LMFDB - Embedded newform 760.2.w.a.267.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [760,2,Mod(267,760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(760, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("760.267"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	760.267
Dual form			760.2.w.a.723.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} +(2.00000 - 2.00000i) q^{3} -2.00000i q^{4} +(1.00000 - 2.00000i) q^{5} +4.00000i q^{6} +(-3.00000 + 3.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} -5.00000i q^{9} +(1.00000 + 3.00000i) q^{10} -4.00000 q^{11} +(-4.00000 - 4.00000i) q^{12} +(-4.00000 - 4.00000i) q^{13} -6.00000i q^{14} +(-2.00000 - 6.00000i) q^{15} -4.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +(5.00000 + 5.00000i) q^{18} -1.00000i q^{19} +(-4.00000 - 2.00000i) q^{20} +12.0000i q^{21} +(4.00000 - 4.00000i) q^{22} +(-5.00000 - 5.00000i) q^{23} +8.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +8.00000 q^{26} +(-4.00000 - 4.00000i) q^{27} +(6.00000 + 6.00000i) q^{28} +10.0000 q^{29} +(8.00000 + 4.00000i) q^{30} -4.00000i q^{31} +(4.00000 - 4.00000i) q^{32} +(-8.00000 + 8.00000i) q^{33} -2.00000 q^{34} +(3.00000 + 9.00000i) q^{35} -10.0000 q^{36} +(1.00000 + 1.00000i) q^{38} -16.0000 q^{39} +(6.00000 - 2.00000i) q^{40} -2.00000 q^{41} +(-12.0000 - 12.0000i) q^{42} +(3.00000 - 3.00000i) q^{43} +8.00000i q^{44} +(-10.0000 - 5.00000i) q^{45} +10.0000 q^{46} +(-5.00000 + 5.00000i) q^{47} +(-8.00000 + 8.00000i) q^{48} -11.0000i q^{49} +(7.00000 + 1.00000i) q^{50} +4.00000 q^{51} +(-8.00000 + 8.00000i) q^{52} +(-2.00000 - 2.00000i) q^{53} +8.00000 q^{54} +(-4.00000 + 8.00000i) q^{55} -12.0000 q^{56} +(-2.00000 - 2.00000i) q^{57} +(-10.0000 + 10.0000i) q^{58} +(-12.0000 + 4.00000i) q^{60} +2.00000i q^{61} +(4.00000 + 4.00000i) q^{62} +(15.0000 + 15.0000i) q^{63} +8.00000i q^{64} +(-12.0000 + 4.00000i) q^{65} -16.0000i q^{66} +(10.0000 + 10.0000i) q^{67} +(2.00000 - 2.00000i) q^{68} -20.0000 q^{69} +(-12.0000 - 6.00000i) q^{70} -8.00000i q^{71} +(10.0000 - 10.0000i) q^{72} +(7.00000 - 7.00000i) q^{73} +(-14.0000 - 2.00000i) q^{75} -2.00000 q^{76} +(12.0000 - 12.0000i) q^{77} +(16.0000 - 16.0000i) q^{78} +8.00000 q^{79} +(-4.00000 + 8.00000i) q^{80} -1.00000 q^{81} +(2.00000 - 2.00000i) q^{82} +(-7.00000 + 7.00000i) q^{83} +24.0000 q^{84} +(3.00000 - 1.00000i) q^{85} +6.00000i q^{86} +(20.0000 - 20.0000i) q^{87} +(-8.00000 - 8.00000i) q^{88} -10.0000i q^{89} +(15.0000 - 5.00000i) q^{90} +24.0000 q^{91} +(-10.0000 + 10.0000i) q^{92} +(-8.00000 - 8.00000i) q^{93} -10.0000i q^{94} +(-2.00000 - 1.00000i) q^{95} -16.0000i q^{96} +(6.00000 + 6.00000i) q^{97} +(11.0000 + 11.0000i) q^{98} +20.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 4 q^{3} + 2 q^{5} - 6 q^{7} + 4 q^{8} + 2 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 4 q^{15} - 8 q^{16} + 2 q^{17} + 10 q^{18} - 8 q^{20} + 8 q^{22} - 10 q^{23} + 16 q^{24} - 6 q^{25} + 16 q^{26}+ \cdots + 22 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^5 - 6 * q^7 + 4 * q^8 + 2 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 4 * q^15 - 8 * q^16 + 2 * q^17 + 10 * q^18 - 8 * q^20 + 8 * q^22 - 10 * q^23 + 16 * q^24 - 6 * q^25 + 16 * q^26 - 8 * q^27 + 12 * q^28 + 20 * q^29 + 16 * q^30 + 8 * q^32 - 16 * q^33 - 4 * q^34 + 6 * q^35 - 20 * q^36 + 2 * q^38 - 32 * q^39 + 12 * q^40 - 4 * q^41 - 24 * q^42 + 6 * q^43 - 20 * q^45 + 20 * q^46 - 10 * q^47 - 16 * q^48 + 14 * q^50 + 8 * q^51 - 16 * q^52 - 4 * q^53 + 16 * q^54 - 8 * q^55 - 24 * q^56 - 4 * q^57 - 20 * q^58 - 24 * q^60 + 8 * q^62 + 30 * q^63 - 24 * q^65 + 20 * q^67 + 4 * q^68 - 40 * q^69 - 24 * q^70 + 20 * q^72 + 14 * q^73 - 28 * q^75 - 4 * q^76 + 24 * q^77 + 32 * q^78 + 16 * q^79 - 8 * q^80 - 2 * q^81 + 4 * q^82 - 14 * q^83 + 48 * q^84 + 6 * q^85 + 40 * q^87 - 16 * q^88 + 30 * q^90 + 48 * q^91 - 20 * q^92 - 16 * q^93 - 4 * q^95 + 12 * q^97 + 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	2.00000	−	2.00000i	1.15470	−	1.15470i	0.169102	−	0.985599i	$-0.445913\pi$
$3$	2.00000	−	2.00000i	1.15470	−	1.15470i	0.985599	−	0.169102i	$-0.0540867\pi$
$4$		−	2.00000i		−	1.00000i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$			4.00000i			1.63299i
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.144370	+	0.989524i	$0.546115\pi$
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.989524	+	0.144370i	$0.953885\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$		−	5.00000i		−	1.66667i
$10$	1.00000	+	3.00000i	0.316228	+	0.948683i
$11$	−4.00000			−1.20605			−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000			−1.20605			−0.603023	+	0.797724i	$0.706037\pi$
$12$	−4.00000	−	4.00000i	−1.15470	−	1.15470i
$13$	−4.00000	−	4.00000i	−1.10940	−	1.10940i	−0.993229	−	0.116171i	$-0.962938\pi$
$13$	−4.00000	−	4.00000i	−1.10940	−	1.10940i	−0.116171	−	0.993229i	$-0.537062\pi$
$14$		−	6.00000i		−	1.60357i
$15$	−2.00000	−	6.00000i	−0.516398	−	1.54919i
$16$	−4.00000			−1.00000
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$	5.00000	+	5.00000i	1.17851	+	1.17851i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−4.00000	−	2.00000i	−0.894427	−	0.447214i
$21$			12.0000i			2.61861i
$22$	4.00000	−	4.00000i	0.852803	−	0.852803i
$23$	−5.00000	−	5.00000i	−1.04257	−	1.04257i	−0.999053	−	0.0435195i	$-0.986143\pi$
$23$	−5.00000	−	5.00000i	−1.04257	−	1.04257i	−0.0435195	−	0.999053i	$-0.513857\pi$
$24$	8.00000			1.63299
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	8.00000			1.56893
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$	6.00000	+	6.00000i	1.13389	+	1.13389i
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$	8.00000	+	4.00000i	1.46059	+	0.730297i
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	−8.00000	+	8.00000i	−1.39262	+	1.39262i
$34$	−2.00000			−0.342997
$35$	3.00000	+	9.00000i	0.507093	+	1.52128i
$36$	−10.0000			−1.66667
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$	1.00000	+	1.00000i	0.162221	+	0.162221i
$39$	−16.0000			−2.56205
$40$	6.00000	−	2.00000i	0.948683	−	0.316228i
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$	−12.0000	−	12.0000i	−1.85164	−	1.85164i
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$			8.00000i			1.20605i
$45$	−10.0000	−	5.00000i	−1.49071	−	0.745356i
$46$	10.0000			1.47442
$47$	−5.00000	+	5.00000i	−0.729325	+	0.729325i	−0.970485	−	0.241160i	$-0.922472\pi$
$47$	−5.00000	+	5.00000i	−0.729325	+	0.729325i	0.241160	+	0.970485i	$0.422472\pi$
$48$	−8.00000	+	8.00000i	−1.15470	+	1.15470i
$49$		−	11.0000i		−	1.57143i
$50$	7.00000	+	1.00000i	0.989949	+	0.141421i
$51$	4.00000			0.560112
$52$	−8.00000	+	8.00000i	−1.10940	+	1.10940i
$53$	−2.00000	−	2.00000i	−0.274721	−	0.274721i	0.556276	−	0.830997i	$-0.312230\pi$
$53$	−2.00000	−	2.00000i	−0.274721	−	0.274721i	−0.830997	+	0.556276i	$0.812230\pi$
$54$	8.00000			1.08866
$55$	−4.00000	+	8.00000i	−0.539360	+	1.07872i
$56$	−12.0000			−1.60357
$57$	−2.00000	−	2.00000i	−0.264906	−	0.264906i
$58$	−10.0000	+	10.0000i	−1.31306	+	1.31306i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$	−12.0000	+	4.00000i	−1.54919	+	0.516398i
$61$			2.00000i			0.256074i	0.991769	+	0.128037i	$0.0408676\pi$
$61$			2.00000i			0.256074i	−0.991769	+	0.128037i	$0.959132\pi$
$62$	4.00000	+	4.00000i	0.508001	+	0.508001i
$63$	15.0000	+	15.0000i	1.88982	+	1.88982i
$64$			8.00000i			1.00000i
$65$	−12.0000	+	4.00000i	−1.48842	+	0.496139i
$66$		−	16.0000i		−	1.96946i
$67$	10.0000	+	10.0000i	1.22169	+	1.22169i	0.967029	+	0.254665i	$0.0819652\pi$
$67$	10.0000	+	10.0000i	1.22169	+	1.22169i	0.254665	+	0.967029i	$0.418035\pi$
$68$	2.00000	−	2.00000i	0.242536	−	0.242536i
$69$	−20.0000			−2.40772
$70$	−12.0000	−	6.00000i	−1.43427	−	0.717137i
