LMFDB - Embedded newform 1274.2.f.k.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(79,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1274.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.f (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:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1274.79
Dual form			1274.2.f.k.1145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} +1.00000 q^{13} -12.0000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{18} +(-3.00000 + 5.19615i) q^{19} +4.00000 q^{20} +1.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(1.50000 + 2.59808i) q^{24} +(-5.50000 - 9.52628i) q^{25} +(-0.500000 + 0.866025i) q^{26} -9.00000 q^{27} -4.00000 q^{29} +(6.00000 - 10.3923i) q^{30} +(3.50000 + 6.06218i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +6.00000 q^{36} +(-4.50000 + 7.79423i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(1.50000 + 2.59808i) q^{39} +(-2.00000 + 3.46410i) q^{40} +3.00000 q^{41} +4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-12.0000 - 20.7846i) q^{45} +(3.50000 + 6.06218i) q^{46} +(3.50000 - 6.06218i) q^{47} -3.00000 q^{48} +11.0000 q^{50} +(-0.500000 - 0.866025i) q^{52} +(4.50000 - 7.79423i) q^{54} +4.00000 q^{55} -18.0000 q^{57} +(2.00000 - 3.46410i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(6.00000 + 10.3923i) q^{60} +(0.500000 - 0.866025i) q^{61} -7.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(1.50000 + 2.59808i) q^{66} +(-0.500000 - 0.866025i) q^{67} +21.0000 q^{69} +16.0000 q^{71} +(-3.00000 + 5.19615i) q^{72} +(2.50000 + 4.33013i) q^{73} +(-4.50000 - 7.79423i) q^{74} +(16.5000 - 28.5788i) q^{75} +6.00000 q^{76} -3.00000 q^{78} +(-5.50000 + 9.52628i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-2.00000 + 3.46410i) q^{86} +(-6.00000 - 10.3923i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-3.00000 + 5.19615i) q^{89} +24.0000 q^{90} -7.00000 q^{92} +(-10.5000 + 18.1865i) q^{93} +(3.50000 + 6.06218i) q^{94} +(-12.0000 - 20.7846i) q^{95} +(1.50000 - 2.59808i) q^{96} +1.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9	$ 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 2 q^{13} - 24 q^{15} - q^{16} - 6 q^{18} - 6 q^{19} + 8 q^{20} + 2 q^{22} + 7 q^{23} + 3 q^{24} - 11 q^{25} - q^{26} - 18 q^{27} - 8 q^{29} + 12 q^{30} + 7 q^{31} - q^{32} + 3 q^{33} + 12 q^{36} - 9 q^{37} - 6 q^{38} + 3 q^{39} - 4 q^{40} + 6 q^{41} + 8 q^{43} - q^{44} - 24 q^{45} + 7 q^{46} + 7 q^{47} - 6 q^{48} + 22 q^{50} - q^{52} + 9 q^{54} + 8 q^{55} - 36 q^{57} + 4 q^{58} - 10 q^{59} + 12 q^{60} + q^{61} - 14 q^{62} + 2 q^{64} - 4 q^{65} + 3 q^{66} - q^{67} + 42 q^{69} + 32 q^{71} - 6 q^{72} + 5 q^{73} - 9 q^{74} + 33 q^{75} + 12 q^{76} - 6 q^{78} - 11 q^{79} - 4 q^{80} - 9 q^{81} - 3 q^{82} - 4 q^{86} - 12 q^{87} - q^{88} - 6 q^{89} + 48 q^{90} - 14 q^{92} - 21 q^{93} + 7 q^{94} - 24 q^{95} + 3 q^{96} + 2 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 2 * q^13 - 24 * q^15 - q^16 - 6 * q^18 - 6 * q^19 + 8 * q^20 + 2 * q^22 + 7 * q^23 + 3 * q^24 - 11 * q^25 - q^26 - 18 * q^27 - 8 * q^29 + 12 * q^30 + 7 * q^31 - q^32 + 3 * q^33 + 12 * q^36 - 9 * q^37 - 6 * q^38 + 3 * q^39 - 4 * q^40 + 6 * q^41 + 8 * q^43 - q^44 - 24 * q^45 + 7 * q^46 + 7 * q^47 - 6 * q^48 + 22 * q^50 - q^52 + 9 * q^54 + 8 * q^55 - 36 * q^57 + 4 * q^58 - 10 * q^59 + 12 * q^60 + q^61 - 14 * q^62 + 2 * q^64 - 4 * q^65 + 3 * q^66 - q^67 + 42 * q^69 + 32 * q^71 - 6 * q^72 + 5 * q^73 - 9 * q^74 + 33 * q^75 + 12 * q^76 - 6 * q^78 - 11 * q^79 - 4 * q^80 - 9 * q^81 - 3 * q^82 - 4 * q^86 - 12 * q^87 - q^88 - 6 * q^89 + 48 * q^90 - 14 * q^92 - 21 * q^93 + 7 * q^94 - 24 * q^95 + 3 * q^96 + 2 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.0599153	+	0.998203i	$0.519083\pi$
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.834512	+	0.550990i	$0.814250\pi$
$6$	−3.00000			−1.22474
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	−2.00000	−	3.46410i	−0.632456	−	1.09545i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	0.780750	−	0.624844i	$-0.214837\pi$
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	−0.931505	+	0.363727i	$0.881504\pi$
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	−12.0000			−3.09839
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−3.00000	−	5.19615i	−0.707107	−	1.22474i
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$	4.00000			0.894427
$21$		0			0
$22$	1.00000			0.213201
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	−0.227167	−	0.973856i	$-0.572946\pi$
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	0.956967	−	0.290196i	$-0.0937204\pi$
$24$	1.50000	+	2.59808i	0.306186	+	0.530330i
$25$	−5.50000	−	9.52628i	−1.10000	−	1.90526i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	−9.00000			−1.73205
$28$		0			0
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$	6.00000	−	10.3923i	1.09545	−	1.89737i
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	0.987829	+	0.155543i	$0.0497126\pi$
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$		0			0
$35$		0			0
$36$	6.00000			1.00000
$37$	−4.50000	+	7.79423i	−0.739795	+	1.28136i	0.212792	+	0.977098i	$0.431744\pi$
$37$	−4.50000	+	7.79423i	−0.739795	+	1.28136i	−0.952587	+	0.304266i	$0.901589\pi$
$38$	−3.00000	−	5.19615i	−0.486664	−	0.842927i
$39$	1.50000	+	2.59808i	0.240192	+	0.416025i
$40$	−2.00000	+	3.46410i	−0.316228	+	0.547723i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−12.0000	−	20.7846i	−1.78885	−	3.09839i
$46$	3.50000	+	6.06218i	0.516047	+	0.893819i
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	−0.489398	−	0.872060i	$-0.662783\pi$
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	0.999926	−	0.0121990i	$-0.00388317\pi$
$48$	−3.00000			−0.433013
$49$		0			0
$50$	11.0000			1.55563
$51$		0			0
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$	4.50000	−	7.79423i	0.612372	−	1.06066i
$55$	4.00000			0.539360
$56$		0			0
$57$	−18.0000			−2.38416
$58$	2.00000	−	3.46410i	0.262613	−	0.454859i
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$	6.00000	+	10.3923i	0.774597	+	1.34164i
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−7.00000			−0.889001
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i	0.833866	−	0.551967i	$-0.186123\pi$
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i	−0.894951	+	0.446165i	$0.852789\pi$
$68$		0			0
$69$	21.0000			2.52810
$70$		0			0
$71$	16.0000			1.89885			0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000			1.89885			0.949425	+	0.313993i	$0.101667\pi$
$72$	−3.00000	+	5.19615i	−0.353553	+	0.612372i
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	0.974424	−	0.224716i	$-0.0721453\pi$
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	−0.681822	+	0.731519i	$0.738812\pi$
$74$	−4.50000	−	7.79423i	−0.523114	−	0.906061i
