LMFDB - Embedded newform 507.2.e.i.484.1

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			484.1
Root			$-0.623490 - 1.07992i$ of defining polynomial
Character	$\chi$	$=$	507.484
Dual form			507.2.e.i.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34601 - 2.33136i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.62349 + 4.54402i) q^{4} -1.04892 q^{5} +(1.34601 - 2.33136i) q^{6} +(-0.277479 + 0.480608i) q^{7} +8.74094 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.34601 - 2.33136i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.62349 + 4.54402i) q^{4} -1.04892 q^{5} +(1.34601 - 2.33136i) q^{6} +(-0.277479 + 0.480608i) q^{7} +8.74094 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.41185 + 2.44540i) q^{10} +(-1.45593 - 2.52174i) q^{11} -5.24698 q^{12} +1.49396 q^{14} +(-0.524459 - 0.908389i) q^{15} +(-6.51842 - 11.2902i) q^{16} +(2.42543 - 4.20096i) q^{17} +2.69202 q^{18} +(0.376510 - 0.652135i) q^{19} +(2.75182 - 4.76630i) q^{20} -0.554958 q^{21} +(-3.91939 + 6.78858i) q^{22} +(-2.88135 - 4.99065i) q^{23} +(4.37047 + 7.56988i) q^{24} -3.89977 q^{25} -1.00000 q^{27} +(-1.45593 - 2.52174i) q^{28} +(0.955927 + 1.65571i) q^{29} +(-1.41185 + 2.44540i) q^{30} -9.51573 q^{31} +(-8.80678 + 15.2538i) q^{32} +(1.45593 - 2.52174i) q^{33} -13.0586 q^{34} +(0.291053 - 0.504118i) q^{35} +(-2.62349 - 4.54402i) q^{36} +(-2.87651 - 4.98226i) q^{37} -2.02715 q^{38} -9.16852 q^{40} +(-2.45593 - 4.25379i) q^{41} +(0.746980 + 1.29381i) q^{42} +(5.54892 - 9.61101i) q^{43} +15.2784 q^{44} +(0.524459 - 0.908389i) q^{45} +(-7.75667 + 13.4349i) q^{46} +0.753020 q^{47} +(6.51842 - 11.2902i) q^{48} +(3.34601 + 5.79546i) q^{49} +(5.24914 + 9.09177i) q^{50} +4.85086 q^{51} -7.58211 q^{53} +(1.34601 + 2.33136i) q^{54} +(1.52715 + 2.64510i) q^{55} +(-2.42543 + 4.20096i) q^{56} +0.753020 q^{57} +(2.57338 - 4.45722i) q^{58} +(-2.04892 + 3.54883i) q^{59} +5.50365 q^{60} +(1.71164 - 2.96464i) q^{61} +(12.8083 + 22.1846i) q^{62} +(-0.277479 - 0.480608i) q^{63} +21.3424 q^{64} -7.83877 q^{66} +(0.936313 + 1.62174i) q^{67} +(12.7262 + 22.0424i) q^{68} +(2.88135 - 4.99065i) q^{69} -1.56704 q^{70} +(5.25182 - 9.09643i) q^{71} +(-4.37047 + 7.56988i) q^{72} +10.4765 q^{73} +(-7.74363 + 13.4124i) q^{74} +(-1.94989 - 3.37730i) q^{75} +(1.97554 + 3.42174i) q^{76} +1.61596 q^{77} +1.33513 q^{79} +(6.83728 + 11.8425i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.61141 + 11.4513i) q^{82} +2.64310 q^{83} +(1.45593 - 2.52174i) q^{84} +(-2.54407 + 4.40646i) q^{85} -29.8756 q^{86} +(-0.955927 + 1.65571i) q^{87} +(-12.7262 - 22.0424i) q^{88} +(-4.96346 - 8.59696i) q^{89} -2.82371 q^{90} +30.2368 q^{92} +(-4.75786 - 8.24086i) q^{93} +(-1.01357 - 1.75556i) q^{94} +(-0.394928 + 0.684035i) q^{95} -17.6136 q^{96} +(-8.53684 + 14.7862i) q^{97} +(9.00753 - 15.6015i) q^{98} +2.91185 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{3} - 11 q^{4} + 12 q^{5} + 3 q^{6} - 2 q^{7} + 24 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 3 * q^3 - 11 * q^4 + 12 * q^5 + 3 * q^6 - 2 * q^7 + 24 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} + 3 q^{3} - 11 q^{4} + 12 q^{5} + 3 q^{6} - 2 q^{7} + 24 q^{8} - 3 q^{9} + q^{10} - 5 q^{11} - 22 q^{12} - 10 q^{14} + 6 q^{15} - 11 q^{16} + q^{17} + 6 q^{18} + 7 q^{19} - 15 q^{20} - 4 q^{21} + 9 q^{22} + 12 q^{24} + 22 q^{25} - 6 q^{27} - 5 q^{28} + 2 q^{29} - q^{30} - 32 q^{31} - 22 q^{32} + 5 q^{33} - 16 q^{34} - 4 q^{35} - 11 q^{36} - 22 q^{37} + 6 q^{40} - 11 q^{41} - 5 q^{42} + 15 q^{43} + 32 q^{44} - 6 q^{45} + 7 q^{46} + 14 q^{47} + 11 q^{48} + 15 q^{49} + 3 q^{50} + 2 q^{51} - 34 q^{53} + 3 q^{54} - 3 q^{55} - q^{56} + 14 q^{57} - 12 q^{58} + 6 q^{59} - 30 q^{60} + 13 q^{61} + 2 q^{62} - 2 q^{63} + 18 q^{66} - 11 q^{67} + 13 q^{68} - 48 q^{70} - 12 q^{72} + 12 q^{73} - 15 q^{74} + 11 q^{75} + 21 q^{76} + 30 q^{77} + 6 q^{79} + 20 q^{80} - 3 q^{81} + 3 q^{82} + 24 q^{83} + 5 q^{84} - 19 q^{85} - 58 q^{86} - 2 q^{87} - 13 q^{88} - q^{89} - 2 q^{90} + 14 q^{92} - 16 q^{93} + 21 q^{95} - 44 q^{96} + 5 q^{97} + 29 q^{98} + 10 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^3 - 11 * q^4 + 12 * q^5 + 3 * q^6 - 2 * q^7 + 24 * q^8 - 3 * q^9 + q^10 - 5 * q^11 - 22 * q^12 - 10 * q^14 + 6 * q^15 - 11 * q^16 + q^17 + 6 * q^18 + 7 * q^19 - 15 * q^20 - 4 * q^21 + 9 * q^22 + 12 * q^24 + 22 * q^25 - 6 * q^27 - 5 * q^28 + 2 * q^29 - q^30 - 32 * q^31 - 22 * q^32 + 5 * q^33 - 16 * q^34 - 4 * q^35 - 11 * q^36 - 22 * q^37 + 6 * q^40 - 11 * q^41 - 5 * q^42 + 15 * q^43 + 32 * q^44 - 6 * q^45 + 7 * q^46 + 14 * q^47 + 11 * q^48 + 15 * q^49 + 3 * q^50 + 2 * q^51 - 34 * q^53 + 3 * q^54 - 3 * q^55 - q^56 + 14 * q^57 - 12 * q^58 + 6 * q^59 - 30 * q^60 + 13 * q^61 + 2 * q^62 - 2 * q^63 + 18 * q^66 - 11 * q^67 + 13 * q^68 - 48 * q^70 - 12 * q^72 + 12 * q^73 - 15 * q^74 + 11 * q^75 + 21 * q^76 + 30 * q^77 + 6 * q^79 + 20 * q^80 - 3 * q^81 + 3 * q^82 + 24 * q^83 + 5 * q^84 - 19 * q^85 - 58 * q^86 - 2 * q^87 - 13 * q^88 - q^89 - 2 * q^90 + 14 * q^92 - 16 * q^93 + 21 * q^95 - 44 * q^96 + 5 * q^97 + 29 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.34601	−	2.33136i	−0.951773	−	1.64852i	−0.741585	−	0.670859i	$-0.765926\pi$
$2$	−1.34601	−	2.33136i	−0.951773	−	1.64852i	−0.210188	−	0.977661i	$-0.567408\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.62349	+	4.54402i	−1.31174	+	2.27201i
$5$	−1.04892			−0.469090			−0.234545	−	0.972105i	$-0.575360\pi$
$5$	−1.04892			−0.469090			−0.234545	+	0.972105i	$0.575360\pi$
$6$	1.34601	−	2.33136i	0.549507	−	0.951773i
$7$	−0.277479	+	0.480608i	−0.104877	+	0.181653i	−0.913688	−	0.406416i	$-0.866778\pi$
$7$	−0.277479	+	0.480608i	−0.104877	+	0.181653i	0.808811	+	0.588069i	$0.200112\pi$
$8$	8.74094			3.09039
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.41185	+	2.44540i	0.446467	+	0.773304i
$11$	−1.45593	−	2.52174i	−0.438979	−	0.760333i	0.558632	−	0.829415i	$-0.311326\pi$
$11$	−1.45593	−	2.52174i	−0.438979	−	0.760333i	−0.997611	+	0.0690822i	$0.977993\pi$
$12$	−5.24698			−1.51467
$13$		0			0
$13$		0			0
$14$	1.49396			0.399277
$15$	−0.524459	−	0.908389i	−0.135415	−	0.234545i
$16$	−6.51842	−	11.2902i	−1.62960	−	2.82256i
$17$	2.42543	−	4.20096i	0.588253	−	1.01888i	−0.406209	−	0.913780i	$-0.633149\pi$
$17$	2.42543	−	4.20096i	0.588253	−	1.01888i	0.994461	−	0.105103i	$-0.0335172\pi$
$18$	2.69202			0.634516
$19$	0.376510	−	0.652135i	0.0863774	−	0.149610i	−0.819600	−	0.572936i	$-0.805804\pi$
$19$	0.376510	−	0.652135i	0.0863774	−	0.149610i	0.905977	+	0.423326i	$0.139138\pi$
$20$	2.75182	−	4.76630i	0.615327	−	1.06578i
$21$	−0.554958			−0.121102
$22$	−3.91939	+	6.78858i	−0.835616	+	1.44733i
$23$	−2.88135	−	4.99065i	−0.600804	−	1.04062i	−0.992700	−	0.120613i	$-0.961514\pi$
$23$	−2.88135	−	4.99065i	−0.600804	−	1.04062i	0.391896	−	0.920010i	$-0.371819\pi$
$24$	4.37047	+	7.56988i	0.892118	+	1.54519i
$25$	−3.89977			−0.779954
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−1.45593	−	2.52174i	−0.275144	−	0.476564i
$29$	0.955927	+	1.65571i	0.177511	+	0.307458i	0.941027	−	0.338330i	$-0.109862\pi$
$29$	0.955927	+	1.65571i	0.177511	+	0.307458i	−0.763516	+	0.645789i	$0.776529\pi$
$30$	−1.41185	+	2.44540i	−0.257768	+	0.446467i
$31$	−9.51573			−1.70908			−0.854538	−	0.519389i	$-0.826159\pi$
$31$	−9.51573			−1.70908			−0.854538	+	0.519389i	$0.826159\pi$
$32$	−8.80678	+	15.2538i	−1.55683	+	2.69652i
$33$	1.45593	−	2.52174i	0.253444	−	0.438979i
$34$	−13.0586			−2.23953
$35$	0.291053	−	0.504118i	0.0491969	−	0.0852115i
$36$	−2.62349	−	4.54402i	−0.437248	−	0.757336i
$37$	−2.87651	−	4.98226i	−0.472895	−	0.819079i	0.526623	−	0.850099i	$-0.323458\pi$
$37$	−2.87651	−	4.98226i	−0.472895	−	0.819079i	−0.999519	+	0.0310199i	$0.990124\pi$
$38$	−2.02715			−0.328847
$39$		0			0
$40$	−9.16852			−1.44967
$41$	−2.45593	−	4.25379i	−0.383551	−	0.664330i	0.608016	−	0.793925i	$-0.291966\pi$
$41$	−2.45593	−	4.25379i	−0.383551	−	0.664330i	−0.991567	+	0.129595i	$0.958632\pi$
$42$	0.746980	+	1.29381i	0.115261	+	0.199639i
$43$	5.54892	−	9.61101i	0.846202	−	1.46566i	−0.0383713	−	0.999264i	$-0.512217\pi$
$43$	5.54892	−	9.61101i	0.846202	−	1.46566i	0.884573	−	0.466401i	$-0.154450\pi$
$44$	15.2784			2.30331
$45$	0.524459	−	0.908389i	0.0781817	−	0.135415i
$46$	−7.75667	+	13.4349i	−1.14366	+	1.98087i
$47$	0.753020			0.109839			0.0549197	−	0.998491i	$-0.482510\pi$
$47$	0.753020			0.109839			0.0549197	+	0.998491i	$0.482510\pi$
$48$	6.51842	−	11.2902i	0.940853	−	1.62960i
$49$	3.34601	+	5.79546i	0.478002	+	0.827923i
$50$	5.24914	+	9.09177i	0.742340	+	1.28577i
$51$	4.85086			0.679256
$52$		0			0
