LMFDB - Embedded newform 975.2.i.l.601.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.i (of order $3$, degree $2$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.3
Root			$0.500000 - 0.385124i$ of defining polynomial
Character	$\chi$	$=$	975.601
Dual form			975.2.i.l.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30084 + 2.25312i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.38437 + 4.12985i) q^{4} +(1.30084 - 2.25312i) q^{6} +(1.80084 - 3.11915i) q^{7} -7.20336 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.30084 + 2.25312i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.38437 + 4.12985i) q^{4} +(1.30084 - 2.25312i) q^{6} +(1.80084 - 3.11915i) q^{7} -7.20336 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.60168 + 4.50624i) q^{11} +4.76873 q^{12} +(-3.01815 + 1.97250i) q^{13} +9.37041 q^{14} +(-4.60168 - 7.97034i) q^{16} +(-1.46789 + 2.54247i) q^{17} -2.60168 q^{18} +(-3.38437 + 5.86190i) q^{19} -3.60168 q^{21} +(-6.76873 + 11.7238i) q^{22} +(2.76873 + 4.79559i) q^{23} +(3.60168 + 6.23829i) q^{24} +(-8.37041 - 4.23435i) q^{26} +1.00000 q^{27} +(8.58773 + 14.8744i) q^{28} +(-0.916472 - 1.58738i) q^{29} +4.10284 q^{31} +(4.76873 - 8.25969i) q^{32} +(2.60168 - 4.50624i) q^{33} -7.63798 q^{34} +(-2.38437 - 4.12985i) q^{36} +(-1.76873 - 3.06354i) q^{37} -17.6101 q^{38} +(3.21731 + 1.62755i) q^{39} +(2.68521 + 4.65091i) q^{41} +(-4.68521 - 8.11502i) q^{42} +(1.58353 - 2.74275i) q^{43} -24.8134 q^{44} +(-7.20336 + 12.4766i) q^{46} -3.80504 q^{47} +(-4.60168 + 7.97034i) q^{48} +(-2.98605 - 5.17198i) q^{49} +2.93579 q^{51} +(-0.949743 - 17.1677i) q^{52} +5.20336 q^{53} +(1.30084 + 2.25312i) q^{54} +(-12.9721 + 22.4683i) q^{56} +6.76873 q^{57} +(2.38437 - 4.12985i) q^{58} +(3.68521 - 6.38297i) q^{59} +(1.71731 - 2.97447i) q^{61} +(5.33714 + 9.24420i) q^{62} +(1.80084 + 3.11915i) q^{63} +6.40672 q^{64} +13.5375 q^{66} +(1.75058 + 3.03210i) q^{67} +(-7.00000 - 12.1244i) q^{68} +(2.76873 - 4.79559i) q^{69} +(4.85226 - 8.40436i) q^{71} +(3.60168 - 6.23829i) q^{72} +0.805037 q^{73} +(4.60168 - 7.97034i) q^{74} +(-16.1391 - 27.9538i) q^{76} +18.7408 q^{77} +(0.518152 + 9.36617i) q^{78} -4.10284 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.98605 + 12.1002i) q^{82} +11.5375 q^{83} +(8.58773 - 14.8744i) q^{84} +8.23966 q^{86} +(-0.916472 + 1.58738i) q^{87} +(-18.7408 - 32.4601i) q^{88} +(-4.91647 - 8.51558i) q^{89} +(0.717312 + 12.9662i) q^{91} -26.4067 q^{92} +(-2.05142 - 3.55317i) q^{93} +(-4.94974 - 8.57321i) q^{94} -9.53747 q^{96} +(-2.78689 + 4.82703i) q^{97} +(7.76873 - 13.4558i) q^{98} -5.20336 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9} + 12 q^{12} - 3 q^{13} + 24 q^{14} - 12 q^{16} - 12 q^{19} - 6 q^{21} - 24 q^{22} + 6 q^{24} - 18 q^{26} + 6 q^{27} + 12 q^{28} - 6 q^{29} + 6 q^{31} + 12 q^{32} - 6 q^{36} + 6 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{42} + 9 q^{43} - 24 q^{44} - 12 q^{46} + 24 q^{47} - 12 q^{48} + 6 q^{49} - 12 q^{52} - 30 q^{56} + 24 q^{57} + 6 q^{58} + 6 q^{59} + 3 q^{61} - 6 q^{62} + 3 q^{63} - 24 q^{64} + 48 q^{66} + 9 q^{67} - 42 q^{68} + 12 q^{71} + 6 q^{72} - 42 q^{73} + 12 q^{74} - 48 q^{76} + 48 q^{77} - 12 q^{78} - 6 q^{79} - 3 q^{81} - 18 q^{82} + 36 q^{83} + 12 q^{84} - 12 q^{86} - 6 q^{87} - 48 q^{88} - 30 q^{89} - 3 q^{91} - 96 q^{92} - 3 q^{93} - 36 q^{94} - 24 q^{96} + 15 q^{97} + 30 q^{98}+O(q^{100}) $ 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9 + 12 * q^12 - 3 * q^13 + 24 * q^14 - 12 * q^16 - 12 * q^19 - 6 * q^21 - 24 * q^22 + 6 * q^24 - 18 * q^26 + 6 * q^27 + 12 * q^28 - 6 * q^29 + 6 * q^31 + 12 * q^32 - 6 * q^36 + 6 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^42 + 9 * q^43 - 24 * q^44 - 12 * q^46 + 24 * q^47 - 12 * q^48 + 6 * q^49 - 12 * q^52 - 30 * q^56 + 24 * q^57 + 6 * q^58 + 6 * q^59 + 3 * q^61 - 6 * q^62 + 3 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 42 * q^68 + 12 * q^71 + 6 * q^72 - 42 * q^73 + 12 * q^74 - 48 * q^76 + 48 * q^77 - 12 * q^78 - 6 * q^79 - 3 * q^81 - 18 * q^82 + 36 * q^83 + 12 * q^84 - 12 * q^86 - 6 * q^87 - 48 * q^88 - 30 * q^89 - 3 * q^91 - 96 * q^92 - 3 * q^93 - 36 * q^94 - 24 * q^96 + 15 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	1.30084	+	2.25312i	0.919832	+	1.59320i	0.799668	+	0.600443i	$0.205009\pi$
$2$	1.30084	+	2.25312i	0.919832	+	1.59320i	0.120165	+	0.992754i	$0.461658\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−2.38437	+	4.12985i	−1.19218	+	2.06492i
$5$		0			0
$5$		0			0
$6$	1.30084	−	2.25312i	0.531066	−	0.919832i
$7$	1.80084	−	3.11915i	0.680653	−	1.17893i	−0.294128	−	0.955766i	$-0.595029\pi$
$7$	1.80084	−	3.11915i	0.680653	−	1.17893i	0.974782	−	0.223160i	$-0.0716373\pi$
$8$	−7.20336			−2.54677
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.60168	+	4.50624i	0.784436	+	1.35868i	0.929336	+	0.369236i	$0.120381\pi$
$11$	2.60168	+	4.50624i	0.784436	+	1.35868i	−0.144900	+	0.989446i	$0.546286\pi$
$12$	4.76873			1.37662
$13$	−3.01815	+	1.97250i	−0.837085	+	0.547073i
$13$	−3.01815	+	1.97250i	−0.837085	+	0.547073i
$14$	9.37041			2.50435
$15$		0			0
$16$	−4.60168	−	7.97034i	−1.15042	−	1.99259i
$17$	−1.46789	+	2.54247i	−0.356017	+	0.616639i	−0.987291	−	0.158920i	$-0.949199\pi$
$17$	−1.46789	+	2.54247i	−0.356017	+	0.616639i	0.631275	+	0.775559i	$0.282532\pi$
$18$	−2.60168			−0.613222
$19$	−3.38437	+	5.86190i	−0.776427	+	1.34481i	0.157562	+	0.987509i	$0.449637\pi$
$19$	−3.38437	+	5.86190i	−0.776427	+	1.34481i	−0.933989	+	0.357302i	$0.883697\pi$
$20$		0			0
$21$	−3.60168			−0.785951
$22$	−6.76873	+	11.7238i	−1.44310	+	2.49952i
$23$	2.76873	+	4.79559i	0.577321	+	0.999949i	0.995785	+	0.0917160i	$0.0292352\pi$
$23$	2.76873	+	4.79559i	0.577321	+	0.999949i	−0.418464	+	0.908233i	$0.637431\pi$
$24$	3.60168	+	6.23829i	0.735190	+	1.27339i
$25$		0			0
$26$	−8.37041	−	4.23435i	−1.64157	−	0.830424i
$27$	1.00000			0.192450
$28$	8.58773	+	14.8744i	1.62293	+	2.81099i
$29$	−0.916472	−	1.58738i	−0.170185	−	0.294768i	0.768300	−	0.640090i	$-0.221103\pi$
$29$	−0.916472	−	1.58738i	−0.170185	−	0.294768i	−0.938484	+	0.345322i	$0.887770\pi$
$30$		0			0
$31$	4.10284			0.736893			0.368446	−	0.929649i	$-0.379890\pi$
$31$	4.10284			0.736893			0.368446	+	0.929649i	$0.379890\pi$
$32$	4.76873	−	8.25969i	0.843001	−	1.46012i
$33$	2.60168	−	4.50624i	0.452894	−	0.784436i
$34$	−7.63798			−1.30990
$35$		0			0
$36$	−2.38437	−	4.12985i	−0.397395	−	0.688308i
$37$	−1.76873	−	3.06354i	−0.290778	−	0.503642i	0.683216	−	0.730217i	$-0.260581\pi$
$37$	−1.76873	−	3.06354i	−0.290778	−	0.503642i	−0.973994	+	0.226574i	$0.927247\pi$
$38$	−17.6101			−2.85673
$39$	3.21731	+	1.62755i	0.515182	+	0.260616i
$40$		0			0
$41$	2.68521	+	4.65091i	0.419359	+	0.726351i	0.995875	−	0.0907349i	$-0.0289216\pi$
$41$	2.68521	+	4.65091i	0.419359	+	0.726351i	−0.576516	+	0.817086i	$0.695588\pi$
$42$	−4.68521	−	8.11502i	−0.722943	−	1.25217i
$43$	1.58353	−	2.74275i	0.241486	−	0.418265i	−0.719652	−	0.694335i	$-0.755699\pi$
$43$	1.58353	−	2.74275i	0.241486	−	0.418265i	0.961138	+	0.276069i	$0.0890320\pi$
$44$	−24.8134			−3.74077
$45$		0			0
$46$	−7.20336	+	12.4766i	−1.06208	+	1.83957i
$47$	−3.80504			−0.555022			−0.277511	−	0.960722i	$-0.589509\pi$
$47$	−3.80504			−0.555022			−0.277511	+	0.960722i	$0.589509\pi$
$48$	−4.60168	+	7.97034i	−0.664195	+	1.15042i
$49$	−2.98605	−	5.17198i	−0.426578	−	0.738855i
$50$		0			0
$51$	2.93579			0.411093
$52$	−0.949743	−	17.1677i	−0.131706	−	2.38073i
$53$	5.20336			0.714736			0.357368	−	0.933964i	$-0.383674\pi$
$53$	5.20336			0.714736			0.357368	+	0.933964i	$0.383674\pi$
$54$	1.30084	+	2.25312i	0.177022	+	0.306611i
$55$		0			0
$56$	−12.9721	+	22.4683i	−1.73347	+	3.00246i
$57$	6.76873			0.896541
$58$	2.38437	−	4.12985i	0.313083	−	0.542275i
$59$	3.68521	−	6.38297i	0.479773	−	0.830991i	−0.519958	−	0.854192i	$-0.674052\pi$
$59$	3.68521	−	6.38297i	0.479773	−	0.830991i	0.999731	+	0.0232007i	$0.00738566\pi$
$60$		0			0