$75$	16.5000	−	28.5788i	1.90526	−	3.30000i
$76$	6.00000			0.688247
$77$		0			0
$78$	−3.00000			−0.339683
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	0.370907	+	0.928670i	$0.379047\pi$
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	−0.989705	+	0.143120i	$0.954286\pi$
$80$	−2.00000	−	3.46410i	−0.223607	−	0.387298i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	−6.00000	−	10.3923i	−0.643268	−	1.11417i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	24.0000			2.52982
$91$		0			0
$92$	−7.00000			−0.729800
$93$	−10.5000	+	18.1865i	−1.08880	+	1.88586i
$94$	3.50000	+	6.06218i	0.360997	+	0.625266i
$95$	−12.0000	−	20.7846i	−1.23117	−	2.13246i
$96$	1.50000	−	2.59808i	0.153093	−	0.265165i
$97$	1.00000			0.101535			0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000			0.101535			0.0507673	+	0.998711i	$0.483833\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	−5.50000	+	9.52628i	−0.550000	+	0.952628i
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	0.714423	−	0.699715i	$-0.246689\pi$
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	−0.963182	+	0.268851i	$0.913356\pi$
$102$		0			0
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$		0			0
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	−0.753010	−	0.658009i	$-0.771399\pi$
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	0.946357	+	0.323122i	$0.104732\pi$
$108$	4.50000	+	7.79423i	0.433013	+	0.750000i
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	0.977769	+	0.209687i	$0.0672444\pi$
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	−0.307290	+	0.951616i	$0.599422\pi$
$110$	−2.00000	+	3.46410i	−0.190693	+	0.330289i
$111$	−27.0000			−2.56273
$112$		0			0
$113$	−7.00000			−0.658505			−0.329252	−	0.944242i	$-0.606797\pi$
$113$	−7.00000			−0.658505			−0.329252	+	0.944242i	$0.606797\pi$
$114$	9.00000	−	15.5885i	0.842927	−	1.45999i
$115$	14.0000	+	24.2487i	1.30551	+	2.26120i
$116$	2.00000	+	3.46410i	0.185695	+	0.321634i
$117$	−3.00000	+	5.19615i	−0.277350	+	0.480384i
$118$	10.0000			0.920575
$119$		0			0
$120$	−12.0000			−1.09545
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	0.500000	+	0.866025i	0.0452679	+	0.0784063i
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$	3.50000	−	6.06218i	0.314309	−	0.544400i
$125$	24.0000			2.14663
$126$		0			0
$127$	−11.0000			−0.976092			−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000			−0.976092			−0.488046	+	0.872818i	$0.662290\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	6.00000	+	10.3923i	0.528271	+	0.914991i
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	−0.636676	−	0.771132i	$-0.719691\pi$
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	0.986157	+	0.165812i	$0.0530244\pi$
$132$	−3.00000			−0.261116
$133$		0			0
$134$	1.00000			0.0863868
$135$	18.0000	−	31.1769i	1.54919	−	2.68328i
$136$		0			0
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$	−10.5000	+	18.1865i	−0.893819	+	1.54814i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$	21.0000			1.76852
$142$	−8.00000	+	13.8564i	−0.671345	+	1.16280i
$143$	−0.500000	−	0.866025i	−0.0418121	−	0.0724207i
$144$	−3.00000	−	5.19615i	−0.250000	−	0.433013i
$145$	8.00000	−	13.8564i	0.664364	−	1.15071i
$146$	−5.00000			−0.413803
$147$		0			0
$148$	9.00000			0.739795
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$	16.5000	+	28.5788i	1.34722	+	2.33345i
$151$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$151$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$152$	−3.00000	+	5.19615i	−0.243332	+	0.421464i
$153$		0			0
$154$		0			0
$155$	−28.0000			−2.24901
$156$	1.50000	−	2.59808i	0.120096	−	0.208013i
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	0.948373	−	0.317156i	$-0.102728\pi$
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	−0.748852	+	0.662738i	$0.769394\pi$
$158$	−5.50000	−	9.52628i	−0.437557	−	0.757870i
$159$		0			0
$160$	4.00000			0.316228
$161$		0			0
$162$	9.00000			0.707107
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$	6.00000	+	10.3923i	0.467099	+	0.809040i
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−18.0000	−	31.1769i	−1.37649	−	2.38416i
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	1.00000	−	1.73205i	0.0760286	−	0.131685i	−0.825505	−	0.564396i	$-0.809109\pi$
$173$	1.00000	−	1.73205i	0.0760286	−	0.131685i	0.901533	+	0.432710i	$0.142443\pi$
$174$	12.0000			0.909718
$175$		0			0
$176$	1.00000			0.0753778
$177$	15.0000	−	25.9808i	1.12747	−	1.95283i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$	−12.0000	+	20.7846i	−0.894427	+	1.54919i
$181$	−15.0000			−1.11494			−0.557471	−	0.830197i	$-0.688228\pi$
$181$	−15.0000			−1.11494			−0.557471	+	0.830197i	$0.688228\pi$
$182$		0			0
$183$	3.00000			0.221766
$184$	3.50000	−	6.06218i	0.258023	−	0.446910i
$185$	−18.0000	−	31.1769i	−1.32339	−	2.29217i
$186$	−10.5000	−	18.1865i	−0.769897	−	1.33350i
$187$		0			0
$188$	−7.00000			−0.510527
$189$		0			0
$190$	24.0000			1.74114
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	1.50000	+	2.59808i	0.108253	+	0.187500i
$193$	−10.0000	−	17.3205i	−0.719816	−	1.24676i	−0.961073	−	0.276296i	$-0.910893\pi$
$193$	−10.0000	−	17.3205i	−0.719816	−	1.24676i	0.241257	−	0.970461i	$-0.422440\pi$
$194$	−0.500000	+	0.866025i	−0.0358979	+	0.0621770i
$195$	−12.0000			−0.859338
$196$		0			0
$197$	−27.0000			−1.92367			−0.961835	−	0.273629i	$-0.911776\pi$
$197$	−27.0000			−1.92367			−0.961835	+	0.273629i	$0.911776\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	−5.50000	−	9.52628i	−0.388909	−	0.673610i
$201$	1.50000	−	2.59808i	0.105802	−	0.183254i
$202$	5.00000			0.351799
$203$		0			0
$204$		0			0
$205$	−6.00000	+	10.3923i	−0.419058	+	0.725830i
$206$	−7.00000	−	12.1244i	−0.487713	−	0.844744i
$207$	21.0000	+	36.3731i	1.45960	+	2.52810i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	6.00000			0.415029
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$		0			0
$213$	24.0000	+	41.5692i	1.64445	+	2.84828i
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	−8.00000	+	13.8564i	−0.545595	+	0.944999i
$216$	−9.00000			−0.612372
$217$		0			0
$218$	−14.0000			−0.948200
$219$	−7.50000	+	12.9904i	−0.506803	+	0.877809i
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$		0			0
$222$	13.5000	−	23.3827i	0.906061	−	1.56934i
$223$	−21.0000			−1.40626			−0.703132	−	0.711059i	$-0.748216\pi$
$223$	−21.0000			−1.40626			−0.703132	+	0.711059i	$0.748216\pi$
$224$		0			0
$225$	66.0000			4.40000
$226$	3.50000	−	6.06218i	0.232817	−	0.403250i
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	0.921903	+	0.387421i	$0.126634\pi$
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	−0.125435	+	0.992102i	$0.540033\pi$
$228$	9.00000	+	15.5885i	0.596040	+	1.03237i
