LMFDB - Embedded newform 507.2.e.i.484.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("507.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$6$
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			484.2
Root			$0.222521 + 0.385418i$ of defining polynomial
Character	$\chi$	$=$	507.484
Dual form			507.2.e.i.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17845 - 2.04113i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.77748 + 3.07868i) q^{4} +3.69202 q^{5} +(1.17845 - 2.04113i) q^{6} +(0.400969 - 0.694498i) q^{7} +3.66487 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.35086 - 7.53590i) q^{10} +(1.42543 + 2.46891i) q^{11} -3.55496 q^{12} -1.89008 q^{14} +(1.84601 + 3.19738i) q^{15} +(-0.763906 - 1.32312i) q^{16} +(-1.46950 + 2.54525i) q^{17} +2.35690 q^{18} +(1.22252 - 2.11747i) q^{19} +(-6.56249 + 11.3666i) q^{20} +0.801938 q^{21} +(3.35958 - 5.81897i) q^{22} +(3.89493 + 6.74621i) q^{23} +(1.83244 + 3.17387i) q^{24} +8.63102 q^{25} -1.00000 q^{27} +(1.42543 + 2.46891i) q^{28} +(-1.92543 - 3.33494i) q^{29} +(4.35086 - 7.53590i) q^{30} +2.34481 q^{31} +(1.86443 - 3.22929i) q^{32} +(-1.42543 + 2.46891i) q^{33} +6.92692 q^{34} +(1.48039 - 2.56410i) q^{35} +(-1.77748 - 3.07868i) q^{36} +(-3.72252 - 6.44760i) q^{37} -5.76271 q^{38} +13.5308 q^{40} +(0.425428 + 0.736862i) q^{41} +(-0.945042 - 1.63686i) q^{42} +(0.807979 - 1.39946i) q^{43} -10.1347 q^{44} +(-1.84601 + 3.19738i) q^{45} +(9.17994 - 15.9001i) q^{46} +2.44504 q^{47} +(0.763906 - 1.32312i) q^{48} +(3.17845 + 5.50523i) q^{49} +(-10.1712 - 17.6171i) q^{50} -2.93900 q^{51} -9.96077 q^{53} +(1.17845 + 2.04113i) q^{54} +(5.26271 + 9.11528i) q^{55} +(1.46950 - 2.54525i) q^{56} +2.44504 q^{57} +(-4.53803 + 7.86010i) q^{58} +(2.69202 - 4.66272i) q^{59} -13.1250 q^{60} +(6.62833 - 11.4806i) q^{61} +(-2.76324 - 4.78607i) q^{62} +(0.400969 + 0.694498i) q^{63} -11.8442 q^{64} +6.71917 q^{66} +(-7.19687 - 12.4653i) q^{67} +(-5.22401 - 9.04826i) q^{68} +(-3.89493 + 6.74621i) q^{69} -6.97823 q^{70} +(-4.06249 + 7.03644i) q^{71} +(-1.83244 + 3.17387i) q^{72} -11.8877 q^{73} +(-8.77359 + 15.1963i) q^{74} +(4.31551 + 7.47468i) q^{75} +(4.34601 + 7.52751i) q^{76} +2.28621 q^{77} +5.40581 q^{79} +(-2.82036 - 4.88500i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00269 - 1.73671i) q^{82} +7.04892 q^{83} +(-1.42543 + 2.46891i) q^{84} +(-5.42543 + 9.39712i) q^{85} -3.80864 q^{86} +(1.92543 - 3.33494i) q^{87} +(5.22401 + 9.04826i) q^{88} +(-0.565843 - 0.980069i) q^{89} +8.70171 q^{90} -27.6926 q^{92} +(1.17241 + 2.03067i) q^{93} +(-2.88135 - 4.99065i) q^{94} +(4.51357 - 7.81774i) q^{95} +3.72886 q^{96} +(2.97219 - 5.14798i) q^{97} +(7.49127 - 12.9753i) q^{98} -2.85086 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 $

$2$	−1.17845	−	2.04113i	−0.833289	−	1.44330i	−0.895416	−	0.445230i	$-0.853122\pi$
$2$	−1.17845	−	2.04113i	−0.833289	−	1.44330i	0.0621278	−	0.998068i	$-0.480211\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.77748	+	3.07868i	−0.888740	+	1.53934i
$5$	3.69202			1.65112			0.825561	−	0.564313i	$-0.190859\pi$
$5$	3.69202			1.65112			0.825561	+	0.564313i	$0.190859\pi$
$6$	1.17845	−	2.04113i	0.481099	−	0.833289i
$7$	0.400969	−	0.694498i	0.151552	−	0.262496i	−0.780246	−	0.625473i	$-0.784906\pi$
$7$	0.400969	−	0.694498i	0.151552	−	0.262496i	0.931798	+	0.362977i	$0.118240\pi$
$8$	3.66487			1.29573
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−4.35086	−	7.53590i	−1.37586	−	2.38306i
$11$	1.42543	+	2.46891i	0.429783	+	0.744405i	0.996854	−	0.0792636i	$-0.0252569\pi$
$11$	1.42543	+	2.46891i	0.429783	+	0.744405i	−0.567071	+	0.823669i	$0.691924\pi$
$12$	−3.55496			−1.02623
$13$		0			0
$13$		0			0
$14$	−1.89008			−0.505146
$15$	1.84601	+	3.19738i	0.476638	+	0.825561i
$16$	−0.763906	−	1.32312i	−0.190976	−	0.330781i
$17$	−1.46950	+	2.54525i	−0.356406	+	0.617314i	−0.987358	−	0.158509i	$-0.949331\pi$
$17$	−1.46950	+	2.54525i	−0.356406	+	0.617314i	0.630951	+	0.775822i	$0.282665\pi$
$18$	2.35690			0.555526
$19$	1.22252	−	2.11747i	0.280466	−	0.485781i	−0.691034	−	0.722822i	$-0.742844\pi$
$19$	1.22252	−	2.11747i	0.280466	−	0.485781i	0.971499	+	0.237042i	$0.0761778\pi$
$20$	−6.56249	+	11.3666i	−1.46742	+	2.54164i
$21$	0.801938			0.174997
$22$	3.35958	−	5.81897i	0.716266	−	1.24061i
$23$	3.89493	+	6.74621i	0.812149	+	1.40668i	0.911357	+	0.411616i	$0.135036\pi$
$23$	3.89493	+	6.74621i	0.812149	+	1.40668i	−0.0992087	+	0.995067i	$0.531631\pi$
$24$	1.83244	+	3.17387i	0.374045	+	0.647864i
$25$	8.63102			1.72620
$26$		0			0
$27$	−1.00000			−0.192450
$28$	1.42543	+	2.46891i	0.269380	+	0.466581i
$29$	−1.92543	−	3.33494i	−0.357543	−	0.619282i	0.630007	−	0.776590i	$-0.283052\pi$
$29$	−1.92543	−	3.33494i	−0.357543	−	0.619282i	−0.987550	+	0.157307i	$0.949719\pi$
$30$	4.35086	−	7.53590i	0.794354	−	1.37586i
$31$	2.34481			0.421141			0.210571	−	0.977579i	$-0.432468\pi$
$31$	2.34481			0.421141			0.210571	+	0.977579i	$0.432468\pi$
$32$	1.86443	−	3.22929i	0.329588	−	0.570862i
$33$	−1.42543	+	2.46891i	−0.248135	+	0.429783i
$34$	6.92692			1.18796
$35$	1.48039	−	2.56410i	0.250231	−	0.433413i
$36$	−1.77748	−	3.07868i	−0.296247	−	0.513114i
$37$	−3.72252	−	6.44760i	−0.611979	−	1.05998i	−0.990907	−	0.134552i	$-0.957040\pi$
$37$	−3.72252	−	6.44760i	−0.611979	−	1.05998i	0.378928	−	0.925426i	$-0.376293\pi$
$38$	−5.76271			−0.934835
$39$		0			0
$40$	13.5308			2.13941
$41$	0.425428	+	0.736862i	0.0664406	+	0.115079i	0.897332	−	0.441356i	$-0.145502\pi$
$41$	0.425428	+	0.736862i	0.0664406	+	0.115079i	−0.830892	+	0.556434i	$0.812169\pi$
$42$	−0.945042	−	1.63686i	−0.145823	−	0.252573i
$43$	0.807979	−	1.39946i	0.123216	−	0.213416i	−0.797818	−	0.602898i	$-0.794013\pi$
$43$	0.807979	−	1.39946i	0.123216	−	0.213416i	0.921034	+	0.389482i	$0.127346\pi$
$44$	−10.1347			−1.52786
$45$	−1.84601	+	3.19738i	−0.275187	+	0.476638i
$46$	9.17994	−	15.9001i	1.35351	−	2.34435i
$47$	2.44504			0.356646			0.178323	−	0.983972i	$-0.442933\pi$
$47$	2.44504			0.356646			0.178323	+	0.983972i	$0.442933\pi$
$48$	0.763906	−	1.32312i	0.110260	−	0.190976i
$49$	3.17845	+	5.50523i	0.454064	+	0.786462i
$50$	−10.1712	−	17.6171i	−1.43843	−	2.49143i
$51$	−2.93900			−0.411542
$52$		0			0
$53$	−9.96077			−1.36822			−0.684109	−	0.729380i	$-0.739809\pi$
$53$	−9.96077			−1.36822			−0.684109	+	0.729380i	$0.739809\pi$
$54$	1.17845	+	2.04113i	0.160366	+	0.277763i
$55$	5.26271	+	9.11528i	0.709624	+	1.22910i
$56$	1.46950	−	2.54525i	0.196370	−	0.340123i
$57$	2.44504			0.323854
$58$	−4.53803	+	7.86010i	−0.595873	+	1.03208i
$59$	2.69202	−	4.66272i	0.350471	−	0.607034i	−0.635861	−	0.771804i	$-0.719355\pi$
$59$	2.69202	−	4.66272i	0.350471	−	0.607034i	0.986332	+	0.164770i	$0.0526881\pi$
$60$	−13.1250			−1.69443
$61$	6.62833	−	11.4806i	0.848671	−	1.46994i	−0.0337232	−	0.999431i	$-0.510736\pi$
$61$	6.62833	−	11.4806i	0.848671	−	1.46994i	0.882394	−	0.470510i	$-0.155930\pi$
$62$	−2.76324	−	4.78607i	−0.350932	−	0.607832i
$63$	0.400969	+	0.694498i	0.0505173	+	0.0874986i
$64$	−11.8442			−1.48052
$65$		0			0
$66$	6.71917			0.827072
$67$	−7.19687	−	12.4653i	−0.879237	−	1.52288i	−0.852180	−	0.523249i	$-0.824720\pi$
$67$	−7.19687	−	12.4653i	−0.879237	−	1.52288i	−0.0270575	−	0.999634i	$-0.508614\pi$
$68$	−5.22401	−	9.04826i	−0.633505	−	1.09726i
$69$	−3.89493	+	6.74621i	−0.468894	+	0.812149i
$70$	−6.97823			−0.834058
$71$	−4.06249	+	7.03644i	−0.482129	+	0.835072i	−0.999790	−	0.0205142i	$-0.993470\pi$
$71$	−4.06249	+	7.03644i	−0.482129	+	0.835072i	0.517661	+	0.855586i	$0.326803\pi$
$72$	−1.83244	+	3.17387i	−0.215955	+	0.374045i
$73$	−11.8877			−1.39135			−0.695674	−	0.718357i	$-0.744894\pi$
$73$	−11.8877			−1.39135			−0.695674	+	0.718357i	$0.744894\pi$
$74$	−8.77359	+	15.1963i	−1.01991	+	1.76654i
$75$	4.31551	+	7.47468i	0.498312	+	0.863102i
$76$	4.34601	+	7.52751i	0.498522	+	0.863465i
$77$	2.28621			0.260538
$78$		0			0
$79$	5.40581			0.608202			0.304101	−	0.952640i	$-0.401644\pi$
$79$	5.40581			0.608202			0.304101	+	0.952640i	$0.401644\pi$