$53$	−7.58211			−1.04148			−0.520741	−	0.853715i	$-0.674344\pi$
$53$	−7.58211			−1.04148			−0.520741	+	0.853715i	$0.674344\pi$
$54$	1.34601	+	2.33136i	0.183169	+	0.317258i
$55$	1.52715	+	2.64510i	0.205920	+	0.356665i
$56$	−2.42543	+	4.20096i	−0.324111	+	0.561377i
$57$	0.753020			0.0997400
$58$	2.57338	−	4.45722i	0.337901	−	0.585261i
$59$	−2.04892	+	3.54883i	−0.266746	+	0.462018i	−0.968020	−	0.250874i	$-0.919282\pi$
$59$	−2.04892	+	3.54883i	−0.266746	+	0.462018i	0.701273	+	0.712892i	$0.252615\pi$
$60$	5.50365			0.710518
$61$	1.71164	−	2.96464i	0.219153	−	0.379583i	−0.735397	−	0.677637i	$-0.763004\pi$
$61$	1.71164	−	2.96464i	0.219153	−	0.379583i	0.954549	+	0.298054i	$0.0963374\pi$
$62$	12.8083	+	22.1846i	1.62665	+	2.81744i
$63$	−0.277479	−	0.480608i	−0.0349591	−	0.0605509i
$64$	21.3424			2.66780
$65$		0			0
$66$	−7.83877			−0.964886
$67$	0.936313	+	1.62174i	0.114389	+	0.198127i	0.917535	−	0.397654i	$-0.130176\pi$
$67$	0.936313	+	1.62174i	0.114389	+	0.198127i	−0.803146	+	0.595782i	$0.796842\pi$
$68$	12.7262	+	22.0424i	1.54327	+	2.67303i
$69$	2.88135	−	4.99065i	0.346874	−	0.600804i
$70$	−1.56704			−0.187297
$71$	5.25182	−	9.09643i	0.623277	−	1.07955i	−0.365595	−	0.930774i	$-0.619134\pi$
$71$	5.25182	−	9.09643i	0.623277	−	1.07955i	0.988871	−	0.148773i	$-0.0475324\pi$
$72$	−4.37047	+	7.56988i	−0.515065	+	0.892118i
$73$	10.4765			1.22618			0.613091	−	0.790012i	$-0.289926\pi$
$73$	10.4765			1.22618			0.613091	+	0.790012i	$0.289926\pi$
$74$	−7.74363	+	13.4124i	−0.900178	+	1.55915i
$75$	−1.94989	−	3.37730i	−0.225153	−	0.389977i
$76$	1.97554	+	3.42174i	0.226610	+	0.392500i
$77$	1.61596			0.184155
$78$		0			0
$79$	1.33513			0.150213			0.0751067	−	0.997176i	$-0.476070\pi$
$79$	1.33513			0.150213			0.0751067	+	0.997176i	$0.476070\pi$
$80$	6.83728	+	11.8425i	0.764431	+	1.32403i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.61141	+	11.4513i	−0.730108	+	1.26458i
$83$	2.64310			0.290118			0.145059	−	0.989423i	$-0.453663\pi$
$83$	2.64310			0.290118			0.145059	+	0.989423i	$0.453663\pi$
$84$	1.45593	−	2.52174i	0.158855	−	0.275144i
$85$	−2.54407	+	4.40646i	−0.275943	+	0.477948i
$86$	−29.8756			−3.22157
$87$	−0.955927	+	1.65571i	−0.102486	+	0.177511i
$88$	−12.7262	−	22.0424i	−1.35661	−	2.34972i
$89$	−4.96346	−	8.59696i	−0.526126	−	0.911276i	−0.999537	−	0.0304348i	$-0.990311\pi$
$89$	−4.96346	−	8.59696i	−0.526126	−	0.911276i	0.473411	−	0.880842i	$-0.343023\pi$
$90$	−2.82371			−0.297645
$91$		0			0
$92$	30.2368			3.15241
$93$	−4.75786	−	8.24086i	−0.493368	−	0.854538i
$94$	−1.01357	−	1.75556i	−0.104542	−	0.181072i
$95$	−0.394928	+	0.684035i	−0.0405188	+	0.0701806i
$96$	−17.6136			−1.79768
$97$	−8.53684	+	14.7862i	−0.866784	+	1.50131i	−0.00151988	+	0.999999i	$0.500484\pi$
$97$	−8.53684	+	14.7862i	−0.866784	+	1.50131i	−0.865264	+	0.501316i	$0.832850\pi$
$98$	9.00753	−	15.6015i	0.909898	−	1.57599i
$99$	2.91185			0.292652
$100$	10.2310	−	17.7206i	1.02310	−	1.77206i
$101$	−3.66152	−	6.34194i	−0.364335	−	0.631047i	0.624334	−	0.781157i	$-0.285370\pi$
$101$	−3.66152	−	6.34194i	−0.364335	−	0.631047i	−0.988669	+	0.150111i	$0.952037\pi$
$102$	−6.52930	−	11.3091i	−0.646497	−	1.11977i
$103$	−4.21983			−0.415792			−0.207896	−	0.978151i	$-0.566662\pi$
$103$	−4.21983			−0.415792			−0.207896	+	0.978151i	$0.566662\pi$
$104$		0			0
$105$	0.582105			0.0568077
$106$	10.2056	+	17.6766i	0.991255	+	1.71690i
$107$	−3.19687	−	5.53713i	−0.309053	−	0.535295i	0.669103	−	0.743170i	$-0.266679\pi$
$107$	−3.19687	−	5.53713i	−0.309053	−	0.535295i	−0.978155	+	0.207875i	$0.933345\pi$
$108$	2.62349	−	4.54402i	0.252445	−	0.437248i
$109$	−3.46011			−0.331418			−0.165709	−	0.986175i	$-0.552991\pi$
$109$	−3.46011			−0.331418			−0.165709	+	0.986175i	$0.552991\pi$
$110$	4.11111	−	7.12066i	0.391979	−	0.678928i
$111$	2.87651	−	4.98226i	0.273026	−	0.472895i
$112$	7.23490			0.683634
$113$	−4.67845	+	8.10331i	−0.440111	+	0.762295i	−0.997697	−	0.0678240i	$-0.978394\pi$
$113$	−4.67845	+	8.10331i	−0.440111	+	0.762295i	0.557586	+	0.830119i	$0.311728\pi$
$114$	−1.01357	−	1.75556i	−0.0949299	−	0.164423i
$115$	3.02230	+	5.23478i	0.281831	+	0.488146i
$116$	−10.0315			−0.931398
$117$		0			0
$118$	11.0315			1.01553
$119$	1.34601	+	2.33136i	0.123389	+	0.213715i
$120$	−4.58426	−	7.94017i	−0.418484	−	0.724835i
$121$	1.26055	−	2.18334i	0.114596	−	0.198486i
$122$	−9.21552			−0.834334
$123$	2.45593	−	4.25379i	0.221443	−	0.383551i
$124$	24.9644	−	43.2396i	2.24187	−	3.88303i
$125$	9.33513			0.834959
$126$	−0.746980	+	1.29381i	−0.0665462	+	0.115261i
$127$	2.24094	+	3.88142i	0.198851	+	0.344420i	0.948156	−	0.317805i	$-0.102946\pi$
$127$	2.24094	+	3.88142i	0.198851	+	0.344420i	−0.749305	+	0.662225i	$0.769612\pi$
$128$	−11.1136	−	19.2493i	−0.982310	−	1.70141i
$129$	11.0978			0.977110
$130$		0			0
$131$	−9.21744			−0.805331			−0.402666	−	0.915347i	$-0.631916\pi$
$131$	−9.21744			−0.805331			−0.402666	+	0.915347i	$0.631916\pi$
$132$	7.63922	+	13.2315i	0.664909	+	1.15166i
$133$	0.208947	+	0.361908i	0.0181180	+	0.0313814i
$134$	2.52057	−	4.36576i	0.217744	−	0.377144i
$135$	1.04892			0.0902764
$136$	21.2005	−	36.7204i	1.81793	−	3.14875i
$137$	3.73490	−	6.46903i	0.319094	−	0.552687i	−0.661205	−	0.750205i	$-0.729955\pi$
$137$	3.73490	−	6.46903i	0.319094	−	0.552687i	0.980299	+	0.197518i	$0.0632881\pi$
$138$	−15.5133			−1.32058
$139$	8.99880	−	15.5864i	0.763269	−	1.32202i	−0.177889	−	0.984051i	$-0.556927\pi$
$139$	8.99880	−	15.5864i	0.763269	−	1.32202i	0.941157	−	0.337969i	$-0.109740\pi$
$140$	1.52715	+	2.64510i	0.129067	+	0.223551i
$141$	0.376510	+	0.652135i	0.0317079	+	0.0549197i
$142$	−28.2760			−2.37287
$143$		0			0
$144$	13.0368			1.08640
$145$	−1.00269	−	1.73671i	−0.0832687	−	0.144226i
$146$	−14.1015	−	24.4245i	−1.16705	−	2.02138i
$147$	−3.34601	+	5.79546i	−0.275974	+	0.478002i
$148$	30.1860			2.48127
$149$	−7.66756	+	13.2806i	−0.628151	+	1.08799i	0.359771	+	0.933041i	$0.382855\pi$
$149$	−7.66756	+	13.2806i	−0.628151	+	1.08799i	−0.987922	+	0.154949i	$0.950479\pi$
$150$	−5.24914	+	9.09177i	−0.428590	+	0.742340i
$151$	2.53079			0.205953			0.102977	−	0.994684i	$-0.467163\pi$
$151$	2.53079			0.205953			0.102977	+	0.994684i	$0.467163\pi$
$152$	3.29105	−	5.70027i	0.266940	−	0.462353i
$153$	2.42543	+	4.20096i	0.196084	+	0.339628i
$154$	−2.17510	−	3.76738i	−0.175274	−	0.303584i
$155$	9.98121			0.801710
$156$		0			0
$157$	17.2392			1.37584			0.687919	−	0.725787i	$-0.258524\pi$
$157$	17.2392			1.37584			0.687919	+	0.725787i	$0.258524\pi$
$158$	−1.79709	−	3.11266i	−0.142969	−	0.247630i
$159$	−3.79105	−	6.56630i	−0.300650	−	0.520741i
$160$	9.23759	−	16.0000i	0.730295	−	1.26491i
$161$	3.19806			0.252043
$162$	−1.34601	+	2.33136i	−0.105753	+	0.183169i
$163$	−7.85354	+	13.6027i	−0.615137	+	1.06545i	0.375223	+	0.926934i	$0.377566\pi$
$163$	−7.85354	+	13.6027i	−0.615137	+	1.06545i	−0.990360	+	0.138514i	$0.955767\pi$
$164$	25.7724			2.01249
$165$	−1.52715	+	2.64510i	−0.118888	+	0.205920i
$166$	−3.55765	−	6.16202i	−0.276127	−	0.478266i
$167$	−2.69806	−	4.67318i	−0.208782	−	0.361622i	0.742549	−	0.669792i	$-0.233617\pi$
$167$	−2.69806	−	4.67318i	−0.208782	−	0.361622i	−0.951331	+	0.308170i	$0.900283\pi$
$168$	−4.85086			−0.374252
$169$		0			0
$170$	13.6974			1.05054
$171$	0.376510	+	0.652135i	0.0287925	+	0.0498700i
$172$	29.1151	+	50.4288i	2.22000	+	3.84516i
$173$	−11.9710	+	20.7344i	−0.910138	+	1.57640i	−0.0962694	+	0.995355i	$0.530691\pi$
$173$	−11.9710	+	20.7344i	−0.910138	+	1.57640i	−0.813868	+	0.581049i	$0.802642\pi$
$174$	5.14675			0.390174
$175$	1.08211	−	1.87426i	0.0817995	−	0.141681i
$176$	−18.9807	+	32.8755i	−1.43072	+	2.47808i
$177$	−4.09783			−0.308012
$178$	−13.3617	+	23.1432i	−1.00150	+	1.73466i
$179$	−9.20440	−	15.9425i	−0.687969	−	1.19160i	−0.972494	−	0.232929i	$-0.925169\pi$
$179$	−9.20440	−	15.9425i	−0.687969	−	1.19160i	0.284525	−	0.958669i	$-0.408164\pi$
$180$	2.75182	+	4.76630i	0.205109	+	0.355259i
$181$	−3.63342			−0.270070			−0.135035	−	0.990841i	$-0.543115\pi$
$181$	−3.63342			−0.270070			−0.135035	+	0.990841i	$0.543115\pi$
$182$		0			0
$183$	3.42327			0.253056
$184$	−25.1857	−	43.6230i	−1.85672	−	3.21593i
$185$	3.01722	+	5.22598i	0.221831	+	0.384222i
$186$	−12.8083	+	22.1846i	−0.939148	+	1.62665i
$187$	−14.1250			−1.03292
$188$	−1.97554	+	3.42174i	−0.144081	+	0.249556i
$189$	0.277479	−	0.480608i	0.0201836	−	0.0349591i
$190$	2.12631			0.154259
$191$	10.5891	−	18.3409i	0.766201	−	1.32710i	−0.173409	−	0.984850i	$-0.555478\pi$
$191$	10.5891	−	18.3409i	0.766201	−	1.32710i	0.939609	−	0.342249i	$-0.111189\pi$
$192$	10.6712	+	18.4831i	0.770128	+	1.33390i
$193$	8.80559	+	15.2517i	0.633840	+	1.09784i	0.986760	+	0.162189i	$0.0518555\pi$