$71$		−	8.00000i		−	0.949425i	−0.880141	−	0.474713i	$-0.842552\pi$
$71$		−	8.00000i		−	0.949425i	0.880141	−	0.474713i	$-0.157448\pi$
$72$	10.0000	−	10.0000i	1.17851	−	1.17851i
$73$	7.00000	−	7.00000i	0.819288	−	0.819288i	−0.166717	−	0.986005i	$-0.553317\pi$
$73$	7.00000	−	7.00000i	0.819288	−	0.819288i	0.986005	+	0.166717i	$0.0533166\pi$
$74$		0			0
$75$	−14.0000	−	2.00000i	−1.61658	−	0.230940i
$76$	−2.00000			−0.229416
$77$	12.0000	−	12.0000i	1.36753	−	1.36753i
$78$	16.0000	−	16.0000i	1.81164	−	1.81164i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−4.00000	+	8.00000i	−0.447214	+	0.894427i
$81$	−1.00000			−0.111111
$82$	2.00000	−	2.00000i	0.220863	−	0.220863i
$83$	−7.00000	+	7.00000i	−0.768350	+	0.768350i	−0.977816	−	0.209466i	$-0.932827\pi$
$83$	−7.00000	+	7.00000i	−0.768350	+	0.768350i	0.209466	+	0.977816i	$0.432827\pi$
$84$	24.0000			2.61861
$85$	3.00000	−	1.00000i	0.325396	−	0.108465i
$86$			6.00000i			0.646997i
$87$	20.0000	−	20.0000i	2.14423	−	2.14423i
$88$	−8.00000	−	8.00000i	−0.852803	−	0.852803i
$89$		−	10.0000i		−	1.06000i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$		−	10.0000i		−	1.06000i	0.847998	−	0.529999i	$-0.177808\pi$
$90$	15.0000	−	5.00000i	1.58114	−	0.527046i
$91$	24.0000			2.51588
$92$	−10.0000	+	10.0000i	−1.04257	+	1.04257i
$93$	−8.00000	−	8.00000i	−0.829561	−	0.829561i
$94$		−	10.0000i		−	1.03142i
$95$	−2.00000	−	1.00000i	−0.205196	−	0.102598i
$96$		−	16.0000i		−	1.63299i
$97$	6.00000	+	6.00000i	0.609208	+	0.609208i	0.942739	−	0.333531i	$-0.108240\pi$
$97$	6.00000	+	6.00000i	0.609208	+	0.609208i	−0.333531	+	0.942739i	$0.608240\pi$
$98$	11.0000	+	11.0000i	1.11117	+	1.11117i
$99$			20.0000i			2.01008i
$100$	−8.00000	+	6.00000i	−0.800000	+	0.600000i
$101$		−	6.00000i		−	0.597022i	−0.954406	−	0.298511i	$-0.903510\pi$
$101$		−	6.00000i		−	0.597022i	0.954406	−	0.298511i	$-0.0964900\pi$
$102$	−4.00000	+	4.00000i	−0.396059	+	0.396059i
$103$	6.00000	+	6.00000i	0.591198	+	0.591198i	0.937955	−	0.346757i	$-0.112717\pi$
$103$	6.00000	+	6.00000i	0.591198	+	0.591198i	−0.346757	+	0.937955i	$0.612717\pi$
$104$		−	16.0000i		−	1.56893i
$105$	24.0000	+	12.0000i	2.34216	+	1.17108i
$106$	4.00000			0.388514
$107$	−4.00000	−	4.00000i	−0.386695	−	0.386695i	0.486812	−	0.873507i	$-0.338160\pi$
$107$	−4.00000	−	4.00000i	−0.386695	−	0.386695i	−0.873507	+	0.486812i	$0.838160\pi$
$108$	−8.00000	+	8.00000i	−0.769800	+	0.769800i
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	−4.00000	−	12.0000i	−0.381385	−	1.14416i
$111$		0			0
$112$	12.0000	−	12.0000i	1.13389	−	1.13389i
$113$	−2.00000	+	2.00000i	−0.188144	+	0.188144i	−0.794893	−	0.606749i	$-0.792473\pi$
$113$	−2.00000	+	2.00000i	−0.188144	+	0.188144i	0.606749	+	0.794893i	$0.292473\pi$
$114$	4.00000			0.374634
$115$	−15.0000	+	5.00000i	−1.39876	+	0.466252i
$116$		−	20.0000i		−	1.85695i
$117$	−20.0000	+	20.0000i	−1.84900	+	1.84900i
$118$		0			0
$119$	−6.00000			−0.550019
$120$	8.00000	−	16.0000i	0.730297	−	1.46059i
$121$	5.00000			0.454545
$122$	−2.00000	−	2.00000i	−0.181071	−	0.181071i
$123$	−4.00000	+	4.00000i	−0.360668	+	0.360668i
$124$	−8.00000			−0.718421
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	−30.0000			−2.67261
$127$	−2.00000	+	2.00000i	−0.177471	+	0.177471i	−0.790253	−	0.612781i	$-0.790051\pi$
$127$	−2.00000	+	2.00000i	−0.177471	+	0.177471i	0.612781	+	0.790253i	$0.290051\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$		−	12.0000i		−	1.05654i
$130$	8.00000	−	16.0000i	0.701646	−	1.40329i
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$	16.0000	+	16.0000i	1.39262	+	1.39262i
$133$	3.00000	+	3.00000i	0.260133	+	0.260133i
$134$	−20.0000			−1.72774
$135$	−12.0000	+	4.00000i	−1.03280	+	0.344265i
$136$			4.00000i			0.342997i
$137$	−5.00000	−	5.00000i	−0.427179	−	0.427179i	0.460487	−	0.887666i	$-0.347675\pi$
$137$	−5.00000	−	5.00000i	−0.427179	−	0.427179i	−0.887666	+	0.460487i	$0.847675\pi$
$138$	20.0000	−	20.0000i	1.70251	−	1.70251i
$139$		−	2.00000i		−	0.169638i	−0.996396	−	0.0848189i	$-0.972969\pi$
$139$		−	2.00000i		−	0.169638i	0.996396	−	0.0848189i	$-0.0270312\pi$
$140$	18.0000	−	6.00000i	1.52128	−	0.507093i
$141$			20.0000i			1.68430i
$142$	8.00000	+	8.00000i	0.671345	+	0.671345i
$143$	16.0000	+	16.0000i	1.33799	+	1.33799i
$144$			20.0000i			1.66667i
$145$	10.0000	−	20.0000i	0.830455	−	1.66091i
$146$			14.0000i			1.15865i
$147$	−22.0000	−	22.0000i	−1.81453	−	1.81453i
$148$		0			0
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$	16.0000	−	12.0000i	1.30639	−	0.979796i
$151$		−	16.0000i		−	1.30206i	−0.759051	−	0.651031i	$-0.774337\pi$
$151$		−	16.0000i		−	1.30206i	0.759051	−	0.651031i	$-0.225663\pi$
$152$	2.00000	−	2.00000i	0.162221	−	0.162221i
$153$	5.00000	−	5.00000i	0.404226	−	0.404226i
$154$			24.0000i			1.93398i
$155$	−8.00000	−	4.00000i	−0.642575	−	0.321288i
$156$			32.0000i			2.56205i
$157$	3.00000	−	3.00000i	0.239426	−	0.239426i	−0.577186	−	0.816612i	$-0.695849\pi$
$157$	3.00000	−	3.00000i	0.239426	−	0.239426i	0.816612	+	0.577186i	$0.195849\pi$
$158$	−8.00000	+	8.00000i	−0.636446	+	0.636446i
$159$	−8.00000			−0.634441
$160$	−4.00000	−	12.0000i	−0.316228	−	0.948683i
$161$	30.0000			2.36433
$162$	1.00000	−	1.00000i	0.0785674	−	0.0785674i
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	−0.666858	−	0.745184i	$-0.732361\pi$
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	0.745184	+	0.666858i	$0.232361\pi$
$164$			4.00000i			0.312348i
$165$	8.00000	+	24.0000i	0.622799	+	1.86840i
$166$		−	14.0000i		−	1.08661i
$167$	−16.0000	+	16.0000i	−1.23812	+	1.23812i	−0.277347	+	0.960770i	$0.589455\pi$
$167$	−16.0000	+	16.0000i	−1.23812	+	1.23812i	−0.960770	+	0.277347i	$0.910545\pi$
$168$	−24.0000	+	24.0000i	−1.85164	+	1.85164i
$169$			19.0000i			1.46154i
$170$	−2.00000	+	4.00000i	−0.153393	+	0.306786i
$171$	−5.00000			−0.382360
$172$	−6.00000	−	6.00000i	−0.457496	−	0.457496i
$173$	−10.0000	−	10.0000i	−0.760286	−	0.760286i	0.216088	−	0.976374i	$-0.430670\pi$
$173$	−10.0000	−	10.0000i	−0.760286	−	0.760286i	−0.976374	+	0.216088i	$0.930670\pi$
$174$			40.0000i			3.03239i
$175$	21.0000	+	3.00000i	1.58745	+	0.226779i
$176$	16.0000			1.20605
$177$		0			0
$178$	10.0000	+	10.0000i	0.749532	+	0.749532i
$179$		−	16.0000i		−	1.19590i	−0.801535	−	0.597948i	$-0.795983\pi$
$179$		−	16.0000i		−	1.19590i	0.801535	−	0.597948i	$-0.204017\pi$
$180$	−10.0000	+	20.0000i	−0.745356	+	1.49071i
$181$		−	10.0000i		−	0.743294i	−0.928374	−	0.371647i	$-0.878793\pi$
$181$		−	10.0000i		−	0.743294i	0.928374	−	0.371647i	$-0.121207\pi$
$182$	−24.0000	+	24.0000i	−1.77900	+	1.77900i
$183$	4.00000	+	4.00000i	0.295689	+	0.295689i
$184$		−	20.0000i		−	1.47442i
$185$		0			0
$186$	16.0000			1.17318
$187$	−4.00000	−	4.00000i	−0.292509	−	0.292509i
$188$	10.0000	+	10.0000i	0.729325	+	0.729325i
$189$	24.0000			1.74574
$190$	3.00000	−	1.00000i	0.217643	−	0.0725476i
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	16.0000	+	16.0000i	1.15470	+	1.15470i
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	−0.457381	−	0.889271i	$-0.651213\pi$
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	0.889271	+	0.457381i	$0.151213\pi$
$194$	−12.0000			−0.861550
$195$	−16.0000	+	32.0000i	−1.14578	+	2.29157i
$196$	−22.0000			−1.57143
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	−0.862423	−	0.506188i	$-0.831054\pi$
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	0.506188	+	0.862423i	$0.331054\pi$
$198$	−20.0000	−	20.0000i	−1.42134	−	1.42134i
$199$	−6.00000			−0.425329			−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000			−0.425329			−0.212664	+	0.977125i	$0.568214\pi$
$200$	2.00000	−	14.0000i	0.141421	−	0.989949i
$201$	40.0000			2.82138
$202$	6.00000	+	6.00000i	0.422159	+	0.422159i
$203$	−30.0000	+	30.0000i	−2.10559	+	2.10559i
$204$		−	8.00000i		−	0.560112i