$80$	−2.82036	−	4.88500i	−0.315325	−	0.546160i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.00269	−	1.73671i	0.110728	−	0.191787i
$83$	7.04892			0.773719			0.386860	−	0.922139i	$-0.373560\pi$
$83$	7.04892			0.773719			0.386860	+	0.922139i	$0.373560\pi$
$84$	−1.42543	+	2.46891i	−0.155527	+	0.269380i
$85$	−5.42543	+	9.39712i	−0.588470	+	1.01926i
$86$	−3.80864			−0.410696
$87$	1.92543	−	3.33494i	0.206427	−	0.357543i
$88$	5.22401	+	9.04826i	0.556882	+	0.964547i
$89$	−0.565843	−	0.980069i	−0.0599793	−	0.103887i	0.834477	−	0.551043i	$-0.185770\pi$
$89$	−0.565843	−	0.980069i	−0.0599793	−	0.103887i	−0.894456	+	0.447156i	$0.852437\pi$
$90$	8.70171			0.917241
$91$		0			0
$92$	−27.6926			−2.88715
$93$	1.17241	+	2.03067i	0.121573	+	0.210571i
$94$	−2.88135	−	4.99065i	−0.297189	−	0.514746i
$95$	4.51357	−	7.81774i	0.463083	−	0.802083i
$96$	3.72886			0.380575
$97$	2.97219	−	5.14798i	0.301780	−	0.522698i	−0.674759	−	0.738038i	$-0.735753\pi$
$97$	2.97219	−	5.14798i	0.301780	−	0.522698i	0.976539	+	0.215340i	$0.0690858\pi$
$98$	7.49127	−	12.9753i	0.756733	−	1.31070i
$99$	−2.85086			−0.286522
$100$	−15.3415	+	26.5722i	−1.53415	+	2.65722i
$101$	−2.31282	−	4.00593i	−0.230134	−	0.398605i	0.727713	−	0.685882i	$-0.240583\pi$
$101$	−2.31282	−	4.00593i	−0.230134	−	0.398605i	−0.957848	+	0.287277i	$0.907250\pi$
$102$	3.46346	+	5.99889i	0.342934	+	0.593978i
$103$	1.20775			0.119003			0.0595016	−	0.998228i	$-0.481049\pi$
$103$	1.20775			0.119003			0.0595016	+	0.998228i	$0.481049\pi$
$104$		0			0
$105$	2.96077			0.288942
$106$	11.7383	+	20.3312i	1.14012	+	1.97475i
$107$	4.76055	+	8.24552i	0.460220	+	0.797124i	0.998972	−	0.0453402i	$-0.0144372\pi$
$107$	4.76055	+	8.24552i	0.460220	+	0.797124i	−0.538752	+	0.842465i	$0.681104\pi$
$108$	1.77748	−	3.07868i	0.171038	−	0.296247i
$109$	−1.78448			−0.170922			−0.0854611	−	0.996342i	$-0.527236\pi$
$109$	−1.78448			−0.170922			−0.0854611	+	0.996342i	$0.527236\pi$
$110$	12.4037	−	21.4838i	1.18264	−	2.04840i
$111$	3.72252	−	6.44760i	0.353326	−	0.611979i
$112$	−1.22521			−0.115771
$113$	−2.47554	+	4.28776i	−0.232879	+	0.403359i	−0.958654	−	0.284573i	$-0.908148\pi$
$113$	−2.47554	+	4.28776i	−0.232879	+	0.403359i	0.725775	+	0.687932i	$0.241481\pi$
$114$	−2.88135	−	4.99065i	−0.269864	−	0.467417i
$115$	14.3802	+	24.9072i	1.34096	+	2.32261i
$116$	13.6896			1.27105
$117$		0			0
$118$	−12.6896			−1.16817
$119$	1.17845	+	2.04113i	0.108028	+	0.187110i
$120$	6.76540	+	11.7180i	0.617593	+	1.06970i
$121$	1.43631	−	2.48777i	0.130574	−	0.226161i
$122$	−31.2446			−2.82875
$123$	−0.425428	+	0.736862i	−0.0383595	+	0.0664406i
$124$	−4.16786	+	7.21894i	−0.374285	+	0.648280i
$125$	13.4058			1.19905
$126$	0.945042	−	1.63686i	0.0841910	−	0.145823i
$127$	−2.83513	−	4.91058i	−0.251577	−	0.435744i	0.712383	−	0.701791i	$-0.247616\pi$
$127$	−2.83513	−	4.91058i	−0.251577	−	0.435744i	−0.963960	+	0.266047i	$0.914282\pi$
$128$	10.2289	+	17.7169i	0.904112	+	1.56597i
$129$	1.61596			0.142277
$130$		0			0
$131$	18.2228			1.59213			0.796067	−	0.605208i	$-0.206910\pi$
$131$	18.2228			1.59213			0.796067	+	0.605208i	$0.206910\pi$
$132$	−5.06734	−	8.77688i	−0.441055	−	0.763930i
$133$	−0.980386	−	1.69808i	−0.0850102	−	0.147242i
$134$	−16.9623	+	29.3795i	−1.46532	+	2.53800i
$135$	−3.69202			−0.317759
$136$	−5.38553	+	9.32802i	−0.461806	+	0.799871i
$137$	−4.72521	+	8.18430i	−0.403702	+	0.699232i	−0.994169	−	0.107829i	$-0.965610\pi$
$137$	−4.72521	+	8.18430i	−0.403702	+	0.699232i	0.590468	+	0.807061i	$0.298943\pi$
$138$	18.3599			1.56290
$139$	−2.00753	+	3.47715i	−0.170277	+	0.294928i	−0.938517	−	0.345234i	$-0.887799\pi$
$139$	−2.00753	+	3.47715i	−0.170277	+	0.294928i	0.768240	+	0.640162i	$0.221133\pi$
$140$	5.26271	+	9.11528i	0.444780	+	0.770382i
$141$	1.22252	+	2.11747i	0.102955	+	0.178323i
$142$	19.1497			1.60701
$143$		0			0
$144$	1.52781			0.127318
$145$	−7.10872	−	12.3127i	−0.590347	−	1.02251i
$146$	14.0090	+	24.2643i	1.15940	+	2.00813i
$147$	−3.17845	+	5.50523i	−0.262154	+	0.454064i
$148$	26.4668			2.17556
$149$	−9.70291	+	16.8059i	−0.794893	+	1.37680i	0.128014	+	0.991772i	$0.459140\pi$
$149$	−9.70291	+	16.8059i	−0.794893	+	1.37680i	−0.922907	+	0.385023i	$0.874194\pi$
$150$	10.1712	−	17.6171i	0.830476	−	1.43843i
$151$	−12.3623			−1.00603			−0.503014	−	0.864278i	$-0.667775\pi$
$151$	−12.3623			−1.00603			−0.503014	+	0.864278i	$0.667775\pi$
$152$	4.48039	−	7.76026i	0.363407	−	0.629440i
$153$	−1.46950	−	2.54525i	−0.118802	−	0.205771i
$154$	−2.69418	−	4.66645i	−0.217103	−	0.376033i
$155$	8.65710			0.695355
$156$		0			0
$157$	−18.6775			−1.49063			−0.745315	−	0.666712i	$-0.767701\pi$
$157$	−18.6775			−1.49063			−0.745315	+	0.666712i	$0.767701\pi$
$158$	−6.37047	−	11.0340i	−0.506807	−	0.877816i
$159$	−4.98039	−	8.62628i	−0.394970	−	0.684109i
$160$	6.88351	−	11.9226i	0.544189	−	0.942563i
$161$	6.24698			0.492331
$162$	−1.17845	+	2.04113i	−0.0925876	+	0.160366i
$163$	−6.16972	+	10.6863i	−0.483250	+	0.837013i	−0.999815	−	0.0192348i	$-0.993877\pi$
$163$	−6.16972	+	10.6863i	−0.483250	+	0.837013i	0.516565	+	0.856248i	$0.327210\pi$
$164$	−3.02475			−0.236194
$165$	−5.26271	+	9.11528i	−0.409701	+	0.709624i
$166$	−8.30678	−	14.3878i	−0.644731	−	1.11671i
$167$	−5.74698	−	9.95406i	−0.444715	−	0.770268i	0.553318	−	0.832970i	$-0.313362\pi$
$167$	−5.74698	−	9.95406i	−0.444715	−	0.770268i	−0.998032	+	0.0627020i	$0.980028\pi$
$168$	2.93900			0.226749
$169$		0			0
$170$	25.5743			1.96146
$171$	1.22252	+	2.11747i	0.0934885	+	0.161927i
$172$	2.87233	+	4.97502i	0.219013	+	0.379342i
$173$	−6.05711	+	10.4912i	−0.460514	+	0.797633i	−0.998987	−	0.0450096i	$-0.985668\pi$
$173$	−6.05711	+	10.4912i	−0.460514	+	0.797633i	0.538473	+	0.842643i	$0.319002\pi$
$174$	−9.07606			−0.688055
$175$	3.46077	−	5.99423i	0.261610	−	0.453121i
$176$	2.17778	−	3.77203i	0.164157	−	0.284328i
$177$	5.38404			0.404689
$178$	−1.33363	+	2.30992i	−0.0999601	+	0.173136i
$179$	0.269282	+	0.466411i	0.0201271	+	0.0348612i	0.875914	−	0.482468i	$-0.160260\pi$
$179$	0.269282	+	0.466411i	0.0201271	+	0.0348612i	−0.855786	+	0.517329i	$0.826926\pi$
$180$	−6.56249	−	11.3666i	−0.489139	−	0.847214i
$181$	−23.2838			−1.73067			−0.865336	−	0.501192i	$-0.832895\pi$
$181$	−23.2838			−1.73067			−0.865336	+	0.501192i	$0.832895\pi$
$182$		0			0
$183$	13.2567			0.979961
$184$	14.2744	+	24.7240i	1.05232	+	1.82268i
$185$	−13.7436	−	23.8047i	−1.01045	−	1.75015i
$186$	2.76324	−	4.78607i	0.202611	−	0.350932i
$187$	−8.37867			−0.612709
$188$	−4.34601	+	7.52751i	−0.316965	+	0.549000i
$189$	−0.400969	+	0.694498i	−0.0291662	+	0.0505173i
$190$	−21.2760			−1.54353
$191$	−8.38285	+	14.5195i	−0.606561	+	1.05060i	0.385241	+	0.922816i	$0.374118\pi$
$191$	−8.38285	+	14.5195i	−0.606561	+	1.05060i	−0.991803	+	0.127779i	$0.959215\pi$
$192$	−5.92208	−	10.2573i	−0.427389	−	0.740259i
$193$	−12.8720	−	22.2949i	−0.926544	−	1.60482i	−0.789059	−	0.614318i	$-0.789431\pi$
$193$	−12.8720	−	22.2949i	−0.926544	−	1.60482i	−0.137485	−	0.990504i	$-0.543902\pi$
$194$	−14.0103			−1.00588
$195$		0			0
$196$	−22.5985			−1.61418
$197$	−10.7104	−	18.5510i	−0.763087	−	1.32171i	−0.941252	−	0.337705i	$-0.890349\pi$
$197$	−10.7104	−	18.5510i	−0.763087	−	1.32171i	0.178165	−	0.984001i	$-0.442984\pi$
$198$	3.35958	+	5.81897i	0.238755	+	0.413536i
$199$	−1.76391	+	3.05517i	−0.125040	+	0.216576i	−0.921749	−	0.387788i	$-0.873239\pi$
$199$	−1.76391	+	3.05517i	−0.125040	+	0.216576i	0.796709	+	0.604364i	$0.206573\pi$
$200$	31.6316			2.23669
$201$	7.19687	−	12.4653i	0.507628	−	0.879237i
$202$	−5.45108	+	9.44155i	−0.383537	+	0.664305i
$203$	−3.08815			−0.216745
$204$	5.22401	−	9.04826i	0.365754	−	0.633505i
$205$	1.57069	+	2.72051i	0.109702	+	0.190009i
$206$	−1.42327	−	2.46518i	−0.0991640	−	0.171757i
$207$	−7.78986			−0.541432
$208$		0			0
$209$	6.97046			0.482157
$210$	−3.48911	−	6.04332i	−0.240772	−	0.417029i
$211$	−0.607760	−	1.05267i	−0.0418399	−	0.0724689i	0.844347	−	0.535797i	$-0.179989\pi$
$211$	−0.607760	−	1.05267i	−0.0418399	−	0.0724689i	−0.886187	+	0.463328i	$0.846655\pi$
