−0.870906	+	0.491449i	$0.836467\pi$
$284$	−1.82843	+	3.16693i	−0.108497	+	0.187923i
$285$	8.00000			0.473879
$286$		0			0
$287$	14.6274			0.863429
$288$	2.20711	−	3.82282i	0.130055	−	0.225262i
$289$	−20.8137	+	36.0504i	−1.22434	+	2.12061i
$290$	1.17157	+	2.02922i	0.0687971	+	0.119160i
$291$	−3.65685			−0.214369
$292$	−0.313708	−	0.543359i	−0.0183584	−	0.0317977i
$293$	1.07107	+	1.85514i	0.0625724	+	0.108379i	0.895615	−	0.444831i	$-0.146736\pi$
$293$	1.07107	+	1.85514i	0.0625724	+	0.108379i	−0.833042	+	0.553210i	$0.813403\pi$
$294$	−0.414214			−0.0241574
$295$	10.8284	+	18.7554i	0.630455	+	1.09198i
$296$	−6.07107	+	10.5154i	−0.352874	+	0.611195i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	−3.79899			−0.220070
$299$		0			0
$300$	−5.48528			−0.316693
$301$	−2.34315	+	4.05845i	−0.135057	+	0.233925i
$302$	0.727922	−	1.26080i	0.0418872	−	0.0725508i
$303$	−3.82843	−	6.63103i	−0.219937	−	0.380943i
$304$	8.48528			0.486664
$305$	−18.8284	−	32.6118i	−1.07811	−	1.86735i
$306$	1.58579	+	2.74666i	0.0906534	+	0.157016i
$307$	22.8284			1.30289			0.651444	−	0.758697i	$-0.274164\pi$
$307$	22.8284			1.30289			0.651444	+	0.758697i	$0.274164\pi$
$308$	−5.17157	−	8.95743i	−0.294678	−	0.510397i
$309$	−1.17157	+	2.02922i	−0.0666485	+	0.115439i
$310$	0.686292	−	1.18869i	0.0389787	−	0.0675132i
$311$	−10.6274			−0.602626			−0.301313	−	0.953525i	$-0.597425\pi$
$311$	−10.6274			−0.602626			−0.301313	+	0.953525i	$0.597425\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	−2.07107	+	3.58719i	−0.116877	+	0.202437i
$315$	4.00000	−	6.92820i	0.225374	−	0.390360i
$316$	−10.3431	−	17.9149i	−0.581847	−	1.00779i
$317$	−8.48528			−0.476581			−0.238290	−	0.971194i	$-0.576587\pi$
$317$	−8.48528			−0.476581			−0.238290	+	0.971194i	$0.576587\pi$
$318$	−0.414214	−	0.717439i	−0.0232279	−	0.0402320i
$319$	−2.00000	−	3.46410i	−0.111979	−	0.193952i
$320$	−11.7990			−0.659584
$321$	5.65685	+	9.79796i	0.315735	+	0.546869i
$322$	2.34315	−	4.05845i	0.130578	−	0.226168i
$323$	−10.8284	+	18.7554i	−0.602510	+	1.04358i
$324$	−1.82843			−0.101579
$325$		0			0
$326$	7.79899			0.431946
$327$	2.65685	−	4.60181i	0.146924	−	0.254480i
$328$	4.10051	−	7.10228i	0.226413	−	0.392158i
$329$	16.4853	+	28.5533i	0.908863	+	1.57420i
$330$	−2.34315			−0.128986
$331$	13.0711	+	22.6398i	0.718451	+	1.24439i	0.961613	+	0.274408i	$0.0884818\pi$
$331$	13.0711	+	22.6398i	0.718451	+	1.24439i	−0.243163	+	0.969986i	$0.578185\pi$
$332$	−3.34315	−	5.79050i	−0.183479	−	0.317795i
$333$	7.65685			0.419593
$334$	0.757359	+	1.31178i	0.0414409	+	0.0717777i
$335$	9.65685	−	16.7262i	0.527610	−	0.913848i
$336$	4.24264	−	7.34847i	0.231455	−	0.400892i
$337$	9.31371			0.507350			0.253675	−	0.967290i	$-0.418361\pi$
$337$	9.31371			0.507350			0.253675	+	0.967290i	$0.418361\pi$
$338$		0			0
$339$	−5.31371			−0.288601
$340$	19.7990	−	34.2929i	1.07375	−	1.85979i
$341$	−1.17157	+	2.02922i	−0.0634442	+	0.109889i
$342$	0.585786	+	1.01461i	0.0316757	+	0.0548639i
$343$	16.9706			0.916324
$344$	1.31371	+	2.27541i	0.0708304	+	0.122682i
$345$	5.65685	+	9.79796i	0.304555	+	0.527504i
$346$	4.82843			0.259578
$347$	4.34315	+	7.52255i	0.233152	+	0.403832i	0.958734	−	0.284304i	$-0.0917626\pi$
$347$	4.34315	+	7.52255i	0.233152	+	0.403832i	−0.725582	+	0.688136i	$0.758429\pi$
$348$	1.82843	−	3.16693i	0.0980140	−	0.169765i
$349$	1.82843	−	3.16693i	0.0978735	−	0.169522i	−0.812931	−	0.582360i	$-0.802129\pi$