$229$	−12.0000	+	20.7846i	−0.792982	+	1.37349i	0.131130	+	0.991365i	$0.458139\pi$
$229$	−12.0000	+	20.7846i	−0.792982	+	1.37349i	−0.924113	+	0.382121i	$0.875194\pi$
$230$	−28.0000			−1.84627
$231$		0			0
$232$	−4.00000			−0.262613
$233$	2.50000	−	4.33013i	0.163780	−	0.283676i	−0.772441	−	0.635086i	$-0.780964\pi$
$233$	2.50000	−	4.33013i	0.163780	−	0.283676i	0.936222	+	0.351410i	$0.114298\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	14.0000	+	24.2487i	0.913259	+	1.58181i
$236$	−5.00000	+	8.66025i	−0.325472	+	0.563735i
$237$	−33.0000			−2.14358
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	6.00000	−	10.3923i	0.387298	−	0.670820i
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$	5.00000	+	8.66025i	0.321412	+	0.556702i
$243$		0			0
$244$	−1.00000			−0.0640184
$245$		0			0
$246$	−9.00000			−0.573819
$247$	−3.00000	+	5.19615i	−0.190885	+	0.330623i
$248$	3.50000	+	6.06218i	0.222250	+	0.384949i
$249$		0			0
$250$	−12.0000	+	20.7846i	−0.758947	+	1.31453i
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$		0			0
$253$	−7.00000			−0.440086
$254$	5.50000	−	9.52628i	0.345101	−	0.597732i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.0000	−	20.7846i	0.748539	−	1.29651i	−0.199983	−	0.979799i	$-0.564089\pi$
$257$	12.0000	−	20.7846i	0.748539	−	1.29651i	0.948523	−	0.316709i	$-0.102578\pi$
$258$	−12.0000			−0.747087
$259$		0			0
$260$	4.00000			0.248069
$261$	12.0000	−	20.7846i	0.742781	−	1.28654i
$262$	4.00000	+	6.92820i	0.247121	+	0.428026i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$		0			0
$266$		0			0
$267$	−18.0000			−1.10158
$268$	−0.500000	+	0.866025i	−0.0305424	+	0.0529009i
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$	18.0000	+	31.1769i	1.09545	+	1.89737i
$271$	−11.5000	+	19.9186i	−0.698575	+	1.20997i	0.270385	+	0.962752i	$0.412849\pi$
$271$	−11.5000	+	19.9186i	−0.698575	+	1.20997i	−0.968960	+	0.247216i	$0.920484\pi$
$272$		0			0
$273$		0			0
$274$	−6.00000			−0.362473
$275$	−5.50000	+	9.52628i	−0.331662	+	0.574456i
$276$	−10.5000	−	18.1865i	−0.632026	−	1.09470i
$277$	9.00000	+	15.5885i	0.540758	+	0.936620i	0.998861	+	0.0477206i	$0.0151957\pi$
$277$	9.00000	+	15.5885i	0.540758	+	0.936620i	−0.458103	+	0.888899i	$0.651471\pi$
$278$	2.00000	−	3.46410i	0.119952	−	0.207763i
$279$	−42.0000			−2.51447
$280$		0			0
$281$	−8.00000			−0.477240			−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000			−0.477240			−0.238620	+	0.971113i	$0.576695\pi$
$282$	−10.5000	+	18.1865i	−0.625266	+	1.08299i
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	0.997076	+	0.0764162i	$0.0243478\pi$
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	−0.432360	+	0.901701i	$0.642319\pi$
$284$	−8.00000	−	13.8564i	−0.474713	−	0.822226i
$285$	36.0000	−	62.3538i	2.13246	−	3.69352i
$286$	1.00000			0.0591312
$287$		0			0
$288$	6.00000			0.353553
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	8.00000	+	13.8564i	0.469776	+	0.813676i
$291$	1.50000	+	2.59808i	0.0879316	+	0.152302i
$292$	2.50000	−	4.33013i	0.146301	−	0.253402i
$293$	26.0000			1.51894			0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000			1.51894			0.759468	+	0.650545i	$0.225459\pi$
$294$		0			0
$295$	40.0000			2.32889
$296$	−4.50000	+	7.79423i	−0.261557	+	0.453030i
$297$	4.50000	+	7.79423i	0.261116	+	0.452267i
$298$	−4.50000	−	7.79423i	−0.260678	−	0.451508i
$299$	3.50000	−	6.06218i	0.202410	−	0.350585i
$300$	−33.0000			−1.90526
$301$		0			0
$302$		0			0
$303$	7.50000	−	12.9904i	0.430864	−	0.746278i
$304$	−3.00000	−	5.19615i	−0.172062	−	0.298020i
$305$	2.00000	+	3.46410i	0.114520	+	0.198354i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$	−42.0000			−2.38930
$310$	14.0000	−	24.2487i	0.795147	−	1.37723i
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	0.880693	+	0.473688i	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$	1.50000	+	2.59808i	0.0849208	+	0.147087i
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$	−5.00000			−0.282166
$315$		0			0
$316$	11.0000			0.618798
$317$	−10.5000	+	18.1865i	−0.589739	+	1.02146i	0.404528	+	0.914526i	$0.367436\pi$
$317$	−10.5000	+	18.1865i	−0.589739	+	1.02146i	−0.994266	+	0.106932i	$0.965897\pi$
$318$		0			0
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$	−2.00000	+	3.46410i	−0.111803	+	0.193649i
$321$	12.0000			0.669775
$322$		0			0
$323$		0			0
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−5.50000	−	9.52628i	−0.305085	−	0.528423i
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	−21.0000	+	36.3731i	−1.16130	+	2.01144i
$328$	3.00000			0.165647
$329$		0			0
$330$	−12.0000			−0.660578
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$332$		0			0
$333$	−27.0000	−	46.7654i	−1.47959	−	2.56273i
$334$		0			0
$335$	4.00000			0.218543
$336$		0			0
$337$	17.0000			0.926049			0.463025	−	0.886345i	$-0.346764\pi$
$337$	17.0000			0.926049			0.463025	+	0.886345i	$0.346764\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$	−10.5000	−	18.1865i	−0.570282	−	0.987757i
$340$		0			0
$341$	3.50000	−	6.06218i	0.189536	−	0.328285i
$342$	36.0000			1.94666
$343$		0			0
$344$	4.00000			0.215666
$345$	−42.0000	+	72.7461i	−2.26120	+	3.91652i
$346$	1.00000	+	1.73205i	0.0537603	+	0.0931156i
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	0.984487	+	0.175457i	$0.0561403\pi$
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	−0.340293	+	0.940319i	$0.610526\pi$
$348$	−6.00000	+	10.3923i	−0.321634	+	0.557086i
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	−9.00000			−0.480384
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	12.5000	+	21.6506i	0.665308	+	1.15235i	0.979202	+	0.202889i	$0.0650330\pi$
$353$	12.5000	+	21.6506i	0.665308	+	1.15235i	−0.313894	+	0.949458i	$0.601634\pi$
$354$	15.0000	+	25.9808i	0.797241	+	1.38086i
$355$	−32.0000	+	55.4256i	−1.69838	+	2.94169i
$356$	6.00000			0.317999
$357$		0			0
$358$	−6.00000			−0.317110
$359$	−6.00000	+	10.3923i	−0.316668	+	0.548485i	−0.979791	−	0.200026i	$-0.935897\pi$
$359$	−6.00000	+	10.3923i	−0.316668	+	0.548485i	0.663123	+	0.748511i	$0.269231\pi$
$360$	−12.0000	−	20.7846i	−0.632456	−	1.09545i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	7.50000	−	12.9904i	0.394191	−	0.682759i
$363$	30.0000			1.57459
$364$		0			0
$365$	−20.0000			−1.04685
$366$	−1.50000	+	2.59808i	−0.0784063	+	0.135804i
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	0.893873	+	0.448320i	$0.147978\pi$
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	−0.0586798	+	0.998277i	$0.518689\pi$
$368$	3.50000	+	6.06218i	0.182450	+	0.316013i
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$	36.0000			1.87155
$371$		0			0
$372$	21.0000			1.08880
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	−0.581122	−	0.813816i	$-0.697386\pi$
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	0.995347	+	0.0963587i	$0.0307196\pi$