$212$	17.7051	−	30.6661i	1.21599	−	2.10615i
$213$	−8.12498			−0.556715
$214$	11.2201	−	19.4338i	0.766992	−	1.32847i
$215$	2.98307	−	5.16684i	0.203444	−	0.352375i
$216$	−3.66487			−0.249363
$217$	0.940198	−	1.62847i	0.0638248	−	0.110548i
$218$	2.10292	+	3.64236i	0.142427	+	0.246692i
$219$	−5.94385	−	10.2950i	−0.401648	−	0.695674i
$220$	−37.4174			−2.52268
$221$		0			0
$222$	−17.5472			−1.17769
$223$	8.69418	+	15.0588i	0.582205	+	1.00841i	0.995218	+	0.0976835i	$0.0311433\pi$
$223$	8.69418	+	15.0588i	0.582205	+	1.00841i	−0.413012	+	0.910725i	$0.635523\pi$
$224$	−1.49516	−	2.58969i	−0.0998993	−	0.173031i
$225$	−4.31551	+	7.47468i	−0.287701	+	0.498312i
$226$	11.6692			0.776223
$227$	−8.70775	+	15.0823i	−0.577954	+	1.00105i	0.417760	+	0.908557i	$0.362815\pi$
$227$	−8.70775	+	15.0823i	−0.577954	+	1.00105i	−0.995714	+	0.0924878i	$0.970518\pi$
$228$	−4.34601	+	7.52751i	−0.287822	+	0.498522i
$229$	18.7603			1.23972			0.619858	−	0.784714i	$-0.287190\pi$
$229$	18.7603			1.23972			0.619858	+	0.784714i	$0.287190\pi$
$230$	33.8925	−	58.7036i	2.23481	−	3.87080i
$231$	1.14310	+	1.97991i	0.0752107	+	0.130269i
$232$	−7.05645	−	12.2221i	−0.463279	−	0.802422i
$233$	3.95108			0.258844			0.129422	−	0.991590i	$-0.458688\pi$
$233$	3.95108			0.258844			0.129422	+	0.991590i	$0.458688\pi$
$234$		0			0
$235$	9.02715			0.588866
$236$	9.57002	+	16.5758i	0.622955	+	1.07899i
$237$	2.70291	+	4.68157i	0.175573	+	0.304101i
$238$	2.77748	−	4.81073i	0.180037	−	0.311834i
$239$	0.818331			0.0529334			0.0264667	−	0.999650i	$-0.491574\pi$
$239$	0.818331			0.0529334			0.0264667	+	0.999650i	$0.491574\pi$
$240$	2.82036	−	4.88500i	0.182053	−	0.315325i
$241$	−3.01626	+	5.22432i	−0.194295	+	0.336528i	−0.946669	−	0.322208i	$-0.895575\pi$
$241$	−3.01626	+	5.22432i	−0.194295	+	0.336528i	0.752375	+	0.658736i	$0.228908\pi$
$242$	−6.77048			−0.435223
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	23.5635	+	40.8131i	1.50850	+	2.61279i
$245$	11.7349	+	20.3254i	0.749715	+	1.29854i
$246$	2.00538			0.127858
$247$		0			0
$248$	8.59345			0.545685
$249$	3.52446	+	6.10454i	0.223353	+	0.386860i
$250$	−15.7981	−	27.3630i	−0.999157	−	1.73059i
$251$	13.4400	−	23.2787i	0.848323	−	1.46934i	−0.0343812	−	0.999409i	$-0.510946\pi$
$251$	13.4400	−	23.2787i	0.848323	−	1.46934i	0.882704	−	0.469929i	$-0.155721\pi$
$252$	−2.85086			−0.179587
$253$	−11.1039	+	19.2325i	−0.698095	+	1.20914i
$254$	−6.68210	+	11.5737i	−0.419272	+	0.726200i
$255$	−10.8509			−0.679507
$256$	12.2642	−	21.2422i	0.766513	−	1.32764i
$257$	4.52661	+	7.84033i	0.282362	+	0.489066i	0.971966	−	0.235121i	$-0.0755486\pi$
$257$	4.52661	+	7.84033i	0.282362	+	0.489066i	−0.689604	+	0.724187i	$0.742215\pi$
$258$	−1.90432	−	3.29838i	−0.118558	−	0.205348i
$259$	−5.97046			−0.370986
$260$		0			0
$261$	3.85086			0.238362
$262$	−21.4746	−	37.1952i	−1.32671	−	2.29793i
$263$	−11.5755	−	20.0494i	−0.713778	−	1.23630i	−0.963429	−	0.267964i	$-0.913649\pi$
$263$	−11.5755	−	20.0494i	−0.713778	−	1.23630i	0.249651	−	0.968336i	$-0.419684\pi$
$264$	−5.22401	+	9.04826i	−0.321516	+	0.556882i
$265$	−36.7754			−2.25909
$266$	−2.31067	+	4.00219i	−0.141676	+	0.245390i
$267$	0.565843	−	0.980069i	0.0346290	−	0.0599793i
$268$	51.1691			3.12565
$269$	1.21044	−	2.09654i	0.0738018	−	0.127828i	−0.826763	−	0.562551i	$-0.809820\pi$
$269$	1.21044	−	2.09654i	0.0738018	−	0.127828i	0.900565	+	0.434722i	$0.143153\pi$
$270$	4.35086	+	7.53590i	0.264785	+	0.458620i
$271$	10.7225	+	18.5720i	0.651347	+	1.12817i	0.982796	+	0.184693i	$0.0591290\pi$
$271$	10.7225	+	18.5720i	0.651347	+	1.12817i	−0.331450	+	0.943473i	$0.607538\pi$
$272$	4.49024			0.272261
$273$		0			0
$274$	22.2737			1.34560
$275$	12.3029	+	21.3092i	0.741893	+	1.28500i
$276$	−13.8463	−	23.9825i	−0.833450	−	1.44358i
$277$	7.40366	−	12.8235i	0.444843	−	0.770490i	−0.553199	−	0.833049i	$-0.686593\pi$
$277$	7.40366	−	12.8235i	0.444843	−	0.770490i	0.998041	+	0.0625593i	$0.0199263\pi$
$278$	9.46309			0.567558
$279$	−1.17241	+	2.03067i	−0.0701902	+	0.121573i
$280$	5.42543	−	9.39712i	0.324231	−	0.561585i
$281$	14.5036			0.865215			0.432608	−	0.901582i	$-0.357594\pi$
$281$	14.5036			0.865215			0.432608	+	0.901582i	$0.357594\pi$
$282$	2.88135	−	4.99065i	0.171582	−	0.297189i
$283$	−12.8361	−	22.2328i	−0.763026	−	1.32160i	−0.941284	−	0.337616i	$-0.890379\pi$
$283$	−12.8361	−	22.2328i	−0.763026	−	1.32160i	0.178258	−	0.983984i	$-0.442954\pi$
$284$	−14.4420	−	25.0143i	−0.856974	−	1.48432i
$285$	9.02715			0.534722
$286$		0			0
$287$	0.682333			0.0402768
$288$	1.86443	+	3.22929i	0.109863	+	0.190287i
$289$	4.18114	+	7.24194i	0.245949	+	0.425997i
$290$	−16.7545	+	29.0197i	−0.983859	+	1.70409i
$291$	5.94438			0.348466
$292$	21.1301	−	36.5984i	1.23655	−	2.14176i
$293$	13.2615	−	22.9696i	0.774746	−	1.34190i	−0.160191	−	0.987086i	$-0.551211\pi$
$293$	13.2615	−	22.9696i	0.774746	−	1.34190i	0.934937	−	0.354813i	$-0.115456\pi$
$294$	14.9825			0.873800
$295$	9.93900	−	17.2149i	0.578671	−	1.00229i
$296$	−13.6426	−	23.6296i	−0.792958	−	1.37344i
$297$	−1.42543	−	2.46891i	−0.0827117	−	0.143261i
$298$	45.7375			2.64950
$299$		0			0
$300$	−30.6829			−1.77148
$301$	−0.647948	−	1.12228i	−0.0373471	−	0.0646871i
$302$	14.5683	+	25.2330i	0.838311	+	1.45200i
$303$	2.31282	−	4.00593i	0.132868	−	0.230134i
$304$	−3.73556			−0.214249
$305$	24.4720	−	42.3867i	1.40126	−	2.42705i
$306$	−3.46346	+	5.99889i	−0.197993	+	0.342934i
$307$	−8.24698			−0.470680			−0.235340	−	0.971913i	$-0.575620\pi$
$307$	−8.24698			−0.470680			−0.235340	+	0.971913i	$0.575620\pi$
$308$	−4.06369	+	7.03851i	−0.231550	+	0.401056i
$309$	0.603875	+	1.04594i	0.0343533	+	0.0595016i
$310$	−10.2019	−	17.6703i	−0.579432	−	1.00361i
$311$	−14.4179			−0.817564			−0.408782	−	0.912632i	$-0.634046\pi$
$311$	−14.4179			−0.817564			−0.408782	+	0.912632i	$0.634046\pi$
$312$		0			0
$313$	14.2338			0.804544			0.402272	−	0.915520i	$-0.368221\pi$
$313$	14.2338			0.804544			0.402272	+	0.915520i	$0.368221\pi$
$314$	22.0105	+	38.1233i	1.24213	+	2.15142i
$315$	1.48039	+	2.56410i	0.0834103	+	0.144471i
$316$	−9.60872	+	16.6428i	−0.540533	+	0.936230i
$317$	−6.84415			−0.384406			−0.192203	−	0.981355i	$-0.561563\pi$
$317$	−6.84415			−0.384406			−0.192203	+	0.981355i	$0.561563\pi$
$318$	−11.7383	+	20.3312i	−0.658248	+	1.14012i
$319$	5.48911	−	9.50743i	0.307331	−	0.532314i
$320$	−43.7289			−2.44452
$321$	−4.76055	+	8.24552i	−0.265708	+	0.460220i
$322$	−7.36174	−	12.7509i	−0.410254	−	0.710580i
$323$	3.59299	+	6.22324i	0.199919	+	0.346270i
$324$	3.55496			0.197498
$325$		0			0
$326$	29.0828			1.61075
$327$	−0.892240	−	1.54540i	−0.0493410	−	0.0854611i
$328$	1.55914	+	2.70051i	0.0860890	+	0.149111i
$329$	0.980386	−	1.69808i	0.0540504	−	0.0936181i
$330$	24.8073			1.36560
$331$	−4.72132	+	8.17757i	−0.259507	+	0.449480i	−0.966110	−	0.258130i	$-0.916894\pi$
$331$	−4.72132	+	8.17757i	−0.259507	+	0.449480i	0.706603	+	0.707611i	$0.250227\pi$
$332$	−12.5293	+	21.7014i	−0.687635	+	1.19102i
$333$	7.44504			0.407986
$334$	−13.5450	+	23.4607i	−0.741151	+	1.28371i
$335$	−26.5710	−	46.0223i	−1.45173	−	2.51447i
$336$	−0.612605	−	1.06106i	−0.0334203	−	0.0578857i
$337$	2.64310			0.143979			0.0719895	−	0.997405i	$-0.477065\pi$
$337$	2.64310			0.143979			0.0719895	+	0.997405i	$0.477065\pi$
$338$		0			0
$339$	−4.95108			−0.268906
$340$	−19.2872	−	33.4064i	−1.04599	−	1.81171i
$341$	3.34236	+	5.78914i	0.180999	+	0.313500i
$342$	2.88135	−	4.99065i	0.155806	−	0.269864i
$343$	10.7114			0.578361
$344$	2.96114	−	5.12884i	0.159654	−	0.276529i
$345$	−14.3802	+	24.9072i	−0.774202	+	1.34096i
$346$	28.5520			1.53496
$347$	5.07942	−	8.79781i	0.272677	−	0.472291i	−0.696869	−	0.717198i	$-0.745424\pi$
$347$	5.07942	−	8.79781i	0.272677	−	0.472291i	0.969547	+	0.244907i	$0.0787575\pi$
$348$	6.84481	+	11.8556i	0.366921	+	0.635525i
$349$	−5.21983	−	9.04102i	−0.279411	−	0.483954i	0.691827	−	0.722063i	$-0.256806\pi$
$349$	−5.21983	−	9.04102i	−0.279411	−	0.483954i	−0.971239	+	0.238109i	$0.923473\pi$
$350$	−16.3134			−0.871986
$351$		0			0
$352$	10.6304			0.566604
