LMFDB - Embedded newform 507.2.e.i.22.3

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			22.3
Root			$0.900969 - 1.56052i$ of defining polynomial
Character	$\chi$	$=$	507.22
Dual form			507.2.e.i.484.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02446 - 1.77441i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.09903 - 1.90358i) q^{4} +3.35690 q^{5} +(-1.02446 - 1.77441i) q^{6} +(-1.12349 - 1.94594i) q^{7} -0.405813 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.43900 - 5.95652i) q^{10} +(-2.46950 + 4.27730i) q^{11} -2.19806 q^{12} -4.60388 q^{14} +(1.67845 - 2.90716i) q^{15} +(1.78232 - 3.08707i) q^{16} +(-0.455927 - 0.789689i) q^{17} -2.04892 q^{18} +(1.90097 + 3.29257i) q^{19} +(-3.68933 - 6.39011i) q^{20} -2.24698 q^{21} +(5.05980 + 8.76383i) q^{22} +(-1.01357 + 1.75556i) q^{23} +(-0.202907 + 0.351445i) q^{24} +6.26875 q^{25} -1.00000 q^{27} +(-2.46950 + 4.27730i) q^{28} +(1.96950 - 3.41127i) q^{29} +(-3.43900 - 5.95652i) q^{30} -8.82908 q^{31} +(-4.05765 - 7.02805i) q^{32} +(2.46950 + 4.27730i) q^{33} -1.86831 q^{34} +(-3.77144 - 6.53232i) q^{35} +(-1.09903 + 1.90358i) q^{36} +(-4.40097 + 7.62270i) q^{37} +7.78986 q^{38} -1.36227 q^{40} +(-3.46950 + 6.00935i) q^{41} +(-2.30194 + 3.98707i) q^{42} +(1.14310 + 1.97991i) q^{43} +10.8562 q^{44} +(-1.67845 - 2.90716i) q^{45} +(2.07673 + 3.59700i) q^{46} +3.80194 q^{47} +(-1.78232 - 3.08707i) q^{48} +(0.975541 - 1.68969i) q^{49} +(6.42208 - 11.1234i) q^{50} -0.911854 q^{51} +0.542877 q^{53} +(-1.02446 + 1.77441i) q^{54} +(-8.28986 + 14.3585i) q^{55} +(0.455927 + 0.789689i) q^{56} +3.80194 q^{57} +(-4.03534 - 6.98942i) q^{58} +(2.35690 + 4.08226i) q^{59} -7.37867 q^{60} +(-1.83997 - 3.18692i) q^{61} +(-9.04503 + 15.6665i) q^{62} +(-1.12349 + 1.94594i) q^{63} -9.49827 q^{64} +10.1196 q^{66} +(0.760553 - 1.31732i) q^{67} +(-1.00216 + 1.73578i) q^{68} +(1.01357 + 1.75556i) q^{69} -15.4547 q^{70} +(-1.18933 - 2.05999i) q^{71} +(0.202907 + 0.351445i) q^{72} +7.41119 q^{73} +(9.01722 + 15.6183i) q^{74} +(3.13437 - 5.42890i) q^{75} +(4.17845 - 7.23728i) q^{76} +11.0978 q^{77} -3.74094 q^{79} +(5.98307 - 10.3630i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.10872 + 12.3127i) q^{82} +2.30798 q^{83} +(2.46950 + 4.27730i) q^{84} +(-1.53050 - 2.65090i) q^{85} +4.68425 q^{86} +(-1.96950 - 3.41127i) q^{87} +(1.00216 - 1.73578i) q^{88} +(5.02930 - 8.71101i) q^{89} -6.87800 q^{90} +4.45580 q^{92} +(-4.41454 + 7.64621i) q^{93} +(3.89493 - 6.74621i) q^{94} +(6.38135 + 11.0528i) q^{95} -8.11529 q^{96} +(8.06465 + 13.9684i) q^{97} +(-1.99880 - 3.46203i) q^{98} +4.93900 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.02446	−	1.77441i	0.724402	−	1.25470i	−0.234818	−	0.972039i	$-0.575449\pi$
$2$	1.02446	−	1.77441i	0.724402	−	1.25470i	0.959220	−	0.282661i	$-0.0912172\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.09903	−	1.90358i	−0.549516	−	0.951789i
$5$	3.35690			1.50125			0.750625	−	0.660729i	$-0.229753\pi$
$5$	3.35690			1.50125			0.750625	+	0.660729i	$0.229753\pi$
$6$	−1.02446	−	1.77441i	−0.418234	−	0.724402i
$7$	−1.12349	−	1.94594i	−0.424639	−	0.735497i	0.571747	−	0.820430i	$-0.306266\pi$
$7$	−1.12349	−	1.94594i	−0.424639	−	0.735497i	−0.996387	+	0.0849330i	$0.972932\pi$
$8$	−0.405813			−0.143477
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	3.43900	−	5.95652i	1.08751	−	1.88362i
$11$	−2.46950	+	4.27730i	−0.744582	+	1.28965i	0.205807	+	0.978593i	$0.434018\pi$
$11$	−2.46950	+	4.27730i	−0.744582	+	1.28965i	−0.950390	+	0.311062i	$0.899315\pi$
$12$	−2.19806			−0.634526
$13$		0			0
$13$		0			0
$14$	−4.60388			−1.23044
$15$	1.67845	−	2.90716i	0.433373	−	0.750625i
$16$	1.78232	−	3.08707i	0.445581	−	0.771769i
$17$	−0.455927	−	0.789689i	−0.110579	−	0.191528i	0.805425	−	0.592698i	$-0.201937\pi$
$17$	−0.455927	−	0.789689i	−0.110579	−	0.191528i	−0.916004	+	0.401170i	$0.868604\pi$
$18$	−2.04892			−0.482934
$19$	1.90097	+	3.29257i	0.436112	+	0.755368i	0.997386	−	0.0722619i	$-0.0230218\pi$
$19$	1.90097	+	3.29257i	0.436112	+	0.755368i	−0.561274	+	0.827630i	$0.689688\pi$
$20$	−3.68933	−	6.39011i	−0.824960	−	1.42887i
$21$	−2.24698			−0.490331
$22$	5.05980	+	8.76383i	1.07875	+	1.86846i
$23$	−1.01357	+	1.75556i	−0.211345	+	0.366060i	−0.952136	−	0.305676i	$-0.901118\pi$
$23$	−1.01357	+	1.75556i	−0.211345	+	0.366060i	0.740791	+	0.671736i	$0.234451\pi$
$24$	−0.202907	+	0.351445i	−0.0414181	+	0.0717383i
$25$	6.26875			1.25375
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−2.46950	+	4.27730i	−0.466692	+	0.808334i
$29$	1.96950	−	3.41127i	0.365727	−	0.633458i	−0.623165	−	0.782090i	$-0.714154\pi$
$29$	1.96950	−	3.41127i	0.365727	−	0.633458i	0.988893	+	0.148632i	$0.0474870\pi$
$30$	−3.43900	−	5.95652i	−0.627873	−	1.08751i
$31$	−8.82908			−1.58575			−0.792875	−	0.609384i	$-0.791417\pi$
$31$	−8.82908			−1.58575			−0.792875	+	0.609384i	$0.791417\pi$
$32$	−4.05765	−	7.02805i	−0.717297	−	1.24240i
$33$	2.46950	+	4.27730i	0.429885	+	0.744582i
$34$	−1.86831			−0.320413
$35$	−3.77144	−	6.53232i	−0.637489	−	1.10416i
$36$	−1.09903	+	1.90358i	−0.183172	+	0.317263i
$37$	−4.40097	+	7.62270i	−0.723515	+	1.25316i	0.236068	+	0.971737i	$0.424141\pi$
$37$	−4.40097	+	7.62270i	−0.723515	+	1.25316i	−0.959582	+	0.281428i	$0.909192\pi$
$38$	7.78986			1.26368
$39$		0			0
$40$	−1.36227			−0.215394
$41$	−3.46950	+	6.00935i	−0.541845	+	0.938503i	0.456953	+	0.889491i	$0.348941\pi$
$41$	−3.46950	+	6.00935i	−0.541845	+	0.938503i	−0.998798	+	0.0490123i	$0.984393\pi$
$42$	−2.30194	+	3.98707i	−0.355197	+	0.615219i
$43$	1.14310	+	1.97991i	0.174322	+	0.301934i	0.939926	−	0.341377i	$-0.110893\pi$
$43$	1.14310	+	1.97991i	0.174322	+	0.301934i	−0.765605	+	0.643311i	$0.777560\pi$
$44$	10.8562			1.63664
$45$	−1.67845	−	2.90716i	−0.250208	−	0.433373i
$46$	2.07673	+	3.59700i	0.306197	+	0.530349i
$47$	3.80194			0.554570			0.277285	−	0.960788i	$-0.410565\pi$
$47$	3.80194			0.554570			0.277285	+	0.960788i	$0.410565\pi$
$48$	−1.78232	−	3.08707i	−0.257256	−	0.445581i
$49$	0.975541	−	1.68969i	0.139363	−	0.241384i
$50$	6.42208	−	11.1234i	0.908219	−	1.57308i
$51$	−0.911854			−0.127685
$52$		0			0
$53$	0.542877			0.0745698			0.0372849	−	0.999305i	$-0.488129\pi$
$53$	0.542877			0.0745698			0.0372849	+	0.999305i	$0.488129\pi$
$54$	−1.02446	+	1.77441i	−0.139411	+	0.241467i
$55$	−8.28986	+	14.3585i	−1.11780	+	1.93609i
$56$	0.455927	+	0.789689i	0.0609258	+	0.105527i
$57$	3.80194			0.503579
$58$	−4.03534	−	6.98942i	−0.529867	−	0.917756i
$59$	2.35690	+	4.08226i	0.306842	+	0.531465i	0.977670	−	0.210148i	$-0.0673944\pi$
$59$	2.35690	+	4.08226i	0.306842	+	0.531465i	−0.670828	+	0.741613i	$0.734061\pi$
$60$	−7.37867			−0.952582
$61$	−1.83997	−	3.18692i	−0.235584	−	0.408043i	0.723858	−	0.689949i	$-0.242367\pi$
$61$	−1.83997	−	3.18692i	−0.235584	−	0.408043i	−0.959442	+	0.281905i	$0.909034\pi$
$62$	−9.04503	+	15.6665i	−1.14872	+	1.98964i
$63$	−1.12349	+	1.94594i	−0.141546	+	0.245166i
$64$	−9.49827			−1.18728
$65$		0			0
$66$	10.1196			1.24564
$67$	0.760553	−	1.31732i	0.0929164	−	0.160936i	−0.815821	−	0.578305i	$-0.803714\pi$
$67$	0.760553	−	1.31732i	0.0929164	−	0.160936i	0.908737	+	0.417369i	$0.137048\pi$
$68$	−1.00216	+	1.73578i	−0.121529	+	0.210495i
$69$	1.01357	+	1.75556i	0.122020	+	0.211345i
$70$	−15.4547			−1.84719
$71$	−1.18933	−	2.05999i	−0.141148	−	0.244475i	0.786781	−	0.617232i	$-0.211746\pi$
$71$	−1.18933	−	2.05999i	−0.141148	−	0.244475i	−0.927929	+	0.372757i	$0.878413\pi$
$72$	0.202907	+	0.351445i	0.0239128	+	0.0414181i
$73$	7.41119			0.867414			0.433707	−	0.901054i	$-0.357205\pi$
$73$	7.41119			0.867414			0.433707	+	0.901054i	$0.357205\pi$
$74$	9.01722	+	15.6183i	1.04823	+	1.81559i
$75$	3.13437	−	5.42890i	0.361926	−	0.626875i
$76$	4.17845	−	7.23728i	0.479301	−	0.830173i
$77$	11.0978			1.26472
$78$		0			0
$79$	−3.74094			−0.420888			−0.210444	−	0.977606i	$-0.567491\pi$
$79$	−3.74094			−0.420888			−0.210444	+	0.977606i	$0.567491\pi$
$80$	5.98307	−	10.3630i	0.668928	−	1.15862i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	7.10872	+	12.3127i	0.785027	+	1.35971i