$374$		0			0
$375$	36.0000	+	62.3538i	1.85903	+	3.21994i
$376$	3.50000	−	6.06218i	0.180499	−	0.312633i
$377$	−4.00000			−0.206010
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$	−12.0000	+	20.7846i	−0.615587	+	1.06623i
$381$	−16.5000	−	28.5788i	−0.845321	−	1.46414i
$382$	4.00000	+	6.92820i	0.204658	+	0.354478i
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	20.0000			1.01797
$387$	−12.0000	+	20.7846i	−0.609994	+	1.05654i
$388$	−0.500000	−	0.866025i	−0.0253837	−	0.0439658i
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.810326	+	0.585980i	$0.199290\pi$
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.102311	+	0.994753i	$0.467376\pi$
$390$	6.00000	−	10.3923i	0.303822	−	0.526235i
$391$		0			0
$392$		0			0
$393$	24.0000			1.21064
$394$	13.5000	−	23.3827i	0.680120	−	1.17800i
$395$	−22.0000	−	38.1051i	−1.10694	−	1.91728i
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	−14.0000	+	24.2487i	−0.702640	+	1.21701i	0.264897	+	0.964277i	$0.414662\pi$
$397$	−14.0000	+	24.2487i	−0.702640	+	1.21701i	−0.967537	+	0.252731i	$0.918671\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	11.0000			0.550000
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	−0.976050	−	0.217545i	$-0.930195\pi$
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	0.676425	+	0.736512i	$0.263528\pi$
$402$	1.50000	+	2.59808i	0.0748132	+	0.129580i
$403$	3.50000	+	6.06218i	0.174347	+	0.301979i
$404$	−2.50000	+	4.33013i	−0.124380	+	0.215432i
$405$	36.0000			1.78885
$406$		0			0
$407$	9.00000			0.446113
$408$		0			0
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	−0.984803	−	0.173675i	$-0.944436\pi$
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	0.341994	−	0.939702i	$-0.388898\pi$
$410$	−6.00000	−	10.3923i	−0.296319	−	0.513239i
$411$	−9.00000	+	15.5885i	−0.443937	+	0.768922i
$412$	14.0000			0.689730
$413$		0			0
$414$	−42.0000			−2.06419
$415$		0			0
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−6.00000	−	10.3923i	−0.293821	−	0.508913i
$418$	−3.00000	+	5.19615i	−0.146735	+	0.254152i
$419$	−15.0000			−0.732798			−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000			−0.732798			−0.366399	+	0.930458i	$0.619409\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	5.00000	−	8.66025i	0.243396	−	0.421575i
$423$	21.0000	+	36.3731i	1.02105	+	1.76852i
$424$		0			0
$425$		0			0
$426$	−48.0000			−2.32561
$427$		0			0
$428$	−4.00000			−0.193347
$429$	1.50000	−	2.59808i	0.0724207	−	0.125436i
$430$	−8.00000	−	13.8564i	−0.385794	−	0.668215i
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	0.563658	−	0.826008i	$-0.309393\pi$
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	−0.997173	+	0.0751385i	$0.976060\pi$
$432$	4.50000	−	7.79423i	0.216506	−	0.375000i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$	48.0000			2.30142
$436$	7.00000	−	12.1244i	0.335239	−	0.580651i
$437$	21.0000	+	36.3731i	1.00457	+	1.73996i
$438$	−7.50000	−	12.9904i	−0.358364	−	0.620704i
$439$	1.00000	−	1.73205i	0.0477274	−	0.0826663i	−0.841175	−	0.540763i	$-0.818135\pi$
$439$	1.00000	−	1.73205i	0.0477274	−	0.0826663i	0.888902	+	0.458097i	$0.151469\pi$
$440$	4.00000			0.190693
$441$		0			0
$442$		0			0
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$	13.5000	+	23.3827i	0.640682	+	1.10969i
$445$	−12.0000	−	20.7846i	−0.568855	−	0.985285i
$446$	10.5000	−	18.1865i	0.497189	−	0.861157i
$447$	−27.0000			−1.27706
$448$		0			0
$449$	−2.00000			−0.0943858			−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000			−0.0943858			−0.0471929	+	0.998886i	$0.515028\pi$
$450$	−33.0000	+	57.1577i	−1.55563	+	2.69444i
$451$	−1.50000	−	2.59808i	−0.0706322	−	0.122339i
$452$	3.50000	+	6.06218i	0.164626	+	0.285141i
$453$		0			0
$454$	−24.0000			−1.12638
$455$		0			0
$456$	−18.0000			−0.842927
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	−0.383437	−	0.923567i	$-0.625260\pi$
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	0.991551	−	0.129718i	$-0.0414071\pi$
$458$	−12.0000	−	20.7846i	−0.560723	−	0.971201i
$459$		0			0
$460$	14.0000	−	24.2487i	0.652753	−	1.13060i
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$	−42.0000	−	72.7461i	−1.94770	−	3.37352i
$466$	2.50000	+	4.33013i	0.115810	+	0.200589i
$467$	−2.00000	+	3.46410i	−0.0925490	+	0.160300i	−0.908583	−	0.417704i	$-0.862835\pi$
$467$	−2.00000	+	3.46410i	−0.0925490	+	0.160300i	0.816034	+	0.578004i	$0.196168\pi$
$468$	6.00000			0.277350
$469$		0			0
$470$	−28.0000			−1.29154
$471$	−7.50000	+	12.9904i	−0.345582	+	0.598565i
$472$	−5.00000	−	8.66025i	−0.230144	−	0.398621i
$473$	−2.00000	−	3.46410i	−0.0919601	−	0.159280i
$474$	16.5000	−	28.5788i	0.757870	−	1.31267i
$475$	66.0000			3.02829
$476$		0			0
$477$		0			0
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$	6.00000	+	10.3923i	0.273861	+	0.474342i
$481$	−4.50000	+	7.79423i	−0.205182	+	0.355386i
$482$	18.0000			0.819878
$483$		0			0
$484$	−10.0000			−0.454545
$485$	−2.00000	+	3.46410i	−0.0908153	+	0.157297i
$486$		0			0
$487$	−19.0000	−	32.9090i	−0.860972	−	1.49125i	−0.870992	−	0.491298i	$-0.836523\pi$
$487$	−19.0000	−	32.9090i	−0.860972	−	1.49125i	0.0100195	−	0.999950i	$-0.496811\pi$
$488$	0.500000	−	0.866025i	0.0226339	−	0.0392031i
$489$	12.0000			0.542659
$490$		0			0
$491$	16.0000			0.722070			0.361035	−	0.932552i	$-0.382424\pi$
$491$	16.0000			0.722070			0.361035	+	0.932552i	$0.382424\pi$
$492$	4.50000	−	7.79423i	0.202876	−	0.351391i
$493$		0			0
$494$	−3.00000	−	5.19615i	−0.134976	−	0.233786i
$495$	−12.0000	+	20.7846i	−0.539360	+	0.934199i
$496$	−7.00000			−0.314309
$497$		0			0
$498$		0			0
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	−0.804627	−	0.593780i	$-0.797635\pi$
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	0.916542	+	0.399937i	$0.130968\pi$
$500$	−12.0000	−	20.7846i	−0.536656	−	0.929516i
$501$		0			0
$502$	1.50000	−	2.59808i	0.0669483	−	0.115958i
$503$	20.0000			0.891756			0.445878	−	0.895094i	$-0.352892\pi$
$503$	20.0000			0.891756			0.445878	+	0.895094i	$0.352892\pi$
$504$		0			0
$505$	20.0000			0.889988
$506$	3.50000	−	6.06218i	0.155594	−	0.269497i
$507$	1.50000	+	2.59808i	0.0666173	+	0.115385i
$508$	5.50000	+	9.52628i	0.244023	+	0.422660i
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$	27.0000	−	46.7654i	1.19208	−	2.06474i
$514$	12.0000	+	20.7846i	0.529297	+	0.916770i
$515$	−28.0000	−	48.4974i	−1.23383	−	2.13705i
$516$	6.00000	−	10.3923i	0.264135	−	0.457496i
$517$	−7.00000			−0.307860
$518$		0			0
$519$	6.00000			0.263371
$520$	−2.00000	+	3.46410i	−0.0877058	+	0.151911i
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	12.0000	+	20.7846i	0.525226	+	0.909718i
$523$	13.5000	−	23.3827i	0.590314	−	1.02245i	−0.403876	−	0.914814i	$-0.632337\pi$
$523$	13.5000	−	23.3827i	0.590314	−	1.02245i	0.994190	−	0.107640i	$-0.0343293\pi$
$524$	−8.00000			−0.349482