$353$	−9.14556	−	15.8406i	−0.486769	−	0.843108i	0.513115	−	0.858320i	$-0.328491\pi$
$353$	−9.14556	−	15.8406i	−0.486769	−	0.843108i	−0.999884	+	0.0152113i	$0.995158\pi$
$354$	−6.34481	−	10.9895i	−0.337223	−	0.584087i
$355$	−14.9988	+	25.9787i	−0.796054	+	1.37881i
$356$	4.02310			0.213224
$357$	−1.17845	+	2.04113i	−0.0623701	+	0.108028i
$358$	0.634670	−	1.09928i	0.0335434	−	0.0580988i
$359$	−15.2731			−0.806081			−0.403041	−	0.915182i	$-0.632047\pi$
$359$	−15.2731			−0.806081			−0.403041	+	0.915182i	$0.632047\pi$
$360$	−6.76540	+	11.7180i	−0.356568	+	0.617593i
$361$	6.51089	+	11.2772i	0.342678	+	0.593536i
$362$	27.4388	+	47.5253i	1.44215	+	2.49788i
$363$	2.87263			0.150774
$364$		0			0
$365$	−43.8896			−2.29729
$366$	−15.6223	−	27.0586i	−0.816590	−	1.41438i
$367$	11.1359	+	19.2879i	0.581288	+	1.00682i	0.995327	+	0.0965606i	$0.0307842\pi$
$367$	11.1359	+	19.2879i	0.581288	+	1.00682i	−0.414040	+	0.910259i	$0.635882\pi$
$368$	5.95071	−	10.3069i	0.310202	−	0.537286i
$369$	−0.850855			−0.0442937
$370$	−32.3923	+	56.1051i	−1.68400	+	2.91677i
$371$	−3.99396	+	6.91774i	−0.207356	+	0.359151i
$372$	−8.33572			−0.432187
$373$	−2.06315	+	3.57349i	−0.106826	+	0.185028i	−0.914483	−	0.404625i	$-0.867402\pi$
$373$	−2.06315	+	3.57349i	−0.106826	+	0.185028i	0.807657	+	0.589653i	$0.200735\pi$
$374$	9.87382	+	17.1020i	0.510563	+	0.884321i
$375$	6.70291	+	11.6098i	0.346137	+	0.599526i
$376$	8.96077			0.462116
$377$		0			0
$378$	1.89008			0.0972154
$379$	5.35354	+	9.27261i	0.274993	+	0.476302i	0.970133	−	0.242572i	$-0.0779911\pi$
$379$	5.35354	+	9.27261i	0.274993	+	0.476302i	−0.695140	+	0.718874i	$0.744658\pi$
$380$	16.0456	+	27.7917i	0.823120	+	1.42569i
$381$	2.83513	−	4.91058i	0.145248	−	0.251577i
$382$	39.5150			2.02176
$383$	−3.26324	+	5.65210i	−0.166744	+	0.288809i	−0.937273	−	0.348596i	$-0.886659\pi$
$383$	−3.26324	+	5.65210i	−0.166744	+	0.288809i	0.770529	+	0.637405i	$0.219992\pi$
$384$	−10.2289	+	17.7169i	−0.521989	+	0.904112i
$385$	8.44073			0.430179
$386$	−30.3379	+	52.5467i	−1.54416	+	2.67456i
$387$	0.807979	+	1.39946i	0.0410719	+	0.0711385i
$388$	10.5660	+	18.3009i	0.536408	+	0.929085i
$389$	−11.7922			−0.597891			−0.298945	−	0.954270i	$-0.596635\pi$
$389$	−11.7922			−0.597891			−0.298945	+	0.954270i	$0.596635\pi$
$390$		0			0
$391$	−22.8944			−1.15782
$392$	11.6486	+	20.1760i	0.588344	+	1.01904i
$393$	9.11141	+	15.7814i	0.459610	+	0.796067i
$394$	−25.2434	+	43.7228i	−1.27174	+	2.20272i
$395$	19.9584			1.00422
$396$	5.06734	−	8.77688i	0.254643	−	0.441055i
$397$	6.27144	−	10.8624i	0.314754	−	0.545171i	−0.664631	−	0.747172i	$-0.731411\pi$
$397$	6.27144	−	10.8624i	0.314754	−	0.545171i	0.979385	+	0.202001i	$0.0647445\pi$
$398$	8.31468			0.416777
$399$	0.980386	−	1.69808i	0.0490807	−	0.0850102i
$400$	−6.59329	−	11.4199i	−0.329664	−	0.570995i
$401$	−8.93512	−	15.4761i	−0.446198	−	0.772838i	0.551936	−	0.833886i	$-0.313889\pi$
$401$	−8.93512	−	15.4761i	−0.446198	−	0.772838i	−0.998135	+	0.0610479i	$0.980556\pi$
$402$	−33.9245			−1.69200
$403$		0			0
$404$	16.4440			0.818118
$405$	−1.84601	−	3.19738i	−0.0917290	−	0.158879i
$406$	3.63922	+	6.30331i	0.180611	+	0.312828i
$407$	10.6124	−	18.3812i	0.526036	−	0.911120i
$408$	−10.7711			−0.533247
$409$	13.9559	−	24.1724i	0.690076	−	1.19525i	−0.281736	−	0.959492i	$-0.590910\pi$
$409$	13.9559	−	24.1724i	0.690076	−	1.19525i	0.971812	−	0.235755i	$-0.0757563\pi$
$410$	3.70195	−	6.41196i	0.182826	−	0.316664i
$411$	−9.45042			−0.466155
$412$	−2.14675	+	3.71828i	−0.105763	+	0.183187i
$413$	−2.15883	−	3.73921i	−0.106229	−	0.183994i
$414$	9.17994	+	15.9001i	0.451169	+	0.781448i
$415$	26.0248			1.27750
$416$		0			0
$417$	−4.01507			−0.196619
$418$	−8.21432	−	14.2276i	−0.401776	−	0.695896i
$419$	8.20171	+	14.2058i	0.400680	+	0.693998i	0.993808	−	0.111110i	$-0.0354407\pi$
$419$	8.20171	+	14.2058i	0.400680	+	0.693998i	−0.593128	+	0.805108i	$0.702107\pi$
$420$	−5.26271	+	9.11528i	−0.256794	+	0.444780i
$421$	−3.03684			−0.148006			−0.0740032	−	0.997258i	$-0.523577\pi$
$421$	−3.03684			−0.148006			−0.0740032	+	0.997258i	$0.523577\pi$
$422$	−1.43243	+	2.48104i	−0.0697295	+	0.120775i
$423$	−1.22252	+	2.11747i	−0.0594410	+	0.102955i
$424$	−36.5050			−1.77284
$425$	−12.6833	+	21.9681i	−0.615230	+	1.06561i
$426$	9.57487	+	16.5842i	0.463904	+	0.803505i
$427$	−5.31551	−	9.20674i	−0.257236	−	0.445545i
$428$	−33.8471			−1.63606
$429$		0			0
$430$	−14.0616			−0.678110
$431$	1.66905	+	2.89089i	0.0803955	+	0.139249i	0.903420	−	0.428757i	$-0.141048\pi$
$431$	1.66905	+	2.89089i	0.0803955	+	0.139249i	−0.823024	+	0.568006i	$0.807715\pi$
$432$	0.763906	+	1.32312i	0.0367534	+	0.0636588i
$433$	−5.95138	+	10.3081i	−0.286005	+	0.495375i	−0.972852	−	0.231426i	$-0.925661\pi$
$433$	−5.95138	+	10.3081i	−0.286005	+	0.495375i	0.686847	+	0.726802i	$0.258994\pi$
$434$	−4.43190			−0.212738
$435$	7.10872	−	12.3127i	0.340837	−	0.590347i
$436$	3.17187	−	5.49385i	0.151905	−	0.263108i
$437$	19.0465			0.911119
$438$	−14.0090	+	24.2643i	−0.669377	+	1.15940i
$439$	−1.85905	−	3.21997i	−0.0887277	−	0.153681i	0.818246	−	0.574868i	$-0.194947\pi$
$439$	−1.85905	−	3.21997i	−0.0887277	−	0.153681i	−0.906974	+	0.421188i	$0.861613\pi$
$440$	19.2872	+	33.4064i	0.919480	+	1.59259i
$441$	−6.35690			−0.302709
$442$		0			0
$443$	1.45712			0.0692300			0.0346150	−	0.999401i	$-0.488979\pi$
$443$	1.45712			0.0692300			0.0346150	+	0.999401i	$0.488979\pi$
$444$	13.2334	+	22.9209i	0.628030	+	1.08778i
$445$	−2.08911	−	3.61844i	−0.0990331	−	0.171530i
$446$	20.4913	−	35.4919i	0.970290	−	1.68059i
$447$	−19.4058			−0.917863
$448$	−4.74914	+	8.22574i	−0.224376	+	0.388630i
$449$	6.06369	−	10.5026i	0.286163	−	0.495649i	−0.686727	−	0.726915i	$-0.740953\pi$
$449$	6.06369	−	10.5026i	0.286163	−	0.495649i	0.972891	+	0.231266i	$0.0742867\pi$
$450$	20.3424			0.958951
$451$	−1.21283	+	2.10069i	−0.0571100	+	0.0989175i
$452$	−8.80045	−	15.2428i	−0.413938	−	0.716962i
$453$	−6.18114	−	10.7060i	−0.290415	−	0.503014i
$454$	41.0465			1.92641
$455$		0			0
$456$	8.96077			0.419627
$457$	1.72401	+	2.98608i	0.0806459	+	0.139683i	0.903528	−	0.428530i	$-0.140968\pi$
$457$	1.72401	+	2.98608i	0.0806459	+	0.139683i	−0.822882	+	0.568213i	$0.807635\pi$
$458$	−22.1081	−	38.2923i	−1.03304	−	1.78928i
$459$	1.46950	−	2.54525i	0.0685904	−	0.118802i
$460$	−102.242			−4.76704
$461$	3.37800	−	5.85087i	0.157329	−	0.272502i	−0.776575	−	0.630024i	$-0.783045\pi$
$461$	3.37800	−	5.85087i	0.157329	−	0.272502i	0.933905	+	0.357522i	$0.116378\pi$
$462$	2.69418	−	4.66645i	0.125344	−	0.217103i
$463$	−7.45175			−0.346312			−0.173156	−	0.984894i	$-0.555396\pi$
$463$	−7.45175			−0.346312			−0.173156	+	0.984894i	$0.555396\pi$
$464$	−2.94169	+	5.09516i	−0.136565	+	0.236537i
$465$	4.32855	+	7.49727i	0.200732	+	0.347678i
$466$	−4.65615	−	8.06468i	−0.215692	−	0.373589i
$467$	32.6098			1.50900			0.754502	−	0.656298i	$-0.227879\pi$
$467$	32.6098			1.50900			0.754502	+	0.656298i	$0.227879\pi$
$468$		0			0
$469$	−11.5429			−0.533001
$470$	−10.6380	−	18.4256i	−0.490695	−	0.849909i
$471$	−9.33877	−	16.1752i	−0.430308	−	0.745315i
$472$	9.86592	−	17.0883i	0.454116	−	0.786552i
$473$	4.60686			0.211824
$474$	6.37047	−	11.0340i	0.292605	−	0.506807i
$475$	10.5516	−	18.2759i	0.484141	−	0.838557i
$476$	−8.37867			−0.384036
$477$	4.98039	−	8.62628i	0.228036	−	0.394970i
$478$	−0.964361	−	1.67032i	−0.0441088	−	0.0763987i
$479$	−1.41454	−	2.45006i	−0.0646321	−	0.111946i	0.831899	−	0.554928i	$-0.187254\pi$
$479$	−1.41454	−	2.45006i	−0.0646321	−	0.111946i	−0.896531	+	0.442982i	$0.853921\pi$
$480$	13.7670			0.628376
$481$		0			0
$482$	14.2180			0.647614
$483$	3.12349	+	5.41004i	0.142124	+	0.246165i
$484$	5.10603	+	8.84391i	0.232092	+	0.401996i
$485$	10.9734	−	19.0065i	0.498276	−	0.863039i
$486$	−2.35690			−0.106911
$487$	20.6468	−	35.7612i	0.935594	−	1.62050i	0.162022	−	0.986787i	$-0.448199\pi$
$487$	20.6468	−	35.7612i	0.935594	−	1.62050i	0.773572	−	0.633709i	$-0.218468\pi$
$488$	24.2920	−	42.0750i	1.09965	−	1.90465i
$489$	−12.3394			−0.558009