$61$	1.71731	−	2.97447i	0.219879	−	0.380842i	−0.734892	−	0.678185i	$-0.762767\pi$
$61$	1.71731	−	2.97447i	0.219879	−	0.380842i	0.954771	+	0.297343i	$0.0961003\pi$
$62$	5.33714	+	9.24420i	0.677818	+	1.17401i
$63$	1.80084	+	3.11915i	0.226884	+	0.392975i
$64$	6.40672			0.800840
$65$		0			0
$66$	13.5375			1.66635
$67$	1.75058	+	3.03210i	0.213868	+	0.370430i	0.952922	−	0.303216i	$-0.0980605\pi$
$67$	1.75058	+	3.03210i	0.213868	+	0.370430i	−0.739054	+	0.673646i	$0.764727\pi$
$68$	−7.00000	−	12.1244i	−0.848875	−	1.47029i
$69$	2.76873	−	4.79559i	0.333316	−	0.577321i
$70$		0			0
$71$	4.85226	−	8.40436i	0.575858	−	0.997415i	−0.420090	−	0.907482i	$-0.638002\pi$
$71$	4.85226	−	8.40436i	0.575858	−	0.997415i	0.995948	−	0.0899322i	$-0.0286650\pi$
$72$	3.60168	−	6.23829i	0.424462	−	0.735190i
$73$	0.805037			0.0942225			0.0471113	−	0.998890i	$-0.484998\pi$
$73$	0.805037			0.0942225			0.0471113	+	0.998890i	$0.484998\pi$
$74$	4.60168	−	7.97034i	0.534934	−	0.926533i
$75$		0			0
$76$	−16.1391	−	27.9538i	−1.85129	−	3.20652i
$77$	18.7408			2.13572
$78$	0.518152	+	9.36617i	0.0586691	+	1.06051i
$79$	−4.10284			−0.461606			−0.230803	−	0.973000i	$-0.574135\pi$
$79$	−4.10284			−0.461606			−0.230803	+	0.973000i	$0.574135\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.98605	+	12.1002i	−0.771480	+	1.33624i
$83$	11.5375			1.26640			0.633201	−	0.773988i	$-0.281741\pi$
$83$	11.5375			1.26640			0.633201	+	0.773988i	$0.281741\pi$
$84$	8.58773	−	14.8744i	0.936998	−	1.62293i
$85$		0			0
$86$	8.23966			0.888506
$87$	−0.916472	+	1.58738i	−0.0982562	+	0.170185i
$88$	−18.7408	−	32.4601i	−1.99778	−	3.46025i
$89$	−4.91647	−	8.51558i	−0.521145	−	0.902650i	−0.999698	−	0.0245908i	$-0.992172\pi$
$89$	−4.91647	−	8.51558i	−0.521145	−	0.902650i	0.478553	−	0.878059i	$-0.341162\pi$
$90$		0			0
$91$	0.717312	+	12.9662i	0.0751947	+	1.35923i
$92$	−26.4067			−2.75309
$93$	−2.05142	−	3.55317i	−0.212723	−	0.368446i
$94$	−4.94974	−	8.57321i	−0.510527	−	0.884259i
$95$		0			0
$96$	−9.53747			−0.973414
$97$	−2.78689	+	4.82703i	−0.282965	+	0.490110i	−0.972114	−	0.234510i	$-0.924651\pi$
$97$	−2.78689	+	4.82703i	−0.282965	+	0.490110i	0.689148	+	0.724620i	$0.257985\pi$
$98$	7.76873	−	13.4558i	0.784761	−	1.35925i
$99$	−5.20336			−0.522957
$100$		0			0
$101$	−1.20336	−	2.08428i	−0.119739	−	0.207393i	0.799925	−	0.600099i	$-0.204872\pi$
$101$	−1.20336	−	2.08428i	−0.119739	−	0.207393i	−0.919664	+	0.392706i	$0.871539\pi$
$102$	3.81899	+	6.61469i	0.378136	+	0.654952i
$103$	−18.4430			−1.81724			−0.908622	−	0.417619i	$-0.862865\pi$
$103$	−18.4430			−1.81724			−0.908622	+	0.417619i	$0.862865\pi$
$104$	21.7408	−	14.2086i	2.13186	−	1.39327i
$105$		0			0
$106$	6.76873	+	11.7238i	0.657438	+	1.13872i
$107$	5.46789	+	9.47067i	0.528601	+	0.915564i	0.999444	+	0.0333471i	$0.0106167\pi$
$107$	5.46789	+	9.47067i	0.528601	+	0.915564i	−0.470842	+	0.882217i	$0.656050\pi$
$108$	−2.38437	+	4.12985i	−0.229436	+	0.397395i
$109$	13.8692			1.32843			0.664217	−	0.747540i	$-0.268765\pi$
$109$	13.8692			1.32843			0.664217	+	0.747540i	$0.268765\pi$
$110$		0			0
$111$	−1.76873	+	3.06354i	−0.167881	+	0.290778i
$112$	−33.1475			−3.13215
$113$	−5.60168	+	9.70239i	−0.526962	+	0.912724i	0.472545	+	0.881307i	$0.343336\pi$
$113$	−5.60168	+	9.70239i	−0.526962	+	0.912724i	−0.999506	+	0.0314176i	$0.989998\pi$
$114$	8.80504	+	15.2508i	0.824667	+	1.42837i
$115$		0			0
$116$	8.74083			0.811565
$117$	−0.199160	−	3.60005i	−0.0184124	−	0.332824i
$118$	19.1755			1.76524
$119$	5.28689	+	9.15715i	0.484648	+	0.839435i
$120$		0			0
$121$	−8.03747	+	13.9213i	−0.730679	+	1.26557i
$122$	8.93579			0.809008
$123$	2.68521	−	4.65091i	0.242117	−	0.419359i
$124$	−9.78269	+	16.9441i	−0.878511	+	1.52163i
$125$		0			0
$126$	−4.68521	+	8.11502i	−0.417391	+	0.722943i
$127$	−1.59748	−	2.76692i	−0.141754	−	0.245524i	0.786403	−	0.617713i	$-0.211941\pi$
$127$	−1.59748	−	2.76692i	−0.141754	−	0.245524i	−0.928157	+	0.372189i	$0.878607\pi$
$128$	−1.20336	−	2.08428i	−0.106363	−	0.184226i
$129$	−3.16706			−0.278844
$130$		0			0
$131$	−4.57377			−0.399612			−0.199806	−	0.979835i	$-0.564031\pi$
$131$	−4.57377			−0.399612			−0.199806	+	0.979835i	$0.564031\pi$
$132$	12.4067	+	21.4891i	1.07987	+	1.87038i
$133$	12.1894	+	21.1127i	1.05696	+	1.83070i
$134$	−4.55445	+	7.88855i	−0.393445	+	0.681467i
$135$		0			0
$136$	10.5738	−	18.3143i	0.906693	−	1.57044i
$137$	5.33714	−	9.24420i	0.455983	−	0.789785i	−0.542761	−	0.839887i	$-0.682621\pi$
$137$	5.33714	−	9.24420i	0.455983	−	0.789785i	0.998744	+	0.0501015i	$0.0159545\pi$
$138$	14.4067			1.22638
$139$	8.07377	−	13.9842i	0.684808	−	1.18612i	−0.288689	−	0.957423i	$-0.593219\pi$
$139$	8.07377	−	13.9842i	0.684808	−	1.18612i	0.973497	−	0.228700i	$-0.0734474\pi$
$140$		0			0
$141$	1.90252	+	3.29526i	0.160221	+	0.277511i
$142$	25.2481			2.11877
$143$	−16.7408	−	8.46870i	−1.39994	−	0.708188i
$144$	9.20336			0.766947
$145$		0			0
$146$	1.04722	+	1.81385i	0.0866689	+	0.150115i
$147$	−2.98605	+	5.17198i	−0.246285	+	0.426578i
$148$	16.8692			1.38664
$149$	4.83294	−	8.37091i	0.395930	−	0.685771i	−0.597289	−	0.802026i	$-0.703756\pi$
$149$	4.83294	−	8.37091i	0.395930	−	0.685771i	0.993219	+	0.116255i	$0.0370889\pi$
$150$		0			0
$151$	−18.7129			−1.52284			−0.761418	−	0.648261i	$-0.775496\pi$
$151$	−18.7129			−1.52284			−0.761418	+	0.648261i	$0.775496\pi$
$152$	24.3788	−	42.2253i	1.97738	−	3.42493i
$153$	−1.46789	−	2.54247i	−0.118672	−	0.205546i
$154$	24.3788	+	42.2253i	1.96450	+	3.40261i
$155$		0			0
$156$	−14.3928	+	9.40633i	−1.15234	+	0.753109i
$157$	10.3704			0.827649			0.413825	−	0.910357i	$-0.364193\pi$
$157$	10.3704			0.827649			0.413825	+	0.910357i	$0.364193\pi$
$158$	−5.33714	−	9.24420i	−0.424600	−	0.735429i
$159$	−2.60168	−	4.50624i	−0.206327	−	0.357368i
$160$		0			0
$161$	19.9442			1.57182
$162$	1.30084	−	2.25312i	0.102204	−	0.177022i
$163$	−5.73663	+	9.93613i	−0.449327	+	0.778258i	−0.998342	−	0.0575546i	$-0.981670\pi$
$163$	−5.73663	+	9.93613i	−0.449327	+	0.778258i	0.549015	+	0.835813i	$0.315003\pi$
$164$	−25.6101			−1.99981
$165$		0			0
$166$	15.0084	+	25.9953i	1.16488	+	2.01763i
$167$	−1.56538	−	2.71131i	−0.121132	−	0.209808i	0.799082	−	0.601222i	$-0.205319\pi$
$167$	−1.56538	−	2.71131i	−0.121132	−	0.209808i	−0.920215	+	0.391414i	$0.871986\pi$
$168$	25.9442			2.00164
$169$	5.21848	−	11.9066i	0.401421	−	0.915893i
$170$		0			0
$171$	−3.38437	−	5.86190i	−0.258809	−	0.448270i
$172$	7.55142	+	13.0794i	0.575791	+	0.997298i
$173$	4.13378	−	7.15992i	0.314286	−	0.544359i	−0.665000	−	0.746844i	$-0.731568\pi$
$173$	4.13378	−	7.15992i	0.314286	−	0.544359i	0.979285	+	0.202485i	$0.0649016\pi$
$174$	−4.76873			−0.361517
$175$		0			0
$176$	23.9442	−	41.4725i	1.80486	−	3.12611i
$177$	−7.37041			−0.553994
$178$	12.7911	−	22.1548i	0.958732	−	1.66057i
$179$	9.22268	+	15.9741i	0.689335	+	1.19396i	0.972053	+	0.234760i	$0.0754306\pi$
$179$	9.22268	+	15.9741i	0.689335	+	1.19396i	−0.282718	+	0.959203i	$0.591236\pi$
$180$		0			0
$181$	21.1028			1.56856			0.784281	−	0.620406i	$-0.213032\pi$
$181$	21.1028			1.56856			0.784281	+	0.620406i	$0.213032\pi$
$182$	−28.2813	+	18.4832i	−2.09635	+	1.37006i
$183$	−3.43462			−0.253895
$184$	−19.9442	−	34.5443i	−1.47030	−	2.54664i
$185$		0			0
$186$	5.33714	−	9.24420i	0.391338	−	0.677818i
$187$	−15.2760			−1.11709
$188$	9.07261	−	15.7142i	0.661688	−	1.14608i
$189$	1.80084	−	3.11915i	0.130992	−	0.226884i
$190$		0			0
$191$	4.35110	−	7.53632i	0.314834	−	0.545309i	−0.664568	−	0.747228i	$-0.731384\pi$
$191$	4.35110	−	7.53632i	0.314834	−	0.545309i	0.979402	+	0.201919i	$0.0647177\pi$
$192$	−3.20336	−	5.54838i	−0.231182	−	0.400420i
$193$	9.63378	+	16.6862i	0.693455	+	1.20110i	0.970699	+	0.240300i	$0.0772457\pi$
$193$	9.63378	+	16.6862i	0.693455	+	1.20110i	−0.277244	+	0.960800i	$0.589421\pi$
$194$	−14.5012			−1.04112
$195$		0			0
$196$	28.4793			2.03424
$197$	−7.57377	−	13.1182i	−0.539609	−	0.934630i	−0.998925	−	0.0463571i	$-0.985239\pi$