$349$	1.82843	−	3.16693i	0.0978735	−	0.169522i	0.910804	+	0.412839i	$0.135463\pi$
$350$	3.51472			0.187870
$351$		0			0
$352$	−8.82843			−0.470557
$353$	−16.7279	+	28.9736i	−0.890337	+	1.54211i	−0.0508663	+	0.998705i	$0.516198\pi$
$353$	−16.7279	+	28.9736i	−0.890337	+	1.54211i	−0.839471	+	0.543404i	$0.817135\pi$
$354$	−1.58579	+	2.74666i	−0.0842836	+	0.145983i
$355$	2.82843	+	4.89898i	0.150117	+	0.260011i
$356$	27.1127			1.43697
$357$	10.8284	+	18.7554i	0.573101	+	0.992640i
$358$	−4.82843	−	8.36308i	−0.255190	−	0.442003i
$359$	−34.9706			−1.84568			−0.922838	−	0.385189i	$-0.874136\pi$
$359$	−34.9706			−1.84568			−0.922838	+	0.385189i	$0.874136\pi$
$360$	−2.24264	−	3.88437i	−0.118198	−	0.204724i
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$	2.89949	−	5.02207i	0.152394	−	0.263954i
$363$	−7.00000			−0.367405
$364$		0			0
$365$	−0.970563			−0.0508016
$366$	2.75736	−	4.77589i	0.144129	−	0.249640i
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	−0.361874	−	0.932227i	$-0.617863\pi$
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	0.988269	−	0.152721i	$-0.0488036\pi$
$368$	6.00000	+	10.3923i	0.312772	+	0.541736i
$369$	−5.17157			−0.269221
$370$	4.48528	+	7.76874i	0.233179	+	0.403877i
$371$	−2.82843	−	4.89898i	−0.146845	−	0.254342i
$372$	−2.14214			−0.111065
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$	3.17157	−	5.49333i	0.163998	−	0.284053i
$375$	2.82843	−	4.89898i	0.146059	−	0.252982i
$376$	18.4853			0.953306
$377$		0			0
$378$	1.17157			0.0602592
$379$	0.242641	−	0.420266i	0.0124636	−	0.0215876i	−0.859726	−	0.510755i	$-0.829366\pi$
$379$	0.242641	−	0.420266i	0.0124636	−	0.0215876i	0.872190	+	0.489167i	$0.162699\pi$
$380$	7.31371	−	12.6677i	0.375185	−	0.649840i
$381$	−2.82843	−	4.89898i	−0.144905	−	0.250982i
$382$	−1.37258			−0.0702275
$383$	15.4853	+	26.8213i	0.791261	+	1.37050i	0.925187	+	0.379513i	$0.123908\pi$
$383$	15.4853	+	26.8213i	0.791261	+	1.37050i	−0.133926	+	0.990991i	$0.542758\pi$
$384$	−5.27817	−	9.14207i	−0.269351	−	0.466529i
$385$	−16.0000			−0.815436
$386$	−1.10051	−	1.90613i	−0.0560142	−	0.0970195i
$387$	0.828427	−	1.43488i	0.0421113	−	0.0729389i
$388$	−3.34315	+	5.79050i	−0.169723	+	0.293968i
$389$	−26.9706			−1.36746			−0.683731	−	0.729734i	$-0.739644\pi$
$389$	−26.9706			−1.36746			−0.683731	+	0.729734i	$0.739644\pi$
$390$		0			0
$391$	−30.6274			−1.54890
$392$	−0.792893	+	1.37333i	−0.0400472	+	0.0693637i
$393$	4.00000	−	6.92820i	0.201773	−	0.349482i
$394$	−0.100505	−	0.174080i	−0.00506337	−	0.00877002i
$395$	−32.0000			−1.61009
$396$	1.82843	+	3.16693i	0.0918819	+	0.159144i
$397$	15.4853	+	26.8213i	0.777184	+	1.34612i	0.933559	+	0.358424i	$0.116686\pi$
$397$	15.4853	+	26.8213i	0.777184	+	1.34612i	−0.156375	+	0.987698i	$0.549981\pi$
$398$	−8.97056			−0.449654
$399$	4.00000	+	6.92820i	0.200250	+	0.346844i
$400$	−4.50000	+	7.79423i	−0.225000	+	0.389711i
$401$	13.0711	−	22.6398i	0.652738	−	1.13058i	−0.329718	−	0.944080i	$-0.606954\pi$
$401$	13.0711	−	22.6398i	0.652738	−	1.13058i	0.982456	−	0.186496i	$-0.0597131\pi$
$402$	2.82843			0.141069
$403$		0			0
$404$	−14.0000			−0.696526
$405$	−1.41421	+	2.44949i	−0.0702728	+	0.121716i
$406$	−1.17157	+	2.02922i	−0.0581442	+	0.100709i
$407$	−7.65685	−	13.2621i	−0.379536	−	0.657376i
$408$	12.1421			0.601125
$409$	−17.4853	−	30.2854i	−0.864592	−	1.49752i	−0.867452	−	0.497521i	$-0.834244\pi$