$83$	2.30798			0.253334			0.126667	−	0.991945i	$-0.459572\pi$
$83$	2.30798			0.253334			0.126667	+	0.991945i	$0.459572\pi$
$84$	2.46950	+	4.27730i	0.269445	+	0.466692i
$85$	−1.53050	−	2.65090i	−0.166006	−	0.287531i
$86$	4.68425			0.505116
$87$	−1.96950	−	3.41127i	−0.211153	−	0.365727i
$88$	1.00216	−	1.73578i	0.106830	−	0.185035i
$89$	5.02930	−	8.71101i	0.533105	−	0.923365i	−0.466147	−	0.884707i	$-0.654358\pi$
$89$	5.02930	−	8.71101i	0.533105	−	0.923365i	0.999253	−	0.0386580i	$-0.0123083\pi$
$90$	−6.87800			−0.725005
$91$		0			0
$92$	4.45580			0.464549
$93$	−4.41454	+	7.64621i	−0.457767	+	0.792875i
$94$	3.89493	−	6.74621i	0.401731	−	0.695819i
$95$	6.38135	+	11.0528i	0.654713	+	1.13400i
$96$	−8.11529			−0.828264
$97$	8.06465	+	13.9684i	0.818841	+	1.41827i	0.906537	+	0.422127i	$0.138716\pi$
$97$	8.06465	+	13.9684i	0.818841	+	1.41827i	−0.0876961	+	0.996147i	$0.527950\pi$
$98$	−1.99880	−	3.46203i	−0.201910	−	0.349718i
$99$	4.93900			0.496388
$100$	−6.88955	−	11.9331i	−0.688955	−	1.19331i
$101$	4.97434	−	8.61582i	0.494966	−	0.857306i	−0.505017	−	0.863109i	$-0.668514\pi$
$101$	4.97434	−	8.61582i	0.494966	−	0.857306i	0.999983	+	0.00580325i	$0.00184724\pi$
$102$	−0.934157	+	1.61801i	−0.0924953	+	0.160207i
$103$	−10.9879			−1.08267			−0.541336	−	0.840806i	$-0.682081\pi$
$103$	−10.9879			−1.08267			−0.541336	+	0.840806i	$0.682081\pi$
$104$		0			0
$105$	−7.54288			−0.736109
$106$	0.556155	−	0.963288i	0.0540185	−	0.0935628i
$107$	4.93631	−	8.54994i	0.477211	−	0.826554i	−0.522448	−	0.852671i	$-0.674981\pi$
$107$	4.93631	−	8.54994i	0.477211	−	0.826554i	0.999659	+	0.0261171i	$0.00831428\pi$
$108$	1.09903	+	1.90358i	0.105754	+	0.183172i
$109$	20.2446			1.93908			0.969540	−	0.244934i	$-0.0787662\pi$
$109$	20.2446			1.93908			0.969540	+	0.244934i	$0.0787662\pi$
$110$	16.9852	+	29.4193i	1.61948	+	2.80502i
$111$	4.40097	+	7.62270i	0.417721	+	0.723515i
$112$	−8.00969			−0.756844
$113$	−4.84601	−	8.39354i	−0.455874	−	0.789598i	0.542864	−	0.839821i	$-0.317340\pi$
$113$	−4.84601	−	8.39354i	−0.455874	−	0.789598i	−0.998738	+	0.0502233i	$0.984007\pi$
$114$	3.89493	−	6.74621i	0.364793	−	0.631841i
$115$	−3.40246	+	5.89324i	−0.317281	+	0.549547i
$116$	−8.65817			−0.803891
$117$		0			0
$118$	9.65817			0.889107
$119$	−1.02446	+	1.77441i	−0.0939120	+	0.162660i
$120$	−0.681136	+	1.17976i	−0.0621790	+	0.107697i
$121$	−6.69687	−	11.5993i	−0.608806	−	1.05448i
$122$	−7.53989			−0.682630
$123$	3.46950	+	6.00935i	0.312834	+	0.541845i
$124$	9.70344	+	16.8068i	0.871395	+	1.50930i
$125$	4.25906			0.380942
$126$	2.30194	+	3.98707i	0.205073	+	0.355197i
$127$	−6.90581	+	11.9612i	−0.612792	+	1.06139i	0.377976	+	0.925815i	$0.376620\pi$
$127$	−6.90581	+	11.9612i	−0.612792	+	1.06139i	−0.990768	+	0.135571i	$0.956713\pi$
$128$	−1.61529	+	2.79777i	−0.142773	+	0.247290i
$129$	2.28621			0.201289
$130$		0			0
$131$	2.99462			0.261641			0.130821	−	0.991406i	$-0.458239\pi$
$131$	2.99462			0.261641			0.130821	+	0.991406i	$0.458239\pi$
$132$	5.42812	−	9.40177i	0.472457	−	0.818319i
$133$	4.27144	−	7.39835i	0.370381	−	0.641518i
$134$	−1.55831	−	2.69907i	−0.134618	−	0.233164i
$135$	−3.35690			−0.288916
$136$	0.185021	+	0.320466i	0.0158654	+	0.0274797i
$137$	−11.5097	−	19.9354i	−0.983339	−	1.70319i	−0.649096	−	0.760706i	$-0.724853\pi$
$137$	−11.5097	−	19.9354i	−0.983339	−	1.70319i	−0.334243	−	0.942487i	$-0.608481\pi$
$138$	4.15346			0.353566
$139$	−0.491271	−	0.850906i	−0.0416690	−	0.0721729i	0.844439	−	0.535652i	$-0.179934\pi$
$139$	−0.491271	−	0.850906i	−0.0416690	−	0.0721729i	−0.886108	+	0.463479i	$0.846601\pi$
$140$	−8.28986	+	14.3585i	−0.700621	+	1.21351i
$141$	1.90097	−	3.29257i	0.160090	−	0.277285i
$142$	−4.87369			−0.408991
$143$		0			0
$144$	−3.56465			−0.297054
$145$	6.61141	−	11.4513i	0.549048	−	0.950978i
$146$	7.59246	−	13.1505i	0.628356	−	1.08835i
$147$	−0.975541	−	1.68969i	−0.0804613	−	0.139363i
$148$	19.3472			1.59033
$149$	−5.12953	−	8.88461i	−0.420228	−	0.727855i	0.575734	−	0.817637i	$-0.304716\pi$
$149$	−5.12953	−	8.88461i	−0.420228	−	0.727855i	−0.995961	+	0.0897817i	$0.971383\pi$
$150$	−6.42208	−	11.1234i	−0.524360	−	0.908219i
$151$	−20.1685			−1.64129			−0.820646	−	0.571438i	$-0.806386\pi$
$151$	−20.1685			−1.64129			−0.820646	+	0.571438i	$0.806386\pi$
$152$	−0.771438	−	1.33617i	−0.0625719	−	0.108378i
$153$	−0.455927	+	0.789689i	−0.0368595	+	0.0638425i
$154$	11.3693	−	19.6922i	0.916162	−	1.58684i
$155$	−29.6383			−2.38061
$156$		0			0
$157$	10.4383			0.833070			0.416535	−	0.909120i	$-0.363244\pi$
$157$	10.4383			0.833070			0.416535	+	0.909120i	$0.363244\pi$
$158$	−3.83244	+	6.63798i	−0.304892	+	0.528089i
$159$	0.271438	−	0.470145i	0.0215265	−	0.0372849i
$160$	−13.6211	−	23.5924i	−1.07684	−	1.86515i
$161$	4.55496			0.358981
$162$	1.02446	+	1.77441i	0.0804891	+	0.139411i
$163$	5.52326	+	9.56657i	0.432615	+	0.749312i	0.997098	−	0.0761335i	$-0.0242575\pi$
$163$	5.52326	+	9.56657i	0.432615	+	0.749312i	−0.564482	+	0.825445i	$0.690924\pi$
$164$	15.2524			1.19101
$165$	8.28986	+	14.3585i	0.645364	+	1.11780i
$166$	2.36443	−	4.09531i	0.183515	−	0.317858i
$167$	−4.05496	+	7.02339i	−0.313782	+	0.543487i	−0.979178	−	0.203004i	$-0.934929\pi$
$167$	−4.05496	+	7.02339i	−0.313782	+	0.543487i	0.665396	+	0.746491i	$0.268263\pi$
$168$	0.911854			0.0703511
$169$		0			0
$170$	−6.27173			−0.481020
$171$	1.90097	−	3.29257i	0.145371	−	0.251789i
$172$	2.51261	−	4.35198i	0.191585	−	0.331835i
$173$	9.02811	+	15.6371i	0.686394	+	1.18887i	0.972996	+	0.230820i	$0.0741409\pi$
$173$	9.02811	+	15.6371i	0.686394	+	1.18887i	−0.286602	+	0.958050i	$0.592526\pi$
$174$	−8.07069			−0.611837
$175$	−7.04288	−	12.1986i	−0.532391	−	0.922129i
$176$	8.80290	+	15.2471i	0.663543	+	1.14929i
$177$	4.71379			0.354310
$178$	−10.3046	−	17.8481i	−0.772364	−	1.33777i
$179$	9.93512	−	17.2081i	0.742585	−	1.28620i	−0.208729	−	0.977974i	$-0.566933\pi$
$179$	9.93512	−	17.2081i	0.742585	−	1.28620i	0.951314	−	0.308222i	$-0.0997340\pi$
$180$	−3.68933	+	6.39011i	−0.274987	+	0.476291i
$181$	−10.0828			−0.749446			−0.374723	−	0.927137i	$-0.622262\pi$
$181$	−10.0828			−0.749446			−0.374723	+	0.927137i	$0.622262\pi$
$182$		0			0
$183$	−3.67994			−0.272029
$184$	0.411322	−	0.712430i	0.0303230	−	0.0525210i
$185$	−14.7736	+	25.5886i	−1.08618	+	1.88131i
$186$	9.04503	+	15.6665i	0.663214	+	1.14872i
$187$	4.50365			0.329339
$188$	−4.17845	−	7.23728i	−0.304745	−	0.527833i
$189$	1.12349	+	1.94594i	0.0817219	+	0.141546i
$190$	26.1497			1.89710
$191$	3.29374	+	5.70493i	0.238327	+	0.412794i	0.960234	−	0.279196i	$-0.0900678\pi$
$191$	3.29374	+	5.70493i	0.238327	+	0.412794i	−0.721908	+	0.691990i	$0.756734\pi$
$192$	−4.74914	+	8.22574i	−0.342739	+	0.593642i
$193$	−5.43362	+	9.41131i	−0.391121	+	0.677441i	−0.992598	−	0.121449i	$-0.961246\pi$
$193$	−5.43362	+	9.41131i	−0.391121	+	0.677441i	0.601477	+	0.798890i	$0.294579\pi$
$194$	33.0476			2.37268
$195$		0			0
$196$	−4.28860			−0.306329
$197$	−4.62080	+	8.00346i	−0.329218	+	0.570223i	−0.982357	−	0.187015i	$-0.940119\pi$
$197$	−4.62080	+	8.00346i	−0.329218	+	0.570223i	0.653139	+	0.757238i	$0.273452\pi$
$198$	5.05980	−	8.76383i	0.359585	−	0.622819i
$199$	0.782323	+	1.35502i	0.0554574	+	0.0960551i	0.892421	−	0.451203i	$-0.149005\pi$
$199$	0.782323	+	1.35502i	0.0554574	+	0.0960551i	−0.836964	+	0.547258i	$0.815672\pi$
$200$	−2.54394			−0.179884
$201$	−0.760553	−	1.31732i	−0.0536453	−	0.0929164i
$202$	−10.1920	−	17.6531i	−0.717108	−	1.24207i
$203$	−8.85086			−0.621208
$204$	1.00216	+	1.73578i	0.0701649	+	0.121529i
$205$	−11.6468	+	20.1728i	−0.813444	+	1.40893i
$206$	−11.2567	+	19.4971i	−0.784289	+	1.35843i
$207$	2.02715			0.140896
$208$		0			0
$209$	−18.7778			−1.29889
$210$	−7.72737	+	13.3842i	−0.533239	+	0.923597i
$211$	−11.6223	+	20.1304i	−0.800112	+	1.38583i	0.119430	+	0.992843i	$0.461893\pi$
$211$	−11.6223	+	20.1304i	−0.800112	+	1.38583i	−0.919542	+	0.392991i	$0.871440\pi$
$212$	−0.596638	−	1.03341i	−0.0409773	−	0.0709747i
$213$	−2.37867			−0.162984
$214$	−10.1141	−	17.5181i	−0.691385	−	1.19751i