$490$	27.6579	−	47.9049i	1.24946	−	2.16412i
$491$	17.3349	+	30.0249i	0.782313	+	1.35501i	0.930591	+	0.366060i	$0.119293\pi$
$491$	17.3349	+	30.0249i	0.782313	+	1.35501i	−0.148279	+	0.988946i	$0.547373\pi$
$492$	−1.51238	−	2.61951i	−0.0681832	−	0.118097i
$493$	11.3177			0.509722
$494$		0			0
$495$	−10.5254			−0.473082
$496$	−1.79122	−	3.10248i	−0.0804280	−	0.139305i
$497$	3.25786	+	5.64279i	0.146135	+	0.253114i
$498$	8.30678	−	14.3878i	0.372236	−	0.644731i
$499$	17.9409			0.803146			0.401573	−	0.915827i	$-0.368464\pi$
$499$	17.9409			0.803146			0.401573	+	0.915827i	$0.368464\pi$
$500$	−23.8286	+	41.2723i	−1.06565	+	1.84575i
$501$	5.74698	−	9.95406i	0.256756	−	0.444715i
$502$	−63.3532			−2.82759
$503$	13.0906	−	22.6736i	0.583681	−	1.01096i	−0.411358	−	0.911474i	$-0.634945\pi$
$503$	13.0906	−	22.6736i	0.583681	−	1.01096i	0.995038	−	0.0994909i	$-0.0317214\pi$
$504$	1.46950	+	2.54525i	0.0654568	+	0.113374i
$505$	−8.53899	−	14.7900i	−0.379980	−	0.658145i
$506$	52.3414			2.32686
$507$		0			0
$508$	20.1575			0.894345
$509$	2.75302	+	4.76837i	0.122025	+	0.211354i	0.920566	−	0.390586i	$-0.127728\pi$
$509$	2.75302	+	4.76837i	0.122025	+	0.211354i	−0.798541	+	0.601941i	$0.794394\pi$
$510$	12.7872	+	22.1480i	0.566225	+	0.980731i
$511$	−4.76659	+	8.25598i	−0.210862	+	0.365223i
$512$	−16.8955			−0.746681
$513$	−1.22252	+	2.11747i	−0.0539756	+	0.0934885i
$514$	10.6688	−	18.4788i	0.470579	−	0.815066i
$515$	4.45904			0.196489
$516$	−2.87233	+	4.97502i	−0.126447	+	0.219013i
$517$	3.48523	+	6.03660i	0.153280	+	0.265489i
$518$	7.03588	+	12.1865i	0.309139	+	0.535444i
$519$	−12.1142			−0.531756
$520$		0			0
$521$	−26.7211			−1.17067			−0.585336	−	0.810791i	$-0.699037\pi$
$521$	−26.7211			−1.17067			−0.585336	+	0.810791i	$0.699037\pi$
$522$	−4.53803	−	7.86010i	−0.198624	−	0.344027i
$523$	−18.2615	−	31.6299i	−0.798520	−	1.38308i	−0.920580	−	0.390555i	$-0.872283\pi$
$523$	−18.2615	−	31.6299i	−0.798520	−	1.38308i	0.122060	−	0.992523i	$-0.461050\pi$
$524$	−32.3907	+	56.1023i	−1.41499	+	2.45084i
$525$	6.92154			0.302081
$526$	−27.2823	+	47.2544i	−1.18957	+	2.06039i
$527$	−3.44571	+	5.96814i	−0.150097	+	0.259976i
$528$	4.35557			0.189552
$529$	−18.8409	+	32.6334i	−0.819171	+	1.41885i
$530$	43.3379	+	75.0634i	1.88248	+	3.26055i
$531$	2.69202	+	4.66272i	0.116824	+	0.202345i
$532$	6.97046			0.302208
$533$		0			0
$534$	−2.66727			−0.115424
$535$	17.5761	+	30.4426i	0.759880	+	1.31615i
$536$	−26.3756	−	45.6839i	−1.13925	−	1.97324i
$537$	−0.269282	+	0.466411i	−0.0116204	+	0.0201271i
$538$	−5.70576			−0.245993
$539$	−9.06129	+	15.6946i	−0.390298	+	0.676015i
$540$	6.56249	−	11.3666i	0.282405	−	0.489139i
$541$	18.4655			0.793893			0.396947	−	0.917842i	$-0.370070\pi$
$541$	18.4655			0.793893			0.396947	+	0.917842i	$0.370070\pi$
$542$	25.2719	−	43.7722i	1.08552	−	1.88018i
$543$	−11.6419	−	20.1644i	−0.499602	−	0.865336i
$544$	5.47956	+	9.49087i	0.234934	+	0.406918i
$545$	−6.58834			−0.282213
$546$		0			0
$547$	39.8471			1.70374			0.851870	−	0.523753i	$-0.175468\pi$
$547$	39.8471			1.70374			0.851870	+	0.523753i	$0.175468\pi$
$548$	−16.7979	−	29.0949i	−0.717572	−	1.24287i
$549$	6.62833	+	11.4806i	0.282890	+	0.489981i
$550$	28.9966	−	50.2237i	1.23642	−	2.14154i
$551$	−9.41550			−0.401114
$552$	−14.2744	+	24.7240i	−0.607560	+	1.05232i
$553$	2.16756	−	3.75433i	0.0921741	−	0.159650i
$554$	−34.8993			−1.48273
$555$	13.7436	−	23.8047i	0.583384	−	1.01045i
$556$	−7.13669	−	12.3611i	−0.302663	−	0.524228i
$557$	−4.60238	−	7.97156i	−0.195009	−	0.337766i	0.751894	−	0.659284i	$-0.229140\pi$
$557$	−4.60238	−	7.97156i	−0.195009	−	0.337766i	−0.946904	+	0.321518i	$0.895807\pi$
$558$	5.52648			0.233955
$559$		0			0
$560$	−4.52350			−0.191153
$561$	−4.18933	−	7.25614i	−0.176874	−	0.306354i
$562$	−17.0918	−	29.6039i	−0.720974	−	1.24876i
$563$	0.487623	−	0.844588i	0.0205509	−	0.0355951i	−0.855567	−	0.517692i	$-0.826791\pi$
$563$	0.487623	−	0.844588i	0.0205509	−	0.0355951i	0.876118	+	0.482097i	$0.160125\pi$
$564$	−8.69202			−0.366000
$565$	−9.13975	+	15.8305i	−0.384512	+	0.665995i
$566$	−30.2533	+	52.4003i	−1.27164	+	2.20255i
$567$	−0.801938			−0.0336782
$568$	−14.8885	+	25.7877i	−0.624708	+	1.08203i
$569$	8.44720	+	14.6310i	0.354125	+	0.613362i	0.986968	−	0.160918i	$-0.0514454\pi$
$569$	8.44720	+	14.6310i	0.354125	+	0.613362i	−0.632843	+	0.774280i	$0.718112\pi$
$570$	−10.6380	−	18.4256i	−0.445578	−	0.771763i
$571$	−44.3226			−1.85484			−0.927421	−	0.374019i	$-0.877979\pi$
$571$	−44.3226			−1.85484			−0.927421	+	0.374019i	$0.877979\pi$
$572$		0			0
$573$	−16.7657			−0.700397
$574$	−0.804094	−	1.39273i	−0.0335622	−	0.0581315i
$575$	33.6172	+	58.2267i	1.40193	+	2.42822i
$576$	5.92208	−	10.2573i	0.246753	−	0.427389i
$577$	3.56704			0.148498			0.0742489	−	0.997240i	$-0.476344\pi$
$577$	3.56704			0.148498			0.0742489	+	0.997240i	$0.476344\pi$
$578$	9.85450	−	17.0685i	0.409893	−	0.709956i
$579$	12.8720	−	22.2949i	0.534940	−	0.926544i
$580$	50.5424			2.09866
$581$	2.82640	−	4.89546i	0.117259	−	0.203098i
$582$	−7.00514	−	12.1333i	−0.290372	−	0.502940i
$583$	−14.1984	−	24.5923i	−0.588036	−	1.01851i
$584$	−43.5669			−1.80281
$585$		0			0
$586$	−62.5120			−2.58235
$587$	8.05861	+	13.9579i	0.332614	+	0.576105i	0.983024	−	0.183479i	$-0.0587360\pi$
$587$	8.05861	+	13.9579i	0.332614	+	0.576105i	−0.650409	+	0.759584i	$0.725403\pi$
$588$	−11.2992	−	19.5709i	−0.465973	−	0.807089i
$589$	2.86658	−	4.96507i	0.118116	−	0.204582i
$590$	−46.8504			−1.92880
$591$	10.7104	−	18.5510i	0.440569	−	0.763087i
$592$	−5.68731	+	9.85071i	−0.233747	+	0.404862i
$593$	−42.8611			−1.76010			−0.880048	−	0.474885i	$-0.842490\pi$
$593$	−42.8611			−1.76010			−0.880048	+	0.474885i	$0.842490\pi$
$594$	−3.35958	+	5.81897i	−0.137845	+	0.238755i
$595$	4.35086	+	7.53590i	0.178368	+	0.308942i
$596$	−34.4934	−	59.7444i	−1.41291	−	2.44722i
$597$	−3.52781			−0.144384
$598$		0			0
$599$	40.9420			1.67284			0.836422	−	0.548086i	$-0.184643\pi$
$599$	40.9420			1.67284			0.836422	+	0.548086i	$0.184643\pi$
$600$	15.8158	+	27.3938i	0.645678	+	1.11835i
$601$	−0.593523	−	1.02801i	−0.0242103	−	0.0419335i	0.853666	−	0.520820i	$-0.174374\pi$
$601$	−0.593523	−	1.02801i	−0.0242103	−	0.0419335i	−0.877877	+	0.478887i	$0.841040\pi$
$602$	−1.52715	+	2.64510i	−0.0622419	+	0.107806i
$603$	14.3937			0.586158
$604$	21.9737	−	38.0595i	0.894096	−	1.54862i
$605$	5.30290	−	9.18489i	0.215593	−	0.373419i
$606$	−10.9022			−0.442870
$607$	−9.99612	+	17.3138i	−0.405730	+	0.702745i	−0.994406	−	0.105624i	$-0.966316\pi$
$607$	−9.99612	+	17.3138i	−0.405730	+	0.702745i	0.588676	+	0.808369i	$0.299649\pi$
$608$	−4.55861	−	7.89574i	−0.184876	−	0.320214i
$609$	−1.54407	−	2.67441i	−0.0625690	−	0.108373i
$610$	−115.356			−4.67062
$611$		0			0
$612$	10.4480			0.422336
$613$	16.6809	+	28.8922i	0.673735	+	1.16694i	0.976837	+	0.213985i	$0.0686445\pi$
$613$	16.6809	+	28.8922i	0.673735	+	1.16694i	−0.303102	+	0.952958i	$0.598022\pi$
$614$	9.71864	+	16.8332i	0.392212	+	0.679332i
$615$	−1.57069	+	2.72051i	−0.0633362	+	0.109702i
$616$	8.37867			0.337586
$617$	−5.81163	+	10.0660i	−0.233967	+	0.405243i	−0.958972	−	0.283501i	$-0.908504\pi$
$617$	−5.81163	+	10.0660i	−0.233967	+	0.405243i	0.725005	+	0.688744i	$0.241838\pi$
$618$	1.42327	−	2.46518i	0.0572524	−	0.0991640i
$619$	−16.5381			−0.664722			−0.332361	−	0.943152i	$-0.607845\pi$
$619$	−16.5381			−0.664722			−0.332361	+	0.943152i	$0.607845\pi$
$620$	−15.3878	+	26.6525i	−0.617990	+	1.07039i
$621$	−3.89493	−	6.74621i	−0.156298	−	0.270716i
$622$	16.9907	+	29.4288i	0.681267	+	1.17999i
$623$	−0.907542			−0.0363599
$624$		0			0
$625$	6.33944			0.253577
$626$	−16.7738	−	29.0531i	−0.670417	−	1.16120i
$627$	3.48523	+	6.03660i	0.139187	+	0.241078i
$628$	33.1989	−	57.5023i	1.32478	−	2.29459i
$629$	21.8810			0.872452
$630$	3.48911	−	6.04332i	0.139010	−	0.240772i
$631$	18.2208	−	31.5593i	0.725358	−	1.25636i	−0.233468	−	0.972364i	$-0.575007\pi$
$631$	18.2208	−	31.5593i	0.725358	−	1.25636i	0.958826	−	0.283993i	$-0.0916592\pi$
$632$	19.8116			0.788064