$409$	−17.4853	−	30.2854i	−0.864592	−	1.49752i	0.00286068	−	0.999996i	$-0.499089\pi$
$410$	−3.02944	−	5.24714i	−0.149613	−	0.259138i
$411$	10.8284			0.534127
$412$	2.14214	+	3.71029i	0.105535	+	0.182793i
$413$	−10.8284	+	18.7554i	−0.532832	+	0.922892i
$414$	−0.828427	+	1.43488i	−0.0407150	+	0.0705204i
$415$	−10.3431			−0.507725
$416$		0			0
$417$	−7.31371			−0.358154
$418$	1.17157	−	2.02922i	0.0573035	−	0.0992526i
$419$	−7.31371	+	12.6677i	−0.357298	+	0.618858i	−0.987508	−	0.157566i	$-0.949635\pi$
$419$	−7.31371	+	12.6677i	−0.357298	+	0.618858i	0.630210	+	0.776424i	$0.282969\pi$
$420$	−7.31371	−	12.6677i	−0.356872	−	0.618121i
$421$	−37.3137			−1.81856			−0.909279	−	0.416186i	$-0.863366\pi$
$421$	−37.3137			−1.81856			−0.909279	+	0.416186i	$0.863366\pi$
$422$	−2.48528	−	4.30463i	−0.120982	−	0.209546i
$423$	−5.82843	−	10.0951i	−0.283388	−	0.490842i
$424$	−3.17157			−0.154025
$425$	−11.4853	−	19.8931i	−0.557118	−	0.964957i
$426$	−0.414214	+	0.717439i	−0.0200687	+	0.0347600i
$427$	18.8284	−	32.6118i	0.911171	−	1.57820i
$428$	20.6863			0.999910
$429$		0			0
$430$	1.94113			0.0936094
$431$	4.17157	−	7.22538i	0.200938	−	0.348034i	−0.747893	−	0.663819i	$-0.768934\pi$
$431$	4.17157	−	7.22538i	0.200938	−	0.348034i	0.948831	+	0.315785i	$0.102268\pi$
$432$	−1.50000	+	2.59808i	−0.0721688	+	0.125000i
$433$	10.6569	+	18.4582i	0.512136	+	0.887045i	0.999901	+	0.0140703i	$0.00447886\pi$
$433$	10.6569	+	18.4582i	0.512136	+	0.887045i	−0.487765	+	0.872975i	$0.662188\pi$
$434$	1.37258			0.0658861
$435$	−2.82843	−	4.89898i	−0.135613	−	0.234888i
$436$	−4.85786	−	8.41407i	−0.232650	−	0.402961i
$437$	−11.3137			−0.541208
$438$	−0.0710678	−	0.123093i	−0.00339575	−	0.00588161i
$439$	−8.48528	+	14.6969i	−0.404980	+	0.701447i	−0.994319	−	0.106439i	$-0.966055\pi$
$439$	−8.48528	+	14.6969i	−0.404980	+	0.701447i	0.589339	+	0.807886i	$0.299388\pi$
$440$	−4.48528	+	7.76874i	−0.213827	+	0.370360i
$441$	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	$0.711349\pi$
$444$	7.00000	−	12.1244i	0.332205	−	0.575396i
$445$	20.9706	−	36.3221i	0.994100	−	1.72183i
$446$	2.58579	+	4.47871i	0.122441	+	0.212073i
$447$	9.17157			0.433801
$448$	−5.89949	−	10.2182i	−0.278725	−	0.482766i
$449$	−15.8995	−	27.5387i	−0.750344	−	1.29963i	−0.947656	−	0.319293i	$-0.896555\pi$
$449$	−15.8995	−	27.5387i	−0.750344	−	1.29963i	0.197313	−	0.980341i	$-0.436779\pi$
$450$	−1.24264			−0.0585786
$451$	5.17157	+	8.95743i	0.243520	+	0.421789i
$452$	−4.85786	+	8.41407i	−0.228495	+	0.395764i
$453$	−1.75736	+	3.04384i	−0.0825679	+	0.143012i
$454$	−7.17157			−0.336579
$455$		0			0
$456$	4.48528			0.210043
$457$	−3.82843	+	6.63103i	−0.179086	+	0.310187i	−0.941568	−	0.336823i	$-0.890647\pi$
$457$	−3.82843	+	6.63103i	−0.179086	+	0.310187i	0.762482	+	0.647010i	$0.223981\pi$
$458$	0.272078	−	0.471253i	0.0127134	−	0.0220202i
$459$	−3.82843	−	6.63103i	−0.178696	−	0.309510i
$460$	20.6863			0.964503
$461$	2.58579	+	4.47871i	0.120432	+	0.208594i	0.919938	−	0.392064i	$-0.128239\pi$
$461$	2.58579	+	4.47871i	0.120432	+	0.208594i	−0.799506	+	0.600658i	$0.794905\pi$
$462$	−1.17157	−	2.02922i	−0.0545065	−	0.0944080i
$463$	24.4853			1.13793			0.568964	−	0.822363i	$-0.307344\pi$
$463$	24.4853			1.13793			0.568964	+	0.822363i	$0.307344\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$	−1.65685	+	2.86976i	−0.0768348	+	0.133082i