$205$	−2.00000	+	4.00000i	−0.139686	+	0.279372i
$206$	−12.0000			−0.836080
$207$	−25.0000	+	25.0000i	−1.73762	+	1.73762i
$208$	16.0000	+	16.0000i	1.10940	+	1.10940i
$209$			4.00000i			0.276686i
$210$	−36.0000	+	12.0000i	−2.48424	+	0.828079i
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−4.00000	+	4.00000i	−0.274721	+	0.274721i
$213$	−16.0000	−	16.0000i	−1.09630	−	1.09630i
$214$	8.00000			0.546869
$215$	−3.00000	−	9.00000i	−0.204598	−	0.613795i
$216$		−	16.0000i		−	1.08866i
$217$	12.0000	+	12.0000i	0.814613	+	0.814613i
$218$	−6.00000	+	6.00000i	−0.406371	+	0.406371i
$219$		−	28.0000i		−	1.89206i
$220$	16.0000	+	8.00000i	1.07872	+	0.539360i
$221$		−	8.00000i		−	0.538138i
$222$		0			0
$223$	10.0000	+	10.0000i	0.669650	+	0.669650i	0.957635	−	0.287985i	$-0.0929854\pi$
$223$	10.0000	+	10.0000i	0.669650	+	0.669650i	−0.287985	+	0.957635i	$0.592985\pi$
$224$			24.0000i			1.60357i
$225$	−20.0000	+	15.0000i	−1.33333	+	1.00000i
$226$		−	4.00000i		−	0.266076i
$227$	16.0000	+	16.0000i	1.06196	+	1.06196i	0.997949	+	0.0640079i	$0.0203883\pi$
$227$	16.0000	+	16.0000i	1.06196	+	1.06196i	0.0640079	+	0.997949i	$0.479612\pi$
$228$	−4.00000	+	4.00000i	−0.264906	+	0.264906i
$229$	24.0000			1.58596			0.792982	−	0.609245i	$-0.208527\pi$
$229$	24.0000			1.58596			0.792982	+	0.609245i	$0.208527\pi$
$230$	10.0000	−	20.0000i	0.659380	−	1.31876i
$231$		−	48.0000i		−	3.15817i
$232$	20.0000	+	20.0000i	1.31306	+	1.31306i
$233$	−19.0000	+	19.0000i	−1.24473	+	1.24473i	−0.286716	+	0.958016i	$0.592563\pi$
$233$	−19.0000	+	19.0000i	−1.24473	+	1.24473i	−0.958016	+	0.286716i	$0.907437\pi$
$234$		−	40.0000i		−	2.61488i
$235$	5.00000	+	15.0000i	0.326164	+	0.978492i
$236$		0			0
$237$	16.0000	−	16.0000i	1.03931	−	1.03931i
$238$	6.00000	−	6.00000i	0.388922	−	0.388922i
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$	8.00000	+	24.0000i	0.516398	+	1.54919i
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$	−5.00000	+	5.00000i	−0.321412	+	0.321412i
$243$	10.0000	−	10.0000i	0.641500	−	0.641500i
$244$	4.00000			0.256074
$245$	−22.0000	−	11.0000i	−1.40553	−	0.702764i
$246$		−	8.00000i		−	0.510061i
$247$	−4.00000	+	4.00000i	−0.254514	+	0.254514i
$248$	8.00000	−	8.00000i	0.508001	−	0.508001i
$249$			28.0000i			1.77443i
$250$	9.00000	−	13.0000i	0.569210	−	0.822192i
$251$	−22.0000			−1.38863			−0.694314	−	0.719672i	$-0.744292\pi$
$251$	−22.0000			−1.38863			−0.694314	+	0.719672i	$0.744292\pi$
$252$	30.0000	−	30.0000i	1.88982	−	1.88982i
$253$	20.0000	+	20.0000i	1.25739	+	1.25739i
$254$		−	4.00000i		−	0.250982i
$255$	4.00000	−	8.00000i	0.250490	−	0.500979i
$256$	16.0000			1.00000
$257$	−20.0000	−	20.0000i	−1.24757	−	1.24757i	−0.956792	−	0.290774i	$-0.906087\pi$
$257$	−20.0000	−	20.0000i	−1.24757	−	1.24757i	−0.290774	−	0.956792i	$-0.593913\pi$
$258$	12.0000	+	12.0000i	0.747087	+	0.747087i
$259$		0			0
$260$	8.00000	+	24.0000i	0.496139	+	1.48842i
$261$		−	50.0000i		−	3.09492i
$262$	−6.00000	+	6.00000i	−0.370681	+	0.370681i
$263$	−7.00000	−	7.00000i	−0.431638	−	0.431638i	0.457547	−	0.889185i	$-0.348728\pi$
$263$	−7.00000	−	7.00000i	−0.431638	−	0.431638i	−0.889185	+	0.457547i	$0.848728\pi$
$264$	−32.0000			−1.96946
$265$	−6.00000	+	2.00000i	−0.368577	+	0.122859i
$266$	−6.00000			−0.367884
$267$	−20.0000	−	20.0000i	−1.22398	−	1.22398i
$268$	20.0000	−	20.0000i	1.22169	−	1.22169i
$269$	14.0000			0.853595			0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000			0.853595			0.426798	+	0.904347i	$0.359642\pi$
$270$	8.00000	−	16.0000i	0.486864	−	0.973729i
$271$		−	2.00000i		−	0.121491i	−0.998153	−	0.0607457i	$-0.980652\pi$
$271$		−	2.00000i		−	0.121491i	0.998153	−	0.0607457i	$-0.0193479\pi$
$272$	−4.00000	−	4.00000i	−0.242536	−	0.242536i
$273$	48.0000	−	48.0000i	2.90509	−	2.90509i
$274$	10.0000			0.604122
$275$	12.0000	+	16.0000i	0.723627	+	0.964836i
$276$			40.0000i			2.40772i
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	−0.611213	−	0.791466i	$-0.709318\pi$
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	0.791466	+	0.611213i	$0.209318\pi$
$278$	2.00000	+	2.00000i	0.119952	+	0.119952i
$279$	−20.0000			−1.19737
$280$	−12.0000	+	24.0000i	−0.717137	+	1.43427i
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−20.0000	−	20.0000i	−1.19098	−	1.19098i
$283$	9.00000	−	9.00000i	0.534994	−	0.534994i	−0.387060	−	0.922055i	$-0.626509\pi$
$283$	9.00000	−	9.00000i	0.534994	−	0.534994i	0.922055	+	0.387060i	$0.126509\pi$
$284$	−16.0000			−0.949425
$285$	−6.00000	+	2.00000i	−0.355409	+	0.118470i
$286$	−32.0000			−1.89220
$287$	6.00000	−	6.00000i	0.354169	−	0.354169i
$288$	−20.0000	−	20.0000i	−1.17851	−	1.17851i
$289$		−	15.0000i		−	0.882353i
$290$	10.0000	+	30.0000i	0.587220	+	1.76166i
$291$	24.0000			1.40690
$292$	−14.0000	−	14.0000i	−0.819288	−	0.819288i
$293$	2.00000	+	2.00000i	0.116841	+	0.116841i	0.763110	−	0.646269i	$-0.223671\pi$
$293$	2.00000	+	2.00000i	0.116841	+	0.116841i	−0.646269	+	0.763110i	$0.723671\pi$
$294$	44.0000			2.56613
$295$		0			0
$296$		0			0
$297$	16.0000	+	16.0000i	0.928414	+	0.928414i
$298$	−12.0000	+	12.0000i	−0.695141	+	0.695141i
$299$			40.0000i			2.31326i
$300$	−4.00000	+	28.0000i	−0.230940	+	1.61658i
$301$			18.0000i			1.03750i
$302$	16.0000	+	16.0000i	0.920697	+	0.920697i
$303$	−12.0000	−	12.0000i	−0.689382	−	0.689382i
$304$			4.00000i			0.229416i
$305$	4.00000	+	2.00000i	0.229039	+	0.114520i
$306$			10.0000i			0.571662i
$307$	−8.00000	−	8.00000i	−0.456584	−	0.456584i	0.440948	−	0.897532i	$-0.354642\pi$
$307$	−8.00000	−	8.00000i	−0.456584	−	0.456584i	−0.897532	+	0.440948i	$0.854642\pi$
$308$	−24.0000	−	24.0000i	−1.36753	−	1.36753i
$309$	24.0000			1.36531
$310$	12.0000	−	4.00000i	0.681554	−	0.227185i
$311$		−	2.00000i		−	0.113410i	−0.998391	−	0.0567048i	$-0.981941\pi$
$311$		−	2.00000i		−	0.113410i	0.998391	−	0.0567048i	$-0.0180594\pi$
$312$	−32.0000	−	32.0000i	−1.81164	−	1.81164i
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$			6.00000i			0.338600i
$315$	45.0000	−	15.0000i	2.53546	−	0.845154i
$316$		−	16.0000i		−	0.900070i
$317$	−12.0000	+	12.0000i	−0.673987	+	0.673987i	−0.958633	−	0.284646i	$-0.908124\pi$
$317$	−12.0000	+	12.0000i	−0.673987	+	0.673987i	0.284646	+	0.958633i	$0.408124\pi$
$318$	8.00000	−	8.00000i	0.448618	−	0.448618i
$319$	−40.0000			−2.23957
$320$	16.0000	+	8.00000i	0.894427	+	0.447214i
$321$	−16.0000			−0.893033
$322$	−30.0000	+	30.0000i	−1.67183	+	1.67183i
$323$	1.00000	−	1.00000i	0.0556415	−	0.0556415i
$324$			2.00000i			0.111111i
$325$	−4.00000	+	28.0000i	−0.221880	+	1.55316i
$326$			2.00000i			0.110770i
$327$	12.0000	−	12.0000i	0.663602	−	0.663602i
$328$	−4.00000	−	4.00000i	−0.220863	−	0.220863i
$329$		−	30.0000i		−	1.65395i
$330$	−32.0000	−	16.0000i	−1.76154	−	0.880771i
$331$	−24.0000			−1.31916			−0.659580	−	0.751635i	$-0.729266\pi$
$331$	−24.0000			−1.31916			−0.659580	+	0.751635i	$0.729266\pi$
$332$	14.0000	+	14.0000i	0.768350	+	0.768350i
$333$		0			0
$334$		−	32.0000i		−	1.75096i
$335$	30.0000	−	10.0000i	1.63908	−	0.546358i
$336$		−	48.0000i		−	2.61861i
$337$	10.0000	+	10.0000i	0.544735	+	0.544735i	0.924913	−	0.380178i	$-0.124137\pi$
$337$	10.0000	+	10.0000i	0.544735	+	0.544735i	−0.380178	+	0.924913i	$0.624137\pi$
$338$	−19.0000	−	19.0000i	−1.03346	−	1.03346i
$339$			8.00000i			0.434500i
$340$	−2.00000	−	6.00000i	−0.108465	−	0.325396i
$341$			16.0000i			0.866449i
$342$	5.00000	−	5.00000i	0.270369	−	0.270369i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	12.0000			0.646997
$345$	−20.0000	+	40.0000i	−1.07676	+	2.15353i
$346$	20.0000			1.07521
$347$	7.00000	+	7.00000i	0.375780	+	0.375780i	0.869577	−	0.493797i	$-0.164392\pi$
$347$	7.00000	+	7.00000i	0.375780	+	0.375780i	−0.493797	+	0.869577i	$0.664392\pi$