$197$	−7.57377	−	13.1182i	−0.539609	−	0.934630i	0.459316	−	0.888273i	$-0.348095\pi$
$198$	−6.76873	−	11.7238i	−0.481033	−	0.833174i
$199$	2.26873	−	3.92956i	0.160826	−	0.278559i	−0.774339	−	0.632771i	$-0.781917\pi$
$199$	2.26873	−	3.92956i	0.160826	−	0.278559i	0.935165	+	0.354212i	$0.115251\pi$
$200$		0			0
$201$	1.75058	−	3.03210i	0.123477	−	0.213868i
$202$	3.13075	−	5.42262i	0.220279	−	0.381534i
$203$	−6.60168			−0.463347
$204$	−7.00000	+	12.1244i	−0.490098	+	0.848875i
$205$		0			0
$206$	−23.9914	−	41.5543i	−1.67156	−	2.89523i
$207$	−5.53747			−0.384881
$208$	29.6101	+	14.9789i	2.05309	+	1.03860i
$209$	−35.2201			−2.43623
$210$		0			0
$211$	11.0738	+	19.1803i	0.762350	+	1.32043i	0.941636	+	0.336632i	$0.109288\pi$
$211$	11.0738	+	19.1803i	0.762350	+	1.32043i	−0.179286	+	0.983797i	$0.557379\pi$
$212$	−12.4067	+	21.4891i	−0.852097	+	1.47587i
$213$	−9.70452			−0.664943
$214$	−14.2257	+	24.6396i	−0.972449	+	1.68433i
$215$		0			0
$216$	−7.20336			−0.490126
$217$	7.38856	−	12.7974i	0.501568	−	0.868742i
$218$	18.0417	+	31.2491i	1.22194	+	2.11645i
$219$	−0.402519	−	0.697183i	−0.0271997	−	0.0471113i
$220$		0			0
$221$	−0.584693	−	10.5690i	−0.0393307	−	0.710946i
$222$	−9.20336			−0.617689
$223$	−3.80504	−	6.59052i	−0.254804	−	0.441334i	0.710038	−	0.704163i	$-0.248678\pi$
$223$	−3.80504	−	6.59052i	−0.254804	−	0.441334i	−0.964842	+	0.262829i	$0.915344\pi$
$224$	−17.1755	−	29.7488i	−1.14758	−	1.98767i
$225$		0			0
$226$	−29.1475			−1.93887
$227$	11.6713	−	20.2152i	0.774648	−	1.34173i	−0.160344	−	0.987061i	$-0.551260\pi$
$227$	11.6713	−	20.2152i	0.774648	−	1.34173i	0.934992	−	0.354669i	$-0.115406\pi$
$228$	−16.1391	+	27.9538i	−1.06884	+	1.85129i
$229$	0.824549			0.0544877			0.0272439	−	0.999629i	$-0.491327\pi$
$229$	0.824549			0.0544877			0.0272439	+	0.999629i	$0.491327\pi$
$230$		0			0
$231$	−9.37041	−	16.2300i	−0.616528	−	1.06786i
$232$	6.60168	+	11.4344i	0.433421	+	0.750708i
$233$	13.4044			0.878150			0.439075	−	0.898450i	$-0.355306\pi$
$233$	13.4044			0.878150			0.439075	+	0.898450i	$0.355306\pi$
$234$	7.85226	−	5.13182i	0.513318	−	0.335477i
$235$		0			0
$236$	17.5738	+	30.4387i	1.14396	+	1.98139i
$237$	2.05142	+	3.55317i	0.133254	+	0.230803i
$238$	−13.7548	+	23.8240i	−0.891590	+	1.54428i
$239$	12.7966			0.827746			0.413873	−	0.910335i	$-0.364176\pi$
$239$	12.7966			0.827746			0.413873	+	0.910335i	$0.364176\pi$
$240$		0			0
$241$	−6.38437	+	11.0580i	−0.411253	+	0.712312i	−0.995027	−	0.0996048i	$-0.968242\pi$
$241$	−6.38437	+	11.0580i	−0.411253	+	0.712312i	0.583774	+	0.811916i	$0.301575\pi$
$242$	−41.8218			−2.68841
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	8.18940	+	14.1845i	0.524273	+	0.908067i
$245$		0			0
$246$	13.9721			0.890828
$247$	−1.34806	−	24.3678i	−0.0857753	−	1.55048i
$248$	−29.5543			−1.87670
$249$	−5.76873	−	9.99174i	−0.365579	−	0.633201i
$250$		0			0
$251$	4.20336	−	7.28043i	0.265314	−	0.459537i	−0.702332	−	0.711849i	$-0.747858\pi$
$251$	4.20336	−	7.28043i	0.265314	−	0.459537i	0.967646	+	0.252313i	$0.0811912\pi$
$252$	−17.1755			−1.08195
$253$	−14.4067	+	24.9532i	−0.905743	+	1.56879i
$254$	4.15613	−	7.19863i	0.260779	−	0.451683i
$255$		0			0
$256$	9.53747	−	16.5194i	0.596092	−	1.03246i
$257$	3.06957	+	5.31666i	0.191475	+	0.331644i	0.945739	−	0.324927i	$-0.105340\pi$
$257$	3.06957	+	5.31666i	0.191475	+	0.331644i	−0.754264	+	0.656571i	$0.772006\pi$
$258$	−4.11983	−	7.13576i	−0.256489	−	0.444253i
$259$	−12.7408			−0.791676
$260$		0			0
$261$	1.83294			0.113456
$262$	−5.94974	−	10.3053i	−0.367576	−	0.636661i
$263$	−2.36505	−	4.09639i	−0.145835	−	0.252594i	0.783849	−	0.620951i	$-0.213254\pi$
$263$	−2.36505	−	4.09639i	−0.145835	−	0.252594i	−0.929684	+	0.368357i	$0.879920\pi$
$264$	−18.7408	+	32.4601i	−1.15342	+	1.99778i
$265$		0			0
$266$	−31.7129	+	54.9284i	−1.94444	+	3.36788i
$267$	−4.91647	+	8.51558i	−0.300883	+	0.521145i
$268$	−16.6961			−1.01988
$269$	2.72151	−	4.71379i	0.165933	−	0.287405i	−0.771053	−	0.636771i	$-0.780270\pi$
$269$	2.72151	−	4.71379i	0.165933	−	0.287405i	0.936986	+	0.349366i	$0.113603\pi$
$270$		0			0
$271$	−12.7397	−	22.0657i	−0.773879	−	1.34040i	−0.935422	−	0.353533i	$-0.884980\pi$
$271$	−12.7397	−	22.0657i	−0.773879	−	1.34040i	0.161543	−	0.986866i	$-0.448353\pi$
$272$	27.0191			1.63827
$273$	10.8704	−	7.10432i	0.657907	−	0.429973i
$274$	27.7711			1.67771
$275$		0			0
$276$	13.2034	+	22.8689i	0.794749	+	1.37655i
$277$	−11.4067	+	19.7570i	−0.685363	+	1.18708i	0.287959	+	0.957643i	$0.407023\pi$
$277$	−11.4067	+	19.7570i	−0.685363	+	1.18708i	−0.973323	+	0.229441i	$0.926310\pi$
$278$	42.0107			2.51964
$279$	−2.05142	+	3.55317i	−0.122815	+	0.212723i
$280$		0			0
$281$	−2.16706			−0.129276			−0.0646378	−	0.997909i	$-0.520589\pi$
$281$	−2.16706			−0.129276			−0.0646378	+	0.997909i	$0.520589\pi$
$282$	−4.94974	+	8.57321i	−0.294753	+	0.510527i
$283$	−14.8734	−	25.7616i	−0.884135	−	1.53137i	−0.846702	−	0.532067i	$-0.821416\pi$
$283$	−14.8734	−	25.7616i	−0.884135	−	1.53137i	−0.0374322	−	0.999299i	$-0.511918\pi$
$284$	23.1391	+	40.0782i	1.37306	+	2.37820i
$285$		0			0
$286$	−2.69613	−	48.7355i	−0.159425	−	2.88179i
$287$	19.3425			1.14175
$288$	4.76873	+	8.25969i	0.281000	+	0.486707i
$289$	4.19057	+	7.25828i	0.246504	+	0.426958i
$290$		0			0
$291$	5.57377			0.326740
$292$	−1.91950	+	3.32468i	−0.112331	+	0.194562i
$293$	16.5428	−	28.6530i	0.966443	−	1.67393i	0.260754	−	0.965405i	$-0.416029\pi$
$293$	16.5428	−	28.6530i	0.966443	−	1.67393i	0.705688	−	0.708522i	$-0.250638\pi$
$294$	−15.5375			−0.906164
$295$		0			0
$296$	12.7408	+	22.0678i	0.740546	+	1.28266i
$297$	2.60168	+	4.50624i	0.150965	+	0.261479i
$298$	25.1475			1.45676
$299$	−17.8158	−	9.01248i	−1.03031	−	0.521205i
$300$		0			0
$301$	−5.70336	−	9.87851i	−0.328736	−	0.569388i
$302$	−24.3425	−	42.1625i	−1.40075	−	2.42618i
$303$	−1.20336	+	2.08428i	−0.0691311	+	0.119739i
$304$	62.2951			3.57287
$305$		0			0
$306$	3.81899	−	6.61469i	0.218317	−	0.378136i
$307$	14.3704			0.820163			0.410081	−	0.912049i	$-0.365500\pi$
$307$	14.3704			0.820163			0.410081	+	0.912049i	$0.365500\pi$
$308$	−44.6850	+	77.3967i	−2.54616	+	4.41009i
$309$	9.22151	+	15.9721i	0.524593	+	0.908622i
$310$		0			0
$311$	−8.70685			−0.493720			−0.246860	−	0.969051i	$-0.579399\pi$
$311$	−8.70685			−0.493720			−0.246860	+	0.969051i	$0.579399\pi$
$312$	−23.1755	−	11.7238i	−1.31205	−	0.663729i
$313$	8.16472			0.461497			0.230749	−	0.973013i	$-0.425882\pi$
$313$	8.16472			0.461497			0.230749	+	0.973013i	$0.425882\pi$
$314$	13.4902	+	23.3658i	0.761299	+	1.31861i
$315$		0			0
$316$	9.78269	−	16.9441i	0.550319	−	0.953181i
$317$	−13.4090			−0.753127			−0.376564	−	0.926391i	$-0.622894\pi$
$317$	−13.4090			−0.753127			−0.376564	+	0.926391i	$0.622894\pi$
$318$	6.76873	−	11.7238i	0.379572	−	0.657438i
$319$	4.76873	−	8.25969i	0.266998	−	0.462454i
$320$		0			0
$321$	5.46789	−	9.47067i	0.305188	−	0.528601i
$322$	25.9442	+	44.9366i	1.44581	+	2.50422i
$323$	−9.93579	−	17.2093i	−0.552842	−	0.957551i
$324$	4.76873			0.264930
$325$		0			0
$326$	−29.8497			−1.65322
$327$	−6.93462	−	12.0111i	−0.383486	−	0.664217i
$328$	−19.3425	−	33.5022i	−1.06801	−	1.84985i
$329$	−6.85226	+	11.8685i	−0.377777	+	0.654330i
$330$		0			0
$331$	−10.7397	+	18.6016i	−0.590305	+	1.02244i	0.403886	+	0.914809i	$0.367659\pi$
$331$	−10.7397	+	18.6016i	−0.590305	+	1.02244i	−0.994191	+	0.107629i	$0.965674\pi$
$332$	−27.5096	+	47.6480i	−1.50978	+	2.61502i
$333$	3.53747			0.193852
$334$	4.07261	−	7.05396i	0.222843	−	0.385976i
$335$		0			0
$336$	16.5738	+	28.7066i	0.904173	+	1.56607i
$337$	7.44535			0.405574			0.202787	−	0.979223i	$-0.435000\pi$
$337$	7.44535			0.405574			0.202787	+	0.979223i	$0.435000\pi$
$338$	33.6154	−	3.73074i	1.82844	−	0.202925i
$339$	11.2034			0.608483
$340$		0			0
$341$	10.6743	+	18.4884i	0.578045	+	1.00120i
$342$	8.80504	−	15.2508i	0.476122	−	0.824667i
$343$	3.70219			0.199900
$344$	−11.4067	+	19.7570i	−0.615009	+	1.06523i
$345$		0			0
$346$	21.5096			1.15636