$466$	1.44365	−	2.50048i	0.0668758	−	0.115832i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$	19.3137			0.891824
$470$	6.82843	−	11.8272i	0.314972	−	0.545547i
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$	6.07107	+	10.5154i	0.279444	+	0.484010i
$473$	−3.31371			−0.152364
$474$	−2.34315	−	4.05845i	−0.107624	−	0.186411i
$475$	−4.24264	−	7.34847i	−0.194666	−	0.337171i
$476$	39.5980			1.81497
$477$	1.00000	+	1.73205i	0.0457869	+	0.0793052i
$478$	−0.414214	+	0.717439i	−0.0189457	+	0.0328149i
$479$	12.6569	−	21.9223i	0.578306	−	1.00166i	−0.417367	−	0.908738i	$-0.637047\pi$
$479$	12.6569	−	21.9223i	0.578306	−	1.00166i	0.995674	−	0.0929182i	$-0.0296195\pi$
$480$	−12.4853			−0.569873
$481$		0			0
$482$	0.142136			0.00647410
$483$	−5.65685	+	9.79796i	−0.257396	+	0.445823i
$484$	−6.39949	+	11.0843i	−0.290886	+	0.503830i
$485$	5.17157	+	8.95743i	0.234829	+	0.406736i
$486$	−0.414214			−0.0187891
$487$	−3.89949	−	6.75412i	−0.176703	−	0.306059i	0.764046	−	0.645161i	$-0.223210\pi$
$487$	−3.89949	−	6.75412i	−0.176703	−	0.306059i	−0.940749	+	0.339103i	$0.889877\pi$
$488$	−10.5563	−	18.2841i	−0.477863	−	0.827684i
$489$	−18.8284			−0.851451
$490$	0.585786	+	1.01461i	0.0264631	+	0.0458355i
$491$	−15.3137	+	26.5241i	−0.691098	+	1.19702i	0.280380	+	0.959889i	$0.409539\pi$
$491$	−15.3137	+	26.5241i	−0.691098	+	1.19702i	−0.971478	+	0.237128i	$0.923794\pi$
$492$	−4.72792	+	8.18900i	−0.213151	+	0.369189i
$493$	15.3137			0.689695
$494$		0			0
$495$	5.65685			0.254257
$496$	−1.75736	+	3.04384i	−0.0789078	+	0.136672i
$497$	−2.82843	+	4.89898i	−0.126872	+	0.219749i
$498$	−0.757359	−	1.31178i	−0.0339381	−	0.0587825i
$499$	−26.1421			−1.17028			−0.585141	−	0.810931i	$-0.698961\pi$
$499$	−26.1421			−1.17028			−0.585141	+	0.810931i	$0.698961\pi$
$500$	−5.17157	−	8.95743i	−0.231280	−	0.400588i
$501$	−1.82843	−	3.16693i	−0.0816881	−	0.141488i
$502$		0			0
$503$	3.65685	+	6.33386i	0.163051	+	0.282413i	0.935961	−	0.352102i	$-0.114533\pi$
$503$	3.65685	+	6.33386i	0.163051	+	0.282413i	−0.772910	+	0.634515i	$0.781200\pi$
$504$	2.24264	−	3.88437i	0.0998952	−	0.173023i
$505$	−10.8284	+	18.7554i	−0.481859	+	0.834604i
$506$	3.31371			0.147312
$507$		0			0
$508$	−10.3431			−0.458903
$509$	5.89949	−	10.2182i	0.261491	−	0.452915i	−0.705148	−	0.709060i	$-0.749119\pi$
$509$	5.89949	−	10.2182i	0.261491	−	0.452915i	0.966638	+	0.256146i	$0.0824527\pi$
$510$	4.48528	−	7.76874i	0.198612	−	0.344005i
$511$	−0.485281	−	0.840532i	−0.0214676	−	0.0371829i
$512$	−22.7574			−1.00574
$513$	−1.41421	−	2.44949i	−0.0624391	−	0.108148i
$514$	−0.899495	−	1.55797i	−0.0396750	−	0.0687192i
$515$	6.62742			0.292039
$516$	−1.51472	−	2.62357i	−0.0666818	−	0.115496i
$517$	−11.6569	+	20.1903i	−0.512668	+	0.887967i
$518$	−4.48528	+	7.76874i	−0.197072	+	0.341339i
$519$	−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	$0.312907\pi$
$522$	0.414214	−	0.717439i	0.0181296	−	0.0314014i
$523$	7.65685	−	13.2621i	0.334811	−	0.579909i	−0.648638	−	0.761097i	$-0.724661\pi$
$523$	7.65685	−	13.2621i	0.334811	−	0.579909i	0.983448	+	0.181188i	$0.0579942\pi$
$524$	−7.31371	−	12.6677i	−0.319501	−	0.553392i
$525$	−8.48528			−0.370328
$526$	2.48528	+	4.30463i	0.108363	+	0.187691i
$527$	−4.48528	−	7.76874i	−0.195382	−	0.338411i
$528$	6.00000			0.261116
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−1.17157	+	2.02922i	−0.0508899	+	0.0881438i
$531$	3.82843	−	6.63103i	0.166140	−	0.287762i