$215$	3.83728	+	6.64637i	0.261700	+	0.453278i
$216$	0.405813			0.0276121
$217$	9.91939	+	17.1809i	0.673372	+	1.16631i
$218$	20.7397	−	35.9223i	1.40467	−	2.43296i
$219$	3.70560	−	6.41828i	0.250401	−	0.433707i
$220$	36.4432			2.45700
$221$		0			0
$222$	18.0344			1.21039
$223$	−5.36927	+	9.29985i	−0.359553	+	0.622764i	−0.987886	−	0.155180i	$-0.950404\pi$
$223$	−5.36927	+	9.29985i	−0.359553	+	0.622764i	0.628333	+	0.777944i	$0.283738\pi$
$224$	−9.11745	+	15.7919i	−0.609185	+	1.05514i
$225$	−3.13437	−	5.42890i	−0.208958	−	0.361926i
$226$	−19.8582			−1.32094
$227$	3.48792	+	6.04125i	0.231501	+	0.400972i	0.958250	−	0.285931i	$-0.0923029\pi$
$227$	3.48792	+	6.04125i	0.231501	+	0.400972i	−0.726749	+	0.686903i	$0.758970\pi$
$228$	−4.17845	−	7.23728i	−0.276724	−	0.479301i
$229$	−16.8049			−1.11050			−0.555250	−	0.831683i	$-0.687378\pi$
$229$	−16.8049			−1.11050			−0.555250	+	0.831683i	$0.687378\pi$
$230$	6.97136	+	12.0748i	0.459678	+	0.796186i
$231$	5.54892	−	9.61101i	0.365092	−	0.632358i
$232$	−0.799249	+	1.38434i	−0.0524733	+	0.0908864i
$233$	8.69202			0.569433			0.284717	−	0.958612i	$-0.408100\pi$
$233$	8.69202			0.569433			0.284717	+	0.958612i	$0.408100\pi$
$234$		0			0
$235$	12.7627			0.832547
$236$	5.18060	−	8.97307i	0.337229	−	0.584097i
$237$	−1.87047	+	3.23975i	−0.121500	+	0.210444i
$238$	2.09903	+	3.63563i	0.136060	+	0.235663i
$239$	−22.9191			−1.48252			−0.741258	−	0.671220i	$-0.765771\pi$
$239$	−22.9191			−1.48252			−0.741258	+	0.671220i	$0.765771\pi$
$240$	−5.98307	−	10.3630i	−0.386206	−	0.668928i
$241$	−10.9901	−	19.0354i	−0.707933	−	1.22618i	−0.965623	−	0.259948i	$-0.916295\pi$
$241$	−10.9901	−	19.0354i	−0.707933	−	1.22618i	0.257690	−	0.966228i	$-0.417039\pi$
$242$	−27.4426			−1.76408
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.04437	+	7.00505i	−0.258914	+	0.448452i
$245$	3.27479	−	5.67210i	0.209219	−	0.362377i
$246$	14.2174			0.906471
$247$		0			0
$248$	3.58296			0.227518
$249$	1.15399	−	1.99877i	0.0731311	−	0.126667i
$250$	4.36323	−	7.55734i	0.275955	−	0.477968i
$251$	−13.3218	−	23.0741i	−0.840868	−	1.45643i	−0.889162	−	0.457592i	$-0.848712\pi$
$251$	−13.3218	−	23.0741i	−0.840868	−	1.45643i	0.0482946	−	0.998833i	$-0.484621\pi$
$252$	4.93900			0.311128
$253$	−5.00604	−	8.67072i	−0.314727	−	0.545123i
$254$	14.1494	+	24.5075i	0.887815	+	1.53774i
$255$	−3.06100			−0.191687
$256$	−6.18867	−	10.7191i	−0.386792	−	0.669943i
$257$	−11.5722	+	20.0436i	−0.721853	+	1.25029i	0.238404	+	0.971166i	$0.423376\pi$
$257$	−11.5722	+	20.0436i	−0.721853	+	1.25029i	−0.960256	+	0.279119i	$0.909957\pi$
$258$	2.34213	−	4.05668i	0.145814	−	0.252558i
$259$	19.7778			1.22893
$260$		0			0
$261$	−3.93900			−0.243818
$262$	3.06787	−	5.31370i	0.189533	−	0.328282i
$263$	9.26420	−	16.0461i	0.571255	−	0.989443i	−0.425182	−	0.905108i	$-0.639790\pi$
$263$	9.26420	−	16.0461i	0.571255	−	0.989443i	0.996437	−	0.0843352i	$-0.0268766\pi$
$264$	−1.00216	−	1.73578i	−0.0616784	−	0.106830i
$265$	1.82238			0.111948
$266$	−8.75182	−	15.1586i	−0.536609	−	0.929434i
$267$	−5.02930	−	8.71101i	−0.307788	−	0.533105i
$268$	−3.34349			−0.204236
$269$	−4.87920	−	8.45102i	−0.297490	−	0.515268i	0.678071	−	0.734996i	$-0.262816\pi$
$269$	−4.87920	−	8.45102i	−0.297490	−	0.515268i	−0.975561	+	0.219729i	$0.929483\pi$
$270$	−3.43900	+	5.95652i	−0.209291	+	0.362503i
$271$	11.4010	−	19.7471i	0.692560	−	1.19955i	−0.278437	−	0.960455i	$-0.589816\pi$
$271$	11.4010	−	19.7471i	0.692560	−	1.19955i	0.970996	−	0.239094i	$-0.0768503\pi$
$272$	−3.25044			−0.197087
$273$		0			0
$274$	−47.1648			−2.84933
$275$	−15.4807	+	26.8133i	−0.933520	+	1.61690i
$276$	2.22790	−	3.85883i	0.134104	−	0.232274i
$277$	11.9852	+	20.7590i	0.720123	+	1.24729i	0.960950	+	0.276721i	$0.0892478\pi$
$277$	11.9852	+	20.7590i	0.720123	+	1.24729i	−0.240828	+	0.970568i	$0.577419\pi$
$278$	−2.01315			−0.120741
$279$	4.41454	+	7.64621i	0.264292	+	0.457767i
$280$	1.53050	+	2.65090i	0.0914648	+	0.158422i
$281$	−4.12498			−0.246076			−0.123038	−	0.992402i	$-0.539264\pi$
$281$	−4.12498			−0.246076			−0.123038	+	0.992402i	$0.539264\pi$
$282$	−3.89493	−	6.74621i	−0.231940	−	0.401731i
$283$	7.82789	−	13.5583i	0.465320	−	0.805957i	−0.533896	−	0.845550i	$-0.679273\pi$
$283$	7.82789	−	13.5583i	0.465320	−	0.805957i	0.999216	+	0.0395927i	$0.0126060\pi$
$284$	−2.61423	+	4.52798i	−0.155126	+	0.268686i
$285$	12.7627			0.755998
$286$		0			0
$287$	15.5918			0.920354
$288$	−4.05765	+	7.02805i	−0.239099	+	0.414132i
$289$	8.08426	−	14.0024i	0.475545	−	0.823668i
$290$	−13.5462	−	23.4628i	−0.795462	−	1.37778i
$291$	16.1293			0.945516
$292$	−8.14513	−	14.1078i	−0.476658	−	0.825595i
$293$	−11.2974	−	19.5677i	−0.660001	−	1.14315i	−0.980615	−	0.195945i	$-0.937223\pi$
$293$	−11.2974	−	19.5677i	−0.660001	−	1.14315i	0.320614	−	0.947210i	$-0.396111\pi$
$294$	−3.99761			−0.233145
$295$	7.91185	+	13.7037i	0.460646	+	0.797862i
$296$	1.78597	−	3.09339i	0.103807	−	0.179800i
$297$	2.46950	−	4.27730i	0.143295	−	0.248194i
$298$	−21.0200			−1.21765
$299$		0			0
$300$	−13.7791			−0.795537
$301$	2.56853	−	4.44883i	0.148048	−	0.256426i
$302$	−20.6618	+	35.7873i	−1.18895	+	2.05933i
$303$	−4.97434	−	8.61582i	−0.285769	−	0.494966i
$304$	13.5526			0.777293
$305$	−6.17659	−	10.6982i	−0.353670	−	0.612575i
$306$	0.934157	+	1.61801i	0.0534022	+	0.0924953i
$307$	−6.55496			−0.374111			−0.187056	−	0.982349i	$-0.559894\pi$
$307$	−6.55496			−0.374111			−0.187056	+	0.982349i	$0.559894\pi$
$308$	−12.1969	−	21.1256i	−0.694981	−	1.20374i
$309$	−5.49396	+	9.51582i	−0.312540	+	0.541336i
$310$	−30.3632	+	52.5907i	−1.72452	+	2.98695i
$311$	−12.0392			−0.682682			−0.341341	−	0.939940i	$-0.610881\pi$
$311$	−12.0392			−0.682682			−0.341341	+	0.939940i	$0.610881\pi$
$312$		0			0
$313$	−33.8950			−1.91586			−0.957929	−	0.287005i	$-0.907340\pi$
$313$	−33.8950			−1.91586			−0.957929	+	0.287005i	$0.907340\pi$
$314$	10.6936	−	18.5219i	0.603477	−	1.04525i
$315$	−3.77144	+	6.53232i	−0.212496	+	0.368055i
$316$	4.11141	+	7.12117i	0.231285	+	0.400597i
$317$	−4.49827			−0.252648			−0.126324	−	0.991989i	$-0.540318\pi$
$317$	−4.49827			−0.252648			−0.126324	+	0.991989i	$0.540318\pi$
$318$	−0.556155	−	0.963288i	−0.0311876	−	0.0540185i
$319$	9.72737	+	16.8483i	0.544628	+	0.943323i
$320$	−31.8847			−1.78241
$321$	−4.93631	−	8.54994i	−0.275518	−	0.477211i
$322$	4.66637	−	8.08238i	0.260046	−	0.450414i
$323$	1.73341	−	3.00235i	0.0964493	−	0.167055i
$324$	2.19806			0.122115
$325$		0			0
$326$	22.6334			1.25355
$327$	10.1223	−	17.5323i	0.559764	−	0.969540i
$328$	1.40797	−	2.43867i	0.0777421	−	0.134653i
$329$	−4.27144	−	7.39835i	−0.235492	−	0.407884i
$330$	33.9705			1.87001
$331$	5.60656	+	9.71085i	0.308165	+	0.533757i	0.977961	−	0.208788i	$-0.0669519\pi$
$331$	5.60656	+	9.71085i	0.308165	+	0.533757i	−0.669796	+	0.742545i	$0.733619\pi$
$332$	−2.53654	−	4.39342i	−0.139211	−	0.241120i
$333$	8.80194			0.482343
$334$	8.30827	+	14.3904i	0.454609	+	0.787405i
$335$	2.55310	−	4.42209i	0.139491	−	0.241605i
$336$	−4.00484	+	6.93659i	−0.218482	+	0.378422i
$337$	7.04892			0.383979			0.191989	−	0.981397i	$-0.438506\pi$
$337$	7.04892			0.383979			0.191989	+	0.981397i	$0.438506\pi$
$338$		0			0
$339$	−9.69202			−0.526398
$340$	−3.36413	+	5.82685i	−0.182446	+	0.316005i
$341$	21.8034	−	37.7646i	1.18072	−	2.04507i
$342$	−3.89493	−	6.74621i	−0.210614	−	0.364793i
$343$	−20.1129			−1.08599
$344$	−0.463887	−	0.803475i	−0.0250111	−	0.0433205i
$345$	3.40246	+	5.89324i	0.183182	+	0.317281i
$346$	36.9957			1.98890
$347$	1.35205	+	2.34182i	0.0725819	+	0.125716i	0.900032	−	0.435823i	$-0.143543\pi$
$347$	1.35205	+	2.34182i	0.0725819	+	0.125716i	−0.827450	+	0.561539i	$0.810209\pi$
$348$	−4.32908	+	7.49819i	−0.232063	+	0.401945i
$349$	0.207751	−	0.359835i	0.0111207	−	0.0192615i	−0.860412	−	0.509600i	$-0.829793\pi$
$349$	0.207751	−	0.359835i	0.0111207	−	0.0192615i	0.871532	+	0.490338i	$0.163127\pi$
$350$	−28.8605			−1.54266
$351$		0			0
$352$	40.0814			2.13635
$353$	16.0836	−	27.8576i	0.856044	−	1.48271i	−0.0196301	−	0.999807i	$-0.506249\pi$