$347$	−12.4733	+	21.6043i	−0.669600	+	1.15978i	0.308417	+	0.951251i	$0.400201\pi$
$347$	−12.4733	+	21.6043i	−0.669600	+	1.15978i	−0.978016	+	0.208529i	$0.933132\pi$
$348$	−4.37041	−	7.56978i	−0.234279	−	0.405783i
$349$	−1.05142	−	1.82112i	−0.0562813	−	0.0974822i	0.836512	−	0.547949i	$-0.184591\pi$
$349$	−1.05142	−	1.82112i	−0.0562813	−	0.0974822i	−0.892793	+	0.450466i	$0.851258\pi$
$350$		0			0
$351$	−3.01815	+	1.97250i	−0.161097	+	0.105284i
$352$	49.6269			2.64512
$353$	9.26990	+	16.0559i	0.493387	+	0.854571i	0.999971	−	0.00761929i	$-0.00242532\pi$
$353$	9.26990	+	16.0559i	0.493387	+	0.854571i	−0.506584	+	0.862191i	$0.669092\pi$
$354$	−9.58773	−	16.6064i	−0.509582	−	0.882622i
$355$		0			0
$356$	46.8907			2.48520
$357$	5.28689	−	9.15715i	0.279812	−	0.484648i
$358$	−23.9944	+	41.5596i	−1.26815	+	2.19649i
$359$	−4.75801			−0.251118			−0.125559	−	0.992086i	$-0.540072\pi$
$359$	−4.75801			−0.251118			−0.125559	+	0.992086i	$0.540072\pi$
$360$		0			0
$361$	−13.4079	−	23.2231i	−0.705678	−	1.22227i
$362$	27.4514	+	47.5472i	1.44281	+	2.49903i
$363$	16.0749			0.843715
$364$	−55.2588	−	27.9538i	−2.89635	−	1.46518i
$365$		0			0
$366$	−4.46789	−	7.73862i	−0.233541	−	0.404504i
$367$	−5.12100	−	8.86983i	−0.267314	−	0.463001i	0.700853	−	0.713305i	$-0.252803\pi$
$367$	−5.12100	−	8.86983i	−0.267314	−	0.463001i	−0.968167	+	0.250304i	$0.919469\pi$
$368$	25.4817	−	44.1355i	1.32832	−	2.30072i
$369$	−5.37041			−0.279573
$370$		0			0
$371$	9.37041	−	16.2300i	0.486488	−	0.842621i
$372$	19.5654			1.01442
$373$	−11.6701	+	20.2132i	−0.604254	+	1.04660i	0.387915	+	0.921695i	$0.373196\pi$
$373$	−11.6701	+	20.2132i	−0.604254	+	1.04660i	−0.992169	+	0.124904i	$0.960138\pi$
$374$	−19.8716	−	34.4186i	−1.02753	−	1.77974i
$375$		0			0
$376$	27.4090			1.41351
$377$	5.89716	+	2.98320i	0.303719	+	0.153643i
$378$	9.37041			0.481962
$379$	17.8286	+	30.8800i	0.915791	+	1.58620i	0.805739	+	0.592271i	$0.201769\pi$
$379$	17.8286	+	30.8800i	0.915791	+	1.58620i	0.110052	+	0.993926i	$0.464898\pi$
$380$		0			0
$381$	−1.59748	+	2.76692i	−0.0818414	+	0.141754i
$382$	22.6403			1.15838
$383$	−15.3092	+	26.5164i	−0.782265	+	1.35492i	0.148354	+	0.988934i	$0.452603\pi$
$383$	−15.3092	+	26.5164i	−0.782265	+	1.35492i	−0.930619	+	0.365989i	$0.880731\pi$
$384$	−1.20336	+	2.08428i	−0.0614086	+	0.106363i
$385$		0			0
$386$	−25.0640	+	43.4121i	−1.27572	+	2.20962i
$387$	1.58353	+	2.74275i	0.0804952	+	0.139422i
$388$	−13.2899	−	23.0188i	−0.674693	−	1.16860i
$389$	25.0191			1.26852			0.634260	−	0.773120i	$-0.281305\pi$
$389$	25.0191			1.26852			0.634260	+	0.773120i	$0.281305\pi$
$390$		0			0
$391$	−16.2568			−0.822144
$392$	21.5096	+	37.2557i	1.08640	+	1.88169i
$393$	2.28689	+	3.96100i	0.115358	+	0.199806i
$394$	19.7045	−	34.1292i	0.992700	−	1.71941i
$395$		0			0
$396$	12.4067	−	21.4891i	0.623461	−	1.07987i
$397$	5.41647	−	9.38161i	0.271845	−	0.470849i	−0.697489	−	0.716595i	$-0.745700\pi$
$397$	5.41647	−	9.38161i	0.271845	−	0.470849i	0.969334	+	0.245746i	$0.0790329\pi$
$398$	11.8050			0.591733
$399$	12.1894	−	21.1127i	0.610233	−	1.05696i
$400$		0			0
$401$	12.2397	+	21.1997i	0.611220	+	1.05866i	0.991035	+	0.133601i	$0.0426541\pi$
$401$	12.2397	+	21.1997i	0.611220	+	1.05866i	−0.379816	+	0.925062i	$0.624013\pi$
$402$	9.10891			0.454311
$403$	−12.3830	+	8.09287i	−0.616842	+	0.403134i
$404$	11.4770			0.571002
$405$		0			0
$406$	−8.58773	−	14.8744i	−0.426202	−	0.738203i
$407$	9.20336	−	15.9407i	0.456194	−	0.790150i
$408$	−21.1475			−1.04696
$409$	−13.3553	+	23.1320i	−0.660377	+	1.14381i	0.320140	+	0.947370i	$0.396270\pi$
$409$	−13.3553	+	23.1320i	−0.660377	+	1.14381i	−0.980517	+	0.196436i	$0.937063\pi$
$410$		0			0
$411$	−10.6743			−0.526524
$412$	43.9749	−	76.1668i	2.16649	−	3.75247i
$413$	−13.2729	−	22.9894i	−0.653118	−	1.13123i
$414$	−7.20336	−	12.4766i	−0.354026	−	0.613191i
$415$		0			0
$416$	1.89949	+	34.3353i	0.0931300	+	1.68343i
$417$	−16.1475			−0.790749
$418$	−45.8158	−	79.3552i	−2.24092	−	3.88139i
$419$	−7.51815	−	13.0218i	−0.367286	−	0.636158i	0.621854	−	0.783133i	$-0.286380\pi$
$419$	−7.51815	−	13.0218i	−0.367286	−	0.636158i	−0.989140	+	0.146975i	$0.953046\pi$
$420$		0			0
$421$	−5.90182			−0.287637			−0.143818	−	0.989604i	$-0.545938\pi$
$421$	−5.90182			−0.287637			−0.143818	+	0.989604i	$0.545938\pi$
$422$	−28.8104	+	49.9011i	−1.40247	+	2.42915i
$423$	1.90252	−	3.29526i	0.0925036	−	0.160221i
$424$	−37.4817			−1.82027
$425$		0			0
$426$	−12.6240	−	21.8655i	−0.611636	−	1.05938i
$427$	−6.18521	−	10.7131i	−0.299323	−	0.518443i
$428$	−52.1499			−2.52076
$429$	1.03630	+	18.7323i	0.0500332	+	0.904406i
$430$		0			0
$431$	−19.6743	−	34.0769i	−0.947677	−	1.64142i	−0.750301	−	0.661097i	$-0.770091\pi$
$431$	−19.6743	−	34.0769i	−0.947677	−	1.64142i	−0.197376	−	0.980328i	$-0.563242\pi$
$432$	−4.60168	−	7.97034i	−0.221398	−	0.383473i
$433$	6.20756	−	10.7518i	0.298316	−	0.516699i	−0.677435	−	0.735583i	$-0.736908\pi$
$433$	6.20756	−	10.7518i	0.298316	−	0.516699i	0.975751	+	0.218884i	$0.0702417\pi$
$434$	38.4454			1.84544
$435$		0			0
$436$	−33.0694	+	57.2778i	−1.58374	+	2.74311i
$437$	−37.4817			−1.79299
$438$	1.04722	−	1.81385i	0.0500383	−	0.0866689i
$439$	−15.9207	−	27.5754i	−0.759852	−	1.31610i	−0.942926	−	0.333003i	$-0.891938\pi$
$439$	−15.9207	−	27.5754i	−0.759852	−	1.31610i	0.183074	−	0.983099i	$-0.441395\pi$
$440$		0			0
$441$	5.97209			0.284385
$442$	23.0526	−	15.0659i	1.09650	−	0.716613i
$443$	1.06421			0.0505622			0.0252811	−	0.999680i	$-0.491952\pi$
$443$	1.06421			0.0505622			0.0252811	+	0.999680i	$0.491952\pi$
$444$	−8.43462	−	14.6092i	−0.400290	−	0.693322i
$445$		0			0
$446$	9.89949	−	17.1464i	0.468754	−	0.811906i
$447$	−9.66589			−0.457181
$448$	11.5375	−	19.9835i	0.545094	−	0.944131i
$449$	−7.70219	+	13.3406i	−0.363489	+	0.629581i	−0.988532	−	0.151009i	$-0.951748\pi$
$449$	−7.70219	+	13.3406i	−0.363489	+	0.629581i	0.625044	+	0.780590i	$0.285081\pi$
$450$		0			0
$451$	−13.9721	+	24.2004i	−0.657920	+	1.13955i
$452$	−26.7129	−	46.2681i	−1.25647	−	2.17627i
$453$	9.35646	+	16.2059i	0.439605	+	0.761418i
$454$	60.7297			2.85019
$455$		0			0
$456$	−48.7576			−2.28328
$457$	−4.78689	−	8.29113i	−0.223921	−	0.387843i	0.732074	−	0.681225i	$-0.238552\pi$
$457$	−4.78689	−	8.29113i	−0.223921	−	0.387843i	−0.955995	+	0.293382i	$0.905219\pi$
$458$	1.07261	+	1.85781i	0.0501196	+	0.0868097i
$459$	−1.46789	+	2.54247i	−0.0685155	+	0.118672i
$460$		0			0
$461$	−8.18637	+	14.1792i	−0.381277	+	0.660392i	−0.991245	−	0.132034i	$-0.957849\pi$
$461$	−8.18637	+	14.1792i	−0.381277	+	0.660392i	0.609968	+	0.792426i	$0.291182\pi$
$462$	24.3788	−	42.2253i	1.13420	−	1.96450i
$463$	24.6487			1.14552			0.572761	−	0.819722i	$-0.305872\pi$
$463$	24.6487			1.14552			0.572761	+	0.819722i	$0.305872\pi$
$464$	−8.43462	+	14.6092i	−0.391568	+	0.678215i
$465$		0			0
$466$	17.4370	+	30.2017i	0.807751	+	1.39907i
$467$	20.3402			0.941231			0.470616	−	0.882338i	$-0.344032\pi$
$467$	20.3402			0.941231			0.470616	+	0.882338i	$0.344032\pi$
$468$	15.3425	+	7.76133i	0.709208	+	0.358768i
$469$	12.6101			0.582279
$470$		0			0
$471$	−5.18521	−	8.98104i	−0.238922	−	0.413825i
$472$	−26.5459	+	45.9788i	−1.22187	+	2.11635i
$473$	16.4793			0.757720
$474$	−5.33714	+	9.24420i	−0.245143	+	0.424600i
$475$		0			0
$476$	−50.4235			−2.31116
$477$	−2.60168	+	4.50624i	−0.119123	+	0.206327i
$478$	16.6464	+	28.8324i	0.761388	+	1.31876i
$479$	0.0811965	+	0.140637i	0.00370996	+	0.00642585i	0.867874	−	0.496784i	$-0.165486\pi$
$479$	0.0811965	+	0.140637i	0.00370996	+	0.00642585i	−0.864164	+	0.503209i	$0.832152\pi$
$480$		0			0
$481$	11.3811	+	5.75739i	0.518935	+	0.262514i
$482$	−33.2201			−1.51314
$483$	−9.97209	−	17.2722i	−0.453746	−	0.785911i
$484$	−38.3286	−	66.3870i	−1.74221	−	3.01759i
$485$		0			0
$486$	−2.60168			−0.118015
$487$	1.28152	−	2.21966i	0.0580713	−	0.100582i	−0.835528	−	0.549447i	$-0.814838\pi$
$487$	1.28152	−	2.21966i	0.0580713	−	0.100582i	0.893600	+	0.448865i	$0.148172\pi$