$193$	8.80559	+	15.2517i	0.633840	+	1.09784i	−0.352920	+	0.935654i	$0.614811\pi$
$194$	45.9627			3.29993
$195$		0			0
$196$	−35.1129			−2.50806
$197$	2.33124	+	4.03783i	0.166094	+	0.287683i	0.937043	−	0.349213i	$-0.113551\pi$
$197$	2.33124	+	4.03783i	0.166094	+	0.287683i	−0.770949	+	0.636897i	$0.780218\pi$
$198$	−3.91939	−	6.78858i	−0.278539	−	0.482443i
$199$	−7.51842	+	13.0223i	−0.532967	+	0.923125i	0.466292	+	0.884631i	$0.345590\pi$
$199$	−7.51842	+	13.0223i	−0.532967	+	0.923125i	−0.999259	+	0.0384944i	$0.987744\pi$
$200$	−34.0877			−2.41036
$201$	−0.936313	+	1.62174i	−0.0660424	+	0.114389i
$202$	−9.85690	+	17.0726i	−0.693529	+	1.20123i
$203$	−1.06100			−0.0744675
$204$	−12.7262	+	22.0424i	−0.891010	+	1.54327i
$205$	2.57606	+	4.46187i	0.179920	+	0.311631i
$206$	5.67994	+	9.83794i	0.395740	+	0.685442i
$207$	5.76271			0.400536
$208$		0			0
$209$	−2.19269			−0.151671
$210$	−0.783520	−	1.35710i	−0.0540680	−	0.0936485i
$211$	0.230054	+	0.398465i	0.0158375	+	0.0274314i	0.873836	−	0.486222i	$-0.161625\pi$
$211$	0.230054	+	0.398465i	0.0158375	+	0.0274314i	−0.857998	+	0.513653i	$0.828292\pi$
$212$	19.8916	−	34.4532i	1.36616	−	2.36626i
$213$	10.5036			0.719698
$214$	−8.60603	+	14.9061i	−0.588296	+	1.01896i
$215$	−5.82036	+	10.0812i	−0.396945	+	0.687529i
$216$	−8.74094			−0.594746
$217$	2.64042	−	4.57333i	0.179243	−	0.310458i
$218$	4.65734	+	8.06675i	0.315435	+	0.546349i
$219$	5.23825	+	9.07292i	0.353968	+	0.613091i
$220$	−16.0258			−1.08046
$221$		0			0
$222$	−15.4873			−1.03944
$223$	8.17510	+	14.1597i	0.547445	+	0.948202i	0.998449	+	0.0556803i	$0.0177328\pi$
$223$	8.17510	+	14.1597i	0.547445	+	0.948202i	−0.451004	+	0.892522i	$0.648934\pi$
$224$	−4.88740	−	8.46522i	−0.326553	−	0.565606i
$225$	1.94989	−	3.37730i	0.129992	−	0.225153i
$226$	25.1890			1.67555
$227$	−3.28017	+	5.68142i	−0.217712	+	0.377089i	−0.954108	−	0.299462i	$-0.903193\pi$
$227$	−3.28017	+	5.68142i	−0.217712	+	0.377089i	0.736396	+	0.676551i	$0.236526\pi$
$228$	−1.97554	+	3.42174i	−0.130833	+	0.226610i
$229$	−3.95539			−0.261380			−0.130690	−	0.991423i	$-0.541719\pi$
$229$	−3.95539			−0.261380			−0.130690	+	0.991423i	$0.541719\pi$
$230$	8.13610	−	14.0921i	0.536479	−	0.929209i
$231$	0.807979	+	1.39946i	0.0531611	+	0.0920777i
$232$	8.35570	+	14.4725i	0.548579	+	0.950166i
$233$	8.35690			0.547478			0.273739	−	0.961804i	$-0.411739\pi$
$233$	8.35690			0.547478			0.273739	+	0.961804i	$0.411739\pi$
$234$		0			0
$235$	−0.789856			−0.0515245
$236$	−10.7506	−	18.6206i	−0.699806	−	1.21210i
$237$	0.667563	+	1.15625i	0.0433629	+	0.0751067i
$238$	3.62349	−	6.27607i	0.234876	−	0.406817i
$239$	20.1008			1.30021			0.650107	−	0.759843i	$-0.274724\pi$
$239$	20.1008			1.30021			0.650107	+	0.759843i	$0.274724\pi$
$240$	−6.83728	+	11.8425i	−0.441345	+	0.764431i
$241$	9.50634	−	16.4655i	0.612357	−	1.06063i	−0.378485	−	0.925607i	$-0.623555\pi$
$241$	9.50634	−	16.4655i	0.612357	−	1.06063i	0.990842	−	0.135026i	$-0.0431118\pi$
$242$	−6.78687			−0.436277
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	8.98092	+	15.5554i	0.574944	+	0.995833i
$245$	−3.50969	−	6.07896i	−0.224226	−	0.388370i
$246$	−13.2228			−0.843056
$247$		0			0
$248$	−83.1764			−5.28171
$249$	1.32155	+	2.28900i	0.0837500	+	0.145059i
$250$	−12.5652	−	21.7635i	−0.794692	−	1.37645i
$251$	0.381887	−	0.661448i	0.0241045	−	0.0417502i	−0.853722	−	0.520730i	$-0.825660\pi$
$251$	0.381887	−	0.661448i	0.0241045	−	0.0417502i	0.877826	+	0.478980i	$0.158993\pi$
$252$	2.91185			0.183430
$253$	−8.39008	+	14.5321i	−0.527480	+	0.913622i
$254$	6.03266	−	10.4489i	0.378522	−	0.655620i
$255$	−5.08815			−0.318632
$256$	−8.57553	+	14.8533i	−0.535971	+	0.928329i
$257$	6.54556	+	11.3373i	0.408301	+	0.707198i	0.994700	−	0.102825i	$-0.0327880\pi$
$257$	6.54556	+	11.3373i	0.408301	+	0.707198i	−0.586398	+	0.810023i	$0.699455\pi$
$258$	−14.9378	−	25.8730i	−0.929987	−	1.61078i
$259$	3.19269			0.198384
$260$		0			0
$261$	−1.91185			−0.118341
$262$	12.4068	+	21.4892i	0.766493	+	1.32760i
$263$	−9.18867	−	15.9152i	−0.566598	−	0.981376i	−0.996899	−	0.0786906i	$-0.974926\pi$
$263$	−9.18867	−	15.9152i	−0.566598	−	0.981376i	0.430301	−	0.902685i	$-0.358407\pi$
$264$	12.7262	−	22.0424i	0.783242	−	1.35661i
$265$	7.95300			0.488549
$266$	0.562491	−	0.974263i	0.0344885	−	0.0597359i
$267$	4.96346	−	8.59696i	0.303759	−	0.526126i
$268$	−9.82563			−0.600196
$269$	−11.8312	+	20.4923i	−0.721363	+	1.24944i	0.239090	+	0.970997i	$0.423151\pi$
$269$	−11.8312	+	20.4923i	−0.721363	+	1.24944i	−0.960453	+	0.278441i	$0.910182\pi$
$270$	−1.41185	−	2.44540i	−0.0859227	−	0.148822i
$271$	9.87651	+	17.1066i	0.599955	+	1.03915i	0.992827	+	0.119560i	$0.0381483\pi$
$271$	9.87651	+	17.1066i	0.599955	+	1.03915i	−0.392872	+	0.919593i	$0.628518\pi$
$272$	−63.2398			−3.83448
$273$		0			0
$274$	−20.1089			−1.21482
$275$	5.67778	+	9.83421i	0.342383	+	0.593025i
$276$	15.1184	+	26.1859i	0.910021	+	1.57620i
$277$	−0.888887	+	1.53960i	−0.0534081	+	0.0925055i	−0.891493	−	0.453034i	$-0.850342\pi$
$277$	−0.888887	+	1.53960i	−0.0534081	+	0.0925055i	0.838085	+	0.545539i	$0.183675\pi$
$278$	−48.4499			−2.90583
$279$	4.75786	−	8.24086i	0.284846	−	0.493368i
$280$	2.54407	−	4.40646i	0.152037	−	0.263337i
$281$	1.62133			0.0967207			0.0483603	−	0.998830i	$-0.484600\pi$
$281$	1.62133			0.0967207			0.0483603	+	0.998830i	$0.484600\pi$
$282$	1.01357	−	1.75556i	0.0603574	−	0.104542i
$283$	−2.49180	−	4.31593i	−0.148122	−	0.256555i	0.782411	−	0.622762i	$-0.213990\pi$
$283$	−2.49180	−	4.31593i	−0.148122	−	0.256555i	−0.930533	+	0.366207i	$0.880656\pi$
$284$	27.5562	+	47.7288i	1.63516	+	2.83218i
$285$	−0.789856			−0.0467870
$286$		0			0
$287$	2.72587			0.160903
$288$	−8.80678	−	15.2538i	−0.518945	−	0.898838i
$289$	−3.26540	−	5.65583i	−0.192082	−	0.332696i
$290$	−2.69926	+	4.67525i	−0.158506	+	0.274540i
$291$	−17.0737			−1.00088
$292$	−27.4850	+	47.6054i	−1.60844	+	2.78590i
$293$	0.0358763	−	0.0621395i	0.00209591	−	0.00363023i	−0.864976	−	0.501814i	$-0.832666\pi$
$293$	0.0358763	−	0.0621395i	0.00209591	−	0.00363023i	0.867071	+	0.498184i	$0.166000\pi$
$294$	18.0151			1.05066
$295$	2.14914	−	3.72243i	0.125128	−	0.216728i
$296$	−25.1434	−	43.5496i	−1.46143	−	2.53127i
$297$	1.45593	+	2.52174i	0.0844815	+	0.146326i
$298$	41.2825			2.39143
$299$		0			0
$300$	20.4620			1.18138
$301$	3.07942	+	5.33371i	0.177495	+	0.307430i
$302$	−3.40648	−	5.90019i	−0.196021	−	0.339518i
$303$	3.66152	−	6.34194i	0.210349	−	0.364335i
$304$	−9.81700			−0.563044
$305$	−1.79536	+	3.10966i	−0.102802	+	0.178059i
$306$	6.52930	−	11.3091i	0.373255	−	0.646497i
$307$	−5.19806			−0.296669			−0.148335	−	0.988937i	$-0.547391\pi$
$307$	−5.19806			−0.296669			−0.148335	+	0.988937i	$0.547391\pi$
$308$	−4.23945	+	7.34294i	−0.241565	+	0.418403i
$309$	−2.10992	−	3.65448i	−0.120029	−	0.207896i
$310$	−13.4348	−	23.2698i	−0.763047	−	1.32164i
$311$	−22.5429			−1.27829			−0.639145	−	0.769087i	$-0.720711\pi$
$311$	−22.5429			−1.27829			−0.639145	+	0.769087i	$0.720711\pi$
$312$		0			0
$313$	22.6612			1.28088			0.640442	−	0.768006i	$-0.278751\pi$
$313$	22.6612			1.28088			0.640442	+	0.768006i	$0.278751\pi$
$314$	−23.2042	−	40.1908i	−1.30949	−	2.26810i
$315$	0.291053	+	0.504118i	0.0163990	+	0.0284038i
$316$	−3.50269	+	6.06683i	−0.197042	+	0.341286i
$317$	26.3424			1.47954			0.739769	−	0.672861i	$-0.234935\pi$
$317$	26.3424			1.47954			0.739769	+	0.672861i	$0.234935\pi$
$318$	−10.2056	+	17.6766i	−0.572301	+	0.991255i
$319$	2.78352	−	4.82120i	0.155847	−	0.269935i
$320$	−22.3864			−1.25144
$321$	3.19687	−	5.53713i	0.178432	−	0.309053i
$322$	−4.30463	−	7.45583i	−0.239887	−	0.415497i
$323$	−1.82640	−	3.16341i	−0.101623	−	0.176017i
$324$	5.24698			0.291499
$325$		0			0
$326$	42.2838			2.34188
$327$	−1.73005	−	2.99654i	−0.0956722	−	0.165709i
$328$	−21.4671	−	37.1821i	−1.18532	−	2.05304i
$329$	−0.208947	+	0.361908i	−0.0115196	+	0.0199526i
$330$	8.22223			0.452619
$331$	5.61476	−	9.72505i	0.308615	−	0.534537i	−0.669445	−	0.742862i	$-0.733468\pi$
$331$	5.61476	−	9.72505i	0.308615	−	0.534537i	0.978060	+	0.208325i	$0.0668011\pi$
$332$	−6.93416	+	12.0103i	−0.380561	+	0.659151i
$333$	5.75302			0.315264
$334$	−7.26324	+	12.5803i	−0.397427	+	0.688364i
$335$	−0.982115	−	1.70107i	−0.0536587	−	0.0929395i
$336$	3.61745	+	6.26561i	0.197348	+	0.341817i
$337$	2.30798			0.125724			0.0628618	−	0.998022i	$-0.479977\pi$
$337$	2.30798			0.125724			0.0628618	+	0.998022i	$0.479977\pi$
$338$		0			0
$339$	−9.35690			−0.508197
$340$	−13.3487	−	23.1206i	−0.723935	−	1.25389i
$341$	13.8542	+	23.9962i	0.750247	+	1.29947i
$342$	1.01357	−	1.75556i	0.0548078	−	0.0949299i
$343$	−7.59850			−0.410280
