LMFDB - Embedded newform 507.2.e.l.484.3

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			484.3
Root			$-0.623490 - 1.07992i$ of defining polynomial
Character	$\chi$	$=$	507.484
Dual form			507.2.e.l.22.3

$q$-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} +(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} + 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}+ \cdots - 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

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	$0.234074\pi$
$2$	1.34601	+	2.33136i	0.951773	+	1.64852i	0.210188	+	0.977661i	$0.432592\pi$
$3$	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	$-0.424640\pi$
$5$	1.04892			0.469090			0.234545	+	0.972105i	$0.424640\pi$
$6$	−1.34601	+	2.33136i	−0.549507	+	0.951773i
$7$	0.277479	−	0.480608i	0.104877	−	0.181653i	−0.808811	−	0.588069i	$-0.799888\pi$
$7$	0.277479	−	0.480608i	0.104877	−	0.181653i	0.913688	+	0.406416i	$0.133222\pi$
$8$	−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	0.997611	−	0.0690822i	$-0.0220071\pi$
$11$	1.45593	+	2.52174i	0.438979	+	0.760333i	−0.558632	+	0.829415i	$0.688674\pi$
$12$	−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	−0.905977	−	0.423326i	$-0.860862\pi$
$19$	−0.376510	+	0.652135i	−0.0863774	+	0.149610i	0.819600	+	0.572936i	$0.194196\pi$
$20$	−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	$-0.173841\pi$
$31$	9.51573			1.70908			0.854538	+	0.519389i	$0.173841\pi$
$32$	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	0.999519	−	0.0310199i	$-0.00987552\pi$
$37$	2.87651	+	4.98226i	0.472895	+	0.819079i	−0.526623	+	0.850099i	$0.676542\pi$
$38$	−2.02715			−0.328847
$39$		0			0
$40$	−9.16852			−1.44967
$41$	2.45593	+	4.25379i	0.383551	+	0.664330i	0.991567	−	0.129595i	$-0.0413676\pi$
$41$	2.45593	+	4.25379i	0.383551	+	0.664330i	−0.608016	+	0.793925i	$0.708034\pi$
$42$	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	$-0.517490\pi$
$47$	−0.753020			−0.109839			−0.0549197	+	0.998491i	$0.517490\pi$
$48$	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	−0.701273	−	0.712892i	$-0.747385\pi$
$59$	2.04892	−	3.54883i	0.266746	−	0.462018i	0.968020	+	0.250874i	$0.0807181\pi$
$60$	−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	0.803146	−	0.595782i	$-0.203158\pi$
$67$	−0.936313	−	1.62174i	−0.114389	−	0.198127i	−0.917535	+	0.397654i	$0.869824\pi$
$68$	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	$0.380866\pi$
$71$	−5.25182	+	9.09643i	−0.623277	+	1.07955i	−0.988871	+	0.148773i	$0.952468\pi$
$72$	4.37047	−	7.56988i	0.515065	−	0.892118i
$73$	−10.4765			−1.22618			−0.613091	−	0.790012i	$-0.710074\pi$
$73$	−10.4765			−1.22618			−0.613091	+	0.790012i	$0.710074\pi$
$74$	−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	$-0.546337\pi$
$83$	−2.64310			−0.290118			−0.145059	+	0.989423i	$0.546337\pi$
$84$	−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	$0.00968919\pi$
$89$	4.96346	+	8.59696i	0.526126	+	0.911276i	−0.473411	+	0.880842i	$0.656977\pi$
$90$	−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	$-0.499516\pi$
$97$	8.53684	−	14.7862i	0.866784	−	1.50131i	0.865264	−	0.501316i	$-0.167150\pi$
$98$	−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	$-0.447009\pi$
$109$	3.46011			0.331418			0.165709	+	0.986175i	$0.447009\pi$