$353$	16.0836	−	27.8576i	0.856044	−	1.48271i	0.875674	−	0.482904i	$-0.160418\pi$
$354$	4.82908	−	8.36422i	0.256663	−	0.444553i
$355$	−3.99247	−	6.91516i	−0.211898	−	0.367018i
$356$	−22.1094			−1.17180
$357$	1.02446	+	1.77441i	0.0542201	+	0.0939120i
$358$	−20.3562	−	35.2580i	−1.07586	−	1.86344i
$359$	22.3521			1.17970			0.589850	−	0.807513i	$-0.299187\pi$
$359$	22.3521			1.17970			0.589850	+	0.807513i	$0.299187\pi$
$360$	0.681136	+	1.17976i	0.0358990	+	0.0621790i
$361$	2.27263	−	3.93632i	0.119612	−	0.207175i
$362$	−10.3294	+	17.8910i	−0.542900	+	0.940331i
$363$	−13.3937			−0.702989
$364$		0			0
$365$	24.8786			1.30221
$366$	−3.76995	+	6.52974i	−0.197058	+	0.341315i
$367$	1.15130	−	1.99411i	0.0600974	−	0.104092i	−0.834411	−	0.551142i	$-0.814192\pi$
$367$	1.15130	−	1.99411i	0.0600974	−	0.104092i	0.894509	+	0.447050i	$0.147526\pi$
$368$	3.61303	+	6.25795i	0.188342	+	0.326218i
$369$	6.93900			0.361230
$370$	30.2699	+	52.4290i	1.57366	+	2.72565i
$371$	−0.609916	−	1.05641i	−0.0316653	−	0.0548459i
$372$	19.4069			1.00620
$373$	9.63802	+	16.6935i	0.499038	+	0.864359i	0.999999	−	0.00111058i	$-0.000353507\pi$
$373$	9.63802	+	16.6935i	0.499038	+	0.864359i	−0.500961	+	0.865470i	$0.667020\pi$
$374$	4.61380	−	7.99134i	0.238574	−	0.413222i
$375$	2.12953	−	3.68846i	0.109968	−	0.190471i
$376$	−1.54288			−0.0795678
$377$		0			0
$378$	4.60388			0.236798
$379$	3.66972	−	6.35614i	0.188501	−	0.326493i	−0.756250	−	0.654283i	$-0.772971\pi$
$379$	3.66972	−	6.35614i	0.188501	−	0.326493i	0.944751	+	0.327790i	$0.106304\pi$
$380$	14.0266	−	24.2948i	0.719550	−	1.24630i
$381$	6.90581	+	11.9612i	0.353796	+	0.612792i
$382$	13.4972			0.690577
$383$	−9.54503	−	16.5325i	−0.487728	−	0.844770i	0.512172	−	0.858883i	$-0.328841\pi$
$383$	−9.54503	−	16.5325i	−0.487728	−	0.844770i	−0.999900	+	0.0141126i	$0.995508\pi$
$384$	1.61529	+	2.79777i	0.0824301	+	0.142773i
$385$	37.2543			1.89865
$386$	11.1330	+	19.2830i	0.566657	+	0.981479i
$387$	1.14310	−	1.97991i	0.0581072	−	0.100645i
$388$	17.7266	−	30.7034i	0.899932	−	1.55873i
$389$	−23.9879			−1.21624			−0.608118	−	0.793847i	$-0.708075\pi$
$389$	−23.9879			−1.21624			−0.608118	+	0.793847i	$0.708075\pi$
$390$		0			0
$391$	1.84846			0.0934807
$392$	−0.395888	+	0.685697i	−0.0199953	+	0.0346329i
$393$	1.49731	−	2.59342i	0.0755294	−	0.130821i
$394$	9.46764	+	16.3984i	0.476973	+	0.826141i
$395$	−12.5579			−0.631859
$396$	−5.42812	−	9.40177i	−0.272773	−	0.472457i
$397$	2.20895	+	3.82601i	0.110864	+	0.192022i	0.916119	−	0.400907i	$-0.131305\pi$
$397$	2.20895	+	3.82601i	0.110864	+	0.192022i	−0.805255	+	0.592929i	$0.797972\pi$
$398$	3.20583			0.160694
$399$	−4.27144	−	7.39835i	−0.213839	−	0.370381i
$400$	11.1729	−	19.3521i	0.558647	−	0.967605i
$401$	10.2044	−	17.6745i	0.509583	−	0.882624i	−0.490355	−	0.871523i	$-0.663133\pi$
$401$	10.2044	−	17.6745i	0.509583	−	0.882624i	0.999938	−	0.0111015i	$-0.00353378\pi$
$402$	−3.11662			−0.155443
$403$		0			0
$404$	−21.8678			−1.08797
$405$	−1.67845	+	2.90716i	−0.0834027	+	0.144458i
$406$	−9.06734	+	15.7051i	−0.450004	+	0.779430i
$407$	−21.7364	−	37.6485i	−1.07743	−	1.86617i
$408$	0.370042			0.0183198
$409$	11.0746	+	19.1817i	0.547602	+	0.948475i	0.998438	+	0.0558682i	$0.0177927\pi$
$409$	11.0746	+	19.1817i	0.547602	+	0.948475i	−0.450836	+	0.892607i	$0.648874\pi$
$410$	23.8632	+	41.3323i	1.17852	+	2.04126i
$411$	−23.0194			−1.13546
$412$	12.0761	+	20.9164i	0.594945	+	1.03047i
$413$	5.29590	−	9.17276i	0.260594	−	0.451362i
$414$	2.07673	−	3.59700i	0.102066	−	0.176783i
$415$	7.74764			0.380317
$416$		0			0
$417$	−0.982542			−0.0481153
$418$	−19.2371	+	33.3196i	−0.940915	+	1.62971i
$419$	−7.37800	+	12.7791i	−0.360439	+	0.624299i	−0.988033	−	0.154242i	$-0.950706\pi$
$419$	−7.37800	+	12.7791i	−0.360439	+	0.624299i	0.627594	+	0.778541i	$0.284040\pi$
$420$	8.28986	+	14.3585i	0.404504	+	0.700621i
$421$	8.47219			0.412909			0.206455	−	0.978456i	$-0.433807\pi$
$421$	8.47219			0.412909			0.206455	+	0.978456i	$0.433807\pi$
$422$	23.8131	+	41.2455i	1.15920	+	2.00780i
$423$	−1.90097	−	3.29257i	−0.0924283	−	0.160090i
$424$	−0.220306			−0.0106990
$425$	−2.85809	−	4.95036i	−0.138638	−	0.240128i
$426$	−2.43685	+	4.22074i	−0.118066	+	0.204496i
$427$	−4.13437	+	7.16095i	−0.200076	+	0.346543i
$428$	−21.7006			−1.04894
$429$		0			0
$430$	15.7245			0.758305
$431$	−1.19591	+	2.07137i	−0.0576048	+	0.0997744i	−0.893390	−	0.449283i	$-0.851680\pi$
$431$	−1.19591	+	2.07137i	−0.0576048	+	0.0997744i	0.835785	+	0.549057i	$0.185013\pi$
$432$	−1.78232	+	3.08707i	−0.0857521	+	0.148527i
$433$	5.21432	+	9.03147i	0.250584	+	0.434025i	0.963687	−	0.267035i	$-0.0860439\pi$
$433$	5.21432	+	9.03147i	0.250584	+	0.434025i	−0.713102	+	0.701060i	$0.752711\pi$
$434$	40.6480			1.95117
$435$	−6.61141	−	11.4513i	−0.316993	−	0.549048i
$436$	−22.2494	−	38.5371i	−1.06555	−	1.84559i
$437$	−7.70709			−0.368680
$438$	−7.59246	−	13.1505i	−0.362782	−	0.628356i
$439$	16.2751	−	28.1893i	0.776767	−	1.34540i	−0.157028	−	0.987594i	$-0.550191\pi$
$439$	16.2751	−	28.1893i	0.776767	−	1.34540i	0.933796	−	0.357807i	$-0.116475\pi$
$440$	3.36413	−	5.82685i	0.160379	−	0.277784i
$441$	−1.95108			−0.0929087
$442$		0			0
$443$	9.58211			0.455260			0.227630	−	0.973748i	$-0.426902\pi$
$443$	9.58211			0.455260			0.227630	+	0.973748i	$0.426902\pi$
$444$	9.67360	−	16.7552i	0.459089	−	0.795165i
$445$	16.8828	−	29.2419i	0.800324	−	1.38620i
$446$	11.0012	+	19.0546i	0.520922	+	0.902263i
$447$	−10.2591			−0.485237
$448$	10.6712	+	18.4831i	0.504167	+	0.873243i
$449$	14.1969	+	24.5897i	0.669992	+	1.16046i	0.977906	+	0.209045i	$0.0670356\pi$
$449$	14.1969	+	24.5897i	0.669992	+	1.16046i	−0.307914	+	0.951414i	$0.599631\pi$
$450$	−12.8442			−0.605479
$451$	−17.1359	−	29.6802i	−0.806896	−	1.39759i
$452$	−10.6518	+	18.4495i	−0.501020	+	0.867792i
$453$	−10.0843	+	17.4665i	−0.473800	+	0.820646i
$454$	14.2929			0.670800
$455$		0			0
$456$	−1.54288			−0.0722518
$457$	−2.49784	+	4.32639i	−0.116844	+	0.202380i	−0.918515	−	0.395385i	$-0.870611\pi$
$457$	−2.49784	+	4.32639i	−0.116844	+	0.202380i	0.801671	+	0.597765i	$0.203944\pi$
$458$	−17.2159	+	29.8189i	−0.804448	+	1.39335i
$459$	0.455927	+	0.789689i	0.0212808	+	0.0368595i
$460$	14.9576			0.697404
$461$	−0.676292	−	1.17137i	−0.0314981	−	0.0545562i	0.849847	−	0.527030i	$-0.176694\pi$
$461$	−0.676292	−	1.17137i	−0.0314981	−	0.0545562i	−0.881345	+	0.472474i	$0.843361\pi$
$462$	−11.3693	−	19.6922i	−0.528946	−	0.916162i
$463$	−3.36467			−0.156369			−0.0781846	−	0.996939i	$-0.524912\pi$
$463$	−3.36467			−0.156369			−0.0781846	+	0.996939i	$0.524912\pi$
$464$	−7.02057	−	12.1600i	−0.325922	−	0.564513i
$465$	−14.8192	+	25.6675i	−0.687222	+	1.19030i
$466$	8.90462	−	15.4232i	0.412498	−	0.714468i
$467$	6.91079			0.319793			0.159897	−	0.987134i	$-0.448884\pi$
$467$	6.91079			0.319793			0.159897	+	0.987134i	$0.448884\pi$
$468$		0			0
$469$	−3.41789			−0.157824
$470$	13.0749	−	22.6463i	0.603099	−	1.04460i
$471$	5.21917	−	9.03987i	0.240487	−	0.416535i
$472$	−0.956459	−	1.65664i	−0.0440246	−	0.0762529i
$473$	−11.2916			−0.519188
$474$	3.83244	+	6.63798i	0.176030	+	0.304892i
$475$	11.9167	+	20.6403i	0.546776	+	0.947043i
$476$	4.50365			0.206424
$477$	−0.271438	−	0.470145i	−0.0124283	−	0.0215265i
$478$	−23.4797	+	40.6681i	−1.07394	+	1.86011i
$479$	−1.75786	+	3.04471i	−0.0803189	+	0.139116i	−0.903387	−	0.428826i	$-0.858927\pi$
$479$	−1.75786	+	3.04471i	−0.0803189	+	0.139116i	0.823068	+	0.567943i	$0.192261\pi$
$480$	−27.2422			−1.24343
$481$		0			0
$482$	−45.0355			−2.05131
$483$	2.27748	−	3.94471i	0.103629	−	0.179490i
$484$	−14.7201	+	25.4960i	−0.669097	+	1.15891i
$485$	27.0722	+	46.8904i	1.22928	+	2.12918i
$486$	2.04892			0.0929408
$487$	6.42394	+	11.1266i	0.291096	+	0.504194i	0.974069	−	0.226250i	$-0.0726467\pi$
$487$	6.42394	+	11.1266i	0.291096	+	0.504194i	−0.682973	+	0.730444i	$0.739313\pi$
$488$	0.746684	+	1.29329i	0.0338008	+	0.0585447i
$489$	11.0465			0.499541
$490$	−6.70978	−	11.6217i	−0.303117	−	0.525014i
$491$	−14.3354	+	24.8297i	−0.646948	+	1.12055i	0.336899	+	0.941541i	$0.390622\pi$