$532$	14.6274			0.634179
$533$		0			0
$534$	6.14214			0.265796
$535$	16.0000	−	27.7128i	0.691740	−	1.19813i
$536$	5.41421	−	9.37769i	0.233858	−	0.405055i
$537$	11.6569	+	20.1903i	0.503030	+	0.871274i
$538$	−7.45584			−0.321444
$539$	−1.00000	−	1.73205i	−0.0430730	−	0.0746047i
$540$	2.58579	+	4.47871i	0.111275	+	0.192733i
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	5.75736	+	9.97204i	0.247300	+	0.428336i
$543$	−7.00000	+	12.1244i	−0.300399	+	0.520306i
$544$	16.8995	−	29.2708i	0.724560	−	1.25497i
$545$	−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	$0.333917\pi$
$548$	9.89949	−	17.1464i	0.422885	−	0.732459i
$549$	−6.65685	+	11.5300i	−0.284108	+	0.492089i
$550$	1.24264	+	2.15232i	0.0529864	+	0.0917751i
$551$	5.65685			0.240990
$552$	3.17157	+	5.49333i	0.134991	+	0.233811i
$553$	−16.0000	−	27.7128i	−0.680389	−	1.17847i
$554$	0.828427			0.0351965
$555$	−10.8284	−	18.7554i	−0.459641	−	0.796122i
$556$	−6.68629	+	11.5810i	−0.283562	+	0.491144i
$557$	−3.89949	+	6.75412i	−0.165227	+	0.286181i	−0.936736	−	0.350037i	$-0.886169\pi$
$557$	−3.89949	+	6.75412i	−0.165227	+	0.286181i	0.771509	+	0.636218i	$0.219502\pi$
$558$	−0.485281			−0.0205436
$559$		0			0
$560$	−24.0000			−1.01419
$561$	−7.65685	+	13.2621i	−0.323273	+	0.559925i
$562$	−4.38478	+	7.59466i	−0.184961	+	0.320361i
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$	−21.3137			−0.897469
$565$	7.51472	+	13.0159i	0.316147	+	0.547582i
$566$	6.00000	+	10.3923i	0.252199	+	0.436821i
$567$	−2.82843			−0.118783
$568$	1.58579	+	2.74666i	0.0665381	+	0.115247i
$569$	21.4853	−	37.2136i	0.900710	−	1.56008i	0.0741351	−	0.997248i	$-0.476380\pi$
$569$	21.4853	−	37.2136i	0.900710	−	1.56008i	0.826575	−	0.562827i	$-0.190286\pi$
$570$	1.65685	−	2.86976i	0.0693980	−	0.120201i
$571$	−12.9706			−0.542801			−0.271401	−	0.962466i	$-0.587487\pi$
$571$	−12.9706			−0.542801			−0.271401	+	0.962466i	$0.587487\pi$
$572$		0			0
$573$	3.31371			0.138432
$574$	3.02944	−	5.24714i	0.126446	−	0.219011i
$575$	6.00000	−	10.3923i	0.250217	−	0.433389i
$576$	2.08579	+	3.61269i	0.0869078	+	0.150529i
$577$	31.9411			1.32973			0.664863	−	0.746965i	$-0.268490\pi$
$577$	31.9411			1.32973			0.664863	+	0.746965i	$0.268490\pi$
$578$	8.62132	+	14.9326i	0.358600	+	0.621113i
$579$	2.65685	+	4.60181i	0.110415	+	0.191245i
$580$	−10.3431			−0.429476
$581$	−5.17157	−	8.95743i	−0.214553	−	0.371617i
$582$	−0.757359	+	1.31178i	−0.0313936	+	0.0543752i
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$	−0.544156			−0.0225173
$585$		0			0
$586$	0.887302			0.0366541
$587$	−5.48528	+	9.50079i	−0.226402	+	0.392139i	−0.956739	−	0.290947i	$-0.906030\pi$
$587$	−5.48528	+	9.50079i	−0.226402	+	0.392139i	0.730337	+	0.683087i	$0.239363\pi$
$588$	0.914214	−	1.58346i	0.0377015	−	0.0653010i
$589$	−1.65685	−	2.86976i	−0.0682695	−	0.118246i
$590$	8.97056			0.369312
$591$	0.242641	+	0.420266i	0.00998090	+	0.0172874i
$592$	−11.4853	−	19.8931i	−0.472042	−	0.817601i
$593$	20.4853			0.841230			0.420615	−	0.907239i	$-0.361814\pi$
$593$	20.4853			0.841230			0.420615	+	0.907239i	$0.361814\pi$
$594$	0.414214	+	0.717439i	0.0169954	+	0.0294369i
$595$	30.6274	−	53.0482i	1.25560	−	2.17477i
$596$	8.38478	−	14.5229i	0.343454	−	0.594879i
$597$	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	$0.658017\pi$
$600$	−2.37868	+	4.11999i	−0.0971092	+	0.168198i