$110$	−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	−0.980299	−	0.197518i	$-0.936712\pi$
$137$	−3.73490	+	6.46903i	−0.319094	+	0.552687i	0.661205	+	0.750205i	$0.270045\pi$
$138$	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	$-0.617145\pi$
$149$	7.66756	−	13.2806i	0.628151	−	1.08799i	0.987922	−	0.154949i	$-0.0495214\pi$
$150$	5.24914	−	9.09177i	0.428590	−	0.742340i
$151$	−2.53079			−0.205953			−0.102977	−	0.994684i	$-0.532837\pi$
$151$	−2.53079			−0.205953			−0.102977	+	0.994684i	$0.532837\pi$
$152$	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	$-0.622434\pi$
$163$	7.85354	−	13.6027i	0.615137	−	1.06545i	0.990360	−	0.138514i	$-0.0442326\pi$
$164$	−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	0.951331	−	0.308170i	$-0.0997166\pi$
$167$	2.69806	+	4.67318i	0.208782	+	0.361622i	−0.742549	+	0.669792i	$0.766383\pi$
$168$	−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	$-0.948144\pi$
$193$	−8.80559	−	15.2517i	−0.633840	−	1.09784i	0.352920	−	0.935654i	$-0.385189\pi$
$194$	45.9627			3.29993
$195$		0			0
$196$	−35.1129			−2.50806
$197$	−2.33124	−	4.03783i	−0.166094	−	0.287683i	0.770949	−	0.636897i	$-0.219782\pi$
$197$	−2.33124	−	4.03783i	−0.166094	−	0.287683i	−0.937043	+	0.349213i	$0.886449\pi$
$198$	−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	$-0.982267\pi$
$223$	−8.17510	−	14.1597i	−0.547445	−	0.948202i	0.451004	−	0.892522i	$-0.351066\pi$
$224$	−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	−0.736396	−	0.676551i	$-0.763474\pi$
$227$	3.28017	−	5.68142i	0.217712	−	0.377089i	0.954108	+	0.299462i	$0.0968072\pi$
$228$	1.97554	−	3.42174i	0.130833	−	0.226610i
$229$	3.95539			0.261380			0.130690	−	0.991423i	$-0.458281\pi$
$229$	3.95539			0.261380			0.130690	+	0.991423i	$0.458281\pi$
$230$	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	$-0.725276\pi$
$239$	−20.1008			−1.30021			−0.650107	+	0.759843i	$0.725276\pi$
$240$	6.83728	−	11.8425i	0.441345	−	0.764431i
$241$	−9.50634	+	16.4655i	−0.612357	+	1.06063i	0.378485	+	0.925607i	$0.376445\pi$
$241$	−9.50634	+	16.4655i	−0.612357	+	1.06063i	−0.990842	+	0.135026i	$0.956888\pi$
$242$	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	$-0.961852\pi$
$271$	−9.87651	−	17.1066i	−0.599955	−	1.03915i	0.392872	−	0.919593i	$-0.371482\pi$
$272$	−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	$-0.515400\pi$
$281$	−1.62133			−0.0967207			−0.0483603	+	0.998830i	$0.515400\pi$
$282$	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	−0.867071	−	0.498184i	$-0.834000\pi$
$293$	−0.0358763	+	0.0621395i	−0.00209591	+	0.00363023i	0.864976	+	0.501814i	$0.167334\pi$
$294$	−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	$-0.452609\pi$
$307$	5.19806			0.296669			0.148335	+	0.988937i	$0.452609\pi$
$308$	−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	$-0.765065\pi$
$317$	−26.3424			−1.47954			−0.739769	+	0.672861i	$0.765065\pi$
$318$	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	−0.978060	−	0.208325i	$-0.933199\pi$
$331$	−5.61476	+	9.72505i	−0.308615	+	0.534537i	0.669445	+	0.742862i	$0.266532\pi$
$332$	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	$0.0551033\pi$
$349$	11.9879	+	20.7637i	0.641699	+	1.11145i	−0.343355	+	0.939206i	$0.611563\pi$
$350$	−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	$-0.909968\pi$