$491$	−14.3354	+	24.8297i	−0.646948	+	1.12055i	−0.983848	+	0.179007i	$0.942712\pi$
$492$	7.62618	−	13.2089i	0.343815	−	0.595504i
$493$	−3.59179			−0.161766
$494$		0			0
$495$	16.5797			0.745203
$496$	−15.7363	+	27.2560i	−0.706580	+	1.22383i
$497$	−2.67241	+	4.62874i	−0.119874	+	0.207628i
$498$	−2.36443	−	4.09531i	−0.105953	−	0.183515i
$499$	−33.5555			−1.50215			−0.751076	−	0.660215i	$-0.770465\pi$
$499$	−33.5555			−1.50215			−0.751076	+	0.660215i	$0.770465\pi$
$500$	−4.68084	−	8.10745i	−0.209334	−	0.362576i
$501$	4.05496	+	7.02339i	0.181162	+	0.313782i
$502$	−54.5907			−2.43650
$503$	−10.7817	−	18.6744i	−0.480730	−	0.832650i	0.519025	−	0.854759i	$-0.326295\pi$
$503$	−10.7817	−	18.6744i	−0.480730	−	0.832650i	−0.999756	+	0.0221094i	$0.992962\pi$
$504$	0.455927	−	0.789689i	0.0203086	−	0.0351755i
$505$	16.6984	−	28.9224i	0.743067	−	1.28703i
$506$	−20.5139			−0.911955
$507$		0			0
$508$	30.3588			1.34695
$509$	4.44504	−	7.69904i	0.197023	−	0.341254i	−0.750539	−	0.660826i	$-0.770206\pi$
$509$	4.44504	−	7.69904i	0.197023	−	0.341254i	0.947562	+	0.319572i	$0.103539\pi$
$510$	−3.13587	+	5.43148i	−0.138859	+	0.240510i
$511$	−8.32640	−	14.4217i	−0.368338	−	0.637980i
$512$	−31.8213			−1.40632
$513$	−1.90097	−	3.29257i	−0.0839298	−	0.145371i
$514$	23.7104	+	41.0677i	1.04582	+	1.81142i
$515$	−36.8853			−1.62536
$516$	−2.51261	−	4.35198i	−0.110612	−	0.191585i
$517$	−9.38889	+	16.2620i	−0.412923	+	0.715203i
$518$	20.2615	−	35.0940i	0.890240	−	1.54194i
$519$	18.0562			0.792580
$520$		0			0
$521$	19.3478			0.847642			0.423821	−	0.905746i	$-0.360688\pi$
$521$	19.3478			0.847642			0.423821	+	0.905746i	$0.360688\pi$
$522$	−4.03534	+	6.98942i	−0.176622	+	0.305919i
$523$	6.29739	−	10.9074i	0.275366	−	0.476947i	−0.694862	−	0.719143i	$-0.744534\pi$
$523$	6.29739	−	10.9074i	0.275366	−	0.476947i	0.970227	+	0.242196i	$0.0778678\pi$
$524$	−3.29118	−	5.70050i	−0.143776	−	0.249027i
$525$	−14.0858			−0.614753
$526$	−18.9816	−	32.8771i	−0.827636	−	1.43351i
$527$	4.02542	+	6.97223i	0.175350	+	0.303715i
$528$	17.6058			0.766194
$529$	9.44534	+	16.3598i	0.410667	+	0.711296i
$530$	1.86695	−	3.23366i	0.0810953	−	0.140461i
$531$	2.35690	−	4.08226i	0.102281	−	0.177155i
$532$	−18.7778			−0.814120
$533$		0			0
$534$	−20.6093			−0.891850
$535$	16.5707	−	28.7013i	0.716413	−	1.24086i
$536$	−0.308643	+	0.534585i	−0.0133313	+	0.0230905i
$537$	−9.93512	−	17.2081i	−0.428732	−	0.742585i
$538$	−19.9941			−0.862009
$539$	4.81820	+	8.34537i	0.207535	+	0.359460i
$540$	3.68933	+	6.39011i	0.158764	+	0.274987i
$541$	29.0019			1.24689			0.623445	−	0.781867i	$-0.285733\pi$
$541$	29.0019			1.24689			0.623445	+	0.781867i	$0.285733\pi$
$542$	−23.3596	−	40.4601i	−1.00338	−	1.73791i
$543$	−5.04138	+	8.73193i	−0.216347	+	0.374723i
$544$	−3.69998	+	6.40856i	−0.158635	+	0.274765i
$545$	67.9590			2.91104
$546$		0			0
$547$	27.7006			1.18439			0.592197	−	0.805793i	$-0.298261\pi$
$547$	27.7006			1.18439			0.592197	+	0.805793i	$0.298261\pi$
$548$	−25.2990	+	43.8192i	−1.08072	+	1.87186i
$549$	−1.83997	+	3.18692i	−0.0785280	+	0.136014i
$550$	31.7186	+	54.9383i	1.35249	+	2.34258i
$551$	14.9758			0.637992
$552$	−0.411322	−	0.712430i	−0.0175070	−	0.0303230i
$553$	4.20291	+	7.27965i	0.178726	+	0.309562i
$554$	49.1135			2.08663
$555$	14.7736	+	25.5886i	0.627104	+	1.08618i
$556$	−1.07984	+	1.87034i	−0.0457956	+	0.0793203i
$557$	−3.40485	+	5.89738i	−0.144268	+	0.249880i	−0.929100	−	0.369829i	$-0.879416\pi$
$557$	−3.40485	+	5.89738i	−0.144268	+	0.249880i	0.784831	+	0.619709i	$0.212749\pi$
$558$	18.0901			0.765814
$559$		0			0
$560$	−26.8877			−1.13621
$561$	2.25182	−	3.90027i	0.0950721	−	0.164670i
$562$	−4.22587	+	7.31943i	−0.178258	+	0.308751i
$563$	9.62618	+	16.6730i	0.405695	+	0.702684i	0.994402	−	0.105662i	$-0.0336962\pi$
$563$	9.62618	+	16.6730i	0.405695	+	0.702684i	−0.588707	+	0.808346i	$0.700363\pi$
$564$	−8.35690			−0.351889
$565$	−16.2676	−	28.1762i	−0.684381	−	1.18538i
$566$	−16.0387	−	27.7798i	−0.674157	−	1.16767i
$567$	2.24698			0.0943643
$568$	0.482647	+	0.835969i	0.0202514	+	0.0350765i
$569$	−3.92423	+	6.79697i	−0.164512	+	0.284944i	−0.936482	−	0.350716i	$-0.885938\pi$
$569$	−3.92423	+	6.79697i	−0.164512	+	0.284944i	0.771970	+	0.635659i	$0.219272\pi$
$570$	13.0749	−	22.6463i	0.547646	−	0.948551i
$571$	29.8568			1.24947			0.624735	−	0.780837i	$-0.285207\pi$
$571$	29.8568			1.24947			0.624735	+	0.780837i	$0.285207\pi$
$572$		0			0
$573$	6.58748			0.275196
$574$	15.9731	−	27.6663i	0.666706	−	1.15477i
$575$	−6.35384	+	11.0052i	−0.264973	+	0.458947i
$576$	4.74914	+	8.22574i	0.197881	+	0.342739i
$577$	8.97823			0.373769			0.186884	−	0.982382i	$-0.440161\pi$
$577$	8.97823			0.373769			0.186884	+	0.982382i	$0.440161\pi$
$578$	−16.5640	−	28.6897i	−0.688971	−	1.19333i
$579$	5.43362	+	9.41131i	0.225814	+	0.391121i
$580$	−29.0646			−1.20684
$581$	−2.59299	−	4.49119i	−0.107575	−	0.186326i
$582$	16.5238	−	28.6201i	0.684933	−	1.18634i
$583$	−1.34063	+	2.32205i	−0.0555234	+	0.0961693i
$584$	−3.00756			−0.124454
$585$		0			0
$586$	−46.2948			−1.91242
$587$	−11.9269	+	20.6580i	−0.492277	+	0.852648i	−0.999960	−	0.00889531i	$-0.997168\pi$
$587$	−11.9269	+	20.6580i	−0.492277	+	0.852648i	0.507684	+	0.861543i	$0.330502\pi$
$588$	−2.14430	+	3.71404i	−0.0884295	+	0.153164i
$589$	−16.7838	−	29.0704i	−0.691565	−	1.19783i
$590$	32.4215			1.33477
$591$	4.62080	+	8.00346i	0.190074	+	0.329218i
$592$	15.6879	+	27.1722i	0.644769	+	1.11677i
$593$	11.9866			0.492230			0.246115	−	0.969241i	$-0.420846\pi$
$593$	11.9866			0.492230			0.246115	+	0.969241i	$0.420846\pi$
$594$	−5.05980	−	8.76383i	−0.207606	−	0.359585i
$595$	−3.43900	+	5.95652i	−0.140985	+	0.244194i
$596$	−11.2750	+	19.5289i	−0.461843	+	0.799936i
$597$	1.56465			0.0640367
$598$		0			0
$599$	29.1142			1.18958			0.594788	−	0.803883i	$-0.297236\pi$
$599$	29.1142			1.18958			0.594788	+	0.803883i	$0.297236\pi$
$600$	−1.27197	+	2.20312i	−0.0519280	+	0.0899419i
$601$	−18.5683	+	32.1612i	−0.757417	+	1.31188i	0.186747	+	0.982408i	$0.440205\pi$
$601$	−18.5683	+	32.1612i	−0.757417	+	1.31188i	−0.944164	+	0.329476i	$0.893128\pi$
$602$	−5.26271	−	9.11528i	−0.214492	−	0.371511i
$603$	−1.52111			−0.0619442
$604$	22.1658	+	38.3924i	0.901915	+	1.56216i
$605$	−22.4807	−	38.9377i	−0.913970	−	1.58304i
$606$	−20.3840			−0.828045
$607$	7.11625	+	12.3257i	0.288840	+	0.500285i	0.973533	−	0.228546i	$-0.0733972\pi$
$607$	7.11625	+	12.3257i	0.288840	+	0.500285i	−0.684693	+	0.728831i	$0.740064\pi$
$608$	15.4269	−	26.7202i	0.625644	−	1.08365i
$609$	−4.42543	+	7.66507i	−0.179327	+	0.310604i
$610$	−25.3106			−1.02480
$611$		0			0
$612$	2.00431			0.0810195
$613$	−15.1570	+	26.2526i	−0.612184	+	1.06033i	0.378687	+	0.925525i	$0.376376\pi$
$613$	−15.1570	+	26.2526i	−0.612184	+	1.06033i	−0.990872	+	0.134810i	$0.956958\pi$
$614$	−6.71528	+	11.6312i	−0.271007	+	0.469398i
$615$	11.6468	+	20.1728i	0.469642	+	0.813444i
$616$	−4.50365			−0.181457
$617$	12.4819	+	21.6192i	0.502501	+	0.870358i	0.999996	+	0.00289086i	$0.000920192\pi$
$617$	12.4819	+	21.6192i	0.502501	+	0.870358i	−0.497494	+	0.867467i	$0.665746\pi$
$618$	11.2567	+	19.4971i	0.452810	+	0.784289i
$619$	35.6122			1.43138			0.715688	−	0.698420i	$-0.246113\pi$
$619$	35.6122			1.43138			0.715688	+	0.698420i	$0.246113\pi$
$620$	32.5734	+	56.4188i	1.30818	+	2.26584i
$621$	1.01357	−	1.75556i	0.0406733	−	0.0704482i
$622$	−12.3337	+	21.3626i	−0.494536	+	0.856561i
$623$	−22.6015			−0.905509
$624$		0			0
$625$	−17.0465			−0.681861
$626$	−34.7240	+	60.1438i	−1.38785	+	2.40383i
$627$	−9.38889	+	16.2620i	−0.374956	+	0.649443i
$628$	−11.4721	−	19.8702i	−0.457785	−	0.792907i
$629$	8.02608			0.320021
$630$	7.72737	+	13.3842i	0.307866	+	0.533239i
$631$	−11.9415	−	20.6832i	−0.475382	−	0.823385i	0.524221	−	0.851582i	$-0.324357\pi$
$631$	−11.9415	−	20.6832i	−0.475382	−	0.823385i	−0.999602	+	0.0281972i	$0.991023\pi$
$632$	1.51812			0.0603877
$633$	11.6223	+	20.1304i	0.461945	+	0.800112i
$634$	−4.60829	+	7.98180i	−0.183019	+	0.316998i