$601$	0.313708	−	0.543359i	0.0127964	−	0.0221641i	−0.859556	−	0.511041i	$-0.829260\pi$
$601$	0.313708	−	0.543359i	0.0127964	−	0.0221641i	0.872353	+	0.488877i	$0.162593\pi$
$602$	0.970563	+	1.68106i	0.0395572	+	0.0685151i
$603$	−6.82843			−0.278075
$604$	3.21320	+	5.56543i	0.130743	+	0.226454i
$605$	9.89949	+	17.1464i	0.402472	+	0.697101i
$606$	−3.17157			−0.128836
$607$	−20.9706	−	36.3221i	−0.851169	−	1.47427i	−0.880154	−	0.474688i	$-0.842561\pi$
$607$	−20.9706	−	36.3221i	−0.851169	−	1.47427i	0.0289853	−	0.999580i	$-0.490772\pi$
$608$	6.24264	−	10.8126i	0.253173	−	0.438508i
$609$	2.82843	−	4.89898i	0.114614	−	0.198517i
$610$	−15.5980			−0.631544
$611$		0			0
$612$	−14.0000			−0.565916
$613$	−23.8284	+	41.2720i	−0.962421	+	1.66696i	−0.246031	+	0.969262i	$0.579127\pi$
$613$	−23.8284	+	41.2720i	−0.962421	+	1.66696i	−0.716390	+	0.697700i	$0.754207\pi$
$614$	4.72792	−	8.18900i	0.190803	−	0.330481i
$615$	7.31371	+	12.6677i	0.294917	+	0.510812i
$616$	−8.97056			−0.361434
$617$	−17.4142	−	30.1623i	−0.701070	−	1.21429i	−0.968091	−	0.250598i	$-0.919373\pi$
$617$	−17.4142	−	30.1623i	−0.701070	−	1.21429i	0.267021	−	0.963691i	$-0.413961\pi$
$618$	0.485281	+	0.840532i	0.0195209	+	0.0338112i
$619$	−23.7990			−0.956562			−0.478281	−	0.878207i	$-0.658740\pi$
$619$	−23.7990			−0.956562			−0.478281	+	0.878207i	$0.658740\pi$
$620$	3.02944	+	5.24714i	0.121665	+	0.210730i
$621$	2.00000	−	3.46410i	0.0802572	−	0.139010i
$622$	−2.20101	+	3.81226i	−0.0882525	+	0.152858i
$623$	41.9411			1.68034
$624$		0			0
$625$	−31.0000			−1.24000
$626$	1.24264	−	2.15232i	0.0496659	−	0.0860239i
$627$	−2.82843	+	4.89898i	−0.112956	+	0.195646i
$628$	−9.14214	−	15.8346i	−0.364811	−	0.631871i
$629$	58.6274			2.33763
$630$	−1.65685	−	2.86976i	−0.0660107	−	0.114334i
$631$	21.5563	+	37.3367i	0.858145	+	1.48635i	0.873697	+	0.486471i	$0.161716\pi$
$631$	21.5563	+	37.3367i	0.858145	+	1.48635i	−0.0155519	+	0.999879i	$0.504951\pi$
$632$	−17.9411			−0.713660
$633$	6.00000	+	10.3923i	0.238479	+	0.413057i
$634$	−1.75736	+	3.04384i	−0.0697937	+	0.120886i
$635$	−8.00000	+	13.8564i	−0.317470	+	0.549875i
$636$	3.65685			0.145004
$637$		0			0
$638$	−1.65685			−0.0655955
$639$	1.00000	−	1.73205i	0.0395594	−	0.0685189i
$640$	−14.9289	+	25.8577i	−0.590118	+	1.02211i
$641$	−15.1421	−	26.2269i	−0.598078	−	1.03590i	−0.993105	−	0.117232i	$-0.962598\pi$
$641$	−15.1421	−	26.2269i	−0.598078	−	1.03590i	0.395026	−	0.918670i	$-0.370736\pi$
$642$	4.68629			0.184953
$643$	11.4142	+	19.7700i	0.450133	+	0.779653i	0.998394	−	0.0566545i	$-0.0180434\pi$
$643$	11.4142	+	19.7700i	0.450133	+	0.779653i	−0.548261	+	0.836307i	$0.684710\pi$
$644$	10.3431	+	17.9149i	0.407577	+	0.705944i
$645$	−4.68629			−0.184523
$646$	4.48528	+	7.76874i	0.176471	+	0.305657i
$647$	−5.65685	+	9.79796i	−0.222394	+	0.385198i	−0.955534	−	0.294880i	$-0.904720\pi$
$647$	−5.65685	+	9.79796i	−0.222394	+	0.385198i	0.733140	+	0.680077i	$0.238054\pi$
$648$	−0.792893	+	1.37333i	−0.0311478	+	0.0539496i
$649$	−15.3137			−0.601116
$650$		0			0
$651$	−3.31371			−0.129874
$652$	−17.2132	+	29.8141i	−0.674121	+	1.16761i
$653$	12.6569	−	21.9223i	0.495301	−	0.857886i	−0.504684	−	0.863304i	$-0.668391\pi$
$653$	12.6569	−	21.9223i	0.495301	−	0.857886i	0.999985	+	0.00541749i	$0.00172445\pi$
$654$	−1.10051	−	1.90613i	−0.0430332	−	0.0745356i
$655$	−22.6274			−0.884126
$656$	7.75736	+	13.4361i	0.302874	+	0.524593i