$353$	−13.5620	−	23.4900i	−0.721830	−	1.25025i	0.238435	−	0.971158i	$-0.423366\pi$
$354$	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	$-0.258401\pi$
$359$	26.0790			1.37640			0.688200	+	0.725521i	$0.258401\pi$
$360$	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	0.995122	−	0.0986504i	$-0.0314526\pi$
$379$	8.02326	+	13.8967i	0.412127	+	0.713825i	−0.582995	+	0.812476i	$0.698119\pi$
$380$	−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	$0.383171\pi$
$383$	−12.3083	+	21.3186i	−0.628923	+	1.08933i	−0.987768	+	0.155930i	$0.950163\pi$
$384$	−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	−0.890477	−	0.455028i	$-0.849629\pi$
$397$	−1.01961	+	1.76602i	−0.0511730	+	0.0886342i	0.839304	+	0.543662i	$0.182963\pi$
$398$	−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	0.847203	−	0.531269i	$-0.178284\pi$
$401$	−0.730718	−	1.26564i	−0.0364903	−	0.0632031i	−0.883694	+	0.468065i	$0.844951\pi$
$402$	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	$0.431933\pi$
$409$	−14.9695	+	25.9279i	−0.740194	+	1.28205i	−0.952407	+	0.304830i	$0.901400\pi$
$410$	−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	$-0.607234\pi$
$421$	−13.5646			−0.661100			−0.330550	+	0.943788i	$0.607234\pi$
$422$	−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	$0.166483\pi$
$431$	17.9731	+	31.1304i	0.865736	+	1.49950i	−0.000578325		1.00000i	$0.500184\pi$
$432$	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	−0.974859	−	0.222824i	$-0.928472\pi$
$449$	−6.23945	+	10.8070i	−0.294458	+	0.510016i	0.680401	+	0.732840i	$0.261806\pi$
$450$	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	$0.107659\pi$
$457$	16.2262	+	28.1045i	0.759028	+	1.31468i	−0.184319	+	0.982867i	$0.559008\pi$
$458$	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	$-0.640938\pi$
$461$	12.2017	−	21.1340i	0.568290	−	0.984308i	0.996735	−	0.0807398i	$-0.0257283\pi$
$462$	−2.17510	+	3.76738i	−0.101195	+	0.175274i
$463$	33.1836			1.54217			0.771086	−	0.636731i	$-0.219714\pi$
$463$	33.1836			1.54217			0.771086	+	0.636731i	$0.219714\pi$
$464$	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	0.754821	−	0.655931i	$-0.227724\pi$
$479$	−4.17241	−	7.22682i	−0.190642	−	0.330202i	−0.945463	+	0.325729i	$0.894390\pi$
$480$	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	−0.983801	−	0.179263i	$-0.942629\pi$
$487$	−7.42931	+	12.8679i	−0.336654	+	0.583102i	0.647147	+	0.762365i	$0.275962\pi$
$488$	−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	$-0.497254\pi$
$499$	0.385371			0.0172516			0.00862579	+	0.999963i	$0.497254\pi$
$500$	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	0.708315	−	0.705896i	$-0.249456\pi$
$509$	−5.80194	−	10.0493i	−0.257166	−	0.445425i	−0.965482	+	0.260471i	$0.916122\pi$
$510$	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	$-0.354985\pi$
$541$	20.4674			0.879962			0.439981	+	0.898007i	$0.354985\pi$
$542$	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	$0.131034\pi$
$557$	18.9928	+	32.8964i	0.804749	+	1.39387i	−0.111711	+	0.993741i	$0.535633\pi$
$558$	−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	$-0.618359\pi$
$577$	−17.4547			−0.726650			−0.363325	+	0.931662i	$0.618359\pi$
$578$	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	0.923390	−	0.383864i	$-0.125407\pi$
$587$	3.13169	+	5.42424i	0.129259	+	0.223882i	−0.794131	+	0.607747i	$0.792074\pi$