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$	1.50000	+	2.59808i	0.0652791	+	0.113067i
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$		0			0
$531$	60.0000			2.60378
$532$		0			0
$533$	3.00000			0.129944
$534$	9.00000	−	15.5885i	0.389468	−	0.674579i
$535$	8.00000	+	13.8564i	0.345870	+	0.599065i
$536$	−0.500000	−	0.866025i	−0.0215967	−	0.0374066i
$537$	−9.00000	+	15.5885i	−0.388379	+	0.672692i
$538$	−9.00000			−0.388018
$539$		0			0
$540$	−36.0000			−1.54919
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−11.5000	−	19.9186i	−0.493967	−	0.855576i
$543$	−22.5000	−	38.9711i	−0.965567	−	1.67241i
$544$		0			0
$545$	−56.0000			−2.39878
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$	−5.50000	−	9.52628i	−0.234521	−	0.406202i
$551$	12.0000	−	20.7846i	0.511217	−	0.885454i
$552$	21.0000			0.893819
$553$		0			0
$554$	−18.0000			−0.764747
$555$	54.0000	−	93.5307i	2.29217	−	3.97016i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$	21.0000	−	36.3731i	0.889001	−	1.53979i
$559$	4.00000			0.169182
$560$		0			0
$561$		0			0
$562$	4.00000	−	6.92820i	0.168730	−	0.292249i
$563$	5.50000	+	9.52628i	0.231797	+	0.401485i	0.958337	−	0.285640i	$-0.0922060\pi$
$563$	5.50000	+	9.52628i	0.231797	+	0.401485i	−0.726540	+	0.687124i	$0.758873\pi$
$564$	−10.5000	−	18.1865i	−0.442130	−	0.765791i
$565$	14.0000	−	24.2487i	0.588984	−	1.02015i
$566$	−19.0000			−0.798630
$567$		0			0
$568$	16.0000			0.671345
$569$	17.5000	−	30.3109i	0.733638	−	1.27070i	−0.221680	−	0.975119i	$-0.571154\pi$
$569$	17.5000	−	30.3109i	0.733638	−	1.27070i	0.955318	−	0.295579i	$-0.0955126\pi$
$570$	36.0000	+	62.3538i	1.50787	+	2.61171i
$571$	−3.00000	−	5.19615i	−0.125546	−	0.217452i	0.796400	−	0.604770i	$-0.206735\pi$
$571$	−3.00000	−	5.19615i	−0.125546	−	0.217452i	−0.921946	+	0.387318i	$0.873402\pi$
$572$	−0.500000	+	0.866025i	−0.0209061	+	0.0362103i
$573$	24.0000			1.00261
$574$		0			0
$575$	−77.0000			−3.21112
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	15.0000	+	25.9808i	0.624458	+	1.08159i	0.988645	+	0.150268i	$0.0480135\pi$
$577$	15.0000	+	25.9808i	0.624458	+	1.08159i	−0.364187	+	0.931326i	$0.618653\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	30.0000	−	51.9615i	1.24676	−	2.15945i
$580$	−16.0000			−0.664364
$581$		0			0
$582$	−3.00000			−0.124354
$583$		0			0
$584$	2.50000	+	4.33013i	0.103451	+	0.179182i
$585$	−12.0000	−	20.7846i	−0.496139	−	0.859338i
$586$	−13.0000	+	22.5167i	−0.537025	+	0.930155i
$587$	−14.0000			−0.577842			−0.288921	−	0.957353i	$-0.593296\pi$
$587$	−14.0000			−0.577842			−0.288921	+	0.957353i	$0.593296\pi$
$588$		0			0
$589$	−42.0000			−1.73058
$590$	−20.0000	+	34.6410i	−0.823387	+	1.42615i
$591$	−40.5000	−	70.1481i	−1.66595	−	2.88551i
$592$	−4.50000	−	7.79423i	−0.184949	−	0.320341i
$593$	7.00000	−	12.1244i	0.287456	−	0.497888i	−0.685746	−	0.727841i	$-0.740524\pi$
$593$	7.00000	−	12.1244i	0.287456	−	0.497888i	0.973202	+	0.229953i	$0.0738573\pi$
$594$	−9.00000			−0.369274
$595$		0			0
$596$	9.00000			0.368654
$597$	6.00000	−	10.3923i	0.245564	−	0.425329i
$598$	3.50000	+	6.06218i	0.143126	+	0.247901i
$599$	14.5000	+	25.1147i	0.592454	+	1.02616i	0.993901	+	0.110278i	$0.0351741\pi$
$599$	14.5000	+	25.1147i	0.592454	+	1.02616i	−0.401447	+	0.915882i	$0.631493\pi$
$600$	16.5000	−	28.5788i	0.673610	−	1.16673i
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$	6.00000			0.244339
$604$		0			0
$605$	20.0000	+	34.6410i	0.813116	+	1.40836i
$606$	7.50000	+	12.9904i	0.304667	+	0.527698i
$607$	3.00000	−	5.19615i	0.121766	−	0.210905i	−0.798698	−	0.601732i	$-0.794478\pi$
$607$	3.00000	−	5.19615i	0.121766	−	0.210905i	0.920464	+	0.390827i	$0.127811\pi$
$608$	6.00000			0.243332
$609$		0			0
$610$	−4.00000			−0.161955
$611$	3.50000	−	6.06218i	0.141595	−	0.245249i
$612$		0			0
$613$	24.5000	+	42.4352i	0.989546	+	1.71394i	0.619671	+	0.784862i	$0.287266\pi$
$613$	24.5000	+	42.4352i	0.989546	+	1.71394i	0.369875	+	0.929082i	$0.379401\pi$
$614$	−2.00000	+	3.46410i	−0.0807134	+	0.139800i
$615$	−36.0000			−1.45166
$616$		0			0
$617$	22.0000			0.885687			0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000			0.885687			0.442843	+	0.896599i	$0.353970\pi$
$618$	21.0000	−	36.3731i	0.844744	−	1.46314i
$619$	11.0000	+	19.0526i	0.442127	+	0.765787i	0.997847	−	0.0655827i	$-0.0208906\pi$
$619$	11.0000	+	19.0526i	0.442127	+	0.765787i	−0.555720	+	0.831370i	$0.687557\pi$
$620$	14.0000	+	24.2487i	0.562254	+	0.973852i
$621$	−31.5000	+	54.5596i	−1.26405	+	2.18940i
$622$	−30.0000			−1.20289
$623$		0			0
$624$	−3.00000			−0.120096
$625$	−20.5000	+	35.5070i	−0.820000	+	1.42028i
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$	9.00000	+	15.5885i	0.359425	+	0.622543i
$628$	2.50000	−	4.33013i	0.0997609	−	0.172791i
$629$		0			0
$630$		0			0
$631$	−2.00000			−0.0796187			−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000			−0.0796187			−0.0398094	+	0.999207i	$0.512675\pi$
$632$	−5.50000	+	9.52628i	−0.218778	+	0.378935i
$633$	−15.0000	−	25.9808i	−0.596196	−	1.03264i
$634$	−10.5000	−	18.1865i	−0.417008	−	0.722280i
$635$	22.0000	−	38.1051i	0.873043	−	1.51216i
$636$		0			0
$637$		0			0
$638$	−4.00000			−0.158362
$639$	−48.0000	+	83.1384i	−1.89885	+	3.28891i
$640$	−2.00000	−	3.46410i	−0.0790569	−	0.136931i
$641$	−3.50000	−	6.06218i	−0.138242	−	0.239442i	0.788589	−	0.614920i	$-0.210812\pi$
$641$	−3.50000	−	6.06218i	−0.138242	−	0.239442i	−0.926831	+	0.375478i	$0.877478\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	16.0000			0.630978			0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000			0.630978			0.315489	+	0.948929i	$0.397831\pi$
$644$		0			0
$645$	−48.0000			−1.89000
$646$		0			0
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	0.776622	−	0.629967i	$-0.216932\pi$
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	−0.933878	+	0.357591i	$0.883598\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−5.00000	+	8.66025i	−0.196267	+	0.339945i
$650$	11.0000			0.431455
$651$		0			0
$652$	−4.00000			−0.156652
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	−0.262515	−	0.964928i	$-0.584552\pi$
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	0.966910	−	0.255119i	$-0.0821147\pi$
$654$	−21.0000	−	36.3731i	−0.821165	−	1.42230i
$655$	16.0000	+	27.7128i	0.625172	+	1.08283i
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	−30.0000			−1.17041
$658$		0			0
$659$	−18.0000			−0.701180			−0.350590	−	0.936529i	$-0.614019\pi$
$659$	−18.0000			−0.701180			−0.350590	+	0.936529i	$0.614019\pi$
$660$	6.00000	−	10.3923i	0.233550	−	0.404520i
$661$	−2.00000	−	3.46410i	−0.0777910	−	0.134738i	0.824506	−	0.565854i	$-0.191453\pi$
$661$	−2.00000	−	3.46410i	−0.0777910	−	0.134738i	−0.902297	+	0.431116i	$0.858120\pi$
$662$	3.50000	+	6.06218i	0.136031	+	0.235613i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	54.0000			2.09246