$657$	0.171573	+	0.297173i	0.00669370	+	0.0115938i
$658$	13.6569			0.532400
$659$	23.6569	+	40.9749i	0.921540	+	1.59615i	0.797033	+	0.603936i	$0.206402\pi$
$659$	23.6569	+	40.9749i	0.921540	+	1.59615i	0.124507	+	0.992219i	$0.460265\pi$
$660$	5.17157	−	8.95743i	0.201303	−	0.348667i
$661$	−17.4853	+	30.2854i	−0.680099	+	1.17797i	0.294852	+	0.955543i	$0.404730\pi$
$661$	−17.4853	+	30.2854i	−0.680099	+	1.17797i	−0.974950	+	0.222422i	$0.928604\pi$
$662$	10.8284			0.420859
$663$		0			0
$664$	−5.79899			−0.225044
$665$	11.3137	−	19.5959i	0.438727	−	0.759897i
$666$	1.58579	−	2.74666i	0.0614480	−	0.106431i
$667$	4.00000	+	6.92820i	0.154881	+	0.268261i
$668$	−6.68629			−0.258700
$669$	−6.24264	−	10.8126i	−0.241354	−	0.418038i
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	26.6274			1.02794
$672$	−6.24264	−	10.8126i	−0.240815	−	0.417104i
$673$	−8.31371	+	14.3998i	−0.320470	+	0.555070i	−0.980585	−	0.196094i	$-0.937174\pi$
$673$	−8.31371	+	14.3998i	−0.320470	+	0.555070i	0.660115	+	0.751164i	$0.270507\pi$
$674$	1.92893	−	3.34101i	0.0742997	−	0.128691i
$675$	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	$0.328601\pi$
$678$	−1.10051	+	1.90613i	−0.0422646	+	0.0732045i
$679$	−5.17157	+	8.95743i	−0.198467	+	0.343754i
$680$	−17.1716	−	29.7420i	−0.658500	−	1.14056i
$681$	17.3137			0.663463
$682$	0.485281	+	0.840532i	0.0185824	+	0.0321856i
$683$	23.9706	+	41.5182i	0.917208	+	1.58865i	0.803636	+	0.595121i	$0.202896\pi$
$683$	23.9706	+	41.5182i	0.917208	+	1.58865i	0.113572	+	0.993530i	$0.463771\pi$
$684$	−5.17157			−0.197740
$685$	−15.3137	−	26.5241i	−0.585107	−	1.01343i
$686$	3.51472	−	6.08767i	0.134193	−	0.232428i
$687$	−0.656854	+	1.13770i	−0.0250606	+	0.0434062i
$688$	−4.97056			−0.189501
$689$		0			0
$690$	4.68629			0.178404
$691$	−2.92893	+	5.07306i	−0.111422	+	0.192988i	−0.916344	−	0.400392i	$-0.868874\pi$
$691$	−2.92893	+	5.07306i	−0.111422	+	0.192988i	0.804922	+	0.593381i	$0.202207\pi$
$692$	−10.6569	+	18.4582i	−0.405113	+	0.701676i
$693$	2.82843	+	4.89898i	0.107443	+	0.186097i
$694$	3.59798			0.136577
$695$	10.3431	+	17.9149i	0.392338	+	0.679549i
$696$	−1.58579	−	2.74666i	−0.0601091	−	0.104112i
$697$	−39.5980			−1.49988
$698$	−0.757359	−	1.31178i	−0.0286665	−	0.0496518i
$699$	−3.48528	+	6.03668i	−0.131825	+	0.228328i
$700$	−7.75736	+	13.4361i	−0.293201	+	0.507838i
$701$	5.02944			0.189959			0.0949796	−	0.995479i	$-0.469721\pi$
$701$	5.02944			0.189959			0.0949796	+	0.995479i	$0.469721\pi$
$702$		0			0
$703$	21.6569			0.816804
$704$	4.17157	−	7.22538i	0.157222	−	0.272317i
$705$	−16.4853	+	28.5533i	−0.620872	+	1.07538i
$706$	6.92893	+	12.0013i	0.260774	+	0.451673i
$707$	−21.6569			−0.814490
$708$	−7.00000	−	12.1244i	−0.263076	−	0.455661i
$709$	−2.31371	−	4.00746i	−0.0868931	−	0.150503i	0.819303	−	0.573360i	$-0.194361\pi$
$709$	−2.31371	−	4.00746i	−0.0868931	−	0.150503i	−0.906196	+	0.422857i	$0.861027\pi$
$710$	2.34315			0.0879367
$711$	5.65685	+	9.79796i	0.212149	+	0.367452i
$712$	11.7574	−	20.3643i	0.440626	−	0.763186i
$713$	2.34315	−	4.05845i	0.0877515	−	0.151990i
$714$	8.97056			0.335715
$715$		0			0
$716$	42.6274			1.59306
$717$	1.00000	−	1.73205i	0.0373457	−	0.0646846i
$718$	−7.24264	+	12.5446i	−0.270293	+	0.468161i
$719$	14.9706	+	25.9298i	0.558308	+	0.967017i	0.997638	+	0.0686918i	$0.0218825\pi$
$719$	14.9706	+	25.9298i	0.558308	+	0.967017i	−0.439330	+	0.898326i	$0.644784\pi$
$720$	8.48528			0.316228