$348$	−40.0000	−	40.0000i	−2.14423	−	2.14423i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	−24.0000	+	18.0000i	−1.28285	+	0.962140i
$351$			32.0000i			1.70803i
$352$	−16.0000	+	16.0000i	−0.852803	+	0.852803i
$353$	−9.00000	+	9.00000i	−0.479022	+	0.479022i	−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−9.00000	+	9.00000i	−0.479022	+	0.479022i	0.425797	+	0.904819i	$0.359994\pi$
$354$		0			0
$355$	−16.0000	−	8.00000i	−0.849192	−	0.424596i
$356$	−20.0000			−1.06000
$357$	−12.0000	+	12.0000i	−0.635107	+	0.635107i
$358$	16.0000	+	16.0000i	0.845626	+	0.845626i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	−10.0000	−	30.0000i	−0.527046	−	1.58114i
$361$	−1.00000			−0.0526316
$362$	10.0000	+	10.0000i	0.525588	+	0.525588i
$363$	10.0000	−	10.0000i	0.524864	−	0.524864i
$364$		−	48.0000i		−	2.51588i
$365$	−7.00000	−	21.0000i	−0.366397	−	1.09919i
$366$	−8.00000			−0.418167
$367$	21.0000	−	21.0000i	1.09619	−	1.09619i	0.101339	−	0.994852i	$-0.467687\pi$
$367$	21.0000	−	21.0000i	1.09619	−	1.09619i	0.994852	−	0.101339i	$-0.0323127\pi$
$368$	20.0000	+	20.0000i	1.04257	+	1.04257i
$369$			10.0000i			0.520579i
$370$		0			0
$371$	12.0000			0.623009
$372$	−16.0000	+	16.0000i	−0.829561	+	0.829561i
$373$	10.0000	+	10.0000i	0.517780	+	0.517780i	0.916899	−	0.399119i	$-0.130684\pi$
$373$	10.0000	+	10.0000i	0.517780	+	0.517780i	−0.399119	+	0.916899i	$0.630684\pi$
$374$	8.00000			0.413670
$375$	−18.0000	+	26.0000i	−0.929516	+	1.34263i
$376$	−20.0000			−1.03142
$377$	−40.0000	−	40.0000i	−2.06010	−	2.06010i
$378$	−24.0000	+	24.0000i	−1.23443	+	1.23443i
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$	−2.00000	+	4.00000i	−0.102598	+	0.205196i
$381$			8.00000i			0.409852i
$382$		0			0
$383$	−12.0000	−	12.0000i	−0.613171	−	0.613171i	0.330600	−	0.943771i	$-0.392749\pi$
$383$	−12.0000	−	12.0000i	−0.613171	−	0.613171i	−0.943771	+	0.330600i	$0.892749\pi$
$384$	−32.0000			−1.63299
$385$	−12.0000	−	36.0000i	−0.611577	−	1.83473i
$386$			12.0000i			0.610784i
$387$	−15.0000	−	15.0000i	−0.762493	−	0.762493i
$388$	12.0000	−	12.0000i	0.609208	−	0.609208i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$	−16.0000	−	48.0000i	−0.810191	−	2.43057i
$391$		−	10.0000i		−	0.505722i
$392$	22.0000	−	22.0000i	1.11117	−	1.11117i
$393$	12.0000	−	12.0000i	0.605320	−	0.605320i
$394$		−	10.0000i		−	0.503793i
$395$	8.00000	−	16.0000i	0.402524	−	0.805047i
$396$	40.0000			2.01008
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	0.953583	+	0.301131i	$0.0973643\pi$
$398$	6.00000	−	6.00000i	0.300753	−	0.300753i
$399$	12.0000			0.600751
$400$	12.0000	+	16.0000i	0.600000	+	0.800000i
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	−40.0000	+	40.0000i	−1.99502	+	1.99502i
$403$	−16.0000	+	16.0000i	−0.797017	+	0.797017i
$404$	−12.0000			−0.597022
$405$	−1.00000	+	2.00000i	−0.0496904	+	0.0993808i
$406$		−	60.0000i		−	2.97775i
$407$		0			0
$408$	8.00000	+	8.00000i	0.396059	+	0.396059i
$409$			34.0000i			1.68119i	0.541663	+	0.840596i	$0.317795\pi$
$409$			34.0000i			1.68119i	−0.541663	+	0.840596i	$0.682205\pi$
$410$	−2.00000	−	6.00000i	−0.0987730	−	0.296319i
$411$	−20.0000			−0.986527
$412$	12.0000	−	12.0000i	0.591198	−	0.591198i
$413$		0			0
$414$		−	50.0000i		−	2.45737i
$415$	7.00000	+	21.0000i	0.343616	+	1.03085i
$416$	−32.0000			−1.56893
$417$	−4.00000	−	4.00000i	−0.195881	−	0.195881i
$418$	−4.00000	−	4.00000i	−0.195646	−	0.195646i
$419$		−	12.0000i		−	0.586238i	−0.956076	−	0.293119i	$-0.905307\pi$
$419$		−	12.0000i		−	0.586238i	0.956076	−	0.293119i	$-0.0946933\pi$
$420$	24.0000	−	48.0000i	1.17108	−	2.34216i
$421$		−	26.0000i		−	1.26716i	−0.773676	−	0.633581i	$-0.781584\pi$
$421$		−	26.0000i		−	1.26716i	0.773676	−	0.633581i	$-0.218416\pi$
$422$	8.00000	−	8.00000i	0.389434	−	0.389434i
$423$	25.0000	+	25.0000i	1.21554	+	1.21554i
$424$		−	8.00000i		−	0.388514i
$425$	1.00000	−	7.00000i	0.0485071	−	0.339550i
$426$	32.0000			1.55041
$427$	−6.00000	−	6.00000i	−0.290360	−	0.290360i
$428$	−8.00000	+	8.00000i	−0.386695	+	0.386695i
$429$	64.0000			3.08995
$430$	12.0000	+	6.00000i	0.578691	+	0.289346i
$431$			12.0000i			0.578020i	0.957326	+	0.289010i	$0.0933260\pi$
$431$			12.0000i			0.578020i	−0.957326	+	0.289010i	$0.906674\pi$
$432$	16.0000	+	16.0000i	0.769800	+	0.769800i
$433$	14.0000	−	14.0000i	0.672797	−	0.672797i	−0.285563	−	0.958360i	$-0.592181\pi$
$433$	14.0000	−	14.0000i	0.672797	−	0.672797i	0.958360	+	0.285563i	$0.0921805\pi$
$434$	−24.0000			−1.15204
$435$	−20.0000	−	60.0000i	−0.958927	−	2.87678i
$436$		−	12.0000i		−	0.574696i
$437$	−5.00000	+	5.00000i	−0.239182	+	0.239182i
$438$	28.0000	+	28.0000i	1.33789	+	1.33789i
$439$	20.0000			0.954548			0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000			0.954548			0.477274	+	0.878755i	$0.341625\pi$
$440$	−24.0000	+	8.00000i	−1.14416	+	0.381385i
$441$	−55.0000			−2.61905
$442$	8.00000	+	8.00000i	0.380521	+	0.380521i
$443$	21.0000	−	21.0000i	0.997740	−	0.997740i	−0.00225734	−	0.999997i	$-0.500719\pi$
$443$	21.0000	−	21.0000i	0.997740	−	0.997740i	0.999997	+	0.00225734i	$0.000718535\pi$
$444$		0			0
$445$	−20.0000	−	10.0000i	−0.948091	−	0.474045i
$446$	−20.0000			−0.947027
$447$	24.0000	−	24.0000i	1.13516	−	1.13516i
$448$	−24.0000	−	24.0000i	−1.13389	−	1.13389i
$449$			10.0000i			0.471929i	0.971762	+	0.235965i	$0.0758249\pi$
$449$			10.0000i			0.471929i	−0.971762	+	0.235965i	$0.924175\pi$
$450$	5.00000	−	35.0000i	0.235702	−	1.64992i
$451$	8.00000			0.376705
$452$	4.00000	+	4.00000i	0.188144	+	0.188144i
$453$	−32.0000	−	32.0000i	−1.50349	−	1.50349i
$454$	−32.0000			−1.50183
$455$	24.0000	−	48.0000i	1.12514	−	2.25027i
$456$		−	8.00000i		−	0.374634i
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	0.263099	−	0.964769i	$-0.415256\pi$
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	−0.964769	+	0.263099i	$0.915256\pi$
$458$	−24.0000	+	24.0000i	−1.12145	+	1.12145i
$459$		−	8.00000i		−	0.373408i
$460$	10.0000	+	30.0000i	0.466252	+	1.39876i
$461$			20.0000i			0.931493i	0.884918	+	0.465746i	$0.154214\pi$
$461$			20.0000i			0.931493i	−0.884918	+	0.465746i	$0.845786\pi$
$462$	48.0000	+	48.0000i	2.23316	+	2.23316i
$463$	9.00000	+	9.00000i	0.418265	+	0.418265i	0.884606	−	0.466340i	$-0.154428\pi$
$463$	9.00000	+	9.00000i	0.418265	+	0.418265i	−0.466340	+	0.884606i	$0.654428\pi$
$464$	−40.0000			−1.85695
$465$	−24.0000	+	8.00000i	−1.11297	+	0.370991i
$466$		−	38.0000i		−	1.76032i
$467$	23.0000	+	23.0000i	1.06431	+	1.06431i	0.997785	+	0.0665285i	$0.0211923\pi$
$467$	23.0000	+	23.0000i	1.06431	+	1.06431i	0.0665285	+	0.997785i	$0.478808\pi$
$468$	40.0000	+	40.0000i	1.84900	+	1.84900i
$469$	−60.0000			−2.77054
$470$	−20.0000	−	10.0000i	−0.922531	−	0.461266i
$471$		−	12.0000i		−	0.552931i
$472$		0			0
$473$	−12.0000	+	12.0000i	−0.551761	+	0.551761i
$474$			32.0000i			1.46981i
$475$	−4.00000	+	3.00000i	−0.183533	+	0.137649i
$476$			12.0000i			0.550019i
$477$	−10.0000	+	10.0000i	−0.457869	+	0.457869i
$478$	−18.0000	+	18.0000i	−0.823301	+	0.823301i
$479$	8.00000			0.365529			0.182765	−	0.983157i	$-0.441495\pi$
$479$	8.00000			0.365529			0.182765	+	0.983157i	$0.441495\pi$
$480$	−32.0000	−	16.0000i	−1.46059	−	0.730297i
$481$		0			0
$482$	14.0000	−	14.0000i	0.637683	−	0.637683i
$483$	60.0000	−	60.0000i	2.73009	−	2.73009i
$484$		−	10.0000i		−	0.454545i
$485$	18.0000	−	6.00000i	0.817338	−	0.272446i
$486$			20.0000i			0.907218i
$487$	−24.0000	+	24.0000i	−1.08754	+	1.08754i	−0.0917629	+	0.995781i	$0.529250\pi$
$487$	−24.0000	+	24.0000i	−1.08754	+	1.08754i	−0.995781	+	0.0917629i	$0.970750\pi$
$488$	−4.00000	+	4.00000i	−0.181071	+	0.181071i
$489$		−	4.00000i		−	0.180886i
$490$	33.0000	−	11.0000i	1.49079	−	0.496929i
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$	8.00000	+	8.00000i	0.360668	+	0.360668i
$493$	10.0000	+	10.0000i	0.450377	+	0.450377i