$667$	−14.0000	+	24.2487i	−0.542082	+	0.938914i
$668$		0			0
$669$	−31.5000	−	54.5596i	−1.21786	−	2.10940i
$670$	−2.00000	+	3.46410i	−0.0772667	+	0.133830i
$671$	−1.00000			−0.0386046
$672$		0			0
$673$	7.00000			0.269830			0.134915	−	0.990857i	$-0.456924\pi$
$673$	7.00000			0.269830			0.134915	+	0.990857i	$0.456924\pi$
$674$	−8.50000	+	14.7224i	−0.327408	+	0.567087i
$675$	49.5000	+	85.7365i	1.90526	+	3.30000i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	19.5000	−	33.7750i	0.749446	−	1.29808i	−0.198643	−	0.980072i	$-0.563653\pi$
$677$	19.5000	−	33.7750i	0.749446	−	1.29808i	0.948089	−	0.318006i	$-0.103013\pi$
$678$	21.0000			0.806500
$679$		0			0
$680$		0			0
$681$	−36.0000	+	62.3538i	−1.37952	+	2.38940i
$682$	3.50000	+	6.06218i	0.134022	+	0.232133i
$683$	−0.500000	−	0.866025i	−0.0191320	−	0.0331375i	0.856301	−	0.516477i	$-0.172757\pi$
$683$	−0.500000	−	0.866025i	−0.0191320	−	0.0331375i	−0.875433	+	0.483340i	$0.839424\pi$
$684$	−18.0000	+	31.1769i	−0.688247	+	1.19208i
$685$	−24.0000			−0.916993
$686$		0			0
$687$	−72.0000			−2.74697
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$		0			0
$690$	−42.0000	−	72.7461i	−1.59891	−	2.76940i
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$	−2.00000			−0.0760286
$693$		0			0
$694$	−24.0000			−0.911028
$695$	8.00000	−	13.8564i	0.303457	−	0.525603i
$696$	−6.00000	−	10.3923i	−0.227429	−	0.393919i
$697$		0			0
$698$	−13.0000	+	22.5167i	−0.492057	+	0.852268i
$699$	15.0000			0.567352
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	4.50000	−	7.79423i	0.169842	−	0.294174i
$703$	−27.0000	−	46.7654i	−1.01832	−	1.76379i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−42.0000	+	72.7461i	−1.58181	+	2.73978i
$706$	−25.0000			−0.940887
$707$		0			0
$708$	−30.0000			−1.12747
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	−0.717769	−	0.696281i	$-0.754837\pi$
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	0.961882	+	0.273466i	$0.0881700\pi$
$710$	−32.0000	−	55.4256i	−1.20094	−	2.08009i
$711$	−33.0000	−	57.1577i	−1.23760	−	2.14358i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	49.0000			1.83506
$714$		0			0
$715$	4.00000			0.149592
$716$	3.00000	−	5.19615i	0.112115	−	0.194189i
$717$	9.00000	+	15.5885i	0.336111	+	0.582162i
$718$	−6.00000	−	10.3923i	−0.223918	−	0.387837i
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	−0.846776	−	0.531949i	$-0.821460\pi$
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	0.884070	+	0.467355i	$0.154793\pi$
$720$	24.0000			0.894427
$721$		0			0
$722$	17.0000			0.632674
$723$	27.0000	−	46.7654i	1.00414	−	1.73922i
$724$	7.50000	+	12.9904i	0.278735	+	0.482784i
$725$	22.0000	+	38.1051i	0.817059	+	1.41519i
$726$	−15.0000	+	25.9808i	−0.556702	+	0.964237i
$727$	26.0000			0.964287			0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000			0.964287			0.482143	+	0.876092i	$0.339858\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	10.0000	−	17.3205i	0.370117	−	0.641061i
$731$		0			0
$732$	−1.50000	−	2.59808i	−0.0554416	−	0.0960277i
$733$	−2.00000	+	3.46410i	−0.0738717	+	0.127950i	−0.900595	−	0.434659i	$-0.856869\pi$
$733$	−2.00000	+	3.46410i	−0.0738717	+	0.127950i	0.826723	+	0.562609i	$0.190202\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	−7.00000			−0.258023
$737$	−0.500000	+	0.866025i	−0.0184177	+	0.0319005i
$738$	−9.00000	−	15.5885i	−0.331295	−	0.573819i
$739$	−12.0000	−	20.7846i	−0.441427	−	0.764574i	0.556369	−	0.830936i	$-0.312194\pi$
$739$	−12.0000	−	20.7846i	−0.441427	−	0.764574i	−0.997796	+	0.0663614i	$0.978861\pi$
$740$	−18.0000	+	31.1769i	−0.661693	+	1.14609i
$741$	−18.0000			−0.661247
$742$		0			0
$743$	16.0000			0.586983			0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000			0.586983			0.293492	+	0.955962i	$0.405183\pi$
$744$	−10.5000	+	18.1865i	−0.384949	+	0.666751i
$745$	−18.0000	−	31.1769i	−0.659469	−	1.14223i
$746$	8.00000	+	13.8564i	0.292901	+	0.507319i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−72.0000			−2.62907
$751$	13.5000	−	23.3827i	0.492622	−	0.853246i	−0.507342	−	0.861745i	$-0.669372\pi$
$751$	13.5000	−	23.3827i	0.492622	−	0.853246i	0.999964	+	0.00849853i	$0.00270520\pi$
$752$	3.50000	+	6.06218i	0.127632	+	0.221065i
$753$	−4.50000	−	7.79423i	−0.163989	−	0.284037i
$754$	2.00000	−	3.46410i	0.0728357	−	0.126155i
$755$		0			0
$756$		0			0
$757$	54.0000			1.96266			0.981332	−	0.192323i	$-0.0616021\pi$
$757$	54.0000			1.96266			0.981332	+	0.192323i	$0.0616021\pi$
$758$	4.00000	−	6.92820i	0.145287	−	0.251644i
$759$	−10.5000	−	18.1865i	−0.381126	−	0.660129i
$760$	−12.0000	−	20.7846i	−0.435286	−	0.753937i
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	−0.0932544	−	0.995642i	$-0.529727\pi$
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	0.908879	−	0.417061i	$-0.136940\pi$
$762$	33.0000			1.19546
$763$		0			0
$764$	−8.00000			−0.289430
$765$		0			0
$766$	−7.50000	−	12.9904i	−0.270986	−	0.469362i
$767$	−5.00000	−	8.66025i	−0.180540	−	0.312704i
$768$	1.50000	−	2.59808i	0.0541266	−	0.0937500i
$769$	−21.0000			−0.757279			−0.378640	−	0.925544i	$-0.623608\pi$
$769$	−21.0000			−0.757279			−0.378640	+	0.925544i	$0.623608\pi$
$770$		0			0
$771$	72.0000			2.59302
$772$	−10.0000	+	17.3205i	−0.359908	+	0.623379i
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	0.964014	−	0.265852i	$-0.0856532\pi$
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	−0.712241	+	0.701935i	$0.752320\pi$
$774$	−12.0000	−	20.7846i	−0.431331	−	0.747087i
$775$	38.5000	−	66.6840i	1.38296	−	2.39536i
$776$	1.00000			0.0358979
$777$		0			0
$778$	−36.0000			−1.29066
$779$	−9.00000	+	15.5885i	−0.322458	+	0.558514i
$780$	6.00000	+	10.3923i	0.214834	+	0.372104i
$781$	−8.00000	−	13.8564i	−0.286263	−	0.495821i
$782$		0			0
$783$	36.0000			1.28654
$784$		0			0
$785$	−20.0000			−0.713831
$786$	−12.0000	+	20.7846i	−0.428026	+	0.741362i
$787$	16.0000	+	27.7128i	0.570338	+	0.987855i	0.996531	+	0.0832226i	$0.0265213\pi$
$787$	16.0000	+	27.7128i	0.570338	+	0.987855i	−0.426193	+	0.904632i	$0.640145\pi$
$788$	13.5000	+	23.3827i	0.480918	+	0.832974i
$789$	36.0000	−	62.3538i	1.28163	−	2.21986i
$790$	44.0000			1.56545
$791$		0			0
$792$	6.00000			0.213201
$793$	0.500000	−	0.866025i	0.0177555	−	0.0307535i
$794$	−14.0000	−	24.2487i	−0.496841	−	0.860555i
$795$		0			0
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	−15.0000			−0.531327			−0.265664	−	0.964066i	$-0.585591\pi$
$797$	−15.0000			−0.531327			−0.265664	+	0.964066i	$0.585591\pi$
$798$		0			0
$799$		0			0
$800$	−5.50000	+	9.52628i	−0.194454	+	0.336805i
$801$	−18.0000	−	31.1769i	−0.635999	−	1.10158i
$802$	−6.00000	−	10.3923i	−0.211867	−	0.366965i
$803$	2.50000	−	4.33013i	0.0882231	−	0.152807i
$804$	−3.00000			−0.105802
$805$		0			0
$806$	−7.00000			−0.246564