$588$	−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	$-0.655628\pi$
$593$	−22.8745			−0.939345			−0.469672	+	0.882841i	$0.655628\pi$
$594$	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	0.955751	−	0.294178i	$-0.0950460\pi$
$613$	5.52393	+	9.56772i	0.223109	+	0.386437i	−0.732641	+	0.680615i	$0.761713\pi$
$614$	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	−0.909104	−	0.416570i	$-0.863232\pi$
$617$	−2.32975	+	4.03524i	−0.0937922	+	0.162453i	0.815312	+	0.579022i	$0.196566\pi$
$618$	5.67994	−	9.83794i	0.228481	−	0.395740i
$619$	−31.9259			−1.28321			−0.641604	−	0.767036i	$-0.721731\pi$
$619$	−31.9259			−1.28321			−0.641604	+	0.767036i	$0.721731\pi$
$620$	−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	$0.454038\pi$
$631$	−19.7207	+	34.1572i	−0.785067	+	1.35978i	−0.928959	+	0.370183i	$0.879295\pi$
$632$	−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	$0.366182\pi$
$643$	−14.8735	+	25.7616i	−0.586552	+	1.01594i	−0.994680	+	0.103013i	$0.967152\pi$
$644$	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	$0.104455\pi$
$661$	19.3451	+	33.5067i	0.752438	+	1.30326i	−0.194201	+	0.980962i	$0.562211\pi$
$662$	−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	−0.666385	−	0.745608i	$-0.732159\pi$
$683$	8.16756	−	14.1466i	0.312523	−	0.541306i	0.978908	+	0.204302i	$0.0654925\pi$
$684$	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	0.976731	−	0.214466i	$-0.0688012\pi$
$691$	7.95526	+	13.7789i	0.302632	+	0.524175i	−0.674099	+	0.738641i	$0.735468\pi$
$692$	−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	−0.680870	−	0.732404i	$-0.738398\pi$
$709$	7.82424	−	13.5520i	0.293846	−	0.508955i	0.974716	+	0.223449i	$0.0717315\pi$
$710$	−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	$-0.833300\pi$
$733$	−46.8907			−1.73195			−0.865973	+	0.500090i	$0.833300\pi$
$734$	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	0.979130	−	0.203236i	$-0.0651457\pi$
$739$	8.52393	+	14.7639i	0.313558	+	0.543098i	−0.665572	+	0.746334i	$0.731812\pi$
$740$	−31.6626			−1.16394
$741$		0			0
$742$	−11.3274			−0.415840
$743$	−5.81618	−	10.0739i	−0.213375	−	0.369576i	0.739394	−	0.673273i	$-0.235112\pi$
$743$	−5.81618	−	10.0739i	−0.213375	−	0.369576i	−0.952769	+	0.303697i	$0.901779\pi$
$744$	−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	$0.411243\pi$
$761$	−19.1712	+	33.2055i	−0.694956	+	1.20370i	−0.970196	+	0.242323i	$0.922091\pi$
$762$	−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	0.831355	−	0.555742i	$-0.187566\pi$
$769$	−1.81940	−	3.15129i	−0.0656091	−	0.113638i	−0.896964	+	0.442104i	$0.854232\pi$
$770$	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	$0.416855\pi$
$773$	−19.6712	+	34.0715i	−0.707524	+	1.22547i	−0.965773	+	0.259389i	$0.916479\pi$
$774$	−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	−0.998580	−	0.0532720i	$-0.983035\pi$
$787$	−12.7126	+	22.0189i	−0.453155	+	0.784888i	0.545425	+	0.838160i	$0.316368\pi$
$788$	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	$-0.472906\pi$
$811$	4.84223			0.170034			0.0850169	+	0.996380i	$0.472906\pi$
$812$	−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	$-0.890277\pi$
$821$	−21.8690	−	37.8783i	−0.763235	−	1.32196i	0.177940	−	0.984041i	$-0.443057\pi$
$822$	−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	$-0.289511\pi$