$344$	48.5027	−	84.0092i	2.61509	−	4.52947i
$345$	−3.02230	+	5.23478i	−0.162715	+	0.281831i
$346$	64.4523			3.46498
$347$	4.56853	−	7.91293i	0.245252	−	0.424788i	−0.716951	−	0.697124i	$-0.754463\pi$
$347$	4.56853	−	7.91293i	0.245252	−	0.424788i	0.962202	+	0.272336i	$0.0877961\pi$
$348$	−5.01573	−	8.68750i	−0.268871	−	0.465699i
$349$	−11.9879	−	20.7637i	−0.641699	−	1.11145i	−0.985053	−	0.172249i	$-0.944897\pi$
$349$	−11.9879	−	20.7637i	−0.641699	−	1.11145i	0.343355	−	0.939206i	$-0.388437\pi$
$350$	−5.82610			−0.311418
$351$		0			0
$352$	51.2881			2.73367
$353$	13.5620	+	23.4900i	0.721830	+	1.25025i	0.960265	+	0.279088i	$0.0900322\pi$
$353$	13.5620	+	23.4900i	0.721830	+	1.25025i	−0.238435	+	0.971158i	$0.576634\pi$
$354$	5.51573	+	9.55352i	0.293158	+	0.507764i
$355$	−5.50873	+	9.54140i	−0.292373	+	0.506405i
$356$	52.0863			2.76057
$357$	−1.34601	+	2.33136i	−0.0712384	+	0.123389i
$358$	−24.7784	+	42.9175i	−1.30958	+	2.26826i
$359$	−26.0790			−1.37640			−0.688200	−	0.725521i	$-0.741599\pi$
$359$	−26.0790			−1.37640			−0.688200	+	0.725521i	$0.741599\pi$
$360$	4.58426	−	7.94017i	0.241612	−	0.418484i
$361$	9.21648	+	15.9634i	0.485078	+	0.840180i
$362$	4.89062	+	8.47080i	0.257045	+	0.445215i
$363$	2.52111			0.132324
$364$		0			0
$365$	−10.9890			−0.575190
$366$	−4.60776	−	7.98088i	−0.240851	−	0.417167i
$367$	−4.78717	−	8.29162i	−0.249888	−	0.432819i	0.713606	−	0.700547i	$-0.247061\pi$
$367$	−4.78717	−	8.29162i	−0.249888	−	0.432819i	−0.963495	+	0.267728i	$0.913727\pi$
$368$	−37.5637	+	65.0623i	−1.95815	+	3.39161i
$369$	4.91185			0.255701
$370$	8.12242	−	14.0685i	0.422265	−	0.731384i
$371$	2.10388	−	3.64402i	0.109228	−	0.189188i
$372$	49.9288			2.58869
$373$	−14.0749	+	24.3784i	−0.728769	+	1.26227i	0.228635	+	0.973512i	$0.426574\pi$
$373$	−14.0749	+	24.3784i	−0.728769	+	1.26227i	−0.957404	+	0.288753i	$0.906759\pi$
$374$	19.0124	+	32.9304i	0.983107	+	1.70279i
$375$	4.66756	+	8.08446i	0.241032	+	0.417480i
$376$	6.58211			0.339446
$377$		0			0
$378$	−1.49396			−0.0768410
$379$	−8.02326	−	13.8967i	−0.412127	−	0.713825i	0.582995	−	0.812476i	$-0.301881\pi$
$379$	−8.02326	−	13.8967i	−0.412127	−	0.713825i	−0.995122	+	0.0986504i	$0.968547\pi$
$380$	−2.07218	−	3.58912i	−0.106301	−	0.184118i
$381$	−2.24094	+	3.88142i	−0.114807	+	0.198851i
$382$	−57.0122			−2.91700
$383$	12.3083	−	21.3186i	0.628923	−	1.08933i	−0.358845	−	0.933397i	$-0.616829\pi$
$383$	12.3083	−	21.3186i	0.628923	−	1.08933i	0.987768	−	0.155930i	$-0.0498374\pi$
$384$	11.1136	−	19.2493i	0.567137	−	0.982310i
$385$	−1.69501			−0.0863855
$386$	23.7048	−	41.0580i	1.20654	−	2.08980i
$387$	5.54892	+	9.61101i	0.282067	+	0.488555i
$388$	−44.7926	−	77.5831i	−2.27400	−	3.93868i
$389$	−17.2198			−0.873080			−0.436540	−	0.899685i	$-0.643796\pi$
$389$	−17.2198			−0.873080			−0.436540	+	0.899685i	$0.643796\pi$
$390$		0			0
$391$	−27.9541			−1.41370
$392$	29.2473	+	50.6578i	1.47721	+	2.55860i
$393$	−4.60872	−	7.98254i	−0.232479	−	0.402666i
$394$	6.27575	−	10.8699i	0.316168	−	0.547619i
$395$	−1.40044			−0.0704636
$396$	−7.63922	+	13.2315i	−0.383885	+	0.664909i
$397$	1.01961	−	1.76602i	0.0511730	−	0.0886342i	−0.839304	−	0.543662i	$-0.817037\pi$
$397$	1.01961	−	1.76602i	0.0511730	−	0.0886342i	0.890477	+	0.455028i	$0.150371\pi$
$398$	40.4795			2.02905
$399$	−0.208947	+	0.361908i	−0.0104605	+	0.0181180i
$400$	25.4203	+	44.0293i	1.27102	+	2.20147i
$401$	0.730718	+	1.26564i	0.0364903	+	0.0632031i	0.883694	−	0.468065i	$-0.155049\pi$
$401$	0.730718	+	1.26564i	0.0364903	+	0.0632031i	−0.847203	+	0.531269i	$0.821716\pi$
$402$	5.04115			0.251430
$403$		0			0
$404$	38.4239			1.91166
$405$	0.524459	+	0.908389i	0.0260606	+	0.0451382i
$406$	1.42812	+	2.47357i	0.0708762	+	0.122761i
$407$	−8.37598	+	14.5076i	−0.415182	+	0.719116i
$408$	42.4010			2.09916
$409$	14.9695	−	25.9279i	0.740194	−	1.28205i	−0.212213	−	0.977224i	$-0.568067\pi$
$409$	14.9695	−	25.9279i	0.740194	−	1.28205i	0.952407	−	0.304830i	$-0.0985998\pi$
$410$	6.93482	−	12.0115i	0.342486	−	0.593204i
$411$	7.46980			0.368458
$412$	11.0707	−	19.1750i	0.545414	−	0.944684i
$413$	−1.13706	−	1.96945i	−0.0559512	−	0.0969104i
$414$	−7.75667	−	13.4349i	−0.381219	−	0.660291i
$415$	−2.77240			−0.136092
$416$		0			0
$417$	17.9976			0.881347
$418$	2.95138	+	5.11194i	0.144357	+	0.250033i
$419$	−3.32371	−	5.75683i	−0.162374	−	0.281240i	0.773346	−	0.633984i	$-0.218582\pi$
$419$	−3.32371	−	5.75683i	−0.162374	−	0.281240i	−0.935720	+	0.352745i	$0.885248\pi$
$420$	−1.52715	+	2.64510i	−0.0745171	+	0.129067i
$421$	13.5646			0.661100			0.330550	−	0.943788i	$-0.392766\pi$
$421$	13.5646			0.661100			0.330550	+	0.943788i	$0.392766\pi$
$422$	0.619309	−	1.07268i	0.0301475	−	0.0522170i
$423$	−0.376510	+	0.652135i	−0.0183066	+	0.0317079i
$424$	−66.2747			−3.21858
$425$	−9.45862	+	16.3828i	−0.458810	+	0.794683i
$426$	−14.1380	−	24.4878i	−0.684989	−	1.18644i
$427$	0.949886	+	1.64525i	0.0459682	+	0.0796193i
$428$	33.5478			1.62159
$429$		0			0
$430$	31.3370			1.51121
$431$	−17.9731	−	31.1304i	−0.865736	−	1.49950i	−0.866314	−	0.499499i	$-0.833517\pi$
$431$	−17.9731	−	31.1304i	−0.865736	−	1.49950i	0.000578325	−	1.00000i	$-0.499816\pi$
$432$	6.51842	+	11.2902i	0.313618	+	0.543201i
$433$	16.2371	−	28.1234i	0.780303	−	1.35152i	−0.151462	−	0.988463i	$-0.548398\pi$
$433$	16.2371	−	28.1234i	0.780303	−	1.35152i	0.931765	−	0.363061i	$-0.118268\pi$
$434$	−14.2161			−0.682395
$435$	1.00269	−	1.73671i	0.0480752	−	0.0832687i
$436$	9.07756	−	15.7228i	0.434736	−	0.752985i
$437$	−4.33944			−0.207583
$438$	14.1015	−	24.4245i	0.673795	−	1.16705i
$439$	−6.41603	−	11.1129i	−0.306221	−	0.530390i	0.671312	−	0.741175i	$-0.265731\pi$
$439$	−6.41603	−	11.1129i	−0.306221	−	0.530390i	−0.977532	+	0.210785i	$0.932398\pi$
$440$	13.3487	+	23.1206i	0.636374	+	1.10223i
$441$	−6.69202			−0.318668
$442$		0			0
$443$	11.9608			0.568273			0.284137	−	0.958784i	$-0.408293\pi$
$443$	11.9608			0.568273			0.284137	+	0.958784i	$0.408293\pi$
$444$	15.0930	+	26.1418i	0.716282	+	1.24064i
$445$	5.20626	+	9.01751i	0.246800	+	0.427471i
$446$	22.0075	−	38.1182i	1.04209	−	1.80495i
$447$	−15.3351			−0.725327
$448$	−5.92208	+	10.2573i	−0.279792	+	0.484614i
$449$	6.23945	−	10.8070i	0.294458	−	0.510016i	−0.680401	−	0.732840i	$-0.738194\pi$
$449$	6.23945	−	10.8070i	0.294458	−	0.510016i	0.974859	+	0.222824i	$0.0715277\pi$
$450$	−10.4983			−0.494893
$451$	−7.15130	+	12.3864i	−0.336742	+	0.583254i
$452$	−24.5477	−	42.5179i	−1.15463	−	1.99987i
$453$	1.26540	+	2.19173i	0.0594536	+	0.102977i
$454$	17.6606			0.828851
$455$		0			0
$456$	6.58211			0.308235
$457$	−16.2262	−	28.1045i	−0.759028	−	1.31468i	−0.943347	−	0.331809i	$-0.892341\pi$
$457$	−16.2262	−	28.1045i	−0.759028	−	1.31468i	0.184319	−	0.982867i	$-0.440992\pi$
$458$	5.32400	+	9.22144i	0.248774	+	0.430890i
$459$	−2.42543	+	4.20096i	−0.113209	+	0.196084i
$460$	−31.7159			−1.47876
$461$	−12.2017	+	21.1340i	−0.568290	+	0.984308i	0.428445	+	0.903568i	$0.359062\pi$
$461$	−12.2017	+	21.1340i	−0.568290	+	0.984308i	−0.996735	+	0.0807398i	$0.974272\pi$
$462$	2.17510	−	3.76738i	0.101195	−	0.175274i
$463$	−33.1836			−1.54217			−0.771086	−	0.636731i	$-0.780286\pi$
$463$	−33.1836			−1.54217			−0.771086	+	0.636731i	$0.780286\pi$
$464$	12.4623	−	21.5853i	0.578546	−	1.00207i
$465$	4.99061	+	8.64398i	0.231434	+	0.400855i
$466$	−11.2485	−	19.4829i	−0.521075	−	0.902529i
$467$	−38.5206			−1.78252			−0.891261	−	0.453490i	$-0.850179\pi$
$467$	−38.5206			−1.78252			−0.891261	+	0.453490i	$0.850179\pi$
$468$		0			0
$469$	−1.03923			−0.0479871
$470$	1.06315	+	1.84144i	0.0490397	+	0.0849392i
$471$	8.61960	+	14.9296i	0.397170	+	0.687919i
$472$	−17.9095	+	31.0201i	−0.824350	+	1.42782i
$473$	−32.3153			−1.48586
$474$	1.79709	−	3.11266i	0.0825432	−	0.142969i
$475$	−1.46830	+	2.54318i	−0.0673704	+	0.116689i
$476$	−14.1250			−0.647417
$477$	3.79105	−	6.56630i	0.173580	−	0.300650i
$478$	−27.0559	−	46.8622i	−1.23751	−	2.14343i
$479$	4.17241	+	7.22682i	0.190642	+	0.330202i	0.945463	−	0.325729i	$-0.105610\pi$
$479$	4.17241	+	7.22682i	0.190642	+	0.330202i	−0.754821	+	0.655931i	$0.772276\pi$
$480$	18.4752			0.843272
$481$		0			0
$482$	−51.1825			−2.33130
$483$	1.59903	+	2.76960i	0.0727584	+	0.126021i
$484$	6.61410	+	11.4560i	0.300641	+	0.520725i
$485$	8.95444	−	15.5095i	0.406600	−	0.704252i
$486$	−2.69202			−0.122113
$487$	7.42931	−	12.8679i	0.336654	−	0.583102i	−0.647147	−	0.762365i	$-0.724038\pi$
$487$	7.42931	−	12.8679i	0.336654	−	0.583102i	0.983801	+	0.179263i	$0.0573713\pi$
$488$	14.9613	−	25.9137i	0.677266	−	1.17306i
$489$	−15.7071			−0.710299
$490$	−9.44816	+	16.3647i	−0.426824	+	0.739281i