$494$		−	8.00000i		−	0.359937i
$495$	40.0000	+	20.0000i	1.79787	+	0.898933i
$496$			16.0000i			0.718421i
$497$	24.0000	+	24.0000i	1.07655	+	1.07655i
$498$	−28.0000	−	28.0000i	−1.25471	−	1.25471i
$499$			6.00000i			0.268597i	0.990941	+	0.134298i	$0.0428781\pi$
$499$			6.00000i			0.268597i	−0.990941	+	0.134298i	$0.957122\pi$
$500$	4.00000	+	22.0000i	0.178885	+	0.983870i
$501$			64.0000i			2.85931i
$502$	22.0000	−	22.0000i	0.981908	−	0.981908i
$503$	−3.00000	−	3.00000i	−0.133763	−	0.133763i	0.637055	−	0.770818i	$-0.280152\pi$
$503$	−3.00000	−	3.00000i	−0.133763	−	0.133763i	−0.770818	+	0.637055i	$0.780152\pi$
$504$			60.0000i			2.67261i
$505$	−12.0000	−	6.00000i	−0.533993	−	0.266996i
$506$	−40.0000			−1.77822
$507$	38.0000	+	38.0000i	1.68764	+	1.68764i
$508$	4.00000	+	4.00000i	0.177471	+	0.177471i
$509$	−10.0000			−0.443242			−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000			−0.443242			−0.221621	+	0.975133i	$0.571135\pi$
$510$	4.00000	+	12.0000i	0.177123	+	0.531369i
$511$			42.0000i			1.85797i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−4.00000	+	4.00000i	−0.176604	+	0.176604i
$514$	40.0000			1.76432
$515$	18.0000	−	6.00000i	0.793175	−	0.264392i
$516$	−24.0000			−1.05654
$517$	20.0000	−	20.0000i	0.879599	−	0.879599i
$518$		0			0
$519$	−40.0000			−1.75581
$520$	−32.0000	−	16.0000i	−1.40329	−	0.701646i
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$	50.0000	+	50.0000i	2.18844	+	2.18844i
$523$	−16.0000	+	16.0000i	−0.699631	+	0.699631i	−0.964331	−	0.264700i	$-0.914727\pi$
$523$	−16.0000	+	16.0000i	−0.699631	+	0.699631i	0.264700	+	0.964331i	$0.414727\pi$
$524$		−	12.0000i		−	0.524222i
$525$	48.0000	−	36.0000i	2.09489	−	1.57117i
$526$	14.0000			0.610429
$527$	4.00000	−	4.00000i	0.174243	−	0.174243i
$528$	32.0000	−	32.0000i	1.39262	−	1.39262i
$529$			27.0000i			1.17391i
$530$	4.00000	−	8.00000i	0.173749	−	0.347498i
$531$		0			0
$532$	6.00000	−	6.00000i	0.260133	−	0.260133i
$533$	8.00000	+	8.00000i	0.346518	+	0.346518i
$534$	40.0000			1.73097
$535$	−12.0000	+	4.00000i	−0.518805	+	0.172935i
$536$			40.0000i			1.72774i
$537$	−32.0000	−	32.0000i	−1.38090	−	1.38090i
$538$	−14.0000	+	14.0000i	−0.603583	+	0.603583i
$539$			44.0000i			1.89521i
$540$	8.00000	+	24.0000i	0.344265	+	1.03280i
$541$			2.00000i			0.0859867i	0.999075	+	0.0429934i	$0.0136894\pi$
$541$			2.00000i			0.0859867i	−0.999075	+	0.0429934i	$0.986311\pi$
$542$	2.00000	+	2.00000i	0.0859074	+	0.0859074i
$543$	−20.0000	−	20.0000i	−0.858282	−	0.858282i
$544$	8.00000			0.342997
$545$	6.00000	−	12.0000i	0.257012	−	0.514024i
$546$			96.0000i			4.10842i
$547$	−24.0000	−	24.0000i	−1.02617	−	1.02617i	−0.999648	−	0.0265176i	$-0.991558\pi$
$547$	−24.0000	−	24.0000i	−1.02617	−	1.02617i	−0.0265176	−	0.999648i	$-0.508442\pi$
$548$	−10.0000	+	10.0000i	−0.427179	+	0.427179i
$549$	10.0000			0.426790
$550$	−28.0000	−	4.00000i	−1.19392	−	0.170561i
$551$		−	10.0000i		−	0.426014i
$552$	−40.0000	−	40.0000i	−1.70251	−	1.70251i
$553$	−24.0000	+	24.0000i	−1.02058	+	1.02058i
$554$			6.00000i			0.254916i
$555$		0			0
$556$	−4.00000			−0.169638
$557$	−21.0000	+	21.0000i	−0.889799	+	0.889799i	−0.994503	−	0.104705i	$-0.966610\pi$
$557$	−21.0000	+	21.0000i	−0.889799	+	0.889799i	0.104705	+	0.994503i	$0.466610\pi$
$558$	20.0000	−	20.0000i	0.846668	−	0.846668i
$559$	−24.0000			−1.01509
$560$	−12.0000	−	36.0000i	−0.507093	−	1.52128i
$561$	−16.0000			−0.675521
$562$	−2.00000	+	2.00000i	−0.0843649	+	0.0843649i
$563$	−8.00000	+	8.00000i	−0.337160	+	0.337160i	−0.855297	−	0.518138i	$-0.826626\pi$
$563$	−8.00000	+	8.00000i	−0.337160	+	0.337160i	0.518138	+	0.855297i	$0.326626\pi$
$564$	40.0000			1.68430
$565$	2.00000	+	6.00000i	0.0841406	+	0.252422i
$566$			18.0000i			0.756596i
$567$	3.00000	−	3.00000i	0.125988	−	0.125988i
$568$	16.0000	−	16.0000i	0.671345	−	0.671345i
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$	4.00000	−	8.00000i	0.167542	−	0.335083i
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$	32.0000	−	32.0000i	1.33799	−	1.33799i
$573$		0			0
$574$			12.0000i			0.500870i
$575$	−5.00000	+	35.0000i	−0.208514	+	1.45960i
$576$	40.0000			1.66667
$577$	3.00000	+	3.00000i	0.124892	+	0.124892i	0.766790	−	0.641898i	$-0.221853\pi$
$577$	3.00000	+	3.00000i	0.124892	+	0.124892i	−0.641898	+	0.766790i	$0.721853\pi$
$578$	15.0000	+	15.0000i	0.623918	+	0.623918i
$579$		−	24.0000i		−	0.997406i
$580$	−40.0000	−	20.0000i	−1.66091	−	0.830455i
$581$		−	42.0000i		−	1.74245i
$582$	−24.0000	+	24.0000i	−0.994832	+	0.994832i
$583$	8.00000	+	8.00000i	0.331326	+	0.331326i
$584$	28.0000			1.15865
$585$	20.0000	+	60.0000i	0.826898	+	2.48069i
$586$	−4.00000			−0.165238
$587$	23.0000	+	23.0000i	0.949312	+	0.949312i	0.998776	−	0.0494643i	$-0.0157514\pi$
$587$	23.0000	+	23.0000i	0.949312	+	0.949312i	−0.0494643	+	0.998776i	$0.515751\pi$
$588$	−44.0000	+	44.0000i	−1.81453	+	1.81453i
$589$	−4.00000			−0.164817
$590$		0			0
$591$			20.0000i			0.822690i
$592$		0			0
$593$	31.0000	−	31.0000i	1.27302	−	1.27302i	0.328521	−	0.944497i	$-0.393450\pi$
$593$	31.0000	−	31.0000i	1.27302	−	1.27302i	0.944497	−	0.328521i	$-0.106550\pi$
$594$	−32.0000			−1.31298
$595$	−6.00000	+	12.0000i	−0.245976	+	0.491952i
$596$		−	24.0000i		−	0.983078i
$597$	−12.0000	+	12.0000i	−0.491127	+	0.491127i
$598$	−40.0000	−	40.0000i	−1.63572	−	1.63572i
$599$	−36.0000			−1.47092			−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000			−1.47092			−0.735460	+	0.677568i	$0.763034\pi$
$600$	−24.0000	−	32.0000i	−0.979796	−	1.30639i
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$	−18.0000	−	18.0000i	−0.733625	−	0.733625i
$603$	50.0000	−	50.0000i	2.03616	−	2.03616i
$604$	−32.0000			−1.30206
$605$	5.00000	−	10.0000i	0.203279	−	0.406558i
$606$	24.0000			0.974933
$607$	−12.0000	+	12.0000i	−0.487065	+	0.487065i	−0.907379	−	0.420314i	$-0.861920\pi$
$607$	−12.0000	+	12.0000i	−0.487065	+	0.487065i	0.420314	+	0.907379i	$0.361920\pi$
$608$	−4.00000	−	4.00000i	−0.162221	−	0.162221i
$609$			120.000i			4.86265i
$610$	−6.00000	+	2.00000i	−0.242933	+	0.0809776i
$611$	40.0000			1.61823
$612$	−10.0000	−	10.0000i	−0.404226	−	0.404226i
$613$	−19.0000	−	19.0000i	−0.767403	−	0.767403i	0.210246	−	0.977649i	$-0.432574\pi$
$613$	−19.0000	−	19.0000i	−0.767403	−	0.767403i	−0.977649	+	0.210246i	$0.932574\pi$
$614$	16.0000			0.645707
$615$	4.00000	+	12.0000i	0.161296	+	0.483887i
$616$	48.0000			1.93398
$617$	−33.0000	−	33.0000i	−1.32853	−	1.32853i	−0.906653	−	0.421877i	$-0.861371\pi$
$617$	−33.0000	−	33.0000i	−1.32853	−	1.32853i	−0.421877	−	0.906653i	$-0.638629\pi$
$618$	−24.0000	+	24.0000i	−0.965422	+	0.965422i
$619$		−	14.0000i		−	0.562708i	−0.959604	−	0.281354i	$-0.909217\pi$
$619$		−	14.0000i		−	0.562708i	0.959604	−	0.281354i	$-0.0907834\pi$
$620$	−8.00000	+	16.0000i	−0.321288	+	0.642575i
$621$			40.0000i			1.60514i
$622$	2.00000	+	2.00000i	0.0801927	+	0.0801927i
$623$	30.0000	+	30.0000i	1.20192	+	1.20192i
$624$	64.0000			2.56205
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$			18.0000i			0.719425i
$627$	8.00000	+	8.00000i	0.319489	+	0.319489i
$628$	−6.00000	−	6.00000i	−0.239426	−	0.239426i
$629$		0			0
$630$	−30.0000	+	60.0000i	−1.19523	+	2.39046i
$631$			26.0000i			1.03504i	0.855670	+	0.517522i	$0.173145\pi$
$631$			26.0000i			1.03504i	−0.855670	+	0.517522i	$0.826855\pi$
$632$	16.0000	+	16.0000i	0.636446	+	0.636446i
$633$	−16.0000	+	16.0000i	−0.635943	+	0.635943i
$634$		−	24.0000i		−	0.953162i
$635$	2.00000	+	6.00000i	0.0793676	+	0.238103i
$636$			16.0000i			0.634441i
$637$	−44.0000	+	44.0000i	−1.74334	+	1.74334i
$638$	40.0000	−	40.0000i	1.58362	−	1.58362i
$639$	−40.0000			−1.58238
$640$	−24.0000	+	8.00000i	−0.948683	+	0.316228i
$641$	2.00000			0.0789953			0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000			0.0789953			0.0394976	+	0.999220i	$0.487424\pi$