$633$	0.607760	−	1.05267i	0.0241563	−	0.0418399i
$634$	8.06547	+	13.9698i	0.320321	+	0.554812i
$635$	−10.4673	−	18.1300i	−0.415384	−	0.719466i
$636$	35.4101			1.40410
$637$		0			0
$638$	−25.8745			−1.02438
$639$	−4.06249	−	7.03644i	−0.160710	−	0.278357i
$640$	37.7652	+	65.4112i	1.49280	+	2.58560i
$641$	−13.6033	+	23.5617i	−0.537300	+	0.930630i	0.461748	+	0.887011i	$0.347222\pi$
$641$	−13.6033	+	23.5617i	−0.537300	+	0.930630i	−0.999048	+	0.0436195i	$0.986111\pi$
$642$	22.4403			0.885646
$643$	2.53481	−	4.39042i	0.0999632	−	0.173141i	−0.811706	−	0.584066i	$-0.801461\pi$
$643$	2.53481	−	4.39042i	0.0999632	−	0.173141i	0.911669	+	0.410925i	$0.134794\pi$
$644$	−11.1039	+	19.2325i	−0.437554	+	0.757866i
$645$	5.96615			0.234917
$646$	8.46830	−	14.6675i	0.333181	−	0.577086i
$647$	−9.66033	−	16.7322i	−0.379787	−	0.657810i	0.611244	−	0.791442i	$-0.290669\pi$
$647$	−9.66033	−	16.7322i	−0.379787	−	0.657810i	−0.991031	+	0.133632i	$0.957336\pi$
$648$	−1.83244	−	3.17387i	−0.0719849	−	0.124682i
$649$	15.3491			0.602506
$650$		0			0
$651$	1.88040			0.0736985
$652$	−21.9331	−	37.9892i	−0.858966	−	1.48777i
$653$	−17.6177	−	30.5148i	−0.689436	−	1.19414i	−0.972021	−	0.234895i	$-0.924525\pi$
$653$	−17.6177	−	30.5148i	−0.689436	−	1.19414i	0.282585	−	0.959242i	$-0.408808\pi$
$654$	−2.10292	+	3.64236i	−0.0822305	+	0.142427i
$655$	67.2790			2.62881
$656$	0.649973	−	1.12579i	0.0253772	−	0.0439546i
$657$	5.94385	−	10.2950i	0.231891	−	0.401648i
$658$	−4.62133			−0.180158
$659$	2.18084	−	3.77733i	0.0849535	−	0.147144i	−0.820418	−	0.571764i	$-0.806259\pi$
$659$	2.18084	−	3.77733i	0.0849535	−	0.147144i	0.905371	+	0.424621i	$0.139592\pi$
$660$	−18.7087	−	32.4044i	−0.728236	−	1.26134i
$661$	7.73543	+	13.3982i	0.300873	+	0.521128i	0.976334	−	0.216268i	$-0.0693885\pi$
$661$	7.73543	+	13.3982i	0.300873	+	0.521128i	−0.675461	+	0.737396i	$0.736055\pi$
$662$	22.2553			0.864978
$663$		0			0
$664$	25.8334			1.00253
$665$	−3.61960	−	6.26934i	−0.140362	−	0.243115i
$666$	−8.77359	−	15.1963i	−0.339970	−	0.588845i
$667$	14.9988	−	25.9787i	0.580756	−	1.00590i
$668$	40.8605			1.58094
$669$	−8.69418	+	15.0588i	−0.336136	+	0.582205i
$670$	−62.6250	+	108.470i	−2.41942	+	4.19055i
$671$	37.7928			1.45898
$672$	1.49516	−	2.58969i	0.0576769	−	0.0998993i
$673$	5.87047	+	10.1680i	0.226290	+	0.391946i	0.956706	−	0.291057i	$-0.0940070\pi$
$673$	5.87047	+	10.1680i	0.226290	+	0.391946i	−0.730416	+	0.683003i	$0.760674\pi$
$674$	−3.11476	−	5.39492i	−0.119976	−	0.207805i
$675$	−8.63102			−0.332208
$676$		0			0
$677$	3.44504			0.132404			0.0662019	−	0.997806i	$-0.478912\pi$
$677$	3.44504			0.132404			0.0662019	+	0.997806i	$0.478912\pi$
$678$	5.83459	+	10.1058i	0.224076	+	0.388111i
$679$	−2.38351	−	4.12836i	−0.0914707	−	0.158432i
$680$	−19.8835	+	34.4393i	−0.762498	+	1.32068i
$681$	−17.4155			−0.667363
$682$	7.87760	−	13.6444i	0.301649	−	0.522471i
$683$	−10.2029	+	17.6720i	−0.390403	+	0.676198i	−0.992503	−	0.122223i	$-0.960998\pi$
$683$	−10.2029	+	17.6720i	−0.390403	+	0.676198i	0.602099	+	0.798421i	$0.294331\pi$
$684$	−8.69202			−0.332348
$685$	−17.4456	+	30.2166i	−0.666561	+	1.15452i
$686$	−12.6228	−	21.8634i	−0.481942	−	0.834748i
$687$	9.38016	+	16.2469i	0.357875	+	0.619858i
$688$	−2.46888			−0.0941251
$689$		0			0
$690$	67.7851			2.58053
$691$	−13.9019	−	24.0788i	−0.528854	−	0.916002i	−0.999434	−	0.0336449i	$-0.989288\pi$
$691$	−13.9019	−	24.0788i	−0.528854	−	0.916002i	0.470580	−	0.882358i	$-0.344045\pi$
$692$	−21.5328	−	37.2959i	−0.818554	−	1.41778i
$693$	−1.14310	+	1.97991i	−0.0434229	+	0.0752107i
$694$	−23.9433			−0.908876
$695$	−7.41185	+	12.8377i	−0.281148	+	0.486962i
$696$	7.05645	−	12.2221i	0.267474	−	0.463279i
$697$	−2.50066			−0.0947194
$698$	−12.3026	+	21.3087i	−0.465660	+	0.806547i
$699$	1.97554	+	3.42174i	0.0747218	+	0.129422i
$700$	12.3029	+	21.3092i	0.465006	+	0.805414i
$701$	11.9715			0.452158			0.226079	−	0.974109i	$-0.427409\pi$
$701$	11.9715			0.452158			0.226079	+	0.974109i	$0.427409\pi$
$702$		0			0
$703$	−18.2034			−0.686556
$704$	−16.8830	−	29.2422i	−0.636301	−	1.10211i
$705$	4.51357	+	7.81774i	0.169991	+	0.294433i
$706$	−21.5551	+	37.3346i	−0.811238	+	1.40510i
$707$	−3.70948			−0.139509
$708$	−9.57002	+	16.5758i	−0.359664	+	0.622955i
$709$	−16.1332	+	27.9435i	−0.605894	+	1.04944i	0.386015	+	0.922492i	$0.373851\pi$
$709$	−16.1332	+	27.9435i	−0.605894	+	1.04944i	−0.991909	+	0.126947i	$0.959482\pi$
$710$	70.7012			2.65337
$711$	−2.70291	+	4.68157i	−0.101367	+	0.175573i
$712$	−2.07374	−	3.59183i	−0.0777169	−	0.134610i
$713$	9.13288	+	15.8186i	0.342029	+	0.592412i
$714$	5.55496			0.207889
$715$		0			0
$716$	−1.91457			−0.0715510
$717$	0.409166	+	0.708696i	0.0152806	+	0.0264667i
$718$	17.9985	+	31.1743i	0.671698	+	1.16342i
$719$	−6.05429	+	10.4863i	−0.225787	+	0.391075i	−0.956555	−	0.291551i	$-0.905829\pi$
$719$	−6.05429	+	10.4863i	−0.225787	+	0.391075i	0.730768	+	0.682626i	$0.239162\pi$
$720$	5.64071			0.210217
$721$	0.484271	−	0.838781i	0.0180352	−	0.0312378i
$722$	15.3455	−	26.5791i	0.571100	−	0.989173i
$723$	−6.03252			−0.224352
$724$	41.3865	−	71.6835i	1.53812	−	2.66410i
$725$	−16.6184	−	28.7839i	−0.617192	−	1.06901i
$726$	−3.38524	−	5.86341i	−0.125638	−	0.217611i
$727$	−16.6200			−0.616402			−0.308201	−	0.951321i	$-0.599727\pi$
$727$	−16.6200			−0.616402			−0.308201	+	0.951321i	$0.599727\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	51.7216	+	89.5845i	1.91430	+	3.31567i
$731$	2.37465	+	4.11301i	0.0878296	+	0.152125i
$732$	−23.5635	+	40.8131i	−0.870930	+	1.50850i
$733$	17.7912			0.657132			0.328566	−	0.944481i	$-0.393435\pi$
$733$	17.7912			0.657132			0.328566	+	0.944481i	$0.393435\pi$
$734$	26.2461	−	45.4595i	0.968760	−	1.67794i
$735$	−11.7349	+	20.3254i	−0.432848	+	0.749715i
$736$	29.0473			1.07070
$737$	20.5172	−	35.5369i	0.755762	−	1.30902i
$738$	1.00269	+	1.73671i	0.0369095	+	0.0639291i
$739$	13.6809	+	23.6960i	0.503260	+	0.871672i	0.999993	+	0.00376844i	$0.00119954\pi$
$739$	13.6809	+	23.6960i	0.503260	+	0.871672i	−0.496733	+	0.867903i	$0.665467\pi$
$740$	97.7160			3.59211
$741$		0			0
$742$	18.8267			0.691150
$743$	−4.19298	−	7.26246i	−0.153826	−	0.266434i	0.778805	−	0.627266i	$-0.215826\pi$
$743$	−4.19298	−	7.26246i	−0.153826	−	0.266434i	−0.932631	+	0.360832i	$0.882493\pi$
$744$	4.29672	+	7.44215i	0.157526	+	0.272842i
$745$	−35.8233	+	62.0478i	−1.31247	+	2.27326i
$746$	9.72528			0.356068
$747$	−3.52446	+	6.10454i	−0.128953	+	0.223353i
$748$	14.8929	−	25.7953i	0.544538	−	0.943168i
$749$	7.63533			0.278989
$750$	15.7981	−	27.3630i	0.576863	−	0.999157i
$751$	19.3889	+	33.5825i	0.707511	+	1.22544i	0.965778	+	0.259371i	$0.0835151\pi$
$751$	19.3889	+	33.5825i	0.707511	+	1.22544i	−0.258267	+	0.966073i	$0.583152\pi$
$752$	−1.86778	−	3.23509i	−0.0681110	−	0.117972i
$753$	26.8799			0.979559
$754$		0			0
$755$	−45.6418			−1.66107
$756$	−1.42543	−	2.46891i	−0.0518423	−	0.0897935i
$757$	−6.48643	−	11.2348i	−0.235753	−	0.408336i	0.723738	−	0.690075i	$-0.242422\pi$
$757$	−6.48643	−	11.2348i	−0.235753	−	0.408336i	−0.959491	+	0.281738i	$0.909089\pi$
$758$	12.6177	−	21.8546i	0.458297	−	0.793794i
$759$	−22.2078			−0.806090
$760$	16.5417	−	28.6510i	0.600030	−	1.03928i
$761$	2.57792	−	4.46510i	0.0934497	−	0.161860i	−0.815511	−	0.578742i	$-0.803544\pi$
$761$	2.57792	−	4.46510i	0.0934497	−	0.161860i	0.908961	+	0.416882i	$0.136877\pi$
$762$	−13.3642			−0.484134
$763$	−0.715521	+	1.23932i	−0.0259036	+	0.0448663i
$764$	−29.8007	−	51.6163i	−1.07815	−	1.86741i
$765$	−5.42543	−	9.39712i	−0.196157	−	0.339753i
$766$	15.3822			0.555783
$767$		0			0
$768$	24.5284			0.885092
$769$	17.7506	+	30.7450i	0.640104	+	1.10869i	0.985409	+	0.170202i	$0.0544421\pi$
$769$	17.7506	+	30.7450i	0.640104	+	1.10869i	−0.345305	+	0.938490i	$0.612225\pi$
$770$	−9.94696	−	17.2286i	−0.358464	−	0.620877i
$771$	−4.52661	+	7.84033i	−0.163022	+	0.282362i
$772$	91.5186			3.29383
$773$	3.07792	−	5.33112i	0.110705	−	0.191747i	−0.805350	−	0.592800i	$-0.798022\pi$
$773$	3.07792	−	5.33112i	0.110705	−	0.191747i	0.916055	+	0.401053i	$0.131356\pi$