$488$	−12.3704	+	21.4262i	−0.559982	+	0.969918i
$489$	11.4733			0.518839
$490$		0			0
$491$	−14.2203	−	24.6304i	−0.641755	−	1.11155i	−0.985041	−	0.172321i	$-0.944873\pi$
$491$	−14.2203	−	24.6304i	−0.641755	−	1.11155i	0.343286	−	0.939231i	$-0.388460\pi$
$492$	12.8050	+	22.1790i	0.577296	+	0.999905i
$493$	5.38114			0.242354
$494$	53.1499	−	34.7359i	2.39133	−	1.56284i
$495$		0			0
$496$	−18.8800	−	32.7011i	−0.847736	−	1.46832i
$497$	−17.4763	−	30.2698i	−0.783919	−	1.35779i
$498$	15.0084	−	25.9953i	0.672542	−	1.16488i
$499$	−27.8605			−1.24721			−0.623603	−	0.781741i	$-0.714332\pi$
$499$	−27.8605			−1.24721			−0.623603	+	0.781741i	$0.714332\pi$
$500$		0			0
$501$	−1.56538	+	2.71131i	−0.0699358	+	0.121132i
$502$	21.8716			0.976176
$503$	15.7129	−	27.2156i	0.700604	−	1.21348i	−0.267650	−	0.963516i	$-0.586247\pi$
$503$	15.7129	−	27.2156i	0.700604	−	1.21348i	0.968255	−	0.249966i	$-0.0804196\pi$
$504$	−12.9721	−	22.4683i	−0.577823	−	1.00082i
$505$		0			0
$506$	−74.9633			−3.33253
$507$	−12.9207	+	1.43397i	−0.573827	+	0.0636850i
$508$	15.2359			0.675985
$509$	−8.11124	−	14.0491i	−0.359524	−	0.622715i	0.628357	−	0.777925i	$-0.283728\pi$
$509$	−8.11124	−	14.0491i	−0.359524	−	0.622715i	−0.987881	+	0.155211i	$0.950394\pi$
$510$		0			0
$511$	1.44974	−	2.51103i	0.0641329	−	0.111081i
$512$	44.8134			1.98049
$513$	−3.38437	+	5.86190i	−0.149423	+	0.258809i
$514$	−7.98605	+	13.8322i	−0.352249	+	0.610114i
$515$		0			0
$516$	7.55142	−	13.0794i	0.332433	−	0.575791i
$517$	−9.89949	−	17.1464i	−0.435379	−	0.754098i
$518$	−16.5738	−	28.7066i	−0.728210	−	1.26130i
$519$	−8.26757			−0.362906
$520$		0			0
$521$	−20.0386			−0.877909			−0.438954	−	0.898509i	$-0.644651\pi$
$521$	−20.0386			−0.877909			−0.438954	+	0.898509i	$0.644651\pi$
$522$	2.38437	+	4.12985i	0.104361	+	0.180758i
$523$	−6.62959	−	11.4828i	−0.289892	−	0.502107i	0.683892	−	0.729583i	$-0.260286\pi$
$523$	−6.62959	−	11.4828i	−0.289892	−	0.502107i	−0.973784	+	0.227476i	$0.926953\pi$
$524$	10.9056	−	18.8890i	0.476411	−	0.825168i
$525$		0			0
$526$	6.15310	−	10.6575i	0.268288	−	0.464688i
$527$	−6.02254	+	10.4314i	−0.262346	+	0.454397i
$528$	−47.8884			−2.08407
$529$	−3.83178	+	6.63684i	−0.166599	+	0.288558i
$530$		0			0
$531$	3.68521	+	6.38297i	0.159924	+	0.276997i
$532$	−116.256			−5.04034
$533$	−17.2783	−	8.74059i	−0.748406	−	0.378597i
$534$	−25.5822			−1.10705
$535$		0			0
$536$	−12.6101	−	21.8413i	−0.544672	−	0.943400i
$537$	9.22268	−	15.9741i	0.397988	−	0.689335i
$538$	14.1610			0.610524
$539$	15.5375	−	26.9117i	0.669246	−	1.15917i
$540$		0			0
$541$	35.6850			1.53422			0.767109	−	0.641516i	$-0.221694\pi$
$541$	35.6850			1.53422			0.767109	+	0.641516i	$0.221694\pi$
$542$	33.1445	−	57.4080i	1.42368	−	2.46588i
$543$	−10.5514	−	18.2756i	−0.452805	−	0.784281i
$544$	14.0000	+	24.2487i	0.600245	+	1.03965i
$545$		0			0
$546$	30.1475	+	15.2508i	1.29020	+	0.652673i
$547$	0.627256			0.0268195			0.0134098	−	0.999910i	$-0.495731\pi$
$547$	0.627256			0.0268195			0.0134098	+	0.999910i	$0.495731\pi$
$548$	25.4514	+	44.0831i	1.08723	+	1.88314i
$549$	1.71731	+	2.97447i	0.0732931	+	0.126947i
$550$		0			0
$551$	12.4067			0.528544
$552$	−19.9442	+	34.5443i	−0.848881	+	1.47030i
$553$	−7.38856	+	12.7974i	−0.314194	+	0.544200i
$554$	−59.3532			−2.52168
$555$		0			0
$556$	38.5017	+	66.6869i	1.63283	+	2.82815i
$557$	4.60401	+	7.97438i	0.195078	+	0.337885i	0.946926	−	0.321451i	$-0.104171\pi$
$557$	4.60401	+	7.97438i	0.195078	+	0.337885i	−0.751848	+	0.659337i	$0.770837\pi$
$558$	−10.6743			−0.451879
$559$	0.630752	+	11.4015i	0.0266780	+	0.482234i
$560$		0			0
$561$	7.63798	+	13.2294i	0.322476	+	0.558545i
$562$	−2.81899	−	4.88264i	−0.118912	−	0.205962i
$563$	1.33411	−	2.31075i	0.0562260	−	0.0973864i	−0.836542	−	0.547902i	$-0.815427\pi$
$563$	1.33411	−	2.31075i	0.0562260	−	0.0973864i	0.892768	+	0.450516i	$0.148760\pi$
$564$	−18.1452			−0.764051
$565$		0			0
$566$	38.6959	−	67.0233i	1.62651	−	2.81720i
$567$	−3.60168			−0.151256
$568$	−34.9526	+	60.5396i	−1.46658	+	2.54019i
$569$	13.0919	+	22.6759i	0.548842	+	0.950622i	0.998354	+	0.0573480i	$0.0182645\pi$
$569$	13.0919	+	22.6759i	0.548842	+	0.950622i	−0.449512	+	0.893274i	$0.648402\pi$
$570$		0			0
$571$	−19.2481			−0.805506			−0.402753	−	0.915309i	$-0.631947\pi$
$571$	−19.2481			−0.805506			−0.402753	+	0.915309i	$0.631947\pi$
$572$	74.8907	−	48.9445i	3.13134	−	2.04647i
$573$	−8.70219			−0.363539
$574$	25.1615	+	43.5810i	1.05022	+	1.81904i
$575$		0			0
$576$	−3.20336	+	5.54838i	−0.133473	+	0.231182i
$577$	−23.8716			−0.993787			−0.496893	−	0.867812i	$-0.665526\pi$
$577$	−23.8716			−0.993787			−0.496893	+	0.867812i	$0.665526\pi$
$578$	−10.9025	+	18.8837i	−0.453485	+	0.785459i
$579$	9.63378	−	16.6862i	0.400366	−	0.693455i
$580$		0			0
$581$	20.7771	−	35.9870i	0.861981	−	1.49299i
$582$	7.25058	+	12.5584i	0.300546	+	0.520562i
$583$	13.5375	+	23.4476i	0.560665	+	0.971100i
$584$	−5.79897			−0.239963
$585$		0			0
$586$	86.0783			3.55586
$587$	14.4377	+	25.0068i	0.595906	+	1.03214i	0.993418	+	0.114542i	$0.0365402\pi$
$587$	14.4377	+	25.0068i	0.595906	+	1.03214i	−0.397513	+	0.917597i	$0.630126\pi$
$588$	−14.2397	−	24.6638i	−0.587234	−	1.01712i
$589$	−13.8855	+	24.0504i	−0.572143	+	0.990981i
$590$		0			0
$591$	−7.57377	+	13.1182i	−0.311543	+	0.539609i
$592$	−16.2783	+	28.1948i	−0.669034	+	1.15880i
$593$	8.74083			0.358943			0.179471	−	0.983763i	$-0.442561\pi$
$593$	8.74083			0.358943			0.179471	+	0.983763i	$0.442561\pi$
$594$	−6.76873	+	11.7238i	−0.277725	+	0.481033i
$595$		0			0
$596$	23.0470	+	39.9186i	0.944043	+	1.63513i
$597$	−4.53747			−0.185706
$598$	−2.86925	−	51.8649i	−0.117332	−	2.12091i
$599$	21.5929			0.882262			0.441131	−	0.897443i	$-0.354577\pi$
$599$	21.5929			0.882262			0.441131	+	0.897443i	$0.354577\pi$
$600$		0			0
$601$	−15.1252	−	26.1976i	−0.616970	−	1.06862i	−0.990036	−	0.140818i	$-0.955027\pi$
$601$	−15.1252	−	26.1976i	−0.616970	−	1.06862i	0.373066	−	0.927805i	$-0.378306\pi$
$602$	14.8383	−	25.7007i	0.604764	−	1.04748i
$603$	−3.50117			−0.142578
$604$	44.6185	−	77.2815i	1.81550	−	3.14454i
$605$		0			0
$606$	−6.26150			−0.254356
$607$	−11.2536	+	19.4918i	−0.456770	+	0.791149i	−0.998788	−	0.0492178i	$-0.984327\pi$
$607$	−11.2536	+	19.4918i	−0.456770	+	0.791149i	0.542018	+	0.840367i	$0.317660\pi$
$608$	32.2783	+	55.9076i	1.30906	+	2.26735i
$609$	3.30084	+	5.71722i	0.133757	+	0.231674i
$610$		0			0
$611$	11.4842	−	7.50544i	0.464600	−	0.303638i
$612$	14.0000			0.565916
$613$	9.38856	+	16.2615i	0.379201	+	0.656795i	0.990946	−	0.134260i	$-0.0428657\pi$
$613$	9.38856	+	16.2615i	0.379201	+	0.656795i	−0.611746	+	0.791055i	$0.709532\pi$
$614$	18.6936	+	32.3783i	0.754412	+	1.30668i
$615$		0			0
$616$	−134.997			−5.43918
$617$	−1.80504	+	3.12642i	−0.0726681	+	0.125865i	−0.900070	−	0.435746i	$-0.856485\pi$
$617$	−1.80504	+	3.12642i	−0.0726681	+	0.125865i	0.827402	+	0.561610i	$0.189818\pi$
$618$	−23.9914	+	41.5543i	−0.965076	+	1.67156i
$619$	2.87158			0.115419			0.0577093	−	0.998333i	$-0.481620\pi$
$619$	2.87158			0.115419			0.0577093	+	0.998333i	$0.481620\pi$
$620$		0			0
$621$	2.76873	+	4.79559i	0.111105	+	0.192440i
$622$	−11.3262	−	19.6176i	−0.454140	−	0.786594i
$623$	−35.4151			−1.41888
$624$	−1.83294	−	33.1325i	−0.0733765	−	1.32636i
$625$		0			0
$626$	10.6210	+	18.3961i	0.424500	+	0.735256i
$627$	17.6101	+	30.5015i	0.703279	+	1.21811i
$628$	−24.7269	+	42.8282i	−0.986710	+	1.70903i
$629$	10.3853			0.414088
$630$		0			0
$631$	−8.49444	+	14.7128i	−0.338158	+	0.585708i	−0.984086	−	0.177691i	$-0.943137\pi$
$631$	−8.49444	+	14.7128i	−0.338158	+	0.585708i	0.645928	+	0.763398i	$0.276471\pi$
$632$	29.5543			1.17561
$633$	11.0738	−	19.1803i	0.440143	−	0.762350i
$634$	−17.4430	−	30.2122i	−0.692751	−	1.19988i
$635$		0			0
$636$	24.8134			0.983917
$637$	19.2141	+	9.71985i	0.761290	+	0.385115i
$638$	24.8134			0.982373
$639$	4.85226	+	8.40436i	0.191953	+	0.332472i
$640$		0			0