$491$	−2.49947	−	4.32920i	−0.112799	−	0.195374i	0.804099	−	0.594496i	$-0.202648\pi$
$491$	−2.49947	−	4.32920i	−0.112799	−	0.195374i	−0.916898	+	0.399122i	$0.869315\pi$
$492$	12.8862	+	22.3196i	0.580955	+	1.00624i
$493$	9.27413			0.417686
$494$		0			0
$495$	−3.05429			−0.137280
$496$	62.0275	+	107.435i	2.78512	+	4.82396i
$497$	2.91454	+	5.04814i	0.130735	+	0.226440i
$498$	3.55765	−	6.16202i	0.159422	−	0.276127i
$499$	−0.385371			−0.0172516			−0.00862579	−	0.999963i	$-0.502746\pi$
$499$	−0.385371			−0.0172516			−0.00862579	+	0.999963i	$0.502746\pi$
$500$	−24.4906	+	42.4190i	−1.09525	+	1.89703i
$501$	2.69806	−	4.67318i	0.120541	−	0.208782i
$502$	−2.05610			−0.0917681
$503$	−11.3089	+	19.5877i	−0.504241	+	0.873370i	0.495747	+	0.868467i	$0.334894\pi$
$503$	−11.3089	+	19.5877i	−0.504241	+	0.873370i	−0.999988	+	0.00490359i	$0.998439\pi$
$504$	−2.42543	−	4.20096i	−0.108037	−	0.187126i
$505$	3.84063	+	6.65217i	0.170906	+	0.296018i
$506$	45.1726			2.00817
$507$		0			0
$508$	−23.5163			−1.04337
$509$	5.80194	+	10.0493i	0.257166	+	0.445425i	0.965482	−	0.260471i	$-0.0838778\pi$
$509$	5.80194	+	10.0493i	0.257166	+	0.445425i	−0.708315	+	0.705896i	$0.750544\pi$
$510$	6.84870	+	11.8623i	0.303265	+	0.525271i
$511$	−2.90701	+	5.03509i	−0.128599	+	0.222739i
$512$	1.71678			0.0758715
$513$	−0.376510	+	0.652135i	−0.0166233	+	0.0287925i
$514$	17.6208	−	30.5201i	0.777220	−	1.34618i
$515$	4.42626			0.195044
$516$	−29.1151	+	50.4288i	−1.28172	+	2.22000i
$517$	−1.09634	−	1.89892i	−0.0482171	−	0.0835145i
$518$	−4.29739	−	7.44330i	−0.188816	−	0.327040i
$519$	−23.9420			−1.05094
$520$		0			0
$521$	−1.62671			−0.0712675			−0.0356337	−	0.999365i	$-0.511345\pi$
$521$	−1.62671			−0.0712675			−0.0356337	+	0.999365i	$0.511345\pi$
$522$	2.57338	+	4.45722i	0.112634	+	0.195087i
$523$	−5.03588	−	8.72239i	−0.220203	−	0.381404i	0.734666	−	0.678429i	$-0.237339\pi$
$523$	−5.03588	−	8.72239i	−0.220203	−	0.381404i	−0.954870	+	0.297025i	$0.904005\pi$
$524$	24.1819	−	41.8842i	1.05639	−	1.82972i
$525$	2.16421			0.0944539
$526$	−24.7361	+	42.8442i	−1.07854	+	1.86809i
$527$	−23.0797	+	39.9752i	−1.00537	+	1.74135i
$528$	−37.9614			−1.65206
$529$	−5.10441	+	8.84109i	−0.221931	+	0.384395i
$530$	−10.7048	−	18.5413i	−0.464988	−	0.805383i
$531$	−2.04892	−	3.54883i	−0.0889154	−	0.154006i
$532$	−2.19269			−0.0950650
$533$		0			0
$534$	−26.7235			−1.15644
$535$	3.35325	+	5.80800i	0.144974	+	0.251102i
$536$	8.18425	+	14.1755i	0.353506	+	0.612290i
$537$	9.20440	−	15.9425i	0.397199	−	0.687969i
$538$	63.6999			2.74630
$539$	9.74309	−	16.8755i	0.419665	−	0.726881i
$540$	−2.75182	+	4.76630i	−0.118420	+	0.205109i
$541$	−20.4674			−0.879962			−0.439981	−	0.898007i	$-0.645015\pi$
$541$	−20.4674			−0.879962			−0.439981	+	0.898007i	$0.645015\pi$
$542$	26.5878	−	46.0514i	1.14204	−	1.97808i
$543$	−1.81671	−	3.14663i	−0.0779624	−	0.135035i
$544$	42.7204	+	73.9939i	1.83162	+	3.17246i
$545$	3.62937			0.155465
$546$		0			0
$547$	−27.5478			−1.17786			−0.588929	−	0.808185i	$-0.700450\pi$
$547$	−27.5478			−1.17786			−0.588929	+	0.808185i	$0.700450\pi$
$548$	19.5969	+	33.9429i	0.837140	+	1.44997i
$549$	1.71164	+	2.96464i	0.0730508	+	0.126528i
$550$	15.2847	−	26.4739i	0.651742	−	1.12885i
$551$	1.43967			0.0613318
$552$	25.1857	−	43.6230i	1.07198	−	1.85672i
$553$	−0.370469	+	0.641672i	−0.0157540	+	0.0272867i
$554$	4.78581			0.203329
$555$	−3.01722	+	5.22598i	−0.128074	+	0.221831i
$556$	47.2165	+	81.7814i	2.00243	+	3.46831i
$557$	−18.9928	−	32.8964i	−0.804749	−	1.39387i	−0.916460	−	0.400126i	$-0.868966\pi$
$557$	−18.9928	−	32.8964i	−0.804749	−	1.39387i	0.111711	−	0.993741i	$-0.464367\pi$
$558$	−25.6165			−1.08443
$559$		0			0
$560$	−7.58881			−0.320686
$561$	−7.06249	−	12.2326i	−0.298179	−	0.516460i
$562$	−2.18233	−	3.77991i	−0.0920562	−	0.159446i
$563$	14.8862	−	25.7837i	0.627378	−	1.08665i	−0.360697	−	0.932683i	$-0.617461\pi$
$563$	14.8862	−	25.7837i	0.627378	−	1.08665i	0.988076	−	0.153968i	$-0.0492054\pi$
$564$	−3.95108			−0.166371
$565$	4.90731	−	8.49970i	0.206452	−	0.357585i
$566$	−6.70799	+	11.6186i	−0.281958	+	0.488365i
$567$	0.554958			0.0233061
$568$	45.9059	−	79.5113i	1.92617	−	3.33622i
$569$	10.9770	+	19.0128i	0.460181	+	0.797057i	0.998970	−	0.0453839i	$-0.0144511\pi$
$569$	10.9770	+	19.0128i	0.460181	+	0.797057i	−0.538788	+	0.842441i	$0.681118\pi$
$570$	1.06315	+	1.84144i	0.0445307	+	0.0771294i
$571$	2.46575			0.103188			0.0515942	−	0.998668i	$-0.483570\pi$
$571$	2.46575			0.103188			0.0515942	+	0.998668i	$0.483570\pi$
$572$		0			0
$573$	21.1782			0.884732
$574$	−3.66905	−	6.35499i	−0.153143	−	0.265252i
$575$	11.2366	+	19.4624i	0.468600	+	0.811639i
$576$	−10.6712	+	18.4831i	−0.444634	+	0.770128i
$577$	17.4547			0.726650			0.363325	−	0.931662i	$-0.381641\pi$
$577$	17.4547			0.726650			0.363325	+	0.931662i	$0.381641\pi$
$578$	−8.79052	+	15.2256i	−0.365637	+	0.633303i
$579$	−8.80559	+	15.2517i	−0.365948	+	0.633840i
$580$	10.5222			0.436909
$581$	−0.733406	+	1.27030i	−0.0304268	+	0.0527008i
$582$	22.9813	+	39.8049i	0.952607	+	1.64996i
$583$	11.0390	+	19.1201i	0.457188	+	0.791873i
$584$	91.5745			3.78938
$585$		0			0
$586$	−0.193159			−0.00797934
$587$	−3.13169	−	5.42424i	−0.129259	−	0.223882i	0.794131	−	0.607747i	$-0.207926\pi$
$587$	−3.13169	−	5.42424i	−0.129259	−	0.223882i	−0.923390	+	0.383864i	$0.874593\pi$
$588$	−17.5565	−	30.4087i	−0.724016	−	1.25403i
$589$	−3.58277	+	6.20554i	−0.147625	+	0.255695i
$590$	−11.5711			−0.476374
$591$	−2.33124	+	4.03783i	−0.0958944	+	0.166094i
$592$	−37.5006	+	64.9529i	−1.54126	+	2.66955i
$593$	22.8745			0.939345			0.469672	−	0.882841i	$-0.344372\pi$
$593$	22.8745			0.939345			0.469672	+	0.882841i	$0.344372\pi$
$594$	3.91939	−	6.78858i	0.160814	−	0.278539i
$595$	−1.41185	−	2.44540i	−0.0578804	−	0.100252i
$596$	−40.2315	−	69.6831i	−1.64795	−	2.85433i
$597$	−15.0368			−0.615417
$598$		0			0
$599$	−1.05621			−0.0431557			−0.0215778	−	0.999767i	$-0.506869\pi$
$599$	−1.05621			−0.0431557			−0.0215778	+	0.999767i	$0.506869\pi$
$600$	−17.0438	−	29.5208i	−0.695812	−	1.20518i
$601$	16.6618	+	28.8591i	0.679650	+	1.17719i	0.975086	+	0.221826i	$0.0712015\pi$
$601$	16.6618	+	28.8591i	0.679650	+	1.17719i	−0.295437	+	0.955362i	$0.595465\pi$
$602$	8.28986	−	14.3585i	0.337869	−	0.585207i
$603$	−1.87263			−0.0762592
$604$	−6.63951	+	11.5000i	−0.270158	+	0.467927i
$605$	−1.32222	+	2.29015i	−0.0537557	+	0.0931076i
$606$	−19.7138			−0.800818
$607$	−8.12014	+	14.0645i	−0.329586	+	0.570860i	−0.982430	−	0.186633i	$-0.940243\pi$
$607$	−8.12014	+	14.0645i	−0.329586	+	0.570860i	0.652844	+	0.757493i	$0.273576\pi$
$608$	6.63169	+	11.4864i	0.268950	+	0.465836i
$609$	−0.530499	−	0.918852i	−0.0214969	−	0.0372338i
$610$	9.66632			0.391378
$611$		0			0
$612$	−25.4523			−1.02885
$613$	−5.52393	−	9.56772i	−0.223109	−	0.386437i	0.732641	−	0.680615i	$-0.238287\pi$
$613$	−5.52393	−	9.56772i	−0.223109	−	0.386437i	−0.955751	+	0.294178i	$0.904954\pi$
$614$	6.99665	+	12.1185i	0.282362	+	0.489065i
$615$	−2.57606	+	4.46187i	−0.103877	+	0.179920i
$616$	14.1250			0.569112
$617$	2.32975	−	4.03524i	0.0937922	−	0.162453i	−0.815312	−	0.579022i	$-0.803434\pi$
$617$	2.32975	−	4.03524i	0.0937922	−	0.162453i	0.909104	+	0.416570i	$0.136768\pi$
$618$	−5.67994	+	9.83794i	−0.228481	+	0.395740i
$619$	31.9259			1.28321			0.641604	−	0.767036i	$-0.278269\pi$
$619$	31.9259			1.28321			0.641604	+	0.767036i	$0.278269\pi$
$620$	−26.1856	+	45.3548i	−1.05164	+	1.82149i
$621$	2.88135	+	4.99065i	0.115625	+	0.200268i
$622$	30.3430	+	52.5555i	1.21664	+	2.10729i
$623$	5.50902			0.220714
$624$		0			0
$625$	9.70709			0.388283
$626$	−30.5022	−	52.8313i	−1.21911	−	2.11156i
$627$	−1.09634	−	1.89892i	−0.0437837	−	0.0758356i
$628$	−45.2269	+	78.3353i	−1.80475	+	3.12592i
$629$	−27.9071			−1.11273
$630$	0.783520	−	1.35710i	0.0312162	−	0.0540680i
$631$	19.7207	−	34.1572i	0.785067	−	1.35978i	−0.143892	−	0.989593i	$-0.545962\pi$
$631$	19.7207	−	34.1572i	0.785067	−	1.35978i	0.928959	−	0.370183i	$-0.120705\pi$
$632$	11.6703			0.464218
$633$	−0.230054	+	0.398465i	−0.00914381	+	0.0158375i
$634$	−35.4572	−	61.4136i	−1.40818	−	2.43905i
$635$	−2.35056	−	4.07129i	−0.0932791	−	0.161564i
$636$	39.7832			1.57750
$637$		0			0
$638$	−14.9866			−0.593325
$639$	5.25182	+	9.09643i	0.207759	+	0.359849i
$640$	11.6572	+	20.1909i	0.460792	+	0.798115i
$641$	−22.7255	+	39.3617i	−0.897603	+	1.55469i	−0.0670544	+	0.997749i	$0.521360\pi$
$641$	−22.7255	+	39.3617i	−0.897603	+	1.55469i	−0.830549	+	0.556946i	$0.811973\pi$
$642$	−17.2121			−0.679306
$643$	14.8735	−	25.7616i	0.586552	−	1.01594i	−0.408128	−	0.912925i	$-0.633818\pi$
$643$	14.8735	−	25.7616i	0.586552	−	1.01594i	0.994680	−	0.103013i	$-0.0328483\pi$