$642$	16.0000	−	16.0000i	0.631470	−	0.631470i
$643$	17.0000	−	17.0000i	0.670415	−	0.670415i	−0.287397	−	0.957812i	$-0.592790\pi$
$643$	17.0000	−	17.0000i	0.670415	−	0.670415i	0.957812	+	0.287397i	$0.0927899\pi$
$644$		−	60.0000i		−	2.36433i
$645$	−24.0000	−	12.0000i	−0.944999	−	0.472500i
$646$			2.00000i			0.0786889i
$647$	33.0000	−	33.0000i	1.29736	−	1.29736i	0.367236	−	0.930128i	$-0.380304\pi$
$647$	33.0000	−	33.0000i	1.29736	−	1.29736i	0.930128	−	0.367236i	$-0.119696\pi$
$648$	−2.00000	−	2.00000i	−0.0785674	−	0.0785674i
$649$		0			0
$650$	−24.0000	−	32.0000i	−0.941357	−	1.25514i
$651$	48.0000			1.88127
$652$	−2.00000	−	2.00000i	−0.0783260	−	0.0783260i
$653$	13.0000	+	13.0000i	0.508729	+	0.508729i	0.914136	−	0.405407i	$-0.132870\pi$
$653$	13.0000	+	13.0000i	0.508729	+	0.508729i	−0.405407	+	0.914136i	$0.632870\pi$
$654$			24.0000i			0.938474i
$655$	6.00000	−	12.0000i	0.234439	−	0.468879i
$656$	8.00000			0.312348
$657$	−35.0000	−	35.0000i	−1.36548	−	1.36548i
$658$	30.0000	+	30.0000i	1.16952	+	1.16952i
$659$			28.0000i			1.09073i	0.838200	+	0.545363i	$0.183608\pi$
$659$			28.0000i			1.09073i	−0.838200	+	0.545363i	$0.816392\pi$
$660$	48.0000	−	16.0000i	1.86840	−	0.622799i
$661$			26.0000i			1.01128i	0.862744	+	0.505641i	$0.168744\pi$
$661$			26.0000i			1.01128i	−0.862744	+	0.505641i	$0.831256\pi$
$662$	24.0000	−	24.0000i	0.932786	−	0.932786i
$663$	−16.0000	−	16.0000i	−0.621389	−	0.621389i
$664$	−28.0000			−1.08661
$665$	9.00000	−	3.00000i	0.349005	−	0.116335i
$666$		0			0
$667$	−50.0000	−	50.0000i	−1.93601	−	1.93601i
$668$	32.0000	+	32.0000i	1.23812	+	1.23812i
$669$	40.0000			1.54649
$670$	−20.0000	+	40.0000i	−0.772667	+	1.54533i
$671$		−	8.00000i		−	0.308837i
$672$	48.0000	+	48.0000i	1.85164	+	1.85164i
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	−0.997386	−	0.0722542i	$-0.976981\pi$
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	0.0722542	+	0.997386i	$0.476981\pi$
$674$	−20.0000			−0.770371
$675$	−4.00000	+	28.0000i	−0.153960	+	1.07772i
$676$	38.0000			1.46154
$677$	22.0000	−	22.0000i	0.845529	−	0.845529i	−0.144043	−	0.989571i	$-0.546010\pi$
$677$	22.0000	−	22.0000i	0.845529	−	0.845529i	0.989571	+	0.144043i	$0.0460103\pi$
$678$	−8.00000	−	8.00000i	−0.307238	−	0.307238i
$679$	−36.0000			−1.38155
$680$	8.00000	+	4.00000i	0.306786	+	0.153393i
$681$	64.0000			2.45249
$682$	−16.0000	−	16.0000i	−0.612672	−	0.612672i
$683$	28.0000	−	28.0000i	1.07139	−	1.07139i	0.0741426	−	0.997248i	$-0.476378\pi$
$683$	28.0000	−	28.0000i	1.07139	−	1.07139i	0.997248	−	0.0741426i	$-0.0236220\pi$
$684$			10.0000i			0.382360i
$685$	−15.0000	+	5.00000i	−0.573121	+	0.191040i
$686$	−24.0000			−0.916324
$687$	48.0000	−	48.0000i	1.83131	−	1.83131i
$688$	−12.0000	+	12.0000i	−0.457496	+	0.457496i
$689$			16.0000i			0.609551i
$690$	−20.0000	−	60.0000i	−0.761387	−	2.28416i
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$	−20.0000	+	20.0000i	−0.760286	+	0.760286i
$693$	−60.0000	−	60.0000i	−2.27921	−	2.27921i
$694$	−14.0000			−0.531433
$695$	−4.00000	−	2.00000i	−0.151729	−	0.0758643i
$696$	80.0000			3.03239
$697$	−2.00000	−	2.00000i	−0.0757554	−	0.0757554i
$698$	−2.00000	+	2.00000i	−0.0757011	+	0.0757011i
$699$			76.0000i			2.87458i
$700$	6.00000	−	42.0000i	0.226779	−	1.58745i
$701$			26.0000i			0.982006i	0.871158	+	0.491003i	$0.163370\pi$
$701$			26.0000i			0.982006i	−0.871158	+	0.491003i	$0.836630\pi$
$702$	−32.0000	−	32.0000i	−1.20776	−	1.20776i
$703$		0			0
$704$		−	32.0000i		−	1.20605i
$705$	40.0000	+	20.0000i	1.50649	+	0.753244i
$706$		−	18.0000i		−	0.677439i
$707$	18.0000	+	18.0000i	0.676960	+	0.676960i
$708$		0			0
$709$	−46.0000			−1.72757			−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000			−1.72757			−0.863783	+	0.503864i	$0.831911\pi$
$710$	24.0000	−	8.00000i	0.900704	−	0.300235i
$711$		−	40.0000i		−	1.50012i
$712$	20.0000	−	20.0000i	0.749532	−	0.749532i
$713$	−20.0000	+	20.0000i	−0.749006	+	0.749006i
$714$		−	24.0000i		−	0.898177i
$715$	48.0000	−	16.0000i	1.79510	−	0.598366i
$716$	−32.0000			−1.19590
$717$	36.0000	−	36.0000i	1.34444	−	1.34444i
$718$	−24.0000	+	24.0000i	−0.895672	+	0.895672i
$719$	−48.0000			−1.79010			−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000			−1.79010			−0.895049	+	0.445968i	$0.852860\pi$
$720$	40.0000	+	20.0000i	1.49071	+	0.745356i
$721$	−36.0000			−1.34071
$722$	1.00000	−	1.00000i	0.0372161	−	0.0372161i
$723$	−28.0000	+	28.0000i	−1.04133	+	1.04133i
$724$	−20.0000			−0.743294
$725$	−30.0000	−	40.0000i	−1.11417	−	1.48556i
$726$			20.0000i			0.742270i
$727$	1.00000	−	1.00000i	0.0370879	−	0.0370879i	−0.688320	−	0.725408i	$-0.741651\pi$
$727$	1.00000	−	1.00000i	0.0370879	−	0.0370879i	0.725408	+	0.688320i	$0.241651\pi$
$728$	48.0000	+	48.0000i	1.77900	+	1.77900i
$729$		−	43.0000i		−	1.59259i
$730$	28.0000	+	14.0000i	1.03633	+	0.518163i
$731$	6.00000			0.221918
$732$	8.00000	−	8.00000i	0.295689	−	0.295689i
$733$	5.00000	+	5.00000i	0.184679	+	0.184679i	0.793391	−	0.608712i	$-0.208314\pi$
$733$	5.00000	+	5.00000i	0.184679	+	0.184679i	−0.608712	+	0.793391i	$0.708314\pi$
$734$			42.0000i			1.55025i
$735$	−66.0000	+	22.0000i	−2.43445	+	0.811482i
$736$	−40.0000			−1.47442
$737$	−40.0000	−	40.0000i	−1.47342	−	1.47342i
$738$	−10.0000	−	10.0000i	−0.368105	−	0.368105i
$739$		−	20.0000i		−	0.735712i	−0.929883	−	0.367856i	$-0.880092\pi$
$739$		−	20.0000i		−	0.735712i	0.929883	−	0.367856i	$-0.119908\pi$
$740$		0			0
$741$			16.0000i			0.587775i
$742$	−12.0000	+	12.0000i	−0.440534	+	0.440534i
$743$	−20.0000	−	20.0000i	−0.733729	−	0.733729i	0.237628	−	0.971356i	$-0.423630\pi$
$743$	−20.0000	−	20.0000i	−0.733729	−	0.733729i	−0.971356	+	0.237628i	$0.923630\pi$
$744$		−	32.0000i		−	1.17318i
$745$	12.0000	−	24.0000i	0.439646	−	0.879292i
$746$	−20.0000			−0.732252
$747$	35.0000	+	35.0000i	1.28058	+	1.28058i
$748$	−8.00000	+	8.00000i	−0.292509	+	0.292509i
$749$	24.0000			0.876941
$750$	−8.00000	−	44.0000i	−0.292119	−	1.60665i
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$	20.0000	−	20.0000i	0.729325	−	0.729325i
$753$	−44.0000	+	44.0000i	−1.60345	+	1.60345i
$754$	80.0000			2.91343
$755$	−32.0000	−	16.0000i	−1.16460	−	0.582300i
$756$		−	48.0000i		−	1.74574i
$757$	9.00000	−	9.00000i	0.327111	−	0.327111i	−0.524376	−	0.851487i	$-0.675701\pi$
$757$	9.00000	−	9.00000i	0.327111	−	0.327111i	0.851487	+	0.524376i	$0.175701\pi$
$758$	−16.0000	−	16.0000i	−0.581146	−	0.581146i
$759$	80.0000			2.90382
$760$	−2.00000	−	6.00000i	−0.0725476	−	0.217643i
$761$	16.0000			0.580000			0.290000	−	0.957027i	$-0.406345\pi$
$761$	16.0000			0.580000			0.290000	+	0.957027i	$0.406345\pi$
$762$	−8.00000	−	8.00000i	−0.289809	−	0.289809i
$763$	−18.0000	+	18.0000i	−0.651644	+	0.651644i
$764$		0			0
$765$	−5.00000	−	15.0000i	−0.180775	−	0.542326i
$766$	24.0000			0.867155
$767$		0			0
$768$	32.0000	−	32.0000i	1.15470	−	1.15470i
$769$		−	2.00000i		−	0.0721218i	−0.999350	−	0.0360609i	$-0.988519\pi$
$769$		−	2.00000i		−	0.0721218i	0.999350	−	0.0360609i	$-0.0114810\pi$
$770$	48.0000	+	24.0000i	1.72980	+	0.864900i
$771$	−80.0000			−2.88113
$772$	−12.0000	−	12.0000i	−0.431889	−	0.431889i
$773$	−16.0000	−	16.0000i	−0.575480	−	0.575480i	0.358175	−	0.933655i	$-0.383399\pi$
$773$	−16.0000	−	16.0000i	−0.575480	−	0.575480i	−0.933655	+	0.358175i	$0.883399\pi$
$774$	30.0000			1.07833
$775$	−16.0000	+	12.0000i	−0.574737	+	0.431053i
$776$			24.0000i			0.861550i
$777$		0			0
$778$	−6.00000	+	6.00000i	−0.215110	+	0.215110i
$779$			2.00000i			0.0716574i
$780$	64.0000	+	32.0000i	2.29157	+	1.14578i
$781$			32.0000i			1.14505i
$782$	10.0000	+	10.0000i	0.357599	+	0.357599i
$783$	−40.0000	−	40.0000i	−1.42948	−	1.42948i
$784$			44.0000i			1.57143i