$641$	8.30620	−	14.3868i	0.328075	−	0.568243i	−0.654055	−	0.756447i	$-0.726933\pi$
$641$	8.30620	−	14.3868i	0.328075	−	0.568243i	0.982130	+	0.188204i	$0.0602667\pi$
$642$	28.4514			1.12289
$643$	22.6701	−	39.2657i	0.894021	−	1.54849i	0.0590094	−	0.998257i	$-0.481206\pi$
$643$	22.6701	−	39.2657i	0.894021	−	1.54849i	0.835012	−	0.550232i	$-0.185461\pi$
$644$	−47.5543	+	82.3664i	−1.87390	+	3.24569i
$645$		0			0
$646$	25.8497	−	44.7731i	1.01704	−	1.76157i
$647$	2.43462	+	4.21689i	0.0957149	+	0.165783i	0.909907	−	0.414813i	$-0.136153\pi$
$647$	2.43462	+	4.21689i	0.0957149	+	0.165783i	−0.814192	+	0.580596i	$0.802820\pi$
$648$	3.60168	+	6.23829i	0.141487	+	0.245063i
$649$	38.3509			1.50540
$650$		0			0
$651$	−14.7771			−0.579161
$652$	−27.3565	−	47.3828i	−1.07136	−	1.85565i
$653$	9.63495	+	16.6882i	0.377045	+	0.653061i	0.990631	−	0.136567i	$-0.0436070\pi$
$653$	9.63495	+	16.6882i	0.377045	+	0.653061i	−0.613586	+	0.789628i	$0.710274\pi$
$654$	18.0417	−	31.2491i	0.705485	−	1.22194i
$655$		0			0
$656$	24.7129	−	42.8040i	0.964877	−	1.67122i
$657$	−0.402519	+	0.697183i	−0.0157038	+	0.0271997i
$658$	−35.6548			−1.38997
$659$	−0.167055	+	0.289348i	−0.00650755	+	0.0112714i	−0.869261	−	0.494354i	$-0.835405\pi$
$659$	−0.167055	+	0.289348i	−0.00650755	+	0.0112714i	0.862753	+	0.505625i	$0.168738\pi$
$660$		0			0
$661$	6.83411	+	11.8370i	0.265816	+	0.460407i	0.967777	−	0.251808i	$-0.0810253\pi$
$661$	6.83411	+	11.8370i	0.265816	+	0.460407i	−0.701961	+	0.712215i	$0.747692\pi$
$662$	−55.8823			−2.17193
$663$	−8.86066	+	5.79085i	−0.344119	+	0.224898i
$664$	−83.1085			−3.22524
$665$		0			0
$666$	4.60168	+	7.97034i	0.178311	+	0.308844i
$667$	5.07494	−	8.79005i	0.196502	−	0.340352i
$668$	14.9297			0.577648
$669$	−3.80504	+	6.59052i	−0.147111	+	0.254804i
$670$		0			0
$671$	17.8716			0.689925
$672$	−17.1755	+	29.7488i	−0.662557	+	1.14758i
$673$	−10.9400	−	18.9486i	−0.421706	−	0.730415i	0.574401	−	0.818574i	$-0.305235\pi$
$673$	−10.9400	−	18.9486i	−0.421706	−	0.730415i	−0.996106	+	0.0881587i	$0.971902\pi$
$674$	9.68521	+	16.7753i	0.373060	+	0.646159i
$675$		0			0
$676$	36.7297	+	49.9412i	1.41268	+	1.92082i
$677$	17.0749			0.656243			0.328122	−	0.944636i	$-0.393584\pi$
$677$	17.0749			0.656243			0.328122	+	0.944636i	$0.393584\pi$
$678$	14.5738	+	25.2425i	0.559702	+	0.969433i
$679$	10.0375	+	17.3854i	0.385203	+	0.667191i
$680$		0			0
$681$	−23.3425			−0.894487
$682$	−27.7711	+	48.1009i	−1.06341	+	1.84188i
$683$	−13.3651	+	23.1489i	−0.511399	+	0.885770i	0.488513	+	0.872556i	$0.337539\pi$
$683$	−13.3651	+	23.1489i	−0.511399	+	0.885770i	−0.999913	+	0.0132133i	$0.995794\pi$
$684$	32.2783			1.23419
$685$		0			0
$686$	4.81596	+	8.34149i	0.183874	+	0.318479i
$687$	−0.412275	−	0.714081i	−0.0157293	−	0.0272439i
$688$	−29.1475			−1.11124
$689$	−15.7045	+	10.2636i	−0.598295	+	0.391013i
$690$		0			0
$691$	−24.3576	−	42.1886i	−0.926608	−	1.60493i	−0.788955	−	0.614451i	$-0.789378\pi$
$691$	−24.3576	−	42.1886i	−0.926608	−	1.60493i	−0.137653	−	0.990481i	$-0.543956\pi$
$692$	19.7129	+	34.1438i	0.749373	+	1.29795i
$693$	−9.37041	+	16.2300i	−0.355953	+	0.616528i
$694$	−64.9028			−2.46368
$695$		0			0
$696$	6.60168	−	11.4344i	0.250236	−	0.433421i
$697$	−15.7664			−0.597195
$698$	2.73546	−	4.73796i	0.103539	−	0.179334i
$699$	−6.70219	−	11.6085i	−0.253500	−	0.439075i
$700$		0			0
$701$	22.9419			0.866502			0.433251	−	0.901273i	$-0.357366\pi$
$701$	22.9419			0.866502			0.433251	+	0.901273i	$0.357366\pi$
$702$	−8.37041	−	4.23435i	−0.315921	−	0.159815i
$703$	23.9442			0.903072
$704$	16.6682	+	28.8702i	0.628207	+	1.08809i
$705$		0			0
$706$	−24.1173	+	41.7724i	−0.907667	+	1.57212i
$707$	−8.66822			−0.326002
$708$	17.5738	−	30.4387i	0.660463	−	1.14396i
$709$	3.57261	−	6.18794i	0.134172	−	0.232393i	−0.791109	−	0.611675i	$-0.790496\pi$
$709$	3.57261	−	6.18794i	0.134172	−	0.232393i	0.925281	+	0.379283i	$0.123829\pi$
$710$		0			0
$711$	2.05142	−	3.55317i	0.0769343	−	0.133254i
$712$	35.4151	+	61.3408i	1.32724	+	2.29884i
$713$	11.3597	+	19.6756i	0.425424	+	0.736855i
$714$	27.5096			1.02952
$715$		0			0
$716$	−87.9610			−3.28726
$717$	−6.39832	−	11.0822i	−0.238950	−	0.413873i
$718$	−6.18940	−	10.7204i	−0.230987	−	0.400080i
$719$	−20.9891	+	36.3542i	−0.782761	+	1.35578i	0.147567	+	0.989052i	$0.452856\pi$
$719$	−20.9891	+	36.3542i	−0.782761	+	1.35578i	−0.930328	+	0.366729i	$0.880478\pi$
$720$		0			0
$721$	−33.2129	+	57.5265i	−1.23691	+	2.14240i
$722$	34.8830	−	60.4191i	1.29821	−	2.24857i
$723$	12.7687			0.474874
$724$	−50.3169	+	87.1515i	−1.87001	+	3.23896i
$725$		0			0
$726$	20.9109	+	36.2188i	0.776077	+	1.34420i
$727$	11.4965			0.426382			0.213191	−	0.977011i	$-0.431614\pi$
$727$	11.4965			0.426382			0.213191	+	0.977011i	$0.431614\pi$
$728$	−5.16706	−	93.4003i	−0.191504	−	3.46164i
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.64890	+	8.05214i	0.171946	+	0.297819i
$732$	8.18940	−	14.1845i	0.302689	−	0.524273i
$733$	−46.1136			−1.70324			−0.851622	−	0.524157i	$-0.824381\pi$
$733$	−46.1136			−1.70324			−0.851622	+	0.524157i	$0.824381\pi$
$734$	13.3232	−	23.0764i	0.491768	−	0.851767i
$735$		0			0
$736$	52.8134			1.94673
$737$	−9.10891	+	15.7771i	−0.335531	+	0.581157i
$738$	−6.98605	−	12.1002i	−0.257160	−	0.445414i
$739$	5.80504	+	10.0546i	0.213542	+	0.369865i	0.952820	−	0.303534i	$-0.0981667\pi$
$739$	5.80504	+	10.0546i	0.213542	+	0.369865i	−0.739279	+	0.673400i	$0.764833\pi$
$740$		0			0
$741$	−20.4291	+	13.3513i	−0.750480	+	0.490474i
$742$	48.7576			1.78995
$743$	6.70756	+	11.6178i	0.246076	+	0.426217i	0.962434	−	0.271517i	$-0.0875253\pi$
$743$	6.70756	+	11.6178i	0.246076	+	0.426217i	−0.716357	+	0.697734i	$0.754192\pi$
$744$	14.7771	+	25.5947i	0.541756	+	0.938349i
$745$		0			0
$746$	−60.7236			−2.22325
$747$	−5.76873	+	9.99174i	−0.211067	+	0.365579i
$748$	36.4235	−	63.0874i	1.33178	−	2.30670i
$749$	39.3872			1.43918
$750$		0			0
$751$	−22.0866	−	38.2550i	−0.805950	−	1.39595i	−0.915648	−	0.401981i	$-0.868322\pi$
$751$	−22.0866	−	38.2550i	−0.805950	−	1.39595i	0.109698	−	0.993965i	$-0.465012\pi$
$752$	17.5096	+	30.3274i	0.638508	+	1.10593i
$753$	−8.40672			−0.306358
$754$	0.949743	+	17.1677i	0.0345876	+	0.625210i
$755$		0			0
$756$	8.58773	+	14.8744i	0.312333	+	0.540976i
$757$	3.98605	+	6.90403i	0.144875	+	0.250931i	0.929326	−	0.369259i	$-0.120389\pi$
$757$	3.98605	+	6.90403i	0.144875	+	0.250931i	−0.784451	+	0.620191i	$0.787055\pi$
$758$	−46.3842	+	80.3397i	−1.68475	+	2.91807i
$759$	28.8134			1.04586
$760$		0			0
$761$	−6.83294	+	11.8350i	−0.247694	+	0.429019i	−0.962886	−	0.269910i	$-0.913006\pi$
$761$	−6.83294	+	11.8350i	−0.247694	+	0.429019i	0.715192	+	0.698928i	$0.246339\pi$
$762$	−8.31227			−0.301122
$763$	24.9763	−	43.2602i	0.904202	−	1.56612i
$764$	20.7492	+	35.9387i	0.750681	+	1.30022i
$765$		0			0
$766$	−79.6594			−2.87821
$767$	1.46789	+	26.5338i	0.0530026	+	0.958081i
$768$	−19.0749			−0.688308
$769$	−8.24522	−	14.2811i	−0.297330	−	0.514991i	0.678194	−	0.734883i	$-0.262763\pi$
$769$	−8.24522	−	14.2811i	−0.297330	−	0.514991i	−0.975524	+	0.219892i	$0.929430\pi$
$770$		0			0
$771$	3.06957	−	5.31666i	0.110548	−	0.191475i
$772$	−91.8819			−3.30690
$773$	−22.8521	+	39.5809i	−0.821932	+	1.42363i	0.0823101	+	0.996607i	$0.473770\pi$
$773$	−22.8521	+	39.5809i	−0.821932	+	1.42363i	−0.904242	+	0.427021i	$0.859563\pi$
$774$	−4.11983	+	7.13576i	−0.148084	+	0.256489i
$775$		0			0
$776$	20.0749	−	34.7708i	0.720648	−	1.24820i
$777$	6.37041	+	11.0339i	0.228537	+	0.395838i
$778$	32.5459	+	56.3711i	1.16683	+	2.02100i
$779$	−36.3509			−1.30241
$780$		0			0
$781$	50.4961			1.80689
$782$	−21.1475	−	36.6286i	−0.756235	−	1.30984i
$783$	−0.916472	−	1.58738i	−0.0327521	−	0.0567282i
$784$	−27.4817	+	47.5996i	−0.981488	+	1.69999i
$785$		0			0
$786$	−5.94974	+	10.3053i	−0.212220	+	0.367576i
$787$	−24.4109	+	42.2809i	−0.870155	+	1.50715i	−0.00831938	+	0.999965i	$0.502648\pi$
$787$	−24.4109	+	42.2809i	−0.870155	+	1.50715i	−0.861836	+	0.507187i	$0.830685\pi$