$644$	−8.39008	+	14.5321i	−0.330616	+	0.572643i
$645$	−11.6407			−0.458353
$646$	−4.91670	+	8.51597i	−0.193445	+	0.335056i
$647$	8.46562	+	14.6629i	0.332818	+	0.576457i	0.983063	−	0.183267i	$-0.0586673\pi$
$647$	8.46562	+	14.6629i	0.332818	+	0.576457i	−0.650245	+	0.759724i	$0.725334\pi$
$648$	−4.37047	−	7.56988i	−0.171688	−	0.297373i
$649$	11.9323			0.468384
$650$		0			0
$651$	5.28083			0.206972
$652$	−41.2074	−	71.3733i	−1.61381	−	2.79519i
$653$	16.5988	+	28.7500i	0.649561	+	1.12507i	0.983228	+	0.182382i	$0.0583806\pi$
$653$	16.5988	+	28.7500i	0.649561	+	1.12507i	−0.333667	+	0.942691i	$0.608286\pi$
$654$	−4.65734	+	8.06675i	−0.182116	+	0.315435i
$655$	9.66833			0.377773
$656$	−32.0175	+	55.4560i	−1.25007	+	2.16519i
$657$	−5.23825	+	9.07292i	−0.204364	+	0.353968i
$658$	1.12498			0.0438564
$659$	21.3286	−	36.9421i	0.830842	−	1.43906i	−0.0665286	−	0.997785i	$-0.521192\pi$
$659$	21.3286	−	36.9421i	0.830842	−	1.43906i	0.897371	−	0.441277i	$-0.145474\pi$
$660$	−8.01291	−	13.8788i	−0.311902	−	0.540230i
$661$	−19.3451	−	33.5067i	−0.752438	−	1.30326i	−0.946638	−	0.322298i	$-0.895545\pi$
$661$	−19.3451	−	33.5067i	−0.752438	−	1.30326i	0.194201	−	0.980962i	$-0.437789\pi$
$662$	−30.2301			−1.17493
$663$		0			0
$664$	23.1032			0.896578
$665$	−0.219169	−	0.379611i	−0.00849899	−	0.0147207i
$666$	−7.74363	−	13.4124i	−0.300059	−	0.519718i
$667$	5.50873	−	9.54140i	0.213299	−	0.369444i
$668$	28.3134			1.09548
$669$	−8.17510	+	14.1597i	−0.316067	+	0.547445i
$670$	−2.64387	+	4.57932i	−0.102142	+	0.176915i
$671$	−9.96807			−0.384813
$672$	4.88740	−	8.46522i	0.188535	−	0.326553i
$673$	1.29709	+	2.24663i	0.0499993	+	0.0866013i	0.889942	−	0.456074i	$-0.150745\pi$
$673$	1.29709	+	2.24663i	0.0499993	+	0.0866013i	−0.839943	+	0.542675i	$0.817411\pi$
$674$	−3.10656	−	5.38073i	−0.119660	−	0.207258i
$675$	3.89977			0.150102
$676$		0			0
$677$	1.75302			0.0673740			0.0336870	−	0.999432i	$-0.489275\pi$
$677$	1.75302			0.0673740			0.0336870	+	0.999432i	$0.489275\pi$
$678$	12.5945	+	21.8143i	0.483688	+	0.837773i
$679$	−4.73759	−	8.20574i	−0.181812	−	0.314907i
$680$	−22.2376	+	38.5166i	−0.852773	+	1.47705i
$681$	−6.56033			−0.251393
$682$	37.2958	−	64.5983i	1.42813	−	2.47360i
$683$	−8.16756	+	14.1466i	−0.312523	+	0.541306i	−0.978908	−	0.204302i	$-0.934508\pi$
$683$	−8.16756	+	14.1466i	−0.312523	+	0.541306i	0.666385	+	0.745608i	$0.267841\pi$
$684$	−3.95108			−0.151073
$685$	−3.91760	+	6.78548i	−0.149684	+	0.259260i
$686$	10.2277	+	17.7148i	0.390494	+	0.676355i
$687$	−1.97770	−	3.42547i	−0.0754539	−	0.130690i
$688$	−144.681			−5.51590
$689$		0			0
$690$	16.2722			0.619472
$691$	−7.95526	−	13.7789i	−0.302632	−	0.524175i	0.674099	−	0.738641i	$-0.264532\pi$
$691$	−7.95526	−	13.7789i	−0.302632	−	0.524175i	−0.976731	+	0.214466i	$0.931199\pi$
$692$	−62.8116	−	108.793i	−2.38774	−	4.13568i
$693$	−0.807979	+	1.39946i	−0.0306926	+	0.0531611i
$694$	−24.5972			−0.933696
$695$	−9.43900	+	16.3488i	−0.358042	+	0.620146i
$696$	−8.35570	+	14.4725i	−0.316722	+	0.548579i
$697$	−23.8267			−0.902500
$698$	−32.2717	+	55.8963i	−1.22150	+	2.11571i
$699$	4.17845	+	7.23728i	0.158043	+	0.273739i
$700$	5.67778	+	9.83421i	0.214600	+	0.371698i
$701$	−20.8635			−0.788005			−0.394002	−	0.919109i	$-0.628910\pi$
$701$	−20.8635			−0.788005			−0.394002	+	0.919109i	$0.628910\pi$
$702$		0			0
$703$	−4.33214			−0.163390
$704$	−31.0730	−	53.8200i	−1.17111	−	2.02842i
$705$	−0.394928	−	0.684035i	−0.0148739	−	0.0257623i
$706$	36.5091	−	63.2356i	1.37404	−	2.37990i
$707$	4.06398			0.152842
$708$	10.7506	−	18.6206i	0.404033	−	0.699806i
$709$	−7.82424	+	13.5520i	−0.293846	+	0.508955i	−0.974716	−	0.223449i	$-0.928268\pi$
$709$	−7.82424	+	13.5520i	−0.293846	+	0.508955i	0.680870	+	0.732404i	$0.261602\pi$
$710$	29.6592			1.11309
$711$	−0.667563	+	1.15625i	−0.0250356	+	0.0433629i
$712$	−43.3853	−	75.1455i	−1.62593	−	2.81620i
$713$	27.4182	+	47.4897i	1.02682	+	1.77850i
$714$	7.24698			0.271211
$715$		0			0
$716$	96.5906			3.60976
$717$	10.0504	+	17.4078i	0.375339	+	0.650107i
$718$	35.1027	+	60.7996i	1.31002	+	2.26902i
$719$	13.5797	−	23.5208i	0.506438	−	0.877176i	−0.493534	−	0.869726i	$-0.664295\pi$
$719$	13.5797	−	23.5208i	0.506438	−	0.877176i	0.999972	−	0.00744977i	$-0.00237136\pi$
$720$	−13.6746			−0.509621
$721$	1.17092	−	2.02808i	0.0436072	−	0.0755298i
$722$	24.8110	−	42.9738i	0.923368	−	1.59932i
$723$	19.0127			0.707089
$724$	9.53223	−	16.5103i	0.354262	−	0.613601i
$725$	−3.72790	−	6.45691i	−0.138451	−	0.239804i
$726$	−3.39344	−	5.87760i	−0.125942	−	0.218138i
$727$	31.7784			1.17859			0.589297	−	0.807916i	$-0.299405\pi$
$727$	31.7784			1.17859			0.589297	+	0.807916i	$0.299405\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	14.7913	+	25.6193i	0.547450	+	0.948212i
$731$	−26.9170	−	46.6216i	−0.995561	−	1.72436i
$732$	−8.98092	+	15.5554i	−0.331944	+	0.574944i
$733$	46.8907			1.73195			0.865973	−	0.500090i	$-0.166700\pi$
$733$	46.8907			1.73195			0.865973	+	0.500090i	$0.166700\pi$
$734$	−12.8872	+	22.3212i	−0.475674	+	0.823891i
$735$	3.50969	−	6.07896i	0.129457	−	0.224226i
$736$	101.502			3.74141
$737$	2.72641	−	4.72227i	0.100428	−	0.173947i
$738$	−6.61141	−	11.4513i	−0.243369	−	0.421528i
$739$	−8.52393	−	14.7639i	−0.313558	−	0.543098i	0.665572	−	0.746334i	$-0.268188\pi$
$739$	−8.52393	−	14.7639i	−0.313558	−	0.543098i	−0.979130	+	0.203236i	$0.934854\pi$
$740$	−31.6626			−1.16394
$741$		0			0
$742$	−11.3274			−0.415840
$743$	5.81618	+	10.0739i	0.213375	+	0.369576i	0.952769	−	0.303697i	$-0.0982211\pi$
$743$	5.81618	+	10.0739i	0.213375	+	0.369576i	−0.739394	+	0.673273i	$0.764888\pi$
$744$	−41.5882	−	72.0329i	−1.52470	−	2.64085i
$745$	8.04264	−	13.9303i	0.294660	−	0.510365i
$746$	75.7797			2.77449
$747$	−1.32155	+	2.28900i	−0.0483531	+	0.0837500i
$748$	37.0567	−	64.1842i	1.35493	−	2.34681i
$749$	3.54825			0.129650
$750$	12.5652	−	21.7635i	0.458815	−	0.794692i
$751$	6.51477	+	11.2839i	0.237727	+	0.411756i	0.960062	−	0.279788i	$-0.0902642\pi$
$751$	6.51477	+	11.2839i	0.237727	+	0.411756i	−0.722334	+	0.691544i	$0.756931\pi$
$752$	−4.90850	−	8.50177i	−0.178995	−	0.310028i
$753$	0.763774			0.0278335
$754$		0			0
$755$	−2.65459			−0.0966106
$756$	1.45593	+	2.52174i	0.0529516	+	0.0917148i
$757$	−11.3949	−	19.7366i	−0.414156	−	0.717339i	0.581184	−	0.813772i	$-0.302590\pi$
$757$	−11.3949	−	19.7366i	−0.414156	−	0.717339i	−0.995339	+	0.0964337i	$0.969256\pi$
$758$	−21.5988	+	37.4102i	−0.784504	+	1.35880i
$759$	−16.7802			−0.609081
$760$	−3.45204	+	5.97911i	−0.125219	+	0.216885i
$761$	19.1712	−	33.2055i	0.694956	−	1.20370i	−0.275240	−	0.961376i	$-0.588757\pi$
$761$	19.1712	−	33.2055i	0.694956	−	1.20370i	0.970196	−	0.242323i	$-0.0779094\pi$
$762$	12.0653			0.437080
$763$	0.960107	−	1.66295i	0.0347582	−	0.0602030i
$764$	55.5608	+	96.2342i	2.01012	+	3.48163i
$765$	−2.54407	−	4.40646i	−0.0919812	−	0.159316i
$766$	−66.2683			−2.39437
$767$		0			0
$768$	−17.1511			−0.618886
$769$	1.81940	+	3.15129i	0.0656091	+	0.113638i	0.896964	−	0.442104i	$-0.145768\pi$
$769$	1.81940	+	3.15129i	0.0656091	+	0.113638i	−0.831355	+	0.555742i	$0.812434\pi$
$770$	2.28150	+	3.95167i	0.0822194	+	0.142408i
$771$	−6.54556	+	11.3373i	−0.235733	+	0.408301i
$772$	−92.4055			−3.32575
$773$	19.6712	−	34.0715i	0.707524	−	1.22547i	−0.258249	−	0.966079i	$-0.583145\pi$
$773$	19.6712	−	34.0715i	0.707524	−	1.22547i	0.965773	−	0.259389i	$-0.0835213\pi$
$774$	14.9378	−	25.8730i	0.536928	−	0.929987i
$775$	37.1092			1.33300
$776$	−74.6200	+	129.246i	−2.67870	+	4.63965i
$777$	1.59634	+	2.76495i	0.0572685	+	0.0991919i
$778$	23.1781	+	40.1456i	0.830974	+	1.43929i
$779$	−3.69873			−0.132521
$780$		0			0
$781$	−30.5851			−1.09442
$782$	37.6265	+	65.1710i	1.34552	+	2.33051i
$783$	−0.955927	−	1.65571i	−0.0341620	−	0.0591704i
$784$	43.6214	−	75.5545i	1.55791	−	2.69837i
$785$	−18.0825			−0.645392
$786$	−12.4068	+	21.4892i	−0.442535	+	0.766493i
$787$	12.7126	−	22.0189i	0.453155	−	0.784888i	−0.545425	−	0.838160i	$-0.683632\pi$
$787$	12.7126	−	22.0189i	0.453155	−	0.784888i	0.998580	+	0.0532720i	$0.0169650\pi$
$788$	−24.4639			−0.871492
$789$	9.18867	−	15.9152i	0.327125	−	0.566598i
$790$	1.88500	+	3.26492i	0.0670654	+	0.116161i
$791$	−2.59634	−	4.49700i	−0.0923153	−	0.159895i
$792$	25.4523			0.904409
$793$		0			0
$794$	−5.48965			−0.194820
$795$	3.97650	+	6.88750i	0.141032	+	0.244275i
$796$	−39.4490	−	68.3276i	−1.39823	−	2.42181i
$797$	−10.3569	+	17.9387i	−0.366860	+	0.635420i	−0.989073	−	0.147428i	$-0.952901\pi$
$797$	−10.3569	+	17.9387i	−0.366860	+	0.635420i	0.622213	+	0.782848i	$0.286234\pi$
$798$	1.12498			0.0398239