$807$	−13.5000	+	23.3827i	−0.475223	+	0.823110i
$808$	−2.50000	−	4.33013i	−0.0879497	−	0.152333i
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	0.808458	−	0.588555i	$-0.200303\pi$
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	−0.913932	+	0.405868i	$0.866969\pi$
$810$	−18.0000	+	31.1769i	−0.632456	+	1.09545i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	−69.0000			−2.41994
$814$	−4.50000	+	7.79423i	−0.157725	+	0.273188i
$815$	8.00000	+	13.8564i	0.280228	+	0.485369i
$816$		0			0
$817$	−12.0000	+	20.7846i	−0.419827	+	0.727161i
$818$	26.0000			0.909069
$819$		0			0
$820$	12.0000			0.419058
$821$	23.0000	−	39.8372i	0.802706	−	1.39033i	−0.115124	−	0.993351i	$-0.536726\pi$
$821$	23.0000	−	39.8372i	0.802706	−	1.39033i	0.917829	−	0.396976i	$-0.129940\pi$
$822$	−9.00000	−	15.5885i	−0.313911	−	0.543710i
$823$	1.50000	+	2.59808i	0.0522867	+	0.0905632i	0.890984	−	0.454034i	$-0.150016\pi$
$823$	1.50000	+	2.59808i	0.0522867	+	0.0905632i	−0.838697	+	0.544598i	$0.816682\pi$
$824$	−7.00000	+	12.1244i	−0.243857	+	0.422372i
$825$	−33.0000			−1.14891
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	21.0000	−	36.3731i	0.729800	−	1.26405i
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$		0			0
$831$	−27.0000	+	46.7654i	−0.936620	+	1.62227i
$832$	1.00000			0.0346688
$833$		0			0
$834$	12.0000			0.415526
$835$		0			0
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$	−31.5000	−	54.5596i	−1.08880	−	1.88586i
$838$	7.50000	−	12.9904i	0.259083	−	0.448745i
$839$	−17.0000			−0.586905			−0.293453	−	0.955974i	$-0.594804\pi$
$839$	−17.0000			−0.586905			−0.293453	+	0.955974i	$0.594804\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−9.50000	+	16.4545i	−0.327392	+	0.567059i
$843$	−12.0000	−	20.7846i	−0.413302	−	0.715860i
$844$	5.00000	+	8.66025i	0.172107	+	0.298098i
$845$	−2.00000	+	3.46410i	−0.0688021	+	0.119169i
$846$	−42.0000			−1.44399
$847$		0			0
$848$		0			0
$849$	−28.5000	+	49.3634i	−0.978117	+	1.69415i
$850$		0			0
$851$	31.5000	+	54.5596i	1.07981	+	1.87028i
$852$	24.0000	−	41.5692i	0.822226	−	1.42414i
$853$	−16.0000			−0.547830			−0.273915	−	0.961754i	$-0.588319\pi$
$853$	−16.0000			−0.547830			−0.273915	+	0.961754i	$0.588319\pi$
$854$		0			0
$855$	144.000			4.92470
$856$	2.00000	−	3.46410i	0.0683586	−	0.118401i
$857$	11.0000	+	19.0526i	0.375753	+	0.650823i	0.990439	−	0.137948i	$-0.0440508\pi$
$857$	11.0000	+	19.0526i	0.375753	+	0.650823i	−0.614687	+	0.788771i	$0.710717\pi$
$858$	1.50000	+	2.59808i	0.0512092	+	0.0886969i
$859$	2.50000	−	4.33013i	0.0852989	−	0.147742i	−0.820220	−	0.572049i	$-0.806149\pi$
$859$	2.50000	−	4.33013i	0.0852989	−	0.147742i	0.905519	+	0.424307i	$0.139482\pi$
$860$	16.0000			0.545595
$861$		0			0
$862$	18.0000			0.613082
$863$	−14.0000	+	24.2487i	−0.476566	+	0.825436i	−0.999639	−	0.0268516i	$-0.991452\pi$
$863$	−14.0000	+	24.2487i	−0.476566	+	0.825436i	0.523074	+	0.852287i	$0.324785\pi$
$864$	4.50000	+	7.79423i	0.153093	+	0.265165i
$865$	4.00000	+	6.92820i	0.136004	+	0.235566i
$866$	17.0000	−	29.4449i	0.577684	−	1.00058i
$867$	51.0000			1.73205
$868$		0			0
$869$	11.0000			0.373149
$870$	−24.0000	+	41.5692i	−0.813676	+	1.40933i
$871$	−0.500000	−	0.866025i	−0.0169419	−	0.0293442i
$872$	7.00000	+	12.1244i	0.237050	+	0.410582i
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$	−42.0000			−1.42067
$875$		0			0
$876$	15.0000			0.506803
$877$	22.5000	−	38.9711i	0.759771	−	1.31596i	−0.183196	−	0.983076i	$-0.558644\pi$
$877$	22.5000	−	38.9711i	0.759771	−	1.31596i	0.942967	−	0.332886i	$-0.108022\pi$
$878$	1.00000	+	1.73205i	0.0337484	+	0.0584539i
$879$	39.0000	+	67.5500i	1.31544	+	2.27840i
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	−14.0000			−0.471138			−0.235569	−	0.971858i	$-0.575695\pi$
$883$	−14.0000			−0.471138			−0.235569	+	0.971858i	$0.575695\pi$
$884$		0			0
$885$	60.0000	+	103.923i	2.01688	+	3.49334i
$886$	−6.00000	−	10.3923i	−0.201574	−	0.349136i
$887$	−19.0000	+	32.9090i	−0.637958	+	1.10497i	0.347923	+	0.937523i	$0.386887\pi$
$887$	−19.0000	+	32.9090i	−0.637958	+	1.10497i	−0.985880	+	0.167452i	$0.946446\pi$
$888$	−27.0000			−0.906061
$889$		0			0
$890$	24.0000			0.804482
$891$	−4.50000	+	7.79423i	−0.150756	+	0.261116i
$892$	10.5000	+	18.1865i	0.351566	+	0.608930i
$893$	21.0000	+	36.3731i	0.702738	+	1.21718i
$894$	13.5000	−	23.3827i	0.451508	−	0.782034i
$895$	−24.0000			−0.802232
$896$		0			0
$897$	21.0000			0.701170
$898$	1.00000	−	1.73205i	0.0333704	−	0.0577993i
$899$	−14.0000	−	24.2487i	−0.466926	−	0.808740i
$900$	−33.0000	−	57.1577i	−1.10000	−	1.90526i
$901$		0			0
$902$	3.00000			0.0998891
$903$		0			0
$904$	−7.00000			−0.232817
$905$	30.0000	−	51.9615i	0.997234	−	1.72726i
$906$		0			0
$907$	15.0000	+	25.9808i	0.498067	+	0.862677i	0.999998	−	0.00223080i	$-0.000710087\pi$
$907$	15.0000	+	25.9808i	0.498067	+	0.862677i	−0.501931	+	0.864908i	$0.667377\pi$
$908$	12.0000	−	20.7846i	0.398234	−	0.689761i
$909$	30.0000			0.995037
$910$		0			0
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$	9.00000	−	15.5885i	0.298020	−	0.516185i
$913$		0			0
$914$	13.0000	+	22.5167i	0.430002	+	0.744785i
$915$	−6.00000	+	10.3923i	−0.198354	+	0.343559i
$916$	24.0000			0.792982
$917$		0			0
$918$		0			0
$919$	−13.5000	+	23.3827i	−0.445324	+	0.771324i	−0.998075	−	0.0620230i	$-0.980245\pi$
$919$	−13.5000	+	23.3827i	−0.445324	+	0.771324i	0.552751	+	0.833347i	$0.313578\pi$
$920$	14.0000	+	24.2487i	0.461566	+	0.799456i
$921$	6.00000	+	10.3923i	0.197707	+	0.342438i
$922$	6.00000	−	10.3923i	0.197599	−	0.342252i
$923$	16.0000			0.526646
$924$		0			0
$925$	99.0000			3.25510
$926$	−8.00000	+	13.8564i	−0.262896	+	0.455350i
$927$	−42.0000	−	72.7461i	−1.37946	−	2.38930i
$928$	2.00000	+	3.46410i	0.0656532	+	0.113715i
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	−0.962431	−	0.271526i	$-0.912472\pi$
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	0.716364	+	0.697727i	$0.245805\pi$
$930$	84.0000			2.75447
$931$		0			0
$932$	−5.00000			−0.163780
$933$	−45.0000	+	77.9423i	−1.47323	+	2.55172i
$934$	−2.00000	−	3.46410i	−0.0654420	−	0.113349i
$935$		0			0
$936$	−3.00000	+	5.19615i	−0.0980581	+	0.169842i
$937$	36.0000			1.17607			0.588034	−	0.808836i	$-0.299902\pi$
$937$	36.0000			1.17607			0.588034	+	0.808836i	$0.299902\pi$
$938$		0			0
$939$	42.0000			1.37062
$940$	14.0000	−	24.2487i	0.456630	−	0.790906i
$941$	−25.0000	−	43.3013i	−0.814977	−	1.41158i	−0.909345	−	0.416044i	$-0.863416\pi$
$941$	−25.0000	−	43.3013i	−0.814977	−	1.41158i	0.0943679	−	0.995537i	$-0.469917\pi$
$942$	−7.50000	−	12.9904i	−0.244363	−	0.423249i
$943$	10.5000	−	18.1865i	0.341927	−	0.592235i
$944$	10.0000			0.325472
$945$		0			0
$946$	4.00000			0.130051
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	−0.992442	−	0.122714i	$-0.960840\pi$