$635$	−23.1821	+	40.1526i	−0.919953	+	1.59341i
$636$	−1.19328			−0.0473165
$637$		0			0
$638$	39.8611			1.57812
$639$	−1.18933	+	2.05999i	−0.0470493	+	0.0814918i
$640$	−5.42237	+	9.39182i	−0.214338	+	0.371244i
$641$	12.3288	+	21.3542i	0.486960	+	0.843440i	0.999888	−	0.0149922i	$-0.00477233\pi$
$641$	12.3288	+	21.3542i	0.486960	+	0.843440i	−0.512927	+	0.858432i	$0.671439\pi$
$642$	−20.2282			−0.798343
$643$	−23.9083	−	41.4103i	−0.942850	−	1.63306i	−0.760000	−	0.649923i	$-0.774801\pi$
$643$	−23.9083	−	41.4103i	−0.942850	−	1.63306i	−0.182850	−	0.983141i	$-0.558532\pi$
$644$	−5.00604	−	8.67072i	−0.197266	−	0.341674i
$645$	7.67456			0.302186
$646$	−3.55161	−	6.15156i	−0.139736	−	0.242030i
$647$	2.69471	−	4.66737i	0.105940	−	0.183493i	−0.808182	−	0.588933i	$-0.799548\pi$
$647$	2.69471	−	4.66737i	0.105940	−	0.183493i	0.914122	+	0.405440i	$0.132882\pi$
$648$	0.202907	−	0.351445i	0.00797092	−	0.0138060i
$649$	−23.2814			−0.913876
$650$		0			0
$651$	19.8388			0.777543
$652$	12.1405	−	21.0279i	0.475458	−	0.823517i
$653$	2.51895	−	4.36295i	0.0985741	−	0.170735i	−0.812521	−	0.582933i	$-0.801905\pi$
$653$	2.51895	−	4.36295i	0.0985741	−	0.170735i	0.911095	+	0.412197i	$0.135239\pi$
$654$	−20.7397	−	35.9223i	−0.810988	−	1.40467i
$655$	10.0526			0.392789
$656$	12.3675	+	21.4212i	0.482871	+	0.836358i
$657$	−3.70560	−	6.41828i	−0.144569	−	0.250401i
$658$	−17.5036			−0.682363
$659$	21.9906	+	38.0888i	0.856632	+	1.48373i	0.875122	+	0.483902i	$0.160781\pi$
$659$	21.9906	+	38.0888i	0.856632	+	1.48373i	−0.0184899	+	0.999829i	$0.505886\pi$
$660$	18.2216	−	31.5608i	0.709276	−	1.22850i
$661$	19.1097	−	33.0989i	0.743280	−	1.28740i	−0.207714	−	0.978190i	$-0.566602\pi$
$661$	19.1097	−	33.0989i	0.743280	−	1.28740i	0.950994	−	0.309210i	$-0.100064\pi$
$662$	22.9748			0.892940
$663$		0			0
$664$	−0.936608			−0.0363474
$665$	14.3388	−	24.8355i	0.556034	−	0.963079i
$666$	9.01722	−	15.6183i	0.349410	−	0.605196i
$667$	3.99247	+	6.91516i	0.154589	+	0.267756i
$668$	17.8261			0.689713
$669$	5.36927	+	9.29985i	0.207588	+	0.359553i
$670$	−5.23109	−	9.06051i	−0.202094	−	0.350038i
$671$	18.1752			0.701647
$672$	9.11745	+	15.7919i	0.351713	+	0.609185i
$673$	3.33244	−	5.77195i	0.128456	−	0.222492i	−0.794623	−	0.607104i	$-0.792331\pi$
$673$	3.33244	−	5.77195i	0.128456	−	0.222492i	0.923079	+	0.384611i	$0.125665\pi$
$674$	7.22132	−	12.5077i	0.278155	−	0.481779i
$675$	−6.26875			−0.241284
$676$		0			0
$677$	4.80194			0.184553			0.0922767	−	0.995733i	$-0.470586\pi$
$677$	4.80194			0.184553			0.0922767	+	0.995733i	$0.470586\pi$
$678$	−9.92908	+	17.1977i	−0.381324	+	0.660472i
$679$	18.1211	−	31.3867i	0.695424	−	1.20451i
$680$	0.621097	+	1.07577i	0.0238180	+	0.0412539i
$681$	6.97584			0.267315
$682$	−44.6734	−	77.3766i	−1.71063	−	2.96290i
$683$	−5.62953	−	9.75063i	−0.215408	−	0.373098i	0.737991	−	0.674811i	$-0.235775\pi$
$683$	−5.62953	−	9.75063i	−0.215408	−	0.373098i	−0.953399	+	0.301713i	$0.902441\pi$
$684$	−8.35690			−0.319534
$685$	−38.6368	−	66.9209i	−1.47624	−	2.55692i
$686$	−20.6048	+	35.6886i	−0.786696	+	1.36260i
$687$	−8.40246	+	14.5535i	−0.320574	+	0.555250i
$688$	8.14952			0.310698
$689$		0			0
$690$	13.9427			0.530790
$691$	12.3572	−	21.4033i	0.470090	−	0.814219i	−0.529325	−	0.848419i	$-0.677555\pi$
$691$	12.3572	−	21.4033i	0.470090	−	0.814219i	0.999415	+	0.0341997i	$0.0108882\pi$
$692$	19.8443	−	34.3714i	0.754369	−	1.30660i
$693$	−5.54892	−	9.61101i	−0.210786	−	0.365092i
$694$	5.54048			0.210314
$695$	−1.64914	−	2.85640i	−0.0625556	−	0.108350i
$696$	0.799249	+	1.38434i	0.0302955	+	0.0524733i
$697$	6.32736			0.239666
$698$	−0.425665	−	0.737273i	−0.0161116	−	0.0279062i
$699$	4.34601	−	7.52751i	0.164381	−	0.284717i
$700$	−15.4807	+	26.8133i	−0.585115	+	1.01345i
$701$	25.8920			0.977927			0.488964	−	0.872304i	$-0.337375\pi$
$701$	25.8920			0.977927			0.488964	+	0.872304i	$0.337375\pi$
$702$		0			0
$703$	−33.4644			−1.26213
$704$	23.4560	−	40.6270i	0.884031	−	1.53119i
$705$	6.38135	−	11.0528i	0.240336	−	0.416274i
$706$	−32.9540	−	57.0779i	−1.24024	−	2.14816i
$707$	−22.3545			−0.840728
$708$	−5.18060	−	8.97307i	−0.194699	−	0.337229i
$709$	−0.0425810	−	0.0737525i	−0.00159916	−	0.00276983i	0.865225	−	0.501384i	$-0.167176\pi$
$709$	−0.0425810	−	0.0737525i	−0.00159916	−	0.00276983i	−0.866824	+	0.498614i	$0.833842\pi$
$710$	−16.3605			−0.613998
$711$	1.87047	+	3.23975i	0.0701481	+	0.121500i
$712$	−2.04096	+	3.53504i	−0.0764881	+	0.132481i
$713$	8.94893	−	15.5000i	0.335140	−	0.580479i
$714$	4.19806			0.157109
$715$		0			0
$716$	−43.6760			−1.63225
$717$	−11.4596	+	19.8486i	−0.427966	+	0.741258i
$718$	22.8988	−	39.6619i	0.854576	−	1.48017i
$719$	−13.5254	−	23.4267i	−0.504413	−	0.873669i	−0.999987	−	0.00510319i	$-0.998376\pi$
$719$	−13.5254	−	23.4267i	−0.504413	−	0.873669i	0.495574	−	0.868566i	$-0.334958\pi$
$720$	−11.9661			−0.445952
$721$	12.3448	+	21.3818i	0.459745	+	0.796302i
$722$	−4.65644	−	8.06519i	−0.173295	−	0.300155i
$723$	−21.9801			−0.817451
$724$	11.0813	+	19.1933i	0.411832	+	0.713315i
$725$	12.3463	−	21.3844i	0.458530	−	0.794198i
$726$	−13.7213	+	23.7660i	−0.509246	+	0.882040i
$727$	−47.1584			−1.74901			−0.874503	−	0.485019i	$-0.838813\pi$
$727$	−47.1584			−1.74901			−0.874503	+	0.485019i	$0.838813\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	25.4871	−	44.1449i	0.943320	−	1.63388i
$731$	1.04234	−	1.80539i	0.0385525	−	0.0667749i
$732$	4.04437	+	7.00505i	0.149484	+	0.258914i
$733$	−9.68186			−0.357608			−0.178804	−	0.983885i	$-0.557223\pi$
$733$	−9.68186			−0.357608			−0.178804	+	0.983885i	$0.557223\pi$
$734$	−2.35892	−	4.08577i	−0.0870693	−	0.150809i
$735$	−3.27479	−	5.67210i	−0.120792	−	0.209219i
$736$	16.4509			0.606388
$737$	3.75637	+	6.50623i	0.138368	+	0.239660i
$738$	7.10872	−	12.3127i	0.261676	−	0.453235i
$739$	−18.1570	+	31.4488i	−0.667915	+	1.15686i	0.310571	+	0.950550i	$0.399480\pi$
$739$	−18.1570	+	31.4488i	−0.667915	+	1.15686i	−0.978486	+	0.206313i	$0.933854\pi$
$740$	64.9466			2.38748
$741$		0			0
$742$	−2.49934			−0.0917535
$743$	20.8768	−	36.1597i	0.765896	−	1.32657i	−0.173876	−	0.984768i	$-0.555629\pi$
$743$	20.8768	−	36.1597i	0.765896	−	1.32657i	0.939772	−	0.341803i	$-0.111037\pi$
$744$	1.79148	−	3.10293i	0.0656788	−	0.113759i
$745$	−17.2193	−	29.8247i	−0.630866	−	1.09269i
$746$	39.4950			1.44602
$747$	−1.15399	−	1.99877i	−0.0422223	−	0.0731311i
$748$	−4.94965	−	8.57304i	−0.180977	−	0.313462i
$749$	−22.1836			−0.810571
$750$	−4.36323	−	7.55734i	−0.159323	−	0.275955i
$751$	11.0963	−	19.2194i	0.404911	−	0.701327i	−0.589400	−	0.807841i	$-0.700636\pi$
$751$	11.0963	−	19.2194i	0.404911	−	0.701327i	0.994311	+	0.106515i	$0.0339691\pi$
$752$	6.77628	−	11.7369i	0.247106	−	0.427999i
$753$	−26.6437			−0.970950
$754$		0			0
$755$	−67.7036			−2.46399
$756$	2.46950	−	4.27730i	0.0898149	−	0.155564i
$757$	−4.61865	+	7.99973i	−0.167868	+	0.290755i	−0.937670	−	0.347527i	$-0.887021\pi$
$757$	−4.61865	+	7.99973i	−0.167868	+	0.290755i	0.769802	+	0.638282i	$0.220355\pi$
$758$	−7.51895	−	13.0232i	−0.273101	−	0.473024i
$759$	−10.0121			−0.363416
$760$	−2.58964	−	4.48538i	−0.0939360	−	0.162702i
$761$	3.75086	+	6.49669i	0.135969	+	0.235505i	0.925967	−	0.377604i	$-0.123252\pi$
$761$	3.75086	+	6.49669i	0.135969	+	0.235505i	−0.789998	+	0.613109i	$0.789919\pi$
$762$	28.2989			1.02516
$763$	−22.7446	−	39.3948i	−0.823409	−	1.42619i
$764$	7.23985	−	12.5398i	0.261929	−	0.453673i
$765$	−1.53050	+	2.65090i	−0.0553353	+	0.0958436i
$766$	−39.1140			−1.41325
$767$		0			0
$768$	−12.3773			−0.446629
$769$	−2.57002	+	4.45141i	−0.0926774	+	0.160522i	−0.908637	−	0.417587i	$-0.862876\pi$
$769$	−2.57002	+	4.45141i	−0.0926774	+	0.160522i	0.815959	+	0.578109i	$0.196209\pi$
$770$	38.1655	−	66.1045i	1.37539	−	2.38224i
$771$	11.5722	+	20.0436i	0.416762	+	0.721853i
$772$	23.8869			0.859708
$773$	4.25086	+	7.36271i	0.152893	+	0.264818i	0.932290	−	0.361712i	$-0.117808\pi$
$773$	4.25086	+	7.36271i	0.152893	+	0.264818i	−0.779397	+	0.626531i	$0.784474\pi$
$774$	−2.34213	−	4.05668i	−0.0841860	−	0.145814i
$775$	−55.3473			−1.98813