$721$	3.31371	+	5.73951i	0.123409	+	0.213751i
$722$	−2.27817	−	3.94591i	−0.0847849	−	0.146852i
$723$	−0.343146			−0.0127617
$724$	12.7990	+	22.1685i	0.475671	+	0.823886i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$	−1.44975	+	2.51104i	−0.0538052	+	0.0931933i
$727$	−10.3431			−0.383606			−0.191803	−	0.981433i	$-0.561433\pi$
$727$	−10.3431			−0.383606			−0.191803	+	0.981433i	$0.561433\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−0.201010	+	0.348160i	−0.00743972	+	0.0128860i
$731$	6.34315	−	10.9867i	0.234610	−	0.406356i
$732$	12.1716	+	21.0818i	0.449874	+	0.779205i
$733$	36.6274			1.35286			0.676432	−	0.736505i	$-0.263525\pi$
$733$	36.6274			1.35286			0.676432	+	0.736505i	$0.263525\pi$
$734$	−4.97056	−	8.60927i	−0.183467	−	0.317774i
$735$	−1.41421	−	2.44949i	−0.0521641	−	0.0903508i
$736$	17.6569			0.650840
$737$	6.82843	+	11.8272i	0.251528	+	0.435660i
$738$	−1.07107	+	1.85514i	−0.0394266	+	0.0682888i
$739$	−9.07107	+	15.7116i	−0.333685	+	0.577959i	−0.983231	−	0.182363i	$-0.941625\pi$
$739$	−9.07107	+	15.7116i	−0.333685	+	0.577959i	0.649547	+	0.760322i	$0.274959\pi$
$740$	−39.5980			−1.45565
$741$		0			0
$742$	−2.34315			−0.0860196
$743$	1.00000	−	1.73205i	0.0366864	−	0.0635428i	−0.847099	−	0.531435i	$-0.821653\pi$
$743$	1.00000	−	1.73205i	0.0366864	−	0.0635428i	0.883786	+	0.467892i	$0.154986\pi$
$744$	−0.928932	+	1.60896i	−0.0340563	+	0.0589873i
$745$	−12.9706	−	22.4657i	−0.475205	−	0.823079i
$746$	−4.14214			−0.151654
$747$	1.82843	+	3.16693i	0.0668987	+	0.115872i
$748$	14.0000	+	24.2487i	0.511891	+	0.886621i
$749$	32.0000			1.16925
$750$	−1.17157	−	2.02922i	−0.0427798	−	0.0740968i
$751$	0.485281	−	0.840532i	0.0177082	−	0.0306714i	−0.857036	−	0.515257i	$-0.827696\pi$
$751$	0.485281	−	0.840532i	0.0177082	−	0.0306714i	0.874744	+	0.484586i	$0.161030\pi$
$752$	−17.4853	+	30.2854i	−0.637623	+	1.10439i
$753$		0			0
$754$		0			0
$755$	9.94113			0.361795
$756$	−2.58579	+	4.47871i	−0.0940441	+	0.162889i
$757$	−25.9706	+	44.9823i	−0.943916	+	1.63491i	−0.186009	+	0.982548i	$0.559555\pi$
$757$	−25.9706	+	44.9823i	−0.943916	+	1.63491i	−0.757907	+	0.652363i	$0.773778\pi$
$758$	−0.100505	−	0.174080i	−0.00365051	−	0.00632287i
$759$	−8.00000			−0.290382
$760$	−6.34315	−	10.9867i	−0.230090	−	0.398528i
$761$	16.2426	+	28.1331i	0.588795	+	1.01982i	0.994391	+	0.105771i	$0.0337309\pi$
$761$	16.2426	+	28.1331i	0.588795	+	1.01982i	−0.405595	+	0.914053i	$0.632936\pi$
$762$	−2.34315			−0.0848832
$763$	−7.51472	−	13.0159i	−0.272051	−	0.471206i
$764$	3.02944	−	5.24714i	0.109601	−	0.189835i
$765$	−10.8284	+	18.7554i	−0.391503	+	0.678102i
$766$	12.8284			0.463510
$767$		0			0
$768$	3.97056			0.143275
$769$	21.0000	−	36.3731i	0.757279	−	1.31165i	−0.186954	−	0.982369i	$-0.559861\pi$
$769$	21.0000	−	36.3731i	0.757279	−	1.31165i	0.944233	−	0.329278i	$-0.106805\pi$
$770$	−3.31371	+	5.73951i	−0.119418	+	0.206838i
$771$	2.17157	+	3.76127i	0.0782073	+	0.135459i
$772$	9.71573			0.349677
$773$	17.0711	+	29.5680i	0.614004	+	1.06349i	0.990558	+	0.137091i	$0.0437753\pi$
$773$	17.0711	+	29.5680i	0.614004	+	1.06349i	−0.376555	+	0.926394i	$0.622891\pi$
$774$	−0.343146	−	0.594346i	−0.0123341

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.e (of order \(3\), degree \(2\), not minimal)

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

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