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	0.602494	+	0.798123i	$0.294174\pi$
$948$	16.5000	+	28.5788i	0.535895	+	0.928198i
$949$	2.50000	+	4.33013i	0.0811534	+	0.140562i
$950$	−33.0000	+	57.1577i	−1.07066	+	1.85444i
$951$	−63.0000			−2.04291
$952$		0			0
$953$	−34.0000			−1.10137			−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000			−1.10137			−0.550684	+	0.834714i	$0.685633\pi$
$954$		0			0
$955$	16.0000	+	27.7128i	0.517748	+	0.896766i
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$	−6.00000	+	10.3923i	−0.193952	+	0.335936i
$958$	−24.0000			−0.775405
$959$		0			0
$960$	−12.0000			−0.387298
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$	−4.50000	−	7.79423i	−0.145086	−	0.251296i
$963$	12.0000	+	20.7846i	0.386695	+	0.669775i
$964$	−9.00000	+	15.5885i	−0.289870	+	0.502070i
$965$	80.0000			2.57529
$966$		0			0
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$	5.00000	−	8.66025i	0.160706	−	0.278351i
$969$		0			0
$970$	−2.00000	−	3.46410i	−0.0642161	−	0.111226i
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$		0			0
$973$		0			0
$974$	38.0000			1.21760
$975$	16.5000	−	28.5788i	0.528423	−	0.915255i
$976$	0.500000	+	0.866025i	0.0160046	+	0.0277208i
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$978$	−6.00000	+	10.3923i	−0.191859	+	0.332309i
$979$	6.00000			0.191761
$980$		0			0
$981$	−84.0000			−2.68191
$982$	−8.00000	+	13.8564i	−0.255290	+	0.442176i
$983$	−20.0000	−	34.6410i	−0.637901	−	1.10488i	−0.985893	−	0.167379i	$-0.946470\pi$
$983$	−20.0000	−	34.6410i	−0.637901	−	1.10488i	0.347992	−	0.937498i	$-0.386864\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$	54.0000	−	93.5307i	1.72058	−	2.98014i
$986$		0			0
$987$		0			0
$988$	6.00000			0.190885
$989$	14.0000	−	24.2487i	0.445174	−	0.771064i
$990$	−12.0000	−	20.7846i	−0.381385	−	0.660578i
$991$	28.5000	+	49.3634i	0.905332	+	1.56808i	0.820470	+	0.571689i	$0.193712\pi$
$991$	28.5000	+	49.3634i	0.905332	+	1.56808i	0.0848618	+	0.996393i	$0.472955\pi$
$992$	3.50000	−	6.06218i	0.111125	−	0.192474i
$993$	21.0000			0.666415
$994$		0			0
$995$	16.0000			0.507234
$996$		0			0
$997$	2.50000	+	4.33013i	0.0791758	+	0.137136i	0.902895	−	0.429862i	$-0.141438\pi$
$997$	2.50000	+	4.33013i	0.0791758	+	0.137136i	−0.823719	+	0.566999i	$0.808104\pi$
$998$	2.50000	+	4.33013i	0.0791361	+	0.137068i
$999$	40.5000	−	70.1481i	1.28136	−	2.21939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.f.k.79.1		2
7.2	even	3		1274.2.a.h.1.1		1
7.3	odd	6		1274.2.f.b.1145.1		2
7.4	even	3	inner	1274.2.f.k.1145.1		2
7.5	odd	6		182.2.a.e.1.1	✓	1
7.6	odd	2		1274.2.f.b.79.1		2
21.5	even	6		1638.2.a.j.1.1		1
28.19	even	6		1456.2.a.a.1.1		1
35.19	odd	6		4550.2.a.a.1.1		1
56.5	odd	6		5824.2.a.b.1.1		1
56.19	even	6		5824.2.a.bf.1.1		1
91.5	even	12		2366.2.d.j.337.1		2
91.12	odd	6		2366.2.a.h.1.1		1
91.47	even	12		2366.2.d.j.337.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.a.e.1.1	✓	1	7.5	odd	6
1274.2.a.h.1.1		1	7.2	even	3
1274.2.f.b.79.1		2	7.6	odd	2
1274.2.f.b.1145.1		2	7.3	odd	6
1274.2.f.k.79.1		2	1.1	even	1	trivial
1274.2.f.k.1145.1		2	7.4	even	3	inner
1456.2.a.a.1.1		1	28.19	even	6
1638.2.a.j.1.1		1	21.5	even	6
2366.2.a.h.1.1		1	91.12	odd	6
2366.2.d.j.337.1		2	91.5	even	12
2366.2.d.j.337.2		2	91.47	even	12
4550.2.a.a.1.1		1	35.19	odd	6
5824.2.a.b.1.1		1	56.5	odd	6
5824.2.a.bf.1.1		1	56.19	even	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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} +1.00000 q^{13} -12.0000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{18} +(-3.00000 + 5.19615i) q^{19} +4.00000 q^{20} +1.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(1.50000 + 2.59808i) q^{24} +(-5.50000 - 9.52628i) q^{25} +(-0.500000 + 0.866025i) q^{26} -9.00000 q^{27} -4.00000 q^{29} +(6.00000 - 10.3923i) q^{30} +(3.50000 + 6.06218i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +6.00000 q^{36} +(-4.50000 + 7.79423i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(1.50000 + 2.59808i) q^{39} +(-2.00000 + 3.46410i) q^{40} +3.00000 q^{41} +4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-12.0000 - 20.7846i) q^{45} +(3.50000 + 6.06218i) q^{46} +(3.50000 - 6.06218i) q^{47} -3.00000 q^{48} +11.0000 q^{50} +(-0.500000 - 0.866025i) q^{52} +(4.50000 - 7.79423i) q^{54} +4.00000 q^{55} -18.0000 q^{57} +(2.00000 - 3.46410i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(6.00000 + 10.3923i) q^{60} +(0.500000 - 0.866025i) q^{61} -7.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(1.50000 + 2.59808i) q^{66} +(-0.500000 - 0.866025i) q^{67} +21.0000 q^{69} +16.0000 q^{71} +(-3.00000 + 5.19615i) q^{72} +(2.50000 + 4.33013i) q^{73} +(-4.50000 - 7.79423i) q^{74} +(16.5000 - 28.5788i) q^{75} +6.00000 q^{76} -3.00000 q^{78} +(-5.50000 + 9.52628i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-2.00000 + 3.46410i) q^{86} +(-6.00000 - 10.3923i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-3.00000 + 5.19615i) q^{89} +24.0000 q^{90} -7.00000 q^{92} +(-10.5000 + 18.1865i) q^{93} +(3.50000 + 6.06218i) q^{94} +(-12.0000 - 20.7846i) q^{95} +(1.50000 - 2.59808i) q^{96} +1.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9	\( 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 2 q^{13} - 24 q^{15} - q^{16} - 6 q^{18} - 6 q^{19} + 8 q^{20} + 2 q^{22} + 7 q^{23} + 3 q^{24} - 11 q^{25} - q^{26} - 18 q^{27} - 8 q^{29} + 12 q^{30} + 7 q^{31} - q^{32} + 3 q^{33} + 12 q^{36} - 9 q^{37} - 6 q^{38} + 3 q^{39} - 4 q^{40} + 6 q^{41} + 8 q^{43} - q^{44} - 24 q^{45} + 7 q^{46} + 7 q^{47} - 6 q^{48} + 22 q^{50} - q^{52} + 9 q^{54} + 8 q^{55} - 36 q^{57} + 4 q^{58} - 10 q^{59} + 12 q^{60} + q^{61} - 14 q^{62} + 2 q^{64} - 4 q^{65} + 3 q^{66} - q^{67} + 42 q^{69} + 32 q^{71} - 6 q^{72} + 5 q^{73} - 9 q^{74} + 33 q^{75} + 12 q^{76} - 6 q^{78} - 11 q^{79} - 4 q^{80} - 9 q^{81} - 3 q^{82} - 4 q^{86} - 12 q^{87} - q^{88} - 6 q^{89} + 48 q^{90} - 14 q^{92} - 21 q^{93} + 7 q^{94} - 24 q^{95} + 3 q^{96} + 2 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 2 * q^13 - 24 * q^15 - q^16 - 6 * q^18 - 6 * q^19 + 8 * q^20 + 2 * q^22 + 7 * q^23 + 3 * q^24 - 11 * q^25 - q^26 - 18 * q^27 - 8 * q^29 + 12 * q^30 + 7 * q^31 - q^32 + 3 * q^33 + 12 * q^36 - 9 * q^37 - 6 * q^38 + 3 * q^39 - 4 * q^40 + 6 * q^41 + 8 * q^43 - q^44 - 24 * q^45 + 7 * q^46 + 7 * q^47 - 6 * q^48 + 22 * q^50 - q^52 + 9 * q^54 + 8 * q^55 - 36 * q^57 + 4 * q^58 - 10 * q^59 + 12 * q^60 + q^61 - 14 * q^62 + 2 * q^64 - 4 * q^65 + 3 * q^66 - q^67 + 42 * q^69 + 32 * q^71 - 6 * q^72 + 5 * q^73 - 9 * q^74 + 33 * q^75 + 12 * q^76 - 6 * q^78 - 11 * q^79 - 4 * q^80 - 9 * q^81 - 3 * q^82 - 4 * q^86 - 12 * q^87 - q^88 - 6 * q^89 + 48 * q^90 - 14 * q^92 - 21 * q^93 + 7 * q^94 - 24 * q^95 + 3 * q^96 + 2 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more