$799$	1.82640	−	3.16341i	0.0646133	−	0.111913i
$800$	34.3444	−	59.4863i	1.21426	−	2.10316i
$801$	9.92692			0.350750
$802$	1.96711	−	3.40713i	0.0694610	−	0.120310i
$803$	−15.2530	−	26.4190i	−0.538267	−	0.932306i
$804$	−4.91281	−	8.50924i	−0.173262	−	0.300098i
$805$	−3.35450			−0.118231
$806$		0			0
$807$	−23.6625			−0.832959
$808$	−32.0051	−	55.4345i	−1.12594	−	1.95018i
$809$	−5.54892	−	9.61101i	−0.195090	−	0.337905i	0.751840	−	0.659345i	$-0.229166\pi$
$809$	−5.54892	−	9.61101i	−0.195090	−	0.337905i	−0.946930	+	0.321440i	$0.895833\pi$
$810$	1.41185	−	2.44540i	0.0496075	−	0.0859227i
$811$	−4.84223			−0.170034			−0.0850169	−	0.996380i	$-0.527094\pi$
$811$	−4.84223			−0.170034			−0.0850169	+	0.996380i	$0.527094\pi$
$812$	2.78352	−	4.82120i	0.0976824	−	0.169191i
$813$	−9.87651	+	17.1066i	−0.346384	+	0.599955i
$814$	45.0966			1.58064
$815$	8.23772	−	14.2681i	0.288555	−	0.499791i
$816$	−31.6199	−	54.7673i	−1.10692	−	1.91724i
$817$	−4.17845	−	7.23728i	−0.146185	−	0.253201i
$818$	−80.5964			−2.81799
$819$		0			0
$820$	−27.0331			−0.944037
$821$	21.8690	+	37.8783i	0.763235	+	1.32196i	0.941175	+	0.337920i	$0.109723\pi$
$821$	21.8690	+	37.8783i	0.763235	+	1.32196i	−0.177940	+	0.984041i	$0.556943\pi$
$822$	−10.0544	−	17.4148i	−0.350688	−	0.607410i
$823$	−6.04988	+	10.4787i	−0.210885	+	0.365264i	−0.951992	−	0.306123i	$-0.900968\pi$
$823$	−6.04988	+	10.4787i	−0.210885	+	0.365264i	0.741106	+	0.671388i	$0.234301\pi$
$824$	−36.8853			−1.28496
$825$	−5.67778	+	9.83421i	−0.197675	+	0.342383i
$826$	−3.06100	+	5.30181i	−0.106506	+	0.184473i
$827$	−35.3212			−1.22824			−0.614120	−	0.789213i	$-0.710489\pi$
$827$	−35.3212			−1.22824			−0.614120	+	0.789213i	$0.710489\pi$
$828$	−15.1184	+	26.1859i	−0.525401	+	0.910021i
$829$	−26.7473	−	46.3276i	−0.928971	−	1.60903i	−0.785047	−	0.619437i	$-0.787361\pi$
$829$	−26.7473	−	46.3276i	−0.928971	−	1.60903i	−0.143925	−	0.989589i	$-0.545972\pi$
$830$	3.73168	+	6.46345i	0.129528	+	0.224350i
$831$	−1.77777			−0.0616703
$832$		0			0
$833$	32.4620			1.12474
$834$	−24.2250	−	41.9589i	−0.838842	−	1.45292i
$835$	2.83004	+	4.90178i	0.0979377	+	0.169633i
$836$	5.75249	−	9.96360i	0.198954	−	0.344598i
$837$	9.51573			0.328912
$838$	−8.94749	+	15.4975i	−0.309086	+	0.535353i
$839$	−11.5761	+	20.0503i	−0.399650	+	0.692214i	−0.993683	−	0.112227i	$-0.964202\pi$
$839$	−11.5761	+	20.0503i	−0.399650	+	0.692214i	0.594033	+	0.804441i	$0.297535\pi$
$840$	5.08815			0.175558
$841$	12.6724	−	21.9493i	0.436980	−	0.756871i
$842$	−18.2582	−	31.6241i	−0.629218	−	1.08984i
$843$	0.810667	+	1.40412i	0.0279209	+	0.0483603i
$844$	−2.41417			−0.0830993
$845$		0			0
$846$	2.02715			0.0696948
$847$	0.699554	+	1.21166i	0.0240370	+	0.0416332i
$848$	49.4233	+	85.6037i	1.69720	+	2.93964i
$849$	2.49180	−	4.31593i	0.0855185	−	0.148122i
$850$	50.9256			1.74673
$851$	−16.5765	+	28.7113i	−0.568235	+	0.984212i
$852$	−27.5562	+	47.7288i	−0.944060	+	1.63516i
$853$	26.7265			0.915097			0.457548	−	0.889185i	$-0.348728\pi$
$853$	26.7265			0.915097			0.457548	+	0.889185i	$0.348728\pi$
$854$	2.55711	−	4.42905i	0.0875026	−	0.151559i
$855$	−0.394928	−	0.684035i	−0.0135063	−	0.0233935i
$856$	−27.9436	−	48.3997i	−0.955093	−	1.65427i
$857$	42.6064			1.45541			0.727703	−	0.685892i	$-0.240588\pi$
$857$	42.6064			1.45541			0.727703	+	0.685892i	$0.240588\pi$
$858$		0			0
$859$	33.6079			1.14669			0.573344	−	0.819315i	$-0.305646\pi$
$859$	33.6079			1.14669			0.573344	+	0.819315i	$0.305646\pi$
$860$	−30.5393	−	52.8956i	−1.04138	−	1.80372i
$861$	1.36294	+	2.36068i	0.0464488	+	0.0804516i
$862$	−48.3841	+	83.8037i	−1.64797	+	2.85437i
$863$	18.7047			0.636715			0.318358	−	0.947971i	$-0.396869\pi$
$863$	18.7047			0.636715			0.318358	+	0.947971i	$0.396869\pi$
$864$	8.80678	−	15.2538i	0.299613	−	0.518945i
$865$	12.5566	−	21.7486i	0.426937	−	0.739476i
$866$	−87.4210			−2.97069
$867$	3.26540	−	5.65583i	0.110899	−	0.192082i
$868$	13.8542	+	23.9962i	0.470242	+	0.814484i
$869$	−1.94385	−	3.36684i	−0.0659404	−	0.114212i
$870$	−5.39852			−0.183027
$871$		0			0
$872$	−30.2446			−1.02421
$873$	−8.53684	−	14.7862i	−0.288928	−	0.500438i
$874$	5.84093	+	10.1168i	0.197572	+	0.342205i
$875$	−2.59030	+	4.48653i	−0.0875682	+	0.151673i
$876$	−54.9700			−1.85726
$877$	−18.4119	+	31.8903i	−0.621724	+	1.07686i	0.367440	+	0.930047i	$0.380234\pi$
$877$	−18.4119	+	31.8903i	−0.621724	+	1.07686i	−0.989165	+	0.146811i	$0.953099\pi$
$878$	−17.2721	+	29.9162i	−0.582905	+	1.00962i
$879$	0.0717525			0.00242015
$880$	19.9092	−	34.4837i	0.671138	−	1.16244i
$881$	20.5625	+	35.6153i	0.692768	+	1.19991i	0.970927	+	0.239374i	$0.0769423\pi$
$881$	20.5625	+	35.6153i	0.692768	+	1.19991i	−0.278159	+	0.960535i	$0.589724\pi$
$882$	9.00753	+	15.6015i	0.303299	+	0.525330i
$883$	30.7482			1.03476			0.517380	−	0.855756i	$-0.326907\pi$
$883$	30.7482			1.03476			0.517380	+	0.855756i	$0.326907\pi$
$884$		0			0
$885$	4.29829			0.144485
$886$	−16.0993	−	27.8849i	−0.540867	−	0.936810i
$887$	−3.79470	−	6.57261i	−0.127414	−	0.220687i	0.795260	−	0.606268i	$-0.207334\pi$
$887$	−3.79470	−	6.57261i	−0.127414	−	0.220687i	−0.922674	+	0.385581i	$0.874001\pi$
$888$	25.1434	−	43.5496i	0.843757	−	1.46143i
$889$	−2.48725			−0.0834198
$890$	14.0154	−	24.2753i	0.469796	−	0.813710i
$891$	−1.45593	+	2.52174i	−0.0487754	+	0.0844815i
$892$	−85.7891			−2.87243
$893$	0.283520	−	0.491071i	0.00948763	−	0.0164331i
$894$	20.6412	+	35.7517i	0.690346	+	1.19572i
$895$	9.65465	+	16.7223i	0.322719	+	0.558967i
$896$	12.3351			0.412088
$897$		0			0
$898$	−33.5934			−1.12103
$899$	−9.09634	−	15.7553i	−0.303380	−	0.525470i
$900$	10.2310	+	17.7206i	0.341034	+	0.590688i
$901$	−18.3898	+	31.8521i	−0.612655	+	1.06115i
$902$	38.5029			1.28201
$903$	−3.07942	+	5.33371i	−0.102477	+	0.177495i
$904$	−40.8940	+	70.8305i	−1.36012	+	2.35579i
$905$	3.81115			0.126687
$906$	3.40648	−	5.90019i	0.113173	−	0.196021i
$907$	−9.66666	−	16.7431i	−0.320976	−	0.555947i	0.659713	−	0.751517i	$-0.270678\pi$
$907$	−9.66666	−	16.7431i	−0.320976	−	0.555947i	−0.980690	+	0.195570i	$0.937344\pi$
$908$	−17.2110	−	29.8103i	−0.571166	−	0.989289i
$909$	7.32304			0.242890
$910$		0			0
$911$	22.7149			0.752577			0.376288	−	0.926503i	$-0.377200\pi$
$911$	22.7149			0.752577			0.376288	+	0.926503i	$0.377200\pi$
$912$	−4.90850	−	8.50177i	−0.162537	−	0.281522i
$913$	−3.84817	−	6.66522i	−0.127356	−	0.220587i
$914$	−43.6812	+	75.6580i	−1.44485	+	2.50255i
$915$	−3.59073			−0.118706
$916$	10.3769	−	17.9734i	0.342864	−	0.593857i
$917$	2.55765	−	4.42997i	0.0844609	−	0.146291i
$918$	13.0586			0.430998
$919$	−7.14556	+	12.3765i	−0.235710	+	0.408262i	−0.959479	−	0.281781i	$-0.909075\pi$
$919$	−7.14556	+	12.3765i	−0.235710	+	0.408262i	0.723769	+	0.690043i	$0.242408\pi$
$920$	26.4178	+	45.7569i	0.870968	+	1.50856i
$921$	−2.59903	−	4.50165i	−0.0856410	−	0.148335i
$922$	65.6945			2.16353
$923$		0			0
$924$	−8.47889			−0.278935
$925$	11.2177	+	19.4297i	0.368837	+	0.638844i
$926$	44.6655	+	77.3629i	1.46780	+	2.54230i
$927$	2.10992	−	3.65448i	0.0692987	−	0.120029i
$928$	−33.6746			−1.10542
$929$	−16.3605	+	28.3373i	−0.536772	+	0.929716i	0.462303	+	0.886722i	$0.347023\pi$
$929$	−16.3605	+	28.3373i	−0.536772	+	0.929716i	−0.999075	+	0.0429946i	$0.986310\pi$
$930$	13.4348	−	23.2698i	0.440545	−	0.763047i
$931$	5.03923			0.165154
$932$	−21.9242	+	37.9739i	−0.718152	+	1.24388i
$933$	−11.2714	−	19.5227i	−0.369010	−	0.639145i
$934$	51.8492	+	89.8054i	1.69656	+	2.93852i
$935$	14.8159			0.484533
$936$		0			0
$937$	−4.01400			−0.131132			−0.0655658	−	0.997848i	$-0.520885\pi$
$937$	−4.01400			−0.131132			−0.0655658	+	0.997848i	$0.520885\pi$
$938$	1.39881	+	2.42282i	0.0456729	+	0.0791077i
$939$	11.3306	+	19.6251i	0.369759	+	0.640442i
$940$	2.07218	−	3.58912i	0.0675870	−	0.117064i
$941$	−28.2669			−0.921476			−0.460738	−	0.887536i	$-0.652415\pi$
$941$	−28.2669			−0.921476			−0.460738	+	0.887536i	$0.652415\pi$
$942$	23.2042	−	40.1908i	0.756032	−	1.30949i
$943$	−14.1528	+	24.5134i	−0.460878	+	0.798265i
$944$	53.4228			1.73876
$945$	−0.291053	+	0.504118i	−0.00946794	+	0.0163990i
$946$	43.4967	+	75.3385i	1.41420	+	2.44947i
$947$	18.9227	+	32.7751i	0.614906	+	1.06505i	0.990401	+	0.138225i	$0.0441396\pi$
$947$	18.9227	+	32.7751i	0.614906	+	1.06505i	−0.375495	+	0.926825i	$0.622527\pi$
$948$	−7.00538			−0.227524
$949$		0			0
$950$	7.90541			0.256485
$951$	13.1712	+	22.8132i	0.427106	+	0.739769i
$952$	11.7654	+	20.3783i	0.381319	+	0.660463i
$953$	20.4128	−	35.3560i	0.661236	−	1.14529i	−0.319055	−	0.947736i	$-0.603366\pi$
$953$	20.4128	−	35.3560i	0.661236	−	1.14529i	0.980291	−	0.197558i	$-0.0633011\pi$
$954$	−20.4112			−0.660837
$955$	−11.1071	+	19.2381i	−0.359417	+	0.622529i