$785$	−3.00000	−	9.00000i	−0.107075	−	0.321224i
$786$			24.0000i			0.856052i
$787$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$787$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$788$	10.0000	+	10.0000i	0.356235	+	0.356235i
$789$	−28.0000			−0.996826
$790$	8.00000	+	24.0000i	0.284627	+	0.853882i
$791$		−	12.0000i		−	0.426671i
$792$	−40.0000	+	40.0000i	−1.42134	+	1.42134i
$793$	8.00000	−	8.00000i	0.284088	−	0.284088i
$794$			26.0000i			0.922705i
$795$	−8.00000	+	16.0000i	−0.283731	+	0.567462i
$796$			12.0000i			0.425329i
$797$	10.0000	−	10.0000i	0.354218	−	0.354218i	−0.507458	−	0.861676i	$-0.669415\pi$
$797$	10.0000	−	10.0000i	0.354218	−	0.354218i	0.861676	+	0.507458i	$0.169415\pi$
$798$	−12.0000	+	12.0000i	−0.424795	+	0.424795i
$799$	−10.0000			−0.353775
$800$	−28.0000	−	4.00000i	−0.989949	−	0.141421i
$801$	−50.0000			−1.76666
$802$	−6.00000	+	6.00000i	−0.211867	+	0.211867i
$803$	−28.0000	+	28.0000i	−0.988099	+	0.988099i
$804$		−	80.0000i		−	2.82138i
$805$	30.0000	−	60.0000i	1.05736	−	2.11472i
$806$		−	32.0000i		−	1.12715i
$807$	28.0000	−	28.0000i	0.985647	−	0.985647i
$808$	12.0000	−	12.0000i	0.422159	−	0.422159i
$809$		−	40.0000i		−	1.40633i	−0.711029	−	0.703163i	$-0.751771\pi$
$809$		−	40.0000i		−	1.40633i	0.711029	−	0.703163i	$-0.248229\pi$
$810$	−1.00000	−	3.00000i	−0.0351364	−	0.105409i
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$	60.0000	+	60.0000i	2.10559	+	2.10559i
$813$	−4.00000	−	4.00000i	−0.140286	−	0.140286i
$814$		0			0
$815$	−1.00000	−	3.00000i	−0.0350285	−	0.105085i
$816$	−16.0000			−0.560112
$817$	−3.00000	−	3.00000i	−0.104957	−	0.104957i
$818$	−34.0000	−	34.0000i	−1.18878	−	1.18878i
$819$		−	120.000i		−	4.19314i
$820$	8.00000	+	4.00000i	0.279372	+	0.139686i
$821$			24.0000i			0.837606i	0.908077	+	0.418803i	$0.137550\pi$
$821$			24.0000i			0.837606i	−0.908077	+	0.418803i	$0.862450\pi$
$822$	20.0000	−	20.0000i	0.697580	−	0.697580i
$823$	−15.0000	−	15.0000i	−0.522867	−	0.522867i	0.395569	−	0.918436i	$-0.370547\pi$
$823$	−15.0000	−	15.0000i	−0.522867	−	0.522867i	−0.918436	+	0.395569i	$0.870547\pi$
$824$			24.0000i			0.836080i
$825$	56.0000	+	8.00000i	1.94967	+	0.278524i
$826$		0			0
$827$	−18.0000	−	18.0000i	−0.625921	−	0.625921i	0.321118	−	0.947039i	$-0.395941\pi$
$827$	−18.0000	−	18.0000i	−0.625921	−	0.625921i	−0.947039	+	0.321118i	$0.895941\pi$
$828$	50.0000	+	50.0000i	1.73762	+	1.73762i
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−28.0000	−	14.0000i	−0.971894	−	0.485947i
$831$		−	12.0000i		−	0.416275i
$832$	32.0000	−	32.0000i	1.10940	−	1.10940i
$833$	11.0000	−	11.0000i	0.381127	−	0.381127i
$834$	8.00000			0.277017
$835$	16.0000	+	48.0000i	0.553703	+	1.66111i
$836$	8.00000			0.276686
$837$	−16.0000	+	16.0000i	−0.553041	+	0.553041i
$838$	12.0000	+	12.0000i	0.414533	+	0.414533i
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$	24.0000	+	72.0000i	0.828079	+	2.48424i
$841$	71.0000			2.44828
$842$	26.0000	+	26.0000i	0.896019	+	0.896019i
$843$	4.00000	−	4.00000i	0.137767	−	0.137767i
$844$			16.0000i			0.550743i
$845$	38.0000	+	19.0000i	1.30724	+	0.653620i
$846$	−50.0000			−1.71904
$847$	−15.0000	+	15.0000i	−0.515406	+	0.515406i
$848$	8.00000	+	8.00000i	0.274721	+	0.274721i
$849$		−	36.0000i		−	1.23552i
$850$	6.00000	+	8.00000i	0.205798	+	0.274398i
$851$		0			0
$852$	−32.0000	+	32.0000i	−1.09630	+	1.09630i
$853$	23.0000	+	23.0000i	0.787505	+	0.787505i	0.981085	−	0.193580i	$-0.0620098\pi$
$853$	23.0000	+	23.0000i	0.787505	+	0.787505i	−0.193580	+	0.981085i	$0.562010\pi$
$854$	12.0000			0.410632
$855$	−5.00000	+	10.0000i	−0.170996	+	0.341993i
$856$		−	16.0000i		−	0.546869i
$857$	24.0000	+	24.0000i	0.819824	+	0.819824i	0.986082	−	0.166258i	$-0.0531684\pi$
$857$	24.0000	+	24.0000i	0.819824	+	0.819824i	−0.166258	+	0.986082i	$0.553168\pi$
$858$	−64.0000	+	64.0000i	−2.18492	+	2.18492i
$859$		−	12.0000i		−	0.409435i	−0.978821	−	0.204717i	$-0.934372\pi$
$859$		−	12.0000i		−	0.409435i	0.978821	−	0.204717i	$-0.0656275\pi$
$860$	−18.0000	+	6.00000i	−0.613795	+	0.204598i
$861$		−	24.0000i		−	0.817918i
$862$	−12.0000	−	12.0000i	−0.408722	−	0.408722i
$863$	−16.0000	−	16.0000i	−0.544646	−	0.544646i	0.380241	−	0.924887i	$-0.375841\pi$
$863$	−16.0000	−	16.0000i	−0.544646	−	0.544646i	−0.924887	+	0.380241i	$0.875841\pi$
$864$	−32.0000			−1.08866
$865$	−30.0000	+	10.0000i	−1.02003	+	0.340010i
$866$			28.0000i			0.951479i
$867$	−30.0000	−	30.0000i	−1.01885	−	1.01885i
$868$	24.0000	−	24.0000i	0.814613	−	0.814613i
$869$	−32.0000			−1.08553
$870$	80.0000	+	40.0000i	2.71225	+	1.35613i
$871$		−	80.0000i		−	2.71070i
$872$	12.0000	+	12.0000i	0.406371	+	0.406371i
$873$	30.0000	−	30.0000i	1.01535	−	1.01535i
$874$		−	10.0000i		−	0.338255i
$875$	27.0000	−	39.0000i	0.912767	−	1.31844i
$876$	−56.0000			−1.89206
$877$	22.0000	−	22.0000i	0.742887	−	0.742887i	−0.230245	−	0.973133i	$-0.573953\pi$
$877$	22.0000	−	22.0000i	0.742887	−	0.742887i	0.973133	+	0.230245i	$0.0739529\pi$
$878$	−20.0000	+	20.0000i	−0.674967	+	0.674967i
$879$	8.00000			0.269833
$880$	16.0000	−	32.0000i	0.539360	−	1.07872i
$881$	−12.0000			−0.404290			−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000			−0.404290			−0.202145	+	0.979356i	$0.564791\pi$
$882$	55.0000	−	55.0000i	1.85195	−	1.85195i
$883$	−9.00000	+	9.00000i	−0.302874	+	0.302874i	−0.842137	−	0.539263i	$-0.818703\pi$
$883$	−9.00000	+	9.00000i	−0.302874	+	0.302874i	0.539263	+	0.842137i	$0.318703\pi$
$884$	−16.0000			−0.538138
$885$		0			0
$886$			42.0000i			1.41102i
$887$	−22.0000	+	22.0000i	−0.738688	+	0.738688i	−0.972324	−	0.233636i	$-0.924937\pi$
$887$	−22.0000	+	22.0000i	−0.738688	+	0.738688i	0.233636	+	0.972324i	$0.424937\pi$
$888$		0			0
$889$		−	12.0000i		−	0.402467i
$890$	30.0000	−	10.0000i	1.00560	−	0.335201i
$891$	4.00000			0.134005
$892$	20.0000	−	20.0000i	0.669650	−	0.669650i
$893$	5.00000	+	5.00000i	0.167319	+	0.167319i
$894$			48.0000i			1.60536i
$895$	−32.0000	−	16.0000i	−1.06964	−	0.534821i
$896$	48.0000			1.60357
$897$	80.0000	+	80.0000i	2.67112	+	2.67112i
$898$	−10.0000	−	10.0000i	−0.333704	−	0.333704i
$899$		−	40.0000i		−	1.33407i
$900$	30.0000	+	40.0000i	1.00000	+	1.33333i
$901$		−	4.00000i		−	0.133259i
$902$	−8.00000	+	8.00000i	−0.266371	+	0.266371i
$903$	36.0000	+	36.0000i	1.19800	+	1.19800i
$904$	−8.00000			−0.266076
$905$	−20.0000	−	10.0000i	−0.664822	−	0.332411i
$906$	64.0000			2.12626
$907$	−4.00000	−	4.00000i	−0.132818	−	0.132818i	0.637573	−	0.770390i	$-0.279939\pi$
$907$	−4.00000	−	4.00000i	−0.132818	−	0.132818i	−0.770390	+	0.637573i	$0.779939\pi$
$908$	32.0000	−	32.0000i	1.06196	−	1.06196i
$909$	−30.0000			−0.995037
$910$	24.0000	+	72.0000i	0.795592	+	2.38678i
$911$		−	8.00000i		−	0.265052i	−0.991180	−	0.132526i	$-0.957691\pi$
$911$		−	8.00000i		−	0.265052i	0.991180	−	0.132526i	$-0.0423088\pi$
$912$	8.00000	+	8.00000i	0.264906	+	0.264906i
$913$	28.0000	−	28.0000i	0.926665	−	0.926665i
$914$	30.0000			0.992312
$915$	12.0000	−	4.00000i	0.396708	−	0.132236i
$916$		−	48.0000i		−	1.58596i
$917$	−18.0000	+	18.0000i	−0.594412	+	0.594412i
$918$	8.00000	+	8.00000i	0.264039	+	0.264039i
$919$	−14.0000			−0.461817			−0.230909	−	0.972975i	$-0.574170\pi$
$919$	−14.0000			−0.461817			−0.230909	+	0.972975i	$0.574170\pi$
$920$	−40.0000	−	20.0000i	−1.31876	−	0.659380i
$921$	−32.0000			−1.05444
$922$	−20.0000	−	20.0000i	−0.658665	−	0.658665i
$923$	−32.0000	+	32.0000i	−1.05329	+	1.05329i
$924$	−96.0000			−3.15817
$925$		0			0
$926$	−18.0000			−0.591517
$927$	30.0000	−	30.0000i	0.985329	−	0.985329i
$928$	40.0000	−	40.0000i	1.31306	−	1.31306i
$929$		−	12.0000i		−	0.393707i	−0.980433	−	0.196854i	$-0.936928\pi$
$929$		−	12.0000i		−	0.393707i	0.980433	−	0.196854i	$-0.0630724\pi$
$930$	16.0000	−	32.0000i	0.524661	−	1.04932i
$931$	−11.0000			−0.360510