$788$	72.2346			2.57325
$789$	−2.36505	+	4.09639i	−0.0841980	+	0.145835i
$790$		0			0
$791$	20.1755	+	34.9449i	0.717356	+	1.24250i
$792$	37.4817			1.33185
$793$	0.684041	+	12.3648i	0.0242910	+	0.439087i
$794$	28.1838			1.00021
$795$		0			0
$796$	10.8190	+	18.7390i	0.383469	+	0.664188i
$797$	6.87461	−	11.9072i	0.243511	−	0.421774i	−0.718201	−	0.695836i	$-0.755034\pi$
$797$	6.87461	−	11.9072i	0.243511	−	0.421774i	0.961712	+	0.274062i	$0.0883674\pi$
$798$	63.4258			2.24525
$799$	5.58539	−	9.67419i	0.197597	−	0.342248i
$800$		0			0
$801$	9.83294			0.347430
$802$	−31.8437	+	55.1549i	−1.12444	+	1.94759i
$803$	2.09445	+	3.62769i	0.0739115	+	0.128018i
$804$	8.34806	+	14.4593i	0.294414	+	0.509939i
$805$		0			0
$806$	−34.3425	−	17.3729i	−1.20966	−	0.611934i
$807$	−5.44302			−0.191603
$808$	8.66822	+	15.0138i	0.304947	+	0.528184i
$809$	−10.1671	−	17.6099i	−0.357455	−	0.619130i	0.630080	−	0.776530i	$-0.283022\pi$
$809$	−10.1671	−	17.6099i	−0.357455	−	0.619130i	−0.987535	+	0.157400i	$0.949689\pi$
$810$		0			0
$811$	22.4817			0.789438			0.394719	−	0.918802i	$-0.370842\pi$
$811$	22.4817			0.789438			0.394719	+	0.918802i	$0.370842\pi$
$812$	15.7408	−	27.2639i	0.552395	−	0.956776i
$813$	−12.7397	+	22.0657i	−0.446799	+	0.773879i
$814$	47.8884			1.67849
$815$		0			0
$816$	−13.5096	−	23.3992i	−0.472929	−	0.819137i
$817$	10.7185	+	18.5649i	0.374992	+	0.649505i
$818$	−69.4924			−2.42974
$819$	−11.5877	−	5.86190i	−0.404908	−	0.204831i
$820$		0			0
$821$	16.3039	+	28.2391i	0.569009	+	0.985553i	0.996664	+	0.0816107i	$0.0260064\pi$
$821$	16.3039	+	28.2391i	0.569009	+	0.985553i	−0.427655	+	0.903942i	$0.640660\pi$
$822$	−13.8855	−	24.0504i	−0.484314	−	0.838856i
$823$	16.7408	−	28.9960i	0.583549	−	1.01074i	−0.411506	−	0.911407i	$-0.634997\pi$
$823$	16.7408	−	28.9960i	0.583549	−	1.01074i	0.995055	−	0.0993287i	$-0.0316695\pi$
$824$	132.852			4.62811
$825$		0			0
$826$	34.5319	−	59.8110i	1.20152	−	2.08109i
$827$	51.0298			1.77448			0.887241	−	0.461306i	$-0.152619\pi$
$827$	51.0298			1.77448			0.887241	+	0.461306i	$0.152619\pi$
$828$	13.2034	−	22.8689i	0.458848	−	0.794749i
$829$	−10.5973	−	18.3550i	−0.368059	−	0.637497i	0.621203	−	0.783650i	$-0.286644\pi$
$829$	−10.5973	−	18.3550i	−0.368059	−	0.637497i	−0.989262	+	0.146153i	$0.953311\pi$
$830$		0			0
$831$	22.8134			0.791389
$832$	−19.3364	+	12.6373i	−0.670370	+	0.438118i
$833$	17.5328			0.607476
$834$	−21.0054	−	36.3824i	−0.727356	−	1.25982i
$835$		0			0
$836$	83.9778	−	145.454i	2.90443	−	5.03062i
$837$	4.10284			0.141815
$838$	19.5598	−	33.8786i	0.675683	−	1.17032i
$839$	−26.9419	+	46.6647i	−0.930136	+	1.61104i	−0.147051	+	0.989129i	$0.546978\pi$
$839$	−26.9419	+	46.6647i	−0.930136	+	1.61104i	−0.783086	+	0.621914i	$0.786355\pi$
$840$		0			0
$841$	12.8202	−	22.2052i	0.442074	−	0.765695i
$842$	−7.67732	−	13.2975i	−0.264578	−	0.458262i
$843$	1.08353	+	1.87672i	0.0373187	+	0.0646378i
$844$	−105.616			−3.63544
$845$		0			0
$846$	9.89949			0.340351
$847$	28.9484	+	50.1401i	0.994678	+	1.72283i
$848$	−23.9442	−	41.4725i	−0.822247	−	1.42417i
$849$	−14.8734	+	25.7616i	−0.510455	+	0.884135i
$850$		0			0
$851$	9.79431	−	16.9642i	0.335745	−	0.581527i
$852$	23.1391	−	40.0782i	0.792734	−	1.37306i
$853$	4.06421			0.139156			0.0695780	−	0.997577i	$-0.477835\pi$
$853$	4.06421			0.139156			0.0695780	+	0.997577i	$0.477835\pi$
$854$	16.0919	−	27.8720i	0.550654	−	0.953761i
$855$		0			0
$856$	−39.3872	−	68.2206i	−1.34623	−	2.33173i
$857$	39.2141			1.33953			0.669764	−	0.742574i	$-0.266395\pi$
$857$	39.2141			1.33953			0.669764	+	0.742574i	$0.266395\pi$
$858$	−40.8581	+	26.7027i	−1.39487	+	0.911614i
$859$	−5.64031			−0.192445			−0.0962225	−	0.995360i	$-0.530676\pi$
$859$	−5.64031			−0.192445			−0.0962225	+	0.995360i	$0.530676\pi$
$860$		0			0
$861$	−9.67125	−	16.7511i	−0.329595	−	0.570876i
$862$	51.1862	−	88.6571i	1.74341	−	3.01967i
$863$	9.66589			0.329031			0.164515	−	0.986375i	$-0.447394\pi$
$863$	9.66589			0.329031			0.164515	+	0.986375i	$0.447394\pi$
$864$	4.76873	−	8.25969i	0.162236	−	0.281000i
$865$		0			0
$866$	32.3001			1.09760
$867$	4.19057	−	7.25828i	0.142319	−	0.246504i
$868$	35.2341	+	61.0273i	1.19592	+	2.07140i
$869$	−10.6743	−	18.4884i	−0.362100	−	0.627176i
$870$		0			0
$871$	−11.2643	−	5.69831i	−0.381678	−	0.193080i
$872$	−99.9052			−3.38322
$873$	−2.78689	−	4.82703i	−0.0943218	−	0.163370i
$874$	−48.7576	−	84.4507i	−1.64925	−	2.85659i
$875$		0			0
$876$	3.83901			0.129708
$877$	7.93579	−	13.7452i	0.267973	−	0.464142i	−0.700366	−	0.713784i	$-0.746980\pi$
$877$	7.93579	−	13.7452i	0.267973	−	0.464142i	0.968338	+	0.249642i	$0.0803130\pi$
$878$	41.4205	−	71.7424i	1.39787	−	2.42119i
$879$	−33.0857			−1.11595
$880$		0			0
$881$	14.6017	+	25.2909i	0.491943	+	0.852070i	0.999957	−	0.00927849i	$-0.00295348\pi$
$881$	14.6017	+	25.2909i	0.491943	+	0.852070i	−0.508014	+	0.861349i	$0.669620\pi$
$882$	7.76873	+	13.4558i	0.261587	+	0.453082i
$883$	−30.4598			−1.02505			−0.512527	−	0.858671i	$-0.671291\pi$
$883$	−30.4598			−1.02505			−0.512527	+	0.858671i	$0.671291\pi$
$884$	45.0424	+	22.7856i	1.51494	+	0.766364i
$885$		0			0
$886$	1.38437	+	2.39779i	0.0465087	+	0.0805555i
$887$	5.79967	+	10.0453i	0.194734	+	0.337289i	0.946813	−	0.321783i	$-0.104282\pi$
$887$	5.79967	+	10.0453i	0.194734	+	0.337289i	−0.752079	+	0.659073i	$0.770949\pi$
$888$	12.7408	−	22.0678i	0.427554	−	0.740546i
$889$	−11.5072			−0.385940
$890$		0			0
$891$	2.60168	−	4.50624i	0.0871595	−	0.150965i
$892$	36.2904			1.21509
$893$	12.8776	−	22.3047i	0.430934	−	0.746399i
$894$	−12.5738	−	21.7784i	−0.420530	−	0.728379i
$895$		0			0
$896$	−8.66822			−0.289585
$897$	1.10284	+	19.9351i	0.0368229	+	0.665615i
$898$	−40.0773			−1.33740
$899$	−3.76014	−	6.51276i	−0.125408	−	0.217213i
$900$		0			0
$901$	−7.63798	+	13.2294i	−0.254458	+	0.440734i
$902$	−72.7018			−2.42071
$903$	−5.70336	+	9.87851i	−0.189796	+	0.328736i
$904$	40.3509	−	69.8898i	1.34205	−	2.32450i
$905$		0			0
$906$	−24.3425	+	42.1625i	−0.808726	+	1.40075i
$907$	21.4593	+	37.1686i	0.712545	+	1.23416i	0.963899	+	0.266268i	$0.0857907\pi$
$907$	21.4593	+	37.1686i	0.712545	+	1.23416i	−0.251354	+	0.967895i	$0.580876\pi$
$908$	55.6571	+	96.4009i	1.84705	+	3.19918i
$909$	2.40672			0.0798257
$910$		0			0
$911$	42.0726			1.39393			0.696964	−	0.717106i	$-0.254534\pi$
$911$	42.0726			1.39393			0.696964	+	0.717106i	$0.254534\pi$
$912$	−31.1475	−	53.9491i	−1.03140	−	1.78643i
$913$	30.0168	+	51.9906i	0.993411	+	1.72064i
$914$	12.4539	−	21.5709i	0.411940	−	0.713501i
$915$		0			0
$916$	−1.96603	+	3.40526i	−0.0649594	+	0.112513i
$917$	−8.23663	+	14.2663i	−0.271997	+	0.471113i
$918$	−7.63798			−0.252091
$919$	−19.5575	+	33.8746i	−0.645142	+	1.11742i	0.339127	+	0.940741i	$0.389868\pi$
$919$	−19.5575	+	33.8746i	−0.645142	+	1.11742i	−0.984269	+	0.176678i	$0.943465\pi$
$920$		0			0
$921$	−7.18521	−	12.4451i	−0.236761	−	0.410081i
$922$	−42.5966			−1.40285
$923$	1.93276	+	34.9367i	0.0636175	+	1.14996i
$924$	89.3700			2.94006
$925$		0			0
$926$	32.0640	+	55.5365i	1.05369	+	1.82504i
$927$	9.22151	−	15.9721i	0.302874	−	0.524593i
$928$	−17.4817			−0.573863
$929$	−5.23127	+	9.06082i	−0.171632	+	0.297276i	−0.938991	−	0.343943i	$-0.888237\pi$
$929$	−5.23127	+	9.06082i	−0.171632	+	0.297276i	0.767358	+	0.641218i	$0.221571\pi$
$930$		0			0
$931$	40.4235			1.32483
$932$	−31.9610	+	55.3580i	−1.04692	+	1.81331i
$933$	4.35343	+	7.54036i	0.142525	+	0.246860i
$934$	26.4593	+	45.8289i	0.865775	+	1.49957i
$935$		0			0
$936$	1.43462	+	25.9324i	0.0468922	+	0.847628i
$937$	−39.6269			−1.29455			−0.647277	−	0.762255i	$-0.724092\pi$
$937$	−39.6269			−1.29455			−0.647277	+	0.762255i	$0.724092\pi$
$938$	16.4037	+	28.4120i	0.535599	+	0.927685i
$939$	−4.08236	−	7.07086i	−0.133223	−	0.230749i
$940$		0			0
$941$	15.3146			0.499242			0.249621	−	0.968344i	$-0.419694\pi$
$941$	15.3146			0.499242			0.249621	+	0.968344i	$0.419694\pi$
$942$	13.4902	−	23.3658i	0.439536	−	0.761299i