$776$	−3.27274	−	5.66855i	−0.117485	−	0.203489i
$777$	9.88889	−	17.1281i	0.354762	−	0.614466i
$778$	−24.5746	+	42.5645i	−0.881043	+	1.52601i
$779$	−26.3817			−0.945221
$780$		0			0
$781$	11.7482			0.420385
$782$	1.89367	−	3.27994i	0.0677176	−	0.117290i
$783$	−1.96950	+	3.41127i	−0.0703842	+	0.121909i
$784$	−3.47746	−	6.02314i	−0.124195	−	0.215112i
$785$	35.0404			1.25065
$786$	−3.06787	−	5.31370i	−0.109427	−	0.189533i
$787$	3.89277	+	6.74248i	0.138762	+	0.240343i	0.927028	−	0.374991i	$-0.122354\pi$
$787$	3.89277	+	6.74248i	0.138762	+	0.240343i	−0.788266	+	0.615335i	$0.789021\pi$
$788$	20.3136			0.723643
$789$	−9.26420	−	16.0461i	−0.329814	−	0.571255i
$790$	−12.8651	+	22.2830i	−0.457719	+	0.792793i
$791$	−10.8889	+	18.8601i	−0.387164	+	0.670588i
$792$	−2.00431			−0.0712201
$793$		0			0
$794$	9.05190			0.321240
$795$	0.911190	−	1.57823i	0.0323166	−	0.0559740i
$796$	1.71960	−	2.97843i	0.0609494	−	0.105568i
$797$	−10.6920	−	18.5191i	−0.378731	−	0.655981i	0.612147	−	0.790744i	$-0.290306\pi$
$797$	−10.6920	−	18.5191i	−0.378731	−	0.655981i	−0.990878	+	0.134763i	$0.956973\pi$
$798$	−17.5036			−0.619622
$799$	−1.73341	−	3.00235i	−0.0613235	−	0.106215i
$800$	−25.4364	−	44.0571i	−0.899312	−	1.55765i
$801$	−10.0586			−0.355403
$802$	−20.9080	−	36.2137i	−0.738286	−	1.27875i
$803$	−18.3019	+	31.6999i	−0.645861	+	1.11866i
$804$	−1.67174	+	2.89554i	−0.0589578	+	0.102118i
$805$	15.2905			0.538920
$806$		0			0
$807$	−9.75840			−0.343512
$808$	−2.01865	+	3.49641i	−0.0710160	+	0.123003i
$809$	−1.14310	+	1.97991i	−0.0401894	+	0.0696101i	−0.885420	−	0.464791i	$-0.846129\pi$
$809$	−1.14310	+	1.97991i	−0.0401894	+	0.0696101i	0.845231	+	0.534401i	$0.179463\pi$
$810$	3.43900	+	5.95652i	0.120834	+	0.209291i
$811$	17.8079			0.625320			0.312660	−	0.949865i	$-0.398780\pi$
$811$	17.8079			0.625320			0.312660	+	0.949865i	$0.398780\pi$
$812$	9.72737	+	16.8483i	0.341364	+	0.591259i
$813$	−11.4010	−	19.7471i	−0.399849	−	0.692560i
$814$	−89.0721			−3.12198
$815$	18.5410	+	32.1140i	0.649463	+	1.12490i
$816$	−1.62522	+	2.81496i	−0.0568940	+	0.0985434i
$817$	−4.34601	+	7.52751i	−0.152048	+	0.263354i
$818$	45.3818			1.58674
$819$		0			0
$820$	51.2006			1.78800
$821$	−6.95271	+	12.0424i	−0.242651	+	0.420284i	−0.961469	−	0.274915i	$-0.911350\pi$
$821$	−6.95271	+	12.0424i	−0.242651	+	0.420284i	0.718817	+	0.695199i	$0.244684\pi$
$822$	−23.5824	+	40.8459i	−0.822531	+	1.42466i
$823$	3.62415	+	6.27722i	0.126330	+	0.218810i	0.922252	−	0.386589i	$-0.126347\pi$
$823$	3.62415	+	6.27722i	0.126330	+	0.218810i	−0.795922	+	0.605399i	$0.793013\pi$
$824$	4.45904			0.155338
$825$	15.4807	+	26.8133i	0.538968	+	0.933520i
$826$	−10.8509	−	18.7942i	−0.377550	−	0.653935i
$827$	54.1191			1.88191			0.940953	−	0.338536i	$-0.109932\pi$
$827$	54.1191			1.88191			0.940953	+	0.338536i	$0.109932\pi$
$828$	−2.22790	−	3.85883i	−0.0774248	−	0.134104i
$829$	2.89589	−	5.01582i	0.100578	−	0.174207i	−0.811345	−	0.584568i	$-0.801264\pi$
$829$	2.89589	−	5.01582i	0.100578	−	0.174207i	0.911923	+	0.410361i	$0.134597\pi$
$830$	7.93714	−	13.7475i	0.275502	−	0.477184i
$831$	23.9705			0.831526
$832$		0			0
$833$	−1.77910			−0.0616422
$834$	−1.00657	+	1.74344i	−0.0348548	+	0.0603703i
$835$	−13.6121	+	23.5768i	−0.471065	+	0.815909i
$836$	20.6374	+	35.7450i	0.713758	+	1.23627i
$837$	8.82908			0.305178
$838$	15.1169	+	26.1833i	0.522205	+	0.904486i
$839$	2.64675	+	4.58431i	0.0913760	+	0.158268i	0.908090	−	0.418774i	$-0.137540\pi$
$839$	2.64675	+	4.58431i	0.0913760	+	0.158268i	−0.816714	+	0.577042i	$0.804207\pi$
$840$	3.06100			0.105614
$841$	6.74214	+	11.6777i	0.232487	+	0.402680i
$842$	8.67941	−	15.0332i	0.299112	−	0.518077i
$843$	−2.06249	+	3.57234i	−0.0710360	+	0.123038i
$844$	51.0930			1.75870
$845$		0			0
$846$	−7.78986			−0.267821
$847$	−15.0477	+	26.0634i	−0.517046	+	0.895550i
$848$	0.967582	−	1.67590i	0.0332269	−	0.0575507i
$849$	−7.82789	−	13.5583i	−0.268652	−	0.465320i
$850$	−11.7120			−0.401718
$851$	−8.92141	−	15.4523i	−0.305822	−	0.529699i
$852$	2.61423	+	4.52798i	0.0895620	+	0.155126i
$853$	−13.5961			−0.465522			−0.232761	−	0.972534i	$-0.574776\pi$
$853$	−13.5961			−0.465522			−0.232761	+	0.972534i	$0.574776\pi$
$854$	8.47099	+	14.6722i	0.289871	+	0.502072i
$855$	6.38135	−	11.0528i	0.218238	−	0.377999i
$856$	−2.00322	+	3.46968i	−0.0684687	+	0.118591i
$857$	−23.8323			−0.814097			−0.407048	−	0.913407i	$-0.633442\pi$
$857$	−23.8323			−0.814097			−0.407048	+	0.913407i	$0.633442\pi$
$858$		0			0
$859$	−26.9861			−0.920754			−0.460377	−	0.887723i	$-0.652286\pi$
$859$	−26.9861			−0.920754			−0.460377	+	0.887723i	$0.652286\pi$
$860$	8.43458	−	14.6091i	0.287617	−	0.498167i
$861$	7.79590	−	13.5029i	0.265683	−	0.460177i
$862$	2.45031	+	4.24407i	0.0834580	+	0.144553i
$863$	−27.0291			−0.920080			−0.460040	−	0.887898i	$-0.652165\pi$
$863$	−27.0291			−0.920080			−0.460040	+	0.887898i	$0.652165\pi$
$864$	4.05765	+	7.02805i	0.138044	+	0.239099i
$865$	30.3064	+	52.4922i	1.03045	+	1.78479i
$866$	21.3674			0.726095
$867$	−8.08426	−	14.0024i	−0.274556	−	0.475545i
$868$	21.8034	−	37.7646i	0.740057	−	1.28182i
$869$	9.23825	−	16.0011i	0.313386	−	0.542801i
$870$	−27.0925			−0.918520
$871$		0			0
$872$	−8.21552			−0.278213
$873$	8.06465	−	13.9684i	0.272947	−	0.472758i
$874$	−7.89559	+	13.6756i	−0.267072	+	0.462583i
$875$	−4.78501	−	8.28788i	−0.161763	−	0.280182i
$876$	−16.2903			−0.550397
$877$	−20.4390	−	35.4014i	−0.690176	−	1.19542i	−0.971780	−	0.235889i	$-0.924200\pi$
$877$	−20.4390	−	35.4014i	−0.690176	−	1.19542i	0.281604	−	0.959531i	$-0.409134\pi$
$878$	−33.3463	−	57.7575i	−1.12538	−	1.94922i
$879$	−22.5948			−0.762103
$880$	29.5504	+	51.1828i	0.996144	+	1.72537i
$881$	11.2482	−	19.4824i	0.378961	−	0.656379i	−0.611951	−	0.790896i	$-0.709615\pi$
$881$	11.2482	−	19.4824i	0.378961	−	0.656379i	0.990911	+	0.134517i	$0.0429482\pi$
$882$	−1.99880	+	3.46203i	−0.0673032	+	0.116573i
$883$	−4.16315			−0.140101			−0.0700505	−	0.997543i	$-0.522316\pi$
$883$	−4.16315			−0.140101			−0.0700505	+	0.997543i	$0.522316\pi$
$884$		0			0
$885$	15.8237			0.531908
$886$	9.81647	−	17.0026i	0.329791	−	0.571214i
$887$	13.1501	−	22.7766i	0.441537	−	0.764765i	−0.556266	−	0.831004i	$-0.687767\pi$
$887$	13.1501	−	22.7766i	0.441537	−	0.764765i	0.997804	+	0.0662389i	$0.0211000\pi$
$888$	−1.78597	−	3.09339i	−0.0599333	−	0.103807i
$889$	31.0344			1.04086
$890$	−34.5916	−	59.9143i	−1.15951	−	2.00833i
$891$	−2.46950	−	4.27730i	−0.0827314	−	0.143295i
$892$	23.6040			0.790320
$893$	7.22737	+	12.5182i	0.241855	+	0.418904i
$894$	−10.5100	+	18.2038i	−0.351506	+	0.608827i
$895$	33.3512	−	57.7659i	1.11481	−	1.93090i
$896$	7.25906			0.242508
$897$		0			0
$898$	58.1764			1.94137
$899$	−17.3889	+	30.1184i	−0.579952	+	1.00451i
$900$	−6.88955	+	11.9331i	−0.229652	+	0.397768i
$901$	−0.247512	−	0.428703i	−0.00824582	−	0.0142822i
$902$	−70.2199			−2.33807
$903$	−2.56853	−	4.44883i	−0.0854754	−	0.148048i
$904$	1.96658	+	3.40621i	0.0654073	+	0.113289i
$905$	−33.8468			−1.12511
$906$	20.6618	+	35.7873i	0.686443	+	1.18895i
$907$	28.9557	−	50.1527i	0.961458	−	1.66529i	0.242613	−	0.970123i	$-0.421995\pi$
$907$	28.9557	−	50.1527i	0.961458	−	1.66529i	0.718845	−	0.695171i	$-0.244671\pi$
$908$	7.66666	−	13.2790i	0.254427	−	0.440681i
$909$	−9.94869			−0.329977
$910$		0			0
$911$	−0.286799			−0.00950208			−0.00475104	−	0.999989i	$-0.501512\pi$
$911$	−0.286799			−0.00950208			−0.00475104	+	0.999989i	$0.501512\pi$
$912$	6.77628	−	11.7369i	0.224385	−	0.388646i
$913$	−5.69955	+	9.87192i	−0.188628	+	0.326713i
$914$	5.11788	+	8.86442i	0.169284	+	0.293209i
$915$	−12.3532			−0.408383
$916$	18.4691	+	31.9895i	0.610237	+	1.05696i
$917$	−3.36443	−	5.82736i	−0.111103	−	0.192436i
$918$	1.86831			0.0616635
$919$	15.5620	+	26.9541i	0.513342	+	0.889134i	0.999880	+	0.0154747i	$0.00492596\pi$
$919$	15.5620	+	26.9541i	0.513342	+	0.889134i	−0.486539	+	0.873659i	$0.661741\pi$
$920$	1.38076	−	2.39155i	0.0455224	−	0.0788472i
$921$	−3.27748	+	5.67676i	−0.107997	+	0.187056i
$922$	−2.77133			−0.0912690