$956$	−52.7343	+	91.3385i	−1.70555	+	2.95410i
$957$	5.56704			0.179957
$958$	11.2322	−	19.4548i	0.362896	−	0.628555i
$959$	2.07271	+	3.59004i	0.0669314	+	0.115929i
$960$	−11.1932	−	19.3872i	−0.361260	−	0.625720i
$961$	59.5491			1.92094
$962$		0			0
$963$	6.39373			0.206035
$964$	49.8796	+	86.3939i	1.60651	+	2.78256i
$965$	−9.23633	−	15.9978i	−0.297328	−	0.514987i
$966$	4.30463	−	7.45583i	0.138499	−	0.239887i
$967$	10.2798			0.330575			0.165288	−	0.986245i	$-0.447145\pi$
$967$	10.2798			0.330575			0.165288	+	0.986245i	$0.447145\pi$
$968$	11.0184	−	19.0845i	0.354145	−	0.613398i
$969$	1.82640	−	3.16341i	0.0586723	−	0.101623i
$970$	−48.2111			−1.54796
$971$	9.74027	−	16.8707i	0.312580	−	0.541405i	−0.666340	−	0.745648i	$-0.732140\pi$
$971$	9.74027	−	16.8707i	0.312580	−	0.541405i	0.978920	+	0.204243i	$0.0654733\pi$
$972$	2.62349	+	4.54402i	0.0841485	+	0.145749i
$973$	4.99396	+	8.64979i	0.160099	+	0.277300i
$974$	−39.9997			−1.28167
$975$		0			0
$976$	−44.6286			−1.42853
$977$	−23.5269	−	40.7498i	−0.752693	−	1.30370i	−0.946513	−	0.322665i	$-0.895421\pi$
$977$	−23.5269	−	40.7498i	−0.752693	−	1.30370i	0.193821	−	0.981037i	$-0.437912\pi$
$978$	21.1419	+	36.6189i	0.676044	+	1.17094i
$979$	−14.4529	+	25.0331i	−0.461916	+	0.800062i
$980$	36.8305			1.17651
$981$	1.73005	−	2.99654i	0.0552364	−	0.0956722i
$982$	−6.72862	+	11.6543i	−0.214719	+	0.371904i
$983$	34.4295			1.09813			0.549065	−	0.835779i	$-0.314984\pi$
$983$	34.4295			1.09813			0.549065	+	0.835779i	$0.314984\pi$
$984$	21.4671	−	37.1821i	0.684346	−	1.18532i
$985$	−2.44528	−	4.23535i	−0.0779131	−	0.134949i
$986$	−12.4831	−	21.6213i	−0.397542	−	0.688563i
$987$	−0.417895			−0.0133017
$988$		0			0
$989$	−63.9536			−2.03361
$990$	4.11111	+	7.12066i	0.130660	+	0.226309i
$991$	−3.65399	−	6.32890i	−0.116073	−	0.201044i	0.802135	−	0.597142i	$-0.203697\pi$
$991$	−3.65399	−	6.32890i	−0.116073	−	0.201044i	−0.918208	+	0.396098i	$0.870364\pi$
$992$	83.8030	−	145.151i	2.66075	−	4.60855i
$993$	11.2295			0.356358
$994$	7.84601	−	13.5897i	0.248860	−	0.431039i
$995$	7.88620	−	13.6593i	0.250009	−	0.433029i
$996$	−13.8683			−0.439434
$997$	17.8458	−	30.9098i	0.565181	−	0.978923i	−0.431851	−	0.901945i	$-0.642140\pi$
$997$	17.8458	−	30.9098i	0.565181	−	0.978923i	0.997033	−	0.0769780i	$-0.0245271\pi$
$998$	0.518713	+	0.898438i	0.0164196	+	0.0284396i
$999$	2.87651	+	4.98226i	0.0910088	+	0.157632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.e.i.484.1		6
13.2	odd	12		507.2.b.f.337.1		6
13.3	even	3		507.2.a.l.1.3	yes	3
13.4	even	6		507.2.e.l.22.3		6
13.5	odd	4		507.2.j.i.361.1		12
13.6	odd	12		507.2.j.i.316.6		12
13.7	odd	12		507.2.j.i.316.1		12
13.8	odd	4		507.2.j.i.361.6		12
13.9	even	3	inner	507.2.e.i.22.1		6
13.10	even	6		507.2.a.i.1.1	✓	3
13.11	odd	12		507.2.b.f.337.6		6
13.12	even	2		507.2.e.l.484.3		6
39.2	even	12		1521.2.b.k.1351.6		6
39.11	even	12		1521.2.b.k.1351.1		6
39.23	odd	6		1521.2.a.s.1.3		3
39.29	odd	6		1521.2.a.n.1.1		3
52.3	odd	6		8112.2.a.cp.1.1		3
52.23	odd	6		8112.2.a.cg.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.i.1.1	✓	3	13.10	even	6
507.2.a.l.1.3	yes	3	13.3	even	3
507.2.b.f.337.1		6	13.2	odd	12
507.2.b.f.337.6		6	13.11	odd	12
507.2.e.i.22.1		6	13.9	even	3	inner
507.2.e.i.484.1		6	1.1	even	1	trivial
507.2.e.l.22.3		6	13.4	even	6
507.2.e.l.484.3		6	13.12	even	2
507.2.j.i.316.1		12	13.7	odd	12
507.2.j.i.316.6		12	13.6	odd	12
507.2.j.i.361.1		12	13.5	odd	4
507.2.j.i.361.6		12	13.8	odd	4
1521.2.a.n.1.1		3	39.29	odd	6
1521.2.a.s.1.3		3	39.23	odd	6
1521.2.b.k.1351.1		6	39.11	even	12
1521.2.b.k.1351.6		6	39.2	even	12
8112.2.a.cg.1.3		3	52.23	odd	6
8112.2.a.cp.1.1		3	52.3	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-1.34601 - 2.33136i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.62349 + 4.54402i) q^{4} -1.04892 q^{5} +(1.34601 - 2.33136i) q^{6} +(-0.277479 + 0.480608i) q^{7} +8.74094 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.34601 - 2.33136i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.62349 + 4.54402i) q^{4} -1.04892 q^{5} +(1.34601 - 2.33136i) q^{6} +(-0.277479 + 0.480608i) q^{7} +8.74094 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.41185 + 2.44540i) q^{10} +(-1.45593 - 2.52174i) q^{11} -5.24698 q^{12} +1.49396 q^{14} +(-0.524459 - 0.908389i) q^{15} +(-6.51842 - 11.2902i) q^{16} +(2.42543 - 4.20096i) q^{17} +2.69202 q^{18} +(0.376510 - 0.652135i) q^{19} +(2.75182 - 4.76630i) q^{20} -0.554958 q^{21} +(-3.91939 + 6.78858i) q^{22} +(-2.88135 - 4.99065i) q^{23} +(4.37047 + 7.56988i) q^{24} -3.89977 q^{25} -1.00000 q^{27} +(-1.45593 - 2.52174i) q^{28} +(0.955927 + 1.65571i) q^{29} +(-1.41185 + 2.44540i) q^{30} -9.51573 q^{31} +(-8.80678 + 15.2538i) q^{32} +(1.45593 - 2.52174i) q^{33} -13.0586 q^{34} +(0.291053 - 0.504118i) q^{35} +(-2.62349 - 4.54402i) q^{36} +(-2.87651 - 4.98226i) q^{37} -2.02715 q^{38} -9.16852 q^{40} +(-2.45593 - 4.25379i) q^{41} +(0.746980 + 1.29381i) q^{42} +(5.54892 - 9.61101i) q^{43} +15.2784 q^{44} +(0.524459 - 0.908389i) q^{45} +(-7.75667 + 13.4349i) q^{46} +0.753020 q^{47} +(6.51842 - 11.2902i) q^{48} +(3.34601 + 5.79546i) q^{49} +(5.24914 + 9.09177i) q^{50} +4.85086 q^{51} -7.58211 q^{53} +(1.34601 + 2.33136i) q^{54} +(1.52715 + 2.64510i) q^{55} +(-2.42543 + 4.20096i) q^{56} +0.753020 q^{57} +(2.57338 - 4.45722i) q^{58} +(-2.04892 + 3.54883i) q^{59} +5.50365 q^{60} +(1.71164 - 2.96464i) q^{61} +(12.8083 + 22.1846i) q^{62} +(-0.277479 - 0.480608i) q^{63} +21.3424 q^{64} -7.83877 q^{66} +(0.936313 + 1.62174i) q^{67} +(12.7262 + 22.0424i) q^{68} +(2.88135 - 4.99065i) q^{69} -1.56704 q^{70} +(5.25182 - 9.09643i) q^{71} +(-4.37047 + 7.56988i) q^{72} +10.4765 q^{73} +(-7.74363 + 13.4124i) q^{74} +(-1.94989 - 3.37730i) q^{75} +(1.97554 + 3.42174i) q^{76} +1.61596 q^{77} +1.33513 q^{79} +(6.83728 + 11.8425i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.61141 + 11.4513i) q^{82} +2.64310 q^{83} +(1.45593 - 2.52174i) q^{84} +(-2.54407 + 4.40646i) q^{85} -29.8756 q^{86} +(-0.955927 + 1.65571i) q^{87} +(-12.7262 - 22.0424i) q^{88} +(-4.96346 - 8.59696i) q^{89} -2.82371 q^{90} +30.2368 q^{92} +(-4.75786 - 8.24086i) q^{93} +(-1.01357 - 1.75556i) q^{94} +(-0.394928 + 0.684035i) q^{95} -17.6136 q^{96} +(-8.53684 + 14.7862i) q^{97} +(9.00753 - 15.6015i) q^{98} +2.91185 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{3} - 11 q^{4} + 12 q^{5} + 3 q^{6} - 2 q^{7} + 24 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 3 * q^3 - 11 * q^4 + 12 * q^5 + 3 * q^6 - 2 * q^7 + 24 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} + 3 q^{3} - 11 q^{4} + 12 q^{5} + 3 q^{6} - 2 q^{7} + 24 q^{8} - 3 q^{9} + q^{10} - 5 q^{11} - 22 q^{12} - 10 q^{14} + 6 q^{15} - 11 q^{16} + q^{17} + 6 q^{18} + 7 q^{19} - 15 q^{20} - 4 q^{21} + 9 q^{22} + 12 q^{24} + 22 q^{25} - 6 q^{27} - 5 q^{28} + 2 q^{29} - q^{30} - 32 q^{31} - 22 q^{32} + 5 q^{33} - 16 q^{34} - 4 q^{35} - 11 q^{36} - 22 q^{37} + 6 q^{40} - 11 q^{41} - 5 q^{42} + 15 q^{43} + 32 q^{44} - 6 q^{45} + 7 q^{46} + 14 q^{47} + 11 q^{48} + 15 q^{49} + 3 q^{50} + 2 q^{51} - 34 q^{53} + 3 q^{54} - 3 q^{55} - q^{56} + 14 q^{57} - 12 q^{58} + 6 q^{59} - 30 q^{60} + 13 q^{61} + 2 q^{62} - 2 q^{63} + 18 q^{66} - 11 q^{67} + 13 q^{68} - 48 q^{70} - 12 q^{72} + 12 q^{73} - 15 q^{74} + 11 q^{75} + 21 q^{76} + 30 q^{77} + 6 q^{79} + 20 q^{80} - 3 q^{81} + 3 q^{82} + 24 q^{83} + 5 q^{84} - 19 q^{85} - 58 q^{86} - 2 q^{87} - 13 q^{88} - q^{89} - 2 q^{90} + 14 q^{92} - 16 q^{93} + 21 q^{95} - 44 q^{96} + 5 q^{97} + 29 q^{98} + 10 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^3 - 11 * q^4 + 12 * q^5 + 3 * q^6 - 2 * q^7 + 24 * q^8 - 3 * q^9 + q^10 - 5 * q^11 - 22 * q^12 - 10 * q^14 + 6 * q^15 - 11 * q^16 + q^17 + 6 * q^18 + 7 * q^19 - 15 * q^20 - 4 * q^21 + 9 * q^22 + 12 * q^24 + 22 * q^25 - 6 * q^27 - 5 * q^28 + 2 * q^29 - q^30 - 32 * q^31 - 22 * q^32 + 5 * q^33 - 16 * q^34 - 4 * q^35 - 11 * q^36 - 22 * q^37 + 6 * q^40 - 11 * q^41 - 5 * q^42 + 15 * q^43 + 32 * q^44 - 6 * q^45 + 7 * q^46 + 14 * q^47 + 11 * q^48 + 15 * q^49 + 3 * q^50 + 2 * q^51 - 34 * q^53 + 3 * q^54 - 3 * q^55 - q^56 + 14 * q^57 - 12 * q^58 + 6 * q^59 - 30 * q^60 + 13 * q^61 + 2 * q^62 - 2 * q^63 + 18 * q^66 - 11 * q^67 + 13 * q^68 - 48 * q^70 - 12 * q^72 + 12 * q^73 - 15 * q^74 + 11 * q^75 + 21 * q^76 + 30 * q^77 + 6 * q^79 + 20 * q^80 - 3 * q^81 + 3 * q^82 + 24 * q^83 + 5 * q^84 - 19 * q^85 - 58 * q^86 - 2 * q^87 - 13 * q^88 - q^89 - 2 * q^90 + 14 * q^92 - 16 * q^93 + 21 * q^95 - 44 * q^96 + 5 * q^97 + 29 * q^98 + 10 * q^99

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