$827$	35.3212			1.22824			0.614120	+	0.789213i	$0.289511\pi$
$828$	−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	−0.594033	−	0.804441i	$-0.702465\pi$
$839$	11.5761	−	20.0503i	0.399650	−	0.692214i	0.993683	+	0.112227i	$0.0357983\pi$
$840$	−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	$-0.651272\pi$
$853$	−26.7265			−0.915097			−0.457548	+	0.889185i	$0.651272\pi$
$854$	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	$-0.603131\pi$
$863$	−18.7047			−0.636715			−0.318358	+	0.947971i	$0.603131\pi$
$864$	−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	$-0.619766\pi$
$877$	18.4119	−	31.8903i	0.621724	−	1.07686i	0.989165	−	0.146811i	$-0.0469008\pi$
$878$	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	$-0.652977\pi$
$929$	16.3605	−	28.3373i	0.536772	−	0.929716i	0.999075	−	0.0429946i	$-0.0136898\pi$
$930$	−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	$-0.347585\pi$
$941$	28.2669			0.921476			0.460738	+	0.887536i	$0.347585\pi$
$942$	−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	$-0.955860\pi$
$947$	−18.9227	−	32.7751i	−0.614906	−	1.06505i	0.375495	−	0.926825i	$-0.377473\pi$
$948$	−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	$-0.552855\pi$
$967$	−10.2798			−0.330575			−0.165288	+	0.986245i	$0.552855\pi$
$968$	−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	$0.104579\pi$
$977$	23.5269	+	40.7498i	0.752693	+	1.30370i	−0.193821	+	0.981037i	$0.562088\pi$
$978$	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	$-0.685016\pi$
$983$	−34.4295			−1.09813			−0.549065	+	0.835779i	$0.685016\pi$
$984$	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.l.484.3		6
13.2	odd	12		507.2.b.f.337.6		6
13.3	even	3		507.2.a.i.1.1	✓	3
13.4	even	6		507.2.e.i.22.1		6
13.5	odd	4		507.2.j.i.361.6		12
13.6	odd	12		507.2.j.i.316.1		12
13.7	odd	12		507.2.j.i.316.6		12
13.8	odd	4		507.2.j.i.361.1		12
13.9	even	3	inner	507.2.e.l.22.3		6
13.10	even	6		507.2.a.l.1.3	yes	3
13.11	odd	12		507.2.b.f.337.1		6
13.12	even	2		507.2.e.i.484.1		6
39.2	even	12		1521.2.b.k.1351.1		6
39.11	even	12		1521.2.b.k.1351.6		6
39.23	odd	6		1521.2.a.n.1.1		3
39.29	odd	6		1521.2.a.s.1.3		3
52.3	odd	6		8112.2.a.cg.1.3		3
52.23	odd	6		8112.2.a.cp.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.i.1.1	✓	3	13.3	even	3
507.2.a.l.1.3	yes	3	13.10	even	6
507.2.b.f.337.1		6	13.11	odd	12
507.2.b.f.337.6		6	13.2	odd	12
507.2.e.i.22.1		6	13.4	even	6
507.2.e.i.484.1		6	13.12	even	2
507.2.e.l.22.3		6	13.9	even	3	inner
507.2.e.l.484.3		6	1.1	even	1	trivial
507.2.j.i.316.1		12	13.6	odd	12
507.2.j.i.316.6		12	13.7	odd	12
507.2.j.i.361.1		12	13.8	odd	4
507.2.j.i.361.6		12	13.5	odd	4
1521.2.a.n.1.1		3	39.23	odd	6
1521.2.a.s.1.3		3	39.29	odd	6
1521.2.b.k.1351.1		6	39.2	even	12
1521.2.b.k.1351.6		6	39.11	even	12
8112.2.a.cg.1.3		3	52.3	odd	6
8112.2.a.cp.1.1		3	52.23	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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 11 q^{4} - 12 q^{5} - 3 q^{6} + 2 q^{7} - 24 q^{8} - 3 q^{9} + q^{10} + 5 q^{11} - 22 q^{12} - 10 q^{14} - 6 q^{15} - 11 q^{16} + q^{17} - 6 q^{18} - 7 q^{19} + 15 q^{20} + 4 q^{21}+ \cdots - 10 q^{99}+O(q^{100}) \) 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

Introduction

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