$923$		0			0
$924$	−24.3937			−0.802495
$925$	−27.5886	+	47.7848i	−0.907107	+	1.57115i
$926$	−3.44696	+	5.97031i	−0.113274	+	0.196197i
$927$	5.49396	+	9.51582i	0.180445	+	0.312540i
$928$	−31.9661			−1.04934
$929$	−3.81336	−	6.60493i	−0.125112	−	0.216701i	0.796665	−	0.604422i	$-0.206596\pi$
$929$	−3.81336	−	6.60493i	−0.125112	−	0.216701i	−0.921777	+	0.387721i	$0.873262\pi$
$930$	30.3632	+	52.5907i	0.995650	+	1.72452i
$931$	7.41789			0.243112
$932$	−9.55280	−	16.5459i	−0.312912	−	0.541980i
$933$	−6.01961	+	10.4263i	−0.197073	+	0.341341i
$934$	7.07982	−	12.2626i	0.231659	−	0.401245i
$935$	15.1183			0.494421
$936$		0			0
$937$	−5.67324			−0.185337			−0.0926683	−	0.995697i	$-0.529540\pi$
$937$	−5.67324			−0.185337			−0.0926683	+	0.995697i	$0.529540\pi$
$938$	−3.50149	+	6.06476i	−0.114328	+	0.198021i
$939$	−16.9475	+	29.3539i	−0.553061	+	0.957929i
$940$	−14.0266	−	24.2948i	−0.457498	−	0.792409i
$941$	41.5394			1.35415			0.677073	−	0.735916i	$-0.263248\pi$
$941$	41.5394			1.35415			0.677073	+	0.735916i	$0.263248\pi$
$942$	−10.6936	−	18.5219i	−0.348418	−	0.603477i
$943$	−7.03319	−	12.1818i	−0.229032	−	0.396695i
$944$	16.8030			0.546891
$945$	3.77144	+	6.53232i	0.122685	+	0.212496i
$946$	−11.5678	+	20.0360i	−0.376100	+	0.651425i
$947$	23.6555	−	40.9725i	0.768700	−	1.33143i	−0.169568	−	0.985518i	$-0.554237\pi$
$947$	23.6555	−	40.9725i	0.768700	−	1.33143i	0.938268	−	0.345909i	$-0.112429\pi$
$948$	8.22282			0.267065
$949$		0			0
$950$	48.8327			1.58434
$951$	−2.24914	+	3.89562i	−0.0729332	+	0.126324i
$952$	0.415739	−	0.720081i	0.0134742	−	0.0233380i
$953$	17.1717	+	29.7423i	0.556247	+	0.963449i	0.997805	+	0.0662159i	$0.0210926\pi$
$953$	17.1717	+	29.7423i	0.556247	+	0.963449i	−0.441558	+	0.897233i	$0.645574\pi$
$954$	−1.11231			−0.0360123
$955$	11.0567	+	19.1508i	0.357788	+	0.619707i
$956$	25.1889	+	43.6284i	0.814666	+	1.41104i
$957$	19.4547			0.628882
$958$	3.60172	+	6.23836i	0.116366	+	0.201552i
$959$	−25.8620	+	44.7944i	−0.835129	+	1.44649i
$960$	−15.9424	+	27.6130i	−0.514537	+	0.891205i
$961$	46.9527			1.51460
$962$		0			0
$963$	−9.87263			−0.318141
$964$	−24.1569	+	41.8409i	−0.778040	+	1.34761i
$965$	−18.2401	+	31.5928i	−0.587170	+	1.01701i
$966$	−4.66637	−	8.08238i	−0.150138	−	0.260046i
$967$	48.5096			1.55996			0.779982	−	0.625802i	$-0.215228\pi$
$967$	48.5096			1.55996			0.779982	+	0.625802i	$0.215228\pi$
$968$	2.71768	+	4.70715i	0.0873494	+	0.151294i
$969$	−1.73341	−	3.00235i	−0.0556850	−	0.0964493i
$970$	110.937			3.56198
$971$	−20.7325	−	35.9098i	−0.665338	−	1.15240i	−0.979194	−	0.202928i	$-0.934954\pi$
$971$	−20.7325	−	35.9098i	−0.665338	−	1.15240i	0.313856	−	0.949471i	$-0.398379\pi$
$972$	1.09903	−	1.90358i	0.0352514	−	0.0610573i
$973$	−1.10388	+	1.91197i	−0.0353886	+	0.0612949i
$974$	26.3242			0.843483
$975$		0			0
$976$	−13.1177			−0.419887
$977$	1.04838	−	1.81586i	0.0335408	−	0.0580944i	−0.848768	−	0.528766i	$-0.822655\pi$
$977$	1.04838	−	1.81586i	0.0335408	−	0.0580944i	0.882309	+	0.470671i	$0.155988\pi$
$978$	11.3167	−	19.6011i	0.361868	−	0.626774i
$979$	24.8397	+	43.0237i	0.793881	+	1.37504i
$980$	−14.3964			−0.459876
$981$	−10.1223	−	17.5323i	−0.323180	−	0.559764i
$982$	29.3721	+	50.8740i	0.937301	+	1.62345i
$983$	25.2336			0.804826			0.402413	−	0.915458i	$-0.368172\pi$
$983$	25.2336			0.804826			0.402413	+	0.915458i	$0.368172\pi$
$984$	−1.40797	−	2.43867i	−0.0448844	−	0.0777421i
$985$	−15.5115	+	26.8668i	−0.494239	+	0.856047i
$986$	−3.67964	+	6.37333i	−0.117184	+	0.202968i
$987$	−8.54288			−0.271923
$988$		0			0
$989$	−4.63448			−0.147368
$990$	16.9852	−	29.4193i	0.539826	−	0.935006i
$991$	−6.02446	+	10.4347i	−0.191373	+	0.331468i	−0.945706	−	0.325025i	$-0.894627\pi$
$991$	−6.02446	+	10.4347i	−0.191373	+	0.331468i	0.754332	+	0.656493i	$0.227961\pi$
$992$	35.8253	+	62.0512i	1.13745	+	1.97013i
$993$	11.2131			0.355838
$994$	5.47554	+	9.48392i	0.173674	+	0.300812i
$995$	2.62618	+	4.54867i	0.0832554	+	0.144203i
$996$	−5.07308			−0.160747
$997$	0.717013	+	1.24190i	0.0227080	+	0.0393314i	0.877156	−	0.480205i	$-0.159438\pi$
$997$	0.717013	+	1.24190i	0.0227080	+	0.0393314i	−0.854448	+	0.519537i	$0.826105\pi$
$998$	−34.3763	+	59.5415i	−1.08816	+	1.88475i
$999$	4.40097	−	7.62270i	0.139240	−	0.241172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.e.i.22.3		6
13.2	odd	12		507.2.j.i.361.4		12
13.3	even	3	inner	507.2.e.i.484.3		6
13.4	even	6		507.2.a.i.1.3	✓	3
13.5	odd	4		507.2.j.i.316.3		12
13.6	odd	12		507.2.b.f.337.4		6
13.7	odd	12		507.2.b.f.337.3		6
13.8	odd	4		507.2.j.i.316.4		12
13.9	even	3		507.2.a.l.1.1	yes	3
13.10	even	6		507.2.e.l.484.1		6
13.11	odd	12		507.2.j.i.361.3		12
13.12	even	2		507.2.e.l.22.1		6
39.17	odd	6		1521.2.a.s.1.1		3
39.20	even	12		1521.2.b.k.1351.4		6
39.32	even	12		1521.2.b.k.1351.3		6
39.35	odd	6		1521.2.a.n.1.3		3
52.35	odd	6		8112.2.a.cp.1.2		3
52.43	odd	6		8112.2.a.cg.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.i.1.3	✓	3	13.4	even	6
507.2.a.l.1.1	yes	3	13.9	even	3
507.2.b.f.337.3		6	13.7	odd	12
507.2.b.f.337.4		6	13.6	odd	12
507.2.e.i.22.3		6	1.1	even	1	trivial
507.2.e.i.484.3		6	13.3	even	3	inner
507.2.e.l.22.1		6	13.12	even	2
507.2.e.l.484.1		6	13.10	even	6
507.2.j.i.316.3		12	13.5	odd	4
507.2.j.i.316.4		12	13.8	odd	4
507.2.j.i.361.3		12	13.11	odd	12
507.2.j.i.361.4		12	13.2	odd	12
1521.2.a.n.1.3		3	39.35	odd	6
1521.2.a.s.1.1		3	39.17	odd	6
1521.2.b.k.1351.3		6	39.32	even	12
1521.2.b.k.1351.4		6	39.20	even	12
8112.2.a.cg.1.2		3	52.43	odd	6
8112.2.a.cp.1.2		3	52.35	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+(1.02446 - 1.77441i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.09903 - 1.90358i) q^{4} +3.35690 q^{5} +(-1.02446 - 1.77441i) q^{6} +(-1.12349 - 1.94594i) q^{7} -0.405813 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.43900 - 5.95652i) q^{10} +(-2.46950 + 4.27730i) q^{11} -2.19806 q^{12} -4.60388 q^{14} +(1.67845 - 2.90716i) q^{15} +(1.78232 - 3.08707i) q^{16} +(-0.455927 - 0.789689i) q^{17} -2.04892 q^{18} +(1.90097 + 3.29257i) q^{19} +(-3.68933 - 6.39011i) q^{20} -2.24698 q^{21} +(5.05980 + 8.76383i) q^{22} +(-1.01357 + 1.75556i) q^{23} +(-0.202907 + 0.351445i) q^{24} +6.26875 q^{25} -1.00000 q^{27} +(-2.46950 + 4.27730i) q^{28} +(1.96950 - 3.41127i) q^{29} +(-3.43900 - 5.95652i) q^{30} -8.82908 q^{31} +(-4.05765 - 7.02805i) q^{32} +(2.46950 + 4.27730i) q^{33} -1.86831 q^{34} +(-3.77144 - 6.53232i) q^{35} +(-1.09903 + 1.90358i) q^{36} +(-4.40097 + 7.62270i) q^{37} +7.78986 q^{38} -1.36227 q^{40} +(-3.46950 + 6.00935i) q^{41} +(-2.30194 + 3.98707i) q^{42} +(1.14310 + 1.97991i) q^{43} +10.8562 q^{44} +(-1.67845 - 2.90716i) q^{45} +(2.07673 + 3.59700i) q^{46} +3.80194 q^{47} +(-1.78232 - 3.08707i) q^{48} +(0.975541 - 1.68969i) q^{49} +(6.42208 - 11.1234i) q^{50} -0.911854 q^{51} +0.542877 q^{53} +(-1.02446 + 1.77441i) q^{54} +(-8.28986 + 14.3585i) q^{55} +(0.455927 + 0.789689i) q^{56} +3.80194 q^{57} +(-4.03534 - 6.98942i) q^{58} +(2.35690 + 4.08226i) q^{59} -7.37867 q^{60} +(-1.83997 - 3.18692i) q^{61} +(-9.04503 + 15.6665i) q^{62} +(-1.12349 + 1.94594i) q^{63} -9.49827 q^{64} +10.1196 q^{66} +(0.760553 - 1.31732i) q^{67} +(-1.00216 + 1.73578i) q^{68} +(1.01357 + 1.75556i) q^{69} -15.4547 q^{70} +(-1.18933 - 2.05999i) q^{71} +(0.202907 + 0.351445i) q^{72} +7.41119 q^{73} +(9.01722 + 15.6183i) q^{74} +(3.13437 - 5.42890i) q^{75} +(4.17845 - 7.23728i) q^{76} +11.0978 q^{77} -3.74094 q^{79} +(5.98307 - 10.3630i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.10872 + 12.3127i) q^{82} +2.30798 q^{83} +(2.46950 + 4.27730i) q^{84} +(-1.53050 - 2.65090i) q^{85} +4.68425 q^{86} +(-1.96950 - 3.41127i) q^{87} +(1.00216 - 1.73578i) q^{88} +(5.02930 - 8.71101i) q^{89} -6.87800 q^{90} +4.45580 q^{92} +(-4.41454 + 7.64621i) q^{93} +(3.89493 - 6.74621i) q^{94} +(6.38135 + 11.0528i) q^{95} -8.11529 q^{96} +(8.06465 + 13.9684i) q^{97} +(-1.99880 - 3.46203i) q^{98} +4.93900 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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