$774$	1.90432	−	3.29838i	0.0684494	−	0.118558i
$775$	20.2381			0.726976
$776$	10.8927	−	18.8667i	0.391025	−	0.677275i
$777$	−2.98523	−	5.17057i	−0.107095	−	0.185493i
$778$	13.8966	+	24.0695i	0.498216	+	0.862935i
$779$	2.08038			0.0745372
$780$		0			0
$781$	−23.1631			−0.828843
$782$	26.9799	+	46.7305i	0.964798	+	1.67108i
$783$	1.92543	+	3.33494i	0.0688092	+	0.119181i
$784$	4.85607	−	8.41096i	0.173431	−	0.300391i
$785$	−68.9579			−2.46121
$786$	21.4746	−	37.1952i	0.765975	−	1.32671i
$787$	−7.10537	+	12.3069i	−0.253279	+	0.438692i	−0.964427	−	0.264351i	$-0.914842\pi$
$787$	−7.10537	+	12.3069i	−0.253279	+	0.438692i	0.711148	+	0.703043i	$0.248176\pi$
$788$	76.1503			2.71274
$789$	11.5755	−	20.0494i	0.412100	−	0.713778i
$790$	−23.5199	−	40.7377i	−0.836801	−	1.44938i
$791$	1.98523	+	3.43852i	0.0705867	+	0.122260i
$792$	−10.4480			−0.371254
$793$		0			0
$794$	−29.5623			−1.04913
$795$	−18.3877	−	31.8484i	−0.652144	−	1.12955i
$796$	−6.27061	−	10.8610i	−0.222256	−	0.384958i
$797$	−5.95108	+	10.3076i	−0.210798	+	0.365113i	−0.951965	−	0.306208i	$-0.900940\pi$
$797$	−5.95108	+	10.3076i	−0.210798	+	0.365113i	0.741166	+	0.671321i	$0.234273\pi$
$798$	−4.62133			−0.163593
$799$	−3.59299	+	6.22324i	−0.127111	+	0.220162i
$800$	16.0919	−	27.8720i	0.568935	−	0.985425i
$801$	1.13169			0.0399862
$802$	−21.0591	+	36.4755i	−0.743624	+	1.28799i
$803$	−16.9450	−	29.3497i	−0.597978	−	1.03573i
$804$	25.5846	+	44.3138i	0.902298	+	1.56283i
$805$	23.0640			0.812899
$806$		0			0
$807$	2.42088			0.0852190
$808$	−8.47621	−	14.6812i	−0.298192	−	0.516483i
$809$	−0.807979	−	1.39946i	−0.0284070	−	0.0492024i	0.851472	−	0.524399i	$-0.175710\pi$
$809$	−0.807979	−	1.39946i	−0.0284070	−	0.0492024i	−0.879879	+	0.475197i	$0.842377\pi$
$810$	−4.35086	+	7.53590i	−0.152873	+	0.264785i
$811$	−51.9657			−1.82476			−0.912381	−	0.409342i	$-0.865758\pi$
$811$	−51.9657			−1.82476			−0.912381	+	0.409342i	$0.865758\pi$
$812$	5.48911	−	9.50743i	0.192630	−	0.333645i
$813$	−10.7225	+	18.5720i	−0.376055	+	0.651347i
$814$	−50.0245			−1.75336
$815$	−22.7787	+	39.4539i	−0.797904	+	1.38201i
$816$	2.24512	+	3.88866i	0.0785949	+	0.136130i
$817$	−1.97554	−	3.42174i	−0.0691154	−	0.119711i
$818$	−65.7853			−2.30013
$819$		0			0
$820$	−11.1675			−0.389985
$821$	−27.4163	−	47.4865i	−0.956837	−	1.65729i	−0.730108	−	0.683331i	$-0.760530\pi$
$821$	−27.4163	−	47.4865i	−0.956837	−	1.65729i	−0.226728	−	0.973958i	$-0.572803\pi$
$822$	11.1368	+	19.2895i	0.388441	+	0.672800i
$823$	23.4257	−	40.5745i	0.816569	−	1.41434i	−0.0916262	−	0.995793i	$-0.529206\pi$
$823$	23.4257	−	40.5745i	0.816569	−	1.41434i	0.908196	−	0.418546i	$-0.137460\pi$
$824$	4.42626			0.154196
$825$	−12.3029	+	21.3092i	−0.428332	+	0.741893i
$826$	−5.08815	+	8.81293i	−0.177039	+	0.306641i
$827$	21.2021			0.737270			0.368635	−	0.929574i	$-0.379825\pi$
$827$	21.2021			0.737270			0.368635	+	0.929574i	$0.379825\pi$
$828$	13.8463	−	23.9825i	0.481192	−	0.833450i
$829$	−9.14861	−	15.8459i	−0.317744	−	0.550350i	0.662273	−	0.749263i	$-0.269592\pi$
$829$	−9.14861	−	15.8459i	−0.317744	−	0.550350i	−0.980017	+	0.198913i	$0.936259\pi$
$830$	−30.6688	−	53.1200i	−1.06453	−	1.84382i
$831$	14.8073			0.513660
$832$		0			0
$833$	−18.6829			−0.647325
$834$	4.73155	+	8.19528i	0.163840	+	0.283779i
$835$	−21.2180	−	36.7506i	−0.734278	−	1.27181i
$836$	−12.3898	+	21.4598i	−0.428512	+	0.742204i
$837$	−2.34481			−0.0810486
$838$	19.3306	−	33.4815i	0.667764	−	1.15660i
$839$	−10.5707	+	18.3090i	−0.364941	+	0.632096i	−0.988767	−	0.149468i	$-0.952244\pi$
$839$	−10.5707	+	18.3090i	−0.364941	+	0.632096i	0.623826	+	0.781563i	$0.285577\pi$
$840$	10.8509			0.374390
$841$	7.08546	−	12.2724i	0.244326	−	0.423185i
$842$	3.57875	+	6.19858i	0.123332	+	0.213617i
$843$	7.25182	+	12.5605i	0.249766	+	0.432608i
$844$	4.32113			0.148739
$845$		0			0
$846$	5.76271			0.198126
$847$	−1.15183	−	1.99503i	−0.0395775	−	0.0685502i
$848$	7.60909	+	13.1793i	0.261297	+	0.452580i
$849$	12.8361	−	22.2328i	0.440533	−	0.763026i
$850$	59.7864			2.05066
$851$	28.9979	−	50.2258i	0.994035	−	1.72172i
$852$	14.4420	−	25.0143i	0.494774	−	0.856974i
$853$	−7.13036			−0.244139			−0.122069	−	0.992522i	$-0.538953\pi$
$853$	−7.13036			−0.244139			−0.122069	+	0.992522i	$0.538953\pi$
$854$	−12.5281	+	21.6993i	−0.428703	+	0.742535i
$855$	4.51357	+	7.81774i	0.154361	+	0.267361i
$856$	17.4468	+	30.2188i	0.596320	+	1.03286i
$857$	−44.7741			−1.52945			−0.764726	−	0.644355i	$-0.777126\pi$
$857$	−44.7741			−1.52945			−0.764726	+	0.644355i	$0.777126\pi$
$858$		0			0
$859$	57.3782			1.95772			0.978859	−	0.204535i	$-0.0655681\pi$
$859$	57.3782			1.95772			0.978859	+	0.204535i	$0.0655681\pi$
$860$	10.6047	+	18.3679i	0.361617	+	0.626340i
$861$	0.341166	+	0.590918i	0.0116269	+	0.0201384i
$862$	3.93379	−	6.81352i	0.133985	−	0.232069i
$863$	−6.67563			−0.227241			−0.113621	−	0.993524i	$-0.536245\pi$
$863$	−6.67563			−0.227241			−0.113621	+	0.993524i	$0.536245\pi$
$864$	−1.86443	+	3.22929i	−0.0634291	+	0.109863i
$865$	−22.3630	+	38.7338i	−0.760365	+	1.31699i
$866$	28.0536			0.953299
$867$	−4.18114	+	7.24194i	−0.141999	+	0.245949i
$868$	3.34236	+	5.78914i	0.113447	+	0.196496i
$869$	7.70560	+	13.3465i	0.261394	+	0.452748i
$870$	−33.5090			−1.13606
$871$		0			0
$872$	−6.53989			−0.221469
$873$	2.97219	+	5.14798i	0.100593	+	0.174233i
$874$	−22.4453	−	38.8765i	−0.759225	−	1.31502i
$875$	5.37531	−	9.31032i	0.181719	−	0.314746i
$876$	42.2602			1.42784
$877$	−12.6491	+	21.9090i	−0.427131	+	0.739813i	−0.996617	−	0.0821883i	$-0.973809\pi$
$877$	−12.6491	+	21.9090i	−0.427131	+	0.739813i	0.569486	+	0.822001i	$0.307142\pi$
$878$	−4.38159	+	7.58914i	−0.147872	+	0.256121i
$879$	26.5230			0.894599
$880$	8.04043	−	13.9264i	0.271043	−	0.469460i
$881$	17.6893	+	30.6388i	0.595969	+	1.03225i	0.993409	+	0.114620i	$0.0365651\pi$
$881$	17.6893	+	30.6388i	0.595969	+	1.03225i	−0.397441	+	0.917628i	$0.630102\pi$
$882$	7.49127	+	12.9753i	0.252244	+	0.436900i
$883$	−11.5851			−0.389869			−0.194935	−	0.980816i	$-0.562449\pi$
$883$	−11.5851			−0.389869			−0.194935	+	0.980816i	$0.562449\pi$
$884$		0			0
$885$	19.8780			0.668192
$886$	−1.71714	−	2.97418i	−0.0576886	−	0.0999196i
$887$	13.6446	+	23.6331i	0.458141	+	0.793523i	0.998863	−	0.0476784i	$-0.0151822\pi$
$887$	13.6446	+	23.6331i	0.458141	+	0.793523i	−0.540722	+	0.841201i	$0.681849\pi$
$888$	13.6426	−	23.6296i	0.457815	−	0.792958i
$889$	−4.54719			−0.152508
$890$	−4.92380	+	8.52828i	−0.165046	+	0.285869i
$891$	1.42543	−	2.46891i	0.0477536	−	0.0827117i
$892$	−61.8149			−2.06972
$893$	2.98911	−	5.17730i	0.100027	−	0.173252i
$894$	22.8687	+	39.6098i	0.764845	+	1.32475i
$895$	0.994196	+	1.72200i	0.0332323	+	0.0575601i
$896$	16.4058			0.548080
$897$		0			0
$898$	−28.5830			−0.953826
$899$	−4.51477	−	7.81981i	−0.150576	−	0.260805i
$900$	−15.3415	−	26.5722i	−0.511382	−	0.885740i
$901$	14.6374	−	25.3526i	0.487641	−	0.844619i
$902$	5.71704			0.190357
$903$	0.647948	−	1.12228i	0.0215624	−	0.0373471i
$904$	−9.07255	+	15.7141i	−0.301748	+	0.522644i
$905$	−85.9643			−2.85755
$906$	−14.5683	+	25.2330i	−0.483999	+	0.838311i
$907$	15.2110	+	26.3462i	0.505072	+	0.874810i	0.999983	+	0.00586661i	$0.00186741\pi$
$907$	15.2110	+	26.3462i	0.505072	+	0.874810i	−0.494911	+	0.868944i	$0.664799\pi$
$908$	−30.9557	−	53.6168i	−1.02730	−	1.77934i
$909$	4.62565			0.153423
$910$		0			0
$911$	53.5719			1.77492			0.887459	−	0.460887i	$-0.152469\pi$
$911$	53.5719			1.77492			0.887459	+	0.460887i	$0.152469\pi$
$912$	−1.86778	−	3.23509i	−0.0618484	−	0.107125i
$913$	10.0477	+	17.4032i	0.332531	+	0.575961i
$914$	4.06332	−	7.03787i	0.134403	−	0.232792i
$915$	48.9439			1.61804
$916$	−33.3461	+	57.7571i	−1.10179	+	1.90835i
$917$	7.30678	−	12.6557i	0.241291	−	0.417929i
$918$	−6.92692			−0.228622
$919$	18.0836	−	31.3217i	0.596523	−	1.03321i	−0.396807	−	0.917902i	$-0.629882\pi$
$919$	18.0836	−	31.3217i	0.596523	−	1.03321i	0.993330	−	0.115306i	$-0.0367848\pi$
$920$	52.7015	+	91.2816i	1.73752	+	3.00947i
$921$	−4.12349	−	7.14209i	−0.135874	−	0.235340i