$932$	38.0000	+	38.0000i	1.24473	+	1.24473i
$933$	−4.00000	−	4.00000i	−0.130954	−	0.130954i
$934$	−46.0000			−1.50517
$935$	−12.0000	+	4.00000i	−0.392442	+	0.130814i
$936$	−80.0000			−2.61488
$937$	21.0000	+	21.0000i	0.686040	+	0.686040i	0.961354	−	0.275314i	$-0.0887819\pi$
$937$	21.0000	+	21.0000i	0.686040	+	0.686040i	−0.275314	+	0.961354i	$0.588782\pi$
$938$	60.0000	−	60.0000i	1.95907	−	1.95907i
$939$		−	36.0000i		−	1.17482i
$940$	30.0000	−	10.0000i	0.978492	−	0.326164i
$941$		−	22.0000i		−	0.717180i	−0.933495	−	0.358590i	$-0.883258\pi$
$941$		−	22.0000i		−	0.717180i	0.933495	−	0.358590i	$-0.116742\pi$
$942$	12.0000	+	12.0000i	0.390981	+	0.390981i
$943$	10.0000	+	10.0000i	0.325645	+	0.325645i
$944$		0			0
$945$	24.0000	−	48.0000i	0.780720	−	1.56144i
$946$		−	24.0000i		−	0.780307i
$947$	7.00000	+	7.00000i	0.227469	+	0.227469i	0.811635	−	0.584165i	$-0.198578\pi$
$947$	7.00000	+	7.00000i	0.227469	+	0.227469i	−0.584165	+	0.811635i	$0.698578\pi$
$948$	−32.0000	−	32.0000i	−1.03931	−	1.03931i
$949$	−56.0000			−1.81784
$950$	1.00000	−	7.00000i	0.0324443	−	0.227110i
$951$			48.0000i			1.55651i
$952$	−12.0000	−	12.0000i	−0.388922	−	0.388922i
$953$	−32.0000	+	32.0000i	−1.03658	+	1.03658i	−0.0372767	+	0.999305i	$0.511868\pi$
$953$	−32.0000	+	32.0000i	−1.03658	+	1.03658i	−0.999305	+	0.0372767i	$0.988132\pi$
$954$		−	20.0000i		−	0.647524i
$955$		0			0
$956$		−	36.0000i		−	1.16432i
$957$	−80.0000	+	80.0000i	−2.58603	+	2.58603i
$958$	−8.00000	+	8.00000i	−0.258468	+	0.258468i
$959$	30.0000			0.968751
$960$	48.0000	−	16.0000i	1.54919	−	0.516398i
$961$	15.0000			0.483871
$962$		0			0
$963$	−20.0000	+	20.0000i	−0.644491	+	0.644491i
$964$			28.0000i			0.901819i
$965$	−6.00000	−	18.0000i	−0.193147	−	0.579441i
$966$			120.000i			3.86094i
$967$	−37.0000	+	37.0000i	−1.18984	+	1.18984i	−0.212728	+	0.977111i	$0.568235\pi$
$967$	−37.0000	+	37.0000i	−1.18984	+	1.18984i	−0.977111	+	0.212728i	$0.931765\pi$
$968$	10.0000	+	10.0000i	0.321412	+	0.321412i
$969$		−	4.00000i		−	0.128499i
$970$	−12.0000	+	24.0000i	−0.385297	+	0.770594i
$971$	−32.0000			−1.02693			−0.513464	−	0.858111i	$-0.671638\pi$
$971$	−32.0000			−1.02693			−0.513464	+	0.858111i	$0.671638\pi$
$972$	−20.0000	−	20.0000i	−0.641500	−	0.641500i
$973$	6.00000	+	6.00000i	0.192351	+	0.192351i
$974$		−	48.0000i		−	1.53802i
$975$	48.0000	+	64.0000i	1.53723	+	2.04964i
$976$		−	8.00000i		−	0.256074i
$977$	32.0000	+	32.0000i	1.02377	+	1.02377i	0.999711	+	0.0240602i	$0.00765934\pi$
$977$	32.0000	+	32.0000i	1.02377	+	1.02377i	0.0240602	+	0.999711i	$0.492341\pi$
$978$	4.00000	+	4.00000i	0.127906	+	0.127906i
$979$			40.0000i			1.27841i
$980$	−22.0000	+	44.0000i	−0.702764	+	1.40553i
$981$		−	30.0000i		−	0.957826i
$982$	30.0000	−	30.0000i	0.957338	−	0.957338i
$983$	−20.0000	−	20.0000i	−0.637901	−	0.637901i	0.312136	−	0.950037i	$-0.398955\pi$
$983$	−20.0000	−	20.0000i	−0.637901	−	0.637901i	−0.950037	+	0.312136i	$0.898955\pi$
$984$	−16.0000			−0.510061
$985$	5.00000	+	15.0000i	0.159313	+	0.477940i
$986$	−20.0000			−0.636930
$987$	−60.0000	−	60.0000i	−1.90982	−	1.90982i
$988$	8.00000	+	8.00000i	0.254514	+	0.254514i
$989$	−30.0000			−0.953945
$990$	−60.0000	+	20.0000i	−1.90693	+	0.635642i
$991$		−	8.00000i		−	0.254128i	−0.991894	−	0.127064i	$-0.959445\pi$
$991$		−	8.00000i		−	0.254128i	0.991894	−	0.127064i	$-0.0405554\pi$
$992$	−16.0000	−	16.0000i	−0.508001	−	0.508001i
$993$	−48.0000	+	48.0000i	−1.52323	+	1.52323i
$994$	−48.0000			−1.52247
$995$	−6.00000	+	12.0000i	−0.190213	+	0.380426i
$996$	56.0000			1.77443
$997$	−41.0000	+	41.0000i	−1.29848	+	1.29848i	−0.369089	+	0.929394i	$0.620330\pi$
$997$	−41.0000	+	41.0000i	−1.29848	+	1.29848i	−0.929394	+	0.369089i	$0.879670\pi$
$998$	−6.00000	−	6.00000i	−0.189927	−	0.189927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.w.a.267.1	✓	2
5.3	odd	4		760.2.w.b.723.1	yes	2
8.3	odd	2		760.2.w.b.267.1	yes	2
40.3	even	4	inner	760.2.w.a.723.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.w.a.267.1	✓	2	1.1	even	1	trivial
760.2.w.a.723.1	yes	2	40.3	even	4	inner
760.2.w.b.267.1	yes	2	8.3	odd	2
760.2.w.b.723.1	yes	2	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(2.00000 - 2.00000i) q^{3} -2.00000i q^{4} +(1.00000 - 2.00000i) q^{5} +4.00000i q^{6} +(-3.00000 + 3.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} -5.00000i q^{9} +(1.00000 + 3.00000i) q^{10} -4.00000 q^{11} +(-4.00000 - 4.00000i) q^{12} +(-4.00000 - 4.00000i) q^{13} -6.00000i q^{14} +(-2.00000 - 6.00000i) q^{15} -4.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +(5.00000 + 5.00000i) q^{18} -1.00000i q^{19} +(-4.00000 - 2.00000i) q^{20} +12.0000i q^{21} +(4.00000 - 4.00000i) q^{22} +(-5.00000 - 5.00000i) q^{23} +8.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +8.00000 q^{26} +(-4.00000 - 4.00000i) q^{27} +(6.00000 + 6.00000i) q^{28} +10.0000 q^{29} +(8.00000 + 4.00000i) q^{30} -4.00000i q^{31} +(4.00000 - 4.00000i) q^{32} +(-8.00000 + 8.00000i) q^{33} -2.00000 q^{34} +(3.00000 + 9.00000i) q^{35} -10.0000 q^{36} +(1.00000 + 1.00000i) q^{38} -16.0000 q^{39} +(6.00000 - 2.00000i) q^{40} -2.00000 q^{41} +(-12.0000 - 12.0000i) q^{42} +(3.00000 - 3.00000i) q^{43} +8.00000i q^{44} +(-10.0000 - 5.00000i) q^{45} +10.0000 q^{46} +(-5.00000 + 5.00000i) q^{47} +(-8.00000 + 8.00000i) q^{48} -11.0000i q^{49} +(7.00000 + 1.00000i) q^{50} +4.00000 q^{51} +(-8.00000 + 8.00000i) q^{52} +(-2.00000 - 2.00000i) q^{53} +8.00000 q^{54} +(-4.00000 + 8.00000i) q^{55} -12.0000 q^{56} +(-2.00000 - 2.00000i) q^{57} +(-10.0000 + 10.0000i) q^{58} +(-12.0000 + 4.00000i) q^{60} +2.00000i q^{61} +(4.00000 + 4.00000i) q^{62} +(15.0000 + 15.0000i) q^{63} +8.00000i q^{64} +(-12.0000 + 4.00000i) q^{65} -16.0000i q^{66} +(10.0000 + 10.0000i) q^{67} +(2.00000 - 2.00000i) q^{68} -20.0000 q^{69} +(-12.0000 - 6.00000i) q^{70} -8.00000i q^{71} +(10.0000 - 10.0000i) q^{72} +(7.00000 - 7.00000i) q^{73} +(-14.0000 - 2.00000i) q^{75} -2.00000 q^{76} +(12.0000 - 12.0000i) q^{77} +(16.0000 - 16.0000i) q^{78} +8.00000 q^{79} +(-4.00000 + 8.00000i) q^{80} -1.00000 q^{81} +(2.00000 - 2.00000i) q^{82} +(-7.00000 + 7.00000i) q^{83} +24.0000 q^{84} +(3.00000 - 1.00000i) q^{85} +6.00000i q^{86} +(20.0000 - 20.0000i) q^{87} +(-8.00000 - 8.00000i) q^{88} -10.0000i q^{89} +(15.0000 - 5.00000i) q^{90} +24.0000 q^{91} +(-10.0000 + 10.0000i) q^{92} +(-8.00000 - 8.00000i) q^{93} -10.0000i q^{94} +(-2.00000 - 1.00000i) q^{95} -16.0000i q^{96} +(6.00000 + 6.00000i) q^{97} +(11.0000 + 11.0000i) q^{98} +20.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 4 q^{3} + 2 q^{5} - 6 q^{7} + 4 q^{8} + 2 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 4 q^{15} - 8 q^{16} + 2 q^{17} + 10 q^{18} - 8 q^{20} + 8 q^{22} - 10 q^{23} + 16 q^{24} - 6 q^{25} + 16 q^{26}+ \cdots + 22 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^5 - 6 * q^7 + 4 * q^8 + 2 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 4 * q^15 - 8 * q^16 + 2 * q^17 + 10 * q^18 - 8 * q^20 + 8 * q^22 - 10 * q^23 + 16 * q^24 - 6 * q^25 + 16 * q^26 - 8 * q^27 + 12 * q^28 + 20 * q^29 + 16 * q^30 + 8 * q^32 - 16 * q^33 - 4 * q^34 + 6 * q^35 - 20 * q^36 + 2 * q^38 - 32 * q^39 + 12 * q^40 - 4 * q^41 - 24 * q^42 + 6 * q^43 - 20 * q^45 + 20 * q^46 - 10 * q^47 - 16 * q^48 + 14 * q^50 + 8 * q^51 - 16 * q^52 - 4 * q^53 + 16 * q^54 - 8 * q^55 - 24 * q^56 - 4 * q^57 - 20 * q^58 - 24 * q^60 + 8 * q^62 + 30 * q^63 - 24 * q^65 + 20 * q^67 + 4 * q^68 - 40 * q^69 - 24 * q^70 + 20 * q^72 + 14 * q^73 - 28 * q^75 - 4 * q^76 + 24 * q^77 + 32 * q^78 + 16 * q^79 - 8 * q^80 - 2 * q^81 + 4 * q^82 - 14 * q^83 + 48 * q^84 + 6 * q^85 + 40 * q^87 - 16 * q^88 + 30 * q^90 + 48 * q^91 - 20 * q^92 - 16 * q^93 - 4 * q^95 + 12 * q^97 + 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more