$943$	−14.8692	+	25.7543i	−0.484209	+	0.838675i
$944$	−67.8326			−2.20776
$945$		0			0
$946$	21.4370	+	37.1299i	0.696976	+	1.20720i
$947$	−16.6433	−	28.8271i	−0.540836	−	0.936756i	−0.998856	−	0.0478138i	$-0.984775\pi$
$947$	−16.6433	−	28.8271i	−0.540836	−	0.936756i	0.458020	−	0.888942i	$-0.348559\pi$
$948$	−19.5654			−0.635454
$949$	−2.42972	+	1.58794i	−0.0788722	+	0.0515466i
$950$		0			0
$951$	6.70452	+	11.6126i	0.217409	+	0.376564i
$952$	−38.0833	−	65.9623i	−1.23429	−	2.13785i
$953$	11.7045	−	20.2728i	0.379147	−	0.656701i	−0.611792	−	0.791019i	$-0.709551\pi$
$953$	11.7045	−	20.2728i	0.379147	−	0.656701i	0.990938	+	0.134318i	$0.0428842\pi$
$954$	−13.5375			−0.438292
$955$		0			0
$956$	−30.5119	+	52.8481i	−0.986825	+	1.70923i
$957$	−9.53747			−0.308303
$958$	−0.211247	+	0.365891i	−0.00682509	+	0.0118214i
$959$	−19.2227	−	33.2947i	−0.620733	−	1.07514i
$960$		0			0
$961$	−14.1667			−0.456989
$962$	1.83294	+	33.1325i	0.0590965	+	1.06824i
$963$	−10.9358			−0.352401
$964$	−30.4454	−	52.7329i	−0.980579	−	1.69841i
$965$		0			0
$966$	25.9442	−	44.9366i	0.834740	−	1.44581i
$967$	−27.8669			−0.896140			−0.448070	−	0.893999i	$-0.647888\pi$
$967$	−27.8669			−0.896140			−0.448070	+	0.893999i	$0.647888\pi$
$968$	57.8968	−	100.280i	1.86087	−	3.22313i
$969$	−9.93579	+	17.2093i	−0.319184	+	0.552842i
$970$		0			0
$971$	2.25917	−	3.91300i	0.0725003	−	0.125574i	−0.827496	−	0.561471i	$-0.810236\pi$
$971$	2.25917	−	3.91300i	0.0725003	−	0.125574i	0.899997	+	0.435897i	$0.143569\pi$
$972$	−2.38437	−	4.12985i	−0.0764786	−	0.132465i
$973$	−29.0791	−	50.3665i	−0.932234	−	1.61468i
$974$	6.66822			0.213664
$975$		0			0
$976$	−31.6101			−1.01181
$977$	−21.2420	−	36.7922i	−0.679592	−	1.17709i	−0.975104	−	0.221748i	$-0.928824\pi$
$977$	−21.2420	−	36.7922i	−0.679592	−	1.17709i	0.295512	−	0.955339i	$-0.404510\pi$
$978$	14.9249	+	25.8506i	0.477245	+	0.826612i
$979$	25.5822	−	44.3096i	0.817610	−	1.41614i
$980$		0			0
$981$	−6.93462	+	12.0111i	−0.221406	+	0.383486i
$982$	36.9968	−	64.0803i	1.18061	−	2.04488i
$983$	−9.87158			−0.314854			−0.157427	−	0.987531i	$-0.550320\pi$
$983$	−9.87158			−0.314854			−0.157427	+	0.987531i	$0.550320\pi$
$984$	−19.3425	+	33.5022i	−0.616617	+	1.06801i
$985$		0			0
$986$	7.00000	+	12.1244i	0.222925	+	0.386118i
$987$	13.7045			0.436220
$988$	103.849	+	52.5344i	3.30389	+	1.67134i
$989$	17.5375			0.557659
$990$		0			0
$991$	−10.5598	−	18.2901i	−0.335444	−	0.581005i	0.648126	−	0.761533i	$-0.275553\pi$
$991$	−10.5598	−	18.2901i	−0.335444	−	0.581005i	−0.983570	+	0.180527i	$0.942220\pi$
$992$	19.5654	−	33.8882i	0.621201	−	1.07595i
$993$	21.4793			0.681626
$994$	45.4677	−	78.7524i	1.44215	−	2.49787i
$995$		0			0
$996$	55.0191			1.74335
$997$	8.54167	−	14.7946i	0.270517	−	0.468550i	−0.698477	−	0.715632i	$-0.746139\pi$
$997$	8.54167	−	14.7946i	0.270517	−	0.468550i	0.968994	+	0.247083i	$0.0794719\pi$
$998$	−36.2420	−	62.7730i	−1.14722	−	1.98704i
$999$	−1.76873	−	3.06354i	−0.0559603	−	0.0969260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.l.601.3		6
5.2	odd	4		975.2.bb.k.874.1		12
5.3	odd	4		975.2.bb.k.874.6		12
5.4	even	2		195.2.i.d.16.1	✓	6
13.9	even	3	inner	975.2.i.l.451.3		6
15.14	odd	2		585.2.j.f.406.3		6
65.9	even	6		195.2.i.d.61.1	yes	6
65.22	odd	12		975.2.bb.k.724.6		12
65.29	even	6		2535.2.a.bb.1.3		3
65.48	odd	12		975.2.bb.k.724.1		12
65.49	even	6		2535.2.a.ba.1.1		3
195.29	odd	6		7605.2.a.bv.1.1		3
195.74	odd	6		585.2.j.f.451.3		6
195.179	odd	6		7605.2.a.bw.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.1	✓	6	5.4	even	2
195.2.i.d.61.1	yes	6	65.9	even	6
585.2.j.f.406.3		6	15.14	odd	2
585.2.j.f.451.3		6	195.74	odd	6
975.2.i.l.451.3		6	13.9	even	3	inner
975.2.i.l.601.3		6	1.1	even	1	trivial
975.2.bb.k.724.1		12	65.48	odd	12
975.2.bb.k.724.6		12	65.22	odd	12
975.2.bb.k.874.1		12	5.2	odd	4
975.2.bb.k.874.6		12	5.3	odd	4
2535.2.a.ba.1.1		3	65.49	even	6
2535.2.a.bb.1.3		3	65.29	even	6
7605.2.a.bv.1.1		3	195.29	odd	6
7605.2.a.bw.1.3		3	195.179	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30084 + 2.25312i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.38437 + 4.12985i) q^{4} +(1.30084 - 2.25312i) q^{6} +(1.80084 - 3.11915i) q^{7} -7.20336 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.30084 + 2.25312i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.38437 + 4.12985i) q^{4} +(1.30084 - 2.25312i) q^{6} +(1.80084 - 3.11915i) q^{7} -7.20336 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.60168 + 4.50624i) q^{11} +4.76873 q^{12} +(-3.01815 + 1.97250i) q^{13} +9.37041 q^{14} +(-4.60168 - 7.97034i) q^{16} +(-1.46789 + 2.54247i) q^{17} -2.60168 q^{18} +(-3.38437 + 5.86190i) q^{19} -3.60168 q^{21} +(-6.76873 + 11.7238i) q^{22} +(2.76873 + 4.79559i) q^{23} +(3.60168 + 6.23829i) q^{24} +(-8.37041 - 4.23435i) q^{26} +1.00000 q^{27} +(8.58773 + 14.8744i) q^{28} +(-0.916472 - 1.58738i) q^{29} +4.10284 q^{31} +(4.76873 - 8.25969i) q^{32} +(2.60168 - 4.50624i) q^{33} -7.63798 q^{34} +(-2.38437 - 4.12985i) q^{36} +(-1.76873 - 3.06354i) q^{37} -17.6101 q^{38} +(3.21731 + 1.62755i) q^{39} +(2.68521 + 4.65091i) q^{41} +(-4.68521 - 8.11502i) q^{42} +(1.58353 - 2.74275i) q^{43} -24.8134 q^{44} +(-7.20336 + 12.4766i) q^{46} -3.80504 q^{47} +(-4.60168 + 7.97034i) q^{48} +(-2.98605 - 5.17198i) q^{49} +2.93579 q^{51} +(-0.949743 - 17.1677i) q^{52} +5.20336 q^{53} +(1.30084 + 2.25312i) q^{54} +(-12.9721 + 22.4683i) q^{56} +6.76873 q^{57} +(2.38437 - 4.12985i) q^{58} +(3.68521 - 6.38297i) q^{59} +(1.71731 - 2.97447i) q^{61} +(5.33714 + 9.24420i) q^{62} +(1.80084 + 3.11915i) q^{63} +6.40672 q^{64} +13.5375 q^{66} +(1.75058 + 3.03210i) q^{67} +(-7.00000 - 12.1244i) q^{68} +(2.76873 - 4.79559i) q^{69} +(4.85226 - 8.40436i) q^{71} +(3.60168 - 6.23829i) q^{72} +0.805037 q^{73} +(4.60168 - 7.97034i) q^{74} +(-16.1391 - 27.9538i) q^{76} +18.7408 q^{77} +(0.518152 + 9.36617i) q^{78} -4.10284 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.98605 + 12.1002i) q^{82} +11.5375 q^{83} +(8.58773 - 14.8744i) q^{84} +8.23966 q^{86} +(-0.916472 + 1.58738i) q^{87} +(-18.7408 - 32.4601i) q^{88} +(-4.91647 - 8.51558i) q^{89} +(0.717312 + 12.9662i) q^{91} -26.4067 q^{92} +(-2.05142 - 3.55317i) q^{93} +(-4.94974 - 8.57321i) q^{94} -9.53747 q^{96} +(-2.78689 + 4.82703i) q^{97} +(7.76873 - 13.4558i) q^{98} -5.20336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9} + 12 q^{12} - 3 q^{13} + 24 q^{14} - 12 q^{16} - 12 q^{19} - 6 q^{21} - 24 q^{22} + 6 q^{24} - 18 q^{26} + 6 q^{27} + 12 q^{28} - 6 q^{29} + 6 q^{31} + 12 q^{32} - 6 q^{36} + 6 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{42} + 9 q^{43} - 24 q^{44} - 12 q^{46} + 24 q^{47} - 12 q^{48} + 6 q^{49} - 12 q^{52} - 30 q^{56} + 24 q^{57} + 6 q^{58} + 6 q^{59} + 3 q^{61} - 6 q^{62} + 3 q^{63} - 24 q^{64} + 48 q^{66} + 9 q^{67} - 42 q^{68} + 12 q^{71} + 6 q^{72} - 42 q^{73} + 12 q^{74} - 48 q^{76} + 48 q^{77} - 12 q^{78} - 6 q^{79} - 3 q^{81} - 18 q^{82} + 36 q^{83} + 12 q^{84} - 12 q^{86} - 6 q^{87} - 48 q^{88} - 30 q^{89} - 3 q^{91} - 96 q^{92} - 3 q^{93} - 36 q^{94} - 24 q^{96} + 15 q^{97} + 30 q^{98}+O(q^{100}) \) 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9 + 12 * q^12 - 3 * q^13 + 24 * q^14 - 12 * q^16 - 12 * q^19 - 6 * q^21 - 24 * q^22 + 6 * q^24 - 18 * q^26 + 6 * q^27 + 12 * q^28 - 6 * q^29 + 6 * q^31 + 12 * q^32 - 6 * q^36 + 6 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^42 + 9 * q^43 - 24 * q^44 - 12 * q^46 + 24 * q^47 - 12 * q^48 + 6 * q^49 - 12 * q^52 - 30 * q^56 + 24 * q^57 + 6 * q^58 + 6 * q^59 + 3 * q^61 - 6 * q^62 + 3 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 42 * q^68 + 12 * q^71 + 6 * q^72 - 42 * q^73 + 12 * q^74 - 48 * q^76 + 48 * q^77 - 12 * q^78 - 6 * q^79 - 3 * q^81 - 18 * q^82 + 36 * q^83 + 12 * q^84 - 12 * q^86 - 6 * q^87 - 48 * q^88 - 30 * q^89 - 3 * q^91 - 96 * q^92 - 3 * q^93 - 36 * q^94 - 24 * q^96 + 15 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more