$922$	−15.9232			−0.524403
$923$		0			0
$924$	−8.12737			−0.267371
$925$	−32.1292	−	55.6493i	−1.05640	−	1.82974i
$926$	8.78150	+	15.2100i	0.288578	+	0.499831i
$927$	−0.603875	+	1.04594i	−0.0198339	+	0.0343533i
$928$	−14.3593			−0.471367
$929$	6.67390	−	11.5595i	0.218964	−	0.379256i	−0.735528	−	0.677494i	$-0.763066\pi$
$929$	6.67390	−	11.5595i	0.218964	−	0.379256i	0.954491	+	0.298239i	$0.0963991\pi$
$930$	10.2019	−	17.6703i	0.334535	−	0.579432i
$931$	15.5429			0.509397
$932$	−7.02297	+	12.1641i	−0.230045	+	0.398449i
$933$	−7.20895	−	12.4863i	−0.236010	−	0.408782i
$934$	−38.4290	−	66.5610i	−1.25744	−	2.17794i
$935$	−30.9342			−1.01166
$936$		0			0
$937$	38.6872			1.26386			0.631928	−	0.775027i	$-0.282264\pi$
$937$	38.6872			1.26386			0.631928	+	0.775027i	$0.282264\pi$
$938$	13.6027	+	23.5605i	0.444143	+	0.769279i
$939$	7.11692	+	12.3269i	0.232252	+	0.402272i
$940$	−16.0456	+	27.7917i	−0.523349	+	0.906466i
$941$	35.7275			1.16468			0.582342	−	0.812944i	$-0.302136\pi$
$941$	35.7275			1.16468			0.582342	+	0.812944i	$0.302136\pi$
$942$	−22.0105	+	38.1233i	−0.717141	+	1.24213i
$943$	−3.31402	+	5.74005i	−0.107919	+	0.186922i
$944$	−8.22580			−0.267727
$945$	−1.48039	+	2.56410i	−0.0481569	+	0.0834103i
$946$	−5.42894	−	9.40321i	−0.176510	−	0.305725i
$947$	8.92178	+	15.4530i	0.289919	+	0.502154i	0.973790	−	0.227448i	$-0.0730383\pi$
$947$	8.92178	+	15.4530i	0.289919	+	0.502154i	−0.683871	+	0.729603i	$0.739705\pi$
$948$	−19.2174			−0.624153
$949$		0			0
$950$	−49.7381			−1.61372
$951$	−3.42208	−	5.92721i	−0.110968	−	0.192203i
$952$	4.31886	+	7.48049i	0.139975	+	0.242444i
$953$	−10.0846	+	17.4670i	−0.326671	+	0.565810i	−0.981849	−	0.189664i	$-0.939260\pi$
$953$	−10.0846	+	17.4670i	−0.326671	+	0.565810i	0.655178	+	0.755474i	$0.272594\pi$
$954$	−23.4765			−0.760080
$955$	−30.9496	+	53.6064i	−1.00151	+	1.73466i
$956$	−1.45457	+	2.51938i	−0.0470440	+	0.0814827i
$957$	10.9782			0.354876
$958$	−3.33393	+	5.77453i	−0.107714	+	0.186567i
$959$	3.78932	+	6.56330i	0.122364	+	0.211940i
$960$	−21.8644	−	37.8703i	−0.705671	−	1.22226i
$961$	−25.5018			−0.822640
$962$		0			0
$963$	−9.52111			−0.306813
$964$	−10.7227	−	18.5722i	−0.345354	−	0.598171i
$965$	−47.5236	−	82.3132i	−1.52984	−	2.64976i
$966$	7.36174	−	12.7509i	0.236860	−	0.410254i
$967$	−32.7894			−1.05444			−0.527218	−	0.849730i	$-0.676765\pi$
$967$	−32.7894			−1.05444			−0.527218	+	0.849730i	$0.676765\pi$
$968$	5.26391	−	9.11735i	0.169188	−	0.293043i
$969$	−3.59299	+	6.22324i	−0.115423	+	0.199919i
$970$	−51.7263			−1.66083
$971$	13.4922	−	23.3692i	0.432986	−	0.749954i	−0.564143	−	0.825677i	$-0.690793\pi$
$971$	13.4922	−	23.3692i	0.432986	−	0.749954i	0.997129	+	0.0757231i	$0.0241265\pi$
$972$	1.77748	+	3.07868i	0.0570127	+	0.0987488i
$973$	1.60992	+	2.78846i	0.0516115	+	0.0893938i
$974$	−97.3245			−3.11848
$975$		0			0
$976$	−20.2537			−0.648305
$977$	8.47853	+	14.6852i	0.271252	+	0.469822i	0.969183	−	0.246343i	$-0.0792290\pi$
$977$	8.47853	+	14.6852i	0.271252	+	0.469822i	−0.697931	+	0.716165i	$0.745896\pi$
$978$	14.5414	+	25.1864i	0.464982	+	0.805373i
$979$	1.61314	−	2.79404i	0.0515561	−	0.0892978i
$980$	−83.4341			−2.66521
$981$	0.892240	−	1.54540i	0.0284870	−	0.0493410i
$982$	40.8565	−	70.7656i	1.30378	−	2.25822i
$983$	−32.6631			−1.04179			−0.520895	−	0.853621i	$-0.674402\pi$
$983$	−32.6631			−1.04179			−0.520895	+	0.853621i	$0.674402\pi$
$984$	−1.55914	+	2.70051i	−0.0497035	+	0.0860890i
$985$	−39.5432	−	68.4908i	−1.25995	−	2.18230i
$986$	−13.3373	−	23.1008i	−0.424746	−	0.735681i
$987$	1.96077			0.0624120
$988$		0			0
$989$	12.5881			0.400277
$990$	12.4037	+	21.4838i	0.394214	+	0.682799i
$991$	−3.82155	−	6.61912i	−0.121396	−	0.210263i	0.798923	−	0.601434i	$-0.205404\pi$
$991$	−3.82155	−	6.61912i	−0.121396	−	0.210263i	−0.920318	+	0.391170i	$0.872070\pi$
$992$	4.37174	−	7.57207i	0.138803	−	0.240414i
$993$	−9.44265			−0.299653
$994$	7.67845	−	13.2995i	0.243546	−	0.421833i
$995$	−6.51238	+	11.2798i	−0.206456	+	0.357593i
$996$	−25.0586			−0.794012
$997$	−18.0628	+	31.2857i	−0.572054	+	0.990827i	0.424301	+	0.905521i	$0.360520\pi$
$997$	−18.0628	+	31.2857i	−0.572054	+	0.990827i	−0.996355	+	0.0853055i	$0.972813\pi$
$998$	−21.1424	−	36.6198i	−0.669252	−	1.15918i
$999$	3.72252	+	6.44760i	0.117775	+	0.203993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.e.i.484.2		6
13.2	odd	12		507.2.b.f.337.2		6
13.3	even	3		507.2.a.l.1.2	yes	3
13.4	even	6		507.2.e.l.22.2		6
13.5	odd	4		507.2.j.i.361.2		12
13.6	odd	12		507.2.j.i.316.5		12
13.7	odd	12		507.2.j.i.316.2		12
13.8	odd	4		507.2.j.i.361.5		12
13.9	even	3	inner	507.2.e.i.22.2		6
13.10	even	6		507.2.a.i.1.2	✓	3
13.11	odd	12		507.2.b.f.337.5		6
13.12	even	2		507.2.e.l.484.2		6
39.2	even	12		1521.2.b.k.1351.5		6
39.11	even	12		1521.2.b.k.1351.2		6
39.23	odd	6		1521.2.a.s.1.2		3
39.29	odd	6		1521.2.a.n.1.2		3
52.3	odd	6		8112.2.a.cp.1.3		3
52.23	odd	6		8112.2.a.cg.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.i.1.2	✓	3	13.10	even	6
507.2.a.l.1.2	yes	3	13.3	even	3
507.2.b.f.337.2		6	13.2	odd	12
507.2.b.f.337.5		6	13.11	odd	12
507.2.e.i.22.2		6	13.9	even	3	inner
507.2.e.i.484.2		6	1.1	even	1	trivial
507.2.e.l.22.2		6	13.4	even	6
507.2.e.l.484.2		6	13.12	even	2
507.2.j.i.316.2		12	13.7	odd	12
507.2.j.i.316.5		12	13.6	odd	12
507.2.j.i.361.2		12	13.5	odd	4
507.2.j.i.361.5		12	13.8	odd	4
1521.2.a.n.1.2		3	39.29	odd	6
1521.2.a.s.1.2		3	39.23	odd	6
1521.2.b.k.1351.2		6	39.11	even	12
1521.2.b.k.1351.5		6	39.2	even	12
8112.2.a.cg.1.1		3	52.23	odd	6
8112.2.a.cp.1.3		3	52.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.17845 - 2.04113i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.77748 + 3.07868i) q^{4} +3.69202 q^{5} +(1.17845 - 2.04113i) q^{6} +(0.400969 - 0.694498i) q^{7} +3.66487 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.35086 - 7.53590i) q^{10} +(1.42543 + 2.46891i) q^{11} -3.55496 q^{12} -1.89008 q^{14} +(1.84601 + 3.19738i) q^{15} +(-0.763906 - 1.32312i) q^{16} +(-1.46950 + 2.54525i) q^{17} +2.35690 q^{18} +(1.22252 - 2.11747i) q^{19} +(-6.56249 + 11.3666i) q^{20} +0.801938 q^{21} +(3.35958 - 5.81897i) q^{22} +(3.89493 + 6.74621i) q^{23} +(1.83244 + 3.17387i) q^{24} +8.63102 q^{25} -1.00000 q^{27} +(1.42543 + 2.46891i) q^{28} +(-1.92543 - 3.33494i) q^{29} +(4.35086 - 7.53590i) q^{30} +2.34481 q^{31} +(1.86443 - 3.22929i) q^{32} +(-1.42543 + 2.46891i) q^{33} +6.92692 q^{34} +(1.48039 - 2.56410i) q^{35} +(-1.77748 - 3.07868i) q^{36} +(-3.72252 - 6.44760i) q^{37} -5.76271 q^{38} +13.5308 q^{40} +(0.425428 + 0.736862i) q^{41} +(-0.945042 - 1.63686i) q^{42} +(0.807979 - 1.39946i) q^{43} -10.1347 q^{44} +(-1.84601 + 3.19738i) q^{45} +(9.17994 - 15.9001i) q^{46} +2.44504 q^{47} +(0.763906 - 1.32312i) q^{48} +(3.17845 + 5.50523i) q^{49} +(-10.1712 - 17.6171i) q^{50} -2.93900 q^{51} -9.96077 q^{53} +(1.17845 + 2.04113i) q^{54} +(5.26271 + 9.11528i) q^{55} +(1.46950 - 2.54525i) q^{56} +2.44504 q^{57} +(-4.53803 + 7.86010i) q^{58} +(2.69202 - 4.66272i) q^{59} -13.1250 q^{60} +(6.62833 - 11.4806i) q^{61} +(-2.76324 - 4.78607i) q^{62} +(0.400969 + 0.694498i) q^{63} -11.8442 q^{64} +6.71917 q^{66} +(-7.19687 - 12.4653i) q^{67} +(-5.22401 - 9.04826i) q^{68} +(-3.89493 + 6.74621i) q^{69} -6.97823 q^{70} +(-4.06249 + 7.03644i) q^{71} +(-1.83244 + 3.17387i) q^{72} -11.8877 q^{73} +(-8.77359 + 15.1963i) q^{74} +(4.31551 + 7.47468i) q^{75} +(4.34601 + 7.52751i) q^{76} +2.28621 q^{77} +5.40581 q^{79} +(-2.82036 - 4.88500i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00269 - 1.73671i) q^{82} +7.04892 q^{83} +(-1.42543 + 2.46891i) q^{84} +(-5.42543 + 9.39712i) q^{85} -3.80864 q^{86} +(1.92543 - 3.33494i) q^{87} +(5.22401 + 9.04826i) q^{88} +(-0.565843 - 0.980069i) q^{89} +8.70171 q^{90} -27.6926 q^{92} +(1.17241 + 2.03067i) q^{93} +(-2.88135 - 4.99065i) q^{94} +(4.51357 - 7.81774i) q^{95} +3.72886 q^{96} +(2.97219 - 5.14798i) q^{97} +(7.49127 - 12.9753i) q^{98} -